It is often said that one should re-declare (certain) Lua functions locally, as this reduces the overhead. But what is the exact rule / principle behind this? How do I know for which functions this should be done and for which it is superfluous? Or should it be done for EVERY function, even your own?
Unfortunately I can't figure it out from the Lua manual.
The principle is that every time you write table.insert for example, the Lua interpreter looks up the "insert" entry in the table called table. Actually, it means _ENV.table.insert - _ENV is where the "global variables" are in Lua 5.2+. Lua 5.1 has something similar but it's not called _ENV. The interpreter looks up the string "table" in _ENV and then looks up the string "insert" in that table. Two table lookups every time you call table.insert, before the function actually gets called.
But if you put it in a local variable then the interpreter gets the function directly from the local variable, which is faster. It still has to look it up, to fill in the local variable.
It is superfluous if you only call the function once within the scope of the local variable, but that is pretty rare. There is no reason to do it for functions which are already declared as local. It also makes the code harder to read, so typically you won't do it except when it actually matters (in code that runs a lot of times).