Details

analyze974.0ms (19.6%)

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)

sample1.1s (21.5%)

Symmetry

(sort x.re y.re)

(sort x.im y.im)

Results

874.0ms	8256×	body	128	valid
138.0ms	1350×	body	128	invalid

Compiler

Compiled 35 to 23 computations (34.3% saved)

simplify17.0ms (0.3%)

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

prune1.0ms (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)

localize5.0ms (0.1%)

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))

rewrite3.0ms (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))

simplify112.0ms (2.2%)

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

prune24.0ms (0.5%)

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

0.0b

Counts

33 → 3

Alt Table

Status	Error	Program
	33.2b	(.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))))
	1.2b	(.f64 (.f64 (cbrt.f64 (-.f64 (.f64 x.re y.re) (.f64 x.im y.im))) (cbrt.f64 (-.f64 (.f64 x.re y.re) (.f64 x.im y.im)))) (cbrt.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 537 to 144 computations (73.2% 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)))

series13.0ms (0.3%)

Counts

1 → 48

Calls

1 calls:

13.0ms

(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)))

simplify79.0ms (1.6%)

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

prune8.0ms (0.2%)

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

0.0b

Counts

24 → 3

Alt Table

Status	Error	Program
	33.2b	(.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))))
▶	1.2b	(.f64 (.f64 (cbrt.f64 (-.f64 (.f64 x.re y.re) (.f64 x.im y.im))) (cbrt.f64 (-.f64 (.f64 x.re y.re) (.f64 x.im y.im)))) (cbrt.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 354 to 95 computations (73.2% saved)

localize9.0ms (0.2%)

Local error

Found 4 expressions with local error:

New	Error	Program
	0.0b	(-.f64 (.f64 x.re y.re) (.f64 x.im y.im))
✓	0.3b	(.f64 (.f64 (cbrt.f64 (-.f64 (.f64 x.re y.re) (.f64 x.im y.im))) (cbrt.f64 (-.f64 (.f64 x.re y.re) (.f64 x.im y.im)))) (cbrt.f64 (-.f64 (.f64 x.re y.re) (.f64 x.im y.im))))
✓	0.5b	(.f64 (cbrt.f64 (-.f64 (.f64 x.re y.re) (.f64 x.im y.im))) (cbrt.f64 (-.f64 (.f64 x.re y.re) (*.f64 x.im y.im))))
✓	1.8b	(cbrt.f64 (-.f64 (.f64 x.re y.re) (.f64 x.im y.im)))

series236.0ms (4.8%)

Counts

3 → 144

Calls

3 calls:

118.0ms

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

88.0ms

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

30.0ms

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

rewrite44.0ms (0.9%)

Algorithm

1×	rewrite-expression-head

Rules

68×	`cbrt-div_binary64`
34×	`flip--_binary64`
34×	`flip3--_binary64`
32×	`frac-times_binary64`
29×	`pow1_binary64`

Counts

3 → 129

Calls

3 calls:

15.0ms

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

8.0ms

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

2.0ms

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

simplify185.0ms (3.7%)

Algorithm

1×	egg-herbie

Rules

787×	`associate-/r*_binary64`
684×	`associate-/l*_binary64`
280×	`fma-def_binary64`
246×	`*-commutative_binary64`
147×	`cancel-sign-sub-inv_binary64`

Counts

273 → 349

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	627	12010
1	2088	11381
2	5859	11381

prune395.0ms (7.9%)

Pruning

4 alts after pruning (2 fresh and 2 done)

	Pruned	Kept	Total
New	650	1	651
Fresh	0	1	1
Picked	0	1	1
Done	0	1	1
Total	650	4	654

Error

Counts

654 → 4

Alt Table

Status	Error	Program
	33.2b	(.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))))
✓	1.2b	(.f64 (.f64 (cbrt.f64 (-.f64 (.f64 x.re y.re) (.f64 x.im y.im))) (cbrt.f64 (-.f64 (.f64 x.re y.re) (.f64 x.im y.im)))) (cbrt.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)))
▶	1.7b	(.f64 (.f64 (.f64 (cbrt.f64 (-.f64 (.f64 x.re y.re) (.f64 y.im x.im))) (cbrt.f64 (cbrt.f64 (-.f64 (.f64 x.re y.re) (.f64 y.im x.im))))) (.f64 (cbrt.f64 (cbrt.f64 (-.f64 (.f64 x.re y.re) (.f64 y.im x.im)))) (cbrt.f64 (cbrt.f64 (-.f64 (.f64 x.re y.re) (.f64 y.im x.im)))))) (cbrt.f64 (-.f64 (.f64 x.re y.re) (.f64 x.im y.im))))

