On my laptop the output is:

Testing edit distance in PyTorch vs. pure Python, with timeit
Running for 2500 iterations, best of 3.
Torch best: 3561.410 usec/loop, Python best: 554.336 usec/loop

Have you tried using numpy?

In any case, it is not surprising that pytorch would be slower than python with these for-loops, given the overhead coming from the pytorch/autograd/tensor infrastructure. You can see for example the performance comparison for filters in torchaudio.

Is your goal in using pytorch to have a differentiable edit_distance?

Note also that the filters mentioned above seem to perform best in pure C++ implementation, as we discussed offline. There is support for C++ extensions, e.g. here or pybind.