Average Error: 0.1 → 0.1
Time: 2.6s
Precision: 64
\[\left(x \cdot y\right) \cdot \left(1 - y\right)\]
↓
\[\left(x \cdot y\right) \cdot 1 + \left(x \cdot y\right) \cdot \left(-y\right)\]
\left(x \cdot y\right) \cdot \left(1 - y\right)
↓
\left(x \cdot y\right) \cdot 1 + \left(x \cdot y\right) \cdot \left(-y\right)
double f(double x, double y) {
        double r36305 = x;
        double r36306 = y;
        double r36307 = r36305 * r36306;
        double r36308 = 1.0;
        double r36309 = r36308 - r36306;
        double r36310 = r36307 * r36309;
        return r36310;
}
↓
double f(double x, double y) {
        double r36311 = x;
        double r36312 = y;
        double r36313 = r36311 * r36312;
        double r36314 = 1.0;
        double r36315 = r36313 * r36314;
        double r36316 = -r36312;
        double r36317 = r36313 * r36316;
        double r36318 = r36315 + r36317;
        return r36318;
}

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

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

Reproduce

herbie shell --seed 2020089 +o rules:numerics
(FPCore (x y)
  :name "Statistics.Distribution.Binomial:$cvariance from math-functions-0.1.5.2"
  :precision binary64
  (* (* x y) (- 1 y)))