I agree these are central components, but to avoid oversimplification and the mistaken belief that modern LLMs do a lot of search during inference: If it was so simple, the traditional computer algebra systems would have reached similar breakthroughs when deployed at large supercomputer centers. This didnt happen because the search space is huge. You definitely also need a fancy learning algorithm. Although these ingredients would suffice (depending on what the learning algorithm is), you probably also want to learn in the absense of a strong verifier at every step, to allow building a fuzzy/erratic sense of the search space that can lead to planning/intuition and allow distant jumps in a targetted direction.

The search space is far too large for a mere order of magnitude to make any difference at all.