Average Error: 0.1 → 0.1
Time: 12.1s
Precision: 64
\[\left(x \cdot y\right) \cdot \left(1 - y\right)\]
↓
\[y \cdot \left(\left(1 - y\right) \cdot x\right)\]
\left(x \cdot y\right) \cdot \left(1 - y\right)
↓
y \cdot \left(\left(1 - y\right) \cdot x\right)
double f(double x, double y) {
        double r19858 = x;
        double r19859 = y;
        double r19860 = r19858 * r19859;
        double r19861 = 1.0;
        double r19862 = r19861 - r19859;
        double r19863 = r19860 * r19862;
        return r19863;
}
↓
double f(double x, double y) {
        double r19864 = y;
        double r19865 = 1.0;
        double r19866 = r19865 - r19864;
        double r19867 = x;
        double r19868 = r19866 * r19867;
        double r19869 = r19864 * r19868;
        return r19869;
}

Error

Bits error versus x

Bits error versus y

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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. Taylor expanded around 0 5.7

    \[\leadsto \color{blue}{1 \cdot \left(x \cdot y\right) - x \cdot {y}^{2}}\]

  3. Simplified5.7

    \[\leadsto \color{blue}{\left(y \cdot \left(1 - y\right)\right) \cdot x}\]
  4. Using strategy rm

  5. Applied associate-*l*0.1

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

  6. Final simplification0.1

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

Reproduce

herbie shell --seed 2019322 
(FPCore (x y)
  :name "Statistics.Distribution.Binomial:$cvariance from math-functions-0.1.5.2"
  :precision binary64
  (* (* x y) (- 1 y)))