Average Error: 0.0 → 0.0
Time: 2.2s
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 r7521013 = x;
        double r7521014 = y;
        double r7521015 = r7521013 * r7521014;
        double r7521016 = 2.0;
        double r7521017 = r7521015 / r7521016;
        return r7521017;
}
↓
double f(double x, double y) {
        double r7521018 = y;
        double r7521019 = 2.0;
        double r7521020 = r7521018 / r7521019;
        double r7521021 = x;
        double r7521022 = r7521020 * r7521021;
        return r7521022;
}

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 2019168 +o rules:numerics
(FPCore (x y)
  :name "Numeric.Interval.Internal:scale from intervals-0.7.1, B"
  (/ (* x y) 2.0))