Metrics for Migdal et al, Equation (51)

start0.0ms (0%)

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

analyze144.0ms (2.9%)

Memory

3.5MiB live, 161.1MiB allocated; 50ms 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)

sample3.2s (64.9%)

Memory

-49.7MiB live, 4 030.1MiB allocated; 1.4s collecting garbage

Samples

1.1s	5 526×	1	invalid
837.0ms	8 256×	0	valid
140.0ms	463×	2	invalid
24.0ms	381×	0	invalid
21.0ms	227×	0	exit

Precisions

Click to see histograms. Total time spent on operations: 1.6s

ival-pow: 637.0ms (40.6% of total)

ival-mult!: 272.0ms (17.3% of total)

ival-div!: 251.0ms (16% of total)

adjust: 190.0ms (12.1% of total)

ival-sqrt: 139.0ms (8.9% of total)

ival-sub!: 79.0ms (5% of total)

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

exact: 0.0ms (0% of total)

Bogosity

explain236.0ms (4.7%)

Memory

21.9MiB live, 392.1MiB allocated; 65ms collecting garbage

FPErrors

Click to see full error table

Ground Truth	Overpredictions	Example	Underpredictions	Example	Subexpression
6	85	(4.196668409962216e-111 1.1937597392430984e+254)	1	(1.096244722358154e-8 2.6389252601283493e+81)	`(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	89	27
`pow.f64`	`(pow.f64 (.f64 (.f64 #s(literal 2 binary64) (PI.f64)) n) (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 2 binary64)))`	oflow-rescue	1	0
↳	`(.f64 (.f64 #s(literal 2 binary64) (PI.f64)) n)`	overflow	2
↳	`(pow.f64 (.f64 (.f64 #s(literal 2 binary64) (PI.f64)) n) (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 2 binary64)))`	overflow	65

Confusion

	Predicted +	Predicted -
+	5	1
-	85	165

Precision

0.05555555555555555

Recall

0.8333333333333334

Confusion?

	Predicted +	Predicted Maybe	Predicted -
+	5	1	0
-	85	26	139

Precision?

0.05128205128205128

Recall?

1.0

Freqs

test

number	freq
0	166
1	90

Total Confusion?

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

Precision?

1.0

Recall?

1.0

Samples

106.0ms

512×

valid

Compiler

Compiled 128 to 43 computations (66.4% saved)

Precisions

Click to see histograms. Total time spent on operations: 26.0ms

ival-pow: 10.0ms (38.9% of total)

ival-div!: 5.0ms (19.4% of total)

ival-sqrt: 4.0ms (15.5% of total)

ival-mult!: 4.0ms (15.5% of total)

ival-sub!: 2.0ms (7.8% of total)

adjust: 0.0ms (0% of total)

preprocess46.0ms (0.9%)

Memory

-20.1MiB live, 10.0MiB allocated; 26ms collecting garbage

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	33	104
1	76	90
2	162	88
3	382	88
4	1615	88

Stop Event

1×	node-limit

Alt Table

Click to see full alt table

Status	Accuracy	Program
▶	99.0%	(.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))))

Compiler

Compiled 32 to 26 computations (18.8% saved)

series108.0ms (2.2%)

Memory

31.7MiB live, 80.7MiB allocated; 50ms collecting garbage

Counts

13 → 34

Calls

Call 1

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

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

Calls

6 calls:

Time	Variable		Point	Expression
52.0ms	n	@	inf	((* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (/ 1 (sqrt k)) 1 (sqrt k) k (pow (* (* 2 (PI)) n) (/ (- 1 k) 2)) (* (* 2 (PI)) n) (* 2 (PI)) 2 (PI) n (/ (- 1 k) 2) (- 1 k))
28.0ms	n	@	0	((* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (/ 1 (sqrt k)) 1 (sqrt k) k (pow (* (* 2 (PI)) n) (/ (- 1 k) 2)) (* (* 2 (PI)) n) (* 2 (PI)) 2 (PI) n (/ (- 1 k) 2) (- 1 k))
21.0ms	n	@	-inf	((* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (/ 1 (sqrt k)) 1 (sqrt k) k (pow (* (* 2 (PI)) n) (/ (- 1 k) 2)) (* (* 2 (PI)) n) (* 2 (PI)) 2 (PI) n (/ (- 1 k) 2) (- 1 k))
3.0ms	k	@	-inf	((* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (/ 1 (sqrt k)) 1 (sqrt k) k (pow (* (* 2 (PI)) n) (/ (- 1 k) 2)) (* (* 2 (PI)) n) (* 2 (PI)) 2 (PI) n (/ (- 1 k) 2) (- 1 k))
3.0ms	k	@	0	((* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (/ 1 (sqrt k)) 1 (sqrt k) k (pow (* (* 2 (PI)) n) (/ (- 1 k) 2)) (* (* 2 (PI)) n) (* 2 (PI)) 2 (PI) n (/ (- 1 k) 2) (- 1 k))

rewrite72.0ms (1.4%)

Memory

-3.0MiB live, 90.5MiB allocated; 8ms collecting garbage

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	181	965
0	195	935
0	833	922

Stop Event

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

Counts

47 → 70

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

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

eval7.0ms (0.2%)

Memory: 16.5MiB live, 16.6MiB allocated; 0ms collecting garbage
Compiler: Compiled 1 740 to 286 computations (83.6% saved)

prune12.0ms (0.2%)

Memory

-23.2MiB live, 22.9MiB allocated; 3ms collecting garbage

Pruning

13 alts after pruning (13 fresh and 0 done)

	Pruned	Kept	Total
New	59	13	72
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	60	13	73

Accuracy

99.9%

Counts

73 → 13

Alt Table

Click to see full alt table

Status	Accuracy	Program
▶	99.1%	(/.f64 (.f64 #s(literal 1 binary64) (pow.f64 (.f64 (*.f64 (PI.f64) #s(literal 2 binary64)) n) (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 2 binary64)))) (sqrt.f64 k))
▶	99.0%	(.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) (pow.f64 (.f64 (*.f64 #s(literal 2 binary64) (PI.f64)) n) #s(approx (/ (- 1 k) 2) (fma.f64 #s(literal -1/2 binary64) k #s(literal 1/2 binary64)))))
	51.8%	(.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) (pow.f64 (.f64 (.f64 #s(literal 2 binary64) (PI.f64)) n) #s(approx (/ (- 1 k) 2) (.f64 #s(literal -1/2 binary64) k))))
▶	98.9%	(.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) (.f64 (pow.f64 (.f64 (.f64 (PI.f64) #s(literal 2 binary64)) n) (/.f64 (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 2 binary64)) #s(literal 2 binary64))) (pow.f64 (.f64 (.f64 (PI.f64) #s(literal 2 binary64)) n) (/.f64 (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 2 binary64)) #s(literal 2 binary64)))))
	74.6%	(.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 (.f64 (PI.f64) #s(literal 2 binary64)) n)) (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 2 binary64)))))
	59.2%	(.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) #s(approx (pow ( (* 2 (PI)) n) (/ (- 1 k) 2)) (fma.f64 (fma.f64 (.f64 k (.f64 (.f64 (sqrt.f64 (.f64 (PI.f64) n)) (pow.f64 (log.f64 (.f64 (.f64 (PI.f64) #s(literal 2 binary64)) n)) #s(literal 2 binary64))) (sqrt.f64 #s(literal 2 binary64)))) #s(literal 1/8 binary64) (.f64 (.f64 #s(literal -1/2 binary64) (sqrt.f64 (.f64 (PI.f64) n))) (.f64 (log.f64 (.f64 (.f64 (PI.f64) #s(literal 2 binary64)) n)) (sqrt.f64 #s(literal 2 binary64))))) k (sqrt.f64 (.f64 (.f64 (PI.f64) #s(literal 2 binary64)) n)))))
	51.4%	(.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) #s(approx (pow ( (* 2 (PI)) n) (/ (- 1 k) 2)) (fma.f64 (.f64 (.f64 (.f64 (log.f64 (.f64 (.f64 (PI.f64) #s(literal 2 binary64)) n)) (sqrt.f64 #s(literal 2 binary64))) k) (sqrt.f64 (.f64 (PI.f64) n))) #s(literal -1/2 binary64) (sqrt.f64 (.f64 (.f64 (PI.f64) #s(literal 2 binary64)) n)))))
	95.5%	(.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) #s(approx (pow ( (* 2 (PI)) n) (/ (- 1 k) 2)) (pow.f64 (exp.f64 #s(literal 1/2 binary64)) (.f64 (log.f64 (.f64 (*.f64 (PI.f64) #s(literal 2 binary64)) n)) (-.f64 #s(literal 1 binary64) k)))))
	50.9%	(.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) #s(approx (pow ( (* 2 (PI)) n) (/ (- 1 k) 2)) (sqrt.f64 (.f64 (.f64 (PI.f64) #s(literal 2 binary64)) n))))
	99.1%	(.f64 (sqrt.f64 (pow.f64 k #s(literal -1 binary64))) (pow.f64 (.f64 (*.f64 #s(literal 2 binary64) (PI.f64)) n) (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 2 binary64))))
	54.8%	#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (/.f64 (fma.f64 (.f64 (.f64 (log.f64 (.f64 (.f64 (PI.f64) #s(literal 2 binary64)) n)) (sqrt.f64 #s(literal 2 binary64))) (sqrt.f64 (.f64 (.f64 (pow.f64 k #s(literal 3 binary64)) n) (PI.f64)))) #s(literal -1/2 binary64) (sqrt.f64 (.f64 (.f64 (*.f64 (PI.f64) n) k) #s(literal 2 binary64)))) k))
▶	40.8%	#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt.f64 (.f64 (/.f64 (.f64 (PI.f64) n) k) #s(literal 2 binary64))))

Compiler

Compiled 744 to 542 computations (27.2% saved)

series111.0ms (2.2%)

Memory

-14.4MiB live, 130.4MiB allocated; 71ms collecting garbage

Counts

35 → 134

Calls

Call 1

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

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

6 calls:

Time	Variable		Point	Expression
54.0ms	k	@	inf	((/ (* 1 (pow (* (* (PI) 2) n) (/ (- 1 k) 2))) (sqrt k)) (* 1 (pow (* (* (PI) 2) n) (/ (- 1 k) 2))) 1 (pow (* (* (PI) 2) n) (/ (- 1 k) 2)) (* (* (PI) 2) n) (* (PI) 2) (PI) 2 n (/ (- 1 k) 2) (- 1 k) k (sqrt k) (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt (* (/ (* (PI) n) k) 2)) (* (/ (* (PI) n) k) 2) (/ (* (PI) n) k) (* (PI) n) (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2)) (* (* 2 (PI)) n) (* 2 (PI)) (/ (- 1 k) 2) (+ (* -1/2 k) 1/2) -1/2 1/2 (* (/ 1 (sqrt k)) (exp (* (log (* (* (PI) 2) n)) (/ (- 1 k) 2)))) (exp (* (log (* (* (PI) 2) n)) (/ (- 1 k) 2))) (* (log (* (* (PI) 2) n)) (/ (- 1 k) 2)) (log (* (* (PI) 2) n)) (* (/ 1 (sqrt k)) (* (pow (* (* (PI) 2) n) (/ (/ (- 1 k) 2) 2)) (pow (* (* (PI) 2) n) (/ (/ (- 1 k) 2) 2)))) (* (pow (* (* (PI) 2) n) (/ (/ (- 1 k) 2) 2)) (pow (* (* (PI) 2) n) (/ (/ (- 1 k) 2) 2))) (pow (* (* (PI) 2) n) (/ (/ (- 1 k) 2) 2)) (/ (/ (- 1 k) 2) 2))
14.0ms	n	@	inf	((/ (* 1 (pow (* (* (PI) 2) n) (/ (- 1 k) 2))) (sqrt k)) (* 1 (pow (* (* (PI) 2) n) (/ (- 1 k) 2))) 1 (pow (* (* (PI) 2) n) (/ (- 1 k) 2)) (* (* (PI) 2) n) (* (PI) 2) (PI) 2 n (/ (- 1 k) 2) (- 1 k) k (sqrt k) (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt (* (/ (* (PI) n) k) 2)) (* (/ (* (PI) n) k) 2) (/ (* (PI) n) k) (* (PI) n) (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2)) (* (* 2 (PI)) n) (* 2 (PI)) (/ (- 1 k) 2) (+ (* -1/2 k) 1/2) -1/2 1/2 (* (/ 1 (sqrt k)) (exp (* (log (* (* (PI) 2) n)) (/ (- 1 k) 2)))) (exp (* (log (* (* (PI) 2) n)) (/ (- 1 k) 2))) (* (log (* (* (PI) 2) n)) (/ (- 1 k) 2)) (log (* (* (PI) 2) n)) (* (/ 1 (sqrt k)) (* (pow (* (* (PI) 2) n) (/ (/ (- 1 k) 2) 2)) (pow (* (* (PI) 2) n) (/ (/ (- 1 k) 2) 2)))) (* (pow (* (* (PI) 2) n) (/ (/ (- 1 k) 2) 2)) (pow (* (* (PI) 2) n) (/ (/ (- 1 k) 2) 2))) (pow (* (* (PI) 2) n) (/ (/ (- 1 k) 2) 2)) (/ (/ (- 1 k) 2) 2))
13.0ms	n	@	-inf	((/ (* 1 (pow (* (* (PI) 2) n) (/ (- 1 k) 2))) (sqrt k)) (* 1 (pow (* (* (PI) 2) n) (/ (- 1 k) 2))) 1 (pow (* (* (PI) 2) n) (/ (- 1 k) 2)) (* (* (PI) 2) n) (* (PI) 2) (PI) 2 n (/ (- 1 k) 2) (- 1 k) k (sqrt k) (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt (* (/ (* (PI) n) k) 2)) (* (/ (* (PI) n) k) 2) (/ (* (PI) n) k) (* (PI) n) (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2)) (* (* 2 (PI)) n) (* 2 (PI)) (/ (- 1 k) 2) (+ (* -1/2 k) 1/2) -1/2 1/2 (* (/ 1 (sqrt k)) (exp (* (log (* (* (PI) 2) n)) (/ (- 1 k) 2)))) (exp (* (log (* (* (PI) 2) n)) (/ (- 1 k) 2))) (* (log (* (* (PI) 2) n)) (/ (- 1 k) 2)) (log (* (* (PI) 2) n)) (* (/ 1 (sqrt k)) (* (pow (* (* (PI) 2) n) (/ (/ (- 1 k) 2) 2)) (pow (* (* (PI) 2) n) (/ (/ (- 1 k) 2) 2)))) (* (pow (* (* (PI) 2) n) (/ (/ (- 1 k) 2) 2)) (pow (* (* (PI) 2) n) (/ (/ (- 1 k) 2) 2))) (pow (* (* (PI) 2) n) (/ (/ (- 1 k) 2) 2)) (/ (/ (- 1 k) 2) 2))
11.0ms	n	@	0	((/ (* 1 (pow (* (* (PI) 2) n) (/ (- 1 k) 2))) (sqrt k)) (* 1 (pow (* (* (PI) 2) n) (/ (- 1 k) 2))) 1 (pow (* (* (PI) 2) n) (/ (- 1 k) 2)) (* (* (PI) 2) n) (* (PI) 2) (PI) 2 n (/ (- 1 k) 2) (- 1 k) k (sqrt k) (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt (* (/ (* (PI) n) k) 2)) (* (/ (* (PI) n) k) 2) (/ (* (PI) n) k) (* (PI) n) (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2)) (* (* 2 (PI)) n) (* 2 (PI)) (/ (- 1 k) 2) (+ (* -1/2 k) 1/2) -1/2 1/2 (* (/ 1 (sqrt k)) (exp (* (log (* (* (PI) 2) n)) (/ (- 1 k) 2)))) (exp (* (log (* (* (PI) 2) n)) (/ (- 1 k) 2))) (* (log (* (* (PI) 2) n)) (/ (- 1 k) 2)) (log (* (* (PI) 2) n)) (* (/ 1 (sqrt k)) (* (pow (* (* (PI) 2) n) (/ (/ (- 1 k) 2) 2)) (pow (* (* (PI) 2) n) (/ (/ (- 1 k) 2) 2)))) (* (pow (* (* (PI) 2) n) (/ (/ (- 1 k) 2) 2)) (pow (* (* (PI) 2) n) (/ (/ (- 1 k) 2) 2))) (pow (* (* (PI) 2) n) (/ (/ (- 1 k) 2) 2)) (/ (/ (- 1 k) 2) 2))
8.0ms	k	@	0	((/ (* 1 (pow (* (* (PI) 2) n) (/ (- 1 k) 2))) (sqrt k)) (* 1 (pow (* (* (PI) 2) n) (/ (- 1 k) 2))) 1 (pow (* (* (PI) 2) n) (/ (- 1 k) 2)) (* (* (PI) 2) n) (* (PI) 2) (PI) 2 n (/ (- 1 k) 2) (- 1 k) k (sqrt k) (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt (* (/ (* (PI) n) k) 2)) (* (/ (* (PI) n) k) 2) (/ (* (PI) n) k) (* (PI) n) (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2)) (* (* 2 (PI)) n) (* 2 (PI)) (/ (- 1 k) 2) (+ (* -1/2 k) 1/2) -1/2 1/2 (* (/ 1 (sqrt k)) (exp (* (log (* (* (PI) 2) n)) (/ (- 1 k) 2)))) (exp (* (log (* (* (PI) 2) n)) (/ (- 1 k) 2))) (* (log (* (* (PI) 2) n)) (/ (- 1 k) 2)) (log (* (* (PI) 2) n)) (* (/ 1 (sqrt k)) (* (pow (* (* (PI) 2) n) (/ (/ (- 1 k) 2) 2)) (pow (* (* (PI) 2) n) (/ (/ (- 1 k) 2) 2)))) (* (pow (* (* (PI) 2) n) (/ (/ (- 1 k) 2) 2)) (pow (* (* (PI) 2) n) (/ (/ (- 1 k) 2) 2))) (pow (* (* (PI) 2) n) (/ (/ (- 1 k) 2) 2)) (/ (/ (- 1 k) 2) 2))

