The main source of time and memory issues is that you build the whole Collatz sequences, whereas for the task you only need their lengths, and unfortunately the laziness doesn't save the day. The simple solution calculating only lengths runs in a few seconds:
simpleCol :: Integer -> Int
simpleCol 1 = 1
simpleCol x | even x = 1 + simpleCol (x `quot` 2)
| otherwise = 1 + simpleCol (3 * x + 1)
problem14 = maximum $ map simpleCol [1 .. 999999]
It also takes much less memory and doesn't need enlarged stack:
$> ./simpleCollatz +RTS -s
simpleCollatz +RTS -s
2,517,321,124 bytes allocated in the heap
217,468 bytes copied during GC
41,860 bytes maximum residency (2 sample(s))
19,580 bytes maximum slop
1 MB total memory in use (0 MB lost due to fragmentation)
Tot time (elapsed) Avg pause Max pause
Gen 0 4804 colls, 0 par 0.00s 0.02s 0.0000s 0.0046s
Gen 1 2 colls, 0 par 0.00s 0.00s 0.0001s 0.0001s
INIT time 0.00s ( 0.00s elapsed)
MUT time 4.47s ( 4.49s elapsed)
GC time 0.00s ( 0.02s elapsed)
EXIT time 0.00s ( 0.00s elapsed)
Total time 4.47s ( 4.52s elapsed)
%GC time 0.0% (0.5% elapsed)
Alloc rate 563,316,615 bytes per MUT second
Productivity 100.0% of total user, 98.9% of total elapsed
To illustrate the proposed solution with caching, there is a nifty technique called memoization. Arguably the easiest way to use it is to install a memoize package:
import Data.Function.Memoize
memoCol :: Integer -> Int
memoCol = memoFix mc where
mc _ 1 = 1
mc f x | even x = 1 + f (x `quot` 2)
| otherwise = 1 + f (3 * x + 1)
This cuts down the both the runtime and memory usage, but also heavily uses GC in order to maintain cached values:
$> ./memoCollatz +RTS -s
memoCollatz +RTS -s
1,577,954,668 bytes allocated in the heap
1,056,591,780 bytes copied during GC
303,942,300 bytes maximum residency (12 sample(s))
341,468 bytes maximum slop
616 MB total memory in use (0 MB lost due to fragmentation)
Tot time (elapsed) Avg pause Max pause
Gen 0 3003 colls, 0 par 1.11s 1.19s 0.0004s 0.0010s
Gen 1 12 colls, 0 par 3.48s 3.65s 0.3043s 1.7065s
INIT time 0.00s ( 0.00s elapsed)
MUT time 7.55s ( 7.50s elapsed)
GC time 4.59s ( 4.84s elapsed)
EXIT time 0.00s ( 0.05s elapsed)
Total time 12.14s ( 12.39s elapsed)
%GC time 37.8% (39.1% elapsed)
Alloc rate 209,087,160 bytes per MUT second
Productivity 62.2% of total user, 60.9% of total elapsed
