Details

Time bar (total: 4.8s)

analyze537.0ms (11.1%)

Algorithm
search
Search
TrueOtherFalseIter
0%50%50%0
0%50%50%1
25%25%50%2
25%25%50%3
31.2%18.7%50%4
31.2%18.7%50%5
34.3%15.6%50%6
34.3%15.6%50%7
35.9%14%50%8
35.9%14%50%9
36.7%13.3%50%10
36.7%13.3%50%11
37.1%12.9%50%12
37.1%12.9%50%13
37.3%12.7%50%14
Compiler

Compiled 20 to 14 computations (30% saved)

sample2.0s (40.8%)

Results
787.0ms6203×body128valid
412.0ms548×body4096valid
411.0ms667×body2048valid
207.0ms475×body1024valid
74.0ms255×body512valid
22.0ms108×body256valid
Compiler

Compiled 57 to 40 computations (29.8% saved)

simplify29.0ms (0.6%)

Algorithm
egg-herbie
Rules
203×fma-def_binary64
142×fma-neg_binary64
51×distribute-rgt-in_binary64
42×cancel-sign-sub-inv_binary64
28×sub-neg_binary64
Counts
1 → 2
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
01315
12015
23315
35015
46915
59815
615115
721115
826315
930515
1034315
1137915
1239615
1341515
1442815
1546515
1647715
1748615
1844915

prune4.0ms (0.1%)

Pruning

1 alts after pruning (1 fresh and 0 done)

PrunedKeptTotal
New112
Fresh101
Picked000
Done000
Total213
Error
13.4b
Counts
3 → 1
Alt Table
StatusErrorProgram
13.4b
(*.f64 1/2 (sqrt.f64 (*.f64 2 (-.f64 (hypot.f64 re im) re))))
Compiler

Compiled 51 to 37 computations (27.5% saved)

localize6.0ms (0.1%)

Local error

Found 3 expressions with local error:

NewErrorProgram
0.0b
(hypot.f64 re im)
0.5b
(sqrt.f64 (*.f64 2 (-.f64 (hypot.f64 re im) re)))
0.6b
(-.f64 (hypot.f64 re im) re)

series56.0ms (1.2%)

Counts
3 → 56
Calls

3 calls:

32.0ms
(sqrt.f64 (*.f64 2 (-.f64 (hypot.f64 re im) re)))
13.0ms
(hypot.f64 re im)
11.0ms
(-.f64 (hypot.f64 re im) re)

rewrite57.0ms (1.2%)

Algorithm
batch-egg-rewrite
Rules
811×log1p-expm1-u_binary64
811×expm1-log1p-u_binary64
410×prod-diff_binary64
96×egg-rr
85×add-sqr-sqrt_binary64
Counts
3 → 96
Calls

3 calls:

56.0ms
(hypot.f64 re im)
56.0ms
(sqrt.f64 (*.f64 2 (-.f64 (hypot.f64 re im) re)))
56.0ms
(-.f64 (hypot.f64 re im) re)
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
0823
117223
2205323
3573523
000
100

simplify70.0ms (1.4%)

Algorithm
egg-herbie
Rules
618×fma-def_binary64
559×fma-neg_binary64
365×associate-/l*_binary64
347×times-frac_binary64
280×cancel-sign-sub-inv_binary64
Counts
152 → 168
Iterations

Useful iterations: 3 (0.0ms)

IterNodesCost
01581505
14891464
215851399
347931395
450571395

prune110.0ms (2.3%)

Pruning

6 alts after pruning (5 fresh and 1 done)

