Average Error: 0.1 → 0.1
Time: 16.5s
Precision: 64
\[0 \lt m \land 0 \lt v \land v \lt 0.25\]
\[\left(\frac{m \cdot \left(1 - m\right)}{v} - 1\right) \cdot \left(1 - m\right)\]
↓
\[\left(1 - m\right) \cdot \left(\frac{m}{\frac{v}{1 - m}} - 1\right)\]
\left(\frac{m \cdot \left(1 - m\right)}{v} - 1\right) \cdot \left(1 - m\right)
↓
\left(1 - m\right) \cdot \left(\frac{m}{\frac{v}{1 - m}} - 1\right)
double f(double m, double v) {
        double r538598 = m;
        double r538599 = 1.0;
        double r538600 = r538599 - r538598;
        double r538601 = r538598 * r538600;
        double r538602 = v;
        double r538603 = r538601 / r538602;
        double r538604 = r538603 - r538599;
        double r538605 = r538604 * r538600;
        return r538605;
}
↓
double f(double m, double v) {
        double r538606 = 1.0;
        double r538607 = m;
        double r538608 = r538606 - r538607;
        double r538609 = v;
        double r538610 = r538609 / r538608;
        double r538611 = r538607 / r538610;
        double r538612 = r538611 - r538606;
        double r538613 = r538608 * r538612;
        return r538613;
}

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 associate-/l*0.1

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

  4. Final simplification0.1

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

Reproduce

herbie shell --seed 2019154 +o rules:numerics
(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)))