a=10^6

While[a > 0,

y=(something complicated related with x and xfinal)

sol = FindRoot[RandomReal[] - (1 - Assuming[x > 0, Exp[y]^(-a)]) == 0, {x, 0,300}];

x1 = (x /. sol);

If[a1>0, x2=(something),x2=(something else)]

Which[x1 < x2, (a=a-1; a1=a1+1; xtrue=x1)
,x1 > x2, (a1=a1-1; xtrue=x2;)];

xfinal = xfinal + xtrue;

AppendTo[alist, {xfinal, a1*(a1 + a)}];

];//AbsoluteTiming

SetDirectory[NotebookDirectory[]];
Export["alist.dat",alist];

a=10^6

While[a > 0,

y=(something complicated related with x and xfinal)

sol = FindRoot[RandomReal[] - (1 - Assuming[x > 0, Exp[y]^(-a)]) == 0, {x, 0,300}];

x1 = (x /. sol);

If[a1>0, x2=(something),x2=(something else)]

Which[x1 < x2, (a=a-1; a1=a1+1; xtrue=x1)
,x1 > x2, (a1=a1-1; xtrue=x2;)];

xfinal = xfinal + xtrue;

alist = {alist, {xfinal, a1(a1+a)}};

];//AbsoluteTiming

alist = Cases[alist, {__}, {-2}];//AbsoluteTiming

SetDirectory[NotebookDirectory[]];
Export["alist.dat",alist];