Hi everyone,
I am Shuvro, a third-year CSE student from Bangladesh. I am planning to apply for the "Efficient Equations of Motion Generation" project this GSoC. Before finalising my proposal I wanted to share some profiling results and ask a few specific questions.
I spent the last few weeks running line_profiler on the real unmodified SymPy 1.15.0.dev source on my machine. For KanesMethod on a 5-link planar pendulum, _form_frstar takes up 94.6% of total kanes_equations() time. The three biggest costs inside it are the dot product loop at line 496 (36.2%), acc() at line 486 (22.6%), and two msubs() calls at lines 512–513 (7.4% combined). For LagrangesMethod at N=4, the jacobian and subs operations at lines 223–224 alone are 49.9% of total form_lagranges_equations() time (4.556s total).
I have three questions based on what I found:

1. Lines 512 and 513 in _form_frstar make two separate msubs() calls with different substitution maps, both walking the same expression tree. I want to merge them into one combined pass. Is there any ordering dependency between those two maps that would make merging unsafe?
2. For LagrangesMethod, lines 223–224 are running on the fully expanded Lagrangian. I want to apply cse() before line 189 and again before line 223 to reduce the expression size before differentiation. Is this the right place to apply it, or is there a pattern already used elsewhere in SymPy I should follow instead?
3. I looked at the Point.acc() source and saw it already caches results in _acc_dict. So the 22.6% cost at line 486 is the first-time computation for each body's masscenter, not a repeated recomputation. Would applying cse() to the velocity expressions before calling .dt(frame) help reduce that first-time cost?
   Happy to share my profiling scripts and full results if that would be useful.
   Thanks,
   Shuvro Bhattacharjee
   Sylhet Engineering College, Bangladesh
   github.com/shuvro-git