Expression to calculate Color Blending Mode on 2 color values?

[Oleg Pirogov]

So you have two color vectors:
[r2, g2, b2, a2] for the top solid (Solid2) corresponding to Blend (also called source)
[r1, g1, b1, a1] for the bottom solid (Solid1) corresponding to Target (also called backdrop)

The formula you’ve found simplifies to
Target + 2*Blend – 1

Linear Light is a separable blend mode, meaning that the formula is applied to each color channel separately.
For instance, for the red channel it will be:
r = r1 + 2*r2 - 1
– same for g and b.

If both the Blend and the Target colors have alphas a1=a2=1, then the resulting color is simply:
[r, g, b, 1]

If not, then it gets worse, cause alphas have to be taken into account.
Let:
C2 = [r2, g2, b2]
C1 = [r1, g1, b1]
B=[r, g, b]
C – resulting RGB vector (without alpha component)
a = a1+a2 – a1*a2 – resulting alpha

Then:
C = (1 – a2/a)*C1+(a2/a)*((1-a1)*C2+a1*B)

And the resulting color vector will be:
[Cr, Cg, Cb, a], where Cr, Cg, Cb are the components of C.

JS code:
color2 = thisComp.layer("Pre-comp 1").sampleImage([1800,100], radius = [.5, .5]);
color1 = thisComp.layer("Pre-comp 1").sampleImage([100,800], radius = [.5, .5]);
C2 = color2.slice(0,3);
C1 = color1.slice(0,3);
a2=color2[3];
a1=color1[3];
a=a2+a1-a2*a1;

function linearLight(r1, r2){
return r1 + 2*r2 - 1;
};

B = [linearLight(C1[0], C2[0]), linearLight(C1[1], C2[1]), linearLight(C1[2], C2[2])];
aC=(a - a2)*C1+(a2)*((1-a1)*C2+a1*B);
z=[aC[0]/a, aC[1]/a, aC[2]/a, a];
It appears that it gives the right result.