Rate > Cost > Instructions
Cost > Area > Cycles
Copper Sulfate (dirty)
Rate is defined as the number of cycles per outputted product ad infinitum. That is to say, your solution needs to loop. So for example, if your solution outputs once every four cycles, it has a rate of four. If it outputs twice every four cycles, it has a rate of two.
For this puzzle, since there are two outputs, the calculated rate is the rate of the slower output. Unless of course both products are outputted at an equal rate. Practically speaking, think of rate as kind of like cycles except you don't have to worry about the cycle count.
Grounded for the day for subordinate behaviour, a 12-year old Maximos Critelli finds himself wandering around his parent's basement, bored. His dad's old weird hex table looks visually interesting though, so he sits by it. Staring into its old, oddly hypnotic surface, he wonders.
He flicks through the tray table on the left; little arms, weird little mechanisms, all so intricate and strange. The bottom tray contains an unopened box labelled "alchemist learner's kit". His dad probably won't care, so he pokes inside. The instructions look long and boring to read. One sentence catches his eye though: "Master the science of alchemy, and you master the fabric of the universe itself". Huh.
The kit also comes with a vial called "reactive water" and some chunks of rust. Maximos is rather intrigued by the idea of turning this junk into whatever "Blue Vitriol" is. I'll let you, the reader, guess how Maximos spent his next 9 hours.