Average Error: 0.1 → 0.1
Time: 1.6m
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 r6498858 = m;
        double r6498859 = 1.0;
        double r6498860 = r6498859 - r6498858;
        double r6498861 = r6498858 * r6498860;
        double r6498862 = v;
        double r6498863 = r6498861 / r6498862;
        double r6498864 = r6498863 - r6498859;
        double r6498865 = r6498864 * r6498860;
        return r6498865;
}
↓
double f(double m, double v) {
        double r6498866 = m;
        double r6498867 = 1.0;
        double r6498868 = r6498867 - r6498866;
        double r6498869 = r6498866 * r6498868;
        double r6498870 = v;
        double r6498871 = r6498869 / r6498870;
        double r6498872 = r6498871 - r6498867;
        double r6498873 = -r6498866;
        double r6498874 = r6498872 * r6498873;
        double r6498875 = r6498874 + r6498872;
        return r6498875;
}


\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 2019102 
(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)))