Details

Time bar (total: 3.5min)

sample15.0ms

Algorithm
intervals
Results
7.0ms257×body80valid

simplify8.0ms

Counts
1 → 1
Iterations

Useful iterations: 1 (3.0ms)

IterNodesCost
048
186
2126
3136
done136

prune8.0ms

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: 28.1b

Counts
2 → 1

localize5.0ms

Local error

Found 1 expressions with local error:

27.0b
(sqrt (* x (+ x x)))

rewrite8.0ms

Algorithm
rewrite-expression-head
Rules
pow1
sqrt-pow1 sqrt-div associate-*r/
add-exp-log add-sqr-sqrt add-cube-cbrt *-un-lft-identity flip3-+ pow1/2 pow-prod-down sqrt-prod add-cbrt-cube flip-+ add-log-exp
Counts
1 → 13
Calls
1 calls:
7.0ms
(sqrt (* x (+ x x)))

series13.0ms

Counts
1 → 3
Calls
1 calls:
13.0ms
(sqrt (* x (+ x x)))

simplify15.7s

Counts
16 → 16
Iterations

Useful iterations: 2 (3.0ms)

IterNodesCost
057
1107
2127
3137
done137
057
1107
2127
3137
done137
0615
11115
21315
31415
done1415
057
1107
2127
3137
done137
0620
11212
2298
3558
4658
5758
6988
71598
83658
913088
done50018
022
done22
034
154
264
done64
0610
1208
2526
31236
42716
57856
628596
done50016
0512
1156
2244
3702
42472
512102
649402
done50002
0510
1134
2191
3201
done201
034
161
done61
033
161
done61
033
161
done61
057
1107
2127
3137
done137
057
1107
2127
3137
done137
044
154
done54
044
154
done54
066
1115
2235
done235

prune43.0ms

Filtered
13 candidates to 16 candidates (-23.1%)
Pruning

7 alts after pruning (7 fresh and 0 done)

PrunedKeptTotal
New9716
Fresh000
Picked101
Done000
Total10717

Merged error: 0.1b

Counts
17 → 7

localize7.0ms

Local error

Found 1 expressions with local error:

27.0b
(pow (* x (+ x x)) 1/2)

rewrite7.0ms

Algorithm
rewrite-expression-head
Rules
pow1 add-exp-log
pow-unpow
add-sqr-sqrt add-cube-cbrt pow-pow *-un-lft-identity pow-exp
pow-to-exp unpow-prod-down pow-prod-down prod-exp add-cbrt-cube unpow1/2 add-log-exp sqr-pow
Counts
1 → 18
Calls
1 calls:
7.0ms
(pow (* x (+ x x)) 1/2)

series32.0ms

Counts
1 → 3
Calls
1 calls:
32.0ms
(pow (* x (+ x x)) 1/2)

simplify58.9s

Counts
21 → 21
Iterations

Useful iterations: 1 (1.0ms)

IterNodesCost
079
1119
2229
3299
4389
5479
6537
71107
83117
914217
done50007
068
1158
2268
3378
4518
5608
6667
71247
83307
914477
done50007
068
1158
2268
3378
4518
5608
6667
71247
83307
914477
done50007
033
161
done61
033
161
done61
0711
11511
22411
34911
410611
526311
688311
7331211
done500011
068
1148
2218
3408
4828
51868
65628
721858
done50008
057
1165
2255
3375
4595
51245
63385
712635
done50005
033
192
2152
3252
4492
51142
63372
712732
done50002
045
1114
2184
3284
4504
51114
63234
712634
done50004
068
1187
2337
3617
41307
53307
611197
done50017
068
1167
2267
3427
4797
51947
66647
730127
done50007
0717
11715
22515
33615
45815
512315
633815
7126015
done500015
068
1167
2247
3357
4577
51207
63397
712737
done50017
0723
12114
2468
31207
43537
512497
done50007
068
1167
2257
3367
4587
51227
63287
712527
done50017
068
1167
2257
3367
4587
51227
63287
712527
done50017
079
1167
2247
3357
4577
51157
63357
712687
done50007
079
1167
2247
3357
4577
51157
63357
712687
done50007
0910
12010
23810
3697
41664
54104
612724
746524
done50014
01112
12311
24711
31099
42506
55564
614254
done50004
01112
12012
24112
310111
42568
57816
626561
727251
done27251

prune39.0ms

Filtered
13 candidates to 21 candidates (-61.5%)
Pruning

7 alts after pruning (6 fresh and 1 done)

PrunedKeptTotal
New21021
Fresh066
Picked011
Done000
Total21728

Merged error: 0.1b

Counts
28 → 7

localize7.0ms

Local error

Found 4 expressions with local error:

0.1b
(sqrt (sqrt (* x (+ x x))))
0.5b
(* (sqrt (sqrt (* x (+ x x)))) (sqrt (sqrt (* x (+ x x)))))
27.0b
(sqrt (* x (+ x x)))
27.0b
(sqrt (* x (+ x x)))

rewrite43.0ms

Algorithm
rewrite-expression-head
Rules
84×sqrt-pow1
71×pow1
33×sqrt-prod
32×sqrt-div
26×add-sqr-sqrt
25×pow-prod-down
22×pow1/2
20×associate-*r/
14×pow-prod-up
13×add-cube-cbrt *-un-lft-identity
flip3-+ swap-sqr flip-+
pow-sqr
associate-*r* associate-*l*
add-exp-log add-cbrt-cube
frac-times add-log-exp unswap-sqr
associate-*l/
pow2 rem-sqrt-square pow-plus sqrt-unprod prod-exp rem-square-sqrt *-commutative cbrt-unprod
Counts
4 → 124
Calls
4 calls:
6.0ms
(sqrt (sqrt (* x (+ x x))))
19.0ms
(* (sqrt (sqrt (* x (+ x x)))) (sqrt (sqrt (* x (+ x x)))))
5.0ms
(sqrt (* x (+ x x)))
6.0ms
(sqrt (* x (+ x x)))

series26.0ms

Counts
4 → 12
Calls
4 calls:
6.0ms
(sqrt (sqrt (* x (+ x x))))
11.0ms
(* (sqrt (sqrt (* x (+ x x)))) (sqrt (sqrt (* x (+ x x)))))
5.0ms
(sqrt (* x (+ x x)))
4.0ms
(sqrt (* x (+ x x)))

simplify2.1min

Counts
136 → 136
Iterations

Useful iterations: 2 (10.0ms)

IterNodesCost
057
1107
2127
3137
done137
057
1107
2127
3137
done137
0615
11115
21315
31415
done1415
057
1107
2127
3137
done137
0620
11212
2298
3558
4658
5758
6988
71598
83658
913088
done50018
022
done22
034
154
264
done64
0610
1208
2526
31236
42716
57856
628596
done50016
0512
1156
2244
3702
42472
512102
649402
done50002
0510
1134
2191
3201
done201
034
161
done61
033
161
done61
033
161
done61
057
1107
2127
3137
done137
057
1107
2127
3137
done137
057
1107
2127
3137
done137
057
1107
2127
3137
done137
0615
11115
21315
31415
done1415
057
1107
2127
3137
done137
0620
11212
2298
3558
4658
5758
6988
71598
83658
913088
done50018
022
done22
034
154
264
done64
0610
1208
2526
31236
42716
57856
628596
done50016
0512
1156
2244
3702
42472
512102
649402
done50002
0510
1134
2191
3201
done201
034
161
done61
033
161
done61
033
161
done61
057
1107
2127
3137
done137
057
1107
2127
3137
done137
023
151
271
done71
055
181
done81
023
161
done61
047
163
271
done71
079
1143
done141
079
1143
done141
055
183
done81
047
183
291
done91
079
1143
done141
0511
1125
2181
done181
0511
1125
2181
done181
079
1143
done141
0511
1125
2181
done181
0511
1125
2181
done181
0513
1105
2135
3145
done145
0615
1116
2146
3156
done156
0411
11511
2489
3869
41347
51635
62045
73665
88375
924115
done50015
0513
1105
2135
3145
done145
0411
11511
2489
3869
41347
51635
62045
73665
88375
924115
done50015
0411
11511
2489
3869
41347
51635
62045
73665
88375
924115
done50015
0411
11511
2489
3869
41347
51635
62045
73665
88375
924115
done50015
0411
11511
2489
3869
41347
51635
62045
73665
88375
924115
done50015
023
161
done61
0717
11310
21610
31710
done1710
0716
1147
2187
3207
done207
0716
1147
2207
3267
4447
5847
61917
75717
822517
done50007
0847
12020
23412
3788
41548
52448
64828
715208
done50018
0833
11315
21615
31715
done1715
0716
1127
2157
3167
done167
0847
12120
2328
3778
41538
52488
64958
715708
done50018
0513
1105
2135
3145
done145
0716
1137
2157
3167
done167
0716
1137
2157
3167
done167
0823
1228
2556
31286
42796
57876
628726
done50016
0727
1176
2274
3732
42522
511992
649542
done50002
01323
13515
2709
31369
42911
57921
629141
done50001
01019
1229
2297
3751
42561
512001
649091
done50001
01323
13515
2709
31389
42971
58331
629081
done50011
01019
1229
2297
3751
42521
512271
done50001
0723
1154
2221
3231
done231
0511
181
done81
0835
11735
22119
33010
44510
57110
614310
735810
8126810
done500010
0717
11217
21417
31517
done1517
0833
11415
21715
31815
done1815
0717
1127
2157
3167
done167
047
done42
0511
174
294
done94
0717
1127
2157
3167
done167
0717
1127
2157
3167
done167
0717
1127
2157
3167
done167
0717
1127
2157
3167
done167
035
151
done51
0615
1116
2146
3156
done156
0717
1127
2157
3167
done167
0717
1127
2157
3167
done167
0717
1127
2157
3167
done167
0717
1127
2157
3167
done167
023
141
done41
0615
1116
2146
3156
done156
0717
1127
2157
3167
done167
0717
1127
2157
3167
done167
0717
1127
2157
3167
done167
0717
1127
2157
3167
done167
0717
1127
2157
3167
done167
0717
1127
2157
3167
done167
0717
1127
2157
3167
done167
0717
1127
2157
3167
done167
033
151
271
done71
033
161
done61
045
193
2111
done111
045
1101
done101
057
1145
2221
done221
057
1145
2221
done221
057
1145
2221
done221
057
1145
2221
done221
0825
11625
22025
32125
done2125
0924
11616
21816
31916
done1916
0811
11411
21611
31711
done1711
0716
11316
21516
31616
done1616
0810
1169
2189
3197
4227
done227
0716
11316
21516
31616
done1616
079
1157
2207
3217
done217
0716
11316
21516
31616
done1616
0816
11416
21616
31716
done1716
0813
11413
21613
31713
done1713
0716
11316
21516
31616
done1616
0615
1116
2146
3156
done156
0716
11316
21516
31616
done1616
0615
1116
2146
3156
done156
01219
13017
25915
311415
427015
579815
6293015
done500015
01119
12313
2299
3309
done301
01219
13017
25915
311615
426815
577215
6282015
done500015
01119
12313
2299
3309
done301
068
1118
2138
3148
done148
068
1118
2138
3148
done148
0717
11217
21417
31517
done1517
068
1118
2138
3148
done148
0723
11314
2189
3239
4299
5399
6609
71179
83249
912509
done50009
0716
1138
2158
3168
done168
068
1118
2138
3148
done148
033
done33
045
165
275
done75
068
1118
2138
3148
done148
068
1118
2138
3148
done148
022
141
done41
057
1107
2127
3137
done137
0711
1219
2537
31227
42727
57697
627907
done50007
0613
1167
2255
3713
42513
512233
done50013
0611
1145
2201
3211
done211
045
171
done71
033
141
done41
033
161
done61
045
1103
2111
done111
045
1103
2111
done111
068
1118
2138
3148
done148
068
1118
2138
3148
done148
044
154
done54
044
154
done54
066
1115
2235
done235
044
154
done54
044
154
done54
066
1115
2235
done235
044
154
done54
044
154
done54
066
1115
2235
done235
02032
16332
222929
384626
4411024
done500024
01828
15228
218825
354525
4240121
done500121
01828
15328
219425
360525
4278421
done500121

