Average Error: 0.0 → 0.0
Time: 2.7s
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 r5013934 = x;
        double r5013935 = y;
        double r5013936 = r5013934 * r5013935;
        double r5013937 = 2.0;
        double r5013938 = r5013936 / r5013937;
        return r5013938;
}
↓
double f(double x, double y) {
        double r5013939 = y;
        double r5013940 = 2.0;
        double r5013941 = r5013939 / r5013940;
        double r5013942 = x;
        double r5013943 = r5013941 * r5013942;
        return r5013943;
}

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 2019170 +o rules:numerics
(FPCore (x y)
  :name "Numeric.Interval.Internal:scale from intervals-0.7.1, B"
  (/ (* x y) 2.0))