Average Error: 30.4 → 30.4
Time: 32.4s
Precision: 64
Internal Precision: 2368
$\sin^{-1} \left(\cos^{-1} \left(\tan^{-1} \left(\tan \left(\cos \left(\sin x\right)\right)\right)\right)\right)$
$\sin^{-1} \left(\cos^{-1} \left(\tan^{-1} \left(\tan \left(\cos \left(\sin x\right)\right)\right)\right)\right)$

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Results

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Derivation

1. Initial program 30.4

$\sin^{-1} \left(\cos^{-1} \left(\tan^{-1} \left(\tan \left(\cos \left(\sin x\right)\right)\right)\right)\right)$
2. Initial simplification30.4

$\leadsto \sin^{-1} \left(\cos^{-1} \left(\tan^{-1} \left(\tan \left(\cos \left(\sin x\right)\right)\right)\right)\right)$
3. Using strategy rm

$\leadsto \color{blue}{\log \left(e^{\sin^{-1} \left(\cos^{-1} \left(\tan^{-1} \left(\tan \left(\cos \left(\sin x\right)\right)\right)\right)\right)}\right)}$
5. Taylor expanded around inf 30.4

$\leadsto \color{blue}{\sin^{-1} \left(\cos^{-1} \left(\tan^{-1} \left(\tan \left(\cos \left(\sin x\right)\right)\right)\right)\right)}$
6. Final simplification30.4

$\leadsto \sin^{-1} \left(\cos^{-1} \left(\tan^{-1} \left(\tan \left(\cos \left(\sin x\right)\right)\right)\right)\right)$

Runtime

Time bar (total: 32.4s)Debug log

herbie shell --seed '#(2775764126 3555076145 3898259844 1891440260 2599947619 1948460636)'
(FPCore (x)
:name "asin (acos (atan (tan (cos (sin (x) ) ) ) ) )"
(asin (acos (atan (tan (cos (sin x)))))))