Details

Time bar (total: 21.7min)

sample20.0ms

Algorithm
intervals
Results
9.0ms256×body80valid

simplify2.0s

Counts
1 → 1
Iterations

Useful iterations: 0 (1.0ms)

IterNodesCost
0917
13617
213017
341117
4121017
done500117

prune3.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

PrunedKeptTotal
New011
Fresh011
Picked000
Done000
Total022

Merged error: 22.0b

Counts
2 → 1

localize9.0ms

Local error

Found 3 expressions with local error:

0.0b
(* (+ x y) (+ x y))
0.0b
(* (* (+ x y) (+ x y)) (+ (+ x y) 1.0))
21.7b
(/ (* x y) (* (* (+ x y) (+ x y)) (+ (+ x y) 1.0)))

rewrite61.0ms

Algorithm
rewrite-expression-head
Rules
60×frac-times flip3-+ flip-+
31×add-exp-log add-cbrt-cube
30×associate-*l/
27×*-un-lft-identity
26×associate-/r/
18×associate-*r/
15×pow1
13×prod-exp cbrt-unprod
11×add-sqr-sqrt
associate-*r* distribute-lft-out
add-cube-cbrt
cbrt-undiv swap-sqr div-exp
associate-*l*
pow-prod-down
add-log-exp
distribute-rgt-in distribute-lft-in *-commutative unswap-sqr
pow2 frac-2neg times-frac pow-plus clear-num associate-/r* pow-sqr pow-prod-up div-inv associate-/l*
Counts
3 → 140
Calls
3 calls:
9.0ms
(* (+ x y) (+ x y))
18.0ms
(* (* (+ x y) (+ x y)) (+ (+ x y) 1.0))
21.0ms
(/ (* x y) (* (* (+ x y) (+ x y)) (+ (+ x y) 1.0)))

series37.0ms

Counts
3 → 9
Calls
3 calls:
4.0ms
(* (+ x y) (+ x y))
10.0ms
(* (* (+ x y) (+ x y)) (+ (+ x y) 1.0))
23.0ms
(/ (* x y) (* (* (+ x y) (+ x y)) (+ (+ x y) 1.0)))

simplify4.9min

Counts
149 → 149
Iterations

Useful iterations: 1 (1.0ms)

