Average Error: 0.2 → 0.2
Time: 14.9s
Precision: 64
\[0.0 \lt m \land 0.0 \lt v \land v \lt 0.25\]
\[\left(\frac{m \cdot \left(1 - m\right)}{v} - 1\right) \cdot m\]
↓
\[1 \cdot \left(\frac{m}{\frac{v}{m}} - m\right) - \frac{{m}^{3}}{v}\]
\left(\frac{m \cdot \left(1 - m\right)}{v} - 1\right) \cdot m
↓
1 \cdot \left(\frac{m}{\frac{v}{m}} - m\right) - \frac{{m}^{3}}{v}
double f(double m, double v) {
        double r11718 = m;
        double r11719 = 1.0;
        double r11720 = r11719 - r11718;
        double r11721 = r11718 * r11720;
        double r11722 = v;
        double r11723 = r11721 / r11722;
        double r11724 = r11723 - r11719;
        double r11725 = r11724 * r11718;
        return r11725;
}
↓
double f(double m, double v) {
        double r11726 = 1.0;
        double r11727 = m;
        double r11728 = v;
        double r11729 = r11728 / r11727;
        double r11730 = r11727 / r11729;
        double r11731 = r11730 - r11727;
        double r11732 = r11726 * r11731;
        double r11733 = 3.0;
        double r11734 = pow(r11727, r11733);
        double r11735 = r11734 / r11728;
        double r11736 = r11732 - r11735;
        return r11736;
}

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. Using strategy rm

  3. Applied clear-num0.2

    \[\leadsto \left(\color{blue}{\frac{1}{\frac{v}{m \cdot \left(1 - m\right)}}} - 1\right) \cdot m\]
  4. Using strategy rm

  5. Applied associate-/r*0.2

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

  6. Taylor expanded around 0 6.7

    \[\leadsto \color{blue}{1 \cdot \frac{{m}^{2}}{v} - \left(1 \cdot m + \frac{{m}^{3}}{v}\right)}\]

  7. Simplified0.2

    \[\leadsto \color{blue}{1 \cdot \left(\frac{m}{\frac{v}{m}} - m\right) - \frac{{m}^{3}}{v}}\]

  8. Final simplification0.2

    \[\leadsto 1 \cdot \left(\frac{m}{\frac{v}{m}} - m\right) - \frac{{m}^{3}}{v}\]

Reproduce

herbie shell --seed 2019350 
(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))