Average Error: 0.1 → 0.1
Time: 15.1s
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 r17237 = x;
        double r17238 = y;
        double r17239 = r17237 * r17238;
        double r17240 = 1.0;
        double r17241 = r17240 - r17238;
        double r17242 = r17239 * r17241;
        return r17242;
}
↓
double f(double x, double y) {
        double r17243 = 1.0;
        double r17244 = y;
        double r17245 = r17243 - r17244;
        double r17246 = x;
        double r17247 = r17246 * r17244;
        double r17248 = r17245 * r17247;
        return r17248;
}

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 2019304 +o rules:numerics
(FPCore (x y)
  :name "Statistics.Distribution.Binomial:$cvariance from math-functions-0.1.5.2"
  :precision binary64
  (* (* x y) (- 1 y)))