Metrics for math.sqrt on complex, real part

start0.0ms (0%)

Memory: 0.3MiB live, 0.3MiB allocated

analyze183.0ms (2.2%)

Memory

-34.0MiB live, 183.9MiB allocated

Algorithm

1×

Search

Probability	Valid	Unknown	Precondition	Infinite	Domain	Can't	Iter
0%	0%	99.9%	0.1%	0%	0%	0%	0
0%	0%	99.9%	0.1%	0%	0%	0%	1
50%	50%	50%	0.1%	0%	0%	0%	2
50%	50%	50%	0.1%	0%	0%	0%	3
50%	50%	50%	0.1%	0%	0%	0%	4
62.5%	62.4%	37.5%	0.1%	0%	0%	0%	5
62.5%	62.4%	37.5%	0.1%	0%	0%	0%	6
68.8%	68.7%	31.2%	0.1%	0%	0%	0%	7
68.8%	68.7%	31.2%	0.1%	0%	0%	0%	8
71.9%	71.8%	28.1%	0.1%	0%	0%	0%	9
71.9%	71.8%	28.1%	0.1%	0%	0%	0%	10
73.4%	73.4%	26.5%	0.1%	0%	0%	0%	11
73.4%	73.4%	26.5%	0.1%	0%	0%	0%	12

Compiler

Compiled 17 to 11 computations (35.3% saved)

sample1.6s (18.6%)

Memory

62.3MiB live, 1 963.0MiB allocated

Samples

504.0ms	6 268×	0	valid
421.0ms	413×	3	valid
157.0ms	799×	2	valid
115.0ms	776×	1	valid

Precisions

Click to see histograms. Total time spent on operations: 889.0ms

ival-hypot: 527.0ms (59.3% of total)

ival-mult: 159.0ms (17.9% of total)

ival-sqrt: 88.0ms (9.9% of total)

ival-add: 59.0ms (6.6% of total)

adjust: 37.0ms (4.2% of total)

exact: 8.0ms (0.9% of total)

ival-true: 7.0ms (0.8% of total)

ival-assert: 4.0ms (0.5% of total)

Bogosity

explain210.0ms (2.5%)

Memory

47.8MiB live, 382.5MiB allocated

FPErrors

Click to see full error table

Ground Truth	Example	Underpredictions	Example	Subexpression
136	-	0	-	`(sqrt.f64 (+.f64 (.f64 re re) (.f64 im im)))`
29	-	0	-	`(+.f64 (sqrt.f64 (+.f64 (.f64 re re) (.f64 im im))) re)`
24	-	1	(-1.3877954642078258e+202 7.705536477537309e-55)	`(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 re re)`
0	-	0	-	`im`
0	-	0	-	`(+.f64 (.f64 re re) (.f64 im im))`
0	-	0	-	`#s(literal 2 binary64)`
0	-	0	-	`(.f64 #s(literal 2 binary64) (+.f64 (sqrt.f64 (+.f64 (.f64 re re) (*.f64 im im))) re))`
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	116	0
↳	`(+.f64 (.f64 re re) (.f64 im im))`	overflow	116
↳	`(*.f64 re re)`	overflow	75
↳	`(*.f64 im im)`	overflow	60
`+.f64`	`(+.f64 (sqrt.f64 (+.f64 (.f64 re re) (.f64 im im))) re)`	cancellation	29	0
`sqrt.f64`	`(sqrt.f64 (.f64 #s(literal 2 binary64) (+.f64 (sqrt.f64 (+.f64 (.f64 re re) (*.f64 im im))) re)))`	uflow-rescue	20	0
↳	`(+.f64 (.f64 re re) (.f64 im im))`	underflow	20
↳	`(*.f64 im im)`	underflow	76
↳	`(sqrt.f64 (.f64 #s(literal 2 binary64) (+.f64 (sqrt.f64 (+.f64 (.f64 re re) (*.f64 im im))) re)))`	underflow	11
↳	`(.f64 #s(literal 2 binary64) (+.f64 (sqrt.f64 (+.f64 (.f64 re re) (*.f64 im im))) re))`	underflow	31
↳	`(*.f64 re re)`	underflow	60
↳	`(+.f64 (sqrt.f64 (+.f64 (.f64 re re) (.f64 im im))) re)`	underflow	31
`sqrt.f64`	`(sqrt.f64 (+.f64 (.f64 re re) (.f64 im im)))`	uflow-rescue	20	0
↳	`(+.f64 (.f64 re re) (.f64 im im))`	underflow	20
↳	`(*.f64 re re)`	underflow	60
↳	`(*.f64 im im)`	underflow	76
`sqrt.f64`	`(sqrt.f64 (.f64 #s(literal 2 binary64) (+.f64 (sqrt.f64 (+.f64 (.f64 re re) (*.f64 im im))) re)))`	oflow-rescue	3	0
↳	`(+.f64 (.f64 re re) (.f64 im im))`	overflow	116
↳	`(*.f64 re re)`	overflow	75
↳	`(*.f64 im im)`	overflow	60
↳	`(.f64 #s(literal 2 binary64) (+.f64 (sqrt.f64 (+.f64 (.f64 re re) (*.f64 im im))) re))`	overflow	3

Confusion

	Predicted +	Predicted -
+	157	0
-	0	99

Precision

1.0

Recall

1.0

Confusion?

	Predicted +	Predicted Maybe	Predicted -
+	157	0	0
-	0	0	99

Precision?

1.0

Recall?

1.0

Freqs

test

number	freq
0	99
1	126
2	31

Total Confusion?

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

Precision?

1.0

Recall?

1.0

Samples

49.0ms	394×	0	valid
26.0ms	36×	3	valid
15.0ms	42×	2	valid
7.0ms	40×	1	valid

Compiler

Compiled 244 to 52 computations (78.7% saved)

Precisions

Click to see histograms. Total time spent on operations: 60.0ms

ival-hypot: 28.0ms (46.9% of total)

ival-mult: 15.0ms (25.1% of total)

ival-add: 6.0ms (10.1% of total)

ival-sqrt: 5.0ms (8.4% of total)

adjust: 4.0ms (6.7% of total)

exact: 1.0ms (1.7% of total)

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

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

preprocess123.0ms (1.5%)

Memory

-10.9MiB live, 23.4MiB allocated

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	30	75
1	94	75
2	169	75
3	259	75
4	396	75
5	523	75
6	645	75
7	745	75
8	773	75
0	12	15
0	20	15
1	30	15
2	32	15
0	32	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: 0.4MiB live, 0.4MiB 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
▶	41.6%	(.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)

simplify3.0ms (0%)

Memory

5.1MiB live, 5.1MiB 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	30	75
2	32	75
0	32	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

localize237.0ms (2.8%)

Memory

10.1MiB live, 81.1MiB allocated

Localize:

Found 4 expressions of interest:

New	Metric	Score
accuracy	0.00390625	(+.f64 (.f64 re re) (.f64 im im))
accuracy	5.281846752426357	(sqrt.f64 (.f64 #s(literal 2 binary64) (+.f64 (sqrt.f64 (+.f64 (.f64 re re) (*.f64 im im))) re)))
accuracy	6.582561687117777	(+.f64 (sqrt.f64 (+.f64 (.f64 re re) (.f64 im im))) re)
accuracy	31.480211570230413	(sqrt.f64 (+.f64 (.f64 re re) (.f64 im im)))

Samples

212.0ms	197×	0	valid
7.0ms	18×	3	valid
6.0ms	21×	2	valid
4.0ms	20×	1	valid

Compiler

Compiled 152 to 26 computations (82.9% saved)

Precisions

Click to see histograms. Total time spent on operations: 217.0ms

ival-mult: 118.0ms (54.4% of total)

ival-hypot: 90.0ms (41.5% of total)

ival-sqrt: 3.0ms (1.4% of total)

ival-add: 3.0ms (1.4% of total)

adjust: 2.0ms (0.9% of total)

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

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

exact: 0.0ms (0% of total)

series92.0ms (1.1%)

Memory

-0.4MiB live, 63.5MiB 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>) () ())) ())
#s(alt #<batchref> (taylor inf 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 (sqrt.f64 (+.f64 (.f64 re re) (.f64 im im))) re) #<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>) () ())) ())
#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>) () ())) ())
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#s(alt #<batchref> (taylor 0 im) (#s(alt #<batchref> (patch (sqrt.f64 (.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 (.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>) () ())) ())
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#s(alt #<batchref> (taylor -inf im) (#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 im) (#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 im) (#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 im) (#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 im) (#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 im) (#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 im) (#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 im) (#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 im) (#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 im) (#s(alt #<batchref> (patch (sqrt.f64 (+.f64 (.f64 re re) (.f64 im im))) #<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 (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
30.0ms	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))
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))
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))
2.0ms	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))

simplify368.0ms (4.4%)

Memory

-8.3MiB live, 325.9MiB allocated

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	500	3104
1	1659	2919
2	5910	2897
0	8080	2716

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 (+ (* 1/16 (* (sqrt (/ 1 (pow im 3))) (* re (sqrt 2)))) (* 1/4 (* (sqrt (/ 1 im)) (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 (+ (* 1/8 (* (sqrt (/ 1 (pow im 3))) (* re (sqrt 2)))) (* 1/2 (* (sqrt (/ 1 im)) (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 im) (* 2 re))
(+ (* 2 im) (* re (+ 2 (/ re im))))
(+ (* 2 im) (* re (+ 2 (* re (+ (* -1/4 (/ (pow re 2) (pow im 3))) (/ 1 im))))))
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 re)
(+ im (* re (+ 1 (* 1/2 (/ re im)))))
(+ im (* re (+ 1 (* re (+ (* -1/8 (/ (pow re 2) (pow im 3))) (* 1/2 (/ 1 im)))))))
(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) (pow (sqrt 2) 2)))
(* re (+ (* 1/8 (* (pow im 2) (sqrt (/ 1 (pow re 5))))) (* 1/2 (* (sqrt (/ 1 re)) (pow (sqrt 2) 2)))))
(* re (+ (* -1/32 (* (pow im 4) (sqrt (/ 1 (pow re 9))))) (+ (* 1/8 (* (pow im 2) (sqrt (/ 1 (pow re 5))))) (* 1/2 (* (sqrt (/ 1 re)) (pow (sqrt 2) 2))))))
(* re (+ (* -1/32 (* (pow im 4) (sqrt (/ 1 (pow re 9))))) (+ (* -1/64 (* (/ (pow im 4) (pow (sqrt 2) 2)) (sqrt (/ 1 (pow re 9))))) (+ (* 1/8 (* (pow im 2) (sqrt (/ 1 (pow re 5))))) (* 1/2 (* (sqrt (/ 1 re)) (pow (sqrt 2) 2)))))))
(* (sqrt re) (pow (sqrt 2) 2))
(* re (+ (* 1/4 (* (pow im 2) (sqrt (/ 1 (pow re 5))))) (* (sqrt (/ 1 re)) (pow (sqrt 2) 2))))
(* re (+ (* -1/16 (* (pow im 4) (sqrt (/ 1 (pow re 9))))) (+ (* 1/4 (* (pow im 2) (sqrt (/ 1 (pow re 5))))) (* (sqrt (/ 1 re)) (pow (sqrt 2) 2)))))
(* re (+ (* -1/16 (* (pow im 4) (sqrt (/ 1 (pow re 9))))) (+ (* -1/32 (* (/ (pow im 4) (pow (sqrt 2) 2)) (sqrt (/ 1 (pow re 9))))) (+ (* 1/4 (* (pow im 2) (sqrt (/ 1 (pow re 5))))) (* (sqrt (/ 1 re)) (pow (sqrt 2) 2))))))
(* 4 re)
(* re (+ 4 (/ (pow im 2) (pow re 2))))
(* re (+ 4 (+ (* -1/4 (/ (pow im 4) (pow re 4))) (/ (pow im 2) (pow re 2)))))
(* re (+ 4 (+ (* -1/4 (/ (pow im 4) (pow re 4))) (+ (* 1/8 (/ (pow im 6) (pow re 6))) (/ (pow im 2) (pow re 2))))))
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)
(* re (+ 2 (* 1/2 (/ (pow im 2) (pow re 2)))))
(* re (+ 2 (+ (* -1/8 (/ (pow im 4) (pow re 4))) (* 1/2 (/ (pow im 2) (pow re 2))))))
(* 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 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) (* (sqrt 1/2) (sqrt 2)))) (sqrt (/ 1 re))))
(+ (* 1/32 (* (/ (* (pow im 3) (* (sqrt -1) (sqrt 2))) (sqrt 1/2)) (sqrt (/ 1 (pow re 5))))) (* 1/2 (* (* im (* (sqrt -1) (* (sqrt 1/2) (sqrt 2)))) (sqrt (/ 1 re)))))
(+ (* -1 (/ (+ (* -1/32 (* (/ (* (pow im 3) (* (sqrt -1) (sqrt 2))) (sqrt 1/2)) (sqrt re))) (* 1/64 (* (/ (* (pow im 5) (* (sqrt -1) (sqrt 2))) (sqrt 1/2)) (sqrt (/ 1 (pow re 3)))))) (pow re 3))) (* 1/2 (* (* im (* (sqrt -1) (* (sqrt 1/2) (sqrt 2)))) (sqrt (/ 1 re)))))
(+ (* -1 (/ (+ (* -1/32 (* (/ (* (pow im 3) (* (sqrt -1) (sqrt 2))) (sqrt 1/2)) (sqrt re))) (+ (* 1/1024 (* (/ (* (pow im 5) (* (sqrt -1) (sqrt 2))) (pow (sqrt 1/2) 3)) (sqrt (/ 1 (pow re 3))))) (* 1/64 (* (/ (* (pow im 5) (* (sqrt -1) (sqrt 2))) (sqrt 1/2)) (sqrt (/ 1 (pow re 3))))))) (pow re 3))) (* 1/2 (* (* im (* (sqrt -1) (* (sqrt 1/2) (sqrt 2)))) (sqrt (/ 1 re)))))
(* (* im (* (sqrt -1) (* (sqrt 1/2) (sqrt 2)))) (sqrt (/ 1 re)))
(+ (* 1/16 (* (/ (* (pow im 3) (* (sqrt -1) (sqrt 2))) (sqrt 1/2)) (sqrt (/ 1 (pow re 5))))) (* (* im (* (sqrt -1) (* (sqrt 1/2) (sqrt 2)))) (sqrt (/ 1 re))))
(+ (* -1 (/ (+ (* -1/16 (* (/ (* (pow im 3) (* (sqrt -1) (sqrt 2))) (sqrt 1/2)) (sqrt re))) (* 1/32 (* (/ (* (pow im 5) (* (sqrt -1) (sqrt 2))) (sqrt 1/2)) (sqrt (/ 1 (pow re 3)))))) (pow re 3))) (* (* im (* (sqrt -1) (* (sqrt 1/2) (sqrt 2)))) (sqrt (/ 1 re))))
(+ (* -1 (/ (+ (* -1/16 (* (/ (* (pow im 3) (* (sqrt -1) (sqrt 2))) (sqrt 1/2)) (sqrt re))) (+ (* 1/512 (* (/ (* (pow im 5) (* (sqrt -1) (sqrt 2))) (pow (sqrt 1/2) 3)) (sqrt (/ 1 (pow re 3))))) (* 1/32 (* (/ (* (pow im 5) (* (sqrt -1) (sqrt 2))) (sqrt 1/2)) (sqrt (/ 1 (pow re 3))))))) (pow re 3))) (* (* im (* (sqrt -1) (* (sqrt 1/2) (sqrt 2)))) (sqrt (/ 1 re))))
(* -1 (/ (pow im 2) re))
(* -1 (/ (+ (* -1/4 (/ (pow im 4) (pow re 2))) (pow im 2)) re))
(* -1 (/ (+ (* -1/4 (/ (pow im 4) (pow re 2))) (+ (* 1/8 (/ (pow im 6) (pow re 4))) (pow im 2))) re))
(* -1 (/ (+ (* -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 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))
(* -1 (/ (+ (* -1/8 (/ (pow im 4) (pow re 2))) (* 1/2 (pow im 2))) re))
(* -1 (/ (+ (* -1/8 (/ (pow im 4) (pow re 2))) (+ (* 1/16 (/ (pow im 6) (pow re 4))) (* 1/2 (pow im 2)))) re))
(* -1 (/ (+ (* -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 im 2) (pow re 2))
(+ (pow im 2) (pow re 2))
(+ (pow im 2) (pow re 2))
(* 1/2 (* (sqrt re) (pow (sqrt 2) 2)))
(+ (* 1/8 (* (pow im 2) (sqrt (/ 1 (pow re 3))))) (* 1/2 (* (sqrt re) (pow (sqrt 2) 2))))
(+ (* 1/2 (* (sqrt re) (pow (sqrt 2) 2))) (* (pow im 2) (+ (* -1/4 (* (* (pow im 2) (+ (* 1/16 (/ 1 (* (pow re 3) (pow (sqrt 2) 2)))) (* 1/8 (/ 1 (pow re 3))))) (sqrt (/ 1 re)))) (* 1/8 (sqrt (/ 1 (pow re 3)))))))
(+ (* 1/2 (* (sqrt re) (pow (sqrt 2) 2))) (* (pow im 2) (+ (* 1/8 (sqrt (/ 1 (pow re 3)))) (* (pow im 2) (+ (* -1/4 (* (sqrt (/ 1 re)) (+ (* 1/16 (/ 1 (* (pow re 3) (pow (sqrt 2) 2)))) (* 1/8 (/ 1 (pow re 3)))))) (* 1/4 (* (* (pow im 2) (- (* 1/16 (/ 1 (pow re 5))) (* -1/4 (/ (+ (* 1/16 (/ 1 (* (pow re 3) (pow (sqrt 2) 2)))) (* 1/8 (/ 1 (pow re 3)))) (* (pow re 2) (pow (sqrt 2) 2)))))) (sqrt (/ 1 re)))))))))
(* (sqrt re) (pow (sqrt 2) 2))
(+ (* 1/4 (* (pow im 2) (sqrt (/ 1 (pow re 3))))) (* (sqrt re) (pow (sqrt 2) 2)))
(+ (* (sqrt re) (pow (sqrt 2) 2)) (* (pow im 2) (+ (* -1/2 (* (* (pow im 2) (+ (* 1/16 (/ 1 (* (pow re 3) (pow (sqrt 2) 2)))) (* 1/8 (/ 1 (pow re 3))))) (sqrt (/ 1 re)))) (* 1/4 (sqrt (/ 1 (pow re 3)))))))
(+ (* (sqrt re) (pow (sqrt 2) 2)) (* (pow im 2) (+ (* 1/4 (sqrt (/ 1 (pow re 3)))) (* (pow im 2) (+ (* -1/2 (* (sqrt (/ 1 re)) (+ (* 1/16 (/ 1 (* (pow re 3) (pow (sqrt 2) 2)))) (* 1/8 (/ 1 (pow re 3)))))) (* 1/2 (* (* (pow im 2) (- (* 1/16 (/ 1 (pow re 5))) (* -1/4 (/ (+ (* 1/16 (/ 1 (* (pow re 3) (pow (sqrt 2) 2)))) (* 1/8 (/ 1 (pow re 3)))) (* (pow re 2) (pow (sqrt 2) 2)))))) (sqrt (/ 1 re)))))))))
(* 4 re)
(+ (* 4 re) (/ (pow im 2) re))
(+ (* 4 re) (* (pow im 2) (+ (* -1/4 (/ (pow im 2) (pow re 3))) (/ 1 re))))
(+ (* 4 re) (* (pow im 2) (+ (* (pow im 2) (- (* 1/8 (/ (pow im 2) (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)))))
(* 2 re)
(+ (* 1/2 (/ (pow im 2) re)) (* 2 re))
(+ (* 2 re) (* (pow im 2) (+ (* -1/8 (/ (pow im 2) (pow re 3))) (* 1/2 (/ 1 re)))))
(+ (* 2 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) (+ 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 (+ (* 1/8 (* (sqrt (/ 1 (pow im 5))) (* (pow re 2) (sqrt 2)))) (+ (* 1/4 (* (sqrt (/ 1 (pow im 3))) (* re (sqrt 2)))) (* 1/2 (* (sqrt (/ 1 im)) (sqrt 2))))))
(* im (+ (* -1/16 (* (sqrt (/ 1 (pow im 5))) (* (pow re 2) (sqrt 2)))) (+ (* 1/8 (* (sqrt (/ 1 (pow im 5))) (* (pow re 2) (sqrt 2)))) (+ (* 1/4 (* (sqrt (/ 1 (pow im 3))) (* re (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 (+ (* 1/4 (* (sqrt (/ 1 (pow im 5))) (* (pow re 2) (sqrt 2)))) (+ (* 1/2 (* (sqrt (/ 1 (pow im 3))) (* re (sqrt 2)))) (* (sqrt (/ 1 im)) (sqrt 2)))))
(* im (+ (* -1/8 (* (sqrt (/ 1 (pow im 5))) (* (pow re 2) (sqrt 2)))) (+ (* 1/4 (* (sqrt (/ 1 (pow im 5))) (* (pow re 2) (sqrt 2)))) (+ (* 1/2 (* (sqrt (/ 1 (pow im 3))) (* re (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 (+ (* -1/4 (/ (pow re 4) (pow im 4))) (+ (* 2 (/ re im)) (/ (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 (/ 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 (+ (* -1/8 (* (sqrt (/ 1 (pow im 5))) (* (pow re 2) (* (sqrt -1) (sqrt 2))))) (+ (* 1/4 (* (sqrt (/ 1 (pow im 3))) (* re (* (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 (+ (* -1/4 (* (sqrt (/ 1 (pow im 5))) (* (pow re 2) (* (sqrt -1) (sqrt 2))))) (+ (* 1/2 (* (sqrt (/ 1 (pow im 3))) (* re (* (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 (/ (+ (* -1 (/ (pow re 2) im)) (* 2 re)) im)))))
(* -1 (* im (+ 2 (* -1 (/ (+ (* -1 (/ (+ (* -1/4 (/ (pow re 4) (pow im 2))) (pow re 2)) im)) (* 2 re)) 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 (* -1 (/ re im)))))
(* -1 (* im (+ 1 (* -1 (/ (+ re (* -1/2 (/ (pow re 2) im))) im)))))
(* -1 (* im (+ 1 (* -1 (/ (+ re (* -1 (/ (+ (* -1/8 (/ (pow re 4) (pow im 2))) (* 1/2 (pow re 2))) im))) 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 1/2 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 #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 -1/16 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 1/8 binary64) (sqrt.f64 #s(literal 2 binary64))) (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 im #s(literal 3 binary64)))))) re)) re (*.f64 (sqrt.f64 #s(literal 2 binary64)) (sqrt.f64 im)))
(*.f64 #s(literal 2 binary64) im)
(*.f64 (+.f64 im re) #s(literal 2 binary64))
(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 #s(literal 1/2 binary64) re) (/.f64 re im) 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 #s(literal 1/2 binary64) re) (/.f64 re im) 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))
(sqrt.f64 re)
(.f64 (fma.f64 (.f64 #s(literal 1/8 binary64) (*.f64 im im)) (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 re #s(literal 5 binary64)))) (sqrt.f64 (/.f64 #s(literal 1 binary64) re))) re)
(.f64 (fma.f64 (.f64 (pow.f64 im #s(literal 4 binary64)) #s(literal -1/32 binary64)) (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 re #s(literal 9 binary64)))) (fma.f64 (.f64 #s(literal 1/8 binary64) (.f64 im im)) (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 re #s(literal 5 binary64)))) (sqrt.f64 (/.f64 #s(literal 1 binary64) re)))) re)
(.f64 (fma.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 re #s(literal 9 binary64)))) (fma.f64 (pow.f64 im #s(literal 4 binary64)) #s(literal -1/32 binary64) (.f64 (/.f64 (pow.f64 im #s(literal 4 binary64)) #s(literal 2 binary64)) #s(literal -1/64 binary64))) (fma.f64 (.f64 #s(literal 1/8 binary64) (.f64 im im)) (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 re #s(literal 5 binary64)))) (sqrt.f64 (/.f64 #s(literal 1 binary64) re)))) re)
(*.f64 (sqrt.f64 re) #s(literal 2 binary64))
(.f64 (fma.f64 (.f64 #s(literal 1/4 binary64) (.f64 im im)) (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 re #s(literal 5 binary64)))) (.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) re)) #s(literal 2 binary64))) re)
(.f64 (fma.f64 (.f64 (pow.f64 im #s(literal 4 binary64)) #s(literal -1/16 binary64)) (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 re #s(literal 9 binary64)))) (fma.f64 (.f64 #s(literal 1/4 binary64) (.f64 im im)) (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 re #s(literal 5 binary64)))) (*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) re)) #s(literal 2 binary64)))) re)
(.f64 (fma.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 re #s(literal 9 binary64)))) (fma.f64 (pow.f64 im #s(literal 4 binary64)) #s(literal -1/16 binary64) (.f64 (/.f64 (pow.f64 im #s(literal 4 binary64)) #s(literal 2 binary64)) #s(literal -1/32 binary64))) (fma.f64 (.f64 #s(literal 1/4 binary64) (.f64 im im)) (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 re #s(literal 5 binary64)))) (*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) re)) #s(literal 2 binary64)))) re)
(*.f64 #s(literal 4 binary64) re)
(*.f64 (fma.f64 (/.f64 im re) (/.f64 im re) #s(literal 4 binary64)) re)
(*.f64 (fma.f64 (/.f64 (pow.f64 im #s(literal 4 binary64)) (pow.f64 re #s(literal 4 binary64))) #s(literal -1/4 binary64) (fma.f64 (/.f64 im re) (/.f64 im re) #s(literal 4 binary64))) re)
(.f64 (+.f64 (fma.f64 (/.f64 (pow.f64 im #s(literal 4 binary64)) (pow.f64 re #s(literal 4 binary64))) #s(literal -1/4 binary64) (fma.f64 (/.f64 im re) (/.f64 im re) #s(literal 4 binary64))) (/.f64 (.f64 (pow.f64 im #s(literal 6 binary64)) #s(literal 1/8 binary64)) (pow.f64 re #s(literal 6 binary64)))) re)
re
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(.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 (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 im #s(literal 3 binary64)))) #s(literal 1/2 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 (neg.f64 im) (fma.f64 #s(literal -2 binary64) (/.f64 re im) #s(literal 2 binary64)))
(.f64 (neg.f64 im) (-.f64 #s(literal 2 binary64) (/.f64 (fma.f64 (/.f64 (neg.f64 re) im) re (.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)))
(neg.f64 im)
(.f64 (neg.f64 im) (fma.f64 (/.f64 (.f64 (/.f64 re im) re) 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 (/.f64 re im) re) 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)
(fma.f64 (/.f64 re im) im (neg.f64 im))
(fma.f64 (/.f64 (fma.f64 #s(literal -1/2 binary64) (*.f64 (/.f64 re im) re) re) im) im (neg.f64 im))
(fma.f64 (/.f64 (-.f64 re (/.f64 (fma.f64 (/.f64 #s(literal -1/8 binary64) im) (/.f64 (pow.f64 re #s(literal 4 binary64)) im) (.f64 #s(literal 1/2 binary64) (.f64 re re))) im)) im) im (neg.f64 im))

