Equation 3 · Astra's 63%-Cheaper Claim Has to Beat a Price Disadvantage Nobody Mentions
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Read the formula alongside the article passage below. Each part has a deeper page with its role in the equation, the supporting passage and nearby citations.
each model’s cache-read rate: 1. Read the equation part by part below; each part has a contextual explanation and a link to its mathematical background.
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What the article says around this equation
Call the cache-hit share s — the fraction of input tokens that are cache reads rather than fresh reads. The blended input-token cost per model, in dollars per million tokens, is (1-s) 10 + s r , where r is each model’s cache-read rate: $1.00 for Astra, $0.25 for Fable 5.1. The ratio of Astra’s blended input cost to Fable 5.1’s, at a given cache-hit share, is:
For background, read the article’s source list.
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