Numerical Workspace
One problem, every method of that engine, side by side.
Compare successful methods using reference error, root residual, or interpolation spread. Each row is recomputed locally.
By CalculatorX · Content updated .
Integral sources and limits
NIST DLMF §3.5 — Quadrature supports the integral rules. ISO 80000-2:2019 Quantities and units — Mathematics supports notation; CRC Standard Mathematical Tables — composite trapezoid, Simpson 1/3, Gauss–Legendre supports formulas. These citations cover the integral path; they do not endorse CalculatorX or validate every Workspace operation.
Decimal underflow, integrand range failures and severe cancellation are rejected. The signed difference from the binary64 analytic baseline is not a certified bound. Full integral input and numerical contract.
Derivative sources and limits
NIST DLMF §3.4 — Differentiation supports difference formulas and truncation/rounding considerations. Polynomial finite steps use exact dyadic intermediates for supplied binary64 inputs; elementary identities retain mathematical h even when x±h rounds to x. The binary64 analytic baseline is not a certified error bound. Derivative input and numerical contract. This source covers the derivative path only.
Interpolation sources and limits
NIST DLMF §3.3 — Interpolation supports polynomial interpolation, divided differences and splines. This source covers the interpolation path. Primary values use bounded exact rational intermediates of the supplied binary64 inputs, then12 significant digits; this does not remove data uncertainty or polynomial oscillation. Unique nodes, 2–100 points (Lagrange at most9); outside-table linear/spline queries are rejected here. Full input and numerical contract.
Optimization sources and limits
SciPy — minimize_scalar supports golden-section and bounded Brent local minimization and their unimodal assumptions. This source covers the optimization path. Each candidate reports whether its internal bracket met tol or stopped at an iteration/resolution limit. Analytic baseline differences are not certified error bounds. Full input, convergence and numerical contract.
Comparisons 5
Trapezoid, Simpson, Gauss, central, forward, backward, Newton, bisection, secant, golden section and Brent, and linear, Lagrange, spline. A single-method session stays at /workspace/function. Two-sided limit and ODE stay on their calculator pages.
Each row is recomputed from the inputs.
| Method | Value | Reference | Difference |
|---|