Details

Time bar (total: 37.4s)

sample157.0ms

Algorithm
intervals
Results
63.0ms51×body1280valid
31.0ms139×body80valid
27.0ms37×body640valid
9.0ms17×body320valid
5.0ms12×body160valid

simplify813.0ms

Counts
1 → 1
Iterations
IterNodes
52093
4624
3188
281
136
017

prune22.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 14.7b

localize31.0ms

Local error

Found 4 expressions with local error:

0.1b
(* (* -2 J) (cos (/ K 2)))
0.2b
(pow (/ U (* (* 2 J) (cos (/ K 2)))) 2)
5.9b
(* (* (* -2 J) (cos (/ K 2))) (sqrt (+ 1 (pow (/ U (* (* 2 J) (cos (/ K 2)))) 2))))
8.7b
(sqrt (+ 1 (pow (/ U (* (* 2 J) (cos (/ K 2)))) 2)))

rewrite331.0ms

Algorithm
rewrite-expression-head
Rules
28×add-exp-log
20×pow1
18×add-cbrt-cube
15×*-un-lft-identity
12×add-sqr-sqrt prod-exp
11×add-cube-cbrt
10×associate-*r*
9×pow-prod-down cbrt-unprod
8×sqrt-prod
7×unpow-prod-down
4×sqrt-div pow-exp insert-posit16 add-log-exp
3×pow-unpow times-frac div-exp
2×flip3-+ associate-*l* associate-*r/ *-commutative flip-+ distribute-lft-out
1×pow-to-exp rem-sqrt-square pow-pow sqrt-pow1 pow1/2 div-inv unpow2 sqr-pow
Counts
4 → 90
Calls
4 calls:
28.0ms
(* (* -2 J) (cos (/ K 2)))
36.0ms
(pow (/ U (* (* 2 J) (cos (/ K 2)))) 2)
182.0ms
(* (* (* -2 J) (cos (/ K 2))) (sqrt (+ 1 (pow (/ U (* (* 2 J) (cos (/ K 2)))) 2))))
82.0ms
(sqrt (+ 1 (pow (/ U (* (* 2 J) (cos (/ K 2)))) 2)))

series612.0ms

Counts
4 → 12
Calls
4 calls:
83.0ms
(* (* -2 J) (cos (/ K 2)))
156.0ms
(pow (/ U (* (* 2 J) (cos (/ K 2)))) 2)
216.0ms
(* (* (* -2 J) (cos (/ K 2))) (sqrt (+ 1 (pow (/ U (* (* 2 J) (cos (/ K 2)))) 2))))
157.0ms
(sqrt (+ 1 (pow (/ U (* (* 2 J) (cos (/ K 2)))) 2)))

simplify2.6s

Counts
102 → 102
Iterations
IterNodes
35702
21419
1436
0179

prune1.4s

Pruning

10 alts after pruning (9 fresh and 1 done)

Merged error: 9.2b

localize33.0ms

Local error

Found 4 expressions with local error:

0.1b
(* J (cos (/ K 2)))
0.2b
(* (/ (/ U 2) (* J (cos (/ K 2)))) (/ (/ U 2) (* J (cos (/ K 2)))))
6.0b
(* (* -2 J) (* (sqrt (+ 1 (* (/ (/ U 2) (* J (cos (/ K 2)))) (/ (/ U 2) (* J (cos (/ K 2))))))) (cos (/ K 2))))
8.7b
(sqrt (+ 1 (* (/ (/ U 2) (* J (cos (/ K 2)))) (/ (/ U 2) (* J (cos (/ K 2)))))))

