Details

Time bar (total: 4.6s)

analyze933.0ms (20.3%)

Algorithm
search
egg-herbie
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
031698
131698
044
144
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
Symmetry

(sort x.re y.re)

(sort x.im y.im)

Compiler

Compiled 8 to 8 computations (0% saved)

sample32.0ms (0.7%)

Algorithm
intervals
Results
6.0ms256×body128valid
1.0ms54×body128invalid
Compiler

Compiled 15 to 19 computations (-26.7% saved)

simplify13.0ms (0.3%)

Algorithm
egg-herbie
Counts
1 → 1
Iterations

Useful iterations: 0 (8.0ms)

IterNodesCost
016014
116014

prune2.0ms (0%)

Pruning

2 alts after pruning (2 fresh and 0 done)

PrunedKeptTotal
New011
Fresh011
Picked000
Done000
Total022
Error
0.0b
Counts
2 → 1
Compiler

Compiled 14 to 14 computations (0% saved)

localize5.0ms (0.1%)

Local error

Found 1 expressions with local error:

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

rewrite19.0ms (0.4%)

Algorithm
rewrite-expression-head
Error
0.0b
Rules
add-log-exp_binary64_799
diff-log_binary64_852 pow1_binary64_821 add-exp-log_binary64_798 add-cbrt-cube_binary64_796 add-cube-cbrt_binary64_795 add-sqr-sqrt_binary64_782 flip3--_binary64_764 *-un-lft-identity_binary64_760 sub-neg_binary64_753 flip--_binary64_735 cancel-sign-sub-inv_binary64_726
Counts
1 → 12
Calls

1 calls:

4.0ms
(-.f64 (*.f64 x.re y.re) (*.f64 x.im y.im))
Compiler

Compiled 187 to 46 computations (75.4% saved)

series146.0ms (3.2%)

Error
0.0b
Counts
1 → 24
Calls

1 calls:

136.0ms
(-.f64 (*.f64 x.re y.re) (*.f64 x.im y.im))
Compiler

Compiled 348 to 259 computations (25.6% saved)

simplify69.0ms (1.5%)

Algorithm
egg-herbie
Counts
36 → 36
Iterations

Useful iterations: 0 (59.0ms)

IterNodesCost
04948517
14948517

prune21.0ms (0.5%)

Pruning

4 alts after pruning (3 fresh and 1 done)

PrunedKeptTotal
New33336
Fresh000
Picked011
Done000
Total33437
Error
0.0b
Counts
37 → 4
Compiler

Compiled 352 to 78 computations (77.8% saved)

localize10.0ms (0.2%)

Local error

Found 4 expressions with local error:

0.0b
(-.f64 (*.f64 y.re x.re) (*.f64 y.im x.im))
0.3b
(*.f64 (sqrt.f64 (-.f64 (*.f64 y.re x.re) (*.f64 y.im x.im))) (sqrt.f64 (-.f64 (*.f64 y.re x.re) (*.f64 y.im x.im))))
1.0b
(sqrt.f64 (-.f64 (*.f64 y.re x.re) (*.f64 y.im x.im)))
1.0b
(sqrt.f64 (-.f64 (*.f64 y.re x.re) (*.f64 y.im x.im)))

rewrite112.0ms (2.4%)

Algorithm
rewrite-expression-head
Error
0.0b
Rules
30×add-sqr-sqrt_binary64_782
24×sqrt-prod_binary64_776
21×pow1_binary64_821
16×sqrt-div_binary64_777
14×add-cube-cbrt_binary64_795 *-un-lft-identity_binary64_760
10×pow1/2_binary64_840 sqrt-pow1_binary64_778
flip3--_binary64_764 flip--_binary64_735
swap-sqr_binary64_727
add-log-exp_binary64_799 add-exp-log_binary64_798 add-cbrt-cube_binary64_796 associate-*l*_binary64_701 associate-*r*_binary64_700
pow-prod-up_binary64_830
rem-sqrt-square_binary64_773 frac-times_binary64_770 unswap-sqr_binary64_728
pow-prod-down_binary64_831 pow-sqr_binary64_733
associate-*l/_binary64_703 associate-*r/_binary64_702
pow2_binary64_841 pow-plus_binary64_823 prod-exp_binary64_809 cbrt-unprod_binary64_793 sqrt-unprod_binary64_780 sqr-abs_binary64_775 rem-square-sqrt_binary64_772 *-commutative_binary64_691 diff-log_binary64_852 sub-neg_binary64_753 cancel-sign-sub-inv_binary64_726
Counts
4 → 100
Calls

