Average Error: 0.1 → 0.1

Time: 1.8m

Precision: 64

Ground Truth: 128

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

⬇

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

Error

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

Derivation

Initial program 0.1
\[\left(\frac{m \cdot \left(1 - m\right)}{v} - 1\right) \cdot \left(1 - m\right)\]
Applied taylor 0.1
\[\leadsto \left(\frac{m - {m}^2}{v} - 1\right) \cdot \left(1 - m\right)\]
Taylor expanded around 0 0.1

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

Runtime

Please include this information when filing a bug report:

herbie --seed '#(2151212895 762856151 3271092982 78694672 3135315502 414136599)'
(FPCore (m v)
  :name "b parameter of renormalized beta distribution"
  :pre (and (< 0 m) (< 0 v) (< v 0.25))
  (* (- (/ (* m (- 1 m)) v) 1) (- 1 m)))