Details

Time bar (total: 13.1s)

analyze2.2s (17%)

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
9.4%90.4%0.2%6
17.2%82.7%0.2%7
19.5%80.3%0.2%8
30.8%69%0.2%9
35.5%64.3%0.2%10
42.4%57.4%0.2%11
47.1%52.7%0.2%12
49%50.8%0.2%13
50.1%49.7%0.2%14
Compiler

Compiled 42 to 20 computations (52.4% saved)

sample206.0ms (1.6%)

Algorithm
intervals
Results
73.0ms34×body512invalid
55.0ms72×body1024invalid
39.0ms245×body128valid
10.0msbody2048invalid
4.0msbody1024valid
3.0msbody256invalid
1.0msbody512valid
1.0msbody128invalid
1.0msbody256valid
Compiler

Compiled 87 to 43 computations (50.6% saved)

simplify74.0ms (0.6%)

Algorithm
egg-herbie
Rules
892×unswap-sqr_binary64
461×associate-/l*_binary64
323×associate-/r*_binary64
296×associate-*l/_binary64
286×associate-*r/_binary64
Counts
1 → 1
Iterations

Useful iterations: 1 (0.0ms)

IterNodesCost
02252
14150
27250
312050
426550
599850
6304550
7408750
8454350
9486850
10493450

prune5.0ms (0%)

Pruning

2 alts after pruning (2 fresh and 0 done)

PrunedKeptTotal
New011
Fresh011
Picked000
Done000
Total022
Error
5.3b
Counts
2 → 2
Alt Table
StatusErrorProgram
8.3b
(*.f64 (/.f64 (pow.f64 (hypot.f64 x.re x.im) y.re) (exp.f64 (*.f64 (atan2.f64 x.im x.re) y.im))) (sin.f64 (fma.f64 (log.f64 (hypot.f64 x.re x.im)) y.im (*.f64 y.re (atan2.f64 x.im x.re)))))
32.5b
(*.f64 (exp.f64 (-.f64 (*.f64 (log.f64 (sqrt.f64 (+.f64 (*.f64 x.re x.re) (*.f64 x.im x.im)))) y.re) (*.f64 (atan2.f64 x.im x.re) y.im))) (sin.f64 (+.f64 (*.f64 (log.f64 (sqrt.f64 (+.f64 (*.f64 x.re x.re) (*.f64 x.im x.im)))) y.im) (*.f64 (atan2.f64 x.im x.re) y.re))))
Compiler

Compiled 169 to 83 computations (50.9% saved)

localize19.0ms (0.1%)

Local error

Found 4 expressions with local error:

0.3b
(/.f64 (pow.f64 (hypot.f64 x.re x.im) y.re) (exp.f64 (*.f64 (atan2.f64 x.im x.re) y.im)))
1.6b
(*.f64 y.re (atan2.f64 x.im x.re))
2.1b
(*.f64 (atan2.f64 x.im x.re) y.im)
33.1b
(sin.f64 (fma.f64 (log.f64 (hypot.f64 x.re x.im)) y.im (*.f64 y.re (atan2.f64 x.im x.re))))

rewrite293.0ms (2.2%)

Algorithm
rewrite-expression-head
Error
2.7b
Rules
31×add-cube-cbrt_binary64
30×pow1_binary64
24×add-sqr-sqrt_binary64
20×add-cbrt-cube_binary64
16×add-exp-log_binary64
Counts
4 → 151
Calls

4 calls:

15.0ms
(*.f64 (atan2.f64 x.im x.re) y.im)
14.0ms
(*.f64 y.re (atan2.f64 x.im x.re))
14.0ms
(/.f64 (pow.f64 (hypot.f64 x.re x.im) y.re) (exp.f64 (*.f64 (atan2.f64 x.im x.re) y.im)))
10.0ms
(sin.f64 (fma.f64 (log.f64 (hypot.f64 x.re x.im)) y.im (*.f64 y.re (atan2.f64 x.im x.re))))
Compiler

Compiled 4150 to 562 computations (86.5% saved)

series266.0ms (2%)

Error
2.8b
Counts
4 → 53
Calls

4 calls:

109.0ms
(/.f64 (pow.f64 (hypot.f64 x.re x.im) y.re) (exp.f64 (*.f64 (atan2.f64 x.im x.re) y.im)))
83.0ms
(sin.f64 (fma.f64 (log.f64 (hypot.f64 x.re x.im)) y.im (*.f64 y.re (atan2.f64 x.im x.re))))
19.0ms
(*.f64 y.re (atan2.f64 x.im x.re))
19.0ms
(*.f64 (atan2.f64 x.im x.re) y.im)
Compiler

Compiled 4867 to 2559 computations (47.4% saved)

simplify170.0ms (1.3%)

Algorithm
egg-herbie
Rules
428×fma-def_binary64
409×fma-neg_binary64
256×unswap-sqr_binary64
253×cancel-sign-sub-inv_binary64
223×associate-*r*_binary64
Counts
204 → 117
Iterations

Useful iterations: 2 (0.0ms)

IterNodesCost
02874655
16824173
221334127
347984127
450024127

prune189.0ms (1.4%)

Pruning

15 alts after pruning (15 fresh and 0 done)

