agm(a, b) := %pi/4*(a + b)/elliptic_kc(((a - b)/(a + b))^2)$

agm(1, 1/sqrt(2)), bfloat, fpprec: 85;
/* 8.472130847939790866064991234821916364814459103269421850605793726597340048341347597232b-1 */