Details

analyze334.0ms

Algorithm

Search

True	Other	False	Iter
0%	50%	50%	0
0%	50%	50%	1
25%	25%	50%	2
25%	25%	50%	3
31.2%	18.7%	50%	4
31.2%	18.7%	50%	5
34.3%	15.6%	50%	6
34.3%	15.6%	50%	7
35.9%	14%	50%	8
35.9%	14%	50%	9
36.7%	13.3%	50%	10
36.7%	13.3%	50%	11
37.1%	12.9%	50%	12
37.1%	12.9%	50%	13
37.3%	12.7%	50%	14

sample34.0ms

Algorithm

intervals

Results

9.0ms	193×	body	80	valid
7.0ms	24×	body	2560	valid
3.0ms	19×	body	640	valid
3.0ms	256×	pre	80	true
2.0ms	7×	body	5120	valid
2.0ms	8×	body	1280	valid
1.0ms	4×	body	320	valid
0.0ms	1×	body	160	valid

simplify32.0ms

Counts

1 → 1

Iterations

Useful iterations: 0 (16.0ms)

Iter	Nodes	Cost
0	157	23
1	157	23

prune2.0ms

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: 41.2b

Counts

2 → 1

localize11.0ms

Local error

Found 4 expressions with local error:

0.0b	(+.f64 (.f64 re re) (.f64 im im))
0.0b	(sqrt.f64 (.f64 2 (-.f64 (sqrt.f64 (+.f64 (.f64 re re) (*.f64 im im))) re)))
0.8b	(-.f64 (sqrt.f64 (+.f64 (.f64 re re) (.f64 im im))) re)
31.4b	(sqrt.f64 (+.f64 (.f64 re re) (.f64 im im)))

rewrite40.0ms

Algorithm

rewrite-expression-head

Rules

10×	`add-sqr-sqrt_binary64`
8×	`add-log-exp_binary64` `pow1_binary64`
7×	`*-un-lft-identity_binary64`
5×	`add-cube-cbrt_binary64` `sqrt-prod_binary64`
4×	`add-exp-log_binary64` `add-cbrt-cube_binary64` `insert-posit16` `sqrt-div_binary64`
3×	`sqrt-pow1_binary64`
2×	`flip3-+_binary64` `pow1/2_binary64` `flip3--_binary64` `associate-*r/_binary64` `difference-of-squares_binary64` `flip--_binary64` `flip-+_binary64`
1×	`pow-prod-down_binary64` `sub-neg_binary64` `diff-log_binary64` `rem-sqrt-square_binary64` `distribute-lft-out--_binary64` `+-commutative_binary64` `sum-log_binary64`

Counts

4 → 57

Calls

4 calls:

6.0ms	(+.f64 (.f64 re re) (.f64 im im))
11.0ms	(sqrt.f64 (.f64 2 (-.f64 (sqrt.f64 (+.f64 (.f64 re re) (*.f64 im im))) re)))
14.0ms	(-.f64 (sqrt.f64 (+.f64 (.f64 re re) (.f64 im im))) re)
7.0ms	(sqrt.f64 (+.f64 (.f64 re re) (.f64 im im)))

series1.4s

Counts

4 → 12

Calls

4 calls:

189.0ms	(+.f64 (.f64 re re) (.f64 im im))
456.0ms	(sqrt.f64 (.f64 2 (-.f64 (sqrt.f64 (+.f64 (.f64 re re) (*.f64 im im))) re)))
407.0ms	(-.f64 (sqrt.f64 (+.f64 (.f64 re re) (.f64 im im))) re)
388.0ms	(sqrt.f64 (+.f64 (.f64 re re) (.f64 im im)))

Iterations

Useful iterations: 0 (5.0ms)

Iter	Nodes	Cost
0	645	567
1	645	567
0	645	567
1	645	567
0	4858	14
1	4858	14
0	763	98
1	763	98
0	763	98
1	763	98
0	4858	14
1	4858	14
0	801	464
1	801	464
0	801	464
1	801	464
0	5120	19
0	573	257
1	573	257
0	573	257
1	573	257
0	1	3
1	1	3

simplify131.0ms

Counts

69 → 69

Iterations

Useful iterations: 0 (102.0ms)

Iter	Nodes	Cost
0	4923	1122
1	4923	1122

prune88.0ms

Filtered

55 candidates to 69 candidates (-25.5%)

Pruning

12 alts after pruning (12 fresh and 0 done)

	Pruned	Kept	Total
New	57	12	69
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	58	12	70

Merged error: 33.8b

Counts

70 → 12

localize14.0ms

Local error

Found 4 expressions with local error:

