Average Error: 0.1 → 0.1
Time: 17.1s
Precision: 64
\[\left(x \cdot y\right) \cdot \left(1.0 - y\right)\]
↓
\[\left(y \cdot x\right) \cdot \left(-y\right) + \left(y \cdot x\right) \cdot 1.0\]
\left(x \cdot y\right) \cdot \left(1.0 - y\right)
↓
\left(y \cdot x\right) \cdot \left(-y\right) + \left(y \cdot x\right) \cdot 1.0
double f(double x, double y) {
        double r1561517 = x;
        double r1561518 = y;
        double r1561519 = r1561517 * r1561518;
        double r1561520 = 1.0;
        double r1561521 = r1561520 - r1561518;
        double r1561522 = r1561519 * r1561521;
        return r1561522;
}
↓
double f(double x, double y) {
        double r1561523 = y;
        double r1561524 = x;
        double r1561525 = r1561523 * r1561524;
        double r1561526 = -r1561523;
        double r1561527 = r1561525 * r1561526;
        double r1561528 = 1.0;
        double r1561529 = r1561525 * r1561528;
        double r1561530 = r1561527 + r1561529;
        return r1561530;
}

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

    \[\left(x \cdot y\right) \cdot \left(1.0 - y\right)\]
  2. Using strategy rm

  3. Applied sub-neg0.1

    \[\leadsto \left(x \cdot y\right) \cdot \color{blue}{\left(1.0 + \left(-y\right)\right)}\]

  4. Applied distribute-rgt-in0.1

    \[\leadsto \color{blue}{1.0 \cdot \left(x \cdot y\right) + \left(-y\right) \cdot \left(x \cdot y\right)}\]

  5. Final simplification0.1

    \[\leadsto \left(y \cdot x\right) \cdot \left(-y\right) + \left(y \cdot x\right) \cdot 1.0\]

Reproduce

herbie shell --seed 2019163 +o rules:numerics
(FPCore (x y)
  :name "Statistics.Distribution.Binomial:$cvariance from math-functions-0.1.5.2"
  (* (* x y) (- 1.0 y)))