17 September 2021 11:53:53.147 PM TEST_INT_TEST FORTRAN90 version Test the TEST_INT library. TEST01 Composite midpoint rule, for 1D finite interval problems. Problem Exact Ints Approx Error 1 1.71828 1 1.64872 0.695606E-01 2 1.70051 0.177691E-01 4 1.71382 0.446655E-02 8 1.71716 0.111816E-02 16 1.71800 0.279636E-03 32 1.71821 0.699151E-04 64 1.71826 0.174791E-04 128 1.71828 0.436981E-05 2 0.700000 1 1.00000 0.300000 2 0.500000 0.200000 4 0.750000 0.500000E-01 8 0.750000 0.500000E-01 16 0.687500 0.125000E-01 32 0.687500 0.125000E-01 64 0.703125 0.312500E-02 128 0.703125 0.312500E-02 3 0.666667 1 0.707107 0.404401E-01 2 0.683013 0.163460E-01 4 0.672977 0.631073E-02 8 0.669032 0.236551E-02 16 0.667537 0.870009E-03 32 0.666983 0.316020E-03 64 0.666781 0.113837E-03 128 0.666707 0.407740E-04 4 0.479428 1 -0.160000 0.639428 2 0.319667 0.159762 4 0.439407 0.400208E-01 8 0.469417 0.100116E-01 16 0.476925 0.250332E-02 32 0.478802 0.625856E-03 64 0.479272 0.156466E-03 128 0.479389 0.391165E-04 5 1.58223 1 2.22222 0.639989 2 1.64948 0.672516E-01 4 1.59690 0.146717E-01 8 1.58594 0.370973E-02 16 1.58316 0.928631E-03 32 1.58247 0.232219E-03 64 1.58229 0.580584E-04 128 1.58225 0.145148E-04 6 1.46045 1 1.41421 0.462336E-01 2 1.00000 0.460447 4 1.49203 0.315826E-01 8 1.47277 0.123277E-01 16 1.46510 0.465635E-02 32 1.46217 0.172127E-02 64 1.46107 0.627348E-03 128 1.46067 0.226500E-03 7 2.00000 1 1.41421 0.585786 2 1.57735 0.422650 4 1.69884 0.301156 8 1.78646 0.213539 16 1.84886 0.151143 32 1.89309 0.106912 64 1.92439 0.756072E-01 128 1.94654 0.534647E-01 8 0.866973 1 0.941176 0.742035E-01 2 0.877876 0.109034E-01 4 0.869605 0.263242E-02 8 0.867626 0.652821E-03 16 0.867136 0.162872E-03 32 0.867014 0.406971E-04 64 0.866983 0.101730E-04 128 0.866976 0.254316E-05 9 1.15470 1 1.00000 0.154701 2 1.33333 0.178633 4 1.14286 0.118434E-01 8 1.15464 0.613631E-04 16 1.15470 0.163057E-08 32 1.15470 0.00000 64 1.15470 0.666134E-15 128 1.15470 0.222045E-15 10 0.693147 1 0.666667 0.264805E-01 2 0.685714 0.743289E-02 4 0.691220 0.192729E-02 8 0.692661 0.486627E-03 16 0.693025 0.121966E-03 32 0.693117 0.305111E-04 64 0.693140 0.762899E-05 128 0.693145 0.190732E-05 11 0.379885 1 0.377541 0.234482E-02 2 0.379322 0.563093E-03 4 0.379746 0.139459E-03 8 0.379851 0.347845E-04 16 0.379877 0.869113E-05 32 0.379883 0.217247E-05 64 0.379885 0.543098E-06 128 0.379885 0.135773E-06 12 0.777505 1 0.770747 0.675759E-02 2 0.775822 0.168250E-02 4 0.777084 0.420201E-03 8 0.777400 0.105024E-03 16 0.777478 0.262543E-04 32 0.777498 0.656347E-05 64 0.777503 0.164086E-05 128 0.777504 0.410215E-06 13 1.65835 1 -1.91785 3.57620 2 1.82228 0.163930 4 1.68215 0.238016E-01 8 1.66365 0.530061E-02 16 1.65964 0.128888E-02 32 1.65867 0.320013E-03 64 1.65843 0.798663E-04 128 1.65837 0.199580E-04 14 0.500000 1 0.00000 0.500000 2 0.00000 0.500000 4 0.00000 0.500000 8 0.00000 0.500000 16 0.962434E-06 0.499999 32 0.477350E-01 0.452265 64 0.423773 0.762275E-01 128 0.499966 0.340341E-04 15 1.00000 1 0.129161E-51 1.00000 2 0.898473E-25 1.00000 4 0.167563E-11 1.00000 8 0.511680E-05 0.999995 16 0.632258E-02 0.993677 32 0.157218 0.842782 64 0.565397 0.434603 128 0.857119 0.142881 16 0.499363 1 0.254241E-01 0.473939 2 0.562605E-01 0.443103 4 0.116750 0.382613 8 0.225744 0.273619 16 0.375544 0.123819 32 0.476020 0.233431E-01 64 0.493313 0.605001E-02 128 0.493635 0.572880E-02 17 0.500000 1 0.241176E-30 0.500000 2 1.00000 0.500000 4 0.500000 0.999201E-15 8 0.500000 0.888178E-15 16 0.500000 0.499600E-15 32 0.500000 0.111022E-15 64 0.500000 0.00000 128 0.500000 0.333067E-15 18 0.170557 1 0.188770 0.182130E-01 2 0.175036 0.447858E-02 4 0.171673 0.111519E-02 8 0.170836 0.278523E-03 16 0.170627 0.696135E-04 32 0.170575 0.174023E-04 64 0.170562 0.435051E-05 128 0.170558 0.108762E-05 19 -1.00000 1 -0.693147 0.306853 2 -0.836988 0.163012 4 -0.915951 0.840485E-01 8 -0.957329 0.426712E-01 16 -0.978502 0.214981E-01 32 -0.989210 0.107897E-01 64 -0.994595 0.540504E-02 128 -0.997295 0.270506E-02 20 1.56440 1 1.99005 0.425653 2 1.59363 0.292291E-01 4 1.57473 0.103302E-01 8 1.56699 0.259103E-02 16 1.56504 0.647799E-03 32 1.56456 0.161950E-03 64 1.56444 0.404874E-04 128 1.56441 0.101219E-04 21 0.210803 1 0.986604E-02 0.200937 2 0.393257 0.182455 4 0.177981 0.328217E-01 8 0.199073 0.117297E-01 16 0.226581 0.157785E-01 32 0.203178 0.762438E-02 64 0.212309 0.150656E-02 128 0.209728 0.107450E-02 22 0.728103 1 0.761905 0.338018E-01 2 0.734977 0.687382E-02 4 0.729839 0.173559E-02 8 0.728537 0.434020E-03 16 0.728211 0.108507E-03 32 0.728130 0.271267E-04 64 0.728110 0.678168E-05 128 0.728105 0.169542E-05 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 0.432480 32 3.04553 2.42081 64 1.56902 0.944307 128 -1.79113 2.41584 24 -0.675475E-02 1 0.112539 0.119294 2 -0.346577E-01 0.279030E-01 4 -0.285088E-01 0.217540E-01 8 -0.172141E-01 0.104593E-01 16 -0.549740E-02 0.125734E-02 32 -0.668040E-02 0.743424E-04 64 -0.665077E-02 0.103973E-03 128 -0.681738E-02 0.626371E-04 25 -1.61086 1 -1.60944 0.142639E-02 2 -1.89712 0.286256 4 -1.50264 0.108226 8 -1.67409 0.632291E-01 16 -1.58156 0.293022E-01 32 -1.62610 0.152315E-01 64 -1.60339 0.747050E-02 128 -1.61464 0.377158E-02 26 7.95493 1 2.31145 5.64347 2 6.28319 1.67174 4 7.92053 0.343944E-01 8 7.95493 0.125169E-05 16 7.95493 0.177636E-14 32 7.95493 0.444089E-14 64 7.95493 0.177636E-14 128 7.95493 0.177636E-14 27 0.841117 1 0.666308 0.174809 2 0.724249 0.116868 4 0.764438 0.766788E-01 8 0.791275 0.498421E-01 16 0.808885 0.322321E-01 32 0.820343 0.207743E-01 64 0.827762 0.133553E-01 128 0.832549 0.856742E-02 28 0.199547E-01 1 0.266686E-15 0.199547E-01 2 0.387556E-16 0.199547E-01 4 0.591821 0.571866 8 0.451165 0.431210 16 -0.412133 0.432088 32 -0.993940E-01 0.119349 64 0.768649E-01 0.569102E-01 128 0.260090E-01 0.605430E-02 29 0.306853 1 0.400000 0.931472E-01 2 0.222222 0.846306E-01 4 0.318148 0.112955E-01 8 0.318377 0.115243E-01 16 0.295446 0.114068E-01 32 0.307020 0.167549E-03 64 0.307024 0.171049E-03 128 0.307025 0.171924E-03 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 0.399198E-01 64 -4.51824 0.932672E-02 128 -4.52528 0.229292E-02 31 2.65164 1 8.00000 5.34836 2 1.60000 1.05164 4 2.40000 0.251635 8 2.64219 0.944525E-02 16 2.65219 0.552195E-03 32 2.65178 0.144012E-03 64 2.65167 0.360336E-04 128 2.65164 0.901032E-05 32 -12.0703 1 0.925377E-15 12.0703 2 -9.28279 2.78756 4 -11.4283 0.642044 8 -11.9138 0.156501 16 -12.0315 0.388662E-01 32 -12.0606 0.970023E-02 64 -12.0679 0.242404E-02 128 -12.0697 0.605945E-03 33 0.886227 1 0.832555 0.536723E-01 2 0.856885 0.293419E-01 4 0.870846 0.153812E-01 8 0.878377 0.785022E-02 16 0.882289 0.393745E-02 32 0.884275 0.195217E-02 64 0.885267 0.960397E-03 128 0.885757 0.470070E-03 34 1085.25 1 219.336 865.917 2 814.086 271.167 4 1014.04 71.2096 8 1067.24 18.0160 16 1080.74 4.51736 32 1084.12 1.13017 64 1084.97 0.282596 128 1085.18 0.706522E-01 35 26.0000 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 25.0640 0.936004 128 26.8277 0.827707 36 100.000 1 1.29346 98.7065 2 2.60003 97.4000 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 14.8250 85.1750 37 3.13580 1 0.119893E-01 3.12381 2 0.391087 2.74471 4 0.419041E-01 3.09389 8 0.188576 2.94722 16 3.40688 0.271079 32 0.361297 2.77450 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 0.490129E-03 16 0.539257 0.333067E-15 32 0.539257 0.444089E-15 64 0.539257 0.333067E-15 128 0.539257 0.111022E-15 39 2.78769 1 2.44949 0.338204 2 2.50665 0.281046 4 2.57506 0.212633 8 2.63340 0.154297 16 2.67756 0.110134 32 2.70956 0.781367E-01 64 2.73238 0.553163E-01 128 2.74856 0.391309E-01 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 0.198310 64 2.59919 0.997649E-01 128 2.94320 0.244240 41 6.09559 1 1.77778 4.31781 2 2.55811 3.53748 4 3.38470 2.71088 8 4.14022 1.95536 16 4.73426 1.36132 32 5.15477 0.940810 64 5.44153 0.654058 128 5.63770 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 -0.300997E-01 1 0.412820E-04 0.301410E-01 2 0.475558E-03 0.305753E-01 4 -0.711483E-02 0.229849E-01 8 -0.206782E-01 0.942150E-02 16 -0.273605E-01 0.273917E-02 32 -0.293871E-01 0.712613E-03 64 -0.299197E-01 0.179960E-03 128 -0.300546E-01 0.451041E-04 45 -0.292707 1 -0.832294 0.539587 2 -0.519258 0.226551 4 -0.421685 0.128978 8 -0.374867 0.821608E-01 16 -0.347869 0.551623E-01 32 -0.330715 0.380086E-01 64 -0.319237 0.265303E-01 128 -0.311345 0.186387E-01 46 6.06909 1 4.65698 1.41211 2 5.86229 0.206799 4 6.06545 0.364535E-02 8 6.06909 0.109543E-05 16 6.06909 0.985878E-13 32 6.06909 0.177636E-14 64 6.06909 0.177636E-14 128 6.06909 0.266454E-14 47 -0.444444 1 -0.490129 0.456846E-01 2 -0.471144 0.266991E-01 4 -0.458076 0.136316E-01 8 -0.450859 0.641469E-02 16 -0.447304 0.285994E-02 32 -0.445672 0.122744E-02 64 -0.444957 0.512182E-03 128 -0.444654 0.209174E-03 48 -4.00000 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 0.556088E-01 128 52.7346 0.612517E-02 50 -0.128137 1 -0.424430E-15 0.128137 2 -0.549306 0.421169 4 0.434294 0.562430 8 -0.233903 0.105766 16 -0.151016 0.228792E-01 32 -0.134366 0.622943E-02 64 -0.129889 0.175260E-02 128 -0.128628 