Function approximation, part 2

P.S. Here are the data.

For newton_10e8.txt (one underscore in the name):

2.00999999999999978683717927197 38035
2.01999999999999957367435854394 23136
2.02999999999999936051153781591 16155
2.03999999999999914734871708788 12260
2.04999999999999893418589635985 10019
2.05999999999999872102307563182 8187
2.06999999999999850786025490379 7172
2.07999999999999829469743417576 6088
2.08999999999999808153461344773 5503
2.0999999999999978683717927197 5029
2.10999999999999765520897199167 4462
2.11999999999999744204615126364 4065
2.12999999999999722888333053561 3803
2.13999999999999701572050980758 3499
2.14999999999999680255768907955 3381
2.15999999999999658939486835152 3114
2.16999999999999637623204762349 2888
2.17999999999999616306922689546 2733
2.18999999999999594990640616743 2596
2.1999999999999957367435854394 2480
2.20999999999999552358076471137 2397
2.21999999999999531041794398334 2183
2.22999999999999509725512325531 2134
2.23999999999999488409230252728 2015
2.24999999999999467092948179925 1989
2.25999999999999445776666107122 1861
2.26999999999999424460384034319 1868
2.27999999999999403144101961516 1845
2.28999999999999381827819888713 1753
2.2999999999999936051153781591 1664
2.30999999999999339195255743107 1581
2.31999999999999317878973670304 1480
2.32999999999999296562691597501 1514
2.33999999999999275246409524698 1416
2.34999999999999253930127451895 1367
2.35999999999999232613845379092 1366
2.36999999999999211297563306289 1264
2.37999999999999189981281233486 1270
2.38999999999999168664999160683 1244
2.3999999999999914734871708788 1289
2.40999999999999126032435015077 1161
2.41999999999999104716152942274 1147
2.42999999999999083399870869471 1192
2.43999999999999062083588796668 1152
2.44999999999999040767306723865 1091
2.45999999999999019451024651062 1074
2.46999999999998998134742578259 1045
2.47999999999998976818460505456 1066
2.48999999999998955502178432653 977
2.4999999999999893418589635985 996
2.50999999999998912869614287047 979
2.51999999999998891553332214244 974
2.52999999999998870237050141441 893
2.53999999999998848920768068638 923
2.54999999999998827604485995835 900
2.55999999999998806288203923032 940
2.56999999999998784971921850229 886
2.57999999999998763655639777426 825
2.58999999999998742339357704623 772
2.5999999999999872102307563182 795
2.60999999999998699706793559017 839
2.61999999999998678390511486214 777
2.62999999999998657074229413411 769
2.63999999999998635757947340608 737
2.64999999999998614441665267805 732
2.65999999999998593125383195002 730
2.66999999999998571809101122199 710
2.67999999999998550492819049396 724
2.68999999999998529176536976593 726
2.6999999999999850786025490379 672
2.70999999999998486543972830987 691
2.71999999999998465227690758184 689
2.72999999999998443911408685381 628
2.73999999999998422595126612578 633
2.74999999999998401278844539775 696
2.75999999999998379962562466972 642
2.76999999999998358646280394169 634
2.77999999999998337329998321366 626
2.78999999999998316013716248563 601
2.7999999999999829469743417576 628
2.80999999999998273381152102957 576
2.81999999999998252064870030154 582
2.82999999999998230748587957351 634
2.83999999999998209432305884548 594
2.84999999999998188116023811745 599
2.85999999999998166799741738942 560
2.86999999999998145483459666139 546
2.87999999999998124167177593336 505
2.88999999999998102850895520533 500
2.89999999999998081534613447729 506
2.90999999999998060218331374926 540
2.91999999999998038902049302123 554
2.9299999999999801758576722932 536
2.93999999999997996269485156517 526
2.94999999999997974953203083714 543
2.95999999999997953636921010911 515
2.96999999999997932320638938108 499
2.97999999999997911004356865305 512
2.98999999999997889688074792502 494
2.99999999999997868371792719699 517

For newton__10e8.txt (two underscores):

