Details

analyze2.0ms (0.1%)

Algorithm

1×

Search

True	Other	False	Iter
0%	99.8%	0.2%	0
99.8%	0%	0.2%	1

Compiler

Compiled 12 to 8 computations (33.3% saved)

sample1.3s (47.1%)

Symmetry

(sort x.re y.re)

(sort x.im y.im)

Results

1.2s

8256×

body

128

valid

Compiler

Compiled 35 to 23 computations (34.3% saved)

simplify15.0ms (0.5%)

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 (0.1%)

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

0.3b

Counts

2 → 1

Alt Table

Status	Error	Program
▶	0.3b	(-.f64 (.f64 x.re y.re) (.f64 x.im y.im))

Compiler

Compiled 33 to 21 computations (36.4% saved)

localize5.0ms (0.2%)

Local error

Found 1 expressions with local error:

New	Error	Program
✓	0.2b	(-.f64 (.f64 x.re y.re) (.f64 x.im y.im))

series9.0ms (0.3%)

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))

simplify132.0ms (4.8%)

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

prune18.0ms (0.7%)

Pruning

2 alts after pruning (2 fresh and 0 done)

	Pruned	Kept	Total
New	30	2	32
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	31	2	33

Error

Counts

33 → 2

Alt Table

Status	Error	Program
	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)))

Status

Error

Program

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 495 to 126 computations (74.5% saved)

localize5.0ms (0.2%)

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)))

series11.0ms (0.4%)

Counts

1 → 48

Calls

1 calls:

11.0ms

(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)))

simplify85.0ms (3.1%)

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

prune9.0ms (0.3%)

Pruning

2 alts after pruning (1 fresh and 1 done)

	Pruned	Kept	Total
New	21	0	21
Fresh	0	1	1
Picked	0	1	1
Done	0	0	0
Total	21	2	23

Error

Counts

23 → 2

Alt Table

Status	Error	Program
▶	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)))

Status

Error

Program

▶

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 312 to 77 computations (75.3% saved)

localize8.0ms (0.3%)

Local error

Found 4 expressions with local error:

New	Error	Program
	0.2b	(-.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))))
✓	15.0b	(cbrt.f64 (-.f64 (.f64 x.re y.re) (.f64 x.im y.im)))

series262.0ms (9.5%)

Counts

3 → 144

Calls

3 calls:

127.0ms

(*.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))))

100.0ms

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

34.0ms

(*.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))))

rewrite46.0ms (1.7%)

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:

14.0ms

(*.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)))

simplify190.0ms (6.9%)

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

prune418.0ms (15.1%)

Pruning

2 alts after pruning (0 fresh and 2 done)

	Pruned	Kept	Total
New	651	0	651
Fresh	0	0	0
Picked	0	1	1
Done	0	1	1
Total	651	2	653

Error

Counts

653 → 2

Alt Table

Status	Error	Program
✓	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)))

Status

Error

Program

✓

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 32694 to 11011 computations (66.3% saved)

regimes174.0ms (6.3%)

Accuracy

Total 0.0b remaining (0.3%)

Threshold costs 0.0b (0.3%)

Counts

19 → 1

Compiler

Compiled 2694 to 1667 computations (38.1% saved)

simplify2.0ms (0.1%)

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

end63.0ms (2.3%)

Remove

(sort x.im y.im)

(sort x.re y.re)

Compiler

Compiled 107 to 59 computations (44.9% 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

analyze2.0ms (0.1%)

sample1.3s (47.1%)

simplify15.0ms (0.5%)

prune1.0ms (0.1%)

localize5.0ms (0.2%)

series9.0ms (0.3%)

rewrite3.0ms (0.1%)

simplify132.0ms (4.8%)

prune18.0ms (0.7%)

localize5.0ms (0.2%)

series11.0ms (0.4%)

rewrite1.0ms (0%)

simplify85.0ms (3.1%)

prune9.0ms (0.3%)

localize8.0ms (0.3%)

series262.0ms (9.5%)

rewrite46.0ms (1.7%)

simplify190.0ms (6.9%)

prune418.0ms (15.1%)

regimes174.0ms (6.3%)

simplify2.0ms (0.1%)

end63.0ms (2.3%)

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