06 October 2025 01:23:36 AM test_int_test(): C version Test test_int(). TEST01 Composite midpoint rule, for 1D finite interval problems. Prob Ints Exact Error Approx 1 1.71828 1 1.64872 0.0695606 2 1.70051 0.0177691 4 1.71382 0.00446655 8 1.71716 0.00111816 16 1.718 0.000279636 32 1.71821 6.99151e-05 64 1.71826 1.74791e-05 128 1.71828 4.36981e-06 2 0.7 1 1 0.3 2 0.5 0.2 4 0.75 0.05 8 0.75 0.05 16 0.6875 0.0125 32 0.6875 0.0125 64 0.703125 0.003125 128 0.703125 0.003125 3 0.666667 1 0.707107 0.0404401 2 0.683013 0.016346 4 0.672977 0.00631073 8 0.669032 0.00236551 16 0.667537 0.000870009 32 0.666983 0.00031602 64 0.666781 0.000113837 128 0.666707 4.0774e-05 4 0.479428 1 -0.16 0.639428 2 0.319667 0.159762 4 0.439407 0.0400208 8 0.469417 0.0100116 16 0.476925 0.00250332 32 0.478802 0.000625856 64 0.479272 0.000156466 128 0.479389 3.91165e-05 5 1.58223 1 2.22222 0.639989 2 1.64948 0.0672516 4 1.5969 0.0146717 8 1.58594 0.00370973 16 1.58316 0.000928631 32 1.58247 0.000232219 64 1.58229 5.80584e-05 128 1.58225 1.45148e-05 6 1.46045 1 0 1.46045 2 1 0.460447 4 0.5 0.960447 8 0.5 0.960447 16 0.5 0.960447 32 0.5 0.960447 64 0.5 0.960447 128 0.5 0.960447 7 2 1 1.41421 0.585786 2 1.57735 0.42265 4 1.69884 0.301156 8 1.78646 0.213539 16 1.84886 0.151143 32 1.89309 0.106912 64 1.92439 0.0756072 128 1.94654 0.0534647 8 0.866973 1 0.941176 0.0742035 2 0.877876 0.0109034 4 0.869605 0.00263242 8 0.867626 0.000652821 16 0.867136 0.000162872 32 0.867014 4.06971e-05 64 0.866983 1.0173e-05 128 0.866976 2.54316e-06 9 1.1547 1 1 0.154701 2 1.33333 0.178633 4 1.14286 0.0118434 8 1.15464 6.13631e-05 16 1.1547 1.63057e-09 32 1.1547 0 64 1.1547 6.66134e-16 128 1.1547 2.22045e-16 10 0.693147 1 0.666667 0.0264805 2 0.685714 0.00743289 4 0.69122 0.00192729 8 0.692661 0.000486627 16 0.693025 0.000121966 32 0.693117 3.05111e-05 64 0.69314 7.62899e-06 128 0.693145 1.90732e-06 11 0.379885 1 0.377541 0.00234482 2 0.379322 0.000563093 4 0.379746 0.000139459 8 0.379851 3.47845e-05 16 0.379877 8.69113e-06 32 0.379883 2.17247e-06 64 0.379885 5.43098e-07 128 0.379885 1.35773e-07 12 0.777505 1 0.770747 0.00675759 2 0.775822 0.0016825 4 0.777084 0.000420201 8 0.7774 0.000105024 16 0.777478 2.62543e-05 32 0.777498 6.56347e-06 64 0.777503 1.64086e-06 128 0.777504 4.10215e-07 13 1.65835 1 -1.91785 3.5762 2 1.82228 0.16393 4 1.68215 0.0238016 8 1.66365 0.00530061 16 1.65964 0.00128888 32 1.65867 0.000320013 64 1.65843 7.98663e-05 128 1.65837 1.9958e-05 14 0.5 1 0 0.5 2 0 0.5 4 0 0.5 8 0 0.5 16 9.62434e-07 0.499999 32 0.047735 0.452265 64 0.423773 0.0762275 128 0.499966 3.40341e-05 15 1 1 1.29161e-52 1 2 8.98473e-26 1 4 1.67563e-12 1 8 5.1168e-06 0.999995 16 0.00632258 0.993677 32 0.157218 0.842782 64 0.565397 0.434603 128 0.857119 0.142881 16 0.493635 1 0.0254241 0.468211 2 0.0562605 0.437374 4 0.11675 0.376885 8 0.225744 0.267891 16 0.375544 0.11809 32 0.47602 0.0176144 64 0.493313 0.000321279 128 0.493635 7.10161e-08 17 0.5 1 2.41176e-31 0.5 2 1 0.5 4 0.5 9.99201e-16 8 0.5 8.88178e-16 16 0.5 4.996e-16 32 0.5 1.11022e-16 64 0.5 0 128 0.5 3.33067e-16 18 0.170557 1 0.18877 0.018213 2 0.175036 0.00447858 4 0.171673 0.00111519 8 0.170836 0.000278523 16 0.170627 6.96135e-05 32 0.170575 1.74023e-05 64 0.170562 4.35051e-06 128 0.170558 1.08762e-06 19 -1 1 -0.693147 0.306853 2 -0.836988 0.163012 4 -0.915951 0.0840485 8 -0.957329 0.0426712 16 -0.978502 0.0214981 32 -0.98921 0.0107897 64 -0.994595 0.00540504 128 -0.997295 0.00270506 20 1.5644 1 1.99005 0.425653 2 1.59363 0.0292291 4 1.57473 0.0103302 8 1.56699 0.00259103 16 1.56504 0.000647799 32 1.56456 0.00016195 64 1.56444 4.04874e-05 128 1.56441 1.01219e-05 21 0.210803 1 0.00986604 0.200937 2 0.393257 0.182455 4 0.177981 0.0328217 8 0.199073 0.0117297 16 0.226581 0.0157785 32 0.203178 0.00762438 64 0.212309 0.00150656 128 0.209728 0.0010745 22 0.728103 1 0.761905 0.0338018 2 0.734977 0.00687382 4 0.729839 0.00173559 8 0.728537 0.00043402 16 0.728211 0.000108507 32 0.72813 2.71267e-05 64 0.72811 6.78168e-06 128 0.728105 1.69542e-06 23 0.624713 1 1.81859 1.19388 2 -0.865646 1.49036 4 2.94334 2.31863 8 -0.265766 0.890479 16 1.05719 0.43248 32 3.04553 2.42081 64 1.56902 0.944307 128 -1.79113 2.41584 24 -0.00675475 1 0.112539 0.119294 2 -0.0346577 0.027903 4 -0.0285088 0.021754 8 -0.0172141 0.0104593 16 -0.0054974 0.00125734 32 -0.0066804 7.43424e-05 64 -0.00665077 0.000103973 128 -0.00681738 6.26371e-05 25 -1.61086 1 -1.60944 0.00142639 2 -1.89712 0.286256 4 -1.50264 0.108226 8 -1.67409 0.0632291 16 -1.58156 0.0293022 32 -1.6261 0.0152315 64 -1.60339 0.0074705 128 -1.61464 0.00377158 26 7.95493 1 2.31145 5.64347 2 6.28319 1.67174 4 7.92053 0.0343944 8 7.95493 1.25169e-06 16 7.95493 1.77636e-15 32 7.95493 4.44089e-15 64 7.95493 1.77636e-15 128 7.95493 1.77636e-15 27 0.841117 1 0.666308 0.174809 2 0.724249 0.116868 4 0.764438 0.0766788 8 0.791275 0.0498421 16 0.808885 0.0322321 32 0.820343 0.0207743 64 0.827762 0.0133553 128 0.832549 0.00856742 28 0.0199547 1 2.66686e-16 0.0199547 2 3.87556e-17 0.0199547 4 0.591821 0.571866 8 0.451165 0.43121 16 -0.412133 0.432088 32 -0.099394 0.119349 64 0.0768649 0.0569102 128 0.026009 0.0060543 29 0.306853 1 0.4 0.0931472 2 0.222222 0.0846306 4 0.318148 0.0112955 8 0.318377 0.0115243 16 0.295446 0.0114068 32 0.30702 0.000167549 64 0.307024 0.000171049 128 0.307025 0.000171924 30 -4.52757 1 -5.48384 0.956268 2 -18.9108 14.3832 4 -15.7321 11.2046 8 0.572087 5.09966 16 -4.31551 0.212061 32 -4.48765 0.0399198 64 -4.51824 0.00932672 128 -4.52528 0.00229292 31 2.65164 1 8 5.34836 2 1.6 1.05164 4 2.4 0.251635 8 2.64219 0.00944525 16 2.65219 0.000552195 32 2.65178 0.000144012 64 2.65167 3.60336e-05 128 2.65164 9.01032e-06 32 -12.0703 1 9.25377e-16 12.0703 2 -9.28279 2.78756 4 -11.4283 0.642044 8 -11.9138 0.156501 16 -12.0315 0.0388662 32 -12.0606 0.00970023 64 -12.0679 0.00242404 128 -12.0697 0.000605945 33 0.886227 1 0.832555 0.0536723 2 0.856885 0.0293419 4 0.870846 0.0153812 8 0.878377 0.00785022 16 0.882289 0.00393745 32 0.884275 0.00195217 64 0.885267 0.000960397 128 0.885757 0.00047007 34 1085.25 1 219.336 865.917 2 814.086 271.167 4 1014.04 71.2096 8 1067.24 18.016 16 1080.74 4.51736 32 1084.12 1.13017 64 1084.97 0.282596 128 1085.18 0.0706522 35 26 1 16.1592 9.84076 2 19.1472 6.85282 4 23.9735 2.02645 8 24.6537 1.34628 16 24.6682 1.33183 32 25.5508 0.449172 64 25.064 0.936004 128 26.8277 0.827707 36 100 1 1.29346 98.7065 2 2.60003 97.4 4 4.18787 95.8121 8 6.00422 93.9958 16 8.00816 91.9918 32 10.1655 89.8345 64 12.4466 87.5534 128 14.825 85.175 37 3.1358 1 0.0119893 3.12381 2 0.391087 2.74471 4 0.0419041 3.09389 8 0.188576 2.94722 16 3.40688 0.271079 32 0.361297 2.7745 64 1.28441 1.85139 128 7.93948 4.80368 38 0.539257 1 -0.457102 0.996359 2 2.54527 2.00601 4 -0.864262 1.40352 8 0.538767 0.000490129 16 0.539257 3.33067e-16 32 0.539257 4.44089e-16 64 0.539257 3.33067e-16 128 0.539257 1.11022e-16 39 2.78769 1 2.44949 0.338204 2 2.50665 0.281046 4 2.57506 0.212633 8 2.6334 0.154297 16 2.67756 0.110134 32 2.70956 0.0781367 64 2.73238 0.0553163 128 2.74856 0.0391309 40 2.69896 1 1.87186 0.827092 2 3.34087 0.641914 4 2.15729 0.541669 8 2.44645 0.252509 16 2.94122 0.242265 32 2.50065 0.19831 64 2.59919 0.0997649 128 2.9432 0.24424 41 6.09559 1 1.77778 4.31781 2 2.55811 3.53748 4 3.3847 2.71088 8 4.14022 1.95536 16 4.73426 1.36132 32 5.15477 0.94081 64 5.44153 0.654058 128 5.6377 0.457888 42 3.98079 1 2.00208 1.97871 2 2.36867 1.61211 4 2.67031 1.31048 8 2.91613 1.06465 16 3.11597 0.864811 32 3.27833 0.702454 64 3.41021 0.570572 128 3.51734 0.463449 43 2.99157 1 1.29248 1.69909 2 1.59381 1.39776 4 1.85063 1.14094 8 2.06307 0.928499 16 2.23681 0.754761 32 2.37831 0.613263 64 2.49337 0.498201 128 2.58687 0.404696 44 -0.0300997 1 4.1282e-05 0.030141 2 0.000475558 0.0305753 4 -0.00711483 0.0229849 8 -0.0206782 0.0094215 16 -0.0273605 0.00273917 32 -0.0293871 0.000712613 64 -0.0299197 0.00017996 128 -0.0300546 4.51041e-05 45 -0.292707 1 -0.832294 0.539587 2 -0.519258 0.226551 4 -0.421685 0.128978 8 -0.374867 0.0821608 16 -0.347869 0.0551623 32 -0.330715 0.0380086 64 -0.319237 0.0265303 128 -0.311345 0.0186387 46 6.06909 1 4.65698 1.41211 2 5.86229 0.206799 4 6.06545 0.00364535 8 6.06909 1.09543e-06 16 6.06909 9.85878e-14 32 6.06909 1.77636e-15 64 6.06909 1.77636e-15 128 6.06909 2.66454e-15 47 -0.444444 1 -0.490129 0.0456846 2 -0.471144 0.0266991 4 -0.458076 0.0136316 8 -0.450859 0.00641469 16 -0.447304 0.00285994 32 -0.445672 0.00122744 64 -0.444957 0.000512182 128 -0.444654 0.000209174 48 -4 1 -0.980258 3.01974 2 -1.55239 2.44761 4 -2.05513 1.94487 8 -2.47535 1.52465 16 -2.81679 1.18321 32 -3.08915 0.910847 64 -3.30351 0.696495 128 -3.47044 0.529561 49 52.7407 1 -11.7769 64.5177 2 42.7807 9.96007 4 50.4805 2.26021 8 52.4691 0.271599 16 51.8217 0.919077 32 52.8604 0.119671 64 52.7964 0.0556088 128 52.7346 0.00612517 50 -0.128137 1 -4.2443e-16 0.128137 2 -0.549306 0.421169 4 0.434294 0.56243 8 -0.233903 0.105766 16 -0.151016 0.0228792 32 -0.134366 0.00622943 64 -0.129889 0.0017526 128 -0.128628 0.000491628 51 -0.197814 1 -0.316254 0.118441 2 -0.203886 0.00607226 4 -0.193089 0.00472476 8 -0.190257 0.00755704 16 -0.189535 0.00827896 32 -0.189346 0.00846785 64 -0.189295 0.00851857 128 -0.189281 0.0085326 52 -0.089944 1 0.0652174 0.155161 2 0.90955 0.999494 4 -0.931213 0.841269 8 0.862596 0.95254 16 -0.971462 0.881518 32 0.828247 0.918191 64 -0.992841 0.902897 128 0.818136 0.90808 53 1.50462 1 1.1547 0.349922 2 2.41703 0.912406 4 1.19237 0.312251 8 1.29604 0.208584 16 1.41033 0.094293 32 1.57604 0.0714202 64 1.43081 0.0738088 128 1.47347 0.0311505 54 1.1547 1 1 0.154701 2 1.33333 0.178633 4 1.14286 0.0118434 8 1.15464 6.13631e-05 16 1.1547 1.63057e-09 32 1.1547 2.22045e-16 64 1.1547 4.44089e-16 128 1.1547 4.44089e-16 55 0.505059 1 0.569783 0.0647242 2 0.5527 0.047641 4 0.512356 0.00729694 8 0.506807 0.00174792 16 0.505491 0.00043264 32 0.505167 0.000107895 64 0.505086 2.69573e-05 128 0.505065 6.7383e-06 56 1.99225 1 2.22222 0.22997 2 2.1843 0.192048 4 2.03847 0.0462196 8 2.00115 0.00889411 16 1.99443 0.002179 32 1.99279 0.000541953 64 1.99239 0.000135315 128 1.99229 3.38181e-05 57 0.4 1 0.353553 0.0464466 2 0.38726 0.0127405 4 0.396607 0.00339318 8 0.399114 0.000885662 16 0.399772 0.000228059 32 0.399942 5.81915e-05 64 0.399985 1.4756e-05 128 0.399996 3.72582e-06 TEST02 Composite Simpson rule, for 1D finite interval problems. Prob Ints Exact Error Approx 1 1.71828 1 1.71886 0.000579323 2 1.71832 3.70135e-05 4 1.71828 2.32624e-06 8 1.71828 1.45593e-07 16 1.71828 9.10273e-09 32 1.71828 5.6897e-10 64 1.71828 3.55616e-11 128 1.71828 2.22244e-12 256 1.71828 1.38334e-13 512 1.71828 9.54792e-15 1024 1.71828 2.22045e-16 2 0.7 1 0.833333 0.133333 2 0.583333 0.116667 4 0.708333 0.00833333 8 0.729167 0.0291667 16 0.697917 0.00208333 32 0.692708 0.00729167 64 0.700521 0.000520833 128 0.701823 0.00182292 256 0.69987 0.000130208 512 0.699544 0.000455729 1024 0.700033 3.25521e-05 3 0.666667 1 0.638071 0.0285955 2 0.656526 0.0101404 4 0.663079 0.00358739 8 0.665398 0.00126848 16 0.666218 0.000448484 32 0.666508 0.000158564 64 0.666611 5.60607e-05 128 0.666647 1.98205e-05 256 0.66666 7.00759e-06 512 0.666664 2.47756e-06 