Details

analyze981.0ms (3.9%)

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

Symmetry

(sort kx ky)

Compiler

Compiled 30 to 30 computations (0% saved)

sample108.0ms (0.4%)

Algorithm

1×

intervals

Results

42.0ms	207×	body	128	valid
23.0ms	25×	body	1024	valid
13.0ms	18×	body	512	valid
3.0ms	6×	body	256	valid

Compiler

Compiled 59 to 63 computations (-6.8% saved)

simplify54.0ms (0.2%)

Algorithm

1×	egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (49.0ms)

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

Error

2.8b

Counts

2 → 1

Compiler

Compiled 50 to 50 computations (0% saved)

localize27.0ms (0.1%)

Local error

Found 4 expressions with local error:

0.3b	(pow.f64 (sin.f64 ky) 2)
0.5b	(/.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))))))
4.5b	(.f64 (pow.f64 (/.f64 (.f64 2 l) Om) 2) (+.f64 (pow.f64 (sin.f64 kx) 2) (pow.f64 (sin.f64 ky) 2)))
8.0b	(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)))))

rewrite335.0ms (1.3%)

Algorithm

1×	rewrite-expression-head

Error

1.9b

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×	`pow1_binary64_139` `prod-exp_binary64_127` `associate-/r*_binary64_22`
5×	`associate-r_binary64_18`
4×	`add-log-exp_binary64_117` `sqrt-div_binary64_95` `pow-exp_binary64_146` `unswap-sqr_binary64_46`
3×	`flip3-+_binary64_81` `flip-+_binary64_52` `div-exp_binary64_129` `unpow2_binary64_143` `sqr-pow_binary64_50` `associate-/l*_binary64_23` `pow-unpow_binary64_155`
2×	`pow-to-exp_binary64_147` `associate-*r/_binary64_20` `div-inv_binary64_75` `distribute-lft-out_binary64_29` `associate-/r/_binary64_24`
1×	`pow1/2_binary64_158` `sqrt-pow1_binary64_96` `rem-sqrt-square_binary64_91` `cbrt-unprod_binary64_111` `distribute-rgt-in_binary64_28` `distribute-lft-in_binary64_27` `*-commutative_binary64_9` `cbrt-undiv_binary64_112` `frac-2neg_binary64_89` `clear-num_binary64_77` `pow-pow_binary64_150`

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)))
10.0ms	(/.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)

Compiler

Compiled 4614 to 3499 computations (24.2% saved)

series3.6s (14.3%)

Error

0.2b

Counts

4 → 52

Calls

4 calls:

1.6s	(/.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))))))
1.2s	(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)))))
703.0ms	(.f64 (pow.f64 (/.f64 (.f64 2 l) Om) 2) (+.f64 (pow.f64 (sin.f64 kx) 2) (pow.f64 (sin.f64 ky) 2)))
31.0ms	(pow.f64 (sin.f64 ky) 2)

Compiler

Compiled 5460 to 4816 computations (11.8% saved)

simplify99.0ms (0.4%)

Algorithm

1×	egg-herbie

Counts

165 → 165

Iterations

Useful iterations: 0 (44.0ms)

Iter	Nodes	Cost
0	4969	5722
1	4969	5722

prune419.0ms (1.7%)

Pruning

3 alts after pruning (3 fresh and 0 done)

	Pruned	Kept	Total
New	162	3	165
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	163	3	166

Error

0.0b

Counts

166 → 3

Compiler

Compiled 5699 to 4190 computations (26.5% saved)

localize21.0ms (0.1%)

Local error

Found 4 expressions with local error:

0.5b	(/.f64 1/2 (sqrt.f64 (+.f64 1 (.f64 (+.f64 (pow.f64 (sin.f64 ky) 2) (pow.f64 (sin.f64 kx) 2)) (pow.f64 (/.f64 (.f64 2 l) Om) 2)))))
1.4b	(log.f64 (exp.f64 (/.f64 1/2 (sqrt.f64 (+.f64 1 (.f64 (+.f64 (pow.f64 (sin.f64 ky) 2) (pow.f64 (sin.f64 kx) 2)) (pow.f64 (/.f64 (.f64 2 l) Om) 2)))))))
4.5b	(.f64 (+.f64 (pow.f64 (sin.f64 ky) 2) (pow.f64 (sin.f64 kx) 2)) (pow.f64 (/.f64 (.f64 2 l) Om) 2))
8.0b	(sqrt.f64 (+.f64 1 (.f64 (+.f64 (pow.f64 (sin.f64 ky) 2) (pow.f64 (sin.f64 kx) 2)) (pow.f64 (/.f64 (.f64 2 l) Om) 2))))

rewrite539.0ms (2.1%)

