Details

analyze2.4s (9.9%)

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)

sample311.0ms (1.3%)

Algorithm

1×

intervals

Results

230.0ms	150×	body	1024	valid
44.0ms	49×	body	512	valid
12.0ms	49×	body	128	valid
5.0ms	8×	body	256	valid

Compiler

Compiled 33 to 32 computations (3% saved)

simplify448.0ms (1.9%)

Algorithm

1×	egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (155.0ms)

Iter	Nodes	Cost
0	5170	26

prune6.0ms (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: 4.9b

Counts

2 → 1

Compiler

Compiled 32 to 28 computations (12.5% saved)

localize30.0ms (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)
4.5b	(sqrt.f64 (+.f64 (pow.f64 (sin.f64 kx) 2) (pow.f64 (sin.f64 ky) 2)))

rewrite89.0ms (0.4%)

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:

38.0ms	(*.f64 (/.f64 (sin.f64 ky) (sqrt.f64 (+.f64 (pow.f64 (sin.f64 kx) 2) (pow.f64 (sin.f64 ky) 2)))) (sin.f64 th))
18.0ms	(sqrt.f64 (+.f64 (pow.f64 (sin.f64 kx) 2) (pow.f64 (sin.f64 ky) 2)))
6.0ms	(pow.f64 (sin.f64 kx) 2)
6.0ms	(pow.f64 (sin.f64 ky) 2)

series1.1s (4.5%)

Counts

4 → 12

Calls

4 calls:

701.0ms	(*.f64 (/.f64 (sin.f64 ky) (sqrt.f64 (+.f64 (pow.f64 (sin.f64 kx) 2) (pow.f64 (sin.f64 ky) 2)))) (sin.f64 th))
291.0ms	(sqrt.f64 (+.f64 (pow.f64 (sin.f64 kx) 2) (pow.f64 (sin.f64 ky) 2)))
42.0ms	(pow.f64 (sin.f64 kx) 2)
42.0ms	(pow.f64 (sin.f64 ky) 2)

simplify148.0ms (0.6%)

Algorithm

1×	egg-herbie

Counts

115 → 115

Iterations

Useful iterations: 0 (103.0ms)

Iter	Nodes	Cost
0	5013	2288

prune364.0ms (1.5%)

Pruning

11 alts after pruning (11 fresh and 0 done)

	Pruned	Kept	Total
New	104	11	115
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	105	11	116

Merged error: 3.3b

Counts

116 → 11

Compiler

Compiled 2988 to 1683 computations (43.7% saved)

localize30.0ms (0.1%)

Local error

Found 4 expressions with local error:

0.2b	(pow.f64 (sin.f64 kx) 2)
0.2b	(pow.f64 (sin.f64 ky) 2)
0.3b	(/.f64 (sin.f64 th) (sqrt.f64 (+.f64 (pow.f64 (sin.f64 kx) 2) (pow.f64 (sin.f64 ky) 2))))
4.5b	(sqrt.f64 (+.f64 (pow.f64 (sin.f64 kx) 2) (pow.f64 (sin.f64 ky) 2)))

rewrite75.0ms (0.3%)

Algorithm

1×	rewrite-expression-head

Rules

46×	`*-un-lft-identity_binary64_78`
27×	`add-sqr-sqrt_binary64_100`
26×	`add-cube-cbrt_binary64_113`
25×	`sqrt-prod_binary64_94`
24×	`times-frac_binary64_84`
16×	`unpow-prod-down_binary64_157`
10×	`distribute-lft-out_binary64_29`
8×	`associate-/r*_binary64_22` `add-exp-log_binary64_116`
7×	`pow1_binary64_139`
6×	`add-cbrt-cube_binary64_114` `pow-unpow_binary64_155`
4×	`add-log-exp_binary64_117` `sqrt-div_binary64_95`
3×	`associate-/l*_binary64_23`
2×	`pow-exp_binary64_146` `pow-to-exp_binary64_147` `flip-+_binary64_52` `unpow2_binary64_143` `sqr-pow_binary64_50` `pow-pow_binary64_150` `associate-/r/_binary64_24` `flip3-+_binary64_81`
1×	`sqrt-pow1_binary64_96` `cbrt-undiv_binary64_112` `div-exp_binary64_129` `rem-sqrt-square_binary64_91` `frac-2neg_binary64_89` `div-inv_binary64_75` `clear-num_binary64_77` `pow1/2_binary64_158`

Counts

4 → 102

Calls

4 calls:

26.0ms	(/.f64 (sin.f64 th) (sqrt.f64 (+.f64 (pow.f64 (sin.f64 kx) 2) (pow.f64 (sin.f64 ky) 2))))
17.0ms	(sqrt.f64 (+.f64 (pow.f64 (sin.f64 kx) 2) (pow.f64 (sin.f64 ky) 2)))
6.0ms	(pow.f64 (sin.f64 ky) 2)
6.0ms	(pow.f64 (sin.f64 kx) 2)

series1.2s (5.1%)

