Average Error: 0.1 → 0
Time: 4.5s
Precision: 64
\[\frac{x \cdot y}{2}\]
↓
\[x \cdot \frac{y}{2}\]
\frac{x \cdot y}{2}
↓
x \cdot \frac{y}{2}
double f(double x, double y) {
        double r71393 = x;
        double r71394 = y;
        double r71395 = r71393 * r71394;
        double r71396 = 2.0;
        double r71397 = r71395 / r71396;
        return r71397;
}
↓
double f(double x, double y) {
        double r71398 = x;
        double r71399 = y;
        double r71400 = 2.0;
        double r71401 = r71399 / r71400;
        double r71402 = r71398 * r71401;
        return r71402;
}

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

    \[\frac{x \cdot y}{2}\]
  2. Using strategy rm

  3. Applied *-un-lft-identity0.1

    \[\leadsto \frac{x \cdot y}{\color{blue}{1 \cdot 2}}\]

  4. Applied times-frac0

    \[\leadsto \color{blue}{\frac{x}{1} \cdot \frac{y}{2}}\]

  5. Simplified0

    \[\leadsto \color{blue}{x} \cdot \frac{y}{2}\]

  6. Final simplification0

    \[\leadsto x \cdot \frac{y}{2}\]

Reproduce

herbie shell --seed 2019325 
(FPCore (x y)
  :name "Numeric.Interval.Internal:scale from intervals-0.7.1, B"
  :precision binary64
  (/ (* x y) 2))