HumanEval/32

 import math


def poly(xs: list, x: float):
    """
    Evaluates polynomial with coefficients xs at point x.
    return xs[0] + xs[1] * x + xs[1] * x^2 + .... xs[n] * x^n
    """
    return sum([coeff * math.pow(x, i) for i, coeff in enumerate(xs)])


def find_zero(xs: list):
    """ xs are coefficients of a polynomial.
    find_zero find x such that poly(x) = 0.
    find_zero returns only only zero point, even if there are many.
    Moreover, find_zero only takes list xs having even number of coefficients
    and largest non zero coefficient as it guarantees
    a solution.
    >>> round(find_zero([1, 2]), 2) # f(x) = 1 + 2x
    -0.5
    >>> round(find_zero([-6, 11, -6, 1]), 2) # (x - 1) * (x - 2) * (x - 3) = -6 + 11x - 6x^2 + x^3
    1.0
    """
 

solution

 

    dxs = [xs[i] * i for i in range(1, len(xs))]
    def func(x):
        return poly(xs, x)
    def derivative(x):
        return poly(dxs, x)
    
    x, tol = 0, 1e-5
    for _ in range(1000):
        fx = func(x)
        dfx = derivative(x)
        if abs(fx) < tol: break
        x = x - fx / dfx

    return x

 

base input

 [[[-10, -2]], [[-3, -6, -7, 7]], [[8, 3]], [[-10, -8]], [[-3, 6, 9, -10]], [[10, 7, 3, -3]], [[8, -2, -10, -5, 3, 1, -2, -6]], [[1, -7, -8, 2]], [[1, 1]], [[-9, 4, 7, -7, 2, -8]], [[10, 9, 1, 8, -4, -8]], [[-3, -1]], [[-3, -7]], [[-2, 4, 10, 1, -5, 1, 1, -4]], [[10, -8, 9, 10, -5, 7]], [[-5, 4, 2, -2]], [[1, -9, -3, -9]], [[2, -2, -8, -4, 8, 1]], [[10, 5, 2, 10]], [[-6, -2, -6, -3, 7, 7, -2, 8]], [[8, 2, 1, -3, -6, 6, 5, -8]], [[-7, -6]], [[3, 9, -8, 2]], [[9, 4, 6, -2, 7, -10, -7, 7]], [[10, 1, -7, -1, 3, -5]], [[-10, -2, 6, -5, 6, -7, 10, -1]], [[-6, 1, -5, 7]], [[9, 1]], [[-10, -7, 1, -1, -3, -9, -3, 8]], [[-8, 5]], [[7, -6]], [[5, 7, -5, -2]], [[-4, 7, -4, -1, 2, 10, 1, 4]], [[-7, -3, -3, -8, 1, -10, 8, 7]], [[8, -3, -10, -8]], [[-3, -8]], [[1, -8]], [[-2, 5, -4, 7]], [[8, 8, 5, -3]], [[3, -4, -7, -7, 3, 1, 3, 3]], [[-9, 10, 10, -7, -9, 2, 1, -7]], [[-4, -4, 7, 4]], [[3, -5, -2, 4]], [[-8, 4, 7, -7]], [[10, 7]], [[-8, -3]], [[3, 5, 5, -4]], [[-9, -5, 2, -10, 2, -2, 4, -1]], [[7, 5, -6, -4, -1, -4, -9, 8]], [[1, -9]], [[8, 5]], [[-9, 6, -8, -5]], [[9, -8]], [[2, -7, 8, -3]], [[9, -8]], [[8, 8, 6, 1, -2, -4, 1, -3]], [[2, -6, 10, -1, 4, 1]], [[-10, 4]], [[-8, 7]], [[6, -2, -6, 1]], [[-3, 1]], [[-5, 4, 7, -1, 9, 10]], [[7, -1]], [[-6, -2]], [[-7, 7]], [[-2, -1, 9, -4]], [[-4, 10, -2, 6, 5, -2]], [[-8, 10]], [[-2, -9, -10, 1, -6, 10, -2, -5]], [[7, 3, 7, -10, -7, -8, -6, 7]], [[1, 8]], [[3, -6, -9, -1]], [[-9, 1, -4, -3, -7, 1]], [[9, -6, -3, -5, -5, 3, -10, -5]], [[3, -3, -2, -5, -7, 2]], [[5, -3]], [[4, 1, -1, -3]], [[-10, -4, 2, 1]], [[-8, -2, 1, 10, 6, 2]], [[-10, -7, -2, -5, 8, -2]], [[-7, 9]], [[1, 1, 3, 9, 6, -7, 2, 8]], [[-2, -9, 3, -10]], [[1, 3, -8, 1]], [[-7, -1, 6, -1, 3, 1]], [[-1, 7, -6, -4, 3, 2, -5, 9]], [[2, 7, -10, -1, -1, -4]], [[8, 9, 10, 1, 4, 4, 4, -4]], [[-5, -8, -1, 6, 10, 9, 1, -8]], [[-1, -3, -4, -6]], [[-9, -3]], [[9, -8, 4, 3, 10, 8, -4, 2]], [[2, -3, -6, 10, -10, -7, 3, -3]], [[6, 4, -9, 7]], [[-7, 4, -6, 4]], [[4, 9, 6, 3, 7, 4]], [[5, 4, -2, -3]], [[6, 5, 10, -3, -2, 4]], [[-1, -3]], [[1, 1, 7, -8, -6, -6]]] 

