Average Error: 0.1 → 0.1
Time: 15.5s
Precision: 64
\[0.0 \lt m \land 0.0 \lt v \land v \lt 0.25\]
\[\left(\frac{m \cdot \left(1 - m\right)}{v} - 1\right) \cdot \left(1 - m\right)\]
↓
\[\left(1 - m\right) \cdot \left(\frac{1 \cdot m + \left(-m\right) \cdot m}{v} - 1\right)\]
\left(\frac{m \cdot \left(1 - m\right)}{v} - 1\right) \cdot \left(1 - m\right)
↓
\left(1 - m\right) \cdot \left(\frac{1 \cdot m + \left(-m\right) \cdot m}{v} - 1\right)
double f(double m, double v) {
        double r1084860 = m;
        double r1084861 = 1.0;
        double r1084862 = r1084861 - r1084860;
        double r1084863 = r1084860 * r1084862;
        double r1084864 = v;
        double r1084865 = r1084863 / r1084864;
        double r1084866 = r1084865 - r1084861;
        double r1084867 = r1084866 * r1084862;
        return r1084867;
}
↓
double f(double m, double v) {
        double r1084868 = 1.0;
        double r1084869 = m;
        double r1084870 = r1084868 - r1084869;
        double r1084871 = r1084868 * r1084869;
        double r1084872 = -r1084869;
        double r1084873 = r1084872 * r1084869;
        double r1084874 = r1084871 + r1084873;
        double r1084875 = v;
        double r1084876 = r1084874 / r1084875;
        double r1084877 = r1084876 - r1084868;
        double r1084878 = r1084870 * r1084877;
        return r1084878;
}

Error

Bits error versus m

Bits error versus v

Try it out

Your Program's Arguments

Results

Enter valid numbers for all inputs

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

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

  4. Applied distribute-rgt-in0.1

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

  5. Final simplification0.1

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

Reproduce

herbie shell --seed 2019172 
(FPCore (m v)
  :name "b parameter of renormalized beta distribution"
  :pre (and (< 0.0 m) (< 0.0 v) (< v 0.25))
  (* (- (/ (* m (- 1.0 m)) v) 1.0) (- 1.0 m)))