rewrite151.0ms

Algorithm
rewrite-expression-head
Rules
148×add-cbrt-cube add-exp-log
88×times-frac
60×cbrt-undiv div-exp
54×prod-exp cbrt-unprod
44×add-sqr-sqrt
39×*-un-lft-identity add-cube-cbrt
26×pow1
21×associate-*r* associate-*l*
17×swap-sqr
10×pow-prod-down
8×div-inv
4×sqrt-div insert-posit16 add-log-exp
3×associate-*l/ associate-*r/ *-commutative sqrt-prod
2×flip3-+ flip-+ unswap-sqr
1×pow2 frac-times rem-sqrt-square sqrt-pow1 pow-plus pow1/2 pow-sqr pow-prod-up
Counts
4 → 179
Calls
4 calls:
13.0ms
(* J (cos (/ K 2)))
65.0ms
(* (/ (/ U 2) (* J (cos (/ K 2)))) (/ (/ U 2) (* J (cos (/ K 2)))))
58.0ms
(* (* -2 J) (* (sqrt (+ 1 (* (/ (/ U 2) (* J (cos (/ K 2)))) (/ (/ U 2) (* J (cos (/ K 2))))))) (cos (/ K 2))))
7.0ms
(sqrt (+ 1 (* (/ (/ U 2) (* J (cos (/ K 2)))) (/ (/ U 2) (* J (cos (/ K 2)))))))

series513.0ms

Counts
4 → 12
Calls
4 calls:
42.0ms
(* J (cos (/ K 2)))
121.0ms
(* (/ (/ U 2) (* J (cos (/ K 2)))) (/ (/ U 2) (* J (cos (/ K 2)))))
188.0ms
(* (* -2 J) (* (sqrt (+ 1 (* (/ (/ U 2) (* J (cos (/ K 2)))) (/ (/ U 2) (* J (cos (/ K 2))))))) (cos (/ K 2))))
161.0ms
(sqrt (+ 1 (* (/ (/ U 2) (* J (cos (/ K 2)))) (/ (/ U 2) (* J (cos (/ K 2)))))))

simplify1.9s

Counts
191 → 191
Iterations
IterNodes
24490
11014
0327

prune2.7s

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 6.9b

localize31.0ms

Local error

Found 4 expressions with local error:

0.1b
(* (* (* -2 J) (sqrt (+ 1 (* (/ (/ U 2) (* J (cos (/ K 2)))) (/ (/ U 2) (* J (cos (/ K 2)))))))) (cos (/ K 2)))
0.2b
(* (/ (/ U 2) (* J (cos (/ K 2)))) (/ (/ U 2) (* J (cos (/ K 2)))))
5.9b
(* (* -2 J) (sqrt (+ 1 (* (/ (/ U 2) (* J (cos (/ K 2)))) (/ (/ U 2) (* J (cos (/ K 2))))))))
8.7b
(sqrt (+ 1 (* (/ (/ U 2) (* J (cos (/ K 2)))) (/ (/ U 2) (* J (cos (/ K 2)))))))

rewrite239.0ms

Algorithm
rewrite-expression-head
Rules
148×add-cbrt-cube add-exp-log
88×times-frac
60×cbrt-undiv div-exp
54×prod-exp cbrt-unprod
43×add-sqr-sqrt
40×*-un-lft-identity add-cube-cbrt
26×pow1 associate-*r*
19×associate-*l*
17×swap-sqr
10×pow-prod-down
8×div-inv
6×sqrt-div sqrt-prod
5×associate-*r/
4×insert-posit16 add-log-exp
3×flip3-+ associate-*l/ *-commutative flip-+
1×pow2 frac-times rem-sqrt-square sqrt-pow1 pow-plus pow1/2 pow-sqr pow-prod-up unswap-sqr
Counts
4 → 183
Calls
4 calls:
104.0ms
(* (* (* -2 J) (sqrt (+ 1 (* (/ (/ U 2) (* J (cos (/ K 2)))) (/ (/ U 2) (* J (cos (/ K 2)))))))) (cos (/ K 2)))
82.0ms
(* (/ (/ U 2) (* J (cos (/ K 2)))) (/ (/ U 2) (* J (cos (/ K 2)))))
41.0ms
(* (* -2 J) (sqrt (+ 1 (* (/ (/ U 2) (* J (cos (/ K 2)))) (/ (/ U 2) (* J (cos (/ K 2))))))))
3.0ms
(sqrt (+ 1 (* (/ (/ U 2) (* J (cos (/ K 2)))) (/ (/ U 2) (* J (cos (/ K 2)))))))

