Details

analyze1.1s (4.1%)

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)

sample130.0ms (0.5%)

Algorithm

1×

intervals

Results

45.0ms	189×	body	128	valid
32.0ms	30×	body	1024	valid
19.0ms	26×	body	512	valid
8.0ms	11×	body	256	valid

Compiler

Compiled 59 to 63 computations (-6.8% saved)

simplify48.0ms (0.2%)

Algorithm

1×	egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (42.0ms)

Iter	Nodes	Cost
0	5325	39

prune9.0ms (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

0.5b

Counts

2 → 1

Compiler

Compiled 50 to 50 computations (0% saved)

localize19.0ms (0.1%)

Local error

Found 4 expressions with local error:

0.3b	(pow.f64 (sin.f64 kx) 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))))))
2.5b	(.f64 (pow.f64 (/.f64 (.f64 2 l) Om) 2) (+.f64 (pow.f64 (sin.f64 kx) 2) (pow.f64 (sin.f64 ky) 2)))
9.6b	(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)))))

rewrite387.0ms (1.5%)

Algorithm

1×	rewrite-expression-head

Error

0.2b

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:

24.0ms	(.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 kx) 2)

Compiler

Compiled 4614 to 3499 computations (24.2% saved)

series4.1s (15.8%)

Error

0.0b

Counts

4 → 56

Calls

4 calls:

1.9s	(/.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))))))
1.3s	(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)))))
678.0ms	(.f64 (pow.f64 (/.f64 (.f64 2 l) Om) 2) (+.f64 (pow.f64 (sin.f64 kx) 2) (pow.f64 (sin.f64 ky) 2)))
30.0ms	(pow.f64 (sin.f64 kx) 2)

Compiler

Compiled 5955 to 5210 computations (12.5% saved)

simplify89.0ms (0.3%)

Algorithm

1×	egg-herbie

Counts

169 → 169

Iterations

Useful iterations: 0 (33.0ms)

Iter	Nodes	Cost
0	5120	5888

prune378.0ms (1.5%)

Pruning

4 alts after pruning (3 fresh and 1 done)

	Pruned	Kept	Total
New	166	3	169
Fresh	0	0	0
Picked	0	1	1
Done	0	0	0
Total	166	4	170

Error

0.0b

Counts

170 → 4

Compiler

Compiled 5837 to 4274 computations (26.8% saved)

localize30.0ms (0.1%)

Local error

Found 4 expressions with local error:

0.4b	(/.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)))))
2.2b	(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)))))))
2.5b	(.f64 (+.f64 (pow.f64 (sin.f64 ky) 2) (pow.f64 (sin.f64 kx) 2)) (pow.f64 (/.f64 (.f64 2 l) Om) 2))
9.6b	(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))))

rewrite520.0ms (2%)

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))
12.0ms	(/.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)))))
12.0ms	(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)))))))
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)

series7.0s (27%)

Error

0.0b

Counts

4 → 69

Calls

4 calls:

3.1s	(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)))))))
1.6s	(/.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)))))
1.2s	(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))))
749.0ms	(.f64 (+.f64 (pow.f64 (sin.f64 ky) 2) (pow.f64 (sin.f64 kx) 2)) (pow.f64 (/.f64 (.f64 2 l) Om) 2))

Compiler

Compiled 7788 to 6844 computations (12.1% saved)

simplify126.0ms (0.5%)

Algorithm

1×	egg-herbie

Counts

198 → 198

Iterations

Useful iterations: 0 (33.0ms)

Iter	Nodes	Cost
0	5029	7519

prune552.0ms (2.1%)

Pruning

4 alts after pruning (2 fresh and 2 done)

	Pruned	Kept	Total
New	197	1	198
Fresh	1	1	2
Picked	0	1	1
Done	0	1	1
Total	198	4	202

Error

0.0b

Counts

202 → 4

Compiler

Compiled 7478 to 5591 computations (25.2% saved)

localize28.0ms (0.1%)

Local error

Found 4 expressions with local error:

2.0b	(log.f64 (exp.f64 (/.f64 1/2 (sqrt.f64 (+.f64 (.f64 4 (/.f64 (.f64 (pow.f64 (sin.f64 kx) 2) (.f64 l l)) (.f64 Om Om))) 1)))))
6.3b	(.f64 (pow.f64 (sin.f64 kx) 2) (.f64 l l))
7.7b	(sqrt.f64 (+.f64 (.f64 4 (/.f64 (.f64 (pow.f64 (sin.f64 kx) 2) (.f64 l l)) (.f64 Om Om))) 1))
17.8b	(/.f64 (.f64 (pow.f64 (sin.f64 kx) 2) (.f64 l l)) (*.f64 Om Om))

rewrite350.0ms (1.4%)

