Average Error: 0.0 → 0
Time: 3.5s
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 r363537 = x;
        double r363538 = y;
        double r363539 = r363538 - r363537;
        double r363540 = 2.0;
        double r363541 = r363539 / r363540;
        double r363542 = r363537 + r363541;
        return r363542;
}
↓
double f(double x, double y) {
        double r363543 = 0.5;
        double r363544 = x;
        double r363545 = y;
        double r363546 = r363544 + r363545;
        double r363547 = r363543 * r363546;
        return r363547;
}

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 2019198 
(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)))