1024 0.666666 8.75949e-07 4 0.479428 1 0.479555 0.000126359 2 0.479555 0.000126834 4 0.479438 9.78384e-06 8 0.479429 6.40567e-07 16 0.479428 4.04901e-08 32 0.479428 2.53773e-09 64 0.479428 1.5872e-10 128 0.479428 9.9219e-12 256 0.479428 6.20393e-13 512 0.479428 3.87468e-14 1024 0.479428 2.27596e-15 5 1.58223 1 1.71137 0.129134 2 1.58497 0.00273629 4 1.58217 5.92977e-05 8 1.58223 1.78421e-06 16 1.58223 9.28413e-08 32 1.58223 5.52189e-09 64 1.58223 3.40781e-10 128 1.58223 2.12323e-11 256 1.58223 1.32605e-12 512 1.58223 8.26006e-14 1024 1.58223 4.88498e-15 6 1.46045 1 0.333333 1.12711 2 0.833333 0.627114 4 0.583333 0.877114 8 0.541667 0.91878 16 0.520833 0.939614 32 0.510417 0.95003 64 0.505208 0.955239 128 0.502604 0.957843 256 0.501302 0.959145 512 0.500651 0.959796 1024 0.500326 0.960122 7 2 1 1.10948 0.890524 2 1.3706 0.629398 4 1.55497 0.445028 8 1.68532 0.314681 16 1.77749 0.222513 32 1.84266 0.15734 64 1.88874 0.111256 128 1.92133 0.0786701 256 1.94437 0.0556282 512 1.96066 0.0393351 1024 1.97219 0.0278141 8 0.866973 1 0.877451 0.010478 2 0.867114 0.000140713 4 0.866981 8.06165e-06 8 0.866973 5.08364e-07 16 0.866973 3.17882e-08 32 0.866973 1.98682e-09 64 0.866973 1.24176e-10 128 0.866973 7.76101e-12 256 0.866973 4.85612e-13 512 0.866973 3.03091e-14 1024 0.866973 2.33147e-15 9 1.1547 1 1 0.154701 2 1.22222 0.0675217 4 1.15079 0.00390689 8 1.15468 2.04533e-05 16 1.1547 5.43522e-10 32 1.1547 2.22045e-16 64 1.1547 6.66134e-16 128 1.1547 2.22045e-16 256 1.1547 0 512 1.1547 0 1024 1.1547 2.22045e-16 10 0.693147 1 0.694444 0.00129726 2 0.693254 0.000106788 4 0.693155 7.35009e-06 8 0.693148 4.72259e-07 16 0.693147 2.97299e-08 32 0.693147 1.86151e-09 64 0.693147 1.16397e-10 128 0.693147 7.27551e-12 256 0.693147 4.55191e-13 512 0.693147 2.79776e-14 1024 0.693147 2.22045e-15 11 0.379885 1 0.379851 3.48103e-05 2 0.379883 1.99648e-06 4 0.379885 1.22395e-07 8 0.379885 7.61369e-09 16 0.379885 4.75298e-10 32 0.379885 2.96973e-11 64 0.379885 1.85579e-12 128 0.379885 1.16018e-13 256 0.379885 7.27196e-15 512 0.379885 3.33067e-16 1024 0.379885 1.66533e-16 12 0.777505 1 0.777494 1.04888e-05 2 0.777504 6.46046e-07 4 0.777505 4.02338e-08 8 0.777505 2.51238e-09 16 0.777505 1.56989e-10 32 0.777505 9.81137e-12 64 0.777505 6.13176e-13 128 0.777505 3.83027e-14 256 0.777505 2.10942e-15 512 0.777505 2.22045e-16 1024 0.777505 2.22045e-16 13 1.65835 1 0.297431 1.36092 2 1.68321 0.024861 4 1.65932 0.000976569 8 1.6584 5.50876e-05 16 1.65835 3.35878e-06 32 1.65835 2.08639e-07 64 1.65835 1.302e-08 128 1.65835 8.13439e-10 256 1.65835 5.0836e-11 512 1.65835 3.17635e-12 1024 1.65835 1.96732e-13 14 0.5 1 11.7851 11.2851 2 5.89256 5.39256 4 2.94628 2.44628 8 1.47314 0.973139 16 0.73657 0.23657 32 0.400108 0.099892 64 0.474613 0.0253867 128 0.499989 1.14855e-05 256 0.5 2.1117e-07 512 0.5 2.11169e-07 1024 0.5 2.11172e-07 15 1 1 41.6667 40.6667 2 20.8333 19.8333 4 10.4167 9.41667 8 5.20834 4.20834 16 2.60838 1.60838 32 1.40795 0.40795 64 1.0547 0.0547035 128 1.00453 0.00453143 256 1.00031 0.000307053 512 1.00002 1.95981e-05 1024 1 1.2314e-06 16 0.493635 1 2.67059 2.17696 2 1.36857 0.874931 4 0.75274 0.259105 8 0.507408 0.0137729 16 0.466443 0.0271921 32 0.487977 0.00565722 64 0.493528 0.000107067 128 0.493635 3.44567e-08 256 0.493635 1.59872e-14 512 0.493635 1.22125e-15 1024 0.493635 3.33067e-16 17 0.5 1 3.21568e-31 0.5 2 0.666667 0.166667 4 0.5 6.66134e-16 8 0.5 7.21645e-16 16 0.5 6.10623e-16 32 0.5 1.66533e-16 64 0.5 0 128 0.5 2.22045e-16 256 0.5 4.44089e-16 512 0.5 1.11022e-16 1024 0.5 2.22045e-16 18 0.170557 1 0.17067 0.00011311 2 0.170564 6.77481e-06 4 0.170558 4.1905e-07 8 0.170557 2.61233e-08 16 0.170557 1.63166e-09 32 0.170557 1.01962e-10 64 0.170557 6.3724e-12 128 0.170557 3.98293e-13 256 0.170557 2.49245e-14 512 0.170557 1.55431e-15 1024 0.170557 0 19 -1 1 -0.462098 0.537902 2 -0.673517 0.326483 4 -0.807895 0.192105 8 -0.889508 0.110492 16 -0.937534 0.0624663 32 -0.965157 0.0348433 64 -0.980773 0.0192267 128 -0.989484 0.0105159 256 -0.994291 0.00570921 512 -0.99692 0.00308024 1024 -0.998347 0.00165294 20 1.5644 1 1.6592 0.0948055 2 1.56034 0.00405345 4 1.56439 1.14072e-05 8 1.5644 5.46947e-08 16 1.5644 8.81228e-11 32 1.5644 6.03884e-11 64 1.5644 4.63163e-12 128 1.5644 3.03091e-13 256 1.5644 1.9762e-14 512 1.5644 1.9984e-15 1024 1.5644 6.66134e-16 21 0.210803 1 0.0183526 0.19245 2 0.269703 0.0589007 4 0.187963 0.0228399 8 0.197033 0.0137695 16 0.216392 0.00558924 32 0.205885 0.00491805 64 0.210619 0.000183926 128 0.209743 0.00105939 256 0.211408 0.000605042 512 0.210662 0.000141014 1024 0.210822 1.93429e-05 22 0.728103 1 0.730159 0.00205582 2 0.72808 2.31851e-05 4 0.728103 1.67247e-07 8 0.728103 2.49305e-09 16 0.728103 3.84832e-11 32 0.728103 5.99631e-13 64 0.728103 9.4369e-15 128 0.728103 2.22045e-16 256 0.728103 1.11022e-16 512 0.728103 1.11022e-16 1024 0.728103 1.11022e-16 23 0.624713 1 1.35264 0.727928 2 -0.203876 0.828589 4 2.00457 1.37985 8 0.334548 0.290165 16 0.916364 0.29165 32 2.31233 1.68762 64 1.69459 1.06988 128 -0.608292 1.233 256 1.21807 0.593356 512 0.721466 0.0967531 1024 0.317796 0.306917 24 -0.00675475 1 0.101552 0.108307 2 0.00891432 0.0156691 4 -0.0087724 0.00201765 8 -0.0111108 0.00435605 16 -0.00635132 0.000403428 32 -0.00671303 4.17187e-05 64 -0.00667696 7.7784e-05 128 -0.00677494 2.01948e-05 256 -0.00674429 1.04602e-05 512 -0.00677533 2.05867e-05 1024 -0.00675909 4.3402e-06 25 -1.61086 1 -1.33307 0.277798 2 -1.66304 0.052176 4 -1.51709 0.0937722 8 -1.62417 0.0133043 16 -1.58744 0.0234208 32 -1.61419 0.00332766 64 -1.60501 0.00585509 128 -1.6117 0.000831922 256 -1.6094 0.00146377 512 -1.61107 0.000207981 1024 -1.6105 0.000365943 26 7.95493 1 7.23413 0.720801 2 7.42061 0.534316 4 7.94346 0.011464 8 7.95493 4.1723e-07 16 7.95493 8.88178e-16 32 7.95493 2.66454e-15 64 7.95493 8.88178e-16 128 7.95493 1.77636e-15 256 7.95493 2.66454e-15 512 7.95493 8.88178e-16 1024 7.95493 5.32907e-15 27 0.841117 1 0.527539 0.313578 2 0.635551 0.205566 4 0.706693 0.134424 8 0.753456 0.0876604 16 0.784106 0.0570113 32 0.804134 0.0369832 64 0.817184 0.0239327 128 0.825665 0.0154521 256 0.831162 0.00995523 512 0.834716 0.00640097 1024 0.837009 0.00410802 28 0.0199547 1 1.81632e-16 0.0199547 2 7.22055e-17 0.0199547 4 0.394547 0.374593 8 0.399413 0.379459 16 -0.150243 0.170198 32 -0.0726952 0.0926499 64 0.0314613 0.0115066 128 0.0202592 0.000304486 256 0.0199711 1.64321e-05 512 0.0199557 9.92424e-07 1024 0.0199547 6.15061e-08 29 0.306853 1 0.35 0.0431472 2 0.256481 0.0503713 4 0.303303 0.00355024 8 0.310878 0.00402518 16 0.29934 0.00751264 32 0.305109 0.00174349 64 0.306067 0.000785639 128 0.306546 0.000306711 256 0.306786 6.72477e-05 512 0.306905 5.24841e-05 1024 0.306965 0.00011235 30 -4.52757 1 4.13186 8.65943 2 -9.62729 5.09972 4 -12.1499 7.62237 8 -3.07156 1.45601 16 -4.50813 0.0194385 32 -4.52658 0.000988914 64 -4.52751 5.89709e-05 128 -4.52757 3.64354e-06 256 -4.52757 2.27071e-07 512 -4.52757 1.41818e-08 1024 -4.52757 8.86207e-10 31 2.65164 1 5.4902 2.83856 2 2.47843 0.173204 4 2.57255 0.0790863 8 2.64773 0.00390076 16 2.65163 8.04438e-06 32 2.65164 4.6673e-08 64 2.65164 2.92119e-09 128 2.65164 1.82665e-10 256 2.65164 1.14184e-11 512 2.65164 7.13207e-13 1024 2.65164 4.17444e-14 32 -12.0703 1 -11.5928 0.477507 2 -11.9849 0.0854023 4 -12.0642 0.00613736 8 -12.07 0.000394993 16 -12.0703 2.48603e-05 32 -12.0703 1.55646e-06 64 -12.0703 9.73205e-08 128 -12.0703 6.08319e-09 256 -12.0703 3.80211e-10 512 -12.0703 2.37605e-11 1024 -12.0703 1.48859e-12 33 0.886227 1 0.555036 0.331191 2 0.710016 0.176211 4 0.792758 0.0934694 8 0.836822 0.0494046 16 0.860208 0.0260189 32 0.872572 0.0136547 64 0.879085 0.00714224 128 0.882502 0.00372443 256 0.88429 0.00193676 512 0.885222 0.0010046 1024 0.885707 0.000519901 34 1085.25 1 1168.59 83.3333 2 1090.46 5.20833 4 1085.58 0.325521 8 1085.27 0.0203451 16 1085.25 0.00127157 32 1085.25 7.94729e-05 64 1085.25 4.96705e-06 128 1085.25 3.10441e-07 256 1085.25 1.94025e-08 512 1085.25 1.21258e-09 1024 1085.25 7.52607e-11 35 26 1 18.645 7.35495 2 19.3941 6.6059 4 22.4882 3.51178 8 23.6843 2.31567 16 24.1787 1.82134 32 25.0119 0.988147 64 24.9568 1.04321 128 26.1862 0.186198 256 25.4696 0.530359 512 25.6227 0.377274 1024 26.2033 0.203309 36 100 1 0.862306 99.1377 2 1.94893 98.0511 4 3.33304 96.667 8 4.97136 95.0286 16 6.82375 93.1763 32 8.8542 91.1458 64 11.0306 88.9694 128 13.3242 86.6758 256 15.7096 84.2904 512 18.1643 81.8357 1024 20.6681 79.3319 37 3.1358 1 0.0117908 3.12401 2 0.264622 2.87118 4 0.0950659 3.04073 8 0.166266 2.96953 16 2.32296 0.812843 32 0.83453 2.30127 64 1.21332 1.92248 128 5.68558 2.54978 256 2.91907 0.21673 512 3.07161 0.0641916 1024 3.13572 7.79468e-05 38 0.539257 1 0.742463 0.203206 2 2.14426 1.605 4 0.071744 0.467513 8 0.539094 0.000163376 16 0.539257 3.33067e-16 32 0.539257 3.33067e-16 64 0.539257 1.11022e-16 128 0.539257 1.11022e-16 256 0.539257 1.11022e-16 512 0.539257 3.33067e-16 1024 0.539257 1.11022e-16 39 2.78769 1 2.12579 0.661901 2 2.32575 0.461947 4 2.46181 0.325888 8 2.55732 0.23037 16 2.6248 0.162891 32 2.67251 0.115181 64 2.70625 0.0814453 128 2.7301 0.0575905 256 2.74697 0.0407226 512 2.7589 0.0287953 1024 2.76733 0.0203613 40 2.69896 1 1.79575 0.903208 2 2.81314 0.114187 4 2.28795 0.411005 8 2.41539 0.283563 16 2.76077 0.0618128 32 2.55728 0.141677 64 2.59466 0.104297 128 2.82626 0.127305 256 2.67225 0.0267032 512 2.66458 0.0343738 1024 2.67214 0.026813 41 6.09559 1 1.18519 4.9104 2 2.0017 4.09388 4 2.83097 3.26462 8 3.61152 2.48407 16 4.2719 1.82369 32 4.78342 1.31216 64 5.16027 0.93532 128 5.43168 0.663909 256 5.62525 0.470334 512 5.7627 0.332885 1024 5.86009 0.235493 42 3.98079 1 1.59652 2.38427 2 2.04369 1.93709 4 2.40727 1.57351 8 2.70267 1.27811 16 2.94263 1.03816 32 3.13754 0.843245 64 3.29586 0.684928 128 3.42445 0.556334 256 3.5289 0.451884 512 3.61374 0.367044 1024 3.68265 0.298132 43 2.99157 1 0.86165 2.12992 2 1.27795 1.71362 4 1.6071 1.38447 8 1.87049 1.12108 16 2.0826 0.908964 32 2.25404 0.73753 64 2.39288 0.598689 128 2.50546 0.486108 256 2.59681 0.394757 512 2.67097 0.320601 1024 2.73118 0.260389 44 -0.0300997 1 -0.126106 0.0960065 2 -0.062743 0.0326433 4 -0.036194 0.00609425 8 -0.0306966 0.000596941 16 -0.0301423 4.26078e-05 32 -0.0301025 2.75693e-06 64 -0.0300999 1.73824e-07 128 -0.0300997 1.08879e-08 256 -0.0300997 6.80868e-10 512 -0.0300997 4.25601e-11 1024 -0.0300997 2.6601e-12 45 -0.292707 1 -0.554862 0.262156 2 -0.484887 0.192181 4 -0.437024 0.144317 8 -0.398143 0.105436 16 -0.368506 0.0757994 32 -0.346752 0.0540451 64 -0.331081 0.0383747 128 -0.319898 0.0271914 256 -0.311954 0.0192472 512 -0.306324 0.0136169 1024 -0.302338 0.00963108 46 6.06909 1 5.74112 0.327975 2 6.00259 0.0665014 4 6.06788 0.00121439 8 6.06909 3.65145e-07 16 6.06909 3.28626e-14 32 6.06909 8.88178e-16 64 6.06909 8.88178e-16 128 6.06909 8.88178e-16 256 6.06909 0 512 6.06909 8.88178e-16 1024 6.06909 8.88178e-16 47 -0.444444 1 -0.326753 0.117692 2 -0.395784 0.0486605 4 -0.424752 0.0196924 8 -0.436603 0.00784168 16 -0.441361 0.00308332 32 -0.443244 0.00120003 64 -0.443981 0.000463132 128 -0.444267 0.000177481 256 -0.444377 6.76061e-05 512 -0.444419 2.56197e-05 1024 -0.444435 9.66509e-06 