Details

analyze785.0ms (5.2%)

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)

sample92.0ms (0.6%)

Algorithm

1×

intervals

Results

34.0ms	205×	body	128	valid
24.0ms	25×	body	1024	valid
9.0ms	15×	body	512	valid
4.0ms	11×	body	256	valid

Compiler

Compiled 59 to 63 computations (-6.8% saved)

simplify47.0ms (0.3%)

Algorithm

1×	egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (42.0ms)

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

1.0b

Counts

2 → 1

Compiler

Compiled 50 to 50 computations (0% saved)

localize19.0ms (0.1%)

Local error

Found 4 expressions with local error:

0.3b	(pow.f64 (sin.f64 ky) 2)
0.8b	(/.f64 1/2 (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))))))
2.5b	(.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)))))

rewrite309.0ms (2.1%)

Algorithm

1×	rewrite-expression-head

Error

0.9b

Rules

33×	`add-sqr-sqrt_binary64_100`
30×	`*-un-lft-identity_binary64_78`
26×	`add-cube-cbrt_binary64_113`
21×	`times-frac_binary64_84`
19×	`add-exp-log_binary64_116`
15×	`sqrt-prod_binary64_94`
13×	`unpow-prod-down_binary64_157`
12×	`associate-l_binary64_19`
8×	`add-cbrt-cube_binary64_114`
6×	`pow1_binary64_139` `prod-exp_binary64_127` `associate-/r*_binary64_22`
5×	`associate-r_binary64_18`
4×	`add-log-exp_binary64_117` `sqrt-div_binary64_95` `pow-exp_binary64_146` `unswap-sqr_binary64_46`
3×	`flip3-+_binary64_81` `flip-+_binary64_52` `div-exp_binary64_129` `unpow2_binary64_143` `sqr-pow_binary64_50` `associate-/l*_binary64_23` `pow-unpow_binary64_155`
2×	`pow-to-exp_binary64_147` `associate-*r/_binary64_20` `div-inv_binary64_75` `distribute-lft-out_binary64_29` `associate-/r/_binary64_24`
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` `cbrt-undiv_binary64_112` `frac-2neg_binary64_89` `clear-num_binary64_77` `pow-pow_binary64_150`

Counts

4 → 113

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	(/.f64 1/2 (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))))))
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 4614 to 3499 computations (24.2% saved)

series3.8s (25.6%)

Error

0.1b

Counts

4 → 61

Calls

4 calls:

2.0s	(/.f64 1/2 (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))))))
1.2s	(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)))))
564.0ms	(.f64 (pow.f64 (/.f64 (.f64 2 l) Om) 2) (+.f64 (pow.f64 (sin.f64 kx) 2) (pow.f64 (sin.f64 ky) 2)))
23.0ms	(pow.f64 (sin.f64 ky) 2)

Compiler

Compiled 7222 to 6152 computations (14.8% saved)

simplify106.0ms (0.7%)

Algorithm

1×	egg-herbie

Counts

174 → 174

Iterations

Useful iterations: 0 (50.0ms)

Iter	Nodes	Cost
0	4997	6592
1	4997	6592

prune393.0ms (2.6%)

Pruning

3 alts after pruning (2 fresh and 1 done)

	Pruned	Kept	Total
New	172	2	174
Fresh	0	0	0
Picked	0	1	1
Done	0	0	0
Total	172	3	175

Error

0.1b

Counts

175 → 3

Compiler

Compiled 6315 to 4526 computations (28.3% saved)

localize24.0ms (0.2%)

Local error

Found 4 expressions with local error:

2.7b	(.f64 (.f64 l l) (+.f64 (pow.f64 (sin.f64 ky) 2) (pow.f64 (sin.f64 kx) 2)))
2.7b	(.f64 (.f64 l l) (+.f64 (pow.f64 (sin.f64 ky) 2) (pow.f64 (sin.f64 kx) 2)))
27.7b	(sqrt.f64 (/.f64 1/4 (.f64 (.f64 l l) (+.f64 (pow.f64 (sin.f64 ky) 2) (pow.f64 (sin.f64 kx) 2)))))
27.9b	(sqrt.f64 (.f64 4 (.f64 (*.f64 l l) (+.f64 (pow.f64 (sin.f64 ky) 2) (pow.f64 (sin.f64 kx) 2)))))

rewrite294.0ms (2%)

