Error

Derivation

1. Initial program 0.1

   \[\left(\frac{m \cdot \left(1 - m\right)}{v} - 1\right) \cdot \left(1 - m\right)\]

2. Taylor expanded around 0 0.1

   \[\leadsto \left(\color{blue}{\left(\frac{m}{v} - \frac{{m}^{2}}{v}\right)} - 1\right) \cdot \left(1 - m\right)\]

3. Simplified0.1

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

5. Applied pow10.1

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

6. Applied pow10.1

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

7. Applied pow-prod-down0.1

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

8. Simplified0.1

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

10. Applied associate-*r/0.1

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

11. Final simplification0.1

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

Reproduce

herbie shell --seed 2019050 
(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)))