Error

Derivation

1. Initial program 0.6

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

2. Initial simplification0.6

   \[\leadsto \cos^{-1} \left(\frac{(\left(-5 \cdot v\right) \cdot v + 1)_*}{(v \cdot v + -1)_*}\right)\]
3. Using strategy rm

4. Applied acos-asin0.6

   \[\leadsto \color{blue}{\frac{\pi}{2} - \sin^{-1} \left(\frac{(\left(-5 \cdot v\right) \cdot v + 1)_*}{(v \cdot v + -1)_*}\right)}\]

5. Taylor expanded around 0 0.6

   \[\leadsto \color{blue}{\frac{1}{2} \cdot \pi - \sin^{-1} \left(\frac{(\left(-5 \cdot v\right) \cdot v + 1)_*}{(v \cdot v + -1)_*}\right)}\]

6. Final simplification0.6

   \[\leadsto \frac{1}{2} \cdot \pi - \sin^{-1} \left(\frac{(\left(-5 \cdot v\right) \cdot v + 1)_*}{(v \cdot v + -1)_*}\right)\]

Runtime

Time bar (total: 26.7s)Debug logProfile

herbie shell --seed 2018296 +o rules:numerics
(FPCore (v)
  :name "Falkner and Boettcher, Appendix B, 1"
  (acos (/ (- 1 (* 5 (* v v))) (- (* v v) 1))))