Equation 3 · Part 1 · Comparing Frontier Model Pricing Without Comparing Apples to Oranges

Symbol p^out_i

p^{\text{out}}_i

p^{\text{out}}_i

What this part means

$p^o$ u $t_i$ 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

$p^o$ u $t_i$ is a part of this expression. Its role is fixed by the surrounding article and by the operations shown in the formula.

Full expressionSymbol p^out_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; let $h_i$ be the fraction of…

Read this part in the article →

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 →

See this notation across published equations →

Sources cited in the article section

These citations provide research context; check each source for the exact claim it supports.