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Derivation

1. Initial program 0.1

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

3. Applied sub-neg0.1

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

4. Applied distribute-rgt-in0.1

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

5. Simplified0.1

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

7. Applied associate-/r/0.1

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

8. Final simplification0.1

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

Runtime

Time bar (total: 31.8s)Debug logProfile

herbie shell --seed 2018274 
(FPCore (m v)
  :name "b parameter of renormalized beta distribution"
  :pre (and (< 0 m) (< 0 v) (< v 0.25))
  (* (- (/ (* m (- 1 m)) v) 1) (- 1 m)))