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\subsection{Experimental results}  We have evaluated the effectiveness of our technique on four benchmarks, namely {\tt odeEuler}, {\tt odeMidpt}, {\tt odeRK4}, and {\tt sim\_anl}. The first three benchmarks solve an ODE for heat treating simulation using the Euler, midpoint, and Range-Kutta method, respectively; the last benchmark minimizes the six-hump camelback function with the method of simulated annealing.    \begin{table}   \begin{tabular}{ c c c c c }  benchmark/ speedup & base (cached) & optimized & optimized (cached) & hand-coded \\   odeEuler & 1.046 & 2.796 & 2.800 & 2 .828 \\   odeMidpt & 1.014 & 2.645 & 2.660 & 2.685 \\   odeRK4 & 1.005 & 2.490 & 2.582 & 2.647 \\   sim_anl & 1.009 & 1.564 & 1.606 & 1.612 \\   \end{tabular}   \caption{Speedup comparison for \feval\ optimization.}   \end{table}