Metrics for math.abs on complex

start0.0ms (0%)

Memory: 0.0MiB live, 0.0MiB allocated; 0ms collecting garbage

analyze0.0ms (0%)

Memory

0.2MiB live, 0.2MiB allocated; 0ms collecting garbage

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)

sample605.0ms (23.3%)

Memory

39.4MiB live, 699.9MiB allocated; 210ms collecting garbage

Samples

411.0ms

8 256×

valid

Precisions

Click to see histograms. Total time spent on operations: 199.0ms

ival-hypot: 197.0ms (99.2% of total)

adjust: 2.0ms (1% of total)

Bogosity

preprocess96.0ms (3.7%)

Memory

9.0MiB live, 58.4MiB allocated; 24ms collecting garbage

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	18	50
1	74	50

Stop Event

1×	iter-limit
1×	node-limit

Alt Table

Click to see full alt table

Status	Accuracy	Program
▶	48.0%	(sqrt.f64 (+.f64 (.f64 re re) (.f64 im im)))

Symmetry

(abs re)

(abs im)

(sort re im)

Compiler

Compiled 16 to 12 computations (25% saved)

series113.0ms (4.4%)

Memory

-15.2MiB live, 74.9MiB allocated; 28ms collecting garbage

Counts

6 → 29

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

Calls

6 calls:

Time	Variable	Point
16.0ms	re	inf
3.0ms	re	-inf
2.0ms	re	0
1.0ms	im	inf
1.0ms	im	0

rewrite190.0ms (7.3%)

Memory

-53.3MiB live, 93.6MiB allocated; 145ms collecting garbage

Counts

6 → 24

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

eval9.0ms (0.3%)

Memory: 16.7MiB live, 16.7MiB allocated; 0ms collecting garbage
Compiler: Compiled 985 to 217 computations (78% saved)

prune5.0ms (0.2%)

Memory

8.9MiB live, 8.9MiB allocated; 0ms collecting garbage

Pruning

9 alts after pruning (8 fresh and 1 done)

	Pruned	Kept	Total
New	41	8	49
Fresh	0	0	0
Picked	0	1	1
Done	0	0	0
Total	41	9	50

Accuracy

97.7%

Counts

50 → 9

Alt Table

Click to see full alt table

Status	Accuracy	Program
▶	0.0%	(*.f64 (sqrt.f64 (+.f64 im re)) (sqrt.f64 (-.f64 re im)))
✓	48.0%	(sqrt.f64 (+.f64 (.f64 re re) (.f64 im im)))
	0.4%	(sqrt.f64 (*.f64 (-.f64 re im) (+.f64 im re)))
▶	47.7%	(sqrt.f64 (*.f64 (+.f64 im re) (-.f64 im re)))
▶	5.1%	#s(approx (sqrt (+ (* re re) (* im im))) (.f64 re (+.f64 #s(literal 1 binary64) (.f64 #s(literal 1/2 binary64) (/.f64 (pow.f64 im #s(literal 2 binary64)) (pow.f64 re #s(literal 2 binary64)))))))
▶	88.0%	#s(approx (sqrt (+ (* re re) (* im im))) (.f64 im (+.f64 #s(literal 1 binary64) (.f64 #s(literal 1/2 binary64) (/.f64 (pow.f64 re #s(literal 2 binary64)) (pow.f64 im #s(literal 2 binary64)))))))
	1.9%	#s(approx (sqrt (+ (* re re) (* im im))) (*.f64 #s(literal -1 binary64) re))
▶	1.2%	#s(approx (sqrt (+ (* re re) (* im im))) (*.f64 #s(literal -1 binary64) im))
	4.5%	#s(approx (sqrt (+ (* re re) (* im im))) (sqrt.f64 (pow.f64 re #s(literal 2 binary64))))

Compiler

Compiled 220 to 164 computations (25.5% saved)

series365.0ms (14.1%)

Memory

-19.2MiB live, 268.4MiB allocated; 54ms collecting garbage

Counts

28 → 157

Calls

Call 1

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

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

Calls

6 calls:

Time	Variable	Point
24.0ms	im	0
22.0ms	re	-inf
15.0ms	im	inf
6.0ms	re	inf
5.0ms	re	0

rewrite232.0ms (8.9%)

