Error

Derivation

1. Initial program 0.5

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

2. Initial simplification0.5

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

4. Applied expm1-log1p-u0.5

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

6. Applied expm1-log1p-u0.5

   \[\leadsto (e^{\color{blue}{(e^{\log_* (1 + \log_* (1 + \cos^{-1} \left(\frac{(\left(-5 \cdot v\right) \cdot v + 1)_*}{(v \cdot v + -1)_*}\right)))} - 1)^*}} - 1)^*\]

7. Final simplification0.5

   \[\leadsto (e^{(e^{\log_* (1 + \log_* (1 + \cos^{-1} \left(\frac{(\left(-5 \cdot v\right) \cdot v + 1)_*}{(v \cdot v + -1)_*}\right)))} - 1)^*} - 1)^*\]

Runtime

Time bar (total: 20.1s)Debug logProfile

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