Details

analyze774.0ms (7.5%)

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)

sample96.0ms (0.9%)

Algorithm

1×

intervals

Results

38.0ms	207×	body	128	valid
19.0ms	22×	body	1024	valid
12.0ms	18×	body	512	valid
3.0ms	9×	body	256	valid

Compiler

Compiled 71 to 63 computations (11.3% saved)

simplify61.0ms (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)

localize27.0ms (0.3%)

Local error

Found 4 expressions with local error:

0.2b	(/.f64 (*.f64 2 l) Om)
0.2b	(pow.f64 (sin.f64 kx) 2)
2.2b	(.f64 (pow.f64 (/.f64 (.f64 2 l) Om) 2) (+.f64 (pow.f64 (sin.f64 kx) 2) (pow.f64 (sin.f64 ky) 2)))
7.1b	(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)))))

rewrite342.0ms (3.3%)

Algorithm

1×	rewrite-expression-head

Error

0.6b

Rules

22×	`add-exp-log_binary64`
20×	`add-sqr-sqrt_binary64`
17×	`*-un-lft-identity_binary64`
13×	`add-cube-cbrt_binary64` `unpow-prod-down_binary64`
12×	`associate-l_binary64`

Counts

4 → 93

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)))
4.0ms	(/.f64 (*.f64 2 l) Om)
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 kx) 2)

Compiler

Compiled 3128 to 2338 computations (25.3% saved)

series426.0ms (4.1%)

Error

0.0b

Counts

4 → 43

Calls

4 calls:

229.0ms	(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)))))
125.0ms	(.f64 (pow.f64 (/.f64 (.f64 2 l) Om) 2) (+.f64 (pow.f64 (sin.f64 kx) 2) (pow.f64 (sin.f64 ky) 2)))
23.0ms	(/.f64 (*.f64 2 l) Om)
10.0ms	(pow.f64 (sin.f64 kx) 2)

Compiler

Compiled 3921 to 3264 computations (16.8% saved)

simplify102.0ms (1%)

Algorithm

1×	egg-herbie

Rules

689×	`times-frac_binary64`
350×	`distribute-rgt-in_binary64`
325×	`unswap-sqr_binary64`
195×	`associate-l_binary64`
188×	`associate-r_binary64`

Counts

136 → 104

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	249	3568
1	621	3350
2	2145	3234
3	5049	3234

prune118.0ms (1.1%)

Pruning

3 alts after pruning (2 fresh and 1 done)

	Pruned	Kept	Total
New	102	2	104
Fresh	0	0	0
Picked	0	1	1
Done	0	0	0
Total	102	3	105

Error

0.0b

Counts

105 → 3

Alt Table

Status	Error	Program
▶	5.3b	(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))))))))
✓	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))))))))
	27.8b	(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 2415 to 1705 computations (29.4% saved)

localize22.0ms (0.2%)

Local error

Found 4 expressions with local error:

4.0b	(/.f64 (pow.f64 (sin.f64 kx) 2) Om)
4.5b	(.f64 (/.f64 (.f64 l l) Om) (+.f64 (/.f64 (pow.f64 (sin.f64 ky) 2) Om) (/.f64 (pow.f64 (sin.f64 kx) 2) Om)))
5.0b	(/.f64 (pow.f64 (sin.f64 ky) 2) Om)
7.0b	(/.f64 (*.f64 l l) Om)

rewrite357.0ms (3.4%)

Algorithm

1×	rewrite-expression-head

Error

0.0b

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:

47.0ms	(.f64 (/.f64 (.f64 l l) Om) (+.f64 (/.f64 (pow.f64 (sin.f64 ky) 2) Om) (/.f64 (pow.f64 (sin.f64 kx) 2) Om)))
5.0ms	(/.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)

series243.0ms (2.3%)

Error

0.0b

Counts

4 → 32

Calls

4 calls:

141.0ms	(.f64 (/.f64 (.f64 l l) Om) (+.f64 (/.f64 (pow.f64 (sin.f64 ky) 2) Om) (/.f64 (pow.f64 (sin.f64 kx) 2) Om)))
28.0ms	(/.f64 (pow.f64 (sin.f64 kx) 2) Om)
28.0ms	(/.f64 (pow.f64 (sin.f64 ky) 2) Om)
25.0ms	(/.f64 (*.f64 l l) Om)

Compiler

Compiled 2340 to 1870 computations (20.1% saved)

simplify151.0ms (1.5%)

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 → 127

Iterations

Useful iterations: 2 (0.0ms)

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

prune129.0ms (1.2%)

Pruning

2 alts after pruning (1 fresh and 1 done)

	Pruned	Kept	Total
New	126	1	127
Fresh	1	0	1
Picked	1	0	1
Done	0	1	1
Total	128	2	130

Error

0.0b

Counts

130 → 2

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))))))))
▶	4.5b	(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 (sin.f64 kx) (/.f64 (sin.f64 kx) Om)))))))))

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))))))))

▶

4.5b

(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 (sin.f64 kx) (/.f64 (sin.f64 kx) Om)))))))))

Compiler

Compiled 2607 to 1523 computations (41.6% saved)

localize21.0ms (0.2%)

Local error

Found 4 expressions with local error:

0.7b	(/.f64 1/2 (+.f64 1 (.f64 2 (.f64 (/.f64 (.f64 l l) Om) (+.f64 (/.f64 (pow.f64 (sin.f64 ky) 2) Om) (.f64 (sin.f64 kx) (/.f64 (sin.f64 kx) Om)))))))
4.5b	(.f64 (/.f64 (.f64 l l) Om) (+.f64 (/.f64 (pow.f64 (sin.f64 ky) 2) Om) (*.f64 (sin.f64 kx) (/.f64 (sin.f64 kx) Om))))
5.0b	(/.f64 (pow.f64 (sin.f64 ky) 2) Om)
7.0b	(/.f64 (*.f64 l l) Om)

rewrite235.0ms (2.3%)

Algorithm

1×	rewrite-expression-head

Error

0.0b

Rules

40×	`times-frac_binary64`
38×	`add-sqr-sqrt_binary64`
34×	`add-cube-cbrt_binary64` `*-un-lft-identity_binary64`
25×	`add-exp-log_binary64`
22×	`add-cbrt-cube_binary64`

Counts

4 → 135

Calls

4 calls:

19.0ms	(.f64 (/.f64 (.f64 l l) Om) (+.f64 (/.f64 (pow.f64 (sin.f64 ky) 2) Om) (*.f64 (sin.f64 kx) (/.f64 (sin.f64 kx) Om))))
5.0ms	(/.f64 (pow.f64 (sin.f64 ky) 2) Om)
5.0ms	(/.f64 1/2 (+.f64 1 (.f64 2 (.f64 (/.f64 (.f64 l l) Om) (+.f64 (/.f64 (pow.f64 (sin.f64 ky) 2) Om) (.f64 (sin.f64 kx) (/.f64 (sin.f64 kx) Om)))))))
5.0ms	(/.f64 (*.f64 l l) Om)

Compiler

Compiled 5584 to 2664 computations (52.3% saved)

series420.0ms (4.1%)

Error

0.0b

Counts

4 → 38

Calls

4 calls:

206.0ms	(/.f64 1/2 (+.f64 1 (.f64 2 (.f64 (/.f64 (.f64 l l) Om) (+.f64 (/.f64 (pow.f64 (sin.f64 ky) 2) Om) (.f64 (sin.f64 kx) (/.f64 (sin.f64 kx) Om)))))))
137.0ms	(.f64 (/.f64 (.f64 l l) Om) (+.f64 (/.f64 (pow.f64 (sin.f64 ky) 2) Om) (*.f64 (sin.f64 kx) (/.f64 (sin.f64 kx) Om))))
26.0ms	(/.f64 (pow.f64 (sin.f64 ky) 2) Om)
24.0ms	(/.f64 (*.f64 l l) Om)

Compiler

Compiled 3042 to 2429 computations (20.2% saved)

simplify135.0ms (1.3%)

Algorithm

1×	egg-herbie

Rules

622×	`distribute-rgt-in_binary64`
592×	`distribute-lft-in_binary64`
216×	`associate-l_binary64`
207×	`associate-*l/_binary64`
205×	`associate-r_binary64`

Counts

173 → 129

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	296	5277
1	736	4571
2	2530	4553
3	5481	4553

prune133.0ms (1.3%)

Pruning

2 alts after pruning (0 fresh and 2 done)

	Pruned	Kept	Total
New	129	0	129
Fresh	0	0	0
Picked	0	1	1
Done	0	1	1
Total	129	2	131

Error

0.0b

Counts

131 → 2

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))))))))
	4.5b	(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 (sin.f64 kx) (/.f64 (sin.f64 kx) Om)))))))))

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))))))))

4.5b

(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 (sin.f64 kx) (/.f64 (sin.f64 kx) Om)))))))))

Compiler

Compiled 3498 to 1964 computations (43.9% saved)

regimes3.7s (35.9%)

Accuracy

Total 0.3b remaining (39.8%)

Threshold costs 0.3b (39.8%)

Compiler

Compiled 77707 to 61368 computations (21% saved)

simplify3.0ms (0%)

Algorithm

1×	egg-herbie

Rules

3×	`*-commutative_binary64` `+-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)

sample2.8s (27.3%)

Algorithm

1×

intervals

Results

1.2s	6410×	body	128	valid
652.0ms	746×	body	1024	valid
363.0ms	581×	body	512	valid
106.0ms	263×	body	256	valid

Compiler

Compiled 133 to 110 computations (17.3% saved)

Details

analyze774.0ms (7.5%)

sample96.0ms (0.9%)

simplify61.0ms (0.6%)

prune5.0ms (0.1%)

localize27.0ms (0.3%)

rewrite342.0ms (3.3%)

series426.0ms (4.1%)

simplify102.0ms (1%)

prune118.0ms (1.1%)

localize22.0ms (0.2%)

rewrite357.0ms (3.4%)

series243.0ms (2.3%)

simplify151.0ms (1.5%)

prune129.0ms (1.2%)

localize21.0ms (0.2%)

rewrite235.0ms (2.3%)

series420.0ms (4.1%)

simplify135.0ms (1.3%)

prune133.0ms (1.3%)

regimes3.7s (35.9%)

simplify3.0ms (0%)

end8.0ms (0.1%)

sample2.8s (27.3%)

Profiling