rewrite78.0ms (1.6%)

Memory

31.8MiB live, 126.9MiB allocated; 6ms collecting garbage

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	411	5105
0	464	4445
0	1713	4381

Stop Event

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

Counts

169 → 303

Calls

Call 1

Inputs
(/.f64 (.f64 #s(literal 1 binary64) (pow.f64 (.f64 (*.f64 (PI.f64) #s(literal 2 binary64)) n) (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 2 binary64)))) (sqrt.f64 k))
(.f64 #s(literal 1 binary64) (pow.f64 (.f64 (*.f64 (PI.f64) #s(literal 2 binary64)) n) (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 2 binary64))))
#s(literal 1 binary64)
(pow.f64 (.f64 (.f64 (PI.f64) #s(literal 2 binary64)) n) (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 2 binary64)))
(.f64 (.f64 (PI.f64) #s(literal 2 binary64)) n)
(*.f64 (PI.f64) #s(literal 2 binary64))
(PI.f64)
#s(literal 2 binary64)
n
(/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 2 binary64))
(-.f64 #s(literal 1 binary64) k)
k
(sqrt.f64 k)
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt.f64 (.f64 (/.f64 (.f64 (PI.f64) n) k) #s(literal 2 binary64))))
(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)
(.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) (pow.f64 (.f64 (*.f64 #s(literal 2 binary64) (PI.f64)) n) #s(approx (/ (- 1 k) 2) (fma.f64 #s(literal -1/2 binary64) k #s(literal 1/2 binary64)))))
(/.f64 #s(literal 1 binary64) (sqrt.f64 k))
(pow.f64 (.f64 (.f64 #s(literal 2 binary64) (PI.f64)) n) #s(approx (/ (- 1 k) 2) (fma.f64 #s(literal -1/2 binary64) k #s(literal 1/2 binary64))))
(.f64 (.f64 #s(literal 2 binary64) (PI.f64)) n)
(*.f64 #s(literal 2 binary64) (PI.f64))
#s(approx (/ (- 1 k) 2) (fma.f64 #s(literal -1/2 binary64) k #s(literal 1/2 binary64)))
(fma.f64 #s(literal -1/2 binary64) k #s(literal 1/2 binary64))
#s(literal -1/2 binary64)
#s(literal 1/2 binary64)
(.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) (exp.f64 (.f64 (log.f64 (.f64 (.f64 (PI.f64) #s(literal 2 binary64)) n)) (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 2 binary64)))))
(exp.f64 (.f64 (log.f64 (.f64 (*.f64 (PI.f64) #s(literal 2 binary64)) n)) (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 2 binary64))))
(.f64 (log.f64 (.f64 (*.f64 (PI.f64) #s(literal 2 binary64)) n)) (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 2 binary64)))
(log.f64 (.f64 (.f64 (PI.f64) #s(literal 2 binary64)) n))
(.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) (.f64 (pow.f64 (.f64 (.f64 (PI.f64) #s(literal 2 binary64)) n) (/.f64 (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 2 binary64)) #s(literal 2 binary64))) (pow.f64 (.f64 (.f64 (PI.f64) #s(literal 2 binary64)) n) (/.f64 (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 2 binary64)) #s(literal 2 binary64)))))
(.f64 (pow.f64 (.f64 (.f64 (PI.f64) #s(literal 2 binary64)) n) (/.f64 (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 2 binary64)) #s(literal 2 binary64))) (pow.f64 (.f64 (*.f64 (PI.f64) #s(literal 2 binary64)) n) (/.f64 (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 2 binary64)) #s(literal 2 binary64))))
(pow.f64 (.f64 (.f64 (PI.f64) #s(literal 2 binary64)) n) (/.f64 (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 2 binary64)) #s(literal 2 binary64)))
(/.f64 (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 2 binary64)) #s(literal 2 binary64))
#s(approx (/ (* 1 (pow (* (* (PI) 2) n) (/ (- 1 k) 2))) (sqrt k)) #s(hole binary64 (* (sqrt (/ (* n (PI)) k)) (sqrt 2))))
#s(approx (/ (* 1 (pow (* (* (PI) 2) n) (/ (- 1 k) 2))) (sqrt 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 (/ (* 1 (pow (* (* (PI) 2) n) (/ (- 1 k) 2))) (sqrt 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 (/ (* 1 (pow (* (* (PI) 2) n) (/ (- 1 k) 2))) (sqrt 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 (* 1 (pow (* (* (PI) 2) n) (/ (- 1 k) 2))) #s(hole binary64 (* (sqrt (* n (PI))) (sqrt 2))))
#s(approx (* 1 (pow (* (* (PI) 2) 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 (* 1 (pow (* (* (PI) 2) 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 (* 1 (pow (* (* (PI) 2) 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 (* (* (PI) 2) n) (/ (- 1 k) 2)) #s(hole binary64 (* (sqrt (* n (PI))) (sqrt 2))))
#s(approx (pow (* (* (PI) 2) 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 (* (* (PI) 2) 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 (* (* (PI) 2) n) (/ (- 1 k) 2)) #s(hole binary64 (+ (* k (+ (* -1/2 (* (sqrt (* n (PI))) (* (log (* 2 (* n (PI)))) (sqrt 2)))) (* k (+ (* -1/48 (* (* k (* (pow (log (* 2 (* n (PI)))) 3) (sqrt 2))) (sqrt (* n (PI))))) (* 1/8 (* (sqrt (* n (PI))) (* (pow (log (* 2 (* n (PI)))) 2) (sqrt 2)))))))) (* (sqrt (* n (PI))) (sqrt 2)))))
#s(approx (/ (- 1 k) 2) #s(hole binary64 1/2))
#s(approx (/ (- 1 k) 2) #s(hole binary64 (+ 1/2 (* -1/2 k))))
#s(approx (- 1 k) #s(hole binary64 1))
#s(approx (- 1 k) #s(hole binary64 (+ 1 (* -1 k))))
#s(approx k #s(hole binary64 k))
#s(approx (sqrt k) #s(hole binary64 (sqrt k)))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) #s(hole binary64 (* (sqrt (/ (* n (PI)) k)) (sqrt 2))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) #s(hole binary64 (/ (+ (* -1/2 (* (sqrt (* (pow k 3) (* n (PI)))) (* (log (* 2 (* n (PI)))) (sqrt 2)))) (* (sqrt (* k (* n (PI)))) (sqrt 2))) k)))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) #s(hole binary64 (/ (+ (* k (+ (* -1/2 (* (sqrt (* k (* n (PI)))) (* (log (* 2 (* n (PI)))) (sqrt 2)))) (* 1/8 (* (sqrt (* (pow k 3) (* n (PI)))) (* (pow (log (* 2 (* n (PI)))) 2) (sqrt 2)))))) (* (sqrt (* k (* n (PI)))) (sqrt 2))) k)))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) #s(hole binary64 (/ (+ (* k (+ (* -1/2 (* (sqrt (* k (* n (PI)))) (* (log (* 2 (* n (PI)))) (sqrt 2)))) (* k (+ (* -1/48 (* (sqrt (* (pow k 3) (* n (PI)))) (* (pow (log (* 2 (* n (PI)))) 3) (sqrt 2)))) (* 1/8 (* (sqrt (* k (* n (PI)))) (* (pow (log (* 2 (* n (PI)))) 2) (sqrt 2)))))))) (* (sqrt (* k (* n (PI)))) (sqrt 2))) k)))
#s(approx (sqrt (* (/ (* (PI) n) k) 2)) #s(hole binary64 (* (sqrt (/ (* n (PI)) k)) (sqrt 2))))
#s(approx (* (/ (* (PI) n) k) 2) #s(hole binary64 (* 2 (/ (* n (PI)) k))))
#s(approx (/ (* (PI) n) k) #s(hole binary64 (/ (* n (PI)) k)))
#s(approx (/ 1 (sqrt k)) #s(hole binary64 (sqrt (/ 1 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 (+ (* -1/2 k) 1/2) #s(hole binary64 1/2))
#s(approx (+ (* -1/2 k) 1/2) #s(hole binary64 (+ 1/2 (* -1/2 k))))
#s(approx (* (/ 1 (sqrt k)) (exp (* (log (* (* (PI) 2) n)) (/ (- 1 k) 2)))) #s(hole binary64 (* (sqrt (/ (* n (PI)) k)) (sqrt 2))))
#s(approx (* (/ 1 (sqrt k)) (exp (* (log (* (* (PI) 2) 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)) (exp (* (log (* (* (PI) 2) 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)) (exp (* (log (* (* (PI) 2) 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 (exp (* (log (* (* (PI) 2) n)) (/ (- 1 k) 2))) #s(hole binary64 (* (sqrt (* n (PI))) (sqrt 2))))
#s(approx (exp (* (log (* (* (PI) 2) 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 (exp (* (log (* (* (PI) 2) 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 (exp (* (log (* (* (PI) 2) 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 (* (log (* (* (PI) 2) n)) (/ (- 1 k) 2)) #s(hole binary64 (* 1/2 (log (* 2 (* n (PI)))))))
#s(approx (* (log (* (* (PI) 2) n)) (/ (- 1 k) 2)) #s(hole binary64 (+ (* -1/2 (* k (log (* 2 (* n (PI)))))) (* 1/2 (log (* 2 (* n (PI))))))))
#s(approx (* (/ 1 (sqrt k)) (* (pow (* (* (PI) 2) n) (/ (/ (- 1 k) 2) 2)) (pow (* (* (PI) 2) n) (/ (/ (- 1 k) 2) 2)))) #s(hole binary64 (* (sqrt (/ (* n (PI)) k)) (sqrt 2))))
#s(approx (* (/ 1 (sqrt k)) (* (pow (* (* (PI) 2) n) (/ (/ (- 1 k) 2) 2)) (pow (* (* (PI) 2) n) (/ (/ (- 1 k) 2) 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) n) (/ (/ (- 1 k) 2) 2)) (pow (* (* (PI) 2) n) (/ (/ (- 1 k) 2) 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 (* (* (PI) 2) n) (/ (/ (- 1 k) 2) 2)) (pow (* (* (PI) 2) n) (/ (/ (- 1 k) 2) 2)))) #s(hole binary64 (/ (+ (* k (+ (* -1/2 (* (sqrt (* k (* n (PI)))) (* (log (* 2 (* n (PI)))) (sqrt 2)))) (* k (+ (* 1/8 (* (sqrt (* k (* n (PI)))) (* (pow (log (* 2 (* n (PI)))) 2) (sqrt 2)))) (* (sqrt (pow k 3)) (+ (* -1/64 (* (sqrt (* n (PI))) (* (pow (log (* 2 (* n (PI)))) 3) (sqrt 2)))) (* -1/192 (* (sqrt (* n (PI))) (* (pow (log (* 2 (* n (PI)))) 3) (sqrt 2)))))))))) (* (sqrt (* k (* n (PI)))) (sqrt 2))) k)))
#s(approx (* (pow (* (* (PI) 2) n) (/ (/ (- 1 k) 2) 2)) (pow (* (* (PI) 2) n) (/ (/ (- 1 k) 2) 2))) #s(hole binary64 (* (sqrt (* n (PI))) (sqrt 2))))
#s(approx (* (pow (* (* (PI) 2) n) (/ (/ (- 1 k) 2) 2)) (pow (* (* (PI) 2) n) (/ (/ (- 1 k) 2) 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) 2) n) (/ (/ (- 1 k) 2) 2)) (pow (* (* (PI) 2) n) (/ (/ (- 1 k) 2) 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)))))
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#s(approx (pow (* (* (PI) 2) n) (/ (/ (- 1 k) 2) 2)) #s(hole binary64 (pow (* 2 (* n (PI))) 1/4)))
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#s(approx (* 1 (pow (* (* (PI) 2) n) (/ (- 1 k) 2))) #s(hole binary64 (exp (* 1/2 (* (log (* 2 (* n (PI)))) (- 1 k))))))
#s(approx (pow (* (* (PI) 2) n) (/ (- 1 k) 2)) #s(hole binary64 (exp (* 1/2 (* (log (* 2 (* n (PI)))) (- 1 k))))))
#s(approx (/ (- 1 k) 2) #s(hole binary64 (* -1/2 k)))
#s(approx (/ (- 1 k) 2) #s(hole binary64 (* k (- (* 1/2 (/ 1 k)) 1/2))))
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#s(approx (- 1 k) #s(hole binary64 (* k (- (/ 1 k) 1))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) #s(hole binary64 (* (sqrt (/ 1 k)) (exp (* 1/2 (* (log (* 2 (* n (PI)))) (- 1 k)))))))
