polynomials_test 27-Feb-2019 08:54:01 polynomials_test MATLAB version. Test polynomials. RANGE_BY_SAMPLING_TEST: Use N sample values of each polynomial over its domain to estimate its minimum Pmin and maximum Pmax N Pmin Pmax butcher: [-1.4393333333, +0.219] 16 -0.9392362348 0.1722153637 32 -1.096808774 0.1619794357 64 -1.218607005 0.1354705999 128 -1.146982586 0.200123647 256 -1.163550893 0.1864259985 512 -1.261186459 0.1643861716 1024 -1.301762549 0.181939832 2048 -1.328901868 0.1806981008 4096 -1.30398538 0.1970596662 8192 -1.333096962 0.1967859621 16384 -1.367394167 0.1955562743 32768 -1.347472355 0.2058122585 65536 -1.365699517 0.2125327583 131072 -1.355741449 0.2123066372 262144 -1.396926957 0.2177005289 524288 -1.397266108 0.2141781022 1048576 -1.39471054 0.2164118703 camel: [ -1.031628453489616, ? ]: 16 2.34293696 286.8335898 32 -0.5656567098 323.5035177 64 -0.9962010179 325.1266789 128 -1.027385874 379.3308185 256 -0.6818695846 307.3754905 512 -1.015374044 352.3236156 1024 -1.00287864 338.5134894 2048 -1.001644111 374.7228438 4096 -1.008459822 375.3418439 8192 -1.030057213 379.9255796 16384 -1.0315199 399.0081893 32768 -1.030716586 393.6800883 65536 -1.031499798 401.2157052 131072 -1.031604928 403.3259929 262144 -1.031451431 400.6543081 524288 -1.031561663 403.3561477 1048576 -1.03160806 403.9333421 camera: [-270397.4, +270202.6] 16 -46966.46863 87607.58773 32 -46583.37426 131880.9884 64 -107842.0561 96384.78574 128 -115095.894 102371.4783 256 -123199.992 125799.9772 512 -132145.0254 166292.1828 1024 -158207.0598 142974.8428 2048 -148419.6789 149261.7396 4096 -167042.0576 152023.3768 8192 -199173.1852 186346.3269 16384 -188996.5906 195186.7777 32768 -226765.1798 232225.4553 65536 -223290.0705 199323.1465 131072 -239475.7762 214594.9647 262144 -223937.433 219707.9062 524288 -226095.1346 221139.3738 1048576 -220739.0299 228089.0193 caprasse: [-3.1800966258, +4.4852773332] 16 -1.122640811 3.568584008 32 -1.647449732 3.56462884 64 -2.303226173 3.346400025 128 -1.409359901 3.38414889 256 -2.188055437 3.744646826 512 -2.156669132 3.949668106 1024 -2.681084075 3.871754895 2048 -2.508913074 3.954812721 4096 -2.708625627 4.240230838 8192 -2.917337055 4.252268658 16384 -2.863663818 4.295687111 32768 -3.057783765 4.344869033 65536 -2.983681702 4.280455175 131072 -3.054743761 4.401290811 262144 -3.026200759 4.387669535 524288 -3.087886456 4.408258398 1048576 -3.055552816 4.460833605 cyclic5: [-30000, +50000] 16 -9991.369907 6422.069083 32 -2145.460004 4624.181633 64 -4222.701274 7624.457565 128 -14992.43919 6112.12361 256 -8174.970236 11483.64356 512 -8628.718062 23099.33817 1024 -13808.80086 14629.6272 2048 -19021.72443 35545.02833 4096 -16946.40579 28357.55695 8192 -17621.7452 26592.28456 16384 -21133.52841 33712.66728 32768 -20793.87133 29474.87736 65536 -23036.08174 27816.00644 131072 -24933.06023 35863.25232 262144 -23580.77258 33465.41057 524288 -24018.55212 42566.08176 1048576 -25467.84219 39498.54646 cyclic7: [-5.0, +7.0] 16 -0.1818128315 0.2943232411 32 -0.1566307448 0.2425566252 64 -0.1613862091 0.5427491584 128 -0.6420509895 0.9047133214 256 -0.3866409939 0.4517013016 512 -0.9462007286 0.5831586333 1024 -1.5731949 0.9667101914 2048 -2.894077843 1.048015102 4096 -1.873678733 1.393726369 8192 -2.614966655 1.362242833 16384 -1.800746927 2.36379899 32768 -2.936911452 1.919211055 65536 -2.477698801 2.107552639 131072 -2.812458641 2.64886998 262144 -3.343510677 3.25534353 524288 -2.477821056 3.326030713 1048576 -2.669923467 3.303197282 cyclic8: [-8.0, +8.0] 16 -0.4040071044 0.05786917277 32 -0.08508165615 0.0622396526 64 -0.04506995837 0.118717916 128 -0.4218346391 0.2745799351 256 -0.2725731752 0.1953586594 512 -0.4612749938 0.4890045447 1024 -0.2750077722 0.55066444 2048 -0.6659820419 0.5284259662 4096 -0.7214659199 0.7541840231 8192 -2.193833684 1.286781661 16384 -0.9603117808 1.292588948 32768 -0.966085627 1.509452859 65536 -1.468336729 1.587438261 131072 -2.345419689 1.848147231 262144 -2.619592599 1.969771506 524288 -2.330561365 2.781625427 1048576 -2.384376073 2.303065784 goldstein_price: [ 3, ? ]: 16 51.12676154 820896.2479 32 105.5459688 203980.5891 64 10.92957343 724262.7837 128 3.817344807 798623.0425 256 9.765102979 867929.2964 512 8.221251128 969804.7232 1024 5.050014183 932723.5592 2048 4.492353885 940076.8531 4096 3.052169259 955370.7013 8192 3.052850987 1001207.627 16384 3.088965056 1004841.246 32768 3.00526769 1007141.08 65536 3.008620381 1012877.892 131072 3.002478186 1012477.438 262144 3.001078639 1014881.033 524288 3.001491298 1015031.333 1048576 3.000262585 1014524.015 hairer: [-1875.25, -48.25] 16 -926.0411179 -155.0324846 32 -1032.123614 -204.2213865 64 -923.2430733 -199.0450683 128 -1315.081641 -135.905696 256 -1023.718237 -114.4337671 512 -1309.290832 -112.6619642 1024 -1316.029618 -97.7389525 2048 -1525.32216 -93.39353897 4096 -1474.126644 -68.40662814 8192 -1491.76719 -73.46822717 16384 -1493.356889 -64.93141755 32768 -1594.938255 -74.16070942 65536 -1678.734462 -73.05326927 131072 -1611.06875 -67.44005 262144 -1659.385907 -58.2896173 524288 -1699.753406 -64.00018544 1048576 -1711.254178 -60.67348512 heart: [-1.36775, +1.74345327935 16 0.1140052593 1.007342859 32 0.3366754628 1.025957486 64 -0.3499218274 1.289240672 128 -0.07225874411 1.052502143 256 -0.4754486392 1.485554943 512 -0.3983935201 1.360331884 1024 -0.4679556199 1.460674034 2048 -0.5101981721 1.416384693 4096 -0.552286899 1.559009544 8192 -0.7789747658 1.575163714 16384 -0.7811037014 1.540810454 32768 -0.8293137161 1.640550256 65536 -0.7699449513 1.656784516 131072 -0.9025015425 1.654347059 262144 -0.9717289694 1.652736872 524288 -0.8253402394 1.63059713 1048576 -0.9570437895 1.685752139 himmelblau: [ 0, ? ]: 16 3.344612463 535.1187975 32 13.65550768 697.0243811 64 1.967193857 653.9187636 128 0.9391154232 833.246507 256 0.9589538353 657.0620917 512 0.7848869657 753.4085761 1024 0.03416051653 723.8703239 2048 0.008669694946 799.5137097 4096 0.09444232334 758.8565032 8192 0.01297949904 801.8225927 16384 0.01188193096 837.8470141 32768 0.006387915561 860.9489768 65536 0.008655583411 869.0417687 131072 6.034563755e-05 881.1186093 262144 0.0005764269044 874.9953325 524288 0.0008305200062 883.8135778 1048576 0.0003036544091 884.9308391 hunecke: [-1436.515078155, +161.120543283] 16 -787.374311 -37.15179156 32 -1101.766472 -73.77956751 64 -1145.158259 -1.121914179 128 -1187.430028 11.15542153 256 -1286.887026 -1.46343509 512 -1235.790156 42.27869517 1024 -1230.098017 66.51978582 2048 -1246.878481 98.97282175 4096 -1340.039759 85.46988876 8192 -1263.167011 98.62275376 16384 -1330.169829 129.8288892 32768 -1342.754365 98.77241454 65536 -1343.667596 116.1091694 131072 -1373.56007 123.7924842 262144 -1384.266376 135.977523 524288 -1412.494981 138.8953855 1048576 -1416.623171 139.3435011 kearfott: [ 0, ? ]: 16 1.890688428 73.3603846 32 0.6002071179 102.1437303 64 1.10893189 76.76005163 128 0.8683045935 97.6338526 256 0.4403239578 109.9642397 512 0.2045063378 122.7198361 1024 0.2308875819 130.9075302 2048 0.2923803795 151.9116666 4096 0.2187191028 158.5862868 8192 0.145415032 157.6793629 16384 0.04625697041 183.6609911 32768 0.06696469032 171.0181402 65536 0.03664279462 168.8297855 131072 0.03048870343 195.9865407 262144 0.01840079095 176.5833542 524288 0.002912729339 198.4442477 1048576 0.003118859558 207.6541432 lv3: [-9.35, +14.8 ] 16 -5.505976006 2.359192519 32 -2.411196489 4.221394903 64 -8.7249261 5.118580012 128 -6.196118255 5.045720063 256 -7.529919236 8.246773071 512 -7.992012879 6.563083491 1024 -6.584624644 8.049174981 2048 -8.76839483 8.190774113 4096 -7.471582786 7.949835791 8192 -8.519852729 8.063633439 16384 -8.789651166 8.158836837 32768 -8.920377623 8.475209322 65536 -9.046798181 8.147452917 131072 -9.009408155 8.498095034 262144 -9.060767317 8.530391987 524288 -8.969659498 8.503243629 1048576 -9.085109029 8.546697262 lv4: [-20.8, +22.8] 16 -6.884893684 4.151084073 32 -1.240729077 5.887408848 64 -8.377417891 8.796272966 128 -8.157045315 11.19769307 256 -8.607705406 7.948720738 512 -7.702569651 10.06555102 1024 -9.890049382 11.02818851 2048 -7.978823916 9.916188162 4096 -11.25760943 12.14712213 8192 -11.73914407 12.8606102 16384 -11.56105265 12.51808081 32768 -10.93875822 14.11446132 65536 -11.22992462 13.27660181 131072 -11.78153073 13.54132999 262144 -11.86689048 13.52270807 524288 -12.25617509 14.39611352 1048576 -12.5438857 13.73974981 magnetism6: [-0.25, +280.0] 16 56.49768538 176.9576672 32 20.37974721 155.4025017 64 13.068286 198.9760108 128 25.95516037 174.6717335 256 22.10666306 191.0768325 512 12.90162943 216.4283606 1024 7.597354659 194.5672584 2048 3.788502143 219.991467 4096 6.67575603 237.3487063 8192 4.261387053 219.9843987 16384 3.135742018 233.3861037 32768 4.552718225 241.1575989 65536 0.832176155 230.8975475 131072 2.191661966 252.8632361 262144 1.014809403 252.2550204 524288 1.238867148 245.623275 1048576 0.4762961256 249.9233468 magnetism7: [-0.25, +330.0] 16 2.61800899 8.614991166 32 0.8401354203 7.790561078 64 0.1041970534 9.155543046 128 0.8584411547 8.633176341 256 0.844812533 9.895126238 512 0.6488536823 9.918250127 1024 0.5583994316 10.07929211 2048 0.2170992297 11.76857085 4096 0.1689974334 10.57275424 8192 0.1073492634 11.30109414 16384 0.05507700358 10.79551285 32768 -0.1122765141 12.18196461 65536 -0.1082084514 10.75991951 131072 -0.1614776301 12.08280139 262144 -0.1262636206 12.31436106 524288 -0.1822241126 11.92265429 1048576 -0.154977993 12.44957874 quadratic: [ -2, ? ]: 16 14839.88234 48437.54628 32 9845.959905 38301.32847 64 9014.247013 42640.41569 128 8896.862825 51065.16435 256 7826.451775 52802.30423 512 5740.192882 50460.37355 1024 3763.537685 55927.90114 2048 4614.095632 56865.9075 4096 2543.616641 63334.06688 8192 3816.785264 67292.04963 16384 2150.438092 59774.27552 32768 2040.147525 