Average Error: 0.1 → 0.1
Time: 2.7s
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 r26971 = x;
        double r26972 = y;
        double r26973 = r26971 * r26972;
        double r26974 = 1.0;
        double r26975 = r26974 - r26972;
        double r26976 = r26973 * r26975;
        return r26976;
}
↓
double f(double x, double y) {
        double r26977 = 1.0;
        double r26978 = y;
        double r26979 = r26977 - r26978;
        double r26980 = x;
        double r26981 = r26980 * r26978;
        double r26982 = r26979 * r26981;
        return r26982;
}

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 2020001 +o rules:numerics
(FPCore (x y)
  :name "Statistics.Distribution.Binomial:$cvariance from math-functions-0.1.5.2"
  :precision binary64
  (* (* x y) (- 1 y)))