In[486]:= FixedPoint[2 + E^-# &, .0] Out[486]= 2.12002823898764 billgosper$ ries/ries -l6 -EW 2.12002823898764 Your target value: T = 2.12002823898764 mrob.com/ries x^x = 5 for x = T + 0.00934424 {53} x-2 = 1/9 for x = T - 0.00891713 {59} ln(x)^2 = W(1) for x = T + 0.00352165 {62} x^4 = e^3 for x = T - 0.00302822 {65} x/3 = 1/sqrt(2) for x = T + 0.0012921 {64} ln(x)^2 = 1/sqrt(pi) for x = T - 0.000644103 {67} e"/x = 1/pi+1 for x = T - 0.000489232 {73} x-1/x = sqrt(e) for x = T + 0.000314826 {67} sqrt(x-2) = ln(sqrt(2)) for x = T + 8.50145e-05 {77} sqrt(x/pi) = sinpi(ln(2)) for x = T + 2.54297e-05 {82} x/sqrt(phi) = 5/3 for x = T + 4.5102e-06 {84} sinpi(cospi(1/x)) = e/pi^2 for x = T + 1.73152e-06 {92} x"/(x-1) = 9"/phi for x = T - 3.21311e-07 {96} x-2 = W(1/e^2) for x = T + 1.33227e-15 {80} (Stopping now because best match is within 1.88e-15 of target value.) W(x) = LambertW(x) = inverse(x=w*e^w) phi = the golden ratio, (1+sqrt(5))/2 sqrt(x) = square root A"/B = Ath root of B pi = 3.14159... (I.e., 2.12002823898764 = 2 + W(e^-2).) But, thanks to El Capitan (which also broke my Macsyma)-:, billgosper$ gcc -o ries ries.c -DRIES_USE_SA_M64 -lm xcrun: error: invalid active developer path (/Library/Developer/CommandLineTools), missing xcrun at: /Library/Developer/CommandLineTools/usr/bin/xcrun until: billgosper$ xcode-select --install --rwg Now if ries just had γ and the Γ function . . . it would probably be too slow!-(