I have experience with GPT-4, and in particular I've used to for math questions in my work occasionally. I'm not sure how Bing chat compares.

For GTP-4, I've noticed the following:

1. How reliable the answer is depends on how easy or obscure the question is. It hasn't lied to me on easy or introductory material, but once your questions start becoming more obscure, and it's less likely to have the answer in the training set, it starts making things up.

• I think of it as search to an extent - it needs to have the answer in the training data to find it. Unlike google, it can usually find an answer even if you don't use the proper terms. But if it doesn't find an answer, it might make something up.
• "Easy or introductory" is relative - I have been able to get good answers for some masters-level math, and some wrong ones for lower-level things. Ultimately it depends on how much resources on the topic have been in the training set.

2. It's actually much more reliable in detecting errors than it's in generating text. So you can open a new chat and ask, "Is the following true: ..." and it will catch most of its own errors. Once it starts catching error, you should know you've left the reliable "easy questions" territory, and even if it can still be useful, exercise much more care.
3. The way you phrase a prompt matters a lot. For example, if you ask it to explain its reasoning step by step, it becomes much more accurate.
4. It is generally good in rephrasing questions to use better terminology.

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Bing chat might be different in some regards. I know that it automatically searches the web for sources, and when generating an answer, and bases its answer on the contents of the sources it found - but I don't have experience with it.

That said, asking for additional sources (besides the search results it found) shouldn't improve the accuracy. It might just give you something you can use to fact-check it.