WesterBenchmarks - Sagemath Wiki

Performance Key
\times	wrong answer/cannot do the problem
s\ sec/ms/\mu s	performs correctly in time s
> s\ sec/ms/\mu s	does not finish in time s
>.<,s or >.<,\times	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.)
\sqrt{2\sqrt{3} + 4} \rightarrow 1 + \sqrt{3}
2\infty - 3 \rightarrow \infty
\frac{e^x-1}{e^{x/2}+1} \rightarrow e^{x/2} - 1
A(x \geq y, y \geq z, z \geq x); x = z?
A(x > y, y > 0); 2x^2 > 2y^2?
\frac{\cos(3x)}{\cos x} \rightarrow \cos^2 x - 3\sin^2 x
\frac{\cos(3x)}{\cos x} \rightarrow 2\cos(2x) - 1
A(x,y > 0); x^{1/n}y^{1/n} - (xy)^{1/n} \rightarrow 0
\log(\tan(\frac{1}{2}x + \frac{\pi}{4})) - \sinh^{-1}(\tan(x)) \rightarrow 0
\log\frac{2\sqrt{r} + 1}{\sqrt{4r + 4\sqrt{r} + 1}} \rightarrow 0