Fri Sep 2 19:11:50 2022 test_int_test() Python version: 3.6.9 Test test_int(). gauss_legendre4_test(): Composite 4-point Gauss-Legendre quadrature rule. N Approx Error Ratio Problem 1 1 1.7182818275 9.329675e-10 2 1.7182818285 3.741674e-12 249.345 4 1.7182818285 1.465494e-14 255.318 8 1.7182818285 2.220446e-16 66 16 1.7182818285 0.000000e+00 */0 32 1.7182818285 0.000000e+00 */0 64 1.7182818285 0.000000e+00 */0 128 1.7182818285 2.220446e-16 0 256 1.7182818285 0.000000e+00 */0 512 1.7182818285 0.000000e+00 */0 1024 1.7182818285 2.220446e-16 0 Exact 1.7182818285 Problem 2 1 0.8260725774 1.260726e-01 2 0.7500000000 5.000000e-02 2.52145 4 0.7065181444 6.518144e-03 7.67089 8 0.6875000000 1.250000e-02 0.521452 16 0.6983704639 1.629536e-03 7.67089 32 0.7031250000 3.125000e-03 0.521452 64 0.7004073840 4.073840e-04 7.67089 128 0.6992187500 7.812500e-04 0.521452 256 0.6998981540 1.018460e-04 7.67089 512 0.7001953125 1.953125e-04 0.521452 1024 0.7000254615 2.546150e-05 7.67089 Exact 0.7000000000 Problem 3 1 0.6678276454 1.160979e-03 2 0.6670771406 4.104740e-04 2.82839 4 0.6668117912 1.451245e-04 2.82843 8 0.6667179759 5.130926e-05 2.82843 16 0.6666848072 1.814056e-05 2.82843 32 0.6666730803 6.413658e-06 2.82843 64 0.6666689342 2.267570e-06 2.82843 128 0.6666674684 8.017072e-07 2.82843 256 0.6666669501 2.834463e-07 2.82843 512 0.6666667669 1.002134e-07 2.82843 1024 0.6666667021 3.543079e-08 2.82843 Exact 0.6666666667 Problem 4 1 0.4794282361 9.399092e-09 2 0.4794282265 1.930694e-10 48.6825 4 0.4794282267 9.782730e-13 197.357 8 0.4794282267 3.941292e-15 248.211 16 0.4794282267 5.551115e-17 71 32 0.4794282267 5.551115e-17 1 64 0.4794282267 5.551115e-17 1 128 0.4794282267 1.110223e-16 0.5 256 0.4794282267 5.551115e-17 2 512 0.4794282267 5.551115e-17 1 1024 0.4794282267 5.551115e-17 1 Exact 0.4794282267 Problem 5 1 1.5850604881 2.827524e-03 2 1.5822136552 1.930856e-05 146.439 4 1.5822330003 3.656264e-08 528.095 8 1.5822329638 3.304668e-11 1106.39 16 1.5822329637 1.458833e-13 226.528 32 1.5822329637 4.440892e-16 328.5 64 1.5822329637 2.220446e-16 2 128 1.5822329637 2.220446e-16 1 256 1.5822329637 2.220446e-16 1 512 1.5822329637 2.220446e-16 1 1024 1.5822329637 2.220446e-16 1 Exact 1.5822329637 Problem 6 1 1.4734441274 1.299700e-02 2 1.4861762298 2.572910e-02 0.505148 4 1.4612680738 8.209420e-04 31.3409 8 1.4607373808 2.902490e-04 2.82841 16 1.4605497503 1.026185e-04 2.82843 32 1.4604834129 3.628113e-05 2.82843 64 1.4604599591 1.282732e-05 2.82843 128 1.4604516669 4.535141e-06 2.82843 256 1.4604487352 1.603414e-06 2.82843 512 1.4604476987 5.668926e-07 2.82843 1024 1.4604473322 2.004268e-07 2.82843 Exact 1.4604471318 Problem 7 1 1.8063425404 1.936575e-01 2 1.8630633707 1.369366e-01 1.41421 4 1.9031711798 9.682882e-02 1.41421 8 1.9315316846 6.846832e-02 1.41421 16 1.9515855899 4.841441e-02 1.41421 32 1.9657658423 3.423416e-02 1.41421 64 1.9757927949 2.420721e-02 1.41421 128 1.9828829212 1.711708e-02 1.41421 256 1.9878963975 1.210360e-02 1.41421 512 1.9914414606 8.558539e-03 1.41421 1024 1.9939481987 6.051801e-03 1.41421 Exact 2.0000000000 Problem 8 1 0.8669556575 1.732989e-05 2 0.8669729312 5.613566e-08 308.714 4 0.8669729875 1.679805e-10 334.18 8 0.8669729873 5.584422e-13 300.802 16 0.8669729873 1.998401e-15 279.444 32 0.8669729873 1.110223e-16 18 64 0.8669729873 0.000000e+00 */0 128 0.8669729873 0.000000e+00 */0 256 0.8669729873 0.000000e+00 */0 512 0.8669729873 1.110223e-16 0 1024 0.8669729873 0.000000e+00 */0 Exact 0.8669729873 Problem 9 1 1.1978133015 4.311276e-02 2 1.2466068790 9.190634e-02 0.469095 4 1.1477459287 6.954610e-03 13.2152 8 1.1546647884 3.574995e-05 194.535 16 1.1547005374 9.499237e-10 37634.6 32 1.1547005384 0.000000e+00 */0 64 1.1547005384 0.000000e+00 */0 128 1.1547005384 0.000000e+00 */0 256 1.1547005384 0.000000e+00 */0 512 1.1547005384 0.000000e+00 */0 1024 1.1547005384 0.000000e+00 */0 Exact 1.1547005384 Problem 10 1 0.6931464174 7.631145e-07 2 0.6931471738 6.806386e-09 112.117 4 0.6931471805 3.723388e-11 182.801 8 0.6931471806 1.619815e-13 229.865 16 0.6931471806 6.661338e-16 243.167 32 0.6931471806 0.000000e+00 */0 64 0.6931471806 0.000000e+00 */0 128 0.6931471806 1.110223e-16 0 256 0.6931471806 1.110223e-16 1 512 0.6931471806 1.110223e-16 1 1024 0.6931471806 0.000000e+00 */0 Exact 0.6931471806 Problem 11 1 0.3798854943 1.272926e-09 2 0.3798854930 3.834044e-12 332.006 4 0.3798854930 1.421085e-14 269.797 8 0.3798854930 0.000000e+00 */0 16 0.3798854930 0.000000e+00 */0 32 0.3798854930 5.551115e-17 0 64 0.3798854930 0.000000e+00 */0 128 0.3798854930 0.000000e+00 */0 256 0.3798854930 0.000000e+00 */0 512 0.3798854930 0.000000e+00 */0 1024 0.3798854930 5.551115e-17 0 Exact 0.3798854930 Problem 12 1 0.7182818355 5.922280e-02 2 0.7182818285 5.922281e-02 1 4 0.7182818285 5.922281e-02 1 8 0.7182818285 5.922281e-02 1 16 0.7182818285 5.922281e-02 1 32 0.7182818285 5.922281e-02 1 64 0.7182818285 5.922281e-02 1 128 0.7182818285 5.922281e-02 1 256 0.7182818285 5.922281e-02 1 512 0.7182818285 5.922281e-02 1 1024 0.7182818285 5.922281e-02 1 Exact 0.7775046341 Problem 13 1 1.6661017652 7.754171e-03 2 1.6583381237 9.470520e-06 818.769 4 1.6583475676 2.657638e-08 356.351 8 1.6583475941 9.438494e-11 281.574 16 1.6583475942 3.601563e-13 262.067 32 1.6583475942 1.554312e-15 231.714 64 1.6583475942 0.000000e+00 */0 128 1.6583475942 2.220446e-16 0 256 1.6583475942 0.000000e+00 */0 512 1.6583475942 0.000000e+00 */0 1024 1.6583475942 0.000000e+00 */0 Exact 1.6583475942 Problem 14 1 0.0000000000 5.000002e-01 2 0.0000000369 5.000002e-01 1 4 0.0270625179 4.729377e-01 1.05722 8 0.4708763285 2.912388e-02 16.2388 16 0.5736380465 7.363784e-02 0.395502 32 0.4932257487 6.774462e-03 10.8699 64 0.5000771817 7.697052e-05 88.0137 128 0.5000000361 1.750487e-07 439.709 256 0.5000000000 2.111660e-07 0.828962 512 0.5000000000 2.111660e-07 1 1024 0.5000000000 2.111660e-07 1 Exact 0.5000002112 Problem 15 1 0.0000012585 9.999987e-01 2 0.0036986627 9.963013e-01 1.00371 4 0.1417853867 8.582146e-01 1.1609 8 0.6210783832 3.789216e-01 2.26489 16 0.9479094143 5.209059e-02 7.27428 32 0.9982230214 1.776979e-03 29.3141 64 0.9999810687 1.893131e-05 93.8645 128 0.9999998955 1.045036e-07 181.155 256 0.9999999996 4.498557e-10 232.305 512 1.0000000000 1.801892e-12 249.657 1024 1.0000000000 7.216450e-15 249.692 Exact 1.0000000000 Problem 16 1 0.2369757743 2.566589e-01 2 0.4005961755 9.303848e-02 2.75863 4 0.5090877053 1.545305e-02 6.02072 8 0.5037194603 1.008481e-02 1.53231 16 0.4931699566 4.646943e-04 21.702 32 0.4936176093 1.704163e-05 27.2682 64 0.4936349812 3.303491e-07 51.5867 128 0.4936346510 1.103804e-10 2992.82 256 0.4936346509 5.551115e-17 1.98844e+06 512 0.4936346509 5.551115e-17 1 1024 0.4936346509 0.000000e+00 */0 Exact 0.4936346509 Problem 17 1 0.9972353096 4.972353e-01 2 0.5159871457 1.598715e-02 31.1022 4 0.5000000000 1.110223e-15 1.43999e+13 8 0.5000000000 6.661338e-16 1.66667 16 0.5000000000 4.440892e-16 1.5 32 0.5000000000 0.000000e+00 */0 64 0.5000000000 1.110223e-16 0 128 0.5000000000 1.110223e-16 1 256 0.5000000000 5.551115e-17 2 512 0.5000000000 0.000000e+00 */0 1024 0.5000000000 1.110223e-16 0 Exact 0.5000000000 Problem 18 1 0.1705573488 6.749800e-10 2 0.1705573495 3.126416e-12 215.896 4 0.1705573495 1.221245e-14 256.002 8 0.1705573495 5.551115e-17 220 16 0.1705573495 0.000000e+00 */0 32 0.1705573495 0.000000e+00 */0 64 0.1705573495 2.775558e-17 0 128 0.1705573495 2.775558e-17 1 256 0.1705573495 0.000000e+00 */0 512 0.1705573495 2.775558e-17 0 1024 0.1705573495 0.000000e+00 */0 Exact 0.1705573495 Problem 19 1 -0.9685359779 3.146402e-02 2 -0.9842679210 1.573208e-02 1.99999 4 -0.9921339600 7.866040e-03 2 8 -0.9960669800 3.933020e-03 2 16 -0.9980334900 1.966510e-03 2 32 -0.9990167450 9.832550e-04 2 64 -0.9995083725 4.916275e-04 2 128 -0.9997541862 2.458138e-04 2 256 -0.9998770931 1.229069e-04 2 512 -0.9999385466 6.145344e-05 2 1024 -0.9999692733 3.072672e-05 2 Exact -1.0000000000 Problem 20 1 1.5622671487 2.129295e-03 2 1.5644059378 9.493715e-06 224.285 4 1.5643964663 2.224436e-08 426.792 8 1.5643964441 2.913225e-13 76356.5 16 1.5643964441 2.220446e-16 1312 32 1.5643964441 0.000000e+00 */0 64 1.5643964441 2.220446e-16 0 128 1.5643964441 0.000000e+00 */0 256 1.5643964441 0.000000e+00 */0 512 1.5643964441 2.220446e-16 0 1024 1.5643964441 2.220446e-16 1 Exact 1.5643964441 Problem 21 1 0.1283744447 8.242829e-02 2 0.1971497387 1.365300e-02 6.03738 4 0.1976779144 1.312482e-02 1.04024 8 0.1976803154 1.312242e-02 1.00018 16 0.2108417318 3.899553e-05 336.511 32 0.2098124772 9.902591e-04 0.0393791 64 0.2099754895 8.272468e-04 1.19705 128 0.2100037145 7.990218e-04 1.03532 256 0.2108428631 4.012676e-05 19.9124 512 0.2108086095 5.873217e-06 6.83216 1024 0.2108026709 6.538999e-08 89.8183 Exact 0.2108027363 Problem 22 1 0.7280895172 1.339604e-05 2 0.7281029523 3.911765e-08 342.455 4 0.7281029132 2.125433e-11 1840.46 8 0.7281029132 8.326673e-14 255.256 16 0.7281029132 3.330669e-16 250 32 0.7281029132 1.110223e-16 3 64 0.7281029132 0.000000e+00 */0 128 0.7281029132 0.000000e+00 */0 256 0.7281029132 0.000000e+00 */0 512 0.7281029132 0.000000e+00 */0 1024 0.7281029132 0.000000e+00 */0 Exact 0.7281029132 Problem 23 1 3.1766518355 2.551939e+00 2 -0.5948891377 1.219602e+00 2.09243 4 2.2527500350 1.628037e+00 0.749125 8 1.8440569077 1.219344e+00 1.33517 16 -3.1885601604 3.813273e+00 0.319763 32 2.4547036767 1.829990e+00 2.08377 64 -2.1449142004 2.769627e+00 0.660735 128 1.2918704801 6.671572e-01 4.15139 256 -1.7313509001 2.356064e+00 0.283166 512 -1.7252108192 2.349924e+00 1.00261 1024 2.7242178218 2.099505e+00 1.11928 Exact 0.6247132564 Problem 24 1 0.0036354153 1.039016e-02 2 0.0152560870 2.201083e-02 0.472048 4 0.0047895323 1.154428e-02 1.90664 8 -0.0056119280 1.142817e-03 10.1016 16 -0.0065932484 1.614971e-04 7.07639 32 -0.0065165818 2.381637e-04 0.678093 64 -0.0067886200 3.387446e-05 7.03077 128 -0.0067308024 2.394314e-05 1.41479 256 -0.0067796654 2.491993e-05 0.960803 512 -0.0067481315 6.614005e-06 3.76775 1024 -0.0067527486 1.996917e-06 3.31211 Exact -0.0067547455 Problem 25 1 -1.8028878166 1.920235e-01 2 -1.5727869092 3.807739e-02 5.04298 4 -1.5657576906 4.510661e-02 0.844164 8 -1.6013447047 9.519597e-03 4.73829 16 -1.5995876461 1.127666e-02 0.844186 32 -1.6084844027 2.379899e-03 4.73829 64 -1.6080451381 2.819164e-03 0.844186 128 -1.6102693272 5.949748e-04 4.73829 256 -1.6101595111 7.047910e-04 0.844186 512 -1.6107155583 1.487437e-04 4.73829 1024 -1.6106881043 1.761977e-04 0.844186 Exact -1.6108643021 Problem 26 1 7.9409163321 1.401019e-02 2 7.9526324233 2.294098e-03 6.10706 4 7.9549630925 3.657153e-05 62.7291 8 7.9549265223 1.336596e-09 27361.7 16 7.9549265210 1.776357e-15 752436 32 7.9549265210 1.776357e-15 1 64 7.9549265210 3.552714e-15 0.5 128 7.9549265210 3.552714e-15 1 256 7.9549265210 3.552714e-15 1 512 7.9549265210 3.552714e-15 1 1024 7.9549265210 1.776357e-15 2 Exact 7.9549265210 Problem 27 1 0.7976637401 4.345318e-02 2 0.8130999230 2.801699e-02 1.55096 4 0.8230932496 1.802367e-02 1.55446 8 0.8295461596 1.157076e-02 1.55769 16 0.8337029464 7.413970e-03 1.56067 32 0.8363746989 4.742218e-03 1.5634 64 0.8380884570 3.028460e-03 1.56588 128 0.8391856771 1.931240e-03 1.56814 256 0.8398869738 1.229943e-03 1.57019 512 0.8403345251 7.823915e-04 1.57203 1024 0.8406197459 4.971707e-04 1.57369 Exact 0.8411169166 Problem 28 1 0.1241909823 1.042363e-01 2 -0.1772555987 1.972103e-01 0.528554 4 0.0948974721 7.494280e-02 2.63148 8 0.2274216912 2.074670e-01 0.361228 16 0.3541056582 3.341510e-01 0.620878 32 0.0225451321 2.590463e-03 128.993 64 0.0199423656 1.230371e-05 210.543 128 0.0199546509 1.838019e-08 669.4 256 0.0199546692 6.043622e-11 304.126 512 0.0199546693 2.267908e-13 266.484 1024 0.0199546693 9.298118e-16 243.91 Exact 0.0199546693 Problem 29 1 0.3461157150 3.926290e-02 2 0.3186293426 1.177652e-02 3.334 4 0.3025417108 4.311109e-03 2.73167 8 0.3105229096 3.670090e-03 1.17466 16 0.3070278451 1.750256e-04 20.9689 32 0.3070250353 1.722159e-04 1.01632 64 0.3070250353 1.722159e-04 1 128 0.3070250353 1.722159e-04 1 256 0.3067751146 7.770480e-05 2.21628 512 0.3069000812 4.726176e-05 1.64414 1024 0.3068454222 7.397290e-06 6.38906 Exact 0.3068528194 Problem 30 1 -23.1023498041 1.857478e+01 2 1.5330145378 6.060584e+00 3.06485 4 -4.1050143786 4.225552e-01 14.3427 8 -4.5304458131 2.876188e-03 146.915 16 -4.5275717566 2.131468e-06 1349.39 32 -4.5275696317 6.586663e-09 323.604 64 -4.5275696252 2.436451e-11 270.338 128 -4.5275696252 7.904788e-14 308.225 256 -4.5275696252 7.993606e-15 9.88889 512 -4.5275696252 7.993606e-15 1 1024 -4.5275696252 2.664535e-15 3 Exact -4.5275696252 Problem 31 1 2.0472850091 6.043503e-01 2 2.6554264456 3.791118e-03 159.412 4 2.6508177651 8.175622e-04 4.6371 8 2.6516451321 9.804786e-06 83.384 16 2.6516353507 2.338863e-08 419.212 32 2.6516353273 8.215650e-14 284684 64 2.6516353273 4.440892e-16 185 128 2.6516353273 4.440892e-16 1 256 2.6516353273 4.440892e-16 1 512 2.6516353273 4.440892e-16 1 1024 2.6516353273 0.000000e+00 */0 Exact 2.6516353273 Problem 32 1 -12.0701894903 1.568261e-04 2 -12.0703430780 3.238376e-06 48.4274 4 -12.0703463014 1.501408e-08 215.689 8 -12.0703463163 6.075673e-11 247.118 16 -12.0703463164 2.451372e-13 247.848 32 -12.0703463164 5.329071e-15 46 64 -12.0703463164 3.552714e-15 1.5 128 -12.0703463164 3.552714e-15 1 256 -12.0703463164 5.329071e-15 0.666667 512 -12.0703463164 3.552714e-15 1.5 1024 -12.0703463164 3.552714e-15 1 Exact -12.0703463164 Problem 33 1 0.8803989373 5.827988e-03 2 0.8833523725 2.874553e-03 2.02744 4 0.8848180410 1.408884e-03 2.0403 8 0.8855392483 6.876771e-04 2.04876 16 0.8858921197 3.348057e-04 2.05396 32 0.8860641466 1.627788e-04 2.05681 64 0.8861478302 7.909524e-05 2.05801 128 0.8861884934 3.843201e-05 2.05806 256 0.8862082449 1.868060e-05 2.05732 512 0.8862178399 9.085563e-06 2.05607 1024 0.8862225032 4.422261e-06 2.05451 Exact 0.8862269255 Problem 34 1 1085.2526666667 4.547474e-13 2 1085.2526666667 0.000000e+00 */0 4 1085.2526666667 0.000000e+00 */0 8 1085.2526666667 2.273737e-13 0 16 1085.2526666667 0.000000e+00 */0 32 1085.2526666667 2.273737e-13 0 64 1085.2526666667 2.273737e-13 1 128 1085.2526666667 2.273737e-13 1 256 1085.2526666667 0.000000e+00 */0 512 1085.2526666667 2.273737e-13 0 1024 1085.2526666667 2.273737e-13 1 Exact 1085.2526666667 Problem 35 1 29.1002123752 3.100212e+00 2 21.4436678601 4.556332e+00 0.680418 4 121.7402202610 9.574022e+01 0.0475906 8 32.2504998896 6.250500e+00 15.3172 16 30.6849543836 4.684954e+00 1.33416 32 26.5430244604 5.430245e-01 8.62752 64 25.8498488780 1.501511e-01 3.61652 128 25.4517981693 5.482018e-01 0.273898 256 25.6420355503 3.579644e-01 1.53144 512 25.8885103174 1.114897e-01 3.21074 1024 25.7865157557 2.134842e-01 0.522238 Exact 26.0000000000 Problem 36 1 6.2985367083 9.370146e+01 2 8.3412710707 9.165873e+01 1.02229 4 10.5306268443 8.946937e+01 1.02447 8 12.8378043397 8.716220e+01 1.02647 16 15.2372048669 8.476280e+01 1.02831 32 17.7061299021 8.229387e+01 1.03 64 20.2245074444 7.977549e+01 1.03157 128 22.7746420287 7.722536e+01 1.03302 256 25.3409864405 7.465901e+01 1.03437 512 27.9099333495 7.209007e+01 1.03564 1024 30.4696252153 6.953037e+01 1.03681 Exact 100.0000000000 Problem 37 1 0.0338324865 3.101966e+00 2 0.0818373833 3.053961e+00 1.01572 4 0.1972906396 2.938508e+00 1.03929 8 1.2129948068 1.922804e+00 1.52824 16 0.6439947048 2.491804e+00 0.771651 32 1.6451820349 1.490617e+00 1.67166 64 3.2377788831 1.019802e-01 14.6167 128 2.5987378446 5.370609e-01 0.189886 256 3.1296098507 6.188858e-03 86.7787 512 3.1357319618 6.674732e-05 92.7207 1024 3.1358016412 2.932078e-06 22.7645 Exact 3.1357987092 Problem 38 1 1.5130472578 9.737903e-01 2 0.4066598555 1.325971e-01 7.34398 4 0.5406945413 1.437627e-03 92.2333 8 0.5392574381 5.233767e-07 2746.83 16 0.5392569147 8.881784e-16 5.8927e+08 32 0.5392569147 4.440892e-16 2 64 0.5392569147 1.110223e-16 4 128 0.5392569147 0.000000e+00 */0 256 0.5392569147 2.220446e-16 0 512 0.5392569147 2.220446e-16 1 1024 0.5392569147 2.220446e-16 1 Exact 0.5392569147 Problem 39 1 6.7813962640 3.993703e+00 2 5.6116337623 2.823940e+00 1.41423 4 4.7845199749 1.996826e+00 1.41421 8 4.1996630890 1.411969e+00 1.41421 16 3.7861068298 9.984131e-01 1.41421 32 3.4936783946 7.059847e-01 1.41421 64 3.2869002650 4.992066e-01 1.41421 128 3.1406860474 3.529923e-01 1.41421 256 3.0372969826 2.496033e-01 1.41421 512 2.9641898738 1.764962e-01 1.41421 1024 2.9124953414 1.248016e-01 1.41421 Exact 2.7876937002 Problem 40 1 2.1050720270 5.938846e-01 2 2.2846802120 4.142764e-01 1.43355 4 2.4172034910 2.817531e-01 1.47035 8 2.6515208879 4.743571e-02 5.93968 16 2.5480581562 1.508984e-01 0.314355 32 2.6057257740 9.323083e-02 1.61855 64 2.6561698690 4.278673e-02 2.17897 128 2.6376123619 6.134424e-02 0.697486 256 2.7490177919 5.006119e-02 1.22539 512 2.6777973985 2.115920e-02 2.36593 1024 2.6842877650 1.466884e-02 1.44246 Exact 2.6989566013 Problem 41 1 4.2944171037 1.801168e+00 2 4.8674841785 1.228101e+00 1.46663 4 5.2529761353 8.426090e-01 1.4575 8 5.5085553261 5.870298e-01 1.43538 16 5.6831381879 4.124469e-01 1.42329 32 5.8047925599 2.907925e-01 1.41835 64 5.8902530944 2.053320e-01 1.41621 128 5.9504939682 1.450911e-01 1.41519 256 5.9930254198 1.025597e-01 1.4147 512 6.0230768643 7.250824e-02 1.41446 1024 6.0443184139 5.126669e-02 1.41433 Exact 6.0955851028 Problem 42 1 2.9673629739 1.013423e+00 2 3.1576446695 8.231416e-01 1.23117 4 3.3121903408 6.685959e-01 1.23115 8 3.4377181914 5.430681e-01 1.23115 16 3.5396780342 4.411082e-01 1.23114 32 3.6224950687 3.582912e-01 1.23114 64 3.6897633846 2.910229e-01 1.23114 128 3.7444022316 2.363840e-01 1.23114 256 3.7887827653 1.920035e-01 1.23114 512 3.8248309599 1.559553e-01 1.23114 1024 3.8541111924 1.266751e-01 1.23114 Exact 3.9807862525 Problem 43 1 2.1071089161 8.844601e-01 2 2.2729568681 7.186121e-01 1.23079 4 2.4077876092 5.837814e-01 1.23096 8 2.5173537402 4.742152e-01 1.23105 16 2.6063700103 3.851990e-01 1.23109 32 2.6786827590 3.128862e-01 1.23112 64 2.7374229926 2.541460e-01 1.23113 128 2.7851367151 2.064323e-01 1.23113 256 2.8238931415 1.676758e-01 1.23114 512 2.8553735328 1.361955e-01 1.23114 1024 2.8809437394 1.106252e-01 1.23114 Exact 2.9915689877 Problem 44 1 -0.0235999952 6.499705e-03 2 -0.0297060647 3.936359e-04 16.512 4 -0.0300941057 5.594865e-06 70.3566 8 -0.0300996671 3.338153e-08 167.604 16 -0.0300997004 1.454571e-10 229.494 32 -0.0300997005 5.837310e-13 249.185 64 -0.0300997005 2.307182e-15 253.006 128 -0.0300997005 3.122502e-17 73.8889 256 -0.0300997005 6.938894e-18 4.5 512 -0.0300997005 1.734723e-17 0.4 1024 -0.0300997005 1.734723e-17 1 Exact -0.0300997005 Problem 45 1 -0.3628589060 7.015220e-02 2 -0.3412681851 4.856148e-02 1.44461 4 -0.3266515040 3.394479e-02 1.4306 8 -0.3165664257 2.385972e-02 1.42268 16 -0.3095269201 1.682021e-02 1.41851 32 -0.3045821977 1.187549e-02 1.41638 64 -0.3010974951 8.390785e-03 1.4153 128 -0.2986376062 5.930896e-03 1.41476 256 -0.2968996785 4.192969e-03 1.41449 512 -0.2956713005 2.964591e-03 1.41435 1024 -0.2948028909 2.096181e-03 1.41428 Exact -0.2927067098 Problem 46 1 6.0633722527 5.718707e-03 2 6.0689035879 1.873716e-04 30.5207 4 6.0690947159 3.756318e-06 49.8817 8 6.0690909607 1.169730e-09 3211.27 16 6.0690909596 8.881784e-16 1.317e+06 32 6.0690909596 8.881784e-16 1 64 6.0690909596 8.881784e-16 1 128 6.0690909596 8.881784e-16 1 256 6.0690909596 8.881784e-16 1 512 6.0690909596 8.881784e-16 1 1024 6.0690909596 8.881784e-16 1 Exact 6.0690909596 Problem 47 1 -0.4488775545 4.433110e-03 2 -0.4462963138 1.851869e-03 2.39386 4 -0.4451997718 7.553274e-04 2.45174 8 -0.4447470579 3.026134e-04 2.49601 16 -0.4445640085 1.195641e-04 2.53097 32 -0.4444911623 4.671790e-05 2.55928 64 -0.4444625335 1.808903e-05 2.58266 128 -0.4444513956 6.951139e-06 2.60231 256 -0.4444470985 2.654069e-06 2.61905 512 -0.4444454523 1.007818e-06 2.63348 1024 -0.4444448253 3.808761e-07 2.64605 Exact -0.4444444444 Problem 48 1 -2.5624608364 1.437539e+00 2 -2.8885886044 1.111411e+00 1.29344 4 -3.1469968378 8.530032e-01 1.30294 8 -3.3493770598 6.506229e-01 1.31106 16 -3.5063817951 4.936182e-01 1.31807 32 -3.6272299101 3.727701e-01 1.32419 64 -3.7196325857 2.803674e-01 1.32958 128 -3.7898856452 2.101144e-01 1.33436 256 -3.8430371369 1.569629e-01 1.33862 512 -3.8830781677 1.169218e-01 1.34246 1024 -3.9131289905 8.687101e-02 1.34592 Exact -4.0000000000 Problem 49 1 52.4910941666 2.496542e-01 2 50.7370083556 2.003740e+00 0.124594 4 52.2435120869 4.972363e-01 4.02975 8 52.5620808722 1.786675e-01 2.78303 16 52.6861419522 5.460643e-02 3.27191 32 52.6313503128 1.093981e-01 0.499154 64 52.7231496725 1.759871e-02 6.21625 128 52.6832957236 5.745266e-02 0.306317 256 52.7117098643 2.903852e-02 1.9785 512 52.7322573165 8.491067e-03 3.41989 1024 52.7377203087 3.028075e-03 