7. One or more computer memory having computer-executable instructions stored thereon that, when executed, direct a computer to perform operations comprising: accessing an arbitrary formula pattern; compiling the arbitrary formula pattern into a testable code sequence, the testable code sequence comprising one or more instructions received from a remote computing device; comparing the testable code sequence, term by term, to known code sequences, the known code sequences being stored in a code sequence database, wherein the code sequence database comprises a combination of formulas with first-order place-holders, formulas with second-order place holders, and first-order patterns; merging known code sequences associated with the testable code sequence to form a code tree; instantiating second-order place-holders by known formulas in the testable code sequence, the known formulas being stored in a functions database, at least one of the known formulas including a pseudo-function that comprises: at least one of the second-order place-holders representing a function symbol of a function in the arbitrary formula pattern; a first variable of the pseudo-function that represents an arity of the function in the arbitrary formula pattern; and a second variable of the pseudo-function that is equal to an offset of a next available register, wherein the next available register is a first register of a plurality of registers that are reserved for storing arguments associated with the function in the arbitrary formula pattern; matching a term of the testable code sequence with a permutation of the term, the permutation comprising a sub-term in a weak second-order pattern stored in a database of patterns; and associating a first occurrence of a matching term in the testable code sequence with the permutation of the matching term.
7. One or more computer memory having computer-executable instructions stored thereon that, when executed, direct a computer to perform operations comprising: accessing an arbitrary formula pattern; compiling the arbitrary formula pattern into a testable code sequence, the testable code sequence comprising one or more instructions received from a remote computing device; comparing the testable code sequence, term by term, to known code sequences, the known code sequences being stored in a code sequence database, wherein the code sequence database comprises a combination of formulas with first-order place-holders, formulas with second-order place holders, and first-order patterns; merging known code sequences associated with the testable code sequence to form a code tree; instantiating second-order place-holders by known formulas in the testable code sequence, the known formulas being stored in a functions database, at least one of the known formulas including a pseudo-function that comprises: at least one of the second-order place-holders representing a function symbol of a function in the arbitrary formula pattern; a first variable of the pseudo-function that represents an arity of the function in the arbitrary formula pattern; and a second variable of the pseudo-function that is equal to an offset of a next available register, wherein the next available register is a first register of a plurality of registers that are reserved for storing arguments associated with the function in the arbitrary formula pattern; matching a term of the testable code sequence with a permutation of the term, the permutation comprising a sub-term in a weak second-order pattern stored in a database of patterns; and associating a first occurrence of a matching term in the testable code sequence with the permutation of the matching term. 8. The one or more computer memory of claim 7 wherein the permutation of the term is stored in the database of patterns.