Details

analyze1.8s

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
0%	93.6%	6.4%	8
9.4%	84.3%	6.4%	9
14.8%	75.7%	9.5%	10
16%	71.4%	12.6%	11
20.9%	65.7%	13.4%	12
24.2%	60.5%	15.3%	13
24.8%	58.6%	16.6%	14

sample128.0ms

Algorithm

intervals

Results

42.0ms	45×	body	1280	valid
32.0ms	44×	body	640	valid
19.0ms	126×	body	80	valid
13.0ms	30×	body	320	valid
3.0ms	23×	body	80	invalid
3.0ms	11×	body	160	valid
1.0ms	1×	body	1280	invalid
0.0ms	3×	body	80	nan

simplify196.0ms

Counts

1 → 1

Iterations

Useful iterations: 0 (51.0ms)

Iter	Nodes	Cost
0	5272	32

prune8.0ms

Filtered

1 candidates to 1 candidates (0.0%)

Pruning

2 alts after pruning (2 fresh and 0 done)

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

Merged error: 13.9b

Counts

2 → 2

localize28.0ms

Local error

Found 4 expressions with local error:

0.1b	(/.f64 F (sin.f64 B))
0.1b	(/.f64 x (tan.f64 B))
6.0b	(.f64 (/.f64 F (sin.f64 B)) (pow.f64 (+.f64 (+.f64 (.f64 F F) 2) (*.f64 x 2)) -1/2))
16.4b	(pow.f64 (+.f64 (+.f64 (.f64 F F) 2) (.f64 x 2)) -1/2)

rewrite244.0ms

Algorithm

rewrite-expression-head

Rules

44×	`add-sqr-sqrt_binary64`
31×	`*-un-lft-identity_binary64` `add-cube-cbrt_binary64`
30×	`times-frac_binary64`
22×	`add-exp-log_binary64`
13×	`add-cbrt-cube_binary64` `associate-l_binary64`
8×	`unpow-prod-down_binary64`
7×	`associate-r_binary64`
6×	`associate-/r_binary64` `unswap-sqr_binary64` `prod-exp_binary64` `associate-/l_binary64`
5×	`pow1_binary64` `div-exp_binary64`
4×	`add-log-exp_binary64` `sqr-pow_binary64` `insert-posit16`
3×	`pow-to-exp_binary64` `pow-unpow_binary64` `cbrt-undiv_binary64` `div-inv_binary64` `pow-exp_binary64`
2×	`cbrt-unprod_binary64` `clear-num_binary64` `frac-2neg_binary64`
1×	`pow-pow_binary64` `associate-/r/_binary64` `tan-quot_binary64` `associate-l/_binary64` `-commutative_binary64`

Counts

4 → 119

Calls

4 calls:

4.0ms	(/.f64 F (sin.f64 B))
5.0ms	(/.f64 x (tan.f64 B))
18.0ms	(.f64 (/.f64 F (sin.f64 B)) (pow.f64 (+.f64 (+.f64 (.f64 F F) 2) (*.f64 x 2)) -1/2))
212.0ms	(pow.f64 (+.f64 (+.f64 (.f64 F F) 2) (.f64 x 2)) -1/2)

series1.2s

Counts

4 → 12

Calls

4 calls:

204.0ms	(/.f64 F (sin.f64 B))
247.0ms	(/.f64 x (tan.f64 B))
320.0ms	(.f64 (/.f64 F (sin.f64 B)) (pow.f64 (+.f64 (+.f64 (.f64 F F) 2) (*.f64 x 2)) -1/2))
422.0ms	(pow.f64 (+.f64 (+.f64 (.f64 F F) 2) (.f64 x 2)) -1/2)

Iterations

Useful iterations: 0 (5.0ms)

Iter	Nodes	Cost
0	475	378
1	475	378
0	475	378
1	475	378
0	4960	24
1	4960	24
0	1245	648
1	1245	648
0	1245	648
1	1245	648
0	1	3
1	1	3
0	861	140
1	861	140
0	861	140
1	861	140
0	1	3
1	1	3
0	662	140
1	662	140
0	662	140
1	662	140
0	1	3
1	1	3

simplify123.0ms

Counts

131 → 131

Iterations

Useful iterations: 0 (88.0ms)

Iter	Nodes	Cost
0	4981	2419
1	4981	2419

prune174.0ms

Filtered

101 candidates to 131 candidates (-29.7%)

Pruning

13 alts after pruning (13 fresh and 0 done)

