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

sample101.0ms

Algorithm

intervals

Results

34.0ms	42×	body	1280	valid
23.0ms	41×	body	640	valid
16.0ms	139×	body	80	valid
8.0ms	21×	body	320	valid
8.0ms	13×	body	160	valid

simplify66.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (63.0ms)

Iter	Nodes	Cost
0	5501	24

prune7.0ms

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: 16.4b

Counts

2 → 1

localize15.0ms

Local error

Found 4 expressions with local error:

0.1b	(.f64 (.f64 -2.0 J) (cos.f64 (/.f64 K 2.0)))
0.2b	(pow.f64 (/.f64 U (.f64 (.f64 2.0 J) (cos.f64 (/.f64 K 2.0)))) 2.0)
7.1b	(.f64 (.f64 (.f64 -2.0 J) (cos.f64 (/.f64 K 2.0))) (sqrt.f64 (+.f64 1.0 (pow.f64 (/.f64 U (.f64 (*.f64 2.0 J) (cos.f64 (/.f64 K 2.0)))) 2.0))))
8.3b	(sqrt.f64 (+.f64 1.0 (pow.f64 (/.f64 U (.f64 (.f64 2.0 J) (cos.f64 (/.f64 K 2.0)))) 2.0)))

rewrite43.0ms

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` `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` `pow-pow_binary64` `sqr-pow_binary64` `sqrt-pow1_binary64` `rem-sqrt-square_binary64` `div-inv_binary64`

Counts

4 → 85

Calls

4 calls:

5.0ms	(.f64 (.f64 -2.0 J) (cos.f64 (/.f64 K 2.0)))
8.0ms	(pow.f64 (/.f64 U (.f64 (.f64 2.0 J) (cos.f64 (/.f64 K 2.0)))) 2.0)
15.0ms	(.f64 (.f64 (.f64 -2.0 J) (cos.f64 (/.f64 K 2.0))) (sqrt.f64 (+.f64 1.0 (pow.f64 (/.f64 U (.f64 (*.f64 2.0 J) (cos.f64 (/.f64 K 2.0)))) 2.0))))
11.0ms	(sqrt.f64 (+.f64 1.0 (pow.f64 (/.f64 U (.f64 (.f64 2.0 J) (cos.f64 (/.f64 K 2.0)))) 2.0)))

series153.0ms

Counts

4 → 12

Calls

4 calls:

10.0ms	(.f64 (.f64 -2.0 J) (cos.f64 (/.f64 K 2.0)))
39.0ms	(pow.f64 (/.f64 U (.f64 (.f64 2.0 J) (cos.f64 (/.f64 K 2.0)))) 2.0)
58.0ms	(.f64 (.f64 (.f64 -2.0 J) (cos.f64 (/.f64 K 2.0))) (sqrt.f64 (+.f64 1.0 (pow.f64 (/.f64 U (.f64 (*.f64 2.0 J) (cos.f64 (/.f64 K 2.0)))) 2.0))))
46.0ms	(sqrt.f64 (+.f64 1.0 (pow.f64 (/.f64 U (.f64 (.f64 2.0 J) (cos.f64 (/.f64 K 2.0)))) 2.0)))

simplify101.0ms

Algorithm

egg-herbie

Counts

97 → 97

Iterations

Useful iterations: 0 (87.0ms)

Iter	Nodes	Cost
0	4939	1613
1	4939	1613

prune165.0ms

Filtered

67 candidates to 97 candidates (-44.8%)

Pruning

10 alts after pruning (9 fresh and 1 done)

	Pruned	Kept	Total
New	88	9	97
Fresh	0	0	0
Picked	0	1	1
Done	0	0	0
Total	88	10	98

Merged error: 6.8b

Counts

98 → 10

localize18.0ms

Local error

Found 4 expressions with local error:

7.2b	(sqrt.f64 (sqrt.f64 (+.f64 1.0 (pow.f64 (/.f64 U (.f64 (.f64 2.0 J) (cos.f64 (/.f64 K 2.0)))) 2.0))))
7.2b	(sqrt.f64 (sqrt.f64 (+.f64 1.0 (pow.f64 (/.f64 U (.f64 (.f64 2.0 J) (cos.f64 (/.f64 K 2.0)))) 2.0))))
8.3b	(sqrt.f64 (+.f64 1.0 (pow.f64 (/.f64 U (.f64 (.f64 2.0 J) (cos.f64 (/.f64 K 2.0)))) 2.0)))
8.3b	(sqrt.f64 (+.f64 1.0 (pow.f64 (/.f64 U (.f64 (.f64 2.0 J) (cos.f64 (/.f64 K 2.0)))) 2.0)))

rewrite38.0ms

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` `flip-+_binary64`

Counts

4 → 76

Calls

4 calls:

11.0ms	(sqrt.f64 (sqrt.f64 (+.f64 1.0 (pow.f64 (/.f64 U (.f64 (.f64 2.0 J) (cos.f64 (/.f64 K 2.0)))) 2.0))))
9.0ms	(sqrt.f64 (sqrt.f64 (+.f64 1.0 (pow.f64 (/.f64 U (.f64 (.f64 2.0 J) (cos.f64 (/.f64 K 2.0)))) 2.0))))
8.0ms	(sqrt.f64 (+.f64 1.0 (pow.f64 (/.f64 U (.f64 (.f64 2.0 J) (cos.f64 (/.f64 K 2.0)))) 2.0)))
8.0ms	(sqrt.f64 (+.f64 1.0 (pow.f64 (/.f64 U (.f64 (.f64 2.0 J) (cos.f64 (/.f64 K 2.0)))) 2.0)))

series249.0ms

Counts

4 → 12

Calls

4 calls:

80.0ms	(sqrt.f64 (sqrt.f64 (+.f64 1.0 (pow.f64 (/.f64 U (.f64 (.f64 2.0 J) (cos.f64 (/.f64 K 2.0)))) 2.0))))
77.0ms	(sqrt.f64 (sqrt.f64 (+.f64 1.0 (pow.f64 (/.f64 U (.f64 (.f64 2.0 J) (cos.f64 (/.f64 K 2.0)))) 2.0))))
47.0ms	(sqrt.f64 (+.f64 1.0 (pow.f64 (/.f64 U (.f64 (.f64 2.0 J) (cos.f64 (/.f64 K 2.0)))) 2.0)))
45.0ms	(sqrt.f64 (+.f64 1.0 (pow.f64 (/.f64 U (.f64 (.f64 2.0 J) (cos.f64 (/.f64 K 2.0)))) 2.0)))

simplify74.0ms

Algorithm

egg-herbie

Counts

88 → 88

Iterations

Useful iterations: 0 (62.0ms)

Iter	Nodes	Cost
0	4904	1580
1	4904	1580

prune177.0ms

Filtered

60 candidates to 88 candidates (-46.7%)

Pruning

10 alts after pruning (8 fresh and 2 done)

	Pruned	Kept	Total
New	88	0	88
Fresh	0	8	8
Picked	0	1	1
Done	0	1	1
Total	88	10	98

Merged error: 6.8b

Counts

98 → 10

localize21.0ms

Local error

Found 4 expressions with local error:

7.4b	(cbrt.f64 (sqrt.f64 (+.f64 1.0 (pow.f64 (/.f64 U (.f64 (.f64 2.0 J) (cos.f64 (/.f64 K 2.0)))) 2.0))))
8.3b	(sqrt.f64 (+.f64 1.0 (pow.f64 (/.f64 U (.f64 (.f64 2.0 J) (cos.f64 (/.f64 K 2.0)))) 2.0)))
8.3b	(sqrt.f64 (+.f64 1.0 (pow.f64 (/.f64 U (.f64 (.f64 2.0 J) (cos.f64 (/.f64 K 2.0)))) 2.0)))
8.3b	(sqrt.f64 (+.f64 1.0 (pow.f64 (/.f64 U (.f64 (.f64 2.0 J) (cos.f64 (/.f64 K 2.0)))) 2.0)))