2.80411 Exact 52.7407483835 Problem 50 1 -0.1830369009 5.490005e-02 2 0.0679213127 1.960582e-01 0.280019 4 -0.1313153499 3.178502e-03 61.6826 8 -0.1284440932 3.072448e-04 10.3452 16 -0.1282159099 7.906152e-05 3.88615 32 -0.1281567272 1.987879e-05 3.97718 64 -0.1281418253 4.976910e-06 3.9942 128 -0.1281380931 1.244682e-06 3.99854 256 -0.1281371596 3.111990e-07 3.99963 512 -0.1281369262 7.780152e-08 3.99991 1024 -0.1281368678 1.945049e-08 3.99998 Exact -0.1281368484 Problem 51 1 -0.1891691460 8.644413e-03 2 -0.1892975285 8.516031e-03 1.01508 4 -0.1892836175 8.529942e-03 0.998369 8 -0.1892783926 8.535167e-03 0.999388 16 -0.1892763997 8.537159e-03 0.999767 32 -0.1892756480 8.537911e-03 0.999912 64 -0.1892753641 8.538195e-03 0.999967 128 -0.1892752561 8.538303e-03 0.999987 256 -0.1892752146 8.538345e-03 0.999995 512 -0.1892751984 8.538361e-03 0.999998 1024 -0.1892751921 8.538367e-03 0.999999 Exact -0.1978135592 Problem 52 1 -0.1658151993 7.587119e-02 2 -16.4349640506 1.634502e+01 0.00464185 4 16.2832112558 1.637316e+01 0.998282 8 -16.4535891173 1.636365e+01 1.00058 16 16.2757792171 1.636572e+01 0.999873 32 -16.4554040579 1.636546e+01 1.00002 64 16.2755328729 1.636548e+01 0.999999 128 -16.4554203982 1.636548e+01 1 256 16.2755323907 1.636548e+01 1 512 -16.4554204046 1.636548e+01 1 1024 16.2755323907 1.636548e+01 1 Exact -0.0899440070 Problem 53 1 1.3351499749 1.694728e-01 2 1.2443433218 2.602794e-01 0.651119 4 2.1383854702 6.337627e-01 0.410689 8 1.3962665159 1.083562e-01 5.84888 16 1.4955031493 9.119613e-03 11.8817 32 1.4504707539 5.415201e-02 0.168408 64 1.4652879192 3.933484e-02 1.37669 128 1.5121358747 7.513112e-03 5.23549 256 1.4894693484 1.515341e-02 0.495803 512 1.4897327732 1.488999e-02 1.01769 1024 1.5013159972 3.306765e-03 4.50289 Exact 1.5046227625 Problem 54 1 1.1978133015 4.311276e-02 2 1.2466068790 9.190634e-02 0.469095 4 1.1477459287 6.954610e-03 13.2152 8 1.1546647884 3.574995e-05 194.535 16 1.1547005374 9.499239e-10 37634.5 32 1.1547005384 2.220446e-16 4.27808e+06 64 1.1547005384 2.220446e-16 1 128 1.1547005384 2.220446e-16 1 256 1.1547005384 2.220446e-16 1 512 1.1547005384 2.220446e-16 1 1024 1.1547005384 2.220446e-16 1 Exact 1.1547005384 Problem 55 1 0.5068639753 1.805343e-03 2 0.5050460432 1.258923e-05 143.404 4 0.5050586311 1.341399e-09 9385.15 8 0.5050586324 8.353762e-12 160.574 16 0.5050586325 3.363976e-14 248.33 32 0.5050586325 1.110223e-16 303 64 0.5050586325 0.000000e+00 */0 128 0.5050586325 1.110223e-16 0 256 0.5050586325 0.000000e+00 */0 512 0.5050586325 0.000000e+00 */0 1024 0.5050586325 0.000000e+00 */0 Exact 0.5050586325 Problem 56 1 1.9787045692 1.354784e-02 2 1.9930197208 7.673128e-04 17.6562 4 1.9922438301 8.577808e-06 89.4532 8 1.9922524167 8.746735e-09 980.687 16 1.9922524080 1.028533e-11 850.409 32 1.9922524080 2.864375e-14 359.078 64 1.9922524080 2.220446e-16 129 128 1.9922524080 0.000000e+00 */0 256 1.9922524080 2.220446e-16 0 512 1.9922524080 2.220446e-16 1 1024 1.9922524080 2.220446e-16 1 Exact 1.9922524080 Problem 57 1 0.3999503850 4.961499e-05 2 0.3999912282 8.771771e-06 5.65621 4 0.3999984493 1.550651e-06 5.65683 8 0.3999997259 2.741190e-07 5.65685 16 0.3999999515 4.845785e-08 5.65685 32 0.3999999914 8.566219e-09 5.65685 64 0.3999999985 1.514308e-09 5.65685 128 0.3999999997 2.676944e-10 5.65685 256 0.4000000000 4.732215e-11 5.65685 512 0.4000000000 8.365475e-12 5.65684 1024 0.4000000000 1.478873e-12 5.65666 Exact 0.4000000000 midpoint_test(): Composite midpoint quadrature rule. N Approx Error Ratio Problem 1 1 1.6487212707 6.956056e-02 2 1.7005127167 1.776911e-02 3.91469 4 1.7138152798 4.466549e-03 3.97826 8 1.7171636650 1.118163e-03 3.99454 16 1.7180021921 2.796364e-04 3.99863 32 1.7182119134 6.991508e-05 3.99966 64 1.7182643493 1.747914e-05 3.99991 128 1.7182774587 4.369809e-06 3.99998 256 1.7182807360 1.092454e-06 3.99999 512 1.7182815553 2.731135e-07 4 1024 1.7182817602 6.827838e-08 4 2048 1.7182818114 1.706960e-08 4 4096 1.7182818242 4.267399e-09 4 8192 1.7182818274 1.066850e-09 4 16384 1.7182818282 2.667122e-10 4 32768 1.7182818284 6.667777e-11 4.00002 65536 1.7182818284 1.666933e-11 4.00003 131072 1.7182818285 4.167333e-12 4 262144 1.7182818285 1.041611e-12 4.00085 524288 1.7182818285 2.602363e-13 4.00256 1048576 1.7182818285 6.461498e-14 4.02749 Exact 1.7182818285 Problem 2 1 1.0000000000 3.000000e-01 2 0.5000000000 2.000000e-01 1.5 4 0.7500000000 5.000000e-02 4 8 0.7500000000 5.000000e-02 1 16 0.6875000000 1.250000e-02 4 32 0.6875000000 1.250000e-02 1 64 0.7031250000 3.125000e-03 4 128 0.7031250000 3.125000e-03 1 256 0.6992187500 7.812500e-04 4 512 0.6992187500 7.812500e-04 1 1024 0.7001953125 1.953125e-04 4 2048 0.7001953125 1.953125e-04 1 4096 0.6999511719 4.882812e-05 4 8192 0.6999511719 4.882812e-05 1 16384 0.7000122070 1.220703e-05 4 32768 0.7000122070 1.220703e-05 1 65536 0.6999969482 3.051758e-06 4 131072 0.6999969482 3.051758e-06 1 262144 0.7000007629 7.629395e-07 4 524288 0.7000007629 7.629395e-07 1 1048576 0.6999998093 1.907349e-07 4 Exact 0.7000000000 Problem 3 1 0.7071067812 4.044011e-02 2 0.6830127019 1.634604e-02 2.474 4 0.6729773970 6.310730e-03 2.5902 8 0.6690321721 2.365505e-03 2.66781 16 0.6675366757 8.700090e-04 2.71894 32 0.6669826865 3.160198e-04 2.75302 64 0.6667805032 1.138365e-04 2.77608 128 0.6667074407 4.077399e-05 2.79189 256 0.6666812141 1.454746e-05 2.80283 512 0.6666718429 5.176221e-06 2.81044 1024 0.6666685050 1.838300e-06 2.81576 2048 0.6666673187 6.519947e-07 2.8195 4096 0.6666668977 2.310293e-07 2.82213 8192 0.6666667485 8.180978e-08 2.82398 16384 0.6666666956 2.895627e-08 2.82529 32768 0.6666666769 1.024563e-08 2.82621 65536 0.6666666703 3.624385e-09 2.82686 131072 0.6666666679 1.281916e-09 2.82732 262144 0.6666666671 4.533512e-10 2.82764 524288 0.6666666668 1.603154e-10 2.82787 1048576 0.6666666667 5.668810e-11 2.82803 Exact 0.6666666667 Problem 4 1 -0.1600000000 6.394282e-01 2 0.3196666522 1.597616e-01 4.00239 4 0.4394073832 4.002084e-02 3.99196 8 0.4694166388 1.001159e-02 3.99745 16 0.4769249100 2.503317e-03 3.99933 32 0.4788023710 6.258557e-04 3.99983 64 0.4792717611 1.564656e-04 3.99996 128 0.4793891102 3.911650e-05 3.99999 256 0.4794184476 9.779132e-06 4 512 0.4794257819 2.444783e-06 4 1024 0.4794276155 6.111959e-07 4 2048 0.4794280739 1.527990e-07 4 4096 0.4794281885 3.819974e-08 4 8192 0.4794282171 9.549936e-09 4 16384 0.4794282243 2.387484e-09 4 32768 0.4794282261 5.968709e-10 4 65536 0.4794282265 1.492176e-10 4 131072 0.4794282267 3.730433e-11 4.00001 262144 0.4794282267 9.326040e-12 4.00002 524288 0.4794282267 2.331524e-12 3.99998 1048576 0.4794282267 5.827561e-13 4.00086 Exact 0.4794282267 Problem 5 1 2.2222222222 6.399893e-01 2 1.6494845361 6.725157e-02 9.51635 4 1.5969046906 1.467173e-02 4.58375 8 1.5859426924 3.709729e-03 3.95493 16 1.5831615948 9.286311e-04 3.99484 32 1.5824651828 2.322191e-04 3.99894 64 1.5822910221 5.805841e-05 3.99975 128 1.5822474786 1.451483e-05 3.99994 256 1.5822365925 3.628720e-06 3.99998 512 1.5822338709 9.071810e-07 4 1024 1.5822331905 2.267953e-07 4 2048 1.5822330204 5.669883e-08 4 4096 1.5822329779 1.417471e-08 4 8192 1.5822329673 3.543677e-09 4 16384 1.5822329646 8.859191e-10 4 32768 1.5822329640 2.214795e-10 4.00001 65536 1.5822329638 5.536971e-11 4.00001 131072 1.5822329637 1.384248e-11 3.99998 262144 1.5822329637 3.460565e-12 4.00006 524288 1.5822329637 8.655299e-13 3.9982 1048576 1.5822329637 2.162714e-13 4.00205 Exact 1.5822329637 Problem 6 1 1.4142135624 4.623357e-02 2 1.0000000000 4.604471e-01 0.10041 4 1.4920296963 3.158256e-02 14.5792 8 1.4727748815 1.232775e-02 2.56191 16 1.4651034810 4.656349e-03 2.64751 32 1.4621684024 1.721271e-03 2.70518 64 1.4610744793 6.273476e-04 2.74373 128 1.4606736315 2.264998e-04 2.76975 256 1.4605283864 8.125462e-05 2.78753 512 1.4604761534 2.902157e-05 2.7998 1024 1.4604574659 1.033411e-05 2.80833 2048 1.4604508038 3.672017e-06 2.81429 4096 1.4604484346 1.302843e-06 2.81846 8192 1.4604475936 4.617721e-07 2.8214 16384 1.4604472953 1.635479e-07 2.82347 32768 1.4604471897 5.789464e-08 2.82492 65536 1.4604471523 2.048677e-08 2.82595 131072 1.4604471390 7.247650e-09 2.82668 262144 1.4604471344 2.563552e-09 2.82719 524288 1.4604471327 9.066325e-10 2.82755 1048576 1.4604471321 3.206126e-10 2.82781 Exact 1.4604471318 Problem 7 1 1.4142135624 5.857864e-01 2 1.5773502692 4.226497e-01 1.38599 4 1.6988440796 3.011559e-01 1.40342 8 1.7864610017 2.135390e-01 1.41031 16 1.8488566846 1.511433e-01 1.41282 32 1.8930883597 1.069116e-01 1.41372 64 1.9243927557 7.560724e-02 1.41404 128 1.9465352800 5.346472e-02 1.41415 256 1.9621941527 3.780585e-02 1.41419 512 1.9732670837 2.673292e-02 1.41421 1024 1.9810969373 1.890306e-02 1.41421 2048 1.9866335071 1.336649e-02 1.41421 4096 1.9905484599 9.451540e-03 1.41421 8192 1.9933167514 6.683249e-03 1.41421 16384 1.9952742294 4.725771e-03 1.41421 32768 1.9966583755 3.341624e-03 1.41421 65536 1.9976371147 2.362885e-03 1.41421 131072 1.9983291878 1.670812e-03 1.41421 262144 1.9988185573 1.181443e-03 1.41421 524288 1.9991645939 8.354061e-04 1.41421 1048576 1.9994092787 5.907213e-04 1.41421 Exact 2.0000000000 Problem 8 1 0.9411764706 7.420348e-02 2 0.8778764332 1.090345e-02 6.80551 4 0.8696054064 2.632419e-03 4.14199 8 0.8676258084 6.528211e-04 4.03237 16 0.8671358590 1.628717e-04 4.00819 32 0.8670136844 4.069706e-05 4.00205 64 0.8669831603 1.017296e-05 4.00051 128 0.8669755305 2.543159e-06 4.00013 256 0.8669736231 6.357846e-07 4.00003 512 0.8669731463 1.589458e-07 4.00001 1024 0.8669730271 3.973644e-08 4 2048 0.8669729973 9.934108e-09 4 4096 0.8669729898 2.483527e-09 4 8192 0.8669729880 6.208818e-10 4 16384 0.8669729875 1.552204e-10 4 32768 0.8669729874 3.880518e-11 3.99999 65536 0.8669729873 9.701351e-12 3.99998 131072 0.8669729873 2.425282e-12 4.00009 262144 0.8669729873 6.066259e-13 3.99799 524288 0.8669729873 1.516565e-13 4 1048576 0.8669729873 3.752554e-14 4.04142 Exact 0.8669729873 Problem 9 1 1.0000000000 1.547005e-01 2 1.3333333333 1.786328e-01 0.866025 4 1.1428571429 1.184340e-02 15.0829 8 1.1546391753 6.136312e-05 193.005 16 1.1547005367 1.630567e-09 37633 32 1.1547005384 0.000000e+00 (*/0) 64 1.1547005384 0.000000e+00 (*/0) 128 1.1547005384 0.000000e+00 (*/0) 256 1.1547005384 0.000000e+00 (*/0) 512 1.1547005384 0.000000e+00 (*/0) 1024 1.1547005384 0.000000e+00 (*/0) 2048 1.1547005384 0.000000e+00 (*/0) 4096 1.1547005384 0.000000e+00 (*/0) 8192 1.1547005384 0.000000e+00 (*/0) 16384 1.1547005384 0.000000e+00 (*/0) 32768 1.1547005384 0.000000e+00 (*/0) 65536 1.1547005384 0.000000e+00 (*/0) 131072 1.1547005384 0.000000e+00 (*/0) 262144 1.1547005384 0.000000e+00 (*/0) 524288 1.1547005384 0.000000e+00 (*/0) 1048576 1.1547005384 6.661338e-16 0 Exact 1.1547005384 Problem 10 1 0.6666666667 2.648051e-02 2 0.6857142857 7.432895e-03 3.56261 4 0.6912198912 1.927289e-03 3.85666 8 0.6926605540 4.866265e-04 3.96051 16 0.6930252143 1.219662e-04 3.98985 32 0.6931166695 3.051106e-05 3.99744 64 0.6931395516 7.628987e-06 3.99936 128 0.6931452732 1.907323e-06 3.99984 256 0.6931467037 4.768356e-07 3.99996 512 0.6931470614 1.192092e-07 3.99999 1024 0.6931471508 2.980232e-08 4 2048 0.6931471731 7.450580e-09 4 4096 0.6931471787 1.862645e-09 4 8192 0.6931471801 4.656613e-10 4 16384 0.6931471804 1.164153e-10 4 32768 0.6931471805 2.910372e-11 4.00002 65536 0.6931471806 7.275958e-12 3.99998 131072 0.6931471806 1.819211e-12 3.99951 262144 0.6931471806 4.546363e-13 4.00147 524288 0.6931471806 1.136868e-13 3.99902 1048576 0.6931471806 2.864375e-14 3.96899 Exact 0.6931471806 Problem 11 1 0.3775406688 2.344824e-03 2 0.3793224000 5.630931e-04 4.16419 4 0.3797460335 1.394595e-04 4.03768 8 0.3798507085 3.478450e-05 4.00924 16 0.3798768019 8.691127e-06 4.0023 32 0.3798833206 2.172470e-06 4.00057 64 0.3798849499 5.430980e-07 4.00014 128 0.3798853573 1.357733e-07 4.00004 256 0.3798854591 3.394324e-08 4.00001 512 0.3798854846 8.485806e-09 4 1024 0.3798854909 2.121451e-09 4 2048 0.3798854925 5.303628e-10 4 4096 0.3798854929 1.325907e-10 4 8192 0.3798854930 3.314771e-11 4 16384 0.3798854930 8.286927e-12 4 32768 0.3798854930 2.071732e-12 4 65536 0.3798854930 5.179746e-13 3.99968 131072 0.3798854930 1.295630e-13 3.99786 262144 0.3798854930 3.241851e-14 3.99658 524288 0.3798854930 7.993606e-15 4.05556 1048576 0.3798854930 2.164935e-15 3.69231 Exact 0.3798854930 Problem 12 1 0.8243606354 4.685600e-02 2 0.7461345333 3.137010e-02 1.49365 4 0.7253315441 5.217309e-02 0.60127 8 0.7200497182 5.745492e-02 0.90807 16 0.7187241430 5.878049e-02 0.977449 32 0.7183924285 5.911221e-02 0.994388 64 0.7183094798 5.919515e-02 0.998599 128 0.7182887414 5.921589e-02 0.99965 256 0.7182835567 5.922108e-02 0.999912 512 0.7182822605 5.922237e-02 0.999978 1024 0.7182819365 5.922270e-02 0.999995 2048 0.7182818555 5.922278e-02 0.999999 4096 0.7182818352 5.922280e-02 1 8192 0.7182818301 5.922280e-02 1 16384 0.7182818289 5.922281e-02 1 32768 0.7182818286 5.922281e-02 1 65536 0.7182818285 5.922281e-02 1 131072 0.7182818285 5.922281e-02 1 262144 0.7182818285 5.922281e-02 1 524288 0.7182818285 5.922281e-02 1 1048576 0.7182818285 5.922281e-02 1 Exact 0.7775046341 Problem 13 1 -1.9178485493 3.576196e+00 2 1.8222776061 1.639300e-01 21.8154 4 1.6821492311 2.380164e-02 6.88734 8 1.6636482082 5.300614e-03 4.49035 16 1.6596364702 1.288876e-03 4.11259 32 1.6586676071 3.200129e-04 4.02758 64 1.6584274605 7.986627e-05 4.00686 128 1.6583675522 1.995802e-05 4.00171 256 1.6583525832 4.988972e-06 4.00043 512 1.6583488414 1.247210e-06 4.00011 1024 1.6583479060 3.118003e-07 4.00003 2048 1.6583476722 7.794995e-08 4.00001 4096 1.6583476137 1.948748e-08 4 8192 1.6583475991 4.871869e-09 4 16384 1.6583475954 1.217968e-09 4 32768 1.6583475945 3.044915e-10 4 65536 1.6583475943 7.612333e-11 3.99998 131072 1.6583475942 1.903033e-11 4.00011 262144 1.6583475942 4.758194e-12 3.99949 524288 1.6583475942 1.189715e-12 3.99944 1048576 1.6583475942 2.984279e-13 3.98661 Exact 1.6583475942 Problem 14 1 0.0000000000 5.000002e-01 2 0.0000000000 5.000002e-01 1 4 0.0000000000 5.000002e-01 1 8 0.0000000000 5.000002e-01 1 16 0.0000009624 4.999992e-01 1 32 0.0477349580 4.522653e-01 1.10554 64 0.4237727535 7.622746e-02 5.9331 128 0.4999661770 3.403412e-05 2239.74 256 0.5000000000 2.111660e-07 161.172 512 0.5000000000 2.111660e-07 1 1024 0.5000000000 2.111660e-07 1 2048 0.5000000000 2.111660e-07 1 4096 0.5000000000 2.111660e-07 1 8192 0.5000000000 2.111660e-07 1 16384 0.5000000000 2.111660e-07 1 32768 0.5000000000 2.111660e-07 1 65536 0.5000000000 2.111660e-07 1 131072 0.5000000000 2.111660e-07 1 262144 0.5000000000 2.111660e-07 1 524288 0.5000000000 2.111660e-07 1 1048576 0.5000000000 2.111660e-07 1 Exact 0.5000002112 Problem 15 1 0.0000000000 1.000000e+00 2 0.0000000000 1.000000e+00 1 4 0.0000000000 1.000000e+00 1 8 0.0000051168 9.999949e-01 1.00001 16 0.0063225818 9.936774e-01 1.00636 32 0.1572182584 8.427817e-01 1.17904 64 0.5653974781 4.346025e-01 1.9392 128 0.8571189287 1.428811e-01 3.04171 256 0.9613417350 3.865826e-02 3.696 512 0.9901345416 9.865458e-03 3.91855 1024 0.9975207839 2.479216e-03 3.97927 2048 0.9993793880 6.206120e-04 3.99479 4096 0.9998447964 1.552036e-04 3.9987 8192 0.9999611959 3.880405e-05 3.99967 16384 0.9999902988 9.701211e-06 3.99992 32768 0.9999975747 2.425315e-06 3.99998 65536 0.9999993937 6.063295e-07 3.99999 131072 0.9999998484 1.515824e-07 4 262144 0.9999999621 3.789561e-08 4 524288 0.9999999905 9.473903e-09 4 1048576 0.9999999976 2.368476e-09 4 Exact 1.0000000000 Problem 16 1 0.0254241123 4.682105e-01 2 0.0562605265 4.373741e-01 1.0705 4 0.1167501124 3.768845e-01 1.1605 8 0.2257441263 2.678905e-01 1.40686 16 0.3755442540 1.180904e-01 2.26852 32 0.4760202743 1.761438e-02 6.70421 64 0.4933133721 3.212788e-04 54.8258 128 0.4936345799 7.101607e-08 4524.03 256 0.4936346590 8.088513e-09 8.77987 512 0.4936346529 2.022139e-09 3.99998 1024 0.4936346514 5.055353e-10 4 2048 0.4936346510 1.263838e-10 4 4096 0.4936346509 3.159600e-11 3.99999 8192 0.4936346509 7.898959e-12 4.00002 16384 0.4936346509 1.974754e-12 3.99997 32768 0.4936346509 4.936607e-13 4.00022 65536 0.4936346509 1.234013e-13 4.00045 131072 0.4936346509 3.091971e-14 3.99102 262144 0.4936346509 7.771561e-15 3.97857 524288 0.4936346509 2.164935e-15 3.58974 1048576 0.4936346509 2.220446e-16 9.75 Exact 0.4936346509 Problem 17 1 0.0000000000 5.000000e-01 2 1.0000000000 5.000000e-01 1 4 0.5000000000 9.992007e-16 5.004e+14 8 0.5000000000 8.881784e-16 1.125 16 0.5000000000 4.996004e-16 1.77778 32 0.5000000000 0.000000e+00 (*/0) 64 0.5000000000 1.110223e-16 0 128 0.5000000000 2.220446e-16 0.5 256 0.5000000000 0.000000e+00 (*/0) 512 0.5000000000 0.000000e+00 (*/0) 1024 0.5000000000 0.000000e+00 (*/0) 2048 0.5000000000 0.000000e+00 (*/0) 4096 0.5000000000 0.000000e+00 (*/0) 8192 0.5000000000 0.000000e+00 (*/0) 16384 0.5000000000 0.000000e+00 (*/0) 32768 0.5000000000 0.000000e+00 (*/0) 65536 0.5000000000 0.000000e+00 (*/0) 131072 0.5000000000 0.000000e+00 (*/0) 262144 0.5000000000 0.000000e+00 (*/0) 524288 0.5000000000 1.110223e-16 0 1048576 0.5000000000 0.000000e+00 (*/0) Exact 0.5000000000 Problem 18 1 0.1887703344 1.821298e-02 2 0.1750359252 4.478576e-03 4.06669 4 0.1716725409 1.115191e-03 4.01597 8 0.1708358722 2.785227e-04 4.00395 16 0.1706269630 6.961354e-05 4.00099 32 0.1705747518 1.740231e-05 4.00025 64 0.1705617000 4.350512e-06 4.00006 128 0.1705584371 1.087624e-06 4.00002 256 0.1705576214 2.719057e-07 4 512 0.1705574175 6.797640e-08 4 1024 0.1705573665 1.699410e-08 4 2048 0.1705573538 4.248525e-09 4 4096 0.1705573506 1.062131e-09 4 8192 0.1705573498 2.655328e-10 4 16384 0.1705573496 6.638320e-11 4 32768 0.1705573495 1.659578e-11 4.00001 65536 0.1705573495 4.148931e-12 4.00001 131072 0.1705573495 1.037226e-12 4.00003 262144 0.1705573495 2.592926e-13 4.00021 524288 0.1705573495 6.483702e-14 3.99914 1048576 0.1705573495 1.615375e-14 4.01375 Exact 0.1705573495 Problem 19 1 -0.6931471806 3.068528e-01 2 -0.8369882168 1.630118e-01 1.8824 4 -0.9159514541 8.404855e-02 1.9395 8 -0.9573287524 4.267125e-02 1.96968 16 -0.9785018740 2.149813e-02 1.98488 32 -0.9892102631 1.078974e-02 1.99246 64 -0.9945949600 5.405040e-03 1.99624 128 -0.9972949369 2.705063e-03 1.99812 256 -0.9986468327 1.353167e-03 1.99906 512 -0.9993232574 6.767426e-04 1.99953 1024 -0.9996615890 3.384110e-04 1.99977 2048 -0.9998307845 1.692155e-04 1.99988 4096 -0.9999153898 8.461021e-05 1.99994 8192 -0.9999576943 4.230573e-05 1.99997 16384 -0.9999788470 2.115302e-05 1.99999 32768 -0.9999894235 1.057655e-05 1.99999 65536 -0.9999947117 5.288284e-06 2 131072 -0.9999973559 2.644144e-06 2 262144 -0.9999986779 1.322073e-06 2 524288 -0.9999993390 6.610365e-07 2 1048576 -0.9999996695 3.305183e-07 2 Exact -1.0000000000 Problem 20 1 1.9900497512 4.256533e-01 2 1.5936254980 2.922905e-02 14.5627 4 1.5747266826 1.033024e-02 2.82947 8 1.5669874771 2.591033e-03 3.98692 16 1.5650442435 6.477994e-04 3.99975 32 1.5645583939 1.619499e-04 4 64 1.5644369315 4.048743e-05 4 128 1.5644065659 1.012185e-05 4 256 1.5643989745 2.530463e-06 4 512 1.5643970767 6.326158e-07 4 1024 1.5643966022 1.581540e-07 4 2048 1.5643964836 3.953849e-08 4 4096 1.5643964540 9.884623e-09 4 8192 1.5643964465 2.471156e-09 4 16384 1.5643964447 6.177889e-10 4 32768 1.5643964442 1.544471e-10 4 65536 1.5643964441 3.861200e-11 3.99998 131072 1.5643964441 9.652945e-12 4.00002 262144 1.5643964441 2.413403e-12 3.99972 524288 1.5643964441 6.032952e-13 4.00037 1048576 1.5643964441 1.507683e-13 4.00147 Exact 1.5643964441 Problem 21 1 0.0098660372 2.009367e-01 2 0.3932572688 1.824545e-01 1.1013 4 0.1779810191 3.282172e-02 5.55896 8 0.1990730187 1.172972e-02 2.79817 16 0.2265812629 1.577853e-02 0.743398 32 0.2031783608 7.624375e-03 2.06948 64 0.2123092922 1.506556e-03 5.0608 128 0.2097282377 1.074499e-03 1.4021 256 0.2122362163 1.433480e-03 0.749574 512 0.2104958032 3.069331e-04 4.67033 1024 0.2108607780 5.804171e-05 5.28815 2048 0.2108027277 8.638047e-09 6719.31 4096 0.2108027389 2.573419e-09 3.35664 8192 0.2108027363 3.612999e-11 71.2267 16384 0.2108027357 5.981918e-10 0.0603987 32768 0.2108027356 7.567723e-10 0.790452 65536 0.2108027355 7.964174e-10 0.950221 131072 0.2108027355 8.063287e-10 0.987708 262144 0.2108027355 8.088065e-10 0.996937 524288 0.2108027355 8.094259e-10 0.999235 1048576 0.2108027355 8.095807e-10 0.999809 Exact 0.2108027363 Problem 22 1 0.7619047619 3.380185e-02 2 0.7349767350 6.873822e-03 4.91748 4 0.7298385067 1.735593e-03 3.9605 8 0.7285369333 4.340201e-04 3.99888 16 0.7282114201 1.085068e-04 3.99993 32 0.7281300400 2.712673e-05 4 64 0.7281096949 6.781684e-06 4 128 0.7281046086 1.695421e-06 4 256 0.7281033371 4.238553e-07 4 512 0.7281030192 1.059638e-07 4 1024 0.7281029397 2.649095e-08 4 2048 0.7281029198 6.622738e-09 4 4096 0.7281029149 1.655685e-09 4 8192 0.7281029136 4.139211e-10 4 16384 