Details

analyze748.0ms

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
12.5%	87.4%	0.1%	5
18.7%	81.1%	0.1%	6
21.8%	71.8%	6.4%	7
31.2%	62.4%	6.4%	8
35.9%	55.4%	8.7%	9
37.8%	48.8%	13.4%	10
42.7%	42.3%	15%	11
47.7%	34.2%	18.1%	12
49.1%	30.4%	20.5%	13
51.9%	25.8%	22.3%	14

sample45.0ms

Algorithm

intervals

Results

10.0ms	31×	body	2560	valid
9.0ms	167×	body	80	valid
8.0ms	30×	body	1280	valid
3.0ms	14×	body	640	valid
2.0ms	6×	body	5120	valid
1.0ms	18×	body	80	invalid
1.0ms	17×	body	80	nan
1.0ms	4×	body	320	valid
0.0ms	4×	body	160	valid

simplify121.0ms

Counts

1 → 1

Iterations

Useful iterations: 0 (103.0ms)

Iter	Nodes	Cost
0	928	24
1	928	24

prune4.0ms

Filtered

1 candidates to 1 candidates (0.0%)

Pruning

1 alts after pruning (1 fresh and 0 done)

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

Merged error: 33.5b

Counts

2 → 1

localize12.0ms

Local error

Found 4 expressions with local error:

0.1b	(/.f64 (-.f64 (sqrt.f64 (-.f64 (.f64 b b) (.f64 (.f64 4 a) c))) b) (.f64 a 2))
0.8b	(-.f64 (.f64 b b) (.f64 (*.f64 4 a) c))
1.0b	(-.f64 (sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c))) b)
21.9b	(sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c)))

rewrite40.0ms

Algorithm

rewrite-expression-head

Rules

20×	`add-sqr-sqrt_binary64_1762`
13×	`*-un-lft-identity_binary64_1777`
9×	`add-cbrt-cube_binary64_1749` `add-exp-log_binary64_1741`
8×	`add-log-exp_binary64_1742`
7×	`add-cube-cbrt_binary64_1748`
6×	`associate-/l*_binary64_1841` `times-frac_binary64_1772` `sqrt-prod_binary64_1756` `difference-of-squares_binary64_1806`
5×	`pow1_binary64_1719`
4×	`flip3--_binary64_1776` `flip--_binary64_1803`
3×	`distribute-lft-out--_binary64_1822`
2×	`cbrt-undiv_binary64_1747` `div-exp_binary64_1726` `diff-log_binary64_1688` `sub-neg_binary64_1781` `sqrt-div_binary64_1757` `associate-/l/_binary64_1843`
1×	`div-sub_binary64_1771` `clear-num_binary64_1780` `div-inv_binary64_1778` `pow1/2_binary64_1709` `prod-exp_binary64_1724` `cbrt-unprod_binary64_1746` `frac-2neg_binary64_1770` `rem-sqrt-square_binary64_1765` `associate-/r*_binary64_1840` `sqrt-pow1_binary64_1758`

Counts

4 → 70

Calls

4 calls:

16.0ms	(/.f64 (-.f64 (sqrt.f64 (-.f64 (.f64 b b) (.f64 (.f64 4 a) c))) b) (.f64 a 2))
6.0ms	(-.f64 (.f64 b b) (.f64 (*.f64 4 a) c))
11.0ms	(-.f64 (sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c))) b)
6.0ms	(sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c)))

series229.0ms

Counts

4 → 12

Calls

4 calls:

59.0ms	(/.f64 (-.f64 (sqrt.f64 (-.f64 (.f64 b b) (.f64 (.f64 4 a) c))) b) (.f64 a 2))
56.0ms	(-.f64 (.f64 b b) (.f64 (*.f64 4 a) c))
56.0ms	(-.f64 (sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c))) b)
57.0ms	(sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c)))

Iterations

Useful iterations: 0 (5.0ms)

Iter	Nodes	Cost
0	45	9
1	45	9
0	45	9
1	45	9
0	1	3
1	1	3
0	67	9
1	67	9
0	67	9
1	67	9
0	1	3
1	1	3
0	42	9
1	42	9
0	42	9
1	42	9
0	1	3
1	1	3
0	77	9
1	77	9
0	77	9
1	77	9
0	1	3
1	1	3

simplify139.0ms

Counts

82 → 82

Iterations

Useful iterations: 0 (108.0ms)