64602.84142 65536 1472.641548 62707.54343 131072 737.0904958 65042.89241 262144 552.4597205 65332.71939 524288 1220.033859 67224.38646 1048576 779.2150834 67670.24279 rd: [-36.71269068, +10.40560403] 16 -25.28086805 4.497116297 32 -21.91160446 6.164186762 64 -31.84507985 5.314029372 128 -28.18593081 8.468599367 256 -32.2239576 9.280755427 512 -34.37184738 8.712661997 1024 -32.76607409 9.430387606 2048 -33.70567456 9.943244789 4096 -33.41258906 10.0578444 8192 -35.70089028 9.514725373 16384 -34.98116712 10.18877346 32768 -35.44273091 10.35038961 65536 -35.46953288 10.30957117 131072 -36.174262 10.29443881 262144 -36.24836969 10.29016873 524288 -36.25222472 10.37149306 1048576 -36.45468642 10.31003619 reimer5: [-5.0, +5.0] 16 -2.361421916 2.704557987 32 -3.972695582 0.986257506 64 -3.217000685 2.032755989 128 -3.483504688 2.88951549 256 -3.194819989 2.763117113 512 -4.477395366 3.370369899 1024 -4.15838999 3.494604936 2048 -4.616521353 3.062676495 4096 -4.432506719 3.206821162 8192 -4.823650023 3.729307995 16384 -4.854054326 4.39754424 32768 -4.564112961 4.469575818 65536 -4.676685955 4.254240181 131072 -4.828277994 4.65359081 262144 -4.919769089 4.530616105 524288 -4.913618108 4.720229217 1048576 -4.925946223 4.699093241 reimer6: [-937501, +937499] 16 -216406.1196 143249.8505 32 -198041.2158 162876.8859 64 -259952.0084 263578.3623 128 -356140.0489 284512.089 256 -392049.9024 351816.816 512 -300184.011 381708.3474 1024 -344592.3377 401510.8525 2048 -318159.9736 405190.3427 4096 -397220.4826 396754.8119 8192 -435313.677 442697.448 16384 -511761.0618 425393.6531 32768 -465225.1855 515696.4921 65536 -537552.4335 470410.11 131072 -520920.8046 493498.4913 262144 -561643.7515 545348.9635 524288 -597021.9616 569344.228 1048576 -544521.8243 614558.7621 rosenbrock: [ 0, ? ]: 16 3279.0466 25302.94453 32 640.123231 37067.04753 64 251.7248232 49858.14266 128 724.1849479 39743.87575 256 111.0103696 53190.69659 512 90.86844074 52432.71283 1024 389.4488942 43715.11226 2048 30.91942906 58801.74504 4096 33.86417839 49426.12446 8192 62.22950547 58722.93201 16384 26.18954261 61525.89623 32768 40.23342493 55536.65555 65536 8.67362244 60633.10559 131072 8.558799195 65560.51067 262144 2.775330825 61103.6659 524288 3.201745928 64586.774 1048576 3.961061056 64452.94159 schwefel: [ 0, ? ]: 16 26.20698845 14952.37685 32 19.24332636 14409.12887 64 27.78131083 14362.91488 128 13.00573185 15596.643 256 2.693938057 18210.45926 512 6.329847001 17679.3988 1024 1.733246677 19542.94178 2048 1.711402766 20728.86981 4096 3.945633822 20875.80899 8192 1.0483197 22272.86669 16384 0.3575255246 22289.12026 32768 0.3632678296 23597.06074 65536 0.04075515688 23006.96345 131072 0.1780585259 23778.34825 262144 0.1595290857 23857.28458 524288 0.04910429572 23952.09488 1048576 0.02833273288 24137.65225 smith1: [ ?, ? ]: 16 31894.87703 261820.2815 32 20766.65283 181182.4803 64 18646.85718 274073.9985 128 8275.672143 401170.8701 256 9830.832006 279646.508 512 6128.948192 356302.3166 1024 4283.764101 374814.1959 2048 205.8468433 361051.7997 4096 1562.047289 429562.6929 8192 208.5012886 432714.4986 16384 2868.328443 441846.2972 32768 -1873.591333 457636.3338 65536 -676.3127945 500037.7835 131072 -1958.482913 490542.9343 262144 -1184.279241 488462.4813 524288 -2307.426881 485044.1633 1048576 -2052.432228 485447.6323 smith2: [ ?, ? ]: 16 -94691.41437 -755.5715445 32 -124454.0286 -70.64406169 64 -184497.4088 -117.3613514 128 -251690.6777 -7.368007913 256 -117923.9421 -13.40702833 512 -206312.4668 31.61313318 1024 -213457.5251 74.94191361 2048 -272728.3135 131.6697951 4096 -246718.7849 173.5016588 8192 -240054.6462 178.4586741 16384 -293327.4482 144.01461 32768 -326207.5833 206.2040368 65536 -304006.3419 221.7402841 131072 -313583.3811 231.3577427 262144 -305065.6922 242.2777611 524288 -321105.6831 279.4288612 1048576 -322752.2198 299.9506699 virasoro: [-29.0, +21.0] 16 -5.095535765 12.38910217 32 -9.328907304 10.02015178 64 -7.559487901 14.2265071 128 -11.84791997 16.42500861 256 -11.17145084 16.60232768 512 -14.35943061 16.91136634 1024 -14.55244956 17.37568103 2048 -15.72789536 18.57021816 4096 -18.10639705 19.24736744 8192 -16.22807994 19.66357965 16384 -17.44105986 19.83234891 32768 -16.99306248 19.93345155 65536 -20.41002263 19.78756216 131072 -19.94418466 20.22108268 262144 -21.62984907 20.42587032 524288 -20.97522433 20.31674168 1048576 -21.55233453 20.54891895 wright: [-30.25, 40.0 ] 16 -10.81769109 -8.325569794 32 -10.8993462 -8.701143985 64 -11.40451116 -8.469731443 128 -11.56755932 -7.667416737 256 -11.25778333 -8.065405719 512 -11.50224087 -8.193169379 1024 -11.63862276 -7.991977062 2048 -11.64480556 -7.742748387 4096 -11.78017849 -7.707492893 8192 -11.88695213 -7.684721959 16384 -11.982057 -7.557812121 32768 -12.0614065 -7.528100813 65536 -12.17380653 -7.464791433 131072 -12.15407048 -7.583746326 262144 -12.08196782 -7.49659552 524288 -12.08095527 -7.460238632 1048576 -12.1654111 -7.483117164 zakharov: [ 0, ? ]:: 16 307.2572513 7805013.819 32 509.6723746 3601280.195 64 28.84753056 12197333.21 128 25.39264337 10302061.91 256 40.42131893 12283122.44 512 15.04679164 12467982.85 1024 16.1921555 15759352.47 2048 2.550197461 17513517.62 4096 10.20800089 16560273.83 8192 7.446913682 18107392.77 16384 5.984833934 23794094.48 32768 1.338112649 21106129.48 65536 2.364084421 22008999.36 131072 2.959038777 24757714.87 262144 1.130631563 25242079.72 524288 1.024112152 24810619.67 1048576 1.535256997 27185776.7 range_by_fmincon_test: Use the MATLAB fmincon() function to seek range. N Pmin Pmax Local minimum found that satisfies the constraints. Optimization completed because the objective function is non-decreasing in feasible directions, to within the default value of the optimality tolerance, and constraints are satisfied to within the default value of the constraint tolerance. <stopping criteria details> Local minimum found that satisfies the constraints. Optimization completed because the objective function is non-decreasing in feasible directions, to within the default value of the optimality tolerance, and constraints are satisfied to within the default value of the constraint tolerance. <stopping criteria details> butcher known: [-1.4393333333, +0.219] Butcher estimated: [ -1.439332949 0.2189993599] polynomials_test Normal end of execution. 27-Feb-2019 08:54:13 polynomials_test 27-Feb-2019 08:56:03 polynomials_test MATLAB version. Test polynomials. RANGE_BY_SAMPLING_TEST: Use N sample values of each polynomial over its domain to estimate its minimum Pmin and maximum Pmax N Pmin Pmax butcher: [-1.4393333333, +0.219] 16 -0.9392362348 0.1722153637 32 -1.096808774 0.1619794357 64 -1.218607005 0.1354705999 128 -1.146982586 0.200123647 256 -1.163550893 0.1864259985 512 -1.261186459 0.1643861716 1024 -1.301762549 0.181939832 2048 -1.328901868 0.1806981008 4096 -1.30398538 0.1970596662 8192 -1.333096962 0.1967859621 16384 -1.367394167 0.1955562743 32768 -1.347472355 0.2058122585 65536 -1.365699517 0.2125327583 131072 -1.355741449 0.2123066372 262144 -1.396926957 0.2177005289 524288 -1.397266108 0.2141781022 1048576 -1.39471054 0.2164118703 camel: [ -1.031628453489616, ? ]: 16 2.34293696 286.8335898 32 -0.5656567098 323.5035177 64 -0.9962010179 325.1266789 128 -1.027385874 379.3308185 256 -0.6818695846 307.3754905 512 -1.015374044 352.3236156 1024 -1.00287864 338.5134894 2048 -1.001644111 374.7228438 4096 -1.008459822 375.3418439 8192 -1.030057213 379.9255796 16384 -1.0315199 399.0081893 32768 -1.030716586 393.6800883 65536 -1.031499798 401.2157052 131072 -1.031604928 403.3259929 262144 -1.031451431 400.6543081 524288 -1.031561663 403.3561477 1048576 -1.03160806 403.9333421 camera: [-270397.4, +270202.6] 16 -46966.46863 87607.58773 32 -46583.37426 131880.9884 64 -107842.0561 96384.78574 128 -115095.894 102371.4783 256 -123199.992 125799.9772 512 -132145.0254 166292.1828 1024 -158207.0598 142974.8428 2048 -148419.6789 149261.7396 4096 -167042.0576 152023.3768 8192 -199173.1852 186346.3269 16384 -188996.5906 195186.7777 32768 -226765.1798 232225.4553 65536 -223290.0705 199323.1465 131072 -239475.7762 214594.9647 262144 -223937.433 219707.9062 524288 -226095.1346 221139.3738 1048576 -220739.0299 228089.0193 caprasse: [-3.1800966258, +4.4852773332] 16 -1.122640811 3.568584008 32 -1.647449732 3.56462884 64 -2.303226173 3.346400025 128 -1.409359901 3.38414889 256 -2.188055437 3.744646826 512 -2.156669132 3.949668106 1024 -2.681084075 3.871754895 2048 -2.508913074 3.954812721 4096 -2.708625627 4.240230838 8192 -2.917337055 4.252268658 16384 -2.863663818 4.295687111 32768 -3.057783765 4.344869033 65536 -2.983681702 4.280455175 131072 -3.054743761 4.401290811 262144 -3.026200759 4.387669535 524288 -3.087886456 4.408258398 1048576 -3.055552816 4.460833605 cyclic5: [-30000, +50000] 16 -9991.369907 6422.069083 32 -2145.460004 4624.181633 64 -4222.701274 7624.457565 128 -14992.43919 6112.12361 256 -8174.970236 11483.64356 512 -8628.718062 23099.33817 1024 -13808.80086 14629.6272 2048 -19021.72443 35545.02833 4096 -16946.40579 28357.55695 8192 -17621.7452 26592.28456 16384 -21133.52841 33712.66728 32768 -20793.87133 29474.87736 65536 -23036.08174 27816.00644 131072 -24933.06023 35863.25232 262144 -23580.77258 33465.41057 524288 -24018.55212 42566.08176 1048576 -25467.84219 39498.54646 cyclic7: [-5.0, +7.0] 16 -0.1818128315 0.2943232411 32 -0.1566307448 0.2425566252 64 -0.1613862091 0.5427491584 128 -0.6420509895 0.9047133214 256 -0.3866409939 0.4517013016 512 -0.9462007286 0.5831586333 1024 -1.5731949 0.9667101914 2048 -2.894077843 1.048015102 4096 -1.873678733 1.393726369 8192 -2.614966655 1.362242833 16384 -1.800746927 2.36379899 32768 -2.936911452 1.919211055 65536 -2.477698801 2.107552639 131072 -2.812458641 2.64886998 262144 -3.343510677 3.25534353 524288 -2.477821056 3.326030713 1048576 -2.669923467 