Average Error: 0.0 → 0
Time: 3.8s
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 r36344 = x;
        double r36345 = y;
        double r36346 = r36345 - r36344;
        double r36347 = 2.0;
        double r36348 = r36346 / r36347;
        double r36349 = r36344 + r36348;
        return r36349;
}
↓
double f(double x, double y) {
        double r36350 = 0.5;
        double r36351 = x;
        double r36352 = y;
        double r36353 = r36351 + r36352;
        double r36354 = r36350 * r36353;
        return r36354;
}

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 2019310 
(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)))