Metrics for Migdal et al, Equation (51)

start0.0ms (0%)

Memory: 0.0MiB live, 0.0MiB allocated

analyze115.0ms (1.2%)

Memory

27.2MiB live, 188.7MiB allocated

Algorithm

1×

Search

Probability	Valid	Unknown	Precondition	Infinite	Domain	Can't	Iter
0%	0%	99.9%	0.1%	0%	0%	0%	0
0%	0%	99.9%	0.1%	0%	0%	0%	1
0%	0%	50%	0.1%	0%	50%	0%	2
50%	25%	25%	0.1%	0%	50%	0%	3
50%	25%	25%	0.1%	0%	50%	0%	4
50%	25%	25%	0.1%	0%	50%	0%	5
50%	25%	25%	0.1%	0%	50%	0%	6
51.6%	25%	23.4%	0.1%	0%	51.5%	0%	7
52.5%	25%	22.6%	0.1%	0%	52.3%	0%	8
53.8%	25%	21.5%	0.1%	0%	53.5%	0%	9
54.5%	25%	20.9%	0.1%	0%	54%	0%	10
55.3%	25%	20.2%	0.1%	0%	54.7%	0%	11
55.7%	25%	19.9%	0.1%	0%	55.1%	0%	12

Compiler

Compiled 18 to 15 computations (16.7% saved)

sample3.3s (35.3%)

Memory

42.2MiB live, 5 038.3MiB allocated

Samples

1.1s	8 256×	0	valid
908.0ms	3 545×	1	invalid
364.0ms	1 827×	1	exit
116.0ms	438×	2	invalid
104.0ms	504×	0	invalid
76.0ms	229×	0	exit

Precisions

Click to see histograms. Total time spent on operations: 2.0s

ival-pow: 541.0ms (27.2% of total)

ival-mult: 506.0ms (25.4% of total)

ival-div: 329.0ms (16.5% of total)

ival-sqrt: 167.0ms (8.4% of total)

ival-pi: 142.0ms (7.1% of total)

ival-sub: 137.0ms (6.9% of total)

adjust: 134.0ms (6.7% of total)

exact: 17.0ms (0.9% of total)

ival-true: 12.0ms (0.6% of total)

ival-assert: 7.0ms (0.4% of total)

Bogosity

explain146.0ms (1.6%)

Memory

-35.9MiB live, 330.9MiB allocated

FPErrors

Click to see full error table

Ground Truth	Overpredictions	Example	Underpredictions	Example	Subexpression
6	94	(3.5196183650888855e-156 1.3214746812306985e-126)	1	(2.5903535525047055e-16 8.296240732519837e+72)	`(pow.f64 (.f64 (.f64 #s(literal 2 binary64) (PI.f64)) n) (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 2 binary64)))`
0	0	-	0	-	`k`
0	0	-	0	-	`n`
0	0	-	0	-	`(/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 2 binary64))`
0	0	-	0	-	`#s(literal 1 binary64)`
0	0	-	0	-	`(.f64 (.f64 #s(literal 2 binary64) (PI.f64)) n)`
0	0	-	0	-	`(sqrt.f64 k)`
0	0	-	0	-	`#s(literal 2 binary64)`
0	0	-	0	-	`(/.f64 #s(literal 1 binary64) (sqrt.f64 k))`
0	0	-	0	-	`(-.f64 #s(literal 1 binary64) k)`
0	0	-	0	-	`(*.f64 #s(literal 2 binary64) (PI.f64))`
0	0	-	0	-	`(.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) (pow.f64 (.f64 (*.f64 #s(literal 2 binary64) (PI.f64)) n) (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 2 binary64))))`
0	0	-	0	-	`(PI.f64)`

Explanations

Click to see full explanations table

Operator	Subexpression	Explanation	Count
`pow.f64`	`(pow.f64 (.f64 (.f64 #s(literal 2 binary64) (PI.f64)) n) (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 2 binary64)))`	sensitivity	99	23

Confusion

	Predicted +	Predicted -
+	5	1
-	94	156

Precision

0.050505050505050504

Recall

0.8333333333333334

Confusion?

	Predicted +	Predicted Maybe	Predicted -
+	5	1	0
-	94	22	134

Precision?

0.04918032786885246

Recall?

1.0

Freqs

test

number	freq
0	157
1	99

Total Confusion?

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

Precision?

1.0

Recall?

1.0

Samples

55.0ms

512×

valid

Compiler

Compiled 128 to 43 computations (66.4% saved)

Precisions

Click to see histograms. Total time spent on operations: 37.0ms

ival-pow: 10.0ms (27% of total)

ival-mult: 9.0ms (24.3% of total)

ival-div: 8.0ms (21.6% of total)

ival-sqrt: 5.0ms (13.5% of total)

ival-sub: 3.0ms (8.1% of total)

ival-pi: 2.0ms (5.4% of total)

exact: 1.0ms (2.7% of total)

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

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

preprocess49.0ms (0.5%)

Memory

22.6MiB live, 64.1MiB allocated

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	31	88
1	82	74
2	193	74
3	383	74
4	607	74
5	878	74
6	1047	74
7	1230	74
8	1285	74
9	1309	74
10	1327	74
11	1331	74
12	1331	74
0	13	16
0	22	16
1	37	14
2	54	14
3	75	14
4	93	14
5	108	14
6	129	14
7	156	14
8	165	14
9	168	14
0	168	13

Stop Event

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

Calls

Call 1

Inputs
(.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) (pow.f64 (.f64 (*.f64 #s(literal 2 binary64) (PI.f64)) n) (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 2 binary64))))

Outputs

(*.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) (pow.f64 (*.f64 (*.f64 #s(literal 2 binary64) (PI.f64)) n) (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 2 binary64))))

(/.f64 (pow.f64 (*.f64 n (*.f64 (PI.f64) #s(literal 2 binary64))) (fma.f64 #s(literal -1/2 binary64) k #s(literal 1/2 binary64))) (sqrt.f64 k))

Compiler

Compiled 16 to 13 computations (18.8% saved)

eval0.0ms (0%)

Memory: 0.4MiB live, 0.4MiB allocated
Compiler: Compiled 0 to 2 computations (-∞% saved)

prune1.0ms (0%)

Memory

2.1MiB live, 2.1MiB allocated

Alt Table

Click to see full alt table

Status	Accuracy	Program
▶	99.4%	(.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) (pow.f64 (.f64 (*.f64 #s(literal 2 binary64) (PI.f64)) n) (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 2 binary64))))

Compiler

Compiled 16 to 13 computations (18.8% saved)

simplify7.0ms (0.1%)

Memory

-24.8MiB live, 14.5MiB allocated

Algorithm

1×	egg-herbie

Localize:

Found 4 expressions of interest:

New	Metric	Score
cost-diff	0	(sqrt.f64 k)
cost-diff	0	(/.f64 #s(literal 1 binary64) (sqrt.f64 k))
cost-diff	320	(.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) (pow.f64 (.f64 (*.f64 #s(literal 2 binary64) (PI.f64)) n) (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 2 binary64))))
cost-diff	512	(/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 2 binary64))

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	13	54
0	22	54
1	37	52
2	54	52
3	75	52
4	93	52
5	108	52
6	129	52
7	156	52
8	165	52
9	168	52
0	168	49

Stop Event

1×	iter limit
1×	saturated
1×	iter limit

Calls

Call 1

Inputs
(.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) (pow.f64 (.f64 (*.f64 #s(literal 2 binary64) (PI.f64)) n) (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 2 binary64))))
(/.f64 #s(literal 1 binary64) (sqrt.f64 k))
#s(literal 1 binary64)
(sqrt.f64 k)
k
(pow.f64 (.f64 (.f64 #s(literal 2 binary64) (PI.f64)) n) (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 2 binary64)))
(.f64 (.f64 #s(literal 2 binary64) (PI.f64)) n)
(*.f64 #s(literal 2 binary64) (PI.f64))
#s(literal 2 binary64)
(PI.f64)
n
(/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 2 binary64))
(-.f64 #s(literal 1 binary64) k)

Outputs
(.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) (pow.f64 (.f64 (*.f64 #s(literal 2 binary64) (PI.f64)) n) (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 2 binary64))))
(/.f64 (pow.f64 (.f64 n (.f64 (PI.f64) #s(literal 2 binary64))) (fma.f64 #s(literal -1/2 binary64) k #s(literal 1/2 binary64))) (sqrt.f64 k))
(/.f64 #s(literal 1 binary64) (sqrt.f64 k))
#s(literal 1 binary64)
(sqrt.f64 k)
k
(pow.f64 (.f64 (.f64 #s(literal 2 binary64) (PI.f64)) n) (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 2 binary64)))
(pow.f64 (.f64 n (.f64 (PI.f64) #s(literal 2 binary64))) (fma.f64 #s(literal -1/2 binary64) k #s(literal 1/2 binary64)))
(.f64 (.f64 #s(literal 2 binary64) (PI.f64)) n)
(.f64 n (.f64 (PI.f64) #s(literal 2 binary64)))
(*.f64 #s(literal 2 binary64) (PI.f64))
(*.f64 (PI.f64) #s(literal 2 binary64))
#s(literal 2 binary64)
(PI.f64)
n
(/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 2 binary64))
(fma.f64 #s(literal -1/2 binary64) k #s(literal 1/2 binary64))
(-.f64 #s(literal 1 binary64) k)

localize37.0ms (0.4%)

Memory

5.7MiB live, 84.0MiB allocated

Localize:

Found 4 expressions of interest:

New	Metric	Score
accuracy	0.205410009768442	(.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) (pow.f64 (.f64 (*.f64 #s(literal 2 binary64) (PI.f64)) n) (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 2 binary64))))
accuracy	0.22265625	(/.f64 #s(literal 1 binary64) (sqrt.f64 k))
accuracy	0.22818734794137574	(pow.f64 (.f64 (.f64 #s(literal 2 binary64) (PI.f64)) n) (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 2 binary64)))
accuracy	0.23828125	(.f64 (.f64 #s(literal 2 binary64) (PI.f64)) n)

Samples

27.0ms

256×

valid

Compiler

Compiled 56 to 15 computations (73.2% saved)

Precisions

Click to see histograms. Total time spent on operations: 17.0ms

ival-pow: 5.0ms (28.6% of total)

ival-mult: 4.0ms (22.9% of total)

ival-div: 3.0ms (17.2% of total)

ival-sqrt: 2.0ms (11.5% of total)

ival-pi: 1.0ms (5.7% of total)

ival-sub: 1.0ms (5.7% of total)

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

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

exact: 0.0ms (0% of total)

series81.0ms (0.9%)

Memory

6.7MiB live, 157.7MiB allocated

Counts

6 → 96

Calls

Call 1

Inputs
#s(alt (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 2 binary64)) (patch (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 2 binary64)) #<representation binary64>) () ())
#s(alt (.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) (pow.f64 (.f64 (.f64 #s(literal 2 binary64) (PI.f64)) n) (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 2 binary64)))) (patch (.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) (pow.f64 (.f64 (.f64 #s(literal 2 binary64) (PI.f64)) n) (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 2 binary64)))) #<representation binary64>) () ())
#s(alt (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) (patch (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) #<representation binary64>) () ())
#s(alt (sqrt.f64 k) (patch (sqrt.f64 k) #<representation binary64>) () ())
#s(alt (.f64 (.f64 #s(literal 2 binary64) (PI.f64)) n) (patch (.f64 (.f64 #s(literal 2 binary64) (PI.f64)) n) #<representation binary64>) () ())
#s(alt (pow.f64 (.f64 (.f64 #s(literal 2 binary64) (PI.f64)) n) (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 2 binary64))) (patch (pow.f64 (.f64 (.f64 #s(literal 2 binary64) (PI.f64)) n) (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 2 binary64))) #<representation binary64>) () ())

Outputs
#s(alt 1/2 (taylor 0 k) (#s(alt (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 2 binary64)) (patch (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 2 binary64)) #<representation binary64>) () ())) ())
#s(alt (+ 1/2 (* -1/2 k)) (taylor 0 k) (#s(alt (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 2 binary64)) (patch (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 2 binary64)) #<representation binary64>) () ())) ())
#s(alt (+ 1/2 (* -1/2 k)) (taylor 0 k) (#s(alt (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 2 binary64)) (patch (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 2 binary64)) #<representation binary64>) () ())) ())
#s(alt (+ 1/2 (* -1/2 k)) (taylor 0 k) (#s(alt (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 2 binary64)) (patch (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 2 binary64)) #<representation binary64>) () ())) ())
#s(alt (* (sqrt (/ (* n (PI)) k)) (sqrt 2)) (taylor 0 k) (#s(alt (.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) (pow.f64 (.f64 (.f64 #s(literal 2 binary64) (PI.f64)) n) (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 2 binary64)))) (patch (.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) (pow.f64 (.f64 (.f64 #s(literal 2 binary64) (PI.f64)) n) (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 2 binary64)))) #<representation binary64>) () ())) ())
#s(alt (/ (+ (* -1/2 (* (sqrt (* (pow k 3) (* n (PI)))) (* (log (* 2 (* n (PI)))) (sqrt 2)))) (* (sqrt (* k (* n (PI)))) (sqrt 2))) k) (taylor 0 k) (#s(alt (.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) (pow.f64 (.f64 (.f64 #s(literal 2 binary64) (PI.f64)) n) (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 2 binary64)))) (patch (.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) (pow.f64 (.f64 (.f64 #s(literal 2 binary64) (PI.f64)) n) (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 2 binary64)))) #<representation binary64>) () ())) ())
#s(alt (/ (+ (* k (+ (* -1/2 (* (sqrt (* k (* n (PI)))) (* (log (* 2 (* n (PI)))) (sqrt 2)))) (* 1/8 (* (sqrt (* (pow k 3) (* n (PI)))) (* (pow (log (* 2 (* n (PI)))) 2) (sqrt 2)))))) (* (sqrt (* k (* n (PI)))) (sqrt 2))) k) (taylor 0 k) (#s(alt (.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) (pow.f64 (.f64 (.f64 #s(literal 2 binary64) (PI.f64)) n) (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 2 binary64)))) (patch (.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) (pow.f64 (.f64 (.f64 #s(literal 2 binary64) (PI.f64)) n) (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 2 binary64)))) #<representation binary64>) () ())) ())
#s(alt (/ (+ (* k (+ (* -1/2 (* (sqrt (* k (* n (PI)))) (* (log (* 2 (* n (PI)))) (sqrt 2)))) (* k (+ (* -1/48 (* (sqrt (* (pow k 3) (* n (PI)))) (* (pow (log (* 2 (* n (PI)))) 3) (sqrt 2)))) (* 1/8 (* (sqrt (* k (* n (PI)))) (* (pow (log (* 2 (* n (PI)))) 2) (sqrt 2)))))))) (* (sqrt (* k (* n (PI)))) (sqrt 2))) k) (taylor 0 k) (#s(alt (.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) (pow.f64 (.f64 (.f64 #s(literal 2 binary64) (PI.f64)) n) (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 2 binary64)))) (patch (.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) (pow.f64 (.f64 (.f64 #s(literal 2 binary64) (PI.f64)) n) (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 2 binary64)))) #<representation binary64>) () ())) ())
#s(alt (sqrt (/ 1 k)) (taylor 0 k) (#s(alt (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) (patch (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) #<representation binary64>) () ())) ())
#s(alt (sqrt (/ 1 k)) (taylor 0 k) (#s(alt (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) (patch (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) #<representation binary64>) () ())) ())
#s(alt (sqrt (/ 1 k)) (taylor 0 k) (#s(alt (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) (patch (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) #<representation binary64>) () ())) ())
#s(alt (sqrt (/ 1 k)) (taylor 0 k) (#s(alt (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) (patch (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) #<representation binary64>) () ())) ())
#s(alt (sqrt k) (taylor 0 k) (#s(alt (sqrt.f64 k) (patch (sqrt.f64 k) #<representation binary64>) () ())) ())
#s(alt (sqrt k) (taylor 0 k) (#s(alt (sqrt.f64 k) (patch (sqrt.f64 k) #<representation binary64>) () ())) ())
#s(alt (sqrt k) (taylor 0 k) (#s(alt (sqrt.f64 k) (patch (sqrt.f64 k) #<representation binary64>) () ())) ())
#s(alt (sqrt k) (taylor 0 k) (#s(alt (sqrt.f64 k) (patch (sqrt.f64 k) #<representation binary64>) () ())) ())
#s(alt (* (sqrt (* n (PI))) (sqrt 2)) (taylor 0 k) (#s(alt (pow.f64 (.f64 (.f64 #s(literal 2 binary64) (PI.f64)) n) (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 2 binary64))) (patch (pow.f64 (.f64 (.f64 #s(literal 2 binary64) (PI.f64)) n) (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 2 binary64))) #<representation binary64>) () ())) ())
#s(alt (+ (* -1/2 (* (* k (* (log (* 2 (* n (PI)))) (sqrt 2))) (sqrt (* n (PI))))) (* (sqrt (* n (PI))) (sqrt 2))) (taylor 0 k) (#s(alt (pow.f64 (.f64 (.f64 #s(literal 2 binary64) (PI.f64)) n) (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 2 binary64))) (patch (pow.f64 (.f64 (.f64 #s(literal 2 binary64) (PI.f64)) n) (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 2 binary64))) #<representation binary64>) () ())) ())
#s(alt (+ (* k (+ (* -1/2 (* (sqrt (* n (PI))) (* (log (* 2 (* n (PI)))) (sqrt 2)))) (* 1/8 (* (* k (* (pow (log (* 2 (* n (PI)))) 2) (sqrt 2))) (sqrt (* n (PI))))))) (* (sqrt (* n (PI))) (sqrt 2))) (taylor 0 k) (#s(alt (pow.f64 (.f64 (.f64 #s(literal 2 binary64) (PI.f64)) n) (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 2 binary64))) (patch (pow.f64 (.f64 (.f64 #s(literal 2 binary64) (PI.f64)) n) (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 2 binary64))) #<representation binary64>) () ())) ())
#s(alt (+ (* k (+ (* -1/2 (* (sqrt (* n (PI))) (* (log (* 2 (* n (PI)))) (sqrt 2)))) (* k (+ (* -1/48 (* (* k (* (pow (log (* 2 (* n (PI)))) 3) (sqrt 2))) (sqrt (* n (PI))))) (* 1/8 (* (sqrt (* n (PI))) (* (pow (log (* 2 (* n (PI)))) 2) (sqrt 2)))))))) (* (sqrt (* n (PI))) (sqrt 2))) (taylor 0 k) (#s(alt (pow.f64 (.f64 (.f64 #s(literal 2 binary64) (PI.f64)) n) (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 2 binary64))) (patch (pow.f64 (.f64 (.f64 #s(literal 2 binary64) (PI.f64)) n) (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 2 binary64))) #<representation binary64>) () ())) ())
#s(alt (* -1/2 k) (taylor inf k) (#s(alt (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 2 binary64)) (patch (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 2 binary64)) #<representation binary64>) () ())) ())
#s(alt (* k (- (* 1/2 (/ 1 k)) 1/2)) (taylor inf k) (#s(alt (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 2 binary64)) (patch (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 2 binary64)) #<representation binary64>) () ())) ())
#s(alt (* k (- (* 1/2 (/ 1 k)) 1/2)) (taylor inf k) (#s(alt (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 2 binary64)) (patch (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 2 binary64)) #<representation binary64>) () ())) ())
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#s(alt (* (sqrt (/ 1 k)) (exp (* 1/2 (* (+ (log (* -2 (PI))) (* -1 (log (/ -1 n)))) (- 1 k))))) (taylor -inf n) (#s(alt (.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) (pow.f64 (.f64 (.f64 #s(literal 2 binary64) (PI.f64)) n) (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 2 binary64)))) (patch (.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) (pow.f64 (.f64 (.f64 #s(literal 2 binary64) (PI.f64)) n) (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 2 binary64)))) #<representation binary64>) () ())) ())
#s(alt (* (sqrt (/ 1 k)) (exp (* 1/2 (* (+ (log (* -2 (PI))) (* -1 (log (/ -1 n)))) (- 1 k))))) (taylor -inf n) (#s(alt (.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) (pow.f64 (.f64 (.f64 #s(literal 2 binary64) (PI.f64)) n) (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 2 binary64)))) (patch (.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) (pow.f64 (.f64 (.f64 #s(literal 2 binary64) (PI.f64)) n) (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 2 binary64)))) #<representation binary64>) () ())) ())
#s(alt (* (sqrt (/ 1 k)) (exp (* 1/2 (* (+ (log (* -2 (PI))) (* -1 (log (/ -1 n)))) (- 1 k))))) (taylor -inf n) (#s(alt (.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) (pow.f64 (.f64 (.f64 #s(literal 2 binary64) (PI.f64)) n) (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 2 binary64)))) (patch (.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) (pow.f64 (.f64 (.f64 #s(literal 2 binary64) (PI.f64)) n) (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 2 binary64)))) #<representation binary64>) () ())) ())
#s(alt (* (sqrt (/ 1 k)) (exp (* 1/2 (* (+ (log (* -2 (PI))) (* -1 (log (/ -1 n)))) (- 1 k))))) (taylor -inf n) (#s(alt (.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) (pow.f64 (.f64 (.f64 #s(literal 2 binary64) (PI.f64)) n) (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 2 binary64)))) (patch (.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) (pow.f64 (.f64 (.f64 #s(literal 2 binary64) (PI.f64)) n) (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 2 binary64)))) #<representation binary64>) () ())) ())
#s(alt (* 2 (* n (PI))) (taylor -inf n) (#s(alt (.f64 (.f64 #s(literal 2 binary64) (PI.f64)) n) (patch (.f64 (.f64 #s(literal 2 binary64) (PI.f64)) n) #<representation binary64>) () ())) ())
#s(alt (* 2 (* n (PI))) (taylor -inf n) (#s(alt (.f64 (.f64 #s(literal 2 binary64) (PI.f64)) n) (patch (.f64 (.f64 #s(literal 2 binary64) (PI.f64)) n) #<representation binary64>) () ())) ())
#s(alt (* 2 (* n (PI))) (taylor -inf n) (#s(alt (.f64 (.f64 #s(literal 2 binary64) (PI.f64)) n) (patch (.f64 (.f64 #s(literal 2 binary64) (PI.f64)) n) #<representation binary64>) () ())) ())
#s(alt (* 2 (* n (PI))) (taylor -inf n) (#s(alt (.f64 (.f64 #s(literal 2 binary64) (PI.f64)) n) (patch (.f64 (.f64 #s(literal 2 binary64) (PI.f64)) n) #<representation binary64>) () ())) ())
#s(alt (exp (* 1/2 (* (+ (log (* -2 (PI))) (* -1 (log (/ -1 n)))) (- 1 k)))) (taylor -inf n) (#s(alt (pow.f64 (.f64 (.f64 #s(literal 2 binary64) (PI.f64)) n) (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 2 binary64))) (patch (pow.f64 (.f64 (.f64 #s(literal 2 binary64) (PI.f64)) n) (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 2 binary64))) #<representation binary64>) () ())) ())
#s(alt (exp (* 1/2 (* (+ (log (* -2 (PI))) (* -1 (log (/ -1 n)))) (- 1 k)))) (taylor -inf n) (#s(alt (pow.f64 (.f64 (.f64 #s(literal 2 binary64) (PI.f64)) n) (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 2 binary64))) (patch (pow.f64 (.f64 (.f64 #s(literal 2 binary64) (PI.f64)) n) (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 2 binary64))) #<representation binary64>) () ())) ())
#s(alt (exp (* 1/2 (* (+ (log (* -2 (PI))) (* -1 (log (/ -1 n)))) (- 1 k)))) (taylor -inf n) (#s(alt (pow.f64 (.f64 (.f64 #s(literal 2 binary64) (PI.f64)) n) (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 2 binary64))) (patch (pow.f64 (.f64 (.f64 #s(literal 2 binary64) (PI.f64)) n) (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 2 binary64))) #<representation binary64>) () ())) ())
#s(alt (exp (* 1/2 (* (+ (log (* -2 (PI))) (* -1 (log (/ -1 n)))) (- 1 k)))) (taylor -inf n) (#s(alt (pow.f64 (.f64 (.f64 #s(literal 2 binary64) (PI.f64)) n) (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 2 binary64))) (patch (pow.f64 (.f64 (.f64 #s(literal 2 binary64) (PI.f64)) n) (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 2 binary64))) #<representation binary64>) () ())) ())

Calls

6 calls:

Time	Variable		Point	Expression
38.0ms	n	@	0	((/ (- 1 k) 2) (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (/ 1 (sqrt k)) (sqrt k) (* (* 2 (PI)) n) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2)))
23.0ms	n	@	-inf	((/ (- 1 k) 2) (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (/ 1 (sqrt k)) (sqrt k) (* (* 2 (PI)) n) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2)))
8.0ms	n	@	inf	((/ (- 1 k) 2) (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (/ 1 (sqrt k)) (sqrt k) (* (* 2 (PI)) n) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2)))
3.0ms	k	@	-inf	((/ (- 1 k) 2) (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (/ 1 (sqrt k)) (sqrt k) (* (* 2 (PI)) n) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2)))
2.0ms	k	@	0	((/ (- 1 k) 2) (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (/ 1 (sqrt k)) (sqrt k) (* (* 2 (PI)) n) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2)))

simplify160.0ms (1.7%)

Memory

2.9MiB live, 244.1MiB allocated

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	128	1158
1	345	1139
2	1013	1017
3	3349	990
4	5543	966
0	8350	945

Stop Event

1×	iter limit
1×	node limit

Counts

96 → 96

Calls

Call 1

Inputs
1/2
(+ 1/2 (* -1/2 k))
(+ 1/2 (* -1/2 k))
(+ 1/2 (* -1/2 k))
(* (sqrt (/ (* n (PI)) k)) (sqrt 2))
(/ (+ (* -1/2 (* (sqrt (* (pow k 3) (* n (PI)))) (* (log (* 2 (* n (PI)))) (sqrt 2)))) (* (sqrt (* k (* n (PI)))) (sqrt 2))) k)
(/ (+ (* k (+ (* -1/2 (* (sqrt (* k (* n (PI)))) (* (log (* 2 (* n (PI)))) (sqrt 2)))) (* 1/8 (* (sqrt (* (pow k 3) (* n (PI)))) (* (pow (log (* 2 (* n (PI)))) 2) (sqrt 2)))))) (* (sqrt (* k (* n (PI)))) (sqrt 2))) k)
(/ (+ (* k (+ (* -1/2 (* (sqrt (* k (* n (PI)))) (* (log (* 2 (* n (PI)))) (sqrt 2)))) (* k (+ (* -1/48 (* (sqrt (* (pow k 3) (* n (PI)))) (* (pow (log (* 2 (* n (PI)))) 3) (sqrt 2)))) (* 1/8 (* (sqrt (* k (* n (PI)))) (* (pow (log (* 2 (* n (PI)))) 2) (sqrt 2)))))))) (* (sqrt (* k (* n (PI)))) (sqrt 2))) k)
(sqrt (/ 1 k))
(sqrt (/ 1 k))
(sqrt (/ 1 k))
(sqrt (/ 1 k))
(sqrt k)
(sqrt k)
(sqrt k)
(sqrt k)
(* (sqrt (* n (PI))) (sqrt 2))
(+ (* -1/2 (* (* k (* (log (* 2 (* n (PI)))) (sqrt 2))) (sqrt (* n (PI))))) (* (sqrt (* n (PI))) (sqrt 2)))
(+ (* k (+ (* -1/2 (* (sqrt (* n (PI))) (* (log (* 2 (* n (PI)))) (sqrt 2)))) (* 1/8 (* (* k (* (pow (log (* 2 (* n (PI)))) 2) (sqrt 2))) (sqrt (* n (PI))))))) (* (sqrt (* n (PI))) (sqrt 2)))
(+ (* k (+ (* -1/2 (* (sqrt (* n (PI))) (* (log (* 2 (* n (PI)))) (sqrt 2)))) (* k (+ (* -1/48 (* (* k (* (pow (log (* 2 (* n (PI)))) 3) (sqrt 2))) (sqrt (* n (PI))))) (* 1/8 (* (sqrt (* n (PI))) (* (pow (log (* 2 (* n (PI)))) 2) (sqrt 2)))))))) (* (sqrt (* n (PI))) (sqrt 2)))
(* -1/2 k)
(* k (- (* 1/2 (/ 1 k)) 1/2))
(* k (- (* 1/2 (/ 1 k)) 1/2))
(* k (- (* 1/2 (/ 1 k)) 1/2))
(* (sqrt (/ 1 k)) (exp (* 1/2 (* (log (* 2 (* n (PI)))) (- 1 k)))))
(* (sqrt (/ 1 k)) (exp (* 1/2 (* (log (* 2 (* n (PI)))) (- 1 k)))))
(* (sqrt (/ 1 k)) (exp (* 1/2 (* (log (* 2 (* n (PI)))) (- 1 k)))))
(* (sqrt (/ 1 k)) (exp (* 1/2 (* (log (* 2 (* n (PI)))) (- 1 k)))))
(sqrt (/ 1 k))
(sqrt (/ 1 k))
(sqrt (/ 1 k))
(sqrt (/ 1 k))
(sqrt k)
(sqrt k)
(sqrt k)
(sqrt k)
(exp (* 1/2 (* (log (* 2 (* n (PI)))) (- 1 k))))
(exp (* 1/2 (* (log (* 2 (* n (PI)))) (- 1 k))))
(exp (* 1/2 (* (log (* 2 (* n (PI)))) (- 1 k))))
(exp (* 1/2 (* (log (* 2 (* n (PI)))) (- 1 k))))
(* -1/2 k)
(* -1 (* k (- 1/2 (* 1/2 (/ 1 k)))))
(* -1 (* k (- 1/2 (* 1/2 (/ 1 k)))))
(* -1 (* k (- 1/2 (* 1/2 (/ 1 k)))))
(* (sqrt (/ 1 k)) (exp (* 1/2 (* (log (* 2 (* n (PI)))) (+ 1 (* -1 k))))))
(* (sqrt (/ 1 k)) (exp (* 1/2 (* (log (* 2 (* n (PI)))) (+ 1 (* -1 k))))))
(* (sqrt (/ 1 k)) (exp (* 1/2 (* (log (* 2 (* n (PI)))) (+ 1 (* -1 k))))))
(* (sqrt (/ 1 k)) (exp (* 1/2 (* (log (* 2 (* n (PI)))) (+ 1 (* -1 k))))))
(sqrt (/ 1 k))
(sqrt (/ 1 k))
(sqrt (/ 1 k))
(sqrt (/ 1 k))
(* -1 (* (sqrt k) (pow (sqrt -1) 2)))
(* -1 (* (sqrt k) (pow (sqrt -1) 2)))
(* -1 (* (sqrt k) (pow (sqrt -1) 2)))
(* -1 (* (sqrt k) (pow (sqrt -1) 2)))
(exp (* 1/2 (* (log (* 2 (* n (PI)))) (+ 1 (* -1 k)))))
(exp (* 1/2 (* (log (* 2 (* n (PI)))) (+ 1 (* -1 k)))))
(exp (* 1/2 (* (log (* 2 (* n (PI)))) (+ 1 (* -1 k)))))
(exp (* 1/2 (* (log (* 2 (* n (PI)))) (+ 1 (* -1 k)))))
(* (sqrt (/ 1 k)) (exp (* 1/2 (* (+ (log n) (log (* 2 (PI)))) (- 1 k)))))
(* (sqrt (/ 1 k)) (exp (* 1/2 (* (+ (log n) (log (* 2 (PI)))) (- 1 k)))))
(* (sqrt (/ 1 k)) (exp (* 1/2 (* (+ (log n) (log (* 2 (PI)))) (- 1 k)))))
(* (sqrt (/ 1 k)) (exp (* 1/2 (* (+ (log n) (log (* 2 (PI)))) (- 1 k)))))
(* 2 (* n (PI)))
(* 2 (* n (PI)))
(* 2 (* n (PI)))
(* 2 (* n (PI)))
(exp (* 1/2 (* (+ (log n) (log (* 2 (PI)))) (- 1 k))))
(exp (* 1/2 (* (+ (log n) (log (* 2 (PI)))) (- 1 k))))
(exp (* 1/2 (* (+ (log n) (log (* 2 (PI)))) (- 1 k))))
(exp (* 1/2 (* (+ (log n) (log (* 2 (PI)))) (- 1 k))))
(* (sqrt (/ 1 k)) (exp (* 1/2 (* (+ (log (* 2 (PI))) (* -1 (log (/ 1 n)))) (- 1 k)))))
(* (sqrt (/ 1 k)) (exp (* 1/2 (* (+ (log (* 2 (PI))) (* -1 (log (/ 1 n)))) (- 1 k)))))
(* (sqrt (/ 1 k)) (exp (* 1/2 (* (+ (log (* 2 (PI))) (* -1 (log (/ 1 n)))) (- 1 k)))))
(* (sqrt (/ 1 k)) (exp (* 1/2 (* (+ (log (* 2 (PI))) (* -1 (log (/ 1 n)))) (- 1 k)))))
(* 2 (* n (PI)))
(* 2 (* n (PI)))
(* 2 (* n (PI)))
(* 2 (* n (PI)))
(exp (* 1/2 (* (+ (log (* 2 (PI))) (* -1 (log (/ 1 n)))) (- 1 k))))
(exp (* 1/2 (* (+ (log (* 2 (PI))) (* -1 (log (/ 1 n)))) (- 1 k))))
(exp (* 1/2 (* (+ (log (* 2 (PI))) (* -1 (log (/ 1 n)))) (- 1 k))))
(exp (* 1/2 (* (+ (log (* 2 (PI))) (* -1 (log (/ 1 n)))) (- 1 k))))
(* (sqrt (/ 1 k)) (exp (* 1/2 (* (+ (log (* -2 (PI))) (* -1 (log (/ -1 n)))) (- 1 k)))))
(* (sqrt (/ 1 k)) (exp (* 1/2 (* (+ (log (* -2 (PI))) (* -1 (log (/ -1 n)))) (- 1 k)))))
(* (sqrt (/ 1 k)) (exp (* 1/2 (* (+ (log (* -2 (PI))) (* -1 (log (/ -1 n)))) (- 1 k)))))
(* (sqrt (/ 1 k)) (exp (* 1/2 (* (+ (log (* -2 (PI))) (* -1 (log (/ -1 n)))) (- 1 k)))))
(* 2 (* n (PI)))
(* 2 (* n (PI)))
(* 2 (* n (PI)))
(* 2 (* n (PI)))
(exp (* 1/2 (* (+ (log (* -2 (PI))) (* -1 (log (/ -1 n)))) (- 1 k))))
(exp (* 1/2 (* (+ (log (* -2 (PI))) (* -1 (log (/ -1 n)))) (- 1 k))))
(exp (* 1/2 (* (+ (log (* -2 (PI))) (* -1 (log (/ -1 n)))) (- 1 k))))
(exp (* 1/2 (* (+ (log (* -2 (PI))) (* -1 (log (/ -1 n)))) (- 1 k))))

Outputs
1/2
#s(literal 1/2 binary64)
(+ 1/2 (* -1/2 k))
(fma.f64 k #s(literal -1/2 binary64) #s(literal 1/2 binary64))
(+ 1/2 (* -1/2 k))
(fma.f64 k #s(literal -1/2 binary64) #s(literal 1/2 binary64))
(+ 1/2 (* -1/2 k))
(fma.f64 k #s(literal -1/2 binary64) #s(literal 1/2 binary64))
(* (sqrt (/ (* n (PI)) k)) (sqrt 2))
(.f64 (sqrt.f64 #s(literal 2 binary64)) (sqrt.f64 (/.f64 (.f64 (PI.f64) n) k)))
(/ (+ (* -1/2 (* (sqrt (* (pow k 3) (* n (PI)))) (* (log (* 2 (* n (PI)))) (sqrt 2)))) (* (sqrt (* k (* n (PI)))) (sqrt 2))) k)
(/.f64 (.f64 (sqrt.f64 #s(literal 2 binary64)) (fma.f64 (.f64 (log.f64 (.f64 (.f64 #s(literal 2 binary64) n) (PI.f64))) (sqrt.f64 (.f64 (.f64 (pow.f64 k #s(literal 3 binary64)) (PI.f64)) n))) #s(literal -1/2 binary64) (sqrt.f64 (.f64 (.f64 (PI.f64) n) k)))) k)
(/ (+ (* k (+ (* -1/2 (* (sqrt (* k (* n (PI)))) (* (log (* 2 (* n (PI)))) (sqrt 2)))) (* 1/8 (* (sqrt (* (pow k 3) (* n (PI)))) (* (pow (log (* 2 (* n (PI)))) 2) (sqrt 2)))))) (* (sqrt (* k (* n (PI)))) (sqrt 2))) k)
(/.f64 (fma.f64 (.f64 #s(literal 1/8 binary64) k) (.f64 (.f64 (pow.f64 (log.f64 (.f64 (.f64 #s(literal 2 binary64) n) (PI.f64))) #s(literal 2 binary64)) (sqrt.f64 #s(literal 2 binary64))) (sqrt.f64 (.f64 (.f64 (pow.f64 k #s(literal 3 binary64)) (PI.f64)) n))) (.f64 (fma.f64 (log.f64 (.f64 (.f64 #s(literal 2 binary64) n) (PI.f64))) (.f64 k #s(literal -1/2 binary64)) #s(literal 1 binary64)) (.f64 (sqrt.f64 (.f64 (.f64 (PI.f64) n) k)) (sqrt.f64 #s(literal 2 binary64))))) k)
(/ (+ (* k (+ (* -1/2 (* (sqrt (* k (* n (PI)))) (* (log (* 2 (* n (PI)))) (sqrt 2)))) (* k (+ (* -1/48 (* (sqrt (* (pow k 3) (* n (PI)))) (* (pow (log (* 2 (* n (PI)))) 3) (sqrt 2)))) (* 1/8 (* (sqrt (* k (* n (PI)))) (* (pow (log (* 2 (* n (PI)))) 2) (sqrt 2)))))))) (* (sqrt (* k (* n (PI)))) (sqrt 2))) k)
(/.f64 (fma.f64 (.f64 k k) (.f64 (.f64 (pow.f64 (log.f64 (.f64 (.f64 #s(literal 2 binary64) n) (PI.f64))) #s(literal 2 binary64)) (sqrt.f64 #s(literal 2 binary64))) (fma.f64 (.f64 #s(literal -1/48 binary64) (sqrt.f64 (.f64 (.f64 (pow.f64 k #s(literal 3 binary64)) (PI.f64)) n))) (log.f64 (.f64 (.f64 #s(literal 2 binary64) n) (PI.f64))) (.f64 #s(literal 1/8 binary64) (sqrt.f64 (.f64 (.f64 (PI.f64) n) k))))) (.f64 (fma.f64 (log.f64 (.f64 (.f64 #s(literal 2 binary64) n) (PI.f64))) (.f64 k #s(literal -1/2 binary64)) #s(literal 1 binary64)) (.f64 (sqrt.f64 (.f64 (.f64 (PI.f64) n) k)) (sqrt.f64 #s(literal 2 binary64))))) k)
(sqrt (/ 1 k))
(sqrt.f64 (/.f64 #s(literal 1 binary64) k))
(sqrt (/ 1 k))
(sqrt.f64 (/.f64 #s(literal 1 binary64) k))
(sqrt (/ 1 k))
(sqrt.f64 (/.f64 #s(literal 1 binary64) k))
(sqrt (/ 1 k))
(sqrt.f64 (/.f64 #s(literal 1 binary64) k))
(sqrt k)
(sqrt.f64 k)
(sqrt k)
(sqrt.f64 k)
(sqrt k)
(sqrt.f64 k)
(sqrt k)
(sqrt.f64 k)
(* (sqrt (* n (PI))) (sqrt 2))
(.f64 (sqrt.f64 (.f64 (PI.f64) n)) (sqrt.f64 #s(literal 2 binary64)))
(+ (* -1/2 (* (* k (* (log (* 2 (* n (PI)))) (sqrt 2))) (sqrt (* n (PI))))) (* (sqrt (* n (PI))) (sqrt 2)))
(.f64 (fma.f64 (log.f64 (.f64 (.f64 #s(literal 2 binary64) n) (PI.f64))) (.f64 k #s(literal -1/2 binary64)) #s(literal 1 binary64)) (.f64 (sqrt.f64 (.f64 (PI.f64) n)) (sqrt.f64 #s(literal 2 binary64))))
(+ (* k (+ (* -1/2 (* (sqrt (* n (PI))) (* (log (* 2 (* n (PI)))) (sqrt 2)))) (* 1/8 (* (* k (* (pow (log (* 2 (* n (PI)))) 2) (sqrt 2))) (sqrt (* n (PI))))))) (* (sqrt (* n (PI))) (sqrt 2)))
(.f64 (sqrt.f64 (.f64 (PI.f64) n)) (fma.f64 k (.f64 (.f64 (log.f64 (.f64 (.f64 #s(literal 2 binary64) n) (PI.f64))) (sqrt.f64 #s(literal 2 binary64))) (fma.f64 (.f64 #s(literal 1/8 binary64) k) (log.f64 (.f64 (*.f64 #s(literal 2 binary64) n) (PI.f64))) #s(literal -1/2 binary64))) (sqrt.f64 #s(literal 2 binary64))))
(+ (* k (+ (* -1/2 (* (sqrt (* n (PI))) (* (log (* 2 (* n (PI)))) (sqrt 2)))) (* k (+ (* -1/48 (* (* k (* (pow (log (* 2 (* n (PI)))) 3) (sqrt 2))) (sqrt (* n (PI))))) (* 1/8 (* (sqrt (* n (PI))) (* (pow (log (* 2 (* n (PI)))) 2) (sqrt 2)))))))) (* (sqrt (* n (PI))) (sqrt 2)))
(fma.f64 (.f64 (sqrt.f64 (.f64 (PI.f64) n)) (fma.f64 k (.f64 (.f64 (pow.f64 (log.f64 (.f64 (.f64 #s(literal 2 binary64) n) (PI.f64))) #s(literal 2 binary64)) (sqrt.f64 #s(literal 2 binary64))) (fma.f64 (.f64 #s(literal -1/48 binary64) k) (log.f64 (.f64 (.f64 #s(literal 2 binary64) n) (PI.f64))) #s(literal 1/8 binary64))) (.f64 (.f64 (sqrt.f64 #s(literal 2 binary64)) #s(literal -1/2 binary64)) (log.f64 (.f64 (.f64 #s(literal 2 binary64) n) (PI.f64)))))) k (.f64 (sqrt.f64 (*.f64 (PI.f64) n)) (sqrt.f64 #s(literal 2 binary64))))
(* -1/2 k)
(*.f64 k #s(literal -1/2 binary64))
(* k (- (* 1/2 (/ 1 k)) 1/2))
(fma.f64 k #s(literal -1/2 binary64) #s(literal 1/2 binary64))
(* k (- (* 1/2 (/ 1 k)) 1/2))
(fma.f64 k #s(literal -1/2 binary64) #s(literal 1/2 binary64))
(* k (- (* 1/2 (/ 1 k)) 1/2))
(fma.f64 k #s(literal -1/2 binary64) #s(literal 1/2 binary64))
(* (sqrt (/ 1 k)) (exp (* 1/2 (* (log (* 2 (* n (PI)))) (- 1 k)))))
(.f64 (pow.f64 (.f64 (*.f64 #s(literal 2 binary64) n) (PI.f64)) (fma.f64 k #s(literal -1/2 binary64) #s(literal 1/2 binary64))) (sqrt.f64 (/.f64 #s(literal 1 binary64) k)))
(* (sqrt (/ 1 k)) (exp (* 1/2 (* (log (* 2 (* n (PI)))) (- 1 k)))))
(.f64 (pow.f64 (.f64 (*.f64 #s(literal 2 binary64) n) (PI.f64)) (fma.f64 k #s(literal -1/2 binary64) #s(literal 1/2 binary64))) (sqrt.f64 (/.f64 #s(literal 1 binary64) k)))
(* (sqrt (/ 1 k)) (exp (* 1/2 (* (log (* 2 (* n (PI)))) (- 1 k)))))
(.f64 (pow.f64 (.f64 (*.f64 #s(literal 2 binary64) n) (PI.f64)) (fma.f64 k #s(literal -1/2 binary64) #s(literal 1/2 binary64))) (sqrt.f64 (/.f64 #s(literal 1 binary64) k)))
(* (sqrt (/ 1 k)) (exp (* 1/2 (* (log (* 2 (* n (PI)))) (- 1 k)))))
(.f64 (pow.f64 (.f64 (*.f64 #s(literal 2 binary64) n) (PI.f64)) (fma.f64 k #s(literal -1/2 binary64) #s(literal 1/2 binary64))) (sqrt.f64 (/.f64 #s(literal 1 binary64) k)))
(sqrt (/ 1 k))
(sqrt.f64 (/.f64 #s(literal 1 binary64) k))
(sqrt (/ 1 k))
(sqrt.f64 (/.f64 #s(literal 1 binary64) k))
(sqrt (/ 1 k))
(sqrt.f64 (/.f64 #s(literal 1 binary64) k))
(sqrt (/ 1 k))
(sqrt.f64 (/.f64 #s(literal 1 binary64) k))
(sqrt k)
(sqrt.f64 k)
(sqrt k)
(sqrt.f64 k)
(sqrt k)
(sqrt.f64 k)
(sqrt k)
(sqrt.f64 k)
(exp (* 1/2 (* (log (* 2 (* n (PI)))) (- 1 k))))
(pow.f64 (.f64 (.f64 #s(literal 2 binary64) n) (PI.f64)) (fma.f64 k #s(literal -1/2 binary64) #s(literal 1/2 binary64)))
(exp (* 1/2 (* (log (* 2 (* n (PI)))) (- 1 k))))
(pow.f64 (.f64 (.f64 #s(literal 2 binary64) n) (PI.f64)) (fma.f64 k #s(literal -1/2 binary64) #s(literal 1/2 binary64)))
(exp (* 1/2 (* (log (* 2 (* n (PI)))) (- 1 k))))
(pow.f64 (.f64 (.f64 #s(literal 2 binary64) n) (PI.f64)) (fma.f64 k #s(literal -1/2 binary64) #s(literal 1/2 binary64)))
(exp (* 1/2 (* (log (* 2 (* n (PI)))) (- 1 k))))
(pow.f64 (.f64 (.f64 #s(literal 2 binary64) n) (PI.f64)) (fma.f64 k #s(literal -1/2 binary64) #s(literal 1/2 binary64)))
(* -1/2 k)
(*.f64 k #s(literal -1/2 binary64))
(* -1 (* k (- 1/2 (* 1/2 (/ 1 k)))))
(fma.f64 k #s(literal -1/2 binary64) #s(literal 1/2 binary64))
(* -1 (* k (- 1/2 (* 1/2 (/ 1 k)))))
(fma.f64 k #s(literal -1/2 binary64) #s(literal 1/2 binary64))
(* -1 (* k (- 1/2 (* 1/2 (/ 1 k)))))
(fma.f64 k #s(literal -1/2 binary64) #s(literal 1/2 binary64))
(* (sqrt (/ 1 k)) (exp (* 1/2 (* (log (* 2 (* n (PI)))) (+ 1 (* -1 k))))))
(.f64 (pow.f64 (.f64 (*.f64 #s(literal 2 binary64) n) (PI.f64)) (fma.f64 k #s(literal -1/2 binary64) #s(literal 1/2 binary64))) (sqrt.f64 (/.f64 #s(literal 1 binary64) k)))
(* (sqrt (/ 1 k)) (exp (* 1/2 (* (log (* 2 (* n (PI)))) (+ 1 (* -1 k))))))
(.f64 (pow.f64 (.f64 (*.f64 #s(literal 2 binary64) n) (PI.f64)) (fma.f64 k #s(literal -1/2 binary64) #s(literal 1/2 binary64))) (sqrt.f64 (/.f64 #s(literal 1 binary64) k)))
(* (sqrt (/ 1 k)) (exp (* 1/2 (* (log (* 2 (* n (PI)))) (+ 1 (* -1 k))))))
(.f64 (pow.f64 (.f64 (*.f64 #s(literal 2 binary64) n) (PI.f64)) (fma.f64 k #s(literal -1/2 binary64) #s(literal 1/2 binary64))) (sqrt.f64 (/.f64 #s(literal 1 binary64) k)))
(* (sqrt (/ 1 k)) (exp (* 1/2 (* (log (* 2 (* n (PI)))) (+ 1 (* -1 k))))))
(.f64 (pow.f64 (.f64 (*.f64 #s(literal 2 binary64) n) (PI.f64)) (fma.f64 k #s(literal -1/2 binary64) #s(literal 1/2 binary64))) (sqrt.f64 (/.f64 #s(literal 1 binary64) k)))
(sqrt (/ 1 k))
(sqrt.f64 (/.f64 #s(literal 1 binary64) k))
(sqrt (/ 1 k))
(sqrt.f64 (/.f64 #s(literal 1 binary64) k))
(sqrt (/ 1 k))
(sqrt.f64 (/.f64 #s(literal 1 binary64) k))
(sqrt (/ 1 k))
(sqrt.f64 (/.f64 #s(literal 1 binary64) k))
(* -1 (* (sqrt k) (pow (sqrt -1) 2)))
(sqrt.f64 k)
(* -1 (* (sqrt k) (pow (sqrt -1) 2)))
(sqrt.f64 k)
(* -1 (* (sqrt k) (pow (sqrt -1) 2)))
(sqrt.f64 k)
(* -1 (* (sqrt k) (pow (sqrt -1) 2)))
(sqrt.f64 k)
(exp (* 1/2 (* (log (* 2 (* n (PI)))) (+ 1 (* -1 k)))))
(pow.f64 (.f64 (.f64 #s(literal 2 binary64) n) (PI.f64)) (fma.f64 k #s(literal -1/2 binary64) #s(literal 1/2 binary64)))
(exp (* 1/2 (* (log (* 2 (* n (PI)))) (+ 1 (* -1 k)))))
(pow.f64 (.f64 (.f64 #s(literal 2 binary64) n) (PI.f64)) (fma.f64 k #s(literal -1/2 binary64) #s(literal 1/2 binary64)))
(exp (* 1/2 (* (log (* 2 (* n (PI)))) (+ 1 (* -1 k)))))
(pow.f64 (.f64 (.f64 #s(literal 2 binary64) n) (PI.f64)) (fma.f64 k #s(literal -1/2 binary64) #s(literal 1/2 binary64)))
(exp (* 1/2 (* (log (* 2 (* n (PI)))) (+ 1 (* -1 k)))))
(pow.f64 (.f64 (.f64 #s(literal 2 binary64) n) (PI.f64)) (fma.f64 k #s(literal -1/2 binary64) #s(literal 1/2 binary64)))
(* (sqrt (/ 1 k)) (exp (* 1/2 (* (+ (log n) (log (* 2 (PI)))) (- 1 k)))))
(.f64 (pow.f64 (.f64 (*.f64 #s(literal 2 binary64) n) (PI.f64)) (fma.f64 k #s(literal -1/2 binary64) #s(literal 1/2 binary64))) (sqrt.f64 (/.f64 #s(literal 1 binary64) k)))
(* (sqrt (/ 1 k)) (exp (* 1/2 (* (+ (log n) (log (* 2 (PI)))) (- 1 k)))))
(.f64 (pow.f64 (.f64 (*.f64 #s(literal 2 binary64) n) (PI.f64)) (fma.f64 k #s(literal -1/2 binary64) #s(literal 1/2 binary64))) (sqrt.f64 (/.f64 #s(literal 1 binary64) k)))
(* (sqrt (/ 1 k)) (exp (* 1/2 (* (+ (log n) (log (* 2 (PI)))) (- 1 k)))))
(.f64 (pow.f64 (.f64 (*.f64 #s(literal 2 binary64) n) (PI.f64)) (fma.f64 k #s(literal -1/2 binary64) #s(literal 1/2 binary64))) (sqrt.f64 (/.f64 #s(literal 1 binary64) k)))
(* (sqrt (/ 1 k)) (exp (* 1/2 (* (+ (log n) (log (* 2 (PI)))) (- 1 k)))))
(.f64 (pow.f64 (.f64 (*.f64 #s(literal 2 binary64) n) (PI.f64)) (fma.f64 k #s(literal -1/2 binary64) #s(literal 1/2 binary64))) (sqrt.f64 (/.f64 #s(literal 1 binary64) k)))
(* 2 (* n (PI)))
(.f64 (.f64 #s(literal 2 binary64) n) (PI.f64))
(* 2 (* n (PI)))
(.f64 (.f64 #s(literal 2 binary64) n) (PI.f64))
(* 2 (* n (PI)))
(.f64 (.f64 #s(literal 2 binary64) n) (PI.f64))
(* 2 (* n (PI)))
(.f64 (.f64 #s(literal 2 binary64) n) (PI.f64))
(exp (* 1/2 (* (+ (log n) (log (* 2 (PI)))) (- 1 k))))
(pow.f64 (.f64 (.f64 #s(literal 2 binary64) n) (PI.f64)) (fma.f64 k #s(literal -1/2 binary64) #s(literal 1/2 binary64)))
(exp (* 1/2 (* (+ (log n) (log (* 2 (PI)))) (- 1 k))))
(pow.f64 (.f64 (.f64 #s(literal 2 binary64) n) (PI.f64)) (fma.f64 k #s(literal -1/2 binary64) #s(literal 1/2 binary64)))
(exp (* 1/2 (* (+ (log n) (log (* 2 (PI)))) (- 1 k))))
(pow.f64 (.f64 (.f64 #s(literal 2 binary64) n) (PI.f64)) (fma.f64 k #s(literal -1/2 binary64) #s(literal 1/2 binary64)))
(exp (* 1/2 (* (+ (log n) (log (* 2 (PI)))) (- 1 k))))
(pow.f64 (.f64 (.f64 #s(literal 2 binary64) n) (PI.f64)) (fma.f64 k #s(literal -1/2 binary64) #s(literal 1/2 binary64)))
(* (sqrt (/ 1 k)) (exp (* 1/2 (* (+ (log (* 2 (PI))) (* -1 (log (/ 1 n)))) (- 1 k)))))
(.f64 (pow.f64 (.f64 (*.f64 #s(literal 2 binary64) n) (PI.f64)) (fma.f64 k #s(literal -1/2 binary64) #s(literal 1/2 binary64))) (sqrt.f64 (/.f64 #s(literal 1 binary64) k)))
(* (sqrt (/ 1 k)) (exp (* 1/2 (* (+ (log (* 2 (PI))) (* -1 (log (/ 1 n)))) (- 1 k)))))
(.f64 (pow.f64 (.f64 (*.f64 #s(literal 2 binary64) n) (PI.f64)) (fma.f64 k #s(literal -1/2 binary64) #s(literal 1/2 binary64))) (sqrt.f64 (/.f64 #s(literal 1 binary64) k)))
(* (sqrt (/ 1 k)) (exp (* 1/2 (* (+ (log (* 2 (PI))) (* -1 (log (/ 1 n)))) (- 1 k)))))
(.f64 (pow.f64 (.f64 (*.f64 #s(literal 2 binary64) n) (PI.f64)) (fma.f64 k #s(literal -1/2 binary64) #s(literal 1/2 binary64))) (sqrt.f64 (/.f64 #s(literal 1 binary64) k)))
(* (sqrt (/ 1 k)) (exp (* 1/2 (* (+ (log (* 2 (PI))) (* -1 (log (/ 1 n)))) (- 1 k)))))
(.f64 (pow.f64 (.f64 (*.f64 #s(literal 2 binary64) n) (PI.f64)) (fma.f64 k #s(literal -1/2 binary64) #s(literal 1/2 binary64))) (sqrt.f64 (/.f64 #s(literal 1 binary64) k)))
(* 2 (* n (PI)))
(.f64 (.f64 #s(literal 2 binary64) n) (PI.f64))
(* 2 (* n (PI)))
(.f64 (.f64 #s(literal 2 binary64) n) (PI.f64))
(* 2 (* n (PI)))
(.f64 (.f64 #s(literal 2 binary64) n) (PI.f64))
(* 2 (* n (PI)))
(.f64 (.f64 #s(literal 2 binary64) n) (PI.f64))
(exp (* 1/2 (* (+ (log (* 2 (PI))) (* -1 (log (/ 1 n)))) (- 1 k))))
(pow.f64 (.f64 (.f64 #s(literal 2 binary64) n) (PI.f64)) (fma.f64 k #s(literal -1/2 binary64) #s(literal 1/2 binary64)))
(exp (* 1/2 (* (+ (log (* 2 (PI))) (* -1 (log (/ 1 n)))) (- 1 k))))
(pow.f64 (.f64 (.f64 #s(literal 2 binary64) n) (PI.f64)) (fma.f64 k #s(literal -1/2 binary64) #s(literal 1/2 binary64)))
(exp (* 1/2 (* (+ (log (* 2 (PI))) (* -1 (log (/ 1 n)))) (- 1 k))))
(pow.f64 (.f64 (.f64 #s(literal 2 binary64) n) (PI.f64)) (fma.f64 k #s(literal -1/2 binary64) #s(literal 1/2 binary64)))
(exp (* 1/2 (* (+ (log (* 2 (PI))) (* -1 (log (/ 1 n)))) (- 1 k))))
(pow.f64 (.f64 (.f64 #s(literal 2 binary64) n) (PI.f64)) (fma.f64 k #s(literal -1/2 binary64) #s(literal 1/2 binary64)))
(* (sqrt (/ 1 k)) (exp (* 1/2 (* (+ (log (* -2 (PI))) (* -1 (log (/ -1 n)))) (- 1 k)))))
(.f64 (pow.f64 (/.f64 (.f64 #s(literal -2 binary64) (PI.f64)) (/.f64 #s(literal -1 binary64) n)) (fma.f64 k #s(literal -1/2 binary64) #s(literal 1/2 binary64))) (sqrt.f64 (/.f64 #s(literal 1 binary64) k)))
(* (sqrt (/ 1 k)) (exp (* 1/2 (* (+ (log (* -2 (PI))) (* -1 (log (/ -1 n)))) (- 1 k)))))
(.f64 (pow.f64 (/.f64 (.f64 #s(literal -2 binary64) (PI.f64)) (/.f64 #s(literal -1 binary64) n)) (fma.f64 k #s(literal -1/2 binary64) #s(literal 1/2 binary64))) (sqrt.f64 (/.f64 #s(literal 1 binary64) k)))
(* (sqrt (/ 1 k)) (exp (* 1/2 (* (+ (log (* -2 (PI))) (* -1 (log (/ -1 n)))) (- 1 k)))))
(.f64 (pow.f64 (/.f64 (.f64 #s(literal -2 binary64) (PI.f64)) (/.f64 #s(literal -1 binary64) n)) (fma.f64 k #s(literal -1/2 binary64) #s(literal 1/2 binary64))) (sqrt.f64 (/.f64 #s(literal 1 binary64) k)))
(* (sqrt (/ 1 k)) (exp (* 1/2 (* (+ (log (* -2 (PI))) (* -1 (log (/ -1 n)))) (- 1 k)))))
(.f64 (pow.f64 (/.f64 (.f64 #s(literal -2 binary64) (PI.f64)) (/.f64 #s(literal -1 binary64) n)) (fma.f64 k #s(literal -1/2 binary64) #s(literal 1/2 binary64))) (sqrt.f64 (/.f64 #s(literal 1 binary64) k)))
(* 2 (* n (PI)))
(.f64 (.f64 #s(literal 2 binary64) n) (PI.f64))
(* 2 (* n (PI)))
(.f64 (.f64 #s(literal 2 binary64) n) (PI.f64))
(* 2 (* n (PI)))
(.f64 (.f64 #s(literal 2 binary64) n) (PI.f64))
(* 2 (* n (PI)))
(.f64 (.f64 #s(literal 2 binary64) n) (PI.f64))
(exp (* 1/2 (* (+ (log (* -2 (PI))) (* -1 (log (/ -1 n)))) (- 1 k))))
(pow.f64 (/.f64 (*.f64 #s(literal -2 binary64) (PI.f64)) (/.f64 #s(literal -1 binary64) n)) (fma.f64 k #s(literal -1/2 binary64) #s(literal 1/2 binary64)))
(exp (* 1/2 (* (+ (log (* -2 (PI))) (* -1 (log (/ -1 n)))) (- 1 k))))
(pow.f64 (/.f64 (*.f64 #s(literal -2 binary64) (PI.f64)) (/.f64 #s(literal -1 binary64) n)) (fma.f64 k #s(literal -1/2 binary64) #s(literal 1/2 binary64)))
(exp (* 1/2 (* (+ (log (* -2 (PI))) (* -1 (log (/ -1 n)))) (- 1 k))))
(pow.f64 (/.f64 (*.f64 #s(literal -2 binary64) (PI.f64)) (/.f64 #s(literal -1 binary64) n)) (fma.f64 k #s(literal -1/2 binary64) #s(literal 1/2 binary64)))
(exp (* 1/2 (* (+ (log (* -2 (PI))) (* -1 (log (/ -1 n)))) (- 1 k))))
(pow.f64 (/.f64 (*.f64 #s(literal -2 binary64) (PI.f64)) (/.f64 #s(literal -1 binary64) n)) (fma.f64 k #s(literal -1/2 binary64) #s(literal 1/2 binary64)))

rewrite179.0ms (1.9%)

Memory

22.3MiB live, 249.2MiB allocated

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	13	43
0	22	43
1	89	40
2	497	38
3	4474	38
0	8599	37

Stop Event

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

Counts

6 → 419

Calls

Call 1

Inputs
(/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 2 binary64))
(.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) (pow.f64 (.f64 (*.f64 #s(literal 2 binary64) (PI.f64)) n) (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 2 binary64))))
(/.f64 #s(literal 1 binary64) (sqrt.f64 k))
(sqrt.f64 k)
(.f64 (.f64 #s(literal 2 binary64) (PI.f64)) n)
(pow.f64 (.f64 (.f64 #s(literal 2 binary64) (PI.f64)) n) (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 2 binary64)))

Outputs
(.f64 (/.f64 (.f64 (fma.f64 (neg.f64 k) k #s(literal 1 binary64)) #s(literal 1/2 binary64)) (-.f64 #s(literal 1 binary64) (pow.f64 k #s(literal 3 binary64)))) (fma.f64 (-.f64 #s(literal 1 binary64) k) k #s(literal 1 binary64)))
(.f64 (/.f64 (.f64 (fma.f64 (neg.f64 k) k #s(literal 1 binary64)) #s(literal 1/2 binary64)) (fma.f64 (neg.f64 k) k #s(literal 1 binary64))) (-.f64 #s(literal 1 binary64) k))
(.f64 (/.f64 (.f64 (-.f64 #s(literal 1 binary64) (pow.f64 k #s(literal 3 binary64))) #s(literal 1/2 binary64)) (-.f64 #s(literal 1 binary64) (pow.f64 (fma.f64 k k k) #s(literal 2 binary64)))) (-.f64 #s(literal 1 binary64) (fma.f64 k k k)))
(.f64 (/.f64 (.f64 (-.f64 #s(literal 1 binary64) (pow.f64 k #s(literal 3 binary64))) #s(literal 1/2 binary64)) (+.f64 (pow.f64 (fma.f64 k k k) #s(literal 3 binary64)) #s(literal 1 binary64))) (fma.f64 (fma.f64 k k k) (-.f64 (fma.f64 k k k) #s(literal 1 binary64)) #s(literal 1 binary64)))
(.f64 (pow.f64 (/.f64 #s(literal -2 binary64) (+.f64 #s(literal -1 binary64) (.f64 k k))) #s(literal -1 binary64)) (pow.f64 (-.f64 #s(literal 1 binary64) k) #s(literal -1 binary64)))
(*.f64 (pow.f64 (/.f64 #s(literal -2 binary64) (+.f64 #s(literal -1 binary64) (pow.f64 k #s(literal 3 binary64)))) #s(literal -1 binary64)) (pow.f64 (fma.f64 (-.f64 #s(literal 1 binary64) k) k #s(literal 1 binary64)) #s(literal -1 binary64)))
(.f64 (.f64 #s(literal 1 binary64) (-.f64 k #s(literal 1 binary64))) #s(literal -1/2 binary64))
(*.f64 (pow.f64 (fma.f64 #s(literal 1/2 binary64) k #s(literal 1/2 binary64)) #s(literal 1/2 binary64)) (pow.f64 (fma.f64 #s(literal 1/2 binary64) k #s(literal 1/2 binary64)) #s(literal 1/2 binary64)))
(.f64 (.f64 #s(literal 2 binary64) (fma.f64 #s(literal 1/2 binary64) k #s(literal 1/2 binary64))) #s(literal 1/2 binary64))
(*.f64 (fma.f64 #s(literal 2 binary64) k #s(literal 2 binary64)) #s(literal 1/4 binary64))
(.f64 (.f64 (fma.f64 (neg.f64 k) k #s(literal 1 binary64)) #s(literal 1/2 binary64)) (pow.f64 (-.f64 #s(literal 1 binary64) k) #s(literal -1 binary64)))
(.f64 (.f64 (-.f64 #s(literal 1 binary64) (pow.f64 k #s(literal 3 binary64))) #s(literal 1/2 binary64)) (pow.f64 (fma.f64 (-.f64 #s(literal 1 binary64) k) k #s(literal 1 binary64)) #s(literal -1 binary64)))
(.f64 (-.f64 #s(literal 1/4 binary64) (.f64 (*.f64 k k) #s(literal 1/4 binary64))) (/.f64 #s(literal -2 binary64) (-.f64 k #s(literal 1 binary64))))
(.f64 (-.f64 #s(literal 1/8 binary64) (.f64 (pow.f64 k #s(literal 3 binary64)) #s(literal 1/8 binary64))) (pow.f64 (fma.f64 (*.f64 #s(literal 1/2 binary64) k) (fma.f64 #s(literal 1/2 binary64) k #s(literal 1/2 binary64)) #s(literal 1/4 binary64)) #s(literal -1 binary64)))
(*.f64 #s(literal 1/4 binary64) (+.f64 (-.f64 #s(literal 1 binary64) k) (-.f64 #s(literal 1 binary64) k)))
(*.f64 #s(literal -1/2 binary64) (-.f64 k #s(literal 1 binary64)))
(.f64 (.f64 #s(literal 1/4 binary64) (-.f64 #s(literal 1 binary64) k)) #s(literal 2 binary64))
(*.f64 (fma.f64 (neg.f64 k) k #s(literal 1 binary64)) (/.f64 #s(literal 1/2 binary64) (-.f64 #s(literal 1 binary64) k)))
(.f64 (fma.f64 (neg.f64 k) k #s(literal 1 binary64)) (.f64 (pow.f64 (-.f64 #s(literal 1 binary64) k) #s(literal -1 binary64)) #s(literal 1/2 binary64)))
(*.f64 (fma.f64 (neg.f64 k) k #s(literal 1 binary64)) (pow.f64 (fma.f64 #s(literal 2 binary64) k #s(literal 2 binary64)) #s(literal -1 binary64)))
(*.f64 (fma.f64 (neg.f64 k) k #s(literal 1 binary64)) (/.f64 (pow.f64 (-.f64 #s(literal 1 binary64) k) #s(literal -1 binary64)) #s(literal 2 binary64)))
(*.f64 (-.f64 #s(literal 1 binary64) (pow.f64 k #s(literal 3 binary64))) (/.f64 #s(literal 1/2 binary64) (fma.f64 (-.f64 #s(literal 1 binary64) k) k #s(literal 1 binary64))))
(.f64 (-.f64 #s(literal 1 binary64) (pow.f64 k #s(literal 3 binary64))) (.f64 (pow.f64 (fma.f64 (-.f64 #s(literal 1 binary64) k) k #s(literal 1 binary64)) #s(literal -1 binary64)) #s(literal 1/2 binary64)))
(*.f64 (-.f64 #s(literal 1 binary64) (pow.f64 k #s(literal 3 binary64))) (pow.f64 (fma.f64 (fma.f64 k k k) #s(literal 2 binary64) #s(literal 2 binary64)) #s(literal -1 binary64)))
(*.f64 (-.f64 #s(literal 1 binary64) (pow.f64 k #s(literal 3 binary64))) (/.f64 (pow.f64 (fma.f64 (-.f64 #s(literal 1 binary64) k) k #s(literal 1 binary64)) #s(literal -1 binary64)) #s(literal 2 binary64)))
(*.f64 (-.f64 k #s(literal 1 binary64)) #s(literal -1/2 binary64))
(*.f64 #s(literal 1/2 binary64) (fma.f64 #s(literal -1/2 binary64) (-.f64 k #s(literal 1 binary64)) (fma.f64 #s(literal 1/2 binary64) k #s(literal 1/2 binary64))))
(*.f64 #s(literal 1/2 binary64) (-.f64 #s(literal 1 binary64) k))
(.f64 #s(literal -1 binary64) (.f64 #s(literal -1/2 binary64) (-.f64 #s(literal 1 binary64) k)))
(*.f64 (fma.f64 #s(literal 1/2 binary64) k #s(literal 1/2 binary64)) #s(literal 1 binary64))
(.f64 #s(literal 2 binary64) (.f64 #s(literal 1/4 binary64) (-.f64 #s(literal 1 binary64) k)))
(*.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 1/2 binary64))
(*.f64 #s(literal 1 binary64) (fma.f64 #s(literal 1/2 binary64) k #s(literal 1/2 binary64)))
(pow.f64 (/.f64 (-.f64 #s(literal 1 binary64) k) (*.f64 (fma.f64 (neg.f64 k) k #s(literal 1 binary64)) #s(literal 1/2 binary64))) #s(literal -1 binary64))
(pow.f64 (/.f64 (fma.f64 (-.f64 #s(literal 1 binary64) k) k #s(literal 1 binary64)) (*.f64 (-.f64 #s(literal 1 binary64) (pow.f64 k #s(literal 3 binary64))) #s(literal 1/2 binary64))) #s(literal -1 binary64))
(pow.f64 (/.f64 (fma.f64 #s(literal 1/2 binary64) k #s(literal 1/2 binary64)) (-.f64 #s(literal 1/4 binary64) (.f64 (.f64 k k) #s(literal 1/4 binary64)))) #s(literal -1 binary64))
(pow.f64 (/.f64 (fma.f64 (.f64 #s(literal 1/2 binary64) k) (fma.f64 #s(literal 1/2 binary64) k #s(literal 1/2 binary64)) #s(literal 1/4 binary64)) (-.f64 #s(literal 1/8 binary64) (.f64 (pow.f64 k #s(literal 3 binary64)) #s(literal 1/8 binary64)))) #s(literal -1 binary64))
(pow.f64 (/.f64 #s(literal -2 binary64) (-.f64 k #s(literal 1 binary64))) #s(literal -1 binary64))
(pow.f64 (fma.f64 #s(literal 1/2 binary64) k #s(literal 1/2 binary64)) #s(literal 1 binary64))
(/.f64 (pow.f64 (/.f64 #s(literal -2 binary64) (+.f64 #s(literal -1 binary64) (*.f64 k k))) #s(literal -1 binary64)) (-.f64 #s(literal 1 binary64) k))
(/.f64 (pow.f64 (/.f64 #s(literal -2 binary64) (+.f64 #s(literal -1 binary64) (pow.f64 k #s(literal 3 binary64)))) #s(literal -1 binary64)) (fma.f64 (-.f64 #s(literal 1 binary64) k) k #s(literal 1 binary64)))
(/.f64 (.f64 (+.f64 #s(literal -1 binary64) (.f64 k k)) #s(literal -1/2 binary64)) (-.f64 #s(literal 1 binary64) k))
(/.f64 (*.f64 (+.f64 #s(literal -1 binary64) (pow.f64 k #s(literal 3 binary64))) #s(literal -1/2 binary64)) (fma.f64 (-.f64 #s(literal 1 binary64) k) k #s(literal 1 binary64)))
(/.f64 (*.f64 (fma.f64 (neg.f64 k) k #s(literal 1 binary64)) #s(literal -1/2 binary64)) (-.f64 k #s(literal 1 binary64)))
(/.f64 (*.f64 (-.f64 #s(literal 1 binary64) (pow.f64 k #s(literal 3 binary64))) #s(literal -1/2 binary64)) (neg.f64 (fma.f64 (-.f64 #s(literal 1 binary64) k) k #s(literal 1 binary64))))
(/.f64 (.f64 (+.f64 #s(literal -1 binary64) (.f64 k k)) #s(literal 1/2 binary64)) (-.f64 k #s(literal 1 binary64)))
(/.f64 (*.f64 (+.f64 #s(literal -1 binary64) (pow.f64 k #s(literal 3 binary64))) #s(literal 1/2 binary64)) (neg.f64 (fma.f64 (-.f64 #s(literal 1 binary64) k) k #s(literal 1 binary64))))
(/.f64 (.f64 #s(literal 1/2 binary64) (+.f64 #s(literal -1 binary64) (.f64 k k))) (-.f64 k #s(literal 1 binary64)))
(/.f64 (*.f64 #s(literal 1/2 binary64) (+.f64 #s(literal -1 binary64) (pow.f64 k #s(literal 3 binary64)))) (neg.f64 (fma.f64 (-.f64 #s(literal 1 binary64) k) k #s(literal 1 binary64))))
(/.f64 (.f64 #s(literal 1 binary64) (.f64 (fma.f64 (neg.f64 k) k #s(literal 1 binary64)) #s(literal 1/2 binary64))) (-.f64 #s(literal 1 binary64) k))
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(pow.f64 (exp.f64 (fma.f64 #s(literal 1/2 binary64) k #s(literal 1/2 binary64))) (log.f64 (.f64 n (.f64 (PI.f64) #s(literal 2 binary64)))))
(pow.f64 (pow.f64 (.f64 n (.f64 (PI.f64) #s(literal 2 binary64))) (*.f64 #s(literal -1/2 binary64) (-.f64 #s(literal 1 binary64) k))) #s(literal -1 binary64))
(pow.f64 (pow.f64 (.f64 n (.f64 (PI.f64) #s(literal 2 binary64))) (fma.f64 #s(literal 2 binary64) k #s(literal 2 binary64))) #s(literal 1/4 binary64))
(pow.f64 (pow.f64 (.f64 n (.f64 (PI.f64) #s(literal 2 binary64))) (-.f64 k #s(literal 1 binary64))) #s(literal -1/2 binary64))
(pow.f64 (pow.f64 (.f64 n (.f64 (PI.f64) #s(literal 2 binary64))) (fma.f64 (neg.f64 k) k #s(literal 1 binary64))) (*.f64 (pow.f64 (-.f64 #s(literal 1 binary64) k) #s(literal -1 binary64)) #s(literal 1/2 binary64)))
(pow.f64 (pow.f64 (.f64 n (.f64 (PI.f64) #s(literal 2 binary64))) (-.f64 #s(literal 1 binary64) (pow.f64 k #s(literal 3 binary64)))) (*.f64 (pow.f64 (fma.f64 (-.f64 #s(literal 1 binary64) k) k #s(literal 1 binary64)) #s(literal -1 binary64)) #s(literal 1/2 binary64)))
(pow.f64 (pow.f64 (.f64 n (.f64 (PI.f64) #s(literal 2 binary64))) (*.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 1/8 binary64))) #s(literal 4 binary64))
(pow.f64 (pow.f64 (.f64 n (.f64 (PI.f64) #s(literal 2 binary64))) #s(literal 2 binary64)) (.f64 (.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 1/8 binary64)) #s(literal 2 binary64)))
(pow.f64 (pow.f64 (.f64 n (.f64 (PI.f64) #s(literal 2 binary64))) #s(literal 2 binary64)) (*.f64 #s(literal 1/4 binary64) (-.f64 #s(literal 1 binary64) k)))
(pow.f64 (pow.f64 (.f64 n (.f64 (PI.f64) #s(literal 2 binary64))) (-.f64 #s(literal 1 binary64) k)) #s(literal 1/2 binary64))
(pow.f64 (sqrt.f64 (.f64 n (.f64 (PI.f64) #s(literal 2 binary64)))) (-.f64 #s(literal 1 binary64) k))
(pow.f64 (pow.f64 (.f64 n (.f64 (PI.f64) #s(literal 2 binary64))) (*.f64 #s(literal 1/4 binary64) (-.f64 #s(literal 1 binary64) k))) #s(literal 2 binary64))
(pow.f64 (pow.f64 (.f64 n (.f64 (PI.f64) #s(literal 2 binary64))) (fma.f64 #s(literal 1/2 binary64) k #s(literal 1/2 binary64))) #s(literal 1 binary64))
(pow.f64 (.f64 n (.f64 (PI.f64) #s(literal 2 binary64))) (.f64 (.f64 #s(literal 2 binary64) (*.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 1/8 binary64))) #s(literal 2 binary64)))
(pow.f64 (.f64 n (.f64 (PI.f64) #s(literal 2 binary64))) (.f64 (fma.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 1/8 binary64) (.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 1/8 binary64))) #s(literal 2 binary64)))
(pow.f64 (.f64 n (.f64 (PI.f64) #s(literal 2 binary64))) (fma.f64 #s(literal 1/2 binary64) k #s(literal 1/2 binary64)))
(/.f64 (pow.f64 (pow.f64 (.f64 n (.f64 (PI.f64) #s(literal 2 binary64))) #s(literal 2 binary64)) (/.f64 (pow.f64 (-.f64 #s(literal 1 binary64) k) #s(literal -1 binary64)) #s(literal 4 binary64))) (pow.f64 (pow.f64 (.f64 n (.f64 (PI.f64) #s(literal 2 binary64))) #s(literal 2 binary64)) (/.f64 (*.f64 k (/.f64 k (-.f64 #s(literal 1 binary64) k))) #s(literal 4 binary64))))
(/.f64 (pow.f64 (pow.f64 (.f64 n (.f64 (PI.f64) #s(literal 2 binary64))) #s(literal 2 binary64)) (/.f64 (pow.f64 (fma.f64 (-.f64 #s(literal 1 binary64) k) k #s(literal 1 binary64)) #s(literal -1 binary64)) #s(literal 4 binary64))) (pow.f64 (pow.f64 (.f64 n (.f64 (PI.f64) #s(literal 2 binary64))) #s(literal 2 binary64)) (/.f64 (/.f64 (pow.f64 k #s(literal 3 binary64)) (fma.f64 (-.f64 #s(literal 1 binary64) k) k #s(literal 1 binary64))) #s(literal 4 binary64))))
(/.f64 (pow.f64 (sqrt.f64 (.f64 n (.f64 (PI.f64) #s(literal 2 binary64)))) (pow.f64 (-.f64 #s(literal 1 binary64) k) #s(literal -1 binary64))) (pow.f64 (sqrt.f64 (.f64 n (.f64 (PI.f64) #s(literal 2 binary64)))) (*.f64 k (/.f64 k (-.f64 #s(literal 1 binary64) k)))))
(/.f64 (pow.f64 (sqrt.f64 (.f64 n (.f64 (PI.f64) #s(literal 2 binary64)))) (pow.f64 (fma.f64 (-.f64 #s(literal 1 binary64) k) k #s(literal 1 binary64)) #s(literal -1 binary64))) (pow.f64 (sqrt.f64 (.f64 n (.f64 (PI.f64) #s(literal 2 binary64)))) (/.f64 (pow.f64 k #s(literal 3 binary64)) (fma.f64 (-.f64 #s(literal 1 binary64) k) k #s(literal 1 binary64)))))
(/.f64 (pow.f64 (sqrt.f64 (.f64 n (.f64 (PI.f64) #s(literal 2 binary64)))) #s(literal 1 binary64)) (pow.f64 (sqrt.f64 (.f64 n (.f64 (PI.f64) #s(literal 2 binary64)))) k))
(/.f64 (pow.f64 (.f64 n (.f64 (PI.f64) #s(literal 2 binary64))) (fma.f64 #s(literal 1/4 binary64) (-.f64 #s(literal 1 binary64) k) #s(literal 1/4 binary64))) (pow.f64 (.f64 n (.f64 (PI.f64) #s(literal 2 binary64))) (*.f64 k #s(literal 1/4 binary64))))
(/.f64 (pow.f64 (.f64 n (.f64 (PI.f64) #s(literal 2 binary64))) (/.f64 #s(literal 1/4 binary64) (fma.f64 #s(literal 1/2 binary64) k #s(literal 1/2 binary64)))) (pow.f64 (.f64 n (.f64 (PI.f64) #s(literal 2 binary64))) (/.f64 (.f64 (.f64 k k) #s(literal 1/4 binary64)) (fma.f64 #s(literal 1/2 binary64) k #s(literal 1/2 binary64)))))
(/.f64 (pow.f64 (.f64 n (.f64 (PI.f64) #s(literal 2 binary64))) (/.f64 #s(literal 1/8 binary64) (fma.f64 (.f64 #s(literal 1/2 binary64) k) (fma.f64 #s(literal 1/2 binary64) k #s(literal 1/2 binary64)) #s(literal 1/4 binary64)))) (pow.f64 (.f64 n (.f64 (PI.f64) #s(literal 2 binary64))) (/.f64 (.f64 (pow.f64 k #s(literal 3 binary64)) #s(literal 1/8 binary64)) (fma.f64 (*.f64 #s(literal 1/2 binary64) k) (fma.f64 #s(literal 1/2 binary64) k #s(literal 1/2 binary64)) #s(literal 1/4 binary64)))))
(/.f64 (pow.f64 (.f64 n (.f64 (PI.f64) #s(literal 2 binary64))) (pow.f64 (fma.f64 #s(literal 2 binary64) k #s(literal 2 binary64)) #s(literal -1 binary64))) (pow.f64 (.f64 n (.f64 (PI.f64) #s(literal 2 binary64))) (/.f64 (*.f64 k k) (fma.f64 #s(literal 2 binary64) k #s(literal 2 binary64)))))
(/.f64 (pow.f64 (.f64 n (.f64 (PI.f64) #s(literal 2 binary64))) (pow.f64 (fma.f64 (fma.f64 k k k) #s(literal 2 binary64) #s(literal 2 binary64)) #s(literal -1 binary64))) (pow.f64 (.f64 n (.f64 (PI.f64) #s(literal 2 binary64))) (/.f64 (pow.f64 k #s(literal 3 binary64)) (fma.f64 (fma.f64 k k k) #s(literal 2 binary64) #s(literal 2 binary64)))))
(/.f64 (pow.f64 (.f64 n (.f64 (PI.f64) #s(literal 2 binary64))) (/.f64 (pow.f64 (-.f64 #s(literal 1 binary64) k) #s(literal -1 binary64)) #s(literal 2 binary64))) (pow.f64 (.f64 n (.f64 (PI.f64) #s(literal 2 binary64))) (/.f64 (*.f64 k (/.f64 k (-.f64 #s(literal 1 binary64) k))) #s(literal 2 binary64))))
(/.f64 (pow.f64 (.f64 n (.f64 (PI.f64) #s(literal 2 binary64))) (/.f64 (pow.f64 (fma.f64 (-.f64 #s(literal 1 binary64) k) k #s(literal 1 binary64)) #s(literal -1 binary64)) #s(literal 2 binary64))) (pow.f64 (.f64 n (.f64 (PI.f64) #s(literal 2 binary64))) (/.f64 (/.f64 (pow.f64 k #s(literal 3 binary64)) (fma.f64 (-.f64 #s(literal 1 binary64) k) k #s(literal 1 binary64))) #s(literal 2 binary64))))
(/.f64 (.f64 (sqrt.f64 n) (pow.f64 (.f64 (PI.f64) #s(literal 2 binary64)) (fma.f64 #s(literal 1/2 binary64) k #s(literal 1/2 binary64)))) (pow.f64 n (*.f64 #s(literal 1/2 binary64) k)))
(/.f64 (.f64 (sqrt.f64 (.f64 (PI.f64) #s(literal 2 binary64))) (pow.f64 n (fma.f64 #s(literal 1/2 binary64) k #s(literal 1/2 binary64)))) (pow.f64 (pow.f64 (*.f64 (PI.f64) #s(literal 2 binary64)) k) #s(literal 1/2 binary64)))
(/.f64 (.f64 (pow.f64 n (fma.f64 #s(literal 1/2 binary64) k #s(literal 1/2 binary64))) (sqrt.f64 (.f64 (PI.f64) #s(literal 2 binary64)))) (pow.f64 (pow.f64 (*.f64 (PI.f64) #s(literal 2 binary64)) k) #s(literal 1/2 binary64)))
(/.f64 (.f64 (pow.f64 (.f64 (PI.f64) #s(literal 2 binary64)) (fma.f64 #s(literal 1/2 binary64) k #s(literal 1/2 binary64))) (sqrt.f64 n)) (pow.f64 n (*.f64 #s(literal 1/2 binary64) k)))
(/.f64 (neg.f64 (sqrt.f64 (.f64 n (.f64 (PI.f64) #s(literal 2 binary64))))) (neg.f64 (pow.f64 (pow.f64 (.f64 n (.f64 (PI.f64) #s(literal 2 binary64))) k) #s(literal 1/2 binary64))))
(/.f64 (.f64 (sqrt.f64 (.f64 n (.f64 (PI.f64) #s(literal 2 binary64)))) #s(literal 1 binary64)) (pow.f64 (pow.f64 (.f64 n (*.f64 (PI.f64) #s(literal 2 binary64))) k) #s(literal 1/2 binary64)))
(/.f64 (.f64 #s(literal 1 binary64) (sqrt.f64 (.f64 n (.f64 (PI.f64) #s(literal 2 binary64))))) (pow.f64 (pow.f64 (.f64 n (*.f64 (PI.f64) #s(literal 2 binary64))) k) #s(literal 1/2 binary64)))
(/.f64 (pow.f64 (.f64 n (.f64 (PI.f64) #s(literal 2 binary64))) #s(literal 1/4 binary64)) (pow.f64 (.f64 n (.f64 (PI.f64) #s(literal 2 binary64))) (-.f64 (.f64 k #s(literal 1/4 binary64)) (.f64 #s(literal 1/4 binary64) (-.f64 #s(literal 1 binary64) k)))))
(/.f64 (sqrt.f64 (.f64 n (.f64 (PI.f64) #s(literal 2 binary64)))) (pow.f64 (pow.f64 (.f64 n (.f64 (PI.f64) #s(literal 2 binary64))) #s(literal 2 binary64)) (*.f64 k #s(literal 1/4 binary64))))
(/.f64 (sqrt.f64 (.f64 n (.f64 (PI.f64) #s(literal 2 binary64)))) (pow.f64 (pow.f64 (.f64 n (.f64 (PI.f64) #s(literal 2 binary64))) k) #s(literal 1/2 binary64)))
(/.f64 #s(literal 1 binary64) (pow.f64 (pow.f64 (.f64 n (.f64 (PI.f64) #s(literal 2 binary64))) #s(literal 2 binary64)) (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal -4 binary64))))
(/.f64 #s(literal 1 binary64) (pow.f64 (sqrt.f64 (.f64 n (.f64 (PI.f64) #s(literal 2 binary64)))) (-.f64 k #s(literal 1 binary64))))
(/.f64 #s(literal 1 binary64) (/.f64 (pow.f64 (pow.f64 (.f64 n (.f64 (PI.f64) #s(literal 2 binary64))) k) #s(literal 1/2 binary64)) (sqrt.f64 (.f64 n (.f64 (PI.f64) #s(literal 2 binary64))))))
(/.f64 #s(literal 1 binary64) (pow.f64 (.f64 n (.f64 (PI.f64) #s(literal 2 binary64))) (*.f64 #s(literal -1/2 binary64) (-.f64 #s(literal 1 binary64) k))))
(sqrt.f64 (pow.f64 (.f64 n (.f64 (PI.f64) #s(literal 2 binary64))) (-.f64 #s(literal 1 binary64) k)))
(exp.f64 (.f64 (log.f64 (exp.f64 (fma.f64 #s(literal 1/2 binary64) k #s(literal 1/2 binary64)))) (log.f64 (.f64 n (*.f64 (PI.f64) #s(literal 2 binary64))))))
(exp.f64 (.f64 (log.f64 (pow.f64 (.f64 n (*.f64 (PI.f64) #s(literal 2 binary64))) (fma.f64 #s(literal 2 binary64) k #s(literal 2 binary64)))) #s(literal 1/4 binary64)))
(exp.f64 (.f64 (log.f64 (pow.f64 (.f64 n (*.f64 (PI.f64) #s(literal 2 binary64))) (-.f64 k #s(literal 1 binary64)))) #s(literal -1/2 binary64)))
(exp.f64 (.f64 (log.f64 (sqrt.f64 (.f64 n (*.f64 (PI.f64) #s(literal 2 binary64))))) (-.f64 #s(literal 1 binary64) k)))
(exp.f64 (fma.f64 (.f64 #s(literal 1/4 binary64) (-.f64 #s(literal 1 binary64) k)) (log.f64 (.f64 n (.f64 (PI.f64) #s(literal 2 binary64)))) (.f64 (.f64 #s(literal 1/4 binary64) (-.f64 #s(literal 1 binary64) k)) (log.f64 (.f64 n (*.f64 (PI.f64) #s(literal 2 binary64)))))))
(exp.f64 (.f64 (.f64 (.f64 #s(literal 1/4 binary64) (-.f64 #s(literal 1 binary64) k)) (log.f64 (.f64 n (*.f64 (PI.f64) #s(literal 2 binary64))))) #s(literal 2 binary64)))
(exp.f64 (.f64 (log.f64 (pow.f64 (.f64 n (.f64 (PI.f64) #s(literal 2 binary64))) #s(literal 2 binary64))) (.f64 #s(literal 1/4 binary64) (-.f64 #s(literal 1 binary64) k))))
(exp.f64 (.f64 (log.f64 (.f64 n (*.f64 (PI.f64) #s(literal 2 binary64)))) (fma.f64 #s(literal 1/2 binary64) k #s(literal 1/2 binary64))))

eval88.0ms (0.9%)

