Can I mark when there is a line break in inline math?

Question

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 \binoppenalty and \relpenalty are the badness contributors that matter. So can we log when these are used?

Answer 1

You didn't mention what constitutes "acceptable", in terms of line breaks inside inline math material. The best I can therefore suggest is that you choose a method for highlighting all inline math material with some lurid color. That way, any unfortunate line break will jump out at you immediately.

If it's mostly overfull lines you're concerned with, you could add the option draft to the \documentclass instruction. That way, a big fat "slug", i.e., a solid rectangle, will be inserted at the end of each overfull line.

\documentclass[draft]{article}
\usepackage[x11names]{xcolor}
\everymath{\color{DarkOrchid3}} % Is "DarkOrchid3 lurid enough?!
\begin{document}

Completely unimportant text 
$ABC_{1234} = ABC_{1234} + ABC_{1234} - ABCDEFGHI_{1234} \times ABC_{1234} - ABC_{1234} \times ABC_{1234} - ABC_{1234} + ABC_{1234} - ABC_{1234} + ABC_{1234} - ABC_{1234} + ABC_{1234} - ABC_{1234}$
Some more text.

Completely unimportant text 
$ABC_{1234} = ABC_{1234} + ABC_{1234} - ABC_{1234} + ABC_{1234} - ABC_{1234} + ABC_{1234} - ABC_{1234} + ABC_{1234}$
Some more unimportant text.
\end{document}

Answer 2

\documentclass{article}

\showoutput
\begin{document}


one two three four $1+2+3=3+2+1$ five six
one two three four $1+2+3=3+2+1$ five
one two three four $1+2+3=3+2+1$ five
one two three four $1+2+3=3+2+1$ five
one two three four $1+2+3=3+2+1$ five
one two three four $1+2+3=3+2+1$ five
one two three  $0+1+2+3+4=4+3+2+1+0=10=5\times(5-1)/2$ 
one two three four 
five six   seven  eight nine ten
\end{document}

Produces

so several inline math lists, two of which are broken over a line.

The log file lists lots of things but in particular it logs the start and end of every inline math (\mathon and \mathoff) and the end of every line (\rightskip). (Actually it does not log the start of math that starts a line as that node is discarded)

So we are only interested in lines that have those commands.

You can search for those with grep or any search tool, in this case

grep '\\mathon\|\\mathoff\|\\rightskip' file.log

produces

....\mathon
....\mathoff
....\mathon

....\glue(\rightskip) 0.0

....\mathoff
....\mathon
....\mathoff
....\glue(\rightskip) 0.0
....\mathoff
....\mathon
....\mathoff
....\glue(\rightskip) 0.0
....\mathon
....\mathoff
....\mathon

....\glue(\rightskip) 0.0

....\mathoff
....\glue(\rightskip) 0.0
....\glue(\rightskip) 0.0

So it is easy to see there are exactly two \rightskip appearing before \mathoff corresponding to two broken math lists.

Note that some \mathon have been discarded at line breaks which complicates a fully automatic test, but the information is basically there. alternatively if you know that binoppenalty and relpenalty are unique you just need to spot those before \rightskip so the two lines that end in a broken math list are both marked by

....\penalty 500
....\glue(\rightskip) 0.0

Here I just used grep and highlighted the rightskip in math by eye but you could find them automatically given a few lines of perl or python or lua or whatever.