PrunedKeptTotal
New10215117
Fresh101
Picked101
Done000
Total10415119
Error
2.6b
Counts
119 → 15
Alt Table
StatusErrorProgram
12.7b
(*.f64 (/.f64 (pow.f64 (hypot.f64 x.re x.im) y.re) (exp.f64 (*.f64 (atan2.f64 x.im x.re) y.im))) (*.f64 (cbrt.f64 (*.f64 (sin.f64 (fma.f64 y.im (log.f64 (hypot.f64 x.im x.re)) (*.f64 y.re (atan2.f64 x.im x.re)))) (sin.f64 (fma.f64 y.im (log.f64 (hypot.f64 x.im x.re)) (*.f64 y.re (atan2.f64 x.im x.re)))))) (cbrt.f64 (sin.f64 (fma.f64 y.im (log.f64 (hypot.f64 x.im x.re)) (*.f64 y.re (atan2.f64 x.im x.re)))))))
39.0b
(*.f64 (/.f64 (pow.f64 (hypot.f64 x.re x.im) y.re) (exp.f64 (*.f64 (atan2.f64 x.im x.re) y.im))) (sin.f64 (-.f64 (*.f64 y.re (atan2.f64 x.im x.re)) (*.f64 y.im (log.f64 (/.f64 -1 x.im))))))
8.5b
(*.f64 (/.f64 (pow.f64 (hypot.f64 x.re x.im) y.re) (exp.f64 (*.f64 (atan2.f64 x.im x.re) y.im))) (sin.f64 (fma.f64 (log.f64 (hypot.f64 x.re x.im)) y.im (*.f64 (*.f64 (cbrt.f64 y.re) (cbrt.f64 y.re)) (*.f64 (atan2.f64 x.im x.re) (cbrt.f64 y.re))))))
17.5b
(*.f64 (/.f64 (pow.f64 (hypot.f64 x.re x.im) y.re) (exp.f64 (*.f64 (atan2.f64 x.im x.re) y.im))) (cbrt.f64 (pow.f64 (sin.f64 (fma.f64 y.im (log.f64 (hypot.f64 x.im x.re)) (*.f64 y.re (atan2.f64 x.im x.re)))) 3)))
40.2b
(*.f64 (/.f64 (pow.f64 (hypot.f64 x.re x.im) y.re) (exp.f64 (*.f64 (atan2.f64 x.im x.re) y.im))) (sin.f64 (fma.f64 (log.f64 x.im) y.im (*.f64 y.re (atan2.f64 x.im x.re)))))
23.4b
(*.f64 (/.f64 (pow.f64 (hypot.f64 x.re x.im) y.re) (exp.f64 (*.f64 (atan2.f64 x.im x.re) y.im))) (sin.f64 (fma.f64 (log.f64 (hypot.f64 x.re x.im)) y.im (sqrt.f64 (*.f64 (pow.f64 y.re 2) (pow.f64 (atan2.f64 x.im x.re) 2))))))
15.7b
(*.f64 (pow.f64 (hypot.f64 x.im x.re) y.re) (sin.f64 (fma.f64 (log.f64 (hypot.f64 x.re x.im)) y.im (*.f64 y.re (atan2.f64 x.im x.re)))))
20.0b
(*.f64 (/.f64 (pow.f64 (hypot.f64 x.re x.im) y.re) (exp.f64 (*.f64 (atan2.f64 x.im x.re) y.im))) (sin.f64 (fma.f64 (log.f64 (hypot.f64 x.re x.im)) y.im (*.f64 (cbrt.f64 (*.f64 (pow.f64 y.re 2) (pow.f64 (atan2.f64 x.im x.re) 2))) (cbrt.f64 (*.f64 y.re (atan2.f64 x.im x.re)))))))
8.6b
(*.f64 (/.f64 (pow.f64 (hypot.f64 x.re x.im) y.re) (exp.f64 (expm1.f64 (log1p.f64 (*.f64 y.im (atan2.f64 x.im x.re)))))) (sin.f64 (fma.f64 (log.f64 (hypot.f64 x.re x.im)) y.im (*.f64 y.re (atan2.f64 x.im x.re)))))
20.8b
(*.f64 (pow.f64 (exp.f64 y.im) (neg.f64 (atan2.f64 x.im x.re))) (sin.f64 (fma.f64 (log.f64 (hypot.f64 x.re x.im)) y.im (*.f64 y.re (atan2.f64 x.im x.re)))))
18.4b
(*.f64 (/.f64 (pow.f64 (hypot.f64 x.re x.im) y.re) (exp.f64 (*.f64 (atan2.f64 x.im x.re) y.im))) (/.f64 (+.f64 (pow.f64 (*.f64 (cos.f64 (*.f64 y.re (atan2.f64 x.im x.re))) (sin.f64 (*.f64 y.im (log.f64 (hypot.f64 x.im x.re))))) 3) (pow.f64 (*.f64 (sin.f64 (*.f64 y.re (atan2.f64 x.im x.re))) (cos.f64 (*.f64 y.im (log.f64 (hypot.f64 x.im x.re))))) 3)) (fma.f64 (sin.f64 (*.f64 y.re (atan2.f64 x.im x.re))) (*.f64 (sin.f64 (*.f64 y.re (atan2.f64 x.im x.re))) (*.f64 (cos.f64 (*.f64 y.im (log.f64 (hypot.f64 x.im x.re)))) (cos.f64 (*.f64 y.im (log.f64 (hypot.f64 x.im x.re)))))) (*.f64 (*.f64 (cos.f64 (*.f64 y.re (atan2.f64 x.im x.re))) (sin.f64 (*.f64 y.im (log.f64 (hypot.f64 x.im x.re))))) (-.f64 (*.f64 (cos.f64 (*.f64 y.re (atan2.f64 x.im x.re))) (sin.f64 (*.f64 y.im (log.f64 (hypot.f64 x.im x.re))))) (*.f64 (sin.f64 (*.f64 y.re (atan2.f64 x.im x.re))) (cos.f64 (*.f64 y.im (log.f64 (hypot.f64 x.im x.re))))))))))
8.5b
(*.f64 (log.f64 (exp.f64 (/.f64 (pow.f64 (hypot.f64 x.im x.re) y.re) (exp.f64 (*.f64 y.im (atan2.f64 x.im x.re)))))) (sin.f64 (fma.f64 (log.f64 (hypot.f64 x.re x.im)) y.im (*.f64 y.re (atan2.f64 x.im x.re)))))
8.7b
(*.f64 (/.f64 (pow.f64 (hypot.f64 x.re x.im) y.re) (exp.f64 (*.f64 (atan2.f64 x.im x.re) y.im))) (*.f64 (*.f64 (cbrt.f64 (sin.f64 (fma.f64 y.im (log.f64 (hypot.f64 x.im x.re)) (*.f64 y.re (atan2.f64 x.im x.re))))) (cbrt.f64 (sin.f64 (fma.f64 y.im (log.f64 (hypot.f64 x.im x.re)) (*.f64 y.re (atan2.f64 x.im x.re)))))) (cbrt.f64 (sin.f64 (fma.f64 y.im (log.f64 (hypot.f64 x.im x.re)) (*.f64 y.re (atan2.f64 x.im x.re)))))))
12.5b
(*.f64 (/.f64 (pow.f64 (hypot.f64 x.re x.im) y.re) (exp.f64 (*.f64 (atan2.f64 x.im x.re) y.im))) (/.f64 (*.f64 (-.f64 (*.f64 (cos.f64 (*.f64 y.re (atan2.f64 x.im x.re))) (sin.f64 (*.f64 y.im (log.f64 (hypot.f64 x.im x.re))))) (*.f64 (sin.f64 (*.f64 y.re (atan2.f64 x.im x.re))) (cos.f64 (*.f64 y.im (log.f64 (hypot.f64 x.im x.re)))))) (fma.f64 (sin.f64 (*.f64 y.re (atan2.f64 x.im x.re))) (cos.f64 (*.f64 y.im (log.f64 (hypot.f64 x.im x.re)))) (*.f64 (cos.f64 (*.f64 y.re (atan2.f64 x.im x.re))) (sin.f64 (*.f64 y.im (log.f64 (hypot.f64 x.im x.re))))))) (-.f64 (*.f64 (cos.f64 (*.f64 y.re (atan2.f64 x.im x.re))) (sin.f64 (*.f64 y.im (log.f64 (hypot.f64 x.im x.re))))) (*.f64 (sin.f64 (*.f64 y.re (atan2.f64 x.im x.re))) (cos.f64 (*.f64 y.im (log.f64 (hypot.f64 x.im x.re))))))))
21.8b
(*.f64 (/.f64 (pow.f64 (hypot.f64 x.re x.im) y.re) (exp.f64 (*.f64 (atan2.f64 x.im x.re) y.im))) (sqrt.f64 (*.f64 (sin.f64 (fma.f64 y.im (log.f64 (hypot.f64 x.im x.re)) (*.f64 y.re (atan2.f64 x.im x.re)))) (sin.f64 (fma.f64 y.im (log.f64 (hypot.f64 x.im x.re)) (*.f64 y.re (atan2.f64 x.im x.re)))))))
Compiler

