Details

Time bar (total: 26.2s)

sample68.0ms

Algorithm
intervals
Results
32.0ms74×body1280valid
7.0ms38×body640valid
7.0ms179×body80valid
4.0ms29×body320valid
1.0ms17×body160valid

simplify3.3s

Counts
1 → 1
Iterations
IterNodes
done5028
83392
7883
6221
593
444
323
216
111
06

prune4.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 28.1b

localize8.0ms

Local error

Found 2 expressions with local error:

0.0b
(exp (* a x))
4.0b
(- (exp (* a x)) 1.0)

rewrite14.0ms

Algorithm
rewrite-expression-head
Rules
6×add-log-exp
4×add-sqr-sqrt *-un-lft-identity
2×pow1 add-cbrt-cube add-exp-log add-cube-cbrt
1×exp-prod sub-neg flip3-- exp-to-pow diff-log flip-- distribute-lft-out-- difference-of-squares rem-exp-log
Counts
2 → 24
Calls
2 calls:
3.0ms
(exp (* a x))
10.0ms
(- (exp (* a x)) 1.0)

series66.0ms

Counts
2 → 6
Calls
2 calls:
14.0ms
(exp (* a x))
52.0ms
(- (exp (* a x)) 1.0)

simplify3.0s

Counts
30 → 30
Iterations
IterNodes
done5002
44038
31117
2310
1116
053

prune163.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 0.0b

localize21.0ms

Local error

Found 4 expressions with local error:

0.3b
(* (* x a) (* x a))
0.3b
(* (* x a) (* (* x a) 1/2))
4.2b
(+ (* x a) (* (* x a) (* (* x a) 1/2)))
12.6b
(+ (* (* (* x a) (* (* x a) (* x a))) 1/6) (+ (* x a) (* (* x a) (* (* x a) 1/2))))

rewrite516.0ms

Algorithm
rewrite-expression-head
Rules
64×pow1
37×add-cbrt-cube add-exp-log
32×pow-prod-down
23×prod-exp cbrt-unprod
11×add-log-exp
4×add-sqr-sqrt sum-log *-un-lft-identity pow-sqr pow-prod-up add-cube-cbrt
2×+-commutative flip3-+ pow-plus associate-*r* associate-*l* *-commutative flip-+
1×pow2 associate-+r+ swap-sqr
Counts
4 → 86
Calls
4 calls:
41.0ms
(* (* x a) (* x a))
80.0ms
(* (* x a) (* (* x a) 1/2))
17.0ms
(+ (* x a) (* (* x a) (* (* x a) 1/2)))
373.0ms
(+ (* (* (* x a) (* (* x a) (* x a))) 1/6) (+ (* x a) (* (* x a) (* (* x a) 1/2))))

series281.0ms

Counts
4 → 12
Calls
4 calls:
36.0ms
(* (* x a) (* x a))
50.0ms
(* (* x a) (* (* x a) 1/2))
66.0ms
(+ (* x a) (* (* x a) (* (* x a) 1/2)))
129.0ms
(+ (* (* (* x a) (* (* x a) (* x a))) 1/6) (+ (* x a) (* (* x a) (* (* x a) 1/2))))

simplify2.3s

Counts
98 → 98
Iterations
IterNodes
done5002
21633
1368
0123

prune310.0ms

Pruning

3 alts after pruning (2 fresh and 1 done)

Merged error: 0.0b

localize8.0ms

Local error

Found 2 expressions with local error:

0.0b
(exp (* x a))
4.0b
(- (exp (* x a)) 1.0)

rewrite23.0ms

Algorithm
rewrite-expression-head
Rules
6×add-log-exp
4×add-sqr-sqrt *-un-lft-identity
2×pow1 add-cbrt-cube add-exp-log add-cube-cbrt
1×exp-prod sub-neg flip3-- exp-to-pow diff-log flip-- distribute-lft-out-- difference-of-squares rem-exp-log
Counts
2 → 24
Calls
2 calls:
6.0ms
(exp (* x a))
16.0ms
(- (exp (* x a)) 1.0)

series79.0ms

Counts
2 → 6
Calls
2 calls:
21.0ms
(exp (* x a))
58.0ms
(- (exp (* x a)) 1.0)

simplify3.6s

Counts
30 → 30
Iterations
IterNodes
done5014
44149
31131
2328
1121
056

prune111.0ms

Pruning

3 alts after pruning (1 fresh and 2 done)

