32.md

Results of GPT-3.5 on HumanEval/32

Date: 18 July, 2023
Model: gpt-3.5-turbo
Temperature: 0.2
Passing runs: 0
Total runs: 10
Success rate: 0%

Prompt

Tokens: 285

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 above is an incomplete Python code fragment. Return the complete and correct code with no additional text.

Correct solution

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
    """begin, end = -1., 1.
    while poly(xs, begin) * poly(xs, end) > 0:
        begin *= 2.0
        end *= 2.0
    while end - begin > 1e-10:
        center = (begin + end) / 2.0
        if poly(xs, center) * poly(xs, begin) > 0:
            begin = center
        else:
            end = center
    return begin

Unit tests

METADATA = {}


def check(candidate):
    import math
    import random
    rng = random.Random(42)
    import copy
    for _ in range(100):
        ncoeff = 2 * rng.randint(1, 4)
        coeffs = []
        for _ in range(ncoeff):
            coeff = rng.randint(-10, 10)
            if coeff == 0:
                coeff = 1
            coeffs.append(coeff)
        solution = candidate(copy.deepcopy(coeffs))
        assert math.fabs(poly(coeffs, solution)) < 1e-4

Runs

❌ Run 1

Start time: 2023-07-18 17:26:24
Duration: 14.76s
Completion tokens: 406
Result: Fail

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.")
    
    def f(x):
        return poly(xs, x)
    
    a = -1
    b = 1
    while abs(b - a) > 1e-9:
        c = (a + b) / 2
        if f(c) == 0:
            return c
        elif f(a) * f(c) < 0:
            b = c
        else:
            a = c
    
    return (a + b) / 2

❌ Run 2

Start time: 2023-07-18 17:26:10
Duration: 14.0s
Completion tokens: 400
Result: Fail

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 number of coefficients must be even.")
    if xs[-1] == 0:
        raise ValueError("The largest non-zero coefficient must be non-zero.")

    # Find the roots of the polynomial
    roots = []
    for i in range(len(xs) - 1):
        if xs[i] == 0:
            continue
        root = -xs[i + 1] / xs[i]
        roots.append(root)

    # Find the unique root
    unique_root = None
    for root in roots:
        if poly(xs, root) == 0:
            unique_root = root
            break

    return unique_root

❌ Run 3

Start time: 2023-07-18 17:25:56
Duration: 13.85s
Completion tokens: 387
Result: Fail

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.")
    
    # Find the zero point using the Newton-Raphson method
    x = 1.0
    while True:
        fx = poly(xs, x)
        f_prime_x = poly([i * coeff for i, coeff in enumerate(xs)][1:], x)
        x -= fx / f_prime_x
        if abs(fx) < 1e-6:
            return x

❌ Run 4

Start time: 2023-07-18 17:25:43
Duration: 13.54s
Completion tokens: 374
Result: Fail

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.")
    
    # Find the roots of the polynomial using numpy
    import numpy as np
    roots = np.roots(xs)
    
    # Filter out complex roots
    real_roots = [root.real for root in roots if np.isreal(root)]
    
    # Return the first real root
    return real_roots[0]

❌ Run 5

Start time: 2023-07-18 17:25:30
Duration: 12.87s
Completion tokens: 354
Result: Fail

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.")
    
    # Find the roots using numpy's roots function
    roots = np.roots(xs)
    
    # Return the first real root
    for root in roots:
        if np.isreal(root):
            return float(np.real(root))

❌ Run 6

Start time: 2023-07-18 17:25:15
Duration: 14.22s
Completion tokens: 406
Result: Fail

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.")
    
    def f(x):
        return poly(xs, x)
    
    a = -1
    b = 1
    while abs(b - a) > 1e-6:
        c = (a + b) / 2
        if f(c) == 0:
            return c
        elif f(a) * f(c) < 0:
            b = c
        else:
            a = c
    
    return (a + b) / 2

❌ Run 7

Start time: 2023-07-18 17:25:01
Duration: 14.13s
Completion tokens: 400
Result: Fail

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.")
    
    # Find the roots of the polynomial
    roots = []
    for i in range(len(xs)-1):
        if xs[i] == 0:
            continue
        root = -xs[i+1] / xs[i]
        roots.append(root)
    
    # Find the unique root
    zero = None
    for root in roots:
        if poly(xs, root) == 0:
            zero = root
            break
    
    return zero

❌ Run 8

Start time: 2023-07-18 17:24:47
Duration: 14.14s
Completion tokens: 406
Result: Fail

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.")
    
    def f(x):
        return poly(xs, x)
    
    a = -1
    b = 1
    while abs(b - a) > 1e-9:
        c = (a + b) / 2
        if f(c) == 0:
            return c
        elif f(a) * f(c) < 0:
            b = c
        else:
            a = c
    
    return (a + b) / 2

❌ Run 9

Start time: 2023-07-18 17:24:32
Duration: 15.45s
Completion tokens: 403
Result: Fail

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.")
    
    # Find the roots of the polynomial
    roots = []
    for i in range(len(xs)-1):
        if xs[i] == 0:
            continue
        root = -xs[i+1] / xs[i]
        roots.append(root)
    
    # Find the unique root
    unique_root = None
    for root in roots:
        if poly(xs, root) == 0:
            unique_root = root
            break
    
    return unique_root

❌ Run 10

Start time: 2023-07-18 17:23:47
Duration: 44.21s
Completion tokens: 364
Result: Fail

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 real root closest to zero
    zero = min(roots, key=lambda r: abs(r.real))
    return zero.real