CortexJS Compute Engine Changelog


Release Date: 2022-11-27

Breaking Changes

  • The expr.symbols property return an array of string. Previously it returned an array of BoxedExpression.


  • Rewrote the rational computation engine to use JavaScript bigint instead of Decimal instances. Performance improvements of up to 100x.
  • expr.freeVars provides the free variables in an expression.
  • Improved performance of prime factorization of big num by x100.
  • Added ["RandomExpression"]
  • Improved accuracy of some operations, for example expr.parse("1e999 + 1").simplify()

Bug Fixes

  • When ce.numericMode === "auto", square roots of negative numbers would return an expression instead of a complex number.
  • The formatting of LaTeX numbers when using ce.latexOptions.notation = "engineering" or "scientific" was incorrect.
  • The trig functions no longer “simplify” to the less simple exponential formulas.
  • The canonical order of polynomials now orders non-lexicographic terms of degree 1 last, i.e. “ax^2+ bx+ c” instead of “x + ax^2 + bx”.
  • Fixed evaluation of inverse functions
  • Fixed expr.isLess, expr.isGreater, expr.isLessEqual, expr.isGreaterEqual and ["Min"], ["Max"]


Release Date: 2022-11-18

Breaking Changes

  • The signature of ce.defineSymbol(), ce.defineFunction() and ce.pushScope() have changed


  • When a constant should be held or substituted with its value can now be more precisely controlled. The hold symbol attribute is now holdUntil and can specify at which stage the substitution should take place.

Bug Fixes

  • Some constants would return a value as bignum or complex even when the numericMode did not allow it.
  • Changing the value or domain of a symbol is now correctly taken into account. Changes can be made with ce.assume(), ce.set() or expr.value.
  • When a symbol does not have a value associated with it, assumptions about it (e.g. “x > 0”) are now correctly tracked and reflected.


Release Date: 2022-11-17

Breaking Changes

  • expr.isLiteral has been removed. Use expr.numericValue !== null and expr.string !== null instead.

Bug Fixes

  • Calling ce.forget() would not affect expressions that previously referenced the symbol.


  • More accurate calculations of some trig functions when using bignums.
  • Improved performance when changing a value with ce.set(). Up to 10x faster when evaluating a simple polynomial in a loop.
  • ce.strict can be set to false to bypass some domain and validity checks.


Release Date: 2022-11-15

Breaking Changes

  • The head of a number expression is always Number. Use expr.domain to be get more specific info about what kind of number this is.
  • By default, and ce.parse() return a canonical expression. A flag can be used if a non-canonical expression is desired.
  • The API surface of BoxedExpression has been reduced. The properties machineValue, bignumValue, asFloat, asSmallInteger, asRational etc… have been replaced with a single numericValue property.
  • parseUnknownSymbol is now parseUnknownIdentifier


  • Support angles in degrees with 30\deg, 30\degree, 30^\circ and \ang{30}.

  • More accurate error expressions, for example if there is a missing closing delimiter an ["Error", ["ErrorCode", "'expected-closing-delimiter'", "')'"]] is produced.

  • ["Expand"] handles more cases

  • The trig functions can now have a regular exponent, i.e.\cos^2(x) in addition to -1 for inverse, and a combination of \prime, \doubleprime and ' for derivatives.

  • ce.assume() handle more expressions and can be used to define new symbols by domain or value.

  • Better error message when parsing, e.g. \sqrt(2) (instead of \sqrt{2})

  • Better simplification for square root expressions:

    • \sqrt{25x^2} -> 5x
  • Improved evaluation of ["Power"] expressions, including for negative arguments and non-integer exponents and complex arguments and exponents.

  • Added Arccot, Arcoth, Arcsch, Arcscc, Arsech and Arccsc

  • expr.solve() returns result for polynomials of order up to 2.

