08-Oct-2025 12:29:14 polynomials_test(): MATLAB/Octave version 6.4.0 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 -0.6252524111 0.08811844322 32 -1.160274066 0.06711735377 64 -1.158737921 0.05104697434 128 -1.127137641 0.1304071345 256 -1.095518639 0.185780906 512 -1.299853732 0.1754977894 1024 -1.359832592 0.187024538 2048 -1.298194792 0.1985953117 4096 -1.337978312 0.2083898043 8192 -1.331243252 0.2066680707 16384 -1.385902953 0.2084793214 32768 -1.348667254 0.2100004991 65536 -1.357293608 0.2180622988 131072 -1.385721589 0.2126621279 262144 -1.388257756 0.2146328949 524288 -1.390975728 0.2152501223 1048576 -1.396759238 0.2165745291 camel: [ -1.031628453489616, ? ]: 16 0.02611396447 210.0373284 32 -0.5303983921 274.221662 64 -0.695542819 322.0737604 128 -0.8269759605 302.4793908 256 -0.9227502754 305.6439815 512 -0.980406387 368.3829829 1024 -0.9577980816 372.879255 2048 -1.023370089 377.6702449 4096 -1.027565032 390.5704989 8192 -1.029635312 388.6247458 16384 -1.030166793 398.3580507 32768 -1.03054683 396.2380169 65536 -1.031508632 403.9563767 131072 -1.031304022 396.4138246 262144 -1.031520209 398.6746037 524288 -1.031582567 404.2781226 1048576 -1.031604738 405.0504378 camera: [-270397.4, +270202.6] 16 -47117.29205 36600.53194 32 -78289.28244 101178.9834 64 -85425.17227 120146.5999 128 -115088.2115 126197.492 256 -128542.5124 143579.6298 512 -200121.762 149218.5618 1024 -160398.7117 131704.5405 2048 -173455.2099 157030.0862 4096 -158639.2541 177953.569 8192 -172727.5172 179838.9982 16384 -192954.6032 186989.6588 32768 -200498.2106 210136.3707 65536 -197874.9861 186767.5728 131072 -213014.4234 230299.7675 262144 -219825.7997 225526.5956 524288 -236426.1295 232378.1545 1048576 -230686.9624 222313.6396 caprasse: [-3.1800966258, +4.4852773332] 16 -1.259729489 2.410952428 32 -0.2889679447 3.241828146 64 -0.639458954 3.440988154 128 -2.281682099 3.33332595 256 -2.576857553 3.717460184 512 -2.415885777 4.086378121 1024 -2.531300471 4.051367643 2048 -2.683695454 4.252622923 4096 -2.904389314 4.283212919 8192 -2.839122929 4.239880986 16384 -2.974979329 4.31208546 32768 -2.919870731 4.351329947 65536 -3.014517393 4.359955838 131072 -3.044147566 4.410073622 262144 -3.095168812 4.382412699 524288 -3.127167519 4.450596557 1048576 -3.148590884 4.407275913 cyclic5: [-30000, +50000] 16 -8300.849935 2533.007494 32 -4613.618968 4812.046321 64 -11130.63528 3850.847308 128 -8645.891121 14276.58456 256 -8108.734858 15497.52814 512 -14141.09804 10597.54167 1024 -17135.47588 14180.25867 2048 -16473.51736 26535.54554 4096 -20765.34514 18810.76993 8192 -19365.11354 23058.13058 16384 -21612.30572 26872.31363 32768 -20743.11631 30538.98975 65536 -24004.29346 31484.41658 131072 -23755.68678 31434.90074 262144 -25079.27485 39556.70022 524288 -25474.82205 36110.20073 1048576 -23933.57122 38133.23488 cyclic7: [-5.0, +7.0] 16 -0.1100132508 0.03549181758 32 -0.2564421179 0.9295655064 64 -0.4054442987 0.3171088521 128 -0.2935507636 0.3480717603 256 -0.4889169434 0.4292917612 512 -0.7794001789 0.3690643791 