Details

analyze2.6s (22.6%)

Algorithm

1×

Search

True	Other	False	Iter
0%	99.6%	0.4%	0
0%	99.6%	0.4%	1
0%	99.6%	0.4%	2
0%	99.6%	0.4%	3
0%	99.6%	0.4%	4
0%	99.6%	0.4%	5
0%	99.6%	0.4%	6
0%	99.6%	0.4%	7
0%	99.6%	0.4%	8
0%	99.6%	0.4%	9
0%	99.6%	0.4%	10
1.6%	98%	0.4%	11
1.6%	98%	0.4%	12
1.6%	98%	0.4%	13
1.6%	98%	0.4%	14

Compiler

Compiled 41 to 29 computations (29.3% saved)

sample1.8s (15.9%)

Results

1.8s

8256×

body

128

valid

Compiler

Compiled 82 to 58 computations (29.3% saved)

preprocess62.0ms (0.5%)

Algorithm

2×	egg-herbie

Rules

736×	`sub-neg_binary64`
625×	`div-sub_binary64`
369×	`fma-def_binary64`
287×	`+-commutative_binary64`
236×	`associate-+l+_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	468	1702
1	1013	1702
2	3250	1702
0	9	9
1	9	9

Stop Event

1×	unsound
1×	node limit

Symmetry

(sort Ev EAccept)

Compiler

Compiled 40 to 28 computations (30% saved)

simplify29.0ms (0.2%)

Algorithm

1×	egg-herbie

Rules

726×	`div-sub_binary64`
231×	`fma-def_binary64`
219×	`exp-diff_binary64`
206×	`exp-sum_binary64`
205×	`associate--r+_binary64`

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	28	46
1	57	46
2	160	44
3	522	44
4	1570	44
5	3701	44

Stop Event

1×	node limit

Counts

1 → 2

prune9.0ms (0.1%)

Pruning

1 alts after pruning (1 fresh and 0 done)

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

Error

0.0b

Counts

3 → 1

Alt Table

Status	Error	Program
▶	0.0b	(+.f64 (/.f64 NdChar (+.f64 1 (exp.f64 (/.f64 (+.f64 Vef (-.f64 mu (-.f64 Ec EDonor))) KbT)))) (/.f64 NaChar (+.f64 1 (exp.f64 (/.f64 (+.f64 Vef (+.f64 Ev (-.f64 EAccept mu))) KbT)))))

Compiler

Compiled 145 to 97 computations (33.1% saved)

localize19.0ms (0.2%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.0b	(/.f64 NdChar (+.f64 1 (exp.f64 (/.f64 (+.f64 Vef (-.f64 mu (-.f64 Ec EDonor))) KbT))))
✓	0.0b	(+.f64 1 (exp.f64 (/.f64 (+.f64 Vef (+.f64 Ev (-.f64 EAccept mu))) KbT)))
✓	0.0b	(/.f64 (+.f64 Vef (-.f64 mu (-.f64 Ec EDonor))) KbT)
✓	0.0b	(exp.f64 (/.f64 (+.f64 Vef (-.f64 mu (-.f64 Ec EDonor))) KbT))

series328.0ms (2.8%)

Counts

4 → 252

Calls

63 calls:

47.0ms	(/.f64 NdChar (+.f64 1 (exp.f64 (/.f64 (+.f64 Vef (-.f64 mu (-.f64 Ec EDonor))) KbT))))	KbT	-inf
45.0ms	(/.f64 NdChar (+.f64 1 (exp.f64 (/.f64 (+.f64 Vef (-.f64 mu (-.f64 Ec EDonor))) KbT))))	KbT	inf
20.0ms	(+.f64 1 (exp.f64 (/.f64 (+.f64 Vef (+.f64 Ev (-.f64 EAccept mu))) KbT)))	KbT	inf
18.0ms	(+.f64 1 (exp.f64 (/.f64 (+.f64 Vef (+.f64 Ev (-.f64 EAccept mu))) KbT)))	KbT	-inf
15.0ms	(exp.f64 (/.f64 (+.f64 Vef (-.f64 mu (-.f64 Ec EDonor))) KbT))	KbT	-inf

rewrite37.0ms (0.3%)

