Details

analyze794.0ms (7.7%)

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 34 to 30 computations (11.8% saved)

sample3.9s (37.5%)

Symmetry

(sort kx ky)

Results

2.0s	6577×	body	128	valid
1.1s	795×	body	1024	valid
521.0ms	539×	body	512	valid
205.0ms	345×	body	256	valid

Compiler

Compiled 101 to 89 computations (11.9% saved)

simplify55.0ms (0.5%)

Algorithm

1×	egg-herbie

Rules

665×	`fma-def_binary64`
575×	`associate-l_binary64`
512×	`unswap-sqr_binary64`
437×	`associate-r_binary64`
369×	`associate-/r/_binary64`

Counts

1 → 2

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	24	42
1	56	37
2	113	37
3	465	37
4	2149	37
5	4982	37
6	4847	37
7	4964	37

prune4.0ms (0%)

Pruning

1 alts after pruning (1 fresh and 0 done)

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

Error

1.8b

Counts

3 → 1

Alt Table

Status	Error	Program
▶	1.8b	(sqrt.f64 (+.f64 1/2 (/.f64 1/2 (sqrt.f64 (fma.f64 (pow.f64 (/.f64 (*.f64 2 l) Om) 2) (+.f64 (pow.f64 (sin.f64 kx) 2) (pow.f64 (sin.f64 ky) 2)) 1)))))

Compiler

Compiled 113 to 95 computations (15.9% saved)

localize16.0ms (0.2%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.3b	(pow.f64 (/.f64 (*.f64 2 l) Om) 2)
✓	0.3b	(pow.f64 (sin.f64 ky) 2)
✓	2.8b	(fma.f64 (pow.f64 (/.f64 (*.f64 2 l) Om) 2) (+.f64 (pow.f64 (sin.f64 kx) 2) (pow.f64 (sin.f64 ky) 2)) 1)
✓	8.9b	(sqrt.f64 (fma.f64 (pow.f64 (/.f64 (*.f64 2 l) Om) 2) (+.f64 (pow.f64 (sin.f64 kx) 2) (pow.f64 (sin.f64 ky) 2)) 1))

series352.0ms (3.4%)

Counts

4 → 124

Calls

4 calls:

223.0ms	(sqrt.f64 (fma.f64 (pow.f64 (/.f64 (*.f64 2 l) Om) 2) (+.f64 (pow.f64 (sin.f64 kx) 2) (pow.f64 (sin.f64 ky) 2)) 1))
115.0ms	(fma.f64 (pow.f64 (/.f64 (*.f64 2 l) Om) 2) (+.f64 (pow.f64 (sin.f64 kx) 2) (pow.f64 (sin.f64 ky) 2)) 1)
11.0ms	(pow.f64 (/.f64 (*.f64 2 l) Om) 2)
3.0ms	(pow.f64 (sin.f64 ky) 2)

rewrite11.0ms (0.1%)

Algorithm

1×	rewrite-expression-head

Rules

11×	`add-sqr-sqrt_binary64`
11×	`add-exp-log_binary64`
10×	`unpow-prod-down_binary64`
10×	`*-un-lft-identity_binary64`
10×	`add-cube-cbrt_binary64`

Counts

4 → 71

Calls

4 calls:

5.0ms	(pow.f64 (/.f64 (*.f64 2 l) Om) 2)
2.0ms	(pow.f64 (sin.f64 ky) 2)
1.0ms	(sqrt.f64 (fma.f64 (pow.f64 (/.f64 (*.f64 2 l) Om) 2) (+.f64 (pow.f64 (sin.f64 kx) 2) (pow.f64 (sin.f64 ky) 2)) 1))
0.0ms	(fma.f64 (pow.f64 (/.f64 (*.f64 2 l) Om) 2) (+.f64 (pow.f64 (sin.f64 kx) 2) (pow.f64 (sin.f64 ky) 2)) 1)

simplify153.0ms (1.5%)

