Details

Time bar (total: 35.0s)

sample203.0ms

Algorithm
intervals
Results
65.0ms53×body1280valid
55.0ms131×body80valid
44.0ms48×body640valid
9.0ms14×body320valid
5.0ms10×body160valid

simplify990.0ms

Counts
1 → 1
Iterations
IterNodes
52067
4616
3185
279
134
017

prune17.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 18.9b

localize38.0ms

Local error

Found 4 expressions with local error:

0.1b
(* (* J 2) (cos (/ K 2)))
0.2b
(* (/ U (* (* J 2) (cos (/ K 2)))) (/ U (* (* J 2) (cos (/ K 2)))))
7.3b
(* (sqrt (+ (* (/ U (* (* J 2) (cos (/ K 2)))) (/ U (* (* J 2) (cos (/ K 2))))) 1)) (* (cos (/ K 2)) (* -2 J)))
11.3b
(sqrt (+ (* (/ U (* (* J 2) (cos (/ K 2)))) (/ U (* (* J 2) (cos (/ K 2))))) 1))

rewrite610.0ms

Algorithm
rewrite-expression-head
Rules
98×add-cbrt-cube add-exp-log
49×prod-exp cbrt-unprod
26×pow1
24×cbrt-undiv div-exp
19×add-sqr-sqrt
16×*-un-lft-identity add-cube-cbrt
14×associate-*l*
12×times-frac
11×associate-*r*
10×pow-prod-down
7×swap-sqr
6×sqrt-prod
4×sqrt-div div-inv add-log-exp
3×associate-*l/ *-commutative
2×flip3-+ flip-+
1×pow2 frac-times rem-sqrt-square sqrt-pow1 pow-plus pow1/2 associate-*r/ pow-sqr pow-prod-up unswap-sqr
Counts
4 → 129
Calls
4 calls:
13.0ms
(* (* J 2) (cos (/ K 2)))
101.0ms
(* (/ U (* (* J 2) (cos (/ K 2)))) (/ U (* (* J 2) (cos (/ K 2)))))
343.0ms
(* (sqrt (+ (* (/ U (* (* J 2) (cos (/ K 2)))) (/ U (* (* J 2) (cos (/ K 2))))) 1)) (* (cos (/ K 2)) (* -2 J)))
149.0ms
(sqrt (+ (* (/ U (* (* J 2) (cos (/ K 2)))) (/ U (* (* J 2) (cos (/ K 2))))) 1))

series603.0ms

Counts
4 → 12
Calls
4 calls:
62.0ms
(* (* J 2) (cos (/ K 2)))
165.0ms
(* (/ U (* (* J 2) (cos (/ K 2)))) (/ U (* (* J 2) (cos (/ K 2)))))
207.0ms
(* (sqrt (+ (* (/ U (* (* J 2) (cos (/ K 2)))) (/ U (* (* J 2) (cos (/ K 2))))) 1)) (* (cos (/ K 2)) (* -2 J)))
169.0ms
(sqrt (+ (* (/ U (* (* J 2) (cos (/ K 2)))) (/ U (* (* J 2) (cos (/ K 2))))) 1))

simplify1.3s

Counts
141 → 141
Iterations
IterNodes
23115
1661
0227

prune2.3s

Pruning

7 alts after pruning (6 fresh and 1 done)

Merged error: 10.2b

localize33.0ms

Local error

Found 4 expressions with local error:

0.1b
(* (* J 2) (cos (/ K 2)))
0.2b
(* (/ U (* (* J 2) (cos (/ K 2)))) (/ U (* (* J 2) (cos (/ K 2)))))
7.4b
(* (* (sqrt (+ (* (/ U (* (* J 2) (cos (/ K 2)))) (/ U (* (* J 2) (cos (/ K 2))))) 1)) (cos (/ K 2))) (* -2 J))
11.3b
(sqrt (+ (* (/ U (* (* J 2) (cos (/ K 2)))) (/ U (* (* J 2) (cos (/ K 2))))) 1))

