10 May 2025 01:24:01 PM TEST_INT_TEST C version Test the TEST_INT library. 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 1.01149 0.706787 2 1.05258 0.6657 4 1.41605 0.302235 8 1.96056 0.242278 16 1.76863 0.0503476 32 1.61585 0.102435 64 1.65508 0.0631971 128 1.67986 0.0384178 256 1.63379 0.0844965 512 1.65223 0.0660537 1024 1.69047 0.0278162 2 0.7 1 0 0.7 2 0 0.7 4 0.25 0.45 8 0.625 0.075 16 0.625 0.075 32 0.59375 0.10625 64 0.609375 0.090625 128 0.625 0.075 256 0.613281 0.0867187 512 0.623047 0.0769531 1024 0.657227 0.0427734 3 0.666667 1 0.106907 0.55976 2 0.203068 0.463598 4 0.433586 0.233081 8 0.695483 0.0288168 16 0.658186 0.00848111 32 0.603201 0.0634658 64 0.623617 0.0430499 128 0.643223 0.023444 256 0.628697 0.0379693 512 0.6359 0.030767 1024 0.652903 0.0137633 4 0.479428 1 1.67179 1.19236 2 1.40216 0.922727 4 1.11305 0.633621 8 1.15289 0.673464 16 0.725866 0.246438 32 0.607721 0.128293 64 0.592149 0.112721 128 0.531128 0.0516999 256 0.469937 0.00949154 512 0.488467 0.00903835 1024 0.495242 0.0158133 5 1.58223 1 0.722945 0.859287 2 0.854551 0.727682 4 1.02465 0.55758 8 0.997536 0.584697 16 1.36887 0.21336 32 1.4815 0.100731 64 1.48908 0.0931504 128 1.52987 0.0523628 256 1.58206 0.00017325 512 1.56801 0.0142182 1024 1.56483 0.0174076 6 1.46045 1 0 1.46045 2 0 1.46045 4 0.5 0.960447 8 1.25 0.210447 16 0.75 0.710447 32 0.4375 1.02295 64 0.46875 0.991697 128 0.5 0.960447 256 0.421875 1.03857 512 0.441406 1.01904 1024 0.488281 0.972166 7 2 1 9.35391 7.35391 2 6.34791 4.34791 4 4.0752 2.0752 8 2.56022 0.560223 16 2.25669 0.256687 32 2.2515 0.251495 64 2.2009 0.200903 128 2.02566 0.0256632 256 2.04399 0.0439883 512 1.98392 0.0160841 1024 1.9388 0.0612004 8 0.866973 1 1 0.133027 2 0.999968 0.132995 4 0.908382 0.0414092 8 0.747103 0.11987 16 0.834252 0.032721 32 0.88768 0.0207067 64 0.877439 0.0104662 128 0.873801 0.00682785 256 0.891507 0.0245342 512 0.884937 0.0179637 1024 0.873567 0.0065939 9 1.1547 1 0.85056 0.30414 2 0.855799 0.298901 4 1.09967 0.0550276 8 1.29698 0.142282 16 1.09588 0.0588189 32 1.05425 0.100449 64 1.14162 0.0130853 128 1.17927 0.0245674 256 1.1411 0.0135963 512 1.1332 0.0215051 1024 1.14138 0.0133168 10 0.693147 1 0.9887 0.295553 2 0.95326 0.260113 4 0.82652 0.133373 8 0.67422 0.0189275 16 0.697184 0.00403728 32 0.731225 0.0380778 64 0.71912 0.0259726 128 0.707686 0.0145392 256 0.716237 0.0230901 512 0.712281 0.0191339 1024 0.702002 0.00885485 11 0.379885 1 0.497143 0.117257 2 0.487387 0.107501 4 0.432714 0.0528282 8 0.359169 0.0207161 16 0.377524 0.00236177 32 0.396515 0.0166299 64 0.390752 0.0108665 128 0.386138 0.00625279 256 0.391315 0.0114299 512 0.389173 0.00928752 1024 0.384047 0.00416162 12 0.777505 1 0.994296 0.216792 2 0.975098 0.197593 4 0.875273 0.0977686 8 0.742992 