Details

analyze519.0ms (6.6%)

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

sample117.0ms (1.5%)

Algorithm

1×

intervals

Results

23.0ms	40×	body	1280	valid
18.0ms	44×	body	1280	invalid
15.0ms	44×	body	640	valid
11.0ms	117×	body	80	invalid
9.0ms	132×	body	80	valid
9.0ms	30×	body	640	invalid
5.0ms	21×	body	320	valid
3.0ms	14×	body	320	invalid
3.0ms	19×	body	160	valid
2.0ms	12×	body	160	invalid

simplify54.0ms (0.7%)

Algorithm

1×	egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (53.0ms)

Iter	Nodes	Cost
0	4815	15
1	4815	15

prune14.0ms (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: 20.0b

Counts

2 → 2

localize14.0ms (0.2%)

Local error

Found 3 expressions with local error:

0.0b	(* (- (exp l) (exp (neg l))) (cos (/ K 2.0)))
0.3b	(* J (* (- (exp l) (exp (neg l))) (cos (/ K 2.0))))
7.8b	(- (exp l) (exp (neg l)))

rewrite23.0ms (0.3%)

Algorithm

1×	rewrite-expression-head

Rules

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

Counts

3 → 57

Calls

3 calls:

9.0ms	(* J (* (- (exp l) (exp (neg l))) (cos (/ K 2.0))))
8.0ms	(* (- (exp l) (exp (neg l))) (cos (/ K 2.0)))
5.0ms	(- (exp l) (exp (neg l)))

series41.0ms (0.5%)

Counts

3 → 9

Calls

3 calls:

23.0ms	(* J (* (- (exp l) (exp (neg l))) (cos (/ K 2.0))))
12.0ms	(* (- (exp l) (exp (neg l))) (cos (/ K 2.0)))
5.0ms	(- (exp l) (exp (neg l)))

simplify41.0ms (0.5%)

Algorithm

1×	egg-herbie

Counts

66 → 66

Iterations

Useful iterations: 0 (35.0ms)

Iter	Nodes	Cost
0	5038	786

prune118.0ms (1.5%)

Pruning

1 alts after pruning (1 fresh and 0 done)

	Pruned	Kept	Total
New	65	1	66
Fresh	1	0	1
Picked	1	0	1
Done	0	0	0
Total	67	1	68

Merged error: 0.1b

Counts

68 → 1

localize19.0ms (0.2%)

Local error

Found 4 expressions with local error:

0.1b	(* (+ l (+ l (+ (* 1/3 (pow l 3)) (* 1/60 (pow l 5))))) (cos (/ K 2.0)))
0.1b	(* 1/60 (pow l 5))
0.1b	(* J (* (+ l (+ l (+ (* 1/3 (pow l 3)) (* 1/60 (pow l 5))))) (cos (/ K 2.0))))
0.1b	(* 1/3 (pow l 3))

rewrite38.0ms (0.5%)

Algorithm

1×	rewrite-expression-head

Rules

28×	`add-sqr-sqrt`
23×	`associate-r`
21×	`add-exp-log`
19×	`*-un-lft-identity`
15×	`add-cbrt-cube`
14×	`add-cube-cbrt` `associate-l`
11×	`pow1`
10×	`prod-exp`
8×	`unpow-prod-down` `unswap-sqr`
6×	`cbrt-unprod`
4×	`cube-prod` `pow-prod-down` `associate-l/` `-commutative` `add-log-exp` `sqr-pow`
3×	`distribute-lft-out`
2×	`pow-to-exp` `flip3-+` `associate-*r/` `pow-exp` `flip-+`
1×	`cube-mult` `unpow3`

Counts

4 → 98

Calls

4 calls:

11.0ms	(* J (* (+ l (+ l (+ (* 1/3 (pow l 3)) (* 1/60 (pow l 5))))) (cos (/ K 2.0))))
11.0ms	(* (+ l (+ l (+ (* 1/3 (pow l 3)) (* 1/60 (pow l 5))))) (cos (/ K 2.0)))
6.0ms	(* 1/3 (pow l 3))
5.0ms	(* 1/60 (pow l 5))

series59.0ms (0.7%)

Counts

4 → 12

Calls

4 calls:

37.0ms	(* J (* (+ l (+ l (+ (* 1/3 (pow l 3)) (* 1/60 (pow l 5))))) (cos (/ K 2.0))))
14.0ms	(* (+ l (+ l (+ (* 1/3 (pow l 3)) (* 1/60 (pow l 5))))) (cos (/ K 2.0)))
4.0ms	(* 1/60 (pow l 5))
4.0ms	(* 1/3 (pow l 3))

simplify49.0ms (0.6%)

Algorithm

1×	egg-herbie

Counts

110 → 110

Iterations

Useful iterations: 0 (38.0ms)

