$$c_{\mathrm{req}} = c_{\mathrm{in}}\,(t_{\mathrm{fresh}} + \alpha\, t_{\mathrm{cached}}) + c_{\mathrm{reason}}\, t_{\mathrm{reason}} + c_{\mathrm{out}}\, t_{\mathrm{out}}$$

Equation 1 · Foundation Models

Building on Frontier Model APIs: Effort, Context, Caching, and Failure Handling

This equation states an equality: the expressions on both sides have the same value under the article’s assumptions.

Write the per-request cost as three separate terms rather than one blended figure: $c_{\mathrm{req}} = c_{\mathrm{in}}\,(t_{\mathrm{fresh}} + \alpha\, t_{\mathrm{cached}}) + c_{\mathrm{reason}}\, t_{\mathrm{reason}} + c_{\mathrm{out}}\, t_{\mathrm{out}}$. where $\alpha$ is the discount applied to cached prefix tokens. Three things become obvious the moment it is written this way.

Meanings in this article

• $\alpha$: the discount applied to cached prefix tokens.

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