Equation 31 · Part 1 · The Token Tax of Giving a Model More Tools
Symbol bars
What this part means
the number of tokens.
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.
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Where the article explains it
A single request pays a fixed tool-use tax the moment any tool is attached, plus roughly tokens for every one of the n tools visible in that request, repeated on every turn because the underlying inference API carries no memory between calls.
The passage around this formula
Putting the pieces together gives a short, honest account of where a tool protocol’s overhead actually lives. A single request pays a fixed tool-use tax the moment any tool is attached, plus roughly tokens for every one of the n tools visible in that request, repeated on every turn because the underlying inference API carries no memory between calls. Lazy discovery — Anthropic’s Tool Search Tool, or a disciplined use of MCP’s own paginated listing — replaces the n in that formula with…
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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