Average Error: 0.1 → 0.1
Time: 17.8s
Precision: 64
\[\left(x \cdot y\right) \cdot \left(1 - y\right)\]
↓
\[\left(x \cdot y\right) \cdot \left(-y\right) + \left(x \cdot y\right) \cdot 1\]
\left(x \cdot y\right) \cdot \left(1 - y\right)
↓
\left(x \cdot y\right) \cdot \left(-y\right) + \left(x \cdot y\right) \cdot 1
double f(double x, double y) {
        double r1938907 = x;
        double r1938908 = y;
        double r1938909 = r1938907 * r1938908;
        double r1938910 = 1.0;
        double r1938911 = r1938910 - r1938908;
        double r1938912 = r1938909 * r1938911;
        return r1938912;
}
↓
double f(double x, double y) {
        double r1938913 = x;
        double r1938914 = y;
        double r1938915 = r1938913 * r1938914;
        double r1938916 = -r1938914;
        double r1938917 = r1938915 * r1938916;
        double r1938918 = 1.0;
        double r1938919 = r1938915 * r1938918;
        double r1938920 = r1938917 + r1938919;
        return r1938920;
}

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 sub-neg0.1

    \[\leadsto \left(x \cdot y\right) \cdot \color{blue}{\left(1 + \left(-y\right)\right)}\]

  4. Applied distribute-lft-in0.1

    \[\leadsto \color{blue}{\left(x \cdot y\right) \cdot 1 + \left(x \cdot y\right) \cdot \left(-y\right)}\]

  5. Final simplification0.1

    \[\leadsto \left(x \cdot y\right) \cdot \left(-y\right) + \left(x \cdot y\right) \cdot 1\]

Reproduce

herbie shell --seed 2019172 
(FPCore (x y)
  :name "Statistics.Distribution.Binomial:$cvariance from math-functions-0.1.5.2"
  (* (* x y) (- 1.0 y)))