Return of the Four Fours

In an attempt to get faster results for the four fours problem mentioned earlier, I've come up with a simpler algorithm that does even more number crunching but somehow computes the precious list faster. Despite being sillier because it computes the same thing twice (or even worse), it'll use waaay less memory.
Oh, and since the algorithm encodes the solutions as stacks of operations, it'll print them accordingly (in reverse polish notation).

I want to see all three four five six seven ones twos threes fours fives sixes sevens eights nines tens

0 =  4 4 4 4 + - -
1 =  4 4 4 4 + - /
2 =  4 4 4 4 * * √ /
3 =  4 4 4 4 + + /
4 =  4 4 4 4 - * +
5 =  4 4 4 4 * + /
6 =  4 4 4 4 + - √ +
7 =  4 4 4 / 4 - +
8 =  4 4 4 4 + + -
9 =  4 4 4 4 / + +
10 =  4 4 4 4 * √ √ + +
12 =  4 4 4 4 * * √ +
14 =  4 4 4 4 √ + + +
15 =  4 4 / 4 4 * -
16 =  4 4 4 4 + + +
17 =  4 4 * 4 4 / +
18 =  4 4 4 4 √ / + *
20 =  4 4 4 4 * √ * +
22 =  4 4 4 * 4 √ + +
24 =  4 4 4 4 * + +
26 =  4 4 4 √ + * 4 √ +
28 =  4 4 4 4 + * -
32 =  4 4 4 4 * * √ *
34 =  4 4 4 + * 4 √ +
36 =  4 4 4 4 + * +
40 =  4 4 4 4 √ + + *
48 =  4 4 4 4 + + *
56 =  4 4 √ 4 4 * - *
60 =  4 4 4 4 * * -
64 =  4 4 4 4 * √ * *
66 =  4 4 4 * * 4 √ +
68 =  4 4 4 4 * * +
72 =  4 4 4 * 4 √ + *
80 =  4 4 4 4 * + *
96 =  4 4 4 4 √ + * *
128 =  4 4 4 4 + * *
256 =  4 4 4 4 * * *