Details

Time bar (total: 8.8s)

analyze1.9s (21.3%)

Algorithm
search
Search
TrueOtherFalseIter
0%99.8%0.2%0
0%99.8%0.2%1
0%99.8%0.2%2
0%99.8%0.2%3
0%99.8%0.2%4
0%99.8%0.2%5
0%99.8%0.2%6
0%99.8%0.2%7
0%99.8%0.2%8
18.7%76.4%4.9%9
18.7%76.4%4.9%10
21.8%72.5%5.7%11
21.8%69.8%8.4%12
32.7%46.6%20.7%13
32.7%46.6%20.7%14
Compiler

Compiled 24 to 20 computations (16.7% saved)

sample64.0ms (0.7%)

Algorithm
intervals
Results
31.0ms256×body128valid
14.0ms134×body128nan
Compiler

Compiled 51 to 43 computations (15.7% saved)

simplify59.0ms (0.7%)

Algorithm
egg-herbie
Rules
564×fma-def_binary64
527×associate-/r/_binary64
522×fma-neg_binary64
484×unswap-sqr_binary64
458×associate-/l/_binary64
Counts
1 → 1
Iterations

Useful iterations: 1 (0.0ms)

IterNodesCost
01729
13327
26327
316527
449227
5167927
6365527
7495027
8504327

prune4.0ms (0%)

Pruning

1 alts after pruning (1 fresh and 0 done)

PrunedKeptTotal
New011
Fresh101
Picked000
Done000
Total112
Error
9.8b
Counts
2 → 1
Alt Table
StatusErrorProgram
9.8b
(asin.f64 (sqrt.f64 (/.f64 (-.f64 1 (pow.f64 (/.f64 Om Omc) 2)) (fma.f64 2 (pow.f64 (/.f64 t l) 2) 1))))
Compiler

Compiled 66 to 54 computations (18.2% saved)

localize13.0ms (0.1%)

Local error

Found 4 expressions with local error:

0.3b
(pow.f64 (/.f64 t l) 2)
0.3b
(/.f64 (-.f64 1 (pow.f64 (/.f64 Om Omc) 2)) (fma.f64 2 (pow.f64 (/.f64 t l) 2) 1))
0.3b
(asin.f64 (sqrt.f64 (/.f64 (-.f64 1 (pow.f64 (/.f64 Om Omc) 2)) (fma.f64 2 (pow.f64 (/.f64 t l) 2) 1))))
9.1b
(sqrt.f64 (/.f64 (-.f64 1 (pow.f64 (/.f64 Om Omc) 2)) (fma.f64 2 (pow.f64 (/.f64 t l) 2) 1)))

rewrite846.0ms (9.6%)

Algorithm
rewrite-expression-head
Error
9.7b
Rules
34×add-cube-cbrt_binary64
17×add-sqr-sqrt_binary64
16×add-cbrt-cube_binary64
15×pow1_binary64
14×add-exp-log_binary64
Counts
4 → 166
Calls

4 calls:

601.0ms
(asin.f64 (sqrt.f64 (/.f64 (-.f64 1 (pow.f64 (/.f64 Om Omc) 2)) (fma.f64 2 (pow.f64 (/.f64 t l) 2) 1))))
16.0ms
(/.f64 (-.f64 1 (pow.f64 (/.f64 Om Omc) 2)) (fma.f64 2 (pow.f64 (/.f64 t l) 2) 1))
12.0ms
(pow.f64 (/.f64 t l) 2)
10.0ms
(sqrt.f64 (/.f64 (-.f64 1 (pow.f64 (/.f64 Om Omc) 2)) (fma.f64 2 (pow.f64 (/.f64 t l) 2) 1)))
Compiler

Compiled 3975 to 2714 computations (31.7% saved)

series206.0ms (2.3%)

Error
1.3b
Counts
4 → 45
Calls

4 calls:

83.0ms
(/.f64 (-.f64 1 (pow.f64 (/.f64 Om Omc) 2)) (fma.f64 2 (pow.f64 (/.f64 t l) 2) 1))
69.0ms
(sqrt.f64 (/.f64 (-.f64 1 (pow.f64 (/.f64 Om Omc) 2)) (fma.f64 2 (pow.f64 (/.f64 t l) 2) 1)))
28.0ms
(asin.f64 (sqrt.f64 (/.f64 (-.f64 1 (pow.f64 (/.f64 Om Omc) 2)) (fma.f64 2 (pow.f64 (/.f64 t l) 2) 1))))
16.0ms
(pow.f64 (/.f64 t l) 2)
Compiler