plus input

 [[[5, 10, -3, 1]], [[1, -20, 156, -864, 2667, -4392, 3744, -1440]], [[0, 2]], [[-1, -1, 1, 1]], [[1, -1, 0, 1]], [[6, -1, 2, 1, -3, 1]], [[-1, 10, 1, 1]], [[-1, -36, 6, -1440, 1, 1]], [[3744, 1, 0, 2]], [[1, -20, 156, -864, 2667, -4391, 3743, -1440]], [[1, -20, 156, -864, 2667, -4391, 3743, -4, -1440, -4391]], [[0, -36, 0, 54, 7, 54]], [[-3, 2]], [[0, -36, 0, -3, 7, 54]], [[-20, 156, -864, 2667, -4391, 3743, -4, -1440, -1440, -4391]], [[6, 1, -1, 2, 1, -3, -4, 1]], [[6, 1, -1, 2, 1, -2, -4, 1]], [[0, 0, 6, -1]], [[0, -36, 0, -4, 7, 54]], [[2667, 6, 1, -1, -2, -4, 1, -1]], [[0, -1, -36, 6, -1440, 1, 1, -36]], [[6, -1, -4392, 2, 1, -3, 1, 1]], [[-36, -20, 6, -1440, 1, 1]], [[2, 5, -36, 1, 54, 7]], [[0, 2667, 0, 0]], [[0, -36, 0, 4, -4, 7, 54, 7]], [[-36, 6, 6, -1441]], [[0, -1, 0, 1]], [[2667, 6, 1, -1, 1, -1]], [[0, 6, -1440, 1, 1, -36]], [[-36, 6, -1440, -36]], [[-1, -36, 6, -1440, 1, 0]], [[6, 1, -1, 1, -3, -4, 1, 6]], [[-4392, -1, 6, -2]], [[2667, 6, 1, -1, -2, 1, -1, 2667]], [[6, -1, 2, 1, -3, 3744]], [[1, -1, 0, -1441]], [[-4, -1, 0, 1]], [[0, -1, 1, 1]], [[-4392, -20, 6, 4]], [[1, 2]], [[6, -1, -4392, 2, 1, 3743, 1, 1]], [[5, 10, 7, 10, -3, 1]], [[0, -20, 0, 0]], [[1, -20, 156, -864, 2667, -4392, 3743, -1440]], [[0, -1, -36, 6, -1440, 1, 1, -36, 0, 1]], [[-3, 6, -2, 6]], [[0, -4391, 0, 0]], [[-1, -36, 1, 0]], [[1, -1, 10, 1]], [[-3, 6, -2, 6, -2, -2]], [[6, -2, 2, 1, -3, 3744]], [[-1, -1, -3, -36, 1, 0]], [[-1, -4391, 0, 0]], [[6, -1, -4392, 2, 1, 1, 1, 6]], [[6, 2, 1, -3, 1, 2]], [[0, -36, 0, -4, -5, 7, 54, -36]], [[0, -36, 0, -3, -5, 7, 54, -36]], [[-36, -19, 6, -1440, 3743, 1]], [[5, 10, 1, 1]], [[1, -4391, 0, 0]], [[6, 2, 1, -3, 1, 1]], [[6, -36]], [[-1, -4391, -1440, 0, 0, -4391]], [[1, 1]], [[-1, 5, 1, 0]], [[1, -4391, 4, 0]], [[-1, -864, 1, 0]], [[0, -4, 0, -4, 6, 54]], [[2, 7, -36, 0, 54, 7]], [[6, -1, -4392, 2, 1, 0, 1, 6]], [[7, -1, -4392, 2, 1, 0, 1, 6]], [[0, -3, 4, 7, 54, -36]], [[6, 10, 1, -1, 2, 1, 1, -2, -4, 1]], [[2667, 6, 1, -1, -2, 1, 0, 2667]], [[-1, -2, -3, -36, 1, 0]], [[-20, 156, 7, -3, -4391, 3743, -4, -1440, -1440, -4391]], [[6, 5, 10, 7, 10, -3, -37, 1]], [[6, 1, -1, -864, 1, -36, -2, -4]], [[7, -1, -4392, -19, 1, 0, 1, 6]], [[0, 2, 0, 1, 54, 7]], [[-1, -4391, -1, 0]], [[0, 0, 0, 0, 0, 1]], [[0, -3, 0, 1]], [[0, 0, 0, 0, 0, 0, 0, 0, 0, -10]], [[0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1]], [[1, -2, 3, -4, 5, -6, 7, -8, 9, -10]], [[-300, 21000, -630000, 9450000, -78840000, 395580000, -1186740000, 1935360000, -1663750000, 725760000]], [[-2, -5, -10, -17, -26, -37]], [[2, 5, 10, 17, 26, 37]], [[0, 2, 0, 3, 0, 4, 0, 5]], [[9, -7, 3, 2, 8, -4, -10, 6, 5, -1]], [[0, -4, 0, 0, 2, 0, 1, 0]], [[0, 2, 0, 3, 0, 4, 8, 5, -5, 0]], [[0, 0]], [[0, 0, -1186740000, 1]], [[1, -2, 3, -4, 5, -6, 7, -8, 9, -11]], [[1, 3, 10, -4, 5, -6, 7, -8, 9, -10]], [[1, 3, 10, -4, 4, 8, 2, -6, 7, -8, 9, -10]], [[0, 2, 0, 3, 0, 4, 0, 26, 5, 0]], [[2, 5, 17, 26, 4, 4]], [[2, 5, 10, 17, 26, 17]], [[3, 5, 17, 26, 4, 4]], [[2, 5, -6, 26, 4, 4]], [[9450000, 9, -7, 3, 2, 8, 2, -4, -10, 6, 5, -1]], [[9450000, 9, -7, 3, 2, 8, 1, -4, -10, 6, 5, -1]], [[5, 17, 26, 3, 4, 4]], [[9450000, 9, 9450000, -7, 3, 2, 6, 8, 2, -4, -10, 6, 5, -1]], [[2, 5, 10, 17, 26, 37, 10, 2]], [[0, 0, 0, 0, 0, 0, 0, -37, 0, -10, 0, 0]], [[9450000, 9, 3, 2, 8, 2, -4, -8, -10, 6, -1, 5]], [[-2, -5, -10, -17]], [[0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0]], [[2, 2, 26, 3, 4, 4]], [[9450000, 9, -7, 3, 2, 6, 1, -4, -10, 6, 5, -1]], [[1, -2, 4, -4, 5, -6, 7, -8, 9, -11]], [[9, -6, 3, 2, 8, -4, -10, 6, 5, -1]], [[5, 17, 26, 3, 4, 26, 4, 26]], [[9450000, 6, 9, -7, 3, 2, 8, 2, -4, -10, 7, 5, -1, 9450000]], [[9450000, 9, -7, 3, 2, 6, 1, -4, -10, 6, 17, -1]], [[-1, -3, 1, -3]], [[26, 1, 0, -1186740000, 1, 0]], [[9450000, 9, -6, 3, -7, 2, 6, 1, -4, -10, 6, 5, -1, 9450000]], [[0, 2, -630000, 3, 0, 4, 0, 5]], [[9, -6, 3, 2, 8, -4, -10, 26, 6, 5, -1, 8]], [[9450000, 9, -6, 3, -7, 2, 6, 1, -4, -10, 6, -11, -1, 9450000]], [[26, -2, 4, -4, 5, -6, 7, -8, 9, -11]], [[0, -78840000, 0, 3, 0, 4, 0, 26, 5, 0]], [[-2, -5, -11, -17]], [[9450000, -2, -7, 3, 2, 8, 1, -4, -10, 6, 5, -1]], [[0, 0, 0, -4, 0, 1]], [[26, 1, 3, -4, 5, -10, 7, 21000, -8, 9, -10, 26]], [[1, 3, 10, -4, -3, 5, -6, 7, -8, 9]], [[-5, 26, 1, 3, -10, -4, 5, -10, 7, 21000, -8, 9, -10, 26]], [[9, -6, 4, 2, 8, -4, -10, 26, 6, 5, -1, 8]], [[1, -630000, 3, -4, 5, -10, 7, -8, -8, 9, -10, 26]], [[9, -6, -8, 2, 8, -4, -10, 26, 6, 5, -1, 8]], [[9450000, 6, 9, 8, 3, 2, 8, 2, -4, -10, 7, 5, -1, 9450000]], [[1, 3, 10, -4, 5, -6, 7, -8, 9, 9, -10, 9]], [[9450000, 6, 9, -7, 3, 2, 8, 2, -4, -10, 7, -22, -1, 9450000]], [[9, -6, -8, 2, -630000, -4, -10, 26, 6, 5, -1, 8, 10, -8]], [[1, -630000, 3, -4, 5, -10, 7, -8, -8, 9, -10, 26, 5, -10]], [[2, 5, 10, 26, 37, 10]], [[26, 1, 3, -4, 4, -10, 7, 21000, -8, 9, -10, 26]], [[1, 3, 10, -4, 5, -6, 7, -8, 9, -10, -8, -8]], [[0, 2, 0, 2, 0, 4, 0, 5]], [[9450000, 9, -7, 3, 2, 1, -4, 6, 5, -1]], [[9, -7, 2, 8, -4, -10, 6, 5, -1186740000, -1]], [[9450000, -2, -7, 3, 2, 8, 1, -2, -4, 6, 5, -1]], [[9450000, 9, -6, 3, -7, 2, 6, 1, -4, -10, 6, -11, -1, 9450000, 9, 6]], [[1, -2, 4, -4, 5, 7, -8, 9]], [[1, 3, -4, 5, -6, 7, -8, 9, -11, -6]], [[5, 10, 17, 26, 37, 10, 2, 2]], [[-10, 10, 0, -83, 0, 0, 0, 1]], [[1, 3, 4, -4, 5, -6, 7, -8, 9, 9, -10, 8]], [[-300, -6, 4, 2, 8, -4, -10, 26, 6, 5, -1, 8]], [[9450000, 9, -6, 3, -7, 2, 6, 2, -4, -10, 6, -11, -1, 9450000]], [[-11, 5, 10, 17, 26, 17]], [[-2, -5, -10, -17, -26, -1186740000, -37, -1186740000]], [[9, -6, 21000, 2, 8, -4, -10, 26, 6, 5, -1, 8]], [[2, 5, 26, 37, 10, 2]], [[9, -7, 3, 2, 8, -4, -10, 6, 5, -1, -1, 2]], [[1, 3, 10, -4, 5, 8, 2, -6, 7, -8, 9, -9]], [[2, 5, 10, 17, 26, 37, 26, 2]], [[0, -78840000, 0, 3, 0, 4, 26, 5, 0, 26]], [[2, 5, -6, 26, -630000, 4]], [[1, -2, 4, -4, 5, -6, 7, 9, -11, -4]], [[9450000, 9, -7, 3, 2, 8, 2, -4, -10, 6, 5, -1, 6, -10]], [[-2, -5, -10, 6, -17, -26, -1186740000, -37, -1186740000, -1186740000]], [[-2, -5, -4, -10, -17, -37]], [[2, 5, -300, 10, 17, 26, 37, 10, 2, 10]], [[9450000, 6, 9, -7, 3, 2, 8, 2, -4, -10, 6, 5, -1, 9450000]], [[0, 0, 0, 2, 0, 1]], [[5, 17, 26, 3, 4, -6, 26, 4, 26, 26]], [[2, 6, 17, 26, 4, 4]], [[17, 6, 9, -7, 3, 2, 8, 2, -4, -10, 7, -22, -1, 9450000]], [[0, 1, 2, -3, -630000, 3, 0, 4, 0, 5]], [[9, -6, 20999, 2, 8, -4, -10, 26, 6, 5, -1, 8]], [[2, 5, 10, 17, -7, 37]], [[-300, -6, 2, 2, 8, -4, -10, -6, 6, 5, -1, 8]], [[1, 3, 80, -4, 5, 8, 2, -6, 7, -8, 9, -9]], [[9450000, 6, 9, -7, 4, 2, 8, 2, -4, -10, 7, -22, -1, 9450000]], [[26, 6, 1, 3, -4, 5, -6, 7, -1186740000, 21000, -8, 9, -10, 21000]], [[0, 2, 0, 3, -4, 0, 4, 8, 5, -5, 0, -5]], [[0, 0, 2, 0, 0, 1]], [[-300, 21000, -630000, 9450000, -78840000, -6, -1186740000, 1935360000, -1663750000, 725760000]], [[26, 1, 2, 80, -4, 5, 8, 2, -6, 7, -8, 9, -9, -8]], [[0, -4, 0, 1, 2, 0, 1, 0]], [[1, 3, 5, -6, 7, -8, 9, -10]], [[5, 10, 17, 37, 26, 2]], [[9450000, 6, 9, -7, 3, 2, 8, 2, -4, -78840000, 6, 5, -1, 9450000]], [[26, -2, 4, -4, 5, -6, -26, -8, 9, -11]], [[1, 10, -3, 5, -6, 7, -8, 9]], [[0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, -37, 0, 0]], [[27, 1, 3, -4, 4, -10, 7, 21000, -9, 9, -10, 26]], [[2, 10, 26, 4, 37, 10]], [[-630000, 3, -4, 5, -11, 7, -8, -8, 9, -10, 37, 26]], [[0, 2, 0, 3, -4, 0, 4, 8, 5, -5, 0, -5, -5, 3]], [[1, 3, 10, -9, -4, 5, -6, 3, 7, -8, 9, -10]], [[0, -37, -78840000, 0, 3, 0, 4, 26, 0, 26]], [[2, 3, 4, 4]], [[-2, -7, 3, 2, 8, 1, -2, -4, 5, -1]], [[9450000, 5, 9, 3, 2, 8, 2, -4, 3, -8, -10, 6, -1, 5]], [[-630000, 2, -630000, 3, 0, 4, 0, 5]], [[1, 3, 80, -4, 17, 8, 2, -6, 7, -8, 9, -9]], [[9, -6, 3, 2, 8, -4, -10, 6, 5, -1, 2, -6]], [[2, -6, 26, 4, 4, 4]], [[0, 2, 0, 3, 0, -37, 8, 5, -5, 0]], [[1, 4, -4, 7, -8, 9]], [[-2, -5, -10, 6, -17, -26, -1186740000, -37, -1186740000, -1186740000, -26, -1186740000]], [[2, 5, -300, 10, 17, 26, 37, 10, 2, 20999]], [[0, 2, 0, 0, 3, -4, 0, 4, 8, 5, -5, 0, -5, -5, 27, 3]], [[0, 0, 0, 0, 0, 0, 0, 0, 0, 26, 0, 0, 0, 0, 1, 1]], [[3, 9450000, 5, 17, 26, 4]], [[-300, 3, -6, 4, 2, 8, -4, -10, 27, 26, 6, 5, -1, 8]], [[2, 5, -300, 17, 26, 17]], [[9450000, 9, -6, 3, -7, 2, 6, 2, -4, 4, 6, -11, -1, 9450000]], [[0, -4, 0, 0, 1, 2, 0, 1, 0, 0]], [[0, -4, 0, 0, 2, 0, 0, 0]], [[-300, 21000, -630000, 9450000, -78840000, -6, 37, 1935360000, -1663750000, 725760000]], [[26, 1, -2, -1186740000, 1, 0]], [[-10, 10, 0, 27, 0, 0, 0, 10]], [[27, 5, 10, 26, 37, 10]], [[0, 2, 0, 3, 0, 4, 8, -26, -5, 0]], [[1, -2, 4, -1663750000, 5, 3, -1, 9]], [[2, 16, 6, 17, 9, 26, 4, 4]], [[1, 10, -3, 5, -6, -1186740000, 9, 7, -8, 9]], [[3, 9450000, -1, 17, 26, 4]], [[2, 5, -300, 17, 26, 37, 10, 2]], [[27, -37, -78840000, 0, 3, 0, 4, 26, 0, 26]], [[1, -2, 3, -4, 5, -6, 7, -8, 9, 3]], [[0, -4, 0, 0, -7, 2, 0, 0]], [[17, 6, 9, -7, 4, 2, 8, -4, -10, 7, -7, -22, -1, 9450000]], [[-2, -3, -11, -17]], [[17, -6, 6, 9, -7, 4, 2, 8, -4, -10, 7, -7, -22, -1, 9450000, 9450000]], [[9449999, 9, -6, 3, -7, 2, 6, 1, -4, -10, 6, -11, -1, 9450000, 9, 6]], [[0, 2, -630000, 3, 1, 0, 0, 5]], [[0, 2, 0, 3, 0, 4, 8, 5, -5, 0, -5, 5]], [[0, -6, -8, 2, 8, -4, -10, 26, 6, 5, -1, 8]], [[-300, 21000, -630000, 9450000, -78840000, 9449999, 395580000, -1186740000, 1935360000, -1663750000, 725760000, -1186740000]], [[-26, 9, -6, 3, -7, 2, 6, -4, -10, 6, -11, -1, 9450000, -26]], [[9, -7, 3, 2, -4, -10, 6, 5, -1, -1, 2, 2]], [[2, 5, 9, 17, 26, 37]], [[2, 5, 10, 26, 37, 5]], [[1, 3, 10, -4, 5, -22, 7, -8, 9, -10, -8, -8, 5, -8]], [[2, 5, 17, 26, 37, 2]], [[-4, 1, -2, 4, -4, 5, -6, 7, 9, -11, -4, -6]], [[3, 5, 17, 26, 4, -9]], [[0, -78840000, 0, 3, 0, 1, 0, 26, 5, 0]], [[1, -300]], [[9450000, 5, 9, 3, 8, 2, -4, 3, -8, -10, 6, -1, 5, -1]], [[27, 5, 26, 37, 10, 26]], [[0, -7, 0, 0, 0, 0, 0, 0, 0, 0, 26, 0, 0, -1, 1, 1]], [[-630000, 3, 5, -11, 7, -8, -8, 9, -10, 37, 26, -10]], [[-2, -3, -11, -16]], [[0, -7, 0, 0, 0, 0, 0, 0, 5, 0, 0, 26, 0, 0, -1, 1, 1, 0]], [[-630000, 2, -630000, 2, 10, 4, 0, 5]], [[1, 3, 10, -4, 5, -6, 8, 7, 10, -8, 9, 9, -10, 9]], [[-2, -5, -11, -18]], [[9, -6, 3, 2, 8, -4, -10, 6, 7, 5, -1, 2, -6, 3]], [[9, -6, 3, 2, 8, -4, -10, -4, 6, -5, 5, -1]], [[-2, -15]], [[2, 10, 26, 17]], [[0, -4, 0, 0, 2, 0, 1, 1]], [[2, 5, 3, 26, 4, 4]], [[0, 2, 0, 0, 4, 0, 1, 26, 5, 0]], [[9, -6, 21000, 2, 8, -4, -10, 26, 6, 5, -1, 1935360000]], [[2, 2, 26, 3, -10, 4]], [[1, 3, 10, 0, -4, 5, -6, 3, 7, -8, 9, -10]], [[0, 2, -630000, 3, 16, 4, 0, 5]], [[1, -2, 4, -1663750000, 5, -4, -1, 9]], [[26, 1, 2, -4, 5, -10, 7, 21000, -8, 9, -10, 26]], [[9450000, 9, -6, 3, -7, -18, 6, 2, -4, -10, 6, -11, -1, 9450000]], [[-10, 20999, 0, -1, 0, 0, 0, 1]], [[9, -6, 3, 8, -10, 6, 5, -1, 2, -6]], [[0, 2, 0, 80, 0, 4, 0, 5]], [[-300, -300, 21000, -630000, 9450000, -78840000, -6, 37, 1935360000, -1663750000, 725760000, -300]], [[2, 5, -300, 10, 17, 26, 37, 2, 20999, 37]], [[-26, 9, -6, 3, -7, 2, -4, -10, 6, -1, 9450000, -26]], [[9, -7, 3, 2, 8, -4, -10, -3, 6, 5, -1, -7]], [[26, 1, 2, 80, -4, 5, 8, 2, -6, 7, -8, 9, -9, -8, -8, 7]], [[-11, 5, 10, 25, 26, 17]], [[1, 3, 10, -4, -7, -3, 5, -6, 7, -8, 9, -3]], [[9, -6, 2, 8, -4, -10, 26, 6, 5, -1, 8, -6]], 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-630000, 1935360000]], [[-300, 21000, -630000, -78840000, 395580000, -1186740000, -1186740000, -1663750000, 725760000, -1186740000]], [[-3, -2, 3, 1935360001, 9449999, -3, 5, -6, 37, 3, -630001, -630000, -8, 9, -10, 3, -10, 9]], [[-300, -78840001, 21000, -630001, -78840000, -36, -1186740000, -36, 1935360000, -1663750000, -630001, -630000]], [[-300, 21000, -630000, 7, 9450000, -78840000, -18, 395580000, 1935360000, -1663750000, 725760000, 9450000, -300, 1935360000]], [[-1, 10, 17, 26, 17, 9, 0, 18]], [[-5, -10, -27, -18, -7, -10]], [[-300, 37, 21000, -630000, 9449999, 20999, -17, 395580000, -1186740000, 1935360000, -1663750000, 725760000, 9450000, -630000, -78840000, -630000, -630000, 9450000]], [[0, 1, 0, -26]], [[2, 5, 10, 37]], [[7, -17, -10, -18, -26, 7]], [[-4, -10, -26, -37, 26, -4]], [[0, 1935360001, 0, 3, 1, 0, 1, 5]], [[-1186740000, 9, -7, 2, 8, -4, 395580001, 7, 5, 6, -4, 9]], [[9, -7, 3, 3, 8, -4, -10, 6, 5, -1]], [[-27, 21000, -630000, -78840000, 395580000, -1186740000, 1935360000, 1, -1663750000, 725760000, 1, -630000]], [[9, -6, 3, 2, 8, -78840001, 6, 5, -1, 2, 3, 9]], [[9, -6, 3, 2, 8, -9, -4, -10, 6, 5, -1, 3]], [[-2, 3, -3, 5, -5, 7, -8, 9, -10, 3]], [[-17, -301, -10, 3, -26, -37]], [[1, -2, 3, -6, 6, -9, 9, -10]], [[-300, 21000, -630001, 9450000, 395580000, -1186740000, -1663750000, 725760000, 9450000, -630000, -1186740000, -1186740000]], [[1, -2, 3, 5, -5, 5, -1663750000, 3, 9, -10]], [[-300, 21000, -78840000, -36, 1935360000, -1663750000, -630001, 9450000, 725760000, -630000, 21000, -630000]], [[1, -26, 3, -3, -6, 8, -9, 9, -10, -26, -3, -26]], [[-2, 3, -2, -4, -6, 7, -8, 9, -10, -3, 1, -8, -6, -6]], [[725759999, -300, 21000, -630001, 9450000, -1186740000, 1935360000, -1663750000, 725760000, 9450000, -630000, -1186740000]], [[1, -630002, 1935360000, 3, -7, -630002, -4, -6, 7, -4, -8, -1663750000, -1186740000, 9, -18, 8, -3, 9]], [[-300, 21000, 0, -630001, -78840000, 395580000, -1186740000, 1935360000, -1663750000, -7, 725760000, -630000, 1935360000, 725760000]], [[-300, -78840001, 21000, -630001, -78840000, -36, -1186740000, -36, 1935360000, -1663750000, -630001, -630000, -300, 1935360000]], [[9, -7, 3, 2, 8, -4, -10, -10, 6, -1, -7, 9]], [[-1, -10, -38, -6, -26, -38]], [[-2, 27, -6, -10, -7, -26, -38, -26]], [[1, -629999, -630002, 1935360001, 37, -7, -4, -6, 7, -4, -8, 26, 9, -10, 17, 9]], [[1, -26, 3, -9, 9, -25]], [[0, 17, 0, 7]], [[1, -27, 3, -4, -6, 8, -9, 9, -10, 3]], [[-8, -6, 3, 2, 8, -4, 725760000, -10, 5, -1, 5, 3]], [[2, -36, 2, -4, 1, 0]], [[7, -38, -10, -17, -26, 4, -37, -17]], [[1, -11, -2, 3, 5, -6, 7, 5, -1663750000, 9, -10, -11]], [[1, -2, 3, 5, 18, 7, -8, -37, -10, -8]], [[0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -10, 0, 0, 0, 0, 1, 0]], [[-9, 3, 5, -6, -8, 9, -10, -8, -8, 3]], [[9, 4, -6, 3, 2, 8, -4, 725760000, -9, 6, 5, -1, 2, 3]], [[-300, 21000, -299, -630001, -78840000, -1186740000, 1935360000, -1663750000, 725760000, -630000, -1663750000, -78840000]], [[-1, 5, 10, 21000, 17, 37]], [[0, 26, 0, 3, -9, 0, 5, -9]], [[-300, 21000, -630000, 9450001, -78840000, 395580000, -1186740000, 1935360000, -1663750000, 725760000, 9450000, -630000, -1186740000, 725760000]], [[-630001, -2, 3, 5, -6, 7, 5, -8, 8, -10]], [[-1, -37, 17, 26, 37, 10]], [[0, 0, 0, 0, -630000, 1, 0, 1, 0, -630000]], [[-1, 10, 17, -1663749999, 9, 0]], [[-300, 21000, -630000, 9450000, -78840000, 395580000, -1186740000, -1186740000, -1663750000, -1663750001, 725760000, 21000]], [[-2, -6, -10, 9, -26, -10, -10, -10]], [[-300, 21000, 27, -78840000, 395580000, -1186740000, 1935360000, 1, -1663750000, 725760000, 1, -630000]], [[-16, -17, -301, -10, 3, -26, -37, 3]], [[-17, -10, 21000, 3, -10, -26, -37, -10]], [[1, -2, 3, -3, -6, 7, -8, -2, -10, 3]], [[-630001, -2, 3, 5, -6, 8, 5, -8, 8, -10]], [[7, -28, -38, -27, -17, -37, 7, -10]]] 

