Average Error: 0.1 → 0.1
Time: 9.9s
Precision: 64
\[0.0 \lt m \land 0.0 \lt v \land v \lt 0.25\]
\[\left(\frac{m \cdot \left(1 - m\right)}{v} - 1\right) \cdot \left(1 - m\right)\]
↓
\[1 \cdot \left(\frac{m \cdot \left(1 - m\right)}{v} - 1\right) + \left(\left(1 \cdot m + \frac{{m}^{3}}{v}\right) - 1 \cdot \frac{{m}^{2}}{v}\right)\]
\left(\frac{m \cdot \left(1 - m\right)}{v} - 1\right) \cdot \left(1 - m\right)
↓
1 \cdot \left(\frac{m \cdot \left(1 - m\right)}{v} - 1\right) + \left(\left(1 \cdot m + \frac{{m}^{3}}{v}\right) - 1 \cdot \frac{{m}^{2}}{v}\right)
double f(double m, double v) {
        double r11762 = m;
        double r11763 = 1.0;
        double r11764 = r11763 - r11762;
        double r11765 = r11762 * r11764;
        double r11766 = v;
        double r11767 = r11765 / r11766;
        double r11768 = r11767 - r11763;
        double r11769 = r11768 * r11764;
        return r11769;
}
↓
double f(double m, double v) {
        double r11770 = 1.0;
        double r11771 = m;
        double r11772 = r11770 - r11771;
        double r11773 = r11771 * r11772;
        double r11774 = v;
        double r11775 = r11773 / r11774;
        double r11776 = r11775 - r11770;
        double r11777 = r11770 * r11776;
        double r11778 = r11770 * r11771;
        double r11779 = 3.0;
        double r11780 = pow(r11771, r11779);
        double r11781 = r11780 / r11774;
        double r11782 = r11778 + r11781;
        double r11783 = 2.0;
        double r11784 = pow(r11771, r11783);
        double r11785 = r11784 / r11774;
        double r11786 = r11770 * r11785;
        double r11787 = r11782 - r11786;
        double r11788 = r11777 + r11787;
        return r11788;
}

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 0.1

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

  3. Applied sub-neg0.1

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

  4. Applied distribute-lft-in0.1

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

  5. Simplified0.1

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

  6. Taylor expanded around 0 0.1

    \[\leadsto 1 \cdot \left(\frac{m \cdot \left(1 - m\right)}{v} - 1\right) + \color{blue}{\left(\left(1 \cdot m + \frac{{m}^{3}}{v}\right) - 1 \cdot \frac{{m}^{2}}{v}\right)}\]

  7. Final simplification0.1

    \[\leadsto 1 \cdot \left(\frac{m \cdot \left(1 - m\right)}{v} - 1\right) + \left(\left(1 \cdot m + \frac{{m}^{3}}{v}\right) - 1 \cdot \frac{{m}^{2}}{v}\right)\]

Reproduce

herbie shell --seed 2020042 
(FPCore (m v)
  :name "b parameter of renormalized beta distribution"
  :precision binary64
  :pre (and (< 0.0 m) (< 0.0 v) (< v 0.25))
  (* (- (/ (* m (- 1 m)) v) 1) (- 1 m)))