Deep learning compilers help address the difficulties of deploying deep learning models on diverse types of hardware. Testing deep learning compilers is highly crucial, because they are impacting countless AI applications that use them for model optimization and deployment. To test deep learning compilers, random testing, the testing method popularly used for compiler testing practices, faces the challenge of generating semantically valid test inputs, i.e., deep learning models that satisfy the semantic model specifications (in short as semantic specifications). To tackle this challenge, in this paper, we propose a novel approach named Isra, including a domain-specific constraint solver that resolves the constraints from the semantic specifications without backtracking. We implement and apply our approach to three popular real-world deep learning compilers including TVM, Glow, and a commercial compiler named SophGo. The evaluation results show that Isra is more effective than the state-of-the-art approaches and the baseline approaches on constructing valid test inputs for compiler-bug detection, and Isra successfully finds 24 previously unknown bugs in released versions of the three compilers. These results indicate Isra's effectiveness and practical value.