Metrics for math.sqrt on complex, imaginary part, im greater than 0 branch

start0.0ms (0%)

Memory: 0.0MiB live, 0.0MiB allocated

analyze98.0ms (1.4%)

Memory

11.6MiB live, 205.8MiB allocated

Algorithm

1×

Search

Probability	Valid	Unknown	Precondition	Infinite	Domain	Can't	Iter
0%	0%	50%	50%	0%	0%	0%	0
0%	0%	50%	50%	0%	0%	0%	1
50%	25%	25%	50%	0%	0%	0%	2
50%	25%	25%	50%	0%	0%	0%	3
62.5%	31.2%	18.7%	50%	0%	0%	0%	4
62.5%	31.2%	18.7%	50%	0%	0%	0%	5
68.8%	34.3%	15.6%	50%	0%	0%	0%	6
68.8%	34.3%	15.6%	50%	0%	0%	0%	7
71.9%	35.9%	14%	50%	0%	0%	0%	8
71.9%	35.9%	14%	50%	0%	0%	0%	9
73.4%	36.7%	13.3%	50%	0%	0%	0%	10
73.4%	36.7%	13.3%	50%	0%	0%	0%	11
74.2%	37.1%	12.9%	50%	0%	0%	0%	12

Compiler

Compiled 19 to 12 computations (36.8% saved)

sample1.5s (21.2%)

Memory

24.9MiB live, 2 208.2MiB allocated

Samples

660.0ms	6 158×	0	valid
198.0ms	814×	2	valid
163.0ms	491×	3	valid
103.0ms	793×	1	valid

Precisions

Click to see histograms. Total time spent on operations: 868.0ms

ival-hypot: 356.0ms (41% of total)

ival-mult: 263.0ms (30.3% of total)

ival-sqrt: 101.0ms (11.6% of total)

ival-sub: 58.0ms (6.7% of total)

adjust: 45.0ms (5.2% of total)

ival->: 29.0ms (3.3% of total)

exact: 12.0ms (1.4% of total)

ival-assert: 3.0ms (0.3% of total)

Bogosity

explain225.0ms (3.1%)

Memory

30.0MiB live, 378.0MiB allocated

FPErrors

Click to see full error table

Ground Truth	Example	Underpredictions	Example	Subexpression
141	-	1	(7.939373432026022e-188 1.3982930247122226e-160)	`(sqrt.f64 (+.f64 (.f64 re re) (.f64 im im)))`
32	-	0	-	`(-.f64 (sqrt.f64 (+.f64 (.f64 re re) (.f64 im im))) re)`
24	-	1	(3.97649159652887e-233 2.3791708003100885e-277)	`(sqrt.f64 (.f64 #s(literal 2 binary64) (-.f64 (sqrt.f64 (+.f64 (.f64 re re) (*.f64 im im))) re)))`
0	-	0	-	`(.f64 #s(literal 1/2 binary64) (sqrt.f64 (.f64 #s(literal 2 binary64) (-.f64 (sqrt.f64 (+.f64 (.f64 re re) (.f64 im im))) re))))`
0	-	0	-	`(.f64 #s(literal 2 binary64) (-.f64 (sqrt.f64 (+.f64 (.f64 re re) (*.f64 im im))) re))`
0	-	0	-	`(*.f64 re re)`
0	-	0	-	`im`
0	-	0	-	`(+.f64 (.f64 re re) (.f64 im im))`
0	-	0	-	`#s(literal 2 binary64)`
0	-	0	-	`re`
0	-	0	-	`#s(literal 1/2 binary64)`
0	-	0	-	`(*.f64 im im)`

Explanations

Click to see full explanations table

Operator	Subexpression	Explanation	Count
`sqrt.f64`	`(sqrt.f64 (+.f64 (.f64 re re) (.f64 im im)))`	oflow-rescue	123	0
↳	`(+.f64 (.f64 re re) (.f64 im im))`	overflow	123
↳	`(*.f64 re re)`	overflow	67
↳	`(*.f64 im im)`	overflow	71
`-.f64`	`(-.f64 (sqrt.f64 (+.f64 (.f64 re re) (.f64 im im))) re)`	cancellation	32	0
`sqrt.f64`	`(sqrt.f64 (.f64 #s(literal 2 binary64) (-.f64 (sqrt.f64 (+.f64 (.f64 re re) (*.f64 im im))) re)))`	uflow-rescue	21	0
↳	`(.f64 #s(literal 2 binary64) (-.f64 (sqrt.f64 (+.f64 (.f64 re re) (*.f64 im im))) re))`	underflow	27
↳	`(sqrt.f64 (.f64 #s(literal 2 binary64) (-.f64 (sqrt.f64 (+.f64 (.f64 re re) (*.f64 im im))) re)))`	underflow	6
↳	`(*.f64 re re)`	underflow	67
↳	`(*.f64 im im)`	underflow	61
↳	`(+.f64 (.f64 re re) (.f64 im im))`	underflow	17
↳	`(-.f64 (sqrt.f64 (+.f64 (.f64 re re) (.f64 im im))) re)`	underflow	27
`sqrt.f64`	`(sqrt.f64 (+.f64 (.f64 re re) (.f64 im im)))`	uflow-rescue	17	0
↳	`(+.f64 (.f64 re re) (.f64 im im))`	underflow	17
↳	`(*.f64 re re)`	underflow	67
↳	`(*.f64 im im)`	underflow	61
`sqrt.f64`	`(sqrt.f64 (.f64 #s(literal 2 binary64) (-.f64 (sqrt.f64 (+.f64 (.f64 re re) (*.f64 im im))) re)))`	oflow-rescue	2	0
↳	`(.f64 #s(literal 2 binary64) (-.f64 (sqrt.f64 (+.f64 (.f64 re re) (*.f64 im im))) re))`	overflow	2
↳	`(*.f64 re re)`	overflow	67
↳	`(*.f64 im im)`	overflow	71
↳	`(+.f64 (.f64 re re) (.f64 im im))`	overflow	123
↳	`(-.f64 (sqrt.f64 (+.f64 (.f64 re re) (.f64 im im))) re)`	overflow	1

Confusion

	Predicted +	Predicted -
+	167	1
-	0	88

Precision

1.0

Recall

0.9940476190476191

Confusion?

	Predicted +	Predicted Maybe	Predicted -
+	167	0	1
-	0	0	88

Precision?

1.0

Recall?

0.9940476190476191

Freqs

test

number	freq
0	89
1	139
2	28

Total Confusion?

	Predicted +	Predicted Maybe	Predicted -
+	1	0	0
-	0	0	0

Precision?

1.0

Recall?

1.0

Samples

41.0ms	394×	0	valid
19.0ms	48×	2	valid
9.0ms	46×	1	valid
9.0ms	24×	3	valid

Compiler

Compiled 244 to 52 computations (78.7% saved)

Precisions

Click to see histograms. Total time spent on operations: 45.0ms

ival-mult: 15.0ms (33% of total)

ival-hypot: 14.0ms (30.8% of total)

ival-sqrt: 5.0ms (11% of total)

adjust: 4.0ms (8.8% of total)

ival-sub: 4.0ms (8.8% of total)

ival-add: 3.0ms (6.6% of total)

ival-assert: 0.0ms (0% of total)

ival-true: 0.0ms (0% of total)

exact: 0.0ms (0% of total)

preprocess68.0ms (0.9%)

Memory

8.0MiB live, 78.3MiB allocated

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	30	77
1	71	75
2	152	75
3	285	75
4	424	75
5	515	75
6	637	75
7	775	75
8	830	75
0	12	15
0	20	15
1	25	15
2	36	15
3	52	15
4	73	15
5	98	15
6	154	15
7	227	15
8	310	15
9	360	15
10	420	15
11	434	15
12	450	15
13	470	15
14	500	15
15	531	15
16	543	15
17	545	15
0	545	10

Stop Event

1×	iter limit
1×	saturated
1×	iter limit
1×	saturated

Calls

Call 1

Inputs
(.f64 #s(literal 1/2 binary64) (sqrt.f64 (.f64 #s(literal 2 binary64) (-.f64 (sqrt.f64 (+.f64 (.f64 re re) (.f64 im im))) re))))

Outputs
(.f64 (sqrt.f64 (.f64 (-.f64 (hypot.f64 im re) re) #s(literal 2 binary64))) #s(literal 1/2 binary64))

Symmetry

(abs im)

Compiler

Compiled 15 to 12 computations (20% saved)

eval0.0ms (0%)

Memory: 0.5MiB live, 0.5MiB allocated
Compiler: Compiled 0 to 2 computations (-∞% saved)

prune1.0ms (0%)

Memory

1.2MiB live, 1.2MiB allocated

Alt Table

Click to see full alt table

Status	Accuracy	Program
▶	37.6%	(.f64 #s(literal 1/2 binary64) (sqrt.f64 (.f64 #s(literal 2 binary64) (-.f64 (sqrt.f64 (+.f64 (.f64 re re) (.f64 im im))) re))))

Compiler

Compiled 15 to 12 computations (20% saved)

simplify32.0ms (0.5%)

Memory

-25.9MiB live, 13.6MiB allocated

Algorithm

1×	egg-herbie

Localize:

Found 4 expressions of interest:

New	Metric	Score
cost-diff	0	(.f64 #s(literal 2 binary64) (-.f64 (sqrt.f64 (+.f64 (.f64 re re) (*.f64 im im))) re))
cost-diff	0	(sqrt.f64 (.f64 #s(literal 2 binary64) (-.f64 (sqrt.f64 (+.f64 (.f64 re re) (*.f64 im im))) re)))
cost-diff	0	(.f64 #s(literal 1/2 binary64) (sqrt.f64 (.f64 #s(literal 2 binary64) (-.f64 (sqrt.f64 (+.f64 (.f64 re re) (.f64 im im))) re))))
cost-diff	128	(+.f64 (.f64 re re) (.f64 im im))

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	12	75
0	20	75
1	25	75
2	36	75
3	52	75
4	73	75
5	98	75
6	154	75
7	227	75
8	310	75
9	360	75
10	420	75
11	434	75
12	450	75
13	470	75
14	500	75
15	531	75
16	543	75
17	545	75
0	545	49

Stop Event

1×	iter limit
1×	saturated
1×	iter limit

Calls

Call 1

Inputs
(.f64 #s(literal 1/2 binary64) (sqrt.f64 (.f64 #s(literal 2 binary64) (-.f64 (sqrt.f64 (+.f64 (.f64 re re) (.f64 im im))) re))))
#s(literal 1/2 binary64)
(sqrt.f64 (.f64 #s(literal 2 binary64) (-.f64 (sqrt.f64 (+.f64 (.f64 re re) (*.f64 im im))) re)))
(.f64 #s(literal 2 binary64) (-.f64 (sqrt.f64 (+.f64 (.f64 re re) (*.f64 im im))) re))
#s(literal 2 binary64)
(-.f64 (sqrt.f64 (+.f64 (.f64 re re) (.f64 im im))) re)
(sqrt.f64 (+.f64 (.f64 re re) (.f64 im im)))
(+.f64 (.f64 re re) (.f64 im im))
(*.f64 re re)
re
(*.f64 im im)
im

Outputs
(.f64 (sqrt.f64 (.f64 (-.f64 (hypot.f64 im re) re) #s(literal 2 binary64))) #s(literal 1/2 binary64))
#s(literal 1/2 binary64)
(sqrt.f64 (*.f64 (-.f64 (hypot.f64 im re) re) #s(literal 2 binary64)))
(*.f64 (-.f64 (hypot.f64 im re) re) #s(literal 2 binary64))
#s(literal 2 binary64)
(-.f64 (hypot.f64 im re) re)
(hypot.f64 im re)
(fma.f64 im im (*.f64 re re))
(*.f64 re re)
re
(*.f64 im im)
im

localize78.0ms (1.1%)

Memory

15.1MiB live, 117.2MiB allocated

Localize:

Found 4 expressions of interest:

New	Metric	Score
accuracy	0.00390625	(.f64 #s(literal 1/2 binary64) (sqrt.f64 (.f64 #s(literal 2 binary64) (-.f64 (sqrt.f64 (+.f64 (.f64 re re) (.f64 im im))) re))))
accuracy	5.359724696450623	(sqrt.f64 (.f64 #s(literal 2 binary64) (-.f64 (sqrt.f64 (+.f64 (.f64 re re) (*.f64 im im))) re)))
accuracy	7.3690282203664905	(-.f64 (sqrt.f64 (+.f64 (.f64 re re) (.f64 im im))) re)
accuracy	32.663371370661785	(sqrt.f64 (+.f64 (.f64 re re) (.f64 im im)))

Samples

33.0ms	24×	2	valid
19.0ms	197×	0	valid
5.0ms	12×	3	valid
4.0ms	23×	1	valid

Compiler

Compiled 152 to 26 computations (82.9% saved)

Precisions

Click to see histograms. Total time spent on operations: 22.0ms

ival-hypot: 7.0ms (31.5% of total)

ival-mult: 7.0ms (31.5% of total)

adjust: 2.0ms (9% of total)

ival-sub: 2.0ms (9% of total)

ival-sqrt: 2.0ms (9% of total)

ival-add: 1.0ms (4.5% of total)

ival-assert: 0.0ms (0% of total)

ival-true: 0.0ms (0% of total)

exact: 0.0ms (0% of total)

series335.0ms (4.7%)

Memory

-52.9MiB live, 47.4MiB allocated

Counts

6 → 144

Calls

Call 1

Inputs
#s(alt #<batchref> (patch (+.f64 (.f64 re re) (.f64 im im)) #<representation binary64>) () ())
#s(alt #<batchref> (patch (.f64 #s(literal 1/2 binary64) (sqrt.f64 (.f64 #s(literal 2 binary64) (-.f64 (sqrt.f64 (+.f64 (.f64 re re) (.f64 im im))) re)))) #<representation binary64>) () ())
#s(alt #<batchref> (patch (sqrt.f64 (.f64 #s(literal 2 binary64) (-.f64 (sqrt.f64 (+.f64 (.f64 re re) (*.f64 im im))) re))) #<representation binary64>) () ())
#s(alt #<batchref> (patch (.f64 #s(literal 2 binary64) (-.f64 (sqrt.f64 (+.f64 (.f64 re re) (*.f64 im im))) re)) #<representation binary64>) () ())
#s(alt #<batchref> (patch (sqrt.f64 (+.f64 (.f64 re re) (.f64 im im))) #<representation binary64>) () ())
#s(alt #<batchref> (patch (-.f64 (sqrt.f64 (+.f64 (.f64 re re) (.f64 im im))) re) #<representation binary64>) () ())

Outputs
#s(alt #<batchref> (taylor 0 re) (#s(alt #<batchref> (patch (+.f64 (.f64 re re) (.f64 im im)) #<representation binary64>) () ())) ())
#s(alt #<batchref> (taylor 0 re) (#s(alt #<batchref> (patch (+.f64 (.f64 re re) (.f64 im im)) #<representation binary64>) () ())) ())
#s(alt #<batchref> (taylor 0 re) (#s(alt #<batchref> (patch (+.f64 (.f64 re re) (.f64 im im)) #<representation binary64>) () ())) ())
#s(alt #<batchref> (taylor 0 re) (#s(alt #<batchref> (patch (+.f64 (.f64 re re) (.f64 im im)) #<representation binary64>) () ())) ())
#s(alt #<batchref> (taylor 0 re) (#s(alt #<batchref> (patch (.f64 #s(literal 1/2 binary64) (sqrt.f64 (.f64 #s(literal 2 binary64) (-.f64 (sqrt.f64 (+.f64 (.f64 re re) (.f64 im im))) re)))) #<representation binary64>) () ())) ())
#s(alt #<batchref> (taylor 0 re) (#s(alt #<batchref> (patch (.f64 #s(literal 1/2 binary64) (sqrt.f64 (.f64 #s(literal 2 binary64) (-.f64 (sqrt.f64 (+.f64 (.f64 re re) (.f64 im im))) re)))) #<representation binary64>) () ())) ())
#s(alt #<batchref> (taylor 0 re) (#s(alt #<batchref> (patch (.f64 #s(literal 1/2 binary64) (sqrt.f64 (.f64 #s(literal 2 binary64) (-.f64 (sqrt.f64 (+.f64 (.f64 re re) (.f64 im im))) re)))) #<representation binary64>) () ())) ())
#s(alt #<batchref> (taylor 0 re) (#s(alt #<batchref> (patch (.f64 #s(literal 1/2 binary64) (sqrt.f64 (.f64 #s(literal 2 binary64) (-.f64 (sqrt.f64 (+.f64 (.f64 re re) (.f64 im im))) re)))) #<representation binary64>) () ())) ())
#s(alt #<batchref> (taylor 0 re) (#s(alt #<batchref> (patch (sqrt.f64 (.f64 #s(literal 2 binary64) (-.f64 (sqrt.f64 (+.f64 (.f64 re re) (*.f64 im im))) re))) #<representation binary64>) () ())) ())
#s(alt #<batchref> (taylor 0 re) (#s(alt #<batchref> (patch (sqrt.f64 (.f64 #s(literal 2 binary64) (-.f64 (sqrt.f64 (+.f64 (.f64 re re) (*.f64 im im))) re))) #<representation binary64>) () ())) ())
#s(alt #<batchref> (taylor 0 re) (#s(alt #<batchref> (patch (sqrt.f64 (.f64 #s(literal 2 binary64) (-.f64 (sqrt.f64 (+.f64 (.f64 re re) (*.f64 im im))) re))) #<representation binary64>) () ())) ())
#s(alt #<batchref> (taylor 0 re) (#s(alt #<batchref> (patch (sqrt.f64 (.f64 #s(literal 2 binary64) (-.f64 (sqrt.f64 (+.f64 (.f64 re re) (*.f64 im im))) re))) #<representation binary64>) () ())) ())
#s(alt #<batchref> (taylor 0 re) (#s(alt #<batchref> (patch (.f64 #s(literal 2 binary64) (-.f64 (sqrt.f64 (+.f64 (.f64 re re) (*.f64 im im))) re)) #<representation binary64>) () ())) ())
#s(alt #<batchref> (taylor 0 re) (#s(alt #<batchref> (patch (.f64 #s(literal 2 binary64) (-.f64 (sqrt.f64 (+.f64 (.f64 re re) (*.f64 im im))) re)) #<representation binary64>) () ())) ())
#s(alt #<batchref> (taylor 0 re) (#s(alt #<batchref> (patch (.f64 #s(literal 2 binary64) (-.f64 (sqrt.f64 (+.f64 (.f64 re re) (*.f64 im im))) re)) #<representation binary64>) () ())) ())
#s(alt #<batchref> (taylor 0 re) (#s(alt #<batchref> (patch (.f64 #s(literal 2 binary64) (-.f64 (sqrt.f64 (+.f64 (.f64 re re) (*.f64 im im))) re)) #<representation binary64>) () ())) ())
#s(alt #<batchref> (taylor 0 re) (#s(alt #<batchref> (patch (sqrt.f64 (+.f64 (.f64 re re) (.f64 im im))) #<representation binary64>) () ())) ())
#s(alt #<batchref> (taylor 0 re) (#s(alt #<batchref> (patch (sqrt.f64 (+.f64 (.f64 re re) (.f64 im im))) #<representation binary64>) () ())) ())
#s(alt #<batchref> (taylor 0 re) (#s(alt #<batchref> (patch (sqrt.f64 (+.f64 (.f64 re re) (.f64 im im))) #<representation binary64>) () ())) ())
#s(alt #<batchref> (taylor 0 re) (#s(alt #<batchref> (patch (sqrt.f64 (+.f64 (.f64 re re) (.f64 im im))) #<representation binary64>) () ())) ())
#s(alt #<batchref> (taylor 0 re) (#s(alt #<batchref> (patch (-.f64 (sqrt.f64 (+.f64 (.f64 re re) (.f64 im im))) re) #<representation binary64>) () ())) ())
#s(alt #<batchref> (taylor 0 re) (#s(alt #<batchref> (patch (-.f64 (sqrt.f64 (+.f64 (.f64 re re) (.f64 im im))) re) #<representation binary64>) () ())) ())
#s(alt #<batchref> (taylor 0 re) (#s(alt #<batchref> (patch (-.f64 (sqrt.f64 (+.f64 (.f64 re re) (.f64 im im))) re) #<representation binary64>) () ())) ())
#s(alt #<batchref> (taylor 0 re) (#s(alt #<batchref> (patch (-.f64 (sqrt.f64 (+.f64 (.f64 re re) (.f64 im im))) re) #<representation binary64>) () ())) ())
#s(alt #<batchref> (taylor inf re) (#s(alt #<batchref> (patch (+.f64 (.f64 re re) (.f64 im im)) #<representation binary64>) () ())) ())
#s(alt #<batchref> (taylor inf re) (#s(alt #<batchref> (patch (+.f64 (.f64 re re) (.f64 im im)) #<representation binary64>) () ())) ())
#s(alt #<batchref> (taylor inf re) (#s(alt #<batchref> (patch (+.f64 (.f64 re re) (.f64 im im)) #<representation binary64>) () ())) ())
#s(alt #<batchref> (taylor inf re) (#s(alt #<batchref> (patch (+.f64 (.f64 re re) (.f64 im im)) #<representation binary64>) () ())) ())
#s(alt #<batchref> (taylor inf re) (#s(alt #<batchref> (patch (.f64 #s(literal 1/2 binary64) (sqrt.f64 (.f64 #s(literal 2 binary64) (-.f64 (sqrt.f64 (+.f64 (.f64 re re) (.f64 im im))) re)))) #<representation binary64>) () ())) ())
#s(alt #<batchref> (taylor inf re) (#s(alt #<batchref> (patch (.f64 #s(literal 1/2 binary64) (sqrt.f64 (.f64 #s(literal 2 binary64) (-.f64 (sqrt.f64 (+.f64 (.f64 re re) (.f64 im im))) re)))) #<representation binary64>) () ())) ())
#s(alt #<batchref> (taylor inf re) (#s(alt #<batchref> (patch (.f64 #s(literal 1/2 binary64) (sqrt.f64 (.f64 #s(literal 2 binary64) (-.f64 (sqrt.f64 (+.f64 (.f64 re re) (.f64 im im))) re)))) #<representation binary64>) () ())) ())
#s(alt #<batchref> (taylor inf re) (#s(alt #<batchref> (patch (.f64 #s(literal 1/2 binary64) (sqrt.f64 (.f64 #s(literal 2 binary64) (-.f64 (sqrt.f64 (+.f64 (.f64 re re) (.f64 im im))) re)))) #<representation binary64>) () ())) ())
#s(alt #<batchref> (taylor inf re) (#s(alt #<batchref> (patch (sqrt.f64 (.f64 #s(literal 2 binary64) (-.f64 (sqrt.f64 (+.f64 (.f64 re re) (*.f64 im im))) re))) #<representation binary64>) () ())) ())
#s(alt #<batchref> (taylor inf re) (#s(alt #<batchref> (patch (sqrt.f64 (.f64 #s(literal 2 binary64) (-.f64 (sqrt.f64 (+.f64 (.f64 re re) (*.f64 im im))) re))) #<representation binary64>) () ())) ())
#s(alt #<batchref> (taylor inf re) (#s(alt #<batchref> (patch (sqrt.f64 (.f64 #s(literal 2 binary64) (-.f64 (sqrt.f64 (+.f64 (.f64 re re) (*.f64 im im))) re))) #<representation binary64>) () ())) ())
#s(alt #<batchref> (taylor inf re) (#s(alt #<batchref> (patch (sqrt.f64 (.f64 #s(literal 2 binary64) (-.f64 (sqrt.f64 (+.f64 (.f64 re re) (*.f64 im im))) re))) #<representation binary64>) () ())) ())
#s(alt #<batchref> (taylor inf re) (#s(alt #<batchref> (patch (.f64 #s(literal 2 binary64) (-.f64 (sqrt.f64 (+.f64 (.f64 re re) (*.f64 im im))) re)) #<representation binary64>) () ())) ())
#s(alt #<batchref> (taylor inf re) (#s(alt #<batchref> (patch (.f64 #s(literal 2 binary64) (-.f64 (sqrt.f64 (+.f64 (.f64 re re) (*.f64 im im))) re)) #<representation binary64>) () ())) ())
#s(alt #<batchref> (taylor inf re) (#s(alt #<batchref> (patch (.f64 #s(literal 2 binary64) (-.f64 (sqrt.f64 (+.f64 (.f64 re re) (*.f64 im im))) re)) #<representation binary64>) () ())) ())
#s(alt #<batchref> (taylor inf re) (#s(alt #<batchref> (patch (.f64 #s(literal 2 binary64) (-.f64 (sqrt.f64 (+.f64 (.f64 re re) (*.f64 im im))) re)) #<representation binary64>) () ())) ())
#s(alt #<batchref> (taylor inf re) (#s(alt #<batchref> (patch (sqrt.f64 (+.f64 (.f64 re re) (.f64 im im))) #<representation binary64>) () ())) ())
#s(alt #<batchref> (taylor inf re) (#s(alt #<batchref> (patch (sqrt.f64 (+.f64 (.f64 re re) (.f64 im im))) #<representation binary64>) () ())) ())
#s(alt #<batchref> (taylor inf re) (#s(alt #<batchref> (patch (sqrt.f64 (+.f64 (.f64 re re) (.f64 im im))) #<representation binary64>) () ())) ())
#s(alt #<batchref> (taylor inf re) (#s(alt #<batchref> (patch (sqrt.f64 (+.f64 (.f64 re re) (.f64 im im))) #<representation binary64>) () ())) ())
#s(alt #<batchref> (taylor inf re) (#s(alt #<batchref> (patch (-.f64 (sqrt.f64 (+.f64 (.f64 re re) (.f64 im im))) re) #<representation binary64>) () ())) ())
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#s(alt #<batchref> (taylor -inf im) (#s(alt #<batchref> (patch (.f64 #s(literal 2 binary64) (-.f64 (sqrt.f64 (+.f64 (.f64 re re) (*.f64 im im))) re)) #<representation binary64>) () ())) ())
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#s(alt #<batchref> (taylor -inf im) (#s(alt #<batchref> (patch (sqrt.f64 (+.f64 (.f64 re re) (.f64 im im))) #<representation binary64>) () ())) ())
#s(alt #<batchref> (taylor -inf im) (#s(alt #<batchref> (patch (-.f64 (sqrt.f64 (+.f64 (.f64 re re) (.f64 im im))) re) #<representation binary64>) () ())) ())
#s(alt #<batchref> (taylor -inf im) (#s(alt #<batchref> (patch (-.f64 (sqrt.f64 (+.f64 (.f64 re re) (.f64 im im))) re) #<representation binary64>) () ())) ())
#s(alt #<batchref> (taylor -inf im) (#s(alt #<batchref> (patch (-.f64 (sqrt.f64 (+.f64 (.f64 re re) (.f64 im im))) re) #<representation binary64>) () ())) ())
#s(alt #<batchref> (taylor -inf im) (#s(alt #<batchref> (patch (-.f64 (sqrt.f64 (+.f64 (.f64 re re) (.f64 im im))) re) #<representation binary64>) () ())) ())

Calls

6 calls:

Time	Variable		Point	Expression
314.0ms	im	@	inf	((+ (* re re) (* im im)) (* 1/2 (sqrt (* 2 (- (sqrt (+ (* re re) (* im im))) re)))) (sqrt (* 2 (- (sqrt (+ (* re re) (* im im))) re))) (* 2 (- (sqrt (+ (* re re) (* im im))) re)) (sqrt (+ (* re re) (* im im))) (- (sqrt (+ (* re re) (* im im))) re))
4.0ms	im	@	0	((+ (* re re) (* im im)) (* 1/2 (sqrt (* 2 (- (sqrt (+ (* re re) (* im im))) re)))) (sqrt (* 2 (- (sqrt (+ (* re re) (* im im))) re))) (* 2 (- (sqrt (+ (* re re) (* im im))) re)) (sqrt (+ (* re re) (* im im))) (- (sqrt (+ (* re re) (* im im))) re))
4.0ms	re	@	inf	((+ (* re re) (* im im)) (* 1/2 (sqrt (* 2 (- (sqrt (+ (* re re) (* im im))) re)))) (sqrt (* 2 (- (sqrt (+ (* re re) (* im im))) re))) (* 2 (- (sqrt (+ (* re re) (* im im))) re)) (sqrt (+ (* re re) (* im im))) (- (sqrt (+ (* re re) (* im im))) re))
3.0ms	re	@	-inf	((+ (* re re) (* im im)) (* 1/2 (sqrt (* 2 (- (sqrt (+ (* re re) (* im im))) re)))) (sqrt (* 2 (- (sqrt (+ (* re re) (* im im))) re))) (* 2 (- (sqrt (+ (* re re) (* im im))) re)) (sqrt (+ (* re re) (* im im))) (- (sqrt (+ (* re re) (* im im))) re))
3.0ms	im	@	-inf	((+ (* re re) (* im im)) (* 1/2 (sqrt (* 2 (- (sqrt (+ (* re re) (* im im))) re)))) (sqrt (* 2 (- (sqrt (+ (* re re) (* im im))) re))) (* 2 (- (sqrt (+ (* re re) (* im im))) re)) (sqrt (+ (* re re) (* im im))) (- (sqrt (+ (* re re) (* im im))) re))

simplify181.0ms (2.5%)

Memory

25.3MiB live, 329.8MiB allocated

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	551	3257
1	1814	3103
2	6380	3088
0	8199	2913

Stop Event

1×	iter limit
1×	node limit

Counts

144 → 138

Calls

Call 1

Inputs
(pow im 2)
(+ (pow im 2) (pow re 2))
(+ (pow im 2) (pow re 2))
(+ (pow im 2) (pow re 2))
(* 1/2 (* (sqrt im) (sqrt 2)))
(+ (* -1/4 (* (sqrt (/ 1 im)) (* re (sqrt 2)))) (* 1/2 (* (sqrt im) (sqrt 2))))
(+ (* 1/2 (* (sqrt im) (sqrt 2))) (* re (+ (* -1/4 (* (sqrt (/ 1 im)) (sqrt 2))) (* 1/16 (* (sqrt (/ 1 (pow im 3))) (* re (sqrt 2)))))))
(+ (* 1/2 (* (sqrt im) (sqrt 2))) (* re (+ (* -1/4 (* (sqrt (/ 1 im)) (sqrt 2))) (* re (+ (* 1/32 (* (sqrt (/ 1 (pow im 5))) (* re (sqrt 2)))) (* 1/16 (* (sqrt (/ 1 (pow im 3))) (sqrt 2))))))))
(* (sqrt im) (sqrt 2))
(+ (* -1/2 (* (sqrt (/ 1 im)) (* re (sqrt 2)))) (* (sqrt im) (sqrt 2)))
(+ (* re (+ (* -1/2 (* (sqrt (/ 1 im)) (sqrt 2))) (* 1/8 (* (sqrt (/ 1 (pow im 3))) (* re (sqrt 2)))))) (* (sqrt im) (sqrt 2)))
(+ (* re (+ (* -1/2 (* (sqrt (/ 1 im)) (sqrt 2))) (* re (+ (* 1/16 (* (sqrt (/ 1 (pow im 5))) (* re (sqrt 2)))) (* 1/8 (* (sqrt (/ 1 (pow im 3))) (sqrt 2))))))) (* (sqrt im) (sqrt 2)))
(* 2 im)
(+ (* -2 re) (* 2 im))
(+ (* 2 im) (* re (- (/ re im) 2)))
(+ (* 2 im) (* re (- (* re (+ (* -1/4 (/ (pow re 2) (pow im 3))) (/ 1 im))) 2)))
im
(+ im (* 1/2 (/ (pow re 2) im)))
(+ im (* (pow re 2) (+ (* -1/8 (/ (pow re 2) (pow im 3))) (* 1/2 (/ 1 im)))))
(+ im (* (pow re 2) (+ (* (pow re 2) (- (* 1/16 (/ (pow re 2) (pow im 5))) (* 1/8 (/ 1 (pow im 3))))) (* 1/2 (/ 1 im)))))
im
(+ im (* -1 re))
(+ im (* re (- (* 1/2 (/ re im)) 1)))
(+ im (* re (- (* re (+ (* -1/8 (/ (pow re 2) (pow im 3))) (* 1/2 (/ 1 im)))) 1)))
(pow re 2)
(* (pow re 2) (+ 1 (/ (pow im 2) (pow re 2))))
(* (pow re 2) (+ 1 (/ (pow im 2) (pow re 2))))
(* (pow re 2) (+ 1 (/ (pow im 2) (pow re 2))))
(* 1/2 (* (* im (* (sqrt 1/2) (sqrt 2))) (sqrt (/ 1 re))))
(+ (* -1/32 (* (/ (* (pow im 3) (sqrt 2)) (sqrt 1/2)) (sqrt (/ 1 (pow re 5))))) (* 1/2 (* (* im (* (sqrt 1/2) (sqrt 2))) (sqrt (/ 1 re)))))
(+ (* -1/32 (* (/ (* (pow im 3) (sqrt 2)) (sqrt 1/2)) (sqrt (/ 1 (pow re 5))))) (+ (* 1/64 (* (/ (* (pow im 5) (sqrt 2)) (sqrt 1/2)) (sqrt (/ 1 (pow re 9))))) (* 1/2 (* (* im (* (sqrt 1/2) (sqrt 2))) (sqrt (/ 1 re))))))
(+ (* -1/32 (* (/ (* (pow im 3) (sqrt 2)) (sqrt 1/2)) (sqrt (/ 1 (pow re 5))))) (+ (* -1/1024 (* (/ (* (pow im 5) (sqrt 2)) (pow (sqrt 1/2) 3)) (sqrt (/ 1 (pow re 9))))) (+ (* 1/64 (* (/ (* (pow im 5) (sqrt 2)) (sqrt 1/2)) (sqrt (/ 1 (pow re 9))))) (* 1/2 (* (* im (* (sqrt 1/2) (sqrt 2))) (sqrt (/ 1 re)))))))
(* (* im (* (sqrt 1/2) (sqrt 2))) (sqrt (/ 1 re)))
(+ (* -1/16 (* (/ (* (pow im 3) (sqrt 2)) (sqrt 1/2)) (sqrt (/ 1 (pow re 5))))) (* (* im (* (sqrt 1/2) (sqrt 2))) (sqrt (/ 1 re))))
(+ (* -1/16 (* (/ (* (pow im 3) (sqrt 2)) (sqrt 1/2)) (sqrt (/ 1 (pow re 5))))) (+ (* 1/32 (* (/ (* (pow im 5) (sqrt 2)) (sqrt 1/2)) (sqrt (/ 1 (pow re 9))))) (* (* im (* (sqrt 1/2) (sqrt 2))) (sqrt (/ 1 re)))))
(+ (* -1/16 (* (/ (* (pow im 3) (sqrt 2)) (sqrt 1/2)) (sqrt (/ 1 (pow re 5))))) (+ (* -1/512 (* (/ (* (pow im 5) (sqrt 2)) (pow (sqrt 1/2) 3)) (sqrt (/ 1 (pow re 9))))) (+ (* 1/32 (* (/ (* (pow im 5) (sqrt 2)) (sqrt 1/2)) (sqrt (/ 1 (pow re 9))))) (* (* im (* (sqrt 1/2) (sqrt 2))) (sqrt (/ 1 re))))))
(/ (pow im 2) re)
(/ (+ (* -1/4 (/ (pow im 4) (pow re 2))) (pow im 2)) re)
(/ (+ (* -1/4 (/ (pow im 4) (pow re 2))) (+ (* 1/8 (/ (pow im 6) (pow re 4))) (pow im 2))) re)
(/ (+ (* -1 (/ (+ (* 1/64 (pow im 8)) (* 1/16 (pow im 8))) (pow re 6))) (+ (* -1/4 (/ (pow im 4) (pow re 2))) (+ (* 1/8 (/ (pow im 6) (pow re 4))) (pow im 2)))) re)
re
(* re (+ 1 (* 1/2 (/ (pow im 2) (pow re 2)))))
(* re (+ 1 (+ (* -1/8 (/ (pow im 4) (pow re 4))) (* 1/2 (/ (pow im 2) (pow re 2))))))
(* re (+ 1 (+ (* -1/8 (/ (pow im 4) (pow re 4))) (+ (* 1/16 (/ (pow im 6) (pow re 6))) (* 1/2 (/ (pow im 2) (pow re 2)))))))
(* 1/2 (/ (pow im 2) re))
(/ (+ (* -1/8 (/ (pow im 4) (pow re 2))) (* 1/2 (pow im 2))) re)
(/ (+ (* -1/8 (/ (pow im 4) (pow re 2))) (+ (* 1/16 (/ (pow im 6) (pow re 4))) (* 1/2 (pow im 2)))) re)
(/ (+ (* -1/2 (/ (+ (* 1/64 (pow im 8)) (* 1/16 (pow im 8))) (pow re 6))) (+ (* -1/8 (/ (pow im 4) (pow re 2))) (+ (* 1/16 (/ (pow im 6) (pow re 4))) (* 1/2 (pow im 2))))) re)
(pow re 2)
(* (pow re 2) (+ 1 (/ (pow im 2) (pow re 2))))
(* (pow re 2) (+ 1 (/ (pow im 2) (pow re 2))))
(* (pow re 2) (+ 1 (/ (pow im 2) (pow re 2))))
(* -1/2 (* (sqrt re) (* (sqrt -1) (pow (sqrt 2) 2))))
(* -1 (* re (+ (* -1/8 (* (* (pow im 2) (sqrt -1)) (sqrt (/ 1 (pow re 5))))) (* 1/2 (* (sqrt (/ 1 re)) (* (sqrt -1) (pow (sqrt 2) 2)))))))
(* -1 (* re (+ (* -1 (/ (+ (* -1/32 (* (* (pow im 4) (sqrt -1)) (sqrt (/ 1 (pow re 3))))) (* 1/8 (* (* (pow im 2) (sqrt -1)) (sqrt re)))) (pow re 3))) (* 1/2 (* (sqrt (/ 1 re)) (* (sqrt -1) (pow (sqrt 2) 2)))))))
(* -1 (* re (+ (* -1 (/ (+ (* -1/32 (* (* (pow im 4) (sqrt -1)) (sqrt (/ 1 (pow re 3))))) (+ (* 1/64 (* (/ (* (pow im 4) (sqrt -1)) (pow (sqrt 2) 2)) (sqrt (/ 1 (pow re 3))))) (* 1/8 (* (* (pow im 2) (sqrt -1)) (sqrt re))))) (pow re 3))) (* 1/2 (* (sqrt (/ 1 re)) (* (sqrt -1) (pow (sqrt 2) 2)))))))
(* -1 (* (sqrt re) (* (sqrt -1) (pow (sqrt 2) 2))))
(* -1 (* re (+ (* -1/4 (* (* (pow im 2) (sqrt -1)) (sqrt (/ 1 (pow re 5))))) (* (sqrt (/ 1 re)) (* (sqrt -1) (pow (sqrt 2) 2))))))
(* -1 (* re (+ (* -1 (/ (+ (* -1/16 (* (* (pow im 4) (sqrt -1)) (sqrt (/ 1 (pow re 3))))) (* 1/4 (* (* (pow im 2) (sqrt -1)) (sqrt re)))) (pow re 3))) (* (sqrt (/ 1 re)) (* (sqrt -1) (pow (sqrt 2) 2))))))
(* -1 (* re (+ (* -1 (/ (+ (* -1/16 (* (* (pow im 4) (sqrt -1)) (sqrt (/ 1 (pow re 3))))) (+ (* 1/32 (* (/ (* (pow im 4) (sqrt -1)) (pow (sqrt 2) 2)) (sqrt (/ 1 (pow re 3))))) (* 1/4 (* (* (pow im 2) (sqrt -1)) (sqrt re))))) (pow re 3))) (* (sqrt (/ 1 re)) (* (sqrt -1) (pow (sqrt 2) 2))))))
(* -4 re)
(* -1 (* re (+ 4 (/ (pow im 2) (pow re 2)))))
(* -1 (* re (+ 4 (+ (* -1/4 (/ (pow im 4) (pow re 4))) (/ (pow im 2) (pow re 2))))))
(* -1 (* re (+ 4 (+ (* -1/4 (/ (pow im 4) (pow re 4))) (+ (* 1/8 (/ (pow im 6) (pow re 6))) (/ (pow im 2) (pow re 2)))))))
(* -1 re)
(* -1 (* re (+ 1 (* 1/2 (/ (pow im 2) (pow re 2))))))
(* -1 (* re (+ 1 (+ (* -1/8 (/ (pow im 4) (pow re 4))) (* 1/2 (/ (pow im 2) (pow re 2)))))))
(* -1 (* re (+ 1 (+ (* -1/8 (/ (pow im 4) (pow re 4))) (+ (* 1/16 (/ (pow im 6) (pow re 6))) (* 1/2 (/ (pow im 2) (pow re 2))))))))
(* -2 re)
(* -1 (* re (+ 2 (* 1/2 (/ (pow im 2) (pow re 2))))))
(* -1 (* re (+ 2 (+ (* -1/8 (/ (pow im 4) (pow re 4))) (* 1/2 (/ (pow im 2) (pow re 2)))))))
(* -1 (* re (+ 2 (+ (* -1/8 (/ (pow im 4) (pow re 4))) (+ (* 1/16 (/ (pow im 6) (pow re 6))) (* 1/2 (/ (pow im 2) (pow re 2))))))))
(pow re 2)
(+ (pow im 2) (pow re 2))
(+ (pow im 2) (pow re 2))
(+ (pow im 2) (pow re 2))
(* 1/2 (* (* im (* (sqrt 1/2) (sqrt 2))) (sqrt (/ 1 re))))
(* im (+ (* -1/32 (* (/ (* (pow im 2) (sqrt 2)) (sqrt 1/2)) (sqrt (/ 1 (pow re 5))))) (* 1/2 (* (sqrt (/ 1 re)) (* (sqrt 1/2) (sqrt 2))))))
(* im (+ (* 1/2 (* (sqrt (/ 1 re)) (* (sqrt 1/2) (sqrt 2)))) (* (pow im 2) (+ (* -1/32 (* (sqrt (/ 1 (pow re 5))) (/ (sqrt 2) (sqrt 1/2)))) (* 1/4 (* (/ (* (pow im 2) (* (sqrt 2) (- (* 1/16 (/ 1 (pow re 5))) (* 1/256 (/ 1 (* (pow re 5) (pow (sqrt 1/2) 2))))))) (sqrt 1/2)) (sqrt re)))))))
(* im (+ (* 1/2 (* (sqrt (/ 1 re)) (* (sqrt 1/2) (sqrt 2)))) (* (pow im 2) (+ (* -1/32 (* (sqrt (/ 1 (pow re 5))) (/ (sqrt 2) (sqrt 1/2)))) (* (pow im 2) (+ (* -1/4 (* (/ (* (pow im 2) (* (sqrt 2) (+ (* -1/16 (/ (- (* 1/16 (/ 1 (pow re 5))) (* 1/256 (/ 1 (* (pow re 5) (pow (sqrt 1/2) 2))))) (* (pow re 2) (pow (sqrt 1/2) 2)))) (* 5/128 (/ 1 (pow re 7)))))) (sqrt 1/2)) (sqrt re))) (* 1/4 (* (sqrt re) (/ (* (sqrt 2) (- (* 1/16 (/ 1 (pow re 5))) (* 1/256 (/ 1 (* (pow re 5) (pow (sqrt 1/2) 2)))))) (sqrt 1/2))))))))))
(* (* im (* (sqrt 1/2) (sqrt 2))) (sqrt (/ 1 re)))
(* im (+ (* -1/16 (* (/ (* (pow im 2) (sqrt 2)) (sqrt 1/2)) (sqrt (/ 1 (pow re 5))))) (* (sqrt (/ 1 re)) (* (sqrt 1/2) (sqrt 2)))))
(* im (+ (* (sqrt (/ 1 re)) (* (sqrt 1/2) (sqrt 2))) (* (pow im 2) (+ (* -1/16 (* (sqrt (/ 1 (pow re 5))) (/ (sqrt 2) (sqrt 1/2)))) (* 1/2 (* (/ (* (pow im 2) (* (sqrt 2) (- (* 1/16 (/ 1 (pow re 5))) (* 1/256 (/ 1 (* (pow re 5) (pow (sqrt 1/2) 2))))))) (sqrt 1/2)) (sqrt re)))))))
(* im (+ (* (sqrt (/ 1 re)) (* (sqrt 1/2) (sqrt 2))) (* (pow im 2) (+ (* -1/16 (* (sqrt (/ 1 (pow re 5))) (/ (sqrt 2) (sqrt 1/2)))) (* (pow im 2) (+ (* -1/2 (* (/ (* (pow im 2) (* (sqrt 2) (+ (* -1/16 (/ (- (* 1/16 (/ 1 (pow re 5))) (* 1/256 (/ 1 (* (pow re 5) (pow (sqrt 1/2) 2))))) (* (pow re 2) (pow (sqrt 1/2) 2)))) (* 5/128 (/ 1 (pow re 7)))))) (sqrt 1/2)) (sqrt re))) (* 1/2 (* (sqrt re) (/ (* (sqrt 2) (- (* 1/16 (/ 1 (pow re 5))) (* 1/256 (/ 1 (* (pow re 5) (pow (sqrt 1/2) 2)))))) (sqrt 1/2))))))))))
(/ (pow im 2) re)
(* (pow im 2) (+ (* -1/4 (/ (pow im 2) (pow re 3))) (/ 1 re)))
(* (pow im 2) (+ (* (pow im 2) (- (* 1/8 (/ (pow im 2) (pow re 5))) (* 1/4 (/ 1 (pow re 3))))) (/ 1 re)))
(* (pow im 2) (+ (* (pow im 2) (- (* (pow im 2) (+ (* -5/64 (/ (pow im 2) (pow re 7))) (* 1/8 (/ 1 (pow re 5))))) (* 1/4 (/ 1 (pow re 3))))) (/ 1 re)))
re
(+ re (* 1/2 (/ (pow im 2) re)))
(+ re (* (pow im 2) (+ (* -1/8 (/ (pow im 2) (pow re 3))) (* 1/2 (/ 1 re)))))
(+ re (* (pow im 2) (+ (* (pow im 2) (- (* 1/16 (/ (pow im 2) (pow re 5))) (* 1/8 (/ 1 (pow re 3))))) (* 1/2 (/ 1 re)))))
(* 1/2 (/ (pow im 2) re))
(* (pow im 2) (+ (* -1/8 (/ (pow im 2) (pow re 3))) (* 1/2 (/ 1 re))))
(* (pow im 2) (+ (* (pow im 2) (- (* 1/16 (/ (pow im 2) (pow re 5))) (* 1/8 (/ 1 (pow re 3))))) (* 1/2 (/ 1 re))))
(* (pow im 2) (+ (* (pow im 2) (- (* (pow im 2) (+ (* -5/128 (/ (pow im 2) (pow re 7))) (* 1/16 (/ 1 (pow re 5))))) (* 1/8 (/ 1 (pow re 3))))) (* 1/2 (/ 1 re))))
(pow im 2)
(* (pow im 2) (+ 1 (/ (pow re 2) (pow im 2))))
(* (pow im 2) (+ 1 (/ (pow re 2) (pow im 2))))
(* (pow im 2) (+ 1 (/ (pow re 2) (pow im 2))))
(* 1/2 (* (sqrt im) (sqrt 2)))
(* im (+ (* -1/4 (* (sqrt (/ 1 (pow im 3))) (* re (sqrt 2)))) (* 1/2 (* (sqrt (/ 1 im)) (sqrt 2)))))
(* im (+ (* -1/4 (* (sqrt (/ 1 (pow im 3))) (* re (sqrt 2)))) (+ (* 1/8 (* (sqrt (/ 1 (pow im 5))) (* (pow re 2) (sqrt 2)))) (* 1/2 (* (sqrt (/ 1 im)) (sqrt 2))))))
(* im (+ (* -1/4 (* (sqrt (/ 1 (pow im 3))) (* re (sqrt 2)))) (+ (* -1/16 (* (sqrt (/ 1 (pow im 5))) (* (pow re 2) (sqrt 2)))) (+ (* 1/8 (* (sqrt (/ 1 (pow im 5))) (* (pow re 2) (sqrt 2)))) (* 1/2 (* (sqrt (/ 1 im)) (sqrt 2)))))))
(* (sqrt im) (sqrt 2))
(* im (+ (* -1/2 (* (sqrt (/ 1 (pow im 3))) (* re (sqrt 2)))) (* (sqrt (/ 1 im)) (sqrt 2))))
(* im (+ (* -1/2 (* (sqrt (/ 1 (pow im 3))) (* re (sqrt 2)))) (+ (* 1/4 (* (sqrt (/ 1 (pow im 5))) (* (pow re 2) (sqrt 2)))) (* (sqrt (/ 1 im)) (sqrt 2)))))
(* im (+ (* -1/2 (* (sqrt (/ 1 (pow im 3))) (* re (sqrt 2)))) (+ (* -1/8 (* (sqrt (/ 1 (pow im 5))) (* (pow re 2) (sqrt 2)))) (+ (* 1/4 (* (sqrt (/ 1 (pow im 5))) (* (pow re 2) (sqrt 2)))) (* (sqrt (/ 1 im)) (sqrt 2))))))
(* 2 im)
(* im (+ 2 (* -2 (/ re im))))
(* im (+ 2 (+ (* -2 (/ re im)) (/ (pow re 2) (pow im 2)))))
(* im (+ 2 (+ (* -2 (/ re im)) (+ (* -1/4 (/ (pow re 4) (pow im 4))) (/ (pow re 2) (pow im 2))))))
im
(* im (+ 1 (* 1/2 (/ (pow re 2) (pow im 2)))))
(* im (+ 1 (+ (* -1/8 (/ (pow re 4) (pow im 4))) (* 1/2 (/ (pow re 2) (pow im 2))))))
(* im (+ 1 (+ (* -1/8 (/ (pow re 4) (pow im 4))) (+ (* 1/16 (/ (pow re 6) (pow im 6))) (* 1/2 (/ (pow re 2) (pow im 2)))))))
im
(* im (+ 1 (* -1 (/ re im))))
(* im (- (+ 1 (* 1/2 (/ (pow re 2) (pow im 2)))) (/ re im)))
(* im (- (+ 1 (+ (* -1/8 (/ (pow re 4) (pow im 4))) (* 1/2 (/ (pow re 2) (pow im 2))))) (/ re im)))
(pow im 2)
(* (pow im 2) (+ 1 (/ (pow re 2) (pow im 2))))
(* (pow im 2) (+ 1 (/ (pow re 2) (pow im 2))))
(* (pow im 2) (+ 1 (/ (pow re 2) (pow im 2))))
(* -1/2 (* (sqrt im) (* (sqrt -1) (sqrt 2))))
(* -1 (* im (+ (* -1/4 (* (sqrt (/ 1 (pow im 3))) (* re (* (sqrt -1) (sqrt 2))))) (* 1/2 (* (sqrt (/ 1 im)) (* (sqrt -1) (sqrt 2)))))))
(* -1 (* im (+ (* -1/4 (* (sqrt (/ 1 (pow im 3))) (* re (* (sqrt -1) (sqrt 2))))) (+ (* -1/8 (* (sqrt (/ 1 (pow im 5))) (* (pow re 2) (* (sqrt -1) (sqrt 2))))) (* 1/2 (* (sqrt (/ 1 im)) (* (sqrt -1) (sqrt 2))))))))
(* -1 (* im (+ (* -1 (/ (+ (* 1/16 (* (sqrt im) (* (pow re 2) (* (sqrt -1) (sqrt 2))))) (* 1/8 (* (sqrt im) (* (pow re 2) (* (sqrt -1) (sqrt 2)))))) (pow im 3))) (+ (* -1/4 (* (sqrt (/ 1 (pow im 3))) (* re (* (sqrt -1) (sqrt 2))))) (* 1/2 (* (sqrt (/ 1 im)) (* (sqrt -1) (sqrt 2))))))))
(* -1 (* (sqrt im) (* (sqrt -1) (sqrt 2))))
(* -1 (* im (+ (* -1/2 (* (sqrt (/ 1 (pow im 3))) (* re (* (sqrt -1) (sqrt 2))))) (* (sqrt (/ 1 im)) (* (sqrt -1) (sqrt 2))))))
(* -1 (* im (+ (* -1/2 (* (sqrt (/ 1 (pow im 3))) (* re (* (sqrt -1) (sqrt 2))))) (+ (* -1/4 (* (sqrt (/ 1 (pow im 5))) (* (pow re 2) (* (sqrt -1) (sqrt 2))))) (* (sqrt (/ 1 im)) (* (sqrt -1) (sqrt 2)))))))
(* -1 (* im (+ (* -1 (/ (+ (* 1/8 (* (sqrt im) (* (pow re 2) (* (sqrt -1) (sqrt 2))))) (* 1/4 (* (sqrt im) (* (pow re 2) (* (sqrt -1) (sqrt 2)))))) (pow im 3))) (+ (* -1/2 (* (sqrt (/ 1 (pow im 3))) (* re (* (sqrt -1) (sqrt 2))))) (* (sqrt (/ 1 im)) (* (sqrt -1) (sqrt 2)))))))
(* -2 im)
(* -1 (* im (+ 2 (* 2 (/ re im)))))
(* -1 (* im (+ 2 (* -1 (/ (+ (* -2 re) (* -1 (/ (pow re 2) im))) im)))))
(* -1 (* im (+ 2 (* -1 (/ (+ (* -2 re) (* -1 (/ (+ (* -1/4 (/ (pow re 4) (pow im 2))) (pow re 2)) im))) im)))))
(* -1 im)
(* -1 (* im (+ 1 (* 1/2 (/ (pow re 2) (pow im 2))))))
(* -1 (* im (+ 1 (+ (* -1/8 (/ (pow re 4) (pow im 4))) (* 1/2 (/ (pow re 2) (pow im 2)))))))
(* -1 (* im (+ 1 (+ (* -1/8 (/ (pow re 4) (pow im 4))) (+ (* 1/16 (/ (pow re 6) (pow im 6))) (* 1/2 (/ (pow re 2) (pow im 2))))))))
(* -1 im)
(* -1 (* im (+ 1 (/ re im))))
(* -1 (* im (+ 1 (* -1 (/ (- (* -1/2 (/ (pow re 2) im)) re) im)))))
(* -1 (* im (+ 1 (* -1 (/ (- (* -1 (/ (+ (* -1/8 (/ (pow re 4) (pow im 2))) (* 1/2 (pow re 2))) im)) re) im)))))

Outputs
(*.f64 im im)
(fma.f64 im im (*.f64 re re))
(fma.f64 im im (*.f64 re re))
(fma.f64 im im (*.f64 re re))
(.f64 (.f64 #s(literal 1/2 binary64) (sqrt.f64 #s(literal 2 binary64))) (sqrt.f64 im))
(fma.f64 (.f64 #s(literal -1/4 binary64) (.f64 (sqrt.f64 #s(literal 2 binary64)) re)) (sqrt.f64 (/.f64 #s(literal 1 binary64) im)) (.f64 (.f64 #s(literal 1/2 binary64) (sqrt.f64 #s(literal 2 binary64))) (sqrt.f64 im)))
(fma.f64 (fma.f64 (.f64 #s(literal -1/4 binary64) (sqrt.f64 #s(literal 2 binary64))) (sqrt.f64 (/.f64 #s(literal 1 binary64) im)) (.f64 (.f64 #s(literal 1/16 binary64) (.f64 (sqrt.f64 #s(literal 2 binary64)) re)) (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 im #s(literal 3 binary64)))))) re (.f64 (.f64 #s(literal 1/2 binary64) (sqrt.f64 #s(literal 2 binary64))) (sqrt.f64 im)))
(fma.f64 (fma.f64 (.f64 #s(literal -1/4 binary64) (sqrt.f64 #s(literal 2 binary64))) (sqrt.f64 (/.f64 #s(literal 1 binary64) im)) (.f64 (fma.f64 (.f64 #s(literal 1/32 binary64) (.f64 (sqrt.f64 #s(literal 2 binary64)) re)) (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 im #s(literal 5 binary64)))) (.f64 (.f64 #s(literal 1/16 binary64) (sqrt.f64 #s(literal 2 binary64))) (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 im #s(literal 3 binary64)))))) re)) re (.f64 (.f64 #s(literal 1/2 binary64) (sqrt.f64 #s(literal 2 binary64))) (sqrt.f64 im)))
(*.f64 (sqrt.f64 #s(literal 2 binary64)) (sqrt.f64 im))
(fma.f64 (.f64 #s(literal -1/2 binary64) (.f64 (sqrt.f64 #s(literal 2 binary64)) re)) (sqrt.f64 (/.f64 #s(literal 1 binary64) im)) (*.f64 (sqrt.f64 #s(literal 2 binary64)) (sqrt.f64 im)))
(fma.f64 (fma.f64 (.f64 #s(literal -1/2 binary64) (sqrt.f64 #s(literal 2 binary64))) (sqrt.f64 (/.f64 #s(literal 1 binary64) im)) (.f64 (.f64 #s(literal 1/8 binary64) (.f64 (sqrt.f64 #s(literal 2 binary64)) re)) (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 im #s(literal 3 binary64)))))) re (*.f64 (sqrt.f64 #s(literal 2 binary64)) (sqrt.f64 im)))
(fma.f64 (fma.f64 (.f64 #s(literal -1/2 binary64) (sqrt.f64 #s(literal 2 binary64))) (sqrt.f64 (/.f64 #s(literal 1 binary64) im)) (.f64 (fma.f64 (.f64 #s(literal 1/8 binary64) (sqrt.f64 #s(literal 2 binary64))) (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 im #s(literal 3 binary64)))) (.f64 (.f64 #s(literal 1/16 binary64) (.f64 (sqrt.f64 #s(literal 2 binary64)) re)) (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 im #s(literal 5 binary64)))))) re)) re (*.f64 (sqrt.f64 #s(literal 2 binary64)) (sqrt.f64 im)))
(*.f64 #s(literal 2 binary64) im)
(fma.f64 #s(literal -2 binary64) re (*.f64 #s(literal 2 binary64) im))
(fma.f64 (-.f64 (/.f64 re im) #s(literal 2 binary64)) re (*.f64 #s(literal 2 binary64) im))
(fma.f64 (fma.f64 (fma.f64 (.f64 re (/.f64 re (pow.f64 im #s(literal 3 binary64)))) #s(literal -1/4 binary64) (/.f64 #s(literal 1 binary64) im)) re #s(literal -2 binary64)) re (.f64 #s(literal 2 binary64) im))
im
(fma.f64 (*.f64 (/.f64 #s(literal 1/2 binary64) im) re) re im)
(fma.f64 (fma.f64 #s(literal -1/8 binary64) (.f64 re (/.f64 re (pow.f64 im #s(literal 3 binary64)))) (/.f64 #s(literal 1/2 binary64) im)) (.f64 re re) im)
(fma.f64 (pow.f64 re #s(literal 4 binary64)) (fma.f64 (.f64 re (/.f64 re (pow.f64 im #s(literal 5 binary64)))) #s(literal 1/16 binary64) (/.f64 #s(literal -1/8 binary64) (pow.f64 im #s(literal 3 binary64)))) (fma.f64 (.f64 (/.f64 #s(literal 1/2 binary64) im) re) re im))
im
(-.f64 im re)
(fma.f64 (fma.f64 (/.f64 #s(literal 1/2 binary64) im) re #s(literal -1 binary64)) re im)
(fma.f64 (fma.f64 (fma.f64 #s(literal -1/8 binary64) (*.f64 re (/.f64 re (pow.f64 im #s(literal 3 binary64)))) (/.f64 #s(literal 1/2 binary64) im)) re #s(literal -1 binary64)) re im)
(*.f64 re re)
(.f64 (fma.f64 (/.f64 im re) (/.f64 im re) #s(literal 1 binary64)) (.f64 re re))
(.f64 (fma.f64 (/.f64 im re) (/.f64 im re) #s(literal 1 binary64)) (.f64 re re))
(.f64 (fma.f64 (/.f64 im re) (/.f64 im re) #s(literal 1 binary64)) (.f64 re re))
(.f64 (.f64 (.f64 #s(literal 1/2 binary64) (.f64 im (sqrt.f64 #s(literal 1/2 binary64)))) (sqrt.f64 #s(literal 2 binary64))) (sqrt.f64 (/.f64 #s(literal 1 binary64) re)))
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(.f64 (fma.f64 (.f64 #s(literal -1/4 binary64) (.f64 (sqrt.f64 #s(literal 2 binary64)) re)) (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 im #s(literal 3 binary64)))) (.f64 (*.f64 #s(literal 1/2 binary64) (sqrt.f64 #s(literal 2 binary64))) (sqrt.f64 (/.f64 #s(literal 1 binary64) im)))) im)
(.f64 (fma.f64 (.f64 #s(literal -1/4 binary64) (.f64 (sqrt.f64 #s(literal 2 binary64)) re)) (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 im #s(literal 3 binary64)))) (fma.f64 (.f64 #s(literal 1/8 binary64) (.f64 (.f64 (sqrt.f64 #s(literal 2 binary64)) re) re)) (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 im #s(literal 5 binary64)))) (.f64 (.f64 #s(literal 1/2 binary64) (sqrt.f64 #s(literal 2 binary64))) (sqrt.f64 (/.f64 #s(literal 1 binary64) im))))) im)
(.f64 (fma.f64 (.f64 #s(literal -1/4 binary64) (.f64 (sqrt.f64 #s(literal 2 binary64)) re)) (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 im #s(literal 3 binary64)))) (fma.f64 (.f64 (.f64 (.f64 (sqrt.f64 #s(literal 2 binary64)) re) re) (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 im #s(literal 5 binary64))))) #s(literal 1/16 binary64) (.f64 (.f64 #s(literal 1/2 binary64) (sqrt.f64 #s(literal 2 binary64))) (sqrt.f64 (/.f64 #s(literal 1 binary64) im))))) im)
(*.f64 (sqrt.f64 #s(literal 2 binary64)) (sqrt.f64 im))
(.f64 (fma.f64 (.f64 #s(literal -1/2 binary64) (.f64 (sqrt.f64 #s(literal 2 binary64)) re)) (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 im #s(literal 3 binary64)))) (.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) im)) (sqrt.f64 #s(literal 2 binary64)))) im)
(.f64 (fma.f64 (.f64 #s(literal -1/2 binary64) (.f64 (sqrt.f64 #s(literal 2 binary64)) re)) (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 im #s(literal 3 binary64)))) (fma.f64 (.f64 #s(literal 1/4 binary64) (.f64 (.f64 (sqrt.f64 #s(literal 2 binary64)) re) re)) (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 im #s(literal 5 binary64)))) (*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) im)) (sqrt.f64 #s(literal 2 binary64))))) im)
(.f64 (fma.f64 (.f64 #s(literal -1/2 binary64) (.f64 (sqrt.f64 #s(literal 2 binary64)) re)) (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 im #s(literal 3 binary64)))) (fma.f64 (.f64 #s(literal 1/8 binary64) (.f64 (.f64 (sqrt.f64 #s(literal 2 binary64)) re) re)) (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 im #s(literal 5 binary64)))) (*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) im)) (sqrt.f64 #s(literal 2 binary64))))) im)
(*.f64 #s(literal 2 binary64) im)
(*.f64 (fma.f64 (/.f64 re im) #s(literal -2 binary64) #s(literal 2 binary64)) im)
(*.f64 (fma.f64 (/.f64 re im) (/.f64 re im) (fma.f64 (/.f64 re im) #s(literal -2 binary64) #s(literal 2 binary64))) im)
(.f64 (+.f64 (fma.f64 (/.f64 (pow.f64 re #s(literal 4 binary64)) (pow.f64 im #s(literal 4 binary64))) #s(literal -1/4 binary64) (/.f64 (.f64 re (/.f64 re im)) im)) (fma.f64 (/.f64 re im) #s(literal -2 binary64) #s(literal 2 binary64))) im)
im
(.f64 (fma.f64 (/.f64 (.f64 re (/.f64 re im)) im) #s(literal 1/2 binary64) #s(literal 1 binary64)) im)
(.f64 (fma.f64 (/.f64 (pow.f64 re #s(literal 4 binary64)) (pow.f64 im #s(literal 4 binary64))) #s(literal -1/8 binary64) (fma.f64 (/.f64 (.f64 re (/.f64 re im)) im) #s(literal 1/2 binary64) #s(literal 1 binary64))) im)
(fma.f64 (fma.f64 (/.f64 (pow.f64 re #s(literal 6 binary64)) (pow.f64 im #s(literal 6 binary64))) #s(literal 1/16 binary64) (fma.f64 (.f64 (/.f64 #s(literal 1/2 binary64) im) re) (/.f64 re im) (/.f64 (.f64 (pow.f64 re #s(literal 4 binary64)) #s(literal -1/8 binary64)) (pow.f64 im #s(literal 4 binary64))))) im im)
im
(*.f64 (-.f64 #s(literal 1 binary64) (/.f64 re im)) im)
(.f64 (fma.f64 (/.f64 (.f64 re (/.f64 re im)) im) #s(literal 1/2 binary64) (-.f64 #s(literal 1 binary64) (/.f64 re im))) im)
(.f64 (-.f64 (fma.f64 (/.f64 (pow.f64 re #s(literal 4 binary64)) (pow.f64 im #s(literal 4 binary64))) #s(literal -1/8 binary64) (fma.f64 (/.f64 (.f64 re (/.f64 re im)) im) #s(literal 1/2 binary64) #s(literal 1 binary64))) (/.f64 re im)) im)
(*.f64 im im)
(.f64 (.f64 (fma.f64 (/.f64 re im) (/.f64 re im) #s(literal 1 binary64)) im) im)
(.f64 (.f64 (fma.f64 (/.f64 re im) (/.f64 re im) #s(literal 1 binary64)) im) im)
(.f64 (.f64 (fma.f64 (/.f64 re im) (/.f64 re im) #s(literal 1 binary64)) im) im)
(.f64 (.f64 #s(literal -1/2 binary64) (sqrt.f64 im)) (*.f64 (sqrt.f64 #s(literal -1 binary64)) (sqrt.f64 #s(literal 2 binary64))))
(.f64 (neg.f64 im) (fma.f64 (.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) im)) (sqrt.f64 #s(literal -1 binary64))) (.f64 (sqrt.f64 #s(literal 2 binary64)) #s(literal 1/2 binary64)) (.f64 (.f64 (.f64 re (sqrt.f64 #s(literal -1 binary64))) (*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 im #s(literal 3 binary64)))) (sqrt.f64 #s(literal 2 binary64)))) #s(literal -1/4 binary64))))
(.f64 (neg.f64 im) (fma.f64 (.f64 (.f64 (.f64 (.f64 (sqrt.f64 #s(literal 2 binary64)) re) re) (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 im #s(literal 5 binary64))))) (sqrt.f64 #s(literal -1 binary64))) #s(literal -1/8 binary64) (fma.f64 (.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) im)) (sqrt.f64 #s(literal -1 binary64))) (.f64 (sqrt.f64 #s(literal 2 binary64)) #s(literal 1/2 binary64)) (.f64 (.f64 (.f64 re (sqrt.f64 #s(literal -1 binary64))) (*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 im #s(literal 3 binary64)))) (sqrt.f64 #s(literal 2 binary64)))) #s(literal -1/4 binary64)))))
(.f64 (neg.f64 im) (-.f64 (fma.f64 (.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) im)) (sqrt.f64 #s(literal -1 binary64))) (.f64 (sqrt.f64 #s(literal 2 binary64)) #s(literal 1/2 binary64)) (.f64 (.f64 (.f64 re (sqrt.f64 #s(literal -1 binary64))) (.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 im #s(literal 3 binary64)))) (sqrt.f64 #s(literal 2 binary64)))) #s(literal -1/4 binary64))) (.f64 (.f64 (.f64 re (.f64 re (sqrt.f64 #s(literal -1 binary64)))) (.f64 (sqrt.f64 #s(literal 2 binary64)) (sqrt.f64 im))) (/.f64 #s(literal 3/16 binary64) (pow.f64 im #s(literal 3 binary64))))))
(.f64 (neg.f64 (sqrt.f64 #s(literal -1 binary64))) (.f64 (sqrt.f64 #s(literal 2 binary64)) (sqrt.f64 im)))
(.f64 (neg.f64 im) (fma.f64 (.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) im)) (sqrt.f64 #s(literal -1 binary64))) (sqrt.f64 #s(literal 2 binary64)) (.f64 (.f64 (.f64 re (sqrt.f64 #s(literal -1 binary64))) (.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 im #s(literal 3 binary64)))) (sqrt.f64 #s(literal 2 binary64)))) #s(literal -1/2 binary64))))
(.f64 (neg.f64 im) (fma.f64 (.f64 (.f64 (.f64 (.f64 (sqrt.f64 #s(literal 2 binary64)) re) re) (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 im #s(literal 5 binary64))))) (sqrt.f64 #s(literal -1 binary64))) #s(literal -1/4 binary64) (fma.f64 (.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) im)) (sqrt.f64 #s(literal -1 binary64))) (sqrt.f64 #s(literal 2 binary64)) (.f64 (.f64 (.f64 re (sqrt.f64 #s(literal -1 binary64))) (.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 im #s(literal 3 binary64)))) (sqrt.f64 #s(literal 2 binary64)))) #s(literal -1/2 binary64)))))
(.f64 (neg.f64 im) (-.f64 (fma.f64 (.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) im)) (sqrt.f64 #s(literal -1 binary64))) (sqrt.f64 #s(literal 2 binary64)) (.f64 (.f64 (.f64 re (sqrt.f64 #s(literal -1 binary64))) (.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 im #s(literal 3 binary64)))) (sqrt.f64 #s(literal 2 binary64)))) #s(literal -1/2 binary64))) (.f64 (.f64 (.f64 re (.f64 re (sqrt.f64 #s(literal -1 binary64)))) (*.f64 (sqrt.f64 #s(literal 2 binary64)) (sqrt.f64 im))) (/.f64 #s(literal 3/8 binary64) (pow.f64 im #s(literal 3 binary64))))))
(*.f64 #s(literal -2 binary64) im)
(*.f64 (neg.f64 im) (fma.f64 (/.f64 re im) #s(literal 2 binary64) #s(literal 2 binary64)))
(.f64 (neg.f64 im) (-.f64 #s(literal 2 binary64) (/.f64 (fma.f64 (neg.f64 re) (/.f64 re im) (.f64 #s(literal -2 binary64) re)) im)))
(.f64 (neg.f64 im) (-.f64 #s(literal 2 binary64) (/.f64 (fma.f64 #s(literal -2 binary64) re (/.f64 (fma.f64 (/.f64 #s(literal -1/4 binary64) im) (/.f64 (pow.f64 re #s(literal 4 binary64)) im) (.f64 re re)) (neg.f64 im))) im)))
(neg.f64 im)
(.f64 (neg.f64 im) (fma.f64 (/.f64 (.f64 re (/.f64 re im)) im) #s(literal 1/2 binary64) #s(literal 1 binary64)))
(.f64 (neg.f64 im) (fma.f64 (/.f64 (pow.f64 re #s(literal 4 binary64)) (pow.f64 im #s(literal 4 binary64))) #s(literal -1/8 binary64) (fma.f64 (/.f64 (.f64 re (/.f64 re im)) im) #s(literal 1/2 binary64) #s(literal 1 binary64))))
(neg.f64 (fma.f64 (fma.f64 (/.f64 (pow.f64 re #s(literal 6 binary64)) (pow.f64 im #s(literal 6 binary64))) #s(literal 1/16 binary64) (fma.f64 (.f64 (/.f64 #s(literal 1/2 binary64) im) re) (/.f64 re im) (/.f64 (.f64 (pow.f64 re #s(literal 4 binary64)) #s(literal -1/8 binary64)) (pow.f64 im #s(literal 4 binary64))))) im im))
(neg.f64 im)
(neg.f64 (fma.f64 (/.f64 re im) im im))
(fma.f64 (/.f64 (-.f64 (.f64 (.f64 re (/.f64 re im)) #s(literal -1/2 binary64)) re) im) im (neg.f64 im))
(neg.f64 (fma.f64 (/.f64 (+.f64 (/.f64 (fma.f64 (/.f64 (pow.f64 re #s(literal 4 binary64)) im) (/.f64 #s(literal -1/8 binary64) im) (.f64 #s(literal 1/2 binary64) (.f64 re re))) im) re) im) im im))

rewrite179.0ms (2.5%)