48 -4 1 -0.653505 3.34649 2 -1.1983 2.8017 4 -1.7105 2.2895 8 -2.16297 1.83703 16 -2.54679 1.45321 32 -2.86336 1.13664 64 -3.11916 0.88084 128 -3.32262 0.677378 256 -3.48246 0.517537 512 -3.60678 0.393219 1024 -3.70267 0.297327 49 52.7407 1 46.491 6.24977 2 53.7288 0.988013 4 53.388 0.64721 8 53.26 0.519241 16 52.4329 0.307831 32 52.8198 0.0790446 64 52.7974 0.0566497 128 52.7557 0.0149733 256 52.7502 0.00945232 512 52.7434 0.00262383 1024 52.7438 0.00304883 50 -0.128137 1 -2.82953e-16 0.128137 2 -0.366204 0.238067 4 0.197978 0.326115 8 -0.129329 0.00119172 16 -0.126358 0.00177901 32 -0.127587 0.000549761 64 -0.127992 0.000144721 128 -0.1281 3.67076e-05 256 -0.128128 9.21486e-06 512 -0.128135 2.30641e-06 1024 -0.128136 5.76791e-07 51 -0.197814 1 -0.210836 0.0130225 2 -0.188633 0.00918066 4 -0.189061 0.00875222 8 -0.189187 0.00862667 16 -0.18924 0.00857313 32 -0.189262 0.00855198 64 -0.18927 0.00854373 128 -0.189273 0.0085405 256 -0.189274 0.00853923 512 -0.189275 0.00853872 1024 -0.189275 0.00853851 52 -0.089944 1 -0.956205 0.866261 2 0.117395 0.207339 4 -0.713703 0.623759 8 0.373414 0.463358 16 -0.6047 0.514756 32 0.411725 0.501669 64 -0.594073 0.504129 128 0.413861 0.503805 256 -0.593779 0.503835 512 0.413889 0.503833 1024 -0.593777 0.503833 53 1.50462 1 1.05432 0.450305 2 1.94606 0.441439 4 1.36511 0.139515 8 1.34785 0.156772 16 1.39814 0.106484 32 1.51471 0.0100869 64 1.44856 0.0560658 128 1.46812 0.0364984 256 1.49902 0.00560466 512 1.48378 0.0208466 1024 1.49802 0.00659783 54 1.1547 1 1 0.154701 2 1.22222 0.0675217 4 1.15079 0.00390689 8 1.15468 2.04533e-05 16 1.1547 5.43522e-10 32 1.1547 0 64 1.1547 4.44089e-16 128 1.1547 4.44089e-16 256 1.1547 2.22045e-16 512 1.1547 2.22045e-16 1024 1.1547 0 55 0.505059 1 0.475874 0.0291847 2 0.51144 0.00638096 4 0.505174 0.000114941 8 0.505065 6.59279e-06 16 0.505059 4.0328e-07 32 0.505059 2.50707e-08 64 0.505059 1.56483e-09 128 0.505059 9.77697e-11 256 0.505059 6.11011e-12 512 0.505059 3.81584e-13 1024 0.505059 2.38698e-14 56 1.99225 1 1.83236 0.159894 2 2.00201 0.00975679 4 1.99594 0.0036835 8 1.99232 6.78812e-05 16 1.99226 4.25503e-06 32 1.99225 2.63392e-07 64 1.99225 1.64189e-08 128 1.99225 1.02549e-09 256 1.99225 6.40825e-11 512 1.99225 4.00391e-12 1024 1.99225 2.5091e-13 57 0.4 1 0.402369 0.00236893 2 0.400432 0.000431916 4 0.400077 7.72494e-05 8 0.400014 1.37135e-05 16 0.400002 2.42785e-06 32 0.4 4.29413e-07 64 0.4 7.59245e-08 128 0.4 1.34226e-08 256 0.4 2.37285e-09 512 0.4 4.19469e-10 1024 0.4 7.41524e-11 TEST03 Monte Carlo rule, for 1D finite interval problems. Prob Ints Exact Error Approx 1 1.71828 1 1.24411 0.474174 2 2.44715 0.728863 4 1.40766 0.310626 8 1.5647 0.153586 16 1.60731 0.110975 32 1.75883 0.040548 64 1.75378 0.0355003 128 1.65865 0.0596283 256 1.75921 0.040933 512 1.7191 0.00081378 1024 1.70321 0.015072 2 0.7 1 1 0.3 2 0.5 0.2 4 0.5 0.2 8 0.625 0.075 16 0.6875 0.0125 32 0.6875 0.0125 64 0.59375 0.10625 128 0.640625 0.059375 256 0.671875 0.028125 512 0.699219 0.00078125 1024 0.689453 0.0105469 3 0.666667 1 0.907125 0.240458 2 0.315327 0.35134 4 0.841345 0.174679 8 0.753368 0.0867013 16 0.650527 0.0161393 32 0.640645 0.0260219 64 0.694655 0.0279886 128 0.657844 0.00882272 256 0.70423 0.0375635 512 0.679307 0.0126399 1024 0.663662 0.00300465 4 0.479428 1 -0.122583 0.602011 2 0.118712 0.360716 4 0.218428 0.261001 8 0.198816 0.280612 16 0.624633 0.145205 32 0.415077 0.0643511 64 0.507103 0.0276743 128 0.471867 0.00756124 256 0.447283 0.0321456 512 0.45722 0.0222079 1024 0.501106 0.0216782 5 1.58223 1 1.20927 0.372966 2 1.71688 0.134642 4 1.65198 0.0697515 8 1.62063 0.0383964 16 1.48392 0.0983104 32 1.57429 0.00794053 64 1.55909 0.0231437 128 1.54117 0.0410628 256 1.59724 0.0150072 512 1.58854 0.00630426 1024 1.59512 0.0128851 6 1.46045 1 2 0.539553 2 0 1.46045 4 1 0.460447 8 0.5 0.960447 16 0.75 0.710447 32 0.25 1.21045 64 0.6875 0.772947 128 0.46875 0.991697 256 0.46875 0.991697 512 0.492188 0.96826 1024 0.447266 1.01318 7 2 1 1.69558 0.304422 2 1.13173 0.86827 4 2.13372 0.133718 8 1.50871 0.491288 16 1.70175 0.298254 32 1.87384 0.126157 64 2.14613 0.14613 128 2.19514 0.195138 256 1.86384 0.13616 512 2.15816 0.158158 1024 1.99081 0.00918679 8 0.866973 1 0.879894 0.0129212 2 0.8398 0.0271728 4 0.839538 0.0274349 8 0.924469 0.0574963 16 0.960999 0.094026 32 0.898863 0.0318899 64 0.872585 0.00561215 128 0.875599 0.00862633 256 0.872747 0.00577418 512 0.86468 0.00229346 1024 0.874162 0.00718866 9 1.1547 1 1.04308 0.111622 2 1.3358 0.181101 4 1.25628 0.101584 8 1.07732 0.0773757 16 1.10583 0.0488715 32 1.15368 0.0010227 64 1.08238 0.0723172 128 1.12967 0.0250272 256 1.17441 0.01971 512 1.17854 0.0238349 1024 1.16807 0.0133734 10 0.693147 1 0.559835 0.133312 2 0.639652 0.0534952 4 0.603226 0.0899215 8 0.687125 0.00602171 16 0.704112 0.0109645 32 0.682407 0.0107403 64 0.676034 0.0171127 128 0.705272 0.0121249 256 0.701114 0.00796721 512 0.689511 0.0036366 1024 0.694591 0.00144358 11 0.379885 1 0.390416 0.0105304 2 0.406906 0.0270209 4 0.362793 0.0170922 8 0.370043 0.00984278 16 0.372398 0.00748702 32 0.367995 0.0118909 64 0.395605 0.0157191 128 0.375239 0.00464653 256 0.378582 0.00130398 512 0.379345 0.000540798 1024 0.377854 0.0020319 12 0.777505 1 0.916689 0.139184 2 0.698972 0.0785329 4 0.683148 0.0943563 8 0.776433 0.0010717 16 0.796358 0.0188529 32 0.783303 0.00579819 64 0.77187 0.00563418 128 0.785736 0.0082318 256 0.778608 0.00110367 512 0.771175 0.00632959 1024 0.772591 0.00491388 13 1.65835 1 9.81533 8.15698 2 4.7222 3.06385 4 0.996646 0.661701 8 0.459505 1.19884 16 0.632555 1.02579 32 0.825467 0.83288 64 2.06311 0.404765 128 1.27491 0.383436 256 1.81079 0.152444 512 1.61166 0.0466864 1024 1.78323 0.124882 14 0.5 1 0 0.5 2 0 0.5 4 0 0.5 8 0 0.5 16 0.918628 0.418628 32 0 0.5 64 0.694817 0.194817 128 0.35663 0.14337 256 0.00426014 0.49574 512 0.555573 0.0555724 1024 0.424636 0.0753638 15 1 1 1.0041e-19 1 2 4.26454e-08 1 4 1.28387e-24 1 8 6.50673e-57 1 16 1.4931e-08 1 32 0.00024684 0.999753 64 2.26996 1.26996 128 0.576344 0.423656 256 0.836376 0.163624 512 1.37181 0.371811 1024 0.85234 0.14766 16 0.493635 1 0.00836605 0.485269 2 0.0324574 0.461177 4 0.763281 0.269647 8 0.0718013 0.421833 16 0.0684542 0.42518 32 0.0633344 0.4303 64 0.37333 0.120305 128 0.37731 0.116325 256 0.532681 0.0390461 512 0.548977 0.055342 1024 0.538155 0.04452 17 0.5 1 0.112213 0.387787 2 0.721376 0.221376 4 0.72553 0.22553 8 0.435381 0.0646193 16 0.49962 0.000379673 32 0.538052 0.0380524 64 0.505943 0.00594288 128 0.51273 0.01273 256 0.498863 0.00113666 512 0.483901 0.0160994 1024 0.501703 0.00170284 18 0.170557 1 0.00962764 0.16093 2 0.190424 0.019867 4 0.185768 0.0152105 8 0.162249 0.00830884 16 0.165049 0.00550811 32 0.167935 0.00262204 64 0.167353 0.0032043 128 0.182861 0.0123036 256 0.166475 0.00408206 512 0.174917 0.00435938 1024 0.17017 0.000387464 19 -1 1 -0.590364 0.409636 2 -1.20764 0.207645 4 -1.64956 0.649557 8 -1.47124 0.471237 16 -1.3619 0.361897 32 -1.0687 0.0687037 64 -0.888355 0.111645 128 -0.951331 0.0486693 256 -0.999389 0.000611077 512 -0.963098 0.0369017 1024 -1.00552 0.00552043 20 1.5644 1 1.98209 0.417696 2 1.66125 0.0968508 4 1.69244 0.128047 8 1.58383 0.0194373 16 1.60282 0.0384209 32 1.52474 0.0396539 64 1.49427 0.0701298 128 1.50597 0.0584312 256 1.55892 0.00547211 512 1.58925 0.0248573 1024 1.58093 0.0165315 21 0.210803 1 0.00284576 0.207957 2 0.414865 0.204062 4 0.166822 0.0439803 8 0.162995 0.0478079 16 0.147157 0.0636461 32 0.23466 0.0238576 64 0.153104 0.0576983 128 0.197086 0.0137167 256 0.228799 0.0179967 512 0.208802 0.00200069 1024 0.209624 0.00117873 22 0.728103 1 0.959255 0.231152 2 0.754851 0.0267479 4 0.825195 0.0970921 8 0.831388 0.103285 16 0.721415 0.00668816 32 0.703208 0.0248947 64 0.701973 0.0261295 128 0.746349 0.0182466 256 0.730345 0.00224168 512 0.714123 0.0139804 1024 0.717525 0.0105779 23 0.624713 1 1.0779 0.453187 2 1.38519 0.760479 4 6.13002 5.5053 8 1.11995 0.495235 16 6.33202 5.70731 32 0.203463 0.42125 64 5.16291 4.5382 128 0.455962 0.168751 256 -132.846 133.47 512 1.878 1.25329 1024 0.407011 0.217703 24 -0.00675475 1 -0.0180202 0.0112655 2 -0.0896348 0.08288 4 -0.0065272 0.00022755 8 -0.00315493 0.00359982 16 -0.000789669 0.00596508 32 0.0128847 0.0196394 64 0.00800497 0.0147597 128 -0.00378494 0.00296981 256 -0.00489441 0.00186033 512 -0.00955934 0.00280459 1024 -0.00676865 1.39077e-05 25 -1.61086 1 -1.4549 0.155964 2 -2.00535 0.394482 4 -1.30258 0.308284 8 -1.43029 0.180575 16 -1.45468 0.156185 32 -1.60491 0.00594958 64 -1.55922 0.0516402 128 -1.63405 0.0231838 256 -1.71093 0.100062 512 -1.64129 0.0304255 1024 -1.59602 0.0148395 26 7.95493 1 4.05946 3.89546 2 11.3206 3.36567 4 9.30023 1.3453 8 7.47169 0.483235 16 8.13095 0.17602 32 7.38764 0.567282 64 7.7957 0.159222 128 7.88017 0.0747538 256 7.82692 0.128005 512 7.83959 0.115333 1024 8.17266 0.217733 27 0.841117 1 0.686179 0.154938 2 0.737776 0.103341 4 0.746696 0.0944212 8 0.93303 0.091913 16 0.814394 0.0267233 32 0.744117 0.0970001 64 0.889105 0.0479885 128 0.76414 0.0769773 256 0.885722 0.0446055 512 0.833287 0.00783012 1024 0.831691 0.00942634 28 0.0199547 1 -0.0085986 0.0285533 2 -0.00231257 0.0222672 4 -0.647683 0.667637 8 0.0250604 0.00510573 16 0.016053 0.00390166 32 -0.0543971 0.0743518 64 0.0248841 0.00492946 128 0.091242 0.0712874 256 0.115731 0.0957763 512 0.00687327 0.0130814 1024 -0.0495241 0.0694788 29 0.306853 1 0.404131 0.0972785 2 0 0.306853 4 0.322005 0.0151523 8 0.428549 0.121696 16 0.317784 0.0109314 32 0.290193 0.0166598 64 0.274939 0.0319135 128 0.288663 0.0181898 256 0.310363 0.00351011 512 0.309796 0.00294298 1024 0.301696 0.0051569 30 -4.52757 1 28.2889 32.8165 2 9.58719 14.1148 4 -19.5834 15.0559 8 -13.5561 9.02857 16 -8.2325 3.70493 32 -3.32872 1.19885 64 -4.92983 0.402258 128 -6.73476 2.20719 256 -3.39305 1.13452 512 -7.6047 3.07713 1024 -4.35208 0.175495 31 2.65164 1 0.703984 1.94765 2 1.23673 1.4149 4 3.67831 1.02668 8 2.67859 0.0269575 16 2.60924 0.0423918 32 2.26466 0.38698 64 3.14715 0.495514 128 2.60313 0.0485056 256 2.83355 0.181916 512 2.74363 0.0919987 1024 2.73173 0.08009 32 -12.0703 1 4.2776 16.3479 2 -15.1272 3.05685 4 -5.59044 6.4799 8 -20.3504 8.28007 16 -6.56116 5.50919 32 -17.0716 5.00123 64 -12.348 0.277675 128 -11.3339 0.736472 256 -10.1116 1.95874 512 -12.148 0.0776411 1024 -11.1571 0.913209 33 0.886227 1 1.84891 0.962681 2 0.52026 0.365967 4 0.743373 0.142854 8 0.928517 0.0422904 16 1.05976 0.173536 32 0.938243 0.0520158 64 0.849995 0.0362316 128 0.861673 0.0245538 256 0.906644 0.0204167 512 0.893704 0.00747755 1024 0.893015 0.00678781 34 1085.25 1 3037.33 1952.08 2 959.606 125.646 4 1375.94 290.691 8 1896.81 811.561 16 956.194 129.058 32 1440.29 355.036 64 1274.47 189.217 128 1111.54 26.2918 256 1107.17 21.9124 512 1203.58 118.33 1024 1089.19 3.94164 35 26 1 20.0303 5.96966 2 16.5818 9.41824 4 18.1763 7.82374 8 22.4113 3.58874 16 22.7179 3.28213 32 33.669 7.66902 64 23.7522 2.24779 128 27.3054 1.30538 256 28.502 2.50202 512 28.282 2.28198 1024 25.9717 0.0283058 36 100 1 6.51885 93.4812 2 0.982325 99.0177 4 0.717924 99.2821 8 11.553 88.447 16 17.3649 82.6351 32 8.13143 91.8686 64 11.2458 88.7542 128 9.10715 90.8928 