Details

analyze1.0s (4.9%)

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)

sample106.0ms (0.5%)

Algorithm

1×

intervals

Results

46.0ms	210×	body	128	valid
22.0ms	22×	body	1024	valid
11.0ms	17×	body	512	valid
3.0ms	7×	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

0.3b

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)
0.4b	(/.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))))))
1.1b	(.f64 (pow.f64 (/.f64 (.f64 2 l) Om) 2) (+.f64 (pow.f64 (sin.f64 kx) 2) (pow.f64 (sin.f64 ky) 2)))
7.7b	(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)))))

rewrite363.0ms (1.8%)

Algorithm

1×	rewrite-expression-head

Error

0.3b

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:

28.0ms	(.f64 (pow.f64 (/.f64 (.f64 2 l) Om) 2) (+.f64 (pow.f64 (sin.f64 kx) 2) (pow.f64 (sin.f64 ky) 2)))
13.0ms	(/.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))))))
6.0ms	(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)))))

Compiler

Compiled 4614 to 3499 computations (24.2% saved)

series3.6s (17.4%)

Error

0.0b

Counts

4 → 55

Calls

4 calls:

1.7s	(/.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)))))
671.0ms	(.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 5736 to 5034 computations (12.2% saved)

simplify77.0ms (0.4%)

Algorithm

1×	egg-herbie

Counts

168 → 168

Iterations

Useful iterations: 0 (27.0ms)

Iter	Nodes	Cost
0	5062	5785

prune345.0ms (1.7%)

Pruning

2 alts after pruning (2 fresh and 0 done)

	Pruned	Kept	Total
New	166	2	168
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	167	2	169

Error

0.0b

Counts

169 → 2

Compiler

Compiled 5744 to 4206 computations (26.8% saved)

localize22.0ms (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)) (pow.f64 (/.f64 (.f64 2 l) Om) 2)))))
1.1b	(.f64 (+.f64 (pow.f64 (sin.f64 ky) 2) (pow.f64 (sin.f64 kx) 2)) (pow.f64 (/.f64 (.f64 2 l) Om) 2))
3.7b	(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)) (pow.f64 (/.f64 (.f64 2 l) Om) 2)))))))
7.7b	(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))))

rewrite444.0ms (2.1%)

Algorithm

1×	rewrite-expression-head

Error

0.0b

Rules

45×	`add-sqr-sqrt_binary64_100`
42×	`*-un-lft-identity_binary64_78`
39×	`times-frac_binary64_84`
38×	`add-cube-cbrt_binary64_113`
25×	`log-pow_binary64_167`
24×	`sqrt-prod_binary64_94` `exp-prod_binary64_130`
18×	`add-exp-log_binary64_116`
12×	`associate-r_binary64_18`
10×	`unpow-prod-down_binary64_157`
8×	`add-cbrt-cube_binary64_114`
6×	`pow1_binary64_139` `sqrt-div_binary64_95` `prod-exp_binary64_127` `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` `unswap-sqr_binary64_46`
3×	`div-inv_binary64_75` `log-prod_binary64_164` `div-exp_binary64_129` `pow-exp_binary64_146` `associate-/l*_binary64_23`
2×	`unpow2_binary64_143` `sqr-pow_binary64_50` `associate-*l/_binary64_21` `distribute-lft-out_binary64_29`
1×	`pow1/2_binary64_158` `sqrt-pow1_binary64_96` `rem-sqrt-square_binary64_91` `rem-log-exp_binary64_119` `pow-to-exp_binary64_147` `cbrt-unprod_binary64_111` `*-commutative_binary64_9` `cbrt-undiv_binary64_112` `frac-2neg_binary64_89` `clear-num_binary64_77`

Counts

4 → 129

Calls

4 calls:

18.0ms	(.f64 (+.f64 (pow.f64 (sin.f64 ky) 2) (pow.f64 (sin.f64 kx) 2)) (pow.f64 (/.f64 (.f64 2 l) Om) 2))
10.0ms	(/.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)))))
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)) (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 6069 to 4682 computations (22.9% saved)

series6.2s (29.9%)

Error

0.0b

Counts

4 → 67

Calls

4 calls:

2.9s	(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)) (pow.f64 (/.f64 (.f64 2 l) Om) 2)))))))
1.4s	(/.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))))
597.0ms	(.f64 (+.f64 (pow.f64 (sin.f64 ky) 2) (pow.f64 (sin.f64 kx) 2)) (pow.f64 (/.f64 (.f64 2 l) Om) 2))

