Average Error: 0.0 → 0
Time: 3.5s
Precision: 64
\[x + \frac{y - x}{2}\]
↓
\[\left(y + x\right) \cdot 0.5\]
x + \frac{y - x}{2}
↓
\left(y + x\right) \cdot 0.5
double f(double x, double y) {
        double r341434 = x;
        double r341435 = y;
        double r341436 = r341435 - r341434;
        double r341437 = 2.0;
        double r341438 = r341436 / r341437;
        double r341439 = r341434 + r341438;
        return r341439;
}
↓
double f(double x, double y) {
        double r341440 = y;
        double r341441 = x;
        double r341442 = r341440 + r341441;
        double r341443 = 0.5;
        double r341444 = r341442 * r341443;
        return r341444;
}

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

    \[x + \frac{y - x}{2}\]

  2. Taylor expanded around 0 0

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

  3. Simplified0

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

  4. Final simplification0

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

Reproduce

herbie shell --seed 2019196 +o rules:numerics
(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)))