Error

Derivation

1. Initial program 1.0

   \[\frac{4}{\left(\left(3 \cdot \pi\right) \cdot \left(1 - v \cdot v\right)\right) \cdot \sqrt{2 - 6 \cdot \left(v \cdot v\right)}}\]

2. Initial simplification0.0

   \[\leadsto \frac{\frac{\frac{\frac{4}{3}}{\pi}}{1 - v \cdot v}}{\sqrt{(-6 \cdot \left(v \cdot v\right) + 2)_*}}\]
3. Using strategy rm

4. Applied *-un-lft-identity0.0

   \[\leadsto \frac{\frac{\frac{\frac{4}{3}}{\pi}}{1 - v \cdot v}}{\sqrt{\color{blue}{1 \cdot (-6 \cdot \left(v \cdot v\right) + 2)_*}}}\]

5. Applied sqrt-prod0.0

   \[\leadsto \frac{\frac{\frac{\frac{4}{3}}{\pi}}{1 - v \cdot v}}{\color{blue}{\sqrt{1} \cdot \sqrt{(-6 \cdot \left(v \cdot v\right) + 2)_*}}}\]

6. Applied div-inv0.0

   \[\leadsto \frac{\color{blue}{\frac{\frac{4}{3}}{\pi} \cdot \frac{1}{1 - v \cdot v}}}{\sqrt{1} \cdot \sqrt{(-6 \cdot \left(v \cdot v\right) + 2)_*}}\]

7. Applied times-frac0.0

   \[\leadsto \color{blue}{\frac{\frac{\frac{4}{3}}{\pi}}{\sqrt{1}} \cdot \frac{\frac{1}{1 - v \cdot v}}{\sqrt{(-6 \cdot \left(v \cdot v\right) + 2)_*}}}\]

8. Simplified0.0

   \[\leadsto \color{blue}{\frac{\frac{4}{3}}{\pi}} \cdot \frac{\frac{1}{1 - v \cdot v}}{\sqrt{(-6 \cdot \left(v \cdot v\right) + 2)_*}}\]

9. Final simplification0.0

   \[\leadsto \frac{\frac{4}{3}}{\pi} \cdot \frac{\frac{1}{1 - v \cdot v}}{\sqrt{(-6 \cdot \left(v \cdot v\right) + 2)_*}}\]

Runtime

Time bar (total: 2.0m)Debug logProfile

herbie shell --seed 2018263 +o rules:numerics
(FPCore (v)
  :name "Falkner and Boettcher, Equation (22+)"
  (/ 4 (* (* (* 3 PI) (- 1 (* v v))) (sqrt (- 2 (* 6 (* v v)))))))