Equation 25 · Part 2 · The Token Tax of Giving a Model More Tools
subscript
subscript
What this part means
The lower label selects a particular version, component, or indexed member of the quantity. For example, x₀ and xₜ can be values at different positions.
Its job in the formula
A subscript distinguishes a version, component, step, or member of a quantity. It does not automatically mean multiplication.
Full expression→subscript→Article meaning
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 a much smaller m , the tools actually retrieved, at the cost of a small fixed search overhead . Separately, and not reducible to a token count at all, the choice the model makes over…
Learn the underlying idea
A subscript is a label attached below a symbol. It often selects a time step, component, category, or member of a sequence.
Open the illustrated subscripts: which member of a family? guide →
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