0.491628E-03 51 -0.197814 1 -0.316254 0.118441 2 -0.203886 0.607226E-02 4 -0.193089 0.472476E-02 8 -0.190257 0.755704E-02 16 -0.189535 0.827896E-02 32 -0.189346 0.846785E-02 64 -0.189295 0.851857E-02 128 -0.189281 0.853260E-02 52 -0.899440E-01 1 0.652174E-01 0.155161 2 0.909550 0.999494 4 -0.931213 0.841269 8 0.862596 0.952540 16 -0.971462 0.881518 32 0.828247 0.918191 64 -0.992841 0.902897 128 0.818136 0.908080 53 1.50462 1 1.15470 0.349922 2 2.41703 0.912406 4 1.19237 0.312251 8 1.29604 0.208584 16 1.41033 0.942930E-01 32 1.57604 0.714202E-01 64 1.43081 0.738088E-01 128 1.47347 0.311505E-01 54 1.15470 1 1.00000 0.154701 2 1.33333 0.178633 4 1.14286 0.118434E-01 8 1.15464 0.613631E-04 16 1.15470 0.163057E-08 32 1.15470 0.222045E-15 64 1.15470 0.444089E-15 128 1.15470 0.444089E-15 55 0.505059 1 0.569783 0.647242E-01 2 0.552700 0.476410E-01 4 0.512356 0.729694E-02 8 0.506807 0.174792E-02 16 0.505491 0.432640E-03 32 0.505167 0.107895E-03 64 0.505086 0.269573E-04 128 0.505065 0.673830E-05 56 1.99225 1 2.22222 0.229970 2 2.18430 0.192048 4 2.03847 0.462196E-01 8 2.00115 0.889411E-02 16 1.99443 0.217900E-02 32 1.99279 0.541953E-03 64 1.99239 0.135315E-03 128 1.99229 0.338181E-04 57 0.400000 1 0.353553 0.464466E-01 2 0.387260 0.127405E-01 4 0.396607 0.339318E-02 8 0.399114 0.885662E-03 16 0.399772 0.228059E-03 32 0.399942 0.581915E-04 64 0.399985 0.147560E-04 128 0.399996 0.372582E-05 TEST02 Composite Simpson rule, for 1D finite interval problems. Problem Exact Ints Approx Error 1 1.71828 1 1.71886 0.579323E-03 2 1.71832 0.370135E-04 4 1.71828 0.232624E-05 8 1.71828 0.145593E-06 16 1.71828 0.910273E-08 32 1.71828 0.568970E-09 64 1.71828 0.355609E-10 128 1.71828 0.222311E-11 2 0.700000 1 0.833333 0.133333 2 0.583333 0.116667 4 0.708333 0.833333E-02 8 0.729167 0.291667E-01 16 0.697917 0.208333E-02 32 0.692708 0.729167E-02 64 0.700521 0.520833E-03 128 0.701823 0.182292E-02 3 0.666667 1 0.638071 0.285955E-01 2 0.656526 0.101404E-01 4 0.663079 0.358739E-02 8 0.665398 0.126848E-02 16 0.666218 0.448484E-03 32 0.666508 0.158564E-03 64 0.666611 0.560607E-04 128 0.666647 0.198205E-04 4 0.479428 1 0.479555 0.126359E-03 2 0.479555 0.126834E-03 4 0.479438 0.978384E-05 8 0.479429 0.640567E-06 16 0.479428 0.404901E-07 32 0.479428 0.253773E-08 64 0.479428 0.158719E-09 128 0.479428 0.992190E-11 5 1.58223 1 1.71137 0.129134 2 1.58497 0.273629E-02 4 1.58217 0.592977E-04 8 1.58223 0.178421E-05 16 1.58223 0.928413E-07 32 1.58223 0.552189E-08 64 1.58223 0.340781E-09 128 1.58223 0.212310E-10 6 1.46045 1 1.58676 0.126312 2 1.22434 0.236103 4 1.44019 0.202552E-01 8 1.45327 0.717288E-02 16 1.45791 0.253683E-02 32 1.45955 0.896960E-03 64 1.46013 0.317127E-03 128 1.46034 0.112121E-03 7 2.00000 1 1.10948 0.890524 2 1.37060 0.629398 4 1.55497 0.445028 8 1.68532 0.314681 16 1.77749 0.222513 32 1.84266 0.157340 64 1.88874 0.111256 128 1.92133 0.786701E-01 8 0.866973 1 0.877451 0.104780E-01 2 0.867114 0.140713E-03 4 0.866981 0.806165E-05 8 0.866973 0.508364E-06 16 0.866973 0.317882E-07 32 0.866973 0.198682E-08 64 0.866973 0.124176E-09 128 0.866973 0.776090E-11 9 1.15470 1 1.00000 0.154701 2 1.22222 0.675217E-01 4 1.15079 0.390689E-02 8 1.15468 0.204533E-04 16 1.15470 0.543522E-09 32 1.15470 0.222045E-15 64 1.15470 0.222045E-15 128 1.15470 0.222045E-15 10 0.693147 1 0.694444 0.129726E-02 2 0.693254 0.106788E-03 4 0.693155 0.735009E-05 8 0.693148 0.472259E-06 16 0.693147 0.297299E-07 32 0.693147 0.186151E-08 64 0.693147 0.116398E-09 128 0.693147 0.727574E-11 11 0.379885 1 0.379851 0.348103E-04 2 0.379883 0.199648E-05 4 0.379885 0.122395E-06 8 0.379885 0.761369E-08 16 0.379885 0.475298E-09 32 0.379885 0.296974E-10 64 0.379885 0.185596E-11 128 0.379885 0.115963E-12 12 0.777505 1 0.777494 0.104888E-04 2 0.777504 0.646046E-06 4 0.777505 0.402338E-07 8 0.777505 0.251238E-08 16 0.777505 0.156989E-09 32 0.777505 0.981137E-11 64 0.777505 0.613176E-12 128 0.777505 0.377476E-13 13 1.65835 1 0.297431 1.36092 2 1.68321 0.248610E-01 4 1.65932 0.976569E-03 8 1.65840 0.550876E-04 16 1.65835 0.335878E-05 32 1.65835 0.208639E-06 64 1.65835 0.130200E-07 128 1.65835 0.813440E-09 14 0.500000 1 11.7851 11.2851 2 5.89256 5.39256 4 2.94628 2.44628 8 1.47314 0.973139 16 0.736570 0.236570 32 0.400108 0.998920E-01 64 0.474613 0.253867E-01 128 0.499989 0.114855E-04 15 1.00000 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 0.407950 64 1.05470 0.547035E-01 128 1.00453 0.453143E-02 16 0.499363 1 2.67059 2.17123 2 1.36857 0.869202 4 0.752740 0.253376 8 0.507408 0.804414E-02 16 0.466443 0.329208E-01 32 0.487977 0.113860E-01 64 0.493528 0.583580E-02 128 0.493635 0.572876E-02 17 0.500000 1 0.321568E-30 0.500000 2 0.666667 0.166667 4 0.500000 0.721645E-15 8 0.500000 0.832667E-15 16 0.500000 0.610623E-15 32 0.500000 0.111022E-15 64 0.500000 0.111022E-15 128 0.500000 0.333067E-15 18 0.170557 1 0.170670 0.113110E-03 2 0.170564 0.677481E-05 4 0.170558 0.419050E-06 8 0.170557 0.261233E-07 16 0.170557 0.163166E-08 32 0.170557 0.101962E-09 64 0.170557 0.637229E-11 128 0.170557 0.398293E-12 19 -1.00000 1 -0.462098 0.537902 2 -0.673517 0.326483 4 -0.807895 0.192105 8 -0.889508 0.110492 16 -0.937534 0.624663E-01 32 -0.965157 0.348433E-01 64 -0.980773 0.192267E-01 128 -0.989484 0.105159E-01 20 1.56440 1 1.65920 0.948055E-01 2 1.56034 0.405345E-02 4 1.56439 0.114072E-04 8 1.56440 0.546947E-07 16 1.56440 0.881231E-10 32 1.56440 0.603884E-10 64 1.56440 0.463141E-11 128 1.56440 0.302869E-12 21 0.210803 1 0.183526E-01 0.192450 2 0.269703 0.589007E-01 4 0.187963 0.228399E-01 8 0.197033 0.137695E-01 16 0.216392 0.558924E-02 32 0.205885 0.491805E-02 64 0.210619 0.183926E-03 128 0.209743 0.105939E-02 22 0.728103 1 0.730159 0.205582E-02 2 0.728080 0.231851E-04 4 0.728103 0.167247E-06 8 0.728103 0.249305E-08 16 0.728103 0.384831E-10 32 0.728103 0.599409E-12 64 0.728103 0.910383E-14 128 0.728103 0.222045E-15 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 0.291650 32 2.31233 1.68762 64 1.69459 1.06988 128 -0.608292 1.23300 24 -0.675475E-02 1 0.101552 0.108307 2 0.891432E-02 0.156691E-01 4 -0.877240E-02 0.201765E-02 8 -0.111108E-01 0.435605E-02 16 -0.635132E-02 0.403428E-03 32 -0.671303E-02 0.417187E-04 64 -0.667696E-02 0.777840E-04 128 -0.677494E-02 0.201948E-04 25 -1.61086 1 -1.33307 0.277798 2 -1.66304 0.521760E-01 4 -1.51709 0.937722E-01 8 -1.62417 0.133043E-01 16 -1.58744 0.234208E-01 32 -1.61419 0.332766E-02 64 -1.60501 0.585509E-02 128 -1.61170 0.831922E-03 26 7.95493 1 7.23413 0.720801 2 7.42061 0.534316 4 7.94346 0.114640E-01 8 7.95493 0.417230E-06 16 7.95493 0.888178E-15 32 7.95493 0.888178E-15 64 7.95493 0.177636E-14 128 7.95493 0.00000 27 0.841117 1 0.527539 0.313578 2 0.635551 0.205566 4 0.706693 0.134424 8 0.753456 0.876604E-01 16 0.784106 0.570113E-01 32 0.804134 0.369832E-01 64 0.817184 0.239327E-01 128 0.825665 0.154521E-01 28 0.199547E-01 1 0.181632E-15 0.199547E-01 2 0.722055E-16 0.199547E-01 4 0.394547 0.374593 8 0.399413 0.379459 16 -0.150243 0.170198 32 -0.726952E-01 0.926499E-01 64 0.314613E-01 0.115066E-01 128 0.202592E-01 0.304486E-03 29 0.306853 1 0.350000 0.431472E-01 2 0.256481 0.503713E-01 4 0.303303 0.355024E-02 8 0.310878 0.402518E-02 16 0.299340 0.751264E-02 32 0.305109 0.174349E-02 64 0.306067 0.785639E-03 128 0.306546 0.306711E-03 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 0.194385E-01 32 -4.52658 0.988914E-03 64 -4.52751 0.589709E-04 128 -4.52757 0.364354E-05 31 2.65164 1 5.49020 2.83856 2 2.47843 0.173204 4 2.57255 0.790863E-01 8 2.64773 0.390076E-02 16 2.65163 0.804438E-05 32 2.65164 0.466730E-07 64 2.65164 0.292119E-08 128 2.65164 0.182664E-09 32 -12.0703 1 -11.5928 0.477507 2 -11.9849 0.854023E-01 4 -12.0642 0.613736E-02 8 -12.0700 0.394993E-03 16 -12.0703 0.248603E-04 32 -12.0703 0.155646E-05 64 -12.0703 0.973205E-07 128 -12.0703 0.608319E-08 33 0.886227 1 0.555036 0.331191 2 0.710016 0.176211 4 0.792758 0.934694E-01 8 0.836822 0.494046E-01 16 0.860208 0.260189E-01 32 0.872572 0.136547E-01 64 0.879085 0.714224E-02 128 0.882502 0.372443E-02 34 1085.25 1 1168.59 83.3333 2 1090.46 5.20833 4 1085.58 0.325521 8 1085.27 0.203451E-01 16 1085.25 0.127157E-02 32 1085.25 0.794729E-04 64 1085.25 0.496705E-05 128 1085.25 0.310441E-06 35 26.0000 1 18.6450 7.35495 2 19.3941 6.60590 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 36 100.000 1 0.862306 99.1377 2 1.94893 98.0511 4 3.33304 96.6670 8 4.97136 95.0286 16 6.82375 93.1763 32 8.85420 91.1458 64 11.0306 88.9694 128 13.3242 86.6758 37 3.13580 1 0.117908E-01 3.12401 2 0.264622 2.87118 4 0.950659E-01 3.04073 8 0.166266 2.96953 16 2.32296 0.812843 32 0.834530 2.30127 64 1.21332 1.92248 128 5.68558 2.54978 38 0.539257 1 0.742463 0.203206 2 2.14426 1.60500 4 0.717440E-01 0.467513 8 0.539094 0.163376E-03 16 0.539257 0.222045E-15 32 0.539257 0.444089E-15 64 0.539257 0.111022E-15 128 0.539257 0.333067E-15 39 2.78769 1 2.12579 0.661901 2 2.32575 0.461947 4 2.46181 0.325888 8 2.55732 0.230370 16 2.62480 0.162891 32 2.67251 0.115181 64 2.70625 0.814453E-01 128 2.73010 0.575905E-01 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 0.618128E-01 32 2.55728 