Average Error: 0.1 → 0.1
Time: 9.9s
Precision: 64
\[0.0 \lt m \land 0.0 \lt v \land v \lt 0.25\]
\[\left(\frac{m \cdot \left(1 - m\right)}{v} - 1\right) \cdot \left(1 - m\right)\]
↓
\[\left(\frac{\frac{m \cdot \left(1 \cdot 1 - m \cdot m\right)}{1 + m}}{v} - 1\right) \cdot \left(1 - m\right)\]
\left(\frac{m \cdot \left(1 - m\right)}{v} - 1\right) \cdot \left(1 - m\right)
↓
\left(\frac{\frac{m \cdot \left(1 \cdot 1 - m \cdot m\right)}{1 + m}}{v} - 1\right) \cdot \left(1 - m\right)
double f(double m, double v) {
        double r33966 = m;
        double r33967 = 1.0;
        double r33968 = r33967 - r33966;
        double r33969 = r33966 * r33968;
        double r33970 = v;
        double r33971 = r33969 / r33970;
        double r33972 = r33971 - r33967;
        double r33973 = r33972 * r33968;
        return r33973;
}
↓
double f(double m, double v) {
        double r33974 = m;
        double r33975 = 1.0;
        double r33976 = r33975 * r33975;
        double r33977 = r33974 * r33974;
        double r33978 = r33976 - r33977;
        double r33979 = r33974 * r33978;
        double r33980 = r33975 + r33974;
        double r33981 = r33979 / r33980;
        double r33982 = v;
        double r33983 = r33981 / r33982;
        double r33984 = r33983 - r33975;
        double r33985 = r33975 - r33974;
        double r33986 = r33984 * r33985;
        return r33986;
}

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 flip--0.1

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

  4. Applied associate-*r/0.1

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

  5. Final simplification0.1

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

Reproduce

herbie shell --seed 2020003 
(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)))