Details

analyze1.2s (9.5%)

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)

sample146.0ms (1.1%)

Algorithm

1×

intervals

Results

98.0ms	143×	body	1024	valid
27.0ms	55×	body	512	valid
5.0ms	20×	body	256	valid
5.0ms	37×	body	128	valid
1.0ms	1×	body	2048	valid

Compiler

Compiled 33 to 32 computations (3% saved)

simplify174.0ms (1.4%)

Algorithm

1×	egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (74.0ms)

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: 4.9b

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

rewrite36.0ms (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:

13.0ms	(/.f64 (sin.f64 ky) (sqrt.f64 (+.f64 (pow.f64 (sin.f64 kx) 2) (pow.f64 (sin.f64 ky) 2))))
8.0ms	(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)

series416.0ms (3.3%)

Counts

4 → 12

Calls

4 calls:

228.0ms	(sqrt.f64 (+.f64 (pow.f64 (sin.f64 kx) 2) (pow.f64 (sin.f64 ky) 2)))
160.0ms	(/.f64 (sin.f64 ky) (sqrt.f64 (+.f64 (pow.f64 (sin.f64 kx) 2) (pow.f64 (sin.f64 ky) 2))))
14.0ms	(pow.f64 (sin.f64 ky) 2)
14.0ms	(pow.f64 (sin.f64 kx) 2)

simplify88.0ms (0.7%)

Algorithm

1×	egg-herbie

Counts

114 → 114

Iterations

Useful iterations: 0 (63.0ms)

Iter	Nodes	Cost
0	4939	2298
1	4939	2298

prune169.0ms (1.3%)

Pruning

11 alts after pruning (11 fresh and 0 done)

	Pruned	Kept	Total
New	103	11	114
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	104	11	115

Merged error: 1.9b

Counts

115 → 11

Compiler

Compiled 2837 to 1616 computations (43% saved)

localize14.0ms (0.1%)

Local error

Found 4 expressions with local error:

0.2b	(/.f64 1 (/.f64 (sqrt.f64 (+.f64 (pow.f64 (sin.f64 kx) 2) (pow.f64 (sin.f64 ky) 2))) (sin.f64 ky)))
0.3b	(pow.f64 (sin.f64 kx) 2)
0.3b	(pow.f64 (sin.f64 ky) 2)
4.5b	(sqrt.f64 (+.f64 (pow.f64 (sin.f64 kx) 2) (pow.f64 (sin.f64 ky) 2)))

rewrite57.0ms (0.4%)

Algorithm

1×	rewrite-expression-head

Rules

180×	`times-frac_binary64_84`
150×	`*-un-lft-identity_binary64_78`
99×	`add-sqr-sqrt_binary64_100`
98×	`add-cube-cbrt_binary64_113`
65×	`sqrt-prod_binary64_94`
32×	`unpow-prod-down_binary64_157`
28×	`associate-/r*_binary64_22`
26×	`distribute-lft-out_binary64_29`
17×	`add-exp-log_binary64_116`
9×	`add-cbrt-cube_binary64_114`
8×	`pow1_binary64_139`
7×	`div-exp_binary64_129`
6×	`pow-unpow_binary64_155`
5×	`div-inv_binary64_75`
4×	`add-log-exp_binary64_117`
3×	`cbrt-undiv_binary64_112` `associate-/l*_binary64_23`
2×	`pow-exp_binary64_146` `pow-to-exp_binary64_147` `unpow2_binary64_143` `1-exp_binary64_122` `sqr-pow_binary64_50` `pow-pow_binary64_150` `rec-exp_binary64_128` `sqrt-div_binary64_95`
1×	`sqrt-pow1_binary64_96` `inv-pow_binary64_163` `flip-+_binary64_52` `rem-sqrt-square_binary64_91` `frac-2neg_binary64_89` `pow-flip_binary64_152` `associate-/r/_binary64_24` `clear-num_binary64_77` `pow1/2_binary64_158` `flip3-+_binary64_81`

