CONDENSED CONSLOIDATED STATEMENTS OF CHANGES IN STOCKHOLDERS' EQUITY (UNAUDITED) - USD ($) $ in Millions	Total	Ordinary Shares	Capital in Excess of Par Value of Ordinary Shares	Accumulated Deficit	Accumulated Other Comprehensive Income (Loss)	Non-controlling Interest
Beginning balance at Dec. 31, 2022	$ 3,276.7	$ 442.2	$ 9,109.7	$ (5,010.0)	$ (1,301.7)	$ 36.5
Increase (Decrease) in Stockholders' Equity [Roll Forward]
Net income	7.8			0.4		7.4
Other comprehensive income (loss)	11.6				13.6	(2.0)
Issuance of ordinary shares, net of shares withheld for tax	(14.6)	2.7	(17.3)
Share-based compensation	11.1		11.1
Shares repurchased and cancelled	(50.0)	(3.3)	(46.7)
Other	0.1			0.1
Ending balance at Mar. 31, 2023	3,242.7	441.6	9,056.8	(5,009.5)	(1,288.1)	41.9
Beginning balance at Dec. 31, 2023	3,172.1	432.9	8,938.9	(4,993.1)	(1,242.0)	35.4
Increase (Decrease) in Stockholders' Equity [Roll Forward]
Net income	160.9			157.1		3.8
Other comprehensive income (loss)	(84.7)				(84.8)	0.1
Issuance of ordinary shares, net of shares withheld for tax	(49.7)	4.3	(54.0)
Share-based compensation	18.5		18.5
Shares repurchased and cancelled	(150.1)	(6.3)	(129.0)	(14.8)
Dividends declared and paid	(21.7)			(21.7)
Other	(0.1)		(0.1)
Ending balance at Mar. 31, 2024	$ 3,045.2	$ 430.9	$ 8,774.3	$ (4,872.5)	$ (1,326.8)	$ 39.3