0.141677 64 2.59466 0.104297 128 2.82626 0.127305 41 6.09559 1 1.18519 4.91040 2 2.00170 4.09388 4 2.83097 3.26462 8 3.61152 2.48407 16 4.27190 1.82369 32 4.78342 1.31216 64 5.16027 0.935320 128 5.43168 0.663909 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 43 2.99157 1 0.861650 2.12992 2 1.27795 1.71362 4 1.60710 1.38447 8 1.87049 1.12108 16 2.08260 0.908964 32 2.25404 0.737530 64 2.39288 0.598689 128 2.50546 0.486108 44 -0.300997E-01 1 -0.126106 0.960065E-01 2 -0.627430E-01 0.326433E-01 4 -0.361940E-01 0.609425E-02 8 -0.306966E-01 0.596941E-03 16 -0.301423E-01 0.426078E-04 32 -0.301025E-01 0.275693E-05 64 -0.300999E-01 0.173824E-06 128 -0.300997E-01 0.108879E-07 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 0.757994E-01 32 -0.346752 0.540451E-01 64 -0.331081 0.383747E-01 128 -0.319898 0.271914E-01 46 6.06909 1 5.74112 0.327975 2 6.00259 0.665014E-01 4 6.06788 0.121439E-02 8 6.06909 0.365145E-06 16 6.06909 0.337508E-13 32 6.06909 0.888178E-15 64 6.06909 0.888178E-15 128 6.06909 0.532907E-14 47 -0.444444 1 -0.326753 0.117692 2 -0.395784 0.486605E-01 4 -0.424752 0.196924E-01 8 -0.436603 0.784168E-02 16 -0.441361 0.308332E-02 32 -0.443244 0.120003E-02 64 -0.443981 0.463132E-03 128 -0.444267 0.177481E-03 48 -4.00000 1 -0.653505 3.34649 2 -1.19830 2.80170 4 -1.71050 2.28950 8 -2.16297 1.83703 16 -2.54679 1.45321 32 -2.86336 1.13664 64 -3.11916 0.880840 128 -3.32262 0.677378 49 52.7407 1 46.4910 6.24977 2 53.7288 0.988013 4 53.3880 0.647210 8 53.2600 0.519241 16 52.4329 0.307831 32 52.8198 0.790446E-01 64 52.7974 0.566497E-01 128 52.7557 0.149733E-01 50 -0.128137 1 -0.282953E-15 0.128137 2 -0.366204 0.238067 4 0.197978 0.326115 8 -0.129329 0.119172E-02 16 -0.126358 0.177901E-02 32 -0.127587 0.549761E-03 64 -0.127992 0.144721E-03 128 -0.128100 0.367076E-04 51 -0.197814 1 -0.210836 0.130225E-01 2 -0.188633 0.918066E-02 4 -0.189061 0.875222E-02 8 -0.189187 0.862667E-02 16 -0.189240 0.857313E-02 32 -0.189262 0.855198E-02 64 -0.189270 0.854373E-02 128 -0.189273 0.854050E-02 52 -0.899440E-01 1 -0.956205 0.866261 2 0.117395 0.207339 4 -0.713703 0.623759 8 0.373414 0.463358 16 -0.604700 0.514756 32 0.411725 0.501669 64 -0.594073 0.504129 128 0.413861 0.503805 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 0.100869E-01 64 1.44856 0.560658E-01 128 1.46812 0.364984E-01 54 1.15470 1 1.00000 0.154701 2 1.22222 0.675217E-01 4 1.15079 0.390689E-02 8 1.15468 0.204533E-04 16 1.15470 0.543522E-09 32 1.15470 0.00000 64 1.15470 0.444089E-15 128 1.15470 0.00000 55 0.505059 1 0.475874 0.291847E-01 2 0.511440 0.638096E-02 4 0.505174 0.114941E-03 8 0.505065 0.659279E-05 16 0.505059 0.403280E-06 32 0.505059 0.250707E-07 64 0.505059 0.156483E-08 128 0.505059 0.977695E-10 56 1.99225 1 1.83236 0.159894 2 2.00201 0.975679E-02 4 1.99594 0.368350E-02 8 1.99232 0.678812E-04 16 1.99226 0.425503E-05 32 1.99225 0.263392E-06 64 1.99225 0.164189E-07 128 1.99225 0.102550E-08 57 0.400000 1 0.402369 0.236893E-02 2 0.400432 0.431916E-03 4 0.400077 0.772494E-04 8 0.400014 0.137135E-04 16 0.400002 0.242785E-05 32 0.400000 0.429413E-06 64 0.400000 0.759245E-07 128 0.400000 0.134226E-07 TEST03 Monte Carlo rule, for 1D finite interval problems. Problem Exact Pts Approx Error 1 1.71828 1 1.24411 0.474174 2 1.92310 0.204820 4 1.97301 0.254728 8 1.61066 0.107625 16 1.58053 0.137755 32 1.61741 0.100873 64 1.68651 0.317724E-01 128 1.72155 0.326625E-02 2 0.700000 1 0.00000 0.700000 2 0.500000 0.200000 4 0.750000 0.500000E-01 8 0.500000 0.200000 16 0.562500 0.137500 32 0.562500 0.137500 64 0.656250 0.437500E-01 128 0.671875 0.281250E-01 3 0.666667 1 0.467352 0.199314 2 0.722634 0.559670E-01 4 0.776376 0.109710 8 0.605775 0.608914E-01 16 0.575543 0.911233E-01 32 0.589211 0.774556E-01 64 0.639049 0.276176E-01 128 0.657455 0.921207E-02 4 0.479428 1 0.448433 0.309949E-01 2 0.943031 0.463603 4 0.607085 0.127656 8 0.613233 0.133805 16 0.625548 0.146119 32 0.666535 0.187106 64 0.551030 0.716022E-01 128 0.550946 0.715179E-01 5 1.58223 1 1.51775 0.644818E-01 2 1.17097 0.411263 4 1.45998 0.122258 8 1.45464 0.127592 16 1.46839 0.113840 32 1.41952 0.162712 64 1.51198 0.702556E-01 128 1.51363 0.686048E-01 6 1.46045 1 0.502647 0.957801 2 1.43987 0.205805E-01 4 1.65300 0.192550 8 1.28494 0.175507 16 1.40113 0.593146E-01 32 1.41781 0.426337E-01 64 1.47158 0.111327E-01 128 1.49855 0.381036E-01 7 2.00000 1 2.13971 0.139713 2 1.58115 0.418852 4 1.39864 0.601362 8 2.00267 0.266797E-02 16 3.42143 1.42143 32 3.09684 1.09684 64 2.44383 0.443827 128 2.17841 0.178408 8 0.866973 1 0.997729 0.130756 2 0.771138 0.958350E-01 4 0.782605 0.843680E-01 8 0.887123 0.201498E-01 16 0.897542 0.305689E-01 32 0.882508 0.155350E-01 64 0.870369 0.339630E-02 128 0.860328 0.664460E-02 9 1.15470 1 0.785276 0.369425 2 1.37338 0.218684 4 1.33399 0.179288 8 1.08734 0.673600E-01 16 1.02429 0.130409 32 1.06988 0.848162E-01 64 1.15144 0.325692E-02 128 1.17670 0.219990E-01 10 0.693147 1 0.820736 0.127589 2 0.665950 0.271969E-01 4 0.629706 0.634409E-01 8 0.732435 0.392882E-01 16 0.743708 0.505605E-01 32 0.736067 0.429194E-01 64 0.707892 0.147453E-01 128 0.697776 0.462876E-02 11 0.379885 1 0.445611 0.657260E-01 2 0.361614 0.182717E-01 4 0.347533 0.323526E-01 8 0.397468 0.175828E-01 16 0.401275 0.213892E-01 32 0.397009 0.171235E-01 64 0.385377 0.549186E-02 128 0.380641 0.755966E-03 12 0.777505 1 0.894763 0.117259 2 0.745840 0.316649E-01 4 0.719731 0.577733E-01 8 0.809459 0.319543E-01 16 0.816684 0.391792E-01 32 0.809155 0.316506E-01 64 0.787776 0.102712E-01 128 0.779222 0.171691E-02 13 1.65835 1 3.74375 2.08540 2 1.79975 0.141398 4 0.897335 0.761013 8 2.62752 0.969172 16 3.03735 1.37900 32 3.06094 1.40259 64 2.31067 0.652327 128 2.09757 0.439227 14 0.500000 1 0.00000 0.500000 2 0.00000 0.500000 4 0.00000 0.500000 8 0.00000 0.500000 16 4.19092 3.69092 32 3.12615 2.62615 64 1.57061 1.07061 128 0.790374 0.290373 15 1.00000 1 0.482475E-21 1.00000 2 0.241237E-21 1.00000 4 0.120619E-21 1.00000 8 0.207065E-05 0.999998 16 9.86810 8.86810 32 6.38807 5.38807 64 3.23943 2.23943 128 1.65647 0.656468 16 0.499363 1 0.132335 0.367028 2 0.696467E-01 0.429717 4 0.421731E-01 0.457190 8 0.268092 0.231271 16 1.39311 0.893745 32 1.53256 1.03320 64 0.964280 0.464917 128 0.748219 0.248855 17 0.500000 1 0.604693E-01 0.439531 2 0.179682 0.320318 4 0.355675 0.144325 8 0.460567 0.394327E-01 16 0.410976 0.890237E-01 32 0.455192 0.448076E-01 64 0.425232 0.747678E-01 128 0.471015 0.289854E-01 18 0.170557 1 0.973297E-01 0.732276E-01 2 0.181409 0.108521E-01 4 0.204691 0.341336E-01 8 0.147516 0.230416E-01 16 0.142320 0.282370E-01 32 0.146237 0.243208E-01 64 0.162340 0.821722E-02 128 0.167832 0.272499E-02 19 -1.00000 1 -1.52134 0.521343 2 -0.783004 0.216996 4 -0.582431 0.417569 8 -1.18611 0.186108 16 -1.52354 0.523535 32 -1.45674 0.456741 64 -1.18058 0.180583 128 -1.08148 0.814760E-01 20 1.56440 1 1.51268 0.517122E-01 2 1.30044 0.263956 4 1.48770 0.766986E-01 8 1.48445 0.799496E-01 16 1.49314 0.712560E-01 32 1.46097 0.103431 64 1.51909 0.453044E-01 128 1.52017 0.442279E-01 21 0.210803 1 0.966829 0.756027 2 0.483415 0.272612 4 0.242432 0.316289E-01 8 0.313597 0.102795 16 0.251835 0.410325E-01 32 0.231460 0.206570E-01 64 0.219722 0.891916E-02 128 0.207244 0.355877E-02 22 0.728103 1 0.952397 0.224294 2 0.657955 0.701480E-01 4 0.621308 0.106794 8 0.779311 0.512081E-01 16 0.783354 0.552510E-01 32 0.767794 0.396907E-01 64 0.738241 0.101382E-01 128 0.724301 0.380175E-02 23 0.624713 1 -4.53732 5.16203 2 -1.81626 2.44098 4 -0.191285 0.815998 8 1.18895 0.564241 16 -15.6964 16.3211 32 -5.86977 6.49449 64 -3.21603 3.84074 128 -0.557993 1.18271 24 -0.675475E-02 1 -0.712906E-01 0.645358E-01 2 -0.434564E-01 0.367016E-01 4 0.137912E-02 0.813387E-02 8 0.493684E-02 0.116916E-01 16 0.115715E-01 0.183262E-01 32 -0.210309E-02 0.465165E-02 64 -0.879170E-02 0.203695E-02 128 -0.165440E-01 0.978925E-02 25 -1.61086 1 -0.730679 0.880185 2 -1.04601 0.564856 4 -1.52858 0.822849E-01 8 -1.14620 0.464664 16 -1.30913 0.301735 32 -1.34130 0.269569 64 -1.53854 0.723203E-01 128 -1.57507 0.357932E-01 26 7.95493 1 7.65234 0.302590 2 12.0522 4.09725 4 9.18457 1.22964 8 9.33124 1.37632 16 9.21033 1.25540 32 9.64174 1.68681 64 8.63318 0.678257 128 8.61616 0.661236 27 0.841117 1 0.934944 0.938266E-01 2 0.722166 0.118951 4 0.654967 0.186150 8 0.869820 0.287027E-01 16 1.21747 0.376355 32 1.14637 0.305249 64 0.966200 0.125084 128 0.895813 0.546964E-01 28 0.199547E-01 1 -0.759317 0.779272 2 -0.386726 0.406681 4 -0.168655 0.188610 8 0.242855 0.222900 16 0.752815 0.732860 32 0.242770 0.222815 64 0.128926 0.108971 128 0.991962E-02 0.100350E-01 29 0.306853 1 0.450772 0.143919 2 0.225386 0.814670E-01 4 0.210285 0.965683E-01 8 0.332007 0.251546E-01 16 0.333390 0.265374E-01 32 0.320204 0.133507E-01 64 0.299712 0.714122E-02 128 0.291202 0.156510E-01 30 -4.52757 1 -35.1856 30.6580 2 -16.0709 11.5433 4 -12.6890 8.16141 8 -12.1622 7.63464 16 -12.1487 7.62112 32 -16.0894 11.5619 64 -11.9607 7.43314 128 -8.12478 3.59721 31 2.65164 1 1.31699 1.33464 2 0.937700 1.71394 4 2.32869 0.322950 8 2.22952 0.422112 16 2.35974 0.291893 32 2.00510 