Details

analyze1.0s (3.9%)

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)

sample117.0ms (0.4%)

Algorithm

1×

intervals

Results

52.0ms	203×	body	128	valid
28.0ms	25×	body	1024	valid
12.0ms	16×	body	512	valid
6.0ms	12×	body	256	valid

Compiler

Compiled 71 to 63 computations (11.3% saved)

simplify65.0ms (0.2%)

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

prune5.0ms (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
✓	0.2b	(/.f64 (*.f64 2 l) Om)
✓	0.2b	(pow.f64 (sin.f64 ky) 2)
✓	2.4b	(fma.f64 (pow.f64 (/.f64 (*.f64 2 l) Om) 2) (+.f64 (pow.f64 (sin.f64 kx) 2) (pow.f64 (sin.f64 ky) 2)) 1)
✓	7.7b	(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))

rewrite71.0ms (0.3%)

Algorithm

1×	rewrite-expression-head

Rules

30×	`add-cube-cbrt_binary64`
17×	`add-sqr-sqrt_binary64`
16×	`add-cbrt-cube_binary64`
15×	`add-exp-log_binary64`
15×	`pow1_binary64`

Counts

4 → 155

Calls

4 calls:

18.0ms	(/.f64 (*.f64 2 l) Om)
18.0ms	(pow.f64 (sin.f64 ky) 2)
14.0ms	(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))
12.0ms	(fma.f64 (pow.f64 (/.f64 (*.f64 2 l) Om) 2) (+.f64 (pow.f64 (sin.f64 kx) 2) (pow.f64 (sin.f64 ky) 2)) 1)

series484.0ms (1.8%)

Counts

4 → 124

Calls

4 calls:

264.0ms	(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))
187.0ms	(fma.f64 (pow.f64 (/.f64 (*.f64 2 l) Om) 2) (+.f64 (pow.f64 (sin.f64 kx) 2) (pow.f64 (sin.f64 ky) 2)) 1)
27.0ms	(/.f64 (*.f64 2 l) Om)
6.0ms	(pow.f64 (sin.f64 ky) 2)

simplify325.0ms (1.2%)

Algorithm

1×	egg-herbie

Rules

302×	`fma-neg_binary64`
246×	`associate-r_binary64`
218×	`fma-def_binary64`
211×	`associate-l_binary64`
198×	`*-commutative_binary64`

Counts

279 → 449

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	395	8921
1	1080	8202
2	4072	8116
3	4963	8116
4	4941	8116

prune366.0ms (1.4%)

Pruning

3 alts after pruning (3 fresh and 0 done)

	Pruned	Kept	Total
New	446	3	449
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	447	3	450

Error

0.0b

Counts

450 → 3

Alt Table

Status	Error	Program
	33.2b	(sqrt.f64 (+.f64 1/2 (/.f64 1/2 (/.f64 (hypot.f64 (.f64 (.f64 2 l) (sin.f64 kx)) (.f64 (.f64 2 l) (sin.f64 ky))) Om))))
	24.7b	(sqrt.f64 (+.f64 1/2 (/.f64 1/2 1)))
▶	1.0b	(sqrt.f64 (+.f64 1/2 (/.f64 1/2 (-.f64 (exp.f64 (log1p.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)))) 1))))

Compiler

Compiled 10726 to 7680 computations (28.4% saved)

localize23.0ms (0.1%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	1.9b	(exp.f64 (log1p.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))))
	2.4b	(fma.f64 (pow.f64 (/.f64 (*.f64 2 l) Om) 2) (+.f64 (pow.f64 (sin.f64 kx) 2) (pow.f64 (sin.f64 ky) 2)) 1)
✓	6.8b	(log1p.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)))
	7.7b	(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))

rewrite32.0ms (0.1%)

Algorithm

1×	rewrite-expression-head

Rules

11×	`add-cube-cbrt_binary64`
9×	`pow1_binary64`
8×	`add-sqr-sqrt_binary64`
7×	`expm1-log1p-u_binary64`
6×	`add-cbrt-cube_binary64`

Counts

2 → 59

Calls

2 calls:

14.0ms

(log1p.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)))

13.0ms

(exp.f64 (log1p.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))))

series8.1s (30.3%)

Counts

2 → 96

Calls

2 calls:

4.1s

(exp.f64 (log1p.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))))

4.0s

(log1p.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)))

simplify264.0ms (1%)