Algorithm

1×	rewrite-expression-head

Error

0.0b

Rules

66×	`add-exp-log_binary64_116`
34×	`prod-exp_binary64_127`
30×	`add-cbrt-cube_binary64_114`
25×	`log-pow_binary64_167`
24×	`add-sqr-sqrt_binary64_100` `exp-prod_binary64_130`
21×	`add-cube-cbrt_binary64_113` `*-un-lft-identity_binary64_78`
19×	`times-frac_binary64_84`
14×	`div-exp_binary64_129`
12×	`cbrt-unprod_binary64_111` `sqrt-prod_binary64_94`
8×	`associate-l_binary64_19`
6×	`pow1_binary64_139` `pow-to-exp_binary64_147` `pow-exp_binary64_146` `cbrt-undiv_binary64_112`
4×	`add-log-exp_binary64_117` `sqrt-div_binary64_95` `unpow-prod-down_binary64_157` `unswap-sqr_binary64_46`
3×	`log-prod_binary64_164`
2×	`div-inv_binary64_75` `flip3-+_binary64_81` `flip-+_binary64_52` `unpow2_binary64_143` `sqr-pow_binary64_50` `associate-/r/_binary64_24`
1×	`frac-2neg_binary64_89` `clear-num_binary64_77` `associate-/l_binary64_23` `associate-/r_binary64_22` `pow1/2_binary64_158` `sqrt-pow1_binary64_96` `rem-sqrt-square_binary64_91` `pow2_binary64_159` `pow-prod-down_binary64_149` `associate-r_binary64_18` `*-commutative_binary64_9` `rem-log-exp_binary64_119`

Counts

4 → 114

Calls

4 calls:

29.0ms	(sqrt.f64 (+.f64 (.f64 4 (/.f64 (.f64 (pow.f64 (sin.f64 kx) 2) (.f64 l l)) (.f64 Om Om))) 1))
17.0ms	(log.f64 (exp.f64 (/.f64 1/2 (sqrt.f64 (+.f64 (.f64 4 (/.f64 (.f64 (pow.f64 (sin.f64 kx) 2) (.f64 l l)) (.f64 Om Om))) 1)))))
13.0ms	(.f64 (pow.f64 (sin.f64 kx) 2) (.f64 l l))
11.0ms	(/.f64 (.f64 (pow.f64 (sin.f64 kx) 2) (.f64 l l)) (*.f64 Om Om))

Compiler

Compiled 4306 to 2753 computations (36.1% saved)

series1.8s (7%)

Error

0.0b

Counts

4 → 46

Calls

4 calls:

941.0ms	(log.f64 (exp.f64 (/.f64 1/2 (sqrt.f64 (+.f64 (.f64 4 (/.f64 (.f64 (pow.f64 (sin.f64 kx) 2) (.f64 l l)) (.f64 Om Om))) 1)))))
350.0ms	(sqrt.f64 (+.f64 (.f64 4 (/.f64 (.f64 (pow.f64 (sin.f64 kx) 2) (.f64 l l)) (.f64 Om Om))) 1))
305.0ms	(/.f64 (.f64 (pow.f64 (sin.f64 kx) 2) (.f64 l l)) (*.f64 Om Om))
137.0ms	(.f64 (pow.f64 (sin.f64 kx) 2) (.f64 l l))

Compiler

Compiled 2788 to 2560 computations (8.2% saved)

simplify100.0ms (0.4%)

Algorithm

1×	egg-herbie

Counts

160 → 160

Iterations

Useful iterations: 0 (61.0ms)

Iter	Nodes	Cost
0	4987	3181
1	4987	3181

prune303.0ms (1.2%)

Pruning

3 alts after pruning (1 fresh and 2 done)

	Pruned	Kept	Total
New	159	1	160
Fresh	1	0	1
Picked	1	0	1
Done	0	2	2
Total	161	3	164

Error

0.0b

Counts

164 → 3

Compiler

Compiled 4425 to 2904 computations (34.4% saved)

localize18.0ms (0.1%)

Local error

Found 4 expressions with local error:

2.0b	(log.f64 (exp.f64 (/.f64 1/2 (sqrt.f64 (+.f64 (.f64 4 (cbrt.f64 (pow.f64 (/.f64 (.f64 l (sin.f64 kx)) Om) 6))) 1)))))
2.1b	(/.f64 (*.f64 l (sin.f64 kx)) Om)
7.7b	(sqrt.f64 (+.f64 (.f64 4 (cbrt.f64 (pow.f64 (/.f64 (.f64 l (sin.f64 kx)) Om) 6))) 1))
17.3b	(cbrt.f64 (pow.f64 (/.f64 (*.f64 l (sin.f64 kx)) Om) 6))

rewrite232.0ms (0.9%)

