Wow, that dither function!

float dither_matrix (float x, float y) { return mix(mix(mix(mix(mix(mix(0.0,32.0,step(1.0,y)),mix(8.0,40.0,step(3.0,y)),step(2.0,y)),mix(mix(2.0,34.0,step(5.0,y)),mix(10.0,42.0,step(7.0,y)),step(6.0,y)),step(4.0,y)),mix(mix(mix(48.0,16.0,step(1.0,y)),mix(56.0,24.0,step(3.0,y)),step(2.0,y)),mix(mix(50.0,18.0,step(5.0,y)),mix(58.0,26.0,step(7.0,y)),step(6.0,y)),step(4.0,y)),step(1.0,x)),mix(mix(mix(mix(12.0,44.0,step(1.0,y)),mix(4.0,36.0,step(3.0,y)),step(2.0,y)),mix(mix(14.0,46.0,step(5.0,y)),mix(6.0,38.0,step(7.0,y)),step(6.0,y)),step(4.0,y)),mix(mix(mix(60.0,28.0,step(1.0,y)),mix(52.0,20.0,step(3.0,y)),step(2.0,y)),mix(mix(62.0,30.0,step(5.0,y)),mix(54.0,22.0,step(7.0,y)),step(6.0,y)),step(4.0,y)),step(3.0,x)),step(2.0,x)),mix(mix(mix(mix(mix(3.0,35.0,step(1.0,y)),mix(11.0,43.0,step(3.0,y)),step(2.0,y)),mix(mix(1.0,33.0,step(5.0,y)),mix(9.0,41.0,step(7.0,y)),step(6.0,y)),step(4.0,y)),mix(mix(mix(51.0,19.0,step(1.0,y)),mix(59.0,27.0,step(3.0,y)),step(2.0,y)),mix(mix(49.0,17.0,step(5.0,y)),mix(57.0,25.0,step(7.0,y)),step(6.0,y)),step(4.0,y)),step(5.0,x)),mix(mix(mix(mix(15.0,47.0,step(1.0,y)),mix(7.0,39.0,step(3.0,y)),step(2.0,y)),mix(mix(13.0,45.0,step(5.0,y)),mix(5.0,37.0,step(7.0,y)),step(6.0,y)),step(4.0,y)),mix(mix(mix(63.0,31.0,step(1.0,y)),mix(55.0,23.0,step(3.0,y)),step(2.0,y)),mix(mix(61.0,29.0,step(5.0,y)),mix(53.0,21.0,step(7.0,y)),step(6.0,y)),step(4.0,y)),step(7.0,x)),step(6.0,x)),step(4.0,x)); }

What exactly is it doing? There must be a faster way to do it!

Same goes for find_closest. Here's an idea: Convert the pixel's RGB value to HSL. Order the palette's color encoded in HSL by hue. Get the color that has the nearest hue (in O(1)). Then there are some simple refinement that you can do later if you have multiple palette colors that have similar hues.