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from collections.abc import Sequence

def evaluate_poly(poly: Sequence[float], x: float) -> float:

"""Evaluate a polynomial f(x) at specified point x and return the value.

Arguments:

poly -- the coefficients of a polynomial as an iterable in order of

ascending degree

x -- the point at which to evaluate the polynomial

>>> evaluate_poly((0.0, 0.0, 5.0, 9.3, 7.0), 10.0)

79800.0

"""

return sum(c * (x**i) for i, c in enumerate(poly))

def horner(poly: Sequence[float], x: float) -> float:

"""Evaluate a polynomial at specified point using Horner's method.

In terms of computational complexity, Horner's method is an efficient method

of evaluating a polynomial. It avoids the use of expensive exponentiation,

and instead uses only multiplication and addition to evaluate the polynomial

in O(n), where n is the degree of the polynomial.

https://en.wikipedia.org/wiki/Horner's_method

Arguments:

poly -- the coefficients of a polynomial as an iterable in order of

ascending degree

x -- the point at which to evaluate the polynomial

>>> horner((0.0, 0.0, 5.0, 9.3, 7.0), 10.0)

79800.0

"""

result = 0.0

for coeff in reversed(poly):

result = result * x + coeff

return result

if __name__ == "__main__":

"""

Example:

>>> poly = (0.0, 0.0, 5.0, 9.3, 7.0) # f(x) = 7.0x^4 + 9.3x^3 + 5.0x^2

>>> x = -13.0

>>> # f(-13) = 7.0(-13)^4 + 9.3(-13)^3 + 5.0(-13)^2 = 180339.9

>>> evaluate_poly(poly, x)

180339.9

"""

poly = (0.0, 0.0, 5.0, 9.3, 7.0)

x = 10.0

print(evaluate_poly(poly, x))

print(horner(poly, x))

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