Freejam Regent — ruling 1

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

Freejam Regent — ruling 2

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.

Freejam Regent — ruling 3

Because improvise isn't an alternative cost, it can be used in conjunction with alternative costs.

Freejam Regent — ruling 4

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

Freejam Regent — ruling 5

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}."

Freejam Regent — ruling 6

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.

Freejam Regent — ruling 7

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

Freejam Regent — ruling 8

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.

Freejam Regent : règles, fonctionnement et interactions (MTG)

Freejam Regent 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 .) Flying : This creature gets +2/+0 until end of turn.

How it works : Freejam Regent

Original English text — Wizards of the Coast / Scryfall

#1February 9, 2017· Wizards of the Coast
Improvise doesn't change a spell's mana cost or mana value.
No other card is named in this ruling.
#2February 9, 2017· 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.
#3February 9, 2017· Wizards of the Coast
Because improvise isn't an alternative cost, it can be used in conjunction with alternative costs.
No other card is named in this ruling.
#4February 9, 2017· 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.
#5February 9, 2017· 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.
#6February 9, 2017· 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.
#7February 9, 2017· 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.
#8February 9, 2017· 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.