Details

analyze1.2s (7.8%)

Algorithm

1×

Search

True	Other	False	Iter
0%	99.9%	0.1%	0
0%	99.9%	0.1%	1
0%	99.9%	0.1%	2
0%	99.9%	0.1%	3
0%	99.9%	0.1%	4
0%	99.9%	0.1%	5
0%	99.9%	0.1%	6
0%	99.9%	0.1%	7
25%	74.9%	0.1%	8
54.6%	45.2%	0.1%	9
56.2%	43.7%	0.1%	10
62.4%	37.4%	0.1%	11
65.9%	33.9%	0.1%	12
66.3%	33.5%	0.1%	13
69%	30.8%	0.1%	14

Compiler

Compiled 17 to 15 computations (11.8% saved)

sample153.0ms (1%)

Algorithm

1×

intervals

Results

110.0ms	144×	body	1024	valid
20.0ms	44×	body	512	valid
6.0ms	50×	body	128	valid
5.0ms	17×	body	256	valid
1.0ms	1×	body	2048	valid

Compiler

Compiled 33 to 32 computations (3% saved)

simplify169.0ms (1.1%)

Algorithm

1×	egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (78.0ms)

Iter	Nodes	Cost
0	5170	26

prune3.0ms (0%)

Pruning

2 alts after pruning (2 fresh and 0 done)

	Kept	Total
New	1	1
Fresh	1	1
Picked	0	0
Done	0	0
Total	2	2

Merged error: 5.2b

Counts

2 → 1

Compiler

Compiled 32 to 28 computations (12.5% saved)

localize13.0ms (0.1%)

Local error

Found 4 expressions with local error:

0.2b	(*.f64 (/.f64 (sin.f64 ky) (sqrt.f64 (+.f64 (pow.f64 (sin.f64 kx) 2) (pow.f64 (sin.f64 ky) 2)))) (sin.f64 th))
0.2b	(pow.f64 (sin.f64 kx) 2)
0.2b	(pow.f64 (sin.f64 ky) 2)
4.8b	(sqrt.f64 (+.f64 (pow.f64 (sin.f64 kx) 2) (pow.f64 (sin.f64 ky) 2)))

rewrite49.0ms (0.3%)

Algorithm

1×	rewrite-expression-head

Rules

41×	`*-un-lft-identity_binary64_78`
34×	`add-sqr-sqrt_binary64_100`
30×	`associate-l_binary64_19`
26×	`times-frac_binary64_84`
25×	`add-cube-cbrt_binary64_113`
21×	`sqrt-prod_binary64_94`
14×	`unpow-prod-down_binary64_157`
11×	`add-exp-log_binary64_116`
9×	`add-cbrt-cube_binary64_114` `pow1_binary64_139`
8×	`distribute-lft-out_binary64_29`
6×	`pow-unpow_binary64_155`
4×	`add-log-exp_binary64_117` `sqrt-div_binary64_95`
3×	`associate-r_binary64_18` `unswap-sqr_binary64_46`
2×	`pow-exp_binary64_146` `pow-to-exp_binary64_147` `cbrt-unprod_binary64_111` `prod-exp_binary64_127` `flip-+_binary64_52` `unpow2_binary64_143` `sqr-pow_binary64_50` `pow-pow_binary64_150` `associate-/r/_binary64_24` `flip3-+_binary64_81`
1×	`-commutative_binary64_9` `sqrt-pow1_binary64_96` `cbrt-undiv_binary64_112` `div-exp_binary64_129` `rem-sqrt-square_binary64_91` `div-inv_binary64_75` `associate-l/_binary64_21` `pow-prod-down_binary64_149` `pow1/2_binary64_158`

Counts

4 → 103

Calls

4 calls:

23.0ms	(*.f64 (/.f64 (sin.f64 ky) (sqrt.f64 (+.f64 (pow.f64 (sin.f64 kx) 2) (pow.f64 (sin.f64 ky) 2)))) (sin.f64 th))
9.0ms	(sqrt.f64 (+.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)

series1.0s (6.4%)