Generations

claude-3-haiku-20240307. fail_base: True, fail_plus: True

  Here's the code to complete the problem:

```python
import math


def poly(xs: list, x: float):
    """
    Evaluates polynomial with coefficients xs at point x.
    return xs[0] + xs[1] * x + xs[1] * x^2 + .... xs[n] * x^n
    """
    return sum([coeff * math.pow(x, i) for i, coeff in enumerate(xs)])


def find_zero(xs: list):
    """ xs are coefficients of a polynomial.
    find_zero find x such that poly(x) = 0.
    find_zero returns only only zero point, even if there are many.
    Moreover, find_zero only takes list xs having even number of coefficients
    and largest non zero coefficient as it guarantees
    a solution.
    >>> round(find_zero([1, 2]), 2) # f(x) = 1 + 2x
    -0.5
    >>> round(find_zero([-6, 11, -6, 1]), 2) # (x - 1) * (x - 2) * (x - 3) = -6 + 11x - 6x^2 + x^3
    1.0
    """
    if len(xs) % 2 != 0:
        raise ValueError("xs must have an even number of coefficients")

    a = xs[-2]
    b = xs[-1]

    if a == 0:
        raise ValueError("Largest coefficient must be non-zero")

    return -b / a

code-millenials-34b. fail_base: True, fail_plus: True

  import math

def poly(xs: list, x: float):
    """
    Evaluates polynomial with coefficients xs at point x.
    return xs[0] + xs[1] * x + xs[1] * x^2 + .... xs[n] * x^n
    """
    return sum([coeff * math.pow(x, i) for i, coeff in enumerate(xs)])

def find_zero(xs: list):
    """ xs are coefficients of a polynomial.
    find_zero find x such that poly(x) = 0.
    find_zero returns only only zero point, even if there are many.
    Moreover, find_zero only takes list xs having even number of coefficients
    and largest non zero coefficient as it guarantees
    a solution.
    >>> round(find_zero([1, 2]), 2) # f(x) = 1 + 2x
    -0.5
    >>> round(find_zero([-6, 11, -6, 1]), 2) # (x - 1) * (x - 2) * (x - 3) = -6 + 11x - 6x^2 + x^3
    1.0
    """
    # Newton's method is used to find the zero of the polynomial
    # Initial guess is the coefficient of the highest degree term
    x = xs[0]
    while abs(poly(xs, x)) > 1e-6:
        x = x - poly(xs, x) / poly(xs, x + 1e-6)
    return x

speechless-coding-7b-16k-tora. fail_base: True, fail_plus: True

  import math


def poly(xs: list, x: float):
    """
    Evaluates polynomial with coefficients xs at point x.
    return xs[0] + xs[1] * x + xs[1] * x^2 + .... xs[n] * x^n
    """
    return sum([coeff * math.pow(x, i) for i, coeff in enumerate(xs)])


def find_zero(xs: list):
    """ xs are coefficients of a polynomial.
    find_zero find x such that poly(x) = 0.
    find_zero returns only zero point, even if there are many.
    Moreover, find_zero only takes list xs having even number of coefficients
    and largest non zero coefficient as it guarantees
    a solution.
    """
    # Check if the list has an even number of coefficients and a non-zero coefficient
    if len(xs) % 2 != 0 or xs[0] == 0:
        raise ValueError("The list must have an even number of coefficients and a non-zero coefficient.")

    # Find the x value that makes the polynomial equal to zero
    x = 0
    while poly(xs, x) != 0:
        x += 0.001

    return x


# Test the function
print(round(find_zero([1, 2]), 2))  # f(x) = 1 + 2x
print(round(find_zero([-6, 11, -6, 1]), 2))  # (x - 1) * (x - 2) * (x - 3) = -6 + 11x - 6x^2 + x^3

claude-3-opus-20240229. fail_base: True, fail_plus: True

  Here's the completed code wrapped in a markdown block:

```python
import math


def poly(xs: list, x: float):
    """
    Evaluates polynomial with coefficients xs at point x.
    return xs[0] + xs[1] * x + xs[1] * x^2 + .... xs[n] * x^n
    """
    return sum([coeff * math.pow(x, i) for i, coeff in enumerate(xs)])


def find_zero(xs: list):
    """ xs are coefficients of a polynomial.
    find_zero find x such that poly(x) = 0.
    find_zero returns only only zero point, even if there are many.
    Moreover, find_zero only takes list xs having even number of coefficients
    and largest non zero coefficient as it guarantees
    a solution.
    >>> round(find_zero([1, 2]), 2) # f(x) = 1 + 2x
    -0.5
    >>> round(find_zero([-6, 11, -6, 1]), 2) # (x - 1) * (x - 2) * (x - 3) = -6 + 11x - 6x^2 + x^3
    1.0
    """
    if len(xs) % 2 != 0 or xs[-1] == 0:
        raise ValueError("Polynomial must have even number of coefficients and non-zero largest coefficient.")

    left, right = -1, 1
    while poly(xs, left) * poly(xs, right) > 0:
        left *= 2
        right *= 2

    while right - left > 1e-10:
        mid = (left + right) / 2
        if poly(xs, mid) * poly(xs, left) <= 0:
            right = mid
        else:
            left = mid

    return left

mixtral-8x7b-instruct. fail_base: True, fail_plus: True

  import math

def poly(xs: list, x: float):
    """
    Evaluates polynomial with coefficients xs at point x.
    return xs[0] + xs[1] * x + xs[1] * x^2 + .... xs[n] * x^n
    """
    return sum([coeff * math.pow(x, i) for i, coeff in enumerate(xs)])

def find_zero(xs: list):
    """ xs are coefficients of a polynomial.
    find_zero finds x such that poly(x) = 0.
    find_zero returns only one zero point, even if there are many.
    Moreover, find_zero only takes list xs having even number of coefficients
    and largest non zero coefficient as it guarantees
    a solution.
    """
    # Calculate the degree of the polynomial
    degree = len(xs) - 1

    # Iterate through possible values of x
    for i in range(degree, -1, -1):
        # Calculate the current value of the polynomial
        current_poly = poly(xs, i/degree)

        # If the polynomial is 0, return the current value of x
        if current_poly == 0:
            return i/degree

mixtral-8x22b-instruct-v0.1. fail_base: True, fail_plus: True

  import math

def poly(xs: list, x: float):
    """
    Evaluates polynomial with coefficients xs at point x.
    return xs[0] + xs[1] * x + xs[1] * x^2 + .... xs[n] * x^n
    """
    return sum([coeff * math.pow(x, i) for i, coeff in enumerate(xs)])

def find_zero(xs: list):
    """ xs are coefficients of a polynomial.
    find_zero find x such that poly(x) = 0.
    find_zero returns only only zero point, even if there are many.
    Moreover, find_zero only takes list xs having even number of coefficients
    and largest non zero coefficient as it guarantees
    a solution.
    """
    # Check if the list has an even number of coefficients
    if len(xs) % 2 != 0:
        raise ValueError("The list of coefficients must have an even number of elements.")

    # Find the largest non-zero coefficient
    max_coeff = max(xs)
    if max_coeff == 0:
        raise ValueError("The list of coefficients must have at least one non-zero element.")

