Average Error: 0.0 → 0.0
Time: 1.3m
Precision: 64
Internal Precision: 384
\[2 \cdot \tan^{-1} \left(\sqrt{\frac{1 - x}{1 + x}}\right)\]
↓
\[2 \cdot \tan^{-1} \left(\sqrt{\frac{1}{1 + x} - \frac{x}{1 + x}}\right)\]

Error

Bits error versus x

Derivation

  1. Initial program 0.0

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

  3. Applied div-sub0.0

    \[\leadsto 2 \cdot \tan^{-1} \left(\sqrt{\color{blue}{\frac{1}{1 + x} - \frac{x}{1 + x}}}\right)\]
  4. Removed slow pow expressions.

Runtime

Time bar (total: 1.3m)Debug log

herbie shell --seed '#(3622638036 3041702260 3649696288 21285302 1742518495 296600799)' 
(FPCore (x)
  :name "arccos"
  (* 2 (atan (sqrt (/ (- 1 x) (+ 1 x))))))