Counts

4 → 33

Calls

4 calls:

733.0ms	(*.f64 (/.f64 (sin.f64 ky) (sqrt.f64 (+.f64 (pow.f64 (sin.f64 kx) 2) (pow.f64 (sin.f64 ky) 2)))) (sin.f64 th))
223.0ms	(sqrt.f64 (+.f64 (pow.f64 (sin.f64 kx) 2) (pow.f64 (sin.f64 ky) 2)))
36.0ms	(pow.f64 (sin.f64 kx) 2)
22.0ms	(pow.f64 (sin.f64 ky) 2)

Compiler

Compiled 1303 to 1081 computations (17% saved)

simplify72.0ms (0.5%)

Algorithm

1×	egg-herbie

Counts

136 → 136

Iterations

Useful iterations: 0 (40.0ms)

Iter	Nodes	Cost
0	4945	2867
1	4945	2867

prune207.0ms (1.3%)

Pruning

14 alts after pruning (14 fresh and 0 done)

	Pruned	Kept	Total
New	122	14	136
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	123	14	137

Merged error: 1.3b

Counts

137 → 14

Compiler

Compiled 3485 to 1992 computations (42.8% saved)

localize14.0ms (0.1%)

Local error

Found 4 expressions with local error:

0.2b	(pow.f64 (sin.f64 ky) 2)
0.2b	(/.f64 (sin.f64 th) (sqrt.f64 (+.f64 (pow.f64 (sin.f64 kx) 2) (pow.f64 (sin.f64 ky) 2))))
0.3b	(*.f64 (sin.f64 ky) (/.f64 (sin.f64 th) (sqrt.f64 (+.f64 (pow.f64 (sin.f64 kx) 2) (pow.f64 (sin.f64 ky) 2)))))
4.8b	(sqrt.f64 (+.f64 (pow.f64 (sin.f64 kx) 2) (pow.f64 (sin.f64 ky) 2)))

rewrite59.0ms (0.4%)

Algorithm

1×	rewrite-expression-head

Rules

72×	`*-un-lft-identity_binary64_78`
50×	`times-frac_binary64_84`
49×	`add-sqr-sqrt_binary64_100`
41×	`sqrt-prod_binary64_94`
40×	`add-cube-cbrt_binary64_113`
30×	`associate-r_binary64_18`
19×	`unpow-prod-down_binary64_157`
16×	`distribute-lft-out_binary64_29`
12×	`add-exp-log_binary64_116`
11×	`add-cbrt-cube_binary64_114`
8×	`associate-/r*_binary64_22` `pow1_binary64_139`
6×	`sqrt-div_binary64_95`
4×	`add-log-exp_binary64_117` `associate-/r/_binary64_24`
3×	`associate-l_binary64_19` `flip-+_binary64_52` `associate-/l*_binary64_23` `unswap-sqr_binary64_46` `pow-unpow_binary64_155` `flip3-+_binary64_81`
2×	`cbrt-unprod_binary64_111` `cbrt-undiv_binary64_112` `prod-exp_binary64_127` `div-exp_binary64_129` `div-inv_binary64_75`
1×	`-commutative_binary64_9` `pow-exp_binary64_146` `pow-to-exp_binary64_147` `sqrt-pow1_binary64_96` `rem-sqrt-square_binary64_91` `unpow2_binary64_143` `frac-2neg_binary64_89` `sqr-pow_binary64_50` `pow-pow_binary64_150` `pow-prod-down_binary64_149` `associate-r/_binary64_20` `clear-num_binary64_77` `pow1/2_binary64_158`

Counts

4 → 134

Calls

4 calls:

21.0ms	(*.f64 (sin.f64 ky) (/.f64 (sin.f64 th) (sqrt.f64 (+.f64 (pow.f64 (sin.f64 kx) 2) (pow.f64 (sin.f64 ky) 2)))))
13.0ms	(/.f64 (sin.f64 th) (sqrt.f64 (+.f64 (pow.f64 (sin.f64 kx) 2) (pow.f64 (sin.f64 ky) 2))))
9.0ms	(sqrt.f64 (+.f64 (pow.f64 (sin.f64 kx) 2) (pow.f64 (sin.f64 ky) 2)))
3.0ms	(pow.f64 (sin.f64 ky) 2)

series1.6s (9.8%)

Counts

4 → 41

Calls

4 calls:

709.0ms	(*.f64 (sin.f64 ky) (/.f64 (sin.f64 th) (sqrt.f64 (+.f64 (pow.f64 (sin.f64 kx) 2) (pow.f64 (sin.f64 ky) 2)))))
580.0ms	(/.f64 (sin.f64 th) (sqrt.f64 (+.f64 (pow.f64 (sin.f64 kx) 2) (pow.f64 (sin.f64 ky) 2))))
246.0ms	(sqrt.f64 (+.f64 (pow.f64 (sin.f64 kx) 2) (pow.f64 (sin.f64 ky) 2)))
22.0ms	(pow.f64 (sin.f64 ky) 2)

Compiler

Compiled 1717 to 1416 computations (17.5% saved)

simplify100.0ms (0.6%)

Algorithm

1×	egg-herbie

Counts

175 → 175

Iterations

Useful iterations: 0 (57.0ms)

Iter	Nodes	Cost
0	4958	4400
1	4958	4400

prune241.0ms (1.5%)

Pruning

13 alts after pruning (12 fresh and 1 done)

	Pruned	Kept	Total
New	174	1	175
Fresh	2	11	13
Picked	0	1	1
Done	0	0	0
Total	176	13	189

Merged error: 1.3b

Counts

189 → 13

Compiler

Compiled 4471 to 2472 computations (44.7% saved)

localize17.0ms (0.1%)

Local error

Found 4 expressions with local error:

0.2b	(pow.f64 (sin.f64 ky) 2)
0.3b	(*.f64 (fabs.f64 (cbrt.f64 (+.f64 (pow.f64 (sin.f64 kx) 2) (pow.f64 (sin.f64 ky) 2)))) (sqrt.f64 (cbrt.f64 (+.f64 (pow.f64 (sin.f64 kx) 2) (pow.f64 (sin.f64 ky) 2)))))
5.4b	(cbrt.f64 (+.f64 (pow.f64 (sin.f64 kx) 2) (pow.f64 (sin.f64 ky) 2)))
5.4b	(cbrt.f64 (+.f64 (pow.f64 (sin.f64 kx) 2) (pow.f64 (sin.f64 ky) 2)))

rewrite49.0ms (0.3%)

Algorithm

1×	rewrite-expression-head

Rules

24×	`*-un-lft-identity_binary64_78`
18×	`add-sqr-sqrt_binary64_100`
16×	`cbrt-prod_binary64_109`
12×	`add-cube-cbrt_binary64_113`
11×	`associate-r_binary64_18`
10×	`sqrt-prod_binary64_94`
9×	`unpow-prod-down_binary64_157`
7×	`add-exp-log_binary64_116` `pow1_binary64_139`
6×	`add-cbrt-cube_binary64_114` `cbrt-div_binary64_110` `distribute-lft-out_binary64_29`
4×	`add-log-exp_binary64_117`
3×	`associate-l_binary64_19` `flip-+_binary64_52` `unswap-sqr_binary64_46` `pow-unpow_binary64_155` `flip3-+_binary64_81`
2×	`pow1/3_binary64_160` `sqrt-div_binary64_95` `associate-*r/_binary64_20`
1×	`*-commutative_binary64_9` `pow-exp_binary64_146` `pow-to-exp_binary64_147` `cbrt-unprod_binary64_111` `prod-exp_binary64_127` `unpow2_binary64_143` `sqr-pow_binary64_50` `pow-pow_binary64_150` `pow-prod-down_binary64_149`

Counts

4 → 78

Calls

4 calls:

16.0ms	(*.f64 (fabs.f64 (cbrt.f64 (+.f64 (pow.f64 (sin.f64 kx) 2) (pow.f64 (sin.f64 ky) 2)))) (sqrt.f64 (cbrt.f64 (+.f64 (pow.f64 (sin.f64 kx) 2) (pow.f64 (sin.f64 ky) 2)))))
11.0ms	(cbrt.f64 (+.f64 (pow.f64 (sin.f64 kx) 2) (pow.f64 (sin.f64 ky) 2)))
9.0ms	(cbrt.f64 (+.f64 (pow.f64 (sin.f64 kx) 2) (pow.f64 (sin.f64 ky) 2)))
3.0ms	(pow.f64 (sin.f64 ky) 2)

series1.5s (9.2%)

Counts

4 → 27

Calls

4 calls:

657.0ms	(*.f64 (fabs.f64 (cbrt.f64 (+.f64 (pow.f64 (sin.f64 kx) 2) (pow.f64 (sin.f64 ky) 2)))) (sqrt.f64 (cbrt.f64 (+.f64 (pow.f64 (sin.f64 kx) 2) (pow.f64 (sin.f64 ky) 2)))))
395.0ms	(cbrt.f64 (+.f64 (pow.f64 (sin.f64 kx) 2) (pow.f64 (sin.f64 ky) 2)))
394.0ms	(cbrt.f64 (+.f64 (pow.f64 (sin.f64 kx) 2) (pow.f64 (sin.f64 ky) 2)))
24.0ms	(pow.f64 (sin.f64 ky) 2)

Compiler

Compiled 1872 to 1549 computations (17.3% saved)

simplify76.0ms (0.5%)

Algorithm

1×	egg-herbie

Counts

105 → 105

Iterations

Useful iterations: 0 (44.0ms)

Iter	Nodes	Cost
0	5425	2729

prune204.0ms (1.3%)

Pruning

13 alts after pruning (11 fresh and 2 done)

	Pruned	Kept	Total
New	105	0	105
Fresh	0	11	11
Picked	0	1	1
Done	0	1	1
Total	105	13	118

Merged error: 1.3b

Counts

118 → 13

Compiler

Compiled 3997 to 2526 computations (36.8% saved)

localize20.0ms (0.1%)

Local error

Found 4 expressions with local error:

0.4b	(cbrt.f64 (/.f64 (sin.f64 ky) (sqrt.f64 (+.f64 (pow.f64 (sin.f64 kx) 2) (pow.f64 (sin.f64 ky) 2)))))
4.8b	(sqrt.f64 (+.f64 (pow.f64 (sin.f64 kx) 2) (pow.f64 (sin.f64 ky) 2)))
4.8b	(sqrt.f64 (+.f64 (pow.f64 (sin.f64 kx) 2) (pow.f64 (sin.f64 ky) 2)))
4.8b	(sqrt.f64 (+.f64 (pow.f64 (sin.f64 kx) 2) (pow.f64 (sin.f64 ky) 2)))

rewrite58.0ms (0.4%)

Algorithm

1×	rewrite-expression-head

Rules

46×	`*-un-lft-identity_binary64_78`
30×	`sqrt-prod_binary64_94` `cbrt-prod_binary64_109`
25×	`add-sqr-sqrt_binary64_100`
24×	`times-frac_binary64_84`
22×	`add-cube-cbrt_binary64_113`
12×	`unpow-prod-down_binary64_157` `distribute-lft-out_binary64_29`
8×	`sqrt-div_binary64_95`
7×	`pow1_binary64_139`
4×	`add-cbrt-cube_binary64_114` `add-log-exp_binary64_117` `flip-+_binary64_52` `add-exp-log_binary64_116` `flip3-+_binary64_81`
3×	`sqrt-pow1_binary64_96` `rem-sqrt-square_binary64_91` `pow1/2_binary64_158`
2×	`associate-/r/_binary64_24`
1×	`cbrt-div_binary64_110` `pow1/3_binary64_160` `div-inv_binary64_75`

