Average Error: 0.0 → 0.0
Time: 2.6s
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 r5734169 = x;
        double r5734170 = y;
        double r5734171 = r5734169 * r5734170;
        double r5734172 = 2.0;
        double r5734173 = r5734171 / r5734172;
        return r5734173;
}
↓
double f(double x, double y) {
        double r5734174 = y;
        double r5734175 = 2.0;
        double r5734176 = r5734174 / r5734175;
        double r5734177 = x;
        double r5734178 = r5734176 * r5734177;
        return r5734178;
}

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))