Details

analyze642.0ms (2.9%)

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)

sample84.0ms (0.4%)

Algorithm

1×

intervals

Results

37.0ms	204×	body	128	valid
23.0ms	28×	body	1024	valid
12.0ms	20×	body	512	valid
1.0ms	4×	body	256	valid

Compiler

Compiled 59 to 63 computations (-6.8% saved)

simplify134.0ms (0.6%)

Algorithm

1×	egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (42.0ms)

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

1.0b

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))))))
1.5b	(.f64 (pow.f64 (/.f64 (.f64 2 l) Om) 2) (+.f64 (pow.f64 (sin.f64 kx) 2) (pow.f64 (sin.f64 ky) 2)))
8.2b	(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)))))

rewrite45.0ms (0.2%)

Algorithm

1×	rewrite-expression-head

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

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)))
9.0ms	(/.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)

series3.1s (14.2%)

Counts

4 → 52

Calls

4 calls:

1.4s	(/.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))))))
1.0s	(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)))))
653.0ms	(.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 kx) 2)

Compiler

Compiled 3787 to 3502 computations (7.5% saved)

simplify80.0ms (0.4%)

Algorithm

1×	egg-herbie

Counts

165 → 165

Iterations

Useful iterations: 0 (32.0ms)

Iter	Nodes	Cost
0	5347	5719

prune351.0ms (1.6%)

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 5698 to 4223 computations (25.9% saved)

localize20.0ms (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 (/.f64 (.f64 2 l) Om) (.f64 (/.f64 (.f64 2 l) Om) (+.f64 (pow.f64 (sin.f64 kx) 2) (pow.f64 (sin.f64 ky) 2)))))))
2.0b	(.f64 (/.f64 (.f64 2 l) Om) (+.f64 (pow.f64 (sin.f64 kx) 2) (pow.f64 (sin.f64 ky) 2)))
8.2b	(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))))))

rewrite46.0ms (0.2%)

Algorithm

1×	rewrite-expression-head

Rules

29×	`*-un-lft-identity_binary64_78`
28×	`add-sqr-sqrt_binary64_100`
25×	`add-cube-cbrt_binary64_113`
21×	`times-frac_binary64_84`
16×	`add-exp-log_binary64_116`
15×	`add-cbrt-cube_binary64_114` `sqrt-prod_binary64_94`
8×	`pow1_binary64_139`
7×	`associate-l_binary64_19`
6×	`associate-/r*_binary64_22`
5×	`unpow-prod-down_binary64_157` `associate-r_binary64_18`
4×	`add-log-exp_binary64_117` `cbrt-unprod_binary64_111` `prod-exp_binary64_127` `flip-+_binary64_52` `sqrt-div_binary64_95` `flip3-+_binary64_81`
3×	`cbrt-undiv_binary64_112` `div-exp_binary64_129` `associate-/l*_binary64_23` `pow-unpow_binary64_155`
2×	`div-inv_binary64_75` `frac-times_binary64_88` `associate-/r/_binary64_24` `associate-*r/_binary64_20` `distribute-lft-out_binary64_29`
1×	`distribute-lft-in_binary64_27` `-commutative_binary64_9` `pow-exp_binary64_146` `pow-to-exp_binary64_147` `sqrt-pow1_binary64_96` `rem-sqrt-square_binary64_91` `unpow2_binary64_143` `distribute-rgt-in_binary64_28` `frac-2neg_binary64_89` `sqr-pow_binary64_50` `pow-pow_binary64_150` `associate-l/_binary64_21` `pow-prod-down_binary64_149` `unswap-sqr_binary64_46` `clear-num_binary64_77` `pow1/2_binary64_158`

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)))
9.0ms	(/.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 kx) 2)

series3.1s (13.9%)

Counts

4 → 52

Calls

4 calls:

1.4s	(/.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)))))))
989.0ms	(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))))))
621.0ms	(.f64 (/.f64 (.f64 2 l) Om) (+.f64 (pow.f64 (sin.f64 kx) 2) (pow.f64 (sin.f64 ky) 2)))
24.0ms	(pow.f64 (sin.f64 kx) 2)

Compiler

Compiled 3855 to 3502 computations (9.2% saved)

simplify98.0ms (0.4%)

Algorithm

1×	egg-herbie

Counts

161 → 161

Iterations

Useful iterations: 0 (51.0ms)

Iter	Nodes	Cost
0	5024	5613

prune332.0ms (1.5%)

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

Error

0.0b

Counts

164 → 3

Compiler

Compiled 5954 to 4115 computations (30.9% saved)

localize24.0ms (0.1%)

Local error

Found 4 expressions with local error:

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))))))
1.5b	(.f64 (pow.f64 (/.f64 (.f64 2 l) Om) 2) (+.f64 (pow.f64 (sin.f64 kx) 2) (pow.f64 (sin.f64 ky) 2)))
2.8b	(log.f64 (exp.f64 (/.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))))))))
8.2b	(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)))))

rewrite52.0ms (0.2%)

Algorithm

1×	rewrite-expression-head

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-l_binary64_19`
10×	`unpow-prod-down_binary64_157`
8×	`add-cbrt-cube_binary64_114`
6×	`prod-exp_binary64_127` `associate-/r*_binary64_22` `sqrt-div_binary64_95` `pow1_binary64_139`
5×	`associate-r_binary64_18`
4×	`add-log-exp_binary64_117` `flip-+_binary64_52` `unswap-sqr_binary64_46` `associate-/r/_binary64_24` `flip3-+_binary64_81`
3×	`pow-exp_binary64_146` `div-exp_binary64_129` `div-inv_binary64_75` `associate-/l*_binary64_23` `log-prod_binary64_164`
2×	`unpow2_binary64_143` `sqr-pow_binary64_50` `associate-*r/_binary64_20` `distribute-lft-out_binary64_29`
1×	`distribute-lft-in_binary64_27` `*-commutative_binary64_9` `pow-to-exp_binary64_147` `sqrt-pow1_binary64_96` `cbrt-unprod_binary64_111` `cbrt-undiv_binary64_112` `rem-sqrt-square_binary64_91` `distribute-rgt-in_binary64_28` `frac-2neg_binary64_89` `rem-log-exp_binary64_119` `clear-num_binary64_77` `pow1/2_binary64_158`

Counts

4 → 131

Calls

4 calls:

16.0ms	(.f64 (pow.f64 (/.f64 (.f64 2 l) Om) 2) (+.f64 (pow.f64 (sin.f64 kx) 2) (pow.f64 (sin.f64 ky) 2)))
9.0ms	(log.f64 (exp.f64 (/.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))))))))
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)))))

series5.2s (23.9%)

Counts

4 → 61

Calls

4 calls:

2.4s	(log.f64 (exp.f64 (/.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	(/.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))))))
1.0s	(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)))))
656.0ms	(.f64 (pow.f64 (/.f64 (.f64 2 l) Om) 2) (+.f64 (pow.f64 (sin.f64 kx) 2) (pow.f64 (sin.f64 ky) 2)))

Compiler

Compiled 4716 to 4385 computations (7% saved)

simplify109.0ms (0.5%)

Algorithm

1×	egg-herbie

Counts

192 → 192

Iterations

Useful iterations: 0 (51.0ms)

Iter	Nodes	Cost
0	5028	7231

prune476.0ms (2.2%)

Pruning

3 alts after pruning (1 fresh and 2 done)

	Pruned	Kept	Total
New	192	0	192
Fresh	0	1	1
Picked	0	1	1
Done	0	1	1
Total	192	3	195

Error

0.0b

Counts

195 → 3

Compiler

Compiled 7253 to 5470 computations (24.6% saved)

localize21.0ms (0.1%)

Local error

Found 4 expressions with local error:

0.4b	(/.f64 1/2 (sqrt.f64 (+.f64 1 (.f64 4 (.f64 (pow.f64 (/.f64 l Om) 2) (+.f64 (pow.f64 (sin.f64 ky) 2) (pow.f64 (sin.f64 (/.f64 -1 kx)) 2)))))))
2.9b	(*.f64 (pow.f64 (/.f64 l Om) 2) (+.f64 (pow.f64 (sin.f64 ky) 2) (pow.f64 (sin.f64 (/.f64 -1 kx)) 2)))
6.5b	(sqrt.f64 (+.f64 1 (.f64 4 (.f64 (pow.f64 (/.f64 l Om) 2) (+.f64 (pow.f64 (sin.f64 ky) 2) (pow.f64 (sin.f64 (/.f64 -1 kx)) 2))))))
26.4b	(sin.f64 (/.f64 -1 kx))

rewrite46.0ms (0.2%)

Algorithm

1×	rewrite-expression-head

Rules

39×	`add-sqr-sqrt_binary64_100`
33×	`*-un-lft-identity_binary64_78`
29×	`add-cube-cbrt_binary64_113`
28×	`times-frac_binary64_84`
18×	`associate-l_binary64_19`
17×	`unpow-prod-down_binary64_157`
15×	`sqrt-prod_binary64_94`
14×	`add-exp-log_binary64_116`
8×	`add-cbrt-cube_binary64_114`
6×	`associate-/r*_binary64_22`
5×	`associate-r_binary64_18` `unswap-sqr_binary64_46` `pow1_binary64_139`
4×	`add-log-exp_binary64_117` `prod-exp_binary64_127` `sqrt-div_binary64_95`
3×	`flip-+_binary64_52` `associate-/l*_binary64_23` `flip3-+_binary64_81`
2×	`pow-exp_binary64_146` `div-exp_binary64_129` `unpow2_binary64_143` `sqr-pow_binary64_50` `div-inv_binary64_75` `associate-/r/_binary64_24` `associate-*r/_binary64_20` `distribute-lft-out_binary64_29`
1×	`distribute-lft-in_binary64_27` `*-commutative_binary64_9` `pow-to-exp_binary64_147` `sqrt-pow1_binary64_96` `cbrt-unprod_binary64_111` `cbrt-undiv_binary64_112` `rem-sqrt-square_binary64_91` `distribute-rgt-in_binary64_28` `frac-2neg_binary64_89` `clear-num_binary64_77` `pow1/2_binary64_158`

