Details

analyze1.4s (4.5%)

Algorithm

1×	search
2×	egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	4998	273
1	4998	273
0	4	4
1	4	4

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)

sample154.0ms (0.5%)

Algorithm

1×

intervals

Results

65.0ms	208×	body	128	valid
31.0ms	22×	body	1024	valid
17.0ms	16×	body	512	valid
7.0ms	10×	body	256	valid

Compiler

Compiled 59 to 63 computations (-6.8% saved)

simplify90.0ms (0.3%)

Algorithm

1×	egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (78.0ms)

Iter	Nodes	Cost
0	5325	39

prune10.0ms (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

0.3b

Counts

2 → 1

Compiler

Compiled 50 to 50 computations (0% saved)

localize47.0ms (0.2%)

Local error

Found 4 expressions with local error:

0.3b	(pow.f64 (sin.f64 kx) 2)
0.4b	(/.f64 1/2 (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))))))
1.6b	(.f64 (pow.f64 (/.f64 (.f64 2 l) Om) 2) (+.f64 (pow.f64 (sin.f64 kx) 2) (pow.f64 (sin.f64 ky) 2)))
7.7b	(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)))))

rewrite88.0ms (0.3%)

Algorithm

1×	rewrite-expression-head

Rules

33×	`add-sqr-sqrt_binary64_100`
30×	`*-un-lft-identity_binary64_78`
26×	`add-cube-cbrt_binary64_113`
21×	`times-frac_binary64_84`
19×	`add-exp-log_binary64_116`
15×	`sqrt-prod_binary64_94`
13×	`unpow-prod-down_binary64_157`
12×	`associate-l_binary64_19`
8×	`add-cbrt-cube_binary64_114`
6×	`prod-exp_binary64_127` `associate-/r*_binary64_22` `pow1_binary64_139`
5×	`associate-r_binary64_18`
4×	`pow-exp_binary64_146` `add-log-exp_binary64_117` `unswap-sqr_binary64_46` `sqrt-div_binary64_95`
3×	`div-exp_binary64_129` `flip-+_binary64_52` `unpow2_binary64_143` `sqr-pow_binary64_50` `associate-/l*_binary64_23` `pow-unpow_binary64_155` `flip3-+_binary64_81`
2×	`pow-to-exp_binary64_147` `div-inv_binary64_75` `associate-/r/_binary64_24` `associate-*r/_binary64_20` `distribute-lft-out_binary64_29`
1×	`distribute-lft-in_binary64_27` `*-commutative_binary64_9` `sqrt-pow1_binary64_96` `cbrt-unprod_binary64_111` `cbrt-undiv_binary64_112` `rem-sqrt-square_binary64_91` `distribute-rgt-in_binary64_28` `frac-2neg_binary64_89` `pow-pow_binary64_150` `clear-num_binary64_77` `pow1/2_binary64_158`

Counts

4 → 113

Calls

4 calls:

34.0ms	(.f64 (pow.f64 (/.f64 (.f64 2 l) Om) 2) (+.f64 (pow.f64 (sin.f64 kx) 2) (pow.f64 (sin.f64 ky) 2)))
14.0ms	(/.f64 1/2 (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))))))
7.0ms	(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)))))
6.0ms	(pow.f64 (sin.f64 kx) 2)

series5.6s (18.7%)

Counts

4 → 55

Calls

4 calls:

2.7s	(/.f64 1/2 (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))))))
1.7s	(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)))))
1.0s	(.f64 (pow.f64 (/.f64 (.f64 2 l) Om) 2) (+.f64 (pow.f64 (sin.f64 kx) 2) (pow.f64 (sin.f64 ky) 2)))
44.0ms	(pow.f64 (sin.f64 kx) 2)

Compiler

Compiled 3971 to 3638 computations (8.4% saved)

simplify148.0ms (0.5%)

Algorithm

1×	egg-herbie

Counts

168 → 168

Iterations

Useful iterations: 0 (62.0ms)

Iter	Nodes	Cost
0	5057	5785

prune703.0ms (2.4%)

Pruning

2 alts after pruning (2 fresh and 0 done)

	Pruned	Kept	Total
New	166	2	168
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	167	2	169

Error

0.0b

Counts

169 → 2

Compiler

Compiled 5746 to 4206 computations (26.8% saved)

localize44.0ms (0.1%)

