Tony Cook emailed me to inform me that Imager has a new "mixing" algorithm for scaling that is much faster than the "normal" algorithm which I used. He was right. Here are some new benchmarks that override the ones in my presentation:
For size = 800:
s/iter Magick2 GD Imager Imlib2 Epeg
Magick2 3.44 -- -8% -29% -56% -76%
GD 3.16 9% -- -22% -52% -74%
Imager 2.46 40% 28% -- -38% -66%
Imlib2 1.52 127% 108% 62% -- -46%
Epeg 0.825 317% 282% 198% 84% --
For size = 210
s/iter GD Imager Imlib2 Magick2 Epeg
GD 2.36 -- -9% -46% -80% -89%
Imager 2.14 10% -- -40% -78% -87%
Imlib2 1.28 85% 68% -- -63% -79%
Magick2 0.469 404% 357% 172% -- -42%
Epeg 0.271 772% 691% 372% 73% --
So it does better, but thumbnail resizing is still nowhere near as good as Image::Magick. I suspect the trick for Image::Magick is to resize using pixel binning when the resize is less than 50%, and then follow up with a bicubic (or similar) resize. But I just don't know. I suspect the algorithm for Image::Magick ("Lanczos") is publicly documented somewhere.