The cost reduction applies to the total cost of the Arcane spell, including any additional costs from cards spliced onto it. However, the cost reduction applies only once to each Arcane spell. For example, if you cast an Arcane spell with mana cost {R} and splice onto it a card whose splice cost is {1}{U}, then the spell costs {U}{R} to cast. If you cast an Arcane spell with mana cost {4}{U} and splice onto it a card whose splice cost is {1}{R}, the spell costs {4}{U}{R} to cast.