Average Error: 0.1 → 0.1
Time: 3.3m
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 r10422840 = m;
        double r10422841 = 1.0;
        double r10422842 = r10422841 - r10422840;
        double r10422843 = r10422840 * r10422842;
        double r10422844 = v;
        double r10422845 = r10422843 / r10422844;
        double r10422846 = r10422845 - r10422841;
        double r10422847 = r10422846 * r10422842;
        return r10422847;
}
↓
double f(double m, double v) {
        double r10422848 = 1.0;
        double r10422849 = m;
        double r10422850 = r10422848 - r10422849;
        double r10422851 = v;
        double r10422852 = r10422851 / r10422850;
        double r10422853 = r10422849 / r10422852;
        double r10422854 = r10422853 - r10422848;
        double r10422855 = r10422850 * r10422854;
        return r10422855;
}

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 2019119 +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)))