Memory

12.0MiB live, 275.1MiB allocated

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	12	65
0	20	65
1	56	65
2	374	65
3	4192	65
0	8391	38

Stop Event

1×	iter limit
1×	node limit
1×	iter limit

Counts

6 → 292

Calls

Call 1

Inputs
(+.f64 (.f64 re re) (.f64 im im))
(.f64 #s(literal 1/2 binary64) (sqrt.f64 (.f64 #s(literal 2 binary64) (-.f64 (sqrt.f64 (+.f64 (.f64 re re) (.f64 im im))) re))))
(sqrt.f64 (.f64 #s(literal 2 binary64) (-.f64 (sqrt.f64 (+.f64 (.f64 re re) (*.f64 im im))) re)))
(.f64 #s(literal 2 binary64) (-.f64 (sqrt.f64 (+.f64 (.f64 re re) (*.f64 im im))) re))
(sqrt.f64 (+.f64 (.f64 re re) (.f64 im im)))
(-.f64 (sqrt.f64 (+.f64 (.f64 re re) (.f64 im im))) re)

Outputs
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eval102.0ms (1.4%)

Memory: -20.1MiB live, 169.6MiB allocated
Compiler: Compiled 12 655 to 2 498 computations (80.3% saved)

prune25.0ms (0.4%)

Memory

-23.6MiB live, 60.6MiB allocated

Pruning

16 alts after pruning (16 fresh and 0 done)

	Pruned	Kept	Total
New	414	16	430
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	415	16	431

Accuracy

99.5%

Counts

431 → 16

Alt Table

Click to see full alt table

Status	Accuracy	Program
	79.8%	(.f64 (.f64 (sqrt.f64 (-.f64 (hypot.f64 im re) re)) #s(literal 1/2 binary64)) (sqrt.f64 #s(literal 2 binary64)))
▶	79.9%	(.f64 (sqrt.f64 (.f64 (-.f64 (hypot.f64 im re) re) #s(literal 2 binary64))) #s(literal 1/2 binary64))
	76.6%	(.f64 #s(literal 1/2 binary64) (sqrt.f64 (.f64 #s(literal 2 binary64) (fma.f64 (sqrt.f64 (hypot.f64 im re)) (sqrt.f64 (hypot.f64 im re)) (neg.f64 re)))))
	37.6%	(.f64 #s(literal 1/2 binary64) (sqrt.f64 (.f64 #s(literal 2 binary64) (-.f64 (sqrt.f64 (fma.f64 re re (*.f64 im im))) re))))
	29.9%	(.f64 #s(literal 1/2 binary64) (sqrt.f64 (.f64 #s(literal 2 binary64) (-.f64 (sqrt.f64 #s(approx (+ (* re re) (* im im)) (.f64 (.f64 (fma.f64 (/.f64 re im) (/.f64 re im) #s(literal 1 binary64)) im) im))) re))))
	53.6%	(.f64 #s(literal 1/2 binary64) (sqrt.f64 (.f64 #s(literal 2 binary64) #s(approx (- (sqrt (+ (* re re) (* im im))) re) (-.f64 im re)))))
	51.1%	(.f64 #s(literal 1/2 binary64) (sqrt.f64 #s(approx ( 2 (- (sqrt (+ (* re re) (* im im))) re)) (fma.f64 (-.f64 (/.f64 re im) #s(literal 2 binary64)) re (*.f64 #s(literal 2 binary64) im)))))
▶	12.9%	(.f64 #s(literal 1/2 binary64) (sqrt.f64 #s(approx ( 2 (- (sqrt (+ (* re re) (* im im))) re)) (/.f64 (*.f64 im im) re))))
	52.5%	(.f64 #s(literal 1/2 binary64) (sqrt.f64 #s(approx ( 2 (- (sqrt (+ (* re re) (* im im))) re)) (*.f64 (fma.f64 (/.f64 re im) #s(literal -2 binary64) #s(literal 2 binary64)) im))))
▶	12.4%	(.f64 #s(literal 1/2 binary64) (sqrt.f64 #s(approx ( 2 (- (sqrt (+ (* re re) (* im im))) re)) (.f64 (fma.f64 (.f64 im (/.f64 im (pow.f64 re #s(literal 3 binary64)))) #s(literal -1/4 binary64) (/.f64 #s(literal 1 binary64) re)) (*.f64 im im)))))
	51.0%	(.f64 #s(literal 1/2 binary64) (sqrt.f64 #s(approx ( 2 (- (sqrt (+ (* re re) (* im im))) re)) (*.f64 #s(literal 2 binary64) im))))
▶	28.1%	(.f64 #s(literal 1/2 binary64) (sqrt.f64 #s(approx ( 2 (- (sqrt (+ (* re re) (* im im))) re)) (*.f64 #s(literal -4 binary64) re))))
	17.5%	(.f64 #s(literal 1/2 binary64) #s(approx (sqrt ( 2 (- (sqrt (+ (* re re) (* im im))) re))) (.f64 (fma.f64 (.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) re)) (sqrt.f64 #s(literal 2 binary64))) (sqrt.f64 #s(literal 1/2 binary64)) (.f64 (.f64 (.f64 #s(literal -1/16 binary64) (.f64 im im)) (/.f64 (sqrt.f64 #s(literal 2 binary64)) (sqrt.f64 #s(literal 1/2 binary64)))) (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 re #s(literal 5 binary64)))))) im)))
	24.5%	(.f64 #s(literal 1/2 binary64) #s(approx (sqrt ( 2 (- (sqrt (+ (* re re) (* im im))) re))) (.f64 (.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) re)) (*.f64 im (sqrt.f64 #s(literal 1/2 binary64)))) (sqrt.f64 #s(literal 2 binary64)))))
	51.0%	(.f64 #s(literal 1/2 binary64) #s(approx (sqrt ( 2 (- (sqrt (+ (* re re) (* im im))) re))) (*.f64 (sqrt.f64 #s(literal 2 binary64)) (sqrt.f64 im))))
▶	24.5%	#s(approx (* 1/2 (sqrt (* 2 (- (sqrt (+ (* re re) (* im im))) re)))) (.f64 (.f64 (.f64 #s(literal 1/2 binary64) (.f64 im (sqrt.f64 #s(literal 1/2 binary64)))) (sqrt.f64 #s(literal 2 binary64))) (sqrt.f64 (/.f64 #s(literal 1 binary64) re))))

Compiler

Compiled 728 to 544 computations (25.3% saved)

simplify115.0ms (1.6%)

Memory

20.2MiB live, 136.5MiB allocated

Algorithm

1×	egg-herbie

Localize:

Found 20 expressions of interest:

New	Metric	Score
cost-diff	0	#s(approx (* 2 (- (sqrt (+ (* re re) (* im im))) re)) (.f64 (fma.f64 (.f64 im (/.f64 im (pow.f64 re #s(literal 3 binary64)))) #s(literal -1/4 binary64) (/.f64 #s(literal 1 binary64) re)) (*.f64 im im)))
cost-diff	0	(sqrt.f64 #s(approx (* 2 (- (sqrt (+ (* re re) (* im im))) re)) (.f64 (fma.f64 (.f64 im (/.f64 im (pow.f64 re #s(literal 3 binary64)))) #s(literal -1/4 binary64) (/.f64 #s(literal 1 binary64) re)) (*.f64 im im))))
cost-diff	0	(.f64 #s(literal 1/2 binary64) (sqrt.f64 #s(approx ( 2 (- (sqrt (+ (* re re) (* im im))) re)) (.f64 (fma.f64 (.f64 im (/.f64 im (pow.f64 re #s(literal 3 binary64)))) #s(literal -1/4 binary64) (/.f64 #s(literal 1 binary64) re)) (*.f64 im im)))))
cost-diff	640	(.f64 (fma.f64 (.f64 im (/.f64 im (pow.f64 re #s(literal 3 binary64)))) #s(literal -1/4 binary64) (/.f64 #s(literal 1 binary64) re)) (*.f64 im im))
cost-diff	0	(.f64 #s(literal 1/2 binary64) (.f64 im (sqrt.f64 #s(literal 1/2 binary64))))
cost-diff	0	(.f64 (.f64 #s(literal 1/2 binary64) (*.f64 im (sqrt.f64 #s(literal 1/2 binary64)))) (sqrt.f64 #s(literal 2 binary64)))
cost-diff	0	(.f64 (.f64 (.f64 #s(literal 1/2 binary64) (.f64 im (sqrt.f64 #s(literal 1/2 binary64)))) (sqrt.f64 #s(literal 2 binary64))) (sqrt.f64 (/.f64 #s(literal 1 binary64) re)))
cost-diff	0	#s(approx (* 1/2 (sqrt (* 2 (- (sqrt (+ (* re re) (* im im))) re)))) (.f64 (.f64 (.f64 #s(literal 1/2 binary64) (.f64 im (sqrt.f64 #s(literal 1/2 binary64)))) (sqrt.f64 #s(literal 2 binary64))) (sqrt.f64 (/.f64 #s(literal 1 binary64) re))))
cost-diff	0	(/.f64 (*.f64 im im) re)
cost-diff	0	#s(approx (* 2 (- (sqrt (+ (* re re) (* im im))) re)) (/.f64 (*.f64 im im) re))
cost-diff	0	(sqrt.f64 #s(approx (* 2 (- (sqrt (+ (* re re) (* im im))) re)) (/.f64 (*.f64 im im) re)))
cost-diff	0	(.f64 #s(literal 1/2 binary64) (sqrt.f64 #s(approx ( 2 (- (sqrt (+ (* re re) (* im im))) re)) (/.f64 (*.f64 im im) re))))
cost-diff	0	(*.f64 #s(literal -4 binary64) re)
cost-diff	0	#s(approx (* 2 (- (sqrt (+ (* re re) (* im im))) re)) (*.f64 #s(literal -4 binary64) re))
cost-diff	0	(sqrt.f64 #s(approx (* 2 (- (sqrt (+ (* re re) (* im im))) re)) (*.f64 #s(literal -4 binary64) re)))
cost-diff	0	(.f64 #s(literal 1/2 binary64) (sqrt.f64 #s(approx ( 2 (- (sqrt (+ (* re re) (* im im))) re)) (*.f64 #s(literal -4 binary64) re))))
cost-diff	0	(-.f64 (hypot.f64 im re) re)
cost-diff	0	(*.f64 (-.f64 (hypot.f64 im re) re) #s(literal 2 binary64))
cost-diff	0	(sqrt.f64 (*.f64 (-.f64 (hypot.f64 im re) re) #s(literal 2 binary64)))
cost-diff	0	(.f64 (sqrt.f64 (.f64 (-.f64 (hypot.f64 im re) re) #s(literal 2 binary64))) #s(literal 1/2 binary64))

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	47	389
0	76	339
1	113	339
2	193	339
3	460	339
4	944	335
5	1442	327
6	1634	327
7	1774	327
8	1881	327
9	2011	327
10	3886	327
11	6579	327
12	7538	327
13	7969	327
0	8087	323

Stop Event

1×	iter limit
1×	node limit
1×	iter limit

Calls

Call 1

Inputs
(.f64 (sqrt.f64 (.f64 (-.f64 (hypot.f64 im re) re) #s(literal 2 binary64))) #s(literal 1/2 binary64))
(sqrt.f64 (*.f64 (-.f64 (hypot.f64 im re) re) #s(literal 2 binary64)))
(*.f64 (-.f64 (hypot.f64 im re) re) #s(literal 2 binary64))
(-.f64 (hypot.f64 im re) re)
(hypot.f64 im re)
im
re
#s(literal 2 binary64)
#s(literal 1/2 binary64)
(.f64 #s(literal 1/2 binary64) (sqrt.f64 #s(approx ( 2 (- (sqrt (+ (* re re) (* im im))) re)) (*.f64 #s(literal -4 binary64) re))))
#s(literal 1/2 binary64)
(sqrt.f64 #s(approx (* 2 (- (sqrt (+ (* re re) (* im im))) re)) (*.f64 #s(literal -4 binary64) re)))
#s(approx (* 2 (- (sqrt (+ (* re re) (* im im))) re)) (*.f64 #s(literal -4 binary64) re))
(*.f64 #s(literal -4 binary64) re)
#s(literal -4 binary64)
re
(.f64 #s(literal 1/2 binary64) (sqrt.f64 #s(approx ( 2 (- (sqrt (+ (* re re) (* im im))) re)) (/.f64 (*.f64 im im) re))))
#s(literal 1/2 binary64)
(sqrt.f64 #s(approx (* 2 (- (sqrt (+ (* re re) (* im im))) re)) (/.f64 (*.f64 im im) re)))
#s(approx (* 2 (- (sqrt (+ (* re re) (* im im))) re)) (/.f64 (*.f64 im im) re))
(/.f64 (*.f64 im im) re)
(*.f64 im im)
im
re
#s(approx (* 1/2 (sqrt (* 2 (- (sqrt (+ (* re re) (* im im))) re)))) (.f64 (.f64 (.f64 #s(literal 1/2 binary64) (.f64 im (sqrt.f64 #s(literal 1/2 binary64)))) (sqrt.f64 #s(literal 2 binary64))) (sqrt.f64 (/.f64 #s(literal 1 binary64) re))))
(.f64 (.f64 (.f64 #s(literal 1/2 binary64) (.f64 im (sqrt.f64 #s(literal 1/2 binary64)))) (sqrt.f64 #s(literal 2 binary64))) (sqrt.f64 (/.f64 #s(literal 1 binary64) re)))
(.f64 (.f64 #s(literal 1/2 binary64) (*.f64 im (sqrt.f64 #s(literal 1/2 binary64)))) (sqrt.f64 #s(literal 2 binary64)))
(.f64 #s(literal 1/2 binary64) (.f64 im (sqrt.f64 #s(literal 1/2 binary64))))
#s(literal 1/2 binary64)
(*.f64 im (sqrt.f64 #s(literal 1/2 binary64)))
im
(sqrt.f64 #s(literal 1/2 binary64))
(sqrt.f64 #s(literal 2 binary64))
#s(literal 2 binary64)
(sqrt.f64 (/.f64 #s(literal 1 binary64) re))
(/.f64 #s(literal 1 binary64) re)
#s(literal 1 binary64)
re
(.f64 #s(literal 1/2 binary64) (sqrt.f64 #s(approx ( 2 (- (sqrt (+ (* re re) (* im im))) re)) (.f64 (fma.f64 (.f64 im (/.f64 im (pow.f64 re #s(literal 3 binary64)))) #s(literal -1/4 binary64) (/.f64 #s(literal 1 binary64) re)) (*.f64 im im)))))
#s(literal 1/2 binary64)
(sqrt.f64 #s(approx (* 2 (- (sqrt (+ (* re re) (* im im))) re)) (.f64 (fma.f64 (.f64 im (/.f64 im (pow.f64 re #s(literal 3 binary64)))) #s(literal -1/4 binary64) (/.f64 #s(literal 1 binary64) re)) (*.f64 im im))))
#s(approx (* 2 (- (sqrt (+ (* re re) (* im im))) re)) (.f64 (fma.f64 (.f64 im (/.f64 im (pow.f64 re #s(literal 3 binary64)))) #s(literal -1/4 binary64) (/.f64 #s(literal 1 binary64) re)) (*.f64 im im)))
(.f64 (fma.f64 (.f64 im (/.f64 im (pow.f64 re #s(literal 3 binary64)))) #s(literal -1/4 binary64) (/.f64 #s(literal 1 binary64) re)) (*.f64 im im))
(fma.f64 (*.f64 im (/.f64 im (pow.f64 re #s(literal 3 binary64)))) #s(literal -1/4 binary64) (/.f64 #s(literal 1 binary64) re))
(*.f64 im (/.f64 im (pow.f64 re #s(literal 3 binary64))))
im
(/.f64 im (pow.f64 re #s(literal 3 binary64)))
(pow.f64 re #s(literal 3 binary64))
re
#s(literal 3 binary64)
#s(literal -1/4 binary64)
(/.f64 #s(literal 1 binary64) re)
#s(literal 1 binary64)
(*.f64 im im)

Outputs
(.f64 #s(literal 1/2 binary64) (sqrt.f64 (.f64 #s(literal 2 binary64) (-.f64 (hypot.f64 re im) re))))
(sqrt.f64 (*.f64 #s(literal 2 binary64) (-.f64 (hypot.f64 re im) re)))
(*.f64 #s(literal 2 binary64) (-.f64 (hypot.f64 re im) re))
(-.f64 (hypot.f64 re im) re)
(hypot.f64 re im)
im
re
#s(literal 2 binary64)
#s(literal 1/2 binary64)
(.f64 (sqrt.f64 #s(approx ( 2 (- (sqrt (+ (* re re) (* im im))) re)) (*.f64 #s(literal -4 binary64) re))) #s(literal 1/2 binary64))
#s(literal 1/2 binary64)
(sqrt.f64 #s(approx (* 2 (- (sqrt (+ (* re re) (* im im))) re)) (*.f64 #s(literal -4 binary64) re)))
#s(approx (* 2 (- (sqrt (+ (* re re) (* im im))) re)) (*.f64 #s(literal -4 binary64) re))
(*.f64 #s(literal -4 binary64) re)
#s(literal -4 binary64)
re
(.f64 (sqrt.f64 #s(approx ( 2 (- (sqrt (+ (* re re) (* im im))) re)) (/.f64 (*.f64 im im) re))) #s(literal 1/2 binary64))
#s(literal 1/2 binary64)
(sqrt.f64 #s(approx (* 2 (- (sqrt (+ (* re re) (* im im))) re)) (/.f64 (*.f64 im im) re)))
#s(approx (* 2 (- (sqrt (+ (* re re) (* im im))) re)) (/.f64 (*.f64 im im) re))
(/.f64 (*.f64 im im) re)
(*.f64 im im)
im
re
#s(approx (* 1/2 (sqrt (* 2 (- (sqrt (+ (* re re) (* im im))) re)))) (.f64 (.f64 (.f64 (.f64 (sqrt.f64 #s(literal 1/2 binary64)) #s(literal 1/2 binary64)) (sqrt.f64 (/.f64 #s(literal 1 binary64) re))) (sqrt.f64 #s(literal 2 binary64))) im))
(.f64 (.f64 (.f64 (.f64 (sqrt.f64 #s(literal 1/2 binary64)) #s(literal 1/2 binary64)) (sqrt.f64 (/.f64 #s(literal 1 binary64) re))) (sqrt.f64 #s(literal 2 binary64))) im)
(.f64 (.f64 (sqrt.f64 #s(literal 2 binary64)) im) (*.f64 (sqrt.f64 #s(literal 1/2 binary64)) #s(literal 1/2 binary64)))
(.f64 (.f64 (sqrt.f64 #s(literal 1/2 binary64)) im) #s(literal 1/2 binary64))
#s(literal 1/2 binary64)
(*.f64 (sqrt.f64 #s(literal 1/2 binary64)) im)
im
(sqrt.f64 #s(literal 1/2 binary64))
(sqrt.f64 #s(literal 2 binary64))
#s(literal 2 binary64)
(sqrt.f64 (/.f64 #s(literal 1 binary64) re))
(/.f64 #s(literal 1 binary64) re)
#s(literal 1 binary64)
re
(.f64 (sqrt.f64 #s(approx ( 2 (- (sqrt (+ (* re re) (* im im))) re)) (*.f64 (fma.f64 (pow.f64 (/.f64 im re) #s(literal 3 binary64)) #s(literal -1/4 binary64) (/.f64 im re)) im))) #s(literal 1/2 binary64))
#s(literal 1/2 binary64)
(sqrt.f64 #s(approx (* 2 (- (sqrt (+ (* re re) (* im im))) re)) (*.f64 (fma.f64 (pow.f64 (/.f64 im re) #s(literal 3 binary64)) #s(literal -1/4 binary64) (/.f64 im re)) im)))
#s(approx (* 2 (- (sqrt (+ (* re re) (* im im))) re)) (*.f64 (fma.f64 (pow.f64 (/.f64 im re) #s(literal 3 binary64)) #s(literal -1/4 binary64) (/.f64 im re)) im))
(*.f64 (fma.f64 (pow.f64 (/.f64 im re) #s(literal 3 binary64)) #s(literal -1/4 binary64) (/.f64 im re)) im)
(fma.f64 #s(literal -1/4 binary64) (*.f64 (/.f64 im (pow.f64 re #s(literal 3 binary64))) im) (/.f64 #s(literal 1 binary64) re))
(*.f64 (/.f64 im (pow.f64 re #s(literal 3 binary64))) im)
im
(/.f64 im (pow.f64 re #s(literal 3 binary64)))
(pow.f64 re #s(literal 3 binary64))
re
#s(literal 3 binary64)
#s(literal -1/4 binary64)
(/.f64 #s(literal 1 binary64) re)
#s(literal 1 binary64)
(*.f64 im im)

localize142.0ms (2%)

Memory

17.6MiB live, 236.5MiB allocated

Localize:

Found 20 expressions of interest:

New	Metric	Score
accuracy	4.803403315353946	(*.f64 im (/.f64 im (pow.f64 re #s(literal 3 binary64))))
accuracy	5.117546358106111	(sqrt.f64 #s(approx (* 2 (- (sqrt (+ (* re re) (* im im))) re)) (.f64 (fma.f64 (.f64 im (/.f64 im (pow.f64 re #s(literal 3 binary64)))) #s(literal -1/4 binary64) (/.f64 #s(literal 1 binary64) re)) (*.f64 im im))))
accuracy	5.898638472431402	(.f64 (fma.f64 (.f64 im (/.f64 im (pow.f64 re #s(literal 3 binary64)))) #s(literal -1/4 binary64) (/.f64 #s(literal 1 binary64) re)) (*.f64 im im))
accuracy	15.598117263001392	#s(approx (* 2 (- (sqrt (+ (* re re) (* im im))) re)) (.f64 (fma.f64 (.f64 im (/.f64 im (pow.f64 re #s(literal 3 binary64)))) #s(literal -1/4 binary64) (/.f64 #s(literal 1 binary64) re)) (*.f64 im im)))
accuracy	0.10546875	(sqrt.f64 (/.f64 #s(literal 1 binary64) re))
accuracy	0.2109375	(.f64 (.f64 #s(literal 1/2 binary64) (*.f64 im (sqrt.f64 #s(literal 1/2 binary64)))) (sqrt.f64 #s(literal 2 binary64)))
accuracy	0.21875	(*.f64 im (sqrt.f64 #s(literal 1/2 binary64)))
accuracy	14.625769161491963	#s(approx (* 1/2 (sqrt (* 2 (- (sqrt (+ (* re re) (* im im))) re)))) (.f64 (.f64 (.f64 #s(literal 1/2 binary64) (.f64 im (sqrt.f64 #s(literal 1/2 binary64)))) (sqrt.f64 #s(literal 2 binary64))) (sqrt.f64 (/.f64 #s(literal 1 binary64) re))))
accuracy	0.00390625	(.f64 #s(literal 1/2 binary64) (sqrt.f64 #s(approx ( 2 (- (sqrt (+ (* re re) (* im im))) re)) (/.f64 (*.f64 im im) re))))
accuracy	5.117546358106111	(sqrt.f64 #s(approx (* 2 (- (sqrt (+ (* re re) (* im im))) re)) (/.f64 (*.f64 im im) re)))
accuracy	5.390296731295094	(/.f64 (*.f64 im im) re)
accuracy	14.422315063784257	#s(approx (* 2 (- (sqrt (+ (* re re) (* im im))) re)) (/.f64 (*.f64 im im) re))
accuracy	0	(*.f64 #s(literal -4 binary64) re)
accuracy	0.00390625	(.f64 #s(literal 1/2 binary64) (sqrt.f64 #s(approx ( 2 (- (sqrt (+ (* re re) (* im im))) re)) (*.f64 #s(literal -4 binary64) re))))
accuracy	5.117546358106111	(sqrt.f64 #s(approx (* 2 (- (sqrt (+ (* re re) (* im im))) re)) (*.f64 #s(literal -4 binary64) re)))
accuracy	29.843329810632497	#s(approx (* 2 (- (sqrt (+ (* re re) (* im im))) re)) (*.f64 #s(literal -4 binary64) re))
accuracy	0	(*.f64 (-.f64 (hypot.f64 im re) re) #s(literal 2 binary64))
accuracy	0.00390625	(.f64 (sqrt.f64 (.f64 (-.f64 (hypot.f64 im re) re) #s(literal 2 binary64))) #s(literal 1/2 binary64))
accuracy	5.117546358106111	(sqrt.f64 (*.f64 (-.f64 (hypot.f64 im re) re) #s(literal 2 binary64)))
accuracy	7.3651219703664905	(-.f64 (hypot.f64 im re) re)

Samples

48.0ms	134×	0	invalid
19.0ms	63×	0	valid
15.0ms	24×	2	valid
10.0ms	23×	1	valid
10.0ms	12×	3	valid

Compiler

Compiled 711 to 86 computations (87.9% saved)

Precisions

Click to see histograms. Total time spent on operations: 76.0ms

ival-mult: 20.0ms (26.3% of total)

ival-div: 15.0ms (19.7% of total)

ival-hypot: 13.0ms (17.1% of total)

ival-sqrt: 12.0ms (15.8% of total)

ival-sub: 6.0ms (7.9% of total)

ival-pow: 4.0ms (5.3% of total)

adjust: 3.0ms (3.9% of total)

ival-add: 1.0ms (1.3% of total)

exact: 1.0ms (1.3% of total)

ival-assert: 0.0ms (0% of total)

ival-true: 0.0ms (0% of total)

series78.0ms (1.1%)

Memory

4.2MiB live, 137.0MiB allocated

Counts

23 → 492

Calls

Call 1

Inputs
#s(alt #<batchref> (patch (.f64 (sqrt.f64 (.f64 (-.f64 (hypot.f64 im re) re) #s(literal 2 binary64))) #s(literal 1/2 binary64)) #<representation binary64>) () ())
#s(alt #<batchref> (patch (sqrt.f64 (*.f64 (-.f64 (hypot.f64 im re) re) #s(literal 2 binary64))) #<representation binary64>) () ())
#s(alt #<batchref> (patch (*.f64 (-.f64 (hypot.f64 im re) re) #s(literal 2 binary64)) #<representation binary64>) () ())
#s(alt #<batchref> (patch (-.f64 (hypot.f64 im re) re) #<representation binary64>) () ())
#s(alt #<batchref> (patch (.f64 #s(literal 1/2 binary64) (sqrt.f64 #s(approx ( 2 (- (sqrt (+ (* re re) (* im im))) re)) (*.f64 #s(literal -4 binary64) re)))) #<representation binary64>) () ())
#s(alt #<batchref> (patch (sqrt.f64 #s(approx (* 2 (- (sqrt (+ (* re re) (* im im))) re)) (*.f64 #s(literal -4 binary64) re))) #<representation binary64>) () ())
#s(alt #<batchref> (patch #s(approx (* 2 (- (sqrt (+ (* re re) (* im im))) re)) (*.f64 #s(literal -4 binary64) re)) #<representation binary64>) () ())
#s(alt #<batchref> (patch (*.f64 #s(literal -4 binary64) re) #<representation binary64>) () ())
#s(alt #<batchref> (patch (.f64 #s(literal 1/2 binary64) (sqrt.f64 #s(approx ( 2 (- (sqrt (+ (* re re) (* im im))) re)) (/.f64 (*.f64 im im) re)))) #<representation binary64>) () ())
#s(alt #<batchref> (patch (sqrt.f64 #s(approx (* 2 (- (sqrt (+ (* re re) (* im im))) re)) (/.f64 (*.f64 im im) re))) #<representation binary64>) () ())
#s(alt #<batchref> (patch #s(approx (* 2 (- (sqrt (+ (* re re) (* im im))) re)) (/.f64 (*.f64 im im) re)) #<representation binary64>) () ())
#s(alt #<batchref> (patch (/.f64 (*.f64 im im) re) #<representation binary64>) () ())
#s(alt #<batchref> (patch #s(approx (* 1/2 (sqrt (* 2 (- (sqrt (+ (* re re) (* im im))) re)))) (.f64 (.f64 (.f64 #s(literal 1/2 binary64) (.f64 im (sqrt.f64 #s(literal 1/2 binary64)))) (sqrt.f64 #s(literal 2 binary64))) (sqrt.f64 (/.f64 #s(literal 1 binary64) re)))) #<representation binary64>) () ())
#s(alt #<batchref> (patch (.f64 (.f64 (.f64 #s(literal 1/2 binary64) (.f64 im (sqrt.f64 #s(literal 1/2 binary64)))) (sqrt.f64 #s(literal 2 binary64))) (sqrt.f64 (/.f64 #s(literal 1 binary64) re))) #<representation binary64>) () ())
#s(alt #<batchref> (patch (.f64 (.f64 #s(literal 1/2 binary64) (*.f64 im (sqrt.f64 #s(literal 1/2 binary64)))) (sqrt.f64 #s(literal 2 binary64))) #<representation binary64>) () ())
#s(alt #<batchref> (patch (.f64 #s(literal 1/2 binary64) (.f64 im (sqrt.f64 #s(literal 1/2 binary64)))) #<representation binary64>) () ())
#s(alt #<batchref> (patch (.f64 (fma.f64 (.f64 im (/.f64 im (pow.f64 re #s(literal 3 binary64)))) #s(literal -1/4 binary64) (/.f64 #s(literal 1 binary64) re)) (*.f64 im im)) #<representation binary64>) () ())
#s(alt #<batchref> (patch (.f64 #s(literal 1/2 binary64) (sqrt.f64 #s(approx ( 2 (- (sqrt (+ (* re re) (* im im))) re)) (.f64 (fma.f64 (.f64 im (/.f64 im (pow.f64 re #s(literal 3 binary64)))) #s(literal -1/4 binary64) (/.f64 #s(literal 1 binary64) re)) (*.f64 im im))))) #<representation binary64>) () ())
#s(alt #<batchref> (patch (sqrt.f64 #s(approx (* 2 (- (sqrt (+ (* re re) (* im im))) re)) (.f64 (fma.f64 (.f64 im (/.f64 im (pow.f64 re #s(literal 3 binary64)))) #s(literal -1/4 binary64) (/.f64 #s(literal 1 binary64) re)) (*.f64 im im)))) #<representation binary64>) () ())
#s(alt #<batchref> (patch #s(approx (* 2 (- (sqrt (+ (* re re) (* im im))) re)) (.f64 (fma.f64 (.f64 im (/.f64 im (pow.f64 re #s(literal 3 binary64)))) #s(literal -1/4 binary64) (/.f64 #s(literal 1 binary64) re)) (*.f64 im im))) #<representation binary64>) () ())
#s(alt #<batchref> (patch (*.f64 im (sqrt.f64 #s(literal 1/2 binary64))) #<representation binary64>) () ())
#s(alt #<batchref> (patch (sqrt.f64 (/.f64 #s(literal 1 binary64) re)) #<representation binary64>) () ())
#s(alt #<batchref> (patch (*.f64 im (/.f64 im (pow.f64 re #s(literal 3 binary64)))) #<representation binary64>) () ())

Outputs
#s(alt #<batchref> (taylor 0 re) (#s(alt #<batchref> (patch (.f64 (sqrt.f64 (.f64 (-.f64 (hypot.f64 im re) re) #s(literal 2 binary64))) #s(literal 1/2 binary64)) #<representation binary64>) () ())) ())
#s(alt #<batchref> (taylor 0 re) (#s(alt #<batchref> (patch (.f64 (sqrt.f64 (.f64 (-.f64 (hypot.f64 im re) re) #s(literal 2 binary64))) #s(literal 1/2 binary64)) #<representation binary64>) () ())) ())
#s(alt #<batchref> (taylor 0 re) (#s(alt #<batchref> (patch (.f64 (sqrt.f64 (.f64 (-.f64 (hypot.f64 im re) re) #s(literal 2 binary64))) #s(literal 1/2 binary64)) #<representation binary64>) () ())) ())
#s(alt #<batchref> (taylor 0 re) (#s(alt #<batchref> (patch (.f64 (sqrt.f64 (.f64 (-.f64 (hypot.f64 im re) re) #s(literal 2 binary64))) #s(literal 1/2 binary64)) #<representation binary64>) () ())) ())
#s(alt #<batchref> (taylor 0 re) (#s(alt #<batchref> (patch (sqrt.f64 (*.f64 (-.f64 (hypot.f64 im re) re) #s(literal 2 binary64))) #<representation binary64>) () ())) ())
#s(alt #<batchref> (taylor 0 re) (#s(alt #<batchref> (patch (sqrt.f64 (*.f64 (-.f64 (hypot.f64 im re) re) #s(literal 2 binary64))) #<representation binary64>) () ())) ())
#s(alt #<batchref> (taylor 0 re) (#s(alt #<batchref> (patch (sqrt.f64 (*.f64 (-.f64 (hypot.f64 im re) re) #s(literal 2 binary64))) #<representation binary64>) () ())) ())
#s(alt #<batchref> (taylor 0 re) (#s(alt #<batchref> (patch (sqrt.f64 (*.f64 (-.f64 (hypot.f64 im re) re) #s(literal 2 binary64))) #<representation binary64>) () ())) ())
#s(alt #<batchref> (taylor 0 re) (#s(alt #<batchref> (patch (*.f64 (-.f64 (hypot.f64 im re) re) #s(literal 2 binary64)) #<representation binary64>) () ())) ())
#s(alt #<batchref> (taylor 0 re) (#s(alt #<batchref> (patch (*.f64 (-.f64 (hypot.f64 im re) re) #s(literal 2 binary64)) #<representation binary64>) () ())) ())
#s(alt #<batchref> (taylor 0 re) (#s(alt #<batchref> (patch (*.f64 (-.f64 (hypot.f64 im re) re) #s(literal 2 binary64)) #<representation binary64>) () ())) ())
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#s(alt #<batchref> (taylor -inf im) (#s(alt #<batchref> (patch (sqrt.f64 #s(approx (* 2 (- (sqrt (+ (* re re) (* im im))) re)) (.f64 (fma.f64 (.f64 im (/.f64 im (pow.f64 re #s(literal 3 binary64)))) #s(literal -1/4 binary64) (/.f64 #s(literal 1 binary64) re)) (*.f64 im im)))) #<representation binary64>) () ())) ())
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#s(alt #<batchref> (taylor -inf im) (#s(alt #<batchref> (patch (*.f64 im (sqrt.f64 #s(literal 1/2 binary64))) #<representation binary64>) () ())) ())
#s(alt #<batchref> (taylor -inf im) (#s(alt #<batchref> (patch (*.f64 im (sqrt.f64 #s(literal 1/2 binary64))) #<representation binary64>) () ())) ())
#s(alt #<batchref> (taylor -inf im) (#s(alt #<batchref> (patch (*.f64 im (/.f64 im (pow.f64 re #s(literal 3 binary64)))) #<representation binary64>) () ())) ())
#s(alt #<batchref> (taylor -inf im) (#s(alt #<batchref> (patch (*.f64 im (/.f64 im (pow.f64 re #s(literal 3 binary64)))) #<representation binary64>) () ())) ())
#s(alt #<batchref> (taylor -inf im) (#s(alt #<batchref> (patch (*.f64 im (/.f64 im (pow.f64 re #s(literal 3 binary64)))) #<representation binary64>) () ())) ())
#s(alt #<batchref> (taylor -inf im) (#s(alt #<batchref> (patch (*.f64 im (/.f64 im (pow.f64 re #s(literal 3 binary64)))) #<representation binary64>) () ())) ())

Calls

6 calls:

Time	Variable		Point	Expression
29.0ms	im	@	-inf	((* (sqrt (* (- (sqrt (+ (* im im) (* re re))) re) 2)) 1/2) (sqrt (* (- (sqrt (+ (* im im) (* re re))) re) 2)) (* (- (sqrt (+ (* im im) (* re re))) re) 2) (- (sqrt (+ (* im im) (* re re))) re) (* 1/2 (sqrt (* 2 (- (sqrt (+ (* re re) (* im im))) re)))) (sqrt (* 2 (- (sqrt (+ (* re re) (* im im))) re))) (* 2 (- (sqrt (+ (* re re) (* im im))) re)) (* -4 re) (* 1/2 (sqrt (* 2 (- (sqrt (+ (* re re) (* im im))) re)))) (sqrt (* 2 (- (sqrt (+ (* re re) (* im im))) re))) (* 2 (- (sqrt (+ (* re re) (* im im))) re)) (/ (* im im) re) (* 1/2 (sqrt (* 2 (- (sqrt (+ (* re re) (* im im))) re)))) (* (* (* 1/2 (* im (sqrt 1/2))) (sqrt 2)) (sqrt (/ 1 re))) (* (* 1/2 (* im (sqrt 1/2))) (sqrt 2)) (* 1/2 (* im (sqrt 1/2))) (* (+ (* (* im (/ im (pow re 3))) -1/4) (/ 1 re)) (* im im)) (* 1/2 (sqrt (* 2 (- (sqrt (+ (* re re) (* im im))) re)))) (sqrt (* 2 (- (sqrt (+ (* re re) (* im im))) re))) (* 2 (- (sqrt (+ (* re re) (* im im))) re)) (* im (sqrt 1/2)) (sqrt (/ 1 re)) (* im (/ im (pow re 3))))
9.0ms	re	@	-inf	((* (sqrt (* (- (sqrt (+ (* im im) (* re re))) re) 2)) 1/2) (sqrt (* (- (sqrt (+ (* im im) (* re re))) re) 2)) (* (- (sqrt (+ (* im im) (* re re))) re) 2) (- (sqrt (+ (* im im) (* re re))) re) (* 1/2 (sqrt (* 2 (- (sqrt (+ (* re re) (* im im))) re)))) (sqrt (* 2 (- (sqrt (+ (* re re) (* im im))) re))) (* 2 (- (sqrt (+ (* re re) (* im im))) re)) (* -4 re) (* 1/2 (sqrt (* 2 (- (sqrt (+ (* re re) (* im im))) re)))) (sqrt (* 2 (- (sqrt (+ (* re re) (* im im))) re))) (* 2 (- (sqrt (+ (* re re) (* im im))) re)) (/ (* im im) re) (* 1/2 (sqrt (* 2 (- (sqrt (+ (* re re) (* im im))) re)))) (* (* (* 1/2 (* im (sqrt 1/2))) (sqrt 2)) (sqrt (/ 1 re))) (* (* 1/2 (* im (sqrt 1/2))) (sqrt 2)) (* 1/2 (* im (sqrt 1/2))) (* (+ (* (* im (/ im (pow re 3))) -1/4) (/ 1 re)) (* im im)) (* 1/2 (sqrt (* 2 (- (sqrt (+ (* re re) (* im im))) re)))) (sqrt (* 2 (- (sqrt (+ (* re re) (* im im))) re))) (* 2 (- (sqrt (+ (* re re) (* im im))) re)) (* im (sqrt 1/2)) (sqrt (/ 1 re)) (* im (/ im (pow re 3))))
5.0ms	im	@	0	((* (sqrt (* (- (sqrt (+ (* im im) (* re re))) re) 2)) 1/2) (sqrt (* (- (sqrt (+ (* im im) (* re re))) re) 2)) (* (- (sqrt (+ (* im im) (* re re))) re) 2) (- (sqrt (+ (* im im) (* re re))) re) (* 1/2 (sqrt (* 2 (- (sqrt (+ (* re re) (* im im))) re)))) (sqrt (* 2 (- (sqrt (+ (* re re) (* im im))) re))) (* 2 (- (sqrt (+ (* re re) (* im im))) re)) (* -4 re) (* 1/2 (sqrt (* 2 (- (sqrt (+ (* re re) (* im im))) re)))) (sqrt (* 2 (- (sqrt (+ (* re re) (* im im))) re))) (* 2 (- (sqrt (+ (* re re) (* im im))) re)) (/ (* im im) re) (* 1/2 (sqrt (* 2 (- (sqrt (+ (* re re) (* im im))) re)))) (* (* (* 1/2 (* im (sqrt 1/2))) (sqrt 2)) (sqrt (/ 1 re))) (* (* 1/2 (* im (sqrt 1/2))) (sqrt 2)) (* 1/2 (* im (sqrt 1/2))) (* (+ (* (* im (/ im (pow re 3))) -1/4) (/ 1 re)) (* im im)) (* 1/2 (sqrt (* 2 (- (sqrt (+ (* re re) (* im im))) re)))) (sqrt (* 2 (- (sqrt (+ (* re re) (* im im))) re))) (* 2 (- (sqrt (+ (* re re) (* im im))) re)) (* im (sqrt 1/2)) (sqrt (/ 1 re)) (* im (/ im (pow re 3))))
4.0ms	im	@	inf	((* (sqrt (* (- (sqrt (+ (* im im) (* re re))) re) 2)) 1/2) (sqrt (* (- (sqrt (+ (* im im) (* re re))) re) 2)) (* (- (sqrt (+ (* im im) (* re re))) re) 2) (- (sqrt (+ (* im im) (* re re))) re) (* 1/2 (sqrt (* 2 (- (sqrt (+ (* re re) (* im im))) re)))) (sqrt (* 2 (- (sqrt (+ (* re re) (* im im))) re))) (* 2 (- (sqrt (+ (* re re) (* im im))) re)) (* -4 re) (* 1/2 (sqrt (* 2 (- (sqrt (+ (* re re) (* im im))) re)))) (sqrt (* 2 (- (sqrt (+ (* re re) (* im im))) re))) (* 2 (- (sqrt (+ (* re re) (* im im))) re)) (/ (* im im) re) (* 1/2 (sqrt (* 2 (- (sqrt (+ (* re re) (* im im))) re)))) (* (* (* 1/2 (* im (sqrt 1/2))) (sqrt 2)) (sqrt (/ 1 re))) (* (* 1/2 (* im (sqrt 1/2))) (sqrt 2)) (* 1/2 (* im (sqrt 1/2))) (* (+ (* (* im (/ im (pow re 3))) -1/4) (/ 1 re)) (* im im)) (* 1/2 (sqrt (* 2 (- (sqrt (+ (* re re) (* im im))) re)))) (sqrt (* 2 (- (sqrt (+ (* re re) (* im im))) re))) (* 2 (- (sqrt (+ (* re re) (* im im))) re)) (* im (sqrt 1/2)) (sqrt (/ 1 re)) (* im (/ im (pow re 3))))
4.0ms	re	@	0	((* (sqrt (* (- (sqrt (+ (* im im) (* re re))) re) 2)) 1/2) (sqrt (* (- (sqrt (+ (* im im) (* re re))) re) 2)) (* (- (sqrt (+ (* im im) (* re re))) re) 2) (- (sqrt (+ (* im im) (* re re))) re) (* 1/2 (sqrt (* 2 (- (sqrt (+ (* re re) (* im im))) re)))) (sqrt (* 2 (- (sqrt (+ (* re re) (* im im))) re))) (* 2 (- (sqrt (+ (* re re) (* im im))) re)) (* -4 re) (* 1/2 (sqrt (* 2 (- (sqrt (+ (* re re) (* im im))) re)))) (sqrt (* 2 (- (sqrt (+ (* re re) (* im im))) re))) (* 2 (- (sqrt (+ (* re re) (* im im))) re)) (/ (* im im) re) (* 1/2 (sqrt (* 2 (- (sqrt (+ (* re re) (* im im))) re)))) (* (* (* 1/2 (* im (sqrt 1/2))) (sqrt 2)) (sqrt (/ 1 re))) (* (* 1/2 (* im (sqrt 1/2))) (sqrt 2)) (* 1/2 (* im (sqrt 1/2))) (* (+ (* (* im (/ im (pow re 3))) -1/4) (/ 1 re)) (* im im)) (* 1/2 (sqrt (* 2 (- (sqrt (+ (* re re) (* im im))) re)))) (sqrt (* 2 (- (sqrt (+ (* re re) (* im im))) re))) (* 2 (- (sqrt (+ (* re re) (* im im))) re)) (* im (sqrt 1/2)) (sqrt (/ 1 re)) (* im (/ im (pow re 3))))

simplify236.0ms (3.3%)

Memory

-12.2MiB live, 266.5MiB allocated

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	535	11617
1	1729	10906
2	6280	10833
0	8162	10390