    # Use the bisection method to find a zero of the polynomial
    a = -1000
    b = 1000
    while b - a > 1e-6:
        c = (a + b) / 2
        if poly(xs, a) * poly(xs, c) <= 0:
            b = c
        else:
            a = c

    return round(c, 2)

# Test cases

code-llama-multi-34b. fail_base: True, fail_plus: True

  import math


def poly(xs: list, x: float):
    """
    Evaluates polynomial with coefficients xs at point x.
    return xs[0] + xs[1] * x + xs[1] * x^2 + .... xs[n] * x^n
    """
    return sum([coeff * math.pow(x, i) for i, coeff in enumerate(xs)])


def find_zero(xs: list):
    """ xs are coefficients of a polynomial.
    find_zero find x such that poly(x) = 0.
    find_zero returns only only zero point, even if there are many.
    Moreover, find_zero only takes list xs having even number of coefficients
    and largest non zero coefficient as it guarantees
    a solution.
    >>> round(find_zero([1, 2]), 2) # f(x) = 1 + 2x
    -0.5
    >>> round(find_zero([-6, 11, -6, 1]), 2) # (x - 1) * (x - 2) * (x - 3) = -6 + 11x - 6x^2 + x^3
    1.0
    """
    if len(xs) % 2 == 1:
        raise ValueError("xs must have even number of coefficients")
    if xs[-1] == 0:
        raise ValueError("xs must have largest non zero coefficient")
    x = 0
    while True:
        y = poly(xs, x)
        if y == 0:
            return x
        x -= y / poly(xs[:-1], x)


if __name__ == "__main__":
    import doctest

    doctest.testmod()

Qwen--Qwen1.5-72B-Chat. fail_base: True, fail_plus: True

  import math


def poly(xs: list, x: float):
    """
    Evaluates polynomial with coefficients xs at point x.
    return xs[0] + xs[1] * x + xs[1] * x^2 + .... xs[n] * x^n
    """
    return sum([coeff * math.pow(x, i) for i, coeff in enumerate(xs)])


def find_zero(xs: list):
    """
    xs are coefficients of a polynomial.
    find_zero finds x such that poly(x) = 0.
    find_zero returns only one zero point, even if there are many.
    Moreover, find_zero only takes list xs having even number of coefficients
    and largest non-zero coefficient as it guarantees a solution.
    """
    if len(xs) % 2 == 1 or xs[-1] == 0:
        raise ValueError("Invalid input: xs must have an even number of coefficients and a non-zero last coefficient")

    roots = []
    for i in range(0, len(xs), 2):
        a = xs[i]
        b = xs[i + 1]
        if a == 0:
            continue
        root = -b / a
        roots.append(root)

    return roots[0]


# Test cases

mistral-large-latest. fail_base: True, fail_plus: True

  Sure, I can help you with that. The problem is asking to find a root of a polynomial function. For a polynomial of an even degree with a non-zero highest coefficient, we can guarantee at least one real root. However, finding roots of a polynomial is generally a complex problem and may not have a simple solution for polynomials of degree greater than 4.

For polynomials of degree 2 or less, we can use the quadratic formula or a simple formula for linear equations. For higher degrees, numerical methods like the Newton-Raphson method or bisection method can be used, but these methods may not always converge to a root or may converge to a complex root.

Here is a simple implementation using the Newton-Raphson method, which is a numerical method for finding roots of a function. This method may not always work, but it's a good starting point.

```python
import math

def poly(xs: list, x: float):
    """
    Evaluates polynomial with coefficients xs at point x.
    return xs[0] + xs[1] * x + xs[1] * x^2 + .... xs[n] * x^n
    """
    return sum([coeff * math.pow(x, i) for i, coeff in enumerate(xs)])

def poly_derivative(xs: list, x: float):
    """
    Evaluates derivative of polynomial with coefficients xs at point x.
    """
    return sum([coeff * i * math.pow(x, i-1) for i, coeff in enumerate(xs) if i > 0])

def find_zero(xs: list):
    """
    xs are coefficients of a polynomial.
    find_zero finds x such that poly(x) = 0.
    find_zero returns only one zero point, even if there are many.
    Moreover, find_zero only takes list xs having even number of coefficients
    and largest non zero coefficient as it guarantees a solution.
    """
    if len(xs) % 2 == 1 or xs[-1] == 0:
        raise ValueError("Coefficients must have an even number and a non-zero highest coefficient")

    # Starting point for Newton-Raphson method
    x0 = 0

    # Maximum number of iterations
    max_iter = 1000

    # Tolerance for convergence
    tol = 1e-9

    for _ in range(max_iter):
        x1 = x0 - poly(xs, x0) / poly_derivative(xs, x0)
        if abs(x1 - x0) < tol:
            return x1
        x0 = x1

    raise RuntimeError("Newton-Raphson method did not converge")
```

This code uses the Newton-Raphson method to find a root of the polynomial. The method starts with an initial guess (x0) and then iteratively refines that guess by computing the tangent line to the function at the current guess and finding the x-intercept of that tangent line. This x-intercept is then used as the next guess. The method stops when the guesses are sufficiently close to each other, indicating that we have found a root, or when we have reached the maximum number of iterations.

HuggingFaceH4--starchat2-15b-v0.1. fail_base: True, fail_plus: True

  import math

def poly(xs: list, x: float):
    """
    Evaluates polynomial with coefficients xs at point x.
    return xs[0] + xs[1] * x + xs[1] * x^2 + .... xs[n] * x^n
    """
    return sum([coeff * math.pow(x, i) for i, coeff in enumerate(xs)])

def find_zero(xs: list):
    """ xs are coefficients of a polynomial.
    find_zero find x such that poly(x) = 0.
    find_zero returns only only zero point, even if there are many.
    Moreover, find_zero only takes list xs having even number of coefficients
    and largest non zero coefficient as it guarantees
    a solution.
    >>> round(find_zero([1, 2]), 2) # f(x) = 1 + 2x
    -0.5
    >>> round(find_zero([-6, 11, -6, 1]), 2) # (x - 1) * (x - 2) * (x - 3) = -6 + 11x - 6x^2 + x^3
    1.0
    """
    # Check if the number of coefficients is even and the largest non-zero coefficient is at the end
    if len(xs) % 2 == 0 and xs[-1] != 0:
        # Use Newton's method to find the root
        x_n = 0  # Initial guess
        while True:
            f_x = poly(xs, x_n)
            f_prime_x = poly([coeff * i for i, coeff in enumerate(xs)][1:], x_n)
            x_n_next = x_n - f_x / f_prime_x
            if abs(x_n_next - x_n) < 1e-6:  # Stop when the difference is small enough
                return round(x_n_next, 2)
            x_n = x_n_next
    else:
        raise ValueError("Invalid input: xs should have even number of coefficients and largest non-zero coefficient at the end.")

# Test cases
assert round(find_zero([1, 2]), 2) == -0.5
assert round(find_zero([-6, 

codegemma-7b. fail_base: True, fail_plus: True

  from typing import List
import math

def poly(xs: List[float], x: float) -> float:
    """
    Evaluates polynomial with coefficients xs at point x.
    return xs[0] + xs[1] * x + xs[1] * x^2 + .... xs[n] * x^n
    """
    return sum([coeff * math.pow(x, i) for i, coeff in enumerate(xs)])

def find_zero(xs: List[float]) -> float:
    """ xs are coefficients of a polynomial.
    find_zero finds x such that poly(x) = 0.
    find_zero returns only only zero point, even if there are many.
    Moreover, find_zero only takes list xs having even number of coefficients
    and largest non zero coefficient as it guarantees
    a solution.
    """
    assert len(xs) % 2 == 0
    
    max_abs = max(abs(c) for c in xs)
    
    if max_abs == 0:
        raise ValueError("The provided polynomial has all coefficients as zero. It is not invertible.")
    
    for x in range(-100, 101):
        if abs(poly(xs, x)) < 1e-6:
            return x

print(round(find_zero([1, 2]), 2)) # f(x) = 1 + 2x
print(round(find_zero([-6, 11, -6, 1]), 2)) # (x - 1) * (x - 2) * (x - 3) = -6 + 11x - 6x^2 + x^3

code-llama-multi-13b. fail_base: True, fail_plus: True

  import math


def poly(xs: list, x: float):
    """
    Evaluates polynomial with coefficients xs at point x.
    return xs[0] + xs[1] * x + xs[1] * x^2 + .... xs[n] * x^n
    """
    return sum([coeff * math.pow(x, i) for i, coeff in enumerate(xs)])


def find_zero(xs: list):
    """ xs are coefficients of a polynomial.
    find_zero find x such that poly(x) = 0.
    find_zero returns only only zero point, even if there are many.
    Moreover, find_zero only takes list xs having even number of coefficients
    and largest non zero coefficient as it guarantees
    a solution.
    >>> round(find_zero([1, 2]), 2) # f(x) = 1 + 2x
    -0.5
    >>> round(find_zero([-6, 11, -6, 1]), 2) # (x - 1) * (x - 2) * (x - 3) = -6 + 11x - 6x^2 + x^3
    1.0
    """
    assert len(xs) % 2 == 0, "xs must have even number of coefficients"
    assert xs[0] != 0, "xs must have largest non zero coefficient"
    xs = xs[::-1]
    xs = [x / xs[0] for x in xs]
    xs = [x for x in xs if x != 0]
    xs = [x for x in xs if x != 1]
    xs = [x for x in xs if x != -1]
    if len(xs) == 0:
        return 0
    if len(xs) == 1:
        return -xs[0]
    if len(xs) == 2:
        return (xs[1] - math.sqrt(xs[1] ** 2 - 4 * xs[0])) / 2
    if len(xs) == 3:
        return (
            -xs[2]
            - math.sqrt(xs[2] ** 2 - 4 * xs[1])
            / (2 * xs[0])
            - math.sqrt(xs[2] ** 2 - 4 * xs[1])
            / (2 * xs[0])
        )
    if len(xs) == 4:
        return (
            -xs[3]
            - math.sqrt(xs[3] ** 2 - 4 * xs[2])
            / (2 * xs[1])
            - math.sqrt(xs[3] ** 2 - 4 * xs[2])
            / (2 * xs[1])
        )
    if len(xs) == 5:
        return (
            -xs[4]
            - math.sqrt(xs[4] ** 2 - 4 * xs[3])
            / (2 * xs[2])
            - math.sqrt(xs[4] ** 2 - 4 * xs[3])
            / (2 * xs[2])
        )
    if len(xs) == 6:
        return (
            -xs[5]
            - math.sqrt(xs[5] ** 2 - 4 * xs[4])
            / (2 * xs[

deepseek-coder-6.7b-instruct. fail_base: True, fail_plus: True

  Here is the Python function in a markdown style code block:

```python
import math

def poly(xs: list, x: float):
    """
    Evaluates polynomial with coefficients xs at point x.
    return xs[0] + xs[1] * x + xs[1] * x^2 + .... xs[n] * x^n
    """
    return sum([coeff * math.pow(x, i) for i, coeff in enumerate(xs)])

def find_zero(xs: list):
    """ xs are coefficients of a polynomial.
    find_zero find x such that poly(x) = 0.
    find_zero returns only only zero point, even if there are many.
    Moreover, find_zero only takes list xs having even number of coefficients
    and largest non zero coefficient as it guarantees
    a solution.
    >>> round(find_zero([1, 2]), 2) # f(x) = 1 + 2x
    -0.5
    >>> round(find_zero([-6, 11, -6, 1]), 2) # (x - 1) * (x - 2) * (x - 3) = -6 + 11x - 6x^2 + x^3
    1.0
    """
```

This code block contains two functions: `poly` and `find_zero`. The `poly` function takes a list of coefficients `xs` and a point `x`, and returns the value of the polynomial at that point. The `find_zero` function takes a list of coefficients `xs`, and returns a root of the polynomial. It only works with lists of even length and assumes that the largest coefficient is non-zero, as these conditions guarantee the existence of a root.

open-hermes-2.5-code-290k-13b. fail_base: True, fail_plus: True

  
import math


def poly(xs: list, x: float):
    """
    Evaluates polynomial with coefficients xs at point x.
    return xs[0] + xs[1] * x + xs[1] * x^2 + .... xs[n] * x^n
    """
    return sum([coeff * math.pow(x, i) for i, coeff in enumerate(xs)])


def find_zero(xs: list):
    """ xs are coefficients of a polynomial.
    find_zero finds x such that poly(x) = 0.
    find_zero returns only only zero point, even if there are many.
    Moreover, find_zero only takes list xs having even number of coefficients
    and largest non zero coefficient as it guarantees
    a solution.
    >>> round(find_zero([1, 2]), 2) # f(x) = 1 + 2x
    -0.5
    >>> round(find_zero([-6, 11, -6, 1]), 2) # (x - 1) * (x - 2) * (x - 3) = -6 + 11x - 6x^2 + x^3
    1.0
    """
    # Check if the input list has an even number of coefficients
    if len(xs) % 2 != 0:
        raise ValueError("Input list must have an even number of coefficients")

    # Find the largest non-zero coefficient
    max_coeff = max(xs)

    # If the largest non-zero coefficient is 0, there is no solution
    if max_coeff == 0:
        raise ValueError("Input list must have a non-zero largest coefficient")

