Average Error: 0.5 → 0.5

Time: 1.1m

Precision: 64

Internal Precision: 576

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

↓

\[\left(\frac{\pi}{2} - \frac{\pi}{2}\right) + \cos^{-1} \left(\frac{1 - \left(v \cdot v\right) \cdot 5}{v \cdot v - 1}\right)\]

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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 acos-asin0.5
\[\leadsto \color{blue}{\frac{\pi}{2} - \sin^{-1} \left(\frac{1 - 5 \cdot \left(v \cdot v\right)}{v \cdot v - 1}\right)}\]
Using strategy rm
Applied asin-acos0.5
\[\leadsto \frac{\pi}{2} - \color{blue}{\left(\frac{\pi}{2} - \cos^{-1} \left(\frac{1 - 5 \cdot \left(v \cdot v\right)}{v \cdot v - 1}\right)\right)}\]
Applied associate--r-0.5
\[\leadsto \color{blue}{\left(\frac{\pi}{2} - \frac{\pi}{2}\right) + \cos^{-1} \left(\frac{1 - 5 \cdot \left(v \cdot v\right)}{v \cdot v - 1}\right)}\]
Final simplification0.5
\[\leadsto \left(\frac{\pi}{2} - \frac{\pi}{2}\right) + \cos^{-1} \left(\frac{1 - \left(v \cdot v\right) \cdot 5}{v \cdot v - 1}\right)\]

herbie shell --seed 2018227 
(FPCore (v)
  :name "Falkner and Boettcher, Appendix B, 1"
  (acos (/ (- 1 (* 5 (* v v))) (- (* v v) 1))))