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

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

4. Applied add-cbrt-cube1.0

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

5. Applied add-cbrt-cube1.0

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

6. Applied cbrt-undiv0.0

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

7. Simplified0.0

   \[\leadsto \sqrt[3]{\color{blue}{\frac{1 - v \cdot v}{\frac{32}{\sqrt{2}}} \cdot \left(\left(1 - v \cdot v\right) \cdot \left(1 - v \cdot v\right)\right)}} \cdot \sqrt{-3 \cdot \left(v \cdot v\right) + 1}\]

8. Final simplification0.0

   \[\leadsto \sqrt[3]{\left(\left(1 - v \cdot v\right) \cdot \left(1 - v \cdot v\right)\right) \cdot \frac{1 - v \cdot v}{\frac{32}{\sqrt{2}}}} \cdot \sqrt{\left(v \cdot v\right) \cdot -3 + 1}\]

Runtime

Time bar (total: 31.5s)Debug logProfile

herbie shell --seed 2018248 
(FPCore (v)
  :name "Falkner and Boettcher, Appendix B, 2"
  (* (* (/ (sqrt 2) 4) (sqrt (- 1 (* 3 (* v v))))) (- 1 (* v v))))