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

↓

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

Error

The X axis uses an exponential scale — Bits error versus `m`

Derivation

Initial program 0.2
\[\left(\frac{m \cdot \left(1 - m\right)}{v} - 1\right) \cdot m\]
Taylor expanded around 0 0.2
\[\leadsto \left(\color{blue}{\left(\frac{m}{v} - \frac{{m}^{2}}{v}\right)} - 1\right) \cdot m\]
Taylor expanded around -inf 62.7
\[\leadsto \color{blue}{\frac{{m}^{2}}{v} - \left(\frac{e^{2 \cdot \left(\log -1 - \log \left(\frac{-1}{m}\right)\right)} \cdot m}{v} + m\right)}\]
Applied simplify0.2
\[\leadsto \color{blue}{(\left(\frac{m}{v}\right) \cdot m + \left(-m\right))_* - \frac{m}{v} \cdot \left(m \cdot m\right)}\]

Runtime

herbie shell --seed '#(1070386091 2509006183 1430610344 1025408621 36622005 1425925650)' +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))