Metrics for math.abs on complex

start0.0ms (0%)

Memory: 0.1MiB live, 0.1MiB allocated

analyze0.0ms (0%)

Memory

0.7MiB live, 0.7MiB allocated

Algorithm

1×

Search

Probability	Valid	Unknown	Precondition	Infinite	Domain	Can't	Iter
0%	0%	99.9%	0.1%	0%	0%	0%	0
100%	99.9%	0%	0.1%	0%	0%	0%	1

Compiler

Compiled 10 to 5 computations (50% saved)

sample726.0ms (17.5%)

Memory

18.6MiB live, 970.2MiB allocated

Samples

429.0ms

8 256×

valid

Precisions

Click to see histograms. Total time spent on operations: 206.0ms

ival-hypot: 197.0ms (95.4% of total)

ival-true: 6.0ms (2.9% of total)

ival-assert: 4.0ms (1.9% of total)

Bogosity

explain118.0ms (2.8%)

Memory

-15.9MiB live, 104.5MiB allocated

FPErrors

Click to see full error table

Ground Truth	Example	Underpredictions	Example	Subexpression
137	-	4	(-6.0899266242930135e-189 -8.667787038236518e-160)	`(sqrt.f64 (+.f64 (.f64 re re) (.f64 im im)))`
0	-	0	-	`(+.f64 (.f64 re re) (.f64 im im))`
0	-	0	-	`(*.f64 re re)`
0	-	0	-	`re`
0	-	0	-	`(*.f64 im im)`
0	-	0	-	`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	115	0
↳	`(+.f64 (.f64 re re) (.f64 im im))`	overflow	115
↳	`(*.f64 re re)`	overflow	67
↳	`(*.f64 im im)`	overflow	68
`sqrt.f64`	`(sqrt.f64 (+.f64 (.f64 re re) (.f64 im im)))`	uflow-rescue	18	0
↳	`(+.f64 (.f64 re re) (.f64 im im))`	underflow	18
↳	`(*.f64 re re)`	underflow	65
↳	`(*.f64 im im)`	underflow	61

Confusion

	Predicted +	Predicted -
+	133	4
-	0	119

Precision

1.0

Recall

0.9708029197080292

Confusion?

	Predicted +	Predicted Maybe	Predicted -
+	133	0	4
-	0	0	119

Precision?

1.0

Recall?

0.9708029197080292

Freqs

test

number	freq
0	123
1	133

Total Confusion?

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

Precision?

1.0

Recall?

1.0

Samples

64.0ms

512×

valid

Compiler

Compiled 81 to 28 computations (65.4% saved)

Precisions

Click to see histograms. Total time spent on operations: 18.0ms

ival-hypot: 9.0ms (49.1% of total)

ival-mult: 7.0ms (38.2% of total)

ival-add: 2.0ms (10.9% of total)

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

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

preprocess16.0ms (0.4%)

Memory

18.1MiB live, 18.1MiB allocated

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	16	42
1	35	42
2	77	42
3	145	42
4	204	42
5	217	42
6	219	42
0	6	8
0	10	8
1	11	8
0	11	3

Stop Event

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

Calls

Call 1

Inputs
(sqrt.f64 (+.f64 (.f64 re re) (.f64 im im)))

Outputs
(hypot.f64 im re)

Symmetry

(abs im)

(abs re)

(sort re im)

Compiler

Compiled 8 to 6 computations (25% saved)

eval0.0ms (0%)

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

prune1.0ms (0%)

Memory

1.4MiB live, 1.4MiB allocated

Alt Table

Click to see full alt table

Status	Accuracy	Program
▶	50.9%	(sqrt.f64 (+.f64 (.f64 re re) (.f64 im im)))

Compiler

Compiled 8 to 6 computations (25% saved)

simplify3.0ms (0.1%)

Memory

5.4MiB live, 5.4MiB allocated

Algorithm

1×	egg-herbie

Localize:

Found 4 expressions of interest:

New	Metric	Score
cost-diff	-5120	(sqrt.f64 (+.f64 (.f64 re re) (.f64 im im)))
cost-diff	0	(*.f64 im im)
cost-diff	0	(*.f64 re re)
cost-diff	128	(+.f64 (.f64 re re) (.f64 im im))

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	6	23
0	10	23
1	11	23
0	11	17

Stop Event

1×	iter limit
1×	saturated
1×	iter limit

Calls

Call 1

Inputs
(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
(hypot.f64 im re)
(fma.f64 im im (*.f64 re re))
(*.f64 re re)
re
(*.f64 im im)
im

localize47.0ms (1.1%)

Memory

0.5MiB live, 75.2MiB allocated

Localize:

Found 4 expressions of interest:

New	Metric	Score
accuracy	0	(*.f64 re re)
accuracy	0	(*.f64 im im)
accuracy	0.00390625	(+.f64 (.f64 re re) (.f64 im im))
accuracy	31.40418597419603	(sqrt.f64 (+.f64 (.f64 re re) (.f64 im im)))

Samples

41.0ms

256×

valid

Compiler

Compiled 48 to 14 computations (70.8% saved)

Precisions

Click to see histograms. Total time spent on operations: 9.0ms

ival-hypot: 4.0ms (44.3% of total)

ival-mult: 3.0ms (33.3% of total)

ival-add: 1.0ms (11.1% of total)

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

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

series11.0ms (0.3%)

