Just a wild guess, but did you check exactly which operations are actually done to high precision? Obviously you will need high-resolution representations of pi and e to get an improved result.
B. On Jul 2, 2015, at 10:28 AM, Ravi Varadhan <ravi.varad...@jhu.edu> wrote: > Hi, > > Ramanujan supposedly discovered that the number, 163, has this interesting > property that exp(sqrt(163)*pi), which is obviously a transcendental number, > is real close to an integer (close to 10^(-12)). > > If I compute this using the Wolfram alpha engine, I get: > 262537412640768743.99999999999925007259719818568887935385... > > When I do this in R 3.1.1 (64-bit windows), I get: > 262537412640768256.0000 > > The absolute error between the exact and R's value is 488, with a relative > error of about 1.9x10^(-15). > > In order to replicate Wolfram Alpha, I tried doing this in "Rmfpr" but I am > unable to get accurate results: > > library(Rmpfr) > > >> exp(sqrt(163) * mpfr(pi, 120)) > > 1 'mpfr' number of precision 120 bits > > [1] 262537412640767837.08771354274620169031 > > The above answer is not only inaccurate, but it is actually worse than the > answer using the usual double precision. Any thoughts as to what I am doing > wrong? > > Thank you, > Ravi > > > > [[alternative HTML version deleted]] > > ______________________________________________ > R-help@r-project.org mailing list -- To UNSUBSCRIBE and more, see > https://stat.ethz.ch/mailman/listinfo/r-help > PLEASE do read the posting guide http://www.R-project.org/posting-guide.html > and provide commented, minimal, self-contained, reproducible code. ______________________________________________ R-help@r-project.org mailing list -- To UNSUBSCRIBE and more, see https://stat.ethz.ch/mailman/listinfo/r-help PLEASE do read the posting guide http://www.R-project.org/posting-guide.html and provide commented, minimal, self-contained, reproducible code.