rewrite255.0ms (3.1%)

Memory

20.8MiB live, 295.0MiB allocated

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	12	65
0	20	65
1	61	65
2	398	65
3	4225	65
0	8344	38

Stop Event

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

Counts

6 → 285

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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eval321.0ms (3.8%)

Memory: -40.9MiB live, 154.6MiB allocated
Compiler: Compiled 12 141 to 2 385 computations (80.4% saved)

prune20.0ms (0.2%)

Memory

16.8MiB live, 55.5MiB allocated

Pruning

17 alts after pruning (17 fresh and 0 done)

	Pruned	Kept	Total
New	406	17	423
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	407	17	424

Accuracy

92.9%

Counts

424 → 17

Alt Table

Click to see full alt table

Status	Accuracy	Program
▶	81.8%	(.f64 (.f64 (sqrt.f64 (+.f64 (hypot.f64 im re) re)) #s(literal 1/2 binary64)) (sqrt.f64 #s(literal 2 binary64)))
▶	81.3%	(.f64 (sqrt.f64 (.f64 (+.f64 (hypot.f64 im re) re) #s(literal 2 binary64))) #s(literal 1/2 binary64))
	52.0%	(.f64 #s(literal 1/2 binary64) (sqrt.f64 (.f64 #s(literal 2 binary64) (fma.f64 (hypot.f64 im re) (/.f64 (hypot.f64 im re) (-.f64 (hypot.f64 im re) re)) (neg.f64 (*.f64 re (/.f64 re (-.f64 (hypot.f64 im re) re))))))))
	41.6%	(.f64 #s(literal 1/2 binary64) (sqrt.f64 (.f64 #s(literal 2 binary64) (+.f64 (sqrt.f64 (fma.f64 re re (*.f64 im im))) re))))
	27.5%	(.f64 #s(literal 1/2 binary64) (sqrt.f64 (.f64 #s(literal 2 binary64) (+.f64 (sqrt.f64 #s(approx (+ (* re re) (* im im)) (.f64 (fma.f64 (/.f64 im re) (/.f64 im re) #s(literal 1 binary64)) (.f64 re re)))) re))))
	7.9%	(.f64 #s(literal 1/2 binary64) (sqrt.f64 (.f64 #s(literal 2 binary64) (+.f64 #s(approx (sqrt (+ (* re re) (* im im))) (.f64 (neg.f64 re) (fma.f64 (/.f64 (.f64 #s(literal 1/2 binary64) im) re) (/.f64 im re) #s(literal 1 binary64)))) re))))
	7.6%	(.f64 #s(literal 1/2 binary64) (sqrt.f64 (.f64 #s(literal 2 binary64) (+.f64 #s(approx (sqrt (+ (* re re) (* im im))) (neg.f64 re)) re))))
	50.8%	(.f64 #s(literal 1/2 binary64) (sqrt.f64 (.f64 #s(literal 2 binary64) #s(approx (+ (sqrt (+ (* re re) (* im im))) re) (+.f64 im re)))))
▶	13.6%	(.f64 #s(literal 1/2 binary64) (sqrt.f64 (.f64 #s(literal 2 binary64) #s(approx (+ (sqrt (+ (* re re) (* im im))) re) (.f64 #s(literal -1/2 binary64) (/.f64 (.f64 im im) re))))))
	47.9%	(.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)))))
	28.9%	(.f64 #s(literal 1/2 binary64) (sqrt.f64 #s(approx ( 2 (+ (sqrt (+ (* re re) (* im im))) re)) (fma.f64 #s(literal 4 binary64) re (/.f64 (*.f64 im im) re)))))
	17.9%	(.f64 #s(literal 1/2 binary64) (sqrt.f64 #s(approx ( 2 (+ (sqrt (+ (* re re) (* im im))) re)) (*.f64 (neg.f64 im) (/.f64 im re)))))
	47.2%	(.f64 #s(literal 1/2 binary64) (sqrt.f64 #s(approx ( 2 (+ (sqrt (+ (* re re) (* im im))) re)) (*.f64 #s(literal 2 binary64) im))))
	75.6%	(.f64 #s(literal 1/2 binary64) (exp.f64 (.f64 (log.f64 (*.f64 (+.f64 (hypot.f64 im re) re) #s(literal 2 binary64))) #s(literal 1/2 binary64))))
	40.9%	(.f64 #s(literal 1/2 binary64) #s(approx (sqrt ( 2 (+ (sqrt (+ (* re re) (* im im))) re))) (.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)))
▶	47.7%	(.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))))
▶	31.4%	#s(approx (* 1/2 (sqrt (* 2 (+ (sqrt (+ (* re re) (* im im))) re)))) (sqrt.f64 re))

Compiler

Compiled 722 to 524 computations (27.4% saved)

simplify8.0ms (0.1%)

Memory

-37.9MiB live, 8.4MiB allocated

Algorithm

1×	egg-herbie

Localize:

Found 18 expressions of interest:

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

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	35	251
0	55	216
1	83	216
2	100	216
3	114	216
4	117	216
5	120	216
0	120	216

Stop Event

1×	iter limit
1×	saturated
1×	iter limit

Calls

Call 1

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

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

localize71.0ms (0.8%)

Memory

38.7MiB live, 116.1MiB allocated

Localize:

Found 18 expressions of interest:

New	Metric	Score
accuracy	0	(*.f64 (+.f64 (hypot.f64 im re) re) #s(literal 2 binary64))
accuracy	0	(.f64 (sqrt.f64 (.f64 (+.f64 (hypot.f64 im re) re) #s(literal 2 binary64))) #s(literal 1/2 binary64))
accuracy	0.00390625	(+.f64 (hypot.f64 im re) re)
accuracy	0.480463542216694	(sqrt.f64 (*.f64 (+.f64 (hypot.f64 im re) re) #s(literal 2 binary64)))
accuracy	0.00390625	(.f64 #s(literal -1/2 binary64) (/.f64 (.f64 im im) re))
accuracy	0.480463542216694	(sqrt.f64 (.f64 #s(literal 2 binary64) #s(approx (+ (sqrt (+ ( re re) (* im im))) re) (.f64 #s(literal -1/2 binary64) (/.f64 (.f64 im im) re)))))
accuracy	4.542908797371661	(/.f64 (*.f64 im im) re)
accuracy	33.453791668159184	#s(approx (+ (sqrt (+ (* re re) (* im im))) re) (.f64 #s(literal -1/2 binary64) (/.f64 (.f64 im im) re)))
accuracy	0	(sqrt.f64 im)
accuracy	0	(sqrt.f64 #s(literal 2 binary64))
accuracy	0.26009750976844204	(*.f64 (sqrt.f64 #s(literal 2 binary64)) (sqrt.f64 im))
accuracy	18.717514330034575	#s(approx (sqrt (* 2 (+ (sqrt (+ (* re re) (* im im))) re))) (*.f64 (sqrt.f64 #s(literal 2 binary64)) (sqrt.f64 im)))
accuracy	0	(sqrt.f64 re)
accuracy	13.873752976854588	#s(approx (* 1/2 (sqrt (* 2 (+ (sqrt (+ (* re re) (* im im))) re)))) (sqrt.f64 re))
accuracy	0	(sqrt.f64 #s(literal 2 binary64))
accuracy	0.00390625	(+.f64 (hypot.f64 im re) re)
accuracy	0.0078125	(sqrt.f64 (+.f64 (hypot.f64 im re) re))
accuracy	0.2421875	(.f64 (.f64 (sqrt.f64 (+.f64 (hypot.f64 im re) re)) #s(literal 1/2 binary64)) (sqrt.f64 #s(literal 2 binary64)))

Samples

28.0ms	136×	0	valid
25.0ms	120×	0	invalid

Compiler

Compiled 507 to 64 computations (87.4% saved)

Precisions

Click to see histograms. Total time spent on operations: 35.0ms

ival-mult: 13.0ms (36.8% of total)

ival-sqrt: 9.0ms (25.5% of total)

ival-hypot: 8.0ms (22.6% of total)

ival-div: 2.0ms (5.7% of total)

ival-add: 2.0ms (5.7% of total)

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

exact: 0.0ms (0% of total)

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

series39.0ms (0.5%)

Memory

-0.5MiB live, 78.8MiB allocated

Counts

20 → 420

Calls

Call 1

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

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

6 calls:

Time	Variable		Point	Expression
5.0ms	im	@	-inf	((* (* (sqrt (+ (sqrt (+ (* im im) (* re re))) re)) 1/2) (sqrt 2)) (* (sqrt (+ (sqrt (+ (* im im) (* re re))) re)) 1/2) (sqrt (+ (sqrt (+ (* im im) (* re re))) re)) (+ (sqrt (+ (* im im) (* re re))) re) (* 1/2 (sqrt (* 2 (+ (sqrt (+ (* re re) (* im im))) re)))) (sqrt re) (* 1/2 (sqrt (* 2 (+ (sqrt (+ (* re re) (* im im))) re)))) (sqrt (* 2 (+ (sqrt (+ (* re re) (* im im))) re))) (* (sqrt 2) (sqrt im)) (sqrt 2) (* 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 (+ (* 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 im) re) (* -1/2 (/ (* im im) re)))
5.0ms	im	@	0	((* (* (sqrt (+ (sqrt (+ (* im im) (* re re))) re)) 1/2) (sqrt 2)) (* (sqrt (+ (sqrt (+ (* im im) (* re re))) re)) 1/2) (sqrt (+ (sqrt (+ (* im im) (* re re))) re)) (+ (sqrt (+ (* im im) (* re re))) re) (* 1/2 (sqrt (* 2 (+ (sqrt (+ (* re re) (* im im))) re)))) (sqrt re) (* 1/2 (sqrt (* 2 (+ (sqrt (+ (* re re) (* im im))) re)))) (sqrt (* 2 (+ (sqrt (+ (* re re) (* im im))) re))) (* (sqrt 2) (sqrt im)) (sqrt 2) (* 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 (+ (* 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 im) re) (* -1/2 (/ (* im im) re)))
3.0ms	re	@	-inf	((* (* (sqrt (+ (sqrt (+ (* im im) (* re re))) re)) 1/2) (sqrt 2)) (* (sqrt (+ (sqrt (+ (* im im) (* re re))) re)) 1/2) (sqrt (+ (sqrt (+ (* im im) (* re re))) re)) (+ (sqrt (+ (* im im) (* re re))) re) (* 1/2 (sqrt (* 2 (+ (sqrt (+ (* re re) (* im im))) re)))) (sqrt re) (* 1/2 (sqrt (* 2 (+ (sqrt (+ (* re re) (* im im))) re)))) (sqrt (* 2 (+ (sqrt (+ (* re re) (* im im))) re))) (* (sqrt 2) (sqrt im)) (sqrt 2) (* 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 (+ (* 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 im) re) (* -1/2 (/ (* im im) re)))
3.0ms	im	@	inf	((* (* (sqrt (+ (sqrt (+ (* im im) (* re re))) re)) 1/2) (sqrt 2)) (* (sqrt (+ (sqrt (+ (* im im) (* re re))) re)) 1/2) (sqrt (+ (sqrt (+ (* im im) (* re re))) re)) (+ (sqrt (+ (* im im) (* re re))) re) (* 1/2 (sqrt (* 2 (+ (sqrt (+ (* re re) (* im im))) re)))) (sqrt re) (* 1/2 (sqrt (* 2 (+ (sqrt (+ (* re re) (* im im))) re)))) (sqrt (* 2 (+ (sqrt (+ (* re re) (* im im))) re))) (* (sqrt 2) (sqrt im)) (sqrt 2) (* 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 (+ (* 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 im) re) (* -1/2 (/ (* im im) re)))
3.0ms	re	@	inf	((* (* (sqrt (+ (sqrt (+ (* im im) (* re re))) re)) 1/2) (sqrt 2)) (* (sqrt (+ (sqrt (+ (* im im) (* re re))) re)) 1/2) (sqrt (+ (sqrt (+ (* im im) (* re re))) re)) (+ (sqrt (+ (* im im) (* re re))) re) (* 1/2 (sqrt (* 2 (+ (sqrt (+ (* re re) (* im im))) re)))) (sqrt re) (* 1/2 (sqrt (* 2 (+ (sqrt (+ (* re re) (* im im))) re)))) (sqrt (* 2 (+ (sqrt (+ (* re re) (* im im))) re))) (* (sqrt 2) (sqrt im)) (sqrt 2) (* 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 (+ (* 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 im) re) (* -1/2 (/ (* im im) re)))

simplify243.0ms (2.9%)

Memory

-27.9MiB live, 408.1MiB allocated

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	667	10506
1	2227	9608
2	7580	9584
0	8496	9148

Stop Event

1×	iter limit
1×	node limit

Counts

420 → 416

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

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

rewrite182.0ms (2.2%)

Memory

9.8MiB live, 248.4MiB allocated

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	35	218
0	55	181
1	155	179
2	675	179
3	6991	179
0	8905	179

Stop Event

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

Counts

20 → 345

Calls

Call 1

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

Outputs
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eval131.0ms (1.6%)

Memory: 25.1MiB live, 206.6MiB allocated
Compiler: Compiled 27 993 to 2 893 computations (89.7% saved)

prune85.0ms (1%)

Memory

-25.7MiB live, 108.1MiB allocated

Pruning

23 alts after pruning (19 fresh and 4 done)

	Pruned	Kept	Total
New	853	14	867
Fresh	7	5	12
Picked	1	4	5
Done	0	0	0
Total	861	23	884

Accuracy

92.9%

Counts

884 → 23

Alt Table

Click to see full alt table

Status	Accuracy	Program
✓	81.8%	(.f64 (.f64 (sqrt.f64 (+.f64 (hypot.f64 im re) re)) #s(literal 1/2 binary64)) (sqrt.f64 #s(literal 2 binary64)))
	51.2%	(.f64 (.f64 (sqrt.f64 #s(approx (+ (sqrt (+ (* im im) (* re re))) re) (+.f64 re im))) #s(literal 1/2 binary64)) (sqrt.f64 #s(literal 2 binary64)))
	52.0%	(.f64 (sqrt.f64 (.f64 (fma.f64 (hypot.f64 re im) (/.f64 (hypot.f64 re im) (-.f64 (hypot.f64 re im) re)) (neg.f64 (*.f64 re (/.f64 re (-.f64 (hypot.f64 re im) re))))) #s(literal 2 binary64))) #s(literal 1/2 binary64))
✓	81.3%	(.f64 (sqrt.f64 (.f64 (+.f64 (hypot.f64 im re) re) #s(literal 2 binary64))) #s(literal 1/2 binary64))
	50.8%	(.f64 (sqrt.f64 (.f64 #s(approx (+ (sqrt (+ (* im im) (* re re))) re) (+.f64 re im)) #s(literal 2 binary64))) #s(literal 1/2 binary64))
	47.9%	(.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))
	28.9%	(.f64 (sqrt.f64 #s(approx ( (+ (sqrt (+ (* im im) (* re re))) re) 2) (fma.f64 #s(literal 4 binary64) re (/.f64 (*.f64 im im) re)))) #s(literal 1/2 binary64))
▶	13.6%	(.f64 (sqrt.f64 #s(approx ( (+ (sqrt (+ (* im im) (* re re))) re) 2) (/.f64 (*.f64 (neg.f64 im) im) re))) #s(literal 1/2 binary64))
▶	47.2%	(.f64 (sqrt.f64 #s(approx ( (+ (sqrt (+ (* im im) (* re re))) re) 2) (*.f64 #s(literal 2 binary64) im))) #s(literal 1/2 binary64))
▶	75.6%	(.f64 (exp.f64 (.f64 (log.f64 (*.f64 #s(literal 2 binary64) (+.f64 (hypot.f64 re im) re))) #s(literal 1/2 binary64))) #s(literal 1/2 binary64))
▶	40.9%	(.f64 #s(approx (sqrt ( (+ (sqrt (+ (* im im) (* re re))) re) 2)) (.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)) #s(literal 1/2 binary64))
▶	41.6%	(.f64 #s(literal 1/2 binary64) (sqrt.f64 (.f64 #s(literal 2 binary64) (+.f64 (sqrt.f64 (fma.f64 re re (*.f64 im im))) re))))
	27.5%	(.f64 #s(literal 1/2 binary64) (sqrt.f64 (.f64 #s(literal 2 binary64) (+.f64 (sqrt.f64 #s(approx (+ (* re re) (* im im)) (.f64 (fma.f64 (/.f64 im re) (/.f64 im re) #s(literal 1 binary64)) (.f64 re re)))) re))))
	7.9%	(.f64 #s(literal 1/2 binary64) (sqrt.f64 (.f64 #s(literal 2 binary64) (+.f64 #s(approx (sqrt (+ (* re re) (* im im))) (.f64 (neg.f64 re) (fma.f64 (/.f64 (.f64 #s(literal 1/2 binary64) im) re) (/.f64 im re) #s(literal 1 binary64)))) re))))
	7.6%	(.f64 #s(literal 1/2 binary64) (sqrt.f64 (.f64 #s(literal 2 binary64) (+.f64 #s(approx (sqrt (+ (* re re) (* im im))) (neg.f64 re)) re))))
	17.9%	(.f64 #s(literal 1/2 binary64) (sqrt.f64 (.f64 #s(literal 2 binary64) #s(approx (+ (sqrt (+ (* re re) (* im im))) re) (/.f64 (*.f64 #s(literal -1/2 binary64) im) (/.f64 re im))))))
	17.9%	(.f64 #s(literal 1/2 binary64) (sqrt.f64 #s(approx ( 2 (+ (sqrt (+ (* re re) (* im im))) re)) (*.f64 (neg.f64 im) (/.f64 im re)))))
	13.2%	(.f64 #s(literal 1/2 binary64) (exp.f64 (.f64 (log.f64 (.f64 #s(approx (+ (sqrt (+ ( re re) (* im im))) re) (.f64 (/.f64 (.f64 im im) re) #s(literal -1/2 binary64))) #s(literal 2 binary64))) #s(literal 1/2 binary64))))
✓	47.7%	(.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))))
	44.7%	(.f64 #s(literal 1/2 binary64) #s(approx (sqrt ( 2 (+ (sqrt (+ (* re re) (* im im))) re))) (.f64 (sqrt.f64 #s(literal 2 binary64)) (exp.f64 (.f64 (log.f64 im) #s(literal 1/2 binary64))))))
	44.5%	(.f64 #s(literal 1/2 binary64) #s(approx (sqrt ( 2 (+ (sqrt (+ (* re re) (* im im))) re))) (exp.f64 (fma.f64 (log.f64 im) #s(literal 1/2 binary64) (*.f64 (log.f64 #s(literal 2 binary64)) #s(literal 1/2 binary64))))))
	44.0%	(.f64 #s(literal 1/2 binary64) #s(approx (sqrt ( 2 (+ (sqrt (+ (* re re) (* im im))) re))) (exp.f64 (.f64 (log.f64 (.f64 #s(literal 2 binary64) im)) #s(literal 1/2 binary64)))))
✓	31.4%	#s(approx (* 1/2 (sqrt (* 2 (+ (sqrt (+ (* re re) (* im im))) re)))) (sqrt.f64 re))

