Details

analyze1.5s (11.6%)

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 34 to 30 computations (11.8% saved)

sample157.0ms (1.2%)

Algorithm

1×

intervals

Symmetry

(sort kx ky)

Results

49.0ms	206×	body	128	valid
30.0ms	24×	body	1024	valid
12.0ms	17×	body	512	valid
4.0ms	9×	body	256	valid

Compiler

Compiled 71 to 63 computations (11.3% saved)

simplify50.0ms (0.4%)

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)

localize19.0ms (0.1%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.3b	(pow.f64 (sin.f64 kx) 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)))
✓	1.4b	(fma.f64 (pow.f64 (/.f64 (*.f64 2 l) Om) 2) (+.f64 (pow.f64 (sin.f64 kx) 2) (pow.f64 (sin.f64 ky) 2)) 1)
✓	8.7b	(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))

series1.1s (8.9%)

Counts

4 → 148

Calls

4 calls:

810.0ms	(/.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)))
217.0ms	(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))
102.0ms	(fma.f64 (pow.f64 (/.f64 (*.f64 2 l) Om) 2) (+.f64 (pow.f64 (sin.f64 kx) 2) (pow.f64 (sin.f64 ky) 2)) 1)
3.0ms	(pow.f64 (sin.f64 kx) 2)

rewrite12.0ms (0.1%)

Algorithm

1×	rewrite-expression-head

Rules

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

Counts

4 → 86

Calls

4 calls:

4.0ms	(/.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	(pow.f64 (sin.f64 kx) 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)

simplify234.0ms (1.8%)

Algorithm

1×	egg-herbie

Rules

417×	`fma-neg_binary64`
342×	`fma-def_binary64`
271×	`associate-r_binary64`
200×	`associate-l_binary64`
200×	`associate-*r/_binary64`

Counts

234 → 225

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	476	14253
1	1374	13174
2	4955	13168
3	5267	13168

prune362.0ms (2.8%)

Pruning

4 alts after pruning (4 fresh and 0 done)

	Pruned	Kept	Total
New	221	4	225
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	222	4	226

Error

0.4b

Counts

226 → 4

Alt Table

Status	Error	Program
▶	1.0b	(sqrt.f64 (+.f64 1/2 (.f64 (sqrt.f64 1/2) (/.f64 (sqrt.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))))))
	23.3b	(sqrt.f64 (+.f64 1/2 1/2))
	33.1b	(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))))))
	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 13146 to 9417 computations (28.4% saved)

localize21.0ms (0.2%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.3b	(/.f64 (sqrt.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)))
✓	0.7b	(.f64 (sqrt.f64 1/2) (/.f64 (sqrt.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))))
	1.4b	(fma.f64 (pow.f64 (/.f64 (*.f64 2 l) Om) 2) (+.f64 (pow.f64 (sin.f64 kx) 2) (pow.f64 (sin.f64 ky) 2)) 1)
	8.7b	(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))

series1.7s (13.2%)

Counts

2 → 96

Calls

2 calls:

847.0ms

(*.f64 (sqrt.f64 1/2) (/.f64 (sqrt.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))))

836.0ms

(/.f64 (sqrt.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)))

rewrite37.0ms (0.3%)

Algorithm

1×	rewrite-expression-head

Rules

94×	`sqrt-prod_binary64`
90×	`add-sqr-sqrt_binary64`
80×	`times-frac_binary64`
57×	`*-un-lft-identity_binary64`
57×	`add-cube-cbrt_binary64`

Counts

2 → 138

Calls

2 calls:

12.0ms

(*.f64 (sqrt.f64 1/2) (/.f64 (sqrt.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))))

4.0ms

(/.f64 (sqrt.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)))

simplify231.0ms (1.8%)

Algorithm

1×	egg-herbie

Rules

465×	`associate-l_binary64`
362×	`fma-def_binary64`
325×	`associate-/l*_binary64`
270×	`times-frac_binary64`
234×	`associate-*r/_binary64`

