Average Error: 0.0 → 0.0
Time: 2.5s
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 r104728 = x;
        double r104729 = y;
        double r104730 = r104728 * r104729;
        double r104731 = 2.0;
        double r104732 = r104730 / r104731;
        return r104732;
}
↓
double f(double x, double y) {
        double r104733 = x;
        double r104734 = y;
        double r104735 = 2.0;
        double r104736 = r104734 / r104735;
        double r104737 = r104733 * r104736;
        return r104737;
}

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