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. Using strategy rm

3. Applied add-cbrt-cube0.0

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

4. Applied add-cbrt-cube0.0

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

5. Applied cbrt-unprod0.0

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

6. Simplified0.0

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

7. Final simplification0.0

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

Runtime

Time bar (total: 48.4s)Debug logProfile

herbie shell --seed 2018221 +o rules:numerics
(FPCore (v)
  :name "Falkner and Boettcher, Appendix B, 2"
  (* (* (/ (sqrt 2) 4) (sqrt (- 1 (* 3 (* v v))))) (- 1 (* v v))))