Model, inspect and explain a mathematical result

These three starters combine editable assumptions, numerical checks and an explanation of the result. Open their .grid source in Grid, then use the I/O view to make the changes below. To inspect a report, use its arrow in Readable cells, switch to Model, then select the Cell tab for method and completion details. A function missing from your connected runtime requires a matching runtime; changing its spelling does not add the capability.

Engineering what-if

Open the nonlinear spring. At load 2, displacement is approximately 1 and compliance is approximately 0.25. Change Load to 10: displacement becomes approximately 2 and compliance becomes approximately 1/13. Check that Residual remains close to zero and Verified is true.

Inspect StiffnessReport. Its automatic derivative describes the local stiffness, evaluated in floating-point arithmetic. Compliance is derived from the equation at a simple root; it is not a prediction for an arbitrary large change in load. The model states this relationship explicitly.

If a root or scalar optimization search exhausts its iteration budget, Grid reports a calculation failure. Check the equation, domain and interval before increasing the budget. A completed bracket search assumes continuity; a small bracket around a pole does not prove a root.

Experimental inference

Open the exponential fit. Inspect Fit to review completion, coefficients, residuals and local parameter intervals. Change Confidence from 0.95 to 0.90 and compare interval widths. Change InitialRate to 1 and verify whether the solver reaches the same fit. Keep a failed solve visible rather than replacing it with a previous answer.

The example assumes independent observation errors with a common unknown variance. These are individual local parameter intervals. They are not prediction intervals, simultaneous intervals or a guarantee of good coverage. Weak identification and model misspecification need scientific judgment even when every reported number is finite. Supply weights or known observation errors only when the selected report's corresponding assumptions fit the data.

Resource allocation

Open the production model. The baseline produces 40 units of X and 20 units of Y, with profit 280. Increase ResourceCapacity from 100 to 110: profit becomes 300. Inspect Report for resource marginal values and Verified for feasibility and objective checks.

The products are divisible and the constraints are linear. A marginal value is local to the current optimization structure; it is not a license to extrapolate indefinitely. Use a fresh solve for each capacity scenario.

Save a comparison someone else can reproduce

In I/O, open Saved scenarios. Enter a scenario name and the results to capture, then choose Save scenario before editing. Save the changed scenario with a descriptive name and inspect its listed input overrides. Use Preview restore and Restore scenario inputs to return to the baseline and confirm the displayed values return. Save the document as a .gridoc, reopen it, and check the selected scenario and result again.

When sharing the document, explain the question, changed input, completion status and assumptions. Keep the source and report with the answer. For a fit, include the observation-error model; for optimization, include feasibility and the meaning of local marginal values.

Recognize a numerical derivative estimate

DERIVATIVE.REPORT((x) => ABS(x), 0) reports a central-difference estimate of zero and a domain-related automatic-differentiation fallback. The classical derivative does not exist there: the two one-sided slopes differ. A symmetric estimate alone does not establish differentiability. Unsupported automatic coverage, in contrast, does not by itself imply a nonsmooth function.

Read the report's value field to reuse that calculation. Inspect the method, step and fallback reason in the report before interpreting an estimate. Ordinary DERIVATIVE keeps its scalar result and fallback policy; the report adds method disclosure without additional function samples.