Compiled 4308 to 1030 computations (76.1% saved)

localize22.0ms (0.2%)

Local error

Found 4 expressions with local error:

0.3b
(/.f64 (pow.f64 (hypot.f64 x.im x.re) y.re) (exp.f64 (*.f64 y.im (atan2.f64 x.im x.re))))
1.6b
(*.f64 y.re (atan2.f64 x.im x.re))
2.1b
(*.f64 y.im (atan2.f64 x.im x.re))
33.1b
(sin.f64 (fma.f64 (log.f64 (hypot.f64 x.re x.im)) y.im (*.f64 y.re (atan2.f64 x.im x.re))))

rewrite454.0ms (3.5%)

Algorithm
rewrite-expression-head
Error
2.6b
Rules
31×add-cube-cbrt_binary64
30×pow1_binary64
24×add-sqr-sqrt_binary64
20×add-cbrt-cube_binary64
16×add-exp-log_binary64
Counts
4 → 151
Calls

4 calls:

15.0ms
(/.f64 (pow.f64 (hypot.f64 x.im x.re) y.re) (exp.f64 (*.f64 y.im (atan2.f64 x.im x.re))))
14.0ms
(*.f64 y.im (atan2.f64 x.im x.re))
13.0ms
(*.f64 y.re (atan2.f64 x.im x.re))
11.0ms
(sin.f64 (fma.f64 (log.f64 (hypot.f64 x.re x.im)) y.im (*.f64 y.re (atan2.f64 x.im x.re))))
Compiler

Compiled 4380 to 690 computations (84.2% saved)

series260.0ms (2%)

Error
2.6b
Counts
4 → 53
Calls

4 calls:

79.0ms
(/.f64 (pow.f64 (hypot.f64 x.im x.re) y.re) (exp.f64 (*.f64 y.im (atan2.f64 x.im x.re))))
73.0ms
(sin.f64 (fma.f64 (log.f64 (hypot.f64 x.re x.im)) y.im (*.f64 y.re (atan2.f64 x.im x.re))))
20.0ms
(*.f64 y.re (atan2.f64 x.im x.re))
20.0ms
(*.f64 y.im (atan2.f64 x.im x.re))
Compiler

Compiled 5117 to 2837 computations (44.6% saved)

simplify161.0ms (1.2%)

Algorithm
egg-herbie
Rules
420×fma-def_binary64
415×fma-neg_binary64
256×unswap-sqr_binary64
253×cancel-sign-sub-inv_binary64
223×associate-*r*_binary64
Counts
204 → 91
Iterations

Useful iterations: 2 (0.0ms)

IterNodesCost
02884659
16834177
221274131
347844131
449944131

prune292.0ms (2.2%)

Pruning

14 alts after pruning (14 fresh and 0 done)

