Details

analyze1.4s (9.7%)

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%)

Algorithm

1×

intervals

Results

105.0ms	145×	body	1024	valid
17.0ms	38×	body	512	valid
7.0ms	54×	body	128	valid
6.0ms	19×	body	256	valid

Compiler

Compiled 33 to 32 computations (3% saved)

simplify181.0ms (1.3%)

Algorithm

1×	egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (82.0ms)

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: 6.5b

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 ky) 2)
0.3b	(pow.f64 (sin.f64 kx) 2)
6.0b	(sqrt.f64 (+.f64 (pow.f64 (sin.f64 kx) 2) (pow.f64 (sin.f64 ky) 2)))

rewrite34.0ms (0.2%)

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:

12.0ms	(/.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)

series279.0ms (2%)

Counts

4 → 12

Calls

4 calls:

157.0ms	(/.f64 (sin.f64 ky) (sqrt.f64 (+.f64 (pow.f64 (sin.f64 kx) 2) (pow.f64 (sin.f64 ky) 2))))
92.0ms	(sqrt.f64 (+.f64 (pow.f64 (sin.f64 kx) 2) (pow.f64 (sin.f64 ky) 2)))
16.0ms	(pow.f64 (sin.f64 ky) 2)
14.0ms	(pow.f64 (sin.f64 kx) 2)

simplify94.0ms (0.7%)

Algorithm

1×	egg-herbie

Counts

114 → 114

Iterations

Useful iterations: 0 (69.0ms)

Iter	Nodes	Cost
0	4939	2298
1	4939	2298

prune168.0ms (1.2%)

Pruning

12 alts after pruning (12 fresh and 0 done)

	Pruned	Kept	Total
New	102	12	114
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	103	12	115

Merged error: 4.5b

Counts

115 → 12

Compiler

Compiled 2847 to 1626 computations (42.9% 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 ky) 2)
0.3b	(pow.f64 (sin.f64 kx) 2)
6.0b	(sqrt.f64 (+.f64 (pow.f64 (sin.f64 kx) 2) (pow.f64 (sin.f64 ky) 2)))

rewrite62.0ms (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:

23.0ms	(/.f64 1 (/.f64 (sqrt.f64 (+.f64 (pow.f64 (sin.f64 kx) 2) (pow.f64 (sin.f64 ky) 2))) (sin.f64 ky)))
9.0ms	(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)

series271.0ms (1.9%)

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)))
80.0ms	(sqrt.f64 (+.f64 (pow.f64 (sin.f64 kx) 2) (pow.f64 (sin.f64 ky) 2)))
19.0ms	(pow.f64 (sin.f64 ky) 2)
13.0ms	(pow.f64 (sin.f64 kx) 2)

simplify119.0ms (0.8%)

Algorithm

1×	egg-herbie

Counts

201 → 201

Iterations

Useful iterations: 0 (66.0ms)

Iter	Nodes	Cost
0	4970	5648
1	4970	5648

prune287.0ms (2%)

Pruning

12 alts after pruning (11 fresh and 1 done)

	Pruned	Kept	Total
New	198	3	201
Fresh	3	8	11
Picked	0	1	1
Done	0	0	0
Total	201	12	213

Merged error: 4.5b

Counts

213 → 12

Compiler

Compiled 5644 to 3331 computations (41% saved)

localize18.0ms (0.1%)

Local error

Found 4 expressions with local error:

0.2b	(/.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)
0.3b	(pow.f64 (sin.f64 kx) 2)
6.0b	(sqrt.f64 (+.f64 (pow.f64 (sin.f64 kx) 2) (pow.f64 (sin.f64 ky) 2)))

rewrite133.0ms (0.9%)

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%)

Counts

4 → 12

Calls

4 calls:

159.0ms	(/.f64 (/.f64 1 (sqrt.f64 (+.f64 (pow.f64 (sin.f64 kx) 2) (pow.f64 (sin.f64 ky) 2)))) (/.f64 1 (sin.f64 ky)))
93.0ms	(sqrt.f64 (+.f64 (pow.f64 (sin.f64 kx) 2) (pow.f64 (sin.f64 ky) 2)))
14.0ms	(pow.f64 (sin.f64 kx) 2)
13.0ms	(pow.f64 (sin.f64 ky) 2)

simplify248.0ms (1.7%)

Algorithm

1×	egg-herbie

Counts

530 → 530

Iterations

Useful iterations: 0 (58.0ms)

Iter	Nodes	Cost
0	5026	22008

prune1.4s (9.7%)

Pruning

12 alts after pruning (10 fresh and 2 done)

	Pruned	Kept	Total
New	530	0	530
Fresh	0	10	10
Picked	0	1	1
Done	0	1	1
Total	530	12	542

Merged error: 4.5b

Counts

542 → 12

Compiler

Compiled 17121 to 10624 computations (37.9% saved)

localize23.0ms (0.2%)

Local error

Found 4 expressions with local error:

0.3b	(pow.f64 (sin.f64 kx) 2)
0.3b	(.f64 (/.f64 (.f64 (cbrt.f64 1) (cbrt.f64 1)) (sqrt.f64 (sqrt.f64 (+.f64 (pow.f64 (sin.f64 kx) 2) (pow.f64 (sin.f64 ky) 2))))) (/.f64 (cbrt.f64 1) (/.f64 (sqrt.f64 (sqrt.f64 (+.f64 (pow.f64 (sin.f64 kx) 2) (pow.f64 (sin.f64 ky) 2)))) (sin.f64 ky))))
6.0b	(sqrt.f64 (+.f64 (pow.f64 (sin.f64 kx) 2) (pow.f64 (sin.f64 ky) 2)))
6.0b	(sqrt.f64 (+.f64 (pow.f64 (sin.f64 kx) 2) (pow.f64 (sin.f64 ky) 2)))

rewrite236.0ms (1.7%)

