Are professional programmers really fast at programming?

I'm majoring in Computer Science at college and I really enjoy what I am doing and I definitely could see myself doing this for a really long time professionally. The problem though is that I always worry that I am not good enough or am not fast enough as other professional programmers out there. I don't have a problem understanding concepts, visualizing the bigger picture, writing code, nor do I go extremely slow. I just worry that I may not go fast enough because I like to take my time on it and make sure it is correct, functional, and most of all I want to make sure I understand what is going on in the code. Do I have to worry about programming speed when it comes to a career? Any programmers have any advice? How fast are you?