As noted, Metric ‘Recompiles Rate’ that appear for instance dimension in PI, is exactly the same as the metric Recompilations/sec the user sees in the SQL Instance Summary.
Compile/sec is not shown in PI, since compiles by themselves do not indicate a problem. High compile rate may indicate a problem only compared to the overall Batch Requests/sec.
There are many trivial conditions where amount of compile raises – such as a new application starting.