Details

analyze992.0ms (6.3%)

Algorithm

1×

Search

True	Other	False	Iter
0%	99.7%	0.3%	0
0%	99.7%	0.3%	1
0%	99.7%	0.3%	2
0%	99.7%	0.3%	3
0%	99.7%	0.3%	4
0%	99.7%	0.3%	5
0%	99.7%	0.3%	6
0%	99.7%	0.3%	7
0%	99.7%	0.3%	8
0%	99.7%	0.3%	9
0%	49.9%	50.1%	10
0%	49.9%	50.1%	11
0%	49.9%	50.1%	12
0%	49.9%	50.1%	13
0%	49.9%	50.1%	14

Compiler

Compiled 25 to 18 computations (28% saved)

sample3.4s (21.5%)

Infinites

41.7% of outputs are infinite.

Results

1.4s	8140×	body	128	invalid
1.4s	7667×	body	128	valid
147.0ms	259×	body	512	valid
86.0ms	240×	body	256	valid
73.0ms	90×	body	1024	valid

Compiler

Compiled 74 to 53 computations (28.4% saved)

simplify64.0ms (0.4%)

Algorithm

1×	egg-herbie

Rules

784×	`fma-def_binary64`
557×	`associate-/l*_binary64`
456×	`unswap-sqr_binary64`
365×	`*-commutative_binary64`
332×	`fma-neg_binary64`

Counts

1 → 2

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	18	26
1	34	25
2	73	25
3	158	25
4	405	25
5	1252	25
6	2771	25
7	4527	25
8	5117	25

prune6.0ms (0%)

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

0.8b

Counts

3 → 1

Alt Table

Status	Error	Program
▶	0.8b	(.f64 x (exp.f64 (fma.f64 y (-.f64 (log.f64 z) t) (.f64 a (-.f64 (log1p.f64 (neg.f64 z)) b)))))

Compiler

Compiled 84 to 54 computations (35.7% saved)

localize27.0ms (0.2%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.0b	(.f64 x (exp.f64 (fma.f64 y (-.f64 (log.f64 z) t) (.f64 a (-.f64 (log1p.f64 (neg.f64 z)) b)))))
✓	0.0b	(*.f64 a (-.f64 (log1p.f64 (neg.f64 z)) b))
✓	0.1b	(exp.f64 (fma.f64 y (-.f64 (log.f64 z) t) (*.f64 a (-.f64 (log1p.f64 (neg.f64 z)) b))))
✓	0.8b	(fma.f64 y (-.f64 (log.f64 z) t) (*.f64 a (-.f64 (log1p.f64 (neg.f64 z)) b)))

series1.4s (8.8%)

Counts

4 → 164

Calls

4 calls:

602.0ms	(.f64 x (exp.f64 (fma.f64 y (-.f64 (log.f64 z) t) (.f64 a (-.f64 (log1p.f64 (neg.f64 z)) b)))))
412.0ms	(fma.f64 y (-.f64 (log.f64 z) t) (*.f64 a (-.f64 (log1p.f64 (neg.f64 z)) b)))
321.0ms	(*.f64 a (-.f64 (log1p.f64 (neg.f64 z)) b))
47.0ms	(exp.f64 (fma.f64 y (-.f64 (log.f64 z) t) (*.f64 a (-.f64 (log1p.f64 (neg.f64 z)) b))))

rewrite20.0ms (0.1%)

Algorithm

1×	rewrite-expression-head

Rules

29×	`add-sqr-sqrt_binary64`
25×	`*-un-lft-identity_binary64`
23×	`add-cube-cbrt_binary64`
18×	`prod-diff_binary64`
13×	`distribute-lft-in_binary64`

Counts

4 → 95

Calls

4 calls:

8.0ms	(*.f64 a (-.f64 (log1p.f64 (neg.f64 z)) b))
4.0ms	(.f64 x (exp.f64 (fma.f64 y (-.f64 (log.f64 z) t) (.f64 a (-.f64 (log1p.f64 (neg.f64 z)) b)))))
1.0ms	(exp.f64 (fma.f64 y (-.f64 (log.f64 z) t) (*.f64 a (-.f64 (log1p.f64 (neg.f64 z)) b))))
0.0ms	(fma.f64 y (-.f64 (log.f64 z) t) (*.f64 a (-.f64 (log1p.f64 (neg.f64 z)) b)))

simplify223.0ms (1.4%)

