Weapon speed makes no difference...it's normalized for that. 1 delay, 2 delay, 15 delay all will proc 2 times a minute. For the 1 delay, the percentage of procing on any given hit is lower.
Haste is not normalized. If you have 100% haste so are attacking twice as fast you will get 4 procs a minute. The percentages of proccing stay the same regardless of the amount of haste so more attacks at the same percent means more procs.
Worth noting, that spell haste isn't normalized, just like melee haste.
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Calaglin, Former Illusionist/Guild Leader of Dissolution on Nektulos
Calaglin, Former Illusionist/Guild Leader of Confirmed on Unrest
you have a 1.0s delay 1 hander vs a 9.0s delay bow. The bow ill proc more only because it hits at a rate that is way longer then the one hander. So even though the bow hits rarely it wont proc more , it has less chances to proc so it is all normalized.