I generally intentionally avoid running the program in my head because that requires too much context: I prefer to think about the change I want to make and the minimal set of preconditions that make the change valid.

Running non-trivial code in your head is far too tedious for daily use. I'd much rather add debug checks for invariants when I want to confirm that the code works the way I expect it to.

The human brain has, what, about 7 registers in medium term memory?

5±3, if I remember right, but of indeterminate size. You can expand it to a couple dozen by moving up and down abstraction levels.

An exercise: I have 36 letters for you to memorize, in order and without mistakes: "The quick brown fox jumped over the lazy dog"

The sentence as a whole only uses 1 of those memory slots. As necessary, you can jump down one abstraction level to get 9 words, or again on a word-by-word basis to get the full 36 letters.

Code is the same. For example, use multiple slots to understand loop conditions, then file it away in a single slot as the whole conceptual loop. Use multiple slots to understand the loop body, in the context of one element; file it away as well. Combine them into a one-slot conceptual understanding of the whole loop. So on and so forth.

As you work with the conceptual models, you'll also end up with them in long-term memory and not have to do this reconstruction each time.

This pattern can continue indefinitely, with conceptual models of whole packages and systems. Most will do it unconsciously at that level as they become familiar with a codebase, but it works at every level, and is the basis of "running code in your head".

I don't always run the code in my head exactly - i do something more important, which is consider the set of possible situations the code can be in, and look for problems.