Iter	Nodes	Cost
0	4883	1450
1	4883	1450

prune321.0ms (4.1%)

Pruning

5 alts after pruning (4 fresh and 1 done)

	Pruned	Kept	Total
New	106	4	110
Fresh	0	0	0
Picked	0	1	1
Done	0	0	0
Total	106	5	111

Merged error: 0.0b

Counts

111 → 5

localize19.0ms (0.2%)

Local error

Found 4 expressions with local error:

0.0b	(+ (* (* J (+ l (+ l (+ (* 1/3 (pow l 3)) (* 1/60 (pow l 5)))))) (cos (/ K 2.0))) U)
0.1b	(* 1/60 (pow l 5))
0.1b	(* (* J (+ l (+ l (+ (* 1/3 (pow l 3)) (* 1/60 (pow l 5)))))) (cos (/ K 2.0)))
0.1b	(* 1/3 (pow l 3))

rewrite38.0ms (0.5%)

Algorithm

1×	rewrite-expression-head

Rules

24×	`add-sqr-sqrt`
22×	`associate-r`
19×	`add-exp-log`
13×	`add-cbrt-cube`
12×	`add-cube-cbrt` `*-un-lft-identity`
9×	`pow1` `prod-exp`
8×	`unpow-prod-down`
7×	`associate-l` `unswap-sqr`
6×	`add-log-exp`
5×	`cbrt-unprod`
4×	`cube-prod` `sqr-pow`
3×	`pow-prod-down` `*-commutative`
2×	`pow-to-exp` `flip3-+` `associate-r/` `associate-l/` `pow-exp` `flip-+`
1×	`+-commutative` `cube-mult` `unpow3` `sum-log`

Counts

4 → 87

Calls

4 calls:

12.0ms	(+ (* (* J (+ l (+ l (+ (* 1/3 (pow l 3)) (* 1/60 (pow l 5)))))) (cos (/ K 2.0))) U)
12.0ms	(* (* J (+ l (+ l (+ (* 1/3 (pow l 3)) (* 1/60 (pow l 5)))))) (cos (/ K 2.0)))
6.0ms	(* 1/3 (pow l 3))
5.0ms	(* 1/60 (pow l 5))

series115.0ms (1.5%)

Counts

4 → 12

Calls

4 calls:

68.0ms	(+ (* (* J (+ l (+ l (+ (* 1/3 (pow l 3)) (* 1/60 (pow l 5)))))) (cos (/ K 2.0))) U)
39.0ms	(* (* J (+ l (+ l (+ (* 1/3 (pow l 3)) (* 1/60 (pow l 5)))))) (cos (/ K 2.0)))
4.0ms	(* 1/60 (pow l 5))
4.0ms	(* 1/3 (pow l 3))

simplify36.0ms (0.5%)

Algorithm

1×	egg-herbie

Counts

99 → 99

Iterations

Useful iterations: 0 (26.0ms)

Iter	Nodes	Cost
0	4935	1331
1	4935	1331

prune278.0ms (3.5%)

Pruning

5 alts after pruning (3 fresh and 2 done)

	Pruned	Kept	Total
New	98	1	99
Fresh	1	2	3
Picked	0	1	1
Done	0	1	1
Total	99	5	104

Merged error: 0.0b

Counts

104 → 5

localize26.0ms (0.3%)

Local error

Found 4 expressions with local error:

0.5b	(* (cbrt (+ (* J (* (+ l (+ l (+ (* 1/3 (pow l 3)) (* 1/60 (pow l 5))))) (cos (/ K 2.0)))) U)) (cbrt (+ (* J (* (+ l (+ l (+ (* 1/3 (pow l 3)) (* 1/60 (pow l 5))))) (cos (/ K 2.0)))) U)))
0.6b	(cbrt (+ (* J (* (+ l (+ l (+ (* 1/3 (pow l 3)) (* 1/60 (pow l 5))))) (cos (/ K 2.0)))) U))
0.6b	(cbrt (+ (* J (* (+ l (+ l (+ (* 1/3 (pow l 3)) (* 1/60 (pow l 5))))) (cos (/ K 2.0)))) U))
0.6b	(cbrt (+ (* J (* (+ l (+ l (+ (* 1/3 (pow l 3)) (* 1/60 (pow l 5))))) (cos (/ K 2.0)))) U))

rewrite69.0ms (0.9%)

Algorithm

1×	rewrite-expression-head

Rules

25×	`cbrt-prod`
23×	`add-sqr-sqrt`
18×	`cbrt-div`
15×	`add-cube-cbrt` `*-un-lft-identity`
11×	`pow1`
9×	`flip3-+` `pow1/3` `flip-+`
6×	`add-exp-log` `swap-sqr` `associate-r` `associate-l`
4×	`frac-times` `add-cbrt-cube` `add-log-exp` `unswap-sqr`
2×	`associate-r/` `pow-prod-down` `associate-l/` `pow-sqr` `pow-prod-up`
1×	`pow2` `pow-plus` `prod-exp` `*-commutative` `cbrt-unprod`