3.303197282 cyclic8: [-8.0, +8.0] 16 -0.4040071044 0.05786917277 32 -0.08508165615 0.0622396526 64 -0.04506995837 0.118717916 128 -0.4218346391 0.2745799351 256 -0.2725731752 0.1953586594 512 -0.4612749938 0.4890045447 1024 -0.2750077722 0.55066444 2048 -0.6659820419 0.5284259662 4096 -0.7214659199 0.7541840231 8192 -2.193833684 1.286781661 16384 -0.9603117808 1.292588948 32768 -0.966085627 1.509452859 65536 -1.468336729 1.587438261 131072 -2.345419689 1.848147231 262144 -2.619592599 1.969771506 524288 -2.330561365 2.781625427 1048576 -2.384376073 2.303065784 goldstein_price: [ 3, ? ]: 16 51.12676154 820896.2479 32 105.5459688 203980.5891 64 10.92957343 724262.7837 128 3.817344807 798623.0425 256 9.765102979 867929.2964 512 8.221251128 969804.7232 1024 5.050014183 932723.5592 2048 4.492353885 940076.8531 4096 3.052169259 955370.7013 8192 3.052850987 1001207.627 16384 3.088965056 1004841.246 32768 3.00526769 1007141.08 65536 3.008620381 1012877.892 131072 3.002478186 1012477.438 262144 3.001078639 1014881.033 524288 3.001491298 1015031.333 1048576 3.000262585 1014524.015 hairer: [-1875.25, -48.25] 16 -926.0411179 -155.0324846 32 -1032.123614 -204.2213865 64 -923.2430733 -199.0450683 128 -1315.081641 -135.905696 256 -1023.718237 -114.4337671 512 -1309.290832 -112.6619642 1024 -1316.029618 -97.7389525 2048 -1525.32216 -93.39353897 4096 -1474.126644 -68.40662814 8192 -1491.76719 -73.46822717 16384 -1493.356889 -64.93141755 32768 -1594.938255 -74.16070942 65536 -1678.734462 -73.05326927 131072 -1611.06875 -67.44005 262144 -1659.385907 -58.2896173 524288 -1699.753406 -64.00018544 1048576 -1711.254178 -60.67348512 heart: [-1.36775, +1.74345327935 16 0.1140052593 1.007342859 32 0.3366754628 1.025957486 64 -0.3499218274 1.289240672 128 -0.07225874411 1.052502143 256 -0.4754486392 1.485554943 512 -0.3983935201 1.360331884 1024 -0.4679556199 1.460674034 2048 -0.5101981721 1.416384693 4096 -0.552286899 1.559009544 8192 -0.7789747658 1.575163714 16384 -0.7811037014 1.540810454 32768 -0.8293137161 1.640550256 65536 -0.7699449513 1.656784516 131072 -0.9025015425 1.654347059 262144 -0.9717289694 1.652736872 524288 -0.8253402394 1.63059713 1048576 -0.9570437895 1.685752139 himmelblau: [ 0, ? ]: 16 3.344612463 535.1187975 32 13.65550768 697.0243811 64 1.967193857 653.9187636 128 0.9391154232 833.246507 256 0.9589538353 657.0620917 512 0.7848869657 753.4085761 1024 0.03416051653 723.8703239 2048 0.008669694946 799.5137097 4096 0.09444232334 758.8565032 8192 0.01297949904 801.8225927 16384 0.01188193096 837.8470141 32768 0.006387915561 860.9489768 65536 0.008655583411 869.0417687 131072 6.034563755e-05 881.1186093 262144 0.0005764269044 874.9953325 524288 0.0008305200062 883.8135778 1048576 0.0003036544091 884.9308391 hunecke: [-1436.515078155, +161.120543283] 16 -787.374311 -37.15179156 32 -1101.766472 -73.77956751 64 -1145.158259 -1.121914179 128 -1187.430028 11.15542153 256 -1286.887026 -1.46343509 512 -1235.790156 42.27869517 1024 -1230.098017 66.51978582 2048 -1246.878481 98.97282175 4096 -1340.039759 85.46988876 8192 -1263.167011 98.62275376 16384 -1330.169829 129.8288892 32768 -1342.754365 98.77241454 65536 -1343.667596 116.1091694 131072 -1373.56007 123.7924842 262144 -1384.266376 135.977523 524288 -1412.494981 138.8953855 1048576 -1416.623171 139.3435011 kearfott: [ 0, ? ]: 16 1.890688428 73.3603846 32 0.6002071179 102.1437303 64 1.10893189 76.76005163 128 0.8683045935 97.6338526 256 0.4403239578 109.9642397 512 0.2045063378 122.7198361 1024 0.2308875819 130.9075302 2048 0.2923803795 151.9116666 4096 0.2187191028 158.5862868 8192 0.145415032 157.6793629 16384 0.04625697041 183.6609911 32768 0.06696469032 171.0181402 65536 0.03664279462 168.8297855 131072 0.03048870343 195.9865407 262144 0.01840079095 176.5833542 524288 0.002912729339 198.4442477 1048576 0.003118859558 207.6541432 lv3: [-9.35, +14.8 ] 16 -5.505976006 2.359192519 32 -2.411196489 4.221394903 64 -8.7249261 5.118580012 128 -6.196118255 5.045720063 256 -7.529919236 8.246773071 512 -7.992012879 6.563083491 1024 -6.584624644 8.049174981 2048 -8.76839483 8.190774113 4096 -7.471582786 7.949835791 8192 -8.519852729 8.063633439 16384 -8.789651166 8.158836837 32768 -8.920377623 8.475209322 65536 -9.046798181 8.147452917 131072 -9.009408155 8.498095034 262144 -9.060767317 8.530391987 524288 -8.969659498 8.503243629 1048576 -9.085109029 8.546697262 lv4: [-20.8, +22.8] 16 -6.884893684 4.151084073 32 -1.240729077 5.887408848 64 -8.377417891 8.796272966 128 -8.157045315 11.19769307 256 -8.607705406 7.948720738 512 -7.702569651 10.06555102 1024 -9.890049382 11.02818851 2048 -7.978823916 9.916188162 4096 -11.25760943 12.14712213 8192 -11.73914407 12.8606102 16384 -11.56105265 12.51808081 32768 -10.93875822 14.11446132 65536 -11.22992462 13.27660181 131072 -11.78153073 13.54132999 262144 -11.86689048 13.52270807 524288 -12.25617509 14.39611352 1048576 -12.5438857 13.73974981 magnetism6: [-0.25, +280.0] 16 56.49768538 176.9576672 32 20.37974721 155.4025017 64 13.068286 198.9760108 128 25.95516037 174.6717335 256 22.10666306 191.0768325 512 12.90162943 216.4283606 1024 7.597354659 194.5672584 2048 3.788502143 219.991467 4096 6.67575603 237.3487063 8192 4.261387053 219.9843987 16384 3.135742018 233.3861037 32768 4.552718225 241.1575989 65536 0.832176155 230.8975475 131072 2.191661966 252.8632361 262144 1.014809403 252.2550204 524288 1.238867148 245.623275 1048576 0.4762961256 249.9233468 magnetism7: [-0.25, +330.0] 16 2.61800899 8.614991166 32 0.8401354203 7.790561078 64 0.1041970534 9.155543046 128 0.8584411547 8.633176341 256 0.844812533 9.895126238 512 0.6488536823 9.918250127 1024 0.5583994316 10.07929211 2048 0.2170992297 11.76857085 4096 0.1689974334 10.57275424 8192 0.1073492634 11.30109414 16384 0.05507700358 10.79551285 32768 -0.1122765141 12.18196461 65536 -0.1082084514 10.75991951 131072 -0.1614776301 12.08280139 262144 -0.1262636206 12.31436106 524288 -0.1822241126 11.92265429 1048576 -0.154977993 12.44957874 quadratic: [ -2, ? ]: 16 14839.88234 48437.54628 32 9845.959905 38301.32847 64 9014.247013 42640.41569 128 8896.862825 51065.16435 256 7826.451775 52802.30423 512 5740.192882 50460.37355 1024 3763.537685 55927.90114 2048 4614.095632 56865.9075 4096 2543.616641 63334.06688 8192 3816.785264 67292.04963 16384 2150.438092 59774.27552 32768 2040.147525 64602.84142 65536 1472.641548 62707.54343 131072 737.0904958 65042.89241 262144 552.4597205 65332.71939 524288 1220.033859 67224.38646 1048576 779.2150834 67670.24279 rd: [-36.71269068, +10.40560403] 16 -25.28086805 4.497116297 32 -21.91160446 6.164186762 64 -31.84507985 5.314029372 128 -28.18593081 8.468599367 256 -32.2239576 9.280755427 512 -34.37184738 8.712661997 1024 -32.76607409 9.430387606 2048 -33.70567456 9.943244789 4096 -33.41258906 10.0578444 8192 -35.70089028 9.514725373 16384 -34.98116712 10.18877346 32768 -35.44273091 10.35038961 65536 -35.46953288 10.30957117 131072 -36.174262 10.29443881 262144 -36.24836969 10.29016873 524288 -36.25222472 10.37149306 1048576 -36.45468642 10.31003619 reimer5: [-5.0, +5.0] 16 -2.361421916 2.704557987 32 -3.972695582 0.986257506 64 -3.217000685 2.032755989 128 -3.483504688 2.88951549 256 -3.194819989 2.763117113 512 -4.477395366 3.370369899 1024 -4.15838999 3.494604936 2048 -4.616521353 3.062676495 4096 -4.432506719 3.206821162 8192 -4.823650023 3.729307995 16384 -4.854054326 4.39754424 32768 -4.564112961 4.469575818 65536 -4.676685955 4.254240181 131072 -4.828277994 4.65359081 262144 -4.919769089 4.530616105 524288 -4.913618108 4.720229217 1048576 -4.925946223 4.699093241 reimer6: [-937501, +937499] 16 -216406.1196 143249.8505 32 -198041.2158 162876.8859 64 -259952.0084 263578.3623 128 -356140.0489 284512.089 256 -392049.9024 351816.816 512 -300184.011 381708.3474 1024 -344592.3377 401510.8525 2048 -318159.9736 405190.3427 4096 -397220.4826 396754.8119 8192 -435313.677 442697.448 16384 -511761.0618 425393.6531 32768 -465225.1855 515696.4921 65536 -537552.4335 470410.11 131072 -520920.8046 493498.4913 262144 -561643.7515 545348.9635 524288 -597021.9616 569344.228 1048576 -544521.8243 614558.7621 rosenbrock: [ 0, ? ]: 16 3279.0466 25302.94453 32 640.123231 37067.04753 64 251.7248232 49858.14266 128 724.1849479 39743.87575 256 111.0103696 53190.69659 512 90.86844074 52432.71283 1024 389.4488942 43715.11226 2048 30.91942906 58801.74504 4096 33.86417839 49426.12446 8192 62.22950547 58722.93201 16384 26.18954261 61525.89623 32768 40.23342493 55536.65555 65536 8.67362244 60633.10559 131072 8.558799195 65560.51067 262144 2.775330825 61103.6659 524288 3.201745928 64586.774 1048576 3.961061056 64452.94159 schwefel: [ 0, ? ]: 16 26.20698845 14952.37685 32 19.24332636 14409.12887 64 27.78131083 14362.91488 128 13.00573185 15596.643 256 2.693938057 18210.45926 512 6.329847001 17679.3988 1024 1.733246677 19542.94178 2048 1.711402766 20728.86981 4096 3.945633822 20875.80899 8192 1.0483197 22272.86669 16384 0.3575255246 22289.12026 32768 0.3632678296 23597.06074 65536 0.04075515688 23006.96345 131072 0.1780585259 23778.34825 262144 0.1595290857 23857.28458 524288 0.04910429572 23952.09488 1048576 0.02833273288 24137.65225 smith1: [ ?, ? ]: 16 31894.87703 261820.2815 32 20766.65283 181182.4803 64 18646.85718 274073.9985 128 8275.672143 401170.8701 256 9830.832006 279646.508 512 6128.948192 356302.3166 1024 4283.764101 374814.1959 2048 205.8468433 361051.7997 4096 1562.047289 429562.6929 8192 208.5012886 432714.4986 16384 2868.328443 441846.2972 32768 -1873.591333 457636.3338 65536 -676.3127945 500037.7835 131072 -1958.482913 490542.9343 262144 -1184.279241 488462.4813 524288 -2307.426881 485044.1633 1048576 -2052.432228 485447.6323 smith2: [ ?, ? ]: 16 -94691.41437 -755.5715445 32 -124454.0286 -70.64406169 64 -184497.4088 -117.3613514 128 -251690.6777 -7.368007913 256 -117923.9421 -13.40702833 