Details

Time bar (total: 11.1min)

sample29.0ms

Algorithm
intervals
Results
17.0ms256×body80valid

simplify3.0ms

Counts
1 → 1
Iterations

Useful iterations: 0 (1.0ms)

IterNodesCost
01012
11112
done1112

prune4.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

PrunedKeptTotal
New011
Fresh011
Picked000
Done000
Total022

Merged error: 35.5b

Counts
2 → 1

localize12.0ms

Local error

Found 2 expressions with local error:

0.6b
(/ (log (sqrt (+ (* re re) (* im im)))) (log 10.0))
32.9b
(sqrt (+ (* re re) (* im im)))

rewrite17.0ms

Algorithm
rewrite-expression-head
Rules
24×times-frac
22×log-pow
20×pow1
16×add-sqr-sqrt
15×add-cube-cbrt *-un-lft-identity
sqrt-pow1 pow1/2 associate-/l*
add-exp-log sqrt-div associate-/r* add-cbrt-cube
sqrt-prod
log-div flip3-+ div-sub flip-+ add-log-exp
cbrt-undiv rem-sqrt-square frac-2neg div-exp clear-num div-inv
Counts
2 → 63
Calls
2 calls:
9.0ms
(/ (log (sqrt (+ (* re re) (* im im)))) (log 10.0))
6.0ms
(sqrt (+ (* re re) (* im im)))

series47.0ms

Counts
2 → 6
Calls
2 calls:
24.0ms
(/ (log (sqrt (+ (* re re) (* im im)))) (log 10.0))
23.0ms
(sqrt (+ (* re re) (* im im)))

simplify33.3s

Counts
69 → 69
Iterations

Useful iterations: 1 (1.0ms)

IterNodesCost
079
189
done89
079
189
done89
0819
1919
done919
079
189
done89
0826
11016
22110
33410
44210
55210
67310
713410
835010
9129510
done500010
0818
1109
done109
079
189
done89
079
189
done89
079
189
done89
022
141
done41
068
178
done78
0912
12712
2648
31198
42618
56978
623128
done50008
01024
13220
28418
317716
430916
572316
6197216
done500016
0816
12116
24412
3908
42158
55768
614838
done50018
068
1118
2188
3338
4588
5998
61578
73258
815708
done50008
033
161
done61
079
189
done89
079
189
done89
01214
11514
21614
done1614
01113
11513
21713
31813
done1813
01113
11213
done1213
01438
12438
25616
312314
420214
531814
677714
7336514
done500014
01227
11327
done1327
01113
11213
done1213
01238
12038
23614
37414
414114
520314
632914
782314
8356214
done500014
01113
11213
done1213
01113
11213
done1213
0810
1910
done910
033
done33
01316
13116
26812
311912
426112
569312
6230812
done500012
01428
13624
29022
318420
431520
572820
6198920
done500020
01220
12520
24816
39412
421912
558012
6149312
done500112
01012
11512
22212
33712
46212
510312
616112
732912
8160412
done500012
033
151
done51
0911
11011
done1011
069
189
done89
01012
11112
done1112
055
done55
01012
11112
done1112
033
151
done51
0911
11011
done1011
023
141
done41
01012
11112
done1112
069
1109
done109
01113
11213
done1213
055
175
done75
01113
11213
done1213
023
141
done41
01012
11112
done1112
045
191
done91
0911
11011
done1011
0811
1159
2209
3259
4299
done299
01012
11112
done1112
077
1125
2155
done155
01012
11112
done1112
045
191
done91
0911
11011
done1011
01123
11621
22221
32721
done2721
01113
11213
done1213
01429
12129
23029
33629
done3629
01214
11314
done1314
01325
11625
21825
31925
done1925
01214
11314
done1314
01123
11621
22221
32721
done2721
01113
11213
done1213
01012
11310
21510
done1510
01113
11213
done1213
01318
11618
done1618
01214
11314
done1314
01214
11314
done1314
01214
11314
done1314
01012
11310
21510
done1510
01113
11213
done1213
023
141
done41
01012
11112
done1112
069
1109
done109
01113
11213
done1213
055
175
done75
01113
11213
done1213
023
141
done41
01012
11112
done1112
044
164
done64
01012
11112
done1112
0911
1129
2149
done149
01217
11517
done1517
01113
11213
done1213
0911
1129
2149
done149
0911
11011
done1011
01012
11112
done1112
0911
11011
done1011
01113
11213
done1213
01113
11213
done1213
01012
11112
done1112
011
done11
011
done11
033
152
done52
088
1117
done115
0910
1198
2285
3455
4485
5495
done495
01010
1209
2308
3528
4948
51538
61868
72018
82238
92378
done2378

prune172.0ms

Filtered
46 candidates to 69 candidates (-50.0%)
Pruning

13 alts after pruning (13 fresh and 0 done)

PrunedKeptTotal
New561369
Fresh000
Picked101
Done000
Total571370

Merged error: 8.2b

Counts
70 → 13

localize15.0ms

Local error

Found 4 expressions with local error:

0.6b
(/ (log (* (* (cbrt (sqrt (+ (* re re) (* im im)))) (cbrt (sqrt (+ (* re re) (* im im))))) (cbrt (sqrt (+ (* re re) (* im im)))))) (log 10.0))
32.9b
(sqrt (+ (* re re) (* im im)))
32.9b
(sqrt (+ (* re re) (* im im)))
32.9b
(sqrt (+ (* re re) (* im im)))

rewrite60.0ms

Algorithm
rewrite-expression-head
Rules
126×pow1
94×log-pow
72×times-frac
60×sqrt-div
54×cbrt-div
45×pow1/3 pow-prod-up
34×add-sqr-sqrt
31×add-cube-cbrt *-un-lft-identity
30×flip3-+ pow-plus flip-+
28×frac-times
26×log-div div-sub
25×pow-prod-down
18×associate-/l*
15×pow-sqr
14×associate-*l/
10×pow2
sqrt-prod
associate-*r/
add-exp-log add-cbrt-cube
pow3
associate-/r* add-log-exp
rem-sqrt-square sqrt-pow1 pow1/2
cbrt-undiv frac-2neg div-exp clear-num div-inv
Counts
4 → 177
Calls
4 calls:
33.0ms
(/ (log (* (* (cbrt (sqrt (+ (* re re) (* im im)))) (cbrt (sqrt (+ (* re re) (* im im))))) (cbrt (sqrt (+ (* re re) (* im im)))))) (log 10.0))
5.0ms
(sqrt (+ (* re re) (* im im)))
4.0ms
(sqrt (+ (* re re) (* im im)))
5.0ms
(sqrt (+ (* re re) (* im im)))

series43.0ms

Counts
4 → 12
Calls
4 calls:
22.0ms
(/ (log (* (* (cbrt (sqrt (+ (* re re) (* im im)))) (cbrt (sqrt (+ (* re re) (* im im))))) (cbrt (sqrt (+ (* re re) (* im im)))))) (log 10.0))
7.0ms
(sqrt (+ (* re re) (* im im)))
7.0ms
(sqrt (+ (* re re) (* im im)))
7.0ms
(sqrt (+ (* re re) (* im im)))

simplify5.8min

Counts
189 → 189
Iterations

Useful iterations: 1 (1.0ms)

