van=facebook.com/LearningCalculus$

tetration(b, n) := if n = 0 then 1 else b^tetration(b, n-1)$
log10(u):=log(u)/log(10)$
z:tetration(%i,4);

I:imagpart(z); R:realpart(z);

a:float(exp((I/(7*R))^(1/4)))$ b:float(%pi)$ print(a,b)$

n_digits_prec : floor(log10(a-b));

fpprec:30$

a:bfloat(log(640320^3+744)/sqrt(163));

n_digits_prec : floor(log10(a-b));

a:bfloat((2143/22)^(1/4));

n_digits_prec : floor(log10(b-a));