29 December 2011 09:29:24 PM TEST_INT_PRB 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 1.41421 0.0462336 2 1 0.460447 4 1.49203 0.0315826 8 1.47277 0.0123277 16 1.4651 0.00465635 32 1.46217 0.00172127 64 1.46107 0.000627348 128 1.46067 0.0002265 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 0.499363 1 0.0254241 0.473939 2 0.0562605 0.443103 4 0.11675 0.382613 8 0.225744 0.273619 16 0.375544 0.123819 32 0.47602 0.0233431 64 0.493313 0.00605001 128 0.493635 0.0057288 17 0.5 1 2.41176e-31 0.5 2 1 0.5 4 0.5 9.4369e-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 1.58719e-10 128 0.479428 9.92173e-12 256 0.479428 6.20393e-13 512 0.479428 3.86913e-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 1.58676 0.126312 2 1.22434 0.236103 4 1.44019 0.0202552 8 1.45327 0.00717288 16 1.45791 0.00253683 32 1.45955 0.00089696 64 1.46013 0.000317127 128 1.46034 0.000112121 256 1.46041 3.96409e-05 512 1.46043 1.40152e-05 1024 1.46044 4.95512e-06 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 0.499363 1 2.67059 2.17123 2 1.36857 0.869202 4 0.75274 0.253376 8 0.507408 0.00804414 16 0.466443 0.0329208 32 0.487977 0.011386 64 0.493528 0.0058358 128 0.493635 0.00572876 256 0.493635 0.00572873 512 0.493635 0.00572873 1024 0.493635 0.00572873 17 0.5 1 3.21568e-31 0.5 2 0.666667 0.166667 4 0.5 6.10623e-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 2.22045e-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 1.97998 0.261696 2 1.92312 0.204834 4 1.71338 0.00489961 8 1.78676 0.0684735 16 1.85582 0.137539 32 1.72404 0.00576048 64 1.75988 0.0415948 128 1.78933 0.0710441 256 1.76697 0.0486866 512 1.73751 0.0192258 1024 1.7429 0.0246221 2 0.7 1 1 0.3 2 1 0.3 4 1 0.3 8 0.875 0.175 16 0.875 0.175 32 0.78125 0.08125 64 0.703125 0.003125 128 0.695312 0.0046875 256 0.710938 0.0109375 512 0.708984 0.00898438 1024 0.713867 0.0138672 3 0.666667 1 0.82649 0.159823 2 0.808192 0.141525 4 0.722995 0.056328 8 0.715098 0.048431 16 0.738964 0.0722978 32 0.665213 0.00145358 64 0.675545 0.00887869 128 0.685174 0.018507 256 0.681837 0.0151705 512 0.672558 0.00589134 1024 0.675331 0.0086644 4 0.479428 1 0.0973299 0.382098 2 0.0276329 0.451795 4 -0.0294385 0.508867 8 0.333232 0.146196 16 0.394896 0.0845325 32 0.478127 0.00130076 64 0.554429 0.0750003 128 0.602578 0.12315 256 0.551346 0.0719179 512 0.507429 0.0280003 1024 0.504562 0.0251337 5 1.58223 1 1.90103 0.3188 2 1.98656 0.404325 4 2.05754 0.475305 8 1.71405 0.131816 16 1.6708 0.0885682 32 1.60404 0.0218114 64 1.52652 0.0557179 128 1.47766 0.104577 256 1.51774 0.0644882 512 1.55544 0.0267941 1024 1.56118 0.0210517 6 1.46045 1 1.86137 0.40092 2 1.79548 0.335029 4 1.45595 0.00449821 8 1.59623 0.135781 16 1.69546 0.235014 32 1.54518 0.0847326 64 1.51698 0.0565326 128 1.55191 0.0914622 