Compiled 3042 to 2540 computations (16.5% saved)

simplify148.0ms (1.7%)

Algorithm
egg-herbie
Rules
719×associate-/l*_binary64
299×fma-def_binary64
221×distribute-rgt-in_binary64
213×associate-/l/_binary64
211×distribute-lft-in_binary64
Counts
211 → 101
Iterations

Useful iterations: 3 (0.0ms)

IterNodesCost
02074627
14614144
214644028
346854016
450114016

prune63.0ms (0.7%)

Pruning

7 alts after pruning (6 fresh and 1 done)

PrunedKeptTotal
New956101
Fresh000
Picked011
Done000
Total957102
Error
0.4b
Counts
102 → 7
Alt Table
StatusErrorProgram
14.2b
(asin.f64 (cbrt.f64 (pow.f64 (/.f64 (-.f64 1 (pow.f64 (/.f64 Om Omc) 2)) (fma.f64 2 (pow.f64 (/.f64 t l) 2) 1)) 3/2)))
43.5b
(asin.f64 (*.f64 (sqrt.f64 (-.f64 1 (pow.f64 (/.f64 Om Omc) 2))) (neg.f64 (/.f64 (*.f64 l (sqrt.f64 1/2)) t))))
39.3b
(asin.f64 (*.f64 (sqrt.f64 (-.f64 1 (pow.f64 (/.f64 Om Omc) 2))) (/.f64 (*.f64 l (sqrt.f64 1/2)) t)))
9.8b
(asin.f64 (sqrt.f64 (/.f64 (-.f64 1 (pow.f64 (/.f64 Om Omc) 2)) (fma.f64 2 (pow.f64 (/.f64 t l) 2) 1))))
10.0b
(asin.f64 (sqrt.f64 (/.f64 (-.f64 1 (pow.f64 (/.f64 Om Omc) 2)) (fma.f64 2 (*.f64 (pow.f64 (cbrt.f64 (/.f64 t l)) 4) (pow.f64 (cbrt.f64 (/.f64 t l)) 2)) 1))))
23.2b
(asin.f64 (sqrt.f64 (*.f64 (-.f64 1 (pow.f64 (/.f64 Om Omc) 2)) (/.f64 1 (fma.f64 2 (/.f64 (*.f64 t t) (*.f64 l l)) 1)))))
14.6b
(cbrt.f64 (pow.f64 (asin.f64 (sqrt.f64 (/.f64 (-.f64 1 (pow.f64 (/.f64 Om Omc) 2)) (fma.f64 2 (pow.f64 (/.f64 t l) 2) 1)))) 3))
Compiler

Compiled 1656 to 1147 computations (30.7% saved)

localize20.0ms (0.2%)

Local error

Found 4 expressions with local error:

0.5b
(pow.f64 (cbrt.f64 (/.f64 t l)) 4)
9.1b
(sqrt.f64 (/.f64 (-.f64 1 (pow.f64 (/.f64 Om Omc) 2)) (fma.f64 2 (*.f64 (pow.f64 (cbrt.f64 (/.f64 t l)) 4) (pow.f64 (cbrt.f64 (/.f64 t l)) 2)) 1)))
16.6b
(cbrt.f64 (/.f64 t l))
16.6b
(cbrt.f64 (/.f64 t l))

rewrite181.0ms (2.1%)

Algorithm
rewrite-expression-head
Error
0.4b
Rules
28×add-cube-cbrt_binary64
18×add-sqr-sqrt_binary64
12×log1p-expm1-u_binary64
12×expm1-log1p-u_binary64
11×pow1/3_binary64
Counts
4 → 147
Calls

4 calls:

15.0ms
(pow.f64 (cbrt.f64 (/.f64 t l)) 4)
13.0ms
(cbrt.f64 (/.f64 t l))
13.0ms
(cbrt.f64 (/.f64 t l))
11.0ms
(sqrt.f64 (/.f64 (-.f64 1 (pow.f64 (/.f64 Om Omc) 2)) (fma.f64 2 (*.f64 (pow.f64 (cbrt.f64 (/.f64 t l)) 4) (pow.f64 (cbrt.f64 (/.f64 t l)) 2)) 1)))
Compiler

