1. A system for rollback support in an exposed-pipeline processing element, the system comprising: the exposed-pipeline processing element comprising rollback support logic, a result buffer, an effective address buffer, and an operand buffer; and the rollback support logic configured to perform a method comprising: storing results of an arithmetic logic unit pipeline of the exposed-pipeline processing element to the result buffer selectively based on determining that a value of the arithmetic logic unit pipeline is used as an operand; storing results of a load-store unit pipeline of the exposed-pipeline processing element to the effective address buffer based on determining that a value of the load-store unit pipeline is used as an operand; storing operands to the operand buffer of the exposed-pipeline processing element; detecting an error associated with execution of an instruction in the exposed-pipeline processing element; determining whether the exposed-pipeline processing element supports replay of the instruction for a predetermined number of cycles; and based on determining that the exposed-pipeline processing element supports replay of the instruction, performing a rollback action in the exposed-pipeline processing element to attempt recovery from the error by selecting one or more of: the result buffer, the effective address buffer, and the operand buffer to replay the instruction for the predetermined number of cycles.