Is results. Report_id indexed? It's failing to find a key and doing a table scan it looks like.
I'm assuming results.id is actually the primary key.
I would use STRAIGHT_JOIN and go with your second query that has the patients_reports table first and secondarily join to the patient table for their name info. Additionally, if I didn't see it, was there an index on the patients_reports table by the PATIENT_ID column either by itself, or as first element of a compound index key?
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