#s(approx (pow (* (* 2 (PI)) n) (/ (- 1 k) 2)) #s(hole binary64 (exp (* 1/2 (* (log (* 2 (* n (PI)))) (- 1 k))))))
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#s(approx (* (pow (* (* (PI) 2) n) (/ (/ (- 1 k) 2) 2)) (pow (* (* (PI) 2) n) (/ (/ (- 1 k) 2) 2))) #s(hole binary64 (pow (exp (* 1/4 (* (log (* 2 (* n (PI)))) (- 1 k)))) 2)))
#s(approx (pow (* (* (PI) 2) n) (/ (/ (- 1 k) 2) 2)) #s(hole binary64 (exp (* 1/4 (* (log (* 2 (* n (PI)))) (- 1 k))))))
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#s(approx (/ (* 1 (pow (* (* (PI) 2) n) (/ (- 1 k) 2))) (sqrt k)) #s(hole binary64 (* (sqrt (/ 1 k)) (exp (* 1/2 (* (log (* 2 (* n (PI)))) (+ 1 (* -1 k))))))))
#s(approx (* 1 (pow (* (* (PI) 2) n) (/ (- 1 k) 2))) #s(hole binary64 (exp (* 1/2 (* (log (* 2 (* n (PI)))) (+ 1 (* -1 k)))))))
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#s(approx (- 1 k) #s(hole binary64 (* -1 (* k (- 1 (/ 1 k))))))
#s(approx (sqrt k) #s(hole binary64 (* -1 (* (sqrt k) (pow (sqrt -1) 2)))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) #s(hole binary64 (* (sqrt (/ 1 k)) (exp (* 1/2 (* (log (* 2 (* n (PI)))) (+ 1 (* -1 k))))))))
#s(approx (sqrt (* (/ (* (PI) n) k) 2)) #s(hole binary64 (* (sqrt (/ (* n (PI)) k)) (* (sqrt -2) (sqrt -1)))))
#s(approx (pow (* (* 2 (PI)) n) (/ (- 1 k) 2)) #s(hole binary64 (exp (* 1/2 (* (log (* 2 (* n (PI)))) (+ 1 (* -1 k)))))))
#s(approx (+ (* -1/2 k) 1/2) #s(hole binary64 (* -1 (* k (- 1/2 (* 1/2 (/ 1 k)))))))
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#s(approx (exp (* (log (* (* (PI) 2) n)) (/ (- 1 k) 2))) #s(hole binary64 (exp (* 1/2 (* (log (* 2 (* n (PI)))) (+ 1 (* -1 k)))))))
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#s(approx (pow (* (* (PI) 2) n) (/ (/ (- 1 k) 2) 2)) #s(hole binary64 (exp (* 1/4 (* (log (* 2 (* n (PI)))) (+ 1 (* -1 k)))))))
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#s(approx (* 1 (pow (* (* (PI) 2) n) (/ (- 1 k) 2))) #s(hole binary64 (exp (* 1/2 (* (+ (log n) (log (* 2 (PI)))) (- 1 k))))))
#s(approx (pow (* (* (PI) 2) n) (/ (- 1 k) 2)) #s(hole binary64 (exp (* 1/2 (* (+ (log n) (log (* 2 (PI)))) (- 1 k))))))
#s(approx (* (* (PI) 2) n) #s(hole binary64 (* 2 (* n (PI)))))
#s(approx n #s(hole binary64 n))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) #s(hole binary64 (* (sqrt (/ 1 k)) (exp (* 1/2 (* (+ (log n) (log (* 2 (PI)))) (- 1 k)))))))
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#s(approx (* (/ 1 (sqrt k)) (exp (* (log (* (* (PI) 2) n)) (/ (- 1 k) 2)))) #s(hole binary64 (* (sqrt (/ 1 k)) (exp (* 1/2 (* (+ (log n) (log (* 2 (PI)))) (- 1 k)))))))
#s(approx (exp (* (log (* (* (PI) 2) n)) (/ (- 1 k) 2))) #s(hole binary64 (exp (* 1/2 (* (+ (log n) (log (* 2 (PI)))) (- 1 k))))))
#s(approx (* (log (* (* (PI) 2) n)) (/ (- 1 k) 2)) #s(hole binary64 (* 1/2 (* (+ (log n) (log (* 2 (PI)))) (- 1 k)))))
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#s(approx (* (/ 1 (sqrt k)) (* (pow (* (* (PI) 2) n) (/ (/ (- 1 k) 2) 2)) (pow (* (* (PI) 2) n) (/ (/ (- 1 k) 2) 2)))) #s(hole binary64 (* (sqrt (/ 1 k)) (pow (exp (* 1/4 (* (+ (log n) (log (* 2 (PI)))) (- 1 k)))) 2))))
#s(approx (* (pow (* (* (PI) 2) n) (/ (/ (- 1 k) 2) 2)) (pow (* (* (PI) 2) n) (/ (/ (- 1 k) 2) 2))) #s(hole binary64 (pow (exp (* 1/4 (* (+ (log n) (log (* 2 (PI)))) (- 1 k)))) 2)))
#s(approx (pow (* (* (PI) 2) n) (/ (/ (- 1 k) 2) 2)) #s(hole binary64 (exp (* 1/4 (* (+ (log n) (log (* 2 (PI)))) (- 1 k))))))
#s(approx (/ (* 1 (pow (* (* (PI) 2) n) (/ (- 1 k) 2))) (sqrt k)) #s(hole binary64 (* (sqrt (/ 1 k)) (exp (* 1/2 (* (+ (log (* 2 (PI))) (* -1 (log (/ 1 n)))) (- 1 k)))))))
#s(approx (* 1 (pow (* (* (PI) 2) n) (/ (- 1 k) 2))) #s(hole binary64 (exp (* 1/2 (* (+ (log (* 2 (PI))) (* -1 (log (/ 1 n)))) (- 1 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 (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)) (exp (* (log (* (* (PI) 2) n)) (/ (- 1 k) 2)))) #s(hole binary64 (* (sqrt (/ 1 k)) (exp (* 1/2 (* (+ (log (* 2 (PI))) (* -1 (log (/ 1 n)))) (- 1 k)))))))
#s(approx (exp (* (log (* (* (PI) 2) n)) (/ (- 1 k) 2))) #s(hole binary64 (exp (* 1/2 (* (+ (log (* 2 (PI))) (* -1 (log (/ 1 n)))) (- 1 k))))))
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#s(approx (exp (* (log (* (* (PI) 2) n)) (/ (- 1 k) 2))) #s(hole binary64 (exp (* 1/2 (* (+ (log (* -2 (PI))) (* -1 (log (/ -1 n)))) (- 1 k))))))
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#s(approx (* (pow (* (* (PI) 2) n) (/ (/ (- 1 k) 2) 2)) (pow (* (* (PI) 2) n) (/ (/ (- 1 k) 2) 2))) #s(hole binary64 (pow (exp (* 1/4 (* (+ (log (* -2 (PI))) (* -1 (log (/ -1 n)))) (- 1 k)))) 2)))
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Outputs
(.f64 (.f64 (pow.f64 (sqrt.f64 k) #s(literal -1 binary64)) (pow.f64 (.f64 (.f64 #s(literal 2 binary64) n) (PI.f64)) (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 4 binary64)))) (pow.f64 (.f64 (.f64 #s(literal 2 binary64) n) (PI.f64)) (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 4 binary64))))
(.f64 (pow.f64 (sqrt.f64 k) #s(literal -1 binary64)) (pow.f64 (.f64 (*.f64 #s(literal 2 binary64) n) (PI.f64)) (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 2 binary64))))
(.f64 (pow.f64 (.f64 (*.f64 #s(literal 2 binary64) n) (PI.f64)) (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 2 binary64))) (pow.f64 (sqrt.f64 k) #s(literal -1 binary64)))
(.f64 #s(literal 1 binary64) (/.f64 (pow.f64 (.f64 (*.f64 #s(literal 2 binary64) n) (PI.f64)) (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 2 binary64))) (sqrt.f64 k)))
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(/.f64 (pow.f64 (.f64 (.f64 #s(literal 2 binary64) n) (PI.f64)) (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 2 binary64))) (sqrt.f64 k))
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(pow.f64 (.f64 (.f64 #s(literal 2 binary64) n) (PI.f64)) (*.f64 #s(literal 2 binary64) (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 4 binary64))))
(pow.f64 (.f64 (.f64 #s(literal 2 binary64) n) (PI.f64)) (+.f64 (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 4 binary64)) (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 4 binary64))))
(pow.f64 (.f64 (.f64 #s(literal 2 binary64) n) (PI.f64)) (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 2 binary64)))
(exp.f64 (.f64 (log.f64 (.f64 (*.f64 #s(literal 2 binary64) n) (PI.f64))) (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 2 binary64))))
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#s(literal 1 binary64)
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(pow.f64 (.f64 (.f64 #s(literal 2 binary64) n) (PI.f64)) (*.f64 #s(literal 2 binary64) (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 4 binary64))))
(pow.f64 (.f64 (.f64 #s(literal 2 binary64) n) (PI.f64)) (+.f64 (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 4 binary64)) (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 4 binary64))))
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#s(approx (* (/ 1 (sqrt k)) (* (pow (* (* (PI) 2) n) (/ (/ (- 1 k) 2) 2)) (pow (* (* (PI) 2) n) (/ (/ (- 1 k) 2) 2)))) (/.f64 (fma.f64 (fma.f64 (.f64 #s(literal 1/8 binary64) (.f64 (pow.f64 k #s(literal 3/2 binary64)) (sqrt.f64 (.f64 (PI.f64) n)))) (.f64 (pow.f64 (log.f64 (.f64 (.f64 #s(literal 2 binary64) n) (PI.f64))) #s(literal 2 binary64)) (sqrt.f64 #s(literal 2 binary64))) (.f64 (.f64 #s(literal -1/2 binary64) (sqrt.f64 (.f64 (.f64 (PI.f64) n) k))) (.f64 (log.f64 (.f64 (.f64 #s(literal 2 binary64) n) (PI.f64))) (sqrt.f64 #s(literal 2 binary64))))) k (sqrt.f64 (.f64 (.f64 (.f64 (PI.f64) n) k) #s(literal 2 binary64)))) k))
#s(approx (* (/ 1 (sqrt k)) (* (pow (* (* (PI) 2) n) (/ (/ (- 1 k) 2) 2)) (pow (* (* (PI) 2) n) (/ (/ (- 1 k) 2) 2)))) (/.f64 (fma.f64 (fma.f64 (fma.f64 (.f64 #s(literal 1/8 binary64) (sqrt.f64 (.f64 (.f64 (PI.f64) n) k))) (.f64 (pow.f64 (log.f64 (.f64 (.f64 #s(literal 2 binary64) n) (PI.f64))) #s(literal 2 binary64)) (sqrt.f64 #s(literal 2 binary64))) (.f64 (.f64 #s(literal -1/48 binary64) (.f64 (pow.f64 k #s(literal 3/2 binary64)) (sqrt.f64 (.f64 (PI.f64) n)))) (.f64 (pow.f64 (log.f64 (.f64 (.f64 #s(literal 2 binary64) n) (PI.f64))) #s(literal 3 binary64)) (sqrt.f64 #s(literal 2 binary64))))) k (.f64 (.f64 #s(literal -1/2 binary64) (sqrt.f64 (.f64 (.f64 (PI.f64) n) k))) (.f64 (log.f64 (.f64 (.f64 #s(literal 2 binary64) n) (PI.f64))) (sqrt.f64 #s(literal 2 binary64))))) k (sqrt.f64 (.f64 (.f64 (*.f64 (PI.f64) n) k) #s(literal 2 binary64)))) k))
#s(approx (* (pow (* (* (PI) 2) n) (/ (/ (- 1 k) 2) 2)) (pow (* (* (PI) 2) n) (/ (/ (- 1 k) 2) 2))) (sqrt.f64 (.f64 (.f64 #s(literal 2 binary64) n) (PI.f64))))
#s(approx (* (pow (* (* (PI) 2) n) (/ (/ (- 1 k) 2) 2)) (pow (* (* (PI) 2) n) (/ (/ (- 1 k) 2) 2))) (fma.f64 (.f64 k (.f64 (.f64 (sqrt.f64 (.f64 (PI.f64) n)) (log.f64 (.f64 (.f64 #s(literal 2 binary64) n) (PI.f64)))) (sqrt.f64 #s(literal 2 binary64)))) #s(literal -1/2 binary64) (sqrt.f64 (.f64 (.f64 #s(literal 2 binary64) n) (PI.f64)))))
#s(approx (* (pow (* (* (PI) 2) n) (/ (/ (- 1 k) 2) 2)) (pow (* (* (PI) 2) n) (/ (/ (- 1 k) 2) 2))) (fma.f64 (fma.f64 (.f64 #s(literal 1/8 binary64) (.f64 (.f64 (pow.f64 (log.f64 (.f64 (.f64 #s(literal 2 binary64) n) (PI.f64))) #s(literal 2 binary64)) k) (sqrt.f64 #s(literal 2 binary64)))) (sqrt.f64 (.f64 (PI.f64) n)) (.f64 (.f64 #s(literal -1/2 binary64) (sqrt.f64 (.f64 (PI.f64) n))) (.f64 (log.f64 (.f64 (.f64 #s(literal 2 binary64) n) (PI.f64))) (sqrt.f64 #s(literal 2 binary64))))) k (sqrt.f64 (.f64 (.f64 #s(literal 2 binary64) n) (PI.f64)))))
