Error

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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 associate-*r*0.5

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

5. Applied add-exp-log0.5

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

7. Applied pow10.5

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

8. Applied log-pow0.5

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

9. Applied exp-prod0.5

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

10. Simplified0.5

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

11. Final simplification0.5

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

Reproduce

herbie shell --seed 2019007 
(FPCore (v)
  :name "Falkner and Boettcher, Appendix B, 1"
  (acos (/ (- 1 (* 5 (* v v))) (- (* v v) 1))))

Details

Time bar (total: 25.4s)Debug log