Average Error: 0.1 → 0.1
Time: 3.2s
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 r29388 = x;
        double r29389 = y;
        double r29390 = r29388 * r29389;
        double r29391 = 1.0;
        double r29392 = r29391 - r29389;
        double r29393 = r29390 * r29392;
        return r29393;
}
↓
double f(double x, double y) {
        double r29394 = x;
        double r29395 = y;
        double r29396 = r29394 * r29395;
        double r29397 = 1.0;
        double r29398 = r29396 * r29397;
        double r29399 = -r29395;
        double r29400 = r29396 * r29399;
        double r29401 = r29398 + r29400;
        return r29401;
}

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 2020062 
(FPCore (x y)
  :name "Statistics.Distribution.Binomial:$cvariance from math-functions-0.1.5.2"
  :precision binary64
  (* (* x y) (- 1 y)))