#s(approx (* (pow (* (* (PI) 2) n) (/ (/ (- 1 k) 2) 2)) (pow (* (* (PI) 2) n) (/ (/ (- 1 k) 2) 2))) (fma.f64 (fma.f64 (fma.f64 (.f64 (.f64 (.f64 (pow.f64 (log.f64 (.f64 (.f64 #s(literal 2 binary64) n) (PI.f64))) #s(literal 3 binary64)) k) (sqrt.f64 #s(literal 2 binary64))) (sqrt.f64 (.f64 (PI.f64) n))) #s(literal -1/48 binary64) (.f64 (.f64 #s(literal 1/8 binary64) (sqrt.f64 (.f64 (PI.f64) n))) (.f64 (pow.f64 (log.f64 (.f64 (.f64 #s(literal 2 binary64) n) (PI.f64))) #s(literal 2 binary64)) (sqrt.f64 #s(literal 2 binary64))))) k (.f64 (.f64 #s(literal -1/2 binary64) (sqrt.f64 (.f64 (PI.f64) n))) (.f64 (log.f64 (.f64 (.f64 #s(literal 2 binary64) n) (PI.f64))) (sqrt.f64 #s(literal 2 binary64))))) k (sqrt.f64 (.f64 (.f64 #s(literal 2 binary64) n) (PI.f64)))))
#s(approx (* (pow (* (* (PI) 2) n) (/ (/ (- 1 k) 2) 2)) (pow (* (* (PI) 2) n) (/ (/ (- 1 k) 2) 2))) (sqrt.f64 (.f64 (.f64 #s(literal 2 binary64) n) (PI.f64))))
#s(approx (* (pow (* (* (PI) 2) n) (/ (/ (- 1 k) 2) 2)) (pow (* (* (PI) 2) n) (/ (/ (- 1 k) 2) 2))) (fma.f64 (.f64 k (.f64 (.f64 (sqrt.f64 (.f64 (PI.f64) n)) (log.f64 (.f64 (.f64 #s(literal 2 binary64) n) (PI.f64)))) (sqrt.f64 #s(literal 2 binary64)))) #s(literal -1/2 binary64) (sqrt.f64 (.f64 (.f64 #s(literal 2 binary64) n) (PI.f64)))))
#s(approx (* (pow (* (* (PI) 2) n) (/ (/ (- 1 k) 2) 2)) (pow (* (* (PI) 2) n) (/ (/ (- 1 k) 2) 2))) (fma.f64 (fma.f64 (.f64 #s(literal 1/8 binary64) (.f64 (.f64 (pow.f64 (log.f64 (.f64 (.f64 #s(literal 2 binary64) n) (PI.f64))) #s(literal 2 binary64)) k) (sqrt.f64 #s(literal 2 binary64)))) (sqrt.f64 (.f64 (PI.f64) n)) (.f64 (.f64 #s(literal -1/2 binary64) (sqrt.f64 (.f64 (PI.f64) n))) (.f64 (log.f64 (.f64 (.f64 #s(literal 2 binary64) n) (PI.f64))) (sqrt.f64 #s(literal 2 binary64))))) k (sqrt.f64 (.f64 (.f64 #s(literal 2 binary64) n) (PI.f64)))))
#s(approx (* (pow (* (* (PI) 2) n) (/ (/ (- 1 k) 2) 2)) (pow (* (* (PI) 2) n) (/ (/ (- 1 k) 2) 2))) (fma.f64 (fma.f64 (fma.f64 (.f64 (.f64 (.f64 (pow.f64 (log.f64 (.f64 (.f64 #s(literal 2 binary64) n) (PI.f64))) #s(literal 3 binary64)) k) (sqrt.f64 #s(literal 2 binary64))) (sqrt.f64 (.f64 (PI.f64) n))) #s(literal -1/48 binary64) (.f64 (.f64 #s(literal 1/8 binary64) (sqrt.f64 (.f64 (PI.f64) n))) (.f64 (pow.f64 (log.f64 (.f64 (.f64 #s(literal 2 binary64) n) (PI.f64))) #s(literal 2 binary64)) (sqrt.f64 #s(literal 2 binary64))))) k (.f64 (.f64 #s(literal -1/2 binary64) (sqrt.f64 (.f64 (PI.f64) n))) (.f64 (log.f64 (.f64 (.f64 #s(literal 2 binary64) n) (PI.f64))) (sqrt.f64 #s(literal 2 binary64))))) k (sqrt.f64 (.f64 (.f64 #s(literal 2 binary64) n) (PI.f64)))))
#s(approx (/ (- 1 k) 2) #s(literal 1/2 binary64))
#s(approx (/ (- 1 k) 2) (fma.f64 #s(literal -1/2 binary64) k #s(literal 1/2 binary64)))
#s(approx (- 1 k) #s(literal 1 binary64))
#s(approx (- 1 k) (fma.f64 #s(literal -1 binary64) k #s(literal 1 binary64)))
#s(approx k k)
#s(approx (sqrt k) (sqrt.f64 k))
#s(approx (* (/ 1 (sqrt k)) (* (pow (* (* (PI) 2) n) (/ (/ (- 1 k) 2) 2)) (pow (* (* (PI) 2) n) (/ (/ (- 1 k) 2) 2)))) (sqrt.f64 (.f64 (/.f64 (.f64 (PI.f64) n) k) #s(literal 2 binary64))))
#s(approx (* (/ 1 (sqrt k)) (* (pow (* (* (PI) 2) n) (/ (/ (- 1 k) 2) 2)) (pow (* (* (PI) 2) n) (/ (/ (- 1 k) 2) 2)))) (/.f64 (fma.f64 (.f64 #s(literal -1/2 binary64) (.f64 (pow.f64 k #s(literal 3/2 binary64)) (sqrt.f64 (.f64 (PI.f64) n)))) (.f64 (log.f64 (.f64 (.f64 #s(literal 2 binary64) n) (PI.f64))) (sqrt.f64 #s(literal 2 binary64))) (sqrt.f64 (.f64 (.f64 (*.f64 (PI.f64) n) k) #s(literal 2 binary64)))) k))
#s(approx (* (/ 1 (sqrt k)) (* (pow (* (* (PI) 2) n) (/ (/ (- 1 k) 2) 2)) (pow (* (* (PI) 2) n) (/ (/ (- 1 k) 2) 2)))) (/.f64 (fma.f64 (fma.f64 (.f64 #s(literal 1/8 binary64) (.f64 (pow.f64 k #s(literal 3/2 binary64)) (sqrt.f64 (.f64 (PI.f64) n)))) (.f64 (pow.f64 (log.f64 (.f64 (.f64 #s(literal 2 binary64) n) (PI.f64))) #s(literal 2 binary64)) (sqrt.f64 #s(literal 2 binary64))) (.f64 (.f64 #s(literal -1/2 binary64) (sqrt.f64 (.f64 (.f64 (PI.f64) n) k))) (.f64 (log.f64 (.f64 (.f64 #s(literal 2 binary64) n) (PI.f64))) (sqrt.f64 #s(literal 2 binary64))))) k (sqrt.f64 (.f64 (.f64 (.f64 (PI.f64) n) k) #s(literal 2 binary64)))) k))
#s(approx (* (/ 1 (sqrt k)) (* (pow (* (* (PI) 2) n) (/ (/ (- 1 k) 2) 2)) (pow (* (* (PI) 2) n) (/ (/ (- 1 k) 2) 2)))) (/.f64 (fma.f64 (fma.f64 (fma.f64 (.f64 #s(literal 1/8 binary64) (sqrt.f64 (.f64 (.f64 (PI.f64) n) k))) (.f64 (pow.f64 (log.f64 (.f64 (.f64 #s(literal 2 binary64) n) (PI.f64))) #s(literal 2 binary64)) (sqrt.f64 #s(literal 2 binary64))) (.f64 (.f64 #s(literal -1/48 binary64) (.f64 (pow.f64 k #s(literal 3/2 binary64)) (sqrt.f64 (.f64 (PI.f64) n)))) (.f64 (pow.f64 (log.f64 (.f64 (.f64 #s(literal 2 binary64) n) (PI.f64))) #s(literal 3 binary64)) (sqrt.f64 #s(literal 2 binary64))))) k (.f64 (.f64 #s(literal -1/2 binary64) (sqrt.f64 (.f64 (.f64 (PI.f64) n) k))) (.f64 (log.f64 (.f64 (.f64 #s(literal 2 binary64) n) (PI.f64))) (sqrt.f64 #s(literal 2 binary64))))) k (sqrt.f64 (.f64 (.f64 (*.f64 (PI.f64) n) k) #s(literal 2 binary64)))) k))
#s(approx (sqrt (* (/ (* (PI) n) k) 2)) (sqrt.f64 (.f64 (/.f64 (.f64 (PI.f64) n) k) #s(literal 2 binary64))))
#s(approx (* (/ (* (PI) n) k) 2) (.f64 (/.f64 (.f64 (PI.f64) n) k) #s(literal 2 binary64)))
#s(approx (/ (* (PI) n) k) (/.f64 (*.f64 (PI.f64) n) k))
#s(approx (/ 1 (sqrt k)) (pow.f64 (sqrt.f64 k) #s(literal -1 binary64)))
#s(approx (* (pow (* (* (PI) 2) n) (/ (/ (- 1 k) 2) 2)) (pow (* (* (PI) 2) n) (/ (/ (- 1 k) 2) 2))) (sqrt.f64 (.f64 (.f64 #s(literal 2 binary64) n) (PI.f64))))
#s(approx (* (pow (* (* (PI) 2) n) (/ (/ (- 1 k) 2) 2)) (pow (* (* (PI) 2) n) (/ (/ (- 1 k) 2) 2))) (fma.f64 (.f64 k (.f64 (.f64 (sqrt.f64 (.f64 (PI.f64) n)) (log.f64 (.f64 (.f64 #s(literal 2 binary64) n) (PI.f64)))) (sqrt.f64 #s(literal 2 binary64)))) #s(literal -1/2 binary64) (sqrt.f64 (.f64 (.f64 #s(literal 2 binary64) n) (PI.f64)))))
#s(approx (* (pow (* (* (PI) 2) n) (/ (/ (- 1 k) 2) 2)) (pow (* (* (PI) 2) n) (/ (/ (- 1 k) 2) 2))) (fma.f64 (fma.f64 (.f64 #s(literal 1/8 binary64) (.f64 (.f64 (pow.f64 (log.f64 (.f64 (.f64 #s(literal 2 binary64) n) (PI.f64))) #s(literal 2 binary64)) k) (sqrt.f64 #s(literal 2 binary64)))) (sqrt.f64 (.f64 (PI.f64) n)) (.f64 (.f64 #s(literal -1/2 binary64) (sqrt.f64 (.f64 (PI.f64) n))) (.f64 (log.f64 (.f64 (.f64 #s(literal 2 binary64) n) (PI.f64))) (sqrt.f64 #s(literal 2 binary64))))) k (sqrt.f64 (.f64 (.f64 #s(literal 2 binary64) n) (PI.f64)))))
#s(approx (* (pow (* (* (PI) 2) n) (/ (/ (- 1 k) 2) 2)) (pow (* (* (PI) 2) n) (/ (/ (- 1 k) 2) 2))) (fma.f64 (fma.f64 (fma.f64 (.f64 (.f64 (.f64 (pow.f64 (log.f64 (.f64 (.f64 #s(literal 2 binary64) n) (PI.f64))) #s(literal 3 binary64)) k) (sqrt.f64 #s(literal 2 binary64))) (sqrt.f64 (.f64 (PI.f64) n))) #s(literal -1/48 binary64) (.f64 (.f64 #s(literal 1/8 binary64) (sqrt.f64 (.f64 (PI.f64) n))) (.f64 (pow.f64 (log.f64 (.f64 (.f64 #s(literal 2 binary64) n) (PI.f64))) #s(literal 2 binary64)) (sqrt.f64 #s(literal 2 binary64))))) k (.f64 (.f64 #s(literal -1/2 binary64) (sqrt.f64 (.f64 (PI.f64) n))) (.f64 (log.f64 (.f64 (.f64 #s(literal 2 binary64) n) (PI.f64))) (sqrt.f64 #s(literal 2 binary64))))) k (sqrt.f64 (.f64 (.f64 #s(literal 2 binary64) n) (PI.f64)))))
#s(approx (+ (* -1/2 k) 1/2) #s(literal 1/2 binary64))
#s(approx (+ (* -1/2 k) 1/2) (fma.f64 #s(literal -1/2 binary64) k #s(literal 1/2 binary64)))
#s(approx (* (/ 1 (sqrt k)) (* (pow (* (* (PI) 2) n) (/ (/ (- 1 k) 2) 2)) (pow (* (* (PI) 2) n) (/ (/ (- 1 k) 2) 2)))) (sqrt.f64 (.f64 (/.f64 (.f64 (PI.f64) n) k) #s(literal 2 binary64))))
#s(approx (* (/ 1 (sqrt k)) (* (pow (* (* (PI) 2) n) (/ (/ (- 1 k) 2) 2)) (pow (* (* (PI) 2) n) (/ (/ (- 1 k) 2) 2)))) (/.f64 (fma.f64 (.f64 #s(literal -1/2 binary64) (.f64 (pow.f64 k #s(literal 3/2 binary64)) (sqrt.f64 (.f64 (PI.f64) n)))) (.f64 (log.f64 (.f64 (.f64 #s(literal 2 binary64) n) (PI.f64))) (sqrt.f64 #s(literal 2 binary64))) (sqrt.f64 (.f64 (.f64 (*.f64 (PI.f64) n) k) #s(literal 2 binary64)))) k))
#s(approx (* (/ 1 (sqrt k)) (* (pow (* (* (PI) 2) n) (/ (/ (- 1 k) 2) 2)) (pow (* (* (PI) 2) n) (/ (/ (- 1 k) 2) 2)))) (/.f64 (fma.f64 (fma.f64 (.f64 #s(literal 1/8 binary64) (.f64 (pow.f64 k #s(literal 3/2 binary64)) (sqrt.f64 (.f64 (PI.f64) n)))) (.f64 (pow.f64 (log.f64 (.f64 (.f64 #s(literal 2 binary64) n) (PI.f64))) #s(literal 2 binary64)) (sqrt.f64 #s(literal 2 binary64))) (.f64 (.f64 #s(literal -1/2 binary64) (sqrt.f64 (.f64 (.f64 (PI.f64) n) k))) (.f64 (log.f64 (.f64 (.f64 #s(literal 2 binary64) n) (PI.f64))) (sqrt.f64 #s(literal 2 binary64))))) k (sqrt.f64 (.f64 (.f64 (.f64 (PI.f64) n) k) #s(literal 2 binary64)))) k))
#s(approx (* (/ 1 (sqrt k)) (* (pow (* (* (PI) 2) n) (/ (/ (- 1 k) 2) 2)) (pow (* (* (PI) 2) n) (/ (/ (- 1 k) 2) 2)))) (/.f64 (fma.f64 (fma.f64 (fma.f64 (.f64 #s(literal 1/8 binary64) (sqrt.f64 (.f64 (.f64 (PI.f64) n) k))) (.f64 (pow.f64 (log.f64 (.f64 (.f64 #s(literal 2 binary64) n) (PI.f64))) #s(literal 2 binary64)) (sqrt.f64 #s(literal 2 binary64))) (.f64 (.f64 #s(literal -1/48 binary64) (.f64 (pow.f64 k #s(literal 3/2 binary64)) (sqrt.f64 (.f64 (PI.f64) n)))) (.f64 (pow.f64 (log.f64 (.f64 (.f64 #s(literal 2 binary64) n) (PI.f64))) #s(literal 3 binary64)) (sqrt.f64 #s(literal 2 binary64))))) k (.f64 (.f64 #s(literal -1/2 binary64) (sqrt.f64 (.f64 (.f64 (PI.f64) n) k))) (.f64 (log.f64 (.f64 (.f64 #s(literal 2 binary64) n) (PI.f64))) (sqrt.f64 #s(literal 2 binary64))))) k (sqrt.f64 (.f64 (.f64 (*.f64 (PI.f64) n) k) #s(literal 2 binary64)))) k))
#s(approx (* (pow (* (* (PI) 2) n) (/ (/ (- 1 k) 2) 2)) (pow (* (* (PI) 2) n) (/ (/ (- 1 k) 2) 2))) (sqrt.f64 (.f64 (.f64 #s(literal 2 binary64) n) (PI.f64))))
