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Equation 1 · The Hidden Infrastructure Bill Behind Every RAG Answer

What does this equation mean?

CRAG(Q)=pstore⋅S  +  Q⋅(pru⋅r(S)+prerank)C_{\mathrm{RAG}}(Q) = p_{\mathrm{store}} \cdot S \;+\; Q \cdot \left( p_{\mathrm{ru}} \cdot r(S) + p_{\mathrm{rerank}} \right)

Read the formula alongside the article passage below. Each part has a deeper page with its role in the equation, the supporting passage and nearby citations.

This equation states an equality: the expressions on both sides have the same value under the article’s assumptions. Read the equation part by part below; each part has a contextual explanation and a link to its mathematical background.

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CRAGC_{\mathrm{RAG}}

Symbol C_RAG

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

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QQ

Symbol Q

monthly query volume, and pstorep_{\mathrm{store}} , prup_{\mathrm{ru}}.

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pstorep_{\mathrm{store}}

Symbol p_store

psp_store is one of the signed contributions combined to compute the quantity on the left.

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SS

Symbol S

index size in gigabytes.

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prup_{\mathrm{ru}}

Symbol p_ru

prp_ru is one of the signed contributions combined to compute the quantity on the left.

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rr

Symbol r

r is one of the signed contributions combined to compute the quantity on the left.

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prerankp_{\mathrm{rerank}}

Symbol p_rerank

the published per-unit rates given earlier.

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=

=

The expressions on both sides represent the same quantity under the stated assumptions.

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multiplication

multiplication

Multiply the quantities on either side.

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addition

addition

Add the term after the plus sign to the term or group before it.

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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

Read it with the definitions, units, and assumptions supplied by the article.

What the article says around this equation

What the convergence does support is a real, worked comparison. Write the retrieval pipeline’s monthly cost, using the terms established above, as a fixed storage component plus a per-query component that itself has two parts: CRAG(Q)=pstore⋅S  +  Q⋅(pru⋅r(S)+prerank)C_{\mathrm{RAG}}(Q) = p_{\mathrm{store}} \cdot S \;+\; Q \cdot \left( p_{\mathrm{ru}} \cdot r(S) + p_{\mathrm{rerank}} \right). where S is index size in gigabytes, r(S) is Pinecone’s documented read units per query as a function of that size, Q is monthly query volume, and pstorep_{\mathrm{store}} , prup_{\mathrm{ru}} , and prerankp_{\mathrm{rerank}} are the published per-unit rates given earlier. Set against it, the cost of skipping retrieval and instead inlining a fixed block of extra context on every single call is

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Sources cited in the article section

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