Details

analyze775.0ms (3.9%)

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)

sample87.0ms (0.4%)

Algorithm

1×

intervals

Results

35.0ms	211×	body	128	valid
15.0ms	19×	body	1024	valid
8.0ms	14×	body	512	valid
4.0ms	12×	body	256	valid

Compiler

Compiled 59 to 63 computations (-6.8% saved)

simplify46.0ms (0.2%)

Algorithm

1×	egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (40.0ms)

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

0.8b

Counts

2 → 1

Compiler

Compiled 50 to 50 computations (0% saved)

localize18.0ms (0.1%)

Local error

Found 4 expressions with local error:

0.2b	(/.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))))))
0.2b	(pow.f64 (sin.f64 ky) 2)
2.0b	(.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)))))

rewrite325.0ms (1.6%)

Algorithm

1×	rewrite-expression-head

Error

0.5b

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` `pow-unpow_binary64_155` `associate-/l*_binary64_23`
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` `pow-pow_binary64_150` `cbrt-undiv_binary64_112` `frac-2neg_binary64_89` `clear-num_binary64_77`

Counts

4 → 113

Calls

4 calls:

17.0ms	(.f64 (pow.f64 (/.f64 (.f64 2 l) Om) 2) (+.f64 (pow.f64 (sin.f64 kx) 2) (pow.f64 (sin.f64 ky) 2)))
7.0ms	(/.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)

series3.2s (16.4%)

Error

0.0b

Counts

4 → 53

Calls

4 calls:

1.5s	(/.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))))))
1.1s	(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)))))
580.0ms	(.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 5625 to 4952 computations (12% saved)

simplify77.0ms (0.4%)

Algorithm

1×	egg-herbie

Counts

166 → 166

Iterations

Useful iterations: 0 (28.0ms)

Iter	Nodes	Cost
0	5060	5792

prune357.0ms (1.8%)

Pruning

3 alts after pruning (3 fresh and 0 done)

	Pruned	Kept	Total
New	163	3	166
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	164	3	167

Error

Counts

167 → 3

Compiler

Compiled 5749 to 4224 computations (26.5% saved)

localize21.0ms (0.1%)

Local error

Found 4 expressions with local error:

0.3b	(/.f64 (sqrt.f64 1/2) (sqrt.f64 (+.f64 1 (.f64 (+.f64 (pow.f64 (sin.f64 ky) 2) (pow.f64 (sin.f64 kx) 2)) (pow.f64 (/.f64 (.f64 2 l) Om) 2)))))
0.7b	(.f64 (sqrt.f64 1/2) (/.f64 (sqrt.f64 1/2) (sqrt.f64 (+.f64 1 (.f64 (+.f64 (pow.f64 (sin.f64 ky) 2) (pow.f64 (sin.f64 kx) 2)) (pow.f64 (/.f64 (*.f64 2 l) Om) 2))))))
2.0b	(.f64 (+.f64 (pow.f64 (sin.f64 ky) 2) (pow.f64 (sin.f64 kx) 2)) (pow.f64 (/.f64 (.f64 2 l) Om) 2))
7.3b	(sqrt.f64 (+.f64 1 (.f64 (+.f64 (pow.f64 (sin.f64 ky) 2) (pow.f64 (sin.f64 kx) 2)) (pow.f64 (/.f64 (.f64 2 l) Om) 2))))

rewrite771.0ms (3.9%)

