Average Error: 0.2 → 0.2
Time: 31.6s
Precision: 64
\[0.0 \lt m \land 0.0 \lt v \land v \lt 0.25\]
\[\left(\frac{m \cdot \left(1 - m\right)}{v} - 1\right) \cdot m\]
↓
\[\left(\frac{m \cdot 1 - m \cdot m}{v} - 1\right) \cdot m\]
\left(\frac{m \cdot \left(1 - m\right)}{v} - 1\right) \cdot m
↓
\left(\frac{m \cdot 1 - m \cdot m}{v} - 1\right) \cdot m
double f(double m, double v) {
        double r1352971 = m;
        double r1352972 = 1.0;
        double r1352973 = r1352972 - r1352971;
        double r1352974 = r1352971 * r1352973;
        double r1352975 = v;
        double r1352976 = r1352974 / r1352975;
        double r1352977 = r1352976 - r1352972;
        double r1352978 = r1352977 * r1352971;
        return r1352978;
}
↓
double f(double m, double v) {
        double r1352979 = m;
        double r1352980 = 1.0;
        double r1352981 = r1352979 * r1352980;
        double r1352982 = r1352979 * r1352979;
        double r1352983 = r1352981 - r1352982;
        double r1352984 = v;
        double r1352985 = r1352983 / r1352984;
        double r1352986 = r1352985 - r1352980;
        double r1352987 = r1352986 * r1352979;
        return r1352987;
}

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 0.2

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

  2. Taylor expanded around 0 0.2

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

  3. Simplified0.2

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

  4. Final simplification0.2

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

Reproduce

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