Details

Time bar (total: 1.0m)

sample783.0ms

Algorithm
intervals
Results
492.0ms1384×body80nan
197.0ms424×body80valid

simplify824.0ms

Counts
1 → 1
Iterations
IterNodes
done2006
31261
2198
158
022

prune14.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 24.5b

localize110.0ms

Local error

Found 4 expressions with local error:

7.9b
(* (* (pow (/ d h) (/ 1 2)) (pow (/ d l) (/ 1 2))) (- 1 (* (* (/ 1 2) (pow (/ (* M D) (* 2 d)) 2)) (/ h l))))
9.4b
(pow (/ d h) (/ 1 2))
11.5b
(pow (/ d l) (/ 1 2))
13.2b
(* (* (/ 1 2) (pow (/ (* M D) (* 2 d)) 2)) (/ h l))

rewrite145.0ms

Algorithm
rewrite-expression-head
Rules
331×add-exp-log
179×prod-exp
99×div-exp
60×pow-exp
45×times-frac
40×add-sqr-sqrt *-un-lft-identity add-cube-cbrt
30×add-cbrt-cube
26×pow-unpow unpow-prod-down
18×pow-to-exp
16×associate-*r*
14×rec-exp 1-exp
13×cbrt-unprod
10×pow1
5×cbrt-undiv div-inv
4×insert-posit16 add-log-exp
3×associate-*l/ associate-*r/
2×distribute-rgt-in sub-neg pow-pow distribute-lft-in associate-*l* pow-prod-down *-commutative sqr-pow
1×frac-times flip3-- flip--
Counts
4 → 208
Calls
4 calls:
39.0ms
(* (* (pow (/ d h) (/ 1 2)) (pow (/ d l) (/ 1 2))) (- 1 (* (* (/ 1 2) (pow (/ (* M D) (* 2 d)) 2)) (/ h l))))
5.0ms
(pow (/ d h) (/ 1 2))
5.0ms
(pow (/ d l) (/ 1 2))
89.0ms
(* (* (/ 1 2) (pow (/ (* M D) (* 2 d)) 2)) (/ h l))

series737.0ms

Counts
4 → 12
Calls
4 calls:
449.0ms
(* (* (pow (/ d h) (/ 1 2)) (pow (/ d l) (/ 1 2))) (- 1 (* (* (/ 1 2) (pow (/ (* M D) (* 2 d)) 2)) (/ h l))))
83.0ms
(pow (/ d h) (/ 1 2))
99.0ms
(pow (/ d l) (/ 1 2))
105.0ms
(* (* (/ 1 2) (pow (/ (* M D) (* 2 d)) 2)) (/ h l))

simplify991.0ms

Counts
220 → 220
Iterations
IterNodes
done2002
11295
0438

prune1.5s

Pruning

21 alts after pruning (21 fresh and 0 done)

Merged error: 11.7b

localize81.0ms

Local error

Found 4 expressions with local error:

4.0b
(/ (* M D) (* 2 d))
7.9b
(* (* (* (sqrt (/ 1 (* (cbrt h) (cbrt h)))) (sqrt (/ d (cbrt h)))) (pow (/ d l) (/ 1 2))) (- 1 (* (* (/ 1 2) (pow (/ (* M D) (* 2 d)) 2)) (/ h l))))
11.5b
(pow (/ d l) (/ 1 2))
13.2b
(* (* (/ 1 2) (pow (/ (* M D) (* 2 d)) 2)) (/ h l))

rewrite724.0ms

Algorithm
rewrite-expression-head
Rules
320×add-exp-log
171×prod-exp
96×div-exp
46×add-cbrt-cube pow-exp
28×times-frac
26×add-sqr-sqrt *-un-lft-identity add-cube-cbrt
20×cbrt-unprod
18×associate-*l/
16×associate-*r*
14×rec-exp 1-exp
13×pow-unpow unpow-prod-down
12×sqrt-div
11×pow-to-exp
10×frac-times
9×pow1 cbrt-undiv
6×associate-*r/
4×flip3-- insert-posit16 div-inv flip-- add-log-exp
2×distribute-rgt-in sub-neg distribute-lft-in associate-*l* pow-prod-down *-commutative
1×clear-num associate-/r* pow-pow frac-2neg associate-/l* sqr-pow
Counts
4 → 193
Calls
4 calls:
22.0ms
(/ (* M D) (* 2 d))
637.0ms
(* (* (* (sqrt (/ 1 (* (cbrt h) (cbrt h)))) (sqrt (/ d (cbrt h)))) (pow (/ d l) (/ 1 2))) (- 1 (* (* (/ 1 2) (pow (/ (* M D) (* 2 d)) 2)) (/ h l))))
10.0ms
(pow (/ d l) (/ 1 2))
46.0ms
(* (* (/ 1 2) (pow (/ (* M D) (* 2 d)) 2)) (/ h l))

