06-Jun-2023 14:28:09 test_int_test() MATLAB/Octave version 5.2.0 Test test_int(). midpoint_test(): Composite midpoint rule, for 1D finite interval problems. Intervals Approx Error Problem 1: 1 1.6487212707 6.956056e-02 2 1.7005127167 1.776911e-02 4 1.7138152798 4.466549e-03 8 1.7171636650 1.118163e-03 16 1.7180021921 2.796364e-04 32 1.7182119134 6.991508e-05 64 1.7182643493 1.747914e-05 128 1.7182774587 4.369809e-06 256 1.7182807360 1.092454e-06 512 1.7182815553 2.731135e-07 1024 1.7182817602 6.827838e-08 2048 1.7182818114 1.706960e-08 4096 1.7182818242 4.267396e-09 8192 1.7182818274 1.066844e-09 16384 1.7182818282 2.667191e-10 32768 1.7182818284 6.667733e-11 65536 1.7182818284 1.668576e-11 131072 1.7182818285 4.146683e-12 262144 1.7182818285 1.036060e-12 524288 1.7182818285 2.458034e-13 1048576 1.7182818285 3.730349e-14 Exact 1.7182818285 Problem 2: 1 1.0000000000 3.000000e-01 2 0.5000000000 2.000000e-01 4 0.7500000000 5.000000e-02 8 0.7500000000 5.000000e-02 16 0.6875000000 1.250000e-02 32 0.6875000000 1.250000e-02 64 0.7031250000 3.125000e-03 128 0.7031250000 3.125000e-03 256 0.6992187500 7.812500e-04 512 0.6992187500 7.812500e-04 1024 0.7001953125 1.953125e-04 2048 0.7001953125 1.953125e-04 4096 0.6999511719 4.882812e-05 8192 0.6999511719 4.882812e-05 16384 0.7000122070 1.220703e-05 32768 0.7000122070 1.220703e-05 65536 0.6999969482 3.051758e-06 131072 0.6999969482 3.051758e-06 262144 0.7000007629 7.629395e-07 524288 0.7000007629 7.629395e-07 1048576 0.6999998093 1.907349e-07 Exact 0.7000000000 Problem 3: 1 0.7071067812 4.044011e-02 2 0.6830127019 1.634604e-02 4 0.6729773970 6.310730e-03 8 0.6690321721 2.365505e-03 16 0.6675366757 8.700090e-04 32 0.6669826865 3.160198e-04 64 0.6667805032 1.138365e-04 128 0.6667074407 4.077399e-05 256 0.6666812141 1.454746e-05 512 0.6666718429 5.176221e-06 1024 0.6666685050 1.838300e-06 2048 0.6666673187 6.519947e-07 4096 0.6666668977 2.310293e-07 8192 0.6666667485 8.180978e-08 16384 0.6666666956 2.895628e-08 32768 0.6666666769 1.024563e-08 65536 0.6666666703 3.624391e-09 131072 0.6666666679 1.281921e-09 262144 0.6666666671 4.533576e-10 524288 0.6666666668 1.603183e-10 1048576 0.6666666667 5.671086e-11 Exact 0.6666666667 Problem 4: 1 -0.1600000000 6.394282e-01 2 0.3196666522 1.597616e-01 4 0.4394073832 4.002084e-02 8 0.4694166388 1.001159e-02 16 0.4769249100 2.503317e-03 32 0.4788023710 6.258557e-04 64 0.4792717611 1.564656e-04 128 0.4793891102 3.911650e-05 256 0.4794184476 9.779132e-06 512 0.4794257819 2.444783e-06 1024 0.4794276155 6.111959e-07 2048 0.4794280739 1.527990e-07 4096 0.4794281885 3.819974e-08 8192 0.4794282171 9.549936e-09 16384 0.4794282243 2.387486e-09 32768 0.4794282261 5.968694e-10 65536 0.4794282265 1.492145e-10 131072 0.4794282267 3.729939e-11 262144 0.4794282267 9.331313e-12 524288 0.4794282267 2.343736e-12 1048576 0.4794282267 5.907497e-13 Exact 0.4794282267 Problem 5: 1 2.2222222222 6.399893e-01 2 1.6494845361 6.725157e-02 4 1.5969046906 1.467173e-02 8 1.5859426924 3.709729e-03 16 1.5831615948 9.286311e-04 32 1.5824651828 2.322191e-04 64 1.5822910221 5.805841e-05 128 1.5822474786 1.451483e-05 256 1.5822365925 3.628720e-06 512 1.5822338709 9.071810e-07 1024 1.5822331905 2.267953e-07 2048 1.5822330204 5.669883e-08 4096 1.5822329779 1.417471e-08 8192 1.5822329673 3.543671e-09 16384 1.5822329646 8.859158e-10 32768 1.5822329640 2.214704e-10 65536 1.5822329638 5.538170e-11 131072 1.5822329637 1.382894e-11 262144 1.5822329637 3.469891e-12 524288 1.5822329637 9.161560e-13 1048576 1.5822329637 1.492140e-13 Exact 1.5822329637 Problem 6: 1 1.4142135624 4.623357e-02 2 1.0000000000 4.604471e-01 4 1.4920296963 3.158256e-02 8 1.4727748815 1.232775e-02 16 1.4651034810 4.656349e-03 32 1.4621684024 1.721271e-03 64 1.4610744793 6.273476e-04 128 1.4606736315 2.264998e-04 256 1.4605283864 8.125462e-05 512 1.4604761534 2.902157e-05 1024 1.4604574659 1.033411e-05 2048 1.4604508038 3.672017e-06 4096 1.4604484346 1.302843e-06 8192 1.4604475936 4.617721e-07 16384 1.4604472953 1.635479e-07 32768 1.4604471897 5.789463e-08 65536 1.4604471523 2.048679e-08 131072 1.4604471390 7.247673e-09 262144 1.4604471344 2.563548e-09 524288 1.4604471327 9.066672e-10 1048576 1.4604471321 3.206264e-10 Exact 1.4604471318 Problem 7: 1 1.4142135624 5.857864e-01 2 1.5773502692 4.226497e-01 4 1.6988440796 3.011559e-01 8 1.7864610017 2.135390e-01 16 1.8488566846 1.511433e-01 32 1.8930883597 1.069116e-01 64 1.9243927557 7.560724e-02 128 1.9465352800 5.346472e-02 256 1.9621941527 3.780585e-02 512 1.9732670837 2.673292e-02 1024 1.9810969373 1.890306e-02 2048 1.9866335071 1.336649e-02 4096 1.9905484599 9.451540e-03 8192 1.9933167514 6.683249e-03 16384 1.9952742294 4.725771e-03 32768 1.9966583755 3.341624e-03 65536 1.9976371147 2.362885e-03 131072 1.9983291878 1.670812e-03 262144 1.9988185573 1.181443e-03 524288 1.9991645939 8.354061e-04 1048576 1.9994092787 5.907213e-04 Exact 2.0000000000 Problem 8: 1 0.9411764706 7.420348e-02 2 0.8778764332 1.090345e-02 4 0.8696054064 2.632419e-03 8 0.8676258084 6.528211e-04 16 0.8671358590 1.628717e-04 32 0.8670136844 4.069706e-05 64 0.8669831603 1.017296e-05 128 0.8669755305 2.543159e-06 256 0.8669736231 6.357846e-07 512 0.8669731463 1.589458e-07 1024 0.8669730271 3.973644e-08 2048 0.8669729973 9.934108e-09 4096 0.8669729898 2.483529e-09 8192 0.8669729880 6.208812e-10 16384 0.8669729875 1.552165e-10 32768 0.8669729874 3.880285e-11 65536 0.8669729873 9.709122e-12 131072 0.8669729873 2.436384e-12 262144 0.8669729873 6.145084e-13 524288 0.8669729873 1.436629e-13 1048576 0.8669729873 4.440892e-14 Exact 0.8669729873 Problem 9: 1 1.0000000000 1.547005e-01 2 1.3333333333 1.786328e-01 4 1.1428571429 1.184340e-02 8 1.1546391753 6.136312e-05 16 1.1547005367 1.630567e-09 32 1.1547005384 0.000000e+00 64 1.1547005384 6.661338e-16 128 1.1547005384 2.220446e-16 256 1.1547005384 2.220446e-16 512 1.1547005384 4.440892e-16 1024 1.1547005384 1.110223e-15 2048 1.1547005384 4.440892e-16 4096 1.1547005384 2.220446e-16 8192 1.1547005384 3.774758e-15 16384 1.1547005384 2.886580e-15 32768 1.1547005384 5.329071e-15 65536 1.1547005384 1.287859e-14 131072 1.1547005384 6.883383e-15 262144 1.1547005384 1.998401e-15 524288 1.1547005384 5.484502e-14 1048576 1.1547005384 3.708145e-14 Exact 1.1547005384 Problem 10: 1 0.6666666667 2.648051e-02 2 0.6857142857 7.432895e-03 4 0.6912198912 1.927289e-03 8 0.6926605540 4.866265e-04 16 0.6930252143 1.219662e-04 32 0.6931166695 3.051106e-05 64 0.6931395516 7.628987e-06 128 0.6931452732 1.907323e-06 256 0.6931467037 4.768356e-07 512 0.6931470614 1.192092e-07 1024 0.6931471508 2.980232e-08 2048 0.6931471731 7.450581e-09 4096 0.6931471787 1.862645e-09 8192 0.6931471801 4.656625e-10 16384 0.6931471804 1.164144e-10 32768 0.6931471805 2.910883e-11 65536 0.6931471806 7.274403e-12 131072 0.6931471806 1.832867e-12 262144 0.6931471806 4.699574e-13 524288 0.6931471806 9.237056e-14 1048576 0.6931471806 4.996004e-15 Exact 0.6931471806 Problem 11: 1 0.3775406688 2.344824e-03 2 0.3793224000 5.630931e-04 4 0.3797460335 1.394595e-04 8 0.3798507085 3.478450e-05 16 0.3798768019 8.691127e-06 32 0.3798833206 2.172470e-06 64 0.3798849499 5.430980e-07 128 0.3798853573 1.357733e-07 256 0.3798854591 3.394324e-08 512 0.3798854846 8.485806e-09 1024 0.3798854909 2.121452e-09 2048 0.3798854925 5.303637e-10 4096 0.3798854929 1.325903e-10 8192 0.3798854930 3.314754e-11 16384 0.3798854930 8.287260e-12 32768 0.3798854930 2.075506e-12 65536 0.3798854930 5.103695e-13 131072 0.3798854930 1.289524e-13 262144 0.3798854930 3.125278e-14 524288 0.3798854930 9.880985e-15 1048576 0.3798854930 1.448841e-14 Exact 0.3798854930 Problem 12: 1 0.7707470413 6.757593e-03 2 0.7758221334 1.682501e-03 4 0.7770844331 4.202010e-04 8 0.7773996103 1.050238e-04 16 0.7774783798 2.625431e-05 32 0.7774980706 6.563475e-06 64 0.7775029932 1.640862e-06 128 0.7775042239 4.102152e-07 256 0.7775045316 1.025538e-07 512 0.7775046085 2.563844e-08 1024 0.7775046277 6.409610e-09 2048 0.7775046325 1.602402e-09 4096 0.7775046337 4.006040e-10 8192 0.7775046340 1.001493e-10 16384 0.7775046341 2.503264e-11 32768 0.7775046341 6.256107e-12 65536 0.7775046341 1.564637e-12 131072 0.7775046341 3.768097e-13 262144 0.7775046341 8.348877e-14 524288 0.7775046341 1.054712e-14 1048576 0.7775046341 1.532108e-14 Exact 0.7775046341 Problem 13: 1 -1.9178485493 3.576196e+00 2 1.8222776061 1.639300e-01 4 1.6821492311 2.380164e-02 8 1.6636482082 5.300614e-03 16 1.6596364702 1.288876e-03 32 1.6586676071 3.200129e-04 64 1.6584274605 7.986627e-05 128 1.6583675522 1.995802e-05 256 1.6583525832 4.988972e-06 512 1.6583488414 1.247210e-06 1024 1.6583479060 3.118003e-07 2048 1.6583476722 7.794995e-08 4096 1.6583476137 1.948748e-08 8192 1.6583475991 4.871854e-09 16384 1.6583475954 1.217971e-09 32768 1.6583475945 3.044940e-10 65536 1.6583475943 7.611356e-11 131072 1.6583475942 1.902589e-11 262144 1.6583475942 4.793721e-12 524288 1.6583475942 1.252110e-12 1048576 1.6583475942 2.378098e-13 Exact 1.6583475942 Problem 14: 1 0.0000000000 5.000002e-01 2 0.0000000000 5.000002e-01 4 0.0000000000 5.000002e-01 8 0.0000000000 5.000002e-01 16 0.0000009624 4.999992e-01 32 0.0477349580 4.522653e-01 64 0.4237727535 7.622746e-02 128 0.4999661770 3.403412e-05 256 0.5000000000 2.111660e-07 512 0.5000000000 2.111660e-07 1024 0.5000000000 2.111660e-07 2048 0.5000000000 2.111660e-07 4096 0.5000000000 2.111660e-07 8192 0.5000000000 2.111660e-07 16384 0.5000000000 2.111660e-07 32768 0.5000000000 2.111660e-07 65536 0.5000000000 2.111660e-07 131072 0.5000000000 2.111660e-07 262144 0.5000000000 2.111660e-07 524288 0.5000000000 2.111660e-07 1048576 0.5000000000 2.111660e-07 Exact 0.5000002112 Problem 15: 1 0.0000000000 1.000000e+00 2 0.0000000000 1.000000e+00 4 0.0000000000 1.000000e+00 8 0.0000051168 9.999949e-01 16 0.0063225818 9.936774e-01 32 0.1572182584 8.427817e-01 64 0.5653974781 4.346025e-01 128 0.8571189287 1.428811e-01 256 0.9613417350 3.865826e-02 512 0.9901345416 9.865458e-03 1024 0.9975207839 2.479216e-03 2048 0.9993793880 6.206120e-04 4096 0.9998447964 1.552036e-04 8192 0.9999611959 3.880405e-05 16384 0.9999902988 9.701211e-06 32768 0.9999975747 2.425315e-06 65536 0.9999993937 6.063296e-07 131072 0.9999998484 1.515825e-07 262144 0.9999999621 3.789566e-08 524288 0.9999999905 9.474002e-09 1048576 0.9999999976 2.368669e-09 Exact 1.0000000000 Problem 16: 1 0.0254241123 4.682105e-01 2 0.0562605265 4.373741e-01 4 0.1167501124 3.768845e-01 8 0.2257441263 2.678905e-01 16 0.3755442540 1.180904e-01 32 0.4760202743 1.761438e-02 64 0.4933133721 3.212788e-04 128 0.4936345799 7.101607e-08 256 0.4936346590 8.088513e-09 512 0.4936346529 2.022139e-09 1024 0.4936346514 5.055357e-10 2048 0.4936346510 1.263832e-10 4096 0.4936346509 3.159578e-11 8192 0.4936346509 7.898293e-12 16384 0.4936346509 1.973643e-12 32768 0.4936346509 4.933831e-13 65536 0.4936346509 1.225131e-13 131072 0.4936346509 3.252953e-14 262144 0.4936346509 6.550316e-15 524288 0.4936346509 1.432188e-14 1048576 0.4936346509 6.328271e-15 Exact 0.4936346509 Problem 17: 1 0.0000000000 5.000000e-01 2 1.0000000000 5.000000e-01 4 0.5000000000 9.992007e-16 8 0.5000000000 8.881784e-16 16 0.5000000000 4.996004e-16 32 0.5000000000 1.110223e-16 64 0.5000000000 0.000000e+00 128 0.5000000000 3.330669e-16 256 0.5000000000 6.106227e-16 512 0.5000000000 0.000000e+00 1024 0.5000000000 3.330669e-16 2048 0.5000000000 0.000000e+00 4096 0.5000000000 2.220446e-16 8192 0.5000000000 5.551115e-16 16384 0.5000000000 3.330669e-16 32768 0.5000000000 2.220446e-16 65536 0.5000000000 3.885781e-16 131072 0.5000000000 6.661338e-16 262144 0.5000000000 2.997602e-15 524288 0.5000000000 1.776357e-15 1048576 0.5000000000 1.165734e-15 Exact 0.5000000000 Problem 18: 1 0.1887703344 1.821298e-02 2 0.1750359252 4.478576e-03 4 0.1716725409 1.115191e-03 8 0.1708358722 2.785227e-04 16 0.1706269630 6.961354e-05 32 0.1705747518 1.740231e-05 64 0.1705617000 4.350512e-06 128 0.1705584371 1.087624e-06 256 0.1705576214 2.719057e-07 512 0.1705574175 6.797640e-08 1024 0.1705573665 1.699410e-08 2048 0.1705573538 4.248525e-09 4096 0.1705573506 1.062131e-09 8192 0.1705573498 2.655332e-10 16384 0.1705573496 6.638229e-11 32768 0.1705573495 1.659611e-11 65536 0.1705573495 4.148543e-12 131072 0.1705573495 1.037642e-12 262144 0.1705573495 2.622069e-13 524288 0.1705573495 6.128431e-14 1048576 0.1705573495 1.779132e-14 Exact 0.1705573495 Problem 19: 1 -0.6931471806 3.068528e-01 2 -0.8369882168 1.630118e-01 4 -0.9159514541 8.404855e-02 8 -0.9573287524 4.267125e-02 16 -0.9785018740 2.149813e-02 32 -0.9892102631 1.078974e-02 64 -0.9945949600 5.405040e-03 128 -0.9972949369 2.705063e-03 256 -0.9986468327 1.353167e-03 512 -0.9993232574 6.767426e-04 1024 -0.9996615890 3.384110e-04 2048 -0.9998307845 1.692155e-04 4096 -0.9999153898 8.461021e-05 8192 -0.9999576943 4.230573e-05 16384 -0.9999788470 2.115302e-05 32768 -0.9999894235 1.057655e-05 65536 -0.9999947117 5.288284e-06 131072 -0.9999973559 2.644144e-06 262144 -0.9999986779 1.322073e-06 524288 -0.9999993390 6.610365e-07 1048576 -0.9999996695 3.305183e-07 Exact -1.0000000000 Problem 20: 1 1.9900497512 4.256533e-01 2 1.5936254980 2.922905e-02 4 1.5747266826 1.033024e-02 8 1.5669874771 2.591033e-03 16 1.5650442435 6.477994e-04 32 1.5645583939 1.619499e-04 64 1.5644369315 4.048743e-05 128 1.5644065659 1.012185e-05 256 1.5643989745 2.530463e-06 512 1.5643970767 6.326158e-07 1024 1.5643966022 1.581540e-07 2048 1.5643964836 3.953849e-08 4096 1.5643964540 9.884623e-09 8192 1.5643964465 2.471145e-09 16384 1.5643964447 6.177827e-10 32768 1.5643964442 1.544509e-10 65536 1.5643964441 3.863665e-11 131072 1.5643964441 9.665158e-12 262144 1.5643964441 2.415623e-12 524288 1.5643964441 5.573320e-13 1048576 1.5643964441 1.856293e-13 Exact 1.5643964441 Problem 21: 1 0.0098660372 2.009367e-01 2 0.3932572688 1.824545e-01 4 0.1779810191 3.282172e-02 8 0.1990730187 1.172972e-02 16 0.2265812629 1.577853e-02 32 0.2031783608 7.624375e-03 64 0.2123092922 1.506556e-03 128 0.2097282377 1.074499e-03 256 0.2122362163 1.433480e-03 512 0.2104958032 3.069331e-04 1024 0.2108607780 5.804171e-05 2048 0.2108027277 8.638047e-09 4096 0.2108027389 2.573418e-09 8192 0.2108027363 3.612957e-11 16384 0.2108027357 5.981911e-10 32768 0.2108027356 7.567720e-10 65536 0.2108027355 7.964145e-10 131072 0.2108027355 8.063273e-10 262144 0.2108027355 8.088092e-10 524288 0.2108027355 8.094266e-10 1048576 0.2108027355 8.095809e-10 Exact 0.2108027363 Problem 22: 1 0.7619047619 3.380185e-02 2 0.7349767350 6.873822e-03 4 0.7298385067 1.735593e-03 8 0.7285369333 4.340201e-04 16 0.7282114201 1.085068e-04 32 0.7281300400 2.712673e-05 64 0.7281096949 6.781684e-06 128 0.7281046086 1.695421e-06 256 0.7281033371 4.238553e-07 512 0.7281030192 1.059638e-07 1024 0.7281029397 2.649095e-08 2048 0.7281029198 6.622739e-09 4096 0.7281029149 1.655686e-09 8192 0.7281029136 4.139248e-10 16384 0.7281029133 1.034807e-10 32768 0.7281029133 2.586864e-11 65536 0.7281029132 6.466050e-12 131072 0.7281029132 1.616707e-12 262144 0.7281029132 3.856915e-13 524288 0.7281029132 1.236788e-13 1048576 0.7281029132 7.760459e-14 Exact 0.7281029132 Problem 23: 1 1.8185948537 1.193882e+00 2 -0.8656463897 1.490360e+00 4 2.9433437559 2.318630e+00 8 -0.2657657328 8.904790e-01 16 1.0571928662 4.324796e-01 32 3.0455251503 2.420812e+00 64 1.5690203168 9.443071e-01 128 -1.7911268097 2.415840e+00 256 1.8355410657 1.210828e+00 512 0.6275327726 2.819516e-03 1024 0.0924779051 