THE DERIVATOR: Automatic Differentiation in Haskell

This is a simple application for automatic differentiation in Haskell. You will never have to do the differentiation homework again to your maths class.

Supported functions

Supports all basic functions:

• Const .. a constant
• X .. a variable that will be differentiated
• Sum a b (or a + b) .. a sum
• Mul a b (or a * b) .. a multiplication
• Poly x n .. x^n, n doesn't have x inside
• Exp x .. e^x
• ExpCustom a x .. a^x
• Ln x .. natural logarithm of x
• Log a x .. logarithm of x to the base a
• Sin x .. sin x
• Cos x .. cos x

Installation and running the program

Install Haskell on your computer, change directory to this folder and run ghci. Then insert your function and use function derivative to differentiate the function. You can also use function eval to evaluate your function (or its derivative) given x of type Double.

Examples

Here is an example of creating and differentiating common functions used in machine learning - sigmoid and tanh.

λ> sigmoid = Poly (Sum 1 (Exp (Mul (-1) X))) (-1)
λ> sigmoid
((1.0 + e^(-1.0 * x)))^-1.0
λ> derivative sigmoid
-1.0 * ((1.0 + e^(-1.0 * x)))^(-2.0) * e^(-1.0 * x) * -1.0
λ> 
λ> 
λ> tanh = 2 * (Poly (Sum 1 (Exp (Mul (-2) X))) (-1)) - 1
λ> derivative tanh
2.0 * -1.0 * ((1.0 + e^(-2.0 * x)))^(-2.0) * e^(-2.0 * x) * -2.0
λ> 
λ> eval 1 (derivative sigmoid)
0.19661193324148188
λ> 
λ> eval 2.5 tanh
0.9866142981514305