Memory

-3.2MiB live, 170.7MiB allocated; 73ms collecting garbage

Counts

28 → 124

Calls

Call 1

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

Outputs
#s(approx 2 (fma.f64 (*.f64 re #s(literal 1/2 binary64)) im im))
(.f64 im (fma.f64 (.f64 re #s(literal 1/2 binary64)) im #s(literal 1 binary64)))
(.f64 (fma.f64 (.f64 re #s(literal 1/2 binary64)) im #s(literal 1 binary64)) (fma.f64 (*.f64 re #s(literal 1/2 binary64)) im im))
(.f64 (fma.f64 (.f64 re #s(literal 1/2 binary64)) im #s(literal 1 binary64)) im)
(.f64 (fma.f64 (.f64 re #s(literal 1/2 binary64)) im im) (fma.f64 (*.f64 re #s(literal 1/2 binary64)) im im))
(.f64 (fma.f64 (.f64 re #s(literal 1/2 binary64)) im im) (fma.f64 (*.f64 re #s(literal 1/2 binary64)) im #s(literal 1 binary64)))
im
(*.f64 #s(literal -1 binary64) im)
(*.f64 im #s(literal -1 binary64))
(*.f64 im #s(literal 1 binary64))
(*.f64 #s(literal 1 binary64) im)
(.f64 (fma.f64 (.f64 re #s(literal 1/2 binary64)) im #s(literal 1 binary64)) #s(literal 1 binary64))
(.f64 (fma.f64 (.f64 re #s(literal 1/2 binary64)) im #s(literal 1 binary64)) (fma.f64 (*.f64 re #s(literal 1/2 binary64)) im #s(literal 1 binary64)))
(.f64 #s(literal 1 binary64) (fma.f64 (.f64 re #s(literal 1/2 binary64)) im #s(literal 1 binary64)))
(.f64 (fma.f64 #s(literal 1/2 binary64) (fma.f64 (.f64 re #s(literal 1/2 binary64)) im (.f64 im re)) #s(literal 1 binary64)) (fma.f64 (.f64 re #s(literal 1/2 binary64)) im #s(literal 1 binary64)))
(.f64 (+.f64 #s(literal 1 binary64) (fabs.f64 (.f64 #s(literal 1/2 binary64) (.f64 im re)))) (-.f64 #s(literal 1 binary64) (fabs.f64 (.f64 #s(literal 1/2 binary64) (*.f64 im re)))))
#s(literal 1 binary64)
#s(literal 2 binary64)
#s(literal 0 binary64)
(*.f64 #s(literal 1 binary64) #s(literal 1 binary64))
(*.f64 #s(literal 1 binary64) #s(literal 3 binary64))
(.f64 #s(literal 1/2 binary64) (.f64 im re))
(.f64 (.f64 re #s(literal 1/2 binary64)) (*.f64 im re))
(.f64 (.f64 re #s(literal 1/2 binary64)) im)
(.f64 (.f64 im #s(literal 1/2 binary64)) re)
(.f64 (.f64 im #s(literal 1/2 binary64)) (*.f64 im re))
#s(literal 1/2 binary64)
(*.f64 #s(literal 1 binary64) #s(literal 1/2 binary64))
(*.f64 #s(literal 1/2 binary64) #s(literal 1 binary64))
(/.f64 #s(literal 1/2 binary64) #s(literal 1 binary64))
(/.f64 (neg.f64 #s(literal 1/2 binary64)) #s(literal 1 binary64))
(*.f64 im re)
(*.f64 re im)
(.f64 (neg.f64 #s(literal -1 binary64)) (.f64 im re))
(.f64 (.f64 re #s(literal -1 binary64)) im)
(.f64 (.f64 im re) (*.f64 im re))
re
(*.f64 re #s(literal 1 binary64))
(*.f64 #s(literal 1 binary64) re)
(*.f64 re re)
(fabs.f64 re)
re
(*.f64 re #s(literal 1 binary64))
(*.f64 #s(literal 1 binary64) re)
(*.f64 re re)
(fabs.f64 re)
#s(literal 1 binary64)
#s(literal 2 binary64)
#s(literal 0 binary64)
(*.f64 #s(literal 1 binary64) #s(literal 1 binary64))
(*.f64 #s(literal 1 binary64) #s(literal 3 binary64))
im
(*.f64 #s(literal -1 binary64) im)
(*.f64 im #s(literal -1 binary64))
(*.f64 im #s(literal 1 binary64))
(*.f64 #s(literal 1 binary64) im)
#s(approx 2 im)
im
(*.f64 #s(literal -1 binary64) im)
(*.f64 im #s(literal -1 binary64))
(*.f64 im #s(literal 1 binary64))
(*.f64 #s(literal 1 binary64) im)
#s(literal -1 binary64)
