The $count stage works on both collections and views, but always gives an exact count. The $collStats stage can produce a faster, estimated count, but it only works on a collection. $collStats also returns other information that might not be relevant or easy to define for a view.

Let's introduce a new stage which:

• like $count, can run anywhere in a pipeline, on a collection or view.
• like $collStats, can provide a fast estimated count.
• lets the user decide whether to allow falling back to a slower, exact count.

Syntax could be something like:

{$approxCount: {
    as: <string>,
    errorWhenNoApproximation: <default to true>,
}}

Implementation notes:

• This would be a new subclass of DocumentSource.
• getNext() can do whatever $collStats does to get the estimated count.
• optimizeAt() can eliminate stages that preserve count. [$project, $approxCount] becomes just [$approxCount].
• If an estimated count is not possible, and allowExact is true, then during optimization it can expand to the same $group stage that $count expands to. Then other optimizations may apply to the $group.
• On a sharded collection, $approxCount can run partially on the shards and partially on the merger. Each shard can run its own $approxCount, and the merger can $group $sum the results.