Average Error: 0.0 → 0.0
Time: 3.2s
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 r4362036 = x;
        double r4362037 = y;
        double r4362038 = r4362036 * r4362037;
        double r4362039 = 2.0;
        double r4362040 = r4362038 / r4362039;
        return r4362040;
}
↓
double f(double x, double y) {
        double r4362041 = y;
        double r4362042 = 2.0;
        double r4362043 = r4362041 / r4362042;
        double r4362044 = x;
        double r4362045 = r4362043 * r4362044;
        return r4362045;
}

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 2019171 
(FPCore (x y)
  :name "Numeric.Interval.Internal:scale from intervals-0.7.1, B"
  (/ (* x y) 2.0))