To save a compressed version of the logfile (suitable for attaching it to a
bugreport), use:
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-DISPLAY=:0 i3-dump-log | gzip -9c > /tmp/i3.log.gz
+DISPLAY=:0 i3-dump-log | bzip2 -c > /tmp/i3.log.bz2
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This command does not depend on i3 (it also works while i3 displays