Compiled 3473 to 2002 computations (42.4% saved)

series243.0ms (2.8%)

Error
0.4b
Counts
4 → 30
Calls

4 calls:

92.0ms
(sqrt.f64 (/.f64 (-.f64 1 (pow.f64 (/.f64 Om Omc) 2)) (fma.f64 2 (*.f64 (pow.f64 (cbrt.f64 (/.f64 t l)) 4) (pow.f64 (cbrt.f64 (/.f64 t l)) 2)) 1)))
57.0ms
(pow.f64 (cbrt.f64 (/.f64 t l)) 4)
39.0ms
(cbrt.f64 (/.f64 t l))
37.0ms
(cbrt.f64 (/.f64 t l))
Compiler

Compiled 2937 to 2422 computations (17.5% saved)

simplify115.0ms (1.3%)

Algorithm
egg-herbie
Rules
619×unswap-sqr_binary64
394×log-prod_binary64
391×fma-def_binary64
258×associate-*r*_binary64
247×associate-*l*_binary64
Counts
177 → 92
Iterations

Useful iterations: 3 (0.0ms)

IterNodesCost
01662441
13281992
26731915
324161824
447171824
554071824

prune73.0ms (0.8%)

Pruning

7 alts after pruning (5 fresh and 2 done)

PrunedKeptTotal
New92092
Fresh055
Picked011
Done011
Total92799
Error
0.4b
Counts
99 → 7
Alt Table
StatusErrorProgram
14.2b
(asin.f64 (cbrt.f64 (pow.f64 (/.f64 (-.f64 1 (pow.f64 (/.f64 Om Omc) 2)) (fma.f64 2 (pow.f64 (/.f64 t l) 2) 1)) 3/2)))
43.5b
(asin.f64 (*.f64 (sqrt.f64 (-.f64 1 (pow.f64 (/.f64 Om Omc) 2))) (neg.f64 (/.f64 (*.f64 l (sqrt.f64 1/2)) t))))
39.3b
(asin.f64 (*.f64 (sqrt.f64 (-.f64 1 (pow.f64 (/.f64 Om Omc) 2))) (/.f64 (*.f64 l (sqrt.f64 1/2)) t)))
9.8b
(asin.f64 (sqrt.f64 (/.f64 (-.f64 1 (pow.f64 (/.f64 Om Omc) 2)) (fma.f64 2 (pow.f64 (/.f64 t l) 2) 1))))
10.0b
(asin.f64 (sqrt.f64 (/.f64 (-.f64 1 (pow.f64 (/.f64 Om Omc) 2)) (fma.f64 2 (*.f64 (pow.f64 (cbrt.f64 (/.f64 t l)) 4) (pow.f64 (cbrt.f64 (/.f64 t l)) 2)) 1))))
23.2b
(asin.f64 (sqrt.f64 (*.f64 (-.f64 1 (pow.f64 (/.f64 Om Omc) 2)) (/.f64 1 (fma.f64 2 (/.f64 (*.f64 t t) (*.f64 l l)) 1)))))
14.6b
(cbrt.f64 (pow.f64 (asin.f64 (sqrt.f64 (/.f64 (-.f64 1 (pow.f64 (/.f64 Om Omc) 2)) (fma.f64 2 (pow.f64 (/.f64 t l) 2) 1)))) 3))
Compiler

Compiled 2010 to 1320 computations (34.3% saved)

localize18.0ms (0.2%)

Local error

Found 4 expressions with local error:

0.3b
(pow.f64 (/.f64 t l) 2)
0.3b
(/.f64 (-.f64 1 (pow.f64 (/.f64 Om Omc) 2)) (fma.f64 2 (pow.f64 (/.f64 t l) 2) 1))
0.3b
(asin.f64 (cbrt.f64 (pow.f64 (/.f64 (-.f64 1 (pow.f64 (/.f64 Om Omc) 2)) (fma.f64 2 (pow.f64 (/.f64 t l) 2) 1)) 3/2)))
13.9b
(cbrt.f64 (pow.f64 (/.f64 (-.f64 1 (pow.f64 (/.f64 Om Omc) 2)) (fma.f64 2 (pow.f64 (/.f64 t l) 2) 1)) 3/2))

rewrite218.0ms (2.5%)