Algorithm

1×	batch-egg-rewrite

Rules

296×	`add-sqr-sqrt_binary64`
294×	`*-un-lft-identity_binary64`
294×	`pow1_binary64`
276×	`add-log-exp_binary64`
274×	`add-cbrt-cube_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	23	67
1	540	67

Stop Event

1×	node limit

Counts

4 → 39

simplify151.0ms (1.3%)

Algorithm

1×	egg-herbie

Rules

853×	`fma-def_binary64`
350×	`+-commutative_binary64`
332×	`*-commutative_binary64`
280×	`associate-+r+_binary64`
157×	`associate-/l*_binary64`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	1002	11669
1	3779	11477

Stop Event

1×	node limit

Counts

291 → 194

prune275.0ms (2.4%)

Pruning

3 alts after pruning (3 fresh and 0 done)

	Pruned	Kept	Total
New	191	3	194
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	192	3	195

Error

Counts

195 → 3

Alt Table

Status	Error	Program
	0.0b	(+.f64 (/.f64 NdChar (+.f64 1 (exp.f64 (/.f64 (+.f64 Vef (-.f64 mu (-.f64 Ec EDonor))) KbT)))) (/.f64 NaChar (cbrt.f64 (.f64 (.f64 (+.f64 1 (exp.f64 (/.f64 (+.f64 (+.f64 Vef Ev) (-.f64 EAccept mu)) KbT))) (+.f64 1 (exp.f64 (/.f64 (+.f64 (+.f64 Vef Ev) (-.f64 EAccept mu)) KbT)))) (+.f64 1 (exp.f64 (/.f64 (+.f64 (+.f64 Vef Ev) (-.f64 EAccept mu)) KbT)))))))
▶	0.0b	(+.f64 (/.f64 NdChar (+.f64 1 (*.f64 (sqrt.f64 (exp.f64 (/.f64 (-.f64 (+.f64 Vef mu) (-.f64 Ec EDonor)) KbT))) (sqrt.f64 (exp.f64 (/.f64 (-.f64 (+.f64 Vef mu) (-.f64 Ec EDonor)) KbT)))))) (/.f64 NaChar (+.f64 1 (exp.f64 (/.f64 (+.f64 Vef (+.f64 Ev (-.f64 EAccept mu))) KbT)))))
	28.4b	(+.f64 (-.f64 (/.f64 NdChar (+.f64 (exp.f64 (/.f64 (+.f64 mu (-.f64 EDonor Ec)) KbT)) 1)) (.f64 (/.f64 Vef KbT) (/.f64 (.f64 (exp.f64 (/.f64 (+.f64 mu (-.f64 EDonor Ec)) KbT)) NdChar) (pow.f64 (+.f64 (exp.f64 (/.f64 (+.f64 mu (-.f64 EDonor Ec)) KbT)) 1) 2)))) (/.f64 NaChar (+.f64 1 (exp.f64 (/.f64 (+.f64 Vef (+.f64 Ev (-.f64 EAccept mu))) KbT)))))

Compiler

Compiled 15780 to 6243 computations (60.4% saved)

localize22.0ms (0.2%)

Local error

Found 4 expressions with local error:

New	Error	Program
	0.0b	(+.f64 1 (exp.f64 (/.f64 (+.f64 Vef (+.f64 Ev (-.f64 EAccept mu))) KbT)))
✓	0.0b	(/.f64 NdChar (+.f64 1 (*.f64 (sqrt.f64 (exp.f64 (/.f64 (-.f64 (+.f64 Vef mu) (-.f64 Ec EDonor)) KbT))) (sqrt.f64 (exp.f64 (/.f64 (-.f64 (+.f64 Vef mu) (-.f64 Ec EDonor)) KbT))))))
✓	0.0b	(/.f64 (-.f64 (+.f64 Vef mu) (-.f64 Ec EDonor)) KbT)
✓	0.0b	(exp.f64 (/.f64 (-.f64 (+.f64 Vef mu) (-.f64 Ec EDonor)) KbT))

series281.0ms (2.4%)

