Metrics for Migdal et al, Equation (51)

start0.0ms (0%)

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

analyze125.0ms (1.3%)

Memory

5.3MiB live, 194.9MiB allocated; 32ms 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)

sample4.8s (51%)

Memory

13.4MiB live, 6 291.0MiB allocated; 2.2s collecting garbage

Samples

1.3s	4 394×	1	invalid
1.2s	8 255×	0	valid
1.1s	1 475×	2	invalid
76.0ms	402×	0	invalid
64.0ms	249×	0	exit
0.0ms	1×	1	valid

Precisions

Click to see histograms. Total time spent on operations: 2.3s

ival-mult: 586.0ms (24.9% of total)

ival-pow: 567.0ms (24.1% of total)

ival-div: 381.0ms (16.2% of total)

ival-sub: 300.0ms (12.8% of total)

ival-sqrt: 177.0ms (7.5% of total)

adjust: 170.0ms (7.2% of total)

ival-pi: 128.0ms (5.4% of total)

exact: 21.0ms (0.9% of total)

ival-true: 13.0ms (0.6% of total)

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

Bogosity

explain199.0ms (2.1%)

Memory

24.0MiB live, 257.7MiB allocated; 42ms collecting garbage

FPErrors

Click to see full error table

Ground Truth	Overpredictions	Example	Underpredictions	Example	Subexpression
4	98	(4.687333719802061e-104 1.0946051714141427e+109)	1	(2.696281092094482e-8 1.5672818909324757e-79)	`(pow.f64 (.f64 (.f64 #s(literal 2 binary64) (PI.f64)) n) (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 2 binary64)))`
0	0	-	0	-	`k`
0	0	-	0	-	`n`
0	0	-	0	-	`(/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 2 binary64))`
0	0	-	0	-	`#s(literal 1 binary64)`
0	0	-	0	-	`(.f64 (.f64 #s(literal 2 binary64) (PI.f64)) n)`
0	0	-	0	-	`(sqrt.f64 k)`
0	0	-	0	-	`#s(literal 2 binary64)`
0	0	-	0	-	`(/.f64 #s(literal 1 binary64) (sqrt.f64 k))`
0	0	-	0	-	`(-.f64 #s(literal 1 binary64) k)`
0	0	-	0	-	`(*.f64 #s(literal 2 binary64) (PI.f64))`
0	0	-	0	-	`(.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) (pow.f64 (.f64 (*.f64 #s(literal 2 binary64) (PI.f64)) n) (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 2 binary64))))`
0	0	-	0	-	`(PI.f64)`

Explanations

Click to see full explanations table

Operator	Subexpression	Explanation	Count
`pow.f64`	`(pow.f64 (.f64 (.f64 #s(literal 2 binary64) (PI.f64)) n) (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 2 binary64)))`	sensitivity	101	22

Confusion

	Predicted +	Predicted -
+	3	1
-	98	154

Precision

0.0297029702970297

Recall

0.75

Confusion?

	Predicted +	Predicted Maybe	Predicted -
+	3	1	0
-	98	21	133

Precision?

0.032520325203252036

Recall?

1.0

Freqs

test

number	freq
0	155
1	101

Total Confusion?

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

Precision?

1.0

Recall?

1.0

Samples

96.0ms

512×

valid

Compiler

Compiled 128 to 43 computations (66.4% saved)

Precisions

Click to see histograms. Total time spent on operations: 78.0ms

ival-sub: 36.0ms (46.2% of total)

ival-mult: 12.0ms (15.4% of total)

ival-sqrt: 10.0ms (12.8% of total)

ival-pow: 10.0ms (12.8% of total)

ival-div: 7.0ms (9% of total)

ival-pi: 2.0ms (2.6% of total)

exact: 1.0ms (1.3% of total)

adjust: 0.0ms (0% of total)

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

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

preprocess296.0ms (3.2%)

Memory

-18.9MiB live, 193.0MiB allocated; 121ms 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)

prune0.0ms (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)

simplify115.0ms (1.2%)

Memory

8.5MiB live, 197.2MiB allocated; 18ms collecting garbage

Localize:

Found 4 expressions of interest:

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

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	13	54
0	22	54
1	37	52
2	58	52
3	136	52
4	533	52
5	3201	52
0	8098	52

Stop Event

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

Calls

Call 1

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

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

localize41.0ms (0.4%)

Memory

-37.6MiB live, 108.6MiB allocated; 9ms collecting garbage

Localize:

Found 4 expressions of interest:

New	Metric	Score
accuracy	0.1640625	(.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) (pow.f64 (.f64 (*.f64 #s(literal 2 binary64) (PI.f64)) n) (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 2 binary64))))
accuracy	0.16630692927829482	(pow.f64 (.f64 (.f64 #s(literal 2 binary64) (PI.f64)) n) (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 2 binary64)))
accuracy	0.265625	(/.f64 #s(literal 1 binary64) (sqrt.f64 k))
accuracy	0.26953125	(.f64 (.f64 #s(literal 2 binary64) (PI.f64)) n)

Samples

29.0ms

256×

valid

Compiler

Compiled 56 to 15 computations (73.2% saved)

Precisions

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

ival-pow: 6.0ms (30.4% of total)

ival-mult: 4.0ms (20.2% of total)

ival-div: 3.0ms (15.2% of total)

ival-sub: 2.0ms (10.1% of total)

ival-sqrt: 2.0ms (10.1% of total)

ival-pi: 1.0ms (5.1% 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)

series132.0ms (1.4%)

Memory

20.7MiB live, 210.0MiB allocated; 18ms collecting garbage

Counts

5 → 22

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

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 (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 (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 (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 (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 (* (/ 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
67.0ms	n	@	0	((* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (/ 1 (sqrt k)) (sqrt k) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2)) (* (* 2 (PI)) n))
33.0ms	n	@	inf	((* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (/ 1 (sqrt k)) (sqrt k) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2)) (* (* 2 (PI)) n))
26.0ms	n	@	-inf	((* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (/ 1 (sqrt k)) (sqrt k) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2)) (* (* 2 (PI)) n))
3.0ms	k	@	-inf	((* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (/ 1 (sqrt k)) (sqrt k) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2)) (* (* 2 (PI)) n))
2.0ms	k	@	0	((* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (/ 1 (sqrt k)) (sqrt k) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2)) (* (* 2 (PI)) n))

simplify126.0ms (1.4%)

Memory

28.4MiB live, 162.9MiB allocated; 12ms collecting garbage

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	147	780
1	415	749
2	1485	713
0	5250	683

Stop Event

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

Counts

22 → 22

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

rewrite200.0ms (2.1%)

Memory

-58.4MiB live, 114.8MiB allocated; 136ms collecting garbage

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	13	38
0	22	38
1	83	35
0	500	35

Stop Event

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

Counts

5 → 58

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

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)))
(*.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)))
(.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)))

eval9.0ms (0.1%)

Memory: 20.3MiB live, 20.3MiB allocated; 0ms collecting garbage
Compiler: Compiled 1 816 to 305 computations (83.2% saved)

prune20.0ms (0.2%)

Memory

-16.4MiB live, 30.6MiB allocated; 2ms collecting garbage

Pruning

15 alts after pruning (15 fresh and 0 done)

	Pruned	Kept	Total
New	60	15	75
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	61	15	76

Accuracy

100.0%

Counts

76 → 15

Alt Table

Click to see full alt table

Status	Accuracy	Program
	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))) (sqrt.f64 k))
	76.7%	(.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))))
	98.9%	(.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)))
	99.5%	(.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) (pow.f64 (fma.f64 (sqrt.f64 (PI.f64)) (.f64 (sqrt.f64 (PI.f64)) n) (*.f64 n (PI.f64))) (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 2 binary64))))
	99.0%	(.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)) (/.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)))))
▶	76.7%	(.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) (.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)))))
	95.8%	(.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)))))
▶	54.1%	(.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) #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)))))
	53.3%	(.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)))))
	99.1%	(.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) #s(approx (pow ( (* 2 (PI)) n) (/ (- 1 k) 2)) (sqrt.f64 (pow.f64 (.f64 (.f64 (PI.f64) n) #s(literal 2 binary64)) (-.f64 #s(literal 1 binary64) k)))))
	57.6%	#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))
▶	99.2%	#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (.f64 (sqrt.f64 (pow.f64 (.f64 (*.f64 (PI.f64) n) #s(literal 2 binary64)) (-.f64 #s(literal 1 binary64) k))) (sqrt.f64 (/.f64 #s(literal 1 binary64) k))))
▶	39.5%	#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 736 to 552 computations (25% saved)

simplify117.0ms (1.3%)

Memory

14.4MiB live, 197.4MiB allocated; 17ms collecting garbage

Localize:

Found 20 expressions of interest:

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

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	49	423
0	82	423
1	128	415
2	207	415
3	485	415
4	2002	415
0	8214	401

Stop Event

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

Calls

Call 1

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

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

localize211.0ms (2.3%)

Memory

-17.1MiB live, 320.5MiB allocated; 25ms collecting garbage

Localize:

Found 20 expressions of interest:

New	Metric	Score
accuracy	0.18359375	(/.f64 #s(literal 1 binary64) (sqrt.f64 k))
accuracy	0.25390625	(.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))))
accuracy	0.5078125	(pow.f64 (*.f64 (PI.f64) #s(literal 2 binary64)) (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 2 binary64)))
accuracy	14.046533023192962	(PI.f64)
accuracy	0.2109375	(*.f64 (PI.f64) n)
accuracy	0.28515625	(.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)))
accuracy	14.046533023192962	(PI.f64)
accuracy	15.119942353472867	#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))))
accuracy	0.1404475845155633	(pow.f64 (.f64 (.f64 (PI.f64) n) #s(literal 2 binary64)) (-.f64 #s(literal 1 binary64) k))
accuracy	0.1640625	(.f64 (sqrt.f64 (pow.f64 (.f64 (*.f64 (PI.f64) n) #s(literal 2 binary64)) (-.f64 #s(literal 1 binary64) k))) (sqrt.f64 (/.f64 #s(literal 1 binary64) k)))
accuracy	0.2109375	(*.f64 (PI.f64) n)
accuracy	14.046533023192962	(PI.f64)
accuracy	0.3590812988422101	(.f64 (sqrt.f64 #s(literal 2 binary64)) (sqrt.f64 (/.f64 (.f64 (PI.f64) n) k)))
accuracy	9.015977063218699	(sqrt.f64 (/.f64 (*.f64 (PI.f64) n) k))
accuracy	14.046533023192962	(PI.f64)
accuracy	15.423160254970837	#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (.f64 (sqrt.f64 #s(literal 2 binary64)) (sqrt.f64 (/.f64 (.f64 (PI.f64) n) k))))
accuracy	0.1640625	(.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)))
accuracy	0.16630692927829482	(pow.f64 (.f64 n (.f64 (PI.f64) #s(literal 2 binary64))) (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 2 binary64)))
accuracy	0.2109375	(.f64 n (.f64 (PI.f64) #s(literal 2 binary64)))
accuracy	14.046533023192962	(PI.f64)

Samples

105.0ms	198×	valid
39.0ms	57×	exit
0.0ms	1×	invalid

Compiler

Compiled 362 to 43 computations (88.1% saved)

Precisions

Click to see histograms. Total time spent on operations: 108.0ms

ival-pow: 44.0ms (40.6% of total)

ival-sqrt: 26.0ms (24% of total)

ival-mult: 23.0ms (21.2% of total)

ival-div: 8.0ms (7.4% of total)

ival-log: 3.0ms (2.8% of total)

ival-add: 2.0ms (1.8% of total)

ival-pi: 1.0ms (0.9% of total)

ival-sub: 1.0ms (0.9% 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)

series235.0ms (2.5%)

Memory

14.0MiB live, 246.2MiB allocated; 34ms collecting garbage

Counts

22 → 109

Calls

Call 1

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

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

Calls

6 calls:

Time	Variable		Point	Expression
75.0ms	n	@	0	((/ (- 1 k) 2) (* (pow (* n (* (PI) 2)) (/ (- 1 k) 2)) (pow k -1/2)) (pow (* n (* (PI) 2)) (/ (- 1 k) 2)) (* n (* (PI) 2)) (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (* (sqrt 2) (sqrt (/ (* (PI) n) k))) (sqrt 2) (sqrt (/ (* (PI) n) k)) (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (* (sqrt (pow (* (* (PI) n) 2) (- 1 k))) (sqrt (/ 1 k))) (sqrt (pow (* (* (PI) n) 2) (- 1 k))) (pow (* (* (PI) n) 2) (- 1 k)) (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (/ 1 (sqrt k)) (sqrt k) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2)) (* (/ 1 (sqrt k)) (* (pow (* (PI) 2) (/ (- 1 k) 2)) (pow n (/ (- 1 k) 2)))) (PI) (* (PI) n) (* (* (+ (* (* (log (* (* (PI) n) 2)) k) -1/2) 1) (sqrt 2)) (sqrt (* (PI) n))) (pow (* (PI) 2) (/ (- 1 k) 2)) (* (pow (* (PI) 2) (/ (- 1 k) 2)) (pow n (/ (- 1 k) 2))))
67.0ms	n	@	-inf	((/ (- 1 k) 2) (* (pow (* n (* (PI) 2)) (/ (- 1 k) 2)) (pow k -1/2)) (pow (* n (* (PI) 2)) (/ (- 1 k) 2)) (* n (* (PI) 2)) (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (* (sqrt 2) (sqrt (/ (* (PI) n) k))) (sqrt 2) (sqrt (/ (* (PI) n) k)) (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (* (sqrt (pow (* (* (PI) n) 2) (- 1 k))) (sqrt (/ 1 k))) (sqrt (pow (* (* (PI) n) 2) (- 1 k))) (pow (* (* (PI) n) 2) (- 1 k)) (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (/ 1 (sqrt k)) (sqrt k) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2)) (* (/ 1 (sqrt k)) (* (pow (* (PI) 2) (/ (- 1 k) 2)) (pow n (/ (- 1 k) 2)))) (PI) (* (PI) n) (* (* (+ (* (* (log (* (* (PI) n) 2)) k) -1/2) 1) (sqrt 2)) (sqrt (* (PI) n))) (pow (* (PI) 2) (/ (- 1 k) 2)) (* (pow (* (PI) 2) (/ (- 1 k) 2)) (pow n (/ (- 1 k) 2))))
43.0ms	n	@	inf	((/ (- 1 k) 2) (* (pow (* n (* (PI) 2)) (/ (- 1 k) 2)) (pow k -1/2)) (pow (* n (* (PI) 2)) (/ (- 1 k) 2)) (* n (* (PI) 2)) (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (* (sqrt 2) (sqrt (/ (* (PI) n) k))) (sqrt 2) (sqrt (/ (* (PI) n) k)) (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (* (sqrt (pow (* (* (PI) n) 2) (- 1 k))) (sqrt (/ 1 k))) (sqrt (pow (* (* (PI) n) 2) (- 1 k))) (pow (* (* (PI) n) 2) (- 1 k)) (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (/ 1 (sqrt k)) (sqrt k) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2)) (* (/ 1 (sqrt k)) (* (pow (* (PI) 2) (/ (- 1 k) 2)) (pow n (/ (- 1 k) 2)))) (PI) (* (PI) n) (* (* (+ (* (* (log (* (* (PI) n) 2)) k) -1/2) 1) (sqrt 2)) (sqrt (* (PI) n))) (pow (* (PI) 2) (/ (- 1 k) 2)) (* (pow (* (PI) 2) (/ (- 1 k) 2)) (pow n (/ (- 1 k) 2))))
29.0ms	k	@	-inf	((/ (- 1 k) 2) (* (pow (* n (* (PI) 2)) (/ (- 1 k) 2)) (pow k -1/2)) (pow (* n (* (PI) 2)) (/ (- 1 k) 2)) (* n (* (PI) 2)) (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (* (sqrt 2) (sqrt (/ (* (PI) n) k))) (sqrt 2) (sqrt (/ (* (PI) n) k)) (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (* (sqrt (pow (* (* (PI) n) 2) (- 1 k))) (sqrt (/ 1 k))) (sqrt (pow (* (* (PI) n) 2) (- 1 k))) (pow (* (* (PI) n) 2) (- 1 k)) (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (/ 1 (sqrt k)) (sqrt k) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2)) (* (/ 1 (sqrt k)) (* (pow (* (PI) 2) (/ (- 1 k) 2)) (pow n (/ (- 1 k) 2)))) (PI) (* (PI) n) (* (* (+ (* (* (log (* (* (PI) n) 2)) k) -1/2) 1) (sqrt 2)) (sqrt (* (PI) n))) (pow (* (PI) 2) (/ (- 1 k) 2)) (* (pow (* (PI) 2) (/ (- 1 k) 2)) (pow n (/ (- 1 k) 2))))
12.0ms	k	@	0	((/ (- 1 k) 2) (* (pow (* n (* (PI) 2)) (/ (- 1 k) 2)) (pow k -1/2)) (pow (* n (* (PI) 2)) (/ (- 1 k) 2)) (* n (* (PI) 2)) (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (* (sqrt 2) (sqrt (/ (* (PI) n) k))) (sqrt 2) (sqrt (/ (* (PI) n) k)) (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (* (sqrt (pow (* (* (PI) n) 2) (- 1 k))) (sqrt (/ 1 k))) (sqrt (pow (* (* (PI) n) 2) (- 1 k))) (pow (* (* (PI) n) 2) (- 1 k)) (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (/ 1 (sqrt k)) (sqrt k) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2)) (* (/ 1 (sqrt k)) (* (pow (* (PI) 2) (/ (- 1 k) 2)) (pow n (/ (- 1 k) 2)))) (PI) (* (PI) n) (* (* (+ (* (* (log (* (* (PI) n) 2)) k) -1/2) 1) (sqrt 2)) (sqrt (* (PI) n))) (pow (* (PI) 2) (/ (- 1 k) 2)) (* (pow (* (PI) 2) (/ (- 1 k) 2)) (pow n (/ (- 1 k) 2))))

simplify178.0ms (1.9%)

Memory

39.6MiB live, 219.4MiB allocated; 34ms collecting garbage

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	534	4454
1	1634	4112
2	7222	4008
0	8216	3868

Stop Event

1×	iter limit
1×	node limit

Counts

109 → 109

Calls

Call 1

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

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

rewrite69.0ms (0.7%)

Memory

-2.8MiB live, 99.5MiB allocated; 17ms collecting garbage

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	49	289
0	82	262
1	245	250
0	1228	250

Stop Event

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

Counts

22 → 361

Calls

Call 1

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

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

eval79.0ms (0.8%)

Memory: -33.0MiB live, 107.4MiB allocated; 25ms collecting garbage
Compiler: Compiled 13 193 to 1 496 computations (88.7% saved)

prune22.0ms (0.2%)

Memory

11.6MiB live, 56.9MiB allocated; 5ms collecting garbage

Pruning

17 alts after pruning (16 fresh and 1 done)

	Pruned	Kept	Total
New	385	13	398
Fresh	7	3	10
Picked	4	1	5
Done	0	0	0
Total	396	17	413

Accuracy

100.0%

Counts

413 → 17

Alt Table

Click to see full alt table

Status	Accuracy	Program
	54.2%	(/.f64 #s(approx (pow (* (* 2 (PI)) n) (/ (- 1 k) 2)) (.f64 (sqrt.f64 (.f64 (.f64 (PI.f64) n) #s(literal 2 binary64))) (fma.f64 (.f64 #s(literal -1/2 binary64) k) (log.f64 (.f64 (.f64 (PI.f64) n) #s(literal 2 binary64))) #s(literal 1 binary64)))) (sqrt.f64 k))
	99.3%	(.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)))))
	53.3%	(.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)))))
	99.5%	(.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) #s(approx ( (pow (* (PI) 2) (/ (- 1 k) 2)) (pow 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)))))
▶	99.6%	#s(approx (* (pow (* n (* (PI) 2)) (/ (- 1 k) 2)) (pow k -1/2)) (.f64 (pow.f64 (/.f64 (.f64 #s(literal -2 binary64) (PI.f64)) (/.f64 #s(literal -1 binary64) n)) (fma.f64 #s(literal -1/2 binary64) k #s(literal 1/2 binary64))) (sqrt.f64 (/.f64 #s(literal 1 binary64) k))))
	57.6%	#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))
	53.5%	#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)))
▶	99.3%	#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (.f64 (sqrt.f64 (/.f64 (.f64 (.f64 (PI.f64) n) #s(literal 2 binary64)) (pow.f64 (.f64 (*.f64 (PI.f64) n) #s(literal 2 binary64)) k))) (sqrt.f64 (/.f64 #s(literal 1 binary64) k))))
	53.5%	#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (.f64 (sqrt.f64 #s(approx (pow ( (* (PI) n) 2) (- 1 k)) (.f64 (.f64 (PI.f64) n) #s(literal 2 binary64)))) (sqrt.f64 (/.f64 #s(literal 1 binary64) k))))
▶	53.3%	#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))))
	53.4%	#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (.f64 (sqrt.f64 #s(literal 2 binary64)) (.f64 (sqrt.f64 (PI.f64)) (/.f64 (sqrt.f64 n) (sqrt.f64 k)))))
	39.5%	#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)))))
	39.5%	#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (.f64 (sqrt.f64 #s(literal 2 binary64)) (sqrt.f64 (/.f64 (.f64 (*.f64 n (sqrt.f64 (PI.f64))) (sqrt.f64 (PI.f64))) k))))
✓	39.5%	#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))))
▶	39.6%	#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))))
	24.0%	#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) #s(approx (* (sqrt (pow (* (* (PI) n) 2) (- 1 k))) (sqrt (/ 1 k))) (.f64 (sqrt.f64 (/.f64 (pow.f64 (.f64 (*.f64 (PI.f64) n) #s(literal 2 binary64)) (-.f64 #s(literal 1 binary64) k)) k)) #s(literal -1 binary64))))
▶	85.4%	#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) #s(approx (* (sqrt (pow (* (* (PI) n) 2) (- 1 k))) (sqrt (/ 1 k))) (sqrt.f64 (/.f64 (pow.f64 (.f64 (.f64 (PI.f64) n) #s(literal 2 binary64)) (-.f64 #s(literal 1 binary64) k)) k))))

Compiler

Compiled 1 064 to 803 computations (24.5% saved)

simplify131.0ms (1.4%)

Memory

-12.6MiB live, 226.5MiB allocated; 39ms collecting garbage

Localize:

Found 20 expressions of interest:

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

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	62	435
0	91	439
1	130	419
2	206	419
3	509	414
4	2169	414
0	8093	414

Stop Event

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

Calls

Call 1

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

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

localize160.0ms (1.7%)

Memory

20.4MiB live, 397.2MiB allocated; 44ms collecting garbage

Localize:

Found 20 expressions of interest:

New	Metric	Score
accuracy	0.0859375	(sqrt.f64 (/.f64 #s(literal 1 binary64) k))
accuracy	0.1640625	(.f64 (sqrt.f64 (/.f64 (.f64 (.f64 (PI.f64) n) #s(literal 2 binary64)) (pow.f64 (.f64 (*.f64 (PI.f64) n) #s(literal 2 binary64)) k))) (sqrt.f64 (/.f64 #s(literal 1 binary64) k)))
accuracy	0.2109375	(*.f64 (PI.f64) n)
accuracy	14.046533023192962	(PI.f64)
accuracy	0.1404475845155633	(pow.f64 (.f64 (.f64 (PI.f64) n) #s(literal 2 binary64)) (-.f64 #s(literal 1 binary64) k))
accuracy	0.2109375	(*.f64 (PI.f64) n)
accuracy	8.980395849524317	(sqrt.f64 (/.f64 (pow.f64 (.f64 (.f64 (PI.f64) n) #s(literal 2 binary64)) (-.f64 #s(literal 1 binary64) k)) k))
accuracy	14.046533023192962	(PI.f64)
accuracy	0.3046875	(/.f64 (sqrt.f64 (*.f64 (PI.f64) n)) (sqrt.f64 k))
accuracy	0.3590812988422101	(.f64 (sqrt.f64 #s(literal 2 binary64)) (/.f64 (sqrt.f64 (.f64 (PI.f64) n)) (sqrt.f64 k)))
accuracy	14.046533023192962	(PI.f64)
accuracy	15.423160254970837	#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (.f64 (sqrt.f64 #s(literal 2 binary64)) (/.f64 (sqrt.f64 (.f64 (PI.f64) n)) (sqrt.f64 k))))
accuracy	0.2109375	(*.f64 (PI.f64) n)
accuracy	9.007739599524317	(sqrt.f64 (.f64 (/.f64 (.f64 (PI.f64) n) k) #s(literal 2 binary64)))
accuracy	14.046533023192962	(PI.f64)
accuracy	15.423160254970837	#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt.f64 (.f64 (/.f64 (.f64 (PI.f64) n) k) #s(literal 2 binary64))))
accuracy	0.1640625	(.f64 (pow.f64 (/.f64 (.f64 #s(literal -2 binary64) (PI.f64)) (/.f64 #s(literal -1 binary64) n)) (fma.f64 #s(literal -1/2 binary64) k #s(literal 1/2 binary64))) (sqrt.f64 (/.f64 #s(literal 1 binary64) k)))
accuracy	0.16630692927829482	(pow.f64 (/.f64 (*.f64 #s(literal -2 binary64) (PI.f64)) (/.f64 #s(literal -1 binary64) n)) (fma.f64 #s(literal -1/2 binary64) k #s(literal 1/2 binary64)))
accuracy	0.2578125	(/.f64 (*.f64 #s(literal -2 binary64) (PI.f64)) (/.f64 #s(literal -1 binary64) n))
accuracy	14.046533023192962	(PI.f64)

