Details

analyze601.0ms (3%)

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)

sample80.0ms (0.4%)

Algorithm

1×

intervals

Results

35.0ms	207×	body	128	valid
15.0ms	21×	body	512	valid
13.0ms	17×	body	1024	valid
4.0ms	11×	body	256	valid

Compiler

Compiled 59 to 63 computations (-6.8% saved)

simplify132.0ms (0.7%)

Algorithm

1×	egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (38.0ms)

Iter	Nodes	Cost
0	5325	39

prune5.0ms (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

Merged error: 0.5b

Counts

2 → 1

Compiler

Compiled 50 to 50 computations (0% saved)

localize18.0ms (0.1%)

Local error

Found 4 expressions with local error:

0.2b	(pow.f64 (sin.f64 ky) 2)
0.3b	(pow.f64 (sin.f64 kx) 2)
1.5b	(.f64 (pow.f64 (/.f64 (.f64 2 l) Om) 2) (+.f64 (pow.f64 (sin.f64 kx) 2) (pow.f64 (sin.f64 ky) 2)))
10.6b	(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)))))

rewrite38.0ms (0.2%)

Algorithm

1×	rewrite-expression-head

Rules

20×	`add-sqr-sqrt_binary64_100`
18×	`add-exp-log_binary64_116`
17×	`*-un-lft-identity_binary64_78`
16×	`unpow-prod-down_binary64_157`
13×	`add-cube-cbrt_binary64_113`
12×	`associate-l_binary64_19`
7×	`pow1_binary64_139`
6×	`add-cbrt-cube_binary64_114` `prod-exp_binary64_127` `pow-unpow_binary64_155`
5×	`pow-exp_binary64_146` `associate-r_binary64_18`
4×	`add-log-exp_binary64_117` `unpow2_binary64_143` `sqr-pow_binary64_50` `unswap-sqr_binary64_46`
3×	`sqrt-prod_binary64_94` `pow-to-exp_binary64_147` `times-frac_binary64_84`
2×	`div-exp_binary64_129` `flip-+_binary64_52` `pow-pow_binary64_150` `sqrt-div_binary64_95` `associate-*r/_binary64_20` `distribute-lft-out_binary64_29` `flip3-+_binary64_81`
1×	`distribute-lft-in_binary64_27` `*-commutative_binary64_9` `sqrt-pow1_binary64_96` `cbrt-unprod_binary64_111` `rem-sqrt-square_binary64_91` `distribute-rgt-in_binary64_28` `div-inv_binary64_75` `pow1/2_binary64_158`

Counts

4 → 90

Calls

4 calls:

19.0ms	(.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 ky) 2)
3.0ms	(pow.f64 (sin.f64 kx) 2)

series1.8s (8.8%)

Counts

4 → 41

Calls

4 calls:

1.1s	(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)))))
657.0ms	(.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)

Compiler

Compiled 2908 to 2678 computations (7.9% saved)

simplify61.0ms (0.3%)

Algorithm

1×	egg-herbie

Counts

131 → 131

Iterations

Useful iterations: 0 (27.0ms)

Iter	Nodes	Cost
0	5010	3394

prune251.0ms (1.2%)

Pruning

3 alts after pruning (3 fresh and 0 done)

	Pruned	Kept	Total
New	128	3	131
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	129	3	132

Merged error: 0b

Counts

132 → 3

Compiler

Compiled 4249 to 3065 computations (27.9% saved)

localize21.0ms (0.1%)

Local error

Found 4 expressions with local error:

0.3b	(pow.f64 (sin.f64 kx) 2)
1.5b	(.f64 (pow.f64 (/.f64 (.f64 2 l) Om) 2) (+.f64 (pow.f64 (sin.f64 kx) 2) (pow.f64 (sin.f64 ky) 2)))
10.6b	(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)))))
15.4b	(cbrt.f64 (pow.f64 (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))

rewrite44.0ms (0.2%)

