Faceted displacement

[guache]

I'm getting a faceted appearance using a disp map, corresponding to the pixels in the disp map. Any way to smooth this out *without* increasing map resolution, increasing shading quality etc? Do I need to create vertex normals from the displaced geometry normals somehow? The displacement map is a float exr image, so color depth is not a problem. The vex code doing the displacement is as follows:

vector mapclr=0;
float mult=1.0;
mapclr=texture(map,s,t);
P+=mult*mapclr.r*normalize(N);
N = computenormal(P);