Details

Time bar (total: 8.1min)

sample68.0ms

Algorithm
intervals
Results
18.0ms34×body2560valid
12.0ms201×body80valid
6.0ms23×body1280valid
6.0ms103×body80nan
2.0ms11×body640valid
2.0msbody5120valid
1.0msbody320valid
0.0msbody160valid

simplify56.0ms

Counts
1 → 1
Iterations

Useful iterations: 2 (5.0ms)

IterNodesCost
01417
12417
24416
37816
49016
59816
done9816

prune9.0ms

Filtered
1 candidates to 1 candidates (0.0%)
Pruning

1 alts after pruning (1 fresh and 0 done)

PrunedKeptTotal
New011
Fresh101
Picked000
Done000
Total112

Merged error: 32.4b

Counts
2 → 1

localize12.0ms

Local error

Found 4 expressions with local error:

0.1b
(/ (/ (- (sqrt (- (* b b) (* 4.0 (* a c)))) b) 2.0) a)
0.8b
(- (sqrt (- (* b b) (* 4.0 (* a c)))) b)
1.4b
(- (* b b) (* 4.0 (* a c)))
22.5b
(sqrt (- (* b b) (* 4.0 (* a c))))

rewrite39.0ms

Algorithm
rewrite-expression-head
Rules
138×times-frac
121×add-sqr-sqrt
94×*-un-lft-identity
68×add-cube-cbrt
26×difference-of-squares
22×associate-/l*
16×sqrt-prod
13×distribute-lft-out--
add-exp-log add-cbrt-cube
add-log-exp
pow1 div-inv
cbrt-undiv flip3-- div-exp associate-/r* flip--
sub-neg sqrt-div diff-log div-sub
rem-sqrt-square frac-2neg sqrt-pow1 pow1/2 clear-num associate-/l/
Counts
4 → 149
Calls
4 calls:
14.0ms
(/ (/ (- (sqrt (- (* b b) (* 4.0 (* a c)))) b) 2.0) a)
8.0ms
(- (sqrt (- (* b b) (* 4.0 (* a c)))) b)
4.0ms
(- (* b b) (* 4.0 (* a c)))
5.0ms
(sqrt (- (* b b) (* 4.0 (* a c))))

series79.0ms

Counts
4 → 12
Calls
4 calls:
29.0ms
(/ (/ (- (sqrt (- (* b b) (* 4.0 (* a c)))) b) 2.0) a)
18.0ms
(- (sqrt (- (* b b) (* 4.0 (* a c)))) b)
10.0ms
(- (* b b) (* 4.0 (* a c)))
22.0ms
(sqrt (- (* b b) (* 4.0 (* a c))))

simplify1.3min

Counts
161 → 161
Iterations

Useful iterations: 1 (1.0ms)