Memory

-24.3MiB live, 21.3MiB allocated

Counts

4 → 72

Calls

Call 1

Inputs
#s(alt #<batchref> (patch (+.f64 (.f64 re re) (.f64 im im)) #<representation binary64>) () ())
#s(alt #<batchref> (patch (*.f64 re re) #<representation binary64>) () ())
#s(alt #<batchref> (patch (*.f64 im im) #<representation binary64>) () ())
#s(alt #<batchref> (patch (sqrt.f64 (+.f64 (.f64 re re) (.f64 im im))) #<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 re re) #<representation binary64>) () ())) ())
#s(alt #<batchref> (taylor 0 re) (#s(alt #<batchref> (patch (*.f64 re re) #<representation binary64>) () ())) ())
#s(alt #<batchref> (taylor 0 re) (#s(alt #<batchref> (patch (*.f64 re re) #<representation binary64>) () ())) ())
#s(alt #<batchref> (taylor 0 re) (#s(alt #<batchref> (patch (*.f64 re 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 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 re re) #<representation binary64>) () ())) ())
#s(alt #<batchref> (taylor inf re) (#s(alt #<batchref> (patch (*.f64 re re) #<representation binary64>) () ())) ())
#s(alt #<batchref> (taylor inf re) (#s(alt #<batchref> (patch (*.f64 re re) #<representation binary64>) () ())) ())
#s(alt #<batchref> (taylor inf re) (#s(alt #<batchref> (patch (*.f64 re 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 (.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 re re) #<representation binary64>) () ())) ())
#s(alt #<batchref> (taylor -inf re) (#s(alt #<batchref> (patch (*.f64 re re) #<representation binary64>) () ())) ())
#s(alt #<batchref> (taylor -inf re) (#s(alt #<batchref> (patch (*.f64 re re) #<representation binary64>) () ())) ())
#s(alt #<batchref> (taylor -inf re) (#s(alt #<batchref> (patch (*.f64 re 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 0 im) (#s(alt #<batchref> (patch (+.f64 (.f64 re re) (.f64 im im)) #<representation binary64>) () ())) ())
#s(alt #<batchref> (taylor 0 im) (#s(alt #<batchref> (patch (+.f64 (.f64 re re) (.f64 im im)) #<representation binary64>) () ())) ())
#s(alt #<batchref> (taylor 0 im) (#s(alt #<batchref> (patch (+.f64 (.f64 re re) (.f64 im im)) #<representation binary64>) () ())) ())
#s(alt #<batchref> (taylor 0 im) (#s(alt #<batchref> (patch (+.f64 (.f64 re re) (.f64 im im)) #<representation binary64>) () ())) ())
#s(alt #<batchref> (taylor 0 im) (#s(alt #<batchref> (patch (*.f64 im im) #<representation binary64>) () ())) ())
#s(alt #<batchref> (taylor 0 im) (#s(alt #<batchref> (patch (*.f64 im im) #<representation binary64>) () ())) ())
#s(alt #<batchref> (taylor 0 im) (#s(alt #<batchref> (patch (*.f64 im im) #<representation binary64>) () ())) ())
#s(alt #<batchref> (taylor 0 im) (#s(alt #<batchref> (patch (*.f64 im im) #<representation binary64>) () ())) ())
#s(alt #<batchref> (taylor 0 im) (#s(alt #<batchref> (patch (sqrt.f64 (+.f64 (.f64 re re) (.f64 im im))) #<representation binary64>) () ())) ())
#s(alt #<batchref> (taylor 0 im) (#s(alt #<batchref> (patch (sqrt.f64 (+.f64 (.f64 re re) (.f64 im im))) #<representation binary64>) () ())) ())
#s(alt #<batchref> (taylor 0 im) (#s(alt #<batchref> (patch (sqrt.f64 (+.f64 (.f64 re re) (.f64 im im))) #<representation binary64>) () ())) ())
#s(alt #<batchref> (taylor 0 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 (.f64 re re) (.f64 im im)) #<representation binary64>) () ())) ())
#s(alt #<batchref> (taylor inf im) (#s(alt #<batchref> (patch (+.f64 (.f64 re re) (.f64 im im)) #<representation binary64>) () ())) ())
#s(alt #<batchref> (taylor inf im) (#s(alt #<batchref> (patch (+.f64 (.f64 re re) (.f64 im im)) #<representation binary64>) () ())) ())
#s(alt #<batchref> (taylor inf im) (#s(alt #<batchref> (patch (+.f64 (.f64 re re) (.f64 im im)) #<representation binary64>) () ())) ())
#s(alt #<batchref> (taylor inf im) (#s(alt #<batchref> (patch (*.f64 im im) #<representation binary64>) () ())) ())
#s(alt #<batchref> (taylor inf im) (#s(alt #<batchref> (patch (*.f64 im im) #<representation binary64>) () ())) ())
#s(alt #<batchref> (taylor inf im) (#s(alt #<batchref> (patch (*.f64 im im) #<representation binary64>) () ())) ())
#s(alt #<batchref> (taylor inf im) (#s(alt #<batchref> (patch (*.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 (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 (sqrt.f64 (+.f64 (.f64 re re) (.f64 im im))) #<representation binary64>) () ())) ())
#s(alt #<batchref> (taylor -inf im) (#s(alt #<batchref> (patch (+.f64 (.f64 re re) (.f64 im im)) #<representation binary64>) () ())) ())
#s(alt #<batchref> (taylor -inf im) (#s(alt #<batchref> (patch (+.f64 (.f64 re re) (.f64 im im)) #<representation binary64>) () ())) ())
#s(alt #<batchref> (taylor -inf im) (#s(alt #<batchref> (patch (+.f64 (.f64 re re) (.f64 im im)) #<representation binary64>) () ())) ())
#s(alt #<batchref> (taylor -inf im) (#s(alt #<batchref> (patch (+.f64 (.f64 re re) (.f64 im im)) #<representation binary64>) () ())) ())
#s(alt #<batchref> (taylor -inf im) (#s(alt #<batchref> (patch (*.f64 im im) #<representation binary64>) () ())) ())
#s(alt #<batchref> (taylor -inf im) (#s(alt #<batchref> (patch (*.f64 im im) #<representation binary64>) () ())) ())
#s(alt #<batchref> (taylor -inf im) (#s(alt #<batchref> (patch (*.f64 im im) #<representation binary64>) () ())) ())
#s(alt #<batchref> (taylor -inf im) (#s(alt #<batchref> (patch (*.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 (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 (sqrt.f64 (+.f64 (.f64 re re) (.f64 im im))) #<representation binary64>) () ())) ())

Calls

6 calls:

Time	Variable		Point	Expression
5.0ms	re	@	inf	((+ (* re re) (* im im)) (* re re) (* im im) (sqrt (+ (* re re) (* im im))))
1.0ms	re	@	0	((+ (* re re) (* im im)) (* re re) (* im im) (sqrt (+ (* re re) (* im im))))
1.0ms	im	@	inf	((+ (* re re) (* im im)) (* re re) (* im im) (sqrt (+ (* re re) (* im im))))
1.0ms	re	@	-inf	((+ (* re re) (* im im)) (* re re) (* im im) (sqrt (+ (* re re) (* im im))))
1.0ms	im	@	0	((+ (* re re) (* im im)) (* re re) (* im im) (sqrt (+ (* re re) (* im im))))

simplify200.0ms (4.8%)

Memory

28.2MiB live, 183.9MiB allocated

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	104	620
1	296	620
2	953	618
3	3667	584
4	6426	582
0	8051	530

Stop Event

1×	iter limit
1×	node limit

Counts

72 → 68

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))
(pow re 2)
(pow re 2)
(pow re 2)
(pow re 2)
im
(+ im (* 1/2 (/ (pow re 2) im)))
(+ im (* (pow re 2) (+ (* -1/8 (/ (pow re 2) (pow im 3))) (* 1/2 (/ 1 im)))))
(+ im (* (pow re 2) (+ (* (pow re 2) (- (* 1/16 (/ (pow re 2) (pow im 5))) (* 1/8 (/ 1 (pow im 3))))) (* 1/2 (/ 1 im)))))
(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))))
(pow re 2)
(pow re 2)
(pow re 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)))))))
(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))))
(pow re 2)
(pow re 2)
(pow re 2)
(pow re 2)
(* -1 re)
(* -1 (* re (+ 1 (* 1/2 (/ (pow im 2) (pow re 2))))))
(* -1 (* re (+ 1 (+ (* -1/8 (/ (pow im 4) (pow re 4))) (* 1/2 (/ (pow im 2) (pow re 2)))))))
(* -1 (* re (+ 1 (+ (* -1/8 (/ (pow im 4) (pow re 4))) (+ (* 1/16 (/ (pow im 6) (pow re 6))) (* 1/2 (/ (pow im 2) (pow re 2))))))))
(pow re 2)
(+ (pow im 2) (pow re 2))
(+ (pow im 2) (pow re 2))
(+ (pow im 2) (pow re 2))
(pow im 2)
(pow im 2)
(pow im 2)
(pow im 2)
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)))))
(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))))
(pow im 2)
(pow im 2)
(pow im 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)))))))
(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))))
(pow im 2)
(pow im 2)
(pow im 2)
(pow im 2)
(* -1 im)
(* -1 (* im (+ 1 (* 1/2 (/ (pow re 2) (pow im 2))))))
(* -1 (* im (+ 1 (+ (* -1/8 (/ (pow re 4) (pow im 4))) (* 1/2 (/ (pow re 2) (pow im 2)))))))
(* -1 (* im (+ 1 (+ (* -1/8 (/ (pow re 4) (pow im 4))) (+ (* 1/16 (/ (pow re 6) (pow im 6))) (* 1/2 (/ (pow re 2) (pow im 2))))))))

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

rewrite175.0ms (4.2%)

Memory

-9.6MiB live, 228.4MiB allocated

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	6	21
0	10	21
1	29	21
2	196	21
3	1788	21
0	8624	15

Stop Event

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

Counts

4 → 245

Calls

Call 1

Inputs
(+.f64 (.f64 re re) (.f64 im im))
(*.f64 re re)
(*.f64 im im)
(sqrt.f64 (+.f64 (.f64 re re) (.f64 im im)))

Outputs
#<batchref>
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eval39.0ms (0.9%)

Memory: -1.9MiB live, 78.6MiB allocated
Compiler: Compiled 8 055 to 991 computations (87.7% saved)

prune11.0ms (0.3%)