Algorithm

1×	egg-herbie

Rules

789×	`fma-def_binary64`
292×	`*-commutative_binary64`
185×	`sub-neg_binary64`
182×	`times-frac_binary64`
175×	`associate-r_binary64`

Counts

259 → 297

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	713	11258
1	2189	10188
2	4843	10188
3	4989	10188

prune395.0ms (2.5%)

Pruning

6 alts after pruning (6 fresh and 0 done)

	Pruned	Kept	Total
New	291	6	297
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	292	6	298

Error

0.0b

Counts

298 → 6

Alt Table

Status	Error	Program
	19.1b	(.f64 (sqrt.f64 (.f64 x (exp.f64 (fma.f64 y (-.f64 (log.f64 z) t) (.f64 a (-.f64 (log1p.f64 (neg.f64 z)) b)))))) (sqrt.f64 (.f64 x (exp.f64 (fma.f64 y (-.f64 (log.f64 z) t) (*.f64 a (-.f64 (log1p.f64 (neg.f64 z)) b)))))))
	0.8b	(.f64 x (pow.f64 (E.f64) (fma.f64 y (-.f64 (log.f64 z) t) (.f64 a (-.f64 (log1p.f64 (neg.f64 z)) b)))))
	0.8b	(.f64 x (.f64 (.f64 (cbrt.f64 (exp.f64 (fma.f64 y (-.f64 (log.f64 z) t) (.f64 a (-.f64 (log1p.f64 (neg.f64 z)) b))))) (cbrt.f64 (exp.f64 (fma.f64 y (-.f64 (log.f64 z) t) (.f64 a (-.f64 (log1p.f64 (neg.f64 z)) b)))))) (cbrt.f64 (exp.f64 (fma.f64 y (-.f64 (log.f64 z) t) (.f64 a (-.f64 (log1p.f64 (neg.f64 z)) b)))))))
	0.8b	(.f64 x (pow.f64 (exp.f64 (.f64 (cbrt.f64 (fma.f64 y (-.f64 (log.f64 z) t) (.f64 a (-.f64 (log1p.f64 (neg.f64 z)) b)))) (cbrt.f64 (fma.f64 y (-.f64 (log.f64 z) t) (.f64 a (-.f64 (log1p.f64 (neg.f64 z)) b)))))) (cbrt.f64 (fma.f64 y (-.f64 (log.f64 z) t) (*.f64 a (-.f64 (log1p.f64 (neg.f64 z)) b))))))
▶	0.8b	(.f64 x (expm1.f64 (log1p.f64 (exp.f64 (fma.f64 y (-.f64 (log.f64 z) t) (.f64 a (-.f64 (log1p.f64 (neg.f64 z)) b)))))))
	1.6b	(.f64 x (exp.f64 (-.f64 (.f64 (log.f64 z) y) (fma.f64 a b (*.f64 y t)))))

Compiler

Compiled 14077 to 5317 computations (62.2% saved)

localize20.0ms (0.1%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.0b	(expm1.f64 (log1p.f64 (exp.f64 (fma.f64 y (-.f64 (log.f64 z) t) (*.f64 a (-.f64 (log1p.f64 (neg.f64 z)) b))))))
	0.1b	(exp.f64 (fma.f64 y (-.f64 (log.f64 z) t) (*.f64 a (-.f64 (log1p.f64 (neg.f64 z)) b))))
✓	0.5b	(log1p.f64 (exp.f64 (fma.f64 y (-.f64 (log.f64 z) t) (*.f64 a (-.f64 (log1p.f64 (neg.f64 z)) b)))))
	0.8b	(fma.f64 y (-.f64 (log.f64 z) t) (*.f64 a (-.f64 (log1p.f64 (neg.f64 z)) b)))

series2.3s (14.6%)