IterNodesCost
079
189
done89
079
189
done89
0819
1919
done919
079
189
done89
0826
11016
22110
33410
44210
55210
67310
713410
835010
9129510
done500010
0818
1109
done109
079
189
done89
079
189
done89
079
189
done89
022
141
done41
068
178
done78
0912
12712
2648
31198
42618
56978
623128
done50008
01024
13220
28418
317716
430916
572316
6197216
done500016
0816
12116
24412
3908
42158
55768
614838
done50018
068
1118
2188
3338
4588
5998
61578
73258
815708
done50008
033
161
done61
079
189
done89
079
189
done89
079
189
done89
079
189
done89
0819
1919
done919
079
189
done89
0826
11016
22110
33410
44210
55210
67310
713410
835010
9129510
done500010
0818
1109
done109
079
189
done89
079
189
done89
079
189
done89
022
141
done41
068
178
done78
0912
12712
2648
31198
42618
56978
623128
done50008
01024
13220
28418
317716
430916
572316
6197216
done500016
0816
12116
24412
3908
42158
55768
614838
done50018
068
1118
2188
3338
4588
5998
61578
73258
815708
done50008
033
161
done61
079
189
done89
079
189
done89
079
189
done89
079
189
done89
0819
1919
done919
079
189
done89
0826
11016
22110
33410
44210
55210
67310
713410
835010
9129510
done500010
0818
1109
done109
079
189
done89
079
189
done89
079
189
done89
022
141
done41
068
178
done78
0912
12712
2648
31198
42618
56978
623128
done50008
01024
13220
28418
317716
430916
572316
6197216
done500016
0816
12116
24412
3908
42158
55768
614838
done50018
068
1118
2188
3338
4588
5998
61578
73258
815708
done50008
033
161
done61
079
189
done89
079
189
done89
01535
12235
22717
33414
45014
57314
612414
725214
868514
9239614
done500014
01434
12234
22816
33613
45413
58313
614413
729613
880413
9277113
done500013
01434
11934
22316
33013
44513
56513
611113
724613
869713
9251813
done500113
017101
131101
27819
319714
456414
5250814
done500014
01569
12069
22433
33127
44627
56627
611027
723727
866227
9243527
done500027
01434
11934
22316
33013
44513
56513
610913
723613
866413
9239613
done500013
015101
127101
25817
313814
438414
5141814
done500014
01434
11934
22316
33013
44513
56513
610913
723613
866413
9239613
done500013
01434
11934
22316
33013
44513
56513
610913
723613
866413
9239613
done500013
01131
11631
22313
33310
45610
58010
613410
729910
883610
9316110
done500110
033
done33
01645
13845
27815
313512
428712
573512
6243312
done500112
01781
14369
29825
319520
434020
576720
6205220
done500120
02149
15649
211437
322226
449626
5133926
6399426
done500126
02065
15357
211653
322834
438334
591634
6240234
done500034
02149
15549
211337
322133
449526
5133926
6400126
done500026
02065
15257
211553
322849
438234
591634
6239634
done500034
02153
15753
211541
322333
449426
5132326
6396326
done500026
02049
15445
211743
322741
438134
591534
6238334
done500034
02149
15749
211737
322133
449626
5133226
6399526
done500026
02065
15457
211753
322849
438134
591634
6238634
done500034
02153
15553
211541
322133
449526
5133426
6400526
done500026
02049
15245
211343
322641
438034
591434
6239834
done500034
02153
15653
211841
322426
449926
5132826
6397526
done500026
02049
15345
211843
322934
438334
591534
6240234
done500034
01557
13257
25619
310612
424212
561612
6157012
done500112
01333
12233
23315
35512
49512
515612
625812
754912
8224712
done500012
01941
14541
28933
315033
429526
575126
6237826
done500026
01655
14047
29425
318923
432623
574523
6201123
done500023
02445
16045
212537
324533
451933
5135633
6405133
done500133
01939
15035
210733
321231
436531
589831
6237631
done500131
02445
16045
212537
323933
451733
5134733
6403233
done500033
01939
15035
210733
321331
436631
589831
6237931
done500031
01849
13849
26541
311533
424126
561326
6153326
done500126
01223
11923
22815
34615
47515
511915
618215
735015
8162615
done500115
01941
14341
28733
314433
428526
571926
6237626
done500026
01655
14047
29425
318923
432623
574523
6201123
done500023
02445
16045
212537
324533
451733
5135333
6404333
done500033
01939
15035
210733
321231
436531
589831
6237631
done500131
02445
16045
212537
323933
451633
5135033
6402533
done500033
01939
15035
210733
321331
436631
589831
6237931
done500031
01849
13649
26541
311733
424326
561126
6152426
done500026
01223
11923
22815
34615
47515
511915
618215
735015
8162615
done500115
01937
14437
28833
314726
428826
571226
6236626
done500126
01529
13725
29123
318421
431521
572621
6198921
done500021
01841
13741
26437
311626
424226
561126
6152826
done500026
01113
11613
22313
33813
46313
510413
616013
732813
8164513
done500113
01941
14441
28833
314526
428426
571226
6232426
done500026
01655
14047
29425
318923
432623
574523
6201123
done500023
02445
16045
212337
323933
450833
5134933
6403833
done500133
01939
15035
210733
321231
436531
589831
6237631
done500131
02445
16045
212537
323933
451333
5134933
6403133
done500033
01939
15035
210733
321331
436631
589831
6237931
done500031
01849
13749
26641
311826
424426
561326
6151926
done500026
01223
11923
22815
34615
47515
511915
618215
735015
8162615
done500115
01937
14337
28733
314833
429126
572826
6239426
done500026
01529
13725
29123
318421
431521
572621
6198921
done500021
01841
13641
26337
311533
424126
561326
6152826
done500026
01113
11613
22313
33813
46313
510413
616013
732813
8164513
done500113
01937
14537
28933
314433
428326
571326
6233226
done500126
01529
13725
29123
318421
431521
572621
6198921
done500021
01841
13841
26737
311733
424326
560726
6152526
done500026
01113
11613
22313
33813
46313
510413
616013
732813
8164513
done500113
057
1111
done111
01012
11112
done1112
0813
1159
2179
done179
01113
11213
done1213
079
1125
2145
done145
01113
11213
done1213
057
1111
done111
01012
11112
done1112
047
1101
done101
01113
11213
done1213
0813
1169
done169
01214
11314
done1314
079
1135
done135
01214
11314
done1314
047
1101
done101
01113
11213
done1213
045
181
done81
01113
11213
done1213
0811
1149
done149
01214
