Equation 23 · Part 1 · The Token Tax of Giving a Model More Tools
Symbol m
What this part means
the session that only ever actually needs.
Its job in the formula
m is a part of this expression. Its role is fixed by the surrounding article and by the operations shown in the formula.
Full expression→Symbol m→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
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 Tool preserves 191,300 tokens of context compared to 122,800 with Claude’s traditional approach,” described as an “85% reduction in token usage while maintaining access to your…
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.