0.7281029133 1.034803e-10 4 32768 0.7281029133 2.587019e-11 3.99998 65536 0.7281029132 6.467604e-12 3.99997 131072 0.7281029132 1.616818e-12 4.00021 262144 0.7281029132 4.041212e-13 4.00082 524288 0.7281029132 1.012523e-13 3.99123 1048576 0.7281029132 2.509104e-14 4.0354 Exact 0.7281029132 Problem 23 1 1.8185948537 1.193882e+00 2 -0.8656463897 1.490360e+00 0.801069 4 2.9433437559 2.318630e+00 0.642776 8 -0.2657657328 8.904790e-01 2.6038 16 1.0571928662 4.324796e-01 2.05901 32 3.0455251503 2.420812e+00 0.178651 64 1.5690203168 9.443071e-01 2.56359 128 -1.7911268097 2.415840e+00 0.390881 256 1.8355410657 1.210828e+00 1.9952 512 0.6275327726 2.819516e-03 429.445 1024 0.0924779051 5.322354e-01 0.0052975 2048 1.1998277173 5.751145e-01 0.925442 4096 -1.9983038239 2.623017e+00 0.219257 8192 -0.0029860215 6.276993e-01 4.17878 16384 3.0328508774 2.408138e+00 0.260658 32768 1.7355675542 1.110854e+00 2.16782 65536 -1.5887123232 2.213426e+00 0.501871 131072 1.2107681983 5.860549e-01 3.77682 262144 1.2836908165 6.589776e-01 0.88934 524288 0.8092565437 1.845433e-01 3.57086 1048576 1.5207032823 8.959900e-01 0.205966 Exact 0.6247132564 Problem 24 1 0.1125393676 1.192941e-01 2 -0.0346577441 2.790300e-02 4.27532 4 -0.0285087682 2.175402e-02 1.28266 8 -0.0172140824 1.045934e-02 2.07987 16 -0.0054974031 1.257342e-03 8.31861 32 -0.0066804031 7.434244e-05 16.9128 64 -0.0066507729 1.039726e-04 0.715019 128 -0.0068173826 6.263709e-05 1.65992 256 -0.0067395683 1.517720e-05 4.12705 512 -0.0067896764 3.493094e-05 0.434491 1024 -0.0067545485 1.969967e-07 177.317 2048 -0.0067606320 5.886469e-06 0.033466 4096 -0.0067489564 5.789078e-06 1.01682 8192 -0.0067549472 2.017274e-07 28.6975 16384 -0.0067550934 3.479291e-07 0.579795 32768 -0.0067548258 8.033392e-08 4.33104 65536 -0.0067548761 1.306297e-07 0.614975 131072 -0.0067545821 1.633901e-07 0.799495 262144 -0.0067547500 4.465815e-09 36.5869 524288 -0.0067547444 1.090458e-09 4.09536 1048576 -0.0067547455 4.761129e-11 22.9033 Exact -0.0067547455 Problem 25 1 -1.6094379124 1.426390e-03 2 -1.8971199849 2.862557e-01 0.00498292 4 -1.5026379513 1.082264e-01 2.64497 8 -1.6740933633 6.322906e-02 1.71166 16 -1.5815621494 2.930215e-02 2.15783 32 -1.6260958417 1.523154e-02 1.92378 64 -1.6033938021 7.470500e-03 2.03889 128 -1.6146358792 3.771577e-03 1.98074 256 -1.6089875959 1.876706e-03 2.00968 512 -1.6118049258 9.406237e-04 1.99517 1024 -1.6103945579 4.697442e-04 2.00242 2048 -1.6110993161 2.350140e-04 1.99879 4096 -1.6107468305 1.174715e-04 2.0006 8192 -1.6109230467 5.874463e-05 1.9997 16384 -1.6108349320 2.937010e-05 2.00015 32768 -1.6108789877 1.468560e-05 1.99992 65536 -1.6108569594 7.342664e-06 2.00004 131072 -1.6108679734 3.671366e-06 1.99998 262144 -1.6108624664 1.835675e-06 2.00001 524288 -1.6108652199 9.178394e-07 2 1048576 -1.6108638431 4.589192e-07 2 Exact -1.6108643021 Problem 26 1 2.3114546996 5.643472e+00 2 6.2831853072 1.671741e+00 3.3758 4 7.9205321056 3.439442e-02 48.605 8 7.9549252693 1.251689e-06 27478.4 16 7.9549265210 1.776357e-15 7.04638e+08 32 7.9549265210 1.776357e-15 1 64 7.9549265210 1.776357e-15 1 128 7.9549265210 1.776357e-15 1 256 7.9549265210 1.776357e-15 1 512 7.9549265210 1.776357e-15 1 1024 7.9549265210 1.776357e-15 1 2048 7.9549265210 1.776357e-15 1 4096 7.9549265210 1.776357e-15 1 8192 7.9549265210 1.776357e-15 1 16384 7.9549265210 1.776357e-15 1 32768 7.9549265210 1.776357e-15 1 65536 7.9549265210 1.776357e-15 1 131072 7.9549265210 0.000000e+00 (*/0) 262144 7.9549265210 1.776357e-15 0 524288 7.9549265210 1.776357e-15 1 1048576 7.9549265210 0.000000e+00 (*/0) Exact 7.9549265210 Problem 27 1 0.6663080565 1.748089e-01 2 0.7242492390 1.168677e-01 1.49578 4 0.7644380733 7.667884e-02 1.52412 8 0.7912747878 4.984213e-02 1.53843 16 0.8088847911 3.223213e-02 1.54635 32 0.8203426165 2.077430e-02 1.55154 64 0.8277615995 1.335532e-02 1.55551 128 0.8325494935 8.567423e-03 1.55885 256 0.8356312893 5.485627e-03 1.56179 512 0.8376104723 3.506444e-03 1.56444 1024 0.8388790002 2.237916e-03 1.56683 2048 0.8396905824 1.426334e-03 1.569 4096 0.8402089748 9.079419e-04 1.57095 8192 0.8405396079 5.773087e-04 1.57271 16384 0.8407502080 3.667086e-04 1.5743 32768 0.8408841921 2.327246e-04 1.57572 65536 0.8409693417 1.475750e-04 1.57699 131072 0.8410234041 9.351257e-05 1.57813 262144 0.8410576995 5.921716e-05 1.57915 524288 0.8410794387 3.747795e-05 1.58005 1048576 0.8410932093 2.370730e-05 1.58086 Exact 0.8411169166 Problem 28 1 0.0000000000 1.995467e-02 2 0.0000000000 1.995467e-02 1 4 0.5918210011 5.718663e-01 0.0348939 8 0.4511649391 4.312103e-01 1.32619 16 -0.4121331799 4.320878e-01 0.997969 32 -0.0993939785 1.193486e-01 3.62038 64 0.0768648954 5.691023e-02 2.09714 128 0.0260089728 6.054304e-03 9.39996 256 0.0212645287 1.309859e-03 4.6221 512 0.0202712987 3.166294e-04 4.13688 1024 0.0200331746 7.850530e-05 4.03322 2048 0.0199742552 1.958595e-05 4.00825 4096 0.0199595632 4.893969e-06 4.00206 8192 0.0199558926 1.223335e-06 4.00051 16384 0.0199549751 3.058240e-07 4.00013 32768 0.0199547457 7.645537e-08 4.00003 65536 0.0199546884 1.911380e-08 4.00001 131072 0.0199546741 4.778449e-09 4 262144 0.0199546705 1.194612e-09 4 524288 0.0199546696 2.986530e-10 4 1048576 0.0199546694 7.466324e-11 4 Exact 0.0199546693 Problem 29 1 0.4000000000 9.314718e-02 2 0.2222222222 8.463060e-02 1.10063 4 0.3181483120 1.129549e-02 7.49242 8 0.3183771388 1.152432e-02 0.980144 16 0.2954460623 1.140676e-02 1.01031 32 0.3070203680 1.675485e-04 68.0803 64 0.3070238684 1.710490e-04 0.979536 128 0.3070247436 1.719241e-04 0.99491 256 0.3070249624 1.721429e-04 0.998729 512 0.3070250171 1.721976e-04 0.999682 1024 0.3070250307 1.722113e-04 0.999921 2048 0.3068454203 7.399115e-06 23.2746 4096 0.3068454212 7.398261e-06 1.00012 8192 0.3068454214 7.398047e-06 1.00003 16384 0.3068454214 7.397994e-06 1.00001 32768 0.3068566483 3.828829e-06 1.93218 65536 0.3068510349 1.784556e-06 2.14554 131072 0.3068538416 1.022143e-06 1.7459 262144 0.3068524382 3.812052e-07 2.68135 524288 0.3068531399 3.204692e-07 1.18952 1048576 0.3068527891 3.036786e-08 10.5529 Exact 0.3068528194 Problem 30 1 -5.4838379729 9.562683e-01 2 -18.9107910688 1.438322e+01 0.066485 4 -15.7321393620 1.120457e+01 1.28369 8 0.5720874945 5.099657e+00 2.19712 16 -4.3155082478 2.120614e-01 24.048 32 -4.4876498204 3.991980e-02 5.31218 64 -4.5182429031 9.326722e-03 4.28015 128 -4.5252767075 2.292918e-03 4.06762 256 -4.5269987878 5.708374e-04 4.01676 512 -4.5274270648 1.425603e-04 4.00418 1024 -4.5275339944 3.563077e-05 4.00104 2048 -4.5275607180 8.907111e-06 4.00026 4096 -4.5275673984 2.226741e-06 4.00007 8192 -4.5275690685 5.566831e-07 4.00002 16384 -4.5275694860 1.391706e-07 4 32768 -4.5275695904 3.479265e-08 4 65536 -4.5275696165 8.698160e-09 4 131072 -4.5275696230 2.174540e-09 4 262144 -4.5275696246 5.436354e-10 4 524288 -4.5275696250 1.359082e-10 4.00002 1048576 -4.5275696251 3.397549e-11 4.00018 Exact -4.5275696252 Problem 31 1 8.0000000000 5.348365e+00 2 1.6000000000 1.051635e+00 5.08576 4 2.4000000000 2.516353e-01 4.1792 8 2.6421900806 9.445247e-03 26.6415 16 2.6521875219 5.521946e-04 17.1049 32 2.6517793393 1.440119e-04 3.83437 64 2.6516713609 3.603360e-05 3.9966 128 2.6516443377 9.010318e-06 3.99915 256 2.6516375800 2.252699e-06 3.99979 512 2.6516358905 5.631823e-07 3.99995 1024 2.6516354681 1.407961e-07 3.99999 2048 2.6516353625 3.519904e-08 4 4096 2.6516353361 8.799762e-09 4 8192 2.6516353295 2.199940e-09 4 16384 2.6516353279 5.499854e-10 4 32768 2.6516353275 1.374958e-10 4.00002 65536 2.6516353274 3.437428e-11 3.99996 131072 2.6516353273 8.593126e-12 4.00021 262144 2.6516353273 2.148060e-12 4.00041 524288 2.6516353273 5.369039e-13 4.00083 1048576 2.6516353273 1.336709e-13 4.01661 Exact 2.6516353273 Problem 32 1 0.0000000000 1.207035e+01 2 -9.2827863646 2.787560e+00 4.33008 4 -11.4283020121 6.420443e-01 4.34169 8 -11.9138457700 1.565005e-01 4.10251 16 -12.0314801341 3.886618e-02 4.02665 32 -12.0606460814 9.700235e-03 4.00673 64 -12.0679222790 2.424037e-03 4.00169 128 -12.0697403709 6.059455e-04 4.00042 256 -12.0701948340 1.514824e-04 4.00011 512 -12.0703084460 3.787035e-05 4.00003 1024 -12.0703368488 9.467571e-06 4.00001 2048 -12.0703439495 2.366892e-06 4 4096 -12.0703457247 5.917229e-07 4 8192 -12.0703461685 1.479307e-07 4 16384 -12.0703462794 3.698268e-08 4 32768 -12.0703463071 9.245673e-09 4 65536 -12.0703463141 2.311420e-09 4 131072 -12.0703463158 5.778560e-10 3.99999 262144 -12.0703463162 1.444658e-10 3.99995 524288 -12.0703463164 3.611866e-11 3.99975 1048576 -12.0703463164 9.030998e-12 3.99941 Exact -12.0703463164 Problem 33 1 0.8325546112 5.367231e-02 2 0.8568850219 2.934190e-02 1.8292 4 0.8708456774 1.538125e-02 1.90764 8 0.8783767062 7.850219e-03 1.95934 16 0.8822894746 3.937451e-03 1.99373 32 0.8842747588 1.952167e-03 2.01696 64 0.8852665285 9.603969e-04 2.03267 128 0.8857568557 4.700697e-04 2.04309 256 0.8859975964 2.293291e-04 2.04976 512 0.8861152608 1.116647e-04 2.05373 1024 0.8861726079 5.431754e-05 2.05578 2048 0.8862005123 2.641311e-05 2.05646 4096 0.8862140799 1.284557e-05 2.0562 8192 0.8862206755 6.249952e-06 2.05531 16384 0.8862238826 3.042829e-06 2.05399 32768 0.8862254429 1.482553e-06 2.05242 65536 0.8862262025 7.229458e-07 2.05071 131072 0.8862265726 3.528393e-07 2.04894 262144 0.8862267531 1.723558e-07 2.04716 524288 0.8862268412 8.426482e-08 2.04541 1048576 0.8862268842 4.123129e-08 2.04371 Exact 0.8862269255 Problem 34 1 219.3360000000 8.659167e+02 2 814.0860000000 2.711667e+02 3.1933 4 1014.0430312500 7.120964e+01 3.80801 8 1067.2366347656 1.801603e+01 3.95257 16 1080.7353072510 4.517359e+00 3.98818 32 1084.1224923477 1.130174e+00 3.99705 64 1084.9700709329 2.825957e-01 3.99926 128 1085.1820144736 7.065219e-02 3.99982 256 1085.2350034147 1.766325e-02 3.99995 512 1085.2482508409 4.415826e-03 3.99999 1024 1085.2515627094 1.103957e-03 4 2048 1085.2523906773 2.759894e-04 4 4096 1085.2525976693 6.899734e-05 4 8192 1085.2526494173 1.724934e-05 4 16384 1085.2526623543 4.312334e-06 4 32768 1085.2526655886 1.078083e-06 4 65536 1085.2526663971 2.695210e-07 4 131072 1085.2526665993 6.738037e-08 3.99999 262144 1085.2526666498 1.684498e-08 4.00003 524288 1085.2526666625 4.211415e-09 3.99984 1048576 1085.2526666656 1.052740e-09 4.00043 Exact 1085.2526666667 Problem 35 1 16.1592351032 9.840765e+00 2 19.1471782056 6.852822e+00 1.43602 4 23.9735468892 2.026453e+00 3.38168 8 24.6537175722 1.346282e+00 1.50522 16 24.6681700578 1.331830e+00 1.01085 32 25.5508281601 4.491718e-01 2.96508 64 25.0639957988 9.360042e-01 0.479882 128 26.8277071303 8.277071e-01 1.13084 256 25.2717388996 7.282611e-01 1.13655 512 25.6497940229 3.502060e-01 2.07952 1024 26.5003665521 5.003666e-01 0.699899 2048 25.7322187177 2.677813e-01 1.86856 4096 25.8376854990 1.623145e-01 1.64977 8192 26.0358308853 3.583089e-02 4.53002 16384 25.9171057743 8.289423e-02 0.432248 32768 26.0026293054 2.629305e-03 31.527 65536 25.9624185083 3.758149e-02 0.0699628 131072 26.0577505058 5.775051e-02 0.650756 262144 25.9759941987 2.400580e-02 2.40569 524288 25.9845454814 1.545452e-02 1.55332 1048576 25.9952701071 4.729893e-03 3.26741 Exact 26.0000000000 Problem 36 1 1.2934583749 9.870654e+01 2 2.6000279311 9.739997e+01 1.01341 4 4.1878742856 9.581213e+01 1.01657 8 6.0042228000 9.399578e+01 1.01932 16 8.0081586153 9.199184e+01 1.02178 32 10.1655324068 8.983447e+01 1.02401 64 12.4465810485 8.755342e+01 1.02605 128 14.8250085341 8.517499e+01 1.02792 256 17.2775287490 8.272247e+01 1.02965 512 19.7835483484 8.021645e+01 1.03124 1024 22.3249025316 7.767510e+01 1.03272 2048 24.8856201273 7.511438e+01 1.03409 4096 27.4517107537 7.254829e+01 1.03537 8192 30.0109710217 6.998903e+01 1.03657 16384 32.5528079059 6.744719e+01 1.03769 32768 35.0680777813 6.493192e+01 1.03874 65536 37.5489398025 6.245106e+01 1.03972 131072 39.9887224219 6.001128e+01 1.04066 262144 42.3818019441 5.761820e+01 1.04153 524288 44.7234921016 5.527651e+01 1.04236 1048576 47.0099437214 5.299006e+01 1.04315 Exact 100.0000000000 Problem 37 1 0.0119892664 3.123809e+00 2 0.3910874583 2.744711e+00 1.13812 4 0.0419040993 3.093895e+00 0.887138 8 0.1885756089 2.947223e+00 1.04977 16 3.4068775614 2.710789e-01 10.8722 32 0.3612971973 2.774502e+00 0.0977036 64 1.2844068359 1.851392e+00 1.4986 128 7.9394804158 4.803682e+00 0.385411 256 2.0992886522 1.036510e+00 4.63448 512 2.9429313385 1.928674e-01 5.37421 1024 3.1356086819 1.900272e-04 1014.95 2048 3.1358206139 2.190470e-05 8.67518 4096 3.1357987096 4.244969e-10 51601.6 8192 3.1357987093 1.251967e-10 3.39064 16384 3.1357987092 3.129941e-11 3.99997 32768 3.1357987092 7.824852e-12 4 65536 3.1357987092 1.955325e-12 4.00182 131072 3.1357987092 4.893863e-13 3.99546 262144 3.1357987092 1.225686e-13 3.99275 524288 3.1357987092 2.975398e-14 4.1194 1048576 3.1357987092 6.661338e-15 4.46667 Exact 3.1357987092 Problem 38 1 -0.4571018373 9.963588e-01 2 2.5452668556 2.006010e+00 0.496687 4 -0.8642620452 1.403519e+00 1.42927 8 0.5387667860 4.901286e-04 2863.57 16 0.5392569147 3.330669e-16 1.47156e+12 32 0.5392569147 2.220446e-16 1.5 64 0.5392569147 0.000000e+00 (*/0) 128 0.5392569147 0.000000e+00 (*/0) 256 0.5392569147 0.000000e+00 (*/0) 512 0.5392569147 0.000000e+00 (*/0) 1024 0.5392569147 0.000000e+00 (*/0) 2048 0.5392569147 0.000000e+00 (*/0) 4096 0.5392569147 0.000000e+00 (*/0) 8192 0.5392569147 0.000000e+00 (*/0) 16384 0.5392569147 0.000000e+00 (*/0) 32768 0.5392569147 0.000000e+00 (*/0) 65536 0.5392569147 0.000000e+00 (*/0) 131072 0.5392569147 0.000000e+00 (*/0) 262144 0.5392569147 1.110223e-16 0 524288 0.5392569147 0.000000e+00 (*/0) 1048576 0.5392569147 2.220446e-16 0 Exact 0.5392569147 Problem 39 1 2.4494897428 3.382040e-01 2 2.5066474768 2.810462e-01 1.20337 4 2.5750605890 2.126331e-01 1.32174 8 2.6333969609 1.542967e-01 1.37808 16 2.6775601879 1.101335e-01 1.401 32 2.7095570376 7.813666e-02 1.4095 64 2.7323773988 5.531630e-02 1.41254 128 2.7485628207 3.913088e-02 1.41362 256 2.7600199022 2.767380e-02 1.414 512 2.7681243480 1.956935e-02 1.41414 1024 2.7738558231 1.383788e-02 1.41419 2048 2.7779087796 9.784921e-03 1.4142 4096 2.7807747005 6.919000e-03 1.41421 8192 2.7828012246 4.892476e-03 1.41421 16384 2.7842341966 3.459504e-03 1.41421 32768 2.7852474615 2.446239e-03 1.41421 65536 2.7859639482 1.729752e-03 1.41421 131072 2.7864705808 1.223119e-03 1.41421 262144 2.7868288242 8.648761e-04 1.41421 524288 2.7870821405 6.115597e-04 1.41421 1048576 2.7872612622 4.324380e-04 1.41421 Exact 2.7876937002 Problem 40 1 1.8718645217 8.270921e-01 2 3.3408706527 6.419141e-01 1.28848 4 2.1572875147 5.416691e-01 1.18507 8 2.4464477885 2.525088e-01 2.14515 16 2.9412211502 2.422645e-01 1.04229 32 2.5006468991 1.983097e-01 1.22165 64 2.5991917321 9.976487e-02 1.98777 128 2.9431962921 2.442397e-01 0.408471 256 2.6244826443 7.447396e-02 3.27953 512 2.6488047835 5.015182e-02 1.48497 1024 2.6719795167 2.697708e-02 1.85905 2048 2.9615987166 2.626421e-01 0.102714 4096 2.6800596270 1.889697e-02 13.8986 8192 2.6856073550 1.334925e-02 1.41558 16384 2.6895539760 9.402625e-03 1.41974 32768 2.6924132043 6.543397e-03 1.43696 65536 2.6946445500 4.312051e-03 1.51747 131072 2.6970679383 1.888663e-03 2.28312 262144 2.7000107369 1.054136e-03 1.79167 524288 2.6974828085 1.473793e-03 0.715254 1048576 2.6985385601 4.180412e-04 3.52547 Exact 2.6989566013 Problem 41 1 1.7777777778 4.317807e+00 2 2.5581058081 3.537479e+00 1.22059 4 3.3847035396 2.710882e+00 1.30492 8 4.1402234849 1.955362e+00 1.38638 16 4.7342619443 1.361323e+00 1.43637 32 5.1547747846 9.408103e-01 1.44697 64 5.4415266898 6.540584e-01 1.43842 128 5.6376969051 4.578882e-01 1.42842 256 5.7735434539 3.220416e-01 1.42183 512 5.8684983545 2.270867e-01 1.41814 1024 5.9352367034 1.603484e-01 1.41621 2048 5.9822821583 1.133029e-01 1.41522 4096 6.0154963747 8.008873e-02 1.41472 8192 6.0389639311 5.662117e-02 1.41447 16384 6.0555514659 4.003364e-02 1.41434 32768 6.0672783121 2.830679e-02 1.41428 65536 6.0755696266 2.001548e-02 1.41425 131072 6.0814321821 1.415292e-02 1.41423 262144 6.0855775325 1.000757e-02 1.41422 524288 6.0885087018 7.076401e-03 1.41422 1048576 6.0905813386 5.003764e-03 1.41422 Exact 6.0955851028 Problem 42 1 2.0020751517 1.978711e+00 2 2.3686712676 1.612115e+00 1.2274 4 2.6703050232 1.310481e+00 1.23017 8 2.9161318148 1.064654e+00 1.2309 16 3.1159747752 8.648115e-01 1.23108 32 3.2783322468 7.024540e-01 1.23113 64 3.4102145135 5.705717e-01 1.23114 128 3.5173376268 4.634486e-01 1.23114 256 3.6043489219 3.764373e-01 1.23114 512 3.6750241137 3.057621e-01 1.23114 1024 3.7324302195 2.483560e-01 1.23114 2048 3.7790584689 2.017278e-01 1.23114 4096 3.8169323767 1.638539e-01 1.23114 8192 3.8476955492 1.330907e-01 1.23114 16384 3.8726830098 1.081032e-01 1.23114 32768 3.8929791346 8.780712e-02 1.23114 65536 3.9094647105 7.132154e-02 1.23114 131072 3.9228551591 5.793109e-02 1.23114 262144 3.9337315831 4.705467e-02 1.23114 524288 3.9425659845 3.822027e-02 1.23114 1048576 3.9497417482 3.104450e-02 1.23114 Exact 3.9807862525 Problem 43 1 1.2924750770 1.699094e+00 2 1.5938054974 1.397763e+00 1.21558 4 1.8506325438 1.140936e+00 1.2251 8 2.0630701787 9.284988e-01 1.2288 16 2.2368078102 7.547612e-01 1.23019 32 2.3783064164 6.132626e-01 1.23073 64 2.4933678792 4.982011e-01 1.23095 128 2.5868733590 4.046956e-01 1.23105 256 2.6628412514 3.287277e-01 1.2311 512 2.7245535757 2.670154e-01 1.23112 1024 2.7746826167 2.168864e-01 1.23113 2048 2.8154013912 1.761676e-01 1.23114 4096 2.8484759169 1.430931e-01 1.23114 8192 2.8753410562 1.162279e-01 1.23114 16384 2.8971624583 9.440653e-02 1.23114 32768 2.9148870044 7.668198e-02 1.23114 65536 2.9292838378 6.228515e-02 1.23114 131072 2.9409777134 5.059127e-02 1.23114 262144 2.9504760983 4.109289e-02 1.23114 524288 2.9581911871 3.337780e-02 1.23114 1048576 2.9644577879 2.711120e-02 1.23114 Exact 2.9915689877 Problem 44 1 0.0000412820 3.014098e-02 2 0.0004755583 3.057526e-02 0.985796 4 -0.0071148265 2.298487e-02 1.33023 8 -0.0206782022 9.421498e-03 2.43962 16 -0.0273605320 2.739168e-03 3.43955 32 -0.0293870880 7.126126e-04 3.84384 64 -0.0299197404 1.799601e-04 3.95984 128 -0.0300545965 4.510406e-05 3.98989 256 -0.0300884174 1.128316e-05 3.99747 512 -0.0300968793 2.821237e-06 3.99937 1024 -0.0300989952 7.053371e-07 3.99984 2048 -0.0300995242 1.763360e-07 3.99996 4096 -0.0300996564 4.408412e-08 3.99999 8192 -0.0300996895 1.102104e-08 4 16384 -0.0300996978 2.755259e-09 4 32768 -0.0300996998 6.888149e-10 4 65536 -0.0300997003 1.722037e-10 4 131072 -0.0300997005 4.305093e-11 4 262144 -0.0300997005 1.076273e-11 4 524288 -0.0300997005 2.690684e-12 4 1048576 -0.0300997005 6.726703e-13 4.00001 Exact -0.0300997005 Problem 45 1 -0.8322936731 5.395870e-01 2 -0.5192575053 2.265508e-01 2.38175 4 -0.4216849058 1.289782e-01 1.7565 8 -0.3748674873 8.216078e-02 1.56983 16 -0.3478689674 5.516226e-02 1.48944 32 -0.3307153132 3.800860e-02 1.45131 64 -0.3192370401 2.653033e-02 1.43265 128 -0.3113453673 1.863866e-02 1.4234 256 -0.3058436079 1.313690e-02 1.4188 512 -0.3019808649 9.274155e-03 1.41651 1024 -0.2992592183 6.552509e-03 1.41536 2048 -0.2973381569 4.631447e-03 1.41479 4096 -0.2959809744 3.274265e-03 1.4145 8192 -0.2950217301 2.315020e-03 1.41436 16384 -0.2943435934 1.636884e-03 1.41429 32768 -0.2938641320 1.157422e-03 1.41425 65536 -0.2935251205 8.184108e-04 1.41423 131072 -0.2932854099 5.787001e-04 1.41422 262144 -0.2931159113 4.092015e-04 1.41422 524288 -0.2929960585 2.893487e-04 1.41422 1048576 -0.2929113100 2.046003e-04 1.41421 Exact -0.2927067098 Problem 46 1 4.6569772858 1.412114e+00 2 5.8622916999 2.067993e-01 6.82843 4 6.0654456064 3.645353e-03 56.7296 8 6.0690898641 1.095435e-06 3327.77 16 6.0690909596 9.947598e-14 1.10121e+07 32 6.0690909596 8.881784e-16 112 64 6.0690909596 8.881784e-16 1 128 6.0690909596 8.881784e-16 1 256 6.0690909596 8.881784e-16 1 512 6.0690909596 8.881784e-16 1 1024 6.0690909596 8.881784e-16 1 2048 6.0690909596 8.881784e-16 1 4096 6.0690909596 8.881784e-16 1 8192 6.0690909596 8.881784e-16 1 16384 6.0690909596 8.881784e-16 1 32768 6.0690909596 0.000000e+00 (*/0) 65536 6.0690909596 0.000000e+00 (*/0) 131072 6.0690909596 8.881784e-16 0 262144 6.0690909596 8.881784e-16 1 524288 6.0690909596 1.776357e-15 0.5 1048576 6.0690909596 8.881784e-16 2 Exact 6.0690909596 Problem 47 1 -0.4901290717 4.568463e-02 2 -0.4711435818 2.669914e-02 1.71109 4 -0.4580760202 1.363158e-02 1.95862 8 -0.4508591302 6.414686e-03 2.12506 16 -0.4473043873 2.859943e-03 2.24294 32 -0.4456718813 1.227437e-03 2.33001 64 -0.4449566262 5.121818e-04 2.39649 128 -0.4446536184 2.091739e-04 2.44859 256 -0.4445284391 8.399468e-05 2.49032 512 -0.4444777182 3.327374e-05 2.52435 1024 -0.4444574800 1.303557e-05 2.55253 2048 -0.4444495045 5.060025e-06 2.57619 4096 -0.4444463934 1.948958e-06 2.59627 8192 -0.4444451902 7.457251e-07 2.61351 16384 -0.4444447282 2.837141e-07 2.62844 32768 -0.4444445519 1.074072e-07 2.64148 65536 -0.4444444849 4.048575e-08 2.65296 131072 -0.4444444596 1.520227e-08 2.66314 262144 -0.4444444501 5.689011e-09 2.67222 524288 -0.4444444466 2.122481e-09 2.68036 1048576 -0.4444444452 7.897006e-10 2.6877 Exact -0.4444444444 Problem 48 1 -0.9802581435 3.019742e+00 2 -1.5523876831 2.447612e+00 1.23375 4 -2.0551250445 1.944875e+00 1.25849 8 -2.4753532003 1.524647e+00 1.27562 16 -2.8167944571 1.183206e+00 1.28857 32 -3.0891534041 9.108466e-01 1.29902 64 -3.3035051263 6.964949e-01 1.30776 128 -3.4704393008 5.295607e-01 1.31523 256 -3.5993376392 4.006624e-01 1.32171 512 -3.6981587365 3.018413e-01 1.32739 1024 -3.7734633046 2.265367e-01 1.33242 2048 -3.8305493980 1.694506e-01 1.33689 4096 -3.8736290165 1.263710e-01 1.3409 8192 -3.9060097443 9.399026e-02 1.34451 16384 -3.9302631980 6.973680e-02 1.34779 32768 -3.9483723967 5.162760e-02 1.35077 65536 -3.9618559443 3.814406e-02 1.35349 131072 -3.9718699608 2.813004e-02 1.35599 262144 -3.9792901449 2.070986e-02 1.35829 524288 -3.9847768616 1.522314e-02 1.36042 1048576 -3.9888261588 1.117384e-02 1.36239 Exact -4.0000000000 Problem 49 1 -11.7769019493 6.451765e+01 2 42.7806817243 9.960067e+00 6.47763 4 50.4805366229 2.260212e+00 4.4067 8 52.4691497254 2.715987e-01 8.32188 16 51.8216714539 9.190769e-01 0.295512 32 52.8604193202 1.196709e-01 7.68003 64 52.7963572218 5.560884e-02 2.15201 128 52.7346232112 6.125172e-03 9.07874 256 52.7421656129 1.417229e-03 4.32193 512 52.7379492032 2.799180e-03 0.506302 1024 52.7426539516 1.905568e-03 1.46895 2048 52.7369024702 3.845913e-03 0.495479 4096 52.7420112387 1.262855e-03 3.04541 8192 52.7410929640 3.445805e-04 3.66491 16384 52.7392203595 1.528024e-03 0.225507 32768 52.7409274707 1.790872e-04 8.53229 65536 52.7408374039 8.902042e-05 2.01175 131072 52.7407918235 4.344006e-05 2.04927 262144 52.7407678936 1.951008e-05 2.22654 524288 52.7407531025 4.719068e-06 4.13431 1048576 52.7407356873 1.269616e-05 0.371693 Exact 52.7407483835 Problem 50 1 -0.0000000000 1.281368e-01 2 -0.5493061443 4.211693e-01 0.304241 4 0.4342936311 5.624305e-01 0.748838 8 -0.2339029924 1.057661e-01 5.31768 16 -0.1510160724 2.287922e-02 4.6228 32 -0.1343662745 6.229426e-03 3.67277 64 -0.1298894445 1.752596e-03 3.5544 128 -0.1286284765 4.916281e-04 3.56488 256 -0.1282734638 1.366154e-04 3.59863 512 -0.1281744538 3.760538e-05 3.63287 1024 -0.1281471144 1.026597e-05 3.66311 2048 -0.1281396312 2.782769e-06 3.68912 4096 -0.1281375982 7.497699e-07 3.7115 8192 -0.1281370494 2.009625e-07 3.73089 16384 -0.1281369020 5.362067e-08 3.74786 32768 -0.1281368626 1.425018e-08 3.76281 65536 -0.1281368522 3.773799e-09 3.77608 131072 -0.1281368494 9.962631e-10 3.78795 262144 -0.1281368487 2.622693e-10 3.79863 524288 -0.1281368485 6.886816e-11 3.80828 1048576 -0.1281368484 1.804226e-11 3.81705 Exact -0.1281368484 Problem 51 1 -0.3162541288 1.184406e-01 2 -0.2038858201 6.072261e-03 19.5052 4 -0.1930887946 4.724765e-03 1.2852 8 -0.1902565179 7.557041e-03 0.625214 16 -0.1895346026 8.278957e-03 0.912801 32 -0.1893457074 8.467852e-03 0.977693 64 -0.1892949882 8.518571e-03 0.994046 128 -0.1892809608 8.532598e-03 0.998356 256 -0.1892769439 8.536615e-03 0.999529 512 -0.1892757467 8.537812e-03 0.99986 1024 -0.1892753740 8.538185e-03 0.999956 2048 -0.1892752526 8.538307e-03 0.999986 4096 -0.1892752112 8.538348e-03 0.999995 8192 -0.1892751966 8.538363e-03 0.999998 16384 -0.1892751912 8.538368e-03 0.999999 32768 -0.1892751892 8.538370e-03 1 65536 -0.1892751884 8.538371e-03 1 131072 -0.1892751881 8.538371e-03 1 262144 -0.1892751880 8.538371e-03 1 524288 -0.1892751879 8.538371e-03 1 1048576 -0.1892751879 8.538371e-03 1 Exact -0.1978135592 Problem 52 1 0.0652173913 1.551614e-01 2 0.9095498515 9.994939e-01 0.15524 4 -0.9312128883 8.412689e-01 1.18808 8 0.8625956384 9.525396e-01 0.883185 16 -0.9714616994 8.815177e-01 1.08057 32 0.8282470422 9.181910e-01 0.960059 64 -0.9928412426 9.028972e-01 1.01694 128 0.8181356668 9.080797e-01 0.994293 256 -0.9965306648 9.065867e-01 1.00165 512 0.8170352985 9.069793e-01 0.999567 1024 -0.9968236924 9.068797e-01 1.00011 2048 0.8169606801 9.069047e-01 0.999972 4096 -0.9968424375 9.068984e-01 1.00001 8192 0.8169559881 9.069000e-01 0.999998 16384 -0.9968436108 9.068996e-01 1 32768 0.8169556947 9.068997e-01 1 65536 -0.9968436842 9.068997e-01 1 131072 0.8169556764 9.068997e-01 1 262144 -0.9968436888 9.068997e-01 1 524288 0.8169556752 9.068997e-01 1 1048576 -0.9968436891 9.068997e-01 1 Exact -0.0899440070 Problem 53 1 1.1547005384 3.499222e-01 2 2.4170288281 9.124061e-01 0.383516 4 1.1923720708 3.122507e-01 2.92203 8 1.2960383042 2.085845e-01 1.497 16 1.4103297596 9.429300e-02 2.21209 32 1.5760429653 7.142020e-02 1.32026 64 1.4308139745 7.380879e-02 0.967638 128 1.4734722198 3.115054e-02 2.36942 256 1.5158019693 1.117921e-02 2.78647 512 1.4803511758 2.427159e-02 0.460588 1024 1.5042930646 3.296979e-04 73.6177 2048 1.4940731168 1.054965e-02 0.031252 4096 1.5396292961 3.500653e-02 0.301362 8192 1.4974853572 7.137405e-03 4.90466 16384 1.4996712517 4.951511e-03 1.44146 32768 1.5014100429 3.212720e-03 1.54122 65536 1.5034872722 1.135490e-03 2.82937 131072 1.5043325042 2.902583e-04 3.912 262144 1.5038168625 8.059000e-04 0.360167 524288 1.5059092855 1.286523e-03 0.626417 1048576 1.5040094721 6.132904e-04 2.09774 Exact 1.5046227625 Problem 54 1 1.0000000000 1.547005e-01 2 1.3333333333 1.786328e-01 0.866025 4 1.1428571429 1.184340e-02 15.0829 8 1.1546391753 6.136312e-05 193.005 16 1.1547005367 1.630567e-09 37633 32 1.1547005384 2.220446e-16 7.34342e+06 64 1.1547005384 2.220446e-16 1 128 1.1547005384 2.220446e-16 1 256 1.1547005384 2.220446e-16 1 512 1.1547005384 2.220446e-16 1 1024 1.1547005384 2.220446e-16 1 2048 1.1547005384 2.220446e-16 1 4096 1.1547005384 2.220446e-16 1 8192 1.1547005384 2.220446e-16 1 16384 1.1547005384 2.220446e-16 1 32768 1.1547005384 2.220446e-16 1 65536 1.1547005384 2.220446e-16 1 131072 1.1547005384 2.220446e-16 1 262144 1.1547005384 2.220446e-16 1 524288 1.1547005384 2.220446e-16 1 1048576 1.1547005384 4.440892e-16 0.5 Exact 1.1547005384 Problem 55 1 0.5697828247 6.472419e-02 2 0.5526996123 4.764098e-02 1.35858 4 0.5123555702 7.296938e-03 6.5289 8 0.5068065504 1.747918e-03 4.17465 16 0.5054912723 4.326398e-04 4.04012 32 0.5051665276 1.078951e-04 4.00982 64 0.5050855898 2.695732e-05 4.00244 128 0.5050653708 6.738303e-06 4.00061 256 0.5050603170 1.684512e-06 4.00015 512 0.5050590536 4.211239e-07 4.00004 1024 0.5050587377 1.052807e-07 4.00001 2048 0.5050586588 2.632016e-08 4 4096 0.5050586390 6.580040e-09 4 8192 0.5050586341 1.645010e-09 4 16384 0.5050586329 4.112525e-10 4 32768 0.5050586326 1.028132e-10 4 65536 0.5050586325 2.570333e-11 4 131072 0.5050586325 6.425860e-12 3.99998 262144 0.5050586325 1.606493e-12 3.99993 524288 0.5050586325 4.015677e-13 4.00055 1048576 0.5050586325 1.004752e-13 3.99669 Exact 0.5050586325 Problem 56 1 2.2222222222 2.299698e-01 2 2.1843003413 1.920479e-01 1.19746 4 2.0384720576 4.621965e-02 4.15511 8 2.0011465141 8.894106e-03 5.19666 16 1.9944314061 2.178998e-03 4.08174 32 1.9927943613 5.419534e-04 4.02064 64 1.9923877234 1.353154e-04 4.00511 128 1.9922862260 3.381808e-05 4.00127 256 1.9922608618 8.453847e-06 4.00032 512 1.9922545214 2.113420e-06 4.00008 1024 1.9922529363 5.283523e-07 4.00002 2048 1.9922525400 1.320879e-07 4 4096 1.9922524410 3.302197e-08 4 8192 1.9922524162 8.255491e-09 4 16384 1.9922524100 2.063873e-09 4 32768 1.9922524085 5.159679e-10 4 65536 1.9922524081 1.289919e-10 4 131072 1.9922524080 3.224820e-11 3.99997 262144 1.9922524080 8.062218e-12 3.99992 524288 1.9922524080 2.015277e-12 4.00055 1048576 1.9922524080 5.047074e-13 3.99296 Exact 1.9922524080 Problem 57 1 0.3535533906 4.644661e-02 2 0.3872595264 1.274047e-02 3.6456 4 0.3966068187 3.393181e-03 3.75473 8 0.3991143378 8.856622e-04 3.83124 16 0.3997719411 2.280589e-04 3.88348 32 0.3999418085 5.819148e-05 3.91911 64 0.3999852440 1.475604e-05 3.94357 128 0.3999962742 3.725821e-06 3.96048 256 0.3999990620 9.379628e-07 3.97225 512 0.3999997644 2.356411e-07 3.98047 1024 0.3999999409 5.911366e-08 3.98624 2048 0.3999999852 1.481437e-08 3.99029 4096 0.3999999963 3.709947e-09 3.99315 8192 0.3999999991 9.286102e-10 3.99516 16384 0.3999999998 2.323512e-10 3.99658 32768 0.3999999999 5.812290e-11 3.99758 65536 0.4000000000 1.453698e-11 3.99828 131072 0.4000000000 3.635314e-12 3.99882 262144 0.4000000000 9.089951e-13 3.99927 524288 0.4000000000 2.272627e-13 3.99976 1048576 0.4000000000 5.678791e-14 4.00196 Exact 0.4000000000 monte_carlo_test(): Monte Carlo quadrature rule. N Approx Error Ratio Problem 1 1 1.6323617909 8.592004e-02 2 1.5384303197 1.798515e-01 0.477728 4 2.0341719936 3.158902e-01 0.569348 8 1.7461777184 2.789589e-02 11.3239 16 1.7218428576 3.561029e-03 7.83366 32 1.5442695787 1.740122e-01 0.0204642 64 1.8418647287 1.235829e-01 1.40806 128 1.6911802643 2.710156e-02 4.55999 256 1.7827271421 6.444531e-02 0.420536 512 1.7069018309 1.138000e-02 5.66303 1024 1.7208021378 2.520309e-03 4.51532 2048 1.7225492641 4.267436e-03 0.590591 4096 1.7233363395 5.054511e-03 0.844283 8192 1.7206298302 2.348002e-03 2.15269 16384 1.7083313703 9.950458e-03 0.235969 32768 1.7180736969 2.081315e-04 47.8085 65536 1.7164285200 1.853308e-03 0.112303 131072 1.7162791255 2.002703e-03 0.925404 262144 1.7179738766 3.079519e-04 6.5033 524288 1.7176394045 6.424239e-04 0.479359 1048576 1.7175677935 7.140350e-04 0.899709 Exact 1.7182818285 Problem 2 1 1.0000000000 3.000000e-01 2 1.0000000000 3.000000e-01 1 4 0.2500000000 4.500000e-01 0.666667 8 0.5000000000 2.000000e-01 2.25 16 0.6250000000 7.500000e-02 2.66667 32 0.6875000000 1.250000e-02 6 64 0.6875000000 1.250000e-02 1 128 0.7578125000 5.781250e-02 0.216216 256 0.7421875000 4.218750e-02 1.37037 512 0.7226562500 2.265625e-02 1.86207 1024 0.6855468750 1.445312e-02 1.56757 2048 0.6953125000 4.687500e-03 3.08333 4096 0.7084960938 8.496094e-03 0.551724 8192 0.6983642578 1.635742e-03 5.19403 16384 0.7070312500 7.031250e-03 0.232639 32768 0.6990051270 9.948730e-04 7.06748 65536 0.7039642334 3.964233e-03 0.250962 131072 0.7032241821 3.224182e-03 1.22953 262144 0.6992416382 7.583618e-04 4.25151 524288 0.7003765106 3.765106e-04 2.01418 1048576 0.6997022629 2.977371e-04 1.26457 Exact 0.7000000000 Problem 3 1 0.8957143037 2.290476e-01 2 0.5919144878 7.475218e-02 3.06409 4 0.6858009820 1.913432e-02 3.90671 8 0.5992874493 6.737922e-02 0.283979 16 0.7196397135 5.297305e-02 1.27195 32 0.6587379593 7.928707e-03 6.68117 64 0.7238251433 5.715848e-02 0.138714 128 0.6835770869 1.691042e-02 3.38007 256 0.6471517034 1.951496e-02 0.866536 512 0.6614818526 5.184814e-03 3.76387 1024 0.6640275152 2.639151e-03 1.96458 2048 0.6644574319 2.209235e-03 1.1946 4096 0.6700090358 3.342369e-03 0.660979 8192 0.6663239603 3.427063e-04 9.75287 16384 0.6679225681 1.255901e-03 0.272877 32768 0.6698245712 3.157905e-03 0.397701 65536 0.6658005419 8.661248e-04 3.64602 131072 0.6660522438 6.144229e-04 1.40966 262144 0.6670885107 4.218440e-04 1.45652 524288 0.6662879035 3.787632e-04 1.11374 1048576 0.6670600692 3.934026e-04 0.962788 Exact 0.6666666667 Problem 4 1 -0.0029365543 4.823648e-01 2 0.5352683589 5.584013e-02 8.63832 4 0.4879754918 8.547265e-03 6.5331 8 0.3692999520 1.101283e-01 0.0776119 16 0.2733630433 2.060652e-01 0.534434 32 0.4647590744 1.466915e-02 14.0475 64 0.3465657611 1.328625e-01 0.110409 128 0.4638664170 1.556181e-02 8.53773 256 0.4693059827 1.012224e-02 1.53739 512 0.5227590413 4.333081e-02 0.233604 1024 0.4762473854 3.180841e-03 13.6224 2048 0.4755587076 3.869519e-03 0.822025 4096 0.4904833063 1.105508e-02 0.350022 8192 0.4773285012 2.099726e-03 5.26501 16384 0.4734298340 5.998393e-03 0.350048 32768 0.4778532846 1.574942e-03 3.80864 65536 0.4823312060 2.902979e-03 0.542526 131072 0.4767530087 2.675218e-03 1.08514 262144 0.4814660821 2.037855e-03 1.31276 524288 0.4798750930 4.468663e-04 4.56032 1048576 0.4789734264 4.548003e-04 0.982555 Exact 0.4794282267 Problem 5 1 2.0948188773 5.125859e-01 2 2.1928751826 6.106422e-01 0.839421 4 1.8823734663 3.001405e-01 2.03452 8 1.5742219522 8.011012e-03 37.466 16 1.3286067200 2.536262e-01 0.0315859 32 1.4895450678 9.268790e-02 2.73635 64 1.6165892265 3.435626e-02 2.69785 128 1.6336224848 5.138952e-02 0.668546 256 1.5954135432 1.318058e-02 3.89888 512 1.5820616607 1.713031e-04 76.943 1024 1.5935825196 1.134956e-02 0.0150934 2048 1.5652458741 1.698709e-02 0.668128 4096 1.5772400232 4.992941e-03 3.40222 8192 1.5801360106 2.096953e-03 2.38105 16384 1.5796922431 2.540721e-03 0.825338 32768 1.5843271761 2.094212e-03 1.21321 65536 1.5815405424 6.924213e-04 3.02448 131072 1.5809797580 1.253206e-03 0.55252 262144 1.5834878077 1.254844e-03 0.998694 524288 1.5825448404 3.118767e-04 4.02353 1048576 1.5823544377 1.214740e-04 2.56744 Exact 1.5822329637 Problem 6 1 0.7809690915 6.794780e-01 2 1.9030160212 4.425689e-01 1.5353 4 1.2531325121 2.073146e-01 2.13477 8 1.5450328715 8.458574e-02 2.45094 16 1.4707787764 1.033164e-02 8.18705 32 1.3698564690 9.059066e-02 0.114048 64 1.5542679612 9.382083e-02 0.965571 128 1.4340147016 2.643243e-02 3.54946 256 1.5445535922 8.410646e-02 0.314273 512 1.4376530704 2.279406e-02 3.68984 1024 1.4430804120 1.736672e-02 1.31251 2048 1.4443902638 1.605687e-02 1.08158 4096 1.4509494035 9.497728e-03 1.6906 8192 1.4587485618 1.698570e-03 5.5916 16384 1.4518851285 8.562003e-03 0.198385 32768 1.4596657727 7.813591e-04 10.9578 65536 1.4613256418 8.785100e-04 0.889414 131072 1.4591950901 1.252042e-03 0.701662 262144 1.4583159217 2.131210e-03 0.587479 524288 1.4611489169 7.017851e-04 3.03684 1048576 1.4598956177 5.515141e-04 1.27247 Exact 1.4604471318 Problem 7 1 1.4178580069 5.821420e-01 2 2.4806612819 4.806613e-01 1.21113 4 2.0364599858 3.645999e-02 13.1833 8 8.0617522693 6.061752e+00 0.00601476 16 3.0787201465 1.078720e+00 5.61939 32 1.8004777815 1.995222e-01 5.40652 64 1.9324345402 6.756546e-02 2.95302 128 1.8691402373 1.308598e-01 0.51632 256 2.0561989191 5.619892e-02 2.32851 512 1.8696093054 1.303907e-01 0.431004 1024 1.9131326570 8.686734e-02 1.50103 2048 2.3216312084 3.216312e-01 0.270084 4096 2.0897890473 8.978905e-02 3.58208 8192 1.9961708235 3.829177e-03 23.4487 16384 1.9696333913 3.036661e-02 0.126098 32768 2.0037238628 3.723863e-03 8.1546 65536 1.9810103737 1.898963e-02 0.1961 131072 2.0079176671 7.917667e-03 2.39839 262144 2.0049153208 4.915321e-03 1.61081 524288 1.9986883330 1.311667e-03 3.74738 1048576 2.0038560922 3.856092e-03 0.340154 Exact 2.0000000000 Problem 8 1 0.7392759145 1.276971e-01 2 0.6243541676 2.426188e-01 0.526328 4 0.9851036169 1.181306e-01 2.05382 8 0.8564028384 1.057015e-02 11.1759 16 0.7902956892 7.667730e-02 0.137852 32 0.8491359177 1.783707e-02 4.29876 64 0.8757827284 8.809741e-03 2.0247 128 0.8789073655 1.193438e-02 0.738182 256 0.8920593162 2.508633e-02 0.475732 512 0.8579895240 8.983463e-03 2.7925 1024 0.8662304980 7.424894e-04 12.0991 2048 0.8698615903 2.888603e-03 0.257041 4096 0.8662878931 6.850943e-04 4.21636 8192 0.8649743708 1.998617e-03 0.342784 16384 0.8689857177 2.012730e-03 0.992988 32768 0.8673570145 3.840272e-04 5.24111 65536 0.8663245071 6.484803e-04 0.592196 131072 0.8667786346 1.943527e-04 3.33662 262144 0.8666283051 3.446823e-04 0.563861 524288 0.8669851552 1.216783e-05 28.3273 1048576 0.8669662829 6.704451e-06 1.81489 Exact 0.8669729873 Problem 9 1 1.3306258573 1.759253e-01 2 1.0531119959 1.015885e-01 1.73174 4 1.0763343002 7.836624e-02 1.29633 8 0.9580494331 1.966511e-01 0.398504 16 1.0274726918 1.272278e-01 1.54566 32 1.1255925128 2.910803e-02 4.37089 64 1.1929130842 3.821255e-02 0.76174 128 1.1094366794 4.526386e-02 0.844218 256 1.1499337892 4.766749e-03 9.49575 512 1.1329660950 2.173444e-02 0.219318 1024 1.1476674343 7.033104e-03 3.09031 2048 1.1483706182 6.329920e-03 1.11109 4096 1.1610318932 6.331355e-03 0.999773 8192 1.1551903170 4.897786e-04 12.927 16384 1.1525691693 2.131369e-03 0.229795 32768 1.1525763528 2.124186e-03 1.00338 65536 1.1559703582 1.269820e-03 1.67282 131072 1.1575151585 2.814620e-03 0.451151 262144 1.1562266879 1.526150e-03 1.84426 524288 1.1544482212 2.523172e-04 6.04854 1048576 1.1540087413 6.917971e-04 0.364727 Exact 1.1547005384 Problem 10 1 0.5645958296 1.285514e-01 2 0.6474753073 4.567187e-02 2.81467 4 0.7766269523 8.347977e-02 0.547101 8 0.6757019954 1.744519e-02 4.78526 16 0.6849945876 8.152593e-03 2.13983 32 0.7135783112 2.043113e-02 0.399028 64 0.7031792139 1.003203e-02 2.03659 128 0.6814978765 1.164930e-02 0.86117 256 0.6875654347 5.581746e-03 2.08704 512 0.6869112340 6.235947e-03 0.895092 1024 0.6910565417 2.090639e-03 2.98279 2048 0.6878796233 5.267557e-03 0.39689 4096 0.6937473282 6.001476e-04 8.7771 8192 0.6927516963 3.954842e-04 1.5175 16384 0.6928011252 3.460553e-04 1.14284 32768 0.6931758513 2.867069e-05 12.07 65536 0.6934079034 2.607229e-04 0.109966 131072 0.6935457537 3.985732e-04 0.65414 262144 0.6933730189 2.258383e-04 1.76486 524288 0.6933301863 1.830058e-04 1.23405 1048576 0.6933669592 2.197786e-04 0.832682 Exact 0.6931471806 Problem 11 1 0.4200404298 4.015494e-02 2 0.3471099433 3.277555e-02 1.22515 4 0.4067939617 2.690847e-02 1.21804 8 0.4093006105 2.941512e-02 0.914784 16 0.3924243464 1.253885e-02 2.34592 32 0.3739973470 5.888146e-03 2.12951 64 0.3755695150 4.315978e-03 1.36427 128 0.3767758759 3.109617e-03 1.38795 256 0.3786680892 1.217404e-03 2.5543 512 0.3789006261 9.848669e-04 1.23611 1024 0.3810988876 1.213395e-03 0.811663 2048 0.3773421163 2.543377e-03 0.47708 4096 0.3800215315 1.360384e-04 18.696 8192 0.3804958630 6.103699e-04 0.222879 16384 0.3795595794 3.259137e-04 1.8728 32768 0.3796865654 1.989276e-04 1.63835 65536 0.3796742789 2.112141e-04 0.941829 131072 0.3797335910 1.519020e-04 1.39046 262144 0.3802289890 3.434960e-04 0.442224 524288 0.3798541531 3.133989e-05 10.9603 1048576 0.3797818836 1.036095e-04 0.302481 Exact 0.3798854930 Problem 12 1 0.9903336950 2.128291e-01 2 0.8503777033 7.287307e-02 2.92054 4 0.7828796042 5.374970e-03 13.5579 8 0.8268407812 4.933615e-02 0.108946 16 0.7666497972 1.085484e-02 4.54508 32 0.7368766822 4.062795e-02 0.267177 64 0.7493540931 2.815054e-02 1.44324 128 0.7286707524 4.883388e-02 0.576455 256 0.6798854281 9.761921e-02 0.500249 512 0.7082570539 6.924758e-02 1.40971 1024 0.7145976204 6.290701e-02 1.10079 2048 0.7141699737 6.333466e-02 0.993248 4096 0.7245783623 5.292627e-02 1.19666 8192 0.7187770896 5.872754e-02 0.901217 16384 0.7154769314 6.202770e-02 0.946795 32768 0.7176016864 5.990295e-02 1.03547 65536 0.7190112660 5.849337e-02 1.0241 131072 0.7182859064 5.921873e-02 0.987751 262144 0.7184716646 5.903297e-02 1.00315 524288 0.7178898534 5.961478e-02 0.99024 1048576 0.7181400322 5.936460e-02 1.00421 Exact 0.7775046341 Problem 13 1 -0.2626131331 1.920961e+00 2 1.0577706303 6.005770e-01 3.19853 4 2.7869219977 1.128574e+00 0.532155 8 1.8654692312 2.071216e-01 5.44885 16 0.3582145943 1.300133e+00 0.159308 32 0.6775504020 9.807972e-01 1.32559 64 1.8041960070 1.458484e-01 6.72477 128 1.6312509341 2.709666e-02 5.38252 256 1.7454840337 8.713644e-02 0.310968 512 1.7279069200 6.955933e-02 1.25269 1024 1.4663095822 1.920380e-01 0.362216 2048 1.6309197076 2.742789e-02 7.00156 4096 1.5952039014 6.314369e-02 0.434373 8192 1.6282485744 3.009902e-02 2.09787 16384 1.6639733389 5.625745e-03 5.35023 32768 1.6524071124 5.940482e-03 0.947018 65536 1.6412784272 1.706917e-02 0.348024 131072 1.6588115878 4.639936e-04 36.7875 262144 1.6461048298 1.224276e-02 0.0378994 524288 1.6565188420 1.828752e-03 6.6946 1048576 1.6553967682 2.950826e-03 0.619742 Exact 1.6583475942 Problem 14 1 0.0000000000 5.000002e-01 2 0.0000000000 5.000002e-01 1 4 0.0000000000 5.000002e-01 1 8 0.0000000000 5.000002e-01 1 16 0.3696374650 1.303627e-01 3.83545 32 0.0000000000 5.000002e-01 0.260725 64 0.0226141776 4.773860e-01 1.04737 128 0.0006229812 4.993772e-01 0.955963 256 0.4279701486 7.203006e-02 6.9329 512 0.4122603861 8.773983e-02 0.820951 1024 0.5183859535 1.838574e-02 4.77217 2048 0.7064991525 2.064989e-01 0.0890355 4096 0.6691596782 1.691595e-01 1.22074 8192 0.4415661219 5.843409e-02 2.89488 16384 0.5063050684 6.304857e-03 9.26811 32768 0.4538654033 4.613481e-02 0.136662 65536 0.5000946197 9.440850e-05 488.672 131072 0.4921304974 7.869714e-03 0.0119964 262144 0.4929881350 7.012076e-03 1.12231 524288 0.4986873666 1.312845e-03 5.34113 1048576 0.5001414458 1.412346e-04 9.29548 Exact 0.5000002112 Problem 15 1 0.0000000000 1.000000e+00 2 0.0000000000 1.000000e+00 1 4 0.0000000000 1.000000e+00 1 8 12.3297452925 1.132975e+01 0.0882632 16 0.0002136252 9.997864e-01 11.3322 32 0.6106589365 3.893411e-01 2.56789 64 0.3016632526 6.983367e-01 0.557526 128 0.1435058892 8.564941e-01 0.815343 256 1.0680231824 6.802318e-02 12.5912 512 0.8867885069 1.132115e-01 0.600851 1024 1.3949834039 3.949834e-01 