Samples

97.0ms	198×	valid
25.0ms	57×	exit
1.0ms	1×	invalid

Compiler

Compiled 340 to 51 computations (85% saved)

Precisions

Click to see histograms. Total time spent on operations: 99.0ms

ival-mult: 27.0ms (27.4% of total)

ival-pow: 27.0ms (27.4% of total)

ival-div: 19.0ms (19.3% of total)

ival-sqrt: 17.0ms (17.2% of total)

ival-sub: 5.0ms (5.1% of total)

ival-pi: 1.0ms (1% of total)

ival-add: 1.0ms (1% of total)

exact: 1.0ms (1% of total)

adjust: 0.0ms (0% of total)

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

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

series103.0ms (1.1%)

Memory

30.3MiB live, 219.6MiB allocated; 51ms collecting garbage

Counts

24 → 110

Calls

Call 1

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

Outputs
#s(approx (* (pow (* n (* (PI) 2)) (/ (- 1 k) 2)) (pow k -1/2)) #s(hole binary64 (* (sqrt (/ (* n (PI)) k)) (sqrt 2))))
#s(approx (* (pow (* n (* (PI) 2)) (/ (- 1 k) 2)) (pow 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 (* (pow (* n (* (PI) 2)) (/ (- 1 k) 2)) (pow 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 (* (pow (* n (* (PI) 2)) (/ (- 1 k) 2)) (pow 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 (* (pow (/ (* -2 (PI)) (/ -1 n)) (+ (* -1/2 k) 1/2)) (sqrt (/ 1 k))) #s(hole binary64 (* (sqrt (/ (* n (PI)) k)) (sqrt 2))))
#s(approx (* (pow (/ (* -2 (PI)) (/ -1 n)) (+ (* -1/2 k) 1/2)) (sqrt (/ 1 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 (* (pow (/ (* -2 (PI)) (/ -1 n)) (+ (* -1/2 k) 1/2)) (sqrt (/ 1 k))) #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 (* (pow (/ (* -2 (PI)) (/ -1 n)) (+ (* -1/2 k) 1/2)) (sqrt (/ 1 k))) #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 (PI)) (/ -1 n)) (+ (* -1/2 k) 1/2)) #s(hole binary64 (* (sqrt (* n (PI))) (sqrt 2))))
#s(approx (pow (/ (* -2 (PI)) (/ -1 n)) (+ (* -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 (/ (* -2 (PI)) (/ -1 n)) (+ (* -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 (/ (* -2 (PI)) (/ -1 n)) (+ (* -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)))))
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Calls

6 calls:

Time	Variable		Point	Expression
28.0ms	n	@	inf	((/ (* -2 (PI)) (/ -1 n)) (* (pow (* n (* (PI) 2)) (/ (- 1 k) 2)) (pow k -1/2)) (* (pow (/ (* -2 (PI)) (/ -1 n)) (+ (* -1/2 k) 1/2)) (sqrt (/ 1 k))) (pow (/ (* -2 (PI)) (/ -1 n)) (+ (* -1/2 k) 1/2)) (* (/ 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) (/ (sqrt (* (PI) n)) (sqrt k))) (sqrt 2) (/ (sqrt (* (PI) n)) (sqrt k)) (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (* (sqrt (pow (* (* (PI) n) 2) (- 1 k))) (sqrt (/ 1 k))) (sqrt (/ (pow (* (* (PI) n) 2) (- 1 k)) k)) (/ (pow (* (* (PI) n) 2) (- 1 k)) k) (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (* (sqrt (/ (* (* (PI) n) 2) (pow (* (* (PI) n) 2) k))) (sqrt (/ 1 k))) (sqrt (/ (* (* (PI) n) 2) (pow (* (* (PI) n) 2) k))) (/ (* (* (PI) n) 2) (pow (* (* (PI) n) 2) k)) (PI) (* (PI) n) (pow (* (* (PI) n) 2) (- 1 k)) (sqrt (/ 1 k)))
28.0ms	n	@	-inf	((/ (* -2 (PI)) (/ -1 n)) (* (pow (* n (* (PI) 2)) (/ (- 1 k) 2)) (pow k -1/2)) (* (pow (/ (* -2 (PI)) (/ -1 n)) (+ (* -1/2 k) 1/2)) (sqrt (/ 1 k))) (pow (/ (* -2 (PI)) (/ -1 n)) (+ (* -1/2 k) 1/2)) (* (/ 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) (/ (sqrt (* (PI) n)) (sqrt k))) (sqrt 2) (/ (sqrt (* (PI) n)) (sqrt k)) (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (* (sqrt (pow (* (* (PI) n) 2) (- 1 k))) (sqrt (/ 1 k))) (sqrt (/ (pow (* (* (PI) n) 2) (- 1 k)) k)) (/ (pow (* (* (PI) n) 2) (- 1 k)) k) (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (* (sqrt (/ (* (* (PI) n) 2) (pow (* (* (PI) n) 2) k))) (sqrt (/ 1 k))) (sqrt (/ (* (* (PI) n) 2) (pow (* (* (PI) n) 2) k))) (/ (* (* (PI) n) 2) (pow (* (* (PI) n) 2) k)) (PI) (* (PI) n) (pow (* (* (PI) n) 2) (- 1 k)) (sqrt (/ 1 k)))
17.0ms	n	@	0	((/ (* -2 (PI)) (/ -1 n)) (* (pow (* n (* (PI) 2)) (/ (- 1 k) 2)) (pow k -1/2)) (* (pow (/ (* -2 (PI)) (/ -1 n)) (+ (* -1/2 k) 1/2)) (sqrt (/ 1 k))) (pow (/ (* -2 (PI)) (/ -1 n)) (+ (* -1/2 k) 1/2)) (* (/ 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) (/ (sqrt (* (PI) n)) (sqrt k))) (sqrt 2) (/ (sqrt (* (PI) n)) (sqrt k)) (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (* (sqrt (pow (* (* (PI) n) 2) (- 1 k))) (sqrt (/ 1 k))) (sqrt (/ (pow (* (* (PI) n) 2) (- 1 k)) k)) (/ (pow (* (* (PI) n) 2) (- 1 k)) k) (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (* (sqrt (/ (* (* (PI) n) 2) (pow (* (* (PI) n) 2) k))) (sqrt (/ 1 k))) (sqrt (/ (* (* (PI) n) 2) (pow (* (* (PI) n) 2) k))) (/ (* (* (PI) n) 2) (pow (* (* (PI) n) 2) k)) (PI) (* (PI) n) (pow (* (* (PI) n) 2) (- 1 k)) (sqrt (/ 1 k)))
14.0ms	k	@	-inf	((/ (* -2 (PI)) (/ -1 n)) (* (pow (* n (* (PI) 2)) (/ (- 1 k) 2)) (pow k -1/2)) (* (pow (/ (* -2 (PI)) (/ -1 n)) (+ (* -1/2 k) 1/2)) (sqrt (/ 1 k))) (pow (/ (* -2 (PI)) (/ -1 n)) (+ (* -1/2 k) 1/2)) (* (/ 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) (/ (sqrt (* (PI) n)) (sqrt k))) (sqrt 2) (/ (sqrt (* (PI) n)) (sqrt k)) (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (* (sqrt (pow (* (* (PI) n) 2) (- 1 k))) (sqrt (/ 1 k))) (sqrt (/ (pow (* (* (PI) n) 2) (- 1 k)) k)) (/ (pow (* (* (PI) n) 2) (- 1 k)) k) (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (* (sqrt (/ (* (* (PI) n) 2) (pow (* (* (PI) n) 2) k))) (sqrt (/ 1 k))) (sqrt (/ (* (* (PI) n) 2) (pow (* (* (PI) n) 2) k))) (/ (* (* (PI) n) 2) (pow (* (* (PI) n) 2) k)) (PI) (* (PI) n) (pow (* (* (PI) n) 2) (- 1 k)) (sqrt (/ 1 k)))
6.0ms	k	@	0	((/ (* -2 (PI)) (/ -1 n)) (* (pow (* n (* (PI) 2)) (/ (- 1 k) 2)) (pow k -1/2)) (* (pow (/ (* -2 (PI)) (/ -1 n)) (+ (* -1/2 k) 1/2)) (sqrt (/ 1 k))) (pow (/ (* -2 (PI)) (/ -1 n)) (+ (* -1/2 k) 1/2)) (* (/ 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) (/ (sqrt (* (PI) n)) (sqrt k))) (sqrt 2) (/ (sqrt (* (PI) n)) (sqrt k)) (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (* (sqrt (pow (* (* (PI) n) 2) (- 1 k))) (sqrt (/ 1 k))) (sqrt (/ (pow (* (* (PI) n) 2) (- 1 k)) k)) (/ (pow (* (* (PI) n) 2) (- 1 k)) k) (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (* (sqrt (/ (* (* (PI) n) 2) (pow (* (* (PI) n) 2) k))) (sqrt (/ 1 k))) (sqrt (/ (* (* (PI) n) 2) (pow (* (* (PI) n) 2) k))) (/ (* (* (PI) n) 2) (pow (* (* (PI) n) 2) k)) (PI) (* (PI) n) (pow (* (* (PI) n) 2) (- 1 k)) (sqrt (/ 1 k)))

simplify301.0ms (3.2%)

Memory

2.9MiB live, 407.8MiB allocated; 100ms collecting garbage

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	487	4375
1	1439	4156
2	6404	4129
0	9010	4016

