function pow_(atom x, integer e)
    atom r = 1
    for i=1 to e do
        r *= x
    end for
    return r
end function

function nth_root(atom y,n)
atom eps = 1e-15   -- relative accuracy
atom x = 1
    while 1 do
--      atom d = ( y / power(x,n-1) - x ) / n
        atom d = ( y / pow_(x,n-1) - x ) / n
        x += d
        atom e = eps*x   -- absolute accuracy
        if d > -e and d < e then exit end if
    end while
    return {y,n,x,power(y,1/n)}
end function

?nth_root(1024,10)
?nth_root(27,3)
?nth_root(2,2)
?nth_root(5642,125)
--?nth_root(7,0.5)  -- needs power(), not pow_()
?nth_root(4913,3)
?nth_root(8,3)
?nth_root(16,2)
?nth_root(16,4)
?nth_root(125,3)
?nth_root(1000000000,3)
?nth_root(1000000000,9)