Average Error: 0.1 → 0.1
Time: 18.3s
Precision: 64
\[0 \lt m \land 0 \lt v \land v \lt 0.25\]
\[\left(\frac{m \cdot \left(1 - m\right)}{v} - 1\right) \cdot \left(1 - m\right)\]
↓
\[\left(1 - m\right) \cdot \left(\frac{m - m \cdot m}{v} - 1\right)\]
\left(\frac{m \cdot \left(1 - m\right)}{v} - 1\right) \cdot \left(1 - m\right)
↓
\left(1 - m\right) \cdot \left(\frac{m - m \cdot m}{v} - 1\right)
double f(double m, double v) {
        double r1098710 = m;
        double r1098711 = 1.0;
        double r1098712 = r1098711 - r1098710;
        double r1098713 = r1098710 * r1098712;
        double r1098714 = v;
        double r1098715 = r1098713 / r1098714;
        double r1098716 = r1098715 - r1098711;
        double r1098717 = r1098716 * r1098712;
        return r1098717;
}
↓
double f(double m, double v) {
        double r1098718 = 1.0;
        double r1098719 = m;
        double r1098720 = r1098718 - r1098719;
        double r1098721 = r1098719 * r1098719;
        double r1098722 = r1098719 - r1098721;
        double r1098723 = v;
        double r1098724 = r1098722 / r1098723;
        double r1098725 = r1098724 - r1098718;
        double r1098726 = r1098720 * r1098725;
        return r1098726;
}

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 0 0.1

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

  3. Simplified0.1

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

  4. Final simplification0.1

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

Reproduce

herbie shell --seed 2019158 
(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)))