PrunedKeptTotal
New1635168
Fresh000
Picked011
Done000
Total1636169
Error
0.1b
Counts
169 → 6
Alt Table
StatusErrorProgram
13.4b
(*.f64 1/2 (sqrt.f64 (*.f64 2 (-.f64 (hypot.f64 re im) re))))
56.6b
(*.f64 1/2 (fma.f64 (sqrt.f64 1/2) (*.f64 (*.f64 im (sqrt.f64 2)) (sqrt.f64 (/.f64 1 re))) (fma.f64 (sqrt.f64 (/.f64 1 (pow.f64 re 9))) (-.f64 (*.f64 1/32 (/.f64 (*.f64 (sqrt.f64 2) (pow.f64 im 5)) (sqrt.f64 1/2))) (*.f64 1/256 (/.f64 (*.f64 (sqrt.f64 2) (pow.f64 im 5)) (sqrt.f64 1/2)))) (*.f64 (sqrt.f64 (/.f64 1 (pow.f64 re 5))) (*.f64 (/.f64 (*.f64 (pow.f64 im 3) (sqrt.f64 2)) (sqrt.f64 1/2)) -1/16)))))
15.3b
(*.f64 1/2 (sqrt.f64 (*.f64 2 (-.f64 (*.f64 (cbrt.f64 (hypot.f64 re im)) (pow.f64 (cbrt.f64 (hypot.f64 re im)) 2)) re))))
13.3b
(*.f64 1/2 (*.f64 (sqrt.f64 (-.f64 (hypot.f64 re im) re)) (sqrt.f64 2)))
56.6b
(*.f64 1/2 (sqrt.f64 (*.f64 2 (*.f64 1/2 (/.f64 (pow.f64 im 2) re)))))
48.1b
(*.f64 1/2 (*.f64 (*.f64 (sqrt.f64 1/2) (*.f64 (sqrt.f64 2) im)) (sqrt.f64 (/.f64 1 re))))
Compiler

Compiled 3730 to 2542 computations (31.8% saved)

localize7.0ms (0.1%)

Local error

Found 4 expressions with local error:

NewErrorProgram
0.0b
(hypot.f64 re im)
0.0b
(sqrt.f64 (-.f64 (hypot.f64 re im) re))
0.3b
(*.f64 (sqrt.f64 (-.f64 (hypot.f64 re im) re)) (sqrt.f64 2))
0.6b
(-.f64 (hypot.f64 re im) re)

series51.0ms (1.1%)

Counts
2 → 16
Calls

2 calls:

31.0ms
(*.f64 (sqrt.f64 (-.f64 (hypot.f64 re im) re)) (sqrt.f64 2))
20.0ms
(sqrt.f64 (-.f64 (hypot.f64 re im) re))

rewrite50.0ms (1%)

Algorithm
batch-egg-rewrite
Rules
865×log1p-expm1-u_binary64
865×expm1-log1p-u_binary64
410×prod-diff_binary64
93×add-sqr-sqrt_binary64
89×add-log-exp_binary64
Counts
2 → 42
Calls

2 calls:

49.0ms
(sqrt.f64 (-.f64 (hypot.f64 re im) re))
49.0ms
(*.f64 (sqrt.f64 (-.f64 (hypot.f64 re im) re)) (sqrt.f64 2))
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
0921
119121
2219821
3606221
000
100

simplify56.0ms (1.2%)

Algorithm
egg-herbie
Rules
712×fma-def_binary64
406×associate-*l*_binary64
402×fma-neg_binary64
293×associate-/l*_binary64
261×associate-*l/_binary64
Counts
58 → 71
Iterations

Useful iterations: 3 (0.0ms)

IterNodesCost
0134948
1408927
21368854
34910852
45120852

prune145.0ms (3%)

Pruning

9 alts after pruning (8 fresh and 1 done)

