Metrics for Migdal et al, Equation (51)

start0.0ms (0%)

Memory: 0.1MiB live, 0.1MiB allocated; 0ms collecting garbage

analyze220.0ms (2.6%)

Memory

-1.1MiB live, 192.1MiB allocated; 37ms collecting garbage

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)

sample4.7s (56%)

Memory

14.1MiB live, 6 574.5MiB allocated; 2.4s collecting garbage

Samples

1.5s	4 440×	1	invalid
1.1s	8 256×	0	valid
1.1s	1 501×	2	invalid
34.0ms	352×	0	invalid
29.0ms	212×	0	exit

Precisions

Click to see histograms. Total time spent on operations: 2.5s

ival-pow: 582.0ms (22.9% of total)

ival-div: 494.0ms (19.5% of total)

ival-mult: 468.0ms (18.4% of total)

adjust: 291.0ms (11.5% of total)

ival-sqrt: 248.0ms (9.8% of total)

ival-pi: 215.0ms (8.5% of total)

ival-sub: 199.0ms (7.8% of total)

exact: 19.0ms (0.7% of total)

ival-true: 15.0ms (0.6% of total)

ival-assert: 7.0ms (0.3% of total)

Bogosity

explain201.0ms (2.4%)

Memory

3.3MiB live, 385.4MiB allocated; 33ms collecting garbage

FPErrors

Click to see full error table

Ground Truth	Overpredictions	Example	Example	Subexpression
3	80	(3.580419787839436e-44 6.250228270273999e+120)	-	`(pow.f64 (.f64 (.f64 #s(literal 2 binary64) (PI.f64)) n) (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 2 binary64)))`
0	0	-	-	`k`
0	0	-	-	`n`
0	0	-	-	`(/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 2 binary64))`
0	0	-	-	`#s(literal 1 binary64)`
0	0	-	-	`(.f64 (.f64 #s(literal 2 binary64) (PI.f64)) n)`
0	0	-	-	`(sqrt.f64 k)`
0	0	-	-	`#s(literal 2 binary64)`
0	0	-	-	`(/.f64 #s(literal 1 binary64) (sqrt.f64 k))`
0	0	-	-	`(-.f64 #s(literal 1 binary64) k)`
0	0	-	-	`(*.f64 #s(literal 2 binary64) (PI.f64))`
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	-	-	`(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	83	34

Confusion

	Predicted +	Predicted -
+	3	0
-	80	173

Precision

0.03614457831325301

Recall

1.0

Confusion?

	Predicted +	Predicted Maybe	Predicted -
+	3	0	0
-	80	34	139

Precision?

0.02564102564102564

Recall?

1.0

Freqs

test

number	freq
0	173
1	83

Total Confusion?

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

Precision?

1.0

Recall?

1.0

Samples

66.0ms

512×

valid

Compiler

Compiled 128 to 43 computations (66.4% saved)

Precisions

Click to see histograms. Total time spent on operations: 47.0ms

ival-mult: 17.0ms (36% of total)

ival-pow: 10.0ms (21.2% of total)

ival-div: 7.0ms (14.8% of total)

ival-sqrt: 7.0ms (14.8% of total)

ival-sub: 3.0ms (6.4% of total)

ival-pi: 2.0ms (4.2% of total)

exact: 1.0ms (2.1% of total)

adjust: 0.0ms (0% of total)

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

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

preprocess274.0ms (3.3%)

Memory

-0.4MiB live, 190.3MiB allocated; 90ms collecting garbage

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	31	88
1	71	76
2	153	74
3	366	74
4	1514	74
5	7430	74
0	13	16
0	22	16
1	37	14
2	58	14
3	136	14
4	533	14
5	3201	14
0	8098	14

Stop Event

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

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))) (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 2 binary64))) (sqrt.f64 k))

Compiler

Compiled 16 to 13 computations (18.8% saved)

eval0.0ms (0%)

Memory: 0.1MiB live, 0.1MiB allocated; 0ms collecting garbage
Compiler: Compiled 0 to 2 computations (-∞% saved)

prune1.0ms (0%)

Memory

1.4MiB live, 1.4MiB allocated; 0ms collecting garbage

Alt Table

Click to see full alt table

Status	Accuracy	Program
▶	99.5%	(.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)

series91.0ms (1.1%)

Memory

-13.8MiB live, 167.2MiB allocated; 28ms collecting garbage

Counts

13 → 34

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
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) #s(hole binary64 (* (sqrt (/ (* n (PI)) k)) (sqrt 2))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) #s(hole binary64 (/ (+ (* -1/2 (* (sqrt (* (pow k 3) (* n (PI)))) (* (log (* 2 (* n (PI)))) (sqrt 2)))) (* (sqrt (* k (* n (PI)))) (sqrt 2))) k)))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) #s(hole binary64 (/ (+ (* 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)))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) #s(hole binary64 (/ (+ (* 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)))
#s(approx (/ 1 (sqrt k)) #s(hole binary64 (sqrt (/ 1 k))))
#s(approx (sqrt k) #s(hole binary64 (sqrt k)))
#s(approx k #s(hole binary64 k))
#s(approx (pow (* (* 2 (PI)) n) (/ (- 1 k) 2)) #s(hole binary64 (* (sqrt (* n (PI))) (sqrt 2))))
#s(approx (pow (* (* 2 (PI)) n) (/ (- 1 k) 2)) #s(hole binary64 (+ (* -1/2 (* (* k (* (log (* 2 (* n (PI)))) (sqrt 2))) (sqrt (* n (PI))))) (* (sqrt (* n (PI))) (sqrt 2)))))
#s(approx (pow (* (* 2 (PI)) n) (/ (- 1 k) 2)) #s(hole 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)))))
#s(approx (pow (* (* 2 (PI)) n) (/ (- 1 k) 2)) #s(hole 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)))))
#s(approx (/ (- 1 k) 2) #s(hole binary64 1/2))
#s(approx (/ (- 1 k) 2) #s(hole binary64 (+ 1/2 (* -1/2 k))))
#s(approx (- 1 k) #s(hole binary64 1))
#s(approx (- 1 k) #s(hole binary64 (+ 1 (* -1 k))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) #s(hole binary64 (* (sqrt (/ 1 k)) (exp (* 1/2 (* (log (* 2 (* n (PI)))) (- 1 k)))))))
#s(approx (pow (* (* 2 (PI)) n) (/ (- 1 k) 2)) #s(hole binary64 (exp (* 1/2 (* (log (* 2 (* n (PI)))) (- 1 k))))))
#s(approx (/ (- 1 k) 2) #s(hole binary64 (* -1/2 k)))
#s(approx (/ (- 1 k) 2) #s(hole binary64 (* k (- (* 1/2 (/ 1 k)) 1/2))))
#s(approx (- 1 k) #s(hole binary64 (* -1 k)))
#s(approx (- 1 k) #s(hole binary64 (* k (- (/ 1 k) 1))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) #s(hole binary64 (* (sqrt (/ 1 k)) (exp (* 1/2 (* (log (* 2 (* n (PI)))) (+ 1 (* -1 k))))))))
#s(approx (sqrt k) #s(hole binary64 (* -1 (* (sqrt k) (pow (sqrt -1) 2)))))
#s(approx (pow (* (* 2 (PI)) n) (/ (- 1 k) 2)) #s(hole binary64 (exp (* 1/2 (* (log (* 2 (* n (PI)))) (+ 1 (* -1 k)))))))
#s(approx (/ (- 1 k) 2) #s(hole binary64 (* -1 (* k (- 1/2 (* 1/2 (/ 1 k)))))))
#s(approx (- 1 k) #s(hole binary64 (* -1 (* k (- 1 (/ 1 k))))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) #s(hole binary64 (* (sqrt (/ 1 k)) (exp (* 1/2 (* (+ (log n) (log (* 2 (PI)))) (- 1 k)))))))
#s(approx (pow (* (* 2 (PI)) n) (/ (- 1 k) 2)) #s(hole binary64 (exp (* 1/2 (* (+ (log n) (log (* 2 (PI)))) (- 1 k))))))
#s(approx (* (* 2 (PI)) n) #s(hole binary64 (* 2 (* n (PI)))))
#s(approx n #s(hole binary64 n))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) #s(hole binary64 (* (sqrt (/ 1 k)) (exp (* 1/2 (* (+ (log (* 2 (PI))) (* -1 (log (/ 1 n)))) (- 1 k)))))))
#s(approx (pow (* (* 2 (PI)) n) (/ (- 1 k) 2)) #s(hole binary64 (exp (* 1/2 (* (+ (log (* 2 (PI))) (* -1 (log (/ 1 n)))) (- 1 k))))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) #s(hole binary64 (* (sqrt (/ 1 k)) (exp (* 1/2 (* (+ (log (* -2 (PI))) (* -1 (log (/ -1 n)))) (- 1 k)))))))
#s(approx (pow (* (* 2 (PI)) n) (/ (- 1 k) 2)) #s(hole binary64 (exp (* 1/2 (* (+ (log (* -2 (PI))) (* -1 (log (/ -1 n)))) (- 1 k))))))

Calls

6 calls:

Time	Variable		Point	Expression
49.0ms	n	@	0	((* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (/ 1 (sqrt k)) 1 (sqrt k) k (pow (* (* 2 (PI)) n) (/ (- 1 k) 2)) (* (* 2 (PI)) n) (* 2 (PI)) 2 (PI) n (/ (- 1 k) 2) (- 1 k))
23.0ms	n	@	-inf	((* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (/ 1 (sqrt k)) 1 (sqrt k) k (pow (* (* 2 (PI)) n) (/ (- 1 k) 2)) (* (* 2 (PI)) n) (* 2 (PI)) 2 (PI) n (/ (- 1 k) 2) (- 1 k))
8.0ms	n	@	inf	((* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (/ 1 (sqrt k)) 1 (sqrt k) k (pow (* (* 2 (PI)) n) (/ (- 1 k) 2)) (* (* 2 (PI)) n) (* 2 (PI)) 2 (PI) n (/ (- 1 k) 2) (- 1 k))
6.0ms	k	@	0	((* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (/ 1 (sqrt k)) 1 (sqrt k) k (pow (* (* 2 (PI)) n) (/ (- 1 k) 2)) (* (* 2 (PI)) n) (* 2 (PI)) 2 (PI) n (/ (- 1 k) 2) (- 1 k))
3.0ms	k	@	-inf	((* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (/ 1 (sqrt k)) 1 (sqrt k) k (pow (* (* 2 (PI)) n) (/ (- 1 k) 2)) (* (* 2 (PI)) n) (* 2 (PI)) 2 (PI) n (/ (- 1 k) 2) (- 1 k))

simplify136.0ms (1.6%)

Memory

3.8MiB live, 186.3MiB allocated; 41ms collecting garbage

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	172	881
1	461	849
2	1662	795
0	5918	777

Stop Event

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

Counts

34 → 34

Calls

Call 1

Inputs
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) #s(hole binary64 (* (sqrt (/ (* n (PI)) k)) (sqrt 2))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) #s(hole binary64 (/ (+ (* -1/2 (* (sqrt (* (pow k 3) (* n (PI)))) (* (log (* 2 (* n (PI)))) (sqrt 2)))) (* (sqrt (* k (* n (PI)))) (sqrt 2))) k)))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) #s(hole binary64 (/ (+ (* 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)))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) #s(hole binary64 (/ (+ (* 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)))
#s(approx (/ 1 (sqrt k)) #s(hole binary64 (sqrt (/ 1 k))))
#s(approx (sqrt k) #s(hole binary64 (sqrt k)))
#s(approx k #s(hole binary64 k))
#s(approx (pow (* (* 2 (PI)) n) (/ (- 1 k) 2)) #s(hole binary64 (* (sqrt (* n (PI))) (sqrt 2))))
#s(approx (pow (* (* 2 (PI)) n) (/ (- 1 k) 2)) #s(hole binary64 (+ (* -1/2 (* (* k (* (log (* 2 (* n (PI)))) (sqrt 2))) (sqrt (* n (PI))))) (* (sqrt (* n (PI))) (sqrt 2)))))
#s(approx (pow (* (* 2 (PI)) n) (/ (- 1 k) 2)) #s(hole 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)))))
#s(approx (pow (* (* 2 (PI)) n) (/ (- 1 k) 2)) #s(hole 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)))))
#s(approx (/ (- 1 k) 2) #s(hole binary64 1/2))
#s(approx (/ (- 1 k) 2) #s(hole binary64 (+ 1/2 (* -1/2 k))))
#s(approx (- 1 k) #s(hole binary64 1))
#s(approx (- 1 k) #s(hole binary64 (+ 1 (* -1 k))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) #s(hole binary64 (* (sqrt (/ 1 k)) (exp (* 1/2 (* (log (* 2 (* n (PI)))) (- 1 k)))))))
#s(approx (pow (* (* 2 (PI)) n) (/ (- 1 k) 2)) #s(hole binary64 (exp (* 1/2 (* (log (* 2 (* n (PI)))) (- 1 k))))))
#s(approx (/ (- 1 k) 2) #s(hole binary64 (* -1/2 k)))
#s(approx (/ (- 1 k) 2) #s(hole binary64 (* k (- (* 1/2 (/ 1 k)) 1/2))))
#s(approx (- 1 k) #s(hole binary64 (* -1 k)))
#s(approx (- 1 k) #s(hole binary64 (* k (- (/ 1 k) 1))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) #s(hole binary64 (* (sqrt (/ 1 k)) (exp (* 1/2 (* (log (* 2 (* n (PI)))) (+ 1 (* -1 k))))))))
#s(approx (sqrt k) #s(hole binary64 (* -1 (* (sqrt k) (pow (sqrt -1) 2)))))
#s(approx (pow (* (* 2 (PI)) n) (/ (- 1 k) 2)) #s(hole binary64 (exp (* 1/2 (* (log (* 2 (* n (PI)))) (+ 1 (* -1 k)))))))
#s(approx (/ (- 1 k) 2) #s(hole binary64 (* -1 (* k (- 1/2 (* 1/2 (/ 1 k)))))))
#s(approx (- 1 k) #s(hole binary64 (* -1 (* k (- 1 (/ 1 k))))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) #s(hole binary64 (* (sqrt (/ 1 k)) (exp (* 1/2 (* (+ (log n) (log (* 2 (PI)))) (- 1 k)))))))
#s(approx (pow (* (* 2 (PI)) n) (/ (- 1 k) 2)) #s(hole binary64 (exp (* 1/2 (* (+ (log n) (log (* 2 (PI)))) (- 1 k))))))
#s(approx (* (* 2 (PI)) n) #s(hole binary64 (* 2 (* n (PI)))))
#s(approx n #s(hole binary64 n))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) #s(hole binary64 (* (sqrt (/ 1 k)) (exp (* 1/2 (* (+ (log (* 2 (PI))) (* -1 (log (/ 1 n)))) (- 1 k)))))))
#s(approx (pow (* (* 2 (PI)) n) (/ (- 1 k) 2)) #s(hole binary64 (exp (* 1/2 (* (+ (log (* 2 (PI))) (* -1 (log (/ 1 n)))) (- 1 k))))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) #s(hole binary64 (* (sqrt (/ 1 k)) (exp (* 1/2 (* (+ (log (* -2 (PI))) (* -1 (log (/ -1 n)))) (- 1 k)))))))
#s(approx (pow (* (* 2 (PI)) n) (/ (- 1 k) 2)) #s(hole binary64 (exp (* 1/2 (* (+ (log (* -2 (PI))) (* -1 (log (/ -1 n)))) (- 1 k))))))

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

rewrite70.0ms (0.8%)

Memory

-1.4MiB live, 96.9MiB allocated; 22ms collecting garbage

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	13	54
0	22	54
1	83	51
0	500	51

Stop Event

1×	iter limit
1×	iter limit
1×	iter limit
1×	unsound
1×	iter limit

Counts

13 → 101

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

eval19.0ms (0.2%)

Memory: -6.4MiB live, 38.1MiB allocated; 8ms collecting garbage
Compiler: Compiled 3 000 to 533 computations (82.2% saved)

prune13.0ms (0.2%)

Memory

35.3MiB live, 35.3MiB allocated; 0ms collecting garbage

Pruning

17 alts after pruning (17 fresh and 0 done)

	Pruned	Kept	Total
New	116	17	133
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	117	17	134

Accuracy

100.0%

Counts

134 → 17

Alt Table

Click to see full alt table

Status	Accuracy	Program
	99.5%	(/.f64 (pow.f64 (.f64 n (.f64 (PI.f64) #s(literal 2 binary64))) (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 2 binary64))) (sqrt.f64 k))
	99.4%	(.f64 (pow.f64 (.f64 n (.f64 (PI.f64) #s(literal 2 binary64))) (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 4 binary64))) (.f64 (pow.f64 (.f64 n (.f64 (PI.f64) #s(literal 2 binary64))) (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 4 binary64))) (pow.f64 k #s(literal -1/2 binary64))))
	99.6%	(.f64 (pow.f64 (.f64 n (*.f64 (PI.f64) #s(literal 2 binary64))) (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 2 binary64))) (pow.f64 k #s(literal -1/2 binary64)))
	99.3%	(.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) (pow.f64 (pow.f64 (.f64 n (*.f64 (PI.f64) #s(literal 2 binary64))) (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 4 binary64))) #s(literal 2 binary64)))
▶	99.3%	(.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) (pow.f64 (.f64 (.f64 (.f64 #s(literal 2 binary64) (sqrt.f64 (PI.f64))) (sqrt.f64 (PI.f64))) n) (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 2 binary64))))
	78.8%	(.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) (pow.f64 (.f64 (.f64 n (.f64 (PI.f64) #s(literal 2 binary64))) (.f64 n (.f64 (PI.f64) #s(literal 2 binary64)))) (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 4 binary64))))
	99.5%	(.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) (fma.f64 #s(literal -1/2 binary64) k #s(literal 1/2 binary64)))))
	52.5%	(.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 #s(literal -1/2 binary64) k))))
	50.0%	(.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))))
▶	99.6%	(.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) (/.f64 (pow.f64 (.f64 n (.f64 (PI.f64) #s(literal 2 binary64))) #s(literal 1/2 binary64)) (pow.f64 (.f64 n (*.f64 (PI.f64) #s(literal 2 binary64))) (/.f64 k #s(literal 2 binary64)))))
	96.2%	(.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) (exp.f64 (.f64 (log.f64 (.f64 n (.f64 (PI.f64) #s(literal 2 binary64)))) (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 2 binary64)))))
	50.0%	(.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)))))
	72.7%	(.f64 (.f64 (pow.f64 k #s(literal -1/2 binary64)) (pow.f64 (*.f64 (PI.f64) #s(literal 2 binary64)) (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 2 binary64)))) (pow.f64 n (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 2 binary64))))
	58.4%	#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (/.f64 (fma.f64 (.f64 (sqrt.f64 #s(literal 2 binary64)) (fma.f64 (.f64 #s(literal 1/8 binary64) (sqrt.f64 (.f64 (.f64 (pow.f64 k #s(literal 3 binary64)) (PI.f64)) n))) (pow.f64 (log.f64 (.f64 (.f64 (PI.f64) n) #s(literal 2 binary64))) #s(literal 2 binary64)) (.f64 (.f64 (sqrt.f64 (.f64 (.f64 (PI.f64) n) k)) #s(literal -1/2 binary64)) (log.f64 (.f64 (.f64 (PI.f64) n) #s(literal 2 binary64)))))) k (.f64 (sqrt.f64 (.f64 (*.f64 (PI.f64) n) k)) (sqrt.f64 #s(literal 2 binary64)))) k))
▶	58.2%	#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 (PI.f64) n) #s(literal 2 binary64))) (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 (sqrt.f64 (/.f64 #s(literal 1 binary64) k)) (pow.f64 (.f64 (*.f64 (PI.f64) n) #s(literal 2 binary64)) (fma.f64 #s(literal -1/2 binary64) k #s(literal 1/2 binary64)))))
▶	38.0%	#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))))

Compiler

Compiled 860 to 642 computations (25.3% saved)

series218.0ms (2.6%)

Memory

6.3MiB live, 342.1MiB allocated; 64ms collecting garbage

Counts

50 → 150

Calls

Call 1

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

Outputs
#s(approx (* (/ 1 (sqrt k)) (/ (pow (* n (* (PI) 2)) 1/2) (pow (* n (* (PI) 2)) (/ k 2)))) #s(hole binary64 (* (sqrt (/ (* n (PI)) k)) (sqrt 2))))
#s(approx (* (/ 1 (sqrt k)) (/ (pow (* n (* (PI) 2)) 1/2) (pow (* n (* (PI) 2)) (/ k 2)))) #s(hole binary64 (/ (+ (* -1/2 (* (sqrt (* (pow k 3) (* n (PI)))) (* (log (* 2 (* n (PI)))) (sqrt 2)))) (* (sqrt (* k (* n (PI)))) (sqrt 2))) k)))
#s(approx (* (/ 1 (sqrt k)) (/ (pow (* n (* (PI) 2)) 1/2) (pow (* n (* (PI) 2)) (/ k 2)))) #s(hole binary64 (/ (+ (* k (+ (* -1 (* (sqrt (* (pow k 3) (* n (PI)))) (+ (* -1/4 (* (pow (log (* 2 (* n (PI)))) 2) (sqrt 2))) (* 1/8 (* (pow (log (* 2 (* n (PI)))) 2) (sqrt 2)))))) (* -1/2 (* (sqrt (* k (* n (PI)))) (* (log (* 2 (* n (PI)))) (sqrt 2)))))) (* (sqrt (* k (* n (PI)))) (sqrt 2))) k)))
#s(approx (* (/ 1 (sqrt k)) (/ (pow (* n (* (PI) 2)) 1/2) (pow (* n (* (PI) 2)) (/ k 2)))) #s(hole binary64 (/ (+ (* k (+ (* -1/2 (* (sqrt (* k (* n (PI)))) (* (log (* 2 (* n (PI)))) (sqrt 2)))) (* k (+ (* -1 (* (sqrt (* k (* n (PI)))) (+ (* -1/4 (* (pow (log (* 2 (* n (PI)))) 2) (sqrt 2))) (* 1/8 (* (pow (log (* 2 (* n (PI)))) 2) (sqrt 2)))))) (* -1 (* (sqrt (* (pow k 3) (* n (PI)))) (+ (* -1/2 (* (log (* 2 (* n (PI)))) (+ (* -1/4 (* (pow (log (* 2 (* n (PI)))) 2) (sqrt 2))) (* 1/8 (* (pow (log (* 2 (* n (PI)))) 2) (sqrt 2)))))) (+ (* -1/16 (* (pow (log (* 2 (* n (PI)))) 3) (sqrt 2))) (* 1/48 (* (pow (log (* 2 (* n (PI)))) 3) (sqrt 2))))))))))) (* (sqrt (* k (* n (PI)))) (sqrt 2))) k)))
#s(approx (/ 1 (sqrt k)) #s(hole binary64 (sqrt (/ 1 k))))
#s(approx (sqrt k) #s(hole binary64 (sqrt k)))
#s(approx k #s(hole binary64 k))
#s(approx (/ (pow (* n (* (PI) 2)) 1/2) (pow (* n (* (PI) 2)) (/ k 2))) #s(hole binary64 (* (sqrt (* n (PI))) (sqrt 2))))
#s(approx (/ (pow (* n (* (PI) 2)) 1/2) (pow (* n (* (PI) 2)) (/ k 2))) #s(hole binary64 (+ (* -1/2 (* (* k (* (log (* 2 (* n (PI)))) (sqrt 2))) (sqrt (* n (PI))))) (* (sqrt (* n (PI))) (sqrt 2)))))
#s(approx (/ (pow (* n (* (PI) 2)) 1/2) (pow (* n (* (PI) 2)) (/ k 2))) #s(hole binary64 (+ (* k (+ (* -1 (* (* k (+ (* -1/4 (* (pow (log (* 2 (* n (PI)))) 2) (sqrt 2))) (* 1/8 (* (pow (log (* 2 (* n (PI)))) 2) (sqrt 2))))) (sqrt (* n (PI))))) (* -1/2 (* (sqrt (* n (PI))) (* (log (* 2 (* n (PI)))) (sqrt 2)))))) (* (sqrt (* n (PI))) (sqrt 2)))))
#s(approx (/ (pow (* n (* (PI) 2)) 1/2) (pow (* n (* (PI) 2)) (/ k 2))) #s(hole binary64 (+ (* k (+ (* -1/2 (* (sqrt (* n (PI))) (* (log (* 2 (* n (PI)))) (sqrt 2)))) (* k (+ (* -1 (* (sqrt (* n (PI))) (+ (* -1/4 (* (pow (log (* 2 (* n (PI)))) 2) (sqrt 2))) (* 1/8 (* (pow (log (* 2 (* n (PI)))) 2) (sqrt 2)))))) (* -1 (* (* k (+ (* -1/2 (* (log (* 2 (* n (PI)))) (+ (* -1/4 (* (pow (log (* 2 (* n (PI)))) 2) (sqrt 2))) (* 1/8 (* (pow (log (* 2 (* n (PI)))) 2) (sqrt 2)))))) (+ (* -1/16 (* (pow (log (* 2 (* n (PI)))) 3) (sqrt 2))) (* 1/48 (* (pow (log (* 2 (* n (PI)))) 3) (sqrt 2)))))) (sqrt (* n (PI))))))))) (* (sqrt (* n (PI))) (sqrt 2)))))
#s(approx (pow (* n (* (PI) 2)) (/ k 2)) #s(hole binary64 1))
#s(approx (pow (* n (* (PI) 2)) (/ k 2)) #s(hole binary64 (+ 1 (* 1/2 (* k (log (* 2 (* n (PI)))))))))
#s(approx (pow (* n (* (PI) 2)) (/ k 2)) #s(hole binary64 (+ 1 (* k (+ (* 1/8 (* k (pow (log (* 2 (* n (PI)))) 2))) (* 1/2 (log (* 2 (* n (PI))))))))))
#s(approx (pow (* n (* (PI) 2)) (/ k 2)) #s(hole binary64 (+ 1 (* k (+ (* 1/2 (log (* 2 (* n (PI))))) (* k (+ (* 1/48 (* k (pow (log (* 2 (* n (PI)))) 3))) (* 1/8 (pow (log (* 2 (* n (PI)))) 2)))))))))
#s(approx (/ k 2) #s(hole binary64 (* 1/2 k)))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) #s(hole binary64 (* (sqrt (/ (* n (PI)) k)) (sqrt 2))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) #s(hole binary64 (/ (+ (* -1/2 (* (sqrt (* (pow k 3) (* n (PI)))) (* (log (* 2 (* n (PI)))) (sqrt 2)))) (* (sqrt (* k (* n (PI)))) (sqrt 2))) k)))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) #s(hole binary64 (/ (+ (* 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)))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) #s(hole binary64 (/ (+ (* 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)))
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#s(approx (* (/ 1 (sqrt k)) (pow (* (* (* 2 (sqrt (PI))) (sqrt (PI))) n) (/ (- 1 k) 2))) #s(hole binary64 (/ (+ (* 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)))
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#s(approx (/ (pow (* n (* (PI) 2)) 1/2) (pow (* n (* (PI) 2)) (/ k 2))) #s(hole binary64 (* (sqrt (* n (PI))) (/ (sqrt 2) (exp (* 1/2 (* k (log (* 2 (* n (PI)))))))))))
#s(approx (pow (* n (* (PI) 2)) (/ k 2)) #s(hole binary64 (exp (* 1/2 (* k (log (* 2 (* n (PI)))))))))
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#s(approx (* (sqrt (/ 1 k)) (pow (* (* (PI) n) 2) (+ (* -1/2 k) 1/2))) #s(hole binary64 (* (sqrt (/ 1 k)) (exp (* (log (* 2 (* n (PI)))) (- 1/2 (* 1/2 k)))))))
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#s(approx (* (/ 1 (sqrt k)) (pow (* (* (* 2 (sqrt (PI))) (sqrt (PI))) n) (/ (- 1 k) 2))) #s(hole binary64 (* (sqrt (/ 1 k)) (exp (* 1/2 (* (log (* 2 (* n (PI)))) (- 1 k)))))))
#s(approx (pow (* (* (* 2 (sqrt (PI))) (sqrt (PI))) n) (/ (- 1 k) 2)) #s(hole binary64 (exp (* 1/2 (* (log (* 2 (* n (PI)))) (- 1 k))))))
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#s(approx (+ (* (* (log (* (* (PI) n) 2)) (sqrt (* (* (pow k 3) (PI)) n))) -1/2) (sqrt (* (* (PI) n) k))) #s(hole binary64 (* (pow k 2) (+ (sqrt (/ (* n (PI)) (pow k 3))) (* -1/2 (* (sqrt (/ (* n (PI)) k)) (log (* 2 (* n (PI))))))))))
#s(approx (sqrt k) #s(hole binary64 (* -1 (* (sqrt k) (pow (sqrt -1) 2)))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) #s(hole binary64 (* (sqrt (/ 1 k)) (exp (* 1/2 (* (log (* 2 (* n (PI)))) (+ 1 (* -1 k))))))))
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#s(approx (* (sqrt (/ 1 k)) (pow (* (* (PI) n) 2) (+ (* -1/2 k) 1/2))) #s(hole binary64 (* (sqrt (/ 1 k)) (* (exp (* (log (* 2 (* n (PI)))) (+ 1/2 (* -1/2 k)))) (pow (sqrt -1) 2)))))
#s(approx (sqrt (/ 1 k)) #s(hole binary64 (* (sqrt (/ 1 k)) (pow (sqrt -1) 2))))
#s(approx (pow (* (* (PI) n) 2) (+ (* -1/2 k) 1/2)) #s(hole binary64 (exp (* (log (* 2 (* n (PI)))) (+ 1/2 (* -1/2 k))))))
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#s(approx (* (/ 1 (sqrt k)) (pow (* (* (* 2 (sqrt (PI))) (sqrt (PI))) n) (/ (- 1 k) 2))) #s(hole binary64 (* (sqrt (/ 1 k)) (exp (* 1/2 (* (log (* 2 (* n (PI)))) (+ 1 (* -1 k))))))))
#s(approx (pow (* (* (* 2 (sqrt (PI))) (sqrt (PI))) n) (/ (- 1 k) 2)) #s(hole binary64 (exp (* 1/2 (* (log (* 2 (* n (PI)))) (+ 1 (* -1 k)))))))
#s(approx (/ (- 1 k) 2) #s(hole binary64 (* -1 (* k (- 1/2 (* 1/2 (/ 1 k)))))))
#s(approx (- 1 k) #s(hole binary64 (* -1 (* k (- 1 (/ 1 k))))))
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#s(approx (* (sqrt 2) (+ (* (* (log (* (* (PI) n) 2)) (sqrt (* (* (pow k 3) (PI)) n))) -1/2) (sqrt (* (* (PI) n) k)))) #s(hole binary64 (* -1/2 (* (sqrt (* (pow k 3) (* n (PI)))) (* (log (* 2 (* n (PI)))) (* (pow (sqrt -1) 2) (sqrt 2)))))))
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#s(approx (+ (* (* (log (* (* (PI) n) 2)) (sqrt (* (* (pow k 3) (PI)) n))) -1/2) (sqrt (* (* (PI) n) k))) #s(hole binary64 (* -1/2 (* (sqrt (* (pow k 3) (* n (PI)))) (* (log (* 2 (* n (PI)))) (pow (sqrt -1) 2))))))
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#s(approx (* (log (* (* (PI) n) 2)) (sqrt (* (* (pow k 3) (PI)) n))) #s(hole binary64 (* (sqrt (* (pow k 3) (* n (PI)))) (* (log (* 2 (* n (PI)))) (pow (sqrt -1) 2)))))
#s(approx (sqrt (* (* (pow k 3) (PI)) n)) #s(hole binary64 (* (sqrt (* (pow k 3) (* n (PI)))) (pow (sqrt -1) 2))))
#s(approx (sqrt (* (* (PI) n) k)) #s(hole binary64 (* -1 (* (sqrt (* k (* n (PI)))) (pow (sqrt -1) 2)))))
#s(approx (* (/ 1 (sqrt k)) (/ (pow (* n (* (PI) 2)) 1/2) (pow (* n (* (PI) 2)) (/ k 2)))) #s(hole binary64 (* (sqrt (/ (* n (PI)) k)) (/ (sqrt 2) (exp (* 1/2 (* k (+ (log n) (log (* 2 (PI)))))))))))
#s(approx (/ (pow (* n (* (PI) 2)) 1/2) (pow (* n (* (PI) 2)) (/ k 2))) #s(hole binary64 (* (sqrt (* n (PI))) (/ (sqrt 2) (exp (* 1/2 (* k (+ (log n) (log (* 2 (PI)))))))))))
#s(approx (pow (* n (* (PI) 2)) 1/2) #s(hole binary64 (* (sqrt (* n (PI))) (sqrt 2))))
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#s(approx n #s(hole binary64 n))
#s(approx (pow (* n (* (PI) 2)) (/ k 2)) #s(hole binary64 (exp (* 1/2 (* k (+ (log n) (log (* 2 (PI)))))))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) #s(hole binary64 (* (sqrt (/ 1 k)) (exp (* 1/2 (* (+ (log n) (log (* 2 (PI)))) (- 1 k)))))))
#s(approx (* (PI) n) #s(hole binary64 (* n (PI))))
#s(approx (* (sqrt (/ 1 k)) (pow (* (* (PI) n) 2) (+ (* -1/2 k) 1/2))) #s(hole binary64 (* (sqrt (/ 1 k)) (exp (* (+ 1/2 (* -1/2 k)) (+ (log n) (log (* 2 (PI)))))))))
#s(approx (pow (* (* (PI) n) 2) (+ (* -1/2 k) 1/2)) #s(hole binary64 (exp (* (+ 1/2 (* -1/2 k)) (+ (log n) (log (* 2 (PI))))))))
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#s(approx (* (/ 1 (sqrt k)) (pow (* (* (* 2 (sqrt (PI))) (sqrt (PI))) n) (/ (- 1 k) 2))) #s(hole binary64 (* (sqrt (/ 1 k)) (exp (* 1/2 (* (+ (log n) (log (* 2 (PI)))) (- 1 k)))))))
#s(approx (pow (* (* (* 2 (sqrt (PI))) (sqrt (PI))) n) (/ (- 1 k) 2)) #s(hole binary64 (exp (* 1/2 (* (+ (log n) (log (* 2 (PI)))) (- 1 k))))))
#s(approx (* (* (* 2 (sqrt (PI))) (sqrt (PI))) n) #s(hole binary64 (* 2 (* n (PI)))))
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#s(approx (+ (* (* (log (* (* (PI) n) 2)) (sqrt (* (* (pow k 3) (PI)) n))) -1/2) (sqrt (* (* (PI) n) k))) #s(hole binary64 (+ (sqrt (* k (* n (PI)))) (* -1/2 (* (sqrt (* (pow k 3) (* n (PI)))) (+ (log n) (log (* 2 (PI)))))))))
#s(approx (* (log (* (* (PI) n) 2)) (sqrt (* (* (pow k 3) (PI)) n))) #s(hole binary64 (* (sqrt (* (pow k 3) (* n (PI)))) (+ (log n) (log (* 2 (PI)))))))
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#s(approx (* (/ 1 (sqrt k)) (/ (pow (* n (* (PI) 2)) 1/2) (pow (* n (* (PI) 2)) (/ k 2)))) #s(hole binary64 (* (sqrt (/ (* n (PI)) k)) (/ (sqrt 2) (exp (* 1/2 (* k (+ (log (* 2 (PI))) (* -1 (log (/ 1 n)))))))))))
#s(approx (/ (pow (* n (* (PI) 2)) 1/2) (pow (* n (* (PI) 2)) (/ k 2))) #s(hole binary64 (* (sqrt (* n (PI))) (/ (sqrt 2) (exp (* 1/2 (* k (+ (log (* 2 (PI))) (* -1 (log (/ 1 n)))))))))))
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#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) #s(hole binary64 (* (sqrt (/ 1 k)) (exp (* 1/2 (* (+ (log (* 2 (PI))) (* -1 (log (/ 1 n)))) (- 1 k)))))))
#s(approx (* (sqrt (/ 1 k)) (pow (* (* (PI) n) 2) (+ (* -1/2 k) 1/2))) #s(hole binary64 (* (sqrt (/ 1 k)) (exp (* (+ 1/2 (* -1/2 k)) (+ (log (* 2 (PI))) (* -1 (log (/ 1 n)))))))))
#s(approx (pow (* (* (PI) n) 2) (+ (* -1/2 k) 1/2)) #s(hole binary64 (exp (* (+ 1/2 (* -1/2 k)) (+ (log (* 2 (PI))) (* -1 (log (/ 1 n))))))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* (* 2 (sqrt (PI))) (sqrt (PI))) n) (/ (- 1 k) 2))) #s(hole binary64 (* (sqrt (/ 1 k)) (exp (* 1/2 (* (+ (log (* 2 (PI))) (* -1 (log (/ 1 n)))) (- 1 k)))))))
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#s(approx (log (* (* (PI) n) 2)) #s(hole binary64 (+ (log (* 2 (PI))) (* -1 (log (/ 1 n))))))
#s(approx (* (/ 1 (sqrt k)) (/ (pow (* n (* (PI) 2)) 1/2) (pow (* n (* (PI) 2)) (/ k 2)))) #s(hole binary64 (* -1 (* (sqrt (/ (* n (PI)) k)) (/ (* (sqrt -2) (sqrt -1)) (exp (* 1/2 (* k (+ (log (* -2 (PI))) (* -1 (log (/ -1 n))))))))))))
#s(approx (/ (pow (* n (* (PI) 2)) 1/2) (pow (* n (* (PI) 2)) (/ k 2))) #s(hole binary64 (* -1 (* (sqrt (* n (PI))) (/ (* (sqrt -2) (sqrt -1)) (exp (* 1/2 (* k (+ (log (* -2 (PI))) (* -1 (log (/ -1 n))))))))))))
#s(approx (pow (* n (* (PI) 2)) 1/2) #s(hole binary64 (* -1 (* (sqrt (* n (PI))) (* (sqrt -2) (sqrt -1))))))
#s(approx (pow (* n (* (PI) 2)) (/ k 2)) #s(hole binary64 (exp (* 1/2 (* k (+ (log (* -2 (PI))) (* -1 (log (/ -1 n)))))))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) #s(hole binary64 (* (sqrt (/ 1 k)) (exp (* 1/2 (* (+ (log (* -2 (PI))) (* -1 (log (/ -1 n)))) (- 1 k)))))))
#s(approx (* (sqrt 2) (sqrt (/ (* (PI) n) k))) #s(hole binary64 (* -1 (* (sqrt (/ (* n (PI)) k)) (* (pow (sqrt -1) 2) (sqrt 2))))))
#s(approx (sqrt (/ (* (PI) n) k)) #s(hole binary64 (* -1 (* (sqrt (/ (* n (PI)) k)) (pow (sqrt -1) 2)))))
#s(approx (* (sqrt (/ 1 k)) (pow (* (* (PI) n) 2) (+ (* -1/2 k) 1/2))) #s(hole binary64 (* (sqrt (/ 1 k)) (exp (* (+ 1/2 (* -1/2 k)) (+ (log (* -2 (PI))) (* -1 (log (/ -1 n)))))))))
#s(approx (pow (* (* (PI) n) 2) (+ (* -1/2 k) 1/2)) #s(hole binary64 (exp (* (+ 1/2 (* -1/2 k)) (+ (log (* -2 (PI))) (* -1 (log (/ -1 n))))))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* (* 2 (sqrt (PI))) (sqrt (PI))) n) (/ (- 1 k) 2))) #s(hole binary64 (* (sqrt (/ 1 k)) (exp (* 1/2 (* (+ (log (* -2 (PI))) (* -1 (log (/ -1 n)))) (- 1 k)))))))
#s(approx (pow (* (* (* 2 (sqrt (PI))) (sqrt (PI))) n) (/ (- 1 k) 2)) #s(hole binary64 (exp (* 1/2 (* (+ (log (* -2 (PI))) (* -1 (log (/ -1 n)))) (- 1 k))))))
#s(approx (/ (* (sqrt 2) (+ (* (* (log (* (* (PI) n) 2)) (sqrt (* (* (pow k 3) (PI)) n))) -1/2) (sqrt (* (* (PI) n) k)))) k) #s(hole binary64 (* -1 (/ (* n (* (sqrt 2) (+ (* -1/2 (* (sqrt (/ (* (pow k 3) (PI)) n)) (* (pow (sqrt -1) 2) (+ (log (* -2 (PI))) (* -1 (log (/ -1 n))))))) (* (sqrt (/ (* k (PI)) n)) (pow (sqrt -1) 2))))) k))))
#s(approx (* (sqrt 2) (+ (* (* (log (* (* (PI) n) 2)) (sqrt (* (* (pow k 3) (PI)) n))) -1/2) (sqrt (* (* (PI) n) k)))) #s(hole binary64 (* -1 (* n (* (sqrt 2) (+ (* -1/2 (* (sqrt (/ (* (pow k 3) (PI)) n)) (* (pow (sqrt -1) 2) (+ (log (* -2 (PI))) (* -1 (log (/ -1 n))))))) (* (sqrt (/ (* k (PI)) n)) (pow (sqrt -1) 2))))))))
#s(approx (+ (* (* (log (* (* (PI) n) 2)) (sqrt (* (* (pow k 3) (PI)) n))) -1/2) (sqrt (* (* (PI) n) k))) #s(hole binary64 (* -1 (* n (+ (* -1/2 (* (sqrt (/ (* (pow k 3) (PI)) n)) (* (pow (sqrt -1) 2) (+ (log (* -2 (PI))) (* -1 (log (/ -1 n))))))) (* (sqrt (/ (* k (PI)) n)) (pow (sqrt -1) 2)))))))
#s(approx (* (log (* (* (PI) n) 2)) (sqrt (* (* (pow k 3) (PI)) n))) #s(hole binary64 (* -1 (* (sqrt (* (pow k 3) (* n (PI)))) (* (pow (sqrt -1) 2) (+ (log (* -2 (PI))) (* -1 (log (/ -1 n)))))))))
#s(approx (log (* (* (PI) n) 2)) #s(hole binary64 (+ (log (* -2 (PI))) (* -1 (log (/ -1 n))))))
#s(approx (sqrt (* (* (pow k 3) (PI)) n)) #s(hole binary64 (* -1 (* (sqrt (* (pow k 3) (* n (PI)))) (pow (sqrt -1) 2)))))

