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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. Initial simplification0.1

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

4. Applied sub-neg0.1

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

5. Applied distribute-rgt-in0.1

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

6. Simplified0.1

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

8. Applied div-inv0.1

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

9. Applied *-un-lft-identity0.1

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

10. Applied times-frac0.1

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

11. Simplified0.1

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

12. Final simplification0.1

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

Runtime

Time bar (total: 1.2m)Debug logProfile

herbie shell --seed 2018242 
(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)))