Average Error: 0.5 → 0.6

Time: 46.4s

Precision: 64

Internal Precision: 576

\[\cos^{-1} \left(\frac{1 - 5 \cdot \left(v \cdot v\right)}{v \cdot v - 1}\right)\]

↓

\[\cos^{-1} \left(\frac{1}{\frac{v \cdot v - 1}{1 - 5 \cdot \left(v \cdot v\right)}}\right)\]

Error

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Initial program 0.5
\[\cos^{-1} \left(\frac{1 - 5 \cdot \left(v \cdot v\right)}{v \cdot v - 1}\right)\]
Using strategy rm
Applied clear-num0.6
\[\leadsto \cos^{-1} \color{blue}{\left(\frac{1}{\frac{v \cdot v - 1}{1 - 5 \cdot \left(v \cdot v\right)}}\right)}\]
Final simplification0.6
\[\leadsto \cos^{-1} \left(\frac{1}{\frac{v \cdot v - 1}{1 - 5 \cdot \left(v \cdot v\right)}}\right)\]

	Baseline	Herbie	Oracle	Span	%
Regimes	0.6	0.6	0.5	0.0	0%

herbie shell --seed 2018295 
(FPCore (v)
  :name "Falkner and Boettcher, Appendix B, 1"
  (acos (/ (- 1 (* 5 (* v v))) (- (* v v) 1))))