Calls

6 calls:

Time	Variable		Point	Expression
64.0ms	n	@	inf	((* (/ 1 (sqrt k)) (/ (pow (* n (* (PI) 2)) 1/2) (pow (* n (* (PI) 2)) (/ k 2)))) (/ 1 (sqrt k)) 1 (sqrt k) k (/ (pow (* n (* (PI) 2)) 1/2) (pow (* n (* (PI) 2)) (/ k 2))) (pow (* n (* (PI) 2)) 1/2) (* n (* (PI) 2)) n (* (PI) 2) (PI) 2 1/2 (pow (* n (* (PI) 2)) (/ k 2)) (/ k 2) (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (* (sqrt 2) (sqrt (/ (* (PI) n) k))) (sqrt 2) (sqrt (/ (* (PI) n) k)) (/ (* (PI) n) k) (* (PI) n) (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (* (sqrt (/ 1 k)) (pow (* (* (PI) n) 2) (+ (* -1/2 k) 1/2))) (sqrt (/ 1 k)) (/ 1 k) (pow (* (* (PI) n) 2) (+ (* -1/2 k) 1/2)) (* (* (PI) n) 2) (+ (* -1/2 k) 1/2) -1/2 (* (/ 1 (sqrt k)) (pow (* (* (* 2 (sqrt (PI))) (sqrt (PI))) n) (/ (- 1 k) 2))) (pow (* (* (* 2 (sqrt (PI))) (sqrt (PI))) n) (/ (- 1 k) 2)) (* (* (* 2 (sqrt (PI))) (sqrt (PI))) n) (* (* 2 (sqrt (PI))) (sqrt (PI))) (* 2 (sqrt (PI))) (sqrt (PI)) (/ (- 1 k) 2) (- 1 k) (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (/ (* (sqrt 2) (+ (* (* (log (* (* (PI) n) 2)) (sqrt (* (* (pow k 3) (PI)) n))) -1/2) (sqrt (* (* (PI) n) k)))) k) (* (sqrt 2) (+ (* (* (log (* (* (PI) n) 2)) (sqrt (* (* (pow k 3) (PI)) n))) -1/2) (sqrt (* (* (PI) n) k)))) (+ (* (* (log (* (* (PI) n) 2)) (sqrt (* (* (pow k 3) (PI)) n))) -1/2) (sqrt (* (* (PI) n) k))) (* (log (* (* (PI) n) 2)) (sqrt (* (* (pow k 3) (PI)) n))) (log (* (* (PI) n) 2)) (sqrt (* (* (pow k 3) (PI)) n)) (* (* (pow k 3) (PI)) n) (* (pow k 3) (PI)) (pow k 3) 3 (sqrt (* (* (PI) n) k)) (* (* (PI) n) k))
53.0ms	n	@	0	((* (/ 1 (sqrt k)) (/ (pow (* n (* (PI) 2)) 1/2) (pow (* n (* (PI) 2)) (/ k 2)))) (/ 1 (sqrt k)) 1 (sqrt k) k (/ (pow (* n (* (PI) 2)) 1/2) (pow (* n (* (PI) 2)) (/ k 2))) (pow (* n (* (PI) 2)) 1/2) (* n (* (PI) 2)) n (* (PI) 2) (PI) 2 1/2 (pow (* n (* (PI) 2)) (/ k 2)) (/ k 2) (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (* (sqrt 2) (sqrt (/ (* (PI) n) k))) (sqrt 2) (sqrt (/ (* (PI) n) k)) (/ (* (PI) n) k) (* (PI) n) (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (* (sqrt (/ 1 k)) (pow (* (* (PI) n) 2) (+ (* -1/2 k) 1/2))) (sqrt (/ 1 k)) (/ 1 k) (pow (* (* (PI) n) 2) (+ (* -1/2 k) 1/2)) (* (* (PI) n) 2) (+ (* -1/2 k) 1/2) -1/2 (* (/ 1 (sqrt k)) (pow (* (* (* 2 (sqrt (PI))) (sqrt (PI))) n) (/ (- 1 k) 2))) (pow (* (* (* 2 (sqrt (PI))) (sqrt (PI))) n) (/ (- 1 k) 2)) (* (* (* 2 (sqrt (PI))) (sqrt (PI))) n) (* (* 2 (sqrt (PI))) (sqrt (PI))) (* 2 (sqrt (PI))) (sqrt (PI)) (/ (- 1 k) 2) (- 1 k) (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (/ (* (sqrt 2) (+ (* (* (log (* (* (PI) n) 2)) (sqrt (* (* (pow k 3) (PI)) n))) -1/2) (sqrt (* (* (PI) n) k)))) k) (* (sqrt 2) (+ (* (* (log (* (* (PI) n) 2)) (sqrt (* (* (pow k 3) (PI)) n))) -1/2) (sqrt (* (* (PI) n) k)))) (+ (* (* (log (* (* (PI) n) 2)) (sqrt (* (* (pow k 3) (PI)) n))) -1/2) (sqrt (* (* (PI) n) k))) (* (log (* (* (PI) n) 2)) (sqrt (* (* (pow k 3) (PI)) n))) (log (* (* (PI) n) 2)) (sqrt (* (* (pow k 3) (PI)) n)) (* (* (pow k 3) (PI)) n) (* (pow k 3) (PI)) (pow k 3) 3 (sqrt (* (* (PI) n) k)) (* (* (PI) n) k))
30.0ms	k	@	-inf	((* (/ 1 (sqrt k)) (/ (pow (* n (* (PI) 2)) 1/2) (pow (* n (* (PI) 2)) (/ k 2)))) (/ 1 (sqrt k)) 1 (sqrt k) k (/ (pow (* n (* (PI) 2)) 1/2) (pow (* n (* (PI) 2)) (/ k 2))) (pow (* n (* (PI) 2)) 1/2) (* n (* (PI) 2)) n (* (PI) 2) (PI) 2 1/2 (pow (* n (* (PI) 2)) (/ k 2)) (/ k 2) (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (* (sqrt 2) (sqrt (/ (* (PI) n) k))) (sqrt 2) (sqrt (/ (* (PI) n) k)) (/ (* (PI) n) k) (* (PI) n) (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (* (sqrt (/ 1 k)) (pow (* (* (PI) n) 2) (+ (* -1/2 k) 1/2))) (sqrt (/ 1 k)) (/ 1 k) (pow (* (* (PI) n) 2) (+ (* -1/2 k) 1/2)) (* (* (PI) n) 2) (+ (* -1/2 k) 1/2) -1/2 (* (/ 1 (sqrt k)) (pow (* (* (* 2 (sqrt (PI))) (sqrt (PI))) n) (/ (- 1 k) 2))) (pow (* (* (* 2 (sqrt (PI))) (sqrt (PI))) n) (/ (- 1 k) 2)) (* (* (* 2 (sqrt (PI))) (sqrt (PI))) n) (* (* 2 (sqrt (PI))) (sqrt (PI))) (* 2 (sqrt (PI))) (sqrt (PI)) (/ (- 1 k) 2) (- 1 k) (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (/ (* (sqrt 2) (+ (* (* (log (* (* (PI) n) 2)) (sqrt (* (* (pow k 3) (PI)) n))) -1/2) (sqrt (* (* (PI) n) k)))) k) (* (sqrt 2) (+ (* (* (log (* (* (PI) n) 2)) (sqrt (* (* (pow k 3) (PI)) n))) -1/2) (sqrt (* (* (PI) n) k)))) (+ (* (* (log (* (* (PI) n) 2)) (sqrt (* (* (pow k 3) (PI)) n))) -1/2) (sqrt (* (* (PI) n) k))) (* (log (* (* (PI) n) 2)) (sqrt (* (* (pow k 3) (PI)) n))) (log (* (* (PI) n) 2)) (sqrt (* (* (pow k 3) (PI)) n)) (* (* (pow k 3) (PI)) n) (* (pow k 3) (PI)) (pow k 3) 3 (sqrt (* (* (PI) n) k)) (* (* (PI) n) k))
27.0ms	k	@	0	((* (/ 1 (sqrt k)) (/ (pow (* n (* (PI) 2)) 1/2) (pow (* n (* (PI) 2)) (/ k 2)))) (/ 1 (sqrt k)) 1 (sqrt k) k (/ (pow (* n (* (PI) 2)) 1/2) (pow (* n (* (PI) 2)) (/ k 2))) (pow (* n (* (PI) 2)) 1/2) (* n (* (PI) 2)) n (* (PI) 2) (PI) 2 1/2 (pow (* n (* (PI) 2)) (/ k 2)) (/ k 2) (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (* (sqrt 2) (sqrt (/ (* (PI) n) k))) (sqrt 2) (sqrt (/ (* (PI) n) k)) (/ (* (PI) n) k) (* (PI) n) (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (* (sqrt (/ 1 k)) (pow (* (* (PI) n) 2) (+ (* -1/2 k) 1/2))) (sqrt (/ 1 k)) (/ 1 k) (pow (* (* (PI) n) 2) (+ (* -1/2 k) 1/2)) (* (* (PI) n) 2) (+ (* -1/2 k) 1/2) -1/2 (* (/ 1 (sqrt k)) (pow (* (* (* 2 (sqrt (PI))) (sqrt (PI))) n) (/ (- 1 k) 2))) (pow (* (* (* 2 (sqrt (PI))) (sqrt (PI))) n) (/ (- 1 k) 2)) (* (* (* 2 (sqrt (PI))) (sqrt (PI))) n) (* (* 2 (sqrt (PI))) (sqrt (PI))) (* 2 (sqrt (PI))) (sqrt (PI)) (/ (- 1 k) 2) (- 1 k) (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (/ (* (sqrt 2) (+ (* (* (log (* (* (PI) n) 2)) (sqrt (* (* (pow k 3) (PI)) n))) -1/2) (sqrt (* (* (PI) n) k)))) k) (* (sqrt 2) (+ (* (* (log (* (* (PI) n) 2)) (sqrt (* (* (pow k 3) (PI)) n))) -1/2) (sqrt (* (* (PI) n) k)))) (+ (* (* (log (* (* (PI) n) 2)) (sqrt (* (* (pow k 3) (PI)) n))) -1/2) (sqrt (* (* (PI) n) k))) (* (log (* (* (PI) n) 2)) (sqrt (* (* (pow k 3) (PI)) n))) (log (* (* (PI) n) 2)) (sqrt (* (* (pow k 3) (PI)) n)) (* (* (pow k 3) (PI)) n) (* (pow k 3) (PI)) (pow k 3) 3 (sqrt (* (* (PI) n) k)) (* (* (PI) n) k))
25.0ms	n	@	-inf	((* (/ 1 (sqrt k)) (/ (pow (* n (* (PI) 2)) 1/2) (pow (* n (* (PI) 2)) (/ k 2)))) (/ 1 (sqrt k)) 1 (sqrt k) k (/ (pow (* n (* (PI) 2)) 1/2) (pow (* n (* (PI) 2)) (/ k 2))) (pow (* n (* (PI) 2)) 1/2) (* n (* (PI) 2)) n (* (PI) 2) (PI) 2 1/2 (pow (* n (* (PI) 2)) (/ k 2)) (/ k 2) (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (* (sqrt 2) (sqrt (/ (* (PI) n) k))) (sqrt 2) (sqrt (/ (* (PI) n) k)) (/ (* (PI) n) k) (* (PI) n) (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (* (sqrt (/ 1 k)) (pow (* (* (PI) n) 2) (+ (* -1/2 k) 1/2))) (sqrt (/ 1 k)) (/ 1 k) (pow (* (* (PI) n) 2) (+ (* -1/2 k) 1/2)) (* (* (PI) n) 2) (+ (* -1/2 k) 1/2) -1/2 (* (/ 1 (sqrt k)) (pow (* (* (* 2 (sqrt (PI))) (sqrt (PI))) n) (/ (- 1 k) 2))) (pow (* (* (* 2 (sqrt (PI))) (sqrt (PI))) n) (/ (- 1 k) 2)) (* (* (* 2 (sqrt (PI))) (sqrt (PI))) n) (* (* 2 (sqrt (PI))) (sqrt (PI))) (* 2 (sqrt (PI))) (sqrt (PI)) (/ (- 1 k) 2) (- 1 k) (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (/ (* (sqrt 2) (+ (* (* (log (* (* (PI) n) 2)) (sqrt (* (* (pow k 3) (PI)) n))) -1/2) (sqrt (* (* (PI) n) k)))) k) (* (sqrt 2) (+ (* (* (log (* (* (PI) n) 2)) (sqrt (* (* (pow k 3) (PI)) n))) -1/2) (sqrt (* (* (PI) n) k)))) (+ (* (* (log (* (* (PI) n) 2)) (sqrt (* (* (pow k 3) (PI)) n))) -1/2) (sqrt (* (* (PI) n) k))) (* (log (* (* (PI) n) 2)) (sqrt (* (* (pow k 3) (PI)) n))) (log (* (* (PI) n) 2)) (sqrt (* (* (pow k 3) (PI)) n)) (* (* (pow k 3) (PI)) n) (* (pow k 3) (PI)) (pow k 3) 3 (sqrt (* (* (PI) n) k)) (* (* (PI) n) k))

simplify221.0ms (2.6%)

Memory

-16.5MiB live, 303.5MiB allocated; 31ms collecting garbage

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	509	5326
1	1477	5070
2	6004	4825
0	8586	4715

Stop Event

1×	iter limit
1×	node limit

Counts

150 → 150

Calls

Call 1

Inputs
#s(approx (* (/ 1 (sqrt k)) (/ (pow (* n (* (PI) 2)) 1/2) (pow (* n (* (PI) 2)) (/ k 2)))) #s(hole binary64 (* (sqrt (/ (* n (PI)) k)) (sqrt 2))))
#s(approx (* (/ 1 (sqrt k)) (/ (pow (* n (* (PI) 2)) 1/2) (pow (* n (* (PI) 2)) (/ k 2)))) #s(hole binary64 (/ (+ (* -1/2 (* (sqrt (* (pow k 3) (* n (PI)))) (* (log (* 2 (* n (PI)))) (sqrt 2)))) (* (sqrt (* k (* n (PI)))) (sqrt 2))) k)))
#s(approx (* (/ 1 (sqrt k)) (/ (pow (* n (* (PI) 2)) 1/2) (pow (* n (* (PI) 2)) (/ k 2)))) #s(hole binary64 (/ (+ (* k (+ (* -1 (* (sqrt (* (pow k 3) (* n (PI)))) (+ (* -1/4 (* (pow (log (* 2 (* n (PI)))) 2) (sqrt 2))) (* 1/8 (* (pow (log (* 2 (* n (PI)))) 2) (sqrt 2)))))) (* -1/2 (* (sqrt (* k (* n (PI)))) (* (log (* 2 (* n (PI)))) (sqrt 2)))))) (* (sqrt (* k (* n (PI)))) (sqrt 2))) k)))
#s(approx (* (/ 1 (sqrt k)) (/ (pow (* n (* (PI) 2)) 1/2) (pow (* n (* (PI) 2)) (/ k 2)))) #s(hole binary64 (/ (+ (* k (+ (* -1/2 (* (sqrt (* k (* n (PI)))) (* (log (* 2 (* n (PI)))) (sqrt 2)))) (* k (+ (* -1 (* (sqrt (* k (* n (PI)))) (+ (* -1/4 (* (pow (log (* 2 (* n (PI)))) 2) (sqrt 2))) (* 1/8 (* (pow (log (* 2 (* n (PI)))) 2) (sqrt 2)))))) (* -1 (* (sqrt (* (pow k 3) (* n (PI)))) (+ (* -1/2 (* (log (* 2 (* n (PI)))) (+ (* -1/4 (* (pow (log (* 2 (* n (PI)))) 2) (sqrt 2))) (* 1/8 (* (pow (log (* 2 (* n (PI)))) 2) (sqrt 2)))))) (+ (* -1/16 (* (pow (log (* 2 (* n (PI)))) 3) (sqrt 2))) (* 1/48 (* (pow (log (* 2 (* n (PI)))) 3) (sqrt 2))))))))))) (* (sqrt (* k (* n (PI)))) (sqrt 2))) k)))
#s(approx (/ 1 (sqrt k)) #s(hole binary64 (sqrt (/ 1 k))))
#s(approx (sqrt k) #s(hole binary64 (sqrt k)))
#s(approx k #s(hole binary64 k))
#s(approx (/ (pow (* n (* (PI) 2)) 1/2) (pow (* n (* (PI) 2)) (/ k 2))) #s(hole binary64 (* (sqrt (* n (PI))) (sqrt 2))))
#s(approx (/ (pow (* n (* (PI) 2)) 1/2) (pow (* n (* (PI) 2)) (/ k 2))) #s(hole binary64 (+ (* -1/2 (* (* k (* (log (* 2 (* n (PI)))) (sqrt 2))) (sqrt (* n (PI))))) (* (sqrt (* n (PI))) (sqrt 2)))))
#s(approx (/ (pow (* n (* (PI) 2)) 1/2) (pow (* n (* (PI) 2)) (/ k 2))) #s(hole binary64 (+ (* k (+ (* -1 (* (* k (+ (* -1/4 (* (pow (log (* 2 (* n (PI)))) 2) (sqrt 2))) (* 1/8 (* (pow (log (* 2 (* n (PI)))) 2) (sqrt 2))))) (sqrt (* n (PI))))) (* -1/2 (* (sqrt (* n (PI))) (* (log (* 2 (* n (PI)))) (sqrt 2)))))) (* (sqrt (* n (PI))) (sqrt 2)))))
#s(approx (/ (pow (* n (* (PI) 2)) 1/2) (pow (* n (* (PI) 2)) (/ k 2))) #s(hole binary64 (+ (* k (+ (* -1/2 (* (sqrt (* n (PI))) (* (log (* 2 (* n (PI)))) (sqrt 2)))) (* k (+ (* -1 (* (sqrt (* n (PI))) (+ (* -1/4 (* (pow (log (* 2 (* n (PI)))) 2) (sqrt 2))) (* 1/8 (* (pow (log (* 2 (* n (PI)))) 2) (sqrt 2)))))) (* -1 (* (* k (+ (* -1/2 (* (log (* 2 (* n (PI)))) (+ (* -1/4 (* (pow (log (* 2 (* n (PI)))) 2) (sqrt 2))) (* 1/8 (* (pow (log (* 2 (* n (PI)))) 2) (sqrt 2)))))) (+ (* -1/16 (* (pow (log (* 2 (* n (PI)))) 3) (sqrt 2))) (* 1/48 (* (pow (log (* 2 (* n (PI)))) 3) (sqrt 2)))))) (sqrt (* n (PI))))))))) (* (sqrt (* n (PI))) (sqrt 2)))))
#s(approx (pow (* n (* (PI) 2)) (/ k 2)) #s(hole binary64 1))
#s(approx (pow (* n (* (PI) 2)) (/ k 2)) #s(hole binary64 (+ 1 (* 1/2 (* k (log (* 2 (* n (PI)))))))))
#s(approx (pow (* n (* (PI) 2)) (/ k 2)) #s(hole binary64 (+ 1 (* k (+ (* 1/8 (* k (pow (log (* 2 (* n (PI)))) 2))) (* 1/2 (log (* 2 (* n (PI))))))))))
#s(approx (pow (* n (* (PI) 2)) (/ k 2)) #s(hole binary64 (+ 1 (* k (+ (* 1/2 (log (* 2 (* n (PI))))) (* k (+ (* 1/48 (* k (pow (log (* 2 (* n (PI)))) 3))) (* 1/8 (pow (log (* 2 (* n (PI)))) 2)))))))))
#s(approx (/ k 2) #s(hole binary64 (* 1/2 k)))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) #s(hole binary64 (* (sqrt (/ (* n (PI)) k)) (sqrt 2))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) #s(hole binary64 (/ (+ (* -1/2 (* (sqrt (* (pow k 3) (* n (PI)))) (* (log (* 2 (* n (PI)))) (sqrt 2)))) (* (sqrt (* k (* n (PI)))) (sqrt 2))) k)))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) #s(hole binary64 (/ (+ (* 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)))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) #s(hole binary64 (/ (+ (* 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)))
#s(approx (* (sqrt 2) (sqrt (/ (* (PI) n) k))) #s(hole binary64 (* (sqrt (/ (* n (PI)) k)) (sqrt 2))))
#s(approx (sqrt (/ (* (PI) n) k)) #s(hole binary64 (sqrt (/ (* n (PI)) k))))
#s(approx (/ (* (PI) n) k) #s(hole binary64 (/ (* n (PI)) k)))
#s(approx (* (sqrt (/ 1 k)) (pow (* (* (PI) n) 2) (+ (* -1/2 k) 1/2))) #s(hole binary64 (* (sqrt (/ (* n (PI)) k)) (sqrt 2))))
#s(approx (* (sqrt (/ 1 k)) (pow (* (* (PI) n) 2) (+ (* -1/2 k) 1/2))) #s(hole binary64 (/ (+ (* -1/2 (* (sqrt (* (pow k 3) (* n (PI)))) (* (log (* 2 (* n (PI)))) (sqrt 2)))) (* (sqrt (* k (* n (PI)))) (sqrt 2))) k)))
#s(approx (* (sqrt (/ 1 k)) (pow (* (* (PI) n) 2) (+ (* -1/2 k) 1/2))) #s(hole binary64 (/ (+ (* 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)))
#s(approx (* (sqrt (/ 1 k)) (pow (* (* (PI) n) 2) (+ (* -1/2 k) 1/2))) #s(hole binary64 (/ (+ (* 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)))
#s(approx (sqrt (/ 1 k)) #s(hole binary64 (sqrt (/ 1 k))))
#s(approx (/ 1 k) #s(hole binary64 (/ 1 k)))
#s(approx (pow (* (* (PI) n) 2) (+ (* -1/2 k) 1/2)) #s(hole binary64 (* (sqrt (* n (PI))) (sqrt 2))))
#s(approx (pow (* (* (PI) n) 2) (+ (* -1/2 k) 1/2)) #s(hole binary64 (+ (* -1/2 (* (* k (* (log (* 2 (* n (PI)))) (sqrt 2))) (sqrt (* n (PI))))) (* (sqrt (* n (PI))) (sqrt 2)))))
#s(approx (pow (* (* (PI) n) 2) (+ (* -1/2 k) 1/2)) #s(hole 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)))))
#s(approx (pow (* (* (PI) n) 2) (+ (* -1/2 k) 1/2)) #s(hole 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)))))
#s(approx (+ (* -1/2 k) 1/2) #s(hole binary64 1/2))
#s(approx (+ (* -1/2 k) 1/2) #s(hole binary64 (+ 1/2 (* -1/2 k))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* (* 2 (sqrt (PI))) (sqrt (PI))) n) (/ (- 1 k) 2))) #s(hole binary64 (* (sqrt (/ (* n (PI)) k)) (sqrt 2))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* (* 2 (sqrt (PI))) (sqrt (PI))) n) (/ (- 1 k) 2))) #s(hole binary64 (/ (+ (* -1/2 (* (sqrt (* (pow k 3) (* n (PI)))) (* (log (* 2 (* n (PI)))) (sqrt 2)))) (* (sqrt (* k (* n (PI)))) (sqrt 2))) k)))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* (* 2 (sqrt (PI))) (sqrt (PI))) n) (/ (- 1 k) 2))) #s(hole binary64 (/ (+ (* 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)))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* (* 2 (sqrt (PI))) (sqrt (PI))) n) (/ (- 1 k) 2))) #s(hole binary64 (/ (+ (* 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)))
#s(approx (pow (* (* (* 2 (sqrt (PI))) (sqrt (PI))) n) (/ (- 1 k) 2)) #s(hole binary64 (* (sqrt (* n (PI))) (sqrt 2))))
#s(approx (pow (* (* (* 2 (sqrt (PI))) (sqrt (PI))) n) (/ (- 1 k) 2)) #s(hole binary64 (+ (* -1/2 (* (* k (* (log (* 2 (* n (PI)))) (sqrt 2))) (sqrt (* n (PI))))) (* (sqrt (* n (PI))) (sqrt 2)))))
#s(approx (pow (* (* (* 2 (sqrt (PI))) (sqrt (PI))) n) (/ (- 1 k) 2)) #s(hole 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)))))
#s(approx (pow (* (* (* 2 (sqrt (PI))) (sqrt (PI))) n) (/ (- 1 k) 2)) #s(hole 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)))))
#s(approx (/ (- 1 k) 2) #s(hole binary64 1/2))
#s(approx (/ (- 1 k) 2) #s(hole binary64 (+ 1/2 (* -1/2 k))))
#s(approx (- 1 k) #s(hole binary64 1))
#s(approx (- 1 k) #s(hole binary64 (+ 1 (* -1 k))))
#s(approx (/ (* (sqrt 2) (+ (* (* (log (* (* (PI) n) 2)) (sqrt (* (* (pow k 3) (PI)) n))) -1/2) (sqrt (* (* (PI) n) k)))) k) #s(hole binary64 (* (sqrt (/ (* n (PI)) k)) (sqrt 2))))
#s(approx (/ (* (sqrt 2) (+ (* (* (log (* (* (PI) n) 2)) (sqrt (* (* (pow k 3) (PI)) n))) -1/2) (sqrt (* (* (PI) n) k)))) k) #s(hole binary64 (/ (+ (* -1/2 (* (sqrt (* (pow k 3) (* n (PI)))) (* (log (* 2 (* n (PI)))) (sqrt 2)))) (* (sqrt (* k (* n (PI)))) (sqrt 2))) k)))
#s(approx (* (sqrt 2) (+ (* (* (log (* (* (PI) n) 2)) (sqrt (* (* (pow k 3) (PI)) n))) -1/2) (sqrt (* (* (PI) n) k)))) #s(hole binary64 (* (sqrt (* k (* n (PI)))) (sqrt 2))))
#s(approx (* (sqrt 2) (+ (* (* (log (* (* (PI) n) 2)) (sqrt (* (* (pow k 3) (PI)) n))) -1/2) (sqrt (* (* (PI) n) k)))) #s(hole binary64 (+ (* -1/2 (* (sqrt (* (pow k 3) (* n (PI)))) (* (log (* 2 (* n (PI)))) (sqrt 2)))) (* (sqrt (* k (* n (PI)))) (sqrt 2)))))
#s(approx (+ (* (* (log (* (* (PI) n) 2)) (sqrt (* (* (pow k 3) (PI)) n))) -1/2) (sqrt (* (* (PI) n) k))) #s(hole binary64 (sqrt (* k (* n (PI))))))
#s(approx (+ (* (* (log (* (* (PI) n) 2)) (sqrt (* (* (pow k 3) (PI)) n))) -1/2) (sqrt (* (* (PI) n) k))) #s(hole binary64 (+ (sqrt (* k (* n (PI)))) (* -1/2 (* (sqrt (* (pow k 3) (* n (PI)))) (log (* 2 (* n (PI)))))))))
#s(approx (* (log (* (* (PI) n) 2)) (sqrt (* (* (pow k 3) (PI)) n))) #s(hole binary64 (* (sqrt (* (pow k 3) (* n (PI)))) (log (* 2 (* n (PI)))))))
#s(approx (sqrt (* (* (pow k 3) (PI)) n)) #s(hole binary64 (sqrt (* (pow k 3) (* n (PI))))))
#s(approx (* (* (pow k 3) (PI)) n) #s(hole binary64 (* (pow k 3) (* n (PI)))))
#s(approx (* (pow k 3) (PI)) #s(hole binary64 (* (pow k 3) (PI))))
#s(approx (pow k 3) #s(hole binary64 (pow k 3)))
#s(approx (sqrt (* (* (PI) n) k)) #s(hole binary64 (sqrt (* k (* n (PI))))))
#s(approx (* (* (PI) n) k) #s(hole binary64 (* k (* n (PI)))))
#s(approx (* (/ 1 (sqrt k)) (/ (pow (* n (* (PI) 2)) 1/2) (pow (* n (* (PI) 2)) (/ k 2)))) #s(hole binary64 (* (sqrt (/ (* n (PI)) k)) (/ (sqrt 2) (exp (* 1/2 (* k (log (* 2 (* n (PI)))))))))))
#s(approx (/ (pow (* n (* (PI) 2)) 1/2) (pow (* n (* (PI) 2)) (/ k 2))) #s(hole binary64 (* (sqrt (* n (PI))) (/ (sqrt 2) (exp (* 1/2 (* k (log (* 2 (* n (PI)))))))))))
#s(approx (pow (* n (* (PI) 2)) (/ k 2)) #s(hole binary64 (exp (* 1/2 (* k (log (* 2 (* n (PI)))))))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) #s(hole binary64 (* (sqrt (/ 1 k)) (exp (* 1/2 (* (log (* 2 (* n (PI)))) (- 1 k)))))))
#s(approx (* (sqrt (/ 1 k)) (pow (* (* (PI) n) 2) (+ (* -1/2 k) 1/2))) #s(hole binary64 (* (sqrt (/ 1 k)) (exp (* (log (* 2 (* n (PI)))) (- 1/2 (* 1/2 k)))))))
#s(approx (pow (* (* (PI) n) 2) (+ (* -1/2 k) 1/2)) #s(hole binary64 (exp (* (log (* 2 (* n (PI)))) (- 1/2 (* 1/2 k))))))
#s(approx (+ (* -1/2 k) 1/2) #s(hole binary64 (* -1/2 k)))
#s(approx (+ (* -1/2 k) 1/2) #s(hole binary64 (* k (- (* 1/2 (/ 1 k)) 1/2))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* (* 2 (sqrt (PI))) (sqrt (PI))) n) (/ (- 1 k) 2))) #s(hole binary64 (* (sqrt (/ 1 k)) (exp (* 1/2 (* (log (* 2 (* n (PI)))) (- 1 k)))))))
#s(approx (pow (* (* (* 2 (sqrt (PI))) (sqrt (PI))) n) (/ (- 1 k) 2)) #s(hole binary64 (exp (* 1/2 (* (log (* 2 (* n (PI)))) (- 1 k))))))
#s(approx (/ (- 1 k) 2) #s(hole binary64 (* -1/2 k)))
#s(approx (/ (- 1 k) 2) #s(hole binary64 (* k (- (* 1/2 (/ 1 k)) 1/2))))
#s(approx (- 1 k) #s(hole binary64 (* -1 k)))
#s(approx (- 1 k) #s(hole binary64 (* k (- (/ 1 k) 1))))
#s(approx (/ (* (sqrt 2) (+ (* (* (log (* (* (PI) n) 2)) (sqrt (* (* (pow k 3) (PI)) n))) -1/2) (sqrt (* (* (PI) n) k)))) k) #s(hole binary64 (* -1/2 (* (sqrt (* k (* n (PI)))) (* (log (* 2 (* n (PI)))) (sqrt 2))))))
#s(approx (/ (* (sqrt 2) (+ (* (* (log (* (* (PI) n) 2)) (sqrt (* (* (pow k 3) (PI)) n))) -1/2) (sqrt (* (* (PI) n) k)))) k) #s(hole binary64 (* k (+ (* -1/2 (* (sqrt (/ (* n (PI)) k)) (* (log (* 2 (* n (PI)))) (sqrt 2)))) (* (sqrt (/ (* n (PI)) (pow k 3))) (sqrt 2))))))
#s(approx (* (sqrt 2) (+ (* (* (log (* (* (PI) n) 2)) (sqrt (* (* (pow k 3) (PI)) n))) -1/2) (sqrt (* (* (PI) n) k)))) #s(hole binary64 (* -1/2 (* (sqrt (* (pow k 3) (* n (PI)))) (* (log (* 2 (* n (PI)))) (sqrt 2))))))
#s(approx (* (sqrt 2) (+ (* (* (log (* (* (PI) n) 2)) (sqrt (* (* (pow k 3) (PI)) n))) -1/2) (sqrt (* (* (PI) n) k)))) #s(hole binary64 (* (pow k 2) (+ (* -1/2 (* (sqrt (/ (* n (PI)) k)) (* (log (* 2 (* n (PI)))) (sqrt 2)))) (* (sqrt (/ (* n (PI)) (pow k 3))) (sqrt 2))))))
#s(approx (+ (* (* (log (* (* (PI) n) 2)) (sqrt (* (* (pow k 3) (PI)) n))) -1/2) (sqrt (* (* (PI) n) k))) #s(hole binary64 (* -1/2 (* (sqrt (* (pow k 3) (* n (PI)))) (log (* 2 (* n (PI))))))))
#s(approx (+ (* (* (log (* (* (PI) n) 2)) (sqrt (* (* (pow k 3) (PI)) n))) -1/2) (sqrt (* (* (PI) n) k))) #s(hole binary64 (* (pow k 2) (+ (sqrt (/ (* n (PI)) (pow k 3))) (* -1/2 (* (sqrt (/ (* n (PI)) k)) (log (* 2 (* n (PI))))))))))
#s(approx (sqrt k) #s(hole binary64 (* -1 (* (sqrt k) (pow (sqrt -1) 2)))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) #s(hole binary64 (* (sqrt (/ 1 k)) (exp (* 1/2 (* (log (* 2 (* n (PI)))) (+ 1 (* -1 k))))))))
#s(approx (* (sqrt 2) (sqrt (/ (* (PI) n) k))) #s(hole binary64 (* (sqrt (/ (* n (PI)) k)) (* (pow (sqrt -1) 2) (sqrt 2)))))
#s(approx (sqrt (/ (* (PI) n) k)) #s(hole binary64 (* (sqrt (/ (* n (PI)) k)) (pow (sqrt -1) 2))))
#s(approx (* (sqrt (/ 1 k)) (pow (* (* (PI) n) 2) (+ (* -1/2 k) 1/2))) #s(hole binary64 (* (sqrt (/ 1 k)) (* (exp (* (log (* 2 (* n (PI)))) (+ 1/2 (* -1/2 k)))) (pow (sqrt -1) 2)))))
#s(approx (sqrt (/ 1 k)) #s(hole binary64 (* (sqrt (/ 1 k)) (pow (sqrt -1) 2))))
#s(approx (pow (* (* (PI) n) 2) (+ (* -1/2 k) 1/2)) #s(hole binary64 (exp (* (log (* 2 (* n (PI)))) (+ 1/2 (* -1/2 k))))))
#s(approx (+ (* -1/2 k) 1/2) #s(hole binary64 (* -1 (* k (- 1/2 (* 1/2 (/ 1 k)))))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* (* 2 (sqrt (PI))) (sqrt (PI))) n) (/ (- 1 k) 2))) #s(hole binary64 (* (sqrt (/ 1 k)) (exp (* 1/2 (* (log (* 2 (* n (PI)))) (+ 1 (* -1 k))))))))
#s(approx (pow (* (* (* 2 (sqrt (PI))) (sqrt (PI))) n) (/ (- 1 k) 2)) #s(hole binary64 (exp (* 1/2 (* (log (* 2 (* n (PI)))) (+ 1 (* -1 k)))))))
#s(approx (/ (- 1 k) 2) #s(hole binary64 (* -1 (* k (- 1/2 (* 1/2 (/ 1 k)))))))
#s(approx (- 1 k) #s(hole binary64 (* -1 (* k (- 1 (/ 1 k))))))
#s(approx (/ (* (sqrt 2) (+ (* (* (log (* (* (PI) n) 2)) (sqrt (* (* (pow k 3) (PI)) n))) -1/2) (sqrt (* (* (PI) n) k)))) k) #s(hole binary64 (* -1/2 (* (sqrt (* k (* n (PI)))) (* (log (* 2 (* n (PI)))) (* (pow (sqrt -1) 2) (sqrt 2)))))))
#s(approx (/ (* (sqrt 2) (+ (* (* (log (* (* (PI) n) 2)) (sqrt (* (* (pow k 3) (PI)) n))) -1/2) (sqrt (* (* (PI) n) k)))) k) #s(hole binary64 (* -1 (* k (+ (* 1/2 (* (sqrt (/ (* n (PI)) k)) (* (log (* 2 (* n (PI)))) (* (pow (sqrt -1) 2) (sqrt 2))))) (* (sqrt (/ (* n (PI)) (pow k 3))) (* (pow (sqrt -1) 2) (sqrt 2))))))))
#s(approx (* (sqrt 2) (+ (* (* (log (* (* (PI) n) 2)) (sqrt (* (* (pow k 3) (PI)) n))) -1/2) (sqrt (* (* (PI) n) k)))) #s(hole binary64 (* -1/2 (* (sqrt (* (pow k 3) (* n (PI)))) (* (log (* 2 (* n (PI)))) (* (pow (sqrt -1) 2) (sqrt 2)))))))
#s(approx (* (sqrt 2) (+ (* (* (log (* (* (PI) n) 2)) (sqrt (* (* (pow k 3) (PI)) n))) -1/2) (sqrt (* (* (PI) n) k)))) #s(hole binary64 (* (pow k 2) (+ (* -1 (* (sqrt (/ (* n (PI)) (pow k 3))) (* (pow (sqrt -1) 2) (sqrt 2)))) (* -1/2 (* (sqrt (/ (* n (PI)) k)) (* (log (* 2 (* n (PI)))) (* (pow (sqrt -1) 2) (sqrt 2)))))))))
#s(approx (+ (* (* (log (* (* (PI) n) 2)) (sqrt (* (* (pow k 3) (PI)) n))) -1/2) (sqrt (* (* (PI) n) k))) #s(hole binary64 (* -1/2 (* (sqrt (* (pow k 3) (* n (PI)))) (* (log (* 2 (* n (PI)))) (pow (sqrt -1) 2))))))
#s(approx (+ (* (* (log (* (* (PI) n) 2)) (sqrt (* (* (pow k 3) (PI)) n))) -1/2) (sqrt (* (* (PI) n) k))) #s(hole binary64 (* (pow k 2) (+ (* -1 (* (sqrt (/ (* n (PI)) (pow k 3))) (pow (sqrt -1) 2))) (* -1/2 (* (sqrt (/ (* n (PI)) k)) (* (log (* 2 (* n (PI)))) (pow (sqrt -1) 2))))))))
#s(approx (* (log (* (* (PI) n) 2)) (sqrt (* (* (pow k 3) (PI)) n))) #s(hole binary64 (* (sqrt (* (pow k 3) (* n (PI)))) (* (log (* 2 (* n (PI)))) (pow (sqrt -1) 2)))))
#s(approx (sqrt (* (* (pow k 3) (PI)) n)) #s(hole binary64 (* (sqrt (* (pow k 3) (* n (PI)))) (pow (sqrt -1) 2))))
#s(approx (sqrt (* (* (PI) n) k)) #s(hole binary64 (* -1 (* (sqrt (* k (* n (PI)))) (pow (sqrt -1) 2)))))
#s(approx (* (/ 1 (sqrt k)) (/ (pow (* n (* (PI) 2)) 1/2) (pow (* n (* (PI) 2)) (/ k 2)))) #s(hole binary64 (* (sqrt (/ (* n (PI)) k)) (/ (sqrt 2) (exp (* 1/2 (* k (+ (log n) (log (* 2 (PI)))))))))))
#s(approx (/ (pow (* n (* (PI) 2)) 1/2) (pow (* n (* (PI) 2)) (/ k 2))) #s(hole binary64 (* (sqrt (* n (PI))) (/ (sqrt 2) (exp (* 1/2 (* k (+ (log n) (log (* 2 (PI)))))))))))
#s(approx (pow (* n (* (PI) 2)) 1/2) #s(hole binary64 (* (sqrt (* n (PI))) (sqrt 2))))
#s(approx (* n (* (PI) 2)) #s(hole binary64 (* 2 (* n (PI)))))
#s(approx n #s(hole binary64 n))
#s(approx (pow (* n (* (PI) 2)) (/ k 2)) #s(hole binary64 (exp (* 1/2 (* k (+ (log n) (log (* 2 (PI)))))))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) #s(hole binary64 (* (sqrt (/ 1 k)) (exp (* 1/2 (* (+ (log n) (log (* 2 (PI)))) (- 1 k)))))))
#s(approx (* (PI) n) #s(hole binary64 (* n (PI))))
#s(approx (* (sqrt (/ 1 k)) (pow (* (* (PI) n) 2) (+ (* -1/2 k) 1/2))) #s(hole binary64 (* (sqrt (/ 1 k)) (exp (* (+ 1/2 (* -1/2 k)) (+ (log n) (log (* 2 (PI)))))))))
#s(approx (pow (* (* (PI) n) 2) (+ (* -1/2 k) 1/2)) #s(hole binary64 (exp (* (+ 1/2 (* -1/2 k)) (+ (log n) (log (* 2 (PI))))))))
#s(approx (* (* (PI) n) 2) #s(hole binary64 (* 2 (* n (PI)))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* (* 2 (sqrt (PI))) (sqrt (PI))) n) (/ (- 1 k) 2))) #s(hole binary64 (* (sqrt (/ 1 k)) (exp (* 1/2 (* (+ (log n) (log (* 2 (PI)))) (- 1 k)))))))
#s(approx (pow (* (* (* 2 (sqrt (PI))) (sqrt (PI))) n) (/ (- 1 k) 2)) #s(hole binary64 (exp (* 1/2 (* (+ (log n) (log (* 2 (PI)))) (- 1 k))))))
#s(approx (* (* (* 2 (sqrt (PI))) (sqrt (PI))) n) #s(hole binary64 (* 2 (* n (PI)))))
#s(approx (/ (* (sqrt 2) (+ (* (* (log (* (* (PI) n) 2)) (sqrt (* (* (pow k 3) (PI)) n))) -1/2) (sqrt (* (* (PI) n) k)))) k) #s(hole binary64 (/ (* (sqrt 2) (+ (sqrt (* k (* n (PI)))) (* -1/2 (* (sqrt (* (pow k 3) (* n (PI)))) (+ (log n) (log (* 2 (PI)))))))) k)))
#s(approx (* (sqrt 2) (+ (* (* (log (* (* (PI) n) 2)) (sqrt (* (* (pow k 3) (PI)) n))) -1/2) (sqrt (* (* (PI) n) k)))) #s(hole binary64 (* (sqrt 2) (+ (sqrt (* k (* n (PI)))) (* -1/2 (* (sqrt (* (pow k 3) (* n (PI)))) (+ (log n) (log (* 2 (PI))))))))))
#s(approx (+ (* (* (log (* (* (PI) n) 2)) (sqrt (* (* (pow k 3) (PI)) n))) -1/2) (sqrt (* (* (PI) n) k))) #s(hole binary64 (+ (sqrt (* k (* n (PI)))) (* -1/2 (* (sqrt (* (pow k 3) (* n (PI)))) (+ (log n) (log (* 2 (PI)))))))))
#s(approx (* (log (* (* (PI) n) 2)) (sqrt (* (* (pow k 3) (PI)) n))) #s(hole binary64 (* (sqrt (* (pow k 3) (* n (PI)))) (+ (log n) (log (* 2 (PI)))))))
#s(approx (log (* (* (PI) n) 2)) #s(hole binary64 (+ (log n) (log (* 2 (PI))))))
#s(approx (* (/ 1 (sqrt k)) (/ (pow (* n (* (PI) 2)) 1/2) (pow (* n (* (PI) 2)) (/ k 2)))) #s(hole binary64 (* (sqrt (/ (* n (PI)) k)) (/ (sqrt 2) (exp (* 1/2 (* k (+ (log (* 2 (PI))) (* -1 (log (/ 1 n)))))))))))
#s(approx (/ (pow (* n (* (PI) 2)) 1/2) (pow (* n (* (PI) 2)) (/ k 2))) #s(hole binary64 (* (sqrt (* n (PI))) (/ (sqrt 2) (exp (* 1/2 (* k (+ (log (* 2 (PI))) (* -1 (log (/ 1 n)))))))))))
#s(approx (pow (* n (* (PI) 2)) (/ k 2)) #s(hole binary64 (exp (* 1/2 (* k (+ (log (* 2 (PI))) (* -1 (log (/ 1 n)))))))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) #s(hole binary64 (* (sqrt (/ 1 k)) (exp (* 1/2 (* (+ (log (* 2 (PI))) (* -1 (log (/ 1 n)))) (- 1 k)))))))
#s(approx (* (sqrt (/ 1 k)) (pow (* (* (PI) n) 2) (+ (* -1/2 k) 1/2))) #s(hole binary64 (* (sqrt (/ 1 k)) (exp (* (+ 1/2 (* -1/2 k)) (+ (log (* 2 (PI))) (* -1 (log (/ 1 n)))))))))
#s(approx (pow (* (* (PI) n) 2) (+ (* -1/2 k) 1/2)) #s(hole binary64 (exp (* (+ 1/2 (* -1/2 k)) (+ (log (* 2 (PI))) (* -1 (log (/ 1 n))))))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* (* 2 (sqrt (PI))) (sqrt (PI))) n) (/ (- 1 k) 2))) #s(hole binary64 (* (sqrt (/ 1 k)) (exp (* 1/2 (* (+ (log (* 2 (PI))) (* -1 (log (/ 1 n)))) (- 1 k)))))))
#s(approx (pow (* (* (* 2 (sqrt (PI))) (sqrt (PI))) n) (/ (- 1 k) 2)) #s(hole binary64 (exp (* 1/2 (* (+ (log (* 2 (PI))) (* -1 (log (/ 1 n)))) (- 1 k))))))
#s(approx (/ (* (sqrt 2) (+ (* (* (log (* (* (PI) n) 2)) (sqrt (* (* (pow k 3) (PI)) n))) -1/2) (sqrt (* (* (PI) n) k)))) k) #s(hole binary64 (/ (* n (* (sqrt 2) (+ (sqrt (/ (* k (PI)) n)) (* -1/2 (* (sqrt (/ (* (pow k 3) (PI)) n)) (+ (log (* 2 (PI))) (* -1 (log (/ 1 n))))))))) k)))
#s(approx (* (sqrt 2) (+ (* (* (log (* (* (PI) n) 2)) (sqrt (* (* (pow k 3) (PI)) n))) -1/2) (sqrt (* (* (PI) n) k)))) #s(hole binary64 (* n (* (sqrt 2) (+ (sqrt (/ (* k (PI)) n)) (* -1/2 (* (sqrt (/ (* (pow k 3) (PI)) n)) (+ (log (* 2 (PI))) (* -1 (log (/ 1 n)))))))))))
#s(approx (+ (* (* (log (* (* (PI) n) 2)) (sqrt (* (* (pow k 3) (PI)) n))) -1/2) (sqrt (* (* (PI) n) k))) #s(hole binary64 (* n (+ (sqrt (/ (* k (PI)) n)) (* -1/2 (* (sqrt (/ (* (pow k 3) (PI)) n)) (+ (log (* 2 (PI))) (* -1 (log (/ 1 n))))))))))
#s(approx (* (log (* (* (PI) n) 2)) (sqrt (* (* (pow k 3) (PI)) n))) #s(hole binary64 (* (sqrt (* (pow k 3) (* n (PI)))) (+ (log (* 2 (PI))) (* -1 (log (/ 1 n)))))))
#s(approx (log (* (* (PI) n) 2)) #s(hole binary64 (+ (log (* 2 (PI))) (* -1 (log (/ 1 n))))))
#s(approx (* (/ 1 (sqrt k)) (/ (pow (* n (* (PI) 2)) 1/2) (pow (* n (* (PI) 2)) (/ k 2)))) #s(hole binary64 (* -1 (* (sqrt (/ (* n (PI)) k)) (/ (* (sqrt -2) (sqrt -1)) (exp (* 1/2 (* k (+ (log (* -2 (PI))) (* -1 (log (/ -1 n))))))))))))
#s(approx (/ (pow (* n (* (PI) 2)) 1/2) (pow (* n (* (PI) 2)) (/ k 2))) #s(hole binary64 (* -1 (* (sqrt (* n (PI))) (/ (* (sqrt -2) (sqrt -1)) (exp (* 1/2 (* k (+ (log (* -2 (PI))) (* -1 (log (/ -1 n))))))))))))
#s(approx (pow (* n (* (PI) 2)) 1/2) #s(hole binary64 (* -1 (* (sqrt (* n (PI))) (* (sqrt -2) (sqrt -1))))))
#s(approx (pow (* n (* (PI) 2)) (/ k 2)) #s(hole binary64 (exp (* 1/2 (* k (+ (log (* -2 (PI))) (* -1 (log (/ -1 n)))))))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) #s(hole binary64 (* (sqrt (/ 1 k)) (exp (* 1/2 (* (+ (log (* -2 (PI))) (* -1 (log (/ -1 n)))) (- 1 k)))))))
#s(approx (* (sqrt 2) (sqrt (/ (* (PI) n) k))) #s(hole binary64 (* -1 (* (sqrt (/ (* n (PI)) k)) (* (pow (sqrt -1) 2) (sqrt 2))))))
#s(approx (sqrt (/ (* (PI) n) k)) #s(hole binary64 (* -1 (* (sqrt (/ (* n (PI)) k)) (pow (sqrt -1) 2)))))
#s(approx (* (sqrt (/ 1 k)) (pow (* (* (PI) n) 2) (+ (* -1/2 k) 1/2))) #s(hole binary64 (* (sqrt (/ 1 k)) (exp (* (+ 1/2 (* -1/2 k)) (+ (log (* -2 (PI))) (* -1 (log (/ -1 n)))))))))
#s(approx (pow (* (* (PI) n) 2) (+ (* -1/2 k) 1/2)) #s(hole binary64 (exp (* (+ 1/2 (* -1/2 k)) (+ (log (* -2 (PI))) (* -1 (log (/ -1 n))))))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* (* 2 (sqrt (PI))) (sqrt (PI))) n) (/ (- 1 k) 2))) #s(hole binary64 (* (sqrt (/ 1 k)) (exp (* 1/2 (* (+ (log (* -2 (PI))) (* -1 (log (/ -1 n)))) (- 1 k)))))))
#s(approx (pow (* (* (* 2 (sqrt (PI))) (sqrt (PI))) n) (/ (- 1 k) 2)) #s(hole binary64 (exp (* 1/2 (* (+ (log (* -2 (PI))) (* -1 (log (/ -1 n)))) (- 1 k))))))
#s(approx (/ (* (sqrt 2) (+ (* (* (log (* (* (PI) n) 2)) (sqrt (* (* (pow k 3) (PI)) n))) -1/2) (sqrt (* (* (PI) n) k)))) k) #s(hole binary64 (* -1 (/ (* n (* (sqrt 2) (+ (* -1/2 (* (sqrt (/ (* (pow k 3) (PI)) n)) (* (pow (sqrt -1) 2) (+ (log (* -2 (PI))) (* -1 (log (/ -1 n))))))) (* (sqrt (/ (* k (PI)) n)) (pow (sqrt -1) 2))))) k))))
#s(approx (* (sqrt 2) (+ (* (* (log (* (* (PI) n) 2)) (sqrt (* (* (pow k 3) (PI)) n))) -1/2) (sqrt (* (* (PI) n) k)))) #s(hole binary64 (* -1 (* n (* (sqrt 2) (+ (* -1/2 (* (sqrt (/ (* (pow k 3) (PI)) n)) (* (pow (sqrt -1) 2) (+ (log (* -2 (PI))) (* -1 (log (/ -1 n))))))) (* (sqrt (/ (* k (PI)) n)) (pow (sqrt -1) 2))))))))
#s(approx (+ (* (* (log (* (* (PI) n) 2)) (sqrt (* (* (pow k 3) (PI)) n))) -1/2) (sqrt (* (* (PI) n) k))) #s(hole binary64 (* -1 (* n (+ (* -1/2 (* (sqrt (/ (* (pow k 3) (PI)) n)) (* (pow (sqrt -1) 2) (+ (log (* -2 (PI))) (* -1 (log (/ -1 n))))))) (* (sqrt (/ (* k (PI)) n)) (pow (sqrt -1) 2)))))))
#s(approx (* (log (* (* (PI) n) 2)) (sqrt (* (* (pow k 3) (PI)) n))) #s(hole binary64 (* -1 (* (sqrt (* (pow k 3) (* n (PI)))) (* (pow (sqrt -1) 2) (+ (log (* -2 (PI))) (* -1 (log (/ -1 n)))))))))
#s(approx (log (* (* (PI) n) 2)) #s(hole binary64 (+ (log (* -2 (PI))) (* -1 (log (/ -1 n))))))
#s(approx (sqrt (* (* (pow k 3) (PI)) n)) #s(hole binary64 (* -1 (* (sqrt (* (pow k 3) (* n (PI)))) (pow (sqrt -1) 2)))))

