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Equation 1 · Part 4 · Building on Frontier Model APIs: Effort, Context, Caching, and Failure Handling

Symbol α

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}},
α\alpha

What this part means

the discount applied to cached prefix tokens.

Its job in the formula

α is one of the signed contributions combined to compute the quantity on the left.

Where the article explains it

where α\alpha is the discount applied to cached prefix tokens.

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

A variable is a named place for a value. Its letter is a local label: x can mean position in one formula and a data point in another.

Open the illustrated variables: a letter stands for a value guide →

See this notation across published equations →

Sources cited in the article section

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