Details

Time bar (total: 3.5s)

analyze741.0ms (21.4%)

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)

sample1.0s (29.4%)

Symmetry

(sort x.re y.re)

(sort x.im y.im)

Results
808.0ms8256×body128valid
147.0ms1412×body128invalid
Compiler

Compiled 35 to 23 computations (34.3% saved)

simplify14.0ms (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)

localize6.0ms (0.2%)

Local error

Found 1 expressions with local error:

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

series8.0ms (0.2%)

Counts
1 → 48
Calls

1 calls:

8.0ms
(-.f64 (*.f64 x.re y.re) (*.f64 x.im y.im))

rewrite47.0ms (1.4%)

Algorithm
batch-egg-rewrite
Rules
890×log1p-expm1-u_binary64
890×expm1-log1p-u_binary64
92×add-sqr-sqrt_binary64
85×add-log-exp_binary64
84×add-cube-cbrt_binary64
Counts
1 → 51
Calls

1 calls:

46.0ms
(-.f64 (*.f64 x.re y.re) (*.f64 x.im y.im))
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
0810
117510
2225410
3541310
000
100

simplify37.0ms (1.1%)

Algorithm
egg-herbie
Rules
172×fma-def_binary64
87×fma-neg_binary64
36×cancel-sign-sub-inv_binary64
23×distribute-rgt-neg-in_binary64
20×sub-neg_binary64
Counts
99 → 55
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
010420
121420
233420
344420
466420
5100420
6152420
7213420
8257420
9279420
10299420
11305420
12274420

prune31.0ms (0.9%)

Pruning

3 alts after pruning (2 fresh and 1 done)

PrunedKeptTotal
New53255
Fresh000
Picked011
Done000
Total53356
Error
0b
Counts
56 → 3
Alt Table
StatusErrorProgram
0.0b
(-.f64 (*.f64 x.re y.re) (*.f64 x.im y.im))
0.2b
(+.f64 (-.f64 (*.f64 x.re y.re) (*.f64 x.im y.im)) (+.f64 (fma.f64 (neg.f64 y.im) x.im (*.f64 x.im y.im)) (fma.f64 (neg.f64 y.im) x.im (*.f64 x.im y.im))))
0.5b
(+.f64 (-.f64 (*.f64 x.re y.re) (*.f64 x.im y.im)) (fma.f64 (neg.f64 (cbrt.f64 (*.f64 x.im y.im))) (pow.f64 (cbrt.f64 (*.f64 x.im y.im)) 2) (*.f64 x.im y.im)))
Compiler

Compiled 1023 to 270 computations (73.6% saved)

localize9.0ms (0.3%)

Local error

Found 2 expressions with local error:

NewErrorProgram
0.0b
(-.f64 (*.f64 x.re y.re) (*.f64 x.im y.im))
53.1b
(fma.f64 (neg.f64 y.im) x.im (*.f64 x.im y.im))

series9.0ms (0.2%)

Counts
1 → 24
Calls

1 calls:

8.0ms
(fma.f64 (neg.f64 y.im) x.im (*.f64 x.im y.im))

rewrite64.0ms (1.8%)

Algorithm
batch-egg-rewrite
Rules
451×log1p-expm1-u_binary64
451×expm1-log1p-u_binary64
425×prod-diff_binary64
337×unpow-prod-down_binary64
258×log-prod_binary64
Counts
1 → 190
Calls

1 calls:

57.0ms
(fma.f64 (neg.f64 y.im) x.im (*.f64 x.im y.im))
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
0610
11227
212097
350327
000
100

simplify10.0ms (0.3%)

Algorithm
egg-herbie
Counts
214 → 191
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
0124
1124

prune210.0ms (6.1%)

Pruning

3 alts after pruning (1 fresh and 2 done)

PrunedKeptTotal
New4370437
Fresh011
Picked011
Done011
Total4373440
Error
0b
Counts
440 → 3
Alt Table
StatusErrorProgram
0.0b
(-.f64 (*.f64 x.re y.re) (*.f64 x.im y.im))
0.2b
(+.f64 (-.f64 (*.f64 x.re y.re) (*.f64 x.im y.im)) (+.f64 (fma.f64 (neg.f64 y.im) x.im (*.f64 x.im y.im)) (fma.f64 (neg.f64 y.im) x.im (*.f64 x.im y.im))))
0.5b
(+.f64 (-.f64 (*.f64 x.re y.re) (*.f64 x.im y.im)) (fma.f64 (neg.f64 (cbrt.f64 (*.f64 x.im y.im))) (pow.f64 (cbrt.f64 (*.f64 x.im y.im)) 2) (*.f64 x.im y.im)))
Compiler