Counts

4 → 189

Calls

4 calls:

16.0ms	(/.f64 1 (/.f64 (sqrt.f64 (+.f64 (pow.f64 (sin.f64 kx) 2) (pow.f64 (sin.f64 ky) 2))) (sin.f64 ky)))
11.0ms	(sqrt.f64 (+.f64 (pow.f64 (sin.f64 kx) 2) (pow.f64 (sin.f64 ky) 2)))
3.0ms	(pow.f64 (sin.f64 kx) 2)
3.0ms	(pow.f64 (sin.f64 ky) 2)

series278.0ms (2.2%)

Counts

4 → 12

Calls

4 calls:

158.0ms	(/.f64 1 (/.f64 (sqrt.f64 (+.f64 (pow.f64 (sin.f64 kx) 2) (pow.f64 (sin.f64 ky) 2))) (sin.f64 ky)))
91.0ms	(sqrt.f64 (+.f64 (pow.f64 (sin.f64 kx) 2) (pow.f64 (sin.f64 ky) 2)))
15.0ms	(pow.f64 (sin.f64 ky) 2)
14.0ms	(pow.f64 (sin.f64 kx) 2)

simplify112.0ms (0.9%)

Algorithm

1×	egg-herbie

Counts

201 → 201

Iterations

Useful iterations: 0 (58.0ms)

Iter	Nodes	Cost
0	4970	5648
1	4970	5648

prune289.0ms (2.3%)

Pruning

11 alts after pruning (11 fresh and 0 done)

	Pruned	Kept	Total
New	198	3	201
Fresh	2	8	10
Picked	1	0	1
Done	0	0	0
Total	201	11	212

Merged error: 1.9b

Counts

212 → 11

Compiler

Compiled 5634 to 3323 computations (41% saved)

localize15.0ms (0.1%)

Local error

Found 4 expressions with local error:

0.3b	(pow.f64 (sin.f64 kx) 2)
0.3b	(/.f64 (/.f64 1 (sqrt.f64 (+.f64 (pow.f64 (sin.f64 kx) 2) (pow.f64 (sin.f64 ky) 2)))) (/.f64 1 (sin.f64 ky)))
0.3b	(pow.f64 (sin.f64 ky) 2)
4.5b	(sqrt.f64 (+.f64 (pow.f64 (sin.f64 kx) 2) (pow.f64 (sin.f64 ky) 2)))

rewrite140.0ms (1.1%)

Algorithm

1×	rewrite-expression-head

Rules

1005×	`times-frac_binary64_84`
608×	`*-un-lft-identity_binary64_78`
437×	`add-sqr-sqrt_binary64_100`
436×	`add-cube-cbrt_binary64_113`
215×	`sqrt-prod_binary64_94`
92×	`unpow-prod-down_binary64_157`
86×	`distribute-lft-out_binary64_29`
46×	`div-inv_binary64_75` `add-exp-log_binary64_116`
32×	`div-exp_binary64_129`
30×	`associate-/l*_binary64_23` `sqrt-div_binary64_95`
29×	`associate-/r/_binary64_24`
16×	`add-cbrt-cube_binary64_114`
15×	`flip-+_binary64_52` `flip3-+_binary64_81`
13×	`associate-/r*_binary64_22`
8×	`cbrt-undiv_binary64_112` `1-exp_binary64_122` `rec-exp_binary64_128`
7×	`pow1_binary64_139`
6×	`pow-unpow_binary64_155`
4×	`add-log-exp_binary64_117`
2×	`pow-exp_binary64_146` `pow-to-exp_binary64_147` `unpow2_binary64_143` `sqr-pow_binary64_50` `pow-pow_binary64_150`
1×	`sqrt-pow1_binary64_96` `rem-sqrt-square_binary64_91` `frac-2neg_binary64_89` `clear-num_binary64_77` `associate-/l/_binary64_25` `pow1/2_binary64_158`

