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Derivation

1. Initial program 0.2

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

2. Initial simplification0.2

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

4. Applied fma-udef0.2

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

5. Applied distribute-lft-in0.2

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

6. Simplified0.2

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

7. Taylor expanded around 0 7.1

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

8. Simplified0.2

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

9. Final simplification0.2

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

Runtime

Time bar (total: 16.7s)Debug logProfile

herbie shell --seed 2018339 +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))