Average Error: 0.0 → 0
Time: 2.9s
Precision: 64
\[x + \frac{y - x}{2}\]
↓
\[0.5 \cdot \left(x + y\right)\]
x + \frac{y - x}{2}
↓
0.5 \cdot \left(x + y\right)
double f(double x, double y) {
        double r287090 = x;
        double r287091 = y;
        double r287092 = r287091 - r287090;
        double r287093 = 2.0;
        double r287094 = r287092 / r287093;
        double r287095 = r287090 + r287094;
        return r287095;
}
↓
double f(double x, double y) {
        double r287096 = 0.5;
        double r287097 = x;
        double r287098 = y;
        double r287099 = r287097 + r287098;
        double r287100 = r287096 * r287099;
        return r287100;
}

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

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

Reproduce

herbie shell --seed 2019303 +o rules:numerics
(FPCore (x y)
  :name "Numeric.Interval.Internal:bisect from intervals-0.7.1, A"
  :precision binary64

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

  (+ x (/ (- y x) 2)))