[VA] Short & Sweet Math Challenge #24: "2019 Spring Special 5-tier"
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04-01-2019, 03:25 PM
(This post was last modified: 04-03-2019 06:01 PM by Albert Chan.)
Post: #22
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RE: [VA] Short & Sweet Math Challenge #24: "2019 Spring Special 5-tier"
Just figured out how to improve cin(x) accuracy for large x
cin(x) = arcsin(cin(sin(x))) = nest(arcsin, cin(nest(sin, x, n)), n) Pick enough nested sin's so cin argument is small, say below 0.1 radian cin[x0_] := Block[ {n=0, x=x0+0.0}, While[Abs[x] ≥ 0.1, x = Sin[x]; n++]; Nest[ArcSin, x - (1/18) x^3 - (7/1080) x^5 - (51/32285) x^7, n] ] Above cin(x) setup give about 12 digits accuracy: x cin(x) cin(cin(cin(x))) - sin(x) 0.0 0.0 +0.0 0.2 0.199553461081 -1.9e-16 0.4 0.396375366278 +1.8e-14 0.6 0.587446695546 -1.1e-16 0.8 0.769025184826 -9.1e-14 1.0 0.935745970819 +1.4e-13 Pi/2. 1.210368344457 +2.6e-13 -0.71 -0.688778525307 -1.6e-13 2.019 1.026923318694 +6.4e-13 Edit: changed x^7 coefficient from -0.00158 to -51/32285 to get better accuracy |
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