Uncertainty

Package: UNCERTAINTY_PACKAGE. Registered by createEngine(); for a slimmer engine, register it explicitly (see choosing packages).

An uncertainty is the give-or-take on a measurement: a reading of 12.3 that could be off by 0.5 either way. Solve lets you attach that tolerance to a number and carries it through the sums, so you do not have to track the error on a second line.

A measurement can carry a tolerance, written ± or the ASCII +/-, and the tolerance travels through the arithmetic so you do not have to track it on a second line. 12.3 ± 0.5 is the number 12.3 with a one-sigma uncertainty of 0.5.

12.3 +/- 0.5 // 12.3 ± 0.5
(12.3 +/- 0.5) * 4 // 49.2 ± 2.0
(10 +/- 1) + (20 +/- 2) // 30 ± 2.24
(100 +/- 5) + 10% // 110 ± 5.5

+, -, * and / propagate it, combining independent errors in quadrature: a sum or difference adds the spreads as sqrt(a² + b²), and a product or quotient adds the relative spreads the same way. A plain number counts as an exact value, so multiplying by one scales the spread; a percentage is a scalar multiply too, so (100 ± 5) + 10% is 110 ± 5.5. The ± binds tighter than + - * /, so 12.3 ± 0.5 * 4 is (12.3 ± 0.5) * 4; parenthesise to group otherwise.

Everything else reads the centre and drops the tolerance: a comparison compares the centres, and sqrt, sin and the like work on the centre alone. Correlated errors are out of scope, and a tolerance on a value with a unit drops the unit: 5m ± 1m is read as 5 ± 1, not carried as metres.