Average Error: 0.6 → 0.6
Time: 1.3m
Precision: 64
Internal Precision: 576
\[\cos^{-1} \left(\frac{1 - 5 \cdot \left(v \cdot v\right)}{v \cdot v - 1}\right)\]
↓
\[\cos^{-1} \left(\frac{1 - \log \left(e^{\left(v \cdot v\right) \cdot 5}\right)}{v \cdot v - 1}\right)\]

Error

Bits error versus v

Try it out

Your Program's Arguments

Results

Enter valid numbers for all inputs

Derivation

  1. Initial program 0.6

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

  3. Applied add-log-exp0.6

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

  4. Final simplification0.6

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

Runtime

Time bar (total: 1.3m)Debug logProfile

herbie shell --seed 2018217 
(FPCore (v)
  :name "Falkner and Boettcher, Appendix B, 1"
  (acos (/ (- 1 (* 5 (* v v))) (- (* v v) 1))))