IterNodesCost
01011
11611
23311
35811
46011
done6011
01011
11611
23311
35811
46011
done6011
01123
11723
23423
35923
46123
done6123
01011
11611
23311
35811
46011
done6011
01132
11820
24412
310712
421312
526412
628912
734912
855012
9147012
done500012
01122
11811
23511
36011
46211
done6211
01011
11611
23311
35811
46011
done6011
01011
11611
23311
35811
46011
done6011
01011
11611
23311
35811
46011
done6011
022
141
done41
0910
11510
23210
35710
45910
done5910
01214
13614
213212
363012
4324512
done500112
01330
13924
212922
338020
453420
556120
666920
7101320
8235120
done500020
01120
13120
29918
337816
4100416
5141216
6185416
7307416
done500016
0910
11410
22010
done2010
033
161
done61
01011
11611
23311
35811
46011
done6011
01011
11611
23311
35811
46011
done6011
01011
12010
23910
39610
425510
583110
6497010
done500010
0910
11510
23210
35710
45910
done5910
0910
11810
24510
310510
421510
565710
6294610
done500010
01021
11621
23321
35821
46021
done6021
0910
11510
23210
35710
45910
done5910
01029
11729
24811
317411
491611
5466111
done500011
0910
11510
23210
35710
45910
done5910
0910
11510
23210
35710
45910
done5910
01113
13513
213111
362211
4313911
done500011
01229
13823
212821
337119
451419
554119
664619
799019
8233419
done500119
066
1146
2356
3536
4546
done546
01019
13019
29817
337815
4101315
5142715
6188615
7303915
done500015
089
1139
2199
done199
066
1146
2356
3536
4546
done546
01214
12013
23913
36713
47213
57813
68213
79813
810213
910713
1011413
1113313
1215413
1316613
1416913
done16913
01113
11913
23713
36213
46413
done6413
01113
12213
24213
37013
48013
58413
610013
710413
810913
911613
1013413
1115513
1217313
1317613
done17613
01227
12027
23827
36327
46527
done6527
01113
11913
23713
36213
46413
done6413
01238
12138
25314
312114
423114
560514
6244814
done500114
01113
11913
23713
36213
46413
done6413
01113
11913
23713
36213
46413
done6413
01316
13316
27216
314016
430316
573616
6259316
done500116
01338
12624
26124
311722
416722
525022
642322
753622
864222
969822
1077022
done77022
022
done22
01125
12213
25513
311213
41607
52446
69746
done50006
01012
11712
23412
35912
46312
done6312
01214
11914
23614
36114
46514
done6514
01214
12014
23814
36314
46514
done6514
01214
11914
23614
36114
46514
done6514
01214
12014
23814
36314
46514
done6514
01012
11812
23612
36112
46312
done6312
022
done22
01619
13019
25919
310219
411719
512519
614019
716619
817519
done17519
01518
13118
25818
310018
411618
512018
612818
714318
816918
917818
done17818
01417
13017
26617
311417
413917
515417
616217
717517
818917
920517
1020917
done20917
01417
12717
25617
39717
410717
511317
611917
712317
813917
914317
1015417
1117117
1219917
1323517
1426217
1527917
1630517
1730717
done30717
01950
14150
214922
360420
4245318
done500118
01750
14350
213520
351018
4213218
done500018
01535
12835
25735
39335
410135
510435
done10435
01417
12717
25617
39417
410217
510517
done10517
01550
13550
29518
333618
4158318
done500018
01417
12717
25617
39417
410217
510517
done10517
01417
12717
25617
39417
410217
510517
done10517
01315
12615
24915
38115
48914
59014
done9014
022
done22
01214
12014
24014
36514
46714
done6714
055
175
2105
done105
01737
13437
26337
39637
49837
done9837
01518
12618
24618
37318
47518
done7518
01634
12934
25134
37934
48134
done8134
01518
12618
24618
37318
47518
done7518
01633
13131
25731
38931
49131
done9131
01417
12517
24517
37217
47417
done7417
01621
12921
24921
37621
47821
done7821
01518
12618
24618
37318
47518
done7518
01518
12618
24618
37318
47518
done7518
01518
12618
24618
37318
47518
done7518
01517
12815
25015
37715
47915
done7915
01417
12517
24517
37217
47417
done7417
01939
13739
29039
320539
433639
537639
done37639
01619
12619
24719
37219
47419
done7419
01836
13436
27536
313736
418236
518636
done18636
01619
12619
24719
37219
47419
done7419
01835
13633
28133
315533
418933
done18933
01518
12518
24618
37118
47318
done7318
01836
13236
26636
312736
417036
518036
done18036
01619
12619
24719
37219
47419
done7419
01733
12933
25833
39633
410833
done10833
01619
12619
24719
37219
47419
done7419
01732
13130
26430
310630
411830
done11830
01518
12518
24618
37118
47318
done7318
01735
13333
28033
316433
418133
done18133
01518
12518
24618
37118
47318
done7318
01632
13030
26830
311530
411830
done11830
01518
12518
24618
37118
47318
done7318
01531
12927
25127
38127
48327
done8327
01417
12417
24517
37017
47217
done7217
01825
13225
26225
311425
412125
done12125
01619
12619
24719
37219
47419
done7419
01722
12922
25322
38822
49022
done9022
01619
12619
24719
37219
47419
done7419
01721
13119
25919
310019
410219
done10219
01518
12518
24618
37118
47318
done7318
01722
12922
25322
38622
48822
done8822
01619
12619
24719
37219
47419
done7419
01619
12619
24719
37219
47419
done7419
01619
12619
24719
37219
47419
done7419
01618
12816
25316
38216
48416
done8416
01518
12518
24618
37118
47318
done7318
01621
13019
25719
39019
49219
done9219
01518
12518
24618
37118
47318
done7318
01518
12716
25116
37616
47816
done7816
01518
12518
24618
37118
47318
done7318
01417
12613
24413
36913
47113
done7113
01417
12417
24517
37017
47217
done7217
0913
11713
22913
35613
46213
done6213
01518
12818
25718
39318
410118
510418
done10418
0810
11410
22010
32810
done2810
01518
12818
25718
39318