Stop Event

1×	iter limit
1×	node limit

Counts

492 → 490

Calls

Call 1

Inputs
(* 1/2 (* (sqrt im) (sqrt 2)))
(+ (* -1/4 (* (sqrt (/ 1 im)) (* re (sqrt 2)))) (* 1/2 (* (sqrt im) (sqrt 2))))
(+ (* 1/2 (* (sqrt im) (sqrt 2))) (* re (+ (* -1/4 (* (sqrt (/ 1 im)) (sqrt 2))) (* 1/16 (* (sqrt (/ 1 (pow im 3))) (* re (sqrt 2)))))))
(+ (* 1/2 (* (sqrt im) (sqrt 2))) (* re (+ (* -1/4 (* (sqrt (/ 1 im)) (sqrt 2))) (* re (+ (* 1/32 (* (sqrt (/ 1 (pow im 5))) (* re (sqrt 2)))) (* 1/16 (* (sqrt (/ 1 (pow im 3))) (sqrt 2))))))))
(* (sqrt im) (sqrt 2))
(+ (* -1/2 (* (sqrt (/ 1 im)) (* re (sqrt 2)))) (* (sqrt im) (sqrt 2)))
(+ (* re (+ (* -1/2 (* (sqrt (/ 1 im)) (sqrt 2))) (* 1/8 (* (sqrt (/ 1 (pow im 3))) (* re (sqrt 2)))))) (* (sqrt im) (sqrt 2)))
(+ (* re (+ (* -1/2 (* (sqrt (/ 1 im)) (sqrt 2))) (* re (+ (* 1/16 (* (sqrt (/ 1 (pow im 5))) (* re (sqrt 2)))) (* 1/8 (* (sqrt (/ 1 (pow im 3))) (sqrt 2))))))) (* (sqrt im) (sqrt 2)))
(* 2 im)
(+ (* -2 re) (* 2 im))
(+ (* 2 im) (* re (- (/ re im) 2)))
(+ (* 2 im) (* re (- (* re (+ (* -1/4 (/ (pow re 2) (pow im 3))) (/ 1 im))) 2)))
im
(+ im (* -1 re))
(+ im (* re (- (* 1/2 (/ re im)) 1)))
(+ im (* re (- (* re (+ (* -1/8 (/ (pow re 2) (pow im 3))) (* 1/2 (/ 1 im)))) 1)))
(* 1/2 (* (sqrt im) (sqrt 2)))
(+ (* -1/4 (* (sqrt (/ 1 im)) (* re (sqrt 2)))) (* 1/2 (* (sqrt im) (sqrt 2))))
(+ (* 1/2 (* (sqrt im) (sqrt 2))) (* re (+ (* -1/4 (* (sqrt (/ 1 im)) (sqrt 2))) (* 1/16 (* (sqrt (/ 1 (pow im 3))) (* re (sqrt 2)))))))
(+ (* 1/2 (* (sqrt im) (sqrt 2))) (* re (+ (* -1/4 (* (sqrt (/ 1 im)) (sqrt 2))) (* re (+ (* 1/32 (* (sqrt (/ 1 (pow im 5))) (* re (sqrt 2)))) (* 1/16 (* (sqrt (/ 1 (pow im 3))) (sqrt 2))))))))
(* (sqrt im) (sqrt 2))
(+ (* -1/2 (* (sqrt (/ 1 im)) (* re (sqrt 2)))) (* (sqrt im) (sqrt 2)))
(+ (* re (+ (* -1/2 (* (sqrt (/ 1 im)) (sqrt 2))) (* 1/8 (* (sqrt (/ 1 (pow im 3))) (* re (sqrt 2)))))) (* (sqrt im) (sqrt 2)))
(+ (* re (+ (* -1/2 (* (sqrt (/ 1 im)) (sqrt 2))) (* re (+ (* 1/16 (* (sqrt (/ 1 (pow im 5))) (* re (sqrt 2)))) (* 1/8 (* (sqrt (/ 1 (pow im 3))) (sqrt 2))))))) (* (sqrt im) (sqrt 2)))
(* 2 im)
(+ (* -2 re) (* 2 im))
(+ (* 2 im) (* re (- (/ re im) 2)))
(+ (* 2 im) (* re (- (* re (+ (* -1/4 (/ (pow re 2) (pow im 3))) (/ 1 im))) 2)))
(* -4 re)
(* -4 re)
(* -4 re)
(* -4 re)
(* 1/2 (* (sqrt im) (sqrt 2)))
(+ (* -1/4 (* (sqrt (/ 1 im)) (* re (sqrt 2)))) (* 1/2 (* (sqrt im) (sqrt 2))))
(+ (* 1/2 (* (sqrt im) (sqrt 2))) (* re (+ (* -1/4 (* (sqrt (/ 1 im)) (sqrt 2))) (* 1/16 (* (sqrt (/ 1 (pow im 3))) (* re (sqrt 2)))))))
(+ (* 1/2 (* (sqrt im) (sqrt 2))) (* re (+ (* -1/4 (* (sqrt (/ 1 im)) (sqrt 2))) (* re (+ (* 1/32 (* (sqrt (/ 1 (pow im 5))) (* re (sqrt 2)))) (* 1/16 (* (sqrt (/ 1 (pow im 3))) (sqrt 2))))))))
(* (sqrt im) (sqrt 2))
(+ (* -1/2 (* (sqrt (/ 1 im)) (* re (sqrt 2)))) (* (sqrt im) (sqrt 2)))
(+ (* re (+ (* -1/2 (* (sqrt (/ 1 im)) (sqrt 2))) (* 1/8 (* (sqrt (/ 1 (pow im 3))) (* re (sqrt 2)))))) (* (sqrt im) (sqrt 2)))
(+ (* re (+ (* -1/2 (* (sqrt (/ 1 im)) (sqrt 2))) (* re (+ (* 1/16 (* (sqrt (/ 1 (pow im 5))) (* re (sqrt 2)))) (* 1/8 (* (sqrt (/ 1 (pow im 3))) (sqrt 2))))))) (* (sqrt im) (sqrt 2)))
(* 2 im)
(+ (* -2 re) (* 2 im))
(+ (* 2 im) (* re (- (/ re im) 2)))
(+ (* 2 im) (* re (- (* re (+ (* -1/4 (/ (pow re 2) (pow im 3))) (/ 1 im))) 2)))
(/ (pow im 2) re)
(/ (pow im 2) re)
(/ (pow im 2) re)
(/ (pow im 2) re)
(* 1/2 (* (sqrt im) (sqrt 2)))
(+ (* -1/4 (* (sqrt (/ 1 im)) (* re (sqrt 2)))) (* 1/2 (* (sqrt im) (sqrt 2))))
(+ (* 1/2 (* (sqrt im) (sqrt 2))) (* re (+ (* -1/4 (* (sqrt (/ 1 im)) (sqrt 2))) (* 1/16 (* (sqrt (/ 1 (pow im 3))) (* re (sqrt 2)))))))
(+ (* 1/2 (* (sqrt im) (sqrt 2))) (* re (+ (* -1/4 (* (sqrt (/ 1 im)) (sqrt 2))) (* re (+ (* 1/32 (* (sqrt (/ 1 (pow im 5))) (* re (sqrt 2)))) (* 1/16 (* (sqrt (/ 1 (pow im 3))) (sqrt 2))))))))
(* 1/2 (* (* im (* (sqrt 1/2) (sqrt 2))) (sqrt (/ 1 re))))
(* 1/2 (* (* im (* (sqrt 1/2) (sqrt 2))) (sqrt (/ 1 re))))
(* 1/2 (* (* im (* (sqrt 1/2) (sqrt 2))) (sqrt (/ 1 re))))
(* 1/2 (* (* im (* (sqrt 1/2) (sqrt 2))) (sqrt (/ 1 re))))
(* -1/4 (/ (pow im 4) (pow re 3)))
(/ (+ (* -1/4 (pow im 4)) (* (pow im 2) (pow re 2))) (pow re 3))
(/ (+ (* -1/4 (pow im 4)) (* (pow im 2) (pow re 2))) (pow re 3))
(/ (+ (* -1/4 (pow im 4)) (* (pow im 2) (pow re 2))) (pow re 3))
(* 1/2 (* (sqrt im) (sqrt 2)))
(+ (* -1/4 (* (sqrt (/ 1 im)) (* re (sqrt 2)))) (* 1/2 (* (sqrt im) (sqrt 2))))
(+ (* 1/2 (* (sqrt im) (sqrt 2))) (* re (+ (* -1/4 (* (sqrt (/ 1 im)) (sqrt 2))) (* 1/16 (* (sqrt (/ 1 (pow im 3))) (* re (sqrt 2)))))))
(+ (* 1/2 (* (sqrt im) (sqrt 2))) (* re (+ (* -1/4 (* (sqrt (/ 1 im)) (sqrt 2))) (* re (+ (* 1/32 (* (sqrt (/ 1 (pow im 5))) (* re (sqrt 2)))) (* 1/16 (* (sqrt (/ 1 (pow im 3))) (sqrt 2))))))))
(* (sqrt im) (sqrt 2))
(+ (* -1/2 (* (sqrt (/ 1 im)) (* re (sqrt 2)))) (* (sqrt im) (sqrt 2)))
(+ (* re (+ (* -1/2 (* (sqrt (/ 1 im)) (sqrt 2))) (* 1/8 (* (sqrt (/ 1 (pow im 3))) (* re (sqrt 2)))))) (* (sqrt im) (sqrt 2)))
(+ (* re (+ (* -1/2 (* (sqrt (/ 1 im)) (sqrt 2))) (* re (+ (* 1/16 (* (sqrt (/ 1 (pow im 5))) (* re (sqrt 2)))) (* 1/8 (* (sqrt (/ 1 (pow im 3))) (sqrt 2))))))) (* (sqrt im) (sqrt 2)))
(* 2 im)
(+ (* -2 re) (* 2 im))
(+ (* 2 im) (* re (- (/ re im) 2)))
(+ (* 2 im) (* re (- (* re (+ (* -1/4 (/ (pow re 2) (pow im 3))) (/ 1 im))) 2)))
(sqrt (/ 1 re))
(sqrt (/ 1 re))
(sqrt (/ 1 re))
(sqrt (/ 1 re))
(/ (pow im 2) (pow re 3))
(/ (pow im 2) (pow re 3))
(/ (pow im 2) (pow re 3))
(/ (pow im 2) (pow re 3))
(* 1/2 (* (* im (* (sqrt 1/2) (sqrt 2))) (sqrt (/ 1 re))))
(+ (* -1/32 (* (/ (* (pow im 3) (sqrt 2)) (sqrt 1/2)) (sqrt (/ 1 (pow re 5))))) (* 1/2 (* (* im (* (sqrt 1/2) (sqrt 2))) (sqrt (/ 1 re)))))
(+ (* -1/32 (* (/ (* (pow im 3) (sqrt 2)) (sqrt 1/2)) (sqrt (/ 1 (pow re 5))))) (+ (* 1/64 (* (/ (* (pow im 5) (sqrt 2)) (sqrt 1/2)) (sqrt (/ 1 (pow re 9))))) (* 1/2 (* (* im (* (sqrt 1/2) (sqrt 2))) (sqrt (/ 1 re))))))
(+ (* -1/32 (* (/ (* (pow im 3) (sqrt 2)) (sqrt 1/2)) (sqrt (/ 1 (pow re 5))))) (+ (* -1/1024 (* (/ (* (pow im 5) (sqrt 2)) (pow (sqrt 1/2) 3)) (sqrt (/ 1 (pow re 9))))) (+ (* 1/64 (* (/ (* (pow im 5) (sqrt 2)) (sqrt 1/2)) (sqrt (/ 1 (pow re 9))))) (* 1/2 (* (* im (* (sqrt 1/2) (sqrt 2))) (sqrt (/ 1 re)))))))
(* (* im (* (sqrt 1/2) (sqrt 2))) (sqrt (/ 1 re)))
(+ (* -1/16 (* (/ (* (pow im 3) (sqrt 2)) (sqrt 1/2)) (sqrt (/ 1 (pow re 5))))) (* (* im (* (sqrt 1/2) (sqrt 2))) (sqrt (/ 1 re))))
(+ (* -1/16 (* (/ (* (pow im 3) (sqrt 2)) (sqrt 1/2)) (sqrt (/ 1 (pow re 5))))) (+ (* 1/32 (* (/ (* (pow im 5) (sqrt 2)) (sqrt 1/2)) (sqrt (/ 1 (pow re 9))))) (* (* im (* (sqrt 1/2) (sqrt 2))) (sqrt (/ 1 re)))))
(+ (* -1/16 (* (/ (* (pow im 3) (sqrt 2)) (sqrt 1/2)) (sqrt (/ 1 (pow re 5))))) (+ (* -1/512 (* (/ (* (pow im 5) (sqrt 2)) (pow (sqrt 1/2) 3)) (sqrt (/ 1 (pow re 9))))) (+ (* 1/32 (* (/ (* (pow im 5) (sqrt 2)) (sqrt 1/2)) (sqrt (/ 1 (pow re 9))))) (* (* im (* (sqrt 1/2) (sqrt 2))) (sqrt (/ 1 re))))))
(/ (pow im 2) re)
(/ (+ (* -1/4 (/ (pow im 4) (pow re 2))) (pow im 2)) re)
(/ (+ (* -1/4 (/ (pow im 4) (pow re 2))) (+ (* 1/8 (/ (pow im 6) (pow re 4))) (pow im 2))) re)
(/ (+ (* -1 (/ (+ (* 1/64 (pow im 8)) (* 1/16 (pow im 8))) (pow re 6))) (+ (* -1/4 (/ (pow im 4) (pow re 2))) (+ (* 1/8 (/ (pow im 6) (pow re 4))) (pow im 2)))) re)
(* 1/2 (/ (pow im 2) re))
(/ (+ (* -1/8 (/ (pow im 4) (pow re 2))) (* 1/2 (pow im 2))) re)
(/ (+ (* -1/8 (/ (pow im 4) (pow re 2))) (+ (* 1/16 (/ (pow im 6) (pow re 4))) (* 1/2 (pow im 2)))) re)
(/ (+ (* -1/2 (/ (+ (* 1/64 (pow im 8)) (* 1/16 (pow im 8))) (pow re 6))) (+ (* -1/8 (/ (pow im 4) (pow re 2))) (+ (* 1/16 (/ (pow im 6) (pow re 4))) (* 1/2 (pow im 2))))) re)
(* 1/2 (* (* im (* (sqrt 1/2) (sqrt 2))) (sqrt (/ 1 re))))
(+ (* -1/32 (* (/ (* (pow im 3) (sqrt 2)) (sqrt 1/2)) (sqrt (/ 1 (pow re 5))))) (* 1/2 (* (* im (* (sqrt 1/2) (sqrt 2))) (sqrt (/ 1 re)))))
(+ (* -1/32 (* (/ (* (pow im 3) (sqrt 2)) (sqrt 1/2)) (sqrt (/ 1 (pow re 5))))) (+ (* 1/64 (* (/ (* (pow im 5) (sqrt 2)) (sqrt 1/2)) (sqrt (/ 1 (pow re 9))))) (* 1/2 (* (* im (* (sqrt 1/2) (sqrt 2))) (sqrt (/ 1 re))))))
(+ (* -1/32 (* (/ (* (pow im 3) (sqrt 2)) (sqrt 1/2)) (sqrt (/ 1 (pow re 5))))) (+ (* -1/1024 (* (/ (* (pow im 5) (sqrt 2)) (pow (sqrt 1/2) 3)) (sqrt (/ 1 (pow re 9))))) (+ (* 1/64 (* (/ (* (pow im 5) (sqrt 2)) (sqrt 1/2)) (sqrt (/ 1 (pow re 9))))) (* 1/2 (* (* im (* (sqrt 1/2) (sqrt 2))) (sqrt (/ 1 re)))))))
(* (* im (* (sqrt 1/2) (sqrt 2))) (sqrt (/ 1 re)))
(+ (* -1/16 (* (/ (* (pow im 3) (sqrt 2)) (sqrt 1/2)) (sqrt (/ 1 (pow re 5))))) (* (* im (* (sqrt 1/2) (sqrt 2))) (sqrt (/ 1 re))))
(+ (* -1/16 (* (/ (* (pow im 3) (sqrt 2)) (sqrt 1/2)) (sqrt (/ 1 (pow re 5))))) (+ (* 1/32 (* (/ (* (pow im 5) (sqrt 2)) (sqrt 1/2)) (sqrt (/ 1 (pow re 9))))) (* (* im (* (sqrt 1/2) (sqrt 2))) (sqrt (/ 1 re)))))
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(/ (+ (* -1/4 (/ (pow im 4) (pow re 2))) (pow im 2)) re)
(/ (+ (* -1/4 (/ (pow im 4) (pow re 2))) (+ (* 1/8 (/ (pow im 6) (pow re 4))) (pow im 2))) re)
(/ (+ (* -1 (/ (+ (* 1/64 (pow im 8)) (* 1/16 (pow im 8))) (pow re 6))) (+ (* -1/4 (/ (pow im 4) (pow re 2))) (+ (* 1/8 (/ (pow im 6) (pow re 4))) (pow im 2)))) re)
(* -4 re)
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(* (* im (* (sqrt 1/2) (sqrt 2))) (sqrt (/ 1 re)))
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(/ (+ (* -1/4 (/ (pow im 4) (pow re 2))) (pow im 2)) re)
(/ (+ (* -1/4 (/ (pow im 4) (pow re 2))) (+ (* 1/8 (/ (pow im 6) (pow re 4))) (pow im 2))) re)
(/ (+ (* -1 (/ (+ (* 1/64 (pow im 8)) (* 1/16 (pow im 8))) (pow re 6))) (+ (* -1/4 (/ (pow im 4) (pow re 2))) (+ (* 1/8 (/ (pow im 6) (pow re 4))) (pow im 2)))) re)
(/ (pow im 2) re)
(/ (pow im 2) re)
(/ (pow im 2) re)
(/ (pow im 2) re)
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(* 1/2 (* (* im (* (sqrt 1/2) (sqrt 2))) (sqrt (/ 1 re))))
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(* (* im (* (sqrt 1/2) (sqrt 2))) (sqrt (/ 1 re)))
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(/ (+ (* -1/4 (/ (pow im 4) (pow re 2))) (pow im 2)) re)
(/ (+ (* -1/4 (/ (pow im 4) (pow re 2))) (+ (* 1/8 (/ (pow im 6) (pow re 4))) (pow im 2))) re)
(/ (+ (* -1 (/ (+ (* 1/64 (pow im 8)) (* 1/16 (pow im 8))) (pow re 6))) (+ (* -1/4 (/ (pow im 4) (pow re 2))) (+ (* 1/8 (/ (pow im 6) (pow re 4))) (pow im 2)))) re)
(sqrt (/ 1 re))
(sqrt (/ 1 re))
(sqrt (/ 1 re))
(sqrt (/ 1 re))
(/ (pow im 2) (pow re 3))
(/ (pow im 2) (pow re 3))
(/ (pow im 2) (pow re 3))
(/ (pow im 2) (pow re 3))
(* -1/2 (* (sqrt re) (* (sqrt -1) (pow (sqrt 2) 2))))
(* -1 (* re (+ (* -1/8 (* (* (pow im 2) (sqrt -1)) (sqrt (/ 1 (pow re 5))))) (* 1/2 (* (sqrt (/ 1 re)) (* (sqrt -1) (pow (sqrt 2) 2)))))))
(* -1 (* re (+ (* -1 (/ (+ (* -1/32 (* (* (pow im 4) (sqrt -1)) (sqrt (/ 1 (pow re 3))))) (* 1/8 (* (* (pow im 2) (sqrt -1)) (sqrt re)))) (pow re 3))) (* 1/2 (* (sqrt (/ 1 re)) (* (sqrt -1) (pow (sqrt 2) 2)))))))
(* -1 (* re (+ (* -1 (/ (+ (* -1/32 (* (* (pow im 4) (sqrt -1)) (sqrt (/ 1 (pow re 3))))) (+ (* 1/64 (* (/ (* (pow im 4) (sqrt -1)) (pow (sqrt 2) 2)) (sqrt (/ 1 (pow re 3))))) (* 1/8 (* (* (pow im 2) (sqrt -1)) (sqrt re))))) (pow re 3))) (* 1/2 (* (sqrt (/ 1 re)) (* (sqrt -1) (pow (sqrt 2) 2)))))))
(* -1 (* (sqrt re) (* (sqrt -1) (pow (sqrt 2) 2))))
(* -1 (* re (+ (* -1/4 (* (* (pow im 2) (sqrt -1)) (sqrt (/ 1 (pow re 5))))) (* (sqrt (/ 1 re)) (* (sqrt -1) (pow (sqrt 2) 2))))))
(* -1 (* re (+ (* -1 (/ (+ (* -1/16 (* (* (pow im 4) (sqrt -1)) (sqrt (/ 1 (pow re 3))))) (* 1/4 (* (* (pow im 2) (sqrt -1)) (sqrt re)))) (pow re 3))) (* (sqrt (/ 1 re)) (* (sqrt -1) (pow (sqrt 2) 2))))))
(* -1 (* re (+ (* -1 (/ (+ (* -1/16 (* (* (pow im 4) (sqrt -1)) (sqrt (/ 1 (pow re 3))))) (+ (* 1/32 (* (/ (* (pow im 4) (sqrt -1)) (pow (sqrt 2) 2)) (sqrt (/ 1 (pow re 3))))) (* 1/4 (* (* (pow im 2) (sqrt -1)) (sqrt re))))) (pow re 3))) (* (sqrt (/ 1 re)) (* (sqrt -1) (pow (sqrt 2) 2))))))
(* -4 re)
(* -1 (* re (+ 4 (/ (pow im 2) (pow re 2)))))
(* -1 (* re (+ 4 (+ (* -1/4 (/ (pow im 4) (pow re 4))) (/ (pow im 2) (pow re 2))))))
(* -1 (* re (+ 4 (+ (* -1/4 (/ (pow im 4) (pow re 4))) (+ (* 1/8 (/ (pow im 6) (pow re 6))) (/ (pow im 2) (pow re 2)))))))
(* -2 re)
(* -1 (* re (+ 2 (* 1/2 (/ (pow im 2) (pow re 2))))))
(* -1 (* re (+ 2 (+ (* -1/8 (/ (pow im 4) (pow re 4))) (* 1/2 (/ (pow im 2) (pow re 2)))))))
(* -1 (* re (+ 2 (+ (* -1/8 (/ (pow im 4) (pow re 4))) (+ (* 1/16 (/ (pow im 6) (pow re 6))) (* 1/2 (/ (pow im 2) (pow re 2))))))))
(* -1/2 (* (sqrt re) (* (sqrt -1) (pow (sqrt 2) 2))))
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(* -1 (* re (+ (* -1 (/ (+ (* -1/32 (* (* (pow im 4) (sqrt -1)) (sqrt (/ 1 (pow re 3))))) (* 1/8 (* (* (pow im 2) (sqrt -1)) (sqrt re)))) (pow re 3))) (* 1/2 (* (sqrt (/ 1 re)) (* (sqrt -1) (pow (sqrt 2) 2)))))))
(* -1 (* re (+ (* -1 (/ (+ (* -1/32 (* (* (pow im 4) (sqrt -1)) (sqrt (/ 1 (pow re 3))))) (+ (* 1/64 (* (/ (* (pow im 4) (sqrt -1)) (pow (sqrt 2) 2)) (sqrt (/ 1 (pow re 3))))) (* 1/8 (* (* (pow im 2) (sqrt -1)) (sqrt re))))) (pow re 3))) (* 1/2 (* (sqrt (/ 1 re)) (* (sqrt -1) (pow (sqrt 2) 2)))))))
(* -1 (* (sqrt re) (* (sqrt -1) (pow (sqrt 2) 2))))
(* -1 (* re (+ (* -1/4 (* (* (pow im 2) (sqrt -1)) (sqrt (/ 1 (pow re 5))))) (* (sqrt (/ 1 re)) (* (sqrt -1) (pow (sqrt 2) 2))))))
(* -1 (* re (+ (* -1 (/ (+ (* -1/16 (* (* (pow im 4) (sqrt -1)) (sqrt (/ 1 (pow re 3))))) (* 1/4 (* (* (pow im 2) (sqrt -1)) (sqrt re)))) (pow re 3))) (* (sqrt (/ 1 re)) (* (sqrt -1) (pow (sqrt 2) 2))))))
(* -1 (* re (+ (* -1 (/ (+ (* -1/16 (* (* (pow im 4) (sqrt -1)) (sqrt (/ 1 (pow re 3))))) (+ (* 1/32 (* (/ (* (pow im 4) (sqrt -1)) (pow (sqrt 2) 2)) (sqrt (/ 1 (pow re 3))))) (* 1/4 (* (* (pow im 2) (sqrt -1)) (sqrt re))))) (pow re 3))) (* (sqrt (/ 1 re)) (* (sqrt -1) (pow (sqrt 2) 2))))))
(* -4 re)
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(* -1 (* re (+ 4 (+ (* -1/4 (/ (pow im 4) (pow re 4))) (/ (pow im 2) (pow re 2))))))
(* -1 (* re (+ 4 (+ (* -1/4 (/ (pow im 4) (pow re 4))) (+ (* 1/8 (/ (pow im 6) (pow re 6))) (/ (pow im 2) (pow re 2)))))))
(* -4 re)
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(* -4 re)
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(* -1 (* re (+ (* -1 (/ (+ (* -1/32 (* (* (pow im 4) (sqrt -1)) (sqrt (/ 1 (pow re 3))))) (* 1/8 (* (* (pow im 2) (sqrt -1)) (sqrt re)))) (pow re 3))) (* 1/2 (* (sqrt (/ 1 re)) (* (sqrt -1) (pow (sqrt 2) 2)))))))
(* -1 (* re (+ (* -1 (/ (+ (* -1/32 (* (* (pow im 4) (sqrt -1)) (sqrt (/ 1 (pow re 3))))) (+ (* 1/64 (* (/ (* (pow im 4) (sqrt -1)) (pow (sqrt 2) 2)) (sqrt (/ 1 (pow re 3))))) (* 1/8 (* (* (pow im 2) (sqrt -1)) (sqrt re))))) (pow re 3))) (* 1/2 (* (sqrt (/ 1 re)) (* (sqrt -1) (pow (sqrt 2) 2)))))))
(* -1 (* (sqrt re) (* (sqrt -1) (pow (sqrt 2) 2))))
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(* -1 (* re (+ (* -1 (/ (+ (* -1/16 (* (* (pow im 4) (sqrt -1)) (sqrt (/ 1 (pow re 3))))) (+ (* 1/32 (* (/ (* (pow im 4) (sqrt -1)) (pow (sqrt 2) 2)) (sqrt (/ 1 (pow re 3))))) (* 1/4 (* (* (pow im 2) (sqrt -1)) (sqrt re))))) (pow re 3))) (* (sqrt (/ 1 re)) (* (sqrt -1) (pow (sqrt 2) 2))))))
(* -4 re)
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(* -1 (* re (+ 4 (+ (* -1/4 (/ (pow im 4) (pow re 4))) (+ (* 1/8 (/ (pow im 6) (pow re 6))) (/ (pow im 2) (pow re 2)))))))
(/ (pow im 2) re)
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(* -1 (* re (+ (* -1 (/ (+ (* -1/32 (* (* (pow im 4) (sqrt -1)) (sqrt (/ 1 (pow re 3))))) (+ (* 1/64 (* (/ (* (pow im 4) (sqrt -1)) (pow (sqrt 2) 2)) (sqrt (/ 1 (pow re 3))))) (* 1/8 (* (* (pow im 2) (sqrt -1)) (sqrt re))))) (pow re 3))) (* 1/2 (* (sqrt (/ 1 re)) (* (sqrt -1) (pow (sqrt 2) 2)))))))
(* 1/2 (* (* im (* (pow (sqrt -1) 2) (* (sqrt 1/2) (sqrt 2)))) (sqrt (/ 1 re))))
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(/ (pow im 2) re)
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(* -1 (* re (+ (* -1 (/ (+ (* -1/32 (* (* (pow im 4) (sqrt -1)) (sqrt (/ 1 (pow re 3))))) (+ (* 1/64 (* (/ (* (pow im 4) (sqrt -1)) (pow (sqrt 2) 2)) (sqrt (/ 1 (pow re 3))))) (* 1/8 (* (* (pow im 2) (sqrt -1)) (sqrt re))))) (pow re 3))) (* 1/2 (* (sqrt (/ 1 re)) (* (sqrt -1) (pow (sqrt 2) 2)))))))
(* -1 (* (sqrt re) (* (sqrt -1) (pow (sqrt 2) 2))))
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(* -1 (* re (+ (* -1 (/ (+ (* -1/16 (* (* (pow im 4) (sqrt -1)) (sqrt (/ 1 (pow re 3))))) (+ (* 1/32 (* (/ (* (pow im 4) (sqrt -1)) (pow (sqrt 2) 2)) (sqrt (/ 1 (pow re 3))))) (* 1/4 (* (* (pow im 2) (sqrt -1)) (sqrt re))))) (pow re 3))) (* (sqrt (/ 1 re)) (* (sqrt -1) (pow (sqrt 2) 2))))))
(* -4 re)
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(* -1 (* re (+ 4 (+ (* -1/4 (/ (pow im 4) (pow re 4))) (+ (* 1/8 (/ (pow im 6) (pow re 6))) (/ (pow im 2) (pow re 2)))))))
(* (sqrt (/ 1 re)) (pow (sqrt -1) 2))
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(/ (pow im 2) (pow re 3))
(/ (pow im 2) (pow re 3))
(/ (pow im 2) (pow re 3))
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(* 1/2 (* (* im (* (sqrt 1/2) (sqrt 2))) (sqrt (/ 1 re))))
(* im (+ (* -1/32 (* (/ (* (pow im 2) (sqrt 2)) (sqrt 1/2)) (sqrt (/ 1 (pow re 5))))) (* 1/2 (* (sqrt (/ 1 re)) (* (sqrt 1/2) (sqrt 2))))))
(* im (+ (* 1/2 (* (sqrt (/ 1 re)) (* (sqrt 1/2) (sqrt 2)))) (* (pow im 2) (+ (* -1/32 (* (sqrt (/ 1 (pow re 5))) (/ (sqrt 2) (sqrt 1/2)))) (* 1/4 (* (/ (* (pow im 2) (* (sqrt 2) (- (* 1/16 (/ 1 (pow re 5))) (* 1/256 (/ 1 (* (pow re 5) (pow (sqrt 1/2) 2))))))) (sqrt 1/2)) (sqrt re)))))))
(* im (+ (* 1/2 (* (sqrt (/ 1 re)) (* (sqrt 1/2) (sqrt 2)))) (* (pow im 2) (+ (* -1/32 (* (sqrt (/ 1 (pow re 5))) (/ (sqrt 2) (sqrt 1/2)))) (* (pow im 2) (+ (* -1/4 (* (/ (* (pow im 2) (* (sqrt 2) (+ (* -1/16 (/ (- (* 1/16 (/ 1 (pow re 5))) (* 1/256 (/ 1 (* (pow re 5) (pow (sqrt 1/2) 2))))) (* (pow re 2) (pow (sqrt 1/2) 2)))) (* 5/128 (/ 1 (pow re 7)))))) (sqrt 1/2)) (sqrt re))) (* 1/4 (* (sqrt re) (/ (* (sqrt 2) (- (* 1/16 (/ 1 (pow re 5))) (* 1/256 (/ 1 (* (pow re 5) (pow (sqrt 1/2) 2)))))) (sqrt 1/2))))))))))
(* (* im (* (sqrt 1/2) (sqrt 2))) (sqrt (/ 1 re)))
(* im (+ (* -1/16 (* (/ (* (pow im 2) (sqrt 2)) (sqrt 1/2)) (sqrt (/ 1 (pow re 5))))) (* (sqrt (/ 1 re)) (* (sqrt 1/2) (sqrt 2)))))
(* im (+ (* (sqrt (/ 1 re)) (* (sqrt 1/2) (sqrt 2))) (* (pow im 2) (+ (* -1/16 (* (sqrt (/ 1 (pow re 5))) (/ (sqrt 2) (sqrt 1/2)))) (* 1/2 (* (/ (* (pow im 2) (* (sqrt 2) (- (* 1/16 (/ 1 (pow re 5))) (* 1/256 (/ 1 (* (pow re 5) (pow (sqrt 1/2) 2))))))) (sqrt 1/2)) (sqrt re)))))))
(* im (+ (* (sqrt (/ 1 re)) (* (sqrt 1/2) (sqrt 2))) (* (pow im 2) (+ (* -1/16 (* (sqrt (/ 1 (pow re 5))) (/ (sqrt 2) (sqrt 1/2)))) (* (pow im 2) (+ (* -1/2 (* (/ (* (pow im 2) (* (sqrt 2) (+ (* -1/16 (/ (- (* 1/16 (/ 1 (pow re 5))) (* 1/256 (/ 1 (* (pow re 5) (pow (sqrt 1/2) 2))))) (* (pow re 2) (pow (sqrt 1/2) 2)))) (* 5/128 (/ 1 (pow re 7)))))) (sqrt 1/2)) (sqrt re))) (* 1/2 (* (sqrt re) (/ (* (sqrt 2) (- (* 1/16 (/ 1 (pow re 5))) (* 1/256 (/ 1 (* (pow re 5) (pow (sqrt 1/2) 2)))))) (sqrt 1/2))))))))))
(/ (pow im 2) re)
(* (pow im 2) (+ (* -1/4 (/ (pow im 2) (pow re 3))) (/ 1 re)))
(* (pow im 2) (+ (* (pow im 2) (- (* 1/8 (/ (pow im 2) (pow re 5))) (* 1/4 (/ 1 (pow re 3))))) (/ 1 re)))
(* (pow im 2) (+ (* (pow im 2) (- (* (pow im 2) (+ (* -5/64 (/ (pow im 2) (pow re 7))) (* 1/8 (/ 1 (pow re 5))))) (* 1/4 (/ 1 (pow re 3))))) (/ 1 re)))
(* 1/2 (/ (pow im 2) re))
(* (pow im 2) (+ (* -1/8 (/ (pow im 2) (pow re 3))) (* 1/2 (/ 1 re))))
(* (pow im 2) (+ (* (pow im 2) (- (* 1/16 (/ (pow im 2) (pow re 5))) (* 1/8 (/ 1 (pow re 3))))) (* 1/2 (/ 1 re))))
(* (pow im 2) (+ (* (pow im 2) (- (* (pow im 2) (+ (* -5/128 (/ (pow im 2) (pow re 7))) (* 1/16 (/ 1 (pow re 5))))) (* 1/8 (/ 1 (pow re 3))))) (* 1/2 (/ 1 re))))
(* 1/2 (* (* im (* (sqrt 1/2) (sqrt 2))) (sqrt (/ 1 re))))
(* im (+ (* -1/32 (* (/ (* (pow im 2) (sqrt 2)) (sqrt 1/2)) (sqrt (/ 1 (pow re 5))))) (* 1/2 (* (sqrt (/ 1 re)) (* (sqrt 1/2) (sqrt 2))))))
(* im (+ (* 1/2 (* (sqrt (/ 1 re)) (* (sqrt 1/2) (sqrt 2)))) (* (pow im 2) (+ (* -1/32 (* (sqrt (/ 1 (pow re 5))) (/ (sqrt 2) (sqrt 1/2)))) (* 1/4 (* (/ (* (pow im 2) (* (sqrt 2) (- (* 1/16 (/ 1 (pow re 5))) (* 1/256 (/ 1 (* (pow re 5) (pow (sqrt 1/2) 2))))))) (sqrt 1/2)) (sqrt re)))))))
(* im (+ (* 1/2 (* (sqrt (/ 1 re)) (* (sqrt 1/2) (sqrt 2)))) (* (pow im 2) (+ (* -1/32 (* (sqrt (/ 1 (pow re 5))) (/ (sqrt 2) (sqrt 1/2)))) (* (pow im 2) (+ (* -1/4 (* (/ (* (pow im 2) (* (sqrt 2) (+ (* -1/16 (/ (- (* 1/16 (/ 1 (pow re 5))) (* 1/256 (/ 1 (* (pow re 5) (pow (sqrt 1/2) 2))))) (* (pow re 2) (pow (sqrt 1/2) 2)))) (* 5/128 (/ 1 (pow re 7)))))) (sqrt 1/2)) (sqrt re))) (* 1/4 (* (sqrt re) (/ (* (sqrt 2) (- (* 1/16 (/ 1 (pow re 5))) (* 1/256 (/ 1 (* (pow re 5) (pow (sqrt 1/2) 2)))))) (sqrt 1/2))))))))))
(* (* im (* (sqrt 1/2) (sqrt 2))) (sqrt (/ 1 re)))
(* im (+ (* -1/16 (* (/ (* (pow im 2) (sqrt 2)) (sqrt 1/2)) (sqrt (/ 1 (pow re 5))))) (* (sqrt (/ 1 re)) (* (sqrt 1/2) (sqrt 2)))))
(* im (+ (* (sqrt (/ 1 re)) (* (sqrt 1/2) (sqrt 2))) (* (pow im 2) (+ (* -1/16 (* (sqrt (/ 1 (pow re 5))) (/ (sqrt 2) (sqrt 1/2)))) (* 1/2 (* (/ (* (pow im 2) (* (sqrt 2) (- (* 1/16 (/ 1 (pow re 5))) (* 1/256 (/ 1 (* (pow re 5) (pow (sqrt 1/2) 2))))))) (sqrt 1/2)) (sqrt re)))))))
(* im (+ (* (sqrt (/ 1 re)) (* (sqrt 1/2) (sqrt 2))) (* (pow im 2) (+ (* -1/16 (* (sqrt (/ 1 (pow re 5))) (/ (sqrt 2) (sqrt 1/2)))) (* (pow im 2) (+ (* -1/2 (* (/ (* (pow im 2) (* (sqrt 2) (+ (* -1/16 (/ (- (* 1/16 (/ 1 (pow re 5))) (* 1/256 (/ 1 (* (pow re 5) (pow (sqrt 1/2) 2))))) (* (pow re 2) (pow (sqrt 1/2) 2)))) (* 5/128 (/ 1 (pow re 7)))))) (sqrt 1/2)) (sqrt re))) (* 1/2 (* (sqrt re) (/ (* (sqrt 2) (- (* 1/16 (/ 1 (pow re 5))) (* 1/256 (/ 1 (* (pow re 5) (pow (sqrt 1/2) 2)))))) (sqrt 1/2))))))))))
(/ (pow im 2) re)
(* (pow im 2) (+ (* -1/4 (/ (pow im 2) (pow re 3))) (/ 1 re)))
(* (pow im 2) (+ (* (pow im 2) (- (* 1/8 (/ (pow im 2) (pow re 5))) (* 1/4 (/ 1 (pow re 3))))) (/ 1 re)))
(* (pow im 2) (+ (* (pow im 2) (- (* (pow im 2) (+ (* -5/64 (/ (pow im 2) (pow re 7))) (* 1/8 (/ 1 (pow re 5))))) (* 1/4 (/ 1 (pow re 3))))) (/ 1 re)))
(* 1/2 (* (* im (* (sqrt 1/2) (sqrt 2))) (sqrt (/ 1 re))))
(* im (+ (* -1/32 (* (/ (* (pow im 2) (sqrt 2)) (sqrt 1/2)) (sqrt (/ 1 (pow re 5))))) (* 1/2 (* (sqrt (/ 1 re)) (* (sqrt 1/2) (sqrt 2))))))
(* im (+ (* 1/2 (* (sqrt (/ 1 re)) (* (sqrt 1/2) (sqrt 2)))) (* (pow im 2) (+ (* -1/32 (* (sqrt (/ 1 (pow re 5))) (/ (sqrt 2) (sqrt 1/2)))) (* 1/4 (* (/ (* (pow im 2) (* (sqrt 2) (- (* 1/16 (/ 1 (pow re 5))) (* 1/256 (/ 1 (* (pow re 5) (pow (sqrt 1/2) 2))))))) (sqrt 1/2)) (sqrt re)))))))
(* im (+ (* 1/2 (* (sqrt (/ 1 re)) (* (sqrt 1/2) (sqrt 2)))) (* (pow im 2) (+ (* -1/32 (* (sqrt (/ 1 (pow re 5))) (/ (sqrt 2) (sqrt 1/2)))) (* (pow im 2) (+ (* -1/4 (* (/ (* (pow im 2) (* (sqrt 2) (+ (* -1/16 (/ (- (* 1/16 (/ 1 (pow re 5))) (* 1/256 (/ 1 (* (pow re 5) (pow (sqrt 1/2) 2))))) (* (pow re 2) (pow (sqrt 1/2) 2)))) (* 5/128 (/ 1 (pow re 7)))))) (sqrt 1/2)) (sqrt re))) (* 1/4 (* (sqrt re) (/ (* (sqrt 2) (- (* 1/16 (/ 1 (pow re 5))) (* 1/256 (/ 1 (* (pow re 5) (pow (sqrt 1/2) 2)))))) (sqrt 1/2))))))))))
(* (* im (* (sqrt 1/2) (sqrt 2))) (sqrt (/ 1 re)))
(* im (+ (* -1/16 (* (/ (* (pow im 2) (sqrt 2)) (sqrt 1/2)) (sqrt (/ 1 (pow re 5))))) (* (sqrt (/ 1 re)) (* (sqrt 1/2) (sqrt 2)))))
(* im (+ (* (sqrt (/ 1 re)) (* (sqrt 1/2) (sqrt 2))) (* (pow im 2) (+ (* -1/16 (* (sqrt (/ 1 (pow re 5))) (/ (sqrt 2) (sqrt 1/2)))) (* 1/2 (* (/ (* (pow im 2) (* (sqrt 2) (- (* 1/16 (/ 1 (pow re 5))) (* 1/256 (/ 1 (* (pow re 5) (pow (sqrt 1/2) 2))))))) (sqrt 1/2)) (sqrt re)))))))
(* im (+ (* (sqrt (/ 1 re)) (* (sqrt 1/2) (sqrt 2))) (* (pow im 2) (+ (* -1/16 (* (sqrt (/ 1 (pow re 5))) (/ (sqrt 2) (sqrt 1/2)))) (* (pow im 2) (+ (* -1/2 (* (/ (* (pow im 2) (* (sqrt 2) (+ (* -1/16 (/ (- (* 1/16 (/ 1 (pow re 5))) (* 1/256 (/ 1 (* (pow re 5) (pow (sqrt 1/2) 2))))) (* (pow re 2) (pow (sqrt 1/2) 2)))) (* 5/128 (/ 1 (pow re 7)))))) (sqrt 1/2)) (sqrt re))) (* 1/2 (* (sqrt re) (/ (* (sqrt 2) (- (* 1/16 (/ 1 (pow re 5))) (* 1/256 (/ 1 (* (pow re 5) (pow (sqrt 1/2) 2)))))) (sqrt 1/2))))))))))
(/ (pow im 2) re)
(* (pow im 2) (+ (* -1/4 (/ (pow im 2) (pow re 3))) (/ 1 re)))
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(* (pow im 2) (+ (* (pow im 2) (- (* (pow im 2) (+ (* -5/64 (/ (pow im 2) (pow re 7))) (* 1/8 (/ 1 (pow re 5))))) (* 1/4 (/ 1 (pow re 3))))) (/ 1 re)))
(/ (pow im 2) re)
(/ (pow im 2) re)
(/ (pow im 2) re)
(/ (pow im 2) re)
(* 1/2 (* (* im (* (sqrt 1/2) (sqrt 2))) (sqrt (/ 1 re))))
(* im (+ (* -1/32 (* (/ (* (pow im 2) (sqrt 2)) (sqrt 1/2)) (sqrt (/ 1 (pow re 5))))) (* 1/2 (* (sqrt (/ 1 re)) (* (sqrt 1/2) (sqrt 2))))))
(* im (+ (* 1/2 (* (sqrt (/ 1 re)) (* (sqrt 1/2) (sqrt 2)))) (* (pow im 2) (+ (* -1/32 (* (sqrt (/ 1 (pow re 5))) (/ (sqrt 2) (sqrt 1/2)))) (* 1/4 (* (/ (* (pow im 2) (* (sqrt 2) (- (* 1/16 (/ 1 (pow re 5))) (* 1/256 (/ 1 (* (pow re 5) (pow (sqrt 1/2) 2))))))) (sqrt 1/2)) (sqrt re)))))))
(* im (+ (* 1/2 (* (sqrt (/ 1 re)) (* (sqrt 1/2) (sqrt 2)))) (* (pow im 2) (+ (* -1/32 (* (sqrt (/ 1 (pow re 5))) (/ (sqrt 2) (sqrt 1/2)))) (* (pow im 2) (+ (* -1/4 (* (/ (* (pow im 2) (* (sqrt 2) (+ (* -1/16 (/ (- (* 1/16 (/ 1 (pow re 5))) (* 1/256 (/ 1 (* (pow re 5) (pow (sqrt 1/2) 2))))) (* (pow re 2) (pow (sqrt 1/2) 2)))) (* 5/128 (/ 1 (pow re 7)))))) (sqrt 1/2)) (sqrt re))) (* 1/4 (* (sqrt re) (/ (* (sqrt 2) (- (* 1/16 (/ 1 (pow re 5))) (* 1/256 (/ 1 (* (pow re 5) (pow (sqrt 1/2) 2)))))) (sqrt 1/2))))))))))
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(/ (pow im 2) re)
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(* im (+ (* 1/2 (* (sqrt (/ 1 re)) (* (sqrt 1/2) (sqrt 2)))) (* (pow im 2) (+ (* -1/32 (* (sqrt (/ 1 (pow re 5))) (/ (sqrt 2) (sqrt 1/2)))) (* 1/4 (* (/ (* (pow im 2) (* (sqrt 2) (- (* 1/16 (/ 1 (pow re 5))) (* 1/256 (/ 1 (* (pow re 5) (pow (sqrt 1/2) 2))))))) (sqrt 1/2)) (sqrt re)))))))
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(* im (+ (* (sqrt (/ 1 re)) (* (sqrt 1/2) (sqrt 2))) (* (pow im 2) (+ (* -1/16 (* (sqrt (/ 1 (pow re 5))) (/ (sqrt 2) (sqrt 1/2)))) (* (pow im 2) (+ (* -1/2 (* (/ (* (pow im 2) (* (sqrt 2) (+ (* -1/16 (/ (- (* 1/16 (/ 1 (pow re 5))) (* 1/256 (/ 1 (* (pow re 5) (pow (sqrt 1/2) 2))))) (* (pow re 2) (pow (sqrt 1/2) 2)))) (* 5/128 (/ 1 (pow re 7)))))) (sqrt 1/2)) (sqrt re))) (* 1/2 (* (sqrt re) (/ (* (sqrt 2) (- (* 1/16 (/ 1 (pow re 5))) (* 1/256 (/ 1 (* (pow re 5) (pow (sqrt 1/2) 2)))))) (sqrt 1/2))))))))))
(/ (pow im 2) re)
(* (pow im 2) (+ (* -1/4 (/ (pow im 2) (pow re 3))) (/ 1 re)))
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(/ (pow im 2) (pow re 3))
(/ (pow im 2) (pow re 3))
(/ (pow im 2) (pow re 3))
(/ (pow im 2) (pow re 3))
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(* im (+ (* -1/4 (* (sqrt (/ 1 (pow im 3))) (* re (sqrt 2)))) (+ (* -1/16 (* (sqrt (/ 1 (pow im 5))) (* (pow re 2) (sqrt 2)))) (+ (* 1/8 (* (sqrt (/ 1 (pow im 5))) (* (pow re 2) (sqrt 2)))) (* 1/2 (* (sqrt (/ 1 im)) (sqrt 2)))))))
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(* 2 im)
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(* im (+ 2 (+ (* -2 (/ re im)) (+ (* -1/4 (/ (pow re 4) (pow im 4))) (/ (pow re 2) (pow im 2))))))
im
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(/ (pow im 2) re)
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(/ (pow im 2) re)
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(* -1 (* im (+ (* -1/2 (* (sqrt (/ 1 (pow im 3))) (* re (* (sqrt -1) (sqrt 2))))) (* (sqrt (/ 1 im)) (* (sqrt -1) (sqrt 2))))))
(* -1 (* im (+ (* -1/2 (* (sqrt (/ 1 (pow im 3))) (* re (* (sqrt -1) (sqrt 2))))) (+ (* -1/4 (* (sqrt (/ 1 (pow im 5))) (* (pow re 2) (* (sqrt -1) (sqrt 2))))) (* (sqrt (/ 1 im)) (* (sqrt -1) (sqrt 2)))))))
(* -1 (* im (+ (* -1 (/ (+ (* 1/8 (* (sqrt im) (* (pow re 2) (* (sqrt -1) (sqrt 2))))) (* 1/4 (* (sqrt im) (* (pow re 2) (* (sqrt -1) (sqrt 2)))))) (pow im 3))) (+ (* -1/2 (* (sqrt (/ 1 (pow im 3))) (* re (* (sqrt -1) (sqrt 2))))) (* (sqrt (/ 1 im)) (* (sqrt -1) (sqrt 2)))))))
(* -2 im)
(* -1 (* im (+ 2 (* 2 (/ re im)))))
(* -1 (* im (+ 2 (* -1 (/ (+ (* -2 re) (* -1 (/ (pow re 2) im))) im)))))
(* -1 (* im (+ 2 (* -1 (/ (+ (* -2 re) (* -1 (/ (+ (* -1/4 (/ (pow re 4) (pow im 2))) (pow re 2)) im))) im)))))
(/ (pow im 2) re)
(/ (pow im 2) re)
(/ (pow im 2) re)
(/ (pow im 2) re)
(* -1/2 (* (sqrt im) (* (sqrt -1) (sqrt 2))))
(* -1 (* im (+ (* -1/4 (* (sqrt (/ 1 (pow im 3))) (* re (* (sqrt -1) (sqrt 2))))) (* 1/2 (* (sqrt (/ 1 im)) (* (sqrt -1) (sqrt 2)))))))
(* -1 (* im (+ (* -1/4 (* (sqrt (/ 1 (pow im 3))) (* re (* (sqrt -1) (sqrt 2))))) (+ (* -1/8 (* (sqrt (/ 1 (pow im 5))) (* (pow re 2) (* (sqrt -1) (sqrt 2))))) (* 1/2 (* (sqrt (/ 1 im)) (* (sqrt -1) (sqrt 2))))))))
(* -1 (* im (+ (* -1 (/ (+ (* 1/16 (* (sqrt im) (* (pow re 2) (* (sqrt -1) (sqrt 2))))) (* 1/8 (* (sqrt im) (* (pow re 2) (* (sqrt -1) (sqrt 2)))))) (pow im 3))) (+ (* -1/4 (* (sqrt (/ 1 (pow im 3))) (* re (* (sqrt -1) (sqrt 2))))) (* 1/2 (* (sqrt (/ 1 im)) (* (sqrt -1) (sqrt 2))))))))
(* 1/2 (* (* im (* (sqrt 1/2) (sqrt 2))) (sqrt (/ 1 re))))
(* 1/2 (* (* im (* (sqrt 1/2) (sqrt 2))) (sqrt (/ 1 re))))
(* 1/2 (* (* im (* (sqrt 1/2) (sqrt 2))) (sqrt (/ 1 re))))
(* 1/2 (* (* im (* (sqrt 1/2) (sqrt 2))) (sqrt (/ 1 re))))
(* 1/2 (* im (* (sqrt 1/2) (sqrt 2))))
(* 1/2 (* im (* (sqrt 1/2) (sqrt 2))))
(* 1/2 (* im (* (sqrt 1/2) (sqrt 2))))
(* 1/2 (* im (* (sqrt 1/2) (sqrt 2))))
(* 1/2 (* im (sqrt 1/2)))
(* 1/2 (* im (sqrt 1/2)))
(* 1/2 (* im (sqrt 1/2)))
(* 1/2 (* im (sqrt 1/2)))
(* -1/4 (/ (pow im 4) (pow re 3)))
(* (pow im 4) (- (/ 1 (* (pow im 2) re)) (* 1/4 (/ 1 (pow re 3)))))
(* (pow im 4) (- (/ 1 (* (pow im 2) re)) (* 1/4 (/ 1 (pow re 3)))))
(* (pow im 4) (- (/ 1 (* (pow im 2) re)) (* 1/4 (/ 1 (pow re 3)))))
(* -1/2 (* (sqrt im) (* (sqrt -1) (sqrt 2))))
(* -1 (* im (+ (* -1/4 (* (sqrt (/ 1 (pow im 3))) (* re (* (sqrt -1) (sqrt 2))))) (* 1/2 (* (sqrt (/ 1 im)) (* (sqrt -1) (sqrt 2)))))))
(* -1 (* im (+ (* -1/4 (* (sqrt (/ 1 (pow im 3))) (* re (* (sqrt -1) (sqrt 2))))) (+ (* -1/8 (* (sqrt (/ 1 (pow im 5))) (* (pow re 2) (* (sqrt -1) (sqrt 2))))) (* 1/2 (* (sqrt (/ 1 im)) (* (sqrt -1) (sqrt 2))))))))
(* -1 (* im (+ (* -1 (/ (+ (* 1/16 (* (sqrt im) (* (pow re 2) (* (sqrt -1) (sqrt 2))))) (* 1/8 (* (sqrt im) (* (pow re 2) (* (sqrt -1) (sqrt 2)))))) (pow im 3))) (+ (* -1/4 (* (sqrt (/ 1 (pow im 3))) (* re (* (sqrt -1) (sqrt 2))))) (* 1/2 (* (sqrt (/ 1 im)) (* (sqrt -1) (sqrt 2))))))))
(* -1 (* (sqrt im) (* (sqrt -1) (sqrt 2))))
(* -1 (* im (+ (* -1/2 (* (sqrt (/ 1 (pow im 3))) (* re (* (sqrt -1) (sqrt 2))))) (* (sqrt (/ 1 im)) (* (sqrt -1) (sqrt 2))))))
(* -1 (* im (+ (* -1/2 (* (sqrt (/ 1 (pow im 3))) (* re (* (sqrt -1) (sqrt 2))))) (+ (* -1/4 (* (sqrt (/ 1 (pow im 5))) (* (pow re 2) (* (sqrt -1) (sqrt 2))))) (* (sqrt (/ 1 im)) (* (sqrt -1) (sqrt 2)))))))
(* -1 (* im (+ (* -1 (/ (+ (* 1/8 (* (sqrt im) (* (pow re 2) (* (sqrt -1) (sqrt 2))))) (* 1/4 (* (sqrt im) (* (pow re 2) (* (sqrt -1) (sqrt 2)))))) (pow im 3))) (+ (* -1/2 (* (sqrt (/ 1 (pow im 3))) (* re (* (sqrt -1) (sqrt 2))))) (* (sqrt (/ 1 im)) (* (sqrt -1) (sqrt 2)))))))
(* -2 im)
(* -1 (* im (+ 2 (* 2 (/ re im)))))
(* -1 (* im (+ 2 (* -1 (/ (+ (* -2 re) (* -1 (/ (pow re 2) im))) im)))))
(* -1 (* im (+ 2 (* -1 (/ (+ (* -2 re) (* -1 (/ (+ (* -1/4 (/ (pow re 4) (pow im 2))) (pow re 2)) im))) im)))))
(* im (sqrt 1/2))
(* im (sqrt 1/2))
(* im (sqrt 1/2))
(* im (sqrt 1/2))
(/ (pow im 2) (pow re 3))
(/ (pow im 2) (pow re 3))
(/ (pow im 2) (pow re 3))
(/ (pow im 2) (pow re 3))

Outputs
(.f64 (.f64 #s(literal 1/2 binary64) (sqrt.f64 #s(literal 2 binary64))) (sqrt.f64 im))
(fma.f64 (.f64 #s(literal 1/2 binary64) (sqrt.f64 #s(literal 2 binary64))) (sqrt.f64 im) (.f64 (.f64 #s(literal -1/4 binary64) (.f64 (sqrt.f64 #s(literal 2 binary64)) re)) (sqrt.f64 (/.f64 #s(literal 1 binary64) im))))
(fma.f64 (fma.f64 (.f64 #s(literal -1/4 binary64) (sqrt.f64 #s(literal 2 binary64))) (sqrt.f64 (/.f64 #s(literal 1 binary64) im)) (.f64 (.f64 re #s(literal 1/16 binary64)) (.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 im #s(literal 3 binary64)))) (sqrt.f64 #s(literal 2 binary64))))) re (.f64 (.f64 #s(literal 1/2 binary64) (sqrt.f64 #s(literal 2 binary64))) (sqrt.f64 im)))
(fma.f64 (fma.f64 (.f64 #s(literal -1/4 binary64) (sqrt.f64 #s(literal 2 binary64))) (sqrt.f64 (/.f64 #s(literal 1 binary64) im)) (.f64 (fma.f64 (.f64 #s(literal 1/32 binary64) (.f64 (sqrt.f64 #s(literal 2 binary64)) re)) (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 im #s(literal 5 binary64)))) (.f64 (.f64 #s(literal 1/16 binary64) (sqrt.f64 #s(literal 2 binary64))) (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 im #s(literal 3 binary64)))))) re)) re (.f64 (.f64 #s(literal 1/2 binary64) (sqrt.f64 #s(literal 2 binary64))) (sqrt.f64 im)))
(*.f64 (sqrt.f64 #s(literal 2 binary64)) (sqrt.f64 im))
(fma.f64 (.f64 re #s(literal -1/2 binary64)) (.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) im)) (sqrt.f64 #s(literal 2 binary64))) (*.f64 (sqrt.f64 #s(literal 2 binary64)) (sqrt.f64 im)))
(fma.f64 (fma.f64 (.f64 re #s(literal 1/8 binary64)) (.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 im #s(literal 3 binary64)))) (sqrt.f64 #s(literal 2 binary64))) (.f64 (.f64 #s(literal -1/2 binary64) (sqrt.f64 #s(literal 2 binary64))) (sqrt.f64 (/.f64 #s(literal 1 binary64) im)))) re (*.f64 (sqrt.f64 #s(literal 2 binary64)) (sqrt.f64 im)))
(fma.f64 (fma.f64 (.f64 #s(literal -1/2 binary64) (sqrt.f64 #s(literal 2 binary64))) (sqrt.f64 (/.f64 #s(literal 1 binary64) im)) (.f64 (fma.f64 (.f64 #s(literal 1/8 binary64) (sqrt.f64 #s(literal 2 binary64))) (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 im #s(literal 3 binary64)))) (.f64 (.f64 #s(literal 1/16 binary64) (.f64 (sqrt.f64 #s(literal 2 binary64)) re)) (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 im #s(literal 5 binary64)))))) re)) re (*.f64 (sqrt.f64 #s(literal 2 binary64)) (sqrt.f64 im)))
(*.f64 #s(literal 2 binary64) im)
(fma.f64 #s(literal -2 binary64) re (*.f64 #s(literal 2 binary64) im))
(fma.f64 (-.f64 (/.f64 re im) #s(literal 2 binary64)) re (*.f64 #s(literal 2 binary64) im))
(fma.f64 (fma.f64 (fma.f64 (.f64 re (/.f64 re (pow.f64 im #s(literal 3 binary64)))) #s(literal -1/4 binary64) (/.f64 #s(literal 1 binary64) im)) re #s(literal -2 binary64)) re (.f64 #s(literal 2 binary64) im))
im
(-.f64 im re)
(fma.f64 (fma.f64 (/.f64 #s(literal 1/2 binary64) im) re #s(literal -1 binary64)) re im)
(fma.f64 (fma.f64 (fma.f64 #s(literal -1/8 binary64) (*.f64 re (/.f64 re (pow.f64 im #s(literal 3 binary64)))) (/.f64 #s(literal 1/2 binary64) im)) re #s(literal -1 binary64)) re im)
(.f64 (.f64 #s(literal 1/2 binary64) (sqrt.f64 #s(literal 2 binary64))) (sqrt.f64 im))
(fma.f64 (.f64 #s(literal 1/2 binary64) (sqrt.f64 #s(literal 2 binary64))) (sqrt.f64 im) (.f64 (.f64 #s(literal -1/4 binary64) (.f64 (sqrt.f64 #s(literal 2 binary64)) re)) (sqrt.f64 (/.f64 #s(literal 1 binary64) im))))
(fma.f64 (fma.f64 (.f64 #s(literal -1/4 binary64) (sqrt.f64 #s(literal 2 binary64))) (sqrt.f64 (/.f64 #s(literal 1 binary64) im)) (.f64 (.f64 re #s(literal 1/16 binary64)) (.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 im #s(literal 3 binary64)))) (sqrt.f64 #s(literal 2 binary64))))) re (.f64 (.f64 #s(literal 1/2 binary64) (sqrt.f64 #s(literal 2 binary64))) (sqrt.f64 im)))
(fma.f64 (fma.f64 (.f64 #s(literal -1/4 binary64) (sqrt.f64 #s(literal 2 binary64))) (sqrt.f64 (/.f64 #s(literal 1 binary64) im)) (.f64 (fma.f64 (.f64 #s(literal 1/32 binary64) (.f64 (sqrt.f64 #s(literal 2 binary64)) re)) (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 im #s(literal 5 binary64)))) (.f64 (.f64 #s(literal 1/16 binary64) (sqrt.f64 #s(literal 2 binary64))) (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 im #s(literal 3 binary64)))))) re)) re (.f64 (.f64 #s(literal 1/2 binary64) (sqrt.f64 #s(literal 2 binary64))) (sqrt.f64 im)))
(*.f64 (sqrt.f64 #s(literal 2 binary64)) (sqrt.f64 im))
(fma.f64 (.f64 re #s(literal -1/2 binary64)) (.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) im)) (sqrt.f64 #s(literal 2 binary64))) (*.f64 (sqrt.f64 #s(literal 2 binary64)) (sqrt.f64 im)))
(fma.f64 (fma.f64 (.f64 re #s(literal 1/8 binary64)) (.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 im #s(literal 3 binary64)))) (sqrt.f64 #s(literal 2 binary64))) (.f64 (.f64 #s(literal -1/2 binary64) (sqrt.f64 #s(literal 2 binary64))) (sqrt.f64 (/.f64 #s(literal 1 binary64) im)))) re (*.f64 (sqrt.f64 #s(literal 2 binary64)) (sqrt.f64 im)))
(fma.f64 (fma.f64 (.f64 #s(literal -1/2 binary64) (sqrt.f64 #s(literal 2 binary64))) (sqrt.f64 (/.f64 #s(literal 1 binary64) im)) (.f64 (fma.f64 (.f64 #s(literal 1/8 binary64) (sqrt.f64 #s(literal 2 binary64))) (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 im #s(literal 3 binary64)))) (.f64 (.f64 #s(literal 1/16 binary64) (.f64 (sqrt.f64 #s(literal 2 binary64)) re)) (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 im #s(literal 5 binary64)))))) re)) re (*.f64 (sqrt.f64 #s(literal 2 binary64)) (sqrt.f64 im)))
(*.f64 #s(literal 2 binary64) im)
(fma.f64 #s(literal -2 binary64) re (*.f64 #s(literal 2 binary64) im))
(fma.f64 (-.f64 (/.f64 re im) #s(literal 2 binary64)) re (*.f64 #s(literal 2 binary64) im))
(fma.f64 (fma.f64 (fma.f64 (.f64 re (/.f64 re (pow.f64 im #s(literal 3 binary64)))) #s(literal -1/4 binary64) (/.f64 #s(literal 1 binary64) im)) re #s(literal -2 binary64)) re (.f64 #s(literal 2 binary64) im))
(*.f64 #s(literal -4 binary64) re)
(*.f64 #s(literal -4 binary64) re)
(*.f64 #s(literal -4 binary64) re)
(*.f64 #s(literal -4 binary64) re)
(.f64 (.f64 #s(literal 1/2 binary64) (sqrt.f64 #s(literal 2 binary64))) (sqrt.f64 im))
(fma.f64 (.f64 #s(literal 1/2 binary64) (sqrt.f64 #s(literal 2 binary64))) (sqrt.f64 im) (.f64 (.f64 #s(literal -1/4 binary64) (.f64 (sqrt.f64 #s(literal 2 binary64)) re)) (sqrt.f64 (/.f64 #s(literal 1 binary64) im))))
(fma.f64 (fma.f64 (.f64 #s(literal -1/4 binary64) (sqrt.f64 #s(literal 2 binary64))) (sqrt.f64 (/.f64 #s(literal 1 binary64) im)) (.f64 (.f64 re #s(literal 1/16 binary64)) (.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 im #s(literal 3 binary64)))) (sqrt.f64 #s(literal 2 binary64))))) re (.f64 (.f64 #s(literal 1/2 binary64) (sqrt.f64 #s(literal 2 binary64))) (sqrt.f64 im)))
(fma.f64 (fma.f64 (.f64 #s(literal -1/4 binary64) (sqrt.f64 #s(literal 2 binary64))) (sqrt.f64 (/.f64 #s(literal 1 binary64) im)) (.f64 (fma.f64 (.f64 #s(literal 1/32 binary64) (.f64 (sqrt.f64 #s(literal 2 binary64)) re)) (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 im #s(literal 5 binary64)))) (.f64 (.f64 #s(literal 1/16 binary64) (sqrt.f64 #s(literal 2 binary64))) (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 im #s(literal 3 binary64)))))) re)) re (.f64 (.f64 #s(literal 1/2 binary64) (sqrt.f64 #s(literal 2 binary64))) (sqrt.f64 im)))
(*.f64 (sqrt.f64 #s(literal 2 binary64)) (sqrt.f64 im))
(fma.f64 (.f64 re #s(literal -1/2 binary64)) (.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) im)) (sqrt.f64 #s(literal 2 binary64))) (*.f64 (sqrt.f64 #s(literal 2 binary64)) (sqrt.f64 im)))
(fma.f64 (fma.f64 (.f64 re #s(literal 1/8 binary64)) (.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 im #s(literal 3 binary64)))) (sqrt.f64 #s(literal 2 binary64))) (.f64 (.f64 #s(literal -1/2 binary64) (sqrt.f64 #s(literal 2 binary64))) (sqrt.f64 (/.f64 #s(literal 1 binary64) im)))) re (*.f64 (sqrt.f64 #s(literal 2 binary64)) (sqrt.f64 im)))
(fma.f64 (fma.f64 (.f64 #s(literal -1/2 binary64) (sqrt.f64 #s(literal 2 binary64))) (sqrt.f64 (/.f64 #s(literal 1 binary64) im)) (.f64 (fma.f64 (.f64 #s(literal 1/8 binary64) (sqrt.f64 #s(literal 2 binary64))) (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 im #s(literal 3 binary64)))) (.f64 (.f64 #s(literal 1/16 binary64) (.f64 (sqrt.f64 #s(literal 2 binary64)) re)) (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 im #s(literal 5 binary64)))))) re)) re (*.f64 (sqrt.f64 #s(literal 2 binary64)) (sqrt.f64 im)))
(*.f64 #s(literal 2 binary64) im)
(fma.f64 #s(literal -2 binary64) re (*.f64 #s(literal 2 binary64) im))
(fma.f64 (-.f64 (/.f64 re im) #s(literal 2 binary64)) re (*.f64 #s(literal 2 binary64) im))
(fma.f64 (fma.f64 (fma.f64 (.f64 re (/.f64 re (pow.f64 im #s(literal 3 binary64)))) #s(literal -1/4 binary64) (/.f64 #s(literal 1 binary64) im)) re #s(literal -2 binary64)) re (.f64 #s(literal 2 binary64) im))
(/.f64 (*.f64 im im) re)
(/.f64 (*.f64 im im) re)
(/.f64 (*.f64 im im) re)
(/.f64 (*.f64 im im) re)
(.f64 (.f64 #s(literal 1/2 binary64) (sqrt.f64 #s(literal 2 binary64))) (sqrt.f64 im))
(fma.f64 (.f64 #s(literal 1/2 binary64) (sqrt.f64 #s(literal 2 binary64))) (sqrt.f64 im) (.f64 (.f64 #s(literal -1/4 binary64) (.f64 (sqrt.f64 #s(literal 2 binary64)) re)) (sqrt.f64 (/.f64 #s(literal 1 binary64) im))))
(fma.f64 (fma.f64 (.f64 #s(literal -1/4 binary64) (sqrt.f64 #s(literal 2 binary64))) (sqrt.f64 (/.f64 #s(literal 1 binary64) im)) (.f64 (.f64 re #s(literal 1/16 binary64)) (.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 im #s(literal 3 binary64)))) (sqrt.f64 #s(literal 2 binary64))))) re (.f64 (.f64 #s(literal 1/2 binary64) (sqrt.f64 #s(literal 2 binary64))) (sqrt.f64 im)))
(fma.f64 (fma.f64 (.f64 #s(literal -1/4 binary64) (sqrt.f64 #s(literal 2 binary64))) (sqrt.f64 (/.f64 #s(literal 1 binary64) im)) (.f64 (fma.f64 (.f64 #s(literal 1/32 binary64) (.f64 (sqrt.f64 #s(literal 2 binary64)) re)) (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 im #s(literal 5 binary64)))) (.f64 (.f64 #s(literal 1/16 binary64) (sqrt.f64 #s(literal 2 binary64))) (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 im #s(literal 3 binary64)))))) re)) re (.f64 (.f64 #s(literal 1/2 binary64) (sqrt.f64 #s(literal 2 binary64))) (sqrt.f64 im)))
(.f64 (.f64 (.f64 #s(literal 1/2 binary64) im) (.f64 (sqrt.f64 #s(literal 1/2 binary64)) (sqrt.f64 #s(literal 2 binary64)))) (sqrt.f64 (/.f64 #s(literal 1 binary64) re)))
(.f64 (.f64 (.f64 #s(literal 1/2 binary64) im) (.f64 (sqrt.f64 #s(literal 1/2 binary64)) (sqrt.f64 #s(literal 2 binary64)))) (sqrt.f64 (/.f64 #s(literal 1 binary64) re)))
(.f64 (.f64 (.f64 #s(literal 1/2 binary64) im) (.f64 (sqrt.f64 #s(literal 1/2 binary64)) (sqrt.f64 #s(literal 2 binary64)))) (sqrt.f64 (/.f64 #s(literal 1 binary64) re)))
(.f64 (.f64 (.f64 #s(literal 1/2 binary64) im) (.f64 (sqrt.f64 #s(literal 1/2 binary64)) (sqrt.f64 #s(literal 2 binary64)))) (sqrt.f64 (/.f64 #s(literal 1 binary64) re)))
(*.f64 (pow.f64 im #s(literal 4 binary64)) (/.f64 #s(literal -1/4 binary64) (pow.f64 re #s(literal 3 binary64))))
(/.f64 (fma.f64 (.f64 (.f64 re re) im) im (*.f64 (pow.f64 im #s(literal 4 binary64)) #s(literal -1/4 binary64))) (pow.f64 re #s(literal 3 binary64)))
(/.f64 (fma.f64 (.f64 (.f64 re re) im) im (*.f64 (pow.f64 im #s(literal 4 binary64)) #s(literal -1/4 binary64))) (pow.f64 re #s(literal 3 binary64)))
(/.f64 (fma.f64 (.f64 (.f64 re re) im) im (*.f64 (pow.f64 im #s(literal 4 binary64)) #s(literal -1/4 binary64))) (pow.f64 re #s(literal 3 binary64)))
(.f64 (.f64 #s(literal 1/2 binary64) (sqrt.f64 #s(literal 2 binary64))) (sqrt.f64 im))
(fma.f64 (.f64 #s(literal 1/2 binary64) (sqrt.f64 #s(literal 2 binary64))) (sqrt.f64 im) (.f64 (.f64 #s(literal -1/4 binary64) (.f64 (sqrt.f64 #s(literal 2 binary64)) re)) (sqrt.f64 (/.f64 #s(literal 1 binary64) im))))
(fma.f64 (fma.f64 (.f64 #s(literal -1/4 binary64) (sqrt.f64 #s(literal 2 binary64))) (sqrt.f64 (/.f64 #s(literal 1 binary64) im)) (.f64 (.f64 re #s(literal 1/16 binary64)) (.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 im #s(literal 3 binary64)))) (sqrt.f64 #s(literal 2 binary64))))) re (.f64 (.f64 #s(literal 1/2 binary64) (sqrt.f64 #s(literal 2 binary64))) (sqrt.f64 im)))
(fma.f64 (fma.f64 (.f64 #s(literal -1/4 binary64) (sqrt.f64 #s(literal 2 binary64))) (sqrt.f64 (/.f64 #s(literal 1 binary64) im)) (.f64 (fma.f64 (.f64 #s(literal 1/32 binary64) (.f64 (sqrt.f64 #s(literal 2 binary64)) re)) (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 im #s(literal 5 binary64)))) (.f64 (.f64 #s(literal 1/16 binary64) (sqrt.f64 #s(literal 2 binary64))) (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 im #s(literal 3 binary64)))))) re)) re (.f64 (.f64 #s(literal 1/2 binary64) (sqrt.f64 #s(literal 2 binary64))) (sqrt.f64 im)))
(*.f64 (sqrt.f64 #s(literal 2 binary64)) (sqrt.f64 im))
(fma.f64 (.f64 re #s(literal -1/2 binary64)) (.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) im)) (sqrt.f64 #s(literal 2 binary64))) (*.f64 (sqrt.f64 #s(literal 2 binary64)) (sqrt.f64 im)))
(fma.f64 (fma.f64 (.f64 re #s(literal 1/8 binary64)) (.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 im #s(literal 3 binary64)))) (sqrt.f64 #s(literal 2 binary64))) (.f64 (.f64 #s(literal -1/2 binary64) (sqrt.f64 #s(literal 2 binary64))) (sqrt.f64 (/.f64 #s(literal 1 binary64) im)))) re (*.f64 (sqrt.f64 #s(literal 2 binary64)) (sqrt.f64 im)))
(fma.f64 (fma.f64 (.f64 #s(literal -1/2 binary64) (sqrt.f64 #s(literal 2 binary64))) (sqrt.f64 (/.f64 #s(literal 1 binary64) im)) (.f64 (fma.f64 (.f64 #s(literal 1/8 binary64) (sqrt.f64 #s(literal 2 binary64))) (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 im #s(literal 3 binary64)))) (.f64 (.f64 #s(literal 1/16 binary64) (.f64 (sqrt.f64 #s(literal 2 binary64)) re)) (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 im #s(literal 5 binary64)))))) re)) re (*.f64 (sqrt.f64 #s(literal 2 binary64)) (sqrt.f64 im)))
(*.f64 #s(literal 2 binary64) im)
(fma.f64 #s(literal -2 binary64) re (*.f64 #s(literal 2 binary64) im))
(fma.f64 (-.f64 (/.f64 re im) #s(literal 2 binary64)) re (*.f64 #s(literal 2 binary64) im))
(fma.f64 (fma.f64 (fma.f64 (.f64 re (/.f64 re (pow.f64 im #s(literal 3 binary64)))) #s(literal -1/4 binary64) (/.f64 #s(literal 1 binary64) im)) re #s(literal -2 binary64)) re (.f64 #s(literal 2 binary64) im))
(sqrt.f64 (/.f64 #s(literal 1 binary64) re))
(sqrt.f64 (/.f64 #s(literal 1 binary64) re))
(sqrt.f64 (/.f64 #s(literal 1 binary64) re))
(sqrt.f64 (/.f64 #s(literal 1 binary64) re))
(*.f64 im (/.f64 im (pow.f64 re #s(literal 3 binary64))))
(*.f64 im (/.f64 im (pow.f64 re #s(literal 3 binary64))))
(*.f64 im (/.f64 im (pow.f64 re #s(literal 3 binary64))))
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(.f64 (neg.f64 im) (fma.f64 (.f64 (.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) im)) #s(literal 1/2 binary64)) (sqrt.f64 #s(literal -1 binary64))) (sqrt.f64 #s(literal 2 binary64)) (fma.f64 (.f64 (.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 im #s(literal 3 binary64)))) #s(literal -1/4 binary64)) (.f64 (sqrt.f64 #s(literal -1 binary64)) (sqrt.f64 #s(literal 2 binary64)))) re (/.f64 (.f64 #s(literal -3/16 binary64) (.f64 (.f64 re (.f64 (sqrt.f64 #s(literal -1 binary64)) re)) (*.f64 (sqrt.f64 #s(literal 2 binary64)) (sqrt.f64 im)))) (pow.f64 im #s(literal 3 binary64))))))
(.f64 (neg.f64 (sqrt.f64 #s(literal -1 binary64))) (.f64 (sqrt.f64 #s(literal 2 binary64)) (sqrt.f64 im)))
(.f64 (neg.f64 im) (fma.f64 (.f64 (sqrt.f64 #s(literal -1 binary64)) (sqrt.f64 (/.f64 #s(literal 1 binary64) im))) (sqrt.f64 #s(literal 2 binary64)) (.f64 (.f64 (.f64 (sqrt.f64 #s(literal -1 binary64)) re) (.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 im #s(literal 3 binary64)))) (sqrt.f64 #s(literal 2 binary64)))) #s(literal -1/2 binary64))))
(.f64 (neg.f64 im) (fma.f64 (.f64 (.f64 (.f64 (.f64 (sqrt.f64 #s(literal 2 binary64)) re) re) (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 im #s(literal 5 binary64))))) (sqrt.f64 #s(literal -1 binary64))) #s(literal -1/4 binary64) (fma.f64 (.f64 (sqrt.f64 #s(literal -1 binary64)) (sqrt.f64 (/.f64 #s(literal 1 binary64) im))) (sqrt.f64 #s(literal 2 binary64)) (.f64 (.f64 (.f64 (sqrt.f64 #s(literal -1 binary64)) re) (.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 im #s(literal 3 binary64)))) (sqrt.f64 #s(literal 2 binary64)))) #s(literal -1/2 binary64)))))
(.f64 (neg.f64 im) (fma.f64 (.f64 (.f64 #s(literal -1/2 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 im #s(literal 3 binary64))))) (.f64 (sqrt.f64 #s(literal -1 binary64)) re)) (sqrt.f64 #s(literal 2 binary64)) (fma.f64 (.f64 (sqrt.f64 #s(literal -1 binary64)) (sqrt.f64 (/.f64 #s(literal 1 binary64) im))) (sqrt.f64 #s(literal 2 binary64)) (/.f64 (.f64 #s(literal -3/8 binary64) (.f64 (.f64 re (.f64 (sqrt.f64 #s(literal -1 binary64)) re)) (.f64 (sqrt.f64 #s(literal 2 binary64)) (sqrt.f64 im)))) (pow.f64 im #s(literal 3 binary64))))))
(*.f64 #s(literal -2 binary64) im)
(.f64 (.f64 (+.f64 (/.f64 re im) #s(literal 1 binary64)) #s(literal -2 binary64)) im)
(.f64 (neg.f64 im) (-.f64 #s(literal 2 binary64) (/.f64 (fma.f64 (neg.f64 re) (/.f64 re im) (.f64 #s(literal -2 binary64) re)) im)))
(.f64 (neg.f64 im) (-.f64 #s(literal 2 binary64) (/.f64 (fma.f64 #s(literal -2 binary64) re (/.f64 (fma.f64 (/.f64 (pow.f64 re #s(literal 4 binary64)) im) (/.f64 #s(literal -1/4 binary64) im) (.f64 re re)) (neg.f64 im))) im)))
(.f64 (.f64 #s(literal -1/2 binary64) (sqrt.f64 im)) (*.f64 (sqrt.f64 #s(literal -1 binary64)) (sqrt.f64 #s(literal 2 binary64))))
(.f64 (neg.f64 im) (fma.f64 (.f64 (sqrt.f64 #s(literal -1 binary64)) (sqrt.f64 (/.f64 #s(literal 1 binary64) im))) (.f64 (sqrt.f64 #s(literal 2 binary64)) #s(literal 1/2 binary64)) (.f64 (.f64 (.f64 (sqrt.f64 #s(literal -1 binary64)) re) (*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 im #s(literal 3 binary64)))) (sqrt.f64 #s(literal 2 binary64)))) #s(literal -1/4 binary64))))
(.f64 (neg.f64 im) (fma.f64 (.f64 (.f64 (.f64 (.f64 (sqrt.f64 #s(literal 2 binary64)) re) re) (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 im #s(literal 5 binary64))))) (sqrt.f64 #s(literal -1 binary64))) #s(literal -1/8 binary64) (fma.f64 (.f64 (sqrt.f64 #s(literal -1 binary64)) (sqrt.f64 (/.f64 #s(literal 1 binary64) im))) (.f64 (sqrt.f64 #s(literal 2 binary64)) #s(literal 1/2 binary64)) (.f64 (.f64 (.f64 (sqrt.f64 #s(literal -1 binary64)) re) (*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 im #s(literal 3 binary64)))) (sqrt.f64 #s(literal 2 binary64)))) #s(literal -1/4 binary64)))))
(.f64 (neg.f64 im) (fma.f64 (.f64 (.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) im)) #s(literal 1/2 binary64)) (sqrt.f64 #s(literal -1 binary64))) (sqrt.f64 #s(literal 2 binary64)) (fma.f64 (.f64 (.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 im #s(literal 3 binary64)))) #s(literal -1/4 binary64)) (.f64 (sqrt.f64 #s(literal -1 binary64)) (sqrt.f64 #s(literal 2 binary64)))) re (/.f64 (.f64 #s(literal -3/16 binary64) (.f64 (.f64 re (.f64 (sqrt.f64 #s(literal -1 binary64)) re)) (*.f64 (sqrt.f64 #s(literal 2 binary64)) (sqrt.f64 im)))) (pow.f64 im #s(literal 3 binary64))))))
(.f64 (neg.f64 (sqrt.f64 #s(literal -1 binary64))) (.f64 (sqrt.f64 #s(literal 2 binary64)) (sqrt.f64 im)))
(.f64 (neg.f64 im) (fma.f64 (.f64 (sqrt.f64 #s(literal -1 binary64)) (sqrt.f64 (/.f64 #s(literal 1 binary64) im))) (sqrt.f64 #s(literal 2 binary64)) (.f64 (.f64 (.f64 (sqrt.f64 #s(literal -1 binary64)) re) (.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 im #s(literal 3 binary64)))) (sqrt.f64 #s(literal 2 binary64)))) #s(literal -1/2 binary64))))
(.f64 (neg.f64 im) (fma.f64 (.f64 (.f64 (.f64 (.f64 (sqrt.f64 #s(literal 2 binary64)) re) re) (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 im #s(literal 5 binary64))))) (sqrt.f64 #s(literal -1 binary64))) #s(literal -1/4 binary64) (fma.f64 (.f64 (sqrt.f64 #s(literal -1 binary64)) (sqrt.f64 (/.f64 #s(literal 1 binary64) im))) (sqrt.f64 #s(literal 2 binary64)) (.f64 (.f64 (.f64 (sqrt.f64 #s(literal -1 binary64)) re) (.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 im #s(literal 3 binary64)))) (sqrt.f64 #s(literal 2 binary64)))) #s(literal -1/2 binary64)))))
(.f64 (neg.f64 im) (fma.f64 (.f64 (.f64 #s(literal -1/2 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 im #s(literal 3 binary64))))) (.f64 (sqrt.f64 #s(literal -1 binary64)) re)) (sqrt.f64 #s(literal 2 binary64)) (fma.f64 (.f64 (sqrt.f64 #s(literal -1 binary64)) (sqrt.f64 (/.f64 #s(literal 1 binary64) im))) (sqrt.f64 #s(literal 2 binary64)) (/.f64 (.f64 #s(literal -3/8 binary64) (.f64 (.f64 re (.f64 (sqrt.f64 #s(literal -1 binary64)) re)) (.f64 (sqrt.f64 #s(literal 2 binary64)) (sqrt.f64 im)))) (pow.f64 im #s(literal 3 binary64))))))
(*.f64 #s(literal -2 binary64) im)
(.f64 (.f64 (+.f64 (/.f64 re im) #s(literal 1 binary64)) #s(literal -2 binary64)) im)
(.f64 (neg.f64 im) (-.f64 #s(literal 2 binary64) (/.f64 (fma.f64 (neg.f64 re) (/.f64 re im) (.f64 #s(literal -2 binary64) re)) im)))
(.f64 (neg.f64 im) (-.f64 #s(literal 2 binary64) (/.f64 (fma.f64 #s(literal -2 binary64) re (/.f64 (fma.f64 (/.f64 (pow.f64 re #s(literal 4 binary64)) im) (/.f64 #s(literal -1/4 binary64) im) (.f64 re re)) (neg.f64 im))) im)))
(/.f64 (*.f64 im im) re)
(/.f64 (*.f64 im im) re)
(/.f64 (*.f64 im im) re)
(/.f64 (*.f64 im im) re)
(.f64 (.f64 #s(literal -1/2 binary64) (sqrt.f64 im)) (*.f64 (sqrt.f64 #s(literal -1 binary64)) (sqrt.f64 #s(literal 2 binary64))))
(.f64 (neg.f64 im) (fma.f64 (.f64 (sqrt.f64 #s(literal -1 binary64)) (sqrt.f64 (/.f64 #s(literal 1 binary64) im))) (.f64 (sqrt.f64 #s(literal 2 binary64)) #s(literal 1/2 binary64)) (.f64 (.f64 (.f64 (sqrt.f64 #s(literal -1 binary64)) re) (*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 im #s(literal 3 binary64)))) (sqrt.f64 #s(literal 2 binary64)))) #s(literal -1/4 binary64))))
(.f64 (neg.f64 im) (fma.f64 (.f64 (.f64 (.f64 (.f64 (sqrt.f64 #s(literal 2 binary64)) re) re) (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 im #s(literal 5 binary64))))) (sqrt.f64 #s(literal -1 binary64))) #s(literal -1/8 binary64) (fma.f64 (.f64 (sqrt.f64 #s(literal -1 binary64)) (sqrt.f64 (/.f64 #s(literal 1 binary64) im))) (.f64 (sqrt.f64 #s(literal 2 binary64)) #s(literal 1/2 binary64)) (.f64 (.f64 (.f64 (sqrt.f64 #s(literal -1 binary64)) re) (*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 im #s(literal 3 binary64)))) (sqrt.f64 #s(literal 2 binary64)))) #s(literal -1/4 binary64)))))
(.f64 (neg.f64 im) (fma.f64 (.f64 (.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) im)) #s(literal 1/2 binary64)) (sqrt.f64 #s(literal -1 binary64))) (sqrt.f64 #s(literal 2 binary64)) (fma.f64 (.f64 (.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 im #s(literal 3 binary64)))) #s(literal -1/4 binary64)) (.f64 (sqrt.f64 #s(literal -1 binary64)) (sqrt.f64 #s(literal 2 binary64)))) re (/.f64 (.f64 #s(literal -3/16 binary64) (.f64 (.f64 re (.f64 (sqrt.f64 #s(literal -1 binary64)) re)) (*.f64 (sqrt.f64 #s(literal 2 binary64)) (sqrt.f64 im)))) (pow.f64 im #s(literal 3 binary64))))))
(.f64 (.f64 (.f64 #s(literal 1/2 binary64) im) (.f64 (sqrt.f64 #s(literal 1/2 binary64)) (sqrt.f64 #s(literal 2 binary64)))) (sqrt.f64 (/.f64 #s(literal 1 binary64) re)))
(.f64 (.f64 (.f64 #s(literal 1/2 binary64) im) (.f64 (sqrt.f64 #s(literal 1/2 binary64)) (sqrt.f64 #s(literal 2 binary64)))) (sqrt.f64 (/.f64 #s(literal 1 binary64) re)))
(.f64 (.f64 (.f64 #s(literal 1/2 binary64) im) (.f64 (sqrt.f64 #s(literal 1/2 binary64)) (sqrt.f64 #s(literal 2 binary64)))) (sqrt.f64 (/.f64 #s(literal 1 binary64) re)))
(.f64 (.f64 (.f64 #s(literal 1/2 binary64) im) (.f64 (sqrt.f64 #s(literal 1/2 binary64)) (sqrt.f64 #s(literal 2 binary64)))) (sqrt.f64 (/.f64 #s(literal 1 binary64) re)))
(.f64 (.f64 #s(literal 1/2 binary64) im) (*.f64 (sqrt.f64 #s(literal 1/2 binary64)) (sqrt.f64 #s(literal 2 binary64))))
(.f64 (.f64 #s(literal 1/2 binary64) im) (*.f64 (sqrt.f64 #s(literal 1/2 binary64)) (sqrt.f64 #s(literal 2 binary64))))
(.f64 (.f64 #s(literal 1/2 binary64) im) (*.f64 (sqrt.f64 #s(literal 1/2 binary64)) (sqrt.f64 #s(literal 2 binary64))))
(.f64 (.f64 #s(literal 1/2 binary64) im) (*.f64 (sqrt.f64 #s(literal 1/2 binary64)) (sqrt.f64 #s(literal 2 binary64))))
(.f64 (.f64 (sqrt.f64 #s(literal 1/2 binary64)) im) #s(literal 1/2 binary64))
(.f64 (.f64 (sqrt.f64 #s(literal 1/2 binary64)) im) #s(literal 1/2 binary64))
(.f64 (.f64 (sqrt.f64 #s(literal 1/2 binary64)) im) #s(literal 1/2 binary64))
(.f64 (.f64 (sqrt.f64 #s(literal 1/2 binary64)) im) #s(literal 1/2 binary64))
(*.f64 (pow.f64 im #s(literal 4 binary64)) (/.f64 #s(literal -1/4 binary64) (pow.f64 re #s(literal 3 binary64))))
(.f64 (-.f64 (/.f64 #s(literal 1 binary64) (.f64 (*.f64 im im) re)) (/.f64 #s(literal 1/4 binary64) (pow.f64 re #s(literal 3 binary64)))) (pow.f64 im #s(literal 4 binary64)))
(.f64 (-.f64 (/.f64 #s(literal 1 binary64) (.f64 (*.f64 im im) re)) (/.f64 #s(literal 1/4 binary64) (pow.f64 re #s(literal 3 binary64)))) (pow.f64 im #s(literal 4 binary64)))
(.f64 (-.f64 (/.f64 #s(literal 1 binary64) (.f64 (*.f64 im im) re)) (/.f64 #s(literal 1/4 binary64) (pow.f64 re #s(literal 3 binary64)))) (pow.f64 im #s(literal 4 binary64)))
(.f64 (.f64 #s(literal -1/2 binary64) (sqrt.f64 im)) (*.f64 (sqrt.f64 #s(literal -1 binary64)) (sqrt.f64 #s(literal 2 binary64))))
(.f64 (neg.f64 im) (fma.f64 (.f64 (sqrt.f64 #s(literal -1 binary64)) (sqrt.f64 (/.f64 #s(literal 1 binary64) im))) (.f64 (sqrt.f64 #s(literal 2 binary64)) #s(literal 1/2 binary64)) (.f64 (.f64 (.f64 (sqrt.f64 #s(literal -1 binary64)) re) (*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 im #s(literal 3 binary64)))) (sqrt.f64 #s(literal 2 binary64)))) #s(literal -1/4 binary64))))
(.f64 (neg.f64 im) (fma.f64 (.f64 (.f64 (.f64 (.f64 (sqrt.f64 #s(literal 2 binary64)) re) re) (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 im #s(literal 5 binary64))))) (sqrt.f64 #s(literal -1 binary64))) #s(literal -1/8 binary64) (fma.f64 (.f64 (sqrt.f64 #s(literal -1 binary64)) (sqrt.f64 (/.f64 #s(literal 1 binary64) im))) (.f64 (sqrt.f64 #s(literal 2 binary64)) #s(literal 1/2 binary64)) (.f64 (.f64 (.f64 (sqrt.f64 #s(literal -1 binary64)) re) (*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 im #s(literal 3 binary64)))) (sqrt.f64 #s(literal 2 binary64)))) #s(literal -1/4 binary64)))))
(.f64 (neg.f64 im) (fma.f64 (.f64 (.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) im)) #s(literal 1/2 binary64)) (sqrt.f64 #s(literal -1 binary64))) (sqrt.f64 #s(literal 2 binary64)) (fma.f64 (.f64 (.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 im #s(literal 3 binary64)))) #s(literal -1/4 binary64)) (.f64 (sqrt.f64 #s(literal -1 binary64)) (sqrt.f64 #s(literal 2 binary64)))) re (/.f64 (.f64 #s(literal -3/16 binary64) (.f64 (.f64 re (.f64 (sqrt.f64 #s(literal -1 binary64)) re)) (*.f64 (sqrt.f64 #s(literal 2 binary64)) (sqrt.f64 im)))) (pow.f64 im #s(literal 3 binary64))))))
(.f64 (neg.f64 (sqrt.f64 #s(literal -1 binary64))) (.f64 (sqrt.f64 #s(literal 2 binary64)) (sqrt.f64 im)))
(.f64 (neg.f64 im) (fma.f64 (.f64 (sqrt.f64 #s(literal -1 binary64)) (sqrt.f64 (/.f64 #s(literal 1 binary64) im))) (sqrt.f64 #s(literal 2 binary64)) (.f64 (.f64 (.f64 (sqrt.f64 #s(literal -1 binary64)) re) (.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 im #s(literal 3 binary64)))) (sqrt.f64 #s(literal 2 binary64)))) #s(literal -1/2 binary64))))
(.f64 (neg.f64 im) (fma.f64 (.f64 (.f64 (.f64 (.f64 (sqrt.f64 #s(literal 2 binary64)) re) re) (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 im #s(literal 5 binary64))))) (sqrt.f64 #s(literal -1 binary64))) #s(literal -1/4 binary64) (fma.f64 (.f64 (sqrt.f64 #s(literal -1 binary64)) (sqrt.f64 (/.f64 #s(literal 1 binary64) im))) (sqrt.f64 #s(literal 2 binary64)) (.f64 (.f64 (.f64 (sqrt.f64 #s(literal -1 binary64)) re) (.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 im #s(literal 3 binary64)))) (sqrt.f64 #s(literal 2 binary64)))) #s(literal -1/2 binary64)))))
(.f64 (neg.f64 im) (fma.f64 (.f64 (.f64 #s(literal -1/2 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 im #s(literal 3 binary64))))) (.f64 (sqrt.f64 #s(literal -1 binary64)) re)) (sqrt.f64 #s(literal 2 binary64)) (fma.f64 (.f64 (sqrt.f64 #s(literal -1 binary64)) (sqrt.f64 (/.f64 #s(literal 1 binary64) im))) (sqrt.f64 #s(literal 2 binary64)) (/.f64 (.f64 #s(literal -3/8 binary64) (.f64 (.f64 re (.f64 (sqrt.f64 #s(literal -1 binary64)) re)) (.f64 (sqrt.f64 #s(literal 2 binary64)) (sqrt.f64 im)))) (pow.f64 im #s(literal 3 binary64))))))
(*.f64 #s(literal -2 binary64) im)
(.f64 (.f64 (+.f64 (/.f64 re im) #s(literal 1 binary64)) #s(literal -2 binary64)) im)
(.f64 (neg.f64 im) (-.f64 #s(literal 2 binary64) (/.f64 (fma.f64 (neg.f64 re) (/.f64 re im) (.f64 #s(literal -2 binary64) re)) im)))
(.f64 (neg.f64 im) (-.f64 #s(literal 2 binary64) (/.f64 (fma.f64 #s(literal -2 binary64) re (/.f64 (fma.f64 (/.f64 (pow.f64 re #s(literal 4 binary64)) im) (/.f64 #s(literal -1/4 binary64) im) (.f64 re re)) (neg.f64 im))) im)))
(*.f64 (sqrt.f64 #s(literal 1/2 binary64)) im)
(*.f64 (sqrt.f64 #s(literal 1/2 binary64)) im)
(*.f64 (sqrt.f64 #s(literal 1/2 binary64)) im)
(*.f64 (sqrt.f64 #s(literal 1/2 binary64)) im)
(*.f64 im (/.f64 im (pow.f64 re #s(literal 3 binary64))))
(*.f64 im (/.f64 im (pow.f64 re #s(literal 3 binary64))))
(*.f64 im (/.f64 im (pow.f64 re #s(literal 3 binary64))))
(*.f64 im (/.f64 im (pow.f64 re #s(literal 3 binary64))))

rewrite180.0ms (2.5%)

Memory

15.1MiB live, 170.2MiB allocated

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	47	329
0	76	279
1	214	274
2	1073	255
0	8351	255

Stop Event

1×	iter limit
1×	node limit
1×	iter limit

Counts

23 → 380

Calls

Call 1

Inputs
(.f64 (sqrt.f64 (.f64 (-.f64 (hypot.f64 im re) re) #s(literal 2 binary64))) #s(literal 1/2 binary64))
(sqrt.f64 (*.f64 (-.f64 (hypot.f64 im re) re) #s(literal 2 binary64)))
(*.f64 (-.f64 (hypot.f64 im re) re) #s(literal 2 binary64))
(-.f64 (hypot.f64 im re) re)
(.f64 #s(literal 1/2 binary64) (sqrt.f64 #s(approx ( 2 (- (sqrt (+ (* re re) (* im im))) re)) (*.f64 #s(literal -4 binary64) re))))
(sqrt.f64 #s(approx (* 2 (- (sqrt (+ (* re re) (* im im))) re)) (*.f64 #s(literal -4 binary64) re)))
#s(approx (* 2 (- (sqrt (+ (* re re) (* im im))) re)) (*.f64 #s(literal -4 binary64) re))
(*.f64 #s(literal -4 binary64) re)
(.f64 #s(literal 1/2 binary64) (sqrt.f64 #s(approx ( 2 (- (sqrt (+ (* re re) (* im im))) re)) (/.f64 (*.f64 im im) re))))
(sqrt.f64 #s(approx (* 2 (- (sqrt (+ (* re re) (* im im))) re)) (/.f64 (*.f64 im im) re)))
#s(approx (* 2 (- (sqrt (+ (* re re) (* im im))) re)) (/.f64 (*.f64 im im) re))
(/.f64 (*.f64 im im) re)
#s(approx (* 1/2 (sqrt (* 2 (- (sqrt (+ (* re re) (* im im))) re)))) (.f64 (.f64 (.f64 #s(literal 1/2 binary64) (.f64 im (sqrt.f64 #s(literal 1/2 binary64)))) (sqrt.f64 #s(literal 2 binary64))) (sqrt.f64 (/.f64 #s(literal 1 binary64) re))))
(.f64 (.f64 (.f64 #s(literal 1/2 binary64) (.f64 im (sqrt.f64 #s(literal 1/2 binary64)))) (sqrt.f64 #s(literal 2 binary64))) (sqrt.f64 (/.f64 #s(literal 1 binary64) re)))
(.f64 (.f64 #s(literal 1/2 binary64) (*.f64 im (sqrt.f64 #s(literal 1/2 binary64)))) (sqrt.f64 #s(literal 2 binary64)))
(.f64 #s(literal 1/2 binary64) (.f64 im (sqrt.f64 #s(literal 1/2 binary64))))
(.f64 (fma.f64 (.f64 im (/.f64 im (pow.f64 re #s(literal 3 binary64)))) #s(literal -1/4 binary64) (/.f64 #s(literal 1 binary64) re)) (*.f64 im im))
(.f64 #s(literal 1/2 binary64) (sqrt.f64 #s(approx ( 2 (- (sqrt (+ (* re re) (* im im))) re)) (.f64 (fma.f64 (.f64 im (/.f64 im (pow.f64 re #s(literal 3 binary64)))) #s(literal -1/4 binary64) (/.f64 #s(literal 1 binary64) re)) (*.f64 im im)))))
(sqrt.f64 #s(approx (* 2 (- (sqrt (+ (* re re) (* im im))) re)) (.f64 (fma.f64 (.f64 im (/.f64 im (pow.f64 re #s(literal 3 binary64)))) #s(literal -1/4 binary64) (/.f64 #s(literal 1 binary64) re)) (*.f64 im im))))
#s(approx (* 2 (- (sqrt (+ (* re re) (* im im))) re)) (.f64 (fma.f64 (.f64 im (/.f64 im (pow.f64 re #s(literal 3 binary64)))) #s(literal -1/4 binary64) (/.f64 #s(literal 1 binary64) re)) (*.f64 im im)))
(*.f64 im (sqrt.f64 #s(literal 1/2 binary64)))
(sqrt.f64 (/.f64 #s(literal 1 binary64) re))
(*.f64 im (/.f64 im (pow.f64 re #s(literal 3 binary64))))