Algorithm
rewrite-expression-head
Error
0.4b
Rules
35×add-cube-cbrt_binary64
15×add-sqr-sqrt_binary64
14×add-cbrt-cube_binary64
14×add-exp-log_binary64
13×pow1_binary64
Counts
4 → 157
Calls

4 calls:

19.0ms
(/.f64 (-.f64 1 (pow.f64 (/.f64 Om Omc) 2)) (fma.f64 2 (pow.f64 (/.f64 t l) 2) 1))
13.0ms
(pow.f64 (/.f64 t l) 2)
10.0ms
(cbrt.f64 (pow.f64 (/.f64 (-.f64 1 (pow.f64 (/.f64 Om Omc) 2)) (fma.f64 2 (pow.f64 (/.f64 t l) 2) 1)) 3/2))
9.0ms
(asin.f64 (cbrt.f64 (pow.f64 (/.f64 (-.f64 1 (pow.f64 (/.f64 Om Omc) 2)) (fma.f64 2 (pow.f64 (/.f64 t l) 2) 1)) 3/2)))
Compiler

Compiled 4126 to 2907 computations (29.5% saved)

series211.0ms (2.4%)

Error
0.4b
Counts
4 → 45
Calls

4 calls:

85.0ms
(/.f64 (-.f64 1 (pow.f64 (/.f64 Om Omc) 2)) (fma.f64 2 (pow.f64 (/.f64 t l) 2) 1))
71.0ms
(cbrt.f64 (pow.f64 (/.f64 (-.f64 1 (pow.f64 (/.f64 Om Omc) 2)) (fma.f64 2 (pow.f64 (/.f64 t l) 2) 1)) 3/2))
27.0ms
(asin.f64 (cbrt.f64 (pow.f64 (/.f64 (-.f64 1 (pow.f64 (/.f64 Om Omc) 2)) (fma.f64 2 (pow.f64 (/.f64 t l) 2) 1)) 3/2)))
15.0ms
(pow.f64 (/.f64 t l) 2)
Compiler

Compiled 3158 to 2652 computations (16% saved)

simplify115.0ms (1.3%)

Algorithm
egg-herbie
Rules
681×associate-/l*_binary64
439×associate-/r*_binary64
295×fma-def_binary64
217×distribute-rgt-in_binary64
213×associate-/l/_binary64
Counts
202 → 93
Iterations

Useful iterations: 2 (0.0ms)

IterNodesCost
02084650
14684231
214584133
349774133

prune66.0ms (0.8%)

Pruning

8 alts after pruning (5 fresh and 3 done)

PrunedKeptTotal
New92193
Fresh044
Picked011
Done022
Total928100
Error
0.4b
Counts
100 → 8
Alt Table
StatusErrorProgram
9.8b
(asin.f64 (sqrt.f64 (/.f64 (-.f64 1 (pow.f64 (/.f64 Om Omc) 2)) (fma.f64 2 (pow.f64 (/.f64 t l) 2) 1))))
14.7b
(*.f64 (sqrt.f64 (asin.f64 (cbrt.f64 (pow.f64 (/.f64 (-.f64 1 (pow.f64 (/.f64 Om Omc) 2)) (fma.f64 2 (pow.f64 (/.f64 t l) 2) 1)) 3/2)))) (sqrt.f64 (asin.f64 (cbrt.f64 (pow.f64 (/.f64 (-.f64 1 (pow.f64 (/.f64 Om Omc) 2)) (fma.f64 2 (pow.f64 (/.f64 t l) 2) 1)) 3/2)))))
14.2b
(asin.f64 (cbrt.f64 (pow.f64 (/.f64 (-.f64 1 (pow.f64 (/.f64 Om Omc) 2)) (fma.f64 2 (pow.f64 (/.f64 t l) 2) 1)) 3/2)))
43.5b
(asin.f64 (*.f64 (sqrt.f64 (-.f64 1 (pow.f64 (/.f64 Om Omc) 2))) (neg.f64 (/.f64 (*.f64 l (sqrt.f64 1/2)) t))))
39.3b
(asin.f64 (*.f64 (sqrt.f64 (-.f64 1 (pow.f64 (/.f64 Om Omc) 2))) (/.f64 (*.f64 l (sqrt.f64 1/2)) t)))
10.0b
(asin.f64 (sqrt.f64 (/.f64 (-.f64 1 (pow.f64 (/.f64 Om Omc) 2)) (fma.f64 2 (*.f64 (pow.f64 (cbrt.f64 (/.f64 t l)) 4) (pow.f64 (cbrt.f64 (/.f64 t l)) 2)) 1))))
23.2b
(asin.f64 (sqrt.f64 (*.f64 (-.f64 1 (pow.f64 (/.f64 Om Omc) 2)) (/.f64 1 (fma.f64 2 (/.f64 (*.f64 t t) (*.f64 l l)) 1)))))
14.6b
(cbrt.f64 (pow.f64 (asin.f64 (sqrt.f64 (/.f64 (-.f64 1 (pow.f64 (/.f64 Om Omc) 2)) (fma.f64 2 (pow.f64 (/.f64 t l) 2) 1)))) 3))
Compiler