512 -206312.4668 31.61313318 1024 -213457.5251 74.94191361 2048 -272728.3135 131.6697951 4096 -246718.7849 173.5016588 8192 -240054.6462 178.4586741 16384 -293327.4482 144.01461 32768 -326207.5833 206.2040368 65536 -304006.3419 221.7402841 131072 -313583.3811 231.3577427 262144 -305065.6922 242.2777611 524288 -321105.6831 279.4288612 1048576 -322752.2198 299.9506699 virasoro: [-29.0, +21.0] 16 -5.095535765 12.38910217 32 -9.328907304 10.02015178 64 -7.559487901 14.2265071 128 -11.84791997 16.42500861 256 -11.17145084 16.60232768 512 -14.35943061 16.91136634 1024 -14.55244956 17.37568103 2048 -15.72789536 18.57021816 4096 -18.10639705 19.24736744 8192 -16.22807994 19.66357965 16384 -17.44105986 19.83234891 32768 -16.99306248 19.93345155 65536 -20.41002263 19.78756216 131072 -19.94418466 20.22108268 262144 -21.62984907 20.42587032 524288 -20.97522433 20.31674168 1048576 -21.55233453 20.54891895 wright: [-30.25, 40.0 ] 16 -10.81769109 -8.325569794 32 -10.8993462 -8.701143985 64 -11.40451116 -8.469731443 128 -11.56755932 -7.667416737 256 -11.25778333 -8.065405719 512 -11.50224087 -8.193169379 1024 -11.63862276 -7.991977062 2048 -11.64480556 -7.742748387 4096 -11.78017849 -7.707492893 8192 -11.88695213 -7.684721959 16384 -11.982057 -7.557812121 32768 -12.0614065 -7.528100813 65536 -12.17380653 -7.464791433 131072 -12.15407048 -7.583746326 262144 -12.08196782 -7.49659552 524288 -12.08095527 -7.460238632 1048576 -12.1654111 -7.483117164 zakharov: [ 0, ? ]:: 16 307.2572513 7805013.819 32 509.6723746 3601280.195 64 28.84753056 12197333.21 128 25.39264337 10302061.91 256 40.42131893 12283122.44 512 15.04679164 12467982.85 1024 16.1921555 15759352.47 2048 2.550197461 17513517.62 4096 10.20800089 16560273.83 8192 7.446913682 18107392.77 16384 5.984833934 23794094.48 32768 1.338112649 21106129.48 65536 2.364084421 22008999.36 131072 2.959038777 24757714.87 262144 1.130631563 25242079.72 524288 1.024112152 24810619.67 1048576 1.535256997 27185776.7 range_by_fmincon_test: Use the MATLAB fmincon() function to seek range. {Error using optimoptions (line 124) Invalid solver specified. Provide a solver name or handle (such as 'fmincon' or @fminunc). Type DOC OPTIMOPTIONS for a list of solvers. Error in range_by_fmincon_test (line 29) options = optimoptions ( 'Display', 'off' ); Error in polynomials_test (line 28) range_by_fmincon_test ( ); } polynomials_test 27-Feb-2019 08:57:33 polynomials_test MATLAB version. Test polynomials. RANGE_BY_SAMPLING_TEST: Use N sample values of each polynomial over its domain to estimate its minimum Pmin and maximum Pmax N Pmin Pmax butcher: [-1.4393333333, +0.219] 16 -0.9392362348 0.1722153637 32 -1.096808774 0.1619794357 64 -1.218607005 0.1354705999 128 -1.146982586 0.200123647 256 -1.163550893 0.1864259985 512 -1.261186459 0.1643861716 1024 -1.301762549 0.181939832 2048 -1.328901868 0.1806981008 4096 -1.30398538 0.1970596662 8192 -1.333096962 0.1967859621 16384 -1.367394167 0.1955562743 32768 -1.347472355 0.2058122585 65536 -1.365699517 0.2125327583 131072 -1.355741449 0.2123066372 262144 -1.396926957 0.2177005289 524288 -1.397266108 0.2141781022 1048576 -1.39471054 0.2164118703 camel: [ -1.031628453489616, ? ]: 16 2.34293696 286.8335898 32 -0.5656567098 323.5035177 64 -0.9962010179 325.1266789 128 -1.027385874 379.3308185 256 -0.6818695846 307.3754905 512 -1.015374044 352.3236156 1024 -1.00287864 338.5134894 2048 -1.001644111 374.7228438 4096 -1.008459822 375.3418439 8192 -1.030057213 379.9255796 16384 -1.0315199 399.0081893 32768 -1.030716586 393.6800883 65536 -1.031499798 401.2157052 131072 -1.031604928 403.3259929 262144 -1.031451431 400.6543081 524288 -1.031561663 403.3561477 1048576 -1.03160806 403.9333421 camera: [-270397.4, +270202.6] 16 -46966.46863 87607.58773 32 -46583.37426 131880.9884 64 -107842.0561 96384.78574 128 -115095.894 102371.4783 256 -123199.992 125799.9772 512 -132145.0254 166292.1828 1024 -158207.0598 142974.8428 2048 -148419.6789 149261.7396 4096 -167042.0576 152023.3768 8192 -199173.1852 186346.3269 16384 -188996.5906 195186.7777 32768 -226765.1798 232225.4553 65536 -223290.0705 199323.1465 131072 -239475.7762 214594.9647 262144 -223937.433 219707.9062 524288 -226095.1346 221139.3738 1048576 -220739.0299 228089.0193 caprasse: [-3.1800966258, +4.4852773332] 16 -1.122640811 3.568584008 32 -1.647449732 3.56462884 64 -2.303226173 3.346400025 128 -1.409359901 3.38414889 256 -2.188055437 3.744646826 512 -2.156669132 3.949668106 1024 -2.681084075 3.871754895 2048 -2.508913074 3.954812721 4096 -2.708625627 4.240230838 8192 -2.917337055 4.252268658 16384 -2.863663818 4.295687111 32768 -3.057783765 4.344869033 65536 -2.983681702 4.280455175 131072 -3.054743761 4.401290811 262144 -3.026200759 4.387669535 524288 -3.087886456 4.408258398 1048576 -3.055552816 4.460833605 cyclic5: [-30000, +50000] 16 -9991.369907 6422.069083 32 -2145.460004 4624.181633 64 -4222.701274 7624.457565 128 -14992.43919 6112.12361 256 -8174.970236 11483.64356 512 -8628.718062 23099.33817 1024 -13808.80086 14629.6272 2048 -19021.72443 35545.02833 4096 -16946.40579 28357.55695 8192 -17621.7452 26592.28456 16384 -21133.52841 33712.66728 32768 -20793.87133 29474.87736 65536 -23036.08174 27816.00644 131072 -24933.06023 35863.25232 262144 -23580.77258 33465.41057 524288 -24018.55212 42566.08176 1048576 -25467.84219 39498.54646 cyclic7: [-5.0, +7.0] 16 -0.1818128315 0.2943232411 32 -0.1566307448 0.2425566252 64 -0.1613862091 0.5427491584 128 -0.6420509895 0.9047133214 256 -0.3866409939 0.4517013016 512 -0.9462007286 0.5831586333 1024 -1.5731949 0.9667101914 2048 -2.894077843 1.048015102 4096 -1.873678733 1.393726369 8192 -2.614966655 1.362242833 16384 -1.800746927 2.36379899 32768 -2.936911452 1.919211055 65536 -2.477698801 2.107552639 131072 -2.812458641 2.64886998 262144 -3.343510677 3.25534353 524288 -2.477821056 3.326030713 1048576 -2.669923467 3.303197282 cyclic8: [-8.0, +8.0] 16 -0.4040071044 0.05786917277 32 -0.08508165615 0.0622396526 64 -0.04506995837 0.118717916 128 -0.4218346391 0.2745799351 256 -0.2725731752 0.1953586594 512 -0.4612749938 0.4890045447 1024 -0.2750077722 0.55066444 2048 -0.6659820419 0.5284259662 4096 -0.7214659199 0.7541840231 8192 -2.193833684 1.286781661 16384 -0.9603117808 1.292588948 32768 -0.966085627 1.509452859 65536 -1.468336729 1.587438261 131072 -2.345419689 1.848147231 262144 -2.619592599 1.969771506 524288 -2.330561365 2.781625427 1048576 -2.384376073 2.303065784 goldstein_price: [ 3, ? ]: 16 51.12676154 820896.2479 32 105.5459688 203980.5891 64 10.92957343 724262.7837 128 3.817344807 798623.0425 256 9.765102979 867929.2964 512 8.221251128 969804.7232 1024 5.050014183 932723.5592 2048 4.492353885 940076.8531 4096 3.052169259 955370.7013 8192 3.052850987 1001207.627 16384 3.088965056 1004841.246 32768 3.00526769 1007141.08 65536 3.008620381 1012877.892 131072 3.002478186 1012477.438 262144 3.001078639 1014881.033 524288 3.001491298 1015031.333 1048576 3.000262585 1014524.015 hairer: [-1875.25, -48.25] 16 -926.0411179 -155.0324846 32 -1032.123614 -204.2213865 64 -923.2430733 -199.0450683 128 -1315.081641 -135.905696 256 -1023.718237 -114.4337671 512 -1309.290832 -112.6619642 1024 -1316.029618 -97.7389525 2048 -1525.32216 -93.39353897 4096 -1474.126644 -68.40662814 8192 -1491.76719 -73.46822717 16384 -1493.356889 -64.93141755 32768 -1594.938255 -74.16070942 65536 -1678.734462 -73.05326927 131072 -1611.06875 -67.44005 262144 -1659.385907 -58.2896173 524288 -1699.753406 -64.00018544 1048576 -1711.254178 -60.67348512 heart: [-1.36775, +1.74345327935 16 0.1140052593 1.007342859 32 0.3366754628 1.025957486 64 -0.3499218274 1.289240672 128 -0.07225874411 1.052502143 256 -0.4754486392 1.485554943 512 -0.3983935201 1.360331884 1024 -0.4679556199 1.460674034 2048 -0.5101981721 1.416384693 4096 -0.552286899 1.559009544 8192 -0.7789747658 1.575163714 16384 -0.7811037014 1.540810454 32768 -0.8293137161 1.640550256 65536 -0.7699449513 1.656784516 131072 -0.9025015425 1.654347059 262144 -0.9717289694 1.652736872 524288 -0.8253402394 1.63059713 1048576 -0.9570437895 1.685752139 himmelblau: [ 0, ? ]: 16 3.344612463 535.1187975 32 13.65550768 697.0243811 64 1.967193857 653.9187636 128 0.9391154232 833.246507 256 0.9589538353 657.0620917 512 0.7848869657 753.4085761 1024 0.03416051653 723.8703239 2048 0.008669694946 799.5137097 4096 0.09444232334 758.8565032 8192 0.01297949904 801.8225927 16384 0.01188193096 837.8470141 32768 0.006387915561 860.9489768 65536 0.008655583411 869.0417687 131072 6.034563755e-05 881.1186093 262144 0.0005764269044 874.9953325 524288 0.0008305200062 883.8135778 1048576 0.0003036544091 884.9308391 hunecke: [-1436.515078155, +161.120543283] 16 -787.374311 -37.15179156 32 -1101.766472 -73.77956751 64 -1145.158259 -1.121914179 128 -1187.430028 11.15542153 256 -1286.887026 -1.46343509 512 -1235.790156 42.27869517 1024 -1230.098017 66.51978582 2048 -1246.878481 98.97282175 4096 -1340.039759 85.46988876 8192 -1263.167011 98.62275376 16384 -1330.169829 129.8288892 32768 -1342.754365 98.77241454 65536 -1343.667596 116.1091694 131072 -1373.56007 123.7924842 262144 -1384.266376 135.977523 524288 -1412.494981 138.8953855 1048576 -1416.623171 139.3435011 kearfott: [ 0, ? ]: 16 1.890688428 73.3603846 32 0.6002071179 102.1437303 64 1.10893189 76.76005163 128 0.8683045935 97.6338526 256 0.4403239578 109.9642397 512 0.2045063378 122.7198361 1024 0.2308875819 130.9075302 2048 0.2923803795 151.9116666 4096 0.2187191028 158.5862868 8192 0.145415032 157.6793629 16384 0.04625697041 183.6609911 32768 0.06696469032 171.0181402 65536 0.03664279462 168.8297855 131072 0.03048870343 195.9865407 262144 0.01840079095 176.5833542 524288 0.002912729339 198.4442477 1048576 0.003118859558 207.6541432 lv3: [-9.35, +14.8 ] 16 -5.505976006 2.359192519 32 -2.411196489 4.221394903 64 -8.7249261 5.118580012 128 -6.196118255 