Average Error: 0.1 → 0.1
Time: 13.4s
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 r26953 = x;
        double r26954 = y;
        double r26955 = r26953 * r26954;
        double r26956 = 1.0;
        double r26957 = r26956 - r26954;
        double r26958 = r26955 * r26957;
        return r26958;
}
↓
double f(double x, double y) {
        double r26959 = 1.0;
        double r26960 = y;
        double r26961 = r26959 - r26960;
        double r26962 = x;
        double r26963 = r26962 * r26960;
        double r26964 = r26961 * r26963;
        return r26964;
}

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 2019347 +o rules:numerics
(FPCore (x y)
  :name "Statistics.Distribution.Binomial:$cvariance from math-functions-0.1.5.2"
  :precision binary64
  (* (* x y) (- 1 y)))