Details

analyze619.0ms (8%)

Algorithm

1×

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)

sample75.0ms (1%)

Algorithm

1×

intervals

Results

37.0ms	217×	body	128	valid
17.0ms	21×	body	1024	valid
5.0ms	9×	body	512	valid
4.0ms	9×	body	256	valid

Compiler

Compiled 59 to 63 computations (-6.8% saved)

simplify135.0ms (1.7%)

Algorithm

1×	egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (39.0ms)

Iter	Nodes	Cost
0	5325	39

prune5.0ms (0.1%)

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

Merged error: 0.5b

Counts

2 → 1

Compiler

Compiled 50 to 50 computations (0% saved)

localize21.0ms (0.3%)

Local error

Found 4 expressions with local error:

0.3b	(pow.f64 (sin.f64 ky) 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))))))
1.7b	(.f64 (pow.f64 (/.f64 (.f64 2 l) Om) 2) (+.f64 (pow.f64 (sin.f64 kx) 2) (pow.f64 (sin.f64 ky) 2)))
7.5b	(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)))))

rewrite42.0ms (0.5%)

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:

16.0ms	(.f64 (pow.f64 (/.f64 (.f64 2 l) Om) 2) (+.f64 (pow.f64 (sin.f64 kx) 2) (pow.f64 (sin.f64 ky) 2)))
6.0ms	(/.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))))))
4.0ms	(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)))))
3.0ms	(pow.f64 (sin.f64 ky) 2)

series1.2s (15.8%)

Counts

4 → 12

Calls

4 calls:

643.0ms	(/.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))))))
399.0ms	(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)))))
164.0ms	(.f64 (pow.f64 (/.f64 (.f64 2 l) Om) 2) (+.f64 (pow.f64 (sin.f64 kx) 2) (pow.f64 (sin.f64 ky) 2)))
15.0ms	(pow.f64 (sin.f64 ky) 2)

simplify80.0ms (1%)

Algorithm

1×	egg-herbie

Counts

125 → 125

Iterations

Useful iterations: 0 (43.0ms)

Iter	Nodes	Cost
0	5030	4123

prune258.0ms (3.3%)

Pruning

2 alts after pruning (2 fresh and 0 done)

	Pruned	Kept	Total
New	123	2	125
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	124	2	126

Merged error: 0.1b

Counts

126 → 2

Compiler

Compiled 4400 to 3334 computations (24.2% saved)

localize21.0ms (0.3%)

Local error

Found 4 expressions with local error:

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)))))))
0.4b	(.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))))
2.0b	(.f64 (/.f64 (.f64 2 l) Om) (+.f64 (pow.f64 (sin.f64 kx) 2) (pow.f64 (sin.f64 ky) 2)))
7.5b	(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))))))

rewrite71.0ms (0.9%)

Algorithm

1×	rewrite-expression-head

Rules

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

Counts

4 → 148

Calls

4 calls:

20.0ms	(.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))))
16.0ms	(.f64 (/.f64 (.f64 2 l) Om) (+.f64 (pow.f64 (sin.f64 kx) 2) (pow.f64 (sin.f64 ky) 2)))
7.0ms	(/.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)))))))
4.0ms	(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))))))

series1.4s (18.2%)

Counts

4 → 12

Calls

4 calls:

644.0ms	(/.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)))))))
397.0ms	(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))))))
194.0ms	(.f64 (/.f64 (.f64 2 l) Om) (+.f64 (pow.f64 (sin.f64 kx) 2) (pow.f64 (sin.f64 ky) 2)))
171.0ms	(.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))))

simplify104.0ms (1.3%)

Algorithm

1×	egg-herbie

Counts

160 → 160

Iterations

Useful iterations: 0 (50.0ms)

Iter	Nodes	Cost
0	4994	5827
1	4994	5827

prune327.0ms (4.2%)

Pruning

2 alts after pruning (1 fresh and 1 done)

	Pruned	Kept	Total
New	160	0	160
Fresh	0	1	1
Picked	0	1	1
Done	0	0	0
Total	160	2	162

Merged error: 0.1b

Counts

162 → 2

Compiler

Compiled 5936 to 4092 computations (31.1% saved)

localize3.0ms (0%)

rewrite0.0ms (0%)

Algorithm

1×	rewrite-expression-head

Rules

Counts

0 → 0

series0.0ms (0%)

Counts: 0 → 0

simplify7.0ms (0.1%)

Algorithm

1×	egg-herbie

Counts

0 → 0

Iterations

Useful iterations: 0 (2.0ms)

Iter	Nodes	Cost
0	0	0

prune1.0ms (0%)

Pruning

2 alts after pruning (0 fresh and 2 done)

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

Merged error: 0.1b

Counts

2 → 2

Compiler

Compiled 0 to 0 computations (0% saved)

regimes531.0ms (6.9%)

Compiler: Compiled 4087 to 4221 computations (-3.3% saved)

bsearch0.0ms (0%)

simplify2.0ms (0%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	29	45
1	29	45

end0.0ms (0%)

sample2.8s (36.3%)

Algorithm

1×

intervals

Results

1.1s	6292×	body	128	valid
684.0ms	799×	body	1024	valid
364.0ms	605×	body	512	valid
123.0ms	304×	body	256	valid

Compiler

Compiled 214 to 216 computations (-0.9% saved)

Details

analyze619.0ms (8%)

sample75.0ms (1%)

simplify135.0ms (1.7%)

prune5.0ms (0.1%)

localize21.0ms (0.3%)

rewrite42.0ms (0.5%)

series1.2s (15.8%)

simplify80.0ms (1%)

prune258.0ms (3.3%)

localize21.0ms (0.3%)

rewrite71.0ms (0.9%)

series1.4s (18.2%)

simplify104.0ms (1.3%)

prune327.0ms (4.2%)

localize3.0ms (0%)

rewrite0.0ms (0%)

series0.0ms (0%)

simplify7.0ms (0.1%)

prune1.0ms (0%)

regimes531.0ms (6.9%)

bsearch0.0ms (0%)

simplify2.0ms (0%)

end0.0ms (0%)

sample2.8s (36.3%)

Profiling