Details

analyze622.0ms (5.5%)

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)

sample93.0ms (0.8%)

Algorithm

1×

intervals

Results

38.0ms	199×	body	128	valid
29.0ms	32×	body	1024	valid
11.0ms	18×	body	512	valid
3.0ms	7×	body	256	valid

Compiler

Compiled 59 to 63 computations (-6.8% saved)

simplify206.0ms (1.8%)

Algorithm

1×	egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (40.0ms)

Iter	Nodes	Cost
0	5325	39

prune8.0ms (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 104 to 104 computations (0% saved)

localize22.0ms (0.2%)

Local error

Found 4 expressions with local error:

0.2b	(pow.f64 (sin.f64 ky) 2)
0.3b	(/.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))))))
1.8b	(.f64 (pow.f64 (/.f64 (.f64 2 l) Om) 2) (+.f64 (pow.f64 (sin.f64 kx) 2) (pow.f64 (sin.f64 ky) 2)))
8.4b	(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)))))

rewrite48.0ms (0.4%)

Algorithm

1×	rewrite-expression-head

Rules

33×	`add-sqr-sqrt_binary64_101`
30×	`*-un-lft-identity_binary64_79`
26×	`add-cube-cbrt_binary64_114`
21×	`times-frac_binary64_85`
19×	`add-exp-log_binary64_117`
15×	`sqrt-prod_binary64_95`
13×	`unpow-prod-down_binary64_158`
12×	`associate-l_binary64_20`
8×	`add-cbrt-cube_binary64_115`
6×	`associate-/r*_binary64_23` `prod-exp_binary64_128` `pow1_binary64_140`
5×	`associate-r_binary64_19`
4×	`pow-exp_binary64_147` `unswap-sqr_binary64_47` `sqrt-div_binary64_96` `add-log-exp_binary64_118`
3×	`div-exp_binary64_130` `pow-unpow_binary64_156` `flip-+_binary64_53` `unpow2_binary64_144` `sqr-pow_binary64_51` `associate-/l*_binary64_24` `flip3-+_binary64_82`
2×	`pow-to-exp_binary64_148` `div-inv_binary64_76` `associate-*r/_binary64_21` `associate-/r/_binary64_25` `distribute-lft-out_binary64_30`
1×	`cbrt-undiv_binary64_113` `pow-pow_binary64_151` `distribute-lft-in_binary64_28` `cbrt-unprod_binary64_112` `rem-sqrt-square_binary64_92` `*-commutative_binary64_10` `sqrt-pow1_binary64_97` `clear-num_binary64_78` `pow1/2_binary64_159` `distribute-rgt-in_binary64_29` `frac-2neg_binary64_90`

Counts

4 → 113

Calls

4 calls:

17.0ms	(.f64 (pow.f64 (/.f64 (.f64 2 l) Om) 2) (+.f64 (pow.f64 (sin.f64 kx) 2) (pow.f64 (sin.f64 ky) 2)))
7.0ms	(/.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)

series2.1s (18.5%)

Counts

4 → 12

Calls

4 calls:

1.1s	(/.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))))))
661.0ms	(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)))))
320.0ms	(.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)

simplify82.0ms (0.7%)

Algorithm

1×	egg-herbie

Counts

125 → 125

Iterations

Useful iterations: 0 (44.0ms)

Iter	Nodes	Cost
0	4957	4125
1	4957	4125

prune296.0ms (2.6%)

Pruning

3 alts after pruning (3 fresh and 0 done)

	Pruned	Kept	Total
New	122	3	125
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	123	3	126

Merged error: 0b

Counts

126 → 3

Compiler

Compiled 4960 to 3845 computations (22.5% saved)

localize26.0ms (0.2%)

Local error

Found 4 expressions with local error:

0.4b	(.f64 (/.f64 (.f64 2 l) Om) (sqrt.f64 (+.f64 (pow.f64 (sin.f64 kx) 2) (pow.f64 (sin.f64 ky) 2))))
2.0b	(sqrt.f64 (+.f64 (pow.f64 (sin.f64 kx) 2) (pow.f64 (sin.f64 ky) 2)))
2.0b	(sqrt.f64 (+.f64 (pow.f64 (sin.f64 kx) 2) (pow.f64 (sin.f64 ky) 2)))
8.4b	(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)))))))

rewrite56.0ms (0.5%)

Algorithm

1×	rewrite-expression-head

Rules

23×	`*-un-lft-identity_binary64_79`
19×	`sqrt-prod_binary64_95`
18×	`add-sqr-sqrt_binary64_101`
13×	`add-exp-log_binary64_117` `add-cbrt-cube_binary64_115`
11×	`add-cube-cbrt_binary64_114`
10×	`sqrt-div_binary64_96`
9×	`pow1_binary64_140`
8×	`associate-r_binary64_19`
7×	`associate-l_binary64_20`
6×	`unpow-prod-down_binary64_158` `distribute-lft-out_binary64_30`
5×	`flip-+_binary64_53` `flip3-+_binary64_82`
4×	`cbrt-unprod_binary64_112` `prod-exp_binary64_128` `add-log-exp_binary64_118`
3×	`times-frac_binary64_85` `rem-sqrt-square_binary64_92` `sqrt-pow1_binary64_97` `pow1/2_binary64_159`
2×	`cbrt-undiv_binary64_113` `div-exp_binary64_130` `frac-times_binary64_89` `associate-*r/_binary64_21` `unswap-sqr_binary64_47`
1×	`div-inv_binary64_76` `associate-l/_binary64_22` `-commutative_binary64_10` `pow-prod-down_binary64_150`

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 (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)))
5.0ms	(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)))))))

series1.3s (12%)

Counts

4 → 12

Calls

4 calls:

666.0ms	(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)))))))
376.0ms	(.f64 (/.f64 (.f64 2 l) Om) (sqrt.f64 (+.f64 (pow.f64 (sin.f64 kx) 2) (pow.f64 (sin.f64 ky) 2))))
158.0ms	(sqrt.f64 (+.f64 (pow.f64 (sin.f64 kx) 2) (pow.f64 (sin.f64 ky) 2)))
148.0ms	(sqrt.f64 (+.f64 (pow.f64 (sin.f64 kx) 2) (pow.f64 (sin.f64 ky) 2)))

simplify65.0ms (0.6%)

Algorithm

1×	egg-herbie

Counts

98 → 98

Iterations

Useful iterations: 0 (40.0ms)

Iter	Nodes	Cost
0	5170	2575

prune240.0ms (2.1%)

Pruning

3 alts after pruning (2 fresh and 1 done)

	Pruned	Kept	Total
New	98	0	98
Fresh	0	2	2
Picked	0	1	1
Done	0	0	0
Total	98	3	101

Merged error: 0b

Counts

101 → 3

Compiler

Compiled 4574 to 3211 computations (29.8% saved)

localize22.0ms (0.2%)

Local error

Found 4 expressions with local error:

0.2b	(pow.f64 (sin.f64 ky) 2)
0.3b	(/.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)))))))
1.6b	(.f64 (/.f64 (.f64 2 l) Om) (+.f64 (pow.f64 (sin.f64 kx) 2) (pow.f64 (sin.f64 ky) 2)))
8.4b	(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))))))

rewrite50.0ms (0.4%)