5.045720063 256 -7.529919236 8.246773071 512 -7.992012879 6.563083491 1024 -6.584624644 8.049174981 2048 -8.76839483 8.190774113 4096 -7.471582786 7.949835791 8192 -8.519852729 8.063633439 16384 -8.789651166 8.158836837 32768 -8.920377623 8.475209322 65536 -9.046798181 8.147452917 131072 -9.009408155 8.498095034 262144 -9.060767317 8.530391987 524288 -8.969659498 8.503243629 1048576 -9.085109029 8.546697262 lv4: [-20.8, +22.8] 16 -6.884893684 4.151084073 32 -1.240729077 5.887408848 64 -8.377417891 8.796272966 128 -8.157045315 11.19769307 256 -8.607705406 7.948720738 512 -7.702569651 10.06555102 1024 -9.890049382 11.02818851 2048 -7.978823916 9.916188162 4096 -11.25760943 12.14712213 8192 -11.73914407 12.8606102 16384 -11.56105265 12.51808081 32768 -10.93875822 14.11446132 65536 -11.22992462 13.27660181 131072 -11.78153073 13.54132999 262144 -11.86689048 13.52270807 524288 -12.25617509 14.39611352 1048576 -12.5438857 13.73974981 magnetism6: [-0.25, +280.0] 16 56.49768538 176.9576672 32 20.37974721 155.4025017 64 13.068286 198.9760108 128 25.95516037 174.6717335 256 22.10666306 191.0768325 512 12.90162943 216.4283606 1024 7.597354659 194.5672584 2048 3.788502143 219.991467 4096 6.67575603 237.3487063 8192 4.261387053 219.9843987 16384 3.135742018 233.3861037 32768 4.552718225 241.1575989 65536 0.832176155 230.8975475 131072 2.191661966 252.8632361 262144 1.014809403 252.2550204 524288 1.238867148 245.623275 1048576 0.4762961256 249.9233468 magnetism7: [-0.25, +330.0] 16 2.61800899 8.614991166 32 0.8401354203 7.790561078 64 0.1041970534 9.155543046 128 0.8584411547 8.633176341 256 0.844812533 9.895126238 512 0.6488536823 9.918250127 1024 0.5583994316 10.07929211 2048 0.2170992297 11.76857085 4096 0.1689974334 10.57275424 8192 0.1073492634 11.30109414 16384 0.05507700358 10.79551285 32768 -0.1122765141 12.18196461 65536 -0.1082084514 10.75991951 131072 -0.1614776301 12.08280139 262144 -0.1262636206 12.31436106 524288 -0.1822241126 11.92265429 1048576 -0.154977993 12.44957874 quadratic: [ -2, ? ]: 16 14839.88234 48437.54628 32 9845.959905 38301.32847 64 9014.247013 42640.41569 128 8896.862825 51065.16435 256 7826.451775 52802.30423 512 5740.192882 50460.37355 1024 3763.537685 55927.90114 2048 4614.095632 56865.9075 4096 2543.616641 63334.06688 8192 3816.785264 67292.04963 16384 2150.438092 59774.27552 32768 2040.147525 64602.84142 65536 1472.641548 62707.54343 131072 737.0904958 65042.89241 262144 552.4597205 65332.71939 524288 1220.033859 67224.38646 1048576 779.2150834 67670.24279 rd: [-36.71269068, +10.40560403] 16 -25.28086805 4.497116297 32 -21.91160446 6.164186762 64 -31.84507985 5.314029372 128 -28.18593081 8.468599367 256 -32.2239576 9.280755427 512 -34.37184738 8.712661997 1024 -32.76607409 9.430387606 2048 -33.70567456 9.943244789 4096 -33.41258906 10.0578444 8192 -35.70089028 9.514725373 16384 -34.98116712 10.18877346 32768 -35.44273091 10.35038961 65536 -35.46953288 10.30957117 131072 -36.174262 10.29443881 262144 -36.24836969 10.29016873 524288 -36.25222472 10.37149306 1048576 -36.45468642 10.31003619 reimer5: [-5.0, +5.0] 16 -2.361421916 2.704557987 32 -3.972695582 0.986257506 64 -3.217000685 2.032755989 128 -3.483504688 2.88951549 256 -3.194819989 2.763117113 512 -4.477395366 3.370369899 1024 -4.15838999 3.494604936 2048 -4.616521353 3.062676495 4096 -4.432506719 3.206821162 8192 -4.823650023 3.729307995 16384 -4.854054326 4.39754424 32768 -4.564112961 4.469575818 65536 -4.676685955 4.254240181 131072 -4.828277994 4.65359081 262144 -4.919769089 4.530616105 524288 -4.913618108 4.720229217 1048576 -4.925946223 4.699093241 reimer6: [-937501, +937499] 16 -216406.1196 143249.8505 32 -198041.2158 162876.8859 64 -259952.0084 263578.3623 128 -356140.0489 284512.089 256 -392049.9024 351816.816 512 -300184.011 381708.3474 1024 -344592.3377 401510.8525 2048 -318159.9736 405190.3427 4096 -397220.4826 396754.8119 8192 -435313.677 442697.448 16384 -511761.0618 425393.6531 32768 -465225.1855 515696.4921 65536 -537552.4335 470410.11 131072 -520920.8046 493498.4913 262144 -561643.7515 545348.9635 524288 -597021.9616 569344.228 1048576 -544521.8243 614558.7621 rosenbrock: [ 0, ? ]: 16 3279.0466 25302.94453 32 640.123231 37067.04753 64 251.7248232 49858.14266 128 724.1849479 39743.87575 256 111.0103696 53190.69659 512 90.86844074 52432.71283 1024 389.4488942 43715.11226 2048 30.91942906 58801.74504 4096 33.86417839 49426.12446 8192 62.22950547 58722.93201 16384 26.18954261 61525.89623 32768 40.23342493 55536.65555 65536 8.67362244 60633.10559 131072 8.558799195 65560.51067 262144 2.775330825 61103.6659 524288 3.201745928 64586.774 1048576 3.961061056 64452.94159 schwefel: [ 0, ? ]: 16 26.20698845 14952.37685 32 19.24332636 14409.12887 64 27.78131083 14362.91488 128 13.00573185 15596.643 256 2.693938057 18210.45926 512 6.329847001 17679.3988 1024 1.733246677 19542.94178 2048 1.711402766 20728.86981 4096 3.945633822 20875.80899 8192 1.0483197 22272.86669 16384 0.3575255246 22289.12026 32768 0.3632678296 23597.06074 65536 0.04075515688 23006.96345 131072 0.1780585259 23778.34825 262144 0.1595290857 23857.28458 524288 0.04910429572 23952.09488 1048576 0.02833273288 24137.65225 smith1: [ ?, ? ]: 16 31894.87703 261820.2815 32 20766.65283 181182.4803 64 18646.85718 274073.9985 128 8275.672143 401170.8701 256 9830.832006 279646.508 512 6128.948192 356302.3166 1024 4283.764101 374814.1959 2048 205.8468433 361051.7997 4096 1562.047289 429562.6929 8192 208.5012886 432714.4986 16384 2868.328443 441846.2972 32768 -1873.591333 457636.3338 65536 -676.3127945 500037.7835 131072 -1958.482913 490542.9343 262144 -1184.279241 488462.4813 524288 -2307.426881 485044.1633 1048576 -2052.432228 485447.6323 smith2: [ ?, ? ]: 16 -94691.41437 -755.5715445 32 -124454.0286 -70.64406169 64 -184497.4088 -117.3613514 128 -251690.6777 -7.368007913 256 -117923.9421 -13.40702833 512 -206312.4668 31.61313318 1024 -213457.5251 74.94191361 2048 -272728.3135 131.6697951 4096 -246718.7849 173.5016588 8192 -240054.6462 178.4586741 16384 -293327.4482 144.01461 32768 -326207.5833 206.2040368 65536 -304006.3419 221.7402841 131072 -313583.3811 231.3577427 262144 -305065.6922 242.2777611 524288 -321105.6831 279.4288612 1048576 -322752.2198 299.9506699 virasoro: [-29.0, +21.0] 16 -5.095535765 12.38910217 32 -9.328907304 10.02015178 64 -7.559487901 14.2265071 128 -11.84791997 16.42500861 256 -11.17145084 16.60232768 512 -14.35943061 16.91136634 1024 -14.55244956 17.37568103 2048 -15.72789536 18.57021816 4096 -18.10639705 19.24736744 8192 -16.22807994 19.66357965 16384 -17.44105986 19.83234891 32768 -16.99306248 19.93345155 65536 -20.41002263 19.78756216 131072 -19.94418466 20.22108268 262144 -21.62984907 20.42587032 524288 -20.97522433 20.31674168 1048576 -21.55233453 20.54891895 wright: [-30.25, 40.0 ] 16 -10.81769109 -8.325569794 32 -10.8993462 -8.701143985 64 -11.40451116 -8.469731443 128 -11.56755932 -7.667416737 256 -11.25778333 -8.065405719 512 -11.50224087 -8.193169379 1024 -11.63862276 -7.991977062 2048 -11.64480556 -7.742748387 4096 -11.78017849 -7.707492893 8192 -11.88695213 -7.684721959 16384 -11.982057 -7.557812121 32768 -12.0614065 -7.528100813 65536 -12.17380653 -7.464791433 131072 -12.15407048 -7.583746326 262144 -12.08196782 -7.49659552 524288 -12.08095527 -7.460238632 1048576 -12.1654111 -7.483117164 zakharov: [ 0, ? ]:: 16 307.2572513 7805013.819 32 509.6723746 3601280.195 64 28.84753056 12197333.21 128 25.39264337 10302061.91 256 40.42131893 12283122.44 512 15.04679164 12467982.85 1024 16.1921555 15759352.47 2048 2.550197461 17513517.62 4096 10.20800089 16560273.83 8192 7.446913682 18107392.77 16384 5.984833934 23794094.48 32768 1.338112649 21106129.48 65536 2.364084421 22008999.36 131072 2.959038777 24757714.87 262144 1.130631563 25242079.72 524288 1.024112152 24810619.67 1048576 1.535256997 27185776.7 range_by_fmincon_test: Use the MATLAB fmincon() function to seek range. {Error using optimfcnchk (line 99) NONLCON must be a function. Error in fmincon (line 421) confcn = optimfcnchk(NONLCON,'fmincon',length(varargin),funValCheck,flags.gradconst,false,true); Error in range_by_fmincon_test (line 36) [ x_min, f_min ] = fmincon ( @butcher_min_fun, x0, [], [], [], [], lb, ub, options ); Error in polynomials_test (line 28) range_by_fmincon_test ( ); } polynomials_test 27-Feb-2019 08:58:11 polynomials_test MATLAB version. Test polynomials. RANGE_BY_SAMPLING_TEST: Use N sample values of each polynomial over its domain to estimate its minimum Pmin and maximum Pmax N Pmin Pmax butcher: [-1.4393333333, +0.219] 16 -0.9392362348 0.1722153637 32 -1.096808774 0.1619794357 64 -1.218607005 0.1354705999 128 -1.146982586 0.200123647 256 -1.163550893 0.1864259985 512 -1.261186459 0.1643861716 1024 -1.301762549 0.181939832 2048 -1.328901868 0.1806981008 4096 -1.30398538 0.1970596662 8192 -1.333096962 0.1967859621 16384 -1.367394167 0.1955562743 32768 -1.347472355 0.2058122585 65536 -1.365699517 0.2125327583 131072 -1.355741449 0.2123066372 262144 -1.396926957 0.2177005289 524288 -1.397266108 0.2141781022 1048576 -1.39471054 0.2164118703 camel: [ -1.031628453489616, ? ]: 16 2.34293696 286.8335898 32 -0.5656567098 323.5035177 64 -0.9962010179 325.1266789 128 -1.027385874 379.3308185 256 -0.6818695846 307.3754905 512 -1.015374044 352.3236156 1024 -1.00287864 338.5134894 2048 -1.001644111 374.7228438 4096 -1.008459822 375.3418439 8192 -1.030057213 379.9255796 16384 -1.0315199 399.0081893 32768 -1.030716586 393.6800883 65536 -1.031499798 401.2157052 131072 -1.031604928 403.3259929 262144 -1.031451431 400.6543081 524288 -1.031561663 403.3561477 1048576 -1.03160806 403.9333421 camera: [-270397.4, +270202.6] 16 -46966.46863 87607.58773 32 -46583.37426 131880.9884 64 -107842.0561 96384.78574 128 -115095.894 102371.4783 256 -123199.992 125799.9772 512 -132145.0254 166292.1828 1024 -158207.0598 