Test Taylor series approximations to sin

sin_approx.py

from math import factorial, pi, sin

def max_diff(f, g, v):
    return max(abs(f(x) - g(x)) for x in v)

def zigrange(x, s=1.0):
    yield 0
    for y in range(1, int(x / s + 0.5) + 1):
        yield y * s;
        yield -y * s;

# Test up to x**9 / (9!)
max_terms = 5

odd = lambda n: 2 * n + 1
terms = [lambda x, i=i:
         (-1)**i * x**(odd(i)) / factorial(odd(i)) for i in range(max_terms)]
apprs = [lambda x, n=n:
         sum(f(x) for f in terms[:n + 1]) for n in range(max_terms)]

for n, appr in enumerate(apprs):
    error = max_diff(sin, appr, zigrange(pi / 2, 1e-3))
    print("With {} terms, the maximum error is {}".format(n + 1, error))


# Results:
# With 1 terms, the maximum error is 0.5710000207413871
# With 2 terms, the maximum error is 0.07521538109194614
# With 3 terms, the maximum error is 0.004528924235860932
# With 4 terms, the maximum error is 0.00015708088474730708
# With 5 terms, the maximum error is 3.5476258620770196e-06