Complex sentence: For this case, a root-finding algorithms such as Newton's method is much simpler than the arithmetic-geometric mean algorithms above while converging at a similar asymptotic rate; the latter algorithms are required for transcendental trigonometric constants, however.
Split into simpler sentences: For this case, a root-finding algorithm such as Newton's method is much simpler than the arithmetic-geometric mean algorithms above while converging at a similar asymptotic rate. The latter algorithms are required for transcendental trigonometric constants, however.