5.322354e-01 2048 1.1998277173 5.751145e-01 4096 -1.9983038239 2.623017e+00 8192 -0.0029860215 6.276993e-01 16384 3.0328508774 2.408138e+00 32768 1.7355675542 1.110854e+00 65536 -1.5887123232 2.213426e+00 131072 1.2107681983 5.860549e-01 262144 1.2836908165 6.589776e-01 524288 0.8092565437 1.845433e-01 1048576 1.5207032823 8.959900e-01 Exact 0.6247132564 Problem 24: 1 0.1125393676 1.192941e-01 2 -0.0346577441 2.790300e-02 4 -0.0285087682 2.175402e-02 8 -0.0172140824 1.045934e-02 16 -0.0054974031 1.257342e-03 32 -0.0066804031 7.434244e-05 64 -0.0066507729 1.039726e-04 128 -0.0068173826 6.263709e-05 256 -0.0067395683 1.517720e-05 512 -0.0067896764 3.493094e-05 1024 -0.0067545485 1.969967e-07 2048 -0.0067606320 5.886469e-06 4096 -0.0067489564 5.789078e-06 8192 -0.0067549472 2.017274e-07 16384 -0.0067550934 3.479291e-07 32768 -0.0067548258 8.033392e-08 65536 -0.0067548761 1.306297e-07 131072 -0.0067545821 1.633901e-07 262144 -0.0067547500 4.465815e-09 524288 -0.0067547444 1.090458e-09 1048576 -0.0067547455 4.761152e-11 Exact -0.0067547455 Problem 25: 1 -1.6094379124 1.426390e-03 2 -1.8971199849 2.862557e-01 4 -1.5026379513 1.082264e-01 8 -1.6740933633 6.322906e-02 16 -1.5815621494 2.930215e-02 32 -1.6260958417 1.523154e-02 64 -1.6033938021 7.470500e-03 128 -1.6146358792 3.771577e-03 256 -1.6089875959 1.876706e-03 512 -1.6118049258 9.406237e-04 1024 -1.6103945579 4.697442e-04 2048 -1.6110993161 2.350140e-04 4096 -1.6107468305 1.174715e-04 8192 -1.6109230467 5.874463e-05 16384 -1.6108349320 2.937010e-05 32768 -1.6108789877 1.468560e-05 65536 -1.6108569594 7.342664e-06 131072 -1.6108679734 3.671366e-06 262144 -1.6108624664 1.835675e-06 524288 -1.6108652199 9.178395e-07 1048576 -1.6108638431 4.589193e-07 Exact -1.6108643021 Problem 26: 1 2.3114546996 5.643472e+00 2 6.2831853072 1.671741e+00 4 7.9205321056 3.439442e-02 8 7.9549252693 1.251689e-06 16 7.9549265210 1.776357e-15 32 7.9549265210 4.440892e-15 64 7.9549265210 0.000000e+00 128 7.9549265210 1.776357e-15 256 7.9549265210 4.440892e-15 512 7.9549265210 1.776357e-15 1024 7.9549265210 8.881784e-15 2048 7.9549265210 8.881784e-16 4096 7.9549265210 1.243450e-14 8192 7.9549265210 2.664535e-15 16384 7.9549265210 6.217249e-15 32768 7.9549265210 2.664535e-14 65536 7.9549265210 1.243450e-14 131072 7.9549265210 5.506706e-14 262144 7.9549265210 9.947598e-14 524288 7.9549265210 8.881784e-14 1048576 7.9549265210 2.886580e-13 Exact 7.9549265210 Problem 27: 1 0.6663080565 1.748089e-01 2 0.7242492390 1.168677e-01 4 0.7644380733 7.667884e-02 8 0.7912747878 4.984213e-02 16 0.8088847911 3.223213e-02 32 0.8203426165 2.077430e-02 64 0.8277615995 1.335532e-02 128 0.8325494935 8.567423e-03 256 0.8356312893 5.485627e-03 512 0.8376104723 3.506444e-03 1024 0.8388790002 2.237916e-03 2048 0.8396905824 1.426334e-03 4096 0.8402089748 9.079419e-04 8192 0.8405396079 5.773087e-04 16384 0.8407502080 3.667086e-04 32768 0.8408841921 2.327246e-04 65536 0.8409693417 1.475750e-04 131072 0.8410234041 9.351257e-05 262144 0.8410576995 5.921716e-05 524288 0.8410794387 3.747795e-05 1048576 0.8410932093 2.370730e-05 Exact 0.8411169166 Problem 28: 1 0.0000000000 1.995467e-02 2 0.0000000000 1.995467e-02 4 0.5918210011 5.718663e-01 8 0.4511649391 4.312103e-01 16 -0.4121331799 4.320878e-01 32 -0.0993939785 1.193486e-01 64 0.0768648954 5.691023e-02 128 0.0260089728 6.054304e-03 256 0.0212645287 1.309859e-03 512 0.0202712987 3.166294e-04 1024 0.0200331746 7.850530e-05 2048 0.0199742552 1.958595e-05 4096 0.0199595632 4.893969e-06 8192 0.0199558926 1.223335e-06 16384 0.0199549751 3.058240e-07 32768 0.0199547457 7.645537e-08 65536 0.0199546884 1.911380e-08 131072 0.0199546741 4.778449e-09 262144 0.0199546705 1.194612e-09 524288 0.0199546696 2.986529e-10 1048576 0.0199546694 7.466390e-11 Exact 0.0199546693 Problem 29: 1 0.4000000000 9.314718e-02 2 0.2222222222 8.463060e-02 4 0.3181483120 1.129549e-02 8 0.3183771388 1.152432e-02 16 0.2954460623 1.140676e-02 32 0.3070203680 1.675485e-04 64 0.3070238684 1.710490e-04 128 0.3070247436 1.719241e-04 256 0.3070249624 1.721429e-04 512 0.3070250171 1.721976e-04 1024 0.3070250307 1.722113e-04 2048 0.3068454203 7.399115e-06 4096 0.3068454212 7.398261e-06 8192 0.3068454214 7.398047e-06 16384 0.3068454214 7.397994e-06 32768 0.3068566483 3.828829e-06 65536 0.3068510349 1.784556e-06 131072 0.3068538416 1.022143e-06 262144 0.3068524382 3.812052e-07 524288 0.3068531399 3.204692e-07 1048576 0.3068527891 3.036788e-08 Exact 0.3068528194 Problem 30: 1 -5.4838379729 9.562683e-01 2 -18.9107910688 1.438322e+01 4 -15.7321393620 1.120457e+01 8 0.5720874945 5.099657e+00 16 -4.3155082478 2.120614e-01 32 -4.4876498204 3.991980e-02 64 -4.5182429031 9.326722e-03 128 -4.5252767075 2.292918e-03 256 -4.5269987878 5.708374e-04 512 -4.5274270648 1.425603e-04 1024 -4.5275339944 3.563077e-05 2048 -4.5275607180 8.907111e-06 4096 -4.5275673984 2.226741e-06 8192 -4.5275690685 5.566831e-07 16384 -4.5275694860 1.391706e-07 32768 -4.5275695904 3.479267e-08 65536 -4.5275696165 8.698170e-09 131072 -4.5275696230 2.174505e-09 262144 -4.5275696246 5.436478e-10 524288 -4.5275696250 1.358407e-10 1048576 -4.5275696251 3.379341e-11 Exact -4.5275696252 Problem 31: 1 8.0000000000 5.348365e+00 2 1.6000000000 1.051635e+00 4 2.4000000000 2.516353e-01 8 2.6421900806 9.445247e-03 16 2.6521875219 5.521946e-04 32 2.6517793393 1.440119e-04 64 2.6516713609 3.603360e-05 128 2.6516443377 9.010318e-06 256 2.6516375800 2.252699e-06 512 2.6516358905 5.631823e-07 1024 2.6516354681 1.407961e-07 2048 2.6516353625 3.519905e-08 4096 2.6516353361 8.799766e-09 8192 2.6516353295 2.199930e-09 16384 2.6516353279 5.499650e-10 32768 2.6516353275 1.375033e-10 65536 2.6516353274 3.438627e-11 131072 2.6516353273 8.588685e-12 262144 2.6516353273 2.088107e-12 524288 2.6516353273 4.432010e-13 1048576 2.6516353273 5.773160e-14 Exact 2.6516353273 Problem 32: 1 0.0000000000 1.207035e+01 2 -9.2827863646 2.787560e+00 4 -11.4283020121 6.420443e-01 8 -11.9138457700 1.565005e-01 16 -12.0314801341 3.886618e-02 32 -12.0606460814 9.700235e-03 64 -12.0679222790 2.424037e-03 128 -12.0697403709 6.059455e-04 256 -12.0701948340 1.514824e-04 512 -12.0703084460 3.787035e-05 1024 -12.0703368488 9.467571e-06 2048 -12.0703439495 2.366892e-06 4096 -12.0703457247 5.917229e-07 8192 -12.0703461685 1.479307e-07 16384 -12.0703462794 3.698267e-08 32768 -12.0703463071 9.245664e-09 65536 -12.0703463141 2.311413e-09 131072 -12.0703463158 5.779111e-10 262144 -12.0703463162 1.444889e-10 524288 -12.0703463164 3.615952e-11 1048576 -12.0703463164 9.036327e-12 Exact -12.0703463164 Problem 33: 1 0.8325546112 5.367231e-02 2 0.8568850219 2.934190e-02 4 0.8708456774 1.538125e-02 8 0.8783767062 7.850219e-03 16 0.8822894746 3.937451e-03 32 0.8842747588 1.952167e-03 64 0.8852665285 9.603969e-04 128 0.8857568557 4.700697e-04 256 0.8859975964 2.293291e-04 512 0.8861152608 1.116647e-04 1024 0.8861726079 5.431754e-05 2048 0.8862005123 2.641311e-05 4096 0.8862140799 1.284557e-05 8192 0.8862206755 6.249952e-06 16384 0.8862238826 3.042829e-06 32768 0.8862254429 1.482553e-06 65536 0.8862262025 7.229458e-07 131072 0.8862265726 3.528393e-07 262144 0.8862267531 1.723558e-07 524288 0.8862268412 8.426482e-08 1048576 0.8862268842 4.123132e-08 Exact 0.8862269255 Problem 34: 1 219.3360000000 8.659167e+02 2 814.0860000000 2.711667e+02 4 1014.0430312500 7.120964e+01 8 1067.2366347656 1.801603e+01 16 1080.7353072510 4.517359e+00 32 1084.1224923477 1.130174e+00 64 1084.9700709329 2.825957e-01 128 1085.1820144736 7.065219e-02 256 1085.2350034147 1.766325e-02 512 1085.2482508409 4.415826e-03 1024 1085.2515627094 1.103957e-03 2048 1085.2523906773 2.759894e-04 4096 1085.2525976693 6.899734e-05 8192 1085.2526494173 1.724934e-05 16384 1085.2526623543 4.312335e-06 32768 1085.2526655886 1.078081e-06 65536 1085.2526663971 2.695231e-07 131072 1085.2526665993 6.738287e-08 262144 1085.2526666498 1.684612e-08 524288 1085.2526666625 4.202548e-09 1048576 1085.2526666656 1.063199e-09 Exact 1085.2526666667 Problem 35: 1 16.1592351032 9.840765e+00 2 19.1471782056 6.852822e+00 4 23.9735468892 2.026453e+00 8 24.6537175722 1.346282e+00 16 24.6681700578 1.331830e+00 32 25.5508281601 4.491718e-01 64 25.0639957988 9.360042e-01 128 26.8277071303 8.277071e-01 256 25.2717388996 7.282611e-01 512 25.6497940229 3.502060e-01 1024 26.5003665521 5.003666e-01 2048 25.7322187177 2.677813e-01 4096 25.8376854990 1.623145e-01 8192 26.0358308853 3.583089e-02 16384 25.9171057743 8.289423e-02 32768 26.0026293054 2.629305e-03 65536 25.9624185083 3.758149e-02 131072 26.0577505058 5.775051e-02 262144 25.9759941987 2.400580e-02 524288 25.9845454814 1.545452e-02 1048576 25.9952701071 4.729893e-03 Exact 26.0000000000 Problem 36: 1 1.2934583749 9.870654e+01 2 2.6000279311 9.739997e+01 4 4.1878742856 9.581213e+01 8 6.0042228000 9.399578e+01 16 8.0081586153 9.199184e+01 32 10.1655324068 8.983447e+01 64 12.4465810485 8.755342e+01 128 14.8250085341 8.517499e+01 256 17.2775287490 8.272247e+01 512 19.7835483484 8.021645e+01 1024 22.3249025316 7.767510e+01 2048 24.8856201273 7.511438e+01 4096 27.4517107537 7.254829e+01 8192 30.0109710217 6.998903e+01 16384 32.5528079059 6.744719e+01 32768 35.0680777813 6.493192e+01 65536 37.5489398025 6.245106e+01 131072 39.9887224219 6.001128e+01 262144 42.3818019441 5.761820e+01 524288 44.7234921016 5.527651e+01 1048576 47.0099437214 5.299006e+01 Exact 100.0000000000 Problem 37: 1 0.0119892664 3.123809e+00 2 0.3910874583 2.744711e+00 4 0.0419040993 3.093895e+00 8 0.1885756089 2.947223e+00 16 3.4068775614 2.710789e-01 32 0.3612971973 2.774502e+00 64 1.2844068359 1.851392e+00 128 7.9394804158 4.803682e+00 256 2.0992886522 1.036510e+00 512 2.9429313385 1.928674e-01 1024 3.1356086819 1.900272e-04 2048 3.1358206139 2.190470e-05 4096 3.1357987096 4.245031e-10 8192 3.1357987093 1.251936e-10 16384 3.1357987092 3.129808e-11 32768 3.1357987092 7.806200e-12 65536 3.1357987092 1.947331e-12 131072 3.1357987092 4.893863e-13 262144 3.1357987092 1.199041e-13 524288 3.1357987092 1.776357e-14 1048576 3.1357987092 1.145750e-13 Exact 3.1357987092 Problem 38: 1 -0.4571018373 9.963588e-01 2 2.5452668556 2.006010e+00 4 -0.8642620452 1.403519e+00 8 0.5387667860 4.901286e-04 16 0.5392569147 3.330669e-16 32 0.5392569147 3.330669e-16 64 0.5392569147 1.110223e-16 128 0.5392569147 2.220446e-16 256 0.5392569147 2.220446e-16 512 0.5392569147 6.661338e-16 1024 0.5392569147 3.330669e-16 2048 0.5392569147 2.220446e-16 4096 0.5392569147 2.442491e-15 8192 0.5392569147 0.000000e+00 16384 0.5392569147 1.221245e-15 32768 0.5392569147 8.881784e-16 65536 0.5392569147 5.551115e-16 131072 0.5392569147 4.440892e-15 262144 0.5392569147 6.550316e-15 524288 0.5392569147 4.329870e-15 1048576 0.5392569147 3.108624e-15 Exact 0.5392569147 Problem 39: 1 2.4494897428 3.382040e-01 2 2.5066474768 2.810462e-01 4 2.5750605890 2.126331e-01 8 2.6333969609 1.542967e-01 16 2.6775601879 1.101335e-01 32 2.7095570376 7.813666e-02 64 2.7323773988 5.531630e-02 128 2.7485628207 3.913088e-02 256 2.7600199022 2.767380e-02 512 2.7681243480 1.956935e-02 1024 2.7738558231 1.383788e-02 2048 2.7779087796 9.784921e-03 4096 2.7807747005 6.919000e-03 8192 2.7828012246 4.892476e-03 16384 2.7842341966 3.459504e-03 32768 2.7852474615 2.446239e-03 65536 2.7859639482 1.729752e-03 131072 2.7864705808 1.223119e-03 262144 2.7868288242 8.648761e-04 524288 2.7870821405 6.115597e-04 1048576 2.7872612622 4.324380e-04 Exact 2.7876937002 Problem 40: 1 1.8718645217 8.270921e-01 2 3.3408706527 6.419141e-01 4 2.1572875147 5.416691e-01 8 2.4464477885 2.525088e-01 16 2.9412211502 2.422645e-01 32 2.5006468991 1.983097e-01 64 2.5991917321 9.976487e-02 128 2.9431962921 2.442397e-01 256 2.6244826443 7.447396e-02 512 2.6488047835 5.015182e-02 1024 2.6719795167 2.697708e-02 2048 2.9615987166 2.626421e-01 4096 2.6800596270 1.889697e-02 8192 2.6856073550 1.334925e-02 16384 2.6895539760 9.402625e-03 32768 2.6924132043 6.543397e-03 65536 2.6946445500 4.312051e-03 131072 2.6970679383 1.888663e-03 262144 2.7000107369 1.054136e-03 524288 2.6974828085 1.473793e-03 1048576 2.6985385601 4.180412e-04 Exact 2.6989566013 Problem 41: 1 1.7777777778 4.317807e+00 2 2.5581058081 3.537479e+00 4 3.3847035396 2.710882e+00 8 4.1402234849 1.955362e+00 16 4.7342619443 1.361323e+00 32 5.1547747846 9.408103e-01 64 5.4415266898 6.540584e-01 128 5.6376969051 4.578882e-01 256 5.7735434539 3.220416e-01 512 5.8684983545 2.270867e-01 1024 5.9352367034 1.603484e-01 2048 5.9822821583 1.133029e-01 4096 6.0154963747 8.008873e-02 8192 6.0389639311 5.662117e-02 16384 6.0555514659 4.003364e-02 32768 6.0672783121 2.830679e-02 65536 6.0755696266 2.001548e-02 131072 6.0814321821 1.415292e-02 262144 6.0855775325 1.000757e-02 524288 6.0885087018 7.076401e-03 1048576 6.0905813386 5.003764e-03 Exact 6.0955851028 Problem 42: 1 2.0020751517 1.978711e+00 2 2.3686712676 1.612115e+00 4 2.6703050232 1.310481e+00 8 2.9161318148 1.064654e+00 16 3.1159747752 8.648115e-01 32 3.2783322468 7.024540e-01 64 3.4102145135 5.705717e-01 128 3.5173376268 4.634486e-01 256 3.6043489219 3.764373e-01 512 3.6750241137 3.057621e-01 1024 3.7324302195 2.483560e-01 2048 3.7790584689 2.017278e-01 4096 3.8169323767 1.638539e-01 8192 3.8476955492 1.330907e-01 16384 3.8726830098 1.081032e-01 32768 3.8929791346 8.780712e-02 65536 3.9094647105 7.132154e-02 131072 3.9228551591 5.793109e-02 262144 3.9337315831 4.705467e-02 524288 3.9425659845 3.822027e-02 1048576 3.9497417482 3.104450e-02 Exact 3.9807862525 Problem 43: 1 1.2924750770 1.699094e+00 2 1.5938054974 1.397763e+00 4 1.8506325438 1.140936e+00 8 2.0630701787 9.284988e-01 16 2.2368078102 7.547612e-01 32 2.3783064164 6.132626e-01 64 2.4933678792 4.982011e-01 128 2.5868733590 4.046956e-01 256 2.6628412514 3.287277e-01 512 2.7245535757 2.670154e-01 1024 2.7746826167 2.168864e-01 2048 2.8154013912 1.761676e-01 4096 2.8484759169 1.430931e-01 8192 2.8753410562 1.162279e-01 16384 2.8971624583 9.440653e-02 32768 2.9148870044 7.668198e-02 65536 2.9292838378 6.228515e-02 131072 2.9409777134 5.059127e-02 262144 2.9504760983 4.109289e-02 524288 2.9581911871 3.337780e-02 1048576 2.9644577879 2.711120e-02 Exact 2.9915689877 Problem 44: 1 0.0000412820 3.014098e-02 2 0.0004755583 3.057526e-02 4 -0.0071148265 2.298487e-02 8 -0.0206782022 9.421498e-03 16 -0.0273605320 2.739168e-03 32 -0.0293870880 7.126126e-04 64 -0.0299197404 1.799601e-04 128 -0.0300545965 4.510406e-05 256 -0.0300884174 1.128316e-05 512 -0.0300968793 2.821237e-06 1024 -0.0300989952 7.053371e-07 2048 -0.0300995242 1.763360e-07 4096 -0.0300996564 4.408412e-08 8192 -0.0300996895 1.102104e-08 16384 -0.0300996978 2.755259e-09 32768 -0.0300996998 6.888149e-10 65536 -0.0300997003 1.722037e-10 131072 -0.0300997005 4.305095e-11 262144 -0.0300997005 1.076277e-11 524288 -0.0300997005 2.690730e-12 1048576 -0.0300997005 6.728750e-13 Exact -0.0300997005 Problem 45: 1 -0.8322936731 5.395870e-01 2 -0.5192575053 2.265508e-01 4 -0.4216849058 1.289782e-01 8 -0.3748674873 8.216078e-02 16 -0.3478689674 5.516226e-02 32 -0.3307153132 3.800860e-02 64 -0.3192370401 2.653033e-02 128 -0.3113453673 1.863866e-02 256 -0.3058436079 1.313690e-02 512 -0.3019808649 9.274155e-03 1024 -0.2992592183 6.552509e-03 2048 -0.2973381569 4.631447e-03 4096 -0.2959809744 3.274265e-03 8192 -0.2950217301 2.315020e-03 16384 -0.2943435934 1.636884e-03 32768 -0.2938641320 1.157422e-03 65536 -0.2935251205 8.184108e-04 131072 -0.2932854099 5.787001e-04 262144 -0.2931159113 