Details

analyze956.0ms (9.8%)

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)

sample123.0ms (1.3%)

Algorithm

1×

intervals

Results

42.0ms	194×	body	128	valid
39.0ms	28×	body	1024	valid
17.0ms	23×	body	512	valid
5.0ms	11×	body	256	valid

Compiler

Compiled 71 to 63 computations (11.3% saved)

simplify64.0ms (0.7%)

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

prune4.0ms (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)

localize18.0ms (0.2%)

Local error

Found 4 expressions with local error:

0.3b	(pow.f64 (sin.f64 kx) 2)
0.3b	(pow.f64 (sin.f64 ky) 2)
4.2b	(.f64 (pow.f64 (/.f64 (.f64 2 l) Om) 2) (+.f64 (pow.f64 (sin.f64 kx) 2) (pow.f64 (sin.f64 ky) 2)))
9.7b	(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)))))

rewrite147.0ms (1.5%)

Algorithm

1×	rewrite-expression-head

Error

0.8b

Rules

20×	`add-sqr-sqrt_binary64`
18×	`add-exp-log_binary64`
17×	`*-un-lft-identity_binary64`
16×	`unpow-prod-down_binary64`
13×	`add-cube-cbrt_binary64`

Counts

4 → 90

Calls

4 calls:

12.0ms	(.f64 (pow.f64 (/.f64 (.f64 2 l) Om) 2) (+.f64 (pow.f64 (sin.f64 kx) 2) (pow.f64 (sin.f64 ky) 2)))
4.0ms	(pow.f64 (sin.f64 kx) 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)))))
2.0ms	(pow.f64 (sin.f64 ky) 2)

Compiler

Compiled 3007 to 2262 computations (24.8% saved)

series327.0ms (3.4%)

Error

0.2b

Counts

4 → 43

Calls

4 calls:

196.0ms	(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)))))
88.0ms	(.f64 (pow.f64 (/.f64 (.f64 2 l) Om) 2) (+.f64 (pow.f64 (sin.f64 kx) 2) (pow.f64 (sin.f64 ky) 2)))
6.0ms	(pow.f64 (sin.f64 ky) 2)
6.0ms	(pow.f64 (sin.f64 kx) 2)

Compiler

Compiled 4274 to 3531 computations (17.4% saved)

simplify96.0ms (1%)

Algorithm

1×	egg-herbie

Rules

408×	`distribute-rgt-in_binary64`
394×	`distribute-lft-in_binary64`
354×	`times-frac_binary64`
312×	`unswap-sqr_binary64`
176×	`associate-r_binary64`

Counts

133 → 102

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	260	3936
1	659	3683
2	2085	3456
3	5098	3456

prune98.0ms (1%)

Pruning

2 alts after pruning (2 fresh and 0 done)

	Pruned	Kept	Total
New	100	2	102
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	101	2	103

Error

Counts

103 → 2

Alt Table

Status	Error	Program
▶	0.8b	(sqrt.f64 (+.f64 1/2 (/.f64 1/2 (sqrt.f64 (+.f64 1 (.f64 (/.f64 (.f64 2 l) Om) (.f64 (+.f64 (pow.f64 (sin.f64 kx) 2) (pow.f64 (sin.f64 ky) 2)) (/.f64 (.f64 2 l) Om))))))))
	25.4b	(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))))))

Status

Error

Program

▶

0.8b

(sqrt.f64 (+.f64 1/2 (/.f64 1/2 (sqrt.f64 (+.f64 1 (*.f64 (/.f64 (*.f64 2 l) Om) (*.f64 (+.f64 (pow.f64 (sin.f64 kx) 2) (pow.f64 (sin.f64 ky) 2)) (/.f64 (*.f64 2 l) Om))))))))

25.4b

(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))))))

Compiler

Compiled 2482 to 1814 computations (26.9% saved)

localize22.0ms (0.2%)

Local error

Found 4 expressions with local error:

