Average Error: 0.0 → 0
Time: 1.4s
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 r1209082 = x;
        double r1209083 = y;
        double r1209084 = r1209083 - r1209082;
        double r1209085 = 2.0;
        double r1209086 = r1209084 / r1209085;
        double r1209087 = r1209082 + r1209086;
        return r1209087;
}
↓
double f(double x, double y) {
        double r1209088 = 0.5;
        double r1209089 = x;
        double r1209090 = y;
        double r1209091 = r1209089 + r1209090;
        double r1209092 = r1209088 * r1209091;
        return r1209092;
}

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 2020047 
(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)))