4.092015e-04 524288 -0.2929960585 2.893487e-04 1048576 -0.2929113100 2.046003e-04 Exact -0.2927067098 Problem 46: 1 4.6569772858 1.412114e+00 2 5.8622916999 2.067993e-01 4 6.0654456064 3.645353e-03 8 6.0690898641 1.095435e-06 16 6.0690909596 9.858780e-14 32 6.0690909596 1.776357e-15 64 6.0690909596 1.776357e-15 128 6.0690909596 2.664535e-15 256 6.0690909596 8.881784e-16 512 6.0690909596 8.881784e-16 1024 6.0690909596 3.552714e-15 2048 6.0690909596 4.440892e-15 4096 6.0690909596 1.776357e-15 8192 6.0690909596 6.217249e-15 16384 6.0690909596 2.664535e-15 32768 6.0690909596 1.154632e-14 65536 6.0690909596 7.105427e-15 131072 6.0690909596 6.483702e-14 262144 6.0690909596 8.881784e-14 524288 6.0690909596 4.707346e-14 1048576 6.0690909596 1.421085e-14 Exact 6.0690909596 Problem 47: 1 -0.4901290717 4.568463e-02 2 -0.4711435818 2.669914e-02 4 -0.4580760202 1.363158e-02 8 -0.4508591302 6.414686e-03 16 -0.4473043873 2.859943e-03 32 -0.4456718813 1.227437e-03 64 -0.4449566262 5.121818e-04 128 -0.4446536184 2.091739e-04 256 -0.4445284391 8.399468e-05 512 -0.4444777182 3.327374e-05 1024 -0.4444574800 1.303557e-05 2048 -0.4444495045 5.060025e-06 4096 -0.4444463934 1.948958e-06 8192 -0.4444451902 7.457251e-07 16384 -0.4444447282 2.837141e-07 32768 -0.4444445519 1.074072e-07 65536 -0.4444444849 4.048575e-08 131072 -0.4444444596 1.520227e-08 262144 -0.4444444501 5.689012e-09 524288 -0.4444444466 2.122484e-09 1048576 -0.4444444452 7.897243e-10 Exact -0.4444444444 Problem 48: 1 -0.9802581435 3.019742e+00 2 -1.5523876831 2.447612e+00 4 -2.0551250445 1.944875e+00 8 -2.4753532003 1.524647e+00 16 -2.8167944571 1.183206e+00 32 -3.0891534041 9.108466e-01 64 -3.3035051263 6.964949e-01 128 -3.4704393008 5.295607e-01 256 -3.5993376392 4.006624e-01 512 -3.6981587365 3.018413e-01 1024 -3.7734633046 2.265367e-01 2048 -3.8305493980 1.694506e-01 4096 -3.8736290165 1.263710e-01 8192 -3.9060097443 9.399026e-02 16384 -3.9302631980 6.973680e-02 32768 -3.9483723967 5.162760e-02 65536 -3.9618559443 3.814406e-02 131072 -3.9718699608 2.813004e-02 262144 -3.9792901449 2.070986e-02 524288 -3.9847768616 1.522314e-02 1048576 -3.9888261588 1.117384e-02 Exact -4.0000000000 Problem 49: 1 -11.7769019493 6.451765e+01 2 42.7806817243 9.960067e+00 4 50.4805366229 2.260212e+00 8 52.4691497254 2.715987e-01 16 51.8216714539 9.190769e-01 32 52.8604193202 1.196709e-01 64 52.7963572218 5.560884e-02 128 52.7346232112 6.125172e-03 256 52.7421656129 1.417229e-03 512 52.7379492032 2.799180e-03 1024 52.7426539516 1.905568e-03 2048 52.7369024702 3.845913e-03 4096 52.7420112387 1.262855e-03 8192 52.7410929640 3.445805e-04 16384 52.7392203595 1.528024e-03 32768 52.7409274707 1.790872e-04 65536 52.7408374039 8.902042e-05 131072 52.7407918235 4.344006e-05 262144 52.7407678936 1.951008e-05 524288 52.7407531025 4.719068e-06 1048576 52.7407356873 1.269616e-05 Exact 52.7407483835 Problem 50: 1 -0.0000000000 1.281368e-01 2 -0.5493061443 4.211693e-01 4 0.4342936311 5.624305e-01 8 -0.2339029924 1.057661e-01 16 -0.1510160724 2.287922e-02 32 -0.1343662745 6.229426e-03 64 -0.1298894445 1.752596e-03 128 -0.1286284765 4.916281e-04 256 -0.1282734638 1.366154e-04 512 -0.1281744538 3.760538e-05 1024 -0.1281471144 1.026597e-05 2048 -0.1281396312 2.782769e-06 4096 -0.1281375982 7.497699e-07 8192 -0.1281370494 2.009625e-07 16384 -0.1281369020 5.362067e-08 32768 -0.1281368626 1.425018e-08 65536 -0.1281368522 3.773798e-09 131072 -0.1281368494 9.962596e-10 262144 -0.1281368487 2.622714e-10 524288 -0.1281368485 6.886419e-11 1048576 -0.1281368484 1.803382e-11 Exact -0.1281368484 Problem 51: 1 -0.3162541288 1.184406e-01 2 -0.2038858201 6.072261e-03 4 -0.1930887946 4.724765e-03 8 -0.1902565179 7.557041e-03 16 -0.1895346026 8.278957e-03 32 -0.1893457074 8.467852e-03 64 -0.1892949882 8.518571e-03 128 -0.1892809608 8.532598e-03 256 -0.1892769439 8.536615e-03 512 -0.1892757467 8.537812e-03 1024 -0.1892753740 8.538185e-03 2048 -0.1892752526 8.538307e-03 4096 -0.1892752112 8.538348e-03 8192 -0.1892751966 8.538363e-03 16384 -0.1892751912 8.538368e-03 32768 -0.1892751892 8.538370e-03 65536 -0.1892751884 8.538371e-03 131072 -0.1892751881 8.538371e-03 262144 -0.1892751880 8.538371e-03 524288 -0.1892751879 8.538371e-03 1048576 -0.1892751879 8.538371e-03 Exact -0.1978135592 Problem 52: 1 0.0652173913 1.551614e-01 2 0.9095498515 9.994939e-01 4 -0.9312128883 8.412689e-01 8 0.8625956384 9.525396e-01 16 -0.9714616994 8.815177e-01 32 0.8282470422 9.181910e-01 64 -0.9928412426 9.028972e-01 128 0.8181356668 9.080797e-01 256 -0.9965306648 9.065867e-01 512 0.8170352985 9.069793e-01 1024 -0.9968236924 9.068797e-01 2048 0.8169606801 9.069047e-01 4096 -0.9968424375 9.068984e-01 8192 0.8169559881 9.069000e-01 16384 -0.9968436108 9.068996e-01 32768 0.8169556947 9.068997e-01 65536 -0.9968436842 9.068997e-01 131072 0.8169556764 9.068997e-01 262144 -0.9968436888 9.068997e-01 524288 0.8169556752 9.068997e-01 1048576 -0.9968436891 9.068997e-01 Exact -0.0899440070 Problem 53: 1 1.1547005384 3.499222e-01 2 2.4170288281 9.124061e-01 4 1.1923720708 3.122507e-01 8 1.2960383042 2.085845e-01 16 1.4103297596 9.429300e-02 32 1.5760429653 7.142020e-02 64 1.4308139745 7.380879e-02 128 1.4734722198 3.115054e-02 256 1.5158019693 1.117921e-02 512 1.4803511758 2.427159e-02 1024 1.5042930646 3.296979e-04 2048 1.4940731168 1.054965e-02 4096 1.5396292961 3.500653e-02 8192 1.4974853572 7.137405e-03 16384 1.4996712517 4.951511e-03 32768 1.5014100429 3.212720e-03 65536 1.5034872722 1.135490e-03 131072 1.5043325042 2.902583e-04 262144 1.5038168625 8.059000e-04 524288 1.5059092855 1.286523e-03 1048576 1.5040094721 6.132904e-04 Exact 1.5046227625 Problem 54: 1 1.0000000000 1.547005e-01 2 1.3333333333 1.786328e-01 4 1.1428571429 1.184340e-02 8 1.1546391753 6.136312e-05 16 1.1547005367 1.630567e-09 32 1.1547005384 2.220446e-16 64 1.1547005384 4.440892e-16 128 1.1547005384 4.440892e-16 256 1.1547005384 4.440892e-16 512 1.1547005384 6.661338e-16 1024 1.1547005384 8.881784e-16 2048 1.1547005384 6.661338e-16 4096 1.1547005384 4.440892e-16 8192 1.1547005384 3.996803e-15 16384 1.1547005384 3.108624e-15 32768 1.1547005384 5.551115e-15 65536 1.1547005384 1.265654e-14 131072 1.1547005384 7.105427e-15 262144 1.1547005384 2.220446e-15 524288 1.1547005384 5.462297e-14 1048576 1.1547005384 3.685940e-14 Exact 1.1547005384 Problem 55: 1 0.5697828247 6.472419e-02 2 0.5526996123 4.764098e-02 4 0.5123555702 7.296938e-03 8 0.5068065504 1.747918e-03 16 0.5054912723 4.326398e-04 32 0.5051665276 1.078951e-04 64 0.5050855898 2.695732e-05 128 0.5050653708 6.738303e-06 256 0.5050603170 1.684512e-06 512 0.5050590536 4.211239e-07 1024 0.5050587377 1.052807e-07 2048 0.5050586588 2.632016e-08 4096 0.5050586390 6.580039e-09 8192 0.5050586341 1.645010e-09 16384 0.5050586329 4.112519e-10 32768 0.5050586326 1.028132e-10 65536 0.5050586325 2.570033e-11 131072 0.5050586325 6.427636e-12 262144 0.5050586325 1.607159e-12 524288 0.5050586325 4.000134e-13 1048576 0.5050586325 8.382184e-14 Exact 0.5050586325 Problem 56: 1 2.2222222222 2.299698e-01 2 2.1843003413 1.920479e-01 4 2.0384720576 4.621965e-02 8 2.0011465141 8.894106e-03 16 1.9944314061 2.178998e-03 32 1.9927943613 5.419534e-04 64 1.9923877234 1.353154e-04 128 1.9922862260 3.381808e-05 256 1.9922608618 8.453847e-06 512 1.9922545214 2.113420e-06 1024 1.9922529363 5.283523e-07 2048 1.9922525400 1.320879e-07 4096 1.9922524410 3.302197e-08 8192 1.9922524162 8.255489e-09 16384 1.9922524100 2.063872e-09 32768 1.9922524085 5.159762e-10 65536 1.9922524081 1.289815e-10 131072 1.9922524080 3.221134e-11 262144 1.9922524080 8.093970e-12 524288 1.9922524080 2.322809e-12 1048576 1.9922524080 1.024292e-12 Exact 1.9922524080 Problem 57: 1 0.3535533906 4.644661e-02 2 0.3872595264 1.274047e-02 4 0.3966068187 3.393181e-03 8 0.3991143378 8.856622e-04 16 0.3997719411 2.280589e-04 32 0.3999418085 5.819148e-05 64 0.3999852440 1.475604e-05 128 0.3999962742 3.725821e-06 256 0.3999990620 9.379628e-07 512 0.3999997644 2.356411e-07 1024 0.3999999409 5.911366e-08 2048 0.3999999852 1.481437e-08 4096 0.3999999963 3.709947e-09 8192 0.3999999991 9.286105e-10 16384 0.3999999998 2.323513e-10 32768 0.3999999999 5.812167e-11 65536 0.4000000000 1.453621e-11 131072 0.4000000000 3.643197e-12 262144 0.4000000000 9.026113e-13 524288 0.4000000000 2.353673e-13 1048576 0.4000000000 8.998358e-14 Exact 0.4000000000 simpson_test(): Composite Simpson rule, for 1D finite interval problems. Problem Exact Ints Approx Error Problem 1 1 1.718861 5.793234e-04 2 1.718319 3.701346e-05 4 1.718284 2.326241e-06 8 1.718282 1.455928e-07 16 1.718282 9.102727e-09 32 1.718282 5.689700e-10 64 1.718282 3.556155e-11 128 1.718282 2.222444e-12 256 1.718282 1.383338e-13 512 1.718282 9.547918e-15 1024 1.718282 2.220446e-16 2048 1.718282 6.661338e-16 4096 1.718282 2.220446e-15 8192 1.718282 2.220446e-15 16384 1.718282 6.661338e-15 32768 1.718282 2.220446e-15 Exact 1.718282 Problem 2 1 0.833333 1.333333e-01 2 0.583333 1.166667e-01 4 0.708333 8.333333e-03 8 0.729167 2.916667e-02 16 0.697917 2.083333e-03 32 0.692708 7.291667e-03 64 0.700521 5.208333e-04 128 0.701823 1.822917e-03 256 0.699870 1.302083e-04 512 0.699544 4.557292e-04 1024 0.700033 3.255208e-05 2048 0.700114 1.139323e-04 4096 0.699992 8.138021e-06 8192 0.699972 2.848307e-05 16384 0.700002 2.034505e-06 32768 0.700007 7.120768e-06 Exact 0.700000 Problem 3 1 0.638071 2.859548e-02 2 0.656526 1.014040e-02 4 0.663079 3.587387e-03 8 0.665398 1.268478e-03 16 0.666218 4.484839e-04 32 0.666508 1.585636e-04 64 0.666611 5.606073e-05 128 0.666647 1.982046e-05 256 0.666660 7.007592e-06 512 0.666664 2.477558e-06 1024 0.666666 8.759490e-07 2048 0.666666 3.096948e-07 4096 0.666667 1.094936e-07 8192 0.666667 3.871184e-08 16384 0.666667 1.368670e-08 32768 0.666667 4.838978e-09 Exact 0.666667 Problem 4 1 0.479555 1.263588e-04 2 0.479555 1.268342e-04 4 0.479438 9.783843e-06 8 0.479429 6.405666e-07 16 0.479428 4.049006e-08 32 0.479428 2.537734e-09 64 0.479428 1.587195e-10 128 0.479428 9.921897e-12 256 0.479428 6.204481e-13 512 0.479428 3.874678e-14 1024 0.479428 2.220446e-15 2048 0.479428 4.440892e-16 4096 0.479428 1.110223e-16 8192 0.479428 2.220446e-16 16384 0.479428 1.332268e-15 32768 0.479428 5.551115e-16 Exact 0.479428 Problem 5 1 1.711367 1.291336e-01 2 1.584969 2.736293e-03 4 1.582174 5.929773e-05 8 1.582231 1.784215e-06 16 1.582233 9.284131e-08 32 1.582233 5.521886e-09 64 1.582233 3.407812e-10 128 1.582233 2.123235e-11 256 1.582233 1.326050e-12 512 1.582233 8.237855e-14 1024 1.582233 4.884981e-15 2048 1.582233 2.886580e-15 4096 1.582233 2.664535e-15 8192 1.582233 4.218847e-15 16384 1.582233 4.440892e-16 32768 1.582233 7.549517e-15 Exact 1.582233 Problem 6 1 1.586760 1.263125e-01 2 1.224344 2.361029e-01 4 1.440192 2.025523e-02 8 1.453274 7.172877e-03 16 1.457910 2.536831e-03 32 1.459550 8.969599e-04 64 1.460130 3.171267e-04 128 1.460335 1.121214e-04 256 1.460407 3.964093e-05 512 1.460433 1.401518e-05 1024 1.460442 4.955116e-06 2048 1.460445 1.751898e-06 4096 1.460447 6.193895e-07 8192 1.460447 2.189873e-07 16384 1.460447 7.742369e-08 32768 1.460447 2.737341e-08 Exact 1.460447 Problem 7 1 1.109476 8.905243e-01 2 1.370602 6.293976e-01 4 1.554972 4.450278e-01 8 1.685319 3.146806e-01 16 1.777487 2.225127e-01 32 1.842660 1.573402e-01 64 1.888744 1.112563e-01 128 1.921330 7.867010e-02 256 1.944372 5.562816e-02 512 1.960665 3.933505e-02 1024 1.972186 2.781408e-02 2048 1.980332 1.966753e-02 4096 1.986093 1.390704e-02 8192 1.990166 9.833763e-03 16384 1.993046 6.953520e-03 32768 1.995083 4.916881e-03 Exact 2.000000 Problem 8 1 0.877451 1.047799e-02 2 0.867114 1.407132e-04 4 0.866981 8.061650e-06 8 0.866973 5.083640e-07 16 0.866973 3.178817e-08 32 0.866973 1.986818e-09 64 0.866973 1.241764e-10 128 0.866973 7.761014e-12 256 0.866973 4.856116e-13 512 0.866973 3.030909e-14 1024 0.866973 2.331468e-15 2048 0.866973 1.110223e-16 4096 0.866973 2.331468e-15 8192 0.866973 6.661338e-16 16384 0.866973 2.886580e-15 32768 0.866973 3.774758e-15 Exact 0.866973 Problem 9 1 1.000000 1.547005e-01 2 1.222222 6.752168e-02 4 1.150794 3.906888e-03 8 1.154680 2.045329e-05 16 1.154701 5.435219e-10 32 1.154701 2.220446e-16 64 1.154701 6.661338e-16 128 1.154701 2.220446e-16 256 1.154701 0.000000e+00 512 1.154701 0.000000e+00 1024 1.154701 2.220446e-16 2048 1.154701 6.661338e-16 4096 1.154701 2.220446e-16 8192 1.154701 3.330669e-15 16384 1.154701 1.332268e-15 32768 1.154701 3.774758e-15 Exact 1.154701 Problem 10 1 0.694444 1.297264e-03 2 0.693254 1.067877e-04 4 0.693155 7.350095e-06 8 0.693148 4.722595e-07 16 0.693147 2.972988e-08 32 0.693147 1.861510e-09 64 0.693147 1.163973e-10 128 0.693147 7.275514e-12 256 0.693147 4.551914e-13 512 0.693147 2.797762e-14 1024 0.693147 2.220446e-15 2048 0.693147 2.220446e-16 4096 0.693147 2.220446e-16 8192 0.693147 2.220446e-16 16384 0.693147 1.110223e-16 32768 0.693147 4.329870e-15 Exact 0.693147 Problem 11 1 0.379851 3.481028e-05 2 0.379883 1.996482e-06 4 0.379885 1.223950e-07 8 0.379885 7.613688e-09 16 0.379885 4.752977e-10 32 0.379885 2.969724e-11 64 0.379885 1.855904e-12 128 0.379885 1.160183e-13 256 0.379885 7.382983e-15 512 0.379885 2.775558e-16 1024 0.379885 1.665335e-16 2048 0.379885 7.771561e-16 4096 0.379885 3.885781e-16 8192 0.379885 5.551115e-17 16384 0.379885 1.665335e-16 32768 0.379885 3.275158e-15 Exact 0.379885 Problem 12 1 0.777494 1.048879e-05 2 0.777504 6.460455e-07 4 0.777505 4.023384e-08 8 0.777505 2.512382e-09 16 0.777505 1.569890e-10 32 0.777505 9.811374e-12 64 0.777505 6.131762e-13 128 0.777505 3.830269e-14 256 0.777505 2.109424e-15 512 0.777505 2.220446e-16 1024 0.777505 1.110223e-16 2048 0.777505 2.220446e-16 4096 0.777505 1.887379e-15 8192 0.777505 1.221245e-15 16384 0.777505 2.442491e-15 32768 0.777505 1.221245e-15 Exact 0.777505 Problem 13 1 0.297431 1.360917e+00 2 1.683209 2.486096e-02 4 1.659324 9.765688e-04 8 1.658403 5.508757e-05 16 1.658351 3.358779e-06 32 1.658348 2.086393e-07 64 1.658348 1.302001e-08 128 1.658348 8.134386e-10 256 1.658348 5.083600e-11 512 1.658348 3.176348e-12 1024 1.658348 1.967315e-13 2048 1.658348 1.731948e-14 4096 1.658348 8.881784e-16 8192 1.658348 9.547918e-15 16384 1.658348 6.439294e-15 32768 1.658348 7.993606e-15 Exact 1.658348 Problem 14 1 11.785113 1.128511e+01 2 5.892557 5.392556e+00 4 2.946278 2.446278e+00 8 1.473139 9.731389e-01 16 0.736570 2.365700e-01 32 0.400108 9.989196e-02 64 0.474613 2.538674e-02 128 0.499989 1.148548e-05 256 0.500000 2.111660e-07 512 0.500000 2.111660e-07 1024 0.500000 2.111660e-07 2048 0.500000 2.111660e-07 4096 0.500000 2.111660e-07 8192 0.500000 2.111660e-07 16384 0.500000 2.111660e-07 32768 0.500000 2.111660e-07 Exact 0.500000 Problem 15 1 41.666667 4.066667e+01 2 20.833333 1.983333e+01 4 10.416667 9.416667e+00 8 5.208337 4.208337e+00 16 2.608383 1.608383e+00 32 1.407950 4.079497e-01 64 1.054703 5.470346e-02 128 1.004531 4.531435e-03 256 1.000307 3.070525e-04 512 1.000020 1.959812e-05 1024 1.000001 1.231396e-06 2048 1.000000 7.706464e-08 4096 1.000000 4.818140e-09 8192 1.000000 3.011582e-10 16384 1.000000 1.882006e-11 32768 1.000000 1.172618e-12 Exact 1.000000 Problem 16 1 2.670592 2.176958e+00 2 1.368566 8.749312e-01 4 0.752740 2.591049e-01 8 0.507408 1.377287e-02 16 0.466443 2.719207e-02 32 0.487977 5.657221e-03 64 0.493528 1.070672e-04 128 0.493635 3.445674e-08 256 0.493635 1.609823e-14 512 0.493635 1.221245e-15 1024 0.493635 3.330669e-16 2048 0.493635 6.106227e-16 4096 0.493635 4.440892e-16 