1024 -0.7198639599 1.557681897 2048 -1.154530728 0.8612633997 4096 -1.353445623 1.539426579 8192 -1.240762562 1.413361001 16384 -1.158232082 1.570394515 32768 -2.008225074 1.641367134 65536 -2.127617791 2.078333779 131072 -3.108941117 2.5145714 262144 -2.848198518 2.217950246 524288 -2.563058375 3.387341784 1048576 -2.881455899 3.559275099 cyclic8: [-8.0, +8.0] 16 -0.07440913001 0.04407640282 32 -0.03234686299 0.3280720424 64 -0.227993427 0.528020598 128 -0.243222868 0.1241342996 256 -0.2145804218 0.3313801622 512 -0.3718011595 0.4224459911 1024 -0.7338251673 0.2959490288 2048 -0.8390063742 0.706214112 4096 -0.8399293467 0.6265799631 8192 -1.274872943 1.264612608 16384 -1.447048876 1.134906323 32768 -0.8457784321 1.76005035 65536 -1.320093986 1.637863293 131072 -2.444244031 1.930883443 262144 -2.134223924 1.671478707 524288 -3.7449491 2.060359639 1048576 -2.51391055 2.623266505 goldstein_price: [ 3, ? ]: 16 198.5565129 129757.1961 32 6.030027818 441113.5589 64 38.23289397 439833.6571 128 4.669779591 791129.0348 256 5.692904508 939580.6818 512 5.379584165 797910.6898 1024 11.65215507 972732.4058 2048 3.375166503 982893.7692 4096 3.135622947 1005602.231 8192 3.264799257 1007269.821 16384 3.037192932 999507.221 32768 3.023028226 1009931.233 65536 3.015937967 1013066.757 131072 3.024137808 1011436.49 262144 3.00017404 1015632.946 524288 3.006215664 1014509.944 1048576 3.000742346 1015149.039 hairer: [-1875.25, -48.25] 16 -881.2969155 -279.8981767 32 -1211.655429 -147.8604838 64 -869.689685 -130.8277312 128 -1025.619716 -142.8770223 256 -1368.693779 -112.247177 512 -1356.851639 -110.178308 1024 -1338.115492 -73.07469997 2048 -1645.939879 -80.7346486 4096 -1441.300176 -86.89702449 8192 -1444.416532 -81.83197192 16384 -1442.913179 -63.09432434 32768 -1576.562998 -79.90288702 65536 -1622.170812 -65.51131346 131072 -1609.348885 -66.17076719 262144 -1624.048676 -65.04575088 524288 -1652.348462 -64.15759377 1048576 -1712.709053 -64.14337577 heart: [-1.36775, +1.74345327935 16 -0.1227166242 1.313913309 32 -0.3018680605 1.247680159 64 -0.127439426 1.359244809 128 -0.09250271799 1.35568311 256 -0.2193195928 1.588378426 512 -0.2327462346 1.391462141 1024 -0.6841367447 1.563598577 2048 -0.4630928297 1.459178144 4096 -0.4500933667 1.529022078 8192 -0.7392045075 1.587962866 16384 -0.6783052882 1.614654335 32768 -0.7447339719 1.605031333 65536 -0.9849989669 1.585281611 131072 -0.9304243954 1.621741882 262144 -0.8652801212 1.673611398 524288 -1.016404571 1.666684551 1048576 -1.045474906 1.666188785 himmelblau: [ 0, ? ]: 16 5.222201644 549.7589178 32 3.346070538 457.077907 64 8.060586387 648.5352371 128 1.33424333 498.2698889 256 0.8966305626 538.8048962 512 1.080714023 643.9621404 1024 0.1186003455 720.4328671 2048 0.09428392149 803.7897398 4096 0.04260767639 803.4778817 8192 0.07505210504 822.1779286 16384 0.01118601859 820.5024891 32768 0.01229320018 873.3952577 65536 0.004038063709 862.7012636 131072 0.0005269245982 874.5882737 262144 0.001435213392 877.2439099 524288 6.702197039e-05 884.6560231 1048576 