Average Error: 0.2 → 0.2
Time: 1.2m
Precision: 64
Internal Precision: 320
\[\left(\frac{m \cdot \left(1 - m\right)}{v} - 1\right) \cdot m\]
↓
\[1 \cdot (\left(\frac{m}{v}\right) \cdot \left(m - m \cdot m\right) + \left(-m\right))_*\]

Error

Bits error versus m

Bits error versus v

Derivation

  1. Initial program 0.2

    \[\left(\frac{m \cdot \left(1 - m\right)}{v} - 1\right) \cdot m\]
  2. Using strategy rm

  3. Applied div-inv0.2

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

  5. Applied *-un-lft-identity0.2

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

  6. Applied associate-*l*0.2

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

  7. Applied simplify0.2

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

Runtime

Time bar (total: 1.2m)Debug logProfile

herbie shell --seed '#(1071119240 1686926585 3481876196 78132896 2080707795 3185793749)' +o rules:numerics
(FPCore (m v)
  :name "a parameter of renormalized beta distribution"
  :pre (and (< 0 m) (< 0 v) (< v 0.25))
  (* (- (/ (* m (- 1 m)) v) 1) m))