Compiled 1666 to 1196 computations (28.2% saved)

localize19.0ms (0.2%)

Local error

Found 4 expressions with local error:

0.3b
(asin.f64 (sqrt.f64 (/.f64 (-.f64 1 (pow.f64 (/.f64 Om Omc) 2)) (fma.f64 2 (pow.f64 (/.f64 t l) 2) 1))))
0.6b
(pow.f64 (asin.f64 (sqrt.f64 (/.f64 (-.f64 1 (pow.f64 (/.f64 Om Omc) 2)) (fma.f64 2 (pow.f64 (/.f64 t l) 2) 1)))) 3)
9.1b
(sqrt.f64 (/.f64 (-.f64 1 (pow.f64 (/.f64 Om Omc) 2)) (fma.f64 2 (pow.f64 (/.f64 t l) 2) 1)))
14.4b
(cbrt.f64 (pow.f64 (asin.f64 (sqrt.f64 (/.f64 (-.f64 1 (pow.f64 (/.f64 Om Omc) 2)) (fma.f64 2 (pow.f64 (/.f64 t l) 2) 1)))) 3))

rewrite168.0ms (1.9%)

Algorithm
rewrite-expression-head
Error
0.4b
Rules
25×add-cube-cbrt_binary64
18×add-sqr-sqrt_binary64
13×pow1_binary64
12×log1p-expm1-u_binary64
12×expm1-log1p-u_binary64
Counts
4 → 148
Calls

4 calls:

13.0ms
(pow.f64 (asin.f64 (sqrt.f64 (/.f64 (-.f64 1 (pow.f64 (/.f64 Om Omc) 2)) (fma.f64 2 (pow.f64 (/.f64 t l) 2) 1)))) 3)
11.0ms
(sqrt.f64 (/.f64 (-.f64 1 (pow.f64 (/.f64 Om Omc) 2)) (fma.f64 2 (pow.f64 (/.f64 t l) 2) 1)))
10.0ms
(asin.f64 (sqrt.f64 (/.f64 (-.f64 1 (pow.f64 (/.f64 Om Omc) 2)) (fma.f64 2 (pow.f64 (/.f64 t l) 2) 1))))
10.0ms
(cbrt.f64 (pow.f64 (asin.f64 (sqrt.f64 (/.f64 (-.f64 1 (pow.f64 (/.f64 Om Omc) 2)) (fma.f64 2 (pow.f64 (/.f64 t l) 2) 1)))) 3))
Compiler

Compiled 3503 to 2549 computations (27.2% saved)

series230.0ms (2.6%)

Error
0.4b
Counts
4 → 48
Calls

4 calls:

83.0ms
(pow.f64 (asin.f64 (sqrt.f64 (/.f64 (-.f64 1 (pow.f64 (/.f64 Om Omc) 2)) (fma.f64 2 (pow.f64 (/.f64 t l) 2) 1)))) 3)
77.0ms
(sqrt.f64 (/.f64 (-.f64 1 (pow.f64 (/.f64 Om Omc) 2)) (fma.f64 2 (pow.f64 (/.f64 t l) 2) 1)))
31.0ms
(asin.f64 (sqrt.f64 (/.f64 (-.f64 1 (pow.f64 (/.f64 Om Omc) 2)) (fma.f64 2 (pow.f64 (/.f64 t l) 2) 1))))
29.0ms
(cbrt.f64 (pow.f64 (asin.f64 (sqrt.f64 (/.f64 (-.f64 1 (pow.f64 (/.f64 Om Omc) 2)) (fma.f64 2 (pow.f64 (/.f64 t l) 2) 1)))) 3))
Compiler

