Error

Derivation

1. Initial program 0.1

   \[\left(\frac{m \cdot \left(1 - m\right)}{v} - 1\right) \cdot \left(1 - m\right)\]
2. Using strategy rm

3. Applied flip--0.1

   \[\leadsto \left(\frac{m \cdot \color{blue}{\frac{1 \cdot 1 - m \cdot m}{1 + m}}}{v} - 1\right) \cdot \left(1 - m\right)\]

4. Applied associate-*r/0.1

   \[\leadsto \left(\frac{\color{blue}{\frac{m \cdot \left(1 \cdot 1 - m \cdot m\right)}{1 + m}}}{v} - 1\right) \cdot \left(1 - m\right)\]
5. Using strategy rm

6. Applied pow10.1

   \[\leadsto \left(\frac{\frac{m \cdot \left(1 \cdot 1 - m \cdot m\right)}{1 + m}}{v} - 1\right) \cdot \color{blue}{{\left(1 - m\right)}^{1}}\]

7. Applied pow10.1

   \[\leadsto \color{blue}{{\left(\frac{\frac{m \cdot \left(1 \cdot 1 - m \cdot m\right)}{1 + m}}{v} - 1\right)}^{1}} \cdot {\left(1 - m\right)}^{1}\]

8. Applied pow-prod-down0.1

   \[\leadsto \color{blue}{{\left(\left(\frac{\frac{m \cdot \left(1 \cdot 1 - m \cdot m\right)}{1 + m}}{v} - 1\right) \cdot \left(1 - m\right)\right)}^{1}}\]

9. Simplified0.1

   \[\leadsto {\color{blue}{\left((\left(\frac{m}{(v \cdot m + v)_*}\right) \cdot \left(1 - m \cdot m\right) + -1)_* \cdot \left(1 - m\right)\right)}}^{1}\]

10. Final simplification0.1

    \[\leadsto \left(1 - m\right) \cdot (\left(\frac{m}{(v \cdot m + v)_*}\right) \cdot \left(1 - m \cdot m\right) + -1)_*\]

Runtime

Time bar (total: 57.5s)Debug logProfile

herbie shell --seed 2018348 +o rules:numerics
(FPCore (m v)
  :name "b parameter of renormalized beta distribution"
  :pre (and (< 0 m) (< 0 v) (< v 0.25))
  (* (- (/ (* m (- 1 m)) v) 1) (- 1 m)))