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);

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: 2 months ago)

User agent: Mozilla/5.0 (iPhone; CPU iPhone OS 18_3_1 like Mac OS X) AppleWebKit/605.1.15 (KHTML, like Gecko) Version/18.3 Mobile/15E148 Safari/604.1

Browser/OS: Mobile Safari 18 on iOS 18.3.1

View result in a separate tab

Test name	Executions per second
Haversine Classic	27056012.0 Ops/sec
Haversine Optimized	33895236.0 Ops/sec
Haversine Mine ATan	26864536.0 Ops/sec
Haversine Mine ASin	33460134.0 Ops/sec
Spherical Law of Cosines	29906486.0 Ops/sec
Equirectangular (a little less accurate)	69828512.0 Ops/sec

Autogenerated LLM Summary (model llama3.2:3b, generated 6 months 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.

Related benchmarks:

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: 7 years ago by: Registered User

Jump to the latest result

Haversine Classic

Haversine Optimized

Haversine Mine ATan

Haversine Mine ASin

Spherical Law of Cosines

Equirectangular (a little less accurate)

Suite status: <idle, ready to run>

Experimental features:

Fastest: N/A

Slowest: N/A

Autogenerated LLM Summary (model llama3.2:3b, generated 6 months ago):