Details

Time bar (total: 3.3s)

analyze1.0s (30.7%)

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
6.2%93.6%0.2%9
12.5%87.3%0.2%10
25%74.9%0.2%11
31.2%63.9%4.9%12
39%50.9%10.1%13
44.8%44.4%10.7%14
Compiler

Compiled 12 to 8 computations (33.3% saved)

sample1.1s (32.3%)

Symmetry

(sort x.re y.re)

(sort x.im y.im)

Results
876.0ms8256×body128valid
127.0ms1324×body128invalid
Compiler

Compiled 35 to 23 computations (34.3% saved)

simplify15.0ms (0.4%)

Algorithm
egg-herbie
Rules
171×fma-def_binary64
87×fma-neg_binary64
36×cancel-sign-sub-inv_binary64
23×distribute-rgt-neg-in_binary64
20×sub-neg_binary64
Counts
1 → 1
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
0810
11610
22710
34410
46610
510010
615210
721310
825710
927910
1029910
1130510
1227410

prune1.0ms (0%)

Pruning

2 alts after pruning (2 fresh and 0 done)

PrunedKeptTotal
New011
Fresh011
Picked000
Done000
Total022
Error
0.0b
Counts
2 → 1
Alt Table
StatusErrorProgram
0.0b
(-.f64 (*.f64 x.re y.re) (*.f64 x.im y.im))
Compiler

Compiled 33 to 21 computations (36.4% saved)

localize5.0ms (0.1%)

Local error

Found 1 expressions with local error:

NewErrorProgram
0.0b
(-.f64 (*.f64 x.re y.re) (*.f64 x.im y.im))

series92.0ms (2.8%)

Counts
1 → 48
Calls

1 calls:

91.0ms
(-.f64 (*.f64 x.re y.re) (*.f64 x.im y.im))

rewrite3.0ms (0.1%)

Algorithm
rewrite-expression-head
Rules
add-log-exp_binary64
cancel-sign-sub-inv_binary64
flip--_binary64
sub-neg_binary64
*-un-lft-identity_binary64
Counts
1 → 16
Calls

1 calls:

3.0ms
(-.f64 (*.f64 x.re y.re) (*.f64 x.im y.im))

simplify115.0ms (3.5%)

Algorithm
egg-herbie
Rules
480×times-frac_binary64
463×fma-def_binary64
444×unsub-neg_binary64
265×sub-neg_binary64
232×distribute-rgt-neg-in_binary64
Counts
64 → 32
Iterations

Useful iterations: 2 (0.0ms)

IterNodesCost
042682
1112658
2347652
3974652
42183652
53451652
64489652
74961652
84995652
94859652

prune16.0ms (0.5%)

Pruning

3 alts after pruning (2 fresh and 1 done)

PrunedKeptTotal
New30232
Fresh000
Picked011
Done000
Total30333
Error
0b
Counts
33 → 3
Alt Table
StatusErrorProgram
0.0b
(-.f64 (*.f64 x.re y.re) (*.f64 x.im y.im))
28.2b
(/.f64 (-.f64 (*.f64 (*.f64 x.re y.re) (*.f64 x.re y.re)) (*.f64 (*.f64 x.im y.im) (*.f64 x.im y.im))) (+.f64 (*.f64 x.re y.re) (*.f64 x.im y.im)))
29.8b
(*.f64 (sqrt.f64 (-.f64 (*.f64 x.re y.re) (*.f64 x.im y.im))) (sqrt.f64 (-.f64 (*.f64 x.re y.re) (*.f64 x.im y.im))))
Compiler

Compiled 520 to 139 computations (73.3% saved)

localize9.0ms (0.3%)

Local error

Found 4 expressions with local error:

NewErrorProgram
0.2b
(*.f64 (*.f64 x.re y.re) (*.f64 x.re y.re))
0.3b
(*.f64 (*.f64 x.im y.im) (*.f64 x.im y.im))
2.1b
(-.f64 (*.f64 (*.f64 x.re y.re) (*.f64 x.re y.re)) (*.f64 (*.f64 x.im y.im) (*.f64 x.im y.im)))
26.9b
(/.f64 (-.f64 (*.f64 (*.f64 x.re y.re) (*.f64 x.re y.re)) (*.f64 (*.f64 x.im y.im) (*.f64 x.im y.im))) (+.f64 (*.f64 x.re y.re) (*.f64 x.im y.im)))

series185.0ms (5.6%)

Counts
4 → 144
Calls

4 calls:

113.0ms
(/.f64 (-.f64 (*.f64 (*.f64 x.re y.re) (*.f64 x.re y.re)) (*.f64 (*.f64 x.im y.im) (*.f64 x.im y.im))) (+.f64 (*.f64 x.re y.re) (*.f64 x.im y.im)))
47.0ms
(-.f64 (*.f64 (*.f64 x.re y.re) (*.f64 x.re y.re)) (*.f64 (*.f64 x.im y.im) (*.f64 x.im y.im)))
14.0ms
(*.f64 (*.f64 x.im y.im) (*.f64 x.im y.im))
10.0ms
(*.f64 (*.f64 x.re y.re) (*.f64 x.re y.re))

rewrite37.0ms (1.1%)

Algorithm
rewrite-expression-head
Rules
82×pow1_binary64
34×pow-prod-down_binary64
30×add-cbrt-cube_binary64
30×add-exp-log_binary64
16×cbrt-unprod_binary64
Counts
4 → 127
Calls

4 calls:

12.0ms
(/.f64 (-.f64 (*.f64 (*.f64 x.re y.re) (*.f64 x.re y.re)) (*.f64 (*.f64 x.im y.im) (*.f64 x.im y.im))) (+.f64 (*.f64 x.re y.re) (*.f64 x.im y.im)))
5.0ms
(-.f64 (*.f64 (*.f64 x.re y.re) (*.f64 x.re y.re)) (*.f64 (*.f64 x.im y.im) (*.f64 x.im y.im)))
5.0ms
(*.f64 (*.f64 x.im y.im) (*.f64 x.im y.im))
5.0ms
(*.f64 (*.f64 x.re y.re) (*.f64 x.re y.re))

simplify159.0ms (4.8%)

Algorithm
egg-herbie
Rules
752×fma-def_binary64
259×associate-*l*_binary64
235×distribute-rgt-in_binary64
227×distribute-lft-in_binary64
220×fma-neg_binary64
Counts
271 → 172
Iterations

Useful iterations: 2 (0.0ms)

IterNodesCost
01684481
14304207
218143971
347683971
449983971
549153971

prune74.0ms (2.2%)

Pruning

3 alts after pruning (1 fresh and 2 done)

PrunedKeptTotal
New1720172
Fresh011
Picked011
Done011
Total1723175
Error
0b
Counts
175 → 3
Alt Table
StatusErrorProgram
0.0b
(-.f64 (*.f64 x.re y.re) (*.f64 x.im y.im))
28.2b
(/.f64 (-.f64 (*.f64 (*.f64 x.re y.re) (*.f64 x.re y.re)) (*.f64 (*.f64 x.im y.im) (*.f64 x.im y.im))) (+.f64 (*.f64 x.re y.re) (*.f64 x.im y.im)))
29.8b
(*.f64 (sqrt.f64 (-.f64 (*.f64 x.re y.re) (*.f64 x.im y.im))) (sqrt.f64 (-.f64 (*.f64 x.re y.re) (*.f64 x.im y.im))))
Compiler

Compiled 5570 to 743 computations (86.7% saved)

localize7.0ms (0.2%)

Local error

Found 3 expressions with local error:

NewErrorProgram
0.0b
(-.f64 (*.f64 x.re y.re) (*.f64 x.im y.im))
0.3b
(*.f64 (sqrt.f64 (-.f64 (*.f64 x.re y.re) (*.f64 x.im y.im))) (sqrt.f64 (-.f64 (*.f64 x.re y.re) (*.f64 x.im y.im))))
0.8b
(sqrt.f64 (-.f64 (*.f64 x.re y.re) (*.f64 x.im y.im)))

series111.0ms (3.4%)

Counts
2 → 56
Calls

2 calls:

69.0ms
(sqrt.f64 (-.f64 (*.f64 x.re y.re) (*.f64 x.im y.im)))
42.0ms
(*.f64 (sqrt.f64 (-.f64 (*.f64 x.re y.re) (*.f64 x.im y.im))) (sqrt.f64 (-.f64 (*.f64 x.re y.re) (*.f64 x.im y.im))))

rewrite23.0ms (0.7%)

Algorithm
rewrite-expression-head
Rules
28×add-sqr-sqrt_binary64
21×sqrt-prod_binary64
18×pow1_binary64
14×sqrt-div_binary64
11×*-un-lft-identity_binary64
Counts
2 → 78
Calls

2 calls:

13.0ms
(*.f64 (sqrt.f64 (-.f64 (*.f64 x.re y.re) (*.f64 x.im y.im))) (sqrt.f64 (-.f64 (*.f64 x.re y.re) (*.f64 x.im y.im))))
3.0ms
(sqrt.f64 (-.f64 (*.f64 x.re y.re) (*.f64 x.im y.im)))

simplify104.0ms (3.1%)

Algorithm
egg-herbie
Rules
554×times-frac_binary64
530×fma-neg_binary64
341×*-commutative_binary64
335×associate-/r*_binary64
324×fma-def_binary64
Counts
134 → 121
Iterations

Useful iterations: 3 (0.0ms)

IterNodesCost
01372619
13332448
211842366
343742332
449812332
549562332

prune85.0ms (2.6%)

Pruning

3 alts after pruning (0 fresh and 3 done)

PrunedKeptTotal
New2260226
Fresh000
Picked011
Done022
Total2263229
Error
0b
Counts
229 → 3
Alt Table
StatusErrorProgram
0.0b
(-.f64 (*.f64 x.re y.re) (*.f64 x.im y.im))
28.2b
(/.f64 (-.f64 (*.f64 (*.f64 x.re y.re) (*.f64 x.re y.re)) (*.f64 (*.f64 x.im y.im) (*.f64 x.im y.im))) (+.f64 (*.f64 x.re y.re) (*.f64 x.im y.im)))
29.8b
(*.f64 (sqrt.f64 (-.f64 (*.f64 x.re y.re) (*.f64 x.im y.im))) (sqrt.f64 (-.f64 (*.f64 x.re y.re) (*.f64 x.im y.im))))
Compiler

Compiled 5986 to 1049 computations (82.5% saved)

regimes121.0ms (3.6%)

Accuracy

Total 0.0b remaining (18.4%)

Threshold costs 0.0b (18.4%)

Counts
15 → 1
Compiler

Compiled 1959 to 1165 computations (40.5% saved)

simplify2.0ms (0.1%)

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
0810
11510
22510
33110
43510
53610
63610

end63.0ms (1.9%)

Remove

(sort x.im y.im)

(sort x.re y.re)

Compiler

Compiled 125 to 69 computations (44.8% saved)

Profiling

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