Counts

4 → 12

Calls

4 calls:

619.0ms	(/.f64 (sin.f64 th) (sqrt.f64 (+.f64 (pow.f64 (sin.f64 kx) 2) (pow.f64 (sin.f64 ky) 2))))
289.0ms	(sqrt.f64 (+.f64 (pow.f64 (sin.f64 kx) 2) (pow.f64 (sin.f64 ky) 2)))
271.0ms	(pow.f64 (sin.f64 kx) 2)
46.0ms	(pow.f64 (sin.f64 ky) 2)

simplify171.0ms (0.7%)

Algorithm

1×	egg-herbie

Counts

114 → 114

Iterations

Useful iterations: 0 (123.0ms)

Iter	Nodes	Cost
0	4954	2324
1	4954	2324

prune274.0ms (1.1%)

Pruning

12 alts after pruning (11 fresh and 1 done)

	Pruned	Kept	Total
New	113	1	114
Fresh	0	10	10
Picked	0	1	1
Done	0	0	0
Total	113	12	125

Merged error: 3.3b

Counts

125 → 12

Compiler

Compiled 2844 to 1593 computations (44% saved)

localize41.0ms (0.2%)

Local error

Found 4 expressions with local error:

0.6b	(cbrt.f64 (sin.f64 kx))
0.6b	(cbrt.f64 (sin.f64 kx))
0.8b	(pow.f64 (cbrt.f64 (sin.f64 kx)) 4)
4.5b	(sqrt.f64 (+.f64 (*.f64 (pow.f64 (cbrt.f64 (sin.f64 kx)) 4) (pow.f64 (cbrt.f64 (sin.f64 kx)) 2)) (pow.f64 (sin.f64 ky) 2)))

rewrite54.0ms (0.2%)

Algorithm

1×	rewrite-expression-head

Rules

11×	`add-sqr-sqrt_binary64_100`
10×	`add-cube-cbrt_binary64_113` `*-un-lft-identity_binary64_78`
9×	`cbrt-prod_binary64_109`
6×	`unpow-prod-down_binary64_157` `pow1_binary64_139`
5×	`add-exp-log_binary64_116`
4×	`add-cbrt-cube_binary64_114` `add-log-exp_binary64_117`
3×	`sqrt-prod_binary64_94` `pow1/3_binary64_160` `pow-unpow_binary64_155`
2×	`pow-pow_binary64_150` `sqrt-div_binary64_95`
1×	`pow-exp_binary64_146` `pow-to-exp_binary64_147` `sqrt-pow1_binary64_96` `flip-+_binary64_52` `rem-sqrt-square_binary64_91` `sqr-pow_binary64_50` `pow1/2_binary64_158` `flip3-+_binary64_81`

Counts

4 → 58

Calls

4 calls:

27.0ms	(sqrt.f64 (+.f64 (*.f64 (pow.f64 (cbrt.f64 (sin.f64 kx)) 4) (pow.f64 (cbrt.f64 (sin.f64 kx)) 2)) (pow.f64 (sin.f64 ky) 2)))
8.0ms	(pow.f64 (cbrt.f64 (sin.f64 kx)) 4)
4.0ms	(cbrt.f64 (sin.f64 kx))
4.0ms	(cbrt.f64 (sin.f64 kx))

series1.1s (4.5%)

Counts

4 → 12

Calls

4 calls:

355.0ms	(pow.f64 (cbrt.f64 (sin.f64 kx)) 4)
276.0ms	(sqrt.f64 (+.f64 (*.f64 (pow.f64 (cbrt.f64 (sin.f64 kx)) 4) (pow.f64 (cbrt.f64 (sin.f64 kx)) 2)) (pow.f64 (sin.f64 ky) 2)))
236.0ms	(cbrt.f64 (sin.f64 kx))
221.0ms	(cbrt.f64 (sin.f64 kx))

simplify104.0ms (0.4%)

Algorithm

1×	egg-herbie

Counts

70 → 70

Iterations

Useful iterations: 0 (73.0ms)

Iter	Nodes	Cost
0	5117	863

prune192.0ms (0.8%)

Pruning

12 alts after pruning (10 fresh and 2 done)

	Pruned	Kept	Total
New	70	0	70
Fresh	0	10	10
Picked	0	1	1
Done	0	1	1
Total	70	12	82

Merged error: 3.3b

Counts

82 → 12

Compiler

Compiled 2070 to 1160 computations (44% saved)

localize55.0ms (0.2%)

Local error

Found 4 expressions with local error:

0.6b	(cbrt.f64 (sqrt.f64 (+.f64 (pow.f64 (sin.f64 kx) 2) (pow.f64 (sin.f64 ky) 2))))
4.5b	(sqrt.f64 (+.f64 (pow.f64 (sin.f64 kx) 2) (pow.f64 (sin.f64 ky) 2)))
4.5b	(sqrt.f64 (+.f64 (pow.f64 (sin.f64 kx) 2) (pow.f64 (sin.f64 ky) 2)))
4.5b	(sqrt.f64 (+.f64 (pow.f64 (sin.f64 kx) 2) (pow.f64 (sin.f64 ky) 2)))

rewrite95.0ms (0.4%)

Algorithm

1×	rewrite-expression-head

Rules

25×	`*-un-lft-identity_binary64_78`
20×	`sqrt-prod_binary64_94`
12×	`add-sqr-sqrt_binary64_100`
9×	`add-cube-cbrt_binary64_113`
8×	`unpow-prod-down_binary64_157` `cbrt-prod_binary64_109` `sqrt-div_binary64_95` `distribute-lft-out_binary64_29`
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×	`cbrt-div_binary64_110`
1×	`pow1/3_binary64_160`

Counts

4 → 69

Calls

4 calls:

19.0ms	(cbrt.f64 (sqrt.f64 (+.f64 (pow.f64 (sin.f64 kx) 2) (pow.f64 (sin.f64 ky) 2))))
18.0ms	(sqrt.f64 (+.f64 (pow.f64 (sin.f64 kx) 2) (pow.f64 (sin.f64 ky) 2)))
18.0ms	(sqrt.f64 (+.f64 (pow.f64 (sin.f64 kx) 2) (pow.f64 (sin.f64 ky) 2)))
17.0ms	(sqrt.f64 (+.f64 (pow.f64 (sin.f64 kx) 2) (pow.f64 (sin.f64 ky) 2)))

series1.3s (5.3%)

Counts

4 → 12

Calls

4 calls:

410.0ms	(cbrt.f64 (sqrt.f64 (+.f64 (pow.f64 (sin.f64 kx) 2) (pow.f64 (sin.f64 ky) 2))))
304.0ms	(sqrt.f64 (+.f64 (pow.f64 (sin.f64 kx) 2) (pow.f64 (sin.f64 ky) 2)))
283.0ms	(sqrt.f64 (+.f64 (pow.f64 (sin.f64 kx) 2) (pow.f64 (sin.f64 ky) 2)))
282.0ms	(sqrt.f64 (+.f64 (pow.f64 (sin.f64 kx) 2) (pow.f64 (sin.f64 ky) 2)))

simplify176.0ms (0.7%)

Algorithm

1×	egg-herbie

Counts

81 → 81

Iterations

Useful iterations: 0 (137.0ms)

Iter	Nodes	Cost
0	4893	1705
1	4893	1705

prune379.0ms (1.6%)

Pruning

12 alts after pruning (9 fresh and 3 done)

	Pruned	Kept	Total
New	81	0	81
Fresh	0	9	9
Picked	0	1	1
Done	0	2	2
Total	81	12	93

Merged error: 3.3b

Counts

93 → 12

Compiler

Compiled 4536 to 2467 computations (45.6% saved)

regimes2.0s (8.2%)

Compiler: Compiled 11388 to 9007 computations (20.9% saved)

bsearch0.0ms (0%)

simplify4.0ms (0%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	16	26
1	16	26

end0.0ms (0%)

sample12.0s (49.9%)

Algorithm

1×

intervals

Results

7.1s	4648×	body	1024	valid
1.3s	1416×	body	512	valid
327.0ms	1399×	body	128	valid
285.0ms	524×	body	256	valid
38.0ms	13×	body	2048	valid

Compiler

Compiled 1289 to 1021 computations (20.8% saved)

Details

analyze2.4s (9.9%)

sample311.0ms (1.3%)

simplify448.0ms (1.9%)

prune6.0ms (0%)

localize30.0ms (0.1%)

rewrite89.0ms (0.4%)

series1.1s (4.5%)

simplify148.0ms (0.6%)

prune364.0ms (1.5%)

localize30.0ms (0.1%)

rewrite75.0ms (0.3%)

series1.2s (5.1%)

simplify171.0ms (0.7%)

prune274.0ms (1.1%)

localize41.0ms (0.2%)

rewrite54.0ms (0.2%)

series1.1s (4.5%)

simplify104.0ms (0.4%)

prune192.0ms (0.8%)

localize55.0ms (0.2%)

rewrite95.0ms (0.4%)

series1.3s (5.3%)

simplify176.0ms (0.7%)

prune379.0ms (1.6%)

regimes2.0s (8.2%)

bsearch0.0ms (0%)

simplify4.0ms (0%)

end0.0ms (0%)

sample12.0s (49.9%)

Profiling