Note that I didn't chose the worst case for grep. But probably not the best either. First thing I tried just now:

$ time grep -R "yoyo\|regexp" linux-3.10.6 > /dev/null real 0m2.138s user 0m1.875s sys 0m0.252s

$ time jrep -R "yoyo|regexp" linux-3.10.6 > /dev/null real 0m0.411s user 0m0.135s sys 0m0.270s