08-Jan-2022 08:57:53 polynomials_test(): MATLAB/Octave version 9.8.0.1380330 (R2020a) Update 2 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 -0.7181795026 0.07112603465 32 -0.9757423819 0.08110601581 64 -1.178628937 0.1080545686 128 -1.146252082 0.1305509409 256 -1.23660164 0.1289856877 512 -1.270558457 0.2029052064 1024 -1.307792272 0.2032847041 2048 -1.34430876 0.1824426066 4096 -1.321078302 0.1921621994 8192 -1.363022764 0.198334819 16384 -1.348690915 0.2000629569 32768 -1.362226961 0.2139947403 65536 -1.372641805 0.213487399 131072 -1.380491209 0.214586688 262144 -1.39795518 0.2118951759 524288 -1.390019377 0.2158707467 1048576 -1.399981679 0.2156896752 camel: [ -1.031628453489616, ? ]: 16 14.5747642 298.2657168 32 -0.394896174 257.7662329 64 -0.6142223677 278.9326849 128 -1.003014498 264.8145553 256 -0.685810084 367.5938968 512 -0.9715903006 370.6675768 1024 -0.9478495934 374.2459989 2048 -1.020567773 370.4862112 4096 -1.031483323 385.6251737 8192 -1.030770659 364.2818703 16384 -1.031401637 382.0708308 32768 -1.029542533 397.5008694 65536 -1.031397931 401.5805489 131072 -1.031599333 400.3681633 262144 -1.031363902 399.7059085 524288 -1.031616739 402.4569011 1048576 -1.031535041 402.311062 camera: [-270397.4, +270202.6] 16 -159163.6282 117665.5687 32 -79171.86553 60059.37214 64 -102795.5238 112538.774 128 -137477.7495 115725.5623 256 -111229.3662 126832.8233 512 -121159.6413 165614.758 1024 -166348.919 160431.9979 2048 -155614.6851 181158.0693 4096 -160555.2185 204711.6205 8192 -178275.1644 220934.1798 16384 -181057.6516 222513.575 32768 -207989.8131 219329.5105 65536 -218109.7311 207412.0962 131072 -202359.1897 224019.5233 262144 -221113.6956 214261.5509 524288 -221545.4223 219237.9659 1048576 -235921.2415 228385.1638 caprasse: [-3.1800966258, +4.4852773332] 16 -1.493610279 3.644531445 32 -2.171145981 3.389555942 64 -1.60252469 3.466107983 128 -2.463729502 3.377962219 256 -2.097249942 3.838792887 512 -2.297115038 4.184848742 1024 -2.721896888 4.048378966 2048 -2.707804868 3.918282304 4096 -2.883526777 4.217572196 8192 -2.872403421 4.334271201 16384 -2.997228038 4.355728694 32768 -3.048581075 4.327600489 65536 -2.964732241 4.331702725 131072 -2.951051252 4.340887238 262144 -3.043716257 4.399556375 524288 -3.117522261 4.430189622 1048576 -3.069234551 4.416755247 cyclic5: [-30000, +50000] 16 -12600.11164 3080.958796 32 -7053.154222 6040.562297 64 -10730.5555 3323.782233 128 -11229.58474 10325.87113 256 -15489.23073 15130.00473 512 -15529.1344 13820.84303 1024 -14583.68303 21021.19787 2048 -19904.27002 23545.53136 4096 -17754.59238 22199.3658 8192 -19273.93289 27688.029 16384 -22221.46645 32448.83818 32768 -23316.17445 31075.55364 65536 -26139.25322 33353.16201 131072 -23898.49196 37641.63682 262144 -22522.82595 34520.39577 524288 -24762.39644 39098.3945 1048576 -25420.25235 42098.21191 cyclic7: [-5.0, +7.0] 16 -0.1672101929 0.6223032522 32 -0.1214841206 0.113171737 64 -0.1695560479 0.4582746732 128 -0.5533975771 0.2850935019 256 -0.3643803897 0.582294863 512 -0.4775881796 0.3680155586 