Average Error: 0.0 → 0
Time: 1.5s
Precision: binary64
\[x + \frac{y - x}{2}\]
↓
\[0.5 \cdot x + 0.5 \cdot y\]
x + \frac{y - x}{2}
↓
0.5 \cdot x + 0.5 \cdot y
(FPCore (x y) :precision binary64 (+ x (/ (- y x) 2.0)))
↓
(FPCore (x y) :precision binary64 (+ (* 0.5 x) (* 0.5 y)))
double code(double x, double y) {
	return x + ((y - x) / 2.0);
}
↓
double code(double x, double y) {
	return (0.5 * x) + (0.5 * y);
}

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. Final simplification0

    \[\leadsto 0.5 \cdot x + 0.5 \cdot y\]

Reproduce

herbie shell --seed 2021176 
(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) 2.0)))