Compiler

Compiled 942 to 686 computations (27.2% saved)

simplify284.0ms (3.4%)

Memory

14.1MiB live, 232.2MiB allocated

Algorithm

1×	egg-herbie

Localize:

Found 20 expressions of interest:

New	Metric	Score
cost-diff	0	(.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)
cost-diff	0	#s(approx (sqrt (* (+ (sqrt (+ (* im im) (* re re))) re) 2)) (.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))
cost-diff	0	(.f64 #s(approx (sqrt ( (+ (sqrt (+ (* im im) (* re re))) re) 2)) (.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)) #s(literal 1/2 binary64))
cost-diff	960	(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))))
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	(/.f64 (*.f64 (neg.f64 im) im) re)
cost-diff	0	#s(approx (* (+ (sqrt (+ (* im im) (* re re))) re) 2) (/.f64 (*.f64 (neg.f64 im) im) re))
cost-diff	0	(sqrt.f64 #s(approx (* (+ (sqrt (+ (* im im) (* re re))) re) 2) (/.f64 (*.f64 (neg.f64 im) im) re)))
cost-diff	0	(.f64 (sqrt.f64 #s(approx ( (+ (sqrt (+ (* im im) (* re re))) re) 2) (/.f64 (*.f64 (neg.f64 im) im) re))) #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	(log.f64 (*.f64 #s(literal 2 binary64) (+.f64 (hypot.f64 re im) re)))
cost-diff	0	(.f64 (log.f64 (.f64 #s(literal 2 binary64) (+.f64 (hypot.f64 re im) re))) #s(literal 1/2 binary64))
cost-diff	0	(.f64 (exp.f64 (.f64 (log.f64 (*.f64 #s(literal 2 binary64) (+.f64 (hypot.f64 re im) re))) #s(literal 1/2 binary64))) #s(literal 1/2 binary64))
cost-diff	12480	(exp.f64 (.f64 (log.f64 (.f64 #s(literal 2 binary64) (+.f64 (hypot.f64 re im) re))) #s(literal 1/2 binary64)))

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	50	403
0	87	361
1	131	357
2	182	357
3	299	349
4	498	349
5	613	349
6	738	349
7	838	349
8	865	349
9	921	349
10	982	349
11	1035	349
12	1413	349
13	2656	349
14	4279	349
15	4646	349
16	4918	349
17	5194	349
18	5210	349
19	5298	349
20	6061	349
21	6936	349
22	7158	349
23	7158	349
24	7846	349
0	8158	345

Stop Event

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

Calls

Call 1

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

localize186.0ms (2.2%)

Memory

22.4MiB live, 295.4MiB allocated

Localize:

Found 20 expressions of interest:

New	Metric	Score
accuracy	6.5399885230405985	(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))))
accuracy	8.152944923097026	(.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)
accuracy	18.8556509233185	(sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 im #s(literal 3 binary64))))
accuracy	33.41070481725686	#s(approx (sqrt (* (+ (sqrt (+ (* im im) (* re re))) re) 2)) (.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))
accuracy	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))))
accuracy	5.281846752426357	(sqrt.f64 (.f64 #s(literal 2 binary64) (+.f64 (sqrt.f64 (fma.f64 re re (.f64 im im))) re)))
accuracy	6.582561687117777	(+.f64 (sqrt.f64 (fma.f64 re re (*.f64 im im))) re)
accuracy	31.480211570230413	(sqrt.f64 (fma.f64 re re (*.f64 im im)))
accuracy	0	(neg.f64 im)
accuracy	5.281846752426357	(sqrt.f64 #s(approx (* (+ (sqrt (+ (* im im) (* re re))) re) 2) (/.f64 (*.f64 (neg.f64 im) im) re)))
accuracy	8.814111667929732	(/.f64 (*.f64 (neg.f64 im) im) re)
accuracy	47.34442058245425	#s(approx (* (+ (sqrt (+ (* im im) (* re re))) re) 2) (/.f64 (*.f64 (neg.f64 im) im) re))
accuracy	0	(.f64 (sqrt.f64 #s(approx ( (+ (sqrt (+ (* im im) (* re re))) re) 2) (*.f64 #s(literal 2 binary64) im))) #s(literal 1/2 binary64))
accuracy	0	(*.f64 #s(literal 2 binary64) im)
accuracy	5.281846752426357	(sqrt.f64 #s(approx (* (+ (sqrt (+ (* im im) (* re re))) re) 2) (*.f64 #s(literal 2 binary64) im)))
accuracy	33.58907360105243	#s(approx (* (+ (sqrt (+ (* im im) (* re re))) re) 2) (*.f64 #s(literal 2 binary64) im))
accuracy	0	(*.f64 #s(literal 2 binary64) (+.f64 (hypot.f64 re im) re))
accuracy	4.843921141370872	(exp.f64 (.f64 (log.f64 (.f64 #s(literal 2 binary64) (+.f64 (hypot.f64 re im) re))) #s(literal 1/2 binary64)))
accuracy	6.582561687117777	(+.f64 (hypot.f64 re im) re)
accuracy	8.232461467787873	(log.f64 (*.f64 #s(literal 2 binary64) (+.f64 (hypot.f64 re im) re)))

Samples

72.0ms	197×	0	valid
37.0ms	18×	3	valid
25.0ms	20×	1	valid
17.0ms	21×	2	valid

Compiler

Compiled 812 to 92 computations (88.7% saved)

Precisions

Click to see histograms. Total time spent on operations: 120.0ms

ival-mult: 27.0ms (22.6% of total)

ival-exp: 22.0ms (18.4% of total)

ival-hypot: 16.0ms (13.4% of total)

ival-pow: 16.0ms (13.4% of total)

ival-sqrt: 15.0ms (12.5% of total)

ival-add: 6.0ms (5% of total)

adjust: 5.0ms (4.2% of total)

ival-div: 5.0ms (4.2% of total)

ival-log: 5.0ms (4.2% of total)

exact: 1.0ms (0.8% of total)

ival-neg: 1.0ms (0.8% of total)

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

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

series126.0ms (1.5%)

Memory

-22.8MiB live, 201.9MiB allocated

Counts

25 → 564

Calls

Call 1

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

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

6 calls:

Time	Variable		Point	Expression
66.0ms	im	@	inf	((exp (* (log (* 2 (+ (sqrt (+ (* re re) (* im im))) re))) 1/2)) (* (exp (* (log (* 2 (+ (sqrt (+ (* re re) (* im im))) re))) 1/2)) 1/2) (* (log (* 2 (+ (sqrt (+ (* re re) (* im im))) re))) 1/2) (log (* 2 (+ (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 (+ (* im im) (* re re))) re) 2) (/ (* (neg im) im) 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) (+ (* (* 1/2 (* (sqrt 2) re)) (sqrt (/ 1 (pow im 3)))) (* (sqrt (/ 1 im)) (sqrt 2))) (* (sqrt (* (+ (sqrt (+ (* im im) (* re re))) re) 2)) 1/2) (sqrt (* (+ (sqrt (+ (* im im) (* re re))) re) 2)) (* (+ (* (* 1/2 (* (sqrt 2) re)) (sqrt (/ 1 (pow im 3)))) (* (sqrt (/ 1 im)) (sqrt 2))) im) (+ (sqrt (+ (* re re) (* im im))) re) (* 2 (+ (sqrt (+ (* re re) (* im im))) re)) (neg im) (sqrt (+ (* re re) (* im im))) (sqrt (/ 1 (pow im 3))))
8.0ms	re	@	-inf	((exp (* (log (* 2 (+ (sqrt (+ (* re re) (* im im))) re))) 1/2)) (* (exp (* (log (* 2 (+ (sqrt (+ (* re re) (* im im))) re))) 1/2)) 1/2) (* (log (* 2 (+ (sqrt (+ (* re re) (* im im))) re))) 1/2) (log (* 2 (+ (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 (+ (* im im) (* re re))) re) 2) (/ (* (neg im) im) 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) (+ (* (* 1/2 (* (sqrt 2) re)) (sqrt (/ 1 (pow im 3)))) (* (sqrt (/ 1 im)) (sqrt 2))) (* (sqrt (* (+ (sqrt (+ (* im im) (* re re))) re) 2)) 1/2) (sqrt (* (+ (sqrt (+ (* im im) (* re re))) re) 2)) (* (+ (* (* 1/2 (* (sqrt 2) re)) (sqrt (/ 1 (pow im 3)))) (* (sqrt (/ 1 im)) (sqrt 2))) im) (+ (sqrt (+ (* re re) (* im im))) re) (* 2 (+ (sqrt (+ (* re re) (* im im))) re)) (neg im) (sqrt (+ (* re re) (* im im))) (sqrt (/ 1 (pow im 3))))
8.0ms	im	@	-inf	((exp (* (log (* 2 (+ (sqrt (+ (* re re) (* im im))) re))) 1/2)) (* (exp (* (log (* 2 (+ (sqrt (+ (* re re) (* im im))) re))) 1/2)) 1/2) (* (log (* 2 (+ (sqrt (+ (* re re) (* im im))) re))) 1/2) (log (* 2 (+ (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 (+ (* im im) (* re re))) re) 2) (/ (* (neg im) im) 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) (+ (* (* 1/2 (* (sqrt 2) re)) (sqrt (/ 1 (pow im 3)))) (* (sqrt (/ 1 im)) (sqrt 2))) (* (sqrt (* (+ (sqrt (+ (* im im) (* re re))) re) 2)) 1/2) (sqrt (* (+ (sqrt (+ (* im im) (* re re))) re) 2)) (* (+ (* (* 1/2 (* (sqrt 2) re)) (sqrt (/ 1 (pow im 3)))) (* (sqrt (/ 1 im)) (sqrt 2))) im) (+ (sqrt (+ (* re re) (* im im))) re) (* 2 (+ (sqrt (+ (* re re) (* im im))) re)) (neg im) (sqrt (+ (* re re) (* im im))) (sqrt (/ 1 (pow im 3))))
6.0ms	im	@	0	((exp (* (log (* 2 (+ (sqrt (+ (* re re) (* im im))) re))) 1/2)) (* (exp (* (log (* 2 (+ (sqrt (+ (* re re) (* im im))) re))) 1/2)) 1/2) (* (log (* 2 (+ (sqrt (+ (* re re) (* im im))) re))) 1/2) (log (* 2 (+ (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 (+ (* im im) (* re re))) re) 2) (/ (* (neg im) im) 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) (+ (* (* 1/2 (* (sqrt 2) re)) (sqrt (/ 1 (pow im 3)))) (* (sqrt (/ 1 im)) (sqrt 2))) (* (sqrt (* (+ (sqrt (+ (* im im) (* re re))) re) 2)) 1/2) (sqrt (* (+ (sqrt (+ (* im im) (* re re))) re) 2)) (* (+ (* (* 1/2 (* (sqrt 2) re)) (sqrt (/ 1 (pow im 3)))) (* (sqrt (/ 1 im)) (sqrt 2))) im) (+ (sqrt (+ (* re re) (* im im))) re) (* 2 (+ (sqrt (+ (* re re) (* im im))) re)) (neg im) (sqrt (+ (* re re) (* im im))) (sqrt (/ 1 (pow im 3))))
4.0ms	re	@	0	((exp (* (log (* 2 (+ (sqrt (+ (* re re) (* im im))) re))) 1/2)) (* (exp (* (log (* 2 (+ (sqrt (+ (* re re) (* im im))) re))) 1/2)) 1/2) (* (log (* 2 (+ (sqrt (+ (* re re) (* im im))) re))) 1/2) (log (* 2 (+ (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 (+ (* im im) (* re re))) re) 2) (/ (* (neg im) im) 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) (+ (* (* 1/2 (* (sqrt 2) re)) (sqrt (/ 1 (pow im 3)))) (* (sqrt (/ 1 im)) (sqrt 2))) (* (sqrt (* (+ (sqrt (+ (* im im) (* re re))) re) 2)) 1/2) (sqrt (* (+ (sqrt (+ (* im im) (* re re))) re) 2)) (* (+ (* (* 1/2 (* (sqrt 2) re)) (sqrt (/ 1 (pow im 3)))) (* (sqrt (/ 1 im)) (sqrt 2))) im) (+ (sqrt (+ (* re re) (* im im))) re) (* 2 (+ (sqrt (+ (* re re) (* im im))) re)) (neg im) (sqrt (+ (* re re) (* im im))) (sqrt (/ 1 (pow im 3))))

simplify249.0ms (3%)

Memory

24.0MiB live, 323.3MiB allocated

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	879	13452
1	2795	12513
0	8608	11912

