We present a mechanism to symbolically gather performance-relevant operation counts from numerically-oriented subprograms (`kernels') expressed in the Loopy programming system, and apply these counts in a simple, linear model of kernel run time. We use a series of `performance-instructive' kernels to fit the parameters of a unified model to the performance characteristics of GPU hardware from multiple hardware generations and vendors. We evaluate the predictive power of the model on a broad array of computational kernels relevant to scientific computing. In terms of the geometric mean, our simple, vendor- and GPU-type-independent model achieves relative accuracy comparable to that of previously published work using hardware specific models.