The complexity here lies in having to craft a comprehensive enough spec. Correctness is one aspect, but another is performance. If the AI craps out code that passes your tests, but does it in really inefficient way then it's still a problem.

Also worth noting that you don't actually need AI to do such things. For example, Barliman is a tool that can do program synthesis. Given a set of tests to pass, it attempts to complete the program for you. Synthesis is performed using logic programming. Not only is it capable of generating code, but it can also reuse code it's already come up with as basis for solving bigger problems.

https://github.com/webyrd/Barliman

here's a talk about how it works https://www.youtube.com/watch?v=er_lLvkklsk