Here is another example of #40
#40 sqr(2^(bit-1))
python pollard-kangaroo-multi.py 40
//privkey = 1003651412950
#40 sqr(2^(bit-2))
python pollard-kangaroo-multi.py 8:3FFFFFFFFF 028dfd0e801ed8d495b6a0b68b38fba4f32d7423af363c717cca6c2ebd1e11a399
//privkey = 179017692118
Addfactor: 824633720832
//result1 = 1003651412950 true
824633720832 is just 0xC000000000
179017692118 is 0x29AE4933D6
1003651412950 is 0xE9AE4933D6
So 0xC000000000 is just the mid point of the normal #40 range 8000000000:FFFFFFFFFF
in other words the #40 sqr(2^(bit-2)) range you are mentioning is just the position of the private key from the mid-point.
You are not doing less work, you've just changed the origin.
Instead of working with the tame kangaroo matching the private key solution, you are working with the corresponding wild kangaroo.
In general terms, it could be explaind like this: for bit key the range is from 2^(bit-1) up to 2^(bit)-1, where the total number of combinations (range length) is 2^(bit-1).
2^(bit-2) is a half of 2^(bit-1), so 2^(bit-1) + 2^(bit-2) is 1.5 * 2^(bit-1) --> the absolute middle of the total range for the (bit) key.