256 33.3721 66.6279 512 14.4727 85.5273 1024 17.4847 82.5153 37 3.1358 1 0.133441 3.00236 2 0.0493791 3.08642 4 0.140371 2.99543 8 0.822593 2.31321 16 0.324265 2.81153 32 0.106858 3.02894 64 0.190956 2.94484 128 0.360728 2.77507 256 2.83606 0.299741 512 5.60418 2.46838 1024 3.59651 0.46071 38 0.539257 1 -2.15355 2.6928 2 1.5954 1.05614 4 1.52317 0.983909 8 1.12902 0.589767 16 0.688554 0.149297 32 0.740047 0.20079 64 0.450337 0.08892 128 0.576782 0.0375248 256 0.462634 0.0766225 512 0.398713 0.140544 1024 0.560063 0.0208066 39 2.78769 1 1.82525 0.962442 2 3.59472 0.807024 4 3.60989 0.822196 8 2.40455 0.383143 16 2.37423 0.413461 32 3.29831 0.510619 64 2.39472 0.39297 128 2.29225 0.495439 256 2.68168 0.106015 512 2.83807 0.0503761 1024 2.74118 0.0465087 40 2.69896 1 1.16936 1.5296 2 2.25936 0.439598 4 1.96704 0.731921 8 2.03542 0.663538 16 3.25992 0.560963 32 2.34359 0.355367 64 2.3858 0.313154 128 3.06167 0.362711 256 2.50583 0.193128 512 2.81463 0.115673 1024 2.56139 0.137565 41 6.09559 1 1.82112 4.27446 2 1.54733 4.54825 4 2.13739 3.9582 8 2.62066 3.47492 16 3.68937 2.40622 32 4.39522 1.70037 64 5.5435 0.55208 128 3.98952 2.10607 256 6.92091 0.825326 512 5.63857 0.457014 1024 6.10814 0.0125585 42 3.98079 1 2.00965 1.97114 2 4.19231 0.211525 4 4.73083 0.750048 8 3.34044 0.640346 16 7.60007 3.61928 32 3.11333 0.867458 64 3.10482 0.875961 128 2.78999 1.1908 256 3.2092 0.771587 512 4.16816 0.187378 1024 4.13348 0.152692 43 2.99157 1 1.1436 1.84797 2 1.31448 1.67709 4 1.22981 1.76176 8 1.99439 0.997175 16 2.44661 0.544959 32 2.09041 0.901163 64 2.32284 0.668729 128 7.26508 4.27351 256 2.20325 0.788319 512 2.76517 0.226398 1024 2.47815 0.513417 44 -0.0300997 1 2.29045e-05 0.0301226 2 4.15923e-05 0.0301413 4 2.74798e-05 0.0301272 8 -0.101137 0.0710375 16 -0.0677881 0.0376884 32 -0.0379798 0.00788014 64 -0.0259852 0.00411447 128 -0.0181356 0.0119641 256 -0.0178194 0.0122803 512 -0.0324306 0.00233087 1024 -0.0266137 0.00348604 45 -0.292707 1 -2.62674 2.33403 2 -2.54971 2.257 4 0.142006 0.434713 8 -0.145866 0.146841 16 0.20653 0.499236 32 -0.394234 0.101527 64 -0.179317 0.11339 128 -0.417463 0.124757 256 -0.466998 0.174291 512 -0.357797 0.0650902 1024 0.00421417 0.296921 46 6.06909 1 5.21778 0.851313 2 5.60235 0.466742 4 6.29395 0.224861 8 5.83017 0.238923 16 6.2303 0.161213 32 6.05125 0.0178431 64 6.09683 0.0277391 128 5.99644 0.0726558 256 6.03891 0.0301821 512 6.12552 0.0564294 1024 6.02896 0.0401285 47 -0.444444 1 -0.231255 0.21319 2 -0.623487 0.179042 4 -0.51692 0.0724751 8 -0.542709 0.0982644 16 -0.500041 0.0555968 32 -0.45072 0.00627602 64 -0.425883 0.0185614 128 -0.4557 0.0112554 256 -0.458999 0.0145543 512 -0.428869 0.0155754 1024 -0.455111 0.0106664 48 -4 1 -11.8644 7.86443 2 -0.966131 3.03387 4 -4.05733 0.0573291 8 -7.76782 3.76782 16 -1.78793 2.21207 32 -5.78692 1.78692 64 -2.14673 1.85327 128 -3.93825 0.0617451 256 -3.108 0.891998 512 -4.10943 0.109435 1024 -4.27285 0.27285 49 52.7407 1 12.0947 40.6461 2 3.1554 49.5853 4 26.7962 25.9445 8 94.4561 41.7154 16 60.3368 7.59601 32 47.9699 4.77088 64 70.9486 18.2078 128 50.7782 1.96255 256 47.9242 4.81657 512 51.4425 1.29821 1024 46.8367 5.9041 50 -0.128137 1 1.83423 1.96237 2 -2.33299 2.20485 4 0.165641 0.293778 8 0.226998 0.355134 16 0.377751 0.505887 32 -0.263464 0.135327 64 -0.20568 0.0775436 128 -0.129919 0.00178181 256 -0.0574783 0.0706585 512 -0.147685 0.0195485 1024 -0.195964 0.0678268 51 -0.197814 1 -0.155578 0.0422358 2 -0.306372 0.108559 4 -0.215235 0.0174215 8 -0.222845 0.0250315 16 -0.1806 0.0172133 32 -0.168529 0.0292841 64 -0.174075 0.0237381 128 -0.193111 0.004703 256 -0.20114 0.00332625 512 -0.188856 0.00895793 1024 -0.186358 0.0114554 52 -0.089944 1 0.00530886 0.0952529 2 0.086102 0.176046 4 16.9157 17.0056 8 -0.130668 0.0407242 16 -17.3079 17.2179 32 -1.11668 1.02674 64 0.592758 0.682702 128 -3.2758 3.18586 256 1.58285 1.6728 512 0.0254693 0.115413 1024 0.485889 0.575833 53 1.50462 1 9.58063 8.07601 2 1.17014 0.334484 4 1.12297 0.381653 8 1.85909 0.354468 16 1.47446 0.0301631 32 1.18079 0.323829 64 2.01136 0.506733 128 1.2567 0.247921 256 1.4227 0.0819251 512 1.50967 0.0050485 1024 1.4778 0.0268198 54 1.1547 1 1.45906 0.304364 2 0.807381 0.34732 4 1.09759 0.0571106 8 1.12021 0.034487 16 1.3655 0.210802 32 1.10816 0.0465373 64 1.12112 0.0335836 128 1.14524 0.00946395 256 1.16084 0.00614328 512 1.14646 0.00824221 1024 1.15954 0.00484077 55 0.505059 1 0.701083 0.196024 2 0.926277 0.421218 4 0.439659 0.0653997 8 0.500523 0.00453537 16 0.361573 0.143485 32 0.501381 0.00367716 64 0.428174 0.0768842 128 0.500086 0.00497231 256 0.494682 0.0103765 512 0.503433 0.00162527 1024 0.489312 0.0157461 56 1.99225 1 2.22142 0.229168 2 1.98555 0.00670296 4 1.92562 0.0666352 8 2.13325 0.140998 16 1.96041 0.0318451 32 1.98416 0.00809676 64 1.95297 0.0392792 128 1.99764 0.00538697 256 2.00699 0.014735 512 1.96888 0.0233702 1024 1.98945 0.00279753 57 0.4 1 0.711664 0.311664 2 0.951292 0.551292 4 0.190631 0.209369 8 0.490832 0.0908324 16 0.446336 0.046336 32 0.415806 0.0158062 64 0.367474 0.032526 128 0.3482 0.0517998 256 0.388045 0.0119553 512 0.415208 0.0152079 1024 0.394757 0.00524333 TEST04 Use a composite 4 point Gauss-Legendre rule, for 1D finite interval problems. Prob Ints Exact Error Approx 1 1.71828 1 1.71828 9.32967e-10 2 1.71828 3.74145e-12 4 1.71828 1.46549e-14 8 1.71828 4.44089e-16 16 1.71828 0 32 1.71828 0 64 1.71828 0 128 1.71828 6.66134e-16 256 1.71828 2.22045e-16 512 1.71828 4.44089e-16 1024 1.71828 1.55431e-15 2 0.7 1 0.826073 0.126073 2 0.75 0.05 4 0.706518 0.00651814 8 0.6875 0.0125 16 0.69837 0.00162954 32 0.703125 0.003125 64 0.700407 0.000407384 128 0.699219 0.00078125 256 0.699898 0.000101846 512 0.700195 0.000195313 1024 0.700025 2.54615e-05 3 0.666667 1 0.667828 0.00116098 2 0.667077 0.000410474 4 0.666812 0.000145125 8 0.666718 5.13093e-05 16 0.666685 1.81406e-05 32 0.666673 6.41366e-06 64 0.666669 2.26757e-06 128 0.666667 8.01707e-07 256 0.666667 2.83446e-07 512 0.666667 1.00213e-07 1024 0.666667 3.54308e-08 4 0.479428 1 0.479428 9.39909e-09 2 0.479428 1.93069e-10 4 0.479428 9.78329e-13 8 0.479428 3.94129e-15 16 0.479428 1.11022e-16 32 0.479428 1.11022e-16 64 0.479428 1.66533e-16 128 0.479428 1.11022e-16 256 0.479428 2.77556e-16 512 0.479428 4.996e-16 1024 0.479428 1.66533e-16 5 1.58223 1 1.58506 0.00282752 2 1.58221 1.93086e-05 4 1.58223 3.65626e-08 8 1.58223 3.30469e-11 16 1.58223 1.45883e-13 32 1.58223 8.88178e-16 64 1.58223 2.22045e-16 128 1.58223 0 256 1.58223 2.22045e-16 512 1.58223 1.11022e-15 1024 1.58223 8.88178e-16 6 1.46045 1 0.347855 1.11259 2 0.5 0.960447 4 0.5 0.960447 8 0.5 0.960447 16 0.5 0.960447 32 0.5 0.960447 64 0.5 0.960447 128 0.5 0.960447 256 0.5 0.960447 512 0.5 0.960447 1024 0.5 0.960447 7 2 1 1.80634 0.193657 2 1.86306 0.136937 4 1.90317 0.0968288 8 1.93153 0.0684683 16 1.95159 0.0484144 32 1.96577 0.0342342 64 1.97579 0.0242072 128 1.98288 0.0171171 256 1.9879 0.0121036 512 1.99144 0.00855854 1024 1.99395 0.0060518 8 0.866973 1 0.866956 1.73299e-05 2 0.866973 5.61357e-08 4 0.866973 1.6798e-10 8 0.866973 5.58442e-13 16 0.866973 2.10942e-15 32 0.866973 1.11022e-16 64 0.866973 1.11022e-16 128 0.866973 2.22045e-16 256 0.866973 3.33067e-16 512 0.866973 4.44089e-16 1024 0.866973 1.11022e-15 9 1.1547 1 1.19781 0.0431128 2 1.24661 0.0919063 4 1.14775 0.00695461 8 1.15466 3.575e-05 16 1.1547 9.49923e-10 32 1.1547 2.22045e-16 64 1.1547 0 128 1.1547 2.22045e-16 256 1.1547 1.33227e-15 512 1.1547 1.11022e-15 1024 1.1547 2.22045e-16 10 0.693147 1 0.693146 7.63114e-07 2 0.693147 6.80639e-09 4 0.693147 3.72339e-11 8 0.693147 1.61871e-13 16 0.693147 7.77156e-16 32 0.693147 2.22045e-16 64 0.693147 1.11022e-16 128 0.693147 4.44089e-16 256 0.693147 4.44089e-16 512 0.693147 7.77156e-16 1024 0.693147 8.88178e-16 11 0.379885 1 0.379885 1.27293e-09 2 0.379885 3.83404e-12 4 0.379885 1.42109e-14 8 0.379885 5.55112e-17 16 0.379885 5.55112e-17 32 0.379885 5.55112e-17 64 0.379885 0 128 0.379885 5.55112e-17 256 0.379885 1.66533e-16 512 0.379885 0 1024 0.379885 1.66533e-16 12 0.777505 1 0.777505 1.36159e-11 2 0.777505 5.06262e-14 4 0.777505 0 8 0.777505 2.22045e-16 16 0.777505 1.11022e-16 32 0.777505 3.33067e-16 64 0.777505 4.44089e-16 128 0.777505 3.33067e-16 256 0.777505 0 512 0.777505 6.66134e-16 1024 0.777505 9.99201e-16 13 1.65835 1 1.6661 0.00775417 2 1.65834 9.47052e-06 4 1.65835 2.65764e-08 8 1.65835 9.43849e-11 16 1.65835 3.59712e-13 32 1.65835 1.9984e-15 64 1.65835 6.66134e-16 128 1.65835 0 256 1.65835 8.88178e-16 512 1.65835 0 1024 1.65835 2.22045e-15 14 0.5 1 0 0.5 2 3.69083e-08 0.5 4 0.0270625 0.472938 8 0.470876 0.0291239 16 0.573638 0.0736378 32 0.493226 0.00677446 64 0.500077 7.69705e-05 128 0.5 1.75058e-07 256 0.5 2.11171e-07 512 0.5 2.11173e-07 1024 0.5 2.11172e-07 15 1 1 1.25847e-06 0.999999 2 0.00369866 0.996301 4 0.141785 0.858215 8 0.621078 0.378922 16 0.947909 0.0520906 32 0.998223 0.00177698 64 0.999981 1.89313e-05 128 1 1.04504e-07 256 1 4.49856e-10 512 1 1.80211e-12 1024 1 7.54952e-15 16 0.493635 1 0.236976 0.256659 2 0.400596 0.0930385 4 0.509088 0.0154531 8 0.503719 0.0100848 16 0.49317 0.000464694 32 0.493618 1.70416e-05 64 0.493635 3.30349e-07 128 0.493635 1.1038e-10 256 0.493635 5.55112e-17 512 0.493635 2.77556e-16 1024 0.493635 5.55112e-17 17 0.5 1 0.997235 0.497235 2 0.515987 0.0159871 4 0.5 9.99201e-16 8 0.5 7.77156e-16 16 0.5 4.996e-16 32 0.5 0 64 0.5 1.11022e-16 128 0.5 5.55112e-17 256 0.5 1.66533e-16 512 0.5 1.11022e-16 1024 0.5 2.22045e-16 18 0.170557 1 0.170557 6.7498e-10 2 0.170557 3.12642e-12 4 0.170557 1.22125e-14 8 0.170557 5.55112e-17 16 0.170557 2.77556e-17 32 0.170557 0 64 0.170557 2.77556e-17 128 0.170557 2.77556e-17 256 0.170557 2.77556e-17 512 0.170557 1.38778e-16 1024 0.170557 8.32667e-17 19 -1 1 -0.968536 0.031464 2 -0.984268 0.0157321 4 -0.992134 0.00786604 8 -0.996067 0.00393302 16 -0.998033 0.00196651 32 -0.999017 0.000983255 64 -0.999508 0.000491628 128 -0.999754 0.000245814 256 -0.999877 0.000122907 512 -0.999939 6.14534e-05 1024 -0.999969 3.07267e-05 20 1.5644 1 1.56227 0.0021293 2 1.56441 9.49371e-06 4 1.5644 2.22444e-08 8 1.5644 2.91323e-13 16 1.5644 4.44089e-16 32 1.5644 2.22045e-16 64 1.5644 4.44089e-16 128 1.5644 6.66134e-16 256 1.5644 2.22045e-16 512 1.5644 6.66134e-16 1024 1.5644 2.22045e-15 21 0.210803 1 0.128374 0.0824283 2 0.19715 0.013653 4 0.197678 0.0131248 8 0.19768 0.0131224 16 0.210842 3.89955e-05 32 0.209812 0.000990259 64 0.209975 0.000827247 128 0.210004 0.000799022 256 0.210843 4.01268e-05 512 0.210809 5.87322e-06 1024 0.210803 6.539e-08 22 0.728103 1 0.72809 1.3396e-05 2 0.728103 3.91176e-08 4 0.728103 2.12543e-11 8 0.728103 8.32667e-14 16 0.728103 5.55112e-16 32 0.728103 1.11022e-16 64 0.728103 1.11022e-16 128 0.728103 0 256 0.728103 8.88178e-16 512 0.728103 1.11022e-16 1024 0.728103 2.22045e-16 23 0.624713 1 3.17665 2.55194 2 -0.594889 1.2196 4 2.25275 1.62804 8 1.84406 1.21934 16 -3.18856 3.81327 32 2.4547 1.82999 64 -2.14491 2.76963 128 1.29187 0.667157 256 -1.73135 2.35606 512 -1.72521 2.34992 1024 2.72422 2.0995 24 -0.00675475 1 0.00363542 0.0103902 2 0.0152561 0.0220108 4 0.00478953 0.0115443 8 -0.00561193 0.00114282 16 -0.00659325 0.000161497 32 -0.00651658 