Stop Event

1×	iter limit
1×	node limit

Counts

564 → 556

Calls

Call 1

Inputs
(* (sqrt im) (sqrt 2))
(+ (* (sqrt im) (sqrt 2)) (* (sqrt (/ 1 im)) (/ re (sqrt 2))))
(+ (* re (+ (* 1/2 (* (sqrt (/ 1 im)) (/ (* re (- (/ 1 im) (/ 1 (* im (pow (sqrt 2) 2))))) (sqrt 2)))) (* (sqrt (/ 1 im)) (/ 1 (sqrt 2))))) (* (sqrt im) (sqrt 2)))
(+ (* re (+ (* re (+ (* 1/2 (* (sqrt (/ 1 im)) (/ (* re (- (/ 1 (* (pow im 2) (pow (sqrt 2) 4))) (/ 1 (* (pow im 2) (pow (sqrt 2) 2))))) (sqrt 2)))) (* 1/2 (* (sqrt (/ 1 im)) (/ (- (/ 1 im) (/ 1 (* im (pow (sqrt 2) 2)))) (sqrt 2)))))) (* (sqrt (/ 1 im)) (/ 1 (sqrt 2))))) (* (sqrt im) (sqrt 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 (+ (* 1/16 (* (sqrt (/ 1 (pow im 3))) (* re (sqrt 2)))) (* 1/4 (* (sqrt (/ 1 im)) (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 (log (* 2 im)))
(+ (* 1/2 (log (* 2 im))) (* 1/2 (/ re im)))
(+ (* 1/2 (log (* 2 im))) (* re (+ (* -1/12 (/ (pow re 2) (pow im 3))) (* 1/2 (/ 1 im)))))
(+ (* 1/2 (log (* 2 im))) (* re (+ (* (pow re 2) (- (* 3/80 (/ (pow re 2) (pow im 5))) (* 1/12 (/ 1 (pow im 3))))) (* 1/2 (/ 1 im)))))
(log (* 2 im))
(+ (log (* 2 im)) (/ re im))
(+ (log (* 2 im)) (* re (+ (* -1/6 (/ (pow re 2) (pow im 3))) (/ 1 im))))
(+ (log (* 2 im)) (* re (+ (* (pow re 2) (- (* 3/40 (/ (pow re 2) (pow im 5))) (* 1/6 (/ 1 (pow im 3))))) (/ 1 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 (+ (* 1/16 (* (sqrt (/ 1 (pow im 3))) (* re (sqrt 2)))) (* 1/4 (* (sqrt (/ 1 im)) (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 (+ (* 1/8 (* (sqrt (/ 1 (pow im 3))) (* re (sqrt 2)))) (* 1/2 (* (sqrt (/ 1 im)) (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 im) (* 2 re))
(+ (* 2 im) (* re (+ 2 (/ re im))))
(+ (* 2 im) (* re (+ 2 (* re (+ (* -1/4 (/ (pow re 2) (pow im 3))) (/ 1 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 (+ (* 1/16 (* (sqrt (/ 1 (pow im 3))) (* re (sqrt 2)))) (* 1/4 (* (sqrt (/ 1 im)) (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 (+ (* 1/8 (* (sqrt (/ 1 (pow im 3))) (* re (sqrt 2)))) (* 1/2 (* (sqrt (/ 1 im)) (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 im) (* 2 re))
(+ (* 2 im) (* re (+ 2 (/ re im))))
(+ (* 2 im) (* re (+ 2 (* re (+ (* -1/4 (/ (pow re 2) (pow im 3))) (/ 1 im))))))
(* -1 (/ (pow im 2) re))
(* -1 (/ (pow im 2) re))
(* -1 (/ (pow im 2) re))
(* -1 (/ (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 (+ (* 1/16 (* (sqrt (/ 1 (pow im 3))) (* re (sqrt 2)))) (* 1/4 (* (sqrt (/ 1 im)) (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 (+ (* 1/8 (* (sqrt (/ 1 (pow im 3))) (* re (sqrt 2)))) (* 1/2 (* (sqrt (/ 1 im)) (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 im) (* 2 re))
(+ (* 2 im) (* re (+ 2 (/ re im))))
(+ (* 2 im) (* re (+ 2 (* re (+ (* -1/4 (/ (pow re 2) (pow im 3))) (/ 1 im))))))
im
(+ im re)
(+ im (* re (+ 1 (* 1/2 (/ re im)))))
(+ im (* re (+ 1 (* re (+ (* -1/8 (/ (pow re 2) (pow im 3))) (* 1/2 (/ 1 im)))))))
(* (sqrt (/ 1 im)) (sqrt 2))
(+ (* 1/2 (* (sqrt (/ 1 (pow im 3))) (* re (sqrt 2)))) (* (sqrt (/ 1 im)) (sqrt 2)))
(+ (* 1/2 (* (sqrt (/ 1 (pow im 3))) (* re (sqrt 2)))) (* (sqrt (/ 1 im)) (sqrt 2)))
(+ (* 1/2 (* (sqrt (/ 1 (pow im 3))) (* re (sqrt 2)))) (* (sqrt (/ 1 im)) (sqrt 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 (+ (* 1/16 (* (sqrt (/ 1 (pow im 3))) (* re (sqrt 2)))) (* 1/4 (* (sqrt (/ 1 im)) (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 (+ (* 1/8 (* (sqrt (/ 1 (pow im 3))) (* re (sqrt 2)))) (* 1/2 (* (sqrt (/ 1 im)) (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 2))
(+ (* 1/2 (* (sqrt (/ 1 im)) (* re (sqrt 2)))) (* (sqrt im) (sqrt 2)))
(+ (* 1/2 (* (sqrt (/ 1 im)) (* re (sqrt 2)))) (* (sqrt im) (sqrt 2)))
(+ (* 1/2 (* (sqrt (/ 1 im)) (* re (sqrt 2)))) (* (sqrt im) (sqrt 2)))
im
(+ im re)
(+ im (* re (+ 1 (* 1/2 (/ re im)))))
(+ im (* re (+ 1 (* re (+ (* -1/8 (/ (pow re 2) (pow im 3))) (* 1/2 (/ 1 im)))))))
(* 2 im)
(+ (* 2 im) (* 2 re))
(+ (* 2 im) (* re (+ 2 (/ re im))))
(+ (* 2 im) (* re (+ 2 (* re (+ (* -1/4 (/ (pow re 2) (pow im 3))) (/ 1 im))))))
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)))))
(* 2 (sqrt re))
(* re (+ (* 1/4 (* (pow im 2) (sqrt (/ 1 (pow re 5))))) (* 2 (sqrt (/ 1 re)))))
(* re (+ (* -1/16 (* (pow im 4) (sqrt (/ 1 (pow re 9))))) (+ (* 1/4 (* (pow im 2) (sqrt (/ 1 (pow re 5))))) (* 2 (sqrt (/ 1 re))))))
(* re (+ (* -1/16 (* (pow im 4) (sqrt (/ 1 (pow re 9))))) (+ (* -1/64 (* (pow im 4) (sqrt (/ 1 (pow re 9))))) (+ (* 1/4 (* (pow im 2) (sqrt (/ 1 (pow re 5))))) (* 2 (sqrt (/ 1 re)))))))
(* 1/2 (* (sqrt re) (pow (sqrt 2) 2)))
(* re (+ (* 1/8 (* (pow im 2) (sqrt (/ 1 (pow re 5))))) (* 1/2 (* (sqrt (/ 1 re)) (pow (sqrt 2) 2)))))
(* re (+ (* -1/32 (* (pow im 4) (sqrt (/ 1 (pow re 9))))) (+ (* 1/8 (* (pow im 2) (sqrt (/ 1 (pow re 5))))) (* 1/2 (* (sqrt (/ 1 re)) (pow (sqrt 2) 2))))))
(* re (+ (* -1/32 (* (pow im 4) (sqrt (/ 1 (pow re 9))))) (+ (* -1/64 (* (/ (pow im 4) (pow (sqrt 2) 2)) (sqrt (/ 1 (pow re 9))))) (+ (* 1/8 (* (pow im 2) (sqrt (/ 1 (pow re 5))))) (* 1/2 (* (sqrt (/ 1 re)) (pow (sqrt 2) 2)))))))
(* 1/2 (+ (log 4) (* -1 (log (/ 1 re)))))
(+ (* 1/8 (/ (pow im 2) (pow re 2))) (* 1/2 (+ (log 4) (* -1 (log (/ 1 re))))))
(+ (* 1/48 (/ (+ (* -3/2 (pow im 4)) (* -3/4 (pow im 4))) (pow re 4))) (+ (* 1/8 (/ (pow im 2) (pow re 2))) (* 1/2 (+ (log 4) (* -1 (log (/ 1 re)))))))
(+ (* 1/1440 (/ (+ (* 15/4 (pow im 6)) (+ (* 45/4 (pow im 6)) (* 45/2 (pow im 6)))) (pow re 6))) (+ (* 1/48 (/ (+ (* -3/2 (pow im 4)) (* -3/4 (pow im 4))) (pow re 4))) (+ (* 1/8 (/ (pow im 2) (pow re 2))) (* 1/2 (+ (log 4) (* -1 (log (/ 1 re))))))))
(+ (log 4) (* -1 (log (/ 1 re))))
(+ (log 4) (+ (* -1 (log (/ 1 re))) (* 1/4 (/ (pow im 2) (pow re 2)))))
(+ (log 4) (+ (* -1 (log (/ 1 re))) (+ (* 1/24 (/ (+ (* -3/2 (pow im 4)) (* -3/4 (pow im 4))) (pow re 4))) (* 1/4 (/ (pow im 2) (pow re 2))))))
(+ (log 4) (+ (* -1 (log (/ 1 re))) (+ (* 1/720 (/ (+ (* 15/4 (pow im 6)) (+ (* 45/4 (pow im 6)) (* 45/2 (pow im 6)))) (pow re 6))) (+ (* 1/24 (/ (+ (* -3/2 (pow im 4)) (* -3/4 (pow im 4))) (pow re 4))) (* 1/4 (/ (pow im 2) (pow re 2)))))))
(* 1/2 (* (sqrt re) (pow (sqrt 2) 2)))
(* re (+ (* 1/8 (* (pow im 2) (sqrt (/ 1 (pow re 5))))) (* 1/2 (* (sqrt (/ 1 re)) (pow (sqrt 2) 2)))))
(* re (+ (* -1/32 (* (pow im 4) (sqrt (/ 1 (pow re 9))))) (+ (* 1/8 (* (pow im 2) (sqrt (/ 1 (pow re 5))))) (* 1/2 (* (sqrt (/ 1 re)) (pow (sqrt 2) 2))))))
(* re (+ (* -1/32 (* (pow im 4) (sqrt (/ 1 (pow re 9))))) (+ (* -1/64 (* (/ (pow im 4) (pow (sqrt 2) 2)) (sqrt (/ 1 (pow re 9))))) (+ (* 1/8 (* (pow im 2) (sqrt (/ 1 (pow re 5))))) (* 1/2 (* (sqrt (/ 1 re)) (pow (sqrt 2) 2)))))))
(* (sqrt re) (pow (sqrt 2) 2))
(* re (+ (* 1/4 (* (pow im 2) (sqrt (/ 1 (pow re 5))))) (* (sqrt (/ 1 re)) (pow (sqrt 2) 2))))
(* re (+ (* -1/16 (* (pow im 4) (sqrt (/ 1 (pow re 9))))) (+ (* 1/4 (* (pow im 2) (sqrt (/ 1 (pow re 5))))) (* (sqrt (/ 1 re)) (pow (sqrt 2) 2)))))
(* re (+ (* -1/16 (* (pow im 4) (sqrt (/ 1 (pow re 9))))) (+ (* -1/32 (* (/ (pow im 4) (pow (sqrt 2) 2)) (sqrt (/ 1 (pow re 9))))) (+ (* 1/4 (* (pow im 2) (sqrt (/ 1 (pow re 5))))) (* (sqrt (/ 1 re)) (pow (sqrt 2) 2))))))
(* 4 re)
(* re (+ 4 (/ (pow im 2) (pow re 2))))
(* re (+ 4 (+ (* -1/4 (/ (pow im 4) (pow re 4))) (/ (pow im 2) (pow re 2)))))
(* 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) (pow (sqrt 2) 2)))
(* re (+ (* 1/8 (* (pow im 2) (sqrt (/ 1 (pow re 5))))) (* 1/2 (* (sqrt (/ 1 re)) (pow (sqrt 2) 2)))))
(* re (+ (* -1/32 (* (pow im 4) (sqrt (/ 1 (pow re 9))))) (+ (* 1/8 (* (pow im 2) (sqrt (/ 1 (pow re 5))))) (* 1/2 (* (sqrt (/ 1 re)) (pow (sqrt 2) 2))))))
(* re (+ (* -1/32 (* (pow im 4) (sqrt (/ 1 (pow re 9))))) (+ (* -1/64 (* (/ (pow im 4) (pow (sqrt 2) 2)) (sqrt (/ 1 (pow re 9))))) (+ (* 1/8 (* (pow im 2) (sqrt (/ 1 (pow re 5))))) (* 1/2 (* (sqrt (/ 1 re)) (pow (sqrt 2) 2)))))))
(* (sqrt re) (pow (sqrt 2) 2))
(* re (+ (* 1/4 (* (pow im 2) (sqrt (/ 1 (pow re 5))))) (* (sqrt (/ 1 re)) (pow (sqrt 2) 2))))
(* re (+ (* -1/16 (* (pow im 4) (sqrt (/ 1 (pow re 9))))) (+ (* 1/4 (* (pow im 2) (sqrt (/ 1 (pow re 5))))) (* (sqrt (/ 1 re)) (pow (sqrt 2) 2)))))
(* re (+ (* -1/16 (* (pow im 4) (sqrt (/ 1 (pow re 9))))) (+ (* -1/32 (* (/ (pow im 4) (pow (sqrt 2) 2)) (sqrt (/ 1 (pow re 9))))) (+ (* 1/4 (* (pow im 2) (sqrt (/ 1 (pow re 5))))) (* (sqrt (/ 1 re)) (pow (sqrt 2) 2))))))
(* 4 re)
(* re (+ 4 (/ (pow im 2) (pow re 2))))
(* re (+ 4 (+ (* -1/4 (/ (pow im 4) (pow re 4))) (/ (pow im 2) (pow re 2)))))
(* 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 (/ (pow im 2) re))
(* -1 (/ (pow im 2) re))
(* -1 (/ (pow im 2) re))
(* -1 (/ (pow im 2) re))
(* 1/2 (* (sqrt re) (pow (sqrt 2) 2)))
(* re (+ (* 1/8 (* (pow im 2) (sqrt (/ 1 (pow re 5))))) (* 1/2 (* (sqrt (/ 1 re)) (pow (sqrt 2) 2)))))
(* re (+ (* -1/32 (* (pow im 4) (sqrt (/ 1 (pow re 9))))) (+ (* 1/8 (* (pow im 2) (sqrt (/ 1 (pow re 5))))) (* 1/2 (* (sqrt (/ 1 re)) (pow (sqrt 2) 2))))))
(* re (+ (* -1/32 (* (pow im 4) (sqrt (/ 1 (pow re 9))))) (+ (* -1/64 (* (/ (pow im 4) (pow (sqrt 2) 2)) (sqrt (/ 1 (pow re 9))))) (+ (* 1/8 (* (pow im 2) (sqrt (/ 1 (pow re 5))))) (* 1/2 (* (sqrt (/ 1 re)) (pow (sqrt 2) 2)))))))
(* (sqrt re) (pow (sqrt 2) 2))
(* re (+ (* 1/4 (* (pow im 2) (sqrt (/ 1 (pow re 5))))) (* (sqrt (/ 1 re)) (pow (sqrt 2) 2))))
(* re (+ (* -1/16 (* (pow im 4) (sqrt (/ 1 (pow re 9))))) (+ (* 1/4 (* (pow im 2) (sqrt (/ 1 (pow re 5))))) (* (sqrt (/ 1 re)) (pow (sqrt 2) 2)))))
(* re (+ (* -1/16 (* (pow im 4) (sqrt (/ 1 (pow re 9))))) (+ (* -1/32 (* (/ (pow im 4) (pow (sqrt 2) 2)) (sqrt (/ 1 (pow re 9))))) (+ (* 1/4 (* (pow im 2) (sqrt (/ 1 (pow re 5))))) (* (sqrt (/ 1 re)) (pow (sqrt 2) 2))))))
(* 4 re)
(* re (+ 4 (/ (pow im 2) (pow re 2))))
(* re (+ 4 (+ (* -1/4 (/ (pow im 4) (pow re 4))) (/ (pow im 2) (pow re 2)))))
(* 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)
(* re (+ 2 (* 1/2 (/ (pow im 2) (pow re 2)))))
(* re (+ 2 (+ (* -1/8 (/ (pow im 4) (pow re 4))) (* 1/2 (/ (pow im 2) (pow re 2))))))
(* 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 (/ 1 (pow im 3))) (* re (sqrt 2))))
(* re (+ (* 1/2 (* (sqrt (/ 1 (pow im 3))) (sqrt 2))) (* (sqrt (/ 1 im)) (/ (sqrt 2) re))))
(* re (+ (* 1/2 (* (sqrt (/ 1 (pow im 3))) (sqrt 2))) (* (sqrt (/ 1 im)) (/ (sqrt 2) re))))
(* re (+ (* 1/2 (* (sqrt (/ 1 (pow im 3))) (sqrt 2))) (* (sqrt (/ 1 im)) (/ (sqrt 2) re))))
(* 1/2 (* (sqrt re) (pow (sqrt 2) 2)))
(* re (+ (* 1/8 (* (pow im 2) (sqrt (/ 1 (pow re 5))))) (* 1/2 (* (sqrt (/ 1 re)) (pow (sqrt 2) 2)))))
(* re (+ (* -1/32 (* (pow im 4) (sqrt (/ 1 (pow re 9))))) (+ (* 1/8 (* (pow im 2) (sqrt (/ 1 (pow re 5))))) (* 1/2 (* (sqrt (/ 1 re)) (pow (sqrt 2) 2))))))
(* re (+ (* -1/32 (* (pow im 4) (sqrt (/ 1 (pow re 9))))) (+ (* -1/64 (* (/ (pow im 4) (pow (sqrt 2) 2)) (sqrt (/ 1 (pow re 9))))) (+ (* 1/8 (* (pow im 2) (sqrt (/ 1 (pow re 5))))) (* 1/2 (* (sqrt (/ 1 re)) (pow (sqrt 2) 2)))))))
(* (sqrt re) (pow (sqrt 2) 2))
(* re (+ (* 1/4 (* (pow im 2) (sqrt (/ 1 (pow re 5))))) (* (sqrt (/ 1 re)) (pow (sqrt 2) 2))))
(* re (+ (* -1/16 (* (pow im 4) (sqrt (/ 1 (pow re 9))))) (+ (* 1/4 (* (pow im 2) (sqrt (/ 1 (pow re 5))))) (* (sqrt (/ 1 re)) (pow (sqrt 2) 2)))))
(* re (+ (* -1/16 (* (pow im 4) (sqrt (/ 1 (pow re 9))))) (+ (* -1/32 (* (/ (pow im 4) (pow (sqrt 2) 2)) (sqrt (/ 1 (pow re 9))))) (+ (* 1/4 (* (pow im 2) (sqrt (/ 1 (pow re 5))))) (* (sqrt (/ 1 re)) (pow (sqrt 2) 2))))))
(* 1/2 (* (sqrt (/ 1 im)) (* re (sqrt 2))))
(* re (+ (* 1/2 (* (sqrt (/ 1 im)) (sqrt 2))) (* (sqrt im) (/ (sqrt 2) re))))
(* re (+ (* 1/2 (* (sqrt (/ 1 im)) (sqrt 2))) (* (sqrt im) (/ (sqrt 2) re))))
(* re (+ (* 1/2 (* (sqrt (/ 1 im)) (sqrt 2))) (* (sqrt im) (/ (sqrt 2) re))))
(* 2 re)
(* re (+ 2 (* 1/2 (/ (pow im 2) (pow re 2)))))
(* re (+ 2 (+ (* -1/8 (/ (pow im 4) (pow re 4))) (* 1/2 (/ (pow im 2) (pow re 2))))))
(* 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)))))))
(* 4 re)
(* re (+ 4 (/ (pow im 2) (pow re 2))))
(* re (+ 4 (+ (* -1/4 (/ (pow im 4) (pow re 4))) (/ (pow im 2) (pow re 2)))))
(* re (+ 4 (+ (* -1/4 (/ (pow im 4) (pow re 4))) (+ (* 1/8 (/ (pow im 6) (pow re 6))) (/ (pow im 2) (pow re 2))))))
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)))))))
(* (* im (sqrt -1)) (sqrt (/ 1 re)))
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(* 1/2 (+ (log (/ -1 re)) (log (pow im 2))))
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(* (* im (* (sqrt -1) (* (sqrt 1/2) (sqrt 2)))) (sqrt (/ 1 re)))
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(* -1 (/ (pow im 2) re))
(* -1 (/ (+ (* -1/4 (/ (pow im 4) (pow re 2))) (pow im 2)) re))
(* -1 (/ (+ (* -1/4 (/ (pow im 4) (pow re 2))) (+ (* 1/8 (/ (pow im 6) (pow re 4))) (pow im 2))) re))
(* -1 (/ (+ (* -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) (* (sqrt 1/2) (sqrt 2)))) (sqrt (/ 1 re))))
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(+ (* -1 (/ (+ (* -1/32 (* (/ (* (pow im 3) (* (sqrt -1) (sqrt 2))) (sqrt 1/2)) (sqrt re))) (+ (* 1/1024 (* (/ (* (pow im 5) (* (sqrt -1) (sqrt 2))) (pow (sqrt 1/2) 3)) (sqrt (/ 1 (pow re 3))))) (* 1/64 (* (/ (* (pow im 5) (* (sqrt -1) (sqrt 2))) (sqrt 1/2)) (sqrt (/ 1 (pow re 3))))))) (pow re 3))) (* 1/2 (* (* im (* (sqrt -1) (* (sqrt 1/2) (sqrt 2)))) (sqrt (/ 1 re)))))
(* (* im (* (sqrt -1) (* (sqrt 1/2) (sqrt 2)))) (sqrt (/ 1 re)))
(+ (* 1/16 (* (/ (* (pow im 3) (* (sqrt -1) (sqrt 2))) (sqrt 1/2)) (sqrt (/ 1 (pow re 5))))) (* (* im (* (sqrt -1) (* (sqrt 1/2) (sqrt 2)))) (sqrt (/ 1 re))))
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(+ (* -1 (/ (+ (* -1/16 (* (/ (* (pow im 3) (* (sqrt -1) (sqrt 2))) (sqrt 1/2)) (sqrt re))) (+ (* 1/512 (* (/ (* (pow im 5) (* (sqrt -1) (sqrt 2))) (pow (sqrt 1/2) 3)) (sqrt (/ 1 (pow re 3))))) (* 1/32 (* (/ (* (pow im 5) (* (sqrt -1) (sqrt 2))) (sqrt 1/2)) (sqrt (/ 1 (pow re 3))))))) (pow re 3))) (* (* im (* (sqrt -1) (* (sqrt 1/2) (sqrt 2)))) (sqrt (/ 1 re))))
(* -1 (/ (pow im 2) re))
(* -1 (/ (+ (* -1/4 (/ (pow im 4) (pow re 2))) (pow im 2)) re))
(* -1 (/ (+ (* -1/4 (/ (pow im 4) (pow re 2))) (+ (* 1/8 (/ (pow im 6) (pow re 4))) (pow im 2))) re))
(* -1 (/ (+ (* -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 (/ (pow im 2) re))
(* -1 (/ (pow im 2) re))
(* -1 (/ (pow im 2) re))
(* -1 (/ (pow im 2) re))
(* 1/2 (* (* im (* (sqrt -1) (* (sqrt 1/2) (sqrt 2)))) (sqrt (/ 1 re))))
(+ (* 1/32 (* (/ (* (pow im 3) (* (sqrt -1) (sqrt 2))) (sqrt 1/2)) (sqrt (/ 1 (pow re 5))))) (* 1/2 (* (* im (* (sqrt -1) (* (sqrt 1/2) (sqrt 2)))) (sqrt (/ 1 re)))))
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(+ (* -1 (/ (+ (* -1/32 (* (/ (* (pow im 3) (* (sqrt -1) (sqrt 2))) (sqrt 1/2)) (sqrt re))) (+ (* 1/1024 (* (/ (* (pow im 5) (* (sqrt -1) (sqrt 2))) (pow (sqrt 1/2) 3)) (sqrt (/ 1 (pow re 3))))) (* 1/64 (* (/ (* (pow im 5) (* (sqrt -1) (sqrt 2))) (sqrt 1/2)) (sqrt (/ 1 (pow re 3))))))) (pow re 3))) (* 1/2 (* (* im (* (sqrt -1) (* (sqrt 1/2) (sqrt 2)))) (sqrt (/ 1 re)))))
(* (* im (* (sqrt -1) (* (sqrt 1/2) (sqrt 2)))) (sqrt (/ 1 re)))
(+ (* 1/16 (* (/ (* (pow im 3) (* (sqrt -1) (sqrt 2))) (sqrt 1/2)) (sqrt (/ 1 (pow re 5))))) (* (* im (* (sqrt -1) (* (sqrt 1/2) (sqrt 2)))) (sqrt (/ 1 re))))
(+ (* -1 (/ (+ (* -1/16 (* (/ (* (pow im 3) (* (sqrt -1) (sqrt 2))) (sqrt 1/2)) (sqrt re))) (* 1/32 (* (/ (* (pow im 5) (* (sqrt -1) (sqrt 2))) (sqrt 1/2)) (sqrt (/ 1 (pow re 3)))))) (pow re 3))) (* (* im (* (sqrt -1) (* (sqrt 1/2) (sqrt 2)))) (sqrt (/ 1 re))))
(+ (* -1 (/ (+ (* -1/16 (* (/ (* (pow im 3) (* (sqrt -1) (sqrt 2))) (sqrt 1/2)) (sqrt re))) (+ (* 1/512 (* (/ (* (pow im 5) (* (sqrt -1) (sqrt 2))) (pow (sqrt 1/2) 3)) (sqrt (/ 1 (pow re 3))))) (* 1/32 (* (/ (* (pow im 5) (* (sqrt -1) (sqrt 2))) (sqrt 1/2)) (sqrt (/ 1 (pow re 3))))))) (pow re 3))) (* (* im (* (sqrt -1) (* (sqrt 1/2) (sqrt 2)))) (sqrt (/ 1 re))))
(* -1 (/ (pow im 2) re))
(* -1 (/ (+ (* -1/4 (/ (pow im 4) (pow re 2))) (pow im 2)) re))
(* -1 (/ (+ (* -1/4 (/ (pow im 4) (pow re 2))) (+ (* 1/8 (/ (pow im 6) (pow re 4))) (pow im 2))) re))
(* -1 (/ (+ (* -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 (/ (+ (* -1/8 (/ (pow im 4) (pow re 2))) (* 1/2 (pow im 2))) re))
(* -1 (/ (+ (* -1/8 (/ (pow im 4) (pow re 2))) (+ (* 1/16 (/ (pow im 6) (pow re 4))) (* 1/2 (pow im 2)))) re))
(* -1 (/ (+ (* -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 (* (sqrt (/ 1 (pow im 3))) (* re (sqrt 2))))
(* -1 (* re (+ (* -1 (* (sqrt (/ 1 im)) (/ (sqrt 2) re))) (* -1/2 (* (sqrt (/ 1 (pow im 3))) (sqrt 2))))))
(* -1 (* re (+ (* -1 (* (sqrt (/ 1 im)) (/ (sqrt 2) re))) (* -1/2 (* (sqrt (/ 1 (pow im 3))) (sqrt 2))))))
(* -1 (* re (+ (* -1 (* (sqrt (/ 1 im)) (/ (sqrt 2) re))) (* -1/2 (* (sqrt (/ 1 (pow im 3))) (sqrt 2))))))
(* 1/2 (* (* im (* (sqrt -1) (* (sqrt 1/2) (sqrt 2)))) (sqrt (/ 1 re))))
(+ (* 1/32 (* (/ (* (pow im 3) (* (sqrt -1) (sqrt 2))) (sqrt 1/2)) (sqrt (/ 1 (pow re 5))))) (* 1/2 (* (* im (* (sqrt -1) (* (sqrt 1/2) (sqrt 2)))) (sqrt (/ 1 re)))))
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(+ (* -1 (/ (+ (* -1/32 (* (/ (* (pow im 3) (* (sqrt -1) (sqrt 2))) (sqrt 1/2)) (sqrt re))) (+ (* 1/1024 (* (/ (* (pow im 5) (* (sqrt -1) (sqrt 2))) (pow (sqrt 1/2) 3)) (sqrt (/ 1 (pow re 3))))) (* 1/64 (* (/ (* (pow im 5) (* (sqrt -1) (sqrt 2))) (sqrt 1/2)) (sqrt (/ 1 (pow re 3))))))) (pow re 3))) (* 1/2 (* (* im (* (sqrt -1) (* (sqrt 1/2) (sqrt 2)))) (sqrt (/ 1 re)))))
(* (* im (* (sqrt -1) (* (sqrt 1/2) (sqrt 2)))) (sqrt (/ 1 re)))
(+ (* 1/16 (* (/ (* (pow im 3) (* (sqrt -1) (sqrt 2))) (sqrt 1/2)) (sqrt (/ 1 (pow re 5))))) (* (* im (* (sqrt -1) (* (sqrt 1/2) (sqrt 2)))) (sqrt (/ 1 re))))
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(+ (* -1 (/ (+ (* -1/16 (* (/ (* (pow im 3) (* (sqrt -1) (sqrt 2))) (sqrt 1/2)) (sqrt re))) (+ (* 1/512 (* (/ (* (pow im 5) (* (sqrt -1) (sqrt 2))) (pow (sqrt 1/2) 3)) (sqrt (/ 1 (pow re 3))))) (* 1/32 (* (/ (* (pow im 5) (* (sqrt -1) (sqrt 2))) (sqrt 1/2)) (sqrt (/ 1 (pow re 3))))))) (pow re 3))) (* (* im (* (sqrt -1) (* (sqrt 1/2) (sqrt 2)))) (sqrt (/ 1 re))))
(* 1/2 (* (sqrt (/ 1 im)) (* re (sqrt 2))))
(* -1 (* re (+ (* -1 (* (sqrt im) (/ (sqrt 2) re))) (* -1/2 (* (sqrt (/ 1 im)) (sqrt 2))))))
(* -1 (* re (+ (* -1 (* (sqrt im) (/ (sqrt 2) re))) (* -1/2 (* (sqrt (/ 1 im)) (sqrt 2))))))
(* -1 (* re (+ (* -1 (* (sqrt im) (/ (sqrt 2) re))) (* -1/2 (* (sqrt (/ 1 im)) (sqrt 2))))))
(* -1/2 (/ (pow im 2) re))
(* -1 (/ (+ (* -1/8 (/ (pow im 4) (pow re 2))) (* 1/2 (pow im 2))) re))
(* -1 (/ (+ (* -1/8 (/ (pow im 4) (pow re 2))) (+ (* 1/16 (/ (pow im 6) (pow re 4))) (* 1/2 (pow im 2)))) re))
(* -1 (/ (+ (* -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 (/ (pow im 2) re))
(* -1 (/ (+ (* -1/4 (/ (pow im 4) (pow re 2))) (pow im 2)) re))
(* -1 (/ (+ (* -1/4 (/ (pow im 4) (pow re 2))) (+ (* 1/8 (/ (pow im 6) (pow re 4))) (pow im 2))) re))
(* -1 (/ (+ (* -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 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 (sqrt re))
(+ (* 1/4 (* (pow im 2) (sqrt (/ 1 (pow re 3))))) (* 2 (sqrt re)))
(+ (* 2 (sqrt re)) (* (pow im 2) (+ (* -5/64 (* (pow im 2) (sqrt (/ 1 (pow re 7))))) (* 1/4 (sqrt (/ 1 (pow re 3)))))))
(+ (* 2 (sqrt re)) (* (pow im 2) (+ (* 1/4 (sqrt (/ 1 (pow re 3)))) (* (pow im 2) (+ (* -5/64 (sqrt (/ 1 (pow re 7)))) (* 21/512 (* (pow im 2) (sqrt (/ 1 (pow re 11))))))))))
(* 1/2 (* (sqrt re) (pow (sqrt 2) 2)))
(+ (* 1/8 (* (pow im 2) (sqrt (/ 1 (pow re 3))))) (* 1/2 (* (sqrt re) (pow (sqrt 2) 2))))
(+ (* 1/2 (* (sqrt re) (pow (sqrt 2) 2))) (* (pow im 2) (+ (* -1/4 (* (* (pow im 2) (+ (* 1/16 (/ 1 (* (pow re 3) (pow (sqrt 2) 2)))) (* 1/8 (/ 1 (pow re 3))))) (sqrt (/ 1 re)))) (* 1/8 (sqrt (/ 1 (pow re 3)))))))
(+ (* 1/2 (* (sqrt re) (pow (sqrt 2) 2))) (* (pow im 2) (+ (* 1/8 (sqrt (/ 1 (pow re 3)))) (* (pow im 2) (+ (* -1/4 (* (sqrt (/ 1 re)) (+ (* 1/16 (/ 1 (* (pow re 3) (pow (sqrt 2) 2)))) (* 1/8 (/ 1 (pow re 3)))))) (* 1/4 (* (* (pow im 2) (- (* 1/16 (/ 1 (pow re 5))) (* -1/4 (/ (+ (* 1/16 (/ 1 (* (pow re 3) (pow (sqrt 2) 2)))) (* 1/8 (/ 1 (pow re 3)))) (* (pow re 2) (pow (sqrt 2) 2)))))) (sqrt (/ 1 re)))))))))
(* 1/2 (log (* 4 re)))
(+ (* 1/8 (/ (pow im 2) (pow re 2))) (* 1/2 (log (* 4 re))))
(+ (* 1/2 (log (* 4 re))) (* (pow im 2) (+ (* -3/64 (/ (pow im 2) (pow re 4))) (* 1/8 (/ 1 (pow re 2))))))
(+ (* 1/2 (log (* 4 re))) (* (pow im 2) (+ (* (pow im 2) (- (* 5/192 (/ (pow im 2) (pow re 6))) (* 3/64 (/ 1 (pow re 4))))) (* 1/8 (/ 1 (pow re 2))))))
(log (* 4 re))
(+ (log (* 4 re)) (* 1/4 (/ (pow im 2) (pow re 2))))
(+ (log (* 4 re)) (* (pow im 2) (+ (* -3/32 (/ (pow im 2) (pow re 4))) (* 1/4 (/ 1 (pow re 2))))))
(+ (log (* 4 re)) (* (pow im 2) (+ (* (pow im 2) (- (* 5/96 (/ (pow im 2) (pow re 6))) (* 3/32 (/ 1 (pow re 4))))) (* 1/4 (/ 1 (pow re 2))))))
(* 1/2 (* (sqrt re) (pow (sqrt 2) 2)))
(+ (* 1/8 (* (pow im 2) (sqrt (/ 1 (pow re 3))))) (* 1/2 (* (sqrt re) (pow (sqrt 2) 2))))
(+ (* 1/2 (* (sqrt re) (pow (sqrt 2) 2))) (* (pow im 2) (+ (* -1/4 (* (* (pow im 2) (+ (* 1/16 (/ 1 (* (pow re 3) (pow (sqrt 2) 2)))) (* 1/8 (/ 1 (pow re 3))))) (sqrt (/ 1 re)))) (* 1/8 (sqrt (/ 1 (pow re 3)))))))
(+ (* 1/2 (* (sqrt re) (pow (sqrt 2) 2))) (* (pow im 2) (+ (* 1/8 (sqrt (/ 1 (pow re 3)))) (* (pow im 2) (+ (* -1/4 (* (sqrt (/ 1 re)) (+ (* 1/16 (/ 1 (* (pow re 3) (pow (sqrt 2) 2)))) (* 1/8 (/ 1 (pow re 3)))))) (* 1/4 (* (* (pow im 2) (- (* 1/16 (/ 1 (pow re 5))) (* -1/4 (/ (+ (* 1/16 (/ 1 (* (pow re 3) (pow (sqrt 2) 2)))) (* 1/8 (/ 1 (pow re 3)))) (* (pow re 2) (pow (sqrt 2) 2)))))) (sqrt (/ 1 re)))))))))
(* (sqrt re) (pow (sqrt 2) 2))
(+ (* 1/4 (* (pow im 2) (sqrt (/ 1 (pow re 3))))) (* (sqrt re) (pow (sqrt 2) 2)))
(+ (* (sqrt re) (pow (sqrt 2) 2)) (* (pow im 2) (+ (* -1/2 (* (* (pow im 2) (+ (* 1/16 (/ 1 (* (pow re 3) (pow (sqrt 2) 2)))) (* 1/8 (/ 1 (pow re 3))))) (sqrt (/ 1 re)))) (* 1/4 (sqrt (/ 1 (pow re 3)))))))
(+ (* (sqrt re) (pow (sqrt 2) 2)) (* (pow im 2) (+ (* 1/4 (sqrt (/ 1 (pow re 3)))) (* (pow im 2) (+ (* -1/2 (* (sqrt (/ 1 re)) (+ (* 1/16 (/ 1 (* (pow re 3) (pow (sqrt 2) 2)))) (* 1/8 (/ 1 (pow re 3)))))) (* 1/2 (* (* (pow im 2) (- (* 1/16 (/ 1 (pow re 5))) (* -1/4 (/ (+ (* 1/16 (/ 1 (* (pow re 3) (pow (sqrt 2) 2)))) (* 1/8 (/ 1 (pow re 3)))) (* (pow re 2) (pow (sqrt 2) 2)))))) (sqrt (/ 1 re)))))))))
(* 4 re)
(+ (* 4 re) (/ (pow im 2) re))
(+ (* 4 re) (* (pow im 2) (+ (* -1/4 (/ (pow im 2) (pow re 3))) (/ 1 re))))
(+ (* 4 re) (* (pow im 2) (+ (* (pow im 2) (- (* 1/8 (/ (pow im 2) (pow re 5))) (* 1/4 (/ 1 (pow re 3))))) (/ 1 re))))
(* 2 im)
(* 2 im)
(* 2 im)
(* 2 im)
(* 1/2 (* (sqrt re) (pow (sqrt 2) 2)))
(+ (* 1/8 (* (pow im 2) (sqrt (/ 1 (pow re 3))))) (* 1/2 (* (sqrt re) (pow (sqrt 2) 2))))
(+ (* 1/2 (* (sqrt re) (pow (sqrt 2) 2))) (* (pow im 2) (+ (* -1/4 (* (* (pow im 2) (+ (* 1/16 (/ 1 (* (pow re 3) (pow (sqrt 2) 2)))) (* 1/8 (/ 1 (pow re 3))))) (sqrt (/ 1 re)))) (* 1/8 (sqrt (/ 1 (pow re 3)))))))
(+ (* 1/2 (* (sqrt re) (pow (sqrt 2) 2))) (* (pow im 2) (+ (* 1/8 (sqrt (/ 1 (pow re 3)))) (* (pow im 2) (+ (* -1/4 (* (sqrt (/ 1 re)) (+ (* 1/16 (/ 1 (* (pow re 3) (pow (sqrt 2) 2)))) (* 1/8 (/ 1 (pow re 3)))))) (* 1/4 (* (* (pow im 2) (- (* 1/16 (/ 1 (pow re 5))) (* -1/4 (/ (+ (* 1/16 (/ 1 (* (pow re 3) (pow (sqrt 2) 2)))) (* 1/8 (/ 1 (pow re 3)))) (* (pow re 2) (pow (sqrt 2) 2)))))) (sqrt (/ 1 re)))))))))
(* (sqrt re) (pow (sqrt 2) 2))
(+ (* 1/4 (* (pow im 2) (sqrt (/ 1 (pow re 3))))) (* (sqrt re) (pow (sqrt 2) 2)))
(+ (* (sqrt re) (pow (sqrt 2) 2)) (* (pow im 2) (+ (* -1/2 (* (* (pow im 2) (+ (* 1/16 (/ 1 (* (pow re 3) (pow (sqrt 2) 2)))) (* 1/8 (/ 1 (pow re 3))))) (sqrt (/ 1 re)))) (* 1/4 (sqrt (/ 1 (pow re 3)))))))
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(* 4 re)
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im
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im
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(* -1 (* im (+ 2 (* -1 (/ (+ (* -1 (/ (+ (* -1/4 (/ (pow re 4) (pow im 2))) (pow re 2)) im)) (* 2 re)) im)))))
(* -1 (/ (pow im 2) re))
(* -1 (/ (pow im 2) re))
(* -1 (/ (pow im 2) re))
(* -1 (/ (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 (+ (* -1/8 (* (sqrt (/ 1 (pow im 5))) (* (pow re 2) (* (sqrt -1) (sqrt 2))))) (+ (* 1/4 (* (sqrt (/ 1 (pow im 3))) (* re (* (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 (+ (* -1/4 (* (sqrt (/ 1 (pow im 5))) (* (pow re 2) (* (sqrt -1) (sqrt 2))))) (+ (* 1/2 (* (sqrt (/ 1 (pow im 3))) (* re (* (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 (/ (+ (* -1 (/ (pow re 2) im)) (* 2 re)) im)))))
(* -1 (* im (+ 2 (* -1 (/ (+ (* -1 (/ (+ (* -1/4 (/ (pow re 4) (pow im 2))) (pow re 2)) im)) (* 2 re)) im)))))
(* -1 im)
(* -1 (* im (+ 1 (* -1 (/ re im)))))
(* -1 (* im (+ 1 (* -1 (/ (+ re (* -1/2 (/ (pow re 2) im))) im)))))
(* -1 (* im (+ 1 (* -1 (/ (+ re (* -1 (/ (+ (* -1/8 (/ (pow re 4) (pow im 2))) (* 1/2 (pow re 2))) im))) im)))))
(* (sqrt (/ 1 im)) (* (pow (sqrt -1) 2) (sqrt 2)))
(+ (* -1/2 (* (sqrt (/ 1 (pow im 3))) (* re (* (pow (sqrt -1) 2) (sqrt 2))))) (* (sqrt (/ 1 im)) (* (pow (sqrt -1) 2) (sqrt 2))))
(+ (* -1/2 (* (sqrt (/ 1 (pow im 3))) (* re (* (pow (sqrt -1) 2) (sqrt 2))))) (* (sqrt (/ 1 im)) (* (pow (sqrt -1) 2) (sqrt 2))))
(+ (* -1/2 (* (sqrt (/ 1 (pow im 3))) (* re (* (pow (sqrt -1) 2) (sqrt 2))))) (* (sqrt (/ 1 im)) (* (pow (sqrt -1) 2) (sqrt 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 (+ (* -1/8 (* (sqrt (/ 1 (pow im 5))) (* (pow re 2) (* (sqrt -1) (sqrt 2))))) (+ (* 1/4 (* (sqrt (/ 1 (pow im 3))) (* re (* (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 (+ (* -1/4 (* (sqrt (/ 1 (pow im 5))) (* (pow re 2) (* (sqrt -1) (sqrt 2))))) (+ (* 1/2 (* (sqrt (/ 1 (pow im 3))) (* re (* (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)))))))
(* (sqrt im) (* (pow (sqrt -1) 2) (sqrt 2)))
(* -1 (* im (+ (* -1 (* (sqrt (/ 1 im)) (* (pow (sqrt -1) 2) (sqrt 2)))) (* 1/2 (* (sqrt (/ 1 (pow im 3))) (* re (* (pow (sqrt -1) 2) (sqrt 2))))))))
(* -1 (* im (+ (* -1 (* (sqrt (/ 1 im)) (* (pow (sqrt -1) 2) (sqrt 2)))) (* 1/2 (* (sqrt (/ 1 (pow im 3))) (* re (* (pow (sqrt -1) 2) (sqrt 2))))))))
(* -1 (* im (+ (* -1 (* (sqrt (/ 1 im)) (* (pow (sqrt -1) 2) (sqrt 2)))) (* 1/2 (* (sqrt (/ 1 (pow im 3))) (* re (* (pow (sqrt -1) 2) (sqrt 2))))))))
(* -1 im)
(* -1 (* im (+ 1 (* -1 (/ re im)))))
(* -1 (* im (+ 1 (* -1 (/ (+ re (* -1/2 (/ (pow re 2) im))) im)))))
(* -1 (* im (+ 1 (* -1 (/ (+ re (* -1 (/ (+ (* -1/8 (/ (pow re 4) (pow im 2))) (* 1/2 (pow re 2))) im))) im)))))
(* -2 im)
(* -1 (* im (+ 2 (* -2 (/ re im)))))
(* -1 (* im (+ 2 (* -1 (/ (+ (* -1 (/ (pow re 2) im)) (* 2 re)) im)))))
(* -1 (* im (+ 2 (* -1 (/ (+ (* -1 (/ (+ (* -1/4 (/ (pow re 4) (pow im 2))) (pow re 2)) im)) (* 2 re)) im)))))
(* -1 im)
(* -1 im)
(* -1 im)
(* -1 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 (* (sqrt (/ 1 (pow im 3))) (pow (sqrt -1) 2)))
(* -1 (* (sqrt (/ 1 (pow im 3))) (pow (sqrt -1) 2)))
(* -1 (* (sqrt (/ 1 (pow im 3))) (pow (sqrt -1) 2)))
(* -1 (* (sqrt (/ 1 (pow im 3))) (pow (sqrt -1) 2)))