Counts

2 → 120

Calls

2 calls:

2.2s

(log1p.f64 (exp.f64 (fma.f64 y (-.f64 (log.f64 z) t) (*.f64 a (-.f64 (log1p.f64 (neg.f64 z)) b)))))

80.0ms

(expm1.f64 (log1p.f64 (exp.f64 (fma.f64 y (-.f64 (log.f64 z) t) (*.f64 a (-.f64 (log1p.f64 (neg.f64 z)) b))))))

rewrite3.0ms (0%)

Algorithm

1×	rewrite-expression-head

Rules

3×	`expm1-log1p-u_binary64`
2×	`*-un-lft-identity_binary64`
2×	`add-sqr-sqrt_binary64`
2×	`add-cube-cbrt_binary64`
2×	`add-cbrt-cube_binary64`

Counts

2 → 22

Calls

2 calls:

1.0ms

(log1p.f64 (exp.f64 (fma.f64 y (-.f64 (log.f64 z) t) (*.f64 a (-.f64 (log1p.f64 (neg.f64 z)) b)))))

1.0ms

(expm1.f64 (log1p.f64 (exp.f64 (fma.f64 y (-.f64 (log.f64 z) t) (*.f64 a (-.f64 (log1p.f64 (neg.f64 z)) b))))))

simplify411.0ms (2.6%)

Algorithm

1×	egg-herbie

Rules

612×	`times-frac_binary64`
589×	`fma-def_binary64`
272×	`*-commutative_binary64`
165×	`+-commutative_binary64`
145×	`sub-neg_binary64`

Counts

142 → 142

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	687	14026
1	2410	12992
2	4969	12992
3	4992	12992

prune965.0ms (6.1%)

Pruning

6 alts after pruning (5 fresh and 1 done)

	Pruned	Kept	Total
New	270	0	270
Fresh	0	5	5
Picked	0	1	1
Done	0	0	0
Total	270	6	276

Error

0.0b

Counts

276 → 6

Alt Table

Status	Error	Program
	19.1b	(.f64 (sqrt.f64 (.f64 x (exp.f64 (fma.f64 y (-.f64 (log.f64 z) t) (.f64 a (-.f64 (log1p.f64 (neg.f64 z)) b)))))) (sqrt.f64 (.f64 x (exp.f64 (fma.f64 y (-.f64 (log.f64 z) t) (*.f64 a (-.f64 (log1p.f64 (neg.f64 z)) b)))))))
▶	0.8b	(.f64 x (pow.f64 (E.f64) (fma.f64 y (-.f64 (log.f64 z) t) (.f64 a (-.f64 (log1p.f64 (neg.f64 z)) b)))))
	0.8b	(.f64 x (.f64 (.f64 (cbrt.f64 (exp.f64 (fma.f64 y (-.f64 (log.f64 z) t) (.f64 a (-.f64 (log1p.f64 (neg.f64 z)) b))))) (cbrt.f64 (exp.f64 (fma.f64 y (-.f64 (log.f64 z) t) (.f64 a (-.f64 (log1p.f64 (neg.f64 z)) b)))))) (cbrt.f64 (exp.f64 (fma.f64 y (-.f64 (log.f64 z) t) (.f64 a (-.f64 (log1p.f64 (neg.f64 z)) b)))))))
	0.8b	(.f64 x (pow.f64 (exp.f64 (.f64 (cbrt.f64 (fma.f64 y (-.f64 (log.f64 z) t) (.f64 a (-.f64 (log1p.f64 (neg.f64 z)) b)))) (cbrt.f64 (fma.f64 y (-.f64 (log.f64 z) t) (.f64 a (-.f64 (log1p.f64 (neg.f64 z)) b)))))) (cbrt.f64 (fma.f64 y (-.f64 (log.f64 z) t) (*.f64 a (-.f64 (log1p.f64 (neg.f64 z)) b))))))
✓	0.8b	(.f64 x (expm1.f64 (log1p.f64 (exp.f64 (fma.f64 y (-.f64 (log.f64 z) t) (.f64 a (-.f64 (log1p.f64 (neg.f64 z)) b)))))))
	1.6b	(.f64 x (exp.f64 (-.f64 (.f64 (log.f64 z) y) (fma.f64 a b (*.f64 y t)))))