0.000238164 64 -0.00678862 3.38745e-05 128 -0.0067308 2.39431e-05 256 -0.00677967 2.49199e-05 512 -0.00674813 6.61401e-06 1024 -0.00675275 1.99692e-06 25 -1.61086 1 -1.80289 0.192024 2 -1.57279 0.0380774 4 -1.56576 0.0451066 8 -1.60134 0.0095196 16 -1.59959 0.0112767 32 -1.60848 0.0023799 64 -1.60805 0.00281916 128 -1.61027 0.000594975 256 -1.61016 0.000704791 512 -1.61072 0.000148744 1024 -1.61069 0.000176198 26 7.95493 1 7.94092 0.0140102 2 7.95263 0.0022941 4 7.95496 3.65715e-05 8 7.95493 1.3366e-09 16 7.95493 2.66454e-15 32 7.95493 2.66454e-15 64 7.95493 8.88178e-16 128 7.95493 8.88178e-16 256 7.95493 1.77636e-15 512 7.95493 5.32907e-15 1024 7.95493 6.21725e-15 27 0.841117 1 0.797664 0.0434532 2 0.8131 0.028017 4 0.823093 0.0180237 8 0.829546 0.0115708 16 0.833703 0.00741397 32 0.836375 0.00474222 64 0.838088 0.00302846 128 0.839186 0.00193124 256 0.839887 0.00122994 512 0.840335 0.000782392 1024 0.84062 0.000497171 28 0.0199547 1 0.124191 0.104236 2 -0.177256 0.19721 4 0.0948975 0.0749428 8 0.227422 0.207467 16 0.354106 0.334151 32 0.0225451 0.00259046 64 0.0199424 1.23037e-05 128 0.0199547 1.83802e-08 256 0.0199547 6.04362e-11 512 0.0199547 2.2678e-13 1024 0.0199547 9.36751e-16 29 0.306853 1 0.346116 0.0392629 2 0.318629 0.0117765 4 0.302542 0.00431111 8 0.310523 0.00367009 16 0.307028 0.000175026 32 0.307025 0.000172216 64 0.307025 0.000172216 128 0.307025 0.000172216 256 0.306775 7.77048e-05 512 0.3069 4.72618e-05 1024 0.306845 7.39729e-06 30 -4.52757 1 -23.1023 18.5748 2 1.53301 6.06058 4 -4.10501 0.422555 8 -4.53045 0.00287619 16 -4.52757 2.13147e-06 32 -4.52757 6.58666e-09 64 -4.52757 2.43627e-11 128 -4.52757 7.72715e-14 256 -4.52757 4.44089e-15 512 -4.52757 1.15463e-14 1024 -4.52757 7.10543e-15 31 2.65164 1 2.04729 0.60435 2 2.65543 0.00379112 4 2.65082 0.000817562 8 2.65165 9.80479e-06 16 2.65164 2.33886e-08 32 2.65164 8.26006e-14 64 2.65164 1.33227e-15 128 2.65164 8.88178e-16 256 2.65164 1.33227e-15 512 2.65164 3.10862e-15 1024 2.65164 2.22045e-15 32 -12.0703 1 -12.0702 0.000156826 2 -12.0703 3.23838e-06 4 -12.0703 1.50141e-08 8 -12.0703 6.07567e-11 16 -12.0703 2.45137e-13 32 -12.0703 5.32907e-15 64 -12.0703 7.10543e-15 128 -12.0703 3.55271e-15 256 -12.0703 1.77636e-15 512 -12.0703 1.77636e-15 1024 -12.0703 1.77636e-15 33 0.886227 1 0.880399 0.00582799 2 0.883352 0.00287455 4 0.884818 0.00140888 8 0.885539 0.000687677 16 0.885892 0.000334806 32 0.886064 0.000162779 64 0.886148 7.90952e-05 128 0.886188 3.8432e-05 256 0.886208 1.86806e-05 512 0.886218 9.08556e-06 1024 0.886223 4.42226e-06 34 1085.25 1 1085.25 4.54747e-13 2 1085.25 0 4 1085.25 2.27374e-13 8 1085.25 0 16 1085.25 0 32 1085.25 0 64 1085.25 2.27374e-13 128 1085.25 2.27374e-13 256 1085.25 0 512 1085.25 0 1024 1085.25 4.54747e-13 35 26 1 29.1002 3.10021 2 21.4437 4.55633 4 121.74 95.7402 8 32.2505 6.2505 16 30.685 4.68495 32 26.543 0.543024 64 25.8498 0.150151 128 25.4518 0.548202 256 25.642 0.357964 512 25.8885 0.11149 1024 25.7865 0.213484 36 100 1 6.29854 93.7015 2 8.34127 91.6587 4 10.5306 89.4694 8 12.8378 87.1622 16 15.2372 84.7628 32 17.7061 82.2939 64 20.2245 79.7755 128 22.7746 77.2254 256 25.341 74.659 512 27.9099 72.0901 1024 30.4696 69.5304 37 3.1358 1 0.0338325 3.10197 2 0.0818374 3.05396 4 0.197291 2.93851 8 1.21299 1.9228 16 0.643995 2.4918 32 1.64518 1.49062 64 3.23778 0.10198 128 2.59874 0.537061 256 3.12961 0.00618886 512 3.13573 6.67473e-05 1024 3.1358 2.93208e-06 38 0.539257 1 1.51305 0.97379 2 0.40666 0.132597 4 0.540695 0.00143763 8 0.539257 5.23377e-07 16 0.539257 7.77156e-16 32 0.539257 4.44089e-16 64 0.539257 3.33067e-16 128 0.539257 1.11022e-16 256 0.539257 1.11022e-16 512 0.539257 4.44089e-16 1024 0.539257 4.44089e-16 39 2.78769 1 6.7814 3.9937 2 5.61163 2.82394 4 4.78452 1.99683 8 4.19966 1.41197 16 3.78611 0.998413 32 3.49368 0.705985 64 3.2869 0.499207 128 3.14069 0.352992 256 3.0373 0.249603 512 2.96419 0.176496 1024 2.9125 0.124802 40 2.69896 1 2.10507 0.593885 2 2.28468 0.414276 4 2.4172 0.281753 8 2.65152 0.0474357 16 2.54806 0.150898 32 2.60573 0.0932308 64 2.65617 0.0427867 128 2.63761 0.0613442 256 2.74902 0.0500612 512 2.6778 0.0211592 1024 2.68429 0.0146688 41 6.09559 1 4.29442 1.80117 2 4.86748 1.2281 4 5.25298 0.842609 8 5.50856 0.58703 16 5.68314 0.412447 32 5.80479 0.290793 64 5.89025 0.205332 128 5.95049 0.145091 256 5.99303 0.10256 512 6.02308 0.0725082 1024 6.04432 0.0512667 42 3.98079 1 2.96736 1.01342 2 3.15764 0.823142 4 3.31219 0.668596 8 3.43772 0.543068 16 3.53968 0.441108 32 3.6225 0.358291 64 3.68976 0.291023 128 3.7444 0.236384 256 3.78878 0.192003 512 3.82483 0.155955 1024 3.85411 0.126675 43 2.99157 1 2.10711 0.88446 2 2.27296 0.718612 4 2.40779 0.583781 8 2.51735 0.474215 16 2.60637 0.385199 32 2.67868 0.312886 64 2.73742 0.254146 128 2.78514 0.206432 256 2.82389 0.167676 512 2.85537 0.136195 1024 2.88094 0.110625 44 -0.0300997 1 -0.0236 0.00649971 2 -0.0297061 0.000393636 4 -0.0300941 5.59487e-06 8 -0.0300997 3.33815e-08 16 -0.0300997 1.45457e-10 32 -0.0300997 5.83738e-13 64 -0.0300997 2.31412e-15 128 -0.0300997 2.42861e-17 256 -0.0300997 6.93889e-18 512 -0.0300997 1.38778e-17 1024 -0.0300997 2.08167e-17 45 -0.292707 1 -0.362859 0.0701522 2 -0.341268 0.0485615 4 -0.326652 0.0339448 8 -0.316566 0.0238597 16 -0.309527 0.0168202 32 -0.304582 0.0118755 64 -0.301097 0.00839079 128 -0.298638 0.0059309 256 -0.2969 0.00419297 512 -0.295671 0.00296459 1024 -0.294803 0.00209618 46 6.06909 1 6.06337 0.00571871 2 6.0689 0.000187372 4 6.06909 3.75632e-06 8 6.06909 1.16973e-09 16 6.06909 0 32 6.06909 1.77636e-15 64 6.06909 8.88178e-16 128 6.06909 2.66454e-15 256 6.06909 6.21725e-15 512 6.06909 5.32907e-15 1024 6.06909 5.32907e-15 47 -0.444444 1 -0.448878 0.00443311 2 -0.446296 0.00185187 4 -0.4452 0.000755327 8 -0.444747 0.000302613 16 -0.444564 0.000119564 32 -0.444491 4.67179e-05 64 -0.444463 1.8089e-05 128 -0.444451 6.95114e-06 256 -0.444447 2.65407e-06 512 -0.444445 1.00782e-06 1024 -0.444445 3.80876e-07 48 -4 1 -2.56246 1.43754 2 -2.88859 1.11141 4 -3.147 0.853003 8 -3.34938 0.650623 16 -3.50638 0.493618 32 -3.62723 0.37277 64 -3.71963 0.280367 128 -3.78989 0.210114 256 -3.84304 0.156963 512 -3.88308 0.116922 1024 -3.91313 0.086871 49 52.7407 1 52.4911 0.249654 2 50.737 2.00374 4 52.2435 0.497236 8 52.5621 0.178668 16 52.6861 0.0546064 32 52.6314 0.109398 64 52.7231 0.0175987 128 52.6833 0.0574527 256 52.7117 0.0290385 512 52.7323 0.00849107 1024 52.7377 0.00302807 50 -0.128137 1 -0.183037 0.0549001 2 0.0679213 0.196058 4 -0.131315 0.0031785 8 -0.128444 0.000307245 16 -0.128216 7.90615e-05 32 -0.128157 1.98788e-05 64 -0.128142 4.97691e-06 128 -0.128138 1.24468e-06 256 -0.128137 3.11199e-07 512 -0.128137 7.78015e-08 1024 -0.128137 1.94505e-08 51 -0.197814 1 -0.189169 0.00864441 2 -0.189298 0.00851603 4 -0.189284 0.00852994 8 -0.189278 0.00853517 16 -0.189276 0.00853716 32 -0.189276 0.00853791 64 -0.189275 0.0085382 128 -0.189275 0.0085383 256 -0.189275 0.00853834 512 -0.189275 0.00853836 1024 -0.189275 0.00853837 52 -0.089944 1 -0.165815 0.0758712 2 -16.435 16.345 4 16.2832 16.3732 8 -16.4536 16.3636 16 16.2758 16.3657 32 -16.4554 16.3655 64 16.2755 16.3655 128 -16.4554 16.3655 256 16.2755 16.3655 512 -16.4554 16.3655 1024 16.2755 16.3655 53 1.50462 1 1.33515 0.169473 2 1.24434 0.260279 4 2.13839 0.633763 8 1.39627 0.108356 16 1.4955 0.00911961 32 1.45047 0.054152 64 1.46529 0.0393348 128 1.51214 0.00751311 256 1.48947 0.0151534 512 1.48973 0.01489 1024 1.50132 0.00330677 54 1.1547 1 1.19781 0.0431128 2 1.24661 0.0919063 4 1.14775 0.00695461 8 1.15466 3.575e-05 16 1.1547 9.49924e-10 32 1.1547 4.44089e-16 64 1.1547 2.22045e-16 128 1.1547 4.44089e-16 256 1.1547 1.55431e-15 512 1.1547 1.33227e-15 1024 1.1547 0 55 0.505059 1 0.506864 0.00180534 2 0.505046 1.25892e-05 4 0.505059 1.3414e-09 8 0.505059 8.35376e-12 16 0.505059 3.35287e-14 32 0.505059 1.11022e-16 64 0.505059 0 128 0.505059 2.22045e-16 256 0.505059 1.11022e-16 512 0.505059 1.11022e-16 1024 0.505059 2.22045e-16 56 1.99225 1 1.9787 0.0135478 2 1.99302 0.000767313 4 1.99224 8.57781e-06 8 1.99225 8.74673e-09 16 1.99225 1.02856e-11 32 1.99225 2.88658e-14 64 1.99225 4.44089e-16 128 1.99225 6.66134e-16 256 1.99225 1.33227e-15 512 1.99225 4.44089e-16 1024 1.99225 8.88178e-16 57 0.4 1 0.39995 4.9615e-05 2 0.399991 8.77177e-06 4 0.399998 1.55065e-06 8 0.4 2.74119e-07 16 0.4 4.84579e-08 32 0.4 8.56622e-09 64 0.4 1.51431e-09 128 0.4 2.67694e-10 256 0.4 4.73221e-11 512 0.4 8.3652e-12 1024 0.4 1.47843e-12 TEST05 Composite trapezoid rule, for 1D finite interval problems. Prob Ints Exact Error Approx 1 1.71828 1 1.85914 0.140859 2 1.75393 0.0356493 4 1.72722 0.00894008 8 1.72052 0.00223676 16 1.71884 0.0005593 32 1.71842 0.000139832 64 1.71832 3.49584e-05 128 1.71829 8.73962e-06 256 1.71828 2.18491e-06 512 1.71828 5.46227e-07 1024 1.71828 1.36557e-07 2 0.7 1 0.5 0.2 2 0.75 0.05 4 0.625 0.075 8 0.6875 0.0125 16 0.71875 0.01875 32 0.703125 0.003125 64 0.695312 0.0046875 128 0.699219 0.00078125 256 0.701172 0.00117188 512 0.700195 0.000195313 1024 0.699707 0.000292969 3 0.666667 1 0.5 0.166667 2 0.603553 0.0631133 4 0.643283 0.0233836 8 0.65813 0.00853645 16 0.663581 0.00308547 32 0.665559 0.00110773 64 0.666271 0.000395855 128 0.666526 0.000141009 256 0.666617 5.01177e-05 512 0.666649 1.77851e-05 1024 0.66666 6.30445e-06 4 0.479428 1 1.75866 1.27924 2 0.799332 0.319904 4 0.559499 0.080071 8 0.499453 0.0200251 16 0.484435 0.00500675 32 0.48068 0.00125172 64 0.479741 0.000312932 128 0.479506 7.8233e-05 256 0.479448 1.95583e-05 512 0.479433 4.88957e-06 1024 0.479429 1.22239e-06 5 1.58223 1 0.689655 0.892578 2 1.45594 0.126294 4 1.55271 0.0295213 8 1.57481 0.00742481 16 1.58038 0.00185754 32 1.58177 0.000464455 64 1.58212 0.000116118 128 1.5822 2.90297e-05 256 1.58223 7.25744e-06 512 1.58223 1.81436e-06 1024 1.58223 4.53591e-07 6 1.46045 1 1 0.460447 2 0.5 0.960447 4 0.75 0.710447 8 0.625 0.835447 16 0.5625 0.897947 32 0.53125 0.929197 64 0.515625 0.944822 128 0.507812 0.952635 256 0.503906 0.956541 512 0.501953 0.958494 1024 0.500977 0.959471 7 2 1 0.5 1.5 2 0.957107 1.04289 4 1.26723 0.732771 8 1.48304 0.516964 16 1.63475 0.365251 32 1.7418 0.258197 64 1.81745 0.182554 128 1.87092 0.129081 256 1.90873 0.0912728 512 1.93546 0.0645393 1024 1.95436 0.0456361 8 0.866973 1 0.75 0.116973 2 0.845588 0.0213848 4 0.861732 0.00524065 8 0.865669 0.00130412 16 0.866647 0.000325648 32 0.866892 8.13882e-05 64 0.866953 2.03455e-05 128 0.866968 5.08629e-06 256 0.866972 1.27157e-06 512 0.866973 3.17892e-07 1024 0.866973 7.94729e-08 9 1.1547 1 1 0.154701 2 1 0.154701 4 1.16667 0.0119661 8 1.15476 6.13664e-05 16 1.1547 1.63057e-09 32 1.1547 4.44089e-16 64 1.1547 4.44089e-16 128 1.1547 0 256 1.1547 6.66134e-16 512 1.1547 6.66134e-16 1024 1.1547 1.77636e-15 10 0.693147 1 0.75 0.0568528 2 0.708333 0.0151862 4 0.697024 0.00387663 8 0.694122 0.00097467 16 0.693391 0.000244022 32 0.693208 6.10277e-05 64 0.693162 1.52583e-05 128 0.693151 3.81467e-06 256 0.693148 9.53672e-07 512 0.693147 2.38418e-07 1024 0.693147 5.96046e-08 11 0.379885 1 0.384471 0.00458522 2 0.381006 0.0011202 4 0.380164 0.000278552 8 0.379955 6.95462e-05 16 0.379903 1.73808e-05 32 0.37989 4.34485e-06 64 0.379887 