11314
done1314
077
1115
done115
01214
11314
done1314
045
181
done81
01113
11213
done1213
047
1101
done101
01113
11213
done1213
0813
1169
done169
01214
11314
done1314
079
1135
done135
01214
11314
done1314
047
1101
done101
01113
11213
done1213
067
1143
2191
done191
01012
11112
done1112
0913
1189
2209
done209
01113
11213
done1213
089
1157
2205
3225
4235
done235
01113
11213
done1213
067
1143
2191
done191
01012
11112
done1112
057
1121
done121
01113
11213
done1213
0913
1189
done189
01214
11314
done1314
089
1155
done155
01214
11314
done1314
057
1121
done121
01113
11213
done1213
033
151
done51
01230
11720
23014
34514
46014
58014
612613
724913
867413
9244513
done500013
069
189
done89
01331
11821
23115
34615
46315
58315
612714
725014
869214
9244414
done500014
055
done55
01331
11821
23115
34615
46315
58315
612714
725014
869214
9244414
done500014
033
151
done51
01230
11720
23014
34514
46014
58014
612613
724913
867413
9244513
done500013
023
141
done41
01333
11833
22215
32912
44412
56412
610812
723212
866812
9243712
done500012
069
1109
done109
01434
11934
22316
33013
44513
56513
610913
723613
866413
9239913
done500113
055
175
done75
01434
11934
22316
33013
44513
56513
610913
723613
866413
9239913
done500113
023
141
done41
01333
11833
22215
32912
44412
56412
610812
723212
866812
9243712
done500012
023
141
done41
01333
11833
22215
32912
44412
56412
610812
723212
866812
9243712
done500012
069
1109
done109
01434
11934
22316
33013
44513
56513
610913
723613
866413
9239913
done500113
055
175
done75
01434
11934
22316
33013
44513
56513
610913
723613
866413
9239913
done500113
023
141
done41
01333
11833
22215
32912
44412
56412
610812
723212
866812
9243712
done500012
033
151
done51
01113
11213
done1213
069
189
done89
01214
11314
done1314
055
done55
01214
11314
done1314
033
151
done51
01113
11213
done1213
047
1101
done101
01113
11213
done1213
0813
1169
done169
01214
11314
done1314
079
1135
done135
01214
11314
done1314
047
1101
done101
01113
11213
done1213
045
181
done81
01113
11213
done1213
0811
1149
done149
01214
11314
done1314
077
1115
done115
01214
11314
done1314
045
181
done81
01113
11213
done1213
047
1101
done101
01113
11213
done1213
0813
1169
done169
01214
11314
done1314
079
1135
done135
01214
11314
done1314
047
1101
done101
01113
11213
done1213
057
1121
done121
01113
11213
done1213
0913
1189
done189
01214
11314
done1314
089
1155
done155
01214
11314
done1314
057
1121
done121
01113
11213
done1213
023
141
done41
01333
11833
22215
32912
44412
56412
610812
723212
866812
9243712
done500012
069
1109
done109
01434
11934
22316
33013
44513
56513
610913
723613
866413
9239913
done500113
055
175
done75
01434
11934
22316
33013
44513
56513
610913
723613
866413
9239913
done500113
023
141
done41
01333
11833
22215
32912
44412
56412
610812
723212
866812
9243712
done500012
01465
12363
23327
34521
45721
57121
611021
722421
860421
9218221
done500121
01434
11934
22316
33013
44313
55913
69813
721313
857913
9215513
done500113
01771
12871
24135
35429
46729
58329
612229
723829
860729
9217129
done500029
01535
12035
22417
33114
44414
56014
610114
721714
859114
9215714
done500014
01667
12367
22931
33725
45025
56625
610525
722025
859125
9217825
done500025
01535
12035
22417
33114
44414
56014
610114
721714
859114
9215714
done500014
01465
12363
23327
34521
45721
57121
611021
722421
860421
9218221
done500121
01434
11934
22316
33013
44313
55913
69813
721313
857913
9215513
done500113
01333
12031
22613
33310
44510
55910
610010
721010
858010
9215310
done500010
01434
11934
22316
33013
44313
55913
69813
721313
857913
9215513
done500113
01639
12339
22721
33418
44718
56318
610218
721818
859218
9216518
done500018
01535
12035
22417
33114
44414
56014
610114
721714
859114
9215714
done500014
01535
12035
22417
33114
44414
56014
610114
721714
859114
9215714
done500014
01535
12035
22417
33114
44414
56014
610114
721714
859114
9215714
done500014
01333
12031
22613
33310
44510
55910
610010
721010
858010
9215310
done500010
01434
11934
22316
33013
44313
55913
69813
721313
857913
9215513
done500113
023
141
done41
01333
11833
22215
32912
44412
56412
610812
723212
866812
9243712
done500012
069
1109
done109
01434
11934
22316
33013
44513
56513
610913
723613
866413
9239913
done500113
055
175
done75
01434
11934
22316
33013
44513
56513
610913
723613
866413
9239913
done500113
023
141
done41
01333
11833
22215
32912
44412
56412
610812
723212
866812
9243712
done500012
044
164
done64
01333
11833
22215
32912
44412
56212
610312
722012
860712
9221612
done500112
01232
11930
22512
3329
4469
5679
61159
72399
86499
923569
done50009
01538
12238
22620
33317
45317
58217
614117
729417
883717
9288917
done500017
01434
11934
22316
33013
44513
56513
610913
723613
866413
9239913
done500113
01232
11930
22512
3329
4469
5679
61159
72399
86499
923569
done50009
01012
11112
done1112
01113
11213
done1213
01113
11213
done1213
01113
11213
done1213
01012
11112
done1112
01113
11213
done1213
01230
11720
23014
34514
46014
57814
612113
724013
861913
9224213
done500013
01333
11833
22215
32912
44412
56212
610312
722012
860712
9221612
done500112
01333
11833
22215
32912
44412
56212
610312
722012
860712
9221612
done500112
01113
11213
done1213
01113
11213
done1213
01113
11213
done1213
01113
11213
done1213
01113
11213
done1213
01333
11833
22215
32912
44412
56212
610312
722012
860712
9221612
done500112
01434
11934
22316
33013
44313
55913
69813
720713
856813
9215513
done500013
01434
11934
22316
33013
44313
55913
69813
720713
856813
9215513
done500013
01333
11833
22215
32912
44412
56212
610312
722012
860712
9221612
done500112
011
done11
011
done11
033
152
done52
011
done11
011
done11
033
152
done52
011
done11
011
done11
033
152
done52
088
1117
done115
0910
1198
2285
3455
4485
5495
done495
01010
1209
2308
3528
4948
51538
61868
72018
82238
92378
done2378