0.0345122 16 0.774278 0.00322617 32 0.807815 0.0303103 64 0.797441 0.0199363 128 0.788938 0.0114338 256 0.798 0.0204955 512 0.7942 0.0166958 1024 0.785018 0.00751372 13 1.65835 1 9.97824 8.3199 2 9.3473 7.68896 4 6.46546 4.80711 8 3.35859 1.70024 16 2.47115 0.812802 32 2.36195 0.703607 64 2.41237 0.754021 128 2.18377 0.525423 256 2.11469 0.456345 512 2.0662 0.407853 1024 1.87705 0.218698 14 0.5 1 9.08605 8.58605 2 4.54303 4.04303 4 2.27151 1.77151 8 1.13576 0.635756 16 0.567878 0.067878 32 0.283939 0.216061 64 0.813779 0.313779 128 0.408841 0.0911597 256 0.317041 0.182959 512 0.182434 0.317567 1024 0.247563 0.252438 15 1 1 14.3561 13.3561 2 7.17806 6.17806 4 3.58903 2.58903 8 1.79451 0.794515 16 0.89757 0.10243 32 0.449332 0.550668 64 1.18128 0.181279 128 0.616073 0.383927 256 0.481773 0.518227 512 0.280826 0.719174 1024 0.431723 0.568277 16 0.493635 1 11.9975 11.5039 2 6.37694 5.88331 4 3.2551 2.76146 8 1.63136 1.13773 16 1.01201 0.518371 32 0.758046 0.264412 64 0.69473 0.201095 128 0.533808 0.0401729 256 0.54301 0.0493756 512 0.459542 0.0340923 1024 0.434418 0.0592162 17 0.5 1 0.950446 0.450446 2 0.972599 0.472599 4 0.818108 0.318108 8 0.598119 0.0981187 16 0.420151 0.0798494 32 0.466431 0.0335689 64 0.4938 0.00620043 128 0.483233 0.0167673 256 0.48587 0.01413 512 0.495903 0.00409724 1024 0.48955 0.01045 18 0.170557 1 0.00568191 0.164875 2 0.0242241 0.146333 4 0.0943295 0.0762278 8 0.177922 0.00736437 16 0.167246 0.00331173 32 0.148611 0.0219466 64 0.15549 0.0150675 128 0.162168 0.00838984 256 0.157722 0.012835 512 0.159767 0.0107904 1024 0.165462 0.00509539 19 -1 1 -4.47159 3.47159 2 -3.44234 2.44234 4 -2.22041 1.22041 8 -1.15411 0.154107 16 -1.13205 0.13205 32 -1.26082 0.260816 64 -1.1857 0.185704 128 -1.08669 0.0866943 256 -1.12332 0.12332 512 -1.0923 0.0923033 1024 -1.03562 0.035621 20 1.5644 1 1.02051 0.543887 2 1.10588 0.458519 4 1.21213 0.352264 8 1.19571 0.368683 16 1.42963 0.134771 32 1.50211 0.0622864 64 1.50524 0.0591574 128 1.5304 0.0339929 256 1.5636 0.000801048 512 1.55475 0.00965124 1024 1.55317 0.0112222 21 0.210803 1 0.0879805 0.122822 2 0.222267 0.0114644 4 0.317955 0.107152 8 0.158979 0.0518234 16 0.201454 0.00934882 32 0.237376 0.0265734 64 0.240242 0.029439 128 0.241621 0.0308184 256 0.256129 0.045326 512 0.25097 0.0401673 1024 0.236117 0.0253141 22 0.728103 1 0.999869 0.271766 2 0.995926 0.267823 4 0.848906 0.120803 8 0.621193 0.10691 16 0.704935 0.0231674 32 0.775219 0.0471164 64 0.756531 0.028428 128 0.744655 0.0165524 256 0.764697 0.0365945 512 0.757391 0.0292881 1024 0.740819 0.0127162 23 0.624713 1 -39.5428 40.1675 2 -25.2724 25.8971 4 -12.1558 12.7805 8 -5.59248 6.21719 16 -4.05904 4.68375 32 -0.145235 0.769948 64 3.07641 2.4517 128 1.395 0.770289 256 0.436516 0.188197 512 0.481973 