Memory: 2.6MiB live, 165.6MiB allocated
Compiler: Compiled 11 182 to 1 552 computations (86.1% saved)

prune108.0ms (1.2%)

Memory

2.4MiB live, 168.1MiB allocated

Pruning

21 alts after pruning (21 fresh and 0 done)

	Pruned	Kept	Total
New	494	21	515
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	495	21	516

Accuracy

100.0%

Counts

516 → 21

Alt Table

Click to see full alt table

Status	Accuracy	Program
	49.7%	(/.f64 (pow.f64 (.f64 n (.f64 (PI.f64) #s(literal 2 binary64))) (fma.f64 #s(literal 1/2 binary64) k #s(literal 1/2 binary64))) (sqrt.f64 k))
	70.8%	(/.f64 (.f64 (/.f64 (pow.f64 (.f64 (PI.f64) #s(literal 2 binary64)) (fma.f64 #s(literal 1/2 binary64) k #s(literal 1/2 binary64))) (sqrt.f64 k)) (sqrt.f64 n)) (pow.f64 n (*.f64 #s(literal 1/2 binary64) k)))
▶	99.8%	(/.f64 (sqrt.f64 (.f64 n (.f64 (PI.f64) #s(literal 2 binary64)))) (.f64 (sqrt.f64 k) (pow.f64 (pow.f64 (.f64 n (*.f64 (PI.f64) #s(literal 2 binary64))) k) #s(literal 1/2 binary64))))
	49.6%	(/.f64 #s(literal 1 binary64) (/.f64 (sqrt.f64 k) (pow.f64 (.f64 n (.f64 (PI.f64) #s(literal 2 binary64))) (fma.f64 #s(literal 1/2 binary64) k #s(literal 1/2 binary64)))))
	49.2%	(.f64 (pow.f64 #s(literal 2 binary64) (fma.f64 #s(literal 1/2 binary64) k #s(literal 1/2 binary64))) (/.f64 (pow.f64 (.f64 n (PI.f64)) (fma.f64 #s(literal 1/2 binary64) k #s(literal 1/2 binary64))) (sqrt.f64 k)))
	49.2%	(.f64 (/.f64 (pow.f64 #s(literal 2 binary64) (fma.f64 #s(literal 1/2 binary64) k #s(literal 1/2 binary64))) (sqrt.f64 k)) (/.f64 (pow.f64 (.f64 n (PI.f64)) (fma.f64 #s(literal 1/2 binary64) k #s(literal 1/2 binary64))) #s(literal 1 binary64)))
▶	99.4%	(.f64 (/.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (pow.f64 k #s(literal -1/2 binary64)))) (pow.f64 (.f64 (*.f64 #s(literal 2 binary64) (PI.f64)) n) (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 2 binary64))))
	99.3%	(.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) (pow.f64 (.f64 (.f64 (.f64 n #s(literal 2 binary64)) (sqrt.f64 (PI.f64))) (sqrt.f64 (PI.f64))) (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 2 binary64))))
	99.4%	(.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) (pow.f64 (.f64 (*.f64 #s(literal 2 binary64) (PI.f64)) n) (fma.f64 k #s(literal -1/2 binary64) #s(literal 1/2 binary64))))
	52.8%	(.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) (pow.f64 (.f64 (.f64 #s(literal 2 binary64) (PI.f64)) n) #s(approx (/ (- 1 k) 2) (.f64 k #s(literal -1/2 binary64)))))
	50.2%	(.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) (pow.f64 (.f64 (*.f64 #s(literal 2 binary64) (PI.f64)) n) #s(approx (/ (- 1 k) 2) #s(literal 1/2 binary64))))
	99.4%	(.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) (/.f64 #s(literal 1 binary64) (pow.f64 (.f64 n (.f64 (PI.f64) #s(literal 2 binary64))) (.f64 #s(literal -1/2 binary64) (-.f64 #s(literal 1 binary64) k)))))
▶	99.3%	(.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) (/.f64 #s(literal 1 binary64) (pow.f64 (sqrt.f64 (.f64 n (*.f64 (PI.f64) #s(literal 2 binary64)))) (-.f64 k #s(literal 1 binary64)))))
	99.6%	(.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) (.f64 (pow.f64 (.f64 n (.f64 (PI.f64) #s(literal 2 binary64))) (.f64 k #s(literal -1/2 binary64))) (sqrt.f64 (.f64 n (*.f64 (PI.f64) #s(literal 2 binary64))))))
	99.4%	(.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) (sqrt.f64 (pow.f64 (.f64 n (*.f64 (PI.f64) #s(literal 2 binary64))) (-.f64 #s(literal 1 binary64) k))))
	50.6%	(.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) #s(approx (pow ( (* 2 (PI)) n) (/ (- 1 k) 2)) (.f64 (fma.f64 (log.f64 (.f64 (.f64 #s(literal 2 binary64) n) (PI.f64))) (.f64 k #s(literal -1/2 binary64)) #s(literal 1 binary64)) (.f64 (sqrt.f64 (.f64 (PI.f64) n)) (sqrt.f64 #s(literal 2 binary64))))))
	62.1%	(.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) #s(approx (pow ( (* 2 (PI)) n) (/ (- 1 k) 2)) (.f64 (sqrt.f64 (.f64 (PI.f64) n)) (fma.f64 k (.f64 (.f64 (log.f64 (.f64 (.f64 #s(literal 2 binary64) n) (PI.f64))) (sqrt.f64 #s(literal 2 binary64))) (fma.f64 (.f64 #s(literal 1/8 binary64) k) (log.f64 (.f64 (*.f64 #s(literal 2 binary64) n) (PI.f64))) #s(literal -1/2 binary64))) (sqrt.f64 #s(literal 2 binary64))))))
	50.1%	(.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) #s(approx (pow ( (* 2 (PI)) n) (/ (- 1 k) 2)) (.f64 (sqrt.f64 (.f64 (PI.f64) n)) (sqrt.f64 #s(literal 2 binary64)))))
	57.3%	#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (/.f64 (.f64 (sqrt.f64 #s(literal 2 binary64)) (fma.f64 (.f64 (log.f64 (.f64 (.f64 #s(literal 2 binary64) n) (PI.f64))) (sqrt.f64 (.f64 (.f64 (pow.f64 k #s(literal 3 binary64)) (PI.f64)) n))) #s(literal -1/2 binary64) (sqrt.f64 (.f64 (.f64 (PI.f64) n) k)))) k))
▶	99.5%	#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (.f64 (pow.f64 (.f64 (*.f64 #s(literal 2 binary64) n) (PI.f64)) (fma.f64 k #s(literal -1/2 binary64) #s(literal 1/2 binary64))) (sqrt.f64 (/.f64 #s(literal 1 binary64) k))))
▶	37.3%	#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (.f64 (sqrt.f64 #s(literal 2 binary64)) (sqrt.f64 (/.f64 (.f64 (PI.f64) n) k))))

Compiler

Compiled 774 to 618 computations (20.2% saved)

simplify17.0ms (0.2%)

Memory

-25.9MiB live, 15.8MiB allocated

Algorithm

1×	egg-herbie

Localize:

Found 20 expressions of interest:

New	Metric	Score
cost-diff	0	(/.f64 #s(literal 1 binary64) (pow.f64 k #s(literal -1/2 binary64)))
cost-diff	0	(.f64 (/.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (pow.f64 k #s(literal -1/2 binary64)))) (pow.f64 (.f64 (*.f64 #s(literal 2 binary64) (PI.f64)) n) (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 2 binary64))))
cost-diff	512	(/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 2 binary64))
cost-diff	1408	(/.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (pow.f64 k #s(literal -1/2 binary64))))
cost-diff	0	(/.f64 #s(literal 1 binary64) (pow.f64 (sqrt.f64 (.f64 n (.f64 (PI.f64) #s(literal 2 binary64)))) (-.f64 k #s(literal 1 binary64))))
cost-diff	0	(sqrt.f64 k)
cost-diff	0	(/.f64 #s(literal 1 binary64) (sqrt.f64 k))
cost-diff	320	(.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) (/.f64 #s(literal 1 binary64) (pow.f64 (sqrt.f64 (.f64 n (*.f64 (PI.f64) #s(literal 2 binary64)))) (-.f64 k #s(literal 1 binary64)))))
cost-diff	0	(.f64 (.f64 #s(literal 2 binary64) n) (PI.f64))
cost-diff	0	(pow.f64 (.f64 (.f64 #s(literal 2 binary64) n) (PI.f64)) (fma.f64 k #s(literal -1/2 binary64) #s(literal 1/2 binary64)))
cost-diff	0	(.f64 (pow.f64 (.f64 (*.f64 #s(literal 2 binary64) n) (PI.f64)) (fma.f64 k #s(literal -1/2 binary64) #s(literal 1/2 binary64))) (sqrt.f64 (/.f64 #s(literal 1 binary64) k)))
cost-diff	0	#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (.f64 (pow.f64 (.f64 (*.f64 #s(literal 2 binary64) n) (PI.f64)) (fma.f64 k #s(literal -1/2 binary64) #s(literal 1/2 binary64))) (sqrt.f64 (/.f64 #s(literal 1 binary64) k))))
cost-diff	0	(sqrt.f64 (/.f64 (*.f64 (PI.f64) n) k))
cost-diff	0	(sqrt.f64 #s(literal 2 binary64))
cost-diff	0	(.f64 (sqrt.f64 #s(literal 2 binary64)) (sqrt.f64 (/.f64 (.f64 (PI.f64) n) k)))
cost-diff	0	#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (.f64 (sqrt.f64 #s(literal 2 binary64)) (sqrt.f64 (/.f64 (.f64 (PI.f64) n) k))))
cost-diff	0	(*.f64 (PI.f64) #s(literal 2 binary64))
cost-diff	0	(.f64 n (.f64 (PI.f64) #s(literal 2 binary64)))
cost-diff	0	(sqrt.f64 (.f64 n (.f64 (PI.f64) #s(literal 2 binary64))))
cost-diff	5824	(pow.f64 (pow.f64 (.f64 n (.f64 (PI.f64) #s(literal 2 binary64))) k) #s(literal 1/2 binary64))

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	52	340
0	88	327
1	138	321
2	169	321
3	191	318
4	214	318
5	238	318
6	283	318
7	309	318
8	318	318
9	321	318
0	321	318

Stop Event

1×	iter limit
1×	saturated
1×	iter limit

Calls

Call 1

Inputs
(/.f64 (sqrt.f64 (.f64 n (.f64 (PI.f64) #s(literal 2 binary64)))) (.f64 (sqrt.f64 k) (pow.f64 (pow.f64 (.f64 n (*.f64 (PI.f64) #s(literal 2 binary64))) k) #s(literal 1/2 binary64))))
(sqrt.f64 (.f64 n (.f64 (PI.f64) #s(literal 2 binary64))))
(.f64 n (.f64 (PI.f64) #s(literal 2 binary64)))
n
(*.f64 (PI.f64) #s(literal 2 binary64))
(PI.f64)
#s(literal 2 binary64)
(.f64 (sqrt.f64 k) (pow.f64 (pow.f64 (.f64 n (*.f64 (PI.f64) #s(literal 2 binary64))) k) #s(literal 1/2 binary64)))
(sqrt.f64 k)
k
(pow.f64 (pow.f64 (.f64 n (.f64 (PI.f64) #s(literal 2 binary64))) k) #s(literal 1/2 binary64))
(pow.f64 (.f64 n (.f64 (PI.f64) #s(literal 2 binary64))) k)
#s(literal 1/2 binary64)
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (.f64 (sqrt.f64 #s(literal 2 binary64)) (sqrt.f64 (/.f64 (.f64 (PI.f64) n) k))))
(.f64 (sqrt.f64 #s(literal 2 binary64)) (sqrt.f64 (/.f64 (.f64 (PI.f64) n) k)))
(sqrt.f64 #s(literal 2 binary64))
#s(literal 2 binary64)
(sqrt.f64 (/.f64 (*.f64 (PI.f64) n) k))
(/.f64 (*.f64 (PI.f64) n) k)
(*.f64 (PI.f64) n)
(PI.f64)
n
k
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (.f64 (pow.f64 (.f64 (*.f64 #s(literal 2 binary64) n) (PI.f64)) (fma.f64 k #s(literal -1/2 binary64) #s(literal 1/2 binary64))) (sqrt.f64 (/.f64 #s(literal 1 binary64) k))))
(.f64 (pow.f64 (.f64 (*.f64 #s(literal 2 binary64) n) (PI.f64)) (fma.f64 k #s(literal -1/2 binary64) #s(literal 1/2 binary64))) (sqrt.f64 (/.f64 #s(literal 1 binary64) k)))
(pow.f64 (.f64 (.f64 #s(literal 2 binary64) n) (PI.f64)) (fma.f64 k #s(literal -1/2 binary64) #s(literal 1/2 binary64)))
(.f64 (.f64 #s(literal 2 binary64) n) (PI.f64))
(*.f64 #s(literal 2 binary64) n)
#s(literal 2 binary64)
n
(PI.f64)
(fma.f64 k #s(literal -1/2 binary64) #s(literal 1/2 binary64))
k
#s(literal -1/2 binary64)
#s(literal 1/2 binary64)
(sqrt.f64 (/.f64 #s(literal 1 binary64) k))
(/.f64 #s(literal 1 binary64) k)
#s(literal 1 binary64)
(.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) (/.f64 #s(literal 1 binary64) (pow.f64 (sqrt.f64 (.f64 n (*.f64 (PI.f64) #s(literal 2 binary64)))) (-.f64 k #s(literal 1 binary64)))))
(/.f64 #s(literal 1 binary64) (sqrt.f64 k))
#s(literal 1 binary64)
(sqrt.f64 k)
k
(/.f64 #s(literal 1 binary64) (pow.f64 (sqrt.f64 (.f64 n (.f64 (PI.f64) #s(literal 2 binary64)))) (-.f64 k #s(literal 1 binary64))))
(pow.f64 (sqrt.f64 (.f64 n (.f64 (PI.f64) #s(literal 2 binary64)))) (-.f64 k #s(literal 1 binary64)))
(sqrt.f64 (.f64 n (.f64 (PI.f64) #s(literal 2 binary64))))
(.f64 n (.f64 (PI.f64) #s(literal 2 binary64)))
n
(*.f64 (PI.f64) #s(literal 2 binary64))
(PI.f64)
#s(literal 2 binary64)
(-.f64 k #s(literal 1 binary64))
(.f64 (/.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (pow.f64 k #s(literal -1/2 binary64)))) (pow.f64 (.f64 (*.f64 #s(literal 2 binary64) (PI.f64)) n) (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 2 binary64))))
(/.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (pow.f64 k #s(literal -1/2 binary64))))
#s(literal 1 binary64)
(/.f64 #s(literal 1 binary64) (pow.f64 k #s(literal -1/2 binary64)))
(pow.f64 k #s(literal -1/2 binary64))
k
#s(literal -1/2 binary64)
(pow.f64 (.f64 (.f64 #s(literal 2 binary64) (PI.f64)) n) (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 2 binary64)))
(.f64 (.f64 #s(literal 2 binary64) (PI.f64)) n)
(*.f64 #s(literal 2 binary64) (PI.f64))
#s(literal 2 binary64)
(PI.f64)
n
(/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 2 binary64))
(-.f64 #s(literal 1 binary64) k)

Outputs
(/.f64 (sqrt.f64 (.f64 n (.f64 (PI.f64) #s(literal 2 binary64)))) (.f64 (sqrt.f64 k) (pow.f64 (pow.f64 (.f64 n (*.f64 (PI.f64) #s(literal 2 binary64))) k) #s(literal 1/2 binary64))))
(/.f64 (/.f64 (sqrt.f64 (.f64 (.f64 #s(literal 2 binary64) (PI.f64)) n)) (sqrt.f64 k)) (sqrt.f64 (pow.f64 (.f64 (.f64 #s(literal 2 binary64) (PI.f64)) n) k)))
(sqrt.f64 (.f64 n (.f64 (PI.f64) #s(literal 2 binary64))))
(sqrt.f64 (.f64 (.f64 #s(literal 2 binary64) (PI.f64)) n))
(.f64 n (.f64 (PI.f64) #s(literal 2 binary64)))
(.f64 (.f64 #s(literal 2 binary64) (PI.f64)) n)
n
(*.f64 (PI.f64) #s(literal 2 binary64))
(*.f64 #s(literal 2 binary64) (PI.f64))
(PI.f64)
#s(literal 2 binary64)
(.f64 (sqrt.f64 k) (pow.f64 (pow.f64 (.f64 n (*.f64 (PI.f64) #s(literal 2 binary64))) k) #s(literal 1/2 binary64)))
(.f64 (sqrt.f64 (pow.f64 (.f64 (*.f64 #s(literal 2 binary64) (PI.f64)) n) k)) (sqrt.f64 k))
(sqrt.f64 k)
k
(pow.f64 (pow.f64 (.f64 n (.f64 (PI.f64) #s(literal 2 binary64))) k) #s(literal 1/2 binary64))
(sqrt.f64 (pow.f64 (.f64 (.f64 #s(literal 2 binary64) (PI.f64)) n) k))
(pow.f64 (.f64 n (.f64 (PI.f64) #s(literal 2 binary64))) k)
(pow.f64 (.f64 (.f64 #s(literal 2 binary64) (PI.f64)) n) k)
#s(literal 1/2 binary64)
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (.f64 (sqrt.f64 #s(literal 2 binary64)) (sqrt.f64 (/.f64 (.f64 (PI.f64) n) k))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (.f64 (sqrt.f64 (/.f64 (.f64 (PI.f64) n) k)) (sqrt.f64 #s(literal 2 binary64))))
(.f64 (sqrt.f64 #s(literal 2 binary64)) (sqrt.f64 (/.f64 (.f64 (PI.f64) n) k)))
(.f64 (sqrt.f64 (/.f64 (.f64 (PI.f64) n) k)) (sqrt.f64 #s(literal 2 binary64)))
(sqrt.f64 #s(literal 2 binary64))
#s(literal 2 binary64)
(sqrt.f64 (/.f64 (*.f64 (PI.f64) n) k))
(/.f64 (*.f64 (PI.f64) n) k)
(*.f64 (PI.f64) n)
(PI.f64)
n
k
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (.f64 (pow.f64 (.f64 (*.f64 #s(literal 2 binary64) n) (PI.f64)) (fma.f64 k #s(literal -1/2 binary64) #s(literal 1/2 binary64))) (sqrt.f64 (/.f64 #s(literal 1 binary64) k))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (.f64 (pow.f64 (.f64 (*.f64 #s(literal 2 binary64) (PI.f64)) n) (fma.f64 #s(literal -1/2 binary64) k #s(literal 1/2 binary64))) (sqrt.f64 (/.f64 #s(literal 1 binary64) k))))
(.f64 (pow.f64 (.f64 (*.f64 #s(literal 2 binary64) n) (PI.f64)) (fma.f64 k #s(literal -1/2 binary64) #s(literal 1/2 binary64))) (sqrt.f64 (/.f64 #s(literal 1 binary64) k)))
(.f64 (pow.f64 (.f64 (*.f64 #s(literal 2 binary64) (PI.f64)) n) (fma.f64 #s(literal -1/2 binary64) k #s(literal 1/2 binary64))) (sqrt.f64 (/.f64 #s(literal 1 binary64) k)))
(pow.f64 (.f64 (.f64 #s(literal 2 binary64) n) (PI.f64)) (fma.f64 k #s(literal -1/2 binary64) #s(literal 1/2 binary64)))
(pow.f64 (.f64 (.f64 #s(literal 2 binary64) (PI.f64)) n) (fma.f64 #s(literal -1/2 binary64) k #s(literal 1/2 binary64)))
(.f64 (.f64 #s(literal 2 binary64) n) (PI.f64))
(.f64 (.f64 #s(literal 2 binary64) (PI.f64)) n)
(*.f64 #s(literal 2 binary64) n)
#s(literal 2 binary64)
n
(PI.f64)
(fma.f64 k #s(literal -1/2 binary64) #s(literal 1/2 binary64))
(fma.f64 #s(literal -1/2 binary64) k #s(literal 1/2 binary64))
k
#s(literal -1/2 binary64)
#s(literal 1/2 binary64)
(sqrt.f64 (/.f64 #s(literal 1 binary64) k))
(/.f64 #s(literal 1 binary64) k)
#s(literal 1 binary64)
(.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) (/.f64 #s(literal 1 binary64) (pow.f64 (sqrt.f64 (.f64 n (*.f64 (PI.f64) #s(literal 2 binary64)))) (-.f64 k #s(literal 1 binary64)))))
(/.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) (pow.f64 (sqrt.f64 (.f64 (.f64 #s(literal 2 binary64) (PI.f64)) n)) (-.f64 k #s(literal 1 binary64))))
(/.f64 #s(literal 1 binary64) (sqrt.f64 k))
#s(literal 1 binary64)
(sqrt.f64 k)
k
(/.f64 #s(literal 1 binary64) (pow.f64 (sqrt.f64 (.f64 n (.f64 (PI.f64) #s(literal 2 binary64)))) (-.f64 k #s(literal 1 binary64))))
(/.f64 #s(literal 1 binary64) (pow.f64 (sqrt.f64 (.f64 (.f64 #s(literal 2 binary64) (PI.f64)) n)) (-.f64 k #s(literal 1 binary64))))
(pow.f64 (sqrt.f64 (.f64 n (.f64 (PI.f64) #s(literal 2 binary64)))) (-.f64 k #s(literal 1 binary64)))
(pow.f64 (sqrt.f64 (.f64 (.f64 #s(literal 2 binary64) (PI.f64)) n)) (-.f64 k #s(literal 1 binary64)))
(sqrt.f64 (.f64 n (.f64 (PI.f64) #s(literal 2 binary64))))
(sqrt.f64 (.f64 (.f64 #s(literal 2 binary64) (PI.f64)) n))
(.f64 n (.f64 (PI.f64) #s(literal 2 binary64)))
(.f64 (.f64 #s(literal 2 binary64) (PI.f64)) n)
n
(*.f64 (PI.f64) #s(literal 2 binary64))
(*.f64 #s(literal 2 binary64) (PI.f64))
(PI.f64)
#s(literal 2 binary64)
(-.f64 k #s(literal 1 binary64))
(.f64 (/.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (pow.f64 k #s(literal -1/2 binary64)))) (pow.f64 (.f64 (*.f64 #s(literal 2 binary64) (PI.f64)) n) (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 2 binary64))))
(.f64 (pow.f64 (.f64 (*.f64 #s(literal 2 binary64) (PI.f64)) n) (fma.f64 #s(literal -1/2 binary64) k #s(literal 1/2 binary64))) (pow.f64 k #s(literal -1/2 binary64)))
(/.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (pow.f64 k #s(literal -1/2 binary64))))
(pow.f64 k #s(literal -1/2 binary64))
#s(literal 1 binary64)
(/.f64 #s(literal 1 binary64) (pow.f64 k #s(literal -1/2 binary64)))
(pow.f64 k #s(literal -1/2 binary64))
k
#s(literal -1/2 binary64)
(pow.f64 (.f64 (.f64 #s(literal 2 binary64) (PI.f64)) n) (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 2 binary64)))
(pow.f64 (.f64 (.f64 #s(literal 2 binary64) (PI.f64)) n) (fma.f64 #s(literal -1/2 binary64) k #s(literal 1/2 binary64)))
(.f64 (.f64 #s(literal 2 binary64) (PI.f64)) n)
(*.f64 #s(literal 2 binary64) (PI.f64))
#s(literal 2 binary64)
(PI.f64)
n
(/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 2 binary64))
(fma.f64 #s(literal -1/2 binary64) k #s(literal 1/2 binary64))
(-.f64 #s(literal 1 binary64) k)

localize142.0ms (1.5%)

Memory

37.2MiB live, 227.7MiB allocated

Localize:

Found 20 expressions of interest:

New	Metric	Score
accuracy	0.19140625	(.f64 (.f64 #s(literal 2 binary64) (PI.f64)) n)
accuracy	0.205410009768442	(.f64 (/.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (pow.f64 k #s(literal -1/2 binary64)))) (pow.f64 (.f64 (*.f64 #s(literal 2 binary64) (PI.f64)) n) (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 2 binary64))))
accuracy	0.22818734794137574	(pow.f64 (.f64 (.f64 #s(literal 2 binary64) (PI.f64)) n) (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 2 binary64)))
accuracy	13.562169815496654	(PI.f64)
accuracy	0.19140625	(.f64 n (.f64 (PI.f64) #s(literal 2 binary64)))
accuracy	0.205410009768442	(.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) (/.f64 #s(literal 1 binary64) (pow.f64 (sqrt.f64 (.f64 n (*.f64 (PI.f64) #s(literal 2 binary64)))) (-.f64 k #s(literal 1 binary64)))))
accuracy	0.3032001213941556	(pow.f64 (sqrt.f64 (.f64 n (.f64 (PI.f64) #s(literal 2 binary64)))) (-.f64 k #s(literal 1 binary64)))
accuracy	13.562169815496654	(PI.f64)
accuracy	0.19140625	(.f64 (.f64 #s(literal 2 binary64) n) (PI.f64))
accuracy	0.205410009768442	(.f64 (pow.f64 (.f64 (*.f64 #s(literal 2 binary64) n) (PI.f64)) (fma.f64 k #s(literal -1/2 binary64) #s(literal 1/2 binary64))) (sqrt.f64 (/.f64 #s(literal 1 binary64) k)))
accuracy	0.22818734794137574	(pow.f64 (.f64 (.f64 #s(literal 2 binary64) n) (PI.f64)) (fma.f64 k #s(literal -1/2 binary64) #s(literal 1/2 binary64)))
accuracy	13.562169815496654	(PI.f64)
accuracy	0.34212875976844204	(.f64 (sqrt.f64 #s(literal 2 binary64)) (sqrt.f64 (/.f64 (.f64 (PI.f64) n) k)))
accuracy	8.329928742813173	(sqrt.f64 (/.f64 (*.f64 (PI.f64) n) k))
accuracy	13.562169815496654	(PI.f64)
accuracy	17.975855259551754	#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (.f64 (sqrt.f64 #s(literal 2 binary64)) (sqrt.f64 (/.f64 (.f64 (PI.f64) n) k))))
accuracy	0.10546875	(sqrt.f64 (.f64 n (.f64 (PI.f64) #s(literal 2 binary64))))
accuracy	0.16472626953688405	(/.f64 (sqrt.f64 (.f64 n (.f64 (PI.f64) #s(literal 2 binary64)))) (.f64 (sqrt.f64 k) (pow.f64 (pow.f64 (.f64 n (*.f64 (PI.f64) #s(literal 2 binary64))) k) #s(literal 1/2 binary64))))
accuracy	0.19140625	(.f64 n (.f64 (PI.f64) #s(literal 2 binary64)))
accuracy	13.562169815496654	(PI.f64)

Samples

86.0ms	200×	0	valid
24.0ms	56×	0	exit

Compiler

Compiled 319 to 45 computations (85.9% saved)

Precisions

Click to see histograms. Total time spent on operations: 85.0ms

ival-pow: 25.0ms (29.2% of total)

ival-mult: 24.0ms (28.1% of total)

ival-div: 18.0ms (21.1% of total)

ival-sqrt: 12.0ms (14% of total)

ival-sub: 3.0ms (3.5% of total)

ival-pi: 1.0ms (1.2% of total)

ival-add: 1.0ms (1.2% of total)

exact: 1.0ms (1.2% of total)

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

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

series175.0ms (1.9%)

Memory

2.5MiB live, 275.8MiB allocated

Counts

25 → 420

Calls

Call 1

Inputs
#s(alt (pow.f64 (pow.f64 (.f64 n (.f64 (PI.f64) #s(literal 2 binary64))) k) #s(literal 1/2 binary64)) (patch (pow.f64 (pow.f64 (.f64 n (.f64 (PI.f64) #s(literal 2 binary64))) k) #s(literal 1/2 binary64)) #<representation binary64>) () ())
#s(alt (sqrt.f64 (.f64 n (.f64 (PI.f64) #s(literal 2 binary64)))) (patch (sqrt.f64 (.f64 n (.f64 (PI.f64) #s(literal 2 binary64)))) #<representation binary64>) () ())
#s(alt (.f64 n (.f64 (PI.f64) #s(literal 2 binary64))) (patch (.f64 n (.f64 (PI.f64) #s(literal 2 binary64))) #<representation binary64>) () ())
#s(alt (.f64 (PI.f64) #s(literal 2 binary64)) (patch (.f64 (PI.f64) #s(literal 2 binary64)) #<representation binary64>) () ())
#s(alt #s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (.f64 (sqrt.f64 #s(literal 2 binary64)) (sqrt.f64 (/.f64 (.f64 (PI.f64) n) k)))) (patch #s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (.f64 (sqrt.f64 #s(literal 2 binary64)) (sqrt.f64 (/.f64 (.f64 (PI.f64) n) k)))) #<representation binary64>) () ())
#s(alt (.f64 (sqrt.f64 #s(literal 2 binary64)) (sqrt.f64 (/.f64 (.f64 (PI.f64) n) k))) (patch (.f64 (sqrt.f64 #s(literal 2 binary64)) (sqrt.f64 (/.f64 (.f64 (PI.f64) n) k))) #<representation binary64>) () ())
#s(alt (sqrt.f64 #s(literal 2 binary64)) (patch (sqrt.f64 #s(literal 2 binary64)) #<representation binary64>) () ())
#s(alt (sqrt.f64 (/.f64 (.f64 (PI.f64) n) k)) (patch (sqrt.f64 (/.f64 (.f64 (PI.f64) n) k)) #<representation binary64>) () ())
#s(alt #s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (.f64 (pow.f64 (.f64 (.f64 #s(literal 2 binary64) n) (PI.f64)) (fma.f64 k #s(literal -1/2 binary64) #s(literal 1/2 binary64))) (sqrt.f64 (/.f64 #s(literal 1 binary64) k)))) (patch #s(approx ( (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (.f64 (pow.f64 (.f64 (*.f64 #s(literal 2 binary64) n) (PI.f64)) (fma.f64 k #s(literal -1/2 binary64) #s(literal 1/2 binary64))) (sqrt.f64 (/.f64 #s(literal 1 binary64) k)))) #<representation binary64>) () ())
#s(alt (.f64 (pow.f64 (.f64 (.f64 #s(literal 2 binary64) n) (PI.f64)) (fma.f64 k #s(literal -1/2 binary64) #s(literal 1/2 binary64))) (sqrt.f64 (/.f64 #s(literal 1 binary64) k))) (patch (.f64 (pow.f64 (.f64 (.f64 #s(literal 2 binary64) n) (PI.f64)) (fma.f64 k #s(literal -1/2 binary64) #s(literal 1/2 binary64))) (sqrt.f64 (/.f64 #s(literal 1 binary64) k))) #<representation binary64>) () ())
#s(alt (pow.f64 (.f64 (.f64 #s(literal 2 binary64) n) (PI.f64)) (fma.f64 k #s(literal -1/2 binary64) #s(literal 1/2 binary64))) (patch (pow.f64 (.f64 (.f64 #s(literal 2 binary64) n) (PI.f64)) (fma.f64 k #s(literal -1/2 binary64) #s(literal 1/2 binary64))) #<representation binary64>) () ())
#s(alt (.f64 (.f64 #s(literal 2 binary64) n) (PI.f64)) (patch (.f64 (.f64 #s(literal 2 binary64) n) (PI.f64)) #<representation binary64>) () ())
#s(alt (.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) (/.f64 #s(literal 1 binary64) (pow.f64 (sqrt.f64 (.f64 n (.f64 (PI.f64) #s(literal 2 binary64)))) (-.f64 k #s(literal 1 binary64))))) (patch (.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) (/.f64 #s(literal 1 binary64) (pow.f64 (sqrt.f64 (.f64 n (.f64 (PI.f64) #s(literal 2 binary64)))) (-.f64 k #s(literal 1 binary64))))) #<representation binary64>) () ())
#s(alt (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) (patch (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) #<representation binary64>) () ())
#s(alt (sqrt.f64 k) (patch (sqrt.f64 k) #<representation binary64>) () ())
#s(alt (/.f64 #s(literal 1 binary64) (pow.f64 (sqrt.f64 (.f64 n (.f64 (PI.f64) #s(literal 2 binary64)))) (-.f64 k #s(literal 1 binary64)))) (patch (/.f64 #s(literal 1 binary64) (pow.f64 (sqrt.f64 (.f64 n (.f64 (PI.f64) #s(literal 2 binary64)))) (-.f64 k #s(literal 1 binary64)))) #<representation binary64>) () ())
#s(alt (/.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (pow.f64 k #s(literal -1/2 binary64)))) (patch (/.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (pow.f64 k #s(literal -1/2 binary64)))) #<representation binary64>) () ())
#s(alt (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 2 binary64)) (patch (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 2 binary64)) #<representation binary64>) () ())
#s(alt (.f64 (/.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (pow.f64 k #s(literal -1/2 binary64)))) (pow.f64 (.f64 (.f64 #s(literal 2 binary64) (PI.f64)) n) (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 2 binary64)))) (patch (.f64 (/.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (pow.f64 k #s(literal -1/2 binary64)))) (pow.f64 (.f64 (.f64 #s(literal 2 binary64) (PI.f64)) n) (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 2 binary64)))) #<representation binary64>) () ())
#s(alt (/.f64 #s(literal 1 binary64) (pow.f64 k #s(literal -1/2 binary64))) (patch (/.f64 #s(literal 1 binary64) (pow.f64 k #s(literal -1/2 binary64))) #<representation binary64>) () ())
#s(alt (PI.f64) (patch (PI.f64) #<representation binary64>) () ())
#s(alt (/.f64 (sqrt.f64 (.f64 n (.f64 (PI.f64) #s(literal 2 binary64)))) (.f64 (sqrt.f64 k) (pow.f64 (pow.f64 (.f64 n (.f64 (PI.f64) #s(literal 2 binary64))) k) #s(literal 1/2 binary64)))) (patch (/.f64 (sqrt.f64 (.f64 n (.f64 (PI.f64) #s(literal 2 binary64)))) (.f64 (sqrt.f64 k) (pow.f64 (pow.f64 (.f64 n (.f64 (PI.f64) #s(literal 2 binary64))) k) #s(literal 1/2 binary64)))) #<representation binary64>) () ())
#s(alt (pow.f64 (sqrt.f64 (.f64 n (.f64 (PI.f64) #s(literal 2 binary64)))) (-.f64 k #s(literal 1 binary64))) (patch (pow.f64 (sqrt.f64 (.f64 n (.f64 (PI.f64) #s(literal 2 binary64)))) (-.f64 k #s(literal 1 binary64))) #<representation binary64>) () ())
#s(alt (pow.f64 (.f64 (.f64 #s(literal 2 binary64) (PI.f64)) n) (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 2 binary64))) (patch (pow.f64 (.f64 (.f64 #s(literal 2 binary64) (PI.f64)) n) (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 2 binary64))) #<representation binary64>) () ())
#s(alt (.f64 (.f64 #s(literal 2 binary64) (PI.f64)) n) (patch (.f64 (.f64 #s(literal 2 binary64) (PI.f64)) n) #<representation binary64>) () ())

Outputs
#s(alt 1 (taylor 0 k) (#s(alt (pow.f64 (pow.f64 (.f64 n (.f64 (PI.f64) #s(literal 2 binary64))) k) #s(literal 1/2 binary64)) (patch (pow.f64 (pow.f64 (.f64 n (.f64 (PI.f64) #s(literal 2 binary64))) k) #s(literal 1/2 binary64)) #<representation binary64>) () ())) ())
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#s(alt (+ 1 (* k (+ (* 1/2 (log (* 2 (* n (PI))))) (* 1/2 (* k (- (* 1/2 (pow (log (* 2 (* n (PI)))) 2)) (* 1/4 (pow (log (* 2 (* n (PI)))) 2)))))))) (taylor 0 k) (#s(alt (pow.f64 (pow.f64 (.f64 n (.f64 (PI.f64) #s(literal 2 binary64))) k) #s(literal 1/2 binary64)) (patch (pow.f64 (pow.f64 (.f64 n (.f64 (PI.f64) #s(literal 2 binary64))) k) #s(literal 1/2 binary64)) #<representation binary64>) () ())) ())
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#s(alt (/ (+ (* k (+ (* -1/2 (* (sqrt (* k (* n (PI)))) (* (log (* 2 (* n (PI)))) (sqrt 2)))) (* k (+ (* -1/48 (* (sqrt (* (pow k 3) (* n (PI)))) (* (pow (log (* 2 (* n (PI)))) 3) (sqrt 2)))) (* 1/8 (* (sqrt (* k (* n (PI)))) (* (pow (log (* 2 (* n (PI)))) 2) (sqrt 2)))))))) (* (sqrt (* k (* n (PI)))) (sqrt 2))) k) (taylor 0 k) (#s(alt #s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (.f64 (sqrt.f64 #s(literal 2 binary64)) (sqrt.f64 (/.f64 (.f64 (PI.f64) n) k)))) (patch #s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (.f64 (sqrt.f64 #s(literal 2 binary64)) (sqrt.f64 (/.f64 (.f64 (PI.f64) n) k)))) #<representation binary64>) () ())) ())
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#s(alt (* (sqrt (/ (* n (PI)) k)) (sqrt 2)) (taylor 0 k) (#s(alt (.f64 (sqrt.f64 #s(literal 2 binary64)) (sqrt.f64 (/.f64 (.f64 (PI.f64) n) k))) (patch (.f64 (sqrt.f64 #s(literal 2 binary64)) (sqrt.f64 (/.f64 (.f64 (PI.f64) n) k))) #<representation binary64>) () ())) ())
#s(alt (* (sqrt (/ (* n (PI)) k)) (sqrt 2)) (taylor 0 k) (#s(alt (.f64 (sqrt.f64 #s(literal 2 binary64)) (sqrt.f64 (/.f64 (.f64 (PI.f64) n) k))) (patch (.f64 (sqrt.f64 #s(literal 2 binary64)) (sqrt.f64 (/.f64 (.f64 (PI.f64) n) k))) #<representation binary64>) () ())) ())
#s(alt (* (sqrt (/ (* n (PI)) k)) (sqrt 2)) (taylor 0 k) (#s(alt (.f64 (sqrt.f64 #s(literal 2 binary64)) (sqrt.f64 (/.f64 (.f64 (PI.f64) n) k))) (patch (.f64 (sqrt.f64 #s(literal 2 binary64)) (sqrt.f64 (/.f64 (.f64 (PI.f64) n) k))) #<representation binary64>) () ())) ())
#s(alt (sqrt (/ (* n (PI)) k)) (taylor 0 k) (#s(alt (sqrt.f64 (/.f64 (.f64 (PI.f64) n) k)) (patch (sqrt.f64 (/.f64 (.f64 (PI.f64) n) k)) #<representation binary64>) () ())) ())
#s(alt (sqrt (/ (* n (PI)) k)) (taylor 0 k) (#s(alt (sqrt.f64 (/.f64 (.f64 (PI.f64) n) k)) (patch (sqrt.f64 (/.f64 (.f64 (PI.f64) n) k)) #<representation binary64>) () ())) ())
#s(alt (sqrt (/ (* n (PI)) k)) (taylor 0 k) (#s(alt (sqrt.f64 (/.f64 (.f64 (PI.f64) n) k)) (patch (sqrt.f64 (/.f64 (.f64 (PI.f64) n) k)) #<representation binary64>) () ())) ())
#s(alt (sqrt (/ (* n (PI)) k)) (taylor 0 k) (#s(alt (sqrt.f64 (/.f64 (.f64 (PI.f64) n) k)) (patch (sqrt.f64 (/.f64 (.f64 (PI.f64) n) k)) #<representation binary64>) () ())) ())
#s(alt (* (sqrt (/ (* n (PI)) k)) (sqrt 2)) (taylor 0 k) (#s(alt #s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (.f64 (pow.f64 (.f64 (.f64 #s(literal 2 binary64) n) (PI.f64)) (fma.f64 k #s(literal -1/2 binary64) #s(literal 1/2 binary64))) (sqrt.f64 (/.f64 #s(literal 1 binary64) k)))) (patch #s(approx ( (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (.f64 (pow.f64 (.f64 (*.f64 #s(literal 2 binary64) n) (PI.f64)) (fma.f64 k #s(literal -1/2 binary64) #s(literal 1/2 binary64))) (sqrt.f64 (/.f64 #s(literal 1 binary64) k)))) #<representation binary64>) () ())) ())
#s(alt (/ (+ (* -1/2 (* (sqrt (* (pow k 3) (* n (PI)))) (* (log (* 2 (* n (PI)))) (sqrt 2)))) (* (sqrt (* k (* n (PI)))) (sqrt 2))) k) (taylor 0 k) (#s(alt #s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (.f64 (pow.f64 (.f64 (.f64 #s(literal 2 binary64) n) (PI.f64)) (fma.f64 k #s(literal -1/2 binary64) #s(literal 1/2 binary64))) (sqrt.f64 (/.f64 #s(literal 1 binary64) k)))) (patch #s(approx ( (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (.f64 (pow.f64 (.f64 (*.f64 #s(literal 2 binary64) n) (PI.f64)) (fma.f64 k #s(literal -1/2 binary64) #s(literal 1/2 binary64))) (sqrt.f64 (/.f64 #s(literal 1 binary64) k)))) #<representation binary64>) () ())) ())
#s(alt (/ (+ (* k (+ (* -1/2 (* (sqrt (* k (* n (PI)))) (* (log (* 2 (* n (PI)))) (sqrt 2)))) (* 1/8 (* (sqrt (* (pow k 3) (* n (PI)))) (* (pow (log (* 2 (* n (PI)))) 2) (sqrt 2)))))) (* (sqrt (* k (* n (PI)))) (sqrt 2))) k) (taylor 0 k) (#s(alt #s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (.f64 (pow.f64 (.f64 (.f64 #s(literal 2 binary64) n) (PI.f64)) (fma.f64 k #s(literal -1/2 binary64) #s(literal 1/2 binary64))) (sqrt.f64 (/.f64 #s(literal 1 binary64) k)))) (patch #s(approx ( (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (.f64 (pow.f64 (.f64 (*.f64 #s(literal 2 binary64) n) (PI.f64)) (fma.f64 k #s(literal -1/2 binary64) #s(literal 1/2 binary64))) (sqrt.f64 (/.f64 #s(literal 1 binary64) k)))) #<representation binary64>) () ())) ())
#s(alt (/ (+ (* k (+ (* -1/2 (* (sqrt (* k (* n (PI)))) (* (log (* 2 (* n (PI)))) (sqrt 2)))) (* k (+ (* -1/48 (* (sqrt (* (pow k 3) (* n (PI)))) (* (pow (log (* 2 (* n (PI)))) 3) (sqrt 2)))) (* 1/8 (* (sqrt (* k (* n (PI)))) (* (pow (log (* 2 (* n (PI)))) 2) (sqrt 2)))))))) (* (sqrt (* k (* n (PI)))) (sqrt 2))) k) (taylor 0 k) (#s(alt #s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (.f64 (pow.f64 (.f64 (.f64 #s(literal 2 binary64) n) (PI.f64)) (fma.f64 k #s(literal -1/2 binary64) #s(literal 1/2 binary64))) (sqrt.f64 (/.f64 #s(literal 1 binary64) k)))) (patch #s(approx ( (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (.f64 (pow.f64 (.f64 (*.f64 #s(literal 2 binary64) n) (PI.f64)) (fma.f64 k #s(literal -1/2 binary64) #s(literal 1/2 binary64))) (sqrt.f64 (/.f64 #s(literal 1 binary64) k)))) #<representation binary64>) () ())) ())
#s(alt (* (sqrt (/ (* n (PI)) k)) (sqrt 2)) (taylor 0 k) (#s(alt (.f64 (pow.f64 (.f64 (.f64 #s(literal 2 binary64) n) (PI.f64)) (fma.f64 k #s(literal -1/2 binary64) #s(literal 1/2 binary64))) (sqrt.f64 (/.f64 #s(literal 1 binary64) k))) (patch (.f64 (pow.f64 (.f64 (.f64 #s(literal 2 binary64) n) (PI.f64)) (fma.f64 k #s(literal -1/2 binary64) #s(literal 1/2 binary64))) (sqrt.f64 (/.f64 #s(literal 1 binary64) k))) #<representation binary64>) () ())) ())
#s(alt (/ (+ (* -1/2 (* (sqrt (* (pow k 3) (* n (PI)))) (* (log (* 2 (* n (PI)))) (sqrt 2)))) (* (sqrt (* k (* n (PI)))) (sqrt 2))) k) (taylor 0 k) (#s(alt (.f64 (pow.f64 (.f64 (.f64 #s(literal 2 binary64) n) (PI.f64)) (fma.f64 k #s(literal -1/2 binary64) #s(literal 1/2 binary64))) (sqrt.f64 (/.f64 #s(literal 1 binary64) k))) (patch (.f64 (pow.f64 (.f64 (.f64 #s(literal 2 binary64) n) (PI.f64)) (fma.f64 k #s(literal -1/2 binary64) #s(literal 1/2 binary64))) (sqrt.f64 (/.f64 #s(literal 1 binary64) k))) #<representation binary64>) () ())) ())
#s(alt (/ (+ (* k (+ (* -1/2 (* (sqrt (* k (* n (PI)))) (* (log (* 2 (* n (PI)))) (sqrt 2)))) (* 1/8 (* (sqrt (* (pow k 3) (* n (PI)))) (* (pow (log (* 2 (* n (PI)))) 2) (sqrt 2)))))) (* (sqrt (* k (* n (PI)))) (sqrt 2))) k) (taylor 0 k) (#s(alt (.f64 (pow.f64 (.f64 (.f64 #s(literal 2 binary64) n) (PI.f64)) (fma.f64 k #s(literal -1/2 binary64) #s(literal 1/2 binary64))) (sqrt.f64 (/.f64 #s(literal 1 binary64) k))) (patch (.f64 (pow.f64 (.f64 (.f64 #s(literal 2 binary64) n) (PI.f64)) (fma.f64 k #s(literal -1/2 binary64) #s(literal 1/2 binary64))) (sqrt.f64 (/.f64 #s(literal 1 binary64) k))) #<representation binary64>) () ())) ())
#s(alt (/ (+ (* k (+ (* -1/2 (* (sqrt (* k (* n (PI)))) (* (log (* 2 (* n (PI)))) (sqrt 2)))) (* k (+ (* -1/48 (* (sqrt (* (pow k 3) (* n (PI)))) (* (pow (log (* 2 (* n (PI)))) 3) (sqrt 2)))) (* 1/8 (* (sqrt (* k (* n (PI)))) (* (pow (log (* 2 (* n (PI)))) 2) (sqrt 2)))))))) (* (sqrt (* k (* n (PI)))) (sqrt 2))) k) (taylor 0 k) (#s(alt (.f64 (pow.f64 (.f64 (.f64 #s(literal 2 binary64) n) (PI.f64)) (fma.f64 k #s(literal -1/2 binary64) #s(literal 1/2 binary64))) (sqrt.f64 (/.f64 #s(literal 1 binary64) k))) (patch (.f64 (pow.f64 (.f64 (.f64 #s(literal 2 binary64) n) (PI.f64)) (fma.f64 k #s(literal -1/2 binary64) #s(literal 1/2 binary64))) (sqrt.f64 (/.f64 #s(literal 1 binary64) k))) #<representation binary64>) () ())) ())
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#s(alt (+ (* k (+ (* -1/2 (* (sqrt (* n (PI))) (* (log (* 2 (* n (PI)))) (sqrt 2)))) (* k (+ (* -1/48 (* (* k (* (pow (log (* 2 (* n (PI)))) 3) (sqrt 2))) (sqrt (* n (PI))))) (* 1/8 (* (sqrt (* n (PI))) (* (pow (log (* 2 (* n (PI)))) 2) (sqrt 2)))))))) (* (sqrt (* n (PI))) (sqrt 2))) (taylor 0 k) (#s(alt (pow.f64 (.f64 (.f64 #s(literal 2 binary64) n) (PI.f64)) (fma.f64 k #s(literal -1/2 binary64) #s(literal 1/2 binary64))) (patch (pow.f64 (.f64 (.f64 #s(literal 2 binary64) n) (PI.f64)) (fma.f64 k #s(literal -1/2 binary64) #s(literal 1/2 binary64))) #<representation binary64>) () ())) ())
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#s(alt (/ (+ (* -1 (* (sqrt (* (pow k 3) (* n (PI)))) (* (log (* (sqrt (* n (PI))) (sqrt 2))) (sqrt 2)))) (* (sqrt (* k (* n (PI)))) (sqrt 2))) k) (taylor 0 k) (#s(alt (.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) (/.f64 #s(literal 1 binary64) (pow.f64 (sqrt.f64 (.f64 n (.f64 (PI.f64) #s(literal 2 binary64)))) (-.f64 k #s(literal 1 binary64))))) (patch (.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) (/.f64 #s(literal 1 binary64) (pow.f64 (sqrt.f64 (.f64 n (.f64 (PI.f64) #s(literal 2 binary64)))) (-.f64 k #s(literal 1 binary64))))) #<representation binary64>) () ())) ())
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#s(alt (exp (* 1/2 (* (+ (log (* -2 (PI))) (* -1 (log (/ -1 n)))) (- 1 k)))) (taylor -inf n) (#s(alt (pow.f64 (.f64 (.f64 #s(literal 2 binary64) (PI.f64)) n) (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 2 binary64))) (patch (pow.f64 (.f64 (.f64 #s(literal 2 binary64) (PI.f64)) n) (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 2 binary64))) #<representation binary64>) () ())) ())
#s(alt (exp (* 1/2 (* (+ (log (* -2 (PI))) (* -1 (log (/ -1 n)))) (- 1 k)))) (taylor -inf n) (#s(alt (pow.f64 (.f64 (.f64 #s(literal 2 binary64) (PI.f64)) n) (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 2 binary64))) (patch (pow.f64 (.f64 (.f64 #s(literal 2 binary64) (PI.f64)) n) (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 2 binary64))) #<representation binary64>) () ())) ())
#s(alt (exp (* 1/2 (* (+ (log (* -2 (PI))) (* -1 (log (/ -1 n)))) (- 1 k)))) (taylor -inf n) (#s(alt (pow.f64 (.f64 (.f64 #s(literal 2 binary64) (PI.f64)) n) (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 2 binary64))) (patch (pow.f64 (.f64 (.f64 #s(literal 2 binary64) (PI.f64)) n) (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 2 binary64))) #<representation binary64>) () ())) ())
#s(alt (exp (* 1/2 (* (+ (log (* -2 (PI))) (* -1 (log (/ -1 n)))) (- 1 k)))) (taylor -inf n) (#s(alt (pow.f64 (.f64 (.f64 #s(literal 2 binary64) (PI.f64)) n) (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 2 binary64))) (patch (pow.f64 (.f64 (.f64 #s(literal 2 binary64) (PI.f64)) n) (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 2 binary64))) #<representation binary64>) () ())) ())
#s(alt (* 2 (* n (PI))) (taylor -inf n) (#s(alt (.f64 (.f64 #s(literal 2 binary64) (PI.f64)) n) (patch (.f64 (.f64 #s(literal 2 binary64) (PI.f64)) n) #<representation binary64>) () ())) ())
#s(alt (* 2 (* n (PI))) (taylor -inf n) (#s(alt (.f64 (.f64 #s(literal 2 binary64) (PI.f64)) n) (patch (.f64 (.f64 #s(literal 2 binary64) (PI.f64)) n) #<representation binary64>) () ())) ())
#s(alt (* 2 (* n (PI))) (taylor -inf n) (#s(alt (.f64 (.f64 #s(literal 2 binary64) (PI.f64)) n) (patch (.f64 (.f64 #s(literal 2 binary64) (PI.f64)) n) #<representation binary64>) () ())) ())
#s(alt (* 2 (* n (PI))) (taylor -inf n) (#s(alt (.f64 (.f64 #s(literal 2 binary64) (PI.f64)) n) (patch (.f64 (.f64 #s(literal 2 binary64) (PI.f64)) n) #<representation binary64>) () ())) ())

Calls

6 calls:

Time	Variable		Point	Expression
47.0ms	n	@	inf	((pow (pow (* n (* (PI) 2)) k) 1/2) (sqrt (* n (* (PI) 2))) (* n (* (PI) 2)) (* (PI) 2) (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (* (sqrt 2) (sqrt (/ (* (PI) n) k))) (sqrt 2) (sqrt (/ (* (PI) n) k)) (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (* (pow (* (* 2 n) (PI)) (+ (* k -1/2) 1/2)) (sqrt (/ 1 k))) (pow (* (* 2 n) (PI)) (+ (* k -1/2) 1/2)) (* (* 2 n) (PI)) (* (/ 1 (sqrt k)) (/ 1 (pow (sqrt (* n (* (PI) 2))) (- k 1)))) (/ 1 (sqrt k)) (sqrt k) (/ 1 (pow (sqrt (* n (* (PI) 2))) (- k 1))) (/ 1 (/ 1 (pow k -1/2))) (/ (- 1 k) 2) (* (/ 1 (/ 1 (pow k -1/2))) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (/ 1 (pow k -1/2)) (PI) (/ (sqrt (* n (* (PI) 2))) (* (sqrt k) (pow (pow (* n (* (PI) 2)) k) 1/2))) (pow (sqrt (* n (* (PI) 2))) (- k 1)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2)) (* (* 2 (PI)) n))
35.0ms	n	@	-inf	((pow (pow (* n (* (PI) 2)) k) 1/2) (sqrt (* n (* (PI) 2))) (* n (* (PI) 2)) (* (PI) 2) (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (* (sqrt 2) (sqrt (/ (* (PI) n) k))) (sqrt 2) (sqrt (/ (* (PI) n) k)) (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (* (pow (* (* 2 n) (PI)) (+ (* k -1/2) 1/2)) (sqrt (/ 1 k))) (pow (* (* 2 n) (PI)) (+ (* k -1/2) 1/2)) (* (* 2 n) (PI)) (* (/ 1 (sqrt k)) (/ 1 (pow (sqrt (* n (* (PI) 2))) (- k 1)))) (/ 1 (sqrt k)) (sqrt k) (/ 1 (pow (sqrt (* n (* (PI) 2))) (- k 1))) (/ 1 (/ 1 (pow k -1/2))) (/ (- 1 k) 2) (* (/ 1 (/ 1 (pow k -1/2))) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (/ 1 (pow k -1/2)) (PI) (/ (sqrt (* n (* (PI) 2))) (* (sqrt k) (pow (pow (* n (* (PI) 2)) k) 1/2))) (pow (sqrt (* n (* (PI) 2))) (- k 1)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2)) (* (* 2 (PI)) n))
30.0ms	n	@	0	((pow (pow (* n (* (PI) 2)) k) 1/2) (sqrt (* n (* (PI) 2))) (* n (* (PI) 2)) (* (PI) 2) (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (* (sqrt 2) (sqrt (/ (* (PI) n) k))) (sqrt 2) (sqrt (/ (* (PI) n) k)) (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (* (pow (* (* 2 n) (PI)) (+ (* k -1/2) 1/2)) (sqrt (/ 1 k))) (pow (* (* 2 n) (PI)) (+ (* k -1/2) 1/2)) (* (* 2 n) (PI)) (* (/ 1 (sqrt k)) (/ 1 (pow (sqrt (* n (* (PI) 2))) (- k 1)))) (/ 1 (sqrt k)) (sqrt k) (/ 1 (pow (sqrt (* n (* (PI) 2))) (- k 1))) (/ 1 (/ 1 (pow k -1/2))) (/ (- 1 k) 2) (* (/ 1 (/ 1 (pow k -1/2))) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (/ 1 (pow k -1/2)) (PI) (/ (sqrt (* n (* (PI) 2))) (* (sqrt k) (pow (pow (* n (* (PI) 2)) k) 1/2))) (pow (sqrt (* n (* (PI) 2))) (- k 1)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2)) (* (* 2 (PI)) n))
11.0ms	k	@	0	((pow (pow (* n (* (PI) 2)) k) 1/2) (sqrt (* n (* (PI) 2))) (* n (* (PI) 2)) (* (PI) 2) (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (* (sqrt 2) (sqrt (/ (* (PI) n) k))) (sqrt 2) (sqrt (/ (* (PI) n) k)) (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (* (pow (* (* 2 n) (PI)) (+ (* k -1/2) 1/2)) (sqrt (/ 1 k))) (pow (* (* 2 n) (PI)) (+ (* k -1/2) 1/2)) (* (* 2 n) (PI)) (* (/ 1 (sqrt k)) (/ 1 (pow (sqrt (* n (* (PI) 2))) (- k 1)))) (/ 1 (sqrt k)) (sqrt k) (/ 1 (pow (sqrt (* n (* (PI) 2))) (- k 1))) (/ 1 (/ 1 (pow k -1/2))) (/ (- 1 k) 2) (* (/ 1 (/ 1 (pow k -1/2))) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (/ 1 (pow k -1/2)) (PI) (/ (sqrt (* n (* (PI) 2))) (* (sqrt k) (pow (pow (* n (* (PI) 2)) k) 1/2))) (pow (sqrt (* n (* (PI) 2))) (- k 1)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2)) (* (* 2 (PI)) n))
8.0ms	k	@	-inf	((pow (pow (* n (* (PI) 2)) k) 1/2) (sqrt (* n (* (PI) 2))) (* n (* (PI) 2)) (* (PI) 2) (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (* (sqrt 2) (sqrt (/ (* (PI) n) k))) (sqrt 2) (sqrt (/ (* (PI) n) k)) (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (* (pow (* (* 2 n) (PI)) (+ (* k -1/2) 1/2)) (sqrt (/ 1 k))) (pow (* (* 2 n) (PI)) (+ (* k -1/2) 1/2)) (* (* 2 n) (PI)) (* (/ 1 (sqrt k)) (/ 1 (pow (sqrt (* n (* (PI) 2))) (- k 1)))) (/ 1 (sqrt k)) (sqrt k) (/ 1 (pow (sqrt (* n (* (PI) 2))) (- k 1))) (/ 1 (/ 1 (pow k -1/2))) (/ (- 1 k) 2) (* (/ 1 (/ 1 (pow k -1/2))) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (/ 1 (pow k -1/2)) (PI) (/ (sqrt (* n (* (PI) 2))) (* (sqrt k) (pow (pow (* n (* (PI) 2)) k) 1/2))) (pow (sqrt (* n (* (PI) 2))) (- k 1)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2)) (* (* 2 (PI)) n))

simplify176.0ms (1.9%)

Memory

7.3MiB live, 268.4MiB allocated

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	366	6588
1	1156	6312
2	4169	5985
0	8518	5919

