Reply to Rainer,
2. Expression-level optimization is the compiler's job, not the programmer's.
Some (many?) of the interesting optimizations that can be applied to expressions with overloaded operators are not algebraic in nature.
Many of the use cases for operator overloading don't work if the compiler is allowed to assume all the same identities it can for scalars (e.g. the transitive identity doesn't hold for matrix math).
Unless you wan to make a way for the programmer to both add and remove expression level optimizations, and require an optimization engine powerful enough to use them, you can't do optimization of expressions with overloaded operators purely in the compiler.