IterNodesCost
01322
12919
26819
315119
430219
559119
6106719
7139519
8142319
done142319
01321
13321
28219
317019
434519
563019
6111419
7143619
8146819
done146819
01220
13920
212420
337419
4112519
5465319
done500019
01221
12918
26018
313018
426818
551818
690718
7138818
8143318
done143318
01220
13320
27018
314918
431218
555218
695218
7142818
8147918
done147918
01119
13919
211519
335818
4110118
5457018
done500018
01018
14018
215418
349518
4146217
done500017
01018
13718
213318
342918
4126818
done500018
01753
17253
249027
3444421
done500021
01753
16753
248225
3443821
done500021
01553
15853
243723
3468323
done500023
01553
17453
249425
3476319
done500019
01553
16953
248323
3475719
done500019
01353
16053
243921
done500019
01137
13837
213237
341537
4121237
done500037
01018
13718
213118
341218
4121518
done500118
01153
14553
223119
3189719
done500019
01018
13718
213118
341218
4121518
done500118
01018
13718
213118
341218
4121518
done500118
044
194
2114
done114
0814
13114
213314
349514
4185414
done500014
059
1149
2279
3439
4629
5789
6859
7879
done879
067
1107
2167
done167
0915
13215
210315
331115
495315
5425815
done500115
0917
13617
213117
346317
4155917
done500017
0611
12111
24211
37111
410211
512811
614311
715411
818011
971811
10466911
done500011
0815
12915
210315
334115
4109315
5479215
done500015
01529
16429
223129
397429
done500029
01531
15831
219231
386531
done500131
01829
16429
221329
3106229
done500129
01831
15831
218631
3100931
done500131
01829
17029
227429
3152929
done500029
01831
16431
223531
3131531
done500031
01529
15129
217929
387429
done500029
01431
14131
214531
384231
done500031
01525
16525
225125
3110325
done500025
01527
15927
221227
397227
done500227
01525
15225
219225
388025
4413425
done500125
01427
14227
215827
385627
done500027
01525
16525
223125
394725
4445225
done500125
01527
15927
219227
388826
done500025
01525
15825
222725
3103025
done500125
01427
14827
218127
393826
done500125
01221
14921
217321
359921
4217921
done500021
01023
13323
212223
357322
4321221
done500021
01325
15425
218925
375325
4325525
done500125
01625
15425
218025
383925
4419825
done500025
01625
16025
224125
3127025
done500125
01225
13725
213225
365025
4336525
done500025
01321
15521
221621
387621
4338621
done500021
01221
13821
214621
365821
4261621
done500021
01321
15521
219421
370721
4262221
done500021
01221
14421
218421
377421
4314521
done500121
0713
12613
29213
329413
493313
5424213
done500013
0713
12613
29213
329413
493313
5424213
done500013
0916
11813
22713
done2713
0915
12215
24713
36413
48313
59813
610513
710713
done10713
0814
13014
210114
331113
495213
5427213
done500013
0814
12914
211014
337214
4123414
done500014
01141
15241
227119
3153513
done500113
01141
14741
226017
3149913
done500113
0929
12829
29429
329829
493829
5426529
done500029
0814
12714
29314
329514
493114
5423314
done500014
0941
13841
222615
3154815
done500115
0814
12714
29314
329514
493114
5423314
done500014
0814
12714
29314
329514
493114
5423314
done500014
01325
15425
218725
388125
done500025
01641
15435
219135
3100433
done500033
01327
14827
215027
367327
done500127
01229
13425
211325
353825
4309825
done500025
01625
15425
216225
383725
done500225
01733
15229
216629
385727
done500027
01627
14827
213727
369327
done500027
01321
13219
29819
341019
4202219
done500019
01625
16025
222325
3130025
done500025
01733
15829
220929
3108227
done500027
01627
15427
218627
397927
done500027
01321
13819
212719
356819
4275519
done500119
01325
14125
213525
368525
4430025
done500125
01225
13823
213023
350721
4260921
done500121
01227
13127
210327
355727
4460926
done500026
0813
11813
25613
319113
461213
5244313
done500113
01321
15521
220021
396821
done500021
01529
14525
214325
363523
4379923
done500123
01323
14923
216323
371223
done500223
01117
12515
26715
324015
483515
5346515
done500015
01321
14221
214121
368521
4350321
done500021
01121
13519
212119
344517
4202217
done500117
01223
13223
210923
355923
4422922
done500021
079
1159
2419
31299
42969
58789
623119
done50009
01321
15521
218021
378621
4410721
done500021
01529
14525
214325
363523
4379923
done500123
01323
14923
214323
363222
4451321
done500021
01117
12515
26715
324015
483515
5346515
done500015
01321
14821
217621
381621
4458021
done500021
01121
13519
212119
344517
4202217
done500117
01223
13823
213223
363422
done500121
079
1159
2419
31299
42969
58789
623119
done50009
0710
11210
22610
done2610
0710
11210
22610
done2610
0511
11911
2515
31165
42755
58445
619095
727395
832635
943285
done50005
069
1169
2379
3849
41499
52069
62549
72809
done2809
0511
1155
2475
31085
42475
55965
615475
730335
847215
done50005
069
1169
2539
31049
41579
52149
62629
72889
done2889
0921
12621
26221
313821
427321
539121
651221
760821
861421
done61421
0814
12114
24814
39514
415814
521714
626514
729114
829514
done29514
069
1187
2457
3927
42377
52707
62987
73087
done3087
069
1187
2457
3927
42377
52707
62987
73087
done3087
069
1187
2457
3927
42377
52707
62987
73087
done3087
069
1169
2519
31189
42519
55729
67779
77979
87999
done7999
01017
13917
213517
349017
4195217
done500017
0819
12319
28019
338218
4250617
done500017
01121
14421
214521
362921
4301021
done500021
01421
14421
212921
360221
4331921
done500021
01421
15021
219021
3101921
done500021
01021
12721
28821
343421
4237521
done500121
01117
14517
216517
371017
4298517
done500117
01017
12817
29517
345317
4194717
done500117
01117
14517
214317
354017
4222717
done500117
01017
13417
213317
356317
4243517
done500017
023
161
done61
047
1117
2247
3407
4597
5757
6827
7847
done847
023
161
done61
059
186
296
done96
058
1148
2296
3466
4656
5806
6876
7896
done896
058
1148
2388
3718
41478
53238
69888
done50008
0623
12623
210511
33625
414835
done50025
0617
11317
22617
34217
46117
57717
68417
78617
done8617
058
1128
2258
3418
4628
5788
6858
7878
done878
0623
12123
2929
32975
410275
done50015
058
1134
2264
3424
4614
5774
6844
7864
done864
058
1134
2264
3424
4614
5774
6844
7864
done864
0715
12715
27315
322415
466515
5245915
done500015
0823
12219
26419
324719
491319
5350619
done500019
01015
12815
26215
319315
479315
5308815
done500015
0915
12013
24913
314013
436113
589213
6219313
7388213
8464813
done500013
01015
13415
210515
341315
4143015
5488315
done500015
0915
12613
27413
320213
449413
5126313
6314313
7477913
done500013
0615
11115
23115
312615
450515
5151615
done500015
047
167
2137
3307
4637
51067
61867
72967
84557
96287
106717
116727
done6727
0619
11119
21311
3226
4456
5716
61436
73586
812866
done50006
059
169
done69
059
163
273
done73
059
163
273
done73
023
141
done41
047
1117
2247
3407
4597
5757
6827
7847
done847
023
141
done41
047
1117
2247
3407
4597
5757
6827
7847
done847
023
141
done41
047
1117
2247
3407
4597
5757
6827
7847
done847
023
141
done41
047
1117
2247
3407
4597
5757
6827
7847
done847
059
163
273
done73
059
163
273
done73
033
161
done61
045
165
2135
done135
045
165
2135
done135
045
1115
2125
done125
045
1115
2125
done125
0613
11013
22013
33213
43413
done3413
058
178
2158
done158
055
193
2203
3283
done283
055
193
2203
3283
done283
058
1138
2148
done148
058
1138
2148
done148
047
1117
2247
3407
4597
5757
6827
7847
done847
047
1117
2247
3407
4597
5757
6827
7847
done847
0811
13011
28811
320711
443311
5101611
6324211
done500111
0711
11311
23511
310611
425911
556211
6187511
done500111
0811
13011
26411
316211
438211
590111
6299611
done500011
0711
11911
25411
314511
433011
592111
6415511
done500011
01421
14019
210517
321513
450211
5104311
6190011
7306811
8440611
done500111
011
done11
011
done11
01317
13315
27415
38215
49915
512015
616015
728515
870515
9252915
done500015
01319
13919
210717
316115
423813
536313
660913
7166013
done500013
01319
13919
210717
316115
423813
536313
660913
7166013
done500013
0913
12513
24813
35613
47311
59411
613411
725411
866711
9251811
done500011
0913
12513
24813
35613
47311
59411
613411
725411
866711
9251811
done500011
0913
12513
24813
35613
47311
59411
613411
725411
866711
9251811
done500011

prune250.0ms

Filtered
118 candidates to 149 candidates (-26.3%)
Pruning

8 alts after pruning (8 fresh and 0 done)

PrunedKeptTotal
New1418149
Fresh000
Picked101
Done000
Total1428150

Merged error: 5.7b

Counts
150 → 8

localize18.0ms

Local error

Found 4 expressions with local error:

0.0b
(/ y (+ x y))
0.0b
(* (/ y (+ x y)) (/ x (- (pow (+ x y) 3) (* (+ x y) (* 1.0 1.0)))))
5.2b
(/ x (- (pow (+ x y) 3) (* (+ x y) (* 1.0 1.0))))
9.8b
(* (* (/ y (+ x y)) (/ x (- (pow (+ x y) 3) (* (+ x y) (* 1.0 1.0))))) (- (+ x y) 1.0))

rewrite101.0ms

Algorithm
rewrite-expression-head
Rules
58×*-un-lft-identity
53×add-sqr-sqrt
52×times-frac
39×add-cube-cbrt
38×add-exp-log add-cbrt-cube
28×associate-*r*
19×associate-*l*
16×associate-/r/
15×associate-*l/
13×prod-exp cbrt-unprod
11×pow1
10×cbrt-undiv frac-times flip3-+ div-exp flip-+
distribute-lft-out--
cube-div associate-/r* frac-sub distribute-lft-out
cube-mult
flip3-- associate-*r/ flip-- associate-/l*
pow-prod-down div-inv add-log-exp unswap-sqr
distribute-rgt-in distribute-lft-in
sub-neg frac-2neg associate--l+ clear-num *-commutative
difference-of-squares
Counts
4 → 178
Calls
4 calls:
6.0ms
(/ y (+ x y))
32.0ms
(* (/ y (+ x y)) (/ x (- (pow (+ x y) 3) (* (+ x y) (* 1.0 1.0)))))
17.0ms
(/ x (- (pow (+ x y) 3) (* (+ x y) (* 1.0 1.0))))
34.0ms
(* (* (/ y (+ x y)) (/ x (- (pow (+ x y) 3) (* (+ x y) (* 1.0 1.0))))) (- (+ x y) 1.0))

series126.0ms

Counts
4 → 12
Calls
4 calls:
6.0ms
(/ y (+ x y))
44.0ms
(* (/ y (+ x y)) (/ x (- (pow (+ x y) 3) (* (+ x y) (* 1.0 1.0)))))
36.0ms
(/ x (- (pow (+ x y) 3) (* (+ x y) (* 1.0 1.0))))
39.0ms
(* (* (/ y (+ x y)) (/ x (- (pow (+ x y) 3) (* (+ x y) (* 1.0 1.0))))) (- (+ x y) 1.0))

simplify4.9min

Counts
190 → 190
Iterations

Useful iterations: 1 (1.0ms)

