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 div-inv0.1

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

6. Applied associate-/r*0.1

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

8. Applied flip3--0.1

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

9. Applied associate-/r/0.1

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

10. Simplified0.1

    \[\leadsto \left(\frac{\frac{m}{v}}{\frac{1}{{1}^{3} - {m}^{3}} \cdot \color{blue}{(m \cdot \left(1 + m\right) + 1)_*}} - 1\right) \cdot \left(1 - m\right)\]
11. Using strategy rm

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

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

13. Applied times-frac0.1

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

14. Simplified0.1

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

15. Simplified0.1

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

16. Final simplification0.1

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

Runtime

Time bar (total: 49.5s)Debug logProfile

herbie shell --seed 2018340 +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)))