Average Error: 0.0 → 0.0
Time: 16.1s
Precision: 64
Internal Precision: 128
\[2 \cdot \tan^{-1} \left(\sqrt{\frac{1 - x}{1 + x}}\right)\]
↓
\[\tan^{-1} \left(\log \left(e^{\sqrt{\frac{1 - x}{1 + x}}}\right)\right) \cdot 2\]

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-log-exp0.0

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

  4. Final simplification0.0

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

Runtime

Time bar (total: 16.1s)Debug logProfile

BaselineHerbieOracleSpan%
Regimes0.00.00.00.00%
herbie shell --seed 2018355 
(FPCore (x)
  :name "arccos"
  (* 2 (atan (sqrt (/ (- 1 x) (+ 1 x))))))