    # Calculate the polynomial value at x = 0
    poly_value_at_zero = poly(xs, 0)

    # Calculate the polynomial value at x = -max_coeff / max_coeff
    zero_point = -max_coeff / max_coeff

    return round(zero_point, 2)

speechless-coder-ds-6.7b. fail_base: True, fail_plus: True

  import math

def poly(xs: list, x: float):
    """
    Evaluates polynomial with coefficients xs at point x.
    return xs[0] + xs[1] * x + xs[1] * x^2 + .... xs[n] * x^n
    """
    return sum([coeff * math.pow(x, i) for i, coeff in enumerate(xs)])

def find_zero(xs: list):
    """ xs are coefficients of a polynomial.
    find_zero find x such that poly(x) = 0.
    find_zero returns only only zero point, even if there are many.
    Moreover, find_zero only takes list xs having even number of coefficients
    and largest non zero coefficient as it guarantees
    a solution.
    >>> round(find_zero([1, 2]), 2) # f(x) = 1 + 2x
    -0.5
    >>> round(find_zero([-6, 11, -6, 1]), 2) # (x - 1) * (x - 2) * (x - 3) = -6 + 11x - 6x^2 + x^3
    1.0
    """
    if len(xs) % 2 != 0:
        raise ValueError("Number of coefficients must be even")
    if max(xs) == 0:
        raise ValueError("Largest coefficient must be non-zero")

    # Use Newton's method to find the zero of the polynomial
    x = 0
    while True:
        f = poly(xs, x)
        if abs(f) < 1e-6:
            return x
        df = sum([i * math.pow(x, i - 1) for i, _ in enumerate(xs)])
        x = x - f / df

codegemma-7b-it. fail_base: True, fail_plus: True

  import math


def poly(xs: list, x: float):
    """
    Evaluates polynomial with coefficients xs at point x.
    return xs[0] + xs[1] * x + xs[1] * x^2 + .... xs[n] * x^n
    """
    return sum([coeff * math.pow(x, i) for i, coeff in enumerate(xs)])


def find_zero(xs: list):
    """ xs are coefficients of a polynomial.
    find_zero find x such that poly(x) = 0.
    find_zero returns only only zero point, even if there are many.
    Moreover, find_zero only takes list xs having even number of coefficients
    and largest non zero coefficient as it guarantees
    a solution.
    >>> round(find_zero([1, 2]), 2) # f(x) = 1 + 2x
    -0.5
    >>> round(find_zero([-6, 11, -6, 1]), 2) # (x - 1) * (x - 2) * (x - 3) = -6 + 11x - 6x^2 + x^3
    1.0
    """
    if len(xs) % 2 != 0 or xs[-1] == 0:
        raise ValueError("Invalid input list")

    def f(x):
        return poly(xs, x)

    def df(x):
        return sum([coeff * i * math.pow(x, i - 1) for i, coeff in enumerate(xs[1:], start=1)])

    def newton(x):
        return x - f(x) / df(x)

    x = 0
    for _ in range(100):
        x = newton(x)
    return x

deepseek-coder-33b. fail_base: True, fail_plus: True

  import math


def poly(xs: list, x: float):
    """
    Evaluates polynomial with coefficients xs at point x.
    return xs[0] + xs[1] * x + xs[1] * x^2 + .... xs[n] * x^n
    """
    return sum([coeff * math.pow(x, i) for i, coeff in enumerate(xs)])


def find_zero(xs: list):
    """ xs are coefficients of a polynomial.
    find_zero find x such that poly(x) = 0.
    find_zero returns only only zero point, even if there are many.
    Moreover, find_zero only takes list xs having even number of coefficients
    and largest non zero coefficient as it guarantees
    a solution.
    >>> round(find_zero([1, 2]), 2) # f(x) = 1 + 2x
    -0.5
    >>> round(find_zero([-6, 11, -6, 1]), 2) # (x - 1) * (x - 2) * (x - 3) = -6 + 11x - 6x^2 + x^3
    1.0
    """
    # find largest non zero coefficient
    n = len(xs)
    for i in range(n - 1, -1, -1):
        if xs[i] != 0:
            break
    # find zero point
    x = 0
    for i in range(n - 1, -1, -1):
        x = x * (n - 1) + xs[i]
    return -x / xs[n - 1]

mistralai--Mistral-7B-Instruct-v0.2. fail_base: True, fail_plus: True

  import math


def poly(xs: list, x: float):
    """
    Evaluates polynomial with coefficients xs at point x.
    return xs[0] + xs[1] * x + xs[1] * x^2 + .... xs[n] * x^n
    """
    return sum([coeff * math.pow(x, i) for i, coeff in enumerate(xs)])


def find_zero(xs: list):
    """ xs are coefficients of a polynomial.
    find_zero find x such that poly(x) = 0.
    find_zero returns only only zero point, even if there are many.
    Moreover, find_zero only takes list xs having even number of coefficients
    and largest non zero coefficient as it guarantees
    a solution.
    >>> round(find_zero([1, 2]), 2) # f(x) = 1 + 2x
    -0.5
    >>> round(find_zero([-6, 11, -6, 1]), 2) # (x - 1) * (x - 2) * (x - 3) = -6 + 11x - 6x^2 + x^3
    1.0
    """
import math
def poly(xs, x):
    """
    Evaluates polynomial with coefficients xs at point x.
    """
    return sum([coeff * math.pow(x, i) for i, coeff in enumerate(xs)])

def find_zero(xs):
    """
    Finds the zero of a polynomial with even number of coefficients.
    """
    if len(xs) % 2 != 0:
        raise ValueError("xs should have an even number of coefficients.")

    n = len(xs) // 2
    a = xs[0]
    b, c = 0, 1
    for _ in range(n):
        b, c = c, a - x * c / b
    return -c / b

xwincoder-34b. fail_base: True, fail_plus: True

  import math


def poly(xs: list, x: float):
    """
    Evaluates polynomial with coefficients xs at point x.
    return xs[0] + xs[1] * x + xs[1] * x^2 + .... xs[n] * x^n
    """
    return sum([coeff * math.pow(x, i) for i, coeff in enumerate(xs)])


def find_zero(xs: list):
    """ xs are coefficients of a polynomial.
    find_zero find x such that poly(x) = 0.
    find_zero returns only only zero point, even if there are many.
    Moreover, find_zero only takes list xs having even number of coefficients
    and largest non zero coefficient as it guarantees
    a solution.
    >>> round(find_zero([1, 2]), 2) # f(x) = 1 + 2x
    -0.5
    >>> round(find_zero([-6, 11, -6, 1]), 2) # (x - 1) * (x - 2) * (x - 3) = -6 + 11x - 6x^2 + x^3
    1.0
    """
    if len(xs) % 2 != 0:
        raise ValueError("The list of coefficients must have an even number of elements.")
    
    if not all(coeff == 0 for coeff in xs[::2]):
        raise ValueError("The largest non-zero coefficient must be at an even index.")
    
    a = xs[-2]
    b = xs[-3]
    return -b / (2 * a)


# Test cases
print(round(find_zero([1, 2]), 2))  # f(x) = 1 + 2x
print(round(find_zero([-6, 11, -6, 1]), 2))  # (x - 1) * (x - 2) * (x - 3) = -6 + 11x - 6x^2 + x^3

code-13b. fail_base: True, fail_plus: True

  import math

def poly(xs: list, x: float):
    """
    Evaluates polynomial with coefficients xs at point x.
    return xs[0] + xs[1] * x + xs[1] * x^2 + .... xs[n] * x^n
    """
    return sum([coeff * math.pow(x, i) for i, coeff in enumerate(xs)])

def find_zero(xs: list):
    """ xs are coefficients of a polynomial.
    find_zero find x such that poly(x) = 0.
    find_zero returns only only zero point, even if there are many.
    Moreover, find_zero only takes list xs having even number of coefficients
    and largest non zero coefficient as it guarantees
    a solution.
    >>> round(find_zero([1, 2]), 2) # f(x) = 1 + 2x
    -0.5
    >>> round(find_zero([-6, 11, -6, 1]), 2) # (x - 1) * (x - 2) * (x - 3) = -6 + 11x - 6x^2 + x^3
    1.0
    """
    # find the zero of the polynomial
    zero = 0
    f = poly(xs, zero)
    if f == 0:
        return zero
    else:
        # if the polynomial is not zero at the zero point,
        # then there is no real zero for this polynomial
        return None

# test cases
print(round(find_zero([1, 2]), 2))  # f(x) = 1 + 2x
print(round(find_zero([-6, 11, -6, 1]), 2))  # (x - 1) * (x - 2) * (x - 3) = -6 + 11x - 6x^2 + x^3

wizardcoder-15b. fail_base: True, fail_plus: True

  Here's the Python script for the problem:

```python
import math


def poly(xs: list, x: float):
    """
    Evaluates polynomial with coefficients xs at point x.
    return xs[0] + xs[1] * x + xs[1] * x^2 + .... xs[n] * x^n
    """
    return sum([coeff * math.pow(x, i) for i, coeff in enumerate(xs)])


def find_zero(xs: list):
    """ xs are coefficients of a polynomial.
    find_zero find x such that poly(x) = 0.
    find_zero returns only only zero point, even if there are many.
    Moreover, find_zero only takes list xs having even number of coefficients
    and largest non zero coefficient as it guarantees
    a solution.
    """
    if len(xs) % 2 != 0:
        raise ValueError("Length of xs should be even")
    max_coeff = max(abs(coeff) for coeff in xs)
    xs = [coeff / max_coeff for coeff in xs]
    for i in range(len(xs) // 2):
        if xs[i] == 0:
            xs[i] = 1
    xs = xs[:len(xs) // 2]
    xs.reverse()
    for i in range(len(xs)):
        xs[i] *= -1
    xs.reverse()
    xs = [coeff * max_coeff for coeff in xs]
    return poly(xs, 0)
```

The `poly` function takes a list of coefficients `xs` and a point `x` and returns the value of the polynomial at that point. The `find_zero` function takes a list of coefficients `xs` and finds the point `x` such that the polynomial `poly(x)` is equal to zero. The function first checks if the length of `xs` is even, and raises a `ValueError` if it is not. It then finds the largest non-zero coefficient in `xs` and divides all the coefficients by that value. It then reverses the list of coefficients and multiplies each coefficient by -1. Finally, it reverses the list of coefficients and multiplies each coefficient by the largest non-zero coefficient found earlier. It then calls the `poly` function with the modified list of coefficients and the point `x=0` to find the zero point.

mistral-7b-codealpaca. fail_base: True, fail_plus: True

  import math


def poly(xs: list, x: float):
    """
    Evaluates polynomial with coefficients xs at point x.
    return xs[0] + xs[1] * x + xs[1] * x^2 + .... xs[n] * x^n
    """
    return sum([coeff * math.pow(x, i) for i, coeff in enumerate(xs)])


def find_zero(xs: list):
    """ xs are coefficients of a polynomial.
    find_zero find x such that poly(x) = 0.
    find_zero returns only only zero point, even if there are many.
    Moreover, find_zero only takes list xs having even number of coefficients
    and largest non zero coefficient as it guarantees
    a solution.
    >>> round(find_zero([1, 2]), 2) # f(x) = 1 + 2x
    -0.5
    >>> round(find_zero([-6, 11, -6, 1]), 2) # (x - 1) * (x - 2) * (x - 3) = -6 + 11x - 6x^2 + x^3
    1.0
    """
    assert len(xs) % 2 == 0, "List of coefficients must have even number of elements"
    assert max(xs) != 0, "All coefficients must be non-zero to have a solution"

    a = xs[0]
    b = xs[1]
    for i in range(2, len(xs)):
        a += xs[i] * (b ** 2)
        b += xs[i] * b

    c = -a // b
    return round(c, 2)

deepseek-coder-33b-instruct. fail_base: True, fail_plus: True

  Here is the Python function implemented in a markdown style code block:

```python
import math

def poly(xs: list, x: float):
    """
    Evaluates polynomial with coefficients xs at point x.
    return xs[0] + xs[1] * x + xs[1] * x^2 + .... xs[n] * x^n
    """
    return sum([coeff * math.pow(x, i) for i, coeff in enumerate(xs)])

def find_zero(xs: list):
    """
    xs are coefficients of a polynomial.
    find_zero find x such that poly(x) = 0.
    find_zero returns only only zero point, even if there are many.
    Moreover, find_zero only takes list xs having even number of coefficients
    and largest non zero coefficient as it guarantees
    a solution.
    >>> round(find_zero([1, 2]), 2) # f(x) = 1 + 2x
    -0.5
    >>> round(find_zero([-6, 11, -6, 1]), 2) # (x - 1) * (x - 2) * (x - 3) = -6 + 11x - 6x^2 + x^3
    1.0
    """
    # Implementation of the function goes here
```

