Details

analyze741.0ms (6.5%)

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)

sample92.0ms (0.8%)

Algorithm

1×

intervals

Results

33.0ms	201×	body	128	valid
16.0ms	19×	body	1024	valid
14.0ms	24×	body	512	valid
4.0ms	12×	body	256	valid

Compiler

Compiled 71 to 63 computations (11.3% saved)

simplify61.0ms (0.5%)

Algorithm

1×	egg-herbie

Rules

575×	`associate-l_binary64`
512×	`unswap-sqr_binary64`
437×	`associate-r_binary64`
407×	`distribute-rgt-out_binary64`
369×	`associate-/r/_binary64`

Counts

1 → 1

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	24	42
1	56	39
2	107	39
3	429	39
4	2037	39
5	4850	39
6	4809	39
7	5523	39

prune5.0ms (0%)

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

Error

1.5b

Counts

2 → 1

Alt Table

Status	Error	Program
▶	1.5b	(sqrt.f64 (+.f64 1/2 (/.f64 1/2 (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))))))))

Compiler

Compiled 87 to 75 computations (13.8% saved)

localize23.0ms (0.2%)

Local error

Found 4 expressions with local error:

0.3b	(pow.f64 (sin.f64 ky) 2)
0.9b	(/.f64 1/2 (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))))))
3.2b	(.f64 (pow.f64 (/.f64 (.f64 2 l) Om) 2) (+.f64 (pow.f64 (sin.f64 kx) 2) (pow.f64 (sin.f64 ky) 2)))
8.5b	(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)))))

rewrite230.0ms (2%)

Algorithm

1×	rewrite-expression-head

Error

0.9b

Rules

33×	`add-sqr-sqrt_binary64`
30×	`*-un-lft-identity_binary64`
26×	`add-cube-cbrt_binary64`
21×	`times-frac_binary64`
19×	`add-exp-log_binary64`

Counts

4 → 113

Calls

4 calls:

16.0ms	(.f64 (pow.f64 (/.f64 (.f64 2 l) Om) 2) (+.f64 (pow.f64 (sin.f64 kx) 2) (pow.f64 (sin.f64 ky) 2)))
6.0ms	(/.f64 1/2 (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	(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)

Compiler

Compiled 4229 to 3201 computations (24.3% saved)

series755.0ms (6.7%)

Error

0.1b

Counts

4 → 57

Calls

4 calls:

326.0ms	(/.f64 1/2 (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))))))
244.0ms	(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)))))
113.0ms	(.f64 (pow.f64 (/.f64 (.f64 2 l) Om) 2) (+.f64 (pow.f64 (sin.f64 kx) 2) (pow.f64 (sin.f64 ky) 2)))
9.0ms	(pow.f64 (sin.f64 ky) 2)

Compiler

Compiled 5986 to 4934 computations (17.6% saved)

simplify154.0ms (1.4%)

Algorithm

1×	egg-herbie

Rules

408×	`distribute-rgt-in_binary64`
396×	`distribute-lft-in_binary64`
359×	`times-frac_binary64`
304×	`unswap-sqr_binary64`
187×	`associate-r_binary64`

Counts

170 → 145

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	303	6615
1	725	6187
2	2201	5993
3	5195	5993

prune182.0ms (1.6%)

Pruning

3 alts after pruning (2 fresh and 1 done)

	Pruned	Kept	Total
New	143	2	145
Fresh	0	0	0
Picked	0	1	1
Done	0	0	0
Total	143	3	146

Error

0.1b

Counts

146 → 3

Alt Table

Status	Error	Program
▶	6.3b	(sqrt.f64 (+.f64 1/2 (/.f64 1/2 (+.f64 1 (.f64 2 (.f64 (/.f64 (*.f64 l l) Om) (+.f64 (/.f64 (pow.f64 (sin.f64 ky) 2) Om) (/.f64 (pow.f64 (sin.f64 kx) 2) Om))))))))
	26.1b	(sqrt.f64 (+.f64 1/2 (/.f64 1/2 (+.f64 (.f64 l (sqrt.f64 (.f64 (/.f64 4 Om) (+.f64 (/.f64 (pow.f64 (sin.f64 ky) 2) Om) (/.f64 (pow.f64 (sin.f64 kx) 2) Om))))) (.f64 1/2 (/.f64 (sqrt.f64 (/.f64 1 (.f64 (/.f64 4 Om) (+.f64 (/.f64 (pow.f64 (sin.f64 ky) 2) Om) (/.f64 (pow.f64 (sin.f64 kx) 2) Om))))) l))))))
✓	1.5b	(sqrt.f64 (+.f64 1/2 (/.f64 1/2 (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))))))))

Compiler

Compiled 3925 to 2871 computations (26.9% saved)

localize24.0ms (0.2%)

Local error

Found 4 expressions with local error:

4.4b	(/.f64 (pow.f64 (sin.f64 kx) 2) Om)
5.4b	(/.f64 (pow.f64 (sin.f64 ky) 2) Om)
5.8b	(.f64 (/.f64 (.f64 l l) Om) (+.f64 (/.f64 (pow.f64 (sin.f64 ky) 2) Om) (/.f64 (pow.f64 (sin.f64 kx) 2) Om)))
7.1b	(/.f64 (*.f64 l l) Om)

rewrite494.0ms (4.4%)

Algorithm

1×	rewrite-expression-head

Error

0.1b

Rules

67×	`times-frac_binary64`
61×	`*-un-lft-identity_binary64`
51×	`add-sqr-sqrt_binary64`
47×	`add-cube-cbrt_binary64`
30×	`unpow-prod-down_binary64`

Counts

4 → 163

Calls

4 calls:

48.0ms	(.f64 (/.f64 (.f64 l l) Om) (+.f64 (/.f64 (pow.f64 (sin.f64 ky) 2) Om) (/.f64 (pow.f64 (sin.f64 kx) 2) Om)))
10.0ms	(/.f64 (pow.f64 (sin.f64 kx) 2) Om)
5.0ms	(/.f64 (pow.f64 (sin.f64 ky) 2) Om)
5.0ms	(/.f64 (*.f64 l l) Om)

Compiler

Compiled 5891 to 3454 computations (41.4% saved)

series226.0ms (2%)

Error

0.1b

Counts

4 → 32

Calls

4 calls:

126.0ms	(.f64 (/.f64 (.f64 l l) Om) (+.f64 (/.f64 (pow.f64 (sin.f64 ky) 2) Om) (/.f64 (pow.f64 (sin.f64 kx) 2) Om)))
29.0ms	(/.f64 (*.f64 l l) Om)
27.0ms	(/.f64 (pow.f64 (sin.f64 kx) 2) Om)
24.0ms	(/.f64 (pow.f64 (sin.f64 ky) 2) Om)

Compiler

Compiled 2340 to 1870 computations (20.1% saved)

simplify151.0ms (1.3%)

Algorithm

1×	egg-herbie

Rules

505×	`associate-/l/_binary64`
369×	`associate-/r/_binary64`
338×	`distribute-rgt-in_binary64`
320×	`distribute-lft-in_binary64`
206×	`associate-*l/_binary64`

Counts

195 → 131

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	281	4132
1	654	3504
2	2154	3414
3	4848	3414
4	4998	3414

prune134.0ms (1.2%)

Pruning

3 alts after pruning (1 fresh and 2 done)

	Pruned	Kept	Total
New	131	0	131
Fresh	0	1	1
Picked	0	1	1
Done	0	1	1
Total	131	3	134

Error

0.1b

Counts

134 → 3

Alt Table

Status	Error	Program
✓	6.3b	(sqrt.f64 (+.f64 1/2 (/.f64 1/2 (+.f64 1 (.f64 2 (.f64 (/.f64 (*.f64 l l) Om) (+.f64 (/.f64 (pow.f64 (sin.f64 ky) 2) Om) (/.f64 (pow.f64 (sin.f64 kx) 2) Om))))))))
▶	26.1b	(sqrt.f64 (+.f64 1/2 (/.f64 1/2 (+.f64 (.f64 l (sqrt.f64 (.f64 (/.f64 4 Om) (+.f64 (/.f64 (pow.f64 (sin.f64 ky) 2) Om) (/.f64 (pow.f64 (sin.f64 kx) 2) Om))))) (.f64 1/2 (/.f64 (sqrt.f64 (/.f64 1 (.f64 (/.f64 4 Om) (+.f64 (/.f64 (pow.f64 (sin.f64 ky) 2) Om) (/.f64 (pow.f64 (sin.f64 kx) 2) Om))))) l))))))
✓	1.5b	(sqrt.f64 (+.f64 1/2 (/.f64 1/2 (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))))))))

Compiler

Compiled 2884 to 1699 computations (41.1% saved)

localize31.0ms (0.3%)

Local error

Found 4 expressions with local error:

5.4b	(/.f64 (pow.f64 (sin.f64 ky) 2) Om)
5.4b	(/.f64 (pow.f64 (sin.f64 ky) 2) Om)
27.9b	(sqrt.f64 (/.f64 1 (*.f64 (/.f64 4 Om) (+.f64 (/.f64 (pow.f64 (sin.f64 ky) 2) Om) (/.f64 (pow.f64 (sin.f64 kx) 2) Om)))))
28.2b	(sqrt.f64 (*.f64 (/.f64 4 Om) (+.f64 (/.f64 (pow.f64 (sin.f64 ky) 2) Om) (/.f64 (pow.f64 (sin.f64 kx) 2) Om))))

rewrite387.0ms (3.4%)

Algorithm

1×	rewrite-expression-head

Error

0.1b

Rules

51×	`times-frac_binary64`
41×	`add-sqr-sqrt_binary64`
40×	`*-un-lft-identity_binary64`
40×	`add-cube-cbrt_binary64`
24×	`unpow-prod-down_binary64`

Counts

4 → 144

Calls

4 calls:

48.0ms	(sqrt.f64 (/.f64 1 (*.f64 (/.f64 4 Om) (+.f64 (/.f64 (pow.f64 (sin.f64 ky) 2) Om) (/.f64 (pow.f64 (sin.f64 kx) 2) Om)))))
43.0ms	(sqrt.f64 (*.f64 (/.f64 4 Om) (+.f64 (/.f64 (pow.f64 (sin.f64 ky) 2) Om) (/.f64 (pow.f64 (sin.f64 kx) 2) Om))))
6.0ms	(/.f64 (pow.f64 (sin.f64 ky) 2) Om)
6.0ms	(/.f64 (pow.f64 (sin.f64 ky) 2) Om)

Compiler

Compiled 8249 to 5463 computations (33.8% saved)

series345.0ms (3%)

Error

0.1b

Counts

4 → 35

Calls

4 calls:

144.0ms	(sqrt.f64 (/.f64 1 (*.f64 (/.f64 4 Om) (+.f64 (/.f64 (pow.f64 (sin.f64 ky) 2) Om) (/.f64 (pow.f64 (sin.f64 kx) 2) Om)))))
102.0ms	(sqrt.f64 (*.f64 (/.f64 4 Om) (+.f64 (/.f64 (pow.f64 (sin.f64 ky) 2) Om) (/.f64 (pow.f64 (sin.f64 kx) 2) Om))))
31.0ms	(/.f64 (pow.f64 (sin.f64 ky) 2) Om)
29.0ms	(/.f64 (pow.f64 (sin.f64 ky) 2) Om)

Compiler

Compiled 4419 to 3222 computations (27.1% saved)

simplify116.0ms (1%)

Algorithm

1×	egg-herbie

Rules

554×	`associate-/l*_binary64`
537×	`times-frac_binary64`
366×	`associate-*l/_binary64`
360×	`associate-l_binary64`
356×	`associate-/r*_binary64`

Counts

179 → 110

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	241	4121
1	501	3688
2	1304	3656
3	4969	3656

prune159.0ms (1.4%)

Pruning

3 alts after pruning (0 fresh and 3 done)

	Pruned	Kept	Total
New	110	0	110
Fresh	0	0	0
Picked	0	1	1
Done	0	2	2
Total	110	3	113

Error

0.1b

Counts

113 → 3

Alt Table

Status	Error	Program
	6.3b	(sqrt.f64 (+.f64 1/2 (/.f64 1/2 (+.f64 1 (.f64 2 (.f64 (/.f64 (*.f64 l l) Om) (+.f64 (/.f64 (pow.f64 (sin.f64 ky) 2) Om) (/.f64 (pow.f64 (sin.f64 kx) 2) Om))))))))
	26.1b	(sqrt.f64 (+.f64 1/2 (/.f64 1/2 (+.f64 (.f64 l (sqrt.f64 (.f64 (/.f64 4 Om) (+.f64 (/.f64 (pow.f64 (sin.f64 ky) 2) Om) (/.f64 (pow.f64 (sin.f64 kx) 2) Om))))) (.f64 1/2 (/.f64 (sqrt.f64 (/.f64 1 (.f64 (/.f64 4 Om) (+.f64 (/.f64 (pow.f64 (sin.f64 ky) 2) Om) (/.f64 (pow.f64 (sin.f64 kx) 2) Om))))) l))))))
	1.5b	(sqrt.f64 (+.f64 1/2 (/.f64 1/2 (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))))))))

Compiler

Compiled 4784 to 3136 computations (34.4% saved)

regimes4.3s (38.1%)

Accuracy

Total 0.5b remaining (80.6%)

Threshold costs 0.5b (80.6%)

Compiler

Compiled 95801 to 74909 computations (21.8% saved)

simplify3.0ms (0%)

Algorithm

1×	egg-herbie

Rules

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

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	22	45
1	30	45
2	29	45

end9.0ms (0.1%)

Remove: (sort kx ky)
Compiler: Compiled 99 to 81 computations (18.2% saved)

sample2.7s (23.8%)

Algorithm

1×

intervals

Results

1.1s	6391×	body	128	valid
619.0ms	757×	body	1024	valid
319.0ms	550×	body	512	valid
111.0ms	302×	body	256	valid

Compiler

Compiled 186 to 151 computations (18.8% saved)

Details

analyze741.0ms (6.5%)

sample92.0ms (0.8%)

simplify61.0ms (0.5%)

prune5.0ms (0%)

localize23.0ms (0.2%)

rewrite230.0ms (2%)

series755.0ms (6.7%)

simplify154.0ms (1.4%)

prune182.0ms (1.6%)

localize24.0ms (0.2%)

rewrite494.0ms (4.4%)

series226.0ms (2%)

simplify151.0ms (1.3%)

prune134.0ms (1.2%)

localize31.0ms (0.3%)

rewrite387.0ms (3.4%)

series345.0ms (3%)

simplify116.0ms (1%)

prune159.0ms (1.4%)

regimes4.3s (38.1%)

simplify3.0ms (0%)

end9.0ms (0.1%)

sample2.7s (23.8%)

Profiling