Average Error: 0.1 → 0.1
Time: 1.3s
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 r24073 = x;
        double r24074 = y;
        double r24075 = r24073 * r24074;
        double r24076 = 1.0;
        double r24077 = r24076 - r24074;
        double r24078 = r24075 * r24077;
        return r24078;
}
↓
double f(double x, double y) {
        double r24079 = x;
        double r24080 = y;
        double r24081 = r24079 * r24080;
        double r24082 = 1.0;
        double r24083 = r24081 * r24082;
        double r24084 = -r24080;
        double r24085 = r24081 * r24084;
        double r24086 = r24083 + r24085;
        return r24086;
}

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 2020060 
(FPCore (x y)
  :name "Statistics.Distribution.Binomial:$cvariance from math-functions-0.1.5.2"
  :precision binary64
  (* (* x y) (- 1 y)))