Average Error: 0.6 → 0.6
Time: 10.8s
Precision: 64
Internal precision: 384
\[\cos^{-1} \left(\frac{1 - 5 \cdot {v}^2}{{v}^2 - 1}\right)\]
⬇
\[\frac{\pi}{2} - \sin^{-1} \left(\frac{1 - 5 \cdot {v}^2}{{v}^2 - 1}\right)\]

Error

Bits error versus v

Derivation

  1. Initial program 0.6

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

  3. Applied acos-asin 0.6

    \[\leadsto \color{blue}{\frac{\pi}{2} - \sin^{-1} \left(\frac{1 - 5 \cdot {v}^2}{{v}^2 - 1}\right)}\]
  4. Removed slow pow expressions

Runtime

Time bar (total: 10.8s) Debug logProfile

Please include this information when filing a bug report:

herbie shell --seed '#(1064524629 4159152179 2999149171 575749698 4006532819 692958815)'
(FPCore (v)
  :name "Falkner and Boettcher, Appendix B, 1"
  (acos (/ (- 1 (* 5 (sqr v))) (- (sqr v) 1))))