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Author: Roquen (posted 2016-10-17 12:09:13, viewed 2751 times)

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rounded power series: x * (1 + x^2 * (-0.16666667163372039794921875 + x^2 * (8.333333767950534820556640625e-3 + x^2 * (-1.98412701138295233249664306640625e-4 + x^2 * (2.755731884462875314056873321533203125e-6 + x^2 * (-2.50521079436794025241397321224212646484375e-8 + x^2 * (1.6059044372074282591711380518972873687744140625e-10 + x^2 * (-7.6471636098127127034729255683487281203269958496093e-13))))))))

unrounded gamedev poly: x * (1 + x^2 * (-0.166666671633720397949 + x^2 * (8.3333337679505348205599999999999999999999999999999e-3 + x^2 * (-1.98412497411482036114e-4 + x^2 * (2.75565571428160183132e-6 + x^2 * (-2.50368472620721149723999999999999999999999999999997e-8 + x^2 * (1.58849267073435385099999999999999999999999999999999e-10 + x^2 * (-6.589255508414326723e-13))))))))

rounded gamedev poly:   x * (1 + x^2 * (-0.16666667163372039794921875 + x^2 * (8.333333767950534820556640625e-3 + x^2 * (-1.98412497411482036113739013671875e-4 + x^2 * (2.75565571428160183131694793701171875e-6 + x^2 * (-2.503684726207211497239768505096435546875e-8 + x^2 * (1.5884926707343538510031066834926605224609375e-10 + x^2 * (-6.5892555084143267229990215128054842352867126464843e-13))))))))
  ~correct at:    [|0|]
  ~max abs error: 1.31273460943000269150518952096334097893005006285736e-8

9th degree:       x * (1 + x^2 * (-0.166666567325592041015625 + x^2 * (8.33301059901714324951171875e-3 + x^2 * (-1.98062291019596159458160400390625e-4 + x^2 * 2.599344725240371190011501312255859375e-6))))
  ~correct at:    [|0, 0.79256761451043724058698073970209919928423900170935, 1.16220082184083256440052086692864742612697272544112, 1.42016657441421605690126154283604989280271990146748, 1.5538724743860520209168735330805973053244414739681|]
  ~max abs error: 4.936001385402732921647839248180389404296875e-9
    @x:           [|0, 0.54569755266103797794788039152138963563837337844245, 0.99015131127217942303038391152180591666394774596793, 1.30591028261308746365371579940055118250969531010133, 1.50339132080777423110506771660915670574730818816504|]

11th degree:      x * (1 + x^2 * (-0.16666667163372039794921875 + x^2 * (8.333346806466579437255859375e-3 + x^2 * (-1.98424444533884525299072265625e-4 + x^2 * (2.759134758889558725059032440185546875e-6 + x^2 * (-2.487414718643776723183691501617431640625e-8))))))
  ~correct at:    [|0, 0.87158448171960894250040795981468838944688804083035, 1.214057137343887707262418803297054710165262628692, 1.44147464176726352290721977077234326296562312262556, 1.55634564357096727758401281119884274480690659774928|]
  ~max abs error: 3.194503273018511890768422745168209075927734375e-10
    @x:           [|0, 0.59416568150400772181981120907712146504328751727028, 1.0486808448568711237116428594557898323845248871983, 1.33860826399204988137558491544491069416308408804594, 1.51248697263475362990455074756254193629864749849073|]

13th degree:      x * (1 + x^2 * (-0.16666667163372039794921875 + x^2 * (8.33335332572460174560546875e-3 + x^2 * (-1.98442008695565164089202880859375e-4 + x^2 * (2.775746679617441259324550628662109375e-6 + x^2 * (-3.1512893627905214088968932628631591796875e-8 + x^2 * 9.559040226037041065865196287631988525390625e-10))))))
  ~correct at:    [|0, 0.76374835875953843531892862889578897505980445837254, 1.0760704113671672534820610556086647876630399180284, 1.314199962439972538862826329427094562641384944913, 1.4772635339638178310515436392738410319671206762485, 1.5603376258227495128117087160707132956528612905478|]
  ~max abs error: 1.89238014147719013635651208460330963134765625e-10
    @x:           [|0, 0.50707120559424903851437563408422983336673708099287, 0.91721518710678010544321024169790015562828231868022, 1.19886946835591125271684027229436316688267831030626, 1.40333450859086749612493104854036125608051414325145, 1.52856155248496071127691482400737298662353783310655|]