Compiler

Compiled 23472 to 10117 computations (56.9% saved)

localize29.0ms (0.2%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.0b	(.f64 x (pow.f64 (E.f64) (fma.f64 y (-.f64 (log.f64 z) t) (.f64 a (-.f64 (log1p.f64 (neg.f64 z)) b)))))
	0.0b	(*.f64 a (-.f64 (log1p.f64 (neg.f64 z)) b))
✓	0.1b	(pow.f64 (E.f64) (fma.f64 y (-.f64 (log.f64 z) t) (*.f64 a (-.f64 (log1p.f64 (neg.f64 z)) b))))
	0.8b	(fma.f64 y (-.f64 (log.f64 z) t) (*.f64 a (-.f64 (log1p.f64 (neg.f64 z)) b)))

series1.3s (8.5%)

Counts

2 → 132

Calls

2 calls:

1.2s	(.f64 x (pow.f64 (E.f64) (fma.f64 y (-.f64 (log.f64 z) t) (.f64 a (-.f64 (log1p.f64 (neg.f64 z)) b)))))
183.0ms	(pow.f64 (E.f64) (fma.f64 y (-.f64 (log.f64 z) t) (*.f64 a (-.f64 (log1p.f64 (neg.f64 z)) b))))

rewrite17.0ms (0.1%)

Algorithm

1×	rewrite-expression-head

Rules

12×	`add-sqr-sqrt_binary64`
9×	`add-exp-log_binary64`
8×	`associate-r_binary64`
7×	`*-un-lft-identity_binary64`
7×	`unpow-prod-down_binary64`

Counts

2 → 50

Calls

2 calls:

9.0ms	(.f64 x (pow.f64 (E.f64) (fma.f64 y (-.f64 (log.f64 z) t) (.f64 a (-.f64 (log1p.f64 (neg.f64 z)) b)))))
3.0ms	(pow.f64 (E.f64) (fma.f64 y (-.f64 (log.f64 z) t) (*.f64 a (-.f64 (log1p.f64 (neg.f64 z)) b))))

simplify230.0ms (1.5%)

Algorithm

1×	egg-herbie

Rules

702×	`associate-l_binary64`
567×	`fma-def_binary64`
250×	`*-commutative_binary64`
170×	`times-frac_binary64`
169×	`cancel-sign-sub-inv_binary64`

Counts

182 → 189

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	524	10089
1	1716	9313
2	4966	9313
3	5018	9313

prune451.0ms (2.9%)

Pruning

6 alts after pruning (5 fresh and 1 done)

	Pruned	Kept	Total
New	324	3	327
Fresh	2	2	4
Picked	1	0	1
Done	0	1	1
Total	327	6	333

Error

0.0b

Counts

333 → 6

Alt Table

Status	Error	Program
▶	0.3b	(.f64 x (pow.f64 (E.f64) (-.f64 (.f64 (log.f64 z) y) (fma.f64 a (+.f64 b z) (*.f64 y t)))))
	19.1b	(.f64 (sqrt.f64 (.f64 x (exp.f64 (fma.f64 y (-.f64 (log.f64 z) t) (.f64 a (-.f64 (log1p.f64 (neg.f64 z)) b)))))) (sqrt.f64 (.f64 x (exp.f64 (fma.f64 y (-.f64 (log.f64 z) t) (*.f64 a (-.f64 (log1p.f64 (neg.f64 z)) b)))))))
	0.8b	(.f64 x (pow.f64 (exp.f64 (.f64 (cbrt.f64 (fma.f64 y (-.f64 (log.f64 z) t) (.f64 a (-.f64 (log1p.f64 (neg.f64 z)) b)))) (cbrt.f64 (fma.f64 y (-.f64 (log.f64 z) t) (.f64 a (-.f64 (log1p.f64 (neg.f64 z)) b)))))) (cbrt.f64 (fma.f64 y (-.f64 (log.f64 z) t) (*.f64 a (-.f64 (log1p.f64 (neg.f64 z)) b))))))
✓	0.8b	(.f64 x (expm1.f64 (log1p.f64 (exp.f64 (fma.f64 y (-.f64 (log.f64 z) t) (.f64 a (-.f64 (log1p.f64 (neg.f64 z)) b)))))))
	31.8b	(.f64 (.f64 (sqrt.f64 x) (pow.f64 (sqrt.f64 (E.f64)) (fma.f64 y (-.f64 (log.f64 z) t) (.f64 a (-.f64 (log1p.f64 (neg.f64 z)) b))))) (.f64 (sqrt.f64 x) (pow.f64 (sqrt.f64 (E.f64)) (fma.f64 y (-.f64 (log.f64 z) t) (*.f64 a (-.f64 (log1p.f64 (neg.f64 z)) b))))))
	19.5b	(exp.f64 (log.f64 (.f64 x (pow.f64 (E.f64) (fma.f64 y (-.f64 (log.f64 z) t) (.f64 a (-.f64 (log1p.f64 (neg.f64 z)) b)))))))