Counts

4 → 518

Calls

4 calls:

27.0ms	(/.f64 (/.f64 1 (sqrt.f64 (+.f64 (pow.f64 (sin.f64 kx) 2) (pow.f64 (sin.f64 ky) 2)))) (/.f64 1 (sin.f64 ky)))
8.0ms	(sqrt.f64 (+.f64 (pow.f64 (sin.f64 kx) 2) (pow.f64 (sin.f64 ky) 2)))
3.0ms	(pow.f64 (sin.f64 kx) 2)
3.0ms	(pow.f64 (sin.f64 ky) 2)

series279.0ms (2.2%)

Counts

4 → 12

Calls

4 calls:

166.0ms	(/.f64 (/.f64 1 (sqrt.f64 (+.f64 (pow.f64 (sin.f64 kx) 2) (pow.f64 (sin.f64 ky) 2)))) (/.f64 1 (sin.f64 ky)))
85.0ms	(sqrt.f64 (+.f64 (pow.f64 (sin.f64 kx) 2) (pow.f64 (sin.f64 ky) 2)))
14.0ms	(pow.f64 (sin.f64 ky) 2)
14.0ms	(pow.f64 (sin.f64 kx) 2)

simplify236.0ms (1.8%)

Algorithm

1×	egg-herbie

Counts

530 → 530

Iterations

Useful iterations: 0 (51.0ms)

Iter	Nodes	Cost
0	5026	22008

prune1.3s (10.4%)

Pruning

11 alts after pruning (10 fresh and 1 done)

	Pruned	Kept	Total
New	530	0	530
Fresh	0	10	10
Picked	0	1	1
Done	0	0	0
Total	530	11	541

Merged error: 1.9b

Counts

541 → 11

Compiler

Compiled 17111 to 10616 computations (38% saved)

localize14.0ms (0.1%)

Local error

Found 4 expressions with local error:

0.3b	(/.f64 1 (+.f64 (pow.f64 (sin.f64 kx) 2) (pow.f64 (sin.f64 ky) 2)))
0.3b	(pow.f64 (sin.f64 ky) 2)
0.3b	(*.f64 (sin.f64 ky) (sqrt.f64 (/.f64 1 (+.f64 (pow.f64 (sin.f64 kx) 2) (pow.f64 (sin.f64 ky) 2)))))
4.6b	(sqrt.f64 (/.f64 1 (+.f64 (pow.f64 (sin.f64 kx) 2) (pow.f64 (sin.f64 ky) 2))))

rewrite62.0ms (0.5%)

Algorithm

1×	rewrite-expression-head

Rules

78×	`*-un-lft-identity_binary64_78`
49×	`add-sqr-sqrt_binary64_100` `times-frac_binary64_84`
45×	`sqrt-prod_binary64_94`
36×	`add-cube-cbrt_binary64_113`
24×	`associate-r_binary64_18`
23×	`unpow-prod-down_binary64_157`
20×	`distribute-lft-out_binary64_29`
11×	`add-exp-log_binary64_116`
10×	`pow1_binary64_139`
8×	`add-cbrt-cube_binary64_114`
6×	`associate-/r/_binary64_24`
5×	`associate-/r*_binary64_22`
4×	`add-log-exp_binary64_117` `unswap-sqr_binary64_46`
3×	`associate-l_binary64_19` `sqrt-pow1_binary64_96` `flip-+_binary64_52` `rem-sqrt-square_binary64_91` `div-inv_binary64_75` `associate-/l*_binary64_23` `pow-unpow_binary64_155` `flip3-+_binary64_81`
2×	`div-exp_binary64_129` `inv-pow_binary64_163` `pow-flip_binary64_152` `sqrt-div_binary64_95`
1×	`-commutative_binary64_9` `pow-exp_binary64_146` `pow-to-exp_binary64_147` `cbrt-unprod_binary64_111` `cbrt-undiv_binary64_112` `prod-exp_binary64_127` `unpow2_binary64_143` `frac-2neg_binary64_89` `1-exp_binary64_122` `sqr-pow_binary64_50` `pow-pow_binary64_150` `rec-exp_binary64_128` `pow-prod-down_binary64_149` `associate-r/_binary64_20` `clear-num_binary64_77` `pow1/2_binary64_158`

