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Income taxes - Reconciliation of the Provision for Income Taxes (Details) - USD ($) $ in Millions | 12 Months Ended
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Dec. 31, 2018 | Dec. 31, 2017 | Dec. 31, 2016
Income Tax Disclosure [Abstract] |  |  |
United States statutory income tax provision (benefit) | $ 30.1 | $ (25.2) | $ 7.2
Income and losses for which no provision or benefit has been recognized | 22.2 | 70.3 | 65.5
Foreign rate differential and other foreign tax expense | 9.5 | (11.3) | (21.1)
Income tax withholdings | 19.3 | 16.8 | 22.8
Permanent items | (5.0) | (3.0) | (4.7)
Enacted rate changes | (2.3) | (0.4) | 3.5
Change in uncertain tax positions | (1.2) | 2.3 | 0.4
Change in valuation allowances due to changes in judgment | (5.9) | (4.6) | (16.4)
Income tax credits, U.S. | (2.4) | (50.4) | 0.0
Provision (benefit) for income taxes | $ 64.3 | $ (5.5) | $ 57.2

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- Definition Amount of current income tax expense (benefit) and deferred income tax expense (benefit) pertaining to continuing operations. + References Reference 1: http://www.xbrl.org/2003/role/disclosureRef -Publisher FASB -Name Accounting Standards Codification -Topic 280 -SubTopic 10 -Section 50 -Paragraph 22 -Subparagraph (h) -URI http://asc.fasb.org/extlink&oid=115929826&loc=d3e8736-108599 Reference 2: http://www.xbrl.org/2003/role/disclosureRef -Publisher FASB -Name Accounting Standards Codification -Topic 235 -SubTopic 10 -Section S99 -Paragraph 1 -Subparagraph (SX 210.4-08(h)) -URI http://asc.fasb.org/extlink&oid=26873400&loc=d3e23780-122690 Reference 3: http://www.xbrl.org/2003/role/disclosureRef -Publisher FASB -Name Accounting Standards Codification -Topic 740 -SubTopic 20 -Section 45 -Paragraph 2 -Subparagraph (a) -URI http://asc.fasb.org/extlink&oid=109238882&loc=d3e38679-109324 + Details
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- Definition Amount of the difference between reported income tax expense (benefit) and expected income tax expense (benefit) computed by applying the domestic federal statutory income tax rates to pretax income (loss) from continuing operations attributable to increase (decrease) in income tax contingencies. Including, but not limited to, domestic tax contingency, foreign tax contingency, state and local tax contingency, and other contingencies. + References Reference 1: http://fasb.org/us-gaap/role/ref/legacyRef -Publisher FASB -Name Accounting Standards Codification -Topic 740 -SubTopic 10 -Section 50 -Paragraph 12 -URI http://asc.fasb.org/extlink&oid=84230637&loc=d3e32687-109319 Reference 2: http://fasb.org/us-gaap/role/ref/legacyRef -Publisher FASB -Name Accounting Standards Codification -Topic 740 -SubTopic 10 -Section 50 -Paragraph 13 -URI http://asc.fasb.org/extlink&oid=84230637&loc=d3e32698-109319 + Details
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- Definition Amount of the difference between reported income tax expense (benefit) and expected income tax expense (benefit) computed by applying the domestic federal statutory income tax rates to pretax income (loss) from continuing operations attributable to tax credits. Including, but not limited to, research credit, foreign tax credit, investment tax credit, and other tax credits. + References Reference 1: http://fasb.org/us-gaap/role/ref/legacyRef -Publisher FASB -Name Accounting Standards Codification -Topic 740 -SubTopic 10 -Section 50 -Paragraph 12 -URI http://asc.fasb.org/extlink&oid=84230637&loc=d3e32687-109319 Reference 2: http://fasb.org/us-gaap/role/ref/legacyRef -Publisher FASB -Name Accounting Standards Codification -Topic 740 -SubTopic 10 -Section 50 -Paragraph 13 -URI http://asc.fasb.org/extlink&oid=84230637&loc=d3e32698-109319 + Details
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