Average Error: 0.2 → 0.3
Time: 21.3s
Precision: 64
\[0.0 \lt m \land 0.0 \lt v \land v \lt 0.25\]
\[\left(\frac{m \cdot \left(1 - m\right)}{v} - 1\right) \cdot m\]
↓
\[\left(1 \cdot \left(\frac{1}{v} \cdot \left(m - {m}^{2}\right)\right) - 1\right) \cdot m\]
\left(\frac{m \cdot \left(1 - m\right)}{v} - 1\right) \cdot m
↓
\left(1 \cdot \left(\frac{1}{v} \cdot \left(m - {m}^{2}\right)\right) - 1\right) \cdot m
double f(double m, double v) {
        double r19711 = m;
        double r19712 = 1.0;
        double r19713 = r19712 - r19711;
        double r19714 = r19711 * r19713;
        double r19715 = v;
        double r19716 = r19714 / r19715;
        double r19717 = r19716 - r19712;
        double r19718 = r19717 * r19711;
        return r19718;
}
↓
double f(double m, double v) {
        double r19719 = 1.0;
        double r19720 = 1.0;
        double r19721 = v;
        double r19722 = r19720 / r19721;
        double r19723 = m;
        double r19724 = 2.0;
        double r19725 = pow(r19723, r19724);
        double r19726 = r19723 - r19725;
        double r19727 = r19722 * r19726;
        double r19728 = r19719 * r19727;
        double r19729 = r19728 - r19719;
        double r19730 = r19729 * r19723;
        return r19730;
}

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 flip--0.2

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

  4. Applied associate-*r/0.2

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

  5. Applied associate-/l/0.2

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

  6. Taylor expanded around 0 0.2

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

  7. Simplified0.2

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

  9. Applied div-inv0.2

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

  10. Applied div-inv0.3

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

  11. Applied distribute-rgt-out--0.3

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

  12. Final simplification0.3

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

Reproduce

herbie shell --seed 2019323 
(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))