Average Error: 0.1 → 0.1
Time: 11.0s
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 r27265 = x;
        double r27266 = y;
        double r27267 = r27265 * r27266;
        double r27268 = 1.0;
        double r27269 = r27268 - r27266;
        double r27270 = r27267 * r27269;
        return r27270;
}
↓
double f(double x, double y) {
        double r27271 = x;
        double r27272 = y;
        double r27273 = r27271 * r27272;
        double r27274 = 1.0;
        double r27275 = r27273 * r27274;
        double r27276 = -r27272;
        double r27277 = r27276 * r27273;
        double r27278 = r27275 + r27277;
        return r27278;
}

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 2019305 +o rules:numerics
(FPCore (x y)
  :name "Statistics.Distribution.Binomial:$cvariance from math-functions-0.1.5.2"
  :precision binary64
  (* (* x y) (- 1 y)))