Please note that the implementation of the `find_zero` function is not provided in the question. You would need to implement this function based on the problem statement.
<|EOT|>

phi-2. fail_base: True, fail_plus: True

  import math


def poly(xs: list, x: float):
    """
    Evaluates polynomial with coefficients xs at point x.
    return xs[0] + xs[1] * x + xs[1] * x^2 + .... xs[n] * x^n
    """
    return sum([coeff * math.pow(x, i) for i, coeff in enumerate(xs)])


def find_zero(xs: list):
    """ xs are coefficients of a polynomial.
    find_zero find x such that poly(x) = 0.
    find_zero returns only only zero point, even if there are many.
    Moreover, find_zero only takes list xs having even number of coefficients
    and largest non zero coefficient as it guarantees
    a solution.
    >>> round(find_zero([1, 2]), 2) # f(x) = 1 + 2x
    -0.5
    >>> round(find_zero([-6, 11, -6, 1]), 2) # (x - 1) * (x - 2) * (x - 3) = -6 + 11x - 6x^2 + x^3
    1.0
    """
    if len(xs) % 2!= 0:
        raise ValueError("find_zero only takes list xs having even number of coefficients")
    if xs[0]!= 0:
        raise ValueError("find_zero only takes list xs having largest non zero coefficient as it guarantees a solution")
    if len(xs) == 2:
        return -xs[1] / xs[0]
    else:
        # find the root of x^2 - x - 6 = 0
        a = xs[1]
        b = -xs[0]
        c = -xs[2]
        delta = b * b - 4 * a * c
        if delta < 0:
            raise ValueError("find_zero only takes list xs having largest non zero coefficient as it guarantees a solution")
        elif delta == 0:
            return -b / (2 * a)
        else:
            return (-b + math.sqrt(delta)) / (2 * a)


def find_roots(xs: list):
    """ xs are coefficients of a polynomial.
    find_roots find all roots of a polynomial.
    find_roots returns only zero points, even if there are many.
    """
    if len(xs) % 2!= 0:
        raise ValueError("find_roots only takes list xs having even number of coefficients")
    if xs[0]!= 0:
        raise ValueError("find_roots only takes list xs having largest non zero coefficient as it guarantees a solution")
    if len(xs) == 2:
        return [-xs[1] / xs[0]]
    else:
        # find the roots of x^2 - x - 6 = 0
        a = xs[1]
        b = -xs[0]
        c = -xs[2]
        delta = b * b - 4 * a * c
        if delta < 0:
            raise ValueError("find_roots only takes list xs having largest non zero coefficient as it guarantees a solution")
        elif delta == 0:
            return [-b / (2 * a)]
        else:
            return [(-b + math.sqrt(delta)) / (2 * a

bigcode--starcoder2-15b-instruct-v0.1. fail_base: True, fail_plus: True

  import math


def poly(xs: list, x: float):
    """
    Evaluates polynomial with coefficients xs at point x.
    return xs[0] + xs[1] * x + xs[1] * x^2 + .... xs[n] * x^n
    """
    return sum([coeff * math.pow(x, i) for i, coeff in enumerate(xs)])


def find_zero(xs: list):
    """ xs are coefficients of a polynomial.
    find_zero find x such that poly(x) = 0.
    find_zero returns only only zero point, even if there are many.
    Moreover, find_zero only takes list xs having even number of coefficients
    and largest non zero coefficient as it guarantees
    a solution.
    >>> round(find_zero([1, 2]), 2) # f(x) = 1 + 2x
    -0.5
    >>> round(find_zero([-6, 11, -6, 1]), 2) # (x - 1) * (x - 2) * (x - 3) = -6 + 11x - 6x^2 + x^3
    1.0
    """
    assert len(xs) % 2 == 0, "xs must have even number of coefficients"
    assert xs[-1] != 0, "largest non zero coefficient must be non zero"
    return -xs[0] / xs[1]

white-rabbit-neo-33b-v1. fail_base: True, fail_plus: True

  import math

def poly(xs: list, x: float):
    """
    Evaluates polynomial with coefficients xs at point x.
    return xs[0] + xs[1] * x + xs[1] * x^2 + .... xs[n] * x^n
    """
    return sum([coeff * math.pow(x, i) for i, coeff in enumerate(xs)])

def find_zero(xs: list):
    """ xs are coefficients of a polynomial.
    find_zero find x such that poly(x) = 0.
    find_zero returns only only zero point, even if there are many.
    Moreover, find_zero only takes list xs having even number of coefficients
    and largest non zero coefficient as it guarantees
    a solution.
    >>> round(find_zero([1, 2]), 2) # f(x) = 1 + 2x
    -0.5
    >>> round(find_zero([-6, 11, -6, 1]), 2) # (x - 1) * (x - 2) * (x - 3) = -6 + 11x - 6x^2 + x^3
    1.0
    """
    # The largest non-zero coefficient is the last one
    largest_coeff = xs[-1]
    # The degree of the polynomial is the length of the list minus 1
    degree = len(xs) - 1
    # The initial guess for the zero point is the largest non-zero coefficient divided by the largest coefficient
    guess = largest_coeff / xs[0]
    # Newton's method to find the zero point
    while True:
        # Evaluate the polynomial at the current guess
        f_guess = poly(xs, guess)
        # If the guess is close enough to zero, return the guess
        if abs(f_guess) < 1e-10:
            return guess
        # Calculate the derivative of the polynomial at the current guess
        f_prime_guess = sum([coeff * math.pow(guess, i - 1) * i for i, coeff in enumerate(xs) if i > 0])
        # Update the guess using Newton's method
        guess = guess - f_guess / f_prime_guess

# Example usage:
print(find_zero([1, 2]))  # Should print -0.5
print(find_zero([-6, 11, -6, 1]))  # Should print 1.0

microsoft--Phi-3-mini-4k-instruct. fail_base: True, fail_plus: True

  import math


def poly(xs: list, x: float) -> float:
    """
    Evaluates polynomial with coefficients xs at point x.
    return xs[0] + xs[1] * x + xs[2] * x^2 + .... xs[n] * x^n
    """
    return sum([coeff * math.pow(x, i) for i, coeff in enumerate(xs)])


def find_zero(xs: list) -> float:
    """
    xs are coefficients of a polynomial.
    find_zero find x such that poly(x) = 0.
    find_zero returns only zero point, even if there are many.
    Moreover, find_zero only takes list xs having even number of coefficients
    and largest non-zero coefficient as it guarantees a solution.
    >>> round(find_zero([1, 2]), 2) # f(x) = 1 + 2x
    -0.5
    >>> round(find_zero([-6, 11, -6, 1]), 2) # (x - 1) * (x - 2) * (x - 3) = -6 + 11x - 6x^2 + x^3
    1.0
    """
    if len(xs) % 2 != 0 or xs[-1] == 0:
        raise ValueError("List must have even number of coefficients and largest non-zero coefficient")

    # Find the largest non-zero coefficient
    largest_coeff = max(filter(lambda x: x != 0, xs))

    # Find the roots of the polynomial (x - largest_coeff) * poly(x) = 0
    # Since the largest non-zero coefficient is the leading coefficient,
    # we can divide the polynomial by (x - largest_coeff) to get a simpler polynomial
    # with a leading coefficient of 1.
    simplified_poly = [coeff / largest_coeff for coeff in xs]

    # Use numpy's roots function to find the roots of the simplified polynomial
    import numpy as np
    roots = np.roots(simplified_poly)

    # Return the first root (

speechless-codellama-34b. fail_base: True, fail_plus: True

  import math

def poly(xs: list, x: float):
    """
    Evaluates polynomial with coefficients xs at point x.
    return xs[0] + xs[1] * x + xs[1] * x^2 + .... xs[n] * x^n
    """
    return sum([coeff * math.pow(x, i) for i, coeff in enumerate(xs)])

def find_zero(xs: list):
    """ xs are coefficients of a polynomial.
    find_zero find x such that poly(x) = 0.
    find_zero returns only one zero point, even if there are many.
    Moreover, find_zero only takes list xs having even number of coefficients
    and largest non zero coefficient as it guarantees
    a solution.
    """
    if len(xs) % 2 != 0 or xs[-1] == 0:
        raise ValueError("xs must have even number of coefficients and largest non zero coefficient must be non-zero")
    x = 0
    while abs(poly(xs, x)) > 1e-6:
        x -= poly(xs, x) / poly(xs, 2*x)
    return x
```

meta-llama-3-70b-instruct. fail_base: True, fail_plus: True

  import math
import numpy as np

def poly(xs: list, x: float):
    """
    Evaluates polynomial with coefficients xs at point x.
    return xs[0] + xs[1] * x + xs[1] * x^2 + .... xs[n] * x^n
    """
    return sum([coeff * math.pow(x, i) for i, coeff in enumerate(xs)])

def find_zero(xs: list):
    """ xs are coefficients of a polynomial.
    find_zero find x such that poly(x) = 0.
    find_zero returns only only zero point, even if there are many.
    Moreover, find_zero only takes list xs having even number of coefficients
    and largest non zero coefficient as it guarantees
    a solution.
    """
    if len(xs) % 2 != 0:
        raise ValueError("xs must have an even number of coefficients")
    roots = np.roots(xs)
    real_roots = roots[np.isreal(roots)]
    return real_roots[0].real

# Test cases
print(round(find_zero([1, 2]), 2))  # f(x) = 1 + 2x
print(round(find_zero([-6, 11, -6, 1]), 2))  # (x - 1) * (x - 2) * (x - 3) = -6 + 11x - 6x^2 + x^3

code-llama-70b-instruct. fail_base: True, fail_plus: True

  import math


def poly(xs: list, x: float):
    """
    Evaluates polynomial with coefficients xs at point x.
    return xs[0] + xs[1] * x + xs[1] * x^2 + .... xs[n] * x^n
    """
    return sum([coeff * math.pow(x, i) for i, coeff in enumerate(xs)])


def find_zero(xs: list):
    """ xs are coefficients of a polynomial.
    find_zero find x such that poly(x) = 0.
    find_zero returns only only zero point, even if there are many.
    Moreover, find_zero only takes list xs having even number of coefficients
    and largest non zero coefficient as it guarantees
    a solution.
    >>> round(find_zero([1, 2]), 2) # f(x) = 1 + 2x
    -0.5
    >>> round(find_zero([-6, 11, -6, 1]), 2) # (x - 1) * (x - 2) * (x - 3) = -6 + 11x - 6x^2 + x^3
    1.0
    """
    if len(xs) % 2 != 0 or xs[-1] == 0:
        raise ValueError("xs must have an even number of coefficients and the largest coefficient must be non-zero")

    x = 0
    while poly(xs, x) != 0:
        x += 0.001

    return x


if __name__ == "__main__":
    import doctest
    doctest.testmod()

opencodeinterpreter-ds-33b. fail_base: True, fail_plus: True

  ```python
import math

def poly(xs: list, x: float):
    """
    Evaluates polynomial with coefficients xs at point x.
    return xs[0] + xs[1] * x + xs[1] * x^2 + .... xs[n] * x^n
    """
    return sum([coeff * math.pow(x, i) for i, coeff in enumerate(xs)])

def find_zero(xs: list):
    """ xs are coefficients of a polynomial.
    find_zero find x such that poly(x) = 0.
    find_zero returns only only zero point, even if there are many.
    Moreover, find_zero only takes list xs having even number of coefficients
    and largest non zero coefficient as it guarantees
    a solution.
    >>> round(find_zero([1, 2]), 2) # f(x) = 1 + 2x
    -0.5
    >>> round(find_zero([-6, 11, -6, 1]), 2) # (x - 1) * (x - 2) * (x - 3) = -6 + 11x - 6x^2 + x^3
    1.0
    """
    # Find the largest non-zero coefficient
    max_coeff = max([coeff for coeff in xs if coeff != 0])

    # Find the index of the largest non-zero coefficient
    max_index = xs.index(max_coeff)

    # If the number of coefficients is even, return the index as the zero point
    if len(xs) % 2 == 0:
        return max_index

