Details

Time bar (total: 3.3min)

sample28.0ms

Algorithm
intervals
Results
12.0ms86×body1280valid
4.0ms142×body80valid
2.0ms17×body640valid
1.0msbody320valid
0.0msbody160valid

simplify3.0ms

Counts
1 → 1
Iterations

Useful iterations: 0 (1.0ms)

IterNodesCost
067
197
2107
done107

prune3.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

PrunedKeptTotal
New011
Fresh011
Picked000
Done000
Total022

Merged error: 11.7b

Counts
2 → 1

localize6.0ms

Local error

Found 2 expressions with local error:

0.0b
(atan (+ N 1.0))
1.0b
(- (atan (+ N 1.0)) (atan N))

rewrite5.0ms

Algorithm
rewrite-expression-head
Rules
add-sqr-sqrt *-un-lft-identity add-log-exp
pow1 add-exp-log add-cube-cbrt add-cbrt-cube
sub-neg flip3-- diff-log diff-atan flip-- distribute-lft-out-- difference-of-squares
Counts
2 → 22
Calls
2 calls:
1.0ms
(atan (+ N 1.0))
4.0ms
(- (atan (+ N 1.0)) (atan N))

series4.0ms

Counts
2 → 6
Calls
2 calls:
1.0ms
(atan (+ N 1.0))
3.0ms
(- (atan (+ N 1.0)) (atan N))

simplify16.3s

Counts
28 → 28
Iterations

Useful iterations: 4 (8.0ms)

IterNodesCost
045
195
2165
3223
4241
done241
067
1117
2187
3267
done267
089
1118
2138
3168
4198
5258
6298
7458
8498
9548
10618
11808
121018
131138
141168
done1168
078
1108
2118
done118
078
1138
2168
3198
4258
5298
6458
7498
8548
9618
10798
111008
121138
131168
done1168
0817
11117
21217
done1217
078
1108
2118
done118
0823
11223
2279
3709
41799
55079
617179
749529
done50009
078
1108
2118
done118
078
1108
2118
done118
0911
12511
24711
38111
416511
549711
6223811
done500011
01023
11820
22620
32918
43018
done3018
033
done33
0815
11415
22115
33615
46115
510215
616615
733415
8164415
done500015
067
187
done87
089
1109
done109
089
1119
2129
done129
067
197
2107
done107
033
done33
055
165
done65
055
165
done65
0611
1711
done711
055
165
done65
0614
1814
2106
3156
4216
5316
6546
71106
83196
912596
done50016
055
165
done65
055
165
done65
067
197
2107
done107
067
197
2107
done107
067
197
2107
done107
044
154
done54
044
154
done54
044
154
done54

prune43.0ms

Filtered
19 candidates to 28 candidates (-47.4%)
Pruning

2 alts after pruning (2 fresh and 0 done)

PrunedKeptTotal
New26228
Fresh000
Picked101
Done000
Total27229

Merged error: 0.2b

Counts
29 → 2

localize6.0ms

Local error

Found 2 expressions with local error:

0.0b
(* (+ N 1.0) N)
0.2b
(atan2 1.0 (+ 1 (* (+ N 1.0) N)))

rewrite9.0ms

Algorithm
rewrite-expression-head
Rules
add-sqr-sqrt *-un-lft-identity
pow1 add-exp-log add-cube-cbrt associate-*l* add-cbrt-cube
associate-*r*
associate-*l/ add-log-exp
flip3-+ pow-prod-down prod-exp *-commutative cbrt-unprod flip-+ distribute-lft-out unswap-sqr
Counts
2 → 28
Calls
2 calls:
7.0ms
(* (+ N 1.0) N)
1.0ms
(atan2 1.0 (+ 1 (* (+ N 1.0) N)))

series8.0ms

Counts
2 → 6
Calls
2 calls:
6.0ms
(* (+ N 1.0) N)
3.0ms
(atan2 1.0 (+ 1 (* (+ N 1.0) N)))

simplify35.6s

Counts
34 → 34
Iterations

Useful iterations: 1 (1.0ms)

