Details

analyze604.0ms (6%)

Algorithm

1×

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

Compiler

Compiled 30 to 30 computations (0% saved)

sample81.0ms (0.8%)

Algorithm

1×

intervals

Results

34.0ms	206×	body	128	valid
21.0ms	27×	body	1024	valid
8.0ms	13×	body	512	valid
4.0ms	10×	body	256	valid

Compiler

Compiled 59 to 63 computations (-6.8% saved)

simplify140.0ms (1.4%)

Algorithm

1×	egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (42.0ms)

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)

localize19.0ms (0.2%)

Local error

Found 4 expressions with local error:

0.3b	(pow.f64 (/.f64 (*.f64 2 l) Om) 2)
0.3b	(pow.f64 (sin.f64 ky) 2)
1.7b	(.f64 (pow.f64 (/.f64 (.f64 2 l) Om) 2) (+.f64 (pow.f64 (sin.f64 kx) 2) (pow.f64 (sin.f64 ky) 2)))
7.8b	(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)))))

rewrite230.0ms (2.3%)

Algorithm

1×	rewrite-expression-head

Error

0.6b

Rules

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

Counts

4 → 96

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)))
8.0ms	(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)))))
3.0ms	(pow.f64 (sin.f64 ky) 2)

Compiler

Compiled 3397 to 2565 computations (24.5% saved)

series1.7s (17%)

Error

Counts

4 → 43

Calls

4 calls:

970.0ms	(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)))))
574.0ms	(.f64 (pow.f64 (/.f64 (.f64 2 l) Om) 2) (+.f64 (pow.f64 (sin.f64 kx) 2) (pow.f64 (sin.f64 ky) 2)))
84.0ms	(pow.f64 (/.f64 (*.f64 2 l) Om) 2)
23.0ms	(pow.f64 (sin.f64 ky) 2)

Compiler

Compiled 4201 to 3730 computations (11.2% saved)

simplify79.0ms (0.8%)

Algorithm

1×	egg-herbie

Counts

139 → 139

Iterations

Useful iterations: 0 (48.0ms)

Iter	Nodes	Cost
0	5070	3283

prune252.0ms (2.5%)

Pruning

2 alts after pruning (1 fresh and 1 done)

	Pruned	Kept	Total
New	138	1	139
Fresh	0	0	0
Picked	0	1	1
Done	0	0	0
Total	138	2	140

Error

Counts

140 → 2

Compiler

Compiled 4242 to 3089 computations (27.2% saved)

localize26.0ms (0.3%)

Local error

Found 4 expressions with local error:

2.7b	(.f64 (.f64 l l) (+.f64 (pow.f64 (sin.f64 ky) 2) (pow.f64 (sin.f64 kx) 2)))
2.7b	(.f64 (.f64 l l) (*.f64 4 (+.f64 (pow.f64 (sin.f64 ky) 2) (pow.f64 (sin.f64 kx) 2))))
27.6b	(sqrt.f64 (.f64 (.f64 l l) (*.f64 4 (+.f64 (pow.f64 (sin.f64 ky) 2) (pow.f64 (sin.f64 kx) 2)))))
27.8b	(sqrt.f64 (/.f64 1/4 (.f64 (.f64 l l) (+.f64 (pow.f64 (sin.f64 ky) 2) (pow.f64 (sin.f64 kx) 2)))))

rewrite309.0ms (3.1%)

Algorithm

1×	rewrite-expression-head

Error

Rules

35×	`pow1_binary64_139`
21×	`add-exp-log_binary64_116` `add-cbrt-cube_binary64_114`
19×	`pow-prod-down_binary64_149`
12×	`associate-*r/_binary64_20`
11×	`*-un-lft-identity_binary64_78` `prod-exp_binary64_127` `cbrt-unprod_binary64_111`
10×	`sqrt-prod_binary64_94`
9×	`add-sqr-sqrt_binary64_100`
7×	`add-cube-cbrt_binary64_113`
6×	`sqrt-pow1_binary64_96` `associate-r_binary64_18`
5×	`distribute-rgt-in_binary64_28` `distribute-lft-in_binary64_27`
4×	`add-log-exp_binary64_117` `flip3-+_binary64_81` `flip-+_binary64_52`
3×	`sqrt-div_binary64_95` `times-frac_binary64_84`
2×	`pow1/2_binary64_158` `associate-/r/_binary64_24` `associate-l_binary64_19` `*-commutative_binary64_9` `unpow-prod-down_binary64_157` `distribute-lft-out_binary64_29`
1×	`div-inv_binary64_75` `rem-sqrt-square_binary64_91` `unswap-sqr_binary64_46`

