Average Error: 0.1 → 0.1
Time: 13.8s
Precision: 64
\[0 \lt m \land 0 \lt v \land v \lt 0.25\]
\[\left(\frac{m \cdot \left(1 - m\right)}{v} - 1\right) \cdot \left(1 - m\right)\]
↓
\[\left(\left(\frac{\left(m \cdot m\right) \cdot m}{v} - \frac{m \cdot m}{v}\right) + m\right) + \left(\frac{\left(1 - m\right) \cdot m}{v} - 1\right)\]
\left(\frac{m \cdot \left(1 - m\right)}{v} - 1\right) \cdot \left(1 - m\right)
↓
\left(\left(\frac{\left(m \cdot m\right) \cdot m}{v} - \frac{m \cdot m}{v}\right) + m\right) + \left(\frac{\left(1 - m\right) \cdot m}{v} - 1\right)
double f(double m, double v) {
        double r437728 = m;
        double r437729 = 1.0;
        double r437730 = r437729 - r437728;
        double r437731 = r437728 * r437730;
        double r437732 = v;
        double r437733 = r437731 / r437732;
        double r437734 = r437733 - r437729;
        double r437735 = r437734 * r437730;
        return r437735;
}
↓
double f(double m, double v) {
        double r437736 = m;
        double r437737 = r437736 * r437736;
        double r437738 = r437737 * r437736;
        double r437739 = v;
        double r437740 = r437738 / r437739;
        double r437741 = r437737 / r437739;
        double r437742 = r437740 - r437741;
        double r437743 = r437742 + r437736;
        double r437744 = 1.0;
        double r437745 = r437744 - r437736;
        double r437746 = r437745 * r437736;
        double r437747 = r437746 / r437739;
        double r437748 = r437747 - r437744;
        double r437749 = r437743 + r437748;
        return r437749;
}

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. Taylor expanded around 0 0.1

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

  6. Simplified0.1

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

  7. Final simplification0.1

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

Reproduce

herbie shell --seed 2019154 
(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)))