Error

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

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

4. Applied add-exp-log0.0

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

5. Applied add-exp-log0.0

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

6. Applied add-exp-log0.0

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

7. Applied prod-exp0.0

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

8. Applied prod-exp0.0

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

9. Final simplification0.0

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

Runtime

Time bar (total: 42.8s)Debug logProfile

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