Memory

2.9MiB live, 39.7MiB allocated

Pruning

7 alts after pruning (7 fresh and 0 done)

	Pruned	Kept	Total
New	306	7	313
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	307	7	314

Accuracy

100.0%

Counts

314 → 7

Alt Table

Click to see full alt table

Status	Accuracy	Program
▶	100.0%	(hypot.f64 re im)
▶	50.9%	(sqrt.f64 (fma.f64 re re (*.f64 im im)))
▶	4.6%	(sqrt.f64 #s(approx (+ (* re re) (* im im)) (*.f64 re re)))
▶	50.5%	(sqrt.f64 #s(approx (+ (* re re) (* im im)) (*.f64 im im)))
	92.7%	#s(approx (sqrt (+ (* re re) (* im im))) (fma.f64 (/.f64 #s(literal 1/2 binary64) im) (*.f64 re re) im))
	6.6%	#s(approx (sqrt (+ (* re re) (* im im))) (fma.f64 (*.f64 #s(literal 1/2 binary64) im) (/.f64 im re) re))
▶	1.8%	#s(approx (sqrt (+ (* re re) (* im im))) (neg.f64 re))

Compiler

Compiled 158 to 108 computations (31.6% saved)

simplify5.0ms (0.1%)

Memory

13.1MiB live, 13.1MiB allocated

Algorithm

1×	egg-herbie

Localize:

Found 12 expressions of interest:

New	Metric	Score
cost-diff	-5120	(sqrt.f64 (fma.f64 re re (*.f64 im im)))
cost-diff	0	(*.f64 im im)
cost-diff	0	(fma.f64 re re (*.f64 im im))
cost-diff	0	(*.f64 re re)
cost-diff	0	#s(approx (+ (* re re) (* im im)) (*.f64 re re))
cost-diff	0	(sqrt.f64 #s(approx (+ (* re re) (* im im)) (*.f64 re re)))
cost-diff	0	(*.f64 im im)
cost-diff	0	#s(approx (+ (* re re) (* im im)) (*.f64 im im))
cost-diff	0	(sqrt.f64 #s(approx (+ (* re re) (* im im)) (*.f64 im im)))
cost-diff	0	(neg.f64 re)
cost-diff	0	#s(approx (sqrt (+ (* re re) (* im im))) (neg.f64 re))
cost-diff	0	(hypot.f64 re im)

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	17	78
0	25	78
1	30	78
2	32	78
3	34	78
4	36	78
5	40	78
6	49	78
7	55	78
8	59	78
0	59	78

Stop Event

1×	iter limit
1×	saturated
1×	iter limit

Calls

Call 1

Inputs
(hypot.f64 re im)
re
im
#s(approx (sqrt (+ (* re re) (* im im))) (neg.f64 re))
(neg.f64 re)
re
(sqrt.f64 #s(approx (+ (* re re) (* im im)) (*.f64 im im)))
#s(approx (+ (* re re) (* im im)) (*.f64 im im))
(*.f64 im im)
im
(sqrt.f64 #s(approx (+ (* re re) (* im im)) (*.f64 re re)))
#s(approx (+ (* re re) (* im im)) (*.f64 re re))
(*.f64 re re)
re
(sqrt.f64 (fma.f64 re re (*.f64 im im)))
(fma.f64 re re (*.f64 im im))
re
(*.f64 im im)
im

Outputs
(hypot.f64 im re)
re
im
#s(approx (sqrt (+ (* re re) (* im im))) (neg.f64 re))
(neg.f64 re)
re
(sqrt.f64 #s(approx (+ (* re re) (* im im)) (*.f64 im im)))
#s(approx (+ (* re re) (* im im)) (*.f64 im im))
(*.f64 im im)
im
(sqrt.f64 #s(approx (+ (* re re) (* im im)) (*.f64 re re)))
#s(approx (+ (* re re) (* im im)) (*.f64 re re))
(*.f64 re re)
re
(hypot.f64 im re)
(fma.f64 im im (*.f64 re re))
re
(*.f64 im im)
im

localize29.0ms (0.7%)

Memory

-25.5MiB live, 52.4MiB allocated

Localize:

Found 12 expressions of interest:

New	Metric	Score
accuracy	0	(*.f64 im im)
accuracy	0.00390625	(fma.f64 re re (*.f64 im im))
accuracy	31.40418597419603	(sqrt.f64 (fma.f64 re re (*.f64 im im)))
accuracy	0	(*.f64 re re)
accuracy	31.40418597419603	(sqrt.f64 #s(approx (+ (* re re) (* im im)) (*.f64 re re)))
accuracy	51.770924600617924	#s(approx (+ (* re re) (* im im)) (*.f64 re re))
accuracy	0	(*.f64 im im)
accuracy	0.28806961482087234	#s(approx (+ (* re re) (* im im)) (*.f64 im im))
accuracy	31.40418597419603	(sqrt.f64 #s(approx (+ (* re re) (* im im)) (*.f64 im im)))
accuracy	0	(neg.f64 re)
accuracy	62.821626141198685	#s(approx (sqrt (+ (* re re) (* im im))) (neg.f64 re))
accuracy	0	(hypot.f64 re im)

Samples

21.0ms

256×

valid

Compiler

Compiled 172 to 26 computations (84.9% saved)

Precisions

Click to see histograms. Total time spent on operations: 11.0ms

ival-hypot: 5.0ms (46.1% of total)

ival-mult: 3.0ms (27.7% of total)

ival-add: 1.0ms (9.2% of total)

ival-neg: 1.0ms (9.2% of total)

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

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

series11.0ms (0.3%)

Memory

22.8MiB live, 22.8MiB allocated

Counts

11 → 228

Calls

Call 1

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

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

Calls

6 calls:

Time	Variable		Point	Expression
1.0ms	re	@	inf	((sqrt (+ (* re re) (* im im))) (sqrt (+ (* re re) (* im im))) (neg re) (sqrt (+ (* re re) (* im im))) (+ (* re re) (* im im)) (* im im) (sqrt (+ (* re re) (* im im))) (+ (* re re) (* im im)) (* re re) (+ (* re re) (* im im)) (sqrt (+ (* re re) (* im im))))
1.0ms	re	@	-inf	((sqrt (+ (* re re) (* im im))) (sqrt (+ (* re re) (* im im))) (neg re) (sqrt (+ (* re re) (* im im))) (+ (* re re) (* im im)) (* im im) (sqrt (+ (* re re) (* im im))) (+ (* re re) (* im im)) (* re re) (+ (* re re) (* im im)) (sqrt (+ (* re re) (* im im))))
1.0ms	im	@	-inf	((sqrt (+ (* re re) (* im im))) (sqrt (+ (* re re) (* im im))) (neg re) (sqrt (+ (* re re) (* im im))) (+ (* re re) (* im im)) (* im im) (sqrt (+ (* re re) (* im im))) (+ (* re re) (* im im)) (* re re) (+ (* re re) (* im im)) (sqrt (+ (* re re) (* im im))))
1.0ms	im	@	inf	((sqrt (+ (* re re) (* im im))) (sqrt (+ (* re re) (* im im))) (neg re) (sqrt (+ (* re re) (* im im))) (+ (* re re) (* im im)) (* im im) (sqrt (+ (* re re) (* im im))) (+ (* re re) (* im im)) (* re re) (+ (* re re) (* im im)) (sqrt (+ (* re re) (* im im))))
0.0ms	re	@	0	((sqrt (+ (* re re) (* im im))) (sqrt (+ (* re re) (* im im))) (neg re) (sqrt (+ (* re re) (* im im))) (+ (* re re) (* im im)) (* im im) (sqrt (+ (* re re) (* im im))) (+ (* re re) (* im im)) (* re re) (+ (* re re) (* im im)) (sqrt (+ (* re re) (* im im))))

simplify182.0ms (4.4%)

Memory

-14.9MiB live, 187.6MiB allocated

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	104	2548
1	296	2548
2	956	2538
3	3681	2368
4	6442	2358
0	8067	2134

