Average Error: 0.0 → 0.0
Time: 6.2s
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 r5259502 = x;
        double r5259503 = y;
        double r5259504 = r5259502 * r5259503;
        double r5259505 = 2.0;
        double r5259506 = r5259504 / r5259505;
        return r5259506;
}
↓
double f(double x, double y) {
        double r5259507 = y;
        double r5259508 = 2.0;
        double r5259509 = r5259507 / r5259508;
        double r5259510 = x;
        double r5259511 = r5259509 * r5259510;
        return r5259511;
}

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