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In Solr I can use the query function query to return a numerical score for a query and I can user that in the context of a bf parameter something like bf=product(query('cat'),query('dog')) to multiply two relevance scores together.
Elasticsearch has search API that is generally more flexible to work with, but I can't figure out how I would accomplish the same feat. I can use _score in a script_function of a function_query but I can only user the _score of the main query. How can I incorporate the score of another query? How can I multiply the scores together?
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You can combine the queries using bool query. Based on your requirement you can use 'should' or 'must' inside the bool clauses. You may want to schearch for both the field you want, and then aggregate by the most important field.
Before scoring documents, Elasticsearch first reduces the set of candidate documents by applying a boolean test that only includes documents that match the query. A score is then calculated for each document in this set, and this score determines how the documents are ordered.
The _score in Elasticsearch is a way of determining how relevant a match is to the query. The default scoring function used by Elasticsearch is actually the default built in to Lucene which is what Elasticsearch runs under the hood.
The bool query is a go-to query because it allows you to construct an advanced query by chaining together several simple ones. The results must match the queries in this clause. If you have multiple queries, every single one must match. Acts as an and operator.
Alternately, if you've got something in that bf that's heavyweight enough you'd rather not run it across the entire set of matches, you could use rescore requests to modify the score of the top N ranked ORIGINAL QUERY results using subsequent scoring passes with your (cat, dog, etc...) scoring-queries.
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