Details

analyze955.0ms (7.5%)

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 34 to 30 computations (11.8% saved)

sample119.0ms (0.9%)

Algorithm

1×

intervals

Results

46.0ms	199×	body	128	valid
32.0ms	27×	body	1024	valid
13.0ms	17×	body	512	valid
6.0ms	13×	body	256	valid

Compiler

Compiled 71 to 63 computations (11.3% saved)

simplify58.0ms (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

1.0b

Counts

3 → 1

Alt Table

Status	Error	Program
▶	1.0b	(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)

localize17.0ms (0.1%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.3b	(pow.f64 (/.f64 (*.f64 2 l) Om) 2)
✓	0.3b	(/.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)))
✓	2.2b	(fma.f64 (pow.f64 (/.f64 (*.f64 2 l) Om) 2) (+.f64 (pow.f64 (sin.f64 kx) 2) (pow.f64 (sin.f64 ky) 2)) 1)
✓	7.5b	(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))

series1.2s (9.4%)

Counts

4 → 168

Calls

4 calls:

859.0ms	(/.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)))
222.0ms	(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))
98.0ms	(fma.f64 (pow.f64 (/.f64 (*.f64 2 l) Om) 2) (+.f64 (pow.f64 (sin.f64 kx) 2) (pow.f64 (sin.f64 ky) 2)) 1)
12.0ms	(pow.f64 (/.f64 (*.f64 2 l) Om) 2)

rewrite16.0ms (0.1%)

Algorithm

1×	rewrite-expression-head

Rules

24×	`add-sqr-sqrt_binary64`
23×	`*-un-lft-identity_binary64`
23×	`add-cube-cbrt_binary64`
21×	`times-frac_binary64`
15×	`sqrt-prod_binary64`

Counts

4 → 92

Calls

4 calls:

4.0ms	(pow.f64 (/.f64 (*.f64 2 l) Om) 2)
3.0ms	(/.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)))
2.0ms	(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)

simplify249.0ms (2%)

Algorithm

1×	egg-herbie

Rules

396×	`fma-neg_binary64`
329×	`fma-def_binary64`
271×	`associate-r_binary64`
206×	`associate-*r/_binary64`
199×	`associate-l_binary64`

Counts

260 → 226

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	493	14676
1	1397	13058
2	4984	13052
3	5283	13052

prune342.0ms (2.7%)

Pruning

4 alts after pruning (3 fresh and 1 done)

	Pruned	Kept	Total
New	223	3	226
Fresh	0	0	0
Picked	0	1	1
Done	0	0	0
Total	223	4	227

Error

Counts

227 → 4

Alt Table

Status	Error	Program
	24.7b	(sqrt.f64 (+.f64 1/2 1/2))
	27.0b	(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)))))
✓	1.0b	(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)))))
▶	1.0b	(sqrt.f64 (+.f64 1/2 (log.f64 (exp.f64 (/.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 12909 to 9573 computations (25.8% saved)

localize21.0ms (0.2%)

Local error

Found 4 expressions with local error:

New	Error	Program
	0.3b	(/.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)))
	2.2b	(fma.f64 (pow.f64 (/.f64 (*.f64 2 l) Om) 2) (+.f64 (pow.f64 (sin.f64 kx) 2) (pow.f64 (sin.f64 ky) 2)) 1)
✓	2.6b	(log.f64 (exp.f64 (/.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)))))
	7.5b	(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))

series916.0ms (7.2%)

Counts

1 → 48

Calls

1 calls:

915.0ms

(log.f64 (exp.f64 (/.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)))))

rewrite11.0ms (0.1%)

Algorithm

1×	rewrite-expression-head

Rules

23×	`log-pow_binary64`
22×	`exp-prod_binary64`
18×	`times-frac_binary64`
15×	`*-un-lft-identity_binary64`
15×	`add-sqr-sqrt_binary64`

Counts

1 → 36

Calls

1 calls:

4.0ms

(log.f64 (exp.f64 (/.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)))))

simplify116.0ms (0.9%)

Algorithm

1×	egg-herbie

Rules

838×	`fma-def_binary64`
318×	`cancel-sign-sub-inv_binary64`
252×	`unswap-sqr_binary64`
197×	`fma-neg_binary64`
161×	`associate-r_binary64`

Counts

84 → 107

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	328	5968
1	839	5642
2	2940	5606
3	4981	5606

prune622.0ms (4.9%)

Pruning

4 alts after pruning (2 fresh and 2 done)

	Pruned	Kept	Total
New	300	0	300
Fresh	0	2	2
Picked	0	1	1
Done	0	1	1
Total	300	4	304

Error

Counts

304 → 4

Alt Table

Status	Error	Program
▶	24.7b	(sqrt.f64 (+.f64 1/2 1/2))
	27.0b	(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)))))
✓	1.0b	(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)))))
✓	1.0b	(sqrt.f64 (+.f64 1/2 (log.f64 (exp.f64 (/.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 19150 to 14202 computations (25.8% saved)

localize4.0ms (0%)

prune10.0ms (0.1%)

Pruning

4 alts after pruning (1 fresh and 3 done)