prune315.0ms

Filtered
99 candidates to 189 candidates (-90.9%)
Pruning

14 alts after pruning (13 fresh and 1 done)

PrunedKeptTotal
New1845189
Fresh4812
Picked011
Done000
Total18814202

Merged error: 8.2b

Counts
202 → 14

localize15.0ms

Local error

Found 4 expressions with local error:

0.2b
(/ 3 (/ (log 10.0) (log (cbrt (sqrt (+ (* re re) (* im im)))))))
0.5b
(cbrt (sqrt (+ (* re re) (* im im))))
0.6b
(/ (log 10.0) (log (cbrt (sqrt (+ (* re re) (* im im))))))
32.9b
(sqrt (+ (* re re) (* im im)))

rewrite33.0ms

Algorithm
rewrite-expression-head
Rules
172×times-frac
84×add-sqr-sqrt
83×add-cube-cbrt *-un-lft-identity
68×log-pow
52×pow1
29×associate-/r*
22×pow1/3
11×add-exp-log add-cbrt-cube
associate-/l*
cbrt-prod sqrt-prod div-inv
cbrt-undiv sqrt-div div-exp add-log-exp
cbrt-div frac-2neg flip3-+ clear-num flip-+
rem-sqrt-square sqrt-pow1 pow1/2 associate-/r/
Counts
4 → 186
Calls
4 calls:
9.0ms
(/ 3 (/ (log 10.0) (log (cbrt (sqrt (+ (* re re) (* im im)))))))
5.0ms
(cbrt (sqrt (+ (* re re) (* im im))))
5.0ms
(/ (log 10.0) (log (cbrt (sqrt (+ (* re re) (* im im))))))
5.0ms
(sqrt (+ (* re re) (* im im)))

series122.0ms

Counts
4 → 12
Calls
4 calls:
38.0ms
(/ 3 (/ (log 10.0) (log (cbrt (sqrt (+ (* re re) (* im im)))))))
25.0ms
(cbrt (sqrt (+ (* re re) (* im im))))
52.0ms
(/ (log 10.0) (log (cbrt (sqrt (+ (* re re) (* im im))))))
7.0ms
(sqrt (+ (* re re) (* im im)))

simplify1.6min

Counts
198 → 198
Iterations

Useful iterations: 1 (1.0ms)

