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1

I would do it this way. c = With[{a = 77617, b = 33096}, Map[ Rationalize, Hold[(333.75 - a^2)*b^6 + a^2*(11*a^2*b^2 - 121*b^4 - 2) + 5.5*b^8 + a/(2.0*b)], {-1}] // ReleaseHold] -(54767/66192) I think this is likely to be pretty close to the way Wolfram|Alpha does it. If you really want the result to 128 decimal places, you can now ...


2

In working with approximate numbers, it is important to ensure that no terms you introduce (e.g. 5.5 or 333.75) are lower precision than you need to work to. Wherever you have exact coefficients, it is good practice to specify these as rational to avoid this problem. The particular problem you have here is that the terms in b^6 and b^8 are almost equal in ...


2

I offer the following slightly modified version as a better illustration of the problem: Clear["Global`*"] guess = N[3/2, 300]; iter = 1000; n = Table[j, {j, 0, iter}]; y = Sin[4^n guess]^2; Grid[Transpose[{n, y}], Frame -> All] ListPlot[y] What see from the Grid is that at each iteration the number of residual digits of precision decreases - we have 2 ...



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