1.08619e-06 128 0.379886 2.71546e-07 256 0.379886 6.78865e-08 512 0.379886 1.69716e-08 1024 0.379885 4.2429e-09 12 0.777505 1 0.790988 0.0134837 2 0.780868 0.00336306 4 0.778345 0.000840281 8 0.777715 0.00021004 16 0.777557 5.25082e-05 32 0.777518 1.31269e-05 64 0.777508 3.28172e-06 128 0.777505 8.2043e-07 256 0.777505 2.05108e-07 512 0.777505 5.12769e-08 1024 0.777505 1.28192e-08 13 1.65835 1 4.72799 3.06964 2 1.40507 0.253277 4 1.61367 0.0446736 8 1.64791 0.010436 16 1.65578 0.00256768 32 1.65771 0.0006394 64 1.65819 0.000159693 128 1.65831 3.99136e-05 256 1.65834 9.97779e-06 512 1.65835 2.49441e-06 1024 1.65835 6.236e-07 14 0.5 1 35.3553 34.8553 2 17.6777 17.1777 4 8.83883 8.33883 8 4.41942 3.91942 16 2.20971 1.70971 32 1.10485 0.604855 64 0.576295 0.0762947 128 0.500034 3.36118e-05 256 0.5 2.11177e-07 512 0.5 2.11172e-07 1024 0.5 2.1117e-07 15 1 1 125 124 2 62.5 61.5 4 31.25 30.25 8 15.625 14.625 16 7.8125 6.8125 32 3.90941 2.90941 64 2.03332 1.03332 128 1.29936 0.299356 256 1.07824 0.0782377 512 1.01979 0.0197897 1024 1.00496 0.00496213 16 0.493635 1 7.96093 7.46729 2 3.99318 3.49954 4 2.02472 1.53108 8 1.07073 0.5771 16 0.648239 0.154605 32 0.511892 0.0182571 64 0.493956 0.000321356 128 0.493635 3.86619e-08 256 0.493635 1.61771e-08 512 0.493635 4.04428e-09 1024 0.493635 1.01107e-09 17 0.5 1 4.82352e-31 0.5 2 3.61764e-31 0.5 4 0.5 0 8 0.5 5.55112e-16 16 0.5 6.66134e-16 32 0.5 6.10623e-16 64 0.5 5.55112e-17 128 0.5 5.55112e-17 256 0.5 0 512 0.5 4.44089e-16 1024 0.5 0 18 0.170557 1 0.134471 0.0360866 2 0.161621 0.00893683 4 0.168328 0.00222913 8 0.17 0.000556967 16 0.170418 0.000139222 32 0.170523 3.48043e-05 64 0.170549 8.701e-06 128 0.170555 2.17525e-06 256 0.170557 5.43811e-07 512 0.170557 1.35953e-07 1024 0.170557 3.39882e-08 19 -1 1 0 1 2 -0.346574 0.653426 4 -0.591781 0.408219 8 -0.753866 0.246134 16 -0.855597 0.144403 32 -0.91705 0.0829503 64 -0.95313 0.04687 128 -0.973862 0.0261375 256 -0.985579 0.0144213 512 -0.992113 0.00788723 1024 -0.995718 0.00428199 20 1.5644 1 0.997506 0.56689 2 1.49378 0.0706185 4 1.5437 0.0206947 8 1.55921 0.00518223 16 1.5631 0.0012956 32 1.56407 0.0003239 64 1.56432 8.09748e-05 128 1.56438 2.02437e-05 256 1.56439 5.06093e-06 512 1.5644 1.26523e-06 1024 1.5644 3.16308e-07 21 0.210803 1 0.0353256 0.175477 2 0.0225958 0.188207 4 0.207927 0.00287618 8 0.192954 0.017849 16 0.196013 0.0147893 32 0.211297 0.000494596 64 0.207238 0.00356489 128 0.209774 0.00102917 256 0.209751 0.00105183 512 0.210994 0.000190824 1024 0.210745 5.80547e-05 22 0.728103 1 0.666667 0.0614362 2 0.714286 0.0138172 4 0.724631 0.00347169 8 0.727235 0.000868048 16 0.727886 0.000217014 32 0.728049 5.42535e-05 64 0.728089 1.35634e-05 128 0.7281 3.39084e-06 256 0.728102 8.47711e-07 512 0.728103 2.11928e-07 1024 0.728103 5.29819e-08 23 0.624713 1 0.420735 0.203978 2 1.11967 0.494952 4 0.127009 0.497704 8 1.53518 0.910463 16 0.634705 0.00999216 32 0.845949 0.221236 64 1.94574 1.32102 128 1.75738 1.13267 256 -0.016874 0.641587 512 0.909334 0.28462 1024 0.768433 0.14372 24 -0.00675475 1 0.0795775 0.0863323 2 0.0960584 0.102813 4 0.0307004 0.0374551 8 0.00109579 0.00785054 16 -0.00805915 0.0013044 32 -0.00677827 2.35289e-05 64 -0.00672934 2.54068e-05 128 -0.00669006 6.46897e-05 256 -0.00675372 1.02631e-06 512 -0.00674664 8.10175e-06 1024 -0.00676816 1.34146e-05 25 -1.61086 1 -0.780324 0.83054 2 -1.19488 0.415983 4 -1.546 0.0648639 8 -1.52432 0.0865451 16 -1.59921 0.011658 32 -1.59038 0.0204801 64 -1.60824 0.00262427 128 -1.60582 0.00504739 256 -1.61023 0.000637905 512 -1.60961 0.00125731 1024 -1.61071 0.000158341 26 7.95493 1 17.0795 9.12454 2 9.69546 1.74054 4 7.98932 0.0343969 8 7.95493 1.25169e-06 16 7.95493 8.88178e-16 32 7.95493 0 64 7.95493 0 128 7.95493 0 256 7.95493 0 512 7.95493 3.55271e-15 1024 7.95493 0 27 0.841117 1 0.25 0.591117 2 0.458154 0.382963 4 0.591202 0.249915 8 0.67782 0.163297 16 0.734547 0.10657 32 0.771716 0.0694009 64 0.796029 0.0450876 128 0.811895 0.0292214 256 0.822222 0.0188944 512 0.828927 0.01219 1024 0.833269 0.00784824 28 0.0199547 1 1.15246e-17 0.0199547 2 1.39105e-16 0.0199547 4 8.89305e-17 0.0199547 8 0.295911 0.275956 16 0.373538 0.353583 32 -0.0192977 0.0392524 64 -0.0593459 0.0793005 128 0.00875952 0.0111951 256 0.0173842 0.00257042 512 0.0193244 0.000630282 1024 0.0197978 0.000156826 29 0.306853 1 0.25 0.0568528 2 0.325 0.0181472 4 0.273611 0.0332417 8 0.29588 0.0109731 16 0.307128 0.000275606 32 0.301287 0.00556558 64 0.304154 0.00269901 128 0.305589 0.00126398 256 0.306307 0.000546029 512 0.306666 0.000186943 1024 0.306845 7.37273e-06 30 -4.52757 1 23.3632 27.8908 2 8.93971 13.4673 4 -4.98554 0.457973 8 -10.3588 5.83127 16 -4.89338 0.365807 32 -4.60444 0.0768729 64 -4.54605 0.0184765 128 -4.53214 0.0045749 256 -4.52871 0.00114099 512 -4.52785 0.000285078 1024 -4.52764 7.12589e-05 31 2.65164 1 0.470588 2.18105 2 4.23529 1.58366 4 2.91765 0.266012 8 2.65882 0.0071882 16 2.65051 0.00112852 32 2.65135 0.000288164 64 2.65156 7.2076e-05 128 2.65162 1.80212e-05 256 2.65163 4.50543e-06 512 2.65163 1.12637e-06 1024 2.65164 2.81592e-07 32 -12.0703 1 -34.7785 22.7082 2 -17.3893 5.31891 4 -13.336 1.26568 8 -12.3822 0.311816 16 -12.148 0.0776578 32 -12.0897 0.0193958 64 -12.0752 0.00484778 128 -12.0716 0.00121187 256 -12.0706 0.000302964 512 -12.0704 7.57406e-05 1024 -12.0704 1.89351e-05 33 0.886227 1 0 0.886227 2 0.416277 0.46995 4 0.636581 0.249646 8 0.753713 0.132514 16 0.816045 0.0701819 32 0.849167 0.0370597 64 0.866721 0.0195059 128 0.875994 0.0102332 256 0.880875 0.00535161 512 0.883436 0.00279047 1024 0.884776 0.00145107 34 1085.25 1 3067.09 1981.83 2 1643.21 557.958 4 1228.65 143.396 8 1121.35 36.0931 16 1094.29 9.03853 32 1087.51 2.26059 64 1085.82 0.565206 128 1085.39 0.141305 256 1085.29 0.0353266 512 1085.26 0.00883166 1024 1085.25 0.00220791 35 26 1 23.6167 2.38333 2 19.888 6.11205 4 19.5176 6.48244 8 21.7456 4.25444 16 23.1996 2.80036 32 23.9339 2.0661 64 24.7424 1.25763 128 24.9032 1.09682 256 25.8654 0.134556 512 25.5686 0.431409 1024 25.6092 0.390807 36 100 1 0 100 2 0.646729 99.3533 4 1.62338 98.3766 8 2.90563 97.0944 16 4.45492 95.5451 32 6.23154 93.7685 64 8.19854 91.8015 128 10.3226 89.6774 256 12.5738 87.4262 512 14.9257 85.0743 1024 17.3546 82.6454 37 3.1358 1 0.0113937 3.1244 2 0.0116915 3.12411 4 0.201389 2.93441 8 0.121647 3.01415 16 0.155111 2.98069 32 1.78099 1.3548 64 1.07115 2.06465 128 1.17778 1.95802 256 4.55863 1.42283 512 3.32896 0.19316 1024 3.13594 0.000146214 38 0.539257 1 3.14159 2.60234 2 1.34225 0.802988 4 1.94376 1.4045 8 0.539747 0.000490129 16 0.539257 3.33067e-16 32 0.539257 3.33067e-16 64 0.539257 3.33067e-16 128 0.539257 1.11022e-16 256 0.539257 2.22045e-16 512 0.539257 0 1024 0.539257 2.22045e-16 39 2.78769 1 1.4784 1.3093 2 1.96394 0.82375 4 2.2353 0.552398 8 2.40518 0.382516 16 2.51929 0.268406 32 2.59842 0.18927 64 2.65399 0.133703 128 2.69318 0.0945098 256 2.72087 0.0668203 512 2.74045 0.0472471 1024 2.75429 0.0334082 40 2.69896 1 1.64352 1.05544 2 1.75769 0.941266 4 2.54928 0.149676 8 2.35328 0.345672 16 2.39987 0.299091 32 2.67054 0.028413 64 2.5856 0.113361 128 2.59239 0.106563 256 2.76779 0.0688383 512 2.69614 0.00281784 1024 2.67247 0.0264848 41 6.09559 1 0 6.09559 2 0.888889 5.2067 4 1.7235 4.37209 8 2.5541 3.54148 16 3.34716 2.74842 32 4.04071 2.05487 64 4.59774 1.49784 128 5.01964 1.07595 256 5.32867 0.766919 512 5.5511 0.54448 1024 5.7098 0.385784 42 3.98079 1 0.785398 3.19539 2 1.39374 2.58705 4 1.8812 2.09958 8 2.27575 1.70503 16 2.59594 1.38484 32 2.85596 1.12483 64 3.06715 0.913641 128 3.23868 0.742106 256 3.37801 0.602777 512 3.49118 0.489607 1024 3.5831 0.397685 43 2.99157 1 0 2.99157 2 0.646238 2.34533 4 1.12002 1.87155 8 1.48533 1.50624 16 1.7742 1.21737 32 2.0055 0.986066 64 2.1919 0.799664 128 2.34264 0.648933 256 2.46475 0.526814 512 2.5638 0.427771 1024 2.64418 0.347393 44 -0.0300997 1 -0.378401 0.348302 2 -0.18918 0.15908 4 -0.0943522 0.0642525 8 -0.0507335 0.0206338 16 -0.0357059 0.00560616 32 -0.0315332 0.0014335 64 -0.0304601 0.000360442 128 -0.0301899 9.02408e-05 256 -0.0301223 2.25684e-05 512 -0.0301053 5.6426e-06 1024 -0.0301011 1.41068e-06 45 -0.292707 1 0 0.292707 2 -0.416147 0.12344 4 -0.467702 0.174995 8 -0.444694 0.151987 16 -0.409781 0.117074 32 -0.378825 0.086118 64 -0.35477 0.0620633 128 -0.337004 0.0442968 256 -0.324174 0.0314677 512 -0.315009 0.0223023 1024 -0.308495 0.0157882 46 6.06909 1 7.90939 1.8403 2 6.28319 0.214094 4 6.07274 0.00364754 8 6.06909 1.09543e-06 16 6.06909 9.85878e-14 32 6.06909 1.77636e-15 64 6.06909 1.77636e-15 128 6.06909 0 256 6.06909 1.77636e-15 512 6.06909 1.77636e-15 1024 6.06909 1.77636e-15 47 -0.444444 1 0 0.444444 2 -0.245065 0.19938 4 -0.358104 0.0863404 8 -0.40809 0.0363544 16 -0.429475 0.0149699 32 -0.438389 0.00605496 64 -0.442031 0.00241376 128 -0.443494 0.00095079 256 -0.444074 0.000370808 512 -0.444301 0.000143407 1024 -0.444389 5.50664e-05 48 -4 1 0 4 2 -0.490129 3.50987 4 -1.02126 2.97874 8 -1.53819 2.46181 16 -2.00677 1.99323 32 -2.41178 1.58822 64 -2.75047 1.24953 128 -3.02699 0.973013 256 -3.24871 0.751287 512 -3.42403 0.575975 1024 -3.56109 0.438908 49 52.7407 1 163.027 110.286 2 75.6249 22.8842 4 59.2028 6.46205 8 54.8417 2.10092 16 53.6554 0.914661 32 52.7385 0.00220799 64 52.7995 0.0587315 128 52.7979 0.0571702 256 52.7663 0.0255225 512 52.7542 0.0134699 1024 52.7461 0.00533534 50 -0.128137 1 0 0.128137 2 -2.12215e-16 0.128137 4 -0.274653 0.146516 8 0.0798203 0.207957 16 -0.0770414 0.0510955 32 -0.114029 0.0141081 64 -0.124197 0.00393935 128 -0.127043 0.00109338 256 -0.127836 0.000300875 512 -0.128055 8.213e-05 1024 -0.128115 2.22623e-05 51 -0.197814 1 0 0.197814 2 -0.158127 0.0396865 4 -0.181006 0.0168071 8 -0.187048 0.0107659 16 -0.188652 0.00916149 32 -0.189093 0.00872022 64 -0.18922 0.00859404 128 -0.189257 0.0085563 256 -0.189269 0.00854445 512 -0.189273 0.00854053 1024 -0.189274 0.00853917 52 -0.089944 1 -2.99905 2.90911 2 -1.46692 1.37697 4 -0.278683 0.188739 8 -0.604948 0.515004 16 0.128824 0.218768 32 -0.421319 0.331375 64 0.203464 0.293408 128 -0.394689 0.304745 256 0.211724 0.301668 512 -0.392404 0.30246 1024 0.212316 0.30226 53 1.50462 1 0.853553 0.651069 2 1.00413 0.500496 4 1.71058 0.205955 8 1.45147 0.0531478 16 1.37376 0.130866 32 1.39204 0.11258 64 1.48404 0.0205797 128 1.45743 0.0471942 256 1.46545 0.0391724 512 1.49063 0.0139966 1024 1.48549 0.0191341 54 1.1547 1 1 0.154701 2 1 0.154701 4 1.16667 0.0119661 8 1.15476 6.13664e-05 16 1.1547 1.63057e-09 32 1.1547 2.22045e-16 64 1.1547 2.22045e-16 128 1.1547 2.22045e-16 256 1.1547 4.44089e-16 512 1.1547 4.44089e-16 1024 1.1547 1.9984e-15 55 0.505059 1 0.288056 0.217002 2 0.42892 0.0761391 4 0.49081 0.0142491 8 0.501583 0.00347606 16 0.504195 0.00086407 32 0.504843 0.000215715 64 0.505005 5.39099e-05 128 0.505045 1.34763e-05 256 0.505055 3.369e-06 512 0.505058 8.42247e-07 1024 0.505058 2.10561e-07 56 1.99225 1 1.05263 0.939621 2 1.63743 0.354826 4 1.91086 0.0813888 8 1.97467 0.0175846 16 1.98791 0.00434523 32 1.99117 0.00108312 64 1.99198 0.000270582 128 1.99218 6.76331e-05 256 1.99224 1.69075e-05 512 1.99225 4.22683e-06 1024 1.99225 1.0567e-06 57 0.4 1 0.5 0.1 2 0.426777 0.0267767 4 