rewrite646.0ms

Algorithm
rewrite-expression-head
Rules
101×add-cbrt-cube add-exp-log
51×prod-exp cbrt-unprod
29×pow1
24×cbrt-undiv div-exp
17×add-sqr-sqrt
14×*-un-lft-identity add-cube-cbrt
12×times-frac pow-prod-down
11×associate-*r*
9×associate-*l*
7×swap-sqr
5×associate-*l/
4×sqrt-div div-inv add-log-exp
3×*-commutative sqrt-prod
2×flip3-+ flip-+
1×pow2 frac-times rem-sqrt-square sqrt-pow1 pow-plus pow1/2 associate-*r/ pow-sqr pow-prod-up unswap-sqr
Counts
4 → 127
Calls
4 calls:
14.0ms
(* (* J 2) (cos (/ K 2)))
108.0ms
(* (/ U (* (* J 2) (cos (/ K 2)))) (/ U (* (* J 2) (cos (/ K 2)))))
344.0ms
(* (* (sqrt (+ (* (/ U (* (* J 2) (cos (/ K 2)))) (/ U (* (* J 2) (cos (/ K 2))))) 1)) (cos (/ K 2))) (* -2 J))
177.0ms
(sqrt (+ (* (/ U (* (* J 2) (cos (/ K 2)))) (/ U (* (* J 2) (cos (/ K 2))))) 1))

series584.0ms

Counts
4 → 12
Calls
4 calls:
77.0ms
(* (* J 2) (cos (/ K 2)))
131.0ms
(* (/ U (* (* J 2) (cos (/ K 2)))) (/ U (* (* J 2) (cos (/ K 2)))))
223.0ms
(* (* (sqrt (+ (* (/ U (* (* J 2) (cos (/ K 2)))) (/ U (* (* J 2) (cos (/ K 2))))) 1)) (cos (/ K 2))) (* -2 J))
153.0ms
(sqrt (+ (* (/ U (* (* J 2) (cos (/ K 2)))) (/ U (* (* J 2) (cos (/ K 2))))) 1))

simplify1.2s

Counts
139 → 139
Iterations
IterNodes
23138
1662
0227

prune1.8s

Pruning

7 alts after pruning (5 fresh and 2 done)

Merged error: 10.2b

localize50.0ms

Local error

Found 4 expressions with local error:

7.3b
(* (sqrt (+ (* (/ U (* (* J 2) (cos (/ K 2)))) (/ U (* (* J 2) (cos (/ K 2))))) 1)) (* (cos (/ K 2)) (* -2 J)))
11.3b
(sqrt (+ (* (/ U (* (* J 2) (cos (/ K 2)))) (/ U (* (* J 2) (cos (/ K 2))))) 1))
11.3b
(sqrt (+ (* (/ U (* (* J 2) (cos (/ K 2)))) (/ U (* (* J 2) (cos (/ K 2))))) 1))
11.3b
(sqrt (+ (* (/ U (* (* J 2) (cos (/ K 2)))) (/ U (* (* J 2) (cos (/ K 2))))) 1))

rewrite835.0ms

Algorithm
rewrite-expression-head
Rules
16×pow1
13×add-cbrt-cube add-exp-log
12×add-sqr-sqrt sqrt-prod
9×*-un-lft-identity add-cube-cbrt
8×sqrt-div
6×associate-*l* pow-prod-down prod-exp cbrt-unprod
4×flip3-+ flip-+ add-log-exp
3×rem-sqrt-square sqrt-pow1 pow1/2
2×associate-*l/
1×associate-*r* *-commutative
Counts
4 → 71
Calls
4 calls:
303.0ms
(* (sqrt (+ (* (/ U (* (* J 2) (cos (/ K 2)))) (/ U (* (* J 2) (cos (/ K 2))))) 1)) (* (cos (/ K 2)) (* -2 J)))
199.0ms
(sqrt (+ (* (/ U (* (* J 2) (cos (/ K 2)))) (/ U (* (* J 2) (cos (/ K 2))))) 1))
165.0ms
(sqrt (+ (* (/ U (* (* J 2) (cos (/ K 2)))) (/ U (* (* J 2) (cos (/ K 2))))) 1))
167.0ms
(sqrt (+ (* (/ U (* (* J 2) (cos (/ K 2)))) (/ U (* (* J 2) (cos (/ K 2))))) 1))

series738.0ms

Counts
4 → 12
Calls
4 calls:
266.0ms
(* (sqrt (+ (* (/ U (* (* J 2) (cos (/ K 2)))) (/ U (* (* J 2) (cos (/ K 2))))) 1)) (* (cos (/ K 2)) (* -2 J)))
146.0ms
(sqrt (+ (* (/ U (* (* J 2) (cos (/ K 2)))) (/ U (* (* J 2) (cos (/ K 2))))) 1))
176.0ms
(sqrt (+ (* (/ U (* (* J 2) (cos (/ K 2)))) (/ U (* (* J 2) (cos (/ K 2))))) 1))
150.0ms
(sqrt (+ (* (/ U (* (* J 2) (cos (/ K 2)))) (/ U (* (* J 2) (cos (/ K 2))))) 1))

simplify2.3s

Counts
83 → 83
Iterations
IterNodes
34717
2860
1245
0100

prune1.5s

Pruning

7 alts after pruning (4 fresh and 3 done)