0.3b	(pow.f64 (sin.f64 ky) 2)
1.3b	(.f64 (/.f64 (.f64 2 l) Om) (.f64 (+.f64 (pow.f64 (sin.f64 kx) 2) (pow.f64 (sin.f64 ky) 2)) (/.f64 (.f64 2 l) Om)))
2.0b	(.f64 (+.f64 (pow.f64 (sin.f64 kx) 2) (pow.f64 (sin.f64 ky) 2)) (/.f64 (.f64 2 l) Om))
9.7b	(sqrt.f64 (+.f64 1 (.f64 (/.f64 (.f64 2 l) Om) (.f64 (+.f64 (pow.f64 (sin.f64 kx) 2) (pow.f64 (sin.f64 ky) 2)) (/.f64 (.f64 2 l) Om)))))

rewrite184.0ms (1.9%)

Algorithm

1×	rewrite-expression-head

Error

Rules

68×	`add-exp-log_binary64`
67×	`add-cbrt-cube_binary64`
32×	`cbrt-unprod_binary64`
32×	`prod-exp_binary64`
16×	`cbrt-undiv_binary64`

Counts

4 → 119

Calls

4 calls:

19.0ms	(.f64 (/.f64 (.f64 2 l) Om) (.f64 (+.f64 (pow.f64 (sin.f64 kx) 2) (pow.f64 (sin.f64 ky) 2)) (/.f64 (.f64 2 l) Om)))
12.0ms	(.f64 (+.f64 (pow.f64 (sin.f64 kx) 2) (pow.f64 (sin.f64 ky) 2)) (/.f64 (.f64 2 l) Om))
3.0ms	(sqrt.f64 (+.f64 1 (.f64 (/.f64 (.f64 2 l) Om) (.f64 (+.f64 (pow.f64 (sin.f64 kx) 2) (pow.f64 (sin.f64 ky) 2)) (/.f64 (.f64 2 l) Om)))))
2.0ms	(pow.f64 (sin.f64 ky) 2)

Compiler

Compiled 5032 to 3494 computations (30.6% saved)

series412.0ms (4.2%)

Error

Counts

4 → 54

Calls

4 calls:

191.0ms	(sqrt.f64 (+.f64 1 (.f64 (/.f64 (.f64 2 l) Om) (.f64 (+.f64 (pow.f64 (sin.f64 kx) 2) (pow.f64 (sin.f64 ky) 2)) (/.f64 (.f64 2 l) Om)))))
94.0ms	(.f64 (/.f64 (.f64 2 l) Om) (.f64 (+.f64 (pow.f64 (sin.f64 kx) 2) (pow.f64 (sin.f64 ky) 2)) (/.f64 (.f64 2 l) Om)))
84.0ms	(.f64 (+.f64 (pow.f64 (sin.f64 kx) 2) (pow.f64 (sin.f64 ky) 2)) (/.f64 (.f64 2 l) Om))
7.0ms	(pow.f64 (sin.f64 ky) 2)

Compiler

Compiled 5186 to 4238 computations (18.3% saved)

simplify176.0ms (1.8%)

Algorithm

1×	egg-herbie

Rules

373×	`associate-/r/_binary64`
359×	`associate-r_binary64`
296×	`associate-l_binary64`
220×	`*-commutative_binary64`
211×	`associate-/l/_binary64`

Counts

173 → 144

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	318	5929
1	832	5382
2	3110	5159
3	4981	5159
4	5022	5159

prune113.0ms (1.2%)

Pruning

2 alts after pruning (1 fresh and 1 done)

	Pruned	Kept	Total
New	143	1	144
Fresh	1	0	1
Picked	0	1	1
Done	0	0	0
Total	144	2	146

