Details

analyze862.0ms (4%)

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)

sample95.0ms (0.4%)

Algorithm

1×

intervals

Results

36.0ms	203×	body	128	valid
19.0ms	24×	body	1024	valid
9.0ms	15×	body	512	valid
8.0ms	14×	body	256	valid

Compiler

Compiled 59 to 63 computations (-6.8% saved)

simplify47.0ms (0.2%)

Algorithm

1×	egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (41.0ms)

Iter	Nodes	Cost
0	5325	39

prune6.0ms (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

1.4b

Counts

2 → 1

Compiler

Compiled 50 to 50 computations (0% saved)

localize25.0ms (0.1%)

Local error

Found 4 expressions with local error:

0.3b	(pow.f64 (sin.f64 ky) 2)
0.3b	(/.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)))
8.7b	(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)))))

rewrite339.0ms (1.6%)

Algorithm

1×	rewrite-expression-head

Error

1.0b

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:

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)

series4.5s (20.8%)

Error

0.5b

Counts

4 → 52

Calls

4 calls:

2.1s	(/.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))))))
1.4s	(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)))))
860.0ms	(.f64 (pow.f64 (/.f64 (.f64 2 l) Om) 2) (+.f64 (pow.f64 (sin.f64 kx) 2) (pow.f64 (sin.f64 ky) 2)))
33.0ms	(pow.f64 (sin.f64 ky) 2)

Compiler

Compiled 5406 to 4776 computations (11.7% saved)

simplify77.0ms (0.4%)

Algorithm

1×	egg-herbie

Counts

165 → 165

Iterations

Useful iterations: 0 (27.0ms)

Iter	Nodes	Cost
0	4997	5689
1	4997	5689

prune399.0ms (1.8%)

Pruning

2 alts after pruning (2 fresh and 0 done)

	Pruned	Kept	Total
New	163	2	165
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	164	2	166

Error

0.2b

Counts

166 → 2

Compiler

Compiled 5674 to 4167 computations (26.6% saved)

localize20.0ms (0.1%)

Local error

Found 4 expressions with local error:

0.3b	(/.f64 1/2 (sqrt.f64 (+.f64 1 (.f64 (/.f64 (.f64 2 l) Om) (.f64 (+.f64 (pow.f64 (sin.f64 ky) 2) (pow.f64 (sin.f64 kx) 2)) (/.f64 (.f64 2 l) Om))))))
0.4b	(.f64 (/.f64 (.f64 2 l) Om) (.f64 (+.f64 (pow.f64 (sin.f64 ky) 2) (pow.f64 (sin.f64 kx) 2)) (/.f64 (.f64 2 l) Om)))
2.2b	(.f64 (+.f64 (pow.f64 (sin.f64 ky) 2) (pow.f64 (sin.f64 kx) 2)) (/.f64 (.f64 2 l) Om))
8.7b	(sqrt.f64 (+.f64 1 (.f64 (/.f64 (.f64 2 l) Om) (.f64 (+.f64 (pow.f64 (sin.f64 ky) 2) (pow.f64 (sin.f64 kx) 2)) (/.f64 (.f64 2 l) Om)))))

rewrite499.0ms (2.3%)

Algorithm

1×	rewrite-expression-head

Error

0.2b

Rules

69×	`add-exp-log_binary64_116` `add-cbrt-cube_binary64_114`
32×	`prod-exp_binary64_127` `cbrt-unprod_binary64_111`
29×	`*-un-lft-identity_binary64_78`
28×	`add-sqr-sqrt_binary64_100`
25×	`add-cube-cbrt_binary64_113`
24×	`times-frac_binary64_84`
17×	`div-exp_binary64_129` `cbrt-undiv_binary64_112`
15×	`sqrt-prod_binary64_94`
12×	`pow1_binary64_139` `associate-l_binary64_19`
11×	`frac-times_binary64_88`
8×	`flip3-+_binary64_81` `flip-+_binary64_52` `associate-r/_binary64_20` `associate-r*_binary64_18`
7×	`associate-*l/_binary64_21`
6×	`associate-/r*_binary64_22`
4×	`add-log-exp_binary64_117` `sqrt-div_binary64_95` `pow-prod-down_binary64_149`
3×	`div-inv_binary64_75` `associate-/l*_binary64_23`
2×	`unpow-prod-down_binary64_157` `distribute-lft-out_binary64_29` `*-commutative_binary64_9` `associate-/r/_binary64_24`
1×	`pow1/2_binary64_158` `sqrt-pow1_binary64_96` `rem-sqrt-square_binary64_91` `unswap-sqr_binary64_46` `frac-2neg_binary64_89` `clear-num_binary64_77`

Counts

4 → 142

Calls

4 calls:

21.0ms	(.f64 (/.f64 (.f64 2 l) Om) (.f64 (+.f64 (pow.f64 (sin.f64 ky) 2) (pow.f64 (sin.f64 kx) 2)) (/.f64 (.f64 2 l) Om)))
19.0ms	(.f64 (+.f64 (pow.f64 (sin.f64 ky) 2) (pow.f64 (sin.f64 kx) 2)) (/.f64 (.f64 2 l) Om))
7.0ms	(/.f64 1/2 (sqrt.f64 (+.f64 1 (.f64 (/.f64 (.f64 2 l) Om) (.f64 (+.f64 (pow.f64 (sin.f64 ky) 2) (pow.f64 (sin.f64 kx) 2)) (/.f64 (.f64 2 l) Om))))))
4.0ms	(sqrt.f64 (+.f64 1 (.f64 (/.f64 (.f64 2 l) Om) (.f64 (+.f64 (pow.f64 (sin.f64 ky) 2) (pow.f64 (sin.f64 kx) 2)) (/.f64 (.f64 2 l) Om)))))