Stop Event

1×	iter limit
1×	node limit

Counts

228 → 208

Calls

Call 1

Inputs
im
(+ im (* 1/2 (/ (pow re 2) im)))
(+ im (* (pow re 2) (+ (* -1/8 (/ (pow re 2) (pow im 3))) (* 1/2 (/ 1 im)))))
(+ im (* (pow re 2) (+ (* (pow re 2) (- (* 1/16 (/ (pow re 2) (pow im 5))) (* 1/8 (/ 1 (pow im 3))))) (* 1/2 (/ 1 im)))))
im
(+ im (* 1/2 (/ (pow re 2) im)))
(+ im (* (pow re 2) (+ (* -1/8 (/ (pow re 2) (pow im 3))) (* 1/2 (/ 1 im)))))
(+ im (* (pow re 2) (+ (* (pow re 2) (- (* 1/16 (/ (pow re 2) (pow im 5))) (* 1/8 (/ 1 (pow im 3))))) (* 1/2 (/ 1 im)))))
(* -1 re)
(* -1 re)
(* -1 re)
(* -1 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)))))
(pow im 2)
(+ (pow im 2) (pow re 2))
(+ (pow im 2) (pow re 2))
(+ (pow im 2) (pow re 2))
im
(+ im (* 1/2 (/ (pow re 2) im)))
(+ im (* (pow re 2) (+ (* -1/8 (/ (pow re 2) (pow im 3))) (* 1/2 (/ 1 im)))))
(+ im (* (pow re 2) (+ (* (pow re 2) (- (* 1/16 (/ (pow re 2) (pow im 5))) (* 1/8 (/ 1 (pow im 3))))) (* 1/2 (/ 1 im)))))
(pow im 2)
(+ (pow im 2) (pow re 2))
(+ (pow im 2) (pow re 2))
(+ (pow im 2) (pow re 2))
(pow re 2)
(pow re 2)
(pow re 2)
(pow re 2)
(pow im 2)
(+ (pow im 2) (pow re 2))
(+ (pow im 2) (pow re 2))
(+ (pow im 2) (pow re 2))
im
(+ im (* 1/2 (/ (pow re 2) im)))
(+ im (* (pow re 2) (+ (* -1/8 (/ (pow re 2) (pow im 3))) (* 1/2 (/ 1 im)))))
(+ im (* (pow re 2) (+ (* (pow re 2) (- (* 1/16 (/ (pow re 2) (pow im 5))) (* 1/8 (/ 1 (pow im 3))))) (* 1/2 (/ 1 im)))))
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)))))))
re
(* re (+ 1 (* 1/2 (/ (pow im 2) (pow re 2)))))
(* re (+ 1 (+ (* -1/8 (/ (pow im 4) (pow re 4))) (* 1/2 (/ (pow im 2) (pow re 2))))))
(* re (+ 1 (+ (* -1/8 (/ (pow im 4) (pow re 4))) (+ (* 1/16 (/ (pow im 6) (pow re 6))) (* 1/2 (/ (pow im 2) (pow re 2)))))))
(* -1 re)
(* -1 re)
(* -1 re)
(* -1 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)))))))
(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))))
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)))))))
(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))))
(pow re 2)
(pow re 2)
(pow re 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))))
re
(* re (+ 1 (* 1/2 (/ (pow im 2) (pow re 2)))))
(* re (+ 1 (+ (* -1/8 (/ (pow im 4) (pow re 4))) (* 1/2 (/ (pow im 2) (pow re 2))))))
(* re (+ 1 (+ (* -1/8 (/ (pow im 4) (pow re 4))) (+ (* 1/16 (/ (pow im 6) (pow re 6))) (* 1/2 (/ (pow im 2) (pow re 2)))))))
(* -1 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 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 re)
(* -1 re)
(* -1 re)
(* -1 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))))))))
(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 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))))))))
(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))))
(pow re 2)
(pow re 2)
(pow re 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 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))))))))
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)))))
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)))))
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)))))
(pow re 2)
(+ (pow im 2) (pow re 2))
(+ (pow im 2) (pow re 2))
(+ (pow im 2) (pow re 2))
(pow im 2)
(pow im 2)
(pow im 2)
(pow im 2)
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)))))
(pow re 2)
(+ (pow im 2) (pow re 2))
(+ (pow im 2) (pow re 2))
(+ (pow im 2) (pow re 2))
(pow re 2)
(+ (pow im 2) (pow re 2))
(+ (pow im 2) (pow re 2))
(+ (pow im 2) (pow re 2))
re
(+ re (* 1/2 (/ (pow im 2) re)))
(+ re (* (pow im 2) (+ (* -1/8 (/ (pow im 2) (pow re 3))) (* 1/2 (/ 1 re)))))
(+ re (* (pow im 2) (+ (* (pow im 2) (- (* 1/16 (/ (pow im 2) (pow re 5))) (* 1/8 (/ 1 (pow re 3))))) (* 1/2 (/ 1 re)))))
im
(* im (+ 1 (* 1/2 (/ (pow re 2) (pow im 2)))))
(* im (+ 1 (+ (* -1/8 (/ (pow re 4) (pow im 4))) (* 1/2 (/ (pow re 2) (pow im 2))))))
(* im (+ 1 (+ (* -1/8 (/ (pow re 4) (pow im 4))) (+ (* 1/16 (/ (pow re 6) (pow im 6))) (* 1/2 (/ (pow re 2) (pow im 2)))))))
im
(* im (+ 1 (* 1/2 (/ (pow re 2) (pow im 2)))))
(* im (+ 1 (+ (* -1/8 (/ (pow re 4) (pow im 4))) (* 1/2 (/ (pow re 2) (pow im 2))))))
(* im (+ 1 (+ (* -1/8 (/ (pow re 4) (pow im 4))) (+ (* 1/16 (/ (pow re 6) (pow im 6))) (* 1/2 (/ (pow re 2) (pow im 2)))))))
im
(* im (+ 1 (* 1/2 (/ (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)))))))
(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))))
(pow im 2)
(pow im 2)
(pow im 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)))))))
(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))))
(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))))
im
(* im (+ 1 (* 1/2 (/ (pow re 2) (pow im 2)))))
(* im (+ 1 (+ (* -1/8 (/ (pow re 4) (pow im 4))) (* 1/2 (/ (pow re 2) (pow im 2))))))
(* im (+ 1 (+ (* -1/8 (/ (pow re 4) (pow im 4))) (+ (* 1/16 (/ (pow re 6) (pow im 6))) (* 1/2 (/ (pow re 2) (pow im 2)))))))
(* -1 im)
(* -1 (* im (+ 1 (* 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 (* 1/2 (/ (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 (* 1/2 (/ (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))))))))
(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))))
(pow im 2)
(pow im 2)
(pow im 2)
(pow im 2)
(* -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))))))))
(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))))
(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 im)
(* -1 (* im (+ 1 (* 1/2 (/ (pow re 2) (pow im 2))))))
(* -1 (* im (+ 1 (+ (* -1/8 (/ (pow re 4) (pow im 4))) (* 1/2 (/ (pow re 2) (pow im 2)))))))
(* -1 (* im (+ 1 (+ (* -1/8 (/ (pow re 4) (pow im 4))) (+ (* 1/16 (/ (pow re 6) (pow im 6))) (* 1/2 (/ (pow re 2) (pow im 2))))))))

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

rewrite175.0ms (4.2%)

Memory

-2.9MiB live, 227.6MiB allocated

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	17	68
0	25	68
1	50	68
2	239	68
3	1976	68
0	8566	68

