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Is this a bug or calculation limitation? Regards  euler.sm (11kb) downloaded 10 time(s). Edited by user 01 April 2021 21:41:23(UTC)
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Hi overlord. It's a numerical round-off issue. For example you can get the same issue in excel, with more or less same values. round-off-error.pdf (205kb) downloaded 14 time(s).Some few notes: - You can estimate the error for floating point arithmetic. For that you can check almost any numerical methods undergraduate page or book. Also can check this article in the wikipedia: Loss of significance. - The primary way is just know the "exact" value and compare it the obtained. That's one big application of your code for the extended arithmetic. - One reason for use books like Numerical Recipes in C and similar is that one assume that the algorithms in the book are optimized for minimize those errors. For instance, in the order of the arithmetic. - This kind of errors make more pedagogical to study first numerical algorithms for integration and then derivatives, and sometimes the function evaluation. Here an example of the Numerical Recipes in C index  Best regards. Alvaro. Edited by user 02 April 2021 00:45:18(UTC)
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 1 user thanked Razonar for this useful post.
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Rank: Advanced Member Groups: Registered
Joined: 23/07/2013(UTC) Posts: 1,126 Was thanked: 507 time(s) in 338 post(s)
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Originally Posted by: Razonar  Hi overlord. It's a numerical round-off issue. For example you can get the same issue in excel, with more or less same values.
Best regards.
Alvaro. Thank you Alvaro, I had only checked this formula only with wolframalpha website. On it, there were no issues, everything was smooth. Then I tried it with SMath and get those results. After your post I calculated with Mathcad and Mathematica. Results are worse over them. Mathematica can not calculate after exp(7). On Mathcad results have same spike and they are settled on 1 after it. So this is basically a limitation. No need to investigate further. Best regards to you Razonar, Thanks again.
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