(*$B- Aufgabe 3.19 *)
PROGRAM newtonhalley;
VAR xa,x,f0,f1,f2:real;

FUNCTION f(x:real):real;
VAR s,t,sa,ta :real; i:integer;
BEGIN
  t:=x; s := x; i:=0;
  REPEAT
    i:=i+1; sa:=s; ta:=t; t:=-ta*x*x/i;
    s := sa+t/(2*i+1)
  UNTIL s=sa;
  f:=s-0.5
END;

FUNCTION fs(x:real):real;
BEGIN  fs:=exp(-sqr(x)) END;

FUNCTION fss(x:real):real;
BEGIN  fss := -exp(-sqr(x))*2*x END;

BEGIN
  x :=0; writeln('mit Newton');
  REPEAT
    xa := x; x:=x-f(x)/fs(x);
    writeln(x)
  UNTIL xa>=x;
  x :=0; writeln('mit Halley');
  REPEAT
    xa := x;
    f0:=f(x); f1:=fs(x); f2:=fss(x);
    x:=x-f0/f1/(1-0.5*f0/f1*f2/f1);
    writeln(x)
  UNTIL xa>=x
END.