Details

analyze759.0ms (4.1%)

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

Symmetry

sort(kx ky)

Compiler

Compiled 30 to 30 computations (0% saved)

sample96.0ms (0.5%)

Algorithm

1×

intervals

Results

32.0ms	191×	body	128	valid
21.0ms	26×	body	1024	valid
12.0ms	22×	body	512	valid
6.0ms	17×	body	256	valid

Compiler

Compiled 59 to 63 computations (-6.8% saved)

simplify46.0ms (0.3%)

Algorithm

1×	egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (41.0ms)

Iter	Nodes	Cost
0	5325	39

prune5.0ms (0%)

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

2.3b

Counts

2 → 1

Compiler

Compiled 50 to 50 computations (0% saved)

localize18.0ms (0.1%)

Local error

Found 4 expressions with local error:

0.3b	(pow.f64 (sin.f64 ky) 2)
0.3b	(pow.f64 (/.f64 (*.f64 2 l) Om) 2)
3.5b	(.f64 (pow.f64 (/.f64 (.f64 2 l) Om) 2) (+.f64 (pow.f64 (sin.f64 kx) 2) (pow.f64 (sin.f64 ky) 2)))
7.3b	(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)))))

rewrite230.0ms (1.3%)

Algorithm

1×	rewrite-expression-head

Error

1.6b

Rules

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

Counts

4 → 96

Calls

4 calls:

20.0ms	(.f64 (pow.f64 (/.f64 (.f64 2 l) Om) 2) (+.f64 (pow.f64 (sin.f64 kx) 2) (pow.f64 (sin.f64 ky) 2)))
6.0ms	(pow.f64 (/.f64 (*.f64 2 l) Om) 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 ky) 2)

Compiler

Compiled 3397 to 2565 computations (24.5% saved)

series1.7s (9.2%)

Error

0.5b

Counts

4 → 43

Calls

4 calls:

951.0ms	(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)))))
552.0ms	(.f64 (pow.f64 (/.f64 (.f64 2 l) Om) 2) (+.f64 (pow.f64 (sin.f64 kx) 2) (pow.f64 (sin.f64 ky) 2)))
90.0ms	(pow.f64 (/.f64 (*.f64 2 l) Om) 2)
23.0ms	(pow.f64 (sin.f64 ky) 2)

Compiler

Compiled 4201 to 3730 computations (11.2% saved)

simplify76.0ms (0.4%)

Algorithm

1×	egg-herbie

Counts

139 → 139

Iterations

Useful iterations: 0 (46.0ms)

Iter	Nodes	Cost
0	5070	3283

prune247.0ms (1.3%)

Pruning

4 alts after pruning (3 fresh and 1 done)

	Pruned	Kept	Total
New	136	3	139
Fresh	0	0	0
Picked	0	1	1
Done	0	0	0
Total	136	4	140

Error

0.1b

Counts

140 → 4

Compiler

Compiled 4302 to 3145 computations (26.9% saved)

localize23.0ms (0.1%)

Local error

Found 4 expressions with local error:

7.1b	(sqrt.f64 (sqrt.f64 (+.f64 1 (.f64 (+.f64 (pow.f64 (sin.f64 ky) 2) (pow.f64 (sin.f64 kx) 2)) (.f64 4 (pow.f64 (/.f64 l Om) 2))))))
7.1b	(sqrt.f64 (sqrt.f64 (+.f64 1 (.f64 (+.f64 (pow.f64 (sin.f64 ky) 2) (pow.f64 (sin.f64 kx) 2)) (.f64 4 (pow.f64 (/.f64 l Om) 2))))))
7.3b	(sqrt.f64 (+.f64 1 (.f64 (+.f64 (pow.f64 (sin.f64 ky) 2) (pow.f64 (sin.f64 kx) 2)) (.f64 4 (pow.f64 (/.f64 l Om) 2)))))
7.3b	(sqrt.f64 (+.f64 1 (.f64 (+.f64 (pow.f64 (sin.f64 ky) 2) (pow.f64 (sin.f64 kx) 2)) (.f64 4 (pow.f64 (/.f64 l Om) 2)))))

rewrite278.0ms (1.5%)

Algorithm

1×	rewrite-expression-head

Error

0.1b

Rules

26×	`sqrt-prod_binary64_94`
16×	`add-sqr-sqrt_binary64_100`
12×	`sqrt-div_binary64_95`
10×	`pow1_binary64_139` `add-cube-cbrt_binary64_113` `sqrt-pow1_binary64_96` `*-un-lft-identity_binary64_78`
6×	`pow1/2_binary64_158` `rem-sqrt-square_binary64_91`
4×	`add-log-exp_binary64_117` `add-exp-log_binary64_116` `add-cbrt-cube_binary64_114` `flip3-+_binary64_81` `flip-+_binary64_52`

Counts

4 → 72

Calls

4 calls:

5.0ms	(sqrt.f64 (sqrt.f64 (+.f64 1 (.f64 (+.f64 (pow.f64 (sin.f64 ky) 2) (pow.f64 (sin.f64 kx) 2)) (.f64 4 (pow.f64 (/.f64 l Om) 2))))))
5.0ms	(sqrt.f64 (sqrt.f64 (+.f64 1 (.f64 (+.f64 (pow.f64 (sin.f64 ky) 2) (pow.f64 (sin.f64 kx) 2)) (.f64 4 (pow.f64 (/.f64 l Om) 2))))))
4.0ms	(sqrt.f64 (+.f64 1 (.f64 (+.f64 (pow.f64 (sin.f64 ky) 2) (pow.f64 (sin.f64 kx) 2)) (.f64 4 (pow.f64 (/.f64 l Om) 2)))))
4.0ms	(sqrt.f64 (+.f64 1 (.f64 (+.f64 (pow.f64 (sin.f64 ky) 2) (pow.f64 (sin.f64 kx) 2)) (.f64 4 (pow.f64 (/.f64 l Om) 2)))))

Compiler

Compiled 4836 to 3429 computations (29.1% saved)

series6.3s (34.4%)

Error

0.1b

Counts

4 → 86

Calls

4 calls:

1.8s	(sqrt.f64 (sqrt.f64 (+.f64 1 (.f64 (+.f64 (pow.f64 (sin.f64 ky) 2) (pow.f64 (sin.f64 kx) 2)) (.f64 4 (pow.f64 (/.f64 l Om) 2))))))
1.8s	(sqrt.f64 (sqrt.f64 (+.f64 1 (.f64 (+.f64 (pow.f64 (sin.f64 ky) 2) (pow.f64 (sin.f64 kx) 2)) (.f64 4 (pow.f64 (/.f64 l Om) 2))))))
1.2s	(sqrt.f64 (+.f64 1 (.f64 (+.f64 (pow.f64 (sin.f64 ky) 2) (pow.f64 (sin.f64 kx) 2)) (.f64 4 (pow.f64 (/.f64 l Om) 2)))))
1.1s	(sqrt.f64 (+.f64 1 (.f64 (+.f64 (pow.f64 (sin.f64 ky) 2) (pow.f64 (sin.f64 kx) 2)) (.f64 4 (pow.f64 (/.f64 l Om) 2)))))

Compiler

Compiled 16630 to 13510 computations (18.8% saved)

simplify78.0ms (0.4%)

Algorithm

1×	egg-herbie

Counts

158 → 158

Iterations

Useful iterations: 0 (23.0ms)

Iter	Nodes	Cost
0	4970	6608
1	4970	6608

prune597.0ms (3.3%)

Pruning

4 alts after pruning (2 fresh and 2 done)

	Pruned	Kept	Total
New	158	0	158
Fresh	0	2	2
Picked	0	1	1
Done	0	1	1
Total	158	4	162

Error

0.1b

Counts

162 → 4

Compiler

Compiled 9246 to 6518 computations (29.5% saved)

localize4.0ms (0%)

rewrite0.0ms (0%)

Algorithm

1×	rewrite-expression-head

Error

0.1b

Counts

0 → 0

Compiler

Compiled 0 to 0 computations (0% saved)

series0.0ms (0%)

Error: 0.1b
Counts: 0 → 0
Compiler: Compiled 0 to 0 computations (0% saved)

simplify6.0ms (0%)

Algorithm

1×	egg-herbie

Counts

0 → 0

Iterations

Useful iterations: 0 (2.0ms)

Iter	Nodes	Cost
0	0	0

prune3.0ms (0%)

Pruning

4 alts after pruning (1 fresh and 3 done)

	Kept	Total
New	0	0
Fresh	1	1
Picked	1	1
Done	2	2
Total	4	4

Error

0.1b

Counts

4 → 4

Compiler

Compiled 50 to 40 computations (20% saved)

localize26.0ms (0.1%)

Local error

Found 4 expressions with local error:

5.2b	(/.f64 (pow.f64 (sin.f64 ky) 2) Om)
5.2b	(/.f64 (pow.f64 (sin.f64 ky) 2) Om)
28.6b	(sqrt.f64 (*.f64 (/.f64 4 Om) (+.f64 (/.f64 (pow.f64 (sin.f64 ky) 2) Om) (/.f64 (pow.f64 (sin.f64 kx) 2) Om))))
28.7b	(sqrt.f64 (/.f64 1 (*.f64 (/.f64 4 Om) (+.f64 (/.f64 (pow.f64 (sin.f64 ky) 2) Om) (/.f64 (pow.f64 (sin.f64 kx) 2) Om)))))

rewrite768.0ms (4.2%)