142974.8428 2048 -148419.6789 149261.7396 4096 -167042.0576 152023.3768 8192 -199173.1852 186346.3269 16384 -188996.5906 195186.7777 32768 -226765.1798 232225.4553 65536 -223290.0705 199323.1465 131072 -239475.7762 214594.9647 262144 -223937.433 219707.9062 524288 -226095.1346 221139.3738 1048576 -220739.0299 228089.0193 caprasse: [-3.1800966258, +4.4852773332] 16 -1.122640811 3.568584008 32 -1.647449732 3.56462884 64 -2.303226173 3.346400025 128 -1.409359901 3.38414889 256 -2.188055437 3.744646826 512 -2.156669132 3.949668106 1024 -2.681084075 3.871754895 2048 -2.508913074 3.954812721 4096 -2.708625627 4.240230838 8192 -2.917337055 4.252268658 16384 -2.863663818 4.295687111 32768 -3.057783765 4.344869033 65536 -2.983681702 4.280455175 131072 -3.054743761 4.401290811 262144 -3.026200759 4.387669535 524288 -3.087886456 4.408258398 1048576 -3.055552816 4.460833605 cyclic5: [-30000, +50000] 16 -9991.369907 6422.069083 32 -2145.460004 4624.181633 64 -4222.701274 7624.457565 128 -14992.43919 6112.12361 256 -8174.970236 11483.64356 512 -8628.718062 23099.33817 1024 -13808.80086 14629.6272 2048 -19021.72443 35545.02833 4096 -16946.40579 28357.55695 8192 -17621.7452 26592.28456 16384 -21133.52841 33712.66728 32768 -20793.87133 29474.87736 65536 -23036.08174 27816.00644 131072 -24933.06023 35863.25232 262144 -23580.77258 33465.41057 524288 -24018.55212 42566.08176 1048576 -25467.84219 39498.54646 cyclic7: [-5.0, +7.0] 16 -0.1818128315 0.2943232411 32 -0.1566307448 0.2425566252 64 -0.1613862091 0.5427491584 128 -0.6420509895 0.9047133214 256 -0.3866409939 0.4517013016 512 -0.9462007286 0.5831586333 1024 -1.5731949 0.9667101914 2048 -2.894077843 1.048015102 4096 -1.873678733 1.393726369 8192 -2.614966655 1.362242833 16384 -1.800746927 2.36379899 32768 -2.936911452 1.919211055 65536 -2.477698801 2.107552639 131072 -2.812458641 2.64886998 262144 -3.343510677 3.25534353 524288 -2.477821056 3.326030713 1048576 -2.669923467 3.303197282 cyclic8: [-8.0, +8.0] 16 -0.4040071044 0.05786917277 32 -0.08508165615 0.0622396526 64 -0.04506995837 0.118717916 128 -0.4218346391 0.2745799351 256 -0.2725731752 0.1953586594 512 -0.4612749938 0.4890045447 1024 -0.2750077722 0.55066444 2048 -0.6659820419 0.5284259662 4096 -0.7214659199 0.7541840231 8192 -2.193833684 1.286781661 16384 -0.9603117808 1.292588948 32768 -0.966085627 1.509452859 65536 -1.468336729 1.587438261 131072 -2.345419689 1.848147231 262144 -2.619592599 1.969771506 524288 -2.330561365 2.781625427 1048576 -2.384376073 2.303065784 goldstein_price: [ 3, ? ]: 16 51.12676154 820896.2479 32 105.5459688 203980.5891 64 10.92957343 724262.7837 128 3.817344807 798623.0425 256 9.765102979 867929.2964 512 8.221251128 969804.7232 1024 5.050014183 932723.5592 2048 4.492353885 940076.8531 4096 3.052169259 955370.7013 8192 3.052850987 1001207.627 16384 3.088965056 1004841.246 32768 3.00526769 1007141.08 65536 3.008620381 1012877.892 131072 3.002478186 1012477.438 262144 3.001078639 1014881.033 524288 3.001491298 1015031.333 1048576 3.000262585 1014524.015 hairer: [-1875.25, -48.25] 16 -926.0411179 -155.0324846 32 -1032.123614 -204.2213865 64 -923.2430733 -199.0450683 128 -1315.081641 -135.905696 256 -1023.718237 -114.4337671 512 -1309.290832 -112.6619642 1024 -1316.029618 -97.7389525 2048 -1525.32216 -93.39353897 4096 -1474.126644 -68.40662814 8192 -1491.76719 -73.46822717 16384 -1493.356889 -64.93141755 32768 -1594.938255 -74.16070942 65536 -1678.734462 -73.05326927 131072 -1611.06875 -67.44005 262144 -1659.385907 -58.2896173 524288 -1699.753406 -64.00018544 1048576 -1711.254178 -60.67348512 heart: [-1.36775, +1.74345327935 16 0.1140052593 1.007342859 32 0.3366754628 1.025957486 64 -0.3499218274 1.289240672 128 -0.07225874411 1.052502143 256 -0.4754486392 1.485554943 512 -0.3983935201 1.360331884 1024 -0.4679556199 1.460674034 2048 -0.5101981721 1.416384693 4096 -0.552286899 1.559009544 8192 -0.7789747658 1.575163714 16384 -0.7811037014 1.540810454 32768 -0.8293137161 1.640550256 65536 -0.7699449513 1.656784516 131072 -0.9025015425 1.654347059 262144 -0.9717289694 1.652736872 524288 -0.8253402394 1.63059713 1048576 -0.9570437895 1.685752139 himmelblau: [ 0, ? ]: 16 3.344612463 535.1187975 32 13.65550768 697.0243811 64 1.967193857 653.9187636 128 0.9391154232 833.246507 256 0.9589538353 657.0620917 512 0.7848869657 753.4085761 1024 0.03416051653 723.8703239 2048 0.008669694946 799.5137097 4096 0.09444232334 758.8565032 8192 0.01297949904 801.8225927 16384 0.01188193096 837.8470141 32768 0.006387915561 860.9489768 65536 0.008655583411 869.0417687 131072 6.034563755e-05 881.1186093 262144 0.0005764269044 874.9953325 524288 0.0008305200062 883.8135778 1048576 0.0003036544091 884.9308391 hunecke: [-1436.515078155, +161.120543283] 16 -787.374311 -37.15179156 32 -1101.766472 -73.77956751 64 -1145.158259 -1.121914179 128 -1187.430028 11.15542153 256 -1286.887026 -1.46343509 512 -1235.790156 42.27869517 1024 -1230.098017 66.51978582 2048 -1246.878481 98.97282175 4096 -1340.039759 85.46988876 8192 -1263.167011 98.62275376 16384 -1330.169829 129.8288892 32768 -1342.754365 98.77241454 65536 -1343.667596 116.1091694 131072 -1373.56007 123.7924842 262144 -1384.266376 135.977523 524288 -1412.494981 138.8953855 1048576 -1416.623171 139.3435011 kearfott: [ 0, ? ]: 16 1.890688428 73.3603846 32 0.6002071179 102.1437303 64 1.10893189 76.76005163 128 0.8683045935 97.6338526 256 0.4403239578 109.9642397 512 0.2045063378 122.7198361 1024 0.2308875819 130.9075302 2048 0.2923803795 151.9116666 4096 0.2187191028 158.5862868 8192 0.145415032 157.6793629 16384 0.04625697041 183.6609911 32768 0.06696469032 171.0181402 65536 0.03664279462 168.8297855 131072 0.03048870343 195.9865407 262144 0.01840079095 176.5833542 524288 0.002912729339 198.4442477 1048576 0.003118859558 207.6541432 lv3: [-9.35, +14.8 ] 16 -5.505976006 2.359192519 32 -2.411196489 4.221394903 64 -8.7249261 5.118580012 128 -6.196118255 5.045720063 256 -7.529919236 8.246773071 512 -7.992012879 6.563083491 1024 -6.584624644 8.049174981 2048 -8.76839483 8.190774113 4096 -7.471582786 7.949835791 8192 -8.519852729 8.063633439 16384 -8.789651166 8.158836837 32768 -8.920377623 8.475209322 65536 -9.046798181 8.147452917 131072 -9.009408155 8.498095034 262144 -9.060767317 8.530391987 524288 -8.969659498 8.503243629 1048576 -9.085109029 8.546697262 lv4: [-20.8, +22.8] 16 -6.884893684 4.151084073 32 -1.240729077 5.887408848 64 -8.377417891 8.796272966 128 -8.157045315 11.19769307 256 -8.607705406 7.948720738 512 -7.702569651 10.06555102 1024 -9.890049382 11.02818851 2048 -7.978823916 9.916188162 4096 -11.25760943 12.14712213 8192 -11.73914407 12.8606102 16384 -11.56105265 12.51808081 32768 -10.93875822 14.11446132 65536 -11.22992462 13.27660181 131072 -11.78153073 13.54132999 262144 -11.86689048 13.52270807 524288 -12.25617509 14.39611352 1048576 -12.5438857 13.73974981 magnetism6: [-0.25, +280.0] 16 56.49768538 176.9576672 32 20.37974721 155.4025017 64 13.068286 198.9760108 128 25.95516037 174.6717335 256 22.10666306 191.0768325 512 12.90162943 216.4283606 1024 7.597354659 194.5672584 2048 3.788502143 219.991467 4096 6.67575603 237.3487063 8192 4.261387053 219.9843987 16384 3.135742018 233.3861037 32768 4.552718225 241.1575989 65536 0.832176155 230.8975475 131072 2.191661966 252.8632361 262144 1.014809403 252.2550204 524288 1.238867148 245.623275 1048576 0.4762961256 249.9233468 magnetism7: [-0.25, +330.0] 16 2.61800899 8.614991166 32 0.8401354203 7.790561078 64 0.1041970534 9.155543046 128 0.8584411547 8.633176341 256 0.844812533 9.895126238 512 0.6488536823 9.918250127 1024 0.5583994316 10.07929211 2048 0.2170992297 11.76857085 4096 0.1689974334 10.57275424 8192 0.1073492634 11.30109414 16384 0.05507700358 10.79551285 32768 -0.1122765141 12.18196461 65536 -0.1082084514 10.75991951 131072 -0.1614776301 12.08280139 262144 -0.1262636206 12.31436106 524288 -0.1822241126 11.92265429 1048576 -0.154977993 12.44957874 quadratic: [ -2, ? ]: 16 14839.88234 48437.54628 32 9845.959905 38301.32847 64 9014.247013 42640.41569 128 8896.862825 51065.16435 256 7826.451775 52802.30423 512 5740.192882 50460.37355 1024 3763.537685 55927.90114 2048 4614.095632 56865.9075 4096 2543.616641 63334.06688 8192 3816.785264 67292.04963 16384 2150.438092 59774.27552 32768 2040.147525 64602.84142 65536 1472.641548 62707.54343 131072 737.0904958 65042.89241 262144 552.4597205 65332.71939 524288 1220.033859 67224.38646 1048576 779.2150834 67670.24279 rd: [-36.71269068, +10.40560403] 16 -25.28086805 4.497116297 32 -21.91160446 6.164186762 64 -31.84507985 5.314029372 128 -28.18593081 8.468599367 256 -32.2239576 9.280755427 512 -34.37184738 8.712661997 1024 -32.76607409 9.430387606 2048 -33.70567456 9.943244789 4096 -33.41258906 10.0578444 8192 -35.70089028 9.514725373 16384 -34.98116712 10.18877346 32768 -35.44273091 10.35038961 65536 -35.46953288 10.30957117 131072 -36.174262 10.29443881 262144 -36.24836969 10.29016873 524288 -36.25222472 10.37149306 1048576 -36.45468642 10.31003619 reimer5: [-5.0, +5.0] 16 -2.361421916 2.704557987 32 -3.972695582 0.986257506 64 -3.217000685 2.032755989 128 -3.483504688 2.88951549 256 -3.194819989 2.763117113 512 -4.477395366 3.370369899 1024 -4.15838999 3.494604936 2048 -4.616521353 3.062676495 4096 -4.432506719 3.206821162 8192 -4.823650023 3.729307995 16384 -4.854054326 4.39754424 32768 -4.564112961 4.469575818 65536 -4.676685955 4.254240181 131072 -4.828277994 4.65359081 262144 -4.919769089 4.530616105 524288 -4.913618108 4.720229217 1048576 -4.925946223 4.699093241 reimer6: [-937501, +937499] 16 -216406.1196 143249.8505 32 -198041.2158 162876.8859 64 -259952.0084 263578.3623 128 -356140.0489 284512.089 256 -392049.9024 351816.816 512 -300184.011 381708.3474 1024 -344592.3377 401510.8525 2048 -318159.9736 405190.3427 4096 -397220.4826 396754.8119 8192 -435313.677 