Counts

4 → 138

Calls

4 calls:

19.0ms	(*.f64 (sin.f64 ky) (sqrt.f64 (/.f64 1 (+.f64 (pow.f64 (sin.f64 kx) 2) (pow.f64 (sin.f64 ky) 2)))))
11.0ms	(sqrt.f64 (/.f64 1 (+.f64 (pow.f64 (sin.f64 kx) 2) (pow.f64 (sin.f64 ky) 2))))
10.0ms	(/.f64 1 (+.f64 (pow.f64 (sin.f64 kx) 2) (pow.f64 (sin.f64 ky) 2)))
3.0ms	(pow.f64 (sin.f64 ky) 2)

series397.0ms (3.1%)

Counts

4 → 12

Calls

4 calls:

162.0ms	(*.f64 (sin.f64 ky) (sqrt.f64 (/.f64 1 (+.f64 (pow.f64 (sin.f64 kx) 2) (pow.f64 (sin.f64 ky) 2)))))
125.0ms	(sqrt.f64 (/.f64 1 (+.f64 (pow.f64 (sin.f64 kx) 2) (pow.f64 (sin.f64 ky) 2))))
97.0ms	(/.f64 1 (+.f64 (pow.f64 (sin.f64 kx) 2) (pow.f64 (sin.f64 ky) 2)))
14.0ms	(pow.f64 (sin.f64 ky) 2)

simplify95.0ms (0.7%)

Algorithm

1×	egg-herbie

Counts

150 → 150

Iterations

Useful iterations: 0 (64.0ms)

Iter	Nodes	Cost
0	4997	3166
1	4997	3166

prune191.0ms (1.5%)

Pruning

11 alts after pruning (9 fresh and 2 done)

	Pruned	Kept	Total
New	148	2	150
Fresh	2	7	9
Picked	0	1	1
Done	0	1	1
Total	150	11	161

Merged error: 1.9b

Counts

161 → 11

Compiler

Compiled 3752 to 2268 computations (39.6% saved)

regimes1.1s (8.4%)

Compiler: Compiled 11190 to 9282 computations (17.1% 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	62	67
1	62	67

end0.0ms (0%)

sample5.9s (46.3%)

Algorithm

1×

intervals

Results

3.3s	4633×	body	1024	valid
654.0ms	1419×	body	512	valid
193.0ms	1401×	body	128	valid
153.0ms	529×	body	256	valid
26.0ms	18×	body	2048	valid

Compiler

Compiled 1279 to 1056 computations (17.4% saved)

Details

analyze1.2s (9.5%)

sample146.0ms (1.1%)

simplify174.0ms (1.4%)

prune3.0ms (0%)

localize13.0ms (0.1%)

rewrite36.0ms (0.3%)

series416.0ms (3.3%)

simplify88.0ms (0.7%)

prune169.0ms (1.3%)

localize14.0ms (0.1%)

rewrite57.0ms (0.4%)

series278.0ms (2.2%)

simplify112.0ms (0.9%)

prune289.0ms (2.3%)

localize15.0ms (0.1%)

rewrite140.0ms (1.1%)

series279.0ms (2.2%)

simplify236.0ms (1.8%)

prune1.3s (10.4%)

localize14.0ms (0.1%)

rewrite62.0ms (0.5%)

series397.0ms (3.1%)

simplify95.0ms (0.7%)

prune191.0ms (1.5%)

regimes1.1s (8.4%)

bsearch4.0ms (0%)

simplify3.0ms (0%)

end0.0ms (0%)

sample5.9s (46.3%)

Profiling