0.14274 1024 0.720999 0.0962856 24 -0.00675475 1 0.137389 0.144144 2 0.101563 0.108318 4 0.0254299 0.0321846 8 -0.0207267 0.0139719 16 -0.00998327 0.00322853 32 -0.00266929 0.00408546 64 0.00800215 0.0147569 128 -0.00520161 0.00155313 256 -0.00644293 0.000311811 512 -0.00648129 0.000273455 1024 -0.00616533 0.000589417 25 -1.61086 1 -0.373137 1.23773 2 -0.433338 1.17753 4 -0.809568 0.801296 8 -1.18251 0.428352 16 -1.44013 0.170731 32 -1.25597 0.354891 64 -1.402 0.208868 128 -1.54396 0.0669033 256 -1.50286 0.108008 512 -1.49016 0.120707 1024 -1.53043 0.0804363 26 7.95493 1 17.0355 9.08058 2 15.8377 7.88281 4 13.7996 5.84463 8 14.2237 6.26882 16 10.2244 2.26952 32 9.11611 1.16118 64 8.92653 0.971599 128 8.43789 0.482959 256 7.89706 0.0578694 512 8.05814 0.103217 1024 8.11609 0.161167 27 0.841117 1 3.01059 2.16948 2 2.175 1.33388 4 1.4879 0.64678 8 1.00332 0.162201 16 0.925625 0.0845081 32 0.938548 0.0974308 64 0.915938 0.0748214 128 0.862865 0.0217485 256 0.871208 0.0300907 512 0.853686 0.0125692 1024 0.83597 0.005147 28 0.0199547 1 -2.53821 2.55816 2 -1.01044 1.03039 4 -1.08157 1.10152 8 -0.540738 0.560693 16 -0.142511 0.162466 32 -0.20424 0.224195 64 0.0591777 0.0392231 128 -0.126079 0.146033 256 -0.0439935 0.0639482 512 -0.0143609 0.0343155 1024 -0.0178154 0.0377701 29 0.306853 1 0.497159 0.190306 2 0.487867 0.181014 4 0.359902 0.0530487 8 0.179951 0.126902 16 0.275362 0.0314907 32 0.331062 0.0242096 64 0.315363 0.00851059 128 0.305712 0.00114069 256 0.328016 0.0211628 512 0.324255 0.0174024 1024 0.313431 0.0065784 30 -4.52757 1 -13.0242 8.49666 2 -35.526 30.9984 4 -12.3733 7.84577 8 -16.6719 12.1444 16 -5.62516 1.09759 32 6.91183 11.4394 64 1.60591 6.13348 128 -5.7457 1.21813 256 -4.36543 0.162143 512 -7.25636 2.72879 1024 -5.73181 1.20424 31 2.65164 1 0.491494 2.16014 2 0.58523 2.06641 4 0.729019 1.92262 8 0.706042 1.94559 16 1.91321 0.738423 32 2.45159 0.200045 64 2.29287 0.358768 128 2.37348 0.278153 256 2.55889 0.0927471 512 2.51035 0.141285 1024 2.56698 0.0846543 32 -12.0703 1 3.25434 15.3247 2 3.62644 15.6968 4 -8.21774 3.8526 8 -31.3653 19.2949 16 -17.5399 5.46955 32 -10.1062 1.96415 64 -11.2499 0.820482 128 -11.3075 0.762858 256 -8.60656 3.46379 512 -9.66767 2.40268 1024 -11.276 0.794336 33 0.886227 1 2.11461 1.22839 2 1.83401 0.947786 4 1.35063 0.464399 8 0.817346 0.0688809 16 0.899781 0.0135539 32 0.999975 0.113748 64 0.961671 0.0754444 128 0.927426 0.0411995 256 0.958848 0.0726215 512 0.941385 0.0551584 1024 0.908504 0.0222766 34 1085.25 1 1.12391 1084.13 2 0.563273 1084.69 4 818.689 266.564 8 2521.28 1436.02 16 1492.67 407.421 32 995.181 90.072 64 1061.6 23.6573 128 1035.89 49.3613 256 834.851 250.402 512 920.457 164.796 1024 1036.09 49.1589 35 26 1 39.1433 13.1433 2 82.1005 56.1005 4 53.6362 