Ravi I am a chemical engineer by training. Is there not something like law of corresponding states in numerical analysis?
Aditya ------------------------------ On Thu 2 Jul, 2015 7:28 AM PDT Ravi Varadhan 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.