0.8b	(-.f64 (sqrt.f64 (+.f64 (.f64 re re) (.f64 im im))) re)
0.8b	(-.f64 (sqrt.f64 (+.f64 (.f64 re re) (.f64 im im))) re)
31.4b	(sqrt.f64 (+.f64 (.f64 re re) (.f64 im im)))
31.4b	(sqrt.f64 (+.f64 (.f64 re re) (.f64 im im)))

rewrite35.0ms

Algorithm

rewrite-expression-head

Rules

16×	`add-sqr-sqrt_binary64`
10×	`*-un-lft-identity_binary64`
8×	`add-log-exp_binary64` `sqrt-prod_binary64`
6×	`pow1_binary64` `add-cube-cbrt_binary64`
4×	`add-exp-log_binary64` `add-cbrt-cube_binary64` `difference-of-squares_binary64` `insert-posit16` `sqrt-div_binary64`
2×	`flip3-+_binary64` `sub-neg_binary64` `pow1/2_binary64` `flip3--_binary64` `diff-log_binary64` `sqrt-pow1_binary64` `rem-sqrt-square_binary64` `distribute-lft-out--_binary64` `flip--_binary64` `flip-+_binary64`

Counts

4 → 62

Calls

4 calls:

10.0ms	(-.f64 (sqrt.f64 (+.f64 (.f64 re re) (.f64 im im))) re)
10.0ms	(-.f64 (sqrt.f64 (+.f64 (.f64 re re) (.f64 im im))) re)
7.0ms	(sqrt.f64 (+.f64 (.f64 re re) (.f64 im im)))
5.0ms	(sqrt.f64 (+.f64 (.f64 re re) (.f64 im im)))

series1.6s

Counts

4 → 12

Calls

4 calls:

408.0ms	(-.f64 (sqrt.f64 (+.f64 (.f64 re re) (.f64 im im))) re)
411.0ms	(-.f64 (sqrt.f64 (+.f64 (.f64 re re) (.f64 im im))) re)
375.0ms	(sqrt.f64 (+.f64 (.f64 re re) (.f64 im im)))
379.0ms	(sqrt.f64 (+.f64 (.f64 re re) (.f64 im im)))

Iterations

Useful iterations: 0 (165.0ms)

Iter	Nodes	Cost
0	645	567
1	645	567
0	645	567
1	645	567
0	4858	14
1	4858	14
0	645	567
1	645	567
0	645	567
1	645	567
0	4858	14
1	4858	14
0	763	98
1	763	98
0	763	98
1	763	98
0	4858	14
1	4858	14
0	763	98
1	763	98
0	763	98
1	763	98
0	4858	14
1	4858	14

simplify106.0ms

Counts

74 → 74

Iterations

Useful iterations: 0 (77.0ms)

Iter	Nodes	Cost
0	5606	1242

prune97.0ms

Filtered

58 candidates to 74 candidates (-27.6%)

Pruning

13 alts after pruning (12 fresh and 1 done)

	Pruned	Kept	Total
New	73	1	74
Fresh	0	11	11
Picked	0	1	1
Done	0	0	0
Total	73	13	86

Merged error: 33.8b

Counts

86 → 13

localize14.0ms

Local error

Found 4 expressions with local error:

0.3b	(pow.f64 (sqrt.f64 (.f64 2 (-.f64 (sqrt.f64 (+.f64 (.f64 re re) (*.f64 im im))) re))) 3)
0.8b	(-.f64 (sqrt.f64 (+.f64 (.f64 re re) (.f64 im im))) re)
20.3b	(cbrt.f64 (pow.f64 (sqrt.f64 (.f64 2 (-.f64 (sqrt.f64 (+.f64 (.f64 re re) (*.f64 im im))) re))) 3))
31.4b	(sqrt.f64 (+.f64 (.f64 re re) (.f64 im im)))

