MathEvaluator is a .NET library that allows you to evaluate and compile any mathematical expressions from a string dynamically.
- Supports different mathematical contexts, such as scientific, programming, and other custom contexts.
- Evaluates Boolean logic, as well as Double, Decimal, and Complex numbers.
- Compiles a math expression string into executable code and produces a delegate that represents the math expression.
- Provides variable support within math expressions.
- Extensible with custom functions and operators.
- Fast and comprehensive. More than 3000 tests are passed, including complex math expressions (for example, -3^4sin(-π/2) or sin-3/cos1).
Evaluating Boolean logical expressions.
Compilation of a Math Expression into a delegate.
dotnet add package MathEvaluator
Alternatively, you can install the package using the NuGet Package Manager Console:
Install-Package MathEvaluator
This math expression evaluator is designed for exceptional performance by leveraging modern .NET features and best practices, which is why it targets .NET Standard 2.1 or higher.
This high-performance evaluator stands out due to its use of ReadOnlySpan<char>, and avoidance of regular expressions. These design choices collectively ensure minimal memory allocation, fast parsing, and efficient execution.
The evaluator uses recursive method calls to handle mathematical operations based on operator precedence and rules, an operator with highest precedence is evaluating first. This approach avoids the overhead associated with stack or queue data structures.
The evaluator uses a prefix tree, also known as a trie (pronounced "try"), for efficient searching of variables, operators, and functions by their keys (names) when providing a specific mathematical context or adding custom variables, operators, and functions is required.
Let's compare, for example, performance of calculating the mathematical expression:
22888.32 * 30 / 323.34 / .5 - -1 / (2 + 22888.32) * 4 - 6
Below are the results of the comparison with the NCalc library:
| Method | Job | Runtime | Mean | Error | StdDev | Gen0 | Allocated |
|---|---|---|---|---|---|---|---|
| MathEvaluator | .NET 6.0 | .NET 6.0 | 654.5 ns | 2.09 ns | 1.63 ns | 0.0067 | 88 B |
| NCalc | .NET 6.0 | .NET 6.0 | 8,408.6 ns | 42.70 ns | 39.94 ns | 0.3967 | 5160 B |
| MathEvaluator | .NET 8.0 | .NET 8.0 | 589.9 ns | 2.58 ns | 2.41 ns | 0.0067 | 88 B |
| NCalc | .NET 8.0 | .NET 8.0 | 6,184.0 ns | 30.74 ns | 28.75 ns | 0.3510 | 4472 B |
NOTE: NCalc includes built-in caching, enabled by default in recent versions. While this can improve benchmark performance, in real-world scenarios, caching may increase memory usage and is not effective if the evaluation results depend on variable values. In such cases, compilation is a better alternative.
Added in version 2.0.0
By using compilation, you can convert any mathematical expression string into a delegate, such as Func<T, TResult> or Func<TResult>, which significantly improves performance when evaluating the expression. However, since compilation takes time, it is beneficial to compile the expression beforehand if you plan to evaluate it multiple times, especially for 200 or more iterations. Refer to the benchmarks for detailed performance insights.