Local error

Found 4 expressions with local error:

0.3b	(pow.f64 (sin.f64 kx) 2)
0.4b	(/.f64 1/2 (sqrt.f64 (+.f64 1 (.f64 (/.f64 (.f64 2 l) Om) (.f64 (/.f64 (.f64 2 l) Om) (+.f64 (pow.f64 (sin.f64 kx) 2) (pow.f64 (sin.f64 ky) 2)))))))
3.1b	(.f64 (/.f64 (.f64 2 l) Om) (+.f64 (pow.f64 (sin.f64 kx) 2) (pow.f64 (sin.f64 ky) 2)))
7.7b	(sqrt.f64 (+.f64 1 (.f64 (/.f64 (.f64 2 l) Om) (.f64 (/.f64 (.f64 2 l) Om) (+.f64 (pow.f64 (sin.f64 kx) 2) (pow.f64 (sin.f64 ky) 2))))))

rewrite79.0ms (0.3%)

Algorithm

1×	rewrite-expression-head

Rules

29×	`*-un-lft-identity_binary64_78`
28×	`add-sqr-sqrt_binary64_100`
25×	`add-cube-cbrt_binary64_113`
21×	`times-frac_binary64_84`
16×	`add-exp-log_binary64_116`
15×	`add-cbrt-cube_binary64_114` `sqrt-prod_binary64_94`
8×	`pow1_binary64_139`
7×	`associate-l_binary64_19`
6×	`associate-/r*_binary64_22`
5×	`unpow-prod-down_binary64_157` `associate-r_binary64_18`
4×	`add-log-exp_binary64_117` `cbrt-unprod_binary64_111` `prod-exp_binary64_127` `flip-+_binary64_52` `sqrt-div_binary64_95` `flip3-+_binary64_81`
3×	`cbrt-undiv_binary64_112` `div-exp_binary64_129` `associate-/l*_binary64_23` `pow-unpow_binary64_155`
2×	`div-inv_binary64_75` `frac-times_binary64_88` `associate-/r/_binary64_24` `associate-*r/_binary64_20` `distribute-lft-out_binary64_29`
1×	`distribute-lft-in_binary64_27` `-commutative_binary64_9` `pow-exp_binary64_146` `pow-to-exp_binary64_147` `sqrt-pow1_binary64_96` `rem-sqrt-square_binary64_91` `unpow2_binary64_143` `distribute-rgt-in_binary64_28` `frac-2neg_binary64_89` `sqr-pow_binary64_50` `pow-pow_binary64_150` `associate-l/_binary64_21` `pow-prod-down_binary64_149` `unswap-sqr_binary64_46` `clear-num_binary64_77` `pow1/2_binary64_158`

Counts

4 → 109

Calls

4 calls:

30.0ms	(.f64 (/.f64 (.f64 2 l) Om) (+.f64 (pow.f64 (sin.f64 kx) 2) (pow.f64 (sin.f64 ky) 2)))
13.0ms	(/.f64 1/2 (sqrt.f64 (+.f64 1 (.f64 (/.f64 (.f64 2 l) Om) (.f64 (/.f64 (.f64 2 l) Om) (+.f64 (pow.f64 (sin.f64 kx) 2) (pow.f64 (sin.f64 ky) 2)))))))
7.0ms	(sqrt.f64 (+.f64 1 (.f64 (/.f64 (.f64 2 l) Om) (.f64 (/.f64 (.f64 2 l) Om) (+.f64 (pow.f64 (sin.f64 kx) 2) (pow.f64 (sin.f64 ky) 2))))))
6.0ms	(pow.f64 (sin.f64 kx) 2)

series5.4s (18%)

Counts

4 → 55

Calls

4 calls:

2.8s	(/.f64 1/2 (sqrt.f64 (+.f64 1 (.f64 (/.f64 (.f64 2 l) Om) (.f64 (/.f64 (.f64 2 l) Om) (+.f64 (pow.f64 (sin.f64 kx) 2) (pow.f64 (sin.f64 ky) 2)))))))
1.6s	(sqrt.f64 (+.f64 1 (.f64 (/.f64 (.f64 2 l) Om) (.f64 (/.f64 (.f64 2 l) Om) (+.f64 (pow.f64 (sin.f64 kx) 2) (pow.f64 (sin.f64 ky) 2))))))
885.0ms	(.f64 (/.f64 (.f64 2 l) Om) (+.f64 (pow.f64 (sin.f64 kx) 2) (pow.f64 (sin.f64 ky) 2)))
43.0ms	(pow.f64 (sin.f64 kx) 2)

