Average Error: 0.1 → 0.1
Time: 12.8s
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 r1878242 = x;
        double r1878243 = y;
        double r1878244 = r1878242 * r1878243;
        double r1878245 = 1.0;
        double r1878246 = r1878245 - r1878243;
        double r1878247 = r1878244 * r1878246;
        return r1878247;
}
↓
double f(double x, double y) {
        double r1878248 = x;
        double r1878249 = y;
        double r1878250 = r1878248 * r1878249;
        double r1878251 = 1.0;
        double r1878252 = r1878250 * r1878251;
        double r1878253 = -r1878249;
        double r1878254 = r1878250 * r1878253;
        double r1878255 = r1878252 + r1878254;
        return r1878255;
}

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 2019174 +o rules:numerics
(FPCore (x y)
  :name "Statistics.Distribution.Binomial:$cvariance from math-functions-0.1.5.2"
  (* (* x y) (- 1.0 y)))