4 calls:

12.0ms
(*.f64 (sqrt.f64 (-.f64 (*.f64 y.re x.re) (*.f64 y.im x.im))) (sqrt.f64 (-.f64 (*.f64 y.re x.re) (*.f64 y.im x.im))))
4.0ms
(sqrt.f64 (-.f64 (*.f64 y.re x.re) (*.f64 y.im x.im)))
4.0ms
(-.f64 (*.f64 y.re x.re) (*.f64 y.im x.im))
4.0ms
(sqrt.f64 (-.f64 (*.f64 y.re x.re) (*.f64 y.im x.im)))
Compiler

Compiled 2860 to 329 computations (88.5% saved)

series513.0ms (11.2%)

Error
0.0b
Counts
4 → 74
Calls

4 calls:

149.0ms
(-.f64 (*.f64 y.re x.re) (*.f64 y.im x.im))
143.0ms
(*.f64 (sqrt.f64 (-.f64 (*.f64 y.re x.re) (*.f64 y.im x.im))) (sqrt.f64 (-.f64 (*.f64 y.re x.re) (*.f64 y.im x.im))))
99.0ms
(sqrt.f64 (-.f64 (*.f64 y.re x.re) (*.f64 y.im x.im)))
87.0ms
(sqrt.f64 (-.f64 (*.f64 y.re x.re) (*.f64 y.im x.im)))
Compiler

Compiled 2916 to 1605 computations (45% saved)

simplify101.0ms (2.2%)

Algorithm
egg-herbie
Counts
174 → 174
Iterations

Useful iterations: 0 (63.0ms)

IterNodesCost
049303017
149303017

prune104.0ms (2.3%)

Pruning

3 alts after pruning (1 fresh and 2 done)

PrunedKeptTotal
New1731174
Fresh202
Picked011
Done011
Total1753178
Error
0.0b
Counts
178 → 3
Compiler

Compiled 2990 to 460 computations (84.6% saved)

localize15.0ms (0.3%)

Local error

Found 4 expressions with local error:

0.2b
(*.f64 (*.f64 y.im x.im) (*.f64 y.im x.im))
1.6b
(-.f64 (*.f64 (pow.f64 x.re 2) (pow.f64 y.re 2)) (*.f64 (*.f64 y.im x.im) (*.f64 y.im x.im)))
14.6b
(*.f64 (pow.f64 x.re 2) (pow.f64 y.re 2))
24.9b
(/.f64 (-.f64 (*.f64 (pow.f64 x.re 2) (pow.f64 y.re 2)) (*.f64 (*.f64 y.im x.im) (*.f64 y.im x.im))) (+.f64 (*.f64 y.im x.im) (*.f64 x.re y.re)))

rewrite193.0ms (4.2%)