0.0001000428366 884.5230401 hunecke: [-1436.515078155, +161.120543283] 16 -680.230692 -57.69799328 32 -1053.619905 -58.31637384 64 -1041.312775 24.30475069 128 -1109.879939 21.3499049 256 -1188.73735 74.8335367 512 -1141.738036 82.67002191 1024 -1251.450073 78.35359436 2048 -1296.924062 63.45586053 4096 -1294.896489 86.09332413 8192 -1293.922283 87.15974872 16384 -1291.286903 113.8978515 32768 -1355.012267 107.1752689 65536 -1363.909564 107.2679007 131072 -1389.377641 140.7580059 262144 -1360.906289 126.8033626 524288 -1385.075719 140.1318139 1048576 -1394.733363 139.8825683 kearfott: [ 0, ? ]: 16 2.163937866 73.10685468 32 1.92234266 77.17534137 64 1.94113191 96.03421187 128 0.353884799 104.3118683 256 0.8576399765 122.8114689 512 0.436734621 116.4818111 1024 0.4802737204 119.6040124 2048 0.1327011143 142.499561 4096 0.1893324526 148.1591234 8192 0.1012396078 162.0128795 16384 0.08543446094 185.6383588 32768 0.009487891947 171.8127634 65536 0.04427566624 178.9201469 131072 0.02248277066 178.6812664 262144 0.009593862418 193.1954407 524288 0.003301118836 185.1652963 1048576 0.006049455003 208.9685969 lv3: [-9.35, +14.8 ] 16 -3.683539196 3.441162916 32 -5.107866384 2.618789593 64 -5.476619064 4.840733717 128 -5.183523116 6.274216861 256 -7.35938594 6.883659472 512 -6.970552284 7.42801099 1024 -5.918399691 7.046555777 2048 -8.030310519 7.198335721 4096 -7.820708833 7.61065246 8192 -8.612619544 7.761957178 16384 -8.875103305 8.002792037 32768 -8.574977517 8.37356029 65536 -9.080040815 8.216366462 131072 -9.103509274 8.41625171 262144 -8.999626067 8.600646083 524288 -9.091269391 8.57367089 1048576 -9.104483588 8.605097375 lv4: [-20.8, +22.8] 16 -3.513551083 7.103716204 32 -3.30321351 10.02439176 64 -4.917321713 5.246857273 128 -5.654426995 7.031222896 256 -4.657320848 8.388562828 512 -8.005521697 9.970495333 1024 -10.72052037 12.17047536 2048 -9.640906188 11.52894508 4096 -8.933326793 12.62348032 8192 -10.12866309 12.90157041 16384 -10.37097865 12.35063755 32768 -10.79873339 13.05096693 65536 -11.63601347 13.83952322 131072 -11.727409 13.39498545 262144 -11.46374348 13.63031565 524288 -11.873483 14.45777834 1048576 -12.59435792 13.87042967 magnetism6: [-0.25, +280.0] 16 44.85573007 135.210617 32 32.48858376 152.3153921 64 46.40876491 159.4657336 128 19.56038939 192.2180015 256 21.09726585 196.6700897 512 9.80927304 202.332551 1024 9.400589747 218.9267089 2048 9.672509211 201.9762277 4096 6.26201059 217.5327098 8192 5.379119693 245.6983553 16384 1.818704971 218.9927493 32768 2.572987273 228.9516101 65536 3.077246177 237.9561279 131072 2.787322883 245.7369975 262144 1.334623739 237.9620235 524288 0.2859339146 250.414807 1048576 0.2508814911 251.882322 magnetism7: [-0.25, +330.0] 16 1.946119651 5.968606775 32 1.11697758 8.810162183 64 0.2858073661 7.414554721 128 0.4342801034 8.99956903 256 0.7050924792 9.987369921 512 0.2823584621 8.875604977 1024 0.248828378 10.85040489 2048 0.1114327335 10.4836488 4096 0.02435834942 11.55924195 8192 0.08063401001 10.5442976 16384 -0.09090911279 10.73367285 