Average Error: 0.0 → 0.0
Time: 2.6s
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 r103427 = x;
        double r103428 = y;
        double r103429 = r103427 * r103428;
        double r103430 = 2.0;
        double r103431 = r103429 / r103430;
        return r103431;
}
↓
double f(double x, double y) {
        double r103432 = x;
        double r103433 = y;
        double r103434 = 2.0;
        double r103435 = r103433 / r103434;
        double r103436 = r103432 * r103435;
        return r103436;
}

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 0.0

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

  3. Applied *-un-lft-identity0.0

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

  4. Applied times-frac0.0

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

  5. Simplified0.0

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

  6. Final simplification0.0

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

Reproduce

herbie shell --seed 2020042 +o rules:numerics
(FPCore (x y)
  :name "Numeric.Interval.Internal:scale from intervals-0.7.1, B"
  :precision binary64
  (/ (* x y) 2))