Average Error: 0.0 → 0.0
Time: 3.4s
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 r14055738 = x;
        double r14055739 = y;
        double r14055740 = r14055738 * r14055739;
        double r14055741 = 2.0;
        double r14055742 = r14055740 / r14055741;
        return r14055742;
}
↓
double f(double x, double y) {
        double r14055743 = x;
        double r14055744 = y;
        double r14055745 = 2.0;
        double r14055746 = r14055744 / r14055745;
        double r14055747 = r14055743 * r14055746;
        return r14055747;
}

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 2019173 +o rules:numerics
(FPCore (x y)
  :name "Numeric.Interval.Internal:scale from intervals-0.7.1, B"
  (/ (* x y) 2.0))