PrunedKeptTotal
New1935198
Fresh134
Picked101
Done011
Total1959204
Error
0.1b
Counts
204 → 9
Alt Table
StatusErrorProgram
13.4b
(*.f64 1/2 (*.f64 (pow.f64 (pow.f64 (-.f64 (hypot.f64 re im) re) 1/4) 2) (sqrt.f64 2)))
56.6b
(*.f64 1/2 (sqrt.f64 (*.f64 2 (*.f64 1/2 (/.f64 (pow.f64 im 2) re)))))
13.4b
(*.f64 1/2 (sqrt.f64 (*.f64 2 (-.f64 (hypot.f64 re im) re))))
13.6b
(*.f64 1/2 (*.f64 (sqrt.f64 (*.f64 (pow.f64 (cbrt.f64 (-.f64 (hypot.f64 re im) re)) 2) (cbrt.f64 (-.f64 (hypot.f64 re im) re)))) (sqrt.f64 2)))
56.6b
(*.f64 1/2 (fma.f64 (sqrt.f64 1/2) (*.f64 (*.f64 im (sqrt.f64 2)) (sqrt.f64 (/.f64 1 re))) (fma.f64 (sqrt.f64 (/.f64 1 (pow.f64 re 9))) (-.f64 (*.f64 1/32 (/.f64 (*.f64 (sqrt.f64 2) (pow.f64 im 5)) (sqrt.f64 1/2))) (*.f64 1/256 (/.f64 (*.f64 (sqrt.f64 2) (pow.f64 im 5)) (sqrt.f64 1/2)))) (*.f64 (sqrt.f64 (/.f64 1 (pow.f64 re 5))) (*.f64 (/.f64 (*.f64 (pow.f64 im 3) (sqrt.f64 2)) (sqrt.f64 1/2)) -1/16)))))
48.1b
(*.f64 1/2 (*.f64 (*.f64 (sqrt.f64 1/2) (*.f64 (sqrt.f64 2) im)) (sqrt.f64 (/.f64 1 re))))
56.8b
(*.f64 1/2 (*.f64 (-.f64 (fma.f64 1/32 (*.f64 (sqrt.f64 (/.f64 1 (pow.f64 re 9))) (/.f64 (pow.f64 im 5) (sqrt.f64 1/2))) (fma.f64 im (*.f64 (sqrt.f64 1/2) (sqrt.f64 (/.f64 1 re))) (*.f64 (*.f64 (sqrt.f64 (/.f64 1 (pow.f64 re 13))) (/.f64 (pow.f64 im 7) (sqrt.f64 1/2))) 1/256))) (fma.f64 1/16 (*.f64 (sqrt.f64 (/.f64 1 (pow.f64 re 5))) (/.f64 (pow.f64 im 3) (sqrt.f64 1/2))) (fma.f64 (sqrt.f64 (/.f64 1 (pow.f64 re 9))) (*.f64 1/256 (/.f64 (pow.f64 im 5) (sqrt.f64 1/2))) (*.f64 (sqrt.f64 (/.f64 1 (pow.f64 re 13))) (+.f64 (*.f64 1/8192 (/.f64 (pow.f64 im 7) (pow.f64 (sqrt.f64 1/2) 5))) (*.f64 5/256 (/.f64 (pow.f64 im 7) (sqrt.f64 1/2)))))))) (sqrt.f64 2)))
48.1b
(*.f64 1/2 (*.f64 (*.f64 (*.f64 (sqrt.f64 1/2) im) (sqrt.f64 (/.f64 1 re))) (sqrt.f64 2)))
56.7b
(*.f64 1/2 (*.f64 (sqrt.f64 (*.f64 1/2 (/.f64 (*.f64 im im) re))) (sqrt.f64 2)))
Compiler

Compiled 4972 to 3525 computations (29.1% saved)

localize10.0ms (0.2%)

Local error

Found 4 expressions with local error:

NewErrorProgram
0.0b
(hypot.f64 re im)
0.3b
(*.f64 (pow.f64 (pow.f64 (-.f64 (hypot.f64 re im) re) 1/4) 2) (sqrt.f64 2))
0.4b
(pow.f64 (pow.f64 (-.f64 (hypot.f64 re im) re) 1/4) 2)
0.6b
(-.f64 (hypot.f64 re im) re)

series71.0ms (1.5%)

Counts
2 → 32
Calls

2 calls:

40.0ms
(pow.f64 (pow.f64 (-.f64 (hypot.f64 re im) re) 1/4) 2)
30.0ms
(*.f64 (pow.f64 (pow.f64 (-.f64 (hypot.f64 re im) re) 1/4) 2) (sqrt.f64 2))

rewrite52.0ms (1.1%)

Algorithm
batch-egg-rewrite
Rules
480×log-prod_binary64
410×prod-diff_binary64
218×fma-def_binary64
190×expm1-udef_binary64
190×log1p-udef_binary64
Counts
2 → 49
Calls

