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Derivation

1. Initial program 0.5

   \[\cos^{-1} \left(\frac{1 - 5 \cdot \left(v \cdot v\right)}{v \cdot v - 1}\right)\]
2. Using strategy rm

3. Applied expm1-log1p-u0.5

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

5. Applied expm1-udef0.5

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

6. Final simplification0.5

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

Runtime

Time bar (total: 23.7s)Debug logProfile

herbie shell --seed 2018290 +o rules:numerics
(FPCore (v)
  :name "Falkner and Boettcher, Appendix B, 1"
  (acos (/ (- 1 (* 5 (* v v))) (- (* v v) 1))))