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Goodwill and Other Intangible Assets, Net | 9 Months Ended
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Sep. 30, 2024
Goodwill and Intangible Assets Disclosure [Abstract] |
Goodwill and Other Intangible Assets, Net | Goodwill and Other Intangible Assets, Net The carrying amount of goodwill was $51.7 million at both September 30, 2024 and December 31, 2023. The gross carrying amount, accumulated amortization and net book value of intangible assets at the end of each period were as follows:
| September 30, 2024 |  | December 31, 2023
(in millions) | Gross Carrying Amount |  | Accumulated Amortization |  | Net Book Value |  | Gross Carrying Amount |  | Accumulated Amortization |  | Net Book Value
Customer relationships | $ | 43.2 |  |  | $ | (32.9) |  |  | $ | 10.3 |  |  | $ | 43.2 |  |  | $ | (30.9) |  |  | $ | 12.3 |
Internal-use software | 51.0 |  |  | (15.1) |  |  | 35.9 |  |  | 43.1 |  |  | (13.9) |  |  | 29.2 |
Developed technology | 27.4 |  |  | (4.4) |  |  | 23.0 |  |  | 27.4 |  |  | (3.0) |  |  | 24.4 |
Patents | 36.2 |  |  | (5.8) |  |  | 30.4 |  |  | 36.2 |  |  | (3.4) |  |  | 32.8 |
Total intangible assets | $ | 157.8 |  |  | $ | (58.2) |  |  | $ | 99.6 |  |  | $ | 149.9 |  |  | $ | (51.2) |  |  | $ | 98.7 |
Amortization expense for intangible assets was $2.5 million and $2.6 million for the three months ended September 30, 2024 and 2023, respectively, and was $7.3 million and $7.7 million for the nine months ended September 30, 2024 and 2023, respectively.

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- Definition The entire disclosure for goodwill and intangible assets. + References Reference 1: http://www.xbrl.org/2009/role/commonPracticeRef -Topic 350 -SubTopic 30 -Name Accounting Standards Codification -Publisher FASB -URI https://asc.fasb.org/350-30/tableOfContent Reference 2: http://www.xbrl.org/2009/role/commonPracticeRef -Topic 350 -SubTopic 20 -Name Accounting Standards Codification -Publisher FASB -URI https://asc.fasb.org/350-20/tableOfContent + Details
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