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Convolutional neural networks (CNNs) provide the best accuracy for disparity estimation. However, CNNs are computationally expensive, making them unfavorable for resource-limited devices with real-time constraints. Recent advances in neural architectures search (NAS) promise opportunities in automated optimization for disparity estimation. However, the main challenge of the NAS methods is the significant amount of computing time to explore a vast search space [e.g., $1.6\times 10^{29}$ ] and costly training candidates. To reduce the NAS computational demand, many proxy-based NAS methods have been proposed. Despite their success, most of them are designed for comparatively small-scale learning tasks. In this article, we propose a fast NAS method, called FastStereoNet, to enable resource-aware NAS within an intractably large search space. FastStereoNet automatically searches for hardware-friendly CNN architectures based on late acceptance hill climbing (LAHC), followed by simulated annealing (SA). FastStereoNet also employs a fine-tuning with a transferred weights mechanism to improve the convergence of the search process. The collection of these ideas provides competitive results in terms of search time and strikes a balance between accuracy and efficiency. Compared to the state of the art, FastStereoNet provides $5.25\times $ reduction in search time and $44.4\times $ reduction in model size. These benefits are attained while yielding a comparable accuracy that enables seamless deployment of disparity estimation on resource-limited devices. Finally, FastStereoNet significantly improves the perception quality of disparity estimation deployed on field-programmable gate array and Intel Neural Compute Stick 2 accelerator in a significantly less onerous manner. [ABSTRACT FROM AUTHOR]