Details

analyze4.0ms (0.2%)

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)

sample1.0s (58.1%)

Symmetry

(sort x.re y.re)

(sort x.im y.im)

Results

912.0ms

8256×

body

128

valid

Compiler

Compiled 35 to 23 computations (34.3% saved)

simplify19.0ms (1.1%)

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

0.5b

Counts

2 → 1

Alt Table

Status	Error	Program
▶	0.5b	(-.f64 (.f64 x.re y.re) (.f64 x.im y.im))

Compiler

Compiled 33 to 21 computations (36.4% saved)

localize5.0ms (0.3%)

Local error

Found 1 expressions with local error:

New	Error	Program
✓	0.5b	(-.f64 (.f64 x.re y.re) (.f64 x.im y.im))

series11.0ms (0.6%)

Counts

1 → 48

Calls

1 calls:

10.0ms

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

rewrite6.0ms (0.3%)

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:

5.0ms

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

simplify172.0ms (9.7%)

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

prune32.0ms (1.8%)

Pruning

3 alts after pruning (2 fresh and 1 done)

	Pruned	Kept	Total
New	30	2	32
Fresh	0	0	0
Picked	0	1	1
Done	0	0	0
Total	30	3	33

Error

Counts

33 → 3

Alt Table

Status	Error	Program
✓	0.5b	(-.f64 (.f64 x.re y.re) (.f64 x.im y.im))
▶	7.8b	(+.f64 (fma.f64 x.re y.re (neg.f64 (.f64 y.im x.im))) (fma.f64 (neg.f64 y.im) x.im (.f64 y.im x.im)))
	33.7b	(*.f64 x.re y.re)

Compiler

Compiled 476 to 129 computations (72.9% saved)

localize19.0ms (1.1%)

Local error

Found 2 expressions with local error:

New	Error	Program
✓	0.5b	(fma.f64 x.re y.re (neg.f64 (*.f64 y.im x.im)))
✓	53.8b	(fma.f64 (neg.f64 y.im) x.im (*.f64 y.im x.im))

series41.0ms (2.3%)

Counts

2 → 72

Calls

2 calls:

24.0ms	(fma.f64 x.re y.re (neg.f64 (*.f64 y.im x.im)))
17.0ms	(fma.f64 (neg.f64 y.im) x.im (*.f64 y.im x.im))

rewrite3.0ms (0.2%)

Algorithm

1×	rewrite-expression-head

Rules

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

Counts

2 → 20

Calls

2 calls:

1.0ms	(fma.f64 (neg.f64 y.im) x.im (*.f64 y.im x.im))
1.0ms	(fma.f64 x.re y.re (neg.f64 (*.f64 y.im x.im)))

simplify149.0ms (8.4%)

Algorithm

1×	egg-herbie

Rules

933×	`unsub-neg_binary64`
447×	`fma-neg_binary64`
374×	`neg-sub0_binary64`
344×	`neg-mul-1_binary64`
300×	`distribute-rgt-out_binary64`

Counts

92 → 40

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	34	709
1	47	661
2	107	605
3	350	605
4	1034	605
5	2015	605
6	3815	605
7	4665	605
8	4890	605

prune37.0ms (2.1%)

Pruning

3 alts after pruning (1 fresh and 2 done)

	Pruned	Kept	Total
New	40	0	40
Fresh	0	1	1
Picked	0	1	1
Done	0	1	1
Total	40	3	43

Error

Counts

43 → 3

Alt Table

Status	Error	Program
✓	0.5b	(-.f64 (.f64 x.re y.re) (.f64 x.im y.im))
✓	7.8b	(+.f64 (fma.f64 x.re y.re (neg.f64 (.f64 y.im x.im))) (fma.f64 (neg.f64 y.im) x.im (.f64 y.im x.im)))
▶	33.7b	(*.f64 x.re y.re)

Compiler

Compiled 769 to 167 computations (78.3% saved)

localize4.0ms (0.2%)

prune3.0ms (0.2%)

Pruning

3 alts after pruning (0 fresh and 3 done)

	Kept	Total
New	0	0
Fresh	0	0
Picked	1	1
Done	2	2
Total	3	3

Error

Counts

3 → 3

Alt Table

Status	Error	Program
✓	0.5b	(-.f64 (.f64 x.re y.re) (.f64 x.im y.im))
✓	7.8b	(+.f64 (fma.f64 x.re y.re (neg.f64 (.f64 y.im x.im))) (fma.f64 (neg.f64 y.im) x.im (.f64 y.im x.im)))
✓	33.7b	(*.f64 x.re y.re)

Compiler

Compiled 37 to 22 computations (40.5% saved)

regimes103.0ms (5.8%)

Accuracy

Total 0.3b remaining (54.2%)

Threshold costs 0.3b (54.2%)

Counts

5 → 1

Compiler

Compiled 468 to 311 computations (33.5% saved)

simplify5.0ms (0.3%)

Algorithm

1×	egg-herbie

Rules

5×	`*-commutative_binary64`
4×	`+-commutative_binary64`
4×	`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	15	10
2	25	10
3	31	10
4	35	10
5	36	10
6	36	10

end131.0ms (7.4%)

Remove

(sort x.im y.im)

(sort x.re y.re)

Compiler

Compiled 103 to 64 computations (37.9% 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

analyze4.0ms (0.2%)

sample1.0s (58.1%)

simplify19.0ms (1.1%)

prune1.0ms (0.1%)

localize5.0ms (0.3%)

series11.0ms (0.6%)

rewrite6.0ms (0.3%)

simplify172.0ms (9.7%)

prune32.0ms (1.8%)

localize19.0ms (1.1%)

series41.0ms (2.3%)

rewrite3.0ms (0.2%)

simplify149.0ms (8.4%)

prune37.0ms (2.1%)

localize4.0ms (0.2%)

prune3.0ms (0.2%)

regimes103.0ms (5.8%)

simplify5.0ms (0.3%)

end131.0ms (7.4%)

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