Algorithm

1×	rewrite-expression-head

Rules

29×	`*-un-lft-identity_binary64_79`
28×	`add-sqr-sqrt_binary64_101`
25×	`add-cube-cbrt_binary64_114`
21×	`times-frac_binary64_85`
16×	`add-exp-log_binary64_117`
15×	`sqrt-prod_binary64_95` `add-cbrt-cube_binary64_115`
8×	`pow1_binary64_140`
7×	`associate-l_binary64_20`
6×	`associate-/r*_binary64_23`
5×	`unpow-prod-down_binary64_158` `associate-r_binary64_19`
4×	`flip-+_binary64_53` `cbrt-unprod_binary64_112` `prod-exp_binary64_128` `sqrt-div_binary64_96` `add-log-exp_binary64_118` `flip3-+_binary64_82`
3×	`cbrt-undiv_binary64_113` `div-exp_binary64_130` `pow-unpow_binary64_156` `associate-/l*_binary64_24`
2×	`div-inv_binary64_76` `frac-times_binary64_89` `associate-*r/_binary64_21` `associate-/r/_binary64_25` `distribute-lft-out_binary64_30`
1×	`pow-exp_binary64_147` `pow-to-exp_binary64_148` `unpow2_binary64_144` `sqr-pow_binary64_51` `pow-pow_binary64_151` `distribute-lft-in_binary64_28` `associate-l/_binary64_22` `unswap-sqr_binary64_47` `rem-sqrt-square_binary64_92` `-commutative_binary64_10` `pow-prod-down_binary64_150` `sqrt-pow1_binary64_97` `clear-num_binary64_78` `pow1/2_binary64_159` `distribute-rgt-in_binary64_29` `frac-2neg_binary64_90`

Counts

4 → 109

Calls

4 calls:

17.0ms	(.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))))))
3.0ms	(pow.f64 (sin.f64 ky) 2)

series2.1s (18.8%)

Counts

4 → 12

Calls

4 calls:

1.1s	(/.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)))))))
659.0ms	(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))))))
355.0ms	(.f64 (/.f64 (.f64 2 l) Om) (+.f64 (pow.f64 (sin.f64 kx) 2) (pow.f64 (sin.f64 ky) 2)))
31.0ms	(pow.f64 (sin.f64 ky) 2)

simplify65.0ms (0.6%)

Algorithm

1×	egg-herbie

Counts

121 → 121

Iterations

Useful iterations: 0 (28.0ms)

Iter	Nodes	Cost
0	5168	4116

prune248.0ms (2.2%)

Pruning

3 alts after pruning (1 fresh and 2 done)

	Pruned	Kept	Total
New	121	0	121
Fresh	0	1	1
Picked	0	1	1
Done	0	1	1
Total	121	3	124

Merged error: 0b

Counts

124 → 3

Compiler

Compiled 4656 to 3272 computations (29.7% saved)

localize3.0ms (0%)

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

3 alts after pruning (0 fresh and 3 done)

	Kept	Total
New	0	0
Fresh	0	0
Picked	1	1
Done	2	2
Total	3	3

Merged error: 0b

Counts

3 → 3

Compiler

Compiled 0 to 0 computations (0% saved)

regimes629.0ms (5.6%)

Compiler: Compiled 5208 to 5285 computations (-1.5% 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%)

sample2.9s (25.9%)

Algorithm

1×

intervals

Results

1.2s	6389×	body	128	valid
703.0ms	756×	body	1024	valid
320.0ms	530×	body	512	valid
142.0ms	325×	body	256	valid

Compiler

Compiled 273 to 272 computations (0.4% saved)

Details

analyze622.0ms (5.5%)

sample93.0ms (0.8%)

simplify206.0ms (1.8%)

prune8.0ms (0.1%)

localize22.0ms (0.2%)

rewrite48.0ms (0.4%)

series2.1s (18.5%)

simplify82.0ms (0.7%)

prune296.0ms (2.6%)

localize26.0ms (0.2%)

rewrite56.0ms (0.5%)

series1.3s (12%)

simplify65.0ms (0.6%)

prune240.0ms (2.1%)

localize22.0ms (0.2%)

rewrite50.0ms (0.4%)

series2.1s (18.8%)

simplify65.0ms (0.6%)

prune248.0ms (2.2%)

localize3.0ms (0%)

rewrite0.0ms (0%)

series0.0ms (0%)

simplify6.0ms (0.1%)

prune1.0ms (0%)

regimes629.0ms (5.6%)

bsearch0.0ms (0%)

simplify2.0ms (0%)

end0.0ms (0%)

sample2.9s (25.9%)

Profiling