Algorithm

1×	egg-herbie

Rules

489×	`cancel-sign-sub-inv_binary64`
331×	`unswap-sqr_binary64`
223×	`fma-neg_binary64`
206×	`associate-r_binary64`
203×	`fma-def_binary64`

Counts

195 → 162

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	367	8243
1	998	7154
2	3578	7147
3	5215	7147

prune254.0ms (2.4%)

Pruning

4 alts after pruning (4 fresh and 0 done)

	Pruned	Kept	Total
New	158	4	162
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	159	4	163

Error

0.2b

Counts

163 → 4

Alt Table

Status	Error	Program
▶	1.8b	(sqrt.f64 (+.f64 1/2 (/.f64 1/2 (cbrt.f64 (pow.f64 (sqrt.f64 (fma.f64 (pow.f64 (/.f64 (*.f64 2 l) Om) 2) (+.f64 (pow.f64 (sin.f64 kx) 2) (pow.f64 (sin.f64 ky) 2)) 1)) 3)))))
	29.7b	(sqrt.f64 (+.f64 1/2 (/.f64 1/2 (fma.f64 1/2 (.f64 Om (sqrt.f64 (/.f64 1/4 (.f64 (.f64 l l) (+.f64 (pow.f64 (sin.f64 kx) 2) (pow.f64 (sin.f64 ky) 2)))))) (/.f64 (sqrt.f64 (.f64 4 (.f64 (.f64 l l) (+.f64 (pow.f64 (sin.f64 kx) 2) (pow.f64 (sin.f64 ky) 2))))) Om)))))
	33.9b	(sqrt.f64 (+.f64 1/2 (/.f64 1/2 (fma.f64 l (sqrt.f64 (.f64 4 (+.f64 (/.f64 (pow.f64 (sin.f64 ky) 2) (.f64 Om Om)) (/.f64 (pow.f64 (sin.f64 kx) 2) (.f64 Om Om))))) (.f64 1/2 (/.f64 (sqrt.f64 (/.f64 1/4 (+.f64 (/.f64 (pow.f64 (sin.f64 ky) 2) (.f64 Om Om)) (/.f64 (pow.f64 (sin.f64 kx) 2) (.f64 Om Om))))) l))))))
	23.4b	(sqrt.f64 (+.f64 1/2 (/.f64 1/2 1)))

Compiler

Compiled 7879 to 5823 computations (26.1% saved)

localize19.0ms (0.2%)

Local error

Found 4 expressions with local error:

New	Error	Program
	0.3b	(pow.f64 (sin.f64 ky) 2)
	2.8b	(fma.f64 (pow.f64 (/.f64 (*.f64 2 l) Om) 2) (+.f64 (pow.f64 (sin.f64 kx) 2) (pow.f64 (sin.f64 ky) 2)) 1)
	8.9b	(sqrt.f64 (fma.f64 (pow.f64 (/.f64 (*.f64 2 l) Om) 2) (+.f64 (pow.f64 (sin.f64 kx) 2) (pow.f64 (sin.f64 ky) 2)) 1))
✓	13.0b	(cbrt.f64 (pow.f64 (sqrt.f64 (fma.f64 (pow.f64 (/.f64 (*.f64 2 l) Om) 2) (+.f64 (pow.f64 (sin.f64 kx) 2) (pow.f64 (sin.f64 ky) 2)) 1)) 3))

series226.0ms (2.2%)

Counts

1 → 48

Calls

1 calls:

226.0ms

(cbrt.f64 (pow.f64 (sqrt.f64 (fma.f64 (pow.f64 (/.f64 (*.f64 2 l) Om) 2) (+.f64 (pow.f64 (sin.f64 kx) 2) (pow.f64 (sin.f64 ky) 2)) 1)) 3))

rewrite5.0ms (0%)

Algorithm

1×	rewrite-expression-head

Rules

18×	`cbrt-prod_binary64`
6×	`cube-prod_binary64`
6×	`*-un-lft-identity_binary64`
6×	`sqrt-prod_binary64`
6×	`add-sqr-sqrt_binary64`

Counts

1 → 29

Calls

1 calls:

2.0ms

(cbrt.f64 (pow.f64 (sqrt.f64 (fma.f64 (pow.f64 (/.f64 (*.f64 2 l) Om) 2) (+.f64 (pow.f64 (sin.f64 kx) 2) (pow.f64 (sin.f64 ky) 2)) 1)) 3))

simplify168.0ms (1.6%)

Algorithm

1×	egg-herbie

Rules

791×	`fma-def_binary64`
415×	`cancel-sign-sub-inv_binary64`
278×	`unswap-sqr_binary64`
177×	`associate-r_binary64`
173×	`fma-neg_binary64`

Counts

77 → 80

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	276	5588
1	773	5371
2	2917	5361
3	4909	5361
4	4987	5361
5	4960	5361

prune389.0ms (3.7%)

Pruning

4 alts after pruning (3 fresh and 1 done)

	Pruned	Kept	Total
New	210	0	210
Fresh	0	3	3
Picked	0	1	1
Done	0	0	0
Total	210	4	214

Error

0.2b

Counts

214 → 4

Alt Table

Status	Error	Program
✓	1.8b	(sqrt.f64 (+.f64 1/2 (/.f64 1/2 (cbrt.f64 (pow.f64 (sqrt.f64 (fma.f64 (pow.f64 (/.f64 (*.f64 2 l) Om) 2) (+.f64 (pow.f64 (sin.f64 kx) 2) (pow.f64 (sin.f64 ky) 2)) 1)) 3)))))
	29.7b	(sqrt.f64 (+.f64 1/2 (/.f64 1/2 (fma.f64 1/2 (.f64 Om (sqrt.f64 (/.f64 1/4 (.f64 (.f64 l l) (+.f64 (pow.f64 (sin.f64 kx) 2) (pow.f64 (sin.f64 ky) 2)))))) (/.f64 (sqrt.f64 (.f64 4 (.f64 (.f64 l l) (+.f64 (pow.f64 (sin.f64 kx) 2) (pow.f64 (sin.f64 ky) 2))))) Om)))))
	33.9b	(sqrt.f64 (+.f64 1/2 (/.f64 1/2 (fma.f64 l (sqrt.f64 (.f64 4 (+.f64 (/.f64 (pow.f64 (sin.f64 ky) 2) (.f64 Om Om)) (/.f64 (pow.f64 (sin.f64 kx) 2) (.f64 Om Om))))) (.f64 1/2 (/.f64 (sqrt.f64 (/.f64 1/4 (+.f64 (/.f64 (pow.f64 (sin.f64 ky) 2) (.f64 Om Om)) (/.f64 (pow.f64 (sin.f64 kx) 2) (.f64 Om Om))))) l))))))
▶	23.4b	(sqrt.f64 (+.f64 1/2 (/.f64 1/2 1)))

Compiler

Compiled 12659 to 9294 computations (26.6% saved)

localize3.0ms (0%)

prune6.0ms (0.1%)

Pruning

4 alts after pruning (2 fresh and 2 done)

	Kept	Total
New	0	0
Fresh	2	2
Picked	1	1
Done	1	1
Total	4	4

Error

0.2b

Counts

4 → 4

Alt Table

Status	Error	Program
✓	1.8b	(sqrt.f64 (+.f64 1/2 (/.f64 1/2 (cbrt.f64 (pow.f64 (sqrt.f64 (fma.f64 (pow.f64 (/.f64 (*.f64 2 l) Om) 2) (+.f64 (pow.f64 (sin.f64 kx) 2) (pow.f64 (sin.f64 ky) 2)) 1)) 3)))))
▶	29.7b	(sqrt.f64 (+.f64 1/2 (/.f64 1/2 (fma.f64 1/2 (.f64 Om (sqrt.f64 (/.f64 1/4 (.f64 (.f64 l l) (+.f64 (pow.f64 (sin.f64 kx) 2) (pow.f64 (sin.f64 ky) 2)))))) (/.f64 (sqrt.f64 (.f64 4 (.f64 (.f64 l l) (+.f64 (pow.f64 (sin.f64 kx) 2) (pow.f64 (sin.f64 ky) 2))))) Om)))))
	33.9b	(sqrt.f64 (+.f64 1/2 (/.f64 1/2 (fma.f64 l (sqrt.f64 (.f64 4 (+.f64 (/.f64 (pow.f64 (sin.f64 ky) 2) (.f64 Om Om)) (/.f64 (pow.f64 (sin.f64 kx) 2) (.f64 Om Om))))) (.f64 1/2 (/.f64 (sqrt.f64 (/.f64 1/4 (+.f64 (/.f64 (pow.f64 (sin.f64 ky) 2) (.f64 Om Om)) (/.f64 (pow.f64 (sin.f64 kx) 2) (.f64 Om Om))))) l))))))
✓	23.4b	(sqrt.f64 (+.f64 1/2 (/.f64 1/2 1)))