8192 0.493635 5.551115e-17 16384 0.493635 1.054712e-15 32768 0.493635 1.110223e-15 Exact 0.493635 Problem 17 1 0.000000 5.000000e-01 2 0.666667 1.666667e-01 4 0.500000 6.661338e-16 8 0.500000 7.216450e-16 16 0.500000 6.106227e-16 32 0.500000 1.665335e-16 64 0.500000 0.000000e+00 128 0.500000 2.220446e-16 256 0.500000 4.440892e-16 512 0.500000 1.110223e-16 1024 0.500000 2.220446e-16 2048 0.500000 0.000000e+00 4096 0.500000 1.665335e-16 8192 0.500000 6.106227e-16 16384 0.500000 0.000000e+00 32768 0.500000 2.220446e-16 Exact 0.500000 Problem 18 1 0.170670 1.131103e-04 2 0.170564 6.774811e-06 4 0.170558 4.190496e-07 8 0.170557 2.612326e-08 16 0.170557 1.631656e-09 32 0.170557 1.019621e-10 64 0.170557 6.372403e-12 128 0.170557 3.982370e-13 256 0.170557 2.495226e-14 512 0.170557 1.554312e-15 1024 0.170557 5.551115e-17 2048 0.170557 1.110223e-16 4096 0.170557 1.110223e-16 8192 0.170557 2.220446e-16 16384 0.170557 4.996004e-16 32768 0.170557 2.775558e-16 Exact 0.170557 Problem 19 1 -0.462098 5.379019e-01 2 -0.673517 3.264833e-01 4 -0.807895 1.921054e-01 8 -0.889508 1.104921e-01 16 -0.937534 6.246626e-02 32 -0.965157 3.484327e-02 64 -0.980773 1.922670e-02 128 -0.989484 1.051589e-02 256 -0.994291 5.709212e-03 512 -0.996920 3.080240e-03 1024 -0.998347 1.652937e-03 2048 -0.999117 8.828768e-04 4096 -0.999530 4.696426e-04 8192 -0.999751 2.489234e-04 16384 -0.999868 1.315128e-04 32768 -0.999931 6.928192e-05 Exact -1.000000 Problem 20 1 1.659202 9.480547e-02 2 1.560343 4.053448e-03 4 1.564385 1.140721e-05 8 1.564396 5.469474e-08 16 1.564396 8.812284e-11 32 1.564396 6.038836e-11 64 1.564396 4.631628e-12 128 1.564396 3.030909e-13 256 1.564396 1.931788e-14 512 1.564396 1.998401e-15 1024 1.564396 6.661338e-16 2048 1.564396 1.332268e-15 4096 1.564396 2.220446e-16 8192 1.564396 8.215650e-15 16384 1.564396 4.662937e-15 32768 1.564396 4.218847e-15 Exact 1.564396 Problem 21 1 0.018353 1.924502e-01 2 0.269703 5.890072e-02 4 0.187963 2.283987e-02 8 0.197033 1.376946e-02 16 0.216392 5.589240e-03 32 0.205885 4.918052e-03 64 0.210619 1.839260e-04 128 0.209743 1.059388e-03 256 0.211408 6.050424e-04 512 0.210662 1.410142e-04 1024 0.210822 1.934289e-05 2048 0.210803 7.929838e-09 4096 0.210803 8.096325e-10 8192 0.210803 8.096322e-10 16384 0.210803 8.096323e-10 32768 0.210803 8.096317e-10 Exact 0.210803 Problem 22 1 0.730159 2.055817e-03 2 0.728080 2.318515e-05 4 0.728103 1.672471e-07 8 0.728103 2.493054e-09 16 0.728103 3.848322e-11 32 0.728103 5.994094e-13 64 0.728103 9.547918e-15 128 0.728103 2.220446e-16 256 0.728103 2.220446e-16 512 0.728103 1.110223e-16 1024 0.728103 1.110223e-16 2048 0.728103 5.551115e-16 4096 0.728103 1.110223e-16 8192 0.728103 2.886580e-15 16384 0.728103 5.551115e-16 32768 0.728103 1.998401e-15 Exact 0.728103 Problem 23 1 1.352642 7.279285e-01 2 -0.203876 8.285891e-01 4 2.004566 1.379852e+00 8 0.334548 2.901649e-01 16 0.916364 2.916505e-01 32 2.312333 1.687620e+00 64 1.694593 1.069879e+00 128 -0.608292 1.233005e+00 256 1.218069 5.933561e-01 512 0.721466 9.675310e-02 1024 0.317796 3.069169e-01 2048 0.943370 3.186571e-01 4096 -1.060489 1.685202e+00 8192 -0.199184 8.238976e-01 16384 1.922806 1.298093e+00 32768 1.612973 9.882597e-01 Exact 0.624713 Problem 24 1 0.101552 1.083068e-01 2 0.008914 1.566906e-02 4 -0.008772 2.017650e-03 8 -0.011111 4.356046e-03 16 -0.006351 4.034282e-04 32 -0.006713 4.171865e-05 64 -0.006677 7.778402e-05 128 -0.006775 2.019483e-05 256 -0.006744 1.046023e-05 512 -0.006775 2.058671e-05 1024 -0.006759 4.340201e-06 2048 -0.006761 6.127246e-06 4096 -0.006753 1.776841e-06 8192 -0.006755 2.109110e-07 16384 -0.006755 3.037870e-07 32768 -0.006755 1.474613e-07 Exact -0.006755 Problem 25 1 -1.333067 2.777977e-01 2 -1.663040 5.217599e-02 4 -1.517092 9.377219e-02 8 -1.624169 1.330434e-02 16 -1.587444 2.342078e-02 32 -1.614192 3.327664e-03 64 -1.605009 5.855091e-03 128 -1.611696 8.319224e-04 256 -1.609401 1.463772e-03 512 -1.611072 2.079806e-04 1024 -1.610498 3.659431e-04 2048 -1.610916 5.199516e-05 4096 -1.610773 9.148578e-05 8192 -1.610877 1.299879e-05 16384 -1.610841 2.287144e-05 32768 -1.610868 3.249697e-06 Exact -1.610864 Problem 26 1 7.234126 7.208006e-01 2 7.420611 5.343158e-01 4 7.943463 1.146397e-02 8 7.954926 4.172296e-07 16 7.954927 8.881784e-16 32 7.954927 2.664535e-15 64 7.954927 8.881784e-16 128 7.954927 1.776357e-15 256 7.954927 2.664535e-15 512 7.954927 8.881784e-16 1024 7.954927 6.217249e-15 2048 7.954927 4.440892e-15 4096 7.954927 4.440892e-15 8192 7.954927 6.217249e-15 16384 7.954927 1.243450e-14 32768 7.954927 7.993606e-15 Exact 7.954927 Problem 27 1 0.527539 3.135782e-01 2 0.635551 2.055661e-01 4 0.706693 1.344243e-01 8 0.753456 8.766044e-02 16 0.784106 5.701128e-02 32 0.804134 3.698315e-02 64 0.817184 2.393274e-02 128 0.825665 1.545210e-02 256 0.831162 9.955230e-03 512 0.834716 6.400973e-03 1024 0.837009 4.108024e-03 2048 0.838485 2.631915e-03 4096 0.839433 1.683530e-03 8192 0.840042 1.075314e-03 16384 0.840431 6.859112e-04 32768 0.840680 4.369872e-04 Exact 0.841117 Problem 28 1 0.000000 1.995467e-02 2 0.000000 1.995467e-02 4 0.394547 3.745927e-01 8 0.399413 3.794588e-01 16 -0.150243 1.701975e-01 32 -0.072695 9.264990e-02 64 0.031461 1.150664e-02 128 0.020259 3.044861e-04 256 0.019971 1.643211e-05 512 0.019956 9.924243e-07 1024 0.019955 6.150613e-08 2048 0.019955 3.836077e-09 4096 0.019955 2.396292e-10 8192 0.019955 1.497498e-11 16384 0.019955 9.358070e-13 32768 0.019955 5.858508e-14 Exact 0.019955 Problem 29 1 0.350000 4.314718e-02 2 0.256481 5.037134e-02 4 0.303303 3.550241e-03 8 0.310878 4.025177e-03 16 0.299340 7.512636e-03 32 0.305109 1.743493e-03 64 0.306067 7.856385e-04 128 0.306546 3.067113e-04 256 0.306786 6.724775e-05 512 0.306905 5.248405e-05 1024 0.306965 1.123500e-04 2048 0.306875 2.254035e-05 4096 0.306860 7.571188e-06 8192 0.306853 8.660587e-08 16384 0.306849 3.655685e-06 32768 0.306855 1.957709e-06 Exact 0.306853 Problem 30 1 4.131858 8.659428e+00 2 -9.627292 5.099722e+00 4 -12.149940 7.622371e+00 8 -3.071555 1.456014e+00 16 -4.508131 1.943855e-02 32 -4.526581 9.889140e-04 64 -4.527511 5.897087e-05 128 -4.527566 3.643536e-06 256 -4.527569 2.270706e-07 512 -4.527570 1.418178e-08 1024 -4.527570 8.862058e-10 2048 -4.527570 5.539125e-11 4096 -4.527570 3.471889e-12 8192 -4.527570 2.291500e-13 16384 -4.527570 1.687539e-14 32768 -4.527570 1.243450e-14 Exact -4.527570 Problem 31 1 5.490196 2.838561e+00 2 2.478431 1.732040e-01 4 2.572549 7.908631e-02 8 2.647735 3.900764e-03 16 2.651627 8.044380e-06 32 2.651635 4.667299e-08 64 2.651635 2.921190e-09 128 2.651635 1.826650e-10 256 2.651635 1.141842e-11 512 2.651635 7.132073e-13 1024 2.651635 4.174439e-14 2048 2.651635 2.220446e-15 4096 2.651635 8.881784e-16 8192 2.651635 6.217249e-15 16384 2.651635 1.465494e-14 32768 2.651635 8.437695e-15 Exact 2.651635 Problem 32 1 -11.592840 4.775068e-01 2 -11.984944 8.540230e-02 4 -12.064209 6.137359e-03 8 -12.069951 3.949931e-04 16 -12.070321 2.486034e-05 32 -12.070345 1.556458e-06 64 -12.070346 9.732054e-08 128 -12.070346 6.083193e-09 256 -12.070346 3.802114e-10 512 -12.070346 2.376055e-11 1024 -12.070346 1.488587e-12 2048 -12.070346 8.526513e-14 4096 -12.070346 3.552714e-15 8192 -12.070346 1.065814e-14 16384 -12.070346 1.776357e-15 32768 -12.070346 1.776357e-14 Exact -12.070346 Problem 33 1 0.555036 3.311905e-01 2 0.710016 1.762111e-01 4 0.792758 9.346942e-02 8 0.836822 4.940465e-02 16 0.860208 2.601892e-02 32 0.872572 1.365466e-02 64 0.879085 7.142235e-03 128 0.882502 3.724431e-03 256 0.884290 1.936757e-03 512 0.885222 1.004600e-03 1024 0.885707 5.199009e-04 2048 0.885958 2.685063e-04 4096 0.886089 1.384147e-04 8192 0.886156 7.123304e-05 16384 0.886190 3.660341e-05 32768 0.886208 1.878294e-05 Exact 0.886227 Problem 34 1 1168.586000 8.333333e+01 2 1090.461000 5.208333e+00 4 1085.578188 3.255208e-01 8 1085.273012 2.034505e-02 16 1085.253938 1.271566e-03 32 1085.252746 7.947286e-05 64 1085.252672 4.967054e-06 128 1085.252667 3.104410e-07 256 1085.252667 1.940248e-08 512 1085.252667 1.212584e-09 1024 1085.252667 7.526069e-11 2048 1085.252667 4.774847e-12 4096 1085.252667 4.547474e-13 8192 1085.252667 1.364242e-12 16384 1085.252667 4.547474e-13 32768 1085.252667 2.046363e-12 Exact 1085.252667 Problem 35 1 18.645046 7.354954e+00 2 19.394102 6.605898e+00 4 22.488219 3.511781e+00 8 23.684330 2.315670e+00 16 24.178659 1.821341e+00 32 25.011853 9.881468e-01 64 24.956786 1.043214e+00 128 26.186198 1.861983e-01 256 25.469641 5.303594e-01 512 25.622726 3.772735e-01 1024 26.203309 2.033086e-01 2048 25.839739 1.602610e-01 4096 25.856290 1.437099e-01 8192 25.979085 2.091530e-02 16384 25.928308 7.169228e-02 32768 25.979722 2.027757e-02 Exact 26.000000 Problem 36 1 0.862306 9.913769e+01 2 1.948928 9.805107e+01 4 3.333042 9.666696e+01 8 4.971357 9.502864e+01 16 6.823747 9.317625e+01 32 8.854202 9.114580e+01 64 11.030566 8.896943e+01 128 13.324192 8.667581e+01 256 15.709614 8.429039e+01 512 18.164251 8.183575e+01 1024 20.668136 7.933186e+01 2048 23.203664 7.679634e+01 4096 25.755369 7.424463e+01 8192 28.309714 7.169029e+01 16384 30.854900 6.914510e+01 32768 33.380701 6.661930e+01 Exact 100.000000 Problem 37 1 0.011791 3.124008e+00 2 0.264622 2.871177e+00 4 0.095066 3.040733e+00 8 0.166266 2.969533e+00 16 2.322955 8.128433e-01 32 0.834530 2.301269e+00 64 1.213320 1.922479e+00 128 5.685579 2.549780e+00 256 2.919069 2.167302e-01 512 3.071607 6.419165e-02 1024 3.135721 7.794677e-05 2048 3.135806 7.300950e-06 4096 3.135799 2.542633e-11 8192 3.135799 1.776357e-15 16384 3.135799 1.776357e-15 32768 3.135799 1.421085e-14 Exact 3.135799 Problem 38 1 0.742463 2.032061e-01 2 2.144260 1.605003e+00 4 0.071744 4.675129e-01 8 0.539094 1.633762e-04 16 0.539257 3.330669e-16 32 0.539257 3.330669e-16 64 0.539257 1.110223e-16 128 0.539257 1.110223e-16 256 0.539257 1.110223e-16 512 0.539257 3.330669e-16 1024 0.539257 1.110223e-16 2048 0.539257 4.440892e-16 4096 0.539257 2.109424e-15 8192 0.539257 3.330669e-16 16384 0.539257 1.554312e-15 32768 0.539257 9.992007e-16 Exact 0.539257 Problem 39 1 2.125792 6.619013e-01 2 2.325746 4.619475e-01 4 2.461806 3.258881e-01 8 2.557324 2.303697e-01 16 2.624803 1.628911e-01 32 2.672513 1.151811e-01 64 2.706248 8.144528e-02 128 2.730103 5.759051e-02 256 2.746971 4.072264e-02 512 2.758898 2.879526e-02 1024 2.767332 2.036132e-02 2048 2.773296 1.439763e-02 4096 2.777513 1.018066e-02 8192 2.780495 7.198814e-03 16384 2.782603 5.090330e-03 32768 2.784094 3.599407e-03 Exact 2.787694 Problem 40 1 1.795749 9.032079e-01 2 2.813144 1.141875e-01 4 2.287952 4.110047e-01 8 2.415393 2.835634e-01 16 2.760769 6.181282e-02 32 2.557279 1.416775e-01 64 2.594660 1.042970e-01 128 2.826262 1.273054e-01 256 2.672253 2.670321e-02 512 2.664583 3.437382e-02 1024 2.672144 2.681300e-02 2048 2.865141 1.661844e-01 4096 2.725677 2.672054e-02 8192 2.706567 7.610270e-03 16384 2.698718 2.384074e-04 32768 2.696042 2.914364e-03 Exact 2.698957 Problem 41 1 1.185185 4.910400e+00 2 2.001700 4.093885e+00 4 2.830968 3.264617e+00 8 3.611516 2.484069e+00 16 4.271895 1.823690e+00 32 4.783421 1.312165e+00 64 5.160266 9.353195e-01 128 5.431676 6.639088e-01 256 5.625251 4.703341e-01 512 5.762700 3.328846e-01 1024 5.860092 2.354935e-01 2048 5.929028 1.665573e-01 4096 5.977798 1.177873e-01 8192 6.012292 8.329298e-02 16384 6.036686 5.889872e-02 32768 6.053937 4.164828e-02 Exact 6.095585 Problem 42 1 1.596516 2.384270e+00 2 2.043693 1.937093e+00 4 2.407271 1.573515e+00 8 2.702673 1.278114e+00 16 2.942631 1.038155e+00 32 3.137541 8.432451e-01 64 3.295858 6.849280e-01 128 3.424452 5.563345e-01 256 3.528902 4.518840e-01 512 3.613742 3.670439e-01 1024 3.682654 2.981323e-01 2048 3.738628 2.421587e-01 4096 3.784092 1.966939e-01 8192 3.821021 1.597651e-01 16384 3.851017 1.297696e-01 32768 3.875381 1.054057e-01 Exact 3.980786 Problem 43 1 0.861650 2.129919e+00 2 1.277950 1.713619e+00 4 1.607096 1.384473e+00 8 1.870489 1.121080e+00 16 2.082605 9.089642e-01 32 2.254039 7.375303e-01 64 2.392880 5.986888e-01 128 2.505461 4.861080e-01 256 2.596812 3.947565e-01 512 2.670968 3.206006e-01 1024 2.731180 2.603886e-01 2048 2.780077 2.114917e-01 4096 2.819789 1.717799e-01 8192 2.852043 1.395264e-01 16384 2.878239 1.133296e-01 32768 2.899517 9.205169e-02 Exact 2.991569 Problem 44 1 -0.126106 9.600653e-02 2 -0.062743 3.264325e-02 4 -0.036194 6.094255e-03 8 -0.030697 5.969408e-04 16 -0.030142 4.260777e-05 32 -0.030102 2.756931e-06 64 -0.030100 1.738244e-07 128 -0.030100 1.088791e-08 256 -0.030100 6.808682e-10 512 -0.030100 4.256011e-11 1024 -0.030100 2.660101e-12 2048 -0.030100 1.662490e-13 4096 -0.030100 1.038405e-14 8192 -0.030100 6.418477e-16 16384 -0.030100 5.898060e-17 32768 -0.030100 5.204170e-17 Exact -0.030100 Problem 45 1 -0.554862 2.621557e-01 2 -0.484887 1.921806e-01 4 -0.437024 1.443173e-01 8 -0.398143 1.054361e-01 16 -0.368506 7.579944e-02 32 -0.346752 5.404508e-02 64 -0.331081 3.837466e-02 128 -0.319898 2.719138e-02 256 -0.311954 1.924718e-02 512 -0.306324 1.361688e-02 1024 -0.302338 9.631085e-03 2048 -0.299518 6.811089e-03 4096 -0.297523 4.816480e-03 8192 -0.296113 3.405876e-03 16384 -0.295115 2.408357e-03 32768 -0.294410 1.702979e-03 Exact -0.292707 Problem 46 1 5.741116 3.279750e-01 2 6.002590 6.650139e-02 4 6.067877 1.214387e-03 8 6.069091 3.651448e-07 16 6.069091 3.197442e-14 32 6.069091 2.664535e-15 64 6.069091 8.881784e-16 128 6.069091 8.881784e-16 256 6.069091 0.000000e+00 512 6.069091 8.881784e-16 1024 6.069091 8.881784e-16 2048 6.069091 2.664535e-15 4096 6.069091 2.664535e-15 8192 6.069091 9.769963e-15 16384 6.069091 7.993606e-15 32768 6.069091 7.105427e-15 Exact 6.069091 Problem 47 1 -0.326753 1.176917e-01 2 -0.395784 4.866054e-02 4 -0.424752 1.969241e-02 8 -0.436603 7.841678e-03 16 -0.441361 3.083325e-03 32 -0.443244 1.200028e-03 64 -0.443981 4.631324e-04 128 -0.444267 1.774805e-04 256 -0.444377 6.760614e-05 512 -0.444419 2.561969e-05 1024 -0.444435 9.665091e-06 2048 -0.444441 3.631790e-06 4096 -0.444443 1.359927e-06 8192 -0.444444 5.076397e-07 16384 -0.444444 1.889646e-07 32768 -0.444444 7.016322e-08 Exact -0.444444 Problem 48 1 -0.653505 3.346495e+00 2 -1.198301 2.801699e+00 4 -1.710503 2.289497e+00 8 -2.162966 1.837034e+00 16 -2.546787 1.453213e+00 32 -2.863363 1.136637e+00 64 -3.119160 8.808404e-01 128 -3.322622 6.773782e-01 256 -3.482463 5.175372e-01 512 -3.606781 3.932191e-01 1024 -3.702673 2.973271e-01 2048 -3.776125 2.238745e-01 4096 -3.832057 1.679428e-01 8192 -3.874430 1.255697e-01 16384 -3.906389 9.361103e-02 32768 -3.930399 6.960112e-02 Exact -4.000000 Problem 49 1 46.490980 6.249769e+00 2 53.728761 9.880130e-01 4 53.387958 6.472098e-01 8 53.259989 5.192411e-01 16 52.432917 3.078310e-01 32 52.819793 7.904463e-02 64 52.797398 5.664972e-02 128 52.755722 1.497327e-02 256 52.750201 9.452317e-03 512 52.743372 2.623833e-03 1024 52.743797 3.048825e-03 2048 52.739391 1.357124e-03 4096 52.741553 8.043270e-04 8192 52.741170 4.214080e-04 16384 52.739883 8.654087e-04 32768 52.740690 5.864225e-05 Exact 52.740748 Problem 50 1 -0.000000 1.281368e-01 2 -0.366204 2.380672e-01 4 0.197978 3.261149e-01 8 -0.129329 1.191720e-03 16 -0.126358 1.779015e-03 32 -0.127587 5.497606e-04 64 -0.127992 1.447206e-04 128 -0.128100 3.670755e-05 256 -0.128128 9.214860e-06 512 -0.128135 2.306410e-06 1024 -0.128136 5.767914e-07 2048 -0.128137 1.442109e-07 4096 -0.128137 3.605362e-08 8192 -0.128137 9.013467e-09 16384 -0.128137 2.253372e-09 32768 -0.128137 5.633434e-10 Exact -0.128137 