Average Error: 0.0 → 0.0
Time: 1.4s
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 r1649531 = x;
        double r1649532 = y;
        double r1649533 = r1649531 * r1649532;
        double r1649534 = 2.0;
        double r1649535 = r1649533 / r1649534;
        return r1649535;
}
↓
double f(double x, double y) {
        double r1649536 = y;
        double r1649537 = 2.0;
        double r1649538 = r1649536 / r1649537;
        double r1649539 = x;
        double r1649540 = r1649538 * r1649539;
        return r1649540;
}

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 2019156 +o rules:numerics
(FPCore (x y)
  :name "Numeric.Interval.Internal:scale from intervals-0.7.1, B"
  (/ (* x y) 2.0))