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

Error

Bits error versus x

Try it out

Your Program's Arguments

Results

Enter valid numbers for all inputs

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
  4. Applied add-log-exp30.4

    \[\leadsto \color{blue}{\log \left(e^{\sin^{-1} \left(\cos^{-1} \left(\tan^{-1} \left(\tan \left(\cos \left(\sin x\right)\right)\right)\right)\right)}\right)}\]
  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)))))))