Problem 51 1 -0.210836 1.302253e-02 2 -0.188633 9.180658e-03 4 -0.189061 8.752215e-03 8 -0.189187 8.626674e-03 16 -0.189240 8.573135e-03 32 -0.189262 8.551976e-03 64 -0.189270 8.543727e-03 128 -0.189273 8.540500e-03 256 -0.189274 8.539227e-03 512 -0.189275 8.538719e-03 1024 -0.189275 8.538514e-03 2048 -0.189275 8.538431e-03 4096 -0.189275 8.538396e-03 8192 -0.189275 8.538382e-03 16384 -0.189275 8.538376e-03 32768 -0.189275 8.538373e-03 Exact -0.197814 Problem 52 1 -0.956205 8.662608e-01 2 0.117395 2.073386e-01 4 -0.713703 6.237589e-01 8 0.373414 4.633584e-01 16 -0.604700 5.147558e-01 32 0.411725 5.016691e-01 64 -0.594073 5.041288e-01 128 0.413861 5.038049e-01 256 -0.593779 5.038353e-01 512 0.413889 5.038330e-01 1024 -0.593777 5.038332e-01 2048 0.413889 5.038332e-01 4096 -0.593777 5.038332e-01 8192 0.413889 5.038332e-01 16384 -0.593777 5.038332e-01 32768 0.413889 5.038332e-01 Exact -0.089944 Problem 53 1 1.054318 4.503046e-01 2 1.946062 4.414388e-01 4 1.365107 1.395154e-01 8 1.347851 1.567722e-01 16 1.398139 1.064840e-01 32 1.514710 1.008695e-02 64 1.448557 5.606575e-02 128 1.468124 3.649844e-02 256 1.499018 5.604658e-03 512 1.483776 2.084659e-02 1024 1.498025 6.597828e-03 2048 1.494346 1.027706e-02 4096 1.524580 1.995743e-02 8192 1.504009 6.139762e-04 16384 1.502204 2.418428e-03 32768 1.502097 2.525775e-03 Exact 1.504623 Problem 54 1 1.000000 1.547005e-01 2 1.222222 6.752168e-02 4 1.150794 3.906888e-03 8 1.154680 2.045329e-05 16 1.154701 5.435221e-10 32 1.154701 0.000000e+00 64 1.154701 4.440892e-16 128 1.154701 4.440892e-16 256 1.154701 2.220446e-16 512 1.154701 2.220446e-16 1024 1.154701 0.000000e+00 2048 1.154701 8.881784e-16 4096 1.154701 0.000000e+00 8192 1.154701 3.552714e-15 16384 1.154701 1.554312e-15 32768 1.154701 3.996803e-15 Exact 1.154701 Problem 55 1 0.475874 2.918466e-02 2 0.511440 6.380958e-03 4 0.505174 1.149409e-04 8 0.505065 6.592792e-06 16 0.505059 4.032796e-07 32 0.505059 2.507072e-08 64 0.505059 1.564833e-09 128 0.505059 9.776968e-11 256 0.505059 6.110112e-12 512 0.505059 3.815837e-13 1024 0.505059 2.386980e-14 2048 0.505059 2.220446e-15 4096 0.505059 2.220446e-16 8192 0.505059 1.110223e-16 16384 0.505059 4.440892e-16 32768 0.505059 0.000000e+00 Exact 0.505059 Problem 56 1 1.832359 1.598937e-01 2 2.002009 9.756786e-03 4 1.995936 3.683504e-03 8 1.992320 6.788119e-05 16 1.992257 4.255033e-06 32 1.992253 2.633920e-07 64 1.992252 1.641886e-08 128 1.992252 1.025495e-09 256 1.992252 6.408252e-11 512 1.992252 4.003908e-12 1024 1.992252 2.509104e-13 2048 1.992252 1.687539e-14 4096 1.992252 2.220446e-15 8192 1.992252 8.881784e-16 16384 1.992252 8.881784e-16 32768 1.992252 3.108624e-15 Exact 1.992252 Problem 57 1 0.402369 2.368927e-03 2 0.400432 4.319160e-04 4 0.400077 7.724945e-05 8 0.400014 1.371347e-05 16 0.400002 2.427846e-06 32 0.400000 4.294134e-07 64 0.400000 7.592448e-08 128 0.400000 1.342257e-08 256 0.400000 2.372852e-09 512 0.400000 4.194686e-10 1024 0.400000 7.415235e-11 2048 0.400000 1.310790e-11 4096 0.400000 2.317757e-12 8192 0.400000 4.096168e-13 16384 0.400000 7.160939e-14 32768 0.400000 1.337819e-14 Exact 0.400000 test_int_test03(): Monte Carlo rule, for 1D finite interval problems. Problem Exact Pts Approx Error 1 1.718282 1 2.409745 6.914632e-01 2 1.486625 2.316570e-01 4 2.117301 3.990191e-01 8 1.681334 3.694764e-02 16 1.763290 4.500791e-02 32 1.660182 5.809978e-02 64 1.667248 5.103406e-02 128 1.666713 5.156903e-02 2 0.700000 1 1.000000 3.000000e-01 2 0.500000 2.000000e-01 4 0.750000 5.000000e-02 8 0.625000 7.500000e-02 16 0.750000 5.000000e-02 32 0.625000 7.500000e-02 64 0.796875 9.687500e-02 128 0.695312 4.687500e-03 3 0.666667 1 0.845237 1.785706e-01 2 0.216456 4.502110e-01 4 0.592965 7.370214e-02 8 0.659682 6.984389e-03 16 0.620510 4.615687e-02 32 0.669162 2.495377e-03 64 0.625622 4.104435e-02 128 0.662498 4.168486e-03 4 0.479428 1 1.073944 5.945155e-01 2 1.562507 1.083079e+00 4 0.928927 4.494989e-01 8 0.274008 2.054207e-01 16 0.696693 2.172648e-01 32 0.530151 5.072292e-02 64 0.364800 1.146281e-01 128 0.487871 8.442659e-03 5 1.582233 1 1.975204 3.929707e-01 2 1.374226 2.080073e-01 4 1.680309 9.807565e-02 8 1.450379 1.318536e-01 16 1.207339 3.748943e-01 32 1.487662 9.457088e-02 64 1.595903 1.366956e-02 128 1.620773 3.853963e-02 6 1.460447 1 1.285062 1.753848e-01 2 1.499838 3.939039e-02 4 1.294490 1.659575e-01 8 1.558422 9.797454e-02 16 1.492298 3.185041e-02 32 1.434707 2.574047e-02 64 1.412024 4.842303e-02 128 1.349197 1.112504e-01 7 2.000000 1 1.150498 8.495016e-01 2 3.629208 1.629208e+00 4 1.620007 3.799935e-01 8 1.394261 6.057394e-01 16 2.248654 2.486542e-01 32 1.981162 1.883752e-02 64 1.749104 2.508960e-01 128 2.067717 6.771666e-02 8 0.866973 1 0.999495 1.325216e-01 2 0.648498 2.184754e-01 4 0.817868 4.910507e-02 8 0.913050 4.607707e-02 16 0.850759 1.621444e-02 32 0.830640 3.633293e-02 64 0.836589 3.038383e-02 128 0.862161 4.812228e-03 9 1.154701 1 0.693971 4.607294e-01 2 1.938216 7.835157e-01 4 1.593245 4.385448e-01 8 1.092752 6.194853e-02 16 1.270758 1.160575e-01 32 1.002905 1.517955e-01 64 1.163163 8.462239e-03 128 1.125960 2.874057e-02 10 0.693147 1 0.810754 1.176067e-01 2 0.741794 4.864682e-02 4 0.654890 3.825750e-02 8 0.615970 7.717673e-02 16 0.671301 2.184577e-02 32 0.708625 1.547832e-02 64 0.708253 1.510614e-02 128 0.706363 1.321602e-02 11 0.379885 1 0.327835 5.205091e-02 2 0.335740 4.414565e-02 4 0.379422 4.632774e-04 8 0.392972 1.308614e-02 16 0.394797 1.491110e-02 32 0.370026 9.859410e-03 64 0.382568 2.682157e-03 128 0.385308 5.422559e-03 12 0.777505 1 0.943964 1.664592e-01 2 0.685161 9.234340e-02 4 0.750166 2.733872e-02 8 0.787795 1.029020e-02 16 0.781576 4.071167e-03 32 0.786993 9.488130e-03 64 0.784865 7.359932e-03 128 0.796333 1.882827e-02 13 1.658348 1 4.252475 2.594127e+00 2 3.708169 2.049821e+00 4 5.408556 3.750208e+00 8 1.413096 2.452514e-01 16 1.476344 1.820037e-01 32 2.370193 7.118452e-01 64 1.570080 8.826786e-02 128 1.088898 5.694493e-01 14 0.500000 1 0.000000 5.000002e-01 2 0.000000 5.000002e-01 4 0.000000 5.000002e-01 8 0.000000 5.000002e-01 16 0.000007 4.999934e-01 32 0.042636 4.573639e-01 64 2.190719 1.690718e+00 128 0.098351 4.016493e-01 15 1.000000 1 0.000000 1.000000e+00 2 0.000000 1.000000e+00 4 0.000000 1.000000e+00 8 0.000007 9.999929e-01 16 2.694046 1.694046e+00 32 0.012928 9.870715e-01 64 0.773096 2.269041e-01 128 1.200041 2.000410e-01 16 0.493635 1 0.008051 4.855834e-01 2 0.193051 3.005838e-01 4 2.711973 2.218338e+00 8 0.733129 2.394947e-01 16 0.568557 7.492267e-02 32 0.442648 5.098696e-02 64 0.553841 6.020675e-02 128 0.427391 6.624317e-02 17 0.500000 1 0.826762 3.267619e-01 2 0.786321 2.863207e-01 4 0.384955 1.150445e-01 8 0.574426 7.442629e-02 16 0.566495 6.649471e-02 32 0.473585 2.641534e-02 64 0.580403 8.040344e-02 128 0.575549 7.554851e-02 18 0.170557 1 0.083041 8.751650e-02 2 0.181173 1.061529e-02 4 0.247639 7.708206e-02 8 0.172323 1.765842e-03 16 0.184801 1.424318e-02 32 0.157689 1.286852e-02 64 0.154502 1.605566e-02 128 0.162319 8.238366e-03 19 -1.000000 1 -0.012343 9.876575e-01 2 -1.570220 5.702201e-01 4 -0.616633 3.833666e-01 8 -1.839450 8.394498e-01 16 -0.859260 1.407400e-01 32 -0.919237 8.076253e-02 64 -0.897518 1.024820e-01 128 -0.971485 2.851488e-02 20 1.564396 1 1.114629 4.497676e-01 2 1.563578 8.185706e-04 4 1.523428 4.096816e-02 8 1.478023 8.637338e-02 16 1.599814 3.541790e-02 32 1.471545 9.285131e-02 64 1.553994 1.040251e-02 128 1.606596 4.219962e-02 21 0.210803 1 0.000016 2.107867e-01 2 0.331541 1.207386e-01 4 0.054362 1.564409e-01 8 0.348687 1.378840e-01 16 0.305885 9.508260e-02 32 0.216080 5.277495e-03 64 0.298960 8.815683e-02 128 0.190496 2.030655e-02 22 0.728103 1 0.764994 3.689126e-02 2 0.651637 7.646543e-02 4 0.632296 9.580723e-02 8 0.742663 1.456048e-02 16 0.722265 5.838253e-03 32 0.692044 3.605844e-02 64 0.683830 4.427249e-02 128 0.746427 1.832376e-02 23 0.624713 1 -3.787100 4.411814e+00 2 12.589224 1.196451e+01 4 1.261986 6.372725e-01 8 1.883502 1.258788e+00 16 0.390600 2.341130e-01 32 2.105242 1.480529e+00 64 5.027128 4.402415e+00 128 1.550260 9.255471e-01 24 -0.006755 1 -0.055280 4.852513e-02 2 0.000429 7.183697e-03 4 -0.012517 5.761771e-03 8 -0.047159 4.040429e-02 16 -0.013064 6.309193e-03 32 -0.002228 4.526415e-03 64 -0.006793 3.821936e-05 128 -0.015666 8.911276e-03 25 -1.610864 1 -1.731279 1.204152e-01 2 -1.616728 5.863596e-03 4 -1.702360 9.149545e-02 8 -1.031185 5.796791e-01 16 -1.507926 1.029383e-01 32 -1.817596 2.067316e-01 64 -1.451588 1.592759e-01 128 -1.554544 5.632053e-02 26 7.954927 1 2.616431 5.338496e+00 2 4.380533 3.574394e+00 4 4.938925 3.016002e+00 8 8.986408 1.031481e+00 16 6.013962 1.940964e+00 32 9.473256 1.518329e+00 64 8.543266 5.883390e-01 128 8.563661 6.087348e-01 27 0.841117 1 0.823011 1.810633e-02 2 0.623416 2.177011e-01 4 0.733099 1.080182e-01 8 0.923770 8.265333e-02 16 0.940061 9.894403e-02 32 0.703244 1.378733e-01 64 0.861721 2.060427e-02 128 0.964613 1.234959e-01 28 0.019955 1 -0.176773 1.967273e-01 2 -0.041734 6.168819e-02 4 -0.215047 2.350018e-01 8 -0.513152 5.331070e-01 16 0.389815 3.698606e-01 32 -0.111133 1.310879e-01 64 -0.096057 1.160118e-01 128 0.015321 4.633440e-03 29 0.306853 1 0.460515 1.536619e-01 2 0.431927 1.250747e-01 4 0.204257 1.025956e-01 8 0.338779 3.192618e-02 16 0.371208 6.435483e-02 32 0.341044 3.419117e-02 64 0.343051 3.619866e-02 128 0.303006 3.846749e-03 30 -4.527570 1 -11.650465 7.122895e+00 2 -28.083025 2.355546e+01 4 -18.028061 1.350049e+01 8 2.837389 7.364959e+00 16 -10.549979 6.022410e+00 32 -7.122277 2.594708e+00 64 -3.639825 8.877445e-01 128 -1.755644 2.771925e+00 31 2.651635 1 0.616448 2.035188e+00 2 1.615212 1.036423e+00 4 3.141273 4.896378e-01 8 3.420941 7.693059e-01 16 1.799458 8.521772e-01 32 3.522653 8.710181e-01 64 2.405081 2.465543e-01 128 2.403832 2.478036e-01 32 -12.070346 1 4.151546 1.622189e+01 2 1.231307 1.330165e+01 4 -6.732039 5.338307e+00 8 2.024095 1.409444e+01 16 -22.157282 1.008694e+01 32 -13.123038 1.052691e+00 64 -8.926011 3.144335e+00 128 -12.104525 3.417883e-02 33 0.886227 1 0.463820 4.224073e-01 2 1.100503 2.142757e-01 4 0.839729 4.649840e-02 8 1.134458 2.482307e-01 16 1.157188 2.709612e-01 32 0.920020 3.379280e-02 64 0.951579 6.535202e-02 128 0.848571 3.765639e-02 34 1085.252667 1 164.900423 9.203522e+02 2 2941.762502 1.856510e+03 4 430.013073 6.552396e+02 8 1082.802037 2.450630e+00 16 712.713105 3.725396e+02 32 941.382343 1.438703e+02 64 1306.984680 2.217320e+02 128 914.442380 1.708103e+02 35 26.000000 1 11.277688 1.472231e+01 2 38.295871 1.229587e+01 4 13.870450 1.212955e+01 8 13.163468 1.283653e+01 16 17.182323 8.817677e+00 32 29.409854 3.409854e+00 64 25.178190 8.218098e-01 128 22.599863 3.400137e+00 36 100.000000 1 0.096833 9.990317e+01 2 0.836597 9.916340e+01 4 7.965227 9.203477e+01 8 1.018906 9.898109e+01 16 1.217902 9.878210e+01 32 7.193402 9.280660e+01 64 25.286084 7.471392e+01 128 213.850667 1.138507e+02 37 3.135799 1 0.020868 3.114930e+00 2 0.551555 2.584243e+00 4 3.940870 8.050710e-01 8 0.467576 2.668223e+00 16 0.066390 3.069408e+00 32 0.155325 2.980473e+00 64 1.514569 1.621230e+00 128 0.180346 2.955453e+00 38 0.539257 1 2.688329 2.149072e+00 2 -0.509367 1.048624e+00 4 1.442116 9.028594e-01 8 1.136022 5.967655e-01 16 0.653001 1.137441e-01 32 -0.137396 6.766525e-01 64 0.430353 1.089044e-01 128 0.674047 1.347901e-01 39 2.787694 1 1.324574 1.463119e+00 2 3.674877 8.871836e-01 4 1.863365 9.243292e-01 8 1.760810 1.026884e+00 16 2.349478 4.382152e-01 32 3.155102 3.674079e-01 64 2.740183 4.751103e-02 128 2.804274 1.658018e-02 40 2.698957 1 2.814925 1.159681e-01 2 1.617801 1.081155e+00 4 2.248637 4.503193e-01 8 3.811428 1.112472e+00 16 3.608992 9.100351e-01 32 2.246308 4.526486e-01 64 2.496870 2.020869e-01 128 2.640423 5.853382e-02 41 6.095585 1 1.696348 4.399237e+00 2 2.754803 3.340782e+00 4 2.169352 3.926233e+00 8 3.860638 2.234947e+00 16 4.551565 1.544020e+00 32 3.860815 2.234770e+00 64 4.165517 1.930068e+00 128 7.329502 1.233917e+00 42 3.980786 1 1.947961 2.032825e+00 2 2.309240 1.671546e+00 4 11.971715 7.990929e+00 8 3.610667 3.701188e-01 16 2.620197 1.360590e+00 32 2.389033 1.591753e+00 64 2.460171 1.520615e+00 128 3.175005 8.057811e-01 43 2.991569 1 1.783044 1.208525e+00 2 0.624858 2.366711e+00 4 1.531893 1.459676e+00 8 2.836239 1.553296e-01 16 4.839943 1.848374e+00 32 4.401997 1.410428e+00 64 3.644358 6.527885e-01 128 2.465327 5.262421e-01 44 -0.030100 1 0.000000 3.010017e-02 2 -0.023244 6.856089e-03 4 0.000075 3.017424e-02 8 -0.045003 1.490281e-02 16 -0.027436 2.663231e-03 32 -0.025758 4.341790e-03 64 -0.037146 7.046689e-03 128 -0.040888 1.078880e-02 45 -0.292707 1 -0.641289 3.485825e-01 2 -0.320602 2.789536e-02 4 -0.552137 2.594299e-01 8 -1.518807 1.226100e+00 16 -0.588914 2.962068e-01 32 1.050919 1.343625e+00 64 -0.241470 5.123706e-02 128 -0.569447 2.767401e-01 46 6.069091 1 4.659425 1.409666e+00 2 5.336833 7.322579e-01 4 6.295671 2.265799e-01 8 6.702271 6.331798e-01 16 5.570284 4.988073e-01 32 6.328331 2.592397e-01 64 5.820619 2.484721e-01 128 5.876928 1.921630e-01 47 -0.444444 1 -0.574301 1.298567e-01 2 -0.687927 2.434828e-01 4 -0.417856 2.658886e-02 8 -0.440259 4.184994e-03 16 -0.459791 1.534663e-02 32 -0.503608 5.916307e-02 64 -0.399900 4.454485e-02 128 -0.459171 1.472663e-02 48 -4.000000 1 -1.588192 2.411808e+00 2 -0.209716 3.790284e+00 4 -7.545662 3.545662e+00 8 -2.009087 1.990913e+00 16 -3.940545 5.945477e-02 32 -1.979889 2.020111e+00 64 -2.205057 1.794943e+00 128 -3.958501 4.149896e-02 49 52.740748 1 -14.450735 6.719148e+01 2 30.074080 2.266667e+01 4 15.913216 3.682753e+01 8 7.665318 4.507543e+01 16 52.340382 4.003665e-01 32 30.527071 2.221368e+01 64 42.726621 1.001413e+01 128 49.652489 3.088260e+00 50 -0.128137 1 0.580785 7.089222e-01 2 0.278124 4.062612e-01 4 0.304598 4.327349e-01 8 -0.028799 9.933773e-02 16 -0.462810 3.346733e-01 32 -0.264835 1.366978e-01 64 -0.222849 9.471215e-02 128 -0.214755 8.661817e-02 51 -0.197814 1 -0.123816 7.399716e-02 2 -0.220894 2.308054e-02 4 -0.130078 6.773574e-02 8 -0.222464 2.465041e-02 16 -0.147754 5.005963e-02 32 -0.165516 3.229792e-02 64 -0.215489 1.767553e-02 128 -0.181251 1.656230e-02 52 -0.089944 1 0.029037 1.189810e-01 2 1.141672 1.231616e+00 4 0.525846 6.157899e-01 8 -0.191602 1.016579e-01 16 -0.841620 7.516762e-01 32 0.107043 1.969869e-01 64 0.540758 6.307016e-01 128 -0.174094 8.414965e-02 53 1.504623 1 1.643445 1.388223e-01 2 1.072668 4.319544e-01 4 1.031955 4.726673e-01 8 1.410317 9.430583e-02 16 1.119256 3.853670e-01 32 1.158953 3.456696e-01 64 1.370138 1.344850e-01 128 1.650553 1.459302e-01 54 1.154701 1 1.933364 7.786631e-01 2 1.139007 1.569306e-02 4 1.700096 5.453957e-01 8 1.162207 7.506012e-03 16 1.216378 6.167779e-02 32 1.212884 5.818299e-02 64 1.157193 2.492074e-03 128 1.193277 3.857629e-02 55 0.505059 1 0.037984 4.670747e-01 2 0.692470 1.874110e-01 4 0.573750 6.869132e-02 8 0.389909 1.151499e-01 16 0.591286 8.622711e-02 32 0.505955 8.964981e-04 64 0.605165 1.001068e-01 128 0.543465 3.840597e-02 56 1.992252 1 2.165910 1.736580e-01 2 2.125789 1.335361e-01 4 1.983659 8.593784e-03 8 1.890692 1.015603e-01 16 1.907420 8.483204e-02 32 1.938146 5.410658e-02 64 1.992792 5.393740e-04 128 1.998487 6.234539e-03 57 0.400000 1 0.100404 2.995959e-01 2 0.433606 3.360620e-02 4 0.402587 2.586624e-03 8 0.555756 1.557561e-01 16 0.330324 6.967620e-02 32 0.348940 5.106030e-02 64 0.341002 5.899787e-02 128 0.369752 3.024758e-02 test_int_test04(): Use a composite 4 point Gauss-Legendre