You will almost certainly find that the standard library functions have been optimised as much as they can, and they will probably outdo anything you code up in C.
Note that this is for the general case. If there is some restriction you're able to put on the functions, or some extra piece of information you have on the data itself, you may be able to get your code to run faster, since you have the advantage of that restriction or information.
For example, I've written C code for malloc
that blew a library-supplied malloc
away because I knew the application would never ask for more than 256 bytes so I just gave 256 bytes on every request. Yes, that was a waste of memory but it allowed speed improvements beyond the general case.
But, for the general case, you're better off sticking with the supplied stuff.