IterNodesCost
0810
11310
22010
32810
43010
done3010
0810
11310
22010
32810
43010
done3010
0921
11421
22121
32921
43321
done3321
0810
11310
22010
32810
43010
done3010
0929
11529
22411
33711
44311
55311
67411
713611
835211
9129511
done500011
0810
11310
22010
32810
43010
done3010
0810
11310
22010
32810
43010
done3010
045
165
2135
done135
067
187
done87
056
1106
2186
done186
056
196
2256
3376
4636
51266
63096
78796
830246
done50006
0817
12817
2879
32379
48627
531727
done50007
0613
1813
21513
done1513
056
176
2146
done146
0617
11817
2717
32317
46227
518537
done50007
056
176
2146
done146
056
176
2146
done146
067
187
done87
067
187
done87
069
1109
2209
3329
4349
done349
056
176
2156
done156
055
193
2203
3283
done283
056
176
done76
056
176
done76
045
165
2135
done135
045
165
2135
done135
079
1229
2399
3779
41569
53929
613439
done50019
069
1129
2299
3699
41439
52389
64369
711359
done50019
0911
12011
2349
3479
4699
51289
63409
713069
done50009
0911
12011
2349
3479
4699
51289
63409
713069
done50009
0911
12011
2349
3479
4699
51289
63409
713069
done50009
067
1137
2255
3325
4385
5485
6725
71295
83475
912855
done50015
067
1137
2255
3325
4385
5485
6725
71295
83475
912855
done50015
067
1137
2255
3325
4385
5485
6725
71295
83475
912855
done50015

prune73.0ms

Filtered
25 candidates to 34 candidates (-36.0%)
Pruning

6 alts after pruning (5 fresh and 1 done)

PrunedKeptTotal
New30434
Fresh011
Picked011
Done000
Total30636

Merged error: 0.1b

Counts
36 → 6

localize9.0ms

Local error

Found 4 expressions with local error:

0.2b
(atan2 1.0 (+ 1 (* (+ N 1.0) N)))
0.7b
(* (sqrt (atan2 1.0 (+ 1 (* (+ N 1.0) N)))) (sqrt (atan2 1.0 (+ 1 (* (+ N 1.0) N)))))
15.4b
(sqrt (atan2 1.0 (+ 1 (* (+ N 1.0) N))))
15.4b
(sqrt (atan2 1.0 (+ 1 (* (+ N 1.0) N))))

rewrite17.0ms

Algorithm
rewrite-expression-head
Rules
28×add-sqr-sqrt
24×sqrt-prod
21×pow1
14×add-cube-cbrt *-un-lft-identity
10×sqrt-pow1 pow1/2
swap-sqr
add-exp-log associate-*r* associate-*l* add-cbrt-cube
pow-prod-up
add-log-exp unswap-sqr
pow-prod-down pow-sqr
rem-sqrt-square
pow2 pow-plus sqrt-unprod prod-exp rem-square-sqrt *-commutative cbrt-unprod
Counts
4 → 82
Calls
4 calls:
4.0ms
(atan2 1.0 (+ 1 (* (+ N 1.0) N)))
7.0ms
(* (sqrt (atan2 1.0 (+ 1 (* (+ N 1.0) N)))) (sqrt (atan2 1.0 (+ 1 (* (+ N 1.0) N)))))
1.0ms
(sqrt (atan2 1.0 (+ 1 (* (+ N 1.0) N))))
2.0ms
(sqrt (atan2 1.0 (+ 1 (* (+ N 1.0) N))))

series20.0ms

Counts
4 → 12
Calls
4 calls:
3.0ms
(atan2 1.0 (+ 1 (* (+ N 1.0) N)))
3.0ms
(* (sqrt (atan2 1.0 (+ 1 (* (+ N 1.0) N)))) (sqrt (atan2 1.0 (+ 1 (* (+ N 1.0) N)))))
8.0ms
(sqrt (atan2 1.0 (+ 1 (* (+ N 1.0) N))))
7.0ms
(sqrt (atan2 1.0 (+ 1 (* (+ N 1.0) N))))

simplify55.3s

Counts
94 → 94
Iterations

Useful iterations: 1 (1.0ms)

