Average Error: 0.1 → 0.1
Time: 7.9s
Precision: 64
\[\left(x \cdot y\right) \cdot \left(1 - y\right)\]
↓
\[1 \cdot \left(x \cdot y\right) + \left(-y\right) \cdot \left(x \cdot y\right)\]
\left(x \cdot y\right) \cdot \left(1 - y\right)
↓
1 \cdot \left(x \cdot y\right) + \left(-y\right) \cdot \left(x \cdot y\right)
double f(double x, double y) {
        double r23212 = x;
        double r23213 = y;
        double r23214 = r23212 * r23213;
        double r23215 = 1.0;
        double r23216 = r23215 - r23213;
        double r23217 = r23214 * r23216;
        return r23217;
}
↓
double f(double x, double y) {
        double r23218 = 1.0;
        double r23219 = x;
        double r23220 = y;
        double r23221 = r23219 * r23220;
        double r23222 = r23218 * r23221;
        double r23223 = -r23220;
        double r23224 = r23223 * r23221;
        double r23225 = r23222 + r23224;
        return r23225;
}

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

    \[\leadsto \color{blue}{1 \cdot \left(x \cdot y\right)} + \left(x \cdot y\right) \cdot \left(-y\right)\]

  6. Simplified0.1

    \[\leadsto 1 \cdot \left(x \cdot y\right) + \color{blue}{\left(-y\right) \cdot \left(x \cdot y\right)}\]

  7. Final simplification0.1

    \[\leadsto 1 \cdot \left(x \cdot y\right) + \left(-y\right) \cdot \left(x \cdot y\right)\]

Reproduce

herbie shell --seed 2019305 
(FPCore (x y)
  :name "Statistics.Distribution.Binomial:$cvariance from math-functions-0.1.5.2"
  :precision binary64
  (* (* x y) (- 1 y)))