Stop Event

1×	iter limit
1×	node limit

Counts

420 → 420

Calls

Call 1

Inputs
1
(+ 1 (* 1/2 (* k (log (* 2 (* n (PI)))))))
(+ 1 (* k (+ (* 1/2 (log (* 2 (* n (PI))))) (* 1/2 (* k (- (* 1/2 (pow (log (* 2 (* n (PI)))) 2)) (* 1/4 (pow (log (* 2 (* n (PI)))) 2))))))))
(+ 1 (* k (+ (* 1/2 (log (* 2 (* n (PI))))) (* k (+ (* 1/2 (* k (- (* 1/6 (pow (log (* 2 (* n (PI)))) 3)) (* 1/2 (* (log (* 2 (* n (PI)))) (- (* 1/2 (pow (log (* 2 (* n (PI)))) 2)) (* 1/4 (pow (log (* 2 (* n (PI)))) 2)))))))) (* 1/2 (- (* 1/2 (pow (log (* 2 (* n (PI)))) 2)) (* 1/4 (pow (log (* 2 (* n (PI)))) 2)))))))))
(* (sqrt (/ (* n (PI)) k)) (sqrt 2))
(/ (+ (* -1/2 (* (sqrt (* (pow k 3) (* n (PI)))) (* (log (* 2 (* n (PI)))) (sqrt 2)))) (* (sqrt (* k (* n (PI)))) (sqrt 2))) k)
(/ (+ (* k (+ (* -1/2 (* (sqrt (* k (* n (PI)))) (* (log (* 2 (* n (PI)))) (sqrt 2)))) (* 1/8 (* (sqrt (* (pow k 3) (* n (PI)))) (* (pow (log (* 2 (* n (PI)))) 2) (sqrt 2)))))) (* (sqrt (* k (* n (PI)))) (sqrt 2))) k)
(/ (+ (* k (+ (* -1/2 (* (sqrt (* k (* n (PI)))) (* (log (* 2 (* n (PI)))) (sqrt 2)))) (* k (+ (* -1/48 (* (sqrt (* (pow k 3) (* n (PI)))) (* (pow (log (* 2 (* n (PI)))) 3) (sqrt 2)))) (* 1/8 (* (sqrt (* k (* n (PI)))) (* (pow (log (* 2 (* n (PI)))) 2) (sqrt 2)))))))) (* (sqrt (* k (* n (PI)))) (sqrt 2))) k)
(* (sqrt (/ (* n (PI)) k)) (sqrt 2))
(* (sqrt (/ (* n (PI)) k)) (sqrt 2))
(* (sqrt (/ (* n (PI)) k)) (sqrt 2))
(* (sqrt (/ (* n (PI)) k)) (sqrt 2))
(sqrt (/ (* n (PI)) k))
(sqrt (/ (* n (PI)) k))
(sqrt (/ (* n (PI)) k))
(sqrt (/ (* n (PI)) k))
(* (sqrt (/ (* n (PI)) k)) (sqrt 2))
(/ (+ (* -1/2 (* (sqrt (* (pow k 3) (* n (PI)))) (* (log (* 2 (* n (PI)))) (sqrt 2)))) (* (sqrt (* k (* n (PI)))) (sqrt 2))) k)
(/ (+ (* k (+ (* -1/2 (* (sqrt (* k (* n (PI)))) (* (log (* 2 (* n (PI)))) (sqrt 2)))) (* 1/8 (* (sqrt (* (pow k 3) (* n (PI)))) (* (pow (log (* 2 (* n (PI)))) 2) (sqrt 2)))))) (* (sqrt (* k (* n (PI)))) (sqrt 2))) k)
(/ (+ (* k (+ (* -1/2 (* (sqrt (* k (* n (PI)))) (* (log (* 2 (* n (PI)))) (sqrt 2)))) (* k (+ (* -1/48 (* (sqrt (* (pow k 3) (* n (PI)))) (* (pow (log (* 2 (* n (PI)))) 3) (sqrt 2)))) (* 1/8 (* (sqrt (* k (* n (PI)))) (* (pow (log (* 2 (* n (PI)))) 2) (sqrt 2)))))))) (* (sqrt (* k (* n (PI)))) (sqrt 2))) k)
(* (sqrt (/ (* n (PI)) k)) (sqrt 2))
(/ (+ (* -1/2 (* (sqrt (* (pow k 3) (* n (PI)))) (* (log (* 2 (* n (PI)))) (sqrt 2)))) (* (sqrt (* k (* n (PI)))) (sqrt 2))) k)
(/ (+ (* k (+ (* -1/2 (* (sqrt (* k (* n (PI)))) (* (log (* 2 (* n (PI)))) (sqrt 2)))) (* 1/8 (* (sqrt (* (pow k 3) (* n (PI)))) (* (pow (log (* 2 (* n (PI)))) 2) (sqrt 2)))))) (* (sqrt (* k (* n (PI)))) (sqrt 2))) k)
(/ (+ (* k (+ (* -1/2 (* (sqrt (* k (* n (PI)))) (* (log (* 2 (* n (PI)))) (sqrt 2)))) (* k (+ (* -1/48 (* (sqrt (* (pow k 3) (* n (PI)))) (* (pow (log (* 2 (* n (PI)))) 3) (sqrt 2)))) (* 1/8 (* (sqrt (* k (* n (PI)))) (* (pow (log (* 2 (* n (PI)))) 2) (sqrt 2)))))))) (* (sqrt (* k (* n (PI)))) (sqrt 2))) k)
(* (sqrt (* n (PI))) (sqrt 2))
(+ (* -1/2 (* (* k (* (log (* 2 (* n (PI)))) (sqrt 2))) (sqrt (* n (PI))))) (* (sqrt (* n (PI))) (sqrt 2)))
(+ (* k (+ (* -1/2 (* (sqrt (* n (PI))) (* (log (* 2 (* n (PI)))) (sqrt 2)))) (* 1/8 (* (* k (* (pow (log (* 2 (* n (PI)))) 2) (sqrt 2))) (sqrt (* n (PI))))))) (* (sqrt (* n (PI))) (sqrt 2)))
(+ (* k (+ (* -1/2 (* (sqrt (* n (PI))) (* (log (* 2 (* n (PI)))) (sqrt 2)))) (* k (+ (* -1/48 (* (* k (* (pow (log (* 2 (* n (PI)))) 3) (sqrt 2))) (sqrt (* n (PI))))) (* 1/8 (* (sqrt (* n (PI))) (* (pow (log (* 2 (* n (PI)))) 2) (sqrt 2)))))))) (* (sqrt (* n (PI))) (sqrt 2)))
(* (sqrt (/ (* n (PI)) k)) (sqrt 2))
(/ (+ (* -1 (* (sqrt (* (pow k 3) (* n (PI)))) (* (log (* (sqrt (* n (PI))) (sqrt 2))) (sqrt 2)))) (* (sqrt (* k (* n (PI)))) (sqrt 2))) k)
(/ (+ (* k (+ (* -1 (* (sqrt (* k (* n (PI)))) (* (log (* (sqrt (* n (PI))) (sqrt 2))) (sqrt 2)))) (* -1 (* (sqrt (pow k 3)) (+ (* -1 (* (sqrt (* n (PI))) (* (pow (log (* (sqrt (* n (PI))) (sqrt 2))) 2) (sqrt 2)))) (* 1/2 (* (sqrt (* n (PI))) (* (pow (log (* (sqrt (* n (PI))) (sqrt 2))) 2) (sqrt 2))))))))) (* (sqrt (* k (* n (PI)))) (sqrt 2))) k)
(/ (+ (* k (+ (* -1 (* (sqrt (* k (* n (PI)))) (* (log (* (sqrt (* n (PI))) (sqrt 2))) (sqrt 2)))) (* k (+ (* -1 (* (sqrt k) (+ (* -1 (* (sqrt (* n (PI))) (* (pow (log (* (sqrt (* n (PI))) (sqrt 2))) 2) (sqrt 2)))) (* 1/2 (* (sqrt (* n (PI))) (* (pow (log (* (sqrt (* n (PI))) (sqrt 2))) 2) (sqrt 2))))))) (* -1 (* (sqrt (pow k 3)) (+ (* -1 (* (log (* (sqrt (* n (PI))) (sqrt 2))) (+ (* -1 (* (sqrt (* n (PI))) (* (pow (log (* (sqrt (* n (PI))) (sqrt 2))) 2) (sqrt 2)))) (* 1/2 (* (sqrt (* n (PI))) (* (pow (log (* (sqrt (* n (PI))) (sqrt 2))) 2) (sqrt 2))))))) (+ (* -1/2 (* (sqrt (* n (PI))) (* (pow (log (* (sqrt (* n (PI))) (sqrt 2))) 3) (sqrt 2)))) (* 1/6 (* (sqrt (* n (PI))) (* (pow (log (* (sqrt (* n (PI))) (sqrt 2))) 3) (sqrt 2)))))))))))) (* (sqrt (* k (* n (PI)))) (sqrt 2))) k)
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(+ (* k (- (* -1 (* k (+ (* -1 (* (sqrt (* n (PI))) (* (pow (log (* (sqrt (* n (PI))) (sqrt 2))) 2) (sqrt 2)))) (* 1/2 (* (sqrt (* n (PI))) (* (pow (log (* (sqrt (* n (PI))) (sqrt 2))) 2) (sqrt 2))))))) (* (sqrt (* n (PI))) (* (log (* (sqrt (* n (PI))) (sqrt 2))) (sqrt 2))))) (* (sqrt (* n (PI))) (sqrt 2)))
(+ (* k (- (* k (- (* -1 (* k (+ (* -1 (* (log (* (sqrt (* n (PI))) (sqrt 2))) (+ (* -1 (* (sqrt (* n (PI))) (* (pow (log (* (sqrt (* n (PI))) (sqrt 2))) 2) (sqrt 2)))) (* 1/2 (* (sqrt (* n (PI))) (* (pow (log (* (sqrt (* n (PI))) (sqrt 2))) 2) (sqrt 2))))))) (+ (* -1/2 (* (sqrt (* n (PI))) (* (pow (log (* (sqrt (* n (PI))) (sqrt 2))) 3) (sqrt 2)))) (* 1/6 (* (sqrt (* n (PI))) (* (pow (log (* (sqrt (* n (PI))) (sqrt 2))) 3) (sqrt 2)))))))) (+ (* -1 (* (sqrt (* n (PI))) (* (pow (log (* (sqrt (* n (PI))) (sqrt 2))) 2) (sqrt 2)))) (* 1/2 (* (sqrt (* n (PI))) (* (pow (log (* (sqrt (* n (PI))) (sqrt 2))) 2) (sqrt 2))))))) (* (sqrt (* n (PI))) (* (log (* (sqrt (* n (PI))) (sqrt 2))) (sqrt 2))))) (* (sqrt (* n (PI))) (sqrt 2)))
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1/2
(+ 1/2 (* -1/2 k))
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(* (sqrt (/ (* n (PI)) k)) (sqrt 2))
(/ (+ (* -1/2 (* (sqrt (* (pow k 3) (* n (PI)))) (* (log (* 2 (* n (PI)))) (sqrt 2)))) (* (sqrt (* k (* n (PI)))) (sqrt 2))) k)
(/ (+ (* k (+ (* -1/2 (* (sqrt (* k (* n (PI)))) (* (log (* 2 (* n (PI)))) (sqrt 2)))) (* 1/8 (* (sqrt (* (pow k 3) (* n (PI)))) (* (pow (log (* 2 (* n (PI)))) 2) (sqrt 2)))))) (* (sqrt (* k (* n (PI)))) (sqrt 2))) k)
(/ (+ (* k (+ (* -1/2 (* (sqrt (* k (* n (PI)))) (* (log (* 2 (* n (PI)))) (sqrt 2)))) (* k (+ (* -1/48 (* (sqrt (* (pow k 3) (* n (PI)))) (* (pow (log (* 2 (* n (PI)))) 3) (sqrt 2)))) (* 1/8 (* (sqrt (* k (* n (PI)))) (* (pow (log (* 2 (* n (PI)))) 2) (sqrt 2)))))))) (* (sqrt (* k (* n (PI)))) (sqrt 2))) k)
(sqrt k)
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(/ (+ (* (sqrt (* k (* n (PI)))) (sqrt 2)) (* (pow k 2) (+ (* -1/2 (* (sqrt (/ k (* n (PI)))) (* (sqrt 2) (+ (* -1 (* n (* (PI) (pow (log (* 2 (* n (PI)))) 2)))) (* 1/2 (* n (* (PI) (pow (log (* 2 (* n (PI)))) 2)))))))) (* -1/2 (* (sqrt (/ (* n (PI)) k)) (* (log (* 2 (* n (PI)))) (sqrt 2))))))) k)
(/ (+ (* (sqrt (* k (* n (PI)))) (sqrt 2)) (* (pow k 2) (+ (* -1/2 (* (sqrt (/ (* n (PI)) k)) (* (log (* 2 (* n (PI)))) (sqrt 2)))) (* k (+ (* -1/2 (* (sqrt (/ 1 (* k (* n (PI))))) (* (sqrt 2) (+ (* -1 (* n (* (PI) (pow (log (* 2 (* n (PI)))) 2)))) (* 1/2 (* n (* (PI) (pow (log (* 2 (* n (PI)))) 2)))))))) (* -1/2 (* (sqrt (/ k (* n (PI)))) (* (sqrt 2) (+ (* -1 (* (log (* 2 (* n (PI)))) (+ (* -1 (* n (* (PI) (pow (log (* 2 (* n (PI)))) 2)))) (* 1/2 (* n (* (PI) (pow (log (* 2 (* n (PI)))) 2))))))) (+ (* -1/2 (* n (* (PI) (pow (log (* 2 (* n (PI)))) 3)))) (+ (* 1/6 (* n (* (PI) (pow (log (* 2 (* n (PI)))) 3)))) (* 1/4 (/ (* n (* (PI) (pow (log (* 2 (* n (PI)))) 2))) k))))))))))))) k)
(* (sqrt (/ 1 (* n (PI)))) (/ 1 (sqrt 2)))
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(+ (* k (+ (* k (+ (* 1/6 (* (/ (* k (pow (log (* (sqrt (* n (PI))) (sqrt 2))) 3)) (sqrt 2)) (sqrt (/ 1 (* n (PI)))))) (* 1/2 (* (sqrt (/ 1 (* n (PI)))) (/ (pow (log (* (sqrt (* n (PI))) (sqrt 2))) 2) (sqrt 2)))))) (* (sqrt (/ 1 (* n (PI)))) (/ (log (* (sqrt (* n (PI))) (sqrt 2))) (sqrt 2))))) (* (sqrt (/ 1 (* n (PI)))) (/ 1 (sqrt 2))))
(* (sqrt (* n (PI))) (sqrt 2))
(+ (* -1/2 (* (* k (* (log (* 2 (* n (PI)))) (sqrt 2))) (sqrt (* n (PI))))) (* (sqrt (* n (PI))) (sqrt 2)))
(+ (* k (+ (* -1/2 (* (sqrt (* n (PI))) (* (log (* 2 (* n (PI)))) (sqrt 2)))) (* 1/8 (* (* k (* (pow (log (* 2 (* n (PI)))) 2) (sqrt 2))) (sqrt (* n (PI))))))) (* (sqrt (* n (PI))) (sqrt 2)))
(+ (* k (+ (* -1/2 (* (sqrt (* n (PI))) (* (log (* 2 (* n (PI)))) (sqrt 2)))) (* k (+ (* -1/48 (* (* k (* (pow (log (* 2 (* n (PI)))) 3) (sqrt 2))) (sqrt (* n (PI))))) (* 1/8 (* (sqrt (* n (PI))) (* (pow (log (* 2 (* n (PI)))) 2) (sqrt 2)))))))) (* (sqrt (* n (PI))) (sqrt 2)))
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1
#s(literal 1 binary64)
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(exp (* (+ (log (* (sqrt (/ (PI) n)) (* (sqrt -2) (sqrt -1)))) (* -1 (log (/ -1 n)))) (- k 1)))
(pow.f64 (.f64 (.f64 (*.f64 (sqrt.f64 #s(literal -2 binary64)) (sqrt.f64 (/.f64 (PI.f64) n))) (sqrt.f64 #s(literal -1 binary64))) (pow.f64 (/.f64 #s(literal -1 binary64) n) #s(literal -1 binary64))) (-.f64 k #s(literal 1 binary64)))
(exp (* (+ (log (* (sqrt (/ (PI) n)) (* (sqrt -2) (sqrt -1)))) (* -1 (log (/ -1 n)))) (- k 1)))
(pow.f64 (.f64 (.f64 (*.f64 (sqrt.f64 #s(literal -2 binary64)) (sqrt.f64 (/.f64 (PI.f64) n))) (sqrt.f64 #s(literal -1 binary64))) (pow.f64 (/.f64 #s(literal -1 binary64) n) #s(literal -1 binary64))) (-.f64 k #s(literal 1 binary64)))
(exp (* (+ (log (* (sqrt (/ (PI) n)) (* (sqrt -2) (sqrt -1)))) (* -1 (log (/ -1 n)))) (- k 1)))
(pow.f64 (.f64 (.f64 (*.f64 (sqrt.f64 #s(literal -2 binary64)) (sqrt.f64 (/.f64 (PI.f64) n))) (sqrt.f64 #s(literal -1 binary64))) (pow.f64 (/.f64 #s(literal -1 binary64) n) #s(literal -1 binary64))) (-.f64 k #s(literal 1 binary64)))
(exp (* (+ (log (* (sqrt (/ (PI) n)) (* (sqrt -2) (sqrt -1)))) (* -1 (log (/ -1 n)))) (- k 1)))
(pow.f64 (.f64 (.f64 (*.f64 (sqrt.f64 #s(literal -2 binary64)) (sqrt.f64 (/.f64 (PI.f64) n))) (sqrt.f64 #s(literal -1 binary64))) (pow.f64 (/.f64 #s(literal -1 binary64) n) #s(literal -1 binary64))) (-.f64 k #s(literal 1 binary64)))
(exp (* 1/2 (* (+ (log (* -2 (PI))) (* -1 (log (/ -1 n)))) (- 1 k))))
(pow.f64 (exp.f64 (fma.f64 #s(literal -1/2 binary64) k #s(literal 1/2 binary64))) (-.f64 (log.f64 (*.f64 #s(literal -2 binary64) (PI.f64))) (log.f64 (/.f64 #s(literal -1 binary64) n))))
(exp (* 1/2 (* (+ (log (* -2 (PI))) (* -1 (log (/ -1 n)))) (- 1 k))))
(pow.f64 (exp.f64 (fma.f64 #s(literal -1/2 binary64) k #s(literal 1/2 binary64))) (-.f64 (log.f64 (*.f64 #s(literal -2 binary64) (PI.f64))) (log.f64 (/.f64 #s(literal -1 binary64) n))))
(exp (* 1/2 (* (+ (log (* -2 (PI))) (* -1 (log (/ -1 n)))) (- 1 k))))
(pow.f64 (exp.f64 (fma.f64 #s(literal -1/2 binary64) k #s(literal 1/2 binary64))) (-.f64 (log.f64 (*.f64 #s(literal -2 binary64) (PI.f64))) (log.f64 (/.f64 #s(literal -1 binary64) n))))
(exp (* 1/2 (* (+ (log (* -2 (PI))) (* -1 (log (/ -1 n)))) (- 1 k))))
(pow.f64 (exp.f64 (fma.f64 #s(literal -1/2 binary64) k #s(literal 1/2 binary64))) (-.f64 (log.f64 (*.f64 #s(literal -2 binary64) (PI.f64))) (log.f64 (/.f64 #s(literal -1 binary64) n))))
(* 2 (* n (PI)))
(.f64 (.f64 (PI.f64) n) #s(literal 2 binary64))
(* 2 (* n (PI)))
(.f64 (.f64 (PI.f64) n) #s(literal 2 binary64))
(* 2 (* n (PI)))
(.f64 (.f64 (PI.f64) n) #s(literal 2 binary64))
(* 2 (* n (PI)))
(.f64 (.f64 (PI.f64) n) #s(literal 2 binary64))

rewrite174.0ms (1.9%)

Memory

-1.9MiB live, 276.3MiB allocated

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	52	245
0	88	214
1	314	205
2	1752	205
0	8371	205

Stop Event

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

Counts

25 → 1 243

Calls

Call 1

Inputs
(pow.f64 (pow.f64 (.f64 n (.f64 (PI.f64) #s(literal 2 binary64))) k) #s(literal 1/2 binary64))
(sqrt.f64 (.f64 n (.f64 (PI.f64) #s(literal 2 binary64))))
(.f64 n (.f64 (PI.f64) #s(literal 2 binary64)))
(*.f64 (PI.f64) #s(literal 2 binary64))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (.f64 (sqrt.f64 #s(literal 2 binary64)) (sqrt.f64 (/.f64 (.f64 (PI.f64) n) k))))
(.f64 (sqrt.f64 #s(literal 2 binary64)) (sqrt.f64 (/.f64 (.f64 (PI.f64) n) k)))
(sqrt.f64 #s(literal 2 binary64))
(sqrt.f64 (/.f64 (*.f64 (PI.f64) n) k))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (.f64 (pow.f64 (.f64 (*.f64 #s(literal 2 binary64) n) (PI.f64)) (fma.f64 k #s(literal -1/2 binary64) #s(literal 1/2 binary64))) (sqrt.f64 (/.f64 #s(literal 1 binary64) k))))
(.f64 (pow.f64 (.f64 (*.f64 #s(literal 2 binary64) n) (PI.f64)) (fma.f64 k #s(literal -1/2 binary64) #s(literal 1/2 binary64))) (sqrt.f64 (/.f64 #s(literal 1 binary64) k)))
(pow.f64 (.f64 (.f64 #s(literal 2 binary64) n) (PI.f64)) (fma.f64 k #s(literal -1/2 binary64) #s(literal 1/2 binary64)))
(.f64 (.f64 #s(literal 2 binary64) n) (PI.f64))
(.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) (/.f64 #s(literal 1 binary64) (pow.f64 (sqrt.f64 (.f64 n (*.f64 (PI.f64) #s(literal 2 binary64)))) (-.f64 k #s(literal 1 binary64)))))
(/.f64 #s(literal 1 binary64) (sqrt.f64 k))
(sqrt.f64 k)
(/.f64 #s(literal 1 binary64) (pow.f64 (sqrt.f64 (.f64 n (.f64 (PI.f64) #s(literal 2 binary64)))) (-.f64 k #s(literal 1 binary64))))
(/.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (pow.f64 k #s(literal -1/2 binary64))))
(/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 2 binary64))
(.f64 (/.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (pow.f64 k #s(literal -1/2 binary64)))) (pow.f64 (.f64 (*.f64 #s(literal 2 binary64) (PI.f64)) n) (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 2 binary64))))
(/.f64 #s(literal 1 binary64) (pow.f64 k #s(literal -1/2 binary64)))
(PI.f64)
(/.f64 (sqrt.f64 (.f64 n (.f64 (PI.f64) #s(literal 2 binary64)))) (.f64 (sqrt.f64 k) (pow.f64 (pow.f64 (.f64 n (*.f64 (PI.f64) #s(literal 2 binary64))) k) #s(literal 1/2 binary64))))
(pow.f64 (sqrt.f64 (.f64 n (.f64 (PI.f64) #s(literal 2 binary64)))) (-.f64 k #s(literal 1 binary64)))
(pow.f64 (.f64 (.f64 #s(literal 2 binary64) (PI.f64)) n) (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 2 binary64)))
(.f64 (.f64 #s(literal 2 binary64) (PI.f64)) n)

Outputs
(.f64 (fabs.f64 (pow.f64 (sqrt.f64 (.f64 (PI.f64) n)) k)) (fabs.f64 (pow.f64 (sqrt.f64 #s(literal 2 binary64)) k)))
(.f64 (fabs.f64 (pow.f64 (sqrt.f64 #s(literal 2 binary64)) k)) (fabs.f64 (pow.f64 (sqrt.f64 (.f64 (PI.f64) n)) k)))
(.f64 (fabs.f64 (pow.f64 (sqrt.f64 (.f64 #s(literal 2 binary64) n)) k)) (fabs.f64 (pow.f64 (sqrt.f64 (PI.f64)) k)))
(.f64 (fabs.f64 (pow.f64 (sqrt.f64 (PI.f64)) k)) (fabs.f64 (pow.f64 (sqrt.f64 (.f64 #s(literal 2 binary64) n)) k)))
(.f64 (sqrt.f64 (pow.f64 (.f64 (PI.f64) n) k)) (sqrt.f64 (pow.f64 #s(literal 2 binary64) k)))
(.f64 (sqrt.f64 (pow.f64 #s(literal 2 binary64) k)) (sqrt.f64 (pow.f64 (.f64 (PI.f64) n) k)))
(.f64 (sqrt.f64 (pow.f64 (.f64 #s(literal 2 binary64) n) k)) (sqrt.f64 (pow.f64 (PI.f64) k)))
(.f64 (sqrt.f64 (pow.f64 (PI.f64) k)) (sqrt.f64 (pow.f64 (.f64 #s(literal 2 binary64) n) k)))
(.f64 (pow.f64 (sqrt.f64 (.f64 (PI.f64) n)) k) (pow.f64 (sqrt.f64 #s(literal 2 binary64)) k))
(.f64 (pow.f64 (sqrt.f64 #s(literal 2 binary64)) k) (pow.f64 (sqrt.f64 (.f64 (PI.f64) n)) k))
(.f64 (pow.f64 (sqrt.f64 (.f64 #s(literal 2 binary64) n)) k) (pow.f64 (sqrt.f64 (PI.f64)) k))
(.f64 (pow.f64 (sqrt.f64 (PI.f64)) k) (pow.f64 (sqrt.f64 (.f64 #s(literal 2 binary64) n)) k))
(.f64 (pow.f64 (sqrt.f64 (.f64 #s(literal 2 binary64) (PI.f64))) k) (pow.f64 (sqrt.f64 n) k))
(.f64 (pow.f64 (sqrt.f64 n) k) (pow.f64 (sqrt.f64 (.f64 #s(literal 2 binary64) (PI.f64))) k))
(.f64 (pow.f64 (sqrt.f64 (.f64 (*.f64 #s(literal 2 binary64) n) (PI.f64))) k) #s(literal 1 binary64))
(.f64 (pow.f64 (pow.f64 (.f64 (.f64 #s(literal 2 binary64) n) (PI.f64)) #s(literal 1/4 binary64)) k) (pow.f64 (pow.f64 (.f64 (*.f64 #s(literal 2 binary64) n) (PI.f64)) #s(literal 1/4 binary64)) k))
(.f64 #s(literal 1 binary64) (pow.f64 (sqrt.f64 (.f64 (*.f64 #s(literal 2 binary64) n) (PI.f64))) k))
(pow.f64 (exp.f64 #s(literal 1/2 binary64)) (.f64 (log.f64 (.f64 (*.f64 #s(literal 2 binary64) n) (PI.f64))) k))
(pow.f64 (pow.f64 (.f64 (.f64 #s(literal 2 binary64) n) (PI.f64)) #s(literal 2 binary64)) (.f64 (.f64 #s(literal 1/2 binary64) k) #s(literal 1/2 binary64)))
(pow.f64 (pow.f64 (.f64 (.f64 #s(literal 2 binary64) n) (PI.f64)) #s(literal 2 binary64)) (*.f64 k #s(literal 1/4 binary64)))
(pow.f64 (pow.f64 (pow.f64 (.f64 (.f64 #s(literal 2 binary64) n) (PI.f64)) #s(literal 2 binary64)) k) #s(literal 1/4 binary64))
(pow.f64 (pow.f64 (sqrt.f64 (.f64 (.f64 #s(literal 2 binary64) n) (PI.f64))) k) #s(literal 1 binary64))
(pow.f64 (pow.f64 (pow.f64 (.f64 (.f64 #s(literal 2 binary64) n) (PI.f64)) #s(literal 1/4 binary64)) k) #s(literal 2 binary64))
(pow.f64 (.f64 (.f64 #s(literal 2 binary64) n) (PI.f64)) (/.f64 (.f64 #s(literal 2 binary64) (.f64 #s(literal 1/2 binary64) k)) #s(literal 2 binary64)))
(pow.f64 (.f64 (.f64 #s(literal 2 binary64) n) (PI.f64)) (/.f64 (fma.f64 #s(literal 1/2 binary64) k (*.f64 #s(literal 1/2 binary64) k)) #s(literal 2 binary64)))
(pow.f64 (.f64 (.f64 #s(literal 2 binary64) n) (PI.f64)) (fma.f64 (.f64 #s(literal 1/2 binary64) k) #s(literal 1/2 binary64) (.f64 (*.f64 #s(literal 1/2 binary64) k) #s(literal 1/2 binary64))))
(pow.f64 (.f64 (.f64 #s(literal 2 binary64) n) (PI.f64)) (fma.f64 k #s(literal 1/4 binary64) (*.f64 k #s(literal 1/4 binary64))))
(pow.f64 (.f64 (.f64 #s(literal 2 binary64) n) (PI.f64)) (.f64 (.f64 k #s(literal 1/4 binary64)) #s(literal 2 binary64)))
(pow.f64 (.f64 (.f64 #s(literal 2 binary64) n) (PI.f64)) (.f64 (.f64 #s(literal 2 binary64) (*.f64 #s(literal 1/2 binary64) k)) #s(literal 1/2 binary64)))
(pow.f64 (.f64 (.f64 #s(literal 2 binary64) n) (PI.f64)) (.f64 (fma.f64 #s(literal 1/2 binary64) k (.f64 #s(literal 1/2 binary64) k)) #s(literal 1/2 binary64)))
(pow.f64 (.f64 (.f64 #s(literal 2 binary64) n) (PI.f64)) (*.f64 #s(literal 1/2 binary64) k))
(pow.f64 (sqrt.f64 (.f64 (.f64 #s(literal 2 binary64) n) (PI.f64))) (fma.f64 #s(literal 1/2 binary64) k (*.f64 #s(literal 1/2 binary64) k)))
(pow.f64 (sqrt.f64 (.f64 (.f64 #s(literal 2 binary64) n) (PI.f64))) k)
(pow.f64 (pow.f64 (.f64 (.f64 #s(literal 2 binary64) n) (PI.f64)) k) #s(literal 1/2 binary64))
(sqrt.f64 (pow.f64 (.f64 (.f64 #s(literal 2 binary64) n) (PI.f64)) k))
(fabs.f64 (neg.f64 (pow.f64 (sqrt.f64 (.f64 (.f64 #s(literal 2 binary64) n) (PI.f64))) k)))
(fabs.f64 (pow.f64 (sqrt.f64 (.f64 (.f64 #s(literal 2 binary64) n) (PI.f64))) k))
(exp.f64 (fma.f64 (.f64 (log.f64 (.f64 (.f64 #s(literal 2 binary64) n) (PI.f64))) k) #s(literal 1/4 binary64) (.f64 (.f64 (log.f64 (.f64 (*.f64 #s(literal 2 binary64) n) (PI.f64))) k) #s(literal 1/4 binary64))))
(exp.f64 (.f64 (.f64 (.f64 (log.f64 (.f64 (*.f64 #s(literal 2 binary64) n) (PI.f64))) k) #s(literal 1/4 binary64)) #s(literal 2 binary64)))
(exp.f64 (.f64 (log.f64 (pow.f64 (pow.f64 (.f64 (*.f64 #s(literal 2 binary64) n) (PI.f64)) #s(literal 2 binary64)) k)) #s(literal 1/4 binary64)))
(exp.f64 (.f64 (log.f64 (pow.f64 (pow.f64 (.f64 (*.f64 #s(literal 2 binary64) n) (PI.f64)) #s(literal 1/4 binary64)) k)) #s(literal 2 binary64)))
(exp.f64 (log.f64 (pow.f64 (sqrt.f64 (.f64 (.f64 #s(literal 2 binary64) n) (PI.f64))) k)))
(.f64 (sqrt.f64 (.f64 (*.f64 #s(literal 2 binary64) n) (sqrt.f64 (PI.f64)))) (pow.f64 (PI.f64) #s(literal 1/4 binary64)))
(.f64 (sqrt.f64 (.f64 (*.f64 #s(literal 2 binary64) n) (pow.f64 (cbrt.f64 (PI.f64)) #s(literal 2 binary64)))) (pow.f64 (PI.f64) #s(literal 1/6 binary64)))
(.f64 (exp.f64 (log.f64 (sqrt.f64 n))) (exp.f64 (log.f64 (sqrt.f64 (.f64 #s(literal 2 binary64) (PI.f64))))))
(.f64 (pow.f64 (.f64 (.f64 #s(literal 2 binary64) n) (PI.f64)) #s(literal 1/4 binary64)) (pow.f64 (.f64 (*.f64 #s(literal 2 binary64) n) (PI.f64)) #s(literal 1/4 binary64)))
(.f64 (pow.f64 (PI.f64) #s(literal 1/4 binary64)) (sqrt.f64 (.f64 (sqrt.f64 (PI.f64)) (*.f64 #s(literal 2 binary64) n))))
(.f64 (sqrt.f64 (.f64 (PI.f64) n)) (sqrt.f64 #s(literal 2 binary64)))
(.f64 (sqrt.f64 (.f64 #s(literal 2 binary64) n)) (sqrt.f64 (PI.f64)))
(.f64 (sqrt.f64 (PI.f64)) (sqrt.f64 (.f64 #s(literal 2 binary64) n)))
(.f64 (sqrt.f64 (.f64 #s(literal 2 binary64) (PI.f64))) (sqrt.f64 n))
(.f64 (sqrt.f64 n) (sqrt.f64 (.f64 #s(literal 2 binary64) (PI.f64))))
(.f64 (cbrt.f64 (PI.f64)) (sqrt.f64 (.f64 (cbrt.f64 (PI.f64)) (*.f64 #s(literal 2 binary64) n))))
(.f64 #s(literal -1 binary64) (neg.f64 (sqrt.f64 (.f64 (*.f64 #s(literal 2 binary64) n) (PI.f64)))))
(.f64 (sqrt.f64 #s(literal 2 binary64)) (sqrt.f64 (.f64 (PI.f64) n)))
(.f64 #s(literal 1 binary64) (sqrt.f64 (.f64 (*.f64 #s(literal 2 binary64) n) (PI.f64))))
(.f64 (sqrt.f64 (.f64 (*.f64 #s(literal 2 binary64) n) (PI.f64))) #s(literal 1 binary64))
(pow.f64 (exp.f64 #s(literal 1/2 binary64)) (log.f64 (.f64 (.f64 #s(literal 2 binary64) n) (PI.f64))))
(pow.f64 (pow.f64 (.f64 (.f64 #s(literal 2 binary64) n) (PI.f64)) #s(literal 1/4 binary64)) #s(literal 2 binary64))
(pow.f64 (pow.f64 (.f64 (.f64 #s(literal 2 binary64) n) (PI.f64)) #s(literal 2 binary64)) #s(literal 1/4 binary64))
(pow.f64 (.f64 (.f64 #s(literal 2 binary64) n) (PI.f64)) #s(literal 1/2 binary64))
(pow.f64 (sqrt.f64 (.f64 (.f64 #s(literal 2 binary64) n) (PI.f64))) #s(literal 1 binary64))
(/.f64 (neg.f64 (sqrt.f64 (.f64 (.f64 #s(literal 2 binary64) n) (PI.f64)))) #s(literal -1 binary64))
(/.f64 #s(literal 1 binary64) (pow.f64 (.f64 (.f64 #s(literal 2 binary64) n) (PI.f64)) #s(literal -1/2 binary64)))
(/.f64 (sqrt.f64 (.f64 (.f64 #s(literal 2 binary64) n) (PI.f64))) #s(literal 1 binary64))
(neg.f64 (neg.f64 (sqrt.f64 (.f64 (.f64 #s(literal 2 binary64) n) (PI.f64)))))
(sqrt.f64 (.f64 (.f64 #s(literal 2 binary64) n) (PI.f64)))
(-.f64 #s(literal 0 binary64) (neg.f64 (sqrt.f64 (.f64 (.f64 #s(literal 2 binary64) n) (PI.f64)))))
(exp.f64 (log.f64 (sqrt.f64 (.f64 (.f64 #s(literal 2 binary64) n) (PI.f64)))))
(.f64 (exp.f64 (log.f64 (.f64 (PI.f64) n))) (exp.f64 (log.f64 #s(literal 2 binary64))))
(.f64 (exp.f64 (log.f64 #s(literal 2 binary64))) (exp.f64 (log.f64 (.f64 (PI.f64) n))))
(.f64 (exp.f64 (log.f64 (.f64 #s(literal 2 binary64) (PI.f64)))) (exp.f64 (log.f64 n)))
(.f64 (exp.f64 (log.f64 (.f64 #s(literal 2 binary64) n))) (PI.f64))
(.f64 (exp.f64 (log.f64 n)) (exp.f64 (log.f64 (.f64 #s(literal 2 binary64) (PI.f64)))))
(.f64 (.f64 (*.f64 #s(literal 2 binary64) n) (sqrt.f64 (PI.f64))) (sqrt.f64 (PI.f64)))
(.f64 (.f64 (*.f64 #s(literal 2 binary64) n) (pow.f64 (cbrt.f64 (PI.f64)) #s(literal 2 binary64))) (cbrt.f64 (PI.f64)))
(.f64 (sqrt.f64 (PI.f64)) (.f64 (sqrt.f64 (PI.f64)) (*.f64 #s(literal 2 binary64) n)))
(.f64 (pow.f64 (cbrt.f64 (PI.f64)) #s(literal 2 binary64)) (.f64 (cbrt.f64 (PI.f64)) (*.f64 #s(literal 2 binary64) n)))
(.f64 (.f64 #s(literal 2 binary64) n) (PI.f64))
(.f64 (.f64 (PI.f64) n) #s(literal 2 binary64))
(.f64 #s(literal 1 binary64) (.f64 (*.f64 #s(literal 2 binary64) n) (PI.f64)))
(.f64 (sqrt.f64 (.f64 (.f64 #s(literal 2 binary64) n) (PI.f64))) (sqrt.f64 (.f64 (*.f64 #s(literal 2 binary64) n) (PI.f64))))
(.f64 (.f64 #s(literal 2 binary64) (PI.f64)) n)
(.f64 #s(literal 2 binary64) (.f64 (PI.f64) n))
(.f64 (PI.f64) (exp.f64 (log.f64 (.f64 #s(literal 2 binary64) n))))
(.f64 (PI.f64) (.f64 #s(literal 2 binary64) n))
(.f64 n (.f64 #s(literal 2 binary64) (PI.f64)))
(pow.f64 (pow.f64 (.f64 (.f64 #s(literal 2 binary64) n) (PI.f64)) #s(literal 2 binary64)) #s(literal 1/2 binary64))
(pow.f64 (.f64 (.f64 #s(literal 2 binary64) n) (PI.f64)) #s(literal 1 binary64))
(pow.f64 (sqrt.f64 (.f64 (.f64 #s(literal 2 binary64) n) (PI.f64))) #s(literal 2 binary64))
(sqrt.f64 (pow.f64 (.f64 (.f64 #s(literal 2 binary64) n) (PI.f64)) #s(literal 2 binary64)))
(exp.f64 (fma.f64 (log.f64 (.f64 (.f64 #s(literal 2 binary64) n) (PI.f64))) #s(literal 1/2 binary64) (log.f64 (sqrt.f64 (.f64 (.f64 #s(literal 2 binary64) n) (PI.f64))))))
(exp.f64 (log.f64 (.f64 (.f64 #s(literal 2 binary64) n) (PI.f64))))
(.f64 (.f64 #s(literal 2 binary64) (sqrt.f64 (PI.f64))) (sqrt.f64 (PI.f64)))
(.f64 (.f64 #s(literal 2 binary64) (pow.f64 (cbrt.f64 (PI.f64)) #s(literal 2 binary64))) (cbrt.f64 (PI.f64)))
(.f64 (sqrt.f64 (PI.f64)) (.f64 (sqrt.f64 (PI.f64)) #s(literal 2 binary64)))
(.f64 (pow.f64 (cbrt.f64 (PI.f64)) #s(literal 2 binary64)) (.f64 (cbrt.f64 (PI.f64)) #s(literal 2 binary64)))
(.f64 #s(literal 1 binary64) (.f64 #s(literal 2 binary64) (PI.f64)))
(*.f64 #s(literal 2 binary64) (PI.f64))
(*.f64 (PI.f64) #s(literal 2 binary64))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt.f64 (.f64 (/.f64 (.f64 (PI.f64) n) k) #s(literal 2 binary64))))
(.f64 (.f64 (sqrt.f64 (.f64 (.f64 #s(literal 2 binary64) n) (PI.f64))) #s(literal -1 binary64)) (/.f64 #s(literal -1 binary64) (sqrt.f64 k)))
(.f64 (neg.f64 (sqrt.f64 (.f64 (*.f64 #s(literal 2 binary64) n) (PI.f64)))) (/.f64 #s(literal -1 binary64) (sqrt.f64 k)))
(.f64 (sqrt.f64 (.f64 #s(literal 2 binary64) (PI.f64))) (sqrt.f64 (/.f64 n k)))
(.f64 (sqrt.f64 n) (sqrt.f64 (/.f64 (.f64 #s(literal 2 binary64) (PI.f64)) k)))
(.f64 (sqrt.f64 (/.f64 (.f64 (PI.f64) n) k)) (sqrt.f64 #s(literal 2 binary64)))
(.f64 (sqrt.f64 #s(literal 2 binary64)) (sqrt.f64 (/.f64 (.f64 (PI.f64) n) k)))
(.f64 #s(literal 1 binary64) (sqrt.f64 (.f64 (/.f64 (*.f64 (PI.f64) n) k) #s(literal 2 binary64))))
(.f64 (sqrt.f64 (.f64 (*.f64 #s(literal 2 binary64) n) (PI.f64))) (pow.f64 k #s(literal -1/2 binary64)))
(pow.f64 (sqrt.f64 (/.f64 k (.f64 (.f64 #s(literal 2 binary64) n) (PI.f64)))) #s(literal -1 binary64))
(pow.f64 (sqrt.f64 (.f64 (/.f64 (.f64 (PI.f64) n) k) #s(literal 2 binary64))) #s(literal 1 binary64))
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(exp.f64 (.f64 (log.f64 (sqrt.f64 (.f64 (.f64 #s(literal 2 binary64) n) (PI.f64)))) (.f64 (-.f64 k #s(literal 1 binary64)) #s(literal -1 binary64))))
(exp.f64 (.f64 (.f64 (log.f64 (.f64 (.f64 #s(literal 2 binary64) n) (PI.f64))) (*.f64 (fma.f64 #s(literal -1/2 binary64) k #s(literal 1/2 binary64)) #s(literal 1/2 binary64))) #s(literal 2 binary64)))
(exp.f64 (.f64 (log.f64 (pow.f64 (.f64 (.f64 #s(literal 2 binary64) n) (PI.f64)) #s(literal 2 binary64))) (.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 1/4 binary64))))
(exp.f64 (.f64 (log.f64 (pow.f64 (.f64 (*.f64 #s(literal 2 binary64) n) (PI.f64)) (-.f64 #s(literal 1 binary64) k))) #s(literal 1/2 binary64)))
(exp.f64 (.f64 (log.f64 (pow.f64 (pow.f64 (.f64 (*.f64 #s(literal 2 binary64) n) (PI.f64)) #s(literal 1/4 binary64)) (-.f64 #s(literal 1 binary64) k))) #s(literal 2 binary64)))
(exp.f64 (.f64 (log.f64 (.f64 (.f64 #s(literal 2 binary64) n) (PI.f64))) (.f64 #s(literal 2 binary64) (*.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 1/4 binary64)))))
(exp.f64 (.f64 (log.f64 (.f64 (.f64 #s(literal 2 binary64) n) (PI.f64))) (fma.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 1/4 binary64) (.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 1/4 binary64)))))
(exp.f64 (.f64 (log.f64 (.f64 (.f64 #s(literal 2 binary64) n) (PI.f64))) (.f64 (fma.f64 #s(literal 1/2 binary64) k #s(literal -1/2 binary64)) #s(literal -1 binary64))))
(exp.f64 (.f64 (log.f64 (pow.f64 (.f64 (.f64 #s(literal 2 binary64) n) (PI.f64)) #s(literal 2 binary64))) (.f64 (fma.f64 #s(literal -1/2 binary64) k #s(literal 1/2 binary64)) #s(literal 1/2 binary64))))
(exp.f64 (.f64 (log.f64 (.f64 (.f64 #s(literal 2 binary64) n) (PI.f64))) (.f64 #s(literal 2 binary64) (*.f64 (fma.f64 #s(literal -1/2 binary64) k #s(literal 1/2 binary64)) #s(literal 1/2 binary64)))))
(exp.f64 (.f64 (log.f64 (.f64 (.f64 #s(literal 2 binary64) n) (PI.f64))) (fma.f64 (fma.f64 #s(literal -1/2 binary64) k #s(literal 1/2 binary64)) #s(literal 1/2 binary64) (.f64 (fma.f64 #s(literal -1/2 binary64) k #s(literal 1/2 binary64)) #s(literal 1/2 binary64)))))
(exp.f64 (neg.f64 (.f64 (fma.f64 #s(literal 1/2 binary64) k #s(literal -1/2 binary64)) (log.f64 (.f64 (*.f64 #s(literal 2 binary64) n) (PI.f64))))))
(exp.f64 (.f64 (.f64 (fma.f64 #s(literal 1/2 binary64) k #s(literal -1/2 binary64)) (log.f64 (.f64 (.f64 #s(literal 2 binary64) n) (PI.f64)))) #s(literal -1 binary64)))
(exp.f64 (.f64 (log.f64 (sqrt.f64 (.f64 (*.f64 #s(literal 2 binary64) n) (PI.f64)))) (-.f64 #s(literal 1 binary64) k)))
(exp.f64 (.f64 (log.f64 (.f64 (*.f64 #s(literal 2 binary64) n) (PI.f64))) (fma.f64 #s(literal -1/2 binary64) k #s(literal 1/2 binary64))))
(exp.f64 (.f64 (.f64 (log.f64 (.f64 (.f64 #s(literal 2 binary64) n) (PI.f64))) (-.f64 k #s(literal 1 binary64))) #s(literal -1/2 binary64)))
(.f64 (exp.f64 (log.f64 (.f64 (PI.f64) n))) (exp.f64 (log.f64 #s(literal 2 binary64))))
(.f64 (exp.f64 (log.f64 #s(literal 2 binary64))) (exp.f64 (log.f64 (.f64 (PI.f64) n))))
(.f64 (exp.f64 (log.f64 (.f64 #s(literal 2 binary64) (PI.f64)))) (exp.f64 (log.f64 n)))
(.f64 (exp.f64 (log.f64 (.f64 #s(literal 2 binary64) n))) (PI.f64))
(.f64 (exp.f64 (log.f64 n)) (exp.f64 (log.f64 (.f64 #s(literal 2 binary64) (PI.f64)))))
(.f64 (.f64 (*.f64 #s(literal 2 binary64) n) (sqrt.f64 (PI.f64))) (sqrt.f64 (PI.f64)))
(.f64 (.f64 (*.f64 #s(literal 2 binary64) n) (pow.f64 (cbrt.f64 (PI.f64)) #s(literal 2 binary64))) (cbrt.f64 (PI.f64)))
(.f64 (sqrt.f64 (PI.f64)) (.f64 (sqrt.f64 (PI.f64)) (*.f64 #s(literal 2 binary64) n)))
(.f64 (pow.f64 (cbrt.f64 (PI.f64)) #s(literal 2 binary64)) (.f64 (cbrt.f64 (PI.f64)) (*.f64 #s(literal 2 binary64) n)))
(.f64 (.f64 #s(literal 2 binary64) n) (PI.f64))
(.f64 (.f64 (PI.f64) n) #s(literal 2 binary64))
(.f64 #s(literal 1 binary64) (.f64 (*.f64 #s(literal 2 binary64) n) (PI.f64)))
(.f64 (sqrt.f64 (.f64 (.f64 #s(literal 2 binary64) n) (PI.f64))) (sqrt.f64 (.f64 (*.f64 #s(literal 2 binary64) n) (PI.f64))))
(.f64 (.f64 #s(literal 2 binary64) (PI.f64)) n)
(.f64 #s(literal 2 binary64) (.f64 (PI.f64) n))
(.f64 (PI.f64) (exp.f64 (log.f64 (.f64 #s(literal 2 binary64) n))))
(.f64 (PI.f64) (.f64 #s(literal 2 binary64) n))
(.f64 n (.f64 #s(literal 2 binary64) (PI.f64)))
(pow.f64 (pow.f64 (.f64 (.f64 #s(literal 2 binary64) n) (PI.f64)) #s(literal 2 binary64)) #s(literal 1/2 binary64))
(pow.f64 (.f64 (.f64 #s(literal 2 binary64) n) (PI.f64)) #s(literal 1 binary64))
(pow.f64 (sqrt.f64 (.f64 (.f64 #s(literal 2 binary64) n) (PI.f64))) #s(literal 2 binary64))
(sqrt.f64 (pow.f64 (.f64 (.f64 #s(literal 2 binary64) n) (PI.f64)) #s(literal 2 binary64)))
(exp.f64 (fma.f64 (log.f64 (.f64 (.f64 #s(literal 2 binary64) n) (PI.f64))) #s(literal 1/2 binary64) (log.f64 (sqrt.f64 (.f64 (.f64 #s(literal 2 binary64) n) (PI.f64))))))
(exp.f64 (log.f64 (.f64 (.f64 #s(literal 2 binary64) n) (PI.f64))))

eval539.0ms (5.8%)

Memory: -221.6MiB live, 411.3MiB allocated
Compiler: Compiled 41 721 to 4 056 computations (90.3% saved)

prune210.0ms (2.2%)

Memory

9.4MiB live, 374.7MiB allocated

Pruning

20 alts after pruning (18 fresh and 2 done)

	Pruned	Kept	Total
New	1 984	18	2 002
Fresh	16	0	16
Picked	3	2	5
Done	0	0	0
Total	2 003	20	2 023

Accuracy

100.0%

Counts

2 023 → 20

Alt Table

Click to see full alt table

Status	Accuracy	Program
▶	99.5%	(/.f64 (pow.f64 (.f64 (.f64 #s(literal 2 binary64) n) (PI.f64)) (fma.f64 #s(literal -1/2 binary64) k #s(literal 1/2 binary64))) (sqrt.f64 k))
	99.4%	(/.f64 (/.f64 #s(literal -1 binary64) (sqrt.f64 k)) (neg.f64 (pow.f64 (.f64 (.f64 #s(literal 2 binary64) n) (PI.f64)) (fma.f64 #s(literal 1/2 binary64) k #s(literal -1/2 binary64)))))
	99.5%	(/.f64 #s(literal 1 binary64) (.f64 (pow.f64 (.f64 (*.f64 #s(literal 2 binary64) n) (PI.f64)) (fma.f64 #s(literal 1/2 binary64) k #s(literal -1/2 binary64))) (sqrt.f64 k)))
	50.1%	(.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) (/.f64 #s(literal 1 binary64) #s(approx (pow (sqrt ( n (* (PI) 2))) (- k 1)) (/.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (*.f64 (PI.f64) n))) (sqrt.f64 #s(literal 2 binary64))))))
▶	99.7%	(.f64 (sqrt.f64 n) (sqrt.f64 (/.f64 (.f64 #s(literal 2 binary64) (PI.f64)) (.f64 (pow.f64 (.f64 (*.f64 #s(literal 2 binary64) n) (PI.f64)) k) k))))
	75.7%	(sqrt.f64 (/.f64 (.f64 (/.f64 (.f64 (PI.f64) n) k) #s(literal 2 binary64)) (pow.f64 (.f64 (.f64 #s(literal 2 binary64) n) (PI.f64)) k)))
	87.0%	(sqrt.f64 (/.f64 (.f64 (.f64 #s(literal 2 binary64) n) (PI.f64)) (.f64 (pow.f64 (.f64 (*.f64 #s(literal 2 binary64) n) (PI.f64)) k) k)))
	50.3%	#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (/.f64 (sqrt.f64 (.f64 (.f64 #s(literal 2 binary64) n) (PI.f64))) (sqrt.f64 k)))
▶	39.0%	#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (/.f64 (sqrt.f64 #s(literal 2 binary64)) (sqrt.f64 (/.f64 k (*.f64 (PI.f64) n)))))
✓	99.5%	#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (.f64 (pow.f64 (.f64 (*.f64 #s(literal 2 binary64) n) (PI.f64)) (fma.f64 k #s(literal -1/2 binary64) #s(literal 1/2 binary64))) (sqrt.f64 (/.f64 #s(literal 1 binary64) k))))
	50.2%	#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (.f64 (sqrt.f64 (.f64 (*.f64 #s(literal 2 binary64) n) (PI.f64))) (pow.f64 k #s(literal -1/2 binary64))))
	37.2%	#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (.f64 (sqrt.f64 (.f64 #s(literal 2 binary64) (PI.f64))) (sqrt.f64 (/.f64 n k))))
	50.3%	#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (.f64 (sqrt.f64 n) (sqrt.f64 (/.f64 (.f64 #s(literal 2 binary64) (PI.f64)) k))))
	50.2%	#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (.f64 (sqrt.f64 #s(literal 2 binary64)) (/.f64 (sqrt.f64 (.f64 (PI.f64) n)) (sqrt.f64 k))))
	50.2%	#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (.f64 (sqrt.f64 #s(literal 2 binary64)) (.f64 (sqrt.f64 n) (sqrt.f64 (/.f64 (PI.f64) k)))))
	37.3%	#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (.f64 (sqrt.f64 #s(literal 2 binary64)) (sqrt.f64 (/.f64 (.f64 (*.f64 (sqrt.f64 (PI.f64)) (sqrt.f64 (PI.f64))) n) k))))
✓	37.3%	#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (.f64 (sqrt.f64 #s(literal 2 binary64)) (sqrt.f64 (/.f64 (.f64 (PI.f64) n) k))))
	50.2%	#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (.f64 (neg.f64 (sqrt.f64 (.f64 (*.f64 #s(literal 2 binary64) n) (PI.f64)))) (/.f64 #s(literal -1 binary64) (sqrt.f64 k))))
▶	50.1%	#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (.f64 #s(approx (pow ( (* 2 n) (PI)) (+ (* k -1/2) 1/2)) (.f64 (sqrt.f64 (.f64 (PI.f64) n)) (sqrt.f64 #s(literal 2 binary64)))) (sqrt.f64 (/.f64 #s(literal 1 binary64) k))))
▶	37.5%	#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt.f64 (.f64 (/.f64 (.f64 (PI.f64) n) k) #s(literal 2 binary64))))

Compiler

Compiled 492 to 449 computations (8.7% saved)

simplify39.0ms (0.4%)

Memory

-26.9MiB live, 12.0MiB allocated

Algorithm

1×	egg-herbie

Localize:

Found 20 expressions of interest:

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

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	51	339
0	79	336
1	118	330
2	155	330
3	199	327
4	223	327
5	237	327
6	258	327
7	295	327
8	325	327
9	331	327
0	331	327

Stop Event

1×	iter limit
1×	saturated
1×	iter limit

Calls

Call 1

Inputs
(.f64 (sqrt.f64 n) (sqrt.f64 (/.f64 (.f64 #s(literal 2 binary64) (PI.f64)) (.f64 (pow.f64 (.f64 (*.f64 #s(literal 2 binary64) n) (PI.f64)) k) k))))
(sqrt.f64 n)
n
(sqrt.f64 (/.f64 (.f64 #s(literal 2 binary64) (PI.f64)) (.f64 (pow.f64 (.f64 (.f64 #s(literal 2 binary64) n) (PI.f64)) k) k)))
(/.f64 (.f64 #s(literal 2 binary64) (PI.f64)) (.f64 (pow.f64 (.f64 (.f64 #s(literal 2 binary64) n) (PI.f64)) k) k))
(*.f64 #s(literal 2 binary64) (PI.f64))
#s(literal 2 binary64)
(PI.f64)
(.f64 (pow.f64 (.f64 (*.f64 #s(literal 2 binary64) n) (PI.f64)) k) k)
(pow.f64 (.f64 (.f64 #s(literal 2 binary64) n) (PI.f64)) k)
(.f64 (.f64 #s(literal 2 binary64) n) (PI.f64))
(*.f64 #s(literal 2 binary64) n)
k
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt.f64 (.f64 (/.f64 (.f64 (PI.f64) n) k) #s(literal 2 binary64))))
(sqrt.f64 (.f64 (/.f64 (.f64 (PI.f64) n) k) #s(literal 2 binary64)))
(.f64 (/.f64 (.f64 (PI.f64) n) k) #s(literal 2 binary64))
(/.f64 (*.f64 (PI.f64) n) k)
(*.f64 (PI.f64) n)
(PI.f64)
n
k
#s(literal 2 binary64)
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (/.f64 (sqrt.f64 #s(literal 2 binary64)) (sqrt.f64 (/.f64 k (*.f64 (PI.f64) n)))))
(/.f64 (sqrt.f64 #s(literal 2 binary64)) (sqrt.f64 (/.f64 k (*.f64 (PI.f64) n))))
(sqrt.f64 #s(literal 2 binary64))
#s(literal 2 binary64)
(sqrt.f64 (/.f64 k (*.f64 (PI.f64) n)))
(/.f64 k (*.f64 (PI.f64) n))
k
(*.f64 (PI.f64) n)
(PI.f64)
n
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (.f64 #s(approx (pow ( (* 2 n) (PI)) (+ (* k -1/2) 1/2)) (.f64 (sqrt.f64 (.f64 (PI.f64) n)) (sqrt.f64 #s(literal 2 binary64)))) (sqrt.f64 (/.f64 #s(literal 1 binary64) k))))
(.f64 #s(approx (pow ( (* 2 n) (PI)) (+ (* k -1/2) 1/2)) (.f64 (sqrt.f64 (.f64 (PI.f64) n)) (sqrt.f64 #s(literal 2 binary64)))) (sqrt.f64 (/.f64 #s(literal 1 binary64) k)))
#s(approx (pow (* (* 2 n) (PI)) (+ (* k -1/2) 1/2)) (.f64 (sqrt.f64 (.f64 (PI.f64) n)) (sqrt.f64 #s(literal 2 binary64))))
(.f64 (sqrt.f64 (.f64 (PI.f64) n)) (sqrt.f64 #s(literal 2 binary64)))
(sqrt.f64 (*.f64 (PI.f64) n))
(*.f64 (PI.f64) n)
(PI.f64)
n
(sqrt.f64 #s(literal 2 binary64))
#s(literal 2 binary64)
(sqrt.f64 (/.f64 #s(literal 1 binary64) k))
(/.f64 #s(literal 1 binary64) k)
#s(literal 1 binary64)
k
(/.f64 (pow.f64 (.f64 (.f64 #s(literal 2 binary64) n) (PI.f64)) (fma.f64 #s(literal -1/2 binary64) k #s(literal 1/2 binary64))) (sqrt.f64 k))
(pow.f64 (.f64 (.f64 #s(literal 2 binary64) n) (PI.f64)) (fma.f64 #s(literal -1/2 binary64) k #s(literal 1/2 binary64)))
(.f64 (.f64 #s(literal 2 binary64) n) (PI.f64))
(*.f64 #s(literal 2 binary64) n)
#s(literal 2 binary64)
n
(PI.f64)
(fma.f64 #s(literal -1/2 binary64) k #s(literal 1/2 binary64))
#s(literal -1/2 binary64)
k
#s(literal 1/2 binary64)
(sqrt.f64 k)

Outputs
(.f64 (sqrt.f64 n) (sqrt.f64 (/.f64 (.f64 #s(literal 2 binary64) (PI.f64)) (.f64 (pow.f64 (.f64 (*.f64 #s(literal 2 binary64) n) (PI.f64)) k) k))))
(.f64 (sqrt.f64 (.f64 (/.f64 (/.f64 #s(literal 2 binary64) (pow.f64 (.f64 (.f64 #s(literal 2 binary64) n) (PI.f64)) k)) k) (PI.f64))) (sqrt.f64 n))
(sqrt.f64 n)
n
(sqrt.f64 (/.f64 (.f64 #s(literal 2 binary64) (PI.f64)) (.f64 (pow.f64 (.f64 (.f64 #s(literal 2 binary64) n) (PI.f64)) k) k)))
(sqrt.f64 (.f64 (/.f64 (/.f64 #s(literal 2 binary64) (pow.f64 (.f64 (*.f64 #s(literal 2 binary64) n) (PI.f64)) k)) k) (PI.f64)))
(/.f64 (.f64 #s(literal 2 binary64) (PI.f64)) (.f64 (pow.f64 (.f64 (.f64 #s(literal 2 binary64) n) (PI.f64)) k) k))
(.f64 (/.f64 (/.f64 #s(literal 2 binary64) (pow.f64 (.f64 (*.f64 #s(literal 2 binary64) n) (PI.f64)) k)) k) (PI.f64))
(*.f64 #s(literal 2 binary64) (PI.f64))
(*.f64 (PI.f64) #s(literal 2 binary64))
#s(literal 2 binary64)
(PI.f64)
(.f64 (pow.f64 (.f64 (*.f64 #s(literal 2 binary64) n) (PI.f64)) k) k)
(pow.f64 (.f64 (.f64 #s(literal 2 binary64) n) (PI.f64)) k)
(.f64 (.f64 #s(literal 2 binary64) n) (PI.f64))
(*.f64 #s(literal 2 binary64) n)
k
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt.f64 (.f64 (/.f64 (.f64 (PI.f64) n) k) #s(literal 2 binary64))))
(sqrt.f64 (.f64 (/.f64 (.f64 (PI.f64) n) k) #s(literal 2 binary64)))
(.f64 (/.f64 (.f64 (PI.f64) n) k) #s(literal 2 binary64))
(/.f64 (*.f64 (PI.f64) n) k)
(*.f64 (PI.f64) n)
(PI.f64)
n
k
#s(literal 2 binary64)
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (/.f64 (sqrt.f64 #s(literal 2 binary64)) (sqrt.f64 (/.f64 k (*.f64 (PI.f64) n)))))
(/.f64 (sqrt.f64 #s(literal 2 binary64)) (sqrt.f64 (/.f64 k (*.f64 (PI.f64) n))))
(sqrt.f64 #s(literal 2 binary64))
#s(literal 2 binary64)
(sqrt.f64 (/.f64 k (*.f64 (PI.f64) n)))
(/.f64 k (*.f64 (PI.f64) n))
k
(*.f64 (PI.f64) n)
(PI.f64)
n
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (.f64 #s(approx (pow ( (* 2 n) (PI)) (+ (* k -1/2) 1/2)) (.f64 (sqrt.f64 (.f64 (PI.f64) n)) (sqrt.f64 #s(literal 2 binary64)))) (sqrt.f64 (/.f64 #s(literal 1 binary64) k))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) k)) #s(approx (pow ( (* 2 n) (PI)) (+ (* k -1/2) 1/2)) (.f64 (sqrt.f64 (.f64 (PI.f64) n)) (sqrt.f64 #s(literal 2 binary64))))))
(.f64 #s(approx (pow ( (* 2 n) (PI)) (+ (* k -1/2) 1/2)) (.f64 (sqrt.f64 (.f64 (PI.f64) n)) (sqrt.f64 #s(literal 2 binary64)))) (sqrt.f64 (/.f64 #s(literal 1 binary64) k)))
(.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) k)) #s(approx (pow ( (* 2 n) (PI)) (+ (* k -1/2) 1/2)) (.f64 (sqrt.f64 (.f64 (PI.f64) n)) (sqrt.f64 #s(literal 2 binary64)))))
#s(approx (pow (* (* 2 n) (PI)) (+ (* k -1/2) 1/2)) (.f64 (sqrt.f64 (.f64 (PI.f64) n)) (sqrt.f64 #s(literal 2 binary64))))
(.f64 (sqrt.f64 (.f64 (PI.f64) n)) (sqrt.f64 #s(literal 2 binary64)))
(sqrt.f64 (*.f64 (PI.f64) n))
(*.f64 (PI.f64) n)
(PI.f64)
n
(sqrt.f64 #s(literal 2 binary64))
#s(literal 2 binary64)
(sqrt.f64 (/.f64 #s(literal 1 binary64) k))
(/.f64 #s(literal 1 binary64) k)
#s(literal 1 binary64)
k
(/.f64 (pow.f64 (.f64 (.f64 #s(literal 2 binary64) n) (PI.f64)) (fma.f64 #s(literal -1/2 binary64) k #s(literal 1/2 binary64))) (sqrt.f64 k))
(pow.f64 (.f64 (.f64 #s(literal 2 binary64) n) (PI.f64)) (fma.f64 #s(literal -1/2 binary64) k #s(literal 1/2 binary64)))
(.f64 (.f64 #s(literal 2 binary64) n) (PI.f64))
(*.f64 #s(literal 2 binary64) n)
#s(literal 2 binary64)
n
(PI.f64)
(fma.f64 #s(literal -1/2 binary64) k #s(literal 1/2 binary64))
#s(literal -1/2 binary64)
k
#s(literal 1/2 binary64)
(sqrt.f64 k)

localize147.0ms (1.6%)

Memory

32.1MiB live, 184.0MiB allocated

Localize:

Found 20 expressions of interest:

New	Metric	Score
accuracy	0.14681625976844204	(/.f64 (pow.f64 (.f64 (.f64 #s(literal 2 binary64) n) (PI.f64)) (fma.f64 #s(literal -1/2 binary64) k #s(literal 1/2 binary64))) (sqrt.f64 k))
accuracy	0.19140625	(.f64 (.f64 #s(literal 2 binary64) n) (PI.f64))
accuracy	0.22818734794137574	(pow.f64 (.f64 (.f64 #s(literal 2 binary64) n) (PI.f64)) (fma.f64 #s(literal -1/2 binary64) k #s(literal 1/2 binary64)))
accuracy	13.562169815496654	(PI.f64)
accuracy	0.205410009768442	(.f64 #s(approx (pow ( (* 2 n) (PI)) (+ (* k -1/2) 1/2)) (.f64 (sqrt.f64 (.f64 (PI.f64) n)) (sqrt.f64 #s(literal 2 binary64)))) (sqrt.f64 (/.f64 #s(literal 1 binary64) k)))
accuracy	0.34117128907376815	(.f64 (sqrt.f64 (.f64 (PI.f64) n)) (sqrt.f64 #s(literal 2 binary64)))
accuracy	13.562169815496654	(PI.f64)
accuracy	18.070942331824988	#s(approx (pow (* (* 2 n) (PI)) (+ (* k -1/2) 1/2)) (.f64 (sqrt.f64 (.f64 (PI.f64) n)) (sqrt.f64 #s(literal 2 binary64))))
accuracy	0.3483200195368841	(/.f64 (sqrt.f64 #s(literal 2 binary64)) (sqrt.f64 (/.f64 k (*.f64 (PI.f64) n))))
accuracy	7.3454033439399335	(sqrt.f64 (/.f64 k (*.f64 (PI.f64) n)))
accuracy	13.562169815496654	(PI.f64)
accuracy	17.975855259551754	#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (/.f64 (sqrt.f64 #s(literal 2 binary64)) (sqrt.f64 (/.f64 k (*.f64 (PI.f64) n)))))
accuracy	0.19140625	(*.f64 (PI.f64) n)
accuracy	8.33353557423163	(sqrt.f64 (.f64 (/.f64 (.f64 (PI.f64) n) k) #s(literal 2 binary64)))
accuracy	13.562169815496654	(PI.f64)
accuracy	17.975855259551754	#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt.f64 (.f64 (/.f64 (.f64 (PI.f64) n) k) #s(literal 2 binary64))))
accuracy	0.12109375	(/.f64 (.f64 #s(literal 2 binary64) (PI.f64)) (.f64 (pow.f64 (.f64 (.f64 #s(literal 2 binary64) n) (PI.f64)) k) k))
accuracy	0.150722509768442	(.f64 (sqrt.f64 n) (sqrt.f64 (/.f64 (.f64 #s(literal 2 binary64) (PI.f64)) (.f64 (pow.f64 (.f64 (*.f64 #s(literal 2 binary64) n) (PI.f64)) k) k))))
accuracy	0.19140625	(.f64 (.f64 #s(literal 2 binary64) n) (PI.f64))
accuracy	13.562169815496654	(PI.f64)

Samples

94.0ms	200×	0	valid
24.0ms	56×	0	exit

Compiler

Compiled 284 to 45 computations (84.2% saved)

Precisions

Click to see histograms. Total time spent on operations: 94.0ms

ival-mult: 44.0ms (46.9% of total)

ival-pow: 17.0ms (18.1% of total)

ival-div: 15.0ms (16% of total)

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

ival-add: 2.0ms (2.1% of total)

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

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

exact: 1.0ms (1.1% of total)

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

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

series92.0ms (1%)

Memory

-11.5MiB live, 137.7MiB allocated

Counts

23 → 420

Calls

Call 1

Inputs
#s(alt (.f64 (sqrt.f64 n) (sqrt.f64 (/.f64 (.f64 #s(literal 2 binary64) (PI.f64)) (.f64 (pow.f64 (.f64 (.f64 #s(literal 2 binary64) n) (PI.f64)) k) k)))) (patch (.f64 (sqrt.f64 n) (sqrt.f64 (/.f64 (.f64 #s(literal 2 binary64) (PI.f64)) (.f64 (pow.f64 (.f64 (.f64 #s(literal 2 binary64) n) (PI.f64)) k) k)))) #<representation binary64>) () ())
#s(alt (sqrt.f64 n) (patch (sqrt.f64 n) #<representation binary64>) () ())
#s(alt (sqrt.f64 (/.f64 (.f64 #s(literal 2 binary64) (PI.f64)) (.f64 (pow.f64 (.f64 (.f64 #s(literal 2 binary64) n) (PI.f64)) k) k))) (patch (sqrt.f64 (/.f64 (.f64 #s(literal 2 binary64) (PI.f64)) (.f64 (pow.f64 (.f64 (.f64 #s(literal 2 binary64) n) (PI.f64)) k) k))) #<representation binary64>) () ())
#s(alt (.f64 #s(literal 2 binary64) (PI.f64)) (patch (.f64 #s(literal 2 binary64) (PI.f64)) #<representation binary64>) () ())
#s(alt #s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt.f64 (.f64 (/.f64 (.f64 (PI.f64) n) k) #s(literal 2 binary64)))) (patch #s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt.f64 (.f64 (/.f64 (.f64 (PI.f64) n) k) #s(literal 2 binary64)))) #<representation binary64>) () ())
#s(alt (sqrt.f64 (.f64 (/.f64 (.f64 (PI.f64) n) k) #s(literal 2 binary64))) (patch (sqrt.f64 (.f64 (/.f64 (.f64 (PI.f64) n) k) #s(literal 2 binary64))) #<representation binary64>) () ())
#s(alt (.f64 (/.f64 (.f64 (PI.f64) n) k) #s(literal 2 binary64)) (patch (.f64 (/.f64 (.f64 (PI.f64) n) k) #s(literal 2 binary64)) #<representation binary64>) () ())
#s(alt (/.f64 (.f64 (PI.f64) n) k) (patch (/.f64 (.f64 (PI.f64) n) k) #<representation binary64>) () ())
#s(alt #s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (/.f64 (sqrt.f64 #s(literal 2 binary64)) (sqrt.f64 (/.f64 k (.f64 (PI.f64) n))))) (patch #s(approx ( (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (/.f64 (sqrt.f64 #s(literal 2 binary64)) (sqrt.f64 (/.f64 k (*.f64 (PI.f64) n))))) #<representation binary64>) () ())
#s(alt (/.f64 (sqrt.f64 #s(literal 2 binary64)) (sqrt.f64 (/.f64 k (.f64 (PI.f64) n)))) (patch (/.f64 (sqrt.f64 #s(literal 2 binary64)) (sqrt.f64 (/.f64 k (.f64 (PI.f64) n)))) #<representation binary64>) () ())
#s(alt (sqrt.f64 #s(literal 2 binary64)) (patch (sqrt.f64 #s(literal 2 binary64)) #<representation binary64>) () ())
#s(alt (sqrt.f64 (/.f64 k (.f64 (PI.f64) n))) (patch (sqrt.f64 (/.f64 k (.f64 (PI.f64) n))) #<representation binary64>) () ())
#s(alt #s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (.f64 #s(approx (pow ( (* 2 n) (PI)) (+ (* k -1/2) 1/2)) (.f64 (sqrt.f64 (.f64 (PI.f64) n)) (sqrt.f64 #s(literal 2 binary64)))) (sqrt.f64 (/.f64 #s(literal 1 binary64) k)))) (patch #s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (.f64 #s(approx (pow ( (* 2 n) (PI)) (+ (* k -1/2) 1/2)) (.f64 (sqrt.f64 (.f64 (PI.f64) n)) (sqrt.f64 #s(literal 2 binary64)))) (sqrt.f64 (/.f64 #s(literal 1 binary64) k)))) #<representation binary64>) () ())
#s(alt (.f64 #s(approx (pow ( (* 2 n) (PI)) (+ (* k -1/2) 1/2)) (.f64 (sqrt.f64 (.f64 (PI.f64) n)) (sqrt.f64 #s(literal 2 binary64)))) (sqrt.f64 (/.f64 #s(literal 1 binary64) k))) (patch (.f64 #s(approx (pow ( (* 2 n) (PI)) (+ (* k -1/2) 1/2)) (.f64 (sqrt.f64 (.f64 (PI.f64) n)) (sqrt.f64 #s(literal 2 binary64)))) (sqrt.f64 (/.f64 #s(literal 1 binary64) k))) #<representation binary64>) () ())
#s(alt #s(approx (pow (* (* 2 n) (PI)) (+ (* k -1/2) 1/2)) (.f64 (sqrt.f64 (.f64 (PI.f64) n)) (sqrt.f64 #s(literal 2 binary64)))) (patch #s(approx (pow (* (* 2 n) (PI)) (+ (* k -1/2) 1/2)) (.f64 (sqrt.f64 (.f64 (PI.f64) n)) (sqrt.f64 #s(literal 2 binary64)))) #<representation binary64>) () ())
#s(alt (.f64 (sqrt.f64 (.f64 (PI.f64) n)) (sqrt.f64 #s(literal 2 binary64))) (patch (.f64 (sqrt.f64 (.f64 (PI.f64) n)) (sqrt.f64 #s(literal 2 binary64))) #<representation binary64>) () ())
#s(alt (/.f64 (pow.f64 (.f64 (.f64 #s(literal 2 binary64) n) (PI.f64)) (fma.f64 #s(literal -1/2 binary64) k #s(literal 1/2 binary64))) (sqrt.f64 k)) (patch (/.f64 (pow.f64 (.f64 (.f64 #s(literal 2 binary64) n) (PI.f64)) (fma.f64 #s(literal -1/2 binary64) k #s(literal 1/2 binary64))) (sqrt.f64 k)) #<representation binary64>) () ())
#s(alt (pow.f64 (.f64 (.f64 #s(literal 2 binary64) n) (PI.f64)) (fma.f64 #s(literal -1/2 binary64) k #s(literal 1/2 binary64))) (patch (pow.f64 (.f64 (.f64 #s(literal 2 binary64) n) (PI.f64)) (fma.f64 #s(literal -1/2 binary64) k #s(literal 1/2 binary64))) #<representation binary64>) () ())
#s(alt (.f64 (.f64 #s(literal 2 binary64) n) (PI.f64)) (patch (.f64 (.f64 #s(literal 2 binary64) n) (PI.f64)) #<representation binary64>) () ())
#s(alt (.f64 #s(literal 2 binary64) n) (patch (.f64 #s(literal 2 binary64) n) #<representation binary64>) () ())
#s(alt (PI.f64) (patch (PI.f64) #<representation binary64>) () ())
#s(alt (/.f64 (.f64 #s(literal 2 binary64) (PI.f64)) (.f64 (pow.f64 (.f64 (.f64 #s(literal 2 binary64) n) (PI.f64)) k) k)) (patch (/.f64 (.f64 #s(literal 2 binary64) (PI.f64)) (.f64 (pow.f64 (.f64 (.f64 #s(literal 2 binary64) n) (PI.f64)) k) k)) #<representation binary64>) () ())
#s(alt (.f64 (PI.f64) n) (patch (.f64 (PI.f64) n) #<representation binary64>) () ())

