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Equation 3 · The Token Tax of Giving a Model More Tools

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sis_i

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the number of tokens. Read the equation part by part below; each part has a contextual explanation and a link to its mathematical background.

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sis_i

Symbol s_i

the number of tokens.

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subscript

subscript

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.

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How to interpret it

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What the article says around this equation

Call this fixed, tool-independent charge τ0\tau_0 . On top of it sits the actual content of the catalogue: for n tools attached to a request, each with a schema costing sis_i tokens for its name, description, and JSON Schema of parameters, the tool-visibility component of a single request’s input is

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