Outputs
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eval143.0ms (2%)

Memory: -29.3MiB live, 135.3MiB allocated
Compiler: Compiled 32 699 to 2 735 computations (91.6% saved)

prune51.0ms (0.7%)

Memory

32.5MiB live, 71.1MiB allocated

Pruning

17 alts after pruning (14 fresh and 3 done)

	Pruned	Kept	Total
New	858	12	870
Fresh	9	2	11
Picked	2	3	5
Done	0	0	0
Total	869	17	886

Accuracy

99.6%

Counts

886 → 17

Alt Table

Click to see full alt table

Status	Accuracy	Program
▶	79.8%	(.f64 (.f64 (sqrt.f64 (-.f64 (hypot.f64 re im) re)) (sqrt.f64 #s(literal 2 binary64))) #s(literal 1/2 binary64))
	76.6%	(.f64 (sqrt.f64 (.f64 (fma.f64 (sqrt.f64 (hypot.f64 re im)) (sqrt.f64 (hypot.f64 re im)) (neg.f64 re)) #s(literal 2 binary64))) #s(literal 1/2 binary64))
✓	79.9%	(.f64 (sqrt.f64 (.f64 (-.f64 (hypot.f64 im re) re) #s(literal 2 binary64))) #s(literal 1/2 binary64))
	53.6%	(.f64 (sqrt.f64 (.f64 #s(approx (- (sqrt (+ (* im im) (* re re))) re) (-.f64 im re)) #s(literal 2 binary64))) #s(literal 1/2 binary64))
	51.1%	(.f64 (sqrt.f64 #s(approx ( (- (sqrt (+ (* im im) (* re re))) re) 2) (fma.f64 (-.f64 (/.f64 re im) #s(literal 2 binary64)) re (*.f64 #s(literal 2 binary64) im)))) #s(literal 1/2 binary64))
▶	52.5%	(.f64 (sqrt.f64 #s(approx ( (- (sqrt (+ (* im im) (* re re))) re) 2) (*.f64 (fma.f64 (/.f64 re im) #s(literal -2 binary64) #s(literal 2 binary64)) im))) #s(literal 1/2 binary64))
▶	51.0%	(.f64 (sqrt.f64 #s(approx ( (- (sqrt (+ (* im im) (* re re))) re) 2) (*.f64 #s(literal 2 binary64) im))) #s(literal 1/2 binary64))
▶	51.0%	(.f64 #s(approx (sqrt ( (- (sqrt (+ (* im im) (* re re))) re) 2)) (*.f64 (sqrt.f64 #s(literal 2 binary64)) (sqrt.f64 im))) #s(literal 1/2 binary64))
	37.6%	(.f64 #s(literal 1/2 binary64) (sqrt.f64 (.f64 #s(literal 2 binary64) (-.f64 (sqrt.f64 (fma.f64 re re (*.f64 im im))) re))))
	29.9%	(.f64 #s(literal 1/2 binary64) (sqrt.f64 (.f64 #s(literal 2 binary64) (-.f64 (sqrt.f64 #s(approx (+ (* re re) (* im im)) (.f64 (.f64 (fma.f64 (/.f64 re im) (/.f64 re im) #s(literal 1 binary64)) im) im))) re))))
✓	12.9%	(.f64 #s(literal 1/2 binary64) (sqrt.f64 #s(approx ( 2 (- (sqrt (+ (* re re) (* im im))) re)) (/.f64 (*.f64 im im) re))))
✓	28.1%	(.f64 #s(literal 1/2 binary64) (sqrt.f64 #s(approx ( 2 (- (sqrt (+ (* re re) (* im im))) re)) (*.f64 #s(literal -4 binary64) re))))
	50.3%	#s(approx (* (sqrt (* (- (sqrt (+ (* im im) (* re re))) re) 2)) 1/2) (fma.f64 (.f64 #s(literal 1/2 binary64) (sqrt.f64 #s(literal 2 binary64))) (sqrt.f64 im) (.f64 (.f64 #s(literal -1/4 binary64) (.f64 (sqrt.f64 #s(literal 2 binary64)) re)) (sqrt.f64 (/.f64 #s(literal 1 binary64) im)))))
	24.7%	#s(approx (* 1/2 (sqrt (* 2 (- (sqrt (+ (* re re) (* im im))) re)))) (/.f64 (*.f64 #s(literal 1/2 binary64) im) (sqrt.f64 re)))
	24.6%	#s(approx (* 1/2 (sqrt (* 2 (- (sqrt (+ (* re re) (* im im))) re)))) (/.f64 #s(literal 1 binary64) (/.f64 (sqrt.f64 re) (*.f64 #s(literal 1/2 binary64) im))))
▶	24.7%	#s(approx (* 1/2 (sqrt (* 2 (- (sqrt (+ (* re re) (* im im))) re)))) (.f64 (.f64 (sqrt.f64 #s(literal 1/2 binary64)) im) (*.f64 #s(literal 1/2 binary64) (sqrt.f64 (/.f64 #s(literal 2 binary64) re)))))
	24.7%	#s(approx (* 1/2 (sqrt (* 2 (- (sqrt (+ (* re re) (* im im))) re)))) (.f64 (.f64 im #s(literal 1/2 binary64)) (sqrt.f64 (/.f64 #s(literal 1 binary64) re))))

Compiler

Compiled 668 to 507 computations (24.1% saved)

simplify109.0ms (1.5%)

Memory

-0.8MiB live, 75.6MiB allocated

Algorithm

1×	egg-herbie

Localize:

Found 20 expressions of interest:

New	Metric	Score
cost-diff	0	(sqrt.f64 #s(literal 1/2 binary64))
cost-diff	0	(*.f64 (sqrt.f64 #s(literal 1/2 binary64)) im)
cost-diff	0	(.f64 (.f64 (sqrt.f64 #s(literal 1/2 binary64)) im) (*.f64 #s(literal 1/2 binary64) (sqrt.f64 (/.f64 #s(literal 2 binary64) re))))
cost-diff	0	#s(approx (* 1/2 (sqrt (* 2 (- (sqrt (+ (* re re) (* im im))) re)))) (.f64 (.f64 (sqrt.f64 #s(literal 1/2 binary64)) im) (*.f64 #s(literal 1/2 binary64) (sqrt.f64 (/.f64 #s(literal 2 binary64) re)))))
cost-diff	0	#s(approx (* (- (sqrt (+ (* im im) (* re re))) re) 2) (*.f64 (fma.f64 (/.f64 re im) #s(literal -2 binary64) #s(literal 2 binary64)) im))
cost-diff	0	(sqrt.f64 #s(approx (* (- (sqrt (+ (* im im) (* re re))) re) 2) (*.f64 (fma.f64 (/.f64 re im) #s(literal -2 binary64) #s(literal 2 binary64)) im)))
cost-diff	0	(.f64 (sqrt.f64 #s(approx ( (- (sqrt (+ (* im im) (* re re))) re) 2) (*.f64 (fma.f64 (/.f64 re im) #s(literal -2 binary64) #s(literal 2 binary64)) im))) #s(literal 1/2 binary64))
cost-diff	896	(*.f64 (fma.f64 (/.f64 re im) #s(literal -2 binary64) #s(literal 2 binary64)) im)
cost-diff	0	(sqrt.f64 #s(literal 2 binary64))
cost-diff	0	(*.f64 (sqrt.f64 #s(literal 2 binary64)) (sqrt.f64 im))
cost-diff	0	#s(approx (sqrt (* (- (sqrt (+ (* im im) (* re re))) re) 2)) (*.f64 (sqrt.f64 #s(literal 2 binary64)) (sqrt.f64 im)))
cost-diff	0	(.f64 #s(approx (sqrt ( (- (sqrt (+ (* im im) (* re re))) re) 2)) (*.f64 (sqrt.f64 #s(literal 2 binary64)) (sqrt.f64 im))) #s(literal 1/2 binary64))
cost-diff	0	(*.f64 #s(literal 2 binary64) im)
cost-diff	0	#s(approx (* (- (sqrt (+ (* im im) (* re re))) re) 2) (*.f64 #s(literal 2 binary64) im))
cost-diff	0	(sqrt.f64 #s(approx (* (- (sqrt (+ (* im im) (* re re))) re) 2) (*.f64 #s(literal 2 binary64) im)))
cost-diff	0	(.f64 (sqrt.f64 #s(approx ( (- (sqrt (+ (* im im) (* re re))) re) 2) (*.f64 #s(literal 2 binary64) im))) #s(literal 1/2 binary64))
cost-diff	0	(-.f64 (hypot.f64 re im) re)
cost-diff	0	(sqrt.f64 (-.f64 (hypot.f64 re im) re))
cost-diff	0	(*.f64 (sqrt.f64 (-.f64 (hypot.f64 re im) re)) (sqrt.f64 #s(literal 2 binary64)))
cost-diff	0	(.f64 (.f64 (sqrt.f64 (-.f64 (hypot.f64 re im) re)) (sqrt.f64 #s(literal 2 binary64))) #s(literal 1/2 binary64))

Iterations

Useful iterations: 6 (0.0ms)

Iter	Nodes	Cost
0	45	295
0	69	255
1	97	255
2	146	255
3	217	255
4	294	251
5	420	247
6	744	243
7	1601	243
8	3264	243
9	5502	243
10	7762	243
0	8201	243

Stop Event

1×	iter limit
1×	node limit
1×	iter limit

Calls

Call 1

Inputs
(.f64 (.f64 (sqrt.f64 (-.f64 (hypot.f64 re im) re)) (sqrt.f64 #s(literal 2 binary64))) #s(literal 1/2 binary64))
(*.f64 (sqrt.f64 (-.f64 (hypot.f64 re im) re)) (sqrt.f64 #s(literal 2 binary64)))
(sqrt.f64 (-.f64 (hypot.f64 re im) re))
(-.f64 (hypot.f64 re im) re)
(hypot.f64 re im)
re
im
(sqrt.f64 #s(literal 2 binary64))
#s(literal 2 binary64)
#s(literal 1/2 binary64)
(.f64 (sqrt.f64 #s(approx ( (- (sqrt (+ (* im im) (* re re))) re) 2) (*.f64 #s(literal 2 binary64) im))) #s(literal 1/2 binary64))
(sqrt.f64 #s(approx (* (- (sqrt (+ (* im im) (* re re))) re) 2) (*.f64 #s(literal 2 binary64) im)))
#s(approx (* (- (sqrt (+ (* im im) (* re re))) re) 2) (*.f64 #s(literal 2 binary64) im))
(*.f64 #s(literal 2 binary64) im)
#s(literal 2 binary64)
im
#s(literal 1/2 binary64)
(.f64 #s(approx (sqrt ( (- (sqrt (+ (* im im) (* re re))) re) 2)) (*.f64 (sqrt.f64 #s(literal 2 binary64)) (sqrt.f64 im))) #s(literal 1/2 binary64))
#s(approx (sqrt (* (- (sqrt (+ (* im im) (* re re))) re) 2)) (*.f64 (sqrt.f64 #s(literal 2 binary64)) (sqrt.f64 im)))
(*.f64 (sqrt.f64 #s(literal 2 binary64)) (sqrt.f64 im))
(sqrt.f64 #s(literal 2 binary64))
#s(literal 2 binary64)
(sqrt.f64 im)
im
#s(literal 1/2 binary64)
(.f64 (sqrt.f64 #s(approx ( (- (sqrt (+ (* im im) (* re re))) re) 2) (*.f64 (fma.f64 (/.f64 re im) #s(literal -2 binary64) #s(literal 2 binary64)) im))) #s(literal 1/2 binary64))
(sqrt.f64 #s(approx (* (- (sqrt (+ (* im im) (* re re))) re) 2) (*.f64 (fma.f64 (/.f64 re im) #s(literal -2 binary64) #s(literal 2 binary64)) im)))
#s(approx (* (- (sqrt (+ (* im im) (* re re))) re) 2) (*.f64 (fma.f64 (/.f64 re im) #s(literal -2 binary64) #s(literal 2 binary64)) im))
(*.f64 (fma.f64 (/.f64 re im) #s(literal -2 binary64) #s(literal 2 binary64)) im)
(fma.f64 (/.f64 re im) #s(literal -2 binary64) #s(literal 2 binary64))
(/.f64 re im)
re
im
#s(literal -2 binary64)
#s(literal 2 binary64)
#s(literal 1/2 binary64)
#s(approx (* 1/2 (sqrt (* 2 (- (sqrt (+ (* re re) (* im im))) re)))) (.f64 (.f64 (sqrt.f64 #s(literal 1/2 binary64)) im) (*.f64 #s(literal 1/2 binary64) (sqrt.f64 (/.f64 #s(literal 2 binary64) re)))))
(.f64 (.f64 (sqrt.f64 #s(literal 1/2 binary64)) im) (*.f64 #s(literal 1/2 binary64) (sqrt.f64 (/.f64 #s(literal 2 binary64) re))))
(*.f64 (sqrt.f64 #s(literal 1/2 binary64)) im)
(sqrt.f64 #s(literal 1/2 binary64))
#s(literal 1/2 binary64)
im
(*.f64 #s(literal 1/2 binary64) (sqrt.f64 (/.f64 #s(literal 2 binary64) re)))
(sqrt.f64 (/.f64 #s(literal 2 binary64) re))
(/.f64 #s(literal 2 binary64) re)
#s(literal 2 binary64)
re

Outputs
(.f64 (.f64 #s(literal 1/2 binary64) (sqrt.f64 #s(literal 2 binary64))) (sqrt.f64 (-.f64 (hypot.f64 im re) re)))
(*.f64 (sqrt.f64 #s(literal 2 binary64)) (sqrt.f64 (-.f64 (hypot.f64 im re) re)))
(sqrt.f64 (-.f64 (hypot.f64 im re) re))
(-.f64 (hypot.f64 im re) re)
(hypot.f64 im re)
re
im
(sqrt.f64 #s(literal 2 binary64))
#s(literal 2 binary64)
#s(literal 1/2 binary64)
(.f64 (sqrt.f64 #s(approx ( (- (sqrt (+ (* im im) (* re re))) re) 2) (*.f64 #s(literal 2 binary64) im))) #s(literal 1/2 binary64))
(sqrt.f64 #s(approx (* (- (sqrt (+ (* im im) (* re re))) re) 2) (*.f64 #s(literal 2 binary64) im)))
#s(approx (* (- (sqrt (+ (* im im) (* re re))) re) 2) (*.f64 #s(literal 2 binary64) im))
(*.f64 #s(literal 2 binary64) im)
#s(literal 2 binary64)
im
#s(literal 1/2 binary64)
(.f64 #s(approx (sqrt ( (- (sqrt (+ (* im im) (* re re))) re) 2)) (*.f64 (sqrt.f64 im) (sqrt.f64 #s(literal 2 binary64)))) #s(literal 1/2 binary64))
#s(approx (sqrt (* (- (sqrt (+ (* im im) (* re re))) re) 2)) (*.f64 (sqrt.f64 im) (sqrt.f64 #s(literal 2 binary64))))
(*.f64 (sqrt.f64 im) (sqrt.f64 #s(literal 2 binary64)))
(sqrt.f64 #s(literal 2 binary64))
#s(literal 2 binary64)
(sqrt.f64 im)
im
#s(literal 1/2 binary64)
(.f64 (sqrt.f64 #s(approx ( (- (sqrt (+ (* im im) (* re re))) re) 2) (*.f64 (-.f64 re im) #s(literal -2 binary64)))) #s(literal 1/2 binary64))
(sqrt.f64 #s(approx (* (- (sqrt (+ (* im im) (* re re))) re) 2) (*.f64 (-.f64 re im) #s(literal -2 binary64))))
#s(approx (* (- (sqrt (+ (* im im) (* re re))) re) 2) (*.f64 (-.f64 re im) #s(literal -2 binary64)))
(*.f64 (-.f64 re im) #s(literal -2 binary64))
(fma.f64 #s(literal -2 binary64) (/.f64 re im) #s(literal 2 binary64))
(/.f64 re im)
re
im
#s(literal -2 binary64)
#s(literal 2 binary64)
#s(literal 1/2 binary64)
#s(approx (* 1/2 (sqrt (* 2 (- (sqrt (+ (* re re) (* im im))) re)))) (.f64 (.f64 (*.f64 (sqrt.f64 #s(literal 1/2 binary64)) im) #s(literal 1/2 binary64)) (sqrt.f64 (/.f64 #s(literal 2 binary64) re))))
(.f64 (.f64 (*.f64 (sqrt.f64 #s(literal 1/2 binary64)) im) #s(literal 1/2 binary64)) (sqrt.f64 (/.f64 #s(literal 2 binary64) re)))
(*.f64 (sqrt.f64 #s(literal 1/2 binary64)) im)
(sqrt.f64 #s(literal 1/2 binary64))
#s(literal 1/2 binary64)
im
(*.f64 (sqrt.f64 (/.f64 #s(literal 2 binary64) re)) #s(literal 1/2 binary64))
(sqrt.f64 (/.f64 #s(literal 2 binary64) re))
(/.f64 #s(literal 2 binary64) re)
#s(literal 2 binary64)
re

localize157.0ms (2.2%)

Memory

-7.4MiB live, 234.6MiB allocated

Localize:

Found 20 expressions of interest:

New	Metric	Score
accuracy	0.05859375	(sqrt.f64 (/.f64 #s(literal 2 binary64) re))
accuracy	0.16796875	(.f64 (.f64 (sqrt.f64 #s(literal 1/2 binary64)) im) (*.f64 #s(literal 1/2 binary64) (sqrt.f64 (/.f64 #s(literal 2 binary64) re))))
accuracy	0.21875	(*.f64 (sqrt.f64 #s(literal 1/2 binary64)) im)
accuracy	14.421590660575248	#s(approx (* 1/2 (sqrt (* 2 (- (sqrt (+ (* re re) (* im im))) re)))) (.f64 (.f64 (sqrt.f64 #s(literal 1/2 binary64)) im) (*.f64 #s(literal 1/2 binary64) (sqrt.f64 (/.f64 #s(literal 2 binary64) re)))))
accuracy	0.00390625	(.f64 (sqrt.f64 #s(approx ( (- (sqrt (+ (* im im) (* re re))) re) 2) (*.f64 (fma.f64 (/.f64 re im) #s(literal -2 binary64) #s(literal 2 binary64)) im))) #s(literal 1/2 binary64))
accuracy	3.300640611041868	(*.f64 (fma.f64 (/.f64 re im) #s(literal -2 binary64) #s(literal 2 binary64)) im)
accuracy	5.117546358106111	(sqrt.f64 #s(approx (* (- (sqrt (+ (* im im) (* re re))) re) 2) (*.f64 (fma.f64 (/.f64 re im) #s(literal -2 binary64) #s(literal 2 binary64)) im)))
accuracy	14.910277075647457	#s(approx (* (- (sqrt (+ (* im im) (* re re))) re) 2) (*.f64 (fma.f64 (/.f64 re im) #s(literal -2 binary64) #s(literal 2 binary64)) im))
accuracy	0	(sqrt.f64 #s(literal 2 binary64))
accuracy	0.00390625	(.f64 #s(approx (sqrt ( (- (sqrt (+ (* im im) (* re re))) re) 2)) (*.f64 (sqrt.f64 #s(literal 2 binary64)) (sqrt.f64 im))) #s(literal 1/2 binary64))
accuracy	0.20541000976844204	(*.f64 (sqrt.f64 #s(literal 2 binary64)) (sqrt.f64 im))
accuracy	14.350717642855344	#s(approx (sqrt (* (- (sqrt (+ (* im im) (* re re))) re) 2)) (*.f64 (sqrt.f64 #s(literal 2 binary64)) (sqrt.f64 im)))
accuracy	0	(*.f64 #s(literal 2 binary64) im)
accuracy	0.00390625	(.f64 (sqrt.f64 #s(approx ( (- (sqrt (+ (* im im) (* re re))) re) 2) (*.f64 #s(literal 2 binary64) im))) #s(literal 1/2 binary64))
accuracy	5.117546358106111	(sqrt.f64 #s(approx (* (- (sqrt (+ (* im im) (* re re))) re) 2) (*.f64 #s(literal 2 binary64) im)))
accuracy	14.40843990491833	#s(approx (* (- (sqrt (+ (* im im) (* re re))) re) 2) (*.f64 #s(literal 2 binary64) im))
accuracy	0.00390625	(.f64 (.f64 (sqrt.f64 (-.f64 (hypot.f64 re im) re)) (sqrt.f64 #s(literal 2 binary64))) #s(literal 1/2 binary64))
accuracy	0.18197250976844204	(*.f64 (sqrt.f64 (-.f64 (hypot.f64 re im) re)) (sqrt.f64 #s(literal 2 binary64)))
accuracy	4.886514455804674	(sqrt.f64 (-.f64 (hypot.f64 re im) re))
accuracy	7.3612157203664905	(-.f64 (hypot.f64 re im) re)

Samples

45.0ms	134×	0	invalid
44.0ms	25×	2	valid
18.0ms	62×	0	valid
10.0ms	12×	3	valid
10.0ms	22×	1	valid
1.0ms	1×	5	exit

Compiler

Compiled 566 to 81 computations (85.7% saved)

Precisions

Click to see histograms. Total time spent on operations: 93.0ms

ival-mult: 52.0ms (55.8% of total)

ival-hypot: 16.0ms (17.2% of total)

ival-sqrt: 13.0ms (13.9% of total)

ival-div: 4.0ms (4.3% of total)

adjust: 3.0ms (3.2% of total)

ival-sub: 3.0ms (3.2% of total)

ival-add: 1.0ms (1.1% of total)

ival-assert: 0.0ms (0% of total)

ival-true: 0.0ms (0% of total)

exact: 0.0ms (0% of total)

series75.0ms (1%)

Memory

-11.6MiB live, 65.0MiB allocated

Counts

21 → 408

Calls

Call 1

Inputs
#s(alt #<batchref> (patch (.f64 (.f64 (sqrt.f64 (-.f64 (hypot.f64 re im) re)) (sqrt.f64 #s(literal 2 binary64))) #s(literal 1/2 binary64)) #<representation binary64>) () ())
#s(alt #<batchref> (patch (*.f64 (sqrt.f64 (-.f64 (hypot.f64 re im) re)) (sqrt.f64 #s(literal 2 binary64))) #<representation binary64>) () ())
#s(alt #<batchref> (patch (sqrt.f64 (-.f64 (hypot.f64 re im) re)) #<representation binary64>) () ())
#s(alt #<batchref> (patch (-.f64 (hypot.f64 re im) re) #<representation binary64>) () ())
#s(alt #<batchref> (patch (.f64 (sqrt.f64 #s(approx ( (- (sqrt (+ (* im im) (* re re))) re) 2) (*.f64 #s(literal 2 binary64) im))) #s(literal 1/2 binary64)) #<representation binary64>) () ())
#s(alt #<batchref> (patch (sqrt.f64 #s(approx (* (- (sqrt (+ (* im im) (* re re))) re) 2) (*.f64 #s(literal 2 binary64) im))) #<representation binary64>) () ())
#s(alt #<batchref> (patch #s(approx (* (- (sqrt (+ (* im im) (* re re))) re) 2) (*.f64 #s(literal 2 binary64) im)) #<representation binary64>) () ())
#s(alt #<batchref> (patch (*.f64 #s(literal 2 binary64) im) #<representation binary64>) () ())
#s(alt #<batchref> (patch (.f64 #s(approx (sqrt ( (- (sqrt (+ (* im im) (* re re))) re) 2)) (*.f64 (sqrt.f64 #s(literal 2 binary64)) (sqrt.f64 im))) #s(literal 1/2 binary64)) #<representation binary64>) () ())
#s(alt #<batchref> (patch #s(approx (sqrt (* (- (sqrt (+ (* im im) (* re re))) re) 2)) (*.f64 (sqrt.f64 #s(literal 2 binary64)) (sqrt.f64 im))) #<representation binary64>) () ())
#s(alt #<batchref> (patch (*.f64 (sqrt.f64 #s(literal 2 binary64)) (sqrt.f64 im)) #<representation binary64>) () ())
#s(alt #<batchref> (patch (sqrt.f64 #s(literal 2 binary64)) #<representation binary64>) () ())
#s(alt #<batchref> (patch (*.f64 (fma.f64 (/.f64 re im) #s(literal -2 binary64) #s(literal 2 binary64)) im) #<representation binary64>) () ())
#s(alt #<batchref> (patch (.f64 (sqrt.f64 #s(approx ( (- (sqrt (+ (* im im) (* re re))) re) 2) (*.f64 (fma.f64 (/.f64 re im) #s(literal -2 binary64) #s(literal 2 binary64)) im))) #s(literal 1/2 binary64)) #<representation binary64>) () ())
#s(alt #<batchref> (patch (sqrt.f64 #s(approx (* (- (sqrt (+ (* im im) (* re re))) re) 2) (*.f64 (fma.f64 (/.f64 re im) #s(literal -2 binary64) #s(literal 2 binary64)) im))) #<representation binary64>) () ())
#s(alt #<batchref> (patch #s(approx (* (- (sqrt (+ (* im im) (* re re))) re) 2) (*.f64 (fma.f64 (/.f64 re im) #s(literal -2 binary64) #s(literal 2 binary64)) im)) #<representation binary64>) () ())
#s(alt #<batchref> (patch #s(approx (* 1/2 (sqrt (* 2 (- (sqrt (+ (* re re) (* im im))) re)))) (.f64 (.f64 (sqrt.f64 #s(literal 1/2 binary64)) im) (*.f64 #s(literal 1/2 binary64) (sqrt.f64 (/.f64 #s(literal 2 binary64) re))))) #<representation binary64>) () ())
#s(alt #<batchref> (patch (.f64 (.f64 (sqrt.f64 #s(literal 1/2 binary64)) im) (*.f64 #s(literal 1/2 binary64) (sqrt.f64 (/.f64 #s(literal 2 binary64) re)))) #<representation binary64>) () ())
#s(alt #<batchref> (patch (*.f64 (sqrt.f64 #s(literal 1/2 binary64)) im) #<representation binary64>) () ())
#s(alt #<batchref> (patch (sqrt.f64 #s(literal 1/2 binary64)) #<representation binary64>) () ())
#s(alt #<batchref> (patch (sqrt.f64 (/.f64 #s(literal 2 binary64) re)) #<representation binary64>) () ())

Outputs
#s(alt #<batchref> (taylor 0 re) (#s(alt #<batchref> (patch (.f64 (.f64 (sqrt.f64 (-.f64 (hypot.f64 re im) re)) (sqrt.f64 #s(literal 2 binary64))) #s(literal 1/2 binary64)) #<representation binary64>) () ())) ())
#s(alt #<batchref> (taylor 0 re) (#s(alt #<batchref> (patch (.f64 (.f64 (sqrt.f64 (-.f64 (hypot.f64 re im) re)) (sqrt.f64 #s(literal 2 binary64))) #s(literal 1/2 binary64)) #<representation binary64>) () ())) ())
#s(alt #<batchref> (taylor 0 re) (#s(alt #<batchref> (patch (.f64 (.f64 (sqrt.f64 (-.f64 (hypot.f64 re im) re)) (sqrt.f64 #s(literal 2 binary64))) #s(literal 1/2 binary64)) #<representation binary64>) () ())) ())
#s(alt #<batchref> (taylor 0 re) (#s(alt #<batchref> (patch (.f64 (.f64 (sqrt.f64 (-.f64 (hypot.f64 re im) re)) (sqrt.f64 #s(literal 2 binary64))) #s(literal 1/2 binary64)) #<representation binary64>) () ())) ())
#s(alt #<batchref> (taylor 0 re) (#s(alt #<batchref> (patch (*.f64 (sqrt.f64 (-.f64 (hypot.f64 re im) re)) (sqrt.f64 #s(literal 2 binary64))) #<representation binary64>) () ())) ())
#s(alt #<batchref> (taylor 0 re) (#s(alt #<batchref> (patch (*.f64 (sqrt.f64 (-.f64 (hypot.f64 re im) re)) (sqrt.f64 #s(literal 2 binary64))) #<representation binary64>) () ())) ())
#s(alt #<batchref> (taylor 0 re) (#s(alt #<batchref> (patch (*.f64 (sqrt.f64 (-.f64 (hypot.f64 re im) re)) (sqrt.f64 #s(literal 2 binary64))) #<representation binary64>) () ())) ())
#s(alt #<batchref> (taylor 0 re) (#s(alt #<batchref> (patch (*.f64 (sqrt.f64 (-.f64 (hypot.f64 re im) re)) (sqrt.f64 #s(literal 2 binary64))) #<representation binary64>) () ())) ())
#s(alt #<batchref> (taylor 0 re) (#s(alt #<batchref> (patch (sqrt.f64 (-.f64 (hypot.f64 re im) re)) #<representation binary64>) () ())) ())
#s(alt #<batchref> (taylor 0 re) (#s(alt #<batchref> (patch (sqrt.f64 (-.f64 (hypot.f64 re im) re)) #<representation binary64>) () ())) ())
#s(alt #<batchref> (taylor 0 re) (#s(alt #<batchref> (patch (sqrt.f64 (-.f64 (hypot.f64 re im) re)) #<representation binary64>) () ())) ())
#s(alt #<batchref> (taylor 0 re) (#s(alt #<batchref> (patch (sqrt.f64 (-.f64 (hypot.f64 re im) re)) #<representation binary64>) () ())) ())
#s(alt #<batchref> (taylor 0 re) (#s(alt #<batchref> (patch (-.f64 (hypot.f64 re im) re) #<representation binary64>) () ())) ())
#s(alt #<batchref> (taylor 0 re) (#s(alt #<batchref> (patch (-.f64 (hypot.f64 re im) re) #<representation binary64>) () ())) ())
#s(alt #<batchref> (taylor 0 re) (#s(alt #<batchref> (patch (-.f64 (hypot.f64 re im) re) #<representation binary64>) () ())) ())
#s(alt #<batchref> (taylor 0 re) (#s(alt #<batchref> (patch (-.f64 (hypot.f64 re im) re) #<representation binary64>) () ())) ())
#s(alt #<batchref> (taylor 0 re) (#s(alt #<batchref> (patch (.f64 (sqrt.f64 #s(approx ( (- (sqrt (+ (* im im) (* re re))) re) 2) (*.f64 #s(literal 2 binary64) im))) #s(literal 1/2 binary64)) #<representation binary64>) () ())) ())
#s(alt #<batchref> (taylor 0 re) (#s(alt #<batchref> (patch (.f64 (sqrt.f64 #s(approx ( (- (sqrt (+ (* im im) (* re re))) re) 2) (*.f64 #s(literal 2 binary64) im))) #s(literal 1/2 binary64)) #<representation binary64>) () ())) ())
#s(alt #<batchref> (taylor 0 re) (#s(alt #<batchref> (patch (.f64 (sqrt.f64 #s(approx ( (- (sqrt (+ (* im im) (* re re))) re) 2) (*.f64 #s(literal 2 binary64) im))) #s(literal 1/2 binary64)) #<representation binary64>) () ())) ())
#s(alt #<batchref> (taylor 0 re) (#s(alt #<batchref> (patch (.f64 (sqrt.f64 #s(approx ( (- (sqrt (+ (* im im) (* re re))) re) 2) (*.f64 #s(literal 2 binary64) im))) #s(literal 1/2 binary64)) #<representation binary64>) () ())) ())
#s(alt #<batchref> (taylor 0 re) (#s(alt #<batchref> (patch (sqrt.f64 #s(approx (* (- (sqrt (+ (* im im) (* re re))) re) 2) (*.f64 #s(literal 2 binary64) im))) #<representation binary64>) () ())) ())
#s(alt #<batchref> (taylor 0 re) (#s(alt #<batchref> (patch (sqrt.f64 #s(approx (* (- (sqrt (+ (* im im) (* re re))) re) 2) (*.f64 #s(literal 2 binary64) im))) #<representation binary64>) () ())) ())
#s(alt #<batchref> (taylor 0 re) (#s(alt #<batchref> (patch (sqrt.f64 #s(approx (* (- (sqrt (+ (* im im) (* re re))) re) 2) (*.f64 #s(literal 2 binary64) im))) #<representation binary64>) () ())) ())
#s(alt #<batchref> (taylor 0 re) (#s(alt #<batchref> (patch (sqrt.f64 #s(approx (* (- (sqrt (+ (* im im) (* re re))) re) 2) (*.f64 #s(literal 2 binary64) im))) #<representation binary64>) () ())) ())
#s(alt #<batchref> (taylor 0 re) (#s(alt #<batchref> (patch #s(approx (* (- (sqrt (+ (* im im) (* re re))) re) 2) (*.f64 #s(literal 2 binary64) im)) #<representation binary64>) () ())) ())
#s(alt #<batchref> (taylor 0 re) (#s(alt #<batchref> (patch #s(approx (* (- (sqrt (+ (* im im) (* re re))) re) 2) (*.f64 #s(literal 2 binary64) im)) #<representation binary64>) () ())) ())
#s(alt #<batchref> (taylor 0 re) (#s(alt #<batchref> (patch #s(approx (* (- (sqrt (+ (* im im) (* re re))) re) 2) (*.f64 #s(literal 2 binary64) im)) #<representation binary64>) () ())) ())
#s(alt #<batchref> (taylor 0 re) (#s(alt #<batchref> (patch #s(approx (* (- (sqrt (+ (* im im) (* re re))) re) 2) (*.f64 #s(literal 2 binary64) im)) #<representation binary64>) () ())) ())
#s(alt #<batchref> (taylor 0 re) (#s(alt #<batchref> (patch (.f64 #s(approx (sqrt ( (- (sqrt (+ (* im im) (* re re))) re) 2)) (*.f64 (sqrt.f64 #s(literal 2 binary64)) (sqrt.f64 im))) #s(literal 1/2 binary64)) #<representation binary64>) () ())) ())
#s(alt #<batchref> (taylor 0 re) (#s(alt #<batchref> (patch (.f64 #s(approx (sqrt ( (- (sqrt (+ (* im im) (* re re))) re) 2)) (*.f64 (sqrt.f64 #s(literal 2 binary64)) (sqrt.f64 im))) #s(literal 1/2 binary64)) #<representation binary64>) () ())) ())
#s(alt #<batchref> (taylor 0 re) (#s(alt #<batchref> (patch (.f64 #s(approx (sqrt ( (- (sqrt (+ (* im im) (* re re))) re) 2)) (*.f64 (sqrt.f64 #s(literal 2 binary64)) (sqrt.f64 im))) #s(literal 1/2 binary64)) #<representation binary64>) () ())) ())
#s(alt #<batchref> (taylor 0 re) (#s(alt #<batchref> (patch (.f64 #s(approx (sqrt ( (- (sqrt (+ (* im im) (* re re))) re) 2)) (*.f64 (sqrt.f64 #s(literal 2 binary64)) (sqrt.f64 im))) #s(literal 1/2 binary64)) #<representation binary64>) () ())) ())
#s(alt #<batchref> (taylor 0 re) (#s(alt #<batchref> (patch #s(approx (sqrt (* (- (sqrt (+ (* im im) (* re re))) re) 2)) (*.f64 (sqrt.f64 #s(literal 2 binary64)) (sqrt.f64 im))) #<representation binary64>) () ())) ())
#s(alt #<batchref> (taylor 0 re) (#s(alt #<batchref> (patch #s(approx (sqrt (* (- (sqrt (+ (* im im) (* re re))) re) 2)) (*.f64 (sqrt.f64 #s(literal 2 binary64)) (sqrt.f64 im))) #<representation binary64>) () ())) ())
#s(alt #<batchref> (taylor 0 re) (#s(alt #<batchref> (patch #s(approx (sqrt (* (- (sqrt (+ (* im im) (* re re))) re) 2)) (*.f64 (sqrt.f64 #s(literal 2 binary64)) (sqrt.f64 im))) #<representation binary64>) () ())) ())
#s(alt #<batchref> (taylor 0 re) (#s(alt #<batchref> (patch #s(approx (sqrt (* (- (sqrt (+ (* im im) (* re re))) re) 2)) (*.f64 (sqrt.f64 #s(literal 2 binary64)) (sqrt.f64 im))) #<representation binary64>) () ())) ())
#s(alt #<batchref> (taylor 0 re) (#s(alt #<batchref> (patch (*.f64 (fma.f64 (/.f64 re im) #s(literal -2 binary64) #s(literal 2 binary64)) im) #<representation binary64>) () ())) ())
#s(alt #<batchref> (taylor 0 re) (#s(alt #<batchref> (patch (*.f64 (fma.f64 (/.f64 re im) #s(literal -2 binary64) #s(literal 2 binary64)) im) #<representation binary64>) () ())) ())
#s(alt #<batchref> (taylor 0 re) (#s(alt #<batchref> (patch (*.f64 (fma.f64 (/.f64 re im) #s(literal -2 binary64) #s(literal 2 binary64)) im) #<representation binary64>) () ())) ())
#s(alt #<batchref> (taylor 0 re) (#s(alt #<batchref> (patch (*.f64 (fma.f64 (/.f64 re im) #s(literal -2 binary64) #s(literal 2 binary64)) im) #<representation binary64>) () ())) ())
#s(alt #<batchref> (taylor 0 re) (#s(alt #<batchref> (patch (.f64 (sqrt.f64 #s(approx ( (- (sqrt (+ (* im im) (* re re))) re) 2) (*.f64 (fma.f64 (/.f64 re im) #s(literal -2 binary64) #s(literal 2 binary64)) im))) #s(literal 1/2 binary64)) #<representation binary64>) () ())) ())
#s(alt #<batchref> (taylor 0 re) (#s(alt #<batchref> (patch (.f64 (sqrt.f64 #s(approx ( (- (sqrt (+ (* im im) (* re re))) re) 2) (*.f64 (fma.f64 (/.f64 re im) #s(literal -2 binary64) #s(literal 2 binary64)) im))) #s(literal 1/2 binary64)) #<representation binary64>) () ())) ())
#s(alt #<batchref> (taylor 0 re) (#s(alt #<batchref> (patch (.f64 (sqrt.f64 #s(approx ( (- (sqrt (+ (* im im) (* re re))) re) 2) (*.f64 (fma.f64 (/.f64 re im) #s(literal -2 binary64) #s(literal 2 binary64)) im))) #s(literal 1/2 binary64)) #<representation binary64>) () ())) ())
#s(alt #<batchref> (taylor 0 re) (#s(alt #<batchref> (patch (.f64 (sqrt.f64 #s(approx ( (- (sqrt (+ (* im im) (* re re))) re) 2) (*.f64 (fma.f64 (/.f64 re im) #s(literal -2 binary64) #s(literal 2 binary64)) im))) #s(literal 1/2 binary64)) #<representation binary64>) () ())) ())
#s(alt #<batchref> (taylor 0 re) (#s(alt #<batchref> (patch (sqrt.f64 #s(approx (* (- (sqrt (+ (* im im) (* re re))) re) 2) (*.f64 (fma.f64 (/.f64 re im) #s(literal -2 binary64) #s(literal 2 binary64)) im))) #<representation binary64>) () ())) ())
#s(alt #<batchref> (taylor 0 re) (#s(alt #<batchref> (patch (sqrt.f64 #s(approx (* (- (sqrt (+ (* im im) (* re re))) re) 2) (*.f64 (fma.f64 (/.f64 re im) #s(literal -2 binary64) #s(literal 2 binary64)) im))) #<representation binary64>) () ())) ())
#s(alt #<batchref> (taylor 0 re) (#s(alt #<batchref> (patch (sqrt.f64 #s(approx (* (- (sqrt (+ (* im im) (* re re))) re) 2) (*.f64 (fma.f64 (/.f64 re im) #s(literal -2 binary64) #s(literal 2 binary64)) im))) #<representation binary64>) () ())) ())
#s(alt #<batchref> (taylor 0 re) (#s(alt #<batchref> (patch (sqrt.f64 #s(approx (* (- (sqrt (+ (* im im) (* re re))) re) 2) (*.f64 (fma.f64 (/.f64 re im) #s(literal -2 binary64) #s(literal 2 binary64)) im))) #<representation binary64>) () ())) ())
#s(alt #<batchref> (taylor 0 re) (#s(alt #<batchref> (patch #s(approx (* (- (sqrt (+ (* im im) (* re re))) re) 2) (*.f64 (fma.f64 (/.f64 re im) #s(literal -2 binary64) #s(literal 2 binary64)) im)) #<representation binary64>) () ())) ())
#s(alt #<batchref> (taylor 0 re) (#s(alt #<batchref> (patch #s(approx (* (- (sqrt (+ (* im im) (* re re))) re) 2) (*.f64 (fma.f64 (/.f64 re im) #s(literal -2 binary64) #s(literal 2 binary64)) im)) #<representation binary64>) () ())) ())
#s(alt #<batchref> (taylor 0 re) (#s(alt #<batchref> (patch #s(approx (* (- (sqrt (+ (* im im) (* re re))) re) 2) (*.f64 (fma.f64 (/.f64 re im) #s(literal -2 binary64) #s(literal 2 binary64)) im)) #<representation binary64>) () ())) ())
#s(alt #<batchref> (taylor 0 re) (#s(alt #<batchref> (patch #s(approx (* (- (sqrt (+ (* im im) (* re re))) re) 2) (*.f64 (fma.f64 (/.f64 re im) #s(literal -2 binary64) #s(literal 2 binary64)) im)) #<representation binary64>) () ())) ())
#s(alt #<batchref> (taylor 0 re) (#s(alt #<batchref> (patch #s(approx (* 1/2 (sqrt (* 2 (- (sqrt (+ (* re re) (* im im))) re)))) (.f64 (.f64 (sqrt.f64 #s(literal 1/2 binary64)) im) (*.f64 #s(literal 1/2 binary64) (sqrt.f64 (/.f64 #s(literal 2 binary64) re))))) #<representation binary64>) () ())) ())
#s(alt #<batchref> (taylor 0 re) (#s(alt #<batchref> (patch #s(approx (* 1/2 (sqrt (* 2 (- (sqrt (+ (* re re) (* im im))) re)))) (.f64 (.f64 (sqrt.f64 #s(literal 1/2 binary64)) im) (*.f64 #s(literal 1/2 binary64) (sqrt.f64 (/.f64 #s(literal 2 binary64) re))))) #<representation binary64>) () ())) ())
#s(alt #<batchref> (taylor 0 re) (#s(alt #<batchref> (patch #s(approx (* 1/2 (sqrt (* 2 (- (sqrt (+ (* re re) (* im im))) re)))) (.f64 (.f64 (sqrt.f64 #s(literal 1/2 binary64)) im) (*.f64 #s(literal 1/2 binary64) (sqrt.f64 (/.f64 #s(literal 2 binary64) re))))) #<representation binary64>) () ())) ())
#s(alt #<batchref> (taylor 0 re) (#s(alt #<batchref> (patch #s(approx (* 1/2 (sqrt (* 2 (- (sqrt (+ (* re re) (* im im))) re)))) (.f64 (.f64 (sqrt.f64 #s(literal 1/2 binary64)) im) (*.f64 #s(literal 1/2 binary64) (sqrt.f64 (/.f64 #s(literal 2 binary64) re))))) #<representation binary64>) () ())) ())
#s(alt #<batchref> (taylor 0 re) (#s(alt #<batchref> (patch (.f64 (.f64 (sqrt.f64 #s(literal 1/2 binary64)) im) (*.f64 #s(literal 1/2 binary64) (sqrt.f64 (/.f64 #s(literal 2 binary64) re)))) #<representation binary64>) () ())) ())
#s(alt #<batchref> (taylor 0 re) (#s(alt #<batchref> (patch (.f64 (.f64 (sqrt.f64 #s(literal 1/2 binary64)) im) (*.f64 #s(literal 1/2 binary64) (sqrt.f64 (/.f64 #s(literal 2 binary64) re)))) #<representation binary64>) () ())) ())
#s(alt #<batchref> (taylor 0 re) (#s(alt #<batchref> (patch (.f64 (.f64 (sqrt.f64 #s(literal 1/2 binary64)) im) (*.f64 #s(literal 1/2 binary64) (sqrt.f64 (/.f64 #s(literal 2 binary64) re)))) #<representation binary64>) () ())) ())
#s(alt #<batchref> (taylor 0 re) (#s(alt #<batchref> (patch (.f64 (.f64 (sqrt.f64 #s(literal 1/2 binary64)) im) (*.f64 #s(literal 1/2 binary64) (sqrt.f64 (/.f64 #s(literal 2 binary64) re)))) #<representation binary64>) () ())) ())
#s(alt #<batchref> (taylor 0 re) (#s(alt #<batchref> (patch (sqrt.f64 (/.f64 #s(literal 2 binary64) re)) #<representation binary64>) () ())) ())
#s(alt #<batchref> (taylor 0 re) (#s(alt #<batchref> (patch (sqrt.f64 (/.f64 #s(literal 2 binary64) re)) #<representation binary64>) () ())) ())
#s(alt #<batchref> (taylor 0 re) (#s(alt #<batchref> (patch (sqrt.f64 (/.f64 #s(literal 2 binary64) re)) #<representation binary64>) () ())) ())
#s(alt #<batchref> (taylor 0 re) (#s(alt #<batchref> (patch (sqrt.f64 (/.f64 #s(literal 2 binary64) re)) #<representation binary64>) () ())) ())
#s(alt #<batchref> (taylor inf re) (#s(alt #<batchref> (patch (.f64 (.f64 (sqrt.f64 (-.f64 (hypot.f64 re im) re)) (sqrt.f64 #s(literal 2 binary64))) #s(literal 1/2 binary64)) #<representation binary64>) () ())) ())
#s(alt #<batchref> (taylor inf re) (#s(alt #<batchref> (patch (.f64 (.f64 (sqrt.f64 (-.f64 (hypot.f64 re im) re)) (sqrt.f64 #s(literal 2 binary64))) #s(literal 1/2 binary64)) #<representation binary64>) () ())) ())
#s(alt #<batchref> (taylor inf re) (#s(alt #<batchref> (patch (.f64 (.f64 (sqrt.f64 (-.f64 (hypot.f64 re im) re)) (sqrt.f64 #s(literal 2 binary64))) #s(literal 1/2 binary64)) #<representation binary64>) () ())) ())
#s(alt #<batchref> (taylor inf re) (#s(alt #<batchref> (patch (.f64 (.f64 (sqrt.f64 (-.f64 (hypot.f64 re im) re)) (sqrt.f64 #s(literal 2 binary64))) #s(literal 1/2 binary64)) #<representation binary64>) () ())) ())
#s(alt #<batchref> (taylor inf re) (#s(alt #<batchref> (patch (*.f64 (sqrt.f64 (-.f64 (hypot.f64 re im) re)) (sqrt.f64 #s(literal 2 binary64))) #<representation binary64>) () ())) ())
#s(alt #<batchref> (taylor inf re) (#s(alt #<batchref> (patch (*.f64 (sqrt.f64 (-.f64 (hypot.f64 re im) re)) (sqrt.f64 #s(literal 2 binary64))) #<representation binary64>) () ())) ())
#s(alt #<batchref> (taylor inf re) (#s(alt #<batchref> (patch (*.f64 (sqrt.f64 (-.f64 (hypot.f64 re im) re)) (sqrt.f64 #s(literal 2 binary64))) #<representation binary64>) () ())) ())
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Calls

6 calls:

Time	Variable		Point	Expression
24.0ms	re	@	-inf	((* (* (sqrt (- (sqrt (+ (* re re) (* im im))) re)) (sqrt 2)) 1/2) (* (sqrt (- (sqrt (+ (* re re) (* im im))) re)) (sqrt 2)) (sqrt (- (sqrt (+ (* re re) (* im im))) re)) (- (sqrt (+ (* re re) (* im im))) re) (* (sqrt (* (- (sqrt (+ (* im im) (* re re))) re) 2)) 1/2) (sqrt (* (- (sqrt (+ (* im im) (* re re))) re) 2)) (* (- (sqrt (+ (* im im) (* re re))) re) 2) (* 2 im) (* (sqrt (* (- (sqrt (+ (* im im) (* re re))) re) 2)) 1/2) (sqrt (* (- (sqrt (+ (* im im) (* re re))) re) 2)) (* (sqrt 2) (sqrt im)) (sqrt 2) (* (+ (* (/ re im) -2) 2) im) (* (sqrt (* (- (sqrt (+ (* im im) (* re re))) re) 2)) 1/2) (sqrt (* (- (sqrt (+ (* im im) (* re re))) re) 2)) (* (- (sqrt (+ (* im im) (* re re))) re) 2) (* 1/2 (sqrt (* 2 (- (sqrt (+ (* re re) (* im im))) re)))) (* (* (sqrt 1/2) im) (* 1/2 (sqrt (/ 2 re)))) (* (sqrt 1/2) im) (sqrt 1/2) (sqrt (/ 2 re)))
9.0ms	im	@	-inf	((* (* (sqrt (- (sqrt (+ (* re re) (* im im))) re)) (sqrt 2)) 1/2) (* (sqrt (- (sqrt (+ (* re re) (* im im))) re)) (sqrt 2)) (sqrt (- (sqrt (+ (* re re) (* im im))) re)) (- (sqrt (+ (* re re) (* im im))) re) (* (sqrt (* (- (sqrt (+ (* im im) (* re re))) re) 2)) 1/2) (sqrt (* (- (sqrt (+ (* im im) (* re re))) re) 2)) (* (- (sqrt (+ (* im im) (* re re))) re) 2) (* 2 im) (* (sqrt (* (- (sqrt (+ (* im im) (* re re))) re) 2)) 1/2) (sqrt (* (- (sqrt (+ (* im im) (* re re))) re) 2)) (* (sqrt 2) (sqrt im)) (sqrt 2) (* (+ (* (/ re im) -2) 2) im) (* (sqrt (* (- (sqrt (+ (* im im) (* re re))) re) 2)) 1/2) (sqrt (* (- (sqrt (+ (* im im) (* re re))) re) 2)) (* (- (sqrt (+ (* im im) (* re re))) re) 2) (* 1/2 (sqrt (* 2 (- (sqrt (+ (* re re) (* im im))) re)))) (* (* (sqrt 1/2) im) (* 1/2 (sqrt (/ 2 re)))) (* (sqrt 1/2) im) (sqrt 1/2) (sqrt (/ 2 re)))
4.0ms	im	@	0	((* (* (sqrt (- (sqrt (+ (* re re) (* im im))) re)) (sqrt 2)) 1/2) (* (sqrt (- (sqrt (+ (* re re) (* im im))) re)) (sqrt 2)) (sqrt (- (sqrt (+ (* re re) (* im im))) re)) (- (sqrt (+ (* re re) (* im im))) re) (* (sqrt (* (- (sqrt (+ (* im im) (* re re))) re) 2)) 1/2) (sqrt (* (- (sqrt (+ (* im im) (* re re))) re) 2)) (* (- (sqrt (+ (* im im) (* re re))) re) 2) (* 2 im) (* (sqrt (* (- (sqrt (+ (* im im) (* re re))) re) 2)) 1/2) (sqrt (* (- (sqrt (+ (* im im) (* re re))) re) 2)) (* (sqrt 2) (sqrt im)) (sqrt 2) (* (+ (* (/ re im) -2) 2) im) (* (sqrt (* (- (sqrt (+ (* im im) (* re re))) re) 2)) 1/2) (sqrt (* (- (sqrt (+ (* im im) (* re re))) re) 2)) (* (- (sqrt (+ (* im im) (* re re))) re) 2) (* 1/2 (sqrt (* 2 (- (sqrt (+ (* re re) (* im im))) re)))) (* (* (sqrt 1/2) im) (* 1/2 (sqrt (/ 2 re)))) (* (sqrt 1/2) im) (sqrt 1/2) (sqrt (/ 2 re)))
3.0ms	im	@	inf	((* (* (sqrt (- (sqrt (+ (* re re) (* im im))) re)) (sqrt 2)) 1/2) (* (sqrt (- (sqrt (+ (* re re) (* im im))) re)) (sqrt 2)) (sqrt (- (sqrt (+ (* re re) (* im im))) re)) (- (sqrt (+ (* re re) (* im im))) re) (* (sqrt (* (- (sqrt (+ (* im im) (* re re))) re) 2)) 1/2) (sqrt (* (- (sqrt (+ (* im im) (* re re))) re) 2)) (* (- (sqrt (+ (* im im) (* re re))) re) 2) (* 2 im) (* (sqrt (* (- (sqrt (+ (* im im) (* re re))) re) 2)) 1/2) (sqrt (* (- (sqrt (+ (* im im) (* re re))) re) 2)) (* (sqrt 2) (sqrt im)) (sqrt 2) (* (+ (* (/ re im) -2) 2) im) (* (sqrt (* (- (sqrt (+ (* im im) (* re re))) re) 2)) 1/2) (sqrt (* (- (sqrt (+ (* im im) (* re re))) re) 2)) (* (- (sqrt (+ (* im im) (* re re))) re) 2) (* 1/2 (sqrt (* 2 (- (sqrt (+ (* re re) (* im im))) re)))) (* (* (sqrt 1/2) im) (* 1/2 (sqrt (/ 2 re)))) (* (sqrt 1/2) im) (sqrt 1/2) (sqrt (/ 2 re)))
3.0ms	re	@	inf	((* (* (sqrt (- (sqrt (+ (* re re) (* im im))) re)) (sqrt 2)) 1/2) (* (sqrt (- (sqrt (+ (* re re) (* im im))) re)) (sqrt 2)) (sqrt (- (sqrt (+ (* re re) (* im im))) re)) (- (sqrt (+ (* re re) (* im im))) re) (* (sqrt (* (- (sqrt (+ (* im im) (* re re))) re) 2)) 1/2) (sqrt (* (- (sqrt (+ (* im im) (* re re))) re) 2)) (* (- (sqrt (+ (* im im) (* re re))) re) 2) (* 2 im) (* (sqrt (* (- (sqrt (+ (* im im) (* re re))) re) 2)) 1/2) (sqrt (* (- (sqrt (+ (* im im) (* re re))) re) 2)) (* (sqrt 2) (sqrt im)) (sqrt 2) (* (+ (* (/ re im) -2) 2) im) (* (sqrt (* (- (sqrt (+ (* im im) (* re re))) re) 2)) 1/2) (sqrt (* (- (sqrt (+ (* im im) (* re re))) re) 2)) (* (- (sqrt (+ (* im im) (* re re))) re) 2) (* 1/2 (sqrt (* 2 (- (sqrt (+ (* re re) (* im im))) re)))) (* (* (sqrt 1/2) im) (* 1/2 (sqrt (/ 2 re)))) (* (sqrt 1/2) im) (sqrt 1/2) (sqrt (/ 2 re)))

simplify259.0ms (3.6%)

Memory

6.6MiB live, 263.0MiB allocated

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	667	11045
1	2184	10318
2	7562	10296
0	8321	9875