Outputs
#s(alt (* (sqrt (/ (* n (PI)) k)) (sqrt 2)) (taylor 0 k) (#s(alt (.f64 (sqrt.f64 n) (sqrt.f64 (/.f64 (.f64 #s(literal 2 binary64) (PI.f64)) (.f64 (pow.f64 (.f64 (.f64 #s(literal 2 binary64) n) (PI.f64)) k) k)))) (patch (.f64 (sqrt.f64 n) (sqrt.f64 (/.f64 (.f64 #s(literal 2 binary64) (PI.f64)) (.f64 (pow.f64 (.f64 (.f64 #s(literal 2 binary64) n) (PI.f64)) k) k)))) #<representation binary64>) () ())) ())
#s(alt (/ (+ (* -1/2 (* (sqrt (* (pow k 3) (* n (PI)))) (* (log (* 2 (* n (PI)))) (sqrt 2)))) (* (sqrt (* k (* n (PI)))) (sqrt 2))) k) (taylor 0 k) (#s(alt (.f64 (sqrt.f64 n) (sqrt.f64 (/.f64 (.f64 #s(literal 2 binary64) (PI.f64)) (.f64 (pow.f64 (.f64 (.f64 #s(literal 2 binary64) n) (PI.f64)) k) k)))) (patch (.f64 (sqrt.f64 n) (sqrt.f64 (/.f64 (.f64 #s(literal 2 binary64) (PI.f64)) (.f64 (pow.f64 (.f64 (.f64 #s(literal 2 binary64) n) (PI.f64)) k) k)))) #<representation binary64>) () ())) ())
#s(alt (/ (+ (* (sqrt (* k (* n (PI)))) (sqrt 2)) (* (pow k 2) (+ (* -1/2 (* (sqrt (/ k (* n (PI)))) (* (sqrt 2) (+ (* -1 (* n (* (PI) (pow (log (* 2 (* n (PI)))) 2)))) (* 1/2 (* n (* (PI) (pow (log (* 2 (* n (PI)))) 2)))))))) (* -1/2 (* (sqrt (/ (* n (PI)) k)) (* (log (* 2 (* n (PI)))) (sqrt 2))))))) k) (taylor 0 k) (#s(alt (.f64 (sqrt.f64 n) (sqrt.f64 (/.f64 (.f64 #s(literal 2 binary64) (PI.f64)) (.f64 (pow.f64 (.f64 (.f64 #s(literal 2 binary64) n) (PI.f64)) k) k)))) (patch (.f64 (sqrt.f64 n) (sqrt.f64 (/.f64 (.f64 #s(literal 2 binary64) (PI.f64)) (.f64 (pow.f64 (.f64 (.f64 #s(literal 2 binary64) n) (PI.f64)) k) k)))) #<representation binary64>) () ())) ())
#s(alt (/ (+ (* (sqrt (* k (* n (PI)))) (sqrt 2)) (* (pow k 2) (+ (* -1/2 (* (sqrt (/ (* n (PI)) k)) (* (log (* 2 (* n (PI)))) (sqrt 2)))) (* k (+ (* -1/2 (* (sqrt (/ 1 (* k (* n (PI))))) (* (sqrt 2) (+ (* -1 (* n (* (PI) (pow (log (* 2 (* n (PI)))) 2)))) (* 1/2 (* n (* (PI) (pow (log (* 2 (* n (PI)))) 2)))))))) (* -1/2 (* (sqrt (/ k (* n (PI)))) (* (sqrt 2) (+ (* -1 (* (log (* 2 (* n (PI)))) (+ (* -1 (* n (* (PI) (pow (log (* 2 (* n (PI)))) 2)))) (* 1/2 (* n (* (PI) (pow (log (* 2 (* n (PI)))) 2))))))) (+ (* -1/2 (* n (* (PI) (pow (log (* 2 (* n (PI)))) 3)))) (+ (* 1/6 (* n (* (PI) (pow (log (* 2 (* n (PI)))) 3)))) (* 1/4 (/ (* n (* (PI) (pow (log (* 2 (* n (PI)))) 2))) k))))))))))))) k) (taylor 0 k) (#s(alt (.f64 (sqrt.f64 n) (sqrt.f64 (/.f64 (.f64 #s(literal 2 binary64) (PI.f64)) (.f64 (pow.f64 (.f64 (.f64 #s(literal 2 binary64) n) (PI.f64)) k) k)))) (patch (.f64 (sqrt.f64 n) (sqrt.f64 (/.f64 (.f64 #s(literal 2 binary64) (PI.f64)) (.f64 (pow.f64 (.f64 (.f64 #s(literal 2 binary64) n) (PI.f64)) k) k)))) #<representation binary64>) () ())) ())
#s(alt (* (sqrt (/ (PI) k)) (sqrt 2)) (taylor 0 k) (#s(alt (sqrt.f64 (/.f64 (.f64 #s(literal 2 binary64) (PI.f64)) (.f64 (pow.f64 (.f64 (.f64 #s(literal 2 binary64) n) (PI.f64)) k) k))) (patch (sqrt.f64 (/.f64 (.f64 #s(literal 2 binary64) (PI.f64)) (.f64 (pow.f64 (.f64 (.f64 #s(literal 2 binary64) n) (PI.f64)) k) k))) #<representation binary64>) () ())) ())
#s(alt (/ (+ (* -1/2 (* (sqrt (* (pow k 3) (PI))) (* (log (* 2 (* n (PI)))) (sqrt 2)))) (* (sqrt (* k (PI))) (sqrt 2))) k) (taylor 0 k) (#s(alt (sqrt.f64 (/.f64 (.f64 #s(literal 2 binary64) (PI.f64)) (.f64 (pow.f64 (.f64 (.f64 #s(literal 2 binary64) n) (PI.f64)) k) k))) (patch (sqrt.f64 (/.f64 (.f64 #s(literal 2 binary64) (PI.f64)) (.f64 (pow.f64 (.f64 (.f64 #s(literal 2 binary64) n) (PI.f64)) k) k))) #<representation binary64>) () ())) ())
#s(alt (/ (+ (* (sqrt (* k (PI))) (sqrt 2)) (* (pow k 2) (+ (* -1/2 (* (sqrt (/ k (PI))) (* (sqrt 2) (+ (* -1 (* (PI) (pow (log (* 2 (* n (PI)))) 2))) (* 1/2 (* (PI) (pow (log (* 2 (* n (PI)))) 2))))))) (* -1/2 (* (sqrt (/ (PI) k)) (* (log (* 2 (* n (PI)))) (sqrt 2))))))) k) (taylor 0 k) (#s(alt (sqrt.f64 (/.f64 (.f64 #s(literal 2 binary64) (PI.f64)) (.f64 (pow.f64 (.f64 (.f64 #s(literal 2 binary64) n) (PI.f64)) k) k))) (patch (sqrt.f64 (/.f64 (.f64 #s(literal 2 binary64) (PI.f64)) (.f64 (pow.f64 (.f64 (.f64 #s(literal 2 binary64) n) (PI.f64)) k) k))) #<representation binary64>) () ())) ())
#s(alt (/ (+ (* (sqrt (* k (PI))) (sqrt 2)) (* (pow k 2) (+ (* -1/2 (* (sqrt (/ (PI) k)) (* (log (* 2 (* n (PI)))) (sqrt 2)))) (* k (+ (* -1/2 (* (sqrt (/ 1 (* k (PI)))) (* (sqrt 2) (+ (* -1 (* (PI) (pow (log (* 2 (* n (PI)))) 2))) (* 1/2 (* (PI) (pow (log (* 2 (* n (PI)))) 2))))))) (* -1/2 (* (sqrt (/ k (PI))) (* (sqrt 2) (+ (* -1 (* (log (* 2 (* n (PI)))) (+ (* -1 (* (PI) (pow (log (* 2 (* n (PI)))) 2))) (* 1/2 (* (PI) (pow (log (* 2 (* n (PI)))) 2)))))) (+ (* -1/2 (* (PI) (pow (log (* 2 (* n (PI)))) 3))) (+ (* 1/6 (* (PI) (pow (log (* 2 (* n (PI)))) 3))) (* 1/4 (/ (* (PI) (pow (log (* 2 (* n (PI)))) 2)) k))))))))))))) k) (taylor 0 k) (#s(alt (sqrt.f64 (/.f64 (.f64 #s(literal 2 binary64) (PI.f64)) (.f64 (pow.f64 (.f64 (.f64 #s(literal 2 binary64) n) (PI.f64)) k) k))) (patch (sqrt.f64 (/.f64 (.f64 #s(literal 2 binary64) (PI.f64)) (.f64 (pow.f64 (.f64 (.f64 #s(literal 2 binary64) n) (PI.f64)) k) k))) #<representation binary64>) () ())) ())
#s(alt (* (sqrt (/ (* n (PI)) k)) (sqrt 2)) (taylor 0 k) (#s(alt #s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt.f64 (.f64 (/.f64 (.f64 (PI.f64) n) k) #s(literal 2 binary64)))) (patch #s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt.f64 (.f64 (/.f64 (.f64 (PI.f64) n) k) #s(literal 2 binary64)))) #<representation binary64>) () ())) ())
#s(alt (/ (+ (* -1/2 (* (sqrt (* (pow k 3) (* n (PI)))) (* (log (* 2 (* n (PI)))) (sqrt 2)))) (* (sqrt (* k (* n (PI)))) (sqrt 2))) k) (taylor 0 k) (#s(alt #s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt.f64 (.f64 (/.f64 (.f64 (PI.f64) n) k) #s(literal 2 binary64)))) (patch #s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt.f64 (.f64 (/.f64 (.f64 (PI.f64) n) k) #s(literal 2 binary64)))) #<representation binary64>) () ())) ())
#s(alt (/ (+ (* k (+ (* -1/2 (* (sqrt (* k (* n (PI)))) (* (log (* 2 (* n (PI)))) (sqrt 2)))) (* 1/8 (* (sqrt (* (pow k 3) (* n (PI)))) (* (pow (log (* 2 (* n (PI)))) 2) (sqrt 2)))))) (* (sqrt (* k (* n (PI)))) (sqrt 2))) k) (taylor 0 k) (#s(alt #s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt.f64 (.f64 (/.f64 (.f64 (PI.f64) n) k) #s(literal 2 binary64)))) (patch #s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt.f64 (.f64 (/.f64 (.f64 (PI.f64) n) k) #s(literal 2 binary64)))) #<representation binary64>) () ())) ())
#s(alt (/ (+ (* k (+ (* -1/2 (* (sqrt (* k (* n (PI)))) (* (log (* 2 (* n (PI)))) (sqrt 2)))) (* k (+ (* -1/48 (* (sqrt (* (pow k 3) (* n (PI)))) (* (pow (log (* 2 (* n (PI)))) 3) (sqrt 2)))) (* 1/8 (* (sqrt (* k (* n (PI)))) (* (pow (log (* 2 (* n (PI)))) 2) (sqrt 2)))))))) (* (sqrt (* k (* n (PI)))) (sqrt 2))) k) (taylor 0 k) (#s(alt #s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt.f64 (.f64 (/.f64 (.f64 (PI.f64) n) k) #s(literal 2 binary64)))) (patch #s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt.f64 (.f64 (/.f64 (.f64 (PI.f64) n) k) #s(literal 2 binary64)))) #<representation binary64>) () ())) ())
#s(alt (* (sqrt (/ (* n (PI)) k)) (sqrt 2)) (taylor 0 k) (#s(alt (sqrt.f64 (.f64 (/.f64 (.f64 (PI.f64) n) k) #s(literal 2 binary64))) (patch (sqrt.f64 (.f64 (/.f64 (.f64 (PI.f64) n) k) #s(literal 2 binary64))) #<representation binary64>) () ())) ())
#s(alt (* (sqrt (/ (* n (PI)) k)) (sqrt 2)) (taylor 0 k) (#s(alt (sqrt.f64 (.f64 (/.f64 (.f64 (PI.f64) n) k) #s(literal 2 binary64))) (patch (sqrt.f64 (.f64 (/.f64 (.f64 (PI.f64) n) k) #s(literal 2 binary64))) #<representation binary64>) () ())) ())
#s(alt (* (sqrt (/ (* n (PI)) k)) (sqrt 2)) (taylor 0 k) (#s(alt (sqrt.f64 (.f64 (/.f64 (.f64 (PI.f64) n) k) #s(literal 2 binary64))) (patch (sqrt.f64 (.f64 (/.f64 (.f64 (PI.f64) n) k) #s(literal 2 binary64))) #<representation binary64>) () ())) ())
#s(alt (* (sqrt (/ (* n (PI)) k)) (sqrt 2)) (taylor 0 k) (#s(alt (sqrt.f64 (.f64 (/.f64 (.f64 (PI.f64) n) k) #s(literal 2 binary64))) (patch (sqrt.f64 (.f64 (/.f64 (.f64 (PI.f64) n) k) #s(literal 2 binary64))) #<representation binary64>) () ())) ())
#s(alt (* 2 (/ (* n (PI)) k)) (taylor 0 k) (#s(alt (.f64 (/.f64 (.f64 (PI.f64) n) k) #s(literal 2 binary64)) (patch (.f64 (/.f64 (.f64 (PI.f64) n) k) #s(literal 2 binary64)) #<representation binary64>) () ())) ())
#s(alt (* 2 (/ (* n (PI)) k)) (taylor 0 k) (#s(alt (.f64 (/.f64 (.f64 (PI.f64) n) k) #s(literal 2 binary64)) (patch (.f64 (/.f64 (.f64 (PI.f64) n) k) #s(literal 2 binary64)) #<representation binary64>) () ())) ())
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#s(alt (* (sqrt (/ k (* n (PI)))) (pow (sqrt -1) 2)) (taylor -inf n) (#s(alt (sqrt.f64 (/.f64 k (.f64 (PI.f64) n))) (patch (sqrt.f64 (/.f64 k (.f64 (PI.f64) n))) #<representation binary64>) () ())) ())
#s(alt (* (sqrt (/ k (* n (PI)))) (pow (sqrt -1) 2)) (taylor -inf n) (#s(alt (sqrt.f64 (/.f64 k (.f64 (PI.f64) n))) (patch (sqrt.f64 (/.f64 k (.f64 (PI.f64) n))) #<representation binary64>) () ())) ())
#s(alt (* (sqrt (/ k (* n (PI)))) (pow (sqrt -1) 2)) (taylor -inf n) (#s(alt (sqrt.f64 (/.f64 k (.f64 (PI.f64) n))) (patch (sqrt.f64 (/.f64 k (.f64 (PI.f64) n))) #<representation binary64>) () ())) ())
#s(alt (* (sqrt (/ k (* n (PI)))) (pow (sqrt -1) 2)) (taylor -inf n) (#s(alt (sqrt.f64 (/.f64 k (.f64 (PI.f64) n))) (patch (sqrt.f64 (/.f64 k (.f64 (PI.f64) n))) #<representation binary64>) () ())) ())
#s(alt (* (sqrt (/ 1 k)) (exp (* 1/2 (* (+ (log (* -2 (PI))) (* -1 (log (/ -1 n)))) (- 1 k))))) (taylor -inf n) (#s(alt #s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (.f64 #s(approx (pow ( (* 2 n) (PI)) (+ (* k -1/2) 1/2)) (.f64 (sqrt.f64 (.f64 (PI.f64) n)) (sqrt.f64 #s(literal 2 binary64)))) (sqrt.f64 (/.f64 #s(literal 1 binary64) k)))) (patch #s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (.f64 #s(approx (pow ( (* 2 n) (PI)) (+ (* k -1/2) 1/2)) (.f64 (sqrt.f64 (.f64 (PI.f64) n)) (sqrt.f64 #s(literal 2 binary64)))) (sqrt.f64 (/.f64 #s(literal 1 binary64) k)))) #<representation binary64>) () ())) ())
#s(alt (* (sqrt (/ 1 k)) (exp (* 1/2 (* (+ (log (* -2 (PI))) (* -1 (log (/ -1 n)))) (- 1 k))))) (taylor -inf n) (#s(alt #s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (.f64 #s(approx (pow ( (* 2 n) (PI)) (+ (* k -1/2) 1/2)) (.f64 (sqrt.f64 (.f64 (PI.f64) n)) (sqrt.f64 #s(literal 2 binary64)))) (sqrt.f64 (/.f64 #s(literal 1 binary64) k)))) (patch #s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (.f64 #s(approx (pow ( (* 2 n) (PI)) (+ (* k -1/2) 1/2)) (.f64 (sqrt.f64 (.f64 (PI.f64) n)) (sqrt.f64 #s(literal 2 binary64)))) (sqrt.f64 (/.f64 #s(literal 1 binary64) k)))) #<representation binary64>) () ())) ())
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#s(alt (* (sqrt (/ 1 k)) (exp (* 1/2 (* (+ (log (* -2 (PI))) (* -1 (log (/ -1 n)))) (- 1 k))))) (taylor -inf n) (#s(alt #s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (.f64 #s(approx (pow ( (* 2 n) (PI)) (+ (* k -1/2) 1/2)) (.f64 (sqrt.f64 (.f64 (PI.f64) n)) (sqrt.f64 #s(literal 2 binary64)))) (sqrt.f64 (/.f64 #s(literal 1 binary64) k)))) (patch #s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (.f64 #s(approx (pow ( (* 2 n) (PI)) (+ (* k -1/2) 1/2)) (.f64 (sqrt.f64 (.f64 (PI.f64) n)) (sqrt.f64 #s(literal 2 binary64)))) (sqrt.f64 (/.f64 #s(literal 1 binary64) k)))) #<representation binary64>) () ())) ())
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#s(alt (* (sqrt (/ 1 k)) (exp (* (+ 1/2 (* -1/2 k)) (+ (log (* -2 (PI))) (* -1 (log (/ -1 n))))))) (taylor -inf n) (#s(alt (.f64 #s(approx (pow ( (* 2 n) (PI)) (+ (* k -1/2) 1/2)) (.f64 (sqrt.f64 (.f64 (PI.f64) n)) (sqrt.f64 #s(literal 2 binary64)))) (sqrt.f64 (/.f64 #s(literal 1 binary64) k))) (patch (.f64 #s(approx (pow ( (* 2 n) (PI)) (+ (* k -1/2) 1/2)) (.f64 (sqrt.f64 (.f64 (PI.f64) n)) (sqrt.f64 #s(literal 2 binary64)))) (sqrt.f64 (/.f64 #s(literal 1 binary64) k))) #<representation binary64>) () ())) ())
#s(alt (* (sqrt (/ 1 k)) (exp (* (+ 1/2 (* -1/2 k)) (+ (log (* -2 (PI))) (* -1 (log (/ -1 n))))))) (taylor -inf n) (#s(alt (.f64 #s(approx (pow ( (* 2 n) (PI)) (+ (* k -1/2) 1/2)) (.f64 (sqrt.f64 (.f64 (PI.f64) n)) (sqrt.f64 #s(literal 2 binary64)))) (sqrt.f64 (/.f64 #s(literal 1 binary64) k))) (patch (.f64 #s(approx (pow ( (* 2 n) (PI)) (+ (* k -1/2) 1/2)) (.f64 (sqrt.f64 (.f64 (PI.f64) n)) (sqrt.f64 #s(literal 2 binary64)))) (sqrt.f64 (/.f64 #s(literal 1 binary64) k))) #<representation binary64>) () ())) ())
#s(alt (* (sqrt (/ 1 k)) (exp (* (+ 1/2 (* -1/2 k)) (+ (log (* -2 (PI))) (* -1 (log (/ -1 n))))))) (taylor -inf n) (#s(alt (.f64 #s(approx (pow ( (* 2 n) (PI)) (+ (* k -1/2) 1/2)) (.f64 (sqrt.f64 (.f64 (PI.f64) n)) (sqrt.f64 #s(literal 2 binary64)))) (sqrt.f64 (/.f64 #s(literal 1 binary64) k))) (patch (.f64 #s(approx (pow ( (* 2 n) (PI)) (+ (* k -1/2) 1/2)) (.f64 (sqrt.f64 (.f64 (PI.f64) n)) (sqrt.f64 #s(literal 2 binary64)))) (sqrt.f64 (/.f64 #s(literal 1 binary64) k))) #<representation binary64>) () ())) ())
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#s(alt (* -1 (* (sqrt (* n (PI))) (* (pow (sqrt -1) 2) (sqrt 2)))) (taylor -inf n) (#s(alt (.f64 (sqrt.f64 (.f64 (PI.f64) n)) (sqrt.f64 #s(literal 2 binary64))) (patch (.f64 (sqrt.f64 (.f64 (PI.f64) n)) (sqrt.f64 #s(literal 2 binary64))) #<representation binary64>) () ())) ())
#s(alt (* -1 (* (sqrt (* n (PI))) (* (pow (sqrt -1) 2) (sqrt 2)))) (taylor -inf n) (#s(alt (.f64 (sqrt.f64 (.f64 (PI.f64) n)) (sqrt.f64 #s(literal 2 binary64))) (patch (.f64 (sqrt.f64 (.f64 (PI.f64) n)) (sqrt.f64 #s(literal 2 binary64))) #<representation binary64>) () ())) ())
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#s(alt (exp (* (+ 1/2 (* -1/2 k)) (+ (log (* -2 (PI))) (* -1 (log (/ -1 n)))))) (taylor -inf n) (#s(alt (pow.f64 (.f64 (.f64 #s(literal 2 binary64) n) (PI.f64)) (fma.f64 #s(literal -1/2 binary64) k #s(literal 1/2 binary64))) (patch (pow.f64 (.f64 (.f64 #s(literal 2 binary64) n) (PI.f64)) (fma.f64 #s(literal -1/2 binary64) k #s(literal 1/2 binary64))) #<representation binary64>) () ())) ())
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#s(alt (* 2 (* n (PI))) (taylor -inf n) (#s(alt (.f64 (.f64 #s(literal 2 binary64) n) (PI.f64)) (patch (.f64 (.f64 #s(literal 2 binary64) n) (PI.f64)) #<representation binary64>) () ())) ())
#s(alt (* 2 (* n (PI))) (taylor -inf n) (#s(alt (.f64 (.f64 #s(literal 2 binary64) n) (PI.f64)) (patch (.f64 (.f64 #s(literal 2 binary64) n) (PI.f64)) #<representation binary64>) () ())) ())
#s(alt (* 2 (* n (PI))) (taylor -inf n) (#s(alt (.f64 (.f64 #s(literal 2 binary64) n) (PI.f64)) (patch (.f64 (.f64 #s(literal 2 binary64) n) (PI.f64)) #<representation binary64>) () ())) ())
#s(alt (* 2 (* n (PI))) (taylor -inf n) (#s(alt (.f64 (.f64 #s(literal 2 binary64) n) (PI.f64)) (patch (.f64 (.f64 #s(literal 2 binary64) n) (PI.f64)) #<representation binary64>) () ())) ())
#s(alt (* 2 n) (taylor -inf n) (#s(alt (.f64 #s(literal 2 binary64) n) (patch (.f64 #s(literal 2 binary64) n) #<representation binary64>) () ())) ())
#s(alt (* 2 n) (taylor -inf n) (#s(alt (.f64 #s(literal 2 binary64) n) (patch (.f64 #s(literal 2 binary64) n) #<representation binary64>) () ())) ())
#s(alt (* 2 n) (taylor -inf n) (#s(alt (.f64 #s(literal 2 binary64) n) (patch (.f64 #s(literal 2 binary64) n) #<representation binary64>) () ())) ())
#s(alt (* 2 n) (taylor -inf n) (#s(alt (.f64 #s(literal 2 binary64) n) (patch (.f64 #s(literal 2 binary64) n) #<representation binary64>) () ())) ())
#s(alt (* 2 (/ (PI) (* k (exp (* k (+ (log (* -2 (PI))) (* -1 (log (/ -1 n))))))))) (taylor -inf n) (#s(alt (/.f64 (.f64 #s(literal 2 binary64) (PI.f64)) (.f64 (pow.f64 (.f64 (.f64 #s(literal 2 binary64) n) (PI.f64)) k) k)) (patch (/.f64 (.f64 #s(literal 2 binary64) (PI.f64)) (.f64 (pow.f64 (.f64 (.f64 #s(literal 2 binary64) n) (PI.f64)) k) k)) #<representation binary64>) () ())) ())
#s(alt (* 2 (/ (PI) (* k (exp (* k (+ (log (* -2 (PI))) (* -1 (log (/ -1 n))))))))) (taylor -inf n) (#s(alt (/.f64 (.f64 #s(literal 2 binary64) (PI.f64)) (.f64 (pow.f64 (.f64 (.f64 #s(literal 2 binary64) n) (PI.f64)) k) k)) (patch (/.f64 (.f64 #s(literal 2 binary64) (PI.f64)) (.f64 (pow.f64 (.f64 (.f64 #s(literal 2 binary64) n) (PI.f64)) k) k)) #<representation binary64>) () ())) ())
#s(alt (* 2 (/ (PI) (* k (exp (* k (+ (log (* -2 (PI))) (* -1 (log (/ -1 n))))))))) (taylor -inf n) (#s(alt (/.f64 (.f64 #s(literal 2 binary64) (PI.f64)) (.f64 (pow.f64 (.f64 (.f64 #s(literal 2 binary64) n) (PI.f64)) k) k)) (patch (/.f64 (.f64 #s(literal 2 binary64) (PI.f64)) (.f64 (pow.f64 (.f64 (.f64 #s(literal 2 binary64) n) (PI.f64)) k) k)) #<representation binary64>) () ())) ())
#s(alt (* 2 (/ (PI) (* k (exp (* k (+ (log (* -2 (PI))) (* -1 (log (/ -1 n))))))))) (taylor -inf n) (#s(alt (/.f64 (.f64 #s(literal 2 binary64) (PI.f64)) (.f64 (pow.f64 (.f64 (.f64 #s(literal 2 binary64) n) (PI.f64)) k) k)) (patch (/.f64 (.f64 #s(literal 2 binary64) (PI.f64)) (.f64 (pow.f64 (.f64 (.f64 #s(literal 2 binary64) n) (PI.f64)) k) k)) #<representation binary64>) () ())) ())
#s(alt (* n (PI)) (taylor -inf n) (#s(alt (.f64 (PI.f64) n) (patch (.f64 (PI.f64) n) #<representation binary64>) () ())) ())
#s(alt (* n (PI)) (taylor -inf n) (#s(alt (.f64 (PI.f64) n) (patch (.f64 (PI.f64) n) #<representation binary64>) () ())) ())
#s(alt (* n (PI)) (taylor -inf n) (#s(alt (.f64 (PI.f64) n) (patch (.f64 (PI.f64) n) #<representation binary64>) () ())) ())
#s(alt (* n (PI)) (taylor -inf n) (#s(alt (.f64 (PI.f64) n) (patch (.f64 (PI.f64) n) #<representation binary64>) () ())) ())

Calls

6 calls:

Time	Variable		Point	Expression
18.0ms	n	@	-inf	((* (sqrt n) (sqrt (/ (* 2 (PI)) (* (pow (* (* 2 n) (PI)) k) k)))) (sqrt n) (sqrt (/ (* 2 (PI)) (* (pow (* (* 2 n) (PI)) k) k))) (* 2 (PI)) (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt (* (/ (* (PI) n) k) 2)) (* (/ (* (PI) n) k) 2) (/ (* (PI) n) k) (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (/ (sqrt 2) (sqrt (/ k (* (PI) n)))) (sqrt 2) (sqrt (/ k (* (PI) n))) (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (* (pow (* (* 2 n) (PI)) (+ (* k -1/2) 1/2)) (sqrt (/ 1 k))) (pow (* (* 2 n) (PI)) (+ (* k -1/2) 1/2)) (* (sqrt (* (PI) n)) (sqrt 2)) (/ (pow (* (* 2 n) (PI)) (+ (* -1/2 k) 1/2)) (sqrt k)) (pow (* (* 2 n) (PI)) (+ (* -1/2 k) 1/2)) (* (* 2 n) (PI)) (* 2 n) (PI) (/ (* 2 (PI)) (* (pow (* (* 2 n) (PI)) k) k)) (* (PI) n))
17.0ms	n	@	inf	((* (sqrt n) (sqrt (/ (* 2 (PI)) (* (pow (* (* 2 n) (PI)) k) k)))) (sqrt n) (sqrt (/ (* 2 (PI)) (* (pow (* (* 2 n) (PI)) k) k))) (* 2 (PI)) (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt (* (/ (* (PI) n) k) 2)) (* (/ (* (PI) n) k) 2) (/ (* (PI) n) k) (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (/ (sqrt 2) (sqrt (/ k (* (PI) n)))) (sqrt 2) (sqrt (/ k (* (PI) n))) (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (* (pow (* (* 2 n) (PI)) (+ (* k -1/2) 1/2)) (sqrt (/ 1 k))) (pow (* (* 2 n) (PI)) (+ (* k -1/2) 1/2)) (* (sqrt (* (PI) n)) (sqrt 2)) (/ (pow (* (* 2 n) (PI)) (+ (* -1/2 k) 1/2)) (sqrt k)) (pow (* (* 2 n) (PI)) (+ (* -1/2 k) 1/2)) (* (* 2 n) (PI)) (* 2 n) (PI) (/ (* 2 (PI)) (* (pow (* (* 2 n) (PI)) k) k)) (* (PI) n))
16.0ms	k	@	inf	((* (sqrt n) (sqrt (/ (* 2 (PI)) (* (pow (* (* 2 n) (PI)) k) k)))) (sqrt n) (sqrt (/ (* 2 (PI)) (* (pow (* (* 2 n) (PI)) k) k))) (* 2 (PI)) (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt (* (/ (* (PI) n) k) 2)) (* (/ (* (PI) n) k) 2) (/ (* (PI) n) k) (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (/ (sqrt 2) (sqrt (/ k (* (PI) n)))) (sqrt 2) (sqrt (/ k (* (PI) n))) (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (* (pow (* (* 2 n) (PI)) (+ (* k -1/2) 1/2)) (sqrt (/ 1 k))) (pow (* (* 2 n) (PI)) (+ (* k -1/2) 1/2)) (* (sqrt (* (PI) n)) (sqrt 2)) (/ (pow (* (* 2 n) (PI)) (+ (* -1/2 k) 1/2)) (sqrt k)) (pow (* (* 2 n) (PI)) (+ (* -1/2 k) 1/2)) (* (* 2 n) (PI)) (* 2 n) (PI) (/ (* 2 (PI)) (* (pow (* (* 2 n) (PI)) k) k)) (* (PI) n))
11.0ms	n	@	0	((* (sqrt n) (sqrt (/ (* 2 (PI)) (* (pow (* (* 2 n) (PI)) k) k)))) (sqrt n) (sqrt (/ (* 2 (PI)) (* (pow (* (* 2 n) (PI)) k) k))) (* 2 (PI)) (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt (* (/ (* (PI) n) k) 2)) (* (/ (* (PI) n) k) 2) (/ (* (PI) n) k) (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (/ (sqrt 2) (sqrt (/ k (* (PI) n)))) (sqrt 2) (sqrt (/ k (* (PI) n))) (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (* (pow (* (* 2 n) (PI)) (+ (* k -1/2) 1/2)) (sqrt (/ 1 k))) (pow (* (* 2 n) (PI)) (+ (* k -1/2) 1/2)) (* (sqrt (* (PI) n)) (sqrt 2)) (/ (pow (* (* 2 n) (PI)) (+ (* -1/2 k) 1/2)) (sqrt k)) (pow (* (* 2 n) (PI)) (+ (* -1/2 k) 1/2)) (* (* 2 n) (PI)) (* 2 n) (PI) (/ (* 2 (PI)) (* (pow (* (* 2 n) (PI)) k) k)) (* (PI) n))
6.0ms	k	@	-inf	((* (sqrt n) (sqrt (/ (* 2 (PI)) (* (pow (* (* 2 n) (PI)) k) k)))) (sqrt n) (sqrt (/ (* 2 (PI)) (* (pow (* (* 2 n) (PI)) k) k))) (* 2 (PI)) (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt (* (/ (* (PI) n) k) 2)) (* (/ (* (PI) n) k) 2) (/ (* (PI) n) k) (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (/ (sqrt 2) (sqrt (/ k (* (PI) n)))) (sqrt 2) (sqrt (/ k (* (PI) n))) (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (* (pow (* (* 2 n) (PI)) (+ (* k -1/2) 1/2)) (sqrt (/ 1 k))) (pow (* (* 2 n) (PI)) (+ (* k -1/2) 1/2)) (* (sqrt (* (PI) n)) (sqrt 2)) (/ (pow (* (* 2 n) (PI)) (+ (* -1/2 k) 1/2)) (sqrt k)) (pow (* (* 2 n) (PI)) (+ (* -1/2 k) 1/2)) (* (* 2 n) (PI)) (* 2 n) (PI) (/ (* 2 (PI)) (* (pow (* (* 2 n) (PI)) k) k)) (* (PI) n))

simplify217.0ms (2.3%)

Memory

-3.5MiB live, 273.8MiB allocated

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	310	6454
1	953	6310
2	3498	5942
0	8257	5879

Stop Event

1×	iter limit
1×	node limit

Counts

420 → 420

Calls

Call 1

Inputs
(* (sqrt (/ (* n (PI)) k)) (sqrt 2))
(/ (+ (* -1/2 (* (sqrt (* (pow k 3) (* n (PI)))) (* (log (* 2 (* n (PI)))) (sqrt 2)))) (* (sqrt (* k (* n (PI)))) (sqrt 2))) k)
(/ (+ (* (sqrt (* k (* n (PI)))) (sqrt 2)) (* (pow k 2) (+ (* -1/2 (* (sqrt (/ k (* n (PI)))) (* (sqrt 2) (+ (* -1 (* n (* (PI) (pow (log (* 2 (* n (PI)))) 2)))) (* 1/2 (* n (* (PI) (pow (log (* 2 (* n (PI)))) 2)))))))) (* -1/2 (* (sqrt (/ (* n (PI)) k)) (* (log (* 2 (* n (PI)))) (sqrt 2))))))) k)
(/ (+ (* (sqrt (* k (* n (PI)))) (sqrt 2)) (* (pow k 2) (+ (* -1/2 (* (sqrt (/ (* n (PI)) k)) (* (log (* 2 (* n (PI)))) (sqrt 2)))) (* k (+ (* -1/2 (* (sqrt (/ 1 (* k (* n (PI))))) (* (sqrt 2) (+ (* -1 (* n (* (PI) (pow (log (* 2 (* n (PI)))) 2)))) (* 1/2 (* n (* (PI) (pow (log (* 2 (* n (PI)))) 2)))))))) (* -1/2 (* (sqrt (/ k (* n (PI)))) (* (sqrt 2) (+ (* -1 (* (log (* 2 (* n (PI)))) (+ (* -1 (* n (* (PI) (pow (log (* 2 (* n (PI)))) 2)))) (* 1/2 (* n (* (PI) (pow (log (* 2 (* n (PI)))) 2))))))) (+ (* -1/2 (* n (* (PI) (pow (log (* 2 (* n (PI)))) 3)))) (+ (* 1/6 (* n (* (PI) (pow (log (* 2 (* n (PI)))) 3)))) (* 1/4 (/ (* n (* (PI) (pow (log (* 2 (* n (PI)))) 2))) k))))))))))))) k)
(* (sqrt (/ (PI) k)) (sqrt 2))
(/ (+ (* -1/2 (* (sqrt (* (pow k 3) (PI))) (* (log (* 2 (* n (PI)))) (sqrt 2)))) (* (sqrt (* k (PI))) (sqrt 2))) k)
(/ (+ (* (sqrt (* k (PI))) (sqrt 2)) (* (pow k 2) (+ (* -1/2 (* (sqrt (/ k (PI))) (* (sqrt 2) (+ (* -1 (* (PI) (pow (log (* 2 (* n (PI)))) 2))) (* 1/2 (* (PI) (pow (log (* 2 (* n (PI)))) 2))))))) (* -1/2 (* (sqrt (/ (PI) k)) (* (log (* 2 (* n (PI)))) (sqrt 2))))))) k)
(/ (+ (* (sqrt (* k (PI))) (sqrt 2)) (* (pow k 2) (+ (* -1/2 (* (sqrt (/ (PI) k)) (* (log (* 2 (* n (PI)))) (sqrt 2)))) (* k (+ (* -1/2 (* (sqrt (/ 1 (* k (PI)))) (* (sqrt 2) (+ (* -1 (* (PI) (pow (log (* 2 (* n (PI)))) 2))) (* 1/2 (* (PI) (pow (log (* 2 (* n (PI)))) 2))))))) (* -1/2 (* (sqrt (/ k (PI))) (* (sqrt 2) (+ (* -1 (* (log (* 2 (* n (PI)))) (+ (* -1 (* (PI) (pow (log (* 2 (* n (PI)))) 2))) (* 1/2 (* (PI) (pow (log (* 2 (* n (PI)))) 2)))))) (+ (* -1/2 (* (PI) (pow (log (* 2 (* n (PI)))) 3))) (+ (* 1/6 (* (PI) (pow (log (* 2 (* n (PI)))) 3))) (* 1/4 (/ (* (PI) (pow (log (* 2 (* n (PI)))) 2)) k))))))))))))) k)
(* (sqrt (/ (* n (PI)) k)) (sqrt 2))
(/ (+ (* -1/2 (* (sqrt (* (pow k 3) (* n (PI)))) (* (log (* 2 (* n (PI)))) (sqrt 2)))) (* (sqrt (* k (* n (PI)))) (sqrt 2))) k)
(/ (+ (* k (+ (* -1/2 (* (sqrt (* k (* n (PI)))) (* (log (* 2 (* n (PI)))) (sqrt 2)))) (* 1/8 (* (sqrt (* (pow k 3) (* n (PI)))) (* (pow (log (* 2 (* n (PI)))) 2) (sqrt 2)))))) (* (sqrt (* k (* n (PI)))) (sqrt 2))) k)
(/ (+ (* k (+ (* -1/2 (* (sqrt (* k (* n (PI)))) (* (log (* 2 (* n (PI)))) (sqrt 2)))) (* k (+ (* -1/48 (* (sqrt (* (pow k 3) (* n (PI)))) (* (pow (log (* 2 (* n (PI)))) 3) (sqrt 2)))) (* 1/8 (* (sqrt (* k (* n (PI)))) (* (pow (log (* 2 (* n (PI)))) 2) (sqrt 2)))))))) (* (sqrt (* k (* n (PI)))) (sqrt 2))) k)
(* (sqrt (/ (* n (PI)) k)) (sqrt 2))
(* (sqrt (/ (* n (PI)) k)) (sqrt 2))
(* (sqrt (/ (* n (PI)) k)) (sqrt 2))
(* (sqrt (/ (* n (PI)) k)) (sqrt 2))
(* 2 (/ (* n (PI)) k))
(* 2 (/ (* n (PI)) k))
(* 2 (/ (* n (PI)) k))
(* 2 (/ (* n (PI)) k))
(/ (* n (PI)) k)
(/ (* n (PI)) k)
(/ (* n (PI)) k)
(/ (* n (PI)) k)
(* (sqrt (/ (* n (PI)) k)) (sqrt 2))
(/ (+ (* -1/2 (* (sqrt (* (pow k 3) (* n (PI)))) (* (log (* 2 (* n (PI)))) (sqrt 2)))) (* (sqrt (* k (* n (PI)))) (sqrt 2))) k)
(/ (+ (* k (+ (* -1/2 (* (sqrt (* k (* n (PI)))) (* (log (* 2 (* n (PI)))) (sqrt 2)))) (* 1/8 (* (sqrt (* (pow k 3) (* n (PI)))) (* (pow (log (* 2 (* n (PI)))) 2) (sqrt 2)))))) (* (sqrt (* k (* n (PI)))) (sqrt 2))) k)
(/ (+ (* k (+ (* -1/2 (* (sqrt (* k (* n (PI)))) (* (log (* 2 (* n (PI)))) (sqrt 2)))) (* k (+ (* -1/48 (* (sqrt (* (pow k 3) (* n (PI)))) (* (pow (log (* 2 (* n (PI)))) 3) (sqrt 2)))) (* 1/8 (* (sqrt (* k (* n (PI)))) (* (pow (log (* 2 (* n (PI)))) 2) (sqrt 2)))))))) (* (sqrt (* k (* n (PI)))) (sqrt 2))) k)
(* (sqrt (/ (* n (PI)) k)) (sqrt 2))
(* (sqrt (/ (* n (PI)) k)) (sqrt 2))
(* (sqrt (/ (* n (PI)) k)) (sqrt 2))
(* (sqrt (/ (* n (PI)) k)) (sqrt 2))
(sqrt (/ k (* n (PI))))
(sqrt (/ k (* n (PI))))
(sqrt (/ k (* n (PI))))
(sqrt (/ k (* n (PI))))
(* (sqrt (/ (* n (PI)) k)) (sqrt 2))
(/ (+ (* -1/2 (* (sqrt (* (pow k 3) (* n (PI)))) (* (log (* 2 (* n (PI)))) (sqrt 2)))) (* (sqrt (* k (* n (PI)))) (sqrt 2))) k)
(/ (+ (* k (+ (* -1/2 (* (sqrt (* k (* n (PI)))) (* (log (* 2 (* n (PI)))) (sqrt 2)))) (* 1/8 (* (sqrt (* (pow k 3) (* n (PI)))) (* (pow (log (* 2 (* n (PI)))) 2) (sqrt 2)))))) (* (sqrt (* k (* n (PI)))) (sqrt 2))) k)
(/ (+ (* k (+ (* -1/2 (* (sqrt (* k (* n (PI)))) (* (log (* 2 (* n (PI)))) (sqrt 2)))) (* k (+ (* -1/48 (* (sqrt (* (pow k 3) (* n (PI)))) (* (pow (log (* 2 (* n (PI)))) 3) (sqrt 2)))) (* 1/8 (* (sqrt (* k (* n (PI)))) (* (pow (log (* 2 (* n (PI)))) 2) (sqrt 2)))))))) (* (sqrt (* k (* n (PI)))) (sqrt 2))) k)
(* (sqrt (/ (* n (PI)) k)) (sqrt 2))
(/ (+ (* -1/2 (* (sqrt (* (pow k 3) (* n (PI)))) (* (log (* 2 (* n (PI)))) (sqrt 2)))) (* (sqrt (* k (* n (PI)))) (sqrt 2))) k)
(/ (+ (* k (+ (* -1/2 (* (sqrt (* k (* n (PI)))) (* (log (* 2 (* n (PI)))) (sqrt 2)))) (* 1/8 (* (sqrt (* (pow k 3) (* n (PI)))) (* (pow (log (* 2 (* n (PI)))) 2) (sqrt 2)))))) (* (sqrt (* k (* n (PI)))) (sqrt 2))) k)
(/ (+ (* k (+ (* -1/2 (* (sqrt (* k (* n (PI)))) (* (log (* 2 (* n (PI)))) (sqrt 2)))) (* k (+ (* -1/48 (* (sqrt (* (pow k 3) (* n (PI)))) (* (pow (log (* 2 (* n (PI)))) 3) (sqrt 2)))) (* 1/8 (* (sqrt (* k (* n (PI)))) (* (pow (log (* 2 (* n (PI)))) 2) (sqrt 2)))))))) (* (sqrt (* k (* n (PI)))) (sqrt 2))) k)
(* (sqrt (* n (PI))) (sqrt 2))
(+ (* -1/2 (* (* k (* (log (* 2 (* n (PI)))) (sqrt 2))) (sqrt (* n (PI))))) (* (sqrt (* n (PI))) (sqrt 2)))
(+ (* k (+ (* -1/2 (* (sqrt (* n (PI))) (* (log (* 2 (* n (PI)))) (sqrt 2)))) (* 1/8 (* (* k (* (pow (log (* 2 (* n (PI)))) 2) (sqrt 2))) (sqrt (* n (PI))))))) (* (sqrt (* n (PI))) (sqrt 2)))
(+ (* k (+ (* -1/2 (* (sqrt (* n (PI))) (* (log (* 2 (* n (PI)))) (sqrt 2)))) (* k (+ (* -1/48 (* (* k (* (pow (log (* 2 (* n (PI)))) 3) (sqrt 2))) (sqrt (* n (PI))))) (* 1/8 (* (sqrt (* n (PI))) (* (pow (log (* 2 (* n (PI)))) 2) (sqrt 2)))))))) (* (sqrt (* n (PI))) (sqrt 2)))
(* (sqrt (/ (* n (PI)) k)) (sqrt 2))
(/ (+ (* -1/2 (* (sqrt (* (pow k 3) (* n (PI)))) (* (log (* 2 (* n (PI)))) (sqrt 2)))) (* (sqrt (* k (* n (PI)))) (sqrt 2))) k)
(/ (+ (* k (+ (* -1/2 (* (sqrt (* k (* n (PI)))) (* (log (* 2 (* n (PI)))) (sqrt 2)))) (* 1/8 (* (sqrt (* (pow k 3) (* n (PI)))) (* (pow (log (* 2 (* n (PI)))) 2) (sqrt 2)))))) (* (sqrt (* k (* n (PI)))) (sqrt 2))) k)
(/ (+ (* k (+ (* -1/2 (* (sqrt (* k (* n (PI)))) (* (log (* 2 (* n (PI)))) (sqrt 2)))) (* k (+ (* -1/48 (* (sqrt (* (pow k 3) (* n (PI)))) (* (pow (log (* 2 (* n (PI)))) 3) (sqrt 2)))) (* 1/8 (* (sqrt (* k (* n (PI)))) (* (pow (log (* 2 (* n (PI)))) 2) (sqrt 2)))))))) (* (sqrt (* k (* n (PI)))) (sqrt 2))) k)
(* (sqrt (* n (PI))) (sqrt 2))
(+ (* -1/2 (* (* k (* (log (* 2 (* n (PI)))) (sqrt 2))) (sqrt (* n (PI))))) (* (sqrt (* n (PI))) (sqrt 2)))
(+ (* k (+ (* -1/2 (* (sqrt (* n (PI))) (* (log (* 2 (* n (PI)))) (sqrt 2)))) (* 1/8 (* (* k (* (pow (log (* 2 (* n (PI)))) 2) (sqrt 2))) (sqrt (* n (PI))))))) (* (sqrt (* n (PI))) (sqrt 2)))
(+ (* k (+ (* -1/2 (* (sqrt (* n (PI))) (* (log (* 2 (* n (PI)))) (sqrt 2)))) (* k (+ (* -1/48 (* (* k (* (pow (log (* 2 (* n (PI)))) 3) (sqrt 2))) (sqrt (* n (PI))))) (* 1/8 (* (sqrt (* n (PI))) (* (pow (log (* 2 (* n (PI)))) 2) (sqrt 2)))))))) (* (sqrt (* n (PI))) (sqrt 2)))
(* 2 (/ (PI) k))
(/ (+ (* -2 (* k (* (PI) (log (* 2 (* n (PI))))))) (* 2 (PI))) k)
(/ (+ (* 2 (PI)) (* k (+ (* -2 (* k (+ (* -1 (* (PI) (pow (log (* 2 (* n (PI)))) 2))) (* 1/2 (* (PI) (pow (log (* 2 (* n (PI)))) 2)))))) (* -2 (* (PI) (log (* 2 (* n (PI))))))))) k)
(/ (+ (* 2 (PI)) (* k (+ (* -2 (* (PI) (log (* 2 (* n (PI)))))) (* k (+ (* -2 (* k (+ (* -1 (* (log (* 2 (* n (PI)))) (+ (* -1 (* (PI) (pow (log (* 2 (* n (PI)))) 2))) (* 1/2 (* (PI) (pow (log (* 2 (* n (PI)))) 2)))))) (+ (* -1/2 (* (PI) (pow (log (* 2 (* n (PI)))) 3))) (* 1/6 (* (PI) (pow (log (* 2 (* n (PI)))) 3))))))) (* -2 (+ (* -1 (* (PI) (pow (log (* 2 (* n (PI)))) 2))) (* 1/2 (* (PI) (pow (log (* 2 (* n (PI)))) 2)))))))))) k)
(* (sqrt (/ (* n (PI)) (* k (pow (* 2 (* n (PI))) k)))) (sqrt 2))
(* (sqrt (/ (* n (PI)) (* k (pow (* 2 (* n (PI))) k)))) (sqrt 2))
(* (sqrt (/ (* n (PI)) (* k (pow (* 2 (* n (PI))) k)))) (sqrt 2))
(* (sqrt (/ (* n (PI)) (* k (pow (* 2 (* n (PI))) k)))) (sqrt 2))
(* (sqrt (/ (PI) (* k (pow (* 2 (* n (PI))) k)))) (sqrt 2))
(* (sqrt (/ (PI) (* k (pow (* 2 (* n (PI))) k)))) (sqrt 2))
(* (sqrt (/ (PI) (* k (pow (* 2 (* n (PI))) k)))) (sqrt 2))
(* (sqrt (/ (PI) (* k (pow (* 2 (* n (PI))) k)))) (sqrt 2))
(* (sqrt (/ 1 k)) (exp (* 1/2 (* (log (* 2 (* n (PI)))) (- 1 k)))))
(* (sqrt (/ 1 k)) (exp (* 1/2 (* (log (* 2 (* n (PI)))) (- 1 k)))))
(* (sqrt (/ 1 k)) (exp (* 1/2 (* (log (* 2 (* n (PI)))) (- 1 k)))))
(* (sqrt (/ 1 k)) (exp (* 1/2 (* (log (* 2 (* n (PI)))) (- 1 k)))))
(* (sqrt (/ (* n (PI)) k)) (sqrt 2))
(* (sqrt (/ (* n (PI)) k)) (sqrt 2))
(* (sqrt (/ (* n (PI)) k)) (sqrt 2))
(* (sqrt (/ (* n (PI)) k)) (sqrt 2))
(* 2 (/ (* n (PI)) k))
(* 2 (/ (* n (PI)) k))
(* 2 (/ (* n (PI)) k))
(* 2 (/ (* n (PI)) k))
(/ (* n (PI)) k)
(/ (* n (PI)) k)
(/ (* n (PI)) k)
(/ (* n (PI)) k)
(* (sqrt (/ 1 k)) (exp (* 1/2 (* (log (* 2 (* n (PI)))) (- 1 k)))))
(* (sqrt (/ 1 k)) (exp (* 1/2 (* (log (* 2 (* n (PI)))) (- 1 k)))))
(* (sqrt (/ 1 k)) (exp (* 1/2 (* (log (* 2 (* n (PI)))) (- 1 k)))))
(* (sqrt (/ 1 k)) (exp (* 1/2 (* (log (* 2 (* n (PI)))) (- 1 k)))))
(* (sqrt (/ (* n (PI)) k)) (sqrt 2))
(* (sqrt (/ (* n (PI)) k)) (sqrt 2))
(* (sqrt (/ (* n (PI)) k)) (sqrt 2))
(* (sqrt (/ (* n (PI)) k)) (sqrt 2))
(sqrt (/ k (* n (PI))))
(sqrt (/ k (* n (PI))))
(sqrt (/ k (* n (PI))))
(sqrt (/ k (* n (PI))))
(* (sqrt (/ 1 k)) (exp (* 1/2 (* (log (* 2 (* n (PI)))) (- 1 k)))))
(* (sqrt (/ 1 k)) (exp (* 1/2 (* (log (* 2 (* n (PI)))) (- 1 k)))))
(* (sqrt (/ 1 k)) (exp (* 1/2 (* (log (* 2 (* n (PI)))) (- 1 k)))))
(* (sqrt (/ 1 k)) (exp (* 1/2 (* (log (* 2 (* n (PI)))) (- 1 k)))))
(* (sqrt (/ 1 k)) (exp (* (log (* 2 (* n (PI)))) (- 1/2 (* 1/2 k)))))
(* (sqrt (/ 1 k)) (exp (* (log (* 2 (* n (PI)))) (- 1/2 (* 1/2 k)))))
(* (sqrt (/ 1 k)) (exp (* (log (* 2 (* n (PI)))) (- 1/2 (* 1/2 k)))))
(* (sqrt (/ 1 k)) (exp (* (log (* 2 (* n (PI)))) (- 1/2 (* 1/2 k)))))
(exp (* (log (* 2 (* n (PI)))) (- 1/2 (* 1/2 k))))
(exp (* (log (* 2 (* n (PI)))) (- 1/2 (* 1/2 k))))
(exp (* (log (* 2 (* n (PI)))) (- 1/2 (* 1/2 k))))
(exp (* (log (* 2 (* n (PI)))) (- 1/2 (* 1/2 k))))
(* (sqrt (/ 1 k)) (exp (* (log (* 2 (* n (PI)))) (- 1/2 (* 1/2 k)))))
(* (sqrt (/ 1 k)) (exp (* (log (* 2 (* n (PI)))) (- 1/2 (* 1/2 k)))))
(* (sqrt (/ 1 k)) (exp (* (log (* 2 (* n (PI)))) (- 1/2 (* 1/2 k)))))
(* (sqrt (/ 1 k)) (exp (* (log (* 2 (* n (PI)))) (- 1/2 (* 1/2 k)))))
(exp (* (log (* 2 (* n (PI)))) (- 1/2 (* 1/2 k))))
(exp (* (log (* 2 (* n (PI)))) (- 1/2 (* 1/2 k))))
(exp (* (log (* 2 (* n (PI)))) (- 1/2 (* 1/2 k))))
(exp (* (log (* 2 (* n (PI)))) (- 1/2 (* 1/2 k))))
(* 2 (/ (PI) (* k (pow (* 2 (* n (PI))) k))))
(* 2 (/ (PI) (* k (pow (* 2 (* n (PI))) k))))
(* 2 (/ (PI) (* k (pow (* 2 (* n (PI))) k))))
(* 2 (/ (PI) (* k (pow (* 2 (* n (PI))) k))))
(* (sqrt (/ (* n (PI)) (* k (pow (* 2 (* n (PI))) k)))) (* (sqrt -2) (sqrt -1)))
(* (sqrt (/ (* n (PI)) (* k (pow (* 2 (* n (PI))) k)))) (* (sqrt -2) (sqrt -1)))
(* (sqrt (/ (* n (PI)) (* k (pow (* 2 (* n (PI))) k)))) (* (sqrt -2) (sqrt -1)))
(* (sqrt (/ (* n (PI)) (* k (pow (* 2 (* n (PI))) k)))) (* (sqrt -2) (sqrt -1)))
(* (sqrt (/ (PI) (* k (pow (* 2 (* n (PI))) k)))) (* (sqrt -2) (sqrt -1)))
(* (sqrt (/ (PI) (* k (pow (* 2 (* n (PI))) k)))) (* (sqrt -2) (sqrt -1)))
(* (sqrt (/ (PI) (* k (pow (* 2 (* n (PI))) k)))) (* (sqrt -2) (sqrt -1)))
(* (sqrt (/ (PI) (* k (pow (* 2 (* n (PI))) k)))) (* (sqrt -2) (sqrt -1)))
(* (sqrt (/ 1 k)) (exp (* 1/2 (* (log (* 2 (* n (PI)))) (+ 1 (* -1 k))))))
(* (sqrt (/ 1 k)) (exp (* 1/2 (* (log (* 2 (* n (PI)))) (+ 1 (* -1 k))))))
(* (sqrt (/ 1 k)) (exp (* 1/2 (* (log (* 2 (* n (PI)))) (+ 1 (* -1 k))))))
(* (sqrt (/ 1 k)) (exp (* 1/2 (* (log (* 2 (* n (PI)))) (+ 1 (* -1 k))))))
(* (sqrt (/ (* n (PI)) k)) (* (sqrt -2) (sqrt -1)))
(* (sqrt (/ (* n (PI)) k)) (* (sqrt -2) (sqrt -1)))
(* (sqrt (/ (* n (PI)) k)) (* (sqrt -2) (sqrt -1)))
(* (sqrt (/ (* n (PI)) k)) (* (sqrt -2) (sqrt -1)))
(* 2 (/ (* n (PI)) k))
(* 2 (/ (* n (PI)) k))
(* 2 (/ (* n (PI)) k))
(* 2 (/ (* n (PI)) k))
(/ (* n (PI)) k)
(/ (* n (PI)) k)
(/ (* n (PI)) k)
(/ (* n (PI)) k)
(* (sqrt (/ 1 k)) (exp (* 1/2 (* (log (* 2 (* n (PI)))) (+ 1 (* -1 k))))))
(* (sqrt (/ 1 k)) (exp (* 1/2 (* (log (* 2 (* n (PI)))) (+ 1 (* -1 k))))))
(* (sqrt (/ 1 k)) (exp (* 1/2 (* (log (* 2 (* n (PI)))) (+ 1 (* -1 k))))))
(* (sqrt (/ 1 k)) (exp (* 1/2 (* (log (* 2 (* n (PI)))) (+ 1 (* -1 k))))))
(* (sqrt (/ (* n (PI)) k)) (sqrt 2))
(* (sqrt (/ (* n (PI)) k)) (sqrt 2))
(* (sqrt (/ (* n (PI)) k)) (sqrt 2))
(* (sqrt (/ (* n (PI)) k)) (sqrt 2))
(* -1 (* (sqrt (/ k (* n (PI)))) (pow (sqrt -1) 2)))
(* -1 (* (sqrt (/ k (* n (PI)))) (pow (sqrt -1) 2)))
(* -1 (* (sqrt (/ k (* n (PI)))) (pow (sqrt -1) 2)))
(* -1 (* (sqrt (/ k (* n (PI)))) (pow (sqrt -1) 2)))
(* (sqrt (/ 1 k)) (exp (* 1/2 (* (log (* 2 (* n (PI)))) (+ 1 (* -1 k))))))
(* (sqrt (/ 1 k)) (exp (* 1/2 (* (log (* 2 (* n (PI)))) (+ 1 (* -1 k))))))
(* (sqrt (/ 1 k)) (exp (* 1/2 (* (log (* 2 (* n (PI)))) (+ 1 (* -1 k))))))
(* (sqrt (/ 1 k)) (exp (* 1/2 (* (log (* 2 (* n (PI)))) (+ 1 (* -1 k))))))
(* (sqrt (/ 1 k)) (* (exp (* (log (* 2 (* n (PI)))) (+ 1/2 (* -1/2 k)))) (pow (sqrt -1) 2)))
(* (sqrt (/ 1 k)) (* (exp (* (log (* 2 (* n (PI)))) (+ 1/2 (* -1/2 k)))) (pow (sqrt -1) 2)))
(* (sqrt (/ 1 k)) (* (exp (* (log (* 2 (* n (PI)))) (+ 1/2 (* -1/2 k)))) (pow (sqrt -1) 2)))
(* (sqrt (/ 1 k)) (* (exp (* (log (* 2 (* n (PI)))) (+ 1/2 (* -1/2 k)))) (pow (sqrt -1) 2)))
(exp (* (log (* 2 (* n (PI)))) (+ 1/2 (* -1/2 k))))
(exp (* (log (* 2 (* n (PI)))) (+ 1/2 (* -1/2 k))))
(exp (* (log (* 2 (* n (PI)))) (+ 1/2 (* -1/2 k))))
(exp (* (log (* 2 (* n (PI)))) (+ 1/2 (* -1/2 k))))
(* (sqrt (/ 1 k)) (exp (* (log (* 2 (* n (PI)))) (+ 1/2 (* -1/2 k)))))
(* (sqrt (/ 1 k)) (exp (* (log (* 2 (* n (PI)))) (+ 1/2 (* -1/2 k)))))
(* (sqrt (/ 1 k)) (exp (* (log (* 2 (* n (PI)))) (+ 1/2 (* -1/2 k)))))
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Outputs
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(/ (+ (* -1/2 (* (sqrt (* (pow k 3) (* n (PI)))) (* (log (* 2 (* n (PI)))) (sqrt 2)))) (* (sqrt (* k (* n (PI)))) (sqrt 2))) k)
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(.f64 (sqrt.f64 (.f64 (/.f64 (PI.f64) (pow.f64 (*.f64 #s(literal -2 binary64) (PI.f64)) k)) (/.f64 (/.f64 n k) (pow.f64 (/.f64 #s(literal -1 binary64) n) (neg.f64 k))))) (sqrt.f64 #s(literal 2 binary64)))
(* -1 (* (sqrt (/ (* n (PI)) (* k (exp (* k (+ (log (* -2 (PI))) (* -1 (log (/ -1 n))))))))) (* (pow (sqrt -1) 2) (sqrt 2))))
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(* -1 (* (sqrt n) (pow (sqrt -1) 2)))
(sqrt.f64 n)
(* -1 (* (sqrt n) (pow (sqrt -1) 2)))
(sqrt.f64 n)
(* -1 (* (sqrt n) (pow (sqrt -1) 2)))
(sqrt.f64 n)
(* -1 (* (sqrt n) (pow (sqrt -1) 2)))
(sqrt.f64 n)
(* (sqrt (/ (PI) (* k (exp (* k (+ (log (* -2 (PI))) (* -1 (log (/ -1 n))))))))) (sqrt 2))
(.f64 (sqrt.f64 (/.f64 (/.f64 (PI.f64) k) (.f64 (pow.f64 (*.f64 #s(literal -2 binary64) (PI.f64)) k) (pow.f64 (/.f64 #s(literal -1 binary64) n) (neg.f64 k))))) (sqrt.f64 #s(literal 2 binary64)))
(* (sqrt (/ (PI) (* k (exp (* k (+ (log (* -2 (PI))) (* -1 (log (/ -1 n))))))))) (sqrt 2))
(.f64 (sqrt.f64 (/.f64 (/.f64 (PI.f64) k) (.f64 (pow.f64 (*.f64 #s(literal -2 binary64) (PI.f64)) k) (pow.f64 (/.f64 #s(literal -1 binary64) n) (neg.f64 k))))) (sqrt.f64 #s(literal 2 binary64)))
(* (sqrt (/ (PI) (* k (exp (* k (+ (log (* -2 (PI))) (* -1 (log (/ -1 n))))))))) (sqrt 2))
(.f64 (sqrt.f64 (/.f64 (/.f64 (PI.f64) k) (.f64 (pow.f64 (*.f64 #s(literal -2 binary64) (PI.f64)) k) (pow.f64 (/.f64 #s(literal -1 binary64) n) (neg.f64 k))))) (sqrt.f64 #s(literal 2 binary64)))
(* (sqrt (/ (PI) (* k (exp (* k (+ (log (* -2 (PI))) (* -1 (log (/ -1 n))))))))) (sqrt 2))
(.f64 (sqrt.f64 (/.f64 (/.f64 (PI.f64) k) (.f64 (pow.f64 (*.f64 #s(literal -2 binary64) (PI.f64)) k) (pow.f64 (/.f64 #s(literal -1 binary64) n) (neg.f64 k))))) (sqrt.f64 #s(literal 2 binary64)))
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(.f64 (pow.f64 (exp.f64 (fma.f64 #s(literal -1/2 binary64) k #s(literal 1/2 binary64))) (-.f64 (log.f64 (.f64 #s(literal -2 binary64) (PI.f64))) (log.f64 (/.f64 #s(literal -1 binary64) n)))) (sqrt.f64 (/.f64 #s(literal 1 binary64) k)))
(* (sqrt (/ 1 k)) (exp (* 1/2 (* (+ (log (* -2 (PI))) (* -1 (log (/ -1 n)))) (- 1 k)))))
(.f64 (pow.f64 (exp.f64 (fma.f64 #s(literal -1/2 binary64) k #s(literal 1/2 binary64))) (-.f64 (log.f64 (.f64 #s(literal -2 binary64) (PI.f64))) (log.f64 (/.f64 #s(literal -1 binary64) n)))) (sqrt.f64 (/.f64 #s(literal 1 binary64) k)))
(* (sqrt (/ 1 k)) (exp (* 1/2 (* (+ (log (* -2 (PI))) (* -1 (log (/ -1 n)))) (- 1 k)))))
(.f64 (pow.f64 (exp.f64 (fma.f64 #s(literal -1/2 binary64) k #s(literal 1/2 binary64))) (-.f64 (log.f64 (.f64 #s(literal -2 binary64) (PI.f64))) (log.f64 (/.f64 #s(literal -1 binary64) n)))) (sqrt.f64 (/.f64 #s(literal 1 binary64) k)))
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(* -1 (* (sqrt (/ (* n (PI)) k)) (* (sqrt -2) (sqrt -1))))
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(* -1 (* (sqrt (/ (* n (PI)) k)) (* (sqrt -2) (sqrt -1))))
(.f64 (neg.f64 (sqrt.f64 #s(literal -2 binary64))) (.f64 (sqrt.f64 #s(literal -1 binary64)) (sqrt.f64 (/.f64 (*.f64 (PI.f64) n) k))))
(* -1 (* (sqrt (/ (* n (PI)) k)) (* (sqrt -2) (sqrt -1))))
(.f64 (neg.f64 (sqrt.f64 #s(literal -2 binary64))) (.f64 (sqrt.f64 #s(literal -1 binary64)) (sqrt.f64 (/.f64 (*.f64 (PI.f64) n) k))))
(* 2 (/ (* n (PI)) k))
(.f64 #s(literal 2 binary64) (/.f64 (.f64 (PI.f64) n) k))
(* 2 (/ (* n (PI)) k))
(.f64 #s(literal 2 binary64) (/.f64 (.f64 (PI.f64) n) k))
(* 2 (/ (* n (PI)) k))
(.f64 #s(literal 2 binary64) (/.f64 (.f64 (PI.f64) n) k))
(* 2 (/ (* n (PI)) k))
(.f64 #s(literal 2 binary64) (/.f64 (.f64 (PI.f64) n) k))
(/ (* n (PI)) k)
(/.f64 (*.f64 (PI.f64) n) k)
(/ (* n (PI)) k)
(/.f64 (*.f64 (PI.f64) n) k)
(/ (* n (PI)) k)
(/.f64 (*.f64 (PI.f64) n) k)
(/ (* n (PI)) k)
(/.f64 (*.f64 (PI.f64) n) k)
(* (sqrt (/ 1 k)) (exp (* 1/2 (* (+ (log (* -2 (PI))) (* -1 (log (/ -1 n)))) (- 1 k)))))
(.f64 (pow.f64 (exp.f64 (fma.f64 #s(literal -1/2 binary64) k #s(literal 1/2 binary64))) (-.f64 (log.f64 (.f64 #s(literal -2 binary64) (PI.f64))) (log.f64 (/.f64 #s(literal -1 binary64) n)))) (sqrt.f64 (/.f64 #s(literal 1 binary64) k)))
(* (sqrt (/ 1 k)) (exp (* 1/2 (* (+ (log (* -2 (PI))) (* -1 (log (/ -1 n)))) (- 1 k)))))
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(* (sqrt (/ 1 k)) (exp (* 1/2 (* (+ (log (* -2 (PI))) (* -1 (log (/ -1 n)))) (- 1 k)))))
(.f64 (pow.f64 (exp.f64 (fma.f64 #s(literal -1/2 binary64) k #s(literal 1/2 binary64))) (-.f64 (log.f64 (.f64 #s(literal -2 binary64) (PI.f64))) (log.f64 (/.f64 #s(literal -1 binary64) n)))) (sqrt.f64 (/.f64 #s(literal 1 binary64) k)))
(* (sqrt (/ 1 k)) (exp (* 1/2 (* (+ (log (* -2 (PI))) (* -1 (log (/ -1 n)))) (- 1 k)))))
(.f64 (pow.f64 (exp.f64 (fma.f64 #s(literal -1/2 binary64) k #s(literal 1/2 binary64))) (-.f64 (log.f64 (.f64 #s(literal -2 binary64) (PI.f64))) (log.f64 (/.f64 #s(literal -1 binary64) n)))) (sqrt.f64 (/.f64 #s(literal 1 binary64) k)))
(* -1 (* (sqrt (/ (* n (PI)) k)) (sqrt 2)))
(.f64 (neg.f64 (sqrt.f64 #s(literal 2 binary64))) (sqrt.f64 (/.f64 (.f64 (PI.f64) n) k)))
(* -1 (* (sqrt (/ (* n (PI)) k)) (sqrt 2)))
(.f64 (neg.f64 (sqrt.f64 #s(literal 2 binary64))) (sqrt.f64 (/.f64 (.f64 (PI.f64) n) k)))
(* -1 (* (sqrt (/ (* n (PI)) k)) (sqrt 2)))
(.f64 (neg.f64 (sqrt.f64 #s(literal 2 binary64))) (sqrt.f64 (/.f64 (.f64 (PI.f64) n) k)))
(* -1 (* (sqrt (/ (* n (PI)) k)) (sqrt 2)))
(.f64 (neg.f64 (sqrt.f64 #s(literal 2 binary64))) (sqrt.f64 (/.f64 (.f64 (PI.f64) n) k)))
(* (sqrt (/ k (* n (PI)))) (pow (sqrt -1) 2))
(neg.f64 (sqrt.f64 (/.f64 k (*.f64 (PI.f64) n))))
(* (sqrt (/ k (* n (PI)))) (pow (sqrt -1) 2))
(neg.f64 (sqrt.f64 (/.f64 k (*.f64 (PI.f64) n))))
(* (sqrt (/ k (* n (PI)))) (pow (sqrt -1) 2))
(neg.f64 (sqrt.f64 (/.f64 k (*.f64 (PI.f64) n))))
(* (sqrt (/ k (* n (PI)))) (pow (sqrt -1) 2))
(neg.f64 (sqrt.f64 (/.f64 k (*.f64 (PI.f64) n))))
(* (sqrt (/ 1 k)) (exp (* 1/2 (* (+ (log (* -2 (PI))) (* -1 (log (/ -1 n)))) (- 1 k)))))
(.f64 (pow.f64 (exp.f64 (fma.f64 #s(literal -1/2 binary64) k #s(literal 1/2 binary64))) (-.f64 (log.f64 (.f64 #s(literal -2 binary64) (PI.f64))) (log.f64 (/.f64 #s(literal -1 binary64) n)))) (sqrt.f64 (/.f64 #s(literal 1 binary64) k)))
(* (sqrt (/ 1 k)) (exp (* 1/2 (* (+ (log (* -2 (PI))) (* -1 (log (/ -1 n)))) (- 1 k)))))
(.f64 (pow.f64 (exp.f64 (fma.f64 #s(literal -1/2 binary64) k #s(literal 1/2 binary64))) (-.f64 (log.f64 (.f64 #s(literal -2 binary64) (PI.f64))) (log.f64 (/.f64 #s(literal -1 binary64) n)))) (sqrt.f64 (/.f64 #s(literal 1 binary64) k)))
(* (sqrt (/ 1 k)) (exp (* 1/2 (* (+ (log (* -2 (PI))) (* -1 (log (/ -1 n)))) (- 1 k)))))
(.f64 (pow.f64 (exp.f64 (fma.f64 #s(literal -1/2 binary64) k #s(literal 1/2 binary64))) (-.f64 (log.f64 (.f64 #s(literal -2 binary64) (PI.f64))) (log.f64 (/.f64 #s(literal -1 binary64) n)))) (sqrt.f64 (/.f64 #s(literal 1 binary64) k)))
(* (sqrt (/ 1 k)) (exp (* 1/2 (* (+ (log (* -2 (PI))) (* -1 (log (/ -1 n)))) (- 1 k)))))
(.f64 (pow.f64 (exp.f64 (fma.f64 #s(literal -1/2 binary64) k #s(literal 1/2 binary64))) (-.f64 (log.f64 (.f64 #s(literal -2 binary64) (PI.f64))) (log.f64 (/.f64 #s(literal -1 binary64) n)))) (sqrt.f64 (/.f64 #s(literal 1 binary64) k)))
(* (sqrt (/ 1 k)) (exp (* (+ 1/2 (* -1/2 k)) (+ (log (* -2 (PI))) (* -1 (log (/ -1 n)))))))
(.f64 (pow.f64 (exp.f64 (fma.f64 #s(literal -1/2 binary64) k #s(literal 1/2 binary64))) (-.f64 (log.f64 (.f64 #s(literal -2 binary64) (PI.f64))) (log.f64 (/.f64 #s(literal -1 binary64) n)))) (sqrt.f64 (/.f64 #s(literal 1 binary64) k)))
(* (sqrt (/ 1 k)) (exp (* (+ 1/2 (* -1/2 k)) (+ (log (* -2 (PI))) (* -1 (log (/ -1 n)))))))
(.f64 (pow.f64 (exp.f64 (fma.f64 #s(literal -1/2 binary64) k #s(literal 1/2 binary64))) (-.f64 (log.f64 (.f64 #s(literal -2 binary64) (PI.f64))) (log.f64 (/.f64 #s(literal -1 binary64) n)))) (sqrt.f64 (/.f64 #s(literal 1 binary64) k)))
(* (sqrt (/ 1 k)) (exp (* (+ 1/2 (* -1/2 k)) (+ (log (* -2 (PI))) (* -1 (log (/ -1 n)))))))
(.f64 (pow.f64 (exp.f64 (fma.f64 #s(literal -1/2 binary64) k #s(literal 1/2 binary64))) (-.f64 (log.f64 (.f64 #s(literal -2 binary64) (PI.f64))) (log.f64 (/.f64 #s(literal -1 binary64) n)))) (sqrt.f64 (/.f64 #s(literal 1 binary64) k)))
(* (sqrt (/ 1 k)) (exp (* (+ 1/2 (* -1/2 k)) (+ (log (* -2 (PI))) (* -1 (log (/ -1 n)))))))
(.f64 (pow.f64 (exp.f64 (fma.f64 #s(literal -1/2 binary64) k #s(literal 1/2 binary64))) (-.f64 (log.f64 (.f64 #s(literal -2 binary64) (PI.f64))) (log.f64 (/.f64 #s(literal -1 binary64) n)))) (sqrt.f64 (/.f64 #s(literal 1 binary64) k)))
(exp (* (+ 1/2 (* -1/2 k)) (+ (log (* -2 (PI))) (* -1 (log (/ -1 n))))))
(pow.f64 (exp.f64 (fma.f64 #s(literal -1/2 binary64) k #s(literal 1/2 binary64))) (-.f64 (log.f64 (*.f64 #s(literal -2 binary64) (PI.f64))) (log.f64 (/.f64 #s(literal -1 binary64) n))))
(exp (* (+ 1/2 (* -1/2 k)) (+ (log (* -2 (PI))) (* -1 (log (/ -1 n))))))
(pow.f64 (exp.f64 (fma.f64 #s(literal -1/2 binary64) k #s(literal 1/2 binary64))) (-.f64 (log.f64 (*.f64 #s(literal -2 binary64) (PI.f64))) (log.f64 (/.f64 #s(literal -1 binary64) n))))
(exp (* (+ 1/2 (* -1/2 k)) (+ (log (* -2 (PI))) (* -1 (log (/ -1 n))))))
(pow.f64 (exp.f64 (fma.f64 #s(literal -1/2 binary64) k #s(literal 1/2 binary64))) (-.f64 (log.f64 (*.f64 #s(literal -2 binary64) (PI.f64))) (log.f64 (/.f64 #s(literal -1 binary64) n))))
(exp (* (+ 1/2 (* -1/2 k)) (+ (log (* -2 (PI))) (* -1 (log (/ -1 n))))))
(pow.f64 (exp.f64 (fma.f64 #s(literal -1/2 binary64) k #s(literal 1/2 binary64))) (-.f64 (log.f64 (*.f64 #s(literal -2 binary64) (PI.f64))) (log.f64 (/.f64 #s(literal -1 binary64) n))))
(* -1 (* (sqrt (* n (PI))) (* (pow (sqrt -1) 2) (sqrt 2))))
(.f64 (sqrt.f64 (.f64 (PI.f64) n)) (sqrt.f64 #s(literal 2 binary64)))
(* -1 (* (sqrt (* n (PI))) (* (pow (sqrt -1) 2) (sqrt 2))))
(.f64 (sqrt.f64 (.f64 (PI.f64) n)) (sqrt.f64 #s(literal 2 binary64)))
(* -1 (* (sqrt (* n (PI))) (* (pow (sqrt -1) 2) (sqrt 2))))
(.f64 (sqrt.f64 (.f64 (PI.f64) n)) (sqrt.f64 #s(literal 2 binary64)))
(* -1 (* (sqrt (* n (PI))) (* (pow (sqrt -1) 2) (sqrt 2))))
(.f64 (sqrt.f64 (.f64 (PI.f64) n)) (sqrt.f64 #s(literal 2 binary64)))
(* (sqrt (/ 1 k)) (exp (* (+ 1/2 (* -1/2 k)) (+ (log (* -2 (PI))) (* -1 (log (/ -1 n)))))))
(.f64 (pow.f64 (exp.f64 (fma.f64 #s(literal -1/2 binary64) k #s(literal 1/2 binary64))) (-.f64 (log.f64 (.f64 #s(literal -2 binary64) (PI.f64))) (log.f64 (/.f64 #s(literal -1 binary64) n)))) (sqrt.f64 (/.f64 #s(literal 1 binary64) k)))
(* (sqrt (/ 1 k)) (exp (* (+ 1/2 (* -1/2 k)) (+ (log (* -2 (PI))) (* -1 (log (/ -1 n)))))))
(.f64 (pow.f64 (exp.f64 (fma.f64 #s(literal -1/2 binary64) k #s(literal 1/2 binary64))) (-.f64 (log.f64 (.f64 #s(literal -2 binary64) (PI.f64))) (log.f64 (/.f64 #s(literal -1 binary64) n)))) (sqrt.f64 (/.f64 #s(literal 1 binary64) k)))
(* (sqrt (/ 1 k)) (exp (* (+ 1/2 (* -1/2 k)) (+ (log (* -2 (PI))) (* -1 (log (/ -1 n)))))))
(.f64 (pow.f64 (exp.f64 (fma.f64 #s(literal -1/2 binary64) k #s(literal 1/2 binary64))) (-.f64 (log.f64 (.f64 #s(literal -2 binary64) (PI.f64))) (log.f64 (/.f64 #s(literal -1 binary64) n)))) (sqrt.f64 (/.f64 #s(literal 1 binary64) k)))
(* (sqrt (/ 1 k)) (exp (* (+ 1/2 (* -1/2 k)) (+ (log (* -2 (PI))) (* -1 (log (/ -1 n)))))))
(.f64 (pow.f64 (exp.f64 (fma.f64 #s(literal -1/2 binary64) k #s(literal 1/2 binary64))) (-.f64 (log.f64 (.f64 #s(literal -2 binary64) (PI.f64))) (log.f64 (/.f64 #s(literal -1 binary64) n)))) (sqrt.f64 (/.f64 #s(literal 1 binary64) k)))
(exp (* (+ 1/2 (* -1/2 k)) (+ (log (* -2 (PI))) (* -1 (log (/ -1 n))))))
(pow.f64 (exp.f64 (fma.f64 #s(literal -1/2 binary64) k #s(literal 1/2 binary64))) (-.f64 (log.f64 (*.f64 #s(literal -2 binary64) (PI.f64))) (log.f64 (/.f64 #s(literal -1 binary64) n))))
(exp (* (+ 1/2 (* -1/2 k)) (+ (log (* -2 (PI))) (* -1 (log (/ -1 n))))))
(pow.f64 (exp.f64 (fma.f64 #s(literal -1/2 binary64) k #s(literal 1/2 binary64))) (-.f64 (log.f64 (*.f64 #s(literal -2 binary64) (PI.f64))) (log.f64 (/.f64 #s(literal -1 binary64) n))))
(exp (* (+ 1/2 (* -1/2 k)) (+ (log (* -2 (PI))) (* -1 (log (/ -1 n))))))
(pow.f64 (exp.f64 (fma.f64 #s(literal -1/2 binary64) k #s(literal 1/2 binary64))) (-.f64 (log.f64 (*.f64 #s(literal -2 binary64) (PI.f64))) (log.f64 (/.f64 #s(literal -1 binary64) n))))
(exp (* (+ 1/2 (* -1/2 k)) (+ (log (* -2 (PI))) (* -1 (log (/ -1 n))))))
(pow.f64 (exp.f64 (fma.f64 #s(literal -1/2 binary64) k #s(literal 1/2 binary64))) (-.f64 (log.f64 (*.f64 #s(literal -2 binary64) (PI.f64))) (log.f64 (/.f64 #s(literal -1 binary64) n))))
(* 2 (* n (PI)))
(.f64 #s(literal 2 binary64) (.f64 (PI.f64) n))
(* 2 (* n (PI)))
(.f64 #s(literal 2 binary64) (.f64 (PI.f64) n))
(* 2 (* n (PI)))
(.f64 #s(literal 2 binary64) (.f64 (PI.f64) n))
(* 2 (* n (PI)))
(.f64 #s(literal 2 binary64) (.f64 (PI.f64) n))
(* 2 n)
(*.f64 #s(literal 2 binary64) n)
(* 2 n)
(*.f64 #s(literal 2 binary64) n)
(* 2 n)
(*.f64 #s(literal 2 binary64) n)
(* 2 n)
(*.f64 #s(literal 2 binary64) n)
(* 2 (/ (PI) (* k (exp (* k (+ (log (* -2 (PI))) (* -1 (log (/ -1 n)))))))))
(.f64 (/.f64 #s(literal 2 binary64) (pow.f64 (.f64 #s(literal -2 binary64) (PI.f64)) k)) (/.f64 (/.f64 (PI.f64) k) (pow.f64 (/.f64 #s(literal -1 binary64) n) (neg.f64 k))))
(* 2 (/ (PI) (* k (exp (* k (+ (log (* -2 (PI))) (* -1 (log (/ -1 n)))))))))
(.f64 (/.f64 #s(literal 2 binary64) (pow.f64 (.f64 #s(literal -2 binary64) (PI.f64)) k)) (/.f64 (/.f64 (PI.f64) k) (pow.f64 (/.f64 #s(literal -1 binary64) n) (neg.f64 k))))
(* 2 (/ (PI) (* k (exp (* k (+ (log (* -2 (PI))) (* -1 (log (/ -1 n)))))))))
(.f64 (/.f64 #s(literal 2 binary64) (pow.f64 (.f64 #s(literal -2 binary64) (PI.f64)) k)) (/.f64 (/.f64 (PI.f64) k) (pow.f64 (/.f64 #s(literal -1 binary64) n) (neg.f64 k))))
(* 2 (/ (PI) (* k (exp (* k (+ (log (* -2 (PI))) (* -1 (log (/ -1 n)))))))))
(.f64 (/.f64 #s(literal 2 binary64) (pow.f64 (.f64 #s(literal -2 binary64) (PI.f64)) k)) (/.f64 (/.f64 (PI.f64) k) (pow.f64 (/.f64 #s(literal -1 binary64) n) (neg.f64 k))))
(* n (PI))
(*.f64 (PI.f64) n)
(* n (PI))
(*.f64 (PI.f64) n)
(* n (PI))
(*.f64 (PI.f64) n)
(* n (PI))
(*.f64 (PI.f64) n)

rewrite139.0ms (1.5%)

Memory

21.7MiB live, 253.9MiB allocated

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	51	263
0	79	256
1	282	246
2	1456	237
0	8595	237

Stop Event

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

Counts

23 → 700

Calls

Call 1

Inputs
(.f64 (sqrt.f64 n) (sqrt.f64 (/.f64 (.f64 #s(literal 2 binary64) (PI.f64)) (.f64 (pow.f64 (.f64 (*.f64 #s(literal 2 binary64) n) (PI.f64)) k) k))))
(sqrt.f64 n)
(sqrt.f64 (/.f64 (.f64 #s(literal 2 binary64) (PI.f64)) (.f64 (pow.f64 (.f64 (.f64 #s(literal 2 binary64) n) (PI.f64)) k) k)))
(*.f64 #s(literal 2 binary64) (PI.f64))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt.f64 (.f64 (/.f64 (.f64 (PI.f64) n) k) #s(literal 2 binary64))))
(sqrt.f64 (.f64 (/.f64 (.f64 (PI.f64) n) k) #s(literal 2 binary64)))
(.f64 (/.f64 (.f64 (PI.f64) n) k) #s(literal 2 binary64))
(/.f64 (*.f64 (PI.f64) n) k)
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (/.f64 (sqrt.f64 #s(literal 2 binary64)) (sqrt.f64 (/.f64 k (*.f64 (PI.f64) n)))))
(/.f64 (sqrt.f64 #s(literal 2 binary64)) (sqrt.f64 (/.f64 k (*.f64 (PI.f64) n))))
(sqrt.f64 #s(literal 2 binary64))
(sqrt.f64 (/.f64 k (*.f64 (PI.f64) n)))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (.f64 #s(approx (pow ( (* 2 n) (PI)) (+ (* k -1/2) 1/2)) (.f64 (sqrt.f64 (.f64 (PI.f64) n)) (sqrt.f64 #s(literal 2 binary64)))) (sqrt.f64 (/.f64 #s(literal 1 binary64) k))))
(.f64 #s(approx (pow ( (* 2 n) (PI)) (+ (* k -1/2) 1/2)) (.f64 (sqrt.f64 (.f64 (PI.f64) n)) (sqrt.f64 #s(literal 2 binary64)))) (sqrt.f64 (/.f64 #s(literal 1 binary64) k)))
#s(approx (pow (* (* 2 n) (PI)) (+ (* k -1/2) 1/2)) (.f64 (sqrt.f64 (.f64 (PI.f64) n)) (sqrt.f64 #s(literal 2 binary64))))
(.f64 (sqrt.f64 (.f64 (PI.f64) n)) (sqrt.f64 #s(literal 2 binary64)))
(/.f64 (pow.f64 (.f64 (.f64 #s(literal 2 binary64) n) (PI.f64)) (fma.f64 #s(literal -1/2 binary64) k #s(literal 1/2 binary64))) (sqrt.f64 k))
(pow.f64 (.f64 (.f64 #s(literal 2 binary64) n) (PI.f64)) (fma.f64 #s(literal -1/2 binary64) k #s(literal 1/2 binary64)))
(.f64 (.f64 #s(literal 2 binary64) n) (PI.f64))
(*.f64 #s(literal 2 binary64) n)
(PI.f64)
(/.f64 (.f64 #s(literal 2 binary64) (PI.f64)) (.f64 (pow.f64 (.f64 (.f64 #s(literal 2 binary64) n) (PI.f64)) k) k))
(*.f64 (PI.f64) n)

