Average Error: 0.1 → 0.1
Time: 35.8s
Precision: 64
\[0 \lt m \land 0 \lt v \land v \lt 0.25\]
\[\left(\frac{m \cdot \left(1 - m\right)}{v} - 1\right) \cdot \left(1 - m\right)\]
↓
\[\left(1 - m\right) \cdot \left(\frac{m - m \cdot m}{v} - 1\right)\]
\left(\frac{m \cdot \left(1 - m\right)}{v} - 1\right) \cdot \left(1 - m\right)
↓
\left(1 - m\right) \cdot \left(\frac{m - m \cdot m}{v} - 1\right)
double f(double m, double v) {
        double r1074965 = m;
        double r1074966 = 1.0;
        double r1074967 = r1074966 - r1074965;
        double r1074968 = r1074965 * r1074967;
        double r1074969 = v;
        double r1074970 = r1074968 / r1074969;
        double r1074971 = r1074970 - r1074966;
        double r1074972 = r1074971 * r1074967;
        return r1074972;
}
↓
double f(double m, double v) {
        double r1074973 = 1.0;
        double r1074974 = m;
        double r1074975 = r1074973 - r1074974;
        double r1074976 = r1074974 * r1074974;
        double r1074977 = r1074974 - r1074976;
        double r1074978 = v;
        double r1074979 = r1074977 / r1074978;
        double r1074980 = r1074979 - r1074973;
        double r1074981 = r1074975 * r1074980;
        return r1074981;
}

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. Taylor expanded around 0 0.1

    \[\leadsto \left(\frac{\color{blue}{m - {m}^{2}}}{v} - 1\right) \cdot \left(1 - m\right)\]

  3. Simplified0.1

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

  4. Final simplification0.1

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

Reproduce

herbie shell --seed 2019158 +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)))