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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 simplification0.2

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

4. Applied div-inv0.2

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

5. Applied *-un-lft-identity0.2

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

6. Applied times-frac0.2

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

7. Simplified0.1

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

8. Simplified0.1

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

9. Final simplification0.1

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

Runtime

Time bar (total: 1.2m)Debug logProfile

herbie shell --seed 2018263 
(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)))