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Equation 17 · Part 5 · The Token Tax of Giving a Model More Tools

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T(n)≈τ0+nsˉT(n) \approx \tau_0 + n\bar{s}
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What this part means

Approximately equal to; the equality is not exact.

Its job in the formula

Approximately equal to; the equality is not exact.

The passage around this formula

Anthropic’s Tool Search Tool is a direct, documented implementation of that idea. The mechanism is described plainly: “You provide all your tool definitions to the API, but mark tools with deferlr_loading: true to make them discoverable on-demand,” with a lightweight search tool — built-in options include BM25-based and regex-based search — querying an index of names and descriptions, and the full definition of a matching tool injected into context only once the model actually requests it [ 5 ] . The search tool itself is not free, but its overhead is small and fixed rather than proportional to catalogue size: “Only the Tool Search Tool loaded upfront (~500 tokens)” [ 5 ] . Applied to the same…

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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 →

Sources cited in the surrounding passage

These citations provide research context; check each source for the exact claim it supports.