Compiler

Compiled 15170 to 5415 computations (64.3% saved)

localize18.0ms (0.1%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.0b	(.f64 x (pow.f64 (E.f64) (-.f64 (.f64 (log.f64 z) y) (fma.f64 a (+.f64 b z) (*.f64 y t)))))
✓	0.1b	(pow.f64 (E.f64) (-.f64 (.f64 (log.f64 z) y) (fma.f64 a (+.f64 b z) (.f64 y t))))
✓	0.3b	(fma.f64 a (+.f64 b z) (*.f64 y t))
✓	0.3b	(*.f64 (log.f64 z) y)

series1.1s (7.1%)

Counts

4 → 200

Calls

4 calls:

842.0ms	(.f64 x (pow.f64 (E.f64) (-.f64 (.f64 (log.f64 z) y) (fma.f64 a (+.f64 b z) (*.f64 y t)))))
218.0ms	(*.f64 (log.f64 z) y)
40.0ms	(pow.f64 (E.f64) (-.f64 (.f64 (log.f64 z) y) (fma.f64 a (+.f64 b z) (.f64 y t))))
15.0ms	(fma.f64 a (+.f64 b z) (*.f64 y t))

rewrite40.0ms (0.3%)

Algorithm

1×	rewrite-expression-head

Rules

22×	`add-sqr-sqrt_binary64`
17×	`associate-r_binary64`
15×	`*-un-lft-identity_binary64`
15×	`add-cube-cbrt_binary64`
14×	`unpow-prod-up_binary64`

Counts

4 → 95

Calls

4 calls:

13.0ms	(.f64 x (pow.f64 (E.f64) (-.f64 (.f64 (log.f64 z) y) (fma.f64 a (+.f64 b z) (*.f64 y t)))))
8.0ms	(pow.f64 (E.f64) (-.f64 (.f64 (log.f64 z) y) (fma.f64 a (+.f64 b z) (.f64 y t))))
6.0ms	(*.f64 (log.f64 z) y)
1.0ms	(fma.f64 a (+.f64 b z) (*.f64 y t))

simplify294.0ms (1.9%)

Algorithm

1×	egg-herbie

Rules

727×	`associate-l_binary64`
443×	`fma-neg_binary64`
435×	`fma-def_binary64`
395×	`*-commutative_binary64`
208×	`+-commutative_binary64`

Counts

295 → 261

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	496	8332
1	1368	7719
2	4581	7719
3	4992	7719

prune633.0ms (4%)

Pruning

7 alts after pruning (5 fresh and 2 done)

	Pruned	Kept	Total
New	259	2	261
Fresh	1	3	4
Picked	0	1	1
Done	0	1	1
Total	260	7	267

