Reverse Engineer — ruling 1

Equipment attached to a creature doesn't become tapped when that creature becomes tapped, and tapping that Equipment doesn't cause the creature to become tapped.

Reverse Engineer — ruling 2

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}.

Reverse Engineer — ruling 3

Improvise doesn't change a spell's mana cost or mana value.

Reverse Engineer — ruling 4

When calculating a spell's total cost, include any alternative costs, additional costs, or anything else that increases or reduces the cost to cast the spell. Improvise applies after the total cost is calculated.

Reverse Engineer — ruling 5

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

Reverse Engineer — ruling 6

Improvise can't be used to pay for anything other than the cost of casting the spell. For example, it can't be used during the resolution of an ability that says “Counter target spell unless its controller pays {3}.”

Reverse Engineer — ruling 7

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.

Reverse Engineer — ruling 8

Tapping an artifact won't cause its abilities to stop applying unless those abilities say so.

Reverse Engineer : règles, fonctionnement et interactions (MTG)

Reverse Engineer is one of those cards players keep asking about. Here is, in plain words, what its official text says, the rulings published by Wizards of the Coast, and the combos players actually run.

Official card text

Improvise (Your artifacts can help cast this spell. Each artifact you tap after you're done activating mana abilities pays for .) Draw three cards.

How it works : Reverse Engineer

Original English text — Wizards of the Coast / Scryfall

#1July 13, 2018· Wizards of the Coast
Equipment attached to a creature doesn't become tapped when that creature becomes tapped, and tapping that Equipment doesn't cause the creature to become tapped.
No other card is named in this ruling.
#2July 13, 2018· Wizards of the Coast
When using improvise to cast a spell with 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 . If you tap two artifacts, you'll have to pay .
No other card is named in this ruling.
#3July 13, 2018· Wizards of the Coast
Improvise doesn't change a spell's mana cost or mana value.
No other card is named in this ruling.
#4July 13, 2018· Wizards of the Coast
When calculating a spell's total cost, include any alternative costs, additional costs, or anything else that increases or reduces the cost to cast the spell. Improvise applies after the total cost is calculated.
No other card is named in this ruling.
#5July 13, 2018· Wizards of the Coast
Improvise can't pay for , , , , , or mana symbols in a spell's total cost.
No other card is named in this ruling.
#6July 13, 2018· Wizards of the Coast
Improvise can't be used to pay for anything other than the cost of casting the spell. For example, it can't be used during the resolution of an ability that says “Counter target spell unless its controller pays .”
No other card is named in this ruling.
#7July 13, 2018· Wizards of the Coast
If an artifact you control has a mana ability with 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.
No other card is named in this ruling.
#8July 13, 2018· Wizards of the Coast
Tapping an artifact won't cause its abilities to stop applying unless those abilities say so.
No other card is named in this ruling.