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

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 0.2

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

  3. Taylor expanded around -inf 62.7

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

  4. Applied simplify0.2

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

Runtime

Time bar (total: 1.1m)Debug logProfile

herbie shell --seed '#(1072107073 2127697367 3936270018 2300570620 2134894798 4023771849)' +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))