  • The pattern.match() function now work correctly for commutative functions, i.e. ce.pattern(['Add', '_a', 'x']).match(ce.parse('x+y')) -> {"_a": "y"}

  • Added ce.let() and ce.set() to declare and assign values to identifiers.

  • Preserve exact calculations involving rationals or square root of rationals.

    • \sqrt{\frac{49}{25}} -> \frac{7}{5}
  • Addition and multiplication provide more consistent results for evaluate() and N(). Evaluate returns an exact result when possible.

    • EXACT
      • 2 + 5 -> 7
      • 2 + 5/7 -> 19/7
      • 2 + √2 -> 2 + √2
      • 2 + √(5/7) -> 2 + √(5/7)
      • 5/7 + 9/11 -> 118/77
      • 5/7 + √2 -> 5/7 + √2
      • 10/14 + √(18/9) -> 5/7 + √2
      • √2 + √5 -> √2 + √5
      • √2 + √2 -> 2√2
      • sin(2) -> sin(2)
      • sin(π/3) -> √3/2
      • 2 + 2.1 -> 4.1
      • 2 + √2.1 -> 3.44914
      • 5/7 + √2.1 -> 2.16342
      • sin(2) + √2.1 -> 2.35844
  • More consistent behavior of the auto numeric mode: calculations are done with bignum and complex in most cases.

  • JsonSerializationOptions has a new option to specify the numeric precision in the MathJSON serialization.

  • Shorthand numbers can now be strings if they do not fit in a float-64:

// Before
["Rational", { "num": "1234567890123456789"}, { "num": "2345678901234567889"}]

// Now
["Rational", "1234567890123456789", "2345678901234567889"]
  • \sum is now correctly parsed and evaluated. This includes creating a local scope with the index and expression value of the sum.

Bugs Fixed

  • The parsing and evaluation of log functions could produce unexpected results
  • The \gamma command now correctly maps to ["Gamma"]
  • Fixed numeric evaluation of the ["Gamma"] function when using bignum
  • #57 Substituting 0 (i.e. with expr.subs({})) did not work.
  • #60 Correctly parse multi-char symbols with underscore, i.e. \mathrm{V_a}
  • Parsing a number with repeating decimals and an exponent would drop the exponent.
  • Correct calculation of complex square roots
    • \sqrt{-49} -> 7i
  • Calculations were not always performed as bignum in "auto" numeric mode if the precision was less than 15. Now, if the numeric mode is "auto", calculations are done as bignum or complex numbers.
  • If an identifier contained multiple strings of digits, it would not be rendered to LaTeX correctly, e.g. V20_20.
  • Correctly return isReal for real numbers


Release Date: 2022-10-02

Breaking Changes

  • Corrected the implementation of expr.toJSON(), expr.valueOf() and added the esoteric [Symbol.toPrimitive]() method. These are used by JavaScript when interacting with other primitive types. A major change is that expr.toJSON() now returns an Expression as an object literal, and not a string serialization of the Expression.

  • Changed from “decimal” to “bignum”. “Decimal” is a confusing name, since it is used to represent both integers and floating point numbers. Its key characteristic is that it is an arbitrary precision number, aka “bignum”. This affects ce.numericMode which now uses bignum instead of decimal', expr.decimalValue->expr.bignumValue, decimalValue()-> bignumValue()`

Bugs Fixed

  • Numerical evaluation of expressions containing complex numbers when in decimal or auto mode produced incorrect results. Example: e^{i\\pi}


Release Date: 2022-09-30

Breaking Changes

  • The ce.latexOptions.preserveLatex default value is now false
  • The first argument of the ["Error"] expression (default value) has been dropped. The first argument is now an error code, either as a string or an ["ErrorCode"] expression.