Algorithm

1×	egg-herbie

Rules

672×	`fma-def_binary64`
533×	`times-frac_binary64`
424×	`associate-/l*_binary64`
374×	`associate-/r*_binary64`
214×	`associate-*l/_binary64`

Counts

155 → 259

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	483	14020
1	1635	13085
2	4986	12984
3	5324	12984

prune515.0ms (1.9%)

Pruning

3 alts after pruning (2 fresh and 1 done)

	Pruned	Kept	Total
New	548	0	548
Fresh	0	2	2
Picked	0	1	1
Done	0	0	0
Total	548	3	551

Error

0.0b

Counts

551 → 3

Alt Table

Status	Error	Program
	33.2b	(sqrt.f64 (+.f64 1/2 (/.f64 1/2 (/.f64 (hypot.f64 (.f64 (.f64 2 l) (sin.f64 kx)) (.f64 (.f64 2 l) (sin.f64 ky))) Om))))
▶	24.7b	(sqrt.f64 (+.f64 1/2 (/.f64 1/2 1)))
✓	1.0b	(sqrt.f64 (+.f64 1/2 (/.f64 1/2 (-.f64 (exp.f64 (log1p.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)))) 1))))

Compiler

Compiled 22777 to 16349 computations (28.2% saved)

localize3.0ms (0%)

rewrite0.0ms (0%)

Algorithm

1×	rewrite-expression-head

Counts

0 → 0

series0.0ms (0%)

Counts: 0 → 0

simplify10.0ms (0%)

Algorithm

1×	egg-herbie

Counts

0 → 0

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	0	0
1	0	0

prune3.0ms (0%)

Pruning

3 alts after pruning (1 fresh and 2 done)

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

Error

0.0b

Counts

3 → 3

Alt Table

Status	Error	Program
▶	33.2b	(sqrt.f64 (+.f64 1/2 (/.f64 1/2 (/.f64 (hypot.f64 (.f64 (.f64 2 l) (sin.f64 kx)) (.f64 (.f64 2 l) (sin.f64 ky))) Om))))
✓	24.7b	(sqrt.f64 (+.f64 1/2 (/.f64 1/2 1)))
✓	1.0b	(sqrt.f64 (+.f64 1/2 (/.f64 1/2 (-.f64 (exp.f64 (log1p.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)))) 1))))

Compiler

Compiled 90 to 76 computations (15.6% saved)

localize13.0ms (0.1%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.3b	(/.f64 1/2 (/.f64 (hypot.f64 (.f64 (.f64 2 l) (sin.f64 kx)) (.f64 (.f64 2 l) (sin.f64 ky))) Om))
✓	0.4b	(.f64 (.f64 2 l) (sin.f64 kx))
✓	1.1b	(/.f64 (hypot.f64 (.f64 (.f64 2 l) (sin.f64 kx)) (.f64 (.f64 2 l) (sin.f64 ky))) Om)
✓	5.6b	(sqrt.f64 (+.f64 1/2 (/.f64 1/2 (/.f64 (hypot.f64 (.f64 (.f64 2 l) (sin.f64 kx)) (.f64 (.f64 2 l) (sin.f64 ky))) Om))))

rewrite80.0ms (0.3%)

Algorithm

1×	rewrite-expression-head

Rules

42×	`add-cube-cbrt_binary64`
28×	`pow1_binary64`
26×	`add-sqr-sqrt_binary64`
24×	`add-exp-log_binary64`
22×	`add-cbrt-cube_binary64`

Counts

4 → 170

Calls

4 calls:

20.0ms	(.f64 (.f64 2 l) (sin.f64 kx))
18.0ms	(/.f64 1/2 (/.f64 (hypot.f64 (.f64 (.f64 2 l) (sin.f64 kx)) (.f64 (.f64 2 l) (sin.f64 ky))) Om))
16.0ms	(sqrt.f64 (+.f64 1/2 (/.f64 1/2 (/.f64 (hypot.f64 (.f64 (.f64 2 l) (sin.f64 kx)) (.f64 (.f64 2 l) (sin.f64 ky))) Om))))
16.0ms	(/.f64 (hypot.f64 (.f64 (.f64 2 l) (sin.f64 kx)) (.f64 (.f64 2 l) (sin.f64 ky))) Om)

series2.0s (7.4%)

Counts

4 → 156

Calls

4 calls:

901.0ms	(/.f64 1/2 (/.f64 (hypot.f64 (.f64 (.f64 2 l) (sin.f64 kx)) (.f64 (.f64 2 l) (sin.f64 ky))) Om))
562.0ms	(sqrt.f64 (+.f64 1/2 (/.f64 1/2 (/.f64 (hypot.f64 (.f64 (.f64 2 l) (sin.f64 kx)) (.f64 (.f64 2 l) (sin.f64 ky))) Om))))
474.0ms	(/.f64 (hypot.f64 (.f64 (.f64 2 l) (sin.f64 kx)) (.f64 (.f64 2 l) (sin.f64 ky))) Om)
35.0ms	(.f64 (.f64 2 l) (sin.f64 kx))

simplify243.0ms (0.9%)

Algorithm

1×	egg-herbie

Rules

493×	`times-frac_binary64`
419×	`associate-/r*_binary64`
374×	`associate-/l*_binary64`
299×	`fma-def_binary64`
224×	`associate-*l/_binary64`

Counts

326 → 559

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	540	11122
1	1611	9901
2	4982	9901
3	4951	9901

prune411.0ms (1.5%)

Pruning

5 alts after pruning (2 fresh and 3 done)

	Pruned	Kept	Total
New	557	2	559
Fresh	0	0	0
Picked	0	1	1
Done	0	2	2
Total	557	5	562

Error

Counts

562 → 5

Alt Table

Status	Error	Program
✓	33.2b	(sqrt.f64 (+.f64 1/2 (/.f64 1/2 (/.f64 (hypot.f64 (.f64 (.f64 2 l) (sin.f64 kx)) (.f64 (.f64 2 l) (sin.f64 ky))) Om))))
	45.6b	(hypot.f64 (sqrt.f64 1/2) (sqrt.f64 (/.f64 1/2 (/.f64 (hypot.f64 (.f64 (.f64 2 l) (sin.f64 kx)) (.f64 (.f64 2 l) (sin.f64 ky))) Om))))
	34.2b	(-.f64 (sqrt.f64 1/2) (.f64 1/4 (.f64 (/.f64 Om (*.f64 (sqrt.f64 1/2) l)) (sqrt.f64 (/.f64 1/4 (+.f64 (pow.f64 (sin.f64 kx) 2) (pow.f64 (sin.f64 ky) 2)))))))
✓	24.7b	(sqrt.f64 (+.f64 1/2 (/.f64 1/2 1)))
✓	1.0b	(sqrt.f64 (+.f64 1/2 (/.f64 1/2 (-.f64 (exp.f64 (log1p.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)))) 1))))

Compiler

Compiled 12430 to 7830 computations (37% saved)

regimes5.3s (20%)

Accuracy

Total 1.1b remaining (97.1%)

Threshold costs 0b (0%)

Compiler

Compiled 60910 to 52041 computations (14.6% saved)

simplify7.0ms (0%)

Algorithm

1×	egg-herbie

Rules

3×	`+-commutative_binary64`
1×	`*-commutative_binary64`
1×	`sub-neg_binary64`
1×	`1-exp_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	24	44
1	32	44
2	33	44
3	31	44

end18.0ms (0.1%)

Remove: (sort kx ky)
Compiler: Compiled 96 to 84 computations (12.5% saved)

sample7.1s (26.8%)

Algorithm

1×

intervals

Results

3.3s	6392×	body	128	valid
1.7s	722×	body	1024	valid
909.0ms	550×	body	512	valid
361.0ms	336×	body	256	valid

Compiler

Compiled 189 to 163 computations (13.8% saved)

Details

analyze1.0s (3.9%)

sample117.0ms (0.4%)

simplify65.0ms (0.2%)

prune5.0ms (0%)

localize17.0ms (0.1%)

rewrite71.0ms (0.3%)

series484.0ms (1.8%)

simplify325.0ms (1.2%)

prune366.0ms (1.4%)

localize23.0ms (0.1%)

rewrite32.0ms (0.1%)

series8.1s (30.3%)

simplify264.0ms (1%)

prune515.0ms (1.9%)

localize3.0ms (0%)

rewrite0.0ms (0%)

series0.0ms (0%)

simplify10.0ms (0%)

prune3.0ms (0%)

localize13.0ms (0.1%)

rewrite80.0ms (0.3%)

series2.0s (7.4%)

simplify243.0ms (0.9%)

prune411.0ms (1.5%)

regimes5.3s (20%)

simplify7.0ms (0%)

end18.0ms (0.1%)

sample7.1s (26.8%)

Profiling