Basic Examples

Find the repeated term in the expression
(a+b+c)
3
+(a+b+c)
2
:

result=
○
SimplifyRepeatedSubexpressions
(a+b+c)
3
+(a+b+c)
2
In[]:=
$11
2
+$11
3
,$11a+b+c
Out[]=

Reconstruct the original expression from the decomposed form:

ReplaceAll@@result
In[]:=
(a+b+c)
2
+(a+b+c)
3
Out[]=

Options

Finding many small common subexpressions may not be helpful:

○
SimplifyRepeatedSubexpressions
[Solve[ax^2+bx+c0,x]]
In[]:=
{{x(-$12+$13)$14$15},{x($12+$13)$14$15}},$12b
2
-4ac
$15
,$13-b,$14
1
a
,$15
1
2
Out[]=

Find only the largest with
"MinLeafCount"
:

○
SimplifyRepeatedSubexpressions
[Solve[ax^2+bx+c0,x],"MinLeafCount"10]
In[]:=
x
-b-$16
2a
,x
-b+$16
2a
,$16
b
2
-4ac
Out[]=

Applications

Remove the discriminant from the quadratic solution equations:

○
SimplifyRepeatedSubexpressions
[Solve[ax^2+bx+c0,x],"MinLeafCount"10]
In[]:=
x
-b-$17
2a
,x
-b+$17
2a
,$17
b
2
-4ac
Out[]=

Properties and Relations

Reconstruct the original expression from the decomposed form by applying
ReplaceAll
:

result=
○
SimplifyRepeatedSubexpressions
(a+b+c)
3
+(a+b+c)
2
In[]:=
$18
2
+$18
3
,$18a+b+c
Out[]=
ReplaceAll@@result
In[]:=
(a+b+c)
2
+(a+b+c)
3
Out[]=

Possible Issues

The
FullForm
of subexpressions must match; in this case no match is found:

○
SimplifyRepeatedSubexpressions
a+b+c+(a+b+c)
2
In[]:=
a+b+c+(a+b+c)
2
Out[]=

This is because the outermost
Plus
has four arguments and not just the
a
,
b
and
c
:

FullForma+b+c+(a+b+c)
2
In[]:=
Plus[a,b,c,Power[Plus[a,b,c],2]]
Out[]//FullForm=

If the input expression contains elements with
HoldAll
,
HoldRest
or
HoldFirst
, the contents will evaluate during the search:

○
SimplifyRepeatedSubexpressions
[Hold[Print[{2+2,2+2}]]]
In[]:=
{4,4}
{4,4}
{Hold[Print[{2+2,2+2}]]}
Out[]=

Neat Examples

Simplify the order three polynomial solution:

○
SimplifyRepeatedSubexpressions
[Solve[ax^3+bx^2+cx+d0,x],"MinLeafCount"30]
In[]:=
x-
b
3a
+
$19
32
1/3
a
-
2
1/3
-b
2
+3ac$20
3a
,x-
b
3a
-
1-
3
$19
62
1/3
a
+
1+
3
-b
2
+3ac$20
32
2/3
a
,x-
b
3a
-
1+
3
$19
62
1/3
a
+
1-
3
-b
2
+3ac$20
32
2/3
a
,$19$21
1/3
,$20
1
$21
1/3
,$21-2b
3
+9abc-27a
2
d+
4-b
2
+3ac
3
+-2b
3
+9abc-27a
2
d
2
Out[]=

And the order four polynomial solution:

○
SimplifyRepeatedSubexpressions
[Solve[ax^4+bx^3+cx^2+dx+e0,x],"MinLeafCount"30]
In[]:=
x-
b
4a
-
$23
2
+$25,x-
b
4a
+
$23
2
+$25,x-
b
4a
-
$22
2
+$24,x-
b
4a
+
$22
2
+$24,$22
b
2
2a
2
-
4c
3a
+
1
4
-
b
3
a
3
+
4bc
a
2
-
8d
a
$27+$29+$30
,$23
b
2
2a
2
-
4c
3a
-
1
4
-
b
3
a
3
+
4bc
a
2
-
8d
a
$27+$29+$30
,$24
$26
2
,$25-
$26
2
,$26
$28
,$27
1
$28
,$28
b
2
4a
2
-
2c
3a
+
$32
32
1/3
a
+
2
1/3
(c
2
-3bd+12ae)$33
3a
,$29-
2
1/3
(c
2
-3bd+12ae)$33
3a
,$30-
$32
32
1/3
a
,$32$34
1/3
,$33
1
$34
1/3
,$342c
3
-9bcd+27ad
2
+27b
2
e-72ace+√-4(c
2
-3bd+12ae)
3
+2c
3
-9bcd+27ad
2
+27b
2
e-72ace
2
Out[]=