Average Error: 0.1 → 0.1
Time: 19.6s
Precision: 64
\[0 \lt m \land 0 \lt v \land v \lt 0.25\]
\[\left(\frac{m \cdot \left(1 - m\right)}{v} - 1\right) \cdot \left(1 - m\right)\]
↓
\[\left(\frac{m \cdot \left(1 - m\right)}{v} - 1\right) + \left(\frac{m}{\frac{v}{m \cdot m}} - \left(m \cdot \frac{m}{v} - m\right)\right)\]
\left(\frac{m \cdot \left(1 - m\right)}{v} - 1\right) \cdot \left(1 - m\right)
↓
\left(\frac{m \cdot \left(1 - m\right)}{v} - 1\right) + \left(\frac{m}{\frac{v}{m \cdot m}} - \left(m \cdot \frac{m}{v} - m\right)\right)
double f(double m, double v) {
        double r1010717 = m;
        double r1010718 = 1.0;
        double r1010719 = r1010718 - r1010717;
        double r1010720 = r1010717 * r1010719;
        double r1010721 = v;
        double r1010722 = r1010720 / r1010721;
        double r1010723 = r1010722 - r1010718;
        double r1010724 = r1010723 * r1010719;
        return r1010724;
}
↓
double f(double m, double v) {
        double r1010725 = m;
        double r1010726 = 1.0;
        double r1010727 = r1010726 - r1010725;
        double r1010728 = r1010725 * r1010727;
        double r1010729 = v;
        double r1010730 = r1010728 / r1010729;
        double r1010731 = r1010730 - r1010726;
        double r1010732 = r1010725 * r1010725;
        double r1010733 = r1010729 / r1010732;
        double r1010734 = r1010725 / r1010733;
        double r1010735 = r1010725 / r1010729;
        double r1010736 = r1010725 * r1010735;
        double r1010737 = r1010736 - r1010725;
        double r1010738 = r1010734 - r1010737;
        double r1010739 = r1010731 + r1010738;
        return r1010739;
}

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-rgt-in0.1

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

  5. Simplified0.1

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

  7. Applied add-sqr-sqrt0.1

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

  8. Applied distribute-rgt-neg-in0.1

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

  9. Applied associate-*l*0.1

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

  10. Taylor expanded around 0 0.1

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

  11. Simplified0.1

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

  12. Final simplification0.1

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

Reproduce

herbie shell --seed 2019133 
(FPCore (m v)
  :name "b parameter of renormalized beta distribution"
  :pre (and (< 0 m) (< 0 v) (< v 0.25))
  (* (- (/ (* m (- 1 m)) v) 1) (- 1 m)))