Algorithm
rewrite-expression-head
Error
0.0b
Rules
43×pow1_binary64_821
32×add-sqr-sqrt_binary64_782
30×add-exp-log_binary64_798
20×add-cbrt-cube_binary64_796
18×pow-prod-down_binary64_831
17×prod-exp_binary64_809
16×add-cube-cbrt_binary64_795 *-un-lft-identity_binary64_760 unswap-sqr_binary64_728
14×unpow-prod-down_binary64_839
10×unpow2_binary64_825 sqr-pow_binary64_732
times-frac_binary64_766 cbrt-unprod_binary64_793 associate-*l*_binary64_701 associate-*r*_binary64_700
add-log-exp_binary64_799 pow-to-exp_binary64_829 pow-exp_binary64_828
pow-prod-up_binary64_830 pow-sqr_binary64_733
associate-/l*_binary64_705 associate-/r*_binary64_704
flip3--_binary64_764 associate-/l/_binary64_707 flip--_binary64_735 associate-/r/_binary64_706 *-commutative_binary64_691 pow-plus_binary64_823
div-exp_binary64_811 cbrt-undiv_binary64_794 frac-2neg_binary64_771 div-sub_binary64_765 clear-num_binary64_759 div-inv_binary64_757 flip3-+_binary64_763 flip-+_binary64_734 diff-log_binary64_852 sub-neg_binary64_753 cancel-sign-sub-inv_binary64_726 pow2_binary64_841 swap-sqr_binary64_727
Counts
4 → 129
Calls

4 calls:

11.0ms
(/.f64 (-.f64 (*.f64 (pow.f64 x.re 2) (pow.f64 y.re 2)) (*.f64 (*.f64 y.im x.im) (*.f64 y.im x.im))) (+.f64 (*.f64 y.im x.im) (*.f64 x.re y.re)))
8.0ms
(*.f64 (pow.f64 x.re 2) (pow.f64 y.re 2))
6.0ms
(*.f64 (*.f64 y.im x.im) (*.f64 y.im x.im))
6.0ms
(-.f64 (*.f64 (pow.f64 x.re 2) (pow.f64 y.re 2)) (*.f64 (*.f64 y.im x.im) (*.f64 y.im x.im)))
Compiler

Compiled 4314 to 1611 computations (62.7% saved)

series986.0ms (21.5%)

Error
0.0b
Counts
4 → 60
Calls

4 calls:

447.0ms
(/.f64 (-.f64 (*.f64 (pow.f64 x.re 2) (pow.f64 y.re 2)) (*.f64 (*.f64 y.im x.im) (*.f64 y.im x.im))) (+.f64 (*.f64 y.im x.im) (*.f64 x.re y.re)))
362.0ms
(-.f64 (*.f64 (pow.f64 x.re 2) (pow.f64 y.re 2)) (*.f64 (*.f64 y.im x.im) (*.f64 y.im x.im)))
72.0ms
(*.f64 (*.f64 y.im x.im) (*.f64 y.im x.im))
66.0ms
(*.f64 (pow.f64 x.re 2) (pow.f64 y.re 2))
Compiler

Compiled 2388 to 1636 computations (31.5% saved)

simplify89.0ms (1.9%)

Algorithm
egg-herbie
Counts
189 → 189
Iterations

Useful iterations: 0 (47.0ms)

IterNodesCost
050094025

prune184.0ms (4%)

Pruning

3 alts after pruning (0 fresh and 3 done)

PrunedKeptTotal
New1890189
Fresh000
Picked011
Done022
Total1893192
Error
0.0b
Counts
192 → 3
Compiler

Compiled 4597 to 1878 computations (59.1% saved)

regimes204.0ms (4.4%)

Accuracy

Total 0.0b remaining (51.2%)

Threshold costs 0.0b (51.2%)

Compiler

Compiled 2141 to 1368 computations (36.1% saved)

bsearch0.0ms (0%)

simplify25.0ms (0.5%)

Algorithm
egg-herbie
Iterations

Useful iterations: 0 (1.0ms)

IterNodesCost
03814
13814
Remove

(sort x.im y.im)

(sort x.re y.re)

Compiler

Compiled 28 to 28 computations (0% saved)

end0.0ms (0%)

sample823.0ms (17.9%)

Algorithm
intervals
Results
201.0ms8000×body128valid
38.0ms1288×body128invalid
Compiler

Compiled 316 to 205 computations (35.1% saved)

Profiling

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