rewrite42.0ms

Algorithm

rewrite-expression-head

Rules

16×	`add-sqr-sqrt_binary64`
14×	`cbrt-prod_binary64`
13×	`*-un-lft-identity_binary64`
11×	`add-cube-cbrt_binary64`
9×	`pow1_binary64`
8×	`unpow-prod-down_binary64` `cube-prod_binary64` `sqrt-prod_binary64`
6×	`add-log-exp_binary64` `sqrt-div_binary64`
5×	`add-exp-log_binary64` `add-cbrt-cube_binary64`
4×	`associate-*r/_binary64` `pow-pow_binary64` `cube-div_binary64` `insert-posit16`
3×	`pow-unpow_binary64` `flip3--_binary64` `sqrt-pow1_binary64` `flip--_binary64`
2×	`cbrt-div_binary64` `pow1/2_binary64` `sqr-pow_binary64` `difference-of-squares_binary64` `unpow3_binary64` `cube-mult_binary64`
1×	`pow-to-exp_binary64` `pow-prod-down_binary64` `flip3-+_binary64` `sub-neg_binary64` `rem-cbrt-cube_binary64` `diff-log_binary64` `sqrt-pow2_binary64` `pow1/3_binary64` `rem-sqrt-square_binary64` `rem-cube-cbrt_binary64` `distribute-lft-out--_binary64` `flip-+_binary64` `pow-exp_binary64`

Counts

4 → 89

Calls

4 calls:

14.0ms	(pow.f64 (sqrt.f64 (.f64 2 (-.f64 (sqrt.f64 (+.f64 (.f64 re re) (*.f64 im im))) re))) 3)
10.0ms	(-.f64 (sqrt.f64 (+.f64 (.f64 re re) (.f64 im im))) re)
6.0ms	(cbrt.f64 (pow.f64 (sqrt.f64 (.f64 2 (-.f64 (sqrt.f64 (+.f64 (.f64 re re) (*.f64 im im))) re))) 3))
6.0ms	(sqrt.f64 (+.f64 (.f64 re re) (.f64 im im)))

series1.5s

Counts

4 → 12

Calls

4 calls:

446.0ms	(pow.f64 (sqrt.f64 (.f64 2 (-.f64 (sqrt.f64 (+.f64 (.f64 re re) (*.f64 im im))) re))) 3)
406.0ms	(-.f64 (sqrt.f64 (+.f64 (.f64 re re) (.f64 im im))) re)
237.0ms	(cbrt.f64 (pow.f64 (sqrt.f64 (.f64 2 (-.f64 (sqrt.f64 (+.f64 (.f64 re re) (*.f64 im im))) re))) 3))
376.0ms	(sqrt.f64 (+.f64 (.f64 re re) (.f64 im im)))

Iterations

Useful iterations: 0 (161.0ms)

Iter	Nodes	Cost
0	645	567
1	645	567
0	645	567
1	645	567
0	4858	14
1	4858	14
0	200	1793
1	200	1793
0	200	1793
1	200	1793
0	5000	19
0	763	98
1	763	98
0	763	98
1	763	98
0	4858	14
1	4858	14
0	964	589
1	964	589
0	964	589
1	964	589
0	7	60
1	7	60

simplify97.0ms

Counts

101 → 101

Iterations

Useful iterations: 0 (60.0ms)

Iter	Nodes	Cost
0	5010	2226

prune89.0ms

Filtered

61 candidates to 101 candidates (-65.6%)

Pruning

16 alts after pruning (15 fresh and 1 done)

	Pruned	Kept	Total
New	97	4	101
Fresh	0	11	11
Picked	1	0	1
Done	0	1	1
Total	98	16	114

Merged error: 33.8b

Counts

114 → 16

localize16.0ms

Local error

Found 4 expressions with local error:

0.3b	(pow.f64 (sqrt.f64 (-.f64 (sqrt.f64 (+.f64 (.f64 re re) (.f64 im im))) re)) 3)
0.8b	(-.f64 (sqrt.f64 (+.f64 (.f64 re re) (.f64 im im))) re)
20.3b	(cbrt.f64 (.f64 (.f64 2 (sqrt.f64 2)) (pow.f64 (sqrt.f64 (-.f64 (sqrt.f64 (+.f64 (.f64 re re) (.f64 im im))) re)) 3)))
31.4b	(sqrt.f64 (+.f64 (.f64 re re) (.f64 im im)))

rewrite53.0ms

Algorithm

rewrite-expression-head

Rules

24×	`add-sqr-sqrt_binary64`
18×	`sqrt-prod_binary64`
16×	`*-un-lft-identity_binary64`
10×	`add-cube-cbrt_binary64`
9×	`unpow-prod-down_binary64` `cube-prod_binary64`
7×	`pow1_binary64`
6×	`add-log-exp_binary64` `difference-of-squares_binary64` `sqrt-div_binary64`
5×	`add-exp-log_binary64` `add-cbrt-cube_binary64`
4×	`cube-div_binary64` `insert-posit16`
3×	`pow-unpow_binary64` `flip3--_binary64` `pow-pow_binary64` `distribute-lft-out--_binary64` `flip--_binary64`
2×	`cbrt-div_binary64` `pow1/2_binary64` `associate-*r/_binary64` `sqrt-pow1_binary64`
1×	`pow-to-exp_binary64` `pow-prod-down_binary64` `flip3-+_binary64` `sub-neg_binary64` `rem-cbrt-cube_binary64` `diff-log_binary64` `sqrt-pow2_binary64` `pow1/3_binary64` `sqr-pow_binary64` `rem-sqrt-square_binary64` `pow3_binary64` `rem-cube-cbrt_binary64` `flip-+_binary64` `cbrt-prod_binary64` `pow-exp_binary64` `unpow3_binary64` `cube-mult_binary64`