32768 -0.0913505482 11.22441729 65536 -0.1036127461 11.80807733 131072 -0.06761324375 11.81381288 262144 -0.1536390107 11.55390847 524288 -0.1629295066 12.14256732 1048576 -0.1092525514 12.00389629 quadratic: [ -2, ? ]: 16 8670.933072 42416.50847 32 6825.214853 41145.45047 64 7811.457778 45950.28552 128 10316.99518 43488.30161 256 3099.412121 54632.52267 512 4991.172881 59522.30037 1024 5624.121 56800.16396 2048 2536.424388 54401.28388 4096 3492.052159 58218.94605 8192 1764.607277 57348.64352 16384 1911.750581 61919.84336 32768 2158.327533 63042.21958 65536 1483.575961 62683.83603 131072 1829.918063 62666.92986 262144 1108.728908 63539.03962 524288 1008.179695 71576.93839 1048576 752.558642 68494.43984 rd: [-36.71269068, +10.40560403] 16 -23.52676354 7.184827384 32 -30.18013563 5.677642916 64 -25.98780854 7.066644974 128 -32.43327523 8.716560157 256 -29.94670476 7.429869342 512 -34.57885456 9.480029606 1024 -34.54448608 8.539688823 2048 -33.5537683 8.85813027 4096 -34.38020382 10.23402708 8192 -34.58698933 9.704453412 16384 -34.67804377 9.89435604 32768 -35.87520028 10.32173229 65536 -35.8329411 10.30174724 131072 -35.6596888 10.2900026 262144 -35.77392119 10.26174195 524288 -36.36154999 10.33295345 1048576 -36.39622592 10.29071177 reimer5: [-5.0, +5.0] 16 -2.875785698 -0.1305979501 32 -3.240284628 1.675051896 64 -4.233684772 1.537955437 128 -2.961305959 2.492988915 256 -3.300896044 1.977560727 512 -3.857803489 2.784070446 1024 -4.35652884 2.530911447 2048 -4.288000299 3.239978324 4096 -4.796319346 3.396311271 8192 -4.487890847 3.551032399 16384 -4.635910451 4.096016782 32768 -4.882085556 4.235412006 65536 -4.723701781 4.599018508 131072 -4.826544802 4.397077855 262144 -4.857824379 4.631471669 524288 -4.94756699 4.627565173 1048576 -4.965193287 4.77583864 reimer6: [-937501, +937499] 16 -293026.5589 176736.0788 32 -332677.3585 204678.1466 64 -245343.3798 232059.4999 128 -224143.3972 315008.9271 256 -308705.4893 334191.3828 512 -347436.8415 417783.826 1024 -332475.1024 342748.6662 2048 -415004.8273 421161.7581 4096 -423256.8686 429926.1701 8192 -407639.7559 410612.6788 16384 -454396.9484 427777.2683 32768 -493834.9697 491932.7251 65536 -501628.1922 556894.4172 131072 -526733.2871 541942.8519 262144 -541908.8977 534707.1364 524288 -605233.5366 551261.4343 1048576 -563487.4511 584352.5836 rosenbrock: [ 0, ? ]: 16 181.5615796 37141.6957 32 880.8798176 24091.21351 64 652.7486474 38382.68857 128 22.91979552 50664.77268 256 56.63514794 39571.09138 512 175.3997853 44582.06028 1024 30.84381418 57151.62492 2048 103.8585489 49022.68141 4096 53.72797849 54633.62216 8192 45.26549749 54680.51703 16384 32.74810894 61964.5991 32768 48.50513057 59950.9015 65536 9.638415524 59566.01414 131072 14.81348147 60204.5903 262144 13.86487307 63252.56171 524288 2.576407538 62613.72807 1048576 3.645995771 65285.55301 schwefel: [ 0, ? ]: 16 63.50174152 10802.07294 32 10.8098732 12079.09858 64 14.22025462 14402.71083 128 13.88263691 14168.94956 256 3.074450716 20624.2978 512 5.308122471 17857.75543 1024 2.262102962 