As one point of comparison, SymPy is comically slow compared to Sage. This is mostly because SymPy is purely Python; Sage on the other hand uses its own derivative of GiNaC [1], Pynac [2], for its internal symbolic expression representation, and then multiple external libraries for non-trivial operations. Symbolic transformations are mostly Maxima [3], for example. Sage literally converts expressions to strings, pipes them through a Maxima process, and then parses the result back. This is still much faster than the pure Python SymPy.

There is an effort to speed up SymPy core, SymEngine [4], but it's been in development for years now, and still isn't integrated into SymPy. Not sure why.

Case in point: 'expand("(2 + 3 * x + 4 * x * y)^60")' takes 5 seconds with SymPy; Sage (Pynac) does the same in 0.02 seconds.

[1] https://www.ginac.de/

[2] http://pynac.org/

[3] http://maxima.sourceforge.net/

[4] https://github.com/symengine/symengine