 We evaluate P-FOO on several production traces, where results show that recent caching systems are  still far from optimal  .
<meaning-changed>  We evaluate P-FOO on several production traces, where results show that recent caching systems are  still far from optimal  .
 We therefore extend FOO to obtain more efficient bounds on OPT, which we call practical flow-based offline optimal (PFOO). We evaluate PFOO on several full production traces and use it to compare OPT to prior online policies. This analysis shows that current caching systems are still far from optimal .