Average Error: 0.0 → 0.0
Time: 2.1s
Precision: 64
\[\frac{x \cdot y}{2}\]
↓
\[\frac{y}{2} \cdot x\]
\frac{x \cdot y}{2}
↓
\frac{y}{2} \cdot x
double f(double x, double y) {
        double r5946479 = x;
        double r5946480 = y;
        double r5946481 = r5946479 * r5946480;
        double r5946482 = 2.0;
        double r5946483 = r5946481 / r5946482;
        return r5946483;
}
↓
double f(double x, double y) {
        double r5946484 = y;
        double r5946485 = 2.0;
        double r5946486 = r5946484 / r5946485;
        double r5946487 = x;
        double r5946488 = r5946486 * r5946487;
        return r5946488;
}

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

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

Reproduce

herbie shell --seed 2019174 +o rules:numerics
(FPCore (x y)
  :name "Numeric.Interval.Internal:scale from intervals-0.7.1, B"
  (/ (* x y) 2.0))