PrunedKeptTotal
New89291
Fresh21214
Picked101
Done000
Total9214106
Error
2.6b
Counts
106 → 14
Alt Table
StatusErrorProgram
12.7b
(*.f64 (/.f64 (pow.f64 (hypot.f64 x.re x.im) y.re) (exp.f64 (*.f64 (atan2.f64 x.im x.re) y.im))) (*.f64 (cbrt.f64 (*.f64 (sin.f64 (fma.f64 y.im (log.f64 (hypot.f64 x.im x.re)) (*.f64 y.re (atan2.f64 x.im x.re)))) (sin.f64 (fma.f64 y.im (log.f64 (hypot.f64 x.im x.re)) (*.f64 y.re (atan2.f64 x.im x.re)))))) (cbrt.f64 (sin.f64 (fma.f64 y.im (log.f64 (hypot.f64 x.im x.re)) (*.f64 y.re (atan2.f64 x.im x.re)))))))
39.0b
(*.f64 (/.f64 (pow.f64 (hypot.f64 x.re x.im) y.re) (exp.f64 (*.f64 (atan2.f64 x.im x.re) y.im))) (sin.f64 (-.f64 (*.f64 y.re (atan2.f64 x.im x.re)) (*.f64 y.im (log.f64 (/.f64 -1 x.im))))))
8.5b
(*.f64 (/.f64 (pow.f64 (hypot.f64 x.re x.im) y.re) (exp.f64 (*.f64 (atan2.f64 x.im x.re) y.im))) (sin.f64 (fma.f64 (log.f64 (hypot.f64 x.re x.im)) y.im (*.f64 (*.f64 (cbrt.f64 y.re) (cbrt.f64 y.re)) (*.f64 (atan2.f64 x.im x.re) (cbrt.f64 y.re))))))
17.5b
(*.f64 (/.f64 (pow.f64 (hypot.f64 x.re x.im) y.re) (exp.f64 (*.f64 (atan2.f64 x.im x.re) y.im))) (cbrt.f64 (pow.f64 (sin.f64 (fma.f64 y.im (log.f64 (hypot.f64 x.im x.re)) (*.f64 y.re (atan2.f64 x.im x.re)))) 3)))
23.4b
(*.f64 (/.f64 (pow.f64 (hypot.f64 x.re x.im) y.re) (exp.f64 (*.f64 (atan2.f64 x.im x.re) y.im))) (sin.f64 (fma.f64 (log.f64 (hypot.f64 x.re x.im)) y.im (sqrt.f64 (*.f64 (pow.f64 y.re 2) (pow.f64 (atan2.f64 x.im x.re) 2))))))
15.7b
(*.f64 (log.f64 (exp.f64 (pow.f64 (hypot.f64 x.im x.re) y.re))) (sin.f64 (fma.f64 (log.f64 (hypot.f64 x.re x.im)) y.im (*.f64 y.re (atan2.f64 x.im x.re)))))
20.0b
(*.f64 (/.f64 (pow.f64 (hypot.f64 x.re x.im) y.re) (exp.f64 (*.f64 (atan2.f64 x.im x.re) y.im))) (sin.f64 (fma.f64 (log.f64 (hypot.f64 x.re x.im)) y.im (*.f64 (cbrt.f64 (*.f64 (pow.f64 y.re 2) (pow.f64 (atan2.f64 x.im x.re) 2))) (cbrt.f64 (*.f64 y.re (atan2.f64 x.im x.re)))))))
8.6b
(*.f64 (/.f64 (pow.f64 (hypot.f64 x.re x.im) y.re) (exp.f64 (expm1.f64 (log1p.f64 (*.f64 y.im (atan2.f64 x.im x.re)))))) (sin.f64 (fma.f64 (log.f64 (hypot.f64 x.re x.im)) y.im (*.f64 y.re (atan2.f64 x.im x.re)))))
20.8b
(*.f64 (pow.f64 (exp.f64 y.im) (neg.f64 (atan2.f64 x.im x.re))) (sin.f64 (fma.f64 (log.f64 (hypot.f64 x.re x.im)) y.im (*.f64 y.re (atan2.f64 x.im x.re)))))
8.7b
(*.f64 (/.f64 (pow.f64 (hypot.f64 x.re x.im) y.re) (exp.f64 (*.f64 (atan2.f64 x.im x.re) y.im))) (*.f64 (*.f64 (cbrt.f64 (sin.f64 (fma.f64 y.im (log.f64 (hypot.f64 x.im x.re)) (*.f64 y.re (atan2.f64 x.im x.re))))) (cbrt.f64 (sin.f64 (fma.f64 y.im (log.f64 (hypot.f64 x.im x.re)) (*.f64 y.re (atan2.f64 x.im x.re)))))) (cbrt.f64 (sin.f64 (fma.f64 y.im (log.f64 (hypot.f64 x.im x.re)) (*.f64 y.re (atan2.f64 x.im x.re)))))))
40.2b
(*.f64 (log.f64 (exp.f64 (/.f64 (pow.f64 (hypot.f64 x.im x.re) y.re) (exp.f64 (*.f64 y.im (atan2.f64 x.im x.re)))))) (sin.f64 (fma.f64 (log.f64 x.im) y.im (*.f64 y.re (atan2.f64 x.im x.re)))))
12.5b
(*.f64 (/.f64 (pow.f64 (hypot.f64 x.re x.im) y.re) (exp.f64 (*.f64 (atan2.f64 x.im x.re) y.im))) (/.f64 (*.f64 (-.f64 (*.f64 (cos.f64 (*.f64 y.re (atan2.f64 x.im x.re))) (sin.f64 (*.f64 y.im (log.f64 (hypot.f64 x.im x.re))))) (*.f64 (sin.f64 (*.f64 y.re (atan2.f64 x.im x.re))) (cos.f64 (*.f64 y.im (log.f64 (hypot.f64 x.im x.re)))))) (fma.f64 (sin.f64 (*.f64 y.re (atan2.f64 x.im x.re))) (cos.f64 (*.f64 y.im (log.f64 (hypot.f64 x.im x.re)))) (*.f64 (cos.f64 (*.f64 y.re (atan2.f64 x.im x.re))) (sin.f64 (*.f64 y.im (log.f64 (hypot.f64 x.im x.re))))))) (-.f64 (*.f64 (cos.f64 (*.f64 y.re (atan2.f64 x.im x.re))) (sin.f64 (*.f64 y.im (log.f64 (hypot.f64 x.im x.re))))) (*.f64 (sin.f64 (*.f64 y.re (atan2.f64 x.im x.re))) (cos.f64 (*.f64 y.im (log.f64 (hypot.f64 x.im x.re))))))))
18.4b
(*.f64 (/.f64 (pow.f64 (hypot.f64 x.re x.im) y.re) (exp.f64 (*.f64 (atan2.f64 x.im x.re) y.im))) (/.f64 (+.f64 (pow.f64 (*.f64 (cos.f64 (*.f64 y.re (atan2.f64 x.im x.re))) (sin.f64 (*.f64 y.im (log.f64 (hypot.f64 x.im x.re))))) 3) (pow.f64 (*.f64 (sin.f64 (*.f64 y.re (atan2.f64 x.im x.re))) (cos.f64 (*.f64 y.im (log.f64 (hypot.f64 x.im x.re))))) 3)) (fma.f64 (sin.f64 (*.f64 y.re (atan2.f64 x.im x.re))) (*.f64 (sin.f64 (*.f64 y.re (atan2.f64 x.im x.re))) (*.f64 (cos.f64 (*.f64 y.im (log.f64 (hypot.f64 x.im x.re)))) (cos.f64 (*.f64 y.im (log.f64 (hypot.f64 x.im x.re)))))) (*.f64 (*.f64 (cos.f64 (*.f64 y.re (atan2.f64 x.im x.re))) (sin.f64 (*.f64 y.im (log.f64 (hypot.f64 x.im x.re))))) (-.f64 (*.f64 (cos.f64 (*.f64 y.re (atan2.f64 x.im x.re))) (sin.f64 (*.f64 y.im (log.f64 (hypot.f64 x.im x.re))))) (*.f64 (sin.f64 (*.f64 y.re (atan2.f64 x.im x.re))) (cos.f64 (*.f64 y.im (log.f64 (hypot.f64 x.im x.re))))))))))
21.8b
(*.f64 (/.f64 (pow.f64 (hypot.f64 x.re x.im) y.re) (exp.f64 (*.f64 (atan2.f64 x.im x.re) y.im))) (sqrt.f64 (*.f64 (sin.f64 (fma.f64 y.im (log.f64 (hypot.f64 x.im x.re)) (*.f64 y.re (atan2.f64 x.im x.re)))) (sin.f64 (fma.f64 y.im (log.f64 (hypot.f64 x.im x.re)) (*.f64 y.re (atan2.f64 x.im x.re)))))))
Compiler