0.646537 64 2.26744 0.384199 128 2.29564 0.355992 32 -12.0703 1 4.82737 16.8977 2 -28.9765 16.9062 4 -24.5197 12.4493 8 -10.2756 1.79479 16 -8.17289 3.89746 32 -10.3781 1.69226 64 -11.5266 0.543738 128 -13.0312 0.960854 33 0.886227 1 1.23343 0.347201 2 0.722384 0.163842 4 0.659146 0.227081 8 0.984075 0.978476E-01 16 1.08443 0.198207 32 1.05291 0.166688 64 0.951162 0.649346E-01 128 0.908234 0.220068E-01 34 1085.25 1 1.11722 1084.14 2 2504.69 1419.43 4 2003.02 917.769 8 1012.17 73.0867 16 803.441 281.811 32 955.438 129.814 64 1017.25 68.0046 128 1136.93 51.6725 35 26.0000 1 28.3259 2.32593 2 19.7475 6.25246 4 16.6645 9.33545 8 31.7751 5.77511 16 30.6987 4.69867 32 29.7599 3.75993 64 26.9678 0.967834 128 24.7026 1.29735 36 100.000 1 5.98229 94.0177 2 3.01439 96.9856 4 1.80482 98.1952 8 7.64573 92.3543 16 123.600 23.5999 32 82.7366 17.2634 64 45.5679 54.4321 128 28.0570 71.9430 37 3.13580 1 0.303783E-02 3.13276 2 0.182326E-01 3.11757 4 0.139405 2.99639 8 0.715353E-01 3.06426 16 0.533229 2.60257 32 0.313135 2.82266 64 0.558874 2.57693 128 0.596582 2.53922 38 0.539257 1 1.09585 0.556589 2 1.26824 0.728979 4 0.174725 0.364532 8 0.987845E-01 0.440472 16 0.638181 0.989241E-01 32 0.301967 0.237290 64 0.395092 0.144165 128 0.418528 0.120729 39 2.78769 1 2.94993 0.162235 2 2.10844 0.679251 4 1.93229 0.855407 8 2.36318 0.424516 16 2.25133 0.536367 32 2.47123 0.316460 64 2.47225 0.315445 128 2.44214 0.345553 40 2.69896 1 1.32806 1.37090 2 1.87344 0.825517 4 2.65562 0.433376E-01 8 2.00482 0.694136 16 2.51814 0.180821 32 2.38415 0.314808 64 2.69654 0.241579E-02 128 2.71738 0.184220E-01 41 6.09559 1 4.30783 1.78776 2 3.35449 2.74110 4 2.45348 3.64211 8 5.05272 1.04287 16 16.8786 10.7830 32 14.3945 8.29887 64 9.44798 3.35240 128 7.47239 1.37680 42 3.98079 1 3.36761 0.613179 2 2.47050 1.51029 4 2.10865 1.87214 8 3.34303 0.637759 16 9.28871 5.30793 32 7.67578 3.69499 64 5.35401 1.37322 128 4.35278 0.371997 43 2.99157 1 0.745489 2.24608 2 4.77820 1.78664 4 3.56526 0.573691 8 2.15436 0.837211 16 1.72962 1.26195 32 1.79722 1.19435 64 1.87674 1.11483 128 2.43528 0.556293 44 -0.300997E-01 1 0.124706E-06 0.300998E-01 2 -0.131833 0.101733 4 -0.673363E-01 0.372366E-01 8 -0.336671E-01 0.356739E-02 16 -0.168035E-01 0.132962E-01 32 -0.137226E-01 0.163771E-01 64 -0.120643E-01 0.180354E-01 128 -0.243778E-01 0.572189E-02 45 -0.292707 1 1.55386 1.84657 2 -1.11960 0.826893 4 -1.52950 1.23680 8 0.206513 0.499220 16 1.67588 1.96858 32 1.28998 1.58268 64 0.401858 0.694565 128 -0.376963E-01 0.255010 46 6.06909 1 6.17748 0.108388 2 6.99241 0.923323 4 6.35149 0.282400 8 6.37430 0.305210 16 6.32610 0.257005 32 6.43930 0.370214 64 6.22961 0.160515 128 6.22460 0.155505 47 -0.444444 1 -0.711003 0.266559 2 -0.377341 0.671033E-01 4 -0.339303 0.105141 8 -0.505305 0.608608E-01 16 -0.473959 0.295146E-01 32 -0.459880 0.154354E-01 64 -0.443739 0.705294E-03 128 -0.434112 0.103321E-01 48 -4.00000 1 -3.25524 0.744762 2 -1.65046 2.34954 4 -1.06894 2.93106 8 -3.19167 0.808331 16 -12.6484 8.64836 32 -10.2009 6.20092 64 -6.43726 2.43726 128 -4.82304 0.823038 49 52.7407 1 -0.924294E-01 52.8332 2 134.833 82.0922 4 104.582 51.8416 8 51.1879 1.55283 16 39.0388 13.7020 32 48.3867 4.35407 64 50.9739 1.76690 128 57.1731 4.43240 50 -0.128137 1 -0.831986 0.703849 2 -0.394099 0.265962 4 -0.998524E-01 0.282844E-01 8 -0.477515 0.349378 16 -0.674316 0.546179 32 -0.378319 0.250182 64 -0.199560 0.714230E-01 128 -0.124855 0.328232E-02 51 -0.197814 1 -0.138483 0.593310E-01 2 -0.914850E-01 0.106329 4 -0.170561 0.272529E-01 8 -0.154114 0.436999E-01 16 -0.164259 0.335549E-01 32 -0.154954 0.428598E-01 64 -0.176959 0.208544E-01 128 -0.177520 0.202940E-01 52 -0.899440E-01 1 3.14212 3.23206 2 1.57224 1.66218 4 0.796015 0.885959 8 -0.113248E-01 0.786192E-01 16 -0.561527 0.471583 32 -0.674917 0.584973 64 -0.141860 0.519158E-01 128 -0.449534 0.359590 53 1.50462 1 0.812322 0.692301 2 0.955918 0.548705 4 1.23604 0.268581 8 1.03375 0.470875 16 1.24088 0.263745 32 1.20226 0.302361 64 1.40958 0.950394E-01 128 1.43944 0.651855E-01 54 1.15470 1 0.785276 0.369425 2 1.37338 0.218684 4 1.33399 0.179288 8 1.08734 0.673600E-01 16 1.02429 0.130409 32 1.06988 0.848162E-01 64 1.15144 0.325692E-02 128 1.17670 0.219990E-01 55 0.505059 1 0.786135E-01 0.426445 2 0.380178 0.124880 4 0.607958 0.102899 8 0.368676 0.136383 16 0.414094 0.909651E-01 32 0.422504 0.825545E-01 64 0.493449 0.116098E-01 128 0.507399 0.234076E-02 56 1.99225 1 2.14615 0.153898 2 1.74975 0.242499 4 1.93964 0.526155E-01 8 1.93197 0.602867E-01 16 1.89477 0.974820E-01 32 1.89152 0.100734 64 1.96467 0.275803E-01 128 1.96289 0.293674E-01 57 0.400000 1 0.102078 0.297922 2 0.518638 0.118638 4 0.553435 0.153435 8 0.333197 0.668035E-01 16 0.319879 0.801206E-01 32 0.342199 0.578012E-01 64 0.382877 0.171225E-01 128 0.403507 0.350747E-02 TEST04 Use a composite 4 point Gauss-Legendre rule, for 1D finite interval problems. Problem Exact Ints Approx Error 1 1.71828 1 1.71828 0.932967E-09 2 1.71828 0.374145E-11 4 1.71828 0.146549E-13 8 1.71828 0.444089E-15 16 1.71828 0.00000 32 1.71828 0.00000 64 1.71828 0.00000 128 1.71828 0.666134E-15 2 0.700000 1 0.826073 0.126073 2 0.750000 0.500000E-01 4 0.706518 0.651814E-02 8 0.687500 0.125000E-01 16 0.698370 0.162954E-02 32 0.703125 0.312500E-02 64 0.700407 0.407384E-03 128 0.699219 0.781250E-03 3 0.666667 1 0.667828 0.116098E-02 2 0.667077 0.410474E-03 4 0.666812 0.145125E-03 8 0.666718 0.513093E-04 16 0.666685 0.181406E-04 32 0.666673 0.641366E-05 64 0.666669 0.226757E-05 128 0.666667 0.801707E-06 4 0.479428 1 0.479428 0.939909E-08 2 0.479428 0.193069E-09 4 0.479428 0.978329E-12 8 0.479428 0.394129E-14 16 0.479428 0.111022E-15 32 0.479428 0.111022E-15 64 0.479428 0.166533E-15 128 0.479428 0.111022E-15 5 1.58223 1 1.58506 0.282752E-02 2 1.58221 0.193086E-04 4 1.58223 0.365626E-07 8 1.58223 0.330469E-10 16 1.58223 0.145883E-12 32 1.58223 0.888178E-15 64 1.58223 0.222045E-15 128 1.58223 0.00000 6 1.46045 1 1.47344 0.129970E-01 2 1.48618 0.257291E-01 4 1.46127 0.820942E-03 8 1.46074 0.290249E-03 16 1.46055 0.102619E-03 32 1.46048 0.362811E-04 64 1.46046 0.128273E-04 128 1.46045 0.453514E-05 7 2.00000 1 1.80634 0.193657 2 1.86306 0.136937 4 1.90317 0.968288E-01 8 1.93153 0.684683E-01 16 1.95159 0.484144E-01 32 1.96577 0.342342E-01 64 1.97579 0.242072E-01 128 1.98288 0.171171E-01 8 0.866973 1 0.866956 0.173299E-04 2 0.866973 0.561357E-07 4 0.866973 0.167980E-09 8 0.866973 0.558442E-12 16 0.866973 0.210942E-14 32 0.866973 0.111022E-15 64 0.866973 0.111022E-15 128 0.866973 0.222045E-15 9 1.15470 1 1.19781 0.431128E-01 2 1.24661 0.919063E-01 4 1.14775 0.695461E-02 8 1.15466 0.357500E-04 16 1.15470 0.949923E-09 32 1.15470 0.222045E-15 64 1.15470 0.00000 128 1.15470 0.222045E-15 10 0.693147 1 0.693146 0.763114E-06 2 0.693147 0.680639E-08 4 0.693147 0.372339E-10 8 0.693147 0.161871E-12 16 0.693147 0.777156E-15 32 0.693147 0.222045E-15 64 0.693147 0.111022E-15 128 0.693147 0.444089E-15 11 0.379885 1 0.379885 0.127293E-08 2 0.379885 0.383404E-11 4 0.379885 0.142109E-13 8 0.379885 0.555112E-16 16 0.379885 0.555112E-16 32 0.379885 0.555112E-16 64 0.379885 0.00000 128 0.379885 0.555112E-16 12 0.777505 1 0.777505 0.136159E-10 2 0.777505 0.506262E-13 4 0.777505 0.00000 8 0.777505 0.222045E-15 16 0.777505 0.111022E-15 32 0.777505 0.333067E-15 64 0.777505 0.444089E-15 128 0.777505 0.333067E-15 13 1.65835 1 1.66610 0.775417E-02 2 1.65834 0.947052E-05 4 1.65835 0.265764E-07 8 1.65835 0.943849E-10 16 1.65835 0.359712E-12 32 1.65835 0.199840E-14 64 1.65835 0.666134E-15 128 1.65835 0.00000 14 0.500000 1 0.00000 0.500000 2 0.369083E-07 0.500000 4 0.270625E-01 0.472938 8 0.470876 0.291239E-01 16 0.573638 0.736378E-01 32 0.493226 0.677446E-02 64 0.500077 0.769705E-04 128 0.500000 0.175058E-06 15 1.00000 1 0.125847E-05 0.999999 2 0.369866E-02 0.996301 4 0.141785 0.858215 8 0.621078 0.378922 16 0.947909 0.520906E-01 32 0.998223 0.177698E-02 64 0.999981 0.189313E-04 128 1.00000 0.104504E-06 16 0.499363 1 0.236976 0.262388 2 0.400596 0.987672E-01 4 0.509088 0.972432E-02 8 0.503719 0.435608E-02 16 0.493170 0.619342E-02 32 0.493618 0.574577E-02 64 0.493635 0.572840E-02 128 0.493635 0.572873E-02 17 0.500000 1 0.997235 0.497235 2 0.515987 0.159871E-01 4 0.500000 0.999201E-15 8 0.500000 0.777156E-15 16 0.500000 0.499600E-15 32 0.500000 0.00000 64 0.500000 0.111022E-15 128 0.500000 0.555112E-16 18 0.170557 1 0.170557 0.674980E-09 2 0.170557 0.312642E-11 4 0.170557 0.122125E-13 8 0.170557 0.555112E-16 16 0.170557 0.277556E-16 32 0.170557 0.00000 64 0.170557 0.277556E-16 128 0.170557 0.277556E-16 19 -1.00000 1 -0.968536 0.314640E-01 2 -0.984268 0.157321E-01 4 -0.992134 0.786604E-02 8 -0.996067 0.393302E-02 16 -0.998033 0.196651E-02 32 -0.999017 0.983255E-03 64 -0.999508 0.491628E-03 128 -0.999754 0.245814E-03 20 1.56440 1 1.56227 0.212930E-02 2 1.56441 0.949371E-05 4 1.56440 0.222444E-07 8 1.56440 0.291323E-12 16 1.56440 0.444089E-15 32 1.56440 0.222045E-15 64 1.56440 0.444089E-15 128 1.56440 0.666134E-15 21 0.210803 1 0.128374 0.824283E-01 2 0.197150 0.136530E-01 4 0.197678 0.131248E-01 8 0.197680 0.131224E-01 