pi_compute.c running (all values are approximate) 
string pi =  3.1415926535897932384626433832795028841971 
21.17f pi =  3.14159265358979312 
g      pi =  3.14159 
4*atan(1) =  3.14159265358979312 
4*(5*atan(1/7) + 2*atan(3/79))
          =  3.14159265358979312 
6*atan(1/sqrt3)  b1=1/sqrt3=0.57735
          =  3.14159265358979356 
12*atan(2-sqrt3)  b2=2-sqrt3=0.267949
          =  3.14159265358979445 

series for atan(x) shows need for x<1/2 for fast convergence
x - x^3/3 + x^5/5 - x^7/7 + x^9/9 ...