#s(literal 1 binary64)
#s(literal 2 binary64)
#s(literal 0 binary64)
(*.f64 #s(literal 1 binary64) #s(literal 1 binary64))
(*.f64 #s(literal 1 binary64) #s(literal 3 binary64))
#s(literal 1 binary64)
#s(literal 2 binary64)
#s(literal 0 binary64)
(*.f64 #s(literal 1 binary64) #s(literal 1 binary64))
(*.f64 #s(literal 1 binary64) #s(literal 3 binary64))
#s(literal 1 binary64)
#s(literal 2 binary64)
#s(literal 0 binary64)
(*.f64 #s(literal 1 binary64) #s(literal 1 binary64))
(*.f64 #s(literal 1 binary64) #s(literal 3 binary64))
#s(literal 1 binary64)
#s(literal 2 binary64)
#s(literal 0 binary64)
(*.f64 #s(literal 1 binary64) #s(literal 1 binary64))
(*.f64 #s(literal 1 binary64) #s(literal 3 binary64))
#s(literal 1 binary64)
#s(literal 2 binary64)
#s(literal 0 binary64)
(*.f64 #s(literal 1 binary64) #s(literal 1 binary64))
(*.f64 #s(literal 1 binary64) #s(literal 3 binary64))
#s(literal 1 binary64)
#s(literal 2 binary64)
#s(literal 0 binary64)
(*.f64 #s(literal 1 binary64) #s(literal 1 binary64))
(*.f64 #s(literal 1 binary64) #s(literal 3 binary64))
#s(literal 1 binary64)
#s(literal 2 binary64)
#s(literal 0 binary64)
(*.f64 #s(literal 1 binary64) #s(literal 1 binary64))
(*.f64 #s(literal 1 binary64) #s(literal 3 binary64))
#s(literal 1 binary64)
#s(literal 2 binary64)
#s(literal 0 binary64)
(*.f64 #s(literal 1 binary64) #s(literal 1 binary64))
(*.f64 #s(literal 1 binary64) #s(literal 3 binary64))
#s(approx 2 (fma.f64 (*.f64 re #s(literal 1/2 binary64)) im re))
(.f64 re (fma.f64 (.f64 re #s(literal 1/2 binary64)) im #s(literal 1 binary64)))
(.f64 (fma.f64 (.f64 re #s(literal 1/2 binary64)) im #s(literal 1 binary64)) (fma.f64 (*.f64 re #s(literal 1/2 binary64)) im re))
(.f64 (fma.f64 (.f64 re #s(literal 1/2 binary64)) im #s(literal 1 binary64)) re)
(.f64 (fma.f64 (.f64 re #s(literal 1/2 binary64)) im re) (fma.f64 (*.f64 re #s(literal 1/2 binary64)) im re))
(.f64 (fma.f64 (.f64 re #s(literal 1/2 binary64)) im re) (fma.f64 (*.f64 re #s(literal 1/2 binary64)) im #s(literal 1 binary64)))
(.f64 (fma.f64 (.f64 re #s(literal 1/2 binary64)) im #s(literal 1 binary64)) #s(literal 1 binary64))
(.f64 (fma.f64 (.f64 re #s(literal 1/2 binary64)) im #s(literal 1 binary64)) (fma.f64 (*.f64 re #s(literal 1/2 binary64)) im #s(literal 1 binary64)))
(.f64 #s(literal 1 binary64) (fma.f64 (.f64 re #s(literal 1/2 binary64)) im #s(literal 1 binary64)))
(.f64 (fma.f64 #s(literal 1/2 binary64) (fma.f64 (.f64 re #s(literal 1/2 binary64)) im (.f64 im re)) #s(literal 1 binary64)) (fma.f64 (.f64 re #s(literal 1/2 binary64)) im #s(literal 1 binary64)))
(.f64 (+.f64 #s(literal 1 binary64) (fabs.f64 (.f64 #s(literal 1/2 binary64) (.f64 im re)))) (-.f64 #s(literal 1 binary64) (fabs.f64 (.f64 #s(literal 1/2 binary64) (*.f64 im re)))))
(.f64 #s(literal 1/2 binary64) (.f64 im re))
(.f64 (.f64 re #s(literal 1/2 binary64)) (*.f64 im re))
(.f64 (.f64 re #s(literal 1/2 binary64)) im)
(.f64 (.f64 im #s(literal 1/2 binary64)) re)
(.f64 (.f64 im #s(literal 1/2 binary64)) (*.f64 im re))
(*.f64 im re)
(*.f64 re im)
(.f64 (neg.f64 #s(literal -1 binary64)) (.f64 im re))
(.f64 (.f64 re #s(literal -1 binary64)) im)
(.f64 (.f64 im re) (*.f64 im re))

eval47.0ms (1.8%)

