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 *-un-lft-identity0.0

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

5. Applied add-sqr-sqrt0.0

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

6. Applied times-frac0.0

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

7. Applied associate-*l*0.0

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

8. Simplified0.0

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

9. Final simplification0.0

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

Runtime

Time bar (total: 34.7s)Debug logProfile

herbie shell --seed 2018285 
(FPCore (v)
  :name "Falkner and Boettcher, Appendix B, 2"
  (* (* (/ (sqrt 2) 4) (sqrt (- 1 (* 3 (* v v))))) (- 1 (* v v))))