410118
510418
done10418
069
1127
2227
3327
done327
01417
12717
25617
39417
410217
510517
done10517
0810
11410
22010
32610
done2610
01518
12818
25718
39318
410118
510418
done10418
077
1117
2147
done147
01518
12818
25718
39318
410118
510418
done10418
056
194
2164
done164
01417
12717
25617
39417
410217
510517
done10517
069
1127
2167
3267
4287
done287
01417
12717
25617
39417
410217
510517
done10517
056
194
2114
3154
done154
01417
12717
25617
39417
410217
510517
done10517
035
171
done71
01316
12616
25516
39116
49916
510216
done10216
01926
13226
26126
311326
412126
done12126
01720
13020
25920
39720
410520
510820
done10820
01823
12923
25223
38523
48723
done8723
01720
13020
25920
39720
410520
510820
done10820
01822
13120
25820
39920
410320
done10320
01619
12919
25819
39619
410619
510919
done10919
01823
12923
25223
38523
48723
done8723
01720
13020
25920
39720
410520
510820
done10820
01720
12620
24620
37120
47320
done7320
01720
13020
25920
39720
410520
510820
done10820
01719
12817
25217
38117
48317
done8317
01619
12919
25819
39619
410619
510919
done10919
01722
13020
25620
38920
49120
done9120
01619
12919
25819
39619
410619
510919
done10919
01619
12717
25017
37517
47717
done7717
01619
12919
25819
39619
410619
510919
done10919
01518
12614
24314
36814
47014
done7014
01518
12818
25718
39318
410118
510418
done10418
01926
13226
26126
311326
412126
done12126
01720
13020
25920
39720
410520
510820
done10820
01823
12923
25223
38523
48723
done8723
01720
13020
25920
39720
410520
510820
done10820
01822
13120
25820
39920
410320
done10320
01619
12919
25819
39619
410619
510919
done10919
01823
12923
25223
38523
48723
done8723
01720
13020
25920
39720
410520
510820
done10820
01720
12620
24620
37120
47320
done7320
01720
13020
25920
39720
410520
510820
done10820
01719
12817
25217
38117
48317
done8317
01619
12919
25819
39619
410619
510919
done10919
01722
13020
25620
38920
49120
done9120
01619
12919
25819
39619
410619
510919
done10919
01619
12717
25017
37517
47717
done7717
01619
12919
25819
39619
410619
510919
done10919
01518
12614
24314
36814
47014
done7014
01518
12818
25718
39318
410118
510418
done10418
0913
11713
22913
35613
46213
done6213
01518
12818
25718
39318
410118
510418
done10418
0810
11410
22010
32810
done2810
01518
12818
25718
39318
410118
510418
done10418
069
1127
2227
3327
done327
01417
12717
25617
39417
410217
510517
done10517
0810
11410
22010
32610
done2610
01518
12818
25718
39318
410118
510418
done10418
077
1117
2147
done147
01518
12818
25718
39318
410118
510418
done10418
056
194
2164
done164
01417
12717
25617
39417
410217
510517
done10517
069
1127
2167
3267
4287
done287
01417
12717
25617
39417
410217
510517
done10517
056
194
2114
3154
done154
01417
12717
25617
39417
410217
510517
done10517
035
171
done71
01316
12616
25516
39116
49916
510216
done10216
057
197
done97
01417
12717
25617
39417
410217
510517
done10517
044
164
done64
01417
12717
25617
39417
410217
510517
done10517
023
141
done41
01316
12616
25516
39116
49916
510216
done10216
01318
12618
25118
38118
48818
done8818
066
1106
2136
done136
01215
12315
24315
37015
47415
done7415
066
1106
2136
done136
01214
12512
24712
37212
47612
done7612
055
195
2125
done125
033
153
done53
01316
12616
24916
37716
48316
58816
69116
79316
done9316
01520
13020
26520
311720
414020
515120
615220
done15220
01417
12717
25617
39417
410217
510517
done10517
01416
12914
25914
39114
49614
done9614
01417
12517
24517
37217
47417
done7417
01417
12517
24517
37217
47417
done7417
01518
12518
24618
37218
47618
57818
67918
done7918
01518
12518
24618
37218
47618
57818
67918
done7918
01417
12417
24517
37117
47517
57717
67817
done7817
01518
12518
24618
37218
47618
57818
67918
done7918
01518
12518
24618
37218
47618
57818
67918
done7918
01417
12417
24517
37117
47517
57717
67817
done7817
01417
12717
25017
37817
48217
58717
69017
79217
done9217
01417
12717
25017
37817
48217
58717
69017
79217
done9217
01316
12616
24916
37716
48316
58816
69116
79316
done9316
01619
12919
25219
38219
48619
59119
69419
79619
done9619
01619
12919
25219
38219
48619
59119
69419
79619
done9619
01518
12818
25118
37918
48318
58818
69118
79318
done9318
01619
12919
25219
38219
48619
59119
69419
79619
done9619
01619
12919
25219
38219
48619
59119
69419
79619
done9619
01518
12818
25118
37918
48318
58818
69118
79318
done9318
01417
12717
25017
37817
48217
58717
69017
79217
done9217
01417
12717
25017
37817
48217
58717
69017
79217
done9217
01316
12616
24916
37716
48316
58816
69116
79316
done9316
01316
12616
24916
37716
48316
58816
69116
79316
done9316
055
195
2123
3183
4253
5303
done303
033
143
done43
01213
12713
27013
313711
421611
523111
625311
731511
853311
9147211
done500011
089
1169
2399
3949
42009
52769
62869
done2869
089
1169
2319
3529
4819
5929
done929
099
1209
2459
3759
4839
5939
61159
71769
83909
913129
done50019
099
1209
2459
3759
4839
5939
61159
71769
83909
913129
done50019
099
1209
2459
3759
4839
5939
61159
71769
83909
913129
done50019
01315
13115
27115
312413
422013
529413
640913
770613
8107913
9218413
done500013
077
1137
2277
3487
4777
5887
done887
01011
11911
24111
36211
49111
510211
done10211
01417
14015
212015
335115
4105713
5294213
done500013
055
185
2115
3155
4165
done165
0911
1199
2369
3549
4669
5699
done699

