TABULA/samples/inversion test
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This is SAMPLE4. To work with this sample, enter $4
inversion test ┌ ┌ ┌ ┌ ┌ ┌ ┌ ┌ ┌ {1} 3 m X[1] ┌ ┌ ├ ├ │ │ ├ ├ ├ ├ │ {2} 5 m X[2] │ │ │ │ │ │ ├ │ ├ │ │ {3} 2 m X[3] │ │ │ │ │ │ │ │ │ │ └>{4} 9.425 m PI * X[1] │ │ │ │ │ │ │ │ │ └> {5} 8 m X[1]+X[2] │ │ │ │ │ │ │ │ └> {6} 10 m X[1]+X[2]+X[3] │ │ │ │ │ │ │ └> {7} 15 m² X[1]*X[2] │ │ │ │ │ │ └> {8} 30 m³ X[1]*X[2]*X[3] ├ ├ │ │ │ └> {9} 9 m² X[1]^2 │ │ │ │ └> {10} 0.333 /m 1/X[1] │ │ │ └> {11} 0.600 / X[1] / X[2] │ │ └> {12} 1.667 / X[2] / X[1] │ └> {13} 0.556 /m X[2] / (X[1]^2) └> {14} 1.800 m (X[1]^2) / X[2]
Rationale
When backfitting values, TABULA takes short cuts, trying out simple inversion heuristics before deploying the most general method.
This t-table is a testbed for such heuristics. It is offered as a factory sample to show you what backfitting can do.
Note particularly how a change to a given computed line will not only change the line(s) it depends on, but all other lines which depend on these changed lines.
When you overtype a computed value, TABULA builds an internal tree of values it must change in consequence. But this tree depends on the line you choose to overtype.
Try it out
- Select item {8}
- Click tool addpc
This increases the value of {8} by 1% - Note what changes, viz. all items change via the backfit made to {1}, {2}, {3}.
- Reload the sample and repeat the above steps. This time try holding one (or more) of the ancestors {1}, {2}, {3}.
Instead of reloading, click Undo (multiple times).
This exercises the heuristic addressed by {9}. To exercise a different heuristic, choose another item: {4} to {14}.