Average Error: 0.0 → 0
Time: 8.6s
Precision: 64
\[x + \frac{y - x}{2}\]
↓
\[\left(x + y\right) \cdot 0.5\]
x + \frac{y - x}{2}
↓
\left(x + y\right) \cdot 0.5
double f(double x, double y) {
        double r22671869 = x;
        double r22671870 = y;
        double r22671871 = r22671870 - r22671869;
        double r22671872 = 2.0;
        double r22671873 = r22671871 / r22671872;
        double r22671874 = r22671869 + r22671873;
        return r22671874;
}
↓
double f(double x, double y) {
        double r22671875 = x;
        double r22671876 = y;
        double r22671877 = r22671875 + r22671876;
        double r22671878 = 0.5;
        double r22671879 = r22671877 * r22671878;
        return r22671879;
}

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

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

  4. Final simplification0

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

Reproduce

herbie shell --seed 2019169 
(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)))