IterNodesCost
01427
14027
214227
350827
4179727
done500027
01427
14027
214227
350827
4179727
done500027
01932
14932
214432
340532
4113032
5325332
done500032
01831
14731
213231
336131
499231
5302131
done500131
01831
14731
212831
334831
497631
5298731
done500031
01730
14530
211830
331330
487130
5277130
done500030
01629
14329
211829
330229
496729
5400929
done500129
01528
14428
215928
357228
4204328
done500128
01528
14328
215528
356528
4204028
done500128
02483
18077
238337
3320133
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02283
17677
233535
3232433
done500033
02283
16783
231435
3223633
done500033
02083
16383
226633
3159733
done500033
01883
15783
226731
3178431
done500031
01657
14257
214457
351057
4179957
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01528
14128
214328
350928
4180428
done500028
01683
15283
227229
3198329
done500029
01528
14128
214328
350928
4180428
done500028
01528
14128
214328
350928
4180428
done500028
01013
13013
28613
328213
493713
5343113
done500013
01535
15033
220233
395431
done500031
0915
12515
27515
331715
4138415
5444315
done500015
01223
13923
213923
354423
4283823
done500023
01117
13317
29817
334017
4134717
done500017
01431
14629
217229
378527
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01019
12819
28719
339719
4206419
done500019
01119
13519
211719
344219
4202119
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01427
14027
212627
346527
4223327
done500127
01021
13119
211817
341617
4174017
done500017
01429
14429
214329
358529
432929
done50009
069
1169
2519
31189
42519
55729
67779
77979
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01325
14125
214525
338225
4125019
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01424
13824
212124
335424
4124624
done500224
01323
13523
210523
327323
487923
5381323
done500023
01425
13825
212025
337425
4127925
done500025
01325
14125
214525
338225
4125019
done500019
01424
13824
212124
335424
4124624
done500224
01325
13525
211425
333725
4112919
done500017
01424
13824
212124
335024
4119124
done500024
01323
13523
210323
326623
486123
5371423
done500123
01425
13825
211625
335725
4123725
done500025
01325
13525
211425
333725
4112919
done500017
01424
13824
212124
335024
4119124
done500024
01635
14435
213335
336735
4126735
done500035
01528
14128
211928
330728
4101028
5478728
done500028
01423
13821
211621
332521
4104421
5424321
done500121
01629
14529
215429
343329
4143929
done500029
01423
13821
211621
332521
4104421
5424321
done500121
01423
13821
211621
332521
4104421
5424321
done500121
01221
13321
210821
326821
475621
5265721
done500021
01531
14331
214131
354831
4299031
done500031
01533
14733
216333
369433
4445613
done500013
079
1169
2529
31229
41769
52209
62929
73919
84949
96489
108669
1110299
1211589
done11589
0813
11913
26413
320813
438413
563111
697711
7302611
done500011
01323
13723
212723
339823
4124623
5491423
done500023
01217
12817
27417
318617
448817
5146317
done500117
01116
12816
27516
319016
449616
5147516
done500016
01116
12516
27016
318116
447816
5142916
done500016
01447
13747
212519
346817
4299717
done500117
01233
12633
27133
318233
447533
5142133
done500033
01116
12516
27016
318116
447816
5142916
done500016
01247
13347
29317
326817
4104817
done500017
01116
12516
27016
318116
447816
5142916
done500016
01116
12516
27016
318116
447816
5142916
done500016
022
done22
01014
12414
27214
321114
469413
5268513
done500013
01435
13435
28835
320335
448835
5143135
done500135
01217
12617
27117
318017
446917
5142917
done500117
01320
12920
27620
318620
447320
5141420
done500020
01217
12617
27117
318017
446917
5142917
done500117
057
195
2155
3205
done205
01116
12516
27016
318116
447816
5142416
done500116
069
199
2119
3129
done129
0914
12114
25514
314114
445214
5129714
done500114
01332
12932
27432
318332
447632
5142732
done500032
01217
12617
27117
318017
446917
5142917
done500117
01217
12617
27117
318017
446917
5142917
done500117
01217
12617
27117
318017
446917
5142917
done500117
044
162
282
done82
01116
12516
27016
318116
447816
5142416
done500116
056
166
done66
0914
12114
25514
314114
445214
5129714
done500114
01331
13131
27631
318531
447631
5142631
done500131
01116
12516
27016
317916
446816
5139816
done500016
01216
12816
27316
318216
447116
5141516
done500016
01116
12516
27016
317916
446816
5139816
done500016
023
141
done41
01015
12415
26915
318015
447115
5141415
done500015
055
185
done85
0813
12013
25413
314013
444913
5129813
done500013
01115
12715
27215
318315
448015
5143615
done500015
01015
12715
28515
322615
462515
5186615
done500015
01231
12831
27331
318231
447531
5139731
done500031
01116
12516
27016
317916
446816
5139816
done500016
033
151
done51
045
155
done55
01116
12816
28616
322716
462416
5185016
done500016
01116
12816
28616
322716
462416
5185016
done500016
01015
12715
28515
322615
462515
5186615
done500015
02049
16545
224445
3132345
done500045
02241
16739
222139
3121539
done500039
02241
17339
226439
3153139
done500039
01633
14433
217933
3113529
done500125
01219
13819
217619
397517
4493717
done500017
01229
13823
214623
363721
4257019
done500119
01221
13121
28521
322021
469121
5281721
done500121
01625
13925
210725
327425
467625
5188625
done500025
01524
13724
210024
325524
465424
5187124
done500124
01524
13724
29724
324824
464024
5182224
done500024
01423
13523
29223
323523
461623
5182723
done500123
01322
13522
210022
326022
482622
5323822
done500022
01322
13422
29322
323822
477322
5335722
done500122
02065
16659
227829
3178525
done500125
01865
16259
223327
3111725
done500025
01865
15365
221127
3104725
done500125
01665
14965
216625
361225
4379723
done500023
01445
13345
28745
322245
469345
5281745
done500145
01322
13222
28622
322122
469622
5282522
done500022
01465
14365
216923
375923
4459923
done500023
01322
13222
28622
322122
469622
5282522
done500022
01322
13222
28622
322122
469622
5282522
done500022
033
143
done43
01017
12517
28417
326017
491417
5351315
done500015
01423
12923
27423
318523
447823
5144123
done500023
01423
12923
27423
318523
447823
5144123
done500023
01524
13224
28024
319324
448124
5141024
done500124
01524
13224
28024
319324
448124
5141024
done500124
01524
13224
28024
319324
448624
5143624
done500124
01524
13224
28024
319324
448624
5143624
done500124
01625
13525
28925
321525
452125
5146825
done500025
01625
13525
28925
321525
452125
5146825
done500025
01439
13339
28639
320539
450939
5144839
done500039
01322
13022
27822
319122
448822
5142622
done500022
01641
14141
212741
332841
484241
5210441
done500041
01526
13626
29926
325126
462726
5167326
done500026
0913
11911
24511
313811
428711
537811
641511
770111
8283211
done500111
0815
11615
23315
36915
413815
520215
625015
732815
843315
955515
10237915
done500015
01538
13638
210038
324838
462338
5164938
done500138
01423
13323
28723
321323
453723
5149423
done500023
0810
1168
2298
3698
41388
51608
done1608
0712
11312
22112
33312
46112
58612
611012
714512
818712
924012
1070812
11279712
done500112
01537
13837
210135
327835
464935
5171935
done500035
01422
13522
28920
323620
454520
5151920
done500020
079
1157
2255
3465
4855
51165
61175
71185
81225
91385
101545
111585
done1585
0711
11511
2239
3659
4909
51239
61499
71969
82899
95429
1017989
done50019
067
1125
2225
done225
057
197
2127
3147
4167
5177
done177
02355
17451
226151
3138051
done500051
02547
17545
223645
3124245
done500045
02547
18145
227945
3156845
done500045
01939
15239
219539
3115535
done500031
01425
14525
219225
3102723
done500019
01435
14529
216729
371927
4312219
done500019
01322
13022
27822
320422
455822
5173022
done500022
01322
13022
27822
320422
455822
5173022
done500022
01423
13323
28723
323023
469623
5281023
done500123
01423
13323
28723
323023
469623
5281023
done500123
01322
13222
28622
322722
469422
5280322
done500122
01322
13222
28622
322722
469422
5280322
done500122
01423
13323
28723
323023
469623
5281023
done500123
01423
13323
28723
323023
469623
5281023
done500123
01322
13222
28622
322722
469422
5280322
done500122
01322
13222
28622
322722
469422
5280322
done500122
01322
13222
28622
322322
468922
5280022
done500122
01322
13222
28622
322322
468922
5280022
done500122
01221
13121
28521
322021
469121
5281721
done500121
01221
13121
28521
322021
469121
5281721
done500121
01221
13121
28521
322021
469121
5281721
done500121
01321
13421
28819
325119
474619
5290719
done500019
01627
14125
211225
329925
484725
5294025
done500125
01219
13119
28619
322819
463119
5202019
done500019
057
197
2127
3147
4167
5177
done177
01117
12817
27617
319617
454817
5174217
done500017
067
197
2107
done107
056
196
2116
3126
done126
056
166
done66
0817
13017
2919
32167
44897
512857
630107
done50007
0613
1713
done713
056
166
done66
0617
11417
2307
3687
41497
52967
65767
713577
847517
done50007
056
166
done66
056
166
done66
022
done22
044
184
2104
3114
done114
0815
11515
22415
33015
done3015
067
177
done77
0710
11010
21210
31310
done1310
067
177
done77
057
195
2155
3205
done205
056
166
done66
057
195
2155
3205
done205
056
166
done66
0712
11012
done1012
067
177
done77
067
177
done77
067
177
done77
044
162
282
done82
056
166
done66
044
162
282
done82
056
166
done66
0711
11211
done1211
056
166
done66
066
196
done96
056
166
done66
023
141
done41
045
155
done55
023
141
done41
045
155
done55
055
185
done85
045
155
done55
0611
1911
done911
056
166
done66
033
151
done51
033
151
done51
056
166
done66
056
166
done66
045
155
done55
079
1219
2309
3479
4889
52009
66049
724369
done50009
069
1119
2209
3379
4629
51039
61619
73299
816199
done50009
01421
14019
210517
321513
450211
5104311
6190011
7306811
8440611
done500111
011
done11
011
done11
01418
13716
210814
324314
448012
589512
6139612
7265012
done500012
011
done11
011
done11
01824
15024
216820
339220
4104618
5257116
done500016
011
done11
011
done11
011
done11
011
done11
011
done11

prune378.0ms

Filtered
157 candidates to 190 candidates (-21.0%)
Pruning

8 alts after pruning (8 fresh and 0 done)