Compiled 3594 to 964 computations (73.2% saved)

localize23.0ms (0.2%)

Local error

Found 4 expressions with local error:

0.8b
(*.f64 (*.f64 (cbrt.f64 y.re) (cbrt.f64 y.re)) (*.f64 (atan2.f64 x.im x.re) (cbrt.f64 y.re)))
1.0b
(*.f64 (atan2.f64 x.im x.re) (cbrt.f64 y.re))
2.1b
(*.f64 (atan2.f64 x.im x.re) y.im)
33.2b
(sin.f64 (fma.f64 (log.f64 (hypot.f64 x.re x.im)) y.im (*.f64 (*.f64 (cbrt.f64 y.re) (cbrt.f64 y.re)) (*.f64 (atan2.f64 x.im x.re) (cbrt.f64 y.re)))))

rewrite337.0ms (2.6%)

Algorithm
rewrite-expression-head
Error
2.6b
Rules
26×add-sqr-sqrt_binary64
25×pow1_binary64
24×add-exp-log_binary64
18×add-cube-cbrt_binary64
17×add-cbrt-cube_binary64
Counts
4 → 139
Calls

4 calls:

16.0ms
(*.f64 (atan2.f64 x.im x.re) (cbrt.f64 y.re))
16.0ms
(*.f64 (*.f64 (cbrt.f64 y.re) (cbrt.f64 y.re)) (*.f64 (atan2.f64 x.im x.re) (cbrt.f64 y.re)))
14.0ms
(*.f64 (atan2.f64 x.im x.re) y.im)
10.0ms
(sin.f64 (fma.f64 (log.f64 (hypot.f64 x.re x.im)) y.im (*.f64 (*.f64 (cbrt.f64 y.re) (cbrt.f64 y.re)) (*.f64 (atan2.f64 x.im x.re) (cbrt.f64 y.re)))))
Compiler

Compiled 4626 to 600 computations (87% saved)

series195.0ms (1.5%)

Error
2.6b
Counts
4 → 44
Calls

4 calls:

75.0ms
(sin.f64 (fma.f64 (log.f64 (hypot.f64 x.re x.im)) y.im (*.f64 (*.f64 (cbrt.f64 y.re) (cbrt.f64 y.re)) (*.f64 (atan2.f64 x.im x.re) (cbrt.f64 y.re)))))
44.0ms
(*.f64 (atan2.f64 x.im x.re) (cbrt.f64 y.re))
28.0ms
(*.f64 (*.f64 (cbrt.f64 y.re) (cbrt.f64 y.re)) (*.f64 (atan2.f64 x.im x.re) (cbrt.f64 y.re)))
22.0ms
(*.f64 (atan2.f64 x.im x.re) y.im)
Compiler

Compiled 3840 to 1966 computations (48.8% saved)

simplify137.0ms (1%)

Algorithm
egg-herbie
Rules
524×prod-exp_binary64
489×fma-neg_binary64
262×fma-def_binary64
256×exp-prod_binary64
256×log-prod_binary64
Counts
183 → 99
Iterations

Useful iterations: 3 (0.0ms)

IterNodesCost
02204188
15062964
215952952
339002938
453752938

prune131.0ms (1%)

Pruning

14 alts after pruning (13 fresh and 1 done)

