A lot of effects in Pathfinder limit extra attacks. Haste states that it does not stack with similar effects.
Are many of the extra attacks granted by mythic powers similar effects? Examples would be the Champion base abilities that grant extra attacks and the 2nd tier ability of mythic initiative.
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The amazing initiative tier ability grants you an extra standard action, as I understand this does not prevent you from using your normal standard/move action as a full attack action, and grant you a hasted attack with that full attack. As it is only an extra standard action you could only make a single additional attack as an attack action (cleave or vital strike) and so would not benefit from haste, so you are only getting one hasted attack.
Like wise the champion abilities all grant you separate actions from your full attack to do a single attack. As none of them interrupt or interfere with your full attack action, they wouldn't appear to interact at all with haste, and not be subject to the haste limitations.
I can't quote RAW that says this isn't the case, but RAW also calls out those attacks as happening outside your normal action and so would seem to not interact.
Two things to look for in terms of extra attacks:
1) An ability that specifically says that it doesn't stack with Haste doesn't stack with Haste.
2) A magic item that grants an extra attack and lists Haste as one of its required spells most likely qualifies as a "similar effect".