Processors with extensible instruction sets are often used today as programmable hardware accelerators for various domains. When extending RISC-V and other similar extensible processor architectures, the task of designing specialized instructions arises. This task can be solved automatically by using instruction synthesis algorithms. In this paper, we consider algorithms that can be used in addition to the known approaches and improve the synthesized instruction sets by recomputing common operations (the result of which is consumed by multiple operations) of a program inside clustered synthesized instructions (common operations clustering algorithm), and by identifying redundant (which have equivalents among the other instructions) synthesized instructions (subsuming functions algorithm). Experimental evaluations of the developed algorithms are presented for the tests from the domains of cryptography and three-dimensional graphics. For Magma cipher test, the common operations clustering algorithm allows reducing the size of the compiled code by 9%, and the subsuming functions algorithm allows reducing the synthesized instruction set extension size by 2 times. For AES cipher test, the common operations clustering algorithm allows reducing the size of the compiled code by 10%, and the subsuming functions algorithm allows reducing the synthesized instruction set extension size by 2.5 times. Finally, for the instruction set extension from Volume Ray-Casting test, the additional use of subsuming functions algorithm allows reducing problem-specific instruction extension set size from 5 to only 2 instructions without losing its functionality.