In order to improve the exploration efficiency of the design space for floating-point expression, a design space exploration method based on heuristic search was proposed. The design space of non-dominated expression was explored firstly during each iteration. At the same time, the non-dominated expression and the dominated expression were added to the non-dominated list and the dominated list respectively. Then the expression in the dominated list was explored after the iteration, the non-dominated expression in the dominated list was selected, and the neighborhood of the non-dominated expression in the dominated list was explored. And the new non-dominated expression was added to the non-dominated list, effectively improving the diversity and randomness of the non-dominated expression. Finally, the non-dominated list was explored again to obtain the final equivalent expression and further improve the performance of optimal expression. Compared with the existing design space exploration methods for floating-point expression, the proposed method has the calculation accuracy increased by 2% to 9%, the calculation time reduced by 5% to 19% and the resource consumption reduced by 4% to 7%. Experimental results show that the proposed method can effectively improve the efficiency of design space exploration.