A Haskell program: what you can get from 1, 2, 3, 4, +, -, *, /, and ^

I forget why I wrote this Haskell program, but it's cluttering up my do-something-with-this folder, so I’ll just publish it.

-- This program calculates all the ways to combine [1,2,3,4] using + - * / and ^
-- to produce *rational* numbers (i.e. no fractional exponents). (It could be so
-- extended given a data type for algebraic numbers (or by using floats instead
-- of exact rationals, but that would be boring).)
--
-- Written September 7, 2009.
-- Revised August 25, 2010 to show the expressions which produce the numbers.
-- Revised August 26, 2010 to use Data.List.permutations and a fold in combine.
-- 
-- In the unlikely event you actually wants to reuse this code, here's a license
-- statement:
-- Copyright 2009-2010 Kevin Reid, under the terms of the MIT X license
-- found at http://www.opensource.org/licenses/mit-license.html

( Code )

I'd include the output here, but that would spam several aggregators, so I'll just show some highlights. The results are listed in increasing numerical order, and only one of the expressions giving each distinct result is shown.

(1 - (2 ^ (3 ^ 4))) = -2417851639229258349412351
(1 - (2 ^ (4 ^ 3))) = -18446744073709551615
(1 - (3 ^ (2 ^ 4))) = -43046720
(1 - (4 ^ (3 ^ 2))) = -262143
(1 - (4 ^ (2 ^ 3))) = -65535
...all integers...
((1 - (2 ^ 4)) * 3) = -45
(((1 / 2) - 4) ^ 3) = -343/8
((1 - (3 ^ 4)) / 2) = -40
(1 - ((3 ^ 4) / 2)) = -79/2
(1 - ((3 ^ 2) * 4)) = -35
...various short fractions...
(1 / (2 - (3 ^ 4))) = -1/79
(((1 + 2) - 3) * 4) = 0
(1 / (2 ^ (3 ^ 4))) = 1/2417851639229258349412352
(2 ^ (1 - (3 ^ 4))) = 1/1208925819614629174706176
(1 / (2 ^ (4 ^ 3))) = 1/18446744073709551616
(2 ^ (1 - (4 ^ 3))) = 1/9223372036854775808
(2 ^ ((1 - 4) ^ 3)) = 1/134217728
...various short fractions...
(((3 ^ 2) + 1) ^ 4) = 10000      (the longest string of zeros produced)
...all integers...
(2 ^ (3 ^ (1 + 4))) = 14134776518227074636666380005943348126619871175004951664972849610340958208
(2 ^ ((1 + 3) ^ 4)) = 115792089237316195423570985008687907853269984665640564039457584007913129639936
Tried 23090 formulas, got 554 unique results.