import timeit
import numpy as np

def test(ty, limit):
    def thing(n, m):
        x = ty('')
        hoisted = ty('a' * m)
        for _ in range(n):
            x += hoisted

    xvals = []
    yvals = []
    for x in range(0, limit, 500):
        y = timeit.timeit(lambda: thing(x, 1000), number=1000)
        print('%d: %r' % (x, y))
        xvals.append(x)
        yvals.append(y)

    return np.polyfit(xvals, yvals, 2)

print(test(str, 10001))
# [  2.20105955e-09   6.90650409e-05   1.87324922e-02]
print(test(bytes, 10001))
# [  2.94627114e-09   6.88720223e-05   1.36304238e-02]
print(test(list, 4001))
# [  1.84068582e-06  -1.62578855e-03   2.01160158e+00]
print(test(bytearray, 10001))
# [  2.89900130e-09   7.34388859e-05   2.80596315e-02]