Performance for compile and evaluate

[sylee957]

I'm using mathjs to generate the mathematical functions dynamically for evaluation,
however, I'm getting issues with the performance

In the benchmark:
https://www.measurethat.net/Benchmarks/Show/28847/0/mathjs-performance

Native Arrow | Native Arrow x 624 ops/sec ±3.83% (55 runs sampled)
Native Function | Native Function x 545 ops/sec ±4.79% (50 runs sampled)
Native inline | Native inline x 923 ops/sec ±7.12% (9 runs sampled)
Mathjs evaluate | Mathjs evaluate x 10.81 ops/sec ±7.63% (32 runs sampled)
Mathjs compile | Mathjs compile x 34.49 ops/sec ±3.38% (46 runs sampled)

Even with compile, the performance is 15 times slower than the dynamically generated JS native function with new Function.
How do I get the numeric evaluation more faster with mathjs?

[josdejong]

Two things here:

1. You can try do something like:

   var mathfn = math.evaluate('fn(x, y, z) = x^2 + y^2 + z^2')
   

   And then run fn(x, y, z) in your benchmark
2. The main reason for the slowness is that for evaluation, mathjs uses a heavy weight functions math.add and math.pow that are capable of handling numbers, BigNumbers, Units, Fractions, Matrices, etc. If you only need numbers, you can speed things up a lot by creating a mathjs instance with lightweight functions. To do that, you can use the plain-number implementation via import {...} from 'mathjs/number' (see docs), or by providing alternative function implementations yourself. Examples:
   • https://mathjs.org/examples/advanced/custom_evaluate_using_import.js.html
   • https://mathjs.org/examples/advanced/custom_evaluate_using_factories.js.html

[Yuxin-Lou]

Thank you very much for building such a powerful math library.
I am a js beginner and I hope to find a way to input a string mathematical expression and then output its calculation result. At the same time I am concerned about performance issues. My code won't require calculations on matrices or large numbers, but it will use a lot of Arithmetic functions.
I found a test in the benchmark ( link to benchmark,) he said eval Performance is higher than evaluate.
But when I executed the following code in the Edge browser console, I found that evaluate is significantly faster than eval.

What might be the reason for this performance difference? And do you have any suggestions about my work?

var script = document.createElement('script');
script.src = 'https://cdnjs.cloudflare.com/ajax/libs/mathjs/6.6.1/math.min.js'; 
document.head.appendChild(script);

var average = 0;
for(var test = 0; test<10; test++){
    var startTime = performance.now();
    for (var i = 0; i < 50000; i++) {
        let x = math.evaluate('sqrt(3^2 + 4^2)');
    }
    var endTime = performance.now();
    var elapsedTime = endTime - startTime;
    average += elapsedTime;
}

console.log("mathjs evaluate average result"+ average/10 + " ms");

var average = 0;
for(var test = 0; test<10; test++){
    var startTime = performance.now();
    for (var i = 0; i < 50000; i++) {
        let x = eval('Math.sqrt(3**2 + 4**2)');
    }
    var endTime = performance.now();
    var elapsedTime = endTime - startTime;
    average += elapsedTime;
}

console.log("eval average result"+ average/10 + " ms");

result is:
mathjs evaluate average result289.2 ms
eval average result726.7199999988079 ms

[josdejong]

First: please test the outcome of your expression let x = eval('Math.sqrt(3^2 + 4^2)'), in JavaScript, the ^ operator will do bitwise XOR and and not exponentiation (that is ** in JavaScript).

Some considerations:

• The mathjs functions support a broad set of data types (numbers, complex numbers, matrices, units, etc). When evaluating math.add(2, 3), it will be slower than a plain 2 + 3 in JavaScript due to type checking overhead. If you don't need all of that, it would be a waste.
• You can also look into the plain number implementation if you only need numbers, that is faster than the full-fledged functions: https://mathjs.org/docs/custom_bundling.html#numbers-only
• Using JavaScript's eval function on dynamic, user provided input comes with security risks, see https://mathjs.org/docs/expressions/security.html

[Yuxin-Lou]

After my testing, importing part of mathjs does not seem to significantly speed up calculations.

import { create, all } from 'mathjs/number'

const math = create(all)

//console.log(math.sqrt(-1)); 
var average = 0;
for(var test = 0; test<50; test++){
    var startTime = performance.now();
    for (var i = 0; i < 50000; i++) {
        let x = math.evaluate('sqrt(3^2 + 4^2)');
    }
    var endTime = performance.now();
    var elapsedTime = endTime - startTime;
    average += elapsedTime;
}

console.log("mathjs evaluate average result"+ average/50 + " ms");

[josdejong]

Using mathjs/number can make evaluation faster. You will most likely not see that back in your benchmark because there you're testing parsing and evaluation at the same time, and parsing is the slowest part of the two.

[Yuxin-Lou]

Thanks for your patient explanation, that helps a lot.