Average Error: 0.1 → 0.1
Time: 16.7s
Precision: 64
\[0 \lt m \land 0 \lt v \land v \lt 0.25\]
\[\left(\frac{m \cdot \left(1 - m\right)}{v} - 1\right) \cdot \left(1 - m\right)\]
↓
\[\left(\left(\frac{m}{v} - \frac{m}{\frac{v}{m}}\right) - 1\right) + \left(\left(\frac{m \cdot \left(m \cdot m\right)}{v} + m\right) - \frac{m}{v} \cdot m\right)\]
\left(\frac{m \cdot \left(1 - m\right)}{v} - 1\right) \cdot \left(1 - m\right)
↓
\left(\left(\frac{m}{v} - \frac{m}{\frac{v}{m}}\right) - 1\right) + \left(\left(\frac{m \cdot \left(m \cdot m\right)}{v} + m\right) - \frac{m}{v} \cdot m\right)
double f(double m, double v) {
        double r687629 = m;
        double r687630 = 1.0;
        double r687631 = r687630 - r687629;
        double r687632 = r687629 * r687631;
        double r687633 = v;
        double r687634 = r687632 / r687633;
        double r687635 = r687634 - r687630;
        double r687636 = r687635 * r687631;
        return r687636;
}
↓
double f(double m, double v) {
        double r687637 = m;
        double r687638 = v;
        double r687639 = r687637 / r687638;
        double r687640 = r687638 / r687637;
        double r687641 = r687637 / r687640;
        double r687642 = r687639 - r687641;
        double r687643 = 1.0;
        double r687644 = r687642 - r687643;
        double r687645 = r687637 * r687637;
        double r687646 = r687637 * r687645;
        double r687647 = r687646 / r687638;
        double r687648 = r687647 + r687637;
        double r687649 = r687639 * r687637;
        double r687650 = r687648 - r687649;
        double r687651 = r687644 + r687650;
        return r687651;
}

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

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

  6. Simplified0.1

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

  7. Taylor expanded around inf 0.1

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

  8. Simplified0.1

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

  9. Final simplification0.1

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

Reproduce

herbie shell --seed 2019135 
(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)))