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Income Taxes (Narrative) (Details) € in Thousands, $ in Thousands |  | 1 Months Ended | 12 Months Ended
--- | --- | --- | ---
Dec. 28, 2012 EUR (€) | Jan. 31, 2019 EUR (€) | Dec. 31, 2018 EUR (€) | Dec. 31, 2013 EUR (€) | Jan. 31, 2012 EUR (€) | Dec. 31, 2018 USD ($) | Dec. 31, 2017 USD ($) | Dec. 31, 2016 USD ($)
Income Taxes [Line Items] |  |  |  |  |  |  |  |
Percentage of earnings from continuing operations before income taxes attributable to the United States |  |  |  |  |  | 37.00% |  |
Valuation allowance against deferred tax asset |  |  |  |  |  | $ 347,786 | $ 362,963 |
Increase (decrease) in the valuation allowance |  |  |  |  |  | (15,177) | 73,885 |
Net operating loss carryforwards and tax credit |  |  |  |  |  | 575,625 | 530,978 |
Net operating loss carryforwards in various foreign jurisdictions |  |  |  |  |  | 1,805,648 |  |
Repatriation transition tax expense |  |  |  |  |  | 133,366 | 105,165 |
Accumulated earnings |  |  |  |  |  | 1,936,000 |  |
TCJA net provisional tax expense |  |  |  |  |  |  | 45,249 |
Related transactions for repatriation transition tax expense |  |  |  |  |  |  | 46,191 |
TCJA revaluation of deferred tax assets and liabilities |  |  |  |  |  |  | 106,107 |
Provisional income tax expense (benefit) |  |  |  |  |  |  | 25,564 |
Transition tax for accumulated foreign earnings, provisional liability |  |  |  |  |  | 132,236 |  |
Gross unrecognized tax benefits |  |  |  |  |  | 1,330,713 | 65,631 | $ 46,434
Unrecognized tax benefits that would impact effective tax rate |  |  |  |  |  | 23,477 |  |
Interest and penalties |  |  |  |  |  | 7,184 | 8,252 |
Accrued/(reversed) interest and penalties |  |  |  |  |  | (1,085) | $ 165 | $ 2,170
Expected decrease in unrecognized tax benefits within next twelve months |  |  |  |  |  | 9,166 |  |
Luxembourg |  |  |  |  |  |  |  |
Income Taxes [Line Items] |  |  |  |  |  |  |  |
Net operating loss carryforwards in various foreign jurisdictions |  |  |  |  |  | $ 1,298,737 |  |
Domestic tax authority |  |  |  |  |  |  |  |
Income Taxes [Line Items] |  |  |  |  |  |  |  |
Effective income tax rate |  |  |  |  |  | 28.70% | 43.10% | 38.50%
Foreign tax authority |  |  |  |  |  |  |  |
Income Taxes [Line Items] |  |  |  |  |  |  |  |
Effective income tax rate |  |  |  |  |  | 11.00% | 3.20% | 10.80%
Foreign tax authority | Tax year 2008 | Belgium |  |  |  |  |  |  |  |
Income Taxes [Line Items] |  |  |  |  |  |  |  |
Foreign tax assessment | € |  |  |  |  | € 30,131 |  |  |
Foreign tax authority | Tax year 2005 | Belgium |  |  |  |  |  |  |  |
Income Taxes [Line Items] |  |  |  |  |  |  |  |
Foreign tax assessment | € |  |  |  | € 46,135 |  |  |  |
Foreign tax authority | Tax year 2009 | Belgium |  |  |  |  |  |  |  |
Income Taxes [Line Items] |  |  |  |  |  |  |  |
Foreign tax assessment | € | € 35,567 |  |  |  |  |  |  |
Foreign tax authority | Tax year 2006 | Belgium |  |  |  |  |  |  |  |
Income Taxes [Line Items] |  |  |  |  |  |  |  |
Foreign tax assessment | € |  |  |  | 38,817 |  |  |  |
Foreign tax authority | Tax year 2007 | Belgium |  |  |  |  |  |  |  |
Income Taxes [Line Items] |  |  |  |  |  |  |  |
Foreign tax assessment | € |  |  |  | 39,635 |  |  |  |
Foreign tax authority | Tax year 2010 | Belgium |  |  |  |  |  |  |  |
Income Taxes [Line Items] |  |  |  |  |  |  |  |
Foreign tax assessment | € |  |  |  | € 43,117 |  |  |  |
Foreign tax authority | Tax year 2011 | Belgium |  |  |  |  |  |  |  |
Income Taxes [Line Items] |  |  |  |  |  |  |  |
Foreign tax assessment | € |  |  | € 37,991 |  |  |  |  |
State |  |  |  |  |  |  |  |
Income Taxes [Line Items] |  |  |  |  |  |  |  |
Net operating loss carryforwards and tax credit |  |  |  |  |  | $ 68,714 |  |
Repatriation transition tax expense |  |  |  |  |  | 1,130 |  |
Foreign subsidiary and state net operating losses and tax credits |  |  |  |  |  |  |  |
Income Taxes [Line Items] |  |  |  |  |  |  |  |
Increase (decrease) in the valuation allowance |  |  |  |  |  | (15,357) | $ 36,792 |
State deferred tax assets |  |  |  |  |  |  |  |
Income Taxes [Line Items] |  |  |  |  |  |  |  |
Valuation allowance against deferred tax asset |  |  |  |  |  | 37,870 |  |
Operating loss carryforward, foreign jurisdiction |  |  |  |  |  |  |  |
Income Taxes [Line Items] |  |  |  |  |  |  |  |
Valuation allowance against deferred tax asset |  |  |  |  |  | $ 309,916 |  |
Subsequent Event | Foreign tax authority | Tax year 2012 | Belgium |  |  |  |  |  |  |  |
Income Taxes [Line Items] |  |  |  |  |  |  |  |
Foreign tax assessment | € |  | € 38,858 |  |  |  |  |  |
Subsequent Event | Foreign tax authority | Tax year 2013 | Belgium |  |  |  |  |  |  |  |
Income Taxes [Line Items] |  |  |  |  |  |  |  |
Foreign tax assessment | € |  | 11,108 |  |  |  |  |  |
Subsequent Event | Foreign tax authority | Tax year 2014 | Belgium |  |  |  |  |  |  |  |
Income Taxes [Line Items] |  |  |  |  |  |  |  |
Foreign tax assessment | € |  | 23,522 |  |  |  |  |  |
Subsequent Event | Foreign tax authority | Tax year 2015 | Belgium |  |  |  |  |  |  |  |
Income Taxes [Line Items] |  |  |  |  |  |  |  |
Foreign tax assessment | € |  | 30,610 |  |  |  |  |  |
Subsequent Event | Foreign tax authority | Tax year 2016 | Belgium |  |  |  |  |  |  |  |
Income Taxes [Line Items] |  |  |  |  |  |  |  |
Foreign tax assessment | € |  | 92,109 |  |  |  |  |  |
Subsequent Event | Foreign tax authority | Tax year 2017 | Belgium |  |  |  |  |  |  |  |
Income Taxes [Line Items] |  |  |  |  |  |  |  |
Foreign tax assessment | € |  | € 78,174 |  |  |  |  |  |

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