Date: 18 July, 2023
Model: gpt-4
Temperature: 0.2
Passing runs: 3
Total runs: 10
Success rate: 30%
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.
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 beginMETADATA = {}
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-4Start time: 2023-07-18 18:48:35
Duration: 26.55s
Completion tokens: 369
Result: Fail
import math
from scipy.optimize import fsolve
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.
"""
return fsolve(poly, 0, args=(xs))
# Test cases
print(round(find_zero([1, 2])[0], 2)) # f(x) = 1 + 2x
print(round(find_zero([-6, 11, -6, 1])[0], 2)) # (x - 1) * (x - 2) * (x - 3) = -6 + 11x - 6x^2 + x^3Start time: 2023-07-18 18:48:09
Duration: 26.54s
Completion tokens: 349
Result: Fail
import math
from scipy.optimize import fsolve
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.
"""
return fsolve(lambda x: poly(xs, x), 0)[0]
# 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^3Start time: 2023-07-18 18:47:33
Duration: 36.24s
Completion tokens: 465
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.
"""
# Define the interval for the bisection method
a = -100
b = 100
# Bisection method
while abs(a - b) > 1e-6:
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
# 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^3Start time: 2023-07-18 18:46:53
Duration: 39.69s
Completion tokens: 522
Result: Pass
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 the derivative of polynomial with coefficients xs at point x.
return xs[1] + 2 * xs[2] * x + 3 * xs[3] * x^2 + .... n * xs[n] * x^(n-1)
"""
return sum([i * coeff * math.pow(x, i - 1) for i, coeff in enumerate(xs) if i > 0])
def find_zero(xs: list, initial_guess=0.0, tolerance=1e-7, max_iterations=1000):
""" 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.
"""
x = initial_guess
for _ in range(max_iterations):
f = poly(xs, x)
if abs(f) < tolerance:
return x
df = poly_derivative(xs, x)
if df == 0:
raise ValueError("Derivative is zero. The Newton-Raphson method fails.")
x -= f / df
raise ValueError("Failed to find a root within the maximum number of iterations.")Start time: 2023-07-18 18:46:21
Duration: 31.76s
Completion tokens: 363
Result: Fail
import math
from scipy.optimize import newton
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.
"""
return newton(lambda x: poly(xs, x), 0)
# 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^3Start time: 2023-07-18 18:45:48
Duration: 33.16s
Completion tokens: 367
Result: Fail
import math
from scipy.optimize import fsolve
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.
"""
return fsolve(poly, 0, args=(xs))
# Test cases
print(round(find_zero([1, 2])[0], 2)) # f(x) = 1 + 2x
print(round(find_zero([-6, 11, -6, 1])[0], 2)) # (x - 1) * (x - 2) * (x - 3) = -6 + 11x - 6x^2 + x^3Start time: 2023-07-18 18:45:18
Duration: 29.92s
Completion tokens: 408
Result: Fail
import math
from scipy.optimize import fsolve
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.
"""
return fsolve(poly, 0, args=(xs))
# Test cases
print(round(find_zero([1, 2])[0], 2)) # f(x) = 1 + 2x
print(round(find_zero([-6, 11, -6, 1])[0], 2)) # (x - 1) * (x - 2) * (x - 3) = -6 + 11x - 6x^2 + x^3Start time: 2023-07-18 18:44:41
Duration: 36.28s
Completion tokens: 485
Result: Pass
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 derivative(xs: list, x: float):
"""
Evaluates derivative of polynomial with coefficients xs at point x.
return xs[1] + 2 * xs[2] * x + 3 * xs[3] * x^2 + .... n * xs[n] * x^(n-1)
"""
return sum([i * coeff * math.pow(x, i - 1) for i, coeff in enumerate(xs[1:], start=1)])
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.
"""
x = 0.0
while abs(poly(xs, x)) > 1e-7:
x = x - poly(xs, x) / derivative(xs, x)
return x
# 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^3Start time: 2023-07-18 18:44:10
Duration: 30.94s
Completion tokens: 359
Result: Fail
import math
from scipy.optimize import fsolve
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.
"""
return fsolve(poly, 0, args=(xs))
# Test cases
print(round(find_zero([1, 2])[0], 2)) # f(x) = 1 + 2x
print(round(find_zero([-6, 11, -6, 1])[0], 2)) # (x - 1) * (x - 2) * (x - 3) = -6 + 11x - 6x^2 + x^3Start time: 2023-07-18 18:43:36
Duration: 34.21s
Completion tokens: 482
Result: Pass
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 the derivative of the polynomial with coefficients xs at point x.
"""
return sum([i * coeff * 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 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.
"""
# Initial guess
x = 0.0
# Tolerance and maximum number of iterations
epsilon = 1e-7
max_iterations = 1000
for _ in range(max_iterations):
f = poly(xs, x)
df = poly_derivative(xs, x)
if abs(f) < epsilon:
return x
x = x - f / df
raise ValueError("No solution found within the maximum number of iterations")
# 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