$score(q,d) = \sum_{t \in q} \frac{tf-idf(t,d)}{|d|}$
It's basically to simplify the query processing.

University of Michigan - Ann Arbor

$score(q,d) = \sum_{t \in q} \frac{tf-idf(t,q)}{\sqrt[2]{\sum_{q_i \in q} tf-idf^2(q_i,q)}} \cdot \frac{tf-idf(t,d)}{\sqrt[2]{\sum_{d_i \in d} tf-idf^2(d_i,d)}} $

TF-IDF Version Document Score

An on-going but a helpful book resource about NLP
https://web.stanford.edu/~jurafsky/slp3/

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