Average Error: 0.0 → 0.0
Time: 526.0ms
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 r112983 = x;
        double r112984 = y;
        double r112985 = r112983 * r112984;
        double r112986 = 2.0;
        double r112987 = r112985 / r112986;
        return r112987;
}
↓
double f(double x, double y) {
        double r112988 = x;
        double r112989 = y;
        double r112990 = 2.0;
        double r112991 = r112989 / r112990;
        double r112992 = r112988 * r112991;
        return r112992;
}

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 2019347 +o rules:numerics
(FPCore (x y)
  :name "Numeric.Interval.Internal:scale from intervals-0.7.1, B"
  :precision binary64
  (/ (* x y) 2))