Average Error: 0.1 → 0.1
Time: 2.2s
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 r13202 = x;
        double r13203 = y;
        double r13204 = r13202 * r13203;
        double r13205 = 1.0;
        double r13206 = r13205 - r13203;
        double r13207 = r13204 * r13206;
        return r13207;
}
↓
double f(double x, double y) {
        double r13208 = 1.0;
        double r13209 = y;
        double r13210 = r13208 - r13209;
        double r13211 = x;
        double r13212 = r13211 * r13209;
        double r13213 = r13210 * r13212;
        return r13213;
}

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 2020024 +o rules:numerics
(FPCore (x y)
  :name "Statistics.Distribution.Binomial:$cvariance from math-functions-0.1.5.2"
  :precision binary64
  (* (* x y) (- 1 y)))