Exact coefficients

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

The numbers in front of the terms of an expression, its coefficients, are kept as exact fractions rather than the approximate floating-point numbers a computer usually uses. This is why 0.1x + 0.2x combines to exactly 0.3x here, and not the 0.30000000000000004x that ordinary floating point would give. Like the other algebra forms, this reads with a trailing arrow to show the simplified result.

The exactness is a property of a term’s coefficient, not of a bare number. A plain 0.1 + 0.2 is still ordinary floating point (0.30000000000000004); it is the coefficient carried by a variable term that stays exact. Money is the other place the engine keeps exact decimals, to the cent (see money precision).

0.1x + 0.2x => // 0.3x
x/3 + x/3 =>   // 2/3x

A coefficient that cannot be written as a short decimal stays a fraction rather than being rounded into one.