Details

analyze728.0ms (6.9%)

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)

sample100.0ms (1%)

Algorithm

1×

intervals

Results

32.0ms	189×	body	128	valid
27.0ms	33×	body	1024	valid
11.0ms	19×	body	512	valid
10.0ms	15×	body	256	valid

Compiler

Compiled 71 to 63 computations (11.3% saved)

simplify63.0ms (0.6%)

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 (0.1%)

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

1.0b

Counts

2 → 1

Alt Table

Status	Error	Program
▶	1.0b	(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)

localize19.0ms (0.2%)

Local error

Found 4 expressions with local error:

0.3b	(pow.f64 (sin.f64 ky) 2)
0.3b	(pow.f64 (/.f64 (*.f64 2 l) Om) 2)
1.4b	(.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)))))

rewrite224.0ms (2.1%)

Algorithm

1×	rewrite-expression-head

Error

0.9b

Rules

23×	`add-exp-log_binary64`
21×	`add-sqr-sqrt_binary64`
20×	`unpow-prod-down_binary64`
18×	`*-un-lft-identity_binary64`
14×	`add-cube-cbrt_binary64`

Counts

4 → 96

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)))
9.0ms	(pow.f64 (/.f64 (*.f64 2 l) Om) 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 3217 to 2424 computations (24.7% saved)

series423.0ms (4%)

Error

0.2b

Counts

4 → 43

Calls

4 calls:

224.0ms	(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)))))
123.0ms	(.f64 (pow.f64 (/.f64 (.f64 2 l) Om) 2) (+.f64 (pow.f64 (sin.f64 kx) 2) (pow.f64 (sin.f64 ky) 2)))
26.0ms	(pow.f64 (/.f64 (*.f64 2 l) Om) 2)
11.0ms	(pow.f64 (sin.f64 ky) 2)

Compiler

Compiled 3947 to 3290 computations (16.6% saved)

simplify141.0ms (1.3%)

Algorithm

1×	egg-herbie

Rules

347×	`distribute-rgt-in_binary64`
338×	`distribute-lft-in_binary64`
335×	`times-frac_binary64`
332×	`unswap-sqr_binary64`
194×	`exp-prod_binary64`

Counts

139 → 114

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	237	3754
1	579	3444
2	1807	3269
3	4667	3269
4	5098	3269

prune131.0ms (1.2%)

Pruning

3 alts after pruning (2 fresh and 1 done)

	Pruned	Kept	Total
New	112	2	114
Fresh	0	0	0
Picked	0	1	1
Done	0	0	0
Total	112	3	115

Error

Counts

115 → 3

Alt Table

Status	Error	Program
▶	1.0b	(sqrt.f64 (+.f64 1/2 (/.f64 1/2 (.f64 (sqrt.f64 (sqrt.f64 (+.f64 1 (.f64 (+.f64 (pow.f64 (sin.f64 ky) 2) (pow.f64 (sin.f64 kx) 2)) (.f64 4 (pow.f64 (/.f64 l Om) 2)))))) (sqrt.f64 (sqrt.f64 (+.f64 1 (.f64 (+.f64 (pow.f64 (sin.f64 ky) 2) (pow.f64 (sin.f64 kx) 2)) (*.f64 4 (pow.f64 (/.f64 l Om) 2))))))))))
	24.2b	(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))))))
✓	1.0b	(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 2447 to 1763 computations (28% saved)

localize26.0ms (0.2%)

Local error

Found 4 expressions with local error:

7.2b	(sqrt.f64 (sqrt.f64 (+.f64 1 (.f64 (+.f64 (pow.f64 (sin.f64 ky) 2) (pow.f64 (sin.f64 kx) 2)) (.f64 4 (pow.f64 (/.f64 l Om) 2))))))
7.2b	(sqrt.f64 (sqrt.f64 (+.f64 1 (.f64 (+.f64 (pow.f64 (sin.f64 ky) 2) (pow.f64 (sin.f64 kx) 2)) (.f64 4 (pow.f64 (/.f64 l Om) 2))))))
8.5b	(sqrt.f64 (+.f64 1 (.f64 (+.f64 (pow.f64 (sin.f64 ky) 2) (pow.f64 (sin.f64 kx) 2)) (.f64 4 (pow.f64 (/.f64 l Om) 2)))))
8.5b	(sqrt.f64 (+.f64 1 (.f64 (+.f64 (pow.f64 (sin.f64 ky) 2) (pow.f64 (sin.f64 kx) 2)) (.f64 4 (pow.f64 (/.f64 l Om) 2)))))

rewrite207.0ms (2%)

