Average Error: 0.1 → 0.1
Time: 9.9s
Precision: 64
\[0.0 \lt m \land 0.0 \lt v \land v \lt 0.25\]
\[\left(\frac{m \cdot \left(1 - m\right)}{v} - 1\right) \cdot \left(1 - m\right)\]
↓
\[\left(\frac{1 \cdot m + m \cdot \left(-m\right)}{v} - 1\right) \cdot \left(1 - m\right)\]
\left(\frac{m \cdot \left(1 - m\right)}{v} - 1\right) \cdot \left(1 - m\right)
↓
\left(\frac{1 \cdot m + m \cdot \left(-m\right)}{v} - 1\right) \cdot \left(1 - m\right)
double f(double m, double v) {
        double r12607 = m;
        double r12608 = 1.0;
        double r12609 = r12608 - r12607;
        double r12610 = r12607 * r12609;
        double r12611 = v;
        double r12612 = r12610 / r12611;
        double r12613 = r12612 - r12608;
        double r12614 = r12613 * r12609;
        return r12614;
}
↓
double f(double m, double v) {
        double r12615 = 1.0;
        double r12616 = m;
        double r12617 = r12615 * r12616;
        double r12618 = -r12616;
        double r12619 = r12616 * r12618;
        double r12620 = r12617 + r12619;
        double r12621 = v;
        double r12622 = r12620 / r12621;
        double r12623 = r12622 - r12615;
        double r12624 = r12615 - r12616;
        double r12625 = r12623 * r12624;
        return r12625;
}

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

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

  4. Applied distribute-lft-in0.1

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

  5. Simplified0.1

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

  6. Final simplification0.1

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

Reproduce

herbie shell --seed 2019350 
(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)))