Benchmark: Math.hypot vs Math.sqrt vs Math.sqrt&pow vs Math.sqrt&**2

Script Preparation code:

function testHypot() {
  for (let i=0; i < 1000; i++){
    for (let j=0; j < 1000; j++) {
      Math.hypot(i - j, j - i)
    }
  }
}
function testSqrt() {
  for (let i=0; i < 1000; i++){
    for (let j=0; j < 1000; j++) {
      Math.sqrt((i-j)*(i-j)+(j-i)*(j-i))
    }
  }
}
function testSqrtPowFn() {
  for (let i=0; i < 1000; i++){
    for (let j=0; j < 1000; j++) {
      Math.sqrt(Math.pow(i-j, 2)+Math.pow(j-i, 2))
    }
  }
}
function testSqrtPowOp() {
  for (let i=0; i < 1000; i++){
    for (let j=0; j < 1000; j++) {
      Math.sqrt((i-j)**2+(j-i)**2)
    }
  }
}

Tests:

Math.hypot
testHypot()
Math.sqrt
testSqrt()
Math.sqrt > Math.pow
testSqrtPowFn()
Math.sqrt > **
testSqrtPowOp()

Rendered benchmark preparation results:

Suite status: <idle, ready to run>

Previous results

Test case name	Result
Math.hypot
Math.sqrt
Math.sqrt > Math.pow
Math.sqrt > **

Fastest: N/A

Slowest: N/A

Latest run results:

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

User agent: Mozilla/5.0 (Windows NT 10.0; Win64; x64) AppleWebKit/537.36 (KHTML, like Gecko) Chrome/130.0.0.0 Safari/537.36

Browser/OS: Chrome 130 on Windows

View result in a separate tab

Test name	Executions per second
Math.hypot	111.0 Ops/sec
Math.sqrt	223.8 Ops/sec
Math.sqrt > Math.pow	541.7 Ops/sec
Math.sqrt > **	64.5 Ops/sec

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

LLMs can make mistakes. Check important info.

The benchmark you provided is testing different mathematical methods to calculate the Euclidean distance between two points in a 2D space: `(i, j)` and `(j, i)`. The goal is to compare these methods in terms of performance, particularly concerning their execution speed, represented as executions per second.

### Comparison of Approaches

1. **Math.hypot**
   - **Description**: This function computes the square root of the sum of the squares of its arguments, effectively calculating the Euclidean distance. It can take two or more grid points.
   - **Pros**: 
     - Designed specifically for this purpose, it's more semantically clear.
     - Handles large numbers gracefully without overflowing, due to its internal handling of squared values.
   - **Cons**: 
     - In terms of raw performance, it may not be as fast as simpler operations in JavaScript.

2. **Math.sqrt** (with `(i-j)*(i-j)+(j-i)*(j-i)`)
   - **Description**: This method calculates the distance by explicitly computing the square of the differences in both dimensions and adding them before taking the square root of the total.
   - **Pros**: 
     - Clear to those familiar with the distance formula.
   - **Cons**: 
     - It involves two multiplications and an addition per iteration, which can slightly slow down performance.

3. **Math.sqrt with Math.pow**
   - **Description**: Uses `Math.pow` to square the numbers before summing and taking the square root.
   - **Pros**: 
     - The use of `Math.pow` may be clearer to some developers who prefer explicit operations.
   - **Cons**: 
     - Generally performs worse than direct multiplication due to the overhead of the function call to `Math.pow`.

4. **Math.sqrt with the exponentiation operator `**`**
   - **Description**: Similar to the above method but uses the exponentiation operator introduced in ECMAScript 2016.
   - **Pros**: 
     - More concise syntax compared to using `Math.pow`.
   - **Cons**: 
     - May not be as performant as simple multiplication, as function calls and operator parsing can introduce overhead.

### Benchmark Results Overview

From the provided benchmark results, the highest execution rate (541.72 executions per second) is observed for the `Math.sqrt > Math.pow` comparison, indicating that using multiplication directly is faster than employing `Math.pow` for this calculation. The performance drops significantly for `Math.hypot`, which only achieved 111.04 executions per second, hinting at its additional overhead compared to the other methods.

### Alternative Considerations

There are several alternative approaches to calculating distances in JavaScript, beyond what's tested here:
- **Manhattan Distance**: If the distance measured doesn't require the Euclidean calculation, using a simpler formula like the Manhattan distance (`Math.abs(i - j) + Math.abs(j - i)`) may be more efficient.
- **Custom Implementations**: Depending on the specific use case, creating custom functions optimized for particular data sets or using SIMD (Single Instruction, Multiple Data) approaches can yield further performance improvements.
- **Typed Arrays**: When dealing with large datasets or high-performance requirements, leveraging typed arrays or WebAssembly may provide additional benefits over JavaScript’s built-in types.

### Conclusion

In summary, the benchmark examines the efficiency of various JavaScript methods for calculating distances. `Math.sqrt` in conjunction with direct multiplication is shown to be the most performant method in this case, while `Math.hypot`, although clear and safe, demonstrates slower execution speeds. It's essential for developers to understand the performance characteristics of different approaches when tackling similar calculations, particularly in performance-sensitive scenarios.

Related benchmarks:

Math.hypot vs Math.sqrt vs Math.sqrt&pow vs Math.sqrt&**2 (version: 1)

Is Math.hypot actually faster than Math.sqrt?

Comparing performance of: Math.hypot vs Math.sqrt vs Math.sqrt > Math.pow vs Math.sqrt > **

Created: one month ago by: Guest

Jump to the latest result

Math.hypot

Math.sqrt

Math.sqrt > Math.pow

Math.sqrt > **

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):