256 1.51709 0.0566455 512 1.49569 0.0352447 1024 1.49414 0.0336972 7 2 1 1.20994 0.790064 2 1.23796 0.762036 4 1.40411 0.595889 8 1.59877 0.401233 16 1.56783 0.432173 32 2.0667 0.0666954 64 1.99322 0.00677854 128 1.91661 0.0833937 256 1.86145 0.138547 512 1.88314 0.116857 1024 1.93261 0.0673936 8 0.866973 1 0.821206 0.0457671 2 0.844801 0.0221721 4 0.908561 0.0415878 8 0.858352 0.00862101 16 0.835402 0.0315711 32 0.867383 0.000410263 64 0.850209 0.0167642 128 0.837596 0.0293775 256 0.847396 0.0195765 512 0.859237 0.00773557 1024 0.858007 0.00896629 9 1.1547 1 0.797856 0.356845 2 0.771644 0.383056 4 0.93698 0.217721 8 0.828238 0.326463 16 0.984287 0.170414 32 1.09141 0.06329 64 1.14414 0.0105603 128 1.13409 0.0206126 256 1.1733 0.0186044 512 1.16841 0.0137121 1024 1.15856 0.00385551 10 0.693147 1 0.594147 0.0990004 2 0.604968 0.0881793 4 0.657928 0.0352188 8 0.663725 0.0294218 16 0.649077 0.0440702 32 0.6922 0.000947367 64 0.687117 0.0060305 128 0.682144 0.0110033 256 0.684552 0.00859495 512 0.689829 0.00331844 1024 0.688019 0.0051282 11 0.379885 1 0.335573 0.0443126 2 0.34223 0.0376553 4 0.370895 0.00899017 8 0.367517 0.0123682 16 0.359086 0.0207994 32 0.378869 0.00101688 64 0.375535 0.00435043 128 0.372423 0.00746202 256 0.374574 0.00531157 512 0.377734 0.00215183 1024 0.376982 0.00290307 12 0.777505 1 0.697042 0.0804628 2 0.708654 0.0688507 4 0.759415 0.0180897 8 0.754827 0.0226773 16 0.739987 0.0375172 32 0.775799 0.00170539 64 0.770016 0.0074891 128 0.764594 0.0129106 256 0.768229 0.00927551 512 0.773769 0.00373607 1024 0.772384 0.00512073 13 1.65835 1 0.762279 0.896068 2 0.346005 1.31234 4 -0.751897 2.41024 8 0.685346 0.973002 16 0.916017 0.74233 32 1.63869 0.0196534 64 1.74822 0.0898746 128 1.88915 0.2308 256 1.7596 0.10125 512 1.76618 0.107832 1024 1.62225 0.0361002 14 0.5 1 0 0.5 2 0 0.5 4 0 0.5 8 0 0.5 16 0 0.5 32 0.604554 0.104554 64 0.319843 0.180158 128 0.160934 0.339066 256 0.108297 0.391703 512 0.0948375 0.405163 1024 0.334309 0.165691 15 1 1 1.70937e-72 1 2 2.26081e-66 1 4 9.74472e-40 1 8 9.46677e-08 1 16 5.52455e-07 0.999999 32 0.806976 0.193024 64 0.475343 0.524657 128 0.258225 0.741775 256 0.190726 0.809274 512 0.173521 0.826479 1024 0.672925 0.327075 16 0.499363 1 0.0136319 0.485731 2 0.0149842 0.484379 4 0.0269702 0.472393 8 0.140543 0.35882 16 0.153817 0.345546 32 0.712621 0.213258 64 0.65237 0.153006 128 0.540638 0.0412743 256 0.447803 0.0515607 512 0.454429 0.0449348 1024 0.488223 0.0111404 17 0.5 1 0.217123 0.282877 2 0.276307 0.223693 4 0.237051 0.262949 8 0.387931 0.112069 16 0.372594 0.127406 32 0.458239 0.041761 64 0.458425 0.0415755 128 0.481962 0.0180385 256 0.516137 0.0161368 512 0.502297 0.0022971 1024 0.511635 0.011635 18 0.170557 1 0.229225 0.0586678 2 0.223454 0.0528964 4 0.192997 0.02244 