Average Error: 0.0 → 0.0
Time: 4.7s
Precision: 64
\[\frac{x \cdot y}{2.0}\]
↓
\[\frac{y}{2.0} \cdot x\]
\frac{x \cdot y}{2.0}
↓
\frac{y}{2.0} \cdot x
double f(double x, double y) {
        double r3896821 = x;
        double r3896822 = y;
        double r3896823 = r3896821 * r3896822;
        double r3896824 = 2.0;
        double r3896825 = r3896823 / r3896824;
        return r3896825;
}
↓
double f(double x, double y) {
        double r3896826 = y;
        double r3896827 = 2.0;
        double r3896828 = r3896826 / r3896827;
        double r3896829 = x;
        double r3896830 = r3896828 * r3896829;
        return r3896830;
}

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

    \[\frac{x \cdot y}{2.0}\]
  2. Using strategy rm

  3. Applied *-un-lft-identity0.0

    \[\leadsto \frac{x \cdot y}{\color{blue}{1 \cdot 2.0}}\]

  4. Applied times-frac0.0

    \[\leadsto \color{blue}{\frac{x}{1} \cdot \frac{y}{2.0}}\]

  5. Simplified0.0

    \[\leadsto \color{blue}{x} \cdot \frac{y}{2.0}\]

  6. Final simplification0.0

    \[\leadsto \frac{y}{2.0} \cdot x\]

Reproduce

herbie shell --seed 2019163 +o rules:numerics
(FPCore (x y)
  :name "Numeric.Interval.Internal:scale from intervals-0.7.1, B"
  (/ (* x y) 2.0))