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. Using strategy rm

3. Applied flip--0.0

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

4. Applied sqrt-div0.0

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

5. Applied frac-times0.0

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

6. Applied associate-*l/0.0

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

7. Simplified0.0

   \[\leadsto \frac{\color{blue}{\left(\left(1 - v \cdot v\right) \cdot \sqrt{2}\right) \cdot \sqrt{1 - {v}^{3} \cdot \left(v \cdot 9\right)}}}{4 \cdot \sqrt{1 + 3 \cdot \left(v \cdot v\right)}}\]

8. Final simplification0.0

   \[\leadsto \frac{\sqrt{1 - {v}^{3} \cdot \left(v \cdot 9\right)} \cdot \left(\left(1 - v \cdot v\right) \cdot \sqrt{2}\right)}{\sqrt{3 \cdot \left(v \cdot v\right) + 1} \cdot 4}\]

Reproduce

herbie shell --seed 2019005 
(FPCore (v)
  :name "Falkner and Boettcher, Appendix B, 2"
  (* (* (/ (sqrt 2) 4) (sqrt (- 1 (* 3 (* v v))))) (- 1 (* v v))))

Details

Time bar (total: 26.1s)Debug log