Details

analyze620.0ms (9.3%)

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)

sample82.0ms (1.2%)

Algorithm

1×

intervals

Results

37.0ms	209×	body	128	valid
18.0ms	20×	body	1024	valid
10.0ms	15×	body	512	valid
5.0ms	12×	body	256	valid

Compiler

Compiled 59 to 63 computations (-6.8% saved)

simplify50.0ms (0.7%)

Algorithm

1×	egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (39.0ms)

Iter	Nodes	Cost
0	5325	39

prune5.0ms (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: 1.0b

Counts

2 → 1

Compiler

Compiled 50 to 50 computations (0% saved)

localize20.0ms (0.3%)

Local error

Found 4 expressions with local error:

0.2b	(pow.f64 (sin.f64 ky) 2)
0.2b	(pow.f64 (sin.f64 kx) 2)
2.5b	(.f64 (pow.f64 (/.f64 (.f64 2 l) Om) 2) (+.f64 (pow.f64 (sin.f64 kx) 2) (pow.f64 (sin.f64 ky) 2)))
9.4b	(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)))))

rewrite35.0ms (0.5%)

Algorithm

1×	rewrite-expression-head

Rules

20×	`add-sqr-sqrt_binary64`
18×	`add-exp-log_binary64`
17×	`*-un-lft-identity_binary64`
16×	`unpow-prod-down_binary64`
13×	`add-cube-cbrt_binary64`
12×	`associate-l_binary64`
7×	`pow1_binary64`
6×	`pow-unpow_binary64` `add-cbrt-cube_binary64` `prod-exp_binary64`
5×	`associate-r_binary64` `pow-exp_binary64`
4×	`add-log-exp_binary64` `unpow2_binary64` `sqr-pow_binary64` `unswap-sqr_binary64`
3×	`pow-to-exp_binary64` `times-frac_binary64` `sqrt-prod_binary64`
2×	`flip3-+_binary64` `distribute-lft-out_binary64` `associate-*r/_binary64` `pow-pow_binary64` `div-exp_binary64` `flip-+_binary64` `sqrt-div_binary64`
1×	`pow1/2_binary64` `cbrt-unprod_binary64` `distribute-lft-in_binary64` `distribute-rgt-in_binary64` `sqrt-pow1_binary64` `rem-sqrt-square_binary64` `div-inv_binary64` `*-commutative_binary64`

Counts

4 → 90

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)))
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)
3.0ms	(pow.f64 (sin.f64 kx) 2)

series976.0ms (14.6%)

Counts

4 → 12

Calls

4 calls:

632.0ms	(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)))))
295.0ms	(.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 ky) 2)
23.0ms	(pow.f64 (sin.f64 kx) 2)

simplify64.0ms (1%)

Algorithm

1×	egg-herbie

Counts

102 → 102

Iterations

Useful iterations: 0 (41.0ms)

Iter	Nodes	Cost
0	4984	2193
1	4984	2193

prune181.0ms (2.7%)

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: 0.8b

Counts

103 → 2

Compiler

Compiled 3218 to 2417 computations (24.9% saved)

localize20.0ms (0.3%)

Local error

Found 4 expressions with local error:

0.2b	(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))))
2.2b	(.f64 (/.f64 (.f64 2 l) Om) (+.f64 (pow.f64 (sin.f64 kx) 2) (pow.f64 (sin.f64 ky) 2)))
9.4b	(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))))))

rewrite66.0ms (1%)

Algorithm

1×	rewrite-expression-head

Rules

68×	`add-exp-log_binary64`
67×	`add-cbrt-cube_binary64`
32×	`cbrt-unprod_binary64` `prod-exp_binary64`
16×	`*-un-lft-identity_binary64` `cbrt-undiv_binary64` `div-exp_binary64`
15×	`add-sqr-sqrt_binary64`
14×	`associate-l_binary64`
13×	`pow1_binary64`
12×	`add-cube-cbrt_binary64`
11×	`associate-*r/_binary64` `frac-times_binary64`
7×	`flip3-+_binary64` `flip-+_binary64`
6×	`associate-r_binary64` `times-frac_binary64`
5×	`distribute-lft-in_binary64` `distribute-rgt-in_binary64` `unpow-prod-down_binary64`
4×	`pow-prod-down_binary64` `add-log-exp_binary64` `associate-*l/_binary64`
3×	`pow-unpow_binary64` `sqrt-prod_binary64`
2×	`distribute-lft-out_binary64` `div-inv_binary64` `sqrt-div_binary64` `*-commutative_binary64`
1×	`pow-to-exp_binary64` `pow1/2_binary64` `unpow2_binary64` `pow-pow_binary64` `sqr-pow_binary64` `sqrt-pow1_binary64` `unswap-sqr_binary64` `rem-sqrt-square_binary64` `pow-exp_binary64`

Counts

4 → 125

Calls

4 calls:

22.0ms	(.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))))
16.0ms	(.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)

series1.3s (19.5%)

Counts

4 → 12

Calls

4 calls:

649.0ms	(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))))))
335.0ms	(.f64 (/.f64 (.f64 2 l) Om) (+.f64 (pow.f64 (sin.f64 kx) 2) (pow.f64 (sin.f64 ky) 2)))
295.0ms	(.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))))
25.0ms	(pow.f64 (sin.f64 kx) 2)

simplify87.0ms (1.3%)

Algorithm

1×	egg-herbie

Counts

137 → 137

Iterations

Useful iterations: 0 (47.0ms)

Iter	Nodes	Cost
0	4965	3724
1	4965	3724

prune258.0ms (3.8%)

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: 0.8b

Counts

139 → 2

Compiler

Compiled 4675 to 3306 computations (29.3% saved)

localize4.0ms (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: 0.8b

Counts

2 → 2

Compiler

Compiled 0 to 0 computations (0% saved)

regimes114.0ms (1.7%)

Compiler: Compiled 451 to 535 computations (-18.6% 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%)

sample2.8s (41.8%)

Algorithm

1×

intervals

Results

1.2s	6337×	body	128	valid
743.0ms	795×	body	1024	valid
365.0ms	566×	body	512	valid
122.0ms	301×	body	256	valid
1.0ms	1×	body	2048	valid

Compiler

Compiled 94 to 98 computations (-4.3% saved)

Details

analyze620.0ms (9.3%)

sample82.0ms (1.2%)

simplify50.0ms (0.7%)

prune5.0ms (0.1%)

localize20.0ms (0.3%)

rewrite35.0ms (0.5%)

series976.0ms (14.6%)

simplify64.0ms (1%)

prune181.0ms (2.7%)

localize20.0ms (0.3%)

rewrite66.0ms (1%)

series1.3s (19.5%)

simplify87.0ms (1.3%)

prune258.0ms (3.8%)

localize4.0ms (0.1%)

rewrite0.0ms (0%)

series0.0ms (0%)

simplify6.0ms (0.1%)

prune1.0ms (0%)

regimes114.0ms (1.7%)

bsearch0.0ms (0%)

simplify2.0ms (0%)

end0.0ms (0%)

sample2.8s (41.8%)

Profiling