Average Error: 0.1 → 0.1
Time: 1.9m
Precision: 64
Internal Precision: 576
\[\left(\frac{m \cdot \left(1 - m\right)}{v} - 1\right) \cdot \left(1 - m\right)\]
↓
\[(\left(\frac{m}{v}\right) \cdot \left(1 - m\right) + \left(-1\right))_* + (\left(-\frac{m}{v}\right) \cdot \left(m - m \cdot m\right) + m)_*\]

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-rgt-in0.1

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

  5. Applied simplify0.1

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

  6. Applied simplify0.1

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

Runtime

Time bar (total: 1.9m)Debug logProfile

herbie shell --seed 2018206 +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)))