Benchmark: Sine Approximation

HTML Preparation code:

<!--your preparation HTML code goes here-->

Script Preparation code:

const arr = Array.from({ length: 100000 }, () => Math.random());

Tests:

Approximation
function sine(v) { return 0.5 - 0.5 * Math.cos(v * Math.PI); } arr.map(el => sine(el));
Math.sin
arr.map(el => Math.sin(el));

Rendered benchmark preparation results:

Suite status: <idle, ready to run>

Previous results

Test case name	Result
Approximation
Math.sin

Fastest: N/A

Slowest: N/A

Latest run results:

Run details: (Test run date: one month ago)

User agent: Mozilla/5.0 (iPhone; CPU iPhone OS 18_3_2 like Mac OS X) AppleWebKit/605.1.15 (KHTML, like Gecko) FxiOS/136.2 Mobile/15E148 Safari/605.1.15

Browser/OS: Mobile Safari 18 on iOS 18.3.2

View result in a separate tab

Test name	Executions per second
Approximation	1001.1 Ops/sec
Math.sin	1587.9 Ops/sec

Autogenerated LLM Summary (model gpt-4o-mini, generated one month ago):

LLMs can make mistakes. Check important info.

The benchmark represented in the provided JSON is designed to compare the performance of two different approaches for calculating the sine of random values: a custom approximation function and the built-in JavaScript `Math.sin` method.

### Benchmark Overview

1. **Preparation:**
   - The benchmark creates an array (`arr`) of 100,000 random numbers using `Math.random()`. This serves as the input for the sine calculations.

2. **Test Cases:**
   - **Approximation:**
     ```javascript
     function sine(v) {
         return 0.5 - 0.5 * Math.cos(v * Math.PI);
     }
     arr.map(el => sine(el));
     ```
     - This test case uses a custom sine approximation function that calculates the sine values based on a mathematical identity involving cosine. Specifically, it leverages the formula:
       \[
       \sin(v) = 0.5 - 0.5 \cdot \cos(v \cdot \pi)
       \]
     - The `map` method is employed to apply the `sine` function to every element of the `arr`.

- **Math.sin:**
     ```javascript
     arr.map(el => Math.sin(el));
     ```
     - This test case invokes the built-in JavaScript function `Math.sin`, which computes the sine of a number directly using the platform-provided implementation.

### Performance Results
The latest benchmark results indicate the following execution rates:
- **Math.sin:** 526.15 executions per second
- **Approximation:** 371.04 executions per second

### Comparison of Approaches

**Pros and Cons:**

1. **Custom Approximation:**
   - **Pros:**
     - Potentially faster for certain inputs, especially in specific contexts where a simpler calculation may give acceptable accuracy.
   - **Cons:**
     - Likely less accurate than the built-in `Math.sin` for edge cases or more extensive ranges, depending on how closely the cosine approximation matches actual sine values.
     - Computational overhead and potential maintenance issues if non-standard implementations of `sine` are used.

2. **Math.sin (Built-in):**
   - **Pros:**
     - Highly optimized and tested method that provides accurate results across a wide range of inputs.
     - Leverages the language's standard library, which likely benefits from performance improvements, hardware optimizations, or JIT compilation.
   - **Cons:**
     - Might be slower in specific cases compared to a tailored approximation for small ranges or when very quick, rough calculations are needed.

### Considerations
While the benchmarks suggest that `Math.sin` is significantly faster in this instance, the choice between using a custom function or the built-in method depends heavily on the specific use case:

- **Accuracy Needs:** If high accuracy is essential, the built-in `Math.sin` is the preferable option.
- **Performance Sensitivity:** If performance is critical and accuracy can be compromised, especially for certain domains or specific ranges of input, a custom approximation could be worth considering.
- **Maintainability and Readability:** Relying on built-in functions generally improves code maintainability and readability since other developers will likely be familiar with these standard implementations.

### Alternatives
Other possible alternatives for sine calculation or performance benchmarking could include:
- **Libraries:** Using libraries like [math.js](https://mathjs.org/) or [d3.js](https://d3js.org/) for mathematical computations, which may provide additional functionality and optimizations.
- **Other Mathematical Approximations:** Implementing various other Taylor series approximations or utilizing hardware-accelerated mathematical libraries (such as SIMD operations) which can further enhance performance.
- **Scripting Engines:** Considerations around executing benchmarks on various JavaScript engines (like Node.js, or alternative browsers) to see if performance metrics vary across environments.

In conclusion, while the benchmark favors the built-in `Math.sin`, understanding the context and trade-offs for accuracy and performance will guide developers in making informed decisions for their specific applications.

Related benchmarks:

Sine Approximation (version: 1)

Comparing performance of: Approximation vs Math.sin

Created: one month ago by: Guest

Jump to the latest result

Approximation

Math.sin

Suite status: <idle, ready to run>

Experimental features:

Fastest: N/A

Slowest: N/A

Autogenerated LLM Summary (model gpt-4o-mini, generated one month ago):