I haven’t had much time with this but I found in testing that by changing the Hellwig2022 model by removing the 0.1 addition from the post adaptation cone response formula and the 0.305 subtraction from the achromatic response formula, the inverse with @bottosson’s compression algorithm is almost identical to inverse with ACES GC algorithm. Nothing seems to change with the ACES GC so it’s not like it improves inverse, but it does have huge impact with the current compression algorithm. See the difference images in the post above to get an idea.
So the formulas would change from:
A = 2R_a + G_a + 0.05 B_a - 0.305
RGB_c=(400 * sign(FLRGB) * FLRGB) / (27.13 + FLRGB) + 0.1
to:
A = 2R_a + G_a + 0.05 B_a
RGB_c=(400 * sign(FLRGB) * FLRGB) / (27.13 + FLRGB)
for achromatic response and post adaptation cone response, respectively. There’s no visible difference in the image.
These changes would be in line with what has been suggested also for CIECAM02 and CAM16, for example in paper Algorithmic improvements for the CIECAM02 and CAM16 color appearance models.