Average Error: 0.1 → 0.1
Time: 18.5s
Precision: 64
\[0.0 \lt m \land 0.0 \lt v \land v \lt 0.25\]
\[\left(\frac{m \cdot \left(1 - m\right)}{v} - 1\right) \cdot \left(1 - m\right)\]
↓
\[\left(\frac{\left(1 - m\right) \cdot m}{v} - 1\right) \cdot \left(1 - m\right)\]
\left(\frac{m \cdot \left(1 - m\right)}{v} - 1\right) \cdot \left(1 - m\right)
↓
\left(\frac{\left(1 - m\right) \cdot m}{v} - 1\right) \cdot \left(1 - m\right)
double f(double m, double v) {
        double r1591884 = m;
        double r1591885 = 1.0;
        double r1591886 = r1591885 - r1591884;
        double r1591887 = r1591884 * r1591886;
        double r1591888 = v;
        double r1591889 = r1591887 / r1591888;
        double r1591890 = r1591889 - r1591885;
        double r1591891 = r1591890 * r1591886;
        return r1591891;
}
↓
double f(double m, double v) {
        double r1591892 = 1.0;
        double r1591893 = m;
        double r1591894 = r1591892 - r1591893;
        double r1591895 = r1591894 * r1591893;
        double r1591896 = v;
        double r1591897 = r1591895 / r1591896;
        double r1591898 = r1591897 - r1591892;
        double r1591899 = r1591898 * r1591894;
        return r1591899;
}

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 *-un-lft-identity0.1

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

  4. Applied associate-/r*0.1

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

  5. Simplified0.1

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

  6. Final simplification0.1

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

Reproduce

herbie shell --seed 2019170 
(FPCore (m v)
  :name "b parameter of renormalized beta distribution"
  :pre (and (< 0.0 m) (< 0.0 v) (< v 0.25))
  (* (- (/ (* m (- 1.0 m)) v) 1.0) (- 1.0 m)))