rewrite35.0ms

Algorithm

rewrite-expression-head

Rules

17×	`*-un-lft-identity_binary64`
16×	`sqrt-prod_binary64`
12×	`add-sqr-sqrt_binary64`
9×	`add-cube-cbrt_binary64`
8×	`sqrt-div_binary64`
7×	`pow1_binary64` `cbrt-prod_binary64`
4×	`flip3-+_binary64` `add-log-exp_binary64` `distribute-lft-out_binary64` `add-exp-log_binary64` `add-cbrt-cube_binary64` `flip-+_binary64`
3×	`pow1/2_binary64` `sqrt-pow1_binary64` `rem-sqrt-square_binary64`
2×	`cbrt-div_binary64`
1×	`pow1/3_binary64`

Counts

4 → 65

Calls

4 calls:

9.0ms	(cbrt.f64 (sqrt.f64 (+.f64 1.0 (pow.f64 (/.f64 U (.f64 (.f64 2.0 J) (cos.f64 (/.f64 K 2.0)))) 2.0))))
8.0ms	(sqrt.f64 (+.f64 1.0 (pow.f64 (/.f64 U (.f64 (.f64 2.0 J) (cos.f64 (/.f64 K 2.0)))) 2.0)))
8.0ms	(sqrt.f64 (+.f64 1.0 (pow.f64 (/.f64 U (.f64 (.f64 2.0 J) (cos.f64 (/.f64 K 2.0)))) 2.0)))
8.0ms	(sqrt.f64 (+.f64 1.0 (pow.f64 (/.f64 U (.f64 (.f64 2.0 J) (cos.f64 (/.f64 K 2.0)))) 2.0)))

series214.0ms

Counts

4 → 12

Calls

4 calls:

77.0ms	(cbrt.f64 (sqrt.f64 (+.f64 1.0 (pow.f64 (/.f64 U (.f64 (.f64 2.0 J) (cos.f64 (/.f64 K 2.0)))) 2.0))))
46.0ms	(sqrt.f64 (+.f64 1.0 (pow.f64 (/.f64 U (.f64 (.f64 2.0 J) (cos.f64 (/.f64 K 2.0)))) 2.0)))
44.0ms	(sqrt.f64 (+.f64 1.0 (pow.f64 (/.f64 U (.f64 (.f64 2.0 J) (cos.f64 (/.f64 K 2.0)))) 2.0)))
46.0ms	(sqrt.f64 (+.f64 1.0 (pow.f64 (/.f64 U (.f64 (.f64 2.0 J) (cos.f64 (/.f64 K 2.0)))) 2.0)))

simplify69.0ms

Algorithm

egg-herbie

Counts

77 → 77

Iterations

Useful iterations: 0 (57.0ms)

Iter	Nodes	Cost
0	4852	1476
1	4852	1476

prune211.0ms

Filtered

57 candidates to 77 candidates (-35.1%)

Pruning

10 alts after pruning (7 fresh and 3 done)

	Pruned	Kept	Total
New	77	0	77
Fresh	0	7	7
Picked	0	1	1
Done	0	2	2
Total	77	10	87

Merged error: 6.8b

Counts

87 → 10

localize19.0ms

Local error

Found 4 expressions with local error:

0.3b	(cbrt.f64 (cos.f64 (/.f64 K 2.0)))
0.3b	(cbrt.f64 (cos.f64 (/.f64 K 2.0)))
7.1b	(.f64 (.f64 (.f64 (.f64 J -2.0) (.f64 (cbrt.f64 (cos.f64 (/.f64 K 2.0))) (cbrt.f64 (cos.f64 (/.f64 K 2.0))))) (cbrt.f64 (cos.f64 (/.f64 K 2.0)))) (sqrt.f64 (+.f64 1.0 (pow.f64 (/.f64 U (.f64 (*.f64 2.0 J) (cos.f64 (/.f64 K 2.0)))) 2.0))))
8.3b	(sqrt.f64 (+.f64 1.0 (pow.f64 (/.f64 U (.f64 (.f64 2.0 J) (cos.f64 (/.f64 K 2.0)))) 2.0)))

rewrite38.0ms

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` `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 → 74

