Benchmark: Power vs Square Root functions

Power vs Square Root functions (version: 1)

Measure the performance of the Power and Square Root functions. Conclusion: The underlying math logic seems to be the same, regardless of the function used.

Comparing performance of: Power function (small number) vs Power function (large number) vs Power function (very large number) vs Square root function (small number) vs Square root function (large number) vs Square root function (very large number)

Created: 5 years ago by: Registered User

Jump to the latest result

Script Preparation code:

// Javascript uses floats for numbers. Generaate some numbers in advance.
var smallNumber = Math.pow(2, 7) + Math.floor(Math.random() * Math.pow(2,7));
var largeNumber = Math.pow(2, 30) + Math.floor(Math.random() * Math.pow(2,30));
var veryLargeNumber = Math.pow(2, 60) + Math.floor(Math.random() * Math.pow(2,60));

Tests:

Power function (small number)
Math.pow(smallNumber, 2);
Power function (large number)
Math.pow(largeNumber, 2);
Power function (very large number)
Math.pow(veryLargeNumber, 2);
Square root function (small number)
Math.sqrt(smallNumber);
Square root function (large number)
Math.sqrt(largeNumber);
Square root function (very large number)
Math.sqrt(veryLargeNumber);

Rendered benchmark preparation results:

Suite status: <idle, ready to run>

Previous results

Test case name	Result
Power function (small number)
Power function (large number)
Power function (very large number)
Square root function (small number)
Square root function (large number)
Square root function (very large number)

Fastest: N/A

Slowest: N/A

Latest run results:

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

User agent: Mozilla/5.0 (X11; Linux x86_64) AppleWebKit/537.36 (KHTML, like Gecko) Chrome/130.0.0.0 Safari/537.36

Browser/OS: Chrome 130 on Linux

View result in a separate tab

Test name	Executions per second
Power function (small number)	10909729.0 Ops/sec
Power function (large number)	10606111.0 Ops/sec
Power function (very large number)	10529201.0 Ops/sec
Square root function (small number)	10913844.0 Ops/sec
Square root function (large number)	10677415.0 Ops/sec
Square root function (very large number)	10822901.0 Ops/sec

Autogenerated LLM Summary (model llama3.2:3b, generated 2 months ago):

LLMs can make mistakes. Check important info.

Let's break down the provided benchmark definition and test cases to understand what's being tested.

**Benchmark Definition:**
The benchmark measures the performance of two mathematical functions: Power (`Math.pow`) and Square Root (`Math.sqrt`). The functions are applied to three different input values: small, large, and very large numbers. These numbers are generated in advance using `Math.random()` to ensure randomness and minimize any effects due to rounding.

**Test Cases:**

1. **Power function (small number)**: Measures the time taken to calculate `Math.pow(smallNumber, 2)`.
2. **Power function (large number)**: Measures the time taken to calculate `Math.pow(largeNumber, 2)`.
3. **Power function (very large number)**: Measures the time taken to calculate `Math.pow(veryLargeNumber, 2)`.
4. **Square root function (small number)**: Measures the time taken to calculate `Math.sqrt(smallNumber)`.
5. **Square root function (large number)**: Measures the time taken to calculate `Math.sqrt(largeNumber)`.
6. **Square root function (very large number)**: Measures the time taken to calculate `Math.sqrt(veryLargeNumber)`.

**Libraries and Features:**
No specific JavaScript libraries or features are used in this benchmark. The built-in `Math` library is sufficient for these simple mathematical operations.

**Comparison of Approaches:**

1. **Power function**: Both approaches (`Math.pow` with exponentiation and recursive exponentiation) have similar performance characteristics, as the underlying math logic is the same.
2. **Square root function**: The `Math.sqrt` function uses a more efficient algorithm than manual calculations (e.g., Babylonian method), resulting in faster execution times.

**Pros and Cons:**

1. **Power function**: No significant differences between exponentiation and recursive exponentiation methods. However, for very large inputs, the recursive approach might lead to stack overflows or performance issues.
2. **Square root function**: Manual calculations using the Babylonian method are generally slower than using `Math.sqrt`, but they provide insight into the underlying algorithm's implementation.

**Alternatives:**
Other approaches to calculate Power and Square Root functions include:

1. **Using a library or framework:** Alternative libraries like Fast Math, FFTW (for large numbers), or specialized libraries for square roots (e.g., QR algorithm) might offer performance improvements.
2. **Parallel processing:** Utilizing multi-core processors or distributed computing to execute the calculations in parallel could further reduce execution times.
3. **Approximation methods**: Using approximations like the Taylor series expansion for power functions or iterative methods for square root functions can provide faster results at the cost of accuracy.

The benchmark results will help identify which approach performs better, but it's essential to consider factors like code complexity, maintainability, and accuracy when choosing an implementation.

Related benchmarks:

Power vs Square Root functions (version: 1)

Measure the performance of the Power and Square Root functions. Conclusion: The underlying math logic seems to be the same, regardless of the function used.

Comparing performance of: Power function (small number) vs Power function (large number) vs Power function (very large number) vs Square root function (small number) vs Square root function (large number) vs Square root function (very large number)

Created: 5 years ago by: Registered User

Jump to the latest result

Power function (small number)

Power function (large number)

Power function (very large number)

Square root function (small number)

Square root function (large number)

Square root function (very large number)

Suite status: <idle, ready to run>

Experimental features:

Fastest: N/A

Slowest: N/A

Autogenerated LLM Summary (model llama3.2:3b, generated 2 months ago):