The recent breakthrough in metamaterial-based optical computing devices (2014 Science 343 160) has inspired a quest for similar systems in acoustics, performing mathematical operations on sound waves. So far, acoustic analog computing has been demonstrated using thin planar metamaterials, carrying out the operator of choice in Fourier domain. These so-called filtering metasurfaces, however, are always accompanied with additional Fourier transform sub-blocks, enlarging the computing system and preventing its applicability in miniaturized architectures. Here, employing a simple high-index acoustic slab waveguide, we propose a highly compact and potentially integrable acoustic computing system and demonstrate its proper functioning by numerical simulations. The system directly performs mathematical operation in spatial domain and is therefore free of any Fourier bulk lens. Such compact computing system is highly promising for various applications including high throughput image processing, ultrafast equation solving, and real time signal processing.