22471.02792 2048 3.539395607 19914.10777 4096 1.512035237 22916.20306 8192 1.338727297 22511.39489 16384 0.212334853 23710.77018 32768 0.006347321878 23158.40732 65536 0.1401015261 23550.06579 131072 0.2149107372 24073.53046 262144 0.04731372201 24005.94575 524288 0.0661466777 24255.50084 1048576 0.008472658638 23867.82651 smith1: [ ?, ? ]: 16 31424.97327 278079.951 32 13551.33991 247839.2621 64 10098.28864 295055.1801 128 4677.350317 330903.9306 256 12022.47967 336013.6581 512 1275.659444 348173.8026 1024 5657.912372 374946.4747 2048 3342.700356 380249.8104 4096 1165.582126 405588.7141 8192 -406.2623363 446775.246 16384 -268.020467 439074.0099 32768 -1439.618092 432542.8232 65536 -63.17615453 460944.457 131072 -1482.670488 466277.0366 262144 -2039.899581 499160.934 524288 -940.7212122 491171.1166 1048576 -1708.358073 485817.8786 smith2: [ ?, ? ]: 16 -206896.6766 -123.0249593 32 -68649.57257 6.996099656 64 -182441.6537 -121.8556371 128 -96732.17289 -81.40967851 256 -152308.8847 44.8027926 512 -255138.7297 34.04673802 1024 -177744.1958 111.0929099 2048 -224240.9042 129.2680103 4096 -274023.4708 149.8697985 8192 -268197.7307 229.7780712 16384 -310692.1666 179.9623319 32768 -262276.3472 224.5262632 65536 -288864.6423 232.091025 131072 -294992.2864 214.6197697 262144 -297453.4201 258.8687246 524288 -303310.1539 266.5686365 1048576 -314433.8386 269.5215861 virasoro: [-29.0, +21.0] 16 -3.426904607 11.00006352 32 -10.84956308 16.15608014 64 -11.20255315 12.57195381 128 -15.83338409 16.12027804 256 -16.39918644 14.84326322 512 -15.11632711 16.38035256 1024 -10.50526596 18.82070826 2048 -14.26499223 18.6482361 4096 -16.84343764 19.31093257 8192 -17.21722286 19.91411371 16384 -17.66068019 19.41935257 32768 -20.71493226 19.79395766 65536 -19.25876964 20.34382389 131072 -23.67107909 20.41835753 262144 -22.47264926 20.83068144 524288 -21.70574464 20.5696015 1048576 -20.30462593 20.71599283 wright: [-30.25, 40.0 ] 16 -11.15584005 -8.655681369 32 -10.84986593 -8.703593226 64 -11.45156926 -8.770311359 128 -11.52535083 -7.706230795 256 -11.2965748 -8.513564499 512 -11.43331346 -8.028843123 1024 -11.76513165 -8.196387797 2048 -11.7054043 -7.742937797 4096 -11.95992171 -7.820708856 8192 -11.97970425 -7.736446701 16384 -12.088312 -7.670518509 32768 -12.08426373 -7.402071105 65536 -12.11707152 -7.581580456 131072 -12.05402457 -7.447433044 262144 -12.12885155 -7.305948375 524288 -12.13165532 -7.485290408 1048576 -12.11959099 -7.418312034 zakharov: [ 0, ? ]:: 16 28.53971448 5603927.155 32 91.42872001 8974329.974 64 38.21263863 10885852.97 128 18.09877208 12362929.26 256 39.07699459 10090026.16 512 6.018247559 15190297.66 1024 17.88925025 18816446.49 2048 11.0599999 19001364.61 4096 13.62872797 22393285.29 8192 9.326104345 17133491.06 16384 3.138187179 20737337.44 32768 0.5155671243 26287628.3 65536 2.682055479 22894020.8 131072 1.286285589 23773803.64 262144 1.980243385 25807474.91 524288 0.7312725203 26134836.64 1048576 1.187070646 28757808.62 polynomials_test(): Normal end of execution. 08-Oct-2025 12:29:25