What are some good online solvers of huge systems of non-linear equations

Question

I'm wondering cause I want to solve a non-linear system of 8 equations. https://quickmath.com/ worked for 6 equations, but for 8 it says "internal error". Can anyone help? This is quite urgent. I want all of the solutions. Thanks!$$\left\{\begin{matrix}
s+w=0
\\t+ws+x=s
\\wv+ty+sz+ux=0
\\wu+v+tx+sy+z=t
\\tz+uy+vx=u
\\uz+vy=0
\\vz=v
\\wt+u+sx+y=0
\end{matrix}\right.$$

Answer 1

Not a full answer, but Wolfram Cloud solves this system and obtains 45 solutions. It refuses to display them all though.

You can sign up and check out yourself.

Though I wonder where and why would you need all 45 solutions.