Error

Counts

146 → 2

Alt Table

Status	Error	Program
▶	25.4b	(sqrt.f64 (+.f64 1/2 (/.f64 1/2 (+.f64 (/.f64 (sqrt.f64 (.f64 4 (.f64 l (.f64 l (+.f64 (pow.f64 (sin.f64 kx) 2) (pow.f64 (sin.f64 ky) 2)))))) Om) (.f64 1/2 (.f64 Om (sqrt.f64 (/.f64 1/4 (.f64 l (*.f64 l (+.f64 (pow.f64 (sin.f64 kx) 2) (pow.f64 (sin.f64 ky) 2))))))))))))
✓	0.8b	(sqrt.f64 (+.f64 1/2 (/.f64 1/2 (sqrt.f64 (+.f64 1 (.f64 (/.f64 (.f64 2 l) Om) (.f64 (+.f64 (pow.f64 (sin.f64 kx) 2) (pow.f64 (sin.f64 ky) 2)) (/.f64 (.f64 2 l) Om))))))))

Status

Error

Program

▶

25.4b

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

✓

0.8b

(sqrt.f64 (+.f64 1/2 (/.f64 1/2 (sqrt.f64 (+.f64 1 (*.f64 (/.f64 (*.f64 2 l) Om) (*.f64 (+.f64 (pow.f64 (sin.f64 kx) 2) (pow.f64 (sin.f64 ky) 2)) (/.f64 (*.f64 2 l) Om))))))))

Compiler

Compiled 3245 to 2223 computations (31.5% saved)

localize26.0ms (0.3%)

Local error

Found 4 expressions with local error:

1.1b	(*.f64 l (+.f64 (pow.f64 (sin.f64 kx) 2) (pow.f64 (sin.f64 ky) 2)))
1.1b	(*.f64 l (+.f64 (pow.f64 (sin.f64 kx) 2) (pow.f64 (sin.f64 ky) 2)))
28.5b	(sqrt.f64 (.f64 4 (.f64 l (*.f64 l (+.f64 (pow.f64 (sin.f64 kx) 2) (pow.f64 (sin.f64 ky) 2))))))
28.8b	(sqrt.f64 (/.f64 1/4 (.f64 l (.f64 l (+.f64 (pow.f64 (sin.f64 kx) 2) (pow.f64 (sin.f64 ky) 2))))))

rewrite190.0ms (1.9%)

Algorithm

1×	rewrite-expression-head

Error

Rules

19×	`pow1_binary64`
18×	`*-un-lft-identity_binary64`
15×	`add-sqr-sqrt_binary64`
14×	`associate-*r/_binary64`
10×	`associate-r_binary64`

Counts

4 → 83

Calls

4 calls:

13.0ms	(sqrt.f64 (/.f64 1/4 (.f64 l (.f64 l (+.f64 (pow.f64 (sin.f64 kx) 2) (pow.f64 (sin.f64 ky) 2))))))
10.0ms	(sqrt.f64 (.f64 4 (.f64 l (*.f64 l (+.f64 (pow.f64 (sin.f64 kx) 2) (pow.f64 (sin.f64 ky) 2))))))
10.0ms	(*.f64 l (+.f64 (pow.f64 (sin.f64 kx) 2) (pow.f64 (sin.f64 ky) 2)))
9.0ms	(*.f64 l (+.f64 (pow.f64 (sin.f64 kx) 2) (pow.f64 (sin.f64 ky) 2)))

Compiler

Compiled 4051 to 2749 computations (32.1% saved)

series275.0ms (2.8%)

Error

Counts

4 → 44

Calls

4 calls:

90.0ms	(sqrt.f64 (/.f64 1/4 (.f64 l (.f64 l (+.f64 (pow.f64 (sin.f64 kx) 2) (pow.f64 (sin.f64 ky) 2))))))
58.0ms	(sqrt.f64 (.f64 4 (.f64 l (*.f64 l (+.f64 (pow.f64 (sin.f64 kx) 2) (pow.f64 (sin.f64 ky) 2))))))
48.0ms	(*.f64 l (+.f64 (pow.f64 (sin.f64 kx) 2) (pow.f64 (sin.f64 ky) 2)))
46.0ms	(*.f64 l (+.f64 (pow.f64 (sin.f64 kx) 2) (pow.f64 (sin.f64 ky) 2)))

