Average Error: 0.1 → 0.1
Time: 11.5s
Precision: 64
\[0.0 \lt m \land 0.0 \lt v \land v \lt 0.25\]
\[\left(\frac{m \cdot \left(1 - m\right)}{v} - 1\right) \cdot \left(1 - m\right)\]
↓
\[\left(1 - m\right) \cdot \left(\frac{m \cdot \left(1 - m\right)}{v} - 1\right)\]
\left(\frac{m \cdot \left(1 - m\right)}{v} - 1\right) \cdot \left(1 - m\right)
↓
\left(1 - m\right) \cdot \left(\frac{m \cdot \left(1 - m\right)}{v} - 1\right)
double f(double m, double v) {
        double r15683 = m;
        double r15684 = 1.0;
        double r15685 = r15684 - r15683;
        double r15686 = r15683 * r15685;
        double r15687 = v;
        double r15688 = r15686 / r15687;
        double r15689 = r15688 - r15684;
        double r15690 = r15689 * r15685;
        return r15690;
}
↓
double f(double m, double v) {
        double r15691 = 1.0;
        double r15692 = m;
        double r15693 = r15691 - r15692;
        double r15694 = r15692 * r15693;
        double r15695 = v;
        double r15696 = r15694 / r15695;
        double r15697 = r15696 - r15691;
        double r15698 = r15693 * r15697;
        return r15698;
}

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 pow10.1

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

  4. Final simplification0.1

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

Reproduce

herbie shell --seed 2019351 +o rules:numerics
(FPCore (m v)
  :name "b parameter of renormalized beta distribution"
  :precision binary64
  :pre (and (< 0.0 m) (< 0.0 v) (< v 0.25))
  (* (- (/ (* m (- 1 m)) v) 1) (- 1 m)))