Details

analyze591.0ms (4.9%)

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)

sample86.0ms (0.7%)

Algorithm

1×

intervals

Results

36.0ms	200×	body	128	valid
22.0ms	26×	body	1024	valid
13.0ms	21×	body	512	valid
3.0ms	9×	body	256	valid

Compiler

Compiled 59 to 63 computations (-6.8% saved)

simplify197.0ms (1.6%)

Algorithm

1×	egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (39.0ms)

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: 1.3b

Counts

2 → 1

Compiler

Compiled 50 to 50 computations (0% saved)

localize20.0ms (0.2%)

Local error

Found 4 expressions with local error:

0.3b	(pow.f64 (sin.f64 kx) 2)
0.6b	(/.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))))))
2.0b	(.f64 (pow.f64 (/.f64 (.f64 2 l) Om) 2) (+.f64 (pow.f64 (sin.f64 kx) 2) (pow.f64 (sin.f64 ky) 2)))
10.1b	(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)))))

rewrite49.0ms (0.4%)

Algorithm

1×	rewrite-expression-head

Rules

33×	`add-sqr-sqrt_binary64_98`
30×	`*-un-lft-identity_binary64_77`
26×	`add-cube-cbrt_binary64_109`
21×	`times-frac_binary64_83`
19×	`add-exp-log_binary64_112`
15×	`sqrt-prod_binary64_92`
13×	`unpow-prod-down_binary64_153`
12×	`associate-l_binary64_20`
8×	`add-cbrt-cube_binary64_110`
6×	`associate-/r*_binary64_23` `pow1_binary64_135` `prod-exp_binary64_123`
5×	`associate-r_binary64_19`
4×	`add-log-exp_binary64_113` `sqrt-div_binary64_93` `pow-exp_binary64_142` `unswap-sqr_binary64_45`
3×	`flip-+_binary64_51` `sqr-pow_binary64_49` `flip3-+_binary64_80` `associate-/l*_binary64_24` `div-exp_binary64_125` `pow-unpow_binary64_151` `unpow2_binary64_139`
2×	`pow-to-exp_binary64_143` `associate-*r/_binary64_21` `associate-/r/_binary64_25` `distribute-lft-out_binary64_30` `div-inv_binary64_74`
1×	`rem-sqrt-square_binary64_90` `sqrt-pow1_binary64_94` `cbrt-unprod_binary64_107` `cbrt-undiv_binary64_108` `distribute-lft-in_binary64_28` `*-commutative_binary64_10` `pow1/2_binary64_154` `clear-num_binary64_76` `distribute-rgt-in_binary64_29` `frac-2neg_binary64_88` `pow-pow_binary64_146`

Counts

4 → 113

Calls

4 calls:

18.0ms	(.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 kx) 2)

series2.0s (17%)

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))))))
652.0ms	(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)))))
297.0ms	(.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)

simplify77.0ms (0.6%)

Algorithm

1×	egg-herbie

Counts

125 → 125

Iterations

Useful iterations: 0 (40.0ms)

Iter	Nodes	Cost
0	4951	4125
1	4951	4125

prune263.0ms (2.2%)

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: 0.0b

Counts

126 → 3

Compiler

Compiled 4428 to 3364 computations (24% saved)

localize20.0ms (0.2%)

Local error

Found 4 expressions with local error:

0.3b	(pow.f64 (sin.f64 kx) 2)
0.6b	(/.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)))))))
3.6b	(.f64 (/.f64 (.f64 2 l) Om) (+.f64 (pow.f64 (sin.f64 kx) 2) (pow.f64 (sin.f64 ky) 2)))
10.1b	(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_77`
28×	`add-sqr-sqrt_binary64_98`
25×	`add-cube-cbrt_binary64_109`
21×	`times-frac_binary64_83`
16×	`add-exp-log_binary64_112`
15×	`sqrt-prod_binary64_92` `add-cbrt-cube_binary64_110`
8×	`pow1_binary64_135`
7×	`associate-l_binary64_20`
6×	`associate-/r*_binary64_23`
5×	`unpow-prod-down_binary64_153` `associate-r_binary64_19`
4×	`add-log-exp_binary64_113` `flip-+_binary64_51` `cbrt-unprod_binary64_107` `sqrt-div_binary64_93` `flip3-+_binary64_80` `prod-exp_binary64_123`
3×	`cbrt-undiv_binary64_108` `associate-/l*_binary64_24` `div-exp_binary64_125` `pow-unpow_binary64_151`
2×	`frac-times_binary64_87` `associate-*r/_binary64_21` `associate-/r/_binary64_25` `distribute-lft-out_binary64_30` `div-inv_binary64_74`
1×	`pow-to-exp_binary64_143` `pow-prod-down_binary64_145` `rem-sqrt-square_binary64_90` `sqrt-pow1_binary64_94` `sqr-pow_binary64_49` `pow-exp_binary64_142` `distribute-lft-in_binary64_28` `associate-l/_binary64_22` `unswap-sqr_binary64_45` `-commutative_binary64_10` `pow1/2_binary64_154` `clear-num_binary64_76` `unpow2_binary64_139` `distribute-rgt-in_binary64_29` `frac-2neg_binary64_88` `pow-pow_binary64_146`

Counts

4 → 109

Calls

4 calls:

18.0ms	(.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 kx) 2)

series2.1s (17.5%)