Algorithm

1×	rewrite-expression-head

Error

0.0b

Rules

45×	`add-sqr-sqrt_binary64_100`
42×	`*-un-lft-identity_binary64_78`
39×	`times-frac_binary64_84`
38×	`add-cube-cbrt_binary64_113`
25×	`log-pow_binary64_167`
24×	`sqrt-prod_binary64_94` `exp-prod_binary64_130`
18×	`add-exp-log_binary64_116`
12×	`associate-r_binary64_18`
10×	`unpow-prod-down_binary64_157`
8×	`add-cbrt-cube_binary64_114`
6×	`pow1_binary64_139` `sqrt-div_binary64_95` `prod-exp_binary64_127` `associate-/r*_binary64_22`
5×	`associate-l_binary64_19`
4×	`add-log-exp_binary64_117` `flip3-+_binary64_81` `flip-+_binary64_52` `unswap-sqr_binary64_46` `associate-/r/_binary64_24`
3×	`div-exp_binary64_129` `pow-exp_binary64_146` `div-inv_binary64_75` `log-prod_binary64_164` `associate-/l*_binary64_23`
2×	`unpow2_binary64_143` `sqr-pow_binary64_50` `associate-*l/_binary64_21` `distribute-lft-out_binary64_29`
1×	`pow1/2_binary64_158` `sqrt-pow1_binary64_96` `rem-sqrt-square_binary64_91` `pow-to-exp_binary64_147` `cbrt-unprod_binary64_111` `*-commutative_binary64_9` `rem-log-exp_binary64_119` `cbrt-undiv_binary64_112` `frac-2neg_binary64_89` `clear-num_binary64_77`

Counts

4 → 129

Calls

4 calls:

17.0ms	(.f64 (+.f64 (pow.f64 (sin.f64 ky) 2) (pow.f64 (sin.f64 kx) 2)) (pow.f64 (/.f64 (.f64 2 l) Om) 2))
13.0ms	(log.f64 (exp.f64 (/.f64 1/2 (sqrt.f64 (+.f64 1 (.f64 (+.f64 (pow.f64 (sin.f64 ky) 2) (pow.f64 (sin.f64 kx) 2)) (pow.f64 (/.f64 (.f64 2 l) Om) 2)))))))
6.0ms	(/.f64 1/2 (sqrt.f64 (+.f64 1 (.f64 (+.f64 (pow.f64 (sin.f64 ky) 2) (pow.f64 (sin.f64 kx) 2)) (pow.f64 (/.f64 (.f64 2 l) Om) 2)))))
4.0ms	(sqrt.f64 (+.f64 1 (.f64 (+.f64 (pow.f64 (sin.f64 ky) 2) (pow.f64 (sin.f64 kx) 2)) (pow.f64 (/.f64 (.f64 2 l) Om) 2))))

Compiler

Compiled 6069 to 4682 computations (22.9% saved)

series6.1s (24%)

Error

0.0b

Counts

4 → 61

Calls

4 calls:

2.5s	(log.f64 (exp.f64 (/.f64 1/2 (sqrt.f64 (+.f64 1 (.f64 (+.f64 (pow.f64 (sin.f64 ky) 2) (pow.f64 (sin.f64 kx) 2)) (pow.f64 (/.f64 (.f64 2 l) Om) 2)))))))
1.4s	(/.f64 1/2 (sqrt.f64 (+.f64 1 (.f64 (+.f64 (pow.f64 (sin.f64 ky) 2) (pow.f64 (sin.f64 kx) 2)) (pow.f64 (/.f64 (.f64 2 l) Om) 2)))))
1.3s	(sqrt.f64 (+.f64 1 (.f64 (+.f64 (pow.f64 (sin.f64 ky) 2) (pow.f64 (sin.f64 kx) 2)) (pow.f64 (/.f64 (.f64 2 l) Om) 2))))
679.0ms	(.f64 (+.f64 (pow.f64 (sin.f64 ky) 2) (pow.f64 (sin.f64 kx) 2)) (pow.f64 (/.f64 (.f64 2 l) Om) 2))