PrunedKeptTotal
New1855190
Fresh437
Picked101
Done000
Total1908198

Merged error: 0.0b

Counts
198 → 8

localize10.0ms

Local error

Found 4 expressions with local error:

0.0b
(/ y (+ x y))
0.0b
(/ (* (/ y (+ x y)) x) (+ x y))
0.1b
(/ (* 1 (/ (* (/ y (+ x y)) x) (+ x y))) (+ (+ x y) 1.0))
8.6b
(* (/ y (+ x y)) x)

rewrite57.0ms

Algorithm
rewrite-expression-head
Rules
54×add-exp-log *-un-lft-identity
40×add-cbrt-cube
34×times-frac
31×add-sqr-sqrt
26×add-cube-cbrt
23×div-exp
18×associate-*l*
16×prod-exp
15×cbrt-undiv distribute-lft-out
13×associate-/r*
10×cbrt-unprod
associate-/r/
pow1
associate-/l*
flip3-+ 1-exp flip-+ div-inv add-log-exp
frac-2neg associate-*r* clear-num
associate-*l/ associate-/l/ unswap-sqr
associate-*r/ pow-prod-down *-commutative
Counts
4 → 136
Calls
4 calls:
6.0ms
(/ y (+ x y))
12.0ms
(/ (* (/ y (+ x y)) x) (+ x y))
24.0ms
(/ (* 1 (/ (* (/ y (+ x y)) x) (+ x y))) (+ (+ x y) 1.0))
10.0ms
(* (/ y (+ x y)) x)

series46.0ms

Counts
4 → 12
Calls
4 calls:
6.0ms
(/ y (+ x y))
12.0ms
(/ (* (/ y (+ x y)) x) (+ x y))
20.0ms
(/ (* 1 (/ (* (/ y (+ x y)) x) (+ x y))) (+ (+ x y) 1.0))
8.0ms
(* (/ y (+ x y)) x)

simplify4.0min

Counts
148 → 148
Iterations

Useful iterations: 1 (1.0ms)

