Materialism predicts that algorithms have an "inside"?

Yes. The scene from within a formal system (like algebra) has certain qualities (equations, variables, functions, etc) that are different from the scene outside (markings on paper, equals sign, BEDMAS, variable names, brackets for function application).

That's not really a materialism thing, it's a math thing.

As a further note, I'll have to say that if all the blue and if the red in my visual experience were squitched around, my hunch tells me that I'd be experiencing something different; not just in the sense of different memory associations but that the visual experience itself would be different. It would not just be that "red" is associated with hot, and that "blue" is associated with cold... The qualia of the visual experience itself would be different.

Hence the part where they are compared to other qualia. Maybe that's not enough, but imagining getting "blue" or "sdfg66df" instead of "red" (which is the evidence you are using) is of course going to return "they are different" because they don't compare equal. Even if the output of the computation ends up being the same.