grammar - How does one know when to use a gerund or an infinitive?

As a native speaker of English, the gerund version of this sentence sounds better:

infinitive:

When used together in chains, extension methods are an unprecedented tool to produce extremely concise code.

gerund:

When used together in chains, extension methods are an unprecedented tool for producing extremely concise code.

But how can I explain to someone learning English how to decide in situations like these whether to use the infinitive or the gerund?

Answer

From EnglishPage.com's article Gerunds and Infinitives Part 1, if you consider "to produce/for producing" as a complement in your phrase:

Both gerunds and infinitives can be used as the subject or the complement of a sentence.

However, as subjects or complements, gerunds usually sound more like normal, spoken English, whereas infinitives sound more abstract.
In the following sentences, gerunds sound more natural and would be more common in everyday English.
Infinitives emphasize the possibility or potential for something and sound more philosophical.

If this sounds confusing, just remember that 90% of the time, you will use a gerund as the subject or complement of a sentence.

Examples:

• Learning is important. normal subject


• To learn is important. abstract subject - less common


• The most important thing is learning. normal complement


• The most important thing is to learn. abstract complement - less common