Error

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 associate-/l*0.1

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

5. Applied flip--0.1

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

6. Applied associate-/r/0.1

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

7. Applied associate-/r*0.1

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

8. Final simplification0.1

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

Reproduce

herbie shell --seed 2019050 +o rules:numerics
(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)))