IDT application note AN33 [IDT89] gives an expression for the average number of cycles per instruction in a RISC system as:

Cave = Pb(1 + b) + Pm(1 + m) + (1 ? Pb ? Pm) where:

pb = probability that an instruction is a branch
b = branch penalty
pm = probability that an instruction is a memory reference
m = memory reference penalty
Explain the validity of this expression. How do you think that it might be improved?

The first term, Pb(1 + b), is the probability of a branch multiplied by the total cost of a branch (i.e., 1 plus the
branch penalty). The second Pm(1 + m) term deals with memory accesses and is the probability of a memory
access multiplied by the total memory access cost. The final term, (1 ? Pb ? Pm), is what’s left over; that is not a
branch and not a memory access.

This formula is limited in the sense that it does not describe the difference between branches that are taken and
not taken and between cache accesses and not?cache accessed. However, its message is clear; reduce both
branches and memory accesses.