Average Error: 0.2 → 0.2
Time: 33.5s
Precision: 64
\[0 \lt m \land 0 \lt v \land v \lt 0.25\]
\[\left(\frac{m \cdot \left(1 - m\right)}{v} - 1\right) \cdot m\]
↓
\[\left(m \cdot \frac{m}{v} - m\right) - \frac{\left(m \cdot m\right) \cdot m}{v}\]
\left(\frac{m \cdot \left(1 - m\right)}{v} - 1\right) \cdot m
↓
\left(m \cdot \frac{m}{v} - m\right) - \frac{\left(m \cdot m\right) \cdot m}{v}
double f(double m, double v) {
        double r643607 = m;
        double r643608 = 1.0;
        double r643609 = r643608 - r643607;
        double r643610 = r643607 * r643609;
        double r643611 = v;
        double r643612 = r643610 / r643611;
        double r643613 = r643612 - r643608;
        double r643614 = r643613 * r643607;
        return r643614;
}
↓
double f(double m, double v) {
        double r643615 = m;
        double r643616 = v;
        double r643617 = r643615 / r643616;
        double r643618 = r643615 * r643617;
        double r643619 = r643618 - r643615;
        double r643620 = r643615 * r643615;
        double r643621 = r643620 * r643615;
        double r643622 = r643621 / r643616;
        double r643623 = r643619 - r643622;
        return r643623;
}

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 inf 6.9

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

  3. Simplified0.2

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

  4. Final simplification0.2

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

Reproduce

herbie shell --seed 2019149 +o rules:numerics
(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))