1. load x into a register
2. spill the register holding x to the stack
3. call f
4. reload the "local" version of x from the stack
5. add
On the other hand, if the order of evaluation can be chosen by the compiler, it can do this:
1. call f
2. load x into a register
3. add
(Details depend on whether the caller or the callee saves x, but you get the idea.)
I think this is done early, during lowering to a "mid-end" intermediate representation (whether SSA or not). This is the best time to do it, since the legality of this reordering is a property of the source language, which you want to forget about in the mid-end. On the other hand, in this particular example (function call vs. global variable access), I don't think there is any reason to delay this; doing the call first should never be worse than loading the global first.
As for deciding other things later, instruction scheduling and global code motion can reorder a lot of things, though calls and memory accesses block many movements.