Outputs
(*.f64 (sqrt.f64 #s(literal 2 binary64)) (sqrt.f64 im))
(fma.f64 (/.f64 re (sqrt.f64 #s(literal 2 binary64))) (sqrt.f64 (/.f64 #s(literal 1 binary64) im)) (*.f64 (sqrt.f64 #s(literal 2 binary64)) (sqrt.f64 im)))
(fma.f64 (fma.f64 (.f64 (.f64 re (/.f64 (-.f64 (/.f64 #s(literal 1 binary64) im) (/.f64 (/.f64 #s(literal 1 binary64) im) #s(literal 2 binary64))) (sqrt.f64 #s(literal 2 binary64)))) (sqrt.f64 (/.f64 #s(literal 1 binary64) im))) #s(literal 1/2 binary64) (/.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) im)) (sqrt.f64 #s(literal 2 binary64)))) re (*.f64 (sqrt.f64 #s(literal 2 binary64)) (sqrt.f64 im)))
(fma.f64 (fma.f64 (.f64 #s(literal 1/2 binary64) re) (.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) im)) (fma.f64 re (/.f64 (-.f64 (/.f64 (/.f64 #s(literal 1 binary64) (.f64 im im)) (pow.f64 (sqrt.f64 #s(literal 2 binary64)) #s(literal 4 binary64))) (/.f64 #s(literal 1 binary64) (.f64 (.f64 im im) #s(literal 2 binary64)))) (sqrt.f64 #s(literal 2 binary64))) (/.f64 (-.f64 (/.f64 #s(literal 1 binary64) im) (/.f64 (/.f64 #s(literal 1 binary64) im) #s(literal 2 binary64))) (sqrt.f64 #s(literal 2 binary64))))) (/.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) im)) (sqrt.f64 #s(literal 2 binary64)))) re (.f64 (sqrt.f64 #s(literal 2 binary64)) (sqrt.f64 im)))
(.f64 (.f64 #s(literal 1/2 binary64) (sqrt.f64 #s(literal 2 binary64))) (sqrt.f64 im))
(fma.f64 (.f64 re #s(literal 1/4 binary64)) (.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) im)) (sqrt.f64 #s(literal 2 binary64))) (.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 1/16 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 -1/32 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 (.f64 #s(literal 1/2 binary64) (sqrt.f64 #s(literal 2 binary64))) (sqrt.f64 im)))
(.f64 (log.f64 (.f64 #s(literal 2 binary64) im)) #s(literal 1/2 binary64))
(.f64 #s(literal 1/2 binary64) (+.f64 (/.f64 re im) (log.f64 (.f64 #s(literal 2 binary64) im))))
(fma.f64 (fma.f64 (/.f64 (.f64 re re) (pow.f64 im #s(literal 3 binary64))) #s(literal -1/12 binary64) (/.f64 #s(literal 1/2 binary64) im)) re (.f64 (log.f64 (*.f64 #s(literal 2 binary64) im)) #s(literal 1/2 binary64)))
(fma.f64 (fma.f64 (fma.f64 (/.f64 (.f64 re re) (pow.f64 im #s(literal 5 binary64))) #s(literal 3/80 binary64) (/.f64 #s(literal -1/12 binary64) (pow.f64 im #s(literal 3 binary64)))) (.f64 re re) (/.f64 #s(literal 1/2 binary64) im)) re (.f64 (log.f64 (.f64 #s(literal 2 binary64) im)) #s(literal 1/2 binary64)))
(log.f64 (*.f64 #s(literal 2 binary64) im))
(+.f64 (/.f64 re im) (log.f64 (*.f64 #s(literal 2 binary64) im)))
(fma.f64 (fma.f64 #s(literal -1/6 binary64) (/.f64 (.f64 re re) (pow.f64 im #s(literal 3 binary64))) (/.f64 #s(literal 1 binary64) im)) re (log.f64 (.f64 #s(literal 2 binary64) im)))
(fma.f64 (pow.f64 re #s(literal 3 binary64)) (fma.f64 #s(literal 3/40 binary64) (/.f64 (.f64 re re) (pow.f64 im #s(literal 5 binary64))) (/.f64 #s(literal -1/6 binary64) (pow.f64 im #s(literal 3 binary64)))) (fma.f64 re (/.f64 #s(literal 1 binary64) im) (log.f64 (.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 re #s(literal 1/4 binary64)) (.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) im)) (sqrt.f64 #s(literal 2 binary64))) (.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 1/16 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 -1/32 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 (.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)
(*.f64 #s(literal 2 binary64) (+.f64 im re))
(fma.f64 (+.f64 (/.f64 re im) #s(literal 2 binary64)) re (*.f64 #s(literal 2 binary64) im))
(fma.f64 (fma.f64 (fma.f64 #s(literal -1/4 binary64) (/.f64 (.f64 re re) (pow.f64 im #s(literal 3 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 re #s(literal 1/4 binary64)) (.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) im)) (sqrt.f64 #s(literal 2 binary64))) (.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 1/16 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 -1/32 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 (.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)
(*.f64 #s(literal 2 binary64) (+.f64 im re))
(fma.f64 (+.f64 (/.f64 re im) #s(literal 2 binary64)) re (*.f64 #s(literal 2 binary64) im))
(fma.f64 (fma.f64 (fma.f64 #s(literal -1/4 binary64) (/.f64 (.f64 re re) (pow.f64 im #s(literal 3 binary64))) (/.f64 #s(literal 1 binary64) im)) re #s(literal 2 binary64)) re (.f64 #s(literal 2 binary64) im))
(/.f64 (*.f64 (neg.f64 im) im) re)
(/.f64 (*.f64 (neg.f64 im) im) re)
(/.f64 (*.f64 (neg.f64 im) im) re)
(/.f64 (*.f64 (neg.f64 im) im) re)
(.f64 (.f64 #s(literal 1/2 binary64) (sqrt.f64 #s(literal 2 binary64))) (sqrt.f64 im))
(fma.f64 (.f64 re #s(literal 1/4 binary64)) (.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) im)) (sqrt.f64 #s(literal 2 binary64))) (.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 1/16 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 -1/32 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 (.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)
(*.f64 #s(literal 2 binary64) (+.f64 im re))
(fma.f64 (+.f64 (/.f64 re im) #s(literal 2 binary64)) re (*.f64 #s(literal 2 binary64) im))
(fma.f64 (fma.f64 (fma.f64 #s(literal -1/4 binary64) (/.f64 (.f64 re re) (pow.f64 im #s(literal 3 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 re im) #s(literal 1/2 binary64) #s(literal 1 binary64)) re im)
(fma.f64 (fma.f64 (fma.f64 #s(literal -1/8 binary64) (/.f64 (*.f64 re re) (pow.f64 im #s(literal 3 binary64))) (/.f64 #s(literal 1/2 binary64) im)) re #s(literal 1 binary64)) re im)
(*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) im)) (sqrt.f64 #s(literal 2 binary64)))
(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))))
(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))))
(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))))
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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 -1/4 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 (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)))) (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 (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 (.f64 (.f64 (.f64 (.f64 (sqrt.f64 #s(literal -1 binary64)) re) re) (sqrt.f64 #s(literal 2 binary64))) (*.f64 (sqrt.f64 im) #s(literal 3/8 binary64))) (pow.f64 im #s(literal 3 binary64)))) (neg.f64 im))
(*.f64 #s(literal -2 binary64) im)
(*.f64 (fma.f64 #s(literal -2 binary64) (/.f64 re im) #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 #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 (*.f64 (neg.f64 im) im) re)
(/.f64 (*.f64 (neg.f64 im) im) re)
(/.f64 (*.f64 (neg.f64 im) im) re)
(/.f64 (*.f64 (neg.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 (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 (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))) (neg.f64 im))
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(.f64 (.f64 (neg.f64 (sqrt.f64 im)) (sqrt.f64 #s(literal -1 binary64))) (sqrt.f64 #s(literal 2 binary64)))
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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 -1/4 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 (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)))) (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 (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 (.f64 (.f64 (.f64 (.f64 (sqrt.f64 #s(literal -1 binary64)) re) re) (sqrt.f64 #s(literal 2 binary64))) (*.f64 (sqrt.f64 im) #s(literal 3/8 binary64))) (pow.f64 im #s(literal 3 binary64)))) (neg.f64 im))
(*.f64 #s(literal -2 binary64) im)
(*.f64 (fma.f64 #s(literal -2 binary64) (/.f64 re im) #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 #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))
(neg.f64 im)
(*.f64 (-.f64 #s(literal 1 binary64) (/.f64 re im)) (neg.f64 im))
(.f64 (-.f64 #s(literal 1 binary64) (/.f64 (fma.f64 #s(literal -1/2 binary64) (/.f64 (.f64 re re) im) re) im)) (neg.f64 im))
(.f64 (-.f64 #s(literal 1 binary64) (/.f64 (-.f64 re (/.f64 (fma.f64 (/.f64 #s(literal -1/8 binary64) im) (/.f64 (pow.f64 re #s(literal 4 binary64)) im) (.f64 (*.f64 #s(literal 1/2 binary64) re) re)) im)) im)) (neg.f64 im))
(*.f64 (sqrt.f64 #s(literal 2 binary64)) (neg.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) im))))
(fma.f64 (.f64 #s(literal -1/2 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 im #s(literal 3 binary64))))) (.f64 (neg.f64 re) (sqrt.f64 #s(literal 2 binary64))) (*.f64 (sqrt.f64 #s(literal 2 binary64)) (neg.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) im)))))
(fma.f64 (.f64 #s(literal -1/2 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 im #s(literal 3 binary64))))) (.f64 (neg.f64 re) (sqrt.f64 #s(literal 2 binary64))) (*.f64 (sqrt.f64 #s(literal 2 binary64)) (neg.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) im)))))
(fma.f64 (.f64 #s(literal -1/2 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 im #s(literal 3 binary64))))) (.f64 (neg.f64 re) (sqrt.f64 #s(literal 2 binary64))) (*.f64 (sqrt.f64 #s(literal 2 binary64)) (neg.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) 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 (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 (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))) (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 (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)))) (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 (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 (.f64 (sqrt.f64 #s(literal -1 binary64)) re) re) (sqrt.f64 #s(literal 2 binary64))) (.f64 (sqrt.f64 im) #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 (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))) (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 (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)))) (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 (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 (.f64 (.f64 (.f64 (.f64 (sqrt.f64 #s(literal -1 binary64)) re) re) (sqrt.f64 #s(literal 2 binary64))) (*.f64 (sqrt.f64 im) #s(literal 3/8 binary64))) (pow.f64 im #s(literal 3 binary64)))) (neg.f64 im))
(*.f64 (sqrt.f64 #s(literal 2 binary64)) (neg.f64 (sqrt.f64 im)))
(.f64 (-.f64 (.f64 (.f64 #s(literal 1/2 binary64) (.f64 (neg.f64 re) (sqrt.f64 #s(literal 2 binary64)))) (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 im #s(literal 3 binary64))))) (*.f64 (sqrt.f64 #s(literal 2 binary64)) (neg.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) im))))) (neg.f64 im))
(.f64 (-.f64 (.f64 (.f64 #s(literal 1/2 binary64) (.f64 (neg.f64 re) (sqrt.f64 #s(literal 2 binary64)))) (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 im #s(literal 3 binary64))))) (*.f64 (sqrt.f64 #s(literal 2 binary64)) (neg.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) im))))) (neg.f64 im))
(.f64 (-.f64 (.f64 (.f64 #s(literal 1/2 binary64) (.f64 (neg.f64 re) (sqrt.f64 #s(literal 2 binary64)))) (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 im #s(literal 3 binary64))))) (*.f64 (sqrt.f64 #s(literal 2 binary64)) (neg.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) im))))) (neg.f64 im))
(neg.f64 im)
(*.f64 (-.f64 #s(literal 1 binary64) (/.f64 re im)) (neg.f64 im))
(.f64 (-.f64 #s(literal 1 binary64) (/.f64 (fma.f64 #s(literal -1/2 binary64) (/.f64 (.f64 re re) im) re) im)) (neg.f64 im))
(.f64 (-.f64 #s(literal 1 binary64) (/.f64 (-.f64 re (/.f64 (fma.f64 (/.f64 #s(literal -1/8 binary64) im) (/.f64 (pow.f64 re #s(literal 4 binary64)) im) (.f64 (*.f64 #s(literal 1/2 binary64) re) re)) im)) im)) (neg.f64 im))
(*.f64 #s(literal -2 binary64) im)
(*.f64 (fma.f64 #s(literal -2 binary64) (/.f64 re im) #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 #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))
(neg.f64 im)
(neg.f64 im)
(neg.f64 im)
(neg.f64 im)
(neg.f64 im)
(.f64 (fma.f64 (/.f64 (.f64 re re) im) (/.f64 #s(literal 1/2 binary64) im) #s(literal 1 binary64)) (neg.f64 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 re) im) (/.f64 #s(literal 1/2 binary64) im) #s(literal 1 binary64))) (neg.f64 im))
(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 re re) im) (/.f64 #s(literal 1/2 binary64) im) (/.f64 (.f64 #s(literal -1/8 binary64) (pow.f64 re #s(literal 4 binary64))) (pow.f64 im #s(literal 4 binary64))))) im im))
(*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 im #s(literal 3 binary64)))) #s(literal 1 binary64))
(*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 im #s(literal 3 binary64)))) #s(literal 1 binary64))
(*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 im #s(literal 3 binary64)))) #s(literal 1 binary64))
(*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 im #s(literal 3 binary64)))) #s(literal 1 binary64))

