Details

analyze601.0ms (8.6%)

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)

sample85.0ms (1.2%)

Algorithm

1×

intervals

Results

38.0ms	203×	body	128	valid
23.0ms	26×	body	1024	valid
7.0ms	12×	body	512	valid
6.0ms	15×	body	256	valid

Compiler

Compiled 59 to 63 computations (-6.8% saved)

simplify199.0ms (2.9%)

Algorithm

1×	egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (41.0ms)

Iter	Nodes	Cost
0	5325	39

prune12.0ms (0.2%)

Pruning

1 alts after pruning (1 fresh and 0 done)

	Pruned	Kept	Total
New	1	0	1
Fresh	0	1	1
Picked	0	0	0
Done	0	0	0
Total	1	1	2

Merged error: 1.0b

Counts

2 → 1

Compiler

Compiled 108 to 108 computations (0% saved)

localize22.0ms (0.3%)

Local error

Found 4 expressions with local error:

0.2b	(pow.f64 (sin.f64 ky) 2)
0.3b	(pow.f64 (sin.f64 kx) 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)))
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)))))

rewrite40.0ms (0.6%)

Algorithm

1×	rewrite-expression-head

Rules

20×	`add-sqr-sqrt_binary64_101`
18×	`add-exp-log_binary64_117`
17×	`*-un-lft-identity_binary64_79`
16×	`unpow-prod-down_binary64_158`
13×	`add-cube-cbrt_binary64_114`
12×	`associate-l_binary64_20`
7×	`pow1_binary64_140`
6×	`add-cbrt-cube_binary64_115` `pow-unpow_binary64_156` `prod-exp_binary64_128`
5×	`pow-exp_binary64_147` `associate-r_binary64_19`
4×	`unpow2_binary64_144` `sqr-pow_binary64_51` `unswap-sqr_binary64_47` `add-log-exp_binary64_118`
3×	`sqrt-prod_binary64_95` `pow-to-exp_binary64_148` `times-frac_binary64_85`
2×	`div-exp_binary64_130` `flip-+_binary64_53` `pow-pow_binary64_151` `associate-*r/_binary64_21` `sqrt-div_binary64_96` `flip3-+_binary64_82` `distribute-lft-out_binary64_30`
1×	`div-inv_binary64_76` `distribute-lft-in_binary64_28` `cbrt-unprod_binary64_112` `rem-sqrt-square_binary64_92` `*-commutative_binary64_10` `sqrt-pow1_binary64_97` `pow1/2_binary64_159` `distribute-rgt-in_binary64_29`

Counts

4 → 90

Calls

4 calls:

19.0ms	(.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)))))
4.0ms	(pow.f64 (sin.f64 kx) 2)
3.0ms	(pow.f64 (sin.f64 ky) 2)

series1.0s (14.8%)

Counts

4 → 12

Calls

4 calls:

669.0ms	(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)))
26.0ms	(pow.f64 (sin.f64 kx) 2)
25.0ms	(pow.f64 (sin.f64 ky) 2)

simplify66.0ms (0.9%)

Algorithm

1×	egg-herbie

Counts

102 → 102

Iterations

Useful iterations: 0 (43.0ms)

Iter	Nodes	Cost
0	4991	2193
1	4991	2193

prune224.0ms (3.2%)

Pruning

2 alts after pruning (2 fresh and 0 done)

	Pruned	Kept	Total
New	100	2	102
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	101	2	103

Merged error: 0.6b

Counts

103 → 2

Compiler

Compiled 3912 to 3089 computations (21% saved)

localize25.0ms (0.4%)

Local error

Found 4 expressions with local error:

0.3b	(pow.f64 (sin.f64 kx) 2)
0.5b	(.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))))
2.4b	(.f64 (/.f64 (.f64 2 l) Om) (+.f64 (pow.f64 (sin.f64 kx) 2) (pow.f64 (sin.f64 ky) 2)))
9.6b	(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))))))

rewrite69.0ms (1%)

