I need to approx (1-x)^0.25 with given accuracy (0.0001 e.g.). I'm using expansion found on Wikipedia for (1+x)^0.25. I need to stop approximating when current expression is less than the accuracy.

long double s(long double x, long double d) {
    long double w = 1;
    long double n = 1; // nth expression in series
    long double tmp = 1;

    // sum while last expression is greater than accuracy
    while (fabsl(tmp) >= d) {
        tmp *= (1.25 / n - 1) * (-x); // the next expression
        w += tmp; // is added to approximation
        n++; 
    } 

    return w;
}

Don't mind long double n. :P This works well when I'm not checking value of current expression but when I'm computing 1000 or more expressions. Domain of the function is <-1;1> and s() calculates approximation well for x in <-1;~0.6>. The bigger the argument is the bigger is the error of calculation. From 0.6 it exceeds the accuracy.

I'm not sure if the problem is clear enough because I don't know English math language well. The thing is what's the matter with while condition and why the function s() doesn't approximate correctly.