8 0.188002 0.0174445 16 0.196051 0.0254939 32 0.171557 0.00099941 64 0.17368 0.00312266 128 0.176102 0.00554498 256 0.174919 0.00436201 512 0.172305 0.00174728 1024 0.173277 0.00271956 19 -1 1 -0.381135 0.618865 2 -0.426424 0.573576 4 -0.663699 0.336301 8 -0.779625 0.220375 16 -0.720534 0.279466 32 -1.04342 0.0434212 64 -1.00279 0.00279067 128 -0.963256 0.0367436 256 -0.949886 0.0501137 512 -0.976537 0.0234629 1024 -0.972367 0.0276328 20 1.5644 1 1.7558 0.191404 2 1.8156 0.251205 4 1.8668 0.302399 8 1.65167 0.0872732 16 1.62245 0.0580492 32 1.57856 0.014163 64 1.52856 0.0358369 128 1.49746 0.0669406 256 1.5228 0.0415941 512 1.54713 0.0172619 1024 1.55102 0.0133733 21 0.210803 1 0.000254668 0.210548 2 0.000542877 0.21026 4 0.0367869 0.174016 8 0.0576716 0.153131 16 0.0455527 0.16525 32 0.117287 0.0935162 64 0.171459 0.0393437 128 0.190737 0.0200653 256 0.204562 0.00624024 512 0.207839 0.0029638 1024 0.203308 0.00749442 22 0.728103 1 0.593709 0.134394 2 0.621353 0.10675 4 0.729253 0.00115043 8 0.695141 0.0329623 16 0.663088 0.0650151 32 0.722424 0.00567858 64 0.709316 0.0187871 128 0.69686 0.0312431 256 0.707274 0.0208289 512 0.719059 0.00904399 1024 0.717536 0.0105668 23 0.624713 1 1.4556 0.830882 2 1.52876 0.904044 4 1.50498 0.880268 8 1.52647 0.901753 16 2.23046 1.60574 32 0.799912 0.175199 64 -0.51406 1.13877 128 -0.0583857 0.683099 256 0.561994 0.0627194 512 1.0419 0.417183 1024 1.9582 1.33349 24 -0.00675475 1 -0.00492922 0.00182552 2 0.00241178 0.00916652 4 -0.0309637 0.0242089 8 -0.0291269 0.0223721 16 -0.003931 0.00282374 32 0.000519993 0.00727474 64 -0.00691002 0.000155272 128 -0.00906916 0.00231442 256 -0.0125942 0.00583947 512 -0.00811375 0.001359 1024 -0.00848006 0.00172531 25 -1.61086 1 -4.0796 2.46874 2 -3.32787 1.71701 4 -2.28133 0.670464 8 -1.83438 0.223513 16 -2.04872 0.437855 32 -1.73257 0.121709 64 -1.59913 0.0117302 128 -1.6317 0.0208377 256 -1.61034 0.000525118 512 -1.65394 0.0430761 1024 -1.64539 0.0345286 26 7.95493 1 4.17753 3.7774 2 3.63048 4.32444 4 3.20828 4.74665 8 6.84915 1.10577 16 7.16322 0.791709 32 7.81459 0.140341 64 8.52639 0.57146 128 9.03694 1.08201 256 8.59701 0.642087 512 8.21828 0.263357 1024 8.17353 0.218608 27 0.841117 1 0.58576 0.255357 2 0.596943 0.244174 4 0.66152 0.179597 8 0.725209 0.115908 16 0.71198 0.129137 32 0.868399 0.0272822 64 0.846643 0.0055265 128 0.824219 0.0168982 256 0.808759 0.0323576 512 0.816863 0.0242541 1024 0.82572 0.0153966 28 0.0199547 1 0.0708659 0.0509112 2 0.0942783 0.0743237 4 -0.128103 0.148057 8 -0.311832 0.331787 16 -0.072782 0.0927367 32 0.0290999 0.00914525 64 -0.036738 0.0566927 128 0.0954926 0.0755379 256 -0.0561764 0.0761311 512 0.0334262 0.0134715 1024 0.0147088 0.00524586 29 0.306853 1 0.372705 0.0658524 2 0.376906 0.0700534 4 0.396182 0.0893292 