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

sample102.0ms

Algorithm

intervals

Results

34.0ms	42×	body	1280	valid
31.0ms	56×	body	640	valid
15.0ms	131×	body	80	valid
8.0ms	21×	body	320	valid
2.0ms	6×	body	160	valid

simplify58.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (56.0ms)

Iter	Nodes	Cost
0	5501	24

prune12.0ms

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: 21.2b

Counts

2 → 1

localize15.0ms

Local error

Found 4 expressions with local error:

0.1b	(* (* -2.0 J) (cos (/ K 2.0)))
0.2b	(pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) 2.0)
7.2b	(* (* (* -2.0 J) (cos (/ K 2.0))) (sqrt (+ 1.0 (pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) 2.0))))
12.7b	(sqrt (+ 1.0 (pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) 2.0)))

rewrite34.0ms

Algorithm

rewrite-expression-head

Rules

28×	`add-exp-log`
20×	`pow1`
18×	`add-cbrt-cube`
15×	`*-un-lft-identity`
12×	`add-sqr-sqrt` `prod-exp`
11×	`add-cube-cbrt`
10×	`associate-r`
9×	`pow-prod-down` `cbrt-unprod`
8×	`sqrt-prod`
7×	`unpow-prod-down`
4×	`sqrt-div` `pow-exp` `add-log-exp`
3×	`pow-unpow` `times-frac` `div-exp`
2×	`flip3-+` `associate-r/` `associate-l` `-commutative` `flip-+` `distribute-lft-out`
1×	`pow-to-exp` `rem-sqrt-square` `pow-pow` `sqrt-pow1` `pow1/2` `div-inv` `sqr-pow`

Counts

4 → 85

Calls

4 calls:

5.0ms	(* (* -2.0 J) (cos (/ K 2.0)))
7.0ms	(pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) 2.0)
13.0ms	(* (* (* -2.0 J) (cos (/ K 2.0))) (sqrt (+ 1.0 (pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) 2.0))))
6.0ms	(sqrt (+ 1.0 (pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) 2.0)))

series115.0ms

Counts

4 → 12

Calls

4 calls:

8.0ms	(* (* -2.0 J) (cos (/ K 2.0)))
31.0ms	(pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) 2.0)
44.0ms	(* (* (* -2.0 J) (cos (/ K 2.0))) (sqrt (+ 1.0 (pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) 2.0))))
33.0ms	(sqrt (+ 1.0 (pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) 2.0)))

simplify62.0ms

Algorithm

egg-herbie

Counts

97 → 97

Iterations

Useful iterations: 0 (50.0ms)

Iter	Nodes	Cost
0	4964	1603
1	4964	1603

prune245.0ms

Filtered

69 candidates to 97 candidates (-40.6%)

Pruning

9 alts after pruning (8 fresh and 1 done)

	Pruned	Kept	Total
New	89	8	97
Fresh	0	0	0
Picked	0	1	1
Done	0	0	0
Total	89	9	98

Merged error: 13.7b

Counts

98 → 9

localize26.0ms

Local error

Found 4 expressions with local error:

1.7b	(sqrt (cbrt (+ 1.0 (pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) 2.0))))
1.9b	(* J (* -2.0 (* (cos (/ K 2.0)) (fabs (cbrt (+ 1.0 (pow (/ U (* 2.0 (* J (cos (/ K 2.0))))) 2.0)))))))
18.4b	(cbrt (+ 1.0 (pow (/ U (* 2.0 (* J (cos (/ K 2.0))))) 2.0)))
18.4b	(cbrt (+ 1.0 (pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) 2.0)))

rewrite30.0ms

Algorithm

rewrite-expression-head

Rules

15×	`*-un-lft-identity`
14×	`pow1`
13×	`add-exp-log` `cbrt-prod` `add-cbrt-cube`
11×	`add-sqr-sqrt`
9×	`add-cube-cbrt`
7×	`sqrt-prod`
6×	`cbrt-div` `pow-prod-down` `prod-exp` `cbrt-unprod`
4×	`add-log-exp`
3×	`flip3-+` `pow1/3` `associate-l` `flip-+` `distribute-lft-out`
2×	`rem-sqrt-square` `sqrt-pow1` `sqrt-div`
1×	`pow1/2` `associate-r` `*-commutative`

Counts

4 → 70

Calls

4 calls:

7.0ms	(sqrt (cbrt (+ 1.0 (pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) 2.0))))
8.0ms	(* J (* -2.0 (* (cos (/ K 2.0)) (fabs (cbrt (+ 1.0 (pow (/ U (* 2.0 (* J (cos (/ K 2.0))))) 2.0)))))))
7.0ms	(cbrt (+ 1.0 (pow (/ U (* 2.0 (* J (cos (/ K 2.0))))) 2.0)))
6.0ms	(cbrt (+ 1.0 (pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) 2.0)))

series212.0ms

Counts

4 → 12

Calls

4 calls:

60.0ms	(sqrt (cbrt (+ 1.0 (pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) 2.0))))
34.0ms	(* J (* -2.0 (* (cos (/ K 2.0)) (fabs (cbrt (+ 1.0 (pow (/ U (* 2.0 (* J (cos (/ K 2.0))))) 2.0)))))))
60.0ms	(cbrt (+ 1.0 (pow (/ U (* 2.0 (* J (cos (/ K 2.0))))) 2.0)))
58.0ms	(cbrt (+ 1.0 (pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) 2.0)))

simplify47.0ms

Algorithm

egg-herbie

Counts

82 → 82

Iterations

Useful iterations: 0 (36.0ms)

Iter	Nodes	Cost
0	5706	1772

prune350.0ms

Filtered

67 candidates to 82 candidates (-22.4%)

Pruning

10 alts after pruning (8 fresh and 2 done)

	Pruned	Kept	Total
New	79	3	82
Fresh	2	5	7
Picked	0	1	1
Done	0	1	1
Total	81	10	91

Merged error: 13.6b

Counts

91 → 10

localize27.0ms

Local error

Found 4 expressions with local error:

1.9b	(* J (* -2.0 (* (cos (/ K 2.0)) (fabs (cbrt (+ 1.0 (pow (/ U (* 2.0 (* J (cos (/ K 2.0))))) 2.0)))))))
7.4b	(cbrt (sqrt (+ 1.0 (pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) 2.0))))
12.7b	(sqrt (+ 1.0 (pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) 2.0)))
18.4b	(cbrt (+ 1.0 (pow (/ U (* 2.0 (* J (cos (/ K 2.0))))) 2.0)))

rewrite30.0ms

Algorithm

rewrite-expression-head

Rules

15×	`*-un-lft-identity`
14×	`pow1`
13×	`add-exp-log` `add-cbrt-cube`
11×	`cbrt-prod`
10×	`add-sqr-sqrt`
9×	`add-cube-cbrt`
8×	`sqrt-prod`
6×	`pow-prod-down` `prod-exp` `cbrt-unprod`
4×	`cbrt-div` `sqrt-div` `add-log-exp`
3×	`flip3-+` `associate-l` `flip-+` `distribute-lft-out`
2×	`pow1/3`
1×	`rem-sqrt-square` `sqrt-pow1` `pow1/2` `associate-r` `*-commutative`

Counts

4 → 68

Calls

4 calls:

8.0ms	(* J (* -2.0 (* (cos (/ K 2.0)) (fabs (cbrt (+ 1.0 (pow (/ U (* 2.0 (* J (cos (/ K 2.0))))) 2.0)))))))
7.0ms	(cbrt (sqrt (+ 1.0 (pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) 2.0))))
6.0ms	(sqrt (+ 1.0 (pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) 2.0)))
6.0ms	(cbrt (+ 1.0 (pow (/ U (* 2.0 (* J (cos (/ K 2.0))))) 2.0)))

series187.0ms

Counts

4 → 12

Calls

4 calls:

36.0ms	(* J (* -2.0 (* (cos (/ K 2.0)) (fabs (cbrt (+ 1.0 (pow (/ U (* 2.0 (* J (cos (/ K 2.0))))) 2.0)))))))
58.0ms	(cbrt (sqrt (+ 1.0 (pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) 2.0))))
35.0ms	(sqrt (+ 1.0 (pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) 2.0)))
59.0ms	(cbrt (+ 1.0 (pow (/ U (* 2.0 (* J (cos (/ K 2.0))))) 2.0)))

simplify58.0ms

Algorithm

egg-herbie

Counts

80 → 80

Iterations

Useful iterations: 0 (47.0ms)

Iter	Nodes	Cost
0	4973	1782
1	4973	1782

prune333.0ms

Filtered

62 candidates to 80 candidates (-29.0%)

