The difference is accuracy, cost, time and more importantly consistency.
In case you noticed, a year ago, LLMs could not reliably count the number of 'R's in strawberry. Now they all do well. Guess how? Instead of training LLMs to do this, it was easier for them to write a small python script and run that. That solved the problem once and for all.
The same thing here, instead of just using LLMs and keep grilling repeatedly, there is a higher chance of getting a workable solution quickly. The best part about formal methods here is, it is self validating.
It checks in seconds, what would have taken hours or even days with LLM only flow.
The difference is accuracy, cost, time and more importantly consistency.
In case you noticed, a year ago, LLMs could not reliably count the number of 'R's in strawberry. Now they all do well. Guess how? Instead of training LLMs to do this, it was easier for them to write a small python script and run that. That solved the problem once and for all.
The same thing here, instead of just using LLMs and keep grilling repeatedly, there is a higher chance of getting a workable solution quickly. The best part about formal methods here is, it is self validating. It checks in seconds, what would have taken hours or even days with LLM only flow.