Benchmark: Haversine Distance tests

Script Preparation code:

var EARTH_RADIUS_M = 6371e3;
var EARTH_DIAMETER_M = EARTH_RADIUS_M * 2;
var DEG_TO_RAD = Math.PI / 180;
var p1 = { lat: 43.63625, lon: -79.40454 };
var p2 = { lat: 43.69851, lon: -79.39699 };

function haversineClassic(lat1, lon1, lat2, lon2) {
  var φ1 = lat1 * DEG_TO_RAD;
  var φ2 = lat2 * DEG_TO_RAD;
  var Δφ = (lat2-lat1) * DEG_TO_RAD;
  var Δλ = (lon2-lon1) * DEG_TO_RAD;

  var a = Math.sin(Δφ/2) * Math.sin(Δφ/2) +
          Math.cos(φ1) * Math.cos(φ2) *
          Math.sin(Δλ/2) * Math.sin(Δλ/2);
  var c = 2 * Math.atan2(Math.sqrt(a), Math.sqrt(1-a));

  var d = EARTH_RADIUS_M * c;
  
  return d;
}

function haversineOptimized(lat1, lon1, lat2, lon2) {
  var p = 0.017453292519943295;    // Math.PI / 180
  var c = Math.cos;
  var a = 0.5 - c((lat2 - lat1) * p)/2 + 
      c(lat1 * p) * c(lat2 * p) * 
      (1 - c((lon2 - lon1) * p))/2;

  return 12742 * Math.asin(Math.sqrt(a)); // 2 * R; R = 6371 km  
}

function haversineMineATan(lat1, lon1, lat2, lon2) {
  var fDP = Math.sin( (lat2 - lat1) * DEG_TO_RAD / 2 );
  var fDL = Math.sin( (lon2 - lon1) * DEG_TO_RAD / 2 );
  var fP1 = Math.cos( lat1 * DEG_TO_RAD );
  var fP2 = Math.cos( lat2 * DEG_TO_RAD );
  var a = fDP * fDP + fP1 * fP2 * fDL * fDL;
  return EARTH_DIAMETER_M * Math.atan2(Math.sqrt(a), Math.sqrt(1-a));
}
function haversineMineASin(lat1, lon1, lat2, lon2) {
  var fDP = Math.sin( (lat2 - lat1) * DEG_TO_RAD / 2 );
  var fDL = Math.sin( (lon2 - lon1) * DEG_TO_RAD / 2 );
  var fP1 = Math.cos( lat1 * DEG_TO_RAD );
  var fP2 = Math.cos( lat2 * DEG_TO_RAD );
  var a = fDP * fDP + fP1 * fP2 * fDL * fDL;
  return EARTH_DIAMETER_M * Math.asin(Math.sqrt(a));
}

function spherical(lat1, lon1, lat2, lon2) {
  var φ1 = lat1 * DEG_TO_RAD, φ2 = lat2 * DEG_TO_RAD, Δλ = (lon2-lon1) * DEG_TO_RAD;
  return Math.acos( Math.sin(φ1) * Math.sin(φ2) + Math.cos(φ1) * Math.cos(φ2) * Math.cos(Δλ) ) * EARTH_RADIUS_M;
}

function equirectangular(lat1, lon1, lat2, lon2) {
  var x = (lon2-lon1)*DEG_TO_RAD * Math.cos( (lat1+lat2)*DEG_TO_RAD/2 );
  var y = (lat2-lat1)*DEG_TO_RAD;
  return EARTH_RADIUS_M * Math.sqrt( x*x + y*y )
}

Tests:

Haversine Classic
haversineClassic(p1.lat, p1.lon, p2.lat, p2.lon);
Haversine Optimized
haversineOptimized(p1.lat, p1.lon, p2.lat, p2.lon);
Haversine Mine ATan
haversineMineATan(p1.lat, p1.lon, p2.lat, p2.lon);
Haversine Mine ASin
haversineMineASin(p1.lat, p1.lon, p2.lat, p2.lon);
Spherical Law of Cosines
spherical(p1.lat, p1.lon, p2.lat, p2.lon);
Equirectangular (a little less accurate)
equirectangular(p1.lat, p1.lon, p2.lat, p2.lon);

Historical Performance Data aggregated from 8 community runs

Desktop Results:

Chrome 8 runs

Equirectangular (a little less accurate)

1.4M/s

Haversine Mine ASin

1.4M/s

Spherical Law of Cosines

1.4M/s

Haversine Classic

1.3M/s

Haversine Mine ATan

1.3M/s

Haversine Optimized

1.3M/s

View exact numbers

✓ Equirectangular (a little less accurate): 1,376,108 ops/sec
• Haversine Mine ASin: 1,366,043 ops/sec
• Spherical Law of Cosines: 1,356,251 ops/sec
• Haversine Classic: 1,283,712 ops/sec
• Haversine Mine ATan: 1,283,222 ops/sec
• Haversine Optimized: 1,282,926 ops/sec

Results show median performance across all community submissions. Run this benchmark yourself to verify on your device.

