Details

analyze623.0ms (5%)

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)

sample89.0ms (0.7%)

Algorithm

1×

intervals

Results

36.0ms	198×	body	128	valid
25.0ms	26×	body	1024	valid
11.0ms	18×	body	512	valid
6.0ms	14×	body	256	valid

Compiler

Compiled 59 to 63 computations (-6.8% saved)

simplify210.0ms (1.7%)

Algorithm

1×	egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (45.0ms)

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: 1.5b

Counts

2 → 1

Compiler

Compiled 50 to 50 computations (0% saved)

localize21.0ms (0.2%)

Local error

Found 4 expressions with local error:

0.3b	(pow.f64 (sin.f64 ky) 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))))))
2.1b	(.f64 (pow.f64 (/.f64 (.f64 2 l) Om) 2) (+.f64 (pow.f64 (sin.f64 kx) 2) (pow.f64 (sin.f64 ky) 2)))
9.9b	(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)))))

rewrite48.0ms (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:

17.0ms	(.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 ky) 2)

series2.1s (16.8%)

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))))))
676.0ms	(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)))))
315.0ms	(.f64 (pow.f64 (/.f64 (.f64 2 l) Om) 2) (+.f64 (pow.f64 (sin.f64 kx) 2) (pow.f64 (sin.f64 ky) 2)))
25.0ms	(pow.f64 (sin.f64 ky) 2)

simplify99.0ms (0.8%)

Algorithm

1×	egg-herbie

Counts

125 → 125

Iterations

Useful iterations: 0 (59.0ms)

Iter	Nodes	Cost
0	4954	4125
1	4954	4125

prune278.0ms (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: 0.1b

Counts

126 → 3

Compiler

Compiled 4443 to 3377 computations (24% saved)

localize28.0ms (0.2%)

Local error

Found 4 expressions with local error:

9.9b	(sqrt.f64 (+.f64 1 (.f64 (pow.f64 (.f64 (cbrt.f64 (/.f64 (.f64 2 l) Om)) (cbrt.f64 (/.f64 (.f64 2 l) Om))) 2) (.f64 (+.f64 (pow.f64 (sin.f64 kx) 2) (pow.f64 (sin.f64 ky) 2)) (pow.f64 (cbrt.f64 (/.f64 (.f64 2 l) Om)) 2)))))
12.8b	(cbrt.f64 (/.f64 (*.f64 2 l) Om))
12.8b	(cbrt.f64 (/.f64 (*.f64 2 l) Om))
12.8b	(cbrt.f64 (/.f64 (*.f64 2 l) Om))

rewrite25.0ms (0.2%)

Algorithm

1×	rewrite-expression-head

Rules

21×	`cbrt-prod_binary64_105`
12×	`add-sqr-sqrt_binary64_98`
11×	`add-cube-cbrt_binary64_109` `*-un-lft-identity_binary64_77`
9×	`times-frac_binary64_83`
5×	`pow1_binary64_135`
4×	`add-exp-log_binary64_112` `add-cbrt-cube_binary64_110` `add-log-exp_binary64_113`
3×	`sqrt-prod_binary64_92` `cbrt-div_binary64_106` `pow1/3_binary64_156` `div-inv_binary64_74`
2×	`sqrt-div_binary64_93`
1×	`rem-sqrt-square_binary64_90` `sqrt-pow1_binary64_94` `flip-+_binary64_51` `flip3-+_binary64_80` `pow1/2_binary64_154`

Counts

4 → 63

Calls

4 calls:

6.0ms	(cbrt.f64 (/.f64 (*.f64 2 l) Om))
4.0ms	(sqrt.f64 (+.f64 1 (.f64 (pow.f64 (.f64 (cbrt.f64 (/.f64 (.f64 2 l) Om)) (cbrt.f64 (/.f64 (.f64 2 l) Om))) 2) (.f64 (+.f64 (pow.f64 (sin.f64 kx) 2) (pow.f64 (sin.f64 ky) 2)) (pow.f64 (cbrt.f64 (/.f64 (.f64 2 l) Om)) 2)))))
3.0ms	(cbrt.f64 (/.f64 (*.f64 2 l) Om))
3.0ms	(cbrt.f64 (/.f64 (*.f64 2 l) Om))

series1.3s (10.5%)

Counts

4 → 12

Calls

4 calls:

913.0ms	(sqrt.f64 (+.f64 1 (.f64 (pow.f64 (.f64 (cbrt.f64 (/.f64 (.f64 2 l) Om)) (cbrt.f64 (/.f64 (.f64 2 l) Om))) 2) (.f64 (+.f64 (pow.f64 (sin.f64 kx) 2) (pow.f64 (sin.f64 ky) 2)) (pow.f64 (cbrt.f64 (/.f64 (.f64 2 l) Om)) 2)))))
143.0ms	(cbrt.f64 (/.f64 (*.f64 2 l) Om))
142.0ms	(cbrt.f64 (/.f64 (*.f64 2 l) Om))
125.0ms	(cbrt.f64 (/.f64 (*.f64 2 l) Om))

simplify75.0ms (0.6%)

Algorithm

1×	egg-herbie

Counts

75 → 75

Iterations

Useful iterations: 0 (55.0ms)

Iter	Nodes	Cost
0	5004	1438

prune183.0ms (1.5%)

Pruning

3 alts after pruning (2 fresh and 1 done)

	Pruned	Kept	Total
New	75	0	75
Fresh	0	2	2
Picked	0	1	1
Done	0	0	0
Total	75	3	78

Merged error: 0.1b

Counts

78 → 3

Compiler

Compiled 3402 to 2585 computations (24% saved)

localize27.0ms (0.2%)

