Average Error: 0.0 → 0.0

Time: 13.7s

Precision: 64

Internal Precision: 320

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

↓

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

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Initial program 0.0
\[2 \cdot \tan^{-1} \left(\sqrt{\frac{1 - x}{1 + x}}\right)\]
Initial simplification0.0
\[\leadsto \tan^{-1} \left(\sqrt{\frac{1 - x}{1 + x}}\right) \cdot 2\]
Using strategy rm
Applied expm1-log1p-u0.0
\[\leadsto \tan^{-1} \left(\sqrt{\color{blue}{(e^{\log_* (1 + \frac{1 - x}{1 + x})} - 1)^*}}\right) \cdot 2\]
Final simplification0.0
\[\leadsto 2 \cdot \tan^{-1} \left(\sqrt{(e^{\log_* (1 + \frac{1 - x}{x + 1})} - 1)^*}\right)\]

	Baseline	Herbie	Oracle	Span	%
Regimes	0.0	0.0	0.0	0.0	100%

herbie shell --seed 2018290 +o rules:numerics
(FPCore (x)
  :name "arccos"
  (* 2 (atan (sqrt (/ (- 1 x) (+ 1 x))))))