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Equation 1 · Part 8 · Building on Frontier Model APIs: Effort, Context, Caching, and Failure Handling

Symbol c_out

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}},
coutc_{\mathrm{out}}

What this part means

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

Its job in the formula

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

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 subscript is a label attached below a symbol. It often selects a time step, component, category, or member of a sequence.

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See this notation across published equations →

Sources cited in the article section

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