fad is a toy implementation of automatic differentiation, which I wrote for fun after reading this paper by Baydin et al.

fad reads a function and a point from stdin. It outputs the value and the derivative of the function at the given point:

echo "x^2 ; x = 4" | ./fad

Function value: 16
Derivative d/dx: 8

You can specify the function using the operators +, -, *, /, ^ and the functions sin, cos, exp and ln. Variables are specified using the characters a-z.

fad supports functions of several variables:

echo "y * cos(z * x) * ln(sin(x) + exp(y) + 3*z^3) ; x = 2, y = 3, z = 1.5" | ./fad

Function value: -10.2103
Derivative d/dx: -2.14345
Derivative d/dy: -5.32034
Derivative d/dz: -4.84349

fad also includes a simple optimizer. The optimizer uses gradient descent with momentum. You run the optimizer by specifying the steps argument, which specifies the number of steps that the gradient descent should run. fad outputs the result of the descent:

echo "x^2 + y^2 + z^2 + 10 ; x = 20, y = 50, z = 100" | ./fad -steps 500

Function value: 10
x: -1.1042e-11
y: -2.76051e-11
z: -5.52101e-11