IterNodesCost
079
189
done89
079
189
done89
0819
1919
done919
079
189
done89
0826
11016
22110
33410
44210
55210
67310
713410
835010
9129510
done500010
0818
1109
done109
079
189
done89
079
189
done89
079
189
done89
022
141
done41
068
178
done78
0912
12712
2648
31198
42618
56978
623128
done50008
01024
13220
28418
317716
430916
572316
6197216
done500016
0816
12116
24412
3908
42158
55768
614838
done50018
068
1118
2188
3338
4588
5998
61578
73258
815708
done50008
033
161
done61
079
189
done89
079
189
done89
01315
11615
21715
done1715
01214
11614
21814
31914
done1914
01214
11314
done1314
01541
12541
25717
312415
420215
532015
677915
7335715
done500015
01329
11429
done1429
01214
11314
done1314
01341
12141
23715
37515
414015
520515
633115
782415
8354415
done500015
01214
11314
done1314
01214
11314
done1314
033
done33
0911
11011
done1011
033
161
done61
01012
11112
done1112
023
141
done41
01113
11213
done1213
01225
11725
done1725
01214
11314
done1314
01113
11413
done1413
01214
11314
done1314
023
141
done41
01113
11213
done1213
069
189
2109
3119
done119
01113
11213
done1213
069
1107
2167
3217
done217
01214
11314
done1314
01531
12231
23131
33731
done3731
01315
11415
done1415
01419
11719
21919
32019
done2019
01315
11415
done1415
069
1107
2167
3217
done217
01214
11314
done1314
055
done55
01113
11213
done1213
055
173
293
done93
01214
11314
done1314
01427
11727
done1727
01315
11415
done1415
01315
11415
done1415
01315
11415
done1415
055
173
293
done93
01214
11314
done1314
033
161
done61
01012
11112
done1112
023
141
done41
01113
11213
done1213
01225
11725
done1725
01214
11314
done1314
01113
11413
done1413
01214
11314
done1314
023
141
done41
01113
11213
done1213
01012
11312
done1312
01113
11213
done1213
044
done44
044
162
282
done82
01326
11626
done1626
01214
11314
done1314
044
162
282
done82
01113
11213
done1213
01214
11314
done1314
01214
11314
done1314
01113
11213
done1213
0810
1910
done910
0810
1910
done910
0920
11020
done1020
0810
1910
done910
0919
11110
done1110
0810
1910
done910
0810
1910
done910
0810
1910
done910
033
152
done52
079
189
done89
0810
1910
done910
0810
1910
done910
022
141
done41
079
189
done89
01013
12813
2659
31189
42589
56839
623219
done50009
01125
13321
28719
318017
431217
572617
6198317
done500117
0917
12217
24313
3899
42149
55859
614949
done50009
079
1129
2199
3349
4599
51009
61569
73249
816539
done50009
0921
11021
done1021
0810
1910
done910
0929
11129
21311
3188
4248
5348
6558
71208
83408
912708
done50008
0810
1910
done910
0810
1910
done910
01618
12318
23118
34418
44818
55618
67118
79718
810618
done10618
01517
12117
22617
33317
44617
55017
65817
77317
89917
910817
done10817
01416
12016
23016
33916
45116
57016
67916
79016
810816
912816
1013416
done13416
01416
11716
22216
33014
44214
56914
613614
729714
886514
9367314
done500014
01947
13643
29319
331317
496917
5244417
done500117
01747
13543
27717
322617
475017
5205017
6377517
done500017
01533
11833
22133
32233
42433
52633
62733
done2733
01416
11716
22016
32116
42316
52516
62616
done2616
01547
12547
26317
323617
494817
5262617
6459217
done500117
01416
11716
22016
32116
42316
52516
62616
done2616
01416
11716
22016
32116
42316
52516
62616
done2616
022
131
done31
01214
11514
done1514
01735
12435
23335
33935
done3935
01517
11617
done1617
01620
11920
22120
32220
done2220
01517
11617
done1617
079
1137
2207
3457
4857
5977
done977
01315
11615
21915
32015
42215
52415
62515
done2515
069
1127
2215
3425
4565
done565
01416
11716
22016
32116
42316
52516
62616
done2616
01631
12531
24029
38729
420029
526329
630729
done30729
01517
11817
22117
32217
42417
52617
62717
done2717
01519
12219
23117
35717
410417
511317
done11317
01517
11817
22117
32217
42417
52617
62717
done2717
069
1127
2215
3425
4565
done565
01416
11716
22016
32116
42316
52516
62616
done2616
01015
11615
23415
37815
412415
514415
614915
715015
done15015
01416
11716
22016
32116
42316
52516
62616
done2616
01015
11813
24113
311613
414713
517113
617313
done17313
01517
11817
22117
32217
42417
52617
62717
done2717
01937
13037
26637
315737
428537
537937
641837
742837
done42837
01618
11918
22218
32318
42518
52718
62818
done2818
01825
12525
24325
38725
413325
515325
615825
715925
done15925
01618
11918
22218
32318
42518
52718
62818
done2818
01015
11813
24113
311613
414713
517113
617313
done17313
01517
11817
22117
32217
42417
52617
62717
done2717
0911
11311
22211
33211
44211
54611
64811
74911
done4911
01416
11716
22016
32116
42316
52516
62616
done2616
0911
1159
2269
3489
4539
5579
6639
7659
done659
01517
11817
22117
32217
42417
52617
62717
done2717
01833
12533
24033
36833
410433
512633
613633
714533
done14533
01618
11918
22218
32318
42518
52718
62818
done2818
01721
12221
23121
34121
45121
55521
65721
75821
done5821
01618
11918
22218
32318
42518
52718
62818
done2818
0911
1159
2269
3489
4539
5579
6639
7659
done659
01517
11817
22117
32217
42417
52617
62717
done2717
079
1137
2207
3457
4857
5977
done977
01315
11615
21915
32015
42215
52415
62515
done2515
069
1127
2215
3425
4565
done565
01416
11716
22016
32116
42316
52516
62616
done2616
01631
12531
24029
38729
420029
526329
630729
done30729
01517
11817
22117
32217
42417
52617
62717
done2717
01519
12219
23117
35717
410417
511317
done11317
01517
11817
22117
32217
42417
52617
62717
done2717
069
1127
2215
3425
4565
done565
01416
11716
22016
32116
42316
52516
62616
done2616
057
195
2155
3205
done205
01416
11716
22016
32116
42316
52516
62616
done2616
068
188
2108
3118
done118
01315
11815
22113
33013
43913
54113
done4113
01632
11932
done1932
01517
11617
done1617
01517
11617
done1617
01517
11617
done1617
066
1104
2134
3224
4274
done274
01315
11615
21915
32015
42215
52415
62515
done2515
056
194
2142
3162
4202
done202
01416
11716
22016
32116
42316
52516
62616
done2616
01528
12228
22926
34526
47126
59626
611526
done11526
01517
11817
22117
32217
42417
52617
62717
done2717
01416
11916
22214
33114
44014
54214
done4214
01517
11817
22117
32217
42417
52617
62717
done2717
056
194
2142
3162
4202
done202
01416
11716
22016
32116
42316
52516
62616
done2616
0912
11312
22112
33412
44212
54812
65112
done5112
01416
11716
22016
32116
42316
52516
62616
done2616
0912
11510
22810
35510
46710
57910
68410
done8410
01517
11817
22117
32217
42417
52617
62717
done2717
01834
12734
24834
37934
410534
513834
616234
717234
817334
done17334
01618
11918
22218
32318
42518
52718
62818
done2818
01722
12222
23022
34322
45122
55722
66022
done6022
01618
11918
22218
32318
42518
52718
62818
done2818
0912
11510
22810
35510
46710
57910
68410
done8410
01517
11817
22117
32217
42417
52617
62717
done2717
088
1108
2138
3148
4168
5188
6198
done198
01416
11716
22016
32116
42316
52516
62616
done2616
088
1126
2186
3236
4256
5286
6326
done326
01517
11817
22117
32217
42417
52617
62717
done2717
01730
12230
22930
33730
44130
55030
65630
76130
86230
done6230
01618
11918
22218
32318
42518
52718
62818
done2818
01618
11918
22218
32318
42518
52718
62818
done2818
01618
11918
22218
32318
42518
52718
62818
done2818
088
1126
2186
3236
4256
5286
6326
done326
01517
11817
22117
32217
42417
52617
62717
done2717
066
1104
2134
3224
4274
done274
01315
11615
21915
32015
42215
52415
62515
done2515
056
194
2142
3162
4202
done202
01416
11716
22016
32116
42316
52516
62616
done2616
01528
12228
22926
34526
47126
59626
611526
done11526
01517
11817
22117
32217
42417
52617
62717
done2717
01416
11916
22214
33114
44014
54214
done4214
01517
11817
22117
32217
42417
52617
62717
done2717
056
194
2142
3162
4202
done202
01416
11716
22016
32116
42316
52516
62616
done2616
044
162
282
done82
01416
11716
22016
32116
42316
52516
62616
done2616
055
done55
01315
11815
22113
33013
43913
54113
done4113
01531
12031
done2031
01416
11516
done1516
01416
11716
done1716
01416
11516
done1516
045
191
done91
01214
11514
21814
31914
42114
52314
62414
done2414
035
161
done61
01315
11615
21915
32015
42215
52415
62515
done2515
01327
12023
22923
34223
45623
55723
done5723
01416
11716
22016
32116
42316
52516
62616
done2616
01215
11711
22211
32411
42511
done2511
01416
11716
22016
32116
42316
52516
62616
done2616
035
161
done61
01315
11615
21915
32015
42215
52415
62515
done2515
0811
11411
2229
3359
4399
5649
61039
71079
done1079
01315
11615
21915
32015
42215
52415
62515
done2515
0711
1139
2249
3339
done339
01416
11716
22016
32116
42316
52516
62616
done2616
01733
12833
24933
38031
414031
521331
done21331
01517
11817
22117
32217
42417
52617
62717
done2717
01621
12321
23121
34419
47119
510919
done10919
01517
11817
22117
32217
42417
52617
62717
done2717
0711
1139
2249
3339
done339
01416
11716
22016
32116
42316
52516
62616
done2616
077
1117
2145
3165
done165
01315
11615
21915
32015
42215
52415
62515
done2515
067
1105
2155
done155
01416
11716
22016
32116
42316
52516
62616
done2616
01629
12329
23029
33827
46227
57927
done7927
01517
11817
22117
32217
42417
52617
62717
done2717
01517
12017
22317
32415
43715
54215
done4215
01517
11817
22117
32217
42417
52617
62717
done2717
067
1105
2155
done155
01416
11716
22016
32116
42316
52516
62616
done2616
045
191
done91
01214
11514
21814
31914
42114
52314
62414
done2414
035
161
done61
01315
11615
21915
32015
42215
52415
62515
done2515
01327
12023
22923
34223
45623
55723
done5723
01416
11716
22016
32116
42316
52516
62616
done2616
01215
11711
22211
32411
42511
done2511
01416
11716
22016
32116
42316
52516
62616
done2616
035
161
done61
01315
11615
21915
32015
42215
52415
62515
done2515
023
141
done41
01315
11615
21915
32015
42215
52415
62515
done2515
044
164
done64
01214
11712
21812
done1812
01315
11815
22115
32213
43513
54213
done4213
01315
11615
21915
done1915
01531
11831
done1831
01416
11516
done1516
055
191
done91
045
181
done81
01427
12125
22625
33025
43625
54925
68025
710325
done10325
01315
11813
21913
done1913
045
181
done81
0811
11211
2219
3379
4419
5449
6509
7529
done529
0811
1149
2279
3459
4519
5609
6759
7789
done789
01733
12633
24733
37833
410433
513833
616233
717233
817333
done17333
01621
12121
22921
34221
45021
55621
65921
done5921
0811
1149
2279
3459
4519
5609
6759
7789
done789
077
197
2135
3175
done175
077
1115
2175
3195
done195
01629
12129
22829
33629
44029
54929
65529
76029
done6029
01517
11817
22117
32217
42417
52617
62717
done2717
077
1115
2175
3195
done195
055
191
done91
045
181
done81
01427
12125
22625
33025
43625
54925
68025
710325
done10325
01315
11813
21913
done1913
045
181
done81
033
151
done51
044
done44
01416
11716
22016
done2016
01416
11716
22016
done2016
01315
11615
21915
done1915
044
done44
011
done11
011
done11
033
152
done52
01212
11911
2229
3467
4787
5897
6907
done907
01314
12412
24010
31057
41947
52667
63307
73387
done3387
01414
12513
23811
31029
42109
53469
65099
76779
87639
99019
109289
done9289
02127
14925
210719
328314
479112
5301212
done500012
01112
12210
2468
31305
42853
56172
619812
done50002
01212
12311
2449
31267
43245
58744
628933
done50003
01212
11911
2309
3537
4825
52485
65905
714715
844645
done50005
01314
12712
25510
31307
42635
59295
630865
done50005
01414
12813
25311
31239
43048
511378
630868
done50018

