I think this is actually a perfect case of an impressive thing being done exactly by mimicry.
Why do LLMs still have trouble on floating point math without forking out to a tool, but they can perform symbolic manipulation just fine?
Because symbolic manipulation is just rote work and textual stepping through symbols. A side poster commented on the number of prior attempts on this problem which were close, but not quite.
Starting from a known "close" solution (which this did), and using exploration to search around the space is exactly something an LLM would and could be good at (clearly).
The "transformer LLMs are next-token predictors with some in-GPU processing of bounded complexity with respect to token count" remains undefeated. Both because that is mathematically what they are, and also because we don't have counterexamples to that effect that don't require some higher-order tooling wrapping the systems.
Why do LLMs still have trouble on floating point math without forking out to a tool, but they can perform symbolic manipulation just fine?
Because symbolic manipulation is just rote work and textual stepping through symbols. A side poster commented on the number of prior attempts on this problem which were close, but not quite.
Starting from a known "close" solution (which this did), and using exploration to search around the space is exactly something an LLM would and could be good at (clearly).
The "transformer LLMs are next-token predictors with some in-GPU processing of bounded complexity with respect to token count" remains undefeated. Both because that is mathematically what they are, and also because we don't have counterexamples to that effect that don't require some higher-order tooling wrapping the systems.
Symbol manipulation is what LLMs are good at.