0.407018 0.00701811 8 0.401812 0.00181246 16 0.400463 0.000463401 32 0.400118 0.000117671 64 0.40003 2.97399e-05 128 0.400007 7.49191e-06 256 0.400002 1.88304e-06 512 0.4 4.72541e-07 1024 0.4 1.1845e-07 TEST06 Halton sequence rule, for 1D finite interval problems. Prob Ints Exact Error Approx 1 1.71828 1 1.64872 0.0695606 2 1.46637 0.251908 4 1.54572 0.172558 8 1.62119 0.097094 16 1.66713 0.051153 32 1.69207 0.0262162 64 1.70502 0.0132666 128 1.71161 0.00667272 256 1.71494 0.0033462 512 1.71661 0.00167556 1024 1.71744 0.000838391 2 0.7 1 1 0.3 2 0.5 0.2 4 0.5 0.2 8 0.625 0.075 16 0.6875 0.0125 32 0.6875 0.0125 64 0.6875 0.0125 128 0.695312 0.0046875 256 0.699219 0.00078125 512 0.699219 0.00078125 1024 0.699219 0.00078125 3 0.666667 1 0.707107 0.0404401 2 0.603553 0.0631133 4 0.606671 0.0599953 8 0.62688 0.0397864 16 0.64338 0.0232869 32 0.65384 0.0128265 64 0.659839 0.00682729 128 0.663108 0.00355898 256 0.664836 0.00183061 512 0.665733 0.000933312 1024 0.666194 0.000473007 4 0.479428 1 -0.16 0.639428 2 0.0798333 0.399595 4 0.349543 0.129885 8 0.443181 0.0362473 16 0.469892 0.00953665 32 0.476984 0.00244373 64 0.47881 0.000618393 128 0.479273 0.000155532 256 0.479389 3.89997e-05 512 0.479418 9.76453e-06 1024 0.479426 2.44296e-06 5 1.58223 1 2.22222 0.639989 2 1.93585 0.35362 4 1.66137 0.0791364 8 1.59962 0.0173903 16 1.58627 0.00403206 32 1.5832 0.000968397 64 1.58247 0.00023716 128 1.58229 5.86742e-05 256 1.58225 1.45917e-05 512 1.58224 3.63832e-06 1024 1.58223 9.0838e-07 6 1.46045 1 0 1.46045 2 0 1.46045 4 0.5 0.960447 8 0.5 0.960447 16 0.5 0.960447 32 0.5 0.960447 64 0.5 0.960447 128 0.5 0.960447 256 0.5 0.960447 512 0.5 0.960447 1024 0.5 0.960447 7 2 1 1.41421 0.585786 2 1.70711 0.292893 4 1.84934 0.150665 8 1.92054 0.0794637 16 1.95705 0.042948 32 1.97618 0.0238223 64 1.98641 0.0135903 128 1.99201 0.00798712 256 1.99516 0.00483757 512 1.99698 0.00301588 1024 1.99807 0.00193023 8 0.866973 1 0.941176 0.0742035 2 0.968643 0.10167 4 0.924171 0.0571983 8 0.896917 0.029944 16 0.882272 0.0152993 32 0.874704 0.00773111 64 0.870859 0.0038859 128 0.868921 0.00194804 256 0.867948 0.000975291 512 0.867461 0.000487963 1024 0.867217 0.000244061 9 1.1547 1 1 0.154701 2 0.833333 0.321367 4 1.3034 0.148696 8 1.11526 0.0394358 16 1.13635 0.0183533 32 1.14874 0.00596066 64 1.15301 0.00169264 128 1.15425 0.000450588 256 1.15458 0.000116204 512 1.15467 2.95034e-05 1024 1.15469 7.43284e-06 10 0.693147 1 0.666667 0.0264805 2 0.733333 0.0401862 4 0.731746 0.0385989 8 0.718019 0.0248717 16 0.707122 0.0139751 32 0.70054 0.00739276 64 0.696948 0.00380038 128 0.695074 0.00192654 256 0.694117 0.000969902 512 0.693634 0.000486614 1024 0.693391 0.000243724 11 0.379885 1 0.377541 0.00234482 2 0.407682 0.0277966 4 0.401244 0.0213585 8 0.392444 0.0125582 16 0.386635 0.00674972 32 0.383378 0.00349257 64 0.381661 0.00177571 128 0.380781 0.000895215 256 0.380335 0.000449447 512 0.380111 0.000225183 1024 0.379998 0.000112707 12 0.777505 1 0.770747 0.00675759 2 0.825475 0.0479703 4 0.815298 0.0377936 8 0.799976 0.0224709 16 0.789649 0.0121443 32 0.783806 0.00630124 64 0.780713 0.00320813 128 0.779123 0.00161848 256 0.778317 0.000812843 512 0.777912 0.000407324 1024 0.777709 0.000203887 13 1.65835 1 -1.91785 3.5762 2 0.23802 1.42033 4 2.32965 0.671298 8 2.22711 0.56876 16 1.97516 0.31681 32 1.82119 0.162841 64 1.7404 0.0820566 128 1.69948 0.0411278 256 1.67893 0.0205813 512 1.66864 0.0102941 1024 1.6635 0.00514779 14 0.5 1 0 0.5 2 0 0.5 4 0 0.5 8 0 0.5 16 9.62434e-07 0.499999 32 0.0477354 0.452265 64 0.447443 0.0525574 128 0.658512 0.158512 256 0.622042 0.122042 512 0.567 0.0669997 1024 0.534269 0.0342684 15 1 1 1.29161e-52 1 2 8.98473e-26 1 4 1.67563e-12 1 8 5.1168e-06 0.999995 16 0.00632514 0.993675 32 0.160317 0.839683 64 0.634214 0.365786 128 1.05835 0.0583476 256 1.18925 0.189254 512 1.15816 0.158158 1024 1.09898 0.0989773 16 0.493635 1 0.0254241 0.468211 2 0.0633178 0.430317 4 0.133803 0.359832 8 0.260413 0.233221 16 0.439725 0.0539093 32 0.571964 0.0783294 64 0.585324 0.0916894 128 0.551211 0.0575762 256 0.52412 0.0304852 512 0.509097 0.0154623 1024 0.501394 0.00775887 17 0.5 1 2.41176e-31 0.5 2 0.5 0 4 0.625 0.125 8 0.518306 0.0183058 16 0.560121 0.0601212 32 0.512577 0.0125767 64 0.513852 0.0138516 128 0.50259 0.00259027 256 0.500356 0.00035628 512 0.500046 4.55996e-05 1024 0.500006 5.73361e-06 18 0.170557 1 0.18877 0.018213 2 0.149113 0.0214442 4 0.14936 0.0211971 8 0.156976 0.0135816 16 0.162975 0.00758234 32 0.166563 0.00399478 64 0.168508 0.00204901 128 0.16952 0.0010375 256 0.170035 0.000522009 512 0.170296 0.000261821 1024 0.170426 0.000131115 19 -1 1 -0.693147 0.306853 2 -1.03972 0.0397208 4 -1.11164 0.111641 8 -1.10044 0.10044 16 -1.07221 0.072206 32 -1.04701 0.0470148 64 -1.02894 0.0289429 128 -1.01718 0.0171842 256 -1.00995 0.00994716 512 -1.00565 0.0056508 1024 -1.00316 0.00316393 20 1.5644 1 1.99005 0.425653 2 1.79184 0.227441 4 1.6133 0.048908 8 1.57572 0.0113226 16 1.56711 0.00271176 32 1.56506 0.000662895 64 1.56456 0.000163838 128 1.56444 4.07234e-05 256 1.56441 1.01514e-05 512 1.5644 2.53415e-06 1024 1.5644 6.33077e-07 21 0.210803 1 0.00986604 0.200937 2 0.398157 0.187354 4 0.348242 0.137439 8 0.216776 0.00597347 16 0.201803 0.00899936 32 0.213172 0.002369 64 0.207969 0.00283406 128 0.210093 0.000710078 256 0.209899 0.000903261 512 0.211065 0.00026244 1024 0.21078 2.2905e-05 22 0.728103 1 0.761905 0.0338018 2 0.849817 0.121714 4 0.804059 0.0759563 8 0.768413 0.0403103 16 0.748658 0.0205553 32 0.738458 0.0103548 64 0.733297 0.00519382 128 0.730704 0.00260066 256 0.729404 0.00130122 512 0.728754 0.000650828 1024 0.728428 0.000325468 23 0.624713 1 1.81859 1.19388 2 -0.604308 1.22902 4 2.00054 1.37583 8 0.906778 0.282065 16 1.71126 1.08655 32 2.67285 2.04814 64 3.38124 2.75653 128 -0.244324 0.869038 256 0.140519 0.484194 512 0.591445 0.0332683 1024 0.141908 0.482805 24 -0.00675475 1 0.112539 0.119294 2 0.031763 0.0385178 4 0.00610608 0.0128608 8 -0.00380504 0.0029497 16 -0.0106717 0.00391697 32 -0.00704533 0.000290585 64 -0.00641674 0.000338009 128 -0.00653424 0.000220505 256 -0.00654189 0.000212858 512 -0.00664371 0.00011104 1024 -0.00671103 4.37145e-05 25 -1.61086 1 -1.60944 0.00142639 2 -1.20397 0.406891 4 -1.48927 0.121599 8 -1.48305 0.12781 16 -1.57558 0.0352817 32 -1.57785 0.0330137 64 -1.6018 0.00906842 128 -1.60255 0.00831343 256 -1.60858 0.00228187 512 -1.60878 0.00208202 1024 -1.61029 0.000571379 26 7.95493 1 2.31145 5.64347 2 4.29732 3.65761 4 6.90521 1.04971 8 7.79845 0.15648 16 7.93461 0.0203153 32 7.95236 0.00256389 64 7.95461 0.000321259 128 7.95489 4.01816e-05 256 7.95492 5.02345e-06 512 7.95493 6.27955e-07 1024 7.95493 7.84952e-08 27 0.841117 1 0.666308 0.174809 2 0.775647 0.0654696 4 0.821595 0.0195221 8 0.839814 0.00130296 16 0.846018 0.00490071 32 0.847237 0.00611997 64 0.846601 0.00548408 128 0.845455 0.00433838 256 0.844333 0.00321638 512 0.843409 0.00229246 1024 0.842709 0.00159169 28 0.0199547 1 2.66686e-16 0.0199547 2 -1.87379e-16 0.0199547 4 0.716186 0.696231 8 0.670908 0.650953 16 0.250049 0.230095 32 -0.193867 0.213821 64 -4.78481e-05 0.0200025 128 0.0538569 0.0339022 256 0.0313443 0.0113897 512 0.0230079 0.00305322 1024 0.0207325 0.000777854 29 0.306853 1 0.4 0.0931472 2 0.422222 0.115369 4 0.328758 0.0219054 8 0.325236 0.018383 16 0.322273 0.0154198 32 0.308979 0.0021258 64 0.30803 0.00117684 128 0.307534 0.000681528 256 0.307281 0.000428628 512 0.307154 0.000300862 1024 0.307089 0.000236649 30 -4.52757 1 -5.48384 0.956268 2 -19.9234 15.3959 4 -11.1497 6.62212 8 -19.6516 15.124 16 -7.41688 2.88931 32 -5.71074 1.18317 64 -5.13966 0.612095 128 -4.84808 0.320507 256 -4.69243 0.164861 512 -4.61126 0.0836929 1024 -4.56974 0.042175 31 2.65164 1 8 5.34836 2 4.8 2.14836 4 3 0.348365 8 2.67547 0.0238364 16 2.65429 0.00265473 32 2.65225 0.00061571 64 2.65178 0.000148947 128 2.65167 3.6634e-05 256 2.65164 9.08433e-06 512 2.65164 2.26189e-06 1024 2.65164 5.64327e-07 32 -12.0703 1 9.25377e-16 12.0703 2 2.43612 14.5065 4 -3.56678 8.50357 8 -7.56613 4.50421 16 -9.75879 2.31156 32 -10.8999 1.17042 64 -11.4815 0.588858 128 -11.775 0.29534 256 -11.9224 0.147898 512 -11.9963 0.0740058 1024 -12.0333 0.0370171 33 0.886227 1 0.832555 0.0536723 2 1.00498 0.118755 4 0.997088 0.110861 8 0.961852 0.0756251 16 0.932398 0.0461712 32 0.912896 0.0266695 64 0.901139 0.0149118 128 0.894391 0.00816388 256 0.890632 0.00440489 512 0.888579 0.00235166 1024 0.887472 0.00124549 34 1085.25 1 219.336 865.917 2 111.306 973.947 4 461.877 623.376 8 737.969 347.284 16 902.628 182.625 32 991.697 93.5561 64 1037.91 47.3378 128 1061.44 23.8086 256 1073.31 11.9392 512 1079.27 5.97833 1024 1082.26 2.99135 35 26 1 16.1592 9.84076 2 20.8371 5.1629 4 26.2844 0.284391 8 28.0057 2.00565 16 24.604 1.39599 32 24.4569 1.54314 64 24.97 1.03001 128 25.0095 0.990508 256 25.9168 0.0831726 512 25.5939 0.406148 1024 25.6217 0.378283 36 100 1 1.29346 98.7065 2 3.06041 96.9396 4 5.00144 94.9986 8 7.10809 92.8919 16 9.35622 90.6438 32 11.7192 88.2808 64 14.1721 85.8279 128 16.6923 83.3077 256 19.2599 80.7401 512 21.8571 78.1429 1024 24.4686 75.5314 37 3.1358 1 0.0119893 3.12381 2 0.00769803 3.1281 4 0.199101 2.9367 8 0.120456 3.01534 16 0.154506 2.98129 32 1.78069 1.35511 64 1.07099 2.06481 128 1.1777 1.9581 256 4.55859 1.42279 512 3.32894 0.193141 1024 3.13594 0.000136635 38 0.539257 1 -0.457102 0.996359 2 1.04408 0.504826 4 0.37548 0.163777 8 0.151004 0.388253 16 0.481922 0.0573345 32 0.53179 0.00746719 64 0.538314 0.000943012 128 0.539139 0.000118179 256 0.539242 1.47818e-05 512 0.539255 1.84802e-06 1024 0.539257 2.31012e-07 39 2.78769 1 2.44949 0.338204 2 2.9568 0.169102 4 2.41342 0.374275 8 2.46057 0.327123 16 2.5406 0.247091 32 2.60767 0.180028 64 2.65828 0.129417 128 2.69525 0.0924481 256 2.72188 0.0658096 512 2.74095 0.0467467 1024 2.75453 0.0331593 40 2.69896 1 1.87186 0.827092 2 1.61926 1.07969 4 2.44604 0.252919 8 2.29486 0.404094 16 2.36912 0.32984 32 2.6548 0.044155 64 2.57763 0.121322 128 2.58839 0.110566 256 2.76579 0.0668315 512 2.69513 0.00382259 1024 2.67197 0.0269875 41 6.09559 1 1.77778 4.31781 2 2.73641 3.35918 4 3.73931 2.35628 8 4.61969 1.47589 16 5.26295 0.832633 32 5.65336 0.442225 64 5.85976 0.235824 128 5.96266 0.13293 256 6.01502 0.0805692 512 6.04365 0.0519321 1024 6.0607 0.0348852 42 3.98079 1 2.00208 1.97871 2 2.53955 1.44123 4 2.91766 1.06313 8 3.17555 0.805234 16 3.35678 0.624009 32 3.48914 0.491649 64 3.58908 0.391704 128 3.66645 0.314336 256 3.72738 0.253405 512 3.77592 0.204871 1024 3.81486 0.165928 43 2.99157 1 1.29248 1.69909 2 1.04404 1.94753 4 1.26978 1.72179 8 1.54655 1.44502 16 1.80038 1.19119 32 2.01703 0.974543 64 2.19708 0.794492 128 2.34499 0.646577 256 2.46584 0.52573 512 2.5643 0.427267 1024 2.64441 0.347158 44 -0.0300997 1 4.1282e-05 0.030141 2 2.07697e-05 0.0301205 4 0.000248103 0.0303478 8 -0.00343336 0.0266663 16 -0.0120558 0.0180439 32 -0.0197082 0.0103915 64 -0.0245476 0.00555208 128 -0.0272337 0.00286602 256 -0.0286441 0.00145556 512 -0.0293663 0.000733422 1024 -0.0297316 0.000368122 45 -0.292707 1 -0.832294 0.539587 2 0.207741 0.500447 4 0.195688 0.488395 8 0.0556507 0.348357 16 -0.0533726 0.239334 32 -0.12734 