Average Error: 0.2 → 0.2
Time: 46.4s
Precision: 64
\[0 \lt m \land 0 \lt v \land v \lt 0.25\]
\[\left(\frac{m \cdot \left(1 - m\right)}{v} - 1\right) \cdot m\]
↓
\[\frac{m}{\frac{v}{m}} - \left(m + \frac{\left(m \cdot m\right) \cdot m}{v}\right)\]
\left(\frac{m \cdot \left(1 - m\right)}{v} - 1\right) \cdot m
↓
\frac{m}{\frac{v}{m}} - \left(m + \frac{\left(m \cdot m\right) \cdot m}{v}\right)
double f(double m, double v) {
        double r730712 = m;
        double r730713 = 1.0;
        double r730714 = r730713 - r730712;
        double r730715 = r730712 * r730714;
        double r730716 = v;
        double r730717 = r730715 / r730716;
        double r730718 = r730717 - r730713;
        double r730719 = r730718 * r730712;
        return r730719;
}
↓
double f(double m, double v) {
        double r730720 = m;
        double r730721 = v;
        double r730722 = r730721 / r730720;
        double r730723 = r730720 / r730722;
        double r730724 = r730720 * r730720;
        double r730725 = r730724 * r730720;
        double r730726 = r730725 / r730721;
        double r730727 = r730720 + r730726;
        double r730728 = r730723 - r730727;
        return r730728;
}

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 clear-num0.2

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

  5. Applied div-inv0.3

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

  6. Applied associate-/r*0.3

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

  7. Taylor expanded around inf 7.0

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

  8. Simplified0.2

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

  9. Final simplification0.2

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

Reproduce

herbie shell --seed 2019151 
(FPCore (m v)
  :name "a parameter of renormalized beta distribution"
  :pre (and (< 0 m) (< 0 v) (< v 0.25))
  (* (- (/ (* m (- 1 m)) v) 1) m))