Algorithm

1×	rewrite-expression-head

Error

0.0b

Rules

25×	`add-sqr-sqrt_binary64_100` `log-pow_binary64_167`
24×	`add-cube-cbrt_binary64_113` `times-frac_binary64_84` `*-un-lft-identity_binary64_78` `exp-prod_binary64_130`
12×	`sqrt-prod_binary64_94`
11×	`cbrt-prod_binary64_109`
9×	`add-exp-log_binary64_116` `add-cbrt-cube_binary64_114`
7×	`unpow-prod-down_binary64_157`
6×	`pow1_binary64_139`
4×	`add-log-exp_binary64_117` `sqrt-div_binary64_95`
3×	`div-inv_binary64_75` `associate-/r*_binary64_22` `log-prod_binary64_164`
2×	`flip3-+_binary64_81` `flip-+_binary64_52` `div-exp_binary64_129` `cbrt-undiv_binary64_112` `associate-/r/_binary64_24`
1×	`pow1/3_binary64_160` `sqr-pow_binary64_50` `pow1/2_binary64_158` `sqrt-pow1_binary64_96` `rem-sqrt-square_binary64_91` `prod-exp_binary64_127` `cbrt-unprod_binary64_111` `frac-2neg_binary64_89` `clear-num_binary64_77` `associate-/l*_binary64_23` `rem-log-exp_binary64_119`

Counts

4 → 91

Calls

4 calls:

19.0ms	(log.f64 (exp.f64 (/.f64 1/2 (sqrt.f64 (+.f64 (.f64 4 (cbrt.f64 (pow.f64 (/.f64 (.f64 l (sin.f64 kx)) Om) 6))) 1)))))
11.0ms	(/.f64 (*.f64 l (sin.f64 kx)) Om)
10.0ms	(sqrt.f64 (+.f64 (.f64 4 (cbrt.f64 (pow.f64 (/.f64 (.f64 l (sin.f64 kx)) Om) 6))) 1))
3.0ms	(cbrt.f64 (pow.f64 (/.f64 (*.f64 l (sin.f64 kx)) Om) 6))

Compiler

Compiled 3130 to 2175 computations (30.5% saved)

series1.8s (6.9%)

Error

0.0b

Counts

4 → 49

Calls

4 calls:

863.0ms	(log.f64 (exp.f64 (/.f64 1/2 (sqrt.f64 (+.f64 (.f64 4 (cbrt.f64 (pow.f64 (/.f64 (.f64 l (sin.f64 kx)) Om) 6))) 1)))))
333.0ms	(cbrt.f64 (pow.f64 (/.f64 (*.f64 l (sin.f64 kx)) Om) 6))
320.0ms	(sqrt.f64 (+.f64 (.f64 4 (cbrt.f64 (pow.f64 (/.f64 (.f64 l (sin.f64 kx)) Om) 6))) 1))
172.0ms	(/.f64 (*.f64 l (sin.f64 kx)) Om)

Compiler

Compiled 2923 to 2695 computations (7.8% saved)

simplify61.0ms (0.2%)

Algorithm

1×	egg-herbie

Counts

140 → 140

Iterations

Useful iterations: 0 (28.0ms)

Iter	Nodes	Cost
0	5058	2759

prune237.0ms (0.9%)

Pruning

3 alts after pruning (0 fresh and 3 done)

	Pruned	Kept	Total
New	140	0	140
Fresh	0	0	0
Picked	0	1	1
Done	0	2	2
Total	140	3	143

Error

0.0b

Counts

143 → 3

Compiler

Compiled 3620 to 2476 computations (31.6% saved)

regimes2.2s (8.4%)

Accuracy

Total 0.7b remaining (94.8%)

Threshold costs 0.7b (94.8%)

Compiler

Compiled 17988 to 17988 computations (0% saved)

bsearch0.0ms (0%)

simplify11.0ms (0%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	29	45
1	29	45

Remove

(sort kx ky)

Compiler

Compiled 58 to 54 computations (6.9% saved)

end0.0ms (0%)

sample4.3s (16.8%)

Algorithm

1×

intervals

Results

1.4s	6428×	body	128	valid
792.0ms	787×	body	1024	valid
383.0ms	518×	body	512	valid
121.0ms	266×	body	256	valid
3.0ms	1×	body	2048	valid

Compiler

Compiled 936 to 931 computations (0.5% saved)

Details

analyze1.1s (4.1%)

sample130.0ms (0.5%)

simplify48.0ms (0.2%)

prune9.0ms (0%)

localize19.0ms (0.1%)

rewrite387.0ms (1.5%)

series4.1s (15.8%)

simplify89.0ms (0.3%)

prune378.0ms (1.5%)

localize30.0ms (0.1%)

rewrite520.0ms (2%)

series7.0s (27%)

simplify126.0ms (0.5%)

prune552.0ms (2.1%)

localize28.0ms (0.1%)

rewrite350.0ms (1.4%)

series1.8s (7%)

simplify100.0ms (0.4%)

prune303.0ms (1.2%)

localize18.0ms (0.1%)

rewrite232.0ms (0.9%)

series1.8s (6.9%)

simplify61.0ms (0.2%)

prune237.0ms (0.9%)

regimes2.2s (8.4%)

bsearch0.0ms (0%)

simplify11.0ms (0%)

end0.0ms (0%)

sample4.3s (16.8%)

Profiling