Memory: 15.2MiB live, 61.1MiB allocated; 4ms collecting garbage
Compiler: Compiled 7 160 to 1 257 computations (82.4% saved)

prune28.0ms (1.1%)

Memory

7.8MiB live, 7.8MiB allocated; 0ms collecting garbage

Pruning

8 alts after pruning (6 fresh and 2 done)

	Pruned	Kept	Total
New	232	5	237
Fresh	2	1	3
Picked	4	1	5
Done	0	1	1
Total	238	8	246

Accuracy

99.9%

Counts

246 → 8

Alt Table

Click to see full alt table

Status	Accuracy	Program
▶	0.0%	(.f64 #s(approx (sqrt (+ im re)) (.f64 re (sqrt.f64 (/.f64 #s(literal 1 binary64) re)))) (sqrt.f64 (-.f64 re im)))
▶	0.0%	(*.f64 #s(approx (sqrt (+ im re)) (sqrt.f64 re)) (sqrt.f64 (-.f64 re im)))
✓	48.0%	(sqrt.f64 (+.f64 (.f64 re re) (.f64 im im)))
▶	1.9%	#s(approx (sqrt (+ (* re re) (* im im))) (*.f64 #s(literal -1 binary64) re))
✓	1.2%	#s(approx (sqrt (+ (* re re) (* im im))) (*.f64 #s(literal -1 binary64) im))
	6.4%	#s(approx (sqrt (+ (* re re) (* im im))) #s(approx (* re (+ 1 (* 1/2 (/ (pow im 2) (pow re 2))))) (+.f64 re (*.f64 #s(literal 1/2 binary64) (/.f64 (pow.f64 im #s(literal 2 binary64)) re)))))
▶	99.6%	#s(approx (sqrt (+ (* re re) (* im im))) #s(approx (* im (+ 1 (* 1/2 (/ (pow re 2) (pow im 2))))) im))
▶	6.1%	#s(approx 2 (fma.f64 (*.f64 re #s(literal 1/2 binary64)) im re))

Compiler

Compiled 228 to 169 computations (25.9% saved)

series206.0ms (8%)

Memory

-20.2MiB live, 83.5MiB allocated; 32ms collecting garbage

Counts

22 → 105

Calls

Call 1

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

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

Calls

6 calls:

Time	Variable	Point
3.0ms	re	inf
3.0ms	re	0
3.0ms	re	-inf
2.0ms	im	inf
2.0ms	im	-inf

rewrite201.0ms (7.8%)