Iter	Nodes	Cost
0	4966	1825
1	4966	1825

prune129.0ms

Filtered

58 candidates to 82 candidates (-41.4%)

Pruning

17 alts after pruning (17 fresh and 0 done)

	Pruned	Kept	Total
New	65	17	82
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	66	17	83

Merged error: 27.6b

Counts

83 → 17

localize14.0ms

Local error

Found 4 expressions with local error:

0.2b	(/.f64 1 (/.f64 (.f64 a 2) (-.f64 (sqrt.f64 (-.f64 (.f64 b b) (.f64 (.f64 4 a) c))) b)))
0.8b	(-.f64 (.f64 b b) (.f64 (*.f64 4 a) c))
1.0b	(-.f64 (sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c))) b)
21.9b	(sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c)))

rewrite47.0ms

Algorithm

rewrite-expression-head

Rules

60×	`times-frac_binary64_1772`
47×	`add-sqr-sqrt_binary64_1762`
36×	`*-un-lft-identity_binary64_1777`
26×	`add-cube-cbrt_binary64_1748`
25×	`add-exp-log_binary64_1741`
13×	`add-cbrt-cube_binary64_1749`
12×	`div-exp_binary64_1726` `associate-/r*_binary64_1840`
10×	`difference-of-squares_binary64_1806`
9×	`associate-/r/_binary64_1842`
8×	`add-log-exp_binary64_1742` `sqrt-prod_binary64_1756`
7×	`flip3--_binary64_1776` `flip--_binary64_1803`
6×	`pow1_binary64_1719`
5×	`cbrt-undiv_binary64_1747` `div-inv_binary64_1778` `distribute-lft-out--_binary64_1822`
3×	`associate-/l*_binary64_1841` `rec-exp_binary64_1725` `prod-exp_binary64_1724` `1-exp_binary64_1737`
2×	`diff-log_binary64_1688` `sub-neg_binary64_1781` `sqrt-div_binary64_1757`
1×	`clear-num_binary64_1780` `pow1/2_binary64_1709` `pow-flip_binary64_1703` `cbrt-unprod_binary64_1746` `frac-2neg_binary64_1770` `rem-sqrt-square_binary64_1765` `inv-pow_binary64_1695` `sqrt-pow1_binary64_1758`

Counts

4 → 116

Calls

4 calls:

18.0ms	(/.f64 1 (/.f64 (.f64 a 2) (-.f64 (sqrt.f64 (-.f64 (.f64 b b) (.f64 (.f64 4 a) c))) b)))
6.0ms	(-.f64 (.f64 b b) (.f64 (*.f64 4 a) c))
11.0ms	(-.f64 (sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c))) b)
6.0ms	(sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c)))

series239.0ms

Counts

4 → 12

Calls

4 calls:

62.0ms	(/.f64 1 (/.f64 (.f64 a 2) (-.f64 (sqrt.f64 (-.f64 (.f64 b b) (.f64 (.f64 4 a) c))) b)))
58.0ms	(-.f64 (.f64 b b) (.f64 (*.f64 4 a) c))
58.0ms	(-.f64 (sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c))) b)
61.0ms	(sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c)))

Iterations

Useful iterations: 0 (6.0ms)

Iter	Nodes	Cost
0	45	9
1	45	9
0	45	9
1	45	9
0	1	3
1	1	3
0	67	9
1	67	9
0	67	9
1	67	9
0	1	3
1	1	3
0	42	9
1	42	9
0	42	9
1	42	9
0	1	3
1	1	3
0	90	9
1	90	9
0	90	9
1	90	9
0	1	3
1	1	3

simplify171.0ms

Counts

128 → 128

Iterations

Useful iterations: 0 (126.0ms)

Iter	Nodes	Cost
0	4981	3782
1	4981	3782

prune138.0ms

Filtered

76 candidates to 128 candidates (-68.4%)

Pruning

19 alts after pruning (19 fresh and 0 done)