Examples of using string extentions:
"22888.32 * 30 / 323.34 / .5 - -1 / (2 + 22888.32) * 4 - 6".Evaluate();
"22888.32 * 30 / 323.34 / .5 - -1 / (2 + 22888.32) * 4 - 6".EvaluateDecimal();
"$22,888.32 * 30 / 323.34 / .5 - - 1 / (2 + $22,888.32) * 4 - 6".Evaluate(null, new CultureInfo("en-US"));
"22’888.32 CHF * 30 / 323.34 / .5 - - 1 / (2 + 22’888.32 CHF) * 4 - 6".EvaluateDecimal(null, new CultureInfo("de-CH"));
"ln(1/-0.5 + √(1/(0.5^2) + 1))".Evaluate(new ScientificMathContext());
"P * (1 + r/n)^d".EvaluateDecimal(new { P = 10000, r = 0.05, n = 365, d = 31 }, new DecimalScientificMathContext());
"4 % 3".Evaluate(new ProgrammingMathContext());
"4 mod 3".Evaluate(new ScientificMathContext());
"4 <> 4 OR 5.4 = 5.4 AND NOT 0 < 1 XOR 1.0 - 1.95 * 2 >= -12.9 + 0.1 / 0.01".EvaluateBoolean(new ProgrammingMathContext());
"¬⊥∧⊤∨¬⊤⇒¬⊤".EvaluateBoolean(new ScientificMathContext());
"sin(2 + 3i) * arctan(4i)/(1 - 6i)".EvaluateComplex(new ComplexScientificMathContext());
Examples of using an instance of the MathExpression class:
new MathExpression("22888.32 * 30 / 323.34 / .5 - -1 / (2 + 22888.32) * 4 - 6").Evaluate();
new MathExpression("22888.32 * 30 / 323.34 / .5 - -1 / (2 + 22888.32) * 4 - 6").EvaluateDecimal();
new MathExpression("$22,888.32 * 30 / 323.34 / .5 - - 1 / (2 + $22,888.32) * 4 - 6", null, new CultureInfo("en-US")).Evaluate();
new MathExpression("22’888.32 CHF * 30 / 323.34 / .5 - - 1 / (2 + 22’888.32 CHF) * 4 - 6", null, new CultureInfo("de-CH")).EvaluateDecimal();
new MathExpression("ln(1/-0.5 + √(1/(0.5^2) + 1))", new ScientificMathContext()).Evaluate();
new MathExpression("P * (1 + r/n)^d", new DecimalScientificMathContext()).EvaluateDecimal(new { P = 10000, r = 0.05, n = 365, d = 31 });
new MathExpression("4 % 3", new ProgrammingMathContext()).Evaluate();
new MathExpression("4 mod 3", new ScientificMathContext()).Evaluate();
new MathExpression("4 <> 4 OR 5.4 = 5.4 AND NOT 0 < 1 XOR 1.0 - 1.95 * 2 >= -12.9 + 0.1 / 0.01", new ProgrammingMathContext()).EvaluateBoolean();
new MathExpression("¬⊥∧⊤∨¬⊤⇒¬⊤", new ScientificMathContext()).EvaluateBoolean();
new MathExpression("sin(2 + 3i) * arctan(4i)/(1 - 6i)", new ComplexScientificMathContext()).EvaluateComplex();
Examples of passing custom variables and functions as parameters:
var x1 = 0.5;
var x2 = -0.5;
var sqrt = Math.Sqrt;
Func<double, double> ln = Math.Log;
var value1 = "ln(1/-x1 + sqrt(1/(x2*x2) + 1))"
.Evaluate(new { x1, x2, sqrt, ln });
var parameters = new MathParameters();
parameters.BindVariable(x1);
parameters.BindVariable(x2);
parameters.BindFunction(Math.Sqrt);
parameters.BindFunction(d => Math.Log(d), "ln");
var value2 = "ln(1/-x1 + Math.Sqrt(1/(x2*x2) + 1))"
.Evaluate(parameters);
Example of using custom context:
var context = new MathContext();
context.BindFunction(Math.Sqrt);
context.BindFunction(d => Math.Log(d), "ln");
"ln(1/-x1 + Math.Sqrt(1/(x2*x2) + 1))"
.Evaluate(new { x1 = 0.5, x2 = -0.5 }, context);
Examples of compilation:
var fn = "ln(1/x1 + √(1/(x2*x2) + 1))"
.Compile(new { x1 = 0.0, x2 = 0.0 }, new ScientificMathContext());
var value = fn(new { x1 = -0.5, x2 = 0.5 });
Added in version 2.1.0
By using the Evaluating event, you can debug or log the steps of a math expression's evaluation. This event is triggered at each step during the evaluation process. The following code demonstrates how to use to this event:
using var expression = new MathExpression("-3^4sin(-PI/2)", new ScientificMathContext());
expression.Evaluating += (object? sender, EvaluatingEventArgs args) =>
{
Console.WriteLine("{0}: {1} = {2};{3}",
args.Step,
args.MathString[args.Start..(args.End + 1)],
args.Value,
args.IsCompleted ? " //completed" : string.Empty);
};
var value = expression.Evaluate();
Output:
1: 3^4 = 81;
2: PI = 3.141592653589793;
3: PI/2 = 1.5707963267948966;
4: -PI/2 = -1.5707963267948966;
5: sin(-PI/2) = -1;
6: 3^4sin(-PI/2) = -81;
7: -3^4sin(-PI/2) = 81; //completed
NOTE: To prevent memory leaks, it’s important to unsubscribe from the event after subscribing to it. The Evaluating event is cleaned up in the Dispose method, so I recommend using the using statement to ensure proper disposal and efficient resource management.
