Following code evaluates functions using Newton's Method. In this case it is f(x)=x^2-401.

To evaluate another function change the variable f0 and df0, which are the function and the derivative of the function, respectively.

            f(x0)
x1 = x0 -  -------
            f'(x0)

            f(x1)
x2 = x1 -  -------
            f'(x1)

... and so forth

// Saved at Newton.hx
// Compiled as haxe -main Newton -neko Newton.n
// Run as neko Newton.n

import neko.Sys;

class Newton{

public static function main(){

neko.Lib.println("Enter Starting Point");
var x0 : Float = Std.parseFloat(neko.Sys.stdin().readLine());

neko.Lib.println("How Many Iterations?");
var count : Int = Std.parseInt(neko.Sys.stdin().readLine());

// Initialization of variables
var f0 : Float;
var df0 : Float;
var p0 : Float;
var p1 : Float;

p0=x0; // Initial guess at x0

for(i in 0...count) 

{

f0=x0*x0-401; // f(x) = x^2-401 or evaluate sqrt(401)
df0=2*x0;     // f'(x) = 2x (derivative of f(x))

p1=p0-(f0/df0);  // p1=p0-(f(x)/f'(x)) Newton's Method Here

neko.Lib.println("p1 = " + p1);
p0=p1; //switch variables for next iteration
x0=p1; //switch variables for next iteration

}
}
}