Equation 22 · Part 4 · The Token Tax of Giving a Model More Tools
Symbol σ
What this part means
the search tool’s own fixed overhead.
Its job in the formula
σ occurs above the fraction bar. The numerator is divided by the entire denominator below it.
Full expression→Symbol σ→Article meaning
Where the article explains it
Applied to the same 58-tool, roughly 55,000-token example described above, that reframes the earlier formula: instead of the full T(n) + n , a session that only ever actually needs m of the n available tools pays approximately + + m , where is the search tool’s own fixed overhead.
The passage around this formula
…55,000-token example described above, that reframes the earlier formula: instead of the full T(n) + n , a session that only ever actually needs m of the n available tools pays approximately + + m , where is the search tool’s own fixed overhead. The fraction of the original tax avoided is . which grows toward its ceiling as m shrinks relative to n . Anthropic reports a measured outcome consistent with that shape at their own scale: “Tool Search…
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.
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Sources cited in the surrounding passage
These citations provide research context; check each source for the exact claim it supports.