cexprtk: Mathematical Expression Parsing and Evaluation in Python

cexprtk is a cython wrapper around the "C++ Mathematical Expression Toolkit Library (ExprTk)" by Arash Partow. Using cexprtk a powerful mathematical expression engine can be incorporated into your python project.

Table of Contents


The latest version of cexprtk can be installed using pip :

    $ pip install cexprtk

Note: Installation requires a compatible C++ compiler to be installed.


The following examples show the major features of cexprtk.

Example: Evaluate a simple equation

The following shows how the arithmetic expression (5+5) * 23 can be evaluated:

    >>> import cexprtk
    >>> cexprtk.evaluate_expression("(5+5) * 23", {})

Example: Using Variables

Variables can be used within expressions by passing a dictionary to the evaluate_expression function. This maps variable names to their values. The expression from the previous example can be re-calculated using variable values:

    >>> import cexprtk
    >>> cexprtk.evaluate_expression("(A+B) * C", {"A" : 5, "B" : 5, "C" : 23})

Example: Re-using expressions

When using the evaluate_expression() function, the mathematical expression is parsed, evaluated and then immediately thrown away. This example shows how to re-use an Expression for multiple evaluations.

  • An expression will be defined to calculate the circumference of circle, this will then be re-used to calculate the value for several different radii.
  • First a Symbol_Table is created containing a variable r (for radius), it is also populated with some useful constants such as π.

    python >>> import cexprtk >>> st = cexprtk.Symbol_Table({'r' : 1.0}, add_constants= True)

  • Now an instance of Expression is created, defining our function:

    python >>> circumference = cexprtk.Expression('2*pi*r', st)

  • The Symbol_Table was initialised with r=1, the expression can be evaluated for this radius simply by calling it:

    python >>> circumference() 6.283185307179586

  • Now update the radius to a value of 3.0 using the dictionary like object returned by the Symbol_Table's .variables property:

    python >>> st.variables['r'] = 3.0 >>> circumference() 18.84955592153876

Example: Defining an unknown symbol resolver

A callback can be passed to the Expression constructor through the unknown_symbol_resolver_callback parameter. This callback is invoked during expression parsing when a variable or constant is encountered that isn't in the Symbol_Table associated with the Expression.

The callback can be used to provide some logic that leads to a new symbol being registered or for an error condition to be flagged.

The Problem: The following example shows a potential use for the symbol resolver:

  • An expression contains variables of the form m_VARIABLENAME and f_VARIABLENAME.
  • m_ or f_ prefix the actual variable name (perhaps indicating gender).
  • VARIABLENAME should be used to look up the desired value in a dictionary.
  • The dictionary value of VARIABLENAME should then be weighted according to its prefix:
    • m_ variables should be multiplied by 0.8.
    • f_ variables should be multiplied by 1.1.

The Solution:

  • First the VARIABLENAME dictionary is defined:

    python variable_values = { 'county_a' : 82, 'county_b' : 76}

  • Now the callback is defined. This takes a single argument, symbol, which gives the name of the missing variable found in the expression:


    def callback(symbol): # Tokenize the symbol name into prefix and VARIABLENAME components. prefix,variablename = symbol.split("_", 1) # Get the value for this VARIABLENAME from the variable_values dict value = variable_values[variablename] # Find the correct weight for the prefix if prefix == 'm': weight = 0.8 elif prefix == 'f': weight = 1.1 else: # Flag an error condition if prefix not found. errormsg = "Unknown prefix "+ str(prefix) return (False, cexprtk.USRSymbolType.VARIABLE, 0.0, errormsg) # Apply the weight to the value *= weight # Indicate success and return value to cexprtk return (True, cexprtk.USRSymbolType.VARIABLE, value, "")


  • All that remains is to register the callback with an instance of Expression and to evaluate an expression. The expression to be evaluated is:

    • (m_county_a - f_county_b)
    • This should give a value of (0.8*82) - (1.1*76) = -18

    python >>> st = cexprtk.Symbol_Table({}) >>> e = cexprtk.Expression("(m_county_a - f_county_b)", st, callback) >>> e.value() -18.0

API Reference

For information about expressions supported by cexprtk please refer to the original C++ ExprTK documentation:

Class Reference

class Expression:

Class representing mathematical expression.