rule, for 1D finite interval problems. Problem Exact Ints Approx Error 1 1.718282 1 1.718282 9.329675e-10 2 1.718282 3.741674e-12 4 1.718282 1.465494e-14 8 1.718282 2.220446e-16 16 1.718282 4.440892e-16 32 1.718282 0.000000e+00 64 1.718282 2.220446e-16 128 1.718282 2.220446e-16 2 0.700000 1 0.826073 1.260726e-01 2 0.750000 5.000000e-02 4 0.706518 6.518144e-03 8 0.687500 1.250000e-02 16 0.698370 1.629536e-03 32 0.703125 3.125000e-03 64 0.700407 4.073840e-04 128 0.699219 7.812500e-04 3 0.666667 1 0.667828 1.160979e-03 2 0.667077 4.104740e-04 4 0.666812 1.451245e-04 8 0.666718 5.130926e-05 16 0.666685 1.814056e-05 32 0.666673 6.413658e-06 64 0.666669 2.267570e-06 128 0.666667 8.017072e-07 4 0.479428 1 0.479428 9.399092e-09 2 0.479428 1.930694e-10 4 0.479428 9.782730e-13 8 0.479428 3.941292e-15 16 0.479428 5.551115e-17 32 0.479428 5.551115e-17 64 0.479428 0.000000e+00 128 0.479428 5.551115e-17 5 1.582233 1 1.585060 2.827524e-03 2 1.582214 1.930856e-05 4 1.582233 3.656264e-08 8 1.582233 3.304690e-11 16 1.582233 1.458833e-13 32 1.582233 2.220446e-16 64 1.582233 2.220446e-16 128 1.582233 8.881784e-16 6 1.460447 1 1.473444 1.299700e-02 2 1.486176 2.572910e-02 4 1.461268 8.209420e-04 8 1.460737 2.902490e-04 16 1.460550 1.026185e-04 32 1.460483 3.628113e-05 64 1.460460 1.282732e-05 128 1.460452 4.535141e-06 7 2.000000 1 1.806343 1.936575e-01 2 1.863063 1.369366e-01 4 1.903171 9.682882e-02 8 1.931532 6.846832e-02 16 1.951586 4.841441e-02 32 1.965766 3.423416e-02 64 1.975793 2.420721e-02 128 1.982883 1.711708e-02 8 0.866973 1 0.866956 1.732989e-05 2 0.866973 5.613566e-08 4 0.866973 1.679805e-10 8 0.866973 5.585532e-13 16 0.866973 1.998401e-15 32 0.866973 1.110223e-16 64 0.866973 0.000000e+00 128 0.866973 2.220446e-16 9 1.154701 1 1.197813 4.311276e-02 2 1.246607 9.190634e-02 4 1.147746 6.954610e-03 8 1.154665 3.574995e-05 16 1.154701 9.499237e-10 32 1.154701 0.000000e+00 64 1.154701 0.000000e+00 128 1.154701 2.220446e-16 10 0.693147 1 0.693146 7.631145e-07 2 0.693147 6.806386e-09 4 0.693147 3.723388e-11 8 0.693147 1.619815e-13 16 0.693147 6.661338e-16 32 0.693147 1.110223e-16 64 0.693147 1.110223e-16 128 0.693147 1.110223e-16 11 0.379885 1 0.379885 1.272926e-09 2 0.379885 3.834044e-12 4 0.379885 1.421085e-14 8 0.379885 5.551115e-17 16 0.379885 0.000000e+00 32 0.379885 0.000000e+00 64 0.379885 0.000000e+00 128 0.379885 5.551115e-17 12 0.777505 1 0.777505 1.361589e-11 2 0.777505 5.062617e-14 4 0.777505 0.000000e+00 8 0.777505 2.220446e-16 16 0.777505 1.110223e-16 32 0.777505 2.220446e-16 64 0.777505 2.220446e-16 128 0.777505 1.110223e-16 13 1.658348 1 1.666102 7.754171e-03 2 1.658338 9.470520e-06 4 1.658348 2.657638e-08 8 1.658348 9.438494e-11 16 1.658348 3.601563e-13 32 1.658348 1.110223e-15 64 1.658348 6.661338e-16 128 1.658348 8.881784e-16 14 0.500000 1 0.000000 5.000002e-01 2 0.000000 5.000002e-01 4 0.027063 4.729377e-01 8 0.470876 2.912388e-02 16 0.573638 7.363784e-02 32 0.493226 6.774462e-03 64 0.500077 7.697052e-05 128 0.500000 1.750487e-07 15 1.000000 1 0.000001 9.999987e-01 2 0.003699 9.963013e-01 4 0.141785 8.582146e-01 8 0.621078 3.789216e-01 16 0.947909 5.209059e-02 32 0.998223 1.776979e-03 64 0.999981 1.893131e-05 128 1.000000 1.045036e-07 16 0.493635 1 0.236976 2.566589e-01 2 0.400596 9.303848e-02 4 0.509088 1.545305e-02 8 0.503719 1.008481e-02 16 0.493170 4.646943e-04 32 0.493618 1.704163e-05 64 0.493635 3.303491e-07 128 0.493635 1.103806e-10 17 0.500000 1 0.997235 4.972353e-01 2 0.515987 1.598715e-02 4 0.500000 1.110223e-15 8 0.500000 6.661338e-16 16 0.500000 3.330669e-16 32 0.500000 0.000000e+00 64 0.500000 0.000000e+00 128 0.500000 5.551115e-17 18 0.170557 1 0.170557 6.749800e-10 2 0.170557 3.126416e-12 4 0.170557 1.221245e-14 8 0.170557 5.551115e-17 16 0.170557 0.000000e+00 32 0.170557 2.775558e-17 64 0.170557 2.775558e-17 128 0.170557 0.000000e+00 19 -1.000000 1 -0.968536 3.146402e-02 2 -0.984268 1.573208e-02 4 -0.992134 7.866040e-03 8 -0.996067 3.933020e-03 16 -0.998033 1.966510e-03 32 -0.999017 9.832550e-04 64 -0.999508 4.916275e-04 128 -0.999754 2.458138e-04 20 1.564396 1 1.562267 2.129295e-03 2 1.564406 9.493715e-06 4 1.564396 2.224436e-08 8 1.564396 2.915446e-13 16 1.564396 0.000000e+00 32 1.564396 0.000000e+00 64 1.564396 2.220446e-16 128 1.564396 4.440892e-16 21 0.210803 1 0.128374 8.242829e-02 2 0.197150 1.365300e-02 4 0.197678 1.312482e-02 8 0.197680 1.312242e-02 16 0.210842 3.899553e-05 32 0.209812 9.902591e-04 64 0.209975 8.272468e-04 128 0.210004 7.990218e-04 22 0.728103 1 0.728090 1.339604e-05 2 0.728103 3.911765e-08 4 0.728103 2.125433e-11 8 0.728103 8.337775e-14 16 0.728103 3.330669e-16 32 0.728103 2.220446e-16 64 0.728103 0.000000e+00 128 0.728103 0.000000e+00 23 0.624713 1 3.176652 2.551939e+00 2 -0.594889 1.219602e+00 4 2.252750 1.628037e+00 8 1.844057 1.219344e+00 16 -3.188560 3.813273e+00 32 2.454704 1.829990e+00 64 -2.144914 2.769627e+00 128 1.291870 6.671572e-01 24 -0.006755 1 0.003635 1.039016e-02 2 0.015256 2.201083e-02 4 0.004790 1.154428e-02 8 -0.005612 1.142817e-03 16 -0.006593 1.614971e-04 32 -0.006517 2.381637e-04 64 -0.006789 3.387446e-05 128 -0.006731 2.394314e-05 25 -1.610864 1 -1.802888 1.920235e-01 2 -1.572787 3.807739e-02 4 -1.565758 4.510661e-02 8 -1.601345 9.519597e-03 16 -1.599588 1.127666e-02 32 -1.608484 2.379899e-03 64 -1.608045 2.819164e-03 128 -1.610269 5.949748e-04 26 7.954927 1 7.940916 1.401019e-02 2 7.952632 2.294098e-03 4 7.954963 3.657153e-05 8 7.954927 1.336596e-09 16 7.954927 8.881784e-16 32 7.954927 1.776357e-15 64 7.954927 1.776357e-15 128 7.954927 8.881784e-16 27 0.841117 1 0.797664 4.345318e-02 2 0.813100 2.801699e-02 4 0.823093 1.802367e-02 8 0.829546 1.157076e-02 16 0.833703 7.413970e-03 32 0.836375 4.742218e-03 64 0.838088 3.028460e-03 128 0.839186 1.931240e-03 28 0.019955 1 0.124191 1.042363e-01 2 -0.177256 1.972103e-01 4 0.094897 7.494280e-02 8 0.227422 2.074670e-01 16 0.354106 3.341510e-01 32 0.022545 2.590463e-03 64 0.019942 1.230371e-05 128 0.019955 1.838019e-08 29 0.306853 1 0.346116 3.926290e-02 2 0.318629 1.177652e-02 4 0.302542 4.311109e-03 8 0.310523 3.670090e-03 16 0.307028 1.750256e-04 32 0.307025 1.722159e-04 64 0.307025 1.722159e-04 128 0.307025 1.722159e-04 30 -4.527570 1 -23.102350 1.857478e+01 2 1.533015 6.060584e+00 4 -4.105014 4.225552e-01 8 -4.530446 2.876188e-03 16 -4.527572 2.131468e-06 32 -4.527570 6.586660e-09 64 -4.527570 2.436096e-11 128 -4.527570 7.549517e-14 31 2.651635 1 2.047285 6.043503e-01 2 2.655426 3.791118e-03 4 2.650818 8.175622e-04 8 2.651645 9.804786e-06 16 2.651635 2.338863e-08 32 2.651635 8.215650e-14 64 2.651635 4.440892e-16 128 2.651635 1.332268e-15 32 -12.070346 1 -12.070189 1.568261e-04 2 -12.070343 3.238376e-06 4 -12.070346 1.501408e-08 8 -12.070346 6.075673e-11 16 -12.070346 2.451372e-13 32 -12.070346 5.329071e-15 64 -12.070346 5.329071e-15 128 -12.070346 3.552714e-15 33 0.886227 1 0.880399 5.827988e-03 2 0.883352 2.874553e-03 4 0.884818 1.408884e-03 8 0.885539 6.876771e-04 16 0.885892 3.348057e-04 32 0.886064 1.627788e-04 64 0.886148 7.909524e-05 128 0.886188 3.843201e-05 34 1085.252667 1 1085.252667 4.547474e-13 2 1085.252667 0.000000e+00 4 1085.252667 0.000000e+00 8 1085.252667 0.000000e+00 16 1085.252667 0.000000e+00 32 1085.252667 2.273737e-13 64 1085.252667 2.273737e-13 128 1085.252667 2.273737e-13 35 26.000000 1 29.100212 3.100212e+00 2 21.443668 4.556332e+00 4 121.740220 9.574022e+01 8 32.250500 6.250500e+00 16 30.684954 4.684954e+00 32 26.543024 5.430245e-01 64 25.849849 1.501511e-01 128 25.451798 5.482018e-01 36 100.000000 1 6.298537 9.370146e+01 2 8.341271 9.165873e+01 4 10.530627 8.946937e+01 8 12.837804 8.716220e+01 16 15.237205 8.476280e+01 32 17.706130 8.229387e+01 64 20.224507 7.977549e+01 128 22.774642 7.722536e+01 37 3.135799 1 0.033832 3.101966e+00 2 0.081837 3.053961e+00 4 0.197291 2.938508e+00 8 1.212995 1.922804e+00 16 0.643995 2.491804e+00 32 1.645182 1.490617e+00 64 3.237779 1.019802e-01 128 2.598738 5.370609e-01 38 0.539257 1 1.513047 9.737903e-01 2 0.406660 1.325971e-01 4 0.540695 1.437627e-03 8 0.539257 5.233767e-07 16 0.539257 9.992007e-16 32 0.539257 4.440892e-16 64 0.539257 3.330669e-16 128 0.539257 1.110223e-16 39 2.787694 1 6.781396 3.993703e+00 2 5.611634 2.823940e+00 4 4.784520 1.996826e+00 8 4.199663 1.411969e+00 16 3.786107 9.984131e-01 32 3.493678 7.059847e-01 64 3.286900 4.992066e-01 128 3.140686 3.529923e-01 40 2.698957 1 2.105072 5.938846e-01 2 2.284680 4.142764e-01 4 2.417203 2.817531e-01 8 2.651521 4.743571e-02 16 2.548058 1.508984e-01 32 2.605726 9.323083e-02 64 2.656170 4.278673e-02 128 2.637612 6.134424e-02 41 6.095585 1 4.294417 1.801168e+00 2 4.867484 1.228101e+00 4 5.252976 8.426090e-01 8 5.508555 5.870298e-01 16 5.683138 4.124469e-01 32 5.804793 2.907925e-01 64 5.890253 2.053320e-01 128 5.950494 1.450911e-01 42 3.980786 1 2.967363 1.013423e+00 2 3.157645 8.231416e-01 4 3.312190 6.685959e-01 8 3.437718 5.430681e-01 16 3.539678 4.411082e-01 32 3.622495 3.582912e-01 64 3.689763 2.910229e-01 128 3.744402 2.363840e-01 43 2.991569 1 2.107109 8.844601e-01 2 2.272957 7.186121e-01 4 2.407788 5.837814e-01 8 2.517354 4.742152e-01 16 2.606370 3.851990e-01 32 2.678683 3.128862e-01 64 2.737423 2.541460e-01 128 2.785137 2.064323e-01 44 -0.030100 1 -0.023600 6.499705e-03 2 -0.029706 3.936359e-04 4 -0.030094 5.594865e-06 8 -0.030100 3.338153e-08 16 -0.030100 1.454571e-10 32 -0.030100 5.837379e-13 64 -0.030100 2.307182e-15 128 -0.030100 2.428613e-17 45 -0.292707 1 -0.362859 7.015220e-02 2 -0.341268 4.856148e-02 4 -0.326652 3.394479e-02 8 -0.316566 2.385972e-02 16 -0.309527 1.682021e-02 32 -0.304582 1.187549e-02 64 -0.301097 8.390785e-03 128 -0.298638 5.930896e-03 46 6.069091 1 6.063372 5.718707e-03 2 6.068904 1.873716e-04 4 6.069095 3.756318e-06 8 6.069091 1.169730e-09 16 6.069091 0.000000e+00 32 6.069091 1.776357e-15 64 6.069091 0.000000e+00 128 6.069091 3.552714e-15 47 -0.444444 1 -0.448878 4.433110e-03 2 -0.446296 1.851869e-03 4 -0.445200 7.553274e-04 8 -0.444747 3.026134e-04 16 -0.444564 1.195641e-04 32 -0.444491 4.671790e-05 64 -0.444463 1.808903e-05 128 -0.444451 6.951139e-06 48 -4.000000 1 -2.562461 1.437539e+00 2 -2.888589 1.111411e+00 4 -3.146997 8.530032e-01 8 -3.349377 6.506229e-01 16 -3.506382 4.936182e-01 32 -3.627230 3.727701e-01 64 -3.719633 2.803674e-01 128 -3.789886 2.101144e-01 49 52.740748 1 52.491094 2.496542e-01 2 50.737008 2.003740e+00 4 52.243512 4.972363e-01 8 52.562081 1.786675e-01 16 52.686142 5.460643e-02 32 52.631350 1.093981e-01 64 52.723150 1.759871e-02 128 52.683296 5.745266e-02 50 -0.128137 1 -0.183037 5.490005e-02 2 0.067921 1.960582e-01 4 -0.131315 3.178502e-03 8 -0.128444 3.072448e-04 16 -0.128216 7.906152e-05 32 -0.128157 1.987879e-05 64 -0.128142 4.976910e-06 128 -0.128138 1.244682e-06 51 -0.197814 1 -0.189169 8.644413e-03 2 -0.189298 8.516031e-03 4 -0.189284 8.529942e-03 8 -0.189278 8.535167e-03 16 -0.189276 8.537159e-03 32 -0.189276 8.537911e-03 64 -0.189275 8.538195e-03 128 -0.189275 8.538303e-03 52 -0.089944 1 -0.165815 7.587119e-02 2 -16.434964 1.634502e+01 4 16.283211 1.637316e+01 8 -16.453589 1.636365e+01 16 16.275779 1.636572e+01 32 -16.455404 1.636546e+01 64 16.275533 1.636548e+01 128 -16.455420 1.636548e+01 53 1.504623 1 1.335150 1.694728e-01 2 1.244343 2.602794e-01 4 2.138385 6.337627e-01 8 1.396267 1.083562e-01 16 1.495503 9.119613e-03 32 1.450471 5.415201e-02 64 1.465288 3.933484e-02 128 1.512136 7.513112e-03 54 1.154701 1 1.197813 4.311276e-02 2 1.246607 9.190634e-02 4 1.147746 6.954610e-03 8 1.154665 3.574995e-05 16 1.154701 9.499239e-10 32 1.154701 2.220446e-16 64 1.154701 2.220446e-16 128 1.154701 4.440892e-16 55 0.505059 1 0.506864 1.805343e-03 2 0.505046 1.258923e-05 4 0.505059 1.341399e-09 8 0.505059 8.353762e-12 16 0.505059 3.363976e-14 32 0.505059 2.220446e-16 64 0.505059 1.110223e-16 128 0.505059 0.000000e+00 56 1.992252 1 1.978705 1.354784e-02 2 1.993020 7.673128e-04 4 1.992244 8.577808e-06 8 1.992252 8.746735e-09 16 1.992252 1.028555e-11 32 1.992252 2.864375e-14 64 1.992252 0.000000e+00 128 1.992252 2.220446e-16 57 0.400000 1 0.399950 4.961499e-05 2 0.399991 8.771771e-06 4 0.399998 1.550651e-06 8 0.400000 2.741190e-07 16 0.400000 4.845785e-08 32 0.400000 8.566219e-09 64 0.400000 1.514308e-09 128 0.400000 2.676945e-10 test_int_test05(): Composite trapezoid rule, for 1D finite interval problems. Problem Exact Ints Approx Error 1 1.718282 4 1.727222 8.940076e-03 8 1.720519 2.236764e-03 16 1.718841 5.593001e-04 32 1.718422 1.398319e-04 64 1.718317 3.495839e-05 128 1.718291 8.739624e-06 2 0.700000 4 0.625000 7.500000e-02 8 0.687500 1.250000e-02 16 0.718750 1.875000e-02 32 0.703125 3.125000e-03 64 0.695312 4.687500e-03 128 0.699219 7.812500e-04 3 0.666667 4 0.643283 2.338362e-02 8 0.658130 8.536445e-03 16 0.663581 3.085470e-03 32 0.665559 1.107730e-03 64 0.666271 3.958553e-04 128 0.666526 1.410094e-04 4 0.479428 4 0.559499 8.007104e-02 8 0.499453 2.002510e-02 16 0.484435 5.006755e-03 32 0.480680 1.251719e-03 64 0.479741 3.129317e-04 128 0.479506 7.823304e-05 5 1.582233 4 1.552712 2.952135e-02 8 1.574808 7.424810e-03 16 1.580375 1.857541e-03 32 1.581769 4.644548e-04 64 1.582117 1.161178e-04 128 1.582204 2.902972e-05 6 1.460447 4 1.336516 1.239308e-01 8 1.414273 4.617413e-02 16 1.443524 1.692319e-02 32 1.454314 6.133421e-03 64 1.458241 2.206075e-03 128 1.459658 7.893638e-04 7 2.000000 4 1.267229 7.327715e-01 8 1.483036 5.169637e-01 16 1.634749 3.652513e-01 32 1.741803 2.581973e-01 64 1.817446 1.825545e-01 128 1.870919 1.290809e-01 8 0.866973 4 0.861732 5.240653e-03 8 0.865669 1.304117e-03 16 0.866647 3.256480e-04 32 0.866892 8.138816e-05 64 0.866953 2.034555e-05 128 0.866968 5.086294e-06 9 1.154701 4 1.166667 1.196613e-02 8 1.154762 6.136638e-05 16 1.154701 1.630567e-09 32 1.154701 4.440892e-16 64 1.154701 4.440892e-16 128 1.154701 0.000000e+00 10 0.693147 4 0.697024 3.876629e-03 8 0.694122 9.746698e-04 16 0.693391 2.440216e-04 32 0.693208 6.102771e-05 64 0.693162 1.525832e-05 128 0.693151 3.814668e-06 11 0.379885 4 0.380164 2.785518e-04 8 0.379955 6.954616e-05 16 0.379903 1.738083e-05 32 0.379890 4.344851e-06 64 0.379887 1.086190e-06 128 0.379886 2.715462e-07 12 0.777505 4 0.778345 8.402813e-04 8 0.777715 2.100401e-04 16 0.777557 5.250815e-05 32 0.777518 1.312692e-05 64 0.777508 3.281723e-06 128 0.777505 8.204302e-07 13 1.658348 4 1.613674 4.467357e-02 8 1.647912 1.043597e-02 16 1.655780 2.567676e-03 32 1.657708 6.393998e-04 64 1.658188 1.596935e-04 128 1.658308 3.991360e-05 14 0.500000 4 8.838835 8.338835e+00 8 4.419417 3.919417e+00 16 2.209709 1.709708e+00 32 1.104855 6.048546e-01 64 0.576295 7.629468e-02 128 0.500034 3.361179e-05 15 1.000000 4 31.250000 3.025000e+01 8 15.625000 1.462500e+01 16 7.812503 6.812503e+00 32 3.909413 2.909413e+00 64 2.033315 1.033315e+00 128 1.299356 2.993564e-01 16 0.493635 4 2.024719 1.531084e+00 8 1.070734 5.770997e-01 16 0.648239 1.546046e-01 32 0.511892 1.825709e-02 64 0.493956 3.213561e-04 128 0.493635 3.866192e-08 17 0.500000 4 0.500000 0.000000e+00 8 0.500000 5.551115e-16 16 0.500000 6.661338e-16 32 0.500000 6.106227e-16 64 0.500000 5.551115e-17 128 0.500000 5.551115e-17 18 0.170557 4 0.168328 2.229126e-03 8 0.170000 5.569671e-04 16 0.170418 1.392222e-04 32 0.170523 3.480432e-05 64 0.170549 8.701004e-06 128 0.170555 2.175246e-06 19 -1.000000 4 -0.591781 4.082191e-01 8 -0.753866 2.461338e-01 16 -0.855597 1.444025e-01 32 -0.917050 8.295033e-02 64 -0.953130 4.687003e-02 128 -0.973862 2.613754e-02 20 