We've got your number [1, 1, 1, 1]

Calculated 14 numbers
1 = ((1 - 1) + (1 * 1))
2 = ((1 + 1) + (1 - 1))
3 = ((1 + 1) + (1 * 1))
4 = ((1 + 1) + (1 + 1))
5 = (((1 + 1) + 1)! - 1)
6 = (1 * (1 + (1 + 1))!)
7 = (1 + (1 + (1 + 1))!)
8 not calculable
9 = (((1  1) - 1) - 1)
10 = (((1  1) * 1) - 1)
11 = ((1 - 1) + (1  1))
12 = ((1 * 1) + (1  1))
13 = ((1 + 1) + (1  1))
14 not calculable
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21 not calculable
22 = ((1  1) + (1  1))
23 not calculable
24 = ((1 + 1) + (1 + 1))!
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I went through 5.6687e+07 expressions in 1673.1928 seconds, you slow, stupid human!