1. A method of optimizing a sequence of operations adapted for execution by a processor, wherein the processor executes an operation set and has a set of registers, and wherein the method comprises: associating symbolic expressions with each of at least a subset of the set of registers, thereby creating a plurality of associated symbolic expressions, wherein each of the plurality of associated symbolic expressions may be emitted as one or more operations; holding a set of dependency indicators that specify, for each particular associated symbolic expression from the plurality of associated symbolic expressions, which of the other associated symbolic expressions must be emitted prior to emitting the particular associated symbolic expression; locating an operation, if any, that is next within the sequence of operations and setting that operation to be a working operation; processing the working operation as follows: a) handling the working operation by a combination of updating, if necessary, any of the associated symbolic expressions and emitting any of the associated symbolic expressions; b) identifying any of the updated associated symbolic expressions that must be emitted prior to emitting any of the other associated symbolic expressions, and then updating the set of dependency indicators to include any such dependencies; and c) identifying any of the updated associated symbolic expressions that no longer need to be emitted prior to emitting any of the other associated symbolic expressions, and then updating the set of dependency indicators to remove any such dependencies; wherein the set of dependency indicators includes a matrix of dependency indicators; wherein each column of the matrix of dependency indicators is associated with a particular register from the set of registers; wherein each row of the matrix of dependency indicators is associated with a particular register from the set of registers; wherein each dependency indicator found in a non-diagonal element of the matrix of dependency indicators indicates that the associated symbolic expression associated with the particular register associated with the row is to be emitted after the emission of the associated symbolic expression associated with the particular register associated with the column; and when any row of the matrix of dependency indicators is read the diagonal element of the row of the matrix of dependency indicators is read normally; and when any column of the matrix of dependency indicators is read, the diagonal element of the column is read as not indicating dependency regardless of the state of the dependency indicator in the diagonal element.