[FEATURE] Update token counting example to include function calling feature

[bakkot]

The new function calling API is neat, but there's no docs anywhere I can find which tell you how many tokens your functions will cost. Can you update the sample notebook to account for provided functions?

[ted-at-openai]

Agree it would be a nice feature. Not sure if I'll have time soon, unfortunately.

[bakkot]

If you can give a rough description of how it works I can try to put together a PR following that description, if that would be useful.

[lopuhin]

After some testing it looks close to the token count of json-encoded function definition, but would be great to know the official answer, to make it possible to adjust the input text so that it fits within the context.

[adri1wald]

@lopuhin is that json-encoded without any indentation? I.e. json.dumps(value) as opposed to e.g. json.dumps(value, indent=2)

[lopuhin]

@adri1wald yes I meant just json.dumps(value)

[ju-bezdek]

FYI @CGamesPlay did great job reverse engeneering it here

[ifsheldon]

+1. Also waiting for an official implementation.

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