8 0.308782 0.00192945 16 0.280907 0.0259463 32 0.317399 0.0105459 64 0.288309 0.018544 128 0.278621 0.0282314 256 0.286346 0.0205067 512 0.297452 0.00940094 1024 0.297081 0.00977132 30 -4.52757 1 6.36259 10.8902 2 -11.5391 7.01155 4 13.5292 18.0568 8 0.352322 4.87989 16 -4.09271 0.434864 32 -6.25194 1.72437 64 -6.77756 2.24999 128 -6.95569 2.42813 256 -6.70241 2.17484 512 -5.12725 0.599681 1024 -3.27102 1.25655 31 2.65164 1 2.54347 0.108164 2 3.28888 0.637248 4 4.26602 1.61439 8 3.37752 0.725885 16 3.23242 0.580781 32 2.76954 0.117908 64 2.45361 0.198028 128 2.20836 0.443275 256 2.3344 0.317238 512 2.52269 0.128941 1024 2.5876 0.0640331 32 -12.0703 1 -14.6125 2.54215 2 -11.5398 0.530527 4 -4.2028 7.86754 8 -12.3512 0.28085 16 -15.6204 3.55006 32 -11.8148 0.255524 64 -14.6741 2.60375 128 -16.6181 4.54775 256 -15.0867 3.01634 512 -13.1753 1.105 1024 -13.4232 1.35289 33 0.886227 1 0.617361 0.268866 2 0.652087 0.23414 4 0.800201 0.0860259 8 0.802561 0.0836655 16 0.750468 0.135759 32 0.894253 0.00802575 64 0.866427 0.0197998 128 0.843566 0.0426611 256 0.85054 0.0356866 512 0.87233 0.0138973 1024 0.867427 0.0188003 34 1085.25 1 1040.69 44.5675 2 855.457 229.796 4 466.726 618.527 8 1048.43 36.8228 16 1291.31 206.055 32 1056.03 29.2196 64 1281.36 196.111 128 1423.49 338.24 256 1310.52 225.266 512 1160.17 74.9135 1024 1185.48 100.231 35 26 1 13.4726 12.5274 2 13.8311 12.1689 4 16.1073 9.89267 8 33.4504 7.45038 16 28.2495 2.24949 32 27.8121 1.81214 64 24.4405 1.55946 128 24.6471 1.3529 256 23.9378 2.06217 512 25.6018 0.398208 1024 25.0059 0.994094 36 100 1 0.537095 99.4629 2 0.629145 99.3709 4 1.33669 98.6633 8 4.03682 95.9632 16 4.13124 95.8688 32 16.9536 83.0464 64 14.2893 85.7107 128 11.5985 88.4015 256 9.85848 90.1415 512 9.9538 90.0462 1024 17.8398 82.1602 37 3.1358 1 0.0932835 3.04252 2 0.0653699 3.07043 4 0.0361745 3.09962 8 0.0572319 3.07857 16 0.384057 2.75174 32 0.228338 2.90746 64 0.477033 2.65877 128 0.381716 2.75408 256 3.1399 0.00410581 512 2.88062 0.255176 1024 3.10114 0.0346591 38 0.539257 1 2.85617 2.31691 2 2.11518 1.57592 4 1.40315 0.863898 8 -0.268935 0.808191 16 0.49983 0.0394267 32 0.884722 0.345465 64 0.827632 0.288375 128 0.622768 0.0835112 256 0.5584 0.0191428 512 0.517551 0.0217064 1024 0.541102 0.00184548 39 2.78769 1 1.69091 1.09679 2 1.77297 1.01472 4 2.86824 0.0805433 8 2.35903 0.428666 16 2.07056 0.71713 32 3.39487 0.607172 64 2.84593 0.0582407 128 2.50627 0.281422 256 2.61769 0.170003 512 2.64669 0.141007 1024 2.66406 0.123637 40 2.69896 1 3.12634 0.427382 2 2.80748 0.108528 4 2.21913 0.47983 8 2.36277 0.336182 16 2.83793 0.138977 32 2.43706 0.261894 64 2.5671 0.131855 128 2.507 0.191958 256 2.72993 0.0309784 512 2.76257 0.0636104 1024 2.71326 0.0143052 41 6.09559 1 1.44133 4.65425 2 1.47253 4.62305 