The best solution that I know of is to program the symbolic expressions in Mathematica, Maple, or SymPy; all of the links go directly to the code generation documentation. All of the programs above can generate code in C or Fortran.
None of the programs above mentions accuracy in IEEE 754 arithmetic; in general, it would be difficult to anticipate all sources of catastrophic cancellation, as @dmckee notes. It's hard to replace human expertise in numerical analysis.
To provide a concrete example, consider calculating the trigonometric functions to high precision for arbitrary inputs in $[0, 2\pi]$. There are many strategies for doing so, some even hardware dependent, as see in the Wikipedia article Trigonometric Tables. All of the algorithms require ingenuity and numerical analysis, even algorithms that depend on lookup tables and Taylor series or interpolation (see the Wikipedia article The Table-Maker's Dilemma). For more detail, see the related Stack Overflow question How do Trigonometric Functions work?.
Software that generated code or routines to calculate arbitrary functions to high accuracy would not only need to be aware of cancellation errors, but also series approximants (Taylor, Padé, Chebyshev, rational, etc.) for calculating functions that are not defined in terms of a finite number of additions, subtractions, multiplications, divisions, and bit shifts. (See Approximation Theory.)