Strong gravitational lensing is a powerful probe of cosmology and the dark matter distribution. Efficient lensing software is already a necessity to fully use its potential and the performance demands will only increase with the upcoming generation of telescopes. In this paper, we present a proof-of-concept study on the impact of High Performance Computing techniques on a performance-critical part of the widely used lens modeling software LENSTOOL. We implement the algorithm once as a highly optimized CPU version and once with graphics card acceleration for a simple parametric lens model. In addition, we study the impact of finite machine precision on the lensing algorithm. While double precision is the default choice for scientific applications, we find that single precision can be sufficiently accurate for our purposes and lead to a big speedup. Therefore we develop and present a mixed precision algorithm which only uses double precision when necessary. We measure the performance of the different implementations and find that the use of High Performance Computing Techniques dramatically improves the code performance both on CPUs and GPUs. Compared to the current LENSTOOL implementation on 12 CPU cores, we obtain speedup factors of up to 170. We achieve this optimal performance by using our mixed precision algorithm on a high-end GPU which is common in modern supercomputers. We also show that these techniques reduce the energy consumption by up to 98%. Furthermore, we demonstrate that a highly competitive speedup can be reached with consumer GPUs. While they are an order of magnitude cheaper than the high-end graphics cards, they are rarely used for scientific computations due to their low double precision performance. However, our mixed precision algorithm unlocks their full potential. Consequently, the consumer GPU delivers a speedup which is only a factor of four lower than the best speedup achieved by a high-end GPU. (C) 2019 Elsevier B.V. All rights reserved.