27.6362 8 32.5393 6.53929 16 27.6601 1.66014 32 29.3728 3.37282 64 39.3579 13.3579 128 32.0688 6.06882 256 29.1132 3.11318 512 30.6533 4.65331 1024 27.9815 1.98148 36 100 1 250.178 150.178 2 135.675 35.6752 4 70.3545 29.6455 8 35.2262 64.7738 16 21.9238 78.0762 32 16.7289 83.2711 64 19.5737 80.4263 128 13.8911 86.1089 256 13.2987 86.7013 512 11.0374 88.9626 1024 11.7294 88.2706 37 3.1358 1 0.00163024 3.13417 2 0.0018235 3.13398 4 0.0344617 3.10134 8 0.0757103 3.06009 16 2.83079 0.305011 32 1.44068 1.69512 64 5.11194 1.97614 128 4.31666 1.18086 256 2.75869 0.377112 512 3.08861 0.0471885 1024 2.26318 0.872623 38 0.539257 1 3.01293 2.47367 2 0.555854 0.0165972 4 -1.14723 1.68649 8 -0.694143 1.2334 16 0.28294 0.256317 32 0.44168 0.0975767 64 0.60424 0.0649832 128 0.553266 0.0140094 256 0.505773 0.0334843 512 0.535098 0.00415915 1024 0.488156 0.051101 39 2.78769 1 1.76253 1.02516 2 1.89391 0.893782 4 1.88102 0.906674 8 1.5966 1.1911 16 2.05348 0.734214 32 2.51922 0.268472 64 2.38334 0.404356 128 2.553 0.234695 256 2.7111 0.0765894 512 2.75093 0.0367642 1024 2.66643 0.121265 40 2.69896 1 1.13668 1.56228 2 1.16773 1.53123 4 1.75096 0.947999 8 2.3649 0.334059 16 2.89505 0.196089 32 2.31293 0.386024 64 2.85678 0.157823 128 2.93918 0.240221 256 2.65423 0.0447268 512 2.61717 0.0817912 1024 2.584 0.114958 41 6.09559 1 63.6273 57.5317 2 37.5727 31.4771 4 20.7656 14.67 8 11.4039 5.30832 16 8.18264 2.08705 32 7.34556 1.24997 64 7.23481 1.13923 128 5.92928 0.166308 256 5.86342 0.232162 512 5.47024 0.625345 1024 5.34624 0.749348 42 3.98079 1 26.1965 22.2157 2 16.2057 12.2249 4 9.56068 5.5799 8 5.57202 1.59124 16 4.42917 0.448383 32 4.1693 0.188512 64 4.15901 0.178226 128 3.63758 0.343205 256 3.6389 0.341889 512 3.45158 0.529211 1024 3.393 0.587786 43 2.99157 1 0.350491 2.64108 2 0.445124 2.54644 4 1.38686 1.60471 8 4.02029 1.02872 16 2.66209 0.329484 32 2.37083 0.620738 64 2.80359 0.187984 128 2.36464 0.626929 256 1.91747 1.0741 512 2.33413 0.657434 1024 2.56866 0.422907 44 -0.0300997 1 1.18387e-10 0.0300997 2 2.22463e-09 0.0300997 4 -0.0064586 0.0236411 8 -0.0814551 0.0513554 16 -0.0406552 0.0105555 32 -0.0369604 0.00686066 64 -0.0449542 0.0148545 128 -0.029448 0.000651727 256 -0.0167423 0.0133574 512 -0.0245143 0.00558541 1024 -0.0303809 0.000281177 45 -0.292707 1 9.398 9.6907 2 6.33907 6.63178 4 3.02622 3.31893 8 -0.160883 0.131824 16 -0.00565281 0.287054 32 0.364708 0.657415 64 0.117728 0.410434 128 -0.0707567 0.22195 256 0.10563 0.398337 512 -0.0530276 0.239679 1024 -0.231557 0.0611492 46 6.06909 1 7.90228 1.83319 2 7.70387 1.63478 4 7.34991 1.28082 8 7.42219 1.3531 16 6.56032 0.491226 32 6.3029 0.233809 64 6.27783 0.208742 128 6.18727 0.118179 256 6.06937 0.000282358 512 6.10148 0.032393 1024 6.10938 0.0402903 47 -0.444444 