Details

analyze790.0ms (7.3%)

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)

sample96.0ms (0.9%)

Algorithm

1×

intervals

Results

35.0ms	201×	body	128	valid
25.0ms	31×	body	1024	valid
8.0ms	15×	body	512	valid
6.0ms	9×	body	256	valid

Compiler

Compiled 59 to 63 computations (-6.8% saved)

simplify47.0ms (0.4%)

Algorithm

1×	egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (41.0ms)

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)

localize18.0ms (0.2%)

Local error

Found 4 expressions with local error:

0.3b	(pow.f64 (sin.f64 kx) 2)
0.3b	(pow.f64 (sin.f64 ky) 2)
2.9b	(.f64 (pow.f64 (/.f64 (.f64 2 l) Om) 2) (+.f64 (pow.f64 (sin.f64 kx) 2) (pow.f64 (sin.f64 ky) 2)))
8.1b	(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)))))

rewrite211.0ms (2%)

Algorithm

1×	rewrite-expression-head

Error

0.9b

Rules

20×	`add-sqr-sqrt_binary64_100`
18×	`add-exp-log_binary64_116`
17×	`*-un-lft-identity_binary64_78`
16×	`unpow-prod-down_binary64_157`
13×	`add-cube-cbrt_binary64_113`
12×	`associate-l_binary64_19`
7×	`pow1_binary64_139`
6×	`add-cbrt-cube_binary64_114` `prod-exp_binary64_127` `pow-unpow_binary64_155`
5×	`pow-exp_binary64_146` `associate-r_binary64_18`
4×	`add-log-exp_binary64_117` `unswap-sqr_binary64_46` `unpow2_binary64_143` `sqr-pow_binary64_50`
3×	`sqrt-prod_binary64_94` `pow-to-exp_binary64_147` `times-frac_binary64_84`
2×	`flip3-+_binary64_81` `sqrt-div_binary64_95` `flip-+_binary64_52` `div-exp_binary64_129` `associate-*r/_binary64_20` `distribute-lft-out_binary64_29` `pow-pow_binary64_150`
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` `div-inv_binary64_75` `*-commutative_binary64_9`

Counts

4 → 90

Calls

4 calls:

19.0ms	(.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)
3.0ms	(pow.f64 (sin.f64 kx) 2)

Compiler

Compiled 3187 to 2402 computations (24.6% saved)

series1.9s (17.7%)

Error

0.4b

Counts

4 → 43

Calls

4 calls:

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)))))
577.0ms	(.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)
23.0ms	(pow.f64 (sin.f64 kx) 2)

Compiler

Compiled 4669 to 4042 computations (13.4% saved)

simplify80.0ms (0.7%)

Algorithm

1×	egg-herbie

Counts

133 → 133

Iterations

Useful iterations: 0 (48.0ms)

Iter	Nodes	Cost
0	5071	3473

prune241.0ms (2.2%)

Pruning

2 alts after pruning (1 fresh and 1 done)

	Pruned	Kept	Total
New	132	1	133
Fresh	0	0	0
Picked	0	1	1
Done	0	0	0
Total	132	2	134

Error

Counts

134 → 2

Compiler

Compiled 4255 to 3072 computations (27.8% saved)

localize27.0ms (0.2%)

Local error

Found 4 expressions with local error:

4.4b	(/.f64 (pow.f64 (sin.f64 ky) 2) Om)
4.4b	(/.f64 (pow.f64 (sin.f64 ky) 2) Om)
29.4b	(sqrt.f64 (*.f64 (/.f64 4 Om) (+.f64 (/.f64 (pow.f64 (sin.f64 ky) 2) Om) (/.f64 (pow.f64 (sin.f64 kx) 2) Om))))
29.8b	(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)))))

rewrite624.0ms (5.8%)

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` `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:

46.0ms	(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)))))
41.0ms	(sqrt.f64 (*.f64 (/.f64 4 Om) (+.f64 (/.f64 (pow.f64 (sin.f64 ky) 2) Om) (/.f64 (pow.f64 (sin.f64 kx) 2) Om))))
8.0ms	(/.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)

series1.6s (14.6%)

Error

Counts

4 → 35

Calls

4 calls:

700.0ms	(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)))))
567.0ms	(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 ky) 2) Om)
115.0ms	(/.f64 (pow.f64 (sin.f64 ky) 2) Om)

Compiler

Compiled 4983 to 3778 computations (24.2% saved)

simplify92.0ms (0.9%)

Algorithm

1×	egg-herbie

Counts

179 → 179

Iterations

Useful iterations: 0 (53.0ms)

Iter	Nodes	Cost
0	4968	3678
1	4968	3678

prune598.0ms (5.5%)

Pruning

2 alts after pruning (0 fresh and 2 done)

	Pruned	Kept	Total
New	179	0	179
Fresh	0	0	0
Picked	0	1	1
Done	0	1	1
Total	179	2	181

Error

Counts

181 → 2

Compiler

Compiled 9839 to 6448 computations (34.5% saved)

regimes1.1s (10.6%)

Accuracy

Total 0.2b remaining (81.7%)

Threshold costs 0.2b (81.7%)

Compiler

Compiled 12544 to 11790 computations (6% saved)

bsearch2.0ms (0%)

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

simplify18.0ms (0.2%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	56	135
1	56	135

Remove

(sort kx ky)

Compiler

Compiled 174 to 138 computations (20.7% saved)

end0.0ms (0%)

sample3.3s (30.6%)

Algorithm

1×

intervals

Results

1.1s	6371×	body	128	valid
639.0ms	747×	body	1024	valid
336.0ms	564×	body	512	valid
129.0ms	318×	body	256	valid

Compiler

Compiled 715 to 656 computations (8.3% saved)

Details

analyze790.0ms (7.3%)

sample96.0ms (0.9%)

simplify47.0ms (0.4%)

prune5.0ms (0%)

localize18.0ms (0.2%)

rewrite211.0ms (2%)

series1.9s (17.7%)

simplify80.0ms (0.7%)

prune241.0ms (2.2%)

localize27.0ms (0.2%)

rewrite624.0ms (5.8%)

series1.6s (14.6%)

simplify92.0ms (0.9%)

prune598.0ms (5.5%)

regimes1.1s (10.6%)

bsearch2.0ms (0%)

simplify18.0ms (0.2%)

end0.0ms (0%)

sample3.3s (30.6%)

Profiling