Equation 5 · Part 1 · Comparing Frontier Model Pricing Without Comparing Apples to Oranges

Symbol i

i

i

What this part means

i is a part of this expression. Its role is fixed by the surrounding article and by the operations shown in the formula.

Its job in the formula

i is a part of this expression. Its role is fixed by the surrounding article and by the operations shown in the formula.

Full expressionSymbol iArticle meaning

The passage around this formula

Collecting every distinction above into one expression makes explicit what a bare price comparison assumes without saying so. For vendor i , let $p^{\text{in}}_i$ and $p^{\text{out}}_i$ be the published input and output rates; let $\kappa_i$ be a tokenizer expansion factor, the number of tokens vendor i ’s own tokenizer needs to encode one fixed reference passage, normalised so $\kappa_i$ = 1 for whichever vendor is used as the baseline;…

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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 article section

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