Software testing is widely used in industry, but its application in the High Performance Computing area has been scarce. Concolic testing, that automates testing via generation of inputs, has been highly successful for desktop applications and thus recent work on the COMPI tool has extended it to MPI programs. However, COMPI has two limitations. First, it requires the user to specify an upper limit on input size – if the chosen limit is too big, considerable time is wasted and if the chosen limit is too small, the branch coverage achieved is limited. Second, COMPI does not support floating point arithmetic that is common in HPC applications. In this paper, we overcome the above limitations as follows. We propose input tuning that eliminates the need for users to set hard limits and generates inputs such that the testing achieves high coverage while avoiding waste of testing time by selecting suitable input sizes. Moreover, we enable handling of floating point data types and operations and demonstrate that the efficiency of constraint solving can be improved if we rely on the use of reals instead of floating point values. Our evaluation demonstrates that with input tuning the coverage we achieve in 10 minutes is typically higher than the coverage achieved in 1 hour when input tuning is not used. Without input tuning, 9.6-57.1% loss in coverage occurs for a real-world physics simulation program. For the physics simulation program, using our floating-point extension that uses reals covers 46 more branches than without using the extension. Also, we cover 122 more branches when solving floating-point constraints using reals rather than directly using floating-point numbers.