Stop Event

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

Counts

11 → 403

Calls

Call 1

Inputs
(hypot.f64 re im)
#s(approx (sqrt (+ (* re re) (* im im))) (neg.f64 re))
(neg.f64 re)
(sqrt.f64 #s(approx (+ (* re re) (* im im)) (*.f64 im im)))
#s(approx (+ (* re re) (* im im)) (*.f64 im im))
(*.f64 im im)
(sqrt.f64 #s(approx (+ (* re re) (* im im)) (*.f64 re re)))
#s(approx (+ (* re re) (* im im)) (*.f64 re re))
(*.f64 re re)
(fma.f64 re re (*.f64 im im))
(sqrt.f64 (fma.f64 re re (*.f64 im im)))

Outputs
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eval68.0ms (1.6%)

Memory: 19.1MiB live, 142.4MiB allocated
Compiler: Compiled 14 221 to 1 206 computations (91.5% saved)

prune24.0ms (0.6%)

Memory

7.0MiB live, 43.4MiB allocated

Pruning

7 alts after pruning (2 fresh and 5 done)

	Pruned	Kept	Total
New	629	0	629
Fresh	0	2	2
Picked	0	5	5
Done	0	0	0
Total	629	7	636

Accuracy

100.0%

Counts

636 → 7

Alt Table

Click to see full alt table

Status	Accuracy	Program
✓	100.0%	(hypot.f64 re im)
✓	50.9%	(sqrt.f64 (fma.f64 re re (*.f64 im im)))
✓	4.6%	(sqrt.f64 #s(approx (+ (* re re) (* im im)) (*.f64 re re)))
✓	50.5%	(sqrt.f64 #s(approx (+ (* re re) (* im im)) (*.f64 im im)))
▶	92.7%	#s(approx (sqrt (+ (* re re) (* im im))) (fma.f64 (/.f64 #s(literal 1/2 binary64) im) (*.f64 re re) im))
▶	6.6%	#s(approx (sqrt (+ (* re re) (* im im))) (fma.f64 (*.f64 #s(literal 1/2 binary64) im) (/.f64 im re) re))
✓	1.8%	#s(approx (sqrt (+ (* re re) (* im im))) (neg.f64 re))

Compiler

Compiled 79 to 54 computations (31.6% saved)

simplify12.0ms (0.3%)

Memory

-33.2MiB live, 6.0MiB allocated

Algorithm

1×	egg-herbie

Localize:

Found 8 expressions of interest:

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

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	15	68
0	23	68
1	37	68
2	57	68
3	71	68
4	79	68
5	82	68
0	82	58

Stop Event

1×	iter limit
1×	saturated
1×	iter limit

Calls

Call 1

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

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

localize35.0ms (0.8%)

Memory

9.2MiB live, 56.5MiB allocated

Localize:

Found 8 expressions of interest:

New	Metric	Score
accuracy	0	(/.f64 #s(literal 1/2 binary64) im)
accuracy	0	(*.f64 re re)
accuracy	0.08034471307362684	#s(approx (sqrt (+ (* re re) (* im im))) (fma.f64 (/.f64 #s(literal 1/2 binary64) im) (*.f64 re re) im))
accuracy	4.590622841935521	(fma.f64 (/.f64 #s(literal 1/2 binary64) im) (*.f64 re re) im)
accuracy	0	(/.f64 im re)
accuracy	0	(*.f64 #s(literal 1/2 binary64) im)
accuracy	0.171875	(fma.f64 (*.f64 #s(literal 1/2 binary64) im) (/.f64 im re) re)
accuracy	59.74899340124488	#s(approx (sqrt (+ (* re re) (* im im))) (fma.f64 (*.f64 #s(literal 1/2 binary64) im) (/.f64 im re) re))

Samples

27.0ms

256×

valid

Compiler

Compiled 122 to 29 computations (76.2% saved)

Precisions

Click to see histograms. Total time spent on operations: 18.0ms

ival-hypot: 7.0ms (37.9% of total)

ival-mult: 6.0ms (32.5% of total)

ival-div: 3.0ms (16.2% of total)

ival-add: 2.0ms (10.8% of total)

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

exact: 0.0ms (0% of total)

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

series16.0ms (0.4%)

Memory

17.9MiB live, 17.9MiB allocated

Counts

8 → 156

Calls

Call 1

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

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

Calls

6 calls:

Time	Variable		Point	Expression
3.0ms	im	@	inf	((sqrt (+ (* re re) (* im im))) (+ (* (* 1/2 im) (/ im re)) re) (* 1/2 im) (/ im re) (sqrt (+ (* re re) (* im im))) (+ (* (/ 1/2 im) (* re re)) im) (/ 1/2 im) (* re re))
2.0ms	im	@	-inf	((sqrt (+ (* re re) (* im im))) (+ (* (* 1/2 im) (/ im re)) re) (* 1/2 im) (/ im re) (sqrt (+ (* re re) (* im im))) (+ (* (/ 1/2 im) (* re re)) im) (/ 1/2 im) (* re re))
2.0ms	re	@	0	((sqrt (+ (* re re) (* im im))) (+ (* (* 1/2 im) (/ im re)) re) (* 1/2 im) (/ im re) (sqrt (+ (* re re) (* im im))) (+ (* (/ 1/2 im) (* re re)) im) (/ 1/2 im) (* re re))
2.0ms	im	@	0	((sqrt (+ (* re re) (* im im))) (+ (* (* 1/2 im) (/ im re)) re) (* 1/2 im) (/ im re) (sqrt (+ (* re re) (* im im))) (+ (* (/ 1/2 im) (* re re)) im) (/ 1/2 im) (* re re))
2.0ms	re	@	-inf	((sqrt (+ (* re re) (* im im))) (+ (* (* 1/2 im) (/ im re)) re) (* 1/2 im) (/ im re) (sqrt (+ (* re re) (* im im))) (+ (* (/ 1/2 im) (* re re)) im) (/ 1/2 im) (* re re))

simplify243.0ms (5.8%)

Memory

0.2MiB live, 190.9MiB allocated

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	123	1432
1	329	1432
2	1044	1428
3	3928	1300
4	7406	1300
0	8403	1200

