Comment #20 on issue 1038 by [email protected]:
(sin(x)*cos(x)).series(x, 0, 1000) takes forever
http://code.google.com/p/sympy/issues/detail?id=1038
Hi,
with taylor in http:github.com/pernici/sympy this issue can be solved.
taylor can be used as series
from sympy import *
from sympy.polys.ltaylor import taylor
x = Symbol('x')
taylor(sin(x),x,0,10)
x - x**3/6 + x**5/120 - x**7/5040 + x**9/362880 + O(x**10)
Below are benchmarks for this problem and variations
for each precision the taylor expansions of these functions are benchmarked
sin(x)
cos(x)*sin(x)
cos(x + x**2)*sin(x - 2*x**2)
cos(x)*sin(x)*cos(2*x)*sin(2*x)
cos(sin(x))*sin(sin(x))
on Intel Core2 Quad Q8200 2.33GHz
times in seconds
on Intel Core2 Quad Q8200 2.33GHz
times in seconds
prec series taylor
10 0.026 0.018
0.10 0.019
0.30 0.04
0.20 0.02
3.4 0.02
100 0.23 0.18
1.7 0.19
19 0.46
4.8 0.21
0.35
200 0.47 0.36
7.9 0.4
167 1.4
32 0.53
1.6
300 0.7 0.5
28 0.7
3.4
1.0
5.0
400 0.9 0.7
81 1.0
6.8
1.8
12
1000 1.9
5.4
98
18
242
Mario
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