Stop Event

1×	iter limit
1×	node limit

Counts

408 → 406

Calls

Call 1

Inputs
(* 1/2 (* (sqrt im) (sqrt 2)))
(+ (* -1/4 (* (sqrt (/ 1 im)) (* re (sqrt 2)))) (* 1/2 (* (sqrt im) (sqrt 2))))
(+ (* 1/2 (* (sqrt im) (sqrt 2))) (* re (+ (* -1/4 (* (sqrt (/ 1 im)) (sqrt 2))) (* 1/16 (* (sqrt (/ 1 (pow im 3))) (* re (sqrt 2)))))))
(+ (* 1/2 (* (sqrt im) (sqrt 2))) (* re (+ (* -1/4 (* (sqrt (/ 1 im)) (sqrt 2))) (* re (+ (* 1/32 (* (sqrt (/ 1 (pow im 5))) (* re (sqrt 2)))) (* 1/16 (* (sqrt (/ 1 (pow im 3))) (sqrt 2))))))))
(* (sqrt im) (sqrt 2))
(+ (* -1/2 (* (sqrt (/ 1 im)) (* re (sqrt 2)))) (* (sqrt im) (sqrt 2)))
(+ (* re (+ (* -1/2 (* (sqrt (/ 1 im)) (sqrt 2))) (* 1/8 (* (sqrt (/ 1 (pow im 3))) (* re (sqrt 2)))))) (* (sqrt im) (sqrt 2)))
(+ (* re (+ (* -1/2 (* (sqrt (/ 1 im)) (sqrt 2))) (* re (+ (* 1/16 (* (sqrt (/ 1 (pow im 5))) (* re (sqrt 2)))) (* 1/8 (* (sqrt (/ 1 (pow im 3))) (sqrt 2))))))) (* (sqrt im) (sqrt 2)))
(sqrt im)
(+ (sqrt im) (* -1/2 (* (sqrt (/ 1 im)) re)))
(+ (sqrt im) (* re (+ (* -1/2 (sqrt (/ 1 im))) (* 1/8 (* (sqrt (/ 1 (pow im 3))) re)))))
(+ (sqrt im) (* re (+ (* -1/2 (sqrt (/ 1 im))) (* re (+ (* 1/16 (* (sqrt (/ 1 (pow im 5))) re)) (* 1/8 (sqrt (/ 1 (pow im 3)))))))))
im
(+ im (* -1 re))
(+ im (* re (- (* 1/2 (/ re im)) 1)))
(+ im (* re (- (* re (+ (* -1/8 (/ (pow re 2) (pow im 3))) (* 1/2 (/ 1 im)))) 1)))
(* 1/2 (* (sqrt im) (sqrt 2)))
(+ (* -1/4 (* (sqrt (/ 1 im)) (* re (sqrt 2)))) (* 1/2 (* (sqrt im) (sqrt 2))))
(+ (* 1/2 (* (sqrt im) (sqrt 2))) (* re (+ (* -1/4 (* (sqrt (/ 1 im)) (sqrt 2))) (* 1/16 (* (sqrt (/ 1 (pow im 3))) (* re (sqrt 2)))))))
(+ (* 1/2 (* (sqrt im) (sqrt 2))) (* re (+ (* -1/4 (* (sqrt (/ 1 im)) (sqrt 2))) (* re (+ (* 1/32 (* (sqrt (/ 1 (pow im 5))) (* re (sqrt 2)))) (* 1/16 (* (sqrt (/ 1 (pow im 3))) (sqrt 2))))))))
(* (sqrt im) (sqrt 2))
(+ (* -1/2 (* (sqrt (/ 1 im)) (* re (sqrt 2)))) (* (sqrt im) (sqrt 2)))
(+ (* re (+ (* -1/2 (* (sqrt (/ 1 im)) (sqrt 2))) (* 1/8 (* (sqrt (/ 1 (pow im 3))) (* re (sqrt 2)))))) (* (sqrt im) (sqrt 2)))
(+ (* re (+ (* -1/2 (* (sqrt (/ 1 im)) (sqrt 2))) (* re (+ (* 1/16 (* (sqrt (/ 1 (pow im 5))) (* re (sqrt 2)))) (* 1/8 (* (sqrt (/ 1 (pow im 3))) (sqrt 2))))))) (* (sqrt im) (sqrt 2)))
(* 2 im)
(+ (* -2 re) (* 2 im))
(+ (* 2 im) (* re (- (/ re im) 2)))
(+ (* 2 im) (* re (- (* re (+ (* -1/4 (/ (pow re 2) (pow im 3))) (/ 1 im))) 2)))
(* 1/2 (* (sqrt im) (sqrt 2)))
(+ (* -1/4 (* (sqrt (/ 1 im)) (* re (sqrt 2)))) (* 1/2 (* (sqrt im) (sqrt 2))))
(+ (* 1/2 (* (sqrt im) (sqrt 2))) (* re (+ (* -1/4 (* (sqrt (/ 1 im)) (sqrt 2))) (* 1/16 (* (sqrt (/ 1 (pow im 3))) (* re (sqrt 2)))))))
(+ (* 1/2 (* (sqrt im) (sqrt 2))) (* re (+ (* -1/4 (* (sqrt (/ 1 im)) (sqrt 2))) (* re (+ (* 1/32 (* (sqrt (/ 1 (pow im 5))) (* re (sqrt 2)))) (* 1/16 (* (sqrt (/ 1 (pow im 3))) (sqrt 2))))))))
(* (sqrt im) (sqrt 2))
(+ (* -1/2 (* (sqrt (/ 1 im)) (* re (sqrt 2)))) (* (sqrt im) (sqrt 2)))
(+ (* re (+ (* -1/2 (* (sqrt (/ 1 im)) (sqrt 2))) (* 1/8 (* (sqrt (/ 1 (pow im 3))) (* re (sqrt 2)))))) (* (sqrt im) (sqrt 2)))
(+ (* re (+ (* -1/2 (* (sqrt (/ 1 im)) (sqrt 2))) (* re (+ (* 1/16 (* (sqrt (/ 1 (pow im 5))) (* re (sqrt 2)))) (* 1/8 (* (sqrt (/ 1 (pow im 3))) (sqrt 2))))))) (* (sqrt im) (sqrt 2)))
(* 2 im)
(+ (* -2 re) (* 2 im))
(+ (* -2 re) (* 2 im))
(+ (* -2 re) (* 2 im))
(* 1/2 (* (sqrt im) (sqrt 2)))
(+ (* -1/4 (* (sqrt (/ 1 im)) (* re (sqrt 2)))) (* 1/2 (* (sqrt im) (sqrt 2))))
(+ (* 1/2 (* (sqrt im) (sqrt 2))) (* re (+ (* -1/4 (* (sqrt (/ 1 im)) (sqrt 2))) (* 1/16 (* (sqrt (/ 1 (pow im 3))) (* re (sqrt 2)))))))
(+ (* 1/2 (* (sqrt im) (sqrt 2))) (* re (+ (* -1/4 (* (sqrt (/ 1 im)) (sqrt 2))) (* re (+ (* 1/32 (* (sqrt (/ 1 (pow im 5))) (* re (sqrt 2)))) (* 1/16 (* (sqrt (/ 1 (pow im 3))) (sqrt 2))))))))
(* (sqrt im) (sqrt 2))
(+ (* -1/2 (* (sqrt (/ 1 im)) (* re (sqrt 2)))) (* (sqrt im) (sqrt 2)))
(+ (* re (+ (* -1/2 (* (sqrt (/ 1 im)) (sqrt 2))) (* 1/8 (* (sqrt (/ 1 (pow im 3))) (* re (sqrt 2)))))) (* (sqrt im) (sqrt 2)))
(+ (* re (+ (* -1/2 (* (sqrt (/ 1 im)) (sqrt 2))) (* re (+ (* 1/16 (* (sqrt (/ 1 (pow im 5))) (* re (sqrt 2)))) (* 1/8 (* (sqrt (/ 1 (pow im 3))) (sqrt 2))))))) (* (sqrt im) (sqrt 2)))
(* 2 im)
(+ (* -2 re) (* 2 im))
(+ (* 2 im) (* re (- (/ re im) 2)))
(+ (* 2 im) (* re (- (* re (+ (* -1/4 (/ (pow re 2) (pow im 3))) (/ 1 im))) 2)))
(* 1/2 (* (sqrt im) (sqrt 2)))
(+ (* -1/4 (* (sqrt (/ 1 im)) (* re (sqrt 2)))) (* 1/2 (* (sqrt im) (sqrt 2))))
(+ (* 1/2 (* (sqrt im) (sqrt 2))) (* re (+ (* -1/4 (* (sqrt (/ 1 im)) (sqrt 2))) (* 1/16 (* (sqrt (/ 1 (pow im 3))) (* re (sqrt 2)))))))
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(* 1/2 (* (* im (* (sqrt 1/2) (sqrt 2))) (sqrt (/ 1 re))))
(* 1/2 (* (* im (* (sqrt 1/2) (sqrt 2))) (sqrt (/ 1 re))))
(* 1/2 (* (* im (* (sqrt 1/2) (sqrt 2))) (sqrt (/ 1 re))))
(* 1/2 (* (* im (* (sqrt 1/2) (sqrt 2))) (sqrt (/ 1 re))))
(* (sqrt (/ 1 re)) (sqrt 2))
(* (sqrt (/ 1 re)) (sqrt 2))
(* (sqrt (/ 1 re)) (sqrt 2))
(* (sqrt (/ 1 re)) (sqrt 2))
(* 1/2 (* (* im (* (sqrt 1/2) (sqrt 2))) (sqrt (/ 1 re))))
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(+ (* -1/32 (* (/ (* (pow im 3) (sqrt 2)) (sqrt 1/2)) (sqrt (/ 1 (pow re 5))))) (+ (* -1/1024 (* (/ (* (pow im 5) (sqrt 2)) (pow (sqrt 1/2) 3)) (sqrt (/ 1 (pow re 9))))) (+ (* 1/64 (* (/ (* (pow im 5) (sqrt 2)) (sqrt 1/2)) (sqrt (/ 1 (pow re 9))))) (* 1/2 (* (* im (* (sqrt 1/2) (sqrt 2))) (sqrt (/ 1 re)))))))
(* (* im (* (sqrt 1/2) (sqrt 2))) (sqrt (/ 1 re)))
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(* (* im (sqrt 1/2)) (sqrt (/ 1 re)))
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(+ (* -1/16 (* (/ (pow im 3) (sqrt 1/2)) (sqrt (/ 1 (pow re 5))))) (+ (* 1/32 (* (/ (pow im 5) (sqrt 1/2)) (sqrt (/ 1 (pow re 9))))) (* (* im (sqrt 1/2)) (sqrt (/ 1 re)))))
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(* 1/2 (/ (pow im 2) re))
(/ (+ (* -1/8 (/ (pow im 4) (pow re 2))) (* 1/2 (pow im 2))) re)
(/ (+ (* -1/8 (/ (pow im 4) (pow re 2))) (+ (* 1/16 (/ (pow im 6) (pow re 4))) (* 1/2 (pow im 2)))) re)
(/ (+ (* -1/2 (/ (+ (* 1/64 (pow im 8)) (* 1/16 (pow im 8))) (pow re 6))) (+ (* -1/8 (/ (pow im 4) (pow re 2))) (+ (* 1/16 (/ (pow im 6) (pow re 4))) (* 1/2 (pow im 2))))) re)
(* 1/2 (* (* im (* (sqrt 1/2) (sqrt 2))) (sqrt (/ 1 re))))
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(* (* im (* (sqrt 1/2) (sqrt 2))) (sqrt (/ 1 re)))
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(+ (* -1/16 (* (/ (* (pow im 3) (sqrt 2)) (sqrt 1/2)) (sqrt (/ 1 (pow re 5))))) (+ (* -1/512 (* (/ (* (pow im 5) (sqrt 2)) (pow (sqrt 1/2) 3)) (sqrt (/ 1 (pow re 9))))) (+ (* 1/32 (* (/ (* (pow im 5) (sqrt 2)) (sqrt 1/2)) (sqrt (/ 1 (pow re 9))))) (* (* im (* (sqrt 1/2) (sqrt 2))) (sqrt (/ 1 re))))))
(/ (pow im 2) re)
(/ (+ (* -1/4 (/ (pow im 4) (pow re 2))) (pow im 2)) re)
(/ (+ (* -1/4 (/ (pow im 4) (pow re 2))) (+ (* 1/8 (/ (pow im 6) (pow re 4))) (pow im 2))) re)
(/ (+ (* -1 (/ (+ (* 1/64 (pow im 8)) (* 1/16 (pow im 8))) (pow re 6))) (+ (* -1/4 (/ (pow im 4) (pow re 2))) (+ (* 1/8 (/ (pow im 6) (pow re 4))) (pow im 2)))) re)
(* 1/2 (* (* im (* (sqrt 1/2) (sqrt 2))) (sqrt (/ 1 re))))
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(+ (* -1/32 (* (/ (* (pow im 3) (sqrt 2)) (sqrt 1/2)) (sqrt (/ 1 (pow re 5))))) (+ (* -1/1024 (* (/ (* (pow im 5) (sqrt 2)) (pow (sqrt 1/2) 3)) (sqrt (/ 1 (pow re 9))))) (+ (* 1/64 (* (/ (* (pow im 5) (sqrt 2)) (sqrt 1/2)) (sqrt (/ 1 (pow re 9))))) (* 1/2 (* (* im (* (sqrt 1/2) (sqrt 2))) (sqrt (/ 1 re)))))))
(* (* im (* (sqrt 1/2) (sqrt 2))) (sqrt (/ 1 re)))
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(+ (* -1/16 (* (/ (* (pow im 3) (sqrt 2)) (sqrt 1/2)) (sqrt (/ 1 (pow re 5))))) (+ (* -1/512 (* (/ (* (pow im 5) (sqrt 2)) (pow (sqrt 1/2) 3)) (sqrt (/ 1 (pow re 9))))) (+ (* 1/32 (* (/ (* (pow im 5) (sqrt 2)) (sqrt 1/2)) (sqrt (/ 1 (pow re 9))))) (* (* im (* (sqrt 1/2) (sqrt 2))) (sqrt (/ 1 re))))))
(* -2 re)
(* re (- (* 2 (/ im re)) 2))
(* re (- (* 2 (/ im re)) 2))
(* re (- (* 2 (/ im re)) 2))
(* 1/2 (* (* im (* (sqrt 1/2) (sqrt 2))) (sqrt (/ 1 re))))
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(+ (* -1/32 (* (/ (* (pow im 3) (sqrt 2)) (sqrt 1/2)) (sqrt (/ 1 (pow re 5))))) (+ (* -1/1024 (* (/ (* (pow im 5) (sqrt 2)) (pow (sqrt 1/2) 3)) (sqrt (/ 1 (pow re 9))))) (+ (* 1/64 (* (/ (* (pow im 5) (sqrt 2)) (sqrt 1/2)) (sqrt (/ 1 (pow re 9))))) (* 1/2 (* (* im (* (sqrt 1/2) (sqrt 2))) (sqrt (/ 1 re)))))))
(* (* im (* (sqrt 1/2) (sqrt 2))) (sqrt (/ 1 re)))
(+ (* -1/16 (* (/ (* (pow im 3) (sqrt 2)) (sqrt 1/2)) (sqrt (/ 1 (pow re 5))))) (* (* im (* (sqrt 1/2) (sqrt 2))) (sqrt (/ 1 re))))
(+ (* -1/16 (* (/ (* (pow im 3) (sqrt 2)) (sqrt 1/2)) (sqrt (/ 1 (pow re 5))))) (+ (* 1/32 (* (/ (* (pow im 5) (sqrt 2)) (sqrt 1/2)) (sqrt (/ 1 (pow re 9))))) (* (* im (* (sqrt 1/2) (sqrt 2))) (sqrt (/ 1 re)))))
(+ (* -1/16 (* (/ (* (pow im 3) (sqrt 2)) (sqrt 1/2)) (sqrt (/ 1 (pow re 5))))) (+ (* -1/512 (* (/ (* (pow im 5) (sqrt 2)) (pow (sqrt 1/2) 3)) (sqrt (/ 1 (pow re 9))))) (+ (* 1/32 (* (/ (* (pow im 5) (sqrt 2)) (sqrt 1/2)) (sqrt (/ 1 (pow re 9))))) (* (* im (* (sqrt 1/2) (sqrt 2))) (sqrt (/ 1 re))))))
(/ (pow im 2) re)
(/ (+ (* -1/4 (/ (pow im 4) (pow re 2))) (pow im 2)) re)
(/ (+ (* -1/4 (/ (pow im 4) (pow re 2))) (+ (* 1/8 (/ (pow im 6) (pow re 4))) (pow im 2))) re)
(/ (+ (* -1 (/ (+ (* 1/64 (pow im 8)) (* 1/16 (pow im 8))) (pow re 6))) (+ (* -1/4 (/ (pow im 4) (pow re 2))) (+ (* 1/8 (/ (pow im 6) (pow re 4))) (pow im 2)))) re)
(* 1/2 (* (* im (* (sqrt 1/2) (sqrt 2))) (sqrt (/ 1 re))))
(+ (* -1/32 (* (/ (* (pow im 3) (sqrt 2)) (sqrt 1/2)) (sqrt (/ 1 (pow re 5))))) (* 1/2 (* (* im (* (sqrt 1/2) (sqrt 2))) (sqrt (/ 1 re)))))
(+ (* -1/32 (* (/ (* (pow im 3) (sqrt 2)) (sqrt 1/2)) (sqrt (/ 1 (pow re 5))))) (+ (* 1/64 (* (/ (* (pow im 5) (sqrt 2)) (sqrt 1/2)) (sqrt (/ 1 (pow re 9))))) (* 1/2 (* (* im (* (sqrt 1/2) (sqrt 2))) (sqrt (/ 1 re))))))
(+ (* -1/32 (* (/ (* (pow im 3) (sqrt 2)) (sqrt 1/2)) (sqrt (/ 1 (pow re 5))))) (+ (* -1/1024 (* (/ (* (pow im 5) (sqrt 2)) (pow (sqrt 1/2) 3)) (sqrt (/ 1 (pow re 9))))) (+ (* 1/64 (* (/ (* (pow im 5) (sqrt 2)) (sqrt 1/2)) (sqrt (/ 1 (pow re 9))))) (* 1/2 (* (* im (* (sqrt 1/2) (sqrt 2))) (sqrt (/ 1 re)))))))
(* 1/2 (* (* im (* (sqrt 1/2) (sqrt 2))) (sqrt (/ 1 re))))
(* 1/2 (* (* im (* (sqrt 1/2) (sqrt 2))) (sqrt (/ 1 re))))
(* 1/2 (* (* im (* (sqrt 1/2) (sqrt 2))) (sqrt (/ 1 re))))
(* 1/2 (* (* im (* (sqrt 1/2) (sqrt 2))) (sqrt (/ 1 re))))
(* (sqrt (/ 1 re)) (sqrt 2))
(* (sqrt (/ 1 re)) (sqrt 2))
(* (sqrt (/ 1 re)) (sqrt 2))
(* (sqrt (/ 1 re)) (sqrt 2))
(* -1/2 (* (sqrt re) (* (sqrt -1) (pow (sqrt 2) 2))))
(* -1 (* re (+ (* -1/8 (* (* (pow im 2) (sqrt -1)) (sqrt (/ 1 (pow re 5))))) (* 1/2 (* (sqrt (/ 1 re)) (* (sqrt -1) (pow (sqrt 2) 2)))))))
(* -1 (* re (+ (* -1 (/ (+ (* -1/32 (* (* (pow im 4) (sqrt -1)) (sqrt (/ 1 (pow re 3))))) (* 1/8 (* (* (pow im 2) (sqrt -1)) (sqrt re)))) (pow re 3))) (* 1/2 (* (sqrt (/ 1 re)) (* (sqrt -1) (pow (sqrt 2) 2)))))))
(* -1 (* re (+ (* -1 (/ (+ (* -1/32 (* (* (pow im 4) (sqrt -1)) (sqrt (/ 1 (pow re 3))))) (+ (* 1/64 (* (/ (* (pow im 4) (sqrt -1)) (pow (sqrt 2) 2)) (sqrt (/ 1 (pow re 3))))) (* 1/8 (* (* (pow im 2) (sqrt -1)) (sqrt re))))) (pow re 3))) (* 1/2 (* (sqrt (/ 1 re)) (* (sqrt -1) (pow (sqrt 2) 2)))))))
(* -1 (* (sqrt re) (* (sqrt -1) (pow (sqrt 2) 2))))
(* -1 (* re (+ (* -1/4 (* (* (pow im 2) (sqrt -1)) (sqrt (/ 1 (pow re 5))))) (* (sqrt (/ 1 re)) (* (sqrt -1) (pow (sqrt 2) 2))))))
(* -1 (* re (+ (* -1 (/ (+ (* -1/16 (* (* (pow im 4) (sqrt -1)) (sqrt (/ 1 (pow re 3))))) (* 1/4 (* (* (pow im 2) (sqrt -1)) (sqrt re)))) (pow re 3))) (* (sqrt (/ 1 re)) (* (sqrt -1) (pow (sqrt 2) 2))))))
(* -1 (* re (+ (* -1 (/ (+ (* -1/16 (* (* (pow im 4) (sqrt -1)) (sqrt (/ 1 (pow re 3))))) (+ (* 1/32 (* (/ (* (pow im 4) (sqrt -1)) (pow (sqrt 2) 2)) (sqrt (/ 1 (pow re 3))))) (* 1/4 (* (* (pow im 2) (sqrt -1)) (sqrt re))))) (pow re 3))) (* (sqrt (/ 1 re)) (* (sqrt -1) (pow (sqrt 2) 2))))))
(* -1 (* (sqrt re) (* (sqrt -1) (sqrt 2))))
(* -1 (* re (+ (* -1/4 (* (/ (* (pow im 2) (sqrt -1)) (sqrt 2)) (sqrt (/ 1 (pow re 5))))) (* (sqrt (/ 1 re)) (* (sqrt -1) (sqrt 2))))))
(* -1 (* re (+ (* -1 (/ (+ (* -1/16 (* (/ (* (pow im 4) (sqrt -1)) (sqrt 2)) (sqrt (/ 1 (pow re 3))))) (* 1/4 (* (/ (* (pow im 2) (sqrt -1)) (sqrt 2)) (sqrt re)))) (pow re 3))) (* (sqrt (/ 1 re)) (* (sqrt -1) (sqrt 2))))))
(* -1 (* re (+ (* -1 (/ (+ (* -1/16 (* (/ (* (pow im 4) (sqrt -1)) (sqrt 2)) (sqrt (/ 1 (pow re 3))))) (+ (* 1/32 (* (/ (* (pow im 4) (sqrt -1)) (pow (sqrt 2) 3)) (sqrt (/ 1 (pow re 3))))) (* 1/4 (* (/ (* (pow im 2) (sqrt -1)) (sqrt 2)) (sqrt re))))) (pow re 3))) (* (sqrt (/ 1 re)) (* (sqrt -1) (sqrt 2))))))
(* -2 re)
(* -1 (* re (+ 2 (* 1/2 (/ (pow im 2) (pow re 2))))))
(* -1 (* re (+ 2 (+ (* -1/8 (/ (pow im 4) (pow re 4))) (* 1/2 (/ (pow im 2) (pow re 2)))))))
(* -1 (* re (+ 2 (+ (* -1/8 (/ (pow im 4) (pow re 4))) (+ (* 1/16 (/ (pow im 6) (pow re 6))) (* 1/2 (/ (pow im 2) (pow re 2))))))))
(* -1/2 (* (sqrt re) (* (sqrt -1) (pow (sqrt 2) 2))))
(* -1 (* re (+ (* -1/8 (* (* (pow im 2) (sqrt -1)) (sqrt (/ 1 (pow re 5))))) (* 1/2 (* (sqrt (/ 1 re)) (* (sqrt -1) (pow (sqrt 2) 2)))))))
(* -1 (* re (+ (* -1 (/ (+ (* -1/32 (* (* (pow im 4) (sqrt -1)) (sqrt (/ 1 (pow re 3))))) (* 1/8 (* (* (pow im 2) (sqrt -1)) (sqrt re)))) (pow re 3))) (* 1/2 (* (sqrt (/ 1 re)) (* (sqrt -1) (pow (sqrt 2) 2)))))))
(* -1 (* re (+ (* -1 (/ (+ (* -1/32 (* (* (pow im 4) (sqrt -1)) (sqrt (/ 1 (pow re 3))))) (+ (* 1/64 (* (/ (* (pow im 4) (sqrt -1)) (pow (sqrt 2) 2)) (sqrt (/ 1 (pow re 3))))) (* 1/8 (* (* (pow im 2) (sqrt -1)) (sqrt re))))) (pow re 3))) (* 1/2 (* (sqrt (/ 1 re)) (* (sqrt -1) (pow (sqrt 2) 2)))))))
(* -1 (* (sqrt re) (* (sqrt -1) (pow (sqrt 2) 2))))
(* -1 (* re (+ (* -1/4 (* (* (pow im 2) (sqrt -1)) (sqrt (/ 1 (pow re 5))))) (* (sqrt (/ 1 re)) (* (sqrt -1) (pow (sqrt 2) 2))))))
(* -1 (* re (+ (* -1 (/ (+ (* -1/16 (* (* (pow im 4) (sqrt -1)) (sqrt (/ 1 (pow re 3))))) (* 1/4 (* (* (pow im 2) (sqrt -1)) (sqrt re)))) (pow re 3))) (* (sqrt (/ 1 re)) (* (sqrt -1) (pow (sqrt 2) 2))))))
(* -1 (* re (+ (* -1 (/ (+ (* -1/16 (* (* (pow im 4) (sqrt -1)) (sqrt (/ 1 (pow re 3))))) (+ (* 1/32 (* (/ (* (pow im 4) (sqrt -1)) (pow (sqrt 2) 2)) (sqrt (/ 1 (pow re 3))))) (* 1/4 (* (* (pow im 2) (sqrt -1)) (sqrt re))))) (pow re 3))) (* (sqrt (/ 1 re)) (* (sqrt -1) (pow (sqrt 2) 2))))))
(* -4 re)
(* -1 (* re (+ 4 (/ (pow im 2) (pow re 2)))))
(* -1 (* re (+ 4 (+ (* -1/4 (/ (pow im 4) (pow re 4))) (/ (pow im 2) (pow re 2))))))
(* -1 (* re (+ 4 (+ (* -1/4 (/ (pow im 4) (pow re 4))) (+ (* 1/8 (/ (pow im 6) (pow re 6))) (/ (pow im 2) (pow re 2)))))))
(* -1/2 (* (sqrt re) (* (sqrt -1) (pow (sqrt 2) 2))))
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(* -1 (* re (+ (* -1 (/ (+ (* -1/32 (* (* (pow im 4) (sqrt -1)) (sqrt (/ 1 (pow re 3))))) (+ (* 1/64 (* (/ (* (pow im 4) (sqrt -1)) (pow (sqrt 2) 2)) (sqrt (/ 1 (pow re 3))))) (* 1/8 (* (* (pow im 2) (sqrt -1)) (sqrt re))))) (pow re 3))) (* 1/2 (* (sqrt (/ 1 re)) (* (sqrt -1) (pow (sqrt 2) 2)))))))
(* -1 (* (sqrt re) (* (sqrt -1) (pow (sqrt 2) 2))))
(* -1 (* re (+ (* -1/4 (* (* (pow im 2) (sqrt -1)) (sqrt (/ 1 (pow re 5))))) (* (sqrt (/ 1 re)) (* (sqrt -1) (pow (sqrt 2) 2))))))
(* -1 (* re (+ (* -1 (/ (+ (* -1/16 (* (* (pow im 4) (sqrt -1)) (sqrt (/ 1 (pow re 3))))) (* 1/4 (* (* (pow im 2) (sqrt -1)) (sqrt re)))) (pow re 3))) (* (sqrt (/ 1 re)) (* (sqrt -1) (pow (sqrt 2) 2))))))
(* -1 (* re (+ (* -1 (/ (+ (* -1/16 (* (* (pow im 4) (sqrt -1)) (sqrt (/ 1 (pow re 3))))) (+ (* 1/32 (* (/ (* (pow im 4) (sqrt -1)) (pow (sqrt 2) 2)) (sqrt (/ 1 (pow re 3))))) (* 1/4 (* (* (pow im 2) (sqrt -1)) (sqrt re))))) (pow re 3))) (* (sqrt (/ 1 re)) (* (sqrt -1) (pow (sqrt 2) 2))))))
(* -2 re)
(* -1 (* re (+ 2 (* -2 (/ im re)))))
(* -1 (* re (+ 2 (* -2 (/ im re)))))
(* -1 (* re (+ 2 (* -2 (/ im re)))))
(* -1/2 (* (sqrt re) (* (sqrt -1) (pow (sqrt 2) 2))))
(* -1 (* re (+ (* -1/8 (* (* (pow im 2) (sqrt -1)) (sqrt (/ 1 (pow re 5))))) (* 1/2 (* (sqrt (/ 1 re)) (* (sqrt -1) (pow (sqrt 2) 2)))))))
(* -1 (* re (+ (* -1 (/ (+ (* -1/32 (* (* (pow im 4) (sqrt -1)) (sqrt (/ 1 (pow re 3))))) (* 1/8 (* (* (pow im 2) (sqrt -1)) (sqrt re)))) (pow re 3))) (* 1/2 (* (sqrt (/ 1 re)) (* (sqrt -1) (pow (sqrt 2) 2)))))))
(* -1 (* re (+ (* -1 (/ (+ (* -1/32 (* (* (pow im 4) (sqrt -1)) (sqrt (/ 1 (pow re 3))))) (+ (* 1/64 (* (/ (* (pow im 4) (sqrt -1)) (pow (sqrt 2) 2)) (sqrt (/ 1 (pow re 3))))) (* 1/8 (* (* (pow im 2) (sqrt -1)) (sqrt re))))) (pow re 3))) (* 1/2 (* (sqrt (/ 1 re)) (* (sqrt -1) (pow (sqrt 2) 2)))))))
(* -1 (* (sqrt re) (* (sqrt -1) (pow (sqrt 2) 2))))
(* -1 (* re (+ (* -1/4 (* (* (pow im 2) (sqrt -1)) (sqrt (/ 1 (pow re 5))))) (* (sqrt (/ 1 re)) (* (sqrt -1) (pow (sqrt 2) 2))))))
(* -1 (* re (+ (* -1 (/ (+ (* -1/16 (* (* (pow im 4) (sqrt -1)) (sqrt (/ 1 (pow re 3))))) (* 1/4 (* (* (pow im 2) (sqrt -1)) (sqrt re)))) (pow re 3))) (* (sqrt (/ 1 re)) (* (sqrt -1) (pow (sqrt 2) 2))))))
(* -1 (* re (+ (* -1 (/ (+ (* -1/16 (* (* (pow im 4) (sqrt -1)) (sqrt (/ 1 (pow re 3))))) (+ (* 1/32 (* (/ (* (pow im 4) (sqrt -1)) (pow (sqrt 2) 2)) (sqrt (/ 1 (pow re 3))))) (* 1/4 (* (* (pow im 2) (sqrt -1)) (sqrt re))))) (pow re 3))) (* (sqrt (/ 1 re)) (* (sqrt -1) (pow (sqrt 2) 2))))))
(* -4 re)
(* -1 (* re (+ 4 (/ (pow im 2) (pow re 2)))))
(* -1 (* re (+ 4 (+ (* -1/4 (/ (pow im 4) (pow re 4))) (/ (pow im 2) (pow re 2))))))
(* -1 (* re (+ 4 (+ (* -1/4 (/ (pow im 4) (pow re 4))) (+ (* 1/8 (/ (pow im 6) (pow re 6))) (/ (pow im 2) (pow re 2)))))))
(* -1/2 (* (sqrt re) (* (sqrt -1) (pow (sqrt 2) 2))))
(* -1 (* re (+ (* -1/8 (* (* (pow im 2) (sqrt -1)) (sqrt (/ 1 (pow re 5))))) (* 1/2 (* (sqrt (/ 1 re)) (* (sqrt -1) (pow (sqrt 2) 2)))))))
(* -1 (* re (+ (* -1 (/ (+ (* -1/32 (* (* (pow im 4) (sqrt -1)) (sqrt (/ 1 (pow re 3))))) (* 1/8 (* (* (pow im 2) (sqrt -1)) (sqrt re)))) (pow re 3))) (* 1/2 (* (sqrt (/ 1 re)) (* (sqrt -1) (pow (sqrt 2) 2)))))))
(* -1 (* re (+ (* -1 (/ (+ (* -1/32 (* (* (pow im 4) (sqrt -1)) (sqrt (/ 1 (pow re 3))))) (+ (* 1/64 (* (/ (* (pow im 4) (sqrt -1)) (pow (sqrt 2) 2)) (sqrt (/ 1 (pow re 3))))) (* 1/8 (* (* (pow im 2) (sqrt -1)) (sqrt re))))) (pow re 3))) (* 1/2 (* (sqrt (/ 1 re)) (* (sqrt -1) (pow (sqrt 2) 2)))))))
(* 1/2 (* (* im (* (sqrt -2) (* (sqrt -1) (sqrt 1/2)))) (sqrt (/ 1 re))))
(* 1/2 (* (* im (* (sqrt -2) (* (sqrt -1) (sqrt 1/2)))) (sqrt (/ 1 re))))
(* 1/2 (* (* im (* (sqrt -2) (* (sqrt -1) (sqrt 1/2)))) (sqrt (/ 1 re))))
(* 1/2 (* (* im (* (sqrt -2) (* (sqrt -1) (sqrt 1/2)))) (sqrt (/ 1 re))))
(* (sqrt (/ 1 re)) (* (sqrt -2) (sqrt -1)))
(* (sqrt (/ 1 re)) (* (sqrt -2) (sqrt -1)))
(* (sqrt (/ 1 re)) (* (sqrt -2) (sqrt -1)))
(* (sqrt (/ 1 re)) (* (sqrt -2) (sqrt -1)))
(* 1/2 (* (* im (* (sqrt 1/2) (sqrt 2))) (sqrt (/ 1 re))))
(* im (+ (* -1/32 (* (/ (* (pow im 2) (sqrt 2)) (sqrt 1/2)) (sqrt (/ 1 (pow re 5))))) (* 1/2 (* (sqrt (/ 1 re)) (* (sqrt 1/2) (sqrt 2))))))
(* im (+ (* 1/2 (* (sqrt (/ 1 re)) (* (sqrt 1/2) (sqrt 2)))) (* (pow im 2) (+ (* -1/32 (* (sqrt (/ 1 (pow re 5))) (/ (sqrt 2) (sqrt 1/2)))) (* 1/4 (* (/ (* (pow im 2) (* (sqrt 2) (- (* 1/16 (/ 1 (pow re 5))) (* 1/256 (/ 1 (* (pow re 5) (pow (sqrt 1/2) 2))))))) (sqrt 1/2)) (sqrt re)))))))
(* im (+ (* 1/2 (* (sqrt (/ 1 re)) (* (sqrt 1/2) (sqrt 2)))) (* (pow im 2) (+ (* -1/32 (* (sqrt (/ 1 (pow re 5))) (/ (sqrt 2) (sqrt 1/2)))) (* (pow im 2) (+ (* -1/4 (* (/ (* (pow im 2) (* (sqrt 2) (+ (* -1/16 (/ (- (* 1/16 (/ 1 (pow re 5))) (* 1/256 (/ 1 (* (pow re 5) (pow (sqrt 1/2) 2))))) (* (pow re 2) (pow (sqrt 1/2) 2)))) (* 5/128 (/ 1 (pow re 7)))))) (sqrt 1/2)) (sqrt re))) (* 1/4 (* (sqrt re) (/ (* (sqrt 2) (- (* 1/16 (/ 1 (pow re 5))) (* 1/256 (/ 1 (* (pow re 5) (pow (sqrt 1/2) 2)))))) (sqrt 1/2))))))))))
(* (* im (* (sqrt 1/2) (sqrt 2))) (sqrt (/ 1 re)))
(* im (+ (* -1/16 (* (/ (* (pow im 2) (sqrt 2)) (sqrt 1/2)) (sqrt (/ 1 (pow re 5))))) (* (sqrt (/ 1 re)) (* (sqrt 1/2) (sqrt 2)))))
(* im (+ (* (sqrt (/ 1 re)) (* (sqrt 1/2) (sqrt 2))) (* (pow im 2) (+ (* -1/16 (* (sqrt (/ 1 (pow re 5))) (/ (sqrt 2) (sqrt 1/2)))) (* 1/2 (* (/ (* (pow im 2) (* (sqrt 2) (- (* 1/16 (/ 1 (pow re 5))) (* 1/256 (/ 1 (* (pow re 5) (pow (sqrt 1/2) 2))))))) (sqrt 1/2)) (sqrt re)))))))
(* im (+ (* (sqrt (/ 1 re)) (* (sqrt 1/2) (sqrt 2))) (* (pow im 2) (+ (* -1/16 (* (sqrt (/ 1 (pow re 5))) (/ (sqrt 2) (sqrt 1/2)))) (* (pow im 2) (+ (* -1/2 (* (/ (* (pow im 2) (* (sqrt 2) (+ (* -1/16 (/ (- (* 1/16 (/ 1 (pow re 5))) (* 1/256 (/ 1 (* (pow re 5) (pow (sqrt 1/2) 2))))) (* (pow re 2) (pow (sqrt 1/2) 2)))) (* 5/128 (/ 1 (pow re 7)))))) (sqrt 1/2)) (sqrt re))) (* 1/2 (* (sqrt re) (/ (* (sqrt 2) (- (* 1/16 (/ 1 (pow re 5))) (* 1/256 (/ 1 (* (pow re 5) (pow (sqrt 1/2) 2)))))) (sqrt 1/2))))))))))
(* (* im (sqrt 1/2)) (sqrt (/ 1 re)))
(* im (+ (* -1/16 (* (/ (pow im 2) (sqrt 1/2)) (sqrt (/ 1 (pow re 5))))) (* (sqrt (/ 1 re)) (sqrt 1/2))))
(* im (+ (* (sqrt (/ 1 re)) (sqrt 1/2)) (* (pow im 2) (+ (* -1/16 (* (sqrt (/ 1 (pow re 5))) (/ 1 (sqrt 1/2)))) (* 1/2 (* (/ (* (pow im 2) (- (* 1/16 (/ 1 (pow re 5))) (* 1/256 (/ 1 (* (pow re 5) (pow (sqrt 1/2) 2)))))) (sqrt 1/2)) (sqrt re)))))))
(* im (+ (* (sqrt (/ 1 re)) (sqrt 1/2)) (* (pow im 2) (+ (* -1/16 (* (sqrt (/ 1 (pow re 5))) (/ 1 (sqrt 1/2)))) (* (pow im 2) (+ (* -1/2 (* (/ (* (pow im 2) (+ (* -1/16 (/ (- (* 1/16 (/ 1 (pow re 5))) (* 1/256 (/ 1 (* (pow re 5) (pow (sqrt 1/2) 2))))) (* (pow re 2) (pow (sqrt 1/2) 2)))) (* 5/128 (/ 1 (pow re 7))))) (sqrt 1/2)) (sqrt re))) (* 1/2 (* (sqrt re) (/ (- (* 1/16 (/ 1 (pow re 5))) (* 1/256 (/ 1 (* (pow re 5) (pow (sqrt 1/2) 2))))) (sqrt 1/2))))))))))
(* 1/2 (/ (pow im 2) re))
(* (pow im 2) (+ (* -1/8 (/ (pow im 2) (pow re 3))) (* 1/2 (/ 1 re))))
(* (pow im 2) (+ (* (pow im 2) (- (* 1/16 (/ (pow im 2) (pow re 5))) (* 1/8 (/ 1 (pow re 3))))) (* 1/2 (/ 1 re))))
(* (pow im 2) (+ (* (pow im 2) (- (* (pow im 2) (+ (* -5/128 (/ (pow im 2) (pow re 7))) (* 1/16 (/ 1 (pow re 5))))) (* 1/8 (/ 1 (pow re 3))))) (* 1/2 (/ 1 re))))
(* 1/2 (* (* im (* (sqrt 1/2) (sqrt 2))) (sqrt (/ 1 re))))
(* im (+ (* -1/32 (* (/ (* (pow im 2) (sqrt 2)) (sqrt 1/2)) (sqrt (/ 1 (pow re 5))))) (* 1/2 (* (sqrt (/ 1 re)) (* (sqrt 1/2) (sqrt 2))))))
(* im (+ (* 1/2 (* (sqrt (/ 1 re)) (* (sqrt 1/2) (sqrt 2)))) (* (pow im 2) (+ (* -1/32 (* (sqrt (/ 1 (pow re 5))) (/ (sqrt 2) (sqrt 1/2)))) (* 1/4 (* (/ (* (pow im 2) (* (sqrt 2) (- (* 1/16 (/ 1 (pow re 5))) (* 1/256 (/ 1 (* (pow re 5) (pow (sqrt 1/2) 2))))))) (sqrt 1/2)) (sqrt re)))))))
(* im (+ (* 1/2 (* (sqrt (/ 1 re)) (* (sqrt 1/2) (sqrt 2)))) (* (pow im 2) (+ (* -1/32 (* (sqrt (/ 1 (pow re 5))) (/ (sqrt 2) (sqrt 1/2)))) (* (pow im 2) (+ (* -1/4 (* (/ (* (pow im 2) (* (sqrt 2) (+ (* -1/16 (/ (- (* 1/16 (/ 1 (pow re 5))) (* 1/256 (/ 1 (* (pow re 5) (pow (sqrt 1/2) 2))))) (* (pow re 2) (pow (sqrt 1/2) 2)))) (* 5/128 (/ 1 (pow re 7)))))) (sqrt 1/2)) (sqrt re))) (* 1/4 (* (sqrt re) (/ (* (sqrt 2) (- (* 1/16 (/ 1 (pow re 5))) (* 1/256 (/ 1 (* (pow re 5) (pow (sqrt 1/2) 2)))))) (sqrt 1/2))))))))))
(* (* im (* (sqrt 1/2) (sqrt 2))) (sqrt (/ 1 re)))
(* im (+ (* -1/16 (* (/ (* (pow im 2) (sqrt 2)) (sqrt 1/2)) (sqrt (/ 1 (pow re 5))))) (* (sqrt (/ 1 re)) (* (sqrt 1/2) (sqrt 2)))))
(* im (+ (* (sqrt (/ 1 re)) (* (sqrt 1/2) (sqrt 2))) (* (pow im 2) (+ (* -1/16 (* (sqrt (/ 1 (pow re 5))) (/ (sqrt 2) (sqrt 1/2)))) (* 1/2 (* (/ (* (pow im 2) (* (sqrt 2) (- (* 1/16 (/ 1 (pow re 5))) (* 1/256 (/ 1 (* (pow re 5) (pow (sqrt 1/2) 2))))))) (sqrt 1/2)) (sqrt re)))))))
(* im (+ (* (sqrt (/ 1 re)) (* (sqrt 1/2) (sqrt 2))) (* (pow im 2) (+ (* -1/16 (* (sqrt (/ 1 (pow re 5))) (/ (sqrt 2) (sqrt 1/2)))) (* (pow im 2) (+ (* -1/2 (* (/ (* (pow im 2) (* (sqrt 2) (+ (* -1/16 (/ (- (* 1/16 (/ 1 (pow re 5))) (* 1/256 (/ 1 (* (pow re 5) (pow (sqrt 1/2) 2))))) (* (pow re 2) (pow (sqrt 1/2) 2)))) (* 5/128 (/ 1 (pow re 7)))))) (sqrt 1/2)) (sqrt re))) (* 1/2 (* (sqrt re) (/ (* (sqrt 2) (- (* 1/16 (/ 1 (pow re 5))) (* 1/256 (/ 1 (* (pow re 5) (pow (sqrt 1/2) 2)))))) (sqrt 1/2))))))))))
(/ (pow im 2) re)
(* (pow im 2) (+ (* -1/4 (/ (pow im 2) (pow re 3))) (/ 1 re)))
(* (pow im 2) (+ (* (pow im 2) (- (* 1/8 (/ (pow im 2) (pow re 5))) (* 1/4 (/ 1 (pow re 3))))) (/ 1 re)))
(* (pow im 2) (+ (* (pow im 2) (- (* (pow im 2) (+ (* -5/64 (/ (pow im 2) (pow re 7))) (* 1/8 (/ 1 (pow re 5))))) (* 1/4 (/ 1 (pow re 3))))) (/ 1 re)))
(* 2 im)
(* 2 im)
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(* 2 im)
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(* im (+ (* -1/32 (* (/ (* (pow im 2) (sqrt 2)) (sqrt 1/2)) (sqrt (/ 1 (pow re 5))))) (* 1/2 (* (sqrt (/ 1 re)) (* (sqrt 1/2) (sqrt 2))))))
(* im (+ (* 1/2 (* (sqrt (/ 1 re)) (* (sqrt 1/2) (sqrt 2)))) (* (pow im 2) (+ (* -1/32 (* (sqrt (/ 1 (pow re 5))) (/ (sqrt 2) (sqrt 1/2)))) (* 1/4 (* (/ (* (pow im 2) (* (sqrt 2) (- (* 1/16 (/ 1 (pow re 5))) (* 1/256 (/ 1 (* (pow re 5) (pow (sqrt 1/2) 2))))))) (sqrt 1/2)) (sqrt re)))))))
(* im (+ (* 1/2 (* (sqrt (/ 1 re)) (* (sqrt 1/2) (sqrt 2)))) (* (pow im 2) (+ (* -1/32 (* (sqrt (/ 1 (pow re 5))) (/ (sqrt 2) (sqrt 1/2)))) (* (pow im 2) (+ (* -1/4 (* (/ (* (pow im 2) (* (sqrt 2) (+ (* -1/16 (/ (- (* 1/16 (/ 1 (pow re 5))) (* 1/256 (/ 1 (* (pow re 5) (pow (sqrt 1/2) 2))))) (* (pow re 2) (pow (sqrt 1/2) 2)))) (* 5/128 (/ 1 (pow re 7)))))) (sqrt 1/2)) (sqrt re))) (* 1/4 (* (sqrt re) (/ (* (sqrt 2) (- (* 1/16 (/ 1 (pow re 5))) (* 1/256 (/ 1 (* (pow re 5) (pow (sqrt 1/2) 2)))))) (sqrt 1/2))))))))))
(* (* im (* (sqrt 1/2) (sqrt 2))) (sqrt (/ 1 re)))
(* im (+ (* -1/16 (* (/ (* (pow im 2) (sqrt 2)) (sqrt 1/2)) (sqrt (/ 1 (pow re 5))))) (* (sqrt (/ 1 re)) (* (sqrt 1/2) (sqrt 2)))))
(* im (+ (* (sqrt (/ 1 re)) (* (sqrt 1/2) (sqrt 2))) (* (pow im 2) (+ (* -1/16 (* (sqrt (/ 1 (pow re 5))) (/ (sqrt 2) (sqrt 1/2)))) (* 1/2 (* (/ (* (pow im 2) (* (sqrt 2) (- (* 1/16 (/ 1 (pow re 5))) (* 1/256 (/ 1 (* (pow re 5) (pow (sqrt 1/2) 2))))))) (sqrt 1/2)) (sqrt re)))))))
(* im (+ (* (sqrt (/ 1 re)) (* (sqrt 1/2) (sqrt 2))) (* (pow im 2) (+ (* -1/16 (* (sqrt (/ 1 (pow re 5))) (/ (sqrt 2) (sqrt 1/2)))) (* (pow im 2) (+ (* -1/2 (* (/ (* (pow im 2) (* (sqrt 2) (+ (* -1/16 (/ (- (* 1/16 (/ 1 (pow re 5))) (* 1/256 (/ 1 (* (pow re 5) (pow (sqrt 1/2) 2))))) (* (pow re 2) (pow (sqrt 1/2) 2)))) (* 5/128 (/ 1 (pow re 7)))))) (sqrt 1/2)) (sqrt re))) (* 1/2 (* (sqrt re) (/ (* (sqrt 2) (- (* 1/16 (/ 1 (pow re 5))) (* 1/256 (/ 1 (* (pow re 5) (pow (sqrt 1/2) 2)))))) (sqrt 1/2))))))))))
(* (sqrt im) (sqrt 2))
(* (sqrt im) (sqrt 2))
(* (sqrt im) (sqrt 2))
(* (sqrt im) (sqrt 2))
(* -2 re)
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(+ (* -2 re) (* 2 im))
(+ (* -2 re) (* 2 im))
(* 1/2 (* (* im (* (sqrt 1/2) (sqrt 2))) (sqrt (/ 1 re))))
(* im (+ (* -1/32 (* (/ (* (pow im 2) (sqrt 2)) (sqrt 1/2)) (sqrt (/ 1 (pow re 5))))) (* 1/2 (* (sqrt (/ 1 re)) (* (sqrt 1/2) (sqrt 2))))))
(* im (+ (* 1/2 (* (sqrt (/ 1 re)) (* (sqrt 1/2) (sqrt 2)))) (* (pow im 2) (+ (* -1/32 (* (sqrt (/ 1 (pow re 5))) (/ (sqrt 2) (sqrt 1/2)))) (* 1/4 (* (/ (* (pow im 2) (* (sqrt 2) (- (* 1/16 (/ 1 (pow re 5))) (* 1/256 (/ 1 (* (pow re 5) (pow (sqrt 1/2) 2))))))) (sqrt 1/2)) (sqrt re)))))))
(* im (+ (* 1/2 (* (sqrt (/ 1 re)) (* (sqrt 1/2) (sqrt 2)))) (* (pow im 2) (+ (* -1/32 (* (sqrt (/ 1 (pow re 5))) (/ (sqrt 2) (sqrt 1/2)))) (* (pow im 2) (+ (* -1/4 (* (/ (* (pow im 2) (* (sqrt 2) (+ (* -1/16 (/ (- (* 1/16 (/ 1 (pow re 5))) (* 1/256 (/ 1 (* (pow re 5) (pow (sqrt 1/2) 2))))) (* (pow re 2) (pow (sqrt 1/2) 2)))) (* 5/128 (/ 1 (pow re 7)))))) (sqrt 1/2)) (sqrt re))) (* 1/4 (* (sqrt re) (/ (* (sqrt 2) (- (* 1/16 (/ 1 (pow re 5))) (* 1/256 (/ 1 (* (pow re 5) (pow (sqrt 1/2) 2)))))) (sqrt 1/2))))))))))
(* (* im (* (sqrt 1/2) (sqrt 2))) (sqrt (/ 1 re)))
(* im (+ (* -1/16 (* (/ (* (pow im 2) (sqrt 2)) (sqrt 1/2)) (sqrt (/ 1 (pow re 5))))) (* (sqrt (/ 1 re)) (* (sqrt 1/2) (sqrt 2)))))
(* im (+ (* (sqrt (/ 1 re)) (* (sqrt 1/2) (sqrt 2))) (* (pow im 2) (+ (* -1/16 (* (sqrt (/ 1 (pow re 5))) (/ (sqrt 2) (sqrt 1/2)))) (* 1/2 (* (/ (* (pow im 2) (* (sqrt 2) (- (* 1/16 (/ 1 (pow re 5))) (* 1/256 (/ 1 (* (pow re 5) (pow (sqrt 1/2) 2))))))) (sqrt 1/2)) (sqrt re)))))))
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(/ (pow im 2) re)
(* (pow im 2) (+ (* -1/4 (/ (pow im 2) (pow re 3))) (/ 1 re)))
(* (pow im 2) (+ (* (pow im 2) (- (* 1/8 (/ (pow im 2) (pow re 5))) (* 1/4 (/ 1 (pow re 3))))) (/ 1 re)))
(* (pow im 2) (+ (* (pow im 2) (- (* (pow im 2) (+ (* -5/64 (/ (pow im 2) (pow re 7))) (* 1/8 (/ 1 (pow re 5))))) (* 1/4 (/ 1 (pow re 3))))) (/ 1 re)))
(* 1/2 (* (* im (* (sqrt 1/2) (sqrt 2))) (sqrt (/ 1 re))))
(* im (+ (* -1/32 (* (/ (* (pow im 2) (sqrt 2)) (sqrt 1/2)) (sqrt (/ 1 (pow re 5))))) (* 1/2 (* (sqrt (/ 1 re)) (* (sqrt 1/2) (sqrt 2))))))
(* im (+ (* 1/2 (* (sqrt (/ 1 re)) (* (sqrt 1/2) (sqrt 2)))) (* (pow im 2) (+ (* -1/32 (* (sqrt (/ 1 (pow re 5))) (/ (sqrt 2) (sqrt 1/2)))) (* 1/4 (* (/ (* (pow im 2) (* (sqrt 2) (- (* 1/16 (/ 1 (pow re 5))) (* 1/256 (/ 1 (* (pow re 5) (pow (sqrt 1/2) 2))))))) (sqrt 1/2)) (sqrt re)))))))
(* im (+ (* 1/2 (* (sqrt (/ 1 re)) (* (sqrt 1/2) (sqrt 2)))) (* (pow im 2) (+ (* -1/32 (* (sqrt (/ 1 (pow re 5))) (/ (sqrt 2) (sqrt 1/2)))) (* (pow im 2) (+ (* -1/4 (* (/ (* (pow im 2) (* (sqrt 2) (+ (* -1/16 (/ (- (* 1/16 (/ 1 (pow re 5))) (* 1/256 (/ 1 (* (pow re 5) (pow (sqrt 1/2) 2))))) (* (pow re 2) (pow (sqrt 1/2) 2)))) (* 5/128 (/ 1 (pow re 7)))))) (sqrt 1/2)) (sqrt re))) (* 1/4 (* (sqrt re) (/ (* (sqrt 2) (- (* 1/16 (/ 1 (pow re 5))) (* 1/256 (/ 1 (* (pow re 5) (pow (sqrt 1/2) 2)))))) (sqrt 1/2))))))))))
(* 1/2 (* (* im (* (sqrt 1/2) (sqrt 2))) (sqrt (/ 1 re))))
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(* 1/2 (* (* im (* (sqrt 1/2) (sqrt 2))) (sqrt (/ 1 re))))
(* 1/2 (* (* im (* (sqrt 1/2) (sqrt 2))) (sqrt (/ 1 re))))
(* im (sqrt 1/2))
(* im (sqrt 1/2))
(* im (sqrt 1/2))
(* im (sqrt 1/2))
(* 1/2 (* (sqrt im) (sqrt 2)))
(* im (+ (* -1/4 (* (sqrt (/ 1 (pow im 3))) (* re (sqrt 2)))) (* 1/2 (* (sqrt (/ 1 im)) (sqrt 2)))))
(* im (+ (* -1/4 (* (sqrt (/ 1 (pow im 3))) (* re (sqrt 2)))) (+ (* 1/8 (* (sqrt (/ 1 (pow im 5))) (* (pow re 2) (sqrt 2)))) (* 1/2 (* (sqrt (/ 1 im)) (sqrt 2))))))
(* im (+ (* -1/4 (* (sqrt (/ 1 (pow im 3))) (* re (sqrt 2)))) (+ (* -1/16 (* (sqrt (/ 1 (pow im 5))) (* (pow re 2) (sqrt 2)))) (+ (* 1/8 (* (sqrt (/ 1 (pow im 5))) (* (pow re 2) (sqrt 2)))) (* 1/2 (* (sqrt (/ 1 im)) (sqrt 2)))))))
(* (sqrt im) (sqrt 2))
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(* im (+ (* -1/2 (* (sqrt (/ 1 (pow im 3))) (* re (sqrt 2)))) (+ (* -1/8 (* (sqrt (/ 1 (pow im 5))) (* (pow re 2) (sqrt 2)))) (+ (* 1/4 (* (sqrt (/ 1 (pow im 5))) (* (pow re 2) (sqrt 2)))) (* (sqrt (/ 1 im)) (sqrt 2))))))
(sqrt im)
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(* im (+ (sqrt (/ 1 im)) (+ (* -1/2 (* (sqrt (/ 1 (pow im 3))) re)) (+ (* -1/8 (* (sqrt (/ 1 (pow im 5))) (pow re 2))) (* 1/4 (* (sqrt (/ 1 (pow im 5))) (pow re 2)))))))
im
(* im (+ 1 (* -1 (/ re im))))
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(* im (+ (* -1/4 (* (sqrt (/ 1 (pow im 3))) (* re (sqrt 2)))) (+ (* -1/16 (* (sqrt (/ 1 (pow im 5))) (* (pow re 2) (sqrt 2)))) (+ (* 1/8 (* (sqrt (/ 1 (pow im 5))) (* (pow re 2) (sqrt 2)))) (* 1/2 (* (sqrt (/ 1 im)) (sqrt 2)))))))
(* (sqrt im) (sqrt 2))
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(* im (+ (* -1/2 (* (sqrt (/ 1 (pow im 3))) (* re (sqrt 2)))) (+ (* 1/4 (* (sqrt (/ 1 (pow im 5))) (* (pow re 2) (sqrt 2)))) (* (sqrt (/ 1 im)) (sqrt 2)))))
(* im (+ (* -1/2 (* (sqrt (/ 1 (pow im 3))) (* re (sqrt 2)))) (+ (* -1/8 (* (sqrt (/ 1 (pow im 5))) (* (pow re 2) (sqrt 2)))) (+ (* 1/4 (* (sqrt (/ 1 (pow im 5))) (* (pow re 2) (sqrt 2)))) (* (sqrt (/ 1 im)) (sqrt 2))))))
(* 2 im)
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(* im (+ 2 (+ (* -2 (/ re im)) (/ (pow re 2) (pow im 2)))))
(* im (+ 2 (+ (* -2 (/ re im)) (+ (* -1/4 (/ (pow re 4) (pow im 4))) (/ (pow re 2) (pow im 2))))))
(* 2 im)
(* 2 im)
(* 2 im)
(* 2 im)
(* 1/2 (* (sqrt im) (sqrt 2)))
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(* im (+ (* -1/4 (* (sqrt (/ 1 (pow im 3))) (* re (sqrt 2)))) (+ (* -1/16 (* (sqrt (/ 1 (pow im 5))) (* (pow re 2) (sqrt 2)))) (+ (* 1/8 (* (sqrt (/ 1 (pow im 5))) (* (pow re 2) (sqrt 2)))) (* 1/2 (* (sqrt (/ 1 im)) (sqrt 2)))))))
(* (sqrt im) (sqrt 2))
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(* (sqrt im) (sqrt 2))
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(* im (+ (* -1/4 (* (sqrt (/ 1 (pow im 3))) (* re (sqrt 2)))) (+ (* -1/16 (* (sqrt (/ 1 (pow im 5))) (* (pow re 2) (sqrt 2)))) (+ (* 1/8 (* (sqrt (/ 1 (pow im 5))) (* (pow re 2) (sqrt 2)))) (* 1/2 (* (sqrt (/ 1 im)) (sqrt 2)))))))
(* (sqrt im) (sqrt 2))
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(* 2 im)
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(* -1 (* (sqrt im) (sqrt -1)))
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(* -1 im)
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(* -1 (* im (+ (* -1/4 (* (sqrt (/ 1 (pow im 3))) (* re (* (sqrt -1) (sqrt 2))))) (* 1/2 (* (sqrt (/ 1 im)) (* (sqrt -1) (sqrt 2)))))))
(* -1 (* im (+ (* -1/4 (* (sqrt (/ 1 (pow im 3))) (* re (* (sqrt -1) (sqrt 2))))) (+ (* -1/8 (* (sqrt (/ 1 (pow im 5))) (* (pow re 2) (* (sqrt -1) (sqrt 2))))) (* 1/2 (* (sqrt (/ 1 im)) (* (sqrt -1) (sqrt 2))))))))
(* -1 (* im (+ (* -1 (/ (+ (* 1/16 (* (sqrt im) (* (pow re 2) (* (sqrt -1) (sqrt 2))))) (* 1/8 (* (sqrt im) (* (pow re 2) (* (sqrt -1) (sqrt 2)))))) (pow im 3))) (+ (* -1/4 (* (sqrt (/ 1 (pow im 3))) (* re (* (sqrt -1) (sqrt 2))))) (* 1/2 (* (sqrt (/ 1 im)) (* (sqrt -1) (sqrt 2))))))))
(* -1 (* (sqrt im) (* (sqrt -1) (sqrt 2))))
(* -1 (* im (+ (* -1/2 (* (sqrt (/ 1 (pow im 3))) (* re (* (sqrt -1) (sqrt 2))))) (* (sqrt (/ 1 im)) (* (sqrt -1) (sqrt 2))))))
(* -1 (* im (+ (* -1/2 (* (sqrt (/ 1 (pow im 3))) (* re (* (sqrt -1) (sqrt 2))))) (+ (* -1/4 (* (sqrt (/ 1 (pow im 5))) (* (pow re 2) (* (sqrt -1) (sqrt 2))))) (* (sqrt (/ 1 im)) (* (sqrt -1) (sqrt 2)))))))
(* -1 (* im (+ (* -1 (/ (+ (* 1/8 (* (sqrt im) (* (pow re 2) (* (sqrt -1) (sqrt 2))))) (* 1/4 (* (sqrt im) (* (pow re 2) (* (sqrt -1) (sqrt 2)))))) (pow im 3))) (+ (* -1/2 (* (sqrt (/ 1 (pow im 3))) (* re (* (sqrt -1) (sqrt 2))))) (* (sqrt (/ 1 im)) (* (sqrt -1) (sqrt 2)))))))
(* -2 im)
(* -1 (* im (+ 2 (* 2 (/ re im)))))
(* -1 (* im (+ 2 (* -1 (/ (+ (* -2 re) (* -1 (/ (pow re 2) im))) im)))))
(* -1 (* im (+ 2 (* -1 (/ (+ (* -2 re) (* -1 (/ (+ (* -1/4 (/ (pow re 4) (pow im 2))) (pow re 2)) im))) im)))))
(* 2 im)
(* 2 im)
(* 2 im)
(* 2 im)
(* -1/2 (* (sqrt im) (* (sqrt -1) (sqrt 2))))
(* -1 (* im (+ (* -1/4 (* (sqrt (/ 1 (pow im 3))) (* re (* (sqrt -1) (sqrt 2))))) (* 1/2 (* (sqrt (/ 1 im)) (* (sqrt -1) (sqrt 2)))))))
(* -1 (* im (+ (* -1/4 (* (sqrt (/ 1 (pow im 3))) (* re (* (sqrt -1) (sqrt 2))))) (+ (* -1/8 (* (sqrt (/ 1 (pow im 5))) (* (pow re 2) (* (sqrt -1) (sqrt 2))))) (* 1/2 (* (sqrt (/ 1 im)) (* (sqrt -1) (sqrt 2))))))))
(* -1 (* im (+ (* -1 (/ (+ (* 1/16 (* (sqrt im) (* (pow re 2) (* (sqrt -1) (sqrt 2))))) (* 1/8 (* (sqrt im) (* (pow re 2) (* (sqrt -1) (sqrt 2)))))) (pow im 3))) (+ (* -1/4 (* (sqrt (/ 1 (pow im 3))) (* re (* (sqrt -1) (sqrt 2))))) (* 1/2 (* (sqrt (/ 1 im)) (* (sqrt -1) (sqrt 2))))))))
(* -1 (* (sqrt im) (* (sqrt -1) (sqrt 2))))
(* -1 (* im (+ (* -1/2 (* (sqrt (/ 1 (pow im 3))) (* re (* (sqrt -1) (sqrt 2))))) (* (sqrt (/ 1 im)) (* (sqrt -1) (sqrt 2))))))
(* -1 (* im (+ (* -1/2 (* (sqrt (/ 1 (pow im 3))) (* re (* (sqrt -1) (sqrt 2))))) (+ (* -1/4 (* (sqrt (/ 1 (pow im 5))) (* (pow re 2) (* (sqrt -1) (sqrt 2))))) (* (sqrt (/ 1 im)) (* (sqrt -1) (sqrt 2)))))))
(* -1 (* im (+ (* -1 (/ (+ (* 1/8 (* (sqrt im) (* (pow re 2) (* (sqrt -1) (sqrt 2))))) (* 1/4 (* (sqrt im) (* (pow re 2) (* (sqrt -1) (sqrt 2)))))) (pow im 3))) (+ (* -1/2 (* (sqrt (/ 1 (pow im 3))) (* re (* (sqrt -1) (sqrt 2))))) (* (sqrt (/ 1 im)) (* (sqrt -1) (sqrt 2)))))))
(* -1 (* (sqrt im) (* (pow (sqrt -1) 2) (sqrt 2))))
(* -1 (* (sqrt im) (* (pow (sqrt -1) 2) (sqrt 2))))
(* -1 (* (sqrt im) (* (pow (sqrt -1) 2) (sqrt 2))))
(* -1 (* (sqrt im) (* (pow (sqrt -1) 2) (sqrt 2))))
(* 2 im)
(* -1 (* im (- (* 2 (/ re im)) 2)))
(* -1 (* im (- (* 2 (/ re im)) 2)))
(* -1 (* im (- (* 2 (/ re im)) 2)))
(* -1/2 (* (sqrt im) (* (sqrt -1) (sqrt 2))))
(* -1 (* im (+ (* -1/4 (* (sqrt (/ 1 (pow im 3))) (* re (* (sqrt -1) (sqrt 2))))) (* 1/2 (* (sqrt (/ 1 im)) (* (sqrt -1) (sqrt 2)))))))
(* -1 (* im (+ (* -1/4 (* (sqrt (/ 1 (pow im 3))) (* re (* (sqrt -1) (sqrt 2))))) (+ (* -1/8 (* (sqrt (/ 1 (pow im 5))) (* (pow re 2) (* (sqrt -1) (sqrt 2))))) (* 1/2 (* (sqrt (/ 1 im)) (* (sqrt -1) (sqrt 2))))))))
(* -1 (* im (+ (* -1 (/ (+ (* 1/16 (* (sqrt im) (* (pow re 2) (* (sqrt -1) (sqrt 2))))) (* 1/8 (* (sqrt im) (* (pow re 2) (* (sqrt -1) (sqrt 2)))))) (pow im 3))) (+ (* -1/4 (* (sqrt (/ 1 (pow im 3))) (* re (* (sqrt -1) (sqrt 2))))) (* 1/2 (* (sqrt (/ 1 im)) (* (sqrt -1) (sqrt 2))))))))
(* -1 (* (sqrt im) (* (sqrt -1) (sqrt 2))))
(* -1 (* im (+ (* -1/2 (* (sqrt (/ 1 (pow im 3))) (* re (* (sqrt -1) (sqrt 2))))) (* (sqrt (/ 1 im)) (* (sqrt -1) (sqrt 2))))))
(* -1 (* im (+ (* -1/2 (* (sqrt (/ 1 (pow im 3))) (* re (* (sqrt -1) (sqrt 2))))) (+ (* -1/4 (* (sqrt (/ 1 (pow im 5))) (* (pow re 2) (* (sqrt -1) (sqrt 2))))) (* (sqrt (/ 1 im)) (* (sqrt -1) (sqrt 2)))))))
(* -1 (* im (+ (* -1 (/ (+ (* 1/8 (* (sqrt im) (* (pow re 2) (* (sqrt -1) (sqrt 2))))) (* 1/4 (* (sqrt im) (* (pow re 2) (* (sqrt -1) (sqrt 2)))))) (pow im 3))) (+ (* -1/2 (* (sqrt (/ 1 (pow im 3))) (* re (* (sqrt -1) (sqrt 2))))) (* (sqrt (/ 1 im)) (* (sqrt -1) (sqrt 2)))))))
(* -2 im)
(* -1 (* im (+ 2 (* 2 (/ re im)))))
(* -1 (* im (+ 2 (* -1 (/ (+ (* -2 re) (* -1 (/ (pow re 2) im))) im)))))
(* -1 (* im (+ 2 (* -1 (/ (+ (* -2 re) (* -1 (/ (+ (* -1/4 (/ (pow re 4) (pow im 2))) (pow re 2)) im))) im)))))
(* -1/2 (* (sqrt im) (* (sqrt -1) (sqrt 2))))
(* -1 (* im (+ (* -1/4 (* (sqrt (/ 1 (pow im 3))) (* re (* (sqrt -1) (sqrt 2))))) (* 1/2 (* (sqrt (/ 1 im)) (* (sqrt -1) (sqrt 2)))))))
(* -1 (* im (+ (* -1/4 (* (sqrt (/ 1 (pow im 3))) (* re (* (sqrt -1) (sqrt 2))))) (+ (* -1/8 (* (sqrt (/ 1 (pow im 5))) (* (pow re 2) (* (sqrt -1) (sqrt 2))))) (* 1/2 (* (sqrt (/ 1 im)) (* (sqrt -1) (sqrt 2))))))))
(* -1 (* im (+ (* -1 (/ (+ (* 1/16 (* (sqrt im) (* (pow re 2) (* (sqrt -1) (sqrt 2))))) (* 1/8 (* (sqrt im) (* (pow re 2) (* (sqrt -1) (sqrt 2)))))) (pow im 3))) (+ (* -1/4 (* (sqrt (/ 1 (pow im 3))) (* re (* (sqrt -1) (sqrt 2))))) (* 1/2 (* (sqrt (/ 1 im)) (* (sqrt -1) (sqrt 2))))))))
(* 1/2 (* (* im (* (sqrt 1/2) (sqrt 2))) (sqrt (/ 1 re))))
(* 1/2 (* (* im (* (sqrt 1/2) (sqrt 2))) (sqrt (/ 1 re))))
(* 1/2 (* (* im (* (sqrt 1/2) (sqrt 2))) (sqrt (/ 1 re))))
(* 1/2 (* (* im (* (sqrt 1/2) (sqrt 2))) (sqrt (/ 1 re))))
(* im (sqrt 1/2))
(* im (sqrt 1/2))
(* im (sqrt 1/2))
(* im (sqrt 1/2))

Outputs
(.f64 (.f64 #s(literal 1/2 binary64) (sqrt.f64 #s(literal 2 binary64))) (sqrt.f64 im))
(fma.f64 (.f64 #s(literal 1/2 binary64) (sqrt.f64 #s(literal 2 binary64))) (sqrt.f64 im) (.f64 (.f64 #s(literal -1/4 binary64) (.f64 (sqrt.f64 #s(literal 2 binary64)) re)) (sqrt.f64 (/.f64 #s(literal 1 binary64) im))))
(fma.f64 (fma.f64 (.f64 #s(literal -1/4 binary64) (sqrt.f64 #s(literal 2 binary64))) (sqrt.f64 (/.f64 #s(literal 1 binary64) im)) (.f64 (.f64 #s(literal 1/16 binary64) (.f64 (sqrt.f64 #s(literal 2 binary64)) re)) (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 im #s(literal 3 binary64)))))) re (.f64 (.f64 #s(literal 1/2 binary64) (sqrt.f64 #s(literal 2 binary64))) (sqrt.f64 im)))
(fma.f64 (fma.f64 (.f64 #s(literal -1/4 binary64) (sqrt.f64 #s(literal 2 binary64))) (sqrt.f64 (/.f64 #s(literal 1 binary64) im)) (.f64 (fma.f64 (.f64 #s(literal 1/32 binary64) (.f64 (sqrt.f64 #s(literal 2 binary64)) re)) (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 im #s(literal 5 binary64)))) (.f64 (.f64 #s(literal 1/16 binary64) (sqrt.f64 #s(literal 2 binary64))) (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 im #s(literal 3 binary64)))))) re)) re (.f64 (.f64 #s(literal 1/2 binary64) (sqrt.f64 #s(literal 2 binary64))) (sqrt.f64 im)))
(*.f64 (sqrt.f64 #s(literal 2 binary64)) (sqrt.f64 im))
(fma.f64 (.f64 #s(literal -1/2 binary64) (.f64 (sqrt.f64 #s(literal 2 binary64)) re)) (sqrt.f64 (/.f64 #s(literal 1 binary64) im)) (*.f64 (sqrt.f64 #s(literal 2 binary64)) (sqrt.f64 im)))
(fma.f64 (fma.f64 (.f64 #s(literal 1/8 binary64) (.f64 (sqrt.f64 #s(literal 2 binary64)) re)) (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 im #s(literal 3 binary64)))) (.f64 (.f64 #s(literal -1/2 binary64) (sqrt.f64 #s(literal 2 binary64))) (sqrt.f64 (/.f64 #s(literal 1 binary64) im)))) re (*.f64 (sqrt.f64 #s(literal 2 binary64)) (sqrt.f64 im)))
(fma.f64 (fma.f64 (.f64 #s(literal -1/2 binary64) (sqrt.f64 #s(literal 2 binary64))) (sqrt.f64 (/.f64 #s(literal 1 binary64) im)) (.f64 (fma.f64 (.f64 #s(literal 1/8 binary64) (sqrt.f64 #s(literal 2 binary64))) (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 im #s(literal 3 binary64)))) (.f64 (.f64 #s(literal 1/16 binary64) (.f64 (sqrt.f64 #s(literal 2 binary64)) re)) (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 im #s(literal 5 binary64)))))) re)) re (*.f64 (sqrt.f64 #s(literal 2 binary64)) (sqrt.f64 im)))
(sqrt.f64 im)
(fma.f64 (*.f64 re #s(literal -1/2 binary64)) (sqrt.f64 (/.f64 #s(literal 1 binary64) im)) (sqrt.f64 im))
(fma.f64 (fma.f64 (.f64 #s(literal 1/8 binary64) re) (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 im #s(literal 3 binary64)))) (.f64 #s(literal -1/2 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) im)))) re (sqrt.f64 im))
(fma.f64 (fma.f64 (fma.f64 (.f64 #s(literal 1/16 binary64) re) (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 im #s(literal 5 binary64)))) (.f64 #s(literal 1/8 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 im #s(literal 3 binary64)))))) re (*.f64 #s(literal -1/2 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) im)))) re (sqrt.f64 im))
im
(-.f64 im re)
(fma.f64 (fma.f64 (/.f64 #s(literal 1/2 binary64) im) re #s(literal -1 binary64)) re im)
(fma.f64 (fma.f64 (fma.f64 (*.f64 re (/.f64 re (pow.f64 im #s(literal 3 binary64)))) #s(literal -1/8 binary64) (/.f64 #s(literal 1/2 binary64) im)) re #s(literal -1 binary64)) re im)
(.f64 (.f64 #s(literal 1/2 binary64) (sqrt.f64 #s(literal 2 binary64))) (sqrt.f64 im))
(fma.f64 (.f64 #s(literal 1/2 binary64) (sqrt.f64 #s(literal 2 binary64))) (sqrt.f64 im) (.f64 (.f64 #s(literal -1/4 binary64) (.f64 (sqrt.f64 #s(literal 2 binary64)) re)) (sqrt.f64 (/.f64 #s(literal 1 binary64) im))))
(fma.f64 (fma.f64 (.f64 #s(literal -1/4 binary64) (sqrt.f64 #s(literal 2 binary64))) (sqrt.f64 (/.f64 #s(literal 1 binary64) im)) (.f64 (.f64 #s(literal 1/16 binary64) (.f64 (sqrt.f64 #s(literal 2 binary64)) re)) (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 im #s(literal 3 binary64)))))) re (.f64 (.f64 #s(literal 1/2 binary64) (sqrt.f64 #s(literal 2 binary64))) (sqrt.f64 im)))
(fma.f64 (fma.f64 (.f64 #s(literal -1/4 binary64) (sqrt.f64 #s(literal 2 binary64))) (sqrt.f64 (/.f64 #s(literal 1 binary64) im)) (.f64 (fma.f64 (.f64 #s(literal 1/32 binary64) (.f64 (sqrt.f64 #s(literal 2 binary64)) re)) (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 im #s(literal 5 binary64)))) (.f64 (.f64 #s(literal 1/16 binary64) (sqrt.f64 #s(literal 2 binary64))) (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 im #s(literal 3 binary64)))))) re)) re (.f64 (.f64 #s(literal 1/2 binary64) (sqrt.f64 #s(literal 2 binary64))) (sqrt.f64 im)))
(*.f64 (sqrt.f64 #s(literal 2 binary64)) (sqrt.f64 im))
(fma.f64 (.f64 #s(literal -1/2 binary64) (.f64 (sqrt.f64 #s(literal 2 binary64)) re)) (sqrt.f64 (/.f64 #s(literal 1 binary64) im)) (*.f64 (sqrt.f64 #s(literal 2 binary64)) (sqrt.f64 im)))
(fma.f64 (fma.f64 (.f64 #s(literal 1/8 binary64) (.f64 (sqrt.f64 #s(literal 2 binary64)) re)) (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 im #s(literal 3 binary64)))) (.f64 (.f64 #s(literal -1/2 binary64) (sqrt.f64 #s(literal 2 binary64))) (sqrt.f64 (/.f64 #s(literal 1 binary64) im)))) re (*.f64 (sqrt.f64 #s(literal 2 binary64)) (sqrt.f64 im)))
(fma.f64 (fma.f64 (.f64 #s(literal -1/2 binary64) (sqrt.f64 #s(literal 2 binary64))) (sqrt.f64 (/.f64 #s(literal 1 binary64) im)) (.f64 (fma.f64 (.f64 #s(literal 1/8 binary64) (sqrt.f64 #s(literal 2 binary64))) (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 im #s(literal 3 binary64)))) (.f64 (.f64 #s(literal 1/16 binary64) (.f64 (sqrt.f64 #s(literal 2 binary64)) re)) (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 im #s(literal 5 binary64)))))) re)) re (*.f64 (sqrt.f64 #s(literal 2 binary64)) (sqrt.f64 im)))
(*.f64 #s(literal 2 binary64) im)
(fma.f64 #s(literal -2 binary64) re (*.f64 #s(literal 2 binary64) im))
(fma.f64 (-.f64 (/.f64 re im) #s(literal 2 binary64)) re (*.f64 #s(literal 2 binary64) im))
(fma.f64 (fma.f64 (fma.f64 (.f64 re (/.f64 re (pow.f64 im #s(literal 3 binary64)))) #s(literal -1/4 binary64) (/.f64 #s(literal 1 binary64) im)) re #s(literal -2 binary64)) re (.f64 #s(literal 2 binary64) im))
(.f64 (.f64 #s(literal 1/2 binary64) (sqrt.f64 #s(literal 2 binary64))) (sqrt.f64 im))
(fma.f64 (.f64 #s(literal 1/2 binary64) (sqrt.f64 #s(literal 2 binary64))) (sqrt.f64 im) (.f64 (.f64 #s(literal -1/4 binary64) (.f64 (sqrt.f64 #s(literal 2 binary64)) re)) (sqrt.f64 (/.f64 #s(literal 1 binary64) im))))
(fma.f64 (fma.f64 (.f64 #s(literal -1/4 binary64) (sqrt.f64 #s(literal 2 binary64))) (sqrt.f64 (/.f64 #s(literal 1 binary64) im)) (.f64 (.f64 #s(literal 1/16 binary64) (.f64 (sqrt.f64 #s(literal 2 binary64)) re)) (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 im #s(literal 3 binary64)))))) re (.f64 (.f64 #s(literal 1/2 binary64) (sqrt.f64 #s(literal 2 binary64))) (sqrt.f64 im)))
(fma.f64 (fma.f64 (.f64 #s(literal -1/4 binary64) (sqrt.f64 #s(literal 2 binary64))) (sqrt.f64 (/.f64 #s(literal 1 binary64) im)) (.f64 (fma.f64 (.f64 #s(literal 1/32 binary64) (.f64 (sqrt.f64 #s(literal 2 binary64)) re)) (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 im #s(literal 5 binary64)))) (.f64 (.f64 #s(literal 1/16 binary64) (sqrt.f64 #s(literal 2 binary64))) (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 im #s(literal 3 binary64)))))) re)) re (.f64 (.f64 #s(literal 1/2 binary64) (sqrt.f64 #s(literal 2 binary64))) (sqrt.f64 im)))
(*.f64 (sqrt.f64 #s(literal 2 binary64)) (sqrt.f64 im))
(fma.f64 (.f64 #s(literal -1/2 binary64) (.f64 (sqrt.f64 #s(literal 2 binary64)) re)) (sqrt.f64 (/.f64 #s(literal 1 binary64) im)) (*.f64 (sqrt.f64 #s(literal 2 binary64)) (sqrt.f64 im)))
(fma.f64 (fma.f64 (.f64 #s(literal 1/8 binary64) (.f64 (sqrt.f64 #s(literal 2 binary64)) re)) (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 im #s(literal 3 binary64)))) (.f64 (.f64 #s(literal -1/2 binary64) (sqrt.f64 #s(literal 2 binary64))) (sqrt.f64 (/.f64 #s(literal 1 binary64) im)))) re (*.f64 (sqrt.f64 #s(literal 2 binary64)) (sqrt.f64 im)))
(fma.f64 (fma.f64 (.f64 #s(literal -1/2 binary64) (sqrt.f64 #s(literal 2 binary64))) (sqrt.f64 (/.f64 #s(literal 1 binary64) im)) (.f64 (fma.f64 (.f64 #s(literal 1/8 binary64) (sqrt.f64 #s(literal 2 binary64))) (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 im #s(literal 3 binary64)))) (.f64 (.f64 #s(literal 1/16 binary64) (.f64 (sqrt.f64 #s(literal 2 binary64)) re)) (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 im #s(literal 5 binary64)))))) re)) re (*.f64 (sqrt.f64 #s(literal 2 binary64)) (sqrt.f64 im)))
(*.f64 #s(literal 2 binary64) im)
(fma.f64 #s(literal -2 binary64) re (*.f64 #s(literal 2 binary64) im))
(fma.f64 #s(literal -2 binary64) re (*.f64 #s(literal 2 binary64) im))
(fma.f64 #s(literal -2 binary64) re (*.f64 #s(literal 2 binary64) im))
(.f64 (.f64 #s(literal 1/2 binary64) (sqrt.f64 #s(literal 2 binary64))) (sqrt.f64 im))
(fma.f64 (.f64 #s(literal 1/2 binary64) (sqrt.f64 #s(literal 2 binary64))) (sqrt.f64 im) (.f64 (.f64 #s(literal -1/4 binary64) (.f64 (sqrt.f64 #s(literal 2 binary64)) re)) (sqrt.f64 (/.f64 #s(literal 1 binary64) im))))
(fma.f64 (fma.f64 (.f64 #s(literal -1/4 binary64) (sqrt.f64 #s(literal 2 binary64))) (sqrt.f64 (/.f64 #s(literal 1 binary64) im)) (.f64 (.f64 #s(literal 1/16 binary64) (.f64 (sqrt.f64 #s(literal 2 binary64)) re)) (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 im #s(literal 3 binary64)))))) re (.f64 (.f64 #s(literal 1/2 binary64) (sqrt.f64 #s(literal 2 binary64))) (sqrt.f64 im)))
(fma.f64 (fma.f64 (.f64 #s(literal -1/4 binary64) (sqrt.f64 #s(literal 2 binary64))) (sqrt.f64 (/.f64 #s(literal 1 binary64) im)) (.f64 (fma.f64 (.f64 #s(literal 1/32 binary64) (.f64 (sqrt.f64 #s(literal 2 binary64)) re)) (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 im #s(literal 5 binary64)))) (.f64 (.f64 #s(literal 1/16 binary64) (sqrt.f64 #s(literal 2 binary64))) (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 im #s(literal 3 binary64)))))) re)) re (.f64 (.f64 #s(literal 1/2 binary64) (sqrt.f64 #s(literal 2 binary64))) (sqrt.f64 im)))
(*.f64 (sqrt.f64 #s(literal 2 binary64)) (sqrt.f64 im))
(fma.f64 (.f64 #s(literal -1/2 binary64) (.f64 (sqrt.f64 #s(literal 2 binary64)) re)) (sqrt.f64 (/.f64 #s(literal 1 binary64) im)) (*.f64 (sqrt.f64 #s(literal 2 binary64)) (sqrt.f64 im)))
(fma.f64 (fma.f64 (.f64 #s(literal 1/8 binary64) (.f64 (sqrt.f64 #s(literal 2 binary64)) re)) (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 im #s(literal 3 binary64)))) (.f64 (.f64 #s(literal -1/2 binary64) (sqrt.f64 #s(literal 2 binary64))) (sqrt.f64 (/.f64 #s(literal 1 binary64) im)))) re (*.f64 (sqrt.f64 #s(literal 2 binary64)) (sqrt.f64 im)))
(fma.f64 (fma.f64 (.f64 #s(literal -1/2 binary64) (sqrt.f64 #s(literal 2 binary64))) (sqrt.f64 (/.f64 #s(literal 1 binary64) im)) (.f64 (fma.f64 (.f64 #s(literal 1/8 binary64) (sqrt.f64 #s(literal 2 binary64))) (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 im #s(literal 3 binary64)))) (.f64 (.f64 #s(literal 1/16 binary64) (.f64 (sqrt.f64 #s(literal 2 binary64)) re)) (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 im #s(literal 5 binary64)))))) re)) re (*.f64 (sqrt.f64 #s(literal 2 binary64)) (sqrt.f64 im)))
(*.f64 #s(literal 2 binary64) im)
(fma.f64 #s(literal -2 binary64) re (*.f64 #s(literal 2 binary64) im))
(fma.f64 (-.f64 (/.f64 re im) #s(literal 2 binary64)) re (*.f64 #s(literal 2 binary64) im))
(fma.f64 (fma.f64 (fma.f64 (.f64 re (/.f64 re (pow.f64 im #s(literal 3 binary64)))) #s(literal -1/4 binary64) (/.f64 #s(literal 1 binary64) im)) re #s(literal -2 binary64)) re (.f64 #s(literal 2 binary64) im))
(.f64 (.f64 #s(literal 1/2 binary64) (sqrt.f64 #s(literal 2 binary64))) (sqrt.f64 im))
(fma.f64 (.f64 #s(literal 1/2 binary64) (sqrt.f64 #s(literal 2 binary64))) (sqrt.f64 im) (.f64 (.f64 #s(literal -1/4 binary64) (.f64 (sqrt.f64 #s(literal 2 binary64)) re)) (sqrt.f64 (/.f64 #s(literal 1 binary64) im))))
(fma.f64 (fma.f64 (.f64 #s(literal -1/4 binary64) (sqrt.f64 #s(literal 2 binary64))) (sqrt.f64 (/.f64 #s(literal 1 binary64) im)) (.f64 (.f64 #s(literal 1/16 binary64) (.f64 (sqrt.f64 #s(literal 2 binary64)) re)) (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 im #s(literal 3 binary64)))))) re (.f64 (.f64 #s(literal 1/2 binary64) (sqrt.f64 #s(literal 2 binary64))) (sqrt.f64 im)))
(fma.f64 (fma.f64 (.f64 #s(literal -1/4 binary64) (sqrt.f64 #s(literal 2 binary64))) (sqrt.f64 (/.f64 #s(literal 1 binary64) im)) (.f64 (fma.f64 (.f64 #s(literal 1/32 binary64) (.f64 (sqrt.f64 #s(literal 2 binary64)) re)) (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 im #s(literal 5 binary64)))) (.f64 (.f64 #s(literal 1/16 binary64) (sqrt.f64 #s(literal 2 binary64))) (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 im #s(literal 3 binary64)))))) re)) re (.f64 (.f64 #s(literal 1/2 binary64) (sqrt.f64 #s(literal 2 binary64))) (sqrt.f64 im)))
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(.f64 (-.f64 #s(literal 2 binary64) (/.f64 (fma.f64 #s(literal -2 binary64) re (/.f64 (fma.f64 (/.f64 (pow.f64 re #s(literal 4 binary64)) im) (/.f64 #s(literal -1/4 binary64) im) (.f64 re re)) (neg.f64 im))) im)) (neg.f64 im))
(*.f64 #s(literal 2 binary64) im)
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(.f64 (.f64 #s(literal -1/2 binary64) (sqrt.f64 im)) (*.f64 (sqrt.f64 #s(literal -1 binary64)) (sqrt.f64 #s(literal 2 binary64))))
(.f64 (neg.f64 im) (fma.f64 (.f64 (sqrt.f64 #s(literal -1 binary64)) (sqrt.f64 (/.f64 #s(literal 1 binary64) im))) (.f64 (sqrt.f64 #s(literal 2 binary64)) #s(literal 1/2 binary64)) (.f64 (.f64 (.f64 (sqrt.f64 #s(literal -1 binary64)) re) (*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 im #s(literal 3 binary64)))) (sqrt.f64 #s(literal 2 binary64)))) #s(literal -1/4 binary64))))
(.f64 (neg.f64 im) (fma.f64 (.f64 (.f64 (.f64 (.f64 (sqrt.f64 #s(literal 2 binary64)) re) re) (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 im #s(literal 5 binary64))))) (sqrt.f64 #s(literal -1 binary64))) #s(literal -1/8 binary64) (fma.f64 (.f64 (sqrt.f64 #s(literal -1 binary64)) (sqrt.f64 (/.f64 #s(literal 1 binary64) im))) (.f64 (sqrt.f64 #s(literal 2 binary64)) #s(literal 1/2 binary64)) (.f64 (.f64 (.f64 (sqrt.f64 #s(literal -1 binary64)) re) (*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 im #s(literal 3 binary64)))) (sqrt.f64 #s(literal 2 binary64)))) #s(literal -1/4 binary64)))))
(.f64 (neg.f64 im) (-.f64 (fma.f64 (.f64 (sqrt.f64 #s(literal -1 binary64)) (sqrt.f64 (/.f64 #s(literal 1 binary64) im))) (.f64 (sqrt.f64 #s(literal 2 binary64)) #s(literal 1/2 binary64)) (.f64 (.f64 (.f64 (sqrt.f64 #s(literal -1 binary64)) re) (.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 im #s(literal 3 binary64)))) (sqrt.f64 #s(literal 2 binary64)))) #s(literal -1/4 binary64))) (.f64 (.f64 (.f64 (.f64 (sqrt.f64 #s(literal -1 binary64)) re) re) (.f64 (sqrt.f64 #s(literal 2 binary64)) (sqrt.f64 im))) (/.f64 #s(literal 3/16 binary64) (pow.f64 im #s(literal 3 binary64))))))
(.f64 (.f64 (neg.f64 (sqrt.f64 im)) (sqrt.f64 #s(literal 2 binary64))) (sqrt.f64 #s(literal -1 binary64)))
(.f64 (neg.f64 im) (fma.f64 (.f64 (sqrt.f64 #s(literal -1 binary64)) (sqrt.f64 (/.f64 #s(literal 1 binary64) im))) (sqrt.f64 #s(literal 2 binary64)) (.f64 (.f64 (.f64 #s(literal -1/2 binary64) (.f64 (sqrt.f64 #s(literal -1 binary64)) re)) (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 im #s(literal 3 binary64))))) (sqrt.f64 #s(literal 2 binary64)))))
(.f64 (neg.f64 im) (fma.f64 (.f64 (.f64 #s(literal -1/4 binary64) (.f64 (.f64 (sqrt.f64 #s(literal -1 binary64)) re) re)) (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 im #s(literal 5 binary64))))) (sqrt.f64 #s(literal 2 binary64)) (fma.f64 (.f64 (sqrt.f64 #s(literal -1 binary64)) (sqrt.f64 (/.f64 #s(literal 1 binary64) im))) (sqrt.f64 #s(literal 2 binary64)) (.f64 (.f64 (.f64 #s(literal -1/2 binary64) (.f64 (sqrt.f64 #s(literal -1 binary64)) re)) (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 im #s(literal 3 binary64))))) (sqrt.f64 #s(literal 2 binary64))))))
(.f64 (neg.f64 im) (-.f64 (fma.f64 (.f64 (sqrt.f64 #s(literal -1 binary64)) (sqrt.f64 (/.f64 #s(literal 1 binary64) im))) (sqrt.f64 #s(literal 2 binary64)) (.f64 (.f64 (.f64 #s(literal -1/2 binary64) (.f64 (sqrt.f64 #s(literal -1 binary64)) re)) (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 im #s(literal 3 binary64))))) (sqrt.f64 #s(literal 2 binary64)))) (.f64 (.f64 (.f64 (.f64 (sqrt.f64 #s(literal -1 binary64)) re) re) (*.f64 (sqrt.f64 #s(literal 2 binary64)) (sqrt.f64 im))) (/.f64 #s(literal 3/8 binary64) (pow.f64 im #s(literal 3 binary64))))))
(neg.f64 (*.f64 (sqrt.f64 #s(literal 2 binary64)) (neg.f64 (sqrt.f64 im))))
(neg.f64 (*.f64 (sqrt.f64 #s(literal 2 binary64)) (neg.f64 (sqrt.f64 im))))
(neg.f64 (*.f64 (sqrt.f64 #s(literal 2 binary64)) (neg.f64 (sqrt.f64 im))))
(neg.f64 (*.f64 (sqrt.f64 #s(literal 2 binary64)) (neg.f64 (sqrt.f64 im))))
(*.f64 #s(literal 2 binary64) im)
(*.f64 (fma.f64 (/.f64 re im) #s(literal 2 binary64) #s(literal -2 binary64)) (neg.f64 im))
(*.f64 (fma.f64 (/.f64 re im) #s(literal 2 binary64) #s(literal -2 binary64)) (neg.f64 im))
(*.f64 (fma.f64 (/.f64 re im) #s(literal 2 binary64) #s(literal -2 binary64)) (neg.f64 im))
(.f64 (.f64 #s(literal -1/2 binary64) (sqrt.f64 im)) (*.f64 (sqrt.f64 #s(literal -1 binary64)) (sqrt.f64 #s(literal 2 binary64))))
(.f64 (neg.f64 im) (fma.f64 (.f64 (sqrt.f64 #s(literal -1 binary64)) (sqrt.f64 (/.f64 #s(literal 1 binary64) im))) (.f64 (sqrt.f64 #s(literal 2 binary64)) #s(literal 1/2 binary64)) (.f64 (.f64 (.f64 (sqrt.f64 #s(literal -1 binary64)) re) (*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 im #s(literal 3 binary64)))) (sqrt.f64 #s(literal 2 binary64)))) #s(literal -1/4 binary64))))
(.f64 (neg.f64 im) (fma.f64 (.f64 (.f64 (.f64 (.f64 (sqrt.f64 #s(literal 2 binary64)) re) re) (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 im #s(literal 5 binary64))))) (sqrt.f64 #s(literal -1 binary64))) #s(literal -1/8 binary64) (fma.f64 (.f64 (sqrt.f64 #s(literal -1 binary64)) (sqrt.f64 (/.f64 #s(literal 1 binary64) im))) (.f64 (sqrt.f64 #s(literal 2 binary64)) #s(literal 1/2 binary64)) (.f64 (.f64 (.f64 (sqrt.f64 #s(literal -1 binary64)) re) (*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 im #s(literal 3 binary64)))) (sqrt.f64 #s(literal 2 binary64)))) #s(literal -1/4 binary64)))))
(.f64 (neg.f64 im) (-.f64 (fma.f64 (.f64 (sqrt.f64 #s(literal -1 binary64)) (sqrt.f64 (/.f64 #s(literal 1 binary64) im))) (.f64 (sqrt.f64 #s(literal 2 binary64)) #s(literal 1/2 binary64)) (.f64 (.f64 (.f64 (sqrt.f64 #s(literal -1 binary64)) re) (.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 im #s(literal 3 binary64)))) (sqrt.f64 #s(literal 2 binary64)))) #s(literal -1/4 binary64))) (.f64 (.f64 (.f64 (.f64 (sqrt.f64 #s(literal -1 binary64)) re) re) (.f64 (sqrt.f64 #s(literal 2 binary64)) (sqrt.f64 im))) (/.f64 #s(literal 3/16 binary64) (pow.f64 im #s(literal 3 binary64))))))
(.f64 (.f64 (neg.f64 (sqrt.f64 im)) (sqrt.f64 #s(literal 2 binary64))) (sqrt.f64 #s(literal -1 binary64)))
(.f64 (neg.f64 im) (fma.f64 (.f64 (sqrt.f64 #s(literal -1 binary64)) (sqrt.f64 (/.f64 #s(literal 1 binary64) im))) (sqrt.f64 #s(literal 2 binary64)) (.f64 (.f64 (.f64 #s(literal -1/2 binary64) (.f64 (sqrt.f64 #s(literal -1 binary64)) re)) (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 im #s(literal 3 binary64))))) (sqrt.f64 #s(literal 2 binary64)))))
(.f64 (neg.f64 im) (fma.f64 (.f64 (.f64 #s(literal -1/4 binary64) (.f64 (.f64 (sqrt.f64 #s(literal -1 binary64)) re) re)) (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 im #s(literal 5 binary64))))) (sqrt.f64 #s(literal 2 binary64)) (fma.f64 (.f64 (sqrt.f64 #s(literal -1 binary64)) (sqrt.f64 (/.f64 #s(literal 1 binary64) im))) (sqrt.f64 #s(literal 2 binary64)) (.f64 (.f64 (.f64 #s(literal -1/2 binary64) (.f64 (sqrt.f64 #s(literal -1 binary64)) re)) (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 im #s(literal 3 binary64))))) (sqrt.f64 #s(literal 2 binary64))))))
(.f64 (neg.f64 im) (-.f64 (fma.f64 (.f64 (sqrt.f64 #s(literal -1 binary64)) (sqrt.f64 (/.f64 #s(literal 1 binary64) im))) (sqrt.f64 #s(literal 2 binary64)) (.f64 (.f64 (.f64 #s(literal -1/2 binary64) (.f64 (sqrt.f64 #s(literal -1 binary64)) re)) (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 im #s(literal 3 binary64))))) (sqrt.f64 #s(literal 2 binary64)))) (.f64 (.f64 (.f64 (.f64 (sqrt.f64 #s(literal -1 binary64)) re) re) (*.f64 (sqrt.f64 #s(literal 2 binary64)) (sqrt.f64 im))) (/.f64 #s(literal 3/8 binary64) (pow.f64 im #s(literal 3 binary64))))))
(*.f64 #s(literal -2 binary64) im)
(*.f64 (fma.f64 (/.f64 re im) #s(literal 2 binary64) #s(literal 2 binary64)) (neg.f64 im))
(.f64 (-.f64 #s(literal 2 binary64) (/.f64 (fma.f64 #s(literal -2 binary64) re (/.f64 (.f64 (neg.f64 re) re) im)) im)) (neg.f64 im))
(.f64 (-.f64 #s(literal 2 binary64) (/.f64 (fma.f64 #s(literal -2 binary64) re (/.f64 (fma.f64 (/.f64 (pow.f64 re #s(literal 4 binary64)) im) (/.f64 #s(literal -1/4 binary64) im) (.f64 re re)) (neg.f64 im))) im)) (neg.f64 im))
(.f64 (.f64 #s(literal -1/2 binary64) (sqrt.f64 im)) (*.f64 (sqrt.f64 #s(literal -1 binary64)) (sqrt.f64 #s(literal 2 binary64))))
(.f64 (neg.f64 im) (fma.f64 (.f64 (sqrt.f64 #s(literal -1 binary64)) (sqrt.f64 (/.f64 #s(literal 1 binary64) im))) (.f64 (sqrt.f64 #s(literal 2 binary64)) #s(literal 1/2 binary64)) (.f64 (.f64 (.f64 (sqrt.f64 #s(literal -1 binary64)) re) (*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 im #s(literal 3 binary64)))) (sqrt.f64 #s(literal 2 binary64)))) #s(literal -1/4 binary64))))
(.f64 (neg.f64 im) (fma.f64 (.f64 (.f64 (.f64 (.f64 (sqrt.f64 #s(literal 2 binary64)) re) re) (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 im #s(literal 5 binary64))))) (sqrt.f64 #s(literal -1 binary64))) #s(literal -1/8 binary64) (fma.f64 (.f64 (sqrt.f64 #s(literal -1 binary64)) (sqrt.f64 (/.f64 #s(literal 1 binary64) im))) (.f64 (sqrt.f64 #s(literal 2 binary64)) #s(literal 1/2 binary64)) (.f64 (.f64 (.f64 (sqrt.f64 #s(literal -1 binary64)) re) (*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 im #s(literal 3 binary64)))) (sqrt.f64 #s(literal 2 binary64)))) #s(literal -1/4 binary64)))))
(.f64 (neg.f64 im) (-.f64 (fma.f64 (.f64 (sqrt.f64 #s(literal -1 binary64)) (sqrt.f64 (/.f64 #s(literal 1 binary64) im))) (.f64 (sqrt.f64 #s(literal 2 binary64)) #s(literal 1/2 binary64)) (.f64 (.f64 (.f64 (sqrt.f64 #s(literal -1 binary64)) re) (.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 im #s(literal 3 binary64)))) (sqrt.f64 #s(literal 2 binary64)))) #s(literal -1/4 binary64))) (.f64 (.f64 (.f64 (.f64 (sqrt.f64 #s(literal -1 binary64)) re) re) (.f64 (sqrt.f64 #s(literal 2 binary64)) (sqrt.f64 im))) (/.f64 #s(literal 3/16 binary64) (pow.f64 im #s(literal 3 binary64))))))
(.f64 (.f64 im #s(literal 1/2 binary64)) (.f64 (.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) re)) (sqrt.f64 #s(literal 2 binary64))) (sqrt.f64 #s(literal 1/2 binary64))))
(.f64 (.f64 im #s(literal 1/2 binary64)) (.f64 (.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) re)) (sqrt.f64 #s(literal 2 binary64))) (sqrt.f64 #s(literal 1/2 binary64))))
(.f64 (.f64 im #s(literal 1/2 binary64)) (.f64 (.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) re)) (sqrt.f64 #s(literal 2 binary64))) (sqrt.f64 #s(literal 1/2 binary64))))
(.f64 (.f64 im #s(literal 1/2 binary64)) (.f64 (.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) re)) (sqrt.f64 #s(literal 2 binary64))) (sqrt.f64 #s(literal 1/2 binary64))))
(*.f64 (sqrt.f64 #s(literal 1/2 binary64)) im)
(*.f64 (sqrt.f64 #s(literal 1/2 binary64)) im)
(*.f64 (sqrt.f64 #s(literal 1/2 binary64)) im)
(*.f64 (sqrt.f64 #s(literal 1/2 binary64)) im)

