Details

analyze600.0ms (8.8%)

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)

sample89.0ms (1.3%)

Algorithm

1×

intervals

Results

33.0ms	194×	body	128	valid
30.0ms	35×	body	1024	valid
10.0ms	17×	body	512	valid
4.0ms	10×	body	256	valid

Compiler

Compiled 59 to 63 computations (-6.8% saved)

simplify197.0ms (2.9%)

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: 0.8b

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)
0.3b	(pow.f64 (sin.f64 kx) 2)
2.2b	(.f64 (pow.f64 (/.f64 (.f64 2 l) Om) 2) (+.f64 (pow.f64 (sin.f64 kx) 2) (pow.f64 (sin.f64 ky) 2)))
11.3b	(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)))))

rewrite40.0ms (0.6%)

Algorithm

1×	rewrite-expression-head

Rules

20×	`add-sqr-sqrt_binary64_98`
18×	`add-exp-log_binary64_112`
17×	`*-un-lft-identity_binary64_77`
16×	`unpow-prod-down_binary64_153`
13×	`add-cube-cbrt_binary64_109`
12×	`associate-l_binary64_20`
7×	`pow1_binary64_135`
6×	`add-cbrt-cube_binary64_110` `pow-unpow_binary64_151` `prod-exp_binary64_123`
5×	`pow-exp_binary64_142` `associate-r_binary64_19`
4×	`add-log-exp_binary64_113` `sqr-pow_binary64_49` `unswap-sqr_binary64_45` `unpow2_binary64_139`
3×	`pow-to-exp_binary64_143` `sqrt-prod_binary64_92` `times-frac_binary64_83`
2×	`flip-+_binary64_51` `sqrt-div_binary64_93` `flip3-+_binary64_80` `associate-*r/_binary64_21` `div-exp_binary64_125` `pow-pow_binary64_146` `distribute-lft-out_binary64_30`
1×	`rem-sqrt-square_binary64_90` `sqrt-pow1_binary64_94` `cbrt-unprod_binary64_107` `distribute-lft-in_binary64_28` `*-commutative_binary64_10` `pow1/2_binary64_154` `distribute-rgt-in_binary64_29` `div-inv_binary64_74`

Counts

4 → 90

Calls

4 calls:

21.0ms	(.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 kx) 2)
3.0ms	(pow.f64 (sin.f64 ky) 2)

series1.0s (14.7%)

Counts

4 → 12

Calls

4 calls:

653.0ms	(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)))))
300.0ms	(.f64 (pow.f64 (/.f64 (.f64 2 l) Om) 2) (+.f64 (pow.f64 (sin.f64 kx) 2) (pow.f64 (sin.f64 ky) 2)))
24.0ms	(pow.f64 (sin.f64 ky) 2)
24.0ms	(pow.f64 (sin.f64 kx) 2)

simplify63.0ms (0.9%)

Algorithm

1×	egg-herbie

Counts

102 → 102

Iterations

Useful iterations: 0 (41.0ms)

Iter	Nodes	Cost
0	4984	2193
1	4984	2193

prune176.0ms (2.6%)

Pruning

2 alts after pruning (2 fresh and 0 done)

	Pruned	Kept	Total
New	100	2	102
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	101	2	103

Merged error: 0.6b

Counts

103 → 2

Compiler

Compiled 3230 to 2425 computations (24.9% saved)

localize23.0ms (0.3%)

Local error

Found 4 expressions with local error:

1.1b	(.f64 (/.f64 (.f64 2 l) Om) (sqrt.f64 (+.f64 (pow.f64 (sin.f64 kx) 2) (pow.f64 (sin.f64 ky) 2))))
2.3b	(sqrt.f64 (+.f64 (pow.f64 (sin.f64 kx) 2) (pow.f64 (sin.f64 ky) 2)))
2.3b	(sqrt.f64 (+.f64 (pow.f64 (sin.f64 kx) 2) (pow.f64 (sin.f64 ky) 2)))
11.3b	(sqrt.f64 (+.f64 1 (.f64 (.f64 (/.f64 (.f64 2 l) Om) (sqrt.f64 (+.f64 (pow.f64 (sin.f64 kx) 2) (pow.f64 (sin.f64 ky) 2)))) (.f64 (/.f64 (*.f64 2 l) Om) (sqrt.f64 (+.f64 (pow.f64 (sin.f64 kx) 2) (pow.f64 (sin.f64 ky) 2)))))))

rewrite60.0ms (0.9%)

