Average Error: 0.1 → 0.1
Time: 15.5s
Precision: 64
\[\left(x \cdot y\right) \cdot \left(1 - y\right)\]
↓
\[\left(y \cdot x\right) \cdot \left(-y\right) + \left(y \cdot x\right) \cdot 1\]
\left(x \cdot y\right) \cdot \left(1 - y\right)
↓
\left(y \cdot x\right) \cdot \left(-y\right) + \left(y \cdot x\right) \cdot 1
double f(double x, double y) {
        double r1450890 = x;
        double r1450891 = y;
        double r1450892 = r1450890 * r1450891;
        double r1450893 = 1.0;
        double r1450894 = r1450893 - r1450891;
        double r1450895 = r1450892 * r1450894;
        return r1450895;
}
↓
double f(double x, double y) {
        double r1450896 = y;
        double r1450897 = x;
        double r1450898 = r1450896 * r1450897;
        double r1450899 = -r1450896;
        double r1450900 = r1450898 * r1450899;
        double r1450901 = 1.0;
        double r1450902 = r1450898 * r1450901;
        double r1450903 = r1450900 + r1450902;
        return r1450903;
}

Error

Bits error versus x

Bits error versus y

Try it out

Your Program's Arguments

Results

Enter valid numbers for all inputs

Derivation

  1. Initial program 0.1

    \[\left(x \cdot y\right) \cdot \left(1 - y\right)\]
  2. Using strategy rm

  3. Applied sub-neg0.1

    \[\leadsto \left(x \cdot y\right) \cdot \color{blue}{\left(1 + \left(-y\right)\right)}\]

  4. Applied distribute-rgt-in0.1

    \[\leadsto \color{blue}{1 \cdot \left(x \cdot y\right) + \left(-y\right) \cdot \left(x \cdot y\right)}\]

  5. Final simplification0.1

    \[\leadsto \left(y \cdot x\right) \cdot \left(-y\right) + \left(y \cdot x\right) \cdot 1\]

Reproduce

herbie shell --seed 2019169 
(FPCore (x y)
  :name "Statistics.Distribution.Binomial:$cvariance from math-functions-0.1.5.2"
  (* (* x y) (- 1.0 y)))