I learnt this the hard way (and said hello to a large living world of non-standard regex implementations). The GNU grep/egrep documentation page documents all their special backslash character support but
\d is not one of them.
That is, the following will not work when trying to match a numeric digit at the beginning of file (for example):
egrep '^\d' file.log
You need to use either of these two alternative forms instead:
egrep '^[:digit:]' file.log (OR,)
egrep '^[0-9]' file.log