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Equation 1 · Part 11 · Building on Frontier Model APIs: Effort, Context, Caching, and Failure Handling

addition

creq=cin (tfresh+α tcached)+creason treason+cout tout,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}},
addition

What this part means

Add the term after the plus sign to the term or group before it.

Its job in the formula

Add the term after the plus sign to the term or group before it.

The passage around this formula

Write the per-request cost as three separate terms rather than one blended figure: creq=cin (tfresh+α tcached)+creason treason+cout toutc_{\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 α\alpha is the discount applied to cached prefix tokens. Three things become obvious the moment it is written this way.

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Learn the underlying idea

Addition combines quantities; subtraction measures the signed difference between them. Parentheses show what is combined before the rest of the expression is evaluated.

Open the illustrated addition and subtraction in an equation guide →

Sources cited in the article section

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