Merged error: 0.0b

localize25.0ms

Local error

Found 4 expressions with local error:

0.3b
(* (* x a) (* x a))
0.3b
(* 1/6 (* x a))
1.2b
(exp (log (+ (* (* (* x a) (* x a)) (+ (* 1/6 (* x a)) 1/2)) (* x a))))
8.4b
(log (+ (* (* (* x a) (* x a)) (+ (* 1/6 (* x a)) 1/2)) (* x a)))

rewrite287.0ms

Algorithm
rewrite-expression-head
Rules
50×pow1
22×add-exp-log
21×add-cbrt-cube
20×pow-prod-down
11×prod-exp cbrt-unprod
8×add-sqr-sqrt *-un-lft-identity add-cube-cbrt
6×log-prod
4×log-div exp-prod associate-*l* pow-sqr pow-prod-up add-log-exp
3×exp-sum
2×flip3-+ pow-plus exp-diff associate-*r* log-pow *-commutative flip-+
1×pow2 swap-sqr rem-log-exp rem-exp-log
Counts
4 → 83
Calls
4 calls:
37.0ms
(* (* x a) (* x a))
22.0ms
(* 1/6 (* x a))
109.0ms
(exp (log (+ (* (* (* x a) (* x a)) (+ (* 1/6 (* x a)) 1/2)) (* x a))))
115.0ms
(log (+ (* (* (* x a) (* x a)) (+ (* 1/6 (* x a)) 1/2)) (* x a)))

series415.0ms

Counts
4 → 12
Calls
4 calls:
36.0ms
(* (* x a) (* x a))
26.0ms
(* 1/6 (* x a))
138.0ms
(exp (log (+ (* (* (* x a) (* x a)) (+ (* 1/6 (* x a)) 1/2)) (* x a))))
215.0ms
(log (+ (* (* (* x a) (* x a)) (+ (* 1/6 (* x a)) 1/2)) (* x a)))

simplify1.9s

Counts
95 → 95
Iterations
IterNodes
done5001
21461
1362
0150

prune315.0ms

Pruning

3 alts after pruning (1 fresh and 2 done)

Merged error: 0.0b

regimes153.0ms

Accuracy

34.4% (13.8b remaining)

Error of 13.8b against oracle of 0.1b and baseline of 21.1b

bsearch355.0ms

Steps
ItersRangePoint
10
8.794406789868183e+101
3.1068034585604e+112
5.1422287804261643e+104
8
-5.048452062299839e-81
-1.7935007776753498e-85
-4.926528827195549e-81
6
-7.034794544076098e-65
-6.211282037120254e-66
-1.3705872472640043e-65
7
-1.6830083676177457e+18
-2.342337183003078e+16
-1.6552683613750236e+18
10
-1.2302458013603981e+72
-7.398073498271572e+53
-3.362393975033818e+63
7
-8.945895949165957e+98
-1.0929183133375652e+97
-2.2209686932120436e+98

simplify6.7s

Iterations
IterNodes
done5001
1344847
1334830
1324670
1314653
1304497
1294480
1284328
1274311
1264163
1254146
1244002
1233985
1223845
1213828
1203692
1193675
1183543
1173526
1163398
1153381
1143257
1133240
1123120
1113103
1102987
1092970
1082858
1072841
1062733
1052716
1042612
1032595
1022495
1012478
1002382
992365
982273
972256
962168
952151
942067
932050
921970
911953
901877
891860
881788
871771
861703
851686
841622
831605
821545
811528
801472
791455
781403
771386
761338
751321
741277
731260
721220
711203
701167
691150
681118
671101
661073
651056
641032
631015
62995
61978
60960
59945
58932
57912
56894
55874
54857
53840
52826
51811
50797
49785
48774
47757
46743
45732
44716
43699
42683
41665
40647
39627
38610
37593
36576
35560
34546
33534
32520
31500
30484
29462
28448
27433
26422
25408
24393
23374
22357
21347
20335
19321
18305
17282
16262
15242
14228
13205
12177
11154
10122
9102
886
779
673
567
458
352
246
143
033

end0.0ms

sample2.2s

Algorithm
intervals
Results
848.0ms2706×body1280valid
642.0ms5424×body80valid
237.0ms1357×body640valid
86.0ms758×body320valid
72.0ms391×body160valid