\(\begin{align} b &= \text{bottom}\\ t &= \text{top} \end{align}\)
\(\text{normal}(b,t) = t\)
\(\text{darken}(b,t) = \text{min}(b,t)\)
\(\text{multiply}(b,t) = bt\)
\(\text{color_burn}(b,t) = \begin{cases} 1&\text{if }b = 1\\ 0&\text{else if }t = 0\\ 1-\min\left(\dfrac{1-b}{t},1\right)&\text{else} \end{cases}\)
\(\text{linear_burn}(b,t) = \text{max}(b+t-1,0)\)
\(\begin{align} Y(R,G,B) &= 0.299R+0.587G+0.114B\\ \text{darker_color}(b,t) &= \begin{cases} b&\text{if }Y(b) \lt Y(t)\\ t&\text{else} \end{cases} \end{align}\)
\(\text{lighten}(b,t) = \text{max}(b,t)\)
\(\begin{align} \text{screen}(b,t) &= 1-(1-b)(1-t)\\ &= b+t-bt \end{align}\)
\(\text{color_dodge}(b,t) = \begin{cases} 0&\text{if }b = 0\\ 1&\text{else if }t = 1\\ \min\left(\dfrac{b}{1-t},1\right)&\text{else} \end{cases}\)
\(\text{linear_dodge}(b,t) = \text{min}(b+t,1)\)
\(\begin{align} Y(R,G,B) &= 0.299R+0.587G+0.114B\\ \text{lighter_color}(b,t) &= \begin{cases} t&\text{if }Y(b) \lt Y(t)\\ b&\text{else} \end{cases} \end{align}\)
\(\text{overlay}(b,t) = \text{hard_light}(t,b)\)
\(\begin{align} D(c) &= \begin{cases} ((16c-12)c+4)c&\text{if }c \le 0.25\\ \sqrt{c}&\text{else} \end{cases}\\ \text{soft_light}(b,t) &= \begin{cases} b-(1-2t)b(1-b)&\text{if }t \le 0.5\\ b+(2t-1)(D(b)-b)&\text{else} \end{cases} \end{align}\)
\(\text{hard_light}(b,t) = \begin{cases} \text{multiply}(b,2t)&\text{if }t \le 0.5\\ \text{screen}(b,2(t-0.5))&\text{else} \end{cases}\)
\(\text{vivid_light}(b,t) = \begin{cases} \text{color_burn}(b,2t)&\text{if }t \le 0.5\\ \text{color_dodge}(b,2(t-0.5))&\text{else} \end{cases}\)
\(\text{linear_light}(b,t) = \begin{cases} \text{linear_burn}(b,2t)&\text{if }t \le 0.5\\ \text{linear_light}(b,2(t-0.5))&\text{else} \end{cases}\)
\(\text{pin_light}(b,t) = \begin{cases} \text{darken}(b,2t)&\text{if }t \le 0.5\\ \text{lighten}(b,2(t-0.5))&\text{else} \end{cases}\)
\(\text{hard_mix}(b,t) = \lfloor b+t \rfloor\)
\(\text{difference}(b,t) = \max(b-t,t-b)\)
\(\text{exclusion}(b,t) = b+t-2bt\)
\(\text{subtract}(b,t) = \text{max}(b-t,0)\)
\(\text{divide}(b,t) = \begin{cases} 0&\text{if }b = 0\\ 1&\text{else if }b \ge t\\ b/t&\text{else} \end{cases}\)
\(\text{hue}(b,t) = b_H,t_S,t_L\)
\(\text{saturation}(b,t) = t_H,b_S,t_L\)
\(\text{color}(b,t) = t_H,t_S,b_L\)
\(\text{luminosity}(b,t) = \text{color}(t,b)\)