Average Error: 0.2 → 0.2
Time: 30.9s
Precision: 64
Internal Precision: 128
\[\left(\frac{m \cdot \left(1 - m\right)}{v} - 1\right) \cdot m\]
↓
\[(\left(1 - m\right) \cdot \left(\frac{m}{v}\right) + -1)_* \cdot m\]

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. Initial simplification0.2

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

  4. Applied *-commutative0.2

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

  5. Final simplification0.2

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

Runtime

Time bar (total: 30.9s)Debug logProfile

herbie shell --seed 2018346 +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))