rewrite215.0ms (2.6%)

Memory

16.4MiB live, 298.9MiB allocated

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	50	333
0	87	273
1	241	260
2	1143	260
0	8341	260

Stop Event

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

Counts

25 → 606

Calls

Call 1

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

Outputs
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eval164.0ms (2%)

Memory: -3.3MiB live, 383.2MiB allocated
Compiler: Compiled 43 493 to 4 497 computations (89.7% saved)

prune46.0ms (0.6%)

Memory

16.5MiB live, 133.3MiB allocated

Pruning

26 alts after pruning (18 fresh and 8 done)

	Pruned	Kept	Total
New	1 153	9	1 162
Fresh	5	9	14
Picked	1	4	5
Done	0	4	4
Total	1 159	26	1 185

Accuracy

94.2%

Counts

1 185 → 26

Alt Table

Click to see full alt table

Status	Accuracy	Program
	46.9%	(.f64 (pow.f64 (pow.f64 #s(approx ( (+ (sqrt (+ (* im im) (* re re))) re) 2) (*.f64 im #s(literal 2 binary64))) #s(literal 1/4 binary64)) #s(literal 2 binary64)) #s(literal 1/2 binary64))
	44.0%	(.f64 (pow.f64 (exp.f64 (log.f64 #s(approx ( (+ (sqrt (+ (* im im) (* re re))) re) 2) (*.f64 im #s(literal 2 binary64))))) #s(literal 1/2 binary64)) #s(literal 1/2 binary64))
✓	81.8%	(.f64 (.f64 (sqrt.f64 (+.f64 (hypot.f64 im re) re)) #s(literal 1/2 binary64)) (sqrt.f64 #s(literal 2 binary64)))
	51.2%	(.f64 (.f64 (sqrt.f64 #s(approx (+ (sqrt (+ (* im im) (* re re))) re) (+.f64 re im))) #s(literal 1/2 binary64)) (sqrt.f64 #s(literal 2 binary64)))
▶	52.0%	(.f64 (sqrt.f64 (.f64 (fma.f64 (hypot.f64 re im) (/.f64 (hypot.f64 re im) (-.f64 (hypot.f64 re im) re)) (neg.f64 (*.f64 re (/.f64 re (-.f64 (hypot.f64 re im) re))))) #s(literal 2 binary64))) #s(literal 1/2 binary64))
✓	81.3%	(.f64 (sqrt.f64 (.f64 (+.f64 (hypot.f64 im re) re) #s(literal 2 binary64))) #s(literal 1/2 binary64))
▶	50.8%	(.f64 (sqrt.f64 (.f64 #s(approx (+ (sqrt (+ (* im im) (* re re))) re) (+.f64 re im)) #s(literal 2 binary64))) #s(literal 1/2 binary64))
	47.9%	(.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))
▶	28.9%	(.f64 (sqrt.f64 #s(approx ( (+ (sqrt (+ (* im im) (* re re))) re) 2) (fma.f64 #s(literal 4 binary64) re (/.f64 (*.f64 im im) re)))) #s(literal 1/2 binary64))
✓	13.6%	(.f64 (sqrt.f64 #s(approx ( (+ (sqrt (+ (* im im) (* re re))) re) 2) (/.f64 (*.f64 (neg.f64 im) im) re))) #s(literal 1/2 binary64))
	17.9%	(.f64 (sqrt.f64 #s(approx ( (+ (sqrt (+ (* im im) (* re re))) re) 2) (/.f64 (neg.f64 im) (/.f64 re im)))) #s(literal 1/2 binary64))
	17.9%	(.f64 (sqrt.f64 #s(approx ( (+ (sqrt (+ (* im im) (* re re))) re) 2) (*.f64 (/.f64 im re) (neg.f64 im)))) #s(literal 1/2 binary64))
✓	47.2%	(.f64 (sqrt.f64 #s(approx ( (+ (sqrt (+ (* im im) (* re re))) re) 2) (*.f64 #s(literal 2 binary64) im))) #s(literal 1/2 binary64))
✓	75.6%	(.f64 (exp.f64 (.f64 (log.f64 (*.f64 #s(literal 2 binary64) (+.f64 (hypot.f64 re im) re))) #s(literal 1/2 binary64))) #s(literal 1/2 binary64))
	13.2%	(.f64 (exp.f64 (.f64 (log.f64 #s(approx (* (+ (sqrt (+ (* im im) (* re re))) re) 2) (/.f64 (*.f64 (neg.f64 im) im) re))) #s(literal 1/2 binary64))) #s(literal 1/2 binary64))
	44.0%	(.f64 (exp.f64 (.f64 (log.f64 #s(approx (* (+ (sqrt (+ (* im im) (* re re))) re) 2) (*.f64 im #s(literal 2 binary64)))) #s(literal 1/2 binary64))) #s(literal 1/2 binary64))
	13.9%	(.f64 (exp.f64 (.f64 #s(approx (log (* 2 (+ (sqrt (+ (* re re) (* im im))) re))) (+.f64 (log.f64 (*.f64 im im)) (log.f64 (/.f64 #s(literal -1 binary64) re)))) #s(literal 1/2 binary64))) #s(literal 1/2 binary64))
	44.5%	(.f64 (exp.f64 (.f64 #s(approx (log (* 2 (+ (sqrt (+ (* re re) (* im im))) re))) (+.f64 (log.f64 im) (log.f64 #s(literal 2 binary64)))) #s(literal 1/2 binary64))) #s(literal 1/2 binary64))
	47.7%	(.f64 #s(approx (sqrt ( (+ (sqrt (+ (* im im) (* re re))) re) 2)) (.f64 #s(approx (+ ( (* 1/2 (* (sqrt 2) re)) (sqrt (/ 1 (pow im 3)))) (* (sqrt (/ 1 im)) (sqrt 2))) (*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) im)) (sqrt.f64 #s(literal 2 binary64)))) im)) #s(literal 1/2 binary64))
✓	41.6%	(.f64 #s(literal 1/2 binary64) (sqrt.f64 (.f64 #s(literal 2 binary64) (+.f64 (sqrt.f64 (fma.f64 re re (*.f64 im im))) re))))
	27.5%	(.f64 #s(literal 1/2 binary64) (sqrt.f64 (.f64 #s(literal 2 binary64) (+.f64 (sqrt.f64 #s(approx (+ (* re re) (* im im)) (.f64 (fma.f64 (/.f64 im re) (/.f64 im re) #s(literal 1 binary64)) (.f64 re re)))) re))))
▶	7.9%	(.f64 #s(literal 1/2 binary64) (sqrt.f64 (.f64 #s(literal 2 binary64) (+.f64 #s(approx (sqrt (+ (* re re) (* im im))) (.f64 (neg.f64 re) (fma.f64 (/.f64 (.f64 #s(literal 1/2 binary64) im) re) (/.f64 im re) #s(literal 1 binary64)))) re))))
	7.6%	(.f64 #s(literal 1/2 binary64) (sqrt.f64 (.f64 #s(literal 2 binary64) (+.f64 #s(approx (sqrt (+ (* re re) (* im im))) (neg.f64 re)) re))))
✓	47.7%	(.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))))
▶	44.7%	(.f64 #s(literal 1/2 binary64) #s(approx (sqrt ( 2 (+ (sqrt (+ (* re re) (* im im))) re))) (.f64 (sqrt.f64 #s(literal 2 binary64)) (exp.f64 (.f64 (log.f64 im) #s(literal 1/2 binary64))))))
✓	31.4%	#s(approx (* 1/2 (sqrt (* 2 (+ (sqrt (+ (* re re) (* im im))) re)))) (sqrt.f64 re))

Compiler

Compiled 1 028 to 753 computations (26.8% saved)

simplify147.0ms (1.8%)

Memory

-57.5MiB live, 85.2MiB allocated

Algorithm

1×	egg-herbie

Localize:

Found 20 expressions of interest:

New	Metric	Score
cost-diff	0	(.f64 (sqrt.f64 #s(literal 2 binary64)) (exp.f64 (.f64 (log.f64 im) #s(literal 1/2 binary64))))
cost-diff	0	#s(approx (sqrt (* 2 (+ (sqrt (+ (* re re) (* im im))) re))) (.f64 (sqrt.f64 #s(literal 2 binary64)) (exp.f64 (.f64 (log.f64 im) #s(literal 1/2 binary64)))))
cost-diff	0	(.f64 #s(literal 1/2 binary64) #s(approx (sqrt ( 2 (+ (sqrt (+ (* re re) (* im im))) re))) (.f64 (sqrt.f64 #s(literal 2 binary64)) (exp.f64 (.f64 (log.f64 im) #s(literal 1/2 binary64))))))
cost-diff	12480	(exp.f64 (*.f64 (log.f64 im) #s(literal 1/2 binary64)))
cost-diff	0	(.f64 #s(literal 2 binary64) (+.f64 #s(approx (sqrt (+ ( re re) (* im im))) (.f64 (neg.f64 re) (fma.f64 (/.f64 (.f64 #s(literal 1/2 binary64) im) re) (/.f64 im re) #s(literal 1 binary64)))) re))
cost-diff	0	(sqrt.f64 (.f64 #s(literal 2 binary64) (+.f64 #s(approx (sqrt (+ ( re re) (* im im))) (.f64 (neg.f64 re) (fma.f64 (/.f64 (.f64 #s(literal 1/2 binary64) im) re) (/.f64 im re) #s(literal 1 binary64)))) re)))
cost-diff	0	(.f64 #s(literal 1/2 binary64) (sqrt.f64 (.f64 #s(literal 2 binary64) (+.f64 #s(approx (sqrt (+ (* re re) (* im im))) (.f64 (neg.f64 re) (fma.f64 (/.f64 (.f64 #s(literal 1/2 binary64) im) re) (/.f64 im re) #s(literal 1 binary64)))) re))))
cost-diff	1024	(.f64 (neg.f64 re) (fma.f64 (/.f64 (.f64 #s(literal 1/2 binary64) im) re) (/.f64 im re) #s(literal 1 binary64)))
cost-diff	0	(fma.f64 #s(literal 4 binary64) re (/.f64 (*.f64 im im) re))
cost-diff	0	#s(approx (* (+ (sqrt (+ (* im im) (* re re))) re) 2) (fma.f64 #s(literal 4 binary64) re (/.f64 (*.f64 im im) re)))
cost-diff	0	(sqrt.f64 #s(approx (* (+ (sqrt (+ (* im im) (* re re))) re) 2) (fma.f64 #s(literal 4 binary64) re (/.f64 (*.f64 im im) re))))
cost-diff	0	(.f64 (sqrt.f64 #s(approx ( (+ (sqrt (+ (* im im) (* re re))) re) 2) (fma.f64 #s(literal 4 binary64) re (/.f64 (*.f64 im im) re)))) #s(literal 1/2 binary64))
cost-diff	0	#s(approx (+ (sqrt (+ (* im im) (* re re))) re) (+.f64 re im))
cost-diff	0	(.f64 #s(approx (+ (sqrt (+ ( im im) (* re re))) re) (+.f64 re im)) #s(literal 2 binary64))
cost-diff	0	(sqrt.f64 (.f64 #s(approx (+ (sqrt (+ ( im im) (* re re))) re) (+.f64 re im)) #s(literal 2 binary64)))
cost-diff	0	(.f64 (sqrt.f64 (.f64 #s(approx (+ (sqrt (+ (* im im) (* re re))) re) (+.f64 re im)) #s(literal 2 binary64))) #s(literal 1/2 binary64))
cost-diff	0	(sqrt.f64 (.f64 (fma.f64 (hypot.f64 re im) (/.f64 (hypot.f64 re im) (-.f64 (hypot.f64 re im) re)) (neg.f64 (.f64 re (/.f64 re (-.f64 (hypot.f64 re im) re))))) #s(literal 2 binary64)))
cost-diff	0	(.f64 (sqrt.f64 (.f64 (fma.f64 (hypot.f64 re im) (/.f64 (hypot.f64 re im) (-.f64 (hypot.f64 re im) re)) (neg.f64 (*.f64 re (/.f64 re (-.f64 (hypot.f64 re im) re))))) #s(literal 2 binary64))) #s(literal 1/2 binary64))
cost-diff	128	(neg.f64 (*.f64 re (/.f64 re (-.f64 (hypot.f64 re im) re))))
cost-diff	20672	(fma.f64 (hypot.f64 re im) (/.f64 (hypot.f64 re im) (-.f64 (hypot.f64 re im) re)) (neg.f64 (*.f64 re (/.f64 re (-.f64 (hypot.f64 re im) re)))))

Iterations

Useful iterations: 8 (0.0ms)

Iter	Nodes	Cost
0	56	513
0	95	470
1	163	466
2	266	466
3	616	461
4	2036	425
5	3995	422
6	5346	416
7	6525	398
8	7853	385
0	8155	385

Stop Event

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

Calls

Call 1

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

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

localize236.0ms (2.8%)

Memory

26.9MiB live, 295.7MiB allocated

Localize:

Found 20 expressions of interest:

New	Metric	Score
accuracy	0	(log.f64 im)
accuracy	0.49837875976844204	(.f64 (sqrt.f64 #s(literal 2 binary64)) (exp.f64 (.f64 (log.f64 im) #s(literal 1/2 binary64))))
accuracy	4.97411364271853	(exp.f64 (*.f64 (log.f64 im) #s(literal 1/2 binary64)))
accuracy	33.04477555103927	#s(approx (sqrt (* 2 (+ (sqrt (+ (* re re) (* im im))) re))) (.f64 (sqrt.f64 #s(literal 2 binary64)) (exp.f64 (.f64 (log.f64 im) #s(literal 1/2 binary64)))))
accuracy	1.6937251845200088	(.f64 (neg.f64 re) (fma.f64 (/.f64 (.f64 #s(literal 1/2 binary64) im) re) (/.f64 im re) #s(literal 1 binary64)))
accuracy	5.281846752426357	(sqrt.f64 (.f64 #s(literal 2 binary64) (+.f64 #s(approx (sqrt (+ ( re re) (* im im))) (.f64 (neg.f64 re) (fma.f64 (/.f64 (.f64 #s(literal 1/2 binary64) im) re) (/.f64 im re) #s(literal 1 binary64)))) re)))
accuracy	6.582561687117777	(+.f64 #s(approx (sqrt (+ (* re re) (* im im))) (.f64 (neg.f64 re) (fma.f64 (/.f64 (.f64 #s(literal 1/2 binary64) im) re) (/.f64 im re) #s(literal 1 binary64)))) re)
accuracy	47.454929522105694	#s(approx (sqrt (+ (* re re) (* im im))) (.f64 (neg.f64 re) (fma.f64 (/.f64 (.f64 #s(literal 1/2 binary64) im) re) (/.f64 im re) #s(literal 1 binary64))))
accuracy	0.0078125	(fma.f64 #s(literal 4 binary64) re (/.f64 (*.f64 im im) re))
accuracy	5.281846752426357	(sqrt.f64 #s(approx (* (+ (sqrt (+ (* im im) (* re re))) re) 2) (fma.f64 #s(literal 4 binary64) re (/.f64 (*.f64 im im) re))))
accuracy	8.814111667929732	(/.f64 (*.f64 im im) re)
accuracy	43.15482657678274	#s(approx (* (+ (sqrt (+ (* im im) (* re re))) re) 2) (fma.f64 #s(literal 4 binary64) re (/.f64 (*.f64 im im) re)))
accuracy	0	(.f64 (sqrt.f64 (.f64 #s(approx (+ (sqrt (+ (* im im) (* re re))) re) (+.f64 re im)) #s(literal 2 binary64))) #s(literal 1/2 binary64))
accuracy	0	(.f64 #s(approx (+ (sqrt (+ ( im im) (* re re))) re) (+.f64 re im)) #s(literal 2 binary64))
accuracy	5.281846752426357	(sqrt.f64 (.f64 #s(approx (+ (sqrt (+ ( im im) (* re re))) re) (+.f64 re im)) #s(literal 2 binary64)))
accuracy	30.78298229449251	#s(approx (+ (sqrt (+ (* im im) (* re re))) re) (+.f64 re im))
accuracy	1.1292240358150403	(/.f64 re (-.f64 (hypot.f64 re im) re))
accuracy	5.281846752426357	(sqrt.f64 (.f64 (fma.f64 (hypot.f64 re im) (/.f64 (hypot.f64 re im) (-.f64 (hypot.f64 re im) re)) (neg.f64 (.f64 re (/.f64 re (-.f64 (hypot.f64 re im) re))))) #s(literal 2 binary64)))
accuracy	8.394750743164549	(-.f64 (hypot.f64 re im) re)
accuracy	24.4672250028011	(fma.f64 (hypot.f64 re im) (/.f64 (hypot.f64 re im) (-.f64 (hypot.f64 re im) re)) (neg.f64 (*.f64 re (/.f64 re (-.f64 (hypot.f64 re im) re)))))