	Pruned	Kept	Total
New	118	13	131
Fresh	1	0	1
Picked	1	0	1
Done	0	0	0
Total	120	13	133

Merged error: 10.8b

Counts

133 → 13

localize20.0ms

Local error

Found 4 expressions with local error:

0.1b	(/.f64 x (tan.f64 B))
0.2b	(.f64 F (pow.f64 (+.f64 (+.f64 (.f64 F F) 2) (*.f64 2 x)) -1/2))
0.4b	(/.f64 (.f64 F (pow.f64 (+.f64 (+.f64 (.f64 F F) 2) (*.f64 2 x)) -1/2)) (sin.f64 B))
16.4b	(pow.f64 (+.f64 (+.f64 (.f64 F F) 2) (.f64 2 x)) -1/2)

rewrite50.0ms

Algorithm

rewrite-expression-head

Rules

24×	`add-sqr-sqrt_binary64`
22×	`add-exp-log_binary64`
19×	`*-un-lft-identity_binary64` `add-cube-cbrt_binary64`
13×	`add-cbrt-cube_binary64`
12×	`times-frac_binary64`
7×	`associate-r_binary64` `unpow-prod-down_binary64`
6×	`associate-/r*_binary64` `prod-exp_binary64`
5×	`pow1_binary64` `div-exp_binary64`
4×	`add-log-exp_binary64` `associate-/l*_binary64` `insert-posit16`
3×	`pow-to-exp_binary64` `pow-unpow_binary64` `cbrt-undiv_binary64` `sqr-pow_binary64` `associate-l_binary64` `unswap-sqr_binary64` `pow-exp_binary64`
2×	`cbrt-unprod_binary64` `clear-num_binary64` `frac-2neg_binary64` `div-inv_binary64`
1×	`pow-pow_binary64` `associate-/r/_binary64` `tan-quot_binary64` `*-commutative_binary64`

Counts

4 → 97

Calls

4 calls:

5.0ms	(/.f64 x (tan.f64 B))
14.0ms	(.f64 F (pow.f64 (+.f64 (+.f64 (.f64 F F) 2) (*.f64 2 x)) -1/2))
17.0ms	(/.f64 (.f64 F (pow.f64 (+.f64 (+.f64 (.f64 F F) 2) (*.f64 2 x)) -1/2)) (sin.f64 B))
11.0ms	(pow.f64 (+.f64 (+.f64 (.f64 F F) 2) (.f64 2 x)) -1/2)

series1.4s

Counts

4 → 12

Calls

4 calls:

245.0ms	(/.f64 x (tan.f64 B))
396.0ms	(.f64 F (pow.f64 (+.f64 (+.f64 (.f64 F F) 2) (*.f64 2 x)) -1/2))
341.0ms	(/.f64 (.f64 F (pow.f64 (+.f64 (+.f64 (.f64 F F) 2) (*.f64 2 x)) -1/2)) (sin.f64 B))
413.0ms	(pow.f64 (+.f64 (+.f64 (.f64 F F) 2) (.f64 2 x)) -1/2)

Iterations

Useful iterations: 0 (5.0ms)

Iter	Nodes	Cost
0	559	378
1	559	378
0	559	378
1	559	378
0	4960	24
1	4960	24
0	1260	1284
1	1260	1284
0	1260	1284
1	1260	1284
0	1	3
1	1	3
0	626	588
1	626	588
0	626	588
1	626	588
0	4996	15
1	4996	15
0	861	140
1	861	140
0	861	140
1	861	140
0	1	3
1	1	3

simplify119.0ms

Counts

109 → 109

Iterations

Useful iterations: 0 (88.0ms)

Iter	Nodes	Cost
0	5073	2031

prune129.0ms

Filtered

78 candidates to 109 candidates (-39.7%)

Pruning

15 alts after pruning (15 fresh and 0 done)

	Pruned	Kept	Total
New	101	8	109
Fresh	5	7	12
Picked	1	0	1
Done	0	0	0
Total	107	15	122

Merged error: 10.7b

Counts

122 → 15

localize23.0ms

Local error

Found 4 expressions with local error:

0.1b	(/.f64 x (tan.f64 B))
0.2b	(.f64 F (/.f64 (pow.f64 (+.f64 (+.f64 (.f64 F F) 2) (*.f64 2 x)) -1/2) (sin.f64 B)))
0.3b	(/.f64 (pow.f64 (+.f64 (+.f64 (.f64 F F) 2) (.f64 2 x)) -1/2) (sin.f64 B))
16.4b	(pow.f64 (+.f64 (+.f64 (.f64 F F) 2) (.f64 2 x)) -1/2)

rewrite54.0ms

Algorithm

rewrite-expression-head

Rules

55×	`add-sqr-sqrt_binary64`
54×	`times-frac_binary64`
45×	`*-un-lft-identity_binary64` `add-cube-cbrt_binary64`
25×	`associate-r_binary64` `unpow-prod-down_binary64`
22×	`add-exp-log_binary64`
13×	`add-cbrt-cube_binary64`
10×	`associate-/l*_binary64`
9×	`sqr-pow_binary64`
7×	`pow1_binary64` `div-exp_binary64`
6×	`associate-/r*_binary64`
4×	`add-log-exp_binary64` `unswap-sqr_binary64` `prod-exp_binary64` `insert-posit16`
3×	`pow-to-exp_binary64` `pow-unpow_binary64` `cbrt-undiv_binary64` `associate-l_binary64` `div-inv_binary64` `pow-exp_binary64`
2×	`cbrt-unprod_binary64` `clear-num_binary64` `frac-2neg_binary64`
1×	`pow-prod-down_binary64` `associate-r/_binary64` `pow-pow_binary64` `associate-/r/_binary64` `tan-quot_binary64` `-commutative_binary64`

Counts

4 → 142

Calls

4 calls:

5.0ms	(/.f64 x (tan.f64 B))
19.0ms	(.f64 F (/.f64 (pow.f64 (+.f64 (+.f64 (.f64 F F) 2) (*.f64 2 x)) -1/2) (sin.f64 B)))
14.0ms	(/.f64 (pow.f64 (+.f64 (+.f64 (.f64 F F) 2) (.f64 2 x)) -1/2) (sin.f64 B))
10.0ms	(pow.f64 (+.f64 (+.f64 (.f64 F F) 2) (.f64 2 x)) -1/2)

series1.5s

Counts

4 → 12

Calls

4 calls:

242.0ms	(/.f64 x (tan.f64 B))
415.0ms	(.f64 F (/.f64 (pow.f64 (+.f64 (+.f64 (.f64 F F) 2) (*.f64 2 x)) -1/2) (sin.f64 B)))
430.0ms	(/.f64 (pow.f64 (+.f64 (+.f64 (.f64 F F) 2) (.f64 2 x)) -1/2) (sin.f64 B))
418.0ms	(pow.f64 (+.f64 (+.f64 (.f64 F F) 2) (.f64 2 x)) -1/2)

Iterations

Useful iterations: 0 (5.0ms)

Iter	Nodes	Cost
0	559	378
1	559	378
0	559	378
1	559	378
0	4960	24
1	4960	24
0	1280	1009
1	1280	1009
0	1280	1009
1	1280	1009
0	1	3
1	1	3
0	1164	1353
1	1164	1353
0	1164	1353
1	1164	1353
0	1	3
1	1	3
0	861	140
1	861	140
0	861	140
1	861	140
0	1	3
1	1	3

simplify135.0ms

Counts

154 → 154

Iterations

Useful iterations: 0 (89.0ms)

Iter	Nodes	Cost
0	4995	3776
1	4995	3776

prune193.0ms

Filtered

114 candidates to 154 candidates (-35.1%)

Pruning

15 alts after pruning (14 fresh and 1 done)

	Pruned	Kept	Total
New	154	0	154
Fresh	0	14	14
Picked	0	1	1
Done	0	0	0
Total	154	15	169

Merged error: 10.7b

Counts

169 → 15

localize22.0ms

Local error

Found 4 expressions with local error:

0.2b	(.f64 F (pow.f64 (+.f64 (+.f64 (.f64 F F) 2) (*.f64 2 x)) -1/2))
0.3b	(/.f64 1 (/.f64 (tan.f64 B) x))
0.4b	(/.f64 (.f64 F (pow.f64 (+.f64 (+.f64 (.f64 F F) 2) (*.f64 2 x)) -1/2)) (sin.f64 B))
16.4b	(pow.f64 (+.f64 (+.f64 (.f64 F F) 2) (.f64 2 x)) -1/2)

