Consider a processor running at $4$ GHz and $1\mathrm{.}5$ Volts. It executes a program that finishes in $100$ seconds, while consuming $20$ W leakage power and $80$ W dynamic power. Let's call this the baseline.

I$\text{'}$m able to engage DFS to scale down the frequency $($and hence power$)$ of the processor. But this usually causes the program to consume more processor energy than the baseline. The only way my processor can consume less energy than the baseline is if the program is highly memory$-$bound.

The program is considered Y$\%$ memory$-$bound if Y$\%$ of the execution time in any baseline is spent accessing memory $--$ note that this portion of the execution time is unaffected by frequency scaling on the processor. Also note that this processor's dynamic power is uniform, i$.$e$.,$ it does not fluctuate up or down depending on whether the program is accessing memory or doing computations.

What is the minimum value of Y such that operating at a frequency of $2$ GHz causes the program to consume less processor energy than the baseline?