prune103.0ms

Filtered
71 candidates to 136 candidates (-91.5%)
Pruning

6 alts after pruning (4 fresh and 2 done)

PrunedKeptTotal
New1351136
Fresh235
Picked011
Done011
Total1376143

Merged error: 0.1b

Counts
143 → 6

localize3.0ms

Local error

Found 1 expressions with local error:

0.4b
(* x (sqrt 2))

rewrite7.0ms

Algorithm
rewrite-expression-head
Rules
add-sqr-sqrt
associate-*r*
add-cube-cbrt *-un-lft-identity sqrt-prod
pow1 add-exp-log associate-*l* add-cbrt-cube
unswap-sqr
pow-prod-down prod-exp *-commutative cbrt-unprod add-log-exp
Counts
1 → 22
Calls
1 calls:
6.0ms
(* x (sqrt 2))

series5.0ms

Counts
1 → 3
Calls
1 calls:
5.0ms
(* x (sqrt 2))

simplify10.7s

Counts
25 → 25
Iterations

Useful iterations: 1 (1.0ms)

IterNodesCost
044
154
done54
066
176
done76
055
195
2105
done105
055
185
2135
3215
4445
51005
62395
76965
826955
done50005
0814
11510
2388
3698
4978
51438
62668
76588
821028
done50008
0611
1711
done711
055
165
done65
0614
11714
2466
3876
41046
51486
62806
77426
827136
done50016
055
165
done65
055
165
done65
066
176
done76
066
176
done76
066
176
done76
066
176
done76
069
199
2119
done119
068
185
done85
055
165
done65
044
173
done73
055
165
done65
033
161
done61
055
165
done65
055
165
done65
044
154
done54
044
154
done54
044
154
done54
044
154
done54

prune36.0ms

Filtered
17 candidates to 25 candidates (-47.1%)
Pruning

9 alts after pruning (6 fresh and 3 done)

PrunedKeptTotal
New22325
Fresh033
Picked011
Done022
Total22931

Merged error: 0.1b

Counts
31 → 9

regimes60.0ms

Accuracy

99.1% (0.3b remaining)

Error of 0.4b against oracle of 0.1b and baseline of 30.7b

bsearch12.0ms

Steps
ItersRangePoint
8
-7.67443757966827e-305
8.126837495347253e-308
1.9786006080648e-310

simplify3.0ms

Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
01216
11816
22016
done2016

end0.0ms

sample366.0ms

Algorithm
intervals
Results
210.0ms8006×body80valid

Profiling

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