prune353.0ms

Filtered
116 candidates to 161 candidates (-38.8%)
Pruning

11 alts after pruning (10 fresh and 1 done)

PrunedKeptTotal
New15110161
Fresh000
Picked011
Done000
Total15111162

Merged error: 6.0b

Counts
162 → 11

localize13.0ms

Local error

Found 4 expressions with local error:

0.2b
(* (- (sqrt (- (* b b) (* 4.0 (* a c)))) b) (/ (/ 1 2.0) a))
0.8b
(- (sqrt (- (* b b) (* 4.0 (* a c)))) b)
1.4b
(- (* b b) (* 4.0 (* a c)))
22.5b
(sqrt (- (* b b) (* 4.0 (* a c))))

rewrite49.0ms

Algorithm
rewrite-expression-head
Rules
71×times-frac
62×add-sqr-sqrt
46×*-un-lft-identity
43×associate-*r*
41×add-cube-cbrt
19×add-exp-log
13×add-cbrt-cube
add-log-exp
pow1
div-exp associate-*l*
flip3-- prod-exp sqrt-prod flip--
div-inv difference-of-squares unswap-sqr
cbrt-undiv cbrt-unprod
frac-times sub-neg sqrt-div diff-log associate-*l/ distribute-lft-out--
rem-sqrt-square rec-exp sqrt-pow1 pow1/2 1-exp associate-*r/ pow-prod-down *-commutative
Counts
4 → 117
Calls
4 calls:
25.0ms
(* (- (sqrt (- (* b b) (* 4.0 (* a c)))) b) (/ (/ 1 2.0) a))
9.0ms
(- (sqrt (- (* b b) (* 4.0 (* a c)))) b)
4.0ms
(- (* b b) (* 4.0 (* a c)))
5.0ms
(sqrt (- (* b b) (* 4.0 (* a c))))

series81.0ms

Counts
4 → 12
Calls
4 calls:
30.0ms
(* (- (sqrt (- (* b b) (* 4.0 (* a c)))) b) (/ (/ 1 2.0) a))
18.0ms
(- (sqrt (- (* b b) (* 4.0 (* a c)))) b)
16.0ms
(- (* b b) (* 4.0 (* a c)))
17.0ms
(sqrt (- (* b b) (* 4.0 (* a c))))

simplify3.1min

Counts
129 → 129
Iterations

Useful iterations: 1 (1.0ms)

