1. A machine translation apparatus comprising: a memory and; at least one processor coupled to the memory, the at least one processor configured to: obtain a first translated sentence generated by translating a first input sentence and a second translated sentence generated by translating a second input sentence, the second input sentence being a sentence into which the first input sentence is rewritten; acquire a difference between the first translated sentence and the second translated sentence; specify a first word in the first translated sentence corresponding to the difference, a second word in the second translated sentence corresponding to the difference and a related word that has a predetermined relationship with the first word and the second word, the related word being included in both of the first translated sentence and the second translated sentence; acquire a first appearance frequency and a second appearance frequency, the first appearance frequency indicating an appearance frequency of a combination of the first word and the related word with the predetermined relationship in a plurality of example sentences, the second appearance frequency indicating an appearance frequency of a combination of the second word and the related word with the predetermined relationship in the plurality of example sentences; generate, when the second appearance frequency is larger by a predetermined value than the first appearance frequency, a translation rule for replacing the first word with the second word; translate an input sentence entered by a user based on the generated translation rule; and output the translated input sentence.