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