I tried all sorts of approaches for sum.

My first approach didn't use a duplicator, meaning it had 18 waste atoms, and that turned out to be really awkward because the waste handling was more expensive than a duplicator.

Then I committed hard to the duplicator and built a solution with an earth-fire catalyst that calcified everything and fed it through.  But that was overengineered, and too expensive for how slow it turned out.

With those designs under my belt, I figured something like 160 cost 120 cycles was attainable, and set out to make it.  I kept having to add expense, so what wanted to be 160/120/50 became 190/92/56.  But that was my new best sum regardless.  Annoyingly, it had no way to loop due to access points.

I was dissatisfied so I started fresh, made a much cheaper design.  Versions of that design from 155g down to 130g were still fast enough to be competitive, but would lose out to my dissatisfying target by around a dozen due to being over 70 area.

Then on the last day, I made a design that did its duplication within the already bonded product.  Identical elements are never adjacent in this product, so that idea didn't seem good on paper.  However, there's one extra salt if I stick 5 inputs together, and if I leave it attached it can aid in duplication.  Break it off as waste and you never need a calcifier.  This turned out to be convenient enough to pass my previous mark on sum.

In the final hour, I managed to find a 6P version that saved my waste bonder at the cost of 6 cycles and 1 area.  I had to make it loop for secondary, which I really enjoyed doing.  Thus, funny carrot factory was created.