Equation 6 · Part 1 · The Token Tax of Giving a Model More Tools

Symbol T

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

T

What this part means

T is a part of this expression. Its role is fixed by the surrounding article and by the operations shown in the formula.

Its job in the formula

T is a part of this expression. Its role is fixed by the surrounding article and by the operations shown in the formula.

Full expressionSymbol TArticle 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 function assigns an output to each allowed input. The expression f(x) means “apply f to x”.

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Sources cited in the article section

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