Average Error: 0.1 → 0.1
Time: 14.6s
Precision: 64
\[\left(x \cdot y\right) \cdot \left(1.0 - y\right)\]
↓
\[\left(x \cdot y\right) \cdot \left(-y\right) + \left(x \cdot y\right) \cdot 1.0\]
\left(x \cdot y\right) \cdot \left(1.0 - y\right)
↓
\left(x \cdot y\right) \cdot \left(-y\right) + \left(x \cdot y\right) \cdot 1.0
double f(double x, double y) {
        double r1557882 = x;
        double r1557883 = y;
        double r1557884 = r1557882 * r1557883;
        double r1557885 = 1.0;
        double r1557886 = r1557885 - r1557883;
        double r1557887 = r1557884 * r1557886;
        return r1557887;
}
↓
double f(double x, double y) {
        double r1557888 = x;
        double r1557889 = y;
        double r1557890 = r1557888 * r1557889;
        double r1557891 = -r1557889;
        double r1557892 = r1557890 * r1557891;
        double r1557893 = 1.0;
        double r1557894 = r1557890 * r1557893;
        double r1557895 = r1557892 + r1557894;
        return r1557895;
}

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

    \[\left(x \cdot y\right) \cdot \left(1.0 - y\right)\]
  2. Using strategy rm

  3. Applied sub-neg0.1

    \[\leadsto \left(x \cdot y\right) \cdot \color{blue}{\left(1.0 + \left(-y\right)\right)}\]

  4. Applied distribute-lft-in0.1

    \[\leadsto \color{blue}{\left(x \cdot y\right) \cdot 1.0 + \left(x \cdot y\right) \cdot \left(-y\right)}\]

  5. Final simplification0.1

    \[\leadsto \left(x \cdot y\right) \cdot \left(-y\right) + \left(x \cdot y\right) \cdot 1.0\]

Reproduce

herbie shell --seed 2019163 +o rules:numerics
(FPCore (x y)
  :name "Statistics.Distribution.Binomial:$cvariance from math-functions-0.1.5.2"
  (* (* x y) (- 1.0 y)))