Has anybody run into an error in TurboTax's calculation of the tax liability?

I don't know what "the IRS's formula" is. There are seven different methods that can be used to calculate the tax on Form 1040 line 16, depending on what types of income you have and other things in your tax return. The IRS instructions for Form 1040 line 16 explain the conditions for determining which of the 7 methods you have to use, starting in the right column on page 33 of the 2024 Instructions for Form 1040.

In TurboTax there is a Tax Smart Worksheet that has 7 checkboxes that show you which method TurboTax used. In the CD/Download TurboTax software you can see the Tax Smart Worksheet in forms mode. It's between lines 15 and 16 in the first section of the Form 1040 or Form 1040-SR Worksheet.

 

If you are using desktop software,

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mentioned above how to look at the Tax Smart Worksheet.   On the other hand, if you are using Online TurboTax, here's how to view the Tax Smart Worksheet mentioned above which shows what method(s) TurboTax is using to calculate your tax.

 

• In Online TurboTax open your return interview, and in the left menu column scroll down to TAX TOOLS, then subtab TOOLS.  
• In the Tools window choose View Tax Summary.
• While on the Tax Summary screen go to left menu column and under Federal tab choose "Preview My 1040".
• This opens up the Form 1040 Worksheet and Schedules 1-3.
• On the Form 1040 Worksheet scroll down to between lines 15 and 16, and there should be a Tax Smart Worksheet that shows what method(s) TurboTax used to figure your tax.