Technologies for automatic reordering of sparse matrices include a computing device to determine a distributivity of an expression defined in a code region of a program code. The expression is determined to be distributive if semantics of the expression are unaffected by a reordering of an input/output of the expression. The computing device performs inter-dependent array analysis on the expression to determine one or more clusters of inter-dependent arrays of the expression, wherein each array of a cluster of the one or more clusters is inter-dependent on each other array of the cluster, and performs bi-directional data flow analysis on the code region by iterative backward and forward propagation of reorderable arrays through expressions in the code region based on the one or more clusters of the inter-dependent arrays. The backward propagation is based on a backward transfer function and the forward propagation is based on a forward transfer function.