IterNodesCost
01011
11611
23311
35811
46011
done6011
01011
11611
23311
35811
46011
done6011
01123
11723
23423
35923
46123
done6123
01011
11611
23311
35811
46011
done6011
01132
11820
24412
310712
421312
526412
628912
734912
855012
9147012
done500012
01122
11811
23511
36011
46211
done6211
01011
11611
23311
35811
46011
done6011
01011
11611
23311
35811
46011
done6011
01011
11611
23311
35811
46011
done6011
022
141
done41
0910
11510
23210
35710
45910
done5910
01214
13614
213212
363012
4324512
done500112
01330
13924
212922
338020
453420
556120
666920
7101320
8235120
done500020
01120
13120
29918
337816
4100416
5141216
6185416
7307416
done500016
0910
11410
22010
done2010
033
161
done61
01011
11611
23311
35811
46011
done6011
01011
11611
23311
35811
46011
done6011
01011
12010
23910
39610
425510
583110
6497010
done500010
0910
11510
23210
35710
45910
done5910
0910
11810
24510
310510
421510
565710
6294610
done500010
01021
11621
23321
35821
46021
done6021
0910
11510
23210
35710
45910
done5910
01029
11729
24811
317411
491611
5466111
done500011
0910
11510
23210
35710
45910
done5910
0910
11510
23210
35710
45910
done5910
01113
13513
213111
362211
4313911
done500011
01229
13823
212821
337119
451419
554119
664619
799019
8233419
done500119
066
1146
2356
3536
4546
done546
01019
13019
29817
337815
4101315
5142715
6188615
7303915
done500015
089
1139
2199
done199
066
1146
2356
3536
4546
done546
01214
12013
23913
36713
47213
57813
68213
79813
810213
910713
1011413
1113313
1215413
1316613
1416913
done16913
01113
11913
23713
36213
46413
done6413
01113
12213
24213
37013
48013
58413
610013
710413
810913
911613
1013413
1115513
1217313
1317613
done17613
01227
12027
23827
36327
46527
done6527
01113
11913
23713
36213
46413
done6413
01238
12138
25314
312114
423114
560514
6244814
done500114
01113
11913
23713
36213
46413
done6413
01113
11913
23713
36213
46413
done6413
01316
13316
27216
314016
430316
573616
6259316
done500116
01338
12624
26124
311722
416722
525022
642322
753622
864222
969822
1077022
done77022
022
done22
01125
12213
25513
311213
41607
52446
69746
done50006
01012
11712
23412
35912
46312
done6312
01214
11914
23614
36114
46514
done6514
01214
12014
23814
36314
46514
done6514
01214
11914
23614
36114
46514
done6514
01214
12014
23814
36314
46514
done6514
01012
11812
23612
36112
46312
done6312
022
done22
01518
13018
26518
315116
431016
543116
654316
759316
862916
963316
done63316
01720
13020
25819
39919
411819
514119
615719
717419
817619
done17619
01821
13520
27719
315819
426219
536519
640019
744719
done44719
01922
13821
27920
316719
426819
537519
641119
745419
done45419
01821
13720
27119
313919
422119
530919
637619
742319
done42319
01720
13320
26719
312018
418518
526718
636518
741618
841918
done41918
01619
13419
27919
318917
440617
561317
687717
7100217
8104117
9104517
done104517
01619
13319
27919
318417
442717
576617
6177217
done500017
02356
15252
217024
373122
4460322
done500022
02156
15256
218724
391322
4493520
done500020
01956
14456
214322
358722
4330718
done500018
01739
13239
26739
315335
432335
544335
655135
760135
864735
965135
done65135
01619
13119
26619
315417
431317
543517
654317
759117
863017
963417
done63417
01756
14256
215620
383718
4477418
done500018
01619
13119
26619
315417
431317
543517
654317
759117
863017
963417
done63417
01619
13119
26619
315417
431317
543517
654317
759117
863017
963417
done63417
01720
14220
29018
324118
471618
5269718
done500118
01440
12826
27726
317624
431224
550824
679824
7111424
8149624
9200724
10220024
11223424
done223424
01529
13117
27915
324315
46339
514668
635848
done50018
01114
11914
24414
36914
47114
done7114
01720
13020
25120
37620
48020
done8020
01720
13020
25120
37620
48020
done8020
01821
13121
25221
38321
48621
done8621
01821
13121
25221
38321
48621
done8621
01922
13421
26321
310919
416919
517419
done17419
01922
13421
26321
310919
416919
517419
done17419
01821
13321
26221
310819
417119
517819
done17819
01821
13321
26221
310819
417119
517819
done17819
01726
13226
26126
310326
411926
512726
done12726
01619
12919
25619
38819
49419
done9419
01928
13828
29128
322328
441628
563928
679728
783628
883728
done83728
01825
13325
26725
314525
422525
529225
634125
734625
done34625
01724
13222
27322
317022
426622
537522
643822
747222
done47222
01823
13323
26823
314423
420723
527223
630723
731423
done31423
01720
13020
25720
310620
413120
514720
615820
done15820
01619
12917
26017
310417
413017
516417
618917
719517
done19517
02130
14428
212526
340024
4118024
5217524
6313724
7371324
8397024
done397024
02027
14125
210223
327321
465421
5102321
6136421
7154421
8165021
done165021
01926
14022
211320
327418
451718
576118
695318
7108718
8109418
done109418
02027
13925
29723
325721
471321
5116121
6151121
7170621
8181621
done181621
01924
13622
28120
319318
440318
557318
669218
774218
878818
979218
done79218
01823
13519
28817
318015
430415
544515
653715
758715
859115
done59115
01826
13722
210420
322718
440718
565118
683718
797418
8100218
done100218
01723
13419
28417
315615
424715
538615
647115
751615
853515
done53515
01622
13314
26012
310312
411812
512612
done12612
02027
13926
29326
326424
482224
5193724
6283824
7353524
8384424
done384424
01924
13623
27623
319121
450021
587421
6117021
7135621
8145521
done145521
01823
13520
28420
319718
439618
562018
678218
793218
897018
done97018
01924
13623
28223
320421
452521
598721
6130421
7154921
8167821
done167821
01821
13320
26820
315418
432418
543318
654018
759018
862518
962918
done62918
01720
13217
27417
314315
424815
536915
644615
750015
851215
done51215
01723
13420
27318
318318
435818
558818
676318
793418
895918
done95918
01620
13117
26115
313215
422115
535415
643515
749315
850815
done50815
01519
13014
25712
310012
411512
512312
done12312
01926
13826
29226
326324
480924
5195624
6284024
7357224
8395424
done395424
01823
13523
27523
319221
449721
587121
6116221
7133521
8143621
done143621
01722
13420
28320
319618
439218
560618
677118
792318
895518
done95518
01823
13523
28123
320321
452421
597821
6130221
7155521
8169421
done169421
01720
13220
26720
315318
431418
542318
652818
757818
862218
962618
done62618
01619
13117
27317
314215
424515
536615
644115
750115
851315
done51315
01622
13320
27218
318218
435818
558718
676618
792018
896118
done96118
01519
13017
26015
313115
422015
535315
643315
750615
852415
done52415
01418
12914
25612
310112
411612
512412
done12412
01520
13020
26418
315318
425918
533618
640418
743018
845318
945518
done45518
01417
12717
25415
311415
415815
518615
620515
720715
820815
done20815
01316
12614
25512
39812
411312
512112
done12112
01520
13020
26418
315318
425918
533618
640418
743018
845318
945518
done45518
01417
12717
25415
311415
415815
518615
620515
720715
820815
done20815
01316
12614
25512
39812
411312
512112
done12112
01214
12312
25012
38612
49912
510312
done10312
01416
12716
25414
311414
415814
518514
620214
720414
820514
done20514
01619
13119
26019
310817
417117
518617
done18617
01619
13119
26019
310817
417117
518617
done18617
01518
13018
26518
315116
431016
543116
654316
759316
862916
963316
done63316
01720
13220
26720
315318
432318
544318
656318
760018
862118
done62118
01720
13220
26720
315318
432318
544318
656318
760018
862118
done62118
01518
13018
26518
315116
431016
543116
654316
759316
862916
963316
done63316
01416
12716
25414
311414
415814
518514
620214
720414
820514
done20514
01822
14522
210122
328020
4115420
done500120
01631
13419
29019
328917
4113211
5292710
done500010
01213
12713
27013
313711
421611
523111
625311
731511
853311
9147211
done500011
089
1169
2399
3949
42009
52769
62869
done2869
089
1169
2319
3529
4819
5929
done929
099
1209
2459
3759
4839
5939
61159
71769
83909
913129
done50019
099
1209
2459
3759
4839
5939
61159
71769
83909
913129
done50019
099
1209
2459
3759
4839
5939
61159
71769
83909
913129
done50019
01315
13115
27115
312413
422013
529413
640913
770613
8107913
9218413
done500013
077
1137
2277
3487
4777
5887
done887
01011
11911
24111
36211
49111
510211
done10211
01417
14015
212015
335115
4105713
5294213
done500013
055
185
2115
3155
4165
done165
0911
1199
2369
3549
4669
5699
done699

prune251.0ms

Filtered
101 candidates to 129 candidates (-27.7%)
Pruning

9 alts after pruning (7 fresh and 2 done)

PrunedKeptTotal
New1272129
Fresh459
Picked011
Done011
Total1319140

Merged error: 6.0b

Counts
140 → 9

localize14.0ms

Local error

Found 4 expressions with local error:

0.2b
(+ (sqrt (- (* b b) (* 4.0 (* a c)))) b)
1.4b
(- (* b b) (* 4.0 (* a c)))
14.7b
(/ (* 4.0 (* a c)) (* a 2.0))
22.5b
(sqrt (- (* b b) (* 4.0 (* a c))))

rewrite28.0ms

Algorithm
rewrite-expression-head
Rules
25×add-exp-log add-cbrt-cube
prod-exp cbrt-unprod
add-log-exp
*-un-lft-identity
cbrt-undiv add-sqr-sqrt div-exp
pow1 add-cube-cbrt
sqrt-prod
flip3-- sqrt-div flip--
+-commutative sub-neg rem-sqrt-square frac-2neg sqrt-pow1 flip3-+ times-frac pow1/2 diff-log clear-num associate-/r* sum-log flip-+ div-inv distribute-lft-out associate-/l*
Counts
4 → 64
Calls
4 calls:
7.0ms
(+ (sqrt (- (* b b) (* 4.0 (* a c)))) b)
4.0ms
(- (* b b) (* 4.0 (* a c)))
10.0ms
(/ (* 4.0 (* a c)) (* a 2.0))
4.0ms
(sqrt (- (* b b) (* 4.0 (* a c))))

series49.0ms

Counts
4 → 12
Calls
4 calls:
17.0ms
(+ (sqrt (- (* b b) (* 4.0 (* a c)))) b)
10.0ms
(- (* b b) (* 4.0 (* a c)))
3.0ms
(/ (* 4.0 (* a c)) (* a 2.0))
18.0ms
(sqrt (- (* b b) (* 4.0 (* a c))))

simplify2.3min

Counts
76 → 76
Iterations

Useful iterations: 1 (1.0ms)

IterNodesCost
01011
11611
23311
35811
46011
done6011
01011
11611
23311
35811
46011
done6011
01123
11723
23423
35923
46123
done6123
01011
11611
23311
35811
46011
done6011
01132
11820
24412
310712
421312
526412
628912
734912
855012
9147012
done500012
01122
11811
23511
36011
46211
done6211
01011
11611
23311
35811
46011
done6011
01011
11611
23311
35811
46011
done6011
01011
11611
23311
35811
46011
done6011
022
141
done41
0910
11510
23210
35710
45910
done5910
01214
13614
213212
363012
4324512
done500112
01330
13924
212922
338020
453420
556120
666920
7101320
8235120
done500020
01120
13120
29918
337816
4100416
5141216
6185416
7307416
done500016
0910
11410
22010
done2010
033
161
done61
01011
11611
23311
35811
46011
done6011
01011
11611
23311
35811
46011
done6011
01214
12314
26014
317114
436410
56558
633208
done50008
01213
12313
25113
312813
429110
55528
630118
done50008
01213
12313
25213
313813
433010
56128
630718
done50008
01112
12312
24512
310812
426010
55058
629478
done50018
01112
12312
25012
312112
43319
55787
625217
done50017
01011
12311
24611
39811
425911
54979
68407
737247
done50017
0910
12410
29310
32988
47086
528966
done50006
0910
12110
27210
32188
44426
514726
done50006
01629
14229
231719
3372313
done500113
01629
14629
233617
3435317
done500017
01629
14629
230317
3360417
done500117
01429
14829
232215
3416915
done500015
01429
14229
229815
3417815
done500015
01229
14429
232113
3483611
done500011
01021
12221
27121
320117
437713
5120513
done500013
0910
12110
27010
32008
43736
511976
done50016
01029
12929
216611
316079
done50009
0910
12110
27010
32008
43736
511976
done50016
0910
12110
27010
32008
43736
511976
done50016
066
1146
2356
3536
4546
done546
044
194
2114
done114
033
done33
055
185
2125
3155
4165
done165
055
1105
2125
done125
089
1209
2639
31739
43037
53565
612355
done50005
067
1127
2277
3525
4753
52043
610893
749743
done50003
067
1157
2365
3663
41563
56013
624403
done50013
01011
12010
23910
39610
425510
583110
6497010
done500010
0910
11510
23210
35710
45910
done5910
0910
11810
24510
310510
421510
565710
6294610
done500010
01021
11621
23321
35821
46021
done6021
0910
11510
23210
35710
45910
done5910
01029
11729
24811
317411
491611
5466111
done500011
0910
11510
23210
35710
45910
done5910
0910
11510
23210
35710
45910
done5910
01113
13513
213111
362211
4313911
done500011
01229
13823
212821
337119
451419
554119
664619
799019
8233419
done500119
066
1146
2356
3536
4546
done546
01019
13019
29817
337815
4101315
5142715
6188615
7303915
done500015
089
1139
2199
done199
066
1146
2356
3536
4546
done546
01214
12113
23913
36413
46613
done6613
01113
11813
23513
36013
46413
done6413
01113
12113
23913
36413
46613
done6613
01227
11927
23627
36127
46527
done6527
01113
11813
23513
36013
46413
done6413
01238
13238
28014
317014
437914
5144414
done500014
01113
11813
23513
36013
46413
done6413
01113
11813
23513
36013
46413
done6413
01316
13216
25816
310916
422516
542716
687516
7273016
done500016
01338
12724
26924
314322
423922
539722
666522
774122
876822
done76822
01125
12213
25513
311213
41607
52446
69746
done50006
01012
11812
23612
36112
46312
done6312
01012
11712
23412
35912
46312
done6312
01213
12713
27013
313711
421611
523111
625311
731511
853311
9147211
done500011
089
1169
2399
3949
42009
52769
62869
done2869
089
1169
2319
3529
4819
5929
done929
033
143
done43
033
143
done43
033
143
done43
099
1209
2459
3759
4839
5939
61159
71769
83909
913129
done50019
099
1209
2459
3759
4839
5939
61159
71769
83909
913129
done50019
099
1209
2459
3759
4839
5939
61159
71769
83909
913129
done50019
01315
13115
28015
315113
423313
528213
637813
754713
881813
9183313
done500013
01011
11911
24211
39711
420311
527911
628911
done28911
077
1137
2277
3487
4777
5887
done887

prune155.0ms

Filtered
64 candidates to 76 candidates (-18.8%)
Pruning

7 alts after pruning (5 fresh and 2 done)

