Average Error: 4.5 → 3.7
Time: 5.7s
Precision: 64
Internal Precision: 320
$\sin^{-1} \left(\cos^{-1} \left(\tan^{-1} \left(\tan \left(\cos \left(\sin 0.1\right)\right)\right)\right)\right)$
$\sin^{-1} \left(\frac{\pi}{2} - \sqrt[3]{\sin^{-1} \left(\tan^{-1} \left(\tan \left(\cos \left(\sin 0.1\right)\right)\right)\right)} \cdot \left(\sqrt[3]{\sin^{-1} \left(\tan^{-1} \left(\tan \left(\cos \left(\sin 0.1\right)\right)\right)\right)} \cdot \sqrt[3]{\sin^{-1} \left(\tan^{-1} \left(\tan \left(\cos \left(\sin 0.1\right)\right)\right)\right)}\right)\right)$

# Try it out

Results

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# Derivation

1. Initial program 4.5

$\sin^{-1} \left(\cos^{-1} \left(\tan^{-1} \left(\tan \left(\cos \left(\sin 0.1\right)\right)\right)\right)\right)$
2. Using strategy rm
3. Applied acos-asin4.4

$\leadsto \sin^{-1} \color{blue}{\left(\frac{\pi}{2} - \sin^{-1} \left(\tan^{-1} \left(\tan \left(\cos \left(\sin 0.1\right)\right)\right)\right)\right)}$
4. Using strategy rm

$\leadsto \sin^{-1} \left(\frac{\pi}{2} - \color{blue}{\left(\sqrt[3]{\sin^{-1} \left(\tan^{-1} \left(\tan \left(\cos \left(\sin 0.1\right)\right)\right)\right)} \cdot \sqrt[3]{\sin^{-1} \left(\tan^{-1} \left(\tan \left(\cos \left(\sin 0.1\right)\right)\right)\right)}\right) \cdot \sqrt[3]{\sin^{-1} \left(\tan^{-1} \left(\tan \left(\cos \left(\sin 0.1\right)\right)\right)\right)}}\right)$
6. Final simplification3.7

$\leadsto \sin^{-1} \left(\frac{\pi}{2} - \sqrt[3]{\sin^{-1} \left(\tan^{-1} \left(\tan \left(\cos \left(\sin 0.1\right)\right)\right)\right)} \cdot \left(\sqrt[3]{\sin^{-1} \left(\tan^{-1} \left(\tan \left(\cos \left(\sin 0.1\right)\right)\right)\right)} \cdot \sqrt[3]{\sin^{-1} \left(\tan^{-1} \left(\tan \left(\cos \left(\sin 0.1\right)\right)\right)\right)}\right)\right)$

# Runtime

Time bar (total: 5.7s)Debug log

herbie shell --seed '#(2775764126 3555076145 3898259844 1891440260 2599947619 1948460636)'
(FPCore ()
:name "asin(acos(atan(tan(cos(sin(0.1))))))"
(asin (acos (atan (tan (cos (sin 0.1)))))))