Compiler

Compiled 245 to 177 computations (27.8% saved)

localize24.0ms (0.2%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	1.4b	(.f64 Om (sqrt.f64 (/.f64 1/4 (.f64 (*.f64 l l) (+.f64 (pow.f64 (sin.f64 kx) 2) (pow.f64 (sin.f64 ky) 2))))))
✓	3.2b	(.f64 (.f64 l l) (+.f64 (pow.f64 (sin.f64 kx) 2) (pow.f64 (sin.f64 ky) 2)))
✓	25.0b	(sqrt.f64 (/.f64 1/4 (.f64 (.f64 l l) (+.f64 (pow.f64 (sin.f64 kx) 2) (pow.f64 (sin.f64 ky) 2)))))
✓	26.0b	(sqrt.f64 (.f64 4 (.f64 (*.f64 l l) (+.f64 (pow.f64 (sin.f64 kx) 2) (pow.f64 (sin.f64 ky) 2)))))

series705.0ms (6.8%)

Counts

4 → 156

Calls

4 calls:

325.0ms	(.f64 Om (sqrt.f64 (/.f64 1/4 (.f64 (*.f64 l l) (+.f64 (pow.f64 (sin.f64 kx) 2) (pow.f64 (sin.f64 ky) 2))))))
248.0ms	(sqrt.f64 (/.f64 1/4 (.f64 (.f64 l l) (+.f64 (pow.f64 (sin.f64 kx) 2) (pow.f64 (sin.f64 ky) 2)))))
85.0ms	(sqrt.f64 (.f64 4 (.f64 (*.f64 l l) (+.f64 (pow.f64 (sin.f64 kx) 2) (pow.f64 (sin.f64 ky) 2)))))
46.0ms	(.f64 (.f64 l l) (+.f64 (pow.f64 (sin.f64 kx) 2) (pow.f64 (sin.f64 ky) 2)))

rewrite52.0ms (0.5%)

Algorithm

1×	rewrite-expression-head

Rules

22×	`pow1_binary64`
20×	`sqrt-prod_binary64`
17×	`associate-r_binary64`
17×	`add-sqr-sqrt_binary64`
15×	`*-un-lft-identity_binary64`

Counts

4 → 97

Calls

4 calls:

15.0ms	(.f64 Om (sqrt.f64 (/.f64 1/4 (.f64 (*.f64 l l) (+.f64 (pow.f64 (sin.f64 kx) 2) (pow.f64 (sin.f64 ky) 2))))))
11.0ms	(sqrt.f64 (/.f64 1/4 (.f64 (.f64 l l) (+.f64 (pow.f64 (sin.f64 kx) 2) (pow.f64 (sin.f64 ky) 2)))))
10.0ms	(sqrt.f64 (.f64 4 (.f64 (*.f64 l l) (+.f64 (pow.f64 (sin.f64 kx) 2) (pow.f64 (sin.f64 ky) 2)))))
10.0ms	(.f64 (.f64 l l) (+.f64 (pow.f64 (sin.f64 kx) 2) (pow.f64 (sin.f64 ky) 2)))

simplify254.0ms (2.5%)

