Details

analyze792.0ms (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)

sample97.0ms (0.5%)

Algorithm

1×

intervals

Results

38.0ms	203×	body	128	valid
23.0ms	29×	body	1024	valid
9.0ms	15×	body	512	valid
3.0ms	9×	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

1.3b

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 (/.f64 (*.f64 2 l) Om) 2)
0.4b	(/.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))))))
3.1b	(.f64 (pow.f64 (/.f64 (.f64 2 l) Om) 2) (+.f64 (pow.f64 (sin.f64 kx) 2) (pow.f64 (sin.f64 ky) 2)))
8.5b	(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)))))

rewrite337.0ms (1.7%)

Algorithm

1×	rewrite-expression-head

Error

1.1b

Rules

34×	`add-sqr-sqrt_binary64_100`
31×	`*-un-lft-identity_binary64_78`
27×	`add-cube-cbrt_binary64_113`
24×	`add-exp-log_binary64_116` `times-frac_binary64_84`
17×	`unpow-prod-down_binary64_157`
15×	`sqrt-prod_binary64_94`
12×	`associate-l_binary64_19`
8×	`add-cbrt-cube_binary64_114`
7×	`prod-exp_binary64_127`
6×	`pow1_binary64_139` `pow-exp_binary64_146` `associate-/r*_binary64_22`
5×	`div-exp_binary64_129` `associate-r_binary64_18`
4×	`add-log-exp_binary64_117` `sqrt-div_binary64_95` `unswap-sqr_binary64_46`
3×	`flip3-+_binary64_81` `flip-+_binary64_52` `unpow2_binary64_143` `sqr-pow_binary64_50` `div-inv_binary64_75` `associate-/l*_binary64_23` `pow-unpow_binary64_155`
2×	`pow-to-exp_binary64_147` `associate-*r/_binary64_20` `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 → 119

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))))))
5.0ms	(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)))))

Compiler

Compiled 4824 to 3662 computations (24.1% saved)

series3.5s (17.6%)

Error

0.6b

Counts

4 → 60

Calls

4 calls:

1.6s	(/.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)))))
571.0ms	(.f64 (pow.f64 (/.f64 (.f64 2 l) Om) 2) (+.f64 (pow.f64 (sin.f64 kx) 2) (pow.f64 (sin.f64 ky) 2)))
96.0ms	(pow.f64 (/.f64 (*.f64 2 l) Om) 2)

Compiler

Compiled 6438 to 5632 computations (12.5% saved)

simplify102.0ms (0.5%)

Algorithm

1×	egg-herbie

Counts

179 → 179

Iterations

Useful iterations: 0 (48.0ms)

Iter	Nodes	Cost
0	4959	6212
1	4959	6212

prune380.0ms (1.9%)

Pruning

3 alts after pruning (2 fresh and 1 done)

	Pruned	Kept	Total
New	177	2	179
Fresh	0	0	0
Picked	0	1	1
Done	0	0	0
Total	177	3	180

Error

Counts

180 → 3

Compiler

Compiled 6163 to 4404 computations (28.5% saved)

localize23.0ms (0.1%)

Local error

Found 4 expressions with local error:

0.4b	(/.f64 1/2 (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))))))
2.9b	(log.f64 (exp.f64 (/.f64 1/2 (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))))))))
3.1b	(.f64 (+.f64 (pow.f64 (sin.f64 ky) 2) (pow.f64 (sin.f64 kx) 2)) (.f64 4 (pow.f64 (/.f64 l Om) 2)))
8.5b	(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)))))

rewrite384.0ms (1.9%)

Algorithm

1×	rewrite-expression-head

Error

Rules

39×	`*-un-lft-identity_binary64_78`
36×	`add-sqr-sqrt_binary64_100` `times-frac_binary64_84`
35×	`add-cube-cbrt_binary64_113`
25×	`log-pow_binary64_167`
24×	`sqrt-prod_binary64_94` `exp-prod_binary64_130`
20×	`add-exp-log_binary64_116`
11×	`add-cbrt-cube_binary64_114`
9×	`prod-exp_binary64_127`
8×	`pow1_binary64_139`
6×	`sqrt-div_binary64_95` `associate-/r*_binary64_22`
5×	`associate-l_binary64_19`
4×	`add-log-exp_binary64_117` `flip3-+_binary64_81` `flip-+_binary64_52` `associate-/r/_binary64_24`
3×	`cbrt-unprod_binary64_111` `log-prod_binary64_164` `associate-/l*_binary64_23`
2×	`div-exp_binary64_129` `pow-exp_binary64_146` `associate-*l/_binary64_21` `unpow-prod-down_binary64_157` `distribute-lft-out_binary64_29` `div-inv_binary64_75`
1×	`pow1/2_binary64_158` `sqrt-pow1_binary64_96` `rem-sqrt-square_binary64_91` `pow-prod-down_binary64_149` `pow-to-exp_binary64_147` `associate-r_binary64_18` `*-commutative_binary64_9` `rem-log-exp_binary64_119` `cbrt-undiv_binary64_112` `frac-2neg_binary64_89` `clear-num_binary64_77`

Counts

4 → 116

Calls

4 calls:

17.0ms	(.f64 (+.f64 (pow.f64 (sin.f64 ky) 2) (pow.f64 (sin.f64 kx) 2)) (.f64 4 (pow.f64 (/.f64 l Om) 2)))
9.0ms	(log.f64 (exp.f64 (/.f64 1/2 (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))))))))
6.0ms	(/.f64 1/2 (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 5574 to 4093 computations (26.6% saved)

series5.9s (29.8%)

Error

Counts

4 → 71

Calls

4 calls:

2.6s	(log.f64 (exp.f64 (/.f64 1/2 (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))))))))
1.5s	(/.f64 1/2 (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)))))
583.0ms	(.f64 (+.f64 (pow.f64 (sin.f64 ky) 2) (pow.f64 (sin.f64 kx) 2)) (.f64 4 (pow.f64 (/.f64 l Om) 2)))

Compiler

Compiled 8182 to 7166 computations (12.4% saved)

simplify88.0ms (0.4%)

Algorithm

1×	egg-herbie

Counts

187 → 187

Iterations

Useful iterations: 0 (27.0ms)

Iter	Nodes	Cost
0	4995	7107
1	4995	7107

prune470.0ms (2.4%)

Pruning

3 alts after pruning (1 fresh and 2 done)

	Pruned	Kept	Total
New	187	0	187
Fresh	0	1	1
Picked	0	1	1
Done	0	1	1
Total	187	3	190

Error

Counts

190 → 3

Compiler

Compiled 6979 to 5112 computations (26.8% saved)

localize29.0ms (0.1%)

Local error

Found 4 expressions with local error:

3.7b	(/.f64 (pow.f64 (sin.f64 kx) 2) Om)
3.7b	(/.f64 (pow.f64 (sin.f64 kx) 2) Om)
30.3b	(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)))))
31.2b	(sqrt.f64 (*.f64 (/.f64 4 Om) (+.f64 (/.f64 (pow.f64 (sin.f64 ky) 2) Om) (/.f64 (pow.f64 (sin.f64 kx) 2) Om))))

rewrite626.0ms (3.2%)

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:

45.0ms	(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)))))
45.0ms	(sqrt.f64 (*.f64 (/.f64 4 Om) (+.f64 (/.f64 (pow.f64 (sin.f64 ky) 2) Om) (/.f64 (pow.f64 (sin.f64 kx) 2) Om))))
9.0ms	(/.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)

series1.5s (7.4%)

Error

Counts

4 → 34

Calls

4 calls:

658.0ms	(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)))))
513.0ms	(sqrt.f64 (*.f64 (/.f64 4 Om) (+.f64 (/.f64 (pow.f64 (sin.f64 ky) 2) Om) (/.f64 (pow.f64 (sin.f64 kx) 2) Om))))
117.0ms	(/.f64 (pow.f64 (sin.f64 kx) 2) Om)
108.0ms	(/.f64 (pow.f64 (sin.f64 kx) 2) Om)

Compiler

Compiled 4804 to 3658 computations (23.9% saved)

simplify79.0ms (0.4%)

Algorithm

1×	egg-herbie

Counts

178 → 178

Iterations

Useful iterations: 0 (41.0ms)

Iter	Nodes	Cost
0	4956	3627
1	4956	3627

prune679.0ms (3.4%)

Pruning

3 alts after pruning (0 fresh and 3 done)

	Pruned	Kept	Total
New	178	0	178
Fresh	0	0	0
Picked	0	1	1
Done	0	2	2
Total	178	3	181

Error

Counts

181 → 3

Compiler

Compiled 9774 to 6410 computations (34.4% saved)

regimes1.4s (6.9%)

Accuracy

Total 0.3b remaining (88.4%)

Threshold costs 0.3b (88.4%)

Compiler

Compiled 16412 to 15539 computations (5.3% saved)

bsearch3.0ms (0%)

Compiler: Compiled 7 to 9 computations (-28.6% saved)

simplify16.0ms (0.1%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	54	132
1	54	132

Remove

(sort kx ky)

Compiler

Compiled 170 to 134 computations (21.2% saved)

end0.0ms (0%)

sample3.4s (17.4%)

Algorithm

1×

intervals

Results

1.1s	6332×	body	128	valid
635.0ms	785×	body	1024	valid
335.0ms	576×	body	512	valid
112.0ms	305×	body	256	valid
2.0ms	2×	body	2048	valid

Compiler

Compiled 913 to 846 computations (7.3% saved)

Details

analyze792.0ms (4%)

sample97.0ms (0.5%)

simplify47.0ms (0.2%)

prune6.0ms (0%)

localize25.0ms (0.1%)

rewrite337.0ms (1.7%)

series3.5s (17.6%)

simplify102.0ms (0.5%)

prune380.0ms (1.9%)

localize23.0ms (0.1%)

rewrite384.0ms (1.9%)

series5.9s (29.8%)

simplify88.0ms (0.4%)

prune470.0ms (2.4%)

localize29.0ms (0.1%)

rewrite626.0ms (3.2%)

series1.5s (7.4%)

simplify79.0ms (0.4%)

prune679.0ms (3.4%)

regimes1.4s (6.9%)

bsearch3.0ms (0%)

simplify16.0ms (0.1%)

end0.0ms (0%)

sample3.4s (17.4%)

Profiling