Most problems in programming seems to be approximate on various levels, rather then analytic. Often, through decades of research or trail and error, we do stumble upon a very good solution, but given the general open-endedness of the problems programming aims to solve, the solution most probably is an approximate one, rather then analytic.
To define what "analytic" means, in my mind it should be a "proven" result, which means there's some fundamental truth to that solution, which makes it one of the or the only correct solution to that problem, for ever (there won't be, or rather can't be, a better solution).
By that above definition, a lot of people would hesitate to call any solution an analytic one, since most solutions in programming are slowly improved upon, and no solution feels like it's a fundamental truth about our reality (mostly cause the problem also seems very artificial, like "what's is the best data structure to store this data").
In the above paragraph, the artificiality that I mentioned could just be abstraction in disguise.