Average Error: 0.1 → 0.1
Time: 3.8s
Precision: 64
\[\left(x \cdot y\right) \cdot \left(1 - y\right)\]
↓
\[\left(1 - y\right) \cdot \left(x \cdot y\right)\]
\left(x \cdot y\right) \cdot \left(1 - y\right)
↓
\left(1 - y\right) \cdot \left(x \cdot y\right)
double f(double x, double y) {
        double r25551 = x;
        double r25552 = y;
        double r25553 = r25551 * r25552;
        double r25554 = 1.0;
        double r25555 = r25554 - r25552;
        double r25556 = r25553 * r25555;
        return r25556;
}
↓
double f(double x, double y) {
        double r25557 = 1.0;
        double r25558 = y;
        double r25559 = r25557 - r25558;
        double r25560 = x;
        double r25561 = r25560 * r25558;
        double r25562 = r25559 * r25561;
        return r25562;
}

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

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

Reproduce

herbie shell --seed 2019304 
(FPCore (x y)
  :name "Statistics.Distribution.Binomial:$cvariance from math-functions-0.1.5.2"
  :precision binary64
  (* (* x y) (- 1 y)))