Average Error: 0.2 → 0.2
Time: 1.1m
Precision: 64
Internal Precision: 384
\[\left(\frac{m \cdot \left(1 - m\right)}{v} - 1\right) \cdot m\]
↓
\[\left(m - m \cdot m\right) \cdot \frac{m}{v} - m\]

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. Taylor expanded around 0 7.1

    \[\leadsto \color{blue}{\frac{{m}^{2}}{v} - \left(\frac{{m}^{3}}{v} + m\right)}\]

  3. Applied simplify0.2

    \[\leadsto \color{blue}{\left(m - m \cdot m\right) \cdot \frac{m}{v} - m}\]
  4. Removed slow pow expressions.

Runtime

Time bar (total: 1.1m)Debug logProfile

herbie shell --seed '#(1063154770 1824007522 645063331 41291047 494775821 1237684644)' 
(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))