Average Error: 0.0 → 0.0
Time: 35.2s
Precision: 64
Internal Precision: 576
\[2 \cdot \tan^{-1} \left(\sqrt{\frac{1 - x}{1 + x}}\right)\]
↓
\[2 \cdot \tan^{-1} \left(\sqrt{\sqrt[3]{\frac{1 - x}{1 + x} \cdot \left(\frac{1 - x}{1 + x} \cdot \frac{1 - x}{1 + x}\right)}}\right)\]

Error

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Results

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Derivation

  1. Initial program 0.0

    \[2 \cdot \tan^{-1} \left(\sqrt{\frac{1 - x}{1 + x}}\right)\]
  2. Using strategy rm

  3. Applied add-cbrt-cube0.0

    \[\leadsto 2 \cdot \tan^{-1} \left(\sqrt{\color{blue}{\sqrt[3]{\left(\frac{1 - x}{1 + x} \cdot \frac{1 - x}{1 + x}\right) \cdot \frac{1 - x}{1 + x}}}}\right)\]

  4. Final simplification0.0

    \[\leadsto 2 \cdot \tan^{-1} \left(\sqrt{\sqrt[3]{\frac{1 - x}{1 + x} \cdot \left(\frac{1 - x}{1 + x} \cdot \frac{1 - x}{1 + x}\right)}}\right)\]

Runtime

Time bar (total: 35.2s)Debug logProfile

herbie shell --seed 2018254 
(FPCore (x)
  :name "arccos"
  (* 2 (atan (sqrt (/ (- 1 x) (+ 1 x))))))