    # If the number of coefficients is odd, return the index of the largest non-zero coefficient
    else:
        return max_index
```

openchat. fail_base: True, fail_plus: True

  import math


def poly(xs: list, x: float):
    """
    Evaluates polynomial with coefficients xs at point x.
    return xs[0] + xs[1] * x + xs[1] * x^2 + .... xs[n] * x^n
    """
    return sum([coeff * math.pow(x, i) for i, coeff in enumerate(xs)])


def find_zero(xs: list):
    """ xs are coefficients of a polynomial.
    find_zero find x such that poly(x) = 0.
    find_zero returns only only zero point, even if there are many.
    Moreover, find_zero only takes list xs having even number of coefficients
    and largest non zero coefficient as it guarantees
    a solution.
    >>> round(find_zero([1, 2]), 2) # f(x) = 1 + 2x
    -0.5
    >>> round(find_zero([-6, 11, -6, 1]), 2) # (x - 1) * (x - 2) * (x - 3) = -6 + 11x - 6x^2 + x^3
    1.0
    """
    # Check if the list has an even number of coefficients
    if len(xs) % 2 != 0:
        raise ValueError("The list of coefficients must have an even number of elements.")

    # Find the largest non-zero coefficient
    max_coeff = max(abs(coeff) for coeff in xs)

    # Find the power of x corresponding to the largest non-zero coefficient
    max_power = len(xs) // 2 - 1

    # Find the zero of the polynomial using the Newton-Raphson method
    x = 1
    for _ in range(100):
        fx = poly(xs, x)
        dfx = poly([i for i, coeff in enumerate(xs) if i != max_power], x)
        x -= fx / dfx

    return round(x, 2)


# Test cases
print(find_zero([1, 2]))  # f(x) = 1 + 2x
print(find_zero([-6, 11, -6, 1]))  # (x - 1) * (x - 2) * (x - 3) = -6 + 11x - 6x^2 + x^3

deepseek-coder-7b-instruct-v1.5. fail_base: True, fail_plus: True

  import math


def poly(xs: list, x: float):
    """
    Evaluates polynomial with coefficients xs at point x.
    return xs[0] + xs[1] * x + xs[1] * x^2 + .... xs[n] * x^n
    """
    return sum([coeff * math.pow(x, i) for i, coeff in enumerate(xs)])


def find_zero(xs: list):
    """ xs are coefficients of a polynomial.
    find_zero find x such that poly(x) = 0.
    find_zero returns only only zero point, even if there are many.
    Moreover, find_zero only takes list xs having even number of coefficients
    and largest non zero coefficient as it guarantees
    a solution.
    >>> round(find_zero([1, 2]), 2) # f(x) = 1 + 2x
    -0.5
    >>> round(find_zero([-6, 11, -6, 1]), 2) # (x - 1) * (x - 2) * (x - 3) = -6 + 11x - 6x^2 + x^3
    1.0
    """
    if len(xs) % 2 != 0:
        raise ValueError("The list must have an even number of coefficients")
    if max(xs) != xs[0]:
        raise ValueError("The largest coefficient must be the first coefficient")

    a = xs[0]
    b = xs[1]
    if a == 0:
        return 0
    if b == 0:
        return -a

    c = xs[2]
    while c != 0:
        a, b, c = b, c, b * b - 4 * a * c
        if c < 0:
            raise ValueError("The polynomial has no real roots")
        root = (-b + math.sqrt(c)) / (2 * a)
        if poly(xs, root) == 0:
            return root

    return None

speechless-starcoder2-7b. fail_base: True, fail_plus: True

  import math

def poly(xs: list, x: float):
    """
    Evaluates polynomial with coefficients xs at point x.
    return xs[0] + xs[1] * x + xs[1] * x^2 + .... xs[n] * x^n
    """
    return sum([coeff * math.pow(x, i) for i, coeff in enumerate(xs)])

def find_zero(xs: list):
    """ xs are coefficients of a polynomial.
    find_zero find x such that poly(x) = 0.
    find_zero returns only only zero point, even if there are many.
    Moreover, find_zero only takes list xs having even number of coefficients
    and largest non zero coefficient as it guarantees
    a solution.
    >>> round(find_zero([1, 2]), 2) # f(x) = 1 + 2x
    -0.5
    >>> round(find_zero([-6, 11, -6, 1]), 2) # (x - 1) * (x - 2) * (x - 3) = -6 + 11x - 6x^2 + x^3
    1.0
    """
    # Check if the list has even number of coefficients
    if len(xs) % 2 != 0:
        raise ValueError("List should have even number of coefficients")

    # Check if the largest non-zero coefficient is positive
    if max(xs) < 0:
        raise ValueError("Largest non-zero coefficient should be positive")

    # Find the zero point using the quadratic formula
    a = xs[1]
    b = xs[0]
    c = -xs[2]
    d = b**2 - 4*a*c
    if d < 0:
        raise ValueError("No real roots")
    elif d == 0:
        return -b / (2*a)
    else:
        return (-b + math.sqrt(d)) / (2*a)

wizardcoder-7b. fail_base: True, fail_plus: True

  Here's the Python script for the given problem:

```python
import math

def poly(xs: list, x: float):
    """
    Evaluates polynomial with coefficients xs at point x.
    return xs[0] + xs[1] * x + xs[1] * x^2 + .... xs[n] * x^n
    """
    return sum([coeff * math.pow(x, i) for i, coeff in enumerate(xs)])

def find_zero(xs: list):
    """ xs are coefficients of a polynomial. 
    find_zero find x such that poly(x) = 0. 
    find_zero returns only zero point, even if there are many. 
    Moreover, find_zero only takes list xs having even number of coefficients
    and largest non zero coefficient as it guarantees 
    a solution. 
    >>> round(find_zero([1, 2]), 2) # f(x) = 1 + 2x
    -0.5
    >>> round(find_zero([-6, 11, -6, 1]), 2) # (x - 1) * (x - 2) * (x - 3) = -6 + 11x - 6x^2 + x^3
    1.0
    """
    if len(xs) % 2 != 0:
        raise ValueError("List must have even number of coefficients")
    if xs[-1] == 0:
        raise ValueError("Largest non-zero coefficient must be non-zero")
    
    # Find the index of the largest non-zero coefficient
    max_coeff_idx = len(xs) - 1
    for i in range(len(xs) - 2, -1, -1):
        if xs[i] != 0:
            max_coeff_idx = i
            break
    
    # Find the value of x such that the polynomial is zero
    x = -xs[max_coeff_idx] / xs[max_coeff_idx - 1]
    
    # Check if the polynomial is indeed zero at x
    if poly(xs, x) != 0:
        raise ValueError("No zero point found")
    
    return x
```

The `poly` function takes a list of coefficients `xs` and a value `x` and returns the value of the polynomial at that point. It uses the formula `sum([coeff * math.pow(x, i) for i, coeff in enumerate(xs)])` to evaluate the polynomial. The `find_zero` function takes a list of coefficients `xs` and returns the value of `x` such that the polynomial is zero. It first checks if the list has an even number of coefficients and if the largest non-zero coefficient is non-zero. If not, it raises a `ValueError`. Then, it finds the index of the largest non-zero coefficient and uses the formula `x = -xs[max_coeff_idx] / xs[max_coeff_idx - 1]` to find the value of `x` such that the polynomial is zero. Finally, it checks if the polynomial is indeed zero at `x` and returns it if it is, otherwise raises a `ValueError`. 

octocoder. fail_base: True, fail_plus: True

  import math


def poly(xs: list, x: float):
    """
    Evaluates polynomial with coefficients xs at point x.
    return xs[0] + xs[1] * x + xs[1] * x^2 + .... xs[n] * x^n
    """
    return sum([coeff * math.pow(x, i) for i, coeff in enumerate(xs)])


def find_zero(xs: list):
    """ xs are coefficients of a polynomial.
    find_zero find x such that poly(x) = 0.
    find_zero returns only only zero point, even if there are many.
    Moreover, find_zero only takes list xs having even number of coefficients
    and largest non zero coefficient as it guarantees
    a solution.
    >>> round(find_zero([1, 2]), 2) # f(x) = 1 + 2x
    -0.5
    >>> round(find_zero([-6, 11, -6, 1]), 2) # (x - 1) * (x - 2) * (x - 3) = -6 + 11x - 6x^2 + x^3
    1.0
    """

    if len(xs) % 2 == 1:
        raise ValueError("find_zero only takes list xs having even number of coefficients")
    if xs[0] == 0:
        raise ValueError("find_zero only takes list xs having largest non zero coefficient as it guarantees a solution")
    xs = xs[::-1]
    n = len(xs) // 2
    a = xs[n]
    b = xs[n - 1]
    c = xs[n - 2]
    d = xs[n - 3]
    x = (b * b - 4 * a * c) / (4 * a * a)
    return x

gemma-1.1-7b-it. fail_base: True, fail_plus: True

  import math


def poly(xs: list, x: float):
    """
    Evaluates polynomial with coefficients xs at point x.
    return xs[0] + xs[1] * x + xs[1] * x^2 + .... xs[n] * x^n
    """
    return sum([coeff * math.pow(x, i) for i, coeff in enumerate(xs)])


def find_zero(xs: list):
    """ xs are coefficients of a polynomial.
    find_zero find x such that poly(x) = 0.
    find_zero returns only only zero point, even if there are many.
    Moreover, find_zero only takes list xs having even number of coefficients
    and largest non zero coefficient as it guarantees
    a solution.
    """
    if len(xs) % 2 != 0:
        raise ValueError("Polynomial must have an even number of coefficients.")
    
    x = -xs[0] / xs[1]
    for i in range(2, len(xs), 2):
        x = x - (poly([xs[i], xs[i+1]], x) / (xs[i] * x + xs[i+1]))
    return round(x, 2)

gpt-3.5-turbo. fail_base: True, fail_plus: True

  Here is the completed code:

```python
import math


def poly(xs: list, x: float):
    """
    Evaluates polynomial with coefficients xs at point x.
    return xs[0] + xs[1] * x + xs[1] * x^2 + .... xs[n] * x^n
    """
    return sum([coeff * math.pow(x, i) for i, coeff in enumerate(xs)])


def find_zero(xs: list):
    """ xs are coefficients of a polynomial.
    find_zero find x such that poly(x) = 0.
    find_zero returns only only zero point, even if there are many.
    Moreover, find_zero only takes list xs having even number of coefficients
    and largest non zero coefficient as it guarantees
    a solution.
    >>> round(find_zero([1, 2]), 2) # f(x) = 1 + 2x
    -0.5
    >>> round(find_zero([-6, 11, -6, 1]), 2) # (x - 1) * (x - 2) * (x - 3) = -6 + 11x - 6x^2 + x^3
    1.0
    """
    if len(xs) % 2 != 0:
        raise ValueError("The list of coefficients must have an even number of elements.")
    if xs[-1] == 0:
        raise ValueError("The largest non-zero coefficient must be non-zero.")
    
    # Use the numpy library to find the roots of the polynomial
    import numpy as np
    roots = np.roots(xs)
    
    # Return the first real root found
    for root in roots:
        if np.isreal(root):
            return float(root.real)
    
    # If no real root is found, raise an exception
    raise ValueError("No real root found for the given polynomial.")
```

This code defines a function `find_zero` that takes a list of polynomial coefficients and finds a zero point of the polynomial. It uses the `numpy` library to find the roots of the polynomial and returns the first real root found. If no real root is found, it raises a `ValueError` exception. The code also includes some input validation to ensure that the list of coefficients has an even number of elements and that the largest non-zero coefficient is non-zero.

codebooga-34b. fail_base: True, fail_plus: True

  import math


def poly(xs: list, x: float):
    """
    Evaluates polynomial with coefficients xs at point x.
    return xs[0] + xs[1] * x + xs[1] * x^2 + .... xs[n] * x^n
    """
    return sum([coeff * math.pow(x, i) for i, coeff in enumerate(xs)])


def find_zero(xs: list):
    """ xs are coefficients of a polynomial.
    find_zero find x such that poly(x) = 0.
    find_zero returns only only zero point, even if there are many.
    Moreover, find_zero only takes list xs having even number of coefficients
    and largest non zero coefficient as it guarantees
    a solution.
    >>> round(find_zero([1, 2]), 2) # f(x) = 1 + 2x
    -0.5
    >>> round(find_zero([-6, 11, -6, 1]), 2) # (x - 1) * (x - 2) * (x - 3) = -6 + 11x - 6x^2 + x^3
    1.0
    """
    if len(xs) % 2 == 1:
        raise ValueError("Polynomial must have even number of coefficients")
    if xs[-1] == 0:
        raise ValueError("Largest coefficient must be non-zero")
    x = -xs[-2] / (2 * xs[-1])
    while abs(poly(xs, x)) > 1e-6:
        x = x - poly(xs, x) / poly_derivative(xs, x)
    return x

deepseek-coder-1.3b-instruct. fail_base: True, fail_plus: True

  Here is the implementation of the function in markdown style:

```python
import math

def poly(xs: list, x: float):
    """
    Evaluates polynomial with coefficients xs at point x.
    return xs[0] + xs[1] * x + xs[1] * x^2 + .... xs[n] * x^n
    """
    return sum([coeff * math.pow(x, i) for i, coeff in enumerate(xs)])

def find_zero(xs: list):
    """ xs are coefficients of a polynomial.
    find_zero find x such that poly(x) = 0.
    find_zero returns only only zero point, even if there are many.
    Moreover, find_zero only takes list xs having even number of coefficients
    and largest non zero coefficient as it guarantees
    a solution.
    >>> round(find_zero([1, 2]), 2) # f(x) = 1 + 2x
    -0.5
    >>> round(find_zero([-6, 11, -6, 1]), 2) # (x - 1) * (x - 2) * (x - 3) = -6 + 11x - 6x^2 + x^3
    1.0
    """
    # Check if the list xs has even number of coefficients
    if len(xs) % 2 != 0:
        raise ValueError("The list xs must have an even number of coefficients")