Algorithm

1×	rewrite-expression-head

Rules

23×	`add-sqr-sqrt_binary64_100`
20×	`*-un-lft-identity_binary64_78`
19×	`unpow-prod-down_binary64_157`
18×	`cbrt-prod_binary64_109`
17×	`add-exp-log_binary64_116`
16×	`add-cube-cbrt_binary64_113`
12×	`associate-l_binary64_19`
9×	`sqrt-prod_binary64_94`
6×	`add-cbrt-cube_binary64_114` `prod-exp_binary64_127` `cube-prod_binary64_106` `pow1_binary64_139`
5×	`associate-r_binary64_18`
4×	`pow-exp_binary64_146` `add-log-exp_binary64_117` `sqr-pow_binary64_50` `unswap-sqr_binary64_46` `sqrt-div_binary64_95`
3×	`flip-+_binary64_52` `unpow2_binary64_143` `times-frac_binary64_84` `pow-unpow_binary64_155` `flip3-+_binary64_81`
2×	`cbrt-div_binary64_110` `pow-to-exp_binary64_147` `cube-div_binary64_107` `div-exp_binary64_129` `associate-*r/_binary64_20` `distribute-lft-out_binary64_29`
1×	`cube-mult_binary64_108` `distribute-lft-in_binary64_27` `*-commutative_binary64_9` `rem-cbrt-cube_binary64_102` `sqrt-pow1_binary64_96` `cbrt-unprod_binary64_111` `rem-sqrt-square_binary64_91` `pow1/3_binary64_160` `distribute-rgt-in_binary64_28` `div-inv_binary64_75` `pow-pow_binary64_150` `pow1/2_binary64_158` `unpow3_binary64_144`

Counts

4 → 101

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)))
6.0ms	(cbrt.f64 (pow.f64 (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))
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)

series2.8s (13.9%)

Counts

4 → 60

Calls

4 calls:

1.1s	(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	(cbrt.f64 (pow.f64 (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))
667.0ms	(.f64 (pow.f64 (/.f64 (.f64 2 l) Om) 2) (+.f64 (pow.f64 (sin.f64 kx) 2) (pow.f64 (sin.f64 ky) 2)))
22.0ms	(pow.f64 (sin.f64 kx) 2)

Compiler

Compiled 4753 to 4308 computations (9.4% saved)

simplify101.0ms (0.5%)

Algorithm

1×	egg-herbie

Counts

161 → 161

Iterations

Useful iterations: 0 (50.0ms)

Iter	Nodes	Cost
0	4980	5656
1	4980	5656

prune359.0ms (1.8%)

Pruning

3 alts after pruning (2 fresh and 1 done)

	Pruned	Kept	Total
New	161	0	161
Fresh	0	2	2
Picked	0	1	1
Done	0	0	0
Total	161	3	164

Merged error: 0b

Counts

164 → 3

Compiler

Compiled 5905 to 4314 computations (26.9% saved)

localize22.0ms (0.1%)

Local error

Found 4 expressions with local error:

6.5b	(sqrt.f64 (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))))))
6.5b	(sqrt.f64 (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))))))
10.6b	(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)))))
10.6b	(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)))))

rewrite30.0ms (0.1%)

Algorithm

1×	rewrite-expression-head

Rules

26×	`sqrt-prod_binary64_94`
16×	`add-sqr-sqrt_binary64_100`
12×	`sqrt-div_binary64_95`
10×	`sqrt-pow1_binary64_96` `add-cube-cbrt_binary64_113` `*-un-lft-identity_binary64_78` `pow1_binary64_139`
6×	`rem-sqrt-square_binary64_91` `pow1/2_binary64_158`
4×	`add-cbrt-cube_binary64_114` `add-log-exp_binary64_117` `flip-+_binary64_52` `add-exp-log_binary64_116` `flip3-+_binary64_81`

Counts

4 → 72

Calls

4 calls:

5.0ms	(sqrt.f64 (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))))))
5.0ms	(sqrt.f64 (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)))))
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)))))

series6.6s (32.7%)

Counts

4 → 86

Calls

4 calls:

2.0s	(sqrt.f64 (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))))))
2.0s	(sqrt.f64 (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))))))
1.3s	(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)))))
1.3s	(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)))))

Compiler

Compiled 11162 to 9358 computations (16.2% saved)

simplify82.0ms (0.4%)

Algorithm

1×	egg-herbie

Counts

158 → 158

Iterations

Useful iterations: 0 (24.0ms)

Iter	Nodes	Cost
0	4990	7006
1	4990	7006

prune629.0ms (3.1%)

Pruning

3 alts after pruning (1 fresh and 2 done)

	Pruned	Kept	Total
New	158	0	158
Fresh	0	1	1
Picked	0	1	1
Done	0	1	1
Total	158	3	161

Merged error: 0b

Counts

161 → 3

Compiler

Compiled 9479 to 6816 computations (28.1% saved)

localize20.0ms (0.1%)

