On 2012-04-26, Phil Carmody <thefatphil@yahoo.co.uk> wrote:

My own favourite light year expression used to be Pi^(29+Pi) metres, 1 part in 132 too large, until I discovered (Pi^8)*10^9 kilometres, 1 Part in 337 too large.

Those are pretty cool too. I would suggest Pi^(8 Pi + 7) meters = 9.436*10^15, which is 1 part in 381 too small. For kilometers, I found Pi^(82/Pi), which is 1 part in 1117 too large. However your approximation has a 10^9, meaning it's really in units of "billion kilometers" AKA terameters, and that's pretty cool. Since I also like things in the form of X^Y^Z, by which I mean X^(Y^Z) not (X^Y)^Z, I suggest: Pi^8^cbrt(3) megameters where cbrt(x) is the cube root of x (1 part in 1233 too large) Pi^(2+1/Pi)^Pi gigameters (1 part in 255 too large) Pi^(2-1/Pi)^4 terameters (1 part in 1433 too large) Note similarity between the last two, which might be a benefit or a hindrance depending on how your associative memory works.

I don't know how those rate using RIES's metrics.

RIES explores somewhat different options from what I've seen most people do when they work out formulas on their own (or with the aid of other tools). For these examples the main difference is that RIES builds up big numbers from smaller numbers. That "82" in my Pi^(82/Pi) is actually given as 9^2+1. Using "ries -i 10" we can see that RIES considers "x/2 = 5" to be the simplest solution for 10, therefore it would substitute "2*5" for the 10 in your second formula. And for 29 similarly we get x-4 = 5^2, thus 29=5^2+4 in RIES's biased world. So your approximations for the light-year distance become "Pi^(5^2+4+Pi)" and "(Pi^8)*(2*5)^9". Translating the expressions into postfix and invoking "ries --eval-expression p5s4+p+^" we get: [p5s4+p+^] = 9.53210232861468e+15; d/dx = 0, complexity = {84} and similarly: [p8^25*9^*] = 9488531016070.57; d/dx = 0, complexity = {102} A 16 points difference isn't a lot, but RIES would consider your "Pi^(29+Pi)" to be simpler. This agrees with the expectation that better approximations come from more "complex" expressions. RIES chokes on really huge numbers (a safeguard against loss-of-precision) so to get all of the ones I suggested above, I took the log to base Pi first. The complexity score for my "Pi^(8*Pi+7)" is 87, and the scores for the others (in order) are 81, 82, 78, and 81. -- Robert Munafo -- mrob.com Follow me at: gplus.to/mrob - fb.com/mrob27 - twitter.com/mrob_27 - mrob27.wordpress.com - youtube.com/user/mrob143 - rilybot.blogspot.com