Details

analyze789.0ms (20.2%)

Algorithm

1×

Search

True	Other	False	Iter
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 (26.8%)

Symmetry

(sort x.re y.re)

(sort x.im y.im)

Results

841.0ms	8256×	body	128	valid
142.0ms	1430×	body	128	invalid

Compiler

Compiled 35 to 23 computations (34.3% saved)

simplify16.0ms (0.4%)

Algorithm

1×	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)

Iter	Nodes	Cost
0	8	10
1	16	10
2	27	10
3	44	10
4	66	10
5	100	10
6	152	10
7	213	10
8	257	10
9	279	10
10	299	10
11	305	10
12	274	10

prune2.0ms (0%)

Pruning

2 alts after pruning (2 fresh and 0 done)

	Kept	Total
New	1	1
Fresh	1	1
Picked	0	0
Done	0	0
Total	2	2

Error

0.0b

Counts

2 → 1

Alt Table

Status	Error	Program
▶	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:

New	Error	Program
✓	0.0b	(-.f64 (.f64 x.re y.re) (.f64 x.im y.im))

series9.0ms (0.2%)

Counts

1 → 48

Calls

1 calls:

9.0ms

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

rewrite4.0ms (0.1%)

Algorithm

1×	rewrite-expression-head

Rules

3×	`add-log-exp_binary64`
1×	`cancel-sign-sub-inv_binary64`
1×	`flip--_binary64`
1×	`sub-neg_binary64`
1×	`*-un-lft-identity_binary64`

Counts

1 → 16

Calls

1 calls:

3.0ms

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

simplify113.0ms (2.9%)

Algorithm

1×	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)

Iter	Nodes	Cost
0	42	682
1	112	658
2	347	652
3	974	652
4	2183	652
5	3451	652
6	4489	652
7	4961	652
8	4995	652
9	4859	652

prune22.0ms (0.6%)

Pruning

3 alts after pruning (3 fresh and 0 done)

	Pruned	Kept	Total
New	29	3	32
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	30	3	33

Error

Counts

33 → 3

Alt Table

Status	Error	Program
	36.0b	(/.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)))))
	31.8b	(.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))))
▶	0.0b	(fma.f64 x.re y.re (neg.f64 (*.f64 x.im y.im)))

Compiler

Compiled 555 to 158 computations (71.5% saved)

localize5.0ms (0.1%)

Local error

Found 1 expressions with local error:

New	Error	Program
✓	0.0b	(fma.f64 x.re y.re (neg.f64 (*.f64 x.im y.im)))

series10.0ms (0.3%)

Counts

1 → 48

Calls

1 calls:

10.0ms

(fma.f64 x.re y.re (neg.f64 (*.f64 x.im y.im)))

rewrite1.0ms (0%)

Algorithm

1×	rewrite-expression-head

Rules

1×	`*-un-lft-identity_binary64`
1×	`add-sqr-sqrt_binary64`
1×	`add-cube-cbrt_binary64`
1×	`add-cbrt-cube_binary64`
1×	`add-exp-log_binary64`

Counts

1 → 10

Calls

1 calls:

0.0ms

(fma.f64 x.re y.re (neg.f64 (*.f64 x.im y.im)))

simplify82.0ms (2.1%)

Algorithm

1×	egg-herbie

Rules

967×	`unsub-neg_binary64`
792×	`times-frac_binary64`
422×	`fma-neg_binary64`
384×	`neg-sub0_binary64`
364×	`neg-mul-1_binary64`

Counts

58 → 21

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	22	568
1	36	547
2	65	547
3	215	547
4	895	547
5	1760	547
6	3723	547
7	4512	547
8	5729	547

prune10.0ms (0.3%)

Pruning

3 alts after pruning (2 fresh and 1 done)

	Pruned	Kept	Total
New	21	0	21
Fresh	0	2	2
Picked	0	1	1
Done	0	0	0
Total	21	3	24

Error

Counts

24 → 3

Alt Table

Status	Error	Program
	36.0b	(/.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)))))
▶	31.8b	(.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))))
✓	0.0b	(fma.f64 x.re y.re (neg.f64 (*.f64 x.im y.im)))

Compiler

Compiled 372 to 109 computations (70.7% saved)

localize7.0ms (0.2%)

Local error

Found 3 expressions with local error:

New	Error	Program
	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))))
✓	0.6b	(sqrt.f64 (-.f64 (.f64 x.re y.re) (.f64 x.im y.im)))

series114.0ms (2.9%)

Counts

2 → 56

Calls

2 calls:

74.0ms	(sqrt.f64 (-.f64 (.f64 x.re y.re) (.f64 x.im y.im)))
40.0ms	(.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))))

rewrite19.0ms (0.5%)

Algorithm

1×	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:

9.0ms	(.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)))

simplify169.0ms (4.3%)

Algorithm

1×	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)

Iter	Nodes	Cost
0	137	2619
1	333	2448
2	1184	2366
3	4374	2332
4	4981	2332
5	4956	2332

prune144.0ms (3.7%)

Pruning

3 alts after pruning (1 fresh and 2 done)