Compiled 3146 to 2663 computations (15.4% saved)

simplify177.0ms (2%)

Algorithm
egg-herbie
Rules
840×fma-def_binary64
795×times-frac_binary64
359×associate-*l*_binary64
311×associate-*r*_binary64
198×exp-prod_binary64
Counts
196 → 103
Iterations

Useful iterations: 2 (0.0ms)

IterNodesCost
01524969
12954333
26274287
323354287
444854287
549064287

prune55.0ms (0.6%)

Pruning

7 alts after pruning (4 fresh and 3 done)

PrunedKeptTotal
New1021103
Fresh134
Picked101
Done033
Total1047111
Error
0.4b
Counts
111 → 7
Alt Table
StatusErrorProgram
43.5b
(asin.f64 (*.f64 (sqrt.f64 (-.f64 1 (pow.f64 (/.f64 Om Omc) 2))) (neg.f64 (/.f64 (*.f64 l (sqrt.f64 1/2)) t))))
14.7b
(*.f64 (cbrt.f64 (cbrt.f64 (pow.f64 (asin.f64 (sqrt.f64 (/.f64 (-.f64 1 (pow.f64 (/.f64 Om Omc) 2)) (fma.f64 2 (pow.f64 (/.f64 t l) 2) 1)))) 3))) (cbrt.f64 (pow.f64 (asin.f64 (sqrt.f64 (/.f64 (-.f64 1 (pow.f64 (/.f64 Om Omc) 2)) (fma.f64 2 (pow.f64 (/.f64 t l) 2) 1)))) 2)))
14.2b
(asin.f64 (cbrt.f64 (pow.f64 (/.f64 (-.f64 1 (pow.f64 (/.f64 Om Omc) 2)) (fma.f64 2 (pow.f64 (/.f64 t l) 2) 1)) 3/2)))
39.3b
(asin.f64 (*.f64 (sqrt.f64 (-.f64 1 (pow.f64 (/.f64 Om Omc) 2))) (/.f64 (*.f64 l (sqrt.f64 1/2)) t)))
9.8b
(asin.f64 (sqrt.f64 (/.f64 (-.f64 1 (pow.f64 (/.f64 Om Omc) 2)) (fma.f64 2 (pow.f64 (/.f64 t l) 2) 1))))
10.0b
(asin.f64 (sqrt.f64 (/.f64 (-.f64 1 (pow.f64 (/.f64 Om Omc) 2)) (fma.f64 2 (*.f64 (pow.f64 (cbrt.f64 (/.f64 t l)) 4) (pow.f64 (cbrt.f64 (/.f64 t l)) 2)) 1))))
23.2b
(asin.f64 (sqrt.f64 (*.f64 (-.f64 1 (pow.f64 (/.f64 Om Omc) 2)) (/.f64 1 (fma.f64 2 (/.f64 (*.f64 t t) (*.f64 l l)) 1)))))
Compiler

Compiled 1477 to 1074 computations (27.3% saved)

regimes1.4s (15.7%)

Accuracy

Total 0.3b remaining (30.5%)

Threshold costs 0.3b (30.5%)

Compiler

Compiled 30118 to 23658 computations (21.4% saved)

bsearch3.0ms (0%)

Compiler

Compiled 7 to 5 computations (28.6% saved)

simplify6.0ms (0.1%)

Algorithm
egg-herbie
Rules
10×*-commutative_binary64
+-commutative_binary64
sub-neg_binary64
neg-sub0_binary64
neg-mul-1_binary64
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
03397
14697
26497
37797
48697
58997
68897

end1.0ms (0%)

Compiler

Compiled 67 to 47 computations (29.9% saved)

sample2.2s (25.2%)

Algorithm
intervals
Results
977.0ms8000×body128valid
532.0ms4626×body128nan
Compiler

Compiled 286 to 222 computations (22.4% saved)

Profiling

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