Average Error: 0.0 → 0.0
Time: 1.5s
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 r139655 = x;
        double r139656 = y;
        double r139657 = r139655 * r139656;
        double r139658 = 2.0;
        double r139659 = r139657 / r139658;
        return r139659;
}
↓
double f(double x, double y) {
        double r139660 = x;
        double r139661 = y;
        double r139662 = 2.0;
        double r139663 = r139661 / r139662;
        double r139664 = r139660 * r139663;
        return r139664;
}

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 2020047 +o rules:numerics
(FPCore (x y)
  :name "Numeric.Interval.Internal:scale from intervals-0.7.1, B"
  :precision binary64
  (/ (* x y) 2))