It seems that decreases error curve always has the same shape. Is there a name for this shape? I assume you could sample just a few points and have a good estim

It seems that decreases error curve always has the same shape. Is there a name for this shape? I assume you could sample just a few points and have a good estimate of what the error will be for any truncation. And, this makes me naively assume you could apply some reversible transformation to the image, before applying this, to reduce some of the "perceptual" error (even if at the expense of numeric error)?