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The function c2hyp (convert to hyperbolic) convert expression with exp function to expression with hyperbolic functions sinh, cosh.
Examples:
(%i6) c2hyp(exp(x));
(%o6) sinh(x) + cosh(x)
(%i7) c2hyp(exp(x)+exp(x^2)+1);
2 2
(%o7) sinh(x ) + cosh(x ) + sinh(x) + cosh(x) + 1
(%i8) c2hyp(exp(x)/(2*exp(y)-3*exp(z)));
sinh(x) + cosh(x)
(%o8) ---------------------------------------------
2 (sinh(y) + cosh(y)) - 3 (sinh(z) + cosh(z))