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Equation 17 · Part 1 · The Token Tax of Giving a Model More Tools

Symbol T

T(n)≈τ0+nsˉT(n) \approx \tau_0 + n\bar{s}
TT

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.

The passage around this formula

…to catalogue size: “Only the Tool Search Tool loaded upfront (~500 tokens)” [ 5 ] . Applied to the same 58-tool, roughly 55,000-token example described above, that reframes the earlier formula: instead of the full T(n) ≈\approx τ0\tau_0 + nsˉ\bar{s} , a session that only ever actually needs m of the n available tools pays approximately τ0\tau_0 + σ\sigma + msˉ\bar{s} , where σ\sigma is the search tool’s own fixed overhead. The fraction of the original tax avoided is

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

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