A very, very simple neural network (with only 1 neuron ;-))

dnn.js

'use strict';

const input = 0.5;
const expected = 0.8;

let weight = 0.5;
const alpha = 0.1;
const iterations = 100;

for (let i = 0; i < iterations; i++) {
  const actual = input * weight;
  const error = (expected - actual) * (expected - actual);

  console.log(`i=${i}, weight=${weight}, prediction=${actual}, error=${error}`);

  const derivative = 2 * (expected - actual);
  const scaledDerivative = alpha * input * derivative;

  weight = weight + scaledDerivative;
}

console.log();
console.log(`f(${input}) = ${input * weight}`);