16 0.210842 0.389955E-04 32 0.209812 0.990259E-03 64 0.209975 0.827247E-03 128 0.210004 0.799022E-03 22 0.728103 1 0.728090 0.133960E-04 2 0.728103 0.391176E-07 4 0.728103 0.212543E-10 8 0.728103 0.832667E-13 16 0.728103 0.555112E-15 32 0.728103 0.111022E-15 64 0.728103 0.111022E-15 128 0.728103 0.00000 23 0.624713 1 3.17665 2.55194 2 -0.594889 1.21960 4 2.25275 1.62804 8 1.84406 1.21934 16 -3.18856 3.81327 32 2.45470 1.82999 64 -2.14491 2.76963 128 1.29187 0.667157 24 -0.675475E-02 1 0.363542E-02 0.103902E-01 2 0.152561E-01 0.220108E-01 4 0.478953E-02 0.115443E-01 8 -0.561193E-02 0.114282E-02 16 -0.659325E-02 0.161497E-03 32 -0.651658E-02 0.238164E-03 64 -0.678862E-02 0.338745E-04 128 -0.673080E-02 0.239431E-04 25 -1.61086 1 -1.80289 0.192024 2 -1.57279 0.380774E-01 4 -1.56576 0.451066E-01 8 -1.60134 0.951960E-02 16 -1.59959 0.112767E-01 32 -1.60848 0.237990E-02 64 -1.60805 0.281916E-02 128 -1.61027 0.594975E-03 26 7.95493 1 7.94092 0.140102E-01 2 7.95263 0.229410E-02 4 7.95496 0.365715E-04 8 7.95493 0.133660E-08 16 7.95493 0.266454E-14 32 7.95493 0.266454E-14 64 7.95493 0.888178E-15 128 7.95493 0.888178E-15 27 0.841117 1 0.797664 0.434532E-01 2 0.813100 0.280170E-01 4 0.823093 0.180237E-01 8 0.829546 0.115708E-01 16 0.833703 0.741397E-02 32 0.836375 0.474222E-02 64 0.838088 0.302846E-02 128 0.839186 0.193124E-02 28 0.199547E-01 1 0.124191 0.104236 2 -0.177256 0.197210 4 0.948975E-01 0.749428E-01 8 0.227422 0.207467 16 0.354106 0.334151 32 0.225451E-01 0.259046E-02 64 0.199424E-01 0.123037E-04 128 0.199547E-01 0.183802E-07 29 0.306853 1 0.346116 0.392629E-01 2 0.318629 0.117765E-01 4 0.302542 0.431111E-02 8 0.310523 0.367009E-02 16 0.307028 0.175026E-03 32 0.307025 0.172216E-03 64 0.307025 0.172216E-03 128 0.307025 0.172216E-03 30 -4.52757 1 -23.1023 18.5748 2 1.53301 6.06058 4 -4.10501 0.422555 8 -4.53045 0.287619E-02 16 -4.52757 0.213147E-05 32 -4.52757 0.658666E-08 64 -4.52757 0.243627E-10 128 -4.52757 0.772715E-13 31 2.65164 1 2.04729 0.604350 2 2.65543 0.379112E-02 4 2.65082 0.817562E-03 8 2.65165 0.980479E-05 16 2.65164 0.233886E-07 32 2.65164 0.826006E-13 64 2.65164 0.133227E-14 128 2.65164 0.888178E-15 32 -12.0703 1 -12.0702 0.156826E-03 2 -12.0703 0.323838E-05 4 -12.0703 0.150141E-07 8 -12.0703 0.607567E-10 16 -12.0703 0.245137E-12 32 -12.0703 0.532907E-14 64 -12.0703 0.710543E-14 128 -12.0703 0.355271E-14 33 0.886227 1 0.880399 0.582799E-02 2 0.883352 0.287455E-02 4 0.884818 0.140888E-02 8 0.885539 0.687677E-03 16 0.885892 0.334806E-03 32 0.886064 0.162779E-03 64 0.886148 0.790952E-04 128 0.886188 0.384320E-04 34 1085.25 1 1085.25 0.454747E-12 2 1085.25 0.00000 4 1085.25 0.227374E-12 8 1085.25 0.00000 16 1085.25 0.00000 32 1085.25 0.00000 64 1085.25 0.227374E-12 128 1085.25 0.227374E-12 35 26.0000 1 29.1002 3.10021 2 21.4437 4.55633 4 121.740 95.7402 8 32.2505 6.25050 16 30.6850 4.68495 32 26.5430 0.543024 64 25.8498 0.150151 128 25.4518 0.548202 36 100.000 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 37 3.13580 1 0.338325E-01 3.10197 2 0.818374E-01 3.05396 4 0.197291 2.93851 8 1.21299 1.92280 16 0.643995 2.49180 32 1.64518 1.49062 64 3.23778 0.101980 128 2.59874 0.537061 38 0.539257 1 1.51305 0.973790 2 0.406660 0.132597 4 0.540695 0.143763E-02 8 0.539257 0.523377E-06 16 0.539257 0.777156E-15 32 0.539257 0.444089E-15 64 0.539257 0.333067E-15 128 0.539257 0.111022E-15 39 2.78769 1 6.78140 3.99370 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 3.28690 0.499207 128 3.14069 0.352992 40 2.69896 1 2.10507 0.593885 2 2.28468 0.414276 4 2.41720 0.281753 8 2.65152 0.474357E-01 16 2.54806 0.150898 32 2.60573 0.932308E-01 64 2.65617 0.427867E-01 128 2.63761 0.613442E-01 41 6.09559 1 4.29442 1.80117 2 4.86748 1.22810 4 5.25298 0.842609 8 5.50856 0.587030 16 5.68314 0.412447 32 5.80479 0.290793 64 5.89025 0.205332 128 5.95049 0.145091 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 3.62250 0.358291 64 3.68976 0.291023 128 3.74440 0.236384 43 2.99157 1 2.10711 0.884460 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 44 -0.300997E-01 1 -0.236000E-01 0.649971E-02 2 -0.297061E-01 0.393636E-03 4 -0.300941E-01 0.559487E-05 8 -0.300997E-01 0.333815E-07 16 -0.300997E-01 0.145457E-09 32 -0.300997E-01 0.583738E-12 64 -0.300997E-01 0.231412E-14 128 -0.300997E-01 0.242861E-16 45 -0.292707 1 -0.362859 0.701522E-01 2 -0.341268 0.485615E-01 4 -0.326652 0.339448E-01 8 -0.316566 0.238597E-01 16 -0.309527 0.168202E-01 32 -0.304582 0.118755E-01 64 -0.301097 0.839079E-02 128 -0.298638 0.593090E-02 46 6.06909 1 6.06337 0.571871E-02 2 6.06890 0.187372E-03 4 6.06909 0.375632E-05 8 6.06909 0.116973E-08 16 6.06909 0.00000 32 6.06909 0.177636E-14 64 6.06909 0.888178E-15 128 6.06909 0.266454E-14 47 -0.444444 1 -0.448878 0.443311E-02 2 -0.446296 0.185187E-02 4 -0.445200 0.755327E-03 8 -0.444747 0.302613E-03 16 -0.444564 0.119564E-03 32 -0.444491 0.467179E-04 64 -0.444463 0.180890E-04 128 -0.444451 0.695114E-05 48 -4.00000 1 -2.56246 1.43754 2 -2.88859 1.11141 4 -3.14700 0.853003 8 -3.34938 0.650623 16 -3.50638 0.493618 32 -3.62723 0.372770 64 -3.71963 0.280367 128 -3.78989 0.210114 49 52.7407 1 52.4911 0.249654 2 50.7370 2.00374 4 52.2435 0.497236 8 52.5621 0.178668 16 52.6861 0.546064E-01 32 52.6314 0.109398 64 52.7231 0.175987E-01 128 52.6833 0.574527E-01 50 -0.128137 1 -0.183037 0.549001E-01 2 0.679213E-01 0.196058 4 -0.131315 0.317850E-02 8 -0.128444 0.307245E-03 16 -0.128216 0.790615E-04 32 -0.128157 0.198788E-04 64 -0.128142 0.497691E-05 128 -0.128138 0.124468E-05 51 -0.197814 1 -0.189169 0.864441E-02 2 -0.189298 0.851603E-02 4 -0.189284 0.852994E-02 8 -0.189278 0.853517E-02 16 -0.189276 0.853716E-02 32 -0.189276 0.853791E-02 64 -0.189275 0.853820E-02 128 -0.189275 0.853830E-02 52 -0.899440E-01 1 -0.165815 0.758712E-01 2 -16.4350 16.3450 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 53 1.50462 1 1.33515 0.169473 2 1.24434 0.260279 4 2.13839 0.633763 8 1.39627 0.108356 16 1.49550 0.911961E-02 32 1.45047 0.541520E-01 64 1.46529 0.393348E-01 128 1.51214 0.751311E-02 54 1.15470 1 1.19781 0.431128E-01 2 1.24661 0.919063E-01 4 1.14775 0.695461E-02 8 1.15466 0.357500E-04 16 1.15470 0.949924E-09 32 1.15470 0.444089E-15 64 1.15470 0.222045E-15 128 1.15470 0.444089E-15 55 0.505059 1 0.506864 0.180534E-02 2 0.505046 0.125892E-04 4 0.505059 0.134140E-08 8 0.505059 0.835376E-11 16 0.505059 0.335287E-13 32 0.505059 0.111022E-15 64 0.505059 0.00000 128 0.505059 0.222045E-15 56 1.99225 1 1.97870 0.135478E-01 2 1.99302 0.767313E-03 4 1.99224 0.857781E-05 8 1.99225 0.874673E-08 16 1.99225 0.102856E-10 32 1.99225 0.288658E-13 64 1.99225 0.444089E-15 128 1.99225 0.444089E-15 57 0.400000 1 0.399950 0.496150E-04 2 0.399991 0.877177E-05 4 0.399998 0.155065E-05 8 0.400000 0.274119E-06 16 0.400000 0.484579E-07 32 0.400000 0.856622E-08 64 0.400000 0.151431E-08 128 0.400000 0.267694E-09 TEST05 Composite trapezoid rule, for 1D finite interval problems. Problem Exact Ints Approx Error 1 1.71828 1 1.85914 0.140859 2 1.75393 0.356493E-01 4 1.72722 0.894008E-02 8 1.72052 0.223676E-02 16 1.71884 0.559300E-03 32 1.71842 0.139832E-03 64 1.71832 0.349584E-04 128 1.71829 0.873962E-05 2 0.700000 1 0.500000 0.200000 2 0.750000 0.500000E-01 4 0.625000 0.750000E-01 8 0.687500 0.125000E-01 16 0.718750 0.187500E-01 32 0.703125 0.312500E-02 64 0.695312 0.468750E-02 128 0.699219 0.781250E-03 3 0.666667 1 0.500000 0.166667 2 0.603553 0.631133E-01 4 0.643283 0.233836E-01 8 0.658130 0.853645E-02 16 0.663581 0.308547E-02 32 0.665559 0.110773E-02 64 0.666271 0.395855E-03 128 0.666526 0.141009E-03 4 0.479428 1 1.75866 1.27924 2 0.799332 0.319904 4 0.559499 0.800710E-01 8 0.499453 0.200251E-01 16 0.484435 0.500675E-02 32 0.480680 0.125172E-02 64 0.479741 0.312932E-03 128 0.479506 0.782330E-04 5 1.58223 1 0.689655 0.892578 2 1.45594 0.126294 4 1.55271 0.295213E-01 8 1.57481 0.742481E-02 16 1.58038 0.185754E-02 32 1.58177 0.464455E-03 64 1.58212 0.116118E-03 128 1.58220 0.290297E-04 6 1.46045 1 1.93185 0.471405 2 1.67303 0.212585 4 1.33652 0.123931 8 1.41427 0.461741E-01 16 1.44352 0.169232E-01 32 1.45431 0.613342E-02 64 1.45824 0.220608E-02 128 1.45966 0.789364E-03 7 2.00000 1 0.500000 1.50000 2 0.957107 1.04289 4 1.26723 0.732771 8 1.48304 0.516964 16 1.63475 0.365251 32 1.74180 0.258197 64 1.81745 0.182554 128 1.87092 0.129081 8 0.866973 1 0.750000 0.116973 2 0.845588 0.213848E-01 4 0.861732 0.524065E-02 8 0.865669 0.130412E-02 16 0.866647 0.325648E-03 32 0.866892 0.813882E-04 64 0.866953 0.203455E-04 128 0.866968 0.508629E-05 9 1.15470 1 1.00000 0.154701 2 1.00000 0.154701 4 1.16667 0.119661E-01 8 1.15476 0.613664E-04 16 1.15470 0.163057E-08 32 1.15470 0.00000 64 1.15470 0.00000 128 1.15470 0.444089E-15 10 0.693147 1 0.750000 0.568528E-01 2 0.708333 0.151862E-01 4 0.697024 0.387663E-02 8 0.694122 0.974670E-03 16 0.693391 0.244022E-03 32 0.693208 0.610277E-04 64 0.693162 0.152583E-04 128 0.693151 0.381467E-05 11 0.379885 1 0.384471 0.458522E-02 2 0.381006 0.112020E-02 4 0.380164 0.278552E-03 8 0.379955 0.695462E-04 16 0.379903 0.173808E-04 32 0.379890 0.434485E-05 64 0.379887 0.108619E-05 