  • Following instantiation, the expression is evaluated calling the expression or invoking its value() method.
  • The variable values used by the Expression can be modified through the variables property of the Symbol_Table instance associated with the expression. The Symbol_Table can be accessed using the Expression.symbol_table property.
Defining unknown symbol-resolver:

The unknown_symbol_resolver_callback argument to the Expression constructor accepts a callable which is invoked whenever a symbol (i.e. a variable or a constant), is not found in the Symbol_Table given by the symbol_table argument. The unknown_symbol_resolver_callback can be used to provide a value for the missing value or to set an error condition.

The callable should have following signature:

    def callback(symbol_name):

Where symbol_name is a string identifying the missing symbol.

The callable should return a tuple of the form:



  • HANDLED_FLAG is a boolean:
    • True indicates that callback was able handle the error condition and that SYMBOL_VALUE should be used for the missing symbol.
    • False, flags and error condition, the reason why the unknown symbol could not be resolved by the callback is described by ERROR_STRING.
  • USR_SYMBOL_TYPE gives type of symbol (constant or variable) that should be added to the symbol_table when unkown symbol is resolved. Value should be one of those given in cexprtk.USRSymbolType. e.g.
    • cexprtk.USRSymbolType.VARIABLE
    • cexprtk.USRSymbolType.CONSTANT
  • SYMBOL_VALUE, floating point value that should be used when resolving missing symbol.
  • ERROR_STRING when HANDLED_FLAG is False this can be used to describe error condition.
def init(self, expression, symbol_table, unknown_symbol_resolver_callback = None):

Instantiate Expression from a text string giving formula and Symbol_Table instance encapsulating variables and constants used by the expression.


  • expression (str) String giving expression to be calculated.
  • symbol_table (Symbol_Table) Object defining variables and constants.
  • unknown_symbol_resolver_callback (callable) See description above.
def value(self):

Evaluate expression using variable values currently set within associated Symbol_Table


  • (float) Value resulting from evaluation of expression.
def call(self):

Equivalent to calling value() method.


  • (float) Value resulting from evaluation of expression.

Read only property that returns Symbol_Table instance associated with this expression.


  • (Symbol_Table) Symbol_Table associated with this Expression.

class Symbol_Table:

Class for providing variable and constant values to Expression instances.

def init(self, variables, constants = {}, add_constants = False):

Instantiate Symbol_Table defining variables and constants for use with Expression class.


  • To instantiate a Symbol_Table with:
    • x = 1
    • y = 5
    • define a constant k = 1.3806488e-23
  • The following code would be used:

    python st = cexprtk.Symbol_Table({'x' : 1, 'y' : 5}, {'k'= 1.3806488e-23})


  • variables (dict) Mapping between variable name and initial variable value.
  • constants (dict) Dictionary containing values that should be added to Symbol_Table as constants. These can be used a variables within expressions but their values cannot be updated following Symbol_Table instantiation.
  • add_constants (bool) If True, add the standard constants pi, inf, epsilon to the 'constants' dictionary before populating the Symbol_Table

Returns dictionary like object containing variable values. Symbol_Table values can be updated through this object.


    >>> import cexprtk
    >>> st = cexprtk.Symbol_Table({'x' : 5, 'y' : 5})
    >>> expression = cexprtk.Expression('x+y', st)
    >>> expression()

Update the value of x in the symbol table and re-evaluate the expression:

    >>> expression.symbol_table.variables['x'] = 11.0
    >>> expression()


  • Dictionary like giving variables stored in this Symbol_Table. Keys are variables names and these map to variable values.

Property giving constants stored in this Symbol_Table.


  • Read-only dictionary like object mapping constant names stored in Symbol_Table to their values.

class USRSymbolType:

Defines constant values used to determine symbol type returned by unknown_symbol_resolver_callback (see Expression constructor documentation for more).


Value that should be returned by an unknown_symbol_resolver_callback to define a variable.


Value that should be returned by an unknown_symbol_resolver_callback to define a constant.

Utility Functions

def check_expression (expression)

Check that expression can be parsed. If successful do nothing, if unsuccessful raise ParseException.


  • expression (str) Formula to be evaluated


  • ParseException: If expression is invalid.

def evaluate_expression (expression, variables)

Evaluate a mathematical formula using the exprtk library and return result.

For more information about supported functions and syntax see the exprtk C++ library website.


  • expression (str) Expression to be evaluated.
  • variables (dict) Dictionary containing variable name, variable value pairs to be used in expression.


  • (float): Evaluated expression


  • ParseException: if expression is invalid.


Cython wrapper by Michael Rushton (, although most credit should go to Arash Partow for creating the underlying ExprTK library.


cexprtk is released under the same terms as the ExprTK library the Common Public License Version 1.0 (CPL).