Details

analyze1.1s

Algorithm

Search

True	Other	False	Iter
0%	99.7%	0.3%	0
0%	99.7%	0.3%	1
0%	99.7%	0.3%	2
0%	99.7%	0.3%	3
0%	99.7%	0.3%	4
0%	99.7%	0.3%	5
0%	99.7%	0.3%	6
0%	99.7%	0.3%	7
0%	74.8%	25.2%	8
0%	74.8%	25.2%	9
0%	74.8%	25.2%	10
0%	74.8%	25.2%	11
0%	74.8%	25.2%	12
24.9%	49.9%	25.2%	13
24.9%	37.4%	37.7%	14

sample80.0ms

Algorithm

intervals

Results

22.0ms	48×	body	1280	valid
12.0ms	160×	body	80	valid
9.0ms	75×	body	80	nan
8.0ms	24×	body	640	valid
7.0ms	10×	body	2560	valid
3.0ms	38×	body	80	invalid
2.0ms	9×	body	320	valid
1.0ms	5×	body	160	valid

simplify82.0ms

Counts

1 → 1

Iterations

Useful iterations: 0 (67.0ms)

Iter	Nodes	Cost
0	717	29
1	717	29

prune3.0ms

Filtered

1 candidates to 1 candidates (0.0%)

Pruning

1 alts after pruning (1 fresh and 0 done)

	Pruned	Kept	Total
New	1	0	1
Fresh	0	1	1
Picked	0	0	0
Done	0	0	0
Total	1	1	2

Merged error: 22.9b

Counts

2 → 1

localize17.0ms

Local error

Found 4 expressions with local error:

0.2b	(/.f64 (*.f64 z t) 3)
0.3b	(.f64 (.f64 2 (sqrt.f64 x)) (cos.f64 (-.f64 y (/.f64 (*.f64 z t) 3))))
0.5b	(/.f64 a (*.f64 b 3))
26.1b	(cos.f64 (-.f64 y (/.f64 (*.f64 z t) 3)))

rewrite31.0ms

Algorithm

rewrite-expression-head

Rules

19×	`add-exp-log_binary64` `add-cbrt-cube_binary64`
9×	`*-un-lft-identity_binary64` `pow1_binary64` `add-cube-cbrt_binary64` `add-sqr-sqrt_binary64`
6×	`times-frac_binary64`
5×	`cbrt-unprod_binary64` `prod-exp_binary64`
4×	`associate-/r_binary64` `add-log-exp_binary64` `cbrt-undiv_binary64` `associate-/l_binary64` `div-exp_binary64` `insert-posit16`
3×	`pow-prod-down_binary64` `associate-r_binary64` `cos-diff_binary64`
2×	`clear-num_binary64` `frac-2neg_binary64` `div-inv_binary64`
1×	`sub-neg_binary64` `distribute-lft-in_binary64` `associate-l_binary64` `distribute-rgt-in_binary64` `cos-sum_binary64` `*-commutative_binary64`

Counts

4 → 75

Calls

4 calls:

8.0ms	(/.f64 (*.f64 z t) 3)
8.0ms	(.f64 (.f64 2 (sqrt.f64 x)) (cos.f64 (-.f64 y (/.f64 (*.f64 z t) 3))))
5.0ms	(/.f64 a (*.f64 b 3))
7.0ms	(cos.f64 (-.f64 y (/.f64 (*.f64 z t) 3)))

series1.1s

Counts

4 → 12

Calls

4 calls:

205.0ms	(/.f64 (*.f64 z t) 3)
394.0ms	(.f64 (.f64 2 (sqrt.f64 x)) (cos.f64 (-.f64 y (/.f64 (*.f64 z t) 3))))
223.0ms	(/.f64 a (*.f64 b 3))
280.0ms	(cos.f64 (-.f64 y (/.f64 (*.f64 z t) 3)))

Iterations

Useful iterations: 0 (5.0ms)

Iter	Nodes	Cost
0	458	375
1	458	375
0	11	9
1	11	9
0	458	375
1	458	375
0	11	9
1	11	9
0	1	3
1	1	3
0	358	276
1	358	276
0	15	9
1	15	9
0	358	276
1	358	276
0	15	9
1	15	9
0	1	3
1	1	3
0	654	735
1	654	735
0	15	9
1	15	9
0	654	735
1	654	735
0	15	9
1	15	9
0	1	3
1	1	3
0	302	213
1	302	213
0	11	9
1	11	9
0	302	213
1	302	213
0	11	9
1	11	9
0	1	3
1	1	3

simplify150.0ms

Counts

87 → 87

Iterations

Useful iterations: 0 (122.0ms)

