Average Error: 0.1 → 0.1
Time: 2.2s
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 r13693 = x;
        double r13694 = y;
        double r13695 = r13693 * r13694;
        double r13696 = 1.0;
        double r13697 = r13696 - r13694;
        double r13698 = r13695 * r13697;
        return r13698;
}
↓
double f(double x, double y) {
        double r13699 = 1.0;
        double r13700 = y;
        double r13701 = r13699 - r13700;
        double r13702 = x;
        double r13703 = r13702 * r13700;
        double r13704 = r13701 * r13703;
        return r13704;
}

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 *-commutative0.1

    \[\leadsto \color{blue}{\left(1 - y\right) \cdot \left(x \cdot y\right)}\]

  4. Final simplification0.1

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

Reproduce

herbie shell --seed 2020034 +o rules:numerics
(FPCore (x y)
  :name "Statistics.Distribution.Binomial:$cvariance from math-functions-0.1.5.2"
  :precision binary64
  (* (* x y) (- 1 y)))