To illustrate the difference between time elapsed including simplification of data structures, consider the following example.
The following records only the time to evaluate the expression after the data structure is already created.
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$\mathrm{time}\left({3}^{1000000}\right)$

The following is the same computation but it also records the time used to create the data structure.
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$\mathrm{st}\u2254\mathrm{time}\left(\right)\:$${3}^{1000000}\:$$\mathrm{time}\left(\right)\mathrm{st}$

The following is the same computation as the one above, but records real time used instead of cpu time.
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$\mathrm{st}\u2254{\mathrm{time}}_{\mathrm{real}}\left(\right)\:$${3}^{1000000}\:$${\mathrm{time}}_{\mathrm{real}}\left(\right)\mathrm{st}$