15th degree:      x * (1 + x^2 * (-0.16666667163372039794921875 + x^2 * (8.333359844982624053955078125e-3 + x^2 * (-1.98465961148031055927276611328125e-4 + x^2 * (2.808531235132250003516674041748046875e-6 + x^2 * (-5.273488312695917556993663311004638671875e-8 + x^2 * (7.5236119556620906223542988300323486328125e-9 + x^2 * (-7.83581810548383828063379041850566864013671875e-10))))))))
  ~correct at:    [|0, 0.67744469062677057348696675183776015019298448396358, 0.96301541753762238572567486435215377965827801337243, 1.19619294824868674854459319738319254941010530068993, 1.37668122315482053884640090175273679846930884676839, 1.5001624546580787317767506309135460944582629982165, 1.56290313065328262180751904926437644200585423664783|]
  ~max abs error: 1.265517968196405718117603100836277008056640625e-10
    @x:           [|0, 0.445757903945418493473873405564943664652576137619919, 0.81527729503524751819347697892055630924683698852077, 1.08029716509517114176720384268458656140880693357667, 1.29052283367181586471294577091423930869811694123295, 1.44467379282931138852994016102050144966051382672205, 1.53901929025935463726514955476622543710797647308924|]

COSINE

8th degree:       0.999999940395355224609375 + x^2 * (-0.499998986721038818359375 + x^2 * (4.1663490235805511474609375e-2 + x^2 * (-1.385320327244699001312255859375e-3 + x^2 * 2.31450176215730607509613037109375e-5)))
  ~correct at:    [|0.27393016104735247655747125869147718036967822593807, 0.71950829261928464111667124290353623125406435256561, 1.112232252402468946800675017837323485397397920774, 1.39995809355010196472107409246817946313809751147373, 1.55147018423991180612577048755073886919114457140298|]
  ~max abs error: 5.9604644775390625e-8
    @x:           [|0, 0.49815319491827494187965000421825414476410209090596, 0.92677619655530824857131147722978677591205387212166, 1.27162126170779507117823282645592445182343471726855, 1.49403676457233321672780593033474140125343055812236|]

10th degree:       1 + x^2 * (-0.5 + x^2 * (4.16666567325592041015625e-2 + x^2 * (-1.388858654536306858062744140625e-3 + x^2 * (2.4770297386567108333110809326171875e-5 + x^2 * (-2.62119527860704693011939525604248046875e-7)))))
  ~correct at:    [|0, 0.8343372487556189937919321224726763094205081462419, 1.1939322083988889549930352763673312299097731447613, 1.43359508958529849796537573547497358949243438252925, 1.55545814815647515503607638559720500315674057636346|]
  ~max abs error: 4.410775356067375696511589922010898590087890625e-10
    @x:           [|0, 0.61805347590661786064890033639003862881562883266625, 1.0335945417691214393124505976599651076837310605955, 1.3290646237912299442942371124061163136623496407905, 1.50974313414484655376058455992300786253629529161893|]

12th degree:       1 + x^2 * (-0.5 + x^2 * (4.16666679084300994873046875e-2 + x^2 * (-1.3888920657336711883544921875e-3 + x^2 * (2.4804394342936575412750244140625e-5 + x^2 * (-2.76562701628790819086134433746337890625e-7 + x^2 * 2.1777040171144790292601101100444793701171875e-9)))))
  ~correct at:    [|0, 0.95047331227991475142361547969743286707733907521238, 1.2557572198235500427322795789187693734673090840407, 1.45681952341198238304438325189060355927636749000359, 1.55809161824714345346607951555209496731908746571|]
  ~max abs error: 5.9785294770353658577732858248054981231689453125e-11
    @x:           [|0, 0.68520468445714544463893872861011862136243861256844, 1.10711976562046912051224696663622200521429976706173, 1.36539755671914406716610500923401614407827121397933, 1.51930878151626878632106567506485318259302345100017|]

14th degree:       1 + x^2 * (-0.5 + x^2 * (4.16666679084300994873046875e-2 + x^2 * (-1.388893462717533111572265625e-3 + x^2 * (2.4807859517750330269336700439453125e-5 + x^2 * (-2.79638925348990596830844879150390625e-7 + x^2 * (3.34695560155751081765629351139068603515625e-9 + x^2 * (-1.61639313045469634744222275912761688232421875e-10)))))))
  ~correct at:    [|0, 0.82662186511584515441052476642585014202759291582466, 1.1190169855550329645174379729888179751064224865686, 1.33791676548204138988347595788702242612752534871722, 1.48623428418224665586562266069902017553385566145323, 1.56135522123297333976011385068629310043750698162349|]
  ~max abs error: 3.100607270933863901518634520471096038818359375e-11
    @x:           [|0, 0.58837399833869077330969943003295749799027788570969, 0.97276892883445247494963595987641454517256408550383, 1.23289310008008244121842034956018174394138392614208, 1.41935940966550789655812762223405549454550372121627, 1.53270323446839620966937041493879326803149031700444|]





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