hree different processors P$1,$ P$2,$ P$3$ executing the same set of instructions. P$1$ has a $3$ GHz clock rate and a CPI of $1\mathrm{.}5.$ P$2$ has $2$ GHz clock rate and CPI of $1\mathrm{.}2.$ P$3$ has $4$ GHz and CPI of $2\mathrm{.}4.$

$[5$ pts$]$ A new generation of these processors have been announced by the vendors of each processor and due to microarchitecture innovations, each decreases its CPI by $25\%($CPI$\_$new$=$CPI$\_$old $/1\mathrm{.}25),$ however due to the added complexity, each processor decreases it frequency by a percentage $\%$ according to the inverse of $2$X of the old CPI $($Clock Freqnew $=$ Clock Freqold $/(1+1/(2\backslash$times CPI$\_$old$))$ which processor has the best performance and which is worst now for this new generation of processors?