series731.0ms

Counts
4 → 12
Calls
4 calls:
206.0ms
(* (* (* -2 J) (sqrt (+ 1 (* (/ (/ U 2) (* J (cos (/ K 2)))) (/ (/ U 2) (* J (cos (/ K 2)))))))) (cos (/ K 2)))
176.0ms
(* (/ (/ U 2) (* J (cos (/ K 2)))) (/ (/ U 2) (* J (cos (/ K 2)))))
167.0ms
(* (* -2 J) (sqrt (+ 1 (* (/ (/ U 2) (* J (cos (/ K 2)))) (/ (/ U 2) (* J (cos (/ K 2))))))))
182.0ms
(sqrt (+ 1 (* (/ (/ U 2) (* J (cos (/ K 2)))) (/ (/ U 2) (* J (cos (/ K 2)))))))

simplify1.8s

Counts
195 → 195
Iterations
IterNodes
24819
11034
0327

prune2.9s

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 6.6b

localize85.0ms

Local error

Found 4 expressions with local error:

0.1b
(* (* (* -2 J) (sqrt (+ 1 (* (* (/ (/ U 2) (* J (cos (/ K 2)))) (/ U J)) (/ (/ 1 2) (cos (/ K 2))))))) (cos (/ K 2)))
0.2b
(* (/ (/ U 2) (* J (cos (/ K 2)))) (/ U J))
5.9b
(* (* -2 J) (sqrt (+ 1 (* (* (/ (/ U 2) (* J (cos (/ K 2)))) (/ U J)) (/ (/ 1 2) (cos (/ K 2)))))))
8.7b
(sqrt (+ 1 (* (* (/ (/ U 2) (* J (cos (/ K 2)))) (/ U J)) (/ (/ 1 2) (cos (/ K 2))))))

rewrite217.0ms

Algorithm
rewrite-expression-head
Rules
59×add-cbrt-cube add-exp-log
32×times-frac
29×add-sqr-sqrt
23×*-un-lft-identity prod-exp add-cube-cbrt cbrt-unprod
22×associate-*r*
21×pow1
19×associate-*l*
17×cbrt-undiv div-exp
10×pow-prod-down
6×sqrt-div sqrt-prod
5×associate-*r/
4×insert-posit16 add-log-exp
3×flip3-+ associate-*l/ *-commutative flip-+ div-inv
2×unswap-sqr
1×frac-times rem-sqrt-square sqrt-pow1 pow1/2
Counts
4 → 129
Calls
4 calls:
103.0ms
(* (* (* -2 J) (sqrt (+ 1 (* (* (/ (/ U 2) (* J (cos (/ K 2)))) (/ U J)) (/ (/ 1 2) (cos (/ K 2))))))) (cos (/ K 2)))
56.0ms
(* (/ (/ U 2) (* J (cos (/ K 2)))) (/ U J))
46.0ms
(* (* -2 J) (sqrt (+ 1 (* (* (/ (/ U 2) (* J (cos (/ K 2)))) (/ U J)) (/ (/ 1 2) (cos (/ K 2)))))))
7.0ms
(sqrt (+ 1 (* (* (/ (/ U 2) (* J (cos (/ K 2)))) (/ U J)) (/ (/ 1 2) (cos (/ K 2))))))

