Average Error: 0.1 → 0.1
Time: 2.9s
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 r24334 = x;
        double r24335 = y;
        double r24336 = r24334 * r24335;
        double r24337 = 1.0;
        double r24338 = r24337 - r24335;
        double r24339 = r24336 * r24338;
        return r24339;
}
↓
double f(double x, double y) {
        double r24340 = x;
        double r24341 = y;
        double r24342 = r24340 * r24341;
        double r24343 = 1.0;
        double r24344 = r24342 * r24343;
        double r24345 = -r24341;
        double r24346 = r24342 * r24345;
        double r24347 = r24344 + r24346;
        return r24347;
}

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 2020021 
(FPCore (x y)
  :name "Statistics.Distribution.Binomial:$cvariance from math-functions-0.1.5.2"
  :precision binary64
  (* (* x y) (- 1 y)))