It isn't exactly common subexpressions. Basically the problem is things like matrix multiplies always get unrolled.

I've used lots of operator overloading based autodiff packages for C++. They are great, but the issue is not how the function is recorded (I used operator overloading myself in my python package) but how it gets executed at runtime. Unless a compiler (or JIT) is called sometime between when the operator overloading happens and execution happens, the function is basically being interpreted at runtime. This is what happens in, e.g. ADOL-C, SACADE, and CPPAD, all of which come with a significant (e.g. 20x) performance penalty as compared with hand-written derivatives.