I have copied the latest version of Graeme Dennes’ Tanh-Sinh Quadrature spreadsheet to my download site:  Click here to download Tanh-Sinh.zip

As before, the download includes full open-source code, and detailed notes by Graeme.

In the new version the Gauss-Kronrod function has been modified to give similar precision to the Tanh-Sinh function.  The result is that on a like for like basis the Tanh-Sinh function now averages 40 times faster than the Gauss-Kronrod function, and in one case it is about 750 times faster!

The screen-shots below show the recalc times and cumulative errors for integration of 55 different functions, using the three different integration methods.  I recommend this spreadsheet to anyone looking for an efficient high precision numerical integration method.

Tanh-Sinh Function; click to view full size

Gauss-Kronrod Function

Romberg Function