When executing the code pasted below in Eclipse, approximately 1 out of 3 times I encounter the following exception:
Exception in thread "main" java.lang.StackOverflowError
    at src.Adder.recursiveSumAllNumbersUpTo(Driver.java:33)
    at src.Adder.recursiveSumAllNumbersUpTo(Driver.java:37)
    ... *(there are 1024 lines in this stack)*
The other 2 times, it spits out the result as intended (the times vary slightly between each run):
Recursive: 467946
Non Recursive: 61282
Difference between recursive and non-recursive: 406664
Sum from recursive add: 19534375
Sum from non-recursive add: 19534375
Why does the exception only happen (seemingly) ~30% of the time?
Here's the code:
public class Driver {
    public static void main(String[] args) {
        Adder adder = new Adder();
        int valueToSumTo = 6250;
        long startTime = System.nanoTime();
        int raSum = adder.recursiveAddAllNumbersUpTo(valueToSumTo);
        long endTime = System.nanoTime();
        long raDif = endTime - startTime;
        System.out.println("Recursive: " + (raDif));
        startTime = System.nanoTime();
        int nonRaSum = adder.nonRecursiveAddAllNumbersUpTo(valueToSumTo);
        endTime = System.nanoTime();
        long nonRaDif = endTime - startTime;
        System.out.println("Non Recursive: " + (nonRaDif));
        System.out.println("Difference between recursive and non-recursive: " + (raDif - nonRaDif));
        System.out.println("Sum from recursive add: " + raSum);
        System.out.println("Sum from non-recursive add: " + nonRaSum);
    }
}
class Adder {
    public int recursiveAddAllNumbersUpTo(int i) {
        if (i == 1) {
            return i;
        }
        return i + recursiveAddAllNumbersUpTo(i - 1);
    }
    public int nonRecursiveAddAllNumbersUpTo(int i) {
        int count = 0;
        for(int num = 1; num <= i; num++) {
            count += num;
        }
        return count;
    }   
}
Everytime a recursive method calls itself, everything goes to the stack and algorithm such as yours requires a very deep stack.
To solve your problem, you should increase your Stack Size.
You can do that by calling the JVM with the -Xss parameter.
If you are using Eclipse you can do that by doing the following:
Try a bigger stack if that configuration is not enough.
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