Algorithm

1×	rewrite-expression-head

Error

0.1b

Rules

25×	`pow1_binary64_139`
16×	`*-un-lft-identity_binary64_78`
14×	`add-exp-log_binary64_116` `add-cbrt-cube_binary64_114`
12×	`pow-prod-down_binary64_149`
11×	`add-sqr-sqrt_binary64_100`
10×	`associate-r/_binary64_20` `sqrt-prod_binary64_94` `associate-r*_binary64_18`
8×	`add-cube-cbrt_binary64_113`
6×	`prod-exp_binary64_127` `cbrt-unprod_binary64_111`
5×	`sqrt-pow1_binary64_96`
4×	`add-log-exp_binary64_117` `flip3-+_binary64_81` `flip-+_binary64_52` `unpow-prod-down_binary64_157` `distribute-lft-out_binary64_29`
3×	`sqrt-div_binary64_95` `times-frac_binary64_84`
2×	`pow1/2_binary64_158` `associate-/r/_binary64_24` `unswap-sqr_binary64_46` `distribute-rgt-in_binary64_28` `distribute-lft-in_binary64_27` `associate-l_binary64_19` `*-commutative_binary64_9`
1×	`div-inv_binary64_75` `rem-sqrt-square_binary64_91`

Counts

4 → 85

Calls

4 calls:

18.0ms	(.f64 (.f64 l l) (+.f64 (pow.f64 (sin.f64 ky) 2) (pow.f64 (sin.f64 kx) 2)))
15.0ms	(.f64 (.f64 l l) (+.f64 (pow.f64 (sin.f64 ky) 2) (pow.f64 (sin.f64 kx) 2)))
15.0ms	(sqrt.f64 (.f64 4 (.f64 (*.f64 l l) (+.f64 (pow.f64 (sin.f64 ky) 2) (pow.f64 (sin.f64 kx) 2)))))
14.0ms	(sqrt.f64 (/.f64 1/4 (.f64 (.f64 l l) (+.f64 (pow.f64 (sin.f64 ky) 2) (pow.f64 (sin.f64 kx) 2)))))

Compiler

Compiled 4687 to 2990 computations (36.2% saved)

series1.6s (10.6%)

Error

0.1b

Counts

4 → 43

Calls

4 calls:

587.0ms	(sqrt.f64 (/.f64 1/4 (.f64 (.f64 l l) (+.f64 (pow.f64 (sin.f64 ky) 2) (pow.f64 (sin.f64 kx) 2)))))
382.0ms	(sqrt.f64 (.f64 4 (.f64 (*.f64 l l) (+.f64 (pow.f64 (sin.f64 ky) 2) (pow.f64 (sin.f64 kx) 2)))))
276.0ms	(.f64 (.f64 l l) (+.f64 (pow.f64 (sin.f64 ky) 2) (pow.f64 (sin.f64 kx) 2)))
254.0ms	(.f64 (.f64 l l) (+.f64 (pow.f64 (sin.f64 ky) 2) (pow.f64 (sin.f64 kx) 2)))

Compiler

Compiled 5517 to 4303 computations (22% saved)

simplify69.0ms (0.5%)

Algorithm

1×	egg-herbie

Counts

128 → 128

Iterations

Useful iterations: 0 (40.0ms)

Iter	Nodes	Cost
0	4971	2869
1	4971	2869

prune300.0ms (2%)

Pruning

3 alts after pruning (1 fresh and 2 done)

	Pruned	Kept	Total
New	128	0	128
Fresh	0	1	1
Picked	0	1	1
Done	0	1	1
Total	128	3	131

Error

0.1b

Counts

131 → 3

Compiler

Compiled 6222 to 4009 computations (35.6% saved)

localize26.0ms (0.2%)

Local error

Found 4 expressions with local error:

9.3b	(/.f64 (pow.f64 (sin.f64 ky) 2) (*.f64 Om Om))
9.3b	(/.f64 (pow.f64 (sin.f64 ky) 2) (*.f64 Om Om))
29.9b	(sqrt.f64 (.f64 4 (+.f64 (/.f64 (pow.f64 (sin.f64 ky) 2) (.f64 Om Om)) (/.f64 (pow.f64 (sin.f64 kx) 2) (*.f64 Om Om)))))
30.3b	(sqrt.f64 (/.f64 1/4 (+.f64 (/.f64 (pow.f64 (sin.f64 ky) 2) (.f64 Om Om)) (/.f64 (pow.f64 (sin.f64 kx) 2) (.f64 Om Om)))))

rewrite464.0ms (3.1%)