  • Much improved LaTeX parser, in particular when parsing invalid LaTeX. The parser now avoids throwing, but will return a partial expression with ["Error"] subexpressions indicating where the problems were.
  • Implemented new domain computation system (similar to type systems in programming languages)
  • Added support for multiple signatures per function (ad-hoc polymorphism)
  • Added FixedPoint, Loop, Product, Sum, Break, Continue, Block, If, Let, Set, Function, Apply, Return
  • Added Min, Max, Clamp
  • Parsing of \sum, \prod, \int.
  • Added parsing of log functions, \lb, \ln, \ln_{10}, \ln_2, etc…
  • Added expr.subexpressions, expr.getSubexpressions(), expr.errors, expr.symbols, expr.isValid`.
  • Symbols can now be used to represent functions, i.e.'Sin').domain correctly returns ["Domain", "Function"].
  • Correctly handle rational numbers with a numerator or denominator outside the range of a 64-bit float.
  • Instead of a Missing symbol an ["Error", "'missing'"] expression is used.
  • Name binding is now done lazily
  • Correctly handle MathJSON numbers with repeating decimals, e.g. 1.(3).
  • Correctly evaluate inverse functions, e.g. ce.parse('\\sin^{-1}(.5)).N()
  • Fixed some LaTeX serialization issues

Read more at Core Reference and [Arithmetic Reference] (

Bugs Fixed

  • #43 If the input of ce.parse() is an empty string, return an empty string for expr.latex or expr.json.latex: that is, ensure verbatim LaTeX round-tripping
  • Evaluating some functions, such as \arccos would result in a crash
  • Correctly handle parsing of multi-token decimal markers, e.g. {,}


Release Date: 2022-04-18


  • Parse more cases of tabular environments
  • Handle simplify and evaluate of inert functions by default
  • Avoid unnecessary wrapping of functions when serializing LaTeX
  • Parse arguments of LaTeX commands (e.g. \vec{})
  • #42 Export static ComputeEngine.getLatexDictionary
  • Parse multi-character constants and variables, e.g. \mathit{speed} and \mathrm{radius}
  • Parse/serialize some LaTeX styling commands: \displaystyle, \tiny and more


Release Date: 2022-04-05


  • Correctly parse tabular content (for example in \begin{pmatrix}...\end{pmatrix}
  • Correctly parse LaTeX groups, i.e. {...}
  • Ensure constructible trigonometric values are canonical
  • Correct and simplify evaluation loop for simplify(), evaluate() and N().
  • #41 Preserve the parsed LaTeX verbatim for top-level expressions
  • #40 Correctly calculate the synthetic LaTeX metadata for numbers
  • Only require Node LTS (16.14.2)
  • Improved documentation, including Dark Mode support


Release Date: 2022-03-27


  • Added option to specify custom LaTeX dictionaries in ComputeEngine constructor
  • expr.valueOf returns rational numbers as [number, number] when applicable
  • The non-ESM builds (compute-engine.min.js) now targets vintage JavaScript for improved compatibility with outdated toolchains (e.g. Webpack 4) and environments. The ESM build (compute-engine.min.esm.js) targets evergreen JavaScript (currently ECMAScript 2020).


Release Date: 2022-03-21

Transition Guide from 0.4.2

The API has changed substantially between 0.4.2 and 0.4.3, however adapting code to the new API is very straightforward.

The two major changes are the introduction of the BoxedExpression class and the removal of top level functions.

Boxed Expression

The BoxedExpression class is a immutable box (wrapper) that encapsulates a MathJSON Expression. It provides some member functions that can be used to manipulate the expression, for example expr.simplify() or expr.evaluate().

The boxed expresson itself is immutable. For example, calling expr.simplify() will return a new, simplified, expression, without modifying expr.

To create a “boxed” expression from a “raw” MathJSON expression, use To create a boxed expression from a LaTeX string, use ce.parse().

To access the “raw” MathJSON expression, use the expr.json property. To serialize the expression to LaTeX, use the expr.latex property.

The top level functions such as parse() and evaluate() are now member functions of the ComputeEngine class or the BoxedExpression class.

