Details

analyze1.9s

Algorithm

Search

True	Other	False	Iter
0%	99.9%	0.1%	0
0%	99.9%	0.1%	1
0%	99.9%	0.1%	2
0%	99.9%	0.1%	3
0%	99.9%	0.1%	4
0%	99.9%	0.1%	5
0%	99.9%	0.1%	6
0%	99.9%	0.1%	7
15.6%	84.3%	0.1%	8
15.6%	84.3%	0.1%	9
15.6%	84.3%	0.1%	10
30.4%	69.4%	0.1%	11
30.4%	69.4%	0.1%	12
30.4%	69.4%	0.1%	13
39.6%	60.3%	0.1%	14

sample110.0ms

Algorithm

intervals

Results

41.0ms	51×	body	1280	valid
26.0ms	47×	body	640	valid
19.0ms	124×	body	80	valid
10.0ms	24×	body	320	valid
2.0ms	10×	body	160	valid

simplify190.0ms

Counts

1 → 1

Iterations

Useful iterations: 0 (173.0ms)

Iter	Nodes	Cost
0	4872	37
1	4872	37

prune4.0ms

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: 18.1b

Counts

2 → 1

localize17.0ms

Local error

Found 4 expressions with local error:

0.1b	(.f64 (.f64 -2 J) (cos.f64 (/.f64 K 2)))
0.2b	(pow.f64 (/.f64 U (.f64 (.f64 2 J) (cos.f64 (/.f64 K 2)))) 2)
6.0b	(.f64 (.f64 (.f64 -2 J) (cos.f64 (/.f64 K 2))) (sqrt.f64 (+.f64 1 (pow.f64 (/.f64 U (.f64 (*.f64 2 J) (cos.f64 (/.f64 K 2)))) 2))))
11.0b	(sqrt.f64 (+.f64 1 (pow.f64 (/.f64 U (.f64 (.f64 2 J) (cos.f64 (/.f64 K 2)))) 2)))

rewrite49.0ms

Algorithm

rewrite-expression-head

Rules

28×	`add-exp-log_binary64`
20×	`pow1_binary64`
18×	`add-cbrt-cube_binary64`
15×	`*-un-lft-identity_binary64`
12×	`prod-exp_binary64` `add-sqr-sqrt_binary64`
11×	`add-cube-cbrt_binary64`
10×	`associate-r_binary64`
9×	`pow-prod-down_binary64` `cbrt-unprod_binary64`
8×	`sqrt-prod_binary64`
7×	`unpow-prod-down_binary64`
4×	`add-log-exp_binary64` `insert-posit16` `pow-exp_binary64` `sqrt-div_binary64`
3×	`pow-unpow_binary64` `times-frac_binary64` `div-exp_binary64`
2×	`flip3-+_binary64` `distribute-lft-out_binary64` `associate-r/_binary64` `associate-l_binary64` `flip-+_binary64` `-commutative_binary64`
1×	`pow-to-exp_binary64` `pow1/2_binary64` `unpow2_binary64` `pow-pow_binary64` `sqr-pow_binary64` `sqrt-pow1_binary64` `rem-sqrt-square_binary64` `div-inv_binary64`

Counts

4 → 90

Calls

4 calls:

6.0ms	(.f64 (.f64 -2 J) (cos.f64 (/.f64 K 2)))
9.0ms	(pow.f64 (/.f64 U (.f64 (.f64 2 J) (cos.f64 (/.f64 K 2)))) 2)
19.0ms	(.f64 (.f64 (.f64 -2 J) (cos.f64 (/.f64 K 2))) (sqrt.f64 (+.f64 1 (pow.f64 (/.f64 U (.f64 (*.f64 2 J) (cos.f64 (/.f64 K 2)))) 2))))
12.0ms	(sqrt.f64 (+.f64 1 (pow.f64 (/.f64 U (.f64 (.f64 2 J) (cos.f64 (/.f64 K 2)))) 2)))

series2.6s

Counts

4 → 12

Calls

4 calls:

371.0ms	(.f64 (.f64 -2 J) (cos.f64 (/.f64 K 2)))
549.0ms	(pow.f64 (/.f64 U (.f64 (.f64 2 J) (cos.f64 (/.f64 K 2)))) 2)
1.0s	(.f64 (.f64 (.f64 -2 J) (cos.f64 (/.f64 K 2))) (sqrt.f64 (+.f64 1 (pow.f64 (/.f64 U (.f64 (*.f64 2 J) (cos.f64 (/.f64 K 2)))) 2))))
666.0ms	(sqrt.f64 (+.f64 1 (pow.f64 (/.f64 U (.f64 (.f64 2 J) (cos.f64 (/.f64 K 2)))) 2)))

Iterations

Useful iterations: 0 (5.0ms)

Iter	Nodes	Cost
0	853	1353
1	853	1353
0	67	458
1	67	458
0	853	1353
1	853	1353
0	67	458
1	67	458
0	5219	33
0	930	1721
1	930	1721
0	4450	9
1	4450	9
0	930	1721
1	930	1721
0	4450	9
1	4450	9
0	1	3
1	1	3
0	730	1194
1	730	1194
0	89	63
1	89	63
0	730	1194
1	730	1194
0	89	63
1	89	63
0	4952	3
1	4952	3
0	406	378
1	406	378
0	43	36
1	43	36
0	406	378
1	406	378
0	43	36
1	43	36
0	5074	3

simplify129.0ms

Counts

102 → 102

Iterations

Useful iterations: 0 (93.0ms)

Iter	Nodes	Cost
0	5365	2368

prune145.0ms

Filtered

66 candidates to 102 candidates (-54.5%)

Pruning

11 alts after pruning (10 fresh and 1 done)

	Pruned	Kept	Total
New	92	10	102
Fresh	0	0	0
Picked	0	1	1
Done	0	0	0
Total	92	11	103

Merged error: 17.1b

Counts

103 → 11

localize17.0ms

Local error

Found 4 expressions with local error:

0.1b	(.f64 (.f64 2 J) (cos.f64 (/.f64 K 2)))
0.2b	(pow.f64 (/.f64 U (.f64 (.f64 2 J) (cos.f64 (/.f64 K 2)))) 2)
6.0b	(.f64 (.f64 -2 J) (.f64 (cos.f64 (/.f64 K 2)) (sqrt.f64 (+.f64 1 (pow.f64 (/.f64 U (.f64 (*.f64 2 J) (cos.f64 (/.f64 K 2)))) 2)))))
11.0b	(sqrt.f64 (+.f64 1 (pow.f64 (/.f64 U (.f64 (.f64 2 J) (cos.f64 (/.f64 K 2)))) 2)))

rewrite51.0ms

Algorithm

rewrite-expression-head

Rules

31×	`add-exp-log_binary64`
23×	`pow1_binary64`
21×	`add-cbrt-cube_binary64`
14×	`prod-exp_binary64`
11×	`pow-prod-down_binary64` `*-un-lft-identity_binary64` `cbrt-unprod_binary64`
10×	`add-sqr-sqrt_binary64`
9×	`add-cube-cbrt_binary64`
7×	`unpow-prod-down_binary64`
4×	`add-log-exp_binary64` `associate-r_binary64` `associate-*r/_binary64` `insert-posit16` `sqrt-prod_binary64` `pow-exp_binary64` `sqrt-div_binary64`
3×	`pow-unpow_binary64` `times-frac_binary64` `div-exp_binary64`
2×	`flip3-+_binary64` `associate-l_binary64` `flip-+_binary64` `*-commutative_binary64`
1×	`pow-to-exp_binary64` `pow1/2_binary64` `distribute-lft-out_binary64` `unpow2_binary64` `pow-pow_binary64` `sqr-pow_binary64` `sqrt-pow1_binary64` `rem-sqrt-square_binary64` `div-inv_binary64`

Counts

4 → 87

Calls

4 calls:

7.0ms	(.f64 (.f64 2 J) (cos.f64 (/.f64 K 2)))
12.0ms	(pow.f64 (/.f64 U (.f64 (.f64 2 J) (cos.f64 (/.f64 K 2)))) 2)
19.0ms	(.f64 (.f64 -2 J) (.f64 (cos.f64 (/.f64 K 2)) (sqrt.f64 (+.f64 1 (pow.f64 (/.f64 U (.f64 (*.f64 2 J) (cos.f64 (/.f64 K 2)))) 2)))))
10.0ms	(sqrt.f64 (+.f64 1 (pow.f64 (/.f64 U (.f64 (.f64 2 J) (cos.f64 (/.f64 K 2)))) 2)))

series2.1s

Counts

4 → 12

Calls

4 calls:

395.0ms	(.f64 (.f64 2 J) (cos.f64 (/.f64 K 2)))
547.0ms	(pow.f64 (/.f64 U (.f64 (.f64 2 J) (cos.f64 (/.f64 K 2)))) 2)
537.0ms	(.f64 (.f64 -2 J) (.f64 (cos.f64 (/.f64 K 2)) (sqrt.f64 (+.f64 1 (pow.f64 (/.f64 U (.f64 (*.f64 2 J) (cos.f64 (/.f64 K 2)))) 2)))))
663.0ms	(sqrt.f64 (+.f64 1 (pow.f64 (/.f64 U (.f64 (.f64 2 J) (cos.f64 (/.f64 K 2)))) 2)))

Iterations

Useful iterations: 0 (5.0ms)

Iter	Nodes	Cost
0	853	1353
1	853	1353
0	67	458
1	67	458
0	853	1353
1	853	1353
0	67	458
1	67	458
0	5219	33
0	977	1753
1	977	1753
0	33	9
1	33	9
0	977	1753
1	977	1753
0	33	9
1	33	9
0	1	3
1	1	3
0	730	1194
1	730	1194
0	89	63
1	89	63
0	730	1194
1	730	1194
0	89	63
1	89	63
0	4952	3
1	4952	3
0	402	378
1	402	378
0	38	36
1	38	36
0	402	378
1	402	378
0	38	36
1	38	36
0	4992	3
1	4992	3

simplify92.0ms

Counts

99 → 99

Iterations

Useful iterations: 0 (58.0ms)

Iter	Nodes	Cost
0	5604	2280

prune117.0ms

Filtered

61 candidates to 99 candidates (-62.3%)

Pruning

14 alts after pruning (12 fresh and 2 done)

	Pruned	Kept	Total
New	95	4	99
Fresh	1	8	9
Picked	0	1	1
Done	0	1	1
Total	96	14	110

Merged error: 17.1b

Counts

110 → 14

localize21.0ms

Local error

Found 4 expressions with local error:

5.9b	(sqrt.f64 (sqrt.f64 (+.f64 1 (pow.f64 (/.f64 U (.f64 (.f64 2 J) (cos.f64 (/.f64 K 2)))) 2))))
5.9b	(sqrt.f64 (sqrt.f64 (+.f64 1 (pow.f64 (/.f64 U (.f64 (.f64 2 J) (cos.f64 (/.f64 K 2)))) 2))))
11.0b	(sqrt.f64 (+.f64 1 (pow.f64 (/.f64 U (.f64 (.f64 2 J) (cos.f64 (/.f64 K 2)))) 2)))
11.0b	(sqrt.f64 (+.f64 1 (pow.f64 (/.f64 U (.f64 (.f64 2 J) (cos.f64 (/.f64 K 2)))) 2)))

rewrite43.0ms

Algorithm

rewrite-expression-head

Rules

32×	`sqrt-prod_binary64`
18×	`*-un-lft-identity_binary64`
16×	`add-sqr-sqrt_binary64`
12×	`sqrt-div_binary64`
10×	`pow1_binary64` `add-cube-cbrt_binary64` `sqrt-pow1_binary64`
6×	`pow1/2_binary64` `rem-sqrt-square_binary64`
4×	`flip3-+_binary64` `add-log-exp_binary64` `distribute-lft-out_binary64` `add-exp-log_binary64` `add-cbrt-cube_binary64` `insert-posit16` `flip-+_binary64`

Counts

4 → 80

Calls

4 calls:

11.0ms	(sqrt.f64 (sqrt.f64 (+.f64 1 (pow.f64 (/.f64 U (.f64 (.f64 2 J) (cos.f64 (/.f64 K 2)))) 2))))
10.0ms	(sqrt.f64 (sqrt.f64 (+.f64 1 (pow.f64 (/.f64 U (.f64 (.f64 2 J) (cos.f64 (/.f64 K 2)))) 2))))
10.0ms	(sqrt.f64 (+.f64 1 (pow.f64 (/.f64 U (.f64 (.f64 2 J) (cos.f64 (/.f64 K 2)))) 2)))
10.0ms	(sqrt.f64 (+.f64 1 (pow.f64 (/.f64 U (.f64 (.f64 2 J) (cos.f64 (/.f64 K 2)))) 2)))

series2.7s

Counts

4 → 12

Calls

4 calls:

707.0ms	(sqrt.f64 (sqrt.f64 (+.f64 1 (pow.f64 (/.f64 U (.f64 (.f64 2 J) (cos.f64 (/.f64 K 2)))) 2))))
704.0ms	(sqrt.f64 (sqrt.f64 (+.f64 1 (pow.f64 (/.f64 U (.f64 (.f64 2 J) (cos.f64 (/.f64 K 2)))) 2))))
663.0ms	(sqrt.f64 (+.f64 1 (pow.f64 (/.f64 U (.f64 (.f64 2 J) (cos.f64 (/.f64 K 2)))) 2)))
666.0ms	(sqrt.f64 (+.f64 1 (pow.f64 (/.f64 U (.f64 (.f64 2 J) (cos.f64 (/.f64 K 2)))) 2)))

Iterations

Useful iterations: 0 (155.0ms)

Iter	Nodes	Cost
0	853	1353
1	853	1353
0	67	458
1	67	458
0	853	1353
1	853	1353
0	67	458
1	67	458
0	5219	33
0	853	1353
1	853	1353
0	67	458
1	67	458
0	853	1353
1	853	1353
0	67	458
1	67	458
0	5219	33
0	926	1489
1	926	1489
0	69	462
1	69	462
0	926	1489
1	926	1489
0	69	462
1	69	462
0	5219	33
0	926	1489
1	926	1489
0	69	462
1	69	462
0	926	1489
1	926	1489
0	69	462
1	69	462
0	5219	33

simplify115.0ms

Counts

92 → 92

Iterations

Useful iterations: 0 (81.0ms)

Iter	Nodes	Cost
0	5030	2436

prune198.0ms

Filtered

68 candidates to 92 candidates (-35.3%)

Pruning

13 alts after pruning (11 fresh and 2 done)

	Pruned	Kept	Total
New	91	1	92
Fresh	1	10	11
Picked	1	0	1
Done	0	2	2
Total	93	13	106

Merged error: 17.1b

Counts

106 → 13

localize25.0ms

Local error

Found 4 expressions with local error:

0.3b	(cbrt.f64 (cos.f64 (/.f64 K 2)))
0.3b	(cbrt.f64 (cos.f64 (/.f64 K 2)))
6.0b	(.f64 (.f64 (.f64 (.f64 J -2) (.f64 (cbrt.f64 (cos.f64 (/.f64 K 2))) (cbrt.f64 (cos.f64 (/.f64 K 2))))) (cbrt.f64 (cos.f64 (/.f64 K 2)))) (sqrt.f64 (+.f64 1 (pow.f64 (/.f64 U (.f64 (*.f64 2 J) (cos.f64 (/.f64 K 2)))) 2))))
11.0b	(sqrt.f64 (+.f64 1 (pow.f64 (/.f64 U (.f64 (.f64 2 J) (cos.f64 (/.f64 K 2)))) 2)))

rewrite45.0ms

Algorithm

rewrite-expression-head

Rules

30×	`pow1_binary64`
29×	`add-exp-log_binary64`
20×	`add-cbrt-cube_binary64`
19×	`pow-prod-down_binary64` `cbrt-unprod_binary64` `prod-exp_binary64`
13×	`*-un-lft-identity_binary64`
10×	`add-sqr-sqrt_binary64`
9×	`add-cube-cbrt_binary64`
8×	`sqrt-prod_binary64`
7×	`associate-r_binary64`
6×	`cbrt-prod_binary64`
4×	`add-log-exp_binary64` `insert-posit16` `sqrt-div_binary64`
2×	`flip3-+_binary64` `distribute-lft-out_binary64` `associate-*r/_binary64` `pow1/3_binary64` `flip-+_binary64`
1×	`pow1/2_binary64` `associate-l_binary64` `sqrt-pow1_binary64` `rem-sqrt-square_binary64` `*-commutative_binary64`

Counts

4 → 78

Calls

4 calls:

