command | tee >(grep rerun)
command | grep rerun

while pdflatex paper.tex | grep -E "rerun LaTeX|run Biber"; do
    biber paper
done

command | tee outfile | grep rerun

while pdflatex paper.tex | tee outfile | grep -E "rerun LaTeX|run Biber"; do

RERUN=1
while [[ $RERUN == 1 ]] ; do
  biber paper
  ! pdflatex paper.tex | tee output.txt && grep -E -q "rerun LaTeX|run Biber" output.txt
  RERUN=$?
done

Normally the exit status is 0 if a line is selected, 1 if no lines were
   selected, and 2 if an error occurred.  However, if the -q or --quiet or
   --silent is used and a line is selected, the exit status is 0  even  if
   an error occurred.