2 calls:

51.0ms
(*.f64 (pow.f64 (pow.f64 (-.f64 (hypot.f64 re im) re) 1/4) 2) (sqrt.f64 2))
51.0ms
(pow.f64 (pow.f64 (-.f64 (hypot.f64 re im) re) 1/4) 2)
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
01125
124121
2254321
3509921
000
100

simplify54.0ms (1.1%)

Algorithm
egg-herbie
Rules
637×associate-/l*_binary64
607×fma-def_binary64
508×associate-/r*_binary64
247×cancel-sign-sub-inv_binary64
214×associate-/r/_binary64
Counts
81 → 100
Iterations

Useful iterations: 2 (0.0ms)

IterNodesCost
01951850
15781737
218321534
352111534

prune173.0ms (3.6%)

Pruning

10 alts after pruning (8 fresh and 2 done)

PrunedKeptTotal
New2261227
Fresh077
Picked011
Done011
Total22610236
Error
0.1b
Counts
236 → 10
Alt Table
StatusErrorProgram
13.4b
(*.f64 1/2 (*.f64 (pow.f64 (pow.f64 (-.f64 (hypot.f64 re im) re) 1/4) 2) (sqrt.f64 2)))
56.6b
(*.f64 1/2 (sqrt.f64 (*.f64 2 (*.f64 1/2 (/.f64 (pow.f64 im 2) re)))))
13.4b
(*.f64 1/2 (sqrt.f64 (*.f64 2 (-.f64 (hypot.f64 re im) re))))
13.6b
(*.f64 1/2 (*.f64 (sqrt.f64 (*.f64 (pow.f64 (cbrt.f64 (-.f64 (hypot.f64 re im) re)) 2) (cbrt.f64 (-.f64 (hypot.f64 re im) re)))) (sqrt.f64 2)))
56.6b
(*.f64 1/2 (fma.f64 (sqrt.f64 1/2) (*.f64 (*.f64 im (sqrt.f64 2)) (sqrt.f64 (/.f64 1 re))) (fma.f64 (sqrt.f64 (/.f64 1 (pow.f64 re 9))) (-.f64 (*.f64 1/32 (/.f64 (*.f64 (sqrt.f64 2) (pow.f64 im 5)) (sqrt.f64 1/2))) (*.f64 1/256 (/.f64 (*.f64 (sqrt.f64 2) (pow.f64 im 5)) (sqrt.f64 1/2)))) (*.f64 (sqrt.f64 (/.f64 1 (pow.f64 re 5))) (*.f64 (/.f64 (*.f64 (pow.f64 im 3) (sqrt.f64 2)) (sqrt.f64 1/2)) -1/16)))))
48.1b
(*.f64 1/2 (*.f64 (*.f64 (sqrt.f64 1/2) (*.f64 (sqrt.f64 2) im)) (sqrt.f64 (/.f64 1 re))))
56.8b
(*.f64 1/2 (*.f64 (-.f64 (fma.f64 1/32 (*.f64 (sqrt.f64 (/.f64 1 (pow.f64 re 9))) (/.f64 (pow.f64 im 5) (sqrt.f64 1/2))) (fma.f64 im (*.f64 (sqrt.f64 1/2) (sqrt.f64 (/.f64 1 re))) (*.f64 (*.f64 (sqrt.f64 (/.f64 1 (pow.f64 re 13))) (/.f64 (pow.f64 im 7) (sqrt.f64 1/2))) 1/256))) (fma.f64 1/16 (*.f64 (sqrt.f64 (/.f64 1 (pow.f64 re 5))) (/.f64 (pow.f64 im 3) (sqrt.f64 1/2))) (fma.f64 (sqrt.f64 (/.f64 1 (pow.f64 re 9))) (*.f64 1/256 (/.f64 (pow.f64 im 5) (sqrt.f64 1/2))) (*.f64 (sqrt.f64 (/.f64 1 (pow.f64 re 13))) (+.f64 (*.f64 1/8192 (/.f64 (pow.f64 im 7) (pow.f64 (sqrt.f64 1/2) 5))) (*.f64 5/256 (/.f64 (pow.f64 im 7) (sqrt.f64 1/2)))))))) (sqrt.f64 2)))
49.1b
(*.f64 1/2 (*.f64 (fma.f64 (*.f64 (*.f64 (/.f64 im re) (/.f64 im re)) (pow.f64 (*.f64 (sqrt.f64 im) (pow.f64 (/.f64 1/2 re) 1/4)) 2)) -1/8 (pow.f64 (*.f64 (sqrt.f64 im) (pow.f64 (/.f64 1/2 re) 1/4)) 2)) (sqrt.f64 2)))
56.7b
(*.f64 1/2 (*.f64 (sqrt.f64 (*.f64 1/2 (/.f64 (*.f64 im im) re))) (sqrt.f64 2)))
48.1b
(*.f64 1/2 (*.f64 (*.f64 (*.f64 (sqrt.f64 1/2) im) (sqrt.f64 (/.f64 1 re))) (sqrt.f64 2)))
Compiler

