Collatz Arithmetic

Is the Half Collatz Conjecture (HCC) trivial, as currently stated?

The definition: > H(n = 2k) = n and H(2k + 1) = 3k + 2

means that time to iterate H until its argument is even is exactly the length of the run of right-most 1 bits.

Collatz itself has the same property:

for some number that ends in ...11111, we can "accelerate" the process by directly calculating the odd branch 5 times directly.

I'm very interested in applying more advanced acceleration techniques to Collatz itself.