Algorithm

1×	rewrite-expression-head

Error

Rules

99×	`add-sqr-sqrt_binary64_100`
97×	`sqrt-prod_binary64_94`
83×	`times-frac_binary64_84`
68×	`*-un-lft-identity_binary64_78`
64×	`add-cube-cbrt_binary64_113`
54×	`associate-r_binary64_18`
23×	`add-exp-log_binary64_116`
14×	`unswap-sqr_binary64_46`
13×	`add-cbrt-cube_binary64_114`
11×	`associate-l_binary64_19`
10×	`unpow-prod-down_binary64_157`
8×	`prod-exp_binary64_127`
7×	`pow1_binary64_139`
6×	`sqrt-div_binary64_95` `associate-/l_binary64_23` `associate-/r_binary64_22`
4×	`add-log-exp_binary64_117` `flip3-+_binary64_81` `flip-+_binary64_52` `div-exp_binary64_129` `associate-/r/_binary64_24`
3×	`pow-exp_binary64_146` `cbrt-unprod_binary64_111` `div-inv_binary64_75`
2×	`unpow2_binary64_143` `sqr-pow_binary64_50` `associate-l/_binary64_21` `distribute-lft-out_binary64_29` `-commutative_binary64_9` `cbrt-undiv_binary64_112` `sqrt-undiv_binary64_99`
1×	`pow1/2_binary64_158` `sqrt-pow1_binary64_96` `rem-sqrt-square_binary64_91` `pow-to-exp_binary64_147` `pow-prod-down_binary64_149` `sqrt-unprod_binary64_98` `associate-*r/_binary64_20` `frac-2neg_binary64_89` `clear-num_binary64_77`

Counts

4 → 188

Calls

4 calls:

26.0ms	(.f64 (sqrt.f64 1/2) (/.f64 (sqrt.f64 1/2) (sqrt.f64 (+.f64 1 (.f64 (+.f64 (pow.f64 (sin.f64 ky) 2) (pow.f64 (sin.f64 kx) 2)) (pow.f64 (/.f64 (*.f64 2 l) Om) 2))))))
18.0ms	(.f64 (+.f64 (pow.f64 (sin.f64 ky) 2) (pow.f64 (sin.f64 kx) 2)) (pow.f64 (/.f64 (.f64 2 l) Om) 2))
8.0ms	(/.f64 (sqrt.f64 1/2) (sqrt.f64 (+.f64 1 (.f64 (+.f64 (pow.f64 (sin.f64 ky) 2) (pow.f64 (sin.f64 kx) 2)) (pow.f64 (/.f64 (.f64 2 l) Om) 2)))))
4.0ms	(sqrt.f64 (+.f64 1 (.f64 (+.f64 (pow.f64 (sin.f64 ky) 2) (pow.f64 (sin.f64 kx) 2)) (pow.f64 (/.f64 (.f64 2 l) Om) 2))))

Compiler

Compiled 9537 to 7514 computations (21.2% saved)

series4.9s (24.6%)

Error

Counts

4 → 65

Calls

4 calls:

1.5s	(.f64 (sqrt.f64 1/2) (/.f64 (sqrt.f64 1/2) (sqrt.f64 (+.f64 1 (.f64 (+.f64 (pow.f64 (sin.f64 ky) 2) (pow.f64 (sin.f64 kx) 2)) (pow.f64 (/.f64 (*.f64 2 l) Om) 2))))))
1.5s	(/.f64 (sqrt.f64 1/2) (sqrt.f64 (+.f64 1 (.f64 (+.f64 (pow.f64 (sin.f64 ky) 2) (pow.f64 (sin.f64 kx) 2)) (pow.f64 (/.f64 (.f64 2 l) Om) 2)))))
1.1s	(sqrt.f64 (+.f64 1 (.f64 (+.f64 (pow.f64 (sin.f64 ky) 2) (pow.f64 (sin.f64 kx) 2)) (pow.f64 (/.f64 (.f64 2 l) Om) 2))))
603.0ms	(.f64 (+.f64 (pow.f64 (sin.f64 ky) 2) (pow.f64 (sin.f64 kx) 2)) (pow.f64 (/.f64 (.f64 2 l) Om) 2))

Compiler

Compiled 7886 to 7036 computations (10.8% saved)

simplify136.0ms (0.7%)

Algorithm

1×	egg-herbie

Counts

253 → 253

Iterations

Useful iterations: 0 (52.0ms)

Iter	Nodes	Cost
0	4977	10845
1	4977	10845

prune895.0ms (4.5%)

Pruning

3 alts after pruning (2 fresh and 1 done)

	Pruned	Kept	Total
New	253	0	253
Fresh	0	2	2
Picked	0	1	1
Done	0	0	0
Total	253	3	256

Error

Counts

256 → 3

Compiler

Compiled 10569 to 8137 computations (23% saved)

localize2.0ms (0%)

rewrite1.0ms (0%)