Algorithm

1×	rewrite-expression-head

Rules

23×	`*-un-lft-identity_binary64_77`
19×	`sqrt-prod_binary64_92`
18×	`add-sqr-sqrt_binary64_98`
13×	`add-exp-log_binary64_112` `add-cbrt-cube_binary64_110`
11×	`add-cube-cbrt_binary64_109`
10×	`sqrt-div_binary64_93`
9×	`pow1_binary64_135`
8×	`associate-r_binary64_19`
7×	`associate-l_binary64_20`
6×	`unpow-prod-down_binary64_153` `distribute-lft-out_binary64_30`
5×	`flip-+_binary64_51` `flip3-+_binary64_80`
4×	`add-log-exp_binary64_113` `cbrt-unprod_binary64_107` `prod-exp_binary64_123`
3×	`rem-sqrt-square_binary64_90` `sqrt-pow1_binary64_94` `times-frac_binary64_83` `pow1/2_binary64_154`
2×	`cbrt-undiv_binary64_108` `frac-times_binary64_87` `associate-*r/_binary64_21` `div-exp_binary64_125` `unswap-sqr_binary64_45`
1×	`pow-prod-down_binary64_145` `associate-l/_binary64_22` `-commutative_binary64_10` `div-inv_binary64_74`

Counts

4 → 86

Calls

4 calls:

18.0ms	(.f64 (/.f64 (.f64 2 l) Om) (sqrt.f64 (+.f64 (pow.f64 (sin.f64 kx) 2) (pow.f64 (sin.f64 ky) 2))))
9.0ms	(sqrt.f64 (+.f64 1 (.f64 (.f64 (/.f64 (.f64 2 l) Om) (sqrt.f64 (+.f64 (pow.f64 (sin.f64 kx) 2) (pow.f64 (sin.f64 ky) 2)))) (.f64 (/.f64 (*.f64 2 l) Om) (sqrt.f64 (+.f64 (pow.f64 (sin.f64 kx) 2) (pow.f64 (sin.f64 ky) 2)))))))
9.0ms	(sqrt.f64 (+.f64 (pow.f64 (sin.f64 kx) 2) (pow.f64 (sin.f64 ky) 2)))
9.0ms	(sqrt.f64 (+.f64 (pow.f64 (sin.f64 kx) 2) (pow.f64 (sin.f64 ky) 2)))

series1.3s (19.4%)

Counts

4 → 12

Calls

4 calls:

661.0ms	(sqrt.f64 (+.f64 1 (.f64 (.f64 (/.f64 (.f64 2 l) Om) (sqrt.f64 (+.f64 (pow.f64 (sin.f64 kx) 2) (pow.f64 (sin.f64 ky) 2)))) (.f64 (/.f64 (*.f64 2 l) Om) (sqrt.f64 (+.f64 (pow.f64 (sin.f64 kx) 2) (pow.f64 (sin.f64 ky) 2)))))))
363.0ms	(.f64 (/.f64 (.f64 2 l) Om) (sqrt.f64 (+.f64 (pow.f64 (sin.f64 kx) 2) (pow.f64 (sin.f64 ky) 2))))
155.0ms	(sqrt.f64 (+.f64 (pow.f64 (sin.f64 kx) 2) (pow.f64 (sin.f64 ky) 2)))
146.0ms	(sqrt.f64 (+.f64 (pow.f64 (sin.f64 kx) 2) (pow.f64 (sin.f64 ky) 2)))

simplify66.0ms (1%)

Algorithm

1×	egg-herbie

Counts

98 → 98

Iterations

Useful iterations: 0 (40.0ms)

Iter	Nodes	Cost
0	5018	2575

prune237.0ms (3.5%)

Pruning

2 alts after pruning (1 fresh and 1 done)

	Pruned	Kept	Total
New	98	0	98
Fresh	0	1	1
Picked	0	1	1
Done	0	0	0
Total	98	2	100

Merged error: 0.6b

Counts

100 → 2

Compiler

Compiled 4547 to 3186 computations (29.9% saved)

localize4.0ms (0.1%)

rewrite0.0ms (0%)

Algorithm

1×	rewrite-expression-head

Rules

Counts

0 → 0

series0.0ms (0%)

Counts: 0 → 0

simplify6.0ms (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: 0.6b

Counts

2 → 2

Compiler

Compiled 0 to 0 computations (0% saved)

regimes131.0ms (1.9%)

Compiler: Compiled 583 to 623 computations (-6.9% saved)

bsearch0.0ms (0%)

simplify2.0ms (0%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	29	65
1	29	65

end0.0ms (0%)

sample2.8s (40.7%)

Algorithm

1×

intervals

Results

1.1s	6277×	body	128	valid
776.0ms	853×	body	1024	valid
336.0ms	557×	body	512	valid
128.0ms	313×	body	256	valid

Compiler

Compiled 118 to 114 computations (3.4% saved)

Details

analyze600.0ms (8.8%)

sample89.0ms (1.3%)

simplify197.0ms (2.9%)

prune5.0ms (0.1%)

localize21.0ms (0.3%)

rewrite40.0ms (0.6%)

series1.0s (14.7%)

simplify63.0ms (0.9%)

prune176.0ms (2.6%)

localize23.0ms (0.3%)

rewrite60.0ms (0.9%)

series1.3s (19.4%)

simplify66.0ms (1%)

prune237.0ms (3.5%)

localize4.0ms (0.1%)

rewrite0.0ms (0%)

series0.0ms (0%)

simplify6.0ms (0.1%)

prune1.0ms (0%)

regimes131.0ms (1.9%)

bsearch0.0ms (0%)

simplify2.0ms (0%)

end0.0ms (0%)

sample2.8s (40.7%)

Profiling