Average Error: 0.2 → 0.2
Time: 12.8s
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 r12655 = m;
        double r12656 = 1.0;
        double r12657 = r12656 - r12655;
        double r12658 = r12655 * r12657;
        double r12659 = v;
        double r12660 = r12658 / r12659;
        double r12661 = r12660 - r12656;
        double r12662 = r12661 * r12655;
        return r12662;
}
↓
double f(double m, double v) {
        double r12663 = 1.0;
        double r12664 = m;
        double r12665 = v;
        double r12666 = r12664 / r12665;
        double r12667 = r12663 * r12666;
        double r12668 = 2.0;
        double r12669 = pow(r12664, r12668);
        double r12670 = r12669 / r12665;
        double r12671 = r12663 + r12670;
        double r12672 = r12667 - r12671;
        double r12673 = r12672 * r12664;
        return r12673;
}

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 +o rules:numerics
(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))