Counts

4 → 89

Calls

4 calls:

19.0ms	(.f64 (.f64 l l) (*.f64 4 (+.f64 (pow.f64 (sin.f64 ky) 2) (pow.f64 (sin.f64 kx) 2))))
15.0ms	(.f64 (.f64 l l) (+.f64 (pow.f64 (sin.f64 ky) 2) (pow.f64 (sin.f64 kx) 2)))
14.0ms	(sqrt.f64 (/.f64 1/4 (.f64 (.f64 l l) (+.f64 (pow.f64 (sin.f64 ky) 2) (pow.f64 (sin.f64 kx) 2)))))
14.0ms	(sqrt.f64 (.f64 (.f64 l l) (*.f64 4 (+.f64 (pow.f64 (sin.f64 ky) 2) (pow.f64 (sin.f64 kx) 2)))))

Compiler

Compiled 4924 to 3137 computations (36.3% saved)

series1.7s (16.7%)

Error

Counts

4 → 44

Calls

4 calls:

615.0ms	(sqrt.f64 (/.f64 1/4 (.f64 (.f64 l l) (+.f64 (pow.f64 (sin.f64 ky) 2) (pow.f64 (sin.f64 kx) 2)))))
368.0ms	(sqrt.f64 (.f64 (.f64 l l) (*.f64 4 (+.f64 (pow.f64 (sin.f64 ky) 2) (pow.f64 (sin.f64 kx) 2)))))
337.0ms	(.f64 (.f64 l l) (*.f64 4 (+.f64 (pow.f64 (sin.f64 ky) 2) (pow.f64 (sin.f64 kx) 2))))
282.0ms	(.f64 (.f64 l l) (+.f64 (pow.f64 (sin.f64 ky) 2) (pow.f64 (sin.f64 kx) 2)))

Compiler

Compiled 5633 to 4396 computations (22% saved)

simplify93.0ms (0.9%)

Algorithm

1×	egg-herbie

Counts

133 → 133

Iterations

Useful iterations: 0 (61.0ms)

Iter	Nodes	Cost
0	4981	3086
1	4981	3086

prune335.0ms (3.3%)

Pruning

2 alts after pruning (0 fresh and 2 done)

	Pruned	Kept	Total
New	133	0	133
Fresh	0	0	0
Picked	0	1	1
Done	0	1	1
Total	133	2	135

Error

Counts

135 → 2

Compiler

Compiled 6378 to 4110 computations (35.6% saved)

regimes1.3s (13%)

Accuracy

Total 0.7b remaining (93.7%)

Threshold costs 0.7b (93.7%)

Compiler

Compiled 14130 to 13168 computations (6.8% saved)

bsearch0.0ms (0%)

simplify3.0ms (0%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	29	65
1	29	65

end0.0ms (0%)

sample3.2s (31.9%)

Algorithm

1×

intervals

Results

1.1s	6385×	body	128	valid
602.0ms	746×	body	1024	valid
313.0ms	540×	body	512	valid
128.0ms	329×	body	256	valid

Compiler

Compiled 755 to 697 computations (7.7% saved)

Details

analyze604.0ms (6%)

sample81.0ms (0.8%)

simplify140.0ms (1.4%)

prune5.0ms (0%)

localize19.0ms (0.2%)

rewrite230.0ms (2.3%)

series1.7s (17%)

simplify79.0ms (0.8%)

prune252.0ms (2.5%)

localize26.0ms (0.3%)

rewrite309.0ms (3.1%)

series1.7s (16.7%)

simplify93.0ms (0.9%)

prune335.0ms (3.3%)

regimes1.3s (13%)

bsearch0.0ms (0%)

simplify3.0ms (0%)

end0.0ms (0%)

sample3.2s (31.9%)

Profiling