Average Error: 0.1 → 0.1
Time: 2.5s
Precision: 64
\[\left(x \cdot y\right) \cdot \left(1 - y\right)\]
↓
\[\left(x \cdot y\right) \cdot 1 + \left(x \cdot y\right) \cdot \left(-y\right)\]
\left(x \cdot y\right) \cdot \left(1 - y\right)
↓
\left(x \cdot y\right) \cdot 1 + \left(x \cdot y\right) \cdot \left(-y\right)
double f(double x, double y) {
        double r35693 = x;
        double r35694 = y;
        double r35695 = r35693 * r35694;
        double r35696 = 1.0;
        double r35697 = r35696 - r35694;
        double r35698 = r35695 * r35697;
        return r35698;
}
↓
double f(double x, double y) {
        double r35699 = x;
        double r35700 = y;
        double r35701 = r35699 * r35700;
        double r35702 = 1.0;
        double r35703 = r35701 * r35702;
        double r35704 = -r35700;
        double r35705 = r35701 * r35704;
        double r35706 = r35703 + r35705;
        return r35706;
}

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

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

Reproduce

herbie shell --seed 2020089 
(FPCore (x y)
  :name "Statistics.Distribution.Binomial:$cvariance from math-functions-0.1.5.2"
  :precision binary64
  (* (* x y) (- 1 y)))