Error

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

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

4. Applied sub-neg0.1

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

5. Applied distribute-rgt-in0.1

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

6. Simplified0.1

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

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

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

9. Applied distribute-lft-out0.1

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

10. Simplified0.1

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

11. Final simplification0.1

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

Runtime

Time bar (total: 28.1s)Debug logProfile

herbie shell --seed 2018295 +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)))