Average Error: 0.1 → 0.1
Time: 8.4s
Precision: 64
\[\left(x \cdot y\right) \cdot \left(1 - y\right)\]
↓
\[\left(x \cdot y\right) \cdot \left(-y\right) + \left(x \cdot y\right) \cdot 1\]
\left(x \cdot y\right) \cdot \left(1 - y\right)
↓
\left(x \cdot y\right) \cdot \left(-y\right) + \left(x \cdot y\right) \cdot 1
double f(double x, double y) {
        double r1817729 = x;
        double r1817730 = y;
        double r1817731 = r1817729 * r1817730;
        double r1817732 = 1.0;
        double r1817733 = r1817732 - r1817730;
        double r1817734 = r1817731 * r1817733;
        return r1817734;
}
↓
double f(double x, double y) {
        double r1817735 = x;
        double r1817736 = y;
        double r1817737 = r1817735 * r1817736;
        double r1817738 = -r1817736;
        double r1817739 = r1817737 * r1817738;
        double r1817740 = 1.0;
        double r1817741 = r1817737 * r1817740;
        double r1817742 = r1817739 + r1817741;
        return r1817742;
}

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-lft-in0.1

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

  5. Final simplification0.1

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

Reproduce

herbie shell --seed 2019174 
(FPCore (x y)
  :name "Statistics.Distribution.Binomial:$cvariance from math-functions-0.1.5.2"
  (* (* x y) (- 1.0 y)))