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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 -inf 0.2

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

4. Applied div-inv0.2

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

5. Taylor expanded around -inf 7.0

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

7. Applied unpow27.0

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

8. Applied associate-/l*0.2

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

9. Final simplification0.2

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

Runtime

Time bar (total: 26.3s)Debug logProfile

herbie shell --seed 2018285 +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))