442697.448 16384 -511761.0618 425393.6531 32768 -465225.1855 515696.4921 65536 -537552.4335 470410.11 131072 -520920.8046 493498.4913 262144 -561643.7515 545348.9635 524288 -597021.9616 569344.228 1048576 -544521.8243 614558.7621 rosenbrock: [ 0, ? ]: 16 3279.0466 25302.94453 32 640.123231 37067.04753 64 251.7248232 49858.14266 128 724.1849479 39743.87575 256 111.0103696 53190.69659 512 90.86844074 52432.71283 1024 389.4488942 43715.11226 2048 30.91942906 58801.74504 4096 33.86417839 49426.12446 8192 62.22950547 58722.93201 16384 26.18954261 61525.89623 32768 40.23342493 55536.65555 65536 8.67362244 60633.10559 131072 8.558799195 65560.51067 262144 2.775330825 61103.6659 524288 3.201745928 64586.774 1048576 3.961061056 64452.94159 schwefel: [ 0, ? ]: 16 26.20698845 14952.37685 32 19.24332636 14409.12887 64 27.78131083 14362.91488 128 13.00573185 15596.643 256 2.693938057 18210.45926 512 6.329847001 17679.3988 1024 1.733246677 19542.94178 2048 1.711402766 20728.86981 4096 3.945633822 20875.80899 8192 1.0483197 22272.86669 16384 0.3575255246 22289.12026 32768 0.3632678296 23597.06074 65536 0.04075515688 23006.96345 131072 0.1780585259 23778.34825 262144 0.1595290857 23857.28458 524288 0.04910429572 23952.09488 1048576 0.02833273288 24137.65225 smith1: [ ?, ? ]: 16 31894.87703 261820.2815 32 20766.65283 181182.4803 64 18646.85718 274073.9985 128 8275.672143 401170.8701 256 9830.832006 279646.508 512 6128.948192 356302.3166 1024 4283.764101 374814.1959 2048 205.8468433 361051.7997 4096 1562.047289 429562.6929 8192 208.5012886 432714.4986 16384 2868.328443 441846.2972 32768 -1873.591333 457636.3338 65536 -676.3127945 500037.7835 131072 -1958.482913 490542.9343 262144 -1184.279241 488462.4813 524288 -2307.426881 485044.1633 1048576 -2052.432228 485447.6323 smith2: [ ?, ? ]: 16 -94691.41437 -755.5715445 32 -124454.0286 -70.64406169 64 -184497.4088 -117.3613514 128 -251690.6777 -7.368007913 256 -117923.9421 -13.40702833 512 -206312.4668 31.61313318 1024 -213457.5251 74.94191361 2048 -272728.3135 131.6697951 4096 -246718.7849 173.5016588 8192 -240054.6462 178.4586741 16384 -293327.4482 144.01461 32768 -326207.5833 206.2040368 65536 -304006.3419 221.7402841 131072 -313583.3811 231.3577427 262144 -305065.6922 242.2777611 524288 -321105.6831 279.4288612 1048576 -322752.2198 299.9506699 virasoro: [-29.0, +21.0] 16 -5.095535765 12.38910217 32 -9.328907304 10.02015178 64 -7.559487901 14.2265071 128 -11.84791997 16.42500861 256 -11.17145084 16.60232768 512 -14.35943061 16.91136634 1024 -14.55244956 17.37568103 2048 -15.72789536 18.57021816 4096 -18.10639705 19.24736744 8192 -16.22807994 19.66357965 16384 -17.44105986 19.83234891 32768 -16.99306248 19.93345155 65536 -20.41002263 19.78756216 131072 -19.94418466 20.22108268 262144 -21.62984907 20.42587032 524288 -20.97522433 20.31674168 1048576 -21.55233453 20.54891895 wright: [-30.25, 40.0 ] 16 -10.81769109 -8.325569794 32 -10.8993462 -8.701143985 64 -11.40451116 -8.469731443 128 -11.56755932 -7.667416737 256 -11.25778333 -8.065405719 512 -11.50224087 -8.193169379 1024 -11.63862276 -7.991977062 2048 -11.64480556 -7.742748387 4096 -11.78017849 -7.707492893 8192 -11.88695213 -7.684721959 16384 -11.982057 -7.557812121 32768 -12.0614065 -7.528100813 65536 -12.17380653 -7.464791433 131072 -12.15407048 -7.583746326 262144 -12.08196782 -7.49659552 524288 -12.08095527 -7.460238632 1048576 -12.1654111 -7.483117164 zakharov: [ 0, ? ]:: 16 307.2572513 7805013.819 32 509.6723746 3601280.195 64 28.84753056 12197333.21 128 25.39264337 10302061.91 256 40.42131893 12283122.44 512 15.04679164 12467982.85 1024 16.1921555 15759352.47 2048 2.550197461 17513517.62 4096 10.20800089 16560273.83 8192 7.446913682 18107392.77 16384 5.984833934 23794094.48 32768 1.338112649 21106129.48 65536 2.364084421 22008999.36 131072 2.959038777 24757714.87 262144 1.130631563 25242079.72 524288 1.024112152 24810619.67 1048576 1.535256997 27185776.7 range_by_fmincon_test: Use the MATLAB fmincon() function to seek range. butcher known: [-1.4393333333, +0.219] Butcher estimated: [ -1.439332949 0.2189993599] polynomials_test Normal end of execution. 27-Feb-2019 08:58:22 polynomials_test 27-Feb-2019 08:59:20 polynomials_test MATLAB version. Test polynomials. RANGE_BY_SAMPLING_TEST: Use N sample values of each polynomial over its domain to estimate its minimum Pmin and maximum Pmax N Pmin Pmax butcher: [-1.4393333333, +0.219] 16 -0.9392362348 0.1722153637 32 -1.096808774 0.1619794357 64 -1.218607005 0.1354705999 128 -1.146982586 0.200123647 256 -1.163550893 0.1864259985 512 -1.261186459 0.1643861716 1024 -1.301762549 0.181939832 2048 -1.328901868 0.1806981008 4096 -1.30398538 0.1970596662 8192 -1.333096962 0.1967859621 16384 -1.367394167 0.1955562743 32768 -1.347472355 0.2058122585 65536 -1.365699517 0.2125327583 131072 -1.355741449 0.2123066372 262144 -1.396926957 0.2177005289 524288 -1.397266108 0.2141781022 1048576 -1.39471054 0.2164118703 camel: [ -1.031628453489616, ? ]: 16 2.34293696 286.8335898 32 -0.5656567098 323.5035177 64 -0.9962010179 325.1266789 128 -1.027385874 379.3308185 256 -0.6818695846 307.3754905 512 -1.015374044 352.3236156 1024 -1.00287864 338.5134894 2048 -1.001644111 374.7228438 4096 -1.008459822 375.3418439 8192 -1.030057213 379.9255796 16384 -1.0315199 399.0081893 32768 -1.030716586 393.6800883 65536 -1.031499798 401.2157052 131072 -1.031604928 403.3259929 262144 -1.031451431 400.6543081 524288 -1.031561663 403.3561477 1048576 -1.03160806 403.9333421 camera: [-270397.4, +270202.6] 16 -46966.46863 87607.58773 32 -46583.37426 131880.9884 64 -107842.0561 96384.78574 128 -115095.894 102371.4783 256 -123199.992 125799.9772 512 -132145.0254 166292.1828 1024 -158207.0598 142974.8428 2048 -148419.6789 149261.7396 4096 -167042.0576 152023.3768 8192 -199173.1852 186346.3269 16384 -188996.5906 195186.7777 32768 -226765.1798 232225.4553 65536 -223290.0705 199323.1465 131072 -239475.7762 214594.9647 262144 -223937.433 219707.9062 524288 -226095.1346 221139.3738 1048576 -220739.0299 228089.0193 caprasse: [-3.1800966258, +4.4852773332] 16 -1.122640811 3.568584008 32 -1.647449732 3.56462884 64 -2.303226173 3.346400025 128 -1.409359901 3.38414889 256 -2.188055437 3.744646826 512 -2.156669132 3.949668106 1024 -2.681084075 3.871754895 2048 -2.508913074 3.954812721 4096 -2.708625627 4.240230838 8192 -2.917337055 4.252268658 16384 -2.863663818 4.295687111 32768 -3.057783765 4.344869033 65536 -2.983681702 4.280455175 131072 -3.054743761 4.401290811 262144 -3.026200759 4.387669535 524288 -3.087886456 4.408258398 1048576 -3.055552816 4.460833605 cyclic5: [-30000, +50000] 16 -9991.369907 6422.069083 32 -2145.460004 4624.181633 64 -4222.701274 7624.457565 128 -14992.43919 6112.12361 256 -8174.970236 11483.64356 512 -8628.718062 23099.33817 1024 -13808.80086 14629.6272 2048 -19021.72443 35545.02833 4096 -16946.40579 28357.55695 8192 -17621.7452 26592.28456 16384 -21133.52841 33712.66728 32768 -20793.87133 29474.87736 65536 -23036.08174 27816.00644 131072 -24933.06023 35863.25232 262144 -23580.77258 33465.41057 524288 -24018.55212 42566.08176 1048576 -25467.84219 39498.54646 cyclic7: [-5.0, +7.0] 16 -0.1818128315 0.2943232411 32 -0.1566307448 0.2425566252 64 -0.1613862091 0.5427491584 128 -0.6420509895 0.9047133214 256 -0.3866409939 0.4517013016 512 -0.9462007286 0.5831586333 1024 -1.5731949 0.9667101914 2048 -2.894077843 1.048015102 4096 -1.873678733 1.393726369 8192 -2.614966655 1.362242833 16384 -1.800746927 2.36379899 32768 -2.936911452 1.919211055 65536 -2.477698801 2.107552639 131072 -2.812458641 2.64886998 262144 -3.343510677 3.25534353 524288 -2.477821056 3.326030713 1048576 -2.669923467 3.303197282 cyclic8: [-8.0, +8.0] 16 -0.4040071044 0.05786917277 32 -0.08508165615 0.0622396526 64 -0.04506995837 0.118717916 128 -0.4218346391 0.2745799351 256 -0.2725731752 0.1953586594 512 -0.4612749938 0.4890045447 1024 -0.2750077722 0.55066444 2048 -0.6659820419 0.5284259662 4096 -0.7214659199 0.7541840231 8192 -2.193833684 1.286781661 16384 -0.9603117808 1.292588948 32768 -0.966085627 1.509452859 65536 -1.468336729 1.587438261 131072 -2.345419689 1.848147231 262144 -2.619592599 1.969771506 524288 -2.330561365 2.781625427 1048576 -2.384376073 2.303065784 goldstein_price: [ 3, ? ]: 16 51.12676154 820896.2479 32 105.5459688 203980.5891 64 10.92957343 724262.7837 128 3.817344807 798623.0425 256 9.765102979 867929.2964 512 8.221251128 969804.7232 1024 5.050014183 932723.5592 2048 4.492353885 940076.8531 4096 3.052169259 955370.7013 8192 3.052850987 1001207.627 16384 3.088965056 1004841.246 32768 3.00526769 1007141.08 65536 3.008620381 1012877.892 131072 3.002478186 1012477.438 262144 3.001078639 1014881.033 524288 3.001491298 1015031.333 1048576 3.000262585 1014524.015 hairer: [-1875.25, -48.25] 16 -926.0411179 -155.0324846 32 -1032.123614 -204.2213865 64 -923.2430733 -199.0450683 128 -1315.081641 -135.905696 256 -1023.718237 -114.4337671 512 -1309.290832 -112.6619642 1024 -1316.029618 -97.7389525 2048 -1525.32216 -93.39353897 4096 -1474.126644 -68.40662814 8192 -1491.76719 -73.46822717 16384 -1493.356889 -64.93141755 32768 -1594.938255 -74.16070942 65536 -1678.734462 -73.05326927 131072 -1611.06875 -67.44005 262144 -1659.385907 -58.2896173 524288 -1699.753406 -64.00018544 1048576 -1711.254178 -60.67348512 heart: [-1.36775, +1.74345327935 16 0.1140052593 1.007342859 32 0.3366754628 1.025957486 64 -0.3499218274 1.289240672 128 -0.07225874411 1.052502143 256 -0.4754486392 1.485554943 512 -0.3983935201 1.360331884 1024 -0.4679556199 1.460674034 2048 -0.5101981721 1.416384693 4096 -0.552286899 1.559009544 8192 -0.7789747658 1.575163714 16384 -0.7811037014 1.540810454 32768 -0.8293137161 1.640550256 65536 -0.7699449513 1.656784516 131072 -0.9025015425 1.654347059 262144 -0.9717289694 1.652736872 524288 -0.8253402394 1.63059713 1048576 -0.9570437895 