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

rewrite107.0ms (1.3%)

Memory

-6.1MiB live, 138.9MiB allocated; 18ms collecting garbage

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	59	446
0	101	415
1	321	401
0	1751	401

Stop Event

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

Counts

50 → 624

Calls

Call 1

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

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

eval180.0ms (2.1%)

Memory: -11.0MiB live, 235.4MiB allocated; 164ms collecting garbage
Compiler: Compiled 27 553 to 3 107 computations (88.7% saved)

prune44.0ms (0.5%)

Memory

9.3MiB live, 105.4MiB allocated; 23ms collecting garbage

Pruning

21 alts after pruning (20 fresh and 1 done)

	Pruned	Kept	Total
New	727	19	746
Fresh	11	1	12
Picked	4	1	5
Done	0	0	0
Total	742	21	763

Accuracy

100.0%

Counts

763 → 21

Alt Table

Click to see full alt table

Status	Accuracy	Program
	76.4%	(/.f64 (sqrt.f64 (.f64 (/.f64 (.f64 (PI.f64) n) k) #s(literal 2 binary64))) (pow.f64 (.f64 (.f64 (PI.f64) n) #s(literal 2 binary64)) (/.f64 k #s(literal 2 binary64))))
▶	52.5%	(.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 #s(literal -1/2 binary64) k))))
	99.5%	(.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) (/.f64 (.f64 (sqrt.f64 (.f64 (PI.f64) n)) (sqrt.f64 #s(literal 2 binary64))) (pow.f64 (.f64 n (*.f64 (PI.f64) #s(literal 2 binary64))) (/.f64 k #s(literal 2 binary64)))))
▶	99.6%	(.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) (/.f64 (sqrt.f64 (.f64 (.f64 (PI.f64) n) #s(literal 2 binary64))) (pow.f64 (.f64 (*.f64 (PI.f64) n) #s(literal 2 binary64)) (/.f64 k #s(literal 2 binary64)))))
	50.0%	(.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) #s(approx (pow ( (* (PI) n) 2) (+ (* -1/2 k) 1/2)) (.f64 (sqrt.f64 (.f64 (PI.f64) n)) (sqrt.f64 #s(literal 2 binary64)))))
	99.5%	#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (/.f64 (.f64 (pow.f64 (.f64 (*.f64 (PI.f64) n) #s(literal 2 binary64)) (fma.f64 #s(literal -1/2 binary64) k #s(literal 1/2 binary64))) #s(literal 1 binary64)) (sqrt.f64 k)))
	67.9%	#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 (PI.f64) n) #s(literal 2 binary64))) (sqrt.f64 (.f64 (.f64 (pow.f64 k #s(literal 3 binary64)) (PI.f64)) n))) #s(literal -1/2 binary64) (.f64 (sqrt.f64 (.f64 (PI.f64) n)) (sqrt.f64 k)))) k))
▶	40.3%	#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (/.f64 (.f64 (sqrt.f64 #s(literal 2 binary64)) #s(approx (+ ( (* (log (* (* (PI) n) 2)) (sqrt (* (* (pow k 3) (PI)) n))) -1/2) (sqrt (* (* (PI) n) k))) (sqrt.f64 (.f64 (.f64 (PI.f64) n) k)))) k))
	50.1%	#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (/.f64 (sqrt.f64 (.f64 (.f64 (PI.f64) n) #s(literal 2 binary64))) (sqrt.f64 k)))
	58.2%	#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (.f64 (fma.f64 (.f64 (sqrt.f64 (.f64 (.f64 (pow.f64 k #s(literal 3 binary64)) (PI.f64)) n)) (log.f64 (.f64 (.f64 (PI.f64) n) #s(literal 2 binary64)))) #s(literal -1/2 binary64) (sqrt.f64 (.f64 (.f64 (PI.f64) n) k))) (/.f64 (sqrt.f64 #s(literal 2 binary64)) k)))
	50.1%	#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (.f64 (pow.f64 k #s(literal -1/2 binary64)) (sqrt.f64 (.f64 (*.f64 (PI.f64) n) #s(literal 2 binary64)))))
	49.9%	#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (.f64 (.f64 (pow.f64 k #s(literal -1/2 binary64)) (sqrt.f64 n)) (sqrt.f64 (*.f64 #s(literal 2 binary64) (PI.f64)))))
✓	99.5%	#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) k)) (pow.f64 (.f64 (*.f64 (PI.f64) n) #s(literal 2 binary64)) (fma.f64 #s(literal -1/2 binary64) k #s(literal 1/2 binary64)))))
	50.1%	#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) k)) (pow.f64 (.f64 (.f64 (PI.f64) n) #s(literal 2 binary64)) #s(approx (+ ( -1/2 k) 1/2) #s(literal 1/2 binary64)))))
	50.0%	#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))))
	38.1%	#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (.f64 (sqrt.f64 #s(literal 2 binary64)) (.f64 (sqrt.f64 (PI.f64)) (sqrt.f64 (/.f64 n k)))))
	38.0%	#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (.f64 (sqrt.f64 #s(literal 2 binary64)) (sqrt.f64 (.f64 (/.f64 n k) (PI.f64)))))
▶	38.1%	#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (.f64 (sqrt.f64 #s(literal 2 binary64)) (sqrt.f64 (.f64 (sqrt.f64 (PI.f64)) (*.f64 (sqrt.f64 (PI.f64)) (/.f64 n k))))))
	38.0%	#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (.f64 (sqrt.f64 #s(literal 2 binary64)) (sqrt.f64 (.f64 n (/.f64 (PI.f64) k)))))
▶	38.2%	#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))))
	76.3%	#s(approx (* (/ 1 (sqrt k)) (/ (pow (* n (* (PI) 2)) 1/2) (pow (* n (* (PI) 2)) (/ k 2)))) (.f64 (/.f64 (sqrt.f64 #s(literal 2 binary64)) (sqrt.f64 (pow.f64 (.f64 (.f64 (PI.f64) n) #s(literal 2 binary64)) k))) (sqrt.f64 (/.f64 (.f64 (PI.f64) n) k))))

Compiler

Compiled 1 230 to 950 computations (22.8% saved)

series80.0ms (1%)

Memory

26.2MiB live, 263.5MiB allocated; 22ms collecting garbage

Counts

39 → 103

Calls

Call 1

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

Outputs
#s(approx (* (/ 1 (sqrt k)) (/ (sqrt (* (* (PI) n) 2)) (pow (* (* (PI) n) 2) (/ k 2)))) #s(hole binary64 (* (sqrt (/ (* n (PI)) k)) (sqrt 2))))
#s(approx (* (/ 1 (sqrt k)) (/ (sqrt (* (* (PI) n) 2)) (pow (* (* (PI) n) 2) (/ k 2)))) #s(hole binary64 (/ (+ (* -1/2 (* (sqrt (* (pow k 3) (* n (PI)))) (* (log (* 2 (* n (PI)))) (sqrt 2)))) (* (sqrt (* k (* n (PI)))) (sqrt 2))) k)))
#s(approx (* (/ 1 (sqrt k)) (/ (sqrt (* (* (PI) n) 2)) (pow (* (* (PI) n) 2) (/ k 2)))) #s(hole binary64 (/ (+ (* k (+ (* -1 (* (sqrt (* (pow k 3) (* n (PI)))) (+ (* -1/4 (* (pow (log (* 2 (* n (PI)))) 2) (sqrt 2))) (* 1/8 (* (pow (log (* 2 (* n (PI)))) 2) (sqrt 2)))))) (* -1/2 (* (sqrt (* k (* n (PI)))) (* (log (* 2 (* n (PI)))) (sqrt 2)))))) (* (sqrt (* k (* n (PI)))) (sqrt 2))) k)))
#s(approx (* (/ 1 (sqrt k)) (/ (sqrt (* (* (PI) n) 2)) (pow (* (* (PI) n) 2) (/ k 2)))) #s(hole binary64 (/ (+ (* k (+ (* -1/2 (* (sqrt (* k (* n (PI)))) (* (log (* 2 (* n (PI)))) (sqrt 2)))) (* k (+ (* -1 (* (sqrt (* k (* n (PI)))) (+ (* -1/4 (* (pow (log (* 2 (* n (PI)))) 2) (sqrt 2))) (* 1/8 (* (pow (log (* 2 (* n (PI)))) 2) (sqrt 2)))))) (* -1 (* (sqrt (* (pow k 3) (* n (PI)))) (+ (* -1/2 (* (log (* 2 (* n (PI)))) (+ (* -1/4 (* (pow (log (* 2 (* n (PI)))) 2) (sqrt 2))) (* 1/8 (* (pow (log (* 2 (* n (PI)))) 2) (sqrt 2)))))) (+ (* -1/16 (* (pow (log (* 2 (* n (PI)))) 3) (sqrt 2))) (* 1/48 (* (pow (log (* 2 (* n (PI)))) 3) (sqrt 2))))))))))) (* (sqrt (* k (* n (PI)))) (sqrt 2))) k)))
#s(approx (/ 1 (sqrt k)) #s(hole binary64 (sqrt (/ 1 k))))
#s(approx (sqrt k) #s(hole binary64 (sqrt k)))
#s(approx k #s(hole binary64 k))
#s(approx (/ (sqrt (* (* (PI) n) 2)) (pow (* (* (PI) n) 2) (/ k 2))) #s(hole binary64 (* (sqrt (* n (PI))) (sqrt 2))))
#s(approx (/ (sqrt (* (* (PI) n) 2)) (pow (* (* (PI) n) 2) (/ k 2))) #s(hole binary64 (+ (* -1/2 (* (* k (* (log (* 2 (* n (PI)))) (sqrt 2))) (sqrt (* n (PI))))) (* (sqrt (* n (PI))) (sqrt 2)))))
#s(approx (/ (sqrt (* (* (PI) n) 2)) (pow (* (* (PI) n) 2) (/ k 2))) #s(hole binary64 (+ (* k (+ (* -1 (* (* k (+ (* -1/4 (* (pow (log (* 2 (* n (PI)))) 2) (sqrt 2))) (* 1/8 (* (pow (log (* 2 (* n (PI)))) 2) (sqrt 2))))) (sqrt (* n (PI))))) (* -1/2 (* (sqrt (* n (PI))) (* (log (* 2 (* n (PI)))) (sqrt 2)))))) (* (sqrt (* n (PI))) (sqrt 2)))))
#s(approx (/ (sqrt (* (* (PI) n) 2)) (pow (* (* (PI) n) 2) (/ k 2))) #s(hole binary64 (+ (* k (+ (* -1/2 (* (sqrt (* n (PI))) (* (log (* 2 (* n (PI)))) (sqrt 2)))) (* k (+ (* -1 (* (sqrt (* n (PI))) (+ (* -1/4 (* (pow (log (* 2 (* n (PI)))) 2) (sqrt 2))) (* 1/8 (* (pow (log (* 2 (* n (PI)))) 2) (sqrt 2)))))) (* -1 (* (* k (+ (* -1/2 (* (log (* 2 (* n (PI)))) (+ (* -1/4 (* (pow (log (* 2 (* n (PI)))) 2) (sqrt 2))) (* 1/8 (* (pow (log (* 2 (* n (PI)))) 2) (sqrt 2)))))) (+ (* -1/16 (* (pow (log (* 2 (* n (PI)))) 3) (sqrt 2))) (* 1/48 (* (pow (log (* 2 (* n (PI)))) 3) (sqrt 2)))))) (sqrt (* n (PI))))))))) (* (sqrt (* n (PI))) (sqrt 2)))))
#s(approx (pow (* (* (PI) n) 2) (/ k 2)) #s(hole binary64 1))
#s(approx (pow (* (* (PI) n) 2) (/ k 2)) #s(hole binary64 (+ 1 (* 1/2 (* k (log (* 2 (* n (PI)))))))))
#s(approx (pow (* (* (PI) n) 2) (/ k 2)) #s(hole binary64 (+ 1 (* k (+ (* 1/8 (* k (pow (log (* 2 (* n (PI)))) 2))) (* 1/2 (log (* 2 (* n (PI))))))))))
#s(approx (pow (* (* (PI) n) 2) (/ k 2)) #s(hole binary64 (+ 1 (* k (+ (* 1/2 (log (* 2 (* n (PI))))) (* k (+ (* 1/48 (* k (pow (log (* 2 (* n (PI)))) 3))) (* 1/8 (pow (log (* 2 (* n (PI)))) 2)))))))))
#s(approx (/ k 2) #s(hole binary64 (* 1/2 k)))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) #s(hole binary64 (* (sqrt (/ (* n (PI)) k)) (sqrt 2))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) #s(hole binary64 (/ (+ (* -1/2 (* (sqrt (* (pow k 3) (* n (PI)))) (* (log (* 2 (* n (PI)))) (sqrt 2)))) (* (sqrt (* k (* n (PI)))) (sqrt 2))) k)))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) #s(hole binary64 (/ (+ (* 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)))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) #s(hole binary64 (/ (+ (* 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)))
#s(approx (sqrt (* (/ (* (PI) n) k) 2)) #s(hole binary64 (* (sqrt (/ (* n (PI)) k)) (sqrt 2))))
#s(approx (* (/ (* (PI) n) k) 2) #s(hole binary64 (* 2 (/ (* n (PI)) k))))
#s(approx (/ (* (PI) n) k) #s(hole binary64 (/ (* n (PI)) k)))
#s(approx (/ (* (sqrt 2) (+ (* (* (log (* (* (PI) n) 2)) (sqrt (* (* (pow k 3) (PI)) n))) -1/2) (sqrt (* (* (PI) n) k)))) k) #s(hole binary64 (* (sqrt (/ (* n (PI)) k)) (sqrt 2))))
#s(approx (/ (* (sqrt 2) (+ (* (* (log (* (* (PI) n) 2)) (sqrt (* (* (pow k 3) (PI)) n))) -1/2) (sqrt (* (* (PI) n) k)))) k) #s(hole binary64 (/ (+ (* -1/2 (* (sqrt (* (pow k 3) (* n (PI)))) (* (log (* 2 (* n (PI)))) (sqrt 2)))) (* (sqrt (* k (* n (PI)))) (sqrt 2))) k)))
#s(approx (* (sqrt 2) (+ (* (* (log (* (* (PI) n) 2)) (sqrt (* (* (pow k 3) (PI)) n))) -1/2) (sqrt (* (* (PI) n) k)))) #s(hole binary64 (* (sqrt (* k (* n (PI)))) (sqrt 2))))
#s(approx (* (sqrt 2) (+ (* (* (log (* (* (PI) n) 2)) (sqrt (* (* (pow k 3) (PI)) n))) -1/2) (sqrt (* (* (PI) n) k)))) #s(hole binary64 (+ (* -1/2 (* (sqrt (* (pow k 3) (* n (PI)))) (* (log (* 2 (* n (PI)))) (sqrt 2)))) (* (sqrt (* k (* n (PI)))) (sqrt 2)))))
#s(approx (+ (* (* (log (* (* (PI) n) 2)) (sqrt (* (* (pow k 3) (PI)) n))) -1/2) (sqrt (* (* (PI) n) k))) #s(hole binary64 (sqrt (* k (* n (PI))))))
#s(approx (+ (* (* (log (* (* (PI) n) 2)) (sqrt (* (* (pow k 3) (PI)) n))) -1/2) (sqrt (* (* (PI) n) k))) #s(hole binary64 (+ (sqrt (* k (* n (PI)))) (* -1/2 (* (sqrt (* (pow k 3) (* n (PI)))) (log (* 2 (* n (PI)))))))))
#s(approx (sqrt (* (* (PI) n) k)) #s(hole binary64 (sqrt (* k (* n (PI))))))
#s(approx (* (* (PI) n) k) #s(hole binary64 (* k (* n (PI)))))
#s(approx (* (sqrt 2) (sqrt (* (sqrt (PI)) (* (sqrt (PI)) (/ n k))))) #s(hole binary64 (* (sqrt (/ (* n (PI)) k)) (sqrt 2))))
#s(approx (sqrt (* (sqrt (PI)) (* (sqrt (PI)) (/ n k)))) #s(hole binary64 (sqrt (/ (* n (PI)) k))))
#s(approx (* (sqrt (PI)) (* (sqrt (PI)) (/ n k))) #s(hole binary64 (/ (* n (PI)) k)))
#s(approx (* (sqrt (PI)) (/ n k)) #s(hole binary64 (* (/ n k) (sqrt (PI)))))
#s(approx (/ n k) #s(hole binary64 (/ n k)))
#s(approx (pow (* (* 2 (PI)) n) (/ (- 1 k) 2)) #s(hole binary64 (* (sqrt (* n (PI))) (sqrt 2))))
#s(approx (pow (* (* 2 (PI)) n) (/ (- 1 k) 2)) #s(hole binary64 (+ (* -1/2 (* (* k (* (log (* 2 (* n (PI)))) (sqrt 2))) (sqrt (* n (PI))))) (* (sqrt (* n (PI))) (sqrt 2)))))
#s(approx (pow (* (* 2 (PI)) n) (/ (- 1 k) 2)) #s(hole 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)))))
#s(approx (pow (* (* 2 (PI)) n) (/ (- 1 k) 2)) #s(hole 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)))))
#s(approx (/ (- 1 k) 2) #s(hole binary64 1/2))
#s(approx (/ (- 1 k) 2) #s(hole binary64 (+ 1/2 (* -1/2 k))))
#s(approx (* -1/2 k) #s(hole binary64 (* -1/2 k)))
#s(approx (* (/ 1 (sqrt k)) (/ (sqrt (* (* (PI) n) 2)) (pow (* (* (PI) n) 2) (/ k 2)))) #s(hole binary64 (* (sqrt (/ (* n (PI)) k)) (/ (sqrt 2) (exp (* 1/2 (* k (log (* 2 (* n (PI)))))))))))
#s(approx (/ (sqrt (* (* (PI) n) 2)) (pow (* (* (PI) n) 2) (/ k 2))) #s(hole binary64 (* (sqrt (* n (PI))) (/ (sqrt 2) (exp (* 1/2 (* k (log (* 2 (* n (PI)))))))))))
#s(approx (pow (* (* (PI) n) 2) (/ k 2)) #s(hole binary64 (exp (* 1/2 (* k (log (* 2 (* n (PI)))))))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) #s(hole binary64 (* (sqrt (/ 1 k)) (exp (* 1/2 (* (log (* 2 (* n (PI)))) (- 1 k)))))))
#s(approx (/ (* (sqrt 2) (+ (* (* (log (* (* (PI) n) 2)) (sqrt (* (* (pow k 3) (PI)) n))) -1/2) (sqrt (* (* (PI) n) k)))) k) #s(hole binary64 (* -1/2 (* (sqrt (* k (* n (PI)))) (* (log (* 2 (* n (PI)))) (sqrt 2))))))
#s(approx (/ (* (sqrt 2) (+ (* (* (log (* (* (PI) n) 2)) (sqrt (* (* (pow k 3) (PI)) n))) -1/2) (sqrt (* (* (PI) n) k)))) k) #s(hole binary64 (* k (+ (* -1/2 (* (sqrt (/ (* n (PI)) k)) (* (log (* 2 (* n (PI)))) (sqrt 2)))) (* (sqrt (/ (* n (PI)) (pow k 3))) (sqrt 2))))))
#s(approx (* (sqrt 2) (+ (* (* (log (* (* (PI) n) 2)) (sqrt (* (* (pow k 3) (PI)) n))) -1/2) (sqrt (* (* (PI) n) k)))) #s(hole binary64 (* -1/2 (* (sqrt (* (pow k 3) (* n (PI)))) (* (log (* 2 (* n (PI)))) (sqrt 2))))))
#s(approx (* (sqrt 2) (+ (* (* (log (* (* (PI) n) 2)) (sqrt (* (* (pow k 3) (PI)) n))) -1/2) (sqrt (* (* (PI) n) k)))) #s(hole binary64 (* (pow k 2) (+ (* -1/2 (* (sqrt (/ (* n (PI)) k)) (* (log (* 2 (* n (PI)))) (sqrt 2)))) (* (sqrt (/ (* n (PI)) (pow k 3))) (sqrt 2))))))
#s(approx (+ (* (* (log (* (* (PI) n) 2)) (sqrt (* (* (pow k 3) (PI)) n))) -1/2) (sqrt (* (* (PI) n) k))) #s(hole binary64 (* -1/2 (* (sqrt (* (pow k 3) (* n (PI)))) (log (* 2 (* n (PI))))))))
#s(approx (+ (* (* (log (* (* (PI) n) 2)) (sqrt (* (* (pow k 3) (PI)) n))) -1/2) (sqrt (* (* (PI) n) k))) #s(hole binary64 (* (pow k 2) (+ (sqrt (/ (* n (PI)) (pow k 3))) (* -1/2 (* (sqrt (/ (* n (PI)) k)) (log (* 2 (* n (PI))))))))))
#s(approx (pow (* (* 2 (PI)) n) (/ (- 1 k) 2)) #s(hole binary64 (exp (* 1/2 (* (log (* 2 (* n (PI)))) (- 1 k))))))
#s(approx (/ (- 1 k) 2) #s(hole binary64 (* -1/2 k)))
#s(approx (/ (- 1 k) 2) #s(hole binary64 (* k (- (* 1/2 (/ 1 k)) 1/2))))
#s(approx (sqrt k) #s(hole binary64 (* -1 (* (sqrt k) (pow (sqrt -1) 2)))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) #s(hole binary64 (* (sqrt (/ 1 k)) (exp (* 1/2 (* (log (* 2 (* n (PI)))) (+ 1 (* -1 k))))))))
#s(approx (sqrt (* (/ (* (PI) n) k) 2)) #s(hole binary64 (* (sqrt (/ (* n (PI)) k)) (* (sqrt -2) (sqrt -1)))))
#s(approx (/ (* (sqrt 2) (+ (* (* (log (* (* (PI) n) 2)) (sqrt (* (* (pow k 3) (PI)) n))) -1/2) (sqrt (* (* (PI) n) k)))) k) #s(hole binary64 (* -1/2 (* (sqrt (* k (* n (PI)))) (* (log (* 2 (* n (PI)))) (* (pow (sqrt -1) 2) (sqrt 2)))))))
#s(approx (/ (* (sqrt 2) (+ (* (* (log (* (* (PI) n) 2)) (sqrt (* (* (pow k 3) (PI)) n))) -1/2) (sqrt (* (* (PI) n) k)))) k) #s(hole binary64 (* -1 (* k (+ (* 1/2 (* (sqrt (/ (* n (PI)) k)) (* (log (* 2 (* n (PI)))) (* (pow (sqrt -1) 2) (sqrt 2))))) (* (sqrt (/ (* n (PI)) (pow k 3))) (* (pow (sqrt -1) 2) (sqrt 2))))))))
#s(approx (* (sqrt 2) (+ (* (* (log (* (* (PI) n) 2)) (sqrt (* (* (pow k 3) (PI)) n))) -1/2) (sqrt (* (* (PI) n) k)))) #s(hole binary64 (* -1/2 (* (sqrt (* (pow k 3) (* n (PI)))) (* (log (* 2 (* n (PI)))) (* (pow (sqrt -1) 2) (sqrt 2)))))))
#s(approx (* (sqrt 2) (+ (* (* (log (* (* (PI) n) 2)) (sqrt (* (* (pow k 3) (PI)) n))) -1/2) (sqrt (* (* (PI) n) k)))) #s(hole binary64 (* (pow k 2) (+ (* -1 (* (sqrt (/ (* n (PI)) (pow k 3))) (* (pow (sqrt -1) 2) (sqrt 2)))) (* -1/2 (* (sqrt (/ (* n (PI)) k)) (* (log (* 2 (* n (PI)))) (* (pow (sqrt -1) 2) (sqrt 2)))))))))
#s(approx (+ (* (* (log (* (* (PI) n) 2)) (sqrt (* (* (pow k 3) (PI)) n))) -1/2) (sqrt (* (* (PI) n) k))) #s(hole binary64 (* -1/2 (* (sqrt (* (pow k 3) (* n (PI)))) (* (log (* 2 (* n (PI)))) (pow (sqrt -1) 2))))))
#s(approx (+ (* (* (log (* (* (PI) n) 2)) (sqrt (* (* (pow k 3) (PI)) n))) -1/2) (sqrt (* (* (PI) n) k))) #s(hole binary64 (* (pow k 2) (+ (* -1 (* (sqrt (/ (* n (PI)) (pow k 3))) (pow (sqrt -1) 2))) (* -1/2 (* (sqrt (/ (* n (PI)) k)) (* (log (* 2 (* n (PI)))) (pow (sqrt -1) 2))))))))
#s(approx (sqrt (* (* (PI) n) k)) #s(hole binary64 (* -1 (* (sqrt (* k (* n (PI)))) (pow (sqrt -1) 2)))))
#s(approx (* (sqrt 2) (sqrt (* (sqrt (PI)) (* (sqrt (PI)) (/ n k))))) #s(hole binary64 (* (sqrt (/ (* n (PI)) k)) (* (pow (sqrt -1) 2) (sqrt 2)))))
#s(approx (sqrt (* (sqrt (PI)) (* (sqrt (PI)) (/ n k)))) #s(hole binary64 (* (sqrt (/ (* n (PI)) k)) (pow (sqrt -1) 2))))
#s(approx (pow (* (* 2 (PI)) n) (/ (- 1 k) 2)) #s(hole binary64 (exp (* 1/2 (* (log (* 2 (* n (PI)))) (+ 1 (* -1 k)))))))
#s(approx (/ (- 1 k) 2) #s(hole binary64 (* -1 (* k (- 1/2 (* 1/2 (/ 1 k)))))))
#s(approx (* (/ 1 (sqrt k)) (/ (sqrt (* (* (PI) n) 2)) (pow (* (* (PI) n) 2) (/ k 2)))) #s(hole binary64 (* (sqrt (/ (* n (PI)) k)) (/ (sqrt 2) (exp (* 1/2 (* k (+ (log n) (log (* 2 (PI)))))))))))
#s(approx (/ (sqrt (* (* (PI) n) 2)) (pow (* (* (PI) n) 2) (/ k 2))) #s(hole binary64 (* (sqrt (* n (PI))) (/ (sqrt 2) (exp (* 1/2 (* k (+ (log n) (log (* 2 (PI)))))))))))
#s(approx (sqrt (* (* (PI) n) 2)) #s(hole binary64 (* (sqrt (* n (PI))) (sqrt 2))))
#s(approx (* (* (PI) n) 2) #s(hole binary64 (* 2 (* n (PI)))))
#s(approx (* (PI) n) #s(hole binary64 (* n (PI))))
#s(approx n #s(hole binary64 n))
#s(approx (pow (* (* (PI) n) 2) (/ k 2)) #s(hole binary64 (exp (* 1/2 (* k (+ (log n) (log (* 2 (PI)))))))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) #s(hole binary64 (* (sqrt (/ 1 k)) (exp (* 1/2 (* (+ (log n) (log (* 2 (PI)))) (- 1 k)))))))
#s(approx (/ (* (sqrt 2) (+ (* (* (log (* (* (PI) n) 2)) (sqrt (* (* (pow k 3) (PI)) n))) -1/2) (sqrt (* (* (PI) n) k)))) k) #s(hole binary64 (/ (* (sqrt 2) (+ (sqrt (* k (* n (PI)))) (* -1/2 (* (sqrt (* (pow k 3) (* n (PI)))) (+ (log n) (log (* 2 (PI)))))))) k)))
#s(approx (* (sqrt 2) (+ (* (* (log (* (* (PI) n) 2)) (sqrt (* (* (pow k 3) (PI)) n))) -1/2) (sqrt (* (* (PI) n) k)))) #s(hole binary64 (* (sqrt 2) (+ (sqrt (* k (* n (PI)))) (* -1/2 (* (sqrt (* (pow k 3) (* n (PI)))) (+ (log n) (log (* 2 (PI))))))))))
#s(approx (+ (* (* (log (* (* (PI) n) 2)) (sqrt (* (* (pow k 3) (PI)) n))) -1/2) (sqrt (* (* (PI) n) k))) #s(hole binary64 (+ (sqrt (* k (* n (PI)))) (* -1/2 (* (sqrt (* (pow k 3) (* n (PI)))) (+ (log n) (log (* 2 (PI)))))))))
#s(approx (pow (* (* 2 (PI)) n) (/ (- 1 k) 2)) #s(hole binary64 (exp (* 1/2 (* (+ (log n) (log (* 2 (PI)))) (- 1 k))))))
#s(approx (* (* 2 (PI)) n) #s(hole binary64 (* 2 (* n (PI)))))
#s(approx (* (/ 1 (sqrt k)) (/ (sqrt (* (* (PI) n) 2)) (pow (* (* (PI) n) 2) (/ k 2)))) #s(hole binary64 (* (sqrt (/ (* n (PI)) k)) (/ (sqrt 2) (exp (* 1/2 (* k (+ (log (* 2 (PI))) (* -1 (log (/ 1 n)))))))))))
#s(approx (/ (sqrt (* (* (PI) n) 2)) (pow (* (* (PI) n) 2) (/ k 2))) #s(hole binary64 (* (sqrt (* n (PI))) (/ (sqrt 2) (exp (* 1/2 (* k (+ (log (* 2 (PI))) (* -1 (log (/ 1 n)))))))))))
#s(approx (pow (* (* (PI) n) 2) (/ k 2)) #s(hole binary64 (exp (* 1/2 (* k (+ (log (* 2 (PI))) (* -1 (log (/ 1 n)))))))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) #s(hole binary64 (* (sqrt (/ 1 k)) (exp (* 1/2 (* (+ (log (* 2 (PI))) (* -1 (log (/ 1 n)))) (- 1 k)))))))
#s(approx (/ (* (sqrt 2) (+ (* (* (log (* (* (PI) n) 2)) (sqrt (* (* (pow k 3) (PI)) n))) -1/2) (sqrt (* (* (PI) n) k)))) k) #s(hole binary64 (/ (* n (* (sqrt 2) (+ (sqrt (/ (* k (PI)) n)) (* -1/2 (* (sqrt (/ (* (pow k 3) (PI)) n)) (+ (log (* 2 (PI))) (* -1 (log (/ 1 n))))))))) k)))
#s(approx (* (sqrt 2) (+ (* (* (log (* (* (PI) n) 2)) (sqrt (* (* (pow k 3) (PI)) n))) -1/2) (sqrt (* (* (PI) n) k)))) #s(hole binary64 (* n (* (sqrt 2) (+ (sqrt (/ (* k (PI)) n)) (* -1/2 (* (sqrt (/ (* (pow k 3) (PI)) n)) (+ (log (* 2 (PI))) (* -1 (log (/ 1 n)))))))))))
#s(approx (+ (* (* (log (* (* (PI) n) 2)) (sqrt (* (* (pow k 3) (PI)) n))) -1/2) (sqrt (* (* (PI) n) k))) #s(hole binary64 (* n (+ (sqrt (/ (* k (PI)) n)) (* -1/2 (* (sqrt (/ (* (pow k 3) (PI)) n)) (+ (log (* 2 (PI))) (* -1 (log (/ 1 n))))))))))
#s(approx (pow (* (* 2 (PI)) n) (/ (- 1 k) 2)) #s(hole binary64 (exp (* 1/2 (* (+ (log (* 2 (PI))) (* -1 (log (/ 1 n)))) (- 1 k))))))
#s(approx (* (/ 1 (sqrt k)) (/ (sqrt (* (* (PI) n) 2)) (pow (* (* (PI) n) 2) (/ k 2)))) #s(hole binary64 (* -1 (* (sqrt (/ (* n (PI)) k)) (/ (* (sqrt -2) (sqrt -1)) (exp (* 1/2 (* k (+ (log (* -2 (PI))) (* -1 (log (/ -1 n))))))))))))
#s(approx (/ (sqrt (* (* (PI) n) 2)) (pow (* (* (PI) n) 2) (/ k 2))) #s(hole binary64 (* -1 (* (sqrt (* n (PI))) (/ (* (sqrt -2) (sqrt -1)) (exp (* 1/2 (* k (+ (log (* -2 (PI))) (* -1 (log (/ -1 n))))))))))))
#s(approx (sqrt (* (* (PI) n) 2)) #s(hole binary64 (* -1 (* (sqrt (* n (PI))) (* (sqrt -2) (sqrt -1))))))
#s(approx (pow (* (* (PI) n) 2) (/ k 2)) #s(hole binary64 (exp (* 1/2 (* k (+ (log (* -2 (PI))) (* -1 (log (/ -1 n)))))))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) #s(hole binary64 (* (sqrt (/ 1 k)) (exp (* 1/2 (* (+ (log (* -2 (PI))) (* -1 (log (/ -1 n)))) (- 1 k)))))))
#s(approx (sqrt (* (/ (* (PI) n) k) 2)) #s(hole binary64 (* -1 (* (sqrt (/ (* n (PI)) k)) (* (sqrt -2) (sqrt -1))))))
#s(approx (/ (* (sqrt 2) (+ (* (* (log (* (* (PI) n) 2)) (sqrt (* (* (pow k 3) (PI)) n))) -1/2) (sqrt (* (* (PI) n) k)))) k) #s(hole binary64 (* -1 (/ (* n (* (sqrt 2) (+ (* -1/2 (* (sqrt (/ (* (pow k 3) (PI)) n)) (* (pow (sqrt -1) 2) (+ (log (* -2 (PI))) (* -1 (log (/ -1 n))))))) (* (sqrt (/ (* k (PI)) n)) (pow (sqrt -1) 2))))) k))))
#s(approx (* (sqrt 2) (+ (* (* (log (* (* (PI) n) 2)) (sqrt (* (* (pow k 3) (PI)) n))) -1/2) (sqrt (* (* (PI) n) k)))) #s(hole binary64 (* -1 (* n (* (sqrt 2) (+ (* -1/2 (* (sqrt (/ (* (pow k 3) (PI)) n)) (* (pow (sqrt -1) 2) (+ (log (* -2 (PI))) (* -1 (log (/ -1 n))))))) (* (sqrt (/ (* k (PI)) n)) (pow (sqrt -1) 2))))))))
#s(approx (+ (* (* (log (* (* (PI) n) 2)) (sqrt (* (* (pow k 3) (PI)) n))) -1/2) (sqrt (* (* (PI) n) k))) #s(hole binary64 (* -1 (* n (+ (* -1/2 (* (sqrt (/ (* (pow k 3) (PI)) n)) (* (pow (sqrt -1) 2) (+ (log (* -2 (PI))) (* -1 (log (/ -1 n))))))) (* (sqrt (/ (* k (PI)) n)) (pow (sqrt -1) 2)))))))
#s(approx (* (sqrt 2) (sqrt (* (sqrt (PI)) (* (sqrt (PI)) (/ n k))))) #s(hole binary64 (* -1 (* (sqrt (/ (* n (PI)) k)) (* (pow (sqrt -1) 2) (sqrt 2))))))
#s(approx (sqrt (* (sqrt (PI)) (* (sqrt (PI)) (/ n k)))) #s(hole binary64 (* -1 (* (sqrt (/ (* n (PI)) k)) (pow (sqrt -1) 2)))))
#s(approx (pow (* (* 2 (PI)) n) (/ (- 1 k) 2)) #s(hole binary64 (exp (* 1/2 (* (+ (log (* -2 (PI))) (* -1 (log (/ -1 n)))) (- 1 k))))))

