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Equation 11 · Part 6 · Building Production RAG: An Advanced Technical Guide

multiplication

Ltotal≈Lretrieve+k⋅ℓrerank+Lgenerate,L_{\mathrm{total}} \approx L_{\mathrm{retrieve}} + k \cdot \ell_{\mathrm{rerank}} + L_{\mathrm{generate}},
multiplication

What this part means

Multiply the quantities on either side.

Its job in the formula

Multiply the quantities on either side.

The passage around this formula

The latency consequence follows from where the reranker sits in the request path. A simplified but useful model of end-to-end latency is Ltotal≈Lretrieve+k⋅ℓrerank+LgenerateL_{\mathrm{total}} \approx L_{\mathrm{retrieve}} + k \cdot \ell_{\mathrm{rerank}} + L_{\mathrm{generate}}. where k is the number of candidates handed to the reranker and ℓrerank\ell_{\mathrm{rerank}} is the marginal latency per candidate scored. Recall generally improves as k grows, because a larger candidate set is more likely to contain the passage that actually answers the query — but k multiplies the one latency term a team most directly controls, so it is not a value to leave at a copied default. It is a dial to be set from a measured recall-versus- k curve against an explicit latency budget, the same way the hybrid weight α\alpha is set from a…

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Learn the underlying idea

Multiplication scales one quantity by another. A dot, a cross, or adjacent symbols can indicate a product.

Open the illustrated multiplication: combining factors guide →

Sources cited in the article section

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