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)))))))
670.0ms	(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))))))
333.0ms	(.f64 (/.f64 (.f64 2 l) Om) (+.f64 (pow.f64 (sin.f64 kx) 2) (pow.f64 (sin.f64 ky) 2)))
23.0ms	(pow.f64 (sin.f64 kx) 2)

simplify62.0ms (0.5%)

Algorithm

1×	egg-herbie

Counts

121 → 121

Iterations

Useful iterations: 0 (25.0ms)

Iter	Nodes	Cost
0	5049	4116

prune250.0ms (2.1%)

Pruning

3 alts after pruning (2 fresh and 1 done)

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

Merged error: 0.0b

Counts

124 → 3

Compiler

Compiled 4683 to 3299 computations (29.6% saved)

localize23.0ms (0.2%)

Local error

Found 4 expressions with local error:

0.6b	(/.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))))))
2.0b	(.f64 (pow.f64 (/.f64 (.f64 2 l) Om) 2) (+.f64 (pow.f64 (sin.f64 kx) 2) (pow.f64 (sin.f64 ky) 2)))
3.5b	(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))))))))
10.1b	(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)))))

rewrite57.0ms (0.5%)

Algorithm

1×	rewrite-expression-head

Rules

45×	`add-sqr-sqrt_binary64_98`
42×	`*-un-lft-identity_binary64_77`
39×	`times-frac_binary64_83`
38×	`add-cube-cbrt_binary64_109`
25×	`log-pow_binary64_163`
24×	`sqrt-prod_binary64_92` `exp-prod_binary64_126`
18×	`add-exp-log_binary64_112`
12×	`associate-l_binary64_20`
10×	`unpow-prod-down_binary64_153`
8×	`add-cbrt-cube_binary64_110`
6×	`associate-/r*_binary64_23` `sqrt-div_binary64_93` `pow1_binary64_135` `prod-exp_binary64_123`
5×	`associate-r_binary64_19`
4×	`add-log-exp_binary64_113` `flip-+_binary64_51` `flip3-+_binary64_80` `unswap-sqr_binary64_45` `associate-/r/_binary64_25`
3×	`log-prod_binary64_160` `pow-exp_binary64_142` `associate-/l*_binary64_24` `div-exp_binary64_125` `div-inv_binary64_74`
2×	`sqr-pow_binary64_49` `associate-*r/_binary64_21` `unpow2_binary64_139` `distribute-lft-out_binary64_30`
1×	`rem-log-exp_binary64_115` `pow-to-exp_binary64_143` `rem-sqrt-square_binary64_90` `sqrt-pow1_binary64_94` `cbrt-unprod_binary64_107` `cbrt-undiv_binary64_108` `distribute-lft-in_binary64_28` `*-commutative_binary64_10` `pow1/2_binary64_154` `clear-num_binary64_76` `distribute-rgt-in_binary64_29` `frac-2neg_binary64_88`

Counts

4 → 131

Calls

4 calls:

18.0ms	(.f64 (pow.f64 (/.f64 (.f64 2 l) Om) 2) (+.f64 (pow.f64 (sin.f64 kx) 2) (pow.f64 (sin.f64 ky) 2)))
10.0ms	(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))))))))
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)))))

series2.8s (23.4%)

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))))))
761.0ms	(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))))))))
674.0ms	(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)))))
298.0ms	(.f64 (pow.f64 (/.f64 (.f64 2 l) Om) 2) (+.f64 (pow.f64 (sin.f64 kx) 2) (pow.f64 (sin.f64 ky) 2)))

simplify87.0ms (0.7%)

Algorithm

1×	egg-herbie

Counts

143 → 143

Iterations

Useful iterations: 0 (41.0ms)

Iter	Nodes	Cost
0	5032	5281

prune355.0ms (3%)

Pruning

3 alts after pruning (1 fresh and 2 done)

	Pruned	Kept	Total
New	143	0	143
Fresh	0	1	1
Picked	0	1	1
Done	0	1	1
Total	143	3	146

Merged error: 0.0b

Counts

146 → 3

Compiler

Compiled 5650 to 4355 computations (22.9% 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: 0.0b

Counts

3 → 3

Compiler

Compiled 0 to 0 computations (0% saved)

regimes256.0ms (2.1%)

Compiler: Compiled 1342 to 1458 computations (-8.6% 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%)

sample2.6s (21.7%)

Algorithm

1×

intervals

Results

1.1s	6404×	body	128	valid
651.0ms	746×	body	1024	valid
324.0ms	537×	body	512	valid
118.0ms	313×	body	256	valid

Compiler

Compiled 119 to 123 computations (-3.4% saved)

Details

analyze591.0ms (4.9%)

sample86.0ms (0.7%)

simplify197.0ms (1.6%)

prune5.0ms (0%)

localize20.0ms (0.2%)

rewrite49.0ms (0.4%)

series2.0s (17%)

simplify77.0ms (0.6%)

prune263.0ms (2.2%)

localize20.0ms (0.2%)

rewrite50.0ms (0.4%)

series2.1s (17.5%)

simplify62.0ms (0.5%)

prune250.0ms (2.1%)

localize23.0ms (0.2%)

rewrite57.0ms (0.5%)

series2.8s (23.4%)

simplify87.0ms (0.7%)

prune355.0ms (3%)

localize3.0ms (0%)

rewrite0.0ms (0%)

series0.0ms (0%)

simplify6.0ms (0.1%)

prune1.0ms (0%)

regimes256.0ms (2.1%)

bsearch0.0ms (0%)

simplify2.0ms (0%)

end0.0ms (0%)

sample2.6s (21.7%)

Profiling