Average Error: 0.0 → 0
Time: 13.6s
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 r20866626 = x;
        double r20866627 = y;
        double r20866628 = r20866627 - r20866626;
        double r20866629 = 2.0;
        double r20866630 = r20866628 / r20866629;
        double r20866631 = r20866626 + r20866630;
        return r20866631;
}
↓
double f(double x, double y) {
        double r20866632 = x;
        double r20866633 = y;
        double r20866634 = r20866632 + r20866633;
        double r20866635 = 0.5;
        double r20866636 = r20866634 * r20866635;
        return r20866636;
}

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

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

Reproduce

herbie shell --seed 2019200 
(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)))