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
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

42.0ms	52×	body	1280	valid
21.0ms	148×	body	80	valid
19.0ms	34×	body	640	valid
5.0ms	14×	body	320	valid
2.0ms	8×	body	160	valid

simplify67.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (64.0ms)

Iter	Nodes	Cost
0	4870	24
1	4870	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: 19.5b

Counts

2 → 1

localize15.0ms

Local error

Found 4 expressions with local error:

0.2b	(.f64 (.f64 -2 J) (cos.f64 (/.f64 K 2)))
0.2b	(.f64 (.f64 2 J) (cos.f64 (/.f64 K 2)))
8.7b	(sqrt.f64 (+.f64 1 (pow.f64 (/.f64 U (.f64 (.f64 2 J) (cos.f64 (/.f64 K 2)))) 2)))
9.5b	(.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))))

rewrite41.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 79

Calls

4 calls:

5.0ms	(.f64 (.f64 -2 J) (cos.f64 (/.f64 K 2)))
6.0ms	(.f64 (.f64 2 J) (cos.f64 (/.f64 K 2)))
8.0ms	(sqrt.f64 (+.f64 1 (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))))

series98.0ms

Counts

4 → 12

Calls

4 calls:

8.0ms	(.f64 (.f64 -2 J) (cos.f64 (/.f64 K 2)))
8.0ms	(.f64 (.f64 2 J) (cos.f64 (/.f64 K 2)))
38.0ms	(sqrt.f64 (+.f64 1 (pow.f64 (/.f64 U (.f64 (.f64 2 J) (cos.f64 (/.f64 K 2)))) 2)))
43.0ms	(.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))))

simplify52.0ms

Algorithm

egg-herbie

Counts

91 → 91

Iterations

Useful iterations: 0 (41.0ms)

Iter	Nodes	Cost
0	5041	1334

prune149.0ms

Filtered

60 candidates to 91 candidates (-51.7%)

Pruning

9 alts after pruning (9 fresh and 0 done)

	Pruned	Kept	Total
New	82	9	91
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	83	9	92

Merged error: 14.7b

Counts

92 → 9

localize25.0ms

Local error

Found 4 expressions with local error:

8.7b	(sqrt.f64 (+.f64 1 (pow.f64 (/.f64 U (.f64 (.f64 2 J) (cos.f64 (/.f64 K 2)))) 2)))
8.7b	(sqrt.f64 (+.f64 1 (pow.f64 (/.f64 U (*.f64 (cos.f64 (/.f64 K 2)) (+.f64 J J))) 2)))
9.5b	(sqrt.f64 (sqrt.f64 (+.f64 1 (pow.f64 (/.f64 U (*.f64 (cos.f64 (/.f64 K 2)) (+.f64 J J))) 2))))
9.5b	(sqrt.f64 (sqrt.f64 (+.f64 1 (pow.f64 (/.f64 U (.f64 (.f64 2 J) (cos.f64 (/.f64 K 2)))) 2))))

rewrite39.0ms

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:

10.0ms	(sqrt.f64 (+.f64 1 (pow.f64 (/.f64 U (.f64 (.f64 2 J) (cos.f64 (/.f64 K 2)))) 2)))
8.0ms	(sqrt.f64 (+.f64 1 (pow.f64 (/.f64 U (*.f64 (cos.f64 (/.f64 K 2)) (+.f64 J J))) 2)))
9.0ms	(sqrt.f64 (sqrt.f64 (+.f64 1 (pow.f64 (/.f64 U (*.f64 (cos.f64 (/.f64 K 2)) (+.f64 J J))) 2))))
9.0ms	(sqrt.f64 (sqrt.f64 (+.f64 1 (pow.f64 (/.f64 U (.f64 (.f64 2 J) (cos.f64 (/.f64 K 2)))) 2))))

series206.0ms

Counts

4 → 12

Calls

4 calls:

37.0ms	(sqrt.f64 (+.f64 1 (pow.f64 (/.f64 U (.f64 (.f64 2 J) (cos.f64 (/.f64 K 2)))) 2)))
33.0ms	(sqrt.f64 (+.f64 1 (pow.f64 (/.f64 U (*.f64 (cos.f64 (/.f64 K 2)) (+.f64 J J))) 2)))
71.0ms	(sqrt.f64 (sqrt.f64 (+.f64 1 (pow.f64 (/.f64 U (*.f64 (cos.f64 (/.f64 K 2)) (+.f64 J J))) 2))))
65.0ms	(sqrt.f64 (sqrt.f64 (+.f64 1 (pow.f64 (/.f64 U (.f64 (.f64 2 J) (cos.f64 (/.f64 K 2)))) 2))))

simplify40.0ms

Algorithm

egg-herbie

Counts

88 → 88

Iterations

Useful iterations: 0 (25.0ms)

Iter	Nodes	Cost
0	4984	1534
1	4984	1534

prune189.0ms

Filtered

66 candidates to 88 candidates (-33.3%)

Pruning

9 alts after pruning (8 fresh and 1 done)

	Pruned	Kept	Total
New	87	1	88
Fresh	1	7	8
Picked	0	1	1
Done	0	0	0
Total	88	9	97

Merged error: 14.7b

Counts

97 → 9

localize33.0ms

Local error

Found 4 expressions with local error:

9.5b	(sqrt.f64 (sqrt.f64 (+.f64 1 (pow.f64 (/.f64 U (*.f64 (cos.f64 (/.f64 K 2)) (+.f64 J J))) 2))))
9.5b	(sqrt.f64 (sqrt.f64 (+.f64 1 (pow.f64 (/.f64 U (*.f64 (+.f64 J J) (cos.f64 (/.f64 K 2)))) 2))))
9.5b	(sqrt.f64 (sqrt.f64 (+.f64 1 (pow.f64 (/.f64 U (*.f64 (+.f64 J J) (cos.f64 (/.f64 K 2)))) 2))))
9.5b	(sqrt.f64 (sqrt.f64 (+.f64 1 (pow.f64 (/.f64 U (*.f64 (+.f64 J J) (cos.f64 (/.f64 K 2)))) 2))))

rewrite40.0ms

Algorithm

rewrite-expression-head

Rules

48×	`sqrt-prod_binary64`
20×	`*-un-lft-identity_binary64` `add-sqr-sqrt_binary64`
16×	`sqrt-pow1_binary64` `sqrt-div_binary64`
12×	`pow1_binary64` `add-cube-cbrt_binary64`
8×	`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 → 88

Calls

4 calls:

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

series271.0ms

Counts

4 → 12

Calls

4 calls:

72.0ms	(sqrt.f64 (sqrt.f64 (+.f64 1 (pow.f64 (/.f64 U (*.f64 (cos.f64 (/.f64 K 2)) (+.f64 J J))) 2))))
65.0ms	(sqrt.f64 (sqrt.f64 (+.f64 1 (pow.f64 (/.f64 U (*.f64 (+.f64 J J) (cos.f64 (/.f64 K 2)))) 2))))
67.0ms	(sqrt.f64 (sqrt.f64 (+.f64 1 (pow.f64 (/.f64 U (*.f64 (+.f64 J J) (cos.f64 (/.f64 K 2)))) 2))))
67.0ms	(sqrt.f64 (sqrt.f64 (+.f64 1 (pow.f64 (/.f64 U (*.f64 (+.f64 J J) (cos.f64 (/.f64 K 2)))) 2))))

simplify60.0ms

Algorithm

egg-herbie

Counts

100 → 100

Iterations

Useful iterations: 0 (47.0ms)

Iter	Nodes	Cost
0	4902	1760
1	4902	1760

prune278.0ms

Filtered

65 candidates to 100 candidates (-53.8%)

Pruning

9 alts after pruning (7 fresh and 2 done)

	Pruned	Kept	Total
New	100	0	100
Fresh	0	7	7
Picked	0	1	1
Done	0	1	1
Total	100	9	109

Merged error: 14.7b

Counts

109 → 9

localize27.0ms

Local error

Found 4 expressions with local error:

8.7b	(sqrt.f64 (+.f64 1 (pow.f64 (/.f64 U (*.f64 (cos.f64 (/.f64 K 2)) (+.f64 J J))) 2)))
9.8b	(cbrt.f64 (sqrt.f64 (+.f64 1 (pow.f64 (/.f64 U (*.f64 (cos.f64 (/.f64 K 2)) (+.f64 J J))) 2))))
9.8b	(cbrt.f64 (sqrt.f64 (+.f64 1 (pow.f64 (/.f64 U (*.f64 (cos.f64 (/.f64 K 2)) (+.f64 J J))) 2))))
9.8b	(cbrt.f64 (sqrt.f64 (+.f64 1 (pow.f64 (/.f64 U (.f64 (.f64 2 J) (cos.f64 (/.f64 K 2)))) 2))))

rewrite40.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 67

Calls

4 calls:

9.0ms	(sqrt.f64 (+.f64 1 (pow.f64 (/.f64 U (*.f64 (cos.f64 (/.f64 K 2)) (+.f64 J J))) 2)))
9.0ms	(cbrt.f64 (sqrt.f64 (+.f64 1 (pow.f64 (/.f64 U (*.f64 (cos.f64 (/.f64 K 2)) (+.f64 J J))) 2))))
9.0ms	(cbrt.f64 (sqrt.f64 (+.f64 1 (pow.f64 (/.f64 U (*.f64 (cos.f64 (/.f64 K 2)) (+.f64 J J))) 2))))
11.0ms	(cbrt.f64 (sqrt.f64 (+.f64 1 (pow.f64 (/.f64 U (.f64 (.f64 2 J) (cos.f64 (/.f64 K 2)))) 2))))

series244.0ms

Counts

4 → 12

Calls

4 calls:

33.0ms	(sqrt.f64 (+.f64 1 (pow.f64 (/.f64 U (*.f64 (cos.f64 (/.f64 K 2)) (+.f64 J J))) 2)))
72.0ms	(cbrt.f64 (sqrt.f64 (+.f64 1 (pow.f64 (/.f64 U (*.f64 (cos.f64 (/.f64 K 2)) (+.f64 J J))) 2))))
70.0ms	(cbrt.f64 (sqrt.f64 (+.f64 1 (pow.f64 (/.f64 U (*.f64 (cos.f64 (/.f64 K 2)) (+.f64 J J))) 2))))
69.0ms	(cbrt.f64 (sqrt.f64 (+.f64 1 (pow.f64 (/.f64 U (.f64 (.f64 2 J) (cos.f64 (/.f64 K 2)))) 2))))

simplify31.0ms

Algorithm

egg-herbie

Counts

79 → 79

Iterations

Useful iterations: 0 (19.0ms)

Iter	Nodes	Cost
0	4964	1701
1	4964	1701

prune205.0ms

Filtered

66 candidates to 79 candidates (-19.7%)

Pruning

9 alts after pruning (7 fresh and 2 done)

	Pruned	Kept	Total
New	78	1	79
Fresh	0	6	6
Picked	1	0	1
Done	0	2	2
Total	79	9	88

Merged error: 14.7b

Counts

88 → 9

regimes346.0ms

Accuracy

0% (5.6b remaining)

Error of 18.5b against oracle of 12.9b and baseline of 18.5b

bsearch0.0ms

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	36	42
1	36	42

end0.0ms

sample3.3s

Algorithm

intervals

Results

1.3s	1491×	body	1280	valid
721.0ms	4317×	body	80	valid
716.0ms	1252×	body	640	valid
249.0ms	616×	body	320	valid
86.0ms	324×	body	160	valid
0.0ms	4×	body	80	invalid

Details

analyze1.8s

sample101.0ms

simplify67.0ms

prune7.0ms

localize15.0ms

rewrite41.0ms

series98.0ms

simplify52.0ms

prune149.0ms

localize25.0ms

rewrite39.0ms

series206.0ms

simplify40.0ms

prune189.0ms

localize33.0ms

rewrite40.0ms

series271.0ms

simplify60.0ms

prune278.0ms

localize27.0ms

rewrite40.0ms

series244.0ms

simplify31.0ms

prune205.0ms

regimes346.0ms

bsearch0.0ms

simplify2.0ms

end0.0ms

sample3.3s

Profiling