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 add-exp-log0.5

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

5. Applied add-sqr-sqrt1.5

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

7. Applied add-sqr-sqrt1.5

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

8. Applied sqrt-prod0.5

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

9. Final simplification0.5

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

Runtime

Time bar (total: 59.9s)Debug logProfile

herbie shell --seed 2018351 
(FPCore (v)
  :name "Falkner and Boettcher, Appendix B, 1"
  (acos (/ (- 1 (* 5 (* v v))) (- (* v v) 1))))