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Derivation

1. Initial program 0.2

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

3. Applied flip3--0.2

   \[\leadsto \left(\frac{m \cdot \color{blue}{\frac{{1}^{3} - {m}^{3}}{1 \cdot 1 + \left(m \cdot m + 1 \cdot m\right)}}}{v} - 1\right) \cdot m\]

4. Applied associate-*r/0.7

   \[\leadsto \left(\frac{\color{blue}{\frac{m \cdot \left({1}^{3} - {m}^{3}\right)}{1 \cdot 1 + \left(m \cdot m + 1 \cdot m\right)}}}{v} - 1\right) \cdot m\]

5. Applied associate-/l/0.7

   \[\leadsto \left(\color{blue}{\frac{m \cdot \left({1}^{3} - {m}^{3}\right)}{v \cdot \left(1 \cdot 1 + \left(m \cdot m + 1 \cdot m\right)\right)}} - 1\right) \cdot m\]

6. Simplified0.7

   \[\leadsto \left(\frac{\color{blue}{m - {m}^{4}}}{v \cdot \left(1 \cdot 1 + \left(m \cdot m + 1 \cdot m\right)\right)} - 1\right) \cdot m\]

7. Final simplification0.7

   \[\leadsto \left(\frac{m - {m}^{4}}{v \cdot \left(1 + \left(m \cdot m + m\right)\right)} - 1\right) \cdot m\]

Runtime

Time bar (total: 22.0s)Debug logProfile

herbie shell --seed 2018297 +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))