Average Error: 0.2 → 0.2
Time: 1.1m
Precision: 64
Internal Precision: 576
\[\left(\frac{m \cdot \left(1 - m\right)}{v} - 1\right) \cdot m\]
↓
\[\frac{m - m \cdot m}{\frac{v}{m}} - m\]

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. 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. Taylor expanded around 0 0.2

    \[\leadsto \left(\color{blue}{\left(m - {m}^{2}\right)} \cdot \frac{1}{v} - 1\right) \cdot m\]

  5. Applied simplify0.2

    \[\leadsto \color{blue}{\frac{m - m \cdot m}{\frac{v}{m}} - m}\]

Runtime

Time bar (total: 1.1m)Debug logProfile

herbie shell --seed '#(1071948828 1180510430 2986424009 997076509 406109801 420189285)' 
(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))