Stop Event

1×	iter limit
1×	node limit

Counts

110 → 110

Calls

Call 1

Inputs
#s(approx (* (pow (* n (* (PI) 2)) (/ (- 1 k) 2)) (pow k -1/2)) #s(hole binary64 (* (sqrt (/ (* n (PI)) k)) (sqrt 2))))
#s(approx (* (pow (* n (* (PI) 2)) (/ (- 1 k) 2)) (pow 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 (* (pow (* n (* (PI) 2)) (/ (- 1 k) 2)) (pow 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 (* (pow (* n (* (PI) 2)) (/ (- 1 k) 2)) (pow 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 (* (pow (/ (* -2 (PI)) (/ -1 n)) (+ (* -1/2 k) 1/2)) (sqrt (/ 1 k))) #s(hole binary64 (* (sqrt (/ (* n (PI)) k)) (sqrt 2))))
#s(approx (* (pow (/ (* -2 (PI)) (/ -1 n)) (+ (* -1/2 k) 1/2)) (sqrt (/ 1 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 (* (pow (/ (* -2 (PI)) (/ -1 n)) (+ (* -1/2 k) 1/2)) (sqrt (/ 1 k))) #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 (* (pow (/ (* -2 (PI)) (/ -1 n)) (+ (* -1/2 k) 1/2)) (sqrt (/ 1 k))) #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 (PI)) (/ -1 n)) (+ (* -1/2 k) 1/2)) #s(hole binary64 (* (sqrt (* n (PI))) (sqrt 2))))
#s(approx (pow (/ (* -2 (PI)) (/ -1 n)) (+ (* -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 (/ (* -2 (PI)) (/ -1 n)) (+ (* -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 (/ (* -2 (PI)) (/ -1 n)) (+ (* -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 (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) (/ (sqrt (* (PI) n)) (sqrt k))) #s(hole binary64 (* (sqrt (/ (* n (PI)) k)) (sqrt 2))))
#s(approx (/ (sqrt (* (PI) n)) (sqrt k)) #s(hole binary64 (sqrt (/ (* n (PI)) k))))
#s(approx (* (sqrt (pow (* (* (PI) n) 2) (- 1 k))) (sqrt (/ 1 k))) #s(hole binary64 (* (sqrt (/ (* n (PI)) k)) (sqrt 2))))
#s(approx (* (sqrt (pow (* (* (PI) n) 2) (- 1 k))) (sqrt (/ 1 k))) #s(hole binary64 (/ (+ (* -1 (* (sqrt (* (pow k 3) (* n (PI)))) (/ (log (* 2 (* n (PI)))) (sqrt 2)))) (* (sqrt (* k (* n (PI)))) (sqrt 2))) k)))
#s(approx (* (sqrt (pow (* (* (PI) n) 2) (- 1 k))) (sqrt (/ 1 k))) #s(hole binary64 (/ (+ (* (sqrt (* k (* n (PI)))) (sqrt 2)) (* (pow k 2) (+ (* -1 (* (sqrt (/ (* n (PI)) k)) (/ (log (* 2 (* n (PI)))) (sqrt 2)))) (* 1/2 (* (sqrt (* k (* n (PI)))) (/ (pow (log (* 2 (* n (PI)))) 2) (sqrt 2))))))) k)))
#s(approx (* (sqrt (pow (* (* (PI) n) 2) (- 1 k))) (sqrt (/ 1 k))) #s(hole binary64 (/ (+ (* (sqrt (* k (* n (PI)))) (sqrt 2)) (* (pow k 2) (+ (* -1 (* (sqrt (/ (* n (PI)) k)) (/ (log (* 2 (* n (PI)))) (sqrt 2)))) (* k (+ (* 1/2 (* (sqrt (/ k (* n (PI)))) (/ (- (* -1/3 (* n (* (PI) (pow (log (* 2 (* n (PI)))) 3)))) (/ (* n (* (PI) (pow (log (* 2 (* n (PI)))) 2))) (* k (pow (sqrt 2) 2)))) (sqrt 2)))) (* 1/2 (* (sqrt (/ (* n (PI)) k)) (/ (pow (log (* 2 (* n (PI)))) 2) (sqrt 2))))))))) k)))
#s(approx (sqrt (/ (pow (* (* (PI) n) 2) (- 1 k)) k)) #s(hole binary64 (* (sqrt (/ (* n (PI)) k)) (sqrt 2))))
#s(approx (sqrt (/ (pow (* (* (PI) n) 2) (- 1 k)) k)) #s(hole binary64 (/ (+ (* -1 (* (sqrt (* (pow k 3) (* n (PI)))) (/ (log (* 2 (* n (PI)))) (sqrt 2)))) (* (sqrt (* k (* n (PI)))) (sqrt 2))) k)))
#s(approx (sqrt (/ (pow (* (* (PI) n) 2) (- 1 k)) k)) #s(hole binary64 (/ (+ (* (sqrt (* k (* n (PI)))) (sqrt 2)) (* (pow k 2) (+ (* -1 (* (sqrt (/ (* n (PI)) k)) (/ (log (* 2 (* n (PI)))) (sqrt 2)))) (* 1/2 (* (sqrt (* k (* n (PI)))) (/ (pow (log (* 2 (* n (PI)))) 2) (sqrt 2))))))) k)))
#s(approx (sqrt (/ (pow (* (* (PI) n) 2) (- 1 k)) k)) #s(hole binary64 (/ (+ (* (sqrt (* k (* n (PI)))) (sqrt 2)) (* (pow k 2) (+ (* -1 (* (sqrt (/ (* n (PI)) k)) (/ (log (* 2 (* n (PI)))) (sqrt 2)))) (* k (+ (* 1/2 (* (sqrt (/ k (* n (PI)))) (/ (- (* -1/3 (* n (* (PI) (pow (log (* 2 (* n (PI)))) 3)))) (/ (* n (* (PI) (pow (log (* 2 (* n (PI)))) 2))) (* k (pow (sqrt 2) 2)))) (sqrt 2)))) (* 1/2 (* (sqrt (/ (* n (PI)) k)) (/ (pow (log (* 2 (* n (PI)))) 2) (sqrt 2))))))))) k)))
#s(approx (/ (pow (* (* (PI) n) 2) (- 1 k)) k) #s(hole binary64 (* 2 (/ (* n (PI)) k))))
#s(approx (/ (pow (* (* (PI) n) 2) (- 1 k)) k) #s(hole binary64 (/ (+ (* -2 (* k (* n (* (PI) (log (* 2 (* n (PI)))))))) (* 2 (* n (PI)))) k)))
#s(approx (/ (pow (* (* (PI) n) 2) (- 1 k)) k) #s(hole binary64 (/ (+ (* 2 (* n (PI))) (* k (+ (* -2 (* n (* (PI) (log (* 2 (* n (PI))))))) (* k (* n (* (PI) (pow (log (* 2 (* n (PI)))) 2))))))) k)))
#s(approx (/ (pow (* (* (PI) n) 2) (- 1 k)) k) #s(hole binary64 (/ (+ (* 2 (* n (PI))) (* k (+ (* -2 (* n (* (PI) (log (* 2 (* n (PI))))))) (* k (+ (* -1/3 (* k (* n (* (PI) (pow (log (* 2 (* n (PI)))) 3))))) (* n (* (PI) (pow (log (* 2 (* n (PI)))) 2)))))))) k)))
#s(approx (* (sqrt (/ (* (* (PI) n) 2) (pow (* (* (PI) n) 2) k))) (sqrt (/ 1 k))) #s(hole binary64 (* (sqrt (/ (* n (PI)) k)) (sqrt 2))))
#s(approx (* (sqrt (/ (* (* (PI) n) 2) (pow (* (* (PI) n) 2) k))) (sqrt (/ 1 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 (/ (* (* (PI) n) 2) (pow (* (* (PI) n) 2) k))) (sqrt (/ 1 k))) #s(hole binary64 (/ (+ (* (sqrt (* k (* n (PI)))) (sqrt 2)) (* (pow k 2) (+ (* -1/2 (* (sqrt (/ k (* n (PI)))) (* (sqrt 2) (+ (* -1 (* n (* (PI) (pow (log (* 2 (* n (PI)))) 2)))) (* 1/2 (* n (* (PI) (pow (log (* 2 (* n (PI)))) 2)))))))) (* -1/2 (* (sqrt (/ (* n (PI)) k)) (* (log (* 2 (* n (PI)))) (sqrt 2))))))) k)))
#s(approx (* (sqrt (/ (* (* (PI) n) 2) (pow (* (* (PI) n) 2) k))) (sqrt (/ 1 k))) #s(hole binary64 (/ (+ (* (sqrt (* k (* n (PI)))) (sqrt 2)) (* (pow k 2) (+ (* -1/2 (* (sqrt (/ (* n (PI)) k)) (* (log (* 2 (* n (PI)))) (sqrt 2)))) (* k (+ (* -1/2 (* (sqrt (/ 1 (* k (* n (PI))))) (* (sqrt 2) (+ (* -1 (* n (* (PI) (pow (log (* 2 (* n (PI)))) 2)))) (* 1/2 (* n (* (PI) (pow (log (* 2 (* n (PI)))) 2)))))))) (* -1/2 (* (sqrt (/ k (* n (PI)))) (* (sqrt 2) (+ (* -1 (* (log (* 2 (* n (PI)))) (+ (* -1 (* n (* (PI) (pow (log (* 2 (* n (PI)))) 2)))) (* 1/2 (* n (* (PI) (pow (log (* 2 (* n (PI)))) 2))))))) (+ (* -1/2 (* n (* (PI) (pow (log (* 2 (* n (PI)))) 3)))) (+ (* 1/6 (* n (* (PI) (pow (log (* 2 (* n (PI)))) 3)))) (* 1/4 (/ (* n (* (PI) (pow (log (* 2 (* n (PI)))) 2))) k))))))))))))) k)))
#s(approx (sqrt (/ (* (* (PI) n) 2) (pow (* (* (PI) n) 2) k))) #s(hole binary64 (* (sqrt (* n (PI))) (sqrt 2))))
#s(approx (sqrt (/ (* (* (PI) n) 2) (pow (* (* (PI) n) 2) k))) #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))) #s(hole binary64 (+ (* k (+ (* -1/2 (* (sqrt (* n (PI))) (* (log (* 2 (* n (PI)))) (sqrt 2)))) (* -1/2 (* (* k (* (sqrt 2) (+ (* -1 (* n (* (PI) (pow (log (* 2 (* n (PI)))) 2)))) (+ (* 1/4 (* n (* (PI) (pow (log (* 2 (* n (PI)))) 2)))) (* 1/2 (* n (* (PI) (pow (log (* 2 (* n (PI)))) 2)))))))) (sqrt (/ 1 (* n (PI)))))))) (* (sqrt (* n (PI))) (sqrt 2)))))
#s(approx (sqrt (/ (* (* (PI) n) 2) (pow (* (* (PI) n) 2) k))) #s(hole binary64 (+ (* k (+ (* -1/2 (* (sqrt (* n (PI))) (* (log (* 2 (* n (PI)))) (sqrt 2)))) (* k (+ (* -1/2 (* (sqrt (/ 1 (* n (PI)))) (* (sqrt 2) (+ (* -1 (* n (* (PI) (pow (log (* 2 (* n (PI)))) 2)))) (+ (* 1/4 (* n (* (PI) (pow (log (* 2 (* n (PI)))) 2)))) (* 1/2 (* n (* (PI) (pow (log (* 2 (* n (PI)))) 2))))))))) (* -1/2 (* (* k (* (sqrt 2) (+ (* -1 (* (log (* 2 (* n (PI)))) (+ (* -1 (* n (* (PI) (pow (log (* 2 (* n (PI)))) 2)))) (* 1/2 (* n (* (PI) (pow (log (* 2 (* n (PI)))) 2))))))) (+ (* -1/2 (* n (* (PI) (pow (log (* 2 (* n (PI)))) 3)))) (+ (* 1/6 (* n (* (PI) (pow (log (* 2 (* n (PI)))) 3)))) (* 1/2 (* (log (* 2 (* n (PI)))) (+ (* -1 (* n (* (PI) (pow (log (* 2 (* n (PI)))) 2)))) (+ (* 1/4 (* n (* (PI) (pow (log (* 2 (* n (PI)))) 2)))) (* 1/2 (* n (* (PI) (pow (log (* 2 (* n (PI)))) 2))))))))))))) (sqrt (/ 1 (* n (PI)))))))))) (* (sqrt (* n (PI))) (sqrt 2)))))
#s(approx (/ (* (* (PI) n) 2) (pow (* (* (PI) n) 2) k)) #s(hole binary64 (* 2 (* n (PI)))))
#s(approx (/ (* (* (PI) n) 2) (pow (* (* (PI) n) 2) k)) #s(hole binary64 (+ (* -2 (* k (* n (* (PI) (log (* 2 (* n (PI)))))))) (* 2 (* n (PI))))))
#s(approx (/ (* (* (PI) n) 2) (pow (* (* (PI) n) 2) k)) #s(hole binary64 (+ (* 2 (* n (PI))) (* k (+ (* -2 (* k (+ (* -1 (* n (* (PI) (pow (log (* 2 (* n (PI)))) 2)))) (* 1/2 (* n (* (PI) (pow (log (* 2 (* n (PI)))) 2))))))) (* -2 (* n (* (PI) (log (* 2 (* n (PI))))))))))))
#s(approx (/ (* (* (PI) n) 2) (pow (* (* (PI) n) 2) k)) #s(hole binary64 (+ (* 2 (* n (PI))) (* k (+ (* -2 (* n (* (PI) (log (* 2 (* n (PI))))))) (* k (+ (* -2 (* k (+ (* -1 (* (log (* 2 (* n (PI)))) (+ (* -1 (* n (* (PI) (pow (log (* 2 (* n (PI)))) 2)))) (* 1/2 (* n (* (PI) (pow (log (* 2 (* n (PI)))) 2))))))) (+ (* -1/2 (* n (* (PI) (pow (log (* 2 (* n (PI)))) 3)))) (* 1/6 (* n (* (PI) (pow (log (* 2 (* n (PI)))) 3)))))))) (* -2 (+ (* -1 (* n (* (PI) (pow (log (* 2 (* n (PI)))) 2)))) (* 1/2 (* n (* (PI) (pow (log (* 2 (* n (PI)))) 2)))))))))))))