IterNodesCost
0911
11411
22111
32911
43311
done3311
0911
11411
22111
32911
43311
done3311
01023
11523
22223
33023
done3023
0911
11411
22111
32911
43311
done3311
01032
11620
22612
33912
44512
55512
67612
713612
834612
9127912
done500012
01022
11611
22311
33111
43511
done3511
0911
11411
22111
32911
43311
done3311
0911
11411
22111
32911
43311
done3311
0911
11411
22111
32911
43311
done3311
022
141
done41
0810
11310
22010
32810
43010
done3010
033
161
done61
0911
11411
22111
32911
43311
done3311
0911
11411
22111
32911
43311
done3311
0911
11411
22111
32911
43311
done3311
0911
11411
22111
32911
43311
done3311
01023
11523
22223
33023
done3023
0911
11411
22111
32911
43311
done3311
01032
11620
22612
33912
44512
55512
67612
713612
834612
9127912
done500012
01022
11611
22311
33111
43511
done3511
0911
11411
22111
32911
43311
done3311
0911
11411
22111
32911
43311
done3311
0911
11411
22111
32911
43311
done3311
022
141
done41
0810
11310
22010
32810
43010
done3010
033
161
done61
0911
11411
22111
32911
43311
done3311
0911
11411
22111
32911
43311
done3311
023
151
271
done71
055
181
done81
023
161
done61
055
183
done81
047
183
291
done91
0819
11319
22019
32819
43019
done3019
0921
1149
2229
3309
done309
0819
11319
22019
32819
43019
done3019
023
161
done61
01023
11713
22513
33313
43713
done3713
01022
11710
22710
33610
done3610
01022
11710
22910
34210
46410
510510
621410
758710
8227010
done500010
01165
12329
24225
36211
49311
517211
639111
7134811
done500011
01145
11621
22421
33221
done3221
01022
11510
22310
33110
43510
done3510
01165
12429
23911
36011
49211
517611
640611
7139711
done500011
0819
11319
22019
32819
43019
done3019
01022
11610
22310
33110
43510
done3510
01022
11610
22310
33110
43510
done3510
01147
12047
22925
34513
46213
58813
616113
737913
8128213
done500013
01023
11523
22223
33023
done3023
01145
11721
22521
33321
43721
done3721
01023
11510
22310
33110
43510
done3510
01023
11510
22310
33110
43510
done3510
01023
11510
22310
33110
43510
done3510
01023
11510
22310
33110
43510
done3510
01023
11510
22310
33110
43510
done3510
035
151
done51
0921
1149
2229
3309
done309
01023
11510
22310
33110
43510
done3510
01023
11510
22310
33110
43510
done3510
01023
11510
22310
33110
43510
done3510
01023
11510
22310
33110
43510
done3510
023
141
done41
0921
1149
2229
3309
done309
01023
11510
22310
33110
43510
done3510
01023
11510
22310
33110
43510
done3510
01023
11510
22310
33110
43510
done3510
01023
11510
22310
33110
43510
done3510
01023
11510
22310
33110
43510
done3510
01023
11510
22310
33110
43510
done3510
01023
11510
22310
33110
43510
done3510
01023
11510
22310
33110
43510
done3510
033
151
271
done71
033
161
done61
045
1101
done101
01134
11934
22834
33634
done3634
01233
11922
22622
33422
done3422
01022
11622
22322
33122
43522
done3522
01013
11612
22312
33110
43810
done3810
01022
11622
22322
33122
43522
done3522
0912
11510
22510
33310
43710
done3710
01022
11622
22322
33122
43522
done3522
01122
11722
22422
33222
done3222
01022
11622
22322
33122
43522
done3522
0921
1149
2229
3309
done309
01022
11622
22322
33122
43522
done3522
0921
1149
2229
3309
done309
0810
11310
22010
32810
43010
done3010
0810
11310
22010
32810
43010
done3010
0921
11421
22121
32921
43321
done3321
0810
11310
22010
32810
43010
done3010
0929
11529
22411
33711
44311
55311
67411
713611
835211
9129511
done500011
0810
11310
22010
32810
43010
done3010
0810
11310
22010
32810
43010
done3010
01012
12112
23510
34810
47010
512910
634910
7138910
done500010
01012
12112
23510
34810
47010
512910
634910
7138910
done500010
01012
12112
23510
34810
47010
512910
634910
7138910
done500010
01012
12112
23510
34810
47010
512910
634910
7138910
done500010
01012
12112
23510
34810
47010
512910
634910
7138910
done500010
01012
12112
23510
34810
47010
512910
634910
7138910
done500010
0911
12011
2349
3479
4699
51289
63409
713069
done50009
0911
12011
2349
3479
4699
51289
63409
713069
done50009
0911
12011
2349
3479
4699
51289
63409
713069
done50009
0911
12011
2349
3479
4699
51289
63409
713069
done50009
0911
12011
2349
3479
4699
51289
63409
713069
done50009
0911
12011
2349
3479
4699
51289
63409
713069
done50009

prune180.0ms

Filtered
51 candidates to 94 candidates (-84.3%)
Pruning

8 alts after pruning (6 fresh and 2 done)

