Mine: x/(100 - (y + x))
Yours: (100 - y)/(100 - z)
where x is "added haste", y is "old haste" and z is "new haste".
Note also by this definition that z = x + y.
My answer is output in the form 0.~ and yours is output in the form 1.~: neither are mathematically correct on their own but we can obviously deduce the actual % from them. In order to make the answers consistent, I am going to add 1 to mine.
Mine: x/(100 - (y + x)) + 1
Yours: (100 - y)/(100 - z)
Immediately we can see that y + x = z, therefore:
Mine: x/(100 - z) + 1
Let's eliminate the x. x + y = z, so z - y = x.
Mine: (z - y)/(100 - z) + 1
Converting 1 to a fraction,
Mine: (z - y)/(100 - z) + (100 - z)/(100 - z)
Adding:
Mine: (z - y + 100 - z)/(100 - z)
Mine: (-y + 100)/(100 - z)
Mine: (100 - y)/(100 - z)
Yours: (100 - y)/(100 - z)
Hurrah :D