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 sub-neg0.1

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

4. Applied distribute-lft-in0.1

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

5. Simplified0.1

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

6. Taylor expanded around 0 0.1

   \[\leadsto \left(\frac{m \cdot \left(1 - m\right)}{v} - 1\right) \cdot 1 + \color{blue}{\left(\left(m + \frac{{m}^{3}}{v}\right) - \frac{{m}^{2}}{v}\right)}\]

7. Simplified0.1

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

8. Final simplification0.1

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

Runtime

Time bar (total: 39.9s)Debug logProfile

herbie shell --seed 2018251 +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)))