Symbol T
T is part of the quantity the equation computes from the expression on the right.
Read this term in its guide →Published equation contexts
Why this formula appears here
Call this fixed, tool-independent charge . On top of it sits the actual content of the catalogue: for n tools attached to a request, each with a schema costing tokens for its name, description, and JSON Schema of parameters, the tool-visibility component of a single request’s input is . which, if schemas run at roughly a uniform average size , simplifies to T(n) + n . Nothing about this term depends on whether the model calls any tool at all; it is the price of the menu, not the price of the order. And critically, because a stateless inference API resends its full input on every request, T(n) is not paid once at the start of a…
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Symbol n
n appears in the bound of this sum. The bound states where the repeated operation starts, ends, or which values it includes.
Read this term in its guide →Symbol i
i appears in the bound of this sum. The bound states where the repeated operation starts, ends, or which values it includes.
Read this term in its guide →Starting index or lower bound: i=1
This label says where the repeated addition, multiplication, or accumulation starts. Read its value or condition together with the article’s description of the index.
Read this term in its guide →Ending index or upper bound: n
This label says where the repeated addition, multiplication, or accumulation stops. It sets the last term or end of the range.
Read this term in its guide →How to interpret it
Read it with the definitions, units, and assumptions supplied by the article.
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Published contexts (1)
A symbol can carry a different meaning in another article. Each occurrence keeps its own guide and term definitions.
Equation 4 · AI Infrastructure
The Token Tax of Giving a Model More Tools
This equation states an equality: the expressions on both sides have the same value under the article’s assumptions.
Call this fixed, tool-independent charge . On top of it sits the actual content of the catalogue: for n tools attached to a request, each with a schema costing tokens for its name, description, and JSON Schema of parameters, the tool-visibility component of a single request’s input is . which, if schemas run at roughly a uniform average size , simplifies to T(n) + n . Nothing about this term depends on whether the model calls any tool at all; it is the price of the menu, not the price of the order. And critically, because a stateless inference API resends its full input on every request, T(n) is not paid once at the start of a…