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Published equation contexts

τ0+σ+msˉ\tau_0 + \sigma + m\bar{s}

Why this formula appears here

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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τ0\tau_0

Symbol tau_0

tau0u_0 is a part of this expression. Its role is fixed by the surrounding article and by the operations shown in the formula.

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sˉ\bar{s}

Symbol bars

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

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Published contexts (1)

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τ0+σ+msˉ\tau_0 + \sigma + m\bar{s}

Equation 20 · AI Infrastructure

The Token Tax of Giving a Model More Tools

This mathematical expression combines the displayed quantities; its precise role follows from the surrounding article text.

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…

Meanings in this article

  • σ\sigma: the search tool’s own fixed overhead.
  • mm: the session that only ever actually needs.
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