/sci/ - Science & Math

In my opinion humans should learn to become more extremophile and I'm interested in small closed ecosystems for that purpose (e.g. space travel, living deep under the ground of Mercury, Moon, ...).
Let's define a human as a biochemical function that transforms the input molecules to the output molecules. One kg of long term average input or output could look like this (made up values):

input = [400g H2O, 350g O2, ...]
output = [300g CO2, 350g H2O, 30g CH4, ...]

Human bioreactor:
[math]f(input) = output, energy[/math]

Im interested in the reverse bioreactor:
[math]f^{-1}(output, energy) = input [/math]

If I could dream it would be great if we could build a [math]f^{-1}[/math] machine that weights 5
200 kg and needs 2 [math]m^3[/math] of space. It would ona long term average take 3kg of human excretions and 5kWh of energy (in the theoretical best case) and produce the molecules to power a human for a day.

What is the closest we are to such a machine (more precisely set of reactors)? In which areas are we already good and where are we really bad? I'm guessing it will involve hydroponics? If so, is hydroponics getting more mass, energy and volume efficient over time?