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TraceScan

TraceScan[f,expr]

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

TraceScan[f,expr,form]

includes only those expressions which match form.

TraceScan[f,expr,s]

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

TraceScan[f,expr,form,fp]

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

TraceScan

TraceScan[f,expr]

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

TraceScan[f,expr,form]

includes only those expressions which match form.

TraceScan[f,expr,s]

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

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)

Print all expressions used for evaluation:

Wolfram Language code: TraceScan[Print, f[1, 2 + 3]]

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

Wolfram Language code: Block[{c = 0}, {TraceScan[c++&, FixedPoint[(# / 2 + 1 / #)&, 1.], (Plus | Times)[__ ? MachineNumberQ]], c}]

A recursive definition for finding Fibonacci numbers:

Wolfram Language code: fib[0] = fib[1] = 1;fib[n_] := fib[n - 1] + fib[n - 2];

Count calls to fib required:

Wolfram Language code: {c = 0;TraceScan[(c++)&, fib[10], fib[_Integer]], c}

Redefine fib so that it saves results:

Wolfram Language code: fib[n_] := (fib[n] = fib[n - 1] + fib[n - 2]);

Count calls to fib required:

Wolfram Language code: {c = 0;TraceScan[(c++)&, fib[10], fib[_Integer]], c}

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

Wolfram Language code: {c = 0;TraceScan[(c++)&, fib[10], fib[_Integer]], c}

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