Outputs
(.f64 (.f64 (pow.f64 (.f64 (/.f64 (.f64 (pow.f64 (.f64 (.f64 #s(literal 2 binary64) n) (PI.f64)) k) k) (PI.f64)) #s(literal 1/2 binary64)) #s(literal -1/4 binary64)) (pow.f64 n #s(literal 1/4 binary64))) (.f64 (pow.f64 (.f64 (/.f64 (.f64 (pow.f64 (.f64 (*.f64 #s(literal 2 binary64) n) (PI.f64)) k) k) (PI.f64)) #s(literal 1/2 binary64)) #s(literal -1/4 binary64)) (pow.f64 n #s(literal 1/4 binary64))))
(.f64 (.f64 (pow.f64 n #s(literal 1/4 binary64)) (pow.f64 (.f64 (/.f64 (.f64 (pow.f64 (.f64 (.f64 #s(literal 2 binary64) n) (PI.f64)) k) k) (PI.f64)) #s(literal 1/2 binary64)) #s(literal -1/4 binary64))) (.f64 (pow.f64 n #s(literal 1/4 binary64)) (pow.f64 (.f64 (/.f64 (.f64 (pow.f64 (.f64 (*.f64 #s(literal 2 binary64) n) (PI.f64)) k) k) (PI.f64)) #s(literal 1/2 binary64)) #s(literal -1/4 binary64))))
(.f64 (.f64 (pow.f64 (.f64 (.f64 #s(literal 2 binary64) n) (PI.f64)) (.f64 k #s(literal -1/4 binary64))) (pow.f64 (.f64 (/.f64 (.f64 (PI.f64) n) k) #s(literal 2 binary64)) #s(literal 1/4 binary64))) (.f64 (pow.f64 (.f64 (.f64 #s(literal 2 binary64) n) (PI.f64)) (.f64 k #s(literal -1/4 binary64))) (pow.f64 (.f64 (/.f64 (*.f64 (PI.f64) n) k) #s(literal 2 binary64)) #s(literal 1/4 binary64))))
(.f64 (.f64 (pow.f64 (.f64 (.f64 #s(literal 2 binary64) n) (PI.f64)) (.f64 (+.f64 #s(literal -1 binary64) k) #s(literal -1/4 binary64))) (pow.f64 k #s(literal -1/4 binary64))) (.f64 (pow.f64 (.f64 (.f64 #s(literal 2 binary64) n) (PI.f64)) (*.f64 (+.f64 #s(literal -1 binary64) k) #s(literal -1/4 binary64))) (pow.f64 k #s(literal -1/4 binary64))))
(.f64 (.f64 (pow.f64 k #s(literal -1/4 binary64)) (pow.f64 (.f64 (.f64 #s(literal 2 binary64) n) (PI.f64)) (.f64 (+.f64 #s(literal -1 binary64) k) #s(literal -1/4 binary64)))) (.f64 (pow.f64 k #s(literal -1/4 binary64)) (pow.f64 (.f64 (.f64 #s(literal 2 binary64) n) (PI.f64)) (*.f64 (+.f64 #s(literal -1 binary64) k) #s(literal -1/4 binary64)))))
(.f64 (pow.f64 (.f64 (.f64 n (/.f64 #s(literal 2 binary64) (pow.f64 (.f64 (.f64 #s(literal 2 binary64) n) (PI.f64)) k))) (/.f64 (PI.f64) k)) #s(literal 1/4 binary64)) (pow.f64 (.f64 (.f64 n (/.f64 #s(literal 2 binary64) (pow.f64 (.f64 (*.f64 #s(literal 2 binary64) n) (PI.f64)) k))) (/.f64 (PI.f64) k)) #s(literal 1/4 binary64)))
(.f64 (pow.f64 (/.f64 (sqrt.f64 k) (pow.f64 (.f64 (.f64 #s(literal 2 binary64) n) (PI.f64)) (fma.f64 #s(literal -1/2 binary64) k #s(literal 1/2 binary64)))) #s(literal -1/2 binary64)) (pow.f64 (/.f64 (sqrt.f64 k) (pow.f64 (.f64 (*.f64 #s(literal 2 binary64) n) (PI.f64)) (fma.f64 #s(literal -1/2 binary64) k #s(literal 1/2 binary64)))) #s(literal -1/2 binary64)))
(.f64 (sqrt.f64 (.f64 n (/.f64 #s(literal 2 binary64) (pow.f64 (.f64 (.f64 #s(literal 2 binary64) n) (PI.f64)) k)))) (sqrt.f64 (/.f64 (PI.f64) k)))
(.f64 (pow.f64 (.f64 n (/.f64 #s(literal 2 binary64) (pow.f64 (.f64 (.f64 #s(literal 2 binary64) n) (PI.f64)) k))) #s(literal 1/2 binary64)) (sqrt.f64 (/.f64 (PI.f64) k)))
(.f64 (.f64 (pow.f64 (.f64 (.f64 #s(literal 2 binary64) n) (PI.f64)) (fma.f64 #s(literal -1/2 binary64) k #s(literal 1/2 binary64))) #s(literal -1 binary64)) (/.f64 #s(literal -1 binary64) (sqrt.f64 k)))
(.f64 (.f64 (pow.f64 k #s(literal -1/2 binary64)) (pow.f64 (.f64 (.f64 #s(literal 2 binary64) n) (PI.f64)) (.f64 (+.f64 #s(literal -1 binary64) k) #s(literal -1/4 binary64)))) (pow.f64 (.f64 (.f64 #s(literal 2 binary64) n) (PI.f64)) (.f64 (+.f64 #s(literal -1 binary64) k) #s(literal -1/4 binary64))))
(.f64 (.f64 (pow.f64 k #s(literal -1/2 binary64)) (pow.f64 (*.f64 (PI.f64) #s(literal 2 binary64)) (fma.f64 #s(literal -1/2 binary64) k #s(literal 1/2 binary64)))) (pow.f64 n (fma.f64 #s(literal -1/2 binary64) k #s(literal 1/2 binary64))))
(.f64 (sqrt.f64 (.f64 #s(literal 2 binary64) n)) (sqrt.f64 (/.f64 (PI.f64) (.f64 (pow.f64 (.f64 (*.f64 #s(literal 2 binary64) n) (PI.f64)) k) k))))
(.f64 (pow.f64 (.f64 (.f64 #s(literal 2 binary64) n) (PI.f64)) (.f64 (+.f64 #s(literal -1 binary64) k) #s(literal -1/4 binary64))) (/.f64 (pow.f64 (.f64 (.f64 #s(literal 2 binary64) n) (PI.f64)) (*.f64 (+.f64 #s(literal -1 binary64) k) #s(literal -1/4 binary64))) (sqrt.f64 k)))
(.f64 (neg.f64 (pow.f64 (.f64 (*.f64 #s(literal 2 binary64) n) (PI.f64)) (fma.f64 #s(literal -1/2 binary64) k #s(literal 1/2 binary64)))) (/.f64 #s(literal -1 binary64) (sqrt.f64 k)))
(.f64 (pow.f64 (.f64 #s(literal 2 binary64) n) (fma.f64 #s(literal -1/2 binary64) k #s(literal 1/2 binary64))) (/.f64 (pow.f64 (PI.f64) (fma.f64 #s(literal -1/2 binary64) k #s(literal 1/2 binary64))) (sqrt.f64 k)))
(.f64 (pow.f64 (.f64 (PI.f64) #s(literal 2 binary64)) (fma.f64 #s(literal -1/2 binary64) k #s(literal 1/2 binary64))) (/.f64 (pow.f64 n (fma.f64 #s(literal -1/2 binary64) k #s(literal 1/2 binary64))) (sqrt.f64 k)))
(.f64 (sqrt.f64 (.f64 (.f64 #s(literal 2 binary64) n) (PI.f64))) (pow.f64 (.f64 (pow.f64 (.f64 (.f64 #s(literal 2 binary64) n) (PI.f64)) k) k) #s(literal -1/2 binary64)))
(.f64 (pow.f64 (pow.f64 (.f64 (.f64 #s(literal 2 binary64) n) (PI.f64)) k) #s(literal -1/2 binary64)) (sqrt.f64 (.f64 (/.f64 (*.f64 (PI.f64) n) k) #s(literal 2 binary64))))
(.f64 #s(literal -1 binary64) (/.f64 #s(literal 1 binary64) (neg.f64 (/.f64 (sqrt.f64 k) (pow.f64 (.f64 (*.f64 #s(literal 2 binary64) n) (PI.f64)) (fma.f64 #s(literal -1/2 binary64) k #s(literal 1/2 binary64)))))))
(.f64 #s(literal -1 binary64) (/.f64 (pow.f64 (.f64 (*.f64 #s(literal 2 binary64) n) (PI.f64)) (fma.f64 #s(literal -1/2 binary64) k #s(literal 1/2 binary64))) (neg.f64 (sqrt.f64 k))))
(.f64 (pow.f64 (.f64 (*.f64 #s(literal 2 binary64) n) (PI.f64)) (fma.f64 #s(literal -1/2 binary64) k #s(literal 1/2 binary64))) (pow.f64 k #s(literal -1/2 binary64)))
(.f64 (pow.f64 k #s(literal -1/2 binary64)) (pow.f64 (pow.f64 (.f64 (.f64 #s(literal 2 binary64) n) (PI.f64)) (.f64 (+.f64 #s(literal -1 binary64) k) #s(literal 1/2 binary64))) #s(literal -1 binary64)))
(.f64 (pow.f64 k #s(literal -1/2 binary64)) (pow.f64 (.f64 (*.f64 #s(literal 2 binary64) n) (PI.f64)) (fma.f64 #s(literal -1/2 binary64) k #s(literal 1/2 binary64))))
(.f64 #s(literal 1 binary64) (/.f64 (pow.f64 (.f64 (*.f64 #s(literal 2 binary64) n) (PI.f64)) (fma.f64 #s(literal -1/2 binary64) k #s(literal 1/2 binary64))) (sqrt.f64 k)))
(.f64 (sqrt.f64 (.f64 (/.f64 (PI.f64) (pow.f64 (.f64 (.f64 #s(literal 2 binary64) n) (PI.f64)) k)) (/.f64 #s(literal 2 binary64) k))) (sqrt.f64 n))
(.f64 (sqrt.f64 n) (sqrt.f64 (.f64 (/.f64 (PI.f64) (pow.f64 (.f64 (.f64 #s(literal 2 binary64) n) (PI.f64)) k)) (/.f64 #s(literal 2 binary64) k))))
(pow.f64 (.f64 (pow.f64 k #s(literal -1 binary64)) (pow.f64 (.f64 (*.f64 #s(literal 2 binary64) n) (PI.f64)) (-.f64 #s(literal 1 binary64) k))) #s(literal 1/2 binary64))
(pow.f64 (.f64 (pow.f64 (.f64 (*.f64 #s(literal 2 binary64) n) (PI.f64)) (-.f64 #s(literal 1 binary64) k)) (pow.f64 k #s(literal -1 binary64))) #s(literal 1/2 binary64))
(pow.f64 (/.f64 (sqrt.f64 k) (pow.f64 (.f64 (.f64 #s(literal 2 binary64) n) (PI.f64)) (fma.f64 #s(literal -1/2 binary64) k #s(literal 1/2 binary64)))) #s(literal -1 binary64))
(pow.f64 (.f64 (.f64 n (/.f64 #s(literal 2 binary64) (pow.f64 (.f64 (.f64 #s(literal 2 binary64) n) (PI.f64)) k))) (/.f64 (PI.f64) k)) #s(literal 1/2 binary64))
(/.f64 (neg.f64 (.f64 (pow.f64 (.f64 (*.f64 #s(literal 2 binary64) n) (PI.f64)) (fma.f64 #s(literal -1/2 binary64) k #s(literal 1/2 binary64))) #s(literal -1 binary64))) (sqrt.f64 k))
(/.f64 (.f64 (sqrt.f64 #s(literal -1 binary64)) (sqrt.f64 (.f64 (.f64 #s(literal 2 binary64) n) (PI.f64)))) (sqrt.f64 (.f64 (neg.f64 k) (pow.f64 (.f64 (.f64 #s(literal 2 binary64) n) (PI.f64)) k))))
(/.f64 (.f64 (sqrt.f64 (.f64 (.f64 #s(literal 2 binary64) n) (PI.f64))) (sqrt.f64 #s(literal -1 binary64))) (sqrt.f64 (.f64 (neg.f64 k) (pow.f64 (.f64 (.f64 #s(literal 2 binary64) n) (PI.f64)) k))))
(/.f64 (.f64 (sqrt.f64 (.f64 (.f64 #s(literal 2 binary64) n) (PI.f64))) #s(literal -1 binary64)) (.f64 (sqrt.f64 (pow.f64 (.f64 (.f64 #s(literal 2 binary64) n) (PI.f64)) k)) (neg.f64 (sqrt.f64 k))))
(/.f64 (.f64 (sqrt.f64 (.f64 (.f64 #s(literal 2 binary64) n) (PI.f64))) #s(literal 1 binary64)) (sqrt.f64 (.f64 (pow.f64 (.f64 (.f64 #s(literal 2 binary64) n) (PI.f64)) k) k)))
(/.f64 (sqrt.f64 (.f64 n (.f64 (PI.f64) (/.f64 #s(literal 2 binary64) (pow.f64 (.f64 (.f64 #s(literal 2 binary64) n) (PI.f64)) k))))) (sqrt.f64 k))
(/.f64 (sqrt.f64 (.f64 n (.f64 #s(literal -2 binary64) (PI.f64)))) (sqrt.f64 (.f64 (neg.f64 k) (pow.f64 (.f64 (*.f64 #s(literal 2 binary64) n) (PI.f64)) k))))
(/.f64 (.f64 (pow.f64 (.f64 (*.f64 #s(literal 2 binary64) n) (PI.f64)) (fma.f64 #s(literal -1/2 binary64) k #s(literal 1/2 binary64))) #s(literal -1 binary64)) (neg.f64 (sqrt.f64 k)))
(/.f64 (neg.f64 (sqrt.f64 (.f64 (.f64 #s(literal 2 binary64) n) (PI.f64)))) (neg.f64 (sqrt.f64 (.f64 (pow.f64 (.f64 (*.f64 #s(literal 2 binary64) n) (PI.f64)) k) k))))
(/.f64 (neg.f64 (pow.f64 (.f64 (.f64 #s(literal 2 binary64) n) (PI.f64)) (fma.f64 #s(literal -1/2 binary64) k #s(literal 1/2 binary64)))) (neg.f64 (sqrt.f64 k)))
(/.f64 (sqrt.f64 (.f64 (.f64 #s(literal 2 binary64) n) (PI.f64))) (sqrt.f64 (.f64 (pow.f64 (.f64 (*.f64 #s(literal 2 binary64) n) (PI.f64)) k) k)))
(/.f64 (pow.f64 (pow.f64 (.f64 (.f64 #s(literal 2 binary64) n) (PI.f64)) k) #s(literal -1/2 binary64)) (sqrt.f64 (.f64 (/.f64 k (.f64 (PI.f64) n)) #s(literal 1/2 binary64))))
(/.f64 #s(literal -1 binary64) (neg.f64 (/.f64 (sqrt.f64 k) (pow.f64 (.f64 (.f64 #s(literal 2 binary64) n) (PI.f64)) (fma.f64 #s(literal -1/2 binary64) k #s(literal 1/2 binary64))))))
(/.f64 (pow.f64 (.f64 (.f64 #s(literal 2 binary64) n) (PI.f64)) (fma.f64 #s(literal -1/2 binary64) k #s(literal 1/2 binary64))) (sqrt.f64 k))
(/.f64 #s(literal 1 binary64) (/.f64 (sqrt.f64 (.f64 (pow.f64 (.f64 (.f64 #s(literal 2 binary64) n) (PI.f64)) k) k)) (sqrt.f64 (.f64 (*.f64 #s(literal 2 binary64) n) (PI.f64)))))
(/.f64 #s(literal 1 binary64) (/.f64 (neg.f64 (sqrt.f64 k)) (.f64 (pow.f64 (.f64 (*.f64 #s(literal 2 binary64) n) (PI.f64)) (fma.f64 #s(literal -1/2 binary64) k #s(literal 1/2 binary64))) #s(literal -1 binary64))))
(/.f64 #s(literal 1 binary64) (neg.f64 (neg.f64 (/.f64 (sqrt.f64 k) (pow.f64 (.f64 (.f64 #s(literal 2 binary64) n) (PI.f64)) (fma.f64 #s(literal -1/2 binary64) k #s(literal 1/2 binary64)))))))
(/.f64 #s(literal 1 binary64) (/.f64 (sqrt.f64 k) (pow.f64 (.f64 (.f64 #s(literal 2 binary64) n) (PI.f64)) (fma.f64 #s(literal -1/2 binary64) k #s(literal 1/2 binary64)))))
(/.f64 (sqrt.f64 n) (sqrt.f64 (.f64 (/.f64 (.f64 (pow.f64 (.f64 (.f64 #s(literal 2 binary64) n) (PI.f64)) k) k) (PI.f64)) #s(literal 1/2 binary64))))
(neg.f64 (/.f64 (pow.f64 (.f64 (.f64 #s(literal 2 binary64) n) (PI.f64)) (fma.f64 #s(literal -1/2 binary64) k #s(literal 1/2 binary64))) (neg.f64 (sqrt.f64 k))))
(sqrt.f64 (.f64 (.f64 n (/.f64 #s(literal 2 binary64) (pow.f64 (.f64 (.f64 #s(literal 2 binary64) n) (PI.f64)) k))) (/.f64 (PI.f64) k)))
(-.f64 (/.f64 #s(literal 0 binary64) (neg.f64 (sqrt.f64 k))) (/.f64 (pow.f64 (.f64 (.f64 #s(literal 2 binary64) n) (PI.f64)) (fma.f64 #s(literal -1/2 binary64) k #s(literal 1/2 binary64))) (neg.f64 (sqrt.f64 k))))
(-.f64 #s(literal 0 binary64) (/.f64 (pow.f64 (.f64 (.f64 #s(literal 2 binary64) n) (PI.f64)) (fma.f64 #s(literal -1/2 binary64) k #s(literal 1/2 binary64))) (neg.f64 (sqrt.f64 k))))
(exp.f64 (-.f64 (.f64 (log.f64 (.f64 (*.f64 #s(literal 2 binary64) n) (PI.f64))) (fma.f64 #s(literal -1/2 binary64) k #s(literal 1/2 binary64))) (log.f64 (sqrt.f64 k))))
(exp.f64 (fma.f64 (log.f64 (.f64 (/.f64 (PI.f64) (pow.f64 (.f64 (.f64 #s(literal 2 binary64) n) (PI.f64)) k)) (/.f64 #s(literal 2 binary64) k))) #s(literal 1/2 binary64) (.f64 (log.f64 n) #s(literal 1/2 binary64))))
(exp.f64 (fma.f64 (log.f64 n) #s(literal 1/2 binary64) (.f64 (log.f64 (.f64 (/.f64 (PI.f64) (pow.f64 (.f64 (.f64 #s(literal 2 binary64) n) (PI.f64)) k)) (/.f64 #s(literal 2 binary64) k))) #s(literal 1/2 binary64))))
(exp.f64 (fma.f64 (log.f64 (.f64 (.f64 #s(literal 2 binary64) n) (PI.f64))) (.f64 #s(literal -1/2 binary64) k) (.f64 (log.f64 (.f64 (/.f64 (.f64 (PI.f64) n) k) #s(literal 2 binary64))) #s(literal 1/2 binary64))))
(exp.f64 (fma.f64 (log.f64 (.f64 (.f64 #s(literal 2 binary64) n) (PI.f64))) (fma.f64 #s(literal -1/2 binary64) k #s(literal 1/2 binary64)) (*.f64 (log.f64 (sqrt.f64 k)) #s(literal -1 binary64))))
(exp.f64 (fma.f64 (log.f64 (.f64 (.f64 #s(literal 2 binary64) n) (PI.f64))) (fma.f64 #s(literal -1/2 binary64) k #s(literal 1/2 binary64)) (*.f64 (neg.f64 (log.f64 k)) #s(literal 1/2 binary64))))
(exp.f64 (fma.f64 (log.f64 (sqrt.f64 k)) #s(literal -1 binary64) (.f64 (log.f64 (.f64 (*.f64 #s(literal 2 binary64) n) (PI.f64))) (fma.f64 #s(literal -1/2 binary64) k #s(literal 1/2 binary64)))))
(exp.f64 (fma.f64 (neg.f64 (log.f64 k)) #s(literal 1/2 binary64) (.f64 (log.f64 (.f64 (*.f64 #s(literal 2 binary64) n) (PI.f64))) (fma.f64 #s(literal -1/2 binary64) k #s(literal 1/2 binary64)))))
(exp.f64 (.f64 (log.f64 (.f64 (.f64 n (/.f64 #s(literal 2 binary64) (pow.f64 (.f64 (*.f64 #s(literal 2 binary64) n) (PI.f64)) k))) (/.f64 (PI.f64) k))) #s(literal 1/2 binary64)))
(exp.f64 (.f64 (log.f64 (/.f64 (sqrt.f64 k) (pow.f64 (.f64 (*.f64 #s(literal 2 binary64) n) (PI.f64)) (fma.f64 #s(literal -1/2 binary64) k #s(literal 1/2 binary64))))) #s(literal -1 binary64)))
(*.f64 (pow.f64 n #s(literal 1/4 binary64)) (pow.f64 n #s(literal 1/4 binary64)))
(pow.f64 (exp.f64 (log.f64 n)) #s(literal 1/2 binary64))
(pow.f64 (*.f64 n n) #s(literal 1/4 binary64))
(pow.f64 (pow.f64 n #s(literal 1/4 binary64)) #s(literal 2 binary64))
(pow.f64 n #s(literal 1/2 binary64))
(sqrt.f64 n)
(exp.f64 (*.f64 (log.f64 n) #s(literal 1/2 binary64)))
(.f64 (sqrt.f64 (/.f64 #s(literal 2 binary64) k)) (sqrt.f64 (/.f64 (PI.f64) (pow.f64 (.f64 (*.f64 #s(literal 2 binary64) n) (PI.f64)) k))))
(.f64 (sqrt.f64 (/.f64 (PI.f64) (pow.f64 (.f64 (*.f64 #s(literal 2 binary64) n) (PI.f64)) k))) (sqrt.f64 (/.f64 #s(literal 2 binary64) k)))
(.f64 (pow.f64 (/.f64 (PI.f64) (pow.f64 (.f64 (*.f64 #s(literal 2 binary64) n) (PI.f64)) k)) #s(literal 1/2 binary64)) (pow.f64 (/.f64 #s(literal 2 binary64) k) #s(literal 1/2 binary64)))
(.f64 (pow.f64 (/.f64 #s(literal 2 binary64) k) #s(literal 1/2 binary64)) (pow.f64 (/.f64 (PI.f64) (pow.f64 (.f64 (*.f64 #s(literal 2 binary64) n) (PI.f64)) k)) #s(literal 1/2 binary64)))
(.f64 (pow.f64 (.f64 (/.f64 (.f64 (pow.f64 (.f64 (.f64 #s(literal 2 binary64) n) (PI.f64)) k) k) (PI.f64)) #s(literal 1/2 binary64)) #s(literal -1/4 binary64)) (pow.f64 (.f64 (/.f64 (.f64 (pow.f64 (.f64 (*.f64 #s(literal 2 binary64) n) (PI.f64)) k) k) (PI.f64)) #s(literal 1/2 binary64)) #s(literal -1/4 binary64)))
(.f64 (neg.f64 (sqrt.f64 (.f64 (PI.f64) #s(literal 2 binary64)))) (/.f64 #s(literal 1 binary64) (neg.f64 (sqrt.f64 (.f64 (pow.f64 (.f64 (*.f64 #s(literal 2 binary64) n) (PI.f64)) k) k)))))
(.f64 (sqrt.f64 (.f64 (PI.f64) (/.f64 #s(literal 2 binary64) (pow.f64 (.f64 (.f64 #s(literal 2 binary64) n) (PI.f64)) k)))) (pow.f64 k #s(literal -1/2 binary64)))
(.f64 (sqrt.f64 (.f64 #s(literal -2 binary64) (PI.f64))) (/.f64 #s(literal 1 binary64) (sqrt.f64 (.f64 (neg.f64 k) (pow.f64 (.f64 (*.f64 #s(literal 2 binary64) n) (PI.f64)) k)))))
(.f64 (sqrt.f64 (.f64 #s(literal -2 binary64) (PI.f64))) (sqrt.f64 (/.f64 #s(literal -1 binary64) (.f64 (pow.f64 (.f64 (*.f64 #s(literal 2 binary64) n) (PI.f64)) k) k))))
(.f64 (sqrt.f64 (.f64 #s(literal -2 binary64) (PI.f64))) (pow.f64 (/.f64 #s(literal -1 binary64) (.f64 (pow.f64 (.f64 (*.f64 #s(literal 2 binary64) n) (PI.f64)) k) k)) #s(literal 1/2 binary64)))
(.f64 (sqrt.f64 (/.f64 (PI.f64) k)) (sqrt.f64 (/.f64 #s(literal 2 binary64) (pow.f64 (.f64 (*.f64 #s(literal 2 binary64) n) (PI.f64)) k))))
(.f64 (sqrt.f64 (/.f64 #s(literal 2 binary64) (pow.f64 (.f64 (*.f64 #s(literal 2 binary64) n) (PI.f64)) k))) (sqrt.f64 (/.f64 (PI.f64) k)))
(.f64 (pow.f64 (.f64 (pow.f64 (.f64 (.f64 #s(literal 2 binary64) n) (PI.f64)) k) k) #s(literal -1/2 binary64)) (sqrt.f64 (*.f64 (PI.f64) #s(literal 2 binary64))))
(.f64 (sqrt.f64 (/.f64 (PI.f64) (.f64 (pow.f64 (.f64 (.f64 #s(literal 2 binary64) n) (PI.f64)) k) k))) (sqrt.f64 #s(literal 2 binary64)))
(.f64 (sqrt.f64 (.f64 (PI.f64) #s(literal 2 binary64))) (pow.f64 (.f64 (pow.f64 (.f64 (*.f64 #s(literal 2 binary64) n) (PI.f64)) k) k) #s(literal -1/2 binary64)))
(.f64 (sqrt.f64 (PI.f64)) (sqrt.f64 (/.f64 #s(literal 2 binary64) (.f64 (pow.f64 (.f64 (.f64 #s(literal 2 binary64) n) (PI.f64)) k) k))))
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(*.f64 (pow.f64 (pow.f64 (PI.f64) #s(literal 5/2 binary64)) #s(literal 1/3 binary64)) (cbrt.f64 (sqrt.f64 (PI.f64))))
(.f64 (pow.f64 (pow.f64 (.f64 (PI.f64) (cbrt.f64 (PI.f64))) #s(literal 2 binary64)) #s(literal 1/3 binary64)) (cbrt.f64 (cbrt.f64 (PI.f64))))
(*.f64 (pow.f64 (pow.f64 (PI.f64) #s(literal 3/2 binary64)) #s(literal 1/3 binary64)) (pow.f64 (pow.f64 (PI.f64) #s(literal 3/2 binary64)) #s(literal 1/3 binary64)))
(*.f64 (pow.f64 (cbrt.f64 (sqrt.f64 (PI.f64))) #s(literal 3 binary64)) (pow.f64 (cbrt.f64 (sqrt.f64 (PI.f64))) #s(literal 3 binary64)))
(*.f64 (pow.f64 (cbrt.f64 (pow.f64 (cbrt.f64 (PI.f64)) #s(literal 2 binary64))) #s(literal 3 binary64)) (pow.f64 (cbrt.f64 (cbrt.f64 (PI.f64))) #s(literal 3 binary64)))
(*.f64 (pow.f64 (PI.f64) #s(literal 1/4 binary64)) (sqrt.f64 (pow.f64 (PI.f64) #s(literal 3/2 binary64))))
(*.f64 (sqrt.f64 (PI.f64)) (log.f64 (exp.f64 (sqrt.f64 (PI.f64)))))
(*.f64 (sqrt.f64 (PI.f64)) (sqrt.f64 (PI.f64)))
(*.f64 (pow.f64 (cbrt.f64 (PI.f64)) #s(literal 2 binary64)) (pow.f64 (pow.f64 (PI.f64) #s(literal 1/6 binary64)) #s(literal 2 binary64)))
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(*.f64 (cbrt.f64 (PI.f64)) (log.f64 (exp.f64 (pow.f64 (cbrt.f64 (PI.f64)) #s(literal 2 binary64)))))
(*.f64 (cbrt.f64 (PI.f64)) (pow.f64 (cbrt.f64 (PI.f64)) #s(literal 2 binary64)))
(*.f64 #s(literal 1 binary64) (PI.f64))
(*.f64 (PI.f64) (log.f64 (E.f64)))
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(sqrt.f64 (*.f64 (PI.f64) (PI.f64)))
(fabs.f64 (PI.f64))
(exp.f64 (*.f64 (log.f64 (sqrt.f64 (PI.f64))) #s(literal 2 binary64)))
(exp.f64 (*.f64 (log.f64 (pow.f64 (PI.f64) #s(literal 3 binary64))) #s(literal 1/3 binary64)))
(exp.f64 (*.f64 (log.f64 (cbrt.f64 (PI.f64))) #s(literal 3 binary64)))
(exp.f64 (log.f64 (PI.f64)))
(log.f64 (exp.f64 (PI.f64)))
(PI.f64)
(.f64 (pow.f64 (/.f64 (pow.f64 (.f64 (.f64 #s(literal 2 binary64) n) (PI.f64)) k) (PI.f64)) #s(literal -1 binary64)) (pow.f64 (.f64 #s(literal 1/2 binary64) k) #s(literal -1 binary64)))
(.f64 (pow.f64 (.f64 #s(literal 1/2 binary64) k) #s(literal -1 binary64)) (pow.f64 (/.f64 (pow.f64 (.f64 (.f64 #s(literal 2 binary64) n) (PI.f64)) k) (PI.f64)) #s(literal -1 binary64)))
(.f64 (/.f64 (.f64 (PI.f64) #s(literal 2 binary64)) k) (pow.f64 (.f64 (.f64 #s(literal 2 binary64) n) (PI.f64)) (neg.f64 k)))
(.f64 (.f64 #s(literal 2 binary64) (/.f64 (PI.f64) k)) (pow.f64 (.f64 (.f64 #s(literal 2 binary64) n) (PI.f64)) (neg.f64 k)))
(.f64 (.f64 (/.f64 #s(literal 2 binary64) (pow.f64 (.f64 (.f64 #s(literal 2 binary64) n) (PI.f64)) k)) (PI.f64)) (pow.f64 k #s(literal -1 binary64)))
(.f64 (pow.f64 (.f64 (.f64 #s(literal 2 binary64) n) (PI.f64)) (neg.f64 k)) (pow.f64 (/.f64 k (.f64 (PI.f64) #s(literal 2 binary64))) #s(literal -1 binary64)))
(.f64 (/.f64 (PI.f64) (pow.f64 (.f64 (*.f64 #s(literal 2 binary64) n) (PI.f64)) k)) (/.f64 #s(literal 2 binary64) k))
(.f64 (/.f64 #s(literal 2 binary64) k) (/.f64 (PI.f64) (pow.f64 (.f64 (*.f64 #s(literal 2 binary64) n) (PI.f64)) k)))
(.f64 (.f64 #s(literal -2 binary64) (/.f64 (PI.f64) (pow.f64 (.f64 (.f64 #s(literal 2 binary64) n) (PI.f64)) k))) (/.f64 #s(literal -1 binary64) k))
(.f64 (/.f64 (PI.f64) (.f64 (pow.f64 (.f64 (.f64 #s(literal 2 binary64) n) (PI.f64)) k) k)) #s(literal 2 binary64))
(.f64 (.f64 (PI.f64) (/.f64 #s(literal 2 binary64) (pow.f64 (.f64 (.f64 #s(literal 2 binary64) n) (PI.f64)) k))) (pow.f64 k #s(literal -1 binary64)))
(.f64 (/.f64 (pow.f64 (.f64 (.f64 #s(literal 2 binary64) n) (PI.f64)) (neg.f64 k)) k) (pow.f64 (pow.f64 (.f64 (PI.f64) #s(literal 2 binary64)) #s(literal -1 binary64)) #s(literal -1 binary64)))
(.f64 (/.f64 (pow.f64 (.f64 (.f64 #s(literal 2 binary64) n) (PI.f64)) (neg.f64 k)) k) (.f64 (PI.f64) #s(literal 2 binary64)))
(.f64 (/.f64 (PI.f64) k) (/.f64 #s(literal 2 binary64) (pow.f64 (.f64 (*.f64 #s(literal 2 binary64) n) (PI.f64)) k)))
(.f64 (/.f64 #s(literal 2 binary64) (pow.f64 (.f64 (*.f64 #s(literal 2 binary64) n) (PI.f64)) k)) (/.f64 (PI.f64) k))
(.f64 (.f64 #s(literal -2 binary64) (PI.f64)) (/.f64 #s(literal -1 binary64) (.f64 (pow.f64 (.f64 (*.f64 #s(literal 2 binary64) n) (PI.f64)) k) k)))
(.f64 #s(literal -1 binary64) (/.f64 #s(literal 1 binary64) (.f64 (.f64 (neg.f64 k) #s(literal 1/2 binary64)) (/.f64 (pow.f64 (.f64 (*.f64 #s(literal 2 binary64) n) (PI.f64)) k) (PI.f64)))))
(.f64 #s(literal -1 binary64) (/.f64 (.f64 #s(literal -2 binary64) (PI.f64)) (.f64 (pow.f64 (.f64 (*.f64 #s(literal 2 binary64) n) (PI.f64)) k) k)))
(.f64 (pow.f64 k #s(literal -1 binary64)) (.f64 (PI.f64) (/.f64 #s(literal 2 binary64) (pow.f64 (.f64 (.f64 #s(literal 2 binary64) n) (PI.f64)) k))))
(.f64 #s(literal 1 binary64) (.f64 (/.f64 (PI.f64) (pow.f64 (.f64 (.f64 #s(literal 2 binary64) n) (PI.f64)) k)) (/.f64 #s(literal 2 binary64) k)))
(.f64 (sqrt.f64 (.f64 (/.f64 (PI.f64) (pow.f64 (.f64 (.f64 #s(literal 2 binary64) n) (PI.f64)) k)) (/.f64 #s(literal 2 binary64) k))) (sqrt.f64 (.f64 (/.f64 (PI.f64) (pow.f64 (.f64 (*.f64 #s(literal 2 binary64) n) (PI.f64)) k)) (/.f64 #s(literal 2 binary64) k))))
(.f64 (.f64 (PI.f64) #s(literal 2 binary64)) (/.f64 (pow.f64 (.f64 (.f64 #s(literal 2 binary64) n) (PI.f64)) (neg.f64 k)) k))
(.f64 (PI.f64) (/.f64 #s(literal 2 binary64) (.f64 (pow.f64 (.f64 (.f64 #s(literal 2 binary64) n) (PI.f64)) k) k)))
(.f64 #s(literal 2 binary64) (/.f64 (PI.f64) (.f64 (pow.f64 (.f64 (.f64 #s(literal 2 binary64) n) (PI.f64)) k) k)))
(pow.f64 (.f64 (/.f64 (.f64 (pow.f64 (.f64 (.f64 #s(literal 2 binary64) n) (PI.f64)) k) k) (PI.f64)) #s(literal 1/2 binary64)) #s(literal -1 binary64))
(/.f64 (neg.f64 (/.f64 (.f64 (PI.f64) #s(literal 2 binary64)) k)) (neg.f64 (pow.f64 (.f64 (*.f64 #s(literal 2 binary64) n) (PI.f64)) k)))
(/.f64 (neg.f64 (.f64 #s(literal 2 binary64) (/.f64 (PI.f64) k))) (neg.f64 (pow.f64 (.f64 (*.f64 #s(literal 2 binary64) n) (PI.f64)) k)))
(/.f64 (neg.f64 (.f64 (/.f64 #s(literal 2 binary64) (pow.f64 (.f64 (*.f64 #s(literal 2 binary64) n) (PI.f64)) k)) (PI.f64))) (neg.f64 k))
(/.f64 (neg.f64 (.f64 #s(literal -2 binary64) (/.f64 (PI.f64) (pow.f64 (.f64 (*.f64 #s(literal 2 binary64) n) (PI.f64)) k)))) k)
(/.f64 (.f64 (/.f64 (.f64 (PI.f64) #s(literal 2 binary64)) (sqrt.f64 (pow.f64 (.f64 (.f64 #s(literal 2 binary64) n) (PI.f64)) k))) #s(literal -1 binary64)) (.f64 (sqrt.f64 (pow.f64 (.f64 (*.f64 #s(literal 2 binary64) n) (PI.f64)) k)) (neg.f64 k)))
(/.f64 (.f64 (/.f64 (.f64 (PI.f64) #s(literal 2 binary64)) (sqrt.f64 (pow.f64 (.f64 (.f64 #s(literal 2 binary64) n) (PI.f64)) k))) #s(literal 1 binary64)) (.f64 (sqrt.f64 (pow.f64 (.f64 (*.f64 #s(literal 2 binary64) n) (PI.f64)) k)) k))
(/.f64 (.f64 (/.f64 (.f64 (PI.f64) #s(literal 2 binary64)) (pow.f64 (.f64 #s(literal 2 binary64) n) k)) #s(literal -1 binary64)) (.f64 (pow.f64 (PI.f64) k) (neg.f64 k)))
(/.f64 (.f64 (/.f64 (.f64 (PI.f64) #s(literal 2 binary64)) (pow.f64 (.f64 #s(literal 2 binary64) n) k)) #s(literal 1 binary64)) (.f64 (pow.f64 (PI.f64) k) k))
(/.f64 (.f64 (.f64 #s(literal -2 binary64) (PI.f64)) #s(literal -1 binary64)) (.f64 (pow.f64 (.f64 (*.f64 #s(literal 2 binary64) n) (PI.f64)) k) k))
(/.f64 (.f64 (.f64 #s(literal -2 binary64) (PI.f64)) #s(literal 1 binary64)) (.f64 (neg.f64 k) (pow.f64 (.f64 (*.f64 #s(literal 2 binary64) n) (PI.f64)) k)))
(/.f64 (.f64 (.f64 (PI.f64) #s(literal 2 binary64)) #s(literal -1 binary64)) (.f64 (neg.f64 k) (pow.f64 (.f64 (*.f64 #s(literal 2 binary64) n) (PI.f64)) k)))
(/.f64 (.f64 (neg.f64 (PI.f64)) (/.f64 #s(literal 2 binary64) (sqrt.f64 (pow.f64 (.f64 (.f64 #s(literal 2 binary64) n) (PI.f64)) k)))) (.f64 (neg.f64 k) (sqrt.f64 (pow.f64 (.f64 (.f64 #s(literal 2 binary64) n) (PI.f64)) k))))
(/.f64 (.f64 (neg.f64 (PI.f64)) (/.f64 #s(literal 2 binary64) (pow.f64 (.f64 #s(literal 2 binary64) n) k))) (*.f64 (neg.f64 k) (pow.f64 (PI.f64) k)))
(/.f64 (.f64 #s(literal 1 binary64) (/.f64 #s(literal 2 binary64) (sqrt.f64 (pow.f64 (.f64 (.f64 #s(literal 2 binary64) n) (PI.f64)) k)))) (.f64 (/.f64 k (PI.f64)) (sqrt.f64 (pow.f64 (.f64 (.f64 #s(literal 2 binary64) n) (PI.f64)) k))))
(/.f64 (.f64 #s(literal 1 binary64) (/.f64 #s(literal 2 binary64) (pow.f64 (.f64 #s(literal 2 binary64) n) k))) (*.f64 (/.f64 k (PI.f64)) (pow.f64 (PI.f64) k)))
(/.f64 (.f64 (PI.f64) (/.f64 #s(literal 2 binary64) (sqrt.f64 (pow.f64 (.f64 (.f64 #s(literal 2 binary64) n) (PI.f64)) k)))) (.f64 k (sqrt.f64 (pow.f64 (.f64 (.f64 #s(literal 2 binary64) n) (PI.f64)) k))))
(/.f64 (.f64 (PI.f64) (/.f64 #s(literal 2 binary64) (pow.f64 (.f64 #s(literal 2 binary64) n) k))) (*.f64 k (pow.f64 (PI.f64) k)))
(/.f64 (.f64 (/.f64 #s(literal 2 binary64) (sqrt.f64 (pow.f64 (.f64 (.f64 #s(literal 2 binary64) n) (PI.f64)) k))) (neg.f64 (PI.f64))) (.f64 (sqrt.f64 (pow.f64 (.f64 (.f64 #s(literal 2 binary64) n) (PI.f64)) k)) (neg.f64 k)))
(/.f64 (.f64 (/.f64 #s(literal 2 binary64) (sqrt.f64 (pow.f64 (.f64 (.f64 #s(literal 2 binary64) n) (PI.f64)) k))) #s(literal 1 binary64)) (.f64 (sqrt.f64 (pow.f64 (.f64 (.f64 #s(literal 2 binary64) n) (PI.f64)) k)) (/.f64 k (PI.f64))))
(/.f64 (.f64 (/.f64 #s(literal 2 binary64) (sqrt.f64 (pow.f64 (.f64 (.f64 #s(literal 2 binary64) n) (PI.f64)) k))) (PI.f64)) (.f64 (sqrt.f64 (pow.f64 (.f64 (.f64 #s(literal 2 binary64) n) (PI.f64)) k)) k))
(/.f64 (.f64 (/.f64 #s(literal 2 binary64) (pow.f64 (.f64 #s(literal 2 binary64) n) k)) (neg.f64 (PI.f64))) (*.f64 (pow.f64 (PI.f64) k) (neg.f64 k)))
(/.f64 (.f64 (/.f64 #s(literal 2 binary64) (pow.f64 (.f64 #s(literal 2 binary64) n) k)) #s(literal 1 binary64)) (*.f64 (pow.f64 (PI.f64) k) (/.f64 k (PI.f64))))
(/.f64 (.f64 (/.f64 #s(literal 2 binary64) (pow.f64 (.f64 #s(literal 2 binary64) n) k)) (PI.f64)) (*.f64 (pow.f64 (PI.f64) k) k))
(/.f64 (.f64 #s(literal 1 binary64) (neg.f64 (PI.f64))) (.f64 (.f64 (pow.f64 (.f64 (*.f64 #s(literal 2 binary64) n) (PI.f64)) k) #s(literal 1/2 binary64)) (neg.f64 k)))
(/.f64 (/.f64 (.f64 (PI.f64) #s(literal 2 binary64)) k) (pow.f64 (.f64 (*.f64 #s(literal 2 binary64) n) (PI.f64)) k))
(/.f64 (.f64 #s(literal 2 binary64) (/.f64 (PI.f64) k)) (pow.f64 (.f64 (*.f64 #s(literal 2 binary64) n) (PI.f64)) k))
(/.f64 (.f64 (/.f64 #s(literal 2 binary64) (pow.f64 (.f64 (*.f64 #s(literal 2 binary64) n) (PI.f64)) k)) (PI.f64)) k)
(/.f64 (.f64 #s(literal -2 binary64) (/.f64 (PI.f64) (pow.f64 (.f64 (*.f64 #s(literal 2 binary64) n) (PI.f64)) k))) (neg.f64 k))
(/.f64 (neg.f64 (PI.f64)) (.f64 (neg.f64 k) (.f64 (pow.f64 (.f64 (.f64 #s(literal 2 binary64) n) (PI.f64)) k) #s(literal 1/2 binary64))))
(/.f64 (.f64 (PI.f64) (/.f64 #s(literal 2 binary64) (pow.f64 (.f64 (*.f64 #s(literal 2 binary64) n) (PI.f64)) k))) k)
(/.f64 (/.f64 (PI.f64) k) (.f64 (pow.f64 (.f64 (*.f64 #s(literal 2 binary64) n) (PI.f64)) k) #s(literal 1/2 binary64)))
(/.f64 (/.f64 #s(literal 2 binary64) (pow.f64 (.f64 (.f64 #s(literal 2 binary64) n) (PI.f64)) k)) (/.f64 k (PI.f64)))
(/.f64 #s(literal -2 binary64) (.f64 (/.f64 k (PI.f64)) (neg.f64 (pow.f64 (.f64 (*.f64 #s(literal 2 binary64) n) (PI.f64)) k))))
(/.f64 #s(literal -2 binary64) (.f64 (neg.f64 (pow.f64 (.f64 (*.f64 #s(literal 2 binary64) n) (PI.f64)) k)) (/.f64 k (PI.f64))))
(/.f64 (.f64 #s(literal -2 binary64) (PI.f64)) (.f64 (neg.f64 k) (pow.f64 (.f64 (.f64 #s(literal 2 binary64) n) (PI.f64)) k)))
(/.f64 #s(literal -1 binary64) (.f64 (/.f64 (pow.f64 (.f64 (.f64 #s(literal 2 binary64) n) (PI.f64)) k) (.f64 (PI.f64) #s(literal 2 binary64))) (neg.f64 k)))
(/.f64 #s(literal -1 binary64) (.f64 (.f64 (neg.f64 k) #s(literal 1/2 binary64)) (/.f64 (pow.f64 (.f64 (.f64 #s(literal 2 binary64) n) (PI.f64)) k) (PI.f64))))
(/.f64 #s(literal 1 binary64) (/.f64 (pow.f64 (.f64 (.f64 #s(literal 2 binary64) n) (PI.f64)) k) (/.f64 (*.f64 (PI.f64) #s(literal 2 binary64)) k)))
(/.f64 #s(literal 1 binary64) (/.f64 (pow.f64 (.f64 (.f64 #s(literal 2 binary64) n) (PI.f64)) k) (*.f64 #s(literal 2 binary64) (/.f64 (PI.f64) k))))
(/.f64 #s(literal 1 binary64) (/.f64 k (.f64 (/.f64 #s(literal 2 binary64) (pow.f64 (.f64 (*.f64 #s(literal 2 binary64) n) (PI.f64)) k)) (PI.f64))))
(/.f64 #s(literal 1 binary64) (neg.f64 (.f64 (.f64 (neg.f64 k) #s(literal 1/2 binary64)) (/.f64 (pow.f64 (.f64 (.f64 #s(literal 2 binary64) n) (PI.f64)) k) (PI.f64)))))
(/.f64 #s(literal 1 binary64) (.f64 (/.f64 (pow.f64 (.f64 (.f64 #s(literal 2 binary64) n) (PI.f64)) k) (.f64 (PI.f64) #s(literal 2 binary64))) k))
(/.f64 #s(literal 1 binary64) (.f64 (/.f64 (.f64 (pow.f64 (.f64 (.f64 #s(literal 2 binary64) n) (PI.f64)) k) k) (PI.f64)) #s(literal 1/2 binary64)))
(/.f64 (.f64 (PI.f64) #s(literal 2 binary64)) (.f64 (pow.f64 (.f64 (.f64 #s(literal 2 binary64) n) (PI.f64)) k) k))
(/.f64 (PI.f64) (.f64 k (.f64 (pow.f64 (.f64 (.f64 #s(literal 2 binary64) n) (PI.f64)) k) #s(literal 1/2 binary64))))
(/.f64 (PI.f64) (.f64 (.f64 (pow.f64 (.f64 (.f64 #s(literal 2 binary64) n) (PI.f64)) k) #s(literal 1/2 binary64)) k))
(/.f64 #s(literal 2 binary64) (.f64 (/.f64 k (PI.f64)) (pow.f64 (.f64 (*.f64 #s(literal 2 binary64) n) (PI.f64)) k)))
(/.f64 #s(literal 2 binary64) (.f64 (pow.f64 (.f64 (*.f64 #s(literal 2 binary64) n) (PI.f64)) k) (/.f64 k (PI.f64))))
(/.f64 #s(literal 2 binary64) (/.f64 (.f64 (pow.f64 (.f64 (*.f64 #s(literal 2 binary64) n) (PI.f64)) k) k) (PI.f64)))
(neg.f64 (/.f64 (.f64 #s(literal -2 binary64) (PI.f64)) (.f64 (pow.f64 (.f64 (.f64 #s(literal 2 binary64) n) (PI.f64)) k) k)))
(-.f64 (/.f64 #s(literal 0 binary64) (.f64 (neg.f64 k) (pow.f64 (.f64 (.f64 #s(literal 2 binary64) n) (PI.f64)) k))) (/.f64 (.f64 #s(literal -2 binary64) (PI.f64)) (.f64 (pow.f64 (.f64 (*.f64 #s(literal 2 binary64) n) (PI.f64)) k) k)))
(-.f64 #s(literal 0 binary64) (/.f64 (.f64 #s(literal -2 binary64) (PI.f64)) (.f64 (pow.f64 (.f64 (.f64 #s(literal 2 binary64) n) (PI.f64)) k) k)))
(exp.f64 (.f64 (log.f64 (.f64 (/.f64 (.f64 (pow.f64 (.f64 (*.f64 #s(literal 2 binary64) n) (PI.f64)) k) k) (PI.f64)) #s(literal 1/2 binary64))) #s(literal -1 binary64)))
(*.f64 (neg.f64 (neg.f64 n)) (PI.f64))
(*.f64 (neg.f64 (neg.f64 (PI.f64))) n)
(.f64 (.f64 n (sqrt.f64 (PI.f64))) (sqrt.f64 (PI.f64)))
(.f64 (.f64 n (pow.f64 (cbrt.f64 (PI.f64)) #s(literal 2 binary64))) (cbrt.f64 (PI.f64)))
(*.f64 (neg.f64 n) (neg.f64 (PI.f64)))
(*.f64 (neg.f64 (PI.f64)) (neg.f64 n))
(.f64 (sqrt.f64 (PI.f64)) (.f64 (sqrt.f64 (PI.f64)) n))
(.f64 (pow.f64 (cbrt.f64 (PI.f64)) #s(literal 2 binary64)) (.f64 (cbrt.f64 (PI.f64)) n))
(.f64 #s(literal -1 binary64) (.f64 (neg.f64 n) (PI.f64)))
(.f64 (.f64 (PI.f64) n) #s(literal 1 binary64))
(.f64 #s(literal 1 binary64) (.f64 (PI.f64) n))
(*.f64 (PI.f64) n)
(*.f64 n (PI.f64))
(/.f64 (*.f64 (neg.f64 n) (PI.f64)) #s(literal -1 binary64))
(/.f64 (*.f64 (PI.f64) n) #s(literal 1 binary64))
(/.f64 #s(literal 1 binary64) (pow.f64 (*.f64 (PI.f64) n) #s(literal -1 binary64)))
(neg.f64 (*.f64 (neg.f64 n) (PI.f64)))
(-.f64 #s(literal 0 binary64) (*.f64 (neg.f64 n) (PI.f64)))

eval206.0ms (2.2%)

Memory: 8.5MiB live, 312.7MiB allocated
Compiler: Compiled 25 197 to 3 651 computations (85.5% saved)

prune219.0ms (2.3%)

Memory

-29.0MiB live, 316.0MiB allocated

Pruning

36 alts after pruning (29 fresh and 7 done)

	Pruned	Kept	Total
New	1 420	21	1 441
Fresh	5	8	13
Picked	0	5	5
Done	0	2	2
Total	1 425	36	1 461

Accuracy

100.0%

Counts

1 461 → 36

Alt Table

Click to see full alt table

Status	Accuracy	Program
✓	99.5%	(/.f64 (pow.f64 (.f64 (.f64 #s(literal 2 binary64) n) (PI.f64)) (fma.f64 #s(literal -1/2 binary64) k #s(literal 1/2 binary64))) (sqrt.f64 k))
	50.2%	(/.f64 #s(approx (pow (* (* 2 n) (PI)) (+ (* -1/2 k) 1/2)) (.f64 (sqrt.f64 (.f64 (PI.f64) n)) (sqrt.f64 #s(literal 2 binary64)))) (sqrt.f64 k))
▶	99.5%	(/.f64 #s(literal 1 binary64) (.f64 (pow.f64 (.f64 (*.f64 #s(literal 2 binary64) n) (PI.f64)) (fma.f64 #s(literal 1/2 binary64) k #s(literal -1/2 binary64))) (sqrt.f64 k)))
	50.1%	(.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) (/.f64 #s(literal 1 binary64) #s(approx (pow (sqrt ( n (* (PI) 2))) (- k 1)) (/.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (*.f64 (PI.f64) n))) (sqrt.f64 #s(literal 2 binary64))))))
✓	99.7%	(.f64 (sqrt.f64 n) (sqrt.f64 (/.f64 (.f64 #s(literal 2 binary64) (PI.f64)) (.f64 (pow.f64 (.f64 (*.f64 #s(literal 2 binary64) n) (PI.f64)) k) k))))
	50.3%	(.f64 (sqrt.f64 n) (sqrt.f64 #s(approx (/ ( 2 (PI)) (* (pow (* (* 2 n) (PI)) k) k)) (*.f64 (/.f64 (PI.f64) k) #s(literal 2 binary64)))))
	50.2%	(.f64 (sqrt.f64 n) #s(approx (sqrt (/ ( 2 (PI)) (* (pow (* (* 2 n) (PI)) k) k))) (*.f64 (sqrt.f64 (/.f64 (PI.f64) k)) (sqrt.f64 #s(literal 2 binary64)))))
	75.7%	(sqrt.f64 (/.f64 (.f64 (/.f64 (.f64 (PI.f64) n) k) #s(literal 2 binary64)) (pow.f64 (.f64 (.f64 #s(literal 2 binary64) n) (PI.f64)) k)))
	87.0%	(sqrt.f64 (/.f64 (.f64 (.f64 #s(literal 2 binary64) n) (PI.f64)) (.f64 (pow.f64 (.f64 (*.f64 #s(literal 2 binary64) n) (PI.f64)) k) k)))
	50.3%	#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (/.f64 (sqrt.f64 (.f64 (.f64 #s(literal 2 binary64) n) (PI.f64))) (sqrt.f64 k)))
	50.2%	#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (/.f64 (sqrt.f64 #s(literal 2 binary64)) (/.f64 (sqrt.f64 (/.f64 k (PI.f64))) (sqrt.f64 n))))
	37.3%	#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (/.f64 (sqrt.f64 #s(literal 2 binary64)) (/.f64 #s(literal 1 binary64) (sqrt.f64 (/.f64 (*.f64 (PI.f64) n) k)))))
	50.1%	#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (/.f64 (sqrt.f64 #s(literal 2 binary64)) (.f64 (neg.f64 (sqrt.f64 k)) (/.f64 #s(literal 1 binary64) (neg.f64 (sqrt.f64 (.f64 (PI.f64) n)))))))
✓	39.0%	#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (/.f64 (sqrt.f64 #s(literal 2 binary64)) (sqrt.f64 (/.f64 k (*.f64 (PI.f64) n)))))
	50.2%	#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (/.f64 #s(literal 1 binary64) (/.f64 (sqrt.f64 k) #s(approx (pow (* (* 2 n) (PI)) (+ (* k -1/2) 1/2)) (sqrt.f64 (.f64 (.f64 #s(literal 2 binary64) n) (PI.f64)))))))
✓	99.5%	#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (.f64 (pow.f64 (.f64 (*.f64 #s(literal 2 binary64) n) (PI.f64)) (fma.f64 k #s(literal -1/2 binary64) #s(literal 1/2 binary64))) (sqrt.f64 (/.f64 #s(literal 1 binary64) k))))
	50.2%	#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (.f64 (sqrt.f64 (/.f64 #s(literal 2 binary64) k)) (sqrt.f64 (.f64 (PI.f64) n))))
▶	37.2%	#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (.f64 (sqrt.f64 (.f64 (PI.f64) #s(literal 2 binary64))) (sqrt.f64 (/.f64 n k))))
	37.3%	#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (.f64 (sqrt.f64 (PI.f64)) (sqrt.f64 (.f64 (/.f64 n k) #s(literal 2 binary64)))))
▶	50.2%	#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (.f64 (sqrt.f64 #s(literal 2 binary64)) (/.f64 (sqrt.f64 (.f64 (PI.f64) n)) (sqrt.f64 k))))
	50.2%	#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (.f64 (sqrt.f64 #s(literal 2 binary64)) (.f64 (sqrt.f64 n) (sqrt.f64 (/.f64 (PI.f64) k)))))
✓	37.3%	#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (.f64 (sqrt.f64 #s(literal 2 binary64)) (sqrt.f64 (/.f64 (.f64 (PI.f64) n) k))))
	50.2%	#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (.f64 (neg.f64 (sqrt.f64 (.f64 (*.f64 #s(literal 2 binary64) n) (PI.f64)))) (/.f64 #s(literal -1 binary64) (sqrt.f64 k))))
✓	50.1%	#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (.f64 #s(approx (pow ( (* 2 n) (PI)) (+ (* k -1/2) 1/2)) (.f64 (sqrt.f64 (.f64 (PI.f64) n)) (sqrt.f64 #s(literal 2 binary64)))) (sqrt.f64 (/.f64 #s(literal 1 binary64) k))))
▶	50.0%	#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (.f64 #s(approx (pow ( (* 2 n) (PI)) (+ (* k -1/2) 1/2)) (.f64 (sqrt.f64 (.f64 (PI.f64) #s(literal 2 binary64))) (sqrt.f64 n))) (sqrt.f64 (/.f64 #s(literal 1 binary64) k))))
	50.1%	#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (.f64 #s(approx (pow ( (* 2 n) (PI)) (+ (* k -1/2) 1/2)) (.f64 (sqrt.f64 (.f64 #s(literal 2 binary64) n)) (sqrt.f64 (PI.f64)))) (sqrt.f64 (/.f64 #s(literal 1 binary64) k))))
	50.3%	#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (.f64 #s(approx (pow ( (* 2 n) (PI)) (+ (* k -1/2) 1/2)) (sqrt.f64 (.f64 (.f64 #s(literal 2 binary64) n) (PI.f64)))) (sqrt.f64 (/.f64 #s(literal 1 binary64) k))))
	37.5%	#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt.f64 (/.f64 (*.f64 (PI.f64) #s(literal 2 binary64)) (/.f64 k n))))
	37.5%	#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt.f64 (/.f64 #s(literal 2 binary64) (/.f64 k (*.f64 (PI.f64) n)))))
	37.2%	#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt.f64 (.f64 (/.f64 (.f64 (*.f64 n (sqrt.f64 (PI.f64))) (sqrt.f64 (PI.f64))) k) #s(literal 2 binary64))))
✓	37.5%	#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt.f64 (.f64 (/.f64 (.f64 (PI.f64) n) k) #s(literal 2 binary64))))
	37.4%	#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt.f64 (*.f64 (/.f64 n (/.f64 k (PI.f64))) #s(literal 2 binary64))))
	37.4%	#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt.f64 (.f64 (/.f64 #s(literal 2 binary64) k) (.f64 (PI.f64) n))))
	37.3%	#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt.f64 (.f64 (.f64 (sqrt.f64 (PI.f64)) (*.f64 (sqrt.f64 (PI.f64)) (/.f64 n k))) #s(literal 2 binary64))))
	37.5%	#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt.f64 (.f64 (.f64 (PI.f64) #s(literal 2 binary64)) (/.f64 n k))))
▶	37.5%	#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt.f64 (.f64 (.f64 #s(literal 2 binary64) (/.f64 (PI.f64) k)) n)))

Compiler

Compiled 775 to 735 computations (5.2% saved)

simplify12.0ms (0.1%)

Memory

16.5MiB live, 16.5MiB allocated

Algorithm

1×	egg-herbie

Localize:

Found 20 expressions of interest:

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

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	52	335
0	80	335
1	117	327
2	140	327
3	169	327
4	198	327
5	215	327
6	241	327
7	275	327
8	286	327
9	290	327
0	290	320

Stop Event

1×	iter limit
1×	saturated
1×	iter limit

Calls

Call 1

Inputs
(/.f64 #s(literal 1 binary64) (.f64 (pow.f64 (.f64 (*.f64 #s(literal 2 binary64) n) (PI.f64)) (fma.f64 #s(literal 1/2 binary64) k #s(literal -1/2 binary64))) (sqrt.f64 k)))
#s(literal 1 binary64)
(.f64 (pow.f64 (.f64 (*.f64 #s(literal 2 binary64) n) (PI.f64)) (fma.f64 #s(literal 1/2 binary64) k #s(literal -1/2 binary64))) (sqrt.f64 k))
(pow.f64 (.f64 (.f64 #s(literal 2 binary64) n) (PI.f64)) (fma.f64 #s(literal 1/2 binary64) k #s(literal -1/2 binary64)))
(.f64 (.f64 #s(literal 2 binary64) n) (PI.f64))
(*.f64 #s(literal 2 binary64) n)
#s(literal 2 binary64)
n
(PI.f64)
(fma.f64 #s(literal 1/2 binary64) k #s(literal -1/2 binary64))
#s(literal 1/2 binary64)
k
#s(literal -1/2 binary64)
(sqrt.f64 k)
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt.f64 (.f64 (.f64 #s(literal 2 binary64) (/.f64 (PI.f64) k)) n)))
(sqrt.f64 (.f64 (.f64 #s(literal 2 binary64) (/.f64 (PI.f64) k)) n))
(.f64 (.f64 #s(literal 2 binary64) (/.f64 (PI.f64) k)) n)
(*.f64 #s(literal 2 binary64) (/.f64 (PI.f64) k))
#s(literal 2 binary64)
(/.f64 (PI.f64) k)
(PI.f64)
k
n
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (.f64 (sqrt.f64 (.f64 (PI.f64) #s(literal 2 binary64))) (sqrt.f64 (/.f64 n k))))
(.f64 (sqrt.f64 (.f64 (PI.f64) #s(literal 2 binary64))) (sqrt.f64 (/.f64 n k)))
(sqrt.f64 (*.f64 (PI.f64) #s(literal 2 binary64)))
(*.f64 (PI.f64) #s(literal 2 binary64))
(PI.f64)
#s(literal 2 binary64)
(sqrt.f64 (/.f64 n k))
(/.f64 n k)
n
k
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (.f64 (sqrt.f64 #s(literal 2 binary64)) (/.f64 (sqrt.f64 (.f64 (PI.f64) n)) (sqrt.f64 k))))
(.f64 (sqrt.f64 #s(literal 2 binary64)) (/.f64 (sqrt.f64 (.f64 (PI.f64) n)) (sqrt.f64 k)))
(sqrt.f64 #s(literal 2 binary64))
#s(literal 2 binary64)
(/.f64 (sqrt.f64 (*.f64 (PI.f64) n)) (sqrt.f64 k))
(sqrt.f64 (*.f64 (PI.f64) n))
(*.f64 (PI.f64) n)
(PI.f64)
n
(sqrt.f64 k)
k
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (.f64 #s(approx (pow ( (* 2 n) (PI)) (+ (* k -1/2) 1/2)) (.f64 (sqrt.f64 (.f64 (PI.f64) #s(literal 2 binary64))) (sqrt.f64 n))) (sqrt.f64 (/.f64 #s(literal 1 binary64) k))))
(.f64 #s(approx (pow ( (* 2 n) (PI)) (+ (* k -1/2) 1/2)) (.f64 (sqrt.f64 (.f64 (PI.f64) #s(literal 2 binary64))) (sqrt.f64 n))) (sqrt.f64 (/.f64 #s(literal 1 binary64) k)))
#s(approx (pow (* (* 2 n) (PI)) (+ (* k -1/2) 1/2)) (.f64 (sqrt.f64 (.f64 (PI.f64) #s(literal 2 binary64))) (sqrt.f64 n)))
(.f64 (sqrt.f64 (.f64 (PI.f64) #s(literal 2 binary64))) (sqrt.f64 n))
(sqrt.f64 (*.f64 (PI.f64) #s(literal 2 binary64)))
(*.f64 (PI.f64) #s(literal 2 binary64))
(PI.f64)
#s(literal 2 binary64)
(sqrt.f64 n)
n
(sqrt.f64 (/.f64 #s(literal 1 binary64) k))
(/.f64 #s(literal 1 binary64) k)
#s(literal 1 binary64)
k

Outputs
(/.f64 #s(literal 1 binary64) (.f64 (pow.f64 (.f64 (*.f64 #s(literal 2 binary64) n) (PI.f64)) (fma.f64 #s(literal 1/2 binary64) k #s(literal -1/2 binary64))) (sqrt.f64 k)))
(/.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) (pow.f64 (.f64 (PI.f64) (.f64 n #s(literal 2 binary64))) (fma.f64 k #s(literal 1/2 binary64) #s(literal -1/2 binary64))))
#s(literal 1 binary64)
(.f64 (pow.f64 (.f64 (*.f64 #s(literal 2 binary64) n) (PI.f64)) (fma.f64 #s(literal 1/2 binary64) k #s(literal -1/2 binary64))) (sqrt.f64 k))
(.f64 (sqrt.f64 k) (pow.f64 (.f64 (PI.f64) (*.f64 n #s(literal 2 binary64))) (fma.f64 k #s(literal 1/2 binary64) #s(literal -1/2 binary64))))
(pow.f64 (.f64 (.f64 #s(literal 2 binary64) n) (PI.f64)) (fma.f64 #s(literal 1/2 binary64) k #s(literal -1/2 binary64)))
(pow.f64 (.f64 (PI.f64) (.f64 n #s(literal 2 binary64))) (fma.f64 k #s(literal 1/2 binary64) #s(literal -1/2 binary64)))
(.f64 (.f64 #s(literal 2 binary64) n) (PI.f64))
(.f64 (PI.f64) (.f64 n #s(literal 2 binary64)))
(*.f64 #s(literal 2 binary64) n)
(*.f64 n #s(literal 2 binary64))
#s(literal 2 binary64)
n
(PI.f64)
(fma.f64 #s(literal 1/2 binary64) k #s(literal -1/2 binary64))
(fma.f64 k #s(literal 1/2 binary64) #s(literal -1/2 binary64))
#s(literal 1/2 binary64)
k
#s(literal -1/2 binary64)
(sqrt.f64 k)
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt.f64 (.f64 (.f64 #s(literal 2 binary64) (/.f64 (PI.f64) k)) n)))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt.f64 (.f64 (.f64 (/.f64 (PI.f64) k) #s(literal 2 binary64)) n)))
(sqrt.f64 (.f64 (.f64 #s(literal 2 binary64) (/.f64 (PI.f64) k)) n))
(sqrt.f64 (.f64 (.f64 (/.f64 (PI.f64) k) #s(literal 2 binary64)) n))
(.f64 (.f64 #s(literal 2 binary64) (/.f64 (PI.f64) k)) n)
(.f64 (.f64 (/.f64 (PI.f64) k) #s(literal 2 binary64)) n)
(*.f64 #s(literal 2 binary64) (/.f64 (PI.f64) k))
(*.f64 (/.f64 (PI.f64) k) #s(literal 2 binary64))
#s(literal 2 binary64)
(/.f64 (PI.f64) k)
(PI.f64)
k
n
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (.f64 (sqrt.f64 (.f64 (PI.f64) #s(literal 2 binary64))) (sqrt.f64 (/.f64 n k))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (.f64 (sqrt.f64 (/.f64 n k)) (sqrt.f64 (.f64 (PI.f64) #s(literal 2 binary64)))))
(.f64 (sqrt.f64 (.f64 (PI.f64) #s(literal 2 binary64))) (sqrt.f64 (/.f64 n k)))
(.f64 (sqrt.f64 (/.f64 n k)) (sqrt.f64 (.f64 (PI.f64) #s(literal 2 binary64))))
(sqrt.f64 (*.f64 (PI.f64) #s(literal 2 binary64)))
(*.f64 (PI.f64) #s(literal 2 binary64))
(PI.f64)
#s(literal 2 binary64)
(sqrt.f64 (/.f64 n k))
(/.f64 n k)
n
k
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (.f64 (sqrt.f64 #s(literal 2 binary64)) (/.f64 (sqrt.f64 (.f64 (PI.f64) n)) (sqrt.f64 k))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (.f64 (/.f64 (sqrt.f64 (.f64 (PI.f64) n)) (sqrt.f64 k)) (sqrt.f64 #s(literal 2 binary64))))
(.f64 (sqrt.f64 #s(literal 2 binary64)) (/.f64 (sqrt.f64 (.f64 (PI.f64) n)) (sqrt.f64 k)))
(.f64 (/.f64 (sqrt.f64 (.f64 (PI.f64) n)) (sqrt.f64 k)) (sqrt.f64 #s(literal 2 binary64)))
(sqrt.f64 #s(literal 2 binary64))
#s(literal 2 binary64)
(/.f64 (sqrt.f64 (*.f64 (PI.f64) n)) (sqrt.f64 k))
(sqrt.f64 (*.f64 (PI.f64) n))
(*.f64 (PI.f64) n)
(PI.f64)
n
(sqrt.f64 k)
k
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (.f64 #s(approx (pow ( (* 2 n) (PI)) (+ (* k -1/2) 1/2)) (.f64 (sqrt.f64 (.f64 (PI.f64) #s(literal 2 binary64))) (sqrt.f64 n))) (sqrt.f64 (/.f64 #s(literal 1 binary64) k))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) k)) #s(approx (pow ( (* 2 n) (PI)) (+ (* k -1/2) 1/2)) (.f64 (sqrt.f64 n) (sqrt.f64 (.f64 (PI.f64) #s(literal 2 binary64)))))))
(.f64 #s(approx (pow ( (* 2 n) (PI)) (+ (* k -1/2) 1/2)) (.f64 (sqrt.f64 (.f64 (PI.f64) #s(literal 2 binary64))) (sqrt.f64 n))) (sqrt.f64 (/.f64 #s(literal 1 binary64) k)))
(.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) k)) #s(approx (pow ( (* 2 n) (PI)) (+ (* k -1/2) 1/2)) (.f64 (sqrt.f64 n) (sqrt.f64 (.f64 (PI.f64) #s(literal 2 binary64))))))
#s(approx (pow (* (* 2 n) (PI)) (+ (* k -1/2) 1/2)) (.f64 (sqrt.f64 (.f64 (PI.f64) #s(literal 2 binary64))) (sqrt.f64 n)))
#s(approx (pow (* (* 2 n) (PI)) (+ (* k -1/2) 1/2)) (.f64 (sqrt.f64 n) (sqrt.f64 (.f64 (PI.f64) #s(literal 2 binary64)))))
(.f64 (sqrt.f64 (.f64 (PI.f64) #s(literal 2 binary64))) (sqrt.f64 n))
(.f64 (sqrt.f64 n) (sqrt.f64 (.f64 (PI.f64) #s(literal 2 binary64))))
(sqrt.f64 (*.f64 (PI.f64) #s(literal 2 binary64)))
(*.f64 (PI.f64) #s(literal 2 binary64))
(PI.f64)
#s(literal 2 binary64)
(sqrt.f64 n)
n
(sqrt.f64 (/.f64 #s(literal 1 binary64) k))
(/.f64 #s(literal 1 binary64) k)
#s(literal 1 binary64)
k

localize182.0ms (2%)

Memory

-5.4MiB live, 198.5MiB allocated

Localize:

Found 20 expressions of interest:

New	Metric	Score
accuracy	0.336601269536884	(.f64 (sqrt.f64 (.f64 (PI.f64) #s(literal 2 binary64))) (sqrt.f64 n))
accuracy	0.78125	(sqrt.f64 (*.f64 (PI.f64) #s(literal 2 binary64)))
accuracy	13.562169815496654	(PI.f64)
accuracy	18.070942331824988	#s(approx (pow (* (* 2 n) (PI)) (+ (* k -1/2) 1/2)) (.f64 (sqrt.f64 (.f64 (PI.f64) #s(literal 2 binary64))) (sqrt.f64 n)))
accuracy	0.217128759768442	(/.f64 (sqrt.f64 (*.f64 (PI.f64) n)) (sqrt.f64 k))
accuracy	0.34212875976844204	(.f64 (sqrt.f64 #s(literal 2 binary64)) (/.f64 (sqrt.f64 (.f64 (PI.f64) n)) (sqrt.f64 k)))
accuracy	13.562169815496654	(PI.f64)
accuracy	17.975855259551754	#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (.f64 (sqrt.f64 #s(literal 2 binary64)) (/.f64 (sqrt.f64 (.f64 (PI.f64) n)) (sqrt.f64 k))))
accuracy	0.78125	(sqrt.f64 (*.f64 (PI.f64) #s(literal 2 binary64)))
accuracy	8.34605022212498	(sqrt.f64 (/.f64 n k))
accuracy	13.562169815496654	(PI.f64)
accuracy	17.975855259551754	#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (.f64 (sqrt.f64 (.f64 (PI.f64) #s(literal 2 binary64))) (sqrt.f64 (/.f64 n k))))
accuracy	0.23828125	(/.f64 (PI.f64) k)
accuracy	8.33353557423163	(sqrt.f64 (.f64 (.f64 #s(literal 2 binary64) (/.f64 (PI.f64) k)) n))
accuracy	13.562169815496654	(PI.f64)
accuracy	17.975855259551754	#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt.f64 (.f64 (.f64 #s(literal 2 binary64) (/.f64 (PI.f64) k)) n)))
accuracy	0.18978500976844204	(.f64 (pow.f64 (.f64 (*.f64 #s(literal 2 binary64) n) (PI.f64)) (fma.f64 #s(literal 1/2 binary64) k #s(literal -1/2 binary64))) (sqrt.f64 k))
accuracy	0.19140625	(.f64 (.f64 #s(literal 2 binary64) n) (PI.f64))
accuracy	0.25158192118546285	(pow.f64 (.f64 (.f64 #s(literal 2 binary64) n) (PI.f64)) (fma.f64 #s(literal 1/2 binary64) k #s(literal -1/2 binary64)))
accuracy	13.562169815496654	(PI.f64)

Samples

79.0ms	200×	0	valid
29.0ms	56×	0	exit

Compiler

Compiled 270 to 46 computations (83% saved)

Precisions

Click to see histograms. Total time spent on operations: 66.0ms

ival-mult: 23.0ms (34.7% of total)

ival-pow: 14.0ms (21.1% of total)

ival-sqrt: 13.0ms (19.6% of total)

ival-div: 11.0ms (16.6% of total)

ival-add: 3.0ms (4.5% of total)

ival-pi: 1.0ms (1.5% of total)

ival-sub: 1.0ms (1.5% of total)

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

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

exact: 0.0ms (0% of total)

series67.0ms (0.7%)

Memory

13.0MiB live, 125.3MiB allocated

Counts

23 → 396

Calls

Call 1

Inputs
#s(alt (.f64 (pow.f64 (.f64 (.f64 #s(literal 2 binary64) n) (PI.f64)) (fma.f64 #s(literal 1/2 binary64) k #s(literal -1/2 binary64))) (sqrt.f64 k)) (patch (.f64 (pow.f64 (.f64 (.f64 #s(literal 2 binary64) n) (PI.f64)) (fma.f64 #s(literal 1/2 binary64) k #s(literal -1/2 binary64))) (sqrt.f64 k)) #<representation binary64>) () ())
#s(alt (pow.f64 (.f64 (.f64 #s(literal 2 binary64) n) (PI.f64)) (fma.f64 #s(literal 1/2 binary64) k #s(literal -1/2 binary64))) (patch (pow.f64 (.f64 (.f64 #s(literal 2 binary64) n) (PI.f64)) (fma.f64 #s(literal 1/2 binary64) k #s(literal -1/2 binary64))) #<representation binary64>) () ())
#s(alt (.f64 (.f64 #s(literal 2 binary64) n) (PI.f64)) (patch (.f64 (.f64 #s(literal 2 binary64) n) (PI.f64)) #<representation binary64>) () ())
#s(alt (.f64 #s(literal 2 binary64) n) (patch (.f64 #s(literal 2 binary64) n) #<representation binary64>) () ())
#s(alt #s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt.f64 (.f64 (.f64 #s(literal 2 binary64) (/.f64 (PI.f64) k)) n))) (patch #s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt.f64 (.f64 (.f64 #s(literal 2 binary64) (/.f64 (PI.f64) k)) n))) #<representation binary64>) () ())
#s(alt (sqrt.f64 (.f64 (.f64 #s(literal 2 binary64) (/.f64 (PI.f64) k)) n)) (patch (sqrt.f64 (.f64 (.f64 #s(literal 2 binary64) (/.f64 (PI.f64) k)) n)) #<representation binary64>) () ())
#s(alt (.f64 (.f64 #s(literal 2 binary64) (/.f64 (PI.f64) k)) n) (patch (.f64 (.f64 #s(literal 2 binary64) (/.f64 (PI.f64) k)) n) #<representation binary64>) () ())
#s(alt (.f64 #s(literal 2 binary64) (/.f64 (PI.f64) k)) (patch (.f64 #s(literal 2 binary64) (/.f64 (PI.f64) k)) #<representation binary64>) () ())
#s(alt #s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (.f64 (sqrt.f64 (.f64 (PI.f64) #s(literal 2 binary64))) (sqrt.f64 (/.f64 n k)))) (patch #s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (.f64 (sqrt.f64 (.f64 (PI.f64) #s(literal 2 binary64))) (sqrt.f64 (/.f64 n k)))) #<representation binary64>) () ())
#s(alt (.f64 (sqrt.f64 (.f64 (PI.f64) #s(literal 2 binary64))) (sqrt.f64 (/.f64 n k))) (patch (.f64 (sqrt.f64 (.f64 (PI.f64) #s(literal 2 binary64))) (sqrt.f64 (/.f64 n k))) #<representation binary64>) () ())
#s(alt (sqrt.f64 (.f64 (PI.f64) #s(literal 2 binary64))) (patch (sqrt.f64 (.f64 (PI.f64) #s(literal 2 binary64))) #<representation binary64>) () ())
#s(alt (.f64 (PI.f64) #s(literal 2 binary64)) (patch (.f64 (PI.f64) #s(literal 2 binary64)) #<representation binary64>) () ())
#s(alt #s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (.f64 (sqrt.f64 #s(literal 2 binary64)) (/.f64 (sqrt.f64 (.f64 (PI.f64) n)) (sqrt.f64 k)))) (patch #s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (.f64 (sqrt.f64 #s(literal 2 binary64)) (/.f64 (sqrt.f64 (.f64 (PI.f64) n)) (sqrt.f64 k)))) #<representation binary64>) () ())
#s(alt (.f64 (sqrt.f64 #s(literal 2 binary64)) (/.f64 (sqrt.f64 (.f64 (PI.f64) n)) (sqrt.f64 k))) (patch (.f64 (sqrt.f64 #s(literal 2 binary64)) (/.f64 (sqrt.f64 (.f64 (PI.f64) n)) (sqrt.f64 k))) #<representation binary64>) () ())
#s(alt (sqrt.f64 #s(literal 2 binary64)) (patch (sqrt.f64 #s(literal 2 binary64)) #<representation binary64>) () ())
#s(alt (/.f64 (sqrt.f64 (.f64 (PI.f64) n)) (sqrt.f64 k)) (patch (/.f64 (sqrt.f64 (.f64 (PI.f64) n)) (sqrt.f64 k)) #<representation binary64>) () ())
#s(alt #s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (.f64 #s(approx (pow ( (* 2 n) (PI)) (+ (* k -1/2) 1/2)) (.f64 (sqrt.f64 (.f64 (PI.f64) #s(literal 2 binary64))) (sqrt.f64 n))) (sqrt.f64 (/.f64 #s(literal 1 binary64) k)))) (patch #s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (.f64 #s(approx (pow ( (* 2 n) (PI)) (+ (* k -1/2) 1/2)) (.f64 (sqrt.f64 (.f64 (PI.f64) #s(literal 2 binary64))) (sqrt.f64 n))) (sqrt.f64 (/.f64 #s(literal 1 binary64) k)))) #<representation binary64>) () ())
#s(alt (.f64 #s(approx (pow ( (* 2 n) (PI)) (+ (* k -1/2) 1/2)) (.f64 (sqrt.f64 (.f64 (PI.f64) #s(literal 2 binary64))) (sqrt.f64 n))) (sqrt.f64 (/.f64 #s(literal 1 binary64) k))) (patch (.f64 #s(approx (pow ( (* 2 n) (PI)) (+ (* k -1/2) 1/2)) (.f64 (sqrt.f64 (.f64 (PI.f64) #s(literal 2 binary64))) (sqrt.f64 n))) (sqrt.f64 (/.f64 #s(literal 1 binary64) k))) #<representation binary64>) () ())
#s(alt #s(approx (pow (* (* 2 n) (PI)) (+ (* k -1/2) 1/2)) (.f64 (sqrt.f64 (.f64 (PI.f64) #s(literal 2 binary64))) (sqrt.f64 n))) (patch #s(approx (pow (* (* 2 n) (PI)) (+ (* k -1/2) 1/2)) (.f64 (sqrt.f64 (.f64 (PI.f64) #s(literal 2 binary64))) (sqrt.f64 n))) #<representation binary64>) () ())
#s(alt (.f64 (sqrt.f64 (.f64 (PI.f64) #s(literal 2 binary64))) (sqrt.f64 n)) (patch (.f64 (sqrt.f64 (.f64 (PI.f64) #s(literal 2 binary64))) (sqrt.f64 n)) #<representation binary64>) () ())
#s(alt (PI.f64) (patch (PI.f64) #<representation binary64>) () ())
#s(alt (/.f64 (PI.f64) k) (patch (/.f64 (PI.f64) k) #<representation binary64>) () ())
#s(alt (sqrt.f64 (/.f64 n k)) (patch (sqrt.f64 (/.f64 n k)) #<representation binary64>) () ())