prune395.0ms

Filtered
132 candidates to 198 candidates (-50.0%)
Pruning

20 alts after pruning (20 fresh and 0 done)

PrunedKeptTotal
New18612198
Fresh4812
Picked101
Done101
Total19220212

Merged error: 8.1b

Counts
212 → 20

localize23.0ms

Local error

Found 4 expressions with local error:

0.6b
(/ (log 10.0) (log (cbrt (* (* (cbrt (sqrt (+ (* re re) (* im im)))) (cbrt (sqrt (+ (* re re) (* im im))))) (cbrt (sqrt (+ (* re re) (* im im))))))))
32.9b
(sqrt (+ (* re re) (* im im)))
32.9b
(sqrt (+ (* re re) (* im im)))
32.9b
(sqrt (+ (* re re) (* im im)))

rewrite22.0ms

Algorithm
rewrite-expression-head
Rules
21×add-sqr-sqrt
20×times-frac
18×pow1 add-cube-cbrt *-un-lft-identity
16×log-pow
sqrt-prod
add-exp-log sqrt-div add-cbrt-cube
pow1/3 associate-/r*
associate-/l* add-log-exp
rem-sqrt-square sqrt-pow1 flip3-+ pow1/2 flip-+
cbrt-undiv frac-2neg div-exp clear-num div-inv
Counts
4 → 86
Calls
4 calls:
5.0ms
(/ (log 10.0) (log (cbrt (* (* (cbrt (sqrt (+ (* re re) (* im im)))) (cbrt (sqrt (+ (* re re) (* im im))))) (cbrt (sqrt (+ (* re re) (* im im))))))))
5.0ms
(sqrt (+ (* re re) (* im im)))
5.0ms
(sqrt (+ (* re re) (* im im)))
5.0ms
(sqrt (+ (* re re) (* im im)))

series66.0ms

Counts
4 → 12
Calls
4 calls:
46.0ms
(/ (log 10.0) (log (cbrt (* (* (cbrt (sqrt (+ (* re re) (* im im)))) (cbrt (sqrt (+ (* re re) (* im im))))) (cbrt (sqrt (+ (* re re) (* im im))))))))
7.0ms
(sqrt (+ (* re re) (* im im)))
7.0ms
(sqrt (+ (* re re) (* im im)))
7.0ms
(sqrt (+ (* re re) (* im im)))

simplify3.0min

Counts
98 → 98
Iterations

Useful iterations: 1 (1.0ms)

