TraceScan

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TraceScan[f,expr]

applies f to all expressions used in the evaluation of expr.

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TraceScan[f,expr,form]

includes only those expressions which match form.

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TraceScan[f,expr,s]

includes all evaluations which use transformation rules associated with the symbol s.

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TraceScan[f,expr,form,fp]

applies f before evaluation and fp after evaluation to expressions used in the evaluation of expr.

Details and Options

All expressions are wrapped in HoldForm to prevent evaluation before f or fp are applied to them.
The function fp is given as an argument for both the form before evaluation and the form after evaluation.
TraceScan[f,expr] returns the result of evaluating expr.

Examples

Basic Examples (3)Summary of the most common use cases

Print all expressions used for evaluation:

In[1]:=1

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https://wolfram.com/xid/0cg4dbqyc-zuxyb

Out[1]=1

Count additions and multiplications of machine numbers needed for a numerical computation:

In[1]:=1

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https://wolfram.com/xid/0cg4dbqyc-k47lf3

Out[1]=1

A recursive definition for finding Fibonacci numbers:

In[1]:=1

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https://wolfram.com/xid/0cg4dbqyc-bjc302

Count calls to fib required:

In[2]:=2

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https://wolfram.com/xid/0cg4dbqyc-dfy82o

Out[2]=2

Redefine fib so that it saves results:

In[3]:=3

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https://wolfram.com/xid/0cg4dbqyc-g5q9ye

Count calls to fib required:

In[4]:=4

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https://wolfram.com/xid/0cg4dbqyc-gtmtw

Out[4]=4

The second time through it takes only one call since the value was saved:

In[5]:=5

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https://wolfram.com/xid/0cg4dbqyc-h4nuy2

Out[5]=5

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