IterNodesCost
057
197
2127
3147
4167
5177
done177
0810
11410
22410
33310
44210
54710
65610
77310
89210
910010
done10010
079
1129
2189
3279
4379
5469
6519
7609
8779
9969
101049
done1049
068
1138
2228
3348
4528
5668
6788
7908
81138
91238
101398
111418
done1418
068
1128
2218
3318
4588
51298
63068
78418
831728
done50008
01123
13923
214413
354711
4207611
done500011
0923
12323
27211
323311
48279
528359
done50009
0717
11117
21417
31617
41817
51917
done1917
068
1108
2138
3158
4178
5188
done188
0723
12123
2759
32909
48379
524099
done50009
068
1108
2138
3158
4178
5188
done188
068
1108
2138
3158
4178
5188
done188
079
199
done99
079
199
done99
0810
11210
21510
31710
41910
52010
done2010
0810
11210
21510
31710
41910
52010
done2010
0711
11311
22111
32911
43811
54411
64911
done4911
068
1108
2138
3158
4178
5188
done188
067
1125
2225
done225
068
188
done88
068
188
done88
079
1119
2149
3169
4189
5199
done199
079
1119
2149
3169
4189
5199
done199
068
1108
2138
3158
4178
5188
done188
068
1108
2138
3158
4178
5188
done188
079
1119
2149
3169
4189
5199
done199
079
1119
2149
3169
4189
5199
done199
068
1108
2138
3158
4178
5188
done188
068
1108
2138
3158
4178
5188
done188
068
1108
2138
3158
4178
5188
done188
068
1108
2138
3158
4178
5188
done188
057
197
2127
3147
4167
5177
done177
057
197
2127
3147
4167
5177
done177
057
197
2127
3147
4167
5177
done177
067
1127
2155
done155
0813
11711
24011
37611
412711
517211
626411
735611
858611
9101311
10342811
done500011
045
175
2135
3185
4225
done225
033
143
done43
01524
13422
210722
342422
497919
5144419
6193119
7209219
done209219
01523
13321
29321
333721
480619
5143219
6198519
7216319
done216319
01422
13320
28320
324720
459918
5115018
6181418
7198318
done198318
01321
13019
27419
322419
462018
5134018
6202518
7246118
8320818
done500018
01625
13724
29922
342522
499419
5147319
6197019
7211919
done211919
01624
13623
28521
333821
482919
5145819
6202119
7221719
done221719
01523
13622
27720
324920
462418
5118318
6185918
7202318
done202318
01422
13321
27219
321719
459918
5134218
6202818
7247918
8272118
9327118
done500018
01321
13119
27719
321519
464119
5151318
6239218
7401518
done500018
01220
13118
29718
338518
4131618
5340317
done500117
01220
12818
28018
330818
488218
5208518
done500118
02159
18755
241327
3330121
done500021
02159
18655
239325
3287225
done500025
01959
18455
238923
3305121
done500121
01759
16155
226121
3154221
done500121
01559
15953
224221
3143019
done500119
01341
12937
28137
330537
486037
5195937
6459537
done500037
01220
12818
28018
330618
486518
5194818
6457318
done500018
01359
13653
213619
374219
done500019
01220
12818
28018
330618
486518
5194818
6457318
done500018
01220
12818
28018
330618
486518
5194818
6457318
done500018
0914
12512
27312
323612
452912
585012
6109912
7296812
done500112
066
1136
2276
3496
4636
5786
61046
71316
81386
91446
101476
done1476
0915
11715
22315
32515
done2515
01018
12118
26118
314318
428018
542218
665718
786418
8306318
done500018
088
1148
2208
3228
done228
01018
12118
26118
314318
428018
542218
665718
786418
8306318
done500018
023
141
done41
0917
12017
26017
319617
449017
5161817
done500017
023
141
done41
0917
12017
26017
319617
449017
5161817
done500017
023
141
done41
0917
12017
26017
319617
449017
5161817
done500017
077
1137
2197
done197
01119
12717
27717
320117
449017
5113217
6305217
done500017
01327
13325
210225
346825
4149225
5307925
done500025
01220
12818
28018
330618
479618
5146118
6248518
done500018
0915
12211
27311
325011
466411
5131811
6327211
done500111
0915
12211
27311
325011
466411
5131811
6327211
done500111
0915
12211
27311
325011
466411
5131811
6327211
done500111
0917
12017
25417
315517
440817
5108117
6316617
done500017
01423
14121
211121
337821
4109721
5340821
done500021
01325
13723
212523
360623
4319023
done500023
069
1179
2629
31249
43339
55879
66609
76679
done6679
0915
11815
24315
39115
416412
520312
625812
731912
832112
done32112
0914
11714
23114
36914
413012
521412
626512
735112
836612
done36612
0813
11713
23013
35813
411111
519011
624311
730311
837111
938111
done38111
0712
11612
23612
39512
418111
529111
638111
748311
8111011
done500011
0712
11312
22312
35412
48712
513012
621012
740112
8141412
done500012
01235
14735
221719
3128613
done500013
01235
14635
219717
391617
done500117
01035
14435
219515
3112313
done500013
0825
11425
22425
35325
47625
510325
613725
717925
872325
9470225
done500025
0712
11312
22312
35212
47512
510212
613612
717812
872212
9465312
done500012
0835
12135
27413
339113
4224113
done500113
0712
11312
22312
35212
47512
510212
613612
717812
872212
9465312
done500012
0712
11312
22312
35212
47512
510212
613612
717812
872212
9465312
done500012
068
1148
2258
3358
4408
5468
6498
done498
044
184
2104
3114
done114
0715
11215
22615
34415
done4415
056
166
done66
0610
1910
22010
done2010
056
166
done66
067
1115
2265
3365
done365
045
155
done55
067
1115
2265
3365
done365
045
155
done55
055
185
done85
0611
11211
22011
34811
48311
512311
619011
728311
8144811
done500111
0817
11917
24317
312417
423817
531317
634417
736217
8177517
done500017
0712
11312
22412
36312
49312
510912
611812
712812
860612
done500012
079
1157
2307
3817
41477
51607
done1607
079
1157
2307
3817
41477
51607
done1607
045
155
done55
01015
13015
25015
310615
420115
551615
6213015
done500015
0915
11915
24815
313715
436415
587213
6231813
done500013
047
1117
2247
3407
4597
5757
6827
7847
done847
067
197
2107
done107
056
196
2116
3126
done126
056
166
done66
0817
13017
2919
32167
44897
512857
630107
done50007
0613
1713
done713
056
166
done66
0617
11417
2307
3687
41497
52967
65767
713577
847517
done50007
056
166
done66
056
166
done66
022
done22
044
184
2104
3114
done114
0815
11515
22415
33015
done3015
067
177
done77
0710
11010
21210
31310
done1310
067
177
done77
057
195
2155
3205
done205
056
166
done66
057
195
2155
3205
done205
056
166
done66
0712
11012
done1012
067
177
done77
067
177
done77
067
177
done77
044
162
282
done82
056
166
done66
044
162
282
done82
056
166
done66
0711
11211
done1211
056
166
done66
066
196
done96
056
166
done66
023
141
done41
045
155
done55
023
141
done41
045
155
done55
055
185
done85
045
155
done55
0611
1911
done911
056
166
done66
033
151
done51
033
151
done51
056
166
done66
056
166
done66
045
155
done55
079
1219
2309
3479
4889
52009
66049
724369
done50009
069
1119
2209
3379
4629
51039
61619
73299
816199
done50009
011
done11
011
done11
011
done11
01421
14019
210517
321513
450211
5104311
6190011
7306811
8440611
done500111
011
done11
011
done11
011
done11
011
done11
011
done11
011
done11
011
done11
011
done11

prune190.0ms

Filtered
110 candidates to 148 candidates (-34.5%)
Pruning

6 alts after pruning (6 fresh and 0 done)

PrunedKeptTotal
New1435148
Fresh617
Picked101
Done000
Total1506156

Merged error: 0.0b

Counts
156 → 6

localize11.0ms

Local error

Found 4 expressions with local error:

0.0b
(/ (* (/ y (+ x y)) x) (+ x y))
0.0b
(/ 1 (+ (+ x y) 1.0))
0.1b
(* (* 1 (/ (* (/ y (+ x y)) x) (+ x y))) (/ 1 (+ (+ x y) 1.0)))
8.6b
(* (/ y (+ x y)) x)

rewrite69.0ms

Algorithm
rewrite-expression-head
Rules
167×add-exp-log
88×prod-exp
79×*-un-lft-identity
65×add-cbrt-cube
57×div-exp
47×times-frac
39×add-sqr-sqrt
34×add-cube-cbrt
26×1-exp cbrt-unprod distribute-lft-out
24×associate-*r*
19×cbrt-undiv associate-*l*
12×pow1
10×rec-exp
associate-/r*
associate-/r/
flip3-+ pow-prod-down flip-+ div-inv associate-/l* add-log-exp
associate-*r/ associate-*l/
frac-2neg clear-num *-commutative unswap-sqr
frac-times pow-flip un-div-inv associate-/l/ inv-pow
Counts
4 → 188
Calls
4 calls:
16.0ms
(/ (* (/ y (+ x y)) x) (+ x y))
8.0ms
(/ 1 (+ (+ x y) 1.0))
24.0ms
(* (* 1 (/ (* (/ y (+ x y)) x) (+ x y))) (/ 1 (+ (+ x y) 1.0)))
10.0ms
(* (/ y (+ x y)) x)

series45.0ms

Counts
4 → 12
Calls
4 calls:
12.0ms
(/ (* (/ y (+ x y)) x) (+ x y))
6.0ms
(/ 1 (+ (+ x y) 1.0))
20.0ms
(* (* 1 (/ (* (/ y (+ x y)) x) (+ x y))) (/ 1 (+ (+ x y) 1.0)))
8.0ms
(* (/ y (+ x y)) x)

simplify7.9min

Counts
200 → 200
Iterations

Useful iterations: 1 (1.0ms)

