1. A method of providing a compressed representation of a number sequence, said method comprising: utilizing a processor to execute computer code configured to perform the steps of: receiving an input number sequence representing an atomic service having a predetermined duration, wherein the input number sequence comprises a plurality of elements, wherein a number of the plurality of elements corresponds to a number of units of time within the predetermined duration represented as an array; determining a set of coefficients describing the input number sequence, via solving at least one algebraic equation, the at least one algebraic equation comprising at least one of: an arithmetic equation, and an exponential equation; accessing a library of stored number sequences, the number sequences comprising at least one of: arithmetic number sequences, and exponential number sequences; determining a representation of the stored number sequences; ascertaining a match of the set of coefficients with respect to the representation of the stored number sequences, wherein the ascertaining a match is performed by partitioning the representation of the stored number sequences into equivalence sets by performing a linear transformation test, a constant multiple test, a constant multiple of a product test, and a constant multiple of sum test on the input number sequence to reduce a number of stored number sequences to be considered when ascertaining a match and increasing a speed for ascertaining a match; the ascertaining a match comprising: determining, by performing the linear transformation test, whether the input number sequence is at least one of: a linear transformation of at least one of the representation of the stored number sequences and a log-linear transformation of at least one of the representation of the stored number sequences by applying a linear or log-linear transformation to a random position of the stored number sequence and comparing the result of the linear or log-linear transformation to a corresponding position of the input number sequence, wherein a match comprises a representation of the stored number sequence passing the linear transformation test; determining, by performing the constant multiple test, whether the input number sequence comprises a constant multiple of at least one of the representation of the stored number sequences, wherein a match comprises a representation of the stored number sequence passing the constant multiple test; determining, by performing the constant multiple of a product test, whether the input number sequence comprises a constant multiple of a product of at least one representation of the stored number sequences, wherein a match comprises a representation of the stored number sequence passing the constant multiple of a product test; determining, by performing the constant multiple of a sum test, whether the input number sequence comprises a constant multiple of a sum of at least one representation of the stored number sequences, wherein a match comprises a representation of the stored number sequence passing the constant multiple of a sum test; and iteratively performing the ascertaining a match for each of the representation of the stored number sequences until a match is found, the match representing a stored number sequence that corresponds to at least a portion of a specialized predictive cost model for the atomic service and providing the at least a portion of a specialized predictive cost model to a user; and in the event a match is not found, adding the input number sequence to the library of stored number sequences.