	Pruned	Kept	Total
New	121	7	128
Fresh	4	12	16
Picked	1	0	1
Done	0	0	0
Total	126	19	145

Merged error: 27.6b

Counts

145 → 19

localize14.0ms

Local error

Found 4 expressions with local error:

0.3b	(/.f64 (/.f64 1/2 a) (/.f64 1 (-.f64 (sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c))) b)))
0.8b	(-.f64 (.f64 b b) (.f64 (*.f64 4 a) c))
1.0b	(-.f64 (sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c))) b)
21.9b	(sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c)))

rewrite95.0ms

Algorithm

rewrite-expression-head

Rules

789×	`times-frac_binary64_1772`
493×	`add-sqr-sqrt_binary64_1762`
406×	`*-un-lft-identity_binary64_1777`
320×	`add-cube-cbrt_binary64_1748`
86×	`difference-of-squares_binary64_1806`
46×	`sqrt-prod_binary64_1756`
43×	`distribute-lft-out--_binary64_1822`
40×	`div-inv_binary64_1778`
29×	`associate-/r/_binary64_1842`
26×	`add-exp-log_binary64_1741`
24×	`associate-/r*_binary64_1840`
17×	`flip3--_binary64_1776` `flip--_binary64_1803`
16×	`div-exp_binary64_1726` `add-cbrt-cube_binary64_1749`
13×	`associate-/l*_binary64_1841`
8×	`cbrt-undiv_binary64_1747` `add-log-exp_binary64_1742`
5×	`pow1_binary64_1719`
2×	`diff-log_binary64_1688` `sub-neg_binary64_1781` `rec-exp_binary64_1725` `1-exp_binary64_1737` `sqrt-div_binary64_1757`
1×	`clear-num_binary64_1780` `pow1/2_binary64_1709` `frac-2neg_binary64_1770` `rem-sqrt-square_binary64_1765` `sqrt-pow1_binary64_1758` `associate-/l/_binary64_1843`

Counts

4 → 413

Calls

4 calls:

28.0ms	(/.f64 (/.f64 1/2 a) (/.f64 1 (-.f64 (sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c))) b)))
6.0ms	(-.f64 (.f64 b b) (.f64 (*.f64 4 a) c))
11.0ms	(-.f64 (sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c))) b)
6.0ms	(sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c)))

series231.0ms

Counts

4 → 12

Calls

4 calls:

60.0ms	(/.f64 (/.f64 1/2 a) (/.f64 1 (-.f64 (sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c))) b)))
57.0ms	(-.f64 (.f64 b b) (.f64 (*.f64 4 a) c))
59.0ms	(-.f64 (sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c))) b)
54.0ms	(sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c)))

Iterations

Useful iterations: 0 (5.0ms)

Iter	Nodes	Cost
0	45	9
1	45	9
0	45	9
1	45	9
0	1	3
1	1	3
0	67	9
1	67	9
0	67	9
1	67	9
0	1	3
1	1	3
0	42	9
1	42	9
0	42	9
1	42	9
0	1	3
1	1	3
0	110	9
1	110	9
0	110	9
1	110	9
0	1	3
1	1	3

simplify271.0ms

Counts

425 → 425

Iterations

Useful iterations: 0 (91.0ms)

Iter	Nodes	Cost
0	5028	21628

prune565.0ms

Filtered

217 candidates to 425 candidates (-95.9%)

Pruning

23 alts after pruning (23 fresh and 0 done)

	Pruned	Kept	Total
New	416	9	425
Fresh	4	14	18
Picked	1	0	1
Done	0	0	0
Total	421	23	444

Merged error: 27.6b

Counts

444 → 23

localize17.0ms

Local error

Found 4 expressions with local error:

1.0b	(-.f64 (sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c))) b)
1.0b	(-.f64 (sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c))) b)
21.9b	(sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c)))
21.9b	(sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c)))

rewrite35.0ms

Algorithm

rewrite-expression-head

Rules

16×	`add-sqr-sqrt_binary64_1762`
10×	`*-un-lft-identity_binary64_1777`
8×	`add-log-exp_binary64_1742` `sqrt-prod_binary64_1756`
6×	`add-cube-cbrt_binary64_1748` `pow1_binary64_1719`
4×	`flip3--_binary64_1776` `add-cbrt-cube_binary64_1749` `sqrt-div_binary64_1757` `difference-of-squares_binary64_1806` `add-exp-log_binary64_1741` `flip--_binary64_1803`
2×	`diff-log_binary64_1688` `sub-neg_binary64_1781` `pow1/2_binary64_1709` `rem-sqrt-square_binary64_1765` `distribute-lft-out--_binary64_1822` `sqrt-pow1_binary64_1758`

Counts

4 → 58

Calls

4 calls:

11.0ms	(-.f64 (sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c))) b)
11.0ms	(-.f64 (sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c))) b)
6.0ms	(sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c)))
6.0ms	(sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c)))

series235.0ms

Counts

4 → 12

Calls

4 calls:

60.0ms	(-.f64 (sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c))) b)
57.0ms	(-.f64 (sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c))) b)
58.0ms	(sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c)))
59.0ms	(sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c)))

Iterations

Useful iterations: 0 (5.0ms)

Iter	Nodes	Cost
0	45	9
1	45	9
0	45	9
1	45	9
0	1	3
1	1	3
0	45	9
1	45	9
0	45	9
1	45	9
0	1	3
1	1	3
0	67	9
1	67	9
0	67	9
1	67	9
0	1	3
1	1	3
0	67	9
1	67	9
0	67	9
1	67	9
0	1	3
1	1	3

simplify142.0ms

Counts

70 → 70

Iterations

Useful iterations: 0 (114.0ms)

Iter	Nodes	Cost
0	5107	1376

prune88.0ms

Filtered

50 candidates to 70 candidates (-40.0%)

Pruning

23 alts after pruning (22 fresh and 1 done)

	Pruned	Kept	Total
New	70	0	70
Fresh	0	22	22
Picked	0	1	1
Done	0	0	0
Total	70	23	93

Merged error: 27.6b

Counts

93 → 23

regimes231.0ms

Accuracy

86.5% (0.9b remaining)

Error of 28.7b against oracle of 27.8b and baseline of 34.4b

bsearch72.0ms

Steps

Iters	Range		Point
6	1.8173103053317733e+102	7.524142696626456e+102	3.302437054159807e+102
9	-1.1728433930348086e+159	-6.078197847532872e+152	-1.3398860289927658e+154

simplify8.0ms

Iterations

Useful iterations: 0 (3.0ms)

Iter	Nodes	Cost
0	83	76
1	83	76

end0.0ms

sample1.4s

Algorithm

intervals

Results

357.0ms	1070×	body	2560	valid
288.0ms	5138×	body	80	valid
233.0ms	896×	body	1280	valid
91.0ms	446×	body	640	valid
46.0ms	107×	body	5120	valid
37.0ms	695×	body	80	nan
33.0ms	217×	body	320	valid
22.0ms	397×	body	80	invalid
13.0ms	126×	body	160	valid

Iter	Nodes	Cost
0	45	9
1	45	9
0	45	9
1	45	9
0	1	3
1	1	3
0	67	9
1	67	9
0	67	9
1	67	9
0	1	3
1	1	3
0	42	9
1	42	9
0	42	9
1	42	9
0	1	3
1	1	3
0	77	9
1	77	9
0	77	9
1	77	9
0	1	3
1	1	3

Iter	Nodes	Cost
0	45	9
1	45	9
0	45	9
1	45	9
0	1	3
1	1	3
0	67	9
1	67	9
0	67	9
1	67	9
0	1	3
1	1	3
0	42	9
1	42	9
0	42	9
1	42	9
0	1	3
1	1	3
0	90	9
1	90	9
0	90	9
1	90	9
0	1	3
1	1	3

Iter	Nodes	Cost
0	45	9
1	45	9
0	45	9
1	45	9
0	1	3
1	1	3
0	67	9
1	67	9
0	67	9
1	67	9
0	1	3
1	1	3
0	42	9
1	42	9
0	42	9
1	42	9
0	1	3
1	1	3
0	110	9
1	110	9
0	110	9
1	110	9
0	1	3
1	1	3

