Is HMM Smoothing more computationally complex than HMM filtering?

Question

Given a sequence of observations $y_1, y_2, \dots, y_n$, of some lates sequence of Markovian states $x_1, x_2, \dots, x_n$:

HMM filtering computes $p(x_k|y_1,\dots,y_k) \\$

HMM smoothing computes $p(x_k|y_1,\dots,y_n). \\$

HMM filtering uses the forward algorithm and HMM smoothing uses forward-backward algorithm (https://en.wikipedia.org/wiki/Hidden_Markov_model#Filtering). Is forward-backward algorithm more complex than forward algorithm? What are the complexities?