REGEXP performance (compare with "LIKE" and "=")

I am using MySQL. I have asked a question about how to query in database for a single word match here.

• There is an answer which suggest me to use REGEXP '[[:<:]]word[[:>:]]'

  It is a good answer, however, I am not sure how is this REGEXP '[[:<:]]word[[:>:]]' thing from performance perspective? If I have a large table, is this way harm the performance of my application?

For example, compare with = operation, e.g. WHERE column_name='value', is the REGEXP operation far more slow than = for large table?

• There is another answer which suggested me to use LIKE, but I think it is not good from performance point of view.

  Then, I googled and found an article which says use LIKE is even faster than REGEXP . I get confused, which way I should use for a single word match query in a large table...

Can I say, = is the fastest operation, then LIKE , and REGEXP is the poorest one from performance perspective?