#s(approx (* (pow (* (* (PI) 2) n) (/ (/ (- 1 k) 2) 2)) (pow (* (* (PI) 2) n) (/ (/ (- 1 k) 2) 2))) (fma.f64 (.f64 k (.f64 (.f64 (sqrt.f64 (.f64 (PI.f64) n)) (log.f64 (.f64 (.f64 #s(literal 2 binary64) n) (PI.f64)))) (sqrt.f64 #s(literal 2 binary64)))) #s(literal -1/2 binary64) (sqrt.f64 (.f64 (.f64 #s(literal 2 binary64) n) (PI.f64)))))
#s(approx (* (pow (* (* (PI) 2) n) (/ (/ (- 1 k) 2) 2)) (pow (* (* (PI) 2) n) (/ (/ (- 1 k) 2) 2))) (fma.f64 (fma.f64 (.f64 #s(literal 1/8 binary64) (.f64 (.f64 (pow.f64 (log.f64 (.f64 (.f64 #s(literal 2 binary64) n) (PI.f64))) #s(literal 2 binary64)) k) (sqrt.f64 #s(literal 2 binary64)))) (sqrt.f64 (.f64 (PI.f64) n)) (.f64 (.f64 #s(literal -1/2 binary64) (sqrt.f64 (.f64 (PI.f64) n))) (.f64 (log.f64 (.f64 (.f64 #s(literal 2 binary64) n) (PI.f64))) (sqrt.f64 #s(literal 2 binary64))))) k (sqrt.f64 (.f64 (.f64 #s(literal 2 binary64) n) (PI.f64)))))
#s(approx (* (pow (* (* (PI) 2) n) (/ (/ (- 1 k) 2) 2)) (pow (* (* (PI) 2) n) (/ (/ (- 1 k) 2) 2))) (fma.f64 (fma.f64 (fma.f64 (.f64 (.f64 (.f64 (pow.f64 (log.f64 (.f64 (.f64 #s(literal 2 binary64) n) (PI.f64))) #s(literal 3 binary64)) k) (sqrt.f64 #s(literal 2 binary64))) (sqrt.f64 (.f64 (PI.f64) n))) #s(literal -1/48 binary64) (.f64 (.f64 #s(literal 1/8 binary64) (sqrt.f64 (.f64 (PI.f64) n))) (.f64 (pow.f64 (log.f64 (.f64 (.f64 #s(literal 2 binary64) n) (PI.f64))) #s(literal 2 binary64)) (sqrt.f64 #s(literal 2 binary64))))) k (.f64 (.f64 #s(literal -1/2 binary64) (sqrt.f64 (.f64 (PI.f64) n))) (.f64 (log.f64 (.f64 (.f64 #s(literal 2 binary64) n) (PI.f64))) (sqrt.f64 #s(literal 2 binary64))))) k (sqrt.f64 (.f64 (.f64 #s(literal 2 binary64) n) (PI.f64)))))
#s(approx (* (log (* (* (PI) 2) n)) (/ (- 1 k) 2)) (.f64 (log.f64 (.f64 (*.f64 #s(literal 2 binary64) n) (PI.f64))) #s(literal 1/2 binary64)))
#s(approx (* (log (* (* (PI) 2) n)) (/ (- 1 k) 2)) (fma.f64 (.f64 #s(literal -1/2 binary64) k) (log.f64 (.f64 (.f64 #s(literal 2 binary64) n) (PI.f64))) (.f64 (log.f64 (.f64 (.f64 #s(literal 2 binary64) n) (PI.f64))) #s(literal 1/2 binary64))))
#s(approx (* (/ 1 (sqrt k)) (* (pow (* (* (PI) 2) n) (/ (/ (- 1 k) 2) 2)) (pow (* (* (PI) 2) n) (/ (/ (- 1 k) 2) 2)))) (sqrt.f64 (.f64 (/.f64 (.f64 (PI.f64) n) k) #s(literal 2 binary64))))
#s(approx (* (/ 1 (sqrt k)) (* (pow (* (* (PI) 2) n) (/ (/ (- 1 k) 2) 2)) (pow (* (* (PI) 2) n) (/ (/ (- 1 k) 2) 2)))) (/.f64 (fma.f64 (.f64 #s(literal -1/2 binary64) (.f64 (pow.f64 k #s(literal 3/2 binary64)) (sqrt.f64 (.f64 (PI.f64) n)))) (.f64 (log.f64 (.f64 (.f64 #s(literal 2 binary64) n) (PI.f64))) (sqrt.f64 #s(literal 2 binary64))) (sqrt.f64 (.f64 (.f64 (*.f64 (PI.f64) n) k) #s(literal 2 binary64)))) k))
#s(approx (* (/ 1 (sqrt k)) (* (pow (* (* (PI) 2) n) (/ (/ (- 1 k) 2) 2)) (pow (* (* (PI) 2) n) (/ (/ (- 1 k) 2) 2)))) (/.f64 (fma.f64 (fma.f64 (.f64 #s(literal 1/8 binary64) (.f64 (pow.f64 k #s(literal 3/2 binary64)) (sqrt.f64 (.f64 (PI.f64) n)))) (.f64 (pow.f64 (log.f64 (.f64 (.f64 #s(literal 2 binary64) n) (PI.f64))) #s(literal 2 binary64)) (sqrt.f64 #s(literal 2 binary64))) (.f64 (.f64 #s(literal -1/2 binary64) (sqrt.f64 (.f64 (.f64 (PI.f64) n) k))) (.f64 (log.f64 (.f64 (.f64 #s(literal 2 binary64) n) (PI.f64))) (sqrt.f64 #s(literal 2 binary64))))) k (sqrt.f64 (.f64 (.f64 (.f64 (PI.f64) n) k) #s(literal 2 binary64)))) k))
#s(approx (* (/ 1 (sqrt k)) (* (pow (* (* (PI) 2) n) (/ (/ (- 1 k) 2) 2)) (pow (* (* (PI) 2) n) (/ (/ (- 1 k) 2) 2)))) (/.f64 (fma.f64 (fma.f64 (fma.f64 (.f64 (.f64 (.f64 (sqrt.f64 (.f64 (PI.f64) n)) (pow.f64 (log.f64 (.f64 (.f64 #s(literal 2 binary64) n) (PI.f64))) #s(literal 3 binary64))) (sqrt.f64 #s(literal 2 binary64))) #s(literal -1/48 binary64)) (pow.f64 k #s(literal 3/2 binary64)) (.f64 (.f64 #s(literal 1/8 binary64) (sqrt.f64 (.f64 (.f64 (PI.f64) n) k))) (.f64 (pow.f64 (log.f64 (.f64 (.f64 #s(literal 2 binary64) n) (PI.f64))) #s(literal 2 binary64)) (sqrt.f64 #s(literal 2 binary64))))) k (.f64 (.f64 #s(literal -1/2 binary64) (sqrt.f64 (.f64 (.f64 (PI.f64) n) k))) (.f64 (log.f64 (.f64 (.f64 #s(literal 2 binary64) n) (PI.f64))) (sqrt.f64 #s(literal 2 binary64))))) k (sqrt.f64 (.f64 (.f64 (*.f64 (PI.f64) n) k) #s(literal 2 binary64)))) k))
#s(approx (* (pow (* (* (PI) 2) n) (/ (/ (- 1 k) 2) 2)) (pow (* (* (PI) 2) n) (/ (/ (- 1 k) 2) 2))) (sqrt.f64 (.f64 (.f64 #s(literal 2 binary64) n) (PI.f64))))
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#s(approx n n)
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#s(approx (* (log (* (* (PI) 2) n)) (/ (- 1 k) 2)) (.f64 (.f64 (fma.f64 (neg.f64 (log.f64 n)) #s(literal -1 binary64) (log.f64 (*.f64 (PI.f64) #s(literal 2 binary64)))) (-.f64 #s(literal 1 binary64) k)) #s(literal 1/2 binary64)))
#s(approx (log (* (* (PI) 2) n)) (fma.f64 (neg.f64 (log.f64 n)) #s(literal -1 binary64) (log.f64 (*.f64 (PI.f64) #s(literal 2 binary64)))))
#s(approx (* (/ 1 (sqrt k)) (* (pow (* (* (PI) 2) n) (/ (/ (- 1 k) 2) 2)) (pow (* (* (PI) 2) n) (/ (/ (- 1 k) 2) 2)))) (.f64 (pow.f64 (pow.f64 (exp.f64 #s(literal 1/4 binary64)) (.f64 (fma.f64 (neg.f64 (log.f64 n)) #s(literal -1 binary64) (log.f64 (*.f64 (PI.f64) #s(literal 2 binary64)))) (-.f64 #s(literal 1 binary64) k))) #s(literal 2 binary64)) (pow.f64 (sqrt.f64 k) #s(literal -1 binary64))))
#s(approx (* (pow (* (* (PI) 2) n) (/ (/ (- 1 k) 2) 2)) (pow (* (* (PI) 2) n) (/ (/ (- 1 k) 2) 2))) (pow.f64 (pow.f64 (exp.f64 #s(literal 1/4 binary64)) (.f64 (fma.f64 (neg.f64 (log.f64 n)) #s(literal -1 binary64) (log.f64 (.f64 (PI.f64) #s(literal 2 binary64)))) (-.f64 #s(literal 1 binary64) k))) #s(literal 2 binary64)))
#s(approx (pow (* (* (PI) 2) n) (/ (/ (- 1 k) 2) 2)) (pow.f64 (exp.f64 #s(literal 1/4 binary64)) (.f64 (fma.f64 (neg.f64 (log.f64 n)) #s(literal -1 binary64) (log.f64 (.f64 (PI.f64) #s(literal 2 binary64)))) (-.f64 #s(literal 1 binary64) k))))
#s(approx (* (/ 1 (sqrt k)) (* (pow (* (* (PI) 2) n) (/ (/ (- 1 k) 2) 2)) (pow (* (* (PI) 2) n) (/ (/ (- 1 k) 2) 2)))) (.f64 (pow.f64 (exp.f64 #s(literal 1/2 binary64)) (.f64 (fma.f64 (log.f64 (/.f64 #s(literal -1 binary64) n)) #s(literal -1 binary64) (log.f64 (*.f64 #s(literal -2 binary64) (PI.f64)))) (-.f64 #s(literal 1 binary64) k))) (pow.f64 (sqrt.f64 k) #s(literal -1 binary64))))
#s(approx (* (pow (* (* (PI) 2) n) (/ (/ (- 1 k) 2) 2)) (pow (* (* (PI) 2) n) (/ (/ (- 1 k) 2) 2))) (pow.f64 (exp.f64 #s(literal 1/2 binary64)) (.f64 (fma.f64 (log.f64 (/.f64 #s(literal -1 binary64) n)) #s(literal -1 binary64) (log.f64 (.f64 #s(literal -2 binary64) (PI.f64)))) (-.f64 #s(literal 1 binary64) k))))
#s(approx (* (pow (* (* (PI) 2) n) (/ (/ (- 1 k) 2) 2)) (pow (* (* (PI) 2) n) (/ (/ (- 1 k) 2) 2))) (pow.f64 (exp.f64 #s(literal 1/2 binary64)) (.f64 (fma.f64 (log.f64 (/.f64 #s(literal -1 binary64) n)) #s(literal -1 binary64) (log.f64 (.f64 #s(literal -2 binary64) (PI.f64)))) (-.f64 #s(literal 1 binary64) k))))
#s(approx (* (/ 1 (sqrt k)) (* (pow (* (* (PI) 2) n) (/ (/ (- 1 k) 2) 2)) (pow (* (* (PI) 2) n) (/ (/ (- 1 k) 2) 2)))) (.f64 (pow.f64 (exp.f64 #s(literal 1/2 binary64)) (.f64 (fma.f64 (log.f64 (/.f64 #s(literal -1 binary64) n)) #s(literal -1 binary64) (log.f64 (*.f64 #s(literal -2 binary64) (PI.f64)))) (-.f64 #s(literal 1 binary64) k))) (pow.f64 (sqrt.f64 k) #s(literal -1 binary64))))
#s(approx (sqrt (* (/ (* (PI) n) k) 2)) (neg.f64 (sqrt.f64 (.f64 (/.f64 (.f64 (PI.f64) n) k) #s(literal 2 binary64)))))
#s(approx (* (pow (* (* (PI) 2) n) (/ (/ (- 1 k) 2) 2)) (pow (* (* (PI) 2) n) (/ (/ (- 1 k) 2) 2))) (pow.f64 (exp.f64 #s(literal 1/2 binary64)) (.f64 (fma.f64 (log.f64 (/.f64 #s(literal -1 binary64) n)) #s(literal -1 binary64) (log.f64 (.f64 #s(literal -2 binary64) (PI.f64)))) (-.f64 #s(literal 1 binary64) k))))
#s(approx (* (/ 1 (sqrt k)) (* (pow (* (* (PI) 2) n) (/ (/ (- 1 k) 2) 2)) (pow (* (* (PI) 2) n) (/ (/ (- 1 k) 2) 2)))) (.f64 (pow.f64 (exp.f64 #s(literal 1/2 binary64)) (.f64 (fma.f64 (log.f64 (/.f64 #s(literal -1 binary64) n)) #s(literal -1 binary64) (log.f64 (*.f64 #s(literal -2 binary64) (PI.f64)))) (-.f64 #s(literal 1 binary64) k))) (pow.f64 (sqrt.f64 k) #s(literal -1 binary64))))
#s(approx (* (pow (* (* (PI) 2) n) (/ (/ (- 1 k) 2) 2)) (pow (* (* (PI) 2) n) (/ (/ (- 1 k) 2) 2))) (pow.f64 (exp.f64 #s(literal 1/2 binary64)) (.f64 (fma.f64 (log.f64 (/.f64 #s(literal -1 binary64) n)) #s(literal -1 binary64) (log.f64 (.f64 #s(literal -2 binary64) (PI.f64)))) (-.f64 #s(literal 1 binary64) k))))
#s(approx (* (log (* (* (PI) 2) n)) (/ (- 1 k) 2)) (.f64 (.f64 #s(literal 1/2 binary64) (fma.f64 (log.f64 (/.f64 #s(literal -1 binary64) n)) #s(literal -1 binary64) (log.f64 (*.f64 #s(literal -2 binary64) (PI.f64))))) (-.f64 #s(literal 1 binary64) k)))
#s(approx (log (* (* (PI) 2) n)) (fma.f64 (log.f64 (/.f64 #s(literal -1 binary64) n)) #s(literal -1 binary64) (log.f64 (*.f64 #s(literal -2 binary64) (PI.f64)))))
#s(approx (* (/ 1 (sqrt k)) (* (pow (* (* (PI) 2) n) (/ (/ (- 1 k) 2) 2)) (pow (* (* (PI) 2) n) (/ (/ (- 1 k) 2) 2)))) (.f64 (pow.f64 (pow.f64 (exp.f64 #s(literal 1/4 binary64)) (.f64 (fma.f64 (log.f64 (/.f64 #s(literal -1 binary64) n)) #s(literal -1 binary64) (log.f64 (*.f64 #s(literal -2 binary64) (PI.f64)))) (-.f64 #s(literal 1 binary64) k))) #s(literal 2 binary64)) (pow.f64 (sqrt.f64 k) #s(literal -1 binary64))))
#s(approx (* (pow (* (* (PI) 2) n) (/ (/ (- 1 k) 2) 2)) (pow (* (* (PI) 2) n) (/ (/ (- 1 k) 2) 2))) (pow.f64 (pow.f64 (exp.f64 #s(literal 1/4 binary64)) (.f64 (fma.f64 (log.f64 (/.f64 #s(literal -1 binary64) n)) #s(literal -1 binary64) (log.f64 (.f64 #s(literal -2 binary64) (PI.f64)))) (-.f64 #s(literal 1 binary64) k))) #s(literal 2 binary64)))
#s(approx (pow (* (* (PI) 2) n) (/ (/ (- 1 k) 2) 2)) (pow.f64 (exp.f64 #s(literal 1/4 binary64)) (.f64 (fma.f64 (log.f64 (/.f64 #s(literal -1 binary64) n)) #s(literal -1 binary64) (log.f64 (.f64 #s(literal -2 binary64) (PI.f64)))) (-.f64 #s(literal 1 binary64) k))))

