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I recently started learning about floating point arithmetic and a how computers have limited precision when dealing with such calculations.

To what degree of accuracy can Wolfram alpha output computations?

I was hoping to check the accuracy of some calculations in C++ by comparing them to answers outputted by Wolfram Alpha.

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When requesting sqrt(2) with "more digits" Wolfram Alpha outputs

sqrt(2)

which far exceeds the accuracy of double-precision floating point variables (in which sqrt(2) is 1.4142135623730951).

WA is also smart about the organization of computation, preventing the loss of significant digits. For example, sqrt(10^100+1)-10^50 outputs a correct value, slightly less than 5e-51. Straightforward execution of the same computation is likely to return exactly 0.

So, the answer is yes: it is reasonable to check the accuracy of floating point computations using Wolfram Alpha.

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