Average Error: 0.1 → 0.1
Time: 3.2s
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 r148 = x;
        double r149 = y;
        double r150 = r148 * r149;
        double r151 = 1.0;
        double r152 = r151 - r149;
        double r153 = r150 * r152;
        return r153;
}
↓
double f(double x, double y) {
        double r154 = 1.0;
        double r155 = y;
        double r156 = r154 - r155;
        double r157 = x;
        double r158 = r157 * r155;
        double r159 = r156 * r158;
        return r159;
}

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 2020025 +o rules:numerics
(FPCore (x y)
  :name "Statistics.Distribution.Binomial:$cvariance from math-functions-0.1.5.2"
  :precision binary64
  (* (* x y) (- 1 y)))