#s(approx (pow (* (* (PI) n) 2) (- 1 k)) #s(hole binary64 (* 2 (* n (PI)))))
#s(approx (pow (* (* (PI) n) 2) (- 1 k)) #s(hole binary64 (+ (* -2 (* k (* n (* (PI) (log (* 2 (* n (PI)))))))) (* 2 (* n (PI))))))
#s(approx (pow (* (* (PI) n) 2) (- 1 k)) #s(hole binary64 (+ (* 2 (* n (PI))) (* k (+ (* -2 (* n (* (PI) (log (* 2 (* n (PI))))))) (* k (* n (* (PI) (pow (log (* 2 (* n (PI)))) 2)))))))))
#s(approx (pow (* (* (PI) n) 2) (- 1 k)) #s(hole binary64 (+ (* 2 (* n (PI))) (* k (+ (* -2 (* n (* (PI) (log (* 2 (* n (PI))))))) (* k (+ (* -1/3 (* k (* n (* (PI) (pow (log (* 2 (* n (PI)))) 3))))) (* n (* (PI) (pow (log (* 2 (* n (PI)))) 2))))))))))
#s(approx (sqrt (/ 1 k)) #s(hole binary64 (sqrt (/ 1 k))))
#s(approx (* (pow (* n (* (PI) 2)) (/ (- 1 k) 2)) (pow k -1/2)) #s(hole binary64 (* (sqrt (/ 1 k)) (exp (* 1/2 (* (log (* 2 (* n (PI)))) (- 1 k)))))))
#s(approx (* (pow (/ (* -2 (PI)) (/ -1 n)) (+ (* -1/2 k) 1/2)) (sqrt (/ 1 k))) #s(hole binary64 (* (sqrt (/ 1 k)) (exp (* (log (* 2 (* n (PI)))) (- 1/2 (* 1/2 k)))))))
#s(approx (pow (/ (* -2 (PI)) (/ -1 n)) (+ (* -1/2 k) 1/2)) #s(hole binary64 (exp (* (log (* 2 (* n (PI)))) (- 1/2 (* 1/2 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 (* (sqrt (pow (* (* (PI) n) 2) (- 1 k))) (sqrt (/ 1 k))) #s(hole binary64 (sqrt (/ (exp (* (log (* 2 (* n (PI)))) (- 1 k))) k))))
#s(approx (sqrt (/ (pow (* (* (PI) n) 2) (- 1 k)) k)) #s(hole binary64 (sqrt (/ (exp (* (log (* 2 (* n (PI)))) (- 1 k))) k))))
#s(approx (/ (pow (* (* (PI) n) 2) (- 1 k)) k) #s(hole binary64 (/ (exp (* (log (* 2 (* n (PI)))) (- 1 k))) k)))
#s(approx (* (sqrt (/ (* (* (PI) n) 2) (pow (* (* (PI) n) 2) k))) (sqrt (/ 1 k))) #s(hole binary64 (* (sqrt (/ (* n (PI)) (* k (pow (* 2 (* n (PI))) k)))) (sqrt 2))))
#s(approx (sqrt (/ (* (* (PI) n) 2) (pow (* (* (PI) n) 2) k))) #s(hole binary64 (* (sqrt (/ (* n (PI)) (pow (* 2 (* n (PI))) k))) (sqrt 2))))
#s(approx (/ (* (* (PI) n) 2) (pow (* (* (PI) n) 2) k)) #s(hole binary64 (* 2 (/ (* n (PI)) (pow (* 2 (* n (PI))) k)))))
#s(approx (pow (* (* (PI) n) 2) (- 1 k)) #s(hole binary64 (exp (* (log (* 2 (* n (PI)))) (- 1 k)))))
#s(approx (* (pow (* n (* (PI) 2)) (/ (- 1 k) 2)) (pow k -1/2)) #s(hole binary64 (* (sqrt (/ 1 k)) (* (exp (* 1/2 (* (log (* 2 (* n (PI)))) (+ 1 (* -1 k))))) (pow (sqrt -1) 2)))))
#s(approx (* (pow (/ (* -2 (PI)) (/ -1 n)) (+ (* -1/2 k) 1/2)) (sqrt (/ 1 k))) #s(hole binary64 (* (sqrt (/ 1 k)) (* (exp (* (log (* 2 (* n (PI)))) (+ 1/2 (* -1/2 k)))) (pow (sqrt -1) 2)))))
#s(approx (pow (/ (* -2 (PI)) (/ -1 n)) (+ (* -1/2 k) 1/2)) #s(hole binary64 (exp (* (log (* 2 (* n (PI)))) (+ 1/2 (* -1/2 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 (sqrt (* (/ (* (PI) n) k) 2)) #s(hole binary64 (* (sqrt (/ (* n (PI)) k)) (* (sqrt -2) (sqrt -1)))))
#s(approx (* (sqrt (pow (* (* (PI) n) 2) (- 1 k))) (sqrt (/ 1 k))) #s(hole binary64 (* (sqrt (/ (exp (* (log (* 2 (* n (PI)))) (+ 1 (* -1 k)))) k)) (pow (sqrt -1) 2))))
#s(approx (sqrt (/ (pow (* (* (PI) n) 2) (- 1 k)) k)) #s(hole binary64 (* (sqrt (/ (exp (* (log (* 2 (* n (PI)))) (+ 1 (* -1 k)))) k)) (pow (sqrt -1) 2))))
#s(approx (/ (pow (* (* (PI) n) 2) (- 1 k)) k) #s(hole binary64 (/ (exp (* (log (* 2 (* n (PI)))) (+ 1 (* -1 k)))) k)))
#s(approx (* (sqrt (/ (* (* (PI) n) 2) (pow (* (* (PI) n) 2) k))) (sqrt (/ 1 k))) #s(hole binary64 (* (sqrt (/ (* n (PI)) (* k (pow (* 2 (* n (PI))) k)))) (* (pow (sqrt -1) 2) (sqrt 2)))))
#s(approx (pow (* (* (PI) n) 2) (- 1 k)) #s(hole binary64 (exp (* (log (* 2 (* n (PI)))) (+ 1 (* -1 k))))))
#s(approx (sqrt (/ 1 k)) #s(hole binary64 (* (sqrt (/ 1 k)) (pow (sqrt -1) 2))))
#s(approx (/ (* -2 (PI)) (/ -1 n)) #s(hole binary64 (* 2 (* n (PI)))))
#s(approx (* (pow (* n (* (PI) 2)) (/ (- 1 k) 2)) (pow k -1/2)) #s(hole binary64 (* (sqrt (/ 1 k)) (exp (* 1/2 (* (+ (log n) (log (* 2 (PI)))) (- 1 k)))))))
#s(approx (* (pow (/ (* -2 (PI)) (/ -1 n)) (+ (* -1/2 k) 1/2)) (sqrt (/ 1 k))) #s(hole binary64 (* (sqrt (/ 1 k)) (exp (* (+ 1/2 (* -1/2 k)) (+ (log n) (log (* 2 (PI)))))))))
#s(approx (pow (/ (* -2 (PI)) (/ -1 n)) (+ (* -1/2 k) 1/2)) #s(hole binary64 (exp (* (+ 1/2 (* -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 (pow (* (* (PI) n) 2) (- 1 k))) (sqrt (/ 1 k))) #s(hole binary64 (sqrt (/ (exp (* (+ (log n) (log (* 2 (PI)))) (- 1 k))) k))))
#s(approx (sqrt (/ (pow (* (* (PI) n) 2) (- 1 k)) k)) #s(hole binary64 (sqrt (/ (exp (* (+ (log n) (log (* 2 (PI)))) (- 1 k))) k))))
#s(approx (/ (pow (* (* (PI) n) 2) (- 1 k)) k) #s(hole binary64 (/ (exp (* (+ (log n) (log (* 2 (PI)))) (- 1 k))) k)))
#s(approx (* (sqrt (/ (* (* (PI) n) 2) (pow (* (* (PI) n) 2) k))) (sqrt (/ 1 k))) #s(hole binary64 (* (sqrt (/ (* n (PI)) (* k (exp (* k (+ (log n) (log (* 2 (PI))))))))) (sqrt 2))))
#s(approx (sqrt (/ (* (* (PI) n) 2) (pow (* (* (PI) n) 2) k))) #s(hole binary64 (* (sqrt (/ (* n (PI)) (exp (* k (+ (log n) (log (* 2 (PI)))))))) (sqrt 2))))
#s(approx (/ (* (* (PI) n) 2) (pow (* (* (PI) n) 2) k)) #s(hole binary64 (* 2 (/ (* n (PI)) (exp (* k (+ (log n) (log (* 2 (PI))))))))))
#s(approx (* (PI) n) #s(hole binary64 (* n (PI))))
#s(approx (pow (* (* (PI) n) 2) (- 1 k)) #s(hole binary64 (exp (* (+ (log n) (log (* 2 (PI)))) (- 1 k)))))
#s(approx (* (pow (* n (* (PI) 2)) (/ (- 1 k) 2)) (pow k -1/2)) #s(hole binary64 (* (sqrt (/ 1 k)) (exp (* 1/2 (* (+ (log (* 2 (PI))) (* -1 (log (/ 1 n)))) (- 1 k)))))))
#s(approx (* (pow (/ (* -2 (PI)) (/ -1 n)) (+ (* -1/2 k) 1/2)) (sqrt (/ 1 k))) #s(hole binary64 (* (sqrt (/ 1 k)) (exp (* (+ 1/2 (* -1/2 k)) (+ (log (* 2 (PI))) (* -1 (log (/ 1 n)))))))))
#s(approx (pow (/ (* -2 (PI)) (/ -1 n)) (+ (* -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 (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 (pow (* (* (PI) n) 2) (- 1 k))) (sqrt (/ 1 k))) #s(hole binary64 (sqrt (/ (exp (* (+ (log (* 2 (PI))) (* -1 (log (/ 1 n)))) (- 1 k))) k))))
#s(approx (sqrt (/ (pow (* (* (PI) n) 2) (- 1 k)) k)) #s(hole binary64 (sqrt (/ (exp (* (+ (log (* 2 (PI))) (* -1 (log (/ 1 n)))) (- 1 k))) k))))
#s(approx (/ (pow (* (* (PI) n) 2) (- 1 k)) k) #s(hole binary64 (/ (exp (* (+ (log (* 2 (PI))) (* -1 (log (/ 1 n)))) (- 1 k))) k)))
#s(approx (* (sqrt (/ (* (* (PI) n) 2) (pow (* (* (PI) n) 2) k))) (sqrt (/ 1 k))) #s(hole binary64 (* (sqrt (/ (* n (PI)) (* k (exp (* k (+ (log (* 2 (PI))) (* -1 (log (/ 1 n))))))))) (sqrt 2))))
#s(approx (sqrt (/ (* (* (PI) n) 2) (pow (* (* (PI) n) 2) k))) #s(hole binary64 (* (sqrt (/ (* n (PI)) (exp (* k (+ (log (* 2 (PI))) (* -1 (log (/ 1 n)))))))) (sqrt 2))))
#s(approx (/ (* (* (PI) n) 2) (pow (* (* (PI) n) 2) k)) #s(hole binary64 (* 2 (/ (* n (PI)) (exp (* k (+ (log (* 2 (PI))) (* -1 (log (/ 1 n))))))))))
#s(approx (pow (* (* (PI) n) 2) (- 1 k)) #s(hole binary64 (exp (* (+ (log (* 2 (PI))) (* -1 (log (/ 1 n)))) (- 1 k)))))
#s(approx (* (pow (* n (* (PI) 2)) (/ (- 1 k) 2)) (pow k -1/2)) #s(hole binary64 (* (sqrt (/ 1 k)) (exp (* 1/2 (* (+ (log (* -2 (PI))) (* -1 (log (/ -1 n)))) (- 1 k)))))))
#s(approx (* (pow (/ (* -2 (PI)) (/ -1 n)) (+ (* -1/2 k) 1/2)) (sqrt (/ 1 k))) #s(hole binary64 (* (sqrt (/ 1 k)) (exp (* (+ 1/2 (* -1/2 k)) (+ (log (* -2 (PI))) (* -1 (log (/ -1 n)))))))))
#s(approx (pow (/ (* -2 (PI)) (/ -1 n)) (+ (* -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 (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) (/ (sqrt (* (PI) n)) (sqrt k))) #s(hole binary64 (* -1 (* (sqrt (/ (* n (PI)) k)) (* (pow (sqrt -1) 2) (sqrt 2))))))
#s(approx (/ (sqrt (* (PI) n)) (sqrt k)) #s(hole binary64 (* -1 (* (sqrt (/ (* n (PI)) k)) (pow (sqrt -1) 2)))))
#s(approx (* (sqrt (pow (* (* (PI) n) 2) (- 1 k))) (sqrt (/ 1 k))) #s(hole binary64 (sqrt (/ (exp (* (+ (log (* -2 (PI))) (* -1 (log (/ -1 n)))) (- 1 k))) k))))
#s(approx (sqrt (/ (pow (* (* (PI) n) 2) (- 1 k)) k)) #s(hole binary64 (sqrt (/ (exp (* (+ (log (* -2 (PI))) (* -1 (log (/ -1 n)))) (- 1 k))) k))))
#s(approx (/ (pow (* (* (PI) n) 2) (- 1 k)) k) #s(hole binary64 (/ (exp (* (+ (log (* -2 (PI))) (* -1 (log (/ -1 n)))) (- 1 k))) k)))
#s(approx (* (sqrt (/ (* (* (PI) n) 2) (pow (* (* (PI) n) 2) k))) (sqrt (/ 1 k))) #s(hole binary64 (* -1 (* (sqrt (/ (* n (PI)) (* k (exp (* k (+ (log (* -2 (PI))) (* -1 (log (/ -1 n))))))))) (* (sqrt -2) (sqrt -1))))))
#s(approx (sqrt (/ (* (* (PI) n) 2) (pow (* (* (PI) n) 2) k))) #s(hole binary64 (* -1 (* (sqrt (/ (* n (PI)) (exp (* k (+ (log (* -2 (PI))) (* -1 (log (/ -1 n)))))))) (* (sqrt -2) (sqrt -1))))))
#s(approx (/ (* (* (PI) n) 2) (pow (* (* (PI) n) 2) k)) #s(hole binary64 (* 2 (/ (* n (PI)) (exp (* k (+ (log (* -2 (PI))) (* -1 (log (/ -1 n))))))))))
#s(approx (pow (* (* (PI) n) 2) (- 1 k)) #s(hole binary64 (exp (* (+ (log (* -2 (PI))) (* -1 (log (/ -1 n)))) (- 1 k)))))

