Average Error: 0.2 → 0.2
Time: 20.8s
Precision: 64
\[0 \lt m \land 0 \lt v \land v \lt 0.25\]
\[\left(\frac{m \cdot \left(1 - m\right)}{v} - 1\right) \cdot m\]
↓
\[\frac{m}{\frac{v}{m}} - \left(m + \frac{m \cdot m}{v} \cdot m\right)\]
\left(\frac{m \cdot \left(1 - m\right)}{v} - 1\right) \cdot m
↓
\frac{m}{\frac{v}{m}} - \left(m + \frac{m \cdot m}{v} \cdot m\right)
double f(double m, double v) {
        double r1005777 = m;
        double r1005778 = 1.0;
        double r1005779 = r1005778 - r1005777;
        double r1005780 = r1005777 * r1005779;
        double r1005781 = v;
        double r1005782 = r1005780 / r1005781;
        double r1005783 = r1005782 - r1005778;
        double r1005784 = r1005783 * r1005777;
        return r1005784;
}
↓
double f(double m, double v) {
        double r1005785 = m;
        double r1005786 = v;
        double r1005787 = r1005786 / r1005785;
        double r1005788 = r1005785 / r1005787;
        double r1005789 = r1005785 * r1005785;
        double r1005790 = r1005789 / r1005786;
        double r1005791 = r1005790 * r1005785;
        double r1005792 = r1005785 + r1005791;
        double r1005793 = r1005788 - r1005792;
        return r1005793;
}

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 6.6

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

  3. Simplified0.2

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

  5. Applied clear-num0.2

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

  6. Applied associate-/r/0.2

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

  7. Simplified0.2

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

  8. Final simplification0.2

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

Reproduce

herbie shell --seed 2019158 
(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))