Counts

4 → 87

Calls

4 calls:

31.0ms	(* (cbrt (+ (* J (* (+ l (+ l (+ (* 1/3 (pow l 3)) (* 1/60 (pow l 5))))) (cos (/ K 2.0)))) U)) (cbrt (+ (* J (* (+ l (+ l (+ (* 1/3 (pow l 3)) (* 1/60 (pow l 5))))) (cos (/ K 2.0)))) U)))
12.0ms	(cbrt (+ (* J (* (+ l (+ l (+ (* 1/3 (pow l 3)) (* 1/60 (pow l 5))))) (cos (/ K 2.0)))) U))
12.0ms	(cbrt (+ (* J (* (+ l (+ l (+ (* 1/3 (pow l 3)) (* 1/60 (pow l 5))))) (cos (/ K 2.0)))) U))
12.0ms	(cbrt (+ (* J (* (+ l (+ l (+ (* 1/3 (pow l 3)) (* 1/60 (pow l 5))))) (cos (/ K 2.0)))) U))

series884.0ms (11.3%)

Counts

4 → 12

Calls

4 calls:

380.0ms	(* (cbrt (+ (* J (* (+ l (+ l (+ (* 1/3 (pow l 3)) (* 1/60 (pow l 5))))) (cos (/ K 2.0)))) U)) (cbrt (+ (* J (* (+ l (+ l (+ (* 1/3 (pow l 3)) (* 1/60 (pow l 5))))) (cos (/ K 2.0)))) U)))
170.0ms	(cbrt (+ (* J (* (+ l (+ l (+ (* 1/3 (pow l 3)) (* 1/60 (pow l 5))))) (cos (/ K 2.0)))) U))
166.0ms	(cbrt (+ (* J (* (+ l (+ l (+ (* 1/3 (pow l 3)) (* 1/60 (pow l 5))))) (cos (/ K 2.0)))) U))
160.0ms	(cbrt (+ (* J (* (+ l (+ l (+ (* 1/3 (pow l 3)) (* 1/60 (pow l 5))))) (cos (/ K 2.0)))) U))

simplify102.0ms (1.3%)

Algorithm

1×	egg-herbie

Counts

99 → 99

Iterations

Useful iterations: 0 (81.0ms)

Iter	Nodes	Cost
0	5244	4123

prune756.0ms (9.6%)

Pruning

5 alts after pruning (2 fresh and 3 done)

	Pruned	Kept	Total
New	99	0	99
Fresh	0	2	2
Picked	0	1	1
Done	0	2	2
Total	99	5	104

Merged error: 0.0b

Counts

104 → 5

regimes433.0ms (5.5%)

Accuracy

Total 0.0b remaining (12.7%)

Threshold costs 0.0b (12.7%)

bsearch0.0ms (0%)

simplify1.0ms (0%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	29	24
1	29	24

end0.0ms (0%)

sample3.7s (46.7%)

Algorithm

1×

intervals

Results

750.0ms	1238×	body	1280	valid
619.0ms	1479×	body	1280	invalid
472.0ms	1320×	body	640	valid
353.0ms	1219×	body	640	invalid
298.0ms	4148×	body	80	valid
243.0ms	3259×	body	80	invalid
190.0ms	812×	body	320	valid
134.0ms	630×	body	320	invalid
75.0ms	482×	body	160	valid
47.0ms	305×	body	160	invalid

Details

analyze519.0ms (6.6%)

sample117.0ms (1.5%)

simplify54.0ms (0.7%)

prune14.0ms (0.2%)

localize14.0ms (0.2%)

rewrite23.0ms (0.3%)

series41.0ms (0.5%)

simplify41.0ms (0.5%)

prune118.0ms (1.5%)

localize19.0ms (0.2%)

rewrite38.0ms (0.5%)

series59.0ms (0.7%)

simplify49.0ms (0.6%)

prune321.0ms (4.1%)

localize19.0ms (0.2%)

rewrite38.0ms (0.5%)

series115.0ms (1.5%)

simplify36.0ms (0.5%)

prune278.0ms (3.5%)

localize26.0ms (0.3%)

rewrite69.0ms (0.9%)

series884.0ms (11.3%)

simplify102.0ms (1.3%)

prune756.0ms (9.6%)

regimes433.0ms (5.5%)

bsearch0.0ms (0%)

simplify1.0ms (0%)

end0.0ms (0%)

sample3.7s (46.7%)

Profiling