Details

analyze679.0ms (4.4%)

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)

sample98.0ms (0.6%)

Algorithm

1×

intervals

Results

42.0ms	198×	body	128	valid
26.0ms	26×	body	1024	valid
12.0ms	18×	body	512	valid
6.0ms	14×	body	256	valid

Compiler

Compiled 59 to 63 computations (-6.8% saved)

simplify212.0ms (1.4%)

Algorithm

1×	egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (41.0ms)

Iter	Nodes	Cost
0	5325	39

prune8.0ms (0.1%)

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 104 to 104 computations (0% saved)

localize22.0ms (0.1%)

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)))))

rewrite46.0ms (0.3%)

Algorithm

1×	rewrite-expression-head

Rules

33×	`add-sqr-sqrt_binary64_101`
30×	`*-un-lft-identity_binary64_79`
26×	`add-cube-cbrt_binary64_114`
21×	`times-frac_binary64_85`
19×	`add-exp-log_binary64_117`
15×	`sqrt-prod_binary64_95`
13×	`unpow-prod-down_binary64_158`
12×	`associate-l_binary64_20`
8×	`add-cbrt-cube_binary64_115`
6×	`associate-/r*_binary64_23` `prod-exp_binary64_128` `pow1_binary64_140`
5×	`associate-r_binary64_19`
4×	`pow-exp_binary64_147` `unswap-sqr_binary64_47` `sqrt-div_binary64_96` `add-log-exp_binary64_118`
3×	`div-exp_binary64_130` `pow-unpow_binary64_156` `flip-+_binary64_53` `unpow2_binary64_144` `sqr-pow_binary64_51` `associate-/l*_binary64_24` `flip3-+_binary64_82`
2×	`pow-to-exp_binary64_148` `div-inv_binary64_76` `associate-*r/_binary64_21` `associate-/r/_binary64_25` `distribute-lft-out_binary64_30`
1×	`cbrt-undiv_binary64_113` `pow-pow_binary64_151` `distribute-lft-in_binary64_28` `cbrt-unprod_binary64_112` `rem-sqrt-square_binary64_92` `*-commutative_binary64_10` `sqrt-pow1_binary64_97` `clear-num_binary64_78` `pow1/2_binary64_159` `distribute-rgt-in_binary64_29` `frac-2neg_binary64_90`

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 ky) 2)

series2.1s (13.9%)

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))))))
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)))))
311.0ms	(.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)

simplify85.0ms (0.6%)

Algorithm

1×	egg-herbie

Counts

125 → 125

Iterations

Useful iterations: 0 (44.0ms)

Iter	Nodes	Cost
0	4957	4125
1	4957	4125

prune381.0ms (2.5%)

Pruning

4 alts after pruning (4 fresh and 0 done)

	Pruned	Kept	Total
New	121	4	125
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	122	4	126

Merged error: 0.1b

Counts

126 → 4

Compiler

Compiled 6358 to 5125 computations (19.4% saved)

localize21.0ms (0.1%)

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

rewrite51.0ms (0.3%)