Algorithm

1×	rewrite-expression-head

Rules

554×	`times-frac_binary64_84`
387×	`add-sqr-sqrt_binary64_100`
332×	`sqrt-prod_binary64_94`
313×	`*-un-lft-identity_binary64_78`
227×	`associate-r_binary64_18`
213×	`add-cube-cbrt_binary64_113`
143×	`cbrt-prod_binary64_109`
52×	`unswap-sqr_binary64_46`
45×	`unpow-prod-down_binary64_157`
42×	`distribute-lft-out_binary64_29`
41×	`add-exp-log_binary64_116`
28×	`add-cbrt-cube_binary64_114`
17×	`associate-l_binary64_19`
15×	`cbrt-undiv_binary64_112` `div-exp_binary64_129`
12×	`cbrt-unprod_binary64_111` `prod-exp_binary64_127`
9×	`pow1_binary64_139`
8×	`div-inv_binary64_75` `sqrt-div_binary64_95`
4×	`add-log-exp_binary64_117`
3×	`flip-+_binary64_52` `pow-unpow_binary64_155` `associate-/r/_binary64_24` `flip3-+_binary64_81`
2×	`sqrt-pow1_binary64_96` `rem-sqrt-square_binary64_91` `pow1/2_binary64_158`
1×	`-commutative_binary64_9` `pow-exp_binary64_146` `pow-to-exp_binary64_147` `unpow2_binary64_143` `sqr-pow_binary64_50` `frac-times_binary64_88` `pow-pow_binary64_150` `associate-l/_binary64_21` `pow-prod-down_binary64_149` `associate-*r/_binary64_20`

Counts

4 → 378

Calls

4 calls:

126.0ms	(.f64 (/.f64 (.f64 (cbrt.f64 1) (cbrt.f64 1)) (sqrt.f64 (sqrt.f64 (+.f64 (pow.f64 (sin.f64 kx) 2) (pow.f64 (sin.f64 ky) 2))))) (/.f64 (cbrt.f64 1) (/.f64 (sqrt.f64 (sqrt.f64 (+.f64 (pow.f64 (sin.f64 kx) 2) (pow.f64 (sin.f64 ky) 2)))) (sin.f64 ky))))
9.0ms	(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 kx) 2)

series369.0ms (2.6%)

Counts

4 → 12

Calls

4 calls:

167.0ms	(.f64 (/.f64 (.f64 (cbrt.f64 1) (cbrt.f64 1)) (sqrt.f64 (sqrt.f64 (+.f64 (pow.f64 (sin.f64 kx) 2) (pow.f64 (sin.f64 ky) 2))))) (/.f64 (cbrt.f64 1) (/.f64 (sqrt.f64 (sqrt.f64 (+.f64 (pow.f64 (sin.f64 kx) 2) (pow.f64 (sin.f64 ky) 2)))) (sin.f64 ky))))
94.0ms	(sqrt.f64 (+.f64 (pow.f64 (sin.f64 kx) 2) (pow.f64 (sin.f64 ky) 2)))
93.0ms	(sqrt.f64 (+.f64 (pow.f64 (sin.f64 kx) 2) (pow.f64 (sin.f64 ky) 2)))
14.0ms	(pow.f64 (sin.f64 kx) 2)

simplify236.0ms (1.7%)

Algorithm

1×	egg-herbie

Counts

390 → 390

Iterations

Useful iterations: 0 (75.0ms)

Iter	Nodes	Cost
0	4979	20479
1	4979	20479

prune1.6s (11.5%)

Pruning

12 alts after pruning (9 fresh and 3 done)

	Pruned	Kept	Total
New	390	0	390
Fresh	0	9	9
Picked	0	1	1
Done	0	2	2
Total	390	12	402

Merged error: 4.5b

Counts

402 → 12

Compiler

Compiled 20149 to 13462 computations (33.2% saved)

regimes845.0ms (6%)

Compiler: Compiled 9566 to 7704 computations (19.5% saved)

bsearch2.0ms (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%)

sample5.8s (40.5%)

Algorithm

1×

intervals

Results

3.3s	4639×	body	1024	valid
654.0ms	1403×	body	512	valid
192.0ms	1417×	body	128	valid
160.0ms	525×	body	256	valid
22.0ms	16×	body	2048	valid

Compiler

Compiled 1095 to 878 computations (19.8% saved)

Details

analyze1.4s (9.7%)

sample146.0ms (1%)

simplify181.0ms (1.3%)

prune3.0ms (0%)

localize13.0ms (0.1%)

rewrite34.0ms (0.2%)

series279.0ms (2%)

simplify94.0ms (0.7%)

prune168.0ms (1.2%)

localize14.0ms (0.1%)

rewrite62.0ms (0.4%)

series271.0ms (1.9%)

simplify119.0ms (0.8%)

prune287.0ms (2%)

localize18.0ms (0.1%)

rewrite133.0ms (0.9%)

series279.0ms (2%)

simplify248.0ms (1.7%)

prune1.4s (9.7%)

localize23.0ms (0.2%)

rewrite236.0ms (1.7%)

series369.0ms (2.6%)

simplify236.0ms (1.7%)

prune1.6s (11.5%)

regimes845.0ms (6%)

bsearch2.0ms (0%)

simplify3.0ms (0%)

end0.0ms (0%)

sample5.8s (40.5%)

Profiling