Do Karnaugh maps yield the simplest solution possible?

I'm learning to use a Karnaugh map, but I'm not sure if I obtained the simplest expression possible. Have a look at this example:

Truth table (inputs are A B C; output is F):

A   B   C   |   F
0   0   0   |   1
0   0   1   |   0
0   1   0   |   1
1   0   0   |   0
0   1   1   |   1
1   0   1   |   1
1   1   0   |   0
1   1   1   |   1

The Karnaugh map looks like this:

AB
--
C|

    00  01  11  10
    --------------
0|  (1  1)  0   (1)
1|  0   (1  1)  (1)

And this yields $\bar{C}\bar{A}+CB+A\bar{B}$. Is there any simpler way of choosing the 1s from the map and getting a simpler result? Are Karnaugh maps guaranteed to always yield the simplest result possible?

Karnaugh maps do not always give the simplest expression possible, but they do always give the simplest "Sum of Products" expression possible (https://web.archive.org/web/20190920201621/https://www.facstaff.bucknell.edu/mastascu/eLessonsHTML/Logic/Logic3.html).

StackExchange Computer Science Q#32462, answer score: 5