Details

analyze700.0ms (9.3%)

Algorithm

1×	search
2×	egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	4998	273
1	4998	273
0	4	4
1	4	4

Search

True	Other	False	Iter
0%	99.8%	0.2%	0
0%	99.8%	0.2%	1
0%	99.8%	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
74.9%	25%	0.2%	7
74.9%	25%	0.2%	8
74.9%	25%	0.2%	9
74.9%	25%	0.2%	10
87.3%	12.5%	0.2%	11
87.3%	12.5%	0.2%	12
87.3%	12.5%	0.2%	13
87.3%	12.5%	0.2%	14

Compiler

Compiled 30 to 30 computations (0% saved)

sample80.0ms (1.1%)

Algorithm

1×

intervals

Results

35.0ms	207×	body	128	valid
15.0ms	19×	body	1024	valid
10.0ms	18×	body	512	valid
4.0ms	12×	body	256	valid

Compiler

Compiled 59 to 63 computations (-6.8% saved)

simplify46.0ms (0.6%)

Algorithm

1×	egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (41.0ms)

Iter	Nodes	Cost
0	5325	39

prune5.0ms (0.1%)

Pruning

1 alts after pruning (1 fresh and 0 done)

	Pruned	Kept	Total
New	0	1	1
Fresh	1	0	1
Picked	0	0	0
Done	0	0	0
Total	1	1	2

Error

0.5b

Counts

2 → 1

Compiler

Compiled 50 to 50 computations (0% saved)

localize23.0ms (0.3%)

Local error

Found 4 expressions with local error:

0.2b	(pow.f64 (sin.f64 ky) 2)
0.3b	(pow.f64 (sin.f64 kx) 2)
2.7b	(.f64 (pow.f64 (/.f64 (.f64 2 l) Om) 2) (+.f64 (pow.f64 (sin.f64 kx) 2) (pow.f64 (sin.f64 ky) 2)))
8.9b	(sqrt.f64 (+.f64 1 (.f64 (pow.f64 (/.f64 (.f64 2 l) Om) 2) (+.f64 (pow.f64 (sin.f64 kx) 2) (pow.f64 (sin.f64 ky) 2)))))

rewrite34.0ms (0.4%)

Algorithm

1×	rewrite-expression-head

Rules

20×	`add-sqr-sqrt_binary64_100`
18×	`add-exp-log_binary64_116`
17×	`*-un-lft-identity_binary64_78`
16×	`unpow-prod-down_binary64_157`
13×	`add-cube-cbrt_binary64_113`
12×	`associate-l_binary64_19`
7×	`pow1_binary64_139`
6×	`add-cbrt-cube_binary64_114` `prod-exp_binary64_127` `pow-unpow_binary64_155`
5×	`pow-exp_binary64_146` `associate-r_binary64_18`
4×	`add-log-exp_binary64_117` `unpow2_binary64_143` `sqr-pow_binary64_50` `unswap-sqr_binary64_46`
3×	`sqrt-prod_binary64_94` `pow-to-exp_binary64_147` `times-frac_binary64_84`
2×	`div-exp_binary64_129` `flip-+_binary64_52` `pow-pow_binary64_150` `sqrt-div_binary64_95` `associate-*r/_binary64_20` `distribute-lft-out_binary64_29` `flip3-+_binary64_81`
1×	`distribute-lft-in_binary64_27` `*-commutative_binary64_9` `sqrt-pow1_binary64_96` `cbrt-unprod_binary64_111` `rem-sqrt-square_binary64_91` `distribute-rgt-in_binary64_28` `div-inv_binary64_75` `pow1/2_binary64_158`

Counts

4 → 90

Calls

4 calls:

16.0ms	(.f64 (pow.f64 (/.f64 (.f64 2 l) Om) 2) (+.f64 (pow.f64 (sin.f64 kx) 2) (pow.f64 (sin.f64 ky) 2)))
3.0ms	(sqrt.f64 (+.f64 1 (.f64 (pow.f64 (/.f64 (.f64 2 l) Om) 2) (+.f64 (pow.f64 (sin.f64 kx) 2) (pow.f64 (sin.f64 ky) 2)))))
3.0ms	(pow.f64 (sin.f64 kx) 2)
3.0ms	(pow.f64 (sin.f64 ky) 2)

series592.0ms (7.8%)

Counts

4 → 12

Calls

4 calls:

386.0ms	(sqrt.f64 (+.f64 1 (.f64 (pow.f64 (/.f64 (.f64 2 l) Om) 2) (+.f64 (pow.f64 (sin.f64 kx) 2) (pow.f64 (sin.f64 ky) 2)))))
178.0ms	(.f64 (pow.f64 (/.f64 (.f64 2 l) Om) 2) (+.f64 (pow.f64 (sin.f64 kx) 2) (pow.f64 (sin.f64 ky) 2)))
14.0ms	(pow.f64 (sin.f64 ky) 2)
14.0ms	(pow.f64 (sin.f64 kx) 2)

simplify67.0ms (0.9%)

Algorithm

1×	egg-herbie

Counts

102 → 102

Iterations

Useful iterations: 0 (43.0ms)

Iter	Nodes	Cost
0	4972	2191
1	4972	2191

prune178.0ms (2.4%)

Pruning

3 alts after pruning (3 fresh and 0 done)

	Pruned	Kept	Total
New	99	3	102
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	100	3	103

Error

0.2b

Counts

103 → 3

Compiler

Compiled 3245 to 2442 computations (24.7% saved)

localize18.0ms (0.2%)

Local error

Found 4 expressions with local error:

0.3b	(pow.f64 (sin.f64 kx) 2)
0.4b	(.f64 (/.f64 (.f64 2 l) Om) (.f64 (/.f64 (.f64 2 l) Om) (+.f64 (pow.f64 (sin.f64 kx) 2) (pow.f64 (sin.f64 ky) 2))))
2.1b	(.f64 (/.f64 (.f64 2 l) Om) (+.f64 (pow.f64 (sin.f64 kx) 2) (pow.f64 (sin.f64 ky) 2)))
8.9b	(sqrt.f64 (+.f64 1 (.f64 (/.f64 (.f64 2 l) Om) (.f64 (/.f64 (.f64 2 l) Om) (+.f64 (pow.f64 (sin.f64 kx) 2) (pow.f64 (sin.f64 ky) 2))))))

rewrite59.0ms (0.8%)

Algorithm

1×	rewrite-expression-head

Rules

68×	`add-exp-log_binary64_116`
67×	`add-cbrt-cube_binary64_114`
32×	`cbrt-unprod_binary64_111` `prod-exp_binary64_127`
16×	`cbrt-undiv_binary64_112` `div-exp_binary64_129` `*-un-lft-identity_binary64_78`
15×	`add-sqr-sqrt_binary64_100`
14×	`associate-l_binary64_19`
13×	`pow1_binary64_139`
12×	`add-cube-cbrt_binary64_113`
11×	`frac-times_binary64_88` `associate-*r/_binary64_20`
7×	`flip-+_binary64_52` `flip3-+_binary64_81`
6×	`times-frac_binary64_84` `associate-r_binary64_18`
5×	`distribute-lft-in_binary64_27` `unpow-prod-down_binary64_157` `distribute-rgt-in_binary64_28`
4×	`add-log-exp_binary64_117` `associate-*l/_binary64_21` `pow-prod-down_binary64_149`
3×	`sqrt-prod_binary64_94` `pow-unpow_binary64_155`
2×	`*-commutative_binary64_9` `div-inv_binary64_75` `sqrt-div_binary64_95` `distribute-lft-out_binary64_29`
1×	`pow-exp_binary64_146` `pow-to-exp_binary64_147` `sqrt-pow1_binary64_96` `rem-sqrt-square_binary64_91` `unpow2_binary64_143` `sqr-pow_binary64_50` `pow-pow_binary64_150` `unswap-sqr_binary64_46` `pow1/2_binary64_158`

Counts

4 → 125

Calls

4 calls:

19.0ms	(.f64 (/.f64 (.f64 2 l) Om) (.f64 (/.f64 (.f64 2 l) Om) (+.f64 (pow.f64 (sin.f64 kx) 2) (pow.f64 (sin.f64 ky) 2))))
15.0ms	(.f64 (/.f64 (.f64 2 l) Om) (+.f64 (pow.f64 (sin.f64 kx) 2) (pow.f64 (sin.f64 ky) 2)))
6.0ms	(sqrt.f64 (+.f64 1 (.f64 (/.f64 (.f64 2 l) Om) (.f64 (/.f64 (.f64 2 l) Om) (+.f64 (pow.f64 (sin.f64 kx) 2) (pow.f64 (sin.f64 ky) 2))))))
3.0ms	(pow.f64 (sin.f64 kx) 2)

series782.0ms (10.3%)

Counts

4 → 12

Calls

4 calls:

