# 
restart;
f:=x->cos(x)-2*x;
df:=D(f);
A1:=a-f(a)/df(a);
A2:=simplify(A1);
phi:=unapply(A2,a);
Digits:=60;
x:=Pi/4;
for i from 1 to 7
do
    x:=evalf(phi(x));
od;
ddf:=D(df);
A4:=a+(-df(a)-sqrt(df(a)^2-4*ddf(a)*f(a)))/(2*ddf(a));
omega:=unapply(A4,a);
x:=Pi/4;
for i from 1 to 7
do
    x:=evalf(omega(x));
od;