4 1.82735 4.26824 8 3.19164 2.90395 16 3.57641 2.51917 32 6.80593 0.710343 64 6.32256 0.226973 128 5.7118 0.383783 256 5.15336 0.942221 512 5.1736 0.921989 1024 5.6935 0.402089 42 3.98079 1 1.71971 2.26108 2 1.75427 2.22652 4 2.00786 1.97293 8 2.51268 1.46811 16 2.48707 1.49372 32 3.85996 0.120823 64 3.63928 0.341509 128 3.40534 0.575446 256 3.22361 0.757175 512 3.25854 0.722251 1024 3.5438 0.436989 43 2.99157 1 1.96447 1.0271 2 1.82828 1.16329 4 1.45439 1.53718 8 1.9162 1.07537 16 4.70065 1.70908 32 3.4682 0.476634 64 3.7856 0.79403 128 3.5958 0.604233 256 3.23187 0.240301 512 2.85788 0.133691 1024 3.30987 0.318302 44 -0.0300997 1 0.000703259 0.030803 2 0.000514562 0.0306143 4 0.000261516 0.0303612 8 -0.00528828 0.0248114 16 -0.0456125 0.0155128 32 -0.0391028 0.0090031 64 -0.0484149 0.0183152 128 -0.0507554 0.0206557 256 -0.0436281 0.0135284 512 -0.0327694 0.00266965 1024 -0.0361646 0.00606494 45 -0.292707 1 -1.97179 1.67908 2 -1.8102 1.51749 4 -0.962994 0.670287 8 -0.814158 0.521451 16 -1.48947 1.19677 32 -0.403212 0.110506 64 -0.543244 0.250537 128 -0.624719 0.332012 256 -0.582995 0.290288 512 -0.453451 0.160744 1024 -0.474974 0.182267 46 6.06909 1 5.30218 0.766914 2 5.12623 0.942866 4 4.98285 1.08624 8 5.79516 0.273935 16 5.86994 0.199154 32 6.01302 0.0560746 64 6.18768 0.118586 128 6.3049 0.235808 256 6.21443 0.145339 512 6.13037 0.0612792 1024 6.11638 0.0472921 47 -0.444444 1 -0.315004 0.12944 2 -0.343804 0.100641 4 -0.458262 0.0138173 8 -0.41612 0.0283241 16 -0.379968 0.0644764 32 -0.430949 0.0134954 64 -0.419023 0.0254214 128 -0.408412 0.0360321 256 -0.422929 0.0215156 512 -0.435899 0.00854509 1024 -0.43294 0.011504 48 -4 1 -0.461149 3.53885 2 -0.529167 3.47083 4 -0.974327 3.02567 8 -1.79783 2.20217 16 -1.74569 2.25431 32 -4.06929 0.0692891 64 -3.69044 0.309564 128 -3.28926 0.710739 256 -2.98559 1.01441 512 -3.05166 0.948341 1024 -3.48087 0.519132 49 52.7407 1 50.3745 2.36625 2 38.2276 14.5132 4 14.5733 38.1675 8 46.0153 6.72549 16 60.7442 8.00345 32 49.7481 2.99269 64 63.7346 10.9938 128 72.4484 19.7076 256 65.9714 13.2307 512 57.3695 4.62879 1024 58.3732 5.63243 50 -0.128137 1 -0.193128 0.064991 2 -0.257655 0.129519 4 -0.154063 0.0259259 8 -0.37851 0.250373 16 -0.301447 0.17331 32 -0.298066 0.169929 64 -0.253104 0.124967 128 -0.215782 0.0876451 256 -0.0975593 0.0305775 512 -0.11017 0.0179665 1024 -0.108876 0.0192609 51 -0.197814 1 -0.290581 0.0927677 2 -0.303103 0.105289 4 -0.288501 0.0906871 8 -0.222899 0.0250854 16 -0.21953 0.0217161 32 -0.197004 0.000809441 64 -0.179777 0.0180364 128 -0.170732 0.0270819 256 -0.177501 0.0203123 512 -0.185339 0.0124741 1024 -0.185667 0.0121467 52 -0.089944 1 0.0125139 0.102458 2 0.0162648 0.106209 4 0.116395 0.206339 8 -0.199282 0.109338 16 -0.218467 0.128523 32 -0.239113 0.149169 