About a year ago I wrote a blog post (HN discussion: https://news.ycombinator.com/item?id=42584400) experimenting if asking Claude to "write code better" repeatedly would indeed cause it to write better code, determined by speed as better code implies more efficient algorithms. I found that it did indeed work (at n=5 iterations), but additionally providing a system prompt also explicitly improved it.
Given with what I've seen from Claude 4.5 Opus, I suspect the following test would be interesting: attempt to have Claude Code + Haiku/Sonnet/Opus implement and benchmark an algorithm with:
- no CLAUDE.md file
- a basic CLAUDE.md file
- an overly nuanced CLAUDE.md file
And then both test the algorithm speed and number of turns it takes to hit that algorithm speed.