	Pruned	Kept	Total
New	226	0	226
Fresh	0	1	1
Picked	0	1	1
Done	0	1	1
Total	226	3	229

Error

Counts

229 → 3

Alt Table

Status	Error	Program
▶	36.0b	(/.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)))))
✓	31.8b	(.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))))
✓	0.0b	(fma.f64 x.re y.re (neg.f64 (*.f64 x.im y.im)))

Compiler

Compiled 6037 to 1072 computations (82.2% saved)

localize15.0ms (0.4%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	1.2b	(-.f64 (pow.f64 (.f64 x.re y.re) 3) (pow.f64 (.f64 x.im y.im) 3))
✓	1.4b	(+.f64 (.f64 (.f64 x.im y.im) (.f64 x.im y.im)) (.f64 (.f64 x.re y.re) (.f64 x.im y.im)))
✓	2.9b	(.f64 (.f64 x.re y.re) (*.f64 x.im y.im))
✓	34.8b	(/.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)))))

series434.0ms (11.1%)

Counts

4 → 192

Calls

4 calls:

201.0ms	(-.f64 (pow.f64 (.f64 x.re y.re) 3) (pow.f64 (.f64 x.im y.im) 3))
176.0ms	(/.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)))))
39.0ms	(+.f64 (.f64 (.f64 x.im y.im) (.f64 x.im y.im)) (.f64 (.f64 x.re y.re) (.f64 x.im y.im)))
18.0ms	(.f64 (.f64 x.re y.re) (*.f64 x.im y.im))

rewrite63.0ms (1.6%)

Algorithm

1×	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:

22.0ms	(/.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)))))
8.0ms	(-.f64 (pow.f64 (.f64 x.re y.re) 3) (pow.f64 (.f64 x.im y.im) 3))
6.0ms	(+.f64 (.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 x.re y.re) (*.f64 x.im y.im))

simplify247.0ms (6.3%)

Algorithm

1×	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)

Iter	Nodes	Cost
0	310	9702
1	614	8966
2	3208	8822
3	5060	8822

prune186.0ms (4.8%)

Pruning

3 alts after pruning (0 fresh and 3 done)

	Pruned	Kept	Total
New	266	0	266
Fresh	0	0	0
Picked	0	1	1
Done	0	2	2
Total	266	3	269

Error

Counts

269 → 3

Alt Table

Status	Error	Program
✓	36.0b	(/.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)))))
✓	31.8b	(.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))))
✓	0.0b	(fma.f64 x.re y.re (neg.f64 (*.f64 x.im y.im)))

Compiler

Compiled 14613 to 3739 computations (74.4% saved)

regimes305.0ms (7.8%)

Accuracy

Total 0.0b remaining (20%)

Threshold costs 0.0b (20%)

Counts

30 → 1

Compiler

Compiled 6227 to 3331 computations (46.5% saved)

simplify3.0ms (0.1%)

Algorithm

1×	egg-herbie

Rules

4×	`+-commutative_binary64`
4×	`*-commutative_binary64`
3×	`sub-neg_binary64`
3×	`neg-sub0_binary64`
3×	`neg-mul-1_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	11	22
1	22	22
2	30	22
3	34	22
4	35	22
5	35	22

end83.0ms (2.1%)

Remove

(sort x.im y.im)

(sort x.re y.re)

Compiler

Compiled 185 to 93 computations (49.7% saved)

Iter	Nodes	Cost
0	8	10
1	16	10
2	27	10
3	44	10
4	66	10
5	100	10
6	152	10
7	213	10
8	257	10
9	279	10
10	299	10
11	305	10
12	274	10

Iter	Nodes	Cost
0	8	10
1	16	10
2	27	10
3	44	10
4	66	10
5	100	10
6	152	10
7	213	10
8	257	10
9	279	10
10	299	10
11	305	10
12	274	10

Details

analyze789.0ms (20.2%)

sample1.0s (26.8%)

simplify16.0ms (0.4%)

prune2.0ms (0%)

localize6.0ms (0.2%)

series9.0ms (0.2%)

rewrite4.0ms (0.1%)

simplify113.0ms (2.9%)

prune22.0ms (0.6%)

localize5.0ms (0.1%)

series10.0ms (0.3%)

rewrite1.0ms (0%)

simplify82.0ms (2.1%)

prune10.0ms (0.3%)

localize7.0ms (0.2%)

series114.0ms (2.9%)

rewrite19.0ms (0.5%)

simplify169.0ms (4.3%)

prune144.0ms (3.7%)

localize15.0ms (0.4%)

series434.0ms (11.1%)

rewrite63.0ms (1.6%)

simplify247.0ms (6.3%)

prune186.0ms (4.8%)

regimes305.0ms (7.8%)

simplify3.0ms (0.1%)

end83.0ms (2.1%)

Profiling

Iter	Nodes	Cost
0	8	10
1	16	10
2	27	10
3	44	10
4	66	10
5	100	10
6	152	10
7	213	10
8	257	10
9	279	10
10	299	10
11	305	10
12	274	10