There are additional member functions to examine the content of a boxed expression. For example, expr.symbol will return null if the expression is not a MathJSON symbol, otherwise it will return the name of the symbol as a string. Similarly, expr.ops return the arguments (operands) of a function, expr.asFloat return null if the expression does not have a numeric value that can be represented by a float, a number otherwise, etc…

Canonical Form

Use expr.canonical to obtain the canonical form of an expression rather than the ce.format() method.

The canonical form is less aggressive in its attempt to simplify than what was performed by ce.format().

The canonical form still accounts for distributive and associative functions, and will collapse some integer constants. However, in some cases it may be necessary to invoke expr.simplify() in order to get the same results as ce.format(expr).

Rational and Division

In addition to machine floating points, arbitrary precision numbers and complex numbers, the Compute Engine now also recognize and process rational numbers.

This is mostly an implementation detail, although you may see ["Rational", 3, 4], for example, in the value of a expr.json property.

If you do not want rational numbers represented in the value of the .json property, you can exclude the Rational function from the serialization of JSON (see below) in which case Divide will be used instead.

Note also that internally (as a result of boxing), Divide is represented as a product of a power with a negative exponent. This makes some pattern detection and simplifications easier. However, when the .json property is accessed, product of powers with a negative exponents are converted to a Divide, unless you have included Divide as an excluded function for serialization.

Similarly, Subtract is converted internally to Add, but may be serialized unless excluded.

Parsing and Serialization Customization

Rather than using a separate instance of the LatexSyntax class to customize the parsing or serialization, use a ComputeEngine instance and its ce.parse() method and the expr.latex property.

Custom dictionaries (to parse/serialize custom LaTeX syntax) can be passed as an argument to the ComputeEngine constructor.

For more advanced customizations, use ce.latexOptions = {...}. For example, to change the formatting options of numbers, how the invisible operator is interpreted, how unknown commands and symbols are interpreted, etc…

Note that there are also now options available for the “serialization” to MathJSON, i.e. when the expr.json property is used. It is possible to control for example if metadata should be included, if shorthand forms are allowed, or whether some functions should be avoided (Divide, Sqrt, Subtract, etc…). These options can be set using ce.jsonSerializationOptions = {...}.

Comparing Expressions

There are more options to compare two expressions.

Previously, match() could be used to check if one expression matched another as a pattern.

If match() returned null, the first expression could not be matched to the second. If it returned an object literal, the two expressions matched.

The top-level match() function is replaced by the expr.match() method. However, there are two other options that may offer better results:

  • expr.isSame(otherExpr) return true if expr and otherExpr are structurally identical. Structural identity is closely related to the concept of pattern matching, that is ["Add", 1, "x"] and ["Add", "x", 1] are not the same, since the order of the arguments is different. It is useful for example to compare some input to an answer that is expected to have a specific form.
  • expr.isEqual(otherExpr) return true if expr and otherExpr are mathematically identical. For example ce.parse("1+1").isEqual(ce.parse("2")) will return true. This is useful if the specific structure of the expression is not important.

It is also possible to evaluate a boolean expression with a relational operator, such as Equal:

console.log(['Equal', expr, 2]).evaluate().symbol);
// -> "True"

// -> true

Before / After

Before After
expr = ["Add", 1, 2] expr =["Add", 1, 2])
expr = ce.evaluate(expr) expr = expr.evaluate()
console.log(expr) console.log(expr.json)
expr = new LatexSyntax().parse("x^2+1") expr = ce.parse("x^2+1")
new LatexSyntax().serialize(expr) expr.latex
ce.simplify(expr) expr.simplify()
await ce.evaluate(expr) expr.evaluate()
ce.N(expr) expr.N()
ce.domain(expr) expr.domain
ce.format(expr...) expr.canonical


Release Date: 2021-06-18


  • In LaTeX, parse \operatorname{foo} as the MathJSON symbol "foo".