Counts

3 → 192

Calls

48 calls:

49.0ms	(/.f64 NdChar (+.f64 1 (*.f64 (sqrt.f64 (exp.f64 (/.f64 (-.f64 (+.f64 Vef mu) (-.f64 Ec EDonor)) KbT))) (sqrt.f64 (exp.f64 (/.f64 (-.f64 (+.f64 Vef mu) (-.f64 Ec EDonor)) KbT))))))	KbT	-inf
44.0ms	(/.f64 NdChar (+.f64 1 (*.f64 (sqrt.f64 (exp.f64 (/.f64 (-.f64 (+.f64 Vef mu) (-.f64 Ec EDonor)) KbT))) (sqrt.f64 (exp.f64 (/.f64 (-.f64 (+.f64 Vef mu) (-.f64 Ec EDonor)) KbT))))))	KbT	inf
16.0ms	(exp.f64 (/.f64 (-.f64 (+.f64 Vef mu) (-.f64 Ec EDonor)) KbT))	KbT	-inf
13.0ms	(exp.f64 (/.f64 (-.f64 (+.f64 Vef mu) (-.f64 Ec EDonor)) KbT))	KbT	inf
9.0ms	(/.f64 NdChar (+.f64 1 (*.f64 (sqrt.f64 (exp.f64 (/.f64 (-.f64 (+.f64 Vef mu) (-.f64 Ec EDonor)) KbT))) (sqrt.f64 (exp.f64 (/.f64 (-.f64 (+.f64 Vef mu) (-.f64 Ec EDonor)) KbT))))))	Ec	inf

rewrite37.0ms (0.3%)

Algorithm

1×	batch-egg-rewrite

Rules

197×	`add-sqr-sqrt_binary64`
194×	`pow1_binary64`
193×	`*-un-lft-identity_binary64`
184×	`add-log-exp_binary64`
183×	`add-cbrt-cube_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	17	49
1	385	49

Stop Event

1×	node limit

Counts

3 → 83

simplify126.0ms (1.1%)

Algorithm

1×	egg-herbie

Rules

686×	`associate-/l*_binary64`
653×	`fma-def_binary64`
264×	`*-commutative_binary64`
233×	`+-commutative_binary64`
187×	`associate-+r+_binary64`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	742	8761
1	2870	8635

Stop Event

1×	node limit

Counts

275 → 193

prune620.0ms (5.4%)

Pruning

3 alts after pruning (2 fresh and 1 done)

	Pruned	Kept	Total
New	367	1	368
Fresh	1	1	2
Picked	0	1	1
Done	0	0	0
Total	368	3	371

Error

Counts

371 → 3

Alt Table

Status	Error	Program
▶	0.0b	(+.f64 (/.f64 NdChar (+.f64 1 (exp.f64 (/.f64 (+.f64 Vef (-.f64 mu (-.f64 Ec EDonor))) KbT)))) (/.f64 NaChar (cbrt.f64 (.f64 (.f64 (+.f64 1 (exp.f64 (/.f64 (+.f64 (+.f64 Vef Ev) (-.f64 EAccept mu)) KbT))) (+.f64 1 (exp.f64 (/.f64 (+.f64 (+.f64 Vef Ev) (-.f64 EAccept mu)) KbT)))) (+.f64 1 (exp.f64 (/.f64 (+.f64 (+.f64 Vef Ev) (-.f64 EAccept mu)) KbT)))))))
✓	0.0b	(+.f64 (/.f64 NdChar (+.f64 1 (*.f64 (sqrt.f64 (exp.f64 (/.f64 (-.f64 (+.f64 Vef mu) (-.f64 Ec EDonor)) KbT))) (sqrt.f64 (exp.f64 (/.f64 (-.f64 (+.f64 Vef mu) (-.f64 Ec EDonor)) KbT)))))) (/.f64 NaChar (+.f64 1 (exp.f64 (/.f64 (+.f64 Vef (+.f64 Ev (-.f64 EAccept mu))) KbT)))))
	0.1b	(+.f64 (pow.f64 (/.f64 (+.f64 1 (exp.f64 (/.f64 (+.f64 (-.f64 (+.f64 Vef mu) Ec) EDonor) KbT))) NdChar) -1) (/.f64 NaChar (+.f64 1 (exp.f64 (/.f64 (+.f64 Vef (+.f64 Ev (-.f64 EAccept mu))) KbT)))))

