Sometimes a line break inside inline math is acceptable and sometimes it detracts from the message. I'd like to be able to see exactly where such breaks (meaning any line break during inline math mode) occur in my final-minus-epsilon draft and decide if any action should be taken to rearrange sentence wording, etc. (based on my manual inspection of the instance). I know there are automated ways to prevent line breaking in inline math, but I don't want to do that. The document is huge, so it's not OK to just manually look through it for such breaks.
Is there a way to mark where these things occur? Ideally by line number in the log. But also OK would be some sort of visual or searchable signal that stands out in the PDF, if somehow that is easier.
Added later: David Carlisle's answer to a related question points out that
\relpenalty are the badness contributors that matter. So can we log when these are used?