Counts

4 → 90

Calls

4 calls:

13.0ms	(cbrt.f64 (/.f64 (sin.f64 ky) (sqrt.f64 (+.f64 (pow.f64 (sin.f64 kx) 2) (pow.f64 (sin.f64 ky) 2)))))
9.0ms	(sqrt.f64 (+.f64 (pow.f64 (sin.f64 kx) 2) (pow.f64 (sin.f64 ky) 2)))
9.0ms	(sqrt.f64 (+.f64 (pow.f64 (sin.f64 kx) 2) (pow.f64 (sin.f64 ky) 2)))
9.0ms	(sqrt.f64 (+.f64 (pow.f64 (sin.f64 kx) 2) (pow.f64 (sin.f64 ky) 2)))

series1.5s (9.3%)

Counts

4 → 39

Calls

4 calls:

794.0ms	(cbrt.f64 (/.f64 (sin.f64 ky) (sqrt.f64 (+.f64 (pow.f64 (sin.f64 kx) 2) (pow.f64 (sin.f64 ky) 2)))))
230.0ms	(sqrt.f64 (+.f64 (pow.f64 (sin.f64 kx) 2) (pow.f64 (sin.f64 ky) 2)))
227.0ms	(sqrt.f64 (+.f64 (pow.f64 (sin.f64 kx) 2) (pow.f64 (sin.f64 ky) 2)))
224.0ms	(sqrt.f64 (+.f64 (pow.f64 (sin.f64 kx) 2) (pow.f64 (sin.f64 ky) 2)))

Compiler

Compiled 3580 to 2584 computations (27.8% saved)

simplify99.0ms (0.6%)

Algorithm

1×	egg-herbie

Counts

129 → 129

Iterations

Useful iterations: 0 (61.0ms)

Iter	Nodes	Cost
0	4966	3443
1	4966	3443

prune351.0ms (2.2%)

Pruning

13 alts after pruning (10 fresh and 3 done)

	Pruned	Kept	Total
New	129	0	129
Fresh	0	10	10
Picked	0	1	1
Done	0	2	2
Total	129	13	142

Merged error: 1.3b

Counts

142 → 13

Compiler

Compiled 6993 to 4103 computations (41.3% saved)

regimes1.1s (7%)

Compiler: Compiled 12371 to 9851 computations (20.4% saved)

bsearch4.0ms (0%)

Compiler: Compiled 13 to 12 computations (7.7% saved)

simplify3.0ms (0%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	20	55
1	20	55

end0.0ms (0%)

sample6.1s (38.3%)

Algorithm

1×

intervals

Results

3.4s	4559×	body	1024	valid
673.0ms	1440×	body	512	valid
203.0ms	1479×	body	128	valid
143.0ms	505×	body	256	valid
20.0ms	17×	body	2048	valid

Compiler

Compiled 1395 to 1108 computations (20.6% saved)

Details

analyze1.2s (7.8%)

sample153.0ms (1%)

simplify169.0ms (1.1%)

prune3.0ms (0%)

localize13.0ms (0.1%)

rewrite49.0ms (0.3%)

series1.0s (6.4%)

simplify72.0ms (0.5%)

prune207.0ms (1.3%)

localize14.0ms (0.1%)

rewrite59.0ms (0.4%)

series1.6s (9.8%)

simplify100.0ms (0.6%)

prune241.0ms (1.5%)

localize17.0ms (0.1%)

rewrite49.0ms (0.3%)

series1.5s (9.2%)

simplify76.0ms (0.5%)

prune204.0ms (1.3%)

localize20.0ms (0.1%)

rewrite58.0ms (0.4%)

series1.5s (9.3%)

simplify99.0ms (0.6%)

prune351.0ms (2.2%)

regimes1.1s (7%)

bsearch4.0ms (0%)

simplify3.0ms (0%)

end0.0ms (0%)

sample6.1s (38.3%)

Profiling