Merged error: 10.2b

localize18.0ms

Local error

Found 1 expressions with local error:

0.1b
(* (cos (/ K 2)) (* -2 J))

rewrite17.0ms

Algorithm
rewrite-expression-head
Rules
6×pow1 add-cbrt-cube add-exp-log
3×associate-*l* pow-prod-down prod-exp cbrt-unprod
2×add-sqr-sqrt *-un-lft-identity add-cube-cbrt
1×associate-*r* *-commutative add-log-exp
Counts
1 → 18
Calls
1 calls:
16.0ms
(* (cos (/ K 2)) (* -2 J))

series74.0ms

Counts
1 → 3
Calls
1 calls:
74.0ms
(* (cos (/ K 2)) (* -2 J))

simplify2.9s

Counts
21 → 21
Iterations
IterNodes
44518
31288
2327
1118
049

prune273.0ms

Pruning

9 alts after pruning (6 fresh and 3 done)

Merged error: 10.2b

regimes476.0ms

Accuracy

12.3% (8.0b remaining)

Error of 16.8b against oracle of 8.8b and baseline of 17.9b

bsearch805.0ms

Steps
ItersRangePoint
8
1.6535927762855964e-123
2.4400236858423746e-120
6.953802795616913e-122
9
5.083019211311129e-150
1.3178450068536785e-144
6.061443602231617e-146
10
2.7467028975914626e-204
1.98895090012e-193
3.946305958295406e-203
7
-7.458630782677963e-197
-3.2929140702196694e-199
-3.995143407100309e-199

simplify9.0s

Iterations
IterNodes
2672004
2661996
2651989
2641981
2631974
2621966
2611959
2601951
2591944
2581936
2571929
2561921
2551914
2541906
2531899
2521891
2511884
2501876
2491869
2481861
2471854
2461846
2451839
2441831
2431824
2421816
2411809
2401801
2391794
2381786
2371779
2361771
2351764
2341756
2331749
2321741
2311734
2301726
2291719
2281711
2271704
2261696
2251689
2241681
2231674
2221666
2211659
2201651
2191644
2181636
2171629
2161621
2151614
2141606
2131599
2121591
2111584
2101576
2091569
2081561
2071554
2061546
2051539
2041531
2031524
2021516
2011509
2001501
1991494
1981486
1971479
1961471
1951464
1941456
1931449
1921441
1911434
1901426
1891419
1881411
1871404
1861396
1851389
1841381
1831374
1821366
1811359
1801351
1791344
1781336
1771329
1761321
1751314
1741306
1731299
1721291
1711284
1701276
1691269
1681261
1671254
1661246
1651239
1641231
1631224
1621216
1611209
1601201
1591194
1581186
1571179
1561171
1551164
1541156
1531149
1521141
1511134
1501126
1491119
1481111
1471104
1461096
1451089
1441081
1431074
1421066
1411059
1401051
1391044
1381036
1371029
1361021
1351014
1341006
133999
132991
131984
130976
129969
128961
127954
126946
125939
124931
123924
122916
121909
120901
119894
118886
117879
116871
115864
114856
113849
112841
111834
110826
109819
108811
107804
106796
105789
104781
103774
102766
101759
100751
99744
98736
97729
96721
95714
94706
93699
92691
91684
90676
89669
88661
87654
86646
85639
84631
83624
82616
81609
80601
79594
78586
77579
76571
75564
74556
73549
72541
71534
70526
69519
68511
67504
66496
65489
64481
63474
62466
61459
60451
59444
58436
57429
56421
55414
54406
53399
52391
51384
50376
49369
48361
47354
46346
45339
44331
43324
42316
41309
40301
39294
38286
37279
36271
35264
34256
33249
32241
31234
30226
29219
28211
27204
26196
25189
24181
23174
22166
21159
20151
19144
18136
17129
16121
15114
14106
1399
1291
1184
1076
969
859
758
655
554
451
348
242
139
030

end0.0ms

sample5.5s

Algorithm
intervals
Results
2.3s1536×body1280valid
1.2s4244×body80valid
1.2s1255×body640valid
444.0ms643×body320valid
143.0ms323×body160valid