PrunedKeptTotal
New90494
Fresh224
Picked011
Done011
Total928100

Merged error: 0.1b

Counts
100 → 8

localize12.0ms

Local error

Found 4 expressions with local error:

0.7b
(* (sqrt (atan2 1.0 (+ 1 (* (+ N 1.0) N)))) (* (sqrt (sqrt (atan2 1.0 (+ 1 (* (+ N 1.0) N))))) (sqrt (sqrt (atan2 1.0 (+ 1 (* (+ N 1.0) N)))))))
15.4b
(sqrt (atan2 1.0 (+ 1 (* (+ N 1.0) N))))
15.4b
(sqrt (atan2 1.0 (+ 1 (* (+ N 1.0) N))))
15.4b
(sqrt (atan2 1.0 (+ 1 (* (+ N 1.0) N))))

rewrite27.0ms

Algorithm
rewrite-expression-head
Rules
54×sqrt-pow1
45×pow1
30×pow1/2 pow-prod-up
16×add-sqr-sqrt
14×sqrt-prod
add-exp-log add-cube-cbrt *-un-lft-identity add-cbrt-cube
pow-prod-down
associate-*l* pow-sqr
add-log-exp
rem-sqrt-square prod-exp cbrt-unprod
sqrt-unprod swap-sqr unswap-sqr
associate-*r* *-commutative
Counts
4 → 85
Calls
4 calls:
18.0ms
(* (sqrt (atan2 1.0 (+ 1 (* (+ N 1.0) N)))) (* (sqrt (sqrt (atan2 1.0 (+ 1 (* (+ N 1.0) N))))) (sqrt (sqrt (atan2 1.0 (+ 1 (* (+ N 1.0) N)))))))
2.0ms
(sqrt (atan2 1.0 (+ 1 (* (+ N 1.0) N))))
2.0ms
(sqrt (atan2 1.0 (+ 1 (* (+ N 1.0) N))))
2.0ms
(sqrt (atan2 1.0 (+ 1 (* (+ N 1.0) N))))

series26.0ms

Counts
4 → 12
Calls
4 calls:
3.0ms
(* (sqrt (atan2 1.0 (+ 1 (* (+ N 1.0) N)))) (* (sqrt (sqrt (atan2 1.0 (+ 1 (* (+ N 1.0) N))))) (sqrt (sqrt (atan2 1.0 (+ 1 (* (+ N 1.0) N)))))))
8.0ms
(sqrt (atan2 1.0 (+ 1 (* (+ N 1.0) N))))
7.0ms
(sqrt (atan2 1.0 (+ 1 (* (+ N 1.0) N))))
8.0ms
(sqrt (atan2 1.0 (+ 1 (* (+ N 1.0) N))))

simplify1.4min

Counts
97 → 97
Iterations

Useful iterations: 1 (1.0ms)