Local error

Found 4 expressions with local error:

0.4b	(pow.f64 (sin.f64 (/.f64 1 kx)) 2)
3.0b	(.f64 (pow.f64 (/.f64 (.f64 2 l) Om) 2) (+.f64 (pow.f64 (sin.f64 (/.f64 1 kx)) 2) (pow.f64 (sin.f64 ky) 2)))
10.6b	(sqrt.f64 (+.f64 1 (.f64 (pow.f64 (/.f64 (.f64 2 l) Om) 2) (+.f64 (pow.f64 (sin.f64 (/.f64 1 kx)) 2) (pow.f64 (sin.f64 ky) 2)))))
24.4b	(sin.f64 (/.f64 1 kx))

rewrite35.0ms (0.2%)

Algorithm

1×	rewrite-expression-head

Rules

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

Counts

4 → 79

Calls

4 calls:

17.0ms	(.f64 (pow.f64 (/.f64 (.f64 2 l) Om) 2) (+.f64 (pow.f64 (sin.f64 (/.f64 1 kx)) 2) (pow.f64 (sin.f64 ky) 2)))
4.0ms	(pow.f64 (sin.f64 (/.f64 1 kx)) 2)
3.0ms	(sqrt.f64 (+.f64 1 (.f64 (pow.f64 (/.f64 (.f64 2 l) Om) 2) (+.f64 (pow.f64 (sin.f64 (/.f64 1 kx)) 2) (pow.f64 (sin.f64 ky) 2)))))
3.0ms	(sin.f64 (/.f64 1 kx))

series1.8s (9.1%)

Counts

4 → 42

Calls

4 calls:

1.1s	(sqrt.f64 (+.f64 1 (.f64 (pow.f64 (/.f64 (.f64 2 l) Om) 2) (+.f64 (pow.f64 (sin.f64 (/.f64 1 kx)) 2) (pow.f64 (sin.f64 ky) 2)))))
743.0ms	(.f64 (pow.f64 (/.f64 (.f64 2 l) Om) 2) (+.f64 (pow.f64 (sin.f64 (/.f64 1 kx)) 2) (pow.f64 (sin.f64 ky) 2)))
20.0ms	(pow.f64 (sin.f64 (/.f64 1 kx)) 2)
19.0ms	(sin.f64 (/.f64 1 kx))

Compiler

Compiled 3050 to 2846 computations (6.7% saved)

simplify62.0ms (0.3%)

Algorithm

1×	egg-herbie

Counts

121 → 121

Iterations

Useful iterations: 0 (27.0ms)

Iter	Nodes	Cost
0	4996	3484
1	4996	3484

prune232.0ms (1.2%)

Pruning

3 alts after pruning (0 fresh and 3 done)

	Pruned	Kept	Total
New	121	0	121
Fresh	0	0	0
Picked	0	1	1
Done	0	2	2
Total	121	3	124

Merged error: 0b

Counts

124 → 3

Compiler

Compiled 4029 to 3142 computations (22% saved)

regimes1.1s (5.3%)

Compiler: Compiled 12786 to 11951 computations (6.5% 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%)

sample3.2s (16.1%)

Algorithm

1×

intervals

Results

1.1s	6340×	body	128	valid
641.0ms	781×	body	1024	valid
324.0ms	557×	body	512	valid
116.0ms	322×	body	256	valid

Compiler

Compiled 664 to 614 computations (7.5% saved)

Details

analyze601.0ms (3%)

sample80.0ms (0.4%)

simplify132.0ms (0.7%)

prune5.0ms (0%)

localize18.0ms (0.1%)

rewrite38.0ms (0.2%)

series1.8s (8.8%)

simplify61.0ms (0.3%)

prune251.0ms (1.2%)

localize21.0ms (0.1%)

rewrite44.0ms (0.2%)

series2.8s (13.9%)

simplify101.0ms (0.5%)

prune359.0ms (1.8%)

localize22.0ms (0.1%)

rewrite30.0ms (0.1%)

series6.6s (32.7%)

simplify82.0ms (0.4%)

prune629.0ms (3.1%)

localize20.0ms (0.1%)

rewrite35.0ms (0.2%)

series1.8s (9.1%)

simplify62.0ms (0.3%)

prune232.0ms (1.2%)

regimes1.1s (5.3%)

bsearch0.0ms (0%)

simplify2.0ms (0%)

end0.0ms (0%)

sample3.2s (16.1%)

Profiling