Average Error: 0.2 → 0.2

Time: 1.8m

Precision: 64

Ground Truth: 128

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

⬇

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

Error

The X axis may use a short exponential scale — Bits error versus m

The X axis may use a short exponential scale — Bits error versus m

The X axis may use a short exponential scale — Bits error versus v

The X axis may use a short exponential scale — Bits error versus v

Derivation

Initial program 0.2
\[\left(\frac{m \cdot \left(1 - m\right)}{v} - 1\right) \cdot m\]
Applied taylor 0.2
\[\leadsto \left(\left(\frac{m}{v} - \frac{{m}^2}{v}\right) - 1\right) \cdot m\]
Taylor expanded around 0 0.2

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

Runtime

Please include this information when filing a bug report:

herbie --seed '#(3426616366 2981820100 1847864186 1782597920 843738639 3677053776)'
(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))