← All parts of this equation

Equation 2 · Part 3 · Astra's 63%-Cheaper Claim Has to Beat a Price Disadvantage Nobody Mentions

multiplication

(1−s)×10+s×r(1-s) \times 10 + s \times r
multiplication

What this part means

Multiply the quantities on either side.

Its job in the formula

Multiply the quantities on either side.

The passage around this formula

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) ×\times 10 + s ×\times 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:

Read this part in the article →

Learn the underlying idea

Multiplication scales one quantity by another. A dot, a cross, or adjacent symbols can indicate a product.

Open the illustrated multiplication: combining factors guide →

The article lists its research sources here.