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D .. background sRGB color, we assume middle gray #808080
b .. recomputed alpha
The old blending expression:
OLD = S * a + D * (1 - a)
The new blending expression:
NEW = sRGB(rgb(S) * b + rgb(D) * (1 - b))
Alpha which would result in the same final value after blend:
b = (rgb(OLD) - rgb(D)) / (rgb(S) - rgb(D))