Memory

18.2MiB live, 163.4MiB allocated; 70ms collecting garbage

Counts

22 → 74

Calls

Call 1

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

Outputs
#s(approx (sqrt (+ re im)) #s(approx (+ (* im (* 1/2 re)) im) im))
#s(approx (+ (* im (* 1/2 re)) im) im)
im
(*.f64 im #s(literal 1 binary64))
(*.f64 #s(literal 1 binary64) im)
(*.f64 im im)
(fabs.f64 im)
#s(approx (sqrt (+ re im)) re)
re
(*.f64 #s(literal -1 binary64) re)
(*.f64 re #s(literal -1 binary64))
(*.f64 re #s(literal 1 binary64))
(*.f64 #s(literal 1 binary64) re)
#s(literal -1 binary64)
re
(*.f64 #s(literal -1 binary64) re)
(*.f64 re #s(literal -1 binary64))
(*.f64 re #s(literal 1 binary64))
(*.f64 #s(literal 1 binary64) re)
#s(approx 0 (fma.f64 (*.f64 re #s(literal 1/2 binary64)) im re))
(*.f64 (fma.f64 im #s(literal 1/2 binary64) #s(literal 1 binary64)) re)
(*.f64 re (fma.f64 im #s(literal 1/2 binary64) #s(literal -1 binary64)))
(.f64 (fma.f64 (.f64 re #s(literal 1/2 binary64)) im re) (fma.f64 (*.f64 re #s(literal 1/2 binary64)) im re))
(.f64 (fma.f64 (.f64 re #s(literal 1/2 binary64)) im re) re)
(.f64 re (fma.f64 (.f64 re #s(literal 1/2 binary64)) im re))
(*.f64 re #s(literal 1/2 binary64))
(*.f64 #s(literal 1/2 binary64) re)
(.f64 (neg.f64 #s(literal -1 binary64)) (.f64 re #s(literal 1/2 binary64)))
(*.f64 (neg.f64 #s(literal 1/2 binary64)) re)
(.f64 (.f64 re #s(literal 1/2 binary64)) re)
#s(literal 1/2 binary64)
(*.f64 #s(literal 1 binary64) #s(literal 1/2 binary64))
(*.f64 #s(literal 1/2 binary64) #s(literal 1 binary64))
(/.f64 #s(literal 1/2 binary64) #s(literal 1 binary64))
(/.f64 (neg.f64 #s(literal 1/2 binary64)) #s(literal 1 binary64))
(*.f64 #s(approx (sqrt (+ re im)) re) (sqrt.f64 (-.f64 re im)))
#s(approx (sqrt (+ re im)) re)
re
(*.f64 #s(literal -1 binary64) re)
(*.f64 re #s(literal -1 binary64))
(*.f64 re #s(literal 1 binary64))
(*.f64 #s(literal 1 binary64) re)
(*.f64 (sqrt.f64 (-.f64 re im)) (sqrt.f64 (-.f64 re im)))
(*.f64 (fabs.f64 (sqrt.f64 (-.f64 re im))) (fabs.f64 (sqrt.f64 (-.f64 re im))))
(*.f64 (sqrt.f64 (fma.f64 (-.f64 re im) im re)) (sqrt.f64 (-.f64 re im)))
(*.f64 (neg.f64 (sqrt.f64 (-.f64 re im))) (neg.f64 (sqrt.f64 (-.f64 re im))))
(*.f64 (sqrt.f64 (-.f64 re im)) (sqrt.f64 (fma.f64 (-.f64 re im) im re)))
(*.f64 (-.f64 re im) (-.f64 re im))
(*.f64 (fma.f64 (-.f64 re im) im re) (-.f64 re im))
(*.f64 (-.f64 re im) (fma.f64 (-.f64 re im) im re))
(+.f64 im re)
(+.f64 re im)
(*.f64 #s(approx (sqrt (+ re im)) re) (sqrt.f64 (-.f64 re im)))
#s(approx (sqrt (+ re im)) re)
re
(*.f64 #s(literal -1 binary64) re)
(*.f64 re #s(literal -1 binary64))
(*.f64 re #s(literal 1 binary64))
(*.f64 #s(literal 1 binary64) re)
re
(*.f64 #s(literal -1 binary64) re)
(*.f64 re #s(literal -1 binary64))
(*.f64 re #s(literal 1 binary64))
(*.f64 #s(literal 1 binary64) re)
re
(*.f64 #s(literal -1 binary64) re)
(*.f64 re #s(literal -1 binary64))
(*.f64 re #s(literal 1 binary64))
(*.f64 #s(literal 1 binary64) re)
#s(literal 1 binary64)
#s(literal 0 binary64)
#s(literal 2 binary64)
(*.f64 #s(literal 1 binary64) #s(literal 3 binary64))
(*.f64 #s(literal 3 binary64) #s(literal 1 binary64))

eval22.0ms (0.9%)

Memory: 1.3MiB live, 49.3MiB allocated; 6ms collecting garbage
Compiler: Compiled 5 821 to 829 computations (85.8% saved)

prune7.0ms (0.3%)

Memory

-30.9MiB live, 14.7MiB allocated; 4ms collecting garbage

Pruning

6 alts after pruning (3 fresh and 3 done)

	Pruned	Kept	Total
New	193	3	196
Fresh	1	0	1
Picked	3	2	5
Done	1	1	2
Total	198	6	204