PrunedKeptTotal
New74276
Fresh336
Picked101
Done022
Total78785

Merged error: 5.9b

Counts
85 → 7

localize13.0ms

Local error

Found 4 expressions with local error:

0.1b
(/ (neg (* 2.0 c)) (+ (sqrt (- (* b b) (* 4.0 (* a c)))) b))
0.2b
(+ (sqrt (- (* b b) (* 4.0 (* a c)))) b)
1.4b
(- (* b b) (* 4.0 (* a c)))
22.5b
(sqrt (- (* b b) (* 4.0 (* a c))))

rewrite35.0ms

Algorithm
rewrite-expression-head
Rules
33×*-un-lft-identity
24×times-frac
18×add-sqr-sqrt
17×add-cube-cbrt
distribute-lft-out add-log-exp
add-exp-log add-cbrt-cube associate-/l*
pow1 distribute-lft-neg-in neg-mul-1 distribute-rgt-neg-in
associate-/r*
sqrt-prod
flip3-- flip3-+ sqrt-div associate-/r/ flip-- flip-+
cbrt-undiv +-commutative neg-sub0 sub-neg rem-sqrt-square frac-2neg sqrt-pow1 pow1/2 diff-log div-sub distribute-frac-neg div-exp clear-num sum-log div-inv
Counts
4 → 89
Calls
4 calls:
16.0ms
(/ (neg (* 2.0 c)) (+ (sqrt (- (* b b) (* 4.0 (* a c)))) b))
8.0ms
(+ (sqrt (- (* b b) (* 4.0 (* a c)))) b)
4.0ms
(- (* b b) (* 4.0 (* a c)))
4.0ms
(sqrt (- (* b b) (* 4.0 (* a c))))

series108.0ms

Counts
4 → 12
Calls
4 calls:
63.0ms
(/ (neg (* 2.0 c)) (+ (sqrt (- (* b b) (* 4.0 (* a c)))) b))
18.0ms
(+ (sqrt (- (* b b) (* 4.0 (* a c)))) b)
10.0ms
(- (* b b) (* 4.0 (* a c)))
17.0ms
(sqrt (- (* b b) (* 4.0 (* a c))))

simplify1.3min

Counts
101 → 101
Iterations

Useful iterations: 1 (1.0ms)

