Average Error: 0.1 → 0.1
Time: 51.2s
Precision: 64
\[0 \lt m \land 0 \lt v \land v \lt 0.25\]
\[\left(\frac{m \cdot \left(1 - m\right)}{v} - 1\right) \cdot \left(1 - m\right)\]
↓
\[\left(1 - m\right) \cdot \left(\left(\frac{m}{v} - \left(\frac{1}{v} \cdot m\right) \cdot m\right) - 1\right)\]
\left(\frac{m \cdot \left(1 - m\right)}{v} - 1\right) \cdot \left(1 - m\right)
↓
\left(1 - m\right) \cdot \left(\left(\frac{m}{v} - \left(\frac{1}{v} \cdot m\right) \cdot m\right) - 1\right)
double f(double m, double v) {
        double r2872714 = m;
        double r2872715 = 1.0;
        double r2872716 = r2872715 - r2872714;
        double r2872717 = r2872714 * r2872716;
        double r2872718 = v;
        double r2872719 = r2872717 / r2872718;
        double r2872720 = r2872719 - r2872715;
        double r2872721 = r2872720 * r2872716;
        return r2872721;
}
↓
double f(double m, double v) {
        double r2872722 = 1.0;
        double r2872723 = m;
        double r2872724 = r2872722 - r2872723;
        double r2872725 = v;
        double r2872726 = r2872723 / r2872725;
        double r2872727 = r2872722 / r2872725;
        double r2872728 = r2872727 * r2872723;
        double r2872729 = r2872728 * r2872723;
        double r2872730 = r2872726 - r2872729;
        double r2872731 = r2872730 - r2872722;
        double r2872732 = r2872724 * r2872731;
        return r2872732;
}

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. Taylor expanded around inf 0.1

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

  3. Simplified0.1

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

  5. Applied div-inv0.1

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

  6. Applied associate-*r*0.1

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

  8. Applied associate-*l*0.1

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

  9. Final simplification0.1

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

Reproduce

herbie shell --seed 2019121 
(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)))