Compiler

Compiled 4860 to 3608 computations (25.8% saved)

simplify108.0ms (1.1%)

Algorithm

1×	egg-herbie

Rules

480×	`associate-/r/_binary64`
322×	`times-frac_binary64`
307×	`distribute-rgt-in_binary64`
300×	`distribute-lft-in_binary64`
293×	`*-commutative_binary64`

Counts

127 → 94

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	156	2844
1	361	2639
2	1148	2615
3	3262	2609
4	5173	2609

prune102.0ms (1%)

Pruning

2 alts after pruning (0 fresh and 2 done)

	Pruned	Kept	Total
New	94	0	94
Fresh	0	0	0
Picked	0	1	1
Done	0	1	1
Total	94	2	96

Error

Counts

96 → 2

Alt Table

Status	Error	Program
	25.4b	(sqrt.f64 (+.f64 1/2 (/.f64 1/2 (+.f64 (/.f64 (sqrt.f64 (.f64 4 (.f64 l (.f64 l (+.f64 (pow.f64 (sin.f64 kx) 2) (pow.f64 (sin.f64 ky) 2)))))) Om) (.f64 1/2 (.f64 Om (sqrt.f64 (/.f64 1/4 (.f64 l (*.f64 l (+.f64 (pow.f64 (sin.f64 kx) 2) (pow.f64 (sin.f64 ky) 2))))))))))))
	0.8b	(sqrt.f64 (+.f64 1/2 (/.f64 1/2 (sqrt.f64 (+.f64 1 (.f64 (/.f64 (.f64 2 l) Om) (.f64 (+.f64 (pow.f64 (sin.f64 kx) 2) (pow.f64 (sin.f64 ky) 2)) (/.f64 (.f64 2 l) Om))))))))

Status

Error

Program

25.4b

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

0.8b

(sqrt.f64 (+.f64 1/2 (/.f64 1/2 (sqrt.f64 (+.f64 1 (*.f64 (/.f64 (*.f64 2 l) Om) (*.f64 (+.f64 (pow.f64 (sin.f64 kx) 2) (pow.f64 (sin.f64 ky) 2)) (/.f64 (*.f64 2 l) Om))))))))

Compiler

Compiled 3612 to 2450 computations (32.2% saved)

regimes2.8s (28.6%)

Accuracy

Total 0.6b remaining (95.7%)

Threshold costs 0.6b (95.7%)

Compiler

Compiled 73211 to 59541 computations (18.7% 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

end8.0ms (0.1%)

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

sample3.5s (35.9%)

Algorithm

1×

intervals

Results

1.5s	6317×	body	128	valid
904.0ms	744×	body	1024	valid
468.0ms	594×	body	512	valid
182.0ms	345×	body	256	valid

Compiler

Compiled 152 to 124 computations (18.4% saved)

Details

analyze956.0ms (9.8%)

sample123.0ms (1.3%)

simplify64.0ms (0.7%)

prune4.0ms (0%)

localize18.0ms (0.2%)

rewrite147.0ms (1.5%)

series327.0ms (3.4%)

simplify96.0ms (1%)

prune98.0ms (1%)

localize22.0ms (0.2%)

rewrite184.0ms (1.9%)

series412.0ms (4.2%)

simplify176.0ms (1.8%)

prune113.0ms (1.2%)

localize26.0ms (0.3%)

rewrite190.0ms (1.9%)

series275.0ms (2.8%)

simplify108.0ms (1.1%)

prune102.0ms (1%)

regimes2.8s (28.6%)

simplify3.0ms (0%)

end8.0ms (0.1%)

sample3.5s (35.9%)

Profiling