Compiler

Compiled 27473 to 9332 computations (66% saved)

localize22.0ms (0.2%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.0b	(*.f64 (+.f64 1 (exp.f64 (/.f64 (+.f64 (+.f64 Vef Ev) (-.f64 EAccept mu)) KbT))) (+.f64 1 (exp.f64 (/.f64 (+.f64 (+.f64 Vef Ev) (-.f64 EAccept mu)) KbT))))
✓	0.0b	(+.f64 1 (exp.f64 (/.f64 (+.f64 (+.f64 Vef Ev) (-.f64 EAccept mu)) KbT)))
	0.0b	(/.f64 (+.f64 Vef (-.f64 mu (-.f64 Ec EDonor))) KbT)
	0.0b	(exp.f64 (/.f64 (+.f64 Vef (-.f64 mu (-.f64 Ec EDonor))) KbT))

series165.0ms (1.4%)

Counts

2 → 120

Calls

30 calls:

30.0ms	(*.f64 (+.f64 1 (exp.f64 (/.f64 (+.f64 (+.f64 Vef Ev) (-.f64 EAccept mu)) KbT))) (+.f64 1 (exp.f64 (/.f64 (+.f64 (+.f64 Vef Ev) (-.f64 EAccept mu)) KbT))))	KbT	-inf
28.0ms	(*.f64 (+.f64 1 (exp.f64 (/.f64 (+.f64 (+.f64 Vef Ev) (-.f64 EAccept mu)) KbT))) (+.f64 1 (exp.f64 (/.f64 (+.f64 (+.f64 Vef Ev) (-.f64 EAccept mu)) KbT))))	KbT	inf
22.0ms	(+.f64 1 (exp.f64 (/.f64 (+.f64 (+.f64 Vef Ev) (-.f64 EAccept mu)) KbT)))	KbT	-inf
21.0ms	(+.f64 1 (exp.f64 (/.f64 (+.f64 (+.f64 Vef Ev) (-.f64 EAccept mu)) KbT)))	KbT	inf
6.0ms	(+.f64 1 (exp.f64 (/.f64 (+.f64 (+.f64 Vef Ev) (-.f64 EAccept mu)) KbT)))	Ev	0

rewrite75.0ms (0.7%)

Algorithm

1×	batch-egg-rewrite

Rules

292×	`log1p-udef_binary64`
173×	`add-sqr-sqrt_binary64`
170×	`*-un-lft-identity_binary64`
170×	`pow1_binary64`
161×	`add-log-exp_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	14	39
1	320	39
2	4953	39

Stop Event

1×	node limit

Counts

2 → 72

simplify91.0ms (0.8%)

Algorithm

1×	egg-herbie

Rules

629×	`fma-def_binary64`
485×	`times-frac_binary64`
314×	`associate-/r*_binary64`
313×	`associate-/l*_binary64`
260×	`+-commutative_binary64`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	561	6880
1	2147	6732

Stop Event

1×	node limit

Counts

192 → 164

prune700.0ms (6.1%)

Pruning

3 alts after pruning (1 fresh and 2 done)

	Pruned	Kept	Total
New	416	0	416
Fresh	0	1	1
Picked	0	1	1
Done	0	1	1
Total	416	3	419