Error

0.0b

Counts

267 → 7

Alt Table

Status	Error	Program
	12.6b	(/.f64 (.f64 x (pow.f64 (E.f64) (.f64 (log.f64 z) y))) (pow.f64 (E.f64) (fma.f64 a (+.f64 b z) (*.f64 y t))))
	19.5b	(exp.f64 (log.f64 (.f64 x (pow.f64 (E.f64) (fma.f64 y (-.f64 (log.f64 z) t) (.f64 a (-.f64 (log1p.f64 (neg.f64 z)) b)))))))
✓	0.3b	(.f64 x (pow.f64 (E.f64) (-.f64 (.f64 (log.f64 z) y) (fma.f64 a (+.f64 b z) (*.f64 y t)))))
	50.3b	(.f64 (.f64 (/.f64 (pow.f64 z y) (exp.f64 (fma.f64 a (+.f64 z b) (.f64 y t)))) x) (pow.f64 (E.f64) (fma.f64 (neg.f64 (sqrt.f64 (fma.f64 a (+.f64 b z) (.f64 y t)))) (sqrt.f64 (fma.f64 a (+.f64 b z) (.f64 y t))) (.f64 (sqrt.f64 (fma.f64 a (+.f64 b z) (.f64 y t))) (sqrt.f64 (fma.f64 a (+.f64 b z) (.f64 y t)))))))
	0.8b	(.f64 x (pow.f64 (exp.f64 (.f64 (cbrt.f64 (fma.f64 y (-.f64 (log.f64 z) t) (.f64 a (-.f64 (log1p.f64 (neg.f64 z)) b)))) (cbrt.f64 (fma.f64 y (-.f64 (log.f64 z) t) (.f64 a (-.f64 (log1p.f64 (neg.f64 z)) b)))))) (cbrt.f64 (fma.f64 y (-.f64 (log.f64 z) t) (*.f64 a (-.f64 (log1p.f64 (neg.f64 z)) b))))))
✓	0.8b	(.f64 x (expm1.f64 (log1p.f64 (exp.f64 (fma.f64 y (-.f64 (log.f64 z) t) (.f64 a (-.f64 (log1p.f64 (neg.f64 z)) b)))))))
	31.8b	(.f64 (.f64 (sqrt.f64 x) (pow.f64 (sqrt.f64 (E.f64)) (fma.f64 y (-.f64 (log.f64 z) t) (.f64 a (-.f64 (log1p.f64 (neg.f64 z)) b))))) (.f64 (sqrt.f64 x) (pow.f64 (sqrt.f64 (E.f64)) (fma.f64 y (-.f64 (log.f64 z) t) (*.f64 a (-.f64 (log1p.f64 (neg.f64 z)) b))))))

Compiler

Compiled 9947 to 2109 computations (78.8% saved)

regimes1.3s (8.1%)

Accuracy

Total 0.5b remaining (95.9%)

Threshold costs 0.5b (95.9%)

Counts

136 → 1

Compiler

Compiled 27605 to 17970 computations (34.9% saved)

simplify3.0ms (0%)

Algorithm

1×	egg-herbie

Rules

4×	`*-commutative_binary64`
3×	`+-commutative_binary64`
2×	`sub-neg_binary64`
1×	`neg-sub0_binary64`
1×	`neg-mul-1_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	16	26
1	24	26
2	30	26
3	32	26
4	33	26
5	32	26

end122.0ms (0.8%)

Compiler: Compiled 304 to 155 computations (49% saved)

Details

analyze992.0ms (6.3%)

sample3.4s (21.5%)

simplify64.0ms (0.4%)

prune6.0ms (0%)

localize27.0ms (0.2%)

series1.4s (8.8%)

rewrite20.0ms (0.1%)

simplify223.0ms (1.4%)

prune395.0ms (2.5%)

localize20.0ms (0.1%)

series2.3s (14.6%)

rewrite3.0ms (0%)

simplify411.0ms (2.6%)

prune965.0ms (6.1%)

localize29.0ms (0.2%)

series1.3s (8.5%)

rewrite17.0ms (0.1%)

simplify230.0ms (1.5%)

prune451.0ms (2.9%)

localize18.0ms (0.1%)

series1.1s (7.1%)

rewrite40.0ms (0.3%)

simplify294.0ms (1.9%)

prune633.0ms (4%)

regimes1.3s (8.1%)

simplify3.0ms (0%)

end122.0ms (0.8%)

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