1.564396 4 1.543702 2.069470e-02 8 1.559214 5.182230e-03 16 1.563101 1.295599e-03 32 1.564073 3.238996e-04 64 1.564315 8.097485e-05 128 1.564376 2.024371e-05 21 0.210803 4 0.207927 2.876183e-03 8 0.192954 1.784895e-02 16 0.196013 1.478933e-02 32 0.211297 4.945963e-04 64 0.207238 3.564890e-03 128 0.209774 1.029167e-03 22 0.728103 4 0.724631 3.471689e-03 8 0.727235 8.680476e-04 16 0.727886 2.170138e-04 32 0.728049 5.425347e-05 64 0.728089 1.356337e-05 128 0.728100 3.390842e-06 23 0.624713 4 0.127009 4.977039e-01 8 1.535177 9.104633e-01 16 0.634705 9.992164e-03 32 0.845949 2.212359e-01 64 1.945737 1.321024e+00 128 1.757379 1.132665e+00 24 -0.006755 4 0.030700 3.745510e-02 8 0.001096 7.850536e-03 16 -0.008059 1.304400e-03 32 -0.006778 2.352891e-05 64 -0.006729 2.540676e-05 128 -0.006690 6.468971e-05 25 -1.610864 4 -1.546000 6.486386e-02 8 -1.524319 8.654511e-02 16 -1.599206 1.165802e-02 32 -1.590384 2.048009e-02 64 -1.608240 2.624274e-03 128 -1.605817 5.047387e-03 26 7.954927 4 7.989323 3.439692e-02 8 7.954928 1.251689e-06 16 7.954927 8.881784e-16 32 7.954927 0.000000e+00 64 7.954927 0.000000e+00 128 7.954927 0.000000e+00 27 0.841117 4 0.591202 2.499153e-01 8 0.677820 1.632971e-01 16 0.734547 1.065696e-01 32 0.771716 6.940086e-02 64 0.796029 4.508758e-02 128 0.811895 2.922145e-02 28 0.019955 4 0.000000 1.995467e-02 8 0.295911 2.759558e-01 16 0.373538 3.535831e-01 32 -0.019298 3.925240e-02 64 -0.059346 7.930052e-02 128 0.008760 1.119515e-02 29 0.306853 4 0.273611 3.324171e-02 8 0.295880 1.097311e-02 16 0.307128 2.756057e-04 32 0.301287 5.565576e-03 64 0.304154 2.699014e-03 128 0.305589 1.263982e-03 30 -4.527570 4 -4.985543 4.579730e-01 8 -10.358841 5.831271e+00 16 -4.893377 3.658071e-01 32 -4.604442 7.687287e-02 64 -4.546046 1.847653e-02 128 -4.532145 4.574905e-03 31 2.651635 4 2.917647 2.660117e-01 8 2.658824 7.188202e-03 16 2.650507 1.128522e-03 32 2.651347 2.881639e-04 64 2.651563 7.207597e-05 128 2.651617 1.802118e-05 32 -12.070346 4 -13.336023 1.265677e+00 8 -12.382162 3.118161e-01 16 -12.148004 7.765778e-02 32 -12.089742 1.939580e-02 64 -12.075194 4.847783e-03 128 -12.071558 1.211873e-03 33 0.886227 4 0.636581 2.496458e-01 8 0.753713 1.325135e-01 16 0.816045 7.018186e-02 32 0.849167 3.705966e-02 64 0.866721 1.950591e-02 128 0.875994 1.023315e-02 34 1085.252667 4 1228.648500 1.433958e+02 8 1121.345766 3.609310e+01 16 1094.291200 9.038534e+00 32 1087.513254 2.260587e+00 64 1085.817873 5.652064e-01 128 1085.393972 1.413053e-01 35 26.000000 4 19.517565 6.482435e+00 8 21.745556 4.254444e+00 16 23.199637 2.800363e+00 32 23.933903 2.066097e+00 64 24.742366 1.257634e+00 128 24.903181 1.096819e+00 36 100.000000 4 1.623379 9.837662e+01 8 2.905626 9.709437e+01 16 4.454925 9.554508e+01 32 6.231542 9.376846e+01 64 8.198537 9.180146e+01 128 10.322559 8.967744e+01 37 3.135799 4 0.201389 2.934409e+00 8 0.121647 3.014152e+00 16 0.155111 2.980688e+00 32 1.780994 1.354804e+00 64 1.071146 2.064653e+00 128 1.177776 1.958022e+00 38 0.539257 4 1.943756 1.404499e+00 8 0.539747 4.901286e-04 16 0.539257 3.330669e-16 32 0.539257 3.330669e-16 64 0.539257 3.330669e-16 128 0.539257 1.110223e-16 39 2.787694 4 2.235296 5.523981e-01 8 2.405178 3.825156e-01 16 2.519288 2.684062e-01 32 2.598424 1.892698e-01 64 2.653990 1.337033e-01 128 2.693184 9.450978e-02 40 2.698957 4 2.549281 1.496758e-01 8 2.353284 3.456725e-01 16 2.399866 2.990906e-01 32 2.670544 2.841305e-02 64 2.585595 1.133614e-01 128 2.592393 1.065631e-01 41 6.095585 4 1.723497 4.372088e+00 8 2.554100 3.541485e+00 16 3.347162 2.748423e+00 32 4.040712 2.054873e+00 64 4.597743 1.497842e+00 128 5.019635 1.075950e+00 42 3.980786 4 1.881204 2.099582e+00 8 2.275754 1.705032e+00 16 2.595943 1.384843e+00 32 2.855959 1.124827e+00 64 3.067146 9.136406e-01 128 3.238680 7.421062e-01 43 2.991569 4 1.120022 1.871547e+00 8 1.485327 1.506242e+00 16 1.774199 1.217370e+00 32 2.005503 9.860658e-01 64 2.191905 7.996642e-01 128 2.342636 6.489326e-01 44 -0.030100 4 -0.094352 6.425251e-02 8 -0.050734 2.063382e-02 16 -0.035706 5.606160e-03 32 -0.031533 1.433496e-03 64 -0.030460 3.604417e-04 128 -0.030190 9.024079e-05 45 -0.292707 4 -0.467702 1.749955e-01 8 -0.444694 1.519868e-01 16 -0.409781 1.170738e-01 32 -0.378825 8.611803e-02 64 -0.354770 6.206332e-02 128 -0.337004 4.429682e-02 46 6.069091 4 6.072739 3.647544e-03 8 6.069092 1.095435e-06 16 6.069091 9.858780e-14 32 6.069091 1.776357e-15 64 6.069091 1.776357e-15 128 6.069091 0.000000e+00 47 -0.444444 4 -0.358104 8.634039e-02 8 -0.408090 3.635440e-02 16 -0.429475 1.496986e-02 32 -0.438389 6.054958e-03 64 -0.442031 2.413761e-03 128 -0.443494 9.507895e-04 48 -4.000000 4 -1.021258 2.978742e+00 8 -1.538192 2.461808e+00 16 -2.006772 1.993228e+00 32 -2.411783 1.588217e+00 64 -2.750468 1.249532e+00 128 -3.026987 9.730132e-01 49 52.740748 4 59.202801 6.462053e+00 8 54.841669 2.100921e+00 16 53.655409 9.146609e-01 32 52.738540 2.207992e-03 64 52.799480 5.873147e-02 128 52.797919 5.717016e-02 50 -0.128137 4 -0.274653 1.465162e-01 8 0.079820 2.079571e-01 16 -0.077041 5.109549e-02 32 -0.114029 1.410813e-02 64 -0.124197 3.939354e-03 128 -0.127043 1.093379e-03 51 -0.197814 4 -0.181006 1.680712e-02 8 -0.187048 1.076594e-02 16 -0.188652 9.161491e-03 32 -0.189093 8.720224e-03 64 -0.189220 8.594038e-03 128 -0.189257 8.556304e-03 52 -0.089944 4 -0.278683 1.887390e-01 8 -0.604948 5.150039e-01 16 0.128824 2.187679e-01 32 -0.421319 3.313749e-01 64 0.203464 2.934081e-01 128 -0.394689 3.047446e-01 53 1.504623 4 1.710578 2.059551e-01 8 1.451475 5.314778e-02 16 1.373757 1.308661e-01 32 1.392043 1.125796e-01 64 1.484043 2.057968e-02 128 1.457429 4.719423e-02 54 1.154701 4 1.166667 1.196613e-02 8 1.154762 6.136638e-05 16 1.154701 1.630567e-09 32 1.154701 2.220446e-16 64 1.154701 2.220446e-16 128 1.154701 2.220446e-16 55 0.505059 4 0.490810 1.424905e-02 8 0.501583 3.476057e-03 16 0.504195 8.640698e-04 32 0.504843 2.157150e-04 64 0.505005 5.390994e-05 128 0.505045 1.347631e-05 56 1.992252 4 1.910864 8.138879e-02 8 1.974668 1.758457e-02 16 1.987907 4.345231e-03 32 1.991169 1.083117e-03 64 1.991982 2.705816e-04 128 1.992185 6.763308e-05 57 0.400000 4 0.407018 7.018111e-03 8 0.401812 1.812465e-03 16 0.400463 4.634013e-04 32 0.400118 1.176712e-04 64 0.400030 2.973986e-05 128 0.400007 7.491909e-06 test_int_test06(): Halton sequence rule, for 1D finite interval problems. Problem Exact Pts Approx Error 1 1.718282 1 1.648721 6.956056e-02 2 1.466373 2.519085e-01 4 1.545724 1.725580e-01 8 1.621188 9.709404e-02 16 1.667129 5.115304e-02 32 1.692066 2.621621e-02 64 1.705015 1.326657e-02 128 1.711609 6.672722e-03 2 0.700000 1 1.000000 3.000000e-01 2 0.500000 2.000000e-01 4 0.500000 2.000000e-01 8 0.625000 7.500000e-02 16 0.687500 1.250000e-02 32 0.687500 1.250000e-02 64 0.687500 1.250000e-02 128 0.695312 4.687500e-03 3 0.666667 1 0.707107 4.044011e-02 2 0.603553 6.311328e-02 4 0.606671 5.999527e-02 8 0.626880 3.978645e-02 16 0.643380 2.328693e-02 32 0.653840 1.282648e-02 64 0.659839 6.827287e-03 128 0.663108 3.558978e-03 4 0.479428 1 -0.160000 6.394282e-01 2 0.079833 3.995949e-01 4 0.349543 1.298850e-01 8 0.443181 3.624730e-02 16 0.469892 9.536647e-03 32 0.476984 2.443730e-03 64 0.478810 6.183934e-04 128 0.479273 1.555319e-04 5 1.582233 1 2.222222 6.399893e-01 2 1.935853 3.536204e-01 4 1.661369 7.913645e-02 8 1.599623 1.739026e-02 16 1.586265 4.032058e-03 32 1.583201 9.683972e-04 64 1.582470 2.371603e-04 128 1.582292 5.867420e-05 6 1.460447 1 1.414214 4.623357e-02 2 0.707107 7.533404e-01 4 1.103553 3.568937e-01 8 1.325885 1.345625e-01 16 1.405463 5.498419e-02 32 1.436734 2.371296e-02 64 1.449805 1.064218e-02 128 1.455527 4.920068e-03 7 2.000000 1 1.414214 5.857864e-01 2 1.707107 2.928932e-01 4 1.849335 1.506647e-01 8 1.920536 7.946370e-02 16 1.957052 4.294796e-02 32 1.976178 2.382233e-02 64 1.986410 1.359029e-02 128 1.992013 7.987115e-03 8 0.866973 1 0.941176 7.420348e-02 2 0.968643 1.016697e-01 4 0.924171 5.719833e-02 8 0.896917 2.994398e-02 16 0.882272 1.529929e-02 32 0.874704 7.731110e-03 64 0.870859 3.885904e-03 128 0.868921 1.948039e-03 9 1.154701 1 1.000000 1.547005e-01 2 0.833333 3.213672e-01 4 1.303396 1.486957e-01 8 1.115265 3.943579e-02 16 1.136347 1.835331e-02 32 1.148740 5.960657e-03 64 1.153008 1.692643e-03 128 1.154250 4.505883e-04 10 0.693147 1 0.666667 2.648051e-02 2 0.733333 4.018615e-02 4 0.731746 3.859885e-02 8 0.718019 2.487173e-02 16 0.707122 1.397508e-02 32 0.700540 7.392758e-03 64 0.696948 3.800384e-03 128 0.695074 1.926541e-03 11 0.379885 1 0.377541 2.344824e-03 2 0.407682 2.779659e-02 4 0.401244 2.135853e-02 8 0.392444 1.255822e-02 16 0.386635 6.749720e-03 32 0.383378 3.492567e-03 64 0.381661 1.775714e-03 128 0.380781 8.952147e-04 12 0.777505 1 0.770747 6.757593e-03 2 0.825475 4.797034e-02 4 0.815298 3.779363e-02 8 0.799976 2.247093e-02 16 0.789649 1.214426e-02 32 0.783806 6.301236e-03 64 0.780713 3.208133e-03 128 0.779123 1.618475e-03 13 1.658348 1 -1.917849 3.576196e+00 2 0.238020 1.420328e+00 4 2.329646 6.712983e-01 8 2.227107 5.687599e-01 16 1.975158 3.168100e-01 32 1.821189 1.628409e-01 64 1.740404 8.205657e-02 128 1.699475 4.112780e-02 14 0.500000 1 0.000000 5.000002e-01 2 0.000000 5.000002e-01 4 0.000000 5.000002e-01 8 0.000000 5.000002e-01 16 0.000001 4.999992e-01 32 0.047735 4.522648e-01 64 0.447443 5.255740e-02 128 0.658512 1.585118e-01 15 1.000000 1 0.000000 1.000000e+00 2 0.000000 1.000000e+00 4 0.000000 1.000000e+00 8 0.000005 9.999949e-01 16 0.006325 9.936749e-01 32 0.160317 8.396828e-01 64 0.634214 3.657855e-01 128 1.058348 5.834756e-02 16 0.493635 1 0.025424 4.682105e-01 2 0.063318 4.303169e-01 4 0.133803 3.598317e-01 8 0.260413 2.332212e-01 16 0.439725 5.390932e-02 32 0.571964 7.832937e-02 64 0.585324 9.168944e-02 128 0.551211 5.757618e-02 17 0.500000 1 0.000000 5.000000e-01 2 0.500000 0.000000e+00 4 0.625000 1.250000e-01 8 0.518306 1.830583e-02 16 0.560121 6.012124e-02 32 0.512577 1.257671e-02 64 0.513852 1.385164e-02 128 0.502590 2.590274e-03 18 0.170557 1 0.188770 1.821298e-02 2 0.149113 2.144424e-02 4 0.149360 2.119710e-02 8 0.156976 1.358159e-02 16 0.162975 7.582337e-03 32 0.166563 3.994781e-03 64 0.168508 2.049009e-03 128 0.169520 1.037499e-03 19 -1.000000 1 -0.693147 3.068528e-01 2 -1.039721 3.972077e-02 4 -1.111641 1.116413e-01 8 -1.100440 1.004398e-01 16 -1.072206 7.220596e-02 32 -1.047015 4.701477e-02 64 -1.028943 2.894294e-02 128 -1.017184 1.718416e-02 20 1.564396 1 1.990050 4.256533e-01 2 1.791838 2.274412e-01 4 1.613304 4.890801e-02 8 1.575719 1.132257e-02 16 1.567108 2.711759e-03 32 1.565059 6.628954e-04 64 1.564560 1.638376e-04 128 1.564437 4.072344e-05 21 0.210803 1 0.009866 2.009367e-01 2 0.398157 1.873541e-01 4 0.348242 1.374389e-01 8 0.216776 5.973467e-03 16 0.201803 8.999362e-03 32 0.213172 2.368996e-03 64 0.207969 2.834056e-03 128 0.210093 7.100785e-04 22 0.728103 1 0.761905 3.380185e-02 2 0.849817 1.217139e-01 4 0.804059 7.595633e-02 8 0.768413 4.031035e-02 16 0.748658 2.055528e-02 32 0.738458 1.035478e-02 64 0.733297 5.193816e-03 128 0.730704 2.600657e-03 23 0.624713 1 1.818595 1.193882e+00 2 -0.604308 1.229021e+00 4 2.000542 1.375829e+00 8 0.906778 2.820647e-01 16 1.711263 1.086550e+00 32 2.672853 2.048140e+00 64 3.381239 2.756525e+00 128 -0.244324 8.690376e-01 24 -0.006755 1 0.112539 1.192941e-01 2 0.031763 3.851777e-02 4 0.006106 1.286082e-02 8 -0.003805 2.949704e-03 16 -0.010672 3.916975e-03 32 -0.007045 2.905855e-04 64 -0.006417 3.380089e-04 128 -0.006534 2.205054e-04 25 -1.610864 1 -1.609438 1.426390e-03 2 -1.203973 4.068915e-01 4 -1.489266 1.215985e-01 8 -1.483054 1.278105e-01 16 -1.575583 3.528170e-02 32 -1.577851 3.301367e-02 64 -1.601796 9.068422e-03 128 -1.602551 8.313426e-03 26 7.954927 1 2.311455 5.643472e+00 2 4.297320 3.657607e+00 4 6.905212 1.049715e+00 8 7.798447 1.564796e-01 16 7.934611 2.031527e-02 32 7.952363 2.563894e-03 64 7.954605 3.212591e-04 128 7.954886 4.018158e-05 27 0.841117 1 0.666308 1.748089e-01 2 0.775647 6.546955e-02 4 0.821595 1.952206e-02 8 0.839814 1.302958e-03 16 0.846018 4.900708e-03 32 0.847237 6.119973e-03 64 0.846601 5.484083e-03 128 0.845455 4.338383e-03 28 0.019955 1 0.000000 1.995467e-02 2 -0.000000 1.995467e-02 4 0.716186 6.962313e-01 8 0.670908 6.509529e-01 16 0.250049 2.300947e-01 32 -0.193867 2.138214e-01 64 -0.000048 2.000252e-02 128 0.053857 3.390224e-02 29 0.306853 1 0.400000 9.314718e-02 2 0.422222 1.153694e-01 4 0.328758 2.190535e-02 8 0.325236 1.838295e-02 16 0.322273 1.541984e-02 32 0.308979 2.125800e-03 64 0.308030 1.176838e-03 128 0.307534 6.815282e-04 30 -4.527570 1 -5.483838 9.562683e-01 2 -19.923423 1.539585e+01 4 -11.149685 6.622115e+00 8 -19.651563 1.512399e+01 16 -7.416875 2.889306e+00 32 -5.710744 1.183174e+00 64 -5.139665 6.120952e-01 128 -4.848076 3.205065e-01 31 2.651635 1 8.000000 5.348365e+00 2 4.800000 2.148365e+00 4 3.000000 3.483647e-01 8 2.675472 2.383637e-02 16 2.654290 2.654734e-03 32 2.652251 6.157099e-04 64 2.651784 1.489473e-04 128 2.651672 3.663398e-05 32 -12.070346 1 0.000000 1.207035e+01 2 2.436122 1.450647e+01 4 -3.566780 8.503567e+00 8 -7.566134 4.504212e+00 16 -9.758786 2.311561e+00 32 -10.899923 1.170423e+00 64 -11.481488 5.888585e-01 128 -11.775006 2.953402e-01 33 0.886227 1 0.832555 5.367231e-02 2 1.004982 1.187554e-01 4 0.997088 1.108610e-01 8 0.961852 7.562515e-02 16 0.932398 4.617118e-02 32 0.912896 2.666953e-02 64 0.901139 1.491178e-02 128 0.894391 8.163877e-03 34 1085.252667 1 219.336000 8.659167e+02 2 111.306000 9.739467e+02 4 461.876977 6.233757e+02 8 737.968657 3.472840e+02 16 902.627981 1.826247e+02 32 991.696523 9.355614e+01 64 1037.914831 4.733784e+01 128 1061.444022 2.380864e+01 35 26.000000 1 16.159235 9.840765e+00 2 20.837103 5.162897e+00 4 26.284391 2.843905e-01 8 28.005654 2.005654e+00 16 24.604009 1.395991e+00 32 24.456862 1.543138e+00 64 24.969991 1.030009e+00 128 25.009492 9.905078e-01 36 100.000000 1 1.293458 9.870654e+01 2 3.060408 9.693959e+01 4 5.001441 9.499856e+01 8 7.108085 9.289191e+01 16 9.356215 9.064378e+01 32 11.719221 8.828078e+01 64 14.172087 8.582791e+01 128 16.692295 8.330770e+01 37 3.135799 1 0.011989 3.123809e+00 2 0.007698 3.128101e+00 4 0.199101 2.936698e+00 8 0.120456 3.015343e+00 16 0.154506 2.981292e+00 32 1.780690 1.355109e+00 64 1.070993 2.064806e+00 128 1.177700 1.958099e+00 38 0.539257 1 -0.457102 9.963588e-01 2 1.044083 5.048256e-01 4 0.375480 1.637773e-01 8 0.151004 3.882531e-01 16 0.481922 5.733448e-02 32 0.531790 7.467186e-03 64 0.538314 9.430116e-04 128 0.539139 1.181787e-04 39 2.787694 1 2.449490 3.382040e-01 2 2.956796 1.691020e-01 4 2.413419 3.742750e-01 8 2.460571 3.271231e-01 16 2.540602 2.470913e-01 32 2.607666 1.800282e-01 64 2.658277 1.294171e-01 128 2.695246 9.244812e-02 40 2.698957 1 1.871865 8.270921e-01 2 1.619264 1.079693e+00 4 2.446037 2.529192e-01 8 2.294863 4.040938e-01 16 2.369116 3.298404e-01 32 2.654802 4.415503e-02 64 2.577635 1.213221e-01 128 2.588391 1.105656e-01 41 6.095585 1 1.777778 4.317807e+00 2 2.736410 3.359175e+00 4 3.739308 2.356277e+00 8 4.619692 1.475894e+00 16 5.262952 8.326333e-01 32 5.653360 4.422247e-01 64 5.859762 2.358236e-01 128 5.962655 1.329300e-01 42 3.980786 1 2.002075 1.978711e+00 2 2.539554 1.441232e+00 4 2.917661 1.063125e+00 8 3.175552 8.052343e-01 16 3.356778 6.240087e-01 32 3.489137 4.916488e-01 64 3.589082 3.917042e-01 128 3.666450 3.143359e-01 43 2.991569 1 1.292475 1.699094e+00 2 1.044043 1.947526e+00 4 1.269775 1.721794e+00 8 1.546547 1.445022e+00 16 1.800382 