Details

Time bar (total: 7.4s)

analyze1.7s (23.3%)

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
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)

sample65.0ms (0.9%)

Algorithm
intervals
Results
14.0ms256×body128valid
2.0ms45×body128invalid
Compiler

Compiled 27 to 19 computations (29.6% saved)

simplify27.0ms (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

prune4.0ms (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)

localize9.0ms (0.1%)

Local error

Found 1 expressions with local error:

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

series16.0ms (0.2%)

Counts
1 → 48
Calls

1 calls:

16.0ms
(-.f64 (*.f64 x.re y.re) (*.f64 x.im y.im))

rewrite6.0ms (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:

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

simplify154.0ms (2.1%)

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

prune26.0ms (0.4%)

Pruning

2 alts after pruning (1 fresh and 1 done)

PrunedKeptTotal
New31132
Fresh000
Picked011
Done000
Total31233
Error
0.0b
Counts
33 → 2
Alt Table
StatusErrorProgram
0.0b
(-.f64 (*.f64 x.re y.re) (*.f64 x.im y.im))
38.4b
(/.f64 (-.f64 (pow.f64 (*.f64 x.re y.re) 3) (pow.f64 (*.f64 x.im y.im) 3)) (+.f64 (*.f64 (*.f64 x.re y.re) (*.f64 x.re y.re)) (+.f64 (*.f64 (*.f64 x.im y.im) (*.f64 x.im y.im)) (*.f64 (*.f64 x.re y.re) (*.f64 x.im y.im)))))
Compiler

Compiled 502 to 133 computations (73.5% saved)

localize28.0ms (0.4%)

Local error

Found 4 expressions with local error:

NewErrorProgram
1.5b
(+.f64 (*.f64 (*.f64 x.im y.im) (*.f64 x.im y.im)) (*.f64 (*.f64 x.re y.re) (*.f64 x.im y.im)))
1.8b
(-.f64 (pow.f64 (*.f64 x.re y.re) 3) (pow.f64 (*.f64 x.im y.im) 3))
4.7b
(*.f64 (*.f64 x.re y.re) (*.f64 x.im y.im))
37.2b
(/.f64 (-.f64 (pow.f64 (*.f64 x.re y.re) 3) (pow.f64 (*.f64 x.im y.im) 3)) (+.f64 (*.f64 (*.f64 x.re y.re) (*.f64 x.re y.re)) (+.f64 (*.f64 (*.f64 x.im y.im) (*.f64 x.im y.im)) (*.f64 (*.f64 x.re y.re) (*.f64 x.im y.im)))))

series455.0ms (6.2%)

Counts
4 → 192
Calls

4 calls:

254.0ms
(/.f64 (-.f64 (pow.f64 (*.f64 x.re y.re) 3) (pow.f64 (*.f64 x.im y.im) 3)) (+.f64 (*.f64 (*.f64 x.re y.re) (*.f64 x.re y.re)) (+.f64 (*.f64 (*.f64 x.im y.im) (*.f64 x.im y.im)) (*.f64 (*.f64 x.re y.re) (*.f64 x.im y.im)))))
118.0ms
(-.f64 (pow.f64 (*.f64 x.re y.re) 3) (pow.f64 (*.f64 x.im y.im) 3))
53.0ms
(+.f64 (*.f64 (*.f64 x.im y.im) (*.f64 x.im y.im)) (*.f64 (*.f64 x.re y.re) (*.f64 x.im y.im)))
30.0ms
(*.f64 (*.f64 x.re y.re) (*.f64 x.im y.im))

rewrite107.0ms (1.4%)

Algorithm
rewrite-expression-head
Rules
64×prod-diff_binary64
56×add-sqr-sqrt_binary64
46×*-un-lft-identity_binary64
38×sqr-pow_binary64
36×add-cube-cbrt_binary64
Counts
4 → 196
Calls

4 calls:

34.0ms
(/.f64 (-.f64 (pow.f64 (*.f64 x.re y.re) 3) (pow.f64 (*.f64 x.im y.im) 3)) (+.f64 (*.f64 (*.f64 x.re y.re) (*.f64 x.re y.re)) (+.f64 (*.f64 (*.f64 x.im y.im) (*.f64 x.im y.im)) (*.f64 (*.f64 x.re y.re) (*.f64 x.im y.im)))))
15.0ms
(-.f64 (pow.f64 (*.f64 x.re y.re) 3) (pow.f64 (*.f64 x.im y.im) 3))
10.0ms
(+.f64 (*.f64 (*.f64 x.im y.im) (*.f64 x.im y.im)) (*.f64 (*.f64 x.re y.re) (*.f64 x.im y.im)))
8.0ms
(*.f64 (*.f64 x.re y.re) (*.f64 x.im y.im))

simplify338.0ms (4.6%)

Algorithm
egg-herbie
Rules
612×times-frac_binary64
531×fma-neg_binary64
394×associate-*l*_binary64
372×associate-*r*_binary64
255×exp-prod_binary64
Counts
388 → 266
Iterations

Useful iterations: 2 (0.0ms)

IterNodesCost
03109702
16148966
232088822
350608822

prune339.0ms (4.6%)

Pruning

3 alts after pruning (1 fresh and 2 done)

PrunedKeptTotal
New2651266
Fresh000
Picked011
Done011
Total2653268
Error
0b
Counts
268 → 3
Alt Table
StatusErrorProgram
38.5b
(/.f64 1 (/.f64 (fma.f64 (*.f64 y.im x.im) (fma.f64 y.im x.im (*.f64 x.re y.re)) (*.f64 (*.f64 x.re y.re) (*.f64 x.re y.re))) (-.f64 (pow.f64 (*.f64 x.re y.re) 3) (pow.f64 (*.f64 y.im x.im) 3))))
0.0b
(-.f64 (*.f64 x.re y.re) (*.f64 x.im y.im))
38.4b
(/.f64 (-.f64 (pow.f64 (*.f64 x.re y.re) 3) (pow.f64 (*.f64 x.im y.im) 3)) (+.f64 (*.f64 (*.f64 x.re y.re) (*.f64 x.re y.re)) (+.f64 (*.f64 (*.f64 x.im y.im) (*.f64 x.im y.im)) (*.f64 (*.f64 x.re y.re) (*.f64 x.im y.im)))))
Compiler

Compiled 14662 to 3764 computations (74.3% saved)

localize32.0ms (0.4%)

Local error

Found 4 expressions with local error:

NewErrorProgram
0.3b
(pow.f64 (*.f64 y.im x.im) 3)
0.5b
(/.f64 1 (/.f64 (fma.f64 (*.f64 y.im x.im) (fma.f64 y.im x.im (*.f64 x.re y.re)) (*.f64 (*.f64 x.re y.re) (*.f64 x.re y.re))) (-.f64 (pow.f64 (*.f64 x.re y.re) 3) (pow.f64 (*.f64 y.im x.im) 3))))
1.8b
(-.f64 (pow.f64 (*.f64 x.re y.re) 3) (pow.f64 (*.f64 y.im x.im) 3))
37.3b
(/.f64 (fma.f64 (*.f64 y.im x.im) (fma.f64 y.im x.im (*.f64 x.re y.re)) (*.f64 (*.f64 x.re y.re) (*.f64 x.re y.re))) (-.f64 (pow.f64 (*.f64 x.re y.re) 3) (pow.f64 (*.f64 y.im x.im) 3)))

series529.0ms (7.2%)

Counts
4 → 168
Calls

4 calls:

246.0ms
(/.f64 1 (/.f64 (fma.f64 (*.f64 y.im x.im) (fma.f64 y.im x.im (*.f64 x.re y.re)) (*.f64 (*.f64 x.re y.re) (*.f64 x.re y.re))) (-.f64 (pow.f64 (*.f64 x.re y.re) 3) (pow.f64 (*.f64 y.im x.im) 3))))
134.0ms
(-.f64 (pow.f64 (*.f64 x.re y.re) 3) (pow.f64 (*.f64 y.im x.im) 3))
126.0ms
(/.f64 (fma.f64 (*.f64 y.im x.im) (fma.f64 y.im x.im (*.f64 x.re y.re)) (*.f64 (*.f64 x.re y.re) (*.f64 x.re y.re))) (-.f64 (pow.f64 (*.f64 x.re y.re) 3) (pow.f64 (*.f64 y.im x.im) 3)))
23.0ms
(pow.f64 (*.f64 y.im x.im) 3)

rewrite162.0ms (2.2%)