1 -0.478045 0.0336004 2 -0.600056 0.155612 4 -0.515593 0.0711489 8 -0.299163 0.145281 16 -0.406098 0.0383466 32 -0.487428 0.0429838 64 -0.469928 0.0254831 128 -0.462472 0.0180279 256 -0.48478 0.0403359 512 -0.478154 0.0337099 1024 -0.46017 0.0157257 48 -4 1 -41.8268 37.8268 2 -24.9456 20.9456 4 -13.6875 9.68746 8 -6.89036 2.89036 16 -5.01197 1.01197 32 -4.59691 0.59691 64 -4.55404 0.554041 128 -3.68464 0.315363 256 -3.69969 0.300314 512 -3.38272 0.617282 1024 -3.27191 0.728087 49 52.7407 1 8.36073e-05 52.7407 2 0.0169479 52.7238 4 44.8002 7.94051 8 136.714 83.973 16 77.7719 25.0311 32 48.8837 3.85703 64 52.9661 0.225384 128 51.3911 1.3497 256 39.8368 12.9039 512 44.6047 8.13604 1024 50.4076 2.3332 50 -0.128137 1 -1.57128 1.44314 2 -1.17508 1.04695 4 -0.157132 0.0289954 8 -0.0805242 0.0476126 16 -0.429543 0.301406 32 -0.532417 0.404281 64 -0.301551 0.173415 128 -0.209557 0.0814204 256 -0.194124 0.0659871 512 -0.207174 0.0790372 1024 -0.166526 0.0383889 51 -0.197814 1 -0.0101444 0.187669 2 -0.0309897 0.166824 4 -0.0720134 0.1258 8 -0.0784202 0.119393 16 -0.147849 0.0499649 32 -0.160762 0.0370511 64 -0.166323 0.0314904 128 -0.177235 0.0205789 256 -0.18613 0.011684 512 -0.183215 0.0145984 1024 -0.184017 0.0137963 52 -0.089944 1 -3.28711 3.19717 2 -2.82127 2.73133 4 -5.23234 5.1424 8 -2.61467 2.52472 16 -1.11222 1.02228 32 0.173779 0.263723 64 -0.929276 0.839332 128 -0.576261 0.486317 256 -1.05367 0.963722 512 0.0366668 0.126611 1024 -0.327705 0.237761 53 1.50462 1 0.711206 0.793417 2 0.726952 0.777671 4 0.909948 0.594675 8 1.0841 0.420526 16 1.21739 0.287234 32 1.15938 0.345242 64 1.34036 0.164259 128 1.47502 0.0295987 256 1.39497 0.109656 512 1.36378 0.140839 1024 1.3917 0.112921 54 1.1547 1 0.85056 0.30414 2 0.855799 0.298901 4 1.09967 0.0550276 8 1.29698 0.142282 16 1.09588 0.0588189 32 1.05425 0.100449 64 1.14162 0.0130853 128 1.17927 0.0245674 256 1.1411 0.0135963 512 1.1332 0.0215051 1024 1.14138 0.0133168 55 0.505059 1 0.00737704 0.497682 2 0.0135508 0.491508 4 0.236093 0.268965 8 0.502123 0.00293576 16 0.483941 0.0211176 32 0.382674 0.122385 64 0.431482 0.0735768 128 0.471083 0.0339755 256 0.454994 0.0500646 512 0.457268 0.0477904 1024 0.479292 0.0257665 56 1.99225 1 1.12965 0.862598 2 1.39397 0.598283 4 1.66183 0.330424 8 1.6222 0.370051 16 1.8558 0.136452 32 1.90648 0.0857687 64 1.92484 0.067408 128 1.97444 0.0178144 256 2.00922 0.0169701 512 1.99595 0.00369327 1024 1.98872 0.00353046 57 0.4 1 0.00122186 0.398778 2 0.0140072 0.385993 4 0.225765 0.174235 8 0.552536 0.152536 16 0.432949 0.0329492 32 0.337811 0.0621887 64 0.361962 0.0380376 128 0.376888 0.0231123 256 0.348538 0.051462 512 0.359534 0.0404658 1024 0.382825 0.0171752 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. 10 May 2025 01:24:01 PM