Samples

68.0ms	55×	2	valid
57.0ms	34×	3	valid
42.0ms	121×	0	valid
28.0ms	45×	1	valid
1.0ms	1×	3	exit

Compiler

Compiled 1 089 to 102 computations (90.6% saved)

Precisions

Click to see histograms. Total time spent on operations: 146.0ms

ival-mult: 51.0ms (34.9% of total)

ival-hypot: 19.0ms (13% of total)

ival-div: 18.0ms (12.3% of total)

adjust: 15.0ms (10.3% of total)

ival-sqrt: 14.0ms (9.6% of total)

ival-add: 10.0ms (6.8% of total)

ival-neg: 7.0ms (4.8% of total)

ival-log: 5.0ms (3.4% of total)

ival-exp: 4.0ms (2.7% of total)

ival-sub: 3.0ms (2.1% of total)

exact: 1.0ms (0.7% of total)

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

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

series125.0ms (1.5%)

Memory

23.8MiB live, 217.7MiB allocated

Counts

26 → 588

Calls

Call 1

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

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

6 calls:

Time	Variable		Point	Expression
42.0ms	im	@	0	((+ (* (sqrt (+ (* re re) (* im im))) (/ (sqrt (+ (* re re) (* im im))) (- (sqrt (+ (* re re) (* im im))) re))) (neg (* re (/ re (- (sqrt (+ (* re re) (* im im))) re))))) (neg (* re (/ re (- (sqrt (+ (* re re) (* im im))) re)))) (* (sqrt (* (+ (* (sqrt (+ (* re re) (* im im))) (/ (sqrt (+ (* re re) (* im im))) (- (sqrt (+ (* re re) (* im im))) re))) (neg (* re (/ re (- (sqrt (+ (* re re) (* im im))) re))))) 2)) 1/2) (sqrt (* (+ (* (sqrt (+ (* re re) (* im im))) (/ (sqrt (+ (* re re) (* im im))) (- (sqrt (+ (* re re) (* im im))) re))) (neg (* re (/ re (- (sqrt (+ (* re re) (* im im))) 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) (* (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) (+ (* 4 re) (/ (* im im) re)) (* (neg re) (+ (* (/ (* 1/2 im) re) (/ im re)) 1)) (* 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)) (exp (* (log im) 1/2)) (* 1/2 (sqrt (* 2 (+ (sqrt (+ (* re re) (* im im))) re)))) (sqrt (* 2 (+ (sqrt (+ (* re re) (* im im))) re))) (* (sqrt 2) (exp (* (log im) 1/2))) (- (sqrt (+ (* re re) (* im im))) re) (/ re (- (sqrt (+ (* re re) (* im im))) re)) (/ (* im im) re) (sqrt (+ (* re re) (* im im))) (+ (sqrt (+ (* re re) (* im im))) re) (log im))
21.0ms	im	@	-inf	((+ (* (sqrt (+ (* re re) (* im im))) (/ (sqrt (+ (* re re) (* im im))) (- (sqrt (+ (* re re) (* im im))) re))) (neg (* re (/ re (- (sqrt (+ (* re re) (* im im))) re))))) (neg (* re (/ re (- (sqrt (+ (* re re) (* im im))) re)))) (* (sqrt (* (+ (* (sqrt (+ (* re re) (* im im))) (/ (sqrt (+ (* re re) (* im im))) (- (sqrt (+ (* re re) (* im im))) re))) (neg (* re (/ re (- (sqrt (+ (* re re) (* im im))) re))))) 2)) 1/2) (sqrt (* (+ (* (sqrt (+ (* re re) (* im im))) (/ (sqrt (+ (* re re) (* im im))) (- (sqrt (+ (* re re) (* im im))) re))) (neg (* re (/ re (- (sqrt (+ (* re re) (* im im))) 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) (* (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) (+ (* 4 re) (/ (* im im) re)) (* (neg re) (+ (* (/ (* 1/2 im) re) (/ im re)) 1)) (* 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)) (exp (* (log im) 1/2)) (* 1/2 (sqrt (* 2 (+ (sqrt (+ (* re re) (* im im))) re)))) (sqrt (* 2 (+ (sqrt (+ (* re re) (* im im))) re))) (* (sqrt 2) (exp (* (log im) 1/2))) (- (sqrt (+ (* re re) (* im im))) re) (/ re (- (sqrt (+ (* re re) (* im im))) re)) (/ (* im im) re) (sqrt (+ (* re re) (* im im))) (+ (sqrt (+ (* re re) (* im im))) re) (log im))
12.0ms	im	@	inf	((+ (* (sqrt (+ (* re re) (* im im))) (/ (sqrt (+ (* re re) (* im im))) (- (sqrt (+ (* re re) (* im im))) re))) (neg (* re (/ re (- (sqrt (+ (* re re) (* im im))) re))))) (neg (* re (/ re (- (sqrt (+ (* re re) (* im im))) re)))) (* (sqrt (* (+ (* (sqrt (+ (* re re) (* im im))) (/ (sqrt (+ (* re re) (* im im))) (- (sqrt (+ (* re re) (* im im))) re))) (neg (* re (/ re (- (sqrt (+ (* re re) (* im im))) re))))) 2)) 1/2) (sqrt (* (+ (* (sqrt (+ (* re re) (* im im))) (/ (sqrt (+ (* re re) (* im im))) (- (sqrt (+ (* re re) (* im im))) re))) (neg (* re (/ re (- (sqrt (+ (* re re) (* im im))) 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) (* (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) (+ (* 4 re) (/ (* im im) re)) (* (neg re) (+ (* (/ (* 1/2 im) re) (/ im re)) 1)) (* 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)) (exp (* (log im) 1/2)) (* 1/2 (sqrt (* 2 (+ (sqrt (+ (* re re) (* im im))) re)))) (sqrt (* 2 (+ (sqrt (+ (* re re) (* im im))) re))) (* (sqrt 2) (exp (* (log im) 1/2))) (- (sqrt (+ (* re re) (* im im))) re) (/ re (- (sqrt (+ (* re re) (* im im))) re)) (/ (* im im) re) (sqrt (+ (* re re) (* im im))) (+ (sqrt (+ (* re re) (* im im))) re) (log im))
5.0ms	re	@	inf	((+ (* (sqrt (+ (* re re) (* im im))) (/ (sqrt (+ (* re re) (* im im))) (- (sqrt (+ (* re re) (* im im))) re))) (neg (* re (/ re (- (sqrt (+ (* re re) (* im im))) re))))) (neg (* re (/ re (- (sqrt (+ (* re re) (* im im))) re)))) (* (sqrt (* (+ (* (sqrt (+ (* re re) (* im im))) (/ (sqrt (+ (* re re) (* im im))) (- (sqrt (+ (* re re) (* im im))) re))) (neg (* re (/ re (- (sqrt (+ (* re re) (* im im))) re))))) 2)) 1/2) (sqrt (* (+ (* (sqrt (+ (* re re) (* im im))) (/ (sqrt (+ (* re re) (* im im))) (- (sqrt (+ (* re re) (* im im))) re))) (neg (* re (/ re (- (sqrt (+ (* re re) (* im im))) 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) (* (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) (+ (* 4 re) (/ (* im im) re)) (* (neg re) (+ (* (/ (* 1/2 im) re) (/ im re)) 1)) (* 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)) (exp (* (log im) 1/2)) (* 1/2 (sqrt (* 2 (+ (sqrt (+ (* re re) (* im im))) re)))) (sqrt (* 2 (+ (sqrt (+ (* re re) (* im im))) re))) (* (sqrt 2) (exp (* (log im) 1/2))) (- (sqrt (+ (* re re) (* im im))) re) (/ re (- (sqrt (+ (* re re) (* im im))) re)) (/ (* im im) re) (sqrt (+ (* re re) (* im im))) (+ (sqrt (+ (* re re) (* im im))) re) (log im))
4.0ms	re	@	-inf	((+ (* (sqrt (+ (* re re) (* im im))) (/ (sqrt (+ (* re re) (* im im))) (- (sqrt (+ (* re re) (* im im))) re))) (neg (* re (/ re (- (sqrt (+ (* re re) (* im im))) re))))) (neg (* re (/ re (- (sqrt (+ (* re re) (* im im))) re)))) (* (sqrt (* (+ (* (sqrt (+ (* re re) (* im im))) (/ (sqrt (+ (* re re) (* im im))) (- (sqrt (+ (* re re) (* im im))) re))) (neg (* re (/ re (- (sqrt (+ (* re re) (* im im))) re))))) 2)) 1/2) (sqrt (* (+ (* (sqrt (+ (* re re) (* im im))) (/ (sqrt (+ (* re re) (* im im))) (- (sqrt (+ (* re re) (* im im))) re))) (neg (* re (/ re (- (sqrt (+ (* re re) (* im im))) 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) (* (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) (+ (* 4 re) (/ (* im im) re)) (* (neg re) (+ (* (/ (* 1/2 im) re) (/ im re)) 1)) (* 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)) (exp (* (log im) 1/2)) (* 1/2 (sqrt (* 2 (+ (sqrt (+ (* re re) (* im im))) re)))) (sqrt (* 2 (+ (sqrt (+ (* re re) (* im im))) re))) (* (sqrt 2) (exp (* (log im) 1/2))) (- (sqrt (+ (* re re) (* im im))) re) (/ re (- (sqrt (+ (* re re) (* im im))) re)) (/ (* im im) re) (sqrt (+ (* re re) (* im im))) (+ (sqrt (+ (* re re) (* im im))) re) (log im))

simplify245.0ms (2.9%)

Memory

15.5MiB live, 368.0MiB allocated

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	947	13738
1	3172	12809
0	9131	12190

Stop Event

1×	iter limit
1×	node limit

Counts

588 → 576

Calls

Call 1

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

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

rewrite220.0ms (2.6%)

Memory

1.8MiB live, 261.5MiB allocated

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	56	412
0	95	369
1	313	311
2	2053	302
0	8603	296

Stop Event

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

Counts

26 → 552

Calls

Call 1

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

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eval637.0ms (7.6%)

Memory: -15.0MiB live, 494.6MiB allocated
Compiler: Compiled 52 818 to 5 579 computations (89.4% saved)

prune53.0ms (0.6%)

Memory

-21.4MiB live, 133.9MiB allocated

Pruning

26 alts after pruning (13 fresh and 13 done)

	Pruned	Kept	Total
New	1 203	0	1 203
Fresh	0	13	13
Picked	0	5	5
Done	0	8	8
Total	1 203	26	1 229

Accuracy

94.2%

Counts

1 229 → 26

Alt Table

Click to see full alt table

Status	Accuracy	Program
	46.9%	(.f64 (pow.f64 (pow.f64 #s(approx ( (+ (sqrt (+ (* im im) (* re re))) re) 2) (*.f64 im #s(literal 2 binary64))) #s(literal 1/4 binary64)) #s(literal 2 binary64)) #s(literal 1/2 binary64))
	44.0%	(.f64 (pow.f64 (exp.f64 (log.f64 #s(approx ( (+ (sqrt (+ (* im im) (* re re))) re) 2) (*.f64 im #s(literal 2 binary64))))) #s(literal 1/2 binary64)) #s(literal 1/2 binary64))
✓	81.8%	(.f64 (.f64 (sqrt.f64 (+.f64 (hypot.f64 im re) re)) #s(literal 1/2 binary64)) (sqrt.f64 #s(literal 2 binary64)))
	51.2%	(.f64 (.f64 (sqrt.f64 #s(approx (+ (sqrt (+ (* im im) (* re re))) re) (+.f64 re im))) #s(literal 1/2 binary64)) (sqrt.f64 #s(literal 2 binary64)))
✓	52.0%	(.f64 (sqrt.f64 (.f64 (fma.f64 (hypot.f64 re im) (/.f64 (hypot.f64 re im) (-.f64 (hypot.f64 re im) re)) (neg.f64 (*.f64 re (/.f64 re (-.f64 (hypot.f64 re im) re))))) #s(literal 2 binary64))) #s(literal 1/2 binary64))
✓	81.3%	(.f64 (sqrt.f64 (.f64 (+.f64 (hypot.f64 im re) re) #s(literal 2 binary64))) #s(literal 1/2 binary64))
✓	50.8%	(.f64 (sqrt.f64 (.f64 #s(approx (+ (sqrt (+ (* im im) (* re re))) re) (+.f64 re im)) #s(literal 2 binary64))) #s(literal 1/2 binary64))
	47.9%	(.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))
✓	28.9%	(.f64 (sqrt.f64 #s(approx ( (+ (sqrt (+ (* im im) (* re re))) re) 2) (fma.f64 #s(literal 4 binary64) re (/.f64 (*.f64 im im) re)))) #s(literal 1/2 binary64))
✓	13.6%	(.f64 (sqrt.f64 #s(approx ( (+ (sqrt (+ (* im im) (* re re))) re) 2) (/.f64 (*.f64 (neg.f64 im) im) re))) #s(literal 1/2 binary64))
	17.9%	(.f64 (sqrt.f64 #s(approx ( (+ (sqrt (+ (* im im) (* re re))) re) 2) (/.f64 (neg.f64 im) (/.f64 re im)))) #s(literal 1/2 binary64))
	17.9%	(.f64 (sqrt.f64 #s(approx ( (+ (sqrt (+ (* im im) (* re re))) re) 2) (*.f64 (/.f64 im re) (neg.f64 im)))) #s(literal 1/2 binary64))
✓	47.2%	(.f64 (sqrt.f64 #s(approx ( (+ (sqrt (+ (* im im) (* re re))) re) 2) (*.f64 #s(literal 2 binary64) im))) #s(literal 1/2 binary64))
✓	75.6%	(.f64 (exp.f64 (.f64 (log.f64 (*.f64 #s(literal 2 binary64) (+.f64 (hypot.f64 re im) re))) #s(literal 1/2 binary64))) #s(literal 1/2 binary64))
	13.2%	(.f64 (exp.f64 (.f64 (log.f64 #s(approx (* (+ (sqrt (+ (* im im) (* re re))) re) 2) (/.f64 (*.f64 (neg.f64 im) im) re))) #s(literal 1/2 binary64))) #s(literal 1/2 binary64))
	44.0%	(.f64 (exp.f64 (.f64 (log.f64 #s(approx (* (+ (sqrt (+ (* im im) (* re re))) re) 2) (*.f64 im #s(literal 2 binary64)))) #s(literal 1/2 binary64))) #s(literal 1/2 binary64))
	13.9%	(.f64 (exp.f64 (.f64 #s(approx (log (* 2 (+ (sqrt (+ (* re re) (* im im))) re))) (+.f64 (log.f64 (*.f64 im im)) (log.f64 (/.f64 #s(literal -1 binary64) re)))) #s(literal 1/2 binary64))) #s(literal 1/2 binary64))
	44.5%	(.f64 (exp.f64 (.f64 #s(approx (log (* 2 (+ (sqrt (+ (* re re) (* im im))) re))) (+.f64 (log.f64 im) (log.f64 #s(literal 2 binary64)))) #s(literal 1/2 binary64))) #s(literal 1/2 binary64))
	47.7%	(.f64 #s(approx (sqrt ( (+ (sqrt (+ (* im im) (* re re))) re) 2)) (.f64 #s(approx (+ ( (* 1/2 (* (sqrt 2) re)) (sqrt (/ 1 (pow im 3)))) (* (sqrt (/ 1 im)) (sqrt 2))) (*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) im)) (sqrt.f64 #s(literal 2 binary64)))) im)) #s(literal 1/2 binary64))
✓	41.6%	(.f64 #s(literal 1/2 binary64) (sqrt.f64 (.f64 #s(literal 2 binary64) (+.f64 (sqrt.f64 (fma.f64 re re (*.f64 im im))) re))))
	27.5%	(.f64 #s(literal 1/2 binary64) (sqrt.f64 (.f64 #s(literal 2 binary64) (+.f64 (sqrt.f64 #s(approx (+ (* re re) (* im im)) (.f64 (fma.f64 (/.f64 im re) (/.f64 im re) #s(literal 1 binary64)) (.f64 re re)))) re))))
✓	7.9%	(.f64 #s(literal 1/2 binary64) (sqrt.f64 (.f64 #s(literal 2 binary64) (+.f64 #s(approx (sqrt (+ (* re re) (* im im))) (.f64 (neg.f64 re) (fma.f64 (/.f64 (.f64 #s(literal 1/2 binary64) im) re) (/.f64 im re) #s(literal 1 binary64)))) re))))
	7.6%	(.f64 #s(literal 1/2 binary64) (sqrt.f64 (.f64 #s(literal 2 binary64) (+.f64 #s(approx (sqrt (+ (* re re) (* im im))) (neg.f64 re)) re))))
✓	47.7%	(.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))))
✓	44.7%	(.f64 #s(literal 1/2 binary64) #s(approx (sqrt ( 2 (+ (sqrt (+ (* re re) (* im im))) re))) (.f64 (sqrt.f64 #s(literal 2 binary64)) (exp.f64 (.f64 (log.f64 im) #s(literal 1/2 binary64))))))
✓	31.4%	#s(approx (* 1/2 (sqrt (* 2 (+ (sqrt (+ (* re re) (* im im))) re)))) (sqrt.f64 re))

Compiler

Compiled 1 518 to 686 computations (54.8% saved)

regimes98.0ms (1.2%)

Memory

-26.2MiB live, 163.7MiB allocated

Counts

41 → 2

Calls

Call 1

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

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

Calls

7 calls:

20.0ms	(.f64 #s(literal 2 binary64) (+.f64 (sqrt.f64 (+.f64 (.f64 re re) (*.f64 im im))) re))
15.0ms	re
13.0ms	(*.f64 im im)
13.0ms	im
11.0ms	(+.f64 (sqrt.f64 (+.f64 (.f64 re re) (.f64 im im))) re)

Results

Accuracy	Segments	Branch
88.6%	2	`re`
81.8%	1	`im`
84.8%	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))))`
84.8%	2	`(sqrt.f64 (.f64 #s(literal 2 binary64) (+.f64 (sqrt.f64 (+.f64 (.f64 re re) (*.f64 im im))) re)))`
83.8%	2	`(.f64 #s(literal 2 binary64) (+.f64 (sqrt.f64 (+.f64 (.f64 re re) (*.f64 im im))) re))`
83.8%	2	`(+.f64 (sqrt.f64 (+.f64 (.f64 re re) (.f64 im im))) re)`
81.8%	1	`(*.f64 im im)`

Compiler

Compiled 55 to 45 computations (18.2% saved)

regimes13.0ms (0.2%)

Memory

-5.7MiB live, 29.7MiB allocated

Counts

24 → 2

Calls

Call 1

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

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

Calls

1 calls:

8.0ms

re

Results

Accuracy	Segments	Branch
88.0%	2	`re`

Compiler

Compiled 1 to 2 computations (-100% saved)

regimes100.0ms (1.2%)

Memory

-3.3MiB live, 119.7MiB allocated

Counts

23 → 4

Calls

Call 1

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

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

Calls

7 calls:

13.0ms	(sqrt.f64 (.f64 #s(literal 2 binary64) (+.f64 (sqrt.f64 (+.f64 (.f64 re re) (*.f64 im im))) re)))
8.0ms	(+.f64 (sqrt.f64 (+.f64 (.f64 re re) (.f64 im im))) re)
7.0ms	re
7.0ms	im
7.0ms	(.f64 #s(literal 1/2 binary64) (sqrt.f64 (.f64 #s(literal 2 binary64) (+.f64 (sqrt.f64 (+.f64 (.f64 re re) (.f64 im im))) re))))

Results

Accuracy	Segments	Branch
63.7%	3	`im`
63.7%	3	`(*.f64 im im)`
67.5%	4	`(.f64 #s(literal 2 binary64) (+.f64 (sqrt.f64 (+.f64 (.f64 re re) (*.f64 im im))) re))`
67.5%	4	`(+.f64 (sqrt.f64 (+.f64 (.f64 re re) (.f64 im im))) re)`
68.1%	4	`(.f64 #s(literal 1/2 binary64) (sqrt.f64 (.f64 #s(literal 2 binary64) (+.f64 (sqrt.f64 (+.f64 (.f64 re re) (.f64 im im))) re))))`
68.1%	4	`(sqrt.f64 (.f64 #s(literal 2 binary64) (+.f64 (sqrt.f64 (+.f64 (.f64 re re) (*.f64 im im))) re)))`
79.1%	4	`re`

Compiler

Compiled 55 to 45 computations (18.2% saved)

regimes7.0ms (0.1%)

Memory

16.6MiB live, 16.6MiB allocated

Counts

17 → 3

Calls

Call 1

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

Outputs

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

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

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

Calls

1 calls:

6.0ms

re

Results

Accuracy	Segments	Branch
74.8%	3	`re`

Compiler

Compiled 1 to 2 computations (-100% saved)

regimes5.0ms (0.1%)

Memory

7.9MiB live, 7.9MiB allocated

Counts

10 → 3

Calls

Call 1

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

Outputs

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

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

Calls

1 calls:

4.0ms

re

Results

Accuracy	Segments	Branch
74.6%	3	`re`

Compiler

Compiled 1 to 2 computations (-100% saved)

regimes4.0ms (0%)

Memory

5.2MiB live, 5.2MiB allocated

Counts

7 → 3

Calls

Call 1

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

Outputs

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

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

Calls

1 calls:

3.0ms

re

Results

Accuracy	Segments	Branch
67.5%	3	`re`

Compiler

Compiled 1 to 2 computations (-100% saved)

regimes3.0ms (0%)

Memory

5.5MiB live, 5.5MiB allocated

Counts

6 → 3

Calls

Call 1

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

Outputs

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

Calls

1 calls:

3.0ms

re

Results

Accuracy	Segments	Branch
67.0%	3	`re`

Compiler

Compiled 1 to 2 computations (-100% saved)

regimes15.0ms (0.2%)

Memory

-5.2MiB live, 30.9MiB allocated

Counts

5 → 2

Calls

Call 1

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

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

Calls

5 calls:

5.0ms	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 1/2 binary64) (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
50.8%	1	`(.f64 #s(literal 2 binary64) (+.f64 (sqrt.f64 (+.f64 (.f64 re re) (*.f64 im im))) re))`
50.8%	1	`(+.f64 (sqrt.f64 (+.f64 (.f64 re re) (.f64 im im))) re)`
50.8%	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))))`
50.8%	1	`(sqrt.f64 (.f64 #s(literal 2 binary64) (+.f64 (sqrt.f64 (+.f64 (.f64 re re) (*.f64 im im))) re)))`
63.4%	2	`re`

