TimeConstraint

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is an option for various functions that specifies the maximum time to spend doing a particular operation.

Details

TimeConstraint->t specifies that a maximum of t seconds of CPU time should be spent doing a particular operation, or trying a particular transformation or part of an algorithm.
TimeConstraint->Infinity specifies that there should be no limit on the CPU time allowed.
In functions such as Simplify and FullSimplify, settings for TimeConstraint give only the maximum time to be spent doing a particular transformation on a particular subpart; the total time spent processing the whole expression may be considerably larger.
Changing the setting for TimeConstraint will never affect the validity of a result obtained from functions like Simplify or FullSimplify, but smaller settings may prevent the simplest possible form from being found.
Since different computer systems run at different speeds, the same setting for TimeConstraint can lead to different results on different systems.

Examples

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Basic Examples (2)Summary of the most common use cases

This takes a long time, due to trigonometric expansion, but does not yield a simplification:

In[1]:=1

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https://wolfram.com/xid/0d6fuqxx3a-bvam7s

Out[1]=1

TimeConstraint limits the time spent on any single transformation:

In[2]:=2

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https://wolfram.com/xid/0d6fuqxx3a-motqv

Out[2]=2

A similar example, where the transformation yields a simplification:

In[1]:=1

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https://wolfram.com/xid/0d6fuqxx3a-cw6v3s

Out[1]=1

In this case, setting TimeConstraint prevents some simplification:

In[2]:=2

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https://wolfram.com/xid/0d6fuqxx3a-dwvevr

Out[2]=2

Scope (1)Survey of the scope of standard use cases

Checking whether a condition follows from assumptions may take a long time:

In[1]:=1

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https://wolfram.com/xid/0d6fuqxx3a-j70lkd

Out[1]=1

If a condition does not follow from assumptions, checking this may still take a long time:

In[2]:=2

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https://wolfram.com/xid/0d6fuqxx3a-r9xhk

Out[2]=2

The time spent on a single condition check is restricted by the value of TimeConstraint:

In[3]:=3

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https://wolfram.com/xid/0d6fuqxx3a-cjsbf1

In[4]:=4

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https://wolfram.com/xid/0d6fuqxx3a-nxr2t

Out[4]=4

With a time constraint of one second, Refine cannot prove that :

In[5]:=5

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https://wolfram.com/xid/0d6fuqxx3a-cdjadt

Out[5]=5

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