0.286623 2048 1.1225467565 1.225468e-01 3.22312 4096 0.8285817287 1.714183e-01 0.714899 8192 0.9124327373 8.756726e-02 1.95756 16384 1.0218200004 2.182000e-02 4.01317 32768 1.0605034662 6.050347e-02 0.360641 65536 1.0012587944 1.258794e-03 48.0646 131072 0.9719543876 2.804561e-02 0.0448838 262144 0.9756859063 2.431409e-02 1.15347 524288 0.9917686268 8.231373e-03 2.95383 1048576 0.9971859794 2.814021e-03 2.92513 Exact 1.0000000000 Problem 16 1 1.7559945570 1.262360e+00 2 0.0499263544 4.437083e-01 2.84502 4 0.0735439581 4.200907e-01 1.05622 8 0.6472248593 1.535902e-01 2.73514 16 0.9021313111 4.084967e-01 0.375989 32 0.9408385137 4.472039e-01 0.913446 64 0.4873787831 6.255868e-03 71.4855 128 0.4132014137 8.043324e-02 0.0777771 256 0.4711983035 2.243635e-02 3.58495 512 0.3943685671 9.926608e-02 0.226022 1024 0.3955206301 9.811402e-02 1.01174 2048 0.5061061377 1.247149e-02 7.86707 4096 0.5122004543 1.856580e-02 0.671745 8192 0.5213374235 2.770277e-02 0.670179 16384 0.5080691975 1.443455e-02 1.9192 32768 0.4818830271 1.175162e-02 1.2283 65536 0.5035311690 9.896518e-03 1.18745 131072 0.4930342048 6.004461e-04 16.4819 262144 0.4878237201 5.810931e-03 0.10333 524288 0.4915723243 2.062327e-03 2.81766 1048576 0.4905910334 3.043617e-03 0.677591 Exact 0.4936346509 Problem 17 1 0.1208055657 3.791944e-01 2 0.6437136426 1.437136e-01 2.63854 4 0.2370229156 2.629771e-01 0.546487 8 0.4407055978 5.929440e-02 4.43511 16 0.3435365189 1.564635e-01 0.378966 32 0.4524478886 4.755211e-02 3.29036 64 0.4608271359 3.917286e-02 1.2139 128 0.4540750708 4.592493e-02 0.852976 256 0.5416858967 4.168590e-02 1.10169 512 0.4653275037 3.467250e-02 1.20228 1024 0.4964587484 3.541252e-03 9.79103 2048 0.5042885077 4.288508e-03 0.825754 4096 0.5027114147 2.711415e-03 1.58165 8192 0.5083263555 8.326355e-03 0.325642 16384 0.5008344780 8.344780e-04 9.97792 32768 0.5017957637 1.795764e-03 0.464693 65536 0.4964113005 3.588700e-03 0.500394 131072 0.5001095007 1.095007e-04 32.7733 262144 0.4993229009 6.770991e-04 0.16172 524288 0.4996924948 3.075052e-04 2.20191 1048576 0.5000760854 7.608545e-05 4.04158 Exact 0.5000000000 Problem 18 1 0.0607709912 1.097864e-01 2 0.1809202130 1.036286e-02 10.5942 4 0.1609133772 9.643972e-03 1.07454 8 0.2071662347 3.660889e-02 0.263433 16 0.1745822063 4.024857e-03 9.0957 32 0.1804513907 9.894041e-03 0.406796 64 0.1787712575 8.213908e-03 1.20455 128 0.1643465410 6.210809e-03 1.32252 256 0.1788085913 8.251242e-03 0.752712 512 0.1722889071 1.731558e-03 4.76521 1024 0.1708181223 2.607728e-04 6.6401 2048 0.1700636228 4.937267e-04 0.528172 4096 0.1706918458 1.344963e-04 3.67093 8192 0.1712015993 6.442498e-04 0.208764 16384 0.1697483630 8.089865e-04 0.796367 32768 0.1705174890 3.986049e-05 20.2954 65536 0.1708601652 3.028157e-04 0.131633 131072 0.1704735904 8.375909e-05 3.61532 262144 0.1706323173 7.496779e-05 1.11727 524288 0.1704847721 7.257744e-05 1.03294 1048576 0.1706120710 5.472150e-05 1.32631 Exact 0.1705573495 Problem 19 1 -0.5900062624 4.099937e-01 2 -0.9994885756 5.114244e-04 801.67 4 -0.2045297354 7.954703e-01 0.000642921 8 -0.7397462715 2.602537e-01 3.05652 16 -1.4484341582 4.484342e-01 0.580361 32 -0.9886149319 1.138507e-02 39.3879 64 -1.2231041945 2.231042e-01 0.0510303 128 -1.0913206789 9.132068e-02 2.44309 256 -1.0517379945 5.173799e-02 1.76506 512 -1.0610779219 6.107792e-02 0.847082 1024 -1.0248423552 2.484236e-02 2.45862 2048 -1.0113876437 1.138764e-02 2.18152 4096 -0.9826380666 1.736193e-02 0.655897 8192 -1.0005387867 5.387867e-04 32.2241 16384 -0.9890431196 1.095688e-02 0.0491734 32768 -1.0021768861 2.176886e-03 5.03328 65536 -1.0045888051 4.588805e-03 0.474391 131072 -1.0024340942 2.434094e-03 1.88522 262144 -0.9977273323 2.272668e-03 1.07103 524288 -1.0003472338 3.472338e-04 6.54507 1048576 -1.0009248841 9.248841e-04 0.375435 Exact -1.0000000000 Problem 20 1 1.4667310278 9.766542e-02 2 1.6222326012 5.783616e-02 1.68866 4 1.4132474799 1.511490e-01 0.382643 8 1.4687382028 9.565824e-02 1.58009 16 1.5099553522 5.444109e-02 1.7571 32 1.5103920007 5.400444e-02 1.00809 64 1.5711272950 6.730851e-03 8.02342 128 1.5081992086 5.619724e-02 0.119772 256 1.5524659363 1.193051e-02 4.71038 512 1.5753527889 1.095634e-02 1.08891 1024 1.5682220833 3.825639e-03 2.86393 2048 1.5549540311 9.442413e-03 0.405155 4096 1.5702117659 5.815322e-03 1.62371 8192 1.5625289799 1.867464e-03 3.11402 16384 1.5672740922 2.877648e-03 0.648955 32768 1.5628774573 1.518987e-03 1.89445 65536 1.5640021725 3.942715e-04 3.85264 131072 1.5654634201 1.066976e-03 0.369522 262144 1.5644092386 1.279452e-05 83.3932 524288 1.5643358874 6.055670e-05 0.211282 1048576 1.5641376072 2.588368e-04 0.233957 Exact 1.5643964441 Problem 21 1 0.0000454036 2.107573e-01 2 0.0099318525 2.008709e-01 1.04922 4 0.0413321509 1.694706e-01 1.18528 8 0.1832999706 2.750277e-02 6.16195 16 0.1783739309 3.242881e-02 0.848097 32 0.1806072078 3.019553e-02 1.07396 64 0.2535536668 4.275093e-02 0.706313 128 0.1584562842 5.234645e-02 0.816692 256 0.1957185011 1.508424e-02 3.47028 512 0.2174372082 6.634472e-03 2.27362 1024 0.1961566605 1.464608e-02 0.452986 2048 0.1984775277 1.232521e-02 1.1883 4096 0.2090410001 1.761736e-03 6.99606 8192 0.2159206223 5.117886e-03 0.344231 16384 0.2055693496 5.233387e-03 0.97793 32768 0.2097068459 1.095890e-03 4.77547 65536 0.2116566129 8.538766e-04 1.28343 131072 0.2100269362 7.758001e-04 1.10064 262144 0.2103163160 4.864203e-04 1.59492 524288 0.2099416155 8.611208e-04 0.564869 1048576 0.2108968900 9.415372e-05 9.1459 Exact 0.2108027363 Problem 22 1 0.9748285893 2.467257e-01 2 0.6670298629 6.107305e-02 4.03985 4 0.6952384786 3.286443e-02 1.85833 8 0.7726998765 4.459696e-02 0.736921 16 0.8872942308 1.591913e-01 0.280147 32 0.8026014923 7.449858e-02 2.13684 64 0.7312542526 3.151339e-03 23.6403 128 0.7172669225 1.083599e-02 0.290822 256 0.7123266821 1.577623e-02 0.686855 512 0.7197392231 8.363690e-03 1.88628 1024 0.7427357666 1.463285e-02 0.571569 2048 0.7333054283 5.202515e-03 2.81265 4096 0.7248189165 3.283997e-03 1.5842 8192 0.7307001711 2.597258e-03 1.26441 16384 0.7291453759 1.042463e-03 2.49146 32768 0.7286762675 5.733543e-04 1.81818 65536 0.7273379289 7.649843e-04 0.749498 131072 0.7289121737 8.092604e-04 0.945288 262144 0.7273669542 7.359590e-04 1.0996 524288 0.7280137355 8.917776e-05 8.25272 1048576 0.7282003443 9.743112e-05 0.91529 Exact 0.7281029132 Problem 23 1 1.5089880637 8.842748e-01 2 1.0448199077 4.201067e-01 2.10488 4 1.3316884337 7.069752e-01 0.594231 8 -0.0832394032 7.079527e-01 0.998619 16 0.4603792614 1.643340e-01 4.30801 32 -13.2979996837 1.392271e+01 0.0118033 64 -1.0600965221 1.684810e+00 8.26367 128 -0.9741590036 1.598872e+00 1.05375 256 0.0876733107 5.370399e-01 2.97719 512 1.0893011969 4.645879e-01 1.15595 1024 1.0446379042 4.199246e-01 1.10636 2048 2.9562443267 2.331531e+00 0.180107 4096 -3.6491447362 4.273858e+00 0.545533 8192 1.9076741729 1.282961e+00 3.33125 16384 11.2757474309 1.065103e+01 0.120454 32768 2.9219344495 2.297221e+00 4.63649 65536 1.1525814483 5.278682e-01 4.35188 131072 0.6562048539 3.149160e-02 16.7622 262144 -2.5045298241 3.129243e+00 0.0100636 524288 0.5584866247 6.622663e-02 47.2505 1048576 -32.0976279590 3.272234e+01 0.0020239 Exact 0.6247132564 Problem 24 1 -0.0285343401 2.177959e-02 2 0.0465912271 5.334597e-02 0.408271 4 0.0201338788 2.688862e-02 1.98396 8 -0.0067452407 9.504794e-06 2828.95 16 -0.0074280771 6.733316e-04 0.0141161 32 0.0007789726 7.533718e-03 0.0893757 64 -0.0101204173 3.365672e-03 2.2384 128 -0.0021642584 4.590487e-03 0.733184 256 -0.0061026573 6.520882e-04 7.03967 512 -0.0076426551 8.879096e-04 0.734408 1024 -0.0079782421 1.223497e-03 0.725715 2048 -0.0057901718 9.645737e-04 1.26843 4096 -0.0069256734 1.709279e-04 5.64316 8192 -0.0069007279 1.459824e-04 1.17088 16384 -0.0064221870 3.325585e-04 0.438968 32768 -0.0062424090 5.123365e-04 0.649102 65536 -0.0070220997 2.673542e-04 1.91632 131072 -0.0069350646 1.803191e-04 1.48267 262144 -0.0066908990 6.384654e-05 2.82426 524288 -0.0067746348 1.988934e-05 3.21009 1048576 -0.0068337533 7.900776e-05 0.251739 Exact -0.0067547455 Problem 25 1 -1.2214709211 3.893934e-01 2 -3.4310579867 1.820194e+00 0.21393 4 -2.5059765761 8.951123e-01 2.03348 8 -1.3350898452 2.757745e-01 3.24581 16 -1.5688410041 4.202330e-02 6.56242 32 -1.5738685372 3.699576e-02 1.13589 64 -1.6446976069 3.383330e-02 1.09347 128 -1.6180462157 7.181914e-03 4.7109 256 -1.5148817829 9.598252e-02 0.0748252 512 -1.6502601835 3.939588e-02 2.43636 1024 -1.6180046229 7.140321e-03 5.51738 2048 -1.6257739213 1.490962e-02 0.478907 4096 -1.5969103508 1.395395e-02 1.06849 8192 -1.6015828909 9.281411e-03 1.50343 16384 -1.6066716232 4.192679e-03 2.21372 32768 -1.6048703795 5.993923e-03 0.699488 65536 -1.6093950077 1.469294e-03 4.07946 131072 -1.6141643642 3.300062e-03 0.445232 262144 -1.6108117762 5.252586e-05 62.8274 524288 -1.6113419381 4.776360e-04 0.10997 1048576 -1.6097209330 1.143369e-03 0.417744 Exact -1.6108643021 Problem 26 1 6.8900769218 1.064850e+00 2 8.0600814014 1.051549e-01 10.1265 4 7.0111312819 9.437952e-01 0.111417 8 5.9426173537 2.012309e+00 0.469011 16 7.0658147412 8.891118e-01 2.26328 32 8.2327621330 2.778356e-01 3.20014 64 7.8621901597 9.273636e-02 2.99597 128 8.6518957837 6.969693e-01 0.133057 256 7.9190682521 3.585827e-02 19.4368 512 7.4603723461 4.945542e-01 0.0725063 1024 7.9882181371 3.329162e-02 14.8552 2048 8.0381496048 8.322308e-02 0.400029 4096 8.0806797990 1.257533e-01 0.661797 8192 7.9037192089 5.120731e-02 2.45577 16384 7.9064021829 4.852434e-02 1.05529 32768 7.9538972610 1.029260e-03 47.1449 65536 7.9562999493 1.373428e-03 0.749409 131072 7.9611707988 6.244278e-03 0.21995 262144 7.9550535515 1.270305e-04 49.1558 524288 7.9565392231 1.612702e-03 0.0787687 1048576 7.9519169191 3.009602e-03 0.535852 Exact 7.9549265210 Problem 27 1 0.5070177930 3.340991e-01 2 0.6205300156 2.205869e-01 1.51459 4 1.3395857957 4.984689e-01 0.442529 8 0.6549425788 1.861743e-01 2.67743 16 0.8683527593 2.723584e-02 6.83564 32 0.7988460943 4.227082e-02 0.644318 64 0.7864621523 5.465476e-02 0.773415 128 0.8442779555 3.161039e-03 17.2901 256 0.8190001592 2.211676e-02 0.142925 512 0.8613027468 2.018583e-02 1.09566 1024 0.8562090535 1.509214e-02 1.33751 2048 0.8411587022 4.178557e-05 361.181 4096 0.8370346982 4.082218e-03 0.010236 8192 0.8396287762 1.488140e-03 2.74317 16384 0.8456186387 4.501722e-03 0.330571 32768 0.8478835295 6.766613e-03 0.665284 65536 0.8402355626 8.813540e-04 7.67752 131072 0.8397316242 1.385292e-03 0.636222 262144 0.8414691658 3.522492e-04 3.93271 524288 0.8415934674 4.765507e-04 0.739164 1048576 0.8417565393 6.396227e-04 0.74505 Exact 0.8411169166 Problem 28 1 0.1351977542 1.152431e-01 2 -0.1047041323 1.246588e-01 0.924468 4 0.2452656907 2.253110e-01 0.553274 8 0.5349714725 5.150168e-01 0.437483 16 -0.1496620999 1.696168e-01 3.03636 32 0.1077919729 8.783730e-02 1.93103 64 -0.0453244930 6.527916e-02 1.34556 128 0.0022974890 1.765718e-02 3.69703 256 0.0132655216 6.689148e-03 2.63968 512 0.0342537427 1.429907e-02 0.467803 1024 0.0828483430 6.289367e-02 0.227353 2048 0.0462607073 2.630604e-02 2.39085 4096 0.0296598950 9.705226e-03 2.7105 8192 0.0234299811 3.475312e-03 2.79262 16384 0.0221697128 2.215044e-03 1.56896 32768 0.0110924581 8.862211e-03 0.249943 65536 0.0181479691 1.806700e-03 4.90519 131072 0.0137684174 6.186252e-03 0.292051 262144 0.0197771705 1.774988e-04 34.8524 524288 0.0196336315 3.210377e-04 0.552891 1048576 0.0183118176 1.642852e-03 0.195415 Exact 0.0199546693 Problem 29 1 0.4670008616 1.601480e-01 2 0.1937701002 1.130827e-01 1.4162 4 0.4006516655 9.379885e-02 1.20559 8 0.3938160116 8.696319e-02 1.0786 16 0.2674482205 3.940460e-02 2.20693 32 0.3476357248 4.078291e-02 0.966204 64 0.2850169020 2.183592e-02 1.8677 128 0.3112051955 4.352376e-03 5.01701 256 0.3107027753 3.849956e-03 1.1305 512 0.3138533842 7.000565e-03 0.549949 1024 0.3053260522 1.526767e-03 4.58522 2048 0.3098630017 3.010182e-03 0.507201 4096 0.3104198120 3.566993e-03 0.843899 8192 0.3082396916 1.386872e-03 2.57197 16384 0.3074775176 6.246982e-04 2.22007 32768 0.3048317916 2.021028e-03 0.309099 65536 0.3060207706 8.320488e-04 2.42898 131072 0.3063308514 5.219681e-04 1.59406 262144 0.3068092530 4.356643e-05 11.981 524288 0.3065133678 3.394516e-04 0.128344 1048576 0.3069134899 6.067049e-05 5.595 Exact 0.3068528194 Problem 30 1 -29.0482377942 2.452067e+01 2 -19.7811403694 1.525357e+01 1.60754 4 10.7636849694 1.529125e+01 0.997536 8 -28.1330598702 2.360549e+01 0.647784 16 -7.6506090462 3.123039e+00 7.5585 32 -9.1169791179 4.589409e+00 0.680488 64 0.1802512152 4.707821e+00 0.974848 128 -1.0469793959 3.480590e+00 1.35259 256 -3.3441851206 1.183385e+00 2.94122 512 -3.5042870099 1.023283e+00 1.15646 1024 -7.1086444390 2.581075e+00 0.396456 2048 -5.6597881227 1.132218e+00 2.27966 4096 -5.4959309197 9.683613e-01 1.16921 8192 -4.6887070516 1.611374e-01 6.00954 16384 -4.3424618512 1.851078e-01 0.870506 32768 -4.4949075617 3.266206e-02 5.66736 65536 -4.3338221988 1.937474e-01 0.168581 131072 -4.4418027483 8.576688e-02 2.259 262144 -4.4707906167 5.677901e-02 1.51054 524288 -4.4976371969 2.993243e-02 1.89691 1048576 -4.4971314518 3.043817e-02 0.983385 Exact -4.5275696252 Problem 31 1 1.9659817430 6.856536e-01 2 1.1081751349 1.543460e+00 0.444231 4 1.9080366098 7.435987e-01 2.07566 8 2.5680028441 8.363248e-02 8.89127 16 2.7101456171 5.851029e-02 1.42936 32 2.3700578708 2.815775e-01 0.207795 64 2.4782282518 1.734071e-01 1.62379 128 3.2499960897 5.983608e-01 0.289804 256 2.5089967444 1.426386e-01 4.19494 512 2.6137095952 3.792573e-02 3.761 1024 2.7008781292 4.924280e-02 0.770178 2048 2.7443606655 9.272534e-02 0.531061 4096 2.6171602037 3.447512e-02 2.68963 8192 2.6171436488 3.449168e-02 0.99952 16384 2.6507323644 9.029630e-04 38.1983 32768 2.6534814588 1.846131e-03 0.489111 65536 2.6499000012 1.735326e-03 1.06385 131072 2.6561516902 4.516363e-03 0.384231 262144 2.6506101532 1.025174e-03 4.40546 524288 2.6534720308 1.836703e-03 0.55816 1048576 2.6537592135 2.123886e-03 0.864784 Exact 2.6516353273 Problem 32 1 2.1321177935 1.420246e+01 2 -19.9571924253 7.886846e+00 1.80078 4 -16.5062682681 4.435922e+00 1.77795 8 -11.2263972709 8.439490e-01 5.25615 16 -14.1870748599 2.116729e+00 0.398704 32 -12.1891726760 1.188264e-01 17.8136 64 -12.1135852556 4.323894e-02 2.74813 128 -14.7706400611 2.700294e+00 0.0160127 256 -12.5715874206 5.012411e-01 5.38722 512 -11.7860680368 2.842783e-01 1.76321 1024 -12.3138427371 2.434964e-01 1.16748 2048 -11.8970185193 1.733278e-01 1.40483 4096 -12.0460437367 2.430258e-02 7.13207 8192 -11.9473957890 1.229505e-01 0.197661 16384 -11.8087744247 2.615719e-01 0.470045 32768 -12.3735933124 3.032470e-01 0.86257 65536 -11.9709776005 9.936872e-02 3.05174 131072 -12.0390587912 3.128753e-02 3.17599 262144 -12.0993116751 2.896536e-02 1.08017 524288 -12.0499720741 2.037424e-02 1.42167 1048576 -12.0567717234 1.357459e-02 1.50091 Exact -12.0703463164 Problem 33 1 1.1049904173 2.187635e-01 2 0.9637073513 7.748043e-02 2.82347 4 0.9726601240 8.643320e-02 0.89642 8 0.7919210303 9.430590e-02 0.91652 16 0.8529439514 3.328297e-02 2.83346 32 0.9675686962 8.134177e-02 0.409174 64 0.8822159736 4.010952e-03 20.2799 128 0.8784836014 7.743324e-03 0.517988 256 0.9432460102 5.701908e-02 0.135802 512 0.8864935981 2.666727e-04 213.817 1024 0.9082087256 2.198180e-02 0.0121315 2048 0.8864312474 2.043220e-04 107.584 4096 0.8811320520 5.094873e-03 0.0401034 8192 0.8902899796 4.063054e-03 1.25395 16384 0.8796557119 6.571214e-03 0.618311 32768 0.8892179371 2.991012e-03 2.19699 65536 0.8860932930 1.336325e-04 22.3824 131072 0.8863902879 1.633625e-04 0.818012 262144 0.8862235592 3.366272e-06 48.5292 524288 0.8870379809 8.110554e-04 0.00415048 1048576 0.8865938629 3.669374e-04 2.21034 Exact 0.8862269255 Problem 34 1 1.5645048487 1.083688e+03 2 2.3815693269 1.082871e+03 1.00075 4 1306.9059783177 2.216533e+02 4.88543 8 502.8724674185 5.823802e+02 0.380599 16 1216.9349830498 1.316823e+02 4.42262 32 826.0531319933 2.591995e+02 0.508035 64 1196.0041237160 1.107515e+02 2.34037 128 1103.5956139840 1.834295e+01 6.03782 256 1229.8767488392 1.446241e+02 0.126832 512 1134.7509322428 4.949827e+01 2.9218 1024 1056.1585100590 2.909416e+01 1.70131 2048 1132.6444521063 4.739179e+01 0.613907 4096 1112.7856076537 2.753294e+01 1.72128 8192 1079.0641919931 6.188475e+00 4.44907 16384 1089.0416174339 3.788951e+00 1.6333 32768 1077.0393255869 8.213341e+00 0.461317 65536 1082.3847847065 2.867882e+00 2.8639 131072 1084.9517637106 3.009030e-01 9.53092 262144 1080.8885132785 4.364153e+00 0.0689488 524288 1087.0035138667 1.750847e+00 2.4926 1048576 1085.0963965582 1.562701e-01 11.204 Exact 1085.2526666667 Problem 35 1 11.2978410709 1.470216e+01 2 51.2188697687 2.521887e+01 0.582982 4 30.8352339443 4.835234e+00 5.21565 8 18.2150066516 7.784993e+00 0.621097 16 23.9378112658 2.062189e+00 3.77511 32 27.1323980725 1.132398e+00 1.82108 64 23.9634477172 2.036552e+00 0.556037 128 25.9177302413 8.226976e-02 24.7546 256 24.4667997479 1.533200e+00 0.0536588 512 23.3236459408 2.676354e+00 0.572869 1024 26.1210427989 1.210428e-01 22.1108 2048 24.6785167391 1.321483e+00 0.0915962 4096 25.3221422266 6.778578e-01 1.9495 8192 25.5312783623 4.687216e-01 1.44618 16384 26.1424772885 1.424773e-01 3.2898 32768 26.8221818514 8.221819e-01 0.173292 65536 26.0339031849 3.390318e-02 24.2509 131072 26.1019601655 1.019602e-01 0.332514 262144 26.1352118010 1.352118e-01 0.754077 524288 25.9085970374 9.140296e-02 1.47929 1048576 26.0136018203 1.360182e-02 6.71991 Exact 26.0000000000 Problem 36 1 0.5940103457 9.940599e+01 2 1.0688426633 9.893116e+01 1.0048 4 248.1792246853 1.481792e+02 0.667645 8 63.7869983212 3.621300e+01 4.09188 16 5.2552122865 9.474479e+01 0.382216 32 17.0365055414 8.296349e+01 1.14201 64 15.1848346640 8.481517e+01 0.978168 128 5.7627690035 9.423723e+01 0.900018 256 9.1490925485 9.085091e+01 1.03727 512 17.8972881343 8.210271e+01 1.10655 1024 16.7607803208 8.323922e+01 0.986346 2048 29.5523226706 7.044768e+01 1.18158 4096 22.1940348485 7.780597e+01 0.905428 8192 84.3119792009 1.568802e+01 4.95958 16384 103.5617142004 3.561714e+00 4.40463 32768 96.5085091869 3.491491e+00 1.02011 65536 35.1471268906 6.485287e+01 0.0538371 131072 39.2962983966 6.070370e+01 1.06835 262144 35.3494629852 6.465054e+01 0.938951 524288 61.7499701705 3.825003e+01 1.69021 1048576 66.4852429827 3.351476e+01 1.14129 Exact 100.0000000000 Problem 37 1 0.0080414161 3.127757e+00 2 0.0033770282 3.132422e+00 0.998511 4 0.3137260596 2.822073e+00 1.10997 8 0.1514873785 2.984311e+00 0.945636 16 0.2200641376 2.915735e+00 1.02352 32 2.9997561390 1.360426e-01 21.4325 64 0.3201527064 2.815646e+00 0.0483166 128 11.0214212243 7.885623e+00 0.357061 256 2.5229960421 6.128027e-01 12.8681 512 2.5434968068 5.923019e-01 1.03461 1024 1.7584879644 1.377311e+00 0.430042 2048 4.5591701455 1.423371e+00 0.96764 4096 3.5223827523 3.865840e-01 3.68192 8192 2.4371700852 6.986286e-01 0.553347 16384 3.2301661463 9.436744e-02 7.40328 32768 3.2327956171 9.699691e-02 0.972891 65536 3.0221123279 1.136864e-01 0.853197 131072 3.3103457704 1.745471e-01 0.651322 262144 3.0214794126 1.143193e-01 1.52684 524288 3.0909180252 4.488068e-02 2.54718 1048576 3.1642126421 2.841393e-02 1.57953 Exact 3.1357987092 Problem 38 1 0.9532053866 4.139485e-01 2 0.5467756930 7.518778e-03 55.0553 4 0.7199362555 1.806793e-01 0.0416139 8 0.4913243462 4.793257e-02 3.76945 16 0.1847102972 3.545466e-01 0.135194 32 0.4667926114 7.246430e-02 4.89271 64 0.6288923117 8.963540e-02 0.808434 128 0.4372487746 1.020081e-01 0.878708 256 0.5775465158 3.828960e-02 2.66412 512 0.5974378149 5.818090e-02 0.658113 1024 0.5976728343 5.841592e-02 0.995977 2048 0.5270867835 1.217013e-02 4.79994 4096 0.5821884880 4.293157e-02 0.283477 8192 0.5093338962 2.992302e-02 1.43473 16384 0.5164732742 2.278364e-02 1.31336 32768 0.5300203189 9.236596e-03 2.46667 65536 0.5402443252 9.874106e-04 9.35436 131072 0.5467540819 7.497167e-03 0.131704 262144 0.5429436789 3.686764e-03 2.03354 524288 0.5360824122 3.174502e-03 1.16137 1048576 0.5389103288 3.465859e-04 9.15935 Exact 0.5392569147 Problem 39 1 1.8144511823 9.732425e-01 2 1.5445924832 1.243101e+00 0.782915 4 2.1113317450 6.763620e-01 1.83792 8 3.7556834858 9.679898e-01 0.698728 16 2.4988448163 2.888489e-01 3.3512 32 3.2937392371 5.060455e-01 0.570796 64 3.2816432379 4.939495e-01 1.02449 128 2.4843702455 3.033235e-01 1.62846 256 2.8606989242 7.300522e-02 4.15482 512 2.6989590630 8.873464e-02 0.822736 1024 2.7820377689 5.655931e-03 15.6888 2048 2.7512208374 3.647286e-02 0.155072 4096 2.7740285946 1.366511e-02 2.66905 8192 2.7767575240 1.093618e-02 1.24953 16384 2.7440689441 4.362476e-02 0.250687 32768 2.7962293313 8.535631e-03 5.1109 65536 2.7813285633 6.365137e-03 1.341 131072 2.7812749502 6.418750e-03 