Iter	Nodes	Cost
0	4925	1105
1	4925	1105

prune156.0ms

Filtered

62 candidates to 87 candidates (-40.3%)

Pruning

21 alts after pruning (21 fresh and 0 done)

	Pruned	Kept	Total
New	66	21	87
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	67	21	88

Merged error: 12.9b

Counts

88 → 21

localize14.0ms

Local error

Found 3 expressions with local error:

0.0b	(-.f64 (.f64 (.f64 2 (sqrt.f64 x)) (cos.f64 (-.f64 y 0))) (/.f64 a (*.f64 b 3)))
0.2b	(.f64 (.f64 2 (sqrt.f64 x)) (cos.f64 (-.f64 y 0)))
0.5b	(/.f64 a (*.f64 b 3))

rewrite26.0ms

Algorithm

rewrite-expression-head

Rules

13×	`add-exp-log_binary64` `add-cbrt-cube_binary64`
8×	`pow1_binary64`
6×	`*-un-lft-identity_binary64` `add-cube-cbrt_binary64` `add-sqr-sqrt_binary64`
5×	`add-log-exp_binary64`
4×	`cbrt-unprod_binary64` `cos-diff_binary64` `prod-exp_binary64`
3×	`pow-prod-down_binary64` `associate-r_binary64` `associate-/l*_binary64` `times-frac_binary64` `insert-posit16`
2×	`cbrt-undiv_binary64` `distribute-lft-in_binary64` `distribute-rgt-in_binary64` `div-exp_binary64` `associate--l+_binary64`
1×	`associate-/r_binary64` `sub-neg_binary64` `flip3--_binary64` `diff-log_binary64` `associate-l_binary64` `clear-num_binary64` `frac-2neg_binary64` `div-inv_binary64` `flip--_binary64` `-commutative_binary64`

Counts

3 → 57

Calls

3 calls:

11.0ms	(-.f64 (.f64 (.f64 2 (sqrt.f64 x)) (cos.f64 (-.f64 y 0))) (/.f64 a (*.f64 b 3)))
8.0ms	(.f64 (.f64 2 (sqrt.f64 x)) (cos.f64 (-.f64 y 0)))
5.0ms	(/.f64 a (*.f64 b 3))

series999.0ms

Counts

3 → 9

Calls

3 calls:

373.0ms	(-.f64 (.f64 (.f64 2 (sqrt.f64 x)) (cos.f64 (-.f64 y 0))) (/.f64 a (*.f64 b 3)))
401.0ms	(.f64 (.f64 2 (sqrt.f64 x)) (cos.f64 (-.f64 y 0)))
225.0ms	(/.f64 a (*.f64 b 3))

Iterations

Useful iterations: 0 (5.0ms)

Iter	Nodes	Cost
0	358	276
1	358	276
0	15	9
1	15	9
0	358	276
1	358	276
0	15	9
1	15	9
0	1	3
1	1	3
0	407	447
1	407	447
0	39	33
1	39	33
0	407	447
1	407	447
0	39	33
1	39	33
0	4935	3
1	4935	3
0	636	723
1	636	723
0	19	9
1	19	9
0	636	723
1	636	723
0	19	9
1	19	9
0	1	3
1	1	3

simplify104.0ms

Counts

66 → 66

Iterations

Useful iterations: 0 (79.0ms)

Iter	Nodes	Cost
0	5129	842

prune108.0ms

Filtered

46 candidates to 66 candidates (-43.5%)

Pruning

27 alts after pruning (27 fresh and 0 done)

	Pruned	Kept	Total
New	54	12	66
Fresh	5	15	20
Picked	1	0	1
Done	0	0	0
Total	60	27	87

Merged error: 12.9b

Counts

87 → 27

localize15.0ms

Local error

Found 3 expressions with local error:

0.0b	(-.f64 (.f64 (.f64 2 (sqrt.f64 x)) (cos.f64 (-.f64 y 0))) (*.f64 (/.f64 1 b) (/.f64 a 3)))
0.2b	(.f64 (.f64 2 (sqrt.f64 x)) (cos.f64 (-.f64 y 0)))
0.3b	(*.f64 (/.f64 1 b) (/.f64 a 3))

rewrite34.0ms

Algorithm

rewrite-expression-head

Rules

35×	`add-sqr-sqrt_binary64`
30×	`add-exp-log_binary64`
25×	`times-frac_binary64`
20×	`*-un-lft-identity_binary64` `add-cbrt-cube_binary64`
18×	`add-cube-cbrt_binary64`
16×	`associate-r_binary64`
14×	`associate-l_binary64`
11×	`prod-exp_binary64`
10×	`pow1_binary64`
8×	`div-exp_binary64`
7×	`cbrt-unprod_binary64`
6×	`unswap-sqr_binary64`
5×	`add-log-exp_binary64`
4×	`pow-prod-down_binary64` `cbrt-undiv_binary64` `cos-diff_binary64`
3×	`insert-posit16`
2×	`1-exp_binary64` `distribute-lft-in_binary64` `distribute-rgt-in_binary64` `rec-exp_binary64` `div-inv_binary64` `associate--l+_binary64` `*-commutative_binary64`
1×	`sub-neg_binary64` `flip3--_binary64` `diff-log_binary64` `associate-r/_binary64` `flip--_binary64` `frac-times_binary64` `associate-l/_binary64`

