  The one-dimensional Schr\"odinger equation with symmetric trigonometric
double-well potential (DWP) is exactly solved via angular oblate spheroidal
function. The results of stringent analytic calculation for the ground state
splitting of hydrogen bond in malonaldehyde are compared with several variants
of approximate semiclassical (WKB) ones. This enables us to compare the
accuracy of various WKB formulas suggested in the literature: 1. ordinary WKB,
i.e., the formula from the Landau and Lifshitz textbook; 2. Garg's formula; 3.
instanton approach. The results obtained provide a new theoretical tool for the
precise quantitative description of experimental data on IR spectroscopy of
malonaldehyde.
