That would indeed be very neat. I think it's also impossible to do in a reasonable way, because how well a compiler does is probably dependent in a huge way on the particular program. There is a huge class of program transformations that are technically correct but far too specific to implement in a general-purpose compiler, and I think how well a compiler does is mostly dependent on how many of those transformations happen to apply to your program at hand.
For example: suppose you have a program that renders a 3D scene from a hardcoded scene description. A compiler might do a lot of stuff to that program, but what it will certainly not do is notice that the whole hardcoded scene can be replaced with a small representation in the form of a distance estimation function, if the rendering algorithm is also changed from raytracing to distance estimation.
A human in a demo scene situation will certainly perform (or at least try to perform) that transformation, if only because distance estimation is well known to often provide compact representations of certain, a priori very complex, scenes.
Also, nitpick:
> Clearly this problem is NP-complete as hell
I think it's almost certainly not even in NP; that would require a polynomial algorithm that, given some evidence that you can choose, proves that a particular program really is optimal. I think that's still impossible (but am gladly proven wrong). If I'm correct, it's not NP-complete, it's NP-hard.
For example: suppose you have a program that renders a 3D scene from a hardcoded scene description. A compiler might do a lot of stuff to that program, but what it will certainly not do is notice that the whole hardcoded scene can be replaced with a small representation in the form of a distance estimation function, if the rendering algorithm is also changed from raytracing to distance estimation.
A human in a demo scene situation will certainly perform (or at least try to perform) that transformation, if only because distance estimation is well known to often provide compact representations of certain, a priori very complex, scenes.
Also, nitpick:
> Clearly this problem is NP-complete as hell
I think it's almost certainly not even in NP; that would require a polynomial algorithm that, given some evidence that you can choose, proves that a particular program really is optimal. I think that's still impossible (but am gladly proven wrong). If I'm correct, it's not NP-complete, it's NP-hard.