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A comment on Differentiable programming from scratch. Parent comment

Re:Differentiable programming from scratch by bmitc on Monday August 01, 2022 @09:37PM (#32314271)
But as far as I know, there is no corresponding dual analysis. The dual numbers do not form a field.

The issue primarily revolves around elementary functions, compositions of them, and polynomials.

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Re:Differentiable programming from scratch by ithinkso on Monday August 01, 2022 @10:42PM (#32314610)
Yeah, I was only trying to explain where the issue (assuming smooth=analytic, that you rightfully pointed out) might have come from
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Re:Differentiable programming from scratch by bmitc on Monday August 01, 2022 @10:55PM (#32314665)
Ahh, gotcha. I'm trying to figure this out myself. I've always been intrigued by automatic differentiation but have never been satisfied by any article addressing its mathematical justification.
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Re:Differentiable programming from scratch by data_maan on Tuesday August 02, 2022 @04:20AM (#32316284)
Neither have I ...
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