Average Error: 0.1 → 0.1
Time: 44.3s
Precision: 64
\[\left(\frac{m \cdot \left(1 - m\right)}{v} - 1\right) \cdot \left(1 - m\right)\]
↓
\[\left(\frac{m \cdot \left(1 - m\right)}{v} - 1\right) \cdot \left(-m\right) + \left(\frac{m \cdot \left(1 - m\right)}{v} - 1\right)\]
double f(double m, double v) {
        double r2833577 = m;
        double r2833578 = 1.0;
        double r2833579 = r2833578 - r2833577;
        double r2833580 = r2833577 * r2833579;
        double r2833581 = v;
        double r2833582 = r2833580 / r2833581;
        double r2833583 = r2833582 - r2833578;
        double r2833584 = r2833583 * r2833579;
        return r2833584;
}
↓
double f(double m, double v) {
        double r2833585 = m;
        double r2833586 = 1.0;
        double r2833587 = r2833586 - r2833585;
        double r2833588 = r2833585 * r2833587;
        double r2833589 = v;
        double r2833590 = r2833588 / r2833589;
        double r2833591 = r2833590 - r2833586;
        double r2833592 = -r2833585;
        double r2833593 = r2833591 * r2833592;
        double r2833594 = r2833593 + r2833591;
        return r2833594;
}


\left(\frac{m \cdot \left(1 - m\right)}{v} - 1\right) \cdot \left(1 - m\right)
↓
\left(\frac{m \cdot \left(1 - m\right)}{v} - 1\right) \cdot \left(-m\right) + \left(\frac{m \cdot \left(1 - m\right)}{v} - 1\right)

Error

Bits error versus m

Bits error versus v

Derivation

  1. Initial program 0.1

    \[\left(\frac{m \cdot \left(1 - m\right)}{v} - 1\right) \cdot \left(1 - m\right)\]
  2. Using strategy rm

  3. Applied sub-neg0.1

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

  4. Applied distribute-lft-in0.1

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

  5. Final simplification0.1

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

Reproduce

herbie shell --seed 2019101 
(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)))