Average Error: 0.1 → 0.1
Time: 19.7s
Precision: 64
\[0 \lt m \land 0 \lt v \land v \lt 0.25\]
\[\left(\frac{m \cdot \left(1 - m\right)}{v} - 1\right) \cdot \left(1 - m\right)\]
↓
\[\left(-m\right) \cdot \left(\frac{m}{\frac{v}{1 - m}} - 1\right) + \left(\frac{m}{\frac{v}{1 - m}} - 1\right)\]
\left(\frac{m \cdot \left(1 - m\right)}{v} - 1\right) \cdot \left(1 - m\right)
↓
\left(-m\right) \cdot \left(\frac{m}{\frac{v}{1 - m}} - 1\right) + \left(\frac{m}{\frac{v}{1 - m}} - 1\right)
double f(double m, double v) {
        double r444746 = m;
        double r444747 = 1.0;
        double r444748 = r444747 - r444746;
        double r444749 = r444746 * r444748;
        double r444750 = v;
        double r444751 = r444749 / r444750;
        double r444752 = r444751 - r444747;
        double r444753 = r444752 * r444748;
        return r444753;
}
↓
double f(double m, double v) {
        double r444754 = m;
        double r444755 = -r444754;
        double r444756 = v;
        double r444757 = 1.0;
        double r444758 = r444757 - r444754;
        double r444759 = r444756 / r444758;
        double r444760 = r444754 / r444759;
        double r444761 = r444760 - r444757;
        double r444762 = r444755 * r444761;
        double r444763 = r444762 + r444761;
        return r444763;
}

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. Using strategy rm

  5. Applied sub-neg0.1

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

  6. Applied distribute-lft-in0.1

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

  7. Simplified0.1

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

  8. Final simplification0.1

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

Reproduce

herbie shell --seed 2019151 
(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)))