Compiler

Compiled 4039 to 3638 computations (9.9% saved)

simplify165.0ms (0.6%)

Algorithm

1×	egg-herbie

Counts

164 → 164

Iterations

Useful iterations: 0 (72.0ms)

Iter	Nodes	Cost
0	5159	5640

prune561.0ms (1.9%)

Pruning

2 alts after pruning (1 fresh and 1 done)

	Pruned	Kept	Total
New	163	1	164
Fresh	1	0	1
Picked	0	1	1
Done	0	0	0
Total	164	2	166

Error

0.0b

Counts

166 → 2

Compiler

Compiled 5972 to 4092 computations (31.5% saved)

localize56.0ms (0.2%)

Local error

Found 4 expressions with local error:

0.9b	(/.f64 1/2 (+.f64 (.f64 l (sqrt.f64 (.f64 (/.f64 4 Om) (/.f64 (+.f64 (pow.f64 (sin.f64 kx) 2) (pow.f64 (sin.f64 ky) 2)) Om)))) (.f64 1/2 (/.f64 (sqrt.f64 (/.f64 1 (.f64 (/.f64 4 Om) (/.f64 (+.f64 (pow.f64 (sin.f64 kx) 2) (pow.f64 (sin.f64 ky) 2)) Om)))) l))))
1.1b	(/.f64 (sqrt.f64 (/.f64 1 (*.f64 (/.f64 4 Om) (/.f64 (+.f64 (pow.f64 (sin.f64 kx) 2) (pow.f64 (sin.f64 ky) 2)) Om)))) l)
29.0b	(sqrt.f64 (*.f64 (/.f64 4 Om) (/.f64 (+.f64 (pow.f64 (sin.f64 kx) 2) (pow.f64 (sin.f64 ky) 2)) Om)))
29.8b	(sqrt.f64 (/.f64 1 (*.f64 (/.f64 4 Om) (/.f64 (+.f64 (pow.f64 (sin.f64 kx) 2) (pow.f64 (sin.f64 ky) 2)) Om))))

rewrite169.0ms (0.6%)

Algorithm

1×	rewrite-expression-head

Rules

63×	`times-frac_binary64_84`
51×	`sqrt-prod_binary64_94`
41×	`add-sqr-sqrt_binary64_100`
40×	`add-cube-cbrt_binary64_113` `*-un-lft-identity_binary64_78`
20×	`associate-/r/_binary64_24`
16×	`associate-/l*_binary64_23`
13×	`associate-*r/_binary64_20`
11×	`pow1_binary64_139`
8×	`add-cbrt-cube_binary64_114` `add-exp-log_binary64_116` `sqrt-div_binary64_95`
7×	`div-inv_binary64_75` `frac-times_binary64_88` `associate-*l/_binary64_21`
6×	`sqrt-pow1_binary64_96` `associate-/r*_binary64_22`
4×	`add-log-exp_binary64_117`
3×	`frac-add_binary64_86`
2×	`cbrt-undiv_binary64_112` `div-exp_binary64_129` `frac-2neg_binary64_89` `pow-flip_binary64_152` `pow-prod-down_binary64_149` `clear-num_binary64_77` `pow1/2_binary64_158`
1×	`inv-pow_binary64_163` `flip-+_binary64_52` `rem-sqrt-square_binary64_91` `associate-/l/_binary64_25` `flip3-+_binary64_81`

Counts

4 → 138

Calls

4 calls:

42.0ms	(/.f64 1/2 (+.f64 (.f64 l (sqrt.f64 (.f64 (/.f64 4 Om) (/.f64 (+.f64 (pow.f64 (sin.f64 kx) 2) (pow.f64 (sin.f64 ky) 2)) Om)))) (.f64 1/2 (/.f64 (sqrt.f64 (/.f64 1 (.f64 (/.f64 4 Om) (/.f64 (+.f64 (pow.f64 (sin.f64 kx) 2) (pow.f64 (sin.f64 ky) 2)) Om)))) l))))
35.0ms	(/.f64 (sqrt.f64 (/.f64 1 (*.f64 (/.f64 4 Om) (/.f64 (+.f64 (pow.f64 (sin.f64 kx) 2) (pow.f64 (sin.f64 ky) 2)) Om)))) l)
28.0ms	(sqrt.f64 (/.f64 1 (*.f64 (/.f64 4 Om) (/.f64 (+.f64 (pow.f64 (sin.f64 kx) 2) (pow.f64 (sin.f64 ky) 2)) Om))))
22.0ms	(sqrt.f64 (*.f64 (/.f64 4 Om) (/.f64 (+.f64 (pow.f64 (sin.f64 kx) 2) (pow.f64 (sin.f64 ky) 2)) Om)))

series5.5s (18.6%)

Counts

4 → 54

Calls

4 calls:

2.6s	(/.f64 1/2 (+.f64 (.f64 l (sqrt.f64 (.f64 (/.f64 4 Om) (/.f64 (+.f64 (pow.f64 (sin.f64 kx) 2) (pow.f64 (sin.f64 ky) 2)) Om)))) (.f64 1/2 (/.f64 (sqrt.f64 (/.f64 1 (.f64 (/.f64 4 Om) (/.f64 (+.f64 (pow.f64 (sin.f64 kx) 2) (pow.f64 (sin.f64 ky) 2)) Om)))) l))))
1.4s	(/.f64 (sqrt.f64 (/.f64 1 (*.f64 (/.f64 4 Om) (/.f64 (+.f64 (pow.f64 (sin.f64 kx) 2) (pow.f64 (sin.f64 ky) 2)) Om)))) l)
837.0ms	(sqrt.f64 (/.f64 1 (*.f64 (/.f64 4 Om) (/.f64 (+.f64 (pow.f64 (sin.f64 kx) 2) (pow.f64 (sin.f64 ky) 2)) Om))))
662.0ms	(sqrt.f64 (*.f64 (/.f64 4 Om) (/.f64 (+.f64 (pow.f64 (sin.f64 kx) 2) (pow.f64 (sin.f64 ky) 2)) Om)))

Compiler

Compiled 4444 to 3651 computations (17.8% saved)

simplify195.0ms (0.7%)

Algorithm

1×	egg-herbie

Counts

192 → 192

Iterations

Useful iterations: 0 (60.0ms)

Iter	Nodes	Cost
0	5033	7955

prune1.2s (4.1%)

Pruning

2 alts after pruning (0 fresh and 2 done)

	Pruned	Kept	Total
New	192	0	192
Fresh	0	0	0
Picked	0	1	1
Done	0	1	1
Total	192	2	194

Error

0.0b

Counts

194 → 2

Compiler

Compiled 10088 to 6854 computations (32.1% saved)

regimes2.0s (6.8%)

Accuracy

Total 0.7b remaining (93.2%)

Threshold costs 0.7b (93.2%)

Compiler

Compiled 11388 to 10704 computations (6% saved)

bsearch0.0ms (0%)

simplify23.0ms (0.1%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	29	65
1	29	65

Compiler

Compiled 82 to 70 computations (14.6% saved)

end0.0ms (0%)

sample6.2s (20.8%)

Algorithm

1×

intervals

Results

2.1s	6359×	body	128	valid
1.2s	766×	body	1024	valid
635.0ms	559×	body	512	valid
241.0ms	315×	body	256	valid
2.0ms	1×	body	2048	valid

Compiler

Compiled 609 to 564 computations (7.4% saved)

Details

analyze1.4s (4.5%)

sample154.0ms (0.5%)

simplify90.0ms (0.3%)

prune10.0ms (0%)

localize47.0ms (0.2%)

rewrite88.0ms (0.3%)

series5.6s (18.7%)

simplify148.0ms (0.5%)

prune703.0ms (2.4%)

localize44.0ms (0.1%)

rewrite79.0ms (0.3%)

series5.4s (18%)

simplify165.0ms (0.6%)

prune561.0ms (1.9%)

localize56.0ms (0.2%)

rewrite169.0ms (0.6%)

series5.5s (18.6%)

simplify195.0ms (0.7%)

prune1.2s (4.1%)

regimes2.0s (6.8%)

bsearch0.0ms (0%)

simplify23.0ms (0.1%)

end0.0ms (0%)

sample6.2s (20.8%)

Profiling