diff --git a/src/reduce.js b/src/reduce.js
index 38be21c..9abf6f7 100644
--- a/src/reduce.js
+++ b/src/reduce.js
@@ -7,19 +7,37 @@
  * @returns {*}
  */
 function reduce(callback, startValue) {
-  let prev = startValue;
-  let startIndex = 0;
+  if (typeof callback !== 'function') {
+    throw new TypeError(callback + ' is not a function');
+  }
+
+  const arr = this;
+  const length = arr.length;
+  let i = 0;
+  let accumulator;
+
+  if (arguments.length >= 2) {
+    accumulator = startValue;
+  } else {
+    // Find first defined element
+    while (i < length && !(i in arr)) {
+      i++;
+    }
 
-  if (arguments.length < 2) {
-    startIndex = 1;
-    prev = this[0];
+    if (i >= length) {
+      throw new TypeError('Reduce of empty array with no initial value');
+    }
+    accumulator = arr[i];
+    i++;
   }
 
-  for (let i = startIndex; i < this.length; i++) {
-    prev = callback(prev, this[i], i, this);
+  for (; i < length; i++) {
+    if (i in arr) {
+      accumulator = callback(accumulator, arr[i], i, arr);
+    }
   }
 
-  return prev;
+  return accumulator;
 }
 
 module.exports = { reduce };
diff --git a/src/reduce.test.js b/src/reduce.test.js
index 47a892f..77a6849 100644
--- a/src/reduce.test.js
+++ b/src/reduce.test.js
@@ -2,18 +2,81 @@
 
 const { reduce } = require('./reduce');
 
-describe('reduce', () => {
-  beforeAll(() => {
-    Array.prototype.reduce2 = reduce; // eslint-disable-line
+describe('custom reduce', () => {
+  const callReduce = (arr, ...args) =>
+    reduce.call(arr, ...args);
+
+  test('reduces with an initial value', () => {
+    const arr = [1, 2, 3];
+    const result = callReduce(arr, (acc, v) => acc + v, 0);
+
+    expect(result).toBe(6);
+  });
+
+  test('reduces without an initial value', () => {
+    const arr = [1, 2, 3];
+    const result = callReduce(arr, (acc, v) => acc + v);
+
+    expect(result).toBe(6);
+  });
+
+  test('uses first element as initial accumulator when none provided', () => {
+    const arr = [5, 10, 15];
+    const result = callReduce(arr, (acc, v) => acc + v);
+
+    expect(result).toBe(30);
+  });
+
+  test('throws TypeError when callback is not a function', () => {
+    const arr = [1, 2, 3];
+
+    expect(() => callReduce(arr, null, 0)).toThrow(TypeError);
   });
 
-  afterAll(() => {
-    delete Array.prototype.reduce2;
+  test('throws TypeError on empty array without initial value', () => {
+    expect(() => callReduce([], (a, b) => a + b)).toThrow(TypeError);
   });
 
-  it('should ', () => {
+  test('passes correct arguments to callback', () => {
+    const arr = [10, 20, 30];
+    const mock = jest.fn((acc, v) => acc + v);
+
+    callReduce(arr, mock, 0);
 
+    expect(mock).toHaveBeenCalledTimes(3);
+    expect(mock.mock.calls[0]).toEqual([0, 10, 0, arr]);
+    expect(mock.mock.calls[1]).toEqual([10, 20, 1, arr]);
+    expect(mock.mock.calls[2]).toEqual([30, 30, 2, arr]);
   });
 
-  // Add tests here
+  test('works with objects', () => {
+    const arr = [{ x: 1 }, { x: 2 }, { x: 3 }];
+    const result = callReduce(arr, (acc, obj) => acc + obj.x, 0);
+
+    expect(result).toBe(6);
+  });
+
+  test('skips empty slots in a sparse array', () => {
+  // eslint-disable-next-line no-sparse-arrays
+    const arr = [1, , 3]; // A sparse array
+    const callback = jest.fn((sum, el) => sum + el);
+    const result = callReduce(arr, callback, 0);
+
+    expect(callback).toHaveBeenCalledTimes(2); // Only indices 0 and 2 exist
+    expect(result).toBe(4); // 0 + 1 + 3
+  });
+
+  test('single-element arr without initial value returns that element', () => {
+    const arr = [42];
+    const result = callReduce(arr, (acc, v) => acc + v);
+
+    expect(result).toBe(42);
+  });
+
+  test('single-element array with initial value applies callback once', () => {
+    const arr = [42];
+    const result = callReduce(arr, (acc, v) => acc + v, 10);
+
+    expect(result).toBe(52);
+  });
 });