Details

analyze591.0ms (9.5%)

Algorithm

1×

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)

sample78.0ms (1.2%)

Algorithm

1×

intervals

Results

36.0ms	207×	body	128	valid
15.0ms	20×	body	1024	valid
11.0ms	19×	body	512	valid
4.0ms	10×	body	256	valid

Compiler

Compiled 59 to 63 computations (-6.8% saved)

simplify130.0ms (2.1%)

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

1.5b

Counts

2 → 1

Compiler

Compiled 50 to 50 computations (0% saved)

localize23.0ms (0.4%)

Local error

Found 4 expressions with local error:

0.3b	(pow.f64 (sin.f64 ky) 2)
0.3b	(pow.f64 (sin.f64 kx) 2)
2.9b	(.f64 (pow.f64 (/.f64 (.f64 2 l) Om) 2) (+.f64 (pow.f64 (sin.f64 kx) 2) (pow.f64 (sin.f64 ky) 2)))
7.8b	(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)))))

rewrite36.0ms (0.6%)

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)))
4.0ms	(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)

series582.0ms (9.3%)

Counts

4 → 12

Calls

4 calls:

391.0ms	(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)))))
163.0ms	(.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 kx) 2)
14.0ms	(pow.f64 (sin.f64 ky) 2)

simplify68.0ms (1.1%)

Algorithm

1×	egg-herbie

Counts

102 → 102

Iterations

Useful iterations: 0 (44.0ms)

Iter	Nodes	Cost
0	4972	2191
1	4972	2191

prune185.0ms (3%)

Pruning

2 alts after pruning (2 fresh and 0 done)

	Pruned	Kept	Total
New	100	2	102
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	101	2	103

Error

0.8b

Counts

103 → 2

Compiler

Compiled 3217 to 2414 computations (25% saved)

localize19.0ms (0.3%)

Local error

Found 4 expressions with local error:

0.3b	(pow.f64 (sin.f64 kx) 2)
0.5b	(.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))))
2.9b	(.f64 (/.f64 (.f64 2 l) Om) (+.f64 (pow.f64 (sin.f64 kx) 2) (pow.f64 (sin.f64 ky) 2)))
7.8b	(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))))))

rewrite63.0ms (1%)

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:

21.0ms	(.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))))
18.0ms	(.f64 (/.f64 (.f64 2 l) Om) (+.f64 (pow.f64 (sin.f64 kx) 2) (pow.f64 (sin.f64 ky) 2)))
4.0ms	(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)

series765.0ms (12.3%)

Counts

4 → 12

Calls

4 calls:

396.0ms	(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))))))
185.0ms	(.f64 (/.f64 (.f64 2 l) Om) (+.f64 (pow.f64 (sin.f64 kx) 2) (pow.f64 (sin.f64 ky) 2)))
170.0ms	(.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)

simplify86.0ms (1.4%)

Algorithm

1×	egg-herbie

Counts

137 → 137

Iterations

Useful iterations: 0 (48.0ms)

Iter	Nodes	Cost
0	4965	3724
1	4965	3724

prune242.0ms (3.9%)

Pruning

2 alts after pruning (1 fresh and 1 done)

	Pruned	Kept	Total
New	137	0	137
Fresh	0	1	1
Picked	0	1	1
Done	0	0	0
Total	137	2	139

Error

0.8b

Counts

139 → 2

Compiler

Compiled 4675 to 3294 computations (29.5% saved)

localize4.0ms (0.1%)

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

prune1.0ms (0%)

Pruning

2 alts after pruning (0 fresh and 2 done)

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

Error

0.8b

Counts

2 → 2

Compiler

Compiled 0 to 0 computations (0% saved)

regimes644.0ms (10.3%)

Accuracy

Total 0.1b remaining (11%)

Threshold costs 0.1b (11%)

Compiler

Compiled 6316 to 6171 computations (2.3% saved)

bsearch0.0ms (0%)

simplify3.0ms (0%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	29	65
1	29	65

end0.0ms (0%)

sample2.7s (43.4%)

Algorithm

1×

intervals

Results

1.1s	6403×	body	128	valid
566.0ms	709×	body	1024	valid
315.0ms	572×	body	512	valid
113.0ms	315×	body	256	valid
1.0ms	1×	body	2048	valid

Compiler

Compiled 345 to 330 computations (4.3% saved)

Details

analyze591.0ms (9.5%)

sample78.0ms (1.2%)

simplify130.0ms (2.1%)

prune5.0ms (0.1%)

localize23.0ms (0.4%)

rewrite36.0ms (0.6%)

series582.0ms (9.3%)

simplify68.0ms (1.1%)

prune185.0ms (3%)

localize19.0ms (0.3%)

rewrite63.0ms (1%)

series765.0ms (12.3%)

simplify86.0ms (1.4%)

prune242.0ms (3.9%)

localize4.0ms (0.1%)

rewrite0.0ms (0%)

series0.0ms (0%)

simplify7.0ms (0.1%)

prune1.0ms (0%)

regimes644.0ms (10.3%)

bsearch0.0ms (0%)

simplify3.0ms (0%)

end0.0ms (0%)

sample2.7s (43.4%)

Profiling