Local error

Found 4 expressions with local error:

0.4b	(/.f64 (sqrt.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))))))
0.7b	(.f64 (sqrt.f64 1/2) (/.f64 (sqrt.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)))))))
2.1b	(.f64 (pow.f64 (/.f64 (.f64 2 l) Om) 2) (+.f64 (pow.f64 (sin.f64 kx) 2) (pow.f64 (sin.f64 ky) 2)))
9.9b	(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)))))

rewrite82.0ms (0.7%)

Algorithm

1×	rewrite-expression-head

Rules

99×	`add-sqr-sqrt_binary64_98`
97×	`sqrt-prod_binary64_92`
83×	`times-frac_binary64_83`
68×	`*-un-lft-identity_binary64_77`
64×	`add-cube-cbrt_binary64_109`
47×	`associate-r_binary64_19`
23×	`add-exp-log_binary64_112`
18×	`associate-l_binary64_20`
14×	`unswap-sqr_binary64_45`
13×	`add-cbrt-cube_binary64_110`
10×	`unpow-prod-down_binary64_153`
8×	`prod-exp_binary64_123`
7×	`pow1_binary64_135`
6×	`associate-/r_binary64_23` `sqrt-div_binary64_93` `associate-/l_binary64_24`
4×	`add-log-exp_binary64_113` `flip-+_binary64_51` `flip3-+_binary64_80` `div-exp_binary64_125` `associate-/r/_binary64_25`
3×	`cbrt-unprod_binary64_107` `pow-exp_binary64_142` `associate-*r/_binary64_21` `div-inv_binary64_74`
2×	`cbrt-undiv_binary64_108` `sqr-pow_binary64_49` `sqrt-undiv_binary64_97` `*-commutative_binary64_10` `unpow2_binary64_139` `distribute-lft-out_binary64_30`
1×	`pow-to-exp_binary64_143` `pow-prod-down_binary64_145` `rem-sqrt-square_binary64_90` `sqrt-pow1_binary64_94` `distribute-lft-in_binary64_28` `pow1/2_binary64_154` `clear-num_binary64_76` `sqrt-unprod_binary64_96` `distribute-rgt-in_binary64_29` `frac-2neg_binary64_88`

Counts

4 → 190

Calls

4 calls:

21.0ms	(.f64 (sqrt.f64 1/2) (/.f64 (sqrt.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)))))))
17.0ms	(.f64 (pow.f64 (/.f64 (.f64 2 l) Om) 2) (+.f64 (pow.f64 (sin.f64 kx) 2) (pow.f64 (sin.f64 ky) 2)))
8.0ms	(/.f64 (sqrt.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)))))

series3.4s (26.9%)

Counts

4 → 12

Calls

4 calls:

1.2s	(.f64 (sqrt.f64 1/2) (/.f64 (sqrt.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 (sqrt.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))))))
681.0ms	(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)))))
310.0ms	(.f64 (pow.f64 (/.f64 (.f64 2 l) Om) 2) (+.f64 (pow.f64 (sin.f64 kx) 2) (pow.f64 (sin.f64 ky) 2)))

simplify117.0ms (0.9%)

Algorithm

1×	egg-herbie

Counts

202 → 202

Iterations

Useful iterations: 0 (45.0ms)

Iter	Nodes	Cost
0	4964	8609
1	4964	8609

prune643.0ms (5.1%)

Pruning

3 alts after pruning (1 fresh and 2 done)

	Pruned	Kept	Total
New	202	0	202
Fresh	0	1	1
Picked	0	1	1
Done	0	1	1
Total	202	3	205

Merged error: 0.1b

Counts

205 → 3

Compiler

Compiled 8718 to 6838 computations (21.6% saved)

localize2.0ms (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: 0.1b

Counts

3 → 3

Compiler

Compiled 0 to 0 computations (0% saved)

regimes275.0ms (2.2%)

Compiler: Compiled 1575 to 1661 computations (-5.5% saved)

bsearch65.0ms (0.5%)

Steps

Iters	Range		Point
8	2.9723502086234665e+167	3.839622508563207e+170	3.7908934159581465e+170

Compiler

Compiled 7 to 9 computations (-28.6% saved)

simplify2.0ms (0%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	35	64
1	35	64

end0.0ms (0%)

sample2.8s (22.6%)

Algorithm

1×

intervals

Results

1.2s	6329×	body	128	valid
731.0ms	791×	body	1024	valid
359.0ms	560×	body	512	valid
131.0ms	319×	body	256	valid
2.0ms	1×	body	2048	valid

Compiler

Compiled 146 to 148 computations (-1.4% saved)

Details

analyze623.0ms (5%)

sample89.0ms (0.7%)

simplify210.0ms (1.7%)

prune5.0ms (0%)

localize21.0ms (0.2%)

rewrite48.0ms (0.4%)

series2.1s (16.8%)

simplify99.0ms (0.8%)

prune278.0ms (2.2%)

localize28.0ms (0.2%)

rewrite25.0ms (0.2%)

series1.3s (10.5%)

simplify75.0ms (0.6%)

prune183.0ms (1.5%)

localize27.0ms (0.2%)

rewrite82.0ms (0.7%)

series3.4s (26.9%)

simplify117.0ms (0.9%)

prune643.0ms (5.1%)

localize2.0ms (0%)

rewrite0.0ms (0%)

series0.0ms (0%)

simplify6.0ms (0.1%)

prune1.0ms (0%)

regimes275.0ms (2.2%)

bsearch65.0ms (0.5%)

simplify2.0ms (0%)

end0.0ms (0%)

sample2.8s (22.6%)

Profiling