eval37.0ms (0.7%)

Memory: -9.2MiB live, 83.7MiB allocated; 5ms collecting garbage
Compiler: Compiled 10 863 to 1 047 computations (90.4% saved)

prune27.0ms (0.5%)

Memory

16.2MiB live, 63.0MiB allocated; 2ms collecting garbage

Pruning

23 alts after pruning (22 fresh and 1 done)

	Pruned	Kept	Total
New	338	18	356
Fresh	4	4	8
Picked	4	1	5
Done	0	0	0
Total	346	23	369

Accuracy

100.0%

Counts

369 → 23

Alt Table

Click to see full alt table

Status	Accuracy	Program
▶	99.0%	(/.f64 (pow.f64 (pow.f64 (.f64 (.f64 #s(literal 2 binary64) n) (PI.f64)) (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 4 binary64))) #s(literal 2 binary64)) (sqrt.f64 k))
	95.8%	(/.f64 (pow.f64 (exp.f64 (log.f64 (.f64 (.f64 #s(literal 2 binary64) n) (PI.f64)))) (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 2 binary64))) (sqrt.f64 k))
	74.6%	(/.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 2 binary64)))) (sqrt.f64 k))
▶	99.1%	(/.f64 (.f64 #s(literal 1 binary64) (pow.f64 (.f64 (*.f64 #s(literal 2 binary64) n) (PI.f64)) #s(approx (/ (- 1 k) 2) (fma.f64 #s(literal -1/2 binary64) k #s(literal 1/2 binary64))))) (sqrt.f64 k))
	59.3%	(/.f64 #s(approx (* (pow (* (* (PI) 2) n) (/ (/ (- 1 k) 2) 2)) (pow (* (* (PI) 2) n) (/ (/ (- 1 k) 2) 2))) (fma.f64 (fma.f64 (.f64 #s(literal 1/8 binary64) (.f64 (.f64 (pow.f64 (log.f64 (.f64 (.f64 #s(literal 2 binary64) n) (PI.f64))) #s(literal 2 binary64)) k) (sqrt.f64 #s(literal 2 binary64)))) (sqrt.f64 (.f64 (PI.f64) n)) (.f64 (.f64 #s(literal -1/2 binary64) (sqrt.f64 (.f64 (PI.f64) n))) (.f64 (log.f64 (.f64 (.f64 #s(literal 2 binary64) n) (PI.f64))) (sqrt.f64 #s(literal 2 binary64))))) k (sqrt.f64 (.f64 (.f64 #s(literal 2 binary64) n) (PI.f64))))) (sqrt.f64 k))
	51.5%	(/.f64 #s(approx (* (pow (* (* (PI) 2) n) (/ (/ (- 1 k) 2) 2)) (pow (* (* (PI) 2) n) (/ (/ (- 1 k) 2) 2))) (fma.f64 (.f64 k (.f64 (.f64 (sqrt.f64 (.f64 (PI.f64) n)) (log.f64 (.f64 (.f64 #s(literal 2 binary64) n) (PI.f64)))) (sqrt.f64 #s(literal 2 binary64)))) #s(literal -1/2 binary64) (sqrt.f64 (.f64 (.f64 #s(literal 2 binary64) n) (PI.f64))))) (sqrt.f64 k))
	51.0%	(/.f64 #s(approx (* (pow (* (* (PI) 2) n) (/ (/ (- 1 k) 2) 2)) (pow (* (* (PI) 2) n) (/ (/ (- 1 k) 2) 2))) (sqrt.f64 (.f64 (.f64 #s(literal 2 binary64) n) (PI.f64)))) (sqrt.f64 k))
▶	51.8%	(.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) (pow.f64 (.f64 (.f64 #s(literal 2 binary64) (PI.f64)) n) #s(approx (/ (- 1 k) 2) (.f64 #s(literal -1/2 binary64) k))))
▶	98.4%	(.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) (.f64 (pow.f64 (.f64 (.f64 (PI.f64) #s(literal 2 binary64)) n) (/.f64 (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 2 binary64)) #s(literal 2 binary64))) (pow.f64 (.f64 (.f64 (PI.f64) #s(literal 2 binary64)) n) #s(approx (/ (/ (- 1 k) 2) 2) (*.f64 (-.f64 (/.f64 #s(literal 1/4 binary64) k) #s(literal 1/4 binary64)) k)))))
	74.4%	(.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) (.f64 (pow.f64 (.f64 (.f64 (PI.f64) #s(literal 2 binary64)) n) (/.f64 (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 2 binary64)) #s(literal 2 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 4 binary64))))))
	96.5%	(.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) (.f64 (pow.f64 (.f64 (.f64 (PI.f64) #s(literal 2 binary64)) n) (/.f64 (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 2 binary64)) #s(literal 2 binary64))) (exp.f64 (.f64 (log.f64 (.f64 (*.f64 #s(literal 2 binary64) n) (PI.f64))) (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 4 binary64))))))
	74.6%	(.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) (.f64 (pow.f64 (*.f64 (PI.f64) #s(literal 2 binary64)) #s(approx (/ (- 1 k) 2) (fma.f64 #s(literal -1/2 binary64) k #s(literal 1/2 binary64)))) (pow.f64 n #s(approx (/ (- 1 k) 2) (fma.f64 #s(literal -1/2 binary64) k #s(literal 1/2 binary64))))))
	95.6%	(.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) (exp.f64 (.f64 (log.f64 (.f64 (.f64 (PI.f64) #s(literal 2 binary64)) n)) #s(approx (/ (- 1 k) 2) (*.f64 (-.f64 (/.f64 #s(literal 1/2 binary64) k) #s(literal 1/2 binary64)) k)))))
	95.8%	(.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) (exp.f64 (.f64 (log.f64 (.f64 (.f64 #s(literal 2 binary64) n) (PI.f64))) #s(approx (/ (- 1 k) 2) (fma.f64 #s(literal -1/2 binary64) k #s(literal 1/2 binary64))))))
	51.4%	(.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) #s(approx (pow ( (* 2 (PI)) n) (/ (- 1 k) 2)) (fma.f64 (.f64 (.f64 (.f64 (log.f64 (.f64 (.f64 (PI.f64) #s(literal 2 binary64)) n)) (sqrt.f64 #s(literal 2 binary64))) k) (sqrt.f64 (.f64 (PI.f64) n))) #s(literal -1/2 binary64) (sqrt.f64 (.f64 (.f64 (PI.f64) #s(literal 2 binary64)) n)))))
	50.9%	(.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) #s(approx (pow ( (* 2 (PI)) n) (/ (- 1 k) 2)) (sqrt.f64 (.f64 (.f64 (PI.f64) #s(literal 2 binary64)) n))))
	93.8%	(.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) #s(approx ( (pow (* (* (PI) 2) n) (/ (/ (- 1 k) 2) 2)) (pow (* (* (PI) 2) n) (/ (/ (- 1 k) 2) 2))) (pow.f64 (pow.f64 (exp.f64 #s(literal 1/4 binary64)) (.f64 (fma.f64 (neg.f64 (log.f64 n)) #s(literal -1 binary64) (log.f64 (.f64 (PI.f64) #s(literal 2 binary64)))) (-.f64 #s(literal 1 binary64) k))) #s(literal 2 binary64))))
	99.1%	(.f64 (sqrt.f64 (pow.f64 k #s(literal -1 binary64))) (pow.f64 (.f64 (*.f64 #s(literal 2 binary64) (PI.f64)) n) #s(approx (/ (- 1 k) 2) (fma.f64 #s(literal -1/2 binary64) k #s(literal 1/2 binary64)))))
	54.8%	#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (/.f64 (fma.f64 (.f64 (.f64 (log.f64 (.f64 (.f64 (PI.f64) #s(literal 2 binary64)) n)) (sqrt.f64 #s(literal 2 binary64))) (sqrt.f64 (.f64 (.f64 (pow.f64 k #s(literal 3 binary64)) n) (PI.f64)))) #s(literal -1/2 binary64) (sqrt.f64 (.f64 (.f64 (*.f64 (PI.f64) n) k) #s(literal 2 binary64)))) k))
	40.7%	#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))))
✓	40.8%	#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))))
	40.8%	#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt.f64 (.f64 (.f64 (PI.f64) (/.f64 n k)) #s(literal 2 binary64))))
▶	40.8%	#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt.f64 (.f64 (.f64 n (/.f64 (PI.f64) k)) #s(literal 2 binary64))))

Compiler

Compiled 1 441 to 994 computations (31% saved)

series50.0ms (1%)

Memory

-33.5MiB live, 110.5MiB allocated; 7ms collecting garbage

Counts

46 → 150

Calls

Call 1

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

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

Calls

6 calls:

Time	Variable		Point	Expression
11.0ms	n	@	inf	((/ (* 1 (pow (* (* 2 n) (PI)) (/ (- 1 k) 2))) (sqrt k)) (* 1 (pow (* (* 2 n) (PI)) (/ (- 1 k) 2))) 1 (pow (* (* 2 n) (PI)) (/ (- 1 k) 2)) (* (* 2 n) (PI)) (* 2 n) 2 n (PI) (/ (- 1 k) 2) (+ (* -1/2 k) 1/2) -1/2 k 1/2 (sqrt k) (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt (* (* n (/ (PI) k)) 2)) (* (* n (/ (PI) k)) 2) (* n (/ (PI) k)) (/ (PI) k) (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2)) (* (* 2 (PI)) n) (* 2 (PI)) (/ (- 1 k) 2) (* -1/2 k) (/ (pow (pow (* (* 2 n) (PI)) (/ (- 1 k) 4)) 2) (sqrt k)) (pow (pow (* (* 2 n) (PI)) (/ (- 1 k) 4)) 2) (pow (* (* 2 n) (PI)) (/ (- 1 k) 4)) (/ (- 1 k) 4) (- 1 k) 4 (* (/ 1 (sqrt k)) (* (pow (* (* (PI) 2) n) (/ (/ (- 1 k) 2) 2)) (pow (* (* (PI) 2) n) (/ (/ (- 1 k) 2) 2)))) (* (pow (* (* (PI) 2) n) (/ (/ (- 1 k) 2) 2)) (pow (* (* (PI) 2) n) (/ (/ (- 1 k) 2) 2))) (pow (* (* (PI) 2) n) (/ (/ (- 1 k) 2) 2)) (* (* (PI) 2) n) (* (PI) 2) (/ (/ (- 1 k) 2) 2) (/ (- 1 k) 2) (pow (* (* (PI) 2) n) (/ (/ (- 1 k) 2) 2)) (/ (/ (- 1 k) 2) 2) (* (- (/ 1/4 k) 1/4) k) (- (/ 1/4 k) 1/4) (/ 1/4 k) 1/4)
10.0ms	n	@	-inf	((/ (* 1 (pow (* (* 2 n) (PI)) (/ (- 1 k) 2))) (sqrt k)) (* 1 (pow (* (* 2 n) (PI)) (/ (- 1 k) 2))) 1 (pow (* (* 2 n) (PI)) (/ (- 1 k) 2)) (* (* 2 n) (PI)) (* 2 n) 2 n (PI) (/ (- 1 k) 2) (+ (* -1/2 k) 1/2) -1/2 k 1/2 (sqrt k) (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt (* (* n (/ (PI) k)) 2)) (* (* n (/ (PI) k)) 2) (* n (/ (PI) k)) (/ (PI) k) (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2)) (* (* 2 (PI)) n) (* 2 (PI)) (/ (- 1 k) 2) (* -1/2 k) (/ (pow (pow (* (* 2 n) (PI)) (/ (- 1 k) 4)) 2) (sqrt k)) (pow (pow (* (* 2 n) (PI)) (/ (- 1 k) 4)) 2) (pow (* (* 2 n) (PI)) (/ (- 1 k) 4)) (/ (- 1 k) 4) (- 1 k) 4 (* (/ 1 (sqrt k)) (* (pow (* (* (PI) 2) n) (/ (/ (- 1 k) 2) 2)) (pow (* (* (PI) 2) n) (/ (/ (- 1 k) 2) 2)))) (* (pow (* (* (PI) 2) n) (/ (/ (- 1 k) 2) 2)) (pow (* (* (PI) 2) n) (/ (/ (- 1 k) 2) 2))) (pow (* (* (PI) 2) n) (/ (/ (- 1 k) 2) 2)) (* (* (PI) 2) n) (* (PI) 2) (/ (/ (- 1 k) 2) 2) (/ (- 1 k) 2) (pow (* (* (PI) 2) n) (/ (/ (- 1 k) 2) 2)) (/ (/ (- 1 k) 2) 2) (* (- (/ 1/4 k) 1/4) k) (- (/ 1/4 k) 1/4) (/ 1/4 k) 1/4)
10.0ms	n	@	0	((/ (* 1 (pow (* (* 2 n) (PI)) (/ (- 1 k) 2))) (sqrt k)) (* 1 (pow (* (* 2 n) (PI)) (/ (- 1 k) 2))) 1 (pow (* (* 2 n) (PI)) (/ (- 1 k) 2)) (* (* 2 n) (PI)) (* 2 n) 2 n (PI) (/ (- 1 k) 2) (+ (* -1/2 k) 1/2) -1/2 k 1/2 (sqrt k) (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt (* (* n (/ (PI) k)) 2)) (* (* n (/ (PI) k)) 2) (* n (/ (PI) k)) (/ (PI) k) (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2)) (* (* 2 (PI)) n) (* 2 (PI)) (/ (- 1 k) 2) (* -1/2 k) (/ (pow (pow (* (* 2 n) (PI)) (/ (- 1 k) 4)) 2) (sqrt k)) (pow (pow (* (* 2 n) (PI)) (/ (- 1 k) 4)) 2) (pow (* (* 2 n) (PI)) (/ (- 1 k) 4)) (/ (- 1 k) 4) (- 1 k) 4 (* (/ 1 (sqrt k)) (* (pow (* (* (PI) 2) n) (/ (/ (- 1 k) 2) 2)) (pow (* (* (PI) 2) n) (/ (/ (- 1 k) 2) 2)))) (* (pow (* (* (PI) 2) n) (/ (/ (- 1 k) 2) 2)) (pow (* (* (PI) 2) n) (/ (/ (- 1 k) 2) 2))) (pow (* (* (PI) 2) n) (/ (/ (- 1 k) 2) 2)) (* (* (PI) 2) n) (* (PI) 2) (/ (/ (- 1 k) 2) 2) (/ (- 1 k) 2) (pow (* (* (PI) 2) n) (/ (/ (- 1 k) 2) 2)) (/ (/ (- 1 k) 2) 2) (* (- (/ 1/4 k) 1/4) k) (- (/ 1/4 k) 1/4) (/ 1/4 k) 1/4)
6.0ms	k	@	0	((/ (* 1 (pow (* (* 2 n) (PI)) (/ (- 1 k) 2))) (sqrt k)) (* 1 (pow (* (* 2 n) (PI)) (/ (- 1 k) 2))) 1 (pow (* (* 2 n) (PI)) (/ (- 1 k) 2)) (* (* 2 n) (PI)) (* 2 n) 2 n (PI) (/ (- 1 k) 2) (+ (* -1/2 k) 1/2) -1/2 k 1/2 (sqrt k) (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt (* (* n (/ (PI) k)) 2)) (* (* n (/ (PI) k)) 2) (* n (/ (PI) k)) (/ (PI) k) (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2)) (* (* 2 (PI)) n) (* 2 (PI)) (/ (- 1 k) 2) (* -1/2 k) (/ (pow (pow (* (* 2 n) (PI)) (/ (- 1 k) 4)) 2) (sqrt k)) (pow (pow (* (* 2 n) (PI)) (/ (- 1 k) 4)) 2) (pow (* (* 2 n) (PI)) (/ (- 1 k) 4)) (/ (- 1 k) 4) (- 1 k) 4 (* (/ 1 (sqrt k)) (* (pow (* (* (PI) 2) n) (/ (/ (- 1 k) 2) 2)) (pow (* (* (PI) 2) n) (/ (/ (- 1 k) 2) 2)))) (* (pow (* (* (PI) 2) n) (/ (/ (- 1 k) 2) 2)) (pow (* (* (PI) 2) n) (/ (/ (- 1 k) 2) 2))) (pow (* (* (PI) 2) n) (/ (/ (- 1 k) 2) 2)) (* (* (PI) 2) n) (* (PI) 2) (/ (/ (- 1 k) 2) 2) (/ (- 1 k) 2) (pow (* (* (PI) 2) n) (/ (/ (- 1 k) 2) 2)) (/ (/ (- 1 k) 2) 2) (* (- (/ 1/4 k) 1/4) k) (- (/ 1/4 k) 1/4) (/ 1/4 k) 1/4)
5.0ms	k	@	-inf	((/ (* 1 (pow (* (* 2 n) (PI)) (/ (- 1 k) 2))) (sqrt k)) (* 1 (pow (* (* 2 n) (PI)) (/ (- 1 k) 2))) 1 (pow (* (* 2 n) (PI)) (/ (- 1 k) 2)) (* (* 2 n) (PI)) (* 2 n) 2 n (PI) (/ (- 1 k) 2) (+ (* -1/2 k) 1/2) -1/2 k 1/2 (sqrt k) (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt (* (* n (/ (PI) k)) 2)) (* (* n (/ (PI) k)) 2) (* n (/ (PI) k)) (/ (PI) k) (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2)) (* (* 2 (PI)) n) (* 2 (PI)) (/ (- 1 k) 2) (* -1/2 k) (/ (pow (pow (* (* 2 n) (PI)) (/ (- 1 k) 4)) 2) (sqrt k)) (pow (pow (* (* 2 n) (PI)) (/ (- 1 k) 4)) 2) (pow (* (* 2 n) (PI)) (/ (- 1 k) 4)) (/ (- 1 k) 4) (- 1 k) 4 (* (/ 1 (sqrt k)) (* (pow (* (* (PI) 2) n) (/ (/ (- 1 k) 2) 2)) (pow (* (* (PI) 2) n) (/ (/ (- 1 k) 2) 2)))) (* (pow (* (* (PI) 2) n) (/ (/ (- 1 k) 2) 2)) (pow (* (* (PI) 2) n) (/ (/ (- 1 k) 2) 2))) (pow (* (* (PI) 2) n) (/ (/ (- 1 k) 2) 2)) (* (* (PI) 2) n) (* (PI) 2) (/ (/ (- 1 k) 2) 2) (/ (- 1 k) 2) (pow (* (* (PI) 2) n) (/ (/ (- 1 k) 2) 2)) (/ (/ (- 1 k) 2) 2) (* (- (/ 1/4 k) 1/4) k) (- (/ 1/4 k) 1/4) (/ 1/4 k) 1/4)

