Details

analyze982.0ms (10.9%)

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)

sample115.0ms (1.3%)

Algorithm

1×

intervals

Results

54.0ms	208×	body	128	valid
23.0ms	20×	body	1024	valid
12.0ms	15×	body	512	valid
6.0ms	13×	body	256	valid

Compiler

Compiled 71 to 63 computations (11.3% saved)

simplify60.0ms (0.7%)

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 → 1

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	0	1	1
Fresh	1	0	1
Picked	0	0	0
Done	0	0	0
Total	1	1	2

Error

1.3b

Counts

2 → 1

Alt Table

Status	Error	Program
▶	1.3b	(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 84 to 72 computations (14.3% saved)

localize18.0ms (0.2%)

Local error

Found 4 expressions with local error:

0.3b	(pow.f64 (/.f64 (*.f64 2 l) Om) 2)
0.3b	(pow.f64 (sin.f64 ky) 2)
2.6b	(fma.f64 (pow.f64 (/.f64 (*.f64 2 l) Om) 2) (+.f64 (pow.f64 (sin.f64 kx) 2) (pow.f64 (sin.f64 ky) 2)) 1)
8.2b	(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))

rewrite198.0ms (2.2%)

Algorithm

1×	rewrite-expression-head

Error

1.3b

Rules

27×	`add-cube-cbrt_binary64`
16×	`add-sqr-sqrt_binary64`
14×	`pow1_binary64`
12×	`add-exp-log_binary64`
12×	`add-cbrt-cube_binary64`

Counts

4 → 151

Calls

4 calls:

15.0ms	(pow.f64 (sin.f64 ky) 2)
14.0ms	(pow.f64 (/.f64 (*.f64 2 l) Om) 2)
12.0ms	(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))
10.0ms	(fma.f64 (pow.f64 (/.f64 (*.f64 2 l) Om) 2) (+.f64 (pow.f64 (sin.f64 kx) 2) (pow.f64 (sin.f64 ky) 2)) 1)

Compiler

Compiled 3786 to 2836 computations (25.1% saved)

series315.0ms (3.5%)

Error

0.2b

Counts

4 → 51

Calls

4 calls:

156.0ms	(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))
103.0ms	(fma.f64 (pow.f64 (/.f64 (*.f64 2 l) Om) 2) (+.f64 (pow.f64 (sin.f64 kx) 2) (pow.f64 (sin.f64 ky) 2)) 1)
19.0ms	(pow.f64 (/.f64 (*.f64 2 l) Om) 2)
7.0ms	(pow.f64 (sin.f64 ky) 2)

Compiler

Compiled 4575 to 3796 computations (17% saved)

simplify100.0ms (1.1%)

Algorithm

1×	egg-herbie

Rules

515×	`fma-def_binary64`
385×	`associate-/l*_binary64`
373×	`times-frac_binary64`
231×	`distribute-rgt-in_binary64`
218×	`distribute-lft-in_binary64`

Counts

202 → 98

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	221	4281
1	503	3900
2	1524	3521
3	5039	3521

prune69.0ms (0.8%)

Pruning

3 alts after pruning (2 fresh and 1 done)

	Pruned	Kept	Total
New	96	2	98
Fresh	0	0	0
Picked	0	1	1
Done	0	0	0
Total	96	3	99

Error

0.2b

Counts

99 → 3

Alt Table

Status	Error	Program
▶	1.3b	(sqrt.f64 (+.f64 1/2 (/.f64 1/2 (cbrt.f64 (pow.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) 3/2)))))
✓	1.3b	(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)))))
	28.9b	(sqrt.f64 (+.f64 1/2 (/.f64 1/2 (fma.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 1932 to 1380 computations (28.6% saved)

localize23.0ms (0.3%)

Local error

Found 4 expressions with local error:

0.3b	(pow.f64 (/.f64 (*.f64 2 l) Om) 2)
0.3b	(pow.f64 (sin.f64 ky) 2)
2.6b	(fma.f64 (pow.f64 (/.f64 (*.f64 2 l) Om) 2) (+.f64 (pow.f64 (sin.f64 kx) 2) (pow.f64 (sin.f64 ky) 2)) 1)
13.8b	(cbrt.f64 (pow.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) 3/2))

rewrite207.0ms (2.3%)

Algorithm

1×	rewrite-expression-head

Error

0.2b

Rules

28×	`add-cube-cbrt_binary64`
14×	`add-sqr-sqrt_binary64`
12×	`add-exp-log_binary64`
12×	`pow1_binary64`
12×	`log1p-expm1-u_binary64`

Counts

4 → 147

Calls

4 calls:

15.0ms	(pow.f64 (sin.f64 ky) 2)
14.0ms	(pow.f64 (/.f64 (*.f64 2 l) Om) 2)
10.0ms	(cbrt.f64 (pow.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) 3/2))
10.0ms	(fma.f64 (pow.f64 (/.f64 (*.f64 2 l) Om) 2) (+.f64 (pow.f64 (sin.f64 kx) 2) (pow.f64 (sin.f64 ky) 2)) 1)

Compiler

Compiled 3947 to 3015 computations (23.6% saved)

series322.0ms (3.6%)

Error

Counts

4 → 51

Calls

4 calls:

154.0ms	(cbrt.f64 (pow.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) 3/2))
107.0ms	(fma.f64 (pow.f64 (/.f64 (*.f64 2 l) Om) 2) (+.f64 (pow.f64 (sin.f64 kx) 2) (pow.f64 (sin.f64 ky) 2)) 1)
21.0ms	(pow.f64 (/.f64 (*.f64 2 l) Om) 2)
7.0ms	(pow.f64 (sin.f64 ky) 2)

Compiler

Compiled 4778 to 3983 computations (16.6% saved)

simplify136.0ms (1.5%)

Algorithm

1×	egg-herbie

Rules

509×	`fma-def_binary64`
385×	`associate-/l*_binary64`
373×	`times-frac_binary64`
263×	`fma-neg_binary64`
214×	`distribute-rgt-in_binary64`

Counts

198 → 90

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	228	4361
1	521	4014
2	1527	3701
3	4988	3701
4	5121	3701

prune63.0ms (0.7%)

Pruning

3 alts after pruning (1 fresh and 2 done)

	Pruned	Kept	Total
New	90	0	90
Fresh	0	1	1
Picked	0	1	1
Done	0	1	1
Total	90	3	93

Error

0.2b

Counts

93 → 3

Alt Table

Status	Error	Program
✓	1.3b	(sqrt.f64 (+.f64 1/2 (/.f64 1/2 (cbrt.f64 (pow.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) 3/2)))))
✓	1.3b	(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)))))
▶	28.9b	(sqrt.f64 (+.f64 1/2 (/.f64 1/2 (fma.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 1840 to 1326 computations (27.9% saved)

localize30.0ms (0.3%)

Local error

Found 4 expressions with local error:

4.4b	(/.f64 (pow.f64 (sin.f64 kx) 2) Om)
4.4b	(/.f64 (pow.f64 (sin.f64 kx) 2) Om)
24.4b	(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)))))
25.2b	(sqrt.f64 (*.f64 (/.f64 4 Om) (+.f64 (/.f64 (pow.f64 (sin.f64 ky) 2) Om) (/.f64 (pow.f64 (sin.f64 kx) 2) Om))))

rewrite275.0ms (3.1%)

Algorithm

1×	rewrite-expression-head

Error

0.2b

Rules

43×	`add-cube-cbrt_binary64`
20×	`add-sqr-sqrt_binary64`
20×	`add-cbrt-cube_binary64`
16×	`pow1_binary64`
12×	`add-exp-log_binary64`

Counts

4 → 174

Calls

4 calls:

17.0ms	(/.f64 (pow.f64 (sin.f64 kx) 2) Om)
15.0ms	(/.f64 (pow.f64 (sin.f64 kx) 2) Om)
12.0ms	(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)))))
12.0ms	(sqrt.f64 (*.f64 (/.f64 4 Om) (+.f64 (/.f64 (pow.f64 (sin.f64 ky) 2) Om) (/.f64 (pow.f64 (sin.f64 kx) 2) Om))))

Compiler

Compiled 7827 to 5214 computations (33.4% saved)

series271.0ms (3%)

Error

0.2b

Counts

4 → 35

Calls

4 calls:

108.0ms	(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)))))
92.0ms	(sqrt.f64 (*.f64 (/.f64 4 Om) (+.f64 (/.f64 (pow.f64 (sin.f64 ky) 2) Om) (/.f64 (pow.f64 (sin.f64 kx) 2) Om))))
24.0ms	(/.f64 (pow.f64 (sin.f64 kx) 2) Om)
23.0ms	(/.f64 (pow.f64 (sin.f64 kx) 2) Om)

Compiler

Compiled 4326 to 3125 computations (27.8% saved)

simplify121.0ms (1.3%)

Algorithm

1×	egg-herbie

Rules

666×	`associate-/l*_binary64`
576×	`associate-/r*_binary64`
291×	`associate-*l/_binary64`
268×	`associate-*r/_binary64`
263×	`fma-def_binary64`

Counts

209 → 88

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	185	3434
1	406	3135
2	1273	3118
3	4817	3118
4	4981	3118

prune101.0ms (1.1%)

Pruning

3 alts after pruning (0 fresh and 3 done)

	Pruned	Kept	Total
New	88	0	88
Fresh	0	0	0
Picked	0	1	1
Done	0	2	2
Total	88	3	91

Error

0.2b

Counts

91 → 3

Alt Table

Status	Error	Program
	1.3b	(sqrt.f64 (+.f64 1/2 (/.f64 1/2 (cbrt.f64 (pow.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) 3/2)))))
	1.3b	(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)))))
	28.9b	(sqrt.f64 (+.f64 1/2 (/.f64 1/2 (fma.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 4075 to 2728 computations (33.1% saved)

regimes1.4s (15.2%)

Accuracy

Total 0.1b remaining (26.9%)

Threshold costs 0.1b (26.9%)

Compiler

Compiled 37614 to 29440 computations (21.7% saved)

bsearch3.0ms (0%)

Compiler: Compiled 11 to 9 computations (18.2% saved)

simplify5.0ms (0.1%)

Algorithm

1×	egg-herbie

Rules

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

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	42	129
1	51	129
2	50	129

end11.0ms (0.1%)

Remove: (sort kx ky)
Compiler: Compiled 264 to 198 computations (25% saved)

sample4.2s (46.6%)

Algorithm

1×

intervals

Results

2.1s	6362×	body	128	valid
973.0ms	787×	body	1024	valid
436.0ms	542×	body	512	valid
182.0ms	309×	body	256	valid

Compiler

Compiled 237 to 189 computations (20.3% saved)

Details

analyze982.0ms (10.9%)

sample115.0ms (1.3%)

simplify60.0ms (0.7%)

prune4.0ms (0%)

localize18.0ms (0.2%)

rewrite198.0ms (2.2%)

series315.0ms (3.5%)

simplify100.0ms (1.1%)

prune69.0ms (0.8%)

localize23.0ms (0.3%)

rewrite207.0ms (2.3%)

series322.0ms (3.6%)

simplify136.0ms (1.5%)

prune63.0ms (0.7%)

localize30.0ms (0.3%)

rewrite275.0ms (3.1%)

series271.0ms (3%)

simplify121.0ms (1.3%)

prune101.0ms (1.1%)

regimes1.4s (15.2%)

bsearch3.0ms (0%)

simplify5.0ms (0.1%)

end11.0ms (0.1%)

sample4.2s (46.6%)

Profiling