Average Error: 0.1 → 0
Time: 3.8s
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 r77433 = x;
        double r77434 = y;
        double r77435 = r77433 * r77434;
        double r77436 = 2.0;
        double r77437 = r77435 / r77436;
        return r77437;
}
↓
double f(double x, double y) {
        double r77438 = x;
        double r77439 = y;
        double r77440 = 2.0;
        double r77441 = r77439 / r77440;
        double r77442 = r77438 * r77441;
        return r77442;
}

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 +o rules:numerics
(FPCore (x y)
  :name "Numeric.Interval.Internal:scale from intervals-0.7.1, B"
  :precision binary64
  (/ (* x y) 2))