PrunedKeptTotal
New99099
Fresh01313
Picked011
Done000
Total9914113
Error
2.6b
Counts
113 → 14
Alt Table
StatusErrorProgram
12.7b
(*.f64 (/.f64 (pow.f64 (hypot.f64 x.re x.im) y.re) (exp.f64 (*.f64 (atan2.f64 x.im x.re) y.im))) (*.f64 (cbrt.f64 (*.f64 (sin.f64 (fma.f64 y.im (log.f64 (hypot.f64 x.im x.re)) (*.f64 y.re (atan2.f64 x.im x.re)))) (sin.f64 (fma.f64 y.im (log.f64 (hypot.f64 x.im x.re)) (*.f64 y.re (atan2.f64 x.im x.re)))))) (cbrt.f64 (sin.f64 (fma.f64 y.im (log.f64 (hypot.f64 x.im x.re)) (*.f64 y.re (atan2.f64 x.im x.re)))))))
39.0b
(*.f64 (/.f64 (pow.f64 (hypot.f64 x.re x.im) y.re) (exp.f64 (*.f64 (atan2.f64 x.im x.re) y.im))) (sin.f64 (-.f64 (*.f64 y.re (atan2.f64 x.im x.re)) (*.f64 y.im (log.f64 (/.f64 -1 x.im))))))
8.5b
(*.f64 (/.f64 (pow.f64 (hypot.f64 x.re x.im) y.re) (exp.f64 (*.f64 (atan2.f64 x.im x.re) y.im))) (sin.f64 (fma.f64 (log.f64 (hypot.f64 x.re x.im)) y.im (*.f64 (*.f64 (cbrt.f64 y.re) (cbrt.f64 y.re)) (*.f64 (atan2.f64 x.im x.re) (cbrt.f64 y.re))))))
17.5b
(*.f64 (/.f64 (pow.f64 (hypot.f64 x.re x.im) y.re) (exp.f64 (*.f64 (atan2.f64 x.im x.re) y.im))) (cbrt.f64 (pow.f64 (sin.f64 (fma.f64 y.im (log.f64 (hypot.f64 x.im x.re)) (*.f64 y.re (atan2.f64 x.im x.re)))) 3)))
23.4b
(*.f64 (/.f64 (pow.f64 (hypot.f64 x.re x.im) y.re) (exp.f64 (*.f64 (atan2.f64 x.im x.re) y.im))) (sin.f64 (fma.f64 (log.f64 (hypot.f64 x.re x.im)) y.im (sqrt.f64 (*.f64 (pow.f64 y.re 2) (pow.f64 (atan2.f64 x.im x.re) 2))))))
15.7b
(*.f64 (log.f64 (exp.f64 (pow.f64 (hypot.f64 x.im x.re) y.re))) (sin.f64 (fma.f64 (log.f64 (hypot.f64 x.re x.im)) y.im (*.f64 y.re (atan2.f64 x.im x.re)))))
20.0b
(*.f64 (/.f64 (pow.f64 (hypot.f64 x.re x.im) y.re) (exp.f64 (*.f64 (atan2.f64 x.im x.re) y.im))) (sin.f64 (fma.f64 (log.f64 (hypot.f64 x.re x.im)) y.im (*.f64 (cbrt.f64 (*.f64 (pow.f64 y.re 2) (pow.f64 (atan2.f64 x.im x.re) 2))) (cbrt.f64 (*.f64 y.re (atan2.f64 x.im x.re)))))))
8.6b
(*.f64 (/.f64 (pow.f64 (hypot.f64 x.re x.im) y.re) (exp.f64 (expm1.f64 (log1p.f64 (*.f64 y.im (atan2.f64 x.im x.re)))))) (sin.f64 (fma.f64 (log.f64 (hypot.f64 x.re x.im)) y.im (*.f64 y.re (atan2.f64 x.im x.re)))))
20.8b
(*.f64 (pow.f64 (exp.f64 y.im) (neg.f64 (atan2.f64 x.im x.re))) (sin.f64 (fma.f64 (log.f64 (hypot.f64 x.re x.im)) y.im (*.f64 y.re (atan2.f64 x.im x.re)))))
8.7b
(*.f64 (/.f64 (pow.f64 (hypot.f64 x.re x.im) y.re) (exp.f64 (*.f64 (atan2.f64 x.im x.re) y.im))) (*.f64 (*.f64 (cbrt.f64 (sin.f64 (fma.f64 y.im (log.f64 (hypot.f64 x.im x.re)) (*.f64 y.re (atan2.f64 x.im x.re))))) (cbrt.f64 (sin.f64 (fma.f64 y.im (log.f64 (hypot.f64 x.im x.re)) (*.f64 y.re (atan2.f64 x.im x.re)))))) (cbrt.f64 (sin.f64 (fma.f64 y.im (log.f64 (hypot.f64 x.im x.re)) (*.f64 y.re (atan2.f64 x.im x.re)))))))
40.2b
(*.f64 (log.f64 (exp.f64 (/.f64 (pow.f64 (hypot.f64 x.im x.re) y.re) (exp.f64 (*.f64 y.im (atan2.f64 x.im x.re)))))) (sin.f64 (fma.f64 (log.f64 x.im) y.im (*.f64 y.re (atan2.f64 x.im x.re)))))
12.5b
(*.f64 (/.f64 (pow.f64 (hypot.f64 x.re x.im) y.re) (exp.f64 (*.f64 (atan2.f64 x.im x.re) y.im))) (/.f64 (*.f64 (-.f64 (*.f64 (cos.f64 (*.f64 y.re (atan2.f64 x.im x.re))) (sin.f64 (*.f64 y.im (log.f64 (hypot.f64 x.im x.re))))) (*.f64 (sin.f64 (*.f64 y.re (atan2.f64 x.im x.re))) (cos.f64 (*.f64 y.im (log.f64 (hypot.f64 x.im x.re)))))) (fma.f64 (sin.f64 (*.f64 y.re (atan2.f64 x.im x.re))) (cos.f64 (*.f64 y.im (log.f64 (hypot.f64 x.im x.re)))) (*.f64 (cos.f64 (*.f64 y.re (atan2.f64 x.im x.re))) (sin.f64 (*.f64 y.im (log.f64 (hypot.f64 x.im x.re))))))) (-.f64 (*.f64 (cos.f64 (*.f64 y.re (atan2.f64 x.im x.re))) (sin.f64 (*.f64 y.im (log.f64 (hypot.f64 x.im x.re))))) (*.f64 (sin.f64 (*.f64 y.re (atan2.f64 x.im x.re))) (cos.f64 (*.f64 y.im (log.f64 (hypot.f64 x.im x.re))))))))
18.4b
(*.f64 (/.f64 (pow.f64 (hypot.f64 x.re x.im) y.re) (exp.f64 (*.f64 (atan2.f64 x.im x.re) y.im))) (/.f64 (+.f64 (pow.f64 (*.f64 (cos.f64 (*.f64 y.re (atan2.f64 x.im x.re))) (sin.f64 (*.f64 y.im (log.f64 (hypot.f64 x.im x.re))))) 3) (pow.f64 (*.f64 (sin.f64 (*.f64 y.re (atan2.f64 x.im x.re))) (cos.f64 (*.f64 y.im (log.f64 (hypot.f64 x.im x.re))))) 3)) (fma.f64 (sin.f64 (*.f64 y.re (atan2.f64 x.im x.re))) (*.f64 (sin.f64 (*.f64 y.re (atan2.f64 x.im x.re))) (*.f64 (cos.f64 (*.f64 y.im (log.f64 (hypot.f64 x.im x.re)))) (cos.f64 (*.f64 y.im (log.f64 (hypot.f64 x.im x.re)))))) (*.f64 (*.f64 (cos.f64 (*.f64 y.re (atan2.f64 x.im x.re))) (sin.f64 (*.f64 y.im (log.f64 (hypot.f64 x.im x.re))))) (-.f64 (*.f64 (cos.f64 (*.f64 y.re (atan2.f64 x.im x.re))) (sin.f64 (*.f64 y.im (log.f64 (hypot.f64 x.im x.re))))) (*.f64 (sin.f64 (*.f64 y.re (atan2.f64 x.im x.re))) (cos.f64 (*.f64 y.im (log.f64 (hypot.f64 x.im x.re))))))))))
21.8b
(*.f64 (/.f64 (pow.f64 (hypot.f64 x.re x.im) y.re) (exp.f64 (*.f64 (atan2.f64 x.im x.re) y.im))) (sqrt.f64 (*.f64 (sin.f64 (fma.f64 y.im (log.f64 (hypot.f64 x.im x.re)) (*.f64 y.re (atan2.f64 x.im x.re)))) (sin.f64 (fma.f64 y.im (log.f64 (hypot.f64 x.im x.re)) (*.f64 y.re (atan2.f64 x.im x.re)))))))
Compiler