rewrite179.0ms (2.5%)

Memory

-24.9MiB live, 209.8MiB allocated

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	45	251
0	69	206
1	188	206
2	882	204
0	8396	204

Stop Event

1×	iter limit
1×	node limit
1×	iter limit

Counts

21 → 301

Calls

Call 1

Inputs
(.f64 (.f64 (sqrt.f64 (-.f64 (hypot.f64 re im) re)) (sqrt.f64 #s(literal 2 binary64))) #s(literal 1/2 binary64))
(*.f64 (sqrt.f64 (-.f64 (hypot.f64 re im) re)) (sqrt.f64 #s(literal 2 binary64)))
(sqrt.f64 (-.f64 (hypot.f64 re im) re))
(-.f64 (hypot.f64 re im) re)
(.f64 (sqrt.f64 #s(approx ( (- (sqrt (+ (* im im) (* re re))) re) 2) (*.f64 #s(literal 2 binary64) im))) #s(literal 1/2 binary64))
(sqrt.f64 #s(approx (* (- (sqrt (+ (* im im) (* re re))) re) 2) (*.f64 #s(literal 2 binary64) im)))
#s(approx (* (- (sqrt (+ (* im im) (* re re))) re) 2) (*.f64 #s(literal 2 binary64) im))
(*.f64 #s(literal 2 binary64) im)
(.f64 #s(approx (sqrt ( (- (sqrt (+ (* im im) (* re re))) re) 2)) (*.f64 (sqrt.f64 #s(literal 2 binary64)) (sqrt.f64 im))) #s(literal 1/2 binary64))
#s(approx (sqrt (* (- (sqrt (+ (* im im) (* re re))) re) 2)) (*.f64 (sqrt.f64 #s(literal 2 binary64)) (sqrt.f64 im)))
(*.f64 (sqrt.f64 #s(literal 2 binary64)) (sqrt.f64 im))
(sqrt.f64 #s(literal 2 binary64))
(*.f64 (fma.f64 (/.f64 re im) #s(literal -2 binary64) #s(literal 2 binary64)) im)
(.f64 (sqrt.f64 #s(approx ( (- (sqrt (+ (* im im) (* re re))) re) 2) (*.f64 (fma.f64 (/.f64 re im) #s(literal -2 binary64) #s(literal 2 binary64)) im))) #s(literal 1/2 binary64))
(sqrt.f64 #s(approx (* (- (sqrt (+ (* im im) (* re re))) re) 2) (*.f64 (fma.f64 (/.f64 re im) #s(literal -2 binary64) #s(literal 2 binary64)) im)))
#s(approx (* (- (sqrt (+ (* im im) (* re re))) re) 2) (*.f64 (fma.f64 (/.f64 re im) #s(literal -2 binary64) #s(literal 2 binary64)) im))
#s(approx (* 1/2 (sqrt (* 2 (- (sqrt (+ (* re re) (* im im))) re)))) (.f64 (.f64 (sqrt.f64 #s(literal 1/2 binary64)) im) (*.f64 #s(literal 1/2 binary64) (sqrt.f64 (/.f64 #s(literal 2 binary64) re)))))
(.f64 (.f64 (sqrt.f64 #s(literal 1/2 binary64)) im) (*.f64 #s(literal 1/2 binary64) (sqrt.f64 (/.f64 #s(literal 2 binary64) re))))
(*.f64 (sqrt.f64 #s(literal 1/2 binary64)) im)
(sqrt.f64 #s(literal 1/2 binary64))
(sqrt.f64 (/.f64 #s(literal 2 binary64) re))

Outputs
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#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
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#<batchref>
#<batchref>
#<batchref>
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#<batchref>
#<batchref>
#<batchref>

eval169.0ms (2.3%)

Memory: 14.1MiB live, 169.7MiB allocated
Compiler: Compiled 26 131 to 2 290 computations (91.2% saved)

prune69.0ms (1%)

Memory

-1.4MiB live, 85.5MiB allocated

Pruning

17 alts after pruning (10 fresh and 7 done)

	Pruned	Kept	Total
New	712	2	714
Fresh	1	8	9
Picked	1	4	5
Done	0	3	3
Total	714	17	731

Accuracy

99.7%

Counts

731 → 17

Alt Table

Click to see full alt table

Status	Accuracy	Program
✓	79.8%	(.f64 (.f64 (sqrt.f64 (-.f64 (hypot.f64 re im) re)) (sqrt.f64 #s(literal 2 binary64))) #s(literal 1/2 binary64))
	53.7%	(.f64 (.f64 (sqrt.f64 #s(approx (- (sqrt (+ (* re re) (* im im))) re) (-.f64 im re))) (sqrt.f64 #s(literal 2 binary64))) #s(literal 1/2 binary64))
▶	76.6%	(.f64 (sqrt.f64 (.f64 (fma.f64 (sqrt.f64 (hypot.f64 re im)) (sqrt.f64 (hypot.f64 re im)) (neg.f64 re)) #s(literal 2 binary64))) #s(literal 1/2 binary64))
✓	79.9%	(.f64 (sqrt.f64 (.f64 (-.f64 (hypot.f64 im re) re) #s(literal 2 binary64))) #s(literal 1/2 binary64))
▶	53.6%	(.f64 (sqrt.f64 (.f64 #s(approx (- (sqrt (+ (* im im) (* re re))) re) (-.f64 im re)) #s(literal 2 binary64))) #s(literal 1/2 binary64))
	51.1%	(.f64 (sqrt.f64 #s(approx ( (- (sqrt (+ (* im im) (* re re))) re) 2) (fma.f64 (-.f64 (/.f64 re im) #s(literal 2 binary64)) re (*.f64 #s(literal 2 binary64) im)))) #s(literal 1/2 binary64))
✓	51.0%	(.f64 (sqrt.f64 #s(approx ( (- (sqrt (+ (* im im) (* re re))) re) 2) (*.f64 #s(literal 2 binary64) im))) #s(literal 1/2 binary64))
✓	51.0%	(.f64 #s(approx (sqrt ( (- (sqrt (+ (* im im) (* re re))) re) 2)) (*.f64 (sqrt.f64 #s(literal 2 binary64)) (sqrt.f64 im))) #s(literal 1/2 binary64))
▶	37.6%	(.f64 #s(literal 1/2 binary64) (sqrt.f64 (.f64 #s(literal 2 binary64) (-.f64 (sqrt.f64 (fma.f64 re re (*.f64 im im))) re))))
	29.9%	(.f64 #s(literal 1/2 binary64) (sqrt.f64 (.f64 #s(literal 2 binary64) (-.f64 (sqrt.f64 #s(approx (+ (* re re) (* im im)) (.f64 (.f64 (fma.f64 (/.f64 re im) (/.f64 re im) #s(literal 1 binary64)) im) im))) re))))
✓	12.9%	(.f64 #s(literal 1/2 binary64) (sqrt.f64 #s(approx ( 2 (- (sqrt (+ (* re re) (* im im))) re)) (/.f64 (*.f64 im im) re))))
✓	28.1%	(.f64 #s(literal 1/2 binary64) (sqrt.f64 #s(approx ( 2 (- (sqrt (+ (* re re) (* im im))) re)) (*.f64 #s(literal -4 binary64) re))))
	24.7%	#s(approx (* 1/2 (sqrt (* 2 (- (sqrt (+ (* re re) (* im im))) re)))) (/.f64 (*.f64 #s(literal 1/2 binary64) im) (sqrt.f64 re)))
▶	24.6%	#s(approx (* 1/2 (sqrt (* 2 (- (sqrt (+ (* re re) (* im im))) re)))) (/.f64 #s(literal 1 binary64) (/.f64 (sqrt.f64 re) (*.f64 #s(literal 1/2 binary64) im))))
	24.6%	#s(approx (* 1/2 (sqrt (* 2 (- (sqrt (+ (* re re) (* im im))) re)))) (.f64 (.f64 (sqrt.f64 #s(literal 1/2 binary64)) im) (.f64 #s(literal 1/2 binary64) (pow.f64 (pow.f64 (.f64 re #s(literal 1/2 binary64)) #s(literal -1/4 binary64)) #s(literal 2 binary64)))))
✓	24.7%	#s(approx (* 1/2 (sqrt (* 2 (- (sqrt (+ (* re re) (* im im))) re)))) (.f64 (.f64 (sqrt.f64 #s(literal 1/2 binary64)) im) (*.f64 #s(literal 1/2 binary64) (sqrt.f64 (/.f64 #s(literal 2 binary64) re)))))
▶	24.7%	#s(approx (* 1/2 (sqrt (* 2 (- (sqrt (+ (* re re) (* im im))) re)))) (.f64 (.f64 im #s(literal 1/2 binary64)) (sqrt.f64 (/.f64 #s(literal 1 binary64) re))))

Compiler

Compiled 574 to 432 computations (24.7% saved)

simplify172.0ms (2.4%)

Memory

-19.8MiB live, 58.7MiB allocated

Algorithm

1×	egg-herbie

Localize:

Found 20 expressions of interest:

New	Metric	Score
cost-diff	0	(-.f64 (sqrt.f64 (fma.f64 re re (*.f64 im im))) re)
cost-diff	0	(.f64 #s(literal 2 binary64) (-.f64 (sqrt.f64 (fma.f64 re re (.f64 im im))) re))
cost-diff	0	(sqrt.f64 (.f64 #s(literal 2 binary64) (-.f64 (sqrt.f64 (fma.f64 re re (.f64 im im))) re)))
cost-diff	0	(.f64 #s(literal 1/2 binary64) (sqrt.f64 (.f64 #s(literal 2 binary64) (-.f64 (sqrt.f64 (fma.f64 re re (*.f64 im im))) re))))
cost-diff	0	(sqrt.f64 re)
cost-diff	0	(/.f64 (sqrt.f64 re) (*.f64 #s(literal 1/2 binary64) im))
cost-diff	0	#s(approx (* 1/2 (sqrt (* 2 (- (sqrt (+ (* re re) (* im im))) re)))) (/.f64 #s(literal 1 binary64) (/.f64 (sqrt.f64 re) (*.f64 #s(literal 1/2 binary64) im))))
cost-diff	704	(/.f64 #s(literal 1 binary64) (/.f64 (sqrt.f64 re) (*.f64 #s(literal 1/2 binary64) im)))
cost-diff	0	(sqrt.f64 (/.f64 #s(literal 1 binary64) re))
cost-diff	0	(*.f64 im #s(literal 1/2 binary64))
cost-diff	0	(.f64 (.f64 im #s(literal 1/2 binary64)) (sqrt.f64 (/.f64 #s(literal 1 binary64) re)))
cost-diff	0	#s(approx (* 1/2 (sqrt (* 2 (- (sqrt (+ (* re re) (* im im))) re)))) (.f64 (.f64 im #s(literal 1/2 binary64)) (sqrt.f64 (/.f64 #s(literal 1 binary64) re))))
cost-diff	0	#s(approx (- (sqrt (+ (* im im) (* re re))) re) (-.f64 im re))
cost-diff	0	(.f64 #s(approx (- (sqrt (+ ( im im) (* re re))) re) (-.f64 im re)) #s(literal 2 binary64))
cost-diff	0	(sqrt.f64 (.f64 #s(approx (- (sqrt (+ ( im im) (* re re))) re) (-.f64 im re)) #s(literal 2 binary64)))
cost-diff	0	(.f64 (sqrt.f64 (.f64 #s(approx (- (sqrt (+ (* im im) (* re re))) re) (-.f64 im re)) #s(literal 2 binary64))) #s(literal 1/2 binary64))
cost-diff	0	(*.f64 (fma.f64 (sqrt.f64 (hypot.f64 re im)) (sqrt.f64 (hypot.f64 re im)) (neg.f64 re)) #s(literal 2 binary64))
cost-diff	0	(sqrt.f64 (*.f64 (fma.f64 (sqrt.f64 (hypot.f64 re im)) (sqrt.f64 (hypot.f64 re im)) (neg.f64 re)) #s(literal 2 binary64)))
cost-diff	0	(.f64 (sqrt.f64 (.f64 (fma.f64 (sqrt.f64 (hypot.f64 re im)) (sqrt.f64 (hypot.f64 re im)) (neg.f64 re)) #s(literal 2 binary64))) #s(literal 1/2 binary64))
cost-diff	8064	(fma.f64 (sqrt.f64 (hypot.f64 re im)) (sqrt.f64 (hypot.f64 re im)) (neg.f64 re))

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	45	269
0	72	225
1	99	225
2	135	221
3	191	221
4	305	221
5	430	221
6	534	221
7	784	221
8	1252	221
9	1612	221
10	1990	221
11	2461	221
12	2788	221
13	2949	221
14	3369	221
15	3603	221
16	3769	221
17	3773	221
18	3773	221
19	3781	221
20	3785	221
0	3785	221

Stop Event

1×	iter limit
1×	saturated
1×	iter limit

Calls

Call 1

Inputs
(.f64 (sqrt.f64 (.f64 (fma.f64 (sqrt.f64 (hypot.f64 re im)) (sqrt.f64 (hypot.f64 re im)) (neg.f64 re)) #s(literal 2 binary64))) #s(literal 1/2 binary64))
(sqrt.f64 (*.f64 (fma.f64 (sqrt.f64 (hypot.f64 re im)) (sqrt.f64 (hypot.f64 re im)) (neg.f64 re)) #s(literal 2 binary64)))
(*.f64 (fma.f64 (sqrt.f64 (hypot.f64 re im)) (sqrt.f64 (hypot.f64 re im)) (neg.f64 re)) #s(literal 2 binary64))
(fma.f64 (sqrt.f64 (hypot.f64 re im)) (sqrt.f64 (hypot.f64 re im)) (neg.f64 re))
(sqrt.f64 (hypot.f64 re im))
(hypot.f64 re im)
re
im
(neg.f64 re)
#s(literal 2 binary64)
#s(literal 1/2 binary64)
(.f64 (sqrt.f64 (.f64 #s(approx (- (sqrt (+ (* im im) (* re re))) re) (-.f64 im re)) #s(literal 2 binary64))) #s(literal 1/2 binary64))
(sqrt.f64 (.f64 #s(approx (- (sqrt (+ ( im im) (* re re))) re) (-.f64 im re)) #s(literal 2 binary64)))
(.f64 #s(approx (- (sqrt (+ ( im im) (* re re))) re) (-.f64 im re)) #s(literal 2 binary64))
#s(approx (- (sqrt (+ (* im im) (* re re))) re) (-.f64 im re))
(-.f64 im re)
im
re
#s(literal 2 binary64)
#s(literal 1/2 binary64)
#s(approx (* 1/2 (sqrt (* 2 (- (sqrt (+ (* re re) (* im im))) re)))) (.f64 (.f64 im #s(literal 1/2 binary64)) (sqrt.f64 (/.f64 #s(literal 1 binary64) re))))
(.f64 (.f64 im #s(literal 1/2 binary64)) (sqrt.f64 (/.f64 #s(literal 1 binary64) re)))
(*.f64 im #s(literal 1/2 binary64))
im
#s(literal 1/2 binary64)
(sqrt.f64 (/.f64 #s(literal 1 binary64) re))
(/.f64 #s(literal 1 binary64) re)
#s(literal 1 binary64)
re
#s(approx (* 1/2 (sqrt (* 2 (- (sqrt (+ (* re re) (* im im))) re)))) (/.f64 #s(literal 1 binary64) (/.f64 (sqrt.f64 re) (*.f64 #s(literal 1/2 binary64) im))))
(/.f64 #s(literal 1 binary64) (/.f64 (sqrt.f64 re) (*.f64 #s(literal 1/2 binary64) im)))
#s(literal 1 binary64)
(/.f64 (sqrt.f64 re) (*.f64 #s(literal 1/2 binary64) im))
(sqrt.f64 re)
re
(*.f64 #s(literal 1/2 binary64) im)
#s(literal 1/2 binary64)
im
(.f64 #s(literal 1/2 binary64) (sqrt.f64 (.f64 #s(literal 2 binary64) (-.f64 (sqrt.f64 (fma.f64 re re (*.f64 im im))) re))))
#s(literal 1/2 binary64)
(sqrt.f64 (.f64 #s(literal 2 binary64) (-.f64 (sqrt.f64 (fma.f64 re re (.f64 im im))) re)))
(.f64 #s(literal 2 binary64) (-.f64 (sqrt.f64 (fma.f64 re re (.f64 im im))) re))
#s(literal 2 binary64)
(-.f64 (sqrt.f64 (fma.f64 re re (*.f64 im im))) re)
(sqrt.f64 (fma.f64 re re (*.f64 im im)))
(fma.f64 re re (*.f64 im im))
re
(*.f64 im im)
im

Outputs
(.f64 (sqrt.f64 (.f64 (-.f64 (hypot.f64 im re) re) #s(literal 2 binary64))) #s(literal 1/2 binary64))
(sqrt.f64 (*.f64 (-.f64 (hypot.f64 im re) re) #s(literal 2 binary64)))
(*.f64 (-.f64 (hypot.f64 im re) re) #s(literal 2 binary64))
(-.f64 (hypot.f64 im re) re)
(sqrt.f64 (hypot.f64 im re))
(hypot.f64 im re)
re
im
(neg.f64 re)
#s(literal 2 binary64)
#s(literal 1/2 binary64)
(.f64 (sqrt.f64 (.f64 #s(approx (- (sqrt (+ (* im im) (* re re))) re) (-.f64 im re)) #s(literal 2 binary64))) #s(literal 1/2 binary64))
(sqrt.f64 (.f64 #s(approx (- (sqrt (+ ( im im) (* re re))) re) (-.f64 im re)) #s(literal 2 binary64)))
(.f64 #s(approx (- (sqrt (+ ( im im) (* re re))) re) (-.f64 im re)) #s(literal 2 binary64))
#s(approx (- (sqrt (+ (* im im) (* re re))) re) (-.f64 im re))
(-.f64 im re)
im
re
#s(literal 2 binary64)
#s(literal 1/2 binary64)
#s(approx (* 1/2 (sqrt (* 2 (- (sqrt (+ (* re re) (* im im))) re)))) (.f64 (.f64 #s(literal 1/2 binary64) im) (sqrt.f64 (/.f64 #s(literal 1 binary64) re))))
(.f64 (.f64 #s(literal 1/2 binary64) im) (sqrt.f64 (/.f64 #s(literal 1 binary64) re)))
(*.f64 #s(literal 1/2 binary64) im)
im
#s(literal 1/2 binary64)
(sqrt.f64 (/.f64 #s(literal 1 binary64) re))
(/.f64 #s(literal 1 binary64) re)
#s(literal 1 binary64)
re
#s(approx (* 1/2 (sqrt (* 2 (- (sqrt (+ (* re re) (* im im))) re)))) (*.f64 (/.f64 #s(literal 1/2 binary64) (sqrt.f64 re)) im))
(*.f64 (/.f64 #s(literal 1/2 binary64) (sqrt.f64 re)) im)
#s(literal 1 binary64)
(*.f64 (/.f64 #s(literal 2 binary64) im) (sqrt.f64 re))
(sqrt.f64 re)
re
(*.f64 #s(literal 1/2 binary64) im)
#s(literal 1/2 binary64)
im
(.f64 (sqrt.f64 (.f64 (-.f64 (hypot.f64 im re) re) #s(literal 2 binary64))) #s(literal 1/2 binary64))
#s(literal 1/2 binary64)
(sqrt.f64 (*.f64 (-.f64 (hypot.f64 im re) re) #s(literal 2 binary64)))
(*.f64 (-.f64 (hypot.f64 im re) re) #s(literal 2 binary64))
#s(literal 2 binary64)
(-.f64 (hypot.f64 im re) re)
(hypot.f64 im re)
(fma.f64 im im (*.f64 re re))
re
(*.f64 im im)
im

localize286.0ms (4%)

Memory

20.7MiB live, 380.8MiB allocated

Localize:

Found 20 expressions of interest:

New	Metric	Score
accuracy	0.00390625	(.f64 #s(literal 1/2 binary64) (sqrt.f64 (.f64 #s(literal 2 binary64) (-.f64 (sqrt.f64 (fma.f64 re re (*.f64 im im))) re))))
accuracy	5.117546358106111	(sqrt.f64 (.f64 #s(literal 2 binary64) (-.f64 (sqrt.f64 (fma.f64 re re (.f64 im im))) re)))
accuracy	7.3651219703664905	(-.f64 (sqrt.f64 (fma.f64 re re (*.f64 im im))) re)
accuracy	15.514305827091935	(sqrt.f64 (fma.f64 re re (*.f64 im im)))
accuracy	0	(sqrt.f64 re)
accuracy	0.11778236266526008	(/.f64 #s(literal 1 binary64) (/.f64 (sqrt.f64 re) (*.f64 #s(literal 1/2 binary64) im)))
accuracy	0.1328125	(/.f64 (sqrt.f64 re) (*.f64 #s(literal 1/2 binary64) im))
accuracy	14.625769161491963	#s(approx (* 1/2 (sqrt (* 2 (- (sqrt (+ (* re re) (* im im))) re)))) (/.f64 #s(literal 1 binary64) (/.f64 (sqrt.f64 re) (*.f64 #s(literal 1/2 binary64) im))))
accuracy	0	(*.f64 im #s(literal 1/2 binary64))
accuracy	0.1015625	(.f64 (.f64 im #s(literal 1/2 binary64)) (sqrt.f64 (/.f64 #s(literal 1 binary64) re)))
accuracy	0.10546875	(sqrt.f64 (/.f64 #s(literal 1 binary64) re))
accuracy	14.625769161491963	#s(approx (* 1/2 (sqrt (* 2 (- (sqrt (+ (* re re) (* im im))) re)))) (.f64 (.f64 im #s(literal 1/2 binary64)) (sqrt.f64 (/.f64 #s(literal 1 binary64) re))))
accuracy	0	(.f64 #s(approx (- (sqrt (+ ( im im) (* re re))) re) (-.f64 im re)) #s(literal 2 binary64))
accuracy	0.00390625	(.f64 (sqrt.f64 (.f64 #s(approx (- (sqrt (+ (* im im) (* re re))) re) (-.f64 im re)) #s(literal 2 binary64))) #s(literal 1/2 binary64))
accuracy	5.117546358106111	(sqrt.f64 (.f64 #s(approx (- (sqrt (+ ( im im) (* re re))) re) (-.f64 im re)) #s(literal 2 binary64)))
accuracy	15.086234846986052	#s(approx (- (sqrt (+ (* im im) (* re re))) re) (-.f64 im re))
accuracy	0.00390625	(.f64 (sqrt.f64 (.f64 (fma.f64 (sqrt.f64 (hypot.f64 re im)) (sqrt.f64 (hypot.f64 re im)) (neg.f64 re)) #s(literal 2 binary64))) #s(literal 1/2 binary64))
accuracy	0.00390625	(sqrt.f64 (hypot.f64 re im))
accuracy	5.117546358106111	(sqrt.f64 (*.f64 (fma.f64 (sqrt.f64 (hypot.f64 re im)) (sqrt.f64 (hypot.f64 re im)) (neg.f64 re)) #s(literal 2 binary64)))
accuracy	14.355175005813898	(fma.f64 (sqrt.f64 (hypot.f64 re im)) (sqrt.f64 (hypot.f64 re im)) (neg.f64 re))

Samples

86.0ms	134×	0	invalid
46.0ms	12×	3	valid
33.0ms	24×	2	valid
31.0ms	63×	0	valid
20.0ms	23×	1	valid

Compiler

Compiled 626 to 83 computations (86.7% saved)

Precisions

Click to see histograms. Total time spent on operations: 171.0ms

ival-mult: 88.0ms (51.6% of total)

ival-hypot: 27.0ms (15.8% of total)

ival-sqrt: 22.0ms (12.9% of total)

ival-sub: 9.0ms (5.3% of total)

ival-div: 7.0ms (4.1% of total)

adjust: 7.0ms (4.1% of total)

ival-add: 7.0ms (4.1% of total)

ival-neg: 2.0ms (1.2% of total)

exact: 1.0ms (0.6% of total)

ival-assert: 0.0ms (0% of total)

ival-true: 0.0ms (0% of total)

series68.0ms (0.9%)

Memory

-1.3MiB live, 113.2MiB allocated

Counts

22 → 492

Calls

Call 1

Inputs
#s(alt #<batchref> (patch (fma.f64 (sqrt.f64 (hypot.f64 re im)) (sqrt.f64 (hypot.f64 re im)) (neg.f64 re)) #<representation binary64>) () ())
#s(alt #<batchref> (patch (.f64 (sqrt.f64 (.f64 (fma.f64 (sqrt.f64 (hypot.f64 re im)) (sqrt.f64 (hypot.f64 re im)) (neg.f64 re)) #s(literal 2 binary64))) #s(literal 1/2 binary64)) #<representation binary64>) () ())
#s(alt #<batchref> (patch (sqrt.f64 (*.f64 (fma.f64 (sqrt.f64 (hypot.f64 re im)) (sqrt.f64 (hypot.f64 re im)) (neg.f64 re)) #s(literal 2 binary64))) #<representation binary64>) () ())
#s(alt #<batchref> (patch (*.f64 (fma.f64 (sqrt.f64 (hypot.f64 re im)) (sqrt.f64 (hypot.f64 re im)) (neg.f64 re)) #s(literal 2 binary64)) #<representation binary64>) () ())
#s(alt #<batchref> (patch (.f64 (sqrt.f64 (.f64 #s(approx (- (sqrt (+ (* im im) (* re re))) re) (-.f64 im re)) #s(literal 2 binary64))) #s(literal 1/2 binary64)) #<representation binary64>) () ())
#s(alt #<batchref> (patch (sqrt.f64 (.f64 #s(approx (- (sqrt (+ ( im im) (* re re))) re) (-.f64 im re)) #s(literal 2 binary64))) #<representation binary64>) () ())
#s(alt #<batchref> (patch (.f64 #s(approx (- (sqrt (+ ( im im) (* re re))) re) (-.f64 im re)) #s(literal 2 binary64)) #<representation binary64>) () ())
#s(alt #<batchref> (patch #s(approx (- (sqrt (+ (* im im) (* re re))) re) (-.f64 im re)) #<representation binary64>) () ())
#s(alt #<batchref> (patch #s(approx (* 1/2 (sqrt (* 2 (- (sqrt (+ (* re re) (* im im))) re)))) (.f64 (.f64 im #s(literal 1/2 binary64)) (sqrt.f64 (/.f64 #s(literal 1 binary64) re)))) #<representation binary64>) () ())
#s(alt #<batchref> (patch (.f64 (.f64 im #s(literal 1/2 binary64)) (sqrt.f64 (/.f64 #s(literal 1 binary64) re))) #<representation binary64>) () ())
#s(alt #<batchref> (patch (*.f64 im #s(literal 1/2 binary64)) #<representation binary64>) () ())
#s(alt #<batchref> (patch (sqrt.f64 (/.f64 #s(literal 1 binary64) re)) #<representation binary64>) () ())
#s(alt #<batchref> (patch (/.f64 #s(literal 1 binary64) (/.f64 (sqrt.f64 re) (*.f64 #s(literal 1/2 binary64) im))) #<representation binary64>) () ())
#s(alt #<batchref> (patch #s(approx (* 1/2 (sqrt (* 2 (- (sqrt (+ (* re re) (* im im))) re)))) (/.f64 #s(literal 1 binary64) (/.f64 (sqrt.f64 re) (*.f64 #s(literal 1/2 binary64) im)))) #<representation binary64>) () ())
#s(alt #<batchref> (patch (/.f64 (sqrt.f64 re) (*.f64 #s(literal 1/2 binary64) im)) #<representation binary64>) () ())
#s(alt #<batchref> (patch (sqrt.f64 re) #<representation binary64>) () ())
#s(alt #<batchref> (patch (.f64 #s(literal 1/2 binary64) (sqrt.f64 (.f64 #s(literal 2 binary64) (-.f64 (sqrt.f64 (fma.f64 re re (*.f64 im im))) re)))) #<representation binary64>) () ())
#s(alt #<batchref> (patch (sqrt.f64 (.f64 #s(literal 2 binary64) (-.f64 (sqrt.f64 (fma.f64 re re (.f64 im im))) re))) #<representation binary64>) () ())
#s(alt #<batchref> (patch (.f64 #s(literal 2 binary64) (-.f64 (sqrt.f64 (fma.f64 re re (.f64 im im))) re)) #<representation binary64>) () ())
#s(alt #<batchref> (patch (-.f64 (sqrt.f64 (fma.f64 re re (*.f64 im im))) re) #<representation binary64>) () ())
#s(alt #<batchref> (patch (sqrt.f64 (hypot.f64 re im)) #<representation binary64>) () ())
#s(alt #<batchref> (patch (sqrt.f64 (fma.f64 re re (*.f64 im im))) #<representation binary64>) () ())

Outputs
#s(alt #<batchref> (taylor 0 re) (#s(alt #<batchref> (patch (fma.f64 (sqrt.f64 (hypot.f64 re im)) (sqrt.f64 (hypot.f64 re im)) (neg.f64 re)) #<representation binary64>) () ())) ())
#s(alt #<batchref> (taylor 0 re) (#s(alt #<batchref> (patch (fma.f64 (sqrt.f64 (hypot.f64 re im)) (sqrt.f64 (hypot.f64 re im)) (neg.f64 re)) #<representation binary64>) () ())) ())
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Calls

6 calls:

Time	Variable		Point	Expression
9.0ms	re	@	-inf	((+ (* (sqrt (sqrt (+ (* re re) (* im im)))) (sqrt (sqrt (+ (* re re) (* im im))))) (neg re)) (* (sqrt (* (+ (* (sqrt (sqrt (+ (* re re) (* im im)))) (sqrt (sqrt (+ (* re re) (* im im))))) (neg re)) 2)) 1/2) (sqrt (* (+ (* (sqrt (sqrt (+ (* re re) (* im im)))) (sqrt (sqrt (+ (* re re) (* im im))))) (neg re)) 2)) (* (+ (* (sqrt (sqrt (+ (* re re) (* im im)))) (sqrt (sqrt (+ (* re re) (* im im))))) (neg re)) 2) (* (sqrt (* (- (sqrt (+ (* im im) (* re re))) re) 2)) 1/2) (sqrt (* (- (sqrt (+ (* im im) (* re re))) re) 2)) (* (- (sqrt (+ (* im im) (* re re))) re) 2) (- (sqrt (+ (* im im) (* re re))) re) (* 1/2 (sqrt (* 2 (- (sqrt (+ (* re re) (* im im))) re)))) (* (* im 1/2) (sqrt (/ 1 re))) (* im 1/2) (sqrt (/ 1 re)) (/ 1 (/ (sqrt re) (* 1/2 im))) (* 1/2 (sqrt (* 2 (- (sqrt (+ (* re re) (* im im))) re)))) (/ (sqrt re) (* 1/2 im)) (sqrt re) (* 1/2 (sqrt (* 2 (- (sqrt (+ (* re re) (* im im))) re)))) (sqrt (* 2 (- (sqrt (+ (* re re) (* im im))) re))) (* 2 (- (sqrt (+ (* re re) (* im im))) re)) (- (sqrt (+ (* re re) (* im im))) re) (sqrt (sqrt (+ (* re re) (* im im)))) (sqrt (+ (* re re) (* im im))))
8.0ms	re	@	inf	((+ (* (sqrt (sqrt (+ (* re re) (* im im)))) (sqrt (sqrt (+ (* re re) (* im im))))) (neg re)) (* (sqrt (* (+ (* (sqrt (sqrt (+ (* re re) (* im im)))) (sqrt (sqrt (+ (* re re) (* im im))))) (neg re)) 2)) 1/2) (sqrt (* (+ (* (sqrt (sqrt (+ (* re re) (* im im)))) (sqrt (sqrt (+ (* re re) (* im im))))) (neg re)) 2)) (* (+ (* (sqrt (sqrt (+ (* re re) (* im im)))) (sqrt (sqrt (+ (* re re) (* im im))))) (neg re)) 2) (* (sqrt (* (- (sqrt (+ (* im im) (* re re))) re) 2)) 1/2) (sqrt (* (- (sqrt (+ (* im im) (* re re))) re) 2)) (* (- (sqrt (+ (* im im) (* re re))) re) 2) (- (sqrt (+ (* im im) (* re re))) re) (* 1/2 (sqrt (* 2 (- (sqrt (+ (* re re) (* im im))) re)))) (* (* im 1/2) (sqrt (/ 1 re))) (* im 1/2) (sqrt (/ 1 re)) (/ 1 (/ (sqrt re) (* 1/2 im))) (* 1/2 (sqrt (* 2 (- (sqrt (+ (* re re) (* im im))) re)))) (/ (sqrt re) (* 1/2 im)) (sqrt re) (* 1/2 (sqrt (* 2 (- (sqrt (+ (* re re) (* im im))) re)))) (sqrt (* 2 (- (sqrt (+ (* re re) (* im im))) re))) (* 2 (- (sqrt (+ (* re re) (* im im))) re)) (- (sqrt (+ (* re re) (* im im))) re) (sqrt (sqrt (+ (* re re) (* im im)))) (sqrt (+ (* re re) (* im im))))
7.0ms	im	@	0	((+ (* (sqrt (sqrt (+ (* re re) (* im im)))) (sqrt (sqrt (+ (* re re) (* im im))))) (neg re)) (* (sqrt (* (+ (* (sqrt (sqrt (+ (* re re) (* im im)))) (sqrt (sqrt (+ (* re re) (* im im))))) (neg re)) 2)) 1/2) (sqrt (* (+ (* (sqrt (sqrt (+ (* re re) (* im im)))) (sqrt (sqrt (+ (* re re) (* im im))))) (neg re)) 2)) (* (+ (* (sqrt (sqrt (+ (* re re) (* im im)))) (sqrt (sqrt (+ (* re re) (* im im))))) (neg re)) 2) (* (sqrt (* (- (sqrt (+ (* im im) (* re re))) re) 2)) 1/2) (sqrt (* (- (sqrt (+ (* im im) (* re re))) re) 2)) (* (- (sqrt (+ (* im im) (* re re))) re) 2) (- (sqrt (+ (* im im) (* re re))) re) (* 1/2 (sqrt (* 2 (- (sqrt (+ (* re re) (* im im))) re)))) (* (* im 1/2) (sqrt (/ 1 re))) (* im 1/2) (sqrt (/ 1 re)) (/ 1 (/ (sqrt re) (* 1/2 im))) (* 1/2 (sqrt (* 2 (- (sqrt (+ (* re re) (* im im))) re)))) (/ (sqrt re) (* 1/2 im)) (sqrt re) (* 1/2 (sqrt (* 2 (- (sqrt (+ (* re re) (* im im))) re)))) (sqrt (* 2 (- (sqrt (+ (* re re) (* im im))) re))) (* 2 (- (sqrt (+ (* re re) (* im im))) re)) (- (sqrt (+ (* re re) (* im im))) re) (sqrt (sqrt (+ (* re re) (* im im)))) (sqrt (+ (* re re) (* im im))))
7.0ms	im	@	-inf	((+ (* (sqrt (sqrt (+ (* re re) (* im im)))) (sqrt (sqrt (+ (* re re) (* im im))))) (neg re)) (* (sqrt (* (+ (* (sqrt (sqrt (+ (* re re) (* im im)))) (sqrt (sqrt (+ (* re re) (* im im))))) (neg re)) 2)) 1/2) (sqrt (* (+ (* (sqrt (sqrt (+ (* re re) (* im im)))) (sqrt (sqrt (+ (* re re) (* im im))))) (neg re)) 2)) (* (+ (* (sqrt (sqrt (+ (* re re) (* im im)))) (sqrt (sqrt (+ (* re re) (* im im))))) (neg re)) 2) (* (sqrt (* (- (sqrt (+ (* im im) (* re re))) re) 2)) 1/2) (sqrt (* (- (sqrt (+ (* im im) (* re re))) re) 2)) (* (- (sqrt (+ (* im im) (* re re))) re) 2) (- (sqrt (+ (* im im) (* re re))) re) (* 1/2 (sqrt (* 2 (- (sqrt (+ (* re re) (* im im))) re)))) (* (* im 1/2) (sqrt (/ 1 re))) (* im 1/2) (sqrt (/ 1 re)) (/ 1 (/ (sqrt re) (* 1/2 im))) (* 1/2 (sqrt (* 2 (- (sqrt (+ (* re re) (* im im))) re)))) (/ (sqrt re) (* 1/2 im)) (sqrt re) (* 1/2 (sqrt (* 2 (- (sqrt (+ (* re re) (* im im))) re)))) (sqrt (* 2 (- (sqrt (+ (* re re) (* im im))) re))) (* 2 (- (sqrt (+ (* re re) (* im im))) re)) (- (sqrt (+ (* re re) (* im im))) re) (sqrt (sqrt (+ (* re re) (* im im)))) (sqrt (+ (* re re) (* im im))))
6.0ms	re	@	0	((+ (* (sqrt (sqrt (+ (* re re) (* im im)))) (sqrt (sqrt (+ (* re re) (* im im))))) (neg re)) (* (sqrt (* (+ (* (sqrt (sqrt (+ (* re re) (* im im)))) (sqrt (sqrt (+ (* re re) (* im im))))) (neg re)) 2)) 1/2) (sqrt (* (+ (* (sqrt (sqrt (+ (* re re) (* im im)))) (sqrt (sqrt (+ (* re re) (* im im))))) (neg re)) 2)) (* (+ (* (sqrt (sqrt (+ (* re re) (* im im)))) (sqrt (sqrt (+ (* re re) (* im im))))) (neg re)) 2) (* (sqrt (* (- (sqrt (+ (* im im) (* re re))) re) 2)) 1/2) (sqrt (* (- (sqrt (+ (* im im) (* re re))) re) 2)) (* (- (sqrt (+ (* im im) (* re re))) re) 2) (- (sqrt (+ (* im im) (* re re))) re) (* 1/2 (sqrt (* 2 (- (sqrt (+ (* re re) (* im im))) re)))) (* (* im 1/2) (sqrt (/ 1 re))) (* im 1/2) (sqrt (/ 1 re)) (/ 1 (/ (sqrt re) (* 1/2 im))) (* 1/2 (sqrt (* 2 (- (sqrt (+ (* re re) (* im im))) re)))) (/ (sqrt re) (* 1/2 im)) (sqrt re) (* 1/2 (sqrt (* 2 (- (sqrt (+ (* re re) (* im im))) re)))) (sqrt (* 2 (- (sqrt (+ (* re re) (* im im))) re))) (* 2 (- (sqrt (+ (* re re) (* im im))) re)) (- (sqrt (+ (* re re) (* im im))) re) (sqrt (sqrt (+ (* re re) (* im im)))) (sqrt (+ (* re re) (* im im))))

simplify234.0ms (3.2%)

Memory

20.0MiB live, 258.4MiB allocated

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	684	11541
1	2227	10811
2	7684	10795
0	8557	10304

