timetosolution

Time to solution (TTS) is a performance metric used in computational science and numerical computing to measure the total wall-clock time required for a program or solver to produce a correct or acceptable result for a given problem. It encompasses all phases from initial setup and data loading through solver iterations to any post-processing and result validation.

In practice, TTS is used to benchmark and compare algorithms, implementations, and hardware platforms. It is relevant across domains such as linear and nonlinear system solvers, eigenvalue problems, optimization routines, and large-scale simulations. TTS provides a holistic view of performance beyond raw operation counts, reflecting real-world user experience.

Several factors influence TTS. Problem size and characteristics, the choice of algorithm and numerical parameters, and the convergence criteria all play major roles. Hardware aspects—processor speed, memory bandwidth, interconnect latency, and parallel scalability—also strongly affect TTS. Software specifics, including data layout, vectorization, and I/O strategies, matter as well. Optimizations to reduce TTS often target algorithmic improvements (e.g., better preconditioners, multigrid methods), enhanced parallelization, hardware acceleration, and improved data locality and communication overlap.

Measurement and reporting practices vary. TTS is typically recorded as the elapsed time to reach a predefined accuracy or convergence check, and is often averaged over multiple runs to mitigate variability. Benchmarks may present strong and weak scaling results for TTS. The metric is problem-dependent and can differ with hardware, software environment, and solver configuration, but remains a central criterion for assessing computational efficiency.