Calls

6 calls:

Time	Variable		Point	Expression
18.0ms	n	@	0	((* (/ 1 (sqrt k)) (/ (sqrt (* (* (PI) n) 2)) (pow (* (* (PI) n) 2) (/ k 2)))) (/ 1 (sqrt k)) 1 (sqrt k) k (/ (sqrt (* (* (PI) n) 2)) (pow (* (* (PI) n) 2) (/ k 2))) (sqrt (* (* (PI) n) 2)) (* (* (PI) n) 2) (* (PI) n) (PI) n 2 (pow (* (* (PI) n) 2) (/ k 2)) (/ k 2) (* (/ 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) (+ (* (* (log (* (* (PI) n) 2)) (sqrt (* (* (pow k 3) (PI)) n))) -1/2) (sqrt (* (* (PI) n) k)))) k) (* (sqrt 2) (+ (* (* (log (* (* (PI) n) 2)) (sqrt (* (* (pow k 3) (PI)) n))) -1/2) (sqrt (* (* (PI) n) k)))) (sqrt 2) (+ (* (* (log (* (* (PI) n) 2)) (sqrt (* (* (pow k 3) (PI)) n))) -1/2) (sqrt (* (* (PI) n) k))) (sqrt (* (* (PI) n) k)) (* (* (PI) n) k) (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (* (sqrt 2) (sqrt (* (sqrt (PI)) (* (sqrt (PI)) (/ n k))))) (sqrt (* (sqrt (PI)) (* (sqrt (PI)) (/ n k)))) (* (sqrt (PI)) (* (sqrt (PI)) (/ n k))) (sqrt (PI)) (* (sqrt (PI)) (/ n k)) (/ n k) (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2)) (* (* 2 (PI)) n) (* 2 (PI)) (/ (- 1 k) 2) (* -1/2 k) -1/2)
18.0ms	n	@	-inf	((* (/ 1 (sqrt k)) (/ (sqrt (* (* (PI) n) 2)) (pow (* (* (PI) n) 2) (/ k 2)))) (/ 1 (sqrt k)) 1 (sqrt k) k (/ (sqrt (* (* (PI) n) 2)) (pow (* (* (PI) n) 2) (/ k 2))) (sqrt (* (* (PI) n) 2)) (* (* (PI) n) 2) (* (PI) n) (PI) n 2 (pow (* (* (PI) n) 2) (/ k 2)) (/ k 2) (* (/ 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) (+ (* (* (log (* (* (PI) n) 2)) (sqrt (* (* (pow k 3) (PI)) n))) -1/2) (sqrt (* (* (PI) n) k)))) k) (* (sqrt 2) (+ (* (* (log (* (* (PI) n) 2)) (sqrt (* (* (pow k 3) (PI)) n))) -1/2) (sqrt (* (* (PI) n) k)))) (sqrt 2) (+ (* (* (log (* (* (PI) n) 2)) (sqrt (* (* (pow k 3) (PI)) n))) -1/2) (sqrt (* (* (PI) n) k))) (sqrt (* (* (PI) n) k)) (* (* (PI) n) k) (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (* (sqrt 2) (sqrt (* (sqrt (PI)) (* (sqrt (PI)) (/ n k))))) (sqrt (* (sqrt (PI)) (* (sqrt (PI)) (/ n k)))) (* (sqrt (PI)) (* (sqrt (PI)) (/ n k))) (sqrt (PI)) (* (sqrt (PI)) (/ n k)) (/ n k) (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2)) (* (* 2 (PI)) n) (* 2 (PI)) (/ (- 1 k) 2) (* -1/2 k) -1/2)
15.0ms	n	@	inf	((* (/ 1 (sqrt k)) (/ (sqrt (* (* (PI) n) 2)) (pow (* (* (PI) n) 2) (/ k 2)))) (/ 1 (sqrt k)) 1 (sqrt k) k (/ (sqrt (* (* (PI) n) 2)) (pow (* (* (PI) n) 2) (/ k 2))) (sqrt (* (* (PI) n) 2)) (* (* (PI) n) 2) (* (PI) n) (PI) n 2 (pow (* (* (PI) n) 2) (/ k 2)) (/ k 2) (* (/ 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) (+ (* (* (log (* (* (PI) n) 2)) (sqrt (* (* (pow k 3) (PI)) n))) -1/2) (sqrt (* (* (PI) n) k)))) k) (* (sqrt 2) (+ (* (* (log (* (* (PI) n) 2)) (sqrt (* (* (pow k 3) (PI)) n))) -1/2) (sqrt (* (* (PI) n) k)))) (sqrt 2) (+ (* (* (log (* (* (PI) n) 2)) (sqrt (* (* (pow k 3) (PI)) n))) -1/2) (sqrt (* (* (PI) n) k))) (sqrt (* (* (PI) n) k)) (* (* (PI) n) k) (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (* (sqrt 2) (sqrt (* (sqrt (PI)) (* (sqrt (PI)) (/ n k))))) (sqrt (* (sqrt (PI)) (* (sqrt (PI)) (/ n k)))) (* (sqrt (PI)) (* (sqrt (PI)) (/ n k))) (sqrt (PI)) (* (sqrt (PI)) (/ n k)) (/ n k) (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2)) (* (* 2 (PI)) n) (* 2 (PI)) (/ (- 1 k) 2) (* -1/2 k) -1/2)
13.0ms	k	@	-inf	((* (/ 1 (sqrt k)) (/ (sqrt (* (* (PI) n) 2)) (pow (* (* (PI) n) 2) (/ k 2)))) (/ 1 (sqrt k)) 1 (sqrt k) k (/ (sqrt (* (* (PI) n) 2)) (pow (* (* (PI) n) 2) (/ k 2))) (sqrt (* (* (PI) n) 2)) (* (* (PI) n) 2) (* (PI) n) (PI) n 2 (pow (* (* (PI) n) 2) (/ k 2)) (/ k 2) (* (/ 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) (+ (* (* (log (* (* (PI) n) 2)) (sqrt (* (* (pow k 3) (PI)) n))) -1/2) (sqrt (* (* (PI) n) k)))) k) (* (sqrt 2) (+ (* (* (log (* (* (PI) n) 2)) (sqrt (* (* (pow k 3) (PI)) n))) -1/2) (sqrt (* (* (PI) n) k)))) (sqrt 2) (+ (* (* (log (* (* (PI) n) 2)) (sqrt (* (* (pow k 3) (PI)) n))) -1/2) (sqrt (* (* (PI) n) k))) (sqrt (* (* (PI) n) k)) (* (* (PI) n) k) (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (* (sqrt 2) (sqrt (* (sqrt (PI)) (* (sqrt (PI)) (/ n k))))) (sqrt (* (sqrt (PI)) (* (sqrt (PI)) (/ n k)))) (* (sqrt (PI)) (* (sqrt (PI)) (/ n k))) (sqrt (PI)) (* (sqrt (PI)) (/ n k)) (/ n k) (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2)) (* (* 2 (PI)) n) (* 2 (PI)) (/ (- 1 k) 2) (* -1/2 k) -1/2)
7.0ms	k	@	inf	((* (/ 1 (sqrt k)) (/ (sqrt (* (* (PI) n) 2)) (pow (* (* (PI) n) 2) (/ k 2)))) (/ 1 (sqrt k)) 1 (sqrt k) k (/ (sqrt (* (* (PI) n) 2)) (pow (* (* (PI) n) 2) (/ k 2))) (sqrt (* (* (PI) n) 2)) (* (* (PI) n) 2) (* (PI) n) (PI) n 2 (pow (* (* (PI) n) 2) (/ k 2)) (/ k 2) (* (/ 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) (+ (* (* (log (* (* (PI) n) 2)) (sqrt (* (* (pow k 3) (PI)) n))) -1/2) (sqrt (* (* (PI) n) k)))) k) (* (sqrt 2) (+ (* (* (log (* (* (PI) n) 2)) (sqrt (* (* (pow k 3) (PI)) n))) -1/2) (sqrt (* (* (PI) n) k)))) (sqrt 2) (+ (* (* (log (* (* (PI) n) 2)) (sqrt (* (* (pow k 3) (PI)) n))) -1/2) (sqrt (* (* (PI) n) k))) (sqrt (* (* (PI) n) k)) (* (* (PI) n) k) (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (* (sqrt 2) (sqrt (* (sqrt (PI)) (* (sqrt (PI)) (/ n k))))) (sqrt (* (sqrt (PI)) (* (sqrt (PI)) (/ n k)))) (* (sqrt (PI)) (* (sqrt (PI)) (/ n k))) (sqrt (PI)) (* (sqrt (PI)) (/ n k)) (/ n k) (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2)) (* (* 2 (PI)) n) (* 2 (PI)) (/ (- 1 k) 2) (* -1/2 k) -1/2)

simplify200.0ms (2.4%)

Memory

-19.6MiB live, 323.8MiB allocated; 41ms collecting garbage

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	433	3797
1	1299	3588
2	5479	3504
0	8807	3423

Stop Event

1×	iter limit
1×	node limit

Counts

103 → 103

Calls

Call 1

Inputs
#s(approx (* (/ 1 (sqrt k)) (/ (sqrt (* (* (PI) n) 2)) (pow (* (* (PI) n) 2) (/ k 2)))) #s(hole binary64 (* (sqrt (/ (* n (PI)) k)) (sqrt 2))))
#s(approx (* (/ 1 (sqrt k)) (/ (sqrt (* (* (PI) n) 2)) (pow (* (* (PI) n) 2) (/ k 2)))) #s(hole binary64 (/ (+ (* -1/2 (* (sqrt (* (pow k 3) (* n (PI)))) (* (log (* 2 (* n (PI)))) (sqrt 2)))) (* (sqrt (* k (* n (PI)))) (sqrt 2))) k)))
#s(approx (* (/ 1 (sqrt k)) (/ (sqrt (* (* (PI) n) 2)) (pow (* (* (PI) n) 2) (/ k 2)))) #s(hole binary64 (/ (+ (* k (+ (* -1 (* (sqrt (* (pow k 3) (* n (PI)))) (+ (* -1/4 (* (pow (log (* 2 (* n (PI)))) 2) (sqrt 2))) (* 1/8 (* (pow (log (* 2 (* n (PI)))) 2) (sqrt 2)))))) (* -1/2 (* (sqrt (* k (* n (PI)))) (* (log (* 2 (* n (PI)))) (sqrt 2)))))) (* (sqrt (* k (* n (PI)))) (sqrt 2))) k)))
#s(approx (* (/ 1 (sqrt k)) (/ (sqrt (* (* (PI) n) 2)) (pow (* (* (PI) n) 2) (/ k 2)))) #s(hole binary64 (/ (+ (* k (+ (* -1/2 (* (sqrt (* k (* n (PI)))) (* (log (* 2 (* n (PI)))) (sqrt 2)))) (* k (+ (* -1 (* (sqrt (* k (* n (PI)))) (+ (* -1/4 (* (pow (log (* 2 (* n (PI)))) 2) (sqrt 2))) (* 1/8 (* (pow (log (* 2 (* n (PI)))) 2) (sqrt 2)))))) (* -1 (* (sqrt (* (pow k 3) (* n (PI)))) (+ (* -1/2 (* (log (* 2 (* n (PI)))) (+ (* -1/4 (* (pow (log (* 2 (* n (PI)))) 2) (sqrt 2))) (* 1/8 (* (pow (log (* 2 (* n (PI)))) 2) (sqrt 2)))))) (+ (* -1/16 (* (pow (log (* 2 (* n (PI)))) 3) (sqrt 2))) (* 1/48 (* (pow (log (* 2 (* n (PI)))) 3) (sqrt 2))))))))))) (* (sqrt (* k (* n (PI)))) (sqrt 2))) k)))
#s(approx (/ 1 (sqrt k)) #s(hole binary64 (sqrt (/ 1 k))))
#s(approx (sqrt k) #s(hole binary64 (sqrt k)))
#s(approx k #s(hole binary64 k))
#s(approx (/ (sqrt (* (* (PI) n) 2)) (pow (* (* (PI) n) 2) (/ k 2))) #s(hole binary64 (* (sqrt (* n (PI))) (sqrt 2))))
#s(approx (/ (sqrt (* (* (PI) n) 2)) (pow (* (* (PI) n) 2) (/ k 2))) #s(hole binary64 (+ (* -1/2 (* (* k (* (log (* 2 (* n (PI)))) (sqrt 2))) (sqrt (* n (PI))))) (* (sqrt (* n (PI))) (sqrt 2)))))
#s(approx (/ (sqrt (* (* (PI) n) 2)) (pow (* (* (PI) n) 2) (/ k 2))) #s(hole binary64 (+ (* k (+ (* -1 (* (* k (+ (* -1/4 (* (pow (log (* 2 (* n (PI)))) 2) (sqrt 2))) (* 1/8 (* (pow (log (* 2 (* n (PI)))) 2) (sqrt 2))))) (sqrt (* n (PI))))) (* -1/2 (* (sqrt (* n (PI))) (* (log (* 2 (* n (PI)))) (sqrt 2)))))) (* (sqrt (* n (PI))) (sqrt 2)))))
#s(approx (/ (sqrt (* (* (PI) n) 2)) (pow (* (* (PI) n) 2) (/ k 2))) #s(hole binary64 (+ (* k (+ (* -1/2 (* (sqrt (* n (PI))) (* (log (* 2 (* n (PI)))) (sqrt 2)))) (* k (+ (* -1 (* (sqrt (* n (PI))) (+ (* -1/4 (* (pow (log (* 2 (* n (PI)))) 2) (sqrt 2))) (* 1/8 (* (pow (log (* 2 (* n (PI)))) 2) (sqrt 2)))))) (* -1 (* (* k (+ (* -1/2 (* (log (* 2 (* n (PI)))) (+ (* -1/4 (* (pow (log (* 2 (* n (PI)))) 2) (sqrt 2))) (* 1/8 (* (pow (log (* 2 (* n (PI)))) 2) (sqrt 2)))))) (+ (* -1/16 (* (pow (log (* 2 (* n (PI)))) 3) (sqrt 2))) (* 1/48 (* (pow (log (* 2 (* n (PI)))) 3) (sqrt 2)))))) (sqrt (* n (PI))))))))) (* (sqrt (* n (PI))) (sqrt 2)))))
#s(approx (pow (* (* (PI) n) 2) (/ k 2)) #s(hole binary64 1))
#s(approx (pow (* (* (PI) n) 2) (/ k 2)) #s(hole binary64 (+ 1 (* 1/2 (* k (log (* 2 (* n (PI)))))))))
#s(approx (pow (* (* (PI) n) 2) (/ k 2)) #s(hole binary64 (+ 1 (* k (+ (* 1/8 (* k (pow (log (* 2 (* n (PI)))) 2))) (* 1/2 (log (* 2 (* n (PI))))))))))
#s(approx (pow (* (* (PI) n) 2) (/ k 2)) #s(hole binary64 (+ 1 (* k (+ (* 1/2 (log (* 2 (* n (PI))))) (* k (+ (* 1/48 (* k (pow (log (* 2 (* n (PI)))) 3))) (* 1/8 (pow (log (* 2 (* n (PI)))) 2)))))))))
#s(approx (/ k 2) #s(hole binary64 (* 1/2 k)))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) #s(hole binary64 (* (sqrt (/ (* n (PI)) k)) (sqrt 2))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) #s(hole binary64 (/ (+ (* -1/2 (* (sqrt (* (pow k 3) (* n (PI)))) (* (log (* 2 (* n (PI)))) (sqrt 2)))) (* (sqrt (* k (* n (PI)))) (sqrt 2))) k)))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) #s(hole binary64 (/ (+ (* 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)))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) #s(hole binary64 (/ (+ (* 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)))
#s(approx (sqrt (* (/ (* (PI) n) k) 2)) #s(hole binary64 (* (sqrt (/ (* n (PI)) k)) (sqrt 2))))
#s(approx (* (/ (* (PI) n) k) 2) #s(hole binary64 (* 2 (/ (* n (PI)) k))))
#s(approx (/ (* (PI) n) k) #s(hole binary64 (/ (* n (PI)) k)))
#s(approx (/ (* (sqrt 2) (+ (* (* (log (* (* (PI) n) 2)) (sqrt (* (* (pow k 3) (PI)) n))) -1/2) (sqrt (* (* (PI) n) k)))) k) #s(hole binary64 (* (sqrt (/ (* n (PI)) k)) (sqrt 2))))
#s(approx (/ (* (sqrt 2) (+ (* (* (log (* (* (PI) n) 2)) (sqrt (* (* (pow k 3) (PI)) n))) -1/2) (sqrt (* (* (PI) n) k)))) k) #s(hole binary64 (/ (+ (* -1/2 (* (sqrt (* (pow k 3) (* n (PI)))) (* (log (* 2 (* n (PI)))) (sqrt 2)))) (* (sqrt (* k (* n (PI)))) (sqrt 2))) k)))
#s(approx (* (sqrt 2) (+ (* (* (log (* (* (PI) n) 2)) (sqrt (* (* (pow k 3) (PI)) n))) -1/2) (sqrt (* (* (PI) n) k)))) #s(hole binary64 (* (sqrt (* k (* n (PI)))) (sqrt 2))))
#s(approx (* (sqrt 2) (+ (* (* (log (* (* (PI) n) 2)) (sqrt (* (* (pow k 3) (PI)) n))) -1/2) (sqrt (* (* (PI) n) k)))) #s(hole binary64 (+ (* -1/2 (* (sqrt (* (pow k 3) (* n (PI)))) (* (log (* 2 (* n (PI)))) (sqrt 2)))) (* (sqrt (* k (* n (PI)))) (sqrt 2)))))
#s(approx (+ (* (* (log (* (* (PI) n) 2)) (sqrt (* (* (pow k 3) (PI)) n))) -1/2) (sqrt (* (* (PI) n) k))) #s(hole binary64 (sqrt (* k (* n (PI))))))
#s(approx (+ (* (* (log (* (* (PI) n) 2)) (sqrt (* (* (pow k 3) (PI)) n))) -1/2) (sqrt (* (* (PI) n) k))) #s(hole binary64 (+ (sqrt (* k (* n (PI)))) (* -1/2 (* (sqrt (* (pow k 3) (* n (PI)))) (log (* 2 (* n (PI)))))))))
#s(approx (sqrt (* (* (PI) n) k)) #s(hole binary64 (sqrt (* k (* n (PI))))))
#s(approx (* (* (PI) n) k) #s(hole binary64 (* k (* n (PI)))))
#s(approx (* (sqrt 2) (sqrt (* (sqrt (PI)) (* (sqrt (PI)) (/ n k))))) #s(hole binary64 (* (sqrt (/ (* n (PI)) k)) (sqrt 2))))
#s(approx (sqrt (* (sqrt (PI)) (* (sqrt (PI)) (/ n k)))) #s(hole binary64 (sqrt (/ (* n (PI)) k))))
#s(approx (* (sqrt (PI)) (* (sqrt (PI)) (/ n k))) #s(hole binary64 (/ (* n (PI)) k)))
#s(approx (* (sqrt (PI)) (/ n k)) #s(hole binary64 (* (/ n k) (sqrt (PI)))))
#s(approx (/ n k) #s(hole binary64 (/ n k)))
#s(approx (pow (* (* 2 (PI)) n) (/ (- 1 k) 2)) #s(hole binary64 (* (sqrt (* n (PI))) (sqrt 2))))
#s(approx (pow (* (* 2 (PI)) n) (/ (- 1 k) 2)) #s(hole binary64 (+ (* -1/2 (* (* k (* (log (* 2 (* n (PI)))) (sqrt 2))) (sqrt (* n (PI))))) (* (sqrt (* n (PI))) (sqrt 2)))))
#s(approx (pow (* (* 2 (PI)) n) (/ (- 1 k) 2)) #s(hole 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)))))
#s(approx (pow (* (* 2 (PI)) n) (/ (- 1 k) 2)) #s(hole 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)))))
#s(approx (/ (- 1 k) 2) #s(hole binary64 1/2))
#s(approx (/ (- 1 k) 2) #s(hole binary64 (+ 1/2 (* -1/2 k))))
#s(approx (* -1/2 k) #s(hole binary64 (* -1/2 k)))
#s(approx (* (/ 1 (sqrt k)) (/ (sqrt (* (* (PI) n) 2)) (pow (* (* (PI) n) 2) (/ k 2)))) #s(hole binary64 (* (sqrt (/ (* n (PI)) k)) (/ (sqrt 2) (exp (* 1/2 (* k (log (* 2 (* n (PI)))))))))))
#s(approx (/ (sqrt (* (* (PI) n) 2)) (pow (* (* (PI) n) 2) (/ k 2))) #s(hole binary64 (* (sqrt (* n (PI))) (/ (sqrt 2) (exp (* 1/2 (* k (log (* 2 (* n (PI)))))))))))
#s(approx (pow (* (* (PI) n) 2) (/ k 2)) #s(hole binary64 (exp (* 1/2 (* k (log (* 2 (* n (PI)))))))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) #s(hole binary64 (* (sqrt (/ 1 k)) (exp (* 1/2 (* (log (* 2 (* n (PI)))) (- 1 k)))))))
#s(approx (/ (* (sqrt 2) (+ (* (* (log (* (* (PI) n) 2)) (sqrt (* (* (pow k 3) (PI)) n))) -1/2) (sqrt (* (* (PI) n) k)))) k) #s(hole binary64 (* -1/2 (* (sqrt (* k (* n (PI)))) (* (log (* 2 (* n (PI)))) (sqrt 2))))))
#s(approx (/ (* (sqrt 2) (+ (* (* (log (* (* (PI) n) 2)) (sqrt (* (* (pow k 3) (PI)) n))) -1/2) (sqrt (* (* (PI) n) k)))) k) #s(hole binary64 (* k (+ (* -1/2 (* (sqrt (/ (* n (PI)) k)) (* (log (* 2 (* n (PI)))) (sqrt 2)))) (* (sqrt (/ (* n (PI)) (pow k 3))) (sqrt 2))))))
#s(approx (* (sqrt 2) (+ (* (* (log (* (* (PI) n) 2)) (sqrt (* (* (pow k 3) (PI)) n))) -1/2) (sqrt (* (* (PI) n) k)))) #s(hole binary64 (* -1/2 (* (sqrt (* (pow k 3) (* n (PI)))) (* (log (* 2 (* n (PI)))) (sqrt 2))))))
#s(approx (* (sqrt 2) (+ (* (* (log (* (* (PI) n) 2)) (sqrt (* (* (pow k 3) (PI)) n))) -1/2) (sqrt (* (* (PI) n) k)))) #s(hole binary64 (* (pow k 2) (+ (* -1/2 (* (sqrt (/ (* n (PI)) k)) (* (log (* 2 (* n (PI)))) (sqrt 2)))) (* (sqrt (/ (* n (PI)) (pow k 3))) (sqrt 2))))))
#s(approx (+ (* (* (log (* (* (PI) n) 2)) (sqrt (* (* (pow k 3) (PI)) n))) -1/2) (sqrt (* (* (PI) n) k))) #s(hole binary64 (* -1/2 (* (sqrt (* (pow k 3) (* n (PI)))) (log (* 2 (* n (PI))))))))
#s(approx (+ (* (* (log (* (* (PI) n) 2)) (sqrt (* (* (pow k 3) (PI)) n))) -1/2) (sqrt (* (* (PI) n) k))) #s(hole binary64 (* (pow k 2) (+ (sqrt (/ (* n (PI)) (pow k 3))) (* -1/2 (* (sqrt (/ (* n (PI)) k)) (log (* 2 (* n (PI))))))))))
#s(approx (pow (* (* 2 (PI)) n) (/ (- 1 k) 2)) #s(hole binary64 (exp (* 1/2 (* (log (* 2 (* n (PI)))) (- 1 k))))))
#s(approx (/ (- 1 k) 2) #s(hole binary64 (* -1/2 k)))
#s(approx (/ (- 1 k) 2) #s(hole binary64 (* k (- (* 1/2 (/ 1 k)) 1/2))))
#s(approx (sqrt k) #s(hole binary64 (* -1 (* (sqrt k) (pow (sqrt -1) 2)))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) #s(hole binary64 (* (sqrt (/ 1 k)) (exp (* 1/2 (* (log (* 2 (* n (PI)))) (+ 1 (* -1 k))))))))
#s(approx (sqrt (* (/ (* (PI) n) k) 2)) #s(hole binary64 (* (sqrt (/ (* n (PI)) k)) (* (sqrt -2) (sqrt -1)))))
#s(approx (/ (* (sqrt 2) (+ (* (* (log (* (* (PI) n) 2)) (sqrt (* (* (pow k 3) (PI)) n))) -1/2) (sqrt (* (* (PI) n) k)))) k) #s(hole binary64 (* -1/2 (* (sqrt (* k (* n (PI)))) (* (log (* 2 (* n (PI)))) (* (pow (sqrt -1) 2) (sqrt 2)))))))
#s(approx (/ (* (sqrt 2) (+ (* (* (log (* (* (PI) n) 2)) (sqrt (* (* (pow k 3) (PI)) n))) -1/2) (sqrt (* (* (PI) n) k)))) k) #s(hole binary64 (* -1 (* k (+ (* 1/2 (* (sqrt (/ (* n (PI)) k)) (* (log (* 2 (* n (PI)))) (* (pow (sqrt -1) 2) (sqrt 2))))) (* (sqrt (/ (* n (PI)) (pow k 3))) (* (pow (sqrt -1) 2) (sqrt 2))))))))
#s(approx (* (sqrt 2) (+ (* (* (log (* (* (PI) n) 2)) (sqrt (* (* (pow k 3) (PI)) n))) -1/2) (sqrt (* (* (PI) n) k)))) #s(hole binary64 (* -1/2 (* (sqrt (* (pow k 3) (* n (PI)))) (* (log (* 2 (* n (PI)))) (* (pow (sqrt -1) 2) (sqrt 2)))))))
#s(approx (* (sqrt 2) (+ (* (* (log (* (* (PI) n) 2)) (sqrt (* (* (pow k 3) (PI)) n))) -1/2) (sqrt (* (* (PI) n) k)))) #s(hole binary64 (* (pow k 2) (+ (* -1 (* (sqrt (/ (* n (PI)) (pow k 3))) (* (pow (sqrt -1) 2) (sqrt 2)))) (* -1/2 (* (sqrt (/ (* n (PI)) k)) (* (log (* 2 (* n (PI)))) (* (pow (sqrt -1) 2) (sqrt 2)))))))))
#s(approx (+ (* (* (log (* (* (PI) n) 2)) (sqrt (* (* (pow k 3) (PI)) n))) -1/2) (sqrt (* (* (PI) n) k))) #s(hole binary64 (* -1/2 (* (sqrt (* (pow k 3) (* n (PI)))) (* (log (* 2 (* n (PI)))) (pow (sqrt -1) 2))))))
#s(approx (+ (* (* (log (* (* (PI) n) 2)) (sqrt (* (* (pow k 3) (PI)) n))) -1/2) (sqrt (* (* (PI) n) k))) #s(hole binary64 (* (pow k 2) (+ (* -1 (* (sqrt (/ (* n (PI)) (pow k 3))) (pow (sqrt -1) 2))) (* -1/2 (* (sqrt (/ (* n (PI)) k)) (* (log (* 2 (* n (PI)))) (pow (sqrt -1) 2))))))))
#s(approx (sqrt (* (* (PI) n) k)) #s(hole binary64 (* -1 (* (sqrt (* k (* n (PI)))) (pow (sqrt -1) 2)))))
#s(approx (* (sqrt 2) (sqrt (* (sqrt (PI)) (* (sqrt (PI)) (/ n k))))) #s(hole binary64 (* (sqrt (/ (* n (PI)) k)) (* (pow (sqrt -1) 2) (sqrt 2)))))
#s(approx (sqrt (* (sqrt (PI)) (* (sqrt (PI)) (/ n k)))) #s(hole binary64 (* (sqrt (/ (* n (PI)) k)) (pow (sqrt -1) 2))))
#s(approx (pow (* (* 2 (PI)) n) (/ (- 1 k) 2)) #s(hole binary64 (exp (* 1/2 (* (log (* 2 (* n (PI)))) (+ 1 (* -1 k)))))))
#s(approx (/ (- 1 k) 2) #s(hole binary64 (* -1 (* k (- 1/2 (* 1/2 (/ 1 k)))))))
#s(approx (* (/ 1 (sqrt k)) (/ (sqrt (* (* (PI) n) 2)) (pow (* (* (PI) n) 2) (/ k 2)))) #s(hole binary64 (* (sqrt (/ (* n (PI)) k)) (/ (sqrt 2) (exp (* 1/2 (* k (+ (log n) (log (* 2 (PI)))))))))))
#s(approx (/ (sqrt (* (* (PI) n) 2)) (pow (* (* (PI) n) 2) (/ k 2))) #s(hole binary64 (* (sqrt (* n (PI))) (/ (sqrt 2) (exp (* 1/2 (* k (+ (log n) (log (* 2 (PI)))))))))))
#s(approx (sqrt (* (* (PI) n) 2)) #s(hole binary64 (* (sqrt (* n (PI))) (sqrt 2))))
#s(approx (* (* (PI) n) 2) #s(hole binary64 (* 2 (* n (PI)))))
#s(approx (* (PI) n) #s(hole binary64 (* n (PI))))
#s(approx n #s(hole binary64 n))
#s(approx (pow (* (* (PI) n) 2) (/ k 2)) #s(hole binary64 (exp (* 1/2 (* k (+ (log n) (log (* 2 (PI)))))))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) #s(hole binary64 (* (sqrt (/ 1 k)) (exp (* 1/2 (* (+ (log n) (log (* 2 (PI)))) (- 1 k)))))))
#s(approx (/ (* (sqrt 2) (+ (* (* (log (* (* (PI) n) 2)) (sqrt (* (* (pow k 3) (PI)) n))) -1/2) (sqrt (* (* (PI) n) k)))) k) #s(hole binary64 (/ (* (sqrt 2) (+ (sqrt (* k (* n (PI)))) (* -1/2 (* (sqrt (* (pow k 3) (* n (PI)))) (+ (log n) (log (* 2 (PI)))))))) k)))
#s(approx (* (sqrt 2) (+ (* (* (log (* (* (PI) n) 2)) (sqrt (* (* (pow k 3) (PI)) n))) -1/2) (sqrt (* (* (PI) n) k)))) #s(hole binary64 (* (sqrt 2) (+ (sqrt (* k (* n (PI)))) (* -1/2 (* (sqrt (* (pow k 3) (* n (PI)))) (+ (log n) (log (* 2 (PI))))))))))
#s(approx (+ (* (* (log (* (* (PI) n) 2)) (sqrt (* (* (pow k 3) (PI)) n))) -1/2) (sqrt (* (* (PI) n) k))) #s(hole binary64 (+ (sqrt (* k (* n (PI)))) (* -1/2 (* (sqrt (* (pow k 3) (* n (PI)))) (+ (log n) (log (* 2 (PI)))))))))
#s(approx (pow (* (* 2 (PI)) n) (/ (- 1 k) 2)) #s(hole binary64 (exp (* 1/2 (* (+ (log n) (log (* 2 (PI)))) (- 1 k))))))
#s(approx (* (* 2 (PI)) n) #s(hole binary64 (* 2 (* n (PI)))))
#s(approx (* (/ 1 (sqrt k)) (/ (sqrt (* (* (PI) n) 2)) (pow (* (* (PI) n) 2) (/ k 2)))) #s(hole binary64 (* (sqrt (/ (* n (PI)) k)) (/ (sqrt 2) (exp (* 1/2 (* k (+ (log (* 2 (PI))) (* -1 (log (/ 1 n)))))))))))
#s(approx (/ (sqrt (* (* (PI) n) 2)) (pow (* (* (PI) n) 2) (/ k 2))) #s(hole binary64 (* (sqrt (* n (PI))) (/ (sqrt 2) (exp (* 1/2 (* k (+ (log (* 2 (PI))) (* -1 (log (/ 1 n)))))))))))
#s(approx (pow (* (* (PI) n) 2) (/ k 2)) #s(hole binary64 (exp (* 1/2 (* k (+ (log (* 2 (PI))) (* -1 (log (/ 1 n)))))))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) #s(hole binary64 (* (sqrt (/ 1 k)) (exp (* 1/2 (* (+ (log (* 2 (PI))) (* -1 (log (/ 1 n)))) (- 1 k)))))))
#s(approx (/ (* (sqrt 2) (+ (* (* (log (* (* (PI) n) 2)) (sqrt (* (* (pow k 3) (PI)) n))) -1/2) (sqrt (* (* (PI) n) k)))) k) #s(hole binary64 (/ (* n (* (sqrt 2) (+ (sqrt (/ (* k (PI)) n)) (* -1/2 (* (sqrt (/ (* (pow k 3) (PI)) n)) (+ (log (* 2 (PI))) (* -1 (log (/ 1 n))))))))) k)))
#s(approx (* (sqrt 2) (+ (* (* (log (* (* (PI) n) 2)) (sqrt (* (* (pow k 3) (PI)) n))) -1/2) (sqrt (* (* (PI) n) k)))) #s(hole binary64 (* n (* (sqrt 2) (+ (sqrt (/ (* k (PI)) n)) (* -1/2 (* (sqrt (/ (* (pow k 3) (PI)) n)) (+ (log (* 2 (PI))) (* -1 (log (/ 1 n)))))))))))
#s(approx (+ (* (* (log (* (* (PI) n) 2)) (sqrt (* (* (pow k 3) (PI)) n))) -1/2) (sqrt (* (* (PI) n) k))) #s(hole binary64 (* n (+ (sqrt (/ (* k (PI)) n)) (* -1/2 (* (sqrt (/ (* (pow k 3) (PI)) n)) (+ (log (* 2 (PI))) (* -1 (log (/ 1 n))))))))))
#s(approx (pow (* (* 2 (PI)) n) (/ (- 1 k) 2)) #s(hole binary64 (exp (* 1/2 (* (+ (log (* 2 (PI))) (* -1 (log (/ 1 n)))) (- 1 k))))))
#s(approx (* (/ 1 (sqrt k)) (/ (sqrt (* (* (PI) n) 2)) (pow (* (* (PI) n) 2) (/ k 2)))) #s(hole binary64 (* -1 (* (sqrt (/ (* n (PI)) k)) (/ (* (sqrt -2) (sqrt -1)) (exp (* 1/2 (* k (+ (log (* -2 (PI))) (* -1 (log (/ -1 n))))))))))))
#s(approx (/ (sqrt (* (* (PI) n) 2)) (pow (* (* (PI) n) 2) (/ k 2))) #s(hole binary64 (* -1 (* (sqrt (* n (PI))) (/ (* (sqrt -2) (sqrt -1)) (exp (* 1/2 (* k (+ (log (* -2 (PI))) (* -1 (log (/ -1 n))))))))))))
#s(approx (sqrt (* (* (PI) n) 2)) #s(hole binary64 (* -1 (* (sqrt (* n (PI))) (* (sqrt -2) (sqrt -1))))))
#s(approx (pow (* (* (PI) n) 2) (/ k 2)) #s(hole binary64 (exp (* 1/2 (* k (+ (log (* -2 (PI))) (* -1 (log (/ -1 n)))))))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) #s(hole binary64 (* (sqrt (/ 1 k)) (exp (* 1/2 (* (+ (log (* -2 (PI))) (* -1 (log (/ -1 n)))) (- 1 k)))))))
#s(approx (sqrt (* (/ (* (PI) n) k) 2)) #s(hole binary64 (* -1 (* (sqrt (/ (* n (PI)) k)) (* (sqrt -2) (sqrt -1))))))
#s(approx (/ (* (sqrt 2) (+ (* (* (log (* (* (PI) n) 2)) (sqrt (* (* (pow k 3) (PI)) n))) -1/2) (sqrt (* (* (PI) n) k)))) k) #s(hole binary64 (* -1 (/ (* n (* (sqrt 2) (+ (* -1/2 (* (sqrt (/ (* (pow k 3) (PI)) n)) (* (pow (sqrt -1) 2) (+ (log (* -2 (PI))) (* -1 (log (/ -1 n))))))) (* (sqrt (/ (* k (PI)) n)) (pow (sqrt -1) 2))))) k))))
#s(approx (* (sqrt 2) (+ (* (* (log (* (* (PI) n) 2)) (sqrt (* (* (pow k 3) (PI)) n))) -1/2) (sqrt (* (* (PI) n) k)))) #s(hole binary64 (* -1 (* n (* (sqrt 2) (+ (* -1/2 (* (sqrt (/ (* (pow k 3) (PI)) n)) (* (pow (sqrt -1) 2) (+ (log (* -2 (PI))) (* -1 (log (/ -1 n))))))) (* (sqrt (/ (* k (PI)) n)) (pow (sqrt -1) 2))))))))
#s(approx (+ (* (* (log (* (* (PI) n) 2)) (sqrt (* (* (pow k 3) (PI)) n))) -1/2) (sqrt (* (* (PI) n) k))) #s(hole binary64 (* -1 (* n (+ (* -1/2 (* (sqrt (/ (* (pow k 3) (PI)) n)) (* (pow (sqrt -1) 2) (+ (log (* -2 (PI))) (* -1 (log (/ -1 n))))))) (* (sqrt (/ (* k (PI)) n)) (pow (sqrt -1) 2)))))))
#s(approx (* (sqrt 2) (sqrt (* (sqrt (PI)) (* (sqrt (PI)) (/ n k))))) #s(hole binary64 (* -1 (* (sqrt (/ (* n (PI)) k)) (* (pow (sqrt -1) 2) (sqrt 2))))))
#s(approx (sqrt (* (sqrt (PI)) (* (sqrt (PI)) (/ n k)))) #s(hole binary64 (* -1 (* (sqrt (/ (* n (PI)) k)) (pow (sqrt -1) 2)))))
#s(approx (pow (* (* 2 (PI)) n) (/ (- 1 k) 2)) #s(hole binary64 (exp (* 1/2 (* (+ (log (* -2 (PI))) (* -1 (log (/ -1 n)))) (- 1 k))))))

