Equation 6 · Part 7 · The Token Tax of Giving a Model More Tools

subscript

T(n) \approx \tau_0 + n\bar{s}

subscript

What this part means

The lower label selects a particular version, component, or indexed member of the quantity. For example, x₀ and xₜ can be values at different positions.

Its job in the formula

A subscript distinguishes a version, component, step, or member of a quantity. It does not automatically mean multiplication.

Full expressionsubscriptArticle meaning

The passage around this formula

which, if schemas run at roughly a uniform average size $\bar{s}$ , simplifies to T(n) $\approx$ $\tau_0$ + n $\bar{s}$ . Nothing about this term depends on whether the model calls any tool at all; it is the price of the menu, not the price of the order. And critically, because a stateless inference API resends its full input on every request, T(n) is not paid once at the start of a session — it is paid again, in full, on every single turn for as long as tools remain attached to the request.

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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.

Open the illustrated subscripts: which member of a family? guide →

Sources cited in the article section

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