1024 -0.8533064899 0.9604203482 2048 -1.298737576 0.7250854497 4096 -1.033848257 1.129818246 8192 -1.934519267 1.421292052 16384 -1.884814785 1.175046462 32768 -1.943557383 1.744208661 65536 -1.714363217 2.522913981 131072 -2.32121181 2.81378236 262144 -2.308282965 2.637813539 524288 -2.885540124 2.625682251 1048576 -2.873757673 3.240683421 cyclic8: [-8.0, +8.0] 16 -0.04042415959 0.08853272652 32 -0.09385458134 0.1979838396 64 -0.08575266318 0.1186090829 128 -0.07341432872 0.1310335797 256 -0.5378933187 0.5861074538 512 -0.3697587491 0.2556642839 1024 -0.3080925807 0.8523610739 2048 -0.6683634724 0.6006914721 4096 -1.318517873 1.130139523 8192 -2.439962194 1.656861413 16384 -0.9676882046 1.430061004 32768 -1.02894762 1.471285264 65536 -2.610152231 1.924380648 131072 -1.521727599 2.460803727 262144 -1.744516845 2.245146291 524288 -2.618275958 2.171727332 1048576 -3.182051048 2.182911062 goldstein_price: [ 3, ? ]: 16 73.89507021 31058.55318 32 67.12933744 736319.9704 64 11.84273767 538680.7997 128 26.72705366 512261.6256 256 6.193986418 949744.4691 512 8.513930059 925261.9758 1024 4.168473753 977765.8215 2048 4.715231723 938974.1982 4096 4.006340264 968749.7899 8192 3.244002786 1012170.204 16384 3.157205928 1009094.009 32768 3.167835358 1010018.478 65536 3.040404455 1008299.247 131072 3.033138917 1012629.377 262144 3.004577387 1013609.975 524288 3.001270198 1014797.54 1048576 3.000704528 1015539.641 hairer: [-1875.25, -48.25] 16 -1060.56832 -142.3207753 32 -1163.079577 -266.3411956 64 -1195.005051 -167.4018103 128 -1255.732726 -98.2886183 256 -1151.805328 -120.1716487 512 -1506.139078 -100.8020039 1024 -1331.466883 -104.2102835 2048 -1422.804503 -96.25938629 4096 -1448.686783 -74.84459472 8192 -1606.175545 -86.00696652 16384 -1512.975009 -72.09174035 32768 -1575.548754 -70.20408159 65536 -1585.353861 -68.38430841 131072 -1578.874598 -64.98290135 262144 -1672.180048 -68.74123575 524288 -1692.600609 -63.11916717 1048576 -1671.896672 -61.36725655 heart: [-1.36775, +1.74345327935 16 0.075445907 1.106103171 32 0.05211221829 1.153101744 64 -0.09702729959 1.199722424 128 -0.03343210655 1.120286622 256 -0.2005398124 1.460778939 512 -0.5268577679 1.421920024 1024 -0.4519534638 1.504104762 2048 -0.5875683309 1.489814775 4096 -0.6639525426 1.544242351 8192 -0.5185123612 1.597330819 16384 -0.8773601128 1.560876326 32768 -0.7290471291 1.628580249 65536 -0.678045118 1.651075223 131072 -0.8535898933 1.627633731 262144 -0.8074623952 1.642127492 524288 -1.00256425 1.677687568 1048576 -0.9489330162 1.669109789 himmelblau: [ 0, ? ]: 16 23.17808922 496.5580418 32 6.453669294 494.3039504 64 9.284779188 511.8403014 128 2.919267354 713.568318 256 0.3591245671 537.4328227 512 0.2122338009 617.2751022 1024 0.004504339303 813.7493604 2048 0.2382268906 709.2351771 4096 0.0594463909 788.1640872 8192 0.05173223394 870.7635785 16384 0.004546150555 835.2306335 32768 0.005603597052 864.3455288 65536 0.00341130043 887.0921237 131072 0.0007683239043 882.4248512 262144 0.002510590013 862.6210903 524288 0.0005727072072 878.315566 1048576 