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

Error

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Your Program's Arguments

    Results

    Enter valid numbers for all inputs

    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
    5. Applied add-cube-cbrt3.7

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