Average Error: 0.1 → 0.1
Time: 15.1s
Precision: 64
\[\left(x \cdot y\right) \cdot \left(1.0 - y\right)\]
↓
\[\left(x \cdot y\right) \cdot \left(-y\right) + \left(x \cdot y\right) \cdot 1.0\]
\left(x \cdot y\right) \cdot \left(1.0 - y\right)
↓
\left(x \cdot y\right) \cdot \left(-y\right) + \left(x \cdot y\right) \cdot 1.0
double f(double x, double y) {
        double r2005427 = x;
        double r2005428 = y;
        double r2005429 = r2005427 * r2005428;
        double r2005430 = 1.0;
        double r2005431 = r2005430 - r2005428;
        double r2005432 = r2005429 * r2005431;
        return r2005432;
}
↓
double f(double x, double y) {
        double r2005433 = x;
        double r2005434 = y;
        double r2005435 = r2005433 * r2005434;
        double r2005436 = -r2005434;
        double r2005437 = r2005435 * r2005436;
        double r2005438 = 1.0;
        double r2005439 = r2005435 * r2005438;
        double r2005440 = r2005437 + r2005439;
        return r2005440;
}

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-lft-in0.1

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

  5. Final simplification0.1

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

Reproduce

herbie shell --seed 2019158 +o rules:numerics
(FPCore (x y)
  :name "Statistics.Distribution.Binomial:$cvariance from math-functions-0.1.5.2"
  (* (* x y) (- 1.0 y)))