Algorithm

1×	egg-herbie

Rules

312×	`associate-r_binary64`
304×	`fma-neg_binary64`
281×	`associate-l_binary64`
257×	`associate-/r*_binary64`
244×	`times-frac_binary64`

Counts

253 → 222

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	361	7391
1	1076	6804
2	4340	6748
3	4897	6748
4	4998	6748
5	4949	6748

prune386.0ms (3.7%)

Pruning

4 alts after pruning (1 fresh and 3 done)

	Pruned	Kept	Total
New	277	0	277
Fresh	0	1	1
Picked	0	1	1
Done	0	2	2
Total	277	4	281

Error

0.2b

Counts

281 → 4

Alt Table

Status	Error	Program
✓	1.8b	(sqrt.f64 (+.f64 1/2 (/.f64 1/2 (cbrt.f64 (pow.f64 (sqrt.f64 (fma.f64 (pow.f64 (/.f64 (*.f64 2 l) Om) 2) (+.f64 (pow.f64 (sin.f64 kx) 2) (pow.f64 (sin.f64 ky) 2)) 1)) 3)))))
✓	29.7b	(sqrt.f64 (+.f64 1/2 (/.f64 1/2 (fma.f64 1/2 (.f64 Om (sqrt.f64 (/.f64 1/4 (.f64 (.f64 l l) (+.f64 (pow.f64 (sin.f64 kx) 2) (pow.f64 (sin.f64 ky) 2)))))) (/.f64 (sqrt.f64 (.f64 4 (.f64 (.f64 l l) (+.f64 (pow.f64 (sin.f64 kx) 2) (pow.f64 (sin.f64 ky) 2))))) Om)))))
	33.9b	(sqrt.f64 (+.f64 1/2 (/.f64 1/2 (fma.f64 l (sqrt.f64 (.f64 4 (+.f64 (/.f64 (pow.f64 (sin.f64 ky) 2) (.f64 Om Om)) (/.f64 (pow.f64 (sin.f64 kx) 2) (.f64 Om Om))))) (.f64 1/2 (/.f64 (sqrt.f64 (/.f64 1/4 (+.f64 (/.f64 (pow.f64 (sin.f64 ky) 2) (.f64 Om Om)) (/.f64 (pow.f64 (sin.f64 kx) 2) (.f64 Om Om))))) l))))))
✓	23.4b	(sqrt.f64 (+.f64 1/2 (/.f64 1/2 1)))

Compiler

Compiled 15248 to 9632 computations (36.8% saved)

regimes2.4s (23.4%)

Accuracy

Total 0.5b remaining (70%)

Threshold costs 0.5b (70%)

Counts

86 → 2

Compiler

Compiled 57656 to 46724 computations (19% saved)

bsearch6.0ms (0.1%)

Compiler: Compiled 21 to 17 computations (19% saved)

simplify4.0ms (0%)

Algorithm

1×	egg-herbie

Rules

4×	`+-commutative_binary64`
4×	`*-commutative_binary64`
1×	`1-exp_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	45	152
1	55	152
2	54	152

end172.0ms (1.7%)

Remove: (sort kx ky)
Compiler: Compiled 551 to 391 computations (29% saved)

Details

analyze794.0ms (7.7%)

sample3.9s (37.5%)

simplify55.0ms (0.5%)

prune4.0ms (0%)

localize16.0ms (0.2%)

series352.0ms (3.4%)

rewrite11.0ms (0.1%)

simplify153.0ms (1.5%)

prune254.0ms (2.4%)

localize19.0ms (0.2%)

series226.0ms (2.2%)

rewrite5.0ms (0%)

simplify168.0ms (1.6%)

prune389.0ms (3.7%)

localize3.0ms (0%)

prune6.0ms (0.1%)

localize24.0ms (0.2%)

series705.0ms (6.8%)

rewrite52.0ms (0.5%)

simplify254.0ms (2.5%)

prune386.0ms (3.7%)

regimes2.4s (23.4%)

bsearch6.0ms (0.1%)

simplify4.0ms (0%)

end172.0ms (1.7%)

Profiling