I'll throw this out as something where it has saved literally weeks of work: debugging pathological behaviour in third-party code. Prompt example: "Today, when I did U, V, and W. I ended up with X happening. I fixed it by doing Y. The second time I tried, Z happened instead (which was the expected behaviour). Can you work out a plausible explanation for why X happened the first time and why Y fixed it? Please keep track of the specific lines of code where the behaviour difference shows up."

This is in a real-time stateful system, not a system where I'd necessarily expect the exact same thing to happen every time. I just wanted to understand why it behaved differently because there wasn't any obvious reason, to me, why it would.

The explanation it came back with was pretty wild. It essentially boiled down to a module not being adequately initialized before it was used the first time and then it maintained its state from then on out. The narrative touched a lot of code, and the source references it provided did an excellent job of walking me through the narrative. I independently validated the explanation using some telemetry data that the LLM didn't have access to. It was correct. This would have taken me a very long time to work out by hand.

Edit: I have done this multiple times and have been blown away each time.