This 100% checks out! I didn't recognize this at all. - "...in ideal arithmetic!" Comparing the two, Newton-Raphson seems rather better conditioned. I guess i

This 100% checks out! I didn't recognize this at all. - "...in ideal arithmetic!" Comparing the two, Newton-Raphson seems rather better conditioned. I guess it's the (1.0 + x^(2^i)) part that holds back the explicit-product version (adding a large float with a small one).