128 0.379886 0.271546E-06 12 0.777505 1 0.790988 0.134837E-01 2 0.780868 0.336306E-02 4 0.778345 0.840281E-03 8 0.777715 0.210040E-03 16 0.777557 0.525082E-04 32 0.777518 0.131269E-04 64 0.777508 0.328172E-05 128 0.777505 0.820430E-06 13 1.65835 1 4.72799 3.06964 2 1.40507 0.253277 4 1.61367 0.446736E-01 8 1.64791 0.104360E-01 16 1.65578 0.256768E-02 32 1.65771 0.639400E-03 64 1.65819 0.159693E-03 128 1.65831 0.399136E-04 14 0.500000 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 0.762947E-01 128 0.500034 0.336118E-04 15 1.00000 1 125.000 124.000 2 62.5000 61.5000 4 31.2500 30.2500 8 15.6250 14.6250 16 7.81250 6.81250 32 3.90941 2.90941 64 2.03332 1.03332 128 1.29936 0.299356 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 0.125284E-01 64 0.493956 0.540737E-02 128 0.493635 0.572869E-02 17 0.500000 1 0.482352E-30 0.500000 2 0.361764E-30 0.500000 4 0.500000 0.00000 8 0.500000 0.555112E-15 16 0.500000 0.721645E-15 32 0.500000 0.499600E-15 64 0.500000 0.222045E-15 128 0.500000 0.00000 18 0.170557 1 0.134471 0.360866E-01 2 0.161621 0.893683E-02 4 0.168328 0.222913E-02 8 0.170000 0.556967E-03 16 0.170418 0.139222E-03 32 0.170523 0.348043E-04 64 0.170549 0.870100E-05 128 0.170555 0.217525E-05 19 -1.00000 1 0.00000 1.00000 2 -0.346574 0.653426 4 -0.591781 0.408219 8 -0.753866 0.246134 16 -0.855597 0.144403 32 -0.917050 0.829503E-01 64 -0.953130 0.468700E-01 128 -0.973862 0.261375E-01 20 1.56440 1 0.997506 0.566890 2 1.49378 0.706185E-01 4 1.54370 0.206947E-01 8 1.55921 0.518223E-02 16 1.56310 0.129560E-02 32 1.56407 0.323900E-03 64 1.56432 0.809748E-04 128 1.56438 0.202437E-04 21 0.210803 1 0.353256E-01 0.175477 2 0.225958E-01 0.188207 4 0.207927 0.287618E-02 8 0.192954 0.178490E-01 16 0.196013 0.147893E-01 32 0.211297 0.494596E-03 64 0.207238 0.356489E-02 128 0.209774 0.102917E-02 22 0.728103 1 0.666667 0.614362E-01 2 0.714286 0.138172E-01 4 0.724631 0.347169E-02 8 0.727235 0.868048E-03 16 0.727886 0.217014E-03 32 0.728049 0.542535E-04 64 0.728089 0.135634E-04 128 0.728100 0.339084E-05 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 0.999216E-02 32 0.845949 0.221236 64 1.94574 1.32102 128 1.75738 1.13267 24 -0.675475E-02 1 0.795775E-01 0.863323E-01 2 0.960584E-01 0.102813 4 0.307004E-01 0.374551E-01 8 0.109579E-02 0.785054E-02 16 -0.805915E-02 0.130440E-02 32 -0.677827E-02 0.235289E-04 64 -0.672934E-02 0.254068E-04 128 -0.669006E-02 0.646897E-04 25 -1.61086 1 -0.780324 0.830540 2 -1.19488 0.415983 4 -1.54600 0.648639E-01 8 -1.52432 0.865451E-01 16 -1.59921 0.116580E-01 32 -1.59038 0.204801E-01 64 -1.60824 0.262427E-02 128 -1.60582 0.504739E-02 26 7.95493 1 17.0795 9.12454 2 9.69546 1.74054 4 7.98932 0.343969E-01 8 7.95493 0.125169E-05 16 7.95493 0.888178E-15 32 7.95493 0.177636E-14 64 7.95493 0.888178E-15 128 7.95493 0.888178E-15 27 0.841117 1 0.250000 0.591117 2 0.458154 0.382963 4 0.591202 0.249915 8 0.677820 0.163297 16 0.734547 0.106570 32 0.771716 0.694009E-01 64 0.796029 0.450876E-01 128 0.811895 0.292214E-01 28 0.199547E-01 1 0.115246E-16 0.199547E-01 2 0.139105E-15 0.199547E-01 4 0.889305E-16 0.199547E-01 8 0.295911 0.275956 16 0.373538 0.353583 32 -0.192977E-01 0.392524E-01 64 -0.593459E-01 0.793005E-01 128 0.875952E-02 0.111951E-01 29 0.306853 1 0.250000 0.568528E-01 2 0.325000 0.181472E-01 4 0.273611 0.332417E-01 8 0.295880 0.109731E-01 16 0.307128 0.275606E-03 32 0.301287 0.556558E-02 64 0.304154 0.269901E-02 128 0.305589 0.126398E-02 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 0.768729E-01 64 -4.54605 0.184765E-01 128 -4.53214 0.457490E-02 31 2.65164 1 0.470588 2.18105 2 4.23529 1.58366 4 2.91765 0.266012 8 2.65882 0.718820E-02 16 2.65051 0.112852E-02 32 2.65135 0.288164E-03 64 2.65156 0.720760E-04 128 2.65162 0.180212E-04 32 -12.0703 1 -34.7785 22.7082 2 -17.3893 5.31891 4 -13.3360 1.26568 8 -12.3822 0.311816 16 -12.1480 0.776578E-01 32 -12.0897 0.193958E-01 64 -12.0752 0.484778E-02 128 -12.0716 0.121187E-02 33 0.886227 1 0.00000 0.886227 2 0.416277 0.469950 4 0.636581 0.249646 8 0.753713 0.132514 16 0.816045 0.701819E-01 32 0.849167 0.370597E-01 64 0.866721 0.195059E-01 128 0.875994 0.102332E-01 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 35 26.0000 1 23.6167 2.38333 2 19.8880 6.11205 4 19.5176 6.48244 8 21.7456 4.25444 16 23.1996 2.80036 32 23.9339 2.06610 64 24.7424 1.25763 128 24.9032 1.09682 36 100.000 1 0.00000 100.000 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 37 3.13580 1 0.113937E-01 3.12440 2 0.116915E-01 3.12411 4 0.201389 2.93441 8 0.121647 3.01415 16 0.155111 2.98069 32 1.78099 1.35480 64 1.07115 2.06465 128 1.17778 1.95802 38 0.539257 1 3.14159 2.60234 2 1.34225 0.802988 4 1.94376 1.40450 8 0.539747 0.490129E-03 16 0.539257 0.222045E-15 32 0.539257 0.222045E-15 64 0.539257 0.222045E-15 128 0.539257 0.222045E-15 39 2.78769 1 1.47840 1.30930 2 1.96394 0.823750 4 2.23530 0.552398 8 2.40518 0.382516 16 2.51929 0.268406 32 2.59842 0.189270 64 2.65399 0.133703 128 2.69318 0.945098E-01 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 0.284130E-01 64 2.58560 0.113361 128 2.59239 0.106563 41 6.09559 1 0.00000 6.09559 2 0.888889 5.20670 4 1.72350 4.37209 8 2.55410 3.54148 16 3.34716 2.74842 32 4.04071 2.05487 64 4.59774 1.49784 128 5.01964 1.07595 42 3.98079 1 0.785398 3.19539 2 1.39374 2.58705 4 1.88120 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 43 2.99157 1 0.00000 2.99157 2 0.646238 2.34533 4 1.12002 1.87155 8 1.48533 1.50624 16 1.77420 1.21737 32 2.00550 0.986066 64 2.19190 0.799664 128 2.34264 0.648933 44 -0.300997E-01 1 -0.378401 0.348302 2 -0.189180 0.159080 4 -0.943522E-01 0.642525E-01 8 -0.507335E-01 0.206338E-01 16 -0.357059E-01 0.560616E-02 32 -0.315332E-01 0.143350E-02 64 -0.304601E-01 0.360442E-03 128 -0.301899E-01 0.902408E-04 45 -0.292707 1 0.00000 0.292707 2 -0.416147 0.123440 4 -0.467702 0.174995 8 -0.444694 0.151987 16 -0.409781 0.117074 32 -0.378825 0.861180E-01 64 -0.354770 0.620633E-01 128 -0.337004 0.442968E-01 46 6.06909 1 7.90939 1.84030 2 6.28319 0.214094 4 6.07274 0.364754E-02 8 6.06909 0.109543E-05 16 6.06909 0.985878E-13 32 6.06909 0.888178E-15 64 6.06909 0.00000 128 6.06909 0.888178E-15 47 -0.444444 1 0.00000 0.444444 2 -0.245065 0.199380 4 -0.358104 0.863404E-01 8 -0.408090 0.363544E-01 16 -0.429475 0.149699E-01 32 -0.438389 0.605496E-02 64 -0.442031 0.241376E-02 128 -0.443494 0.950790E-03 48 -4.00000 1 0.00000 4.00000 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 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 0.220799E-02 64 52.7995 0.587315E-01 128 52.7979 0.571702E-01 50 -0.128137 1 0.00000 0.128137 2 -0.212215E-15 0.128137 4 -0.274653 0.146516 8 0.798203E-01 0.207957 16 -0.770414E-01 0.510955E-01 32 -0.114029 0.141081E-01 64 -0.124197 0.393935E-02 128 -0.127043 0.109338E-02 51 -0.197814 1 0.00000 0.197814 2 -0.158127 0.396865E-01 4 -0.181006 0.168071E-01 8 -0.187048 0.107659E-01 16 -0.188652 0.916149E-02 32 -0.189093 0.872022E-02 64 -0.189220 0.859404E-02 128 -0.189257 0.855630E-02 52 -0.899440E-01 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 53 1.50462 1 0.853553 0.651069 2 1.00413 0.500496 4 1.71058 0.205955 8 1.45147 0.531478E-01 16 1.37376 0.130866 32 1.39204 0.112580 64 1.48404 0.205797E-01 128 1.45743 0.471942E-01 54 1.15470 1 1.00000 0.154701 2 1.00000 0.154701 4 1.16667 0.119661E-01 8 1.15476 0.613664E-04 16 1.15470 0.163057E-08 32 1.15470 0.222045E-15 64 1.15470 0.222045E-15 128 1.15470 0.222045E-15 55 0.505059 1 0.288056 0.217002 2 0.428920 0.761391E-01 4 0.490810 0.142491E-01 8 0.501583 0.347606E-02 16 0.504195 0.864070E-03 32 0.504843 0.215715E-03 64 0.505005 0.539099E-04 128 0.505045 0.134763E-04 56 1.99225 1 1.05263 0.939621 2 1.63743 0.354826 4 1.91086 0.813888E-01 8 1.97467 0.175846E-01 16 1.98791 0.434523E-02 32 1.99117 0.108312E-02 64 1.99198 0.270582E-03 128 1.99218 0.676331E-04 57 0.400000 1 0.500000 0.100000 2 0.426777 0.267767E-01 4 0.407018 0.701811E-02 8 0.401812 0.181246E-02 16 0.400463 0.463401E-03 32 0.400118 0.117671E-03 64 0.400030 0.297399E-04 128 0.400007 0.749191E-05 TEST06 Halton sequence rule, for 1D finite interval problems. Problem Exact Pts Approx Error 1 1.71828 1 1.64872 0.695606E-01 2 1.46637 0.251908 4 1.54572 0.172558 8 1.62119 0.970940E-01 16 1.66713 0.511530E-01 32 1.69207 0.262162E-01 64 1.70502 0.132666E-01 128 1.71161 0.667272E-02 2 0.700000 1 1.00000 0.300000 2 0.500000 0.200000 4 0.500000 0.200000 8 0.625000 0.750000E-01 16 0.687500 0.125000E-01 32 0.687500 0.125000E-01 64 0.687500 0.125000E-01 128 0.695312 0.468750E-02 3 0.666667 1 0.707107 0.404401E-01 2 0.603553 0.631133E-01 4 0.606671 0.599953E-01 8 0.626880 0.397864E-01 16 0.643380 0.232869E-01 32 0.653840 0.128265E-01 64 0.659839 0.682729E-02 128 0.663108 0.355898E-02 4 0.479428 1 -0.160000 0.639428 2 0.798333E-01 0.399595 4 0.349543 0.129885 8 0.443181 0.362473E-01 16 0.469892 0.953665E-02 32 0.476984 0.244373E-02 64 0.478810 0.618393E-03 128 0.479273 0.155532E-03 5 1.58223 1 2.22222 0.639989 2 1.93585 0.353620 4 1.66137 0.791364E-01 8 1.59962 0.173903E-01 16 1.58627 0.403206E-02 32 1.58320 0.968397E-03 64 1.58247 