This worked for me, it doesn't require 10^12 iterations: My implementation-

cin >>u0>>b;
//double a = reccur(1000000);

double f_val = u0;
double pf_val;
for(unsigned long long i=1;i<=1000001; i++){
    pf_val = f_val;
    f_val = fn_1(pf_val);
    if(f_val == pf_val)
    break;

}
//double b = fn_1(f_val);
cout<<setprecision(16)<<f_val + pf_val;
return 0;