Average Error: 0.1 → 0.1
Time: 20.8s
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 r605847 = m;
        double r605848 = 1.0;
        double r605849 = r605848 - r605847;
        double r605850 = r605847 * r605849;
        double r605851 = v;
        double r605852 = r605850 / r605851;
        double r605853 = r605852 - r605848;
        double r605854 = r605853 * r605849;
        return r605854;
}
↓
double f(double m, double v) {
        double r605855 = 1.0;
        double r605856 = m;
        double r605857 = r605855 - r605856;
        double r605858 = v;
        double r605859 = r605858 / r605857;
        double r605860 = r605856 / r605859;
        double r605861 = r605860 - r605855;
        double r605862 = r605857 * r605861;
        return r605862;
}

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 2019138 +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)))