Outputs
#s(alt (* (sqrt (/ k (* n (PI)))) (sqrt 1/2)) (taylor 0 k) (#s(alt (.f64 (pow.f64 (.f64 (.f64 #s(literal 2 binary64) n) (PI.f64)) (fma.f64 #s(literal 1/2 binary64) k #s(literal -1/2 binary64))) (sqrt.f64 k)) (patch (.f64 (pow.f64 (.f64 (.f64 #s(literal 2 binary64) n) (PI.f64)) (fma.f64 #s(literal 1/2 binary64) k #s(literal -1/2 binary64))) (sqrt.f64 k)) #<representation binary64>) () ())) ())
#s(alt (+ (* 1/2 (* (sqrt (/ (pow k 3) (* n (PI)))) (* (log (* 2 (* n (PI)))) (sqrt 1/2)))) (* (sqrt (/ k (* n (PI)))) (sqrt 1/2))) (taylor 0 k) (#s(alt (.f64 (pow.f64 (.f64 (.f64 #s(literal 2 binary64) n) (PI.f64)) (fma.f64 #s(literal 1/2 binary64) k #s(literal -1/2 binary64))) (sqrt.f64 k)) (patch (.f64 (pow.f64 (.f64 (.f64 #s(literal 2 binary64) n) (PI.f64)) (fma.f64 #s(literal 1/2 binary64) k #s(literal -1/2 binary64))) (sqrt.f64 k)) #<representation binary64>) () ())) ())
#s(alt (+ (* k (+ (* 1/8 (* (sqrt (/ (pow k 3) (* n (PI)))) (* (pow (log (* 2 (* n (PI)))) 2) (sqrt 1/2)))) (* 1/2 (* (sqrt (/ k (* n (PI)))) (* (log (* 2 (* n (PI)))) (sqrt 1/2)))))) (* (sqrt (/ k (* n (PI)))) (sqrt 1/2))) (taylor 0 k) (#s(alt (.f64 (pow.f64 (.f64 (.f64 #s(literal 2 binary64) n) (PI.f64)) (fma.f64 #s(literal 1/2 binary64) k #s(literal -1/2 binary64))) (sqrt.f64 k)) (patch (.f64 (pow.f64 (.f64 (.f64 #s(literal 2 binary64) n) (PI.f64)) (fma.f64 #s(literal 1/2 binary64) k #s(literal -1/2 binary64))) (sqrt.f64 k)) #<representation binary64>) () ())) ())
#s(alt (+ (* k (+ (* 1/2 (* (sqrt (/ k (* n (PI)))) (* (log (* 2 (* n (PI)))) (sqrt 1/2)))) (* k (+ (* 1/48 (* (sqrt (/ (pow k 3) (* n (PI)))) (* (pow (log (* 2 (* n (PI)))) 3) (sqrt 1/2)))) (* 1/8 (* (sqrt (/ k (* n (PI)))) (* (pow (log (* 2 (* n (PI)))) 2) (sqrt 1/2)))))))) (* (sqrt (/ k (* n (PI)))) (sqrt 1/2))) (taylor 0 k) (#s(alt (.f64 (pow.f64 (.f64 (.f64 #s(literal 2 binary64) n) (PI.f64)) (fma.f64 #s(literal 1/2 binary64) k #s(literal -1/2 binary64))) (sqrt.f64 k)) (patch (.f64 (pow.f64 (.f64 (.f64 #s(literal 2 binary64) n) (PI.f64)) (fma.f64 #s(literal 1/2 binary64) k #s(literal -1/2 binary64))) (sqrt.f64 k)) #<representation binary64>) () ())) ())
#s(alt (* (sqrt (/ 1 (* n (PI)))) (sqrt 1/2)) (taylor 0 k) (#s(alt (pow.f64 (.f64 (.f64 #s(literal 2 binary64) n) (PI.f64)) (fma.f64 #s(literal 1/2 binary64) k #s(literal -1/2 binary64))) (patch (pow.f64 (.f64 (.f64 #s(literal 2 binary64) n) (PI.f64)) (fma.f64 #s(literal 1/2 binary64) k #s(literal -1/2 binary64))) #<representation binary64>) () ())) ())
#s(alt (+ (* 1/2 (* (* k (* (log (* 2 (* n (PI)))) (sqrt 1/2))) (sqrt (/ 1 (* n (PI)))))) (* (sqrt (/ 1 (* n (PI)))) (sqrt 1/2))) (taylor 0 k) (#s(alt (pow.f64 (.f64 (.f64 #s(literal 2 binary64) n) (PI.f64)) (fma.f64 #s(literal 1/2 binary64) k #s(literal -1/2 binary64))) (patch (pow.f64 (.f64 (.f64 #s(literal 2 binary64) n) (PI.f64)) (fma.f64 #s(literal 1/2 binary64) k #s(literal -1/2 binary64))) #<representation binary64>) () ())) ())
#s(alt (+ (* k (+ (* 1/8 (* (* k (* (pow (log (* 2 (* n (PI)))) 2) (sqrt 1/2))) (sqrt (/ 1 (* n (PI)))))) (* 1/2 (* (sqrt (/ 1 (* n (PI)))) (* (log (* 2 (* n (PI)))) (sqrt 1/2)))))) (* (sqrt (/ 1 (* n (PI)))) (sqrt 1/2))) (taylor 0 k) (#s(alt (pow.f64 (.f64 (.f64 #s(literal 2 binary64) n) (PI.f64)) (fma.f64 #s(literal 1/2 binary64) k #s(literal -1/2 binary64))) (patch (pow.f64 (.f64 (.f64 #s(literal 2 binary64) n) (PI.f64)) (fma.f64 #s(literal 1/2 binary64) k #s(literal -1/2 binary64))) #<representation binary64>) () ())) ())
#s(alt (+ (* k (+ (* 1/2 (* (sqrt (/ 1 (* n (PI)))) (* (log (* 2 (* n (PI)))) (sqrt 1/2)))) (* k (+ (* 1/48 (* (* k (* (pow (log (* 2 (* n (PI)))) 3) (sqrt 1/2))) (sqrt (/ 1 (* n (PI)))))) (* 1/8 (* (sqrt (/ 1 (* n (PI)))) (* (pow (log (* 2 (* n (PI)))) 2) (sqrt 1/2)))))))) (* (sqrt (/ 1 (* n (PI)))) (sqrt 1/2))) (taylor 0 k) (#s(alt (pow.f64 (.f64 (.f64 #s(literal 2 binary64) n) (PI.f64)) (fma.f64 #s(literal 1/2 binary64) k #s(literal -1/2 binary64))) (patch (pow.f64 (.f64 (.f64 #s(literal 2 binary64) n) (PI.f64)) (fma.f64 #s(literal 1/2 binary64) k #s(literal -1/2 binary64))) #<representation binary64>) () ())) ())
#s(alt (* (sqrt (/ (* n (PI)) k)) (sqrt 2)) (taylor 0 k) (#s(alt #s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt.f64 (.f64 (.f64 #s(literal 2 binary64) (/.f64 (PI.f64) k)) n))) (patch #s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt.f64 (.f64 (.f64 #s(literal 2 binary64) (/.f64 (PI.f64) k)) n))) #<representation binary64>) () ())) ())
#s(alt (/ (+ (* -1/2 (* (sqrt (* (pow k 3) (* n (PI)))) (* (log (* 2 (* n (PI)))) (sqrt 2)))) (* (sqrt (* k (* n (PI)))) (sqrt 2))) k) (taylor 0 k) (#s(alt #s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt.f64 (.f64 (.f64 #s(literal 2 binary64) (/.f64 (PI.f64) k)) n))) (patch #s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt.f64 (.f64 (.f64 #s(literal 2 binary64) (/.f64 (PI.f64) k)) n))) #<representation binary64>) () ())) ())
#s(alt (/ (+ (* k (+ (* -1/2 (* (sqrt (* k (* n (PI)))) (* (log (* 2 (* n (PI)))) (sqrt 2)))) (* 1/8 (* (sqrt (* (pow k 3) (* n (PI)))) (* (pow (log (* 2 (* n (PI)))) 2) (sqrt 2)))))) (* (sqrt (* k (* n (PI)))) (sqrt 2))) k) (taylor 0 k) (#s(alt #s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt.f64 (.f64 (.f64 #s(literal 2 binary64) (/.f64 (PI.f64) k)) n))) (patch #s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt.f64 (.f64 (.f64 #s(literal 2 binary64) (/.f64 (PI.f64) k)) n))) #<representation binary64>) () ())) ())
#s(alt (/ (+ (* k (+ (* -1/2 (* (sqrt (* k (* n (PI)))) (* (log (* 2 (* n (PI)))) (sqrt 2)))) (* k (+ (* -1/48 (* (sqrt (* (pow k 3) (* n (PI)))) (* (pow (log (* 2 (* n (PI)))) 3) (sqrt 2)))) (* 1/8 (* (sqrt (* k (* n (PI)))) (* (pow (log (* 2 (* n (PI)))) 2) (sqrt 2)))))))) (* (sqrt (* k (* n (PI)))) (sqrt 2))) k) (taylor 0 k) (#s(alt #s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt.f64 (.f64 (.f64 #s(literal 2 binary64) (/.f64 (PI.f64) k)) n))) (patch #s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt.f64 (.f64 (.f64 #s(literal 2 binary64) (/.f64 (PI.f64) k)) n))) #<representation binary64>) () ())) ())
#s(alt (* (sqrt (/ (* n (PI)) k)) (sqrt 2)) (taylor 0 k) (#s(alt (sqrt.f64 (.f64 (.f64 #s(literal 2 binary64) (/.f64 (PI.f64) k)) n)) (patch (sqrt.f64 (.f64 (.f64 #s(literal 2 binary64) (/.f64 (PI.f64) k)) n)) #<representation binary64>) () ())) ())
#s(alt (* (sqrt (/ (* n (PI)) k)) (sqrt 2)) (taylor 0 k) (#s(alt (sqrt.f64 (.f64 (.f64 #s(literal 2 binary64) (/.f64 (PI.f64) k)) n)) (patch (sqrt.f64 (.f64 (.f64 #s(literal 2 binary64) (/.f64 (PI.f64) k)) n)) #<representation binary64>) () ())) ())
#s(alt (* (sqrt (/ (* n (PI)) k)) (sqrt 2)) (taylor 0 k) (#s(alt (sqrt.f64 (.f64 (.f64 #s(literal 2 binary64) (/.f64 (PI.f64) k)) n)) (patch (sqrt.f64 (.f64 (.f64 #s(literal 2 binary64) (/.f64 (PI.f64) k)) n)) #<representation binary64>) () ())) ())
#s(alt (* (sqrt (/ (* n (PI)) k)) (sqrt 2)) (taylor 0 k) (#s(alt (sqrt.f64 (.f64 (.f64 #s(literal 2 binary64) (/.f64 (PI.f64) k)) n)) (patch (sqrt.f64 (.f64 (.f64 #s(literal 2 binary64) (/.f64 (PI.f64) k)) n)) #<representation binary64>) () ())) ())
#s(alt (* 2 (/ (* n (PI)) k)) (taylor 0 k) (#s(alt (.f64 (.f64 #s(literal 2 binary64) (/.f64 (PI.f64) k)) n) (patch (.f64 (.f64 #s(literal 2 binary64) (/.f64 (PI.f64) k)) n) #<representation binary64>) () ())) ())
#s(alt (* 2 (/ (* n (PI)) k)) (taylor 0 k) (#s(alt (.f64 (.f64 #s(literal 2 binary64) (/.f64 (PI.f64) k)) n) (patch (.f64 (.f64 #s(literal 2 binary64) (/.f64 (PI.f64) k)) n) #<representation binary64>) () ())) ())
#s(alt (* 2 (/ (* n (PI)) k)) (taylor 0 k) (#s(alt (.f64 (.f64 #s(literal 2 binary64) (/.f64 (PI.f64) k)) n) (patch (.f64 (.f64 #s(literal 2 binary64) (/.f64 (PI.f64) k)) n) #<representation binary64>) () ())) ())
#s(alt (* 2 (/ (* n (PI)) k)) (taylor 0 k) (#s(alt (.f64 (.f64 #s(literal 2 binary64) (/.f64 (PI.f64) k)) n) (patch (.f64 (.f64 #s(literal 2 binary64) (/.f64 (PI.f64) k)) n) #<representation binary64>) () ())) ())
#s(alt (* 2 (/ (PI) k)) (taylor 0 k) (#s(alt (.f64 #s(literal 2 binary64) (/.f64 (PI.f64) k)) (patch (.f64 #s(literal 2 binary64) (/.f64 (PI.f64) k)) #<representation binary64>) () ())) ())
#s(alt (* 2 (/ (PI) k)) (taylor 0 k) (#s(alt (.f64 #s(literal 2 binary64) (/.f64 (PI.f64) k)) (patch (.f64 #s(literal 2 binary64) (/.f64 (PI.f64) k)) #<representation binary64>) () ())) ())
#s(alt (* 2 (/ (PI) k)) (taylor 0 k) (#s(alt (.f64 #s(literal 2 binary64) (/.f64 (PI.f64) k)) (patch (.f64 #s(literal 2 binary64) (/.f64 (PI.f64) k)) #<representation binary64>) () ())) ())
#s(alt (* 2 (/ (PI) k)) (taylor 0 k) (#s(alt (.f64 #s(literal 2 binary64) (/.f64 (PI.f64) k)) (patch (.f64 #s(literal 2 binary64) (/.f64 (PI.f64) k)) #<representation binary64>) () ())) ())
#s(alt (* (sqrt (/ (* n (PI)) k)) (sqrt 2)) (taylor 0 k) (#s(alt #s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (.f64 (sqrt.f64 (.f64 (PI.f64) #s(literal 2 binary64))) (sqrt.f64 (/.f64 n k)))) (patch #s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (.f64 (sqrt.f64 (.f64 (PI.f64) #s(literal 2 binary64))) (sqrt.f64 (/.f64 n k)))) #<representation binary64>) () ())) ())
#s(alt (/ (+ (* -1/2 (* (sqrt (* (pow k 3) (* n (PI)))) (* (log (* 2 (* n (PI)))) (sqrt 2)))) (* (sqrt (* k (* n (PI)))) (sqrt 2))) k) (taylor 0 k) (#s(alt #s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (.f64 (sqrt.f64 (.f64 (PI.f64) #s(literal 2 binary64))) (sqrt.f64 (/.f64 n k)))) (patch #s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (.f64 (sqrt.f64 (.f64 (PI.f64) #s(literal 2 binary64))) (sqrt.f64 (/.f64 n k)))) #<representation binary64>) () ())) ())
#s(alt (/ (+ (* k (+ (* -1/2 (* (sqrt (* k (* n (PI)))) (* (log (* 2 (* n (PI)))) (sqrt 2)))) (* 1/8 (* (sqrt (* (pow k 3) (* n (PI)))) (* (pow (log (* 2 (* n (PI)))) 2) (sqrt 2)))))) (* (sqrt (* k (* n (PI)))) (sqrt 2))) k) (taylor 0 k) (#s(alt #s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (.f64 (sqrt.f64 (.f64 (PI.f64) #s(literal 2 binary64))) (sqrt.f64 (/.f64 n k)))) (patch #s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (.f64 (sqrt.f64 (.f64 (PI.f64) #s(literal 2 binary64))) (sqrt.f64 (/.f64 n k)))) #<representation binary64>) () ())) ())
#s(alt (/ (+ (* k (+ (* -1/2 (* (sqrt (* k (* n (PI)))) (* (log (* 2 (* n (PI)))) (sqrt 2)))) (* k (+ (* -1/48 (* (sqrt (* (pow k 3) (* n (PI)))) (* (pow (log (* 2 (* n (PI)))) 3) (sqrt 2)))) (* 1/8 (* (sqrt (* k (* n (PI)))) (* (pow (log (* 2 (* n (PI)))) 2) (sqrt 2)))))))) (* (sqrt (* k (* n (PI)))) (sqrt 2))) k) (taylor 0 k) (#s(alt #s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (.f64 (sqrt.f64 (.f64 (PI.f64) #s(literal 2 binary64))) (sqrt.f64 (/.f64 n k)))) (patch #s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (.f64 (sqrt.f64 (.f64 (PI.f64) #s(literal 2 binary64))) (sqrt.f64 (/.f64 n k)))) #<representation binary64>) () ())) ())
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#s(alt (* -1 (* (sqrt (/ n k)) (pow (sqrt -1) 2))) (taylor -inf n) (#s(alt (sqrt.f64 (/.f64 n k)) (patch (sqrt.f64 (/.f64 n k)) #<representation binary64>) () ())) ())
#s(alt (* -1 (* (sqrt (/ n k)) (pow (sqrt -1) 2))) (taylor -inf n) (#s(alt (sqrt.f64 (/.f64 n k)) (patch (sqrt.f64 (/.f64 n k)) #<representation binary64>) () ())) ())
#s(alt (* -1 (* (sqrt (/ n k)) (pow (sqrt -1) 2))) (taylor -inf n) (#s(alt (sqrt.f64 (/.f64 n k)) (patch (sqrt.f64 (/.f64 n k)) #<representation binary64>) () ())) ())

Calls

6 calls:

Time	Variable		Point	Expression
13.0ms	n	@	inf	((* (pow (* (* 2 n) (PI)) (+ (* 1/2 k) -1/2)) (sqrt k)) (pow (* (* 2 n) (PI)) (+ (* 1/2 k) -1/2)) (* (* 2 n) (PI)) (* 2 n) (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt (* (* 2 (/ (PI) k)) n)) (* (* 2 (/ (PI) k)) n) (* 2 (/ (PI) k)) (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (* (sqrt (* (PI) 2)) (sqrt (/ n k))) (sqrt (* (PI) 2)) (* (PI) 2) (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (* (sqrt 2) (/ (sqrt (* (PI) n)) (sqrt k))) (sqrt 2) (/ (sqrt (* (PI) n)) (sqrt k)) (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (* (pow (* (* 2 n) (PI)) (+ (* k -1/2) 1/2)) (sqrt (/ 1 k))) (pow (* (* 2 n) (PI)) (+ (* k -1/2) 1/2)) (* (sqrt (* (PI) 2)) (sqrt n)) (PI) (/ (PI) k) (sqrt (/ n k)))
12.0ms	n	@	-inf	((* (pow (* (* 2 n) (PI)) (+ (* 1/2 k) -1/2)) (sqrt k)) (pow (* (* 2 n) (PI)) (+ (* 1/2 k) -1/2)) (* (* 2 n) (PI)) (* 2 n) (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt (* (* 2 (/ (PI) k)) n)) (* (* 2 (/ (PI) k)) n) (* 2 (/ (PI) k)) (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (* (sqrt (* (PI) 2)) (sqrt (/ n k))) (sqrt (* (PI) 2)) (* (PI) 2) (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (* (sqrt 2) (/ (sqrt (* (PI) n)) (sqrt k))) (sqrt 2) (/ (sqrt (* (PI) n)) (sqrt k)) (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (* (pow (* (* 2 n) (PI)) (+ (* k -1/2) 1/2)) (sqrt (/ 1 k))) (pow (* (* 2 n) (PI)) (+ (* k -1/2) 1/2)) (* (sqrt (* (PI) 2)) (sqrt n)) (PI) (/ (PI) k) (sqrt (/ n k)))
11.0ms	n	@	0	((* (pow (* (* 2 n) (PI)) (+ (* 1/2 k) -1/2)) (sqrt k)) (pow (* (* 2 n) (PI)) (+ (* 1/2 k) -1/2)) (* (* 2 n) (PI)) (* 2 n) (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt (* (* 2 (/ (PI) k)) n)) (* (* 2 (/ (PI) k)) n) (* 2 (/ (PI) k)) (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (* (sqrt (* (PI) 2)) (sqrt (/ n k))) (sqrt (* (PI) 2)) (* (PI) 2) (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (* (sqrt 2) (/ (sqrt (* (PI) n)) (sqrt k))) (sqrt 2) (/ (sqrt (* (PI) n)) (sqrt k)) (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (* (pow (* (* 2 n) (PI)) (+ (* k -1/2) 1/2)) (sqrt (/ 1 k))) (pow (* (* 2 n) (PI)) (+ (* k -1/2) 1/2)) (* (sqrt (* (PI) 2)) (sqrt n)) (PI) (/ (PI) k) (sqrt (/ n k)))
8.0ms	k	@	-inf	((* (pow (* (* 2 n) (PI)) (+ (* 1/2 k) -1/2)) (sqrt k)) (pow (* (* 2 n) (PI)) (+ (* 1/2 k) -1/2)) (* (* 2 n) (PI)) (* 2 n) (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt (* (* 2 (/ (PI) k)) n)) (* (* 2 (/ (PI) k)) n) (* 2 (/ (PI) k)) (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (* (sqrt (* (PI) 2)) (sqrt (/ n k))) (sqrt (* (PI) 2)) (* (PI) 2) (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (* (sqrt 2) (/ (sqrt (* (PI) n)) (sqrt k))) (sqrt 2) (/ (sqrt (* (PI) n)) (sqrt k)) (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (* (pow (* (* 2 n) (PI)) (+ (* k -1/2) 1/2)) (sqrt (/ 1 k))) (pow (* (* 2 n) (PI)) (+ (* k -1/2) 1/2)) (* (sqrt (* (PI) 2)) (sqrt n)) (PI) (/ (PI) k) (sqrt (/ n k)))
3.0ms	k	@	0	((* (pow (* (* 2 n) (PI)) (+ (* 1/2 k) -1/2)) (sqrt k)) (pow (* (* 2 n) (PI)) (+ (* 1/2 k) -1/2)) (* (* 2 n) (PI)) (* 2 n) (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt (* (* 2 (/ (PI) k)) n)) (* (* 2 (/ (PI) k)) n) (* 2 (/ (PI) k)) (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (* (sqrt (* (PI) 2)) (sqrt (/ n k))) (sqrt (* (PI) 2)) (* (PI) 2) (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (* (sqrt 2) (/ (sqrt (* (PI) n)) (sqrt k))) (sqrt 2) (/ (sqrt (* (PI) n)) (sqrt k)) (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (* (pow (* (* 2 n) (PI)) (+ (* k -1/2) 1/2)) (sqrt (/ 1 k))) (pow (* (* 2 n) (PI)) (+ (* k -1/2) 1/2)) (* (sqrt (* (PI) 2)) (sqrt n)) (PI) (/ (PI) k) (sqrt (/ n k)))

simplify274.0ms (2.9%)

Memory

-24.2MiB live, 221.4MiB allocated

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	229	5438
1	664	5334
2	2127	4952
3	3537	4864
4	7689	4848
0	8977	4792

Stop Event

1×	iter limit
1×	node limit

Counts

396 → 396

Calls

Call 1

Inputs
(* (sqrt (/ k (* n (PI)))) (sqrt 1/2))
(+ (* 1/2 (* (sqrt (/ (pow k 3) (* n (PI)))) (* (log (* 2 (* n (PI)))) (sqrt 1/2)))) (* (sqrt (/ k (* n (PI)))) (sqrt 1/2)))
(+ (* k (+ (* 1/8 (* (sqrt (/ (pow k 3) (* n (PI)))) (* (pow (log (* 2 (* n (PI)))) 2) (sqrt 1/2)))) (* 1/2 (* (sqrt (/ k (* n (PI)))) (* (log (* 2 (* n (PI)))) (sqrt 1/2)))))) (* (sqrt (/ k (* n (PI)))) (sqrt 1/2)))
(+ (* k (+ (* 1/2 (* (sqrt (/ k (* n (PI)))) (* (log (* 2 (* n (PI)))) (sqrt 1/2)))) (* k (+ (* 1/48 (* (sqrt (/ (pow k 3) (* n (PI)))) (* (pow (log (* 2 (* n (PI)))) 3) (sqrt 1/2)))) (* 1/8 (* (sqrt (/ k (* n (PI)))) (* (pow (log (* 2 (* n (PI)))) 2) (sqrt 1/2)))))))) (* (sqrt (/ k (* n (PI)))) (sqrt 1/2)))
(* (sqrt (/ 1 (* n (PI)))) (sqrt 1/2))
(+ (* 1/2 (* (* k (* (log (* 2 (* n (PI)))) (sqrt 1/2))) (sqrt (/ 1 (* n (PI)))))) (* (sqrt (/ 1 (* n (PI)))) (sqrt 1/2)))
(+ (* k (+ (* 1/8 (* (* k (* (pow (log (* 2 (* n (PI)))) 2) (sqrt 1/2))) (sqrt (/ 1 (* n (PI)))))) (* 1/2 (* (sqrt (/ 1 (* n (PI)))) (* (log (* 2 (* n (PI)))) (sqrt 1/2)))))) (* (sqrt (/ 1 (* n (PI)))) (sqrt 1/2)))
(+ (* k (+ (* 1/2 (* (sqrt (/ 1 (* n (PI)))) (* (log (* 2 (* n (PI)))) (sqrt 1/2)))) (* k (+ (* 1/48 (* (* k (* (pow (log (* 2 (* n (PI)))) 3) (sqrt 1/2))) (sqrt (/ 1 (* n (PI)))))) (* 1/8 (* (sqrt (/ 1 (* n (PI)))) (* (pow (log (* 2 (* n (PI)))) 2) (sqrt 1/2)))))))) (* (sqrt (/ 1 (* n (PI)))) (sqrt 1/2)))
(* (sqrt (/ (* n (PI)) k)) (sqrt 2))
(/ (+ (* -1/2 (* (sqrt (* (pow k 3) (* n (PI)))) (* (log (* 2 (* n (PI)))) (sqrt 2)))) (* (sqrt (* k (* n (PI)))) (sqrt 2))) k)
(/ (+ (* k (+ (* -1/2 (* (sqrt (* k (* n (PI)))) (* (log (* 2 (* n (PI)))) (sqrt 2)))) (* 1/8 (* (sqrt (* (pow k 3) (* n (PI)))) (* (pow (log (* 2 (* n (PI)))) 2) (sqrt 2)))))) (* (sqrt (* k (* n (PI)))) (sqrt 2))) k)
(/ (+ (* k (+ (* -1/2 (* (sqrt (* k (* n (PI)))) (* (log (* 2 (* n (PI)))) (sqrt 2)))) (* k (+ (* -1/48 (* (sqrt (* (pow k 3) (* n (PI)))) (* (pow (log (* 2 (* n (PI)))) 3) (sqrt 2)))) (* 1/8 (* (sqrt (* k (* n (PI)))) (* (pow (log (* 2 (* n (PI)))) 2) (sqrt 2)))))))) (* (sqrt (* k (* n (PI)))) (sqrt 2))) k)
(* (sqrt (/ (* n (PI)) k)) (sqrt 2))
(* (sqrt (/ (* n (PI)) k)) (sqrt 2))
(* (sqrt (/ (* n (PI)) k)) (sqrt 2))
(* (sqrt (/ (* n (PI)) k)) (sqrt 2))
(* 2 (/ (* n (PI)) k))
(* 2 (/ (* n (PI)) k))
(* 2 (/ (* n (PI)) k))
(* 2 (/ (* n (PI)) k))
(* 2 (/ (PI) k))
(* 2 (/ (PI) k))
(* 2 (/ (PI) k))
(* 2 (/ (PI) k))
(* (sqrt (/ (* n (PI)) k)) (sqrt 2))
(/ (+ (* -1/2 (* (sqrt (* (pow k 3) (* n (PI)))) (* (log (* 2 (* n (PI)))) (sqrt 2)))) (* (sqrt (* k (* n (PI)))) (sqrt 2))) k)
(/ (+ (* k (+ (* -1/2 (* (sqrt (* k (* n (PI)))) (* (log (* 2 (* n (PI)))) (sqrt 2)))) (* 1/8 (* (sqrt (* (pow k 3) (* n (PI)))) (* (pow (log (* 2 (* n (PI)))) 2) (sqrt 2)))))) (* (sqrt (* k (* n (PI)))) (sqrt 2))) k)
(/ (+ (* k (+ (* -1/2 (* (sqrt (* k (* n (PI)))) (* (log (* 2 (* n (PI)))) (sqrt 2)))) (* k (+ (* -1/48 (* (sqrt (* (pow k 3) (* n (PI)))) (* (pow (log (* 2 (* n (PI)))) 3) (sqrt 2)))) (* 1/8 (* (sqrt (* k (* n (PI)))) (* (pow (log (* 2 (* n (PI)))) 2) (sqrt 2)))))))) (* (sqrt (* k (* n (PI)))) (sqrt 2))) k)
(* (sqrt (/ (* n (PI)) k)) (sqrt 2))
(* (sqrt (/ (* n (PI)) k)) (sqrt 2))
(* (sqrt (/ (* n (PI)) k)) (sqrt 2))
(* (sqrt (/ (* n (PI)) k)) (sqrt 2))
(* (sqrt (/ (* n (PI)) k)) (sqrt 2))
(/ (+ (* -1/2 (* (sqrt (* (pow k 3) (* n (PI)))) (* (log (* 2 (* n (PI)))) (sqrt 2)))) (* (sqrt (* k (* n (PI)))) (sqrt 2))) k)
(/ (+ (* k (+ (* -1/2 (* (sqrt (* k (* n (PI)))) (* (log (* 2 (* n (PI)))) (sqrt 2)))) (* 1/8 (* (sqrt (* (pow k 3) (* n (PI)))) (* (pow (log (* 2 (* n (PI)))) 2) (sqrt 2)))))) (* (sqrt (* k (* n (PI)))) (sqrt 2))) k)
(/ (+ (* k (+ (* -1/2 (* (sqrt (* k (* n (PI)))) (* (log (* 2 (* n (PI)))) (sqrt 2)))) (* k (+ (* -1/48 (* (sqrt (* (pow k 3) (* n (PI)))) (* (pow (log (* 2 (* n (PI)))) 3) (sqrt 2)))) (* 1/8 (* (sqrt (* k (* n (PI)))) (* (pow (log (* 2 (* n (PI)))) 2) (sqrt 2)))))))) (* (sqrt (* k (* n (PI)))) (sqrt 2))) k)
(* (sqrt (/ (* n (PI)) k)) (sqrt 2))
(* (sqrt (/ (* n (PI)) k)) (sqrt 2))
(* (sqrt (/ (* n (PI)) k)) (sqrt 2))
(* (sqrt (/ (* n (PI)) k)) (sqrt 2))
(sqrt (/ (* n (PI)) k))
(sqrt (/ (* n (PI)) k))
(sqrt (/ (* n (PI)) k))
(sqrt (/ (* n (PI)) k))
(* (sqrt (/ (* n (PI)) k)) (sqrt 2))
(/ (+ (* -1/2 (* (sqrt (* (pow k 3) (* n (PI)))) (* (log (* 2 (* n (PI)))) (sqrt 2)))) (* (sqrt (* k (* n (PI)))) (sqrt 2))) k)
(/ (+ (* k (+ (* -1/2 (* (sqrt (* k (* n (PI)))) (* (log (* 2 (* n (PI)))) (sqrt 2)))) (* 1/8 (* (sqrt (* (pow k 3) (* n (PI)))) (* (pow (log (* 2 (* n (PI)))) 2) (sqrt 2)))))) (* (sqrt (* k (* n (PI)))) (sqrt 2))) k)
(/ (+ (* k (+ (* -1/2 (* (sqrt (* k (* n (PI)))) (* (log (* 2 (* n (PI)))) (sqrt 2)))) (* k (+ (* -1/48 (* (sqrt (* (pow k 3) (* n (PI)))) (* (pow (log (* 2 (* n (PI)))) 3) (sqrt 2)))) (* 1/8 (* (sqrt (* k (* n (PI)))) (* (pow (log (* 2 (* n (PI)))) 2) (sqrt 2)))))))) (* (sqrt (* k (* n (PI)))) (sqrt 2))) k)
(* (sqrt (/ (* n (PI)) k)) (sqrt 2))
(/ (+ (* -1/2 (* (sqrt (* (pow k 3) (* n (PI)))) (* (log (* 2 (* n (PI)))) (sqrt 2)))) (* (sqrt (* k (* n (PI)))) (sqrt 2))) k)
(/ (+ (* k (+ (* -1/2 (* (sqrt (* k (* n (PI)))) (* (log (* 2 (* n (PI)))) (sqrt 2)))) (* 1/8 (* (sqrt (* (pow k 3) (* n (PI)))) (* (pow (log (* 2 (* n (PI)))) 2) (sqrt 2)))))) (* (sqrt (* k (* n (PI)))) (sqrt 2))) k)
(/ (+ (* k (+ (* -1/2 (* (sqrt (* k (* n (PI)))) (* (log (* 2 (* n (PI)))) (sqrt 2)))) (* k (+ (* -1/48 (* (sqrt (* (pow k 3) (* n (PI)))) (* (pow (log (* 2 (* n (PI)))) 3) (sqrt 2)))) (* 1/8 (* (sqrt (* k (* n (PI)))) (* (pow (log (* 2 (* n (PI)))) 2) (sqrt 2)))))))) (* (sqrt (* k (* n (PI)))) (sqrt 2))) k)
(* (sqrt (* n (PI))) (sqrt 2))
(+ (* -1/2 (* (* k (* (log (* 2 (* n (PI)))) (sqrt 2))) (sqrt (* n (PI))))) (* (sqrt (* n (PI))) (sqrt 2)))
(+ (* k (+ (* -1/2 (* (sqrt (* n (PI))) (* (log (* 2 (* n (PI)))) (sqrt 2)))) (* 1/8 (* (* k (* (pow (log (* 2 (* n (PI)))) 2) (sqrt 2))) (sqrt (* n (PI))))))) (* (sqrt (* n (PI))) (sqrt 2)))
(+ (* k (+ (* -1/2 (* (sqrt (* n (PI))) (* (log (* 2 (* n (PI)))) (sqrt 2)))) (* k (+ (* -1/48 (* (* k (* (pow (log (* 2 (* n (PI)))) 3) (sqrt 2))) (sqrt (* n (PI))))) (* 1/8 (* (sqrt (* n (PI))) (* (pow (log (* 2 (* n (PI)))) 2) (sqrt 2)))))))) (* (sqrt (* n (PI))) (sqrt 2)))
(/ (PI) k)
(/ (PI) k)
(/ (PI) k)
(/ (PI) k)
(sqrt (/ n k))
(sqrt (/ n k))
(sqrt (/ n k))
(sqrt (/ n k))
(* (sqrt k) (exp (* (log (* 2 (* n (PI)))) (- (* 1/2 k) 1/2))))
(* (sqrt k) (exp (* (log (* 2 (* n (PI)))) (- (* 1/2 k) 1/2))))
(* (sqrt k) (exp (* (log (* 2 (* n (PI)))) (- (* 1/2 k) 1/2))))
(* (sqrt k) (exp (* (log (* 2 (* n (PI)))) (- (* 1/2 k) 1/2))))
(exp (* (log (* 2 (* n (PI)))) (- (* 1/2 k) 1/2)))
(exp (* (log (* 2 (* n (PI)))) (- (* 1/2 k) 1/2)))
(exp (* (log (* 2 (* n (PI)))) (- (* 1/2 k) 1/2)))
(exp (* (log (* 2 (* n (PI)))) (- (* 1/2 k) 1/2)))
(* (sqrt (/ 1 k)) (exp (* 1/2 (* (log (* 2 (* n (PI)))) (- 1 k)))))
(* (sqrt (/ 1 k)) (exp (* 1/2 (* (log (* 2 (* n (PI)))) (- 1 k)))))
(* (sqrt (/ 1 k)) (exp (* 1/2 (* (log (* 2 (* n (PI)))) (- 1 k)))))
(* (sqrt (/ 1 k)) (exp (* 1/2 (* (log (* 2 (* n (PI)))) (- 1 k)))))
(* (sqrt (/ (* n (PI)) k)) (sqrt 2))
(* (sqrt (/ (* n (PI)) k)) (sqrt 2))
(* (sqrt (/ (* n (PI)) k)) (sqrt 2))
(* (sqrt (/ (* n (PI)) k)) (sqrt 2))
(* 2 (/ (* n (PI)) k))
(* 2 (/ (* n (PI)) k))
(* 2 (/ (* n (PI)) k))
(* 2 (/ (* n (PI)) k))
(* 2 (/ (PI) k))
(* 2 (/ (PI) k))
(* 2 (/ (PI) k))
(* 2 (/ (PI) k))
(* (sqrt (/ 1 k)) (exp (* 1/2 (* (log (* 2 (* n (PI)))) (- 1 k)))))
(* (sqrt (/ 1 k)) (exp (* 1/2 (* (log (* 2 (* n (PI)))) (- 1 k)))))
(* (sqrt (/ 1 k)) (exp (* 1/2 (* (log (* 2 (* n (PI)))) (- 1 k)))))
(* (sqrt (/ 1 k)) (exp (* 1/2 (* (log (* 2 (* n (PI)))) (- 1 k)))))
(* (sqrt (/ (* n (PI)) k)) (sqrt 2))
(* (sqrt (/ (* n (PI)) k)) (sqrt 2))
(* (sqrt (/ (* n (PI)) k)) (sqrt 2))
(* (sqrt (/ (* n (PI)) k)) (sqrt 2))
(* (sqrt (/ 1 k)) (exp (* 1/2 (* (log (* 2 (* n (PI)))) (- 1 k)))))
(* (sqrt (/ 1 k)) (exp (* 1/2 (* (log (* 2 (* n (PI)))) (- 1 k)))))
(* (sqrt (/ 1 k)) (exp (* 1/2 (* (log (* 2 (* n (PI)))) (- 1 k)))))
(* (sqrt (/ 1 k)) (exp (* 1/2 (* (log (* 2 (* n (PI)))) (- 1 k)))))
(* (sqrt (/ (* n (PI)) k)) (sqrt 2))
(* (sqrt (/ (* n (PI)) k)) (sqrt 2))
(* (sqrt (/ (* n (PI)) k)) (sqrt 2))
(* (sqrt (/ (* n (PI)) k)) (sqrt 2))
(sqrt (/ (* n (PI)) k))
(sqrt (/ (* n (PI)) k))
(sqrt (/ (* n (PI)) k))
(sqrt (/ (* n (PI)) k))
(* (sqrt (/ 1 k)) (exp (* 1/2 (* (log (* 2 (* n (PI)))) (- 1 k)))))
(* (sqrt (/ 1 k)) (exp (* 1/2 (* (log (* 2 (* n (PI)))) (- 1 k)))))
(* (sqrt (/ 1 k)) (exp (* 1/2 (* (log (* 2 (* n (PI)))) (- 1 k)))))
(* (sqrt (/ 1 k)) (exp (* 1/2 (* (log (* 2 (* n (PI)))) (- 1 k)))))
(* (sqrt (/ 1 k)) (exp (* (log (* 2 (* n (PI)))) (- 1/2 (* 1/2 k)))))
(* (sqrt (/ 1 k)) (exp (* (log (* 2 (* n (PI)))) (- 1/2 (* 1/2 k)))))
(* (sqrt (/ 1 k)) (exp (* (log (* 2 (* n (PI)))) (- 1/2 (* 1/2 k)))))
(* (sqrt (/ 1 k)) (exp (* (log (* 2 (* n (PI)))) (- 1/2 (* 1/2 k)))))
(exp (* (log (* 2 (* n (PI)))) (- 1/2 (* 1/2 k))))
(exp (* (log (* 2 (* n (PI)))) (- 1/2 (* 1/2 k))))
(exp (* (log (* 2 (* n (PI)))) (- 1/2 (* 1/2 k))))
(exp (* (log (* 2 (* n (PI)))) (- 1/2 (* 1/2 k))))
(/ (PI) k)
(/ (PI) k)
(/ (PI) k)
(/ (PI) k)
(sqrt (/ n k))
(sqrt (/ n k))
(sqrt (/ n k))
(sqrt (/ n k))
(* -1 (* (sqrt k) (* (exp (* -1 (* (log (* 2 (* n (PI)))) (+ 1/2 (* -1/2 k))))) (pow (sqrt -1) 2))))
(* -1 (* (sqrt k) (* (exp (* -1 (* (log (* 2 (* n (PI)))) (+ 1/2 (* -1/2 k))))) (pow (sqrt -1) 2))))
(* -1 (* (sqrt k) (* (exp (* -1 (* (log (* 2 (* n (PI)))) (+ 1/2 (* -1/2 k))))) (pow (sqrt -1) 2))))
(* -1 (* (sqrt k) (* (exp (* -1 (* (log (* 2 (* n (PI)))) (+ 1/2 (* -1/2 k))))) (pow (sqrt -1) 2))))
(exp (* -1 (* (log (* 2 (* n (PI)))) (+ 1/2 (* -1/2 k)))))
(exp (* -1 (* (log (* 2 (* n (PI)))) (+ 1/2 (* -1/2 k)))))
(exp (* -1 (* (log (* 2 (* n (PI)))) (+ 1/2 (* -1/2 k)))))
(exp (* -1 (* (log (* 2 (* n (PI)))) (+ 1/2 (* -1/2 k)))))
(* (sqrt (/ 1 k)) (exp (* 1/2 (* (log (* 2 (* n (PI)))) (+ 1 (* -1 k))))))
(* (sqrt (/ 1 k)) (exp (* 1/2 (* (log (* 2 (* n (PI)))) (+ 1 (* -1 k))))))
(* (sqrt (/ 1 k)) (exp (* 1/2 (* (log (* 2 (* n (PI)))) (+ 1 (* -1 k))))))
(* (sqrt (/ 1 k)) (exp (* 1/2 (* (log (* 2 (* n (PI)))) (+ 1 (* -1 k))))))
(* (sqrt (/ (* n (PI)) k)) (* (sqrt -2) (sqrt -1)))
(* (sqrt (/ (* n (PI)) k)) (* (sqrt -2) (sqrt -1)))
(* (sqrt (/ (* n (PI)) k)) (* (sqrt -2) (sqrt -1)))
(* (sqrt (/ (* n (PI)) k)) (* (sqrt -2) (sqrt -1)))
(* 2 (/ (* n (PI)) k))
(* 2 (/ (* n (PI)) k))
(* 2 (/ (* n (PI)) k))
(* 2 (/ (* n (PI)) k))
(* 2 (/ (PI) k))
(* 2 (/ (PI) k))
(* 2 (/ (PI) k))
(* 2 (/ (PI) k))
(* (sqrt (/ 1 k)) (exp (* 1/2 (* (log (* 2 (* n (PI)))) (+ 1 (* -1 k))))))
(* (sqrt (/ 1 k)) (exp (* 1/2 (* (log (* 2 (* n (PI)))) (+ 1 (* -1 k))))))
(* (sqrt (/ 1 k)) (exp (* 1/2 (* (log (* 2 (* n (PI)))) (+ 1 (* -1 k))))))
(* (sqrt (/ 1 k)) (exp (* 1/2 (* (log (* 2 (* n (PI)))) (+ 1 (* -1 k))))))
(* (sqrt (/ (* n (PI)) k)) (* (pow (sqrt -1) 2) (sqrt 2)))
(* (sqrt (/ (* n (PI)) k)) (* (pow (sqrt -1) 2) (sqrt 2)))
(* (sqrt (/ (* n (PI)) k)) (* (pow (sqrt -1) 2) (sqrt 2)))
(* (sqrt (/ (* n (PI)) k)) (* (pow (sqrt -1) 2) (sqrt 2)))
(* (sqrt (/ 1 k)) (exp (* 1/2 (* (log (* 2 (* n (PI)))) (+ 1 (* -1 k))))))
(* (sqrt (/ 1 k)) (exp (* 1/2 (* (log (* 2 (* n (PI)))) (+ 1 (* -1 k))))))
(* (sqrt (/ 1 k)) (exp (* 1/2 (* (log (* 2 (* n (PI)))) (+ 1 (* -1 k))))))
(* (sqrt (/ 1 k)) (exp (* 1/2 (* (log (* 2 (* n (PI)))) (+ 1 (* -1 k))))))
(* (sqrt (/ (* n (PI)) k)) (sqrt 2))
(* (sqrt (/ (* n (PI)) k)) (sqrt 2))
(* (sqrt (/ (* n (PI)) k)) (sqrt 2))
(* (sqrt (/ (* n (PI)) k)) (sqrt 2))
(sqrt (/ (* n (PI)) k))
(sqrt (/ (* n (PI)) k))
(sqrt (/ (* n (PI)) k))
(sqrt (/ (* n (PI)) k))
(* (sqrt (/ 1 k)) (exp (* 1/2 (* (log (* 2 (* n (PI)))) (+ 1 (* -1 k))))))
(* (sqrt (/ 1 k)) (exp (* 1/2 (* (log (* 2 (* n (PI)))) (+ 1 (* -1 k))))))
(* (sqrt (/ 1 k)) (exp (* 1/2 (* (log (* 2 (* n (PI)))) (+ 1 (* -1 k))))))
(* (sqrt (/ 1 k)) (exp (* 1/2 (* (log (* 2 (* n (PI)))) (+ 1 (* -1 k))))))
(* (sqrt (/ 1 k)) (* (exp (* (log (* 2 (* n (PI)))) (+ 1/2 (* -1/2 k)))) (pow (sqrt -1) 2)))
(* (sqrt (/ 1 k)) (* (exp (* (log (* 2 (* n (PI)))) (+ 1/2 (* -1/2 k)))) (pow (sqrt -1) 2)))
(* (sqrt (/ 1 k)) (* (exp (* (log (* 2 (* n (PI)))) (+ 1/2 (* -1/2 k)))) (pow (sqrt -1) 2)))
(* (sqrt (/ 1 k)) (* (exp (* (log (* 2 (* n (PI)))) (+ 1/2 (* -1/2 k)))) (pow (sqrt -1) 2)))
(exp (* (log (* 2 (* n (PI)))) (+ 1/2 (* -1/2 k))))
(exp (* (log (* 2 (* n (PI)))) (+ 1/2 (* -1/2 k))))
(exp (* (log (* 2 (* n (PI)))) (+ 1/2 (* -1/2 k))))
(exp (* (log (* 2 (* n (PI)))) (+ 1/2 (* -1/2 k))))
(/ (PI) k)
(/ (PI) k)
(/ (PI) k)
(/ (PI) k)
(* (sqrt (/ n k)) (pow (sqrt -1) 2))
(* (sqrt (/ n k)) (pow (sqrt -1) 2))
(* (sqrt (/ n k)) (pow (sqrt -1) 2))
(* (sqrt (/ n k)) (pow (sqrt -1) 2))
(* (sqrt k) (exp (* (+ (log n) (log (* 2 (PI)))) (- (* 1/2 k) 1/2))))
(* (sqrt k) (exp (* (+ (log n) (log (* 2 (PI)))) (- (* 1/2 k) 1/2))))
(* (sqrt k) (exp (* (+ (log n) (log (* 2 (PI)))) (- (* 1/2 k) 1/2))))
(* (sqrt k) (exp (* (+ (log n) (log (* 2 (PI)))) (- (* 1/2 k) 1/2))))
(exp (* (+ (log n) (log (* 2 (PI)))) (- (* 1/2 k) 1/2)))
(exp (* (+ (log n) (log (* 2 (PI)))) (- (* 1/2 k) 1/2)))
(exp (* (+ (log n) (log (* 2 (PI)))) (- (* 1/2 k) 1/2)))
(exp (* (+ (log n) (log (* 2 (PI)))) (- (* 1/2 k) 1/2)))
(* 2 (* n (PI)))
(* 2 (* n (PI)))
(* 2 (* n (PI)))
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(* 2 n)
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(* (sqrt (/ 1 k)) (exp (* 1/2 (* (+ (log n) (log (* 2 (PI)))) (- 1 k)))))
(* (sqrt (/ 1 k)) (exp (* 1/2 (* (+ (log n) (log (* 2 (PI)))) (- 1 k)))))
(* (sqrt (/ 1 k)) (exp (* 1/2 (* (+ (log n) (log (* 2 (PI)))) (- 1 k)))))
(* (sqrt (/ 1 k)) (exp (* 1/2 (* (+ (log n) (log (* 2 (PI)))) (- 1 k)))))
(* (sqrt (/ (* n (PI)) k)) (sqrt 2))
(* (sqrt (/ (* n (PI)) k)) (sqrt 2))
(* (sqrt (/ (* n (PI)) k)) (sqrt 2))
(* (sqrt (/ (* n (PI)) k)) (sqrt 2))
(* 2 (/ (* n (PI)) k))
(* 2 (/ (* n (PI)) k))
(* 2 (/ (* n (PI)) k))
(* 2 (/ (* n (PI)) k))
(* (sqrt (/ 1 k)) (exp (* 1/2 (* (+ (log n) (log (* 2 (PI)))) (- 1 k)))))
(* (sqrt (/ 1 k)) (exp (* 1/2 (* (+ (log n) (log (* 2 (PI)))) (- 1 k)))))
(* (sqrt (/ 1 k)) (exp (* 1/2 (* (+ (log n) (log (* 2 (PI)))) (- 1 k)))))
(* (sqrt (/ 1 k)) (exp (* 1/2 (* (+ (log n) (log (* 2 (PI)))) (- 1 k)))))
(* (sqrt (/ (* n (PI)) k)) (sqrt 2))
(* (sqrt (/ (* n (PI)) k)) (sqrt 2))
(* (sqrt (/ (* n (PI)) k)) (sqrt 2))
(* (sqrt (/ (* n (PI)) k)) (sqrt 2))
(* (sqrt (/ 1 k)) (exp (* 1/2 (* (+ (log n) (log (* 2 (PI)))) (- 1 k)))))
(* (sqrt (/ 1 k)) (exp (* 1/2 (* (+ (log n) (log (* 2 (PI)))) (- 1 k)))))
(* (sqrt (/ 1 k)) (exp (* 1/2 (* (+ (log n) (log (* 2 (PI)))) (- 1 k)))))
(* (sqrt (/ 1 k)) (exp (* 1/2 (* (+ (log n) (log (* 2 (PI)))) (- 1 k)))))
(* (sqrt (/ (* n (PI)) k)) (sqrt 2))
(* (sqrt (/ (* n (PI)) k)) (sqrt 2))
(* (sqrt (/ (* n (PI)) k)) (sqrt 2))
(* (sqrt (/ (* n (PI)) k)) (sqrt 2))
(sqrt (/ (* n (PI)) k))
(sqrt (/ (* n (PI)) k))
(sqrt (/ (* n (PI)) k))
(sqrt (/ (* n (PI)) k))
(* (sqrt (/ 1 k)) (exp (* 1/2 (* (+ (log n) (log (* 2 (PI)))) (- 1 k)))))
(* (sqrt (/ 1 k)) (exp (* 1/2 (* (+ (log n) (log (* 2 (PI)))) (- 1 k)))))
(* (sqrt (/ 1 k)) (exp (* 1/2 (* (+ (log n) (log (* 2 (PI)))) (- 1 k)))))
(* (sqrt (/ 1 k)) (exp (* 1/2 (* (+ (log n) (log (* 2 (PI)))) (- 1 k)))))
(* (sqrt (/ 1 k)) (exp (* (+ 1/2 (* -1/2 k)) (+ (log n) (log (* 2 (PI)))))))
(* (sqrt (/ 1 k)) (exp (* (+ 1/2 (* -1/2 k)) (+ (log n) (log (* 2 (PI)))))))
(* (sqrt (/ 1 k)) (exp (* (+ 1/2 (* -1/2 k)) (+ (log n) (log (* 2 (PI)))))))
(* (sqrt (/ 1 k)) (exp (* (+ 1/2 (* -1/2 k)) (+ (log n) (log (* 2 (PI)))))))
(exp (* (+ 1/2 (* -1/2 k)) (+ (log n) (log (* 2 (PI))))))
(exp (* (+ 1/2 (* -1/2 k)) (+ (log n) (log (* 2 (PI))))))
(exp (* (+ 1/2 (* -1/2 k)) (+ (log n) (log (* 2 (PI))))))
(exp (* (+ 1/2 (* -1/2 k)) (+ (log n) (log (* 2 (PI))))))
(* (sqrt (* n (PI))) (sqrt 2))
(* (sqrt (* n (PI))) (sqrt 2))
(* (sqrt (* n (PI))) (sqrt 2))
(* (sqrt (* n (PI))) (sqrt 2))
(sqrt (/ n k))
(sqrt (/ n k))
(sqrt (/ n k))
(sqrt (/ n k))
(* (sqrt k) (exp (* (+ (log (* 2 (PI))) (* -1 (log (/ 1 n)))) (- (* 1/2 k) 1/2))))
(* (sqrt k) (exp (* (+ (log (* 2 (PI))) (* -1 (log (/ 1 n)))) (- (* 1/2 k) 1/2))))
(* (sqrt k) (exp (* (+ (log (* 2 (PI))) (* -1 (log (/ 1 n)))) (- (* 1/2 k) 1/2))))
(* (sqrt k) (exp (* (+ (log (* 2 (PI))) (* -1 (log (/ 1 n)))) (- (* 1/2 k) 1/2))))
(exp (* (+ (log (* 2 (PI))) (* -1 (log (/ 1 n)))) (- (* 1/2 k) 1/2)))
(exp (* (+ (log (* 2 (PI))) (* -1 (log (/ 1 n)))) (- (* 1/2 k) 1/2)))
(exp (* (+ (log (* 2 (PI))) (* -1 (log (/ 1 n)))) (- (* 1/2 k) 1/2)))
(exp (* (+ (log (* 2 (PI))) (* -1 (log (/ 1 n)))) (- (* 1/2 k) 1/2)))
(* 2 (* n (PI)))
(* 2 (* n (PI)))
(* 2 (* n (PI)))
(* 2 (* n (PI)))
(* 2 n)
(* 2 n)
(* 2 n)
(* 2 n)
(* (sqrt (/ 1 k)) (exp (* 1/2 (* (+ (log (* 2 (PI))) (* -1 (log (/ 1 n)))) (- 1 k)))))
(* (sqrt (/ 1 k)) (exp (* 1/2 (* (+ (log (* 2 (PI))) (* -1 (log (/ 1 n)))) (- 1 k)))))
(* (sqrt (/ 1 k)) (exp (* 1/2 (* (+ (log (* 2 (PI))) (* -1 (log (/ 1 n)))) (- 1 k)))))
(* (sqrt (/ 1 k)) (exp (* 1/2 (* (+ (log (* 2 (PI))) (* -1 (log (/ 1 n)))) (- 1 k)))))
(* (sqrt (/ (* n (PI)) k)) (sqrt 2))
(* (sqrt (/ (* n (PI)) k)) (sqrt 2))
(* (sqrt (/ (* n (PI)) k)) (sqrt 2))
(* (sqrt (/ (* n (PI)) k)) (sqrt 2))
(* 2 (/ (* n (PI)) k))
(* 2 (/ (* n (PI)) k))
(* 2 (/ (* n (PI)) k))
(* 2 (/ (* n (PI)) k))
(* (sqrt (/ 1 k)) (exp (* 1/2 (* (+ (log (* 2 (PI))) (* -1 (log (/ 1 n)))) (- 1 k)))))
(* (sqrt (/ 1 k)) (exp (* 1/2 (* (+ (log (* 2 (PI))) (* -1 (log (/ 1 n)))) (- 1 k)))))
(* (sqrt (/ 1 k)) (exp (* 1/2 (* (+ (log (* 2 (PI))) (* -1 (log (/ 1 n)))) (- 1 k)))))
(* (sqrt (/ 1 k)) (exp (* 1/2 (* (+ (log (* 2 (PI))) (* -1 (log (/ 1 n)))) (- 1 k)))))
(* (sqrt (/ (* n (PI)) k)) (sqrt 2))
(* (sqrt (/ (* n (PI)) k)) (sqrt 2))
(* (sqrt (/ (* n (PI)) k)) (sqrt 2))
(* (sqrt (/ (* n (PI)) k)) (sqrt 2))
(* (sqrt (/ 1 k)) (exp (* 1/2 (* (+ (log (* 2 (PI))) (* -1 (log (/ 1 n)))) (- 1 k)))))
(* (sqrt (/ 1 k)) (exp (* 1/2 (* (+ (log (* 2 (PI))) (* -1 (log (/ 1 n)))) (- 1 k)))))
(* (sqrt (/ 1 k)) (exp (* 1/2 (* (+ (log (* 2 (PI))) (* -1 (log (/ 1 n)))) (- 1 k)))))
(* (sqrt (/ 1 k)) (exp (* 1/2 (* (+ (log (* 2 (PI))) (* -1 (log (/ 1 n)))) (- 1 k)))))
(* (sqrt (/ (* n (PI)) k)) (sqrt 2))
(* (sqrt (/ (* n (PI)) k)) (sqrt 2))
(* (sqrt (/ (* n (PI)) k)) (sqrt 2))
(* (sqrt (/ (* n (PI)) k)) (sqrt 2))
(sqrt (/ (* n (PI)) k))
(sqrt (/ (* n (PI)) k))
(sqrt (/ (* n (PI)) k))
(sqrt (/ (* n (PI)) k))
(* (sqrt (/ 1 k)) (exp (* 1/2 (* (+ (log (* 2 (PI))) (* -1 (log (/ 1 n)))) (- 1 k)))))
(* (sqrt (/ 1 k)) (exp (* 1/2 (* (+ (log (* 2 (PI))) (* -1 (log (/ 1 n)))) (- 1 k)))))
(* (sqrt (/ 1 k)) (exp (* 1/2 (* (+ (log (* 2 (PI))) (* -1 (log (/ 1 n)))) (- 1 k)))))
(* (sqrt (/ 1 k)) (exp (* 1/2 (* (+ (log (* 2 (PI))) (* -1 (log (/ 1 n)))) (- 1 k)))))
(* (sqrt (/ 1 k)) (exp (* (+ 1/2 (* -1/2 k)) (+ (log (* 2 (PI))) (* -1 (log (/ 1 n)))))))
(* (sqrt (/ 1 k)) (exp (* (+ 1/2 (* -1/2 k)) (+ (log (* 2 (PI))) (* -1 (log (/ 1 n)))))))
(* (sqrt (/ 1 k)) (exp (* (+ 1/2 (* -1/2 k)) (+ (log (* 2 (PI))) (* -1 (log (/ 1 n)))))))
(* (sqrt (/ 1 k)) (exp (* (+ 1/2 (* -1/2 k)) (+ (log (* 2 (PI))) (* -1 (log (/ 1 n)))))))
(exp (* (+ 1/2 (* -1/2 k)) (+ (log (* 2 (PI))) (* -1 (log (/ 1 n))))))
(exp (* (+ 1/2 (* -1/2 k)) (+ (log (* 2 (PI))) (* -1 (log (/ 1 n))))))
(exp (* (+ 1/2 (* -1/2 k)) (+ (log (* 2 (PI))) (* -1 (log (/ 1 n))))))
(exp (* (+ 1/2 (* -1/2 k)) (+ (log (* 2 (PI))) (* -1 (log (/ 1 n))))))
(* (sqrt (* n (PI))) (sqrt 2))
(* (sqrt (* n (PI))) (sqrt 2))
(* (sqrt (* n (PI))) (sqrt 2))
(* (sqrt (* n (PI))) (sqrt 2))
(sqrt (/ n k))
(sqrt (/ n k))
(sqrt (/ n k))
(sqrt (/ n k))
(* (sqrt k) (exp (* (+ (log (* -2 (PI))) (* -1 (log (/ -1 n)))) (- (* 1/2 k) 1/2))))
(* (sqrt k) (exp (* (+ (log (* -2 (PI))) (* -1 (log (/ -1 n)))) (- (* 1/2 k) 1/2))))
(* (sqrt k) (exp (* (+ (log (* -2 (PI))) (* -1 (log (/ -1 n)))) (- (* 1/2 k) 1/2))))
(* (sqrt k) (exp (* (+ (log (* -2 (PI))) (* -1 (log (/ -1 n)))) (- (* 1/2 k) 1/2))))
(exp (* (+ (log (* -2 (PI))) (* -1 (log (/ -1 n)))) (- (* 1/2 k) 1/2)))
(exp (* (+ (log (* -2 (PI))) (* -1 (log (/ -1 n)))) (- (* 1/2 k) 1/2)))
(exp (* (+ (log (* -2 (PI))) (* -1 (log (/ -1 n)))) (- (* 1/2 k) 1/2)))
(exp (* (+ (log (* -2 (PI))) (* -1 (log (/ -1 n)))) (- (* 1/2 k) 1/2)))
(* 2 (* n (PI)))
(* 2 (* n (PI)))
(* 2 (* n (PI)))
(* 2 (* n (PI)))
(* 2 n)
(* 2 n)
(* 2 n)
(* 2 n)
(* (sqrt (/ 1 k)) (exp (* 1/2 (* (+ (log (* -2 (PI))) (* -1 (log (/ -1 n)))) (- 1 k)))))
(* (sqrt (/ 1 k)) (exp (* 1/2 (* (+ (log (* -2 (PI))) (* -1 (log (/ -1 n)))) (- 1 k)))))
(* (sqrt (/ 1 k)) (exp (* 1/2 (* (+ (log (* -2 (PI))) (* -1 (log (/ -1 n)))) (- 1 k)))))
(* (sqrt (/ 1 k)) (exp (* 1/2 (* (+ (log (* -2 (PI))) (* -1 (log (/ -1 n)))) (- 1 k)))))
(* -1 (* (sqrt (/ (* n (PI)) k)) (* (sqrt -2) (sqrt -1))))
(* -1 (* (sqrt (/ (* n (PI)) k)) (* (sqrt -2) (sqrt -1))))
(* -1 (* (sqrt (/ (* n (PI)) k)) (* (sqrt -2) (sqrt -1))))
(* -1 (* (sqrt (/ (* n (PI)) k)) (* (sqrt -2) (sqrt -1))))
(* 2 (/ (* n (PI)) k))
(* 2 (/ (* n (PI)) k))
(* 2 (/ (* n (PI)) k))
(* 2 (/ (* n (PI)) k))
(* (sqrt (/ 1 k)) (exp (* 1/2 (* (+ (log (* -2 (PI))) (* -1 (log (/ -1 n)))) (- 1 k)))))
(* (sqrt (/ 1 k)) (exp (* 1/2 (* (+ (log (* -2 (PI))) (* -1 (log (/ -1 n)))) (- 1 k)))))
(* (sqrt (/ 1 k)) (exp (* 1/2 (* (+ (log (* -2 (PI))) (* -1 (log (/ -1 n)))) (- 1 k)))))
(* (sqrt (/ 1 k)) (exp (* 1/2 (* (+ (log (* -2 (PI))) (* -1 (log (/ -1 n)))) (- 1 k)))))
(* -1 (* (sqrt (/ (* n (PI)) k)) (* (pow (sqrt -1) 2) (sqrt 2))))
(* -1 (* (sqrt (/ (* n (PI)) k)) (* (pow (sqrt -1) 2) (sqrt 2))))
(* -1 (* (sqrt (/ (* n (PI)) k)) (* (pow (sqrt -1) 2) (sqrt 2))))
(* -1 (* (sqrt (/ (* n (PI)) k)) (* (pow (sqrt -1) 2) (sqrt 2))))
(* (sqrt (/ 1 k)) (exp (* 1/2 (* (+ (log (* -2 (PI))) (* -1 (log (/ -1 n)))) (- 1 k)))))
(* (sqrt (/ 1 k)) (exp (* 1/2 (* (+ (log (* -2 (PI))) (* -1 (log (/ -1 n)))) (- 1 k)))))
(* (sqrt (/ 1 k)) (exp (* 1/2 (* (+ (log (* -2 (PI))) (* -1 (log (/ -1 n)))) (- 1 k)))))
(* (sqrt (/ 1 k)) (exp (* 1/2 (* (+ (log (* -2 (PI))) (* -1 (log (/ -1 n)))) (- 1 k)))))
(* -1 (* (sqrt (/ (* n (PI)) k)) (* (pow (sqrt -1) 2) (sqrt 2))))
(* -1 (* (sqrt (/ (* n (PI)) k)) (* (pow (sqrt -1) 2) (sqrt 2))))
(* -1 (* (sqrt (/ (* n (PI)) k)) (* (pow (sqrt -1) 2) (sqrt 2))))
(* -1 (* (sqrt (/ (* n (PI)) k)) (* (pow (sqrt -1) 2) (sqrt 2))))
(* -1 (* (sqrt (/ (* n (PI)) k)) (pow (sqrt -1) 2)))
(* -1 (* (sqrt (/ (* n (PI)) k)) (pow (sqrt -1) 2)))
(* -1 (* (sqrt (/ (* n (PI)) k)) (pow (sqrt -1) 2)))
(* -1 (* (sqrt (/ (* n (PI)) k)) (pow (sqrt -1) 2)))
(* (sqrt (/ 1 k)) (exp (* 1/2 (* (+ (log (* -2 (PI))) (* -1 (log (/ -1 n)))) (- 1 k)))))
(* (sqrt (/ 1 k)) (exp (* 1/2 (* (+ (log (* -2 (PI))) (* -1 (log (/ -1 n)))) (- 1 k)))))
(* (sqrt (/ 1 k)) (exp (* 1/2 (* (+ (log (* -2 (PI))) (* -1 (log (/ -1 n)))) (- 1 k)))))
(* (sqrt (/ 1 k)) (exp (* 1/2 (* (+ (log (* -2 (PI))) (* -1 (log (/ -1 n)))) (- 1 k)))))
(* (sqrt (/ 1 k)) (exp (* (+ 1/2 (* -1/2 k)) (+ (log (* -2 (PI))) (* -1 (log (/ -1 n)))))))
(* (sqrt (/ 1 k)) (exp (* (+ 1/2 (* -1/2 k)) (+ (log (* -2 (PI))) (* -1 (log (/ -1 n)))))))
(* (sqrt (/ 1 k)) (exp (* (+ 1/2 (* -1/2 k)) (+ (log (* -2 (PI))) (* -1 (log (/ -1 n)))))))
(* (sqrt (/ 1 k)) (exp (* (+ 1/2 (* -1/2 k)) (+ (log (* -2 (PI))) (* -1 (log (/ -1 n)))))))
(exp (* (+ 1/2 (* -1/2 k)) (+ (log (* -2 (PI))) (* -1 (log (/ -1 n))))))
(exp (* (+ 1/2 (* -1/2 k)) (+ (log (* -2 (PI))) (* -1 (log (/ -1 n))))))
(exp (* (+ 1/2 (* -1/2 k)) (+ (log (* -2 (PI))) (* -1 (log (/ -1 n))))))
(exp (* (+ 1/2 (* -1/2 k)) (+ (log (* -2 (PI))) (* -1 (log (/ -1 n))))))
(* -1 (* (sqrt (* n (PI))) (* (pow (sqrt -1) 2) (sqrt 2))))
(* -1 (* (sqrt (* n (PI))) (* (pow (sqrt -1) 2) (sqrt 2))))
(* -1 (* (sqrt (* n (PI))) (* (pow (sqrt -1) 2) (sqrt 2))))
(* -1 (* (sqrt (* n (PI))) (* (pow (sqrt -1) 2) (sqrt 2))))
(* -1 (* (sqrt (/ n k)) (pow (sqrt -1) 2)))
(* -1 (* (sqrt (/ n k)) (pow (sqrt -1) 2)))
(* -1 (* (sqrt (/ n k)) (pow (sqrt -1) 2)))
(* -1 (* (sqrt (/ n k)) (pow (sqrt -1) 2)))