Stop Event

1×	iter limit
1×	node limit

Counts

156 → 142

Calls

Call 1

Inputs
im
(+ im (* 1/2 (/ (pow re 2) im)))
(+ im (* (pow re 2) (+ (* -1/8 (/ (pow re 2) (pow im 3))) (* 1/2 (/ 1 im)))))
(+ im (* (pow re 2) (+ (* (pow re 2) (- (* 1/16 (/ (pow re 2) (pow im 5))) (* 1/8 (/ 1 (pow im 3))))) (* 1/2 (/ 1 im)))))
(* 1/2 (/ (pow im 2) re))
(/ (+ (* 1/2 (pow im 2)) (pow re 2)) re)
(/ (+ (* 1/2 (pow im 2)) (pow re 2)) re)
(/ (+ (* 1/2 (pow im 2)) (pow re 2)) re)
(/ im re)
(/ im re)
(/ im re)
(/ im 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 (* 1/2 (/ (pow re 2) im)))
(+ im (* 1/2 (/ (pow re 2) im)))
(+ im (* 1/2 (/ (pow re 2) im)))
(pow re 2)
(pow re 2)
(pow re 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)))))))
re
(* re (+ 1 (* 1/2 (/ (pow im 2) (pow re 2)))))
(* re (+ 1 (* 1/2 (/ (pow im 2) (pow re 2)))))
(* re (+ 1 (* 1/2 (/ (pow im 2) (pow re 2)))))
(/ im re)
(/ im re)
(/ im re)
(/ im re)
re
(* re (+ 1 (* 1/2 (/ (pow im 2) (pow re 2)))))
(* re (+ 1 (+ (* -1/8 (/ (pow im 4) (pow re 4))) (* 1/2 (/ (pow im 2) (pow re 2))))))
(* re (+ 1 (+ (* -1/8 (/ (pow im 4) (pow re 4))) (+ (* 1/16 (/ (pow im 6) (pow re 6))) (* 1/2 (/ (pow im 2) (pow re 2)))))))
(* 1/2 (/ (pow re 2) im))
(* (pow re 2) (+ (* 1/2 (/ 1 im)) (/ im (pow re 2))))
(* (pow re 2) (+ (* 1/2 (/ 1 im)) (/ im (pow re 2))))
(* (pow re 2) (+ (* 1/2 (/ 1 im)) (/ im (pow re 2))))
(pow re 2)
(pow re 2)
(pow re 2)
(pow re 2)
(* -1 re)
(* -1 (* re (+ 1 (* 1/2 (/ (pow im 2) (pow re 2))))))
(* -1 (* re (+ 1 (+ (* -1/8 (/ (pow im 4) (pow re 4))) (* 1/2 (/ (pow im 2) (pow re 2)))))))
(* -1 (* re (+ 1 (+ (* -1/8 (/ (pow im 4) (pow re 4))) (+ (* 1/16 (/ (pow im 6) (pow re 6))) (* 1/2 (/ (pow im 2) (pow re 2))))))))
re
(* -1 (* re (- (* -1/2 (/ (pow im 2) (pow re 2))) 1)))
(* -1 (* re (- (* -1/2 (/ (pow im 2) (pow re 2))) 1)))
(* -1 (* re (- (* -1/2 (/ (pow im 2) (pow re 2))) 1)))
(/ im re)
(/ im re)
(/ im re)
(/ im 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 re 2) im))
(* (pow re 2) (+ (* 1/2 (/ 1 im)) (/ im (pow re 2))))
(* (pow re 2) (+ (* 1/2 (/ 1 im)) (/ im (pow re 2))))
(* (pow re 2) (+ (* 1/2 (/ 1 im)) (/ im (pow re 2))))
(pow re 2)
(pow re 2)
(pow re 2)
(pow re 2)
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)))))
re
(+ re (* 1/2 (/ (pow im 2) re)))
(+ re (* 1/2 (/ (pow im 2) re)))
(+ re (* 1/2 (/ (pow im 2) re)))
(* 1/2 im)
(* 1/2 im)
(* 1/2 im)
(* 1/2 im)
(/ im re)
(/ im re)
(/ im re)
(/ im re)
re
(+ re (* 1/2 (/ (pow im 2) re)))
(+ re (* (pow im 2) (+ (* -1/8 (/ (pow im 2) (pow re 3))) (* 1/2 (/ 1 re)))))
(+ re (* (pow im 2) (+ (* (pow im 2) (- (* 1/16 (/ (pow im 2) (pow re 5))) (* 1/8 (/ 1 (pow re 3))))) (* 1/2 (/ 1 re)))))
(* 1/2 (/ (pow re 2) im))
(/ (+ (* 1/2 (pow re 2)) (pow im 2)) im)
(/ (+ (* 1/2 (pow re 2)) (pow im 2)) im)
(/ (+ (* 1/2 (pow re 2)) (pow im 2)) im)
(/ 1/2 im)
(/ 1/2 im)
(/ 1/2 im)
(/ 1/2 im)
im
(* im (+ 1 (* 1/2 (/ (pow re 2) (pow im 2)))))
(* im (+ 1 (+ (* -1/8 (/ (pow re 4) (pow im 4))) (* 1/2 (/ (pow re 2) (pow im 2))))))
(* im (+ 1 (+ (* -1/8 (/ (pow re 4) (pow im 4))) (+ (* 1/16 (/ (pow re 6) (pow im 6))) (* 1/2 (/ (pow re 2) (pow im 2)))))))
(* 1/2 (/ (pow im 2) re))
(* (pow im 2) (+ (* 1/2 (/ 1 re)) (/ re (pow im 2))))
(* (pow im 2) (+ (* 1/2 (/ 1 re)) (/ re (pow im 2))))
(* (pow im 2) (+ (* 1/2 (/ 1 re)) (/ re (pow im 2))))
(* 1/2 im)
(* 1/2 im)
(* 1/2 im)
(* 1/2 im)
(/ im re)
(/ im re)
(/ im re)
(/ im re)
im
(* im (+ 1 (* 1/2 (/ (pow re 2) (pow im 2)))))
(* im (+ 1 (+ (* -1/8 (/ (pow re 4) (pow im 4))) (* 1/2 (/ (pow re 2) (pow im 2))))))
(* im (+ 1 (+ (* -1/8 (/ (pow re 4) (pow im 4))) (+ (* 1/16 (/ (pow re 6) (pow im 6))) (* 1/2 (/ (pow re 2) (pow im 2)))))))
im
(* im (+ 1 (* 1/2 (/ (pow re 2) (pow im 2)))))
(* im (+ 1 (* 1/2 (/ (pow re 2) (pow im 2)))))
(* im (+ 1 (* 1/2 (/ (pow re 2) (pow im 2)))))
(/ 1/2 im)
(/ 1/2 im)
(/ 1/2 im)
(/ 1/2 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))))))))
(* 1/2 (/ (pow im 2) re))
(* (pow im 2) (+ (* 1/2 (/ 1 re)) (/ re (pow im 2))))
(* (pow im 2) (+ (* 1/2 (/ 1 re)) (/ re (pow im 2))))
(* (pow im 2) (+ (* 1/2 (/ 1 re)) (/ re (pow im 2))))
(* 1/2 im)
(* 1/2 im)
(* 1/2 im)
(* 1/2 im)
(/ im re)
(/ im re)
(/ im re)
(/ im 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))))))))
im
(* -1 (* im (- (* -1/2 (/ (pow re 2) (pow im 2))) 1)))
(* -1 (* im (- (* -1/2 (/ (pow re 2) (pow im 2))) 1)))
(* -1 (* im (- (* -1/2 (/ (pow re 2) (pow im 2))) 1)))
(/ 1/2 im)
(/ 1/2 im)
(/ 1/2 im)
(/ 1/2 im)

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

rewrite263.0ms (6.3%)

Memory

-13.3MiB live, 241.3MiB allocated

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	15	62
0	23	62
1	91	62
2	647	62
0	8182	52

Stop Event

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

Counts

8 → 239

Calls

Call 1

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

Outputs
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eval156.0ms (3.8%)

Memory: -30.2MiB live, 58.1MiB allocated
Compiler: Compiled 11 725 to 954 computations (91.9% saved)

prune11.0ms (0.3%)

Memory

17.4MiB live, 17.4MiB allocated

Pruning

5 alts after pruning (1 fresh and 4 done)

	Pruned	Kept	Total
New	380	1	381
Fresh	0	0	0
Picked	2	0	2
Done	1	4	5
Total	383	5	388

Accuracy

100.0%

Counts

388 → 5

Alt Table

Click to see full alt table

Status	Accuracy	Program
✓	50.9%	(sqrt.f64 (fma.f64 re re (*.f64 im im)))
✓	4.6%	(sqrt.f64 #s(approx (+ (* re re) (* im im)) (*.f64 re re)))
✓	50.5%	(sqrt.f64 #s(approx (+ (* re re) (* im im)) (*.f64 im im)))
▶	99.9%	#s(approx (sqrt (+ (* re re) (* im im))) (fma.f64 (*.f64 (/.f64 re im) re) #s(literal 1/2 binary64) im))
✓	1.8%	#s(approx (sqrt (+ (* re re) (* im im))) (neg.f64 re))

Compiler

Compiled 59 to 40 computations (32.2% saved)

simplify4.0ms (0.1%)

Memory

0.7MiB live, 0.7MiB allocated

Algorithm

1×	egg-herbie

Localize:

Found 4 expressions of interest:

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

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	11	36
0	15	36
1	22	36
2	35	36
3	41	36
4	44	36
5	47	36
0	47	31

Stop Event

1×	iter limit
1×	saturated
1×	iter limit

Calls

Call 1

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

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

localize37.0ms (0.9%)

Memory

-2.2MiB live, 35.2MiB allocated

Localize:

Found 4 expressions of interest:

New	Metric	Score
accuracy	0	(fma.f64 (*.f64 (/.f64 re im) re) #s(literal 1/2 binary64) im)
accuracy	0	(/.f64 re im)
accuracy	0.08034471307362684	#s(approx (sqrt (+ (* re re) (* im im))) (fma.f64 (*.f64 (/.f64 re im) re) #s(literal 1/2 binary64) im))
accuracy	0.140625	(*.f64 (/.f64 re im) re)

Samples

31.0ms

256×

valid

Compiler

Compiled 66 to 21 computations (68.2% saved)

Precisions

Click to see histograms. Total time spent on operations: 11.0ms

ival-hypot: 4.0ms (37.1% of total)

ival-mult: 3.0ms (27.8% of total)

ival-div: 2.0ms (18.5% of total)

ival-add: 1.0ms (9.3% of total)

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

exact: 0.0ms (0% of total)

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

series9.0ms (0.2%)

Memory

10.0MiB live, 10.0MiB allocated

Counts

4 → 96

Calls

Call 1

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

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

Calls

6 calls:

Time	Variable		Point	Expression
1.0ms	im	@	-inf	((sqrt (+ (* re re) (* im im))) (+ (* (* (/ re im) re) 1/2) im) (* (/ re im) re) (/ re im))
1.0ms	re	@	-inf	((sqrt (+ (* re re) (* im im))) (+ (* (* (/ re im) re) 1/2) im) (* (/ re im) re) (/ re im))
1.0ms	re	@	inf	((sqrt (+ (* re re) (* im im))) (+ (* (* (/ re im) re) 1/2) im) (* (/ re im) re) (/ re im))
1.0ms	im	@	0	((sqrt (+ (* re re) (* im im))) (+ (* (* (/ re im) re) 1/2) im) (* (/ re im) re) (/ re im))
1.0ms	re	@	0	((sqrt (+ (* re re) (* im im))) (+ (* (* (/ re im) re) 1/2) im) (* (/ re im) re) (/ re im))

simplify261.0ms (6.3%)

Memory

-10.2MiB live, 137.3MiB allocated

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	111	788
1	302	788
2	977	786
3	3647	750
4	7515	750
0	8245	700

Stop Event

1×	iter limit
1×	node limit

Counts

96 → 89

Calls

Call 1

Inputs
im
(+ im (* 1/2 (/ (pow re 2) im)))
(+ im (* (pow re 2) (+ (* -1/8 (/ (pow re 2) (pow im 3))) (* 1/2 (/ 1 im)))))
(+ im (* (pow re 2) (+ (* (pow re 2) (- (* 1/16 (/ (pow re 2) (pow im 5))) (* 1/8 (/ 1 (pow im 3))))) (* 1/2 (/ 1 im)))))
im
(+ im (* 1/2 (/ (pow re 2) im)))
(+ im (* 1/2 (/ (pow re 2) im)))
(+ im (* 1/2 (/ (pow re 2) im)))
(/ (pow re 2) im)
(/ (pow re 2) im)
(/ (pow re 2) im)
(/ (pow re 2) im)
(/ re im)
(/ re im)
(/ re im)
(/ re im)
re
(* re (+ 1 (* 1/2 (/ (pow im 2) (pow re 2)))))
(* re (+ 1 (+ (* -1/8 (/ (pow im 4) (pow re 4))) (* 1/2 (/ (pow im 2) (pow re 2))))))
(* re (+ 1 (+ (* -1/8 (/ (pow im 4) (pow re 4))) (+ (* 1/16 (/ (pow im 6) (pow re 6))) (* 1/2 (/ (pow im 2) (pow re 2)))))))
(* 1/2 (/ (pow re 2) im))
(* (pow re 2) (+ (* 1/2 (/ 1 im)) (/ im (pow re 2))))
(* (pow re 2) (+ (* 1/2 (/ 1 im)) (/ im (pow re 2))))
(* (pow re 2) (+ (* 1/2 (/ 1 im)) (/ im (pow re 2))))
(/ (pow re 2) im)
(/ (pow re 2) im)
(/ (pow re 2) im)
(/ (pow re 2) im)
(/ re im)
(/ re im)
(/ re im)
(/ re im)
(* -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 re 2) im))
(* (pow re 2) (+ (* 1/2 (/ 1 im)) (/ im (pow re 2))))
(* (pow re 2) (+ (* 1/2 (/ 1 im)) (/ im (pow re 2))))
(* (pow re 2) (+ (* 1/2 (/ 1 im)) (/ im (pow re 2))))
(/ (pow re 2) im)
(/ (pow re 2) im)
(/ (pow re 2) im)
(/ (pow re 2) im)
(/ re im)
(/ re im)
(/ re im)
(/ re im)
re
(+ re (* 1/2 (/ (pow im 2) re)))
(+ re (* (pow im 2) (+ (* -1/8 (/ (pow im 2) (pow re 3))) (* 1/2 (/ 1 re)))))
(+ re (* (pow im 2) (+ (* (pow im 2) (- (* 1/16 (/ (pow im 2) (pow re 5))) (* 1/8 (/ 1 (pow re 3))))) (* 1/2 (/ 1 re)))))
(* 1/2 (/ (pow re 2) im))
(/ (+ (* 1/2 (pow re 2)) (pow im 2)) im)
(/ (+ (* 1/2 (pow re 2)) (pow im 2)) im)
(/ (+ (* 1/2 (pow re 2)) (pow im 2)) im)
(/ (pow re 2) im)
(/ (pow re 2) im)
(/ (pow re 2) im)
(/ (pow re 2) im)
(/ re im)
(/ re im)
(/ re im)
(/ re im)
im
(* im (+ 1 (* 1/2 (/ (pow re 2) (pow im 2)))))
(* im (+ 1 (+ (* -1/8 (/ (pow re 4) (pow im 4))) (* 1/2 (/ (pow re 2) (pow im 2))))))
(* im (+ 1 (+ (* -1/8 (/ (pow re 4) (pow im 4))) (+ (* 1/16 (/ (pow re 6) (pow im 6))) (* 1/2 (/ (pow re 2) (pow im 2)))))))
im
(* im (+ 1 (* 1/2 (/ (pow re 2) (pow im 2)))))
(* im (+ 1 (* 1/2 (/ (pow re 2) (pow im 2)))))
(* im (+ 1 (* 1/2 (/ (pow re 2) (pow im 2)))))
(/ (pow re 2) im)
(/ (pow re 2) im)
(/ (pow re 2) im)
(/ (pow re 2) im)
(/ re im)
(/ re im)
(/ re im)
(/ 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))))))))
im
(* -1 (* im (- (* -1/2 (/ (pow re 2) (pow im 2))) 1)))
(* -1 (* im (- (* -1/2 (/ (pow re 2) (pow im 2))) 1)))
(* -1 (* im (- (* -1/2 (/ (pow re 2) (pow im 2))) 1)))
(/ (pow re 2) im)
(/ (pow re 2) im)
(/ (pow re 2) im)
(/ (pow re 2) im)
(/ re im)
(/ re im)
(/ re im)
(/ re im)

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

rewrite357.0ms (8.6%)

Memory

-6.3MiB live, 288.4MiB allocated

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	11	33
0	15	33
1	58	33
2	418	33
3	4804	33
0	8212	28

Stop Event

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

Counts

4 → 158

Calls

Call 1

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

Outputs
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eval59.0ms (1.4%)

Memory: -6.4MiB live, 71.2MiB allocated
Compiler: Compiled 6 965 to 713 computations (89.8% saved)

prune12.0ms (0.3%)

Memory

18.0MiB live, 18.0MiB allocated

Pruning

5 alts after pruning (0 fresh and 5 done)

	Pruned	Kept	Total
New	247	0	247
Fresh	0	0	0
Picked	0	1	1
Done	0	4	4
Total	247	5	252

