Average Error: 0.0 → 0
Time: 9.2s
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 r24157657 = x;
        double r24157658 = y;
        double r24157659 = r24157658 - r24157657;
        double r24157660 = 2.0;
        double r24157661 = r24157659 / r24157660;
        double r24157662 = r24157657 + r24157661;
        return r24157662;
}
↓
double f(double x, double y) {
        double r24157663 = x;
        double r24157664 = y;
        double r24157665 = r24157663 + r24157664;
        double r24157666 = 0.5;
        double r24157667 = r24157665 * r24157666;
        return r24157667;
}

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 2019170 
(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)))