Average Error: 0.1 → 0.1
Time: 15.9s
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 r1209810 = x;
        double r1209811 = y;
        double r1209812 = r1209810 * r1209811;
        double r1209813 = 1.0;
        double r1209814 = r1209813 - r1209811;
        double r1209815 = r1209812 * r1209814;
        return r1209815;
}
↓
double f(double x, double y) {
        double r1209816 = x;
        double r1209817 = y;
        double r1209818 = r1209816 * r1209817;
        double r1209819 = -r1209817;
        double r1209820 = r1209818 * r1209819;
        double r1209821 = 1.0;
        double r1209822 = r1209818 * r1209821;
        double r1209823 = r1209820 + r1209822;
        return r1209823;
}

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 2019172 +o rules:numerics
(FPCore (x y)
  :name "Statistics.Distribution.Binomial:$cvariance from math-functions-0.1.5.2"
  (* (* x y) (- 1.0 y)))