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

rewrite105.0ms (1.1%)

Memory

-6.8MiB live, 149.3MiB allocated; 46ms collecting garbage

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	62	355
0	91	321
1	271	292
0	1508	292

Stop Event

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

Counts

24 → 388

Calls

Call 1

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

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

eval70.0ms (0.7%)

Memory: -5.6MiB live, 233.2MiB allocated; 30ms collecting garbage
Compiler: Compiled 17 962 to 1 828 computations (89.8% saved)

prune107.0ms (1.1%)

Memory

-34.0MiB live, 95.9MiB allocated; 70ms collecting garbage

Pruning

22 alts after pruning (16 fresh and 6 done)

	Pruned	Kept	Total
New	417	10	427
Fresh	5	6	11
Picked	0	5	5
Done	0	1	1
Total	422	22	444

Accuracy

100.0%

Counts

444 → 22

Alt Table

Click to see full alt table

Status	Accuracy	Program
▶	99.5%	(.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) #s(approx ( (pow (* (PI) 2) (/ (- 1 k) 2)) (pow 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)))))
✓	99.6%	#s(approx (* (pow (* n (* (PI) 2)) (/ (- 1 k) 2)) (pow k -1/2)) (.f64 (pow.f64 (/.f64 (.f64 #s(literal -2 binary64) (PI.f64)) (/.f64 #s(literal -1 binary64) n)) (fma.f64 #s(literal -1/2 binary64) k #s(literal 1/2 binary64))) (sqrt.f64 (/.f64 #s(literal 1 binary64) k))))
	53.4%	#s(approx (* (pow (* n (* (PI) 2)) (/ (- 1 k) 2)) (pow k -1/2)) (.f64 #s(approx (pow (/ ( -2 (PI)) (/ -1 n)) (+ (* -1/2 k) 1/2)) (.f64 (sqrt.f64 (.f64 (PI.f64) n)) (sqrt.f64 #s(literal 2 binary64)))) (sqrt.f64 (/.f64 #s(literal 1 binary64) k))))
	53.3%	#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (/.f64 (.f64 (sqrt.f64 #s(literal 2 binary64)) (neg.f64 (sqrt.f64 (.f64 (PI.f64) n)))) (neg.f64 (sqrt.f64 k))))
▶	53.5%	#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)))
✓	99.3%	#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (.f64 (sqrt.f64 (/.f64 (.f64 (.f64 (PI.f64) n) #s(literal 2 binary64)) (pow.f64 (.f64 (*.f64 (PI.f64) n) #s(literal 2 binary64)) k))) (sqrt.f64 (/.f64 #s(literal 1 binary64) k))))
	53.5%	#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (.f64 (sqrt.f64 #s(approx (pow ( (* (PI) n) 2) (- 1 k)) (.f64 (.f64 (PI.f64) n) #s(literal 2 binary64)))) (sqrt.f64 (/.f64 #s(literal 1 binary64) k))))
✓	53.3%	#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))))
	53.4%	#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (.f64 (sqrt.f64 #s(literal 2 binary64)) (.f64 (sqrt.f64 (PI.f64)) (/.f64 (sqrt.f64 n) (sqrt.f64 k)))))
	39.5%	#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)))))
✓	39.5%	#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))))
	39.4%	#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt.f64 (.f64 (/.f64 (.f64 (*.f64 n (sqrt.f64 (PI.f64))) (sqrt.f64 (PI.f64))) k) #s(literal 2 binary64))))
✓	39.6%	#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))))
	39.6%	#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))))
▶	39.5%	#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt.f64 (.f64 (.f64 (sqrt.f64 (PI.f64)) (*.f64 (sqrt.f64 (PI.f64)) (/.f64 n k))) #s(literal 2 binary64))))
	39.6%	#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt.f64 (.f64 (.f64 (PI.f64) n) (/.f64 #s(literal 2 binary64) k))))
	39.6%	#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))))
▶	39.7%	#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt.f64 (.f64 n (/.f64 (.f64 #s(literal 2 binary64) (PI.f64)) k))))
▶	24.0%	#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) #s(approx (* (sqrt (pow (* (* (PI) n) 2) (- 1 k))) (sqrt (/ 1 k))) (.f64 (sqrt.f64 (/.f64 (pow.f64 (.f64 (*.f64 (PI.f64) n) #s(literal 2 binary64)) (-.f64 #s(literal 1 binary64) k)) k)) #s(literal -1 binary64))))
✓	85.4%	#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) #s(approx (* (sqrt (pow (* (* (PI) n) 2) (- 1 k))) (sqrt (/ 1 k))) (sqrt.f64 (/.f64 (pow.f64 (.f64 (.f64 (PI.f64) n) #s(literal 2 binary64)) (-.f64 #s(literal 1 binary64) k)) k))))
	85.5%	#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) #s(approx (* (sqrt (pow (* (* (PI) n) 2) (- 1 k))) (sqrt (/ 1 k))) (sqrt.f64 (/.f64 (.f64 (.f64 (PI.f64) n) #s(literal 2 binary64)) (.f64 (pow.f64 (.f64 (*.f64 (PI.f64) n) #s(literal 2 binary64)) k) k)))))
	39.8%	#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) #s(approx (* (sqrt (pow (* (* (PI) n) 2) (- 1 k))) (sqrt (/ 1 k))) (sqrt.f64 (/.f64 #s(approx (pow (* (* (PI) n) 2) (- 1 k)) (.f64 #s(literal -2 binary64) (fma.f64 (.f64 (log.f64 (.f64 (.f64 (PI.f64) n) #s(literal 2 binary64))) (.f64 (PI.f64) n)) k (.f64 (neg.f64 (PI.f64)) n)))) k))))

Compiler

Compiled 1 274 to 943 computations (26% saved)

simplify154.0ms (1.6%)

Memory

29.9MiB live, 170.2MiB allocated; 14ms collecting garbage

Localize:

Found 20 expressions of interest:

New	Metric	Score
cost-diff	0	(sqrt.f64 (/.f64 (pow.f64 (.f64 (.f64 (PI.f64) n) #s(literal 2 binary64)) (-.f64 #s(literal 1 binary64) k)) k))
cost-diff	0	#s(approx (* (sqrt (pow (* (* (PI) n) 2) (- 1 k))) (sqrt (/ 1 k))) (.f64 (sqrt.f64 (/.f64 (pow.f64 (.f64 (*.f64 (PI.f64) n) #s(literal 2 binary64)) (-.f64 #s(literal 1 binary64) k)) k)) #s(literal -1 binary64)))
cost-diff	0	#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) #s(approx (* (sqrt (pow (* (* (PI) n) 2) (- 1 k))) (sqrt (/ 1 k))) (.f64 (sqrt.f64 (/.f64 (pow.f64 (.f64 (*.f64 (PI.f64) n) #s(literal 2 binary64)) (-.f64 #s(literal 1 binary64) k)) k)) #s(literal -1 binary64))))
cost-diff	1	(.f64 (sqrt.f64 (/.f64 (pow.f64 (.f64 (*.f64 (PI.f64) n) #s(literal 2 binary64)) (-.f64 #s(literal 1 binary64) k)) k)) #s(literal -1 binary64))
cost-diff	0	(.f64 (.f64 (sqrt.f64 (PI.f64)) (*.f64 (sqrt.f64 (PI.f64)) (/.f64 n k))) #s(literal 2 binary64))
cost-diff	0	(sqrt.f64 (.f64 (.f64 (sqrt.f64 (PI.f64)) (*.f64 (sqrt.f64 (PI.f64)) (/.f64 n k))) #s(literal 2 binary64)))
cost-diff	0	#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt.f64 (.f64 (.f64 (sqrt.f64 (PI.f64)) (*.f64 (sqrt.f64 (PI.f64)) (/.f64 n k))) #s(literal 2 binary64))))
cost-diff	4	(.f64 (sqrt.f64 (PI.f64)) (.f64 (sqrt.f64 (PI.f64)) (/.f64 n k)))
cost-diff	0	(.f64 (.f64 (PI.f64) n) #s(literal 2 binary64))
cost-diff	0	(sqrt.f64 (.f64 (.f64 (PI.f64) n) #s(literal 2 binary64)))
cost-diff	0	(/.f64 (sqrt.f64 (.f64 (.f64 (PI.f64) n) #s(literal 2 binary64))) (sqrt.f64 k))
cost-diff	0	#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)))
cost-diff	0	(/.f64 (*.f64 #s(literal 2 binary64) (PI.f64)) k)
cost-diff	0	(.f64 n (/.f64 (.f64 #s(literal 2 binary64) (PI.f64)) k))
cost-diff	0	(sqrt.f64 (.f64 n (/.f64 (.f64 #s(literal 2 binary64) (PI.f64)) k)))
cost-diff	0	#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt.f64 (.f64 n (/.f64 (.f64 #s(literal 2 binary64) (PI.f64)) k))))
cost-diff	0	#s(approx (* (pow (* (PI) 2) (/ (- 1 k) 2)) (pow 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))))
cost-diff	0	(sqrt.f64 k)
cost-diff	0	(/.f64 #s(literal 1 binary64) (sqrt.f64 k))
cost-diff	2	(.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) #s(approx ( (pow (* (PI) 2) (/ (- 1 k) 2)) (pow 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)))))

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	58	419
0	86	407
1	125	390
2	209	390
3	557	382
4	2345	382
5	7940	382
0	8022	382

Stop Event

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

Calls

Call 1

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

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

localize182.0ms (2%)

Memory

-18.9MiB live, 211.6MiB allocated; 31ms collecting garbage

Localize:

Found 20 expressions of interest:

New	Metric	Score
accuracy	0.2109375	(*.f64 (PI.f64) n)
accuracy	8.980395849524317	(sqrt.f64 (/.f64 (pow.f64 (.f64 (.f64 (PI.f64) n) #s(literal 2 binary64)) (-.f64 #s(literal 1 binary64) k)) k))
accuracy	14.046533023192962	(PI.f64)
accuracy	34.36850253633733	#s(approx (* (sqrt (pow (* (* (PI) n) 2) (- 1 k))) (sqrt (/ 1 k))) (.f64 (sqrt.f64 (/.f64 (pow.f64 (.f64 (*.f64 (PI.f64) n) #s(literal 2 binary64)) (-.f64 #s(literal 1 binary64) k)) k)) #s(literal -1 binary64)))
accuracy	0.7734375	(sqrt.f64 (PI.f64))
accuracy	9.007739599524317	(sqrt.f64 (.f64 (.f64 (sqrt.f64 (PI.f64)) (*.f64 (sqrt.f64 (PI.f64)) (/.f64 n k))) #s(literal 2 binary64)))
accuracy	14.046533023192962	(PI.f64)
accuracy	15.423160254970837	#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt.f64 (.f64 (.f64 (sqrt.f64 (PI.f64)) (*.f64 (sqrt.f64 (PI.f64)) (/.f64 n k))) #s(literal 2 binary64))))
accuracy	0.2109375	(*.f64 (PI.f64) n)
accuracy	0.29296875	(/.f64 (sqrt.f64 (.f64 (.f64 (PI.f64) n) #s(literal 2 binary64))) (sqrt.f64 k))
accuracy	14.046533023192962	(PI.f64)
accuracy	15.423160254970837	#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)))
accuracy	0.20703125	(/.f64 (*.f64 #s(literal 2 binary64) (PI.f64)) k)
accuracy	9.007739599524317	(sqrt.f64 (.f64 n (/.f64 (.f64 #s(literal 2 binary64) (PI.f64)) k)))
accuracy	14.046533023192962	(PI.f64)
accuracy	15.423160254970837	#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt.f64 (.f64 n (/.f64 (.f64 #s(literal 2 binary64) (PI.f64)) k))))
accuracy	0.16630692927829482	(pow.f64 (.f64 (.f64 (PI.f64) n) #s(literal 2 binary64)) (fma.f64 #s(literal -1/2 binary64) k #s(literal 1/2 binary64)))
accuracy	0.18359375	(/.f64 #s(literal 1 binary64) (sqrt.f64 k))
accuracy	0.2109375	(*.f64 (PI.f64) n)
accuracy	14.046533023192962	(PI.f64)

Samples

108.0ms	198×	valid
40.0ms	57×	exit
0.0ms	1×	invalid

Compiler

Compiled 323 to 47 computations (85.4% saved)

Precisions

Click to see histograms. Total time spent on operations: 118.0ms

ival-mult: 49.0ms (41.7% of total)

ival-sqrt: 32.0ms (27.2% of total)

ival-pow: 21.0ms (17.9% of total)

ival-div: 12.0ms (10.2% of total)

ival-pi: 1.0ms (0.9% of total)

ival-add: 1.0ms (0.9% of total)

ival-sub: 1.0ms (0.9% of total)

exact: 1.0ms (0.9% of total)

adjust: 0.0ms (0% of total)

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

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

series142.0ms (1.5%)

Memory

1.9MiB live, 191.8MiB allocated; 39ms collecting garbage

Counts

24 → 80

Calls

Call 1

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

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

Calls

6 calls:

Time	Variable		Point	Expression
62.0ms	n	@	-inf	((* (/ 1 (sqrt k)) (* (pow (* (PI) 2) (/ (- 1 k) 2)) (pow n (/ (- 1 k) 2)))) (/ 1 (sqrt k)) (sqrt k) (* (pow (* (PI) 2) (/ (- 1 k) 2)) (pow n (/ (- 1 k) 2))) (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt (* n (/ (* 2 (PI)) k))) (* n (/ (* 2 (PI)) k)) (/ (* 2 (PI)) k) (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (/ (sqrt (* (* (PI) n) 2)) (sqrt k)) (sqrt (* (* (PI) n) 2)) (* (* (PI) n) 2) (* (sqrt (PI)) (* (sqrt (PI)) (/ n k))) (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt (* (* (sqrt (PI)) (* (sqrt (PI)) (/ n k))) 2)) (* (* (sqrt (PI)) (* (sqrt (PI)) (/ n k))) 2) (* (sqrt (/ (pow (* (* (PI) n) 2) (- 1 k)) k)) -1) (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (* (sqrt (pow (* (* (PI) n) 2) (- 1 k))) (sqrt (/ 1 k))) (sqrt (/ (pow (* (* (PI) n) 2) (- 1 k)) k)) (PI) (* (PI) n) (pow (* (* (PI) n) 2) (+ (* -1/2 k) 1/2)) (sqrt (PI)))
35.0ms	n	@	inf	((* (/ 1 (sqrt k)) (* (pow (* (PI) 2) (/ (- 1 k) 2)) (pow n (/ (- 1 k) 2)))) (/ 1 (sqrt k)) (sqrt k) (* (pow (* (PI) 2) (/ (- 1 k) 2)) (pow n (/ (- 1 k) 2))) (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt (* n (/ (* 2 (PI)) k))) (* n (/ (* 2 (PI)) k)) (/ (* 2 (PI)) k) (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (/ (sqrt (* (* (PI) n) 2)) (sqrt k)) (sqrt (* (* (PI) n) 2)) (* (* (PI) n) 2) (* (sqrt (PI)) (* (sqrt (PI)) (/ n k))) (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt (* (* (sqrt (PI)) (* (sqrt (PI)) (/ n k))) 2)) (* (* (sqrt (PI)) (* (sqrt (PI)) (/ n k))) 2) (* (sqrt (/ (pow (* (* (PI) n) 2) (- 1 k)) k)) -1) (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (* (sqrt (pow (* (* (PI) n) 2) (- 1 k))) (sqrt (/ 1 k))) (sqrt (/ (pow (* (* (PI) n) 2) (- 1 k)) k)) (PI) (* (PI) n) (pow (* (* (PI) n) 2) (+ (* -1/2 k) 1/2)) (sqrt (PI)))
29.0ms	n	@	0	((* (/ 1 (sqrt k)) (* (pow (* (PI) 2) (/ (- 1 k) 2)) (pow n (/ (- 1 k) 2)))) (/ 1 (sqrt k)) (sqrt k) (* (pow (* (PI) 2) (/ (- 1 k) 2)) (pow n (/ (- 1 k) 2))) (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt (* n (/ (* 2 (PI)) k))) (* n (/ (* 2 (PI)) k)) (/ (* 2 (PI)) k) (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (/ (sqrt (* (* (PI) n) 2)) (sqrt k)) (sqrt (* (* (PI) n) 2)) (* (* (PI) n) 2) (* (sqrt (PI)) (* (sqrt (PI)) (/ n k))) (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt (* (* (sqrt (PI)) (* (sqrt (PI)) (/ n k))) 2)) (* (* (sqrt (PI)) (* (sqrt (PI)) (/ n k))) 2) (* (sqrt (/ (pow (* (* (PI) n) 2) (- 1 k)) k)) -1) (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (* (sqrt (pow (* (* (PI) n) 2) (- 1 k))) (sqrt (/ 1 k))) (sqrt (/ (pow (* (* (PI) n) 2) (- 1 k)) k)) (PI) (* (PI) n) (pow (* (* (PI) n) 2) (+ (* -1/2 k) 1/2)) (sqrt (PI)))
5.0ms	k	@	-inf	((* (/ 1 (sqrt k)) (* (pow (* (PI) 2) (/ (- 1 k) 2)) (pow n (/ (- 1 k) 2)))) (/ 1 (sqrt k)) (sqrt k) (* (pow (* (PI) 2) (/ (- 1 k) 2)) (pow n (/ (- 1 k) 2))) (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt (* n (/ (* 2 (PI)) k))) (* n (/ (* 2 (PI)) k)) (/ (* 2 (PI)) k) (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (/ (sqrt (* (* (PI) n) 2)) (sqrt k)) (sqrt (* (* (PI) n) 2)) (* (* (PI) n) 2) (* (sqrt (PI)) (* (sqrt (PI)) (/ n k))) (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt (* (* (sqrt (PI)) (* (sqrt (PI)) (/ n k))) 2)) (* (* (sqrt (PI)) (* (sqrt (PI)) (/ n k))) 2) (* (sqrt (/ (pow (* (* (PI) n) 2) (- 1 k)) k)) -1) (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (* (sqrt (pow (* (* (PI) n) 2) (- 1 k))) (sqrt (/ 1 k))) (sqrt (/ (pow (* (* (PI) n) 2) (- 1 k)) k)) (PI) (* (PI) n) (pow (* (* (PI) n) 2) (+ (* -1/2 k) 1/2)) (sqrt (PI)))
4.0ms	k	@	0	((* (/ 1 (sqrt k)) (* (pow (* (PI) 2) (/ (- 1 k) 2)) (pow n (/ (- 1 k) 2)))) (/ 1 (sqrt k)) (sqrt k) (* (pow (* (PI) 2) (/ (- 1 k) 2)) (pow n (/ (- 1 k) 2))) (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt (* n (/ (* 2 (PI)) k))) (* n (/ (* 2 (PI)) k)) (/ (* 2 (PI)) k) (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (/ (sqrt (* (* (PI) n) 2)) (sqrt k)) (sqrt (* (* (PI) n) 2)) (* (* (PI) n) 2) (* (sqrt (PI)) (* (sqrt (PI)) (/ n k))) (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt (* (* (sqrt (PI)) (* (sqrt (PI)) (/ n k))) 2)) (* (* (sqrt (PI)) (* (sqrt (PI)) (/ n k))) 2) (* (sqrt (/ (pow (* (* (PI) n) 2) (- 1 k)) k)) -1) (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (* (sqrt (pow (* (* (PI) n) 2) (- 1 k))) (sqrt (/ 1 k))) (sqrt (/ (pow (* (* (PI) n) 2) (- 1 k)) k)) (PI) (* (PI) n) (pow (* (* (PI) n) 2) (+ (* -1/2 k) 1/2)) (sqrt (PI)))

simplify212.0ms (2.3%)

Memory

23.5MiB live, 257.7MiB allocated; 46ms collecting garbage

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	431	3419
1	1312	3176
2	5562	2979
0	8132	2876

Stop Event

1×	iter limit
1×	node limit

Counts

80 → 80

Calls

Call 1

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

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

rewrite81.0ms (0.9%)

Memory

-22.5MiB live, 83.9MiB allocated; 7ms collecting garbage

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	58	338
0	86	296
1	255	278
0	1346	278

Stop Event

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

Counts

24 → 262

Calls

Call 1

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

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

eval46.0ms (0.5%)

Memory: -3.4MiB live, 85.2MiB allocated; 12ms collecting garbage
Compiler: Compiled 14 112 to 1 517 computations (89.3% saved)

prune47.0ms (0.5%)

Memory

33.3MiB live, 79.3MiB allocated; 4ms collecting garbage

Pruning

25 alts after pruning (18 fresh and 7 done)

	Pruned	Kept	Total
New	339	11	350
Fresh	4	7	11
Picked	1	4	5
Done	3	3	6
Total	347	25	372