rewrite79.0ms (1.6%)

Memory

38.1MiB live, 134.0MiB allocated; 5ms collecting garbage

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	431	5498
0	489	4821
0	1756	4751

Stop Event

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

Counts

196 → 325

Calls

Call 1

Inputs
(/.f64 (.f64 #s(literal 1 binary64) (pow.f64 (.f64 (*.f64 #s(literal 2 binary64) n) (PI.f64)) #s(approx (/ (- 1 k) 2) (fma.f64 #s(literal -1/2 binary64) k #s(literal 1/2 binary64))))) (sqrt.f64 k))
(.f64 #s(literal 1 binary64) (pow.f64 (.f64 (*.f64 #s(literal 2 binary64) n) (PI.f64)) #s(approx (/ (- 1 k) 2) (fma.f64 #s(literal -1/2 binary64) k #s(literal 1/2 binary64)))))
#s(literal 1 binary64)
(pow.f64 (.f64 (.f64 #s(literal 2 binary64) n) (PI.f64)) #s(approx (/ (- 1 k) 2) (fma.f64 #s(literal -1/2 binary64) k #s(literal 1/2 binary64))))
(.f64 (.f64 #s(literal 2 binary64) n) (PI.f64))
(*.f64 #s(literal 2 binary64) n)
#s(literal 2 binary64)
n
(PI.f64)
#s(approx (/ (- 1 k) 2) (fma.f64 #s(literal -1/2 binary64) k #s(literal 1/2 binary64)))
(fma.f64 #s(literal -1/2 binary64) k #s(literal 1/2 binary64))
#s(literal -1/2 binary64)
k
#s(literal 1/2 binary64)
(sqrt.f64 k)
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt.f64 (.f64 (.f64 n (/.f64 (PI.f64) k)) #s(literal 2 binary64))))
(sqrt.f64 (.f64 (.f64 n (/.f64 (PI.f64) k)) #s(literal 2 binary64)))
(.f64 (.f64 n (/.f64 (PI.f64) k)) #s(literal 2 binary64))
(*.f64 n (/.f64 (PI.f64) k))
(/.f64 (PI.f64) k)
(.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) (pow.f64 (.f64 (.f64 #s(literal 2 binary64) (PI.f64)) n) #s(approx (/ (- 1 k) 2) (.f64 #s(literal -1/2 binary64) k))))
(/.f64 #s(literal 1 binary64) (sqrt.f64 k))
(pow.f64 (.f64 (.f64 #s(literal 2 binary64) (PI.f64)) n) #s(approx (/ (- 1 k) 2) (*.f64 #s(literal -1/2 binary64) k)))
(.f64 (.f64 #s(literal 2 binary64) (PI.f64)) n)
(*.f64 #s(literal 2 binary64) (PI.f64))
#s(approx (/ (- 1 k) 2) (*.f64 #s(literal -1/2 binary64) k))
(*.f64 #s(literal -1/2 binary64) k)
(/.f64 (pow.f64 (pow.f64 (.f64 (.f64 #s(literal 2 binary64) n) (PI.f64)) (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 4 binary64))) #s(literal 2 binary64)) (sqrt.f64 k))
(pow.f64 (pow.f64 (.f64 (.f64 #s(literal 2 binary64) n) (PI.f64)) (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 4 binary64))) #s(literal 2 binary64))
(pow.f64 (.f64 (.f64 #s(literal 2 binary64) n) (PI.f64)) (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 4 binary64)))
(/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 4 binary64))
(-.f64 #s(literal 1 binary64) k)
#s(literal 4 binary64)
(.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) (.f64 (pow.f64 (.f64 (.f64 (PI.f64) #s(literal 2 binary64)) n) (/.f64 (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 2 binary64)) #s(literal 2 binary64))) (pow.f64 (.f64 (.f64 (PI.f64) #s(literal 2 binary64)) n) #s(approx (/ (/ (- 1 k) 2) 2) (*.f64 (-.f64 (/.f64 #s(literal 1/4 binary64) k) #s(literal 1/4 binary64)) k)))))
(.f64 (pow.f64 (.f64 (.f64 (PI.f64) #s(literal 2 binary64)) n) (/.f64 (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 2 binary64)) #s(literal 2 binary64))) (pow.f64 (.f64 (.f64 (PI.f64) #s(literal 2 binary64)) n) #s(approx (/ (/ (- 1 k) 2) 2) (.f64 (-.f64 (/.f64 #s(literal 1/4 binary64) k) #s(literal 1/4 binary64)) k))))
(pow.f64 (.f64 (.f64 (PI.f64) #s(literal 2 binary64)) n) (/.f64 (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 2 binary64)) #s(literal 2 binary64)))
(.f64 (.f64 (PI.f64) #s(literal 2 binary64)) n)
(*.f64 (PI.f64) #s(literal 2 binary64))
(/.f64 (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 2 binary64)) #s(literal 2 binary64))
(/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 2 binary64))
(pow.f64 (.f64 (.f64 (PI.f64) #s(literal 2 binary64)) n) #s(approx (/ (/ (- 1 k) 2) 2) (*.f64 (-.f64 (/.f64 #s(literal 1/4 binary64) k) #s(literal 1/4 binary64)) k)))
#s(approx (/ (/ (- 1 k) 2) 2) (*.f64 (-.f64 (/.f64 #s(literal 1/4 binary64) k) #s(literal 1/4 binary64)) k))
(*.f64 (-.f64 (/.f64 #s(literal 1/4 binary64) k) #s(literal 1/4 binary64)) k)
(-.f64 (/.f64 #s(literal 1/4 binary64) k) #s(literal 1/4 binary64))
(/.f64 #s(literal 1/4 binary64) k)
#s(literal 1/4 binary64)
#s(approx (/ (* 1 (pow (* (* 2 n) (PI)) (/ (- 1 k) 2))) (sqrt k)) #s(hole binary64 (* (sqrt (/ (* n (PI)) k)) (sqrt 2))))
#s(approx (/ (* 1 (pow (* (* 2 n) (PI)) (/ (- 1 k) 2))) (sqrt 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 (/ (* 1 (pow (* (* 2 n) (PI)) (/ (- 1 k) 2))) (sqrt 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 (/ (* 1 (pow (* (* 2 n) (PI)) (/ (- 1 k) 2))) (sqrt 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 (* 1 (pow (* (* 2 n) (PI)) (/ (- 1 k) 2))) #s(hole binary64 (* (sqrt (* n (PI))) (sqrt 2))))
#s(approx (* 1 (pow (* (* 2 n) (PI)) (/ (- 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 (* 1 (pow (* (* 2 n) (PI)) (/ (- 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 (* 1 (pow (* (* 2 n) (PI)) (/ (- 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 n) (PI)) (/ (- 1 k) 2)) #s(hole binary64 (* (sqrt (* n (PI))) (sqrt 2))))
#s(approx (pow (* (* 2 n) (PI)) (/ (- 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 n) (PI)) (/ (- 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 n) (PI)) (/ (- 1 k) 2)) #s(hole binary64 (+ (* k (+ (* -1/2 (* (sqrt (* n (PI))) (* (log (* 2 (* n (PI)))) (sqrt 2)))) (* k (+ (* -1/48 (* (* k (* (pow (log (* 2 (* n (PI)))) 3) (sqrt 2))) (sqrt (* n (PI))))) (* 1/8 (* (sqrt (* n (PI))) (* (pow (log (* 2 (* n (PI)))) 2) (sqrt 2)))))))) (* (sqrt (* n (PI))) (sqrt 2)))))
#s(approx (/ (- 1 k) 2) #s(hole binary64 1/2))
#s(approx (/ (- 1 k) 2) #s(hole binary64 (+ 1/2 (* -1/2 k))))
#s(approx (+ (* -1/2 k) 1/2) #s(hole binary64 1/2))
#s(approx (+ (* -1/2 k) 1/2) #s(hole binary64 (+ 1/2 (* -1/2 k))))
#s(approx k #s(hole binary64 k))
#s(approx (sqrt k) #s(hole binary64 (sqrt k)))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) #s(hole binary64 (* (sqrt (/ (* n (PI)) k)) (sqrt 2))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) #s(hole binary64 (/ (+ (* -1/2 (* (sqrt (* (pow k 3) (* n (PI)))) (* (log (* 2 (* n (PI)))) (sqrt 2)))) (* (sqrt (* k (* n (PI)))) (sqrt 2))) k)))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) #s(hole binary64 (/ (+ (* k (+ (* -1/2 (* (sqrt (* k (* n (PI)))) (* (log (* 2 (* n (PI)))) (sqrt 2)))) (* 1/8 (* (sqrt (* (pow k 3) (* n (PI)))) (* (pow (log (* 2 (* n (PI)))) 2) (sqrt 2)))))) (* (sqrt (* k (* n (PI)))) (sqrt 2))) k)))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) #s(hole binary64 (/ (+ (* k (+ (* -1/2 (* (sqrt (* k (* n (PI)))) (* (log (* 2 (* n (PI)))) (sqrt 2)))) (* k (+ (* -1/48 (* (sqrt (* (pow k 3) (* n (PI)))) (* (pow (log (* 2 (* n (PI)))) 3) (sqrt 2)))) (* 1/8 (* (sqrt (* k (* n (PI)))) (* (pow (log (* 2 (* n (PI)))) 2) (sqrt 2)))))))) (* (sqrt (* k (* n (PI)))) (sqrt 2))) k)))
#s(approx (sqrt (* (* n (/ (PI) k)) 2)) #s(hole binary64 (* (sqrt (/ (* n (PI)) k)) (sqrt 2))))
#s(approx (* (* n (/ (PI) k)) 2) #s(hole binary64 (* 2 (/ (* n (PI)) k))))
#s(approx (* n (/ (PI) k)) #s(hole binary64 (/ (* n (PI)) k)))
#s(approx (/ (PI) k) #s(hole binary64 (/ (PI) k)))
#s(approx (/ 1 (sqrt k)) #s(hole binary64 (sqrt (/ 1 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 (* -1/2 k) #s(hole binary64 (* -1/2 k)))
#s(approx (/ (pow (pow (* (* 2 n) (PI)) (/ (- 1 k) 4)) 2) (sqrt k)) #s(hole binary64 (* (sqrt (/ (* n (PI)) k)) (sqrt 2))))
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#s(approx (pow (* (* 2 n) (PI)) (/ (- 1 k) 4)) #s(hole binary64 (pow (* 2 (* n (PI))) 1/4)))
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#s(approx (pow (* (* 2 n) (PI)) (/ (- 1 k) 4)) #s(hole binary64 (+ (* k (+ (* -1/4 (* (pow (* 2 (* n (PI))) 1/4) (log (* 2 (* n (PI)))))) (* k (+ (* -1/384 (* (pow (* 2 (* n (PI))) 1/4) (* k (pow (log (* 2 (* n (PI)))) 3)))) (* 1/32 (* (pow (* 2 (* n (PI))) 1/4) (pow (log (* 2 (* n (PI)))) 2))))))) (pow (* 2 (* n (PI))) 1/4))))
#s(approx (/ (- 1 k) 4) #s(hole binary64 1/4))
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#s(approx (* (/ 1 (sqrt k)) (* (pow (* (* (PI) 2) n) (/ (/ (- 1 k) 2) 2)) (pow (* (* (PI) 2) n) (/ (/ (- 1 k) 2) 2)))) #s(hole binary64 (* (sqrt (/ (* n (PI)) k)) (sqrt 2))))
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#s(approx (* (pow (* (* (PI) 2) n) (/ (/ (- 1 k) 2) 2)) (pow (* (* (PI) 2) n) (/ (/ (- 1 k) 2) 2))) #s(hole binary64 (* (sqrt (* n (PI))) (sqrt 2))))
#s(approx (* (pow (* (* (PI) 2) n) (/ (/ (- 1 k) 2) 2)) (pow (* (* (PI) 2) n) (/ (/ (- 1 k) 2) 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) 2) n) (/ (/ (- 1 k) 2) 2)) (pow (* (* (PI) 2) n) (/ (/ (- 1 k) 2) 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) 2) n) (/ (/ (- 1 k) 2) 2)) (pow (* (* (PI) 2) n) (/ (/ (- 1 k) 2) 2))) #s(hole binary64 (+ (* k (+ (* -1/2 (* (sqrt (* n (PI))) (* (log (* 2 (* n (PI)))) (sqrt 2)))) (* k (+ (* 1/8 (* (sqrt (* n (PI))) (* (pow (log (* 2 (* n (PI)))) 2) (sqrt 2)))) (* k (+ (* -1/64 (* (sqrt (* n (PI))) (* (pow (log (* 2 (* n (PI)))) 3) (sqrt 2)))) (* -1/192 (* (sqrt (* n (PI))) (* (pow (log (* 2 (* n (PI)))) 3) (sqrt 2)))))))))) (* (sqrt (* n (PI))) (sqrt 2)))))
#s(approx (pow (* (* (PI) 2) n) (/ (/ (- 1 k) 2) 2)) #s(hole binary64 (pow (* 2 (* n (PI))) 1/4)))
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#s(approx (/ (/ (- 1 k) 2) 2) #s(hole binary64 1/4))
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#s(approx (* (- (/ 1/4 k) 1/4) k) #s(hole binary64 1/4))
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#s(approx (- (/ 1/4 k) 1/4) #s(hole binary64 (/ 1/4 k)))
#s(approx (- (/ 1/4 k) 1/4) #s(hole binary64 (/ (+ 1/4 (* -1/4 k)) k)))
#s(approx (/ 1/4 k) #s(hole binary64 (/ 1/4 k)))