392.0ms	(sqrt.f64 (+.f64 1 (.f64 (/.f64 (.f64 2 l) Om) (.f64 (/.f64 (.f64 2 l) Om) (+.f64 (pow.f64 (sin.f64 kx) 2) (pow.f64 (sin.f64 ky) 2))))))
198.0ms	(.f64 (/.f64 (.f64 2 l) Om) (+.f64 (pow.f64 (sin.f64 kx) 2) (pow.f64 (sin.f64 ky) 2)))
178.0ms	(.f64 (/.f64 (.f64 2 l) Om) (.f64 (/.f64 (.f64 2 l) Om) (+.f64 (pow.f64 (sin.f64 kx) 2) (pow.f64 (sin.f64 ky) 2))))
14.0ms	(pow.f64 (sin.f64 kx) 2)

simplify88.0ms (1.2%)

Algorithm

1×	egg-herbie

Counts

137 → 137

Iterations

Useful iterations: 0 (49.0ms)

Iter	Nodes	Cost
0	4965	3724
1	4965	3724

prune253.0ms (3.3%)

Pruning

3 alts after pruning (2 fresh and 1 done)

	Pruned	Kept	Total
New	137	0	137
Fresh	0	2	2
Picked	0	1	1
Done	0	0	0
Total	137	3	140

Error

0.2b

Counts

140 → 3

Compiler

Compiled 4703 to 3322 computations (29.4% saved)

localize23.0ms (0.3%)

Local error

Found 4 expressions with local error:

0.3b	(pow.f64 (sin.f64 kx) 2)
2.7b	(.f64 (pow.f64 (/.f64 (.f64 2 l) Om) 2) (+.f64 (pow.f64 (sin.f64 kx) 2) (pow.f64 (sin.f64 ky) 2)))
8.9b	(sqrt.f64 (+.f64 1 (.f64 (pow.f64 (/.f64 (.f64 2 l) Om) 2) (+.f64 (pow.f64 (sin.f64 kx) 2) (pow.f64 (sin.f64 ky) 2)))))
12.6b	(cbrt.f64 (pow.f64 (sqrt.f64 (+.f64 1 (.f64 (pow.f64 (/.f64 (.f64 2 l) Om) 2) (+.f64 (pow.f64 (sin.f64 kx) 2) (pow.f64 (sin.f64 ky) 2))))) 3))

rewrite40.0ms (0.5%)

Algorithm

1×	rewrite-expression-head

Rules

23×	`add-sqr-sqrt_binary64_100`
20×	`*-un-lft-identity_binary64_78`
19×	`unpow-prod-down_binary64_157`
18×	`cbrt-prod_binary64_109`
17×	`add-exp-log_binary64_116`
16×	`add-cube-cbrt_binary64_113`
12×	`associate-l_binary64_19`
9×	`sqrt-prod_binary64_94`
6×	`add-cbrt-cube_binary64_114` `prod-exp_binary64_127` `cube-prod_binary64_106` `pow1_binary64_139`
5×	`associate-r_binary64_18`
4×	`pow-exp_binary64_146` `add-log-exp_binary64_117` `sqr-pow_binary64_50` `unswap-sqr_binary64_46` `sqrt-div_binary64_95`
3×	`flip-+_binary64_52` `unpow2_binary64_143` `times-frac_binary64_84` `pow-unpow_binary64_155` `flip3-+_binary64_81`
2×	`cbrt-div_binary64_110` `pow-to-exp_binary64_147` `cube-div_binary64_107` `div-exp_binary64_129` `associate-*r/_binary64_20` `distribute-lft-out_binary64_29`
1×	`cube-mult_binary64_108` `distribute-lft-in_binary64_27` `*-commutative_binary64_9` `rem-cbrt-cube_binary64_102` `sqrt-pow1_binary64_96` `cbrt-unprod_binary64_111` `rem-sqrt-square_binary64_91` `pow1/3_binary64_160` `distribute-rgt-in_binary64_28` `div-inv_binary64_75` `pow-pow_binary64_150` `pow1/2_binary64_158` `unpow3_binary64_144`

Counts

4 → 101

Calls

4 calls:

16.0ms	(.f64 (pow.f64 (/.f64 (.f64 2 l) Om) 2) (+.f64 (pow.f64 (sin.f64 kx) 2) (pow.f64 (sin.f64 ky) 2)))
6.0ms	(cbrt.f64 (pow.f64 (sqrt.f64 (+.f64 1 (.f64 (pow.f64 (/.f64 (.f64 2 l) Om) 2) (+.f64 (pow.f64 (sin.f64 kx) 2) (pow.f64 (sin.f64 ky) 2))))) 3))
3.0ms	(sqrt.f64 (+.f64 1 (.f64 (pow.f64 (/.f64 (.f64 2 l) Om) 2) (+.f64 (pow.f64 (sin.f64 kx) 2) (pow.f64 (sin.f64 ky) 2)))))
3.0ms	(pow.f64 (sin.f64 kx) 2)

series962.0ms (12.7%)

Counts

4 → 12

Calls

4 calls:

385.0ms	(cbrt.f64 (pow.f64 (sqrt.f64 (+.f64 1 (.f64 (pow.f64 (/.f64 (.f64 2 l) Om) 2) (+.f64 (pow.f64 (sin.f64 kx) 2) (pow.f64 (sin.f64 ky) 2))))) 3))
383.0ms	(sqrt.f64 (+.f64 1 (.f64 (pow.f64 (/.f64 (.f64 2 l) Om) 2) (+.f64 (pow.f64 (sin.f64 kx) 2) (pow.f64 (sin.f64 ky) 2)))))
177.0ms	(.f64 (pow.f64 (/.f64 (.f64 2 l) Om) 2) (+.f64 (pow.f64 (sin.f64 kx) 2) (pow.f64 (sin.f64 ky) 2)))
17.0ms	(pow.f64 (sin.f64 kx) 2)

simplify57.0ms (0.8%)

Algorithm

1×	egg-herbie

Counts

113 → 113

Iterations

Useful iterations: 0 (24.0ms)

Iter	Nodes	Cost
0	5068	3472

prune229.0ms (3%)

Pruning

3 alts after pruning (1 fresh and 2 done)

	Pruned	Kept	Total
New	113	0	113
Fresh	0	1	1
Picked	0	1	1
Done	0	1	1
Total	113	3	116

Error

0.2b

Counts

116 → 3

Compiler

Compiled 4050 to 3104 computations (23.4% saved)

localize3.0ms (0%)

rewrite0.0ms (0%)

Algorithm

1×	rewrite-expression-head

Rules

Counts

0 → 0

series0.0ms (0%)

Counts: 0 → 0

simplify7.0ms (0.1%)

Algorithm

1×	egg-herbie

Counts

0 → 0

Iterations

Useful iterations: 0 (2.0ms)

Iter	Nodes	Cost
0	0	0

prune0.0ms (0%)

Pruning

3 alts after pruning (0 fresh and 3 done)

	Kept	Total
New	0	0
Fresh	0	0
Picked	1	1
Done	2	2
Total	3	3

Error

0.2b

Counts

3 → 3

Compiler

Compiled 0 to 0 computations (0% saved)

regimes576.0ms (7.6%)

Accuracy

Total 0.1b remaining (10.5%)

Threshold costs 0.1b (10.5%)

Compiler

Compiled 5231 to 5219 computations (0.2% saved)

bsearch0.0ms (0%)

simplify3.0ms (0%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	29	45
1	29	45

end0.0ms (0%)

sample2.7s (36.1%)

Algorithm

1×

intervals

Results

1.1s	6353×	body	128	valid
603.0ms	757×	body	1024	valid
313.0ms	544×	body	512	valid
125.0ms	345×	body	256	valid
1.0ms	1×	body	2048	valid

Compiler

Compiled 270 to 266 computations (1.5% saved)

Details

analyze700.0ms (9.3%)

sample80.0ms (1.1%)

simplify46.0ms (0.6%)

prune5.0ms (0.1%)

localize23.0ms (0.3%)

rewrite34.0ms (0.4%)

series592.0ms (7.8%)

simplify67.0ms (0.9%)

prune178.0ms (2.4%)

localize18.0ms (0.2%)

rewrite59.0ms (0.8%)

series782.0ms (10.3%)

simplify88.0ms (1.2%)

prune253.0ms (3.3%)

localize23.0ms (0.3%)

rewrite40.0ms (0.5%)

series962.0ms (12.7%)

simplify57.0ms (0.8%)

prune229.0ms (3%)

localize3.0ms (0%)

rewrite0.0ms (0%)

series0.0ms (0%)

simplify7.0ms (0.1%)

prune0.0ms (0%)

regimes576.0ms (7.6%)

bsearch0.0ms (0%)

simplify3.0ms (0%)

end0.0ms (0%)

sample2.7s (36.1%)

Profiling