Average Error: 0.2 → 0.2
Time: 10.1s
Precision: 64
\[0.0 \lt m \land 0.0 \lt v \land v \lt 0.25\]
\[\left(\frac{m \cdot \left(1 - m\right)}{v} - 1\right) \cdot m\]
↓
\[\left(1 \cdot \frac{m}{v} - \left(1 + \frac{{m}^{2}}{v}\right)\right) \cdot m\]
\left(\frac{m \cdot \left(1 - m\right)}{v} - 1\right) \cdot m
↓
\left(1 \cdot \frac{m}{v} - \left(1 + \frac{{m}^{2}}{v}\right)\right) \cdot m
double f(double m, double v) {
        double r11943 = m;
        double r11944 = 1.0;
        double r11945 = r11944 - r11943;
        double r11946 = r11943 * r11945;
        double r11947 = v;
        double r11948 = r11946 / r11947;
        double r11949 = r11948 - r11944;
        double r11950 = r11949 * r11943;
        return r11950;
}
↓
double f(double m, double v) {
        double r11951 = 1.0;
        double r11952 = m;
        double r11953 = v;
        double r11954 = r11952 / r11953;
        double r11955 = r11951 * r11954;
        double r11956 = 2.0;
        double r11957 = pow(r11952, r11956);
        double r11958 = r11957 / r11953;
        double r11959 = r11951 + r11958;
        double r11960 = r11955 - r11959;
        double r11961 = r11960 * r11952;
        return r11961;
}

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

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

  3. Final simplification0.2

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

Reproduce

herbie shell --seed 2020047 
(FPCore (m v)
  :name "a parameter of renormalized beta distribution"
  :precision binary64
  :pre (and (< 0.0 m) (< 0.0 v) (< v 0.25))
  (* (- (/ (* m (- 1 m)) v) 1) m))