Algorithm
rewrite-expression-head
Rules
234×times-frac_binary64
191×add-sqr-sqrt_binary64
157×*-un-lft-identity_binary64
123×add-cube-cbrt_binary64
87×sqr-pow_binary64
Counts
4 → 336
Calls

4 calls:

20.0ms
(/.f64 1 (/.f64 (fma.f64 (*.f64 y.im x.im) (fma.f64 y.im x.im (*.f64 x.re y.re)) (*.f64 (*.f64 x.re y.re) (*.f64 x.re y.re))) (-.f64 (pow.f64 (*.f64 x.re y.re) 3) (pow.f64 (*.f64 y.im x.im) 3))))
16.0ms
(-.f64 (pow.f64 (*.f64 x.re y.re) 3) (pow.f64 (*.f64 y.im x.im) 3))
13.0ms
(/.f64 (fma.f64 (*.f64 y.im x.im) (fma.f64 y.im x.im (*.f64 x.re y.re)) (*.f64 (*.f64 x.re y.re) (*.f64 x.re y.re))) (-.f64 (pow.f64 (*.f64 x.re y.re) 3) (pow.f64 (*.f64 y.im x.im) 3)))
4.0ms
(pow.f64 (*.f64 y.im x.im) 3)

simplify1.0s (14%)

Algorithm
egg-herbie
Rules
455×exp-prod_binary64
369×unswap-sqr_binary64
301×fma-neg_binary64
276×times-frac_binary64
213×log-prod_binary64
Counts
504 → 401
Iterations

Useful iterations: 3 (0.0ms)

IterNodesCost
036821957
167220572
2342419280
3449319279
4513419279

prune549.0ms (7.5%)

Pruning

3 alts after pruning (0 fresh and 3 done)

PrunedKeptTotal
New4010401
Fresh000
Picked011
Done022
Total4013404
Error
0b
Counts
404 → 3
Alt Table
StatusErrorProgram
38.5b
(/.f64 1 (/.f64 (fma.f64 (*.f64 y.im x.im) (fma.f64 y.im x.im (*.f64 x.re y.re)) (*.f64 (*.f64 x.re y.re) (*.f64 x.re y.re))) (-.f64 (pow.f64 (*.f64 x.re y.re) 3) (pow.f64 (*.f64 y.im x.im) 3))))
0.0b
(-.f64 (*.f64 x.re y.re) (*.f64 x.im y.im))
38.4b
(/.f64 (-.f64 (pow.f64 (*.f64 x.re y.re) 3) (pow.f64 (*.f64 x.im y.im) 3)) (+.f64 (*.f64 (*.f64 x.re y.re) (*.f64 x.re y.re)) (+.f64 (*.f64 (*.f64 x.im y.im) (*.f64 x.im y.im)) (*.f64 (*.f64 x.re y.re) (*.f64 x.im y.im)))))
Compiler

Compiled 22958 to 6994 computations (69.5% saved)

regimes292.0ms (4%)

Accuracy

Total 0.0b remaining (22.3%)

Threshold costs 0.0b (22.3%)

Counts
13 → 1
Compiler

Compiled 3156 to 1529 computations (51.6% saved)

simplify5.0ms (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

end77.0ms (1%)

Remove

(sort x.im y.im)

(sort x.re y.re)

Compiler

Compiled 55 to 35 computations (36.4% saved)

sample1.4s (18.9%)

Algorithm
intervals
Results
540.0ms8000×body128valid
87.0ms1346×body128invalid
Compiler

Compiled 112 to 60 computations (46.4% saved)

Profiling

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