Saheeli's Directive

Improvise can't pay for {W}, {U}, {B}, {R}, {G}, or {C} mana symbols in a spell's total cost.

When using improvise to cast a spell with {X} in its mana cost, first choose the value for X. That choice, plus any cost increases or decreases, will determine the spell's total cost. Then you can tap artifacts you control to help pay that cost. For example, if you cast Saheeli's Directive and choose X to be 3, the total cost is {3}{R}{R}{R}. If you tap two artifacts, you'll have to pay {1}{R}{R}{R}.

If an artifact you control has a mana ability with {T} in the cost, activating that ability while casting a spell with improvise will result in the artifact being tapped when you pay the spell's costs. You won't be able to tap it again for improvise. Similarly, if you sacrifice an artifact to activate a mana ability while casting a spell with improvise, that artifact won't be on the battlefield when you pay the spell's costs, so you won't be able to tap it for improvise.