Average Error: 0.2 → 0.2
Time: 5.8s
Precision: 64
\[0.0 \lt m \land 0.0 \lt v \land v \lt 0.25\]
\[\left(\frac{m \cdot \left(1 - m\right)}{v} - 1\right) \cdot m\]
↓
\[\left(\left(1 \cdot \frac{m}{v} - \frac{{m}^{2}}{v}\right) - 1\right) \cdot m\]
\left(\frac{m \cdot \left(1 - m\right)}{v} - 1\right) \cdot m
↓
\left(\left(1 \cdot \frac{m}{v} - \frac{{m}^{2}}{v}\right) - 1\right) \cdot m
double f(double m, double v) {
        double r14680 = m;
        double r14681 = 1.0;
        double r14682 = r14681 - r14680;
        double r14683 = r14680 * r14682;
        double r14684 = v;
        double r14685 = r14683 / r14684;
        double r14686 = r14685 - r14681;
        double r14687 = r14686 * r14680;
        return r14687;
}
↓
double f(double m, double v) {
        double r14688 = 1.0;
        double r14689 = m;
        double r14690 = v;
        double r14691 = r14689 / r14690;
        double r14692 = r14688 * r14691;
        double r14693 = 2.0;
        double r14694 = pow(r14689, r14693);
        double r14695 = r14694 / r14690;
        double r14696 = r14692 - r14695;
        double r14697 = r14696 - r14688;
        double r14698 = r14697 * r14689;
        return r14698;
}

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 associate-/l*0.2

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

  4. Taylor expanded around 0 0.2

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

  5. Final simplification0.2

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

Reproduce

herbie shell --seed 2020025 +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))