Counts

4 → 108

Calls

4 calls:

18.0ms	(*.f64 (pow.f64 (/.f64 l Om) 2) (+.f64 (pow.f64 (sin.f64 ky) 2) (pow.f64 (sin.f64 (/.f64 -1 kx)) 2)))
6.0ms	(/.f64 1/2 (sqrt.f64 (+.f64 1 (.f64 4 (.f64 (pow.f64 (/.f64 l Om) 2) (+.f64 (pow.f64 (sin.f64 ky) 2) (pow.f64 (sin.f64 (/.f64 -1 kx)) 2)))))))
3.0ms	(sqrt.f64 (+.f64 1 (.f64 4 (.f64 (pow.f64 (/.f64 l Om) 2) (+.f64 (pow.f64 (sin.f64 ky) 2) (pow.f64 (sin.f64 (/.f64 -1 kx)) 2))))))
3.0ms	(sin.f64 (/.f64 -1 kx))

series3.3s (15.1%)

Counts

4 → 56

Calls

4 calls:

1.4s	(/.f64 1/2 (sqrt.f64 (+.f64 1 (.f64 4 (.f64 (pow.f64 (/.f64 l Om) 2) (+.f64 (pow.f64 (sin.f64 ky) 2) (pow.f64 (sin.f64 (/.f64 -1 kx)) 2)))))))
1.3s	(sqrt.f64 (+.f64 1 (.f64 4 (.f64 (pow.f64 (/.f64 l Om) 2) (+.f64 (pow.f64 (sin.f64 ky) 2) (pow.f64 (sin.f64 (/.f64 -1 kx)) 2))))))
620.0ms	(*.f64 (pow.f64 (/.f64 l Om) 2) (+.f64 (pow.f64 (sin.f64 ky) 2) (pow.f64 (sin.f64 (/.f64 -1 kx)) 2)))
16.0ms	(sin.f64 (/.f64 -1 kx))

Compiler

Compiled 4481 to 4143 computations (7.5% saved)

simplify82.0ms (0.4%)

Algorithm

1×	egg-herbie

Counts

164 → 164

Iterations

Useful iterations: 0 (33.0ms)

Iter	Nodes	Cost
0	5357	6381

prune395.0ms (1.8%)

Pruning

3 alts after pruning (0 fresh and 3 done)

	Pruned	Kept	Total
New	164	0	164
Fresh	0	0	0
Picked	0	1	1
Done	0	2	2
Total	164	3	167

Error

0.0b

Counts

167 → 3

Compiler

Compiled 6101 to 4665 computations (23.5% saved)

regimes1.0s (4.6%)

Accuracy

Total 0.6b remaining (92.6%)

Threshold costs 0.6b (92.6%)

Compiler

Compiled 11800 to 11401 computations (3.4% 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%)

sample3.2s (14.4%)

Algorithm

1×

intervals

Results

1.2s	6311×	body	128	valid
668.0ms	806×	body	1024	valid
333.0ms	557×	body	512	valid
129.0ms	326×	body	256	valid

Compiler

Compiled 613 to 587 computations (4.2% saved)

Details

analyze642.0ms (2.9%)

sample84.0ms (0.4%)

simplify134.0ms (0.6%)

prune5.0ms (0%)

localize19.0ms (0.1%)

rewrite45.0ms (0.2%)

series3.1s (14.2%)

simplify80.0ms (0.4%)

prune351.0ms (1.6%)

localize20.0ms (0.1%)

rewrite46.0ms (0.2%)

series3.1s (13.9%)

simplify98.0ms (0.4%)

prune332.0ms (1.5%)

localize24.0ms (0.1%)

rewrite52.0ms (0.2%)

series5.2s (23.9%)

simplify109.0ms (0.5%)

prune476.0ms (2.2%)

localize21.0ms (0.1%)

rewrite46.0ms (0.2%)

series3.3s (15.1%)

simplify82.0ms (0.4%)

prune395.0ms (1.8%)

regimes1.0s (4.6%)

bsearch0.0ms (0%)

simplify2.0ms (0%)

end0.0ms (0%)

sample3.2s (14.4%)

Profiling