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Income Taxes - Reconciliation of Liability for Uncertain Tax Positions (Detail) - USD ($) $ in Millions | 12 Months Ended
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Dec. 31, 2021 | Dec. 31, 2020 | Dec. 31, 2019
Reconciliation of Unrecognized Tax Benefits, Excluding Amounts Pertaining to Examined Tax Returns [Roll Forward] |  |  |
Balance at the beginning of the year | $ 100.7 | $ 109.1 | $ 119.3
Additions for tax positions related to the current year | 41.4 | 15.6 | 17.5
Additions for tax positions of prior years | 34.9 | 6.2 | 2.8
Reductions for tax positions of prior years | (1.5) | (0.3) | (1.3)
Reductions related to settlements with taxing authorities | (0.1) | (0.5) | (0.9)
Reductions due to statute expirations | (28.4) | (29.4) | (28.3)
Balance at the end of the year | $ 147.0 | $ 100.7 | $ 109.1

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- Definition A roll forward is a reconciliation of a concept from the beginning of a period to the end of a period. + References No definition available. + Details
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- Definition Amount of unrecognized tax benefits. + References Reference 1: http://www.xbrl.org/2003/role/disclosureRef -Publisher FASB -Name Accounting Standards Codification -Topic 740 -SubTopic 10 -Section 45 -Paragraph 10B -URI http://asc.fasb.org/extlink&oid=123427490&loc=SL37586934-109318 Reference 2: http://www.xbrl.org/2003/role/disclosureRef -Publisher FASB -Name Accounting Standards Codification -Topic 740 -SubTopic 10 -Section 50 -Paragraph 15A -Subparagraph (a) -URI http://asc.fasb.org/extlink&oid=121826272&loc=SL6600010-109319 + Details
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