Average Error: 0.2 → 0.2
Time: 19.4s
Precision: 64
\[0 \lt m \land 0 \lt v \land v \lt 0.25\]
\[\left(\frac{m \cdot \left(1 - m\right)}{v} - 1\right) \cdot m\]
↓
\[\frac{m}{\frac{v}{m}} - \left(\frac{m}{\frac{\frac{v}{m}}{m}} + m\right)\]
\left(\frac{m \cdot \left(1 - m\right)}{v} - 1\right) \cdot m
↓
\frac{m}{\frac{v}{m}} - \left(\frac{m}{\frac{\frac{v}{m}}{m}} + m\right)
double f(double m, double v) {
        double r992751 = m;
        double r992752 = 1.0;
        double r992753 = r992752 - r992751;
        double r992754 = r992751 * r992753;
        double r992755 = v;
        double r992756 = r992754 / r992755;
        double r992757 = r992756 - r992752;
        double r992758 = r992757 * r992751;
        return r992758;
}
↓
double f(double m, double v) {
        double r992759 = m;
        double r992760 = v;
        double r992761 = r992760 / r992759;
        double r992762 = r992759 / r992761;
        double r992763 = r992761 / r992759;
        double r992764 = r992759 / r992763;
        double r992765 = r992764 + r992759;
        double r992766 = r992762 - r992765;
        return r992766;
}

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 6.7

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

  3. Simplified0.2

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

  5. Applied associate-/r*0.2

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

  6. Final simplification0.2

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

Reproduce

herbie shell --seed 2019162 
(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))