9.559338431e-05 885.5943265 hunecke: [-1436.515078155, +161.120543283] 16 -838.117561 -46.73590289 32 -952.3515309 -8.814665691 64 -1058.146611 -37.38168822 128 -1210.992241 -22.38206034 256 -1069.951764 22.03291526 512 -1194.054238 37.18921714 1024 -1286.83685 42.77857707 2048 -1293.697878 89.95464611 4096 -1268.444601 77.78257354 8192 -1283.48597 78.84410313 16384 -1298.738877 122.281176 32768 -1307.722798 115.4642266 65536 -1314.566741 124.2985645 131072 -1334.232142 146.3415579 262144 -1405.982822 139.3231663 524288 -1384.776591 142.0782333 1048576 -1391.389068 141.8936608 kearfott: [ 0, ? ]: 16 3.364821282 54.91044313 32 2.629573786 58.49421578 64 0.5346547486 106.9105469 128 0.2487969608 114.8407084 256 0.7723128575 173.3692131 512 0.4038425688 143.1063996 1024 0.2278987779 108.3936644 2048 0.1199827859 130.5416346 4096 0.1509238057 148.8622599 8192 0.04685255008 164.8587562 16384 0.06684203307 153.4637627 32768 0.05430924737 181.832433 65536 0.03225996859 199.6630394 131072 0.009191138005 185.7990233 262144 0.01518800721 192.4955549 524288 0.005560054479 194.3898726 1048576 0.01067758321 194.9505098 lv3: [-9.35, +14.8 ] 16 -5.894887472 3.358607529 32 -3.648973362 4.17250096 64 -4.299903039 5.328340969 128 -6.435737116 6.243813522 256 -7.849737483 7.602689805 512 -8.272751358 7.392350629 1024 -7.918855011 7.224526121 2048 -8.021002745 8.045320438 4096 -7.695720232 7.906144875 8192 -8.812498736 7.99470523 16384 -8.477729599 8.302064301 32768 -8.81040792 8.136439484 65536 -8.806575838 8.265962008 131072 -8.898357746 8.603846547 262144 -9.006406208 8.513610219 524288 -9.036536589 8.545101819 1048576 -8.998905384 8.52164727 lv4: [-20.8, +22.8] 16 -1.917251385 3.672375497 32 -5.201621498 9.792733712 64 -5.602449718 9.995819007 128 -7.055153794 9.075941612 256 -8.080415577 8.228378185 512 -10.52241512 8.533603571 1024 -7.831728745 11.33458101 2048 -8.982153345 14.42046565 4096 -9.137215959 12.43100807 8192 -11.01438725 11.86519285 16384 -11.29471866 12.37344208 32768 -11.51471766 13.63867921 65536 -11.2784273 13.2552773 131072 -11.64002241 13.36987263 262144 -11.73628685 13.99346065 524288 -12.06854164 13.79644299 1048576 -12.21270028 14.32422035 magnetism6: [-0.25, +280.0] 16 44.14938804 126.8236887 32 32.86554454 139.7880935 64 15.30751809 155.3643451 128 18.75745786 157.275629 256 9.919410827 204.8354561 512 12.53067527 221.6994032 1024 6.030978389 202.3158521 2048 4.698048148 219.5100786 4096 2.933131507 205.6465737 8192 7.149399684 216.3430352 16384 3.757383843 225.8767802 32768 3.068898875 235.0731154 65536 2.488720152 227.1835847 131072 2.998299759 239.0560585 262144 2.355692095 240.9891051 524288 1.058762969 244.5489362 1048576 0.568246983 251.1523558 magnetism7: [-0.25, +330.0] 16 1.474213841 7.993075301 32 1.030675337 7.351978511 64 0.6472419036 8.029723091 128 0.3236925629 8.361192112 256 0.2866512858 8.552979128 512 0.4961169067 10.17990018 1024 -0.01258452319 9.128606672 2048 0.04892652198 11.08472469 4096 0.2879636084 9.967494708 8192 -0.02173237991 10.85141887 16384 0.07796023603 