0.991647 262144 2.7855828979 2.110802e-03 3.04091 524288 2.7845980217 3.095679e-03 0.681854 1048576 2.7879210639 2.273636e-04 13.6155 Exact 2.7876937002 Problem 40 1 3.8145843795 1.115628e+00 2 1.8746021284 8.243545e-01 1.35334 4 1.9272481466 7.717085e-01 1.06822 8 1.7307232245 9.682334e-01 0.797027 16 2.9873782503 2.884216e-01 3.35701 32 4.0080278976 1.309071e+00 0.220325 64 2.6189112082 8.004539e-02 16.3541 128 2.4701768888 2.287797e-01 0.34988 256 2.4419747968 2.569818e-01 0.890256 512 2.6705463488 2.841025e-02 9.04539 1024 6.4856425760 3.786686e+00 0.00750267 2048 2.6452798192 5.367678e-02 70.5461 4096 2.7038546234 4.898022e-03 10.9589 8192 2.7346240688 3.566747e-02 0.137325 16384 2.6689426377 3.001396e-02 1.18836 32768 2.6842629707 1.469363e-02 2.04265 65536 2.6940330175 4.923584e-03 2.98434 131072 2.6824061788 1.655042e-02 0.29749 262144 2.6784596844 2.049692e-02 0.807459 524288 2.6974846014 1.472000e-03 13.9245 1048576 2.7019087596 2.952158e-03 0.498618 Exact 2.6989566013 Problem 41 1 2.3592772431 3.736308e+00 2 4.8364761072 1.259109e+00 2.96742 4 13.7503719955 7.654787e+00 0.164486 8 2.5080318684 3.587553e+00 2.13371 16 9.7041620770 3.608577e+00 0.994174 32 4.2974511794 1.798134e+00 2.00685 64 2.6234630373 3.472122e+00 0.517878 128 14.6330299768 8.537445e+00 0.406693 256 5.9272671572 1.683179e-01 50.7221 512 6.0814533695 1.413173e-02 11.9106 1024 6.3233683694 2.277833e-01 0.0620403 2048 6.2712154689 1.756304e-01 1.29695 4096 6.6710894639 5.755044e-01 0.305176 8192 6.4049092478 3.093241e-01 1.86052 16384 6.1265566634 3.097156e-02 9.98736 32768 6.0438380691 5.174703e-02 0.598519 65536 6.1846669141 8.908181e-02 0.580893 131072 6.1038251486 8.240046e-03 10.8108 262144 6.0545940841 4.099102e-02 0.201021 524288 6.0723955168 2.318959e-02 1.76765 1048576 6.0896832568 5.901846e-03 3.92921 Exact 6.0955851028 Problem 42 1 1.6402828027 2.340503e+00 2 2.1433478873 1.837438e+00 1.27379 4 3.1637285298 8.170577e-01 2.24885 8 3.4484375489 5.323487e-01 1.53482 16 3.7061009002 2.746854e-01 1.93803 32 2.9429652186 1.037821e+00 0.264675 64 5.4910733155 1.510287e+00 0.687168 128 3.0317554355 9.490308e-01 1.5914 256 5.7390284135 1.758242e+00 0.539761 512 3.4876343220 4.931519e-01 3.56532 1024 5.1779064373 1.197120e+00 0.411949 2048 3.9954809459 1.469469e-02 81.4662 4096 3.9413969238 3.938933e-02 0.373063 8192 3.7725225471 2.082637e-01 0.189132 16384 3.9855311455 4.744893e-03 43.8922 32768 4.3144444540 3.336582e-01 0.0142208 65536 3.8205358565 1.602504e-01 2.08211 131072 3.8541077208 1.266785e-01 1.26502 262144 3.8375748957 1.432114e-01 0.884556 524288 3.8760518208 1.047344e-01 1.36738 1048576 3.9020286280 7.875762e-02 1.32983 Exact 3.9807862525 Problem 43 1 15.3712741067 1.237971e+01 2 1.1035649847 1.888004e+00 6.55703 4 4.2485011146 1.256932e+00 1.50207 8 1.2665982954 1.724971e+00 0.728669 16 2.9459919429 4.557704e-02 37.8474 32 2.3815533580 6.100156e-01 0.0747146 64 2.4253121459 5.662568e-01 1.07728 128 2.4728885093 5.186805e-01 1.09173 256 2.7508179628 2.407510e-01 2.15443 512 2.7982062928 1.933627e-01 1.24507 1024 2.4489188076 5.426502e-01 0.35633 2048 2.7456055589 2.459634e-01 2.20622 4096 3.4146486079 4.230796e-01 0.581364 8192 2.5794699596 4.120990e-01 1.02665 16384 2.8942339460 9.733504e-02 4.23382 32768 3.0800431227 8.847413e-02 1.10015 65536 2.8481456764 1.434233e-01 0.616874 131072 2.8873523053 1.042167e-01 1.3762 262144 2.9594370458 3.213194e-02 3.2434 524288 2.8922945740 9.927441e-02 0.323668 1048576 2.9790752119 1.249378e-02 7.94591 Exact 2.9915689877 Problem 44 1 0.0006240976 3.072380e-02 2 0.0002742402 3.037394e-02 1.01152 4 0.0001324719 3.023217e-02 1.00469 8 -0.0107114354 1.938827e-02 1.5593 16 -0.0066305070 2.346919e-02 0.826116 32 -0.0307422212 6.425206e-04 36.5268 64 -0.0359320501 5.832350e-03 0.110165 128 -0.0155559845 1.454372e-02 0.401022 256 -0.0213443635 8.755337e-03 1.66113 512 -0.0261043778 3.995323e-03 2.1914 1024 -0.0305158853 4.161847e-04 9.59988 2048 -0.0291101372 9.895633e-04 0.420574 4096 -0.0314405046 1.340804e-03 0.738037 8192 -0.0316039935 1.504293e-03 0.891318 16384 -0.0305748693 4.751688e-04 3.16581 32768 -0.0290778260 1.021875e-03 0.464997 65536 -0.0303087615 2.090610e-04 4.88793 131072 -0.0297061733 3.935272e-04 0.531249 262144 -0.0305651059 4.654054e-04 0.845558 524288 -0.0301310623 3.136177e-05 14.8399 1048576 -0.0300351378 6.456268e-05 0.485757 Exact -0.0300997005 Problem 45 1 1.8416934776 2.134400e+00 2 0.5437850960 8.364918e-01 2.55161 4 -0.3286083066 3.590160e-02 23.2996 8 -0.1605420735 1.321646e-01 0.271643 16 -0.8642389910 5.715323e-01 0.231246 32 0.5549668088 8.476735e-01 0.674236 64 -0.1620690894 1.306376e-01 6.48874 128 -0.4153114179 1.226047e-01 1.06552 256 -0.2094027511 8.330396e-02 1.47178 512 -0.3821122586 8.940555e-02 0.931754 1024 -0.1321930300 1.605137e-01 0.556996 2048 -0.4663569292 1.736502e-01 0.924351 4096 -0.3194866199 2.677991e-02 6.48435 8192 -0.2788829435 1.382377e-02 1.93724 16384 -0.3013152327 8.608523e-03 1.60582 32768 -0.2579826851 3.472402e-02 0.247913 65536 -0.3083581779 1.565147e-02 2.21858 131072 -0.3051087664 1.240206e-02 1.26201 262144 -0.2839413934 8.765316e-03 1.4149 524288 -0.2921463183 5.603914e-04 15.6414 1048576 -0.2972749513 4.568242e-03 0.122671 Exact -0.2927067098 Problem 46 1 7.3577439415 1.288653e+00 2 7.2481070525 1.179016e+00 1.09299 4 5.5329966297 5.360943e-01 2.19927 8 6.1391277864 7.003683e-02 7.65446 16 5.7717367267 2.973542e-01 0.235533 32 5.8767402498 1.923507e-01 1.5459 64 6.2857043214 2.166134e-01 0.887991 128 6.0380125666 3.107839e-02 6.9699 256 5.9677156340 1.013753e-01 0.306568 512 6.0228439858 4.624697e-02 2.19204 1024 6.0997816880 3.069073e-02 1.50687 2048 6.0548235797 1.426738e-02 2.15111 4096 6.0532123753 1.587858e-02 0.89853 8192 6.0728764344 3.785475e-03 4.19461 16384 6.0645748196 4.516140e-03 0.83821 32768 6.0702875776 1.196618e-03 3.77409 65536 6.0671151695 1.975790e-03 0.60564 131072 6.0668347471 2.256212e-03 0.875711 262144 6.0727878109 3.696851e-03 0.610307 524288 6.0701887229 1.097763e-03 3.36762 1048576 6.0685408346 5.501250e-04 1.99548 Exact 6.0690909596 Problem 47 1 -0.2002009944 2.442435e-01 2 -0.2575071749 1.869373e-01 1.30655 4 -0.4294017969 1.504265e-02 12.4272 8 -0.4138352990 3.060915e-02 0.491443 16 -0.4104073680 3.403708e-02 0.899288 32 -0.4401403242 4.304120e-03 7.90802 64 -0.4529733694 8.528925e-03 0.50465 128 -0.4857792104 4.133477e-02 0.206338 256 -0.4269556564 1.748879e-02 2.3635 512 -0.4551781351 1.073369e-02 1.62934 1024 -0.4436460409 7.984036e-04 13.4439 2048 -0.4492596592 4.815215e-03 0.165809 4096 -0.4480717345 3.627290e-03 1.3275 8192 -0.4467512663 2.306822e-03 1.57242 16384 -0.4449862572 5.418127e-04 4.2576 32768 -0.4444261804 1.826405e-05 29.6655 65536 -0.4444917304 4.728593e-05 0.386247 131072 -0.4454964819 1.052037e-03 0.044947 262144 -0.4449623197 5.178752e-04 2.03145 524288 -0.4440791227 3.653217e-04 1.41759 1048576 -0.4441606176 2.838269e-04 1.28713 Exact -0.4444444444 Problem 48 1 -2.0064169831 1.993583e+00 2 -0.7758585335 3.224141e+00 0.61833 4 -7.0054761057 3.005476e+00 1.07276 8 -4.3852187193 3.852187e-01 7.802 16 -2.7477926754 1.252207e+00 0.307632 32 -2.2926269199 1.707373e+00 0.733412 64 -2.4811666641 1.518833e+00 1.12413 128 -3.4798203967 5.201796e-01 2.91982 256 -5.0516461350 1.051646e+00 0.494634 512 -3.8923107105 1.076893e-01 9.76556 1024 -4.5603111547 5.603112e-01 0.192196 2048 -3.8891863462 1.108137e-01 5.05634 4096 -3.6077708199 3.922292e-01 0.282523 8192 -4.0763533559 7.635336e-02 5.13703 16384 -3.9211752649 7.882474e-02 0.968647 32768 -3.9130656535 8.693435e-02 0.906716 65536 -4.0287217060 2.872171e-02 3.02678 131072 -3.9034166239 9.658338e-02 0.297377 262144 -4.0721010111 7.210101e-02 1.33956 524288 -4.0802875824 8.028758e-02 0.898034 1048576 -4.0024425239 2.442524e-03 32.8707 Exact -4.0000000000 Problem 49 1 -0.1248015914 5.286555e+01 2 -3.9227835953 5.666353e+01 0.932973 4 -4.3348813856 5.707563e+01 0.99278 8 8.7378185555 4.400293e+01 1.29709 16 44.6810288770 8.059720e+00 5.45961 32 46.2463927220 6.494356e+00 1.24103 64 67.3833237585 1.464258e+01 0.443526 128 55.0285651208 2.287817e+00 6.40024 256 59.6847071250 6.943959e+00 0.329469 512 52.5755334975 1.652149e-01 42.0299 1024 50.3062966979 2.434452e+00 0.0678653 2048 56.5528178028 3.812069e+00 0.638617 4096 50.3037264080 2.437022e+00 1.56423 8192 52.3618802378 3.788681e-01 6.43237 16384 53.1651348330 4.243864e-01 0.892743 32768 51.6872663984 1.053482e+00 0.402842 65536 52.8714423111 1.306939e-01 8.06068 131072 52.6498598822 9.088850e-02 1.43796 262144 52.9915709529 2.508226e-01 0.362362 524288 52.6922272055 4.852118e-02 5.16934 1048576 52.8632763565 1.225280e-01 0.396001 Exact 52.7407483835 Problem 50 1 -1.1484216153 1.020285e+00 2 0.0987042502 2.268411e-01 4.4978 4 -0.1582368346 3.009999e-02 7.53625 8 0.4546188014 5.827556e-01 0.0516511 16 -0.3662083588 2.380715e-01 2.44782 32 -0.6421912696 5.140544e-01 0.463125 64 -0.0637606563 6.437619e-02 7.98516 128 -0.2604067768 1.322699e-01 0.486703 256 -0.1971490572 6.901221e-02 1.91662 512 -0.1129389568 1.519789e-02 4.54091 1024 -0.1078868965 2.024995e-02 0.750515 2048 -0.1689550848 4.081824e-02 0.496101 4096 -0.1079472937 2.018955e-02 2.02175 8192 -0.1407061045 1.256926e-02 1.60626 16384 -0.1369860664 8.849218e-03 1.42038 32768 -0.1375953131 9.458465e-03 0.935587 65536 -0.1290292573 8.924089e-04 10.5988 131072 -0.1273705655 7.662829e-04 1.16459 262144 -0.1283691275 2.322791e-04 3.29897 524288 -0.1278034601 3.333883e-04 0.696722 1048576 -0.1283128494 1.760010e-04 1.89424 Exact -0.1281368484 Problem 51 1 -0.2488500293 5.103647e-02 2 -0.0737862275 1.240273e-01 0.411494 4 -0.2618412246 6.402767e-02 1.93709 8 -0.2067970138 8.983455e-03 7.12729 16 -0.2076915773 9.878018e-03 0.909439 32 -0.2018196067 4.006048e-03 2.46578 64 -0.2019232943 4.109735e-03 0.97477 128 -0.1910705124 6.743047e-03 0.609477 256 -0.1975536723 2.598869e-04 25.9461 512 -0.1888357502 8.977809e-03 0.0289477 1024 -0.1922826968 5.530862e-03 1.62322 2048 -0.1810637061 1.674985e-02 0.330204 4096 -0.1872093928 1.060417e-02 1.57955 8192 -0.1884672938 9.346265e-03 1.13459 16384 -0.1882355482 9.578011e-03 0.975804 32768 -0.1887313099 9.082249e-03 1.05459 65536 -0.1900200083 7.793551e-03 1.16535 131072 -0.1894252756 8.388284e-03 0.9291 262144 -0.1890571790 8.756380e-03 0.957962 524288 -0.1889541556 8.859404e-03 0.988371 1048576 -0.1892783800 8.535179e-03 1.03799 Exact -0.1978135592 Problem 52 1 0.0332180953 1.231621e-01 2 0.2671579664 3.571020e-01 0.344893 4 -8.5406458811 8.450702e+00 0.0422571 8 0.0203919740 1.103360e-01 76.5906 16 0.5657519395 6.556959e-01 0.168273 32 -0.4401027134 3.501587e-01 1.87257 64 -1.4616123779 1.371668e+00 0.255279 128 -0.2494942386 1.595502e-01 8.59709 256 -0.2735858008 1.836418e-01 0.868812 512 0.1046764472 1.946205e-01 0.943589 1024 0.1355230839 2.254671e-01 0.863188 2048 0.1519053418 2.418493e-01 0.932263 4096 0.1857001296 2.756441e-01 0.877397 8192 -1.5090352458 1.419091e+00 0.19424 16384 -0.6720868835 5.821429e-01 2.4377 32768 0.1392641906 2.292082e-01 2.5398 65536 -0.7180487816 6.281048e-01 0.36492 131072 0.1752949905 2.652390e-01 2.36807 262144 -0.0107994601 7.914455e-02 3.35132 524288 0.3904384293 4.803824e-01 0.164753 1048576 0.0708631167 1.608071e-01 2.98732 Exact -0.0899440070 Problem 53 1 2.3799901053 8.753673e-01 2 1.0832795446 4.213432e-01 2.07756 4 1.8778120725 3.731893e-01 1.12903 8 1.7527059535 2.480832e-01 1.50429 16 1.3893698480 1.152529e-01 2.15251 32 1.5710619532 6.643919e-02 1.73471 64 1.7089884868 2.043657e-01 0.325099 128 1.6488840335 1.442613e-01 1.41664 256 1.4623479532 4.227481e-02 3.41246 512 1.5727545095 6.813175e-02 0.620486 1024 1.5179974978 1.337474e-02 5.09406 2048 1.4872977917 1.732497e-02 0.771992 4096 1.5245303107 1.990755e-02 0.870271 8192 1.4632034457 4.141932e-02 0.480634 16384 1.5162821650 1.165940e-02 3.55244 32768 1.4940012542 1.062151e-02 1.09772 65536 1.5015716340 3.051128e-03 3.48117 131072 1.5051966159 5.738534e-04 5.31691 262144 1.5039087189 7.140435e-04 0.803667 524288 1.5024331732 2.189589e-03 0.326108 1048576 1.5046506835 2.792106e-05 78.4207 Exact 1.5046227625 Problem 54 1 0.6798213928 4.748791e-01 2 0.8267665312 3.279340e-01 1.44809 4 1.4659488301 3.112483e-01 1.05361 8 1.3571187747 2.024182e-01 1.53765 16 1.1139459958 4.075454e-02 4.96677 32 1.0146691299 1.400314e-01 0.291039 64 1.1043175367 5.038300e-02 2.77934 128 1.1373715795 1.732896e-02 2.90745 256 1.1831213388 2.842080e-02 0.609728 512 1.1053778074 4.932273e-02 0.576221 1024 1.1475597047 7.140834e-03 6.90714 2048 1.1660293922 1.132885e-02 0.630323 4096 1.1514779151 3.222623e-03 3.51541 8192 1.1610724316 6.371893e-03 0.505756 16384 1.1593098697 4.609331e-03 1.38239 32768 1.1554216767 7.211384e-04 6.39174 65536 1.1545591343 1.414041e-04 5.09984 131072 1.1545994134 1.011249e-04 1.39831 262144 1.1544319408 2.685976e-04 0.376492 524288 1.1549247717 2.242333e-04 1.19785 1048576 1.1543872650 3.132734e-04 0.715775 Exact 1.1547005384 Problem 55 1 0.0458382917 4.592203e-01 2 0.4088401538 9.621848e-02 4.77268 4 0.2707079423 2.343507e-01 0.410575 8 0.3871445259 1.179141e-01 1.98747 16 0.4034575077 1.016011e-01 1.16056 32 0.5388583806 3.379975e-02 3.00597 64 0.4626843378 4.237429e-02 0.797647 128 0.5303260652 2.526743e-02 1.67703 256 0.5263512747 2.129264e-02 1.18667 512 0.5236443256 1.858569e-02 1.14565 1024 0.5028620798 2.196553e-03 8.4613 2048 0.5021260737 2.932559e-03 0.749023 4096 0.5067108423 1.652210e-03 1.77493 8192 0.5017066434 3.351989e-03 0.492904 16384 0.5033711412 1.687491e-03 1.98637 32768 0.5033847916 1.673841e-03 1.00816 65536 0.5055554484 4.968159e-04 3.36914 131072 0.5059933334 9.347009e-04 0.531524 262144 0.5051974708 1.388384e-04 6.7323 524288 0.5051535998 9.496738e-05 1.46196 1048576 0.5054036510 3.450186e-04 0.275253 Exact 0.5050586325 Problem 56 1 2.1194015548 1.271491e-01 2 2.2190837137 2.268313e-01 0.560545 4 1.9507635247 4.148888e-02 5.46728 8 2.1319636062 1.397112e-01 0.296962 16 2.0606761126 6.842370e-02 2.04185 32 1.9094439620 8.280845e-02 0.826289 64 1.9474580754 4.479433e-02 1.84864 128 1.9683896478 2.386276e-02 1.87716 256 2.0096468307 1.739442e-02 1.37186 512 1.9915687173 6.836906e-04 25.4419 1024 1.9981279851 5.875577e-03 0.116361 2048 1.9954207321 3.168324e-03 1.85447 4096 2.0016775940 9.425186e-03 0.336155 8192 1.9924928223 2.404143e-04 39.2039 16384 1.9922525532 1.452899e-07 1654.72 32768 1.9912276829 1.024725e-03 0.000141784 65536 1.9924610854 2.086775e-04 4.91057 131072 1.9939141516 1.661744e-03 0.125577 262144 1.9923124754 6.006743e-05 27.6646 524288 1.9919024813 3.499266e-04 0.171657 1048576 1.9923939173 1.415093e-04 2.47282 Exact 1.9922524080 Problem 57 1 0.0246254622 3.753745e-01 2 0.3307897840 6.921022e-02 5.42369 4 0.3369561070 6.304389e-02 1.09781 8 0.2835931397 1.164069e-01 0.541582 16 0.3130976602 8.690234e-02 1.33951 32 0.4389765739 3.897657e-02 2.2296 64 0.3907447660 9.255234e-03 4.2113 128 0.3517498391 4.825016e-02 0.191818 256 0.4337654590 3.376546e-02 1.42898 512 0.3845033932 1.549661e-02 2.17889 1024 0.4034710867 3.471087e-03 4.46448 2048 0.3959832182 4.016782e-03 0.864146 4096 0.3891001438 1.089986e-02 0.368517 8192 0.4075006429 7.500643e-03 1.45319 16384 0.3991360558 8.639442e-04 8.68186 32768 0.3998774081 1.225919e-04 7.04732 65536 0.4013815783 1.381578e-03 0.0887332 131072 0.3994666430 5.333570e-04 2.59034 262144 0.4000531013 5.310131e-05 10.0441 524288 0.3994993017 5.006983e-04 0.106055 1048576 0.4002282928 2.282928e-04 2.19323 Exact 0.4000000000 trapezoid_test(): Composite trapezoid quadrature rule. N Approx Error Ratio Problem 1 1 1.8591409142 1.408591e-01 2 1.7539310925 3.564926e-02 3.95125 4 1.7272219046 8.940076e-03 3.98758 8 1.7205185922 2.236764e-03 3.99688 16 1.7188411286 5.593001e-04 3.99922 32 1.7184216603 1.398319e-04 3.9998 64 1.7183167869 3.495839e-05 3.99995 128 1.7182905681 8.739624e-06 3.99999 256 1.7182840134 2.184908e-06 4 512 1.7182823747 5.462270e-07 4 1024 1.7182819650 1.365568e-07 4 2048 1.7182818626 3.413919e-08 4 4096 1.7182818370 8.534798e-09 4 8192 1.7182818306 2.133700e-09 4 16384 1.7182818290 5.334249e-10 4 32768 1.7182818286 1.333564e-10 3.99999 65536 1.7182818285 3.333889e-11 4.00003 131072 1.7182818285 8.334666e-12 4.00003 262144 1.7182818285 2.083445e-12 4.00043 524288 1.7182818285 5.206946e-13 4.00128 1048576 1.7182818285 1.303402e-13 3.99489 Exact 1.7182818285 Problem 2 1 0.5000000000 2.000000e-01 2 0.7500000000 5.000000e-02 4 4 0.6250000000 7.500000e-02 0.666667 8 0.6875000000 1.250000e-02 6 16 0.7187500000 1.875000e-02 0.666667 32 0.7031250000 3.125000e-03 6 64 0.6953125000 4.687500e-03 0.666667 128 0.6992187500 7.812500e-04 6 256 0.7011718750 1.171875e-03 0.666667 512 0.7001953125 1.953125e-04 6 1024 0.6997070312 2.929687e-04 0.666667 2048 0.6999511719 4.882812e-05 6 4096 0.7000732422 7.324219e-05 0.666667 8192 0.7000122070 1.220703e-05 6 16384 0.6999816895 1.831055e-05 0.666667 32768 0.6999969482 3.051758e-06 6 65536 0.7000045776 4.577637e-06 0.666667 131072 0.7000007629 7.629395e-07 6 262144 0.6999988556 1.144409e-06 0.666667 524288 0.6999998093 1.907349e-07 6 1048576 0.7000002861 2.861023e-07 0.666667 Exact 0.7000000000 Problem 3 1 0.5000000000 1.666667e-01 2 0.6035533906 6.311328e-02 2.64075 4 0.6432830462 2.338362e-02 2.69904 8 0.6581302216 8.536445e-03 2.73927 16 0.6635811969 3.085470e-03 2.76666 32 0.6655589363 1.107730e-03 2.7854 64 0.6662708114 3.958553e-04 2.79832 128 0.6665256573 1.410094e-04 2.8073 256 0.6666165490 5.011769e-05 2.81356 512 0.6666488815 1.778512e-05 2.81796 1024 0.6666603622 6.304448e-06 2.82104 2048 0.6666644336 2.233074e-06 2.82322 4096 0.6666658761 7.905395e-07 2.82475 8192 0.6666663869 2.797551e-07 2.82583 16384 0.6666665677 9.897266e-08 2.82659 32768 0.6666666317 3.500819e-08 2.82713 65536 0.6666666543 1.238128e-08 2.82751 131072 0.6666666623 4.378449e-09 2.82778 262144 0.6666666651 1.548267e-09 2.82797 524288 0.6666666661 5.474575e-10 2.8281 1048576 0.6666666665 1.935710e-10 2.8282 Exact 0.6666666667 Problem 4 1 1.7586637563 1.279236e+00 2 0.7993318782 3.199037e-01 3.99882 4 0.5594992652 8.007104e-02 3.99525 8 0.4994533242 2.002510e-02 3.99853 16 0.4844349815 5.006755e-03 3.99962 32 0.4806799458 1.251719e-03 3.9999 64 0.4797411584 3.129317e-04 3.99998 128 0.4795064597 7.823304e-05 3.99999 256 0.4794477850 1.955827e-05 4 512 0.4794331163 4.889567e-06 4 1024 0.4794294491 1.222392e-06 4 2048 0.4794285323 3.055980e-07 4 4096 0.4794283031 7.639949e-08 4 8192 0.4794282458 1.909987e-08 4 16384 0.4794282315 4.774968e-09 4 32768 0.4794282279 1.193742e-09 4 65536 0.4794282270 2.984356e-10 4 131072 0.4794282268 7.460882e-11 4 262144 0.4794282267 1.865247e-11 3.99994 524288 0.4794282267 4.663325e-12 3.99982 1048576 0.4794282267 1.165734e-12 4.00033 Exact 0.4794282267 Problem 5 1 0.6896551724 8.925778e-01 2 1.4559386973 1.262943e-01 7.06745 4 1.5527116167 2.952135e-02 4.27807 8 1.5748081537 7.424810e-03 3.97604 16 1.5803754231 1.857541e-03 3.99712 32 1.5817685089 4.644548e-04 3.9994 64 1.5821168459 1.161178e-04 3.99986 128 1.5822039340 2.902972e-05 3.99996 256 1.5822257063 7.257445e-06 3.99999 512 1.5822311494 1.814362e-06 4 1024 1.5822325101 4.535906e-07 4 2048 1.5822328503 1.133977e-07 4 4096 1.5822329354 2.834942e-08 4 8192 1.5822329566 7.087354e-09 4 16384 1.5822329620 1.771838e-09 4 32768 1.5822329633 4.429597e-10 4 65536 1.5822329636 1.107403e-10 3.99999 131072 1.5822329637 2.768519e-11 3.99998 262144 1.5822329637 6.921352e-12 3.99997 524288 1.5822329637 1.730838e-12 3.99885 1048576 1.5822329637 4.325429e-13 4.00154 Exact 1.5822329637 Problem 6 1 1.9318516526 4.714045e-01 2 1.6730326075 2.125855e-01 2.21748 4 1.3365163037 1.239308e-01 1.71536 8 1.4142730000 4.617413e-02 2.68399 16 1.4435239408 1.692319e-02 2.72845 32 1.4543137109 6.133421e-03 2.75918 64 1.4582410566 2.206075e-03 2.78024 128 1.4596577680 7.893638e-04 2.79475 256 1.4601656998 2.814320e-04 2.80481 512 1.4603470431 1.000887e-04 2.81183 1024 1.4604115982 3.553356e-05 2.81674 2048 1.4604345321 1.259973e-05 2.82018 4096 1.4604426679 4.463855e-06 2.82261 8192 1.4604455513 1.580506e-06 2.82432 16384 1.4604465724 5.593669e-07 2.82553 32768 1.4604469339 1.979095e-07 2.82638 65536 1.4604470618 7.000743e-08 2.82698 131072 1.4604471070 2.476033e-08 2.8274 262144 1.4604471230 8.756339e-09 2.8277 524288 1.4604471287 3.096393e-09 2.82792 1048576 1.4604471307 1.094880e-09 2.82807 Exact 1.4604471318 Problem 7 1 0.5000000000 1.500000e+00 2 0.9571067812 1.042893e+00 1.43831 4 1.2672285252 7.327715e-01 1.42322 8 1.4830363024 5.169637e-01 1.41745 16 1.6347486521 3.652513e-01 1.41536 32 1.7418026683 2.581973e-01 1.41462 64 1.8174455140 1.825545e-01 1.41436 128 1.8709191349 1.290809e-01 1.41426 256 1.9087272074 9.127279e-02 1.41423 512 1.9354606800 6.453932e-02 1.41422 1024 