Thanks for all the clarifications. They helped me to better understand your process with CGPT. I think CGPT probably correctly diagnosed its previous mistake, when you pressed further. It confused the attenuation function with cases from its training where spreading and absorption compete, which results in a function with a maximum in the interior. This is unlike the actual situation being tabulated, where both spreading and absorption decrease the pressure with increasing distance.
Well you sent me off at a tangent there. But if you look at the article you linked it differentiates between sound pressure (p) (Proportional to distance) and SPL which is a dB rating = 20Log10(p1/p2) so SPL therefore correct as per the equation, given that d is proportional to p. (Note the reference distance (d0) is 1m - so not included in the equation as a divisor) (if I am reading it right)
I guessed you had normalized the distance d with 1 m, which is customary in acoustics as the Wikipedia page mentions, and log(1) = 0. Your equation for delta(SPL) agrees with the Wikipedia formulas individually, but the distance d needs correct interpretation. The distance d in the first (spreading) term on the RHS of your equation is the radial distance of the prediction point from the point source of sound, while the d in the absorption term is the radial distance between the prediction and anchor points (because the difference in SPL due to absorption occurs over that distance). The Wikipedia page uses "r" to denote the same quantity as your first "d". Also, p is inversely proportional to d, not directly proportional.
You could anchor the function at, say, 1 m, i.e. d=1, by specifying the value of SPL there as SPL1, and use that SPL1 as the reference SPL in the formula for delta(SPL); you could anchor the function at any point d1, it does not have to be at d=1. Then you can evaluate the delta(SPL) corresponding to any other point, say d2, using the formula
delta(SPL) = SPL1-SPL2 = 20*[log(d2)-log(d1)] + alpha*(d2-d1)]
=20*log(d2) + alpha*(d2-1) if you pick d1=1.
I used alpha to denote your abs, and I used log to denote log10. Note that the delta(SPL) is the difference between the SPL values at d1 and d2, but the d2 in the log term is the difference in radius between d2 and the sound source. Also, the formula should not be used for predictions close to the source, as it predicts unphysical values, and indeed the function has a singularity at the source.