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[Dieter]

(09-06-2017 09:45 PM)vanLudwig Wrote:  0.333283335000000 -> 0.333333335000000
2.302990159819040 -> 2.302585159819040

Then I changed from 10,000 iterations to 25,000 iterations. That improved the x^2 by two digits; it only improved the 1/x by half a digit.

0.333333335000000 -> 0.333333333600000
2.302585159819040 -> 2.302585103686040

So that's 25 000 iterations giving roughly 8–9 correct digits.

For the record: a standard Romberg implementation like the one in the WP34s requires merely 61 function calls for the x² integral or 511 calls for 1/x to return results with full 16-digit accuracy.

You really should switch to a better method. And virtually anything is better than rectangular or trapezoid.

Dieter