Error

Try it out

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 flip--0.0

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

5. Applied associate-*r/0.0

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

6. Applied associate-*l/0.0

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

7. Simplified0.0

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

8. Final simplification0.0

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

Runtime

Time bar (total: 1.4m)Debug logProfile

herbie shell --seed 2018230 
(FPCore (v)
  :name "Falkner and Boettcher, Appendix B, 2"
  (* (* (/ (sqrt 2) 4) (sqrt (- 1 (* 3 (* v v))))) (- 1 (* v v))))