Average Error: 0.1 → 0.1
Time: 21.5s
Precision: 64
Internal Precision: 128
\[\left(\frac{m \cdot \left(1 - m\right)}{v} - 1\right) \cdot \left(1 - m\right)\]
↓
\[(\left(\frac{m \cdot \left(1 - m\right)}{v}\right) \cdot \left(-m\right) + m)_* + \left(\frac{m \cdot \left(1 - m\right)}{v} - 1\right)\]

Error

Bits error versus m

Bits error versus v

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. Using strategy rm

  7. Applied associate-*r/0.1

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

  8. Final simplification0.1

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

Reproduce

herbie shell --seed 2019030 +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)))