Algorithm

1×	rewrite-expression-head

Error

Rules

26×	`sqrt-prod_binary64`
16×	`add-sqr-sqrt_binary64`
12×	`sqrt-div_binary64`
10×	`pow1_binary64` `add-cube-cbrt_binary64` `sqrt-pow1_binary64` `*-un-lft-identity_binary64`
6×	`pow1/2_binary64` `rem-sqrt-square_binary64`

Counts

4 → 72

Calls

4 calls:

7.0ms	(sqrt.f64 (sqrt.f64 (+.f64 1 (.f64 (+.f64 (pow.f64 (sin.f64 ky) 2) (pow.f64 (sin.f64 kx) 2)) (.f64 4 (pow.f64 (/.f64 l Om) 2))))))
5.0ms	(sqrt.f64 (sqrt.f64 (+.f64 1 (.f64 (+.f64 (pow.f64 (sin.f64 ky) 2) (pow.f64 (sin.f64 kx) 2)) (.f64 4 (pow.f64 (/.f64 l Om) 2))))))
3.0ms	(sqrt.f64 (+.f64 1 (.f64 (+.f64 (pow.f64 (sin.f64 ky) 2) (pow.f64 (sin.f64 kx) 2)) (.f64 4 (pow.f64 (/.f64 l Om) 2)))))
3.0ms	(sqrt.f64 (+.f64 1 (.f64 (+.f64 (pow.f64 (sin.f64 ky) 2) (pow.f64 (sin.f64 kx) 2)) (.f64 4 (pow.f64 (/.f64 l Om) 2)))))

Compiler

Compiled 4312 to 3055 computations (29.2% saved)

series1.5s (14.3%)

Error

Counts

4 → 86

Calls

4 calls:

400.0ms	(sqrt.f64 (sqrt.f64 (+.f64 1 (.f64 (+.f64 (pow.f64 (sin.f64 ky) 2) (pow.f64 (sin.f64 kx) 2)) (.f64 4 (pow.f64 (/.f64 l Om) 2))))))
398.0ms	(sqrt.f64 (sqrt.f64 (+.f64 1 (.f64 (+.f64 (pow.f64 (sin.f64 ky) 2) (pow.f64 (sin.f64 kx) 2)) (.f64 4 (pow.f64 (/.f64 l Om) 2))))))
279.0ms	(sqrt.f64 (+.f64 1 (.f64 (+.f64 (pow.f64 (sin.f64 ky) 2) (pow.f64 (sin.f64 kx) 2)) (.f64 4 (pow.f64 (/.f64 l Om) 2)))))
276.0ms	(sqrt.f64 (+.f64 1 (.f64 (+.f64 (pow.f64 (sin.f64 ky) 2) (pow.f64 (sin.f64 kx) 2)) (.f64 4 (pow.f64 (/.f64 l Om) 2)))))

Compiler

Compiled 16010 to 12646 computations (21% saved)

simplify169.0ms (1.6%)

Algorithm

1×	egg-herbie

Rules

432×	`times-frac_binary64`
342×	`associate-/l*_binary64`
321×	`associate-/r*_binary64`
262×	`distribute-rgt-in_binary64`
258×	`distribute-lft-in_binary64`

Counts

158 → 128

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	193	7760
1	479	7328
2	1463	6608
3	4970	6608

prune245.0ms (2.3%)

Pruning

3 alts after pruning (1 fresh and 2 done)

	Pruned	Kept	Total
New	128	0	128
Fresh	0	1	1
Picked	0	1	1
Done	0	1	1
Total	128	3	131

Error

Counts

131 → 3

Alt Table

Status	Error	Program
✓	1.0b	(sqrt.f64 (+.f64 1/2 (/.f64 1/2 (.f64 (sqrt.f64 (sqrt.f64 (+.f64 1 (.f64 (+.f64 (pow.f64 (sin.f64 ky) 2) (pow.f64 (sin.f64 kx) 2)) (.f64 4 (pow.f64 (/.f64 l Om) 2)))))) (sqrt.f64 (sqrt.f64 (+.f64 1 (.f64 (+.f64 (pow.f64 (sin.f64 ky) 2) (pow.f64 (sin.f64 kx) 2)) (*.f64 4 (pow.f64 (/.f64 l Om) 2))))))))))
▶	24.2b	(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))))))
✓	1.0b	(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 6585 to 4614 computations (29.9% saved)

localize29.0ms (0.3%)

Local error

Found 4 expressions with local error:

5.4b	(/.f64 (pow.f64 (sin.f64 kx) 2) Om)
5.4b	(/.f64 (pow.f64 (sin.f64 kx) 2) Om)
30.4b	(sqrt.f64 (*.f64 (/.f64 4 Om) (+.f64 (/.f64 (pow.f64 (sin.f64 ky) 2) Om) (/.f64 (pow.f64 (sin.f64 kx) 2) Om))))
30.9b	(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)))))

rewrite435.0ms (4.1%)

Algorithm

1×	rewrite-expression-head

Error

Rules

51×	`times-frac_binary64`
41×	`add-sqr-sqrt_binary64`
40×	`add-cube-cbrt_binary64` `*-un-lft-identity_binary64`
24×	`unpow-prod-down_binary64`
16×	`associate-/l*_binary64`

Counts

4 → 144

Calls

4 calls:

45.0ms	(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)))))
45.0ms	(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 kx) 2) Om)
6.0ms	(/.f64 (pow.f64 (sin.f64 kx) 2) Om)

Compiler

Compiled 8249 to 5463 computations (33.8% saved)

series386.0ms (3.7%)

Error

Counts

4 → 38

Calls

4 calls:

147.0ms	(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)))))
128.0ms	(sqrt.f64 (*.f64 (/.f64 4 Om) (+.f64 (/.f64 (pow.f64 (sin.f64 ky) 2) Om) (/.f64 (pow.f64 (sin.f64 kx) 2) Om))))
34.0ms	(/.f64 (pow.f64 (sin.f64 kx) 2) Om)
33.0ms	(/.f64 (pow.f64 (sin.f64 kx) 2) Om)

Compiler

Compiled 4899 to 3539 computations (27.8% saved)

simplify130.0ms (1.2%)

Algorithm

1×	egg-herbie

Rules

818×	`associate-/l*_binary64`
633×	`associate-/r*_binary64`
311×	`associate-/r/_binary64`
180×	`associate-/l/_binary64`
151×	`cancel-sign-sub-inv_binary64`

Counts

182 → 113

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	281	4382
1	618	3981
2	1830	3899
3	4987	3899

prune175.0ms (1.7%)

Pruning

3 alts after pruning (0 fresh and 3 done)

	Pruned	Kept	Total
New	113	0	113
Fresh	0	0	0
Picked	0	1	1
Done	0	2	2
Total	113	3	116

Error

Counts

116 → 3

Alt Table

Status	Error	Program
	1.0b	(sqrt.f64 (+.f64 1/2 (/.f64 1/2 (.f64 (sqrt.f64 (sqrt.f64 (+.f64 1 (.f64 (+.f64 (pow.f64 (sin.f64 ky) 2) (pow.f64 (sin.f64 kx) 2)) (.f64 4 (pow.f64 (/.f64 l Om) 2)))))) (sqrt.f64 (sqrt.f64 (+.f64 1 (.f64 (+.f64 (pow.f64 (sin.f64 ky) 2) (pow.f64 (sin.f64 kx) 2)) (*.f64 4 (pow.f64 (/.f64 l Om) 2))))))))))
	24.2b	(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))))))
	1.0b	(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 5106 to 3344 computations (34.5% saved)

regimes2.6s (24.4%)

Accuracy

Total 0.5b remaining (73.5%)

Threshold costs 0.5b (73.5%)

Compiler

Compiled 53788 to 43739 computations (18.7% saved)

simplify3.0ms (0%)

Algorithm

1×	egg-herbie

Rules

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

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	23	65
1	30	65
2	29	65

end9.0ms (0.1%)

Remove: (sort kx ky)
Compiler: Compiled 135 to 105 computations (22.2% saved)

sample2.8s (26.6%)

Algorithm

1×

intervals

Results

1.1s	6345×	body	128	valid
672.0ms	806×	body	1024	valid
310.0ms	520×	body	512	valid
128.0ms	329×	body	256	valid

Compiler

Compiled 218 to 175 computations (19.7% saved)

Details

analyze728.0ms (6.9%)

sample100.0ms (1%)

simplify63.0ms (0.6%)

prune5.0ms (0.1%)

localize19.0ms (0.2%)

rewrite224.0ms (2.1%)

series423.0ms (4%)

simplify141.0ms (1.3%)

prune131.0ms (1.2%)

localize26.0ms (0.2%)

rewrite207.0ms (2%)

series1.5s (14.3%)

simplify169.0ms (1.6%)

prune245.0ms (2.3%)

localize29.0ms (0.3%)

rewrite435.0ms (4.1%)

series386.0ms (3.7%)

simplify130.0ms (1.2%)

prune175.0ms (1.7%)

regimes2.6s (24.4%)

simplify3.0ms (0%)

end9.0ms (0.1%)

sample2.8s (26.6%)

Profiling