Compiler

Compiled 7390 to 6518 computations (11.8% saved)

simplify134.0ms (0.6%)

Algorithm

1×	egg-herbie

Counts

196 → 196

Iterations

Useful iterations: 0 (40.0ms)

Iter	Nodes	Cost
0	4966	7334
1	4966	7334

prune615.0ms (3%)

Pruning

2 alts after pruning (1 fresh and 1 done)

	Pruned	Kept	Total
New	196	0	196
Fresh	0	1	1
Picked	0	1	1
Done	0	0	0
Total	196	2	198

Error

0.0b

Counts

198 → 2

Compiler

Compiled 7323 to 5477 computations (25.2% saved)

localize27.0ms (0.1%)

Local error

Found 4 expressions with local error:

4.8b	(/.f64 (pow.f64 (sin.f64 kx) 2) Om)
4.8b	(/.f64 (pow.f64 (sin.f64 kx) 2) Om)
29.9b	(sqrt.f64 (*.f64 (/.f64 4 Om) (+.f64 (/.f64 (pow.f64 (sin.f64 ky) 2) Om) (/.f64 (pow.f64 (sin.f64 kx) 2) Om))))
30.0b	(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)))))

rewrite695.0ms (3.4%)

Algorithm

1×	rewrite-expression-head

Error

0.0b

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

Compiler

Compiled 8686 to 5765 computations (33.6% saved)

series1.7s (8%)

Error

0.0b

Counts

4 → 36

Calls

4 calls:

767.0ms	(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)))))
569.0ms	(sqrt.f64 (*.f64 (/.f64 4 Om) (+.f64 (/.f64 (pow.f64 (sin.f64 ky) 2) Om) (/.f64 (pow.f64 (sin.f64 kx) 2) Om))))
121.0ms	(/.f64 (pow.f64 (sin.f64 kx) 2) Om)
114.0ms	(/.f64 (pow.f64 (sin.f64 kx) 2) Om)

Compiler

Compiled 5107 to 3869 computations (24.2% saved)

simplify61.0ms (0.3%)

Algorithm

1×	egg-herbie

Counts

180 → 180

Iterations

Useful iterations: 0 (23.0ms)

Iter	Nodes	Cost
0	5090	3825

prune565.0ms (2.7%)

Pruning

2 alts after pruning (0 fresh and 2 done)

	Pruned	Kept	Total
New	180	0	180
Fresh	0	0	0
Picked	0	1	1
Done	0	1	1
Total	180	2	182

Error

0.0b

Counts

182 → 2

Compiler

Compiled 9963 to 6531 computations (34.4% saved)

regimes1.1s (5.1%)

Accuracy

Total 1.1b remaining (97.3%)

Threshold costs 0b (0%)

Compiler

Compiled 10583 to 10225 computations (3.4% saved)

bsearch0.0ms (0%)

simplify12.0ms (0.1%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	30	43
1	30	43

Remove

(sort kx ky)

Compiler

Compiled 54 to 54 computations (0% saved)

end0.0ms (0%)

sample3.7s (17.7%)

Algorithm

1×

intervals

Results

1.3s	6302×	body	128	valid
773.0ms	776×	body	1024	valid
414.0ms	598×	body	512	valid
154.0ms	323×	body	256	valid
3.0ms	1×	body	2048	valid

Compiler

Compiled 574 to 554 computations (3.5% saved)

Details

analyze1.0s (4.9%)

sample106.0ms (0.5%)

simplify46.0ms (0.2%)

prune5.0ms (0%)

localize19.0ms (0.1%)

rewrite363.0ms (1.8%)

series3.6s (17.4%)

simplify77.0ms (0.4%)

prune345.0ms (1.7%)

localize22.0ms (0.1%)

rewrite444.0ms (2.1%)

series6.2s (29.9%)

simplify134.0ms (0.6%)

prune615.0ms (3%)

localize27.0ms (0.1%)

rewrite695.0ms (3.4%)

series1.7s (8%)

simplify61.0ms (0.3%)

prune565.0ms (2.7%)

regimes1.1s (5.1%)

bsearch0.0ms (0%)

simplify12.0ms (0.1%)

end0.0ms (0%)

sample3.7s (17.7%)

Profiling