series2.6s

Counts
4 → 12
Calls
4 calls:
38.0ms
(/ (* M D) (* 2 d))
2.3s
(* (* (* (sqrt (/ 1 (* (cbrt h) (cbrt h)))) (sqrt (/ d (cbrt h)))) (pow (/ d l) (/ 1 2))) (- 1 (* (* (/ 1 2) (pow (/ (* M D) (* 2 d)) 2)) (/ h l))))
93.0ms
(pow (/ d l) (/ 1 2))
123.0ms
(* (* (/ 1 2) (pow (/ (* M D) (* 2 d)) 2)) (/ h l))

simplify1.2s

Counts
205 → 205
Iterations
IterNodes
done2011
11428
0472

prune1.6s

Pruning

24 alts after pruning (24 fresh and 0 done)

Merged error: 10.7b

localize110.0ms

Local error

Found 4 expressions with local error:

2.0b
(sqrt (/ d (cbrt l)))
4.0b
(/ (* M D) (* 2 d))
7.9b
(* (* (* (sqrt (/ 1 (* (cbrt h) (cbrt h)))) (sqrt (/ d (cbrt h)))) (* (sqrt (/ (/ 1 (cbrt l)) (cbrt l))) (sqrt (/ d (cbrt l))))) (- 1 (* (* (/ 1 2) (pow (/ (* M D) (* 2 d)) 2)) (/ h l))))
13.2b
(* (* (/ 1 2) (pow (/ (* M D) (* 2 d)) 2)) (/ h l))

rewrite865.0ms

Algorithm
rewrite-expression-head
Rules
305×add-exp-log
163×prod-exp
97×sqrt-div
93×div-exp
82×frac-times
55×add-cbrt-cube
51×associate-*l/
40×pow-exp
36×associate-*r/
30×add-sqr-sqrt times-frac
27×cbrt-unprod
25×pow1 *-un-lft-identity add-cube-cbrt
22×sqrt-prod
16×flip3-- associate-*r* flip--
14×rec-exp 1-exp pow-prod-down
10×cbrt-prod
9×cbrt-undiv
8×pow-to-exp
4×insert-posit16 add-log-exp
3×rem-sqrt-square div-inv
2×distribute-rgt-in sub-neg distribute-lft-in associate-*l* *-commutative
1×clear-num associate-/r* frac-2neg sqrt-pow1 pow1/2 associate-/l*
Counts
4 → 228
Calls
4 calls:
3.0ms
(sqrt (/ d (cbrt l)))
11.0ms
(/ (* M D) (* 2 d))
788.0ms
(* (* (* (sqrt (/ 1 (* (cbrt h) (cbrt h)))) (sqrt (/ d (cbrt h)))) (* (sqrt (/ (/ 1 (cbrt l)) (cbrt l))) (sqrt (/ d (cbrt l))))) (- 1 (* (* (/ 1 2) (pow (/ (* M D) (* 2 d)) 2)) (/ h l))))
57.0ms
(* (* (/ 1 2) (pow (/ (* M D) (* 2 d)) 2)) (/ h l))

series2.2s

Counts
4 → 12
Calls
4 calls:
216.0ms
(sqrt (/ d (cbrt l)))
45.0ms
(/ (* M D) (* 2 d))
1.9s
(* (* (* (sqrt (/ 1 (* (cbrt h) (cbrt h)))) (sqrt (/ d (cbrt h)))) (* (sqrt (/ (/ 1 (cbrt l)) (cbrt l))) (sqrt (/ d (cbrt l))))) (- 1 (* (* (/ 1 2) (pow (/ (* M D) (* 2 d)) 2)) (/ h l))))
112.0ms
(* (* (/ 1 2) (pow (/ (* M D) (* 2 d)) 2)) (/ h l))

simplify1.9s

Counts
240 → 240
Iterations
IterNodes
done2000
11901
0632

prune2.3s

Pruning

27 alts after pruning (27 fresh and 0 done)

Merged error: 8.0b

localize110.0ms

Local error

Found 4 expressions with local error:

4.9b
(/ M (/ 2 (/ D d)))
5.2b
(/ (* h (* (/ M (/ 2 (/ D d))) (/ M (/ 2 (/ D d))))) (* 2 l))
7.7b
(* h (* (/ M (/ 2 (/ D d))) (/ M (/ 2 (/ D d)))))
7.9b
(* (* (* (sqrt (/ 1 (* (cbrt h) (cbrt h)))) (sqrt (/ d (cbrt h)))) (* (sqrt (/ (/ 1 (cbrt l)) (cbrt l))) (sqrt (/ d (cbrt l))))) (- 1 (/ (* h (* (/ M (/ 2 (/ D d))) (/ M (/ 2 (/ D d))))) (* 2 l))))

rewrite1.1s

Algorithm
rewrite-expression-head
Rules
397×times-frac
381×add-cbrt-cube add-exp-log
195×add-sqr-sqrt
194×*-un-lft-identity
191×add-cube-cbrt
186×cbrt-undiv div-exp
130×prod-exp cbrt-unprod
96×sqrt-div
83×frac-times
50×associate-*l/
45×associate-/r*
43×associate-*r/
27×pow1
18×div-inv
16×flip3-- pow-prod-down flip--
7×associate-*r*
5×associate-/r/
4×associate-*l* insert-posit16 associate-/l* add-log-exp
3×associate-/l/
2×distribute-rgt-in clear-num sub-neg frac-2neg distribute-lft-in *-commutative difference-of-squares
1×distribute-lft-out-- unswap-sqr
Counts
4 → 421
Calls
4 calls:
16.0ms
(/ M (/ 2 (/ D d)))
76.0ms
(/ (* h (* (/ M (/ 2 (/ D d))) (/ M (/ 2 (/ D d))))) (* 2 l))
59.0ms
(* h (* (/ M (/ 2 (/ D d))) (/ M (/ 2 (/ D d)))))
892.0ms
(* (* (* (sqrt (/ 1 (* (cbrt h) (cbrt h)))) (sqrt (/ d (cbrt h)))) (* (sqrt (/ (/ 1 (cbrt l)) (cbrt l))) (sqrt (/ d (cbrt l))))) (- 1 (/ (* h (* (/ M (/ 2 (/ D d))) (/ M (/ 2 (/ D d))))) (* 2 l))))

series2.3s

Counts
4 → 12
Calls
4 calls:
56.0ms
(/ M (/ 2 (/ D d)))
164.0ms
(/ (* h (* (/ M (/ 2 (/ D d))) (/ M (/ 2 (/ D d))))) (* 2 l))
153.0ms
(* h (* (/ M (/ 2 (/ D d))) (/ M (/ 2 (/ D d)))))
1.9s
(* (* (* (sqrt (/ 1 (* (cbrt h) (cbrt h)))) (sqrt (/ d (cbrt h)))) (* (sqrt (/ (/ 1 (cbrt l)) (cbrt l))) (sqrt (/ d (cbrt l))))) (- 1 (/ (* h (* (/ M (/ 2 (/ D d))) (/ M (/ 2 (/ D d))))) (* 2 l))))

simplify2.6s

Counts
433 → 433
Iterations
IterNodes
done2000
0943

prune5.4s

Pruning

27 alts after pruning (27 fresh and 0 done)

Merged error: 7.4b

regimes2.6s

Accuracy

12.7% (4.9b remaining)