Outputs
#s(approx (* (/ 1 (sqrt k)) (/ (sqrt (* (* (PI) n) 2)) (pow (* (* (PI) n) 2) (/ k 2)))) #s(hole binary64 (* (sqrt (/ (* n (PI)) k)) (sqrt 2))))
#s(approx (* (/ 1 (sqrt k)) (/ (sqrt (* (* (PI) n) 2)) (pow (* (* (PI) n) 2) (/ k 2)))) (.f64 (sqrt.f64 #s(literal 2 binary64)) (sqrt.f64 (/.f64 (.f64 (PI.f64) n) k))))
#s(approx (* (/ 1 (sqrt k)) (/ (sqrt (* (* (PI) n) 2)) (pow (* (* (PI) n) 2) (/ k 2)))) #s(hole binary64 (/ (+ (* -1/2 (* (sqrt (* (pow k 3) (* n (PI)))) (* (log (* 2 (* n (PI)))) (sqrt 2)))) (* (sqrt (* k (* n (PI)))) (sqrt 2))) k)))
#s(approx (* (/ 1 (sqrt k)) (/ (sqrt (* (* (PI) n) 2)) (pow (* (* (PI) n) 2) (/ k 2)))) (.f64 (fma.f64 (.f64 (sqrt.f64 (.f64 (.f64 (pow.f64 k #s(literal 3 binary64)) (PI.f64)) n)) #s(literal -1/2 binary64)) (log.f64 (.f64 (.f64 (PI.f64) #s(literal 2 binary64)) n)) (sqrt.f64 (.f64 (.f64 (PI.f64) n) k))) (/.f64 (sqrt.f64 #s(literal 2 binary64)) k)))
#s(approx (* (/ 1 (sqrt k)) (/ (sqrt (* (* (PI) n) 2)) (pow (* (* (PI) n) 2) (/ k 2)))) #s(hole binary64 (/ (+ (* k (+ (* -1 (* (sqrt (* (pow k 3) (* n (PI)))) (+ (* -1/4 (* (pow (log (* 2 (* n (PI)))) 2) (sqrt 2))) (* 1/8 (* (pow (log (* 2 (* n (PI)))) 2) (sqrt 2)))))) (* -1/2 (* (sqrt (* k (* n (PI)))) (* (log (* 2 (* n (PI)))) (sqrt 2)))))) (* (sqrt (* k (* n (PI)))) (sqrt 2))) k)))
#s(approx (* (/ 1 (sqrt k)) (/ (sqrt (* (* (PI) n) 2)) (pow (* (* (PI) n) 2) (/ k 2)))) (/.f64 (fma.f64 (fma.f64 (.f64 (.f64 (sqrt.f64 (.f64 (.f64 (PI.f64) n) k)) #s(literal -1/2 binary64)) (log.f64 (.f64 (.f64 (PI.f64) #s(literal 2 binary64)) n))) (sqrt.f64 #s(literal 2 binary64)) (.f64 (.f64 #s(literal 1/8 binary64) (sqrt.f64 (.f64 (.f64 (pow.f64 k #s(literal 3 binary64)) (PI.f64)) n))) (.f64 (pow.f64 (log.f64 (.f64 (.f64 (PI.f64) #s(literal 2 binary64)) n)) #s(literal 2 binary64)) (sqrt.f64 #s(literal 2 binary64))))) k (.f64 (sqrt.f64 (.f64 (.f64 (PI.f64) n) k)) (sqrt.f64 #s(literal 2 binary64)))) k))
#s(approx (* (/ 1 (sqrt k)) (/ (sqrt (* (* (PI) n) 2)) (pow (* (* (PI) n) 2) (/ k 2)))) #s(hole binary64 (/ (+ (* k (+ (* -1/2 (* (sqrt (* k (* n (PI)))) (* (log (* 2 (* n (PI)))) (sqrt 2)))) (* k (+ (* -1 (* (sqrt (* k (* n (PI)))) (+ (* -1/4 (* (pow (log (* 2 (* n (PI)))) 2) (sqrt 2))) (* 1/8 (* (pow (log (* 2 (* n (PI)))) 2) (sqrt 2)))))) (* -1 (* (sqrt (* (pow k 3) (* n (PI)))) (+ (* -1/2 (* (log (* 2 (* n (PI)))) (+ (* -1/4 (* (pow (log (* 2 (* n (PI)))) 2) (sqrt 2))) (* 1/8 (* (pow (log (* 2 (* n (PI)))) 2) (sqrt 2)))))) (+ (* -1/16 (* (pow (log (* 2 (* n (PI)))) 3) (sqrt 2))) (* 1/48 (* (pow (log (* 2 (* n (PI)))) 3) (sqrt 2))))))))))) (* (sqrt (* k (* n (PI)))) (sqrt 2))) k)))
#s(approx (* (/ 1 (sqrt k)) (/ (sqrt (* (* (PI) n) 2)) (pow (* (* (PI) n) 2) (/ k 2)))) (/.f64 (fma.f64 (fma.f64 (.f64 (.f64 (sqrt.f64 (.f64 (.f64 (PI.f64) n) k)) #s(literal -1/2 binary64)) (log.f64 (.f64 (.f64 (PI.f64) #s(literal 2 binary64)) n))) (sqrt.f64 #s(literal 2 binary64)) (.f64 (fma.f64 (.f64 #s(literal -1/8 binary64) (.f64 (pow.f64 (log.f64 (.f64 (.f64 (PI.f64) #s(literal 2 binary64)) n)) #s(literal 2 binary64)) (sqrt.f64 (.f64 (.f64 (PI.f64) n) k)))) (sqrt.f64 #s(literal 2 binary64)) (.f64 (fma.f64 #s(literal -1/24 binary64) (.f64 (pow.f64 (log.f64 (.f64 (.f64 (PI.f64) #s(literal 2 binary64)) n)) #s(literal 3 binary64)) (sqrt.f64 #s(literal 2 binary64))) (.f64 (.f64 (.f64 (pow.f64 (log.f64 (.f64 (.f64 (PI.f64) #s(literal 2 binary64)) n)) #s(literal 3 binary64)) (sqrt.f64 #s(literal 2 binary64))) #s(literal -1/8 binary64)) #s(literal -1/2 binary64))) (sqrt.f64 (.f64 (.f64 (pow.f64 k #s(literal 3 binary64)) (PI.f64)) n)))) (neg.f64 k))) k (.f64 (sqrt.f64 (.f64 (*.f64 (PI.f64) n) k)) (sqrt.f64 #s(literal 2 binary64)))) k))
#s(approx (/ 1 (sqrt k)) #s(hole binary64 (sqrt (/ 1 k))))
#s(approx (/ 1 (sqrt k)) (sqrt.f64 (/.f64 #s(literal 1 binary64) k)))
#s(approx (sqrt k) #s(hole binary64 (sqrt k)))
#s(approx (sqrt k) (sqrt.f64 k))
#s(approx k #s(hole binary64 k))
#s(approx k k)
#s(approx (/ (sqrt (* (* (PI) n) 2)) (pow (* (* (PI) n) 2) (/ k 2))) #s(hole binary64 (* (sqrt (* n (PI))) (sqrt 2))))
#s(approx (/ (sqrt (* (* (PI) n) 2)) (pow (* (* (PI) n) 2) (/ k 2))) (.f64 (sqrt.f64 (.f64 (PI.f64) n)) (sqrt.f64 #s(literal 2 binary64))))
#s(approx (/ (sqrt (* (* (PI) n) 2)) (pow (* (* (PI) n) 2) (/ k 2))) #s(hole binary64 (+ (* -1/2 (* (* k (* (log (* 2 (* n (PI)))) (sqrt 2))) (sqrt (* n (PI))))) (* (sqrt (* n (PI))) (sqrt 2)))))
#s(approx (/ (sqrt (* (* (PI) n) 2)) (pow (* (* (PI) n) 2) (/ k 2))) (.f64 (sqrt.f64 (.f64 (PI.f64) n)) (fma.f64 (.f64 (.f64 #s(literal -1/2 binary64) k) (log.f64 (.f64 (.f64 (PI.f64) #s(literal 2 binary64)) n))) (sqrt.f64 #s(literal 2 binary64)) (sqrt.f64 #s(literal 2 binary64)))))
#s(approx (/ (sqrt (* (* (PI) n) 2)) (pow (* (* (PI) n) 2) (/ k 2))) #s(hole binary64 (+ (* k (+ (* -1 (* (* k (+ (* -1/4 (* (pow (log (* 2 (* n (PI)))) 2) (sqrt 2))) (* 1/8 (* (pow (log (* 2 (* n (PI)))) 2) (sqrt 2))))) (sqrt (* n (PI))))) (* -1/2 (* (sqrt (* n (PI))) (* (log (* 2 (* n (PI)))) (sqrt 2)))))) (* (sqrt (* n (PI))) (sqrt 2)))))
#s(approx (/ (sqrt (* (* (PI) n) 2)) (pow (* (* (PI) n) 2) (/ k 2))) (fma.f64 (neg.f64 k) (.f64 (.f64 k (sqrt.f64 (.f64 (PI.f64) n))) (.f64 (.f64 #s(literal -1/8 binary64) (sqrt.f64 #s(literal 2 binary64))) (pow.f64 (log.f64 (.f64 (.f64 (PI.f64) #s(literal 2 binary64)) n)) #s(literal 2 binary64)))) (.f64 (sqrt.f64 (.f64 (PI.f64) n)) (fma.f64 (.f64 (.f64 #s(literal -1/2 binary64) k) (log.f64 (.f64 (*.f64 (PI.f64) #s(literal 2 binary64)) n))) (sqrt.f64 #s(literal 2 binary64)) (sqrt.f64 #s(literal 2 binary64))))))
#s(approx (/ (sqrt (* (* (PI) n) 2)) (pow (* (* (PI) n) 2) (/ k 2))) #s(hole binary64 (+ (* k (+ (* -1/2 (* (sqrt (* n (PI))) (* (log (* 2 (* n (PI)))) (sqrt 2)))) (* k (+ (* -1 (* (sqrt (* n (PI))) (+ (* -1/4 (* (pow (log (* 2 (* n (PI)))) 2) (sqrt 2))) (* 1/8 (* (pow (log (* 2 (* n (PI)))) 2) (sqrt 2)))))) (* -1 (* (* k (+ (* -1/2 (* (log (* 2 (* n (PI)))) (+ (* -1/4 (* (pow (log (* 2 (* n (PI)))) 2) (sqrt 2))) (* 1/8 (* (pow (log (* 2 (* n (PI)))) 2) (sqrt 2)))))) (+ (* -1/16 (* (pow (log (* 2 (* n (PI)))) 3) (sqrt 2))) (* 1/48 (* (pow (log (* 2 (* n (PI)))) 3) (sqrt 2)))))) (sqrt (* n (PI))))))))) (* (sqrt (* n (PI))) (sqrt 2)))))
#s(approx (/ (sqrt (* (* (PI) n) 2)) (pow (* (* (PI) n) 2) (/ k 2))) (-.f64 (.f64 (sqrt.f64 (.f64 (PI.f64) n)) (fma.f64 (.f64 (.f64 #s(literal -1/2 binary64) k) (log.f64 (.f64 (.f64 (PI.f64) #s(literal 2 binary64)) n))) (sqrt.f64 #s(literal 2 binary64)) (sqrt.f64 #s(literal 2 binary64)))) (.f64 (.f64 (sqrt.f64 (.f64 (PI.f64) n)) (fma.f64 (.f64 #s(literal -1/8 binary64) (pow.f64 (log.f64 (.f64 (.f64 (PI.f64) #s(literal 2 binary64)) n)) #s(literal 2 binary64))) (sqrt.f64 #s(literal 2 binary64)) (.f64 (fma.f64 #s(literal -1/24 binary64) (.f64 (pow.f64 (log.f64 (.f64 (.f64 (PI.f64) #s(literal 2 binary64)) n)) #s(literal 3 binary64)) (sqrt.f64 #s(literal 2 binary64))) (.f64 (.f64 (.f64 (pow.f64 (log.f64 (.f64 (.f64 (PI.f64) #s(literal 2 binary64)) n)) #s(literal 3 binary64)) (sqrt.f64 #s(literal 2 binary64))) #s(literal -1/8 binary64)) #s(literal -1/2 binary64))) k))) (.f64 k k))))
#s(approx (pow (* (* (PI) n) 2) (/ k 2)) #s(hole binary64 1))
#s(approx (pow (* (* (PI) n) 2) (/ k 2)) #s(literal 1 binary64))
#s(approx (pow (* (* (PI) n) 2) (/ k 2)) #s(hole binary64 (+ 1 (* 1/2 (* k (log (* 2 (* n (PI)))))))))
#s(approx (pow (* (* (PI) n) 2) (/ k 2)) (fma.f64 (.f64 #s(literal 1/2 binary64) k) (log.f64 (.f64 (*.f64 (PI.f64) #s(literal 2 binary64)) n)) #s(literal 1 binary64)))
#s(approx (pow (* (* (PI) n) 2) (/ k 2)) #s(hole binary64 (+ 1 (* k (+ (* 1/8 (* k (pow (log (* 2 (* n (PI)))) 2))) (* 1/2 (log (* 2 (* n (PI))))))))))
#s(approx (pow (* (* (PI) n) 2) (/ k 2)) (fma.f64 (fma.f64 (.f64 #s(literal 1/8 binary64) k) (pow.f64 (log.f64 (.f64 (.f64 (PI.f64) #s(literal 2 binary64)) n)) #s(literal 2 binary64)) (.f64 #s(literal 1/2 binary64) (log.f64 (.f64 (.f64 (PI.f64) #s(literal 2 binary64)) n)))) k #s(literal 1 binary64)))
#s(approx (pow (* (* (PI) n) 2) (/ k 2)) #s(hole binary64 (+ 1 (* k (+ (* 1/2 (log (* 2 (* n (PI))))) (* k (+ (* 1/48 (* k (pow (log (* 2 (* n (PI)))) 3))) (* 1/8 (pow (log (* 2 (* n (PI)))) 2)))))))))
#s(approx (pow (* (* (PI) n) 2) (/ k 2)) (fma.f64 (fma.f64 (fma.f64 (.f64 #s(literal 1/48 binary64) k) (pow.f64 (log.f64 (.f64 (.f64 (PI.f64) #s(literal 2 binary64)) n)) #s(literal 3 binary64)) (.f64 #s(literal 1/8 binary64) (pow.f64 (log.f64 (.f64 (.f64 (PI.f64) #s(literal 2 binary64)) n)) #s(literal 2 binary64)))) k (.f64 #s(literal 1/2 binary64) (log.f64 (.f64 (*.f64 (PI.f64) #s(literal 2 binary64)) n)))) k #s(literal 1 binary64)))
#s(approx (/ k 2) #s(hole binary64 (* 1/2 k)))
#s(approx (/ k 2) (*.f64 #s(literal 1/2 binary64) k))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) #s(hole binary64 (* (sqrt (/ (* n (PI)) k)) (sqrt 2))))
#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))) #s(hole binary64 (/ (+ (* -1/2 (* (sqrt (* (pow k 3) (* n (PI)))) (* (log (* 2 (* n (PI)))) (sqrt 2)))) (* (sqrt (* k (* n (PI)))) (sqrt 2))) k)))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (.f64 (fma.f64 (.f64 (sqrt.f64 (.f64 (.f64 (pow.f64 k #s(literal 3 binary64)) (PI.f64)) n)) #s(literal -1/2 binary64)) (log.f64 (.f64 (.f64 (PI.f64) #s(literal 2 binary64)) n)) (sqrt.f64 (.f64 (.f64 (PI.f64) n) k))) (/.f64 (sqrt.f64 #s(literal 2 binary64)) k)))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) #s(hole binary64 (/ (+ (* 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)))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (/.f64 (fma.f64 (fma.f64 (.f64 (.f64 (sqrt.f64 (.f64 (.f64 (PI.f64) n) k)) #s(literal -1/2 binary64)) (log.f64 (.f64 (.f64 (PI.f64) #s(literal 2 binary64)) n))) (sqrt.f64 #s(literal 2 binary64)) (.f64 (.f64 #s(literal 1/8 binary64) (sqrt.f64 (.f64 (.f64 (pow.f64 k #s(literal 3 binary64)) (PI.f64)) n))) (.f64 (pow.f64 (log.f64 (.f64 (.f64 (PI.f64) #s(literal 2 binary64)) n)) #s(literal 2 binary64)) (sqrt.f64 #s(literal 2 binary64))))) k (.f64 (sqrt.f64 (.f64 (.f64 (PI.f64) n) k)) (sqrt.f64 #s(literal 2 binary64)))) k))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) #s(hole binary64 (/ (+ (* 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)))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (/.f64 (fma.f64 (fma.f64 (.f64 (.f64 (sqrt.f64 (.f64 (.f64 (PI.f64) n) k)) #s(literal -1/2 binary64)) (sqrt.f64 #s(literal 2 binary64))) (log.f64 (.f64 (.f64 (PI.f64) #s(literal 2 binary64)) n)) (.f64 (fma.f64 (.f64 (pow.f64 (log.f64 (.f64 (.f64 (PI.f64) #s(literal 2 binary64)) n)) #s(literal 2 binary64)) (sqrt.f64 (.f64 (.f64 (PI.f64) n) k))) (.f64 (sqrt.f64 #s(literal 2 binary64)) #s(literal 1/8 binary64)) (.f64 (.f64 (pow.f64 (log.f64 (.f64 (.f64 (PI.f64) #s(literal 2 binary64)) n)) #s(literal 3 binary64)) (sqrt.f64 (.f64 (.f64 (pow.f64 k #s(literal 3 binary64)) (PI.f64)) n))) (.f64 (sqrt.f64 #s(literal 2 binary64)) #s(literal -1/48 binary64)))) k)) k (.f64 (sqrt.f64 (.f64 (*.f64 (PI.f64) n) k)) (sqrt.f64 #s(literal 2 binary64)))) k))
#s(approx (sqrt (* (/ (* (PI) n) k) 2)) #s(hole binary64 (* (sqrt (/ (* n (PI)) k)) (sqrt 2))))
#s(approx (sqrt (* (/ (* (PI) n) k) 2)) (.f64 (sqrt.f64 #s(literal 2 binary64)) (sqrt.f64 (/.f64 (.f64 (PI.f64) n) k))))
#s(approx (* (/ (* (PI) n) k) 2) #s(hole binary64 (* 2 (/ (* n (PI)) k))))
#s(approx (* (/ (* (PI) n) k) 2) (.f64 (/.f64 (.f64 (PI.f64) n) k) #s(literal 2 binary64)))
#s(approx (/ (* (PI) n) k) #s(hole binary64 (/ (* n (PI)) k)))
#s(approx (* (sqrt (PI)) (* (sqrt (PI)) (/ n k))) (/.f64 (*.f64 (PI.f64) n) k))
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#s(approx (pow (* (* 2 (PI)) n) (/ (- 1 k) 2)) #s(hole binary64 (exp (* 1/2 (* (log (* 2 (* n (PI)))) (+ 1 (* -1 k)))))))
#s(approx (pow (* (* 2 (PI)) n) (/ (- 1 k) 2)) (pow.f64 (.f64 (.f64 (PI.f64) #s(literal 2 binary64)) n) (fma.f64 #s(literal -1/2 binary64) k #s(literal 1/2 binary64))))
#s(approx (/ (- 1 k) 2) #s(hole binary64 (* -1 (* k (- 1/2 (* 1/2 (/ 1 k)))))))
#s(approx (/ (- 1 k) 2) (*.f64 (neg.f64 k) (-.f64 #s(literal 1/2 binary64) (/.f64 #s(literal 1/2 binary64) k))))
#s(approx (* (/ 1 (sqrt k)) (/ (sqrt (* (* (PI) n) 2)) (pow (* (* (PI) n) 2) (/ k 2)))) #s(hole binary64 (* (sqrt (/ (* n (PI)) k)) (/ (sqrt 2) (exp (* 1/2 (* k (+ (log n) (log (* 2 (PI)))))))))))
#s(approx (* (/ 1 (sqrt k)) (/ (sqrt (* (* (PI) n) 2)) (pow (* (* (PI) n) 2) (/ k 2)))) (.f64 (/.f64 (sqrt.f64 #s(literal 2 binary64)) (pow.f64 (sqrt.f64 (exp.f64 k)) (+.f64 (log.f64 n) (log.f64 (.f64 (PI.f64) #s(literal 2 binary64)))))) (sqrt.f64 (/.f64 (*.f64 (PI.f64) n) k))))
#s(approx (/ (sqrt (* (* (PI) n) 2)) (pow (* (* (PI) n) 2) (/ k 2))) #s(hole binary64 (* (sqrt (* n (PI))) (/ (sqrt 2) (exp (* 1/2 (* k (+ (log n) (log (* 2 (PI)))))))))))
#s(approx (/ (sqrt (* (* (PI) n) 2)) (pow (* (* (PI) n) 2) (/ k 2))) (.f64 (/.f64 (sqrt.f64 #s(literal 2 binary64)) (pow.f64 (sqrt.f64 (exp.f64 k)) (+.f64 (log.f64 n) (log.f64 (.f64 (PI.f64) #s(literal 2 binary64)))))) (sqrt.f64 (*.f64 (PI.f64) n))))
#s(approx (sqrt (* (* (PI) n) 2)) #s(hole binary64 (* (sqrt (* n (PI))) (sqrt 2))))
#s(approx (sqrt (* (* (PI) n) 2)) (.f64 (sqrt.f64 (.f64 (PI.f64) n)) (sqrt.f64 #s(literal 2 binary64))))
#s(approx (* (* (PI) n) 2) #s(hole binary64 (* 2 (* n (PI)))))
#s(approx (* (* (PI) n) 2) (.f64 (.f64 (PI.f64) #s(literal 2 binary64)) n))
#s(approx (* (PI) n) #s(hole binary64 (* n (PI))))
#s(approx (* (PI) n) (*.f64 (PI.f64) n))
#s(approx n #s(hole binary64 n))
#s(approx n n)
#s(approx (pow (* (* (PI) n) 2) (/ k 2)) #s(hole binary64 (exp (* 1/2 (* k (+ (log n) (log (* 2 (PI)))))))))
#s(approx (pow (* (* (PI) n) 2) (/ k 2)) (pow.f64 (sqrt.f64 (exp.f64 k)) (+.f64 (log.f64 n) (log.f64 (*.f64 (PI.f64) #s(literal 2 binary64))))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) #s(hole binary64 (* (sqrt (/ 1 k)) (exp (* 1/2 (* (+ (log n) (log (* 2 (PI)))) (- 1 k)))))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (.f64 (pow.f64 (exp.f64 (fma.f64 #s(literal -1/2 binary64) k #s(literal 1/2 binary64))) (+.f64 (log.f64 n) (log.f64 (.f64 (PI.f64) #s(literal 2 binary64))))) (sqrt.f64 (/.f64 #s(literal 1 binary64) k))))
#s(approx (/ (* (sqrt 2) (+ (* (* (log (* (* (PI) n) 2)) (sqrt (* (* (pow k 3) (PI)) n))) -1/2) (sqrt (* (* (PI) n) k)))) k) #s(hole binary64 (/ (* (sqrt 2) (+ (sqrt (* k (* n (PI)))) (* -1/2 (* (sqrt (* (pow k 3) (* n (PI)))) (+ (log n) (log (* 2 (PI)))))))) k)))
#s(approx (/ (* (sqrt 2) (+ (* (* (log (* (* (PI) n) 2)) (sqrt (* (* (pow k 3) (PI)) n))) -1/2) (sqrt (* (* (PI) n) k)))) k) (.f64 (fma.f64 (.f64 (+.f64 (log.f64 n) (log.f64 (.f64 (PI.f64) #s(literal 2 binary64)))) (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))) (/.f64 (sqrt.f64 #s(literal 2 binary64)) k)))
#s(approx (* (sqrt 2) (+ (* (* (log (* (* (PI) n) 2)) (sqrt (* (* (pow k 3) (PI)) n))) -1/2) (sqrt (* (* (PI) n) k)))) #s(hole binary64 (* (sqrt 2) (+ (sqrt (* k (* n (PI)))) (* -1/2 (* (sqrt (* (pow k 3) (* n (PI)))) (+ (log n) (log (* 2 (PI))))))))))
#s(approx (* (sqrt 2) (+ (* (* (log (* (* (PI) n) 2)) (sqrt (* (* (pow k 3) (PI)) n))) -1/2) (sqrt (* (* (PI) n) k)))) (.f64 (fma.f64 (.f64 (+.f64 (log.f64 n) (log.f64 (.f64 (PI.f64) #s(literal 2 binary64)))) (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))) (sqrt.f64 #s(literal 2 binary64))))
#s(approx (+ (* (* (log (* (* (PI) n) 2)) (sqrt (* (* (pow k 3) (PI)) n))) -1/2) (sqrt (* (* (PI) n) k))) #s(hole binary64 (+ (sqrt (* k (* n (PI)))) (* -1/2 (* (sqrt (* (pow k 3) (* n (PI)))) (+ (log n) (log (* 2 (PI)))))))))
#s(approx (+ (* (* (log (* (* (PI) n) 2)) (sqrt (* (* (pow k 3) (PI)) n))) -1/2) (sqrt (* (* (PI) n) k))) (fma.f64 (.f64 (+.f64 (log.f64 n) (log.f64 (.f64 (PI.f64) #s(literal 2 binary64)))) (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))))
#s(approx (pow (* (* 2 (PI)) n) (/ (- 1 k) 2)) #s(hole binary64 (exp (* 1/2 (* (+ (log n) (log (* 2 (PI)))) (- 1 k))))))
#s(approx (pow (* (* 2 (PI)) n) (/ (- 1 k) 2)) (pow.f64 (exp.f64 (fma.f64 #s(literal -1/2 binary64) k #s(literal 1/2 binary64))) (+.f64 (log.f64 n) (log.f64 (*.f64 (PI.f64) #s(literal 2 binary64))))))
#s(approx (* (* 2 (PI)) n) #s(hole binary64 (* 2 (* n (PI)))))
#s(approx (* (* (PI) n) 2) (.f64 (.f64 (PI.f64) #s(literal 2 binary64)) n))
#s(approx (* (/ 1 (sqrt k)) (/ (sqrt (* (* (PI) n) 2)) (pow (* (* (PI) n) 2) (/ k 2)))) #s(hole binary64 (* (sqrt (/ (* n (PI)) k)) (/ (sqrt 2) (exp (* 1/2 (* k (+ (log (* 2 (PI))) (* -1 (log (/ 1 n)))))))))))
#s(approx (* (/ 1 (sqrt k)) (/ (sqrt (* (* (PI) n) 2)) (pow (* (* (PI) n) 2) (/ k 2)))) (.f64 (/.f64 (sqrt.f64 #s(literal 2 binary64)) (pow.f64 (sqrt.f64 (exp.f64 k)) (+.f64 (log.f64 n) (log.f64 (.f64 (PI.f64) #s(literal 2 binary64)))))) (sqrt.f64 (/.f64 (*.f64 (PI.f64) n) k))))
#s(approx (/ (sqrt (* (* (PI) n) 2)) (pow (* (* (PI) n) 2) (/ k 2))) #s(hole binary64 (* (sqrt (* n (PI))) (/ (sqrt 2) (exp (* 1/2 (* k (+ (log (* 2 (PI))) (* -1 (log (/ 1 n)))))))))))
#s(approx (/ (sqrt (* (* (PI) n) 2)) (pow (* (* (PI) n) 2) (/ k 2))) (.f64 (/.f64 (sqrt.f64 #s(literal 2 binary64)) (pow.f64 (sqrt.f64 (exp.f64 k)) (+.f64 (log.f64 n) (log.f64 (.f64 (PI.f64) #s(literal 2 binary64)))))) (sqrt.f64 (*.f64 (PI.f64) n))))
#s(approx (pow (* (* (PI) n) 2) (/ k 2)) #s(hole binary64 (exp (* 1/2 (* k (+ (log (* 2 (PI))) (* -1 (log (/ 1 n)))))))))
#s(approx (pow (* (* (PI) n) 2) (/ k 2)) (pow.f64 (sqrt.f64 (exp.f64 k)) (+.f64 (log.f64 n) (log.f64 (*.f64 (PI.f64) #s(literal 2 binary64))))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) #s(hole binary64 (* (sqrt (/ 1 k)) (exp (* 1/2 (* (+ (log (* 2 (PI))) (* -1 (log (/ 1 n)))) (- 1 k)))))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (.f64 (pow.f64 (exp.f64 (fma.f64 #s(literal -1/2 binary64) k #s(literal 1/2 binary64))) (+.f64 (log.f64 n) (log.f64 (.f64 (PI.f64) #s(literal 2 binary64))))) (sqrt.f64 (/.f64 #s(literal 1 binary64) k))))
#s(approx (/ (* (sqrt 2) (+ (* (* (log (* (* (PI) n) 2)) (sqrt (* (* (pow k 3) (PI)) n))) -1/2) (sqrt (* (* (PI) n) k)))) k) #s(hole binary64 (/ (* n (* (sqrt 2) (+ (sqrt (/ (* k (PI)) n)) (* -1/2 (* (sqrt (/ (* (pow k 3) (PI)) n)) (+ (log (* 2 (PI))) (* -1 (log (/ 1 n))))))))) k)))
#s(approx (/ (* (sqrt 2) (+ (* (* (log (* (* (PI) n) 2)) (sqrt (* (* (pow k 3) (PI)) n))) -1/2) (sqrt (* (* (PI) n) k)))) k) (.f64 (.f64 (fma.f64 (.f64 (sqrt.f64 (/.f64 (.f64 (pow.f64 k #s(literal 3 binary64)) (PI.f64)) n)) (+.f64 (log.f64 n) (log.f64 (.f64 (PI.f64) #s(literal 2 binary64))))) #s(literal -1/2 binary64) (sqrt.f64 (/.f64 (.f64 (PI.f64) k) n))) (sqrt.f64 #s(literal 2 binary64))) (/.f64 n k)))
#s(approx (* (sqrt 2) (+ (* (* (log (* (* (PI) n) 2)) (sqrt (* (* (pow k 3) (PI)) n))) -1/2) (sqrt (* (* (PI) n) k)))) #s(hole binary64 (* n (* (sqrt 2) (+ (sqrt (/ (* k (PI)) n)) (* -1/2 (* (sqrt (/ (* (pow k 3) (PI)) n)) (+ (log (* 2 (PI))) (* -1 (log (/ 1 n)))))))))))
#s(approx (* (sqrt 2) (+ (* (* (log (* (* (PI) n) 2)) (sqrt (* (* (pow k 3) (PI)) n))) -1/2) (sqrt (* (* (PI) n) k)))) (.f64 (.f64 (sqrt.f64 #s(literal 2 binary64)) n) (fma.f64 (.f64 (sqrt.f64 (/.f64 (.f64 (pow.f64 k #s(literal 3 binary64)) (PI.f64)) n)) (+.f64 (log.f64 n) (log.f64 (.f64 (PI.f64) #s(literal 2 binary64))))) #s(literal -1/2 binary64) (sqrt.f64 (/.f64 (.f64 (PI.f64) k) n)))))
#s(approx (+ (* (* (log (* (* (PI) n) 2)) (sqrt (* (* (pow k 3) (PI)) n))) -1/2) (sqrt (* (* (PI) n) k))) #s(hole binary64 (* n (+ (sqrt (/ (* k (PI)) n)) (* -1/2 (* (sqrt (/ (* (pow k 3) (PI)) n)) (+ (log (* 2 (PI))) (* -1 (log (/ 1 n))))))))))
#s(approx (+ (* (* (log (* (* (PI) n) 2)) (sqrt (* (* (pow k 3) (PI)) n))) -1/2) (sqrt (* (* (PI) n) k))) (.f64 (fma.f64 (.f64 (sqrt.f64 (/.f64 (.f64 (pow.f64 k #s(literal 3 binary64)) (PI.f64)) n)) (+.f64 (log.f64 n) (log.f64 (.f64 (PI.f64) #s(literal 2 binary64))))) #s(literal -1/2 binary64) (sqrt.f64 (/.f64 (*.f64 (PI.f64) k) n))) n))
#s(approx (pow (* (* 2 (PI)) n) (/ (- 1 k) 2)) #s(hole binary64 (exp (* 1/2 (* (+ (log (* 2 (PI))) (* -1 (log (/ 1 n)))) (- 1 k))))))
#s(approx (pow (* (* 2 (PI)) n) (/ (- 1 k) 2)) (pow.f64 (exp.f64 (fma.f64 #s(literal -1/2 binary64) k #s(literal 1/2 binary64))) (+.f64 (log.f64 n) (log.f64 (*.f64 (PI.f64) #s(literal 2 binary64))))))
#s(approx (* (/ 1 (sqrt k)) (/ (sqrt (* (* (PI) n) 2)) (pow (* (* (PI) n) 2) (/ k 2)))) #s(hole binary64 (* -1 (* (sqrt (/ (* n (PI)) k)) (/ (* (sqrt -2) (sqrt -1)) (exp (* 1/2 (* k (+ (log (* -2 (PI))) (* -1 (log (/ -1 n))))))))))))
#s(approx (* (/ 1 (sqrt k)) (/ (sqrt (* (* (PI) n) 2)) (pow (* (* (PI) n) 2) (/ k 2)))) (.f64 (neg.f64 (sqrt.f64 (/.f64 (.f64 (PI.f64) n) k))) (/.f64 (.f64 (sqrt.f64 #s(literal -2 binary64)) (sqrt.f64 #s(literal -1 binary64))) (pow.f64 (sqrt.f64 (exp.f64 k)) (-.f64 (log.f64 (.f64 #s(literal -2 binary64) (PI.f64))) (log.f64 (/.f64 #s(literal -1 binary64) n)))))))
#s(approx (/ (sqrt (* (* (PI) n) 2)) (pow (* (* (PI) n) 2) (/ k 2))) #s(hole binary64 (* -1 (* (sqrt (* n (PI))) (/ (* (sqrt -2) (sqrt -1)) (exp (* 1/2 (* k (+ (log (* -2 (PI))) (* -1 (log (/ -1 n))))))))))))
#s(approx (/ (sqrt (* (* (PI) n) 2)) (pow (* (* (PI) n) 2) (/ k 2))) (.f64 (neg.f64 (sqrt.f64 (.f64 (PI.f64) n))) (/.f64 (.f64 (sqrt.f64 #s(literal -2 binary64)) (sqrt.f64 #s(literal -1 binary64))) (pow.f64 (sqrt.f64 (exp.f64 k)) (-.f64 (log.f64 (.f64 #s(literal -2 binary64) (PI.f64))) (log.f64 (/.f64 #s(literal -1 binary64) n)))))))
#s(approx (sqrt (* (* (PI) n) 2)) #s(hole binary64 (* -1 (* (sqrt (* n (PI))) (* (sqrt -2) (sqrt -1))))))
#s(approx (sqrt (* (* (PI) n) 2)) (.f64 (.f64 (sqrt.f64 #s(literal -2 binary64)) (sqrt.f64 (*.f64 (PI.f64) n))) (neg.f64 (sqrt.f64 #s(literal -1 binary64)))))
#s(approx (pow (* (* (PI) n) 2) (/ k 2)) #s(hole binary64 (exp (* 1/2 (* k (+ (log (* -2 (PI))) (* -1 (log (/ -1 n)))))))))
#s(approx (pow (* (* (PI) n) 2) (/ k 2)) (pow.f64 (sqrt.f64 (exp.f64 k)) (-.f64 (log.f64 (*.f64 #s(literal -2 binary64) (PI.f64))) (log.f64 (/.f64 #s(literal -1 binary64) n)))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) #s(hole binary64 (* (sqrt (/ 1 k)) (exp (* 1/2 (* (+ (log (* -2 (PI))) (* -1 (log (/ -1 n)))) (- 1 k)))))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (.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))))
#s(approx (sqrt (* (/ (* (PI) n) k) 2)) #s(hole binary64 (* -1 (* (sqrt (/ (* n (PI)) k)) (* (sqrt -2) (sqrt -1))))))
#s(approx (sqrt (* (/ (* (PI) n) k) 2)) (.f64 (.f64 (sqrt.f64 #s(literal -2 binary64)) (sqrt.f64 (/.f64 (*.f64 (PI.f64) n) k))) (neg.f64 (sqrt.f64 #s(literal -1 binary64)))))
#s(approx (/ (* (sqrt 2) (+ (* (* (log (* (* (PI) n) 2)) (sqrt (* (* (pow k 3) (PI)) n))) -1/2) (sqrt (* (* (PI) n) k)))) k) #s(hole binary64 (* -1 (/ (* n (* (sqrt 2) (+ (* -1/2 (* (sqrt (/ (* (pow k 3) (PI)) n)) (* (pow (sqrt -1) 2) (+ (log (* -2 (PI))) (* -1 (log (/ -1 n))))))) (* (sqrt (/ (* k (PI)) n)) (pow (sqrt -1) 2))))) k))))
#s(approx (/ (* (sqrt 2) (+ (* (* (log (* (* (PI) n) 2)) (sqrt (* (* (pow k 3) (PI)) n))) -1/2) (sqrt (* (* (PI) n) k)))) k) (/.f64 (.f64 (.f64 (sqrt.f64 #s(literal 2 binary64)) n) (fma.f64 (.f64 (sqrt.f64 (/.f64 (.f64 (pow.f64 k #s(literal 3 binary64)) (PI.f64)) n)) #s(literal -1/2 binary64)) (fma.f64 (log.f64 (.f64 #s(literal -2 binary64) (PI.f64))) #s(literal -1 binary64) (log.f64 (/.f64 #s(literal -1 binary64) n))) (.f64 (sqrt.f64 (/.f64 (*.f64 (PI.f64) k) n)) #s(literal -1 binary64)))) (neg.f64 k)))
#s(approx (* (sqrt 2) (+ (* (* (log (* (* (PI) n) 2)) (sqrt (* (* (pow k 3) (PI)) n))) -1/2) (sqrt (* (* (PI) n) k)))) #s(hole binary64 (* -1 (* n (* (sqrt 2) (+ (* -1/2 (* (sqrt (/ (* (pow k 3) (PI)) n)) (* (pow (sqrt -1) 2) (+ (log (* -2 (PI))) (* -1 (log (/ -1 n))))))) (* (sqrt (/ (* k (PI)) n)) (pow (sqrt -1) 2))))))))
#s(approx (* (sqrt 2) (+ (* (* (log (* (* (PI) n) 2)) (sqrt (* (* (pow k 3) (PI)) n))) -1/2) (sqrt (* (* (PI) n) k)))) (.f64 (.f64 (neg.f64 n) (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 -1/2 binary64)) (fma.f64 (log.f64 (.f64 #s(literal -2 binary64) (PI.f64))) #s(literal -1 binary64) (log.f64 (/.f64 #s(literal -1 binary64) n))) (.f64 (sqrt.f64 (/.f64 (*.f64 (PI.f64) k) n)) #s(literal -1 binary64)))))
#s(approx (+ (* (* (log (* (* (PI) n) 2)) (sqrt (* (* (pow k 3) (PI)) n))) -1/2) (sqrt (* (* (PI) n) k))) #s(hole binary64 (* -1 (* n (+ (* -1/2 (* (sqrt (/ (* (pow k 3) (PI)) n)) (* (pow (sqrt -1) 2) (+ (log (* -2 (PI))) (* -1 (log (/ -1 n))))))) (* (sqrt (/ (* k (PI)) n)) (pow (sqrt -1) 2)))))))
#s(approx (+ (* (* (log (* (* (PI) n) 2)) (sqrt (* (* (pow k 3) (PI)) n))) -1/2) (sqrt (* (* (PI) n) k))) (.f64 (neg.f64 n) (fma.f64 (.f64 (sqrt.f64 (/.f64 (.f64 (pow.f64 k #s(literal 3 binary64)) (PI.f64)) n)) #s(literal -1/2 binary64)) (fma.f64 (log.f64 (.f64 #s(literal -2 binary64) (PI.f64))) #s(literal -1 binary64) (log.f64 (/.f64 #s(literal -1 binary64) n))) (.f64 (sqrt.f64 (/.f64 (.f64 (PI.f64) k) n)) #s(literal -1 binary64)))))
#s(approx (* (sqrt 2) (sqrt (* (sqrt (PI)) (* (sqrt (PI)) (/ n k))))) #s(hole binary64 (* -1 (* (sqrt (/ (* n (PI)) k)) (* (pow (sqrt -1) 2) (sqrt 2))))))
#s(approx (* (sqrt 2) (sqrt (* (sqrt (PI)) (* (sqrt (PI)) (/ n k))))) (.f64 (.f64 (sqrt.f64 (/.f64 (*.f64 (PI.f64) n) k)) #s(literal 1 binary64)) (sqrt.f64 #s(literal 2 binary64))))
#s(approx (sqrt (* (sqrt (PI)) (* (sqrt (PI)) (/ n k)))) #s(hole binary64 (* -1 (* (sqrt (/ (* n (PI)) k)) (pow (sqrt -1) 2)))))
#s(approx (sqrt (* (sqrt (PI)) (* (sqrt (PI)) (/ n k)))) (.f64 (sqrt.f64 (/.f64 (.f64 (PI.f64) n) k)) #s(literal 1 binary64)))
#s(approx (pow (* (* 2 (PI)) n) (/ (- 1 k) 2)) #s(hole binary64 (exp (* 1/2 (* (+ (log (* -2 (PI))) (* -1 (log (/ -1 n)))) (- 1 k))))))
#s(approx (pow (* (* 2 (PI)) n) (/ (- 1 k) 2)) (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)))))