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

Error

Counts

4 → 4

Alt Table

Status	Error	Program
✓	24.7b	(sqrt.f64 (+.f64 1/2 1/2))
▶	27.0b	(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)))))
✓	1.0b	(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)))))
✓	1.0b	(sqrt.f64 (+.f64 1/2 (log.f64 (exp.f64 (/.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 160 to 126 computations (21.3% saved)

localize47.0ms (0.4%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	1.2b	(/.f64 (sqrt.f64 (.f64 4 (.f64 (*.f64 l l) (+.f64 (pow.f64 (sin.f64 kx) 2) (pow.f64 (sin.f64 ky) 2))))) Om)
✓	2.3b	(.f64 (.f64 l l) (+.f64 (pow.f64 (sin.f64 kx) 2) (pow.f64 (sin.f64 ky) 2)))
✓	27.4b	(sqrt.f64 (.f64 4 (.f64 (*.f64 l l) (+.f64 (pow.f64 (sin.f64 kx) 2) (pow.f64 (sin.f64 ky) 2)))))
✓	27.5b	(sqrt.f64 (/.f64 1/4 (.f64 (.f64 l l) (+.f64 (pow.f64 (sin.f64 kx) 2) (pow.f64 (sin.f64 ky) 2)))))

series1.0s (8.1%)

Counts

4 → 156

Calls

4 calls:

454.0ms	(sqrt.f64 (/.f64 1/4 (.f64 (.f64 l l) (+.f64 (pow.f64 (sin.f64 kx) 2) (pow.f64 (sin.f64 ky) 2)))))
319.0ms	(/.f64 (sqrt.f64 (.f64 4 (.f64 (*.f64 l l) (+.f64 (pow.f64 (sin.f64 kx) 2) (pow.f64 (sin.f64 ky) 2))))) Om)
158.0ms	(sqrt.f64 (.f64 4 (.f64 (*.f64 l l) (+.f64 (pow.f64 (sin.f64 kx) 2) (pow.f64 (sin.f64 ky) 2)))))
96.0ms	(.f64 (.f64 l l) (+.f64 (pow.f64 (sin.f64 kx) 2) (pow.f64 (sin.f64 ky) 2)))

rewrite106.0ms (0.8%)

Algorithm

1×	rewrite-expression-head

Rules

20×	`*-un-lft-identity_binary64`
20×	`pow1_binary64`
18×	`add-sqr-sqrt_binary64`
16×	`add-cube-cbrt_binary64`
15×	`times-frac_binary64`

Counts

4 → 101

Calls

4 calls:

26.0ms	(/.f64 (sqrt.f64 (.f64 4 (.f64 (*.f64 l l) (+.f64 (pow.f64 (sin.f64 kx) 2) (pow.f64 (sin.f64 ky) 2))))) Om)
23.0ms	(.f64 (.f64 l l) (+.f64 (pow.f64 (sin.f64 kx) 2) (pow.f64 (sin.f64 ky) 2)))
21.0ms	(sqrt.f64 (.f64 4 (.f64 (*.f64 l l) (+.f64 (pow.f64 (sin.f64 kx) 2) (pow.f64 (sin.f64 ky) 2)))))
20.0ms	(sqrt.f64 (/.f64 1/4 (.f64 (.f64 l l) (+.f64 (pow.f64 (sin.f64 kx) 2) (pow.f64 (sin.f64 ky) 2)))))

simplify344.0ms (2.7%)

Algorithm

1×	egg-herbie

Rules

276×	`fma-neg_binary64`
234×	`associate-r_binary64`
234×	`associate-/r*_binary64`
225×	`times-frac_binary64`
222×	`associate-l_binary64`

Counts

257 → 237

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	380	7760
1	1078	6797
2	4061	6715
3	4915	6715
4	4953	6715

prune832.0ms (6.6%)

Pruning

4 alts after pruning (0 fresh and 4 done)

	Pruned	Kept	Total
New	292	0	292
Fresh	0	0	0
Picked	0	1	1
Done	0	3	3
Total	292	4	296

Error

Counts

296 → 4

Alt Table

Status	Error	Program
✓	24.7b	(sqrt.f64 (+.f64 1/2 1/2))
✓	27.0b	(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)))))
✓	1.0b	(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)))))
✓	1.0b	(sqrt.f64 (+.f64 1/2 (log.f64 (exp.f64 (/.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 16057 to 10031 computations (37.5% saved)

regimes2.1s (16.6%)

Accuracy

Total 0.7b remaining (64.9%)

Threshold costs 0.7b (64.9%)

Counts

62 → 1

Compiler

Compiled 44905 to 34798 computations (22.5% saved)

simplify2.0ms (0%)

Algorithm

1×	egg-herbie

Rules

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

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	21	37
1	26	37
2	25	37

end8.0ms (0.1%)

Remove: (sort kx ky)
Compiler: Compiled 84 to 72 computations (14.3% saved)

sample3.5s (27.9%)

Algorithm

1×

intervals

Results

1.5s	6386×	body	128	valid
897.0ms	750×	body	1024	valid
427.0ms	545×	body	512	valid
219.0ms	319×	body	256	valid

Compiler

Compiled 179 to 150 computations (16.2% saved)

Details

analyze955.0ms (7.5%)

sample119.0ms (0.9%)

simplify58.0ms (0.5%)

prune4.0ms (0%)

localize17.0ms (0.1%)

series1.2s (9.4%)

rewrite16.0ms (0.1%)

simplify249.0ms (2%)

prune342.0ms (2.7%)

localize21.0ms (0.2%)

series916.0ms (7.2%)

rewrite11.0ms (0.1%)

simplify116.0ms (0.9%)

prune622.0ms (4.9%)

localize4.0ms (0%)

prune10.0ms (0.1%)

localize47.0ms (0.4%)

series1.0s (8.1%)

rewrite106.0ms (0.8%)

simplify344.0ms (2.7%)

prune832.0ms (6.6%)

regimes2.1s (16.6%)

simplify2.0ms (0%)

end8.0ms (0.1%)

sample3.5s (27.9%)

Profiling