I would just add that Mathematica-style term rewriting (e.g. analytical integration, or equation solving) is done with _semantics-preserving_ symbolic solvers, which are hand-made and human-reviewed to guarantee correctness.

LLM style pattern matching and rewriting does not preserve semantics, except accidentally due to an overwhelming amount of examples.

Trouble sneaks in when the pattern matching is only correct most of the time. Eg, if some code for regex-based search missed anywhere from 0.1% to 10% of matches, with the miss rate depending on the regex and no obvious way to know which regexes have worse miss rates, the utility of your regex-based search would be limited. LLMs are like this, but their generality makes them useful in spite of this limitation.