1.9543638819 4.563612e-02 1.41422 2048 1.9677304096 3.226959e-02 1.41421 4096 1.9771819583 2.281804e-02 1.41421 8192 1.9838652091 1.613479e-02 1.41421 16384 1.9885909802 1.140902e-02 1.41421 32768 1.9919326048 8.067395e-03 1.41421 65536 1.9942954902 5.704510e-03 1.41421 131072 1.9959663024 4.033698e-03 1.41421 262144 1.9971477451 2.852255e-03 1.41421 524288 1.9979831512 2.016849e-03 1.41421 1048576 1.9985738725 1.426127e-03 1.41421 Exact 2.0000000000 Problem 8 1 0.7500000000 1.169730e-01 2 0.8455882353 2.138475e-02 5.46992 4 0.8617323342 5.240653e-03 4.08055 8 0.8656688703 1.304117e-03 4.01855 16 0.8666473394 3.256480e-04 4.00468 32 0.8668915992 8.138816e-05 4.00117 64 0.8669526418 2.034555e-05 4.00029 128 0.8669679010 5.086294e-06 4.00007 256 0.8669717158 1.271568e-06 4.00002 512 0.8669726694 3.178916e-07 4 1024 0.8669729079 7.947287e-08 4 2048 0.8669729675 1.986822e-08 4 4096 0.8669729824 4.967054e-09 4 8192 0.8669729861 1.241763e-09 4 16384 0.8669729870 3.104409e-10 4 32768 0.8669729873 7.761014e-11 4 65536 0.8669729873 1.940248e-11 4.00001 131072 0.8669729873 4.850675e-12 3.99995 262144 0.8669729873 1.212586e-12 4.00027 524288 0.8669729873 3.034240e-13 3.99634 1048576 0.8669729873 7.571721e-14 4.00733 Exact 0.8669729873 Problem 9 1 1.0000000000 1.547005e-01 2 1.0000000000 1.547005e-01 1 4 1.1666666667 1.196613e-02 12.9282 8 1.1547619048 6.136638e-05 194.995 16 1.1547005400 1.630567e-09 37635 32 1.1547005384 4.440892e-16 3.67171e+06 64 1.1547005384 2.220446e-16 2 128 1.1547005384 0.000000e+00 (*/0) 256 1.1547005384 0.000000e+00 (*/0) 512 1.1547005384 0.000000e+00 (*/0) 1024 1.1547005384 0.000000e+00 (*/0) 2048 1.1547005384 0.000000e+00 (*/0) 4096 1.1547005384 0.000000e+00 (*/0) 8192 1.1547005384 0.000000e+00 (*/0) 16384 1.1547005384 0.000000e+00 (*/0) 32768 1.1547005384 0.000000e+00 (*/0) 65536 1.1547005384 0.000000e+00 (*/0) 131072 1.1547005384 0.000000e+00 (*/0) 262144 1.1547005384 4.440892e-16 0 524288 1.1547005384 4.440892e-16 1 1048576 1.1547005384 4.440892e-16 1 Exact 1.1547005384 Problem 10 1 0.7500000000 5.685282e-02 2 0.7083333333 1.518615e-02 3.74373 4 0.6970238095 3.876629e-03 3.91736 8 0.6941218504 9.746698e-04 3.97738 16 0.6933912022 2.440216e-04 3.99419 32 0.6932082083 6.102771e-05 3.99854 64 0.6931624389 1.525832e-05 3.99963 128 0.6931509952 3.814668e-06 3.99991 256 0.6931481342 9.536725e-07 3.99998 512 0.6931474190 2.384185e-07 3.99999 1024 0.6931472402 5.960464e-08 4 2048 0.6931471955 1.490116e-08 4 4096 0.6931471843 3.725290e-09 4 8192 0.6931471815 9.313226e-10 4 16384 0.6931471808 2.328308e-10 4 32768 0.6931471806 5.820777e-11 3.99999 65536 0.6931471806 1.455192e-11 4.00001 131072 0.6931471806 3.638201e-12 3.99976 262144 0.6931471806 9.096057e-13 3.99976 524288 0.6931471806 2.274847e-13 3.99854 1048576 0.6931471806 5.639933e-14 4.03346 Exact 0.6931471806 Problem 11 1 0.3844707107 4.585218e-03 2 0.3810056897 1.120197e-03 4.09323 4 0.3801640449 2.785518e-04 4.0215 8 0.3799550392 6.954616e-05 4.00528 16 0.3799028739 1.738083e-05 4.00131 32 0.3798898379 4.344851e-06 4.00033 64 0.3798865792 1.086190e-06 4.00008 128 0.3798857646 2.715462e-07 4.00002 256 0.3798855609 6.788647e-08 4.00001 512 0.3798855100 1.697161e-08 4 1024 0.3798854973 4.242902e-09 4 2048 0.3798854941 1.060726e-09 4 4096 0.3798854933 2.651814e-10 4 8192 0.3798854931 6.629536e-11 4 16384 0.3798854931 1.657380e-11 4.00001 32768 0.3798854930 4.143463e-12 3.99999 65536 0.3798854930 1.035838e-12 4.00011 131072 0.3798854930 2.589595e-13 4 262144 0.3798854930 6.467049e-14 4.00429 524288 0.3798854930 1.604272e-14 4.03114 1048576 0.3798854930 4.052314e-15 3.9589 Exact 0.3798854930 Problem 12 1 1.0000000000 2.224954e-01 2 0.9121803177 1.346757e-01 1.65208 4 0.8291574255 5.165279e-02 2.60733 8 0.7772444848 2.601493e-04 198.551 16 0.7486471015 2.885753e-02 0.00901495 32 0.7336856223 4.381901e-02 0.658562 64 0.7260390254 5.146561e-02 0.851423 128 0.7221742526 5.533038e-02 0.930151 256 0.7202314970 5.727314e-02 0.966079 512 0.7192575268 5.824711e-02 0.983279 1024 0.7187698937 5.873474e-02 0.991698 2048 0.7185259151 5.897872e-02 0.995863 4096 0.7184038853 5.910075e-02 0.997935 8192 0.7183428602 5.916177e-02 0.998969 16384 0.7183123452 5.919229e-02 0.999484 32768 0.7182970870 5.920755e-02 0.999742 65536 0.7182894578 5.921518e-02 0.999871 131072 0.7182856431 5.921899e-02 0.999936 262144 0.7182837358 5.922090e-02 0.999968 524288 0.7182827821 5.922185e-02 0.999984 1048576 0.7182823053 5.922233e-02 0.999992 Exact 0.7775046341 Problem 13 1 4.7279894446 3.069642e+00 2 1.4050704476 2.532771e-01 12.1197 4 1.6136740268 4.467357e-02 5.66951 8 1.6479116290 1.043597e-02 4.28073 16 1.6557799186 2.567676e-03 4.06436 32 1.6577081944 6.393998e-04 4.01576 64 1.6581879007 1.596935e-04 4.00392 128 1.6583076806 3.991360e-05 4.00098 256 1.6583376164 9.977791e-06 4.00024 512 1.6583450998 2.494410e-06 4.00006 1024 1.6583469706 6.236000e-07 4.00002 2048 1.6583474383 1.558999e-07 4 4096 1.6583475552 3.897495e-08 4 8192 1.6583475845 9.743738e-09 4 16384 1.6583475918 2.435935e-09 4 32768 1.6583475936 6.089835e-10 4 65536 1.6583475941 1.522460e-10 4 131072 1.6583475942 3.806155e-11 3.99999 262144 1.6583475942 9.515722e-12 3.99986 524288 1.6583475942 2.379208e-12 3.99953 1048576 1.6583475942 5.939693e-13 4.00561 Exact 1.6583475942 Problem 14 1 35.3553390593 3.485534e+01 2 17.6776695297 1.717767e+01 2.02911 4 8.8388347648 8.338835e+00 2.05996 8 4.4194173824 3.919417e+00 2.12757 16 2.2097086912 1.709708e+00 2.29245 32 1.1048548268 6.048546e-01 2.82664 64 0.5762948924 7.629468e-02 7.92787 128 0.5000338230 3.361179e-05 2269.88 256 0.5000000000 2.111660e-07 159.172 512 0.5000000000 2.111660e-07 1 1024 0.5000000000 2.111660e-07 1 2048 0.5000000000 2.111660e-07 1 4096 0.5000000000 2.111660e-07 1 8192 0.5000000000 2.111660e-07 1 16384 0.5000000000 2.111660e-07 1 32768 0.5000000000 2.111660e-07 1 65536 0.5000000000 2.111660e-07 1 131072 0.5000000000 2.111660e-07 1 262144 0.5000000000 2.111660e-07 1 524288 0.5000000000 2.111660e-07 1 1048576 0.5000000000 2.111660e-07 1 Exact 0.5000002112 Problem 15 1 125.0000000000 1.240000e+02 2 62.5000000000 6.150000e+01 2.01626 4 31.2500000000 3.025000e+01 2.03306 8 15.6250000000 1.462500e+01 2.06838 16 7.8125025584 6.812503e+00 2.14679 32 3.9094125701 2.909413e+00 2.34154 64 2.0333154143 1.033315e+00 2.81561 128 1.2993564462 2.993564e-01 3.45179 256 1.0782376874 7.823769e-02 3.82624 512 1.0197897112 1.978971e-02 3.95345 1024 1.0049621264 4.962126e-03 3.98815 2048 1.0012414551 1.241455e-03 3.99702 4096 1.0003104216 3.104216e-04 3.99926 8192 1.0000776090 7.760901e-05 3.99981 16384 1.0000194025 1.940248e-05 3.99995 32768 1.0000048506 4.850634e-06 3.99999 65536 1.0000012127 1.212659e-06 4 131072 1.0000003032 3.031649e-07 4 262144 1.0000000758 7.579122e-08 4 524288 1.0000000189 1.894781e-08 4 1048576 1.0000000047 4.736951e-09 4 Exact 1.0000000000 Problem 16 1 7.9609289807 7.467294e+00 2 3.9931765465 3.499542e+00 2.13379 4 2.0247185365 1.531084e+00 2.28566 8 1.0707343245 5.770997e-01 2.65307 16 0.6482392254 1.546046e-01 3.73275 32 0.5118917397 1.825709e-02 8.46819 64 0.4939560070 3.213561e-04 56.8126 128 0.4936346896 3.866192e-08 8311.95 256 0.4936346347 1.617707e-08 2.38992 512 0.4936346469 4.044280e-09 3.99999 1024 0.4936346499 1.011071e-09 4 2048 0.4936346506 2.527678e-10 4 4096 0.4936346508 6.319195e-11 4 8192 0.4936346509 1.579797e-11 4 16384 0.4936346509 3.949452e-12 4.00004 32768 0.4936346509 9.873768e-13 3.99994 65536 0.4936346509 2.469691e-13 3.99798 131072 0.4936346509 6.178391e-14 3.9973 262144 0.4936346509 1.537659e-14 4.01805 524288 0.4936346509 3.830269e-15 4.01449 1048576 0.4936346509 1.054712e-15 3.63158 Exact 0.4936346509 Problem 17 1 0.0000000000 5.000000e-01 2 0.0000000000 5.000000e-01 1 4 0.5000000000 0.000000e+00 (*/0) 8 0.5000000000 5.551115e-16 0 16 0.5000000000 6.106227e-16 0.909091 32 0.5000000000 6.106227e-16 1 64 0.5000000000 2.775558e-16 2.2 128 0.5000000000 1.110223e-16 2.5 256 0.5000000000 1.110223e-16 1 512 0.5000000000 0.000000e+00 (*/0) 1024 0.5000000000 0.000000e+00 (*/0) 2048 0.5000000000 0.000000e+00 (*/0) 4096 0.5000000000 0.000000e+00 (*/0) 8192 0.5000000000 0.000000e+00 (*/0) 16384 0.5000000000 0.000000e+00 (*/0) 32768 0.5000000000 0.000000e+00 (*/0) 65536 0.5000000000 0.000000e+00 (*/0) 131072 0.5000000000 0.000000e+00 (*/0) 262144 0.5000000000 0.000000e+00 (*/0) 524288 0.5000000000 0.000000e+00 (*/0) 1048576 0.5000000000 5.551115e-17 0 Exact 0.5000000000 Problem 18 1 0.1344707107 3.608664e-02 2 0.1616205225 8.936827e-03 4.03797 4 0.1683282239 2.229126e-03 4.00912 8 0.1700003824 5.569671e-04 4.00226 16 0.1704181273 1.392222e-04 4.00056 32 0.1705225452 3.480432e-05 4.00014 64 0.1705486485 8.701004e-06 4.00004 128 0.1705551743 2.175246e-06 4.00001 256 0.1705568057 5.438113e-07 4 512 0.1705572135 1.359528e-07 4 1024 0.1705573155 3.398820e-08 4 2048 0.1705573410 8.497050e-09 4 4096 0.1705573474 2.124262e-09 4 8192 0.1705573490 5.310656e-10 4 16384 0.1705573494 1.327664e-10 4 32768 0.1705573495 3.319162e-11 4 65536 0.1705573495 8.297890e-12 4.00001 131072 0.1705573495 2.074479e-12 3.99999 262144 0.1705573495 5.186407e-13 3.99984 524288 0.1705573495 1.296185e-13 4.00128 1048576 0.1705573495 3.236300e-14 4.00515 Exact 0.1705573495 Problem 19 1 0.0000000000 1.000000e+00 2 -0.3465735903 6.534264e-01 1.53039 4 -0.5917809035 4.082191e-01 1.60068 8 -0.7538661788 2.461338e-01 1.65853 16 -0.8555974656 1.444025e-01 1.7045 32 -0.9170496698 8.295033e-02 1.74083 64 -0.9531299664 4.687003e-02 1.76979 128 -0.9738624632 2.613754e-02 1.79321 256 -0.9855787001 1.442130e-02 1.81243 512 -0.9921127664 7.887234e-03 1.82844 1024 -0.9957180119 4.281988e-03 1.84196 2048 -0.9976898004 2.310200e-03 1.85351 4096 -0.9987602925 1.239708e-03 1.8635 8192 -0.9993378411 6.621589e-04 1.87222 16384 -0.9996477677 3.522323e-04 1.87989 32768 -0.9998133073 1.866927e-04 1.8867 65536 -0.9999013654 9.863460e-05 1.89277 131072 -0.9999480386 5.196144e-05 1.89823 262144 -0.9999726972 2.730279e-05 1.90315 524288 -0.9999856876 1.431243e-05 1.90763 1048576 -0.9999925133 7.486735e-06 1.91171 Exact -1.0000000000 Problem 20 1 0.9975062344 5.668902e-01 2 1.4937779928 7.061845e-02 8.02751 4 1.5437017454 2.069470e-02 3.41239 8 1.5592142140 5.182230e-03 3.9934 16 1.5631008455 1.295599e-03 3.99987 32 1.5640725445 3.238996e-04 4 64 1.5643154692 8.097485e-05 4 128 1.5643762004 2.024371e-05 4 256 1.5643913831 5.060927e-06 4 512 1.5643951788 1.265232e-06 4 1024 1.5643961278 3.163079e-07 4 2048 1.5643963650 7.907698e-08 4 4096 1.5643964243 1.976924e-08 4 8192 1.5643964391 4.942311e-09 4 16384 1.5643964428 1.235577e-09 4 32768 1.5643964438 3.088942e-10 4 65536 1.5643964440 7.722356e-11 4 131072 1.5643964440 1.930611e-11 3.99995 262144 1.5643964441 4.826584e-12 3.99995 524288 1.5643964441 1.206812e-12 3.99945 1048576 1.5643964441 3.008704e-13 4.01107 Exact 1.5643964441 Problem 21 1 0.0353256375 1.754771e-01 2 0.0225958373 1.882069e-01 0.932363 4 0.2079265530 2.876183e-03 65.4363 8 0.1929537861 1.784895e-02 0.16114 16 0.1960134024 1.478933e-02 1.20688 32 0.2112973327 4.945963e-04 29.9018 64 0.2072378467 3.564890e-03 0.138741 128 0.2097735695 1.029167e-03 3.46386 256 0.2097509036 1.051833e-03 0.978451 512 0.2109935599 1.908236e-04 5.51207 1024 0.2107446816 5.805474e-05 3.28696 2048 0.2108027298 6.513419e-09 8913.1 4096 0.2108027287 7.575733e-09 0.859774 8192 0.2108027338 2.501157e-09 3.02889 16384 0.2108027351 1.232514e-09 2.02931 32768 0.2108027354 9.153527e-10 1.34649 65536 0.2108027355 8.360625e-10 1.09484 131072 0.2108027355 8.162399e-10 1.02429 262144 0.2108027355 8.112842e-10 1.00611 524288 0.2108027355 8.100453e-10 1.00153 1048576 0.2108027355 8.097357e-10 1.00038 Exact 0.2108027363 Problem 22 1 0.6666666667 6.143625e-02 2 0.7142857143 1.381720e-02 4.44636 4 0.7246312246 3.471689e-03 3.97996 8 0.7272348656 8.680476e-04 3.99942 16 0.7278858995 2.170138e-04 3.99997 32 0.7280486598 5.425347e-05 4 64 0.7280893499 1.356337e-05 4 128 0.7280995224 3.390842e-06 4 256 0.7281020655 8.477105e-07 4 512 0.7281027013 2.119276e-07 4 1024 0.7281028602 5.298191e-08 4 2048 0.7281029000 1.324548e-08 4 4096 0.7281029099 3.311369e-09 4 8192 0.7281029124 8.278421e-10 4 16384 0.7281029130 2.069606e-10 4 32768 0.7281029132 5.174017e-11 4 65536 0.7281029132 1.293510e-11 3.99998 131072 0.7281029132 3.233636e-12 4.00017 262144 0.7281029132 8.085754e-13 3.99918 524288 0.7281029132 2.020606e-13 4.00165 1048576 0.7281029132 5.062617e-14 3.99123 Exact 0.7281029132 Problem 23 1 0.4207354924 2.039778e-01 2 1.1196651730 4.949519e-01 0.412116 4 0.1270093917 4.977039e-01 0.994471 8 1.5351765738 9.104633e-01 0.546649 16 0.6347054205 9.992164e-03 91.1177 32 0.8459491433 2.212359e-01 0.0451652 64 1.9457371468 1.321024e+00 0.167473 128 1.7573787318 1.132665e+00 1.1663 256 -0.0168740390 6.415873e-01 1.76541 512 0.9093335134 2.846203e-01 2.25419 1024 0.7684331430 1.437199e-01 1.98038 2048 0.4304555240 1.942577e-01 0.739841 4096 0.8151416207 1.904284e-01 1.02011 8192 -0.5915811016 1.216294e+00 0.156564 16384 -0.2972835616 9.219968e-01 1.3192 32768 1.3677836579 7.430704e-01 1.24079 65536 1.5516756061 9.269623e-01 0.801619 131072 -0.0185183586 6.432316e-01 1.4411 262144 0.5961249199 2.858834e-02 22.4998 524288 0.9399078682 3.151946e-01 0.0907006 1048576 0.8745822059 2.498689e-01 1.26144 Exact 0.6247132564 Problem 24 1 0.0795775213 8.633227e-02 2 0.0960584445 1.028132e-01 0.8397 4 0.0307003502 3.745510e-02 2.74497 8 0.0010957910 7.850536e-03 4.77102 16 -0.0080591457 1.304400e-03 6.0185 32 -0.0067782744 2.352891e-05 55.4382 64 -0.0067293387 2.540676e-05 0.926088 128 -0.0066900558 6.468971e-05 0.392748 256 -0.0067537192 1.026307e-06 63.0315 512 -0.0067466437 8.101752e-06 0.126677 1024 -0.0067681601 1.341460e-05 0.603951 2048 -0.0067613543 6.608799e-06 2.02981 4096 -0.0067609931 6.247634e-06 1.05781 8192 -0.0067549748 2.292781e-07 27.2492 16384 -0.0067549610 2.155027e-07 1.06392 32768 -0.0067550272 2.817159e-07 0.764965 65536 -0.0067549265 1.810249e-07 1.55623 131072 -0.0067549013 1.558273e-07 1.1617 262144 -0.0067547417 3.781424e-09 41.2086 524288 -0.0067547458 3.421953e-10 11.0505 1048576 -0.0067547451 3.741311e-10 0.91464 Exact -0.0067547455 Problem 25 1 -0.7803238741 8.305404e-01 2 -1.1948808933 4.159834e-01 1.99657 4 -1.5460004391 6.486386e-02 6.41318 8 -1.5243191952 8.654511e-02 0.74948 16 -1.5992062793 1.165802e-02 7.42365 32 -1.5903842143 2.048009e-02 0.569237 64 -1.6082400280 2.624274e-03 7.8041 128 -1.6058169151 5.047387e-03 0.519927 256 -1.6102263971 6.379049e-04 7.91244 512 -1.6096069965 1.257306e-03 0.507359 1024 -1.6107059611 1.583409e-04 7.9405 2048 -1.6105502595 3.140426e-04 0.504202 4096 -1.6108247878 3.951427e-05 7.94757 8192 -1.6107858092 7.849290e-05 0.503412 16384 -1.6108544279 9.874132e-06 7.94935 32768 -1.6108446799 1.962212e-05 0.503214 65536 -1.6108618338 2.468256e-06 7.94979 131072 -1.6108593966 4.905460e-06 0.503165 262144 -1.6108636850 6.170467e-07 7.9499 524288 -1.6108630757 1.226361e-06 0.503153 1048576 -1.6108641478 1.542606e-07 7.94993 Exact -1.6108643021 Problem 26 1 17.0794684453 9.124542e+00 2 9.6954615725 1.740535e+00 5.24238 4 7.9893234398 3.439692e-02 50.6015 8 7.9549277727 1.251689e-06 27480.4 16 7.9549265210 1.776357e-15 7.04638e+08 32 7.9549265210 1.776357e-15 1 64 7.9549265210 0.000000e+00 (*/0) 128 7.9549265210 8.881784e-16 0 256 7.9549265210 1.776357e-15 0.5 512 7.9549265210 0.000000e+00 (*/0) 1024 7.9549265210 0.000000e+00 (*/0) 2048 7.9549265210 1.776357e-15 0 4096 7.9549265210 2.664535e-15 0.666667 8192 7.9549265210 0.000000e+00 (*/0) 16384 7.9549265210 1.776357e-15 0 32768 7.9549265210 0.000000e+00 (*/0) 65536 7.9549265210 1.776357e-15 0 131072 7.9549265210 1.776357e-15 1 262144 7.9549265210 1.776357e-15 1 524288 7.9549265210 2.664535e-15 0.666667 1048576 7.9549265210 8.881784e-16 3 Exact 7.9549265210 Problem 27 1 0.2500000000 5.911169e-01 2 0.4581540282 3.829629e-01 1.54354 4 0.5912016336 2.499153e-01 1.53237 8 0.6778198535 1.632971e-01 1.53043 16 0.7345473206 1.065696e-01 1.5323 32 0.7717160558 6.940086e-02 1.53557 64 0.7960293362 4.508758e-02 1.53925 128 0.8118954678 2.922145e-02 1.54296 256 0.8222224807 1.889444e-02 1.54656 512 0.8289268850 1.219003e-02 1.54999 1024 0.8332686786 7.848238e-03 1.55322 2048 0.8360738394 5.043077e-03 1.55624 4096 0.8378822109 3.234706e-03 1.55905 8192 0.8390455928 2.071324e-03 1.56166 16384 0.8397926004 1.324316e-03 1.56407 32768 0.8402714042 8.455124e-04 1.56629 65536 0.8405777981 5.391185e-04 1.56832 131072 0.8407735699 3.433467e-04 1.57019 262144 0.8408984870 2.184297e-04 1.57189 524288 0.8409780932 1.388234e-04 1.57344 1048576 0.8410287660 8.815068e-05 1.57484 Exact 0.8411169166 Problem 28 1 0.0000000000 1.995467e-02 2 0.0000000000 1.995467e-02 1 4 0.0000000000 1.995467e-02 1 8 0.2959105006 2.759558e-01 0.0723111 16 0.3735377198 3.535831e-01 0.780455 32 -0.0192977300 3.925240e-02 9.00793 64 -0.0593458542 7.930052e-02 0.494983 128 0.0087595206 1.119515e-02 7.08347 256 0.0173842467 2.570423e-03 4.35537 512 0.0193243877 6.302816e-04 4.07821 1024 0.0197978432 1.568261e-04 4.01898 2048 0.0199155089 3.916039e-05 4.00471 4096 0.0199448821 9.787220e-06 4.00118 8192 0.0199522227 2.446625e-06 4.00029 16384 0.0199540576 6.116451e-07 4.00007 32768 0.0199545164 1.529106e-07 4.00002 65536 0.0199546311 3.822760e-08 4 131072 0.0199546597 9.556897e-09 4 262144 0.0199546669 2.389224e-09 4 524288 0.0199546687 5.973060e-10 4 1048576 0.0199546691 1.493265e-10 4 Exact 0.0199546693 Problem 29 1 0.2500000000 5.685282e-02 2 0.3250000000 1.814718e-02 3.13287 4 0.2736111111 3.324171e-02 0.545916 8 0.2958797115 1.097311e-02 3.02938 16 0.3071284252 2.756057e-04 39.8145 32 0.3012872437 5.565576e-03 0.0495197 64 0.3041538059 2.699014e-03 2.06208 128 0.3055888371 1.263982e-03 2.13533 256 0.3063067904 5.460291e-04 2.31486 512 0.3066658764 1.869431e-04 2.92083 1024 0.3068454467 7.372730e-06 25.356 2048 0.3069352387 8.241928e-05 0.0894539 4096 0.3068903295 3.751008e-05 2.19726 8192 0.3068678754 1.505591e-05 2.49139 16384 0.3068566484 3.828932e-06 3.93214 32768 0.3068510349 1.784531e-06 2.14562 65536 0.3068538416 1.022149e-06 1.74586 131072 0.3068524382 3.812036e-07 2.68137 262144 0.3068531399 3.204696e-07 1.18952 524288 0.3068527891 3.036776e-08 10.553 1048576 0.3068529645 1.450507e-07 0.20936 Exact 0.3068528194 Problem 30 1 23.3632498009 2.789082e+01 2 8.9397059140 1.346728e+01 2.07101 4 -4.9855425774 4.579730e-01 29.4063 8 -10.3588409697 5.831271e+00 0.0785374 16 -4.8933767376 3.658071e-01 15.9408 32 -4.6044424927 7.687287e-02 4.7586 64 -4.5460461566 1.847653e-02 4.16057 128 -4.5321445299 4.574905e-03 4.03867 256 -4.5287106187 1.140994e-03 4.00958 512 -4.5278547032 2.850781e-04 4.00239 1024 -4.5276408840 7.125888e-05 4.0006 2048 -4.5275874392 1.781406e-05 4.00015 4096 -4.5275740786 4.453472e-06 4.00004 8192 -4.5275707385 1.113366e-06 4.00001 16384 -4.5275699035 2.783412e-07 4 32768 -4.5275696947 6.958530e-08 4 65536 -4.5275696426 1.739632e-08 4 131072 -4.5275696295 4.349082e-09 4 262144 -4.5275696262 1.087272e-09 3.99999 524288 -4.5275696254 2.718163e-10 4.00003 1048576 -4.5275696252 6.795542e-11 3.99992 Exact -4.5275696252 Problem 31 1 0.4705882353 2.181047e+00 2 4.2352941176 1.583659e+00 1.37722 4 2.9176470588 2.660117e-01 5.95334 8 2.6588235294 7.188202e-03 37.0067 16 2.6505068050 1.128522e-03 6.36957 32 2.6513471635 2.881639e-04 3.91625 64 2.6515632514 7.207597e-05 3.99806 128 2.6516173062 1.802118e-05 3.99951 256 2.6516308219 4.505433e-06 3.99988 512 2.6516342010 1.126367e-06 3.99997 1024 2.6516350457 2.815922e-07 3.99999 2048 2.6516352569 7.039809e-08 4 4096 2.6516353097 1.759953e-08 4 8192 2.6516353229 4.399882e-09 4 16384 2.6516353262 1.099970e-09 4 32768 2.6516353271 2.749925e-10 4 65536 2.6516353273 6.874767e-11 4.00003 131072 2.6516353273 1.718758e-11 3.99984 262144 2.6516353273 4.297895e-12 3.99907 524288 2.6516353273 1.074252e-12 4.00083 1048576 2.6516353273 2.677858e-13 4.01161 Exact 2.6516353273 Problem 32 1 -34.7785186603 2.270817e+01 2 -17.3892593301 5.318913e+00 4.26933 4 -13.3360228474 1.265677e+00 4.20243 8 -12.3821624298 3.118161e-01 4.05905 16 -12.1480040999 7.765778e-02 4.01526 32 -12.0897421170 1.939580e-02 4.00385 64 -12.0751940992 4.847783e-03 4.00096 128 -12.0715581891 1.211873e-03 4.00024 256 -12.0706492800 3.029636e-04 4.00006 512 -12.0704220570 7.574062e-05 4.00002 1024 -12.0703652515 1.893514e-05 4 2048 -12.0703510502 4.733783e-06 4 4096 -12.0703474998 1.183446e-06 4 8192 -12.0703466123 2.958614e-07 4 16384 -12.0703463904 7.396535e-08 4 32768 -12.0703463349 1.849134e-08 4 65536 -12.0703463210 4.622832e-09 4 131072 -12.0703463175 1.155707e-09 4 262144 -12.0703463167 2.889280e-10 3.99998 524288 -12.0703463165 7.223022e-11 4.0001 1048576 -12.0703463164 1.805489e-11 4.00059 Exact -12.0703463164 