1.191187e+00 32 2.017026 9.745428e-01 64 2.197077 7.944920e-01 128 2.344992 6.465773e-01 44 -0.030100 1 0.000041 3.014098e-02 2 0.000021 3.012047e-02 4 0.000248 3.034780e-02 8 -0.003433 2.666634e-02 16 -0.012056 1.804392e-02 32 -0.019708 1.039154e-02 64 -0.024548 5.552078e-03 128 -0.027234 2.866019e-03 45 -0.292707 1 -0.832294 5.395870e-01 2 0.207741 5.004472e-01 4 0.195688 4.883946e-01 8 0.055651 3.483574e-01 16 -0.053373 2.393341e-01 32 -0.127340 1.653663e-01 64 -0.177385 1.153213e-01 128 -0.211774 8.093275e-02 46 6.069091 1 4.656977 1.412114e+00 2 5.259634 8.094565e-01 4 5.889265 1.798260e-01 8 6.043492 2.559851e-02 16 6.065796 3.294769e-03 32 6.068676 4.149125e-04 64 6.069039 5.196072e-05 128 6.069084 6.498117e-06 47 -0.444444 1 -0.490129 4.568463e-02 2 -0.591638 1.471937e-01 4 -0.541902 9.745802e-02 8 -0.494733 5.028899e-02 16 -0.467766 2.332147e-02 32 -0.454635 1.019068e-02 64 -0.448732 4.287223e-03 128 -0.446201 1.756817e-03 48 -4.000000 1 -0.980258 3.019742e+00 2 -1.876423 2.123577e+00 4 -2.491646 1.508354e+00 8 -2.924486 1.075514e+00 16 -3.232095 7.679049e-01 32 -3.451504 5.484958e-01 64 -3.608194 3.918057e-01 128 -3.720134 2.798660e-01 49 52.740748 1 -11.776902 6.451765e+01 2 -6.181932 5.892268e+01 4 18.464652 3.427610e+01 8 34.464907 1.827584e+01 16 43.466343 9.274405e+00 32 47.643961 5.096787e+00 64 50.252187 2.488561e+00 128 51.524272 1.216476e+00 50 -0.128137 1 -0.000000 1.281368e-01 2 -0.693147 5.650103e-01 4 0.092944 2.210806e-01 8 -0.240372 1.122351e-01 16 -0.257145 1.290079e-01 32 -0.175294 4.715699e-02 64 -0.142619 1.448170e-02 128 -0.132347 4.209659e-03 51 -0.197814 1 -0.316254 1.184406e-01 2 -0.239320 4.150694e-02 4 -0.199346 1.532829e-03 8 -0.191640 6.173633e-03 16 -0.189932 7.882014e-03 32 -0.189482 8.331984e-03 64 -0.189345 8.468169e-03 128 -0.189300 8.513326e-03 52 -0.089944 1 0.065217 1.551614e-01 2 0.938269 1.028213e+00 4 -0.542113 4.521693e-01 8 -0.481150 3.912058e-01 16 0.177168 2.671118e-01 32 -0.418401 3.284571e-01 64 0.191450 2.813936e-01 128 -0.406989 3.170451e-01 53 1.504623 1 1.154701 3.499222e-01 2 0.994379 5.102437e-01 4 1.687021 1.823984e-01 8 1.436163 6.845962e-02 16 1.365322 1.393006e-01 32 1.387643 1.169800e-01 64 1.481798 2.282432e-02 128 1.456295 4.832751e-02 54 1.154701 1 1.000000 1.547005e-01 2 0.833333 3.213672e-01 4 1.303396 1.486957e-01 8 1.115265 3.943579e-02 16 1.136347 1.835331e-02 32 1.148740 5.960657e-03 64 1.153008 1.692643e-03 128 1.154250 4.505883e-04 55 0.505059 1 0.569783 6.472419e-02 2 0.337591 1.674676e-01 4 0.426228 7.883082e-02 8 0.467352 3.770701e-02 16 0.486789 1.826964e-02 32 0.496085 8.973755e-03 64 0.500614 4.444947e-03 128 0.502847 2.211794e-03 56 1.992252 1 2.222222 2.299698e-01 2 2.203261 2.110089e-01 4 2.111537 1.192845e-01 8 2.028439 3.618707e-02 16 2.001285 9.032624e-03 32 1.994474 2.221457e-03 64 1.992801 5.488011e-04 128 1.992389 1.362654e-04 57 0.400000 1 0.353553 4.644661e-02 2 0.239277 1.607233e-01 4 0.293067 1.069333e-01 8 0.341266 5.873441e-02 16 0.369559 3.044133e-02 32 0.384554 1.544629e-02 64 0.392228 7.771971e-03 128 0.396103 3.896851e-03 test_int_test07(): Evenly spaced point sequence rule, for 1D finite interval problems. Problem Exact Pts Approx Error 1 1.718282 1 1.648721 6.956056e-02 2 1.859141 1.408591e-01 4 1.765407 4.712525e-02 8 1.738445 2.016348e-02 16 1.727682 9.400274e-03 32 1.722828 4.546189e-03 64 1.720518 2.236436e-03 128 1.719391 1.109270e-03 2 0.700000 1 1.000000 3.000000e-01 2 0.500000 2.000000e-01 4 0.750000 5.000000e-02 8 0.625000 7.500000e-02 16 0.687500 1.250000e-02 32 0.687500 1.250000e-02 64 0.703125 3.125000e-03 128 0.695312 4.687500e-03 3 0.666667 1 0.707107 4.044011e-02 2 0.500000 1.666667e-01 4 0.598462 6.820495e-02 8 0.636755 2.991118e-02 16 0.653069 1.359781e-02 32 0.660334 6.333127e-03 64 0.663664 3.003070e-03 128 0.665223 1.443637e-03 4 0.479428 1 -0.160000 6.394282e-01 2 1.758664 1.279236e+00 4 0.905961 4.265328e-01 8 0.662218 1.827894e-01 16 0.564721 8.529274e-02 32 0.520696 4.126821e-02 64 0.499734 2.030595e-02 128 0.489501 1.007288e-02 5 1.582233 1 2.222222 6.399893e-01 2 0.689655 8.925778e-01 4 1.321908 2.603246e-01 8 1.462178 1.200547e-01 16 1.524466 5.776743e-02 32 1.553860 2.837249e-02 64 1.568168 1.406449e-02 128 1.575230 7.002522e-03 6 1.460447 1 1.414214 4.623357e-02 2 1.931852 4.714045e-01 4 1.626485 1.660383e-01 8 1.531748 7.130072e-02 16 1.493423 3.297614e-02 32 1.476237 1.578962e-02 64 1.468145 7.697627e-03 128 1.464237 3.790140e-03 7 2.000000 1 1.414214 5.857864e-01 2 0.500000 1.500000e+00 4 0.989199 1.010801e+00 8 1.328790 6.712100e-01 16 1.552581 4.474191e-01 32 1.698992 3.010079e-01 64 1.795440 2.045604e-01 128 1.859706 1.402944e-01 8 0.866973 1 0.941176 7.420348e-02 2 0.750000 1.169730e-01 4 0.830714 3.625888e-02 8 0.850860 1.611275e-02 16 0.859315 7.658188e-03 32 0.863234 3.739420e-03 64 0.865125 1.848371e-03 128 0.866054 9.189778e-04 9 1.154701 1 1.000000 1.547005e-01 2 1.000000 1.547005e-01 4 1.115385 3.931592e-02 8 1.135363 1.933759e-02 16 1.144231 1.046977e-02 32 1.149866 4.834392e-03 64 1.152283 2.417196e-03 128 1.153492 1.208598e-03 10 0.693147 1 0.666667 2.648051e-02 2 0.750000 5.685282e-02 4 0.712500 1.935282e-02 8 0.701367 8.219855e-03 16 0.696961 3.813574e-03 32 0.694987 1.839646e-03 64 0.694051 9.038258e-04 128 0.693595 4.480074e-04 11 0.379885 1 0.377541 2.344824e-03 2 0.384471 4.585218e-03 4 0.381404 1.518218e-03 8 0.380538 6.526442e-04 16 0.380191 3.051159e-04 32 0.380033 1.477731e-04 64 0.379958 7.274746e-05 128 0.379922 3.609570e-05 12 0.777505 1 0.770747 6.757593e-03 2 0.790988 1.348372e-02 4 0.781996 4.491472e-03 8 0.779430 1.925514e-03 16 0.778403 8.987412e-04 32 0.777940 4.349166e-04 64 0.777719 2.140169e-04 128 0.777611 1.061684e-04 13 1.658348 1 -1.917849 3.576196e+00 2 4.727989 3.069642e+00 4 2.361375 7.030279e-01 8 2.030047 3.716991e-01 16 1.847459 1.891118e-01 32 1.753614 9.526623e-02 64 1.706149 4.780092e-02 128 1.682289 2.394135e-02 14 0.500000 1 0.000000 5.000002e-01 2 35.355339 3.485534e+01 4 17.677670 1.717767e+01 8 8.838835 8.338835e+00 16 4.419417 3.919417e+00 32 2.209709 1.709709e+00 64 1.125966 6.259655e-01 128 0.772347 2.723465e-01 15 1.000000 1 0.000000 1.000000e+00 2 125.000000 1.240000e+02 4 62.500000 6.150000e+01 8 31.250000 3.025000e+01 16 15.625001 1.462500e+01 32 7.814958 6.814958e+00 64 3.981526 2.981526e+00 128 2.270193 1.270193e+00 16 0.493635 1 0.025424 4.682105e-01 2 7.960929 7.467294e+00 4 3.998315 3.504680e+00 8 2.047575 1.553940e+00 16 1.128165 6.345299e-01 32 0.747092 2.534570e-01 64 0.610670 1.170352e-01 128 0.551973 5.833829e-02 17 0.500000 1 0.000000 5.000000e-01 2 0.000000 5.000000e-01 4 0.375000 1.250000e-01 8 0.437500 6.250000e-02 16 0.468750 3.125000e-02 32 0.484375 1.562500e-02 64 0.492188 7.812500e-03 128 0.496094 3.906250e-03 18 0.170557 1 0.188770 1.821298e-02 2 0.134471 3.608664e-02 4 0.158562 1.199557e-02 8 0.165410 5.147400e-03 16 0.168153 2.403920e-03 32 0.169394 1.163635e-03 64 0.169985 5.726928e-04 128 0.170273 2.841192e-04 19 -1.000000 1 -0.693147 3.068528e-01 2 0.000000 1.000000e+00 4 -0.376019 6.239807e-01 8 -0.637026 3.629738e-01 16 -0.795093 2.049074e-01 32 -0.886293 1.137069e-01 64 -0.937628 6.237232e-02 128 -0.966081 3.391944e-02 20 1.564396 1 1.990050 4.256533e-01 2 0.997506 5.668902e-01 4 1.394721 1.696752e-01 8 1.487613 7.678366e-02 16 1.527584 3.681261e-02 32 1.546347 1.804967e-02 64 1.555457 8.939920e-03 128 1.559947 4.449233e-03 21 0.210803 1 0.009866 2.009367e-01 2 0.035326 1.754771e-01 4 0.078499 1.323033e-01 8 0.170559 4.024388e-02 16 0.310878 1.000748e-01 32 0.193596 1.720640e-02 64 0.207936 2.866316e-03 128 0.208410 2.393123e-03 22 0.728103 1 0.761905 3.380185e-02 2 0.666667 6.143625e-02 4 0.708116 1.998647e-02 8 0.719431 8.671579e-03 16 0.724032 4.071247e-03 32 0.726127 1.975886e-03 64 0.727129 9.737200e-04 128 0.727620 4.833882e-04 23 0.624713 1 1.818595 1.193882e+00 2 0.420735 2.039778e-01 4 0.690268 6.555512e-02 8 1.259266 6.345526e-01 16 1.492156 8.674432e-01 32 0.177477 4.472359e-01 64 1.062671 4.379575e-01 128 1.758547 1.133834e+00 24 -0.006755 1 0.112539 1.192941e-01 2 0.079578 8.633227e-02 4 0.048197 5.495181e-02 8 0.000000 6.754800e-03 16 0.002885 9.639585e-03 32 -0.003858 2.897022e-03 64 -0.005620 1.135066e-03 128 -0.006105 6.492877e-04 25 -1.610864 1 -1.609438 1.426390e-03 2 -0.780324 8.305404e-01 4 -1.491287 1.195775e-01 8 -1.560150 5.071394e-02 16 -1.513982 9.688189e-02 32 -1.569472 4.139217e-02 64 -1.605308 5.556671e-03 128 -1.608111 2.753540e-03 26 7.954927 1 2.311455 5.643472e+00 2 17.079468 9.124542e+00 4 10.445206 2.490280e+00 8 9.095512 1.140585e+00 16 8.525210 5.702839e-01 32 8.240068 2.851419e-01 64 8.097497 1.425710e-01 128 8.026212 7.128548e-02 27 0.841117 1 0.666308 1.748089e-01 2 0.250000 5.911169e-01 4 0.469662 3.714545e-01 8 0.612128 2.289894e-01 16 0.700205 1.409123e-01 32 0.754075 8.704187e-02 64 0.787059 5.405754e-02 128 0.807363 3.375428e-02 28 0.019955 1 0.000000 1.995467e-02 2 0.000000 1.995467e-02 4 -0.146891 1.668453e-01 8 0.379678 3.597231e-01 16 0.106812 8.685716e-02 32 -0.035872 5.582634e-02 64 -0.064245 8.419944e-02 128 0.008494 1.146113e-02 29 0.306853 1 0.400000 9.314718e-02 2 0.250000 5.685282e-02 4 0.325893 1.904004e-02 8 0.321655 1.480234e-02 16 0.297084 9.769156e-03 32 0.307781 9.279477e-04 64 0.307397 5.441429e-04 128 0.307210 3.567286e-04 30 -4.527570 1 -5.483838 9.562683e-01 2 23.363250 2.789082e+01 4 5.223729 9.751298e+00 8 26.816814 3.134438e+01 16 -3.188586 1.338984e+00 32 -3.735613 7.919565e-01 64 -4.110553 4.170165e-01 128 -4.314284 2.132859e-01 31 2.651635 1 8.000000 5.348365e+00 2 0.470588 2.181047e+00 4 1.675294 9.763412e-01 8 2.351374 3.002611e-01 16 2.514048 1.375872e-01 32 2.583180 6.845517e-02 64 2.617483 3.415208e-02 128 2.634578 1.705759e-02 32 -12.070346 1 0.000000 1.207035e+01 2 -34.778519 2.270817e+01 4 -19.459127 7.388780e+00 8 -15.265777 3.195431e+00 16 -13.572457 1.502110e+00 32 -12.799999 7.296523e-01 64 -12.430086 3.597399e-01 128 -12.248975 1.786290e-01 33 0.886227 1 0.832555 5.367231e-02 2 0.000000 8.862269e-01 4 0.421227 4.649998e-01 8 0.644434 2.417928e-01 16 0.761023 1.252042e-01 32 0.821563 6.466430e-02 64 0.852896 3.333118e-02 128 0.869076 1.715142e-02 34 1085.252667 1 219.336000 8.659167e+02 2 3067.086000 1.981833e+03 4 1770.555136 6.853025e+02 8 1374.202618 2.889500e+02 16 1218.757605 1.335049e+02 32 1149.518446 6.426578e+01 64 1116.792990 3.154032e+01 128 1100.878158 1.562549e+01 35 26.000000 1 16.159235 9.840765e+00 2 23.616667 2.383333e+00 4 20.435678 5.564322e+00 8 21.324608 4.675392e+00 16 23.718053 2.281947e+00 32 23.739622 2.260378e+00 64 25.112786 8.872145e-01 128 24.869005 1.130995e+00 36 100.000000 1 1.293458 9.870654e+01 2 0.000000 1.000000e+02 4 0.884241 9.911576e+01 8 2.307015 9.769298e+01 16 4.031697 9.596830e+01 32 5.953683 9.404632e+01 64 8.024609 9.197539e+01 128 10.217309 8.978269e+01 37 3.135799 1 0.011989 3.123809e+00 2 0.011394 3.124405e+00 4 0.024209 3.111590e+00 8 0.055103 3.080695e+00 16 0.329992 2.805807e+00 32 0.360474 2.775324e+00 64 0.587094 2.548705e+00 128 1.985503 1.150296e+00 38 0.539257 1 -0.457102 9.963588e-01 2 3.141593 2.602336e+00 4 2.826002 2.286745e+00 8 0.870153 3.308956e-01 16 0.701903 1.626460e-01 32 0.620580 8.132299e-02 64 0.579918 4.066150e-02 128 0.559588 2.033075e-02 39 2.787694 1 2.449490 3.382040e-01 2 1.478398 1.309296e+00 4 1.172212 1.615482e+00 8 2.265288 5.224058e-01 16 1.997653 7.900407e-01 32 2.560475 2.272182e-01 64 2.404938 3.827556e-01 128 2.683325 1.043690e-01 40 2.698957 1 1.871865 8.270921e-01 2 1.643517 1.055439e+00 4 1.919117 7.798393e-01 8 2.158562 5.403948e-01 16 2.453254 2.457029e-01 32 2.475271 2.236860e-01 64 2.532539 1.664178e-01 128 2.614038 8.491855e-02 41 6.095585 1 1.777778 4.317807e+00 2 0.000000 6.095585e+00 4 1.033546 5.062040e+00 8 2.095788 3.999797e+00 16 3.071841 3.023744e+00 32 3.886435 2.209150e+00 64 4.514982 1.580603e+00 128 4.976359 1.119226e+00 42 3.980786 1 2.002075 1.978711e+00 2 0.785398 3.195388e+00 4 1.464939 2.515847e+00 8 2.028449 1.952338e+00 16 2.457399 1.523387e+00 32 2.780825 1.199961e+00 64 3.027234 9.535521e-01 128 3.217779 7.630070e-01 43 2.991569 1 1.292475 1.699094e+00 2 0.000000 2.991569e+00 4 0.704369 2.287200e+00 8 1.243933 1.747636e+00 16 1.640592 1.350977e+00 32 1.933597 1.057972e+00 64 2.153907 8.376620e-01 128 2.322813 6.687563e-01 44 -0.030100 1 0.000041 3.014098e-02 2 -0.378401 3.483015e-01 4 -0.189055 1.589550e-01 8 -0.096497 6.639768e-02 16 -0.057824 2.772451e-02 32 -0.042463 1.236342e-02 64 -0.035908 5.808352e-03 128 -0.032912 2.812056e-03 45 -0.292707 1 -0.832294 5.395870e-01 2 0.000000 2.927067e-01 4 -0.346883 5.417636e-02 8 -0.394601 1.018940e-01 16 -0.387156 9.444921e-02 32 -0.368216 7.550940e-02 64 -0.349691 5.698464e-02 128 -0.334540 4.183346e-02 46 6.069091 1 4.656977 1.412114e+00 2 7.909393 1.840302e+00 4 6.549987 4.808962e-01 8 6.299136 2.300451e-01 16 6.184110 1.150189e-01 32 6.126600 5.750945e-02 64 6.097846 2.875472e-02 128 6.083468 1.437736e-02 47 -0.444444 1 -0.490129 4.568463e-02 2 0.000000 4.444444e-01 4 -0.241336 2.031082e-01 8 -0.351240 9.320469e-02 16 -0.401411 4.303310e-02 32 -0.424439 2.000501e-02 64 -0.435073 9.371004e-03 128 -0.440019 4.425637e-03 48 -4.000000 1 -0.980258 3.019742e+00 2 0.000000 4.000000e+00 4 -0.599861 3.400139e+00 8 -1.261411 2.738589e+00 16 -1.842848 2.157152e+00 32 -2.319859 1.680141e+00 64 -2.700621 1.299379e+00 128 -3.000553 9.994466e-01 49 52.740748 1 -11.776902 6.451765e+01 2 163.026743 1.102860e+02 4 92.263929 3.952318e+01 8 69.436515 1.669577e+01 16 60.224989 7.484241e+00 32 56.518783 3.778035e+00 64 54.751230 2.010482e+00 128 53.607414 8.666653e-01 50 -0.128137 1 -0.000000 1.281368e-01 2 0.000000 1.281368e-01 4 0.150071 2.782076e-01 8 0.140544 2.686811e-01 16 -0.065993 6.214353e-02 32 -0.109643 1.849418e-02 64 -0.122143 5.994159e-03 128 -0.126035 2.101807e-03 51 -0.197814 1 -0.316254 1.184406e-01 2 0.000000 1.978136e-01 4 -0.131153 6.666069e-02 8 -0.163113 3.470009e-02 16 -0.176789 2.102470e-02 32 -0.183174 1.463943e-02 64 -0.186262 1.155206e-02 128 -0.187778 1.003510e-02 52 -0.089944 1 0.065217 1.551614e-01 2 -2.999049 2.909105e+00 4 -1.359615 1.269671e+00 8 -1.468146 1.378202e+00 16 -0.357605 2.676610e-01 32 -1.089059 9.991148e-01 64 -0.144402 5.445846e-02 128 -1.014948 9.250043e-01 53 1.504623 1 1.154701 3.499222e-01 2 0.853553 6.510694e-01 4 1.183240 3.213825e-01 8 1.408103 9.652003e-02 16 2.020843 5.162206e-01 32 1.389216 1.154068e-01 64 1.493769 1.085403e-02 128 1.636591 1.319678e-01 54 1.154701 1 1.000000 1.547005e-01 2 1.000000 1.547005e-01 4 1.115385 3.931592e-02 8 1.135363 1.933759e-02 16 1.144231 1.046977e-02 32 1.149866 4.834392e-03 64 1.152283 2.417196e-03 128 1.153492 1.208598e-03 55 0.505059 1 0.569783 6.472419e-02 2 0.288056 2.170024e-01 4 0.431284 7.377438e-02 8 0.473951 3.110739e-02 16 0.490574 1.448456e-02 32 0.498055 7.004004e-03 64 0.501613 3.445428e-03 128 0.503350 1.708913e-03 56 1.992252 1 2.222222 2.299698e-01 2 1.052632 9.396208e-01 4 1.635736 3.565164e-01 8 1.854581 1.376714e-01 16 1.928889 6.336374e-02 32 1.961771 3.048128e-02 64 1.977296 1.495645e-02 128 1.984843 7.408953e-03 57 0.400000 1 0.353553 4.644661e-02 2 0.500000 1.000000e-01 4 0.434195 3.419529e-02 8 0.414560 1.456032e-02 16 0.406743 6.743425e-03 32 0.403246 3.246394e-03 64 0.401593 1.592706e-03 128 0.400789 7.888004e-04 test_int_test() Normal end of execution. 06-Jun-2023 14:28:20