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Rate (1/sec) = (result_amount / (recipe_time / machine_speed)) * productivity
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Rate (1/sec) = (result_amount / (recipe_time / machine_speed)) * productivity - (input_amount / (recipe_time / machine_speed))
Productivity of machine: 50%
If my calculations correct:
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Rate = (2 / (15 / 2)) * 1.5 = 0.4
Rate (catalytic) = (2 / (15 / 2)) * 1.5 - 1 / (15 / 2) = 0.26666
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Rate (catalytic, incorrect) = (2 / (15 / 2)) * 1.5 - 1 / 15 = 0.33333