Accuracy

100.0%

Counts

252 → 5

Alt Table

Click to see full alt table

Status	Accuracy	Program
✓	50.9%	(sqrt.f64 (fma.f64 re re (*.f64 im im)))
✓	4.6%	(sqrt.f64 #s(approx (+ (* re re) (* im im)) (*.f64 re re)))
✓	50.5%	(sqrt.f64 #s(approx (+ (* re re) (* im im)) (*.f64 im im)))
✓	99.9%	#s(approx (sqrt (+ (* re re) (* im im))) (fma.f64 (*.f64 (/.f64 re im) re) #s(literal 1/2 binary64) im))
✓	1.8%	#s(approx (sqrt (+ (* re re) (* im im))) (neg.f64 re))

Compiler

Compiled 163 to 71 computations (56.4% saved)

regimes21.0ms (0.5%)

Memory

12.5MiB live, 12.5MiB allocated

Counts

9 → 1

Calls

Call 1

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

Outputs
(hypot.f64 re im)

Calls

6 calls:

4.0ms	im
4.0ms	re
3.0ms	(sqrt.f64 (+.f64 (.f64 re re) (.f64 im im)))
3.0ms	(*.f64 im im)
3.0ms	(+.f64 (.f64 re re) (.f64 im im))

Results

Accuracy	Segments	Branch
100.0%	1	`re`
100.0%	1	`im`
100.0%	1	`(sqrt.f64 (+.f64 (.f64 re re) (.f64 im im)))`
100.0%	1	`(+.f64 (.f64 re re) (.f64 im im))`
100.0%	1	`(*.f64 re re)`
100.0%	1	`(*.f64 im im)`

Compiler

Compiled 23 to 21 computations (8.7% saved)

regimes68.0ms (1.6%)

Memory

-30.9MiB live, 11.8MiB allocated

Counts

8 → 1

Calls

Call 1

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

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

Calls

6 calls:

52.0ms	(+.f64 (.f64 re re) (.f64 im im))
3.0ms	im
3.0ms	re
3.0ms	(*.f64 im im)
3.0ms	(sqrt.f64 (+.f64 (.f64 re re) (.f64 im im)))

Results

Accuracy	Segments	Branch
99.9%	1	`re`
99.9%	1	`im`
99.9%	1	`(sqrt.f64 (+.f64 (.f64 re re) (.f64 im im)))`
99.9%	1	`(+.f64 (.f64 re re) (.f64 im im))`
99.9%	1	`(*.f64 re re)`
99.9%	1	`(*.f64 im im)`

Compiler

Compiled 23 to 21 computations (8.7% saved)

regimes14.0ms (0.3%)

Memory

10.6MiB live, 10.6MiB allocated

Counts

5 → 1

Calls

Call 1

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

Outputs
(sqrt.f64 (fma.f64 re re (*.f64 im im)))

Calls

6 calls:

2.0ms	re
2.0ms	im
2.0ms	(sqrt.f64 (+.f64 (.f64 re re) (.f64 im im)))
2.0ms	(+.f64 (.f64 re re) (.f64 im im))
2.0ms	(*.f64 im im)

Results

Accuracy	Segments	Branch
50.9%	1	`re`
50.9%	1	`im`
50.9%	1	`(sqrt.f64 (+.f64 (.f64 re re) (.f64 im im)))`
50.9%	1	`(+.f64 (.f64 re re) (.f64 im im))`
50.9%	1	`(*.f64 re re)`
50.9%	1	`(*.f64 im im)`

Compiler

Compiled 23 to 21 computations (8.7% saved)

regimes11.0ms (0.3%)

Memory

9.5MiB live, 9.5MiB allocated

Counts

3 → 1

Calls

Call 1

Inputs
#s(approx (sqrt (+ (* re re) (* im im))) (neg.f64 re))
(sqrt.f64 #s(approx (+ (* re re) (* im im)) (*.f64 im im)))
(sqrt.f64 #s(approx (+ (* re re) (* im im)) (*.f64 re re)))

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

Calls

6 calls:

2.0ms	re
2.0ms	im
2.0ms	(sqrt.f64 (+.f64 (.f64 re re) (.f64 im im)))
2.0ms	(*.f64 im im)
2.0ms	(+.f64 (.f64 re re) (.f64 im im))

Results

Accuracy	Segments	Branch
50.5%	1	`re`
50.5%	1	`(sqrt.f64 (+.f64 (.f64 re re) (.f64 im im)))`
50.5%	1	`(+.f64 (.f64 re re) (.f64 im im))`
50.5%	1	`(*.f64 re re)`
50.5%	1	`(*.f64 im im)`
50.5%	1	`im`

Compiler

Compiled 23 to 21 computations (8.7% saved)

regimes8.0ms (0.2%)

Memory

8.7MiB live, 8.7MiB allocated

Accuracy

Total -0.0b remaining (-0%)

Threshold costs -0b (-0%)

Counts

1 → 1

Calls

Call 1

Inputs
#s(approx (sqrt (+ (* re re) (* im im))) (neg.f64 re))

Outputs
#s(approx (sqrt (+ (* re re) (* im im))) (neg.f64 re))

Calls

6 calls:

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

Results

Accuracy	Segments	Branch
1.8%	1	`re`
1.8%	1	`(*.f64 re re)`
1.8%	1	`im`
1.8%	1	`(sqrt.f64 (+.f64 (.f64 re re) (.f64 im im)))`
1.8%	1	`(+.f64 (.f64 re re) (.f64 im im))`
1.8%	1	`(*.f64 im im)`

Compiler

Compiled 23 to 21 computations (8.7% saved)

simplify63.0ms (1.5%)

Memory

-20.9MiB live, 19.1MiB allocated

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	19	50
1	24	50
2	26	50
3	27	50

Stop Event

1×

saturated

Calls

Call 1

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

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

soundness616.0ms (14.8%)

Memory

-11.2MiB live, 146.5MiB allocated

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	6	21
0	10	21
1	29	21
2	196	21
3	1788	21
0	8624	15
0	15	62
0	23	62
1	91	62
2	647	62
0	8182	52
0	104	620
1	296	620
2	953	618
3	3667	584
4	6426	582
0	8051	530

Stop Event

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

Compiler

Compiled 107 to 58 computations (45.8% saved)

preprocess39.0ms (0.9%)

Memory

21.5MiB live, 140.4MiB allocated

Remove

(sort re im)

(abs re)

(abs im)

Compiler

Compiled 134 to 68 computations (49.3% saved)

end0.0ms (0%)

Memory: 0.0MiB live, 0.0MiB allocated

start0.0ms (0%)

analyze0.0ms (0%)

sample726.0ms (17.5%)

explain118.0ms (2.8%)

preprocess16.0ms (0.4%)

eval0.0ms (0%)

prune1.0ms (0%)

simplify3.0ms (0.1%)

localize47.0ms (1.1%)

series11.0ms (0.3%)

simplify200.0ms (4.8%)

rewrite175.0ms (4.2%)

eval39.0ms (0.9%)

prune11.0ms (0.3%)

simplify5.0ms (0.1%)

localize29.0ms (0.7%)

series11.0ms (0.3%)

simplify182.0ms (4.4%)

rewrite175.0ms (4.2%)

eval68.0ms (1.6%)

prune24.0ms (0.6%)

simplify12.0ms (0.3%)

localize35.0ms (0.8%)

series16.0ms (0.4%)

simplify243.0ms (5.8%)

rewrite263.0ms (6.3%)

eval156.0ms (3.8%)

prune11.0ms (0.3%)

simplify4.0ms (0.1%)

localize37.0ms (0.9%)

series9.0ms (0.2%)

simplify261.0ms (6.3%)

rewrite357.0ms (8.6%)

eval59.0ms (1.4%)

prune12.0ms (0.3%)

regimes21.0ms (0.5%)

regimes68.0ms (1.6%)

regimes14.0ms (0.3%)

regimes11.0ms (0.3%)

regimes8.0ms (0.2%)

simplify63.0ms (1.5%)

soundness616.0ms (14.8%)

preprocess39.0ms (0.9%)

end0.0ms (0%)

Profiling