Consider the following two similar-looking queries:

db.coll.find({a: {$eq: "constant"}})

db.coll.find({$expr: {$eq: ["$a", "constant"]}})

The queries are quite similar in meaning (though not identical) and both can use an index on {a: 1}. Therefore, you might expect that in both cases the "constant" gets auto-parameterized. However, this is not the case in the current implementation of auto-parameterization for the SBE plan cache. The constant in the first query will get auto-parameterized, but the constant beneath the $expr will not. In fact, we never auto-parameterize anything inside a $expr at the moment.

One place where this can come up is if the $lookup join predicate is expressed using $expr. As an example, consider this $lookup used in TPC-H query 18:

db.getSiblingDB('tpch').orders.aggregate([
    {
        "$lookup": {
            "from": "lineitem",
            "let": {"o_orderkey": "$o_orderkey"},
            "as": "lineitem",
            "pipeline": [
                {"$match": {"$expr": {"$eq": ["$$o_orderkey", "$l_orderkey"]}}},
                {"$group": {"_id": "$l_orderkey", "sum(l_quantity)": {"$sum": "$l_quantity"}}},
                {"$match": {"$expr": {"$gt": ["$sum(l_quantity)", 300]}}},
                {"$project": {"_id": 0, "o_orderkey": "$_id", "sum(l_quantity)": 1}}
            ]
        }
    },
    ...
]);

For every document from the scan of the orders collection, a query is internally composed against the lineitems collection. This query will include the equality predicate "o_orderkey == l_orderkey", expressed using $expr. Each such query will have a different constant substituted for "o_orderkey", and therefore without auto-parameterization of $expr will result in a different plan cache key. Note that this behavior will go away once we implement SERVER-69103, which will prevent SBE from being used on the inner side of a DocumentSourceLookup.

In order to constrain the scope of this improvement, I imagine it we would only implement it for simple equalities and inequalities expressed using $expr. I believe it will require work to make sure that the plans generated by sbe_stage_builder_expression.cpp refer to runtime environment slots that can be rebound rather than inlining constants into the plan.