Stop Event

1×	iter limit
1×	node limit

Counts

492 → 482

Calls

Call 1

Inputs
im
(+ im (* -1 re))
(+ im (* re (- (* 1/2 (/ re im)) 1)))
(+ im (* re (- (* re (+ (* -1/8 (/ (pow re 2) (pow im 3))) (* 1/2 (/ 1 im)))) 1)))
(* 1/2 (* (sqrt im) (sqrt 2)))
(+ (* -1/4 (* (sqrt (/ 1 im)) (* re (sqrt 2)))) (* 1/2 (* (sqrt im) (sqrt 2))))
(+ (* 1/2 (* (sqrt im) (sqrt 2))) (* re (+ (* -1/4 (* (sqrt (/ 1 im)) (sqrt 2))) (* 1/16 (* (sqrt (/ 1 (pow im 3))) (* re (sqrt 2)))))))
(+ (* 1/2 (* (sqrt im) (sqrt 2))) (* re (+ (* -1/4 (* (sqrt (/ 1 im)) (sqrt 2))) (* re (+ (* 1/32 (* (sqrt (/ 1 (pow im 5))) (* re (sqrt 2)))) (* 1/16 (* (sqrt (/ 1 (pow im 3))) (sqrt 2))))))))
(* (sqrt im) (sqrt 2))
(+ (* -1/2 (* (sqrt (/ 1 im)) (* re (sqrt 2)))) (* (sqrt im) (sqrt 2)))
(+ (* re (+ (* -1/2 (* (sqrt (/ 1 im)) (sqrt 2))) (* 1/8 (* (sqrt (/ 1 (pow im 3))) (* re (sqrt 2)))))) (* (sqrt im) (sqrt 2)))
(+ (* re (+ (* -1/2 (* (sqrt (/ 1 im)) (sqrt 2))) (* re (+ (* 1/16 (* (sqrt (/ 1 (pow im 5))) (* re (sqrt 2)))) (* 1/8 (* (sqrt (/ 1 (pow im 3))) (sqrt 2))))))) (* (sqrt im) (sqrt 2)))
(* 2 im)
(+ (* -2 re) (* 2 im))
(+ (* 2 im) (* re (- (/ re im) 2)))
(+ (* 2 im) (* re (- (* re (+ (* -1/4 (/ (pow re 2) (pow im 3))) (/ 1 im))) 2)))
(* 1/2 (* (sqrt im) (sqrt 2)))
(+ (* -1/4 (* (sqrt (/ 1 im)) (* re (sqrt 2)))) (* 1/2 (* (sqrt im) (sqrt 2))))
(+ (* 1/2 (* (sqrt im) (sqrt 2))) (* re (+ (* -1/4 (* (sqrt (/ 1 im)) (sqrt 2))) (* 1/16 (* (sqrt (/ 1 (pow im 3))) (* re (sqrt 2)))))))
(+ (* 1/2 (* (sqrt im) (sqrt 2))) (* re (+ (* -1/4 (* (sqrt (/ 1 im)) (sqrt 2))) (* re (+ (* 1/32 (* (sqrt (/ 1 (pow im 5))) (* re (sqrt 2)))) (* 1/16 (* (sqrt (/ 1 (pow im 3))) (sqrt 2))))))))
(* (sqrt im) (sqrt 2))
(+ (* -1/2 (* (sqrt (/ 1 im)) (* re (sqrt 2)))) (* (sqrt im) (sqrt 2)))
(+ (* re (+ (* -1/2 (* (sqrt (/ 1 im)) (sqrt 2))) (* 1/8 (* (sqrt (/ 1 (pow im 3))) (* re (sqrt 2)))))) (* (sqrt im) (sqrt 2)))
(+ (* re (+ (* -1/2 (* (sqrt (/ 1 im)) (sqrt 2))) (* re (+ (* 1/16 (* (sqrt (/ 1 (pow im 5))) (* re (sqrt 2)))) (* 1/8 (* (sqrt (/ 1 (pow im 3))) (sqrt 2))))))) (* (sqrt im) (sqrt 2)))
(* 2 im)
(+ (* -2 re) (* 2 im))
(+ (* 2 im) (* re (- (/ re im) 2)))
(+ (* 2 im) (* re (- (* re (+ (* -1/4 (/ (pow re 2) (pow im 3))) (/ 1 im))) 2)))
im
(+ im (* -1 re))
(+ im (* re (- (* 1/2 (/ re im)) 1)))
(+ im (* re (- (* re (+ (* -1/8 (/ (pow re 2) (pow im 3))) (* 1/2 (/ 1 im)))) 1)))
(* 1/2 (* (sqrt im) (sqrt 2)))
(+ (* -1/4 (* (sqrt (/ 1 im)) (* re (sqrt 2)))) (* 1/2 (* (sqrt im) (sqrt 2))))
(+ (* 1/2 (* (sqrt im) (sqrt 2))) (* re (+ (* -1/4 (* (sqrt (/ 1 im)) (sqrt 2))) (* 1/16 (* (sqrt (/ 1 (pow im 3))) (* re (sqrt 2)))))))
(+ (* 1/2 (* (sqrt im) (sqrt 2))) (* re (+ (* -1/4 (* (sqrt (/ 1 im)) (sqrt 2))) (* re (+ (* 1/32 (* (sqrt (/ 1 (pow im 5))) (* re (sqrt 2)))) (* 1/16 (* (sqrt (/ 1 (pow im 3))) (sqrt 2))))))))
(* 1/2 (* im (sqrt (/ 1 re))))
(* 1/2 (* im (sqrt (/ 1 re))))
(* 1/2 (* im (sqrt (/ 1 re))))
(* 1/2 (* im (sqrt (/ 1 re))))
(sqrt (/ 1 re))
(sqrt (/ 1 re))
(sqrt (/ 1 re))
(sqrt (/ 1 re))
(* 1/2 (* im (sqrt (/ 1 re))))
(* 1/2 (* im (sqrt (/ 1 re))))
(* 1/2 (* im (sqrt (/ 1 re))))
(* 1/2 (* im (sqrt (/ 1 re))))
(* 1/2 (* (sqrt im) (sqrt 2)))
(+ (* -1/4 (* (sqrt (/ 1 im)) (* re (sqrt 2)))) (* 1/2 (* (sqrt im) (sqrt 2))))
(+ (* 1/2 (* (sqrt im) (sqrt 2))) (* re (+ (* -1/4 (* (sqrt (/ 1 im)) (sqrt 2))) (* 1/16 (* (sqrt (/ 1 (pow im 3))) (* re (sqrt 2)))))))
(+ (* 1/2 (* (sqrt im) (sqrt 2))) (* re (+ (* -1/4 (* (sqrt (/ 1 im)) (sqrt 2))) (* re (+ (* 1/32 (* (sqrt (/ 1 (pow im 5))) (* re (sqrt 2)))) (* 1/16 (* (sqrt (/ 1 (pow im 3))) (sqrt 2))))))))
(* 2 (* (/ 1 im) (sqrt re)))
(* 2 (* (/ 1 im) (sqrt re)))
(* 2 (* (/ 1 im) (sqrt re)))
(* 2 (* (/ 1 im) (sqrt re)))
(sqrt re)
(sqrt re)
(sqrt re)
(sqrt re)
(* 1/2 (* (sqrt im) (sqrt 2)))
(+ (* -1/4 (* (sqrt (/ 1 im)) (* re (sqrt 2)))) (* 1/2 (* (sqrt im) (sqrt 2))))
(+ (* 1/2 (* (sqrt im) (sqrt 2))) (* re (+ (* -1/4 (* (sqrt (/ 1 im)) (sqrt 2))) (* 1/16 (* (sqrt (/ 1 (pow im 3))) (* re (sqrt 2)))))))
(+ (* 1/2 (* (sqrt im) (sqrt 2))) (* re (+ (* -1/4 (* (sqrt (/ 1 im)) (sqrt 2))) (* re (+ (* 1/32 (* (sqrt (/ 1 (pow im 5))) (* re (sqrt 2)))) (* 1/16 (* (sqrt (/ 1 (pow im 3))) (sqrt 2))))))))
(* (sqrt im) (sqrt 2))
(+ (* -1/2 (* (sqrt (/ 1 im)) (* re (sqrt 2)))) (* (sqrt im) (sqrt 2)))
(+ (* re (+ (* -1/2 (* (sqrt (/ 1 im)) (sqrt 2))) (* 1/8 (* (sqrt (/ 1 (pow im 3))) (* re (sqrt 2)))))) (* (sqrt im) (sqrt 2)))
(+ (* re (+ (* -1/2 (* (sqrt (/ 1 im)) (sqrt 2))) (* re (+ (* 1/16 (* (sqrt (/ 1 (pow im 5))) (* re (sqrt 2)))) (* 1/8 (* (sqrt (/ 1 (pow im 3))) (sqrt 2))))))) (* (sqrt im) (sqrt 2)))
(* 2 im)
(+ (* -2 re) (* 2 im))
(+ (* 2 im) (* re (- (/ re im) 2)))
(+ (* 2 im) (* re (- (* re (+ (* -1/4 (/ (pow re 2) (pow im 3))) (/ 1 im))) 2)))
im
(+ im (* -1 re))
(+ im (* re (- (* 1/2 (/ re im)) 1)))
(+ im (* re (- (* re (+ (* -1/8 (/ (pow re 2) (pow im 3))) (* 1/2 (/ 1 im)))) 1)))
(* (pow 1 1/4) (sqrt im))
(+ (* 1/4 (* (pow 1 1/4) (* (sqrt (/ 1 (pow im 3))) (pow re 2)))) (* (pow 1 1/4) (sqrt im)))
(+ (* (pow 1 1/4) (sqrt im)) (* (pow re 2) (+ (* -3/32 (* (pow 1 1/4) (* (sqrt (/ 1 (pow im 7))) (pow re 2)))) (* 1/4 (* (pow 1 1/4) (sqrt (/ 1 (pow im 3))))))))
(+ (* (pow 1 1/4) (sqrt im)) (* (pow re 2) (+ (* 1/4 (* (pow 1 1/4) (sqrt (/ 1 (pow im 3))))) (* (pow re 2) (+ (* -3/32 (* (pow 1 1/4) (sqrt (/ 1 (pow im 7))))) (* 7/128 (* (pow 1 1/4) (* (sqrt (/ 1 (pow im 11))) (pow re 2)))))))))
im
(+ im (* 1/2 (/ (pow re 2) im)))
(+ im (* (pow re 2) (+ (* -1/8 (/ (pow re 2) (pow im 3))) (* 1/2 (/ 1 im)))))
(+ im (* (pow re 2) (+ (* (pow re 2) (- (* 1/16 (/ (pow re 2) (pow im 5))) (* 1/8 (/ 1 (pow im 3))))) (* 1/2 (/ 1 im)))))
(* 1/2 (/ (pow im 2) re))
(/ (+ (* -1/8 (/ (pow im 4) (pow re 2))) (* 1/2 (pow im 2))) re)
(/ (+ (* -1/8 (/ (pow im 4) (pow re 2))) (+ (* 1/16 (/ (pow im 6) (pow re 4))) (* 1/2 (pow im 2)))) re)
(/ (+ (* -1/2 (/ (+ (* 1/64 (pow im 8)) (* 1/16 (pow im 8))) (pow re 6))) (+ (* -1/8 (/ (pow im 4) (pow re 2))) (+ (* 1/16 (/ (pow im 6) (pow re 4))) (* 1/2 (pow im 2))))) re)
(* 1/2 (* (* im (* (sqrt 1/2) (sqrt 2))) (sqrt (/ 1 re))))
(+ (* -1/32 (* (/ (* (pow im 3) (sqrt 2)) (sqrt 1/2)) (sqrt (/ 1 (pow re 5))))) (* 1/2 (* (* im (* (sqrt 1/2) (sqrt 2))) (sqrt (/ 1 re)))))
(+ (* -1/32 (* (/ (* (pow im 3) (sqrt 2)) (sqrt 1/2)) (sqrt (/ 1 (pow re 5))))) (+ (* 1/64 (* (/ (* (pow im 5) (sqrt 2)) (sqrt 1/2)) (sqrt (/ 1 (pow re 9))))) (* 1/2 (* (* im (* (sqrt 1/2) (sqrt 2))) (sqrt (/ 1 re))))))
(+ (* -1/32 (* (/ (* (pow im 3) (sqrt 2)) (sqrt 1/2)) (sqrt (/ 1 (pow re 5))))) (+ (* -1/1024 (* (/ (* (pow im 5) (sqrt 2)) (pow (sqrt 1/2) 3)) (sqrt (/ 1 (pow re 9))))) (+ (* 1/64 (* (/ (* (pow im 5) (sqrt 2)) (sqrt 1/2)) (sqrt (/ 1 (pow re 9))))) (* 1/2 (* (* im (* (sqrt 1/2) (sqrt 2))) (sqrt (/ 1 re)))))))
(* (* im (* (sqrt 1/2) (sqrt 2))) (sqrt (/ 1 re)))
(+ (* -1/16 (* (/ (* (pow im 3) (sqrt 2)) (sqrt 1/2)) (sqrt (/ 1 (pow re 5))))) (* (* im (* (sqrt 1/2) (sqrt 2))) (sqrt (/ 1 re))))
(+ (* -1/16 (* (/ (* (pow im 3) (sqrt 2)) (sqrt 1/2)) (sqrt (/ 1 (pow re 5))))) (+ (* 1/32 (* (/ (* (pow im 5) (sqrt 2)) (sqrt 1/2)) (sqrt (/ 1 (pow re 9))))) (* (* im (* (sqrt 1/2) (sqrt 2))) (sqrt (/ 1 re)))))
(+ (* -1/16 (* (/ (* (pow im 3) (sqrt 2)) (sqrt 1/2)) (sqrt (/ 1 (pow re 5))))) (+ (* -1/512 (* (/ (* (pow im 5) (sqrt 2)) (pow (sqrt 1/2) 3)) (sqrt (/ 1 (pow re 9))))) (+ (* 1/32 (* (/ (* (pow im 5) (sqrt 2)) (sqrt 1/2)) (sqrt (/ 1 (pow re 9))))) (* (* im (* (sqrt 1/2) (sqrt 2))) (sqrt (/ 1 re))))))
(/ (pow im 2) re)
(/ (+ (* -1/4 (/ (pow im 4) (pow re 2))) (pow im 2)) re)
(/ (+ (* -1/4 (/ (pow im 4) (pow re 2))) (+ (* 1/8 (/ (pow im 6) (pow re 4))) (pow im 2))) re)
(/ (+ (* -1 (/ (+ (* 1/64 (pow im 8)) (* 1/16 (pow im 8))) (pow re 6))) (+ (* -1/4 (/ (pow im 4) (pow re 2))) (+ (* 1/8 (/ (pow im 6) (pow re 4))) (pow im 2)))) re)
(* 1/2 (* (* im (* (sqrt 1/2) (sqrt 2))) (sqrt (/ 1 re))))
(+ (* -1/32 (* (/ (* (pow im 3) (sqrt 2)) (sqrt 1/2)) (sqrt (/ 1 (pow re 5))))) (* 1/2 (* (* im (* (sqrt 1/2) (sqrt 2))) (sqrt (/ 1 re)))))
(+ (* -1/32 (* (/ (* (pow im 3) (sqrt 2)) (sqrt 1/2)) (sqrt (/ 1 (pow re 5))))) (+ (* 1/64 (* (/ (* (pow im 5) (sqrt 2)) (sqrt 1/2)) (sqrt (/ 1 (pow re 9))))) (* 1/2 (* (* im (* (sqrt 1/2) (sqrt 2))) (sqrt (/ 1 re))))))
(+ (* -1/32 (* (/ (* (pow im 3) (sqrt 2)) (sqrt 1/2)) (sqrt (/ 1 (pow re 5))))) (+ (* -1/1024 (* (/ (* (pow im 5) (sqrt 2)) (pow (sqrt 1/2) 3)) (sqrt (/ 1 (pow re 9))))) (+ (* 1/64 (* (/ (* (pow im 5) (sqrt 2)) (sqrt 1/2)) (sqrt (/ 1 (pow re 9))))) (* 1/2 (* (* im (* (sqrt 1/2) (sqrt 2))) (sqrt (/ 1 re)))))))
(* (* im (* (sqrt 1/2) (sqrt 2))) (sqrt (/ 1 re)))
(+ (* -1/16 (* (/ (* (pow im 3) (sqrt 2)) (sqrt 1/2)) (sqrt (/ 1 (pow re 5))))) (* (* im (* (sqrt 1/2) (sqrt 2))) (sqrt (/ 1 re))))
(+ (* -1/16 (* (/ (* (pow im 3) (sqrt 2)) (sqrt 1/2)) (sqrt (/ 1 (pow re 5))))) (+ (* 1/32 (* (/ (* (pow im 5) (sqrt 2)) (sqrt 1/2)) (sqrt (/ 1 (pow re 9))))) (* (* im (* (sqrt 1/2) (sqrt 2))) (sqrt (/ 1 re)))))
(+ (* -1/16 (* (/ (* (pow im 3) (sqrt 2)) (sqrt 1/2)) (sqrt (/ 1 (pow re 5))))) (+ (* -1/512 (* (/ (* (pow im 5) (sqrt 2)) (pow (sqrt 1/2) 3)) (sqrt (/ 1 (pow re 9))))) (+ (* 1/32 (* (/ (* (pow im 5) (sqrt 2)) (sqrt 1/2)) (sqrt (/ 1 (pow re 9))))) (* (* im (* (sqrt 1/2) (sqrt 2))) (sqrt (/ 1 re))))))
(/ (pow im 2) re)
(/ (+ (* -1/4 (/ (pow im 4) (pow re 2))) (pow im 2)) re)
(/ (+ (* -1/4 (/ (pow im 4) (pow re 2))) (+ (* 1/8 (/ (pow im 6) (pow re 4))) (pow im 2))) re)
(/ (+ (* -1 (/ (+ (* 1/64 (pow im 8)) (* 1/16 (pow im 8))) (pow re 6))) (+ (* -1/4 (/ (pow im 4) (pow re 2))) (+ (* 1/8 (/ (pow im 6) (pow re 4))) (pow im 2)))) re)
(* 1/2 (/ (pow im 2) re))
(/ (+ (* -1/8 (/ (pow im 4) (pow re 2))) (* 1/2 (pow im 2))) re)
(/ (+ (* -1/8 (/ (pow im 4) (pow re 2))) (+ (* 1/16 (/ (pow im 6) (pow re 4))) (* 1/2 (pow im 2)))) re)
(/ (+ (* -1/2 (/ (+ (* 1/64 (pow im 8)) (* 1/16 (pow im 8))) (pow re 6))) (+ (* -1/8 (/ (pow im 4) (pow re 2))) (+ (* 1/16 (/ (pow im 6) (pow re 4))) (* 1/2 (pow im 2))))) re)
(* 1/2 (* (* im (* (sqrt 1/2) (sqrt 2))) (sqrt (/ 1 re))))
(+ (* -1/32 (* (/ (* (pow im 3) (sqrt 2)) (sqrt 1/2)) (sqrt (/ 1 (pow re 5))))) (* 1/2 (* (* im (* (sqrt 1/2) (sqrt 2))) (sqrt (/ 1 re)))))
(+ (* -1/32 (* (/ (* (pow im 3) (sqrt 2)) (sqrt 1/2)) (sqrt (/ 1 (pow re 5))))) (+ (* 1/64 (* (/ (* (pow im 5) (sqrt 2)) (sqrt 1/2)) (sqrt (/ 1 (pow re 9))))) (* 1/2 (* (* im (* (sqrt 1/2) (sqrt 2))) (sqrt (/ 1 re))))))
(+ (* -1/32 (* (/ (* (pow im 3) (sqrt 2)) (sqrt 1/2)) (sqrt (/ 1 (pow re 5))))) (+ (* -1/1024 (* (/ (* (pow im 5) (sqrt 2)) (pow (sqrt 1/2) 3)) (sqrt (/ 1 (pow re 9))))) (+ (* 1/64 (* (/ (* (pow im 5) (sqrt 2)) (sqrt 1/2)) (sqrt (/ 1 (pow re 9))))) (* 1/2 (* (* im (* (sqrt 1/2) (sqrt 2))) (sqrt (/ 1 re)))))))
(* 1/2 (* im (sqrt (/ 1 re))))
(* 1/2 (* im (sqrt (/ 1 re))))
(* 1/2 (* im (sqrt (/ 1 re))))
(* 1/2 (* im (sqrt (/ 1 re))))
(sqrt (/ 1 re))
(sqrt (/ 1 re))
(sqrt (/ 1 re))
(sqrt (/ 1 re))
(* 1/2 (* im (sqrt (/ 1 re))))
(* 1/2 (* im (sqrt (/ 1 re))))
(* 1/2 (* im (sqrt (/ 1 re))))
(* 1/2 (* im (sqrt (/ 1 re))))
(* 1/2 (* (* im (* (sqrt 1/2) (sqrt 2))) (sqrt (/ 1 re))))
(+ (* -1/32 (* (/ (* (pow im 3) (sqrt 2)) (sqrt 1/2)) (sqrt (/ 1 (pow re 5))))) (* 1/2 (* (* im (* (sqrt 1/2) (sqrt 2))) (sqrt (/ 1 re)))))
(+ (* -1/32 (* (/ (* (pow im 3) (sqrt 2)) (sqrt 1/2)) (sqrt (/ 1 (pow re 5))))) (+ (* 1/64 (* (/ (* (pow im 5) (sqrt 2)) (sqrt 1/2)) (sqrt (/ 1 (pow re 9))))) (* 1/2 (* (* im (* (sqrt 1/2) (sqrt 2))) (sqrt (/ 1 re))))))
(+ (* -1/32 (* (/ (* (pow im 3) (sqrt 2)) (sqrt 1/2)) (sqrt (/ 1 (pow re 5))))) (+ (* -1/1024 (* (/ (* (pow im 5) (sqrt 2)) (pow (sqrt 1/2) 3)) (sqrt (/ 1 (pow re 9))))) (+ (* 1/64 (* (/ (* (pow im 5) (sqrt 2)) (sqrt 1/2)) (sqrt (/ 1 (pow re 9))))) (* 1/2 (* (* im (* (sqrt 1/2) (sqrt 2))) (sqrt (/ 1 re)))))))
(* 2 (* (/ 1 im) (sqrt re)))
(* 2 (* (/ 1 im) (sqrt re)))
(* 2 (* (/ 1 im) (sqrt re)))
(* 2 (* (/ 1 im) (sqrt re)))
(sqrt re)
(sqrt re)
(sqrt re)
(sqrt re)
(* 1/2 (* (* im (* (sqrt 1/2) (sqrt 2))) (sqrt (/ 1 re))))
(+ (* -1/32 (* (/ (* (pow im 3) (sqrt 2)) (sqrt 1/2)) (sqrt (/ 1 (pow re 5))))) (* 1/2 (* (* im (* (sqrt 1/2) (sqrt 2))) (sqrt (/ 1 re)))))
(+ (* -1/32 (* (/ (* (pow im 3) (sqrt 2)) (sqrt 1/2)) (sqrt (/ 1 (pow re 5))))) (+ (* 1/64 (* (/ (* (pow im 5) (sqrt 2)) (sqrt 1/2)) (sqrt (/ 1 (pow re 9))))) (* 1/2 (* (* im (* (sqrt 1/2) (sqrt 2))) (sqrt (/ 1 re))))))
(+ (* -1/32 (* (/ (* (pow im 3) (sqrt 2)) (sqrt 1/2)) (sqrt (/ 1 (pow re 5))))) (+ (* -1/1024 (* (/ (* (pow im 5) (sqrt 2)) (pow (sqrt 1/2) 3)) (sqrt (/ 1 (pow re 9))))) (+ (* 1/64 (* (/ (* (pow im 5) (sqrt 2)) (sqrt 1/2)) (sqrt (/ 1 (pow re 9))))) (* 1/2 (* (* im (* (sqrt 1/2) (sqrt 2))) (sqrt (/ 1 re)))))))
(* (* im (* (sqrt 1/2) (sqrt 2))) (sqrt (/ 1 re)))
(+ (* -1/16 (* (/ (* (pow im 3) (sqrt 2)) (sqrt 1/2)) (sqrt (/ 1 (pow re 5))))) (* (* im (* (sqrt 1/2) (sqrt 2))) (sqrt (/ 1 re))))
(+ (* -1/16 (* (/ (* (pow im 3) (sqrt 2)) (sqrt 1/2)) (sqrt (/ 1 (pow re 5))))) (+ (* 1/32 (* (/ (* (pow im 5) (sqrt 2)) (sqrt 1/2)) (sqrt (/ 1 (pow re 9))))) (* (* im (* (sqrt 1/2) (sqrt 2))) (sqrt (/ 1 re)))))
(+ (* -1/16 (* (/ (* (pow im 3) (sqrt 2)) (sqrt 1/2)) (sqrt (/ 1 (pow re 5))))) (+ (* -1/512 (* (/ (* (pow im 5) (sqrt 2)) (pow (sqrt 1/2) 3)) (sqrt (/ 1 (pow re 9))))) (+ (* 1/32 (* (/ (* (pow im 5) (sqrt 2)) (sqrt 1/2)) (sqrt (/ 1 (pow re 9))))) (* (* im (* (sqrt 1/2) (sqrt 2))) (sqrt (/ 1 re))))))
(/ (pow im 2) re)
(/ (+ (* -1/4 (/ (pow im 4) (pow re 2))) (pow im 2)) re)
(/ (+ (* -1/4 (/ (pow im 4) (pow re 2))) (+ (* 1/8 (/ (pow im 6) (pow re 4))) (pow im 2))) re)
(/ (+ (* -1 (/ (+ (* 1/64 (pow im 8)) (* 1/16 (pow im 8))) (pow re 6))) (+ (* -1/4 (/ (pow im 4) (pow re 2))) (+ (* 1/8 (/ (pow im 6) (pow re 4))) (pow im 2)))) re)
(* 1/2 (/ (pow im 2) re))
(/ (+ (* -1/8 (/ (pow im 4) (pow re 2))) (* 1/2 (pow im 2))) re)
(/ (+ (* -1/8 (/ (pow im 4) (pow re 2))) (+ (* 1/16 (/ (pow im 6) (pow re 4))) (* 1/2 (pow im 2)))) re)
(/ (+ (* -1/2 (/ (+ (* 1/64 (pow im 8)) (* 1/16 (pow im 8))) (pow re 6))) (+ (* -1/8 (/ (pow im 4) (pow re 2))) (+ (* 1/16 (/ (pow im 6) (pow re 4))) (* 1/2 (pow im 2))))) re)
(sqrt re)
(+ (sqrt re) (* 1/4 (* (pow im 2) (sqrt (/ 1 (pow re 3))))))
(+ (sqrt re) (+ (* 1/4 (* (pow im 2) (sqrt (/ 1 (pow re 3))))) (* (sqrt (/ 1 (pow re 7))) (+ (* -1/8 (pow im 4)) (* 1/32 (pow im 4))))))
(+ (sqrt re) (+ (* 1/4 (* (pow im 2) (sqrt (/ 1 (pow re 3))))) (+ (* (sqrt (/ 1 (pow re 7))) (+ (* -1/8 (pow im 4)) (* 1/32 (pow im 4)))) (* (sqrt (/ 1 (pow re 11))) (+ (* -1/32 (pow im 6)) (+ (* 1/384 (pow im 6)) (* 1/12 (pow im 6))))))))
re
(* re (+ 1 (* 1/2 (/ (pow im 2) (pow re 2)))))
(* re (+ 1 (+ (* -1/8 (/ (pow im 4) (pow re 4))) (* 1/2 (/ (pow im 2) (pow re 2))))))
(* re (+ 1 (+ (* -1/8 (/ (pow im 4) (pow re 4))) (+ (* 1/16 (/ (pow im 6) (pow re 6))) (* 1/2 (/ (pow im 2) (pow re 2)))))))
(* -2 re)
(* -1 (* re (+ 2 (* 1/2 (/ (pow im 2) (pow re 2))))))
(* -1 (* re (+ 2 (+ (* -1/8 (/ (pow im 4) (pow re 4))) (* 1/2 (/ (pow im 2) (pow re 2)))))))
(* -1 (* re (+ 2 (+ (* -1/8 (/ (pow im 4) (pow re 4))) (+ (* 1/16 (/ (pow im 6) (pow re 6))) (* 1/2 (/ (pow im 2) (pow re 2))))))))
(* -1/2 (* (sqrt re) (* (sqrt -1) (pow (sqrt 2) 2))))
(* -1 (* re (+ (* -1/8 (* (* (pow im 2) (sqrt -1)) (sqrt (/ 1 (pow re 5))))) (* 1/2 (* (sqrt (/ 1 re)) (* (sqrt -1) (pow (sqrt 2) 2)))))))
(* -1 (* re (+ (* -1 (/ (+ (* -1/32 (* (* (pow im 4) (sqrt -1)) (sqrt (/ 1 (pow re 3))))) (* 1/8 (* (* (pow im 2) (sqrt -1)) (sqrt re)))) (pow re 3))) (* 1/2 (* (sqrt (/ 1 re)) (* (sqrt -1) (pow (sqrt 2) 2)))))))
(* -1 (* re (+ (* -1 (/ (+ (* -1/32 (* (* (pow im 4) (sqrt -1)) (sqrt (/ 1 (pow re 3))))) (+ (* 1/64 (* (/ (* (pow im 4) (sqrt -1)) (pow (sqrt 2) 2)) (sqrt (/ 1 (pow re 3))))) (* 1/8 (* (* (pow im 2) (sqrt -1)) (sqrt re))))) (pow re 3))) (* 1/2 (* (sqrt (/ 1 re)) (* (sqrt -1) (pow (sqrt 2) 2)))))))
(* -1 (* (sqrt re) (* (sqrt -1) (pow (sqrt 2) 2))))
(* -1 (* re (+ (* -1/4 (* (* (pow im 2) (sqrt -1)) (sqrt (/ 1 (pow re 5))))) (* (sqrt (/ 1 re)) (* (sqrt -1) (pow (sqrt 2) 2))))))
(* -1 (* re (+ (* -1 (/ (+ (* -1/16 (* (* (pow im 4) (sqrt -1)) (sqrt (/ 1 (pow re 3))))) (* 1/4 (* (* (pow im 2) (sqrt -1)) (sqrt re)))) (pow re 3))) (* (sqrt (/ 1 re)) (* (sqrt -1) (pow (sqrt 2) 2))))))
(* -1 (* re (+ (* -1 (/ (+ (* -1/16 (* (* (pow im 4) (sqrt -1)) (sqrt (/ 1 (pow re 3))))) (+ (* 1/32 (* (/ (* (pow im 4) (sqrt -1)) (pow (sqrt 2) 2)) (sqrt (/ 1 (pow re 3))))) (* 1/4 (* (* (pow im 2) (sqrt -1)) (sqrt re))))) (pow re 3))) (* (sqrt (/ 1 re)) (* (sqrt -1) (pow (sqrt 2) 2))))))
(* -4 re)
(* -1 (* re (+ 4 (/ (pow im 2) (pow re 2)))))
(* -1 (* re (+ 4 (+ (* -1/4 (/ (pow im 4) (pow re 4))) (/ (pow im 2) (pow re 2))))))
(* -1 (* re (+ 4 (+ (* -1/4 (/ (pow im 4) (pow re 4))) (+ (* 1/8 (/ (pow im 6) (pow re 6))) (/ (pow im 2) (pow re 2)))))))
(* -1/2 (* (sqrt re) (* (sqrt -1) (pow (sqrt 2) 2))))
(* -1 (* re (+ (* -1/8 (* (* (pow im 2) (sqrt -1)) (sqrt (/ 1 (pow re 5))))) (* 1/2 (* (sqrt (/ 1 re)) (* (sqrt -1) (pow (sqrt 2) 2)))))))
(* -1 (* re (+ (* -1 (/ (+ (* -1/32 (* (* (pow im 4) (sqrt -1)) (sqrt (/ 1 (pow re 3))))) (* 1/8 (* (* (pow im 2) (sqrt -1)) (sqrt re)))) (pow re 3))) (* 1/2 (* (sqrt (/ 1 re)) (* (sqrt -1) (pow (sqrt 2) 2)))))))
(* -1 (* re (+ (* -1 (/ (+ (* -1/32 (* (* (pow im 4) (sqrt -1)) (sqrt (/ 1 (pow re 3))))) (+ (* 1/64 (* (/ (* (pow im 4) (sqrt -1)) (pow (sqrt 2) 2)) (sqrt (/ 1 (pow re 3))))) (* 1/8 (* (* (pow im 2) (sqrt -1)) (sqrt re))))) (pow re 3))) (* 1/2 (* (sqrt (/ 1 re)) (* (sqrt -1) (pow (sqrt 2) 2)))))))
(* -1 (* (sqrt re) (* (sqrt -1) (pow (sqrt 2) 2))))
(* -1 (* re (+ (* -1/4 (* (* (pow im 2) (sqrt -1)) (sqrt (/ 1 (pow re 5))))) (* (sqrt (/ 1 re)) (* (sqrt -1) (pow (sqrt 2) 2))))))
(* -1 (* re (+ (* -1 (/ (+ (* -1/16 (* (* (pow im 4) (sqrt -1)) (sqrt (/ 1 (pow re 3))))) (* 1/4 (* (* (pow im 2) (sqrt -1)) (sqrt re)))) (pow re 3))) (* (sqrt (/ 1 re)) (* (sqrt -1) (pow (sqrt 2) 2))))))
(* -1 (* re (+ (* -1 (/ (+ (* -1/16 (* (* (pow im 4) (sqrt -1)) (sqrt (/ 1 (pow re 3))))) (+ (* 1/32 (* (/ (* (pow im 4) (sqrt -1)) (pow (sqrt 2) 2)) (sqrt (/ 1 (pow re 3))))) (* 1/4 (* (* (pow im 2) (sqrt -1)) (sqrt re))))) (pow re 3))) (* (sqrt (/ 1 re)) (* (sqrt -1) (pow (sqrt 2) 2))))))
(* -4 re)
(* -1 (* re (+ 4 (/ (pow im 2) (pow re 2)))))
(* -1 (* re (+ 4 (+ (* -1/4 (/ (pow im 4) (pow re 4))) (/ (pow im 2) (pow re 2))))))
(* -1 (* re (+ 4 (+ (* -1/4 (/ (pow im 4) (pow re 4))) (+ (* 1/8 (/ (pow im 6) (pow re 6))) (/ (pow im 2) (pow re 2)))))))
(* -2 re)
(* -1 (* re (+ 2 (* 1/2 (/ (pow im 2) (pow re 2))))))
(* -1 (* re (+ 2 (+ (* -1/8 (/ (pow im 4) (pow re 4))) (* 1/2 (/ (pow im 2) (pow re 2)))))))
(* -1 (* re (+ 2 (+ (* -1/8 (/ (pow im 4) (pow re 4))) (+ (* 1/16 (/ (pow im 6) (pow re 6))) (* 1/2 (/ (pow im 2) (pow re 2))))))))
(* -1/2 (* (sqrt re) (* (sqrt -1) (pow (sqrt 2) 2))))
(* -1 (* re (+ (* -1/8 (* (* (pow im 2) (sqrt -1)) (sqrt (/ 1 (pow re 5))))) (* 1/2 (* (sqrt (/ 1 re)) (* (sqrt -1) (pow (sqrt 2) 2)))))))
(* -1 (* re (+ (* -1 (/ (+ (* -1/32 (* (* (pow im 4) (sqrt -1)) (sqrt (/ 1 (pow re 3))))) (* 1/8 (* (* (pow im 2) (sqrt -1)) (sqrt re)))) (pow re 3))) (* 1/2 (* (sqrt (/ 1 re)) (* (sqrt -1) (pow (sqrt 2) 2)))))))
(* -1 (* re (+ (* -1 (/ (+ (* -1/32 (* (* (pow im 4) (sqrt -1)) (sqrt (/ 1 (pow re 3))))) (+ (* 1/64 (* (/ (* (pow im 4) (sqrt -1)) (pow (sqrt 2) 2)) (sqrt (/ 1 (pow re 3))))) (* 1/8 (* (* (pow im 2) (sqrt -1)) (sqrt re))))) (pow re 3))) (* 1/2 (* (sqrt (/ 1 re)) (* (sqrt -1) (pow (sqrt 2) 2)))))))
(* 1/2 (* (* im (pow (sqrt -1) 2)) (sqrt (/ 1 re))))
(* 1/2 (* (* im (pow (sqrt -1) 2)) (sqrt (/ 1 re))))
(* 1/2 (* (* im (pow (sqrt -1) 2)) (sqrt (/ 1 re))))
(* 1/2 (* (* im (pow (sqrt -1) 2)) (sqrt (/ 1 re))))
(* (sqrt (/ 1 re)) (pow (sqrt -1) 2))
(* (sqrt (/ 1 re)) (pow (sqrt -1) 2))
(* (sqrt (/ 1 re)) (pow (sqrt -1) 2))
(* (sqrt (/ 1 re)) (pow (sqrt -1) 2))
(* 1/2 (* im (sqrt (/ 1 re))))
(* 1/2 (* im (sqrt (/ 1 re))))
(* 1/2 (* im (sqrt (/ 1 re))))
(* 1/2 (* im (sqrt (/ 1 re))))
(* -1/2 (* (sqrt re) (* (sqrt -1) (pow (sqrt 2) 2))))
(* -1 (* re (+ (* -1/8 (* (* (pow im 2) (sqrt -1)) (sqrt (/ 1 (pow re 5))))) (* 1/2 (* (sqrt (/ 1 re)) (* (sqrt -1) (pow (sqrt 2) 2)))))))
(* -1 (* re (+ (* -1 (/ (+ (* -1/32 (* (* (pow im 4) (sqrt -1)) (sqrt (/ 1 (pow re 3))))) (* 1/8 (* (* (pow im 2) (sqrt -1)) (sqrt re)))) (pow re 3))) (* 1/2 (* (sqrt (/ 1 re)) (* (sqrt -1) (pow (sqrt 2) 2)))))))
(* -1 (* re (+ (* -1 (/ (+ (* -1/32 (* (* (pow im 4) (sqrt -1)) (sqrt (/ 1 (pow re 3))))) (+ (* 1/64 (* (/ (* (pow im 4) (sqrt -1)) (pow (sqrt 2) 2)) (sqrt (/ 1 (pow re 3))))) (* 1/8 (* (* (pow im 2) (sqrt -1)) (sqrt re))))) (pow re 3))) (* 1/2 (* (sqrt (/ 1 re)) (* (sqrt -1) (pow (sqrt 2) 2)))))))
(* -2 (* (/ (pow (sqrt -1) 2) im) (sqrt re)))
(* -2 (* (/ (pow (sqrt -1) 2) im) (sqrt re)))
(* -2 (* (/ (pow (sqrt -1) 2) im) (sqrt re)))
(* -2 (* (/ (pow (sqrt -1) 2) im) (sqrt re)))
(* -1 (* (sqrt re) (pow (sqrt -1) 2)))
(* -1 (* (sqrt re) (pow (sqrt -1) 2)))
(* -1 (* (sqrt re) (pow (sqrt -1) 2)))
(* -1 (* (sqrt re) (pow (sqrt -1) 2)))
(* -1/2 (* (sqrt re) (* (sqrt -1) (pow (sqrt 2) 2))))
(* -1 (* re (+ (* -1/8 (* (* (pow im 2) (sqrt -1)) (sqrt (/ 1 (pow re 5))))) (* 1/2 (* (sqrt (/ 1 re)) (* (sqrt -1) (pow (sqrt 2) 2)))))))
(* -1 (* re (+ (* -1 (/ (+ (* -1/32 (* (* (pow im 4) (sqrt -1)) (sqrt (/ 1 (pow re 3))))) (* 1/8 (* (* (pow im 2) (sqrt -1)) (sqrt re)))) (pow re 3))) (* 1/2 (* (sqrt (/ 1 re)) (* (sqrt -1) (pow (sqrt 2) 2)))))))
(* -1 (* re (+ (* -1 (/ (+ (* -1/32 (* (* (pow im 4) (sqrt -1)) (sqrt (/ 1 (pow re 3))))) (+ (* 1/64 (* (/ (* (pow im 4) (sqrt -1)) (pow (sqrt 2) 2)) (sqrt (/ 1 (pow re 3))))) (* 1/8 (* (* (pow im 2) (sqrt -1)) (sqrt re))))) (pow re 3))) (* 1/2 (* (sqrt (/ 1 re)) (* (sqrt -1) (pow (sqrt 2) 2)))))))
(* -1 (* (sqrt re) (* (sqrt -1) (pow (sqrt 2) 2))))
(* -1 (* re (+ (* -1/4 (* (* (pow im 2) (sqrt -1)) (sqrt (/ 1 (pow re 5))))) (* (sqrt (/ 1 re)) (* (sqrt -1) (pow (sqrt 2) 2))))))
(* -1 (* re (+ (* -1 (/ (+ (* -1/16 (* (* (pow im 4) (sqrt -1)) (sqrt (/ 1 (pow re 3))))) (* 1/4 (* (* (pow im 2) (sqrt -1)) (sqrt re)))) (pow re 3))) (* (sqrt (/ 1 re)) (* (sqrt -1) (pow (sqrt 2) 2))))))
(* -1 (* re (+ (* -1 (/ (+ (* -1/16 (* (* (pow im 4) (sqrt -1)) (sqrt (/ 1 (pow re 3))))) (+ (* 1/32 (* (/ (* (pow im 4) (sqrt -1)) (pow (sqrt 2) 2)) (sqrt (/ 1 (pow re 3))))) (* 1/4 (* (* (pow im 2) (sqrt -1)) (sqrt re))))) (pow re 3))) (* (sqrt (/ 1 re)) (* (sqrt -1) (pow (sqrt 2) 2))))))
(* -4 re)
(* -1 (* re (+ 4 (/ (pow im 2) (pow re 2)))))
(* -1 (* re (+ 4 (+ (* -1/4 (/ (pow im 4) (pow re 4))) (/ (pow im 2) (pow re 2))))))
(* -1 (* re (+ 4 (+ (* -1/4 (/ (pow im 4) (pow re 4))) (+ (* 1/8 (/ (pow im 6) (pow re 6))) (/ (pow im 2) (pow re 2)))))))
(* -2 re)
(* -1 (* re (+ 2 (* 1/2 (/ (pow im 2) (pow re 2))))))
(* -1 (* re (+ 2 (+ (* -1/8 (/ (pow im 4) (pow re 4))) (* 1/2 (/ (pow im 2) (pow re 2)))))))
(* -1 (* re (+ 2 (+ (* -1/8 (/ (pow im 4) (pow re 4))) (+ (* 1/16 (/ (pow im 6) (pow re 6))) (* 1/2 (/ (pow im 2) (pow re 2))))))))
(* (sqrt re) (sqrt -1))
(+ (* 1/4 (* (* (pow im 2) (sqrt -1)) (sqrt (/ 1 (pow re 3))))) (* (sqrt re) (sqrt -1)))
(+ (* 1/4 (* (* (pow im 2) (sqrt -1)) (sqrt (/ 1 (pow re 3))))) (+ (* (sqrt re) (sqrt -1)) (* (sqrt (/ 1 (pow re 7))) (* (sqrt -1) (+ (* -1/8 (pow im 4)) (* 1/32 (pow im 4)))))))
(+ (* 1/4 (* (* (pow im 2) (sqrt -1)) (sqrt (/ 1 (pow re 3))))) (+ (* (sqrt re) (sqrt -1)) (+ (* (sqrt (/ 1 (pow re 7))) (* (sqrt -1) (+ (* -1/8 (pow im 4)) (* 1/32 (pow im 4))))) (* (sqrt (/ 1 (pow re 11))) (* (sqrt -1) (+ (* -1/32 (pow im 6)) (+ (* 1/384 (pow im 6)) (* 1/12 (pow im 6)))))))))
(* -1 re)
(* -1 (* re (+ 1 (* 1/2 (/ (pow im 2) (pow re 2))))))
(* -1 (* re (+ 1 (+ (* -1/8 (/ (pow im 4) (pow re 4))) (* 1/2 (/ (pow im 2) (pow re 2)))))))
(* -1 (* re (+ 1 (+ (* -1/8 (/ (pow im 4) (pow re 4))) (+ (* 1/16 (/ (pow im 6) (pow re 6))) (* 1/2 (/ (pow im 2) (pow re 2))))))))
(* 1/2 (/ (pow im 2) re))
(* (pow im 2) (+ (* -1/8 (/ (pow im 2) (pow re 3))) (* 1/2 (/ 1 re))))
(* (pow im 2) (+ (* (pow im 2) (- (* 1/16 (/ (pow im 2) (pow re 5))) (* 1/8 (/ 1 (pow re 3))))) (* 1/2 (/ 1 re))))
(* (pow im 2) (+ (* (pow im 2) (- (* (pow im 2) (+ (* -5/128 (/ (pow im 2) (pow re 7))) (* 1/16 (/ 1 (pow re 5))))) (* 1/8 (/ 1 (pow re 3))))) (* 1/2 (/ 1 re))))
(* 1/2 (* (* im (* (sqrt 1/2) (sqrt 2))) (sqrt (/ 1 re))))
(* im (+ (* -1/32 (* (/ (* (pow im 2) (sqrt 2)) (sqrt 1/2)) (sqrt (/ 1 (pow re 5))))) (* 1/2 (* (sqrt (/ 1 re)) (* (sqrt 1/2) (sqrt 2))))))
(* im (+ (* 1/2 (* (sqrt (/ 1 re)) (* (sqrt 1/2) (sqrt 2)))) (* (pow im 2) (+ (* -1/32 (* (sqrt (/ 1 (pow re 5))) (/ (sqrt 2) (sqrt 1/2)))) (* 1/4 (* (/ (* (pow im 2) (* (sqrt 2) (- (* 1/16 (/ 1 (pow re 5))) (* 1/256 (/ 1 (* (pow re 5) (pow (sqrt 1/2) 2))))))) (sqrt 1/2)) (sqrt re)))))))
(* im (+ (* 1/2 (* (sqrt (/ 1 re)) (* (sqrt 1/2) (sqrt 2)))) (* (pow im 2) (+ (* -1/32 (* (sqrt (/ 1 (pow re 5))) (/ (sqrt 2) (sqrt 1/2)))) (* (pow im 2) (+ (* -1/4 (* (/ (* (pow im 2) (* (sqrt 2) (+ (* -1/16 (/ (- (* 1/16 (/ 1 (pow re 5))) (* 1/256 (/ 1 (* (pow re 5) (pow (sqrt 1/2) 2))))) (* (pow re 2) (pow (sqrt 1/2) 2)))) (* 5/128 (/ 1 (pow re 7)))))) (sqrt 1/2)) (sqrt re))) (* 1/4 (* (sqrt re) (/ (* (sqrt 2) (- (* 1/16 (/ 1 (pow re 5))) (* 1/256 (/ 1 (* (pow re 5) (pow (sqrt 1/2) 2)))))) (sqrt 1/2))))))))))
(* (* im (* (sqrt 1/2) (sqrt 2))) (sqrt (/ 1 re)))
(* im (+ (* -1/16 (* (/ (* (pow im 2) (sqrt 2)) (sqrt 1/2)) (sqrt (/ 1 (pow re 5))))) (* (sqrt (/ 1 re)) (* (sqrt 1/2) (sqrt 2)))))
(* im (+ (* (sqrt (/ 1 re)) (* (sqrt 1/2) (sqrt 2))) (* (pow im 2) (+ (* -1/16 (* (sqrt (/ 1 (pow re 5))) (/ (sqrt 2) (sqrt 1/2)))) (* 1/2 (* (/ (* (pow im 2) (* (sqrt 2) (- (* 1/16 (/ 1 (pow re 5))) (* 1/256 (/ 1 (* (pow re 5) (pow (sqrt 1/2) 2))))))) (sqrt 1/2)) (sqrt re)))))))
(* im (+ (* (sqrt (/ 1 re)) (* (sqrt 1/2) (sqrt 2))) (* (pow im 2) (+ (* -1/16 (* (sqrt (/ 1 (pow re 5))) (/ (sqrt 2) (sqrt 1/2)))) (* (pow im 2) (+ (* -1/2 (* (/ (* (pow im 2) (* (sqrt 2) (+ (* -1/16 (/ (- (* 1/16 (/ 1 (pow re 5))) (* 1/256 (/ 1 (* (pow re 5) (pow (sqrt 1/2) 2))))) (* (pow re 2) (pow (sqrt 1/2) 2)))) (* 5/128 (/ 1 (pow re 7)))))) (sqrt 1/2)) (sqrt re))) (* 1/2 (* (sqrt re) (/ (* (sqrt 2) (- (* 1/16 (/ 1 (pow re 5))) (* 1/256 (/ 1 (* (pow re 5) (pow (sqrt 1/2) 2)))))) (sqrt 1/2))))))))))
(/ (pow im 2) re)
(* (pow im 2) (+ (* -1/4 (/ (pow im 2) (pow re 3))) (/ 1 re)))
(* (pow im 2) (+ (* (pow im 2) (- (* 1/8 (/ (pow im 2) (pow re 5))) (* 1/4 (/ 1 (pow re 3))))) (/ 1 re)))
(* (pow im 2) (+ (* (pow im 2) (- (* (pow im 2) (+ (* -5/64 (/ (pow im 2) (pow re 7))) (* 1/8 (/ 1 (pow re 5))))) (* 1/4 (/ 1 (pow re 3))))) (/ 1 re)))
(* 1/2 (* (* im (* (sqrt 1/2) (sqrt 2))) (sqrt (/ 1 re))))
(* im (+ (* -1/32 (* (/ (* (pow im 2) (sqrt 2)) (sqrt 1/2)) (sqrt (/ 1 (pow re 5))))) (* 1/2 (* (sqrt (/ 1 re)) (* (sqrt 1/2) (sqrt 2))))))
(* im (+ (* 1/2 (* (sqrt (/ 1 re)) (* (sqrt 1/2) (sqrt 2)))) (* (pow im 2) (+ (* -1/32 (* (sqrt (/ 1 (pow re 5))) (/ (sqrt 2) (sqrt 1/2)))) (* 1/4 (* (/ (* (pow im 2) (* (sqrt 2) (- (* 1/16 (/ 1 (pow re 5))) (* 1/256 (/ 1 (* (pow re 5) (pow (sqrt 1/2) 2))))))) (sqrt 1/2)) (sqrt re)))))))
(* im (+ (* 1/2 (* (sqrt (/ 1 re)) (* (sqrt 1/2) (sqrt 2)))) (* (pow im 2) (+ (* -1/32 (* (sqrt (/ 1 (pow re 5))) (/ (sqrt 2) (sqrt 1/2)))) (* (pow im 2) (+ (* -1/4 (* (/ (* (pow im 2) (* (sqrt 2) (+ (* -1/16 (/ (- (* 1/16 (/ 1 (pow re 5))) (* 1/256 (/ 1 (* (pow re 5) (pow (sqrt 1/2) 2))))) (* (pow re 2) (pow (sqrt 1/2) 2)))) (* 5/128 (/ 1 (pow re 7)))))) (sqrt 1/2)) (sqrt re))) (* 1/4 (* (sqrt re) (/ (* (sqrt 2) (- (* 1/16 (/ 1 (pow re 5))) (* 1/256 (/ 1 (* (pow re 5) (pow (sqrt 1/2) 2)))))) (sqrt 1/2))))))))))
(* (* im (* (sqrt 1/2) (sqrt 2))) (sqrt (/ 1 re)))
(* im (+ (* -1/16 (* (/ (* (pow im 2) (sqrt 2)) (sqrt 1/2)) (sqrt (/ 1 (pow re 5))))) (* (sqrt (/ 1 re)) (* (sqrt 1/2) (sqrt 2)))))
(* im (+ (* (sqrt (/ 1 re)) (* (sqrt 1/2) (sqrt 2))) (* (pow im 2) (+ (* -1/16 (* (sqrt (/ 1 (pow re 5))) (/ (sqrt 2) (sqrt 1/2)))) (* 1/2 (* (/ (* (pow im 2) (* (sqrt 2) (- (* 1/16 (/ 1 (pow re 5))) (* 1/256 (/ 1 (* (pow re 5) (pow (sqrt 1/2) 2))))))) (sqrt 1/2)) (sqrt re)))))))
(* im (+ (* (sqrt (/ 1 re)) (* (sqrt 1/2) (sqrt 2))) (* (pow im 2) (+ (* -1/16 (* (sqrt (/ 1 (pow re 5))) (/ (sqrt 2) (sqrt 1/2)))) (* (pow im 2) (+ (* -1/2 (* (/ (* (pow im 2) (* (sqrt 2) (+ (* -1/16 (/ (- (* 1/16 (/ 1 (pow re 5))) (* 1/256 (/ 1 (* (pow re 5) (pow (sqrt 1/2) 2))))) (* (pow re 2) (pow (sqrt 1/2) 2)))) (* 5/128 (/ 1 (pow re 7)))))) (sqrt 1/2)) (sqrt re))) (* 1/2 (* (sqrt re) (/ (* (sqrt 2) (- (* 1/16 (/ 1 (pow re 5))) (* 1/256 (/ 1 (* (pow re 5) (pow (sqrt 1/2) 2)))))) (sqrt 1/2))))))))))
(/ (pow im 2) re)
(* (pow im 2) (+ (* -1/4 (/ (pow im 2) (pow re 3))) (/ 1 re)))
(* (pow im 2) (+ (* (pow im 2) (- (* 1/8 (/ (pow im 2) (pow re 5))) (* 1/4 (/ 1 (pow re 3))))) (/ 1 re)))
(* (pow im 2) (+ (* (pow im 2) (- (* (pow im 2) (+ (* -5/64 (/ (pow im 2) (pow re 7))) (* 1/8 (/ 1 (pow re 5))))) (* 1/4 (/ 1 (pow re 3))))) (/ 1 re)))
(* 1/2 (/ (pow im 2) re))
(* (pow im 2) (+ (* -1/8 (/ (pow im 2) (pow re 3))) (* 1/2 (/ 1 re))))
(* (pow im 2) (+ (* (pow im 2) (- (* 1/16 (/ (pow im 2) (pow re 5))) (* 1/8 (/ 1 (pow re 3))))) (* 1/2 (/ 1 re))))
(* (pow im 2) (+ (* (pow im 2) (- (* (pow im 2) (+ (* -5/128 (/ (pow im 2) (pow re 7))) (* 1/16 (/ 1 (pow re 5))))) (* 1/8 (/ 1 (pow re 3))))) (* 1/2 (/ 1 re))))
(* 1/2 (* (* im (* (sqrt 1/2) (sqrt 2))) (sqrt (/ 1 re))))
(* im (+ (* -1/32 (* (/ (* (pow im 2) (sqrt 2)) (sqrt 1/2)) (sqrt (/ 1 (pow re 5))))) (* 1/2 (* (sqrt (/ 1 re)) (* (sqrt 1/2) (sqrt 2))))))
(* im (+ (* 1/2 (* (sqrt (/ 1 re)) (* (sqrt 1/2) (sqrt 2)))) (* (pow im 2) (+ (* -1/32 (* (sqrt (/ 1 (pow re 5))) (/ (sqrt 2) (sqrt 1/2)))) (* 1/4 (* (/ (* (pow im 2) (* (sqrt 2) (- (* 1/16 (/ 1 (pow re 5))) (* 1/256 (/ 1 (* (pow re 5) (pow (sqrt 1/2) 2))))))) (sqrt 1/2)) (sqrt re)))))))
(* im (+ (* 1/2 (* (sqrt (/ 1 re)) (* (sqrt 1/2) (sqrt 2)))) (* (pow im 2) (+ (* -1/32 (* (sqrt (/ 1 (pow re 5))) (/ (sqrt 2) (sqrt 1/2)))) (* (pow im 2) (+ (* -1/4 (* (/ (* (pow im 2) (* (sqrt 2) (+ (* -1/16 (/ (- (* 1/16 (/ 1 (pow re 5))) (* 1/256 (/ 1 (* (pow re 5) (pow (sqrt 1/2) 2))))) (* (pow re 2) (pow (sqrt 1/2) 2)))) (* 5/128 (/ 1 (pow re 7)))))) (sqrt 1/2)) (sqrt re))) (* 1/4 (* (sqrt re) (/ (* (sqrt 2) (- (* 1/16 (/ 1 (pow re 5))) (* 1/256 (/ 1 (* (pow re 5) (pow (sqrt 1/2) 2)))))) (sqrt 1/2))))))))))
(* 1/2 (* im (sqrt (/ 1 re))))
(* 1/2 (* im (sqrt (/ 1 re))))
(* 1/2 (* im (sqrt (/ 1 re))))
(* 1/2 (* im (sqrt (/ 1 re))))
(* 1/2 im)
(* 1/2 im)
(* 1/2 im)
(* 1/2 im)
(* 1/2 (* im (sqrt (/ 1 re))))
(* 1/2 (* im (sqrt (/ 1 re))))
(* 1/2 (* im (sqrt (/ 1 re))))
(* 1/2 (* im (sqrt (/ 1 re))))
(* 1/2 (* (* im (* (sqrt 1/2) (sqrt 2))) (sqrt (/ 1 re))))
(* im (+ (* -1/32 (* (/ (* (pow im 2) (sqrt 2)) (sqrt 1/2)) (sqrt (/ 1 (pow re 5))))) (* 1/2 (* (sqrt (/ 1 re)) (* (sqrt 1/2) (sqrt 2))))))
(* im (+ (* 1/2 (* (sqrt (/ 1 re)) (* (sqrt 1/2) (sqrt 2)))) (* (pow im 2) (+ (* -1/32 (* (sqrt (/ 1 (pow re 5))) (/ (sqrt 2) (sqrt 1/2)))) (* 1/4 (* (/ (* (pow im 2) (* (sqrt 2) (- (* 1/16 (/ 1 (pow re 5))) (* 1/256 (/ 1 (* (pow re 5) (pow (sqrt 1/2) 2))))))) (sqrt 1/2)) (sqrt re)))))))
(* im (+ (* 1/2 (* (sqrt (/ 1 re)) (* (sqrt 1/2) (sqrt 2)))) (* (pow im 2) (+ (* -1/32 (* (sqrt (/ 1 (pow re 5))) (/ (sqrt 2) (sqrt 1/2)))) (* (pow im 2) (+ (* -1/4 (* (/ (* (pow im 2) (* (sqrt 2) (+ (* -1/16 (/ (- (* 1/16 (/ 1 (pow re 5))) (* 1/256 (/ 1 (* (pow re 5) (pow (sqrt 1/2) 2))))) (* (pow re 2) (pow (sqrt 1/2) 2)))) (* 5/128 (/ 1 (pow re 7)))))) (sqrt 1/2)) (sqrt re))) (* 1/4 (* (sqrt re) (/ (* (sqrt 2) (- (* 1/16 (/ 1 (pow re 5))) (* 1/256 (/ 1 (* (pow re 5) (pow (sqrt 1/2) 2)))))) (sqrt 1/2))))))))))
(* 2 (* (/ 1 im) (sqrt re)))
(* 2 (* (/ 1 im) (sqrt re)))
(* 2 (* (/ 1 im) (sqrt re)))
(* 2 (* (/ 1 im) (sqrt re)))
(* 1/2 (* (* im (* (sqrt 1/2) (sqrt 2))) (sqrt (/ 1 re))))
(* im (+ (* -1/32 (* (/ (* (pow im 2) (sqrt 2)) (sqrt 1/2)) (sqrt (/ 1 (pow re 5))))) (* 1/2 (* (sqrt (/ 1 re)) (* (sqrt 1/2) (sqrt 2))))))
(* im (+ (* 1/2 (* (sqrt (/ 1 re)) (* (sqrt 1/2) (sqrt 2)))) (* (pow im 2) (+ (* -1/32 (* (sqrt (/ 1 (pow re 5))) (/ (sqrt 2) (sqrt 1/2)))) (* 1/4 (* (/ (* (pow im 2) (* (sqrt 2) (- (* 1/16 (/ 1 (pow re 5))) (* 1/256 (/ 1 (* (pow re 5) (pow (sqrt 1/2) 2))))))) (sqrt 1/2)) (sqrt re)))))))
(* im (+ (* 1/2 (* (sqrt (/ 1 re)) (* (sqrt 1/2) (sqrt 2)))) (* (pow im 2) (+ (* -1/32 (* (sqrt (/ 1 (pow re 5))) (/ (sqrt 2) (sqrt 1/2)))) (* (pow im 2) (+ (* -1/4 (* (/ (* (pow im 2) (* (sqrt 2) (+ (* -1/16 (/ (- (* 1/16 (/ 1 (pow re 5))) (* 1/256 (/ 1 (* (pow re 5) (pow (sqrt 1/2) 2))))) (* (pow re 2) (pow (sqrt 1/2) 2)))) (* 5/128 (/ 1 (pow re 7)))))) (sqrt 1/2)) (sqrt re))) (* 1/4 (* (sqrt re) (/ (* (sqrt 2) (- (* 1/16 (/ 1 (pow re 5))) (* 1/256 (/ 1 (* (pow re 5) (pow (sqrt 1/2) 2)))))) (sqrt 1/2))))))))))
(* (* im (* (sqrt 1/2) (sqrt 2))) (sqrt (/ 1 re)))
(* im (+ (* -1/16 (* (/ (* (pow im 2) (sqrt 2)) (sqrt 1/2)) (sqrt (/ 1 (pow re 5))))) (* (sqrt (/ 1 re)) (* (sqrt 1/2) (sqrt 2)))))
(* im (+ (* (sqrt (/ 1 re)) (* (sqrt 1/2) (sqrt 2))) (* (pow im 2) (+ (* -1/16 (* (sqrt (/ 1 (pow re 5))) (/ (sqrt 2) (sqrt 1/2)))) (* 1/2 (* (/ (* (pow im 2) (* (sqrt 2) (- (* 1/16 (/ 1 (pow re 5))) (* 1/256 (/ 1 (* (pow re 5) (pow (sqrt 1/2) 2))))))) (sqrt 1/2)) (sqrt re)))))))
(* im (+ (* (sqrt (/ 1 re)) (* (sqrt 1/2) (sqrt 2))) (* (pow im 2) (+ (* -1/16 (* (sqrt (/ 1 (pow re 5))) (/ (sqrt 2) (sqrt 1/2)))) (* (pow im 2) (+ (* -1/2 (* (/ (* (pow im 2) (* (sqrt 2) (+ (* -1/16 (/ (- (* 1/16 (/ 1 (pow re 5))) (* 1/256 (/ 1 (* (pow re 5) (pow (sqrt 1/2) 2))))) (* (pow re 2) (pow (sqrt 1/2) 2)))) (* 5/128 (/ 1 (pow re 7)))))) (sqrt 1/2)) (sqrt re))) (* 1/2 (* (sqrt re) (/ (* (sqrt 2) (- (* 1/16 (/ 1 (pow re 5))) (* 1/256 (/ 1 (* (pow re 5) (pow (sqrt 1/2) 2)))))) (sqrt 1/2))))))))))
(/ (pow im 2) re)
(* (pow im 2) (+ (* -1/4 (/ (pow im 2) (pow re 3))) (/ 1 re)))
(* (pow im 2) (+ (* (pow im 2) (- (* 1/8 (/ (pow im 2) (pow re 5))) (* 1/4 (/ 1 (pow re 3))))) (/ 1 re)))
(* (pow im 2) (+ (* (pow im 2) (- (* (pow im 2) (+ (* -5/64 (/ (pow im 2) (pow re 7))) (* 1/8 (/ 1 (pow re 5))))) (* 1/4 (/ 1 (pow re 3))))) (/ 1 re)))
(* 1/2 (/ (pow im 2) re))
(* (pow im 2) (+ (* -1/8 (/ (pow im 2) (pow re 3))) (* 1/2 (/ 1 re))))
(* (pow im 2) (+ (* (pow im 2) (- (* 1/16 (/ (pow im 2) (pow re 5))) (* 1/8 (/ 1 (pow re 3))))) (* 1/2 (/ 1 re))))
(* (pow im 2) (+ (* (pow im 2) (- (* (pow im 2) (+ (* -5/128 (/ (pow im 2) (pow re 7))) (* 1/16 (/ 1 (pow re 5))))) (* 1/8 (/ 1 (pow re 3))))) (* 1/2 (/ 1 re))))
(* (pow 1 1/4) (sqrt re))
(+ (* 1/4 (* (pow 1 1/4) (* (pow im 2) (sqrt (/ 1 (pow re 3)))))) (* (pow 1 1/4) (sqrt re)))
(+ (* (pow 1 1/4) (sqrt re)) (* (pow im 2) (+ (* -3/32 (* (pow 1 1/4) (* (pow im 2) (sqrt (/ 1 (pow re 7)))))) (* 1/4 (* (pow 1 1/4) (sqrt (/ 1 (pow re 3))))))))
(+ (* (pow 1 1/4) (sqrt re)) (* (pow im 2) (+ (* 1/4 (* (pow 1 1/4) (sqrt (/ 1 (pow re 3))))) (* (pow im 2) (+ (* -3/32 (* (pow 1 1/4) (sqrt (/ 1 (pow re 7))))) (* 7/128 (* (pow 1 1/4) (* (pow im 2) (sqrt (/ 1 (pow re 11)))))))))))
re
(+ re (* 1/2 (/ (pow im 2) re)))
(+ re (* (pow im 2) (+ (* -1/8 (/ (pow im 2) (pow re 3))) (* 1/2 (/ 1 re)))))
(+ re (* (pow im 2) (+ (* (pow im 2) (- (* 1/16 (/ (pow im 2) (pow re 5))) (* 1/8 (/ 1 (pow re 3))))) (* 1/2 (/ 1 re)))))
im
(* im (+ 1 (* -1 (/ re im))))
(* im (- (+ 1 (* 1/2 (/ (pow re 2) (pow im 2)))) (/ re im)))
(* im (- (+ 1 (+ (* -1/8 (/ (pow re 4) (pow im 4))) (* 1/2 (/ (pow re 2) (pow im 2))))) (/ re im)))
(* 1/2 (* (sqrt im) (sqrt 2)))
(* im (+ (* -1/4 (* (sqrt (/ 1 (pow im 3))) (* re (sqrt 2)))) (* 1/2 (* (sqrt (/ 1 im)) (sqrt 2)))))
(* im (+ (* -1/4 (* (sqrt (/ 1 (pow im 3))) (* re (sqrt 2)))) (+ (* 1/8 (* (sqrt (/ 1 (pow im 5))) (* (pow re 2) (sqrt 2)))) (* 1/2 (* (sqrt (/ 1 im)) (sqrt 2))))))
(* im (+ (* -1/4 (* (sqrt (/ 1 (pow im 3))) (* re (sqrt 2)))) (+ (* -1/16 (* (sqrt (/ 1 (pow im 5))) (* (pow re 2) (sqrt 2)))) (+ (* 1/8 (* (sqrt (/ 1 (pow im 5))) (* (pow re 2) (sqrt 2)))) (* 1/2 (* (sqrt (/ 1 im)) (sqrt 2)))))))
(* (sqrt im) (sqrt 2))
(* im (+ (* -1/2 (* (sqrt (/ 1 (pow im 3))) (* re (sqrt 2)))) (* (sqrt (/ 1 im)) (sqrt 2))))
(* im (+ (* -1/2 (* (sqrt (/ 1 (pow im 3))) (* re (sqrt 2)))) (+ (* 1/4 (* (sqrt (/ 1 (pow im 5))) (* (pow re 2) (sqrt 2)))) (* (sqrt (/ 1 im)) (sqrt 2)))))
(* im (+ (* -1/2 (* (sqrt (/ 1 (pow im 3))) (* re (sqrt 2)))) (+ (* -1/8 (* (sqrt (/ 1 (pow im 5))) (* (pow re 2) (sqrt 2)))) (+ (* 1/4 (* (sqrt (/ 1 (pow im 5))) (* (pow re 2) (sqrt 2)))) (* (sqrt (/ 1 im)) (sqrt 2))))))
(* 2 im)
(* im (+ 2 (* -2 (/ re im))))
(* im (+ 2 (+ (* -2 (/ re im)) (/ (pow re 2) (pow im 2)))))
(* im (+ 2 (+ (* -2 (/ re im)) (+ (* -1/4 (/ (pow re 4) (pow im 4))) (/ (pow re 2) (pow im 2))))))
(* 1/2 (* (sqrt im) (sqrt 2)))
(* im (+ (* -1/4 (* (sqrt (/ 1 (pow im 3))) (* re (sqrt 2)))) (* 1/2 (* (sqrt (/ 1 im)) (sqrt 2)))))
(* im (+ (* -1/4 (* (sqrt (/ 1 (pow im 3))) (* re (sqrt 2)))) (+ (* 1/8 (* (sqrt (/ 1 (pow im 5))) (* (pow re 2) (sqrt 2)))) (* 1/2 (* (sqrt (/ 1 im)) (sqrt 2))))))
(* im (+ (* -1/4 (* (sqrt (/ 1 (pow im 3))) (* re (sqrt 2)))) (+ (* -1/16 (* (sqrt (/ 1 (pow im 5))) (* (pow re 2) (sqrt 2)))) (+ (* 1/8 (* (sqrt (/ 1 (pow im 5))) (* (pow re 2) (sqrt 2)))) (* 1/2 (* (sqrt (/ 1 im)) (sqrt 2)))))))
(* (sqrt im) (sqrt 2))
(* im (+ (* -1/2 (* (sqrt (/ 1 (pow im 3))) (* re (sqrt 2)))) (* (sqrt (/ 1 im)) (sqrt 2))))
(* im (+ (* -1/2 (* (sqrt (/ 1 (pow im 3))) (* re (sqrt 2)))) (+ (* 1/4 (* (sqrt (/ 1 (pow im 5))) (* (pow re 2) (sqrt 2)))) (* (sqrt (/ 1 im)) (sqrt 2)))))
(* im (+ (* -1/2 (* (sqrt (/ 1 (pow im 3))) (* re (sqrt 2)))) (+ (* -1/8 (* (sqrt (/ 1 (pow im 5))) (* (pow re 2) (sqrt 2)))) (+ (* 1/4 (* (sqrt (/ 1 (pow im 5))) (* (pow re 2) (sqrt 2)))) (* (sqrt (/ 1 im)) (sqrt 2))))))
(* 2 im)
(* im (+ 2 (* -2 (/ re im))))
(* im (+ 2 (+ (* -2 (/ re im)) (/ (pow re 2) (pow im 2)))))
(* im (+ 2 (+ (* -2 (/ re im)) (+ (* -1/4 (/ (pow re 4) (pow im 4))) (/ (pow re 2) (pow im 2))))))
im
(* im (+ 1 (* -1 (/ re im))))
(* im (- (+ 1 (* 1/2 (/ (pow re 2) (pow im 2)))) (/ re im)))
(* im (- (+ 1 (+ (* -1/8 (/ (pow re 4) (pow im 4))) (* 1/2 (/ (pow re 2) (pow im 2))))) (/ re im)))
(* 1/2 (* (sqrt im) (sqrt 2)))
(* im (+ (* -1/4 (* (sqrt (/ 1 (pow im 3))) (* re (sqrt 2)))) (* 1/2 (* (sqrt (/ 1 im)) (sqrt 2)))))
(* im (+ (* -1/4 (* (sqrt (/ 1 (pow im 3))) (* re (sqrt 2)))) (+ (* 1/8 (* (sqrt (/ 1 (pow im 5))) (* (pow re 2) (sqrt 2)))) (* 1/2 (* (sqrt (/ 1 im)) (sqrt 2))))))
(* im (+ (* -1/4 (* (sqrt (/ 1 (pow im 3))) (* re (sqrt 2)))) (+ (* -1/16 (* (sqrt (/ 1 (pow im 5))) (* (pow re 2) (sqrt 2)))) (+ (* 1/8 (* (sqrt (/ 1 (pow im 5))) (* (pow re 2) (sqrt 2)))) (* 1/2 (* (sqrt (/ 1 im)) (sqrt 2)))))))
(* 1/2 (* im (sqrt (/ 1 re))))
(* 1/2 (* im (sqrt (/ 1 re))))
(* 1/2 (* im (sqrt (/ 1 re))))
(* 1/2 (* im (sqrt (/ 1 re))))
(* 1/2 im)
(* 1/2 im)
(* 1/2 im)
(* 1/2 im)
(* 1/2 (* im (sqrt (/ 1 re))))
(* 1/2 (* im (sqrt (/ 1 re))))
(* 1/2 (* im (sqrt (/ 1 re))))
(* 1/2 (* im (sqrt (/ 1 re))))
(* 1/2 (* (sqrt im) (sqrt 2)))
(* im (+ (* -1/4 (* (sqrt (/ 1 (pow im 3))) (* re (sqrt 2)))) (* 1/2 (* (sqrt (/ 1 im)) (sqrt 2)))))
(* im (+ (* -1/4 (* (sqrt (/ 1 (pow im 3))) (* re (sqrt 2)))) (+ (* 1/8 (* (sqrt (/ 1 (pow im 5))) (* (pow re 2) (sqrt 2)))) (* 1/2 (* (sqrt (/ 1 im)) (sqrt 2))))))
(* im (+ (* -1/4 (* (sqrt (/ 1 (pow im 3))) (* re (sqrt 2)))) (+ (* -1/16 (* (sqrt (/ 1 (pow im 5))) (* (pow re 2) (sqrt 2)))) (+ (* 1/8 (* (sqrt (/ 1 (pow im 5))) (* (pow re 2) (sqrt 2)))) (* 1/2 (* (sqrt (/ 1 im)) (sqrt 2)))))))
(* 2 (* (/ 1 im) (sqrt re)))
(* 2 (* (/ 1 im) (sqrt re)))
(* 2 (* (/ 1 im) (sqrt re)))
(* 2 (* (/ 1 im) (sqrt re)))
(* 1/2 (* (sqrt im) (sqrt 2)))
(* im (+ (* -1/4 (* (sqrt (/ 1 (pow im 3))) (* re (sqrt 2)))) (* 1/2 (* (sqrt (/ 1 im)) (sqrt 2)))))
(* im (+ (* -1/4 (* (sqrt (/ 1 (pow im 3))) (* re (sqrt 2)))) (+ (* 1/8 (* (sqrt (/ 1 (pow im 5))) (* (pow re 2) (sqrt 2)))) (* 1/2 (* (sqrt (/ 1 im)) (sqrt 2))))))
(* im (+ (* -1/4 (* (sqrt (/ 1 (pow im 3))) (* re (sqrt 2)))) (+ (* -1/16 (* (sqrt (/ 1 (pow im 5))) (* (pow re 2) (sqrt 2)))) (+ (* 1/8 (* (sqrt (/ 1 (pow im 5))) (* (pow re 2) (sqrt 2)))) (* 1/2 (* (sqrt (/ 1 im)) (sqrt 2)))))))
(* (sqrt im) (sqrt 2))
(* im (+ (* -1/2 (* (sqrt (/ 1 (pow im 3))) (* re (sqrt 2)))) (* (sqrt (/ 1 im)) (sqrt 2))))
(* im (+ (* -1/2 (* (sqrt (/ 1 (pow im 3))) (* re (sqrt 2)))) (+ (* 1/4 (* (sqrt (/ 1 (pow im 5))) (* (pow re 2) (sqrt 2)))) (* (sqrt (/ 1 im)) (sqrt 2)))))
(* im (+ (* -1/2 (* (sqrt (/ 1 (pow im 3))) (* re (sqrt 2)))) (+ (* -1/8 (* (sqrt (/ 1 (pow im 5))) (* (pow re 2) (sqrt 2)))) (+ (* 1/4 (* (sqrt (/ 1 (pow im 5))) (* (pow re 2) (sqrt 2)))) (* (sqrt (/ 1 im)) (sqrt 2))))))
(* 2 im)
(* im (+ 2 (* -2 (/ re im))))
(* im (+ 2 (+ (* -2 (/ re im)) (/ (pow re 2) (pow im 2)))))
(* im (+ 2 (+ (* -2 (/ re im)) (+ (* -1/4 (/ (pow re 4) (pow im 4))) (/ (pow re 2) (pow im 2))))))
im
(* im (+ 1 (* -1 (/ re im))))
(* im (- (+ 1 (* 1/2 (/ (pow re 2) (pow im 2)))) (/ re im)))
(* im (- (+ 1 (+ (* -1/8 (/ (pow re 4) (pow im 4))) (* 1/2 (/ (pow re 2) (pow im 2))))) (/ re im)))
(sqrt im)
(+ (sqrt im) (* 1/4 (* (sqrt (/ 1 (pow im 3))) (pow re 2))))
(+ (sqrt im) (+ (* 1/4 (* (sqrt (/ 1 (pow im 3))) (pow re 2))) (* (sqrt (/ 1 (pow im 7))) (+ (* -1/8 (pow re 4)) (* 1/32 (pow re 4))))))
(+ (sqrt im) (+ (* 1/4 (* (sqrt (/ 1 (pow im 3))) (pow re 2))) (+ (* (sqrt (/ 1 (pow im 7))) (+ (* -1/8 (pow re 4)) (* 1/32 (pow re 4)))) (* (sqrt (/ 1 (pow im 11))) (+ (* -1/32 (pow re 6)) (+ (* 1/384 (pow re 6)) (* 1/12 (pow re 6))))))))
im
(* im (+ 1 (* 1/2 (/ (pow re 2) (pow im 2)))))
(* im (+ 1 (+ (* -1/8 (/ (pow re 4) (pow im 4))) (* 1/2 (/ (pow re 2) (pow im 2))))))
(* im (+ 1 (+ (* -1/8 (/ (pow re 4) (pow im 4))) (+ (* 1/16 (/ (pow re 6) (pow im 6))) (* 1/2 (/ (pow re 2) (pow im 2)))))))
(* -1 im)
(* -1 (* im (+ 1 (/ re im))))
(* -1 (* im (+ 1 (* -1 (/ (- (* -1/2 (/ (pow re 2) im)) re) im)))))
(* -1 (* im (+ 1 (* -1 (/ (- (* -1 (/ (+ (* -1/8 (/ (pow re 4) (pow im 2))) (* 1/2 (pow re 2))) im)) re) im)))))
(* -1/2 (* (sqrt im) (* (sqrt -1) (sqrt 2))))
(* -1 (* im (+ (* -1/4 (* (sqrt (/ 1 (pow im 3))) (* re (* (sqrt -1) (sqrt 2))))) (* 1/2 (* (sqrt (/ 1 im)) (* (sqrt -1) (sqrt 2)))))))
(* -1 (* im (+ (* -1/4 (* (sqrt (/ 1 (pow im 3))) (* re (* (sqrt -1) (sqrt 2))))) (+ (* -1/8 (* (sqrt (/ 1 (pow im 5))) (* (pow re 2) (* (sqrt -1) (sqrt 2))))) (* 1/2 (* (sqrt (/ 1 im)) (* (sqrt -1) (sqrt 2))))))))
(* -1 (* im (+ (* -1 (/ (+ (* 1/16 (* (sqrt im) (* (pow re 2) (* (sqrt -1) (sqrt 2))))) (* 1/8 (* (sqrt im) (* (pow re 2) (* (sqrt -1) (sqrt 2)))))) (pow im 3))) (+ (* -1/4 (* (sqrt (/ 1 (pow im 3))) (* re (* (sqrt -1) (sqrt 2))))) (* 1/2 (* (sqrt (/ 1 im)) (* (sqrt -1) (sqrt 2))))))))
(* -1 (* (sqrt im) (* (sqrt -1) (sqrt 2))))
(* -1 (* im (+ (* -1/2 (* (sqrt (/ 1 (pow im 3))) (* re (* (sqrt -1) (sqrt 2))))) (* (sqrt (/ 1 im)) (* (sqrt -1) (sqrt 2))))))
(* -1 (* im (+ (* -1/2 (* (sqrt (/ 1 (pow im 3))) (* re (* (sqrt -1) (sqrt 2))))) (+ (* -1/4 (* (sqrt (/ 1 (pow im 5))) (* (pow re 2) (* (sqrt -1) (sqrt 2))))) (* (sqrt (/ 1 im)) (* (sqrt -1) (sqrt 2)))))))
(* -1 (* im (+ (* -1 (/ (+ (* 1/8 (* (sqrt im) (* (pow re 2) (* (sqrt -1) (sqrt 2))))) (* 1/4 (* (sqrt im) (* (pow re 2) (* (sqrt -1) (sqrt 2)))))) (pow im 3))) (+ (* -1/2 (* (sqrt (/ 1 (pow im 3))) (* re (* (sqrt -1) (sqrt 2))))) (* (sqrt (/ 1 im)) (* (sqrt -1) (sqrt 2)))))))
(* -2 im)
(* -1 (* im (+ 2 (* 2 (/ re im)))))
(* -1 (* im (+ 2 (* -1 (/ (+ (* -2 re) (* -1 (/ (pow re 2) im))) im)))))
(* -1 (* im (+ 2 (* -1 (/ (+ (* -2 re) (* -1 (/ (+ (* -1/4 (/ (pow re 4) (pow im 2))) (pow re 2)) im))) im)))))
(* -1/2 (* (sqrt im) (* (sqrt -1) (sqrt 2))))
(* -1 (* im (+ (* -1/4 (* (sqrt (/ 1 (pow im 3))) (* re (* (sqrt -1) (sqrt 2))))) (* 1/2 (* (sqrt (/ 1 im)) (* (sqrt -1) (sqrt 2)))))))
(* -1 (* im (+ (* -1/4 (* (sqrt (/ 1 (pow im 3))) (* re (* (sqrt -1) (sqrt 2))))) (+ (* -1/8 (* (sqrt (/ 1 (pow im 5))) (* (pow re 2) (* (sqrt -1) (sqrt 2))))) (* 1/2 (* (sqrt (/ 1 im)) (* (sqrt -1) (sqrt 2))))))))
(* -1 (* im (+ (* -1 (/ (+ (* 1/16 (* (sqrt im) (* (pow re 2) (* (sqrt -1) (sqrt 2))))) (* 1/8 (* (sqrt im) (* (pow re 2) (* (sqrt -1) (sqrt 2)))))) (pow im 3))) (+ (* -1/4 (* (sqrt (/ 1 (pow im 3))) (* re (* (sqrt -1) (sqrt 2))))) (* 1/2 (* (sqrt (/ 1 im)) (* (sqrt -1) (sqrt 2))))))))
(* -1 (* (sqrt im) (* (sqrt -1) (sqrt 2))))
(* -1 (* im (+ (* -1/2 (* (sqrt (/ 1 (pow im 3))) (* re (* (sqrt -1) (sqrt 2))))) (* (sqrt (/ 1 im)) (* (sqrt -1) (sqrt 2))))))
(* -1 (* im (+ (* -1/2 (* (sqrt (/ 1 (pow im 3))) (* re (* (sqrt -1) (sqrt 2))))) (+ (* -1/4 (* (sqrt (/ 1 (pow im 5))) (* (pow re 2) (* (sqrt -1) (sqrt 2))))) (* (sqrt (/ 1 im)) (* (sqrt -1) (sqrt 2)))))))
(* -1 (* im (+ (* -1 (/ (+ (* 1/8 (* (sqrt im) (* (pow re 2) (* (sqrt -1) (sqrt 2))))) (* 1/4 (* (sqrt im) (* (pow re 2) (* (sqrt -1) (sqrt 2)))))) (pow im 3))) (+ (* -1/2 (* (sqrt (/ 1 (pow im 3))) (* re (* (sqrt -1) (sqrt 2))))) (* (sqrt (/ 1 im)) (* (sqrt -1) (sqrt 2)))))))
(* -2 im)
(* -1 (* im (+ 2 (* 2 (/ re im)))))
(* -1 (* im (+ 2 (* -1 (/ (+ (* -2 re) (* -1 (/ (pow re 2) im))) im)))))
(* -1 (* im (+ 2 (* -1 (/ (+ (* -2 re) (* -1 (/ (+ (* -1/4 (/ (pow re 4) (pow im 2))) (pow re 2)) im))) im)))))
(* -1 im)
(* -1 (* im (+ 1 (/ re im))))
(* -1 (* im (+ 1 (* -1 (/ (- (* -1/2 (/ (pow re 2) im)) re) im)))))
(* -1 (* im (+ 1 (* -1 (/ (- (* -1 (/ (+ (* -1/8 (/ (pow re 4) (pow im 2))) (* 1/2 (pow re 2))) im)) re) im)))))
(* -1/2 (* (sqrt im) (* (sqrt -1) (sqrt 2))))
(* -1 (* im (+ (* -1/4 (* (sqrt (/ 1 (pow im 3))) (* re (* (sqrt -1) (sqrt 2))))) (* 1/2 (* (sqrt (/ 1 im)) (* (sqrt -1) (sqrt 2)))))))
(* -1 (* im (+ (* -1/4 (* (sqrt (/ 1 (pow im 3))) (* re (* (sqrt -1) (sqrt 2))))) (+ (* -1/8 (* (sqrt (/ 1 (pow im 5))) (* (pow re 2) (* (sqrt -1) (sqrt 2))))) (* 1/2 (* (sqrt (/ 1 im)) (* (sqrt -1) (sqrt 2))))))))
(* -1 (* im (+ (* -1 (/ (+ (* 1/16 (* (sqrt im) (* (pow re 2) (* (sqrt -1) (sqrt 2))))) (* 1/8 (* (sqrt im) (* (pow re 2) (* (sqrt -1) (sqrt 2)))))) (pow im 3))) (+ (* -1/4 (* (sqrt (/ 1 (pow im 3))) (* re (* (sqrt -1) (sqrt 2))))) (* 1/2 (* (sqrt (/ 1 im)) (* (sqrt -1) (sqrt 2))))))))
(* 1/2 (* im (sqrt (/ 1 re))))
(* 1/2 (* im (sqrt (/ 1 re))))
(* 1/2 (* im (sqrt (/ 1 re))))
(* 1/2 (* im (sqrt (/ 1 re))))
(* 1/2 im)
(* 1/2 im)
(* 1/2 im)
(* 1/2 im)
(* 1/2 (* im (sqrt (/ 1 re))))
(* 1/2 (* im (sqrt (/ 1 re))))
(* 1/2 (* im (sqrt (/ 1 re))))
(* 1/2 (* im (sqrt (/ 1 re))))
(* -1/2 (* (sqrt im) (* (sqrt -1) (sqrt 2))))
(* -1 (* im (+ (* -1/4 (* (sqrt (/ 1 (pow im 3))) (* re (* (sqrt -1) (sqrt 2))))) (* 1/2 (* (sqrt (/ 1 im)) (* (sqrt -1) (sqrt 2)))))))
(* -1 (* im (+ (* -1/4 (* (sqrt (/ 1 (pow im 3))) (* re (* (sqrt -1) (sqrt 2))))) (+ (* -1/8 (* (sqrt (/ 1 (pow im 5))) (* (pow re 2) (* (sqrt -1) (sqrt 2))))) (* 1/2 (* (sqrt (/ 1 im)) (* (sqrt -1) (sqrt 2))))))))
(* -1 (* im (+ (* -1 (/ (+ (* 1/16 (* (sqrt im) (* (pow re 2) (* (sqrt -1) (sqrt 2))))) (* 1/8 (* (sqrt im) (* (pow re 2) (* (sqrt -1) (sqrt 2)))))) (pow im 3))) (+ (* -1/4 (* (sqrt (/ 1 (pow im 3))) (* re (* (sqrt -1) (sqrt 2))))) (* 1/2 (* (sqrt (/ 1 im)) (* (sqrt -1) (sqrt 2))))))))
(* 2 (* (/ 1 im) (sqrt re)))
(* 2 (* (/ 1 im) (sqrt re)))
(* 2 (* (/ 1 im) (sqrt re)))
(* 2 (* (/ 1 im) (sqrt re)))
(* -1/2 (* (sqrt im) (* (sqrt -1) (sqrt 2))))
(* -1 (* im (+ (* -1/4 (* (sqrt (/ 1 (pow im 3))) (* re (* (sqrt -1) (sqrt 2))))) (* 1/2 (* (sqrt (/ 1 im)) (* (sqrt -1) (sqrt 2)))))))
(* -1 (* im (+ (* -1/4 (* (sqrt (/ 1 (pow im 3))) (* re (* (sqrt -1) (sqrt 2))))) (+ (* -1/8 (* (sqrt (/ 1 (pow im 5))) (* (pow re 2) (* (sqrt -1) (sqrt 2))))) (* 1/2 (* (sqrt (/ 1 im)) (* (sqrt -1) (sqrt 2))))))))
(* -1 (* im (+ (* -1 (/ (+ (* 1/16 (* (sqrt im) (* (pow re 2) (* (sqrt -1) (sqrt 2))))) (* 1/8 (* (sqrt im) (* (pow re 2) (* (sqrt -1) (sqrt 2)))))) (pow im 3))) (+ (* -1/4 (* (sqrt (/ 1 (pow im 3))) (* re (* (sqrt -1) (sqrt 2))))) (* 1/2 (* (sqrt (/ 1 im)) (* (sqrt -1) (sqrt 2))))))))
(* -1 (* (sqrt im) (* (sqrt -1) (sqrt 2))))
(* -1 (* im (+ (* -1/2 (* (sqrt (/ 1 (pow im 3))) (* re (* (sqrt -1) (sqrt 2))))) (* (sqrt (/ 1 im)) (* (sqrt -1) (sqrt 2))))))
(* -1 (* im (+ (* -1/2 (* (sqrt (/ 1 (pow im 3))) (* re (* (sqrt -1) (sqrt 2))))) (+ (* -1/4 (* (sqrt (/ 1 (pow im 5))) (* (pow re 2) (* (sqrt -1) (sqrt 2))))) (* (sqrt (/ 1 im)) (* (sqrt -1) (sqrt 2)))))))
(* -1 (* im (+ (* -1 (/ (+ (* 1/8 (* (sqrt im) (* (pow re 2) (* (sqrt -1) (sqrt 2))))) (* 1/4 (* (sqrt im) (* (pow re 2) (* (sqrt -1) (sqrt 2)))))) (pow im 3))) (+ (* -1/2 (* (sqrt (/ 1 (pow im 3))) (* re (* (sqrt -1) (sqrt 2))))) (* (sqrt (/ 1 im)) (* (sqrt -1) (sqrt 2)))))))
(* -2 im)
(* -1 (* im (+ 2 (* 2 (/ re im)))))
(* -1 (* im (+ 2 (* -1 (/ (+ (* -2 re) (* -1 (/ (pow re 2) im))) im)))))
(* -1 (* im (+ 2 (* -1 (/ (+ (* -2 re) (* -1 (/ (+ (* -1/4 (/ (pow re 4) (pow im 2))) (pow re 2)) im))) im)))))
(* -1 im)
(* -1 (* im (+ 1 (/ re im))))
(* -1 (* im (+ 1 (* -1 (/ (- (* -1/2 (/ (pow re 2) im)) re) im)))))
(* -1 (* im (+ 1 (* -1 (/ (- (* -1 (/ (+ (* -1/8 (/ (pow re 4) (pow im 2))) (* 1/2 (pow re 2))) im)) re) im)))))
(* (sqrt im) (sqrt -1))
(+ (* 1/4 (* (sqrt (/ 1 (pow im 3))) (* (pow re 2) (sqrt -1)))) (* (sqrt im) (sqrt -1)))
(+ (* 1/4 (* (sqrt (/ 1 (pow im 3))) (* (pow re 2) (sqrt -1)))) (+ (* (sqrt im) (sqrt -1)) (* (sqrt (/ 1 (pow im 7))) (* (sqrt -1) (+ (* -1/8 (pow re 4)) (* 1/32 (pow re 4)))))))
(+ (* 1/4 (* (sqrt (/ 1 (pow im 3))) (* (pow re 2) (sqrt -1)))) (+ (* (sqrt im) (sqrt -1)) (+ (* (sqrt (/ 1 (pow im 7))) (* (sqrt -1) (+ (* -1/8 (pow re 4)) (* 1/32 (pow re 4))))) (* (sqrt (/ 1 (pow im 11))) (* (sqrt -1) (+ (* -1/32 (pow re 6)) (+ (* 1/384 (pow re 6)) (* 1/12 (pow re 6)))))))))
(* -1 im)
(* -1 (* im (+ 1 (* 1/2 (/ (pow re 2) (pow im 2))))))
(* -1 (* im (+ 1 (+ (* -1/8 (/ (pow re 4) (pow im 4))) (* 1/2 (/ (pow re 2) (pow im 2)))))))
(* -1 (* im (+ 1 (+ (* -1/8 (/ (pow re 4) (pow im 4))) (+ (* 1/16 (/ (pow re 6) (pow im 6))) (* 1/2 (/ (pow re 2) (pow im 2))))))))

