Error

Derivation

1. Initial program 0.1

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

2. Taylor expanded around -inf 0.1

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

3. Simplified0.1

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

5. Applied sub-neg0.1

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

6. Applied distribute-lft-in0.1

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

7. Simplified0.1

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

8. Final simplification0.1

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

Reproduce

herbie shell --seed 2019007 +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)))

Details

Time bar (total: 37.7s)Debug log