Problem 33 1 0.0000000000 8.862269e-01 2 0.4162773056 4.699496e-01 1.88579 4 0.6365811637 2.496458e-01 1.88247 8 0.7537134206 1.325135e-01 1.88393 16 0.8160450634 7.018186e-02 1.88814 32 0.8491672690 3.705966e-02 1.89375 64 0.8667210139 1.950591e-02 1.89992 128 0.8759937712 1.023315e-02 1.90615 256 0.8808753135 5.351612e-03 1.91216 512 0.8834364549 2.790471e-03 1.91782 1024 0.8847758579 1.451068e-03 1.92305 2048 0.8854742329 7.526926e-04 1.92784 4096 0.8858373726 3.895528e-04 1.9322 8192 0.8860257262 2.011992e-04 1.93615 16384 0.8861232009 1.037246e-04 1.93974 32768 0.8861735417 5.338370e-05 1.943 65536 0.8861994923 2.743313e-05 1.94596 131072 0.8862128474 1.407804e-05 1.94865 262144 0.8862197100 7.215438e-06 1.9511 524288 0.8862232316 3.693897e-06 1.95334 1048576 0.8862250364 1.889081e-06 1.95539 Exact 0.8862269255 Problem 34 1 3067.0860000000 1.981833e+03 2 1643.2110000000 5.579583e+02 3.55194 4 1228.6485000000 1.433958e+02 3.89104 8 1121.3457656250 3.609310e+01 3.97294 16 1094.2912001953 9.038534e+00 3.99325 32 1087.5132537231 2.260587e+00 3.99831 64 1085.8178730354 5.652064e-01 3.99958 128 1085.3939719841 1.413053e-01 3.99989 256 1085.2879932289 3.532656e-02 3.99997 512 1085.2614983218 8.831655e-03 3.99999 1024 1085.2548745814 2.207915e-03 4 2048 1085.2532186454 5.519787e-04 4 4096 1085.2528046614 1.379947e-04 4 8192 1085.2527011653 3.449867e-05 4 16384 1085.2526752913 8.624668e-06 4 32768 1085.2526688228 2.156167e-06 4 65536 1085.2526672057 5.390416e-07 4 131072 1085.2526668014 1.347605e-07 4 262144 1085.2526667004 3.368996e-08 4.00002 524288 1085.2526666751 8.422603e-09 3.99995 1048576 1085.2526666688 2.105480e-09 4.00032 Exact 1085.2526666667 Problem 35 1 23.6166666667 2.383333e+00 2 19.8879508849 6.112049e+00 0.38994 4 19.5175645453 6.482435e+00 0.942863 8 21.7455557172 4.254444e+00 1.52369 16 23.1996366447 2.800363e+00 1.51925 32 23.9339033513 2.066097e+00 1.35539 64 24.7423657557 1.257634e+00 1.64284 128 24.9031807773 1.096819e+00 1.14662 256 25.8654439538 1.345560e-01 8.15139 512 25.5685914267 4.314086e-01 0.311899 1024 25.6091927248 3.908073e-01 1.10389 2048 26.0547796384 5.477964e-02 7.13417 4096 25.8934991781 1.065008e-01 0.514359 8192 25.8655923385 1.344077e-01 0.792372 16384 25.9507116119 4.928839e-02 2.72696 32768 25.9339086931 6.609131e-02 0.745762 65536 25.9682689992 3.173100e-02 2.08286 131072 25.9653437538 3.465625e-02 0.915593 262144 26.0115471298 1.154713e-02 3.00129 524288 25.9937706643 6.229336e-03 1.85367 1048576 25.9891580728 1.084193e-02 0.57456 Exact 26.0000000000 Problem 36 1 0.0000000000 1.000000e+02 2 0.6467291875 9.935327e+01 1.00651 4 1.6233785593 9.837662e+01 1.00993 8 2.9056264224 9.709437e+01 1.01321 16 4.4549246112 9.554508e+01 1.01622 32 6.2315416133 9.376846e+01 1.01895 64 8.1985370100 9.180146e+01 1.02143 128 10.3225590293 8.967744e+01 1.02369 256 12.5737837817 8.742622e+01 1.02575 512 14.9256562653 8.507434e+01 1.02764 1024 17.3546023069 8.264540e+01 1.02939 2048 19.8397524192 8.016025e+01 1.031 4096 22.3626862733 7.763731e+01 1.0325 8192 24.9071985135 7.509280e+01 1.03388 16384 27.4590847676 7.254092e+01 1.03518 32768 30.0059463368 6.999405e+01 1.03639 65536 32.5370120590 6.746299e+01 1.03752 131072 35.0429759308 6.495702e+01 1.03858 262144 37.5158491763 6.248415e+01 1.03958 524288 39.9488255602 6.005117e+01 1.04052 1048576 42.3361588309 5.766384e+01 1.0414 Exact 100.0000000000 Problem 37 1 0.0113937264 3.124405e+00 2 0.0116914964 3.124107e+00 1.0001 4 0.2013894773 2.934409e+00 1.06465 8 0.1216467883 3.014152e+00 0.973544 16 0.1551111986 2.980688e+00 1.01123 32 1.7809943800 1.354804e+00 2.20009 64 1.0711457886 2.064653e+00 0.65619 128 1.1777763123 1.958022e+00 1.05446 256 4.5586283640 1.422830e+00 1.37615 512 3.3289585081 1.931598e-01 7.36608 1024 3.1359449233 1.462141e-04 1321.07 2048 3.1357768026 2.190655e-05 6.67445 4096 3.1357987082 9.252821e-10 23675.5 8192 3.1357987089 2.503930e-10 3.69532 16384 3.1357987091 6.259793e-11 4.00002 32768 3.1357987091 1.564926e-11 4.00006 65536 3.1357987092 3.911982e-12 4.00034 131072 3.1357987092 9.778844e-13 4.00045 262144 3.1357987092 2.442491e-13 4.00364 524288 3.1357987092 5.995204e-14 4.07407 1048576 3.1357987092 1.465494e-14 4.09091 Exact 3.1357987092 Problem 38 1 3.1415926536 2.602336e+00 2 1.3422454081 8.029885e-01 3.24081 4 1.9437561319 1.404499e+00 0.571726 8 0.5397470433 4.901286e-04 2865.57 16 0.5392569147 3.330669e-16 1.47156e+12 32 0.5392569147 3.330669e-16 1 64 0.5392569147 3.330669e-16 1 128 0.5392569147 1.110223e-16 3 256 0.5392569147 0.000000e+00 (*/0) 512 0.5392569147 0.000000e+00 (*/0) 1024 0.5392569147 0.000000e+00 (*/0) 2048 0.5392569147 0.000000e+00 (*/0) 4096 0.5392569147 0.000000e+00 (*/0) 8192 0.5392569147 0.000000e+00 (*/0) 16384 0.5392569147 0.000000e+00 (*/0) 32768 0.5392569147 0.000000e+00 (*/0) 65536 0.5392569147 0.000000e+00 (*/0) 131072 0.5392569147 0.000000e+00 (*/0) 262144 0.5392569147 0.000000e+00 (*/0) 524288 0.5392569147 1.110223e-16 0 1048576 0.5392569147 1.110223e-16 1 Exact 0.5392569147 Problem 39 1 1.4783978395 1.309296e+00 2 1.9639437911 8.237499e-01 1.58943 4 2.2352956340 5.523981e-01 1.49123 8 2.4051781115 3.825156e-01 1.44412 16 2.5192875362 2.684062e-01 1.42514 32 2.5984238620 1.892698e-01 1.41811 64 2.6539904498 1.337033e-01 1.4156 128 2.6931839243 9.450978e-02 1.4147 256 2.7208733725 6.682033e-02 1.41439 512 2.7404466374 4.724706e-02 1.41427 1024 2.7542854927 3.340821e-02 1.41424 2048 2.7640706579 2.362304e-02 1.41422 4096 2.7709897187 1.670398e-02 1.41422 8192 2.7758822096 1.181149e-02 1.41421 16384 2.7793417171 8.351983e-03 1.41421 32768 2.7817879568 5.905743e-03 1.41421 65536 2.7835177092 4.175991e-03 1.41421 131072 2.7847408287 2.952872e-03 1.41421 262144 2.7856057047 2.087996e-03 1.41421 524288 2.7862172645 1.476436e-03 1.41421 1048576 2.7866497025 1.043998e-03 1.41421 Exact 2.7876937002 Problem 40 1 1.6435171944 1.055439e+00 2 1.7576908581 9.412657e-01 1.1213 4 2.5492807554 1.496758e-01 6.28869 8 2.3532841350 3.456725e-01 0.432999 16 2.3998659617 2.990906e-01 1.15574 32 2.6705435560 2.841305e-02 10.5265 64 2.5855952275 1.133614e-01 0.250641 128 2.5923934798 1.065631e-01 1.0638 256 2.7677948859 6.883828e-02 1.54802 512 2.6961387651 2.817836e-03 24.4295 1024 2.6724717743 2.648483e-02 0.106394 2048 2.6722256455 2.673096e-02 0.990792 4096 2.8169121811 1.179556e-01 0.226619 8192 2.7484859040 4.952930e-02 2.38153 16384 2.7170466295 1.809003e-02 2.73793 32768 2.7033003027 4.343701e-03 4.16466 65536 2.6978567535 1.099848e-03 3.94937 131072 2.6962506518 2.705950e-03 0.406455 262144 2.6966592950 2.297306e-03 1.17788 524288 2.6983350159 6.215853e-04 3.69588 1048576 2.6979089122 1.047689e-03 0.593292 Exact 2.6989566013 Problem 41 1 0.0000000000 6.095585e+00 2 0.8888888889 5.206696e+00 1.17072 4 1.7234973485 4.372088e+00 1.19089 8 2.5541004440 3.541485e+00 1.23454 16 3.3471619645 2.748423e+00 1.28855 32 4.0407119544 2.054873e+00 1.33751 64 4.5977433695 1.497842e+00 1.37189 128 5.0196350297 1.075950e+00 1.39211 256 5.3286659674 7.669191e-01 1.40295 512 5.5511047106 5.444804e-01 1.40853 1024 5.7098015326 3.857836e-01 1.41136 2048 5.8225191180 2.730660e-01 1.41279 4096 5.9024006382 1.931845e-01 1.4135 8192 5.9589485064 1.366366e-01 1.41386 16384 5.9989562187 9.662888e-02 1.41403 32768 6.0272538423 6.833126e-02 1.41412 65536 6.0472660772 4.831903e-02 1.41417 131072 6.0614178519 3.416725e-02 1.41419 262144 6.0714250170 2.416009e-02 1.4142 524288 6.0785012748 1.708383e-02 1.41421 1048576 6.0835049883 1.208011e-02 1.41421 Exact 6.0955851028 Problem 42 1 0.7853981634 3.195388e+00 2 1.3937366575 2.587050e+00 1.23515 4 1.8812039626 2.099582e+00 1.23217 8 2.2757544929 1.705032e+00 1.2314 16 2.5959431538 1.384843e+00 1.23121 32 2.8559589645 1.124827e+00 1.23116 64 3.0671456057 9.136406e-01 1.23115 128 3.2386800596 7.421062e-01 1.23115 256 3.3780088432 6.027774e-01 1.23114 512 3.4911788826 4.896074e-01 1.23114 1024 3.5831014981 3.976848e-01 1.23114 2048 3.6577658588 3.230204e-01 1.23114 4096 3.7184121638 2.623741e-01 1.23114 8192 3.7676722703 2.131140e-01 1.23114 16384 3.8076839098 1.731023e-01 1.23114 32768 3.8401834598 1.406028e-01 1.23114 65536 3.8665812972 1.142050e-01 1.23114 131072 3.8880230039 9.276325e-02 1.23114 262144 3.9054390815 7.534717e-02 1.23114 524288 3.9195853323 6.120092e-02 1.23114 1048576 3.9310756584 4.971059e-02 1.23114 Exact 3.9807862525 Problem 43 1 0.0000000000 2.991569e+00 2 0.6462375385 2.345331e+00 1.27554 4 1.1200215180 1.871547e+00 1.25315 8 1.4853270309 1.506242e+00 1.24253 16 1.7741986048 1.217370e+00 1.23729 32 2.0055032075 9.860658e-01 1.23457 64 2.1919048119 7.996642e-01 1.2331 128 2.3426363456 6.489326e-01 1.23228 256 2.4647548523 5.268141e-01 1.23181 512 2.5637980518 4.277709e-01 1.23153 1024 2.6441758137 3.473932e-01 1.23137 2048 2.7094292152 2.821398e-01 1.23128 4096 2.7624153032 2.291537e-01 1.23123 8192 2.8054456101 1.861234e-01 1.23119 16384 2.8403933331 1.511757e-01 1.23117 32768 2.8687778957 1.227911e-01 1.23116 65536 2.8918324501 9.973654e-02 1.23115 131072 2.9105581439 8.101084e-02 1.23115 262144 2.9257679287 6.580106e-02 1.23115 524288 2.9381220135 5.344697e-02 1.23115 1048576 2.9481566003 4.341239e-02 1.23115 Exact 2.9915689877 Problem 44 1 -0.3784012477 3.483015e-01 2 -0.1891799828 1.590803e-01 2.18947 4 -0.0943522123 6.425251e-02 2.47586 8 -0.0507335194 2.063382e-02 3.11394 16 -0.0357058608 5.606160e-03 3.68056 32 -0.0315331964 1.433496e-03 3.91083 64 -0.0304601422 3.604417e-04 3.97705 128 -0.0301899413 9.024079e-05 3.99422 256 -0.0301222689 2.256836e-05 3.99855 512 -0.0301053431 5.642601e-06 3.99964 1024 -0.0301011112 1.410682e-06 3.99991 2048 -0.0301000532 3.526726e-07 3.99998 4096 -0.0300997887 8.816826e-08 3.99999 8192 -0.0300997226 2.204207e-08 4 16384 -0.0300997060 5.510519e-09 4 32768 -0.0300997019 1.377630e-09 4 65536 -0.0300997009 3.444074e-10 4 131072 -0.0300997006 8.610186e-11 4 262144 -0.0300997005 2.152546e-11 4 524288 -0.0300997005 5.381365e-12 4 1048576 -0.0300997005 1.345337e-12 4.00001 Exact -0.0300997005 Problem 45 1 0.0000000000 2.927067e-01 2 -0.4161468365 1.234401e-01 2.37124 4 -0.4677021709 1.749955e-01 0.70539 8 -0.4446935384 1.519868e-01 1.15139 16 -0.4097805128 1.170738e-01 1.29821 32 -0.3788247401 8.611803e-02 1.35946 64 -0.3547700267 6.206332e-02 1.38758 128 -0.3370035334 4.429682e-02 1.40108 256 -0.3241744503 3.146774e-02 1.40769 512 -0.3150090291 2.230232e-02 1.41096 1024 -0.3084949470 1.578824e-02 1.41259 2048 -0.3038770827 1.117037e-02 1.4134 4096 -0.3006076198 7.900910e-03 1.41381 8192 -0.2982942971 5.587587e-03 1.41401 16384 -0.2966580136 3.951304e-03 1.41411 32768 -0.2955008035 2.794094e-03 1.41416 65536 -0.2946824678 1.975758e-03 1.41419 131072 -0.2941037941 1.397084e-03 1.4142 262144 -0.2936946020 9.878923e-04 1.41421 524288 -0.2934052566 6.985469e-04 1.41421 1048576 -0.2932006576 4.939478e-04 1.41421 Exact -0.2927067098 Problem 46 1 7.9093933286 1.840302e+00 2 6.2831853072 2.140943e-01 8.59575 4 6.0727385036 3.647544e-03 58.6955 8 6.0690920550 1.095435e-06 3329.77 16 6.0690909596 9.858780e-14 1.11113e+07 32 6.0690909596 1.776357e-15 55.5 64 6.0690909596 1.776357e-15 1 128 6.0690909596 8.881784e-16 2 256 6.0690909596 0.000000e+00 (*/0) 512 6.0690909596 8.881784e-16 0 1024 6.0690909596 8.881784e-16 1 2048 6.0690909596 8.881784e-16 1 4096 6.0690909596 8.881784e-16 1 8192 6.0690909596 8.881784e-16 1 16384 6.0690909596 8.881784e-16 1 32768 6.0690909596 8.881784e-16 1 65536 6.0690909596 8.881784e-16 1 131072 6.0690909596 1.776357e-15 0.5 262144 6.0690909596 8.881784e-16 2 524288 6.0690909596 1.776357e-15 0.5 1048576 6.0690909596 8.881784e-16 2 Exact 6.0690909596 Problem 47 1 0.0000000000 4.444444e-01 2 -0.2450645359 1.993799e-01 2.22913 4 -0.3581040588 8.634039e-02 2.30923 8 -0.4080900395 3.635440e-02 2.37496 16 -0.4294745848 1.496986e-02 2.42851 32 -0.4383894861 6.054958e-03 2.47233 64 -0.4420306837 2.413761e-03 2.50852 128 -0.4434936549 9.507895e-04 2.53869 256 -0.4440736367 3.708078e-04 2.5641 512 -0.4443010379 1.434066e-04 2.58571 1024 -0.4443893780 5.506641e-05 2.60425 2048 -0.4444234290 2.101542e-05 2.62029 4096 -0.4444364667 7.977697e-06 2.63427 8192 -0.4444414301 3.014369e-06 2.64656 16384 -0.4444433101 1.134322e-06 2.65742 32768 -0.4444440191 4.253040e-07 2.66709 65536 -0.4444442855 1.589484e-07 2.67574 131072 -0.4444443852 5.923133e-08 2.68352 262144 -0.4444444224 2.201453e-08 2.69056 524288 -0.4444444363 8.162761e-09 2.69695 1048576 -0.4444444414 3.020140e-09 2.70278 Exact -0.4444444444 Problem 48 1 0.0000000000 4.000000e+00 2 -0.4901290717 3.509871e+00 1.13964 4 -1.0212583774 2.978742e+00 1.17831 8 -1.5381917110 2.461808e+00 1.20998 16 -2.0067724556 1.993228e+00 1.23509 32 -2.4117834563 1.588217e+00 1.25501 64 -2.7504684302 1.249532e+00 1.27105 128 -3.0269867783 9.730132e-01 1.28419 256 -3.2487130395 7.512870e-01 1.29513 512 -3.4240253394 5.759747e-01 1.30438 1024 -3.5610920379 4.389080e-01 1.31229 2048 -3.6672776713 3.327223e-01 1.31914 4096 -3.7489135347 2.510865e-01 1.32513 8192 -3.8112712756 1.887287e-01 1.33041 16384 -3.8586405100 1.413595e-01 1.3351 32768 -3.8944518540 1.055481e-01 1.33929 65536 -3.9214121253 7.858787e-02 1.34306 131072 -3.9416340348 5.836597e-02 1.34647 262144 -3.9567519978 4.324800e-02 1.34956 524288 -3.9680210713 3.197893e-02 1.35239 1048576 -3.9763989665 2.360103e-02 1.35498 Exact -4.0000000000 Problem 49 1 163.0267434748 1.102860e+02 2 75.6249207627 2.288417e+01 4.81931 4 59.2028012435 6.462053e+00 3.54132 8 54.8416689332 2.100921e+00 3.07582 16 53.6554093293 9.146609e-01 2.29694 32 52.7385403916 2.207992e-03 414.25 64 52.7994798559 5.873147e-02 0.0375947 128 52.7979185388 5.717016e-02 1.02731 256 52.7662708750 2.552249e-02 2.23999 512 52.7542182440 1.346986e-02 1.89479 1024 52.7460837236 5.335340e-03 2.52465 2048 52.7443688376 3.620454e-03 1.47367 4096 52.7406356539 1.127296e-04 32.1163 8192 52.7413234463 5.750628e-04 0.19603 16384 52.7412082052 4.598217e-04 1.25062 32768 52.7402142823 5.341011e-04 0.860926 65536 52.7405708765 1.775070e-04 3.0089 131072 52.7407041402 4.424327e-05 4.01207 262144 52.7407479819 4.016073e-07 110.166 524288 52.7407579377 9.554236e-06 0.0420345 1048576 52.7407555201 7.136652e-06 1.33876 Exact 52.7407483835 Problem 50 1 0.0000000000 1.281368e-01 2 -0.0000000000 1.281368e-01 1 4 -0.2746530722 1.465162e-01 0.874557 8 0.0798202795 2.079571e-01 0.70455 16 -0.0770413564 5.109549e-02 4.06997 32 -0.1140287144 1.410813e-02 3.6217 64 -0.1241974944 3.939354e-03 3.58133 128 -0.1270434695 1.093379e-03 3.60292 256 -0.1278359730 3.008754e-04 3.63399 512 -0.1280547184 8.213000e-05 3.6634 1024 -0.1281145861 2.226231e-05 3.6892 2048 -0.1281308502 5.998170e-06 3.71152 4096 -0.1281352407 1.607701e-06 3.7309 8192 -0.1281364194 4.289654e-07 3.74786 16384 -0.1281367344 1.140014e-07 3.76281 32768 -0.1281368182 3.019039e-08 3.77608 65536 -0.1281368404 7.970105e-09 3.78795 131072 -0.1281368463 2.098153e-09 3.79863 262144 -0.1281368478 5.509449e-10 3.80828 524288 -0.1281368483 1.443379e-10 3.81705 1048576 -0.1281368484 3.773490e-11 3.82505 Exact -0.1281368484 Problem 51 1 0.0000000000 1.978136e-01 2 -0.1581270644 3.968649e-02 4.9844 4 -0.1810064423 1.680712e-02 2.36129 8 -0.1870476185 1.076594e-02 1.56114 16 -0.1886520682 9.161491e-03 1.17513 32 -0.1890933354 8.720224e-03 1.0506 64 -0.1892195214 8.594038e-03 1.01468 128 -0.1892572548 8.556304e-03 1.00441 256 -0.1892691078 8.544451e-03 1.00139 512 -0.1892730258 8.540533e-03 1.00046 1024 -0.1892743863 8.539173e-03 1.00016 2048 -0.1892748801 8.538679e-03 1.00006 4096 -0.1892750663 8.538493e-03 1.00002 8192 -0.1892751388 8.538420e-03 1.00001 16384 -0.1892751677 8.538391e-03 1 32768 -0.1892751795 8.538380e-03 1 65536 -0.1892751843 8.538375e-03 1 131072 -0.1892751864 8.538373e-03 1 262144 -0.1892751872 8.538372e-03 1 524288 -0.1892751876 8.538372e-03 1 1048576 -0.1892751878 8.538371e-03 1 Exact -0.1978135592 Problem 52 1 -2.9990491284 2.909105e+00 2 -1.4669158685 1.376972e+00 2.11268 4 -0.2786830085 1.887390e-01 7.29564 8 -0.6049479484 5.150039e-01 0.366481 16 0.1288238450 2.187679e-01 2.35411 32 -0.4213189272 3.313749e-01 0.660182 64 0.2034640575 2.934081e-01 1.1294 128 -0.3946885926 3.047446e-01 0.9628 256 0.2117235371 3.016675e-01 1.0102 512 -0.3924035639 3.024596e-01 0.997381 1024 0.2123158673 3.022599e-01 1.00066 2048 -0.3922539125 3.023099e-01 0.999835 4096 0.2123533838 3.022974e-01 1.00004 8192 -0.3922445268 3.023005e-01 0.99999 16384 0.2123557306 3.022997e-01 1 32768 -0.3922439401 3.022999e-01 0.999999 65536 0.2123558773 3.022999e-01 1 131072 -0.3922439034 3.022999e-01 1 262144 0.2123558865 3.022999e-01 1 524288 -0.3922439011 3.022999e-01 1 1048576 0.2123558870 3.022999e-01 1 Exact -0.0899440070 Problem 53 1 0.8535533906 6.510694e-01 2 1.0041269645 5.004958e-01 1.30085 4 1.7105778963 2.059551e-01 2.43012 8 1.4514749836 5.314778e-02 3.87514 16 1.3737566439 1.308661e-01 0.406123 32 1.3920432018 1.125796e-01 1.16243 64 1.4840430835 2.057968e-02 5.47042 128 1.4574285290 4.719423e-02 0.436063 256 1.4654503744 3.917239e-02 1.20478 512 1.4906261719 1.399659e-02 2.79871 1024 1.4854886738 1.913409e-02 0.7315 2048 1.4948908692 9.731893e-03 1.96612 4096 1.4944819930 1.014077e-02 0.95968 8192 1.5170556446 1.243288e-02 0.815641 16384 1.5072705009 2.647738e-03 4.69566 32768 1.5034708763 1.151886e-03 2.29861 65536 1.5024404596 2.182303e-03 0.527831 131072 1.5029638659 1.658897e-03 1.31551 262144 1.5036481850 9.745774e-04 1.70217 524288 1.5037325238 8.902387e-04 1.09474 1048576 1.5048209046 1.981422e-04 4.49293 Exact 1.5046227625 Problem 54 1 1.0000000000 1.547005e-01 2 1.0000000000 1.547005e-01 1 4 1.1666666667 1.196613e-02 12.9282 8 1.1547619048 6.136638e-05 194.995 16 1.1547005400 1.630567e-09 37635 32 1.1547005384 2.220446e-16 7.34342e+06 64 1.1547005384 0.000000e+00 (*/0) 128 1.1547005384 2.220446e-16 0 256 1.1547005384 2.220446e-16 1 512 1.1547005384 2.220446e-16 1 1024 1.1547005384 2.220446e-16 1 2048 1.1547005384 2.220446e-16 1 4096 1.1547005384 2.220446e-16 1 8192 1.1547005384 2.220446e-16 1 16384 1.1547005384 2.220446e-16 1 32768 1.1547005384 2.220446e-16 1 65536 1.1547005384 2.220446e-16 1 131072 1.1547005384 2.220446e-16 1 262144 1.1547005384 2.220446e-16 1 524288 1.1547005384 2.220446e-16 1 1048576 1.1547005384 6.661338e-16 0.333333 Exact 1.1547005384 Problem 55 1 0.2880562701 2.170024e-01 2 0.4289195474 7.613909e-02 2.85008 4 0.4908095798 1.424905e-02 5.34345 8 0.5015825750 3.476057e-03 4.0992 16 0.5041945627 8.640698e-04 4.02289 32 0.5048429175 2.157150e-04 4.00561 64 0.5050047225 5.390994e-05 4.0014 128 0.5050451561 1.347631e-05 4.00035 256 0.5050552634 3.369005e-06 4.00009 512 0.5050577902 8.422466e-07 4.00002 1024 0.5050584219 2.105614e-07 4.00001 2048 0.5050585798 5.264032e-08 4 4096 0.5050586193 1.316008e-08 4 8192 0.5050586292 3.290020e-09 4 16384 0.5050586316 8.225050e-10 4 32768 0.5050586322 2.056263e-10 4 65536 0.5050586324 5.140655e-11 4 131072 0.5050586324 1.285161e-11 4.00001 262144 0.5050586325 3.212985e-12 3.9999 524288 0.5050586325 8.033574e-13 3.99945 1048576 0.5050586325 2.008393e-13 4 Exact 0.5050586325 Problem 56 1 1.0526315789 9.396208e-01 2 1.6374269006 3.548255e-01 2.64812 4 1.9108636209 8.138879e-02 4.35964 8 1.9746678393 1.758457e-02 4.62842 16 1.9879071767 4.345231e-03 4.04687 32 1.9911692914 1.083117e-03 4.01179 64 1.9919818264 2.705816e-04 4.00292 128 1.9921847749 6.763308e-05 4.00073 256 1.9922355004 1.690750e-05 4.00018 512 1.9922481811 4.226827e-06 4.00005 1024 1.9922513512 1.056704e-06 4.00001 2048 1.9922521438 2.641758e-07 4 4096 1.9922523419 6.604393e-08 4 8192 1.9922523914 1.651098e-08 4 16384 1.9922524038 4.127745e-09 4 32768 1.9922524069 1.031937e-09 4 65536 1.9922524077 2.579841e-10 4 131072 1.9922524079 6.449619e-11 3.99999 262144 1.9922524079 1.612377e-11 4.00007 524288 1.9922524079 4.030776e-12 4.00017 1048576 1.9922524079 1.007638e-12 4.00022 Exact 1.9922524080 Problem 57 1 0.5000000000 1.000000e-01 2 0.4267766953 2.677670e-02 3.73459 4 0.4070181109 7.018111e-03 3.81537 8 0.4018124648 1.812465e-03 3.87214 16 0.4004634013 4.634013e-04 3.91122 32 0.4001176712 1.176712e-04 3.9381 64 0.4000297399 2.973986e-05 3.95668 128 0.4000074919 7.491909e-06 3.9696 256 0.4000018830 1.883044e-06 3.97862 512 0.4000004725 4.725407e-07 3.98494 1024 0.4000001184 1.184498e-07 3.98938 2048 0.4000000297 2.966806e-08 3.9925 4096 0.4000000074 7.426846e-09 3.99471 8192 0.4000000019 1.858449e-09 3.99626 16384 0.4000000005 4.649195e-10 3.99736 32768 0.4000000001 1.162842e-10 3.99813 65536 0.4000000000 2.908068e-11 3.99868 131072 0.4000000000 7.271850e-12 3.99908 262144 0.4000000000 1.818268e-12 3.99933 524288 0.4000000000 4.545808e-13 3.99988 1048576 0.4000000000 1.136313e-13 4.00049 Exact 0.4000000000 test_int_test() Normal end of execution. Fri Sep 2 19:12:18 2022