64 -0.213782 0.123838 128 -0.0295169 0.0604271 256 0.511995 0.601939 512 0.20607 0.296014 1024 -0.213359 0.123415 53 1.50462 1 2.44542 0.940796 2 2.05277 0.54815 4 1.52331 0.0186867 8 1.35122 0.153404 16 1.70401 0.199383 32 1.48635 0.0182725 64 1.64296 0.138334 128 1.67908 0.174455 256 1.82592 0.321301 512 1.69624 0.191613 1024 1.58998 0.0853613 54 1.1547 1 0.797856 0.356845 2 0.771644 0.383056 4 0.93698 0.217721 8 0.828238 0.326463 16 0.984287 0.170414 32 1.09141 0.06329 64 1.14414 0.0105603 128 1.13409 0.0206126 256 1.1733 0.0186044 512 1.16841 0.0137121 1024 1.15856 0.00385551 55 0.505059 1 0.960504 0.455445 2 0.913613 0.408554 4 0.632382 0.127323 8 0.602454 0.0973954 16 0.658829 0.153771 32 0.534028 0.0289691 64 0.519475 0.0144166 128 0.5251 0.0200411 256 0.517483 0.0124244 512 0.51689 0.0118317 1024 0.51335 0.00829166 56 1.99225 1 2.21629 0.224034 2 2.21897 0.226716 4 2.22045 0.228196 8 2.06108 0.0688283 16 2.01747 0.0252168 32 1.96445 0.0278049 64 1.93935 0.0529023 128 1.92147 0.070787 256 1.95579 0.0364654 512 1.98025 0.0120016 1024 1.97764 0.0146134 57 0.4 1 0.564564 0.164564 2 0.528702 0.128702 4 0.39466 0.00534036 8 0.442161 0.0421612 16 0.485301 0.0853013 32 0.40529 0.00529026 64 0.426266 0.0262659 128 0.444105 0.0441046 256 0.429802 0.0298017 512 0.412081 0.0120813 1024 0.415075 0.0150753 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 9.78273e-13 8 0.479428 3.94129e-15 16 0.479428 1.11022e-16 32 0.479428 5.55112e-17 64 0.479428 1.66533e-16 128 0.479428 1.11022e-16 256 0.479428 2.22045e-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 1.47344 0.012997 2 1.48618 0.0257291 4 1.46127 0.000820942 8 1.46074 0.000290249 16 1.46055 0.000102619 32 1.46048 3.62811e-05 64 1.46046 1.28273e-05 128 1.46045 4.53514e-06 256 1.46045 1.60341e-06 512 1.46045 5.66893e-07 1024 1.46045 2.00427e-07 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 4.44089e-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 3.59934e-13 32 1.65835 1.77636e-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 0.499363 1 0.236976 0.262388 2 0.400596 0.0987672 4 0.509088 0.00972432 8 0.503719 0.00435608 16 0.49317 0.00619342 32 0.493618 0.00574577 64 0.493635 0.0057284 128 0.493635 0.00572873 256 0.493635 0.00572873 512 0.493635 0.00572873 1024 0.493635 0.00572873 17 0.5 1 0.997235 0.497235 2 0.515987 0.0159871 4 0.5 9.99201e-16 8 0.5 6.66134e-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 3.33067e-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 6.614e-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 9.50628e-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 2.4361e-11 128 -4.52757 7.90479e-14 256 -4.52757 4.44089e-15 512 -4.52757 8.88178e-15 1024 -4.52757 8.88178e-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 