Average Error: 0.1 → 0.1
Time: 10.7s
Precision: 64
\[\left(x \cdot y\right) \cdot \left(1 - y\right)\]
↓
\[\left(x \cdot y\right) \cdot 1 + \left(-y\right) \cdot \left(x \cdot y\right)\]
\left(x \cdot y\right) \cdot \left(1 - y\right)
↓
\left(x \cdot y\right) \cdot 1 + \left(-y\right) \cdot \left(x \cdot y\right)
double f(double x, double y) {
        double r20918 = x;
        double r20919 = y;
        double r20920 = r20918 * r20919;
        double r20921 = 1.0;
        double r20922 = r20921 - r20919;
        double r20923 = r20920 * r20922;
        return r20923;
}
↓
double f(double x, double y) {
        double r20924 = x;
        double r20925 = y;
        double r20926 = r20924 * r20925;
        double r20927 = 1.0;
        double r20928 = r20926 * r20927;
        double r20929 = -r20925;
        double r20930 = r20929 * r20926;
        double r20931 = r20928 + r20930;
        return r20931;
}

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. Simplified0.1

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

  6. Final simplification0.1

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

Reproduce

herbie shell --seed 2019198 +o rules:numerics
(FPCore (x y)
  :name "Statistics.Distribution.Binomial:$cvariance from math-functions-0.1.5.2"
  (* (* x y) (- 1.0 y)))