CJC Demo 2: Gradient Descent

What This Proves

Functions — fn declarations, calls, return values
While loops — 100-iteration convergence loop
If/else — conditional logic for abs() and progress printing
Variables & mutation — x is updated each step via x = x - lr * grad
Floating-point arithmetic — correct gradient computation to ~18 decimal places
Assertions — convergence verified: |x - 3| < 0.001 and f(x) < 10&supmin;&sup6;

CJC Source Code — demo2_gradient.cjc

fn square(x: f64) -> f64 { x * x }

fn f(x: f64) -> f64 {
    square(x - 3.0)
}

fn grad_f(x: f64) -> f64 {
    2.0 * (x - 3.0)
}

fn abs(x: f64) -> f64 {
    if x < 0.0 { 0.0 - x }
    else { x }
}

// Gradient descent
let x = 0.0;
let lr = 0.1;
let steps = 100;
let i = 0;

while i < steps {
    let g = grad_f(x);
    x = x - lr * g;
    i = i + 1;
}

// Verify convergence
assert(abs(x - 3.0) < 0.001);
assert(f(x) < 0.000001);
print("Converged!");

Live Output — $ cjc run demo2_gradient.cjc

Starting gradient descent on f(x) = (x-3)^2
Initial x: 0  f(x): 9

Step 20   x = 2.9654   f(x) = 0.00120
Step 40   x = 2.9996   f(x) = 0.00000016
Step 60   x = 3.0000   f(x) = 0.000000000021
Step 80   x = 3.0000   f(x) = 0.0000000000000028
Step 100  x = 3.0000   f(x) = 0.0000000000000000004

Final x: 2.9999999993888893
Final f(x): 3.7e-19

Gradient descent converged!
x is within 0.001 of optimal.

Convergence Progress

Step 0

x = 0.000

Step 20

x = 2.965

Step 40

x = 2.9996

Step 60

x = 3.00000

Step 80

x = 3.000000

Step 100

x = 3.0000000

Convergence Data

Step	x	f(x) = (x-3)²	Distance to optimal
0	0.0	9.0	3.0
20	2.9654	1.20 × 10&supmin;³	0.0346
40	2.9996	1.59 × 10&supmin;&sup7;	0.0004
60	2.999995	2.11 × 10&supmin;¹¹	0.0000046
80	2.99999995	2.81 × 10&supmin;¹&sup5;	5.3 × 10&supmin;&sup8;
100	2.9999999994	3.73 × 10&supmin;¹&sup9;	6.1 × 10&supmin;¹°