Error of 12.8b against oracle of 7.9b and baseline of 13.5b

bsearch5.0ms

simplify4.2s

Iterations
IterNodes
done2001
6191998
6181995
6171992
6161989
6151986
6141983
6131980
6121977
6111974
6101971
6091968
6081965
6071962
6061959
6051956
6041953
6031950
6021947
6011944
6001941
5991938
5981935
5971932
5961929
5951926
5941923
5931920
5921917
5911914
5901911
5891908
5881905
5871902
5861899
5851896
5841893
5831890
5821887
5811884
5801881
5791878
5781875
5771872
5761869
5751866
5741863
5731860
5721857
5711854
5701851
5691848
5681845
5671842
5661839
5651836
5641833
5631830
5621827
5611824
5601821
5591818
5581815
5571812
5561809
5551806
5541803
5531800
5521797
5511794
5501791
5491788
5481785
5471782
5461779
5451776
5441773
5431770
5421767
5411764
5401761
5391758
5381755
5371752
5361749
5351746
5341743
5331740
5321737
5311734
5301731
5291728
5281725
5271722
5261719
5251716
5241713
5231710
5221707
5211704
5201701
5191698
5181695
5171692
5161689
5151686
5141683
5131680
5121677
5111674
5101671
5091668
5081665
5071662
5061659
5051656
5041653
5031650
5021647
5011644
5001641
4991638
4981635
4971632
4961629
4951626
4941623
4931620
4921617
4911614
4901611
4891608
4881605
4871602
4861599
4851596
4841593
4831590
4821587
4811584
4801581
4791578
4781575
4771572
4761569
4751566
4741563
4731560
4721557
4711554
4701551
4691548
4681545
4671542
4661539
4651536
4641533
4631530
4621527
4611524
4601521
4591518
4581515
4571512
4561509
4551506
4541503
4531500
4521497
4511494
4501491
4491488
4481485
4471482
4461479
4451476
4441473
4431470
4421467
4411464
4401461
4391458
4381455
4371452
4361449
4351446
4341443
4331440
4321437
4311434
4301431
4291428
4281425
4271422
4261419
4251416
4241413
4231410
4221407
4211404
4201401
4191398
4181395
4171392
4161389
4151386
4141383
4131380
4121377
4111374
4101371
4091368
4081365
4071362
4061359
4051356
4041353
4031350
4021347
4011344
4001341
3991338
3981335
3971332
3961329
3951326
3941323
3931320
3921317
3911314
3901311
3891308
3881305
3871302
3861299
3851296
3841293
3831290
3821287
3811284
3801281
3791278
3781275
3771272
3761269
3751266
3741263
3731260
3721257
3711254
3701251
3691248
3681245
3671242
3661239
3651236
3641233
3631230
3621227
3611224
3601221
3591218
3581215
3571212
3561209
3551206
3541203
3531200
3521197
3511194
3501191
3491188
3481185
3471182
3461179
3451176
3441173
3431170
3421167
3411164
3401161
3391158
3381155
3371152
3361149
3351146
3341143
3331140
3321137
3311134
3301131
3291128
3281125
3271122
3261119
3251116
3241113
3231110
3221107
3211104
3201101
3191098
3181095
3171092
3161089
3151086
3141083
3131080
3121077
3111074
3101071
3091068
3081065
3071062
3061059
3051056
3041053
3031050
3021047
3011044
3001041
2991038
2981035
2971032
2961029
2951026
2941023
2931020
2921017
2911014
2901011
2891008
2881005
2871002
286999
285996
284993
283990
282987
281984
280981
279978
278975
277972
276969
275966
274963
273960
272957
271954
270951
269948
268945
267942
266939
265936
264933
263930
262927
261924
260921
259918
258915
257912
256909
255906
254903
253900
252897
251894
250891
249888
248885
247882
246879
245876
244873
243870
242867
241864
240861
239858
238855
237852
236849
235846
234843
233840
232837
231834
230831
229828
228825
227822
226819
225816
224813
223810
222807
221804
220801
219798
218795
217792
216789
215786
214783
213780
212777
211774
210771
209768
208765
207762
206759
205756
204753
203750
202747
201744
200741
199738
198735
197732
196729
195726
194723
193720
192717
191714
190711
189708
188705
187702
186699
185696
184693
183690
182687
181684
180681
179678
178675
177672
176669
175666
174663
173660
172657
171654
170651
169648
168645
167642
166639
165636
164633
163630
162627
161624
160621
159618
158615
157612
156609
155606
154603
153600
152597
151594
150591
149588
148585
147582
146579
145576
144573
143570
142567
141564
140561
139558
138555
137552
136549
135546
134543
133540
132537
131534
130531
129528
128525
127522
126519
125516
124513
123510
122507
121504
120501
119498
118495
117492
116489
115486
114483
113480
112477
111474
110471
109468
108465
107462
106459
105456
104453
103450
102447
101444
100441
99438
98435
97432
96429
95426
94423
93420
92417
91414
90411
89408
88405
87402
86399
85396
84393
83390
82387
81384
80381
79378
78375
77372
76369
75366
74363
73360
72357
71354
70351
69348
68345
67342
66339
65336
64333
63330
62327
61324
60321
59318
58315
57312
56309
55306
54303
53300
52297
51294
50291
49288
48285
47282
46279
45276
44273
43270
42267
41264
40261
39258
38255
37252
36249
35246
34243
33240
32237
31234
30231
29228
28225
27222
26219
25216
24213
23210
22207
21204
20201
19198
18195
17192
16189
15186
14183
13180
12177
11174
10171
9168
8165
7162
6159
5156
4142
3117
297
189
062

end0.0ms

sample23.7s

Algorithm
intervals
Results
15.6s37697×body80nan
5.3s12790×body80valid