IterNodesCost
01011
11611
23311
35811
46011
done6011
01011
11611
23311
35811
46011
done6011
01123
11723
23423
35923
46123
done6123
01011
11611
23311
35811
46011
done6011
01132
11820
24412
310712
421312
526412
628912
734912
855012
9147012
done500012
01122
11811
23511
36011
46211
done6211
01011
11611
23311
35811
46011
done6011
01011
11611
23311
35811
46011
done6011
01011
11611
23311
35811
46011
done6011
022
141
done41
0910
11510
23210
35710
45910
done5910
01214
13614
213212
363012
4324512
done500112
01330
13924
212922
338020
453420
556120
666920
7101320
8235120
done500020
01120
13120
29918
337816
4100416
5141216
6185416
7307416
done500016
0910
11410
22010
done2010
033
161
done61
01011
11611
23311
35811
46011
done6011
01011
11611
23311
35811
46011
done6011
01011
12010
23910
39610
425510
583110
6497010
done500010
0910
11510
23210
35710
45910
done5910
0910
11810
24510
310510
421510
565710
6294610
done500010
01021
11621
23321
35821
46021
done6021
0910
11510
23210
35710
45910
done5910
01029
11729
24811
317411
491611
5466111
done500011
0910
11510
23210
35710
45910
done5910
0910
11510
23210
35710
45910
done5910
01113
13513
213111
362211
4313911
done500011
01229
13823
212821
337119
451419
554119
664619
799019
8233419
done500119
066
1146
2356
3536
4546
done546
01019
13019
29817
337815
4101315
5142715
6188615
7303915
done500015
089
1139
2199
done199
066
1146
2356
3536
4546
done546
01214
12113
23913
36413
46613
done6613
01113
11813
23513
36013
46413
done6413
01113
12113
23913
36413
46613
done6613
01227
11927
23627
36127
46527
done6527
01113
11813
23513
36013
46413
done6413
01238
13238
28014
317014
437914
5144414
done500014
01113
11813
23513
36013
46413
done6413
01113
11813
23513
36013
46413
done6413
01316
13216
25816
310916
422516
542716
687516
7273016
done500016
01338
12724
26924
314322
423922
539722
666522
774122
876822
done76822
01125
12213
25513
311213
41607
52446
69746
done50006
01012
11812
23612
36112
46312
done6312
01012
11712
23412
35912
46312
done6312
01619
13019
25519
39419
411019
511619
612819
714619
817219
920819
1023819
1125119
1228219
1328519
done28519
01518
13218
26518
311718
416118
518618
620218
722618
826218
929218
1030518
1133618
1233918
done33918
01518
12918
25718
39418
411318
513918
618318
729418
858118
9134118
10387818
done500118
01853
15851
222821
3148419
done500119
01637
13037
25537
39237
410437
510737
done10737
01518
12918
25418
38918
410118
510418
done10418
01653
13753
210919
343919
4244419
done500119
01518
12918
25418
38918
410118
510418
done10418
01518
12918
25418
38918
410118
510418
done10418
055
1103
2173
3263
done263
01113
12113
24013
36613
46813
done6813
01214
1191
2361
3611
4651
done651
01316
12316
24416
37216
47716
done7716
01839
13639
26339
39439
49839
done9839
01619
12819
24619
37119
47319
done7319
01725
13125
25125
37725
47925
done7925
01619
12819
24619
37119
47319
done7319
0813
11711
22511
33011
done3011
01518
12718
24518
37018
47218
done7218
0813
11711
22511
33011
done3011
01518
12718
24518
37018
47218
done7218
01733
13133
24933
37433
47633
done7633
01619
12819
24619
37119
47319
done7319
01619
12819
24619
37119
47319
done7319
01619
12819
24619
37119
47319
done7319
077
1145
2185
done185
01518
12718
24518
37018
47218
done7218
077
1145
2185
done185
01518
12718
24518
37018
47218
done7218
01429
12529
24229
36729
47129
done7129
01518
12918
25418
38918
410118
510418
done10418
01315
12215
23915
36415
46615
done6615
01518
12918
25418
38918
410118
510418
done10418
023
141
done41
01417
12817
25317
39017
410217
510517
done10517
023
141
done41
01417
12817
25317
39017
410217
510517
done10517
01429
12329
24029
36529
46729
done6729
01417
12417
24517
37517
47817
done7817
01315
12015
23715
36215
46615
done6615
01417
12417
24517
37517
47817
done7817
033
151
done51
01316
12316
24416
37216
47716
done7716
033
151
done51
01316
12316
24416
37216
47716
done7716
01530
12630
24630
37330
47530
done7530
01215
11915
23615
36115
46515
done6515
01416
12316
24016
36516
46716
done6716
01215
11915
23615
36115
46515
done6515
044
182
2122
done122
01114
11814
23514
36014
46414
done6414
044
182
2122
done122
01114
11814
23514
36014
46414
done6414
01429
12329
24029
36529
46729
done6729
01316
12216
23816
36316
46516
done6516
01315
12015
23715
36215
46615
done6615
01316
12216
23816
36316
46516
done6516
033
151
done51
01215
12115
23715
36215
46415
done6415
033
151
done51
01215
12115
23715
36215
46415
done6415
01214
12114
23814
36314
46514
done6514
01417
12617
24817
37717
47917
done7917
01316
12316
24416
37216
47716
done7716
01632
13232
27232
314032
417532
518232
done18232
01518
12918
25418
38918
410118
510418
done10418
066
1154
2284
3454
4724
5774
done774
066
1154
2284
3454
4724
5774
done774
01518
12718
24518
37018
47218
done7218
01518
12718
24518
37018
47218
done7218
01417
12617
24817
37717
47917
done7917
01316
12316
24216
36716
47116
done7116
01114
11814
23514
36014
46414
done6414
01215
11915
23515
36015
46415
done6415
01721
14321
27721
314021
426421
550921
697121
7299921
done500021
01530
13318
28818
323218
442512
574311
621778
done50018
01213
12713
27013
313711
421611
523111
625311
731511
853311
9147211
done500011
089
1169
2399
3949
42009
52769
62869
done2869
089
1169
2319
3529
4819
5929
done929
099
1209
2459
3759
4839
5939
61159
71769
83909
913129
done50019
099
1209
2459
3759
4839
5939
61159
71769
83909
913129
done50019
099
1209
2459
3759
4839
5939
61159
71769
83909
913129
done50019
01315
13115
28015
315113
423313
528213
637813
754713
881813
9183313
done500013
01011
11911
24211
39711
420311
527911
628911
done28911
077
1137
2277
3487
4777
5887
done887
011
done11
055
185
2115
3155
4165
done165
01520
13818
210816
325716
469516
5257116
done500016

prune171.0ms

Filtered
81 candidates to 101 candidates (-24.7%)
Pruning

9 alts after pruning (6 fresh and 3 done)

PrunedKeptTotal
New983101
Fresh134
Picked011
Done022
Total999108

Merged error: 5.9b

Counts
108 → 9

regimes343.0ms

Accuracy

96.2% (0.9b remaining)

Error of 6.6b against oracle of 5.6b and baseline of 29.9b

bsearch104.0ms

Steps
ItersRangePoint
6
8.452635886898758e+130
9.412684251322846e+131
1.1115227370785376e+131
9
-4.034898188869506e-219
-6.5582180480617695e-226
-1.909915866640199e-222
8
-3.3260857371803445e+155
-4.675996499956814e+152
-3.629137574162212e+153

simplify6.0ms

Iterations

Useful iterations: 0 (1.0ms)

IterNodesCost
03359
14559
24759
done4759

end0.0ms

sample1.9s

Algorithm
intervals
Results
363.0ms1002×body2560valid
359.0ms5928×body80valid
261.0ms947×body1280valid
192.0ms2954×body80nan
103.0ms421×body640valid
46.0ms101×body5120valid
39.0ms236×body320valid
11.0ms99×body160valid

Profiling

Loading profile data...