Compiler

Compiled 6734 to 6000 computations (10.9% saved)

simplify129.0ms (0.5%)

Algorithm

1×	egg-herbie

Counts

190 → 190

Iterations

Useful iterations: 0 (59.0ms)

Iter	Nodes	Cost
0	4977	7175
1	4977	7175

prune588.0ms (2.3%)

Pruning

4 alts after pruning (3 fresh and 1 done)

	Pruned	Kept	Total
New	189	1	190
Fresh	0	2	2
Picked	0	1	1
Done	0	0	0
Total	189	4	193

Error

0.0b

Counts

193 → 4

Compiler

Compiled 7256 to 5466 computations (24.7% saved)

localize37.0ms (0.1%)

Local error

Found 4 expressions with local error:

4.5b	(.f64 (+.f64 (pow.f64 (sin.f64 kx) 2) (pow.f64 (sin.f64 ky) 2)) (pow.f64 (/.f64 (.f64 2 l) Om) 2))
4.5b	(.f64 (+.f64 (pow.f64 (sin.f64 kx) 2) (pow.f64 (sin.f64 ky) 2)) (pow.f64 (/.f64 (.f64 2 l) Om) 2))
8.0b	(sqrt.f64 (+.f64 1 (.f64 (+.f64 (pow.f64 (sin.f64 kx) 2) (pow.f64 (sin.f64 ky) 2)) (pow.f64 (/.f64 (.f64 2 l) Om) 2))))
8.0b	(sqrt.f64 (+.f64 1 (.f64 (+.f64 (pow.f64 (sin.f64 kx) 2) (pow.f64 (sin.f64 ky) 2)) (pow.f64 (/.f64 (.f64 2 l) Om) 2))))

rewrite628.0ms (2.5%)

Algorithm

1×	rewrite-expression-head

Error

0.0b

Rules

28×	`add-exp-log_binary64_116` `add-sqr-sqrt_binary64_100`
24×	`associate-r_binary64_18`
22×	`*-un-lft-identity_binary64_78`
20×	`unpow-prod-down_binary64_157`
14×	`add-cube-cbrt_binary64_113`
12×	`prod-exp_binary64_127`
10×	`associate-l_binary64_19`
8×	`add-cbrt-cube_binary64_114` `unswap-sqr_binary64_46`
6×	`pow1_binary64_139` `sqrt-prod_binary64_94` `pow-exp_binary64_146` `times-frac_binary64_84`
4×	`add-log-exp_binary64_117` `flip3-+_binary64_81` `sqrt-div_binary64_95` `flip-+_binary64_52` `div-exp_binary64_129` `unpow2_binary64_143` `sqr-pow_binary64_50` `associate-*l/_binary64_21` `distribute-lft-out_binary64_29`
2×	`pow1/2_binary64_158` `sqrt-pow1_binary64_96` `rem-sqrt-square_binary64_91` `pow-to-exp_binary64_147` `cbrt-unprod_binary64_111` `div-inv_binary64_75` `*-commutative_binary64_9`

Counts

4 → 104

Calls

4 calls:

28.0ms	(.f64 (+.f64 (pow.f64 (sin.f64 kx) 2) (pow.f64 (sin.f64 ky) 2)) (pow.f64 (/.f64 (.f64 2 l) Om) 2))
22.0ms	(.f64 (+.f64 (pow.f64 (sin.f64 kx) 2) (pow.f64 (sin.f64 ky) 2)) (pow.f64 (/.f64 (.f64 2 l) Om) 2))
4.0ms	(sqrt.f64 (+.f64 1 (.f64 (+.f64 (pow.f64 (sin.f64 kx) 2) (pow.f64 (sin.f64 ky) 2)) (pow.f64 (/.f64 (.f64 2 l) Om) 2))))
4.0ms	(sqrt.f64 (+.f64 1 (.f64 (+.f64 (pow.f64 (sin.f64 kx) 2) (pow.f64 (sin.f64 ky) 2)) (pow.f64 (/.f64 (.f64 2 l) Om) 2))))

Compiler

Compiled 7098 to 5450 computations (23.2% saved)

series4.3s (16.9%)

Error

0.0b

Counts

4 → 70

Calls

4 calls:

1.3s	(sqrt.f64 (+.f64 1 (.f64 (+.f64 (pow.f64 (sin.f64 kx) 2) (pow.f64 (sin.f64 ky) 2)) (pow.f64 (/.f64 (.f64 2 l) Om) 2))))
1.2s	(sqrt.f64 (+.f64 1 (.f64 (+.f64 (pow.f64 (sin.f64 kx) 2) (pow.f64 (sin.f64 ky) 2)) (pow.f64 (/.f64 (.f64 2 l) Om) 2))))
709.0ms	(.f64 (+.f64 (pow.f64 (sin.f64 kx) 2) (pow.f64 (sin.f64 ky) 2)) (pow.f64 (/.f64 (.f64 2 l) Om) 2))
686.0ms	(.f64 (+.f64 (pow.f64 (sin.f64 kx) 2) (pow.f64 (sin.f64 ky) 2)) (pow.f64 (/.f64 (.f64 2 l) Om) 2))

Compiler

Compiled 12876 to 10858 computations (15.7% saved)

simplify80.0ms (0.3%)

Algorithm

1×	egg-herbie

Counts

174 → 174

Iterations

Useful iterations: 0 (24.0ms)

Iter	Nodes	Cost
0	5100	5822

prune976.0ms (3.9%)

Pruning

4 alts after pruning (2 fresh and 2 done)

	Pruned	Kept	Total
New	174	0	174
Fresh	0	2	2
Picked	0	1	1
Done	0	1	1
Total	174	4	178

Error

0.0b

Counts

178 → 4

Compiler

Compiled 10762 to 8119 computations (24.6% saved)

localize2.0ms (0%)

rewrite0.0ms (0%)

Algorithm

1×	rewrite-expression-head

Error

0.0b

Counts

0 → 0

Compiler

Compiled 0 to 0 computations (0% saved)

series0.0ms (0%)

Error: 0.0b
Counts: 0 → 0
Compiler: Compiled 0 to 0 computations (0% saved)

simplify11.0ms (0%)

Algorithm

1×	egg-herbie

Counts

0 → 0

Iterations

Useful iterations: 0 (3.0ms)

Iter	Nodes	Cost
0	0	0

prune1.0ms (0%)

Pruning

4 alts after pruning (1 fresh and 3 done)

	Kept	Total
New	0	0
Fresh	1	1
Picked	1	1
Done	2	2
Total	4	4

Error

0.0b

Counts

4 → 4

Compiler

Compiled 0 to 0 computations (0% saved)

regimes1.8s (7.2%)

Accuracy

Total 0.5b remaining (90.5%)

Threshold costs 0.5b (90.5%)

Compiler

Compiled 16879 to 15987 computations (5.3% saved)

bsearch2.0ms (0%)

Compiler: Compiled 7 to 9 computations (-28.6% saved)

simplify16.0ms (0.1%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	56	136
1	56	136

Remove

(sort kx ky)

Compiler

Compiled 174 to 138 computations (20.7% saved)

end0.0ms (0%)

sample4.4s (17.6%)

Algorithm

1×

intervals

Results

1.4s	6350×	body	128	valid
787.0ms	789×	body	1024	valid
391.0ms	542×	body	512	valid
148.0ms	318×	body	256	valid
8.0ms	1×	body	2048	valid

Compiler

Compiled 927 to 860 computations (7.2% saved)

Details

analyze981.0ms (3.9%)

sample108.0ms (0.4%)

simplify54.0ms (0.2%)

prune5.0ms (0%)

localize27.0ms (0.1%)

rewrite335.0ms (1.3%)

series3.6s (14.3%)

simplify99.0ms (0.4%)

prune419.0ms (1.7%)

localize21.0ms (0.1%)

rewrite539.0ms (2.1%)

series6.1s (24%)

simplify129.0ms (0.5%)

prune588.0ms (2.3%)

localize37.0ms (0.1%)

rewrite628.0ms (2.5%)

series4.3s (16.9%)

simplify80.0ms (0.3%)

prune976.0ms (3.9%)

localize2.0ms (0%)

rewrite0.0ms (0%)

series0.0ms (0%)

simplify11.0ms (0%)

prune1.0ms (0%)

regimes1.8s (7.2%)

bsearch2.0ms (0%)

simplify16.0ms (0.1%)

end0.0ms (0%)

sample4.4s (17.6%)

Profiling