IterNodesCost
057
197
2127
3147
4167
5177
done177
0810
11410
22410
33310
44210
54710
65610
77310
89210
910010
done10010
079
1129
2189
3279
4379
5469
6519
7609
8779
9969
101049
done1049
068
1138
2228
3348
4528
5668
6788
7908
81138
91238
101398
111418
done1418
068
1128
2218
3318
4588
51298
63068
78418
831728
done50008
01123
13923
214413
354711
4207611
done500011
0923
12323
27211
323311
48279
528359
done50009
0717
11117
21417
31617
41817
51917
done1917
068
1108
2138
3158
4178
5188
done188
0723
12123
2759
32909
48379
524099
done50009
068
1108
2138
3158
4178
5188
done188
068
1108
2138
3158
4178
5188
done188
079
199
done99
079
199
done99
0810
11210
21510
31710
41910
52010
done2010
0810
11210
21510
31710
41910
52010
done2010
0711
11311
22111
32911
43811
54411
64911
done4911
068
1108
2138
3158
4178
5188
done188
067
1125
2225
done225
068
188
done88
068
188
done88
079
1119
2149
3169
4189
5199
done199
079
1119
2149
3169
4189
5199
done199
068
1108
2138
3158
4178
5188
done188
068
1108
2138
3158
4178
5188
done188
079
1119
2149
3169
4189
5199
done199
079
1119
2149
3169
4189
5199
done199
068
1108
2138
3158
4178
5188
done188
068
1108
2138
3158
4178
5188
done188
068
1108
2138
3158
4178
5188
done188
068
1108
2138
3158
4178
5188
done188
057
197
2127
3147
4167
5177
done177
057
197
2127
3147
4167
5177
done177
057
197
2127
3147
4167
5177
done177
067
1127
2155
done155
0813
11711
24011
37611
412711
517211
626411
735611
858611
9101311
10342811
done500011
045
175
2135
3185
4225
done225
033
143
done43
01221
13117
29417
331317
485117
5182617
6408517
done500017
01221
13117
29417
331317
485117
5182617
6408517
done500017
01625
13522
211722
347122
4101719
5149019
6196819
7212719
done212719
01626
13822
211822
345122
4111219
5175319
6211419
done211419
01827
14122
212722
345622
4110219
5174719
6210919
done210919
01726
14023
211422
343322
4108019
5173019
6209119
done209119
01624
13421
210321
337821
486119
5149619
6204419
7222019
done222019
01625
13721
210421
335421
493419
5178019
6226519
7230419
done230419
01826
14021
211321
336421
492719
5177419
6224419
7228119
done228119
01725
13922
210021
334521
493219
5176719
6225619
7229519
done229519
01523
13420
29120
327220
464818
5120418
6186718
7204418
done204418
01524
13720
29220
325820
470118
5145218
6214218
7234418
done234418
01725
14020
210120
326920
470818
5146118
6213418
7230918
done230918
01624
13921
29020
324620
469718
5144718
6213518
7232418
done232418
01422
13119
27919
324319
465018
5137918
6206618
7241718
8311318
done500018
01423
13419
28019
323319
471418
5162518
6234718
7256218
8313018
done500018
01624
13719
28919
324219
471518
5162218
6233818
7254918
8260618
9315818
done500018
01523
13620
28119
322719
471318
5165318
6235318
7256018
8261718
9316718
done500118
01726
13824
210422
346722
4101819
5148219
6196019
7211019
done211019
01827
14125
211022
342522
4107519
5172919
6209519
done209519
01728
14126
211422
342622
4106419
5172019
6208319
done208319
01727
14025
210622
342722
4108219
5173519
6210019
done210019
01725
13723
29021
337421
484819
5147519
6202119
7221519
done221519
01826
14024
29621
333221
489119
5172819
6221119
7224919
done224919
01727
14025
210021
334021
490919
5174819
6223719
7227519
done227519
01726
13924
29221
334121
492919
5177519
6226219
7230019
done230019
01624
13722
28220
327020
462918
5118918
6183218
7199918
done199918
01725
14023
28820
324620
467818
5141418
6207418
7226718
done226718
01626
14024
29220
324820
467218
5141018
6208718
7226818
done226818
01625
13923
28420
325120
468818
5143718
6211018
7230918
done230918
01523
13421
27519
323119
461918
5134518
6204218
7248218
8272018
9327618
done500018
01624
13722
28219
321919
467918
5160518
6236318
7255518
8261218
9316218
done500018
01525
13723
28619
322319
469118
5162418
6236718
7257318
8263018
9318818
done500018
01524
13622
27919
322519
469318
5163418
6239618
7260618
8266318
9321818
done500018
01422
13219
27919
322219
459619
5146918
6232818
7395618
done500018
01523
13520
28419
322719
467919
5169518
6260618
7394118
done500018
01524
13521
28719
323019
467819
5169618
6260718
7393118
done500118
01423
13420
28519
322919
468019
5169318
6260818
7393518
done500118
01322
13518
211318
340018
4129218
5324417
done500017
01322
13418
210718
335118
4108218
5297518
done500018
02265
19257
240927
3281621
done500121
02265
18061
234029
3230523
done500023
02265
19157
238925
3241025
done500125
02265
17961
231927
3188227
done500025
02065
18957
238523
3257421
done500021
02065
17761
231025
3205923
done500023
01865
16657
225121
3130121
done500121
01865
15461
217923
389223
done500121
01865
16655
224021
3118821
done500121
01665
15259
215823
377423
done500021
01445
13337
29637
331537
485937
5182637
6409837
done500037
01322
13218
29518
331618
486518
5184518
6411518
done500018
01465
14353
218919
3106719
done500019
01322
13218
29518
331618
486518
5184518
6411518
done500018
01322
13218
29518
331618
486518
5184518
6411518
done500018
0811
1187
2397
3747
4907
51067
61087
done1087
069
1169
2519
31189
42519
55729
67779
77979
87999
done7999
01431
13329
29829
334929
477929
5135029
6172329
done500029
01322
13020
28420
326120
452720
581920
6102620
7307420
done500120
01633
14129
212625
337525
4109425
5227825
6348325