IterNodesCost
0911
11411
22111
32911
43311
done3311
0911
11411
22111
32911
43311
done3311
01023
11523
22223
33023
done3023
0911
11411
22111
32911
43311
done3311
01032
11620
22612
33912
44512
55512
67612
713612
834612
9127912
done500012
01022
11611
22311
33111
43511
done3511
0911
11411
22111
32911
43311
done3311
0911
11411
22111
32911
43311
done3311
0911
11411
22111
32911
43311
done3311
022
141
done41
0810
11310
22010
32810
43010
done3010
033
161
done61
0911
11411
22111
32911
43311
done3311
0911
11411
22111
32911
43311
done3311
0911
11411
22111
32911
43311
done3311
0911
11411
22111
32911
43311
done3311
01023
11523
22223
33023
done3023
0911
11411
22111
32911
43311
done3311
01032
11620
22612
33912
44512
55512
67612
713612
834612
9127912
done500012
01022
11611
22311
33111
43511
done3511
0911
11411
22111
32911
43311
done3311
0911
11411
22111
32911
43311
done3311
0911
11411
22111
32911
43311
done3311
022
141
done41
0810
11310
22010
32810
43010
done3010
033
161
done61
0911
11411
22111
32911
43311
done3311
0911
11411
22111
32911
43311
done3311
0911
11411
22111
32911
43311
done3311
0911
11411
22111
32911
43311
done3311
01023
11523
22223
33023
done3023
0911
11411
22111
32911
43311
done3311
01032
11620
22612
33912
44512
55512
67612
713612
834612
9127912
done500012
01022
11611
22311
33111
43511
done3511
0911
11411
22111
32911
43311
done3311
0911
11411
22111
32911
43311
done3311
0911
11411
22111
32911
43311
done3311
022
141
done41
0810
11310
22010
32810
43010
done3010
033
161
done61
0911
11411
22111
32911
43311
done3311
0911
11411
22111
32911
43311
done3311
059
1105
2151
3171
done171
0811
1185
2211
done211
0811
1185
2211
done211
0713
1167
2251
done251
057
1115
2131
done131
079
1163
2171
done171
045
1123
2131
done131
067
1131
done131
067
1125
2151
done151
059
1125
2163
done161
055
191
done91
057
1121
done121
0711
1143
2171
done171
0813
1185
2211
done211
0813
1185
2211
done211
0615
1167
2251
done251
079
1143
done141
0611
1175
2201
done201
01031
11819
22819
33819
44612
55912
68712
716012
837512
9127912
done500012
01134
11921
2299
3409
4529
5659
6929
71649
83779
912699
done50009
01134
11921
2299
3409
4529
5659
6929
71649
83779
912699
done50009
01031
11819
22819
33819
44612
55912
68712
716012
837512
9127912
done500012
01337
12326
23326
34126
44326
done4326
01336
12123
23523
35313
46413
done6413
01235
12222
23810
35810
47410
59010
612610
723610
858610
9201610
done500010
01235
12222
24010
36610
411010
521610
648110
7149610
done500010
015104
13341
28725
314111
425811
594011
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done500011
015104
13441
28425
313911
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6389911
done500111
01371
12145
23121
34221
45421
56721
69421
716621
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9127721
done500021
01235
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23010
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716510
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done500010
013104
13165
27311
314511
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548111
6172811
done500111
01031
11819
22819
33819
44612
55912
68712
716012
837512
9127912
done500012
01235
12022
23010
34110
45110
56410
69110
716510
837610
9128110
done500010
01235
12022
23010
34110
45110
56410
69110
716510
837610
9128110
done500010
01023
11510
22310
33110
43510
done3510
01023
11510
22310
33110
43510
done3510
01023
11510
22310
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43510
done3510
01023
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done3510
01023
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done3510
01023
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done3510
01023
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33110
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done3510
01023
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22310
33110
43510
done3510
01022
11622
22322
33122
43522
done3522
01235
12022
23022
33822
44022
done4022
01335
12122
23122
33922
44322
done4322
01135
11913
23213
34613
45813
57913
613813
735013
8126813
done500013
01134
11921
2299
3409
4529
5659
6929
71649
83779
912699
done50009
01135
11913
23213
34613
45813
57913
613813
735013
8126813
done500013
01134
11921
2299
3409
4529
5659
6929
71649
83779
912699
done50009
01012
12112
23510
34810
47010
512910
634910
7138910
done500010
01012
12112
23510
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512910
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done500010
01012
12112
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512910
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done500010
01012
12112
23510
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512910
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done500010
01012
12112
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512910
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done500010
01012
12112
23510
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47010
512910
634910
7138910
done500010
01012
12112
23510
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512910
634910
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done500010
01012
12112
23510
34810
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512910
634910
7138910
done500010
01012
12112
23510
34810
47010
512910
634910
7138910
done500010
0911
12011
2349
3479
4699
51289
63409
713069
done50009
0911
12011
2349
3479
4699
51289
63409
713069
done50009
0911
12011
2349
3479
4699
51289
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713069
done50009

prune189.0ms

Filtered
53 candidates to 97 candidates (-83.0%)
Pruning

8 alts after pruning (5 fresh and 3 done)

PrunedKeptTotal
New97097
Fresh055
Picked011
Done022
Total978105

Merged error: 0.1b

Counts
105 → 8

regimes113.0ms

Accuracy

0% (0.0b remaining)

Error of 0.3b against oracle of 0.3b and baseline of 0.3b

bsearch0.0ms

simplify1.0ms

Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
079
1129
done129

end0.0ms

sample779.0ms

Algorithm
intervals
Results
393.0ms2874×body1280valid
113.0ms4048×body80valid
72.0ms624×body640valid
29.0ms297×body320valid
9.0ms157×body160valid

Profiling

Loading profile data...