Accuracy

99.9%

Counts

204 → 6

Alt Table

Click to see full alt table

Status	Accuracy	Program
▶	1.1%	(.f64 #s(approx (sqrt (+ im re)) (.f64 re (sqrt.f64 (/.f64 #s(literal 1 binary64) re)))) (sqrt.f64 (-.f64 re (*.f64 im im))))
✓	48.0%	(sqrt.f64 (+.f64 (.f64 re re) (.f64 im im)))
✓	1.9%	#s(approx (sqrt (+ (* re re) (* im im))) (*.f64 #s(literal -1 binary64) re))
▶	99.6%	#s(approx (sqrt (+ (* re re) (* im im))) #s(approx (* im (+ 1 (* 1/2 (/ (pow re 2) (pow im 2))))) (fabs.f64 im)))
✓	99.6%	#s(approx (sqrt (+ (* re re) (* im im))) #s(approx (* im (+ 1 (* 1/2 (/ (pow re 2) (pow im 2))))) im))
▶	4.9%	#s(approx (sqrt (+ (* re re) (* im im))) re)

Compiler

Compiled 97 to 70 computations (27.8% saved)

series192.0ms (7.4%)

Memory

38.1MiB live, 131.0MiB allocated; 49ms collecting garbage

Counts

15 → 101

Calls

Call 1

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

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

Calls

6 calls:

Time	Variable	Point
3.0ms	re	inf
3.0ms	im	inf
2.0ms	re	-inf
2.0ms	re	0
2.0ms	im	-inf

rewrite176.0ms (6.8%)

Memory

12.1MiB live, 104.7MiB allocated; 23ms collecting garbage

Counts

15 → 55

Calls

Call 1

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

Outputs
#s(approx (sqrt (+ re im)) re)
re
(*.f64 re #s(literal 1 binary64))
(*.f64 #s(literal 1 binary64) re)
(*.f64 re re)
(fabs.f64 re)
#s(approx (sqrt (+ re im)) #s(approx (+ (* (* re im) 1/2) im) im))
#s(approx (+ (* (* re im) 1/2) im) im)
im
(*.f64 im im)
(*.f64 im #s(literal 1 binary64))
(*.f64 #s(literal 1 binary64) im)
(fabs.f64 im)
im
(*.f64 im im)
(*.f64 im #s(literal 1 binary64))
(*.f64 #s(literal 1 binary64) im)
(fabs.f64 im)
(*.f64 #s(approx (sqrt (+ re im)) re) (sqrt.f64 (-.f64 re im)))
#s(approx (sqrt (+ re im)) re)
re
(*.f64 re #s(literal 1 binary64))
(*.f64 #s(literal 1 binary64) re)
(*.f64 re re)
(fabs.f64 re)
re
(*.f64 re #s(literal 1 binary64))
(*.f64 #s(literal 1 binary64) re)
(*.f64 re re)
(fabs.f64 re)
re
(*.f64 re #s(literal 1 binary64))
(*.f64 #s(literal 1 binary64) re)
(*.f64 re re)
(fabs.f64 re)
#s(literal 1 binary64)
#s(literal 0 binary64)
#s(literal 2 binary64)
(*.f64 #s(literal 1 binary64) #s(literal 3 binary64))
(*.f64 #s(literal 3 binary64) #s(literal 1 binary64))
(*.f64 (sqrt.f64 (-.f64 re im)) (sqrt.f64 (-.f64 re im)))
(*.f64 (fabs.f64 (sqrt.f64 (-.f64 re im))) (fabs.f64 (sqrt.f64 (-.f64 re im))))
(*.f64 (sqrt.f64 (fma.f64 (-.f64 re im) im re)) (sqrt.f64 (-.f64 re im)))
(*.f64 (neg.f64 (sqrt.f64 (-.f64 re im))) (neg.f64 (sqrt.f64 (-.f64 re im))))
(+.f64 (cosh.f64 (.f64 (log.f64 (-.f64 re im)) #s(literal 1/2 binary64))) (sinh.f64 (.f64 (log.f64 (-.f64 re im)) #s(literal 1/2 binary64))))
(*.f64 (-.f64 re im) (-.f64 re im))
(*.f64 (fma.f64 (-.f64 re im) im re) (-.f64 re im))
(*.f64 (-.f64 re im) (fma.f64 (-.f64 re im) im re))
(+.f64 im re)
(+.f64 re im)
im
(*.f64 im im)
(*.f64 im #s(literal 1 binary64))
(*.f64 #s(literal 1 binary64) im)
(fabs.f64 im)

eval15.0ms (0.6%)