done500125
01526
13622
210318
328118
478818
5137618
6190518
done500018
01221
13015
28611
320311
454611
5101111
6149811
7424811
done500011
01221
13015
28611
320311
454611
5101111
6149811
7424811
done500011
01221
13015
28611
320311
454611
5101111
6149811
7424811
done500011
01530
13625
210725
340625
4131525
5263925
6444625
done500125
01423
13318
29618
331518
478718
5131418
6197318
done500118
01118
12711
26411
321411
454711
5101011
6152711
7436111
done500111
01118
12711
26411
321411
454711
5101011
6152711
7436111
done500111
01118
12711
26411
321411
454711
5101011
6152711
7436111
done500111
01429
13525
210625
340425
4131225
5264725
6448525
done500125
01322
13218
29518
331618
479818
5134118
6198818
done500018
01017
12611
26311
321311
454411
5102311
6153111
7425711
done500111
01017
12611
26311
321311
454411
5102311
6153111
7425711
done500111
01017
12611
26311
321311
454411
5102311
6153111
7425711
done500111
0915
12111
25011
313511
427011
536211
646511
7153011
done500011
0915
12111
25011
313511
427011
536211
646511
7153011
done500011
01525
14521
212621
338821
4108321
5326721
done500021
01427
14123
213123
352423
4249323
done500023
01119
12719
26317
322717
468117
5152117
6335717
done500117
0915
12111
25011
313511
427011
536211
646511
7153011
done500011
01117
12813
28813
323613
442313
566113
6108513
7183913
done500013
022
151
done51
077
1117
2177
done177
088
1147
2247
3267
4327
5377
done377
099
1178
2247
3307
4367
5417
done417
088
1187
2257
3317
4337
5397
6447
done447
088
1148
2208
3228
done228
01123
13719
21219
34699
423479
done50019
0917
11517
22117
done2117
088
1148
2208
3228
done228
0923
12223
2449
3839
41239
53219
610599
done50019
088
1148
2208
3228
done228
088
1148
2208
3228
done228
022
151
done51
066
1136
2276
3496
4636
5786
61046
71316
81386
91446
101476
done1476
01119
12317
23815
34415
done4415
099
1158
2218
done218
01012
11810
2268
3278
done278
099
1158
2218
done218
047
183
2121
done121
088
1147
2207
done207
047
183
2121
done121
088
1147
2207
done207
047
183
2121
done121
088
1147
2207
done207
01016
11815
22415
done2415
099
1158
2218
done218
099
1158
2218
done218
099
1158
2218
done218
034
151
done51
088
1147
2207
done207
034
151
done51
088
1147
2207
done207
034
151
done51
088
1147
2207
done207
0915
11715
22315
32515
done2515
088
1148
2208
3228
done228
088
1148
2208
3228
done228
088
1148
2208
3228
done228
023
141
done41
077
1137
2197
done197
023
141
done41
077
1137
2197
done197
023
141
done41
077
1137
2197
done197
077
1137
2197
done197
077
1135
2215
done215
0915
11715
22315
32515
done2515
088
1148
2208
3228
done228
023
141
done41
023
141
done41
023
141
done41
088
1147
2207
done207
088
1147
2207
done207
077
1135
2215
done215
01011
12711
25211
310911
425011
571311
6264311
done500011
0913
12313
25713
314313
445813
5130213
done500013
0915
11815
24315
39115
416412
520312
625812
731912
832112
done32112
0914
11714
23114
36914
413012
521412
626512
735112
836612
done36612
0813
11713
23013
35813
411111
519011
624311
730311
837111
938111
done38111
0712
11612
23612
39512
418111
529111
638111
748311
8111011
done500011
0712
11312
22312
35412
48712
513012
621012
740112
8141412
done500012
01235
14735
221719
3128613
done500013
01235
14635
219717
391617
done500117
01035
14435
219515
3112313
done500013
0825
11425
22425
35325
47625
510325
613725
717925
872325
9470225
done500025
0712
11312
22312
35212
47512
510212
613612
717812
872212
9465312
done500012
0835
12135
27413
339113
4224113
done500113
0712
11312
22312
35212
47512
510212
613612
717812
872212
9465312
done500012
0712
11312
22312
35212
47512
510212
613612
717812
872212
9465312
done500012
068
1148
2258
3358
4408
5468
6498
done498
044
184
2104
3114
done114
0715
11215
22615
34415
done4415
056
166
done66
0610
1910
22010
done2010
056
166
done66
067
1115
2265
3365
done365
045
155
done55
067
1115
2265
3365
done365
045
155
done55
055
185
done85
0611
11211
22011
34811
48311
512311
619011
728311
8144811
done500111
0817
11917
24317
312417
423817
531317
634417
736217
8177517
done500017
0712
11312
22412
36312
49312
510912
611812
712812
860612
done500012
079
1157
2307
3817
41477
51607
done1607
079
1157
2307
3817
41477
51607
done1607
045
155
done55
01015
13015
25015
310615
420115
551615
6213015
done500015
0915
11915
24815
313715
436415
587213
6231813
done500013
047
1117
2247
3407
4597
5757
6827
7847
done847
011
done11
011
done11
011
done11
01421
14019
210517
321513
450211
5104311
6190011
7306811
8440611
done500111
011
done11
011
done11
079
1167
2317
3597
4807
51327
62157
72917
83447
94077
105267
119537
1212907
done12907
011
done11
011
done11
011
done11
011
done11
011
done11

prune206.0ms

Filtered
125 candidates to 200 candidates (-60.0%)
Pruning

7 alts after pruning (6 fresh and 1 done)

PrunedKeptTotal
New1991200
Fresh055
Picked011
Done000
Total1997206

Merged error: 0b

Counts
206 → 7

regimes102.0ms

Accuracy

0% (0.1b remaining)

Error of 0.1b against oracle of 0.0b and baseline of 0.1b

bsearch0.0ms

simplify2.0ms

Iterations

Useful iterations: 1 (1.0ms)

IterNodesCost
01221
11919
done1919

end0.0ms

sample810.0ms

Algorithm
intervals
Results
308.0ms8000×body80valid

Profiling

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