Average Error: 0.1 → 0.1
Time: 9.5s
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 r1487305 = x;
        double r1487306 = y;
        double r1487307 = r1487305 * r1487306;
        double r1487308 = 1.0;
        double r1487309 = r1487308 - r1487306;
        double r1487310 = r1487307 * r1487309;
        return r1487310;
}
↓
double f(double x, double y) {
        double r1487311 = x;
        double r1487312 = y;
        double r1487313 = r1487311 * r1487312;
        double r1487314 = -r1487312;
        double r1487315 = r1487313 * r1487314;
        double r1487316 = 1.0;
        double r1487317 = r1487313 * r1487316;
        double r1487318 = r1487315 + r1487317;
        return r1487318;
}

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 2019171 
(FPCore (x y)
  :name "Statistics.Distribution.Binomial:$cvariance from math-functions-0.1.5.2"
  (* (* x y) (- 1.0 y)))