Pruning

10 alts after pruning (7 fresh and 3 done)

	Pruned	Kept	Total
New	80	0	80
Fresh	0	7	7
Picked	0	1	1
Done	0	2	2
Total	80	10	90

Merged error: 13.6b

Counts

90 → 10

localize23.0ms

Local error

Found 4 expressions with local error:

0.3b	(cbrt (cos (/ K 2.0)))
0.3b	(cbrt (cos (/ K 2.0)))
7.2b	(* (* (* J (* -2.0 (* (cbrt (cos (/ K 2.0))) (cbrt (cos (/ K 2.0)))))) (cbrt (cos (/ K 2.0)))) (sqrt (+ 1.0 (pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) 2.0))))
12.7b	(sqrt (+ 1.0 (pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) 2.0)))

rewrite32.0ms

Algorithm

rewrite-expression-head

Rules

25×	`pow1`
24×	`add-exp-log`
18×	`add-cbrt-cube`
15×	`pow-prod-down` `prod-exp` `cbrt-unprod`
13×	`*-un-lft-identity`
10×	`add-sqr-sqrt`
9×	`add-cube-cbrt`
8×	`sqrt-prod`
7×	`associate-r`
6×	`cbrt-prod`
4×	`sqrt-div` `add-log-exp`
2×	`flip3-+` `pow1/3` `associate-*r/` `flip-+` `distribute-lft-out`
1×	`rem-sqrt-square` `sqrt-pow1` `pow1/2` `associate-l` `*-commutative`

Counts

4 → 71

Calls

4 calls:

1.0ms	(cbrt (cos (/ K 2.0)))
1.0ms	(cbrt (cos (/ K 2.0)))
20.0ms	(* (* (* J (* -2.0 (* (cbrt (cos (/ K 2.0))) (cbrt (cos (/ K 2.0)))))) (cbrt (cos (/ K 2.0)))) (sqrt (+ 1.0 (pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) 2.0))))
6.0ms	(sqrt (+ 1.0 (pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) 2.0)))

series113.0ms

Counts

4 → 12

Calls

4 calls:

17.0ms	(cbrt (cos (/ K 2.0)))
17.0ms	(cbrt (cos (/ K 2.0)))
45.0ms	(* (* (* J (* -2.0 (* (cbrt (cos (/ K 2.0))) (cbrt (cos (/ K 2.0)))))) (cbrt (cos (/ K 2.0)))) (sqrt (+ 1.0 (pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) 2.0))))
33.0ms	(sqrt (+ 1.0 (pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) 2.0)))

simplify66.0ms

Algorithm

egg-herbie

Counts

83 → 83

Iterations

Useful iterations: 0 (56.0ms)

Iter	Nodes	Cost
0	4980	1358
1	4980	1358

prune214.0ms

Filtered

55 candidates to 83 candidates (-50.9%)

Pruning

11 alts after pruning (8 fresh and 3 done)

	Pruned	Kept	Total
New	81	2	83
Fresh	0	6	6
Picked	1	0	1
Done	0	3	3
Total	82	11	93

Merged error: 13.6b

Counts

93 → 11

regimes787.0ms

Accuracy

90% (0.5b remaining)

Error of 13.6b against oracle of 13.1b and baseline of 18.4b

bsearch1.0ms

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	45	99
1	45	99

end0.0ms

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

sample3.0s

Algorithm

intervals

Results

1.2s	1477×	body	1280	valid
708.0ms	1243×	body	640	valid
521.0ms	4366×	body	80	valid
242.0ms	610×	body	320	valid
78.0ms	304×	body	160	valid
2.0ms	2×	body	640	invalid
1.0ms	1×	body	1280	invalid
0.0ms	1×	body	160	invalid
0.0ms	1×	body	80	invalid

Details

analyze1.8s

sample102.0ms

simplify58.0ms

prune12.0ms

localize15.0ms

rewrite34.0ms

series115.0ms

simplify62.0ms

prune245.0ms

localize26.0ms

rewrite30.0ms

series212.0ms

simplify47.0ms

prune350.0ms

localize27.0ms

rewrite30.0ms

series187.0ms

simplify58.0ms

prune333.0ms

localize23.0ms

rewrite32.0ms

series113.0ms

simplify66.0ms

prune214.0ms

regimes787.0ms

bsearch1.0ms

simplify2.0ms

end0.0ms

analyze1.8s

sample3.0s

Profiling