0.237160E-03 128 1.58229 0.586742E-04 6 1.46045 1 1.41421 0.462336E-01 2 0.707107 0.753340 4 1.10355 0.356894 8 1.32588 0.134562 16 1.40546 0.549842E-01 32 1.43673 0.237130E-01 64 1.44980 0.106422E-01 128 1.45553 0.492007E-02 7 2.00000 1 1.41421 0.585786 2 1.70711 0.292893 4 1.84934 0.150665 8 1.92054 0.794637E-01 16 1.95705 0.429480E-01 32 1.97618 0.238223E-01 64 1.98641 0.135903E-01 128 1.99201 0.798712E-02 8 0.866973 1 0.941176 0.742035E-01 2 0.968643 0.101670 4 0.924171 0.571983E-01 8 0.896917 0.299440E-01 16 0.882272 0.152993E-01 32 0.874704 0.773111E-02 64 0.870859 0.388590E-02 128 0.868921 0.194804E-02 9 1.15470 1 1.00000 0.154701 2 0.833333 0.321367 4 1.30340 0.148696 8 1.11526 0.394358E-01 16 1.13635 0.183533E-01 32 1.14874 0.596066E-02 64 1.15301 0.169264E-02 128 1.15425 0.450588E-03 10 0.693147 1 0.666667 0.264805E-01 2 0.733333 0.401862E-01 4 0.731746 0.385989E-01 8 0.718019 0.248717E-01 16 0.707122 0.139751E-01 32 0.700540 0.739276E-02 64 0.696948 0.380038E-02 128 0.695074 0.192654E-02 11 0.379885 1 0.377541 0.234482E-02 2 0.407682 0.277966E-01 4 0.401244 0.213585E-01 8 0.392444 0.125582E-01 16 0.386635 0.674972E-02 32 0.383378 0.349257E-02 64 0.381661 0.177571E-02 128 0.380781 0.895215E-03 12 0.777505 1 0.770747 0.675759E-02 2 0.825475 0.479703E-01 4 0.815298 0.377936E-01 8 0.799976 0.224709E-01 16 0.789649 0.121443E-01 32 0.783806 0.630124E-02 64 0.780713 0.320813E-02 128 0.779123 0.161848E-02 13 1.65835 1 -1.91785 3.57620 2 0.238020 1.42033 4 2.32965 0.671298 8 2.22711 0.568760 16 1.97516 0.316810 32 1.82119 0.162841 64 1.74040 0.820566E-01 128 1.69948 0.411278E-01 14 0.500000 1 0.00000 0.500000 2 0.00000 0.500000 4 0.00000 0.500000 8 0.00000 0.500000 16 0.962434E-06 0.499999 32 0.477354E-01 0.452265 64 0.447443 0.525574E-01 128 0.658512 0.158512 15 1.00000 1 0.129161E-51 1.00000 2 0.898473E-25 1.00000 4 0.167563E-11 1.00000 8 0.511680E-05 0.999995 16 0.632514E-02 0.993675 32 0.160317 0.839683 64 0.634214 0.365786 128 1.05835 0.583476E-01 16 0.499363 1 0.254241E-01 0.473939 2 0.633178E-01 0.436046 4 0.133803 0.365560 8 0.260413 0.238950 16 0.439725 0.596381E-01 32 0.571964 0.726006E-01 64 0.585324 0.859607E-01 128 0.551211 0.518475E-01 17 0.500000 1 0.241176E-30 0.500000 2 0.500000 0.00000 4 0.625000 0.125000 8 0.518306 0.183058E-01 16 0.560121 0.601212E-01 32 0.512577 0.125767E-01 64 0.513852 0.138516E-01 128 0.502590 0.259027E-02 18 0.170557 1 0.188770 0.182130E-01 2 0.149113 0.214442E-01 4 0.149360 0.211971E-01 8 0.156976 0.135816E-01 16 0.162975 0.758234E-02 32 0.166563 0.399478E-02 64 0.168508 0.204901E-02 128 0.169520 0.103750E-02 19 -1.00000 1 -0.693147 0.306853 2 -1.03972 0.397208E-01 4 -1.11164 0.111641 8 -1.10044 0.100440 16 -1.07221 0.722060E-01 32 -1.04701 0.470148E-01 64 -1.02894 0.289429E-01 128 -1.01718 0.171842E-01 20 1.56440 1 1.99005 0.425653 2 1.79184 0.227441 4 1.61330 0.489080E-01 8 1.57572 0.113226E-01 16 1.56711 0.271176E-02 32 1.56506 0.662895E-03 64 1.56456 0.163838E-03 128 1.56444 0.407234E-04 21 0.210803 1 0.986604E-02 0.200937 2 0.398157 0.187354 4 0.348242 0.137439 8 0.216776 0.597347E-02 16 0.201803 0.899936E-02 32 0.213172 0.236900E-02 64 0.207969 0.283406E-02 128 0.210093 0.710078E-03 22 0.728103 1 0.761905 0.338018E-01 2 0.849817 0.121714 4 0.804059 0.759563E-01 8 0.768413 0.403103E-01 16 0.748658 0.205553E-01 32 0.738458 0.103548E-01 64 0.733297 0.519382E-02 128 0.730704 0.260066E-02 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 24 -0.675475E-02 1 0.112539 0.119294 2 0.317630E-01 0.385178E-01 4 0.610608E-02 0.128608E-01 8 -0.380504E-02 0.294970E-02 16 -0.106717E-01 0.391697E-02 32 -0.704533E-02 0.290585E-03 64 -0.641674E-02 0.338009E-03 128 -0.653424E-02 0.220505E-03 25 -1.61086 1 -1.60944 0.142639E-02 2 -1.20397 0.406891 4 -1.48927 0.121599 8 -1.48305 0.127810 16 -1.57558 0.352817E-01 32 -1.57785 0.330137E-01 64 -1.60180 0.906842E-02 128 -1.60255 0.831343E-02 26 7.95493 1 2.31145 5.64347 2 4.29732 3.65761 4 6.90521 1.04971 8 7.79845 0.156480 16 7.93461 0.203153E-01 32 7.95236 0.256389E-02 64 7.95461 0.321259E-03 128 7.95489 0.401816E-04 27 0.841117 1 0.666308 0.174809 2 0.775647 0.654696E-01 4 0.821595 0.195221E-01 8 0.839814 0.130296E-02 16 0.846018 0.490071E-02 32 0.847237 0.611997E-02 64 0.846601 0.548408E-02 128 0.845455 0.433838E-02 28 0.199547E-01 1 0.266686E-15 0.199547E-01 2 -0.187379E-15 0.199547E-01 4 0.716186 0.696231 8 0.670908 0.650953 16 0.250049 0.230095 32 -0.193867 0.213821 64 -0.478481E-04 0.200025E-01 128 0.538569E-01 0.339022E-01 29 0.306853 1 0.400000 0.931472E-01 2 0.422222 0.115369 4 0.328758 0.219054E-01 8 0.325236 0.183830E-01 16 0.322273 0.154198E-01 32 0.308979 0.212580E-02 64 0.308030 0.117684E-02 128 0.307534 0.681528E-03 30 -4.52757 1 -5.48384 0.956268 2 -19.9234 15.3959 4 -11.1497 6.62212 8 -19.6516 15.1240 16 -7.41688 2.88931 32 -5.71074 1.18317 64 -5.13966 0.612095 128 -4.84808 0.320507 31 2.65164 1 8.00000 5.34836 2 4.80000 2.14836 4 3.00000 0.348365 8 2.67547 0.238364E-01 16 2.65429 0.265473E-02 32 2.65225 0.615710E-03 64 2.65178 0.148947E-03 128 2.65167 0.366340E-04 32 -12.0703 1 0.925377E-15 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 -11.7750 0.295340 33 0.886227 1 0.832555 0.536723E-01 2 1.00498 0.118755 4 0.997088 0.110861 8 0.961852 0.756251E-01 16 0.932398 0.461712E-01 32 0.912896 0.266695E-01 64 0.901139 0.149118E-01 128 0.894391 0.816388E-02 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 35 26.0000 1 16.1592 9.84076 2 20.8371 5.16290 4 26.2844 0.284391 8 28.0057 2.00565 16 24.6040 1.39599 32 24.4569 1.54314 64 24.9700 1.03001 128 25.0095 0.990508 36 100.000 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 37 3.13580 1 0.119893E-01 3.12381 2 0.769803E-02 3.12810 4 0.199101 2.93670 8 0.120456 3.01534 16 0.154506 2.98129 32 1.78069 1.35511 64 1.07099 2.06481 128 1.17770 1.95810 38 0.539257 1 -0.457102 0.996359 2 1.04408 0.504826 4 0.375480 0.163777 8 0.151004 0.388253 16 0.481922 0.573345E-01 32 0.531790 0.746719E-02 64 0.538314 0.943012E-03 128 0.539139 0.118179E-03 39 2.78769 1 2.44949 0.338204 2 2.95680 0.169102 4 2.41342 0.374275 8 2.46057 0.327123 16 2.54060 0.247091 32 2.60767 0.180028 64 2.65828 0.129417 128 2.69525 0.924481E-01 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 0.329840 32 2.65480 0.441550E-01 64 2.57763 0.121322 128 2.58839 0.110566 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 0.132930 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 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 44 -0.300997E-01 1 0.412820E-04 0.301410E-01 2 0.207697E-04 0.301205E-01 4 0.248103E-03 0.303478E-01 8 -0.343336E-02 0.266663E-01 16 -0.120558E-01 0.180439E-01 32 -0.197082E-01 0.103915E-01 64 -0.245476E-01 0.555208E-02 128 -0.272337E-01 0.286602E-02 45 -0.292707 1 -0.832294 0.539587 2 0.207741 0.500447 4 0.195688 0.488395 8 0.556507E-01 0.348357 16 -0.533726E-01 0.239334 32 -0.127340 0.165366 64 -0.177385 0.115321 128 -0.211774 0.809327E-01 46 6.06909 1 4.65698 1.41211 2 5.25963 0.809456 4 5.88926 0.179826 8 6.04349 0.255985E-01 16 6.06580 0.329477E-02 32 6.06868 0.414912E-03 64 6.06904 0.519607E-04 128 6.06908 0.649812E-05 47 -0.444444 1 -0.490129 0.456846E-01 2 -0.591638 0.147194 4 -0.541902 0.974580E-01 8 -0.494733 0.502890E-01 16 -0.467766 0.233215E-01 32 -0.454635 0.101907E-01 64 -0.448732 0.428722E-02 128 -0.446201 0.175682E-02 48 -4.00000 1 -0.980258 3.01974 2 -1.87642 2.12358 4 -2.49165 1.50835 8 -2.92449 1.07551 16 -3.23210 0.767905 32 -3.45150 0.548496 64 -3.60819 0.391806 128 -3.72013 0.279866 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 47.6440 5.09679 64 50.2522 2.48856 128 51.5243 1.21648 50 -0.128137 1 -0.424430E-15 0.128137 2 -0.693147 0.565010 4 0.929437E-01 0.221081 8 -0.240372 0.112235 16 -0.257145 0.129008 32 -0.175294 0.471570E-01 64 -0.142619 0.144817E-01 128 -0.132347 0.420966E-02 51 -0.197814 1 -0.316254 0.118441 2 -0.239320 0.415069E-01 4 -0.199346 0.153283E-02 8 -0.191640 0.617363E-02 16 -0.189932 0.788201E-02 32 -0.189482 0.833198E-02 64 -0.189345 0.846817E-02 128 -0.189300 0.851333E-02 52 -0.899440E-01 1 0.652174E-01 0.155161 2 0.938269 1.02821 4 -0.542113 0.452169 8 -0.481150 0.391206 16 0.177168 0.267112 32 -0.418401 0.328457 64 0.191450 0.281394 128 -0.406989 0.317045 53 1.50462 1 1.15470 0.349922 2 0.994379 0.510244 4 1.68702 0.182398 8 1.43616 0.684596E-01 16 1.36532 0.139301 32 1.38764 0.116980 64 1.48180 0.228243E-01 128 1.45630 0.483275E-01 54 1.15470 1 1.00000 0.154701 2 0.833333 0.321367 4 1.30340 0.148696 8 1.11526 0.394358E-01 16 1.13635 0.183533E-01 32 1.14874 0.596066E-02 64 1.15301 0.169264E-02 128 1.15425 0.450588E-03 55 0.505059 1 0.569783 0.647242E-01 2 0.337591 0.167468 4 0.426228 0.788308E-01 8 0.467352 0.377070E-01 16 0.486789 0.182696E-01 32 0.496085 0.897375E-02 64 0.500614 0.444495E-02 128 0.502847 0.221179E-02 56 1.99225 1 2.22222 0.229970 2 2.20326 0.211009 4 2.11154 0.119284 8 2.02844 0.361871E-01 16 2.00129 0.903262E-02 32 1.99447 0.222146E-02 64 1.99280 0.548801E-03 128 1.99239 0.136265E-03 57 0.400000 1 0.353553 0.464466E-01 2 0.239277 0.160723 4 