1.685752139 himmelblau: [ 0, ? ]: 16 3.344612463 535.1187975 32 13.65550768 697.0243811 64 1.967193857 653.9187636 128 0.9391154232 833.246507 256 0.9589538353 657.0620917 512 0.7848869657 753.4085761 1024 0.03416051653 723.8703239 2048 0.008669694946 799.5137097 4096 0.09444232334 758.8565032 8192 0.01297949904 801.8225927 16384 0.01188193096 837.8470141 32768 0.006387915561 860.9489768 65536 0.008655583411 869.0417687 131072 6.034563755e-05 881.1186093 262144 0.0005764269044 874.9953325 524288 0.0008305200062 883.8135778 1048576 0.0003036544091 884.9308391 hunecke: [-1436.515078155, +161.120543283] 16 -787.374311 -37.15179156 32 -1101.766472 -73.77956751 64 -1145.158259 -1.121914179 128 -1187.430028 11.15542153 256 -1286.887026 -1.46343509 512 -1235.790156 42.27869517 1024 -1230.098017 66.51978582 2048 -1246.878481 98.97282175 4096 -1340.039759 85.46988876 8192 -1263.167011 98.62275376 16384 -1330.169829 129.8288892 32768 -1342.754365 98.77241454 65536 -1343.667596 116.1091694 131072 -1373.56007 123.7924842 262144 -1384.266376 135.977523 524288 -1412.494981 138.8953855 1048576 -1416.623171 139.3435011 kearfott: [ 0, ? ]: 16 1.890688428 73.3603846 32 0.6002071179 102.1437303 64 1.10893189 76.76005163 128 0.8683045935 97.6338526 256 0.4403239578 109.9642397 512 0.2045063378 122.7198361 1024 0.2308875819 130.9075302 2048 0.2923803795 151.9116666 4096 0.2187191028 158.5862868 8192 0.145415032 157.6793629 16384 0.04625697041 183.6609911 32768 0.06696469032 171.0181402 65536 0.03664279462 168.8297855 131072 0.03048870343 195.9865407 262144 0.01840079095 176.5833542 524288 0.002912729339 198.4442477 1048576 0.003118859558 207.6541432 lv3: [-9.35, +14.8 ] 16 -5.505976006 2.359192519 32 -2.411196489 4.221394903 64 -8.7249261 5.118580012 128 -6.196118255 5.045720063 256 -7.529919236 8.246773071 512 -7.992012879 6.563083491 1024 -6.584624644 8.049174981 2048 -8.76839483 8.190774113 4096 -7.471582786 7.949835791 8192 -8.519852729 8.063633439 16384 -8.789651166 8.158836837 32768 -8.920377623 8.475209322 65536 -9.046798181 8.147452917 131072 -9.009408155 8.498095034 262144 -9.060767317 8.530391987 524288 -8.969659498 8.503243629 1048576 -9.085109029 8.546697262 lv4: [-20.8, +22.8] 16 -6.884893684 4.151084073 32 -1.240729077 5.887408848 64 -8.377417891 8.796272966 128 -8.157045315 11.19769307 256 -8.607705406 7.948720738 512 -7.702569651 10.06555102 1024 -9.890049382 11.02818851 2048 -7.978823916 9.916188162 4096 -11.25760943 12.14712213 8192 -11.73914407 12.8606102 16384 -11.56105265 12.51808081 32768 -10.93875822 14.11446132 65536 -11.22992462 13.27660181 131072 -11.78153073 13.54132999 262144 -11.86689048 13.52270807 524288 -12.25617509 14.39611352 1048576 -12.5438857 13.73974981 magnetism6: [-0.25, +280.0] 16 56.49768538 176.9576672 32 20.37974721 155.4025017 64 13.068286 198.9760108 128 25.95516037 174.6717335 256 22.10666306 191.0768325 512 12.90162943 216.4283606 1024 7.597354659 194.5672584 2048 3.788502143 219.991467 4096 6.67575603 237.3487063 8192 4.261387053 219.9843987 16384 3.135742018 233.3861037 32768 4.552718225 241.1575989 65536 0.832176155 230.8975475 131072 2.191661966 252.8632361 262144 1.014809403 252.2550204 524288 1.238867148 245.623275 1048576 0.4762961256 249.9233468 magnetism7: [-0.25, +330.0] 16 2.61800899 8.614991166 32 0.8401354203 7.790561078 64 0.1041970534 9.155543046 128 0.8584411547 8.633176341 256 0.844812533 9.895126238 512 0.6488536823 9.918250127 1024 0.5583994316 10.07929211 2048 0.2170992297 11.76857085 4096 0.1689974334 10.57275424 8192 0.1073492634 11.30109414 16384 0.05507700358 10.79551285 32768 -0.1122765141 12.18196461 65536 -0.1082084514 10.75991951 131072 -0.1614776301 12.08280139 262144 -0.1262636206 12.31436106 524288 -0.1822241126 11.92265429 1048576 -0.154977993 12.44957874 quadratic: [ -2, ? ]: 16 14839.88234 48437.54628 32 9845.959905 38301.32847 64 9014.247013 42640.41569 128 8896.862825 51065.16435 256 7826.451775 52802.30423 512 5740.192882 50460.37355 1024 3763.537685 55927.90114 2048 4614.095632 56865.9075 4096 2543.616641 63334.06688 8192 3816.785264 67292.04963 16384 2150.438092 59774.27552 32768 2040.147525 64602.84142 65536 1472.641548 62707.54343 131072 737.0904958 65042.89241 262144 552.4597205 65332.71939 524288 1220.033859 67224.38646 1048576 779.2150834 67670.24279 rd: [-36.71269068, +10.40560403] 16 -25.28086805 4.497116297 32 -21.91160446 6.164186762 64 -31.84507985 5.314029372 128 -28.18593081 8.468599367 256 -32.2239576 9.280755427 512 -34.37184738 8.712661997 1024 -32.76607409 9.430387606 2048 -33.70567456 9.943244789 4096 -33.41258906 10.0578444 8192 -35.70089028 9.514725373 16384 -34.98116712 10.18877346 32768 -35.44273091 10.35038961 65536 -35.46953288 10.30957117 131072 -36.174262 10.29443881 262144 -36.24836969 10.29016873 524288 -36.25222472 10.37149306 1048576 -36.45468642 10.31003619 reimer5: [-5.0, +5.0] 16 -2.361421916 2.704557987 32 -3.972695582 0.986257506 64 -3.217000685 2.032755989 128 -3.483504688 2.88951549 256 -3.194819989 2.763117113 512 -4.477395366 3.370369899 1024 -4.15838999 3.494604936 2048 -4.616521353 3.062676495 4096 -4.432506719 3.206821162 8192 -4.823650023 3.729307995 16384 -4.854054326 4.39754424 32768 -4.564112961 4.469575818 65536 -4.676685955 4.254240181 131072 -4.828277994 4.65359081 262144 -4.919769089 4.530616105 524288 -4.913618108 4.720229217 1048576 -4.925946223 4.699093241 reimer6: [-937501, +937499] 16 -216406.1196 143249.8505 32 -198041.2158 162876.8859 64 -259952.0084 263578.3623 128 -356140.0489 284512.089 256 -392049.9024 351816.816 512 -300184.011 381708.3474 1024 -344592.3377 401510.8525 2048 -318159.9736 405190.3427 4096 -397220.4826 396754.8119 8192 -435313.677 442697.448 16384 -511761.0618 425393.6531 32768 -465225.1855 515696.4921 65536 -537552.4335 470410.11 131072 -520920.8046 493498.4913 262144 -561643.7515 545348.9635 524288 -597021.9616 569344.228 1048576 -544521.8243 614558.7621 rosenbrock: [ 0, ? ]: 16 3279.0466 25302.94453 32 640.123231 37067.04753 64 251.7248232 49858.14266 128 724.1849479 39743.87575 256 111.0103696 53190.69659 512 90.86844074 52432.71283 1024 389.4488942 43715.11226 2048 30.91942906 58801.74504 4096 33.86417839 49426.12446 8192 62.22950547 58722.93201 16384 26.18954261 61525.89623 32768 40.23342493 55536.65555 65536 8.67362244 60633.10559 131072 8.558799195 65560.51067 262144 2.775330825 61103.6659 524288 3.201745928 64586.774 1048576 3.961061056 64452.94159 schwefel: [ 0, ? ]: 16 26.20698845 14952.37685 32 19.24332636 14409.12887 64 27.78131083 14362.91488 128 13.00573185 15596.643 256 2.693938057 18210.45926 512 6.329847001 17679.3988 1024 1.733246677 19542.94178 2048 1.711402766 20728.86981 4096 3.945633822 20875.80899 8192 1.0483197 22272.86669 16384 0.3575255246 22289.12026 32768 0.3632678296 23597.06074 65536 0.04075515688 23006.96345 131072 0.1780585259 23778.34825 262144 0.1595290857 23857.28458 524288 0.04910429572 23952.09488 1048576 0.02833273288 24137.65225 smith1: [ ?, ? ]: 16 31894.87703 261820.2815 32 20766.65283 181182.4803 64 18646.85718 274073.9985 128 8275.672143 401170.8701 256 9830.832006 279646.508 512 6128.948192 356302.3166 1024 4283.764101 374814.1959 2048 205.8468433 361051.7997 4096 1562.047289 429562.6929 8192 208.5012886 432714.4986 16384 2868.328443 441846.2972 32768 -1873.591333 457636.3338 65536 -676.3127945 500037.7835 131072 -1958.482913 490542.9343 262144 -1184.279241 488462.4813 524288 -2307.426881 485044.1633 1048576 -2052.432228 485447.6323 smith2: [ ?, ? ]: 16 -94691.41437 -755.5715445 32 -124454.0286 -70.64406169 64 -184497.4088 -117.3613514 128 -251690.6777 -7.368007913 256 -117923.9421 -13.40702833 512 -206312.4668 31.61313318 1024 -213457.5251 74.94191361 2048 -272728.3135 131.6697951 4096 -246718.7849 173.5016588 8192 -240054.6462 178.4586741 16384 -293327.4482 144.01461 32768 -326207.5833 206.2040368 65536 -304006.3419 221.7402841 131072 -313583.3811 231.3577427 262144 -305065.6922 242.2777611 524288 -321105.6831 279.4288612 1048576 -322752.2198 299.9506699 virasoro: [-29.0, +21.0] 16 -5.095535765 12.38910217 32 -9.328907304 10.02015178 64 -7.559487901 14.2265071 128 -11.84791997 16.42500861 256 -11.17145084 16.60232768 512 -14.35943061 16.91136634 1024 -14.55244956 17.37568103 2048 -15.72789536 18.57021816 4096 -18.10639705 19.24736744 8192 -16.22807994 19.66357965 16384 -17.44105986 19.83234891 32768 -16.99306248 19.93345155 65536 -20.41002263 19.78756216 131072 -19.94418466 20.22108268 262144 -21.62984907 20.42587032 524288 -20.97522433 20.31674168 1048576 -21.55233453 20.54891895 wright: [-30.25, 40.0 ] 16 -10.81769109 -8.325569794 32 -10.8993462 -8.701143985 64 -11.40451116 -8.469731443 128 -11.56755932 -7.667416737 256 -11.25778333 -8.065405719 512 -11.50224087 -8.193169379 1024 -11.63862276 -7.991977062 2048 -11.64480556 -7.742748387 4096 -11.78017849 -7.707492893 8192 -11.88695213 -7.684721959 16384 -11.982057 -7.557812121 32768 -12.0614065 -7.528100813 65536 -12.17380653 -7.464791433 131072 -12.15407048 -7.583746326 262144 -12.08196782 -7.49659552 524288 -12.08095527 -7.460238632 1048576 -12.1654111 -7.483117164 zakharov: [ 0, ? ]:: 16 307.2572513 7805013.819 32 509.6723746 3601280.195 64 28.84753056 12197333.21 128 25.39264337 10302061.91 256 40.42131893 12283122.44 512 15.04679164 12467982.85 1024 16.1921555 15759352.47 2048 2.550197461 17513517.62 4096 10.20800089 16560273.83 8192 7.446913682 18107392.77 16384 5.984833934 23794094.48 32768 1.338112649 21106129.48 65536 2.364084421 22008999.36 131072 2.959038777 24757714.87 262144 1.130631563 25242079.72 524288 1.024112152 24810619.67 1048576 1.535256997 27185776.7 range_by_fmincon_test: Use the MATLAB fmincon() function to seek range. butcher known: [ -1.439333333 0.219] Butcher estimated: [ -1.439332949 0.2189993599] polynomials_test Normal end of execution. 27-Feb-2019 08:59:31 diary