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//! # Overview
//! ## Number Diff - An all-purpose tool for calculus
//!
//!
//!
//! ### Functions
//! Number Diff is built around a calculus-like function, that is, a function that takes an
//! f64 as an argument, returning an f64 according to some specific rule. In the current state of
//! the crate, functions are limited to ƒ: ℝ ⟶ ℝ (have a look at the [supported
//! functions](#supported-functions) for which functions can be used).  
//! There are plans to expand to ƒ: ℂ ⟶ ℂ in the not so distant future.
//!
//! #### Usage
//! Functions are represented by the Function struct. The Function struct can be created by either
//! parsing a string or combining functions using standard operations. A Function
//! instance can then be used with the call(x) method (or when using the nightly feature, Function
//! instances can be called directly).
//!
//! Check out [some examples](https://github.com/HellFelix/number-diff/tree/main/examples)!
//!
//! ## Supported functions
//! | Function | Parsing Identifier | In-code Function |
//! |:----------:|:-------------------:|:-----------------:|
//! | sin      | "sin(_)"            | [sin()](crate::sin) |
//! | cos       | "cos(_)"            | [cos()](crate::cos) |
//! | tan       | "tan(_)"            | [tan()](crate::tan) |
//! | sec       | "sec(_)"            | [sec()](crate::sec) |
//! | csc       | "csc(_)"            | [csc()](crate::csc) |
//! | cot       | "cot(_)"            | [cot()](crate::cot) |
//! | asin      | "asin(_)"            | [asin()](crate::asin) |
//! | acos      | "acos(_)"            | [acos()](crate::acos) |
//! | atan      | "atan(_)"            | [atan()](crate::atan) |
//! | sinh      | "sinh(_)"            | [sinh()](crate::sinh) |
//! | cosh      | "cosh(_)"            | [cosh()](crate::cosh) |
//! | tanh      | "tanh(_)"            | [tanh()](crate::tanh) |
//! | natural log|"ln(_)"            | [ln()](crate::ln) |
//! | absolute value|"abs(_)"           | [abs()](crate::abs) |
//! | square root|"sqrt(_)"            | [sqrt()](crate::sqrt) |
//! | factorial | "_!"              | [factorial()](crate::factorial) |
//! | addition | "_ + _ "            | [+](core::ops::Add) |
//! | subtraction| "_ - _"            | [-](core::ops::Sub)  |
//! | multiplication| "_ * _"       | [*](core::ops::Mul) |
//! | division   | "_ / _"           | [/](core::ops::Div) |
//! | contant | "1", "-12", "3.14", etc. | [f64](f64) |
//! | independent variable | "x"    | [Function::default()](crate::Function::default) |
//!
//! Note that "_" in the table above refers to any other function of the ones provided above. Note also that the
//! operations (+, -, *, /) cannot be applied to each other. Attempting to apply an operation to
//! another operation will make the parser return a [Parsing Error](crate::Error::ParseError).
//!
//! ### Derivatives
//! All of the [supported functions](#supported-functions) are [smooth functions](https://en.wikipedia.org/wiki/Smoothness) which in turn
//! means that once initialized, a [Function](crate::Function) is guaranteed to be a smooth function and so are all of its
//! derivatives.
//!
//! Derivatives are calculated analytically. The provided derivative function will always be the
//! the exact derivative of the original function (although not always in simplest form).
//!
//! Note that in its current state, differentiating might in some rare cases return NaN for
//! certain input values where simplification fails to avoid a division by zero.
//!
//! Function instances can be differentiated using the [differentiate()
//! method](crate::Function::differentiate) or using the [derivative_of()
//! function](crate::derivative_of).
//!
//! ### Integrals
//! Integration is stable for the most part. With a standard precision of 1000, integration uses
//! Simpson's rule in order to find an approximate value of the integral.
//!
//! For usage examples, check out the [integration documentation](crate::Integrate)!
//!
//! Note that while integrating over an interval (including the bounds of integration) inside of which the value of the
//! specified function is undefined, the resulting value might be [NaN](f64::NAN).
//!
//! Also, integrating over an interval (including the bounds of integration) inside of which the value of the
//! specified function is infinit, the resulting value might be [inf](f64::INFINITY) even though
//! the integral should converge.
//!
//! ### Series Expansions
//! See [this article](https://en.wikipedia.org/wiki/Series_expansion) for an explanation of series
//! expansions.
//!
//! #### Current stability of series expansions
//!
//! | Expansion Technique | Stability | Usage       |
//! |:-------------------:|:---------:|:-----------:|
//! | Taylor series       | Stable ✅ | [get_taylor_expansion()](crate::Function::get_taylor_expansion)|
//! | Maclaurin series    | Stable ✅ | [get_maclaurin_expansion()](crate::Function::get_maclaurin_expansion)|
//! | Fourier series      | Unimplemented ❌| N/A |

#![cfg_attr(feature = "nightly", feature(unboxed_closures))]
#![cfg_attr(feature = "nightly", feature(fn_traits))]
#![cfg_attr(feature = "nightly", feature(tuple_trait))]

mod functions;
pub use functions::calc::Elementary;

mod utils;
pub use utils::include::*;

mod simplify;

type Func = Box<dyn Fn(f64) -> f64 + 'static>;

#[derive(Debug)]
pub enum Error {
    ParseError(String),
    SimplifyError(Elementary, String),
    InternalError(String),
    ExpansionError(String),
    InputError(String),
}