Memory: -29.1MiB live, 16.4MiB allocated; 4ms collecting garbage
Compiler: Compiled 4 597 to 734 computations (84% saved)

prune4.0ms (0.2%)

Memory

5.3MiB live, 5.3MiB allocated; 0ms collecting garbage

Pruning

6 alts after pruning (1 fresh and 5 done)

	Pruned	Kept	Total
New	127	1	128
Fresh	0	0	0
Picked	0	3	3
Done	1	2	3
Total	128	6	134

Accuracy

99.9%

Counts

134 → 6

Alt Table

Click to see full alt table

Status	Accuracy	Program
✓	1.1%	(.f64 #s(approx (sqrt (+ im re)) (.f64 re (sqrt.f64 (/.f64 #s(literal 1 binary64) re)))) (sqrt.f64 (-.f64 re (*.f64 im im))))
✓	48.0%	(sqrt.f64 (+.f64 (.f64 re re) (.f64 im im)))
	4.9%	#s(approx (sqrt (+ (* re re) (* im im))) (fabs.f64 re))
✓	99.6%	#s(approx (sqrt (+ (* re re) (* im im))) #s(approx (* im (+ 1 (* 1/2 (/ (pow re 2) (pow im 2))))) (fabs.f64 im)))
✓	99.6%	#s(approx (sqrt (+ (* re re) (* im im))) #s(approx (* im (+ 1 (* 1/2 (/ (pow re 2) (pow im 2))))) im))
✓	4.9%	#s(approx (sqrt (+ (* re re) (* im im))) re)

Compiler

Compiled 96 to 69 computations (28.1% saved)

regimes44.0ms (1.7%)

Memory

0.3MiB live, 49.6MiB allocated; 13ms collecting garbage

Accuracy

Total -0.0b remaining (-0%)

Threshold costs -0b (-0%)

Counts

1 → 1

18 → 1

Calls

Call 1

Inputs
#s(approx (sqrt (+ (* re re) (* im im))) re)

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

Call 2

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

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

Calls

12 calls:

12.0ms	(*.f64 re re)
5.0ms	re
5.0ms	im
4.0ms	(*.f64 im im)
4.0ms	(+.f64 (.f64 re re) (.f64 im im))

Results

Accuracy	Segments	Branch
4.9%	1	`(*.f64 im im)`
4.9%	1	`(*.f64 re re)`
4.9%	1	`(+.f64 (.f64 re re) (.f64 im im))`
4.9%	1	`(sqrt.f64 (+.f64 (.f64 re re) (.f64 im im)))`
4.9%	1	`re`
4.9%	1	`im`
99.6%	1	`(*.f64 im im)`
99.6%	1	`(*.f64 re re)`
99.6%	1	`(+.f64 (.f64 re re) (.f64 im im))`
99.6%	1	`(sqrt.f64 (+.f64 (.f64 re re) (.f64 im im)))`
99.6%	1	`re`
99.6%	1	`im`

Compiler

Compiled 316 to 126 computations (60.1% saved)

derivations0.0ms (0%)

Memory

0.6MiB live, 0.6MiB allocated; 0ms collecting garbage

Stop Event

1×

fuel

Compiler

Compiled 34 to 18 computations (47.1% saved)

preprocess34.0ms (1.3%)

Memory

1.0MiB live, 47.4MiB allocated; 3ms collecting garbage

Remove

(abs im)

(sort re im)

Compiler

Compiled 306 to 210 computations (31.4% saved)

end0.0ms (0%)

Memory: 0.0MiB live, 0.0MiB allocated; 0ms collecting garbage

start0.0ms (0%)

analyze0.0ms (0%)

sample605.0ms (23.3%)

preprocess96.0ms (3.7%)

series113.0ms (4.4%)

rewrite190.0ms (7.3%)

eval9.0ms (0.3%)

prune5.0ms (0.2%)

series365.0ms (14.1%)

rewrite232.0ms (8.9%)

eval47.0ms (1.8%)

prune28.0ms (1.1%)

series206.0ms (8%)

rewrite201.0ms (7.8%)

eval22.0ms (0.9%)

prune7.0ms (0.3%)

series192.0ms (7.4%)

rewrite176.0ms (6.8%)

eval15.0ms (0.6%)

prune4.0ms (0.2%)

regimes44.0ms (1.7%)

derivations0.0ms (0%)

preprocess34.0ms (1.3%)

end0.0ms (0%)

Profiling