I don't think this is right. "chortle" is not = "burst out laughing". Here is the definition and etymology of "chortle" from OED, + quotations:
A factitious word introduced by the author of Through the Looking-Glass, and jocularly used by others after him, app. with some suggestion of chuckle, and of snort. Also trans., to utter or sing with a 'chortling' intonation. Also n., an act of 'chortling'.
1871 'L. Carroll' Through Looking-glass i. 24 'O frabjous day! Callooh! Callay!' He chortled in his joy.
1876 W. Besant & J. Rice Golden Butterfly III. ii. 25 It makes the cynic and the worldly-minded man to chuckle and chortle with an open joy.
1886 Referee 18 Aug. (Ware), Mr. Wilford Morgan has been engaged to chortle the famous song, 'Here's to the maiden of bashful fifteen'.
1887 Athenĉum 3 Dec. 751/1 A means of exciting cynical 'chortling'.
1888 Daily News 10 Jan. 5/2 So may chortle the Anthropophagi.
1889 Referee 29 Dec., Many present on Boxing Night fully expected that when he appeared he would chortle a chansonette or two.
1903 'A. McNeill' Egregious Eng. 28 He would tell you‥that he attributed his success‥(5) to marrying Mrs. Business-Manthis last, of course, with a chortle.