Compiled 6477 to 4677 computations (27.8% saved)

localize10.0ms (0.2%)

Local error

Found 4 expressions with local error:

NewErrorProgram
0.3b
(*.f64 (sqrt.f64 (*.f64 (pow.f64 (cbrt.f64 (-.f64 (hypot.f64 re im) re)) 2) (cbrt.f64 (-.f64 (hypot.f64 re im) re)))) (sqrt.f64 2))
0.3b
(pow.f64 (cbrt.f64 (-.f64 (hypot.f64 re im) re)) 2)
0.4b
(cbrt.f64 (-.f64 (hypot.f64 re im) re))
0.6b
(-.f64 (hypot.f64 re im) re)

series106.0ms (2.2%)

Counts
3 → 56
Calls

3 calls:

40.0ms
(pow.f64 (cbrt.f64 (-.f64 (hypot.f64 re im) re)) 2)
35.0ms
(*.f64 (sqrt.f64 (*.f64 (pow.f64 (cbrt.f64 (-.f64 (hypot.f64 re im) re)) 2) (cbrt.f64 (-.f64 (hypot.f64 re im) re)))) (sqrt.f64 2))
30.0ms
(cbrt.f64 (-.f64 (hypot.f64 re im) re))

rewrite55.0ms (1.1%)

Algorithm
batch-egg-rewrite
Rules
486×log-prod_binary64
410×prod-diff_binary64
245×fma-def_binary64
185×expm1-udef_binary64
185×log1p-udef_binary64
Counts
3 → 69
Calls

3 calls:

54.0ms
(*.f64 (sqrt.f64 (*.f64 (pow.f64 (cbrt.f64 (-.f64 (hypot.f64 re im) re)) 2) (cbrt.f64 (-.f64 (hypot.f64 re im) re)))) (sqrt.f64 2))
54.0ms
(pow.f64 (cbrt.f64 (-.f64 (hypot.f64 re im) re)) 2)
54.0ms
(cbrt.f64 (-.f64 (hypot.f64 re im) re))
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
01233
123433
2252433
3512633
000
100

simplify77.0ms (1.6%)

Algorithm
egg-herbie
Rules
747×associate-/l*_binary64
403×cancel-sign-sub-inv_binary64
237×associate-/r/_binary64
210×fma-neg_binary64
208×fma-def_binary64
Counts
125 → 154
Iterations

Useful iterations: 2 (0.0ms)

IterNodesCost
02843077
18572892
225422743
353892743

prune280.0ms (5.8%)

Pruning

10 alts after pruning (7 fresh and 3 done)

