Error

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 associate-/l*0.2

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

5. Applied div-inv0.2

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

6. Applied associate-/r*0.2

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

8. Applied flip--0.2

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

9. Applied associate-/r/0.2

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

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

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

11. Applied times-frac0.2

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

12. Simplified0.2

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

13. Simplified0.2

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

14. Final simplification0.2

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

Runtime

Time bar (total: 23.2s)Debug logProfile

herbie shell --seed 2018340 +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))