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Derivation

1. Initial program 0.2

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

2. Taylor expanded around 0 7.1

   \[\leadsto \color{blue}{\frac{{m}^{2}}{v} - \left(m + \frac{{m}^{3}}{v}\right)}\]

3. Simplified0.2

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

5. Applied sub-neg0.2

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

6. Applied distribute-lft-in0.2

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

7. Simplified0.2

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

8. Final simplification0.2

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

Runtime

Time bar (total: 28.1s)Debug logProfile

herbie shell --seed 2018221 
(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))