Algorithm

1×	rewrite-expression-head

Error

0.1b

Rules

50×	`times-frac_binary64_84`
41×	`*-un-lft-identity_binary64_78`
30×	`add-exp-log_binary64_116`
29×	`sqrt-prod_binary64_94`
26×	`add-sqr-sqrt_binary64_100`
23×	`add-cube-cbrt_binary64_113`
18×	`unpow-prod-down_binary64_157`
16×	`associate-/l*_binary64_23`
14×	`add-cbrt-cube_binary64_114`
12×	`div-exp_binary64_129`
9×	`div-inv_binary64_75` `distribute-lft-out_binary64_29`
8×	`pow1_binary64_139`
6×	`prod-exp_binary64_127`
4×	`add-log-exp_binary64_117` `sqrt-div_binary64_95` `pow-to-exp_binary64_147` `pow-exp_binary64_146` `cbrt-undiv_binary64_112` `unpow2_binary64_143` `sqr-pow_binary64_50`
3×	`sqrt-pow1_binary64_96` `distribute-rgt-out_binary64_31` `associate-/r/_binary64_24` `associate-*r/_binary64_20`
2×	`pow1/2_binary64_158` `frac-add_binary64_86` `flip3-+_binary64_81` `flip-+_binary64_52` `rem-sqrt-square_binary64_91` `cbrt-unprod_binary64_111` `frac-2neg_binary64_89` `clear-num_binary64_77` `associate-/r*_binary64_22`
1×	`pow-prod-down_binary64_149`

Counts

4 → 124

Calls

4 calls:

21.0ms	(sqrt.f64 (.f64 4 (+.f64 (/.f64 (pow.f64 (sin.f64 ky) 2) (.f64 Om Om)) (/.f64 (pow.f64 (sin.f64 kx) 2) (*.f64 Om Om)))))
21.0ms	(sqrt.f64 (/.f64 1/4 (+.f64 (/.f64 (pow.f64 (sin.f64 ky) 2) (.f64 Om Om)) (/.f64 (pow.f64 (sin.f64 kx) 2) (.f64 Om Om)))))
7.0ms	(/.f64 (pow.f64 (sin.f64 ky) 2) (*.f64 Om Om))
7.0ms	(/.f64 (pow.f64 (sin.f64 ky) 2) (*.f64 Om Om))

Compiler

Compiled 7750 to 4531 computations (41.5% saved)

series1.5s (10.2%)

Error

0.1b

Counts

4 → 35

Calls

4 calls:

730.0ms	(sqrt.f64 (/.f64 1/4 (+.f64 (/.f64 (pow.f64 (sin.f64 ky) 2) (.f64 Om Om)) (/.f64 (pow.f64 (sin.f64 kx) 2) (.f64 Om Om)))))
493.0ms	(sqrt.f64 (.f64 4 (+.f64 (/.f64 (pow.f64 (sin.f64 ky) 2) (.f64 Om Om)) (/.f64 (pow.f64 (sin.f64 kx) 2) (*.f64 Om Om)))))
118.0ms	(/.f64 (pow.f64 (sin.f64 ky) 2) (*.f64 Om Om))
114.0ms	(/.f64 (pow.f64 (sin.f64 ky) 2) (*.f64 Om Om))

Compiler

Compiled 5207 to 3760 computations (27.8% saved)

simplify80.0ms (0.5%)

Algorithm

1×	egg-herbie

Counts

159 → 159

Iterations

Useful iterations: 0 (44.0ms)

Iter	Nodes	Cost
0	5004	3565

prune626.0ms (4.2%)

Pruning

3 alts after pruning (0 fresh and 3 done)

	Pruned	Kept	Total
New	159	0	159
Fresh	0	0	0
Picked	0	1	1
Done	0	2	2
Total	159	3	162

Error

0.1b

Counts

162 → 3

Compiler

Compiled 8843 to 5318 computations (39.9% saved)

regimes1.1s (7.2%)

Accuracy

Total 0.8b remaining (81.1%)

Threshold costs 0.8b (81.1%)

Compiler

Compiled 13585 to 12315 computations (9.3% saved)

bsearch0.0ms (0%)

simplify11.0ms (0.1%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	28	39
1	28	39

Remove

(sort kx ky)

Compiler

Compiled 50 to 50 computations (0% saved)

end0.0ms (0%)

sample3.3s (22.2%)

Algorithm

1×

intervals

Results

1.1s	6339×	body	128	valid
697.0ms	797×	body	1024	valid
328.0ms	546×	body	512	valid
118.0ms	317×	body	256	valid
1.0ms	1×	body	2048	valid

Compiler

Compiled 730 to 662 computations (9.3% saved)

Details

analyze785.0ms (5.2%)

sample92.0ms (0.6%)

simplify47.0ms (0.3%)

prune5.0ms (0%)

localize19.0ms (0.1%)

rewrite309.0ms (2.1%)

series3.8s (25.6%)

simplify106.0ms (0.7%)

prune393.0ms (2.6%)

localize24.0ms (0.2%)

rewrite294.0ms (2%)

series1.6s (10.6%)

simplify69.0ms (0.5%)

prune300.0ms (2%)

localize26.0ms (0.2%)

rewrite464.0ms (3.1%)

series1.5s (10.2%)

simplify80.0ms (0.5%)

prune626.0ms (4.2%)

regimes1.1s (7.2%)

bsearch0.0ms (0%)

simplify11.0ms (0.1%)

end0.0ms (0%)

sample3.3s (22.2%)

Profiling