-- reformatted version of this post:
-- http://codereview.stackexchange.com/questions/128225/large-mysql-query-takes-about-15-seconds-to-execute/128234#128225
SELECT
    usr.first,
    usr.last,
    ivn.id,
    IFNULL(ivn.vendor, doc.unattached_vendor) AS vendor,
    IFNULL(ivn.originalskunumber, doc.skunumber) AS skunumber,
    doc.date_sent,
    doc.document_type,
    doc.document_id,
    doc.description,
    doc.qty,
    doc.triage_notes,
    doc.status,
    doc.arrival_date,
    doc.id AS document_row
FROM documents AS doc
    LEFT JOIN inventory AS ivn
        ON (CASE
            WHEN doc.document_type = 'Invoice'
                THEN ivn.skunumber = doc.skunumber
            WHEN doc.document_type = 'Purchase Order'
                THEN ivn.originalskunumber = doc.skunumber
        END)
    INNER JOIN users AS usr
        ON usr.uid = doc.customer_id
WHERE doc.document_type <> 'Quote'
    AND doc.header_item = '0'
    AND doc.active_document = '1'
    AND doc.active_item = '1'
    AND (CASE
        WHEN doc.document_type = 'Invoice' AND doc.skunumber IS NOT NULL
            THEN (doc.document_id, LEFT(doc.skunumber, 3)) NOT IN (
                SELECT
                    trailing_doc,
                    LPAD(vendor_code, 3, '0') AS vendor_code
                FROM documents
                WHERE active_document = '1'
                    AND active_item = '1'
                    AND trailing_doc IS NOT NULL
                    AND vendor_code IS NOT NULL
            )
        WHEN doc.document_type = 'Purchase Order'
            THEN 1
        ELSE 1
    END)
        AND (CASE
            WHEN doc.document_type = 'Invoice'
                THEN doc.document_id IN (
                    SELECT DISTINCT document_id
                    FROM payments
                    WHERE active_payment = '1'
                        AND payment_amount > 0
                )
            WHEN doc.document_type = 'Purchase Order'
                THEN 1
        END)
    AND (CASE
        WHEN ivn.id IS NULL AND document_id IN (
            SELECT DISTINCT trailing_doc
            FROM documents
            WHERE document_type = 'Purchase Order'
                AND active_document = '1'
                AND active_item = '1'
                AND trailing_doc > ''
        )
            THEN 0
        ELSE 1
    END)
GROUP BY doc.document_id, ivn.originalskunumber