Haskell - simple way to cache a function call

I have functions like:

millionsOfCombinations = [[a, b, c, d] | 
  a <- filter (...some filter...) someListOfAs, 
  b <- (...some other filter...) someListOfBs, 
  c <- someListOfCs, d <- someListOfDs]

aLotOfCombinationsOfCombinations = [[comb1, comb2, comb3] | 
  comb1 <- millionsOfCombinations, 
  comb2 <- millionsOfCombinations,
  comb3 <- someList,
  ...around 10 function calls to find if
    [comb1, comb2, comb3] is actually useful]

Evaluating millionsOfCombinations takes 40s. on a very fast workstation. Evaluating aLotOfCombinationsOfCombinations!!0 took 2 days :-(

How can I speed up this code? So far I've had 2 ideas - use a profiler. Tried running myapp +RTS -sstderr after compiling with GHC, but get a blank screen and don't want to wait days for it to finish.

2nd thought was to somehow cache millionsOfCombinations. Do I understand correctly that for each value in aLotOfCombinationsOfCombinations, millionsOfCombinations gets evaluated multiple times? If that is so, how can I cache the result? Obviously I've just started learning Haskell. I know there is a way to do call caching with a monad, but I still don't understand those things.