2.46914e-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 9.99201e-16 32 0.539257 3.33067e-16 64 0.539257 3.33067e-16 128 0.539257 2.22045e-16 256 0.539257 1.11022e-16 512 0.539257 2.22045e-16 1024 0.539257 5.55112e-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 2.31065e-15 128 -0.0300997 2.77556e-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 2.22045e-16 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 4.44089e-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 1.93185 0.471405 2 1.67303 0.212585 4 1.33652 0.123931 8 1.41427 0.0461741 16 1.44352 0.0169232 32 1.45431 0.00613342 64 1.45824 0.00220608 128 1.45966 0.000789364 256 1.46017 0.000281432 512 1.46035 0.000100089 1024 1.46041 3.55336e-05 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 0.499363 1 7.96093 7.46157 2 3.99318 3.49381 4 2.02472 1.52536 8 1.07073 0.571371 16 0.648239 0.148876 32 0.511892 0.0125284 64 0.493956 0.00540737 128 0.493635 0.00572869 256 0.493635 0.00572875 512 0.493635 0.00572873 1024 0.493635 0.00572873 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 1.11022e-16 128 0.5 5.55112e-17 256 0.5 0 512 0.5 5.55112e-16 1024 0.5 5.55112e-17 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 2.22045e-16 32 0.539257 3.33067e-16 64 0.539257 3.33067e-16 128 0.539257 2.22045e-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 1.41421 0.0462336 2 0.707107 0.75334 4 1.10355 0.356894 8 1.32588 0.134562 16 1.40546 0.0549842 32 1.43673 0.023713 64 1.4498 0.0106422 128 1.45553 0.00492007 256 1.45812 0.00232508 512 1.45933 0.0011165 1024 1.4599 0.000542389 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 0.499363 1 0.0254241 0.473939 2 0.0633178 0.436046 4 0.133803 0.36556 8 0.260413 0.23895 16 0.439725 0.0596381 32 0.571964 0.0726006 64 0.585324 0.0859607 128 0.551211 0.0518475 256 0.52412 0.0247565 512 0.509097 0.00973359 1024 0.501394 0.00203014 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 1.41421 0.0462336 2 1.93185 0.471405 4 1.62649 0.166038 8 1.53175 0.0713007 16 1.49342 0.0329761 32 1.47624 0.0157896 64 1.46814 0.00769763 128 1.46424 0.00379014 256 1.46232 0.00187691 512 1.46138 0.000932655 1024 1.46091 0.000464429 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 0.499363 1 0.0254241 0.473939 2 7.96093 7.46157 4 3.99831 3.49895 8 2.04757 1.54821 16 1.12816 0.628801 32 0.747092 0.247728 64 0.61067 0.111306 128 0.551973 0.0526096 256 0.522804 0.0234404 512 0.508219 0.00885583 1024 0.500927 0.00156355 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 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0.0621435 32 -0.109643 0.0184942 64 -0.122143 0.00599416 128 -0.126035 0.00210181 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_PRB Normal end of execution. 29 December 2011 09:29:24 PM