10.64053115 32768 0.03519038051 10.8975848 65536 -0.03556012445 11.60577792 131072 -0.1247938096 11.36655334 262144 -0.1777695439 11.71086024 524288 -0.1099771632 11.81808312 1048576 -0.1944596092 12.09174648 quadratic: [ -2, ? ]: 16 11560.73941 39347.35799 32 14164.05626 56253.47127 64 9856.500968 54178.26338 128 5416.816289 46799.88039 256 5910.140802 48295.89519 512 5159.251445 55144.7589 1024 7038.839694 61263.19299 2048 2587.615258 59922.10363 4096 3352.468761 53132.12684 8192 3458.068934 64746.79337 16384 1622.054538 58329.05538 32768 1853.858757 61289.04337 65536 1574.396406 60551.17008 131072 1367.270782 63669.13329 262144 825.1420244 65501.28192 524288 1185.059931 66421.47325 1048576 684.3839888 68119.9064 rd: [-36.71269068, +10.40560403] 16 -29.10888726 3.990525866 32 -24.71816541 3.958809453 64 -26.53472602 7.952664662 128 -24.49575591 8.597441394 256 -35.10471989 8.426628503 512 -30.94003588 7.976245591 1024 -35.30449345 9.575103018 2048 -32.95011983 9.673334862 4096 -34.35128776 9.923433082 8192 -36.06313096 10.18059212 16384 -35.24669504 10.09217882 32768 -35.78678042 9.866752353 65536 -35.91314626 10.18310533 131072 -36.54770895 10.2229981 262144 -36.11416114 10.25453623 524288 -36.2579979 10.29967302 1048576 -36.49771687 10.33744959 reimer5: [-5.0, +5.0] 16 -1.836934484 0.4781977785 32 -3.802205081 1.818203762 64 -3.448783507 1.041429911 128 -3.043120356 1.742420228 256 -3.502484954 2.404710252 512 -3.749485917 2.573852921 1024 -4.127566038 3.781213483 2048 -4.240934123 3.765256689 4096 -4.617017418 3.542661998 8192 -4.670447592 3.979704711 16384 -4.670906588 3.771961407 32768 -4.81119135 4.482729177 65536 -4.867181196 4.550873673 131072 -4.886504398 4.641483414 262144 -4.891425108 4.659909252 524288 -4.964546404 4.553124882 1048576 -4.966064883 4.695844888 reimer6: [-937501, +937499] 16 -223948.7452 260946.4802 32 -168148.9337 138404.4639 64 -220030.5044 193819.5394 128 -295207.551 219457.7146 256 -430866.9472 380212.4554 512 -328572.0436 339438.9263 1024 -350232.8487 365900.7983 2048 -441983.7423 367853.1663 4096 -373436.0806 374211.5665 8192 -414868.1741 462899.3988 16384 -477951.7529 480574.0585 32768 -470707.7908 514148.0678 65536 -570744.5998 560388.604 131072 -494624.0304 535517.0627 262144 -584188.1888 576876.4629 524288 -580122.6589 624254.064 1048576 -569114.8555 580699.5617 rosenbrock: [ 0, ? ]: 16 1213.44151 23415.77472 32 1600.28742 31563.43126 64 432.858281 35823.91662 128 358.4819767 40552.90869 256 33.50987061 49227.75849 512 189.8703404 50358.64247 1024 157.8113502 49882.4195 2048 35.48043904 53382.83317 4096 88.9175478 52192.12584 8192 50.85232507 52658.224 16384 15.9979462 57382.69267 32768 8.519841358 59671.71717 65536 5.442087648 61457.16198 131072 9.202860084 63563.622 262144 6.386746055 63185.97798 524288 8.895336153 63064.12718 1048576 7.759941471 66188.74328 schwefel: [ 0, ? ]: 16 123.0325946 12095.34177 32 27.81852113 15703.04806 64 11.89755816 12885.35344 128 7.926084099 16636.85654 256 1.279487159 18059.77558 512 2.837764281 20641.14719 1024 7.55615879 