Average Error: 0.2 → 0.2
Time: 11.0s
Precision: 64
\[0 \lt m \land 0 \lt v \land v \lt 0.25\]
\[\left(\frac{m \cdot \left(1 - m\right)}{v} - 1\right) \cdot m\]
↓
\[\left(\left(\frac{m}{v} - \frac{m \cdot m}{v}\right) - 1\right) \cdot m\]
\left(\frac{m \cdot \left(1 - m\right)}{v} - 1\right) \cdot m
↓
\left(\left(\frac{m}{v} - \frac{m \cdot m}{v}\right) - 1\right) \cdot m
double f(double m, double v) {
        double r497982 = m;
        double r497983 = 1.0;
        double r497984 = r497983 - r497982;
        double r497985 = r497982 * r497984;
        double r497986 = v;
        double r497987 = r497985 / r497986;
        double r497988 = r497987 - r497983;
        double r497989 = r497988 * r497982;
        return r497989;
}
↓
double f(double m, double v) {
        double r497990 = m;
        double r497991 = v;
        double r497992 = r497990 / r497991;
        double r497993 = r497990 * r497990;
        double r497994 = r497993 / r497991;
        double r497995 = r497992 - r497994;
        double r497996 = 1.0;
        double r497997 = r497995 - r497996;
        double r497998 = r497997 * r497990;
        return r497998;
}

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

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

  3. Simplified0.2

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

  4. Final simplification0.2

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

Reproduce

herbie shell --seed 2019156 
(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))