You don't need to repeat the verb. You can, but you don't have to - and they don't. That's part of what makes this one hard.

to X <in the same way as> to Y.

First, the "to X" and "to Y" parts are parallel, as they should be, because they are the two things being compared.

Second, this is an example of an elliptical construction, in which we can infer the missing meaning:

Formulas do not apply to X in the same way as (they do) to Y.

The fact that we have a comparison ("in the same way as") and the necessary parts are properly parallel allows us to make the inference.

An elliptical construction lacks some word (or words) that are nevertheless easily able to be inferred. See this if you're interested in more detail: https://en.wikipedia.org/wiki/Elliptical_clause