If you do in the clear the first 400 iterations, say, and then run another 800 iterations on ciphertexts…
Done. I had to change some parameters of the experiments and therefore you will see slightly different plots than the one at the beginning of the post, but the gist is the same.
This is the precision plot with all the steps performed in ciphertext.
This is when the first 120 steps are done in plaintext in standard float32 and the remaining ones in ciphertext (note that the plot starts with step 120).
They are basically the same. The first one performed 494 steps, and the second one 584 (there was enough precision for a few more, but the PC crashed).