Added in version 2.2.0
Complex numbers are written in the form a ± bi, where a is the real part and bi is the imaginary part. In mathematical expressions involving complex numbers, it's advisable to use parentheses () to ensure clarity and obtain the expected result.
| Notation | Precedence | |
|---|---|---|
| Addition | + | 0 |
| Subtraction, Negativity | - | 0 |
| Multiplication | * | 100 |
| Division | / | 100 |
| Parentheses | ( ) | 200 |
| Currency symbol | depends on culture info |
| Notation | Precedence | |
|---|---|---|
| Addition | + | 0 |
| Subtraction, Negativity | - | 0 |
| Multiplication | * | 100 |
| Division | / | 100 |
| Parentheses | ( ) | 200 |
| Currency symbol | depends on culture info | |
| Exponentiation | ** | 400 |
| Modulus | % | 100 |
| Floor Division | // | 100 |
| Logical constants | true, false, True, False, TRUE, FALSE | 300 |
| Equality | = | -100 |
| Inequality | <> | -100 |
| Less than | < | -100 |
| Greater than | > | -100 |
| Less than or equal | <= | -100 |
| Greater than or equal | >= | -100 |
| Logical negation | not, Not, NOT | -200 |
| Logical AND | and, And, AND | -300 |
| Logical exclusive OR | xor, Xor, XOR | -400 |
| Logical OR | or, Or, OR | -500 |
Conditional operation: IIF(condition, valueIfTrue, valueIfFalse), where the valueIfTrue and valueIfFalse args are optional |
iif, Iif, IIF | 200 |
| Notation | Precedence | |
|---|---|---|
| Addition | + | 0 |
| Subtraction, Negativity | - | 0 |
| Multiplication | *, ×, or · | 100 |
| Division | / or ÷ | 100 |
| Parentheses | ( ) | 200 |
| Currency symbol | depends on culture info | |
| Exponentiation | ^ | 400 |
| Modulus | mod, Mod, MOD, modulo, Modulo, or MODULO | 100 |
| Floor Division | // | 100 |
| Absolute | | |, abs, Abs, ABS | 200 |
| Ceiling | ⌈ ⌉ | 200 |
| Floor | ⌊ ⌋ | 200 |
| Square root, cube root, fourth root | √, ∛, ∜ | 200 |
| Natural logarithmic base | e | 300 |
| Natural logarithm | ln, Ln, LN | 200 |
| Common logarithm (base 10) | log, Log, LOG | 200 |
| Factorial | ! | 500 |
| Infinity | ∞ | 300 |
| Logical constants | true, false, True, False, TRUE, FALSE, T, F, ⊤, ⊥ | 300 |
| Equality | = | -100 |
| Inequality | ≠ | -100 |
| Less than | < | -100 |
| Greater than | > | -100 |
| Less than or equal | ≤, ⪯ | -100 |
| Greater than or equal | ≥, ⪰ | -100 |
| Logical negation | ¬, not, Not, NOT | 500 for ¬, -200 |
| Logical AND | ∧, and, And, AND | -300 |
| Logical exclusive OR | ⊕, xor, Xor, XOR | -400 |
| Logical OR | ∨, or, Or, OR | -500 |
| Logical implication | →, ⇒, ←, ⟸ | -800 |
| Logical biconditional equivalence | ↔, ⇔ | -900 |
| Logical biconditional inequivalence | ↮, ⇎ | -900 |
