I’m trying to calculate the Effective Memory Access Time (EMAT) for a system described in the following problem:

Problem Setup

1. The system uses Intel Ice Lake Client micro-architecture with multiple TLBs.
2. Page size: 4 KiB.
3. TLB structure:
   • L1-D TLB: 64 entries, access time = 1 ns.
   • L2 TLB: 2048 entries, access time = 5 ns.
4. Parameters:
   • Memory access time (( Delta t_{mem} )) = 100 ns.
   • On a TLB miss, 4 additional memory accesses are required.
5. Hit rates:
   • L1-D TLB hit rate (( rho_{TLB,L1-D} )) = 30%.
   • L2 TLB hit rate (( rho_{TLB,L2} )) = 98%.

What to Calculate

The Effective Memory Access Time (EMAT), which combines the contributions of hits and misses across the two TLB levels and memory access.

My Attempt

1. EMAT Formula Setup:

   • If there’s an L1-D hit, EMAT is the L1-D access time.
   • If there’s an L1-D miss but an L2 hit, EMAT includes both TLB access times.
   • On a complete miss, include memory access time for additional loads.

   Formula:

   EMAT = (ρ_TLB,L1-D * Δt_TLB,L1-D) + 
          ((1 - ρ_TLB,L1-D) * (ρ_TLB,L2 * (Δt_TLB,L1-D + Δt_TLB,L2) + 
          (1 - ρ_TLB,L2) * (Δt_TLB,L1-D + Δt_TLB,L2 + 4 * Δt_mem)))
   

2. Plugging in Values:

   EMAT = (0.30 * 1) + 
          (0.70 * (0.98 * (1 + 5) + 
          0.02 * (1 + 5 + 4 * 100)))
   

3. Stuck on Simplification:
   I’m struggling to simplify this correctly and ensure the logic is accurate.

What I Need Help With

1. Is my formula for EMAT correct based on the problem setup?
2. How do I simplify the equation to get the final value?
3. Are there any mistakes in my interpretation of the hit/miss calculations?

Thanks in advance for your help!