Google Books Ngram Viewer

Graph these comma-separated phrases:
case-insensitive
between and from the corpus with smoothing of .  
Search in Google Books:

1800 - 1868 1869 - 1913 1914 - 1922 1923 - 1967 1968 - 2000 eat your cake and have English
1800 - 1907 1908 - 1976 1977 - 1984 1985 - 1992 1993 - 2000 have your cake and eat English
1800 - 1865 1866 - 1944 1945 - 1949 1950 - 1974 1975 - 2000 keep your cake and eat English
1800 - 1886 1887 - 1913 1914 - 1917 1918 - 1958 1959 - 2000 eat your cake and keep English

Run your own experiment! Raw data is available for download here.
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