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 add-exp-log0.0

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

5. Applied add-exp-log0.0

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

6. Applied div-exp0.0

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

7. Final simplification0.0

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

Reproduce

herbie shell --seed 2018360 +o rules:numerics
(FPCore (v)
  :name "Falkner and Boettcher, Equation (22+)"
  (/ 4 (* (* (* 3 PI) (- 1 (* v v))) (sqrt (- 2 (* 6 (* v v)))))))

Details

Time bar (total: 30.6s)Debug log