rewrite54.0ms

Algorithm

rewrite-expression-head

Rules

78×	`times-frac_binary64`
58×	`add-sqr-sqrt_binary64`
53×	`*-un-lft-identity_binary64` `add-cube-cbrt_binary64`
31×	`add-exp-log_binary64`
16×	`associate-/r*_binary64` `add-cbrt-cube_binary64`
11×	`div-exp_binary64`
7×	`associate-r_binary64` `unpow-prod-down_binary64`
6×	`pow1_binary64` `prod-exp_binary64` `div-inv_binary64`
5×	`cbrt-undiv_binary64`
4×	`add-log-exp_binary64` `associate-/l*_binary64` `insert-posit16`
3×	`pow-to-exp_binary64` `pow-unpow_binary64` `sqr-pow_binary64` `associate-l_binary64` `unswap-sqr_binary64` `pow-exp_binary64`
2×	`cbrt-unprod_binary64` `1-exp_binary64` `clear-num_binary64` `frac-2neg_binary64` `rec-exp_binary64`
1×	`pow-pow_binary64` `associate-/r/_binary64` `inv-pow_binary64` `pow-flip_binary64` `*-commutative_binary64`

Counts

4 → 145

Calls

4 calls:

14.0ms	(.f64 F (pow.f64 (+.f64 (+.f64 (.f64 F F) 2) (*.f64 2 x)) -1/2))
7.0ms	(/.f64 1 (/.f64 (tan.f64 B) x))
15.0ms	(/.f64 (.f64 F (pow.f64 (+.f64 (+.f64 (.f64 F F) 2) (*.f64 2 x)) -1/2)) (sin.f64 B))
11.0ms	(pow.f64 (+.f64 (+.f64 (.f64 F F) 2) (.f64 2 x)) -1/2)

series1.6s

Counts

4 → 12

Calls

4 calls:

392.0ms	(.f64 F (pow.f64 (+.f64 (+.f64 (.f64 F F) 2) (*.f64 2 x)) -1/2))
404.0ms	(/.f64 1 (/.f64 (tan.f64 B) x))
342.0ms	(/.f64 (.f64 F (pow.f64 (+.f64 (+.f64 (.f64 F F) 2) (*.f64 2 x)) -1/2)) (sin.f64 B))
417.0ms	(pow.f64 (+.f64 (+.f64 (.f64 F F) 2) (.f64 2 x)) -1/2)

Iterations

Useful iterations: 0 (5.0ms)

Iter	Nodes	Cost
0	559	378
1	559	378
0	559	378
1	559	378
0	4960	24
1	4960	24
0	1260	1284
1	1260	1284
0	1260	1284
1	1260	1284
0	1	3
1	1	3
0	1645	194
1	1645	194
0	1645	194
1	1645	194
0	1	3
1	1	3
0	626	588
1	626	588
0	626	588
1	626	588
0	4996	15
1	4996	15

simplify174.0ms

Counts

157 → 157

Iterations

Useful iterations: 0 (132.0ms)

Iter	Nodes	Cost
0	4979	2942
1	4979	2942

prune133.0ms

Filtered

97 candidates to 157 candidates (-61.9%)

Pruning

17 alts after pruning (16 fresh and 1 done)

	Pruned	Kept	Total
New	154	3	157
Fresh	0	13	13
Picked	1	0	1
Done	0	1	1
Total	155	17	172

Merged error: 10.7b

Counts

172 → 17

regimes142.0ms

Accuracy

0% (0.4b remaining)

Error of 10.6b against oracle of 10.1b and baseline of 10.6b

bsearch0.0ms

simplify10.0ms

Iterations

Useful iterations: 0 (2.0ms)

Iter	Nodes	Cost
0	38	32
1	38	32

end0.0ms

sample3.6s

Algorithm

intervals

Results

1.4s	1605×	body	1280	valid
819.0ms	1373×	body	640	valid
556.0ms	3976×	body	80	valid
284.0ms	689×	body	320	valid
106.0ms	357×	body	160	valid
104.0ms	707×	body	80	invalid
12.0ms	115×	body	80	nan
2.0ms	2×	body	1280	invalid
1.0ms	1×	body	640	invalid

Details

analyze1.8s

sample128.0ms

simplify196.0ms

prune8.0ms

localize28.0ms

rewrite244.0ms

series1.2s

simplify123.0ms

prune174.0ms

localize20.0ms

rewrite50.0ms

series1.4s

simplify119.0ms

prune129.0ms

localize23.0ms

rewrite54.0ms

series1.5s

simplify135.0ms

prune193.0ms

localize22.0ms

rewrite54.0ms

series1.6s

simplify174.0ms

prune133.0ms

regimes142.0ms

bsearch0.0ms

simplify10.0ms

end0.0ms

sample3.6s

Profiling