OK, maybe it's time to rephrase the question.
I'm shopping for a new 50mm f/0.45 lens. I've narrowed down my choices to the FlareMaster and the PurpleFringer. Both are 50/0.45s, they're the same size & weight, take the same size filters, etc. Setting them side-by-side, they appear identical. But the FlareMaster has 9 elements in 5 groups, and the PurpleFringer has 8 elements in 6 groups.
Which one should I choose, and why?
You may be kidding yourself.
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Any f/0.45 lens worthy of purchase probably has more than 9 elements.
Adding more elements is the hardest way, of design, of manufacture, of assembly, of justifying the purchase cost. It is done only because it is necessary for decent performance. Many buy the one with the highest performance. And zooms tremendously complicate everything, additional corrections have to be present for all focal lengths too.
In the early days (speaking of 1960s, when the earliest computer ray tracing was just beginning), Nikon used to publish detailed specs of every lens, including the cross sectional view of all the elements. Number of elements and groups was the FIRST line on the spec page, aperture was second. FWIW, there were mighty few zoom lenses at that time.
Longer telephoto lenses likely were four elements. And also not wider than f/4, which allowed four elements. A 400mm FX lens has a diagonal field of view of six degrees. Tiny angles, so light coming in at a greater angle was of no concern.
Wider lenses, wider than say 50mm, and wider than f/2.8, used many more elements (even back then).
50mm f/1.4 was 7 elements.
35mm f/2.8 was 7 elements.
24mm f/2.8 was 9 elements. (all typically a couple fewer groups)
20mm f/3.5 was 11 elements. (this was in the early 1960s - there is nothing new here).
These were NOT zooms.
Fnumber = focal length / aperture diameter.... so f/2.8 was a large diameter lens at 24mm. Large means that all those light rays from the outer extremes (far from center line) came in at a larger angle than those in the center. These angles require much more correction. This is what the extra elements address. Modern coatings reduce the downside, but groups also minimize internal reflections at the air-glass surfaces.
A 24 mm lens has a diagonal field of view of 84 degrees (FX), and 20 mm (FX) is 94 degrees. Compared to six degrees, these angles are an extreme concern about the rays not tracking right (not being sharp), requiring the additional correction and expense of more elements. A zoom, esp a wide zoom, will require more.
So instead, count your blessings.
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