Path tra­cing is now the stand­ard meth­od used to gen­er­ate real­ist­ic im­agery in many do­mains, e.g., film, spe­cial ef­fects, ar­chi­tec­ture etc. Path guid­ing has re­cently emerged as a power­ful strategy to counter the no­tori­ously long com­pu­ta­tion times re­quired to render such im­ages. We present a prac­tic­al path guid­ing al­gorithm that per­forms product sampling, i.e., samples pro­por­tion­al to the product of the bi­d­irec­tion­al scat­ter­ing dis­tri­bu­tion func­tion (BSDF) and in­com­ing ra­di­ance. We use a spa­tial-dir­ec­tion­al sub­di­vi­sion to rep­res­ent in­com­ing ra­di­ance, and in­tro­duce the use of Lin­early Trans­formed Co­sines (LTCs) to rep­res­ent the BSDF dur­ing path guid­ing, thus en­abling ef­fi­cient product sampling. Des­pite the com­pu­ta­tion­al ef­fi­ciency of LTCs, sev­er­al op­tim­iz­a­tions are needed to make our meth­od cost ef­fect­ive. In par­tic­u­lar, we show how we can use vec­tor­iz­a­tion, pre­com­pu­ta­tion, as well as strategies to op­tim­ize mul­tiple im­port­ance sampling and Rus­si­an roul­ette to im­prove per­form­ance. We eval­u­ate our meth­od on sev­er­al scenes, demon­strat­ing con­sist­ent im­prove­ment in ef­fi­ciency com­pared to pre­vi­ous work, es­pe­cially in scenes with sig­ni­fic­ant glossy inter-re­flec­tion.