0.165366 64 -0.177385 0.115321 128 -0.211774 0.0809327 256 -0.235702 0.0570044 512 -0.252479 0.0402277 1024 -0.26429 0.0284166 46 6.06909 1 4.65698 1.41211 2 5.25963 0.809456 4 5.88926 0.179826 8 6.04349 0.0255985 16 6.0658 0.00329477 32 6.06868 0.000414912 64 6.06904 5.19607e-05 128 6.06908 6.49812e-06 256 6.06909 8.12359e-07 512 6.06909 1.01548e-07 1024 6.06909 1.26936e-08 47 -0.444444 1 -0.490129 0.0456846 2 -0.591638 0.147194 4 -0.541902 0.097458 8 -0.494733 0.050289 16 -0.467766 0.0233215 32 -0.454635 0.0101907 64 -0.448732 0.00428722 128 -0.446201 0.00175682 256 -0.445151 0.000706136 512 -0.444724 0.000279657 1024 -0.444554 0.000109467 48 -4 1 -0.980258 3.01974 2 -1.87642 2.12358 4 -2.49165 1.50835 8 -2.92449 1.07551 16 -3.2321 0.767905 32 -3.4515 0.548496 64 -3.60819 0.391806 128 -3.72013 0.279866 256 -3.80011 0.199892 512 -3.85724 0.142758 1024 -3.89806 0.101944 49 52.7407 1 -11.7769 64.5177 2 -6.18193 58.9227 4 18.4647 34.2761 8 34.4649 18.2758 16 43.4663 9.27441 32 47.644 5.09679 64 50.2522 2.48856 128 51.5243 1.21648 256 52.1294 0.611301 512 52.4358 0.304942 1024 52.5869 0.15387 50 -0.128137 1 -4.2443e-16 0.128137 2 -0.693147 0.56501 4 0.0929437 0.221081 8 -0.240372 0.112235 16 -0.257145 0.129008 32 -0.175294 0.047157 64 -0.142619 0.0144817 128 -0.132347 0.00420966 256 -0.12933 0.00119342 512 -0.12847 0.000333146 1024 -0.128229 9.19521e-05 51 -0.197814 1 -0.316254 0.118441 2 -0.23932 0.0415069 4 -0.199346 0.00153283 8 -0.19164 0.00617363 16 -0.189932 0.00788201 32 -0.189482 0.00833198 64 -0.189345 0.00846817 128 -0.1893 0.00851333 256 -0.189284 0.00852916 512 -0.189279 0.00853491 1024 -0.189277 0.00853704 52 -0.089944 1 0.0652174 0.155161 2 0.938269 1.02821 4 -0.542113 0.452169 8 -0.48115 0.391206 16 0.177168 0.267112 32 -0.418401 0.328457 64 0.19145 0.281394 128 -0.406989 0.317045 256 0.203233 0.293177 512 -0.397387 0.307443 1024 0.209615 0.299559 53 1.50462 1 1.1547 0.349922 2 0.994379 0.510244 4 1.68702 0.182398 8 1.43616 0.0684596 16 1.36532 0.139301 32 1.38764 0.11698 64 1.4818 0.0228243 128 1.4563 0.0483275 256 1.46488 0.0397417 512 1.49034 0.0142819 1024 1.48535 0.0192769 54 1.1547 1 1 0.154701 2 0.833333 0.321367 4 1.3034 0.148696 8 1.11526 0.0394358 16 1.13635 0.0183533 32 1.14874 0.00596066 64 1.15301 0.00169264 128 1.15425 0.000450588 256 1.15458 0.000116204 512 1.15467 2.95034e-05 1024 1.15469 7.43284e-06 55 0.505059 1 0.569783 0.0647242 2 0.337591 0.167468 4 0.426228 0.0788308 8 0.467352 0.037707 16 0.486789 0.0182696 32 0.496085 0.00897375 64 0.500614 0.00444495 128 0.502847 0.00221179 256 0.503955 0.0011032 512 0.504508 0.000550925 1024 0.504783 0.000275293 56 1.99225 1 2.22222 0.22997 2 2.20326 0.211009 4 2.11154 0.119284 8 2.02844 0.0361871 16 2.00129 0.00903262 32 1.99447 0.00222146 64 1.9928 0.000548801 128 1.99239 0.000136265 256 1.99229 3.39426e-05 512 1.99226 8.46978e-06 1024 1.99225 2.11543e-06 57 0.4 1 0.353553 0.0464466 2 0.239277 0.160723 4 0.293067 0.106933 8 0.341266 0.0587344 16 0.369559 0.0304413 32 0.384554 0.0154463 64 0.392228 0.00777197 128 0.396103 0.00389685 256 0.398049 0.0019509 512 0.399024 0.00097603 1024 0.399512 0.000488152 TEST07 Evenly spaced point sequence rule, for 1D finite interval problems. Prob Ints Exact Error Approx 1 1.71828 1 1.64872 0.0695606 2 1.85914 0.140859 4 1.76541 0.0471252 8 1.73845 0.0201635 16 1.72768 0.00940027 32 1.72283 0.00454619 64 1.72052 0.00223644 128 1.71939 0.00110927 256 1.71883 0.000552424 512 1.71856 0.000275663 1024 1.71842 0.000137694 2 0.7 1 1 0.3 2 0.5 0.2 4 0.75 0.05 8 0.625 0.075 16 0.6875 0.0125 32 0.6875 0.0125 64 0.703125 0.003125 128 0.695312 0.0046875 256 0.699219 0.00078125 512 0.699219 0.00078125 1024 0.700195 0.000195313 3 0.666667 1 0.707107 0.0404401 2 0.5 0.166667 4 0.598462 0.068205 8 0.636755 0.0299112 16 0.653069 0.0135978 32 0.660334 0.00633313 64 0.663664 0.00300307 128 0.665223 0.00144364 256 0.665965 0.000701256 512 0.666323 0.000343323 1024 0.666498 0.000169068 4 0.479428 1 -0.16 0.639428 2 1.75866 1.27924 4 0.905961 0.426533 8 0.662218 0.182789 16 0.564721 0.0852927 32 0.520696 0.0412682 64 0.499734 0.020306 128 0.489501 0.0100729 256 0.484445 0.00501665 512 0.481932 0.00250341 1024 0.480679 0.00125048 5 1.58223 1 2.22222 0.639989 2 0.689655 0.892578 4 1.32191 0.260325 8 1.46218 0.120055 16 1.52447 0.0577674 32 1.55386 0.0283725 64 1.56817 0.0140645 128 1.57523 0.00700252 256 1.57874 0.00349392 512 1.58049 0.00174513 1024 1.58136 0.000872112 6 1.46045 1 0 1.46045 2 1 0.460447 4 0.5 0.960447 8 0.5 0.960447 16 0.5 0.960447 32 0.5 0.960447 64 0.5 0.960447 128 0.5 0.960447 256 0.5 0.960447 512 0.5 0.960447 1024 0.5 0.960447 7 2 1 1.41421 0.585786 2 0.5 1.5 4 0.989199 1.0108 8 1.32879 0.67121 16 1.55258 0.447419 32 1.69899 0.301008 64 1.79544 0.20456 128 1.85971 0.140294 256 1.90305 0.0969537 512 1.93259 0.067406 1024 1.95292 0.0470787 8 0.866973 1 0.941176 0.0742035 2 0.75 0.116973 4 0.830714 0.0362589 8 0.85086 0.0161128 16 0.859315 0.00765819 32 0.863234 0.00373942 64 0.865125 0.00184837 128 0.866054 0.000918978 256 0.866515 0.000458202 512 0.866744 0.000228781 1024 0.866859 0.000114311 9 1.1547 1 1 0.154701 2 1 0.154701 4 1.11538 0.0393159 8 1.13536 0.0193376 16 1.14423 0.0104698 32 1.14987 0.00483439 64 1.15228 0.0024172 128 1.15349 0.0012086 256 1.1541 0.000604299 512 1.1544 0.000302149 1024 1.15455 0.000151075 10 0.693147 1 0.666667 0.0264805 2 0.75 0.0568528 4 0.7125 0.0193528 8 0.701367 0.00821986 16 0.696961 0.00381357 32 0.694987 0.00183965 64 0.694051 0.000903826 128 0.693595 0.000448007 256 0.69337 0.000223039 512 0.693258 0.00011128 1024 0.693203 5.558e-05 11 0.379885 1 0.377541 0.00234482 2 0.384471 0.00458522 4 0.381404 0.00151822 8 0.380538 0.000652644 16 0.380191 0.000305116 32 0.380033 0.000147773 64 0.379958 7.27475e-05 128 0.379922 3.60957e-05 256 0.379903 1.79792e-05 512 0.379894 8.97251e-06 1024 0.37989 4.482e-06 12 0.777505 1 0.770747 0.00675759 2 0.790988 0.0134837 4 0.781996 0.00449147 8 0.77943 0.00192551 16 0.778403 0.000898741 32 0.77794 0.000434917 64 0.777719 0.000214017 128 0.777611 0.000106168 256 0.777558 5.28767e-05 512 0.777531 2.63868e-05 1024 0.777518 1.31805e-05 13 1.65835 1 -1.91785 3.5762 2 4.72799 3.06964 4 2.36138 0.703028 8 2.03005 0.371699 16 1.84746 0.189112 32 1.75361 0.0952662 64 1.70615 0.0478009 128 1.68229 0.0239413 256 1.67033 0.0119808 512 1.66434 0.00599289 1024 1.66134 0.00299707 14 0.5 1 0 0.5 2 35.3553 34.8553 4 17.6777 17.1777 8 8.83883 8.33883 16 4.41942 3.91942 32 2.20971 1.70971 64 1.12597 0.625966 128 0.772347 0.272347 256 0.636154 0.136153 512 0.568077 0.0680766 1024 0.534038 0.0340382 15 1 1 1.29161e-52 1 2 125 124 4 62.5 61.5 8 31.25 30.25 16 15.625 14.625 32 7.81496 6.81496 64 3.98153 2.98153 128 2.27019 1.27019 256 1.56291 0.56291 512 1.26202 0.262016 1024 1.12606 0.126061 16 0.493635 1 0.0254241 0.468211 2 7.96093 7.46729 4 3.99831 3.50468 8 2.04757 1.55394 16 1.12816 0.63453 32 0.747092 0.253457 64 0.61067 0.117035 128 0.551973 0.0583383 256 0.522804 0.0291691 512 0.508219 0.0145846 1024 0.500927 0.00729228 17 0.5 1 2.41176e-31 0.5 2 4.82352e-31 0.5 4 0.375 0.125 8 0.4375 0.0625 16 0.46875 0.03125 32 0.484375 0.015625 64 0.492188 0.0078125 128 0.496094 0.00390625 256 0.498047 0.00195312 512 0.499023 0.000976563 1024 0.499512 0.000488281 18 0.170557 1 0.18877 0.018213 2 0.134471 0.0360866 4 0.158562 0.0119956 8 0.16541 0.0051474 16 0.168153 0.00240392 32 0.169394 0.00116363 64 0.169985 0.000572693 128 0.170273 0.000284119 256 0.170416 0.000141509 512 0.170487 7.06179e-05 1024 0.170522 3.52749e-05 19 -1 1 -0.693147 0.306853 2 0 1 4 -0.376019 0.623981 8 -0.637026 0.362974 16 -0.795093 0.204907 32 -0.886293 0.113707 64 -0.937628 0.0623723 128 -0.966081 0.0339194 256 -0.98168 0.0183199 512 -0.990162 0.00983845 1024 -0.994742 0.00525807 20 1.5644 1 1.99005 0.425653 2 0.997506 0.56689 4 1.39472 0.169675 8 1.48761 0.0767837 16 1.52758 0.0368126 32 1.54635 0.0180497 64 1.55546 0.00893992 128 1.55995 0.00444923 256 1.56218 0.0022195 512 1.56329 0.00110848 1024 1.56384 0.00055392 21 0.210803 1 0.00986604 0.200937 2 0.0353256 0.175477 4 0.0784994 0.132303 8 0.170559 0.0402439 16 0.310878 0.100075 32 0.193596 0.0172064 64 0.207936 0.00286632 128 0.20841 0.00239312 256 0.212959 0.00215655 512 0.209823 0.000979384 1024 0.210653 0.000149284 22 0.728103 1 0.761905 0.0338018 2 0.666667 0.0614362 4 0.708116 0.0199865 8 0.719431 0.00867158 16 0.724032 0.00407125 32 0.726127 0.00197589 64 0.727129 0.00097372 128 0.72762 0.000483388 256 0.727862 0.000240836 512 0.727983 0.000120205 1024 0.728043 6.00494e-05 23 0.624713 1 1.81859 1.19388 2 0.420735 0.203978 4 0.690268 0.0655551 8 1.25927 0.634553 16 1.49216 0.867443 32 0.177477 0.447236 64 1.06267 0.437957 128 1.75855 1.13383 256 0.62411 0.000602846 512 1.77143 1.14672 1024 0.321249 0.303464 24 -0.00675475 1 0.112539 0.119294 2 0.0795775 0.0863323 4 0.0481971 0.0549518 8 5.45908e-08 0.0067548 16 0.00288484 0.00963959 32 -0.00385772 0.00289702 64 -0.00561968 0.00113507 128 -0.00610546 0.000649288 256 -0.00639721 0.000357535 512 -0.00656949 0.000185254 1024 -0.00668246 7.22879e-05 25 -1.61086 1 -1.60944 0.00142639 2 -0.780324 0.83054 4 -1.49129 0.119577 8 -1.56015 0.0507139 16 -1.51398 0.0968819 32 -1.56947 0.0413922 64 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256 -0.127334 0.000802433 512 -0.127804 0.000332538 1024 -0.127989 0.000147415 51 -0.197814 1 -0.316254 0.118441 2 0 0.197814 4 -0.131153 0.0666607 8 -0.163113 0.0347001 16 -0.176789 0.0210247 32 -0.183174 0.0146394 64 -0.186262 0.0115521 128 -0.187778 0.0100351 256 -0.18853 0.00928382 512 -0.188903 0.00891021 1024 -0.18909 0.00872401 52 -0.089944 1 0.0652174 0.155161 2 -2.99905 2.90911 4 -1.35961 1.26967 8 -1.46815 1.3782 16 -0.357605 0.267661 32 -1.08906 0.999115 64 -0.144402 0.0544585 128 -1.01495 0.925004 256 -0.101942 0.0119985 512 -1.00091 0.91097 1024 -0.092825 0.00288098 53 1.50462 1 1.1547 0.349922 2 0.853553 0.651069 4 1.18324 0.321382 8 1.4081 0.09652 16 2.02084 0.516221 32 1.38922 0.115407 64 1.49377 0.010854 128 1.63659 0.131968 256 1.46664 0.0379818 512 1.51917 0.0145478 1024 1.50532 0.000702162 54 1.1547 1 1 0.154701 2 1 0.154701 4 1.11538 0.0393159 8 1.13536 0.0193376 16 1.14423 0.0104698 32 1.14987 0.00483439 64 1.15228 0.0024172 128 1.15349 0.0012086 256 1.1541 0.000604299 512 1.1544 0.000302149 1024 1.15455 0.000151075 55 0.505059 1 0.569783 0.0647242 2 0.288056 0.217002 4 0.431284 0.0737744 8 0.473951 0.0311074 16 0.490574 0.0144846 32 0.498055 0.007004 64 0.501613 0.00344543 128 0.50335 0.00170891 256 0.504208 0.000851048 512 0.504634 0.000424677 1024 0.504847 0.000212127 56 1.99225 1 2.22222 0.22997 2 1.05263 0.939621 4 1.63574 0.356516 8 1.85458 0.137671 16 1.92889 0.0633637 32 1.96177 0.0304813 64 1.9773 0.0149565 128 1.98484 0.00740895 256 1.98857 0.00368737 512 1.99041 0.00183943 1024 1.99133 0.000918656 57 0.4 1 0.353553 0.0464466 2 0.5 0.1 4 0.434195 0.0341953 8 0.41456 0.0145603 16 0.406743 0.00674343 32 0.403246 0.00324639 64 0.401593 0.00159271 128 0.400789 0.0007888 256 0.400393 0.000392515 512 0.400196 0.000195786 1024 0.400098 9.77748e-05 test_int_test(): Normal end of execution. 06 October 2025 01:23:36 AM