Algorithm

1×	rewrite-expression-head

Rules

29×	`*-un-lft-identity_binary64_79`
28×	`add-sqr-sqrt_binary64_101`
25×	`add-cube-cbrt_binary64_114`
21×	`times-frac_binary64_85`
16×	`add-exp-log_binary64_117`
15×	`sqrt-prod_binary64_95` `add-cbrt-cube_binary64_115`
8×	`pow1_binary64_140`
7×	`associate-l_binary64_20`
6×	`associate-/r*_binary64_23`
5×	`unpow-prod-down_binary64_158` `associate-r_binary64_19`
4×	`flip-+_binary64_53` `cbrt-unprod_binary64_112` `prod-exp_binary64_128` `sqrt-div_binary64_96` `add-log-exp_binary64_118` `flip3-+_binary64_82`
3×	`cbrt-undiv_binary64_113` `div-exp_binary64_130` `pow-unpow_binary64_156` `associate-/l*_binary64_24`
2×	`div-inv_binary64_76` `frac-times_binary64_89` `associate-*r/_binary64_21` `associate-/r/_binary64_25` `distribute-lft-out_binary64_30`
1×	`pow-exp_binary64_147` `pow-to-exp_binary64_148` `unpow2_binary64_144` `sqr-pow_binary64_51` `pow-pow_binary64_151` `distribute-lft-in_binary64_28` `associate-l/_binary64_22` `unswap-sqr_binary64_47` `rem-sqrt-square_binary64_92` `-commutative_binary64_10` `pow-prod-down_binary64_150` `sqrt-pow1_binary64_97` `clear-num_binary64_78` `pow1/2_binary64_159` `distribute-rgt-in_binary64_29` `frac-2neg_binary64_90`

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)))
8.0ms	(/.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 ky) 2)

series2.1s (13.8%)

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)))))))
661.0ms	(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))))))
343.0ms	(.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 ky) 2)

simplify64.0ms (0.4%)

Algorithm

1×	egg-herbie

Counts

121 → 121

Iterations

Useful iterations: 0 (26.0ms)

Iter	Nodes	Cost
0	5168	4116

prune250.0ms (1.6%)

Pruning

4 alts after pruning (3 fresh and 1 done)

	Pruned	Kept	Total
New	121	0	121
Fresh	0	3	3
Picked	0	1	1
Done	0	0	0
Total	121	4	125

Merged error: 0.1b

Counts

125 → 4

Compiler

Compiled 4727 to 3339 computations (29.4% 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))

rewrite24.0ms (0.2%)

Algorithm

1×	rewrite-expression-head

Rules

21×	`cbrt-prod_binary64_110`
12×	`add-sqr-sqrt_binary64_101`
11×	`add-cube-cbrt_binary64_114` `*-un-lft-identity_binary64_79`
9×	`times-frac_binary64_85`
5×	`pow1_binary64_140`
4×	`add-exp-log_binary64_117` `add-cbrt-cube_binary64_115` `add-log-exp_binary64_118`
3×	`sqrt-prod_binary64_95` `div-inv_binary64_76` `cbrt-div_binary64_111` `pow1/3_binary64_161`
2×	`sqrt-div_binary64_96`
1×	`flip-+_binary64_53` `rem-sqrt-square_binary64_92` `sqrt-pow1_binary64_97` `pow1/2_binary64_159` `flip3-+_binary64_82`

Counts

4 → 63

Calls

4 calls:

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))
3.0ms	(cbrt.f64 (/.f64 (*.f64 2 l) Om))

series1.3s (8.6%)

Counts

4 → 12

Calls

4 calls:

912.0ms	(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)))))
139.0ms	(cbrt.f64 (/.f64 (*.f64 2 l) Om))
136.0ms	(cbrt.f64 (/.f64 (*.f64 2 l) Om))
130.0ms	(cbrt.f64 (/.f64 (*.f64 2 l) Om))

simplify74.0ms (0.5%)

Algorithm

1×	egg-herbie

Counts

75 → 75

Iterations

Useful iterations: 0 (55.0ms)

Iter	Nodes	Cost
0	4988	1438
1	4988	1438

prune177.0ms (1.2%)

Pruning

4 alts after pruning (2 fresh and 2 done)

	Pruned	Kept	Total
New	75	0	75
Fresh	0	2	2
Picked	0	1	1
Done	0	1	1
Total	75	4	79

Merged error: 0.1b

Counts

79 → 4

Compiler

Compiled 3402 to 2585 computations (24% saved)

localize25.0ms (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)))))

rewrite87.0ms (0.6%)

