The present invention makes it possible to detect an approximation error amount in approximating and encoding axis-dependent data that depends on the coordinate value of each axis of an industrial machine. An approximation error detection device 1 comprises an approximation error amount detection unit 11 that detects an approximation error amount with an absolute value greater than or equal to a predetermined threshold among approximation error amounts in performing model approximation encoding of axis-dependent data on the basis of a part of the axis-dependent data that depends on the coordinate value of each axis of an industrial machine, and on a linear combination model that approximates the axis-dependent data as a linear combination of data on each axis of the industrial machine.