Rendered benchmark preparation results:

Suite status: <idle, ready to run>

Previous results

Test case name	Result
Haversine Classic
Haversine Optimized
Haversine Mine ATan
Haversine Mine ASin
Spherical Law of Cosines
Equirectangular (a little less accurate)

Fastest: N/A

Slowest: N/A

Latest run results:

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

User agent: Mozilla/5.0 (Macintosh; Intel Mac OS X 10_15_7) AppleWebKit/537.36 (KHTML, like Gecko) Chrome/136.0.0.0 Safari/537.36

Browser/OS: Chrome 136 on Mac OS X 10.15.7

View result in a separate tab

Spherical Law of Cosines

220.8M/s

Equirectangular (a little less accurate)

218.1M/s

Haversine Mine ATan

217.1M/s

Haversine Mine ASin

216.0M/s

Haversine Optimized

208.2M/s

Haversine Classic

202.3M/s

View exact numbers

Test name	Executions per second
✓ Spherical Law of Cosines	220,757,264 Ops/sec
Equirectangular (a little less accurate)	218,050,736 Ops/sec
Haversine Mine ATan	217,073,456 Ops/sec
Haversine Mine ASin	215,958,144 Ops/sec
Haversine Optimized	208,201,456 Ops/sec
Haversine Classic	202,259,088 Ops/sec

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

LLMs can make mistakes. Check important info.

It seems like you're trying to benchmark the performance of different methods for calculating distances between two points on Earth's surface.

Here's my analysis:

**Methods:**

1. `haversineClassic(p1.lat, p1.lon, p2.lat, p2.lon);`: This is a traditional implementation of the Haversine formula.
2. `haversineOptimized(p1.lat, p1.lon, p2.lat, p2.lon);`: This is an optimized version of the Haversine formula.
3. `haversineMineATan(p1.lat, p1.lon, p2.lat, p2(lon));`: This method uses a tangent half-angle approximation for the Haversine formula.
4. `haversineMineASin(p1.lat, p1.lon, p2.lat, p2.lon);`: This method uses a sine half-angle approximation for the Haversine formula.
5. `spherical(p1.lat, p1.lon, p2.lat, p2.lon);`: This is an implementation of the spherical law of cosines.
6. `equirectangular(p1.lat, p1.lon, p2.lat, p2.lon);`: This method uses an equirectangular projection (a simpler approximation of the Earth's surface).

**Benchmark Results:**

The latest benchmark results show that:

* `haversineOptimized` is the fastest method, with approximately 1009763 executions per second.
* `equirectangular` is less accurate but also relatively fast, with around 807031 executions per second.
* `spherical` is faster than `haversineClassic`, but slower than `haversineOptimized`.
* `haversineMineASin` and `haversineMineATan` are slower than all the above methods.

**Conclusion:**

Based on these results, it seems that the optimized Haversine formula (`haversineOptimized`) is the best choice for calculating distances between two points on Earth's surface. This method offers a good balance between accuracy and performance.

However, if you need an alternative approach with even better performance (e.g., for very large datasets), you could consider using the spherical law of cosines (`spherical`).

Keep in mind that these results are specific to this particular implementation and testing environment, so it's essential to verify them on your own before making any conclusions.

Haversine Distance tests (version: 4)

Comparing performance of: `Haversine Classic vs Haversine Optimized vs Haversine Mine ATan vs Haversine Mine ASin vs Spherical Law of Cosines vs Equirectangular (a little less accurate)`

Created: 8 years ago by: Registered User

Go to the latest result

Haversine Classic

Haversine Optimized

Haversine Mine ATan

Haversine Mine ASin

Spherical Law of Cosines

Equirectangular (a little less accurate)

Historical Performance Data aggregated from 8 community runs

Desktop Results:

Chrome 8 runs

Suite status: <idle, ready to run>

Fastest: N/A

Slowest: N/A

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

Haversine Distance tests (version: 4)

Comparing performance of: Haversine Classic vs Haversine Optimized vs Haversine Mine ATan vs Haversine Mine ASin vs Spherical Law of Cosines vs Equirectangular (a little less accurate)

Created: 8 years ago by: Registered User

Go to the latest result

Haversine Classic

Haversine Optimized

Haversine Mine ATan

Haversine Mine ASin

Spherical Law of Cosines

Equirectangular (a little less accurate)

Historical Performance Data aggregated from 8 community runs

Desktop Results:

Chrome 8 runs

Suite status: <idle, ready to run>

Fastest: N/A

Slowest: N/A

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

Comparing performance of: `Haversine Classic vs Haversine Optimized vs Haversine Mine ATan vs Haversine Mine ASin vs Spherical Law of Cosines vs Equirectangular (a little less accurate)`