I've been doing this for 7+ years now and others may find it useful.
People have been using "gray water" by recycling it into the garden and lawn. "Gray water" being anything that doesn't contain human or animal waste - water from the sinks and showers.
I wanted to do that, but it was too much hassle with my single story house and elevation or lack of it - would take a holding tank and a pump to move it - and there's enough nutrients there to insure that it would not be esthetically pleasant.
But . . . the wash machine is another story. Mine uses ~20 gallons per cycle - one wash / one rinse is 40 gallons. The beauty of it is it has a pump to remove the water and the water is nutrient rich.
The discharge hose on mine is 1" and I used a "T" connector to mate it to a 3/4" poly tube that I ran out to a flower garden. Cost was minimal and it took less than a day to run the tubing under the house and underground out to the garden. Quick work with a mattock to bury the tubing 18" underground - no rocks in the soil.
The straight shot from the "T" goes to the 3/4" and the branch goes to the normal cup sink the washer normally discharges to - via a short piece of 1/2" sweated copper with a 90 degree bend (to add a small amount of restriction)
3/4" tubing works like a champ because it has a smooth bore and only takes a 20" radius bend so there's very little restriction and no need for a check valve or vacuum breaker or anything fancier than a T connector. It is also cheap.The branch in the T insures that any back flow - from a higher elevation goes into the cup sink and if the end of the discharge hose has water in it and freezes - the water from the machine still has a place to go.
No watering, no fertilizing, and it maintains a 250 square foot flower garden and a tree or two. One or two loads of laundry a week that I have to do anyway.