Compiled 3588 to 900 computations (74.9% saved)

localize44.0ms (0.3%)

Local error

Found 4 expressions with local error:

1.6b
(*.f64 y.re (atan2.f64 x.im x.re))
1.7b
(expm1.f64 (log1p.f64 (*.f64 y.im (atan2.f64 x.im x.re))))
2.1b
(*.f64 y.im (atan2.f64 x.im x.re))
33.1b
(sin.f64 (fma.f64 (log.f64 (hypot.f64 x.re x.im)) y.im (*.f64 y.re (atan2.f64 x.im x.re))))

rewrite322.0ms (2.5%)

Algorithm
rewrite-expression-head
Error
2.6b
Rules
30×pow1_binary64
24×add-sqr-sqrt_binary64
20×add-cube-cbrt_binary64
16×add-exp-log_binary64
16×add-cbrt-cube_binary64
Counts
4 → 137
Calls

4 calls:

13.0ms
(*.f64 y.im (atan2.f64 x.im x.re))
12.0ms
(*.f64 y.re (atan2.f64 x.im x.re))
11.0ms
(sin.f64 (fma.f64 (log.f64 (hypot.f64 x.re x.im)) y.im (*.f64 y.re (atan2.f64 x.im x.re))))
10.0ms
(expm1.f64 (log1p.f64 (*.f64 y.im (atan2.f64 x.im x.re))))
Compiler

Compiled 3755 to 615 computations (83.6% saved)

series212.0ms (1.6%)

Error
2.6b
Counts
4 → 46
Calls

4 calls:

72.0ms
(sin.f64 (fma.f64 (log.f64 (hypot.f64 x.re x.im)) y.im (*.f64 y.re (atan2.f64 x.im x.re))))
68.0ms
(expm1.f64 (log1p.f64 (*.f64 y.im (atan2.f64 x.im x.re))))
19.0ms
(*.f64 y.re (atan2.f64 x.im x.re))
19.0ms
(*.f64 y.im (atan2.f64 x.im x.re))
Compiler

Compiled 4047 to 2139 computations (47.1% saved)

simplify128.0ms (1%)

Algorithm
egg-herbie
Rules
408×prod-exp_binary64
394×*-commutative_binary64
297×fma-def_binary64
280×fma-neg_binary64
242×times-frac_binary64
Counts
183 → 87
Iterations

Useful iterations: 3 (0.0ms)

IterNodesCost
02243215
14772925
213332915
341122893
451532893

prune162.0ms (1.2%)

Pruning

14 alts after pruning (12 fresh and 2 done)