Outputs
im
(-.f64 im re)
(fma.f64 (fma.f64 (/.f64 #s(literal 1/2 binary64) im) re #s(literal -1 binary64)) re im)
(fma.f64 (fma.f64 (fma.f64 (*.f64 re (/.f64 re (pow.f64 im #s(literal 3 binary64)))) #s(literal -1/8 binary64) (/.f64 #s(literal 1/2 binary64) im)) re #s(literal -1 binary64)) re im)
(.f64 (.f64 #s(literal 1/2 binary64) (sqrt.f64 #s(literal 2 binary64))) (sqrt.f64 im))
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(.f64 (fma.f64 (.f64 (.f64 (.f64 (.f64 (sqrt.f64 #s(literal 2 binary64)) re) re) (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 im #s(literal 5 binary64))))) (sqrt.f64 #s(literal -1 binary64))) #s(literal -1/8 binary64) (fma.f64 (.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) im)) (sqrt.f64 #s(literal -1 binary64))) (.f64 (sqrt.f64 #s(literal 2 binary64)) #s(literal 1/2 binary64)) (.f64 (.f64 (.f64 re (sqrt.f64 #s(literal -1 binary64))) (*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 im #s(literal 3 binary64)))) (sqrt.f64 #s(literal 2 binary64)))) #s(literal -1/4 binary64)))) (neg.f64 im))
(.f64 (-.f64 (fma.f64 (.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) im)) (sqrt.f64 #s(literal -1 binary64))) (.f64 (sqrt.f64 #s(literal 2 binary64)) #s(literal 1/2 binary64)) (.f64 (.f64 (.f64 re (sqrt.f64 #s(literal -1 binary64))) (.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 im #s(literal 3 binary64)))) (sqrt.f64 #s(literal 2 binary64)))) #s(literal -1/4 binary64))) (.f64 (.f64 (.f64 (.f64 (sqrt.f64 #s(literal -1 binary64)) (sqrt.f64 #s(literal 2 binary64))) (.f64 re re)) (sqrt.f64 im)) (/.f64 #s(literal 3/16 binary64) (pow.f64 im #s(literal 3 binary64))))) (neg.f64 im))
(*.f64 (/.f64 (sqrt.f64 re) im) #s(literal 2 binary64))
(*.f64 (/.f64 (sqrt.f64 re) im) #s(literal 2 binary64))
(*.f64 (/.f64 (sqrt.f64 re) im) #s(literal 2 binary64))
(*.f64 (/.f64 (sqrt.f64 re) im) #s(literal 2 binary64))
(.f64 (.f64 #s(literal -1/2 binary64) (sqrt.f64 im)) (*.f64 (sqrt.f64 #s(literal -1 binary64)) (sqrt.f64 #s(literal 2 binary64))))
(.f64 (fma.f64 (.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) im)) (sqrt.f64 #s(literal -1 binary64))) (.f64 (sqrt.f64 #s(literal 2 binary64)) #s(literal 1/2 binary64)) (.f64 (.f64 (.f64 re (sqrt.f64 #s(literal -1 binary64))) (*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 im #s(literal 3 binary64)))) (sqrt.f64 #s(literal 2 binary64)))) #s(literal -1/4 binary64))) (neg.f64 im))
(.f64 (fma.f64 (.f64 (.f64 (.f64 (.f64 (sqrt.f64 #s(literal 2 binary64)) re) re) (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 im #s(literal 5 binary64))))) (sqrt.f64 #s(literal -1 binary64))) #s(literal -1/8 binary64) (fma.f64 (.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) im)) (sqrt.f64 #s(literal -1 binary64))) (.f64 (sqrt.f64 #s(literal 2 binary64)) #s(literal 1/2 binary64)) (.f64 (.f64 (.f64 re (sqrt.f64 #s(literal -1 binary64))) (*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 im #s(literal 3 binary64)))) (sqrt.f64 #s(literal 2 binary64)))) #s(literal -1/4 binary64)))) (neg.f64 im))
(.f64 (-.f64 (fma.f64 (.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) im)) (sqrt.f64 #s(literal -1 binary64))) (.f64 (sqrt.f64 #s(literal 2 binary64)) #s(literal 1/2 binary64)) (.f64 (.f64 (.f64 re (sqrt.f64 #s(literal -1 binary64))) (.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 im #s(literal 3 binary64)))) (sqrt.f64 #s(literal 2 binary64)))) #s(literal -1/4 binary64))) (.f64 (.f64 (.f64 (.f64 (sqrt.f64 #s(literal -1 binary64)) (sqrt.f64 #s(literal 2 binary64))) (.f64 re re)) (sqrt.f64 im)) (/.f64 #s(literal 3/16 binary64) (pow.f64 im #s(literal 3 binary64))))) (neg.f64 im))
(.f64 (.f64 (neg.f64 (sqrt.f64 im)) (sqrt.f64 #s(literal -1 binary64))) (sqrt.f64 #s(literal 2 binary64)))
(.f64 (fma.f64 (.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) im)) (sqrt.f64 #s(literal -1 binary64))) (sqrt.f64 #s(literal 2 binary64)) (.f64 (.f64 (.f64 re (sqrt.f64 #s(literal -1 binary64))) (.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 im #s(literal 3 binary64)))) (sqrt.f64 #s(literal 2 binary64)))) #s(literal -1/2 binary64))) (neg.f64 im))
(.f64 (fma.f64 (.f64 (.f64 (.f64 (.f64 (sqrt.f64 #s(literal 2 binary64)) re) re) (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 im #s(literal 5 binary64))))) (sqrt.f64 #s(literal -1 binary64))) #s(literal -1/4 binary64) (fma.f64 (.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) im)) (sqrt.f64 #s(literal -1 binary64))) (sqrt.f64 #s(literal 2 binary64)) (.f64 (.f64 (.f64 re (sqrt.f64 #s(literal -1 binary64))) (.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 im #s(literal 3 binary64)))) (sqrt.f64 #s(literal 2 binary64)))) #s(literal -1/2 binary64)))) (neg.f64 im))
(.f64 (-.f64 (fma.f64 (.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) im)) (sqrt.f64 #s(literal -1 binary64))) (sqrt.f64 #s(literal 2 binary64)) (.f64 (.f64 (.f64 re (sqrt.f64 #s(literal -1 binary64))) (.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 im #s(literal 3 binary64)))) (sqrt.f64 #s(literal 2 binary64)))) #s(literal -1/2 binary64))) (.f64 (.f64 (.f64 (.f64 (sqrt.f64 #s(literal -1 binary64)) (sqrt.f64 #s(literal 2 binary64))) (*.f64 re re)) (sqrt.f64 im)) (/.f64 #s(literal 3/8 binary64) (pow.f64 im #s(literal 3 binary64))))) (neg.f64 im))
(*.f64 #s(literal -2 binary64) im)
(*.f64 (fma.f64 (/.f64 re im) #s(literal 2 binary64) #s(literal 2 binary64)) (neg.f64 im))
(.f64 (-.f64 #s(literal 2 binary64) (/.f64 (fma.f64 #s(literal -2 binary64) re (/.f64 (.f64 (neg.f64 re) re) im)) im)) (neg.f64 im))
(.f64 (-.f64 #s(literal 2 binary64) (/.f64 (fma.f64 #s(literal -2 binary64) re (/.f64 (fma.f64 (/.f64 (pow.f64 re #s(literal 4 binary64)) im) (/.f64 #s(literal -1/4 binary64) im) (.f64 re re)) (neg.f64 im))) im)) (neg.f64 im))
(neg.f64 im)
(neg.f64 (fma.f64 (/.f64 re im) im im))
(.f64 (-.f64 #s(literal 1 binary64) (/.f64 (-.f64 (.f64 (*.f64 re (/.f64 re im)) #s(literal -1/2 binary64)) re) im)) (neg.f64 im))
(neg.f64 (fma.f64 (/.f64 (-.f64 (/.f64 (fma.f64 (/.f64 #s(literal -1/8 binary64) im) (/.f64 (pow.f64 re #s(literal 4 binary64)) im) (.f64 (.f64 re re) #s(literal 1/2 binary64))) (neg.f64 im)) re) (neg.f64 im)) im im))
(*.f64 (sqrt.f64 #s(literal -1 binary64)) (sqrt.f64 im))
(fma.f64 (.f64 (.f64 #s(literal 1/4 binary64) (.f64 re re)) (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 im #s(literal 3 binary64))))) (sqrt.f64 #s(literal -1 binary64)) (.f64 (sqrt.f64 #s(literal -1 binary64)) (sqrt.f64 im)))
(fma.f64 (.f64 (.f64 (pow.f64 re #s(literal 4 binary64)) #s(literal -3/32 binary64)) (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 im #s(literal 7 binary64))))) (sqrt.f64 #s(literal -1 binary64)) (fma.f64 (.f64 (.f64 #s(literal 1/4 binary64) (.f64 re re)) (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 im #s(literal 3 binary64))))) (sqrt.f64 #s(literal -1 binary64)) (.f64 (sqrt.f64 #s(literal -1 binary64)) (sqrt.f64 im))))
(fma.f64 (.f64 (.f64 #s(literal 1/4 binary64) (.f64 re re)) (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 im #s(literal 3 binary64))))) (sqrt.f64 #s(literal -1 binary64)) (fma.f64 (.f64 (.f64 (pow.f64 re #s(literal 6 binary64)) #s(literal 7/128 binary64)) (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 im #s(literal 11 binary64))))) (sqrt.f64 #s(literal -1 binary64)) (fma.f64 (.f64 (.f64 (pow.f64 re #s(literal 4 binary64)) #s(literal -3/32 binary64)) (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 im #s(literal 7 binary64))))) (sqrt.f64 #s(literal -1 binary64)) (.f64 (sqrt.f64 #s(literal -1 binary64)) (sqrt.f64 im)))))
(neg.f64 im)
(.f64 (neg.f64 im) (fma.f64 (/.f64 (.f64 re (/.f64 re im)) im) #s(literal 1/2 binary64) #s(literal 1 binary64)))
(.f64 (neg.f64 im) (fma.f64 (/.f64 (pow.f64 re #s(literal 4 binary64)) (pow.f64 im #s(literal 4 binary64))) #s(literal -1/8 binary64) (fma.f64 (/.f64 (.f64 re (/.f64 re im)) im) #s(literal 1/2 binary64) #s(literal 1 binary64))))
(neg.f64 (fma.f64 (fma.f64 (pow.f64 re #s(literal 4 binary64)) (/.f64 #s(literal -1/8 binary64) (pow.f64 im #s(literal 4 binary64))) (fma.f64 (.f64 (/.f64 #s(literal 1/2 binary64) im) re) (/.f64 re im) (/.f64 (.f64 (pow.f64 re #s(literal 6 binary64)) #s(literal 1/16 binary64)) (pow.f64 im #s(literal 6 binary64))))) im im))

rewrite110.0ms (1.5%)

Memory

-7.1MiB live, 191.4MiB allocated

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	45	226
0	72	182
1	201	173
2	1021	173
0	9859	173

Stop Event

1×	iter limit
1×	node limit
1×	iter limit

Counts

22 → 680

Calls

Call 1

Inputs
(fma.f64 (sqrt.f64 (hypot.f64 re im)) (sqrt.f64 (hypot.f64 re im)) (neg.f64 re))
(.f64 (sqrt.f64 (.f64 (fma.f64 (sqrt.f64 (hypot.f64 re im)) (sqrt.f64 (hypot.f64 re im)) (neg.f64 re)) #s(literal 2 binary64))) #s(literal 1/2 binary64))
(sqrt.f64 (*.f64 (fma.f64 (sqrt.f64 (hypot.f64 re im)) (sqrt.f64 (hypot.f64 re im)) (neg.f64 re)) #s(literal 2 binary64)))
(*.f64 (fma.f64 (sqrt.f64 (hypot.f64 re im)) (sqrt.f64 (hypot.f64 re im)) (neg.f64 re)) #s(literal 2 binary64))
(.f64 (sqrt.f64 (.f64 #s(approx (- (sqrt (+ (* im im) (* re re))) re) (-.f64 im re)) #s(literal 2 binary64))) #s(literal 1/2 binary64))
(sqrt.f64 (.f64 #s(approx (- (sqrt (+ ( im im) (* re re))) re) (-.f64 im re)) #s(literal 2 binary64)))
(.f64 #s(approx (- (sqrt (+ ( im im) (* re re))) re) (-.f64 im re)) #s(literal 2 binary64))
#s(approx (- (sqrt (+ (* im im) (* re re))) re) (-.f64 im re))
#s(approx (* 1/2 (sqrt (* 2 (- (sqrt (+ (* re re) (* im im))) re)))) (.f64 (.f64 im #s(literal 1/2 binary64)) (sqrt.f64 (/.f64 #s(literal 1 binary64) re))))
(.f64 (.f64 im #s(literal 1/2 binary64)) (sqrt.f64 (/.f64 #s(literal 1 binary64) re)))
(*.f64 im #s(literal 1/2 binary64))
(sqrt.f64 (/.f64 #s(literal 1 binary64) re))
(/.f64 #s(literal 1 binary64) (/.f64 (sqrt.f64 re) (*.f64 #s(literal 1/2 binary64) im)))
#s(approx (* 1/2 (sqrt (* 2 (- (sqrt (+ (* re re) (* im im))) re)))) (/.f64 #s(literal 1 binary64) (/.f64 (sqrt.f64 re) (*.f64 #s(literal 1/2 binary64) im))))
(/.f64 (sqrt.f64 re) (*.f64 #s(literal 1/2 binary64) im))
(sqrt.f64 re)
(.f64 #s(literal 1/2 binary64) (sqrt.f64 (.f64 #s(literal 2 binary64) (-.f64 (sqrt.f64 (fma.f64 re re (*.f64 im im))) re))))
(sqrt.f64 (.f64 #s(literal 2 binary64) (-.f64 (sqrt.f64 (fma.f64 re re (.f64 im im))) re)))
(.f64 #s(literal 2 binary64) (-.f64 (sqrt.f64 (fma.f64 re re (.f64 im im))) re))
(-.f64 (sqrt.f64 (fma.f64 re re (*.f64 im im))) re)
(sqrt.f64 (hypot.f64 re im))
(sqrt.f64 (fma.f64 re re (*.f64 im im)))

Outputs
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eval167.0ms (2.3%)

Memory: 13.3MiB live, 242.6MiB allocated
Compiler: Compiled 40 242 to 4 085 computations (89.8% saved)

prune50.0ms (0.7%)

Memory

5.5MiB live, 83.5MiB allocated

Pruning

18 alts after pruning (6 fresh and 12 done)

	Pruned	Kept	Total
New	1 207	2	1 209
Fresh	1	4	5
Picked	0	5	5
Done	0	7	7
Total	1 208	18	1 226

Accuracy

99.7%

Counts

1 226 → 18

Alt Table

Click to see full alt table

Status	Accuracy	Program
✓	79.8%	(.f64 (.f64 (sqrt.f64 (-.f64 (hypot.f64 re im) re)) (sqrt.f64 #s(literal 2 binary64))) #s(literal 1/2 binary64))
	53.7%	(.f64 (.f64 (sqrt.f64 #s(approx (- (sqrt (+ (* re re) (* im im))) re) (-.f64 im re))) (sqrt.f64 #s(literal 2 binary64))) #s(literal 1/2 binary64))
✓	76.6%	(.f64 (sqrt.f64 (.f64 (fma.f64 (sqrt.f64 (hypot.f64 re im)) (sqrt.f64 (hypot.f64 re im)) (neg.f64 re)) #s(literal 2 binary64))) #s(literal 1/2 binary64))
✓	79.9%	(.f64 (sqrt.f64 (.f64 (-.f64 (hypot.f64 im re) re) #s(literal 2 binary64))) #s(literal 1/2 binary64))
✓	53.6%	(.f64 (sqrt.f64 (.f64 #s(approx (- (sqrt (+ (* im im) (* re re))) re) (-.f64 im re)) #s(literal 2 binary64))) #s(literal 1/2 binary64))
	51.1%	(.f64 (sqrt.f64 #s(approx ( (- (sqrt (+ (* im im) (* re re))) re) 2) (fma.f64 (-.f64 (/.f64 re im) #s(literal 2 binary64)) re (*.f64 #s(literal 2 binary64) im)))) #s(literal 1/2 binary64))
✓	51.0%	(.f64 (sqrt.f64 #s(approx ( (- (sqrt (+ (* im im) (* re re))) re) 2) (*.f64 #s(literal 2 binary64) im))) #s(literal 1/2 binary64))
✓	51.0%	(.f64 #s(approx (sqrt ( (- (sqrt (+ (* im im) (* re re))) re) 2)) (*.f64 (sqrt.f64 #s(literal 2 binary64)) (sqrt.f64 im))) #s(literal 1/2 binary64))
✓	37.6%	(.f64 #s(literal 1/2 binary64) (sqrt.f64 (.f64 #s(literal 2 binary64) (-.f64 (sqrt.f64 (fma.f64 re re (*.f64 im im))) re))))
	29.9%	(.f64 #s(literal 1/2 binary64) (sqrt.f64 (.f64 #s(literal 2 binary64) (-.f64 (sqrt.f64 #s(approx (+ (* re re) (* im im)) (.f64 (.f64 (fma.f64 (/.f64 re im) (/.f64 re im) #s(literal 1 binary64)) im) im))) re))))
✓	12.9%	(.f64 #s(literal 1/2 binary64) (sqrt.f64 #s(approx ( 2 (- (sqrt (+ (* re re) (* im im))) re)) (/.f64 (*.f64 im im) re))))
✓	28.1%	(.f64 #s(literal 1/2 binary64) (sqrt.f64 #s(approx ( 2 (- (sqrt (+ (* re re) (* im im))) re)) (*.f64 #s(literal -4 binary64) re))))
	24.7%	#s(approx (* 1/2 (sqrt (* 2 (- (sqrt (+ (* re re) (* im im))) re)))) (/.f64 (*.f64 #s(literal 1/2 binary64) im) (sqrt.f64 re)))
	8.7%	#s(approx (* 1/2 (sqrt (* 2 (- (sqrt (+ (* re re) (* im im))) re)))) (/.f64 #s(literal 1 binary64) (/.f64 (/.f64 (sqrt.f64 (pow.f64 re #s(literal 3 binary64))) (sqrt.f64 (fma.f64 re re #s(literal 0 binary64)))) (*.f64 #s(literal 1/2 binary64) im))))
✓	24.6%	#s(approx (* 1/2 (sqrt (* 2 (- (sqrt (+ (* re re) (* im im))) re)))) (/.f64 #s(literal 1 binary64) (/.f64 (sqrt.f64 re) (*.f64 #s(literal 1/2 binary64) im))))
	24.7%	#s(approx (* 1/2 (sqrt (* 2 (- (sqrt (+ (* re re) (* im im))) re)))) (*.f64 (/.f64 #s(literal 1/2 binary64) (sqrt.f64 re)) im))
✓	24.7%	#s(approx (* 1/2 (sqrt (* 2 (- (sqrt (+ (* re re) (* im im))) re)))) (.f64 (.f64 (sqrt.f64 #s(literal 1/2 binary64)) im) (*.f64 #s(literal 1/2 binary64) (sqrt.f64 (/.f64 #s(literal 2 binary64) re)))))
✓	24.7%	#s(approx (* 1/2 (sqrt (* 2 (- (sqrt (+ (* re re) (* im im))) re)))) (.f64 (.f64 im #s(literal 1/2 binary64)) (sqrt.f64 (/.f64 #s(literal 1 binary64) re))))

Compiler

Compiled 1 125 to 484 computations (57% saved)

regimes117.0ms (1.6%)

Memory

-40.6MiB live, 93.9MiB allocated

Counts

33 → 2

Calls

Call 1

Inputs
(.f64 #s(literal 1/2 binary64) (sqrt.f64 #s(approx ( 2 (- (sqrt (+ (* re re) (* im im))) re)) (*.f64 #s(literal -4 binary64) re))))
(.f64 #s(literal 1/2 binary64) (sqrt.f64 #s(approx ( 2 (- (sqrt (+ (* re re) (* im im))) re)) (*.f64 #s(literal 2 binary64) im))))
(.f64 (sqrt.f64 #s(approx ( (- (sqrt (+ (* im im) (* re re))) re) 2) (*.f64 #s(literal 2 binary64) im))) #s(literal 1/2 binary64))
(.f64 #s(literal 1/2 binary64) (sqrt.f64 (.f64 #s(literal 2 binary64) #s(approx (- (sqrt (+ (* re re) (* im im))) re) (-.f64 im re)))))
(.f64 (sqrt.f64 (.f64 #s(approx (- (sqrt (+ (* im im) (* re re))) re) (-.f64 im re)) #s(literal 2 binary64))) #s(literal 1/2 binary64))
#s(approx (* 1/2 (sqrt (* 2 (- (sqrt (+ (* re re) (* im im))) re)))) (*.f64 (/.f64 #s(literal 1/2 binary64) (sqrt.f64 re)) im))
#s(approx (* 1/2 (sqrt (* 2 (- (sqrt (+ (* re re) (* im im))) re)))) (/.f64 (*.f64 #s(literal 1/2 binary64) im) (sqrt.f64 re)))
(.f64 #s(literal 1/2 binary64) #s(approx (sqrt ( 2 (- (sqrt (+ (* re re) (* im im))) re))) (*.f64 (sqrt.f64 #s(literal 2 binary64)) (sqrt.f64 im))))
(.f64 #s(approx (sqrt ( (- (sqrt (+ (* im im) (* re re))) re) 2)) (*.f64 (sqrt.f64 #s(literal 2 binary64)) (sqrt.f64 im))) #s(literal 1/2 binary64))
#s(approx (* 1/2 (sqrt (* 2 (- (sqrt (+ (* re re) (* im im))) re)))) (.f64 (.f64 im #s(literal 1/2 binary64)) (sqrt.f64 (/.f64 #s(literal 1 binary64) re))))
(.f64 #s(literal 1/2 binary64) (sqrt.f64 #s(approx ( 2 (- (sqrt (+ (* re re) (* im im))) re)) (/.f64 (*.f64 im im) re))))
(.f64 (.f64 (sqrt.f64 #s(approx (- (sqrt (+ (* re re) (* im im))) re) (-.f64 im re))) (sqrt.f64 #s(literal 2 binary64))) #s(literal 1/2 binary64))
#s(approx (* 1/2 (sqrt (* 2 (- (sqrt (+ (* re re) (* im im))) re)))) (/.f64 #s(literal 1 binary64) (/.f64 (sqrt.f64 re) (*.f64 #s(literal 1/2 binary64) im))))
(.f64 #s(literal 1/2 binary64) (sqrt.f64 #s(approx ( 2 (- (sqrt (+ (* re re) (* im im))) re)) (*.f64 (fma.f64 (/.f64 re im) #s(literal -2 binary64) #s(literal 2 binary64)) im))))
(.f64 (sqrt.f64 #s(approx ( (- (sqrt (+ (* im im) (* re re))) re) 2) (*.f64 (fma.f64 (/.f64 re im) #s(literal -2 binary64) #s(literal 2 binary64)) im))) #s(literal 1/2 binary64))
(.f64 #s(literal 1/2 binary64) (sqrt.f64 #s(approx ( 2 (- (sqrt (+ (* re re) (* im im))) re)) (fma.f64 (-.f64 (/.f64 re im) #s(literal 2 binary64)) re (*.f64 #s(literal 2 binary64) im)))))
(.f64 (sqrt.f64 #s(approx ( (- (sqrt (+ (* im im) (* re re))) re) 2) (fma.f64 (-.f64 (/.f64 re im) #s(literal 2 binary64)) re (*.f64 #s(literal 2 binary64) im)))) #s(literal 1/2 binary64))
(.f64 #s(literal 1/2 binary64) (sqrt.f64 (.f64 #s(literal 2 binary64) (-.f64 (sqrt.f64 (fma.f64 re re (*.f64 im im))) re))))
#s(approx (* 1/2 (sqrt (* 2 (- (sqrt (+ (* re re) (* im im))) re)))) (.f64 (.f64 (sqrt.f64 #s(literal 1/2 binary64)) im) (*.f64 #s(literal 1/2 binary64) (sqrt.f64 (/.f64 #s(literal 2 binary64) re)))))
(.f64 #s(literal 1/2 binary64) (sqrt.f64 (.f64 #s(literal 2 binary64) (-.f64 (sqrt.f64 (+.f64 (.f64 re re) (.f64 im im))) re))))
#s(approx (* 1/2 (sqrt (* 2 (- (sqrt (+ (* re re) (* im im))) re)))) (.f64 (.f64 (.f64 #s(literal 1/2 binary64) (.f64 im (sqrt.f64 #s(literal 1/2 binary64)))) (sqrt.f64 #s(literal 2 binary64))) (sqrt.f64 (/.f64 #s(literal 1 binary64) re))))
(.f64 #s(literal 1/2 binary64) #s(approx (sqrt ( 2 (- (sqrt (+ (* re re) (* im im))) re))) (.f64 (.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) re)) (*.f64 im (sqrt.f64 #s(literal 1/2 binary64)))) (sqrt.f64 #s(literal 2 binary64)))))
(.f64 #s(literal 1/2 binary64) (sqrt.f64 (.f64 #s(literal 2 binary64) (-.f64 (sqrt.f64 #s(approx (+ (* re re) (* im im)) (.f64 (.f64 (fma.f64 (/.f64 re im) (/.f64 re im) #s(literal 1 binary64)) im) im))) re))))
#s(approx (* (sqrt (* (- (sqrt (+ (* im im) (* re re))) re) 2)) 1/2) (fma.f64 (.f64 #s(literal 1/2 binary64) (sqrt.f64 #s(literal 2 binary64))) (sqrt.f64 im) (.f64 (.f64 #s(literal -1/4 binary64) (.f64 (sqrt.f64 #s(literal 2 binary64)) re)) (sqrt.f64 (/.f64 #s(literal 1 binary64) im)))))
(.f64 (sqrt.f64 (.f64 (-.f64 (hypot.f64 im re) re) #s(literal 2 binary64))) #s(literal 1/2 binary64))
(.f64 (.f64 (sqrt.f64 (-.f64 (hypot.f64 im re) re)) #s(literal 1/2 binary64)) (sqrt.f64 #s(literal 2 binary64)))
(.f64 (.f64 (sqrt.f64 (-.f64 (hypot.f64 re im) re)) (sqrt.f64 #s(literal 2 binary64))) #s(literal 1/2 binary64))
(.f64 #s(literal 1/2 binary64) (sqrt.f64 #s(approx ( 2 (- (sqrt (+ (* re re) (* im im))) re)) (.f64 (fma.f64 (.f64 im (/.f64 im (pow.f64 re #s(literal 3 binary64)))) #s(literal -1/4 binary64) (/.f64 #s(literal 1 binary64) re)) (*.f64 im im)))))
#s(approx (* 1/2 (sqrt (* 2 (- (sqrt (+ (* re re) (* im im))) re)))) (/.f64 #s(literal 1 binary64) (/.f64 (/.f64 (sqrt.f64 (pow.f64 re #s(literal 3 binary64))) (sqrt.f64 (fma.f64 re re #s(literal 0 binary64)))) (*.f64 #s(literal 1/2 binary64) im))))
#s(approx (* 1/2 (sqrt (* 2 (- (sqrt (+ (* re re) (* im im))) re)))) (.f64 (.f64 (sqrt.f64 #s(literal 1/2 binary64)) im) (.f64 #s(literal 1/2 binary64) (pow.f64 (pow.f64 (.f64 re #s(literal 1/2 binary64)) #s(literal -1/4 binary64)) #s(literal 2 binary64)))))
(.f64 #s(literal 1/2 binary64) #s(approx (sqrt ( 2 (- (sqrt (+ (* re re) (* im im))) re))) (.f64 (fma.f64 (.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) re)) (sqrt.f64 #s(literal 2 binary64))) (sqrt.f64 #s(literal 1/2 binary64)) (.f64 (.f64 (.f64 #s(literal -1/16 binary64) (.f64 im im)) (/.f64 (sqrt.f64 #s(literal 2 binary64)) (sqrt.f64 #s(literal 1/2 binary64)))) (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 re #s(literal 5 binary64)))))) im)))
(.f64 #s(literal 1/2 binary64) (sqrt.f64 (.f64 #s(literal 2 binary64) (fma.f64 (sqrt.f64 (hypot.f64 im re)) (sqrt.f64 (hypot.f64 im re)) (neg.f64 re)))))
(.f64 (sqrt.f64 (.f64 (fma.f64 (sqrt.f64 (hypot.f64 re im)) (sqrt.f64 (hypot.f64 re im)) (neg.f64 re)) #s(literal 2 binary64))) #s(literal 1/2 binary64))

Outputs

(*.f64 (sqrt.f64 (*.f64 (-.f64 (hypot.f64 im re) re) #s(literal 2 binary64))) #s(literal 1/2 binary64))

#s(approx (* 1/2 (sqrt (* 2 (- (sqrt (+ (* re re) (* im im))) re)))) (*.f64 (*.f64 im #s(literal 1/2 binary64)) (sqrt.f64 (/.f64 #s(literal 1 binary64) re))))

Calls

7 calls:

36.0ms	re
31.0ms	(.f64 #s(literal 1/2 binary64) (sqrt.f64 (.f64 #s(literal 2 binary64) (-.f64 (sqrt.f64 (+.f64 (.f64 re re) (.f64 im im))) re))))
13.0ms	(*.f64 im im)
9.0ms	im
8.0ms	(.f64 #s(literal 2 binary64) (-.f64 (sqrt.f64 (+.f64 (.f64 re re) (*.f64 im im))) re))

Results

Accuracy	Segments	Branch
92.4%	2	`re`
79.9%	1	`im`
89.6%	2	`(.f64 #s(literal 1/2 binary64) (sqrt.f64 (.f64 #s(literal 2 binary64) (-.f64 (sqrt.f64 (+.f64 (.f64 re re) (.f64 im im))) re))))`
89.6%	2	`(sqrt.f64 (.f64 #s(literal 2 binary64) (-.f64 (sqrt.f64 (+.f64 (.f64 re re) (*.f64 im im))) re)))`
89.6%	3	`(.f64 #s(literal 2 binary64) (-.f64 (sqrt.f64 (+.f64 (.f64 re re) (*.f64 im im))) re))`
89.6%	3	`(-.f64 (sqrt.f64 (+.f64 (.f64 re re) (.f64 im im))) re)`
79.9%	1	`(*.f64 im im)`

Compiler

Compiled 55 to 45 computations (18.2% saved)

regimes55.0ms (0.8%)

Memory

27.1MiB live, 66.4MiB allocated

Counts

24 → 3

Calls

Call 1

Inputs
(.f64 #s(literal 1/2 binary64) (sqrt.f64 #s(approx ( 2 (- (sqrt (+ (* re re) (* im im))) re)) (*.f64 #s(literal -4 binary64) re))))
(.f64 #s(literal 1/2 binary64) (sqrt.f64 #s(approx ( 2 (- (sqrt (+ (* re re) (* im im))) re)) (*.f64 #s(literal 2 binary64) im))))
(.f64 (sqrt.f64 #s(approx ( (- (sqrt (+ (* im im) (* re re))) re) 2) (*.f64 #s(literal 2 binary64) im))) #s(literal 1/2 binary64))
(.f64 #s(literal 1/2 binary64) (sqrt.f64 (.f64 #s(literal 2 binary64) #s(approx (- (sqrt (+ (* re re) (* im im))) re) (-.f64 im re)))))
(.f64 (sqrt.f64 (.f64 #s(approx (- (sqrt (+ (* im im) (* re re))) re) (-.f64 im re)) #s(literal 2 binary64))) #s(literal 1/2 binary64))
#s(approx (* 1/2 (sqrt (* 2 (- (sqrt (+ (* re re) (* im im))) re)))) (*.f64 (/.f64 #s(literal 1/2 binary64) (sqrt.f64 re)) im))
#s(approx (* 1/2 (sqrt (* 2 (- (sqrt (+ (* re re) (* im im))) re)))) (/.f64 (*.f64 #s(literal 1/2 binary64) im) (sqrt.f64 re)))
(.f64 #s(literal 1/2 binary64) #s(approx (sqrt ( 2 (- (sqrt (+ (* re re) (* im im))) re))) (*.f64 (sqrt.f64 #s(literal 2 binary64)) (sqrt.f64 im))))
(.f64 #s(approx (sqrt ( (- (sqrt (+ (* im im) (* re re))) re) 2)) (*.f64 (sqrt.f64 #s(literal 2 binary64)) (sqrt.f64 im))) #s(literal 1/2 binary64))
#s(approx (* 1/2 (sqrt (* 2 (- (sqrt (+ (* re re) (* im im))) re)))) (.f64 (.f64 im #s(literal 1/2 binary64)) (sqrt.f64 (/.f64 #s(literal 1 binary64) re))))
(.f64 #s(literal 1/2 binary64) (sqrt.f64 #s(approx ( 2 (- (sqrt (+ (* re re) (* im im))) re)) (/.f64 (*.f64 im im) re))))
(.f64 (.f64 (sqrt.f64 #s(approx (- (sqrt (+ (* re re) (* im im))) re) (-.f64 im re))) (sqrt.f64 #s(literal 2 binary64))) #s(literal 1/2 binary64))
#s(approx (* 1/2 (sqrt (* 2 (- (sqrt (+ (* re re) (* im im))) re)))) (/.f64 #s(literal 1 binary64) (/.f64 (sqrt.f64 re) (*.f64 #s(literal 1/2 binary64) im))))
(.f64 #s(literal 1/2 binary64) (sqrt.f64 #s(approx ( 2 (- (sqrt (+ (* re re) (* im im))) re)) (*.f64 (fma.f64 (/.f64 re im) #s(literal -2 binary64) #s(literal 2 binary64)) im))))
(.f64 (sqrt.f64 #s(approx ( (- (sqrt (+ (* im im) (* re re))) re) 2) (*.f64 (fma.f64 (/.f64 re im) #s(literal -2 binary64) #s(literal 2 binary64)) im))) #s(literal 1/2 binary64))
(.f64 #s(literal 1/2 binary64) (sqrt.f64 #s(approx ( 2 (- (sqrt (+ (* re re) (* im im))) re)) (fma.f64 (-.f64 (/.f64 re im) #s(literal 2 binary64)) re (*.f64 #s(literal 2 binary64) im)))))
(.f64 (sqrt.f64 #s(approx ( (- (sqrt (+ (* im im) (* re re))) re) 2) (fma.f64 (-.f64 (/.f64 re im) #s(literal 2 binary64)) re (*.f64 #s(literal 2 binary64) im)))) #s(literal 1/2 binary64))
(.f64 #s(literal 1/2 binary64) (sqrt.f64 (.f64 #s(literal 2 binary64) (-.f64 (sqrt.f64 (fma.f64 re re (*.f64 im im))) re))))
#s(approx (* 1/2 (sqrt (* 2 (- (sqrt (+ (* re re) (* im im))) re)))) (.f64 (.f64 (sqrt.f64 #s(literal 1/2 binary64)) im) (*.f64 #s(literal 1/2 binary64) (sqrt.f64 (/.f64 #s(literal 2 binary64) re)))))
(.f64 #s(literal 1/2 binary64) (sqrt.f64 (.f64 #s(literal 2 binary64) (-.f64 (sqrt.f64 (+.f64 (.f64 re re) (.f64 im im))) re))))
#s(approx (* 1/2 (sqrt (* 2 (- (sqrt (+ (* re re) (* im im))) re)))) (.f64 (.f64 (.f64 #s(literal 1/2 binary64) (.f64 im (sqrt.f64 #s(literal 1/2 binary64)))) (sqrt.f64 #s(literal 2 binary64))) (sqrt.f64 (/.f64 #s(literal 1 binary64) re))))
(.f64 #s(literal 1/2 binary64) #s(approx (sqrt ( 2 (- (sqrt (+ (* re re) (* im im))) re))) (.f64 (.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) re)) (*.f64 im (sqrt.f64 #s(literal 1/2 binary64)))) (sqrt.f64 #s(literal 2 binary64)))))
(.f64 #s(literal 1/2 binary64) (sqrt.f64 (.f64 #s(literal 2 binary64) (-.f64 (sqrt.f64 #s(approx (+ (* re re) (* im im)) (.f64 (.f64 (fma.f64 (/.f64 re im) (/.f64 re im) #s(literal 1 binary64)) im) im))) re))))
#s(approx (* (sqrt (* (- (sqrt (+ (* im im) (* re re))) re) 2)) 1/2) (fma.f64 (.f64 #s(literal 1/2 binary64) (sqrt.f64 #s(literal 2 binary64))) (sqrt.f64 im) (.f64 (.f64 #s(literal -1/4 binary64) (.f64 (sqrt.f64 #s(literal 2 binary64)) re)) (sqrt.f64 (/.f64 #s(literal 1 binary64) im)))))

Outputs

(*.f64 #s(literal 1/2 binary64) (sqrt.f64 #s(approx (* 2 (- (sqrt (+ (* re re) (* im im))) re)) (*.f64 #s(literal -4 binary64) re))))

(*.f64 (*.f64 (sqrt.f64 #s(approx (- (sqrt (+ (* re re) (* im im))) re) (-.f64 im re))) (sqrt.f64 #s(literal 2 binary64))) #s(literal 1/2 binary64))

#s(approx (* 1/2 (sqrt (* 2 (- (sqrt (+ (* re re) (* im im))) re)))) (*.f64 (*.f64 im #s(literal 1/2 binary64)) (sqrt.f64 (/.f64 #s(literal 1 binary64) re))))

Calls

7 calls:

13.0ms	(.f64 #s(literal 2 binary64) (-.f64 (sqrt.f64 (+.f64 (.f64 re re) (*.f64 im im))) re))
7.0ms	im
7.0ms	re
6.0ms	(.f64 #s(literal 1/2 binary64) (sqrt.f64 (.f64 #s(literal 2 binary64) (-.f64 (sqrt.f64 (+.f64 (.f64 re re) (.f64 im im))) re))))
6.0ms	(sqrt.f64 (.f64 #s(literal 2 binary64) (-.f64 (sqrt.f64 (+.f64 (.f64 re re) (*.f64 im im))) re)))

Results

Accuracy	Segments	Branch
66.1%	4	`im`
62.6%	3	`(*.f64 im im)`
72.7%	3	`(.f64 #s(literal 2 binary64) (-.f64 (sqrt.f64 (+.f64 (.f64 re re) (*.f64 im im))) re))`
72.7%	3	`(-.f64 (sqrt.f64 (+.f64 (.f64 re re) (.f64 im im))) re)`
73.5%	3	`(.f64 #s(literal 1/2 binary64) (sqrt.f64 (.f64 #s(literal 2 binary64) (-.f64 (sqrt.f64 (+.f64 (.f64 re re) (.f64 im im))) re))))`
73.5%	3	`(sqrt.f64 (.f64 #s(literal 2 binary64) (-.f64 (sqrt.f64 (+.f64 (.f64 re re) (*.f64 im im))) re)))`
81.7%	3	`re`

Compiler

Compiled 55 to 45 computations (18.2% saved)

regimes5.0ms (0.1%)

Memory

6.8MiB live, 6.8MiB allocated

Counts

11 → 3

Calls

Call 1

Inputs
(.f64 #s(literal 1/2 binary64) (sqrt.f64 #s(approx ( 2 (- (sqrt (+ (* re re) (* im im))) re)) (*.f64 #s(literal -4 binary64) re))))
(.f64 #s(literal 1/2 binary64) (sqrt.f64 #s(approx ( 2 (- (sqrt (+ (* re re) (* im im))) re)) (*.f64 #s(literal 2 binary64) im))))
(.f64 (sqrt.f64 #s(approx ( (- (sqrt (+ (* im im) (* re re))) re) 2) (*.f64 #s(literal 2 binary64) im))) #s(literal 1/2 binary64))
(.f64 #s(literal 1/2 binary64) (sqrt.f64 (.f64 #s(literal 2 binary64) #s(approx (- (sqrt (+ (* re re) (* im im))) re) (-.f64 im re)))))
(.f64 (sqrt.f64 (.f64 #s(approx (- (sqrt (+ (* im im) (* re re))) re) (-.f64 im re)) #s(literal 2 binary64))) #s(literal 1/2 binary64))
#s(approx (* 1/2 (sqrt (* 2 (- (sqrt (+ (* re re) (* im im))) re)))) (*.f64 (/.f64 #s(literal 1/2 binary64) (sqrt.f64 re)) im))
#s(approx (* 1/2 (sqrt (* 2 (- (sqrt (+ (* re re) (* im im))) re)))) (/.f64 (*.f64 #s(literal 1/2 binary64) im) (sqrt.f64 re)))
(.f64 #s(literal 1/2 binary64) #s(approx (sqrt ( 2 (- (sqrt (+ (* re re) (* im im))) re))) (*.f64 (sqrt.f64 #s(literal 2 binary64)) (sqrt.f64 im))))
(.f64 #s(approx (sqrt ( (- (sqrt (+ (* im im) (* re re))) re) 2)) (*.f64 (sqrt.f64 #s(literal 2 binary64)) (sqrt.f64 im))) #s(literal 1/2 binary64))
#s(approx (* 1/2 (sqrt (* 2 (- (sqrt (+ (* re re) (* im im))) re)))) (.f64 (.f64 im #s(literal 1/2 binary64)) (sqrt.f64 (/.f64 #s(literal 1 binary64) re))))
(.f64 #s(literal 1/2 binary64) (sqrt.f64 #s(approx ( 2 (- (sqrt (+ (* re re) (* im im))) re)) (/.f64 (*.f64 im im) re))))

Outputs

(*.f64 #s(literal 1/2 binary64) (sqrt.f64 #s(approx (* 2 (- (sqrt (+ (* re re) (* im im))) re)) (*.f64 #s(literal -4 binary64) re))))

(*.f64 #s(literal 1/2 binary64) (sqrt.f64 (*.f64 #s(literal 2 binary64) #s(approx (- (sqrt (+ (* re re) (* im im))) re) (-.f64 im re)))))

#s(approx (* 1/2 (sqrt (* 2 (- (sqrt (+ (* re re) (* im im))) re)))) (*.f64 (*.f64 im #s(literal 1/2 binary64)) (sqrt.f64 (/.f64 #s(literal 1 binary64) re))))

Calls

1 calls:

4.0ms

re

Results

Accuracy	Segments	Branch
81.6%	3	`re`

Compiler

Compiled 1 to 2 computations (-100% saved)

regimes15.0ms (0.2%)

Memory

-32.9MiB live, 6.5MiB allocated

Counts

9 → 3

Calls

Call 1

Inputs
(.f64 #s(literal 1/2 binary64) (sqrt.f64 #s(approx ( 2 (- (sqrt (+ (* re re) (* im im))) re)) (*.f64 #s(literal -4 binary64) re))))
(.f64 #s(literal 1/2 binary64) (sqrt.f64 #s(approx ( 2 (- (sqrt (+ (* re re) (* im im))) re)) (*.f64 #s(literal 2 binary64) im))))
(.f64 (sqrt.f64 #s(approx ( (- (sqrt (+ (* im im) (* re re))) re) 2) (*.f64 #s(literal 2 binary64) im))) #s(literal 1/2 binary64))
(.f64 #s(literal 1/2 binary64) (sqrt.f64 (.f64 #s(literal 2 binary64) #s(approx (- (sqrt (+ (* re re) (* im im))) re) (-.f64 im re)))))
(.f64 (sqrt.f64 (.f64 #s(approx (- (sqrt (+ (* im im) (* re re))) re) (-.f64 im re)) #s(literal 2 binary64))) #s(literal 1/2 binary64))
#s(approx (* 1/2 (sqrt (* 2 (- (sqrt (+ (* re re) (* im im))) re)))) (*.f64 (/.f64 #s(literal 1/2 binary64) (sqrt.f64 re)) im))
#s(approx (* 1/2 (sqrt (* 2 (- (sqrt (+ (* re re) (* im im))) re)))) (/.f64 (*.f64 #s(literal 1/2 binary64) im) (sqrt.f64 re)))
(.f64 #s(literal 1/2 binary64) #s(approx (sqrt ( 2 (- (sqrt (+ (* re re) (* im im))) re))) (*.f64 (sqrt.f64 #s(literal 2 binary64)) (sqrt.f64 im))))
(.f64 #s(approx (sqrt ( (- (sqrt (+ (* im im) (* re re))) re) 2)) (*.f64 (sqrt.f64 #s(literal 2 binary64)) (sqrt.f64 im))) #s(literal 1/2 binary64))

Outputs

(*.f64 #s(literal 1/2 binary64) (sqrt.f64 #s(approx (* 2 (- (sqrt (+ (* re re) (* im im))) re)) (*.f64 #s(literal -4 binary64) re))))

(*.f64 #s(literal 1/2 binary64) (sqrt.f64 (*.f64 #s(literal 2 binary64) #s(approx (- (sqrt (+ (* re re) (* im im))) re) (-.f64 im re)))))

#s(approx (* 1/2 (sqrt (* 2 (- (sqrt (+ (* re re) (* im im))) re)))) (/.f64 (*.f64 #s(literal 1/2 binary64) im) (sqrt.f64 re)))

Calls

1 calls:

14.0ms

re

Results

Accuracy	Segments	Branch
81.6%	3	`re`

Compiler

Compiled 1 to 2 computations (-100% saved)

regimes3.0ms (0%)

Memory

4.9MiB live, 4.9MiB allocated

Counts

6 → 3

Calls

Call 1

Inputs
(.f64 #s(literal 1/2 binary64) (sqrt.f64 #s(approx ( 2 (- (sqrt (+ (* re re) (* im im))) re)) (*.f64 #s(literal -4 binary64) re))))
(.f64 #s(literal 1/2 binary64) (sqrt.f64 #s(approx ( 2 (- (sqrt (+ (* re re) (* im im))) re)) (*.f64 #s(literal 2 binary64) im))))
(.f64 (sqrt.f64 #s(approx ( (- (sqrt (+ (* im im) (* re re))) re) 2) (*.f64 #s(literal 2 binary64) im))) #s(literal 1/2 binary64))
(.f64 #s(literal 1/2 binary64) (sqrt.f64 (.f64 #s(literal 2 binary64) #s(approx (- (sqrt (+ (* re re) (* im im))) re) (-.f64 im re)))))
(.f64 (sqrt.f64 (.f64 #s(approx (- (sqrt (+ (* im im) (* re re))) re) (-.f64 im re)) #s(literal 2 binary64))) #s(literal 1/2 binary64))
#s(approx (* 1/2 (sqrt (* 2 (- (sqrt (+ (* re re) (* im im))) re)))) (*.f64 (/.f64 #s(literal 1/2 binary64) (sqrt.f64 re)) im))

Outputs

(*.f64 #s(literal 1/2 binary64) (sqrt.f64 #s(approx (* 2 (- (sqrt (+ (* re re) (* im im))) re)) (*.f64 #s(literal -4 binary64) re))))

(*.f64 #s(literal 1/2 binary64) (sqrt.f64 (*.f64 #s(literal 2 binary64) #s(approx (- (sqrt (+ (* re re) (* im im))) re) (-.f64 im re)))))

#s(approx (* 1/2 (sqrt (* 2 (- (sqrt (+ (* re re) (* im im))) re)))) (*.f64 (/.f64 #s(literal 1/2 binary64) (sqrt.f64 re)) im))

Calls

1 calls:

3.0ms

re

Results

Accuracy	Segments	Branch
81.6%	3	`re`

Compiler

Compiled 1 to 2 computations (-100% saved)

regimes12.0ms (0.2%)

Memory

18.5MiB live, 18.5MiB allocated

Counts

5 → 2

Calls

Call 1

Inputs
(.f64 #s(literal 1/2 binary64) (sqrt.f64 #s(approx ( 2 (- (sqrt (+ (* re re) (* im im))) re)) (*.f64 #s(literal -4 binary64) re))))
(.f64 #s(literal 1/2 binary64) (sqrt.f64 #s(approx ( 2 (- (sqrt (+ (* re re) (* im im))) re)) (*.f64 #s(literal 2 binary64) im))))
(.f64 (sqrt.f64 #s(approx ( (- (sqrt (+ (* im im) (* re re))) re) 2) (*.f64 #s(literal 2 binary64) im))) #s(literal 1/2 binary64))
(.f64 #s(literal 1/2 binary64) (sqrt.f64 (.f64 #s(literal 2 binary64) #s(approx (- (sqrt (+ (* re re) (* im im))) re) (-.f64 im re)))))
(.f64 (sqrt.f64 (.f64 #s(approx (- (sqrt (+ (* im im) (* re re))) re) (-.f64 im re)) #s(literal 2 binary64))) #s(literal 1/2 binary64))

Outputs

(*.f64 #s(literal 1/2 binary64) (sqrt.f64 #s(approx (* 2 (- (sqrt (+ (* re re) (* im im))) re)) (*.f64 #s(literal -4 binary64) re))))

(*.f64 #s(literal 1/2 binary64) (sqrt.f64 #s(approx (* 2 (- (sqrt (+ (* re re) (* im im))) re)) (*.f64 #s(literal 2 binary64) im))))

Calls

5 calls:

2.0ms	re
2.0ms	(.f64 #s(literal 1/2 binary64) (sqrt.f64 (.f64 #s(literal 2 binary64) (-.f64 (sqrt.f64 (+.f64 (.f64 re re) (.f64 im im))) re))))
2.0ms	(sqrt.f64 (.f64 #s(literal 2 binary64) (-.f64 (sqrt.f64 (+.f64 (.f64 re re) (*.f64 im im))) re)))
2.0ms	(.f64 #s(literal 2 binary64) (-.f64 (sqrt.f64 (+.f64 (.f64 re re) (*.f64 im im))) re))
2.0ms	(-.f64 (sqrt.f64 (+.f64 (.f64 re re) (.f64 im im))) re)

Results

Accuracy	Segments	Branch
53.6%	1	`(.f64 #s(literal 2 binary64) (-.f64 (sqrt.f64 (+.f64 (.f64 re re) (*.f64 im im))) re))`
53.6%	1	`(-.f64 (sqrt.f64 (+.f64 (.f64 re re) (.f64 im im))) re)`
53.6%	1	`(.f64 #s(literal 1/2 binary64) (sqrt.f64 (.f64 #s(literal 2 binary64) (-.f64 (sqrt.f64 (+.f64 (.f64 re re) (.f64 im im))) re))))`
53.6%	1	`(sqrt.f64 (.f64 #s(literal 2 binary64) (-.f64 (sqrt.f64 (+.f64 (.f64 re re) (*.f64 im im))) re)))`
65.8%	2	`re`

Compiler

Compiled 51 to 40 computations (21.6% saved)

regimes41.0ms (0.6%)

Memory

-22.8MiB live, 17.6MiB allocated

Accuracy

Total 0.0b remaining (0%)

Threshold costs 0b (0%)

Counts

1 → 1

Calls

Call 1

Inputs
(.f64 #s(literal 1/2 binary64) (sqrt.f64 #s(approx ( 2 (- (sqrt (+ (* re re) (* im im))) re)) (*.f64 #s(literal -4 binary64) re))))

Outputs
(.f64 #s(literal 1/2 binary64) (sqrt.f64 #s(approx ( 2 (- (sqrt (+ (* re re) (* im im))) re)) (*.f64 #s(literal -4 binary64) re))))

Calls

7 calls:

32.0ms	(sqrt.f64 (.f64 #s(literal 2 binary64) (-.f64 (sqrt.f64 (+.f64 (.f64 re re) (*.f64 im im))) re)))
1.0ms	(.f64 #s(literal 1/2 binary64) (sqrt.f64 (.f64 #s(literal 2 binary64) (-.f64 (sqrt.f64 (+.f64 (.f64 re re) (.f64 im im))) re))))
1.0ms	re
1.0ms	im
1.0ms	(.f64 #s(literal 2 binary64) (-.f64 (sqrt.f64 (+.f64 (.f64 re re) (*.f64 im im))) re))

Results

Accuracy	Segments	Branch
28.1%	1	`(.f64 #s(literal 1/2 binary64) (sqrt.f64 (.f64 #s(literal 2 binary64) (-.f64 (sqrt.f64 (+.f64 (.f64 re re) (.f64 im im))) re))))`
28.1%	1	`(sqrt.f64 (.f64 #s(literal 2 binary64) (-.f64 (sqrt.f64 (+.f64 (.f64 re re) (*.f64 im im))) re)))`
28.1%	1	`(.f64 #s(literal 2 binary64) (-.f64 (sqrt.f64 (+.f64 (.f64 re re) (*.f64 im im))) re))`
28.1%	1	`(-.f64 (sqrt.f64 (+.f64 (.f64 re re) (.f64 im im))) re)`
28.1%	1	`(*.f64 im im)`
28.1%	1	`im`
28.1%	1	`re`

Compiler

Compiled 55 to 45 computations (18.2% saved)

bsearch23.0ms (0.3%)

Memory

26.9MiB live, 26.9MiB allocated

Algorithm

1×	binary-search

Stop Event

1×	narrow-enough

Steps

Time	Left	Right
21.0ms	2.4206010711984968e-43	6.599658330427372e-34

Samples

6.0ms	91×	0	valid
5.0ms	29×	2	valid
3.0ms	23×	1	valid
0.0ms	1×	3	valid

Compiler

Compiled 324 to 284 computations (12.3% saved)

Precisions

Click to see histograms. Total time spent on operations: 10.0ms

ival-hypot: 4.0ms (38.5% of total)

ival-mult: 2.0ms (19.2% of total)

ival-sqrt: 2.0ms (19.2% of total)

adjust: 1.0ms (9.6% of total)

ival-sub: 1.0ms (9.6% of total)

ival-assert: 0.0ms (0% of total)

ival-true: 0.0ms (0% of total)

exact: 0.0ms (0% of total)

bsearch28.0ms (0.4%)

Memory

-16.6MiB live, 22.4MiB allocated

Algorithm

2×	binary-search

Stop Event

1×	narrow-enough
1×	narrow-enough

Steps

Time	Left	Right
1.0ms	2.4206010711984968e-43	6.599658330427372e-34
25.0ms	-3.046502773812066e+116	-3.783392661007313e+107

Samples

19.0ms

144×

valid

Compiler

Compiled 765 to 626 computations (18.2% saved)

Precisions

Click to see histograms. Total time spent on operations: 15.0ms

ival-hypot: 12.0ms (78.6% of total)

ival-mult: 2.0ms (13.1% of total)

ival-sub: 1.0ms (6.5% of total)

ival-sqrt: 1.0ms (6.5% of total)

ival-true: 0.0ms (0% of total)

exact: 0.0ms (0% of total)

ival-assert: 0.0ms (0% of total)

bsearch3.0ms (0%)

Memory

4.5MiB live, 4.5MiB allocated

Algorithm

2×	binary-search

Stop Event

1×	narrow-enough
1×	narrow-enough

Steps

Time	Left	Right
1.0ms	2.4206010711984968e-43	6.599658330427372e-34
1.0ms	-3.046502773812066e+116	-3.783392661007313e+107

Compiler

Compiled 747 to 608 computations (18.6% saved)

bsearch3.0ms (0%)

Memory

4.5MiB live, 4.5MiB allocated

Algorithm

2×	binary-search

Stop Event

1×	narrow-enough
1×	narrow-enough

Steps

Time	Left	Right
1.0ms	2.4206010711984968e-43	6.599658330427372e-34
1.0ms	-3.046502773812066e+116	-3.783392661007313e+107

Compiler

Compiled 729 to 590 computations (19.1% saved)

bsearch3.0ms (0%)

Memory

4.3MiB live, 4.3MiB allocated

Algorithm

2×	binary-search

Stop Event

1×	narrow-enough
1×	narrow-enough

Steps

Time	Left	Right
1.0ms	2.4206010711984968e-43	6.599658330427372e-34
1.0ms	-3.046502773812066e+116	-3.783392661007313e+107

Compiler

Compiled 729 to 590 computations (19.1% saved)

bsearch31.0ms (0.4%)

Memory

-13.8MiB live, 25.3MiB allocated

Algorithm

1×	binary-search

Stop Event

1×	narrow-enough

Steps

Time	Left	Right
29.0ms	-0.2767695399033431	-1.0309862892243928e-22

Samples

12.0ms

176×

valid

Compiler

Compiled 436 to 366 computations (16.1% saved)

Precisions

Click to see histograms. Total time spent on operations: 7.0ms

ival-hypot: 3.0ms (40% of total)

ival-mult: 2.0ms (26.7% of total)

ival-sub: 1.0ms (13.3% of total)

ival-sqrt: 1.0ms (13.3% of total)

ival-true: 0.0ms (0% of total)

exact: 0.0ms (0% of total)

ival-assert: 0.0ms (0% of total)

simplify34.0ms (0.5%)

Memory

0.6MiB live, 39.8MiB allocated

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	64	376
1	83	376
2	88	376
3	90	376
4	91	376

Stop Event

1×

saturated

Calls

Call 1

Inputs
(if (<=.f64 re #s(literal 5378326025377723/23384026197294446691258957323460528314494920687616 binary64)) (.f64 (sqrt.f64 (.f64 (-.f64 (hypot.f64 im re) re) #s(literal 2 binary64))) #s(literal 1/2 binary64)) #s(approx (* 1/2 (sqrt (* 2 (- (sqrt (+ (* re re) (* im im))) re)))) (.f64 (.f64 im #s(literal 1/2 binary64)) (sqrt.f64 (/.f64 #s(literal 1 binary64) re)))))
(if (<=.f64 re #s(literal -94999999999999997232870298406541298545373491695516008397252966957081828940906596263511907052906414358602448896 binary64)) (.f64 #s(literal 1/2 binary64) (sqrt.f64 #s(approx ( 2 (- (sqrt (+ (* re re) (* im im))) re)) (.f64 #s(literal -4 binary64) re)))) (if (<=.f64 re #s(literal 5378326025377723/23384026197294446691258957323460528314494920687616 binary64)) (.f64 (.f64 (sqrt.f64 #s(approx (- (sqrt (+ ( re re) (* im im))) re) (-.f64 im re))) (sqrt.f64 #s(literal 2 binary64))) #s(literal 1/2 binary64)) #s(approx (* 1/2 (sqrt (* 2 (- (sqrt (+ (* re re) (* im im))) re)))) (.f64 (.f64 im #s(literal 1/2 binary64)) (sqrt.f64 (/.f64 #s(literal 1 binary64) re))))))
(if (<=.f64 re #s(literal -94999999999999997232870298406541298545373491695516008397252966957081828940906596263511907052906414358602448896 binary64)) (.f64 #s(literal 1/2 binary64) (sqrt.f64 #s(approx ( 2 (- (sqrt (+ (* re re) (* im im))) re)) (.f64 #s(literal -4 binary64) re)))) (if (<=.f64 re #s(literal 5378326025377723/23384026197294446691258957323460528314494920687616 binary64)) (.f64 #s(literal 1/2 binary64) (sqrt.f64 (.f64 #s(literal 2 binary64) #s(approx (- (sqrt (+ ( re re) (* im im))) re) (-.f64 im re))))) #s(approx (* 1/2 (sqrt (* 2 (- (sqrt (+ (* re re) (* im im))) re)))) (.f64 (.f64 im #s(literal 1/2 binary64)) (sqrt.f64 (/.f64 #s(literal 1 binary64) re))))))
(if (<=.f64 re #s(literal -94999999999999997232870298406541298545373491695516008397252966957081828940906596263511907052906414358602448896 binary64)) (.f64 #s(literal 1/2 binary64) (sqrt.f64 #s(approx ( 2 (- (sqrt (+ (* re re) (* im im))) re)) (.f64 #s(literal -4 binary64) re)))) (if (<=.f64 re #s(literal 5378326025377723/23384026197294446691258957323460528314494920687616 binary64)) (.f64 #s(literal 1/2 binary64) (sqrt.f64 (.f64 #s(literal 2 binary64) #s(approx (- (sqrt (+ ( re re) (* im im))) re) (-.f64 im re))))) #s(approx (* 1/2 (sqrt (* 2 (- (sqrt (+ (* re re) (* im im))) re)))) (/.f64 (*.f64 #s(literal 1/2 binary64) im) (sqrt.f64 re)))))
(if (<=.f64 re #s(literal -94999999999999997232870298406541298545373491695516008397252966957081828940906596263511907052906414358602448896 binary64)) (.f64 #s(literal 1/2 binary64) (sqrt.f64 #s(approx ( 2 (- (sqrt (+ (* re re) (* im im))) re)) (.f64 #s(literal -4 binary64) re)))) (if (<=.f64 re #s(literal 5378326025377723/23384026197294446691258957323460528314494920687616 binary64)) (.f64 #s(literal 1/2 binary64) (sqrt.f64 (.f64 #s(literal 2 binary64) #s(approx (- (sqrt (+ ( re re) (* im im))) re) (-.f64 im re))))) #s(approx (* 1/2 (sqrt (* 2 (- (sqrt (+ (* re re) (* im im))) re)))) (*.f64 (/.f64 #s(literal 1/2 binary64) (sqrt.f64 re)) im))))
(if (<=.f64 re #s(literal -6611313076017503/4722366482869645213696 binary64)) (.f64 #s(literal 1/2 binary64) (sqrt.f64 #s(approx ( 2 (- (sqrt (+ (* re re) (* im im))) re)) (.f64 #s(literal -4 binary64) re)))) (.f64 #s(literal 1/2 binary64) (sqrt.f64 #s(approx (* 2 (- (sqrt (+ (* re re) (* im im))) re)) (*.f64 #s(literal 2 binary64) im)))))
(.f64 #s(literal 1/2 binary64) (sqrt.f64 #s(approx ( 2 (- (sqrt (+ (* re re) (* im im))) re)) (*.f64 #s(literal -4 binary64) re))))

Outputs
(if (<=.f64 re #s(literal 5378326025377723/23384026197294446691258957323460528314494920687616 binary64)) (.f64 #s(literal 1/2 binary64) (sqrt.f64 (.f64 #s(literal 2 binary64) (-.f64 (hypot.f64 im re) re)))) #s(approx (* 1/2 (sqrt (* 2 (- (sqrt (+ (* re re) (* im im))) re)))) (.f64 (.f64 #s(literal 1/2 binary64) im) (sqrt.f64 (/.f64 #s(literal 1 binary64) re)))))
(if (<=.f64 re #s(literal -94999999999999997232870298406541298545373491695516008397252966957081828940906596263511907052906414358602448896 binary64)) (.f64 (sqrt.f64 #s(approx ( 2 (- (sqrt (+ (* re re) (* im im))) re)) (.f64 #s(literal -4 binary64) re))) #s(literal 1/2 binary64)) (if (<=.f64 re #s(literal 5378326025377723/23384026197294446691258957323460528314494920687616 binary64)) (.f64 (.f64 (sqrt.f64 #s(literal 2 binary64)) (sqrt.f64 #s(approx (- (sqrt (+ ( re re) (* im im))) re) (-.f64 im re)))) #s(literal 1/2 binary64)) #s(approx (* 1/2 (sqrt (* 2 (- (sqrt (+ (* re re) (* im im))) re)))) (.f64 (.f64 #s(literal 1/2 binary64) im) (sqrt.f64 (/.f64 #s(literal 1 binary64) re))))))
(if (<=.f64 re #s(literal -94999999999999997232870298406541298545373491695516008397252966957081828940906596263511907052906414358602448896 binary64)) (.f64 (sqrt.f64 #s(approx ( 2 (- (sqrt (+ (* re re) (* im im))) re)) (.f64 #s(literal -4 binary64) re))) #s(literal 1/2 binary64)) (if (<=.f64 re #s(literal 5378326025377723/23384026197294446691258957323460528314494920687616 binary64)) (.f64 (sqrt.f64 (.f64 #s(approx (- (sqrt (+ ( re re) (* im im))) re) (-.f64 im re)) #s(literal 2 binary64))) #s(literal 1/2 binary64)) #s(approx (* 1/2 (sqrt (* 2 (- (sqrt (+ (* re re) (* im im))) re)))) (.f64 (.f64 #s(literal 1/2 binary64) im) (sqrt.f64 (/.f64 #s(literal 1 binary64) re))))))
(if (<=.f64 re #s(literal -94999999999999997232870298406541298545373491695516008397252966957081828940906596263511907052906414358602448896 binary64)) (.f64 (sqrt.f64 #s(approx ( 2 (- (sqrt (+ (* re re) (* im im))) re)) (.f64 #s(literal -4 binary64) re))) #s(literal 1/2 binary64)) (if (<=.f64 re #s(literal 5378326025377723/23384026197294446691258957323460528314494920687616 binary64)) (.f64 (sqrt.f64 (.f64 #s(approx (- (sqrt (+ ( re re) (* im im))) re) (-.f64 im re)) #s(literal 2 binary64))) #s(literal 1/2 binary64)) #s(approx (* 1/2 (sqrt (* 2 (- (sqrt (+ (* re re) (* im im))) re)))) (/.f64 (*.f64 #s(literal 1/2 binary64) im) (sqrt.f64 re)))))
(if (<=.f64 re #s(literal -94999999999999997232870298406541298545373491695516008397252966957081828940906596263511907052906414358602448896 binary64)) (.f64 (sqrt.f64 #s(approx ( 2 (- (sqrt (+ (* re re) (* im im))) re)) (.f64 #s(literal -4 binary64) re))) #s(literal 1/2 binary64)) (if (<=.f64 re #s(literal 5378326025377723/23384026197294446691258957323460528314494920687616 binary64)) (.f64 (sqrt.f64 (.f64 #s(approx (- (sqrt (+ ( re re) (* im im))) re) (-.f64 im re)) #s(literal 2 binary64))) #s(literal 1/2 binary64)) #s(approx (* 1/2 (sqrt (* 2 (- (sqrt (+ (* re re) (* im im))) re)))) (*.f64 (/.f64 #s(literal 1/2 binary64) (sqrt.f64 re)) im))))
(if (<=.f64 re #s(literal -6611313076017503/4722366482869645213696 binary64)) (.f64 (sqrt.f64 #s(approx ( 2 (- (sqrt (+ (* re re) (* im im))) re)) (.f64 #s(literal -4 binary64) re))) #s(literal 1/2 binary64)) (.f64 (sqrt.f64 #s(approx (* 2 (- (sqrt (+ (* re re) (* im im))) re)) (*.f64 #s(literal 2 binary64) im))) #s(literal 1/2 binary64)))
(.f64 (sqrt.f64 #s(approx ( 2 (- (sqrt (+ (* re re) (* im im))) re)) (*.f64 #s(literal -4 binary64) re))) #s(literal 1/2 binary64))

soundness871.0ms (12.1%)

Memory

-0.3MiB live, 592.6MiB allocated

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	47	329
0	76	279
1	214	274
2	1073	255
0	8351	255
0	551	3257
1	1814	3103
2	6380	3088
0	8199	2913
0	667	11045
1	2184	10318
2	7562	10296
0	8321	9875
0	12	65
0	20	65
1	56	65
2	374	65
3	4192	65
0	8391	38
0	45	226
0	72	182
1	201	173
2	1021	173
0	9859	173

Stop Event

1×	fuel
1×	iter limit
1×	node limit
1×	iter limit
1×	iter limit
1×	node limit
1×	iter limit
1×	iter limit
1×	node limit
1×	iter limit
1×	node limit
1×	iter limit
1×	node limit
1×	iter limit

Compiler

Compiled 837 to 411 computations (50.9% saved)

preprocess62.0ms (0.9%)

Memory: 6.1MiB live, 127.7MiB allocated
Remove: (abs im)
Compiler: Compiled 934 to 266 computations (71.5% saved)

end0.0ms (0%)

Memory: 0.0MiB live, 0.0MiB allocated

Iter	Nodes	Cost
0	30	77
1	71	75
2	152	75
3	285	75
4	424	75
5	515	75
6	637	75
7	775	75
8	830	75
0	12	15
0	20	15
1	25	15
2	36	15
3	52	15
4	73	15
5	98	15
6	154	15
7	227	15
8	310	15
9	360	15
10	420	15
11	434	15
12	450	15
13	470	15
14	500	15
15	531	15
16	543	15
17	545	15
0	545	10

Iter	Nodes	Cost
0	12	75
0	20	75
1	25	75
2	36	75
3	52	75
4	73	75
5	98	75
6	154	75
7	227	75
8	310	75
9	360	75
10	420	75
11	434	75
12	450	75
13	470	75
14	500	75
15	531	75
16	543	75
17	545	75
0	545	49

Iter	Nodes	Cost
0	30	77
1	71	75
2	152	75
3	285	75
4	424	75
5	515	75
6	637	75
7	775	75
8	830	75
0	12	15
0	20	15
1	25	15
2	36	15
3	52	15
4	73	15
5	98	15
6	154	15
7	227	15
8	310	15
9	360	15
10	420	15
11	434	15
12	450	15
13	470	15
14	500	15
15	531	15
16	543	15
17	545	15
0	545	10

Iter	Nodes	Cost
0	12	75
0	20	75
1	25	75
2	36	75
3	52	75
4	73	75
5	98	75
6	154	75
7	227	75
8	310	75
9	360	75
10	420	75
11	434	75
12	450	75
13	470	75
14	500	75
15	531	75
16	543	75
17	545	75
0	545	49

start0.0ms (0%)

analyze98.0ms (1.4%)

sample1.5s (21.2%)

explain225.0ms (3.1%)

preprocess68.0ms (0.9%)

eval0.0ms (0%)

prune1.0ms (0%)

simplify32.0ms (0.5%)

localize78.0ms (1.1%)

series335.0ms (4.7%)

simplify181.0ms (2.5%)

rewrite179.0ms (2.5%)

eval102.0ms (1.4%)

prune25.0ms (0.4%)

simplify115.0ms (1.6%)

localize142.0ms (2%)

series78.0ms (1.1%)

simplify236.0ms (3.3%)

rewrite180.0ms (2.5%)

eval143.0ms (2%)

prune51.0ms (0.7%)

simplify109.0ms (1.5%)

localize157.0ms (2.2%)

series75.0ms (1%)

simplify259.0ms (3.6%)

rewrite179.0ms (2.5%)

eval169.0ms (2.3%)

prune69.0ms (1%)

simplify172.0ms (2.4%)

localize286.0ms (4%)

series68.0ms (0.9%)

simplify234.0ms (3.2%)

rewrite110.0ms (1.5%)

eval167.0ms (2.3%)

prune50.0ms (0.7%)

regimes117.0ms (1.6%)

regimes55.0ms (0.8%)

regimes5.0ms (0.1%)

regimes15.0ms (0.2%)

regimes3.0ms (0%)

regimes12.0ms (0.2%)

regimes41.0ms (0.6%)

bsearch23.0ms (0.3%)

bsearch28.0ms (0.4%)

bsearch3.0ms (0%)

bsearch3.0ms (0%)

bsearch3.0ms (0%)

bsearch31.0ms (0.4%)

simplify34.0ms (0.5%)

soundness871.0ms (12.1%)

preprocess62.0ms (0.9%)

end0.0ms (0%)

Profiling

Iter	Nodes	Cost
0	30	77
1	71	75
2	152	75
3	285	75
4	424	75
5	515	75
6	637	75
7	775	75
8	830	75
0	12	15
0	20	15
1	25	15
2	36	15
3	52	15
4	73	15
5	98	15
6	154	15
7	227	15
8	310	15
9	360	15
10	420	15
11	434	15
12	450	15
13	470	15
14	500	15
15	531	15
16	543	15
17	545	15
0	545	10

Iter	Nodes	Cost
0	12	75
0	20	75
1	25	75
2	36	75
3	52	75
4	73	75
5	98	75
6	154	75
7	227	75
8	310	75
9	360	75
10	420	75
11	434	75
12	450	75
13	470	75
14	500	75
15	531	75
16	543	75
17	545	75
0	545	49