Algorithm

1×	rewrite-expression-head

Error

0.1b

Rules

51×	`times-frac_binary64_84`
41×	`add-sqr-sqrt_binary64_100`
40×	`add-cube-cbrt_binary64_113` `*-un-lft-identity_binary64_78`
24×	`unpow-prod-down_binary64_157`
16×	`associate-/l*_binary64_23`
15×	`sqrt-prod_binary64_94`
14×	`add-exp-log_binary64_116`
11×	`pow1_binary64_139`
8×	`add-cbrt-cube_binary64_114` `sqrt-div_binary64_95` `unpow2_binary64_143` `sqr-pow_binary64_50`
7×	`associate-/r/_binary64_24`
6×	`sqrt-pow1_binary64_96` `frac-times_binary64_88` `associate-r/_binary64_20` `div-exp_binary64_129` `associate-/r_binary64_22`
4×	`add-log-exp_binary64_117` `frac-add_binary64_86` `flip3-+_binary64_81` `flip-+_binary64_52`
3×	`div-inv_binary64_75`
2×	`pow1/2_binary64_158` `pow-prod-down_binary64_149` `pow-flip_binary64_152` `associate-*l/_binary64_21` `pow-to-exp_binary64_147` `pow-exp_binary64_146` `cbrt-undiv_binary64_112` `frac-2neg_binary64_89` `clear-num_binary64_77`
1×	`inv-pow_binary64_163` `rem-sqrt-square_binary64_91`

Counts

4 → 144

Calls

4 calls:

50.0ms	(sqrt.f64 (/.f64 1 (*.f64 (/.f64 4 Om) (+.f64 (/.f64 (pow.f64 (sin.f64 ky) 2) Om) (/.f64 (pow.f64 (sin.f64 kx) 2) Om)))))
48.0ms	(sqrt.f64 (*.f64 (/.f64 4 Om) (+.f64 (/.f64 (pow.f64 (sin.f64 ky) 2) Om) (/.f64 (pow.f64 (sin.f64 kx) 2) Om))))
6.0ms	(/.f64 (pow.f64 (sin.f64 ky) 2) Om)
6.0ms	(/.f64 (pow.f64 (sin.f64 ky) 2) Om)

Compiler

Compiled 8686 to 5765 computations (33.6% saved)

series1.5s (8.2%)

Error

0.1b

Counts

4 → 35

Calls

4 calls:

663.0ms	(sqrt.f64 (/.f64 1 (*.f64 (/.f64 4 Om) (+.f64 (/.f64 (pow.f64 (sin.f64 ky) 2) Om) (/.f64 (pow.f64 (sin.f64 kx) 2) Om)))))
544.0ms	(sqrt.f64 (*.f64 (/.f64 4 Om) (+.f64 (/.f64 (pow.f64 (sin.f64 ky) 2) Om) (/.f64 (pow.f64 (sin.f64 kx) 2) Om))))
110.0ms	(/.f64 (pow.f64 (sin.f64 ky) 2) Om)
107.0ms	(/.f64 (pow.f64 (sin.f64 ky) 2) Om)

Compiler

Compiled 4983 to 3778 computations (24.2% saved)

simplify78.0ms (0.4%)

Algorithm

1×	egg-herbie

Counts

179 → 179

Iterations

Useful iterations: 0 (38.0ms)

Iter	Nodes	Cost
0	4975	3678
1	4975	3678

prune587.0ms (3.2%)

Pruning

4 alts after pruning (0 fresh and 4 done)

	Pruned	Kept	Total
New	179	0	179
Fresh	0	0	0
Picked	0	1	1
Done	0	3	3
Total	179	4	183

Error

0.1b

Counts

183 → 4

Compiler

Compiled 9839 to 6448 computations (34.5% saved)

regimes1.4s (7.9%)

Accuracy

Total 0.4b remaining (84.7%)

Threshold costs 0.4b (84.7%)

Compiler

Compiled 18685 to 17085 computations (8.6% saved)

bsearch3.0ms (0%)

Compiler: Compiled 5 to 7 computations (-40% saved)

simplify15.0ms (0.1%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	55	135
1	55	135

Removed

((sort kx ky))

Compiler

Compiled 174 to 134 computations (23% saved)

end0.0ms (0%)

sample3.5s (18.8%)

Algorithm

1×

intervals

Results

1.1s	6343×	body	128	valid
635.0ms	776×	body	1024	valid
311.0ms	548×	body	512	valid
128.0ms	332×	body	256	valid
1.0ms	1×	body	2048	valid

Compiler

Compiled 1018 to 914 computations (10.2% saved)

Details

analyze759.0ms (4.1%)

sample96.0ms (0.5%)

simplify46.0ms (0.3%)

prune5.0ms (0%)

localize18.0ms (0.1%)

rewrite230.0ms (1.3%)

series1.7s (9.2%)

simplify76.0ms (0.4%)

prune247.0ms (1.3%)

localize23.0ms (0.1%)

rewrite278.0ms (1.5%)

series6.3s (34.4%)

simplify78.0ms (0.4%)

prune597.0ms (3.3%)

localize4.0ms (0%)

rewrite0.0ms (0%)

series0.0ms (0%)

simplify6.0ms (0%)

prune3.0ms (0%)

localize26.0ms (0.1%)

rewrite768.0ms (4.2%)

series1.5s (8.2%)

simplify78.0ms (0.4%)

prune587.0ms (3.2%)

regimes1.4s (7.9%)

bsearch3.0ms (0%)

simplify15.0ms (0.1%)

end0.0ms (0%)

sample3.5s (18.8%)

Profiling