Outputs
(* (sqrt (/ k (* n (PI)))) (sqrt 1/2))
(.f64 (sqrt.f64 #s(literal 1/2 binary64)) (sqrt.f64 (/.f64 k (.f64 (PI.f64) n))))
(+ (* 1/2 (* (sqrt (/ (pow k 3) (* n (PI)))) (* (log (* 2 (* n (PI)))) (sqrt 1/2)))) (* (sqrt (/ k (* n (PI)))) (sqrt 1/2)))
(.f64 (sqrt.f64 #s(literal 1/2 binary64)) (fma.f64 #s(literal 1/2 binary64) (.f64 (log.f64 (.f64 #s(literal 2 binary64) (.f64 (PI.f64) n))) (sqrt.f64 (/.f64 (/.f64 (pow.f64 k #s(literal 3 binary64)) n) (PI.f64)))) (sqrt.f64 (/.f64 k (*.f64 (PI.f64) n)))))
(+ (* k (+ (* 1/8 (* (sqrt (/ (pow k 3) (* n (PI)))) (* (pow (log (* 2 (* n (PI)))) 2) (sqrt 1/2)))) (* 1/2 (* (sqrt (/ k (* n (PI)))) (* (log (* 2 (* n (PI)))) (sqrt 1/2)))))) (* (sqrt (/ k (* n (PI)))) (sqrt 1/2)))
(fma.f64 (.f64 (sqrt.f64 #s(literal 1/2 binary64)) (fma.f64 (.f64 #s(literal 1/8 binary64) (sqrt.f64 (/.f64 (/.f64 (pow.f64 k #s(literal 3 binary64)) n) (PI.f64)))) (pow.f64 (log.f64 (.f64 #s(literal 2 binary64) (.f64 (PI.f64) n))) #s(literal 2 binary64)) (.f64 #s(literal 1/2 binary64) (.f64 (log.f64 (.f64 #s(literal 2 binary64) (.f64 (PI.f64) n))) (sqrt.f64 (/.f64 k (.f64 (PI.f64) n))))))) k (.f64 (sqrt.f64 #s(literal 1/2 binary64)) (sqrt.f64 (/.f64 k (*.f64 (PI.f64) n)))))
(+ (* k (+ (* 1/2 (* (sqrt (/ k (* n (PI)))) (* (log (* 2 (* n (PI)))) (sqrt 1/2)))) (* k (+ (* 1/48 (* (sqrt (/ (pow k 3) (* n (PI)))) (* (pow (log (* 2 (* n (PI)))) 3) (sqrt 1/2)))) (* 1/8 (* (sqrt (/ k (* n (PI)))) (* (pow (log (* 2 (* n (PI)))) 2) (sqrt 1/2)))))))) (* (sqrt (/ k (* n (PI)))) (sqrt 1/2)))
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(* (sqrt (/ 1 (* n (PI)))) (sqrt 1/2))
(.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (.f64 (PI.f64) n))) (sqrt.f64 #s(literal 1/2 binary64)))
(+ (* 1/2 (* (* k (* (log (* 2 (* n (PI)))) (sqrt 1/2))) (sqrt (/ 1 (* n (PI)))))) (* (sqrt (/ 1 (* n (PI)))) (sqrt 1/2)))
(.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (.f64 (PI.f64) n))) (.f64 (fma.f64 (.f64 #s(literal 1/2 binary64) k) (log.f64 (.f64 #s(literal 2 binary64) (.f64 (PI.f64) n))) #s(literal 1 binary64)) (sqrt.f64 #s(literal 1/2 binary64))))
(+ (* k (+ (* 1/8 (* (* k (* (pow (log (* 2 (* n (PI)))) 2) (sqrt 1/2))) (sqrt (/ 1 (* n (PI)))))) (* 1/2 (* (sqrt (/ 1 (* n (PI)))) (* (log (* 2 (* n (PI)))) (sqrt 1/2)))))) (* (sqrt (/ 1 (* n (PI)))) (sqrt 1/2)))
(.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (.f64 (PI.f64) n))) (fma.f64 (.f64 #s(literal 1/2 binary64) (.f64 (log.f64 (.f64 #s(literal 2 binary64) (.f64 (PI.f64) n))) (sqrt.f64 #s(literal 1/2 binary64)))) k (fma.f64 k (.f64 (.f64 #s(literal 1/8 binary64) k) (.f64 (pow.f64 (log.f64 (.f64 #s(literal 2 binary64) (*.f64 (PI.f64) n))) #s(literal 2 binary64)) (sqrt.f64 #s(literal 1/2 binary64)))) (sqrt.f64 #s(literal 1/2 binary64)))))
(+ (* k (+ (* 1/2 (* (sqrt (/ 1 (* n (PI)))) (* (log (* 2 (* n (PI)))) (sqrt 1/2)))) (* k (+ (* 1/48 (* (* k (* (pow (log (* 2 (* n (PI)))) 3) (sqrt 1/2))) (sqrt (/ 1 (* n (PI)))))) (* 1/8 (* (sqrt (/ 1 (* n (PI)))) (* (pow (log (* 2 (* n (PI)))) 2) (sqrt 1/2)))))))) (* (sqrt (/ 1 (* n (PI)))) (sqrt 1/2)))
(fma.f64 (.f64 k k) (.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (.f64 (PI.f64) n))) (fma.f64 (.f64 #s(literal 1/48 binary64) k) (.f64 (pow.f64 (log.f64 (.f64 #s(literal 2 binary64) (.f64 (PI.f64) n))) #s(literal 3 binary64)) (sqrt.f64 #s(literal 1/2 binary64))) (.f64 #s(literal 1/8 binary64) (.f64 (pow.f64 (log.f64 (.f64 #s(literal 2 binary64) (.f64 (PI.f64) n))) #s(literal 2 binary64)) (sqrt.f64 #s(literal 1/2 binary64)))))) (.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (.f64 (PI.f64) n))) (.f64 (fma.f64 (.f64 #s(literal 1/2 binary64) k) (log.f64 (.f64 #s(literal 2 binary64) (*.f64 (PI.f64) n))) #s(literal 1 binary64)) (sqrt.f64 #s(literal 1/2 binary64)))))
(* (sqrt (/ (* n (PI)) k)) (sqrt 2))
(.f64 (sqrt.f64 #s(literal 2 binary64)) (sqrt.f64 (/.f64 (.f64 (PI.f64) n) k)))
(/ (+ (* -1/2 (* (sqrt (* (pow k 3) (* n (PI)))) (* (log (* 2 (* n (PI)))) (sqrt 2)))) (* (sqrt (* k (* n (PI)))) (sqrt 2))) k)
(/.f64 (.f64 (sqrt.f64 #s(literal 2 binary64)) (fma.f64 #s(literal -1/2 binary64) (.f64 (sqrt.f64 (.f64 (.f64 (pow.f64 k #s(literal 3 binary64)) (PI.f64)) n)) (log.f64 (.f64 #s(literal 2 binary64) (.f64 (PI.f64) n)))) (sqrt.f64 (.f64 (.f64 (PI.f64) n) k)))) k)
(/ (+ (* k (+ (* -1/2 (* (sqrt (* k (* n (PI)))) (* (log (* 2 (* n (PI)))) (sqrt 2)))) (* 1/8 (* (sqrt (* (pow k 3) (* n (PI)))) (* (pow (log (* 2 (* n (PI)))) 2) (sqrt 2)))))) (* (sqrt (* k (* n (PI)))) (sqrt 2))) k)
(/.f64 (fma.f64 (.f64 (sqrt.f64 #s(literal 2 binary64)) (fma.f64 (.f64 (sqrt.f64 (.f64 (.f64 (pow.f64 k #s(literal 3 binary64)) (PI.f64)) n)) #s(literal 1/8 binary64)) (pow.f64 (log.f64 (.f64 #s(literal 2 binary64) (.f64 (PI.f64) n))) #s(literal 2 binary64)) (.f64 #s(literal -1/2 binary64) (.f64 (sqrt.f64 (.f64 (.f64 (PI.f64) n) k)) (log.f64 (.f64 #s(literal 2 binary64) (.f64 (PI.f64) n))))))) k (.f64 (sqrt.f64 (.f64 (*.f64 (PI.f64) n) k)) (sqrt.f64 #s(literal 2 binary64)))) k)
(/ (+ (* k (+ (* -1/2 (* (sqrt (* k (* n (PI)))) (* (log (* 2 (* n (PI)))) (sqrt 2)))) (* k (+ (* -1/48 (* (sqrt (* (pow k 3) (* n (PI)))) (* (pow (log (* 2 (* n (PI)))) 3) (sqrt 2)))) (* 1/8 (* (sqrt (* k (* n (PI)))) (* (pow (log (* 2 (* n (PI)))) 2) (sqrt 2)))))))) (* (sqrt (* k (* n (PI)))) (sqrt 2))) k)
(/.f64 (fma.f64 (fma.f64 (.f64 (sqrt.f64 #s(literal 2 binary64)) (fma.f64 (.f64 (sqrt.f64 (.f64 (.f64 (PI.f64) n) k)) #s(literal 1/8 binary64)) (pow.f64 (log.f64 (.f64 #s(literal 2 binary64) (.f64 (PI.f64) n))) #s(literal 2 binary64)) (.f64 (.f64 #s(literal -1/48 binary64) (sqrt.f64 (.f64 (.f64 (pow.f64 k #s(literal 3 binary64)) (PI.f64)) n))) (pow.f64 (log.f64 (.f64 #s(literal 2 binary64) (.f64 (PI.f64) n))) #s(literal 3 binary64))))) k (.f64 (.f64 (.f64 (sqrt.f64 (.f64 (.f64 (PI.f64) n) k)) #s(literal -1/2 binary64)) (log.f64 (.f64 #s(literal 2 binary64) (.f64 (PI.f64) n)))) (sqrt.f64 #s(literal 2 binary64)))) k (.f64 (sqrt.f64 (.f64 (.f64 (PI.f64) n) k)) (sqrt.f64 #s(literal 2 binary64)))) k)
(* (sqrt (/ (* n (PI)) k)) (sqrt 2))
(.f64 (sqrt.f64 #s(literal 2 binary64)) (sqrt.f64 (/.f64 (.f64 (PI.f64) n) k)))
(* (sqrt (/ (* n (PI)) k)) (sqrt 2))
(.f64 (sqrt.f64 #s(literal 2 binary64)) (sqrt.f64 (/.f64 (.f64 (PI.f64) n) k)))
(* (sqrt (/ (* n (PI)) k)) (sqrt 2))
(.f64 (sqrt.f64 #s(literal 2 binary64)) (sqrt.f64 (/.f64 (.f64 (PI.f64) n) k)))
(* (sqrt (/ (* n (PI)) k)) (sqrt 2))
(.f64 (sqrt.f64 #s(literal 2 binary64)) (sqrt.f64 (/.f64 (.f64 (PI.f64) n) k)))
(* 2 (/ (* n (PI)) k))
(.f64 (/.f64 (.f64 (PI.f64) n) k) #s(literal 2 binary64))
(* 2 (/ (* n (PI)) k))
(.f64 (/.f64 (.f64 (PI.f64) n) k) #s(literal 2 binary64))
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(.f64 (pow.f64 (.f64 #s(literal 2 binary64) (*.f64 (PI.f64) n)) (fma.f64 #s(literal -1/2 binary64) k #s(literal 1/2 binary64))) (sqrt.f64 (/.f64 #s(literal 1 binary64) k)))
(* (sqrt (/ 1 k)) (exp (* (+ 1/2 (* -1/2 k)) (+ (log (* 2 (PI))) (* -1 (log (/ 1 n)))))))
(.f64 (pow.f64 (.f64 #s(literal 2 binary64) (*.f64 (PI.f64) n)) (fma.f64 #s(literal -1/2 binary64) k #s(literal 1/2 binary64))) (sqrt.f64 (/.f64 #s(literal 1 binary64) k)))
(* (sqrt (/ 1 k)) (exp (* (+ 1/2 (* -1/2 k)) (+ (log (* 2 (PI))) (* -1 (log (/ 1 n)))))))
(.f64 (pow.f64 (.f64 #s(literal 2 binary64) (*.f64 (PI.f64) n)) (fma.f64 #s(literal -1/2 binary64) k #s(literal 1/2 binary64))) (sqrt.f64 (/.f64 #s(literal 1 binary64) k)))
(exp (* (+ 1/2 (* -1/2 k)) (+ (log (* 2 (PI))) (* -1 (log (/ 1 n))))))
(pow.f64 (.f64 #s(literal 2 binary64) (.f64 (PI.f64) n)) (fma.f64 #s(literal -1/2 binary64) k #s(literal 1/2 binary64)))
(exp (* (+ 1/2 (* -1/2 k)) (+ (log (* 2 (PI))) (* -1 (log (/ 1 n))))))
(pow.f64 (.f64 #s(literal 2 binary64) (.f64 (PI.f64) n)) (fma.f64 #s(literal -1/2 binary64) k #s(literal 1/2 binary64)))
(exp (* (+ 1/2 (* -1/2 k)) (+ (log (* 2 (PI))) (* -1 (log (/ 1 n))))))
(pow.f64 (.f64 #s(literal 2 binary64) (.f64 (PI.f64) n)) (fma.f64 #s(literal -1/2 binary64) k #s(literal 1/2 binary64)))
(exp (* (+ 1/2 (* -1/2 k)) (+ (log (* 2 (PI))) (* -1 (log (/ 1 n))))))
(pow.f64 (.f64 #s(literal 2 binary64) (.f64 (PI.f64) n)) (fma.f64 #s(literal -1/2 binary64) k #s(literal 1/2 binary64)))
(* (sqrt (* n (PI))) (sqrt 2))
(.f64 (sqrt.f64 (.f64 (PI.f64) n)) (sqrt.f64 #s(literal 2 binary64)))
(* (sqrt (* n (PI))) (sqrt 2))
(.f64 (sqrt.f64 (.f64 (PI.f64) n)) (sqrt.f64 #s(literal 2 binary64)))
(* (sqrt (* n (PI))) (sqrt 2))
(.f64 (sqrt.f64 (.f64 (PI.f64) n)) (sqrt.f64 #s(literal 2 binary64)))
(* (sqrt (* n (PI))) (sqrt 2))
(.f64 (sqrt.f64 (.f64 (PI.f64) n)) (sqrt.f64 #s(literal 2 binary64)))
(sqrt (/ n k))
(sqrt.f64 (/.f64 n k))
(sqrt (/ n k))
(sqrt.f64 (/.f64 n k))
(sqrt (/ n k))
(sqrt.f64 (/.f64 n k))
(sqrt (/ n k))
(sqrt.f64 (/.f64 n k))
(* (sqrt k) (exp (* (+ (log (* -2 (PI))) (* -1 (log (/ -1 n)))) (- (* 1/2 k) 1/2))))
(.f64 (pow.f64 (.f64 #s(literal -2 binary64) (/.f64 (PI.f64) (/.f64 #s(literal -1 binary64) n))) (fma.f64 #s(literal 1/2 binary64) k #s(literal -1/2 binary64))) (sqrt.f64 k))
(* (sqrt k) (exp (* (+ (log (* -2 (PI))) (* -1 (log (/ -1 n)))) (- (* 1/2 k) 1/2))))
(.f64 (pow.f64 (.f64 #s(literal -2 binary64) (/.f64 (PI.f64) (/.f64 #s(literal -1 binary64) n))) (fma.f64 #s(literal 1/2 binary64) k #s(literal -1/2 binary64))) (sqrt.f64 k))
(* (sqrt k) (exp (* (+ (log (* -2 (PI))) (* -1 (log (/ -1 n)))) (- (* 1/2 k) 1/2))))
(.f64 (pow.f64 (.f64 #s(literal -2 binary64) (/.f64 (PI.f64) (/.f64 #s(literal -1 binary64) n))) (fma.f64 #s(literal 1/2 binary64) k #s(literal -1/2 binary64))) (sqrt.f64 k))
(* (sqrt k) (exp (* (+ (log (* -2 (PI))) (* -1 (log (/ -1 n)))) (- (* 1/2 k) 1/2))))
(.f64 (pow.f64 (.f64 #s(literal -2 binary64) (/.f64 (PI.f64) (/.f64 #s(literal -1 binary64) n))) (fma.f64 #s(literal 1/2 binary64) k #s(literal -1/2 binary64))) (sqrt.f64 k))
(exp (* (+ (log (* -2 (PI))) (* -1 (log (/ -1 n)))) (- (* 1/2 k) 1/2)))
(pow.f64 (*.f64 #s(literal -2 binary64) (/.f64 (PI.f64) (/.f64 #s(literal -1 binary64) n))) (fma.f64 #s(literal 1/2 binary64) k #s(literal -1/2 binary64)))
(exp (* (+ (log (* -2 (PI))) (* -1 (log (/ -1 n)))) (- (* 1/2 k) 1/2)))
(pow.f64 (*.f64 #s(literal -2 binary64) (/.f64 (PI.f64) (/.f64 #s(literal -1 binary64) n))) (fma.f64 #s(literal 1/2 binary64) k #s(literal -1/2 binary64)))
(exp (* (+ (log (* -2 (PI))) (* -1 (log (/ -1 n)))) (- (* 1/2 k) 1/2)))
(pow.f64 (*.f64 #s(literal -2 binary64) (/.f64 (PI.f64) (/.f64 #s(literal -1 binary64) n))) (fma.f64 #s(literal 1/2 binary64) k #s(literal -1/2 binary64)))
(exp (* (+ (log (* -2 (PI))) (* -1 (log (/ -1 n)))) (- (* 1/2 k) 1/2)))
(pow.f64 (*.f64 #s(literal -2 binary64) (/.f64 (PI.f64) (/.f64 #s(literal -1 binary64) n))) (fma.f64 #s(literal 1/2 binary64) k #s(literal -1/2 binary64)))
(* 2 (* n (PI)))
(.f64 #s(literal 2 binary64) (.f64 (PI.f64) n))
(* 2 (* n (PI)))
(.f64 #s(literal 2 binary64) (.f64 (PI.f64) n))
(* 2 (* n (PI)))
(.f64 #s(literal 2 binary64) (.f64 (PI.f64) n))
(* 2 (* n (PI)))
(.f64 #s(literal 2 binary64) (.f64 (PI.f64) n))
(* 2 n)
(*.f64 #s(literal 2 binary64) n)
(* 2 n)
(*.f64 #s(literal 2 binary64) n)
(* 2 n)
(*.f64 #s(literal 2 binary64) n)
(* 2 n)
(*.f64 #s(literal 2 binary64) n)
(* (sqrt (/ 1 k)) (exp (* 1/2 (* (+ (log (* -2 (PI))) (* -1 (log (/ -1 n)))) (- 1 k)))))
(.f64 (pow.f64 (.f64 #s(literal -2 binary64) (/.f64 (PI.f64) (/.f64 #s(literal -1 binary64) n))) (fma.f64 #s(literal -1/2 binary64) k #s(literal 1/2 binary64))) (sqrt.f64 (/.f64 #s(literal 1 binary64) k)))
(* (sqrt (/ 1 k)) (exp (* 1/2 (* (+ (log (* -2 (PI))) (* -1 (log (/ -1 n)))) (- 1 k)))))
(.f64 (pow.f64 (.f64 #s(literal -2 binary64) (/.f64 (PI.f64) (/.f64 #s(literal -1 binary64) n))) (fma.f64 #s(literal -1/2 binary64) k #s(literal 1/2 binary64))) (sqrt.f64 (/.f64 #s(literal 1 binary64) k)))
(* (sqrt (/ 1 k)) (exp (* 1/2 (* (+ (log (* -2 (PI))) (* -1 (log (/ -1 n)))) (- 1 k)))))
(.f64 (pow.f64 (.f64 #s(literal -2 binary64) (/.f64 (PI.f64) (/.f64 #s(literal -1 binary64) n))) (fma.f64 #s(literal -1/2 binary64) k #s(literal 1/2 binary64))) (sqrt.f64 (/.f64 #s(literal 1 binary64) k)))
(* (sqrt (/ 1 k)) (exp (* 1/2 (* (+ (log (* -2 (PI))) (* -1 (log (/ -1 n)))) (- 1 k)))))
(.f64 (pow.f64 (.f64 #s(literal -2 binary64) (/.f64 (PI.f64) (/.f64 #s(literal -1 binary64) n))) (fma.f64 #s(literal -1/2 binary64) k #s(literal 1/2 binary64))) (sqrt.f64 (/.f64 #s(literal 1 binary64) k)))
(* -1 (* (sqrt (/ (* n (PI)) k)) (* (sqrt -2) (sqrt -1))))
(.f64 (neg.f64 (sqrt.f64 #s(literal -2 binary64))) (.f64 (sqrt.f64 #s(literal -1 binary64)) (sqrt.f64 (/.f64 (*.f64 (PI.f64) n) k))))
(* -1 (* (sqrt (/ (* n (PI)) k)) (* (sqrt -2) (sqrt -1))))
(.f64 (neg.f64 (sqrt.f64 #s(literal -2 binary64))) (.f64 (sqrt.f64 #s(literal -1 binary64)) (sqrt.f64 (/.f64 (*.f64 (PI.f64) n) k))))
(* -1 (* (sqrt (/ (* n (PI)) k)) (* (sqrt -2) (sqrt -1))))
(.f64 (neg.f64 (sqrt.f64 #s(literal -2 binary64))) (.f64 (sqrt.f64 #s(literal -1 binary64)) (sqrt.f64 (/.f64 (*.f64 (PI.f64) n) k))))
(* -1 (* (sqrt (/ (* n (PI)) k)) (* (sqrt -2) (sqrt -1))))
(.f64 (neg.f64 (sqrt.f64 #s(literal -2 binary64))) (.f64 (sqrt.f64 #s(literal -1 binary64)) (sqrt.f64 (/.f64 (*.f64 (PI.f64) n) k))))
(* 2 (/ (* n (PI)) k))
(.f64 (/.f64 (.f64 (PI.f64) n) k) #s(literal 2 binary64))
(* 2 (/ (* n (PI)) k))
(.f64 (/.f64 (.f64 (PI.f64) n) k) #s(literal 2 binary64))
(* 2 (/ (* n (PI)) k))
(.f64 (/.f64 (.f64 (PI.f64) n) k) #s(literal 2 binary64))
(* 2 (/ (* n (PI)) k))
(.f64 (/.f64 (.f64 (PI.f64) n) k) #s(literal 2 binary64))
(* (sqrt (/ 1 k)) (exp (* 1/2 (* (+ (log (* -2 (PI))) (* -1 (log (/ -1 n)))) (- 1 k)))))
(.f64 (pow.f64 (.f64 #s(literal -2 binary64) (/.f64 (PI.f64) (/.f64 #s(literal -1 binary64) n))) (fma.f64 #s(literal -1/2 binary64) k #s(literal 1/2 binary64))) (sqrt.f64 (/.f64 #s(literal 1 binary64) k)))
(* (sqrt (/ 1 k)) (exp (* 1/2 (* (+ (log (* -2 (PI))) (* -1 (log (/ -1 n)))) (- 1 k)))))
(.f64 (pow.f64 (.f64 #s(literal -2 binary64) (/.f64 (PI.f64) (/.f64 #s(literal -1 binary64) n))) (fma.f64 #s(literal -1/2 binary64) k #s(literal 1/2 binary64))) (sqrt.f64 (/.f64 #s(literal 1 binary64) k)))
(* (sqrt (/ 1 k)) (exp (* 1/2 (* (+ (log (* -2 (PI))) (* -1 (log (/ -1 n)))) (- 1 k)))))
(.f64 (pow.f64 (.f64 #s(literal -2 binary64) (/.f64 (PI.f64) (/.f64 #s(literal -1 binary64) n))) (fma.f64 #s(literal -1/2 binary64) k #s(literal 1/2 binary64))) (sqrt.f64 (/.f64 #s(literal 1 binary64) k)))
(* (sqrt (/ 1 k)) (exp (* 1/2 (* (+ (log (* -2 (PI))) (* -1 (log (/ -1 n)))) (- 1 k)))))
(.f64 (pow.f64 (.f64 #s(literal -2 binary64) (/.f64 (PI.f64) (/.f64 #s(literal -1 binary64) n))) (fma.f64 #s(literal -1/2 binary64) k #s(literal 1/2 binary64))) (sqrt.f64 (/.f64 #s(literal 1 binary64) k)))
(* -1 (* (sqrt (/ (* n (PI)) k)) (* (pow (sqrt -1) 2) (sqrt 2))))
(.f64 (sqrt.f64 #s(literal 2 binary64)) (sqrt.f64 (/.f64 (.f64 (PI.f64) n) k)))
(* -1 (* (sqrt (/ (* n (PI)) k)) (* (pow (sqrt -1) 2) (sqrt 2))))
(.f64 (sqrt.f64 #s(literal 2 binary64)) (sqrt.f64 (/.f64 (.f64 (PI.f64) n) k)))
(* -1 (* (sqrt (/ (* n (PI)) k)) (* (pow (sqrt -1) 2) (sqrt 2))))
(.f64 (sqrt.f64 #s(literal 2 binary64)) (sqrt.f64 (/.f64 (.f64 (PI.f64) n) k)))
(* -1 (* (sqrt (/ (* n (PI)) k)) (* (pow (sqrt -1) 2) (sqrt 2))))
(.f64 (sqrt.f64 #s(literal 2 binary64)) (sqrt.f64 (/.f64 (.f64 (PI.f64) n) k)))
(* (sqrt (/ 1 k)) (exp (* 1/2 (* (+ (log (* -2 (PI))) (* -1 (log (/ -1 n)))) (- 1 k)))))
(.f64 (pow.f64 (.f64 #s(literal -2 binary64) (/.f64 (PI.f64) (/.f64 #s(literal -1 binary64) n))) (fma.f64 #s(literal -1/2 binary64) k #s(literal 1/2 binary64))) (sqrt.f64 (/.f64 #s(literal 1 binary64) k)))
(* (sqrt (/ 1 k)) (exp (* 1/2 (* (+ (log (* -2 (PI))) (* -1 (log (/ -1 n)))) (- 1 k)))))
(.f64 (pow.f64 (.f64 #s(literal -2 binary64) (/.f64 (PI.f64) (/.f64 #s(literal -1 binary64) n))) (fma.f64 #s(literal -1/2 binary64) k #s(literal 1/2 binary64))) (sqrt.f64 (/.f64 #s(literal 1 binary64) k)))
(* (sqrt (/ 1 k)) (exp (* 1/2 (* (+ (log (* -2 (PI))) (* -1 (log (/ -1 n)))) (- 1 k)))))
(.f64 (pow.f64 (.f64 #s(literal -2 binary64) (/.f64 (PI.f64) (/.f64 #s(literal -1 binary64) n))) (fma.f64 #s(literal -1/2 binary64) k #s(literal 1/2 binary64))) (sqrt.f64 (/.f64 #s(literal 1 binary64) k)))
(* (sqrt (/ 1 k)) (exp (* 1/2 (* (+ (log (* -2 (PI))) (* -1 (log (/ -1 n)))) (- 1 k)))))
(.f64 (pow.f64 (.f64 #s(literal -2 binary64) (/.f64 (PI.f64) (/.f64 #s(literal -1 binary64) n))) (fma.f64 #s(literal -1/2 binary64) k #s(literal 1/2 binary64))) (sqrt.f64 (/.f64 #s(literal 1 binary64) k)))
(* -1 (* (sqrt (/ (* n (PI)) k)) (* (pow (sqrt -1) 2) (sqrt 2))))
(.f64 (sqrt.f64 #s(literal 2 binary64)) (sqrt.f64 (/.f64 (.f64 (PI.f64) n) k)))
(* -1 (* (sqrt (/ (* n (PI)) k)) (* (pow (sqrt -1) 2) (sqrt 2))))
(.f64 (sqrt.f64 #s(literal 2 binary64)) (sqrt.f64 (/.f64 (.f64 (PI.f64) n) k)))
(* -1 (* (sqrt (/ (* n (PI)) k)) (* (pow (sqrt -1) 2) (sqrt 2))))
(.f64 (sqrt.f64 #s(literal 2 binary64)) (sqrt.f64 (/.f64 (.f64 (PI.f64) n) k)))
(* -1 (* (sqrt (/ (* n (PI)) k)) (* (pow (sqrt -1) 2) (sqrt 2))))
(.f64 (sqrt.f64 #s(literal 2 binary64)) (sqrt.f64 (/.f64 (.f64 (PI.f64) n) k)))
(* -1 (* (sqrt (/ (* n (PI)) k)) (pow (sqrt -1) 2)))
(sqrt.f64 (/.f64 (*.f64 (PI.f64) n) k))
(* -1 (* (sqrt (/ (* n (PI)) k)) (pow (sqrt -1) 2)))
(sqrt.f64 (/.f64 (*.f64 (PI.f64) n) k))
(* -1 (* (sqrt (/ (* n (PI)) k)) (pow (sqrt -1) 2)))
(sqrt.f64 (/.f64 (*.f64 (PI.f64) n) k))
(* -1 (* (sqrt (/ (* n (PI)) k)) (pow (sqrt -1) 2)))
(sqrt.f64 (/.f64 (*.f64 (PI.f64) n) k))
(* (sqrt (/ 1 k)) (exp (* 1/2 (* (+ (log (* -2 (PI))) (* -1 (log (/ -1 n)))) (- 1 k)))))
(.f64 (pow.f64 (.f64 #s(literal -2 binary64) (/.f64 (PI.f64) (/.f64 #s(literal -1 binary64) n))) (fma.f64 #s(literal -1/2 binary64) k #s(literal 1/2 binary64))) (sqrt.f64 (/.f64 #s(literal 1 binary64) k)))
(* (sqrt (/ 1 k)) (exp (* 1/2 (* (+ (log (* -2 (PI))) (* -1 (log (/ -1 n)))) (- 1 k)))))
(.f64 (pow.f64 (.f64 #s(literal -2 binary64) (/.f64 (PI.f64) (/.f64 #s(literal -1 binary64) n))) (fma.f64 #s(literal -1/2 binary64) k #s(literal 1/2 binary64))) (sqrt.f64 (/.f64 #s(literal 1 binary64) k)))
(* (sqrt (/ 1 k)) (exp (* 1/2 (* (+ (log (* -2 (PI))) (* -1 (log (/ -1 n)))) (- 1 k)))))
(.f64 (pow.f64 (.f64 #s(literal -2 binary64) (/.f64 (PI.f64) (/.f64 #s(literal -1 binary64) n))) (fma.f64 #s(literal -1/2 binary64) k #s(literal 1/2 binary64))) (sqrt.f64 (/.f64 #s(literal 1 binary64) k)))
(* (sqrt (/ 1 k)) (exp (* 1/2 (* (+ (log (* -2 (PI))) (* -1 (log (/ -1 n)))) (- 1 k)))))
(.f64 (pow.f64 (.f64 #s(literal -2 binary64) (/.f64 (PI.f64) (/.f64 #s(literal -1 binary64) n))) (fma.f64 #s(literal -1/2 binary64) k #s(literal 1/2 binary64))) (sqrt.f64 (/.f64 #s(literal 1 binary64) k)))
(* (sqrt (/ 1 k)) (exp (* (+ 1/2 (* -1/2 k)) (+ (log (* -2 (PI))) (* -1 (log (/ -1 n)))))))
(.f64 (pow.f64 (.f64 #s(literal -2 binary64) (/.f64 (PI.f64) (/.f64 #s(literal -1 binary64) n))) (fma.f64 #s(literal -1/2 binary64) k #s(literal 1/2 binary64))) (sqrt.f64 (/.f64 #s(literal 1 binary64) k)))
(* (sqrt (/ 1 k)) (exp (* (+ 1/2 (* -1/2 k)) (+ (log (* -2 (PI))) (* -1 (log (/ -1 n)))))))
(.f64 (pow.f64 (.f64 #s(literal -2 binary64) (/.f64 (PI.f64) (/.f64 #s(literal -1 binary64) n))) (fma.f64 #s(literal -1/2 binary64) k #s(literal 1/2 binary64))) (sqrt.f64 (/.f64 #s(literal 1 binary64) k)))
(* (sqrt (/ 1 k)) (exp (* (+ 1/2 (* -1/2 k)) (+ (log (* -2 (PI))) (* -1 (log (/ -1 n)))))))
(.f64 (pow.f64 (.f64 #s(literal -2 binary64) (/.f64 (PI.f64) (/.f64 #s(literal -1 binary64) n))) (fma.f64 #s(literal -1/2 binary64) k #s(literal 1/2 binary64))) (sqrt.f64 (/.f64 #s(literal 1 binary64) k)))
(* (sqrt (/ 1 k)) (exp (* (+ 1/2 (* -1/2 k)) (+ (log (* -2 (PI))) (* -1 (log (/ -1 n)))))))
(.f64 (pow.f64 (.f64 #s(literal -2 binary64) (/.f64 (PI.f64) (/.f64 #s(literal -1 binary64) n))) (fma.f64 #s(literal -1/2 binary64) k #s(literal 1/2 binary64))) (sqrt.f64 (/.f64 #s(literal 1 binary64) k)))
(exp (* (+ 1/2 (* -1/2 k)) (+ (log (* -2 (PI))) (* -1 (log (/ -1 n))))))
(pow.f64 (*.f64 #s(literal -2 binary64) (/.f64 (PI.f64) (/.f64 #s(literal -1 binary64) n))) (fma.f64 #s(literal -1/2 binary64) k #s(literal 1/2 binary64)))
(exp (* (+ 1/2 (* -1/2 k)) (+ (log (* -2 (PI))) (* -1 (log (/ -1 n))))))
(pow.f64 (*.f64 #s(literal -2 binary64) (/.f64 (PI.f64) (/.f64 #s(literal -1 binary64) n))) (fma.f64 #s(literal -1/2 binary64) k #s(literal 1/2 binary64)))
(exp (* (+ 1/2 (* -1/2 k)) (+ (log (* -2 (PI))) (* -1 (log (/ -1 n))))))
(pow.f64 (*.f64 #s(literal -2 binary64) (/.f64 (PI.f64) (/.f64 #s(literal -1 binary64) n))) (fma.f64 #s(literal -1/2 binary64) k #s(literal 1/2 binary64)))
(exp (* (+ 1/2 (* -1/2 k)) (+ (log (* -2 (PI))) (* -1 (log (/ -1 n))))))
(pow.f64 (*.f64 #s(literal -2 binary64) (/.f64 (PI.f64) (/.f64 #s(literal -1 binary64) n))) (fma.f64 #s(literal -1/2 binary64) k #s(literal 1/2 binary64)))
(* -1 (* (sqrt (* n (PI))) (* (pow (sqrt -1) 2) (sqrt 2))))
(.f64 (sqrt.f64 (.f64 (PI.f64) n)) (sqrt.f64 #s(literal 2 binary64)))
(* -1 (* (sqrt (* n (PI))) (* (pow (sqrt -1) 2) (sqrt 2))))
(.f64 (sqrt.f64 (.f64 (PI.f64) n)) (sqrt.f64 #s(literal 2 binary64)))
(* -1 (* (sqrt (* n (PI))) (* (pow (sqrt -1) 2) (sqrt 2))))
(.f64 (sqrt.f64 (.f64 (PI.f64) n)) (sqrt.f64 #s(literal 2 binary64)))
(* -1 (* (sqrt (* n (PI))) (* (pow (sqrt -1) 2) (sqrt 2))))
(.f64 (sqrt.f64 (.f64 (PI.f64) n)) (sqrt.f64 #s(literal 2 binary64)))
(* -1 (* (sqrt (/ n k)) (pow (sqrt -1) 2)))
(sqrt.f64 (/.f64 n k))
(* -1 (* (sqrt (/ n k)) (pow (sqrt -1) 2)))
(sqrt.f64 (/.f64 n k))
(* -1 (* (sqrt (/ n k)) (pow (sqrt -1) 2)))
(sqrt.f64 (/.f64 n k))
(* -1 (* (sqrt (/ n k)) (pow (sqrt -1) 2)))
(sqrt.f64 (/.f64 n k))

rewrite153.0ms (1.6%)

Memory

33.0MiB live, 226.7MiB allocated

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	51	263
0	78	252
1	260	240
2	1428	236
0	8265	233

Stop Event

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

Counts

23 → 636

Calls

Call 1

Inputs
(.f64 (pow.f64 (.f64 (*.f64 #s(literal 2 binary64) n) (PI.f64)) (fma.f64 #s(literal 1/2 binary64) k #s(literal -1/2 binary64))) (sqrt.f64 k))
(pow.f64 (.f64 (.f64 #s(literal 2 binary64) n) (PI.f64)) (fma.f64 #s(literal 1/2 binary64) k #s(literal -1/2 binary64)))
(.f64 (.f64 #s(literal 2 binary64) n) (PI.f64))
(*.f64 #s(literal 2 binary64) n)
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt.f64 (.f64 (.f64 #s(literal 2 binary64) (/.f64 (PI.f64) k)) n)))
(sqrt.f64 (.f64 (.f64 #s(literal 2 binary64) (/.f64 (PI.f64) k)) n))
(.f64 (.f64 #s(literal 2 binary64) (/.f64 (PI.f64) k)) n)
(*.f64 #s(literal 2 binary64) (/.f64 (PI.f64) k))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (.f64 (sqrt.f64 (.f64 (PI.f64) #s(literal 2 binary64))) (sqrt.f64 (/.f64 n k))))
(.f64 (sqrt.f64 (.f64 (PI.f64) #s(literal 2 binary64))) (sqrt.f64 (/.f64 n k)))
(sqrt.f64 (*.f64 (PI.f64) #s(literal 2 binary64)))
(*.f64 (PI.f64) #s(literal 2 binary64))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (.f64 (sqrt.f64 #s(literal 2 binary64)) (/.f64 (sqrt.f64 (.f64 (PI.f64) n)) (sqrt.f64 k))))
(.f64 (sqrt.f64 #s(literal 2 binary64)) (/.f64 (sqrt.f64 (.f64 (PI.f64) n)) (sqrt.f64 k)))
(sqrt.f64 #s(literal 2 binary64))
(/.f64 (sqrt.f64 (*.f64 (PI.f64) n)) (sqrt.f64 k))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (.f64 #s(approx (pow ( (* 2 n) (PI)) (+ (* k -1/2) 1/2)) (.f64 (sqrt.f64 (.f64 (PI.f64) #s(literal 2 binary64))) (sqrt.f64 n))) (sqrt.f64 (/.f64 #s(literal 1 binary64) k))))
(.f64 #s(approx (pow ( (* 2 n) (PI)) (+ (* k -1/2) 1/2)) (.f64 (sqrt.f64 (.f64 (PI.f64) #s(literal 2 binary64))) (sqrt.f64 n))) (sqrt.f64 (/.f64 #s(literal 1 binary64) k)))
#s(approx (pow (* (* 2 n) (PI)) (+ (* k -1/2) 1/2)) (.f64 (sqrt.f64 (.f64 (PI.f64) #s(literal 2 binary64))) (sqrt.f64 n)))
(.f64 (sqrt.f64 (.f64 (PI.f64) #s(literal 2 binary64))) (sqrt.f64 n))
(PI.f64)
(/.f64 (PI.f64) k)
(sqrt.f64 (/.f64 n k))

Outputs
(.f64 (.f64 (pow.f64 k #s(literal 1/4 binary64)) (pow.f64 (.f64 (PI.f64) (.f64 n #s(literal 2 binary64))) (.f64 (fma.f64 k #s(literal 1/2 binary64) #s(literal -1/2 binary64)) #s(literal 1/2 binary64)))) (.f64 (pow.f64 k #s(literal 1/4 binary64)) (pow.f64 (.f64 (PI.f64) (.f64 n #s(literal 2 binary64))) (*.f64 (fma.f64 k #s(literal 1/2 binary64) #s(literal -1/2 binary64)) #s(literal 1/2 binary64)))))
(.f64 (.f64 (pow.f64 (.f64 (PI.f64) (.f64 n #s(literal 2 binary64))) (.f64 (fma.f64 k #s(literal 1/2 binary64) #s(literal -1/2 binary64)) #s(literal 1/2 binary64))) (pow.f64 k #s(literal 1/4 binary64))) (.f64 (pow.f64 (.f64 (PI.f64) (.f64 n #s(literal 2 binary64))) (*.f64 (fma.f64 k #s(literal 1/2 binary64) #s(literal -1/2 binary64)) #s(literal 1/2 binary64))) (pow.f64 k #s(literal 1/4 binary64))))
(.f64 (.f64 (sqrt.f64 k) (pow.f64 (.f64 (PI.f64) (.f64 n #s(literal 2 binary64))) (.f64 (fma.f64 k #s(literal 1/2 binary64) #s(literal -1/2 binary64)) #s(literal 1/2 binary64)))) (pow.f64 (.f64 (PI.f64) (.f64 n #s(literal 2 binary64))) (.f64 (fma.f64 k #s(literal 1/2 binary64) #s(literal -1/2 binary64)) #s(literal 1/2 binary64))))
(.f64 (.f64 (sqrt.f64 k) (pow.f64 (*.f64 n #s(literal 2 binary64)) (fma.f64 k #s(literal 1/2 binary64) #s(literal -1/2 binary64)))) (pow.f64 (PI.f64) (fma.f64 k #s(literal 1/2 binary64) #s(literal -1/2 binary64))))
(.f64 (.f64 (sqrt.f64 k) (sqrt.f64 (pow.f64 (.f64 (PI.f64) (.f64 n #s(literal 2 binary64))) k))) (pow.f64 (.f64 (PI.f64) (.f64 n #s(literal 2 binary64))) #s(literal -1/2 binary64)))
(.f64 (pow.f64 (.f64 (PI.f64) (.f64 n #s(literal 2 binary64))) (.f64 (fma.f64 k #s(literal 1/2 binary64) #s(literal -1/2 binary64)) #s(literal 1/2 binary64))) (.f64 (pow.f64 (.f64 (PI.f64) (.f64 n #s(literal 2 binary64))) (.f64 (fma.f64 k #s(literal 1/2 binary64) #s(literal -1/2 binary64)) #s(literal 1/2 binary64))) (sqrt.f64 k)))
(.f64 (pow.f64 (.f64 n #s(literal 2 binary64)) (fma.f64 k #s(literal 1/2 binary64) #s(literal -1/2 binary64))) (*.f64 (pow.f64 (PI.f64) (fma.f64 k #s(literal 1/2 binary64) #s(literal -1/2 binary64))) (sqrt.f64 k)))
(.f64 (sqrt.f64 (pow.f64 (.f64 (PI.f64) (.f64 n #s(literal 2 binary64))) k)) (.f64 (pow.f64 (.f64 (PI.f64) (.f64 n #s(literal 2 binary64))) #s(literal -1/2 binary64)) (sqrt.f64 k)))
(.f64 (sqrt.f64 k) (pow.f64 (.f64 (PI.f64) (*.f64 n #s(literal 2 binary64))) (fma.f64 k #s(literal 1/2 binary64) #s(literal -1/2 binary64))))
(.f64 (pow.f64 (.f64 (PI.f64) (*.f64 n #s(literal 2 binary64))) (fma.f64 k #s(literal 1/2 binary64) #s(literal -1/2 binary64))) (sqrt.f64 k))
(/.f64 (pow.f64 (.f64 (PI.f64) (.f64 n #s(literal 2 binary64))) (fma.f64 k #s(literal 1/2 binary64) #s(literal -1/2 binary64))) (pow.f64 k #s(literal -1/2 binary64)))
(exp.f64 (fma.f64 (log.f64 k) #s(literal 1/2 binary64) (.f64 (log.f64 (.f64 (PI.f64) (*.f64 n #s(literal 2 binary64)))) (fma.f64 k #s(literal 1/2 binary64) #s(literal -1/2 binary64)))))
(exp.f64 (fma.f64 (log.f64 (.f64 (PI.f64) (.f64 n #s(literal 2 binary64)))) (fma.f64 k #s(literal 1/2 binary64) #s(literal -1/2 binary64)) (log.f64 (sqrt.f64 k))))
(.f64 (.f64 (pow.f64 (.f64 (PI.f64) (.f64 n #s(literal 2 binary64))) #s(literal -1/4 binary64)) (pow.f64 (.f64 (PI.f64) (.f64 n #s(literal 2 binary64))) (.f64 (.f64 k #s(literal 1/2 binary64)) #s(literal 1/2 binary64)))) (.f64 (pow.f64 (.f64 (PI.f64) (.f64 n #s(literal 2 binary64))) #s(literal -1/4 binary64)) (pow.f64 (.f64 (PI.f64) (.f64 n #s(literal 2 binary64))) (.f64 (*.f64 k #s(literal 1/2 binary64)) #s(literal 1/2 binary64)))))
(.f64 (.f64 (pow.f64 (.f64 (PI.f64) (.f64 n #s(literal 2 binary64))) (.f64 (.f64 k #s(literal 1/2 binary64)) #s(literal 1/2 binary64))) (pow.f64 (.f64 (PI.f64) (.f64 n #s(literal 2 binary64))) #s(literal -1/4 binary64))) (.f64 (pow.f64 (.f64 (PI.f64) (.f64 n #s(literal 2 binary64))) (.f64 (.f64 k #s(literal 1/2 binary64)) #s(literal 1/2 binary64))) (pow.f64 (.f64 (PI.f64) (*.f64 n #s(literal 2 binary64))) #s(literal -1/4 binary64))))
(.f64 (pow.f64 (pow.f64 (.f64 (PI.f64) (.f64 n #s(literal 2 binary64))) (.f64 (fma.f64 k #s(literal 1/2 binary64) #s(literal -1/2 binary64)) #s(literal 1/2 binary64))) #s(literal 1 binary64)) (pow.f64 (pow.f64 (.f64 (PI.f64) (.f64 n #s(literal 2 binary64))) (*.f64 (fma.f64 k #s(literal 1/2 binary64) #s(literal -1/2 binary64)) #s(literal 1/2 binary64))) #s(literal 1 binary64)))
(.f64 (pow.f64 (.f64 (PI.f64) (.f64 n #s(literal 2 binary64))) (/.f64 (.f64 #s(literal 2 binary64) (.f64 (fma.f64 k #s(literal 1/2 binary64) #s(literal -1/2 binary64)) #s(literal 1/2 binary64))) #s(literal 2 binary64))) (pow.f64 (.f64 (PI.f64) (.f64 n #s(literal 2 binary64))) (/.f64 (.f64 #s(literal 2 binary64) (*.f64 (fma.f64 k #s(literal 1/2 binary64) #s(literal -1/2 binary64)) #s(literal 1/2 binary64))) #s(literal 2 binary64))))
(.f64 (pow.f64 (.f64 (PI.f64) (.f64 n #s(literal 2 binary64))) (/.f64 (fma.f64 (fma.f64 k #s(literal 1/2 binary64) #s(literal -1/2 binary64)) #s(literal 1/2 binary64) (.f64 (fma.f64 k #s(literal 1/2 binary64) #s(literal -1/2 binary64)) #s(literal 1/2 binary64))) #s(literal 2 binary64))) (pow.f64 (.f64 (PI.f64) (.f64 n #s(literal 2 binary64))) (/.f64 (fma.f64 (fma.f64 k #s(literal 1/2 binary64) #s(literal -1/2 binary64)) #s(literal 1/2 binary64) (*.f64 (fma.f64 k #s(literal 1/2 binary64) #s(literal -1/2 binary64)) #s(literal 1/2 binary64))) #s(literal 2 binary64))))
(.f64 (exp.f64 (.f64 (.f64 k #s(literal 1/2 binary64)) (log.f64 (.f64 (PI.f64) (.f64 n #s(literal 2 binary64)))))) (exp.f64 (.f64 #s(literal -1/2 binary64) (log.f64 (.f64 (PI.f64) (.f64 n #s(literal 2 binary64)))))))
(.f64 (exp.f64 (.f64 #s(literal -1/2 binary64) (log.f64 (.f64 (PI.f64) (.f64 n #s(literal 2 binary64)))))) (exp.f64 (.f64 (.f64 k #s(literal 1/2 binary64)) (log.f64 (.f64 (PI.f64) (.f64 n #s(literal 2 binary64)))))))
(.f64 (pow.f64 (pow.f64 (.f64 (PI.f64) #s(literal 2 binary64)) (.f64 (fma.f64 k #s(literal 1/2 binary64) #s(literal -1/2 binary64)) #s(literal 1/2 binary64))) #s(literal 2 binary64)) (pow.f64 (pow.f64 n (.f64 (fma.f64 k #s(literal 1/2 binary64) #s(literal -1/2 binary64)) #s(literal 1/2 binary64))) #s(literal 2 binary64)))
(.f64 (pow.f64 (pow.f64 n (.f64 (fma.f64 k #s(literal 1/2 binary64) #s(literal -1/2 binary64)) #s(literal 1/2 binary64))) #s(literal 2 binary64)) (pow.f64 (pow.f64 (.f64 (PI.f64) #s(literal 2 binary64)) (.f64 (fma.f64 k #s(literal 1/2 binary64) #s(literal -1/2 binary64)) #s(literal 1/2 binary64))) #s(literal 2 binary64)))
(.f64 (pow.f64 (pow.f64 #s(literal 2 binary64) (.f64 (fma.f64 k #s(literal 1/2 binary64) #s(literal -1/2 binary64)) #s(literal 1/2 binary64))) #s(literal 2 binary64)) (pow.f64 (pow.f64 (.f64 (PI.f64) n) (.f64 (fma.f64 k #s(literal 1/2 binary64) #s(literal -1/2 binary64)) #s(literal 1/2 binary64))) #s(literal 2 binary64)))
(.f64 (pow.f64 (.f64 (.f64 n #s(literal 2 binary64)) (sqrt.f64 (PI.f64))) (.f64 #s(literal 2 binary64) (*.f64 (fma.f64 k #s(literal 1/2 binary64) #s(literal -1/2 binary64)) #s(literal 1/2 binary64)))) (pow.f64 (sqrt.f64 (PI.f64)) (fma.f64 k #s(literal 1/2 binary64) #s(literal -1/2 binary64))))
(.f64 (pow.f64 (.f64 (.f64 n #s(literal 2 binary64)) (pow.f64 (cbrt.f64 (PI.f64)) #s(literal 2 binary64))) (.f64 #s(literal 2 binary64) (.f64 (fma.f64 k #s(literal 1/2 binary64) #s(literal -1/2 binary64)) #s(literal 1/2 binary64)))) (pow.f64 (cbrt.f64 (PI.f64)) (.f64 #s(literal 2 binary64) (*.f64 (fma.f64 k #s(literal 1/2 binary64) #s(literal -1/2 binary64)) #s(literal 1/2 binary64)))))
(.f64 (pow.f64 (pow.f64 (cbrt.f64 (PI.f64)) #s(literal 2 binary64)) (.f64 #s(literal 2 binary64) (.f64 (fma.f64 k #s(literal 1/2 binary64) #s(literal -1/2 binary64)) #s(literal 1/2 binary64)))) (pow.f64 (.f64 (cbrt.f64 (PI.f64)) (.f64 n #s(literal 2 binary64))) (.f64 #s(literal 2 binary64) (*.f64 (fma.f64 k #s(literal 1/2 binary64) #s(literal -1/2 binary64)) #s(literal 1/2 binary64)))))
(.f64 (pow.f64 #s(literal 1 binary64) (.f64 #s(literal 2 binary64) (.f64 (fma.f64 k #s(literal 1/2 binary64) #s(literal -1/2 binary64)) #s(literal 1/2 binary64)))) (pow.f64 (.f64 (PI.f64) (*.f64 n #s(literal 2 binary64))) (fma.f64 k #s(literal 1/2 binary64) #s(literal -1/2 binary64))))
(.f64 (pow.f64 (.f64 (PI.f64) #s(literal 2 binary64)) (.f64 #s(literal 2 binary64) (.f64 (fma.f64 k #s(literal 1/2 binary64) #s(literal -1/2 binary64)) #s(literal 1/2 binary64)))) (pow.f64 n (.f64 #s(literal 2 binary64) (.f64 (fma.f64 k #s(literal 1/2 binary64) #s(literal -1/2 binary64)) #s(literal 1/2 binary64)))))
(.f64 (pow.f64 n (.f64 #s(literal 2 binary64) (.f64 (fma.f64 k #s(literal 1/2 binary64) #s(literal -1/2 binary64)) #s(literal 1/2 binary64)))) (pow.f64 (.f64 (PI.f64) #s(literal 2 binary64)) (.f64 #s(literal 2 binary64) (.f64 (fma.f64 k #s(literal 1/2 binary64) #s(literal -1/2 binary64)) #s(literal 1/2 binary64)))))
(.f64 (pow.f64 (.f64 (PI.f64) n) (.f64 #s(literal 2 binary64) (.f64 (fma.f64 k #s(literal 1/2 binary64) #s(literal -1/2 binary64)) #s(literal 1/2 binary64)))) (pow.f64 #s(literal 2 binary64) (.f64 #s(literal 2 binary64) (.f64 (fma.f64 k #s(literal 1/2 binary64) #s(literal -1/2 binary64)) #s(literal 1/2 binary64)))))
(.f64 (pow.f64 #s(literal 2 binary64) (.f64 #s(literal 2 binary64) (.f64 (fma.f64 k #s(literal 1/2 binary64) #s(literal -1/2 binary64)) #s(literal 1/2 binary64)))) (pow.f64 (.f64 (PI.f64) n) (.f64 #s(literal 2 binary64) (.f64 (fma.f64 k #s(literal 1/2 binary64) #s(literal -1/2 binary64)) #s(literal 1/2 binary64)))))
(.f64 (pow.f64 (.f64 (.f64 n #s(literal 2 binary64)) (sqrt.f64 (PI.f64))) (fma.f64 (fma.f64 k #s(literal 1/2 binary64) #s(literal -1/2 binary64)) #s(literal 1/2 binary64) (.f64 (fma.f64 k #s(literal 1/2 binary64) #s(literal -1/2 binary64)) #s(literal 1/2 binary64)))) (pow.f64 (sqrt.f64 (PI.f64)) (fma.f64 (fma.f64 k #s(literal 1/2 binary64) #s(literal -1/2 binary64)) #s(literal 1/2 binary64) (*.f64 (fma.f64 k #s(literal 1/2 binary64) #s(literal -1/2 binary64)) #s(literal 1/2 binary64)))))
(.f64 (pow.f64 (.f64 (.f64 n #s(literal 2 binary64)) (pow.f64 (cbrt.f64 (PI.f64)) #s(literal 2 binary64))) (fma.f64 (fma.f64 k #s(literal 1/2 binary64) #s(literal -1/2 binary64)) #s(literal 1/2 binary64) (.f64 (fma.f64 k #s(literal 1/2 binary64) #s(literal -1/2 binary64)) #s(literal 1/2 binary64)))) (pow.f64 (cbrt.f64 (PI.f64)) (fma.f64 (fma.f64 k #s(literal 1/2 binary64) #s(literal -1/2 binary64)) #s(literal 1/2 binary64) (*.f64 (fma.f64 k #s(literal 1/2 binary64) #s(literal -1/2 binary64)) #s(literal 1/2 binary64)))))
(.f64 (pow.f64 (sqrt.f64 (PI.f64)) (fma.f64 (fma.f64 k #s(literal 1/2 binary64) #s(literal -1/2 binary64)) #s(literal 1/2 binary64) (.f64 (fma.f64 k #s(literal 1/2 binary64) #s(literal -1/2 binary64)) #s(literal 1/2 binary64)))) (pow.f64 (.f64 (sqrt.f64 (PI.f64)) (.f64 n #s(literal 2 binary64))) (fma.f64 (fma.f64 k #s(literal 1/2 binary64) #s(literal -1/2 binary64)) #s(literal 1/2 binary64) (*.f64 (fma.f64 k #s(literal 1/2 binary64) #s(literal -1/2 binary64)) #s(literal 1/2 binary64)))))
(.f64 (pow.f64 (pow.f64 (cbrt.f64 (PI.f64)) #s(literal 2 binary64)) (fma.f64 (fma.f64 k #s(literal 1/2 binary64) #s(literal -1/2 binary64)) #s(literal 1/2 binary64) (.f64 (fma.f64 k #s(literal 1/2 binary64) #s(literal -1/2 binary64)) #s(literal 1/2 binary64)))) (pow.f64 (.f64 (cbrt.f64 (PI.f64)) (.f64 n #s(literal 2 binary64))) (fma.f64 (fma.f64 k #s(literal 1/2 binary64) #s(literal -1/2 binary64)) #s(literal 1/2 binary64) (*.f64 (fma.f64 k #s(literal 1/2 binary64) #s(literal -1/2 binary64)) #s(literal 1/2 binary64)))))
(.f64 (pow.f64 #s(literal 1 binary64) (fma.f64 (fma.f64 k #s(literal 1/2 binary64) #s(literal -1/2 binary64)) #s(literal 1/2 binary64) (.f64 (fma.f64 k #s(literal 1/2 binary64) #s(literal -1/2 binary64)) #s(literal 1/2 binary64)))) (pow.f64 (.f64 (PI.f64) (.f64 n #s(literal 2 binary64))) (fma.f64 k #s(literal 1/2 binary64) #s(literal -1/2 binary64))))
(.f64 (pow.f64 (.f64 (PI.f64) #s(literal 2 binary64)) (fma.f64 (fma.f64 k #s(literal 1/2 binary64) #s(literal -1/2 binary64)) #s(literal 1/2 binary64) (.f64 (fma.f64 k #s(literal 1/2 binary64) #s(literal -1/2 binary64)) #s(literal 1/2 binary64)))) (pow.f64 n (fma.f64 (fma.f64 k #s(literal 1/2 binary64) #s(literal -1/2 binary64)) #s(literal 1/2 binary64) (.f64 (fma.f64 k #s(literal 1/2 binary64) #s(literal -1/2 binary64)) #s(literal 1/2 binary64)))))
(.f64 (pow.f64 n (fma.f64 (fma.f64 k #s(literal 1/2 binary64) #s(literal -1/2 binary64)) #s(literal 1/2 binary64) (.f64 (fma.f64 k #s(literal 1/2 binary64) #s(literal -1/2 binary64)) #s(literal 1/2 binary64)))) (pow.f64 (.f64 (PI.f64) #s(literal 2 binary64)) (fma.f64 (fma.f64 k #s(literal 1/2 binary64) #s(literal -1/2 binary64)) #s(literal 1/2 binary64) (.f64 (fma.f64 k #s(literal 1/2 binary64) #s(literal -1/2 binary64)) #s(literal 1/2 binary64)))))
(.f64 (pow.f64 (.f64 (PI.f64) n) (fma.f64 (fma.f64 k #s(literal 1/2 binary64) #s(literal -1/2 binary64)) #s(literal 1/2 binary64) (.f64 (fma.f64 k #s(literal 1/2 binary64) #s(literal -1/2 binary64)) #s(literal 1/2 binary64)))) (pow.f64 #s(literal 2 binary64) (fma.f64 (fma.f64 k #s(literal 1/2 binary64) #s(literal -1/2 binary64)) #s(literal 1/2 binary64) (.f64 (fma.f64 k #s(literal 1/2 binary64) #s(literal -1/2 binary64)) #s(literal 1/2 binary64)))))
(.f64 (pow.f64 #s(literal 2 binary64) (fma.f64 (fma.f64 k #s(literal 1/2 binary64) #s(literal -1/2 binary64)) #s(literal 1/2 binary64) (.f64 (fma.f64 k #s(literal 1/2 binary64) #s(literal -1/2 binary64)) #s(literal 1/2 binary64)))) (pow.f64 (.f64 (PI.f64) n) (fma.f64 (fma.f64 k #s(literal 1/2 binary64) #s(literal -1/2 binary64)) #s(literal 1/2 binary64) (.f64 (fma.f64 k #s(literal 1/2 binary64) #s(literal -1/2 binary64)) #s(literal 1/2 binary64)))))
(.f64 (pow.f64 (.f64 (*.f64 n #s(literal 2 binary64)) (sqrt.f64 (PI.f64))) (fma.f64 k #s(literal 1/2 binary64) #s(literal -1/2 binary64))) (pow.f64 (sqrt.f64 (PI.f64)) (fma.f64 k #s(literal 1/2 binary64) #s(literal -1/2 binary64))))
(.f64 (pow.f64 (.f64 (*.f64 n #s(literal 2 binary64)) (pow.f64 (cbrt.f64 (PI.f64)) #s(literal 2 binary64))) (fma.f64 k #s(literal 1/2 binary64) #s(literal -1/2 binary64))) (pow.f64 (cbrt.f64 (PI.f64)) (fma.f64 k #s(literal 1/2 binary64) #s(literal -1/2 binary64))))
(.f64 (pow.f64 (.f64 (PI.f64) #s(literal 2 binary64)) (fma.f64 k #s(literal 1/2 binary64) #s(literal -1/2 binary64))) (pow.f64 n (fma.f64 k #s(literal 1/2 binary64) #s(literal -1/2 binary64))))
(.f64 (pow.f64 (.f64 (PI.f64) n) (fma.f64 k #s(literal 1/2 binary64) #s(literal -1/2 binary64))) (pow.f64 #s(literal 2 binary64) (fma.f64 k #s(literal 1/2 binary64) #s(literal -1/2 binary64))))
(.f64 (pow.f64 (pow.f64 (cbrt.f64 (PI.f64)) #s(literal 2 binary64)) (fma.f64 k #s(literal 1/2 binary64) #s(literal -1/2 binary64))) (pow.f64 (.f64 (cbrt.f64 (PI.f64)) (*.f64 n #s(literal 2 binary64))) (fma.f64 k #s(literal 1/2 binary64) #s(literal -1/2 binary64))))
(.f64 (pow.f64 n (fma.f64 k #s(literal 1/2 binary64) #s(literal -1/2 binary64))) (pow.f64 (.f64 (PI.f64) #s(literal 2 binary64)) (fma.f64 k #s(literal 1/2 binary64) #s(literal -1/2 binary64))))
(.f64 (pow.f64 #s(literal 2 binary64) (fma.f64 k #s(literal 1/2 binary64) #s(literal -1/2 binary64))) (pow.f64 (.f64 (PI.f64) n) (fma.f64 k #s(literal 1/2 binary64) #s(literal -1/2 binary64))))
(.f64 (pow.f64 (sqrt.f64 (PI.f64)) (fma.f64 k #s(literal 1/2 binary64) #s(literal -1/2 binary64))) (pow.f64 (.f64 (sqrt.f64 (PI.f64)) (.f64 n #s(literal 2 binary64))) (.f64 #s(literal 2 binary64) (*.f64 (fma.f64 k #s(literal 1/2 binary64) #s(literal -1/2 binary64)) #s(literal 1/2 binary64)))))
(.f64 (pow.f64 (sqrt.f64 (PI.f64)) (fma.f64 k #s(literal 1/2 binary64) #s(literal -1/2 binary64))) (pow.f64 (.f64 (sqrt.f64 (PI.f64)) (*.f64 n #s(literal 2 binary64))) (fma.f64 k #s(literal 1/2 binary64) #s(literal -1/2 binary64))))
(.f64 (pow.f64 (.f64 (PI.f64) (.f64 n #s(literal 2 binary64))) (.f64 (fma.f64 k #s(literal 1/2 binary64) #s(literal -1/2 binary64)) #s(literal 1/2 binary64))) (pow.f64 (.f64 (PI.f64) (.f64 n #s(literal 2 binary64))) (*.f64 (fma.f64 k #s(literal 1/2 binary64) #s(literal -1/2 binary64)) #s(literal 1/2 binary64))))
(.f64 (pow.f64 (PI.f64) (fma.f64 k #s(literal 1/2 binary64) #s(literal -1/2 binary64))) (pow.f64 (.f64 n #s(literal 2 binary64)) (fma.f64 k #s(literal 1/2 binary64) #s(literal -1/2 binary64))))
(.f64 (pow.f64 (.f64 n #s(literal 2 binary64)) (fma.f64 k #s(literal 1/2 binary64) #s(literal -1/2 binary64))) (pow.f64 (PI.f64) (fma.f64 k #s(literal 1/2 binary64) #s(literal -1/2 binary64))))
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(.f64 (sqrt.f64 (pow.f64 (.f64 (PI.f64) (.f64 n #s(literal 2 binary64))) k)) (pow.f64 (.f64 (PI.f64) (*.f64 n #s(literal 2 binary64))) #s(literal -1/2 binary64)))
(.f64 #s(literal 1 binary64) (pow.f64 (.f64 (PI.f64) (*.f64 n #s(literal 2 binary64))) (fma.f64 k #s(literal 1/2 binary64) #s(literal -1/2 binary64))))
(pow.f64 (exp.f64 (fma.f64 k #s(literal 1/2 binary64) #s(literal -1/2 binary64))) (log.f64 (.f64 (PI.f64) (.f64 n #s(literal 2 binary64)))))
(pow.f64 (pow.f64 (pow.f64 (.f64 (PI.f64) (.f64 n #s(literal 2 binary64))) #s(literal 2 binary64)) (fma.f64 k #s(literal 1/2 binary64) #s(literal -1/2 binary64))) #s(literal 1/2 binary64))
(pow.f64 (pow.f64 (.f64 (PI.f64) (.f64 n #s(literal 2 binary64))) (fma.f64 (pow.f64 k #s(literal 3 binary64)) #s(literal 1/8 binary64) #s(literal -1/8 binary64))) (pow.f64 (fma.f64 (.f64 k k) #s(literal 1/4 binary64) (-.f64 #s(literal 1/4 binary64) (.f64 k #s(literal -1/4 binary64)))) #s(literal -1 binary64)))
(pow.f64 (pow.f64 (.f64 (PI.f64) (.f64 n #s(literal 2 binary64))) (fma.f64 (*.f64 k k) #s(literal 1/4 binary64) #s(literal -1/4 binary64))) (pow.f64 (fma.f64 k #s(literal 1/2 binary64) #s(literal 1/2 binary64)) #s(literal -1 binary64)))
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(.f64 (pow.f64 (PI.f64) #s(literal 1/4 binary64)) (sqrt.f64 (.f64 (sqrt.f64 (PI.f64)) (*.f64 n #s(literal 2 binary64)))))
(.f64 (pow.f64 (PI.f64) #s(literal 1/4 binary64)) (pow.f64 (.f64 (sqrt.f64 (PI.f64)) (*.f64 n #s(literal 2 binary64))) #s(literal 1/2 binary64)))
(.f64 (pow.f64 (.f64 (PI.f64) (.f64 n #s(literal 2 binary64))) #s(literal 1/4 binary64)) (pow.f64 (.f64 (PI.f64) (*.f64 n #s(literal 2 binary64))) #s(literal 1/4 binary64)))
(.f64 (sqrt.f64 (.f64 n #s(literal 2 binary64))) (sqrt.f64 (PI.f64)))
(.f64 (sqrt.f64 (PI.f64)) (sqrt.f64 (.f64 n #s(literal 2 binary64))))
(.f64 (cbrt.f64 (PI.f64)) (sqrt.f64 (.f64 (cbrt.f64 (PI.f64)) (*.f64 n #s(literal 2 binary64)))))
(.f64 (cbrt.f64 (PI.f64)) (pow.f64 (.f64 (cbrt.f64 (PI.f64)) (*.f64 n #s(literal 2 binary64))) #s(literal 1/2 binary64)))
(.f64 (sqrt.f64 n) (sqrt.f64 (.f64 (PI.f64) #s(literal 2 binary64))))
(.f64 (sqrt.f64 (.f64 (PI.f64) n)) (sqrt.f64 #s(literal 2 binary64)))
(.f64 (sqrt.f64 #s(literal 2 binary64)) (sqrt.f64 (.f64 (PI.f64) n)))
(.f64 (sqrt.f64 (.f64 (PI.f64) #s(literal 2 binary64))) (sqrt.f64 n))
(.f64 #s(literal 1 binary64) (sqrt.f64 (.f64 (PI.f64) (*.f64 n #s(literal 2 binary64)))))
(pow.f64 (pow.f64 (.f64 (PI.f64) (.f64 n #s(literal 2 binary64))) #s(literal 1/4 binary64)) #s(literal 2 binary64))
(pow.f64 (pow.f64 (.f64 (PI.f64) (.f64 n #s(literal 2 binary64))) #s(literal 2 binary64)) #s(literal 1/4 binary64))
(pow.f64 (.f64 (PI.f64) (.f64 n #s(literal 2 binary64))) #s(literal 1/2 binary64))
(sqrt.f64 (.f64 (PI.f64) (.f64 n #s(literal 2 binary64))))
(exp.f64 (fma.f64 (log.f64 n) #s(literal 1/2 binary64) (.f64 (log.f64 (.f64 (PI.f64) #s(literal 2 binary64))) #s(literal 1/2 binary64))))
(exp.f64 (fma.f64 (log.f64 (.f64 (PI.f64) n)) #s(literal 1/2 binary64) (.f64 (log.f64 #s(literal 2 binary64)) #s(literal 1/2 binary64))))
(exp.f64 (fma.f64 (log.f64 #s(literal 2 binary64)) #s(literal 1/2 binary64) (.f64 (log.f64 (.f64 (PI.f64) n)) #s(literal 1/2 binary64))))
(exp.f64 (fma.f64 (log.f64 (.f64 (PI.f64) #s(literal 2 binary64))) #s(literal 1/2 binary64) (.f64 (log.f64 n) #s(literal 1/2 binary64))))
(exp.f64 (.f64 (log.f64 (.f64 (PI.f64) (*.f64 n #s(literal 2 binary64)))) #s(literal 1/2 binary64)))
(.f64 (.f64 (cbrt.f64 (PI.f64)) (cbrt.f64 (sqrt.f64 (PI.f64)))) (*.f64 (cbrt.f64 (PI.f64)) (cbrt.f64 (sqrt.f64 (PI.f64)))))
(.f64 (.f64 (cbrt.f64 (sqrt.f64 (PI.f64))) (cbrt.f64 (PI.f64))) (*.f64 (cbrt.f64 (sqrt.f64 (PI.f64))) (cbrt.f64 (PI.f64))))
(*.f64 (sqrt.f64 (pow.f64 (cbrt.f64 (PI.f64)) #s(literal 5 binary64))) (pow.f64 (PI.f64) #s(literal 1/6 binary64)))
(*.f64 (sqrt.f64 (pow.f64 (cbrt.f64 (PI.f64)) #s(literal 4 binary64))) (cbrt.f64 (PI.f64)))
(*.f64 (sqrt.f64 (pow.f64 (PI.f64) #s(literal 3/2 binary64))) (pow.f64 (PI.f64) #s(literal 1/4 binary64)))
(*.f64 (cbrt.f64 (pow.f64 (PI.f64) #s(literal 5/2 binary64))) (cbrt.f64 (sqrt.f64 (PI.f64))))
(.f64 (cbrt.f64 (pow.f64 (.f64 (PI.f64) (cbrt.f64 (PI.f64))) #s(literal 2 binary64))) (cbrt.f64 (cbrt.f64 (PI.f64))))
(*.f64 (cbrt.f64 (pow.f64 (PI.f64) #s(literal 3/2 binary64))) (cbrt.f64 (pow.f64 (PI.f64) #s(literal 3/2 binary64))))
(*.f64 (exp.f64 (log.f64 (sqrt.f64 (PI.f64)))) (exp.f64 (log.f64 (sqrt.f64 (PI.f64)))))
(*.f64 (exp.f64 (log.f64 (pow.f64 (cbrt.f64 (PI.f64)) #s(literal 2 binary64)))) (exp.f64 (log.f64 (cbrt.f64 (PI.f64)))))
(*.f64 (pow.f64 (pow.f64 (PI.f64) #s(literal 5/2 binary64)) #s(literal 1/3 binary64)) (cbrt.f64 (sqrt.f64 (PI.f64))))
(.f64 (pow.f64 (pow.f64 (.f64 (PI.f64) (cbrt.f64 (PI.f64))) #s(literal 2 binary64)) #s(literal 1/3 binary64)) (cbrt.f64 (cbrt.f64 (PI.f64))))
(*.f64 (pow.f64 (pow.f64 (PI.f64) #s(literal 3/2 binary64)) #s(literal 1/3 binary64)) (pow.f64 (pow.f64 (PI.f64) #s(literal 3/2 binary64)) #s(literal 1/3 binary64)))
(*.f64 (pow.f64 (cbrt.f64 (sqrt.f64 (PI.f64))) #s(literal 3 binary64)) (pow.f64 (cbrt.f64 (sqrt.f64 (PI.f64))) #s(literal 3 binary64)))
(*.f64 (pow.f64 (cbrt.f64 (pow.f64 (cbrt.f64 (PI.f64)) #s(literal 2 binary64))) #s(literal 3 binary64)) (pow.f64 (cbrt.f64 (cbrt.f64 (PI.f64))) #s(literal 3 binary64)))
(*.f64 (pow.f64 (PI.f64) #s(literal 1/4 binary64)) (sqrt.f64 (pow.f64 (PI.f64) #s(literal 3/2 binary64))))
(*.f64 (sqrt.f64 (PI.f64)) (log.f64 (exp.f64 (sqrt.f64 (PI.f64)))))
(*.f64 (sqrt.f64 (PI.f64)) (sqrt.f64 (PI.f64)))
(*.f64 (pow.f64 (cbrt.f64 (PI.f64)) #s(literal 2 binary64)) (pow.f64 (pow.f64 (PI.f64) #s(literal 1/6 binary64)) #s(literal 2 binary64)))
(*.f64 (pow.f64 (cbrt.f64 (PI.f64)) #s(literal 2 binary64)) (cbrt.f64 (PI.f64)))
(.f64 (cbrt.f64 (PI.f64)) (sqrt.f64 (.f64 (cbrt.f64 (PI.f64)) (PI.f64))))
(*.f64 (cbrt.f64 (PI.f64)) (log.f64 (exp.f64 (pow.f64 (cbrt.f64 (PI.f64)) #s(literal 2 binary64)))))
(*.f64 (cbrt.f64 (PI.f64)) (pow.f64 (cbrt.f64 (PI.f64)) #s(literal 2 binary64)))
(*.f64 #s(literal -1 binary64) (neg.f64 (PI.f64)))
(*.f64 #s(literal 1 binary64) (PI.f64))
(*.f64 (PI.f64) (log.f64 (E.f64)))
(*.f64 (PI.f64) #s(literal 1 binary64))
(pow.f64 (E.f64) (log.f64 (PI.f64)))
(pow.f64 (sqrt.f64 (PI.f64)) #s(literal 2 binary64))
(pow.f64 (pow.f64 (PI.f64) #s(literal 3 binary64)) #s(literal 1/3 binary64))
(pow.f64 (*.f64 (PI.f64) (PI.f64)) #s(literal 1/2 binary64))
(pow.f64 (cbrt.f64 (PI.f64)) #s(literal 3 binary64))
(pow.f64 (PI.f64) #s(literal 1 binary64))
(neg.f64 (neg.f64 (PI.f64)))
(cbrt.f64 (pow.f64 (PI.f64) #s(literal 3 binary64)))
(sqrt.f64 (*.f64 (PI.f64) (PI.f64)))
(-.f64 #s(literal 0 binary64) (neg.f64 (PI.f64)))
(fabs.f64 (PI.f64))
(exp.f64 (*.f64 (log.f64 (sqrt.f64 (PI.f64))) #s(literal 2 binary64)))
(exp.f64 (*.f64 (log.f64 (pow.f64 (PI.f64) #s(literal 3 binary64))) #s(literal 1/3 binary64)))
(exp.f64 (*.f64 (log.f64 (cbrt.f64 (PI.f64))) #s(literal 3 binary64)))
(exp.f64 (log.f64 (PI.f64)))
(log.f64 (/.f64 #s(literal 1 binary64) (exp.f64 (neg.f64 (PI.f64)))))
(log.f64 (exp.f64 (PI.f64)))
(PI.f64)
(*.f64 (/.f64 (neg.f64 (sqrt.f64 (PI.f64))) #s(literal -1 binary64)) (/.f64 (sqrt.f64 (PI.f64)) k))
(*.f64 (/.f64 (neg.f64 (pow.f64 (cbrt.f64 (PI.f64)) #s(literal 2 binary64))) #s(literal -1 binary64)) (/.f64 (cbrt.f64 (PI.f64)) k))
(*.f64 (/.f64 (cbrt.f64 (PI.f64)) #s(literal 1 binary64)) (/.f64 (pow.f64 (cbrt.f64 (PI.f64)) #s(literal 2 binary64)) k))
(*.f64 (/.f64 (pow.f64 (cbrt.f64 (PI.f64)) #s(literal 2 binary64)) #s(literal 1 binary64)) (/.f64 (cbrt.f64 (PI.f64)) k))
(*.f64 (/.f64 (PI.f64) #s(literal 1 binary64)) (pow.f64 k #s(literal -1 binary64)))
(*.f64 (/.f64 (sqrt.f64 (PI.f64)) #s(literal 1 binary64)) (/.f64 (sqrt.f64 (PI.f64)) k))
(*.f64 (/.f64 (sqrt.f64 (PI.f64)) #s(literal -1 binary64)) (/.f64 (neg.f64 (sqrt.f64 (PI.f64))) k))
(*.f64 (/.f64 (pow.f64 (cbrt.f64 (PI.f64)) #s(literal 2 binary64)) #s(literal -1 binary64)) (/.f64 (neg.f64 (cbrt.f64 (PI.f64))) k))
(*.f64 (/.f64 (pow.f64 (cbrt.f64 (PI.f64)) #s(literal 2 binary64)) k) (/.f64 (cbrt.f64 (PI.f64)) #s(literal 1 binary64)))
(*.f64 (/.f64 (PI.f64) #s(literal -1 binary64)) (/.f64 #s(literal -1 binary64) k))
(*.f64 (sqrt.f64 (/.f64 (PI.f64) k)) (sqrt.f64 (/.f64 (PI.f64) k)))
(*.f64 (/.f64 (sqrt.f64 (PI.f64)) k) (/.f64 (sqrt.f64 (PI.f64)) #s(literal 1 binary64)))
(*.f64 (/.f64 (cbrt.f64 (PI.f64)) k) (/.f64 (pow.f64 (cbrt.f64 (PI.f64)) #s(literal 2 binary64)) #s(literal 1 binary64)))
(.f64 (.f64 (PI.f64) #s(literal -1 binary64)) (/.f64 #s(literal -1 binary64) k))
(*.f64 (neg.f64 (PI.f64)) (/.f64 #s(literal -1 binary64) k))
(*.f64 (sqrt.f64 (PI.f64)) (/.f64 (sqrt.f64 (PI.f64)) k))
(*.f64 (pow.f64 (cbrt.f64 (PI.f64)) #s(literal 2 binary64)) (/.f64 (cbrt.f64 (PI.f64)) k))
(*.f64 #s(literal -1 binary64) (/.f64 #s(literal 1 binary64) (neg.f64 (/.f64 k (PI.f64)))))
(*.f64 #s(literal -1 binary64) (/.f64 (neg.f64 (PI.f64)) k))
(*.f64 (pow.f64 k #s(literal -1 binary64)) (/.f64 (PI.f64) #s(literal 1 binary64)))
(*.f64 (pow.f64 k #s(literal -1 binary64)) (pow.f64 (pow.f64 (PI.f64) #s(literal -1 binary64)) #s(literal -1 binary64)))
(*.f64 (pow.f64 k #s(literal -1 binary64)) (PI.f64))
(*.f64 (/.f64 (PI.f64) k) #s(literal 1 binary64))
(*.f64 #s(literal 1 binary64) (/.f64 (PI.f64) k))
(*.f64 (PI.f64) (pow.f64 k #s(literal -1 binary64)))
(pow.f64 (/.f64 k (PI.f64)) #s(literal -1 binary64))
(/.f64 (neg.f64 (*.f64 (PI.f64) #s(literal -1 binary64))) k)
(/.f64 (*.f64 (PI.f64) #s(literal -1 binary64)) (neg.f64 k))
(/.f64 (neg.f64 (PI.f64)) (neg.f64 k))
(/.f64 #s(literal -1 binary64) (neg.f64 (/.f64 k (PI.f64))))
(/.f64 #s(literal 1 binary64) (/.f64 (neg.f64 k) (*.f64 (PI.f64) #s(literal -1 binary64))))
(/.f64 #s(literal 1 binary64) (neg.f64 (neg.f64 (/.f64 k (PI.f64)))))
(/.f64 #s(literal 1 binary64) (/.f64 k (PI.f64)))
(/.f64 (PI.f64) k)
(neg.f64 (/.f64 (neg.f64 (PI.f64)) k))
(-.f64 (/.f64 #s(literal 0 binary64) (neg.f64 k)) (/.f64 (neg.f64 (PI.f64)) k))
(-.f64 #s(literal 0 binary64) (/.f64 (neg.f64 (PI.f64)) k))
(exp.f64 (fma.f64 (log.f64 k) #s(literal -1 binary64) (log.f64 (PI.f64))))
(exp.f64 (+.f64 (log.f64 (PI.f64)) (neg.f64 (log.f64 k))))
(exp.f64 (*.f64 (log.f64 (/.f64 k (PI.f64))) #s(literal -1 binary64)))
(*.f64 (/.f64 (pow.f64 n #s(literal 1/4 binary64)) (pow.f64 k #s(literal 1/4 binary64))) (/.f64 (pow.f64 n #s(literal 1/4 binary64)) (pow.f64 k #s(literal 1/4 binary64))))
(*.f64 (/.f64 (pow.f64 n #s(literal 1/4 binary64)) (sqrt.f64 k)) (/.f64 (pow.f64 n #s(literal 1/4 binary64)) #s(literal 1 binary64)))
(*.f64 (pow.f64 (/.f64 k n) #s(literal -1/4 binary64)) (pow.f64 (/.f64 k n) #s(literal -1/4 binary64)))
(*.f64 (neg.f64 (sqrt.f64 n)) (/.f64 #s(literal -1 binary64) (sqrt.f64 k)))
(*.f64 (sqrt.f64 (neg.f64 n)) (/.f64 #s(literal 1 binary64) (sqrt.f64 (neg.f64 k))))
(*.f64 (sqrt.f64 (neg.f64 n)) (sqrt.f64 (/.f64 #s(literal -1 binary64) k)))
(*.f64 (sqrt.f64 (neg.f64 n)) (pow.f64 (/.f64 #s(literal -1 binary64) k) #s(literal 1/2 binary64)))
(*.f64 (pow.f64 k #s(literal -1/2 binary64)) (sqrt.f64 n))
(*.f64 (sqrt.f64 n) (pow.f64 k #s(literal -1/2 binary64)))
(*.f64 #s(literal 1 binary64) (sqrt.f64 (/.f64 n k)))
(pow.f64 (exp.f64 (log.f64 (/.f64 n k))) #s(literal 1/2 binary64))
(pow.f64 (*.f64 (/.f64 n k) (/.f64 n k)) #s(literal 1/4 binary64))
(pow.f64 (pow.f64 (/.f64 k n) #s(literal -1/4 binary64)) #s(literal 2 binary64))
(pow.f64 (sqrt.f64 (/.f64 k n)) #s(literal -1 binary64))
(pow.f64 (/.f64 k n) #s(literal -1/2 binary64))
(pow.f64 (/.f64 n k) #s(literal 1/2 binary64))
(/.f64 (neg.f64 (neg.f64 (sqrt.f64 n))) (sqrt.f64 k))
(/.f64 (neg.f64 (sqrt.f64 (neg.f64 n))) (neg.f64 (sqrt.f64 (neg.f64 k))))
(/.f64 (sqrt.f64 (*.f64 n #s(literal -1 binary64))) (sqrt.f64 (neg.f64 k)))
(/.f64 (neg.f64 (sqrt.f64 n)) (neg.f64 (sqrt.f64 k)))
(/.f64 (sqrt.f64 (neg.f64 n)) (sqrt.f64 (neg.f64 k)))
(/.f64 (sqrt.f64 #s(literal -1 binary64)) (sqrt.f64 (neg.f64 (/.f64 k n))))
(/.f64 #s(literal -1 binary64) (neg.f64 (sqrt.f64 (/.f64 k n))))
(/.f64 (sqrt.f64 n) (sqrt.f64 k))
(/.f64 #s(literal 1 binary64) (/.f64 (sqrt.f64 (/.f64 k n)) #s(literal 1 binary64)))
(/.f64 #s(literal 1 binary64) (sqrt.f64 (/.f64 k n)))
(sqrt.f64 (/.f64 n k))
(exp.f64 (-.f64 (*.f64 (log.f64 n) #s(literal 1/2 binary64)) (log.f64 (sqrt.f64 k))))
(exp.f64 (fma.f64 (log.f64 n) #s(literal 1/2 binary64) (*.f64 (neg.f64 (log.f64 k)) #s(literal 1/2 binary64))))
(exp.f64 (fma.f64 (log.f64 n) #s(literal 1/2 binary64) (*.f64 (log.f64 (sqrt.f64 k)) #s(literal -1 binary64))))
(exp.f64 (*.f64 (log.f64 (/.f64 n k)) #s(literal 1/2 binary64)))

eval277.0ms (3%)

Memory: -22.8MiB live, 369.9MiB allocated
Compiler: Compiled 19 696 to 3 239 computations (83.6% saved)

prune188.0ms (2%)

Memory

7.2MiB live, 364.2MiB allocated

Pruning

49 alts after pruning (37 fresh and 12 done)

	Pruned	Kept	Total
New	1 219	19	1 238
Fresh	6	18	24
Picked	0	5	5
Done	0	7	7
Total	1 225	49	1 274

Accuracy

100.0%

Counts

1 274 → 49

Alt Table

Click to see full alt table

Status	Accuracy	Program
✓	99.5%	(/.f64 (pow.f64 (.f64 (.f64 #s(literal 2 binary64) n) (PI.f64)) (fma.f64 #s(literal -1/2 binary64) k #s(literal 1/2 binary64))) (sqrt.f64 k))
	50.2%	(/.f64 #s(approx (pow (* (* 2 n) (PI)) (+ (* -1/2 k) 1/2)) (.f64 (sqrt.f64 (.f64 (PI.f64) n)) (sqrt.f64 #s(literal 2 binary64)))) (sqrt.f64 k))
✓	99.5%	(/.f64 #s(literal 1 binary64) (.f64 (pow.f64 (.f64 (*.f64 #s(literal 2 binary64) n) (PI.f64)) (fma.f64 #s(literal 1/2 binary64) k #s(literal -1/2 binary64))) (sqrt.f64 k)))
	50.1%	(/.f64 #s(literal 1 binary64) (.f64 #s(approx (pow ( (* 2 n) (PI)) (+ (* 1/2 k) -1/2)) (.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (.f64 (PI.f64) n))) (sqrt.f64 #s(literal 1/2 binary64)))) (sqrt.f64 k)))
	38.9%	(/.f64 #s(literal 1 binary64) #s(approx (* (pow (* (* 2 n) (PI)) (+ (* 1/2 k) -1/2)) (sqrt k)) (.f64 (sqrt.f64 #s(literal 1/2 binary64)) (sqrt.f64 (/.f64 k (.f64 (PI.f64) n))))))
	50.1%	(.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) (/.f64 #s(literal 1 binary64) #s(approx (pow (sqrt ( n (* (PI) 2))) (- k 1)) (/.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (*.f64 (PI.f64) n))) (sqrt.f64 #s(literal 2 binary64))))))
✓	99.7%	(.f64 (sqrt.f64 n) (sqrt.f64 (/.f64 (.f64 #s(literal 2 binary64) (PI.f64)) (.f64 (pow.f64 (.f64 (*.f64 #s(literal 2 binary64) n) (PI.f64)) k) k))))
	50.3%	(.f64 (sqrt.f64 n) (sqrt.f64 #s(approx (/ ( 2 (PI)) (* (pow (* (* 2 n) (PI)) k) k)) (*.f64 (/.f64 (PI.f64) k) #s(literal 2 binary64)))))
	50.2%	(.f64 (sqrt.f64 n) #s(approx (sqrt (/ ( 2 (PI)) (* (pow (* (* 2 n) (PI)) k) k))) (*.f64 (sqrt.f64 (/.f64 (PI.f64) k)) (sqrt.f64 #s(literal 2 binary64)))))
	75.7%	(sqrt.f64 (/.f64 (.f64 (/.f64 (.f64 (PI.f64) n) k) #s(literal 2 binary64)) (pow.f64 (.f64 (.f64 #s(literal 2 binary64) n) (PI.f64)) k)))
	87.0%	(sqrt.f64 (/.f64 (.f64 (.f64 #s(literal 2 binary64) n) (PI.f64)) (.f64 (pow.f64 (.f64 (*.f64 #s(literal 2 binary64) n) (PI.f64)) k) k)))
	50.3%	#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (/.f64 (sqrt.f64 (.f64 (.f64 #s(literal 2 binary64) n) (PI.f64))) (sqrt.f64 k)))
	38.9%	#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (/.f64 (sqrt.f64 (*.f64 (PI.f64) #s(literal 2 binary64))) (sqrt.f64 (/.f64 k n))))
	50.2%	#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (/.f64 (sqrt.f64 #s(literal 2 binary64)) (/.f64 (sqrt.f64 (/.f64 k (PI.f64))) (sqrt.f64 n))))
	37.3%	#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (/.f64 (sqrt.f64 #s(literal 2 binary64)) (/.f64 #s(literal 1 binary64) (sqrt.f64 (/.f64 (*.f64 (PI.f64) n) k)))))
	50.1%	#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (/.f64 (sqrt.f64 #s(literal 2 binary64)) (.f64 (neg.f64 (sqrt.f64 k)) (/.f64 #s(literal 1 binary64) (neg.f64 (sqrt.f64 (.f64 (PI.f64) n)))))))
✓	39.0%	#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (/.f64 (sqrt.f64 #s(literal 2 binary64)) (sqrt.f64 (/.f64 k (*.f64 (PI.f64) n)))))
	38.9%	#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (/.f64 #s(literal 1 binary64) (/.f64 (sqrt.f64 (/.f64 k (*.f64 (PI.f64) n))) (sqrt.f64 #s(literal 2 binary64)))))
	50.2%	#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (/.f64 #s(literal 1 binary64) (/.f64 (sqrt.f64 k) #s(approx (pow (* (* 2 n) (PI)) (+ (* k -1/2) 1/2)) (sqrt.f64 (.f64 (.f64 #s(literal 2 binary64) n) (PI.f64)))))))
✓	99.5%	#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (.f64 (pow.f64 (.f64 (*.f64 #s(literal 2 binary64) n) (PI.f64)) (fma.f64 k #s(literal -1/2 binary64) #s(literal 1/2 binary64))) (sqrt.f64 (/.f64 #s(literal 1 binary64) k))))
	50.1%	#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (.f64 (/.f64 (sqrt.f64 (.f64 n #s(literal 2 binary64))) (sqrt.f64 k)) (/.f64 (sqrt.f64 (PI.f64)) #s(literal 1 binary64))))
	50.2%	#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (.f64 (/.f64 (sqrt.f64 #s(literal 2 binary64)) (sqrt.f64 k)) (/.f64 (sqrt.f64 (.f64 (PI.f64) n)) #s(literal 1 binary64))))
	37.3%	#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (.f64 (.f64 (sqrt.f64 (PI.f64)) (sqrt.f64 #s(literal 2 binary64))) (sqrt.f64 (/.f64 n k))))
	50.2%	#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (.f64 (sqrt.f64 (/.f64 (PI.f64) k)) (sqrt.f64 (.f64 n #s(literal 2 binary64)))))
	50.2%	#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (.f64 (sqrt.f64 (/.f64 #s(literal 2 binary64) k)) (sqrt.f64 (.f64 (PI.f64) n))))
	50.2%	#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (.f64 (sqrt.f64 (.f64 (PI.f64) n)) (*.f64 (pow.f64 k #s(literal -1/2 binary64)) (sqrt.f64 #s(literal 2 binary64)))))
	50.0%	#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (.f64 (sqrt.f64 (.f64 (PI.f64) #s(literal 2 binary64))) (/.f64 (sqrt.f64 n) (sqrt.f64 k))))
	38.8%	#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (.f64 (sqrt.f64 (.f64 (PI.f64) #s(literal 2 binary64))) (/.f64 #s(literal 1 binary64) (sqrt.f64 (/.f64 k n)))))
✓	37.2%	#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (.f64 (sqrt.f64 (.f64 (PI.f64) #s(literal 2 binary64))) (sqrt.f64 (/.f64 n k))))
	37.3%	#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (.f64 (sqrt.f64 (PI.f64)) (sqrt.f64 (.f64 (/.f64 n k) #s(literal 2 binary64)))))
	50.2%	#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (.f64 (sqrt.f64 #s(literal 2 binary64)) (/.f64 (sqrt.f64 (.f64 (*.f64 (sqrt.f64 (PI.f64)) (sqrt.f64 (PI.f64))) n)) (sqrt.f64 k))))
✓	50.2%	#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (.f64 (sqrt.f64 #s(literal 2 binary64)) (/.f64 (sqrt.f64 (.f64 (PI.f64) n)) (sqrt.f64 k))))
	50.2%	#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (.f64 (sqrt.f64 #s(literal 2 binary64)) (.f64 (sqrt.f64 (/.f64 (PI.f64) k)) (sqrt.f64 n))))
✓	37.3%	#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (.f64 (sqrt.f64 #s(literal 2 binary64)) (sqrt.f64 (/.f64 (.f64 (PI.f64) n) k))))
	37.3%	#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (.f64 (sqrt.f64 #s(literal 2 binary64)) (sqrt.f64 (.f64 (pow.f64 k #s(literal -1 binary64)) (*.f64 (PI.f64) n)))))
	50.2%	#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (.f64 (neg.f64 (sqrt.f64 (.f64 (*.f64 #s(literal 2 binary64) n) (PI.f64)))) (/.f64 #s(literal -1 binary64) (sqrt.f64 k))))
	50.1%	#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (.f64 #s(approx (pow ( (* 2 n) (PI)) (+ (* k -1/2) 1/2)) (.f64 (.f64 (sqrt.f64 (PI.f64)) (sqrt.f64 #s(literal 2 binary64))) (sqrt.f64 n))) (sqrt.f64 (/.f64 #s(literal 1 binary64) k))))
✓	50.1%	#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (.f64 #s(approx (pow ( (* 2 n) (PI)) (+ (* k -1/2) 1/2)) (.f64 (sqrt.f64 (.f64 (PI.f64) n)) (sqrt.f64 #s(literal 2 binary64)))) (sqrt.f64 (/.f64 #s(literal 1 binary64) k))))
✓	50.0%	#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (.f64 #s(approx (pow ( (* 2 n) (PI)) (+ (* k -1/2) 1/2)) (.f64 (sqrt.f64 (.f64 (PI.f64) #s(literal 2 binary64))) (sqrt.f64 n))) (sqrt.f64 (/.f64 #s(literal 1 binary64) k))))
	50.3%	#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (.f64 #s(approx (pow ( (* 2 n) (PI)) (+ (* k -1/2) 1/2)) (sqrt.f64 (.f64 (.f64 #s(literal 2 binary64) n) (PI.f64)))) (sqrt.f64 (/.f64 #s(literal 1 binary64) k))))
	37.5%	#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt.f64 (/.f64 (*.f64 (PI.f64) #s(literal 2 binary64)) (/.f64 k n))))
	37.5%	#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt.f64 (/.f64 #s(literal 2 binary64) (/.f64 k (*.f64 (PI.f64) n)))))
✓	37.5%	#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt.f64 (.f64 (/.f64 (.f64 (PI.f64) n) k) #s(literal 2 binary64))))
	37.5%	#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt.f64 (.f64 (/.f64 (.f64 n #s(literal 2 binary64)) k) (/.f64 (PI.f64) #s(literal 1 binary64)))))
	37.5%	#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt.f64 (.f64 (/.f64 n k) (.f64 (PI.f64) #s(literal 2 binary64)))))
	37.5%	#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt.f64 (*.f64 (/.f64 #s(literal 2 binary64) (/.f64 k (PI.f64))) n)))
	37.4%	#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt.f64 (.f64 (/.f64 #s(literal 2 binary64) k) (.f64 (PI.f64) n))))
	37.5%	#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt.f64 (.f64 (.f64 (PI.f64) (/.f64 #s(literal 2 binary64) k)) n)))
✓	37.5%	#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt.f64 (.f64 (.f64 #s(literal 2 binary64) (/.f64 (PI.f64) k)) n)))