2.00999999999999978683717927197 47749.629301071850932203233242
2.01999999999999957367435854394 45600.5419677955796942114830017
2.02999999999999936051153781591 43548.1794978041652939282357693
2.03999999999999914734871708788 41588.1885551337181823328137398
2.04999999999999893418589635985 39716.4117362142715137451887131
2.05999999999999872102307563182 37928.8787514594223466701805592
2.06999999999999850786025490379 36221.7980037497545708902180195
2.07999999999999829469743417576 34591.5485459471019566990435123
2.08999999999999808153461344773 33034.6724003800991340540349483
2.0999999999999978683717927197 31547.8672240099767805077135563
2.10999999999999765520897199167 30127.9793037182171246968209743
2.11999999999999744204615126364 28771.9968668581896054092794657
2.12999999999999722888333053561 27477.0436928815834107808768749
2.13999999999999701572050980758 26240.3730124889916623942553997
2.14999999999999680255768907955 25059.3616813639891915954649448
2.15999999999999658939486835152 23931.5046161322970874607563019
2.16999999999999637623204762349 22854.4094807441360899247229099
2.17999999999999616306922689546 21825.7916120086847513448446989
2.18999999999999594990640616743 20843.4691735171618347521871328
2.1999999999999957367435854394 19905.3585276752564823254942894
2.20999999999999552358076471137 19009.4698160284533514641225338
2.21999999999999531041794398334 18153.9027385054614569526165724
2.22999999999999509725512325531 17336.8425226269755512475967407
2.23999999999999488409230252728 16556.5560741299450455699115992
2.24999999999999467092948179925 15811.3883008422872080700471997
2.25999999999999445776666107122 15099.7586020104663475649431348
2.26999999999999424460384034319 14420.1575156334129133028909564
2.27999999999999403144101961516 13771.1435166912142449291422963
2.28999999999999381827819888713 13151.3399594772854470647871494
2.2999999999999936051153781591 12559.4321575482717889826744795
2.30999999999999339195255743107 11994.1645950978181645041331649
2.31999999999999317878973670304 11454.3382638392267836024984717
2.32999999999999296562691597501 10938.8081197481187700759619474
2.33999999999999275246409524698 10446.4806542705482570454478264
2.34999999999999253930127451895 9976.31157484474169905297458172
2.35999999999999232613845379092 9527.30358981657263939268887043
2.36999999999999211297563306289 9098.50429305024772475007921457
2.37999999999999189981281233486 8689.00414374720276100561022758
2.38999999999999168664999160683 8297.93453718812270381022244692
2.3999999999999914734871708788 7924.46596230587965692393481731
2.40999999999999126032435015077 7567.80624218134653347078710794
2.41999999999999104716152942274 7227.19885372993576311273500323
2.42999999999999083399870869471 6901.92132301471701794071123004
2.43999999999999062083588796668 6591.28369278232094075065106153
2.44999999999999040767306723865 6294.62705897111482045147567987
2.45999999999999019451024651062 6011.3221730873365231673233211
2.46999999999998998134742578259 5740.7681074846786941634491086
2.47999999999998976818460505456 5482.39098071618445828789845109
2.48999999999998955502178432653 5235.64274025474969675997272134
2.4999999999999893418589635985 5000.00000000024556356947869062
2.50999999999998912869614287047 4774.96293010741919715655967593
2.51999999999998891553332214244 4560.05419677978170511778444052
2.52999999999998870237050141441 4354.81794978063044254668056965
2.53999999999998848920768068638 4158.81885551357572694541886449
2.54999999999998827604485995835 3971.64117362162232893751934171
2.55999999999998806288203923032 3792.8878751461274987377692014
2.56999999999998784971921850229 3622.17980037515371805056929588
2.57999999999998763655639777426 3459.15485459487990738125517964
2.58999999999998742339357704623 3303.46724003817189441178925335
2.5999999999999872102307563182 3154.78672240115247404901310802
2.60999999999998699706793559017 3012.79793037196941440925002098
2.61999999999998678390511486214 2877.19968668595993221970275044
2.62999999999998657074229413411 2747.70436928829303724342025816
2.63999999999998635757947340608 2624.03730124902813258813694119
2.64999999999998614441665267805 2505.9361681365217009442858398
2.65999999999998593125383195002 2393.15046161334703356260433793
2.66999999999998571809101122199 2285.44094807452574968920089304
2.67999999999998550492819049396 2182.57916120097570455982349813
2.68999999999998529176536976593 2084.34691735181831973022781312
2.6999999999999850786025490379 1990.53585276762328248878475279
2.70999999999998486543972830987 1900.94698160293887667648959905
2.71999999999998465227690758184 1815.39027385063513975183013827
2.72999999999998443911408685381 1733.68425226278259287937544286
2.73999999999998422595126612578 1655.65560741307604075700510293
2.74999999999998401278844539775 1581.13883008430639165453612804
2.75999999999998379962562466972 1509.97586020112089499889407307
2.76999999999998358646280394169 1442.0157515634120954928221181
2.77999999999998337329998321366 1377.11435166918886352505069226
2.78999999999998316013716248563 1315.13399594779298240609932691
2.7999999999999829469743417576 1255.94321575488879716431256384
2.80999999999998273381152102957 1199.41645950984070623235311359
2.81999999999998252064870030154 1145.43382638397883965808432549
2.82999999999998230748587957351 1093.88081197486553719500079751
2.83999999999998209432305884548 1044.64806542710607573098968714
2.84999999999998188116023811745 997.631157484523214407090563327
2.85999999999998166799741738942 952.730358981704171128512825817
2.86999999999998145483459666139 909.850429305069610563805326819
2.87999999999998124167177593336 868.900414374762817715236451477
2.88999999999998102850895520533 829.793453718852902056823950261
2.89999999999998081534613447729 792.446596230626937540364451706
2.90999999999998060218331374926 756.780624218171851680381223559
2.91999999999998038902049302123 722.719885373029114816745277494
2.9299999999999801758576722932 690.192132301505466784874442965
2.93999999999997996269485156517 659.128369278264472086448222399
2.94999999999997974953203083714 629.462705897142427602375391871
2.95999999999997953636921010911 601.132217308763188157172407955
2.96999999999997932320638938108 574.076810748496086489467415959
2.97999999999997911004356865305 548.239098071645344134594779462
2.98999999999997889688074792502 523.564274025500708376057446003
2.99999999999997868371792719699 500.000000000049112713895738125

P.P.S. The code is at:

https://github.com/sjhalayka/numerical_newtonian_gravity

As you can see from the code, newton__10e8.txt contains the following values:

n / (2.0 * pow(receiver_pos.x, D))

as D goes from 2.01 to 3.0.

Well, i tried some very quick manual curve fitting using polynomals:

(At least i think that's how they call this)

But those math programs we talked about last time can do this much better. You only need to learn a bit about the syntax they require.

I wrote a paper to accompany the code. :)

It's at:

https://github.com/sjhalayka/papers/blob/main/numerical_anisotropic_newtonian_gravitation/bezier_escape.pdf