Etar, you are funny person.
Yes, you just overestimate the rate. It is known that due to pollard kanagaroo method it is possible to perform less bruteforce operations. And roughly it is square root from the total length.
You just count the operations which are not actually performed. You use the method which is good due to birthday paradox. However, due to this methond you just need less operations.
So, your actual speed is not 2.2Ph/s but the square root from this amount, i.e. approx. 47 Mh/s in total.
You can write your vision of speed in example#2 in
https://bitcointalk.org/index.php?topic=5238719.msg54181362#msg54181362