rewrite88.0ms (1%)

Memory

20.3MiB live, 110.9MiB allocated; 6ms collecting garbage

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	61	415
0	93	397
1	265	376
0	1361	372

Stop Event

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

Counts

39 → 366

Calls

Call 1

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

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

eval71.0ms (0.8%)

Memory: -17.8MiB live, 166.9MiB allocated; 23ms collecting garbage
Compiler: Compiled 17 498 to 1 912 computations (89.1% saved)

prune67.0ms (0.8%)

Memory

-2.9MiB live, 97.5MiB allocated; 10ms collecting garbage

Pruning

31 alts after pruning (28 fresh and 3 done)

	Pruned	Kept	Total
New	507	20	527
Fresh	7	8	15
Picked	3	2	5
Done	0	1	1
Total	517	31	548

Accuracy

100.0%

Counts

548 → 31

Alt Table

Click to see full alt table

Status	Accuracy	Program
	52.5%	(/.f64 (pow.f64 (.f64 #s(literal 2 binary64) (.f64 n (PI.f64))) #s(approx (/ (- 1 k) 2) (*.f64 #s(literal -1/2 binary64) k))) (sqrt.f64 k))
	76.4%	(/.f64 (sqrt.f64 (/.f64 (.f64 #s(literal 2 binary64) (.f64 n (PI.f64))) k)) (pow.f64 (.f64 #s(literal 2 binary64) (.f64 n (PI.f64))) (/.f64 k #s(literal 2 binary64))))
	99.6%	(.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) (/.f64 (sqrt.f64 (.f64 (.f64 (PI.f64) n) #s(literal 2 binary64))) (pow.f64 (.f64 (.f64 (PI.f64) n) #s(literal 2 binary64)) #s(approx (/ k 2) (.f64 #s(literal 1/2 binary64) k)))))
▶	50.0%	(.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) (/.f64 (sqrt.f64 (.f64 (.f64 (PI.f64) n) #s(literal 2 binary64))) #s(approx (pow ( (* (PI) n) 2) (/ k 2)) #s(literal 1 binary64))))
	50.0%	(.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) #s(approx (pow ( (* (PI) n) 2) (+ (* -1/2 k) 1/2)) (.f64 (sqrt.f64 (.f64 (PI.f64) n)) (sqrt.f64 #s(literal 2 binary64)))))
▶	99.7%	(.f64 #s(approx (/ 1 (sqrt k)) (sqrt.f64 (/.f64 #s(literal 1 binary64) k))) (/.f64 (sqrt.f64 (.f64 (.f64 (PI.f64) n) #s(literal 2 binary64))) (pow.f64 (.f64 (*.f64 (PI.f64) n) #s(literal 2 binary64)) (/.f64 k #s(literal 2 binary64)))))
	99.5%	#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (/.f64 (.f64 (pow.f64 (.f64 (*.f64 (PI.f64) n) #s(literal 2 binary64)) (fma.f64 #s(literal -1/2 binary64) k #s(literal 1/2 binary64))) #s(literal 1 binary64)) (sqrt.f64 k)))
	50.0%	#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (/.f64 (.f64 (sqrt.f64 #s(literal 2 binary64)) #s(approx (+ ( (* (log (* (* (PI) n) 2)) (sqrt (* (* (pow k 3) (PI)) n))) -1/2) (sqrt (* (* (PI) n) k))) (.f64 (sqrt.f64 (.f64 n (PI.f64))) (sqrt.f64 k)))) k))
	40.3%	#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (/.f64 (.f64 (sqrt.f64 #s(literal 2 binary64)) #s(approx (+ ( (* (log (* (* (PI) n) 2)) (sqrt (* (* (pow k 3) (PI)) n))) -1/2) (sqrt (* (* (PI) n) k))) (.f64 (sqrt.f64 (PI.f64)) (sqrt.f64 (.f64 n k))))) k))
	40.3%	#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (/.f64 (.f64 (sqrt.f64 #s(literal 2 binary64)) #s(approx (+ ( (* (log (* (* (PI) n) 2)) (sqrt (* (* (pow k 3) (PI)) n))) -1/2) (sqrt (* (* (PI) n) k))) (sqrt.f64 (.f64 (.f64 k (PI.f64)) n)))) k))
	27.2%	#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (/.f64 (.f64 (sqrt.f64 #s(literal 2 binary64)) #s(approx (+ ( (* (log (* (* (PI) n) 2)) (sqrt (* (* (pow k 3) (PI)) n))) -1/2) (sqrt (* (* (PI) n) k))) (sqrt.f64 (sqrt.f64 (.f64 (.f64 (.f64 n (PI.f64)) k) (.f64 (*.f64 n (PI.f64)) k)))))) k))
▶	50.1%	#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (/.f64 (sqrt.f64 (.f64 (.f64 (PI.f64) n) #s(literal 2 binary64))) (sqrt.f64 k)))
	40.2%	#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (.f64 (/.f64 #s(approx (+ ( (* (log (* (* (PI) n) 2)) (sqrt (* (* (pow k 3) (PI)) n))) -1/2) (sqrt (* (* (PI) n) k))) (sqrt.f64 (.f64 (.f64 n (PI.f64)) k))) k) (sqrt.f64 #s(literal 2 binary64))))
	49.9%	#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (.f64 (.f64 (pow.f64 k #s(literal -1/2 binary64)) (sqrt.f64 n)) (sqrt.f64 (*.f64 #s(literal 2 binary64) (PI.f64)))))
✓	99.5%	#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) k)) (pow.f64 (.f64 (*.f64 (PI.f64) n) #s(literal 2 binary64)) (fma.f64 #s(literal -1/2 binary64) k #s(literal 1/2 binary64)))))
	38.0%	#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (.f64 (sqrt.f64 (.f64 (/.f64 n k) (PI.f64))) (sqrt.f64 #s(literal 2 binary64))))
	50.0%	#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))))
	38.1%	#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (.f64 (sqrt.f64 #s(literal 2 binary64)) (.f64 (sqrt.f64 (PI.f64)) (sqrt.f64 (/.f64 n k)))))
	38.0%	#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (.f64 (sqrt.f64 #s(literal 2 binary64)) (sqrt.f64 (.f64 (sqrt.f64 (PI.f64)) (/.f64 (*.f64 (sqrt.f64 (PI.f64)) n) k)))))
✓	38.1%	#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (.f64 (sqrt.f64 #s(literal 2 binary64)) (sqrt.f64 (.f64 (sqrt.f64 (PI.f64)) (*.f64 (sqrt.f64 (PI.f64)) (/.f64 n k))))))
	38.0%	#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (.f64 (sqrt.f64 #s(literal 2 binary64)) (sqrt.f64 (.f64 n (/.f64 (PI.f64) k)))))
	40.3%	#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (.f64 #s(approx (+ ( (* (log (* (* (PI) n) 2)) (sqrt (* (* (pow k 3) (PI)) n))) -1/2) (sqrt (* (* (PI) n) k))) (sqrt.f64 (.f64 (.f64 n (PI.f64)) k))) (/.f64 (sqrt.f64 #s(literal 2 binary64)) k)))
	38.0%	#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt.f64 (.f64 (/.f64 (.f64 (*.f64 (sqrt.f64 (PI.f64)) n) (sqrt.f64 (PI.f64))) k) #s(literal 2 binary64))))
✓	38.2%	#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))))
	38.0%	#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt.f64 (.f64 (.f64 (/.f64 n k) (sqrt.f64 (PI.f64))) (*.f64 (sqrt.f64 (PI.f64)) #s(literal 2 binary64)))))
	38.1%	#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt.f64 (.f64 (.f64 (/.f64 n k) (PI.f64)) #s(literal 2 binary64))))
▶	38.0%	#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt.f64 (.f64 (.f64 (*.f64 (/.f64 n k) (sqrt.f64 (PI.f64))) (sqrt.f64 (PI.f64))) #s(literal 2 binary64))))
	38.1%	#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt.f64 (.f64 (.f64 n (/.f64 (PI.f64) k)) #s(literal 2 binary64))))
	38.1%	#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt.f64 (.f64 (.f64 n (PI.f64)) (/.f64 #s(literal 2 binary64) k))))
▶	38.1%	#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt.f64 (.f64 (PI.f64) (/.f64 (.f64 #s(literal 2 binary64) n) k))))
	76.3%	#s(approx (* (/ 1 (sqrt k)) (/ (pow (* n (* (PI) 2)) 1/2) (pow (* n (* (PI) 2)) (/ k 2)))) (.f64 (/.f64 (sqrt.f64 #s(literal 2 binary64)) (sqrt.f64 (pow.f64 (.f64 (.f64 (PI.f64) n) #s(literal 2 binary64)) k))) (sqrt.f64 (/.f64 (.f64 (PI.f64) n) k))))

Compiler

Compiled 1 909 to 1 433 computations (24.9% saved)

series69.0ms (0.8%)

Memory

32.2MiB live, 119.3MiB allocated; 20ms collecting garbage

Counts

34 → 61

Calls

Call 1

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

Outputs
#s(approx (* (/ 1 (sqrt k)) (/ (sqrt (* (* (PI) n) 2)) (pow (* (* (PI) n) 2) (/ k 2)))) #s(hole binary64 (* (sqrt (/ (* n (PI)) k)) (sqrt 2))))
#s(approx (* (/ 1 (sqrt k)) (/ (sqrt (* (* (PI) n) 2)) (pow (* (* (PI) n) 2) (/ k 2)))) #s(hole binary64 (/ (+ (* -1/2 (* (sqrt (* (pow k 3) (* n (PI)))) (* (log (* 2 (* n (PI)))) (sqrt 2)))) (* (sqrt (* k (* n (PI)))) (sqrt 2))) k)))
#s(approx (* (/ 1 (sqrt k)) (/ (sqrt (* (* (PI) n) 2)) (pow (* (* (PI) n) 2) (/ k 2)))) #s(hole binary64 (/ (+ (* k (+ (* -1 (* (sqrt (* (pow k 3) (* n (PI)))) (+ (* -1/4 (* (pow (log (* 2 (* n (PI)))) 2) (sqrt 2))) (* 1/8 (* (pow (log (* 2 (* n (PI)))) 2) (sqrt 2)))))) (* -1/2 (* (sqrt (* k (* n (PI)))) (* (log (* 2 (* n (PI)))) (sqrt 2)))))) (* (sqrt (* k (* n (PI)))) (sqrt 2))) k)))
#s(approx (* (/ 1 (sqrt k)) (/ (sqrt (* (* (PI) n) 2)) (pow (* (* (PI) n) 2) (/ k 2)))) #s(hole binary64 (/ (+ (* k (+ (* -1/2 (* (sqrt (* k (* n (PI)))) (* (log (* 2 (* n (PI)))) (sqrt 2)))) (* k (+ (* -1 (* (sqrt (* k (* n (PI)))) (+ (* -1/4 (* (pow (log (* 2 (* n (PI)))) 2) (sqrt 2))) (* 1/8 (* (pow (log (* 2 (* n (PI)))) 2) (sqrt 2)))))) (* -1 (* (sqrt (* (pow k 3) (* n (PI)))) (+ (* -1/2 (* (log (* 2 (* n (PI)))) (+ (* -1/4 (* (pow (log (* 2 (* n (PI)))) 2) (sqrt 2))) (* 1/8 (* (pow (log (* 2 (* n (PI)))) 2) (sqrt 2)))))) (+ (* -1/16 (* (pow (log (* 2 (* n (PI)))) 3) (sqrt 2))) (* 1/48 (* (pow (log (* 2 (* n (PI)))) 3) (sqrt 2))))))))))) (* (sqrt (* k (* n (PI)))) (sqrt 2))) k)))
#s(approx (/ 1 (sqrt k)) #s(hole binary64 (sqrt (/ 1 k))))
#s(approx (sqrt (/ 1 k)) #s(hole binary64 (sqrt (/ 1 k))))
#s(approx (/ 1 k) #s(hole binary64 (/ 1 k)))
#s(approx k #s(hole binary64 k))
#s(approx (/ (sqrt (* (* (PI) n) 2)) (pow (* (* (PI) n) 2) (/ k 2))) #s(hole binary64 (* (sqrt (* n (PI))) (sqrt 2))))
#s(approx (/ (sqrt (* (* (PI) n) 2)) (pow (* (* (PI) n) 2) (/ k 2))) #s(hole binary64 (+ (* -1/2 (* (* k (* (log (* 2 (* n (PI)))) (sqrt 2))) (sqrt (* n (PI))))) (* (sqrt (* n (PI))) (sqrt 2)))))
#s(approx (/ (sqrt (* (* (PI) n) 2)) (pow (* (* (PI) n) 2) (/ k 2))) #s(hole binary64 (+ (* k (+ (* -1 (* (* k (+ (* -1/4 (* (pow (log (* 2 (* n (PI)))) 2) (sqrt 2))) (* 1/8 (* (pow (log (* 2 (* n (PI)))) 2) (sqrt 2))))) (sqrt (* n (PI))))) (* -1/2 (* (sqrt (* n (PI))) (* (log (* 2 (* n (PI)))) (sqrt 2)))))) (* (sqrt (* n (PI))) (sqrt 2)))))
#s(approx (/ (sqrt (* (* (PI) n) 2)) (pow (* (* (PI) n) 2) (/ k 2))) #s(hole binary64 (+ (* k (+ (* -1/2 (* (sqrt (* n (PI))) (* (log (* 2 (* n (PI)))) (sqrt 2)))) (* k (+ (* -1 (* (sqrt (* n (PI))) (+ (* -1/4 (* (pow (log (* 2 (* n (PI)))) 2) (sqrt 2))) (* 1/8 (* (pow (log (* 2 (* n (PI)))) 2) (sqrt 2)))))) (* -1 (* (* k (+ (* -1/2 (* (log (* 2 (* n (PI)))) (+ (* -1/4 (* (pow (log (* 2 (* n (PI)))) 2) (sqrt 2))) (* 1/8 (* (pow (log (* 2 (* n (PI)))) 2) (sqrt 2)))))) (+ (* -1/16 (* (pow (log (* 2 (* n (PI)))) 3) (sqrt 2))) (* 1/48 (* (pow (log (* 2 (* n (PI)))) 3) (sqrt 2)))))) (sqrt (* n (PI))))))))) (* (sqrt (* n (PI))) (sqrt 2)))))
#s(approx (pow (* (* (PI) n) 2) (/ k 2)) #s(hole binary64 1))
#s(approx (pow (* (* (PI) n) 2) (/ k 2)) #s(hole binary64 (+ 1 (* 1/2 (* k (log (* 2 (* n (PI)))))))))
#s(approx (pow (* (* (PI) n) 2) (/ k 2)) #s(hole binary64 (+ 1 (* k (+ (* 1/8 (* k (pow (log (* 2 (* n (PI)))) 2))) (* 1/2 (log (* 2 (* n (PI))))))))))
#s(approx (pow (* (* (PI) n) 2) (/ k 2)) #s(hole binary64 (+ 1 (* k (+ (* 1/2 (log (* 2 (* n (PI))))) (* k (+ (* 1/48 (* k (pow (log (* 2 (* n (PI)))) 3))) (* 1/8 (pow (log (* 2 (* n (PI)))) 2)))))))))
#s(approx (/ k 2) #s(hole binary64 (* 1/2 k)))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) #s(hole binary64 (* (sqrt (/ (* n (PI)) k)) (sqrt 2))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) #s(hole binary64 (/ (+ (* -1/2 (* (sqrt (* (pow k 3) (* n (PI)))) (* (log (* 2 (* n (PI)))) (sqrt 2)))) (* (sqrt (* k (* n (PI)))) (sqrt 2))) k)))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) #s(hole binary64 (/ (+ (* 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)))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) #s(hole binary64 (/ (+ (* 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)))
#s(approx (sqrt (* (PI) (/ (* 2 n) k))) #s(hole binary64 (* (sqrt (/ (* n (PI)) k)) (sqrt 2))))
#s(approx (* (PI) (/ (* 2 n) k)) #s(hole binary64 (* 2 (/ (* n (PI)) k))))
#s(approx (/ (* 2 n) k) #s(hole binary64 (* 2 (/ n k))))
#s(approx (/ (sqrt (* (* (PI) n) 2)) (sqrt k)) #s(hole binary64 (* (sqrt (/ (* n (PI)) k)) (sqrt 2))))
#s(approx (sqrt k) #s(hole binary64 (sqrt k)))
#s(approx (sqrt (* (* (* (/ n k) (sqrt (PI))) (sqrt (PI))) 2)) #s(hole binary64 (* (sqrt (/ (* n (PI)) k)) (sqrt 2))))
#s(approx (* (* (* (/ n k) (sqrt (PI))) (sqrt (PI))) 2) #s(hole binary64 (* 2 (/ (* n (PI)) k))))
#s(approx (* (* (/ n k) (sqrt (PI))) (sqrt (PI))) #s(hole binary64 (/ (* n (PI)) k)))
#s(approx (* (/ n k) (sqrt (PI))) #s(hole binary64 (* (/ n k) (sqrt (PI)))))
#s(approx (/ n k) #s(hole binary64 (/ n k)))
#s(approx (* (/ 1 (sqrt k)) (/ (sqrt (* (* (PI) n) 2)) (pow (* (* (PI) n) 2) (/ k 2)))) #s(hole binary64 (* (sqrt (/ (* n (PI)) k)) (/ (sqrt 2) (exp (* 1/2 (* k (log (* 2 (* n (PI)))))))))))
#s(approx (/ (sqrt (* (* (PI) n) 2)) (pow (* (* (PI) n) 2) (/ k 2))) #s(hole binary64 (* (sqrt (* n (PI))) (/ (sqrt 2) (exp (* 1/2 (* k (log (* 2 (* n (PI)))))))))))
#s(approx (pow (* (* (PI) n) 2) (/ k 2)) #s(hole binary64 (exp (* 1/2 (* k (log (* 2 (* n (PI)))))))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) #s(hole binary64 (* (sqrt (/ 1 k)) (exp (* 1/2 (* (log (* 2 (* n (PI)))) (- 1 k)))))))
#s(approx (sqrt (/ 1 k)) #s(hole binary64 (* (sqrt (/ 1 k)) (pow (sqrt -1) 2))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) #s(hole binary64 (* (sqrt (/ 1 k)) (exp (* 1/2 (* (log (* 2 (* n (PI)))) (+ 1 (* -1 k))))))))
#s(approx (sqrt (* (PI) (/ (* 2 n) k))) #s(hole binary64 (* (sqrt (/ (* n (PI)) k)) (* (sqrt -2) (sqrt -1)))))
#s(approx (sqrt k) #s(hole binary64 (* -1 (* (sqrt k) (pow (sqrt -1) 2)))))
#s(approx (sqrt (* (* (* (/ n k) (sqrt (PI))) (sqrt (PI))) 2)) #s(hole binary64 (* (sqrt (/ (* n (PI)) k)) (* (sqrt -2) (sqrt -1)))))
#s(approx (* (/ 1 (sqrt k)) (/ (sqrt (* (* (PI) n) 2)) (pow (* (* (PI) n) 2) (/ k 2)))) #s(hole binary64 (* (sqrt (/ (* n (PI)) k)) (/ (sqrt 2) (exp (* 1/2 (* k (+ (log n) (log (* 2 (PI)))))))))))
#s(approx (/ (sqrt (* (* (PI) n) 2)) (pow (* (* (PI) n) 2) (/ k 2))) #s(hole binary64 (* (sqrt (* n (PI))) (/ (sqrt 2) (exp (* 1/2 (* k (+ (log n) (log (* 2 (PI)))))))))))
#s(approx (sqrt (* (* (PI) n) 2)) #s(hole binary64 (* (sqrt (* n (PI))) (sqrt 2))))
#s(approx (* (* (PI) n) 2) #s(hole binary64 (* 2 (* n (PI)))))
#s(approx (* (PI) n) #s(hole binary64 (* n (PI))))
#s(approx n #s(hole binary64 n))
#s(approx (pow (* (* (PI) n) 2) (/ k 2)) #s(hole binary64 (exp (* 1/2 (* k (+ (log n) (log (* 2 (PI)))))))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) #s(hole binary64 (* (sqrt (/ 1 k)) (exp (* 1/2 (* (+ (log n) (log (* 2 (PI)))) (- 1 k)))))))
#s(approx (* 2 n) #s(hole binary64 (* 2 n)))
#s(approx (* (/ 1 (sqrt k)) (/ (sqrt (* (* (PI) n) 2)) (pow (* (* (PI) n) 2) (/ k 2)))) #s(hole binary64 (* (sqrt (/ (* n (PI)) k)) (/ (sqrt 2) (exp (* 1/2 (* k (+ (log (* 2 (PI))) (* -1 (log (/ 1 n)))))))))))
#s(approx (/ (sqrt (* (* (PI) n) 2)) (pow (* (* (PI) n) 2) (/ k 2))) #s(hole binary64 (* (sqrt (* n (PI))) (/ (sqrt 2) (exp (* 1/2 (* k (+ (log (* 2 (PI))) (* -1 (log (/ 1 n)))))))))))
#s(approx (pow (* (* (PI) n) 2) (/ k 2)) #s(hole binary64 (exp (* 1/2 (* k (+ (log (* 2 (PI))) (* -1 (log (/ 1 n)))))))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) #s(hole binary64 (* (sqrt (/ 1 k)) (exp (* 1/2 (* (+ (log (* 2 (PI))) (* -1 (log (/ 1 n)))) (- 1 k)))))))
#s(approx (* (/ 1 (sqrt k)) (/ (sqrt (* (* (PI) n) 2)) (pow (* (* (PI) n) 2) (/ k 2)))) #s(hole binary64 (* -1 (* (sqrt (/ (* n (PI)) k)) (/ (* (sqrt -2) (sqrt -1)) (exp (* 1/2 (* k (+ (log (* -2 (PI))) (* -1 (log (/ -1 n))))))))))))
#s(approx (/ (sqrt (* (* (PI) n) 2)) (pow (* (* (PI) n) 2) (/ k 2))) #s(hole binary64 (* -1 (* (sqrt (* n (PI))) (/ (* (sqrt -2) (sqrt -1)) (exp (* 1/2 (* k (+ (log (* -2 (PI))) (* -1 (log (/ -1 n))))))))))))
#s(approx (sqrt (* (* (PI) n) 2)) #s(hole binary64 (* -1 (* (sqrt (* n (PI))) (* (sqrt -2) (sqrt -1))))))
#s(approx (pow (* (* (PI) n) 2) (/ k 2)) #s(hole binary64 (exp (* 1/2 (* k (+ (log (* -2 (PI))) (* -1 (log (/ -1 n)))))))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) #s(hole binary64 (* (sqrt (/ 1 k)) (exp (* 1/2 (* (+ (log (* -2 (PI))) (* -1 (log (/ -1 n)))) (- 1 k)))))))
#s(approx (sqrt (* (PI) (/ (* 2 n) k))) #s(hole binary64 (* -1 (* (sqrt (/ (* n (PI)) k)) (* (sqrt -2) (sqrt -1))))))
#s(approx (/ (sqrt (* (* (PI) n) 2)) (sqrt k)) #s(hole binary64 (* -1 (* (sqrt (/ (* n (PI)) k)) (* (sqrt -2) (sqrt -1))))))
#s(approx (sqrt (* (* (* (/ n k) (sqrt (PI))) (sqrt (PI))) 2)) #s(hole binary64 (* -1 (* (sqrt (/ (* n (PI)) k)) (* (sqrt -2) (sqrt -1))))))

Calls

6 calls:

Time	Variable		Point	Expression
24.0ms	n	@	0	((* (/ 1 (sqrt k)) (/ (sqrt (* (* (PI) n) 2)) (pow (* (* (PI) n) 2) (/ k 2)))) (/ 1 (sqrt k)) (sqrt (/ 1 k)) (/ 1 k) 1 k (/ (sqrt (* (* (PI) n) 2)) (pow (* (* (PI) n) 2) (/ k 2))) (sqrt (* (* (PI) n) 2)) (* (* (PI) n) 2) (* (PI) n) (PI) n 2 (pow (* (* (PI) n) 2) (/ k 2)) (/ k 2) (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt (* (PI) (/ (* 2 n) k))) (* (PI) (/ (* 2 n) k)) (/ (* 2 n) k) (* 2 n) (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (/ (sqrt (* (* (PI) n) 2)) (sqrt k)) (sqrt k) (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt (* (* (* (/ n k) (sqrt (PI))) (sqrt (PI))) 2)) (* (* (* (/ n k) (sqrt (PI))) (sqrt (PI))) 2) (* (* (/ n k) (sqrt (PI))) (sqrt (PI))) (* (/ n k) (sqrt (PI))) (/ n k) (sqrt (PI)) (* (/ 1 (sqrt k)) (/ (sqrt (* (* (PI) n) 2)) (pow (* (* (PI) n) 2) (/ k 2)))) (/ 1 (sqrt k)) (/ (sqrt (* (* (PI) n) 2)) (pow (* (* (PI) n) 2) (/ k 2))) (pow (* (* (PI) n) 2) (/ k 2)))
18.0ms	n	@	-inf	((* (/ 1 (sqrt k)) (/ (sqrt (* (* (PI) n) 2)) (pow (* (* (PI) n) 2) (/ k 2)))) (/ 1 (sqrt k)) (sqrt (/ 1 k)) (/ 1 k) 1 k (/ (sqrt (* (* (PI) n) 2)) (pow (* (* (PI) n) 2) (/ k 2))) (sqrt (* (* (PI) n) 2)) (* (* (PI) n) 2) (* (PI) n) (PI) n 2 (pow (* (* (PI) n) 2) (/ k 2)) (/ k 2) (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt (* (PI) (/ (* 2 n) k))) (* (PI) (/ (* 2 n) k)) (/ (* 2 n) k) (* 2 n) (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (/ (sqrt (* (* (PI) n) 2)) (sqrt k)) (sqrt k) (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt (* (* (* (/ n k) (sqrt (PI))) (sqrt (PI))) 2)) (* (* (* (/ n k) (sqrt (PI))) (sqrt (PI))) 2) (* (* (/ n k) (sqrt (PI))) (sqrt (PI))) (* (/ n k) (sqrt (PI))) (/ n k) (sqrt (PI)) (* (/ 1 (sqrt k)) (/ (sqrt (* (* (PI) n) 2)) (pow (* (* (PI) n) 2) (/ k 2)))) (/ 1 (sqrt k)) (/ (sqrt (* (* (PI) n) 2)) (pow (* (* (PI) n) 2) (/ k 2))) (pow (* (* (PI) n) 2) (/ k 2)))
12.0ms	n	@	inf	((* (/ 1 (sqrt k)) (/ (sqrt (* (* (PI) n) 2)) (pow (* (* (PI) n) 2) (/ k 2)))) (/ 1 (sqrt k)) (sqrt (/ 1 k)) (/ 1 k) 1 k (/ (sqrt (* (* (PI) n) 2)) (pow (* (* (PI) n) 2) (/ k 2))) (sqrt (* (* (PI) n) 2)) (* (* (PI) n) 2) (* (PI) n) (PI) n 2 (pow (* (* (PI) n) 2) (/ k 2)) (/ k 2) (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt (* (PI) (/ (* 2 n) k))) (* (PI) (/ (* 2 n) k)) (/ (* 2 n) k) (* 2 n) (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (/ (sqrt (* (* (PI) n) 2)) (sqrt k)) (sqrt k) (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt (* (* (* (/ n k) (sqrt (PI))) (sqrt (PI))) 2)) (* (* (* (/ n k) (sqrt (PI))) (sqrt (PI))) 2) (* (* (/ n k) (sqrt (PI))) (sqrt (PI))) (* (/ n k) (sqrt (PI))) (/ n k) (sqrt (PI)) (* (/ 1 (sqrt k)) (/ (sqrt (* (* (PI) n) 2)) (pow (* (* (PI) n) 2) (/ k 2)))) (/ 1 (sqrt k)) (/ (sqrt (* (* (PI) n) 2)) (pow (* (* (PI) n) 2) (/ k 2))) (pow (* (* (PI) n) 2) (/ k 2)))
6.0ms	k	@	-inf	((* (/ 1 (sqrt k)) (/ (sqrt (* (* (PI) n) 2)) (pow (* (* (PI) n) 2) (/ k 2)))) (/ 1 (sqrt k)) (sqrt (/ 1 k)) (/ 1 k) 1 k (/ (sqrt (* (* (PI) n) 2)) (pow (* (* (PI) n) 2) (/ k 2))) (sqrt (* (* (PI) n) 2)) (* (* (PI) n) 2) (* (PI) n) (PI) n 2 (pow (* (* (PI) n) 2) (/ k 2)) (/ k 2) (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt (* (PI) (/ (* 2 n) k))) (* (PI) (/ (* 2 n) k)) (/ (* 2 n) k) (* 2 n) (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (/ (sqrt (* (* (PI) n) 2)) (sqrt k)) (sqrt k) (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt (* (* (* (/ n k) (sqrt (PI))) (sqrt (PI))) 2)) (* (* (* (/ n k) (sqrt (PI))) (sqrt (PI))) 2) (* (* (/ n k) (sqrt (PI))) (sqrt (PI))) (* (/ n k) (sqrt (PI))) (/ n k) (sqrt (PI)) (* (/ 1 (sqrt k)) (/ (sqrt (* (* (PI) n) 2)) (pow (* (* (PI) n) 2) (/ k 2)))) (/ 1 (sqrt k)) (/ (sqrt (* (* (PI) n) 2)) (pow (* (* (PI) n) 2) (/ k 2))) (pow (* (* (PI) n) 2) (/ k 2)))
3.0ms	k	@	inf	((* (/ 1 (sqrt k)) (/ (sqrt (* (* (PI) n) 2)) (pow (* (* (PI) n) 2) (/ k 2)))) (/ 1 (sqrt k)) (sqrt (/ 1 k)) (/ 1 k) 1 k (/ (sqrt (* (* (PI) n) 2)) (pow (* (* (PI) n) 2) (/ k 2))) (sqrt (* (* (PI) n) 2)) (* (* (PI) n) 2) (* (PI) n) (PI) n 2 (pow (* (* (PI) n) 2) (/ k 2)) (/ k 2) (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt (* (PI) (/ (* 2 n) k))) (* (PI) (/ (* 2 n) k)) (/ (* 2 n) k) (* 2 n) (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (/ (sqrt (* (* (PI) n) 2)) (sqrt k)) (sqrt k) (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt (* (* (* (/ n k) (sqrt (PI))) (sqrt (PI))) 2)) (* (* (* (/ n k) (sqrt (PI))) (sqrt (PI))) 2) (* (* (/ n k) (sqrt (PI))) (sqrt (PI))) (* (/ n k) (sqrt (PI))) (/ n k) (sqrt (PI)) (* (/ 1 (sqrt k)) (/ (sqrt (* (* (PI) n) 2)) (pow (* (* (PI) n) 2) (/ k 2)))) (/ 1 (sqrt k)) (/ (sqrt (* (* (PI) n) 2)) (pow (* (* (PI) n) 2) (/ k 2))) (pow (* (* (PI) n) 2) (/ k 2)))

simplify169.0ms (2%)

Memory

-26.3MiB live, 221.9MiB allocated; 74ms collecting garbage

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	283	1860
1	831	1779
2	3379	1715
0	8723	1690

Stop Event

1×	iter limit
1×	node limit

Counts

61 → 61

Calls

Call 1

Inputs
#s(approx (* (/ 1 (sqrt k)) (/ (sqrt (* (* (PI) n) 2)) (pow (* (* (PI) n) 2) (/ k 2)))) #s(hole binary64 (* (sqrt (/ (* n (PI)) k)) (sqrt 2))))
#s(approx (* (/ 1 (sqrt k)) (/ (sqrt (* (* (PI) n) 2)) (pow (* (* (PI) n) 2) (/ k 2)))) #s(hole binary64 (/ (+ (* -1/2 (* (sqrt (* (pow k 3) (* n (PI)))) (* (log (* 2 (* n (PI)))) (sqrt 2)))) (* (sqrt (* k (* n (PI)))) (sqrt 2))) k)))
#s(approx (* (/ 1 (sqrt k)) (/ (sqrt (* (* (PI) n) 2)) (pow (* (* (PI) n) 2) (/ k 2)))) #s(hole binary64 (/ (+ (* k (+ (* -1 (* (sqrt (* (pow k 3) (* n (PI)))) (+ (* -1/4 (* (pow (log (* 2 (* n (PI)))) 2) (sqrt 2))) (* 1/8 (* (pow (log (* 2 (* n (PI)))) 2) (sqrt 2)))))) (* -1/2 (* (sqrt (* k (* n (PI)))) (* (log (* 2 (* n (PI)))) (sqrt 2)))))) (* (sqrt (* k (* n (PI)))) (sqrt 2))) k)))
#s(approx (* (/ 1 (sqrt k)) (/ (sqrt (* (* (PI) n) 2)) (pow (* (* (PI) n) 2) (/ k 2)))) #s(hole binary64 (/ (+ (* k (+ (* -1/2 (* (sqrt (* k (* n (PI)))) (* (log (* 2 (* n (PI)))) (sqrt 2)))) (* k (+ (* -1 (* (sqrt (* k (* n (PI)))) (+ (* -1/4 (* (pow (log (* 2 (* n (PI)))) 2) (sqrt 2))) (* 1/8 (* (pow (log (* 2 (* n (PI)))) 2) (sqrt 2)))))) (* -1 (* (sqrt (* (pow k 3) (* n (PI)))) (+ (* -1/2 (* (log (* 2 (* n (PI)))) (+ (* -1/4 (* (pow (log (* 2 (* n (PI)))) 2) (sqrt 2))) (* 1/8 (* (pow (log (* 2 (* n (PI)))) 2) (sqrt 2)))))) (+ (* -1/16 (* (pow (log (* 2 (* n (PI)))) 3) (sqrt 2))) (* 1/48 (* (pow (log (* 2 (* n (PI)))) 3) (sqrt 2))))))))))) (* (sqrt (* k (* n (PI)))) (sqrt 2))) k)))
#s(approx (/ 1 (sqrt k)) #s(hole binary64 (sqrt (/ 1 k))))
#s(approx (sqrt (/ 1 k)) #s(hole binary64 (sqrt (/ 1 k))))
#s(approx (/ 1 k) #s(hole binary64 (/ 1 k)))
#s(approx k #s(hole binary64 k))
#s(approx (/ (sqrt (* (* (PI) n) 2)) (pow (* (* (PI) n) 2) (/ k 2))) #s(hole binary64 (* (sqrt (* n (PI))) (sqrt 2))))
#s(approx (/ (sqrt (* (* (PI) n) 2)) (pow (* (* (PI) n) 2) (/ k 2))) #s(hole binary64 (+ (* -1/2 (* (* k (* (log (* 2 (* n (PI)))) (sqrt 2))) (sqrt (* n (PI))))) (* (sqrt (* n (PI))) (sqrt 2)))))
#s(approx (/ (sqrt (* (* (PI) n) 2)) (pow (* (* (PI) n) 2) (/ k 2))) #s(hole binary64 (+ (* k (+ (* -1 (* (* k (+ (* -1/4 (* (pow (log (* 2 (* n (PI)))) 2) (sqrt 2))) (* 1/8 (* (pow (log (* 2 (* n (PI)))) 2) (sqrt 2))))) (sqrt (* n (PI))))) (* -1/2 (* (sqrt (* n (PI))) (* (log (* 2 (* n (PI)))) (sqrt 2)))))) (* (sqrt (* n (PI))) (sqrt 2)))))
#s(approx (/ (sqrt (* (* (PI) n) 2)) (pow (* (* (PI) n) 2) (/ k 2))) #s(hole binary64 (+ (* k (+ (* -1/2 (* (sqrt (* n (PI))) (* (log (* 2 (* n (PI)))) (sqrt 2)))) (* k (+ (* -1 (* (sqrt (* n (PI))) (+ (* -1/4 (* (pow (log (* 2 (* n (PI)))) 2) (sqrt 2))) (* 1/8 (* (pow (log (* 2 (* n (PI)))) 2) (sqrt 2)))))) (* -1 (* (* k (+ (* -1/2 (* (log (* 2 (* n (PI)))) (+ (* -1/4 (* (pow (log (* 2 (* n (PI)))) 2) (sqrt 2))) (* 1/8 (* (pow (log (* 2 (* n (PI)))) 2) (sqrt 2)))))) (+ (* -1/16 (* (pow (log (* 2 (* n (PI)))) 3) (sqrt 2))) (* 1/48 (* (pow (log (* 2 (* n (PI)))) 3) (sqrt 2)))))) (sqrt (* n (PI))))))))) (* (sqrt (* n (PI))) (sqrt 2)))))
#s(approx (pow (* (* (PI) n) 2) (/ k 2)) #s(hole binary64 1))
#s(approx (pow (* (* (PI) n) 2) (/ k 2)) #s(hole binary64 (+ 1 (* 1/2 (* k (log (* 2 (* n (PI)))))))))
#s(approx (pow (* (* (PI) n) 2) (/ k 2)) #s(hole binary64 (+ 1 (* k (+ (* 1/8 (* k (pow (log (* 2 (* n (PI)))) 2))) (* 1/2 (log (* 2 (* n (PI))))))))))
#s(approx (pow (* (* (PI) n) 2) (/ k 2)) #s(hole binary64 (+ 1 (* k (+ (* 1/2 (log (* 2 (* n (PI))))) (* k (+ (* 1/48 (* k (pow (log (* 2 (* n (PI)))) 3))) (* 1/8 (pow (log (* 2 (* n (PI)))) 2)))))))))
#s(approx (/ k 2) #s(hole binary64 (* 1/2 k)))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) #s(hole binary64 (* (sqrt (/ (* n (PI)) k)) (sqrt 2))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) #s(hole binary64 (/ (+ (* -1/2 (* (sqrt (* (pow k 3) (* n (PI)))) (* (log (* 2 (* n (PI)))) (sqrt 2)))) (* (sqrt (* k (* n (PI)))) (sqrt 2))) k)))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) #s(hole binary64 (/ (+ (* 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)))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) #s(hole binary64 (/ (+ (* 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)))
#s(approx (sqrt (* (PI) (/ (* 2 n) k))) #s(hole binary64 (* (sqrt (/ (* n (PI)) k)) (sqrt 2))))
#s(approx (* (PI) (/ (* 2 n) k)) #s(hole binary64 (* 2 (/ (* n (PI)) k))))
#s(approx (/ (* 2 n) k) #s(hole binary64 (* 2 (/ n k))))
#s(approx (/ (sqrt (* (* (PI) n) 2)) (sqrt k)) #s(hole binary64 (* (sqrt (/ (* n (PI)) k)) (sqrt 2))))
#s(approx (sqrt k) #s(hole binary64 (sqrt k)))
#s(approx (sqrt (* (* (* (/ n k) (sqrt (PI))) (sqrt (PI))) 2)) #s(hole binary64 (* (sqrt (/ (* n (PI)) k)) (sqrt 2))))
#s(approx (* (* (* (/ n k) (sqrt (PI))) (sqrt (PI))) 2) #s(hole binary64 (* 2 (/ (* n (PI)) k))))
#s(approx (* (* (/ n k) (sqrt (PI))) (sqrt (PI))) #s(hole binary64 (/ (* n (PI)) k)))
#s(approx (* (/ n k) (sqrt (PI))) #s(hole binary64 (* (/ n k) (sqrt (PI)))))
#s(approx (/ n k) #s(hole binary64 (/ n k)))
#s(approx (* (/ 1 (sqrt k)) (/ (sqrt (* (* (PI) n) 2)) (pow (* (* (PI) n) 2) (/ k 2)))) #s(hole binary64 (* (sqrt (/ (* n (PI)) k)) (/ (sqrt 2) (exp (* 1/2 (* k (log (* 2 (* n (PI)))))))))))
#s(approx (/ (sqrt (* (* (PI) n) 2)) (pow (* (* (PI) n) 2) (/ k 2))) #s(hole binary64 (* (sqrt (* n (PI))) (/ (sqrt 2) (exp (* 1/2 (* k (log (* 2 (* n (PI)))))))))))
#s(approx (pow (* (* (PI) n) 2) (/ k 2)) #s(hole binary64 (exp (* 1/2 (* k (log (* 2 (* n (PI)))))))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) #s(hole binary64 (* (sqrt (/ 1 k)) (exp (* 1/2 (* (log (* 2 (* n (PI)))) (- 1 k)))))))
#s(approx (sqrt (/ 1 k)) #s(hole binary64 (* (sqrt (/ 1 k)) (pow (sqrt -1) 2))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) #s(hole binary64 (* (sqrt (/ 1 k)) (exp (* 1/2 (* (log (* 2 (* n (PI)))) (+ 1 (* -1 k))))))))
#s(approx (sqrt (* (PI) (/ (* 2 n) k))) #s(hole binary64 (* (sqrt (/ (* n (PI)) k)) (* (sqrt -2) (sqrt -1)))))
#s(approx (sqrt k) #s(hole binary64 (* -1 (* (sqrt k) (pow (sqrt -1) 2)))))
#s(approx (sqrt (* (* (* (/ n k) (sqrt (PI))) (sqrt (PI))) 2)) #s(hole binary64 (* (sqrt (/ (* n (PI)) k)) (* (sqrt -2) (sqrt -1)))))
#s(approx (* (/ 1 (sqrt k)) (/ (sqrt (* (* (PI) n) 2)) (pow (* (* (PI) n) 2) (/ k 2)))) #s(hole binary64 (* (sqrt (/ (* n (PI)) k)) (/ (sqrt 2) (exp (* 1/2 (* k (+ (log n) (log (* 2 (PI)))))))))))
#s(approx (/ (sqrt (* (* (PI) n) 2)) (pow (* (* (PI) n) 2) (/ k 2))) #s(hole binary64 (* (sqrt (* n (PI))) (/ (sqrt 2) (exp (* 1/2 (* k (+ (log n) (log (* 2 (PI)))))))))))
#s(approx (sqrt (* (* (PI) n) 2)) #s(hole binary64 (* (sqrt (* n (PI))) (sqrt 2))))
#s(approx (* (* (PI) n) 2) #s(hole binary64 (* 2 (* n (PI)))))
#s(approx (* (PI) n) #s(hole binary64 (* n (PI))))
#s(approx n #s(hole binary64 n))
#s(approx (pow (* (* (PI) n) 2) (/ k 2)) #s(hole binary64 (exp (* 1/2 (* k (+ (log n) (log (* 2 (PI)))))))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) #s(hole binary64 (* (sqrt (/ 1 k)) (exp (* 1/2 (* (+ (log n) (log (* 2 (PI)))) (- 1 k)))))))
#s(approx (* 2 n) #s(hole binary64 (* 2 n)))
#s(approx (* (/ 1 (sqrt k)) (/ (sqrt (* (* (PI) n) 2)) (pow (* (* (PI) n) 2) (/ k 2)))) #s(hole binary64 (* (sqrt (/ (* n (PI)) k)) (/ (sqrt 2) (exp (* 1/2 (* k (+ (log (* 2 (PI))) (* -1 (log (/ 1 n)))))))))))
#s(approx (/ (sqrt (* (* (PI) n) 2)) (pow (* (* (PI) n) 2) (/ k 2))) #s(hole binary64 (* (sqrt (* n (PI))) (/ (sqrt 2) (exp (* 1/2 (* k (+ (log (* 2 (PI))) (* -1 (log (/ 1 n)))))))))))
#s(approx (pow (* (* (PI) n) 2) (/ k 2)) #s(hole binary64 (exp (* 1/2 (* k (+ (log (* 2 (PI))) (* -1 (log (/ 1 n)))))))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) #s(hole binary64 (* (sqrt (/ 1 k)) (exp (* 1/2 (* (+ (log (* 2 (PI))) (* -1 (log (/ 1 n)))) (- 1 k)))))))
#s(approx (* (/ 1 (sqrt k)) (/ (sqrt (* (* (PI) n) 2)) (pow (* (* (PI) n) 2) (/ k 2)))) #s(hole binary64 (* -1 (* (sqrt (/ (* n (PI)) k)) (/ (* (sqrt -2) (sqrt -1)) (exp (* 1/2 (* k (+ (log (* -2 (PI))) (* -1 (log (/ -1 n))))))))))))
#s(approx (/ (sqrt (* (* (PI) n) 2)) (pow (* (* (PI) n) 2) (/ k 2))) #s(hole binary64 (* -1 (* (sqrt (* n (PI))) (/ (* (sqrt -2) (sqrt -1)) (exp (* 1/2 (* k (+ (log (* -2 (PI))) (* -1 (log (/ -1 n))))))))))))
#s(approx (sqrt (* (* (PI) n) 2)) #s(hole binary64 (* -1 (* (sqrt (* n (PI))) (* (sqrt -2) (sqrt -1))))))
#s(approx (pow (* (* (PI) n) 2) (/ k 2)) #s(hole binary64 (exp (* 1/2 (* k (+ (log (* -2 (PI))) (* -1 (log (/ -1 n)))))))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) #s(hole binary64 (* (sqrt (/ 1 k)) (exp (* 1/2 (* (+ (log (* -2 (PI))) (* -1 (log (/ -1 n)))) (- 1 k)))))))
#s(approx (sqrt (* (PI) (/ (* 2 n) k))) #s(hole binary64 (* -1 (* (sqrt (/ (* n (PI)) k)) (* (sqrt -2) (sqrt -1))))))
#s(approx (/ (sqrt (* (* (PI) n) 2)) (sqrt k)) #s(hole binary64 (* -1 (* (sqrt (/ (* n (PI)) k)) (* (sqrt -2) (sqrt -1))))))
#s(approx (sqrt (* (* (* (/ n k) (sqrt (PI))) (sqrt (PI))) 2)) #s(hole binary64 (* -1 (* (sqrt (/ (* n (PI)) k)) (* (sqrt -2) (sqrt -1))))))

Outputs
#s(approx (* (/ 1 (sqrt k)) (/ (sqrt (* (* (PI) n) 2)) (pow (* (* (PI) n) 2) (/ k 2)))) #s(hole binary64 (* (sqrt (/ (* n (PI)) k)) (sqrt 2))))
#s(approx (* (/ 1 (sqrt k)) (/ (sqrt (* (* (PI) n) 2)) (pow (* (* (PI) n) 2) (/ k 2)))) (.f64 (sqrt.f64 #s(literal 2 binary64)) (sqrt.f64 (/.f64 (.f64 (PI.f64) n) k))))
#s(approx (* (/ 1 (sqrt k)) (/ (sqrt (* (* (PI) n) 2)) (pow (* (* (PI) n) 2) (/ k 2)))) #s(hole binary64 (/ (+ (* -1/2 (* (sqrt (* (pow k 3) (* n (PI)))) (* (log (* 2 (* n (PI)))) (sqrt 2)))) (* (sqrt (* k (* n (PI)))) (sqrt 2))) k)))
#s(approx (* (/ 1 (sqrt k)) (/ (sqrt (* (* (PI) n) 2)) (pow (* (* (PI) n) 2) (/ k 2)))) (/.f64 (fma.f64 (.f64 (.f64 (log.f64 (.f64 (.f64 (PI.f64) #s(literal 2 binary64)) n)) (sqrt.f64 #s(literal 2 binary64))) (sqrt.f64 (.f64 (.f64 (pow.f64 k #s(literal 3 binary64)) (PI.f64)) n))) #s(literal -1/2 binary64) (.f64 (sqrt.f64 (.f64 (*.f64 (PI.f64) n) k)) (sqrt.f64 #s(literal 2 binary64)))) k))
#s(approx (* (/ 1 (sqrt k)) (/ (sqrt (* (* (PI) n) 2)) (pow (* (* (PI) n) 2) (/ k 2)))) #s(hole binary64 (/ (+ (* k (+ (* -1 (* (sqrt (* (pow k 3) (* n (PI)))) (+ (* -1/4 (* (pow (log (* 2 (* n (PI)))) 2) (sqrt 2))) (* 1/8 (* (pow (log (* 2 (* n (PI)))) 2) (sqrt 2)))))) (* -1/2 (* (sqrt (* k (* n (PI)))) (* (log (* 2 (* n (PI)))) (sqrt 2)))))) (* (sqrt (* k (* n (PI)))) (sqrt 2))) k)))
#s(approx (* (/ 1 (sqrt k)) (/ (sqrt (* (* (PI) n) 2)) (pow (* (* (PI) n) 2) (/ k 2)))) (/.f64 (fma.f64 (fma.f64 (.f64 (.f64 (sqrt.f64 (.f64 (.f64 (PI.f64) n) k)) #s(literal -1/2 binary64)) (log.f64 (.f64 (.f64 (PI.f64) #s(literal 2 binary64)) n))) (sqrt.f64 #s(literal 2 binary64)) (.f64 (.f64 (.f64 #s(literal 1/8 binary64) (sqrt.f64 #s(literal 2 binary64))) (pow.f64 (log.f64 (.f64 (.f64 (PI.f64) #s(literal 2 binary64)) n)) #s(literal 2 binary64))) (sqrt.f64 (.f64 (.f64 (pow.f64 k #s(literal 3 binary64)) (PI.f64)) n)))) k (.f64 (sqrt.f64 (.f64 (.f64 (PI.f64) n) k)) (sqrt.f64 #s(literal 2 binary64)))) k))
#s(approx (* (/ 1 (sqrt k)) (/ (sqrt (* (* (PI) n) 2)) (pow (* (* (PI) n) 2) (/ k 2)))) #s(hole binary64 (/ (+ (* k (+ (* -1/2 (* (sqrt (* k (* n (PI)))) (* (log (* 2 (* n (PI)))) (sqrt 2)))) (* k (+ (* -1 (* (sqrt (* k (* n (PI)))) (+ (* -1/4 (* (pow (log (* 2 (* n (PI)))) 2) (sqrt 2))) (* 1/8 (* (pow (log (* 2 (* n (PI)))) 2) (sqrt 2)))))) (* -1 (* (sqrt (* (pow k 3) (* n (PI)))) (+ (* -1/2 (* (log (* 2 (* n (PI)))) (+ (* -1/4 (* (pow (log (* 2 (* n (PI)))) 2) (sqrt 2))) (* 1/8 (* (pow (log (* 2 (* n (PI)))) 2) (sqrt 2)))))) (+ (* -1/16 (* (pow (log (* 2 (* n (PI)))) 3) (sqrt 2))) (* 1/48 (* (pow (log (* 2 (* n (PI)))) 3) (sqrt 2))))))))))) (* (sqrt (* k (* n (PI)))) (sqrt 2))) k)))
#s(approx (* (/ 1 (sqrt k)) (/ (sqrt (* (* (PI) n) 2)) (pow (* (* (PI) n) 2) (/ k 2)))) (/.f64 (fma.f64 (fma.f64 (fma.f64 (.f64 (.f64 #s(literal 1/8 binary64) (sqrt.f64 (.f64 (.f64 (PI.f64) n) k))) (pow.f64 (log.f64 (.f64 (.f64 (PI.f64) #s(literal 2 binary64)) n)) #s(literal 2 binary64))) (sqrt.f64 #s(literal 2 binary64)) (.f64 (fma.f64 (.f64 (.f64 (pow.f64 (log.f64 (.f64 (.f64 (PI.f64) #s(literal 2 binary64)) n)) #s(literal 3 binary64)) (sqrt.f64 #s(literal 2 binary64))) #s(literal 1/8 binary64)) #s(literal -1/2 binary64) (.f64 #s(literal 1/24 binary64) (.f64 (pow.f64 (log.f64 (.f64 (.f64 (PI.f64) #s(literal 2 binary64)) n)) #s(literal 3 binary64)) (sqrt.f64 #s(literal 2 binary64))))) (sqrt.f64 (.f64 (.f64 (pow.f64 k #s(literal 3 binary64)) (PI.f64)) n)))) k (.f64 (.f64 (.f64 (sqrt.f64 (.f64 (.f64 (PI.f64) n) k)) #s(literal -1/2 binary64)) (log.f64 (.f64 (.f64 (PI.f64) #s(literal 2 binary64)) n))) (sqrt.f64 #s(literal 2 binary64)))) k (.f64 (sqrt.f64 (.f64 (*.f64 (PI.f64) n) k)) (sqrt.f64 #s(literal 2 binary64)))) k))
#s(approx (/ 1 (sqrt k)) #s(hole binary64 (sqrt (/ 1 k))))
#s(approx (/ 1 (sqrt k)) (sqrt.f64 (/.f64 #s(literal 1 binary64) k)))
#s(approx (sqrt (/ 1 k)) #s(hole binary64 (sqrt (/ 1 k))))
#s(approx (sqrt (/ 1 k)) (sqrt.f64 (/.f64 #s(literal 1 binary64) k)))
#s(approx (/ 1 k) #s(hole binary64 (/ 1 k)))
#s(approx (/ 1 k) (/.f64 #s(literal 1 binary64) k))
#s(approx k #s(hole binary64 k))
#s(approx k k)
#s(approx (/ (sqrt (* (* (PI) n) 2)) (pow (* (* (PI) n) 2) (/ k 2))) #s(hole binary64 (* (sqrt (* n (PI))) (sqrt 2))))
#s(approx (/ (sqrt (* (* (PI) n) 2)) (pow (* (* (PI) n) 2) (/ k 2))) (.f64 (sqrt.f64 (.f64 (PI.f64) n)) (sqrt.f64 #s(literal 2 binary64))))
#s(approx (/ (sqrt (* (* (PI) n) 2)) (pow (* (* (PI) n) 2) (/ k 2))) #s(hole binary64 (+ (* -1/2 (* (* k (* (log (* 2 (* n (PI)))) (sqrt 2))) (sqrt (* n (PI))))) (* (sqrt (* n (PI))) (sqrt 2)))))
#s(approx (/ (sqrt (* (* (PI) n) 2)) (pow (* (* (PI) n) 2) (/ k 2))) (.f64 (sqrt.f64 (.f64 (PI.f64) n)) (fma.f64 (.f64 #s(literal -1/2 binary64) k) (.f64 (log.f64 (.f64 (.f64 (PI.f64) #s(literal 2 binary64)) n)) (sqrt.f64 #s(literal 2 binary64))) (sqrt.f64 #s(literal 2 binary64)))))
#s(approx (/ (sqrt (* (* (PI) n) 2)) (pow (* (* (PI) n) 2) (/ k 2))) #s(hole binary64 (+ (* k (+ (* -1 (* (* k (+ (* -1/4 (* (pow (log (* 2 (* n (PI)))) 2) (sqrt 2))) (* 1/8 (* (pow (log (* 2 (* n (PI)))) 2) (sqrt 2))))) (sqrt (* n (PI))))) (* -1/2 (* (sqrt (* n (PI))) (* (log (* 2 (* n (PI)))) (sqrt 2)))))) (* (sqrt (* n (PI))) (sqrt 2)))))
#s(approx (/ (sqrt (* (* (PI) n) 2)) (pow (* (* (PI) n) 2) (/ k 2))) (fma.f64 (.f64 (.f64 (sqrt.f64 (.f64 (PI.f64) n)) k) (.f64 (.f64 #s(literal 1/8 binary64) (sqrt.f64 #s(literal 2 binary64))) (pow.f64 (log.f64 (.f64 (.f64 (PI.f64) #s(literal 2 binary64)) n)) #s(literal 2 binary64)))) k (.f64 (sqrt.f64 (.f64 (PI.f64) n)) (fma.f64 (.f64 #s(literal -1/2 binary64) k) (.f64 (log.f64 (.f64 (*.f64 (PI.f64) #s(literal 2 binary64)) n)) (sqrt.f64 #s(literal 2 binary64))) (sqrt.f64 #s(literal 2 binary64))))))
#s(approx (/ (sqrt (* (* (PI) n) 2)) (pow (* (* (PI) n) 2) (/ k 2))) #s(hole binary64 (+ (* k (+ (* -1/2 (* (sqrt (* n (PI))) (* (log (* 2 (* n (PI)))) (sqrt 2)))) (* k (+ (* -1 (* (sqrt (* n (PI))) (+ (* -1/4 (* (pow (log (* 2 (* n (PI)))) 2) (sqrt 2))) (* 1/8 (* (pow (log (* 2 (* n (PI)))) 2) (sqrt 2)))))) (* -1 (* (* k (+ (* -1/2 (* (log (* 2 (* n (PI)))) (+ (* -1/4 (* (pow (log (* 2 (* n (PI)))) 2) (sqrt 2))) (* 1/8 (* (pow (log (* 2 (* n (PI)))) 2) (sqrt 2)))))) (+ (* -1/16 (* (pow (log (* 2 (* n (PI)))) 3) (sqrt 2))) (* 1/48 (* (pow (log (* 2 (* n (PI)))) 3) (sqrt 2)))))) (sqrt (* n (PI))))))))) (* (sqrt (* n (PI))) (sqrt 2)))))
#s(approx (/ (sqrt (* (* (PI) n) 2)) (pow (* (* (PI) n) 2) (/ k 2))) (fma.f64 (sqrt.f64 (.f64 (PI.f64) n)) (fma.f64 (.f64 #s(literal -1/2 binary64) k) (.f64 (log.f64 (.f64 (.f64 (PI.f64) #s(literal 2 binary64)) n)) (sqrt.f64 #s(literal 2 binary64))) (sqrt.f64 #s(literal 2 binary64))) (.f64 (.f64 k k) (.f64 (neg.f64 (sqrt.f64 (.f64 (PI.f64) n))) (fma.f64 (.f64 #s(literal -1/8 binary64) (pow.f64 (log.f64 (.f64 (.f64 (PI.f64) #s(literal 2 binary64)) n)) #s(literal 2 binary64))) (sqrt.f64 #s(literal 2 binary64)) (.f64 (fma.f64 #s(literal -1/24 binary64) (.f64 (pow.f64 (log.f64 (.f64 (.f64 (PI.f64) #s(literal 2 binary64)) n)) #s(literal 3 binary64)) (sqrt.f64 #s(literal 2 binary64))) (.f64 (.f64 (.f64 (pow.f64 (log.f64 (.f64 (*.f64 (PI.f64) #s(literal 2 binary64)) n)) #s(literal 3 binary64)) (sqrt.f64 #s(literal 2 binary64))) #s(literal 1/8 binary64)) #s(literal 1/2 binary64))) k))))))
#s(approx (pow (* (* (PI) n) 2) (/ k 2)) #s(hole binary64 1))
#s(approx (pow (* (* (PI) n) 2) (/ k 2)) #s(literal 1 binary64))
#s(approx (pow (* (* (PI) n) 2) (/ k 2)) #s(hole binary64 (+ 1 (* 1/2 (* k (log (* 2 (* n (PI)))))))))
#s(approx (pow (* (* (PI) n) 2) (/ k 2)) (fma.f64 (.f64 #s(literal 1/2 binary64) k) (log.f64 (.f64 (*.f64 (PI.f64) #s(literal 2 binary64)) n)) #s(literal 1 binary64)))
#s(approx (pow (* (* (PI) n) 2) (/ k 2)) #s(hole binary64 (+ 1 (* k (+ (* 1/8 (* k (pow (log (* 2 (* n (PI)))) 2))) (* 1/2 (log (* 2 (* n (PI))))))))))
#s(approx (pow (* (* (PI) n) 2) (/ k 2)) (fma.f64 (fma.f64 (.f64 #s(literal 1/8 binary64) k) (pow.f64 (log.f64 (.f64 (.f64 (PI.f64) #s(literal 2 binary64)) n)) #s(literal 2 binary64)) (.f64 #s(literal 1/2 binary64) (log.f64 (.f64 (.f64 (PI.f64) #s(literal 2 binary64)) n)))) k #s(literal 1 binary64)))
#s(approx (pow (* (* (PI) n) 2) (/ k 2)) #s(hole binary64 (+ 1 (* k (+ (* 1/2 (log (* 2 (* n (PI))))) (* k (+ (* 1/48 (* k (pow (log (* 2 (* n (PI)))) 3))) (* 1/8 (pow (log (* 2 (* n (PI)))) 2)))))))))
#s(approx (pow (* (* (PI) n) 2) (/ k 2)) (fma.f64 (fma.f64 (fma.f64 (.f64 #s(literal 1/48 binary64) k) (pow.f64 (log.f64 (.f64 (.f64 (PI.f64) #s(literal 2 binary64)) n)) #s(literal 3 binary64)) (.f64 #s(literal 1/8 binary64) (pow.f64 (log.f64 (.f64 (.f64 (PI.f64) #s(literal 2 binary64)) n)) #s(literal 2 binary64)))) k (.f64 #s(literal 1/2 binary64) (log.f64 (.f64 (*.f64 (PI.f64) #s(literal 2 binary64)) n)))) k #s(literal 1 binary64)))
#s(approx (/ k 2) #s(hole binary64 (* 1/2 k)))
#s(approx (/ k 2) (*.f64 #s(literal 1/2 binary64) k))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) #s(hole binary64 (* (sqrt (/ (* n (PI)) k)) (sqrt 2))))
#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))) #s(hole binary64 (/ (+ (* -1/2 (* (sqrt (* (pow k 3) (* n (PI)))) (* (log (* 2 (* n (PI)))) (sqrt 2)))) (* (sqrt (* k (* n (PI)))) (sqrt 2))) k)))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (/.f64 (fma.f64 (.f64 (.f64 (log.f64 (.f64 (.f64 (PI.f64) #s(literal 2 binary64)) n)) (sqrt.f64 #s(literal 2 binary64))) (sqrt.f64 (.f64 (.f64 (pow.f64 k #s(literal 3 binary64)) (PI.f64)) n))) #s(literal -1/2 binary64) (.f64 (sqrt.f64 (.f64 (*.f64 (PI.f64) n) k)) (sqrt.f64 #s(literal 2 binary64)))) k))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) #s(hole binary64 (/ (+ (* 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)))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (/.f64 (fma.f64 (fma.f64 (.f64 (.f64 (sqrt.f64 (.f64 (.f64 (PI.f64) n) k)) #s(literal -1/2 binary64)) (log.f64 (.f64 (.f64 (PI.f64) #s(literal 2 binary64)) n))) (sqrt.f64 #s(literal 2 binary64)) (.f64 (.f64 (.f64 #s(literal 1/8 binary64) (sqrt.f64 #s(literal 2 binary64))) (pow.f64 (log.f64 (.f64 (.f64 (PI.f64) #s(literal 2 binary64)) n)) #s(literal 2 binary64))) (sqrt.f64 (.f64 (.f64 (pow.f64 k #s(literal 3 binary64)) (PI.f64)) n)))) k (.f64 (sqrt.f64 (.f64 (.f64 (PI.f64) n) k)) (sqrt.f64 #s(literal 2 binary64)))) k))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) #s(hole binary64 (/ (+ (* 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)))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (/.f64 (fma.f64 (fma.f64 (fma.f64 (.f64 (.f64 #s(literal 1/8 binary64) (sqrt.f64 (.f64 (.f64 (PI.f64) n) k))) (pow.f64 (log.f64 (.f64 (.f64 (PI.f64) #s(literal 2 binary64)) n)) #s(literal 2 binary64))) (sqrt.f64 #s(literal 2 binary64)) (.f64 (.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 (.f64 (PI.f64) #s(literal 2 binary64)) n)) #s(literal 3 binary64))) (sqrt.f64 #s(literal 2 binary64)))) k (.f64 (.f64 (.f64 (sqrt.f64 (.f64 (.f64 (PI.f64) n) k)) #s(literal -1/2 binary64)) (log.f64 (.f64 (.f64 (PI.f64) #s(literal 2 binary64)) n))) (sqrt.f64 #s(literal 2 binary64)))) k (.f64 (sqrt.f64 (.f64 (*.f64 (PI.f64) n) k)) (sqrt.f64 #s(literal 2 binary64)))) k))
#s(approx (sqrt (* (PI) (/ (* 2 n) k))) #s(hole binary64 (* (sqrt (/ (* n (PI)) k)) (sqrt 2))))
#s(approx (sqrt (* (* (* (/ n k) (sqrt (PI))) (sqrt (PI))) 2)) (.f64 (sqrt.f64 #s(literal 2 binary64)) (sqrt.f64 (/.f64 (.f64 (PI.f64) n) k))))
#s(approx (* (PI) (/ (* 2 n) k)) #s(hole binary64 (* 2 (/ (* n (PI)) k))))
#s(approx (* (* (* (/ n k) (sqrt (PI))) (sqrt (PI))) 2) (.f64 (/.f64 (.f64 #s(literal 2 binary64) n) k) (PI.f64)))
#s(approx (/ (* 2 n) k) #s(hole binary64 (* 2 (/ n k))))
#s(approx (/ (* 2 n) k) (/.f64 (*.f64 #s(literal 2 binary64) n) k))
#s(approx (/ (sqrt (* (* (PI) n) 2)) (sqrt k)) #s(hole binary64 (* (sqrt (/ (* n (PI)) k)) (sqrt 2))))
#s(approx (/ (sqrt (* (* (PI) n) 2)) (sqrt k)) (.f64 (sqrt.f64 #s(literal 2 binary64)) (sqrt.f64 (/.f64 (.f64 (PI.f64) n) k))))
#s(approx (sqrt k) #s(hole binary64 (sqrt k)))
#s(approx (sqrt k) (sqrt.f64 k))
#s(approx (sqrt (* (* (* (/ n k) (sqrt (PI))) (sqrt (PI))) 2)) #s(hole binary64 (* (sqrt (/ (* n (PI)) k)) (sqrt 2))))
#s(approx (sqrt (* (* (* (/ n k) (sqrt (PI))) (sqrt (PI))) 2)) (.f64 (sqrt.f64 #s(literal 2 binary64)) (sqrt.f64 (/.f64 (.f64 (PI.f64) n) k))))
#s(approx (* (* (* (/ n k) (sqrt (PI))) (sqrt (PI))) 2) #s(hole binary64 (* 2 (/ (* n (PI)) k))))
#s(approx (* (* (* (/ n k) (sqrt (PI))) (sqrt (PI))) 2) (.f64 (/.f64 (.f64 #s(literal 2 binary64) n) k) (PI.f64)))
#s(approx (* (* (/ n k) (sqrt (PI))) (sqrt (PI))) #s(hole binary64 (/ (* n (PI)) k)))
#s(approx (* (* (/ n k) (sqrt (PI))) (sqrt (PI))) (/.f64 (*.f64 (PI.f64) n) k))
#s(approx (* (/ n k) (sqrt (PI))) #s(hole binary64 (* (/ n k) (sqrt (PI)))))
#s(approx (* (/ n k) (sqrt (PI))) (*.f64 (sqrt.f64 (PI.f64)) (/.f64 n k)))
#s(approx (/ n k) #s(hole binary64 (/ n k)))
#s(approx (/ n k) (/.f64 n k))
#s(approx (* (/ 1 (sqrt k)) (/ (sqrt (* (* (PI) n) 2)) (pow (* (* (PI) n) 2) (/ k 2)))) #s(hole binary64 (* (sqrt (/ (* n (PI)) k)) (/ (sqrt 2) (exp (* 1/2 (* k (log (* 2 (* n (PI)))))))))))
#s(approx (* (/ 1 (sqrt k)) (/ (sqrt (* (* (PI) n) 2)) (pow (* (* (PI) n) 2) (/ k 2)))) (.f64 (/.f64 (sqrt.f64 #s(literal 2 binary64)) (sqrt.f64 (pow.f64 (.f64 (.f64 (PI.f64) #s(literal 2 binary64)) n) k))) (sqrt.f64 (/.f64 (.f64 (PI.f64) n) k))))
#s(approx (/ (sqrt (* (* (PI) n) 2)) (pow (* (* (PI) n) 2) (/ k 2))) #s(hole binary64 (* (sqrt (* n (PI))) (/ (sqrt 2) (exp (* 1/2 (* k (log (* 2 (* n (PI)))))))))))
#s(approx (/ (sqrt (* (* (PI) n) 2)) (pow (* (* (PI) n) 2) (/ k 2))) (.f64 (/.f64 (sqrt.f64 #s(literal 2 binary64)) (sqrt.f64 (pow.f64 (.f64 (.f64 (PI.f64) #s(literal 2 binary64)) n) k))) (sqrt.f64 (.f64 (PI.f64) n))))
#s(approx (pow (* (* (PI) n) 2) (/ k 2)) #s(hole binary64 (exp (* 1/2 (* k (log (* 2 (* n (PI)))))))))
#s(approx (pow (* (* (PI) n) 2) (/ k 2)) (sqrt.f64 (pow.f64 (.f64 (.f64 (PI.f64) #s(literal 2 binary64)) n) k)))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) #s(hole binary64 (* (sqrt (/ 1 k)) (exp (* 1/2 (* (log (* 2 (* n (PI)))) (- 1 k)))))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) k)) (pow.f64 (.f64 (*.f64 (PI.f64) #s(literal 2 binary64)) n) (fma.f64 #s(literal -1/2 binary64) k #s(literal 1/2 binary64)))))
#s(approx (sqrt (/ 1 k)) #s(hole binary64 (* (sqrt (/ 1 k)) (pow (sqrt -1) 2))))
#s(approx (sqrt (/ 1 k)) (*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) k)) #s(literal -1 binary64)))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) #s(hole binary64 (* (sqrt (/ 1 k)) (exp (* 1/2 (* (log (* 2 (* n (PI)))) (+ 1 (* -1 k))))))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) k)) (pow.f64 (.f64 (*.f64 (PI.f64) #s(literal 2 binary64)) n) (fma.f64 #s(literal -1/2 binary64) k #s(literal 1/2 binary64)))))
#s(approx (sqrt (* (PI) (/ (* 2 n) k))) #s(hole binary64 (* (sqrt (/ (* n (PI)) k)) (* (sqrt -2) (sqrt -1)))))
#s(approx (sqrt (* (* (* (/ n k) (sqrt (PI))) (sqrt (PI))) 2)) (.f64 (.f64 (sqrt.f64 (/.f64 (*.f64 (PI.f64) n) k)) (sqrt.f64 #s(literal -1 binary64))) (sqrt.f64 #s(literal -2 binary64))))
#s(approx (sqrt k) #s(hole binary64 (* -1 (* (sqrt k) (pow (sqrt -1) 2)))))
#s(approx (sqrt k) (*.f64 (sqrt.f64 k) #s(literal 1 binary64)))
#s(approx (sqrt (* (* (* (/ n k) (sqrt (PI))) (sqrt (PI))) 2)) #s(hole binary64 (* (sqrt (/ (* n (PI)) k)) (* (sqrt -2) (sqrt -1)))))
#s(approx (sqrt (* (* (* (/ n k) (sqrt (PI))) (sqrt (PI))) 2)) (.f64 (.f64 (sqrt.f64 (/.f64 (*.f64 (PI.f64) n) k)) (sqrt.f64 #s(literal -1 binary64))) (sqrt.f64 #s(literal -2 binary64))))
#s(approx (* (/ 1 (sqrt k)) (/ (sqrt (* (* (PI) n) 2)) (pow (* (* (PI) n) 2) (/ k 2)))) #s(hole binary64 (* (sqrt (/ (* n (PI)) k)) (/ (sqrt 2) (exp (* 1/2 (* k (+ (log n) (log (* 2 (PI)))))))))))
#s(approx (* (/ 1 (sqrt k)) (/ (sqrt (* (* (PI) n) 2)) (pow (* (* (PI) n) 2) (/ k 2)))) (.f64 (/.f64 (sqrt.f64 #s(literal 2 binary64)) (pow.f64 (sqrt.f64 (exp.f64 k)) (+.f64 (log.f64 (.f64 (PI.f64) #s(literal 2 binary64))) (log.f64 n)))) (sqrt.f64 (/.f64 (*.f64 (PI.f64) n) k))))
#s(approx (/ (sqrt (* (* (PI) n) 2)) (pow (* (* (PI) n) 2) (/ k 2))) #s(hole binary64 (* (sqrt (* n (PI))) (/ (sqrt 2) (exp (* 1/2 (* k (+ (log n) (log (* 2 (PI)))))))))))
#s(approx (/ (sqrt (* (* (PI) n) 2)) (pow (* (* (PI) n) 2) (/ k 2))) (.f64 (/.f64 (sqrt.f64 #s(literal 2 binary64)) (pow.f64 (sqrt.f64 (exp.f64 k)) (+.f64 (log.f64 (.f64 (PI.f64) #s(literal 2 binary64))) (log.f64 n)))) (sqrt.f64 (*.f64 (PI.f64) n))))
#s(approx (sqrt (* (* (PI) n) 2)) #s(hole binary64 (* (sqrt (* n (PI))) (sqrt 2))))
#s(approx (sqrt (* (* (PI) n) 2)) (.f64 (sqrt.f64 (.f64 (PI.f64) n)) (sqrt.f64 #s(literal 2 binary64))))
#s(approx (* (* (PI) n) 2) #s(hole binary64 (* 2 (* n (PI)))))
#s(approx (* (* (PI) n) 2) (.f64 (.f64 (PI.f64) #s(literal 2 binary64)) n))
#s(approx (* (PI) n) #s(hole binary64 (* n (PI))))
#s(approx (* (PI) n) (*.f64 (PI.f64) n))
#s(approx n #s(hole binary64 n))
#s(approx n n)
#s(approx (pow (* (* (PI) n) 2) (/ k 2)) #s(hole binary64 (exp (* 1/2 (* k (+ (log n) (log (* 2 (PI)))))))))
#s(approx (pow (* (* (PI) n) 2) (/ k 2)) (pow.f64 (sqrt.f64 (exp.f64 k)) (+.f64 (log.f64 (*.f64 (PI.f64) #s(literal 2 binary64))) (log.f64 n))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) #s(hole binary64 (* (sqrt (/ 1 k)) (exp (* 1/2 (* (+ (log n) (log (* 2 (PI)))) (- 1 k)))))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (.f64 (pow.f64 (exp.f64 (fma.f64 #s(literal -1/2 binary64) k #s(literal 1/2 binary64))) (+.f64 (log.f64 (.f64 (PI.f64) #s(literal 2 binary64))) (log.f64 n))) (sqrt.f64 (/.f64 #s(literal 1 binary64) k))))
#s(approx (* 2 n) #s(hole binary64 (* 2 n)))
#s(approx (* 2 n) (*.f64 #s(literal 2 binary64) n))
#s(approx (* (/ 1 (sqrt k)) (/ (sqrt (* (* (PI) n) 2)) (pow (* (* (PI) n) 2) (/ k 2)))) #s(hole binary64 (* (sqrt (/ (* n (PI)) k)) (/ (sqrt 2) (exp (* 1/2 (* k (+ (log (* 2 (PI))) (* -1 (log (/ 1 n)))))))))))
#s(approx (* (/ 1 (sqrt k)) (/ (sqrt (* (* (PI) n) 2)) (pow (* (* (PI) n) 2) (/ k 2)))) (.f64 (/.f64 (sqrt.f64 #s(literal 2 binary64)) (pow.f64 (sqrt.f64 (exp.f64 k)) (+.f64 (log.f64 (.f64 (PI.f64) #s(literal 2 binary64))) (log.f64 n)))) (sqrt.f64 (/.f64 (*.f64 (PI.f64) n) k))))
#s(approx (/ (sqrt (* (* (PI) n) 2)) (pow (* (* (PI) n) 2) (/ k 2))) #s(hole binary64 (* (sqrt (* n (PI))) (/ (sqrt 2) (exp (* 1/2 (* k (+ (log (* 2 (PI))) (* -1 (log (/ 1 n)))))))))))
#s(approx (/ (sqrt (* (* (PI) n) 2)) (pow (* (* (PI) n) 2) (/ k 2))) (.f64 (/.f64 (sqrt.f64 #s(literal 2 binary64)) (pow.f64 (sqrt.f64 (exp.f64 k)) (+.f64 (log.f64 (.f64 (PI.f64) #s(literal 2 binary64))) (log.f64 n)))) (sqrt.f64 (*.f64 (PI.f64) n))))
#s(approx (pow (* (* (PI) n) 2) (/ k 2)) #s(hole binary64 (exp (* 1/2 (* k (+ (log (* 2 (PI))) (* -1 (log (/ 1 n)))))))))
#s(approx (pow (* (* (PI) n) 2) (/ k 2)) (pow.f64 (sqrt.f64 (exp.f64 k)) (+.f64 (log.f64 (*.f64 (PI.f64) #s(literal 2 binary64))) (log.f64 n))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) #s(hole binary64 (* (sqrt (/ 1 k)) (exp (* 1/2 (* (+ (log (* 2 (PI))) (* -1 (log (/ 1 n)))) (- 1 k)))))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (.f64 (pow.f64 (exp.f64 (fma.f64 #s(literal -1/2 binary64) k #s(literal 1/2 binary64))) (+.f64 (log.f64 (.f64 (PI.f64) #s(literal 2 binary64))) (log.f64 n))) (sqrt.f64 (/.f64 #s(literal 1 binary64) k))))
#s(approx (* (/ 1 (sqrt k)) (/ (sqrt (* (* (PI) n) 2)) (pow (* (* (PI) n) 2) (/ k 2)))) #s(hole binary64 (* -1 (* (sqrt (/ (* n (PI)) k)) (/ (* (sqrt -2) (sqrt -1)) (exp (* 1/2 (* k (+ (log (* -2 (PI))) (* -1 (log (/ -1 n))))))))))))
#s(approx (* (/ 1 (sqrt k)) (/ (sqrt (* (* (PI) n) 2)) (pow (* (* (PI) n) 2) (/ k 2)))) (.f64 (/.f64 (.f64 (neg.f64 (sqrt.f64 #s(literal -1 binary64))) (sqrt.f64 #s(literal -2 binary64))) (pow.f64 (sqrt.f64 (exp.f64 k)) (-.f64 (log.f64 (.f64 #s(literal -2 binary64) (PI.f64))) (log.f64 (/.f64 #s(literal -1 binary64) n))))) (sqrt.f64 (/.f64 (.f64 (PI.f64) n) k))))
#s(approx (/ (sqrt (* (* (PI) n) 2)) (pow (* (* (PI) n) 2) (/ k 2))) #s(hole binary64 (* -1 (* (sqrt (* n (PI))) (/ (* (sqrt -2) (sqrt -1)) (exp (* 1/2 (* k (+ (log (* -2 (PI))) (* -1 (log (/ -1 n))))))))))))
#s(approx (/ (sqrt (* (* (PI) n) 2)) (pow (* (* (PI) n) 2) (/ k 2))) (.f64 (/.f64 (.f64 (neg.f64 (sqrt.f64 #s(literal -1 binary64))) (sqrt.f64 #s(literal -2 binary64))) (pow.f64 (sqrt.f64 (exp.f64 k)) (-.f64 (log.f64 (.f64 #s(literal -2 binary64) (PI.f64))) (log.f64 (/.f64 #s(literal -1 binary64) n))))) (sqrt.f64 (.f64 (PI.f64) n))))
#s(approx (sqrt (* (* (PI) n) 2)) #s(hole binary64 (* -1 (* (sqrt (* n (PI))) (* (sqrt -2) (sqrt -1))))))
#s(approx (sqrt (* (* (PI) n) 2)) (.f64 (neg.f64 (sqrt.f64 #s(literal -2 binary64))) (.f64 (sqrt.f64 #s(literal -1 binary64)) (sqrt.f64 (*.f64 (PI.f64) n)))))
#s(approx (pow (* (* (PI) n) 2) (/ k 2)) #s(hole binary64 (exp (* 1/2 (* k (+ (log (* -2 (PI))) (* -1 (log (/ -1 n)))))))))
#s(approx (pow (* (* (PI) n) 2) (/ k 2)) (pow.f64 (sqrt.f64 (exp.f64 k)) (-.f64 (log.f64 (*.f64 #s(literal -2 binary64) (PI.f64))) (log.f64 (/.f64 #s(literal -1 binary64) n)))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) #s(hole binary64 (* (sqrt (/ 1 k)) (exp (* 1/2 (* (+ (log (* -2 (PI))) (* -1 (log (/ -1 n)))) (- 1 k)))))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (.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))))
#s(approx (sqrt (* (PI) (/ (* 2 n) k))) #s(hole binary64 (* -1 (* (sqrt (/ (* n (PI)) k)) (* (sqrt -2) (sqrt -1))))))
#s(approx (sqrt (* (* (* (/ n k) (sqrt (PI))) (sqrt (PI))) 2)) (.f64 (neg.f64 (sqrt.f64 #s(literal -2 binary64))) (.f64 (sqrt.f64 #s(literal -1 binary64)) (sqrt.f64 (/.f64 (*.f64 (PI.f64) n) k)))))
#s(approx (/ (sqrt (* (* (PI) n) 2)) (sqrt k)) #s(hole binary64 (* -1 (* (sqrt (/ (* n (PI)) k)) (* (sqrt -2) (sqrt -1))))))
#s(approx (/ (sqrt (* (* (PI) n) 2)) (sqrt k)) (.f64 (neg.f64 (sqrt.f64 #s(literal -2 binary64))) (.f64 (sqrt.f64 #s(literal -1 binary64)) (sqrt.f64 (/.f64 (*.f64 (PI.f64) n) k)))))
#s(approx (sqrt (* (* (* (/ n k) (sqrt (PI))) (sqrt (PI))) 2)) #s(hole binary64 (* -1 (* (sqrt (/ (* n (PI)) k)) (* (sqrt -2) (sqrt -1))))))
#s(approx (sqrt (* (* (* (/ n k) (sqrt (PI))) (sqrt (PI))) 2)) (.f64 (neg.f64 (sqrt.f64 #s(literal -2 binary64))) (.f64 (sqrt.f64 #s(literal -1 binary64)) (sqrt.f64 (/.f64 (*.f64 (PI.f64) n) k)))))

