Details

analyze509.0ms (8.7%)

Algorithm

1×

Search

True	Other	False	Iter
0%	99.8%	0.2%	0
0%	99.8%	0.2%	1
49.9%	49.9%	0.2%	2
49.9%	49.9%	0.2%	3
49.9%	49.9%	0.2%	4
49.9%	49.9%	0.2%	5
49.9%	49.9%	0.2%	6
49.9%	49.9%	0.2%	7
53%	46.8%	0.2%	8
57.7%	42.1%	0.2%	9
61.6%	38.2%	0.2%	10
63.5%	30%	6.4%	11
63.5%	30%	6.4%	12
67.6%	25.9%	6.4%	13
68.9%	24.7%	6.4%	14

sample108.0ms (1.8%)

Algorithm

1×

intervals

Results

23.0ms	39×	body	1280	valid
14.0ms	45×	body	640	valid
13.0ms	141×	body	80	valid
13.0ms	34×	body	1280	invalid
11.0ms	39×	body	640	invalid
6.0ms	97×	body	80	invalid
4.0ms	19×	body	320	valid
2.0ms	10×	body	320	invalid
2.0ms	12×	body	160	valid
2.0ms	11×	body	160	invalid

simplify67.0ms (1.1%)

Algorithm

1×	egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (65.0ms)

Iter	Nodes	Cost
0	4815	15
1	4815	15

prune9.0ms (0.2%)

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: 15.7b

Counts

2 → 1

localize14.0ms (0.2%)

Local error

Found 2 expressions with local error:

0.0b	(* (* J (- (exp l) (exp (neg l)))) (cos (/ K 2.0)))
4.9b	(- (exp l) (exp (neg l)))

rewrite15.0ms (0.3%)

Algorithm

1×	rewrite-expression-head

Rules

7×	`pow1` `add-exp-log` `add-cbrt-cube`
5×	`add-sqr-sqrt` `*-un-lft-identity`
4×	`add-log-exp`
3×	`add-cube-cbrt` `associate-r` `pow-prod-down` `prod-exp` `cbrt-unprod`
2×	`flip3--` `associate-r/` `associate-l/` `flip--`
1×	`sub-neg` `sinh-undef` `diff-log` `associate-l` `*-commutative` `distribute-lft-out--` `difference-of-squares`

Counts

2 → 34

Calls

2 calls:

9.0ms	(* (* J (- (exp l) (exp (neg l)))) (cos (/ K 2.0)))
5.0ms	(- (exp l) (exp (neg l)))

series27.0ms (0.5%)

Counts

2 → 6

Calls

2 calls:

22.0ms	(* (* J (- (exp l) (exp (neg l)))) (cos (/ K 2.0)))
5.0ms	(- (exp l) (exp (neg l)))

simplify68.0ms (1.2%)

Algorithm

1×	egg-herbie

Counts

40 → 40

Iterations

Useful iterations: 0 (63.0ms)

Iter	Nodes	Cost
0	4905	467
1	4905	467

prune76.0ms (1.3%)

Pruning

1 alts after pruning (1 fresh and 0 done)

	Pruned	Kept	Total
New	39	1	40
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	40	1	41

Merged error: 0.1b

Counts

41 → 1

localize12.0ms (0.2%)

Local error

Found 2 expressions with local error:

0.0b	(sinh l)
0.1b	(* (* J (* 2 (sinh l))) (cos (/ K 2.0)))

rewrite9.0ms (0.2%)

Algorithm

1×	rewrite-expression-head

Rules

11×	`pow1` `add-exp-log` `add-cbrt-cube`
6×	`pow-prod-down` `prod-exp` `cbrt-unprod`
3×	`add-sqr-sqrt` `add-cube-cbrt` `-un-lft-identity` `associate-r*`
2×	`sinh-def` `associate-*r/` `add-log-exp`
1×	`associate-l` `associate-l/` `-commutative`

Counts

2 → 30

Calls

2 calls:

7.0ms	(* (* J (* 2 (sinh l))) (cos (/ K 2.0)))
1.0ms	(sinh l)

series33.0ms (0.6%)

Counts

2 → 6

Calls

2 calls:

26.0ms	(* (* J (* 2 (sinh l))) (cos (/ K 2.0)))
8.0ms	(sinh l)

simplify51.0ms (0.9%)

Algorithm

1×	egg-herbie

Counts

36 → 36

Iterations

Useful iterations: 0 (47.0ms)

Iter	Nodes	Cost
0	4952	344
1	4952	344

prune88.0ms (1.5%)

Pruning

5 alts after pruning (4 fresh and 1 done)

	Pruned	Kept	Total
New	32	4	36
Fresh	0	0	0
Picked	0	1	1
Done	0	0	0
Total	32	5	37

Merged error: 0.0b

Counts

37 → 5

localize12.0ms (0.2%)

Local error

Found 3 expressions with local error:

0.0b	(sinh l)
0.1b	(* J (* (* 2 (sinh l)) (cos (/ K 2.0))))
0.1b	(* (* 2 (sinh l)) (cos (/ K 2.0)))

rewrite15.0ms (0.3%)

Algorithm

1×	rewrite-expression-head

Rules

17×	`pow1` `add-exp-log` `add-cbrt-cube`
9×	`pow-prod-down` `prod-exp` `cbrt-unprod`
5×	`add-sqr-sqrt` `add-cube-cbrt` `*-un-lft-identity`
4×	`associate-r` `associate-l`
3×	`sinh-def` `associate-*r/` `add-log-exp`
2×	`associate-l/` `-commutative`

Counts

3 → 49

Calls

3 calls:

7.0ms	(* J (* (* 2 (sinh l)) (cos (/ K 2.0))))
5.0ms	(* (* 2 (sinh l)) (cos (/ K 2.0)))
1.0ms	(sinh l)

series50.0ms (0.9%)

Counts

3 → 9

Calls

3 calls:

27.0ms	(* J (* (* 2 (sinh l)) (cos (/ K 2.0))))
16.0ms	(* (* 2 (sinh l)) (cos (/ K 2.0)))
7.0ms	(sinh l)

simplify37.0ms (0.6%)

Algorithm

1×	egg-herbie

Counts

58 → 58

Iterations

Useful iterations: 0 (32.0ms)

Iter	Nodes	Cost
0	5112	561

prune119.0ms (2%)

Pruning

5 alts after pruning (4 fresh and 1 done)

	Pruned	Kept	Total
New	57	1	58
Fresh	0	3	3
Picked	0	1	1
Done	1	0	1
Total	58	5	63

Merged error: 0.0b

Counts

63 → 5

localize16.0ms (0.3%)

Local error

Found 4 expressions with local error:

0.5b	(* (cbrt (* (* J (* 2 (sinh l))) (cos (/ K 2.0)))) (cbrt (* (* J (* 2 (sinh l))) (cos (/ K 2.0)))))
14.8b	(cbrt (* (* J (* 2 (sinh l))) (cos (/ K 2.0))))
14.8b	(cbrt (* (* J (* 2 (sinh l))) (cos (/ K 2.0))))
14.8b	(cbrt (* (* J (* 2 (sinh l))) (cos (/ K 2.0))))

rewrite25.0ms (0.4%)

Algorithm

1×	rewrite-expression-head

Rules

15×	`associate-*r/`
11×	`pow1`
10×	`add-sqr-sqrt`
9×	`pow1/3`
8×	`add-cube-cbrt` `-un-lft-identity` `associate-l/`
7×	`cbrt-prod` `sinh-def` `cbrt-div`
6×	`add-exp-log`
4×	`swap-sqr` `associate-r` `associate-l` `add-cbrt-cube` `add-log-exp`
2×	`pow-prod-down` `pow-sqr` `pow-prod-up`
1×	`pow2` `frac-times` `pow-plus` `prod-exp` `*-commutative` `cbrt-unprod` `unswap-sqr`

Counts

4 → 64

Calls

4 calls:

8.0ms	(* (cbrt (* (* J (* 2 (sinh l))) (cos (/ K 2.0)))) (cbrt (* (* J (* 2 (sinh l))) (cos (/ K 2.0)))))
5.0ms	(cbrt (* (* J (* 2 (sinh l))) (cos (/ K 2.0))))
5.0ms	(cbrt (* (* J (* 2 (sinh l))) (cos (/ K 2.0))))
5.0ms	(cbrt (* (* J (* 2 (sinh l))) (cos (/ K 2.0))))

series261.0ms (4.4%)

Counts

4 → 12

Calls

4 calls:

82.0ms	(* (cbrt (* (* J (* 2 (sinh l))) (cos (/ K 2.0)))) (cbrt (* (* J (* 2 (sinh l))) (cos (/ K 2.0)))))
60.0ms	(cbrt (* (* J (* 2 (sinh l))) (cos (/ K 2.0))))
60.0ms	(cbrt (* (* J (* 2 (sinh l))) (cos (/ K 2.0))))
59.0ms	(cbrt (* (* J (* 2 (sinh l))) (cos (/ K 2.0))))

simplify40.0ms (0.7%)

Algorithm

1×	egg-herbie

Counts

76 → 76

Iterations

Useful iterations: 0 (30.0ms)

Iter	Nodes	Cost
0	5155	1198

prune264.0ms (4.5%)

Pruning

6 alts after pruning (4 fresh and 2 done)

	Pruned	Kept	Total
New	75	1	76
Fresh	0	3	3
Picked	0	1	1
Done	0	1	1
Total	75	6	81

Merged error: 0b

Counts

81 → 6

regimes434.0ms (7.4%)

Accuracy

Total 0.0b remaining (33.6%)

Threshold costs 0.0b (33.6%)

bsearch0.0ms (0%)

simplify1.0ms (0%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	17	13
1	17	13

end0.0ms (0%)

sample3.5s (59.8%)

Algorithm

1×

intervals

Results

677.0ms	1166×	body	1280	valid
603.0ms	1530×	body	1280	invalid
465.0ms	1389×	body	640	valid
336.0ms	1233×	body	640	invalid
297.0ms	4145×	body	80	valid
225.0ms	3355×	body	80	invalid
190.0ms	858×	body	320	valid
128.0ms	619×	body	320	invalid
63.0ms	442×	body	160	valid
47.0ms	328×	body	160	invalid

Details

analyze509.0ms (8.7%)

sample108.0ms (1.8%)

simplify67.0ms (1.1%)

prune9.0ms (0.2%)

localize14.0ms (0.2%)

rewrite15.0ms (0.3%)

series27.0ms (0.5%)

simplify68.0ms (1.2%)

prune76.0ms (1.3%)

localize12.0ms (0.2%)

rewrite9.0ms (0.2%)

series33.0ms (0.6%)

simplify51.0ms (0.9%)

prune88.0ms (1.5%)

localize12.0ms (0.2%)

rewrite15.0ms (0.3%)

series50.0ms (0.9%)

simplify37.0ms (0.6%)

prune119.0ms (2%)

localize16.0ms (0.3%)

rewrite25.0ms (0.4%)

series261.0ms (4.4%)

simplify40.0ms (0.7%)

prune264.0ms (4.5%)

regimes434.0ms (7.4%)

bsearch0.0ms (0%)

simplify1.0ms (0%)

end0.0ms (0%)

sample3.5s (59.8%)

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