Counts

4 → 85

Calls

4 calls:

13.0ms	(pow.f64 (sqrt.f64 (-.f64 (sqrt.f64 (+.f64 (.f64 re re) (.f64 im im))) re)) 3)
13.0ms	(-.f64 (sqrt.f64 (+.f64 (.f64 re re) (.f64 im im))) re)
18.0ms	(cbrt.f64 (.f64 (.f64 2 (sqrt.f64 2)) (pow.f64 (sqrt.f64 (-.f64 (sqrt.f64 (+.f64 (.f64 re re) (.f64 im im))) re)) 3)))
5.0ms	(sqrt.f64 (+.f64 (.f64 re re) (.f64 im im)))

series1.5s

Counts

4 → 12

Calls

4 calls:

435.0ms	(pow.f64 (sqrt.f64 (-.f64 (sqrt.f64 (+.f64 (.f64 re re) (.f64 im im))) re)) 3)
407.0ms	(-.f64 (sqrt.f64 (+.f64 (.f64 re re) (.f64 im im))) re)
264.0ms	(cbrt.f64 (.f64 (.f64 2 (sqrt.f64 2)) (pow.f64 (sqrt.f64 (-.f64 (sqrt.f64 (+.f64 (.f64 re re) (.f64 im im))) re)) 3)))
376.0ms	(sqrt.f64 (+.f64 (.f64 re re) (.f64 im im)))

Iterations

Useful iterations: 0 (163.0ms)

Iter	Nodes	Cost
0	645	567
1	645	567
0	645	567
1	645	567
0	4858	14
1	4858	14
0	206	1838
1	206	1838
0	206	1838
1	206	1838
0	4963	29
1	4963	29
0	763	98
1	763	98
0	763	98
1	763	98
0	4858	14
1	4858	14
0	992	508
1	992	508
0	992	508
1	992	508
0	7	51
1	7	51

simplify121.0ms

Counts

97 → 97

Iterations

Useful iterations: 0 (84.0ms)

Iter	Nodes	Cost
0	4794	2159
1	4794	2159

prune78.0ms

Filtered

61 candidates to 97 candidates (-59.0%)

Pruning

16 alts after pruning (15 fresh and 1 done)

	Pruned	Kept	Total
New	94	3	97
Fresh	2	12	14
Picked	1	0	1
Done	0	1	1
Total	97	16	113

Merged error: 33.8b

Counts

113 → 16

regimes321.0ms

Accuracy

86.9% (1.0b remaining)

Error of 32.3b against oracle of 31.3b and baseline of 38.9b

bsearch38.0ms

Steps

Iters	Range		Point
6	-1.473967036525412e-305	-2.0143593938637136e-306	-2.04639252831783e-306
7	-2.4980386653994362e+154	-1.2006993849600361e+153	-1.361077344108107e+154

simplify8.0ms

Iterations

Useful iterations: 0 (3.0ms)

Iter	Nodes	Cost
0	64	93
1	64	93

end0.0ms

sample1.0s

Algorithm

intervals

Results

280.0ms	6040×	body	80	valid
186.0ms	682×	body	2560	valid
104.0ms	475×	body	1280	valid
103.0ms	8000×	pre	80	true
88.0ms	258×	body	5120	valid
49.0ms	287×	body	640	valid
24.0ms	170×	body	320	valid
8.0ms	88×	body	160	valid

Details

analyze334.0ms

sample34.0ms

simplify32.0ms

prune2.0ms

localize11.0ms

rewrite40.0ms

series1.4s

simplify131.0ms

prune88.0ms

localize14.0ms

rewrite35.0ms

series1.6s

simplify106.0ms

prune97.0ms

localize14.0ms

rewrite42.0ms

series1.5s

simplify97.0ms

prune89.0ms

localize16.0ms

rewrite53.0ms

series1.5s

simplify121.0ms

prune78.0ms

regimes321.0ms

bsearch38.0ms

simplify8.0ms

end0.0ms

sample1.0s

Profiling