Counts

3 → 92

Calls

3 calls:

9.0ms	(-.f64 (.f64 (.f64 2 (sqrt.f64 x)) (cos.f64 (-.f64 y 0))) (*.f64 (/.f64 1 b) (/.f64 a 3)))
8.0ms	(.f64 (.f64 2 (sqrt.f64 x)) (cos.f64 (-.f64 y 0)))
12.0ms	(*.f64 (/.f64 1 b) (/.f64 a 3))

series1.1s

Counts

3 → 9

Calls

3 calls:

368.0ms	(-.f64 (.f64 (.f64 2 (sqrt.f64 x)) (cos.f64 (-.f64 y 0))) (*.f64 (/.f64 1 b) (/.f64 a 3)))
398.0ms	(.f64 (.f64 2 (sqrt.f64 x)) (cos.f64 (-.f64 y 0)))
328.0ms	(*.f64 (/.f64 1 b) (/.f64 a 3))

Iterations

Useful iterations: 0 (168.0ms)

Iter	Nodes	Cost
0	365	357
1	365	357
0	13	9
1	13	9
0	365	357
1	365	357
0	13	9
1	13	9
0	5388	36
0	407	447
1	407	447
0	39	33
1	39	33
0	407	447
1	407	447
0	39	33
1	39	33
0	4935	3
1	4935	3
0	652	804
1	652	804
0	13	9
1	13	9
0	652	804
1	652	804
0	13	9
1	13	9
0	1	3
1	1	3

simplify127.0ms

Counts

101 → 101

Iterations

Useful iterations: 0 (97.0ms)

Iter	Nodes	Cost
0	4961	1320
1	4961	1320

prune126.0ms

Filtered

71 candidates to 101 candidates (-42.3%)

Pruning

27 alts after pruning (27 fresh and 0 done)

	Pruned	Kept	Total
New	97	4	101
Fresh	3	23	26
Picked	1	0	1
Done	0	0	0
Total	101	27	128

Merged error: 12.8b

Counts

128 → 27

localize13.0ms

Local error

Found 3 expressions with local error:

0.0b	(-.f64 (.f64 (.f64 2 (sqrt.f64 x)) (cos.f64 (-.f64 y 0))) (/.f64 (/.f64 a 3) b))
0.2b	(/.f64 (/.f64 a 3) b)
0.2b	(.f64 (.f64 2 (sqrt.f64 x)) (cos.f64 (-.f64 y 0)))

rewrite39.0ms

Algorithm

rewrite-expression-head

Rules

75×	`times-frac_binary64`
46×	`*-un-lft-identity_binary64` `add-cube-cbrt_binary64` `add-sqr-sqrt_binary64`
13×	`add-exp-log_binary64` `add-cbrt-cube_binary64` `associate-/l*_binary64`
8×	`pow1_binary64`
5×	`add-log-exp_binary64` `div-inv_binary64`
4×	`cos-diff_binary64`
3×	`pow-prod-down_binary64` `associate-/r_binary64` `cbrt-unprod_binary64` `associate-r*_binary64` `cbrt-undiv_binary64` `prod-exp_binary64` `div-exp_binary64` `insert-posit16`
2×	`distribute-lft-in_binary64` `distribute-rgt-in_binary64` `associate--l+_binary64`
1×	`associate-/l/_binary64` `sub-neg_binary64` `flip3--_binary64` `diff-log_binary64` `associate-l_binary64` `clear-num_binary64` `frac-2neg_binary64` `flip--_binary64` `*-commutative_binary64`

Counts

3 → 106

Calls

3 calls:

17.0ms	(-.f64 (.f64 (.f64 2 (sqrt.f64 x)) (cos.f64 (-.f64 y 0))) (/.f64 (/.f64 a 3) b))
7.0ms	(/.f64 (/.f64 a 3) b)
9.0ms	(.f64 (.f64 2 (sqrt.f64 x)) (cos.f64 (-.f64 y 0)))

series1.2s

Counts

3 → 9

Calls

3 calls:

474.0ms	(-.f64 (.f64 (.f64 2 (sqrt.f64 x)) (cos.f64 (-.f64 y 0))) (/.f64 (/.f64 a 3) b))
316.0ms	(/.f64 (/.f64 a 3) b)
402.0ms	(.f64 (.f64 2 (sqrt.f64 x)) (cos.f64 (-.f64 y 0)))

Iterations

Useful iterations: 0 (166.0ms)

Iter	Nodes	Cost
0	407	447
1	407	447
0	39	33
1	39	33
0	407	447
1	407	447
0	39	33
1	39	33
0	4935	3
1	4935	3
0	314	264
1	314	264
0	25	24
1	25	24
0	314	264
1	314	264
0	25	24
1	25	24
0	4938	3
1	4938	3
0	604	711
1	604	711
0	34	27
1	34	27
0	604	711
1	604	711
0	34	27
1	34	27
0	4884	3
1	4884	3

simplify126.0ms

Counts

115 → 115

Iterations

Useful iterations: 0 (92.0ms)

Iter	Nodes	Cost
0	5092	1830

prune109.0ms

Filtered

90 candidates to 115 candidates (-27.8%)

Pruning

27 alts after pruning (26 fresh and 1 done)

	Pruned	Kept	Total
New	115	0	115
Fresh	0	26	26
Picked	0	1	1
Done	0	0	0
Total	115	27	142

Merged error: 12.8b

Counts

142 → 27

regimes936.0ms

Accuracy

0% (2.1b remaining)

Error of 16.6b against oracle of 14.5b and baseline of 16.6b

bsearch0.0ms

simplify6.0ms

Iterations

Useful iterations: 0 (2.0ms)

Iter	Nodes	Cost
0	40	20
1	40	20

end0.0ms

sample2.5s

Algorithm

intervals

Results

735.0ms	1564×	body	1280	valid
351.0ms	4468×	body	80	valid
307.0ms	928×	body	640	valid
265.0ms	356×	body	2560	valid
175.0ms	2267×	body	80	nan
116.0ms	459×	body	320	valid
85.0ms	1154×	body	80	invalid
39.0ms	225×	body	160	valid

Iter	Nodes	Cost
0	458	375
1	458	375
0	11	9
1	11	9
0	458	375
1	458	375
0	11	9
1	11	9
0	1	3
1	1	3
0	358	276
1	358	276
0	15	9
1	15	9
0	358	276
1	358	276
0	15	9
1	15	9
0	1	3
1	1	3
0	654	735
1	654	735
0	15	9
1	15	9
0	654	735
1	654	735
0	15	9
1	15	9
0	1	3
1	1	3
0	302	213
1	302	213
0	11	9
1	11	9
0	302	213
1	302	213
0	11	9
1	11	9
0	1	3
1	1	3

Iter	Nodes	Cost
0	458	375
1	458	375
0	11	9
1	11	9
0	458	375
1	458	375
0	11	9
1	11	9
0	1	3
1	1	3
0	358	276
1	358	276
0	15	9
1	15	9
0	358	276
1	358	276
0	15	9
1	15	9
0	1	3
1	1	3
0	654	735
1	654	735
0	15	9
1	15	9
0	654	735
1	654	735
0	15	9
1	15	9
0	1	3
1	1	3
0	302	213
1	302	213
0	11	9
1	11	9
0	302	213
1	302	213
0	11	9
1	11	9
0	1	3
1	1	3

Details

analyze1.1s

sample80.0ms

simplify82.0ms

prune3.0ms

localize17.0ms

rewrite31.0ms

series1.1s

simplify150.0ms

prune156.0ms

localize14.0ms

rewrite26.0ms

series999.0ms

simplify104.0ms

prune108.0ms

localize15.0ms

rewrite34.0ms

series1.1s

simplify127.0ms

prune126.0ms

localize13.0ms

rewrite39.0ms

series1.2s

simplify126.0ms

prune109.0ms

regimes936.0ms

bsearch0.0ms

simplify6.0ms

end0.0ms

sample2.5s

Profiling

Iter	Nodes	Cost
0	458	375
1	458	375
0	11	9
1	11	9
0	458	375
1	458	375
0	11	9
1	11	9
0	1	3
1	1	3
0	358	276
1	358	276
0	15	9
1	15	9
0	358	276
1	358	276
0	15	9
1	15	9
0	1	3
1	1	3
0	654	735
1	654	735
0	15	9
1	15	9
0	654	735
1	654	735
0	15	9
1	15	9
0	1	3
1	1	3
0	302	213
1	302	213
0	11	9
1	11	9
0	302	213
1	302	213
0	11	9
1	11	9
0	1	3
1	1	3