Compiled 18678 to 2232 computations (88.1% saved)

localize14.0ms (0.4%)

Local error

Found 4 expressions with local error:

NewErrorProgram
0.0b
(-.f64 (*.f64 x.re y.re) (*.f64 x.im y.im))
0.5b
(pow.f64 (cbrt.f64 (*.f64 x.im y.im)) 2)
8.0b
(cbrt.f64 (*.f64 x.im y.im))
52.6b
(fma.f64 (neg.f64 (cbrt.f64 (*.f64 x.im y.im))) (pow.f64 (cbrt.f64 (*.f64 x.im y.im)) 2) (*.f64 x.im y.im))

series809.0ms (23.4%)

Counts
3 → 72
Calls

3 calls:

328.0ms
(pow.f64 (cbrt.f64 (*.f64 x.im y.im)) 2)
311.0ms
(cbrt.f64 (*.f64 x.im y.im))
171.0ms
(fma.f64 (neg.f64 (cbrt.f64 (*.f64 x.im y.im))) (pow.f64 (cbrt.f64 (*.f64 x.im y.im)) 2) (*.f64 x.im y.im))

rewrite47.0ms (1.4%)

Algorithm
batch-egg-rewrite
Rules
881×prod-diff_binary64
645×log1p-expm1-u_binary64
645×expm1-log1p-u_binary64
88×add-sqr-sqrt_binary64
87×egg-rr
Counts
3 → 87
Calls

3 calls:

46.0ms
(pow.f64 (cbrt.f64 (*.f64 x.im y.im)) 2)
46.0ms
(cbrt.f64 (*.f64 x.im y.im))
45.0ms
(fma.f64 (neg.f64 (cbrt.f64 (*.f64 x.im y.im))) (pow.f64 (cbrt.f64 (*.f64 x.im y.im)) 2) (*.f64 x.im y.im))
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
0938
118325
2172225
3547625
000
100

simplify109.0ms (3.2%)

Algorithm
egg-herbie
Rules
492×associate-*l*_binary64
409×associate-*r*_binary64
282×unswap-sqr_binary64
268×distribute-neg-out_binary64
253×exp-diff_binary64
Counts
159 → 109
Iterations

Useful iterations: 4 (0.0ms)

IterNodesCost
0561296
11511296
22591180
3712720
42652542
53774542
64807542
74972542
84889542

prune120.0ms (3.5%)

Pruning

3 alts after pruning (0 fresh and 3 done)

PrunedKeptTotal
New2120212
Fresh000
Picked011
Done022
Total2123215
Error
0b
Counts
215 → 3
Alt Table
StatusErrorProgram
0.0b
(-.f64 (*.f64 x.re y.re) (*.f64 x.im y.im))
0.2b
(+.f64 (-.f64 (*.f64 x.re y.re) (*.f64 x.im y.im)) (+.f64 (fma.f64 (neg.f64 y.im) x.im (*.f64 x.im y.im)) (fma.f64 (neg.f64 y.im) x.im (*.f64 x.im y.im))))
0.5b
(+.f64 (-.f64 (*.f64 x.re y.re) (*.f64 x.im y.im)) (fma.f64 (neg.f64 (cbrt.f64 (*.f64 x.im y.im))) (pow.f64 (cbrt.f64 (*.f64 x.im y.im)) 2) (*.f64 x.im y.im)))
Compiler

Compiled 5961 to 1601 computations (73.1% saved)

regimes85.0ms (2.5%)

Accuracy

Total 0.0b remaining (33.7%)

Threshold costs 0.0b (33.7%)

Counts
11 → 1
Compiler

Compiled 1392 to 801 computations (42.5% 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

end67.0ms (1.9%)

Remove

(sort x.im y.im)

(sort x.re y.re)

Compiler

Compiled 131 to 73 computations (44.3% saved)

Profiling

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