Compiler

Compiled 51 to 40 computations (21.6% saved)

regimes14.0ms (0.2%)

Memory

-12.2MiB live, 29.3MiB allocated

Accuracy

Total -0.0b remaining (-0%)

Threshold costs -0b (-0%)

Counts

1 → 1

Calls

Call 1

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

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

Calls

7 calls:

6.0ms	(+.f64 (sqrt.f64 (+.f64 (.f64 re re) (.f64 im im))) re)
1.0ms	im
1.0ms	(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

Results

Accuracy	Segments	Branch
31.4%	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))))`
31.4%	1	`(sqrt.f64 (.f64 #s(literal 2 binary64) (+.f64 (sqrt.f64 (+.f64 (.f64 re re) (*.f64 im im))) re)))`
31.4%	1	`(.f64 #s(literal 2 binary64) (+.f64 (sqrt.f64 (+.f64 (.f64 re re) (*.f64 im im))) re))`
31.4%	1	`(+.f64 (sqrt.f64 (+.f64 (.f64 re re) (.f64 im im))) re)`
31.4%	1	`im`
31.4%	1	`(*.f64 im im)`
31.4%	1	`re`

Compiler

Compiled 55 to 45 computations (18.2% saved)

bsearch35.0ms (0.4%)

Memory

21.9MiB live, 58.6MiB allocated

Algorithm

1×	binary-search

Stop Event

1×	narrow-enough

Steps

Time	Left	Right
32.0ms	-7.638802419308949e+103	-1.3150612295317632e+96

Samples

13.0ms	42×	3	valid
6.0ms	33×	2	valid
3.0ms	25×	1	valid
3.0ms	44×	0	valid

Compiler

Compiled 315 to 266 computations (15.6% saved)

Precisions

Click to see histograms. Total time spent on operations: 20.0ms

ival-hypot: 10.0ms (49.2% of total)

ival-mult: 4.0ms (19.7% of total)

adjust: 2.0ms (9.8% of total)

ival-sqrt: 2.0ms (9.8% of total)

ival-add: 2.0ms (9.8% of total)

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

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

exact: 0.0ms (0% of total)

bsearch2.0ms (0%)

Memory

5.0MiB live, 5.0MiB allocated

Algorithm

1×	binary-search

Stop Event

1×	narrow-enough

Steps

Time	Left	Right
1.0ms	-7.638802419308949e+103	-1.3150612295317632e+96

Compiler

Compiled 306 to 257 computations (16% saved)

bsearch62.0ms (0.7%)

Memory

-26.5MiB live, 86.7MiB allocated

Algorithm

3×	binary-search

Stop Event

1×	narrow-enough
1×	narrow-enough
1×	narrow-enough

Steps

Time	Left	Right
3.0ms	8.73148651141569e+124	1.0528830658640517e+125
17.0ms	8.414058740941632e-135	8.163122943675298e-122
24.0ms	-1.3150612295317632e+96	-1.963547097950184e+94

Samples

15.0ms	235×	0	valid
8.0ms	31×	3	valid
4.0ms	21×	2	valid
2.0ms	17×	1	valid

Compiler

Compiled 716 to 579 computations (19.1% saved)

Precisions

Click to see histograms. Total time spent on operations: 21.0ms

ival-hypot: 9.0ms (42.8% of total)

ival-mult: 5.0ms (23.8% of total)

ival-sqrt: 3.0ms (14.3% of total)

adjust: 2.0ms (9.5% of total)

ival-add: 2.0ms (9.5% of total)

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

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

exact: 0.0ms (0% of total)

bsearch23.0ms (0.3%)

Memory

1.5MiB live, 37.9MiB allocated

Algorithm

2×	binary-search

Stop Event

1×	narrow-enough
1×	narrow-enough

Steps

Time	Left	Right
19.0ms	3.993164702472411	2843380432381271.5
1.0ms	-1.3150612295317632e+96	-1.963547097950184e+94

Samples

13.0ms

160×

valid

Compiler

Compiled 692 to 555 computations (19.8% saved)

Precisions

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

ival-hypot: 3.0ms (44.8% of total)

ival-mult: 2.0ms (29.8% of total)

ival-add: 1.0ms (14.9% of total)

ival-sqrt: 1.0ms (14.9% of total)

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

exact: 0.0ms (0% of total)

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

bsearch20.0ms (0.2%)

Memory

14.6MiB live, 47.2MiB allocated

Algorithm

2×	binary-search

Stop Event

1×	narrow-enough
1×	narrow-enough

Steps

Time	Left	Right
18.0ms	8.163122943675298e-122	2.4454115722931997e-120
1.0ms	-1.3150612295317632e+96	-1.963547097950184e+94

Samples

13.0ms

112×

valid

Compiler

Compiled 592 to 490 computations (17.2% saved)

Precisions

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

ival-hypot: 8.0ms (76.5% of total)

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

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

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

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

exact: 0.0ms (0% of total)

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

bsearch23.0ms (0.3%)

Memory

7.8MiB live, 44.9MiB allocated

Algorithm

2×	binary-search

Stop Event

1×	narrow-enough
1×	narrow-enough

Steps

Time	Left	Right
1.0ms	8.163122943675298e-122	2.4454115722931997e-120
20.0ms	-3.652554945795608e+188	-1.3976548818622396e+188

Samples

9.0ms	22×	3	valid
3.0ms	28×	1	valid
3.0ms	16×	2	valid
1.0ms	14×	0	valid

Compiler

Compiled 486 to 410 computations (15.6% saved)

Precisions

Click to see histograms. Total time spent on operations: 13.0ms

ival-hypot: 5.0ms (37.8% of total)

adjust: 4.0ms (30.3% of total)

ival-mult: 2.0ms (15.1% of total)

ival-add: 1.0ms (7.6% of total)

ival-sqrt: 1.0ms (7.6% of total)

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

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

exact: 0.0ms (0% of total)

bsearch60.0ms (0.7%)

Memory

5.0MiB live, 100.6MiB allocated

Algorithm

2×	binary-search

Stop Event

1×	narrow-enough
1×	narrow-enough

Steps

Time	Left	Right
1.0ms	3.993164702472411	2843380432381271.5
55.0ms	-1.5160032370912138e+168	-2.6980409488854193e+155

Samples

27.0ms	32×	2	valid
13.0ms	47×	3	valid
6.0ms	46×	1	valid
2.0ms	35×	0	valid

Compiler

Compiled 758 to 614 computations (19% saved)

Precisions

Click to see histograms. Total time spent on operations: 41.0ms

ival-hypot: 29.0ms (70% of total)

adjust: 4.0ms (9.7% of total)

ival-mult: 4.0ms (9.7% of total)

ival-sqrt: 3.0ms (7.2% of total)

ival-add: 2.0ms (4.8% of total)

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

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

exact: 0.0ms (0% of total)

bsearch2.0ms (0%)

Memory

-34.9MiB live, 4.1MiB allocated

Algorithm

1×	binary-search

Stop Event

1×	narrow-enough

Steps

Time	Left	Right
2.0ms	8.163122943675298e-122	2.4454115722931997e-120

Compiler

Compiled 277 to 231 computations (16.6% saved)

simplify75.0ms (0.9%)

Memory

1.9MiB live, 82.1MiB allocated

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	92	483
1	122	483
2	132	483
3	142	483
4	145	483
5	146	483

Stop Event

1×

saturated

Calls

Call 1

Inputs
(if (<=.f64 re #s(literal -37999999999999996330438299274272929756954877531250474667873998804734840580260146605501758494797201408 binary64)) (.f64 #s(literal 1/2 binary64) (sqrt.f64 #s(approx ( 2 (+ (sqrt (+ (* re re) (* im im))) re)) (.f64 (neg.f64 im) (/.f64 im re))))) (.f64 (*.f64 (sqrt.f64 (+.f64 (hypot.f64 im re) re)) #s(literal 1/2 binary64)) (sqrt.f64 #s(literal 2 binary64))))
(if (<=.f64 re #s(literal -37999999999999996330438299274272929756954877531250474667873998804734840580260146605501758494797201408 binary64)) (.f64 #s(literal 1/2 binary64) (sqrt.f64 #s(approx ( 2 (+ (sqrt (+ (* re re) (* im im))) re)) (.f64 (neg.f64 im) (/.f64 im re))))) (.f64 (sqrt.f64 (*.f64 (+.f64 (hypot.f64 im re) re) #s(literal 2 binary64))) #s(literal 1/2 binary64)))
(if (<=.f64 re #s(literal -244999999999999993837584819370852251538329038353478492664836801869466833436622191033220522311680 binary64)) (.f64 #s(literal 1/2 binary64) (sqrt.f64 #s(approx ( 2 (+ (sqrt (+ (* re re) (* im im))) re)) (.f64 (neg.f64 im) (/.f64 im re))))) (if (<=.f64 re #s(literal 6193549123826929/399583814440447005616844445413525287135820562261116307309972090832047582568929999375399181192126972308457847183540047730617340886948900519205142528 binary64)) (.f64 (.f64 (sqrt.f64 #s(approx (+ (sqrt (+ ( im im) (* re re))) re) (+.f64 re im))) #s(literal 1/2 binary64)) (sqrt.f64 #s(literal 2 binary64))) (if (<=.f64 re #s(literal 99999999999999992486776161899288204254467086983483846143922597222529419997579302660316349376281765375153005841365553228283904 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)))) (sqrt.f64 re)))))
(if (<=.f64 re #s(literal -244999999999999993837584819370852251538329038353478492664836801869466833436622191033220522311680 binary64)) (.f64 #s(literal 1/2 binary64) (sqrt.f64 #s(approx ( 2 (+ (sqrt (+ (* re re) (* im im))) re)) (.f64 (neg.f64 im) (/.f64 im re))))) (if (<=.f64 re #s(literal 130000000 binary64)) (.f64 (.f64 (sqrt.f64 #s(approx (+ (sqrt (+ ( im im) (* re re))) re) (+.f64 re im))) #s(literal 1/2 binary64)) (sqrt.f64 #s(literal 2 binary64))) #s(approx (* 1/2 (sqrt (* 2 (+ (sqrt (+ (* re re) (* im im))) re)))) (sqrt.f64 re))))
(if (<=.f64 re #s(literal -244999999999999993837584819370852251538329038353478492664836801869466833436622191033220522311680 binary64)) (.f64 #s(literal 1/2 binary64) (sqrt.f64 #s(approx ( 2 (+ (sqrt (+ (* re re) (* im im))) re)) (.f64 (neg.f64 im) (/.f64 im re))))) (if (<=.f64 re #s(literal 6047298186139449/5814709794364855124394590463104036274829130885498544482251921593445114304907183386609528405710108524486100172850129423468276813028917248 binary64)) (.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)))) #s(approx ( 1/2 (sqrt (* 2 (+ (sqrt (+ (* re re) (* im im))) re)))) (sqrt.f64 re))))
(if (<=.f64 re #s(literal -244999999999999999474547332333365177975247339597486571602204594117640338619890731449681012569351257214231657901297225938225015927314805525400501422911373846310793823157096536030777530384384 binary64)) (.f64 #s(literal 1/2 binary64) (sqrt.f64 (.f64 #s(literal 2 binary64) (+.f64 #s(approx (sqrt (+ (* re re) (* im im))) (neg.f64 re)) re)))) (if (<=.f64 re #s(literal 6047298186139449/5814709794364855124394590463104036274829130885498544482251921593445114304907183386609528405710108524486100172850129423468276813028917248 binary64)) (.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)))) #s(approx ( 1/2 (sqrt (* 2 (+ (sqrt (+ (* re re) (* im im))) re)))) (sqrt.f64 re))))
(if (<=.f64 re #s(literal -129999999999999989922573080752896642554346043659439402419741479764367625104846996163833301760675601044541091390211386148124492604507885760562484254946699086135296 binary64)) (.f64 #s(literal 1/2 binary64) (sqrt.f64 (.f64 #s(literal 2 binary64) (+.f64 #s(approx (sqrt (+ (* re re) (* im im))) (neg.f64 re)) re)))) (if (<=.f64 re #s(literal 130000000 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)))) (sqrt.f64 re))))
(if (<=.f64 re #s(literal 6047298186139449/5814709794364855124394590463104036274829130885498544482251921593445114304907183386609528405710108524486100172850129423468276813028917248 binary64)) (.f64 #s(literal 1/2 binary64) (sqrt.f64 #s(approx ( 2 (+ (sqrt (+ (* re re) (* im im))) re)) (.f64 #s(literal 2 binary64) im)))) #s(approx ( 1/2 (sqrt (* 2 (+ (sqrt (+ (* re re) (* im im))) re)))) (sqrt.f64 re)))
#s(approx (* 1/2 (sqrt (* 2 (+ (sqrt (+ (* re re) (* im im))) re)))) (sqrt.f64 re))

Outputs
(if (<=.f64 re #s(literal -37999999999999996330438299274272929756954877531250474667873998804734840580260146605501758494797201408 binary64)) (.f64 (sqrt.f64 #s(approx ( 2 (+ (sqrt (+ (* re re) (* im im))) re)) (.f64 (/.f64 (neg.f64 im) re) im))) #s(literal 1/2 binary64)) (.f64 (sqrt.f64 #s(literal 2 binary64)) (*.f64 (sqrt.f64 (+.f64 (hypot.f64 im re) re)) #s(literal 1/2 binary64))))
(if (<=.f64 re #s(literal -37999999999999996330438299274272929756954877531250474667873998804734840580260146605501758494797201408 binary64)) (.f64 (sqrt.f64 #s(approx ( 2 (+ (sqrt (+ (* re re) (* im im))) re)) (.f64 (/.f64 (neg.f64 im) re) im))) #s(literal 1/2 binary64)) (.f64 (sqrt.f64 (*.f64 (+.f64 (hypot.f64 im re) re) #s(literal 2 binary64))) #s(literal 1/2 binary64)))
(if (<=.f64 re #s(literal -244999999999999993837584819370852251538329038353478492664836801869466833436622191033220522311680 binary64)) (.f64 (sqrt.f64 #s(approx ( 2 (+ (sqrt (+ (* re re) (* im im))) re)) (.f64 (/.f64 (neg.f64 im) re) im))) #s(literal 1/2 binary64)) (if (<=.f64 re #s(literal 6193549123826929/399583814440447005616844445413525287135820562261116307309972090832047582568929999375399181192126972308457847183540047730617340886948900519205142528 binary64)) (.f64 (.f64 (sqrt.f64 #s(approx (+ (sqrt (+ ( im im) (* re re))) re) (+.f64 im re))) #s(literal 1/2 binary64)) (sqrt.f64 #s(literal 2 binary64))) (if (<=.f64 re #s(literal 99999999999999992486776161899288204254467086983483846143922597222529419997579302660316349376281765375153005841365553228283904 binary64)) (.f64 (sqrt.f64 (.f64 (+.f64 (sqrt.f64 (fma.f64 re re (.f64 im im))) re) #s(literal 2 binary64))) #s(literal 1/2 binary64)) #s(approx ( 1/2 (sqrt (* 2 (+ (sqrt (+ (* re re) (* im im))) re)))) (sqrt.f64 re)))))
(if (<=.f64 re #s(literal -244999999999999993837584819370852251538329038353478492664836801869466833436622191033220522311680 binary64)) (.f64 (sqrt.f64 #s(approx ( 2 (+ (sqrt (+ (* re re) (* im im))) re)) (.f64 (/.f64 (neg.f64 im) re) im))) #s(literal 1/2 binary64)) (if (<=.f64 re #s(literal 130000000 binary64)) (.f64 (.f64 (sqrt.f64 #s(approx (+ (sqrt (+ ( im im) (* re re))) re) (+.f64 im re))) #s(literal 1/2 binary64)) (sqrt.f64 #s(literal 2 binary64))) #s(approx (* 1/2 (sqrt (* 2 (+ (sqrt (+ (* re re) (* im im))) re)))) (sqrt.f64 re))))
(if (<=.f64 re #s(literal -244999999999999993837584819370852251538329038353478492664836801869466833436622191033220522311680 binary64)) (.f64 (sqrt.f64 #s(approx ( 2 (+ (sqrt (+ (* re re) (* im im))) re)) (.f64 (/.f64 (neg.f64 im) re) im))) #s(literal 1/2 binary64)) (if (<=.f64 re #s(literal 6047298186139449/5814709794364855124394590463104036274829130885498544482251921593445114304907183386609528405710108524486100172850129423468276813028917248 binary64)) (.f64 #s(approx (sqrt (* 2 (+ (sqrt (+ (* re re) (* im im))) re))) (.f64 (sqrt.f64 im) (sqrt.f64 #s(literal 2 binary64)))) #s(literal 1/2 binary64)) #s(approx ( 1/2 (sqrt (* 2 (+ (sqrt (+ (* re re) (* im im))) re)))) (sqrt.f64 re))))
(if (<=.f64 re #s(literal -244999999999999999474547332333365177975247339597486571602204594117640338619890731449681012569351257214231657901297225938225015927314805525400501422911373846310793823157096536030777530384384 binary64)) (.f64 (sqrt.f64 (.f64 (+.f64 #s(approx (sqrt (+ (* re re) (* im im))) (neg.f64 re)) re) #s(literal 2 binary64))) #s(literal 1/2 binary64)) (if (<=.f64 re #s(literal 6047298186139449/5814709794364855124394590463104036274829130885498544482251921593445114304907183386609528405710108524486100172850129423468276813028917248 binary64)) (.f64 #s(approx (sqrt ( 2 (+ (sqrt (+ (* re re) (* im im))) re))) (.f64 (sqrt.f64 im) (sqrt.f64 #s(literal 2 binary64)))) #s(literal 1/2 binary64)) #s(approx ( 1/2 (sqrt (* 2 (+ (sqrt (+ (* re re) (* im im))) re)))) (sqrt.f64 re))))
(if (<=.f64 re #s(literal -129999999999999989922573080752896642554346043659439402419741479764367625104846996163833301760675601044541091390211386148124492604507885760562484254946699086135296 binary64)) (.f64 (sqrt.f64 (.f64 (+.f64 #s(approx (sqrt (+ (* re re) (* im im))) (neg.f64 re)) re) #s(literal 2 binary64))) #s(literal 1/2 binary64)) (if (<=.f64 re #s(literal 130000000 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)))) (sqrt.f64 re))))
(if (<=.f64 re #s(literal 6047298186139449/5814709794364855124394590463104036274829130885498544482251921593445114304907183386609528405710108524486100172850129423468276813028917248 binary64)) (.f64 (sqrt.f64 #s(approx ( 2 (+ (sqrt (+ (* re re) (* im im))) re)) (.f64 im #s(literal 2 binary64)))) #s(literal 1/2 binary64)) #s(approx ( 1/2 (sqrt (* 2 (+ (sqrt (+ (* re re) (* im im))) re)))) (sqrt.f64 re)))
#s(approx (* 1/2 (sqrt (* 2 (+ (sqrt (+ (* re re) (* im im))) re)))) (sqrt.f64 re))

soundness665.0ms (8%)

Memory

20.2MiB live, 661.7MiB allocated

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	12	65
0	20	65
1	61	65
2	398	65
3	4225	65
0	8344	38
0	667	10506
1	2227	9608
2	7580	9584
0	8496	9148
0	500	3104
1	1659	2919
2	5910	2897
0	8080	2716

Stop Event

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

Compiler

Compiled 735 to 296 computations (59.7% saved)

preprocess71.0ms (0.8%)

Memory: -18.9MiB live, 137.3MiB allocated
Remove: (abs im)
Compiler: Compiled 1 148 to 304 computations (73.5% saved)

end0.0ms (0%)

Memory: 0.0MiB live, 0.0MiB allocated

Iter	Nodes	Cost
0	30	75
1	94	75
2	169	75
3	259	75
4	396	75
5	523	75
6	645	75
7	745	75
8	773	75
0	12	15
0	20	15
1	30	15
2	32	15
0	32	10

Iter	Nodes	Cost
0	30	75
1	94	75
2	169	75
3	259	75
4	396	75
5	523	75
6	645	75
7	745	75
8	773	75
0	12	15
0	20	15
1	30	15
2	32	15
0	32	10

start0.0ms (0%)

analyze183.0ms (2.2%)

sample1.6s (18.6%)

explain210.0ms (2.5%)

preprocess123.0ms (1.5%)

eval0.0ms (0%)

prune1.0ms (0%)

simplify3.0ms (0%)

localize237.0ms (2.8%)

series92.0ms (1.1%)

simplify368.0ms (4.4%)

rewrite255.0ms (3.1%)

eval321.0ms (3.8%)

prune20.0ms (0.2%)

simplify8.0ms (0.1%)

localize71.0ms (0.8%)

series39.0ms (0.5%)

simplify243.0ms (2.9%)

rewrite182.0ms (2.2%)

eval131.0ms (1.6%)

prune85.0ms (1%)

simplify284.0ms (3.4%)

localize186.0ms (2.2%)

series126.0ms (1.5%)

simplify249.0ms (3%)

rewrite215.0ms (2.6%)

eval164.0ms (2%)

prune46.0ms (0.6%)

simplify147.0ms (1.8%)

localize236.0ms (2.8%)

series125.0ms (1.5%)

simplify245.0ms (2.9%)

rewrite220.0ms (2.6%)

eval637.0ms (7.6%)

prune53.0ms (0.6%)

regimes98.0ms (1.2%)

regimes13.0ms (0.2%)

regimes100.0ms (1.2%)

regimes7.0ms (0.1%)

regimes5.0ms (0.1%)

regimes4.0ms (0%)

regimes3.0ms (0%)

regimes15.0ms (0.2%)

regimes14.0ms (0.2%)

bsearch35.0ms (0.4%)

bsearch2.0ms (0%)

bsearch62.0ms (0.7%)

bsearch23.0ms (0.3%)

bsearch20.0ms (0.2%)

bsearch23.0ms (0.3%)

bsearch60.0ms (0.7%)

bsearch2.0ms (0%)

simplify75.0ms (0.9%)

soundness665.0ms (8%)

preprocess71.0ms (0.8%)

end0.0ms (0%)

Profiling

Iter	Nodes	Cost
0	30	75
1	94	75
2	169	75
3	259	75
4	396	75
5	523	75
6	645	75
7	745	75
8	773	75
0	12	15
0	20	15
1	30	15
2	32	15
0	32	10