Compiler

Compiled 1 677 to 899 computations (46.4% saved)

regimes133.0ms (1.4%)

Memory

-14.7MiB live, 161.9MiB allocated

Counts

80 → 1

Calls

Call 1

Inputs
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt.f64 (.f64 (.f64 #s(literal 2 binary64) (/.f64 (PI.f64) k)) n)))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt.f64 (.f64 (.f64 (PI.f64) #s(literal 2 binary64)) (/.f64 n k))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt.f64 (.f64 (.f64 (PI.f64) (/.f64 #s(literal 2 binary64) k)) n)))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt.f64 (.f64 (/.f64 #s(literal 2 binary64) k) (.f64 (PI.f64) n))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt.f64 (.f64 (/.f64 n k) (.f64 (PI.f64) #s(literal 2 binary64)))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt.f64 (.f64 (/.f64 (.f64 (PI.f64) n) k) #s(literal 2 binary64))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt.f64 (*.f64 (/.f64 #s(literal 2 binary64) (/.f64 k (PI.f64))) n)))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt.f64 (*.f64 (/.f64 n (/.f64 k (PI.f64))) #s(literal 2 binary64))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt.f64 (/.f64 #s(literal 2 binary64) (/.f64 k (*.f64 (PI.f64) n)))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt.f64 (/.f64 (*.f64 (PI.f64) #s(literal 2 binary64)) (/.f64 k n))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (.f64 (sqrt.f64 #s(literal 2 binary64)) (sqrt.f64 (/.f64 (.f64 (PI.f64) n) k))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (.f64 (sqrt.f64 n) (sqrt.f64 (/.f64 (.f64 #s(literal 2 binary64) (PI.f64)) k))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (.f64 (sqrt.f64 (PI.f64)) (sqrt.f64 (.f64 (/.f64 n k) #s(literal 2 binary64)))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (.f64 (sqrt.f64 (.f64 #s(literal 2 binary64) (PI.f64))) (sqrt.f64 (/.f64 n k))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (.f64 (sqrt.f64 (.f64 (PI.f64) #s(literal 2 binary64))) (sqrt.f64 (/.f64 n k))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (.f64 (sqrt.f64 (/.f64 #s(literal 2 binary64) k)) (sqrt.f64 (.f64 (PI.f64) n))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (.f64 (sqrt.f64 (/.f64 (PI.f64) k)) (sqrt.f64 (.f64 n #s(literal 2 binary64)))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (/.f64 (sqrt.f64 (.f64 (.f64 #s(literal 2 binary64) n) (PI.f64))) (sqrt.f64 k)))
(.f64 (sqrt.f64 n) (sqrt.f64 #s(approx (/ ( 2 (PI)) (* (pow (* (* 2 n) (PI)) k) k)) (*.f64 (/.f64 (PI.f64) k) #s(literal 2 binary64)))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt.f64 (.f64 (/.f64 (.f64 n #s(literal 2 binary64)) k) (/.f64 (PI.f64) #s(literal 1 binary64)))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (.f64 #s(approx (pow ( (* 2 n) (PI)) (+ (* k -1/2) 1/2)) (sqrt.f64 (.f64 (.f64 #s(literal 2 binary64) n) (PI.f64)))) (sqrt.f64 (/.f64 #s(literal 1 binary64) k))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (/.f64 (sqrt.f64 #s(literal 2 binary64)) (sqrt.f64 (/.f64 k (*.f64 (PI.f64) n)))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (/.f64 (sqrt.f64 (*.f64 (PI.f64) #s(literal 2 binary64))) (sqrt.f64 (/.f64 k n))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (.f64 (neg.f64 (sqrt.f64 (.f64 (*.f64 #s(literal 2 binary64) n) (PI.f64)))) (/.f64 #s(literal -1 binary64) (sqrt.f64 k))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (.f64 (sqrt.f64 #s(literal 2 binary64)) (.f64 (sqrt.f64 n) (sqrt.f64 (/.f64 (PI.f64) k)))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (.f64 (sqrt.f64 #s(literal 2 binary64)) (.f64 (sqrt.f64 (/.f64 (PI.f64) k)) (sqrt.f64 n))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (.f64 (sqrt.f64 #s(literal 2 binary64)) (/.f64 (sqrt.f64 (.f64 (PI.f64) n)) (sqrt.f64 k))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (.f64 (sqrt.f64 (.f64 (PI.f64) #s(literal 2 binary64))) (/.f64 (sqrt.f64 n) (sqrt.f64 k))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (.f64 (.f64 (sqrt.f64 (PI.f64)) (sqrt.f64 #s(literal 2 binary64))) (sqrt.f64 (/.f64 n k))))
(.f64 (sqrt.f64 n) #s(approx (sqrt (/ ( 2 (PI)) (* (pow (* (* 2 n) (PI)) k) k))) (*.f64 (sqrt.f64 (/.f64 (PI.f64) k)) (sqrt.f64 #s(literal 2 binary64)))))
(/.f64 #s(approx (pow (* (* 2 n) (PI)) (+ (* -1/2 k) 1/2)) (.f64 (sqrt.f64 (.f64 (PI.f64) n)) (sqrt.f64 #s(literal 2 binary64)))) (sqrt.f64 k))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (.f64 (sqrt.f64 (.f64 (PI.f64) #s(literal 2 binary64))) (/.f64 #s(literal 1 binary64) (sqrt.f64 (/.f64 k n)))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (/.f64 #s(literal 1 binary64) (/.f64 (sqrt.f64 k) #s(approx (pow (* (* 2 n) (PI)) (+ (* k -1/2) 1/2)) (sqrt.f64 (.f64 (.f64 #s(literal 2 binary64) n) (PI.f64)))))))
(/.f64 #s(literal 1 binary64) #s(approx (* (pow (* (* 2 n) (PI)) (+ (* 1/2 k) -1/2)) (sqrt k)) (.f64 (sqrt.f64 #s(literal 1/2 binary64)) (sqrt.f64 (/.f64 k (.f64 (PI.f64) n))))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt.f64 (.f64 (.f64 (sqrt.f64 (PI.f64)) (*.f64 (sqrt.f64 (PI.f64)) (/.f64 n k))) #s(literal 2 binary64))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt.f64 (.f64 (/.f64 (.f64 (*.f64 n (sqrt.f64 (PI.f64))) (sqrt.f64 (PI.f64))) k) #s(literal 2 binary64))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (.f64 #s(approx (pow ( (* 2 n) (PI)) (+ (* k -1/2) 1/2)) (.f64 (sqrt.f64 (.f64 #s(literal 2 binary64) n)) (sqrt.f64 (PI.f64)))) (sqrt.f64 (/.f64 #s(literal 1 binary64) k))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (.f64 #s(approx (pow ( (* 2 n) (PI)) (+ (* k -1/2) 1/2)) (.f64 (sqrt.f64 (.f64 (PI.f64) #s(literal 2 binary64))) (sqrt.f64 n))) (sqrt.f64 (/.f64 #s(literal 1 binary64) k))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (.f64 #s(approx (pow ( (* 2 n) (PI)) (+ (* k -1/2) 1/2)) (.f64 (sqrt.f64 (.f64 (PI.f64) n)) (sqrt.f64 #s(literal 2 binary64)))) (sqrt.f64 (/.f64 #s(literal 1 binary64) k))))
(.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) #s(approx (pow ( (* 2 (PI)) n) (/ (- 1 k) 2)) (.f64 (sqrt.f64 (.f64 (PI.f64) n)) (sqrt.f64 #s(literal 2 binary64)))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (/.f64 #s(literal 1 binary64) (/.f64 (sqrt.f64 (/.f64 k (*.f64 (PI.f64) n))) (sqrt.f64 #s(literal 2 binary64)))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (/.f64 (sqrt.f64 #s(literal 2 binary64)) (/.f64 #s(literal 1 binary64) (sqrt.f64 (/.f64 (*.f64 (PI.f64) n) k)))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (.f64 (/.f64 (sqrt.f64 #s(literal 2 binary64)) (sqrt.f64 k)) (/.f64 (sqrt.f64 (.f64 (PI.f64) n)) #s(literal 1 binary64))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (.f64 (/.f64 (sqrt.f64 (.f64 n #s(literal 2 binary64))) (sqrt.f64 k)) (/.f64 (sqrt.f64 (PI.f64)) #s(literal 1 binary64))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (/.f64 (sqrt.f64 #s(literal 2 binary64)) (/.f64 (sqrt.f64 (/.f64 k (PI.f64))) (sqrt.f64 n))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (.f64 #s(approx (pow ( (* 2 n) (PI)) (+ (* k -1/2) 1/2)) (.f64 (.f64 (sqrt.f64 (PI.f64)) (sqrt.f64 #s(literal 2 binary64))) (sqrt.f64 n))) (sqrt.f64 (/.f64 #s(literal 1 binary64) k))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (.f64 (sqrt.f64 #s(literal 2 binary64)) (sqrt.f64 (/.f64 (.f64 (*.f64 (sqrt.f64 (PI.f64)) (sqrt.f64 (PI.f64))) n) k))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (/.f64 (sqrt.f64 #s(literal 2 binary64)) (.f64 (neg.f64 (sqrt.f64 k)) (/.f64 #s(literal 1 binary64) (neg.f64 (sqrt.f64 (.f64 (PI.f64) n)))))))
(/.f64 #s(literal 1 binary64) (.f64 #s(approx (pow ( (* 2 n) (PI)) (+ (* 1/2 k) -1/2)) (.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (.f64 (PI.f64) n))) (sqrt.f64 #s(literal 1/2 binary64)))) (sqrt.f64 k)))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (.f64 (sqrt.f64 #s(literal 2 binary64)) (/.f64 (sqrt.f64 (.f64 (*.f64 (sqrt.f64 (PI.f64)) (sqrt.f64 (PI.f64))) n)) (sqrt.f64 k))))
(.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) (/.f64 #s(literal 1 binary64) #s(approx (pow (sqrt ( n (* (PI) 2))) (- k 1)) (/.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (*.f64 (PI.f64) n))) (sqrt.f64 #s(literal 2 binary64))))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (.f64 (sqrt.f64 (.f64 (*.f64 #s(literal 2 binary64) n) (PI.f64))) (pow.f64 k #s(literal -1/2 binary64))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (.f64 (sqrt.f64 #s(literal 2 binary64)) (sqrt.f64 (.f64 (pow.f64 k #s(literal -1 binary64)) (*.f64 (PI.f64) n)))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (.f64 (sqrt.f64 (.f64 (PI.f64) n)) (*.f64 (pow.f64 k #s(literal -1/2 binary64)) (sqrt.f64 #s(literal 2 binary64)))))
(.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) (pow.f64 (.f64 (*.f64 #s(literal 2 binary64) (PI.f64)) n) #s(approx (/ (- 1 k) 2) #s(literal 1/2 binary64))))
(/.f64 (pow.f64 (.f64 n (.f64 (PI.f64) #s(literal 2 binary64))) (fma.f64 #s(literal 1/2 binary64) k #s(literal 1/2 binary64))) (sqrt.f64 k))
(/.f64 (pow.f64 (.f64 (.f64 #s(literal 2 binary64) n) (PI.f64)) (fma.f64 #s(literal -1/2 binary64) k #s(literal 1/2 binary64))) (sqrt.f64 k))
(.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) (pow.f64 (.f64 (.f64 #s(literal 2 binary64) (PI.f64)) n) #s(approx (/ (- 1 k) 2) (.f64 k #s(literal -1/2 binary64)))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (.f64 (pow.f64 (.f64 (*.f64 #s(literal 2 binary64) n) (PI.f64)) (fma.f64 k #s(literal -1/2 binary64) #s(literal 1/2 binary64))) (sqrt.f64 (/.f64 #s(literal 1 binary64) k))))
(.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) (pow.f64 (.f64 (*.f64 #s(literal 2 binary64) (PI.f64)) n) (fma.f64 k #s(literal -1/2 binary64) #s(literal 1/2 binary64))))
(/.f64 #s(literal 1 binary64) (.f64 (pow.f64 (.f64 (*.f64 #s(literal 2 binary64) n) (PI.f64)) (fma.f64 #s(literal 1/2 binary64) k #s(literal -1/2 binary64))) (sqrt.f64 k)))
(sqrt.f64 (/.f64 (.f64 (.f64 #s(literal 2 binary64) n) (PI.f64)) (.f64 (pow.f64 (.f64 (*.f64 #s(literal 2 binary64) n) (PI.f64)) k) k)))
(/.f64 #s(literal 1 binary64) (/.f64 (sqrt.f64 k) (pow.f64 (.f64 n (.f64 (PI.f64) #s(literal 2 binary64))) (fma.f64 #s(literal 1/2 binary64) k #s(literal 1/2 binary64)))))
(.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) (sqrt.f64 (pow.f64 (.f64 n (*.f64 (PI.f64) #s(literal 2 binary64))) (-.f64 #s(literal 1 binary64) k))))
(.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) (pow.f64 (.f64 (*.f64 #s(literal 2 binary64) (PI.f64)) n) (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 2 binary64))))
(/.f64 (/.f64 #s(literal -1 binary64) (sqrt.f64 k)) (neg.f64 (pow.f64 (.f64 (.f64 #s(literal 2 binary64) n) (PI.f64)) (fma.f64 #s(literal 1/2 binary64) k #s(literal -1/2 binary64)))))
(sqrt.f64 (/.f64 (.f64 (/.f64 (.f64 (PI.f64) n) k) #s(literal 2 binary64)) (pow.f64 (.f64 (.f64 #s(literal 2 binary64) n) (PI.f64)) k)))
(.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) (/.f64 #s(literal 1 binary64) (pow.f64 (.f64 n (.f64 (PI.f64) #s(literal 2 binary64))) (.f64 #s(literal -1/2 binary64) (-.f64 #s(literal 1 binary64) k)))))
(.f64 (sqrt.f64 n) (sqrt.f64 (/.f64 (.f64 #s(literal 2 binary64) (PI.f64)) (.f64 (pow.f64 (.f64 (*.f64 #s(literal 2 binary64) n) (PI.f64)) k) k))))
(.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) (/.f64 #s(literal 1 binary64) (pow.f64 (sqrt.f64 (.f64 n (*.f64 (PI.f64) #s(literal 2 binary64)))) (-.f64 k #s(literal 1 binary64)))))
(.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) (.f64 (pow.f64 (.f64 n (.f64 (PI.f64) #s(literal 2 binary64))) (.f64 k #s(literal -1/2 binary64))) (sqrt.f64 (.f64 n (*.f64 (PI.f64) #s(literal 2 binary64))))))
(.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) (pow.f64 (.f64 (.f64 (.f64 n #s(literal 2 binary64)) (sqrt.f64 (PI.f64))) (sqrt.f64 (PI.f64))) (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 2 binary64))))
(.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) #s(approx (pow ( (* 2 (PI)) n) (/ (- 1 k) 2)) (.f64 (fma.f64 (log.f64 (.f64 (.f64 #s(literal 2 binary64) n) (PI.f64))) (.f64 k #s(literal -1/2 binary64)) #s(literal 1 binary64)) (.f64 (sqrt.f64 (.f64 (PI.f64) n)) (sqrt.f64 #s(literal 2 binary64))))))
(.f64 (pow.f64 #s(literal 2 binary64) (fma.f64 #s(literal 1/2 binary64) k #s(literal 1/2 binary64))) (/.f64 (pow.f64 (.f64 n (PI.f64)) (fma.f64 #s(literal 1/2 binary64) k #s(literal 1/2 binary64))) (sqrt.f64 k)))
(.f64 (/.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (pow.f64 k #s(literal -1/2 binary64)))) (pow.f64 (.f64 (*.f64 #s(literal 2 binary64) (PI.f64)) n) (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 2 binary64))))
(.f64 (/.f64 (pow.f64 #s(literal 2 binary64) (fma.f64 #s(literal 1/2 binary64) k #s(literal 1/2 binary64))) (sqrt.f64 k)) (/.f64 (pow.f64 (.f64 n (PI.f64)) (fma.f64 #s(literal 1/2 binary64) k #s(literal 1/2 binary64))) #s(literal 1 binary64)))
(/.f64 (sqrt.f64 (.f64 n (.f64 (PI.f64) #s(literal 2 binary64)))) (.f64 (sqrt.f64 k) (pow.f64 (pow.f64 (.f64 n (*.f64 (PI.f64) #s(literal 2 binary64))) k) #s(literal 1/2 binary64))))
(/.f64 (.f64 (/.f64 (pow.f64 (.f64 (PI.f64) #s(literal 2 binary64)) (fma.f64 #s(literal 1/2 binary64) k #s(literal 1/2 binary64))) (sqrt.f64 k)) (sqrt.f64 n)) (pow.f64 n (*.f64 #s(literal 1/2 binary64) k)))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (/.f64 (.f64 (sqrt.f64 #s(literal 2 binary64)) (fma.f64 (.f64 (log.f64 (.f64 (.f64 #s(literal 2 binary64) n) (PI.f64))) (sqrt.f64 (.f64 (.f64 (pow.f64 k #s(literal 3 binary64)) (PI.f64)) n))) #s(literal -1/2 binary64) (sqrt.f64 (.f64 (.f64 (PI.f64) n) k)))) k))
(.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) #s(approx (pow ( (* 2 (PI)) n) (/ (- 1 k) 2)) (.f64 (sqrt.f64 (.f64 (PI.f64) n)) (fma.f64 k (.f64 (.f64 (log.f64 (.f64 (.f64 #s(literal 2 binary64) n) (PI.f64))) (sqrt.f64 #s(literal 2 binary64))) (fma.f64 (.f64 #s(literal 1/8 binary64) k) (log.f64 (.f64 (*.f64 #s(literal 2 binary64) n) (PI.f64))) #s(literal -1/2 binary64))) (sqrt.f64 #s(literal 2 binary64))))))

Outputs
(/.f64 (sqrt.f64 (.f64 n (.f64 (PI.f64) #s(literal 2 binary64)))) (.f64 (sqrt.f64 k) (pow.f64 (pow.f64 (.f64 n (*.f64 (PI.f64) #s(literal 2 binary64))) k) #s(literal 1/2 binary64))))

Calls

4 calls:

57.0ms	k
27.0ms	n
24.0ms	(.f64 (.f64 #s(literal 2 binary64) (PI.f64)) n)
21.0ms	(.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) (pow.f64 (.f64 (*.f64 #s(literal 2 binary64) (PI.f64)) n) (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 2 binary64))))

Results

Accuracy	Segments	Branch
99.8%	1	`k`
99.8%	1	`n`
99.8%	1	`(.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) (pow.f64 (.f64 (*.f64 #s(literal 2 binary64) (PI.f64)) n) (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 2 binary64))))`
99.8%	1	`(.f64 (.f64 #s(literal 2 binary64) (PI.f64)) n)`

Compiler

Compiled 23 to 23 computations (0% saved)

regimes89.0ms (0.9%)

Memory

21.0MiB live, 140.0MiB allocated

Counts

76 → 1

Calls

Call 1

Inputs
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt.f64 (.f64 (.f64 #s(literal 2 binary64) (/.f64 (PI.f64) k)) n)))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt.f64 (.f64 (.f64 (PI.f64) #s(literal 2 binary64)) (/.f64 n k))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt.f64 (.f64 (.f64 (PI.f64) (/.f64 #s(literal 2 binary64) k)) n)))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt.f64 (.f64 (/.f64 #s(literal 2 binary64) k) (.f64 (PI.f64) n))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt.f64 (.f64 (/.f64 n k) (.f64 (PI.f64) #s(literal 2 binary64)))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt.f64 (.f64 (/.f64 (.f64 (PI.f64) n) k) #s(literal 2 binary64))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt.f64 (*.f64 (/.f64 #s(literal 2 binary64) (/.f64 k (PI.f64))) n)))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt.f64 (*.f64 (/.f64 n (/.f64 k (PI.f64))) #s(literal 2 binary64))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt.f64 (/.f64 #s(literal 2 binary64) (/.f64 k (*.f64 (PI.f64) n)))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt.f64 (/.f64 (*.f64 (PI.f64) #s(literal 2 binary64)) (/.f64 k n))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (.f64 (sqrt.f64 #s(literal 2 binary64)) (sqrt.f64 (/.f64 (.f64 (PI.f64) n) k))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (.f64 (sqrt.f64 n) (sqrt.f64 (/.f64 (.f64 #s(literal 2 binary64) (PI.f64)) k))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (.f64 (sqrt.f64 (PI.f64)) (sqrt.f64 (.f64 (/.f64 n k) #s(literal 2 binary64)))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (.f64 (sqrt.f64 (.f64 #s(literal 2 binary64) (PI.f64))) (sqrt.f64 (/.f64 n k))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (.f64 (sqrt.f64 (.f64 (PI.f64) #s(literal 2 binary64))) (sqrt.f64 (/.f64 n k))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (.f64 (sqrt.f64 (/.f64 #s(literal 2 binary64) k)) (sqrt.f64 (.f64 (PI.f64) n))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (.f64 (sqrt.f64 (/.f64 (PI.f64) k)) (sqrt.f64 (.f64 n #s(literal 2 binary64)))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (/.f64 (sqrt.f64 (.f64 (.f64 #s(literal 2 binary64) n) (PI.f64))) (sqrt.f64 k)))
(.f64 (sqrt.f64 n) (sqrt.f64 #s(approx (/ ( 2 (PI)) (* (pow (* (* 2 n) (PI)) k) k)) (*.f64 (/.f64 (PI.f64) k) #s(literal 2 binary64)))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt.f64 (.f64 (/.f64 (.f64 n #s(literal 2 binary64)) k) (/.f64 (PI.f64) #s(literal 1 binary64)))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (.f64 #s(approx (pow ( (* 2 n) (PI)) (+ (* k -1/2) 1/2)) (sqrt.f64 (.f64 (.f64 #s(literal 2 binary64) n) (PI.f64)))) (sqrt.f64 (/.f64 #s(literal 1 binary64) k))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (/.f64 (sqrt.f64 #s(literal 2 binary64)) (sqrt.f64 (/.f64 k (*.f64 (PI.f64) n)))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (/.f64 (sqrt.f64 (*.f64 (PI.f64) #s(literal 2 binary64))) (sqrt.f64 (/.f64 k n))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (.f64 (neg.f64 (sqrt.f64 (.f64 (*.f64 #s(literal 2 binary64) n) (PI.f64)))) (/.f64 #s(literal -1 binary64) (sqrt.f64 k))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (.f64 (sqrt.f64 #s(literal 2 binary64)) (.f64 (sqrt.f64 n) (sqrt.f64 (/.f64 (PI.f64) k)))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (.f64 (sqrt.f64 #s(literal 2 binary64)) (.f64 (sqrt.f64 (/.f64 (PI.f64) k)) (sqrt.f64 n))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (.f64 (sqrt.f64 #s(literal 2 binary64)) (/.f64 (sqrt.f64 (.f64 (PI.f64) n)) (sqrt.f64 k))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (.f64 (sqrt.f64 (.f64 (PI.f64) #s(literal 2 binary64))) (/.f64 (sqrt.f64 n) (sqrt.f64 k))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (.f64 (.f64 (sqrt.f64 (PI.f64)) (sqrt.f64 #s(literal 2 binary64))) (sqrt.f64 (/.f64 n k))))
(.f64 (sqrt.f64 n) #s(approx (sqrt (/ ( 2 (PI)) (* (pow (* (* 2 n) (PI)) k) k))) (*.f64 (sqrt.f64 (/.f64 (PI.f64) k)) (sqrt.f64 #s(literal 2 binary64)))))
(/.f64 #s(approx (pow (* (* 2 n) (PI)) (+ (* -1/2 k) 1/2)) (.f64 (sqrt.f64 (.f64 (PI.f64) n)) (sqrt.f64 #s(literal 2 binary64)))) (sqrt.f64 k))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (.f64 (sqrt.f64 (.f64 (PI.f64) #s(literal 2 binary64))) (/.f64 #s(literal 1 binary64) (sqrt.f64 (/.f64 k n)))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (/.f64 #s(literal 1 binary64) (/.f64 (sqrt.f64 k) #s(approx (pow (* (* 2 n) (PI)) (+ (* k -1/2) 1/2)) (sqrt.f64 (.f64 (.f64 #s(literal 2 binary64) n) (PI.f64)))))))
(/.f64 #s(literal 1 binary64) #s(approx (* (pow (* (* 2 n) (PI)) (+ (* 1/2 k) -1/2)) (sqrt k)) (.f64 (sqrt.f64 #s(literal 1/2 binary64)) (sqrt.f64 (/.f64 k (.f64 (PI.f64) n))))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt.f64 (.f64 (.f64 (sqrt.f64 (PI.f64)) (*.f64 (sqrt.f64 (PI.f64)) (/.f64 n k))) #s(literal 2 binary64))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt.f64 (.f64 (/.f64 (.f64 (*.f64 n (sqrt.f64 (PI.f64))) (sqrt.f64 (PI.f64))) k) #s(literal 2 binary64))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (.f64 #s(approx (pow ( (* 2 n) (PI)) (+ (* k -1/2) 1/2)) (.f64 (sqrt.f64 (.f64 #s(literal 2 binary64) n)) (sqrt.f64 (PI.f64)))) (sqrt.f64 (/.f64 #s(literal 1 binary64) k))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (.f64 #s(approx (pow ( (* 2 n) (PI)) (+ (* k -1/2) 1/2)) (.f64 (sqrt.f64 (.f64 (PI.f64) #s(literal 2 binary64))) (sqrt.f64 n))) (sqrt.f64 (/.f64 #s(literal 1 binary64) k))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (.f64 #s(approx (pow ( (* 2 n) (PI)) (+ (* k -1/2) 1/2)) (.f64 (sqrt.f64 (.f64 (PI.f64) n)) (sqrt.f64 #s(literal 2 binary64)))) (sqrt.f64 (/.f64 #s(literal 1 binary64) k))))
(.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) #s(approx (pow ( (* 2 (PI)) n) (/ (- 1 k) 2)) (.f64 (sqrt.f64 (.f64 (PI.f64) n)) (sqrt.f64 #s(literal 2 binary64)))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (/.f64 #s(literal 1 binary64) (/.f64 (sqrt.f64 (/.f64 k (*.f64 (PI.f64) n))) (sqrt.f64 #s(literal 2 binary64)))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (/.f64 (sqrt.f64 #s(literal 2 binary64)) (/.f64 #s(literal 1 binary64) (sqrt.f64 (/.f64 (*.f64 (PI.f64) n) k)))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (.f64 (/.f64 (sqrt.f64 #s(literal 2 binary64)) (sqrt.f64 k)) (/.f64 (sqrt.f64 (.f64 (PI.f64) n)) #s(literal 1 binary64))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (.f64 (/.f64 (sqrt.f64 (.f64 n #s(literal 2 binary64))) (sqrt.f64 k)) (/.f64 (sqrt.f64 (PI.f64)) #s(literal 1 binary64))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (/.f64 (sqrt.f64 #s(literal 2 binary64)) (/.f64 (sqrt.f64 (/.f64 k (PI.f64))) (sqrt.f64 n))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (.f64 #s(approx (pow ( (* 2 n) (PI)) (+ (* k -1/2) 1/2)) (.f64 (.f64 (sqrt.f64 (PI.f64)) (sqrt.f64 #s(literal 2 binary64))) (sqrt.f64 n))) (sqrt.f64 (/.f64 #s(literal 1 binary64) k))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (.f64 (sqrt.f64 #s(literal 2 binary64)) (sqrt.f64 (/.f64 (.f64 (*.f64 (sqrt.f64 (PI.f64)) (sqrt.f64 (PI.f64))) n) k))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (/.f64 (sqrt.f64 #s(literal 2 binary64)) (.f64 (neg.f64 (sqrt.f64 k)) (/.f64 #s(literal 1 binary64) (neg.f64 (sqrt.f64 (.f64 (PI.f64) n)))))))
(/.f64 #s(literal 1 binary64) (.f64 #s(approx (pow ( (* 2 n) (PI)) (+ (* 1/2 k) -1/2)) (.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (.f64 (PI.f64) n))) (sqrt.f64 #s(literal 1/2 binary64)))) (sqrt.f64 k)))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (.f64 (sqrt.f64 #s(literal 2 binary64)) (/.f64 (sqrt.f64 (.f64 (*.f64 (sqrt.f64 (PI.f64)) (sqrt.f64 (PI.f64))) n)) (sqrt.f64 k))))
(.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) (/.f64 #s(literal 1 binary64) #s(approx (pow (sqrt ( n (* (PI) 2))) (- k 1)) (/.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (*.f64 (PI.f64) n))) (sqrt.f64 #s(literal 2 binary64))))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (.f64 (sqrt.f64 (.f64 (*.f64 #s(literal 2 binary64) n) (PI.f64))) (pow.f64 k #s(literal -1/2 binary64))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (.f64 (sqrt.f64 #s(literal 2 binary64)) (sqrt.f64 (.f64 (pow.f64 k #s(literal -1 binary64)) (*.f64 (PI.f64) n)))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (.f64 (sqrt.f64 (.f64 (PI.f64) n)) (*.f64 (pow.f64 k #s(literal -1/2 binary64)) (sqrt.f64 #s(literal 2 binary64)))))
(.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) (pow.f64 (.f64 (*.f64 #s(literal 2 binary64) (PI.f64)) n) #s(approx (/ (- 1 k) 2) #s(literal 1/2 binary64))))
(/.f64 (pow.f64 (.f64 n (.f64 (PI.f64) #s(literal 2 binary64))) (fma.f64 #s(literal 1/2 binary64) k #s(literal 1/2 binary64))) (sqrt.f64 k))
(/.f64 (pow.f64 (.f64 (.f64 #s(literal 2 binary64) n) (PI.f64)) (fma.f64 #s(literal -1/2 binary64) k #s(literal 1/2 binary64))) (sqrt.f64 k))
(.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) (pow.f64 (.f64 (.f64 #s(literal 2 binary64) (PI.f64)) n) #s(approx (/ (- 1 k) 2) (.f64 k #s(literal -1/2 binary64)))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (.f64 (pow.f64 (.f64 (*.f64 #s(literal 2 binary64) n) (PI.f64)) (fma.f64 k #s(literal -1/2 binary64) #s(literal 1/2 binary64))) (sqrt.f64 (/.f64 #s(literal 1 binary64) k))))
(.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) (pow.f64 (.f64 (*.f64 #s(literal 2 binary64) (PI.f64)) n) (fma.f64 k #s(literal -1/2 binary64) #s(literal 1/2 binary64))))
(/.f64 #s(literal 1 binary64) (.f64 (pow.f64 (.f64 (*.f64 #s(literal 2 binary64) n) (PI.f64)) (fma.f64 #s(literal 1/2 binary64) k #s(literal -1/2 binary64))) (sqrt.f64 k)))
(sqrt.f64 (/.f64 (.f64 (.f64 #s(literal 2 binary64) n) (PI.f64)) (.f64 (pow.f64 (.f64 (*.f64 #s(literal 2 binary64) n) (PI.f64)) k) k)))
(/.f64 #s(literal 1 binary64) (/.f64 (sqrt.f64 k) (pow.f64 (.f64 n (.f64 (PI.f64) #s(literal 2 binary64))) (fma.f64 #s(literal 1/2 binary64) k #s(literal 1/2 binary64)))))
(.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) (sqrt.f64 (pow.f64 (.f64 n (*.f64 (PI.f64) #s(literal 2 binary64))) (-.f64 #s(literal 1 binary64) k))))
(.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) (pow.f64 (.f64 (*.f64 #s(literal 2 binary64) (PI.f64)) n) (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 2 binary64))))
(/.f64 (/.f64 #s(literal -1 binary64) (sqrt.f64 k)) (neg.f64 (pow.f64 (.f64 (.f64 #s(literal 2 binary64) n) (PI.f64)) (fma.f64 #s(literal 1/2 binary64) k #s(literal -1/2 binary64)))))
(sqrt.f64 (/.f64 (.f64 (/.f64 (.f64 (PI.f64) n) k) #s(literal 2 binary64)) (pow.f64 (.f64 (.f64 #s(literal 2 binary64) n) (PI.f64)) k)))
(.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) (/.f64 #s(literal 1 binary64) (pow.f64 (.f64 n (.f64 (PI.f64) #s(literal 2 binary64))) (.f64 #s(literal -1/2 binary64) (-.f64 #s(literal 1 binary64) k)))))
(.f64 (sqrt.f64 n) (sqrt.f64 (/.f64 (.f64 #s(literal 2 binary64) (PI.f64)) (.f64 (pow.f64 (.f64 (*.f64 #s(literal 2 binary64) n) (PI.f64)) k) k))))
(.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) (/.f64 #s(literal 1 binary64) (pow.f64 (sqrt.f64 (.f64 n (*.f64 (PI.f64) #s(literal 2 binary64)))) (-.f64 k #s(literal 1 binary64)))))
(.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) (.f64 (pow.f64 (.f64 n (.f64 (PI.f64) #s(literal 2 binary64))) (.f64 k #s(literal -1/2 binary64))) (sqrt.f64 (.f64 n (*.f64 (PI.f64) #s(literal 2 binary64))))))
(.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) (pow.f64 (.f64 (.f64 (.f64 n #s(literal 2 binary64)) (sqrt.f64 (PI.f64))) (sqrt.f64 (PI.f64))) (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 2 binary64))))
(.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) #s(approx (pow ( (* 2 (PI)) n) (/ (- 1 k) 2)) (.f64 (fma.f64 (log.f64 (.f64 (.f64 #s(literal 2 binary64) n) (PI.f64))) (.f64 k #s(literal -1/2 binary64)) #s(literal 1 binary64)) (.f64 (sqrt.f64 (.f64 (PI.f64) n)) (sqrt.f64 #s(literal 2 binary64))))))
(.f64 (pow.f64 #s(literal 2 binary64) (fma.f64 #s(literal 1/2 binary64) k #s(literal 1/2 binary64))) (/.f64 (pow.f64 (.f64 n (PI.f64)) (fma.f64 #s(literal 1/2 binary64) k #s(literal 1/2 binary64))) (sqrt.f64 k)))
(.f64 (/.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (pow.f64 k #s(literal -1/2 binary64)))) (pow.f64 (.f64 (*.f64 #s(literal 2 binary64) (PI.f64)) n) (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 2 binary64))))
(.f64 (/.f64 (pow.f64 #s(literal 2 binary64) (fma.f64 #s(literal 1/2 binary64) k #s(literal 1/2 binary64))) (sqrt.f64 k)) (/.f64 (pow.f64 (.f64 n (PI.f64)) (fma.f64 #s(literal 1/2 binary64) k #s(literal 1/2 binary64))) #s(literal 1 binary64)))

Outputs
(.f64 (sqrt.f64 n) (sqrt.f64 (/.f64 (.f64 #s(literal 2 binary64) (PI.f64)) (.f64 (pow.f64 (.f64 (*.f64 #s(literal 2 binary64) n) (PI.f64)) k) k))))

Calls

4 calls:

22.0ms	k
22.0ms	(.f64 (.f64 #s(literal 2 binary64) (PI.f64)) n)
22.0ms	n
19.0ms	(.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) (pow.f64 (.f64 (*.f64 #s(literal 2 binary64) (PI.f64)) n) (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 2 binary64))))

Results

Accuracy	Segments	Branch
99.7%	1	`k`
99.7%	1	`n`
99.7%	1	`(.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) (pow.f64 (.f64 (*.f64 #s(literal 2 binary64) (PI.f64)) n) (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 2 binary64))))`
99.7%	1	`(.f64 (.f64 #s(literal 2 binary64) (PI.f64)) n)`

Compiler

Compiled 23 to 23 computations (0% saved)

regimes84.0ms (0.9%)

Memory

-13.2MiB live, 144.7MiB allocated

Counts

68 → 1

Calls

Call 1

Inputs
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt.f64 (.f64 (.f64 #s(literal 2 binary64) (/.f64 (PI.f64) k)) n)))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt.f64 (.f64 (.f64 (PI.f64) #s(literal 2 binary64)) (/.f64 n k))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt.f64 (.f64 (.f64 (PI.f64) (/.f64 #s(literal 2 binary64) k)) n)))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt.f64 (.f64 (/.f64 #s(literal 2 binary64) k) (.f64 (PI.f64) n))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt.f64 (.f64 (/.f64 n k) (.f64 (PI.f64) #s(literal 2 binary64)))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt.f64 (.f64 (/.f64 (.f64 (PI.f64) n) k) #s(literal 2 binary64))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt.f64 (*.f64 (/.f64 #s(literal 2 binary64) (/.f64 k (PI.f64))) n)))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt.f64 (*.f64 (/.f64 n (/.f64 k (PI.f64))) #s(literal 2 binary64))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt.f64 (/.f64 #s(literal 2 binary64) (/.f64 k (*.f64 (PI.f64) n)))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt.f64 (/.f64 (*.f64 (PI.f64) #s(literal 2 binary64)) (/.f64 k n))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (.f64 (sqrt.f64 #s(literal 2 binary64)) (sqrt.f64 (/.f64 (.f64 (PI.f64) n) k))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (.f64 (sqrt.f64 n) (sqrt.f64 (/.f64 (.f64 #s(literal 2 binary64) (PI.f64)) k))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (.f64 (sqrt.f64 (PI.f64)) (sqrt.f64 (.f64 (/.f64 n k) #s(literal 2 binary64)))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (.f64 (sqrt.f64 (.f64 #s(literal 2 binary64) (PI.f64))) (sqrt.f64 (/.f64 n k))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (.f64 (sqrt.f64 (.f64 (PI.f64) #s(literal 2 binary64))) (sqrt.f64 (/.f64 n k))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (.f64 (sqrt.f64 (/.f64 #s(literal 2 binary64) k)) (sqrt.f64 (.f64 (PI.f64) n))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (.f64 (sqrt.f64 (/.f64 (PI.f64) k)) (sqrt.f64 (.f64 n #s(literal 2 binary64)))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (/.f64 (sqrt.f64 (.f64 (.f64 #s(literal 2 binary64) n) (PI.f64))) (sqrt.f64 k)))
(.f64 (sqrt.f64 n) (sqrt.f64 #s(approx (/ ( 2 (PI)) (* (pow (* (* 2 n) (PI)) k) k)) (*.f64 (/.f64 (PI.f64) k) #s(literal 2 binary64)))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt.f64 (.f64 (/.f64 (.f64 n #s(literal 2 binary64)) k) (/.f64 (PI.f64) #s(literal 1 binary64)))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (.f64 #s(approx (pow ( (* 2 n) (PI)) (+ (* k -1/2) 1/2)) (sqrt.f64 (.f64 (.f64 #s(literal 2 binary64) n) (PI.f64)))) (sqrt.f64 (/.f64 #s(literal 1 binary64) k))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (/.f64 (sqrt.f64 #s(literal 2 binary64)) (sqrt.f64 (/.f64 k (*.f64 (PI.f64) n)))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (/.f64 (sqrt.f64 (*.f64 (PI.f64) #s(literal 2 binary64))) (sqrt.f64 (/.f64 k n))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (.f64 (neg.f64 (sqrt.f64 (.f64 (*.f64 #s(literal 2 binary64) n) (PI.f64)))) (/.f64 #s(literal -1 binary64) (sqrt.f64 k))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (.f64 (sqrt.f64 #s(literal 2 binary64)) (.f64 (sqrt.f64 n) (sqrt.f64 (/.f64 (PI.f64) k)))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (.f64 (sqrt.f64 #s(literal 2 binary64)) (.f64 (sqrt.f64 (/.f64 (PI.f64) k)) (sqrt.f64 n))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (.f64 (sqrt.f64 #s(literal 2 binary64)) (/.f64 (sqrt.f64 (.f64 (PI.f64) n)) (sqrt.f64 k))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (.f64 (sqrt.f64 (.f64 (PI.f64) #s(literal 2 binary64))) (/.f64 (sqrt.f64 n) (sqrt.f64 k))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (.f64 (.f64 (sqrt.f64 (PI.f64)) (sqrt.f64 #s(literal 2 binary64))) (sqrt.f64 (/.f64 n k))))
(.f64 (sqrt.f64 n) #s(approx (sqrt (/ ( 2 (PI)) (* (pow (* (* 2 n) (PI)) k) k))) (*.f64 (sqrt.f64 (/.f64 (PI.f64) k)) (sqrt.f64 #s(literal 2 binary64)))))
(/.f64 #s(approx (pow (* (* 2 n) (PI)) (+ (* -1/2 k) 1/2)) (.f64 (sqrt.f64 (.f64 (PI.f64) n)) (sqrt.f64 #s(literal 2 binary64)))) (sqrt.f64 k))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (.f64 (sqrt.f64 (.f64 (PI.f64) #s(literal 2 binary64))) (/.f64 #s(literal 1 binary64) (sqrt.f64 (/.f64 k n)))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (/.f64 #s(literal 1 binary64) (/.f64 (sqrt.f64 k) #s(approx (pow (* (* 2 n) (PI)) (+ (* k -1/2) 1/2)) (sqrt.f64 (.f64 (.f64 #s(literal 2 binary64) n) (PI.f64)))))))
(/.f64 #s(literal 1 binary64) #s(approx (* (pow (* (* 2 n) (PI)) (+ (* 1/2 k) -1/2)) (sqrt k)) (.f64 (sqrt.f64 #s(literal 1/2 binary64)) (sqrt.f64 (/.f64 k (.f64 (PI.f64) n))))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt.f64 (.f64 (.f64 (sqrt.f64 (PI.f64)) (*.f64 (sqrt.f64 (PI.f64)) (/.f64 n k))) #s(literal 2 binary64))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt.f64 (.f64 (/.f64 (.f64 (*.f64 n (sqrt.f64 (PI.f64))) (sqrt.f64 (PI.f64))) k) #s(literal 2 binary64))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (.f64 #s(approx (pow ( (* 2 n) (PI)) (+ (* k -1/2) 1/2)) (.f64 (sqrt.f64 (.f64 #s(literal 2 binary64) n)) (sqrt.f64 (PI.f64)))) (sqrt.f64 (/.f64 #s(literal 1 binary64) k))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (.f64 #s(approx (pow ( (* 2 n) (PI)) (+ (* k -1/2) 1/2)) (.f64 (sqrt.f64 (.f64 (PI.f64) #s(literal 2 binary64))) (sqrt.f64 n))) (sqrt.f64 (/.f64 #s(literal 1 binary64) k))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (.f64 #s(approx (pow ( (* 2 n) (PI)) (+ (* k -1/2) 1/2)) (.f64 (sqrt.f64 (.f64 (PI.f64) n)) (sqrt.f64 #s(literal 2 binary64)))) (sqrt.f64 (/.f64 #s(literal 1 binary64) k))))
(.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) #s(approx (pow ( (* 2 (PI)) n) (/ (- 1 k) 2)) (.f64 (sqrt.f64 (.f64 (PI.f64) n)) (sqrt.f64 #s(literal 2 binary64)))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (/.f64 #s(literal 1 binary64) (/.f64 (sqrt.f64 (/.f64 k (*.f64 (PI.f64) n))) (sqrt.f64 #s(literal 2 binary64)))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (/.f64 (sqrt.f64 #s(literal 2 binary64)) (/.f64 #s(literal 1 binary64) (sqrt.f64 (/.f64 (*.f64 (PI.f64) n) k)))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (.f64 (/.f64 (sqrt.f64 #s(literal 2 binary64)) (sqrt.f64 k)) (/.f64 (sqrt.f64 (.f64 (PI.f64) n)) #s(literal 1 binary64))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (.f64 (/.f64 (sqrt.f64 (.f64 n #s(literal 2 binary64))) (sqrt.f64 k)) (/.f64 (sqrt.f64 (PI.f64)) #s(literal 1 binary64))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (/.f64 (sqrt.f64 #s(literal 2 binary64)) (/.f64 (sqrt.f64 (/.f64 k (PI.f64))) (sqrt.f64 n))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (.f64 #s(approx (pow ( (* 2 n) (PI)) (+ (* k -1/2) 1/2)) (.f64 (.f64 (sqrt.f64 (PI.f64)) (sqrt.f64 #s(literal 2 binary64))) (sqrt.f64 n))) (sqrt.f64 (/.f64 #s(literal 1 binary64) k))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (.f64 (sqrt.f64 #s(literal 2 binary64)) (sqrt.f64 (/.f64 (.f64 (*.f64 (sqrt.f64 (PI.f64)) (sqrt.f64 (PI.f64))) n) k))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (/.f64 (sqrt.f64 #s(literal 2 binary64)) (.f64 (neg.f64 (sqrt.f64 k)) (/.f64 #s(literal 1 binary64) (neg.f64 (sqrt.f64 (.f64 (PI.f64) n)))))))
(/.f64 #s(literal 1 binary64) (.f64 #s(approx (pow ( (* 2 n) (PI)) (+ (* 1/2 k) -1/2)) (.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (.f64 (PI.f64) n))) (sqrt.f64 #s(literal 1/2 binary64)))) (sqrt.f64 k)))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (.f64 (sqrt.f64 #s(literal 2 binary64)) (/.f64 (sqrt.f64 (.f64 (*.f64 (sqrt.f64 (PI.f64)) (sqrt.f64 (PI.f64))) n)) (sqrt.f64 k))))
(.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) (/.f64 #s(literal 1 binary64) #s(approx (pow (sqrt ( n (* (PI) 2))) (- k 1)) (/.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (*.f64 (PI.f64) n))) (sqrt.f64 #s(literal 2 binary64))))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (.f64 (sqrt.f64 (.f64 (*.f64 #s(literal 2 binary64) n) (PI.f64))) (pow.f64 k #s(literal -1/2 binary64))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (.f64 (sqrt.f64 #s(literal 2 binary64)) (sqrt.f64 (.f64 (pow.f64 k #s(literal -1 binary64)) (*.f64 (PI.f64) n)))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (.f64 (sqrt.f64 (.f64 (PI.f64) n)) (*.f64 (pow.f64 k #s(literal -1/2 binary64)) (sqrt.f64 #s(literal 2 binary64)))))
(.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) (pow.f64 (.f64 (*.f64 #s(literal 2 binary64) (PI.f64)) n) #s(approx (/ (- 1 k) 2) #s(literal 1/2 binary64))))
(/.f64 (pow.f64 (.f64 n (.f64 (PI.f64) #s(literal 2 binary64))) (fma.f64 #s(literal 1/2 binary64) k #s(literal 1/2 binary64))) (sqrt.f64 k))
(/.f64 (pow.f64 (.f64 (.f64 #s(literal 2 binary64) n) (PI.f64)) (fma.f64 #s(literal -1/2 binary64) k #s(literal 1/2 binary64))) (sqrt.f64 k))
(.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) (pow.f64 (.f64 (.f64 #s(literal 2 binary64) (PI.f64)) n) #s(approx (/ (- 1 k) 2) (.f64 k #s(literal -1/2 binary64)))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (.f64 (pow.f64 (.f64 (*.f64 #s(literal 2 binary64) n) (PI.f64)) (fma.f64 k #s(literal -1/2 binary64) #s(literal 1/2 binary64))) (sqrt.f64 (/.f64 #s(literal 1 binary64) k))))
(.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) (pow.f64 (.f64 (*.f64 #s(literal 2 binary64) (PI.f64)) n) (fma.f64 k #s(literal -1/2 binary64) #s(literal 1/2 binary64))))
(/.f64 #s(literal 1 binary64) (.f64 (pow.f64 (.f64 (*.f64 #s(literal 2 binary64) n) (PI.f64)) (fma.f64 #s(literal 1/2 binary64) k #s(literal -1/2 binary64))) (sqrt.f64 k)))
(sqrt.f64 (/.f64 (.f64 (.f64 #s(literal 2 binary64) n) (PI.f64)) (.f64 (pow.f64 (.f64 (*.f64 #s(literal 2 binary64) n) (PI.f64)) k) k)))
(/.f64 #s(literal 1 binary64) (/.f64 (sqrt.f64 k) (pow.f64 (.f64 n (.f64 (PI.f64) #s(literal 2 binary64))) (fma.f64 #s(literal 1/2 binary64) k #s(literal 1/2 binary64)))))
(.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) (sqrt.f64 (pow.f64 (.f64 n (*.f64 (PI.f64) #s(literal 2 binary64))) (-.f64 #s(literal 1 binary64) k))))
(.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) (pow.f64 (.f64 (*.f64 #s(literal 2 binary64) (PI.f64)) n) (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 2 binary64))))
(/.f64 (/.f64 #s(literal -1 binary64) (sqrt.f64 k)) (neg.f64 (pow.f64 (.f64 (.f64 #s(literal 2 binary64) n) (PI.f64)) (fma.f64 #s(literal 1/2 binary64) k #s(literal -1/2 binary64)))))
(sqrt.f64 (/.f64 (.f64 (/.f64 (.f64 (PI.f64) n) k) #s(literal 2 binary64)) (pow.f64 (.f64 (.f64 #s(literal 2 binary64) n) (PI.f64)) k)))
(.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) (/.f64 #s(literal 1 binary64) (pow.f64 (.f64 n (.f64 (PI.f64) #s(literal 2 binary64))) (.f64 #s(literal -1/2 binary64) (-.f64 #s(literal 1 binary64) k)))))

Outputs
(/.f64 (pow.f64 (.f64 (.f64 #s(literal 2 binary64) n) (PI.f64)) (fma.f64 #s(literal -1/2 binary64) k #s(literal 1/2 binary64))) (sqrt.f64 k))

Calls

4 calls:

22.0ms	k
21.0ms	n
20.0ms	(.f64 (.f64 #s(literal 2 binary64) (PI.f64)) n)
18.0ms	(.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) (pow.f64 (.f64 (*.f64 #s(literal 2 binary64) (PI.f64)) n) (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 2 binary64))))

Results

Accuracy	Segments	Branch
99.5%	1	`k`
99.5%	1	`n`
99.5%	1	`(.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) (pow.f64 (.f64 (*.f64 #s(literal 2 binary64) (PI.f64)) n) (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 2 binary64))))`
99.5%	1	`(.f64 (.f64 #s(literal 2 binary64) (PI.f64)) n)`

Compiler

Compiled 23 to 23 computations (0% saved)

regimes100.0ms (1.1%)

Memory

7.7MiB live, 121.4MiB allocated

Counts

56 → 1

Calls

Call 1

Inputs
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt.f64 (.f64 (.f64 #s(literal 2 binary64) (/.f64 (PI.f64) k)) n)))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt.f64 (.f64 (.f64 (PI.f64) #s(literal 2 binary64)) (/.f64 n k))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt.f64 (.f64 (.f64 (PI.f64) (/.f64 #s(literal 2 binary64) k)) n)))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt.f64 (.f64 (/.f64 #s(literal 2 binary64) k) (.f64 (PI.f64) n))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt.f64 (.f64 (/.f64 n k) (.f64 (PI.f64) #s(literal 2 binary64)))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt.f64 (.f64 (/.f64 (.f64 (PI.f64) n) k) #s(literal 2 binary64))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt.f64 (*.f64 (/.f64 #s(literal 2 binary64) (/.f64 k (PI.f64))) n)))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt.f64 (*.f64 (/.f64 n (/.f64 k (PI.f64))) #s(literal 2 binary64))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt.f64 (/.f64 #s(literal 2 binary64) (/.f64 k (*.f64 (PI.f64) n)))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt.f64 (/.f64 (*.f64 (PI.f64) #s(literal 2 binary64)) (/.f64 k n))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (.f64 (sqrt.f64 #s(literal 2 binary64)) (sqrt.f64 (/.f64 (.f64 (PI.f64) n) k))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (.f64 (sqrt.f64 n) (sqrt.f64 (/.f64 (.f64 #s(literal 2 binary64) (PI.f64)) k))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (.f64 (sqrt.f64 (PI.f64)) (sqrt.f64 (.f64 (/.f64 n k) #s(literal 2 binary64)))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (.f64 (sqrt.f64 (.f64 #s(literal 2 binary64) (PI.f64))) (sqrt.f64 (/.f64 n k))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (.f64 (sqrt.f64 (.f64 (PI.f64) #s(literal 2 binary64))) (sqrt.f64 (/.f64 n k))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (.f64 (sqrt.f64 (/.f64 #s(literal 2 binary64) k)) (sqrt.f64 (.f64 (PI.f64) n))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (.f64 (sqrt.f64 (/.f64 (PI.f64) k)) (sqrt.f64 (.f64 n #s(literal 2 binary64)))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (/.f64 (sqrt.f64 (.f64 (.f64 #s(literal 2 binary64) n) (PI.f64))) (sqrt.f64 k)))
(.f64 (sqrt.f64 n) (sqrt.f64 #s(approx (/ ( 2 (PI)) (* (pow (* (* 2 n) (PI)) k) k)) (*.f64 (/.f64 (PI.f64) k) #s(literal 2 binary64)))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt.f64 (.f64 (/.f64 (.f64 n #s(literal 2 binary64)) k) (/.f64 (PI.f64) #s(literal 1 binary64)))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (.f64 #s(approx (pow ( (* 2 n) (PI)) (+ (* k -1/2) 1/2)) (sqrt.f64 (.f64 (.f64 #s(literal 2 binary64) n) (PI.f64)))) (sqrt.f64 (/.f64 #s(literal 1 binary64) k))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (/.f64 (sqrt.f64 #s(literal 2 binary64)) (sqrt.f64 (/.f64 k (*.f64 (PI.f64) n)))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (/.f64 (sqrt.f64 (*.f64 (PI.f64) #s(literal 2 binary64))) (sqrt.f64 (/.f64 k n))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (.f64 (neg.f64 (sqrt.f64 (.f64 (*.f64 #s(literal 2 binary64) n) (PI.f64)))) (/.f64 #s(literal -1 binary64) (sqrt.f64 k))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (.f64 (sqrt.f64 #s(literal 2 binary64)) (.f64 (sqrt.f64 n) (sqrt.f64 (/.f64 (PI.f64) k)))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (.f64 (sqrt.f64 #s(literal 2 binary64)) (.f64 (sqrt.f64 (/.f64 (PI.f64) k)) (sqrt.f64 n))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (.f64 (sqrt.f64 #s(literal 2 binary64)) (/.f64 (sqrt.f64 (.f64 (PI.f64) n)) (sqrt.f64 k))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (.f64 (sqrt.f64 (.f64 (PI.f64) #s(literal 2 binary64))) (/.f64 (sqrt.f64 n) (sqrt.f64 k))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (.f64 (.f64 (sqrt.f64 (PI.f64)) (sqrt.f64 #s(literal 2 binary64))) (sqrt.f64 (/.f64 n k))))
(.f64 (sqrt.f64 n) #s(approx (sqrt (/ ( 2 (PI)) (* (pow (* (* 2 n) (PI)) k) k))) (*.f64 (sqrt.f64 (/.f64 (PI.f64) k)) (sqrt.f64 #s(literal 2 binary64)))))
(/.f64 #s(approx (pow (* (* 2 n) (PI)) (+ (* -1/2 k) 1/2)) (.f64 (sqrt.f64 (.f64 (PI.f64) n)) (sqrt.f64 #s(literal 2 binary64)))) (sqrt.f64 k))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (.f64 (sqrt.f64 (.f64 (PI.f64) #s(literal 2 binary64))) (/.f64 #s(literal 1 binary64) (sqrt.f64 (/.f64 k n)))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (/.f64 #s(literal 1 binary64) (/.f64 (sqrt.f64 k) #s(approx (pow (* (* 2 n) (PI)) (+ (* k -1/2) 1/2)) (sqrt.f64 (.f64 (.f64 #s(literal 2 binary64) n) (PI.f64)))))))
(/.f64 #s(literal 1 binary64) #s(approx (* (pow (* (* 2 n) (PI)) (+ (* 1/2 k) -1/2)) (sqrt k)) (.f64 (sqrt.f64 #s(literal 1/2 binary64)) (sqrt.f64 (/.f64 k (.f64 (PI.f64) n))))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt.f64 (.f64 (.f64 (sqrt.f64 (PI.f64)) (*.f64 (sqrt.f64 (PI.f64)) (/.f64 n k))) #s(literal 2 binary64))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt.f64 (.f64 (/.f64 (.f64 (*.f64 n (sqrt.f64 (PI.f64))) (sqrt.f64 (PI.f64))) k) #s(literal 2 binary64))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (.f64 #s(approx (pow ( (* 2 n) (PI)) (+ (* k -1/2) 1/2)) (.f64 (sqrt.f64 (.f64 #s(literal 2 binary64) n)) (sqrt.f64 (PI.f64)))) (sqrt.f64 (/.f64 #s(literal 1 binary64) k))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (.f64 #s(approx (pow ( (* 2 n) (PI)) (+ (* k -1/2) 1/2)) (.f64 (sqrt.f64 (.f64 (PI.f64) #s(literal 2 binary64))) (sqrt.f64 n))) (sqrt.f64 (/.f64 #s(literal 1 binary64) k))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (.f64 #s(approx (pow ( (* 2 n) (PI)) (+ (* k -1/2) 1/2)) (.f64 (sqrt.f64 (.f64 (PI.f64) n)) (sqrt.f64 #s(literal 2 binary64)))) (sqrt.f64 (/.f64 #s(literal 1 binary64) k))))
(.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) #s(approx (pow ( (* 2 (PI)) n) (/ (- 1 k) 2)) (.f64 (sqrt.f64 (.f64 (PI.f64) n)) (sqrt.f64 #s(literal 2 binary64)))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (/.f64 #s(literal 1 binary64) (/.f64 (sqrt.f64 (/.f64 k (*.f64 (PI.f64) n))) (sqrt.f64 #s(literal 2 binary64)))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (/.f64 (sqrt.f64 #s(literal 2 binary64)) (/.f64 #s(literal 1 binary64) (sqrt.f64 (/.f64 (*.f64 (PI.f64) n) k)))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (.f64 (/.f64 (sqrt.f64 #s(literal 2 binary64)) (sqrt.f64 k)) (/.f64 (sqrt.f64 (.f64 (PI.f64) n)) #s(literal 1 binary64))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (.f64 (/.f64 (sqrt.f64 (.f64 n #s(literal 2 binary64))) (sqrt.f64 k)) (/.f64 (sqrt.f64 (PI.f64)) #s(literal 1 binary64))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (/.f64 (sqrt.f64 #s(literal 2 binary64)) (/.f64 (sqrt.f64 (/.f64 k (PI.f64))) (sqrt.f64 n))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (.f64 #s(approx (pow ( (* 2 n) (PI)) (+ (* k -1/2) 1/2)) (.f64 (.f64 (sqrt.f64 (PI.f64)) (sqrt.f64 #s(literal 2 binary64))) (sqrt.f64 n))) (sqrt.f64 (/.f64 #s(literal 1 binary64) k))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (.f64 (sqrt.f64 #s(literal 2 binary64)) (sqrt.f64 (/.f64 (.f64 (*.f64 (sqrt.f64 (PI.f64)) (sqrt.f64 (PI.f64))) n) k))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (/.f64 (sqrt.f64 #s(literal 2 binary64)) (.f64 (neg.f64 (sqrt.f64 k)) (/.f64 #s(literal 1 binary64) (neg.f64 (sqrt.f64 (.f64 (PI.f64) n)))))))
(/.f64 #s(literal 1 binary64) (.f64 #s(approx (pow ( (* 2 n) (PI)) (+ (* 1/2 k) -1/2)) (.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (.f64 (PI.f64) n))) (sqrt.f64 #s(literal 1/2 binary64)))) (sqrt.f64 k)))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (.f64 (sqrt.f64 #s(literal 2 binary64)) (/.f64 (sqrt.f64 (.f64 (*.f64 (sqrt.f64 (PI.f64)) (sqrt.f64 (PI.f64))) n)) (sqrt.f64 k))))
(.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) (/.f64 #s(literal 1 binary64) #s(approx (pow (sqrt ( n (* (PI) 2))) (- k 1)) (/.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (*.f64 (PI.f64) n))) (sqrt.f64 #s(literal 2 binary64))))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (.f64 (sqrt.f64 (.f64 (*.f64 #s(literal 2 binary64) n) (PI.f64))) (pow.f64 k #s(literal -1/2 binary64))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (.f64 (sqrt.f64 #s(literal 2 binary64)) (sqrt.f64 (.f64 (pow.f64 k #s(literal -1 binary64)) (*.f64 (PI.f64) n)))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (.f64 (sqrt.f64 (.f64 (PI.f64) n)) (*.f64 (pow.f64 k #s(literal -1/2 binary64)) (sqrt.f64 #s(literal 2 binary64)))))
(.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) (pow.f64 (.f64 (*.f64 #s(literal 2 binary64) (PI.f64)) n) #s(approx (/ (- 1 k) 2) #s(literal 1/2 binary64))))
(/.f64 (pow.f64 (.f64 n (.f64 (PI.f64) #s(literal 2 binary64))) (fma.f64 #s(literal 1/2 binary64) k #s(literal 1/2 binary64))) (sqrt.f64 k))

Outputs
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (/.f64 (sqrt.f64 (.f64 (.f64 #s(literal 2 binary64) n) (PI.f64))) (sqrt.f64 k)))

Calls

4 calls:

47.0ms	k
17.0ms	n
17.0ms	(.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) (pow.f64 (.f64 (*.f64 #s(literal 2 binary64) (PI.f64)) n) (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 2 binary64))))
16.0ms	(.f64 (.f64 #s(literal 2 binary64) (PI.f64)) n)

Results

Accuracy	Segments	Branch
50.3%	1	`k`
50.3%	1	`n`
50.3%	1	`(.f64 (.f64 #s(literal 2 binary64) (PI.f64)) n)`
50.3%	1	`(.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) (pow.f64 (.f64 (*.f64 #s(literal 2 binary64) (PI.f64)) n) (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 2 binary64))))`

Compiler

Compiled 23 to 23 computations (0% saved)

regimes48.0ms (0.5%)

Memory

1.0MiB live, 43.3MiB allocated

Counts

17 → 1

Calls

Call 1

Inputs
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt.f64 (.f64 (.f64 #s(literal 2 binary64) (/.f64 (PI.f64) k)) n)))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt.f64 (.f64 (.f64 (PI.f64) #s(literal 2 binary64)) (/.f64 n k))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt.f64 (.f64 (.f64 (PI.f64) (/.f64 #s(literal 2 binary64) k)) n)))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt.f64 (.f64 (/.f64 #s(literal 2 binary64) k) (.f64 (PI.f64) n))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt.f64 (.f64 (/.f64 n k) (.f64 (PI.f64) #s(literal 2 binary64)))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt.f64 (.f64 (/.f64 (.f64 (PI.f64) n) k) #s(literal 2 binary64))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt.f64 (*.f64 (/.f64 #s(literal 2 binary64) (/.f64 k (PI.f64))) n)))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt.f64 (*.f64 (/.f64 n (/.f64 k (PI.f64))) #s(literal 2 binary64))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt.f64 (/.f64 #s(literal 2 binary64) (/.f64 k (*.f64 (PI.f64) n)))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt.f64 (/.f64 (*.f64 (PI.f64) #s(literal 2 binary64)) (/.f64 k n))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (.f64 (sqrt.f64 #s(literal 2 binary64)) (sqrt.f64 (/.f64 (.f64 (PI.f64) n) k))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (.f64 (sqrt.f64 n) (sqrt.f64 (/.f64 (.f64 #s(literal 2 binary64) (PI.f64)) k))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (.f64 (sqrt.f64 (PI.f64)) (sqrt.f64 (.f64 (/.f64 n k) #s(literal 2 binary64)))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (.f64 (sqrt.f64 (.f64 #s(literal 2 binary64) (PI.f64))) (sqrt.f64 (/.f64 n k))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (.f64 (sqrt.f64 (.f64 (PI.f64) #s(literal 2 binary64))) (sqrt.f64 (/.f64 n k))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (.f64 (sqrt.f64 (/.f64 #s(literal 2 binary64) k)) (sqrt.f64 (.f64 (PI.f64) n))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (.f64 (sqrt.f64 (/.f64 (PI.f64) k)) (sqrt.f64 (.f64 n #s(literal 2 binary64)))))

Outputs
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (.f64 (sqrt.f64 n) (sqrt.f64 (/.f64 (.f64 #s(literal 2 binary64) (PI.f64)) k))))

Calls

4 calls:

30.0ms	n
6.0ms	(.f64 (.f64 #s(literal 2 binary64) (PI.f64)) n)
6.0ms	k
5.0ms	(.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) (pow.f64 (.f64 (*.f64 #s(literal 2 binary64) (PI.f64)) n) (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 2 binary64))))

Results

Accuracy	Segments	Branch
50.3%	1	`(.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) (pow.f64 (.f64 (*.f64 #s(literal 2 binary64) (PI.f64)) n) (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 2 binary64))))`
50.3%	1	`n`
50.3%	1	`(.f64 (.f64 #s(literal 2 binary64) (PI.f64)) n)`
50.3%	1	`k`

Compiler

Compiled 23 to 23 computations (0% saved)

regimes19.0ms (0.2%)

Memory

3.7MiB live, 40.4MiB allocated

Counts

11 → 1

Calls

Call 1

Inputs
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt.f64 (.f64 (.f64 #s(literal 2 binary64) (/.f64 (PI.f64) k)) n)))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt.f64 (.f64 (.f64 (PI.f64) #s(literal 2 binary64)) (/.f64 n k))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt.f64 (.f64 (.f64 (PI.f64) (/.f64 #s(literal 2 binary64) k)) n)))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt.f64 (.f64 (/.f64 #s(literal 2 binary64) k) (.f64 (PI.f64) n))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt.f64 (.f64 (/.f64 n k) (.f64 (PI.f64) #s(literal 2 binary64)))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt.f64 (.f64 (/.f64 (.f64 (PI.f64) n) k) #s(literal 2 binary64))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt.f64 (*.f64 (/.f64 #s(literal 2 binary64) (/.f64 k (PI.f64))) n)))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt.f64 (*.f64 (/.f64 n (/.f64 k (PI.f64))) #s(literal 2 binary64))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt.f64 (/.f64 #s(literal 2 binary64) (/.f64 k (*.f64 (PI.f64) n)))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt.f64 (/.f64 (*.f64 (PI.f64) #s(literal 2 binary64)) (/.f64 k n))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (.f64 (sqrt.f64 #s(literal 2 binary64)) (sqrt.f64 (/.f64 (.f64 (PI.f64) n) k))))

Outputs
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt.f64 (.f64 (/.f64 (.f64 (PI.f64) n) k) #s(literal 2 binary64))))

Calls

4 calls:

7.0ms	k
4.0ms	n
4.0ms	(.f64 (.f64 #s(literal 2 binary64) (PI.f64)) n)
4.0ms	(.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) (pow.f64 (.f64 (*.f64 #s(literal 2 binary64) (PI.f64)) n) (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 2 binary64))))

Results

Accuracy	Segments	Branch
37.5%	1	`(.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) (pow.f64 (.f64 (*.f64 #s(literal 2 binary64) (PI.f64)) n) (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 2 binary64))))`
37.5%	1	`k`
37.5%	1	`n`
37.5%	1	`(.f64 (.f64 #s(literal 2 binary64) (PI.f64)) n)`

Compiler

Compiled 23 to 23 computations (0% saved)

regimes12.0ms (0.1%)

Memory

-13.0MiB live, 24.4MiB allocated

Accuracy

Total -0.1b remaining (-0.2%)

Threshold costs -0.1b (-0.2%)

Counts

5 → 1

Calls

Call 1

Inputs
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt.f64 (.f64 (.f64 #s(literal 2 binary64) (/.f64 (PI.f64) k)) n)))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt.f64 (.f64 (.f64 (PI.f64) #s(literal 2 binary64)) (/.f64 n k))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt.f64 (.f64 (.f64 (PI.f64) (/.f64 #s(literal 2 binary64) k)) n)))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt.f64 (.f64 (/.f64 #s(literal 2 binary64) k) (.f64 (PI.f64) n))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt.f64 (.f64 (/.f64 n k) (.f64 (PI.f64) #s(literal 2 binary64)))))

Outputs
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt.f64 (.f64 (.f64 #s(literal 2 binary64) (/.f64 (PI.f64) k)) n)))

Calls

4 calls:

5.0ms	(.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) (pow.f64 (.f64 (*.f64 #s(literal 2 binary64) (PI.f64)) n) (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 2 binary64))))
2.0ms	(.f64 (.f64 #s(literal 2 binary64) (PI.f64)) n)
2.0ms	k
2.0ms	n

Results

Accuracy	Segments	Branch
37.5%	1	`(.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) (pow.f64 (.f64 (*.f64 #s(literal 2 binary64) (PI.f64)) n) (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 2 binary64))))`
37.5%	1	`n`
37.5%	1	`(.f64 (.f64 #s(literal 2 binary64) (PI.f64)) n)`
37.5%	1	`k`

Compiler

Compiled 23 to 23 computations (0% saved)

simplify23.0ms (0.2%)

Memory

13.6MiB live, 51.5MiB allocated

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	53	151
1	69	151

Stop Event

1×

saturated

Calls

Call 1

Inputs
(/.f64 (sqrt.f64 (.f64 n (.f64 (PI.f64) #s(literal 2 binary64)))) (.f64 (sqrt.f64 k) (pow.f64 (pow.f64 (.f64 n (*.f64 (PI.f64) #s(literal 2 binary64))) k) #s(literal 1/2 binary64))))
(.f64 (sqrt.f64 n) (sqrt.f64 (/.f64 (.f64 #s(literal 2 binary64) (PI.f64)) (.f64 (pow.f64 (.f64 (*.f64 #s(literal 2 binary64) n) (PI.f64)) k) k))))
(/.f64 (pow.f64 (.f64 (.f64 #s(literal 2 binary64) n) (PI.f64)) (fma.f64 #s(literal -1/2 binary64) k #s(literal 1/2 binary64))) (sqrt.f64 k))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (/.f64 (sqrt.f64 (.f64 (.f64 #s(literal 2 binary64) n) (PI.f64))) (sqrt.f64 k)))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (.f64 (sqrt.f64 n) (sqrt.f64 (/.f64 (.f64 #s(literal 2 binary64) (PI.f64)) k))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt.f64 (.f64 (/.f64 (.f64 (PI.f64) n) k) #s(literal 2 binary64))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt.f64 (.f64 (.f64 #s(literal 2 binary64) (/.f64 (PI.f64) k)) n)))

Outputs
(/.f64 (sqrt.f64 (.f64 n (.f64 (PI.f64) #s(literal 2 binary64)))) (.f64 (sqrt.f64 k) (pow.f64 (pow.f64 (.f64 n (*.f64 (PI.f64) #s(literal 2 binary64))) k) #s(literal 1/2 binary64))))
(/.f64 (sqrt.f64 (.f64 (.f64 #s(literal 2 binary64) (PI.f64)) n)) (.f64 (pow.f64 (pow.f64 (.f64 (*.f64 #s(literal 2 binary64) (PI.f64)) n) k) #s(literal 1/2 binary64)) (sqrt.f64 k)))
(.f64 (sqrt.f64 n) (sqrt.f64 (/.f64 (.f64 #s(literal 2 binary64) (PI.f64)) (.f64 (pow.f64 (.f64 (*.f64 #s(literal 2 binary64) n) (PI.f64)) k) k))))
(.f64 (sqrt.f64 (/.f64 (.f64 #s(literal 2 binary64) (PI.f64)) (.f64 (pow.f64 (.f64 (*.f64 #s(literal 2 binary64) n) (PI.f64)) k) k))) (sqrt.f64 n))
(/.f64 (pow.f64 (.f64 (.f64 #s(literal 2 binary64) n) (PI.f64)) (fma.f64 #s(literal -1/2 binary64) k #s(literal 1/2 binary64))) (sqrt.f64 k))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (/.f64 (sqrt.f64 (.f64 (.f64 #s(literal 2 binary64) n) (PI.f64))) (sqrt.f64 k)))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (.f64 (sqrt.f64 n) (sqrt.f64 (/.f64 (.f64 #s(literal 2 binary64) (PI.f64)) k))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (.f64 (sqrt.f64 (/.f64 (.f64 #s(literal 2 binary64) (PI.f64)) k)) (sqrt.f64 n)))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt.f64 (.f64 (/.f64 (.f64 (PI.f64) n) k) #s(literal 2 binary64))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt.f64 (.f64 (.f64 #s(literal 2 binary64) (/.f64 (PI.f64) k)) n)))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt.f64 (.f64 (.f64 (/.f64 (PI.f64) k) #s(literal 2 binary64)) n)))

soundness754.0ms (8.1%)

Memory

1.2MiB live, 604.6MiB allocated

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	52	245
0	88	214
1	314	205
2	1752	205
0	8371	205
0	128	1158
1	345	1139
2	1013	1017
3	3349	990
4	5543	966
0	8350	945
0	51	263
0	79	256
1	282	246
2	1456	237
0	8595	237
0	13	43
0	22	43
1	89	40
2	497	38
3	4474	38
0	8599	37

Stop Event

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

Compiler

Compiled 220 to 166 computations (24.5% saved)

preprocess166.0ms (1.8%)

Memory: 0.2MiB live, 125.3MiB allocated
Compiler: Compiled 206 to 110 computations (46.6% saved)

end0.0ms (0%)

Memory: 0.0MiB live, 0.0MiB allocated

Iter	Nodes	Cost
0	13	54
0	22	54
1	37	52
2	54	52
3	75	52
4	93	52
5	108	52
6	129	52
7	156	52
8	165	52
9	168	52
0	168	49

Iter	Nodes	Cost
0	52	340
0	88	327
1	138	321
2	169	321
3	191	318
4	214	318
5	238	318
6	283	318
7	309	318
8	318	318
9	321	318
0	321	318

Iter	Nodes	Cost
0	51	339
0	79	336
1	118	330
2	155	330
3	199	327
4	223	327
5	237	327
6	258	327
7	295	327
8	325	327
9	331	327
0	331	327

Iter	Nodes	Cost
0	52	335
0	80	335
1	117	327
2	140	327
3	169	327
4	198	327
5	215	327
6	241	327
7	275	327
8	286	327
9	290	327
0	290	320

Iter	Nodes	Cost
0	13	54
0	22	54
1	37	52
2	54	52
3	75	52
4	93	52
5	108	52
6	129	52
7	156	52
8	165	52
9	168	52
0	168	49

Iter	Nodes	Cost
0	52	340
0	88	327
1	138	321
2	169	321
3	191	318
4	214	318
5	238	318
6	283	318
7	309	318
8	318	318
9	321	318
0	321	318

Iter	Nodes	Cost
0	51	339
0	79	336
1	118	330
2	155	330
3	199	327
4	223	327
5	237	327
6	258	327
7	295	327
8	325	327
9	331	327
0	331	327

Iter	Nodes	Cost
0	52	335
0	80	335
1	117	327
2	140	327
3	169	327
4	198	327
5	215	327
6	241	327
7	275	327
8	286	327
9	290	327
0	290	320

start0.0ms (0%)

analyze115.0ms (1.2%)

sample3.3s (35.3%)

explain146.0ms (1.6%)

preprocess49.0ms (0.5%)

eval0.0ms (0%)

prune1.0ms (0%)

simplify7.0ms (0.1%)

localize37.0ms (0.4%)

series81.0ms (0.9%)

simplify160.0ms (1.7%)

rewrite179.0ms (1.9%)

eval88.0ms (0.9%)

prune108.0ms (1.2%)

simplify17.0ms (0.2%)

localize142.0ms (1.5%)

series175.0ms (1.9%)

simplify176.0ms (1.9%)

rewrite174.0ms (1.9%)

eval539.0ms (5.8%)

prune210.0ms (2.2%)

simplify39.0ms (0.4%)

localize147.0ms (1.6%)

series92.0ms (1%)

simplify217.0ms (2.3%)

rewrite139.0ms (1.5%)

eval206.0ms (2.2%)

prune219.0ms (2.3%)

simplify12.0ms (0.1%)

localize182.0ms (2%)

series67.0ms (0.7%)

simplify274.0ms (2.9%)

rewrite153.0ms (1.6%)

eval277.0ms (3%)

prune188.0ms (2%)

regimes133.0ms (1.4%)

regimes89.0ms (0.9%)

regimes84.0ms (0.9%)

regimes100.0ms (1.1%)

regimes48.0ms (0.5%)

regimes19.0ms (0.2%)

regimes12.0ms (0.1%)

simplify23.0ms (0.2%)

soundness754.0ms (8.1%)

preprocess166.0ms (1.8%)

end0.0ms (0%)

Profiling

Iter	Nodes	Cost
0	13	54
0	22	54
1	37	52
2	54	52
3	75	52
4	93	52
5	108	52
6	129	52
7	156	52
8	165	52
9	168	52
0	168	49

Iter	Nodes	Cost
0	52	340
0	88	327
1	138	321
2	169	321
3	191	318
4	214	318
5	238	318
6	283	318
7	309	318
8	318	318
9	321	318
0	321	318

Iter	Nodes	Cost
0	51	339
0	79	336
1	118	330
2	155	330
3	199	327
4	223	327
5	237	327
6	258	327
7	295	327
8	325	327
9	331	327
0	331	327

Iter	Nodes	Cost
0	52	335
0	80	335
1	117	327
2	140	327
3	169	327
4	198	327
5	215	327
6	241	327
7	275	327
8	286	327
9	290	327
0	290	320