Error

Counts

419 → 3

Alt Table

Status	Error	Program
✓	0.0b	(+.f64 (/.f64 NdChar (+.f64 1 (exp.f64 (/.f64 (+.f64 Vef (-.f64 mu (-.f64 Ec EDonor))) KbT)))) (/.f64 NaChar (cbrt.f64 (.f64 (.f64 (+.f64 1 (exp.f64 (/.f64 (+.f64 (+.f64 Vef Ev) (-.f64 EAccept mu)) KbT))) (+.f64 1 (exp.f64 (/.f64 (+.f64 (+.f64 Vef Ev) (-.f64 EAccept mu)) KbT)))) (+.f64 1 (exp.f64 (/.f64 (+.f64 (+.f64 Vef Ev) (-.f64 EAccept mu)) KbT)))))))
✓	0.0b	(+.f64 (/.f64 NdChar (+.f64 1 (*.f64 (sqrt.f64 (exp.f64 (/.f64 (-.f64 (+.f64 Vef mu) (-.f64 Ec EDonor)) KbT))) (sqrt.f64 (exp.f64 (/.f64 (-.f64 (+.f64 Vef mu) (-.f64 Ec EDonor)) KbT)))))) (/.f64 NaChar (+.f64 1 (exp.f64 (/.f64 (+.f64 Vef (+.f64 Ev (-.f64 EAccept mu))) KbT)))))
▶	0.1b	(+.f64 (pow.f64 (/.f64 (+.f64 1 (exp.f64 (/.f64 (+.f64 (-.f64 (+.f64 Vef mu) Ec) EDonor) KbT))) NdChar) -1) (/.f64 NaChar (+.f64 1 (exp.f64 (/.f64 (+.f64 Vef (+.f64 Ev (-.f64 EAccept mu))) KbT)))))

Compiler

Compiled 37872 to 12793 computations (66.2% saved)

localize21.0ms (0.2%)

Local error

Found 4 expressions with local error:

New	Error	Program
	0.0b	(+.f64 1 (exp.f64 (/.f64 (+.f64 Vef (+.f64 Ev (-.f64 EAccept mu))) KbT)))
✓	0.0b	(/.f64 (+.f64 (-.f64 (+.f64 Vef mu) Ec) EDonor) KbT)
✓	0.0b	(exp.f64 (/.f64 (+.f64 (-.f64 (+.f64 Vef mu) Ec) EDonor) KbT))
✓	0.3b	(pow.f64 (/.f64 (+.f64 1 (exp.f64 (/.f64 (+.f64 (-.f64 (+.f64 Vef mu) Ec) EDonor) KbT))) NdChar) -1)

series520.0ms (4.5%)

Counts

3 → 192

Calls

48 calls:

167.0ms	(pow.f64 (/.f64 (+.f64 1 (exp.f64 (/.f64 (+.f64 (-.f64 (+.f64 Vef mu) Ec) EDonor) KbT))) NdChar) -1)	KbT	inf
156.0ms	(pow.f64 (/.f64 (+.f64 1 (exp.f64 (/.f64 (+.f64 (-.f64 (+.f64 Vef mu) Ec) EDonor) KbT))) NdChar) -1)	KbT	-inf
14.0ms	(exp.f64 (/.f64 (+.f64 (-.f64 (+.f64 Vef mu) Ec) EDonor) KbT))	KbT	-inf
13.0ms	(exp.f64 (/.f64 (+.f64 (-.f64 (+.f64 Vef mu) Ec) EDonor) KbT))	KbT	inf
11.0ms	(pow.f64 (/.f64 (+.f64 1 (exp.f64 (/.f64 (+.f64 (-.f64 (+.f64 Vef mu) Ec) EDonor) KbT))) NdChar) -1)	Vef	inf

rewrite40.0ms (0.3%)

Algorithm

1×	batch-egg-rewrite

Rules

203×	`add-sqr-sqrt_binary64`
199×	`pow1_binary64`
198×	`*-un-lft-identity_binary64`
189×	`add-log-exp_binary64`
188×	`add-cbrt-cube_binary64`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	17	52
1	382	49

Stop Event

1×	node limit

Counts

3 → 81

simplify133.0ms (1.2%)

Algorithm

1×	egg-herbie

Rules

398×	`*-commutative_binary64`
327×	`+-commutative_binary64`
281×	`associate-+r+_binary64`
258×	`fma-def_binary64`
179×	`associate-*r/_binary64`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	1041	10759
1	4169	10638