Algorithm

1×	rewrite-expression-head

Rules

99×	`add-sqr-sqrt_binary64_101`
97×	`sqrt-prod_binary64_95`
83×	`times-frac_binary64_85`
68×	`*-un-lft-identity_binary64_79`
64×	`add-cube-cbrt_binary64_114`
47×	`associate-r_binary64_19`
23×	`add-exp-log_binary64_117`
18×	`associate-l_binary64_20`
14×	`unswap-sqr_binary64_47`
13×	`add-cbrt-cube_binary64_115`
10×	`unpow-prod-down_binary64_158`
8×	`prod-exp_binary64_128`
7×	`pow1_binary64_140`
6×	`associate-/r_binary64_23` `associate-/l_binary64_24` `sqrt-div_binary64_96`
4×	`div-exp_binary64_130` `flip-+_binary64_53` `associate-/r/_binary64_25` `add-log-exp_binary64_118` `flip3-+_binary64_82`
3×	`pow-exp_binary64_147` `div-inv_binary64_76` `associate-*r/_binary64_21` `cbrt-unprod_binary64_112`
2×	`cbrt-undiv_binary64_113` `unpow2_binary64_144` `sqr-pow_binary64_51` `*-commutative_binary64_10` `distribute-lft-out_binary64_30` `sqrt-undiv_binary64_100`
1×	`pow-to-exp_binary64_148` `sqrt-unprod_binary64_99` `distribute-lft-in_binary64_28` `rem-sqrt-square_binary64_92` `pow-prod-down_binary64_150` `sqrt-pow1_binary64_97` `clear-num_binary64_78` `pow1/2_binary64_159` `distribute-rgt-in_binary64_29` `frac-2neg_binary64_90`

Counts

4 → 190

Calls

4 calls:

26.0ms	(.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)))))))
18.0ms	(.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)))))

series3.3s (21.7%)

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))))))
670.0ms	(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)))

simplify97.0ms (0.6%)

Algorithm

1×	egg-herbie

Counts

202 → 202

Iterations

Useful iterations: 0 (28.0ms)

Iter	Nodes	Cost
0	4971	8609
1	4971	8609

prune652.0ms (4.2%)

Pruning

4 alts after pruning (1 fresh and 3 done)

	Pruned	Kept	Total
New	202	0	202
Fresh	0	1	1
Picked	0	1	1
Done	0	2	2
Total	202	4	206

Merged error: 0.1b

Counts

206 → 4

Compiler

Compiled 8714 to 6830 computations (21.6% saved)

regimes306.0ms (2%)

Compiler: Compiled 2010 to 2066 computations (-2.8% saved)

bsearch76.0ms (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%)

sample3.0s (19.5%)

Algorithm

1×

intervals

Results

1.3s	6329×	body	128	valid
778.0ms	791×	body	1024	valid
384.0ms	560×	body	512	valid
136.0ms	319×	body	256	valid
2.0ms	1×	body	2048	valid

Compiler

Compiled 175 to 175 computations (0% saved)

Details

analyze679.0ms (4.4%)

sample98.0ms (0.6%)

simplify212.0ms (1.4%)

prune8.0ms (0.1%)

localize22.0ms (0.1%)

rewrite46.0ms (0.3%)

series2.1s (13.9%)

simplify85.0ms (0.6%)

prune381.0ms (2.5%)

localize21.0ms (0.1%)

rewrite51.0ms (0.3%)

series2.1s (13.8%)

simplify64.0ms (0.4%)

prune250.0ms (1.6%)

localize28.0ms (0.2%)

rewrite24.0ms (0.2%)

series1.3s (8.6%)

simplify74.0ms (0.5%)

prune177.0ms (1.2%)

localize25.0ms (0.2%)

rewrite87.0ms (0.6%)

series3.3s (21.7%)

simplify97.0ms (0.6%)

prune652.0ms (4.2%)

regimes306.0ms (2%)

bsearch76.0ms (0.5%)

simplify2.0ms (0%)

end0.0ms (0%)

sample3.0s (19.5%)

Profiling