Iter	Nodes	Cost
0	45	9
1	45	9
0	45	9
1	45	9
0	1	3
1	1	3
0	45	9
1	45	9
0	45	9
1	45	9
0	1	3
1	1	3
0	67	9
1	67	9
0	67	9
1	67	9
0	1	3
1	1	3
0	67	9
1	67	9
0	67	9
1	67	9
0	1	3
1	1	3

Iter	Nodes	Cost
0	45	9
1	45	9
0	45	9
1	45	9
0	1	3
1	1	3
0	67	9
1	67	9
0	67	9
1	67	9
0	1	3
1	1	3
0	42	9
1	42	9
0	42	9
1	42	9
0	1	3
1	1	3
0	77	9
1	77	9
0	77	9
1	77	9
0	1	3
1	1	3

Iter	Nodes	Cost
0	45	9
1	45	9
0	45	9
1	45	9
0	1	3
1	1	3
0	67	9
1	67	9
0	67	9
1	67	9
0	1	3
1	1	3
0	42	9
1	42	9
0	42	9
1	42	9
0	1	3
1	1	3
0	90	9
1	90	9
0	90	9
1	90	9
0	1	3
1	1	3

Iter	Nodes	Cost
0	45	9
1	45	9
0	45	9
1	45	9
0	1	3
1	1	3
0	67	9
1	67	9
0	67	9
1	67	9
0	1	3
1	1	3
0	42	9
1	42	9
0	42	9
1	42	9
0	1	3
1	1	3
0	110	9
1	110	9
0	110	9
1	110	9
0	1	3
1	1	3

Iter	Nodes	Cost
0	45	9
1	45	9
0	45	9
1	45	9
0	1	3
1	1	3
0	45	9
1	45	9
0	45	9
1	45	9
0	1	3
1	1	3
0	67	9
1	67	9
0	67	9
1	67	9
0	1	3
1	1	3
0	67	9
1	67	9
0	67	9
1	67	9
0	1	3
1	1	3

Details

analyze748.0ms

sample45.0ms

simplify121.0ms

prune4.0ms

localize12.0ms

rewrite40.0ms

series229.0ms

simplify139.0ms

prune129.0ms

localize14.0ms

rewrite47.0ms

series239.0ms

simplify171.0ms

prune138.0ms

localize14.0ms

rewrite95.0ms

series231.0ms

simplify271.0ms

prune565.0ms

localize17.0ms

rewrite35.0ms

series235.0ms

simplify142.0ms

prune88.0ms

regimes231.0ms

bsearch72.0ms

simplify8.0ms

end0.0ms

sample1.4s

Profiling

Iter	Nodes	Cost
0	45	9
1	45	9
0	45	9
1	45	9
0	1	3
1	1	3
0	67	9
1	67	9
0	67	9
1	67	9
0	1	3
1	1	3
0	42	9
1	42	9
0	42	9
1	42	9
0	1	3
1	1	3
0	77	9
1	77	9
0	77	9
1	77	9
0	1	3
1	1	3

Iter	Nodes	Cost
0	45	9
1	45	9
0	45	9
1	45	9
0	1	3
1	1	3
0	67	9
1	67	9
0	67	9
1	67	9
0	1	3
1	1	3
0	42	9
1	42	9
0	42	9
1	42	9
0	1	3
1	1	3
0	90	9
1	90	9
0	90	9
1	90	9
0	1	3
1	1	3

Iter	Nodes	Cost
0	45	9
1	45	9
0	45	9
1	45	9
0	1	3
1	1	3
0	67	9
1	67	9
0	67	9
1	67	9
0	1	3
1	1	3
0	42	9
1	42	9
0	42	9
1	42	9
0	1	3
1	1	3
0	110	9
1	110	9
0	110	9
1	110	9
0	1	3
1	1	3

Iter	Nodes	Cost
0	45	9
1	45	9
0	45	9
1	45	9
0	1	3
1	1	3
0	45	9
1	45	9
0	45	9
1	45	9
0	1	3
1	1	3
0	67	9
1	67	9
0	67	9
1	67	9
0	1	3
1	1	3
0	67	9
1	67	9
0	67	9
1	67	9
0	1	3
1	1	3