Algorithm

1×	rewrite-expression-head

Rules

68×	`add-exp-log_binary64_117`
67×	`add-cbrt-cube_binary64_115`
32×	`cbrt-unprod_binary64_112` `prod-exp_binary64_128`
16×	`cbrt-undiv_binary64_113` `div-exp_binary64_130` `*-un-lft-identity_binary64_79`
15×	`add-sqr-sqrt_binary64_101`
14×	`associate-l_binary64_20`
13×	`pow1_binary64_140`
12×	`add-cube-cbrt_binary64_114`
11×	`frac-times_binary64_89` `associate-*r/_binary64_21`
7×	`flip-+_binary64_53` `flip3-+_binary64_82`
6×	`times-frac_binary64_85` `associate-r_binary64_19`
5×	`distribute-lft-in_binary64_28` `unpow-prod-down_binary64_158` `distribute-rgt-in_binary64_29`
4×	`associate-*l/_binary64_22` `pow-prod-down_binary64_150` `add-log-exp_binary64_118`
3×	`sqrt-prod_binary64_95` `pow-unpow_binary64_156`
2×	`div-inv_binary64_76` `*-commutative_binary64_10` `sqrt-div_binary64_96` `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` `unswap-sqr_binary64_47` `rem-sqrt-square_binary64_92` `sqrt-pow1_binary64_97` `pow1/2_binary64_159`

Counts

4 → 125

Calls

4 calls:

23.0ms	(.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))))
18.0ms	(.f64 (/.f64 (.f64 2 l) Om) (+.f64 (pow.f64 (sin.f64 kx) 2) (pow.f64 (sin.f64 ky) 2)))
5.0ms	(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)

series1.4s (19.9%)

Counts

4 → 12

Calls

4 calls:

675.0ms	(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))))))
350.0ms	(.f64 (/.f64 (.f64 2 l) Om) (+.f64 (pow.f64 (sin.f64 kx) 2) (pow.f64 (sin.f64 ky) 2)))
335.0ms	(.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))))
29.0ms	(pow.f64 (sin.f64 kx) 2)

simplify82.0ms (1.2%)

Algorithm

1×	egg-herbie

Counts

137 → 137

Iterations

Useful iterations: 0 (48.0ms)

Iter	Nodes	Cost
0	5045	3741

prune317.0ms (4.5%)

Pruning

2 alts after pruning (1 fresh and 1 done)

	Pruned	Kept	Total
New	137	0	137
Fresh	0	1	1
Picked	0	1	1
Done	0	0	0
Total	137	2	139

Merged error: 0.6b

Counts

139 → 2

Compiler

Compiled 5238 to 3853 computations (26.4% saved)

localize6.0ms (0.1%)

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

2 alts after pruning (0 fresh and 2 done)

	Kept	Total
New	0	0
Fresh	0	0
Picked	1	1
Done	1	1
Total	2	2

Merged error: 0.6b

Counts

2 → 2

Compiler

Compiled 0 to 0 computations (0% saved)

regimes115.0ms (1.6%)

Compiler: Compiled 539 to 623 computations (-15.6% saved)

bsearch0.0ms (0%)

simplify3.0ms (0%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	31	48
1	31	48

end0.0ms (0%)

sample2.7s (38.5%)

Algorithm

1×

intervals

Results

1.1s	6290×	body	128	valid
727.0ms	811×	body	1024	valid
322.0ms	544×	body	512	valid
139.0ms	355×	body	256	valid

Compiler

Compiled 104 to 108 computations (-3.8% saved)

Details

analyze601.0ms (8.6%)

sample85.0ms (1.2%)

simplify199.0ms (2.9%)

prune12.0ms (0.2%)

localize22.0ms (0.3%)

rewrite40.0ms (0.6%)

series1.0s (14.8%)

simplify66.0ms (0.9%)

prune224.0ms (3.2%)

localize25.0ms (0.4%)

rewrite69.0ms (1%)

series1.4s (19.9%)

simplify82.0ms (1.2%)

prune317.0ms (4.5%)

localize6.0ms (0.1%)

rewrite0.0ms (0%)

series0.0ms (0%)

simplify6.0ms (0.1%)

prune1.0ms (0%)

regimes115.0ms (1.6%)

bsearch0.0ms (0%)

simplify3.0ms (0%)

end0.0ms (0%)

sample2.7s (38.5%)

Profiling