# Optimization benchmarks
Results for the [`optimization`](optimization.rs) suite (`cargo bench -- optimization`).
The accuracy table reports how close each solver lands to the known solution; the latency table
reports wall-clock medians on the machine noted in [README.md](README.md).
## Accuracy
Reported below are the final **objective** (half the sum of squared residuals) and the largest **parameter error** across the recovered parameters versus the known truth. A "0.0" is an exact result to the last bit; a dash marks a pure-minimization problem with no reference parameter vector.
Levenberg-Marquardt:
| Linear least squares, fit $$y = a + bt$$ | 0.0 | 0.0 | Linear residual: the exact least-squares solution |
| Exponential decay, $$a\,e^{bt}$$ fit | 0.0 | 0.0 | Zero-residual data; a and b recovered exactly |
| Rosenbrock residual | 0.0 | 0.0 | Zero-residual; the minimum (1, 1) is reached exactly |
| Damped sinusoids, 12 parameters | 6e-31 | 2e-16 | All twelve parameters to ~1 ulp |
| Trigonometric (Moré-Garbow-Hillstrom), 6 vars | 1e-31 | — | Global minimum of zero reached to machine precision |
Gauss-Newton:
| Linear least squares, fit $$y = a + bt$$ | 0.0 | 0.0 | Reaches the exact solution in a single step |
| Rosenbrock residual | 0.0 | 0.0 | Zero-residual; the minimum (1, 1) is reached exactly |
| Geometric circle fit, 3 parameters | 1e-30 | 0.0 | Center (2, -1) and radius 3 exact to machine precision |
| Two Gaussian peaks, 6 parameters | 0.0 | 0.0 | All six peak parameters recovered exactly |
On these noiseless problems both solvers hit the minimizer to the last few bits; the only nonzero figures are the hardest fits (the 12-parameter sinusoid sum and the 3-parameter circle), where accumulated rounding leaves the objective around `1e-30` and the parameters within ~1 ulp. Accuracy here is bounded by floating-point rounding, not by the algorithm.
## Latency
Median of criterion's estimate; wall-clock and therefore machine- and build-specific (see the
[environment note](README.md#environment)).
Gauss-Newton, linear least squares (3×2) | 0.23 µs |
Gauss-Newton, Rosenbrock (near start) | 0.26 µs |
Gauss-Newton, circle fit (3 params, 40 residuals) | 56 µs |
Levenberg-Marquardt, exponential decay fit (2 params) | 1.4 µs |
Levenberg-Marquardt, Rosenbrock | 6.2 µs |
Levenberg-Marquardt, trigonometric (6 vars) | 45 µs |
Levenberg-Marquardt, damped sinusoids (12 params, 60 residuals) | 14 ms |