Average Error: 0.1 → 0.1
Time: 2.8s
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 r22883 = x;
        double r22884 = y;
        double r22885 = r22883 * r22884;
        double r22886 = 1.0;
        double r22887 = r22886 - r22884;
        double r22888 = r22885 * r22887;
        return r22888;
}
↓
double f(double x, double y) {
        double r22889 = 1.0;
        double r22890 = y;
        double r22891 = r22889 - r22890;
        double r22892 = x;
        double r22893 = r22892 * r22890;
        double r22894 = r22891 * r22893;
        return r22894;
}

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 2020018 +o rules:numerics
(FPCore (x y)
  :name "Statistics.Distribution.Binomial:$cvariance from math-functions-0.1.5.2"
  :precision binary64
  (* (* x y) (- 1 y)))