Compiler

Compiled 32838 to 11061 computations (66.3% saved)

localize16.0ms (0.3%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.6b	(.f64 (cbrt.f64 (cbrt.f64 (-.f64 (.f64 x.re y.re) (.f64 y.im x.im)))) (cbrt.f64 (cbrt.f64 (-.f64 (.f64 x.re y.re) (*.f64 y.im x.im)))))
✓	0.6b	(cbrt.f64 (cbrt.f64 (-.f64 (.f64 x.re y.re) (.f64 y.im x.im))))
	1.8b	(cbrt.f64 (-.f64 (.f64 x.re y.re) (.f64 x.im y.im)))
✓	1.8b	(cbrt.f64 (-.f64 (.f64 x.re y.re) (.f64 y.im x.im)))

series300.0ms (6%)

Counts

3 → 144

Calls

3 calls:

120.0ms

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

91.0ms

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

89.0ms

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

rewrite26.0ms (0.5%)

Algorithm

1×	rewrite-expression-head

Rules

66×	`cbrt-prod_binary64`
36×	`add-sqr-sqrt_binary64`
30×	`cbrt-div_binary64`
18×	`*-un-lft-identity_binary64`
18×	`add-cube-cbrt_binary64`

Counts

3 → 97

Calls

3 calls:

10.0ms

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

3.0ms

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

2.0ms

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

simplify313.0ms (6.3%)

Algorithm

1×	egg-herbie

Rules

424×	`fma-def_binary64`
318×	`*-commutative_binary64`
219×	`cancel-sign-sub-inv_binary64`
206×	`fma-neg_binary64`
199×	`sub-neg_binary64`

Counts

241 → 344

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	825	13649
1	2839	12947
2	4921	12945
3	4983	12945

prune811.0ms (16.3%)

Pruning

4 alts after pruning (1 fresh and 3 done)

	Pruned	Kept	Total
New	923	0	923
Fresh	0	1	1
Picked	0	1	1
Done	0	2	2
Total	923	4	927

Error

Counts

927 → 4

Alt Table

Status	Error	Program
	33.2b	(.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))))
✓	1.2b	(.f64 (.f64 (cbrt.f64 (-.f64 (.f64 x.re y.re) (.f64 x.im y.im))) (cbrt.f64 (-.f64 (.f64 x.re y.re) (.f64 x.im y.im)))) (cbrt.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)))
✓	1.7b	(.f64 (.f64 (.f64 (cbrt.f64 (-.f64 (.f64 x.re y.re) (.f64 y.im x.im))) (cbrt.f64 (cbrt.f64 (-.f64 (.f64 x.re y.re) (.f64 y.im x.im))))) (.f64 (cbrt.f64 (cbrt.f64 (-.f64 (.f64 x.re y.re) (.f64 y.im x.im)))) (cbrt.f64 (cbrt.f64 (-.f64 (.f64 x.re y.re) (.f64 y.im x.im)))))) (cbrt.f64 (-.f64 (.f64 x.re y.re) (.f64 x.im y.im))))

Compiler

Compiled 72608 to 23411 computations (67.8% saved)

regimes242.0ms (4.9%)

Accuracy

Total 0.0b remaining (31.2%)

Threshold costs 0.0b (31.2%)

Counts

30 → 1

Compiler

Compiled 6491 to 3148 computations (51.5% saved)

simplify2.0ms (0%)

Algorithm

1×	egg-herbie

Rules

4×	`*-commutative_binary64`
3×	`+-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	8	10
1	17	10
2	25	10
3	30	10
4	32	10
5	32	10

end72.0ms (1.4%)

Remove

(sort x.im y.im)

(sort x.re y.re)

Compiler

Compiled 179 to 84 computations (53.1% 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

analyze974.0ms (19.6%)

sample1.1s (21.5%)

simplify17.0ms (0.3%)

prune1.0ms (0%)

localize5.0ms (0.1%)

series9.0ms (0.2%)

rewrite3.0ms (0.1%)

simplify112.0ms (2.2%)

prune24.0ms (0.5%)

localize5.0ms (0.1%)

series13.0ms (0.3%)

rewrite1.0ms (0%)

simplify79.0ms (1.6%)

prune8.0ms (0.2%)

localize9.0ms (0.2%)

series236.0ms (4.8%)

rewrite44.0ms (0.9%)

simplify185.0ms (3.7%)

prune395.0ms (7.9%)

localize16.0ms (0.3%)

series300.0ms (6%)

rewrite26.0ms (0.5%)

simplify313.0ms (6.3%)

prune811.0ms (16.3%)

regimes242.0ms (4.9%)

simplify2.0ms (0%)

end72.0ms (1.4%)

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