PrunedKeptTotal
New3771378
Fresh167
Picked011
Done022
Total37810388
Error
0.1b
Counts
388 → 10
Alt Table
StatusErrorProgram
54.8b
(*.f64 1/2 (fma.f64 (sqrt.f64 1/2) (*.f64 (*.f64 im (sqrt.f64 2)) (sqrt.f64 (/.f64 1 re))) (*.f64 (sqrt.f64 (/.f64 1 (pow.f64 re 5))) (*.f64 (/.f64 (*.f64 (sqrt.f64 2) (pow.f64 im 3)) (sqrt.f64 1/2)) -1/16))))
48.1b
(*.f64 1/2 (*.f64 (*.f64 (*.f64 (sqrt.f64 1/2) im) (sqrt.f64 (/.f64 1 re))) (sqrt.f64 2)))
13.4b
(*.f64 1/2 (*.f64 (pow.f64 (pow.f64 (-.f64 (hypot.f64 re im) re) 1/4) 2) (sqrt.f64 2)))
56.6b
(*.f64 1/2 (sqrt.f64 (*.f64 2 (*.f64 1/2 (/.f64 (pow.f64 im 2) re)))))
13.4b
(*.f64 1/2 (sqrt.f64 (*.f64 2 (-.f64 (hypot.f64 re im) re))))
13.6b
(*.f64 1/2 (*.f64 (sqrt.f64 (*.f64 (pow.f64 (cbrt.f64 (-.f64 (hypot.f64 re im) re)) 2) (cbrt.f64 (-.f64 (hypot.f64 re im) re)))) (sqrt.f64 2)))
48.1b
(*.f64 1/2 (*.f64 (*.f64 (sqrt.f64 1/2) (*.f64 (sqrt.f64 2) im)) (sqrt.f64 (/.f64 1 re))))
56.8b
(*.f64 1/2 (*.f64 (-.f64 (fma.f64 1/32 (*.f64 (sqrt.f64 (/.f64 1 (pow.f64 re 9))) (/.f64 (pow.f64 im 5) (sqrt.f64 1/2))) (fma.f64 im (*.f64 (sqrt.f64 1/2) (sqrt.f64 (/.f64 1 re))) (*.f64 (*.f64 (sqrt.f64 (/.f64 1 (pow.f64 re 13))) (/.f64 (pow.f64 im 7) (sqrt.f64 1/2))) 1/256))) (fma.f64 1/16 (*.f64 (sqrt.f64 (/.f64 1 (pow.f64 re 5))) (/.f64 (pow.f64 im 3) (sqrt.f64 1/2))) (fma.f64 (sqrt.f64 (/.f64 1 (pow.f64 re 9))) (*.f64 1/256 (/.f64 (pow.f64 im 5) (sqrt.f64 1/2))) (*.f64 (sqrt.f64 (/.f64 1 (pow.f64 re 13))) (+.f64 (*.f64 1/8192 (/.f64 (pow.f64 im 7) (pow.f64 (sqrt.f64 1/2) 5))) (*.f64 5/256 (/.f64 (pow.f64 im 7) (sqrt.f64 1/2)))))))) (sqrt.f64 2)))
49.1b
(*.f64 1/2 (*.f64 (fma.f64 (*.f64 (*.f64 (/.f64 im re) (/.f64 im re)) (pow.f64 (*.f64 (sqrt.f64 im) (pow.f64 (/.f64 1/2 re) 1/4)) 2)) -1/8 (pow.f64 (*.f64 (sqrt.f64 im) (pow.f64 (/.f64 1/2 re) 1/4)) 2)) (sqrt.f64 2)))
56.7b
(*.f64 1/2 (*.f64 (sqrt.f64 (*.f64 1/2 (/.f64 (*.f64 im im) re))) (sqrt.f64 2)))
Compiler

Compiled 13376 to 8240 computations (38.4% saved)

regimes581.0ms (12%)

Accuracy

Total 6.4b remaining (98.3%)

Threshold costs 0b (0%)

Counts
59 → 2
Compiler

Compiled 8133 to 6573 computations (19.2% saved)

bsearch2.0ms (0%)

Compiler

Compiled 12 to 7 computations (41.7% saved)

simplify3.0ms (0.1%)

Algorithm
egg-herbie
Rules
*-commutative_binary64
+-commutative_binary64
sub-neg_binary64
*-lft-identity_binary64
neg-sub0_binary64
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
02959
14159
24659
34859
44959
54859

end205.0ms (4.3%)

Compiler

Compiled 366 to 295 computations (19.4% saved)

Profiling

Loading profile data...