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.