Counts

234 → 244

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	547	17019
1	1617	15940
2	5121	15940

prune610.0ms (4.8%)

Pruning

4 alts after pruning (3 fresh and 1 done)

	Pruned	Kept	Total
New	342	0	342
Fresh	0	3	3
Picked	0	1	1
Done	0	0	0
Total	342	4	346

Error

0.4b

Counts

346 → 4

Alt Table

Status	Error	Program
✓	1.0b	(sqrt.f64 (+.f64 1/2 (.f64 (sqrt.f64 1/2) (/.f64 (sqrt.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))))))
	23.3b	(sqrt.f64 (+.f64 1/2 1/2))
	33.1b	(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))))))
▶	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 22524 to 16822 computations (25.3% saved)

localize22.0ms (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)))
	1.4b	(fma.f64 (pow.f64 (/.f64 (*.f64 2 l) Om) 2) (+.f64 (pow.f64 (sin.f64 kx) 2) (pow.f64 (sin.f64 ky) 2)) 1)
✓	3.6b	(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)))))
	8.7b	(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))

series802.0ms (6.3%)

Counts

1 → 48

Calls

1 calls:

802.0ms

(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)))))

rewrite10.0ms (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)))))

simplify113.0ms (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

prune513.0ms (4%)

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

0.4b

Counts

304 → 4

Alt Table

Status	Error	Program
✓	1.0b	(sqrt.f64 (+.f64 1/2 (.f64 (sqrt.f64 1/2) (/.f64 (sqrt.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))))))
▶	23.3b	(sqrt.f64 (+.f64 1/2 1/2))
	33.1b	(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))))))
✓	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 19394 to 14052 computations (27.5% saved)

localize2.0ms (0%)

prune5.0ms (0%)

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

0.4b

Counts

4 → 4

Alt Table

Status	Error	Program
✓	1.0b	(sqrt.f64 (+.f64 1/2 (.f64 (sqrt.f64 1/2) (/.f64 (sqrt.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))))))
✓	23.3b	(sqrt.f64 (+.f64 1/2 1/2))
	33.1b	(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))))))
✓	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 125 to 98 computations (21.6% saved)

regimes1.7s (13.5%)

Accuracy

Total 0.6b remaining (56.2%)

Threshold costs 0.6b (56.2%)

Counts

76 → 1

Compiler

Compiled 44430 to 37781 computations (15% saved)

simplify2.0ms (0%)

Algorithm

1×	egg-herbie

Rules

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

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	23	42
1	29	42
2	28	42

end6.0ms (0%)

Remove: (sort kx ky)
Compiler: Compiled 93 to 81 computations (12.9% saved)

sample3.6s (27.8%)

Algorithm

1×

intervals

Results

1.6s	6328×	body	128	valid
961.0ms	818×	body	1024	valid
407.0ms	514×	body	512	valid
168.0ms	340×	body	256	valid

Compiler

Compiled 194 to 159 computations (18% saved)

Details

analyze1.5s (11.6%)

sample157.0ms (1.2%)

simplify50.0ms (0.4%)

prune4.0ms (0%)

localize19.0ms (0.1%)

series1.1s (8.9%)

rewrite12.0ms (0.1%)

simplify234.0ms (1.8%)

prune362.0ms (2.8%)

localize21.0ms (0.2%)

series1.7s (13.2%)

rewrite37.0ms (0.3%)

simplify231.0ms (1.8%)

prune610.0ms (4.8%)

localize22.0ms (0.2%)

series802.0ms (6.3%)

rewrite10.0ms (0.1%)

simplify113.0ms (0.9%)

prune513.0ms (4%)

localize2.0ms (0%)

prune5.0ms (0%)

regimes1.7s (13.5%)

simplify2.0ms (0%)

end6.0ms (0%)

sample3.6s (27.8%)

Profiling