PrunedKeptTotal
New87087
Fresh01212
Picked011
Done011
Total8714101
Error
2.6b
Counts
101 → 14
Alt Table
StatusErrorProgram
12.7b
(*.f64 (/.f64 (pow.f64 (hypot.f64 x.re x.im) y.re) (exp.f64 (*.f64 (atan2.f64 x.im x.re) y.im))) (*.f64 (cbrt.f64 (*.f64 (sin.f64 (fma.f64 y.im (log.f64 (hypot.f64 x.im x.re)) (*.f64 y.re (atan2.f64 x.im x.re)))) (sin.f64 (fma.f64 y.im (log.f64 (hypot.f64 x.im x.re)) (*.f64 y.re (atan2.f64 x.im x.re)))))) (cbrt.f64 (sin.f64 (fma.f64 y.im (log.f64 (hypot.f64 x.im x.re)) (*.f64 y.re (atan2.f64 x.im x.re)))))))
39.0b
(*.f64 (/.f64 (pow.f64 (hypot.f64 x.re x.im) y.re) (exp.f64 (*.f64 (atan2.f64 x.im x.re) y.im))) (sin.f64 (-.f64 (*.f64 y.re (atan2.f64 x.im x.re)) (*.f64 y.im (log.f64 (/.f64 -1 x.im))))))
8.5b
(*.f64 (/.f64 (pow.f64 (hypot.f64 x.re x.im) y.re) (exp.f64 (*.f64 (atan2.f64 x.im x.re) y.im))) (sin.f64 (fma.f64 (log.f64 (hypot.f64 x.re x.im)) y.im (*.f64 (*.f64 (cbrt.f64 y.re) (cbrt.f64 y.re)) (*.f64 (atan2.f64 x.im x.re) (cbrt.f64 y.re))))))
17.5b
(*.f64 (/.f64 (pow.f64 (hypot.f64 x.re x.im) y.re) (exp.f64 (*.f64 (atan2.f64 x.im x.re) y.im))) (cbrt.f64 (pow.f64 (sin.f64 (fma.f64 y.im (log.f64 (hypot.f64 x.im x.re)) (*.f64 y.re (atan2.f64 x.im x.re)))) 3)))
23.4b
(*.f64 (/.f64 (pow.f64 (hypot.f64 x.re x.im) y.re) (exp.f64 (*.f64 (atan2.f64 x.im x.re) y.im))) (sin.f64 (fma.f64 (log.f64 (hypot.f64 x.re x.im)) y.im (sqrt.f64 (*.f64 (pow.f64 y.re 2) (pow.f64 (atan2.f64 x.im x.re) 2))))))
15.7b
(*.f64 (log.f64 (exp.f64 (pow.f64 (hypot.f64 x.im x.re) y.re))) (sin.f64 (fma.f64 (log.f64 (hypot.f64 x.re x.im)) y.im (*.f64 y.re (atan2.f64 x.im x.re)))))
20.0b
(*.f64 (/.f64 (pow.f64 (hypot.f64 x.re x.im) y.re) (exp.f64 (*.f64 (atan2.f64 x.im x.re) y.im))) (sin.f64 (fma.f64 (log.f64 (hypot.f64 x.re x.im)) y.im (*.f64 (cbrt.f64 (*.f64 (pow.f64 y.re 2) (pow.f64 (atan2.f64 x.im x.re) 2))) (cbrt.f64 (*.f64 y.re (atan2.f64 x.im x.re)))))))
8.6b
(*.f64 (/.f64 (pow.f64 (hypot.f64 x.re x.im) y.re) (exp.f64 (expm1.f64 (log1p.f64 (*.f64 y.im (atan2.f64 x.im x.re)))))) (sin.f64 (fma.f64 (log.f64 (hypot.f64 x.re x.im)) y.im (*.f64 y.re (atan2.f64 x.im x.re)))))
20.8b
(*.f64 (pow.f64 (exp.f64 y.im) (neg.f64 (atan2.f64 x.im x.re))) (sin.f64 (fma.f64 (log.f64 (hypot.f64 x.re x.im)) y.im (*.f64 y.re (atan2.f64 x.im x.re)))))
8.7b
(*.f64 (/.f64 (pow.f64 (hypot.f64 x.re x.im) y.re) (exp.f64 (*.f64 (atan2.f64 x.im x.re) y.im))) (*.f64 (*.f64 (cbrt.f64 (sin.f64 (fma.f64 y.im (log.f64 (hypot.f64 x.im x.re)) (*.f64 y.re (atan2.f64 x.im x.re))))) (cbrt.f64 (sin.f64 (fma.f64 y.im (log.f64 (hypot.f64 x.im x.re)) (*.f64 y.re (atan2.f64 x.im x.re)))))) (cbrt.f64 (sin.f64 (fma.f64 y.im (log.f64 (hypot.f64 x.im x.re)) (*.f64 y.re (atan2.f64 x.im x.re)))))))
40.2b
(*.f64 (log.f64 (exp.f64 (/.f64 (pow.f64 (hypot.f64 x.im x.re) y.re) (exp.f64 (*.f64 y.im (atan2.f64 x.im x.re)))))) (sin.f64 (fma.f64 (log.f64 x.im) y.im (*.f64 y.re (atan2.f64 x.im x.re)))))
12.5b
(*.f64 (/.f64 (pow.f64 (hypot.f64 x.re x.im) y.re) (exp.f64 (*.f64 (atan2.f64 x.im x.re) y.im))) (/.f64 (*.f64 (-.f64 (*.f64 (cos.f64 (*.f64 y.re (atan2.f64 x.im x.re))) (sin.f64 (*.f64 y.im (log.f64 (hypot.f64 x.im x.re))))) (*.f64 (sin.f64 (*.f64 y.re (atan2.f64 x.im x.re))) (cos.f64 (*.f64 y.im (log.f64 (hypot.f64 x.im x.re)))))) (fma.f64 (sin.f64 (*.f64 y.re (atan2.f64 x.im x.re))) (cos.f64 (*.f64 y.im (log.f64 (hypot.f64 x.im x.re)))) (*.f64 (cos.f64 (*.f64 y.re (atan2.f64 x.im x.re))) (sin.f64 (*.f64 y.im (log.f64 (hypot.f64 x.im x.re))))))) (-.f64 (*.f64 (cos.f64 (*.f64 y.re (atan2.f64 x.im x.re))) (sin.f64 (*.f64 y.im (log.f64 (hypot.f64 x.im x.re))))) (*.f64 (sin.f64 (*.f64 y.re (atan2.f64 x.im x.re))) (cos.f64 (*.f64 y.im (log.f64 (hypot.f64 x.im x.re))))))))
18.4b
(*.f64 (/.f64 (pow.f64 (hypot.f64 x.re x.im) y.re) (exp.f64 (*.f64 (atan2.f64 x.im x.re) y.im))) (/.f64 (+.f64 (pow.f64 (*.f64 (cos.f64 (*.f64 y.re (atan2.f64 x.im x.re))) (sin.f64 (*.f64 y.im (log.f64 (hypot.f64 x.im x.re))))) 3) (pow.f64 (*.f64 (sin.f64 (*.f64 y.re (atan2.f64 x.im x.re))) (cos.f64 (*.f64 y.im (log.f64 (hypot.f64 x.im x.re))))) 3)) (fma.f64 (sin.f64 (*.f64 y.re (atan2.f64 x.im x.re))) (*.f64 (sin.f64 (*.f64 y.re (atan2.f64 x.im x.re))) (*.f64 (cos.f64 (*.f64 y.im (log.f64 (hypot.f64 x.im x.re)))) (cos.f64 (*.f64 y.im (log.f64 (hypot.f64 x.im x.re)))))) (*.f64 (*.f64 (cos.f64 (*.f64 y.re (atan2.f64 x.im x.re))) (sin.f64 (*.f64 y.im (log.f64 (hypot.f64 x.im x.re))))) (-.f64 (*.f64 (cos.f64 (*.f64 y.re (atan2.f64 x.im x.re))) (sin.f64 (*.f64 y.im (log.f64 (hypot.f64 x.im x.re))))) (*.f64 (sin.f64 (*.f64 y.re (atan2.f64 x.im x.re))) (cos.f64 (*.f64 y.im (log.f64 (hypot.f64 x.im x.re))))))))))
21.8b
(*.f64 (/.f64 (pow.f64 (hypot.f64 x.re x.im) y.re) (exp.f64 (*.f64 (atan2.f64 x.im x.re) y.im))) (sqrt.f64 (*.f64 (sin.f64 (fma.f64 y.im (log.f64 (hypot.f64 x.im x.re)) (*.f64 y.re (atan2.f64 x.im x.re)))) (sin.f64 (fma.f64 y.im (log.f64 (hypot.f64 x.im x.re)) (*.f64 y.re (atan2.f64 x.im x.re)))))))
Compiler

Compiled 2758 to 636 computations (76.9% saved)

regimes1.8s (13.5%)

Accuracy

Total 0.3b remaining (8.9%)

Threshold costs 0.3b (8.9%)

Compiler

Compiled 40272 to 20950 computations (48% saved)

simplify5.0ms (0%)

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

Useful iterations: 0 (0.0ms)

IterNodesCost
01852
12752
23752
34352
44752
54852
64852

end1.0ms (0%)

Compiler

Compiled 30 to 15 computations (50% saved)

sample5.0s (38%)

Algorithm
intervals
Results
1.8s2468×body1024invalid
1.2s7566×body128valid
453.0ms921×body512invalid
208.0ms172×body2048invalid
136.0ms185×body1024valid
112.0ms363×body256invalid
74.0ms135×body512valid
74.0ms463×body128invalid
35.0ms101×body256valid
16.0ms13×body2048valid
Compiler

Compiled 744 to 314 computations (57.8% saved)

Profiling

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