Precision with small numbers

Question

Hi I'm working on a program that will approximate values of derivatives at a point.
The code for my differentiation function (where f is the function and a is the point) is:
public double Diff(String f, double a){
     double answer;
     x=a+h;
     answer=Evaluate(f);
     x=a;
     answer=answer-Evaluate(f);
     answer=answer/h;
     return answer;
h is a double with a really small value (10^-50 or so)
x is also a double.
my Evaluate function is:
public double Evaluate(String expression){
myParser.addVariable("x",x);
myParser.parseExpression(expression);
double answer=myParser.getValue();
return answer;
It uses JEP to evaluate the equation at x. myParser is an instance of the JEP class.
My problem is that the answers I get are wildly inaccurate. 6 and 7 usually produce the same answer. Anything over 50 always gives me 0. I don't know why this is and how I can solve it. Any help would be appreciated.

Answer 1

A double has a precision of 16-17 digits. If you have 2 you can't add a 1 at the 50'th fractional position as you try to do now. You can add a one at the 15'th fractional position at the most, like
System.out.println(2.0+1.0E-50); // double has too little precision for this
System.out.println(2.0+1.0E-15); // double has just enougth precision for thisSo you will have to use a much smaller h, like 10^6 or something. Or you will have to use BigDecimal to get more precision.