c++ - Can different optimization levels lead to functionally different code?

Question

I am curious about the liberties that a compiler has when optimizing. Let's limit this question to GCC and C/C++ (any version, any flavour of standard):

Is it possible to write code which behaves differently depending on which optimization level it was compiled with?

The example I have in mind is printing different bits of text in various constructors in C++ and getting a difference depending on whether copies are elided (though I've not been able to make such a thing work).

Counting clock cycles is not permitted. If you have an example for a non-GCC compiler, I'd be curious, too, but I can't check it. Bonus points for an example in C. :-)

Edit: The example code should be standard compliant and not contain undefined behaviour from the outset.

Edit 2: Got some great answers already! Let me up the stakes a bit: The code must constitute a well-formed program and be standards-compliant, and it must compile to correct, deterministic programs in every optimization level. (That excludes things like race-conditions in ill-formed multithreaded code.) Also I appreciate that floating point rounding may be affected, but let's discount that.

I just hit 800 reputation, so I think I shall blow 50 reputation as bounty on the first complete example to conform to (the spirit) of those conditions; 25 if it involves abusing strict aliasing. (Subject to someone showing me how to send bounty to someone else.)

Answer 1

The portion of the C++ standard that applies is §1.9 "Program execution". It reads, in part:

conforming implementations are required to emulate (only) the observable behavior of the abstract machine as explained below. ...

A conforming implementation executing a well-formed program shall produce the same observable behavior as one of the possible execution sequences of the corresponding instance of the abstract machine with the same program and the same input. ...

The observable behavior of the abstract machine is its sequence of reads and writes to volatile data and calls to library I/O functions. ...

So, yes, code may behave differently at different optimization levels, but (assuming that all levels produce a conforming compiler), but they cannot behave observably differently.

EDIT: Allow me to correct my conclusion: Yes, code may behave differently at different optimization levels as long as each behavior is observably identical to one of the behaviors of the standard's abstract machine.