WesterBenchmarks - Sagemath Wiki

Performance Key
×	wrong answer/cannot do the problem
s sec/ms/μs	performs correctly in time s
>s sec/ms/μs	does not finish in time s
>.<,s or >.<,×	very difficult to convince system to do what you want (regardless of performance)

Problem	Maple	Mathematica	GiNaC	Maxima	Sage	Symbolics	Notes (such as code used/version etc.)
√2√3+4→1+√3					×
2∞−3→∞					s 47.2 µs
ex−1ex/2+1→ex/2−1					s 2.59 ms
A(x≥y,y≥z,z≥x);x=z?					s 1.57 ms
A(x>y,y>0);2x2>2y2?
cosxcos(3x)→cos2x−3sin2x
cosxcos(3x)→2cos(2x)−1
A(x,y>0);x1/ny1/n−(xy)1/n→0
log(tan(21x+4π))−sinh−1(tan(x))→0
log2√r+1√4r+4√r+1→0
√x\|z\|√xy\|z\|2→√x√xy/→√y					s 2.11 ms		Note √x=±√x
2x=0+1→2x+1=1
S(e2x+2ex+1=z,x)					s 4.85 ms
S((x+1)(sin2x+1)2cos3(3x)=0,x)
M−1, where M=[[x,1],[y,ez]]					s 3.93 ms
∑nk=1k3→4n2(n+1)2					s 24.6 ms
∑∞k=1(1k2+1k3)→6π2+ζ(3)
∏nk=1k→n!					s 5.82 ms
limn→∞(1+n1)n→e					s 6.93 ms
limx→0xsinx→1					s 5.95 ms
limx→0x21−cosx→21
d2dx2y(x(t))→dx2d2y(dtdx)2+dxdydt2d2x
ddx(∫1x3+2dx)→1x3+2
∫1a+bcosxdx(a<b)
ddx∫1a+bcosxdx=1a+bcosx
ddx\|x\|→x\|x\|
∫\|x\|dx→2x\|x\|
∫x√1+x+√1−xdx→3(1+x)3/2+(1−x)3/2
∫2√1+x+√1−xdx→3(1+x)3/2+(1−x)3/2
∫1−1x1dx→0 (p.v.)
∫1−11x2dx→ (div)
∫01√x+x1−2dx→34
∫12√x+x1−2dx→34−√8
\int_0^2\sqrt{x + \frac1x - 2}dx \rightarrow \frac{8-\sqrt8}3
A(a>0); \int_{-\infty}^\infty\frac{\cos x}{x^2+a^2}dx \rightarrow \frac\pi ae^{-a}
A(0 < a < 1); \int_0^\infty\frac{t^{a-1}}{t+1}dt \rightarrow \frac{\pi}{\sin(\pi a)}
T(\frac1{\sqrt{1-(x/c)^2}},x=0)
T((\log x)^ae^{-bx},x=1)
T(\log(\sinh z) + \log(\cosh(z + w)))
T(\log(\frac{\sin x}{x}), x=0)					s 5.19 ms		at order 20