Average Error: 0.5 → 0.5
Time: 1.5m
Precision: 64
Internal Precision: 384
\[\cos^{-1} \left(\frac{1 - 5 \cdot \left(v \cdot v\right)}{v \cdot v - 1}\right)\]
↓
\[\cos^{-1} \left(\log \left(e^{\frac{1 - 5 \cdot \left(v \cdot v\right)}{v \cdot v - 1}}\right)\right)\]

Error

Bits error versus v

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 add-log-exp0.5

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

Runtime

Time bar (total: 1.5m)Debug logProfile

herbie shell --seed '#(1070706311 3771791028 4128836681 4194990999 2341756049 504035650)' 
(FPCore (v)
  :name "Falkner and Boettcher, Appendix B, 1"
  (acos (/ (- 1 (* 5 (* v v))) (- (* v v) 1))))