Equation 10 · Part 1 · Comparing Frontier Model Pricing Without Comparing Apples to Oranges

Symbol C_i

C_i \;=\; \kappa_i\Big[(1-h_i)\,p^{\text{in}}_i + h_i\, p^{\text{in}}_i\,\gamma_i\Big] \;+\; \rho_i\, p^{\text{out}}_i .

C_i

What this part means

$C_i$ is part of the quantity the equation computes from the expression on the right.

Its job in the formula

$C_i$ is part of the quantity the equation computes from the expression on the right.

Full expressionSymbol C_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 input served from cache and $\gamma_i$ the cache-read multiplier; and let $\rho_i$ be the ratio of total output tokens generated, visible answer plus hidden reasoning, to the visible answer alone. A workload’s realised cost per completed task…

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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.

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Sources cited in the article section

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