I remember having a similar sort of realization early in my career when trying to implement some horribly convoluted business logic in SQL (I no longer remember the actual details of what I was trying to do, just the epiphany which resulted; I think it had something to do with proration of insurance premiums and commissions): I realized that if I simply pre-computed the value of the function in question and shoved it into a table (requiring "only" a couple million rows or so), then I could use a join in place of function application, and be done with it. An obvious idea in retrospect, but the sudden dredging of the set-theoretic formulation of functions--that they are simply collections of tuples--from deep within my memory was certainly startling at the time.

I've seen this as a "solution" to implementing a function for fibbonacci numbers. The array of all of the fibbonacci numbers that can fit into a 32-bit integer is not particularly large, so sticking it into a static local variable is easy to do.