1.0ms	(cbrt.f64 (cos.f64 (/.f64 K 2)))
1.0ms	(cbrt.f64 (cos.f64 (/.f64 K 2)))
29.0ms	(.f64 (.f64 (.f64 (.f64 J -2) (.f64 (cbrt.f64 (cos.f64 (/.f64 K 2))) (cbrt.f64 (cos.f64 (/.f64 K 2))))) (cbrt.f64 (cos.f64 (/.f64 K 2)))) (sqrt.f64 (+.f64 1 (pow.f64 (/.f64 U (.f64 (*.f64 2 J) (cos.f64 (/.f64 K 2)))) 2))))
10.0ms	(sqrt.f64 (+.f64 1 (pow.f64 (/.f64 U (.f64 (.f64 2 J) (cos.f64 (/.f64 K 2)))) 2)))

series2.2s

Counts

4 → 12

Calls

4 calls:

460.0ms	(cbrt.f64 (cos.f64 (/.f64 K 2)))
462.0ms	(cbrt.f64 (cos.f64 (/.f64 K 2)))
591.0ms	(.f64 (.f64 (.f64 (.f64 J -2) (.f64 (cbrt.f64 (cos.f64 (/.f64 K 2))) (cbrt.f64 (cos.f64 (/.f64 K 2))))) (cbrt.f64 (cos.f64 (/.f64 K 2)))) (sqrt.f64 (+.f64 1 (pow.f64 (/.f64 U (.f64 (*.f64 2 J) (cos.f64 (/.f64 K 2)))) 2))))
656.0ms	(sqrt.f64 (+.f64 1 (pow.f64 (/.f64 U (.f64 (.f64 2 J) (cos.f64 (/.f64 K 2)))) 2)))

Iterations

Useful iterations: 0 (6.0ms)

Iter	Nodes	Cost
0	853	1353
1	853	1353
0	67	458
1	67	458
0	853	1353
1	853	1353
0	67	458
1	67	458
0	5219	33
0	1124	2184
1	1124	2184
0	426	747
1	426	747
0	1124	2184
1	1124	2184
0	426	747
1	426	747
0	1	3
1	1	3
0	56	1645
1	56	1645
0	587	1612
1	587	1612
0	56	1645
1	56	1645
0	587	1612
1	587	1612
0	4891	54
1	4891	54
0	56	1645
1	56	1645
0	587	1612
1	587	1612
0	56	1645
1	56	1645
0	587	1612
1	587	1612
0	4891	54
1	4891	54

simplify95.0ms

Counts

90 → 90

Iterations

Useful iterations: 0 (57.0ms)

Iter	Nodes	Cost
0	5227	2303

prune143.0ms

Filtered

61 candidates to 90 candidates (-47.5%)

Pruning

17 alts after pruning (14 fresh and 3 done)

	Pruned	Kept	Total
New	86	4	90
Fresh	0	10	10
Picked	0	1	1
Done	0	2	2
Total	86	17	103

Merged error: 17.1b

Counts

103 → 17

regimes267.0ms

Accuracy

0% (1.1b remaining)

Error of 18.3b against oracle of 17.3b and baseline of 18.3b

bsearch0.0ms

simplify6.0ms

Iterations

Useful iterations: 0 (2.0ms)

Iter	Nodes	Cost
0	26	37
1	26	37

end0.0ms

sample3.0s

Algorithm

intervals

Results

1.3s	1519×	body	1280	valid
669.0ms	1175×	body	640	valid
497.0ms	4382×	body	80	valid
241.0ms	591×	body	320	valid
86.0ms	333×	body	160	valid
1.0ms	1×	body	1280	invalid
0.0ms	3×	body	80	invalid

Details

analyze1.9s

sample110.0ms

simplify190.0ms

prune4.0ms

localize17.0ms

rewrite49.0ms

series2.6s

simplify129.0ms

prune145.0ms

localize17.0ms

rewrite51.0ms

series2.1s

simplify92.0ms

prune117.0ms

localize21.0ms

rewrite43.0ms

series2.7s

simplify115.0ms

prune198.0ms

localize25.0ms

rewrite45.0ms

series2.2s

simplify95.0ms

prune143.0ms

regimes267.0ms

bsearch0.0ms

simplify6.0ms

end0.0ms

sample3.0s

Profiling