18653.99872 2048 1.679185973 20783.03948 4096 1.359225784 21569.16623 8192 0.6976082199 23068.84544 16384 0.3217042241 23011.50728 32768 0.2182613724 23843.30024 65536 0.3064804135 23363.23895 131072 0.1539401737 23401.34988 262144 0.118465703 24004.66366 524288 0.01797020087 23810.91764 1048576 0.06678932026 24169.87747 smith1: [ ?, ? ]: 16 26466.05576 220659.7316 32 10374.47191 248999.2609 64 8242.636669 254392.0763 128 13522.01997 292865.5463 256 10390.81263 402336.1169 512 3710.769013 384927.8744 1024 5150.175004 376077.1843 2048 3216.069591 360656.0134 4096 -97.60035633 376564.8672 8192 2292.722216 425405.3699 16384 -753.3546181 418427.7617 32768 -497.5475931 436044.7717 65536 664.4595026 450768.8167 131072 -222.0056807 500612.2992 262144 -1676.352753 491567.1259 524288 -950.8407036 479468.211 1048576 -1852.989501 487644.5424 smith2: [ ?, ? ]: 16 -141940.9966 12.61554553 32 -164864.5106 -135.6102602 64 -107729.8597 -125.1086234 128 -111351.2482 92.56235643 256 -142114.0919 19.20098949 512 -223052.2497 76.62444364 1024 -179416.6875 49.5107625 2048 -295667.5748 86.27701354 4096 -269607.4036 205.7093873 8192 -260811.9739 181.4164423 16384 -298029.7851 222.5549832 32768 -285481.2841 228.2758663 65536 -303502.0545 246.1825917 131072 -291918.8636 213.6737519 262144 -323647.7968 243.8957491 524288 -316629.11 287.0959071 1048576 -313129.9978 293.9342219 virasoro: [-29.0, +21.0] 16 -11.36431567 12.99878771 32 -6.634055889 14.20905579 64 -8.1807698 16.41449407 128 -8.835726974 18.37939737 256 -13.79278724 16.11007138 512 -15.21905424 15.74868827 1024 -12.60126054 19.10975061 2048 -12.66049237 17.28272157 4096 -15.61136646 18.87745326 8192 -17.04176407 19.59217579 16384 -17.80011979 19.67824707 32768 -20.26348819 20.14293021 65536 -19.56253453 20.45097374 131072 -18.82568146 20.47409569 262144 -22.46575642 20.62297675 524288 -22.10733442 20.46400699 1048576 -20.73607176 20.65088399 wright: [-30.25, 40.0 ] 16 -10.60713613 -8.504876823 32 -11.00714508 -7.715461912 64 -11.28335879 -8.356090815 128 -11.37436431 -8.190184779 256 -11.79091748 -8.38741939 512 -11.46806627 -8.319117896 1024 -11.85192528 -7.873188621 2048 -11.92295224 -8.054531732 4096 -11.84786828 -7.806482587 8192 -11.88321468 -7.652292434 16384 -11.99040035 -7.556423286 32768 -12.04767902 -7.613240329 65536 -12.01783576 -7.488294673 131072 -12.06350469 -7.523543758 262144 -12.04117265 -7.436311026 524288 -12.10916348 -7.4869409 1048576 -12.14070365 -7.415952942 zakharov: [ 0, ? ]:: 16 89.09402883 5701270.763 32 54.13439743 5710573.233 64 28.25174305 8035880.058 128 22.35194281 5026414.217 256 23.79784845 12614654.28 512 28.78799757 19564792.68 1024 21.93614419 16077942.05 2048 12.4702355 17254234.31 4096 6.707568405 21512650.38 8192 7.804968888 19899459.23 16384 1.872391677 24073139.16 32768 3.489980171 21048743.89 65536 2.781362221 23806021.41 131072 1.252064015 25198175.43 262144 1.18995401 26550834.2 524288 1.686899768 26319424.65 1048576 0.3560812413 26240553.5 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. 08-Jan-2022 08:58:05