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Equation 20 · Part 4 · The Token Tax of Giving a Model More Tools

Symbol bars

τ0+σ+msˉ\tau_0 + \sigma + m\bar{s}
sˉ\bar{s}

What this part means

bars 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

bars 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

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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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.

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Sources cited in the surrounding passage

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