Error

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Derivation

1. Initial program 0.0

   \[\left(\frac{\sqrt{2}}{4} \cdot \sqrt{1 - 3 \cdot \left(v \cdot v\right)}\right) \cdot \left(1 - v \cdot v\right)\]

2. Initial simplification0.0

   \[\leadsto \left(\frac{\sqrt{2}}{4} \cdot \left(1 - v \cdot v\right)\right) \cdot \sqrt{1 - v \cdot \left(3 \cdot v\right)}\]
3. Using strategy rm

4. Applied add-exp-log0.0

   \[\leadsto \left(\frac{\sqrt{2}}{4} \cdot \left(1 - v \cdot v\right)\right) \cdot \color{blue}{e^{\log \left(\sqrt{1 - v \cdot \left(3 \cdot v\right)}\right)}}\]

5. Applied add-exp-log0.0

   \[\leadsto \left(\frac{\sqrt{2}}{4} \cdot \color{blue}{e^{\log \left(1 - v \cdot v\right)}}\right) \cdot e^{\log \left(\sqrt{1 - v \cdot \left(3 \cdot v\right)}\right)}\]

6. Applied add-exp-log0.0

   \[\leadsto \left(\color{blue}{e^{\log \left(\frac{\sqrt{2}}{4}\right)}} \cdot e^{\log \left(1 - v \cdot v\right)}\right) \cdot e^{\log \left(\sqrt{1 - v \cdot \left(3 \cdot v\right)}\right)}\]

7. Applied prod-exp0.0

   \[\leadsto \color{blue}{e^{\log \left(\frac{\sqrt{2}}{4}\right) + \log \left(1 - v \cdot v\right)}} \cdot e^{\log \left(\sqrt{1 - v \cdot \left(3 \cdot v\right)}\right)}\]

8. Applied prod-exp0.0

   \[\leadsto \color{blue}{e^{\left(\log \left(\frac{\sqrt{2}}{4}\right) + \log \left(1 - v \cdot v\right)\right) + \log \left(\sqrt{1 - v \cdot \left(3 \cdot v\right)}\right)}}\]

9. Final simplification0.0

   \[\leadsto e^{\left(\log \left(\frac{\sqrt{2}}{4}\right) + \log \left(1 - v \cdot v\right)\right) + \log \left(\sqrt{1 - \left(3 \cdot v\right) \cdot v}\right)}\]

Runtime

Time bar (total: 1.2m)Debug logProfile

herbie shell --seed 2018219 
(FPCore (v)
  :name "Falkner and Boettcher, Appendix B, 2"
  (* (* (/ (sqrt 2) 4) (sqrt (- 1 (* 3 (* v v))))) (- 1 (* v v))))