0.293067 0.106933 8 0.341266 0.587344E-01 16 0.369559 0.304413E-01 32 0.384554 0.154463E-01 64 0.392228 0.777197E-02 128 0.396103 0.389685E-02 TEST07 Evenly spaced point sequence rule, for 1D finite interval problems. Problem Exact Pts Approx Error 1 1.71828 1 1.64872 0.695606E-01 2 1.85914 0.140859 4 1.76541 0.471252E-01 8 1.73845 0.201635E-01 16 1.72768 0.940027E-02 32 1.72283 0.454619E-02 64 1.72052 0.223644E-02 128 1.71939 0.110927E-02 2 0.700000 1 1.00000 0.300000 2 0.500000 0.200000 4 0.750000 0.500000E-01 8 0.625000 0.750000E-01 16 0.687500 0.125000E-01 32 0.687500 0.125000E-01 64 0.703125 0.312500E-02 128 0.695312 0.468750E-02 3 0.666667 1 0.707107 0.404401E-01 2 0.500000 0.166667 4 0.598462 0.682050E-01 8 0.636755 0.299112E-01 16 0.653069 0.135978E-01 32 0.660334 0.633313E-02 64 0.663664 0.300307E-02 128 0.665223 0.144364E-02 4 0.479428 1 -0.160000 0.639428 2 1.75866 1.27924 4 0.905961 0.426533 8 0.662218 0.182789 16 0.564721 0.852927E-01 32 0.520696 0.412682E-01 64 0.499734 0.203060E-01 128 0.489501 0.100729E-01 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 0.577674E-01 32 1.55386 0.283725E-01 64 1.56817 0.140645E-01 128 1.57523 0.700252E-02 6 1.46045 1 1.41421 0.462336E-01 2 1.93185 0.471405 4 1.62649 0.166038 8 1.53175 0.713007E-01 16 1.49342 0.329761E-01 32 1.47624 0.157896E-01 64 1.46814 0.769763E-02 128 1.46424 0.379014E-02 7 2.00000 1 1.41421 0.585786 2 0.500000 1.50000 4 0.989199 1.01080 8 1.32879 0.671210 16 1.55258 0.447419 32 1.69899 0.301008 64 1.79544 0.204560 128 1.85971 0.140294 8 0.866973 1 0.941176 0.742035E-01 2 0.750000 0.116973 4 0.830714 0.362589E-01 8 0.850860 0.161128E-01 16 0.859315 0.765819E-02 32 0.863234 0.373942E-02 64 0.865125 0.184837E-02 128 0.866054 0.918978E-03 9 1.15470 1 1.00000 0.154701 2 1.00000 0.154701 4 1.11538 0.393159E-01 8 1.13536 0.193376E-01 16 1.14423 0.104698E-01 32 1.14987 0.483439E-02 64 1.15228 0.241720E-02 128 1.15349 0.120860E-02 10 0.693147 1 0.666667 0.264805E-01 2 0.750000 0.568528E-01 4 0.712500 0.193528E-01 8 0.701367 0.821986E-02 16 0.696961 0.381357E-02 32 0.694987 0.183965E-02 64 0.694051 0.903826E-03 128 0.693595 0.448007E-03 11 0.379885 1 0.377541 0.234482E-02 2 0.384471 0.458522E-02 4 0.381404 0.151822E-02 8 0.380538 0.652644E-03 16 0.380191 0.305116E-03 32 0.380033 0.147773E-03 64 0.379958 0.727475E-04 128 0.379922 0.360957E-04 12 0.777505 1 0.770747 0.675759E-02 2 0.790988 0.134837E-01 4 0.781996 0.449147E-02 8 0.779430 0.192551E-02 16 0.778403 0.898741E-03 32 0.777940 0.434917E-03 64 0.777719 0.214017E-03 128 0.777611 0.106168E-03 13 1.65835 1 -1.91785 3.57620 2 4.72799 3.06964 4 2.36138 0.703028 8 2.03005 0.371699 16 1.84746 0.189112 32 1.75361 0.952662E-01 64 1.70615 0.478009E-01 128 1.68229 0.239413E-01 14 0.500000 1 0.00000 0.500000 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 15 1.00000 1 0.129161E-51 1.00000 2 125.000 124.000 4 62.5000 61.5000 8 31.2500 30.2500 16 15.6250 14.6250 32 7.81496 6.81496 64 3.98153 2.98153 128 2.27019 1.27019 16 0.499363 1 0.254241E-01 0.473939 2 7.96093 7.46157 4 3.99831 3.49895 8 2.04757 1.54821 16 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8.52521 0.570284 32 8.24007 0.285142 64 8.09750 0.142571 128 8.02621 0.712855E-01 27 0.841117 1 0.666308 0.174809 2 0.250000 0.591117 4 0.469662 0.371455 8 0.612128 0.228989 16 0.700205 0.140912 32 0.754075 0.870419E-01 64 0.787059 0.540575E-01 128 0.807363 0.337543E-01 28 0.199547E-01 1 0.266686E-15 0.199547E-01 2 0.115246E-16 0.199547E-01 4 -0.146891 0.166845 8 0.379678 0.359723 16 0.106812 0.868572E-01 32 -0.358717E-01 0.558263E-01 64 -0.642448E-01 0.841994E-01 128 0.849354E-02 0.114611E-01 29 0.306853 1 0.400000 0.931472E-01 2 0.250000 0.568528E-01 4 0.325893 0.190400E-01 8 0.321655 0.148023E-01 16 0.297084 0.976916E-02 32 0.307781 0.927948E-03 64 0.307397 0.544143E-03 128 0.307210 0.356729E-03 30 -4.52757 1 -5.48384 0.956268 2 23.3632 27.8908 4 5.22373 9.75130 8 26.8168 31.3444 16 -3.18859 1.33898 32 -3.73561 0.791957 64 -4.11055 0.417017 128 -4.31428 0.213286 31 2.65164 1 8.00000 5.34836 2 0.470588 2.18105 4 1.67529 0.976341 8 2.35137 0.300261 16 2.51405 0.137587 32 2.58318 0.684552E-01 64 2.61748 0.341521E-01 128 2.63458 0.170576E-01 32 -12.0703 1 0.925377E-15 12.0703 2 -34.7785 22.7082 4 -19.4591 7.38878 8 -15.2658 3.19543 16 -13.5725 1.50211 32 -12.8000 0.729652 64 -12.4301 0.359740 128 -12.2490 0.178629 33 0.886227 1 0.832555 0.536723E-01 2 0.00000 0.886227 4 0.421227 0.465000 8 0.644434 0.241793 16 0.761023 0.125204 32 0.821563 0.646643E-01 64 0.852896 0.333312E-01 128 0.869076 0.171514E-01 34 1085.25 1 219.336 865.917 2 3067.09 1981.83 4 1770.56 685.302 8 1374.20 288.950 16 1218.76 133.505 32 1149.52 64.2658 64 1116.79 31.5403 128 1100.88 15.6255 35 26.0000 1 16.1592 9.84076 2 23.6167 2.38333 4 20.4357 5.56432 8 21.3246 4.67539 16 23.7181 2.28195 32 23.7396 2.26038 64 25.1128 0.887214 128 24.8690 1.13099 36 100.000 1 1.29346 98.7065 2 0.00000 100.000 4 0.884241 99.1158 8 2.30702 97.6930 16 4.03170 95.9683 32 5.95368 94.0463 64 8.02461 91.9754 128 10.2173 89.7827 37 3.13580 1 0.119893E-01 3.12381 2 0.113937E-01 3.12440 4 0.242087E-01 3.11159 8 0.551034E-01 3.08070 16 0.329992 2.80581 32 0.360474 2.77532 64 0.587094 2.54871 128 1.98550 1.15030 38 0.539257 1 -0.457102 0.996359 2 3.14159 2.60234 4 2.82600 2.28675 8 0.870153 0.330896 16 0.701903 0.162646 32 0.620580 0.813230E-01 64 0.579918 0.406615E-01 128 0.559588 0.203307E-01 39 2.78769 1 2.44949 0.338204 2 1.47840 1.30930 4 1.17221 1.61548 8 2.26529 0.522406 16 1.99765 0.790041 32 2.56048 0.227218 64 2.40494 0.382756 128 2.68332 0.104369 40 2.69896 1 1.87186 0.827092 2 1.64352 1.05544 4 1.91912 0.779839 8 2.15856 0.540395 16 2.45325 0.245703 32 2.47527 0.223686 64 2.53254 0.166418 128 2.61404 0.849185E-01 41 6.09559 1 1.77778 4.31781 2 0.00000 6.09559 4 1.03355 5.06204 8 2.09579 3.99980 16 3.07184 3.02374 32 3.88644 2.20915 64 4.51498 1.58060 128 4.97636 1.11923 42 3.98079 1 2.00208 1.97871 2 0.785398 3.19539 4 1.46494 2.51585 8 2.02845 1.95234 16 2.45740 1.52339 32 2.78083 1.19996 64 3.02723 0.953552 128 3.21778 0.763007 43 2.99157 1 1.29248 1.69909 2 0.00000 2.99157 4 0.704369 2.28720 8 1.24393 1.74764 16 1.64059 1.35098 32 1.93360 1.05797 64 2.15391 0.837662 128 2.32281 0.668756 44 -0.300997E-01 1 0.412820E-04 0.301410E-01 2 -0.378401 0.348302 4 -0.189055 0.158955 8 -0.964974E-01 0.663977E-01 16 -0.578242E-01 0.277245E-01 32 -0.424631E-01 0.123634E-01 64 -0.359081E-01 0.580835E-02 128 -0.329118E-01 0.281206E-02 45 -0.292707 1 -0.832294 0.539587 2 0.00000 0.292707 4 -0.346883 0.541764E-01 8 -0.394601 0.101894 16 -0.387156 0.944492E-01 32 -0.368216 0.755094E-01 64 -0.349691 0.569846E-01 128 -0.334540 0.418335E-01 46 6.06909 1 4.65698 1.41211 2 7.90939 1.84030 4 6.54999 0.480896 8 6.29914 0.230045 16 6.18411 0.115019 32 6.12660 0.575094E-01 64 6.09785 0.287547E-01 128 6.08347 0.143774E-01 47 -0.444444 1 -0.490129 0.456846E-01 2 0.00000 0.444444 4 -0.241336 0.203108 8 -0.351240 0.932047E-01 16 -0.401411 0.430331E-01 32 -0.424439 0.200050E-01 64 -0.435073 0.937100E-02 128 -0.440019 0.442564E-02 48 -4.00000 1 -0.980258 3.01974 2 0.00000 4.00000 4 -0.599861 3.40014 8 -1.26141 2.73859 16 -1.84285 2.15715 32 -2.31986 1.68014 64 -2.70062 1.29938 128 -3.00055 0.999447 49 52.7407 1 -11.7769 64.5177 2 163.027 110.286 4 92.2639 39.5232 8 69.4365 16.6958 16 60.2250 7.48424 32 56.5188 3.77803 64 54.7512 2.01048 128 53.6074 0.866665 50 -0.128137 1 -0.424430E-15 0.128137 2 0.00000 0.128137 4 0.150071 0.278208 8 0.140544 0.268681 16 -0.659933E-01 0.621435E-01 32 -0.109643 0.184942E-01 64 -0.122143 0.599416E-02 128 -0.126035 0.210181E-02 51 -0.197814 1 -0.316254 0.118441 2 0.00000 0.197814 4 -0.131153 0.666607E-01 8 -0.163113 0.347001E-01 16 -0.176789 0.210247E-01 32 -0.183174 0.146394E-01 64 -0.186262 0.115521E-01 128 -0.187778 0.100351E-01 52 -0.899440E-01 1 0.652174E-01 0.155161 2 -2.99905 2.90911 4 -1.35961 1.26967 8 -1.46815 1.37820 16 -0.357605 0.267661 32 -1.08906 0.999115 64 -0.144402 0.544585E-01 128 -1.01495 0.925004 53 1.50462 1 1.15470 0.349922 2 0.853553 0.651069 4 1.18324 0.321382 8 1.40810 0.965200E-01 16 2.02084 0.516221 32 1.38922 0.115407 64 1.49377 0.108540E-01 128 1.63659 0.131968 54 1.15470 1 1.00000 0.154701 2 1.00000 0.154701 4 1.11538 0.393159E-01 8 1.13536 0.193376E-01 16 1.14423 0.104698E-01 32 1.14987 0.483439E-02 64 1.15228 0.241720E-02 128 1.15349 0.120860E-02 55 0.505059 1 0.569783 0.647242E-01 2 0.288056 0.217002 4 0.431284 0.737744E-01 8 0.473951 0.311074E-01 16 0.490574 0.144846E-01 32 0.498055 0.700400E-02 64 0.501613 0.344543E-02 128 0.503350 0.170891E-02 56 1.99225 1 2.22222 0.229970 2 1.05263 0.939621 4 1.63574 0.356516 8 1.85458 0.137671 16 1.92889 0.633637E-01 32 1.96177 0.304813E-01 64 1.97730 0.149565E-01 128 1.98484 0.740895E-02 57 0.400000 1 0.353553 0.464466E-01 2 0.500000 0.100000 4 0.434195 0.341953E-01 8 0.414560 0.145603E-01 16 0.406743 0.674343E-02 32 0.403246 0.324639E-02 64 0.401593 0.159271E-02 128 0.400789 0.788800E-03 TEST_INT_TEST Normal end of execution. 17 September 2021 11:53:53.173 PM