Description : Haste potions increases unit's working efficiency ( it isn't displayed in number values though ), as well as quite likely increases unit's attack speed or damage. It also stacks with Work-A-Lot potions and Obey Spell ( all three can be used in combination, creating insane efficiency boosts, which is gamebreaking ).
Replication steps : The best way to see this is to use haste potion on units who are interacting with props, such as archive and alchemy lab. Simply drop it on unit or group of units and observe the results. You can also use it in combat and see the positive effect it is granting to your units.
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