Compiler

Compiled 6964 to 4909 computations (29.5% saved)

series5.3s (24.4%)

Error

0.2b

Counts

4 → 63

Calls

4 calls:

2.1s	(/.f64 1/2 (sqrt.f64 (+.f64 1 (.f64 (/.f64 (.f64 2 l) Om) (.f64 (+.f64 (pow.f64 (sin.f64 ky) 2) (pow.f64 (sin.f64 kx) 2)) (/.f64 (.f64 2 l) Om))))))
1.4s	(sqrt.f64 (+.f64 1 (.f64 (/.f64 (.f64 2 l) Om) (.f64 (+.f64 (pow.f64 (sin.f64 ky) 2) (pow.f64 (sin.f64 kx) 2)) (/.f64 (.f64 2 l) Om)))))
869.0ms	(.f64 (/.f64 (.f64 2 l) Om) (.f64 (+.f64 (pow.f64 (sin.f64 ky) 2) (pow.f64 (sin.f64 kx) 2)) (/.f64 (.f64 2 l) Om)))
751.0ms	(.f64 (+.f64 (pow.f64 (sin.f64 ky) 2) (pow.f64 (sin.f64 kx) 2)) (/.f64 (.f64 2 l) Om))

Compiler

Compiled 6392 to 5600 computations (12.4% saved)

simplify113.0ms (0.5%)

Algorithm

1×	egg-herbie

Counts

205 → 205

Iterations

Useful iterations: 0 (50.0ms)

Iter	Nodes	Cost
0	5072	7478

prune450.0ms (2.1%)

Pruning

2 alts after pruning (1 fresh and 1 done)

	Pruned	Kept	Total
New	205	0	205
Fresh	0	1	1
Picked	0	1	1
Done	0	0	0
Total	205	2	207

Error

0.2b

Counts

207 → 2

Compiler

Compiled 7328 to 5112 computations (30.2% saved)

localize28.0ms (0.1%)

Local error

Found 4 expressions with local error:

4.2b	(/.f64 (pow.f64 (sin.f64 ky) 2) Om)
4.2b	(/.f64 (pow.f64 (sin.f64 ky) 2) Om)
26.6b	(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)))))
26.7b	(sqrt.f64 (*.f64 (/.f64 4 Om) (+.f64 (/.f64 (pow.f64 (sin.f64 ky) 2) Om) (/.f64 (pow.f64 (sin.f64 kx) 2) Om))))

rewrite638.0ms (3%)

Algorithm

1×	rewrite-expression-head

Error

0.2b

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:

51.0ms	(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)

series2.2s (10%)

Error

0.2b

Counts

4 → 34

Calls

4 calls:

984.0ms	(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)))))
771.0ms	(sqrt.f64 (*.f64 (/.f64 4 Om) (+.f64 (/.f64 (pow.f64 (sin.f64 ky) 2) Om) (/.f64 (pow.f64 (sin.f64 kx) 2) Om))))
169.0ms	(/.f64 (pow.f64 (sin.f64 ky) 2) Om)
162.0ms	(/.f64 (pow.f64 (sin.f64 ky) 2) Om)

Compiler

Compiled 4804 to 3658 computations (23.9% saved)

simplify88.0ms (0.4%)

Algorithm

1×	egg-herbie

Counts

178 → 178

Iterations

Useful iterations: 0 (51.0ms)

Iter	Nodes	Cost
0	4968	3627
1	4968	3627

prune780.0ms (3.6%)

Pruning

2 alts after pruning (0 fresh and 2 done)

	Pruned	Kept	Total
New	178	0	178
Fresh	0	0	0
Picked	0	1	1
Done	0	1	1
Total	178	2	180

Error

0.2b

Counts

180 → 2

Compiler

Compiled 9774 to 6410 computations (34.4% saved)

regimes1.6s (7.6%)

Accuracy

Total 0.7b remaining (91.2%)

Threshold costs 0.7b (91.2%)

Compiler

Compiled 18575 to 17359 computations (6.5% saved)

bsearch0.0ms (0%)

simplify15.0ms (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 (16.5%)

Algorithm

1×

intervals

Results

1.1s	6374×	body	128	valid
643.0ms	760×	body	1024	valid
326.0ms	547×	body	512	valid
132.0ms	319×	body	256	valid

Compiler

Compiled 986 to 913 computations (7.4% saved)

Details

analyze862.0ms (4%)

sample95.0ms (0.4%)

simplify47.0ms (0.2%)

prune6.0ms (0%)

localize25.0ms (0.1%)

rewrite339.0ms (1.6%)

series4.5s (20.8%)

simplify77.0ms (0.4%)

prune399.0ms (1.8%)

localize20.0ms (0.1%)

rewrite499.0ms (2.3%)

series5.3s (24.4%)

simplify113.0ms (0.5%)

prune450.0ms (2.1%)

localize28.0ms (0.1%)

rewrite638.0ms (3%)

series2.2s (10%)

simplify88.0ms (0.4%)

prune780.0ms (3.6%)

regimes1.6s (7.6%)

bsearch0.0ms (0%)

simplify15.0ms (0.1%)

end0.0ms (0%)

sample3.6s (16.5%)

Profiling