    # Find the largest non-zero coefficient
    coeff = max(filter(lambda x: x != 0, xs))

    # Find the solution x such that poly(x) = 0
    x = (-1)**(xs.index(coeff) % 2) * coeff

    return x
```

This function first checks if the list xs has an even number of coefficients. If not, it raises a ValueError. Then it finds the largest non-zero coefficient in the list. The solution x is found by taking the negative of the coefficient if the index of the largest non-zero coefficient in the list is even, otherwise it takes the coefficient itself. Finally, it returns

speechless-mistral-7b. fail_base: True, fail_plus: True

  import math

def poly(xs: list, x: float):
    """
    Evaluates polynomial with coefficients xs at point x.
    return xs[0] + xs[1] * x + xs[1] * x^2 + .... xs[n] * x^n
    """
    return sum([coeff * math.pow(x, i) for i, coeff in enumerate(xs)])


def find_zero(xs: list):
    """ xs are coefficients of a polynomial.
    find_zero find x such that poly(x) = 0.
    find_zero returns only only zero point, even if there are many.
    Moreover, find_zero only takes list xs having even number of coefficients
    and largest non zero coefficient as it guarantees
    a solution.
    >>> round(find_zero([1, 2]), 2) # f(x) = 1 + 2x
    -0.5
    >>> round(find_zero([-6, 11, -6, 1]), 2) # (x - 1) * (x - 2) * (x - 3) = -6 + 11x - 6x^2 + x^3
    1.0
    """
    # Check if the list has an even number of coefficients
    if len(xs) % 2 != 0:
        raise ValueError("The list of coefficients must have an even number of elements.")

    # Find the largest non-zero coefficient
    max_coeff = max(abs(coeff) for coeff in xs)

    # Find the zero point
    zero_point = -(xs[0] / max_coeff)

    return zero_point
```

xdan-l1-chat. fail_base: True, fail_plus: True

  import math


def poly(xs: list, x: float):
    """
    Evaluates polynomial with coefficients xs at point x.
    return xs[0] + xs[1] * x + xs[1] * x^2 + .... xs[n] * x^n
    """
    return sum([coeff * math.pow(x, i) for i, coeff in enumerate(xs)])


def find_zero(xs: list):
    """ xs are coefficients of a polynomial.
    find_zero find x such that poly(x) = 0.
    find_zero returns only only zero point, even if there are many.
    Moreover, find_zero only takes list xs having even number of coefficients
    and largest non zero coefficient as it guarantees
    a solution.
    """
    assert len(xs) % 2 == 0, "xs must have even number of coefficients"
    assert max(abs(coeff) for coeff in xs) != 0, "xs must have non-zero coefficients"

    # Calculate the degree of the polynomial
    degree = len(xs) // 2 - 1

    # Use the Horner's method to find the zero
    x = 1
    for i in range(degree + 1):
        x = (x - xs[i] / (xs[i + 1] if i + 1 < len(xs) else 1))

    return round(x, 2)

solar-10.7b-instruct. fail_base: True, fail_plus: True

  import math


def poly(xs: list, x: float):
    """
    Evaluates polynomial with coefficients xs at point x.
    return xs[0] + xs[1] * x + xs[1] * x^2 + .... xs[n] * x^n
    """
    return sum([coeff * math.pow(x, i) for i, coeff in enumerate(xs)])


def find_zero(xs: list):
    """ xs are coefficients of a polynomial.
    find_zero find x such that poly(x) = 0.
    find_zero returns only only zero point, even if there are many.
    Moreover, find_zero only takes list xs having even number of coefficients
    and largest non zero coefficient as it guarantees
    a solution.
    >>> round(find_zero([1, 2]), 2) # f(x) = 1 + 2x
    -0.5
    >>> round(find_zero([-6, 11, -6, 1]), 2) # (x - 1) * (x - 2) * (x - 3) = -6 + 11x - 6x^2 + x^3
    1.0
    """
import math


def poly(xs: list, x: float):
    """
    Evaluates polynomial with coefficients xs at point x.
    return xs[0] + xs[1] * x + xs[1] * x^2 + .... xs[n] * x^n
    """
    return sum([coeff * math.pow(x, i) for i, coeff in enumerate(xs)])


def find_zero(xs: list):
    """ xs are coefficients of a polynomial.
    find_zero find x such that poly(x) = 0.
    find_zero returns only only zero point, even if there are many.
    Moreover, find_zero only takes list xs having even number of coefficients
    and largest non zero coefficient as it guarantees
    a solution.
    """
    if len(xs) % 2 != 0 or not xs or not xs[0]:
        raise ValueError("Invalid input, xs should have an even number of coefficients and the first coefficient should be non-zero.")

    # Calculate the degree of the polynomial
    degree = len(xs) // 2

    # Calculate the discriminant
    discriminant = (-1) ** (degree + 1) * reduce(lambda x, y: x * y, xs[1:degree * -1::-2], 1)

    # Calculate the value of x using the quadratic formula
    if degree == 1:
        return -xs[1]
    elif degree > 1:
        if discriminant > 0:
            # Two real solutions
            real_solutions = [(-bs + math.sqrt(discriminant)) / (2 * as_, (-bs - math.sqrt(discriminant)) / (2 * as_)]
            return real_solutions[0]
        elif discriminant == 0:
            # One real solution
            return -bs / (2 * as_)
        else:
            # Two complex conjugate solutions
            return complex(-bs / (2 * as_))


print(round(find_zero([1, 2]), 2))
print(round(find_zero([

claude-3-sonnet-20240229. fail_base: True, fail_plus: True

  Here's the code to complete the `find_zero` function:

```python
import math

def poly(xs: list, x: float):
    """
    Evaluates polynomial with coefficients xs at point x.
    return xs[0] + xs[1] * x + xs[1] * x^2 + .... xs[n] * x^n
    """
    return sum([coeff * math.pow(x, i) for i, coeff in enumerate(xs)])

def find_zero(xs: list):
    """ xs are coefficients of a polynomial.
    find_zero find x such that poly(x) = 0.
    find_zero returns only only zero point, even if there are many.
    Moreover, find_zero only takes list xs having even number of coefficients
    and largest non zero coefficient as it guarantees
    a solution.
    >>> round(find_zero([1, 2]), 2) # f(x) = 1 + 2x
    -0.5
    >>> round(find_zero([-6, 11, -6, 1]), 2) # (x - 1) * (x - 2) * (x - 3) = -6 + 11x - 6x^2 + x^3
    1.0
    """
    # Check if the list has an even number of coefficients
    if len(xs) % 2 != 0:
        raise ValueError("The list of coefficients must have an even number of elements.")

    # Find the largest non-zero coefficient
    max_coeff = max(abs(x) for x in xs)
    if max_coeff == 0:
        raise ValueError("The polynomial has no non-zero coefficients.")

    # Initialize the search interval
    a, b = -1, 1

    # Find the interval where the polynomial changes sign
    while poly(xs, a) * poly(xs, b) > 0:
        a -= 1
        b += 1

    # Use the bisection method to find the zero
    tolerance = 1e-9
    while abs(b - a) > tolerance:
        c = (a + b) / 2
        if poly(xs, c) == 0:
            return c
        elif poly(xs, a) * poly(xs, c) < 0:
            b = c
        else:
            a = c

    return (a + b) / 2

code-33b. fail_base: True, fail_plus: True

  import math

def poly(xs: list, x: float):
    """
    Evaluates polynomial with coefficients xs at point x.
    return xs[0] + xs[1] * x + xs[1] * x^2 + .... xs[n] * x^n
    """
    return sum([coeff * math.pow(x, i) for i, coeff in enumerate(xs)])


def find_zero(xs: list):
    """ xs are coefficients of a polynomial.
    find_zero find x such that poly(x) = 0.
    find_zero returns only only zero point, even if there are many.
    Moreover, find_zero only takes list xs having even number of coefficients
    and largest non zero coefficient as it guarantees
    a solution.
    >>> round(find_zero([1, 2]), 2) # f(x) = 1 + 2x
    -0.5
    >>> round(find_zero([-6, 11, -6, 1]), 2) # (x - 1) * (x - 2) * (x - 3) = -6 + 11x - 6x^2 + x^3
    1.0
    """
    if len(xs) % 2 == 0:
        for x in range(-100, 101):
            y = poly(xs, x)
            if abs(y) < 1e-6:  # here we are checking if y is very close to zero
                return x
    return None

starcoder2-15b-oci. fail_base: True, fail_plus: True

  import math


def poly(xs: list, x: float):
    """
    Evaluates polynomial with coefficients xs at point x.
    return xs[0] + xs[1] * x + xs[1] * x^2 + .... xs[n] * x^n
    """
    return sum([coeff * math.pow(x, i) for i, coeff in enumerate(xs)])


def find_zero(xs: list):
    """ xs are coefficients of a polynomial.
    find_zero find x such that poly(x) = 0.
    find_zero returns only only zero point, even if there are many.
    Moreover, find_zero only takes list xs having even number of coefficients
    and largest non zero coefficient as it guarantees
    a solution.
    >>> round(find_zero([1, 2]), 2) # f(x) = 1 + 2x
    -0.5
    >>> round(find_zero([-6, 11, -6, 1]), 2) # (x - 1) * (x - 2) * (x - 3) = -6 + 11x - 6x^2 + x^3
    1.0
    """

    if len(xs) % 2 != 0:
        raise ValueError("xs must have even number of coefficients")
    if xs[-1] == 0:
        raise ValueError("xs must have largest non zero coefficient")

    # TODO: implement find_zero
    return 0.0

speechless-starcoder2-15b. fail_base: True, fail_plus: True

  import math

def poly(xs: list, x: float):
    """
    Evaluates polynomial with coefficients xs at point x.
    return xs[0] + xs[1] * x + xs[1] * x^2 + .... xs[n] * x^n
    """
    return sum([coeff * math.pow(x, i) for i, coeff in enumerate(xs)])


def find_zero(xs: list):
    """ xs are coefficients of a polynomial.
    find_zero find x such that poly(x) = 0.
    find_zero returns only only zero point, even if there are many.
    Moreover, find_zero only takes list xs having even number of coefficients
    and largest non zero coefficient as it guarantees
    a solution.
    >>> round(find_zero([1, 2]), 2) # f(x) = 1 + 2x
    -0.5
    >>> round(find_zero([-6, 11, -6, 1]), 2) # (x - 1) * (x - 2) * (x - 3) = -6 + 11x - 6x^2 + x^3
    1.0
    """
    # Check if the list has even number of coefficients
    if len(xs) % 2 != 0:
        raise ValueError("The list should have even number of coefficients")

    # Check if the largest non zero coefficient is positive
    if xs[-1] < 0:
        raise ValueError("The largest non zero coefficient should be positive")

    # Find the zero point
    x = 0
    while poly(xs, x) != 0:
        x += 0.001

    return x

python-code-13b. fail_base: True, fail_plus: True

  import math


def poly(xs: list, x: float):
    """
    Evaluates polynomial with coefficients xs at point x.
    return xs[0] + xs[1] * x + xs[1] * x^2 + .... xs[n] * x^n
    """
    return sum([coeff * math.pow(x, i) for i, coeff in enumerate(xs)])


def find_zero(xs: list):
    """ xs are coefficients of a polynomial.
    find_zero find x such that poly(x) = 0.
    find_zero returns only only zero point, even if there are many.
    Moreover, find_zero only takes list xs having even number of coefficients
    and largest non zero coefficient as it guarantees
    a solution.
    >>> round(find_zero([1, 2]), 2) # f(x) = 1 + 2x
    -0.5
    >>> round(find_zero([-6, 11, -6, 1]), 2) # (x - 1) * (x - 2) * (x - 3) = -6 + 11x - 6x^2 + x^3
    1.0
    """
    n = len(xs)
    if n % 2 != 0 or abs(max(xs)) < 1e-10:
        raise ValueError("xs should have even number of coefficients and largest non zero coefficient should be close to 1")
    guess = (xs[0] + xs[1]) / 2  # initial guess
    while True:
        if poly(guess) == 0:
            return round(guess, 2)
        elif guess > 1e10:
            guess = (xs[0] + xs[1]) / 2  # restart with initial guess
        else:
            i = 1
            while i < n:
                guess = (guess + xs[i]) / 2
                i += 1
            return round(guess, 2)


# Testing
print(round(find_zero([1, 2]), 2))  # f(x) = 1 + 2x
print(round(find_zero([-6, 11, -6, 1]), 2))  # (x - 1) * (x - 2) * (x - 3) = -6 + 11x - 6x^2 + x^3

opencodeinterpreter-ds-6.7b. fail_base: True, fail_plus: True

  ```python
import math

def poly(xs: list, x: float):
    """
    Evaluates polynomial with coefficients xs at point x.
    return xs[0] + xs[1] * x + xs[1] * x^2 + .... xs[n] * x^n
    """
    return sum([coeff * math.pow(x, i) for i, coeff in enumerate(xs)])


def find_zero(xs: list):
    """ xs are coefficients of a polynomial.
    find_zero find x such that poly(x) = 0.
    find_zero returns only only zero point, even if there are many.
    Moreover, find_zero only takes list xs having even number of coefficients
    and largest non zero coefficient as it guarantees
    a solution.
    >>> round(find_zero([1, 2]), 2) # f(x) = 1 + 2x
    -0.5
    >>> round(find_zero([-6, 11, -6, 1]), 2) # (x - 1) * (x - 2) * (x - 3) = -6 + 11x - 6x^2 + x^3
    1.0
    """
    if len(xs) % 2 != 0:
        raise ValueError("The list of coefficients must have an even number of elements.")
    if max(xs) == 0:
        raise ValueError("The largest coefficient must be non-zero.")
    
    # Use the Newton-Raphson method to find a zero of the polynomial
    x = 0
    while True:
        f_x = poly(xs, x)
        if abs(f_x) < 1e-6:
            return x
        f_prime_x = sum([i * coeff * math.pow(x, i-1) for i, coeff in enumerate(xs)])
        x = x - f_x / f_prime_x
```