Math of Cache Hit Ratios

gistfile1.txt

The formulas to generate the relevant values of Cache Hit ratios (and sundry):

The variables:
1. % is the cache hit ratio
2. H is the raw number of cache hits
3. M is the raw number of cache misses
4. T is the total number of requests.

The formulas:
'''% = H / T'''
Cache hit ratio is the number of hits divided by the total number of requests

'''H = T * %'''
The number of hits is the total number of hits multiplied by the cache hit ratio (.05 for a 5% cache hit ratio)

'''M = T - H'''
Misses is the total number of requests - the number of hits

'''T = M + H'''
Total number of requests is the number of misses + the number of hits.

Some of the above are obvious.  But, what's interesting is that given the above formulas, some highschool algebra and time, 
you can solve for any of the four, given any two of the others:

Given % and T (fairly obvious):
'''M = T * (T * %)'''
'''H = T * %'''

Given % and H (fairly obvious):
'''T = H / %'''
'''M = (H / %) - H'''

Given % and M (these are slightly tricky):
'''H = (% * M) / ( 1 - %)'''
'''T = ( (% * M) / (1 - %) ) + M'''

Given H and M (these are givens):
'''% = H / (H + M)'''
'''T = H + M'''

Given H and T (these are givens as well):
'''% = H / T'''
'''M = T - H'''

Given M and T (straightforward):
'''% = (T - M) / T'''
'''H = T - M'''