#s(approx (/ (* 1 (pow (* (* 2 n) (PI)) (/ (- 1 k) 2))) (sqrt k)) #s(hole binary64 (* (sqrt (/ 1 k)) (exp (* 1/2 (* (log (* 2 (* n (PI)))) (- 1 k)))))))
#s(approx (* 1 (pow (* (* 2 n) (PI)) (/ (- 1 k) 2))) #s(hole binary64 (exp (* 1/2 (* (log (* 2 (* n (PI)))) (- 1 k))))))
#s(approx (pow (* (* 2 n) (PI)) (/ (- 1 k) 2)) #s(hole binary64 (exp (* 1/2 (* (log (* 2 (* n (PI)))) (- 1 k))))))
#s(approx (/ (- 1 k) 2) #s(hole binary64 (* -1/2 k)))
#s(approx (/ (- 1 k) 2) #s(hole binary64 (* k (- (* 1/2 (/ 1 k)) 1/2))))
#s(approx (+ (* -1/2 k) 1/2) #s(hole binary64 (* -1/2 k)))
#s(approx (+ (* -1/2 k) 1/2) #s(hole binary64 (* k (- (* 1/2 (/ 1 k)) 1/2))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (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 (/ (pow (pow (* (* 2 n) (PI)) (/ (- 1 k) 4)) 2) (sqrt k)) #s(hole binary64 (* (sqrt (/ 1 k)) (pow (exp (* 1/4 (* (log (* 2 (* n (PI)))) (- 1 k)))) 2))))
#s(approx (pow (pow (* (* 2 n) (PI)) (/ (- 1 k) 4)) 2) #s(hole binary64 (pow (exp (* 1/4 (* (log (* 2 (* n (PI)))) (- 1 k)))) 2)))
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#s(approx (/ (- 1 k) 4) #s(hole binary64 (* k (- (* 1/4 (/ 1 k)) 1/4))))
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#s(approx (* (/ 1 (sqrt k)) (* (pow (* (* (PI) 2) n) (/ (/ (- 1 k) 2) 2)) (pow (* (* (PI) 2) n) (/ (/ (- 1 k) 2) 2)))) #s(hole binary64 (* (sqrt (/ 1 k)) (pow (exp (* 1/4 (* (log (* 2 (* n (PI)))) (- 1 k)))) 2))))
#s(approx (* (pow (* (* (PI) 2) n) (/ (/ (- 1 k) 2) 2)) (pow (* (* (PI) 2) n) (/ (/ (- 1 k) 2) 2))) #s(hole binary64 (pow (exp (* 1/4 (* (log (* 2 (* n (PI)))) (- 1 k)))) 2)))
#s(approx (pow (* (* (PI) 2) n) (/ (/ (- 1 k) 2) 2)) #s(hole binary64 (exp (* 1/4 (* (log (* 2 (* n (PI)))) (- 1 k))))))
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#s(approx (/ (/ (- 1 k) 2) 2) #s(hole binary64 (* k (- (* 1/4 (/ 1 k)) 1/4))))
#s(approx (* (- (/ 1/4 k) 1/4) k) #s(hole binary64 (* -1/4 k)))
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#s(approx (- (/ 1/4 k) 1/4) #s(hole binary64 (- (* 1/4 (/ 1 k)) 1/4)))
#s(approx (/ (* 1 (pow (* (* 2 n) (PI)) (/ (- 1 k) 2))) (sqrt k)) #s(hole binary64 (* (sqrt (/ 1 k)) (exp (* 1/2 (* (log (* 2 (* n (PI)))) (+ 1 (* -1 k))))))))
#s(approx (* 1 (pow (* (* 2 n) (PI)) (/ (- 1 k) 2))) #s(hole binary64 (exp (* 1/2 (* (log (* 2 (* n (PI)))) (+ 1 (* -1 k)))))))
#s(approx (pow (* (* 2 n) (PI)) (/ (- 1 k) 2)) #s(hole binary64 (exp (* 1/2 (* (log (* 2 (* n (PI)))) (+ 1 (* -1 k)))))))
#s(approx (/ (- 1 k) 2) #s(hole binary64 (* -1 (* k (- 1/2 (* 1/2 (/ 1 k)))))))
#s(approx (+ (* -1/2 k) 1/2) #s(hole binary64 (* -1 (* k (- 1/2 (* 1/2 (/ 1 k)))))))
#s(approx (sqrt k) #s(hole binary64 (* -1 (* (sqrt k) (pow (sqrt -1) 2)))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) #s(hole binary64 (* (sqrt (/ 1 k)) (exp (* 1/2 (* (log (* 2 (* n (PI)))) (+ 1 (* -1 k))))))))
#s(approx (sqrt (* (* n (/ (PI) k)) 2)) #s(hole binary64 (* (sqrt (/ (* n (PI)) k)) (* (sqrt -2) (sqrt -1)))))
#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 (pow (* (* 2 n) (PI)) (/ (- 1 k) 4)) 2) (sqrt k)) #s(hole binary64 (* (sqrt (/ 1 k)) (pow (exp (* 1/4 (* (log (* 2 (* n (PI)))) (+ 1 (* -1 k))))) 2))))
#s(approx (pow (pow (* (* 2 n) (PI)) (/ (- 1 k) 4)) 2) #s(hole binary64 (pow (exp (* 1/4 (* (log (* 2 (* n (PI)))) (+ 1 (* -1 k))))) 2)))
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#s(approx (* (/ 1 (sqrt k)) (* (pow (* (* (PI) 2) n) (/ (/ (- 1 k) 2) 2)) (pow (* (* (PI) 2) n) (/ (/ (- 1 k) 2) 2)))) #s(hole binary64 (* (sqrt (/ 1 k)) (pow (exp (* 1/4 (* (log (* 2 (* n (PI)))) (+ 1 (* -1 k))))) 2))))
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#s(approx (pow (* (* (PI) 2) n) (/ (/ (- 1 k) 2) 2)) #s(hole binary64 (exp (* 1/4 (* (log (* 2 (* n (PI)))) (+ 1 (* -1 k)))))))
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#s(approx (/ (* 1 (pow (* (* 2 n) (PI)) (/ (- 1 k) 2))) (sqrt k)) #s(hole binary64 (* (sqrt (/ 1 k)) (exp (* 1/2 (* (+ (log n) (log (* 2 (PI)))) (- 1 k)))))))
#s(approx (* 1 (pow (* (* 2 n) (PI)) (/ (- 1 k) 2))) #s(hole binary64 (exp (* 1/2 (* (+ (log n) (log (* 2 (PI)))) (- 1 k))))))
#s(approx (pow (* (* 2 n) (PI)) (/ (- 1 k) 2)) #s(hole binary64 (exp (* 1/2 (* (+ (log n) (log (* 2 (PI)))) (- 1 k))))))
#s(approx (* (* 2 n) (PI)) #s(hole binary64 (* 2 (* n (PI)))))
#s(approx (* 2 n) #s(hole binary64 (* 2 n)))
#s(approx n #s(hole binary64 n))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) #s(hole binary64 (* (sqrt (/ 1 k)) (exp (* 1/2 (* (+ (log 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 (/ (pow (pow (* (* 2 n) (PI)) (/ (- 1 k) 4)) 2) (sqrt k)) #s(hole binary64 (* (sqrt (/ 1 k)) (pow (exp (* 1/4 (* (+ (log n) (log (* 2 (PI)))) (- 1 k)))) 2))))
#s(approx (pow (pow (* (* 2 n) (PI)) (/ (- 1 k) 4)) 2) #s(hole binary64 (pow (exp (* 1/4 (* (+ (log n) (log (* 2 (PI)))) (- 1 k)))) 2)))
#s(approx (pow (* (* 2 n) (PI)) (/ (- 1 k) 4)) #s(hole binary64 (exp (* 1/4 (* (+ (log n) (log (* 2 (PI)))) (- 1 k))))))
#s(approx (* (/ 1 (sqrt k)) (* (pow (* (* (PI) 2) n) (/ (/ (- 1 k) 2) 2)) (pow (* (* (PI) 2) n) (/ (/ (- 1 k) 2) 2)))) #s(hole binary64 (* (sqrt (/ 1 k)) (pow (exp (* 1/4 (* (+ (log n) (log (* 2 (PI)))) (- 1 k)))) 2))))
#s(approx (* (pow (* (* (PI) 2) n) (/ (/ (- 1 k) 2) 2)) (pow (* (* (PI) 2) n) (/ (/ (- 1 k) 2) 2))) #s(hole binary64 (pow (exp (* 1/4 (* (+ (log n) (log (* 2 (PI)))) (- 1 k)))) 2)))
#s(approx (pow (* (* (PI) 2) n) (/ (/ (- 1 k) 2) 2)) #s(hole binary64 (exp (* 1/4 (* (+ (log n) (log (* 2 (PI)))) (- 1 k))))))
#s(approx (* (* (PI) 2) n) #s(hole binary64 (* 2 (* n (PI)))))
#s(approx (/ (* 1 (pow (* (* 2 n) (PI)) (/ (- 1 k) 2))) (sqrt k)) #s(hole binary64 (* (sqrt (/ 1 k)) (exp (* 1/2 (* (+ (log (* 2 (PI))) (* -1 (log (/ 1 n)))) (- 1 k)))))))
#s(approx (* 1 (pow (* (* 2 n) (PI)) (/ (- 1 k) 2))) #s(hole binary64 (exp (* 1/2 (* (+ (log (* 2 (PI))) (* -1 (log (/ 1 n)))) (- 1 k))))))
#s(approx (pow (* (* 2 n) (PI)) (/ (- 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))))))
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#s(approx (pow (pow (* (* 2 n) (PI)) (/ (- 1 k) 4)) 2) #s(hole binary64 (pow (exp (* 1/4 (* (+ (log (* 2 (PI))) (* -1 (log (/ 1 n)))) (- 1 k)))) 2)))
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#s(approx (* (/ 1 (sqrt k)) (* (pow (* (* (PI) 2) n) (/ (/ (- 1 k) 2) 2)) (pow (* (* (PI) 2) n) (/ (/ (- 1 k) 2) 2)))) #s(hole binary64 (* (sqrt (/ 1 k)) (pow (exp (* 1/4 (* (+ (log (* 2 (PI))) (* -1 (log (/ 1 n)))) (- 1 k)))) 2))))
#s(approx (* (pow (* (* (PI) 2) n) (/ (/ (- 1 k) 2) 2)) (pow (* (* (PI) 2) n) (/ (/ (- 1 k) 2) 2))) #s(hole binary64 (pow (exp (* 1/4 (* (+ (log (* 2 (PI))) (* -1 (log (/ 1 n)))) (- 1 k)))) 2)))
#s(approx (pow (* (* (PI) 2) n) (/ (/ (- 1 k) 2) 2)) #s(hole binary64 (exp (* 1/4 (* (+ (log (* 2 (PI))) (* -1 (log (/ 1 n)))) (- 1 k))))))
#s(approx (/ (* 1 (pow (* (* 2 n) (PI)) (/ (- 1 k) 2))) (sqrt k)) #s(hole binary64 (* (sqrt (/ 1 k)) (exp (* 1/2 (* (+ (log (* -2 (PI))) (* -1 (log (/ -1 n)))) (- 1 k)))))))
#s(approx (* 1 (pow (* (* 2 n) (PI)) (/ (- 1 k) 2))) #s(hole binary64 (exp (* 1/2 (* (+ (log (* -2 (PI))) (* -1 (log (/ -1 n)))) (- 1 k))))))
#s(approx (pow (* (* 2 n) (PI)) (/ (- 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 (* (* n (/ (PI) k)) 2)) #s(hole binary64 (* -1 (* (sqrt (/ (* n (PI)) k)) (* (sqrt -2) (sqrt -1))))))
#s(approx (pow (* (* 2 (PI)) n) (/ (- 1 k) 2)) #s(hole binary64 (exp (* 1/2 (* (+ (log (* -2 (PI))) (* -1 (log (/ -1 n)))) (- 1 k))))))
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#s(approx (pow (pow (* (* 2 n) (PI)) (/ (- 1 k) 4)) 2) #s(hole binary64 (pow (exp (* 1/4 (* (+ (log (* -2 (PI))) (* -1 (log (/ -1 n)))) (- 1 k)))) 2)))
#s(approx (pow (* (* 2 n) (PI)) (/ (- 1 k) 4)) #s(hole binary64 (exp (* 1/4 (* (+ (log (* -2 (PI))) (* -1 (log (/ -1 n)))) (- 1 k))))))
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#s(approx (* (pow (* (* (PI) 2) n) (/ (/ (- 1 k) 2) 2)) (pow (* (* (PI) 2) n) (/ (/ (- 1 k) 2) 2))) #s(hole binary64 (pow (exp (* 1/4 (* (+ (log (* -2 (PI))) (* -1 (log (/ -1 n)))) (- 1 k)))) 2)))
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Outputs
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(.f64 n (.f64 (PI.f64) #s(literal 2 binary64)))
(.f64 #s(literal 2 binary64) (.f64 (PI.f64) n))
(fma.f64 (PI.f64) n (*.f64 (PI.f64) n))
(fma.f64 n (PI.f64) (*.f64 (PI.f64) n))
(+.f64 (.f64 (PI.f64) n) (.f64 (PI.f64) n))
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(-.f64 (/.f64 #s(literal 1/4 binary64) k) #s(literal 1/4 binary64))
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#s(literal 1/4 binary64)
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#s(approx (/ (/ (- 1 k) 2) 2) #s(literal 1/4 binary64))
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#s(approx (- 1 k) #s(literal 1 binary64))
#s(approx (- 1 k) (fma.f64 #s(literal -1 binary64) k #s(literal 1 binary64)))
#s(approx (/ (* 1 (pow (* (* 2 n) (PI)) (/ (- 1 k) 2))) (sqrt k)) (sqrt.f64 (.f64 (/.f64 (.f64 (PI.f64) n) k) #s(literal 2 binary64))))
#s(approx (/ (* 1 (pow (* (* 2 n) (PI)) (/ (- 1 k) 2))) (sqrt k)) (/.f64 (fma.f64 (.f64 #s(literal -1/2 binary64) (.f64 (pow.f64 k #s(literal 3/2 binary64)) (sqrt.f64 (.f64 (PI.f64) n)))) (.f64 (log.f64 (.f64 (.f64 (PI.f64) n) #s(literal 2 binary64))) (sqrt.f64 #s(literal 2 binary64))) (sqrt.f64 (.f64 (.f64 (*.f64 (PI.f64) n) k) #s(literal 2 binary64)))) k))
#s(approx (/ (* 1 (pow (* (* 2 n) (PI)) (/ (- 1 k) 2))) (sqrt k)) (/.f64 (fma.f64 (fma.f64 (.f64 #s(literal 1/8 binary64) (.f64 (pow.f64 k #s(literal 3/2 binary64)) (sqrt.f64 (.f64 (PI.f64) n)))) (.f64 (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 #s(literal -1/2 binary64) (sqrt.f64 (.f64 (.f64 (PI.f64) n) k))) (.f64 (log.f64 (.f64 (.f64 (PI.f64) n) #s(literal 2 binary64))) (sqrt.f64 #s(literal 2 binary64))))) k (sqrt.f64 (.f64 (.f64 (.