Delve is a static ability that functions while the spell that has delve is on the stack. "Delve" means "As an additional cost to cast this spell, you may exile any number of cards from your graveyard. Each card exiled this way reduces the cost to cast this spell by {1}." Using the delve ability follows the rules for paying additional costs in rules 601.2b and 601.2e-g.

Delve is a static ability that functions while the spell with delve is on the stack. "Delve" means "For each generic mana in this spell's total cost, you may exile a card from your graveyard rather than pay that mana." The delve ability isn't an additional or alternative cost and applies only after the total cost of the spell with delve is determined.