series633.0ms

Counts
4 → 12
Calls
4 calls:
199.0ms
(* (* (* -2 J) (sqrt (+ 1 (* (* (/ (/ U 2) (* J (cos (/ K 2)))) (/ U J)) (/ (/ 1 2) (cos (/ K 2))))))) (cos (/ K 2)))
160.0ms
(* (/ (/ U 2) (* J (cos (/ K 2)))) (/ U J))
143.0ms
(* (* -2 J) (sqrt (+ 1 (* (* (/ (/ U 2) (* J (cos (/ K 2)))) (/ U J)) (/ (/ 1 2) (cos (/ K 2)))))))
130.0ms
(sqrt (+ 1 (* (* (/ (/ U 2) (* J (cos (/ K 2)))) (/ U J)) (/ (/ 1 2) (cos (/ K 2))))))

simplify1.6s

Counts
141 → 141
Iterations
IterNodes
23540
1794
0265

prune2.2s

Pruning

8 alts after pruning (7 fresh and 1 done)

Merged error: 6.6b

regimes840.0ms

Accuracy

2.4% (9.1b remaining)

Error of 17.2b against oracle of 8.1b and baseline of 17.5b

bsearch608.0ms

Steps
ItersRangePoint
7
1.4164713777351023e-204
8.081446115883691e-203
2.7142743861140305e-203
9
5.72348940587065e-280
2.6667659591502725e-273
5.818795322276243e-280
8
-9.285204783010109e-243
-2.0614872448970783e-245
-3.5882868254156677e-244
7
-2.3850235703365113e-177
-1.5339474964348196e-179
-7.065412618436453e-178

simplify8.3s

Iterations
IterNodes
2662004
2651997
2641989
2631982
2621974
2611967
2601959
2591952
2581944
2571937
2561929
2551922
2541914
2531907
2521899
2511892
2501884
2491877
2481869
2471862
2461854
2451847
2441839
2431832
2421824
2411817
2401809
2391802
2381794
2371787
2361779
2351772
2341764
2331757
2321749
2311742
2301734
2291727
2281719
2271712
2261704
2251697
2241689
2231682
2221674
2211667
2201659
2191652
2181644
2171637
2161629
2151622
2141614
2131607
2121599
2111592
2101584
2091577
2081569
2071562
2061554
2051547
2041539
2031532
2021524
2011517
2001509
1991502
1981494
1971487
1961479
1951472
1941464
1931457
1921449
1911442
1901434
1891427
1881419
1871412
1861404
1851397
1841389
1831382
1821374
1811367
1801359
1791352
1781344
1771337
1761329
1751322
1741314
1731307
1721299
1711292
1701284
1691277
1681269
1671262
1661254
1651247
1641239
1631232
1621224
1611217
1601209
1591202
1581194
1571187
1561179
1551172
1541164
1531157
1521149
1511142
1501134
1491127
1481119
1471112
1461104
1451097
1441089
1431082
1421074
1411067
1401059
1391052
1381044
1371037
1361029
1351022
1341014
1331007
132999
131992
130984
129977
128969
127962
126954
125947
124939
123932
122924
121917
120909
119902
118894
117887
116879
115872
114864
113857
112849
111842
110834
109827
108819
107812
106804
105797
104789
103782
102774
101767
100759
99752
98744
97737
96729
95722
94714
93707
92699
91692
90684
89677
88669
87662
86654
85647
84639
83632
82624
81617
80609
79602
78594
77587
76579
75572
74564
73557
72549
71542
70534
69527
68519
67512
66504
65497
64489
63482
62474
61467
60459
59452
58444
57437
56429
55422
54414
53407
52399
51392
50384
49377
48369
47362
46354
45347
44339
43332
42324
41317
40309
39302
38294
37287
36279
35272
34264
33257
32249
31242
30234
29227
28219
27212
26204
25197
24189
23182
22174
21167
20159
19152
18144
17137
16129
15122
14114
13107
1299
1192
1084
977
867
766
663
562
459
356
250
147
034

end0.0ms

sample6.0s

Algorithm
intervals
Results
2.4s1531×body1280valid
1.3s1258×body640valid
1.0s4261×body80valid
869.0ms644×body320valid
157.0ms308×body160valid