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Income Taxes - Tax rate reconciliation (Details) | 6 Months Ended
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Jun. 30, 2024 | Jun. 30, 2023
Income Taxes |  |
Federal income tax expense (benefit) at statutory rate | 21.00% | (21.00%)
Effect of: |  |
GILTI provisions | 17.60% |
Tax effects of foreign operations | 7.10% | 3.80%
Change in valuation allowance | 6.40% | 51.30%
Increase in unrecognized tax benefits (ASC 740) | 5.50% | 2.60%
State income tax net of federal benefit | 0.80% | 0.40%
Foreign rate differential | (1.40%) | (1.50%)
Effect of stock-based compensation | (2.90%) | (22.70%)
Return to provision true up | (3.20%) | (0.60%)
Deemed interest | (5.20%) | (7.10%)
Foreign operations permanent differences - foreign exchange gains and losses | (7.90%) | 4.70%
Other | 4.20% | 6.20%
Effective tax rate | 42.00% | 16.10%
U.S. federal |  |
Income Taxes |  |
Federal income tax expense (benefit) at statutory rate | 21.00% |

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- Definition Percentage 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 changes in the valuation allowance for deferred tax assets. + References Reference 1: http://www.xbrl.org/2003/role/exampleRef -Topic 740 -SubTopic 10 -Name Accounting Standards Codification -Section 55 -Paragraph 231 -Publisher FASB -URI https://asc.fasb.org/1943274/2147482663/740-10-55-231 Reference 2: http://www.xbrl.org/2003/role/disclosureRef -Topic 740 -SubTopic 10 -Name Accounting Standards Codification -Section 50 -Paragraph 12A -Subparagraph (a)(6) -Publisher FASB -URI https://asc.fasb.org/1943274/2147482685/740-10-50-12A Reference 3: http://www.xbrl.org/2009/role/commonPracticeRef -Topic 740 -SubTopic 10 -Name Accounting Standards Codification -Section 50 -Paragraph 12 -Publisher FASB -URI https://asc.fasb.org/1943274/2147482685/740-10-50-12 Reference 4: http://www.xbrl.org/2009/role/commonPracticeRef -Topic 235 -SubTopic 10 -Name Accounting Standards Codification -Section S99 -Paragraph 1 -Subparagraph (SX 210.4-08(h)(2)) -Publisher FASB -URI https://asc.fasb.org/1943274/2147480678/235-10-S99-1 + Details
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