Algorithm

1×	rewrite-expression-head

Error

Counts

0 → 0

Compiler

Compiled 0 to 0 computations (0% saved)

series1.0ms (0%)

Error: 0b
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

3 alts after pruning (1 fresh and 2 done)

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

Error

Counts

3 → 3

Compiler

Compiled 50 to 40 computations (20% saved)

localize27.0ms (0.1%)

Local error

Found 4 expressions with local error:

4.0b	(/.f64 (pow.f64 (sin.f64 kx) 2) Om)
4.0b	(/.f64 (pow.f64 (sin.f64 kx) 2) Om)
25.2b	(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)))))
25.3b	(sqrt.f64 (*.f64 (/.f64 4 Om) (+.f64 (/.f64 (pow.f64 (sin.f64 ky) 2) Om) (/.f64 (pow.f64 (sin.f64 kx) 2) Om))))

rewrite600.0ms (3%)

Algorithm

1×	rewrite-expression-head

Error

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` `associate-*l/_binary64_21` `pow-flip_binary64_152` `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:

52.0ms	(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)))))
49.0ms	(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 kx) 2) Om)
6.0ms	(/.f64 (pow.f64 (sin.f64 kx) 2) Om)

Compiler

Compiled 8686 to 5765 computations (33.6% saved)

series1.6s (8.3%)

Error

Counts

4 → 36

Calls

4 calls:

774.0ms	(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)))))
523.0ms	(sqrt.f64 (*.f64 (/.f64 4 Om) (+.f64 (/.f64 (pow.f64 (sin.f64 ky) 2) Om) (/.f64 (pow.f64 (sin.f64 kx) 2) Om))))
124.0ms	(/.f64 (pow.f64 (sin.f64 kx) 2) Om)
120.0ms	(/.f64 (pow.f64 (sin.f64 kx) 2) Om)

Compiler

Compiled 5182 to 3926 computations (24.2% saved)

simplify60.0ms (0.3%)

Algorithm

1×	egg-herbie

Counts

180 → 180

Iterations

Useful iterations: 0 (23.0ms)

Iter	Nodes	Cost
0	5144	3765

prune588.0ms (3%)

Pruning

3 alts after pruning (0 fresh and 3 done)

	Pruned	Kept	Total
New	180	0	180
Fresh	0	0	0
Picked	0	1	1
Done	0	2	2
Total	180	3	183

Error

Counts

183 → 3

Compiler

Compiled 9924 to 6504 computations (34.5% saved)

regimes1.6s (8.2%)

Accuracy

Total 0.8b remaining (95%)

Threshold costs 0.8b (95%)

Compiler

Compiled 21400 to 20192 computations (5.6% saved)

bsearch0.0ms (0%)

simplify12.0ms (0.1%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	29	65
1	29	65

Remove

(sort kx ky)

Compiler

Compiled 82 to 70 computations (14.6% saved)

end0.0ms (0%)

sample3.6s (18.2%)

Algorithm

1×

intervals

Results

1.1s	6338×	body	128	valid
643.0ms	766×	body	1024	valid
346.0ms	581×	body	512	valid
116.0ms	315×	body	256	valid

Compiler

Compiled 1082 to 1011 computations (6.6% saved)

Details

analyze775.0ms (3.9%)

sample87.0ms (0.4%)

simplify46.0ms (0.2%)

prune5.0ms (0%)

localize18.0ms (0.1%)

rewrite325.0ms (1.6%)

series3.2s (16.4%)

simplify77.0ms (0.4%)

prune357.0ms (1.8%)

localize21.0ms (0.1%)

rewrite771.0ms (3.9%)

series4.9s (24.6%)

simplify136.0ms (0.7%)

prune895.0ms (4.5%)

localize2.0ms (0%)

rewrite1.0ms (0%)

series1.0ms (0%)

simplify6.0ms (0%)

prune3.0ms (0%)

localize27.0ms (0.1%)

rewrite600.0ms (3%)

series1.6s (8.3%)

simplify60.0ms (0.3%)

prune588.0ms (3%)

regimes1.6s (8.2%)

bsearch0.0ms (0%)

simplify12.0ms (0.1%)

end0.0ms (0%)

sample3.6s (18.2%)

Profiling