rewrite61.0ms (0.7%)

Memory

26.8MiB live, 119.1MiB allocated; 10ms collecting garbage

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	47	302
0	74	284
1	201	259
0	991	259

Stop Event

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

Counts

34 → 369

Calls

Call 1

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

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

eval66.0ms (0.8%)

Memory: -35.9MiB live, 156.6MiB allocated; 18ms collecting garbage
Compiler: Compiled 14 653 to 1 602 computations (89.1% saved)

prune78.0ms (0.9%)

Memory

27.3MiB live, 176.2MiB allocated; 6ms collecting garbage

Pruning

37 alts after pruning (31 fresh and 6 done)

	Pruned	Kept	Total
New	480	15	495
Fresh	7	16	23
Picked	2	3	5
Done	0	3	3
Total	489	37	526

Accuracy

100.0%

Counts

526 → 37

Alt Table

Click to see full alt table

Status	Accuracy	Program
	52.5%	(/.f64 (pow.f64 (.f64 #s(literal 2 binary64) (.f64 n (PI.f64))) #s(approx (/ (- 1 k) 2) (*.f64 #s(literal -1/2 binary64) k))) (sqrt.f64 k))
	76.4%	(/.f64 (sqrt.f64 (/.f64 (.f64 #s(literal 2 binary64) (.f64 n (PI.f64))) k)) (pow.f64 (.f64 #s(literal 2 binary64) (.f64 n (PI.f64))) (/.f64 k #s(literal 2 binary64))))
	49.8%	(.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) (/.f64 (.f64 (sqrt.f64 (.f64 #s(literal 2 binary64) (PI.f64))) (sqrt.f64 n)) #s(approx (pow ( (* (PI) n) 2) (/ k 2)) #s(literal 1 binary64))))
	49.9%	(.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) (/.f64 (sqrt.f64 (.f64 (.f64 (.f64 (sqrt.f64 (PI.f64)) n) (sqrt.f64 (PI.f64))) #s(literal 2 binary64))) #s(approx (pow (* (* (PI) n) 2) (/ k 2)) #s(literal 1 binary64))))
✓	50.0%	(.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) (/.f64 (sqrt.f64 (.f64 (.f64 (PI.f64) n) #s(literal 2 binary64))) #s(approx (pow ( (* (PI) n) 2) (/ k 2)) #s(literal 1 binary64))))
	50.0%	(.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) #s(approx (pow ( (* (PI) n) 2) (+ (* -1/2 k) 1/2)) (.f64 (sqrt.f64 (.f64 (PI.f64) n)) (sqrt.f64 #s(literal 2 binary64)))))
	99.7%	(.f64 #s(approx (/ 1 (sqrt k)) (sqrt.f64 (/.f64 #s(literal 1 binary64) k))) (/.f64 (sqrt.f64 (.f64 (.f64 (PI.f64) n) #s(literal 2 binary64))) (pow.f64 (.f64 (.f64 (PI.f64) n) #s(literal 2 binary64)) #s(approx (/ k 2) (.f64 #s(literal 1/2 binary64) k)))))
	50.0%	(.f64 #s(approx (/ 1 (sqrt k)) (sqrt.f64 (/.f64 #s(literal 1 binary64) k))) #s(approx (/ (sqrt ( (* (PI) n) 2)) (pow (* (* (PI) n) 2) (/ k 2))) (.f64 (sqrt.f64 (.f64 (PI.f64) n)) (sqrt.f64 #s(literal 2 binary64)))))
	99.5%	#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (/.f64 (.f64 (pow.f64 (.f64 (*.f64 (PI.f64) n) #s(literal 2 binary64)) (fma.f64 #s(literal -1/2 binary64) k #s(literal 1/2 binary64))) #s(literal 1 binary64)) (sqrt.f64 k)))
	50.1%	#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (/.f64 (.f64 (sqrt.f64 (.f64 n (PI.f64))) (sqrt.f64 #s(literal 2 binary64))) (sqrt.f64 k)))
	49.8%	#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (/.f64 (.f64 (sqrt.f64 (.f64 #s(literal 2 binary64) (PI.f64))) (sqrt.f64 n)) (sqrt.f64 k)))
	50.0%	#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (/.f64 (.f64 (sqrt.f64 (PI.f64)) (sqrt.f64 (.f64 #s(literal 2 binary64) n))) (sqrt.f64 k)))
	50.0%	#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (/.f64 (.f64 (sqrt.f64 #s(literal 2 binary64)) #s(approx (+ ( (* (log (* (* (PI) n) 2)) (sqrt (* (* (pow k 3) (PI)) n))) -1/2) (sqrt (* (* (PI) n) k))) (.f64 (sqrt.f64 (.f64 n (PI.f64))) (sqrt.f64 k)))) k))
	40.3%	#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (/.f64 (.f64 (sqrt.f64 #s(literal 2 binary64)) #s(approx (+ ( (* (log (* (* (PI) n) 2)) (sqrt (* (* (pow k 3) (PI)) n))) -1/2) (sqrt (* (* (PI) n) k))) (sqrt.f64 (.f64 (.f64 k (PI.f64)) n)))) k))
	27.2%	#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (/.f64 (.f64 (sqrt.f64 #s(literal 2 binary64)) #s(approx (+ ( (* (log (* (* (PI) n) 2)) (sqrt (* (* (pow k 3) (PI)) n))) -1/2) (sqrt (* (* (PI) n) k))) (sqrt.f64 (sqrt.f64 (.f64 (.f64 (.f64 n (PI.f64)) k) (.f64 (*.f64 n (PI.f64)) k)))))) k))
	49.9%	#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (/.f64 (sqrt.f64 (.f64 (.f64 (*.f64 (sqrt.f64 (PI.f64)) n) (sqrt.f64 (PI.f64))) #s(literal 2 binary64))) (sqrt.f64 k)))
✓	50.1%	#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (/.f64 (sqrt.f64 (.f64 (.f64 (PI.f64) n) #s(literal 2 binary64))) (sqrt.f64 k)))
	40.2%	#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (.f64 (/.f64 #s(approx (+ ( (* (log (* (* (PI) n) 2)) (sqrt (* (* (pow k 3) (PI)) n))) -1/2) (sqrt (* (* (PI) n) k))) (sqrt.f64 (.f64 (.f64 n (PI.f64)) k))) k) (sqrt.f64 #s(literal 2 binary64))))
	49.9%	#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (.f64 (.f64 (pow.f64 k #s(literal -1/2 binary64)) (sqrt.f64 n)) (sqrt.f64 (*.f64 #s(literal 2 binary64) (PI.f64)))))
	37.9%	#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (.f64 (sqrt.f64 (/.f64 (.f64 #s(literal 2 binary64) n) k)) (sqrt.f64 (PI.f64))))
✓	99.5%	#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) k)) (pow.f64 (.f64 (*.f64 (PI.f64) n) #s(literal 2 binary64)) (fma.f64 #s(literal -1/2 binary64) k #s(literal 1/2 binary64)))))
	38.0%	#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (.f64 (sqrt.f64 (.f64 (/.f64 n k) (PI.f64))) (sqrt.f64 #s(literal 2 binary64))))
	50.1%	#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (.f64 (sqrt.f64 (.f64 n (PI.f64))) (/.f64 (sqrt.f64 #s(literal 2 binary64)) (sqrt.f64 k))))
	38.1%	#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (.f64 (sqrt.f64 #s(literal 2 binary64)) (.f64 (sqrt.f64 (PI.f64)) (sqrt.f64 (/.f64 n k)))))
✓	38.1%	#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (.f64 (sqrt.f64 #s(literal 2 binary64)) (sqrt.f64 (.f64 (sqrt.f64 (PI.f64)) (*.f64 (sqrt.f64 (PI.f64)) (/.f64 n k))))))
	38.0%	#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (.f64 (sqrt.f64 #s(literal 2 binary64)) (sqrt.f64 (.f64 n (/.f64 (PI.f64) k)))))
	40.3%	#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (.f64 #s(approx (+ ( (* (log (* (* (PI) n) 2)) (sqrt (* (* (pow k 3) (PI)) n))) -1/2) (sqrt (* (* (PI) n) k))) (sqrt.f64 (.f64 (.f64 n (PI.f64)) k))) (/.f64 (sqrt.f64 #s(literal 2 binary64)) k)))
✓	38.2%	#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))))
	38.1%	#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt.f64 (.f64 (/.f64 n k) (.f64 #s(literal 2 binary64) (PI.f64)))))
	38.0%	#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt.f64 (.f64 (.f64 (/.f64 (*.f64 (sqrt.f64 (PI.f64)) n) k) (sqrt.f64 (PI.f64))) #s(literal 2 binary64))))
	38.0%	#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt.f64 (.f64 (.f64 (/.f64 n k) (sqrt.f64 (PI.f64))) (*.f64 (sqrt.f64 (PI.f64)) #s(literal 2 binary64)))))
✓	38.0%	#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt.f64 (.f64 (.f64 (*.f64 (/.f64 n k) (sqrt.f64 (PI.f64))) (sqrt.f64 (PI.f64))) #s(literal 2 binary64))))
	38.0%	#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt.f64 (.f64 (.f64 (*.f64 n (/.f64 (sqrt.f64 (PI.f64)) k)) (sqrt.f64 (PI.f64))) #s(literal 2 binary64))))
	38.1%	#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt.f64 (.f64 (.f64 n (/.f64 (PI.f64) k)) #s(literal 2 binary64))))
	38.1%	#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt.f64 (.f64 (.f64 n (PI.f64)) (/.f64 #s(literal 2 binary64) k))))
	38.1%	#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt.f64 (*.f64 (PI.f64) (/.f64 (+.f64 n n) k))))
	38.1%	#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt.f64 (.f64 (PI.f64) (.f64 n (/.f64 #s(literal 2 binary64) k)))))

Compiler

Compiled 3 245 to 1 214 computations (62.6% saved)

regimes143.0ms (1.7%)

Memory

-9.8MiB live, 130.6MiB allocated; 14ms collecting garbage

Counts

72 → 1

Calls

Call 1

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

Outputs

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

Calls

4 calls:

51.0ms	(.f64 (.f64 #s(literal 2 binary64) (PI.f64)) n)
51.0ms	n
20.0ms	k
15.0ms	(.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	`(.f64 (.f64 #s(literal 2 binary64) (PI.f64)) 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	`k`
99.7%	1	`n`

Compiler

Compiled 23 to 23 computations (0% saved)

regimes108.0ms (1.3%)

Memory

-2.3MiB live, 89.8MiB allocated; 4ms collecting garbage

Counts

56 → 1

Calls

Call 1

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

Outputs

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

Calls

4 calls:

49.0ms	(.f64 (.f64 #s(literal 2 binary64) (PI.f64)) n)
14.0ms	n
14.0ms	k
12.0ms	(.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	`(.f64 (.f64 #s(literal 2 binary64) (PI.f64)) 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	`k`
99.5%	1	`n`

Compiler

Compiled 23 to 23 computations (0% saved)

regimes59.0ms (0.7%)

Memory

-18.5MiB live, 86.4MiB allocated; 12ms collecting garbage

Counts

48 → 1

Calls

Call 1

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

Outputs

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

Calls

4 calls:

16.0ms	(.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))))
15.0ms	k
12.0ms	(.f64 (.f64 #s(literal 2 binary64) (PI.f64)) n)
12.0ms	n

Results

Accuracy	Segments	Branch
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)`
99.5%	1	`k`
99.5%	1	`n`

Compiler

Compiled 23 to 23 computations (0% saved)

regimes83.0ms (1%)

Memory

4.6MiB live, 94.7MiB allocated; 8ms collecting garbage

Counts

47 → 2

Calls

Call 1

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

Outputs

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

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

Calls

4 calls:

43.0ms	(.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))))
14.0ms	(.f64 (.f64 #s(literal 2 binary64) (PI.f64)) n)
12.0ms	k
12.0ms	n

Results

Accuracy	Segments	Branch
97.7%	3	`(.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))))`
97.7%	2	`k`
60.7%	4	`(.f64 (.f64 #s(literal 2 binary64) (PI.f64)) n)`
60.7%	4	`n`

Compiler

Compiled 23 to 23 computations (0% saved)

regimes72.0ms (0.9%)

Memory

0.5MiB live, 94.7MiB allocated; 18ms collecting garbage

Counts

45 → 2

Calls

Call 1

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

Outputs

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

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

Calls

4 calls:

29.0ms	n
11.0ms	(.f64 (.f64 #s(literal 2 binary64) (PI.f64)) n)
11.0ms	k
10.0ms	(.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
50.1%	1	`(.f64 (.f64 #s(literal 2 binary64) (PI.f64)) n)`
50.1%	1	`n`
53.6%	2	`(.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))))`
53.4%	2	`k`

Compiler

Compiled 23 to 23 computations (0% saved)

regimes44.0ms (0.5%)

Memory

20.8MiB live, 111.0MiB allocated; 5ms collecting garbage

Counts

39 → 1

Calls

Call 1

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

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

Calls

4 calls:

12.0ms	(.f64 (.f64 #s(literal 2 binary64) (PI.f64)) n)
11.0ms	k
10.0ms	n
9.0ms	(.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
50.1%	1	`(.f64 (.f64 #s(literal 2 binary64) (PI.f64)) n)`
50.1%	1	`n`
50.1%	1	`k`
50.1%	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)

regimes17.0ms (0.2%)

Memory

-6.3MiB live, 40.0MiB allocated; 2ms collecting garbage

Counts

13 → 1

Calls

Call 1

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

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:

5.0ms	(.f64 (.f64 #s(literal 2 binary64) (PI.f64)) n)
4.0ms	k
4.0ms	n
3.0ms	(.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
38.2%	1	`(.f64 (.f64 #s(literal 2 binary64) (PI.f64)) n)`
38.2%	1	`n`
38.2%	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))))`
38.2%	1	`k`

Compiler

Compiled 23 to 23 computations (0% saved)

regimes10.0ms (0.1%)

Memory

17.7MiB live, 17.7MiB allocated; 0ms collecting garbage

Accuracy

Total -0.1b remaining (-0.2%)

Threshold costs -0.1b (-0.2%)

Counts

7 → 1

Calls

Call 1

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

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

Calls

4 calls:

2.0ms	(.f64 (.f64 #s(literal 2 binary64) (PI.f64)) n)
2.0ms	n
2.0ms	k
2.0ms	(.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
38.1%	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))))`
38.1%	1	`k`
38.1%	1	`(.f64 (.f64 #s(literal 2 binary64) (PI.f64)) n)`
38.1%	1	`n`

Compiler

Compiled 23 to 23 computations (0% saved)

bsearch29.0ms (0.3%)

Memory

-33.5MiB live, 23.1MiB allocated; 5ms collecting garbage

Algorithm

1×	binary-search

Stop Event

1×	narrow-enough

Steps

Time	Left	Right
27.0ms	0.3017255395323611	11916.15478715421

Samples

22.0ms

128×

valid

Compiler

Compiled 379 to 338 computations (10.8% saved)

Precisions

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

ival-div: 2.0ms (23.2% of total)

ival-mult: 2.0ms (23.2% of total)

ival-pow: 2.0ms (23.2% of total)

ival-sub: 1.0ms (11.6% of total)

ival-sqrt: 1.0ms (11.6% of total)

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

adjust: 0.0ms (0% of total)

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

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

exact: 0.0ms (0% of total)

bsearch1.0ms (0%)

Memory

0.3MiB live, 0.3MiB allocated; 0ms collecting garbage

Algorithm

1×	left-value

Steps

Time	Left	Right
0.0ms	2.8618329187414476e+206	1.2195360040598931e+208

Compiler

Compiled 19 to 18 computations (5.3% saved)

simplify52.0ms (0.6%)

Memory

20.5MiB live, 66.6MiB allocated; 3ms collecting garbage

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	90	322
1	123	306
2	193	306
3	432	306
4	1972	306
5	6494	306

Stop Event

1×	node limit

Calls

Call 1

Inputs
(.f64 #s(approx (/ 1 (sqrt k)) (sqrt.f64 (/.f64 #s(literal 1 binary64) k))) (/.f64 (sqrt.f64 (.f64 (.f64 (PI.f64) n) #s(literal 2 binary64))) (pow.f64 (.f64 (.f64 (PI.f64) n) #s(literal 2 binary64)) #s(approx (/ k 2) (.f64 #s(literal 1/2 binary64) k)))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (/.f64 (.f64 (pow.f64 (.f64 (*.f64 (PI.f64) n) #s(literal 2 binary64)) (fma.f64 #s(literal -1/2 binary64) k #s(literal 1/2 binary64))) #s(literal 1 binary64)) (sqrt.f64 k)))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) k)) (pow.f64 (.f64 (*.f64 (PI.f64) n) #s(literal 2 binary64)) (fma.f64 #s(literal -1/2 binary64) k #s(literal 1/2 binary64)))))
(if (<=.f64 k #s(literal 1 binary64)) #s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (.f64 (pow.f64 k #s(literal -1/2 binary64)) (sqrt.f64 (.f64 (.f64 (PI.f64) n) #s(literal 2 binary64))))) (/.f64 (pow.f64 (.f64 #s(literal 2 binary64) (.f64 n (PI.f64))) #s(approx (/ (- 1 k) 2) (.f64 #s(literal -1/2 binary64) k))) (sqrt.f64 k)))
(if (<=.f64 (.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)))) #s(literal 500000000000000019446788775544194215653686246476010066671511910038456471446924483815399828039388506936632301559706066456765853057047187808270091836106344701772172931313084717722832279038279731096611203317760 binary64)) #s(approx ( (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (/.f64 (sqrt.f64 (.f64 (.f64 (PI.f64) n) #s(literal 2 binary64))) (sqrt.f64 k))) #s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (/.f64 (.f64 (sqrt.f64 #s(literal 2 binary64)) #s(approx (+ ( (* (log (* (* (PI) n) 2)) (sqrt (* (* (pow k 3) (PI)) n))) -1/2) (sqrt (* (* (PI) n) k))) (sqrt.f64 (sqrt.f64 (.f64 (.f64 (.f64 n (PI.f64)) k) (.f64 (*.f64 n (PI.f64)) k)))))) k)))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (/.f64 (sqrt.f64 (.f64 (.f64 (PI.f64) n) #s(literal 2 binary64))) (sqrt.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 (PI.f64) (/.f64 (+.f64 n n) k))))

Outputs
(.f64 #s(approx (/ 1 (sqrt k)) (sqrt.f64 (/.f64 #s(literal 1 binary64) k))) (/.f64 (sqrt.f64 (.f64 (.f64 (PI.f64) n) #s(literal 2 binary64))) (pow.f64 (.f64 (.f64 (PI.f64) n) #s(literal 2 binary64)) #s(approx (/ k 2) (.f64 #s(literal 1/2 binary64) k)))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (/.f64 (.f64 (pow.f64 (.f64 (*.f64 (PI.f64) n) #s(literal 2 binary64)) (fma.f64 #s(literal -1/2 binary64) k #s(literal 1/2 binary64))) #s(literal 1 binary64)) (sqrt.f64 k)))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (/.f64 (pow.f64 (.f64 (.f64 (PI.f64) n) #s(literal 2 binary64)) (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 #s(literal 1 binary64) k)) (pow.f64 (.f64 (*.f64 (PI.f64) n) #s(literal 2 binary64)) (fma.f64 #s(literal -1/2 binary64) k #s(literal 1/2 binary64)))))
(if (<=.f64 k #s(literal 1 binary64)) #s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (.f64 (pow.f64 k #s(literal -1/2 binary64)) (sqrt.f64 (.f64 (.f64 (PI.f64) n) #s(literal 2 binary64))))) (/.f64 (pow.f64 (.f64 #s(literal 2 binary64) (.f64 n (PI.f64))) #s(approx (/ (- 1 k) 2) (.f64 #s(literal -1/2 binary64) k))) (sqrt.f64 k)))
(if (<=.f64 (.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)))) #s(literal 500000000000000019446788775544194215653686246476010066671511910038456471446924483815399828039388506936632301559706066456765853057047187808270091836106344701772172931313084717722832279038279731096611203317760 binary64)) #s(approx ( (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (/.f64 (sqrt.f64 (.f64 (.f64 (PI.f64) n) #s(literal 2 binary64))) (sqrt.f64 k))) #s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (/.f64 (.f64 (sqrt.f64 #s(literal 2 binary64)) #s(approx (+ ( (* (log (* (* (PI) n) 2)) (sqrt (* (* (pow k 3) (PI)) n))) -1/2) (sqrt (* (* (PI) n) k))) (sqrt.f64 (sqrt.f64 (.f64 (.f64 (.f64 n (PI.f64)) k) (.f64 (*.f64 n (PI.f64)) k)))))) k)))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (/.f64 (sqrt.f64 (.f64 (.f64 (PI.f64) n) #s(literal 2 binary64))) (sqrt.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 (PI.f64) (/.f64 (+.f64 n n) k))))

derivations243.0ms (2.9%)

Memory

22.6MiB live, 260.6MiB allocated; 12ms collecting garbage

Stop Event

1×

fuel

Compiler

Compiled 322 to 92 computations (71.4% saved)

preprocess92.0ms (1.1%)

Memory: -30.3MiB live, 81.9MiB allocated; 45ms collecting garbage
Compiler: Compiled 676 to 210 computations (68.9% saved)

end0.0ms (0%)

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

start0.0ms (0%)

analyze220.0ms (2.6%)

sample4.7s (56%)

explain201.0ms (2.4%)

preprocess274.0ms (3.3%)

eval0.0ms (0%)

prune1.0ms (0%)

series91.0ms (1.1%)

simplify136.0ms (1.6%)

rewrite70.0ms (0.8%)

eval19.0ms (0.2%)

prune13.0ms (0.2%)

series218.0ms (2.6%)

simplify221.0ms (2.6%)

rewrite107.0ms (1.3%)

eval180.0ms (2.1%)

prune44.0ms (0.5%)

series80.0ms (1%)

simplify200.0ms (2.4%)

rewrite88.0ms (1%)

eval71.0ms (0.8%)

prune67.0ms (0.8%)

series69.0ms (0.8%)

simplify169.0ms (2%)

rewrite61.0ms (0.7%)

eval66.0ms (0.8%)

prune78.0ms (0.9%)

regimes143.0ms (1.7%)

regimes108.0ms (1.3%)

regimes59.0ms (0.7%)

regimes83.0ms (1%)

regimes72.0ms (0.9%)

regimes44.0ms (0.5%)

regimes17.0ms (0.2%)

regimes10.0ms (0.1%)

bsearch29.0ms (0.3%)

bsearch1.0ms (0%)

simplify52.0ms (0.6%)

derivations243.0ms (2.9%)

preprocess92.0ms (1.1%)

end0.0ms (0%)

Profiling