1. A method for providing rollback support in an exposed-pipeline processing element, the method comprising: storing results of an arithmetic logic unit pipeline of the exposed-pipeline processing element to a 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 an effective address buffer based on determining that a value of the load-store unit pipeline is used as an operand; storing operands to an operand buffer of the exposed-pipeline processing element; detecting, by rollback support logic, an error associated with execution of an instruction in the exposed-pipeline processing element; determining, by the rollback support logic, 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.