Being lazy, I would be using the machine for most of the drying. Probably the line-drying (actually a folding wooden clothes drying rack) would be used on clothes that weren't quite dry, like waistbands on slacks.

The drying cycle is supposed to be quite energy efficient as it relies on extracting the water and sending it down the drain, rather than using high heat to evaporate the water (540 calories per gram of water!). The end of the wash cycle centrifuges the clothes at 1,200 RPM so they aren't all that wet to begin with.

tanstaafl.