We present a domain specific language compiler, diesel, for basic linear algebra and neural network computations, that accepts input expressions in an intuitive form and generates high performing code for GPUs. The current trend is to represent a neural network as a computation DAG, where each node in the DAG corresponds to a single operation such as matrix-matrix multiplication, and map the individual operations to hand tuned library functions provided by standard libraries such as CuBLAS and CuDNN. While this method takes advantage of readily available optimized library codes to achieve good performance for individual operations, it is not possible to optimize across operations. As opposed to this, given a computation composed of several operations, diesel generates (a set) of efficient device functions, where the code is optimized for the computation as a whole, using polyhedral compilation techniques. In addition, there are cases where the code needs to be specialized for a specific problem sizes to achieve optimal performance. While standard libraries are written for parametric problem sizes (where problem sizes are provided at runtime), diesel can accept problem sizes at compile time and generate specialized codes. Experimental results show that the performance achieved by diesel generated code for individual operations are comparable to the highly tuned versions provided by standard libraries, while for composite computations, diesel outperforms other tools.