| Logical equivalence | ≡ | -1000 |
| Logical inequivalence | ≢ | -1000 |
| Degree | ° | 500 |
| Pi constant | π, pi, Pi, PI | 300 |
| Tau constant | τ | 300 |
| Sine | sin, Sin, SIN | 200 |
| Cosine | cos, Cos, COS | 200 |
| Tangent | tan, Tan, TAN | 200 |
| Secant | sec, Sec, SEC | 200 |
| Cosecant | csc, Csc, CSC | 200 |
| Cotangent | cot, Cot, COT | 200 |
| Hyperbolic sine | sinh, Sinh, SINH | 200 |
| Hyperbolic cosine | cosh, Cosh, COSH | 200 |
| Hyperbolic tangent | tanh, Tanh, TANH | 200 |
| Hyperbolic secant | sech, Sech, SECH | 200 |
| Hyperbolic cosecant | csch, Csch, CSCH | 200 |
| Hyperbolic cotangent | coth, Coth, COTH | 200 |
| Inverse sine | arcsin, Arcsin, ARCSIN, sin^-1, Sin^-1, SIN^-1 | 200 |
| Inverse cosine | arccos, Arccos, ARCCOS, cos^-1, Cos^-1, COS^-1 | 200 |
| Inverse tangent | arctan, Arctan, ARCTAN, tan^-1, Tan^-1, TAN^-1 | 200 |
| Inverse secant | arcsec, Arcsec, ARCSEC, sec^-1, Sec^-1, SEC^-1 | 200 |
| Inverse cosecant | arccsc, Arccsc, ARCCSC, csc^-1, Csc^-1, CSC^-1 | 200 |
| Inverse cotangent | arccot, Arccot, ARCCOT, cot^-1, Cot^-1, COT^-1 | 200 |
| Inverse Hyperbolic sine | arsinh, Arsinh, ARSINH, sinh^-1, Sinh^-1, SINH^-1 | 200 |
| Inverse Hyperbolic cosine | arcosh, Arcosh, ARCOSH, cosh^-1, Cosh^-1, COSH^-1 | 200 |
| Inverse Hyperbolic tangent | artanh, Artanh, ARTANH, tanh^-1, Tanh^-1, TANH^-1 | 200 |
| Inverse Hyperbolic secant | arsech, Arsech, ARSECH, sech^-1, Sech^-1, SECH^-1 | 200 |
| Inverse Hyperbolic cosecant | arcsch, Arcsch, ARCSCH, csch^-1, Csch^-1, CSCH^-1 | 200 |
| Inverse Hyperbolic cotangent | arcoth, Arcoth, ARCOTH, coth^-1, Coth^-1, COTH^-1 | 200 |
DotNetStandartMathContext is the .NET Standart 2.1 programming math context supports all constants and functions provided by the System.Math and System.Numerics.Complex class, and supports equlity, comparision, logical boolean operators.
Example of evaluating C# expression:
"-2 * Math.Log(1/0.5f + Math.Sqrt(1/Math.Pow(0.5d, 2) + 1L))".Evaluate(new DotNetStandartMathContext());
NOTE: More math functions could be added to the math expression evaluator based on user needs.
Contributions are welcome! Please fork the repository and submit pull requests for any enhancements or bug fixes. If you enjoy my work and find it valuable, please consider becoming my sponsor on GitHub. Your support will enable me to share more open-source code. Together, we can make a positive impact in the developer community!
This project is licensed under the Apache License, Version 2.0 - see the LICENSE file for details.
If you have any questions or suggestions, feel free to open an issue or contact me directly.