Suspiciously precise floats, or, how I got Claude's real limits

2 months ago

Claude's subscription plans offer better value than the API, with the 5× plan being the sweet spot.
The 20× plan provides only twice as much weekly usage as the 5× plan, despite the name suggesting more.
Cache reads are free on subscription plans, significantly increasing their value compared to the API.
Credits are used internally to track plan usage, with specific formulas converting tokens to credits for different models.
The author discovered exact usage limits by analyzing unrounded floats in Claude's API responses.
The Stern-Brocot tree was used to recover the simplest fractions from the unrounded floats, revealing the true limits.
The findings suggest that subscription plans offer up to 36.7× more value than the API, especially with warm caches.
The author developed a Chrome extension to monitor usage limits with full precision, leveraging the unrounded floats.

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