Average Error: 0.0 → 0
Time: 3.5s
Precision: 64
\[x + \frac{y - x}{2.0}\]
↓
\[\left(y + x\right) \cdot 0.5\]
x + \frac{y - x}{2.0}
↓
\left(y + x\right) \cdot 0.5
double f(double x, double y) {
        double r9686771 = x;
        double r9686772 = y;
        double r9686773 = r9686772 - r9686771;
        double r9686774 = 2.0;
        double r9686775 = r9686773 / r9686774;
        double r9686776 = r9686771 + r9686775;
        return r9686776;
}
↓
double f(double x, double y) {
        double r9686777 = y;
        double r9686778 = x;
        double r9686779 = r9686777 + r9686778;
        double r9686780 = 0.5;
        double r9686781 = r9686779 * r9686780;
        return r9686781;
}

Error

Bits error versus x

Bits error versus y

Try it out

Your Program's Arguments

Results

Enter valid numbers for all inputs

Target

Original0.0
Target0
Herbie0
\[0.5 \cdot \left(x + y\right)\]

Derivation

  1. Initial program 0.0

    \[x + \frac{y - x}{2.0}\]

  2. Taylor expanded around 0 0

    \[\leadsto \color{blue}{0.5 \cdot x + 0.5 \cdot y}\]

  3. Simplified0

    \[\leadsto \color{blue}{\left(x + y\right) \cdot 0.5}\]

  4. Final simplification0

    \[\leadsto \left(y + x\right) \cdot 0.5\]

Reproduce

herbie shell --seed 2019156 
(FPCore (x y)
  :name "Numeric.Interval.Internal:bisect from intervals-0.7.1, A"

  :herbie-target
  (* 0.5 (+ x y))

  (+ x (/ (- y x) 2.0)))