Stop Event

1×	node limit

Counts

273 → 192

prune413.0ms (3.6%)

Pruning

3 alts after pruning (0 fresh and 3 done)

	Pruned	Kept	Total
New	248	0	248
Fresh	0	0	0
Picked	0	1	1
Done	0	2	2
Total	248	3	251

Error

Counts

251 → 3

Alt Table

Status	Error	Program
✓	0.0b	(+.f64 (/.f64 NdChar (+.f64 1 (exp.f64 (/.f64 (+.f64 Vef (-.f64 mu (-.f64 Ec EDonor))) KbT)))) (/.f64 NaChar (cbrt.f64 (.f64 (.f64 (+.f64 1 (exp.f64 (/.f64 (+.f64 (+.f64 Vef Ev) (-.f64 EAccept mu)) KbT))) (+.f64 1 (exp.f64 (/.f64 (+.f64 (+.f64 Vef Ev) (-.f64 EAccept mu)) KbT)))) (+.f64 1 (exp.f64 (/.f64 (+.f64 (+.f64 Vef Ev) (-.f64 EAccept mu)) KbT)))))))
✓	0.0b	(+.f64 (/.f64 NdChar (+.f64 1 (*.f64 (sqrt.f64 (exp.f64 (/.f64 (-.f64 (+.f64 Vef mu) (-.f64 Ec EDonor)) KbT))) (sqrt.f64 (exp.f64 (/.f64 (-.f64 (+.f64 Vef mu) (-.f64 Ec EDonor)) KbT)))))) (/.f64 NaChar (+.f64 1 (exp.f64 (/.f64 (+.f64 Vef (+.f64 Ev (-.f64 EAccept mu))) KbT)))))
✓	0.1b	(+.f64 (pow.f64 (/.f64 (+.f64 1 (exp.f64 (/.f64 (+.f64 (-.f64 (+.f64 Vef mu) Ec) EDonor) KbT))) NdChar) -1) (/.f64 NaChar (+.f64 1 (exp.f64 (/.f64 (+.f64 Vef (+.f64 Ev (-.f64 EAccept mu))) KbT)))))

Compiler

Compiled 20612 to 8775 computations (57.4% saved)

regimes2.8s (24.4%)

Accuracy

Total 0.0b remaining (17.3%)

Threshold costs 0.0b (17.3%)

Counts

210 → 1

Compiler

Compiled 96780 to 63898 computations (34% saved)

simplify3.0ms (0%)

Algorithm

1×	egg-herbie

Rules

13×	`+-commutative_binary64`
8×	`sub-neg_binary64`
6×	`cancel-sign-sub-inv_binary64`
5×	`neg-sub0_binary64`
5×	`neg-mul-1_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	28	48
1	42	48
2	55	48
3	70	48
4	88	48
5	94	48

Stop Event

1×

saturated

end92.0ms (0.8%)

Stop Event

1×

done

Remove

(sort Ev EAccept)

Compiler

Compiled 316 to 201 computations (36.4% saved)

Details

analyze2.6s (22.6%)

sample1.8s (15.9%)

preprocess62.0ms (0.5%)

simplify29.0ms (0.2%)

prune9.0ms (0.1%)

localize19.0ms (0.2%)

series328.0ms (2.8%)

rewrite37.0ms (0.3%)

simplify151.0ms (1.3%)

prune275.0ms (2.4%)

localize22.0ms (0.2%)

series281.0ms (2.4%)

rewrite37.0ms (0.3%)

simplify126.0ms (1.1%)

prune620.0ms (5.4%)

localize22.0ms (0.2%)

series165.0ms (1.4%)

rewrite75.0ms (0.7%)

simplify91.0ms (0.8%)

prune700.0ms (6.1%)

localize21.0ms (0.2%)

series520.0ms (4.5%)

rewrite40.0ms (0.3%)

simplify133.0ms (1.2%)

prune413.0ms (3.6%)

regimes2.8s (24.4%)

simplify3.0ms (0%)

end92.0ms (0.8%)

Profiling