Calls

4 calls:

1.0ms	(cbrt.f64 (cos.f64 (/.f64 K 2.0)))
1.0ms	(cbrt.f64 (cos.f64 (/.f64 K 2.0)))
25.0ms	(.f64 (.f64 (.f64 (.f64 J -2.0) (.f64 (cbrt.f64 (cos.f64 (/.f64 K 2.0))) (cbrt.f64 (cos.f64 (/.f64 K 2.0))))) (cbrt.f64 (cos.f64 (/.f64 K 2.0)))) (sqrt.f64 (+.f64 1.0 (pow.f64 (/.f64 U (.f64 (*.f64 2.0 J) (cos.f64 (/.f64 K 2.0)))) 2.0))))
8.0ms	(sqrt.f64 (+.f64 1.0 (pow.f64 (/.f64 U (.f64 (.f64 2.0 J) (cos.f64 (/.f64 K 2.0)))) 2.0)))

series140.0ms

Counts

4 → 12

Calls

4 calls:

18.0ms	(cbrt.f64 (cos.f64 (/.f64 K 2.0)))
18.0ms	(cbrt.f64 (cos.f64 (/.f64 K 2.0)))
56.0ms	(.f64 (.f64 (.f64 (.f64 J -2.0) (.f64 (cbrt.f64 (cos.f64 (/.f64 K 2.0))) (cbrt.f64 (cos.f64 (/.f64 K 2.0))))) (cbrt.f64 (cos.f64 (/.f64 K 2.0)))) (sqrt.f64 (+.f64 1.0 (pow.f64 (/.f64 U (.f64 (*.f64 2.0 J) (cos.f64 (/.f64 K 2.0)))) 2.0))))
47.0ms	(sqrt.f64 (+.f64 1.0 (pow.f64 (/.f64 U (.f64 (.f64 2.0 J) (cos.f64 (/.f64 K 2.0)))) 2.0)))

simplify49.0ms

Algorithm

egg-herbie

Counts

86 → 86

Iterations

Useful iterations: 0 (38.0ms)

Iter	Nodes	Cost
0	5548	1442

prune107.0ms

Filtered

51 candidates to 86 candidates (-68.6%)

Pruning

13 alts after pruning (10 fresh and 3 done)

	Pruned	Kept	Total
New	82	4	86
Fresh	0	6	6
Picked	1	0	1
Done	0	3	3
Total	83	13	96

Merged error: 6.8b

Counts

96 → 13

regimes583.0ms

Accuracy

95.5% (0.4b remaining)

Error of 9.2b against oracle of 8.8b and baseline of 18.1b

bsearch1.0ms

simplify3.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (2.0ms)

Iter	Nodes	Cost
0	78	86
1	78	86

end0.0ms

sample3.1s

Algorithm

intervals

Results

1.2s	1486×	body	1280	valid
728.0ms	1264×	body	640	valid
499.0ms	4328×	body	80	valid
259.0ms	613×	body	320	valid
84.0ms	309×	body	160	valid
0.0ms	2×	body	80	invalid

Details

analyze1.9s

sample101.0ms

simplify66.0ms

prune7.0ms

localize15.0ms

rewrite43.0ms

series153.0ms

simplify101.0ms

prune165.0ms

localize18.0ms

rewrite38.0ms

series249.0ms

simplify74.0ms

prune177.0ms

localize21.0ms

rewrite35.0ms

series214.0ms

simplify69.0ms

prune211.0ms

localize19.0ms

rewrite38.0ms

series140.0ms

simplify49.0ms

prune107.0ms

regimes583.0ms

bsearch1.0ms

simplify3.0ms

end0.0ms

sample3.1s

Profiling