Error

Derivation

1. Initial program 0.2

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

2. Simplified0.2

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

4. Applied sub-neg0.2

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

5. Applied distribute-lft-in0.2

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

6. Simplified0.2

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

7. Taylor expanded around 0 0.2

   \[\leadsto m \cdot \frac{m}{v} + \color{blue}{\left(-\left(m + \frac{{m}^{3}}{v}\right)\right)}\]

8. Simplified0.2

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

9. Final simplification0.2

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

Reproduce

herbie shell --seed 2019093 +o rules:numerics
(FPCore (m v)
  :name "a parameter of renormalized beta distribution"
  :pre (and (< 0 m) (< 0 v) (< v 0.25))
  (* (- (/ (* m (- 1 m)) v) 1) m))