Accuracy

100.0%

Counts

372 → 25

Alt Table

Click to see full alt table

Status	Accuracy	Program
✓	99.5%	(.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) #s(approx ( (pow (* (PI) 2) (/ (- 1 k) 2)) (pow 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)))))
	53.4%	#s(approx (* (pow (* n (* (PI) 2)) (/ (- 1 k) 2)) (pow k -1/2)) (.f64 #s(approx (pow (/ ( -2 (PI)) (/ -1 n)) (+ (* -1/2 k) 1/2)) (.f64 (sqrt.f64 (.f64 (PI.f64) n)) (sqrt.f64 #s(literal 2 binary64)))) (sqrt.f64 (/.f64 #s(literal 1 binary64) k))))
	53.3%	#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (/.f64 (.f64 (sqrt.f64 (.f64 (PI.f64) n)) (sqrt.f64 #s(literal 2 binary64))) (sqrt.f64 k)))
	53.2%	#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (/.f64 (.f64 (sqrt.f64 (.f64 (PI.f64) #s(literal 2 binary64))) (sqrt.f64 n)) (sqrt.f64 k)))
	53.3%	#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (/.f64 (.f64 (sqrt.f64 (PI.f64)) (sqrt.f64 (.f64 n #s(literal 2 binary64)))) (sqrt.f64 k)))
✓	53.5%	#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)))
✓	99.3%	#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (.f64 (sqrt.f64 (/.f64 (.f64 (.f64 (PI.f64) n) #s(literal 2 binary64)) (pow.f64 (.f64 (*.f64 (PI.f64) n) #s(literal 2 binary64)) k))) (sqrt.f64 (/.f64 #s(literal 1 binary64) k))))
	53.2%	#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (.f64 (sqrt.f64 (/.f64 (.f64 (PI.f64) #s(literal 2 binary64)) k)) (sqrt.f64 n)))
	39.5%	#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))))
	53.3%	#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (.f64 (sqrt.f64 (.f64 (PI.f64) n)) (/.f64 (sqrt.f64 #s(literal 2 binary64)) (sqrt.f64 k))))
	39.6%	#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (.f64 (sqrt.f64 (sqrt.f64 (PI.f64))) (sqrt.f64 (.f64 (/.f64 n k) (*.f64 (sqrt.f64 (PI.f64)) #s(literal 2 binary64))))))
	53.5%	#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (.f64 (sqrt.f64 #s(approx (pow ( (* (PI) n) 2) (- 1 k)) (.f64 (.f64 (PI.f64) n) #s(literal 2 binary64)))) (sqrt.f64 (/.f64 #s(literal 1 binary64) k))))
	53.4%	#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (.f64 (sqrt.f64 #s(literal 2 binary64)) (.f64 (sqrt.f64 (PI.f64)) (/.f64 (sqrt.f64 n) (sqrt.f64 k)))))
	39.5%	#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)))))
✓	39.6%	#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))))
	39.5%	#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)))))
	39.6%	#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))))
✓	39.5%	#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt.f64 (.f64 (.f64 (sqrt.f64 (PI.f64)) (*.f64 (sqrt.f64 (PI.f64)) (/.f64 n k))) #s(literal 2 binary64))))
	39.6%	#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt.f64 (.f64 (PI.f64) (/.f64 (.f64 n #s(literal 2 binary64)) k))))
✓	39.7%	#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt.f64 (.f64 n (/.f64 (.f64 #s(literal 2 binary64) (PI.f64)) k))))
	39.6%	#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt.f64 (.f64 n (.f64 (PI.f64) (/.f64 #s(literal 2 binary64) k)))))
✓	85.4%	#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) #s(approx (* (sqrt (pow (* (* (PI) n) 2) (- 1 k))) (sqrt (/ 1 k))) (sqrt.f64 (/.f64 (pow.f64 (.f64 (.f64 (PI.f64) n) #s(literal 2 binary64)) (-.f64 #s(literal 1 binary64) k)) k))))
	85.5%	#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) #s(approx (* (sqrt (pow (* (* (PI) n) 2) (- 1 k))) (sqrt (/ 1 k))) (sqrt.f64 (/.f64 (.f64 (.f64 (PI.f64) n) #s(literal 2 binary64)) (.f64 (pow.f64 (.f64 (*.f64 (PI.f64) n) #s(literal 2 binary64)) k) k)))))
	39.8%	#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) #s(approx (* (sqrt (pow (* (* (PI) n) 2) (- 1 k))) (sqrt (/ 1 k))) (sqrt.f64 (/.f64 #s(approx (pow (* (* (PI) n) 2) (- 1 k)) (.f64 #s(literal -2 binary64) (fma.f64 (.f64 (log.f64 (.f64 (.f64 (PI.f64) n) #s(literal 2 binary64))) (.f64 (PI.f64) n)) k (.f64 (neg.f64 (PI.f64)) n)))) k))))
	24.0%	#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) #s(approx (* (sqrt (pow (* (* (PI) n) 2) (- 1 k))) (sqrt (/ 1 k))) (neg.f64 (sqrt.f64 (/.f64 (pow.f64 (.f64 (.f64 (PI.f64) n) #s(literal 2 binary64)) (-.f64 #s(literal 1 binary64) k)) k)))))

Compiler

Compiled 2 276 to 873 computations (61.6% saved)

regimes84.0ms (0.9%)

Memory

8.4MiB live, 105.0MiB allocated; 13ms collecting garbage

Counts

50 → 1

Calls

Call 1

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

Outputs
(.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)))

Calls

4 calls:

41.0ms	n
16.0ms	k
12.0ms	(.f64 (.f64 #s(literal 2 binary64) (PI.f64)) n)
11.0ms	(.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
99.6%	1	`(.f64 (.f64 #s(literal 2 binary64) (PI.f64)) n)`
99.6%	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))))`
99.6%	1	`k`
99.6%	1	`n`

Compiler

Compiled 23 to 23 computations (0% saved)

regimes49.0ms (0.5%)

Memory

-1.5MiB live, 87.5MiB allocated; 7ms collecting garbage

Counts

42 → 1

Calls

Call 1

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

Outputs
(/.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))

Calls

4 calls:

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))))
11.0ms	(.f64 (.f64 #s(literal 2 binary64) (PI.f64)) n)
11.0ms	n
10.0ms	k

Results

Accuracy	Segments	Branch
99.6%	1	`(.f64 (.f64 #s(literal 2 binary64) (PI.f64)) n)`
99.6%	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))))`
99.6%	1	`n`
99.6%	1	`k`

Compiler

Compiled 23 to 23 computations (0% saved)

regimes49.0ms (0.5%)

Memory

-0.9MiB live, 55.0MiB allocated; 6ms collecting garbage

Counts

31 → 1

Calls

Call 1

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

Outputs

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

Calls

4 calls:

24.0ms	n
8.0ms	k
8.0ms	(.f64 (.f64 #s(literal 2 binary64) (PI.f64)) n)
7.0ms	(.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)

regimes36.0ms (0.4%)

Memory

-24.8MiB live, 67.0MiB allocated; 5ms collecting garbage

Counts

30 → 2

Calls

Call 1

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

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

Calls

4 calls:

10.0ms	k
9.0ms	n
8.0ms	(.f64 (.f64 #s(literal 2 binary64) (PI.f64)) n)
7.0ms	(.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
99.2%	2	`k`
85.4%	1	`(.f64 (.f64 #s(literal 2 binary64) (PI.f64)) n)`
99.3%	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))))`
85.4%	1	`n`

Compiler

Compiled 23 to 23 computations (0% saved)

regimes46.0ms (0.5%)

Memory

-3.5MiB live, 43.3MiB allocated; 2ms collecting garbage

Counts

27 → 1

Calls

Call 1

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

Calls

4 calls:

24.0ms	n
7.0ms	(.f64 (.f64 #s(literal 2 binary64) (PI.f64)) n)
7.0ms	k
6.0ms	(.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
53.5%	1	`(.f64 (.f64 #s(literal 2 binary64) (PI.f64)) n)`
53.5%	1	`n`
53.5%	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))))`
53.5%	1	`k`

Compiler

Compiled 23 to 23 computations (0% saved)

regimes14.0ms (0.1%)

Memory

21.5MiB live, 21.5MiB allocated; 0ms collecting garbage

Counts

10 → 1

Calls

Call 1

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

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

Calls

4 calls:

3.0ms	k
3.0ms	(.f64 (.f64 #s(literal 2 binary64) (PI.f64)) n)
3.0ms	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
53.2%	1	`k`
53.2%	1	`(.f64 (.f64 #s(literal 2 binary64) (PI.f64)) n)`
53.2%	1	`n`
53.2%	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))))`

Compiler

Compiled 23 to 23 computations (0% saved)

regimes28.0ms (0.3%)

Memory

-34.7MiB live, 19.5MiB allocated; 13ms collecting garbage

Counts

9 → 1

Calls

Call 1

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

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

Calls

4 calls:

19.0ms	(.f64 (.f64 #s(literal 2 binary64) (PI.f64)) n)
3.0ms	k
3.0ms	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
39.7%	1	`k`
39.7%	1	`(.f64 (.f64 #s(literal 2 binary64) (PI.f64)) n)`
39.7%	1	`n`
39.7%	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))))`

Compiler

Compiled 23 to 23 computations (0% saved)

regimes4.0ms (0%)

Memory

10.2MiB live, 10.2MiB allocated; 0ms collecting garbage

Accuracy

Total -0.0b remaining (-0%)

Threshold costs -0b (-0%)

Counts

1 → 1

Calls

Call 1

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

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

Calls

4 calls:

1.0ms	(.f64 (.f64 #s(literal 2 binary64) (PI.f64)) n)
1.0ms	n
1.0ms	(.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))))
1.0ms	k

Results

Accuracy	Segments	Branch
39.6%	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))))`
39.6%	1	`k`
39.6%	1	`(.f64 (.f64 #s(literal 2 binary64) (PI.f64)) n)`
39.6%	1	`n`

Compiler

Compiled 23 to 23 computations (0% saved)

bsearch24.0ms (0.3%)

Memory

-7.2MiB live, 37.1MiB allocated; 5ms collecting garbage

Algorithm

1×	binary-search

Stop Event

1×	narrow-enough

Steps

Time	Left	Right
22.0ms	8.163282699141772e-31	1.3631959982157052e-25

Samples

13.0ms

144×

valid

Compiler

Compiled 658 to 504 computations (23.4% saved)

Precisions

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

ival-pow: 3.0ms (31.4% of total)

ival-div: 2.0ms (20.9% of total)

ival-mult: 2.0ms (20.9% of total)

ival-pi: 1.0ms (10.5% of total)

ival-sub: 1.0ms (10.5% of total)

ival-sqrt: 1.0ms (10.5% 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)

simplify48.0ms (0.5%)

Memory

18.9MiB live, 62.9MiB allocated; 5ms collecting garbage

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	69	239
1	90	227
2	119	227
3	244	227
4	1157	227
5	4706	227

Stop Event

1×	node limit

Calls

Call 1

Inputs
(.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 (.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)) #s(approx ( (pow (* (PI) 2) (/ (- 1 k) 2)) (pow 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)))))
(if (<=.f64 k #s(literal 4816960962882615/356811923176489970264571492362373784095686656 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))) #s(approx (* (sqrt (pow (* (* (PI) n) 2) (- 1 k))) (sqrt (/ 1 k))) (sqrt.f64 (/.f64 (pow.f64 (.f64 (.f64 (PI.f64) n) #s(literal 2 binary64)) (-.f64 #s(literal 1 binary64) 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))) (.f64 (sqrt.f64 (/.f64 (.f64 (PI.f64) #s(literal 2 binary64)) k)) (sqrt.f64 n)))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt.f64 (.f64 n (/.f64 (.f64 #s(literal 2 binary64) (PI.f64)) k))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt.f64 (.f64 n (.f64 (PI.f64) (/.f64 #s(literal 2 binary64) k)))))

Outputs
(.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 (.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)) #s(approx ( (pow (* (PI) 2) (/ (- 1 k) 2)) (pow 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)))))
(if (<=.f64 k #s(literal 4816960962882615/356811923176489970264571492362373784095686656 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))) #s(approx (* (sqrt (pow (* (* (PI) n) 2) (- 1 k))) (sqrt (/ 1 k))) (sqrt.f64 (/.f64 (pow.f64 (.f64 (.f64 (PI.f64) n) #s(literal 2 binary64)) (-.f64 #s(literal 1 binary64) 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))) (.f64 (sqrt.f64 (/.f64 (.f64 (PI.f64) #s(literal 2 binary64)) k)) (sqrt.f64 n)))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt.f64 (.f64 n (/.f64 (.f64 #s(literal 2 binary64) (PI.f64)) k))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt.f64 (.f64 n (.f64 (PI.f64) (/.f64 #s(literal 2 binary64) k)))))

derivations136.0ms (1.5%)

Memory

-20.6MiB live, 126.4MiB allocated; 8ms collecting garbage

Stop Event

1×

fuel

Compiler

Compiled 239 to 71 computations (70.3% saved)

preprocess39.0ms (0.4%)

Memory: 18.6MiB live, 64.4MiB allocated; 4ms collecting garbage
Compiler: Compiled 510 to 168 computations (67.1% saved)

end0.0ms (0%)

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

start0.0ms (0%)

analyze125.0ms (1.3%)

sample4.8s (51%)

explain199.0ms (2.1%)

preprocess296.0ms (3.2%)

eval0.0ms (0%)

prune0.0ms (0%)

simplify115.0ms (1.2%)

localize41.0ms (0.4%)

series132.0ms (1.4%)

simplify126.0ms (1.4%)

rewrite200.0ms (2.1%)

eval9.0ms (0.1%)

prune20.0ms (0.2%)

simplify117.0ms (1.3%)

localize211.0ms (2.3%)

series235.0ms (2.5%)

simplify178.0ms (1.9%)

rewrite69.0ms (0.7%)

eval79.0ms (0.8%)

prune22.0ms (0.2%)

simplify131.0ms (1.4%)

localize160.0ms (1.7%)

series103.0ms (1.1%)

simplify301.0ms (3.2%)

rewrite105.0ms (1.1%)

eval70.0ms (0.7%)

prune107.0ms (1.1%)

simplify154.0ms (1.6%)

localize182.0ms (2%)

series142.0ms (1.5%)

simplify212.0ms (2.3%)

rewrite81.0ms (0.9%)

eval46.0ms (0.5%)

prune47.0ms (0.5%)

regimes84.0ms (0.9%)

regimes49.0ms (0.5%)

regimes49.0ms (0.5%)

regimes36.0ms (0.4%)

regimes46.0ms (0.5%)

regimes14.0ms (0.1%)

regimes28.0ms (0.3%)

regimes4.0ms (0%)

bsearch24.0ms (0.3%)

simplify48.0ms (0.5%)

derivations136.0ms (1.5%)

preprocess39.0ms (0.4%)

end0.0ms (0%)

Profiling