IterNodesCost
079
189
done89
079
189
done89
0819
1919
done919
079
189
done89
0826
11016
22110
33410
44210
55210
67310
713410
835010
9129510
done500010
0818
1109
done109
079
189
done89
079
189
done89
079
189
done89
022
141
done41
068
178
done78
0912
12712
2648
31198
42618
56978
623128
done50008
01024
13220
28418
317716
430916
572316
6197216
done500016
0816
12116
24412
3908
42158
55768
614838
done50018
068
1118
2188
3338
4588
5998
61578
73258
815708
done50008
033
161
done61
079
189
done89
079
189
done89
079
189
done89
079
189
done89
0819
1919
done919
079
189
done89
0826
11016
22110
33410
44210
55210
67310
713410
835010
9129510
done500010
0818
1109
done109
079
189
done89
079
189
done89
079
189
done89
022
141
done41
068
178
done78
0912
12712
2648
31198
42618
56978
623128
done50008
01024
13220
28418
317716
430916
572316
6197216
done500016
0816
12116
24412
3908
42158
55768
614838
done50018
068
1118
2188
3338
4588
5998
61578
73258
815708
done50008
033
161
done61
079
189
done89
079
189
done89
079
189
done89
079
189
done89
0819
1919
done919
079
189
done89
0826
11016
22110
33410
44210
55210
67310
713410
835010
9129510
done500010
0818
1109
done109
079
189
done89
079
189
done89
079
189
done89
022
141
done41
068
178
done78
0912
12712
2648
31198
42618
56978
623128
done50008
01024
13220
28418
317716
430916
572316
6197216
done500016
0816
12116
24412
3908
42158
55768
614838
done50018
068
1118
2188
3338
4588
5998
61578
73258
815708
done50008
033
161
done61
079
189
done89
079
189
done89
01636
12036
22318
32815
43415
54415
66515
712515
833415
9125815
done500115
01535
12035
22417
33014
43614
54614
66714
712314
832514
9123414
done500014
01535
11735
21917
32414
43014
54014
66114
712314
833014
9124914
done500014
018104
129104
26220
313115
421315
533915
681415
7343815
done500015
01671
11871
22035
32529
43129
54129
66229
712029
832529
9125029
done500029
01535
11735
21917
32414
43014
54014
66114
712314
833014
9124914
done500014
016104
125104
24218
38215
415215
522615
637215
792115
8384215
done500115
01535
11735
21917
32414
43014
54014
66114
712314
833014
9124914
done500014
01535
11735
21917
32414
43014
54014
66114
712314
833014
9124914
done500014
033
done33
01232
11432
21614
32111
42711
53711
65811
711811
833411
9126411
done500011
033
161
done61
01333
11833
22215
32912
44412
56212
610312
722012
860712
9221612
done500112
023
141
done41
01434
11634
21816
32313
42913
53913
66013
711613
831813
9123113
done500013
01567
12167
22331
32825
43425
54425
66725
713125
834825
9128725
done500125
01535
11735
21917
32414
43014
54014
66114
712314
833014
9124914
done500014
01434
11834
22016
32513
43113
54113
66413
712013
833113
9126313
done500013
01535
11735
21917
32414
43014
54014
66114
712314
833014
9124914
done500014
023
141
done41
01434
11634
21816
32313
42913
53913
66013
711613
831813
9123113
done500013
069
189
2109
3119
done119
01434
11934
22316
33013
44513
56313
610413
722513
860713
9222113
done500013
069
1107
2167
3217
done217
01535
11735
21917
32414
43014
54014
66114
712314
833014
9124514
done500014
01873
12673
23737
34831
45431
56431
68531
714531
835931
9128331
done500031
01636
11836
22018
32515
43115
54115
66415
712015
832615
9125815
done500015
01740
12140
22522
33119
43719
54719
66819
712919
833519
9126319
done500019
01636
11836
22018
32515
43115
54115
66415
712015
832615
9125815
done500015
069
1107
2167
3217
done217
01535
11735
21917
32414
43014
54014
66114
712314
833014
9124514
done500014
055
done55
01434
11934
22316
33013
44513
56313
610413
722513
860713
9222113
done500013
055
173
293
done93
01535
11735
21917
32414
43014
54014
66114
712314
833014
9124514
done500014
01769
12169
22333
32827
43427
54427
66527
712527
833427
9125827
done500127
01636
11836
22018
32515
43115
54115
66415
712015
832615
9125815
done500015
01636
11836
22018
32515
43115
54115
66415
712015
832615
9125815
done500015
01636
11836
22018
32515
43115
54115
66415
712015
832615
9125815
done500015
055
173
293
done93
01535
11735
21917
32414
43014
54014
66114
712314
833014
9124514
done500014
033
161
done61
01333
11833
22215
32912
44412
56212
610312
722012
860712
9221612
done500112
023
141
done41
01434
11634
21816
32313
42913
53913
66013
711613
831813
9123113
done500013
01567
12167
22331
32825
43425
54425
66725
713125
834825
9128725
done500125
01535
11735
21917
32414
43014
54014
66114
712314
833014
9124914
done500014
01434
11834
22016
32513
43113
54113
66413
712013
833113
9126313
done500013
01535
11735
21917
32414
43014
54014
66114
712314
833014
9124914
done500014
023
141
done41
01434
11634
21816
32313
42913
53913
66013
711613
831813
9123113
done500013
01333
11733
21915
32412
43012
54012
66112
712512
833612
9126612
done500012
01434
11634
21816
32313
42913
53913
66013
711813
833613
9126113
done500013
044
done44
044
162
282
done82
01668
12068
22232
32726
43326
54326
66426
712426
833126
9125926
done500026
01535
11735
21917
32414
43014
54014
66114
712314
833014
9124914
done500014
044
162
282
done82
01434
11634
21816
32313
42913
53913
66013
711813
833613
9126113
done500013
01535
11735
21917
32414
43014
54014
66114
712614
833814
9126414
done500114
01535
11735
21917
32414
43014
54014
66114
712614
833814
9126414
done500114
01434
11634
21816
32313
42913
53913
66013
711813
833613
9126113
done500013
011
done11
011
done11
033
152
done52
011
done11
011
done11
033
152
done52
011
done11
011
done11
033
152
done52
01212
11911
2229
3467
4787
5897
6907
done907
01314
12412
24010
31057
41947
52667
63307
73387
done3387
01414
12513
23811
31029
42109
53469
65099
76779
87639
99019
109289
done9289

prune160.0ms

Filtered
70 candidates to 98 candidates (-40.0%)
Pruning

20 alts after pruning (19 fresh and 1 done)

PrunedKeptTotal
New98098
Fresh01919
Picked011
Done000
Total9820118

Merged error: 8.1b

Counts
118 → 20

regimes1.5s

Accuracy

56.4% (10.7b remaining)

Error of 17.8b against oracle of 7.1b and baseline of 31.7b

bsearch86.0ms

Steps
ItersRangePoint
9
2.4540169358802756e+30
3.519108532790208e+36
3.466178613033722e+36
8
3.8885538970219946e-190
3.3867492948767555e-187
4.1020592309585383e-190
9
-1.5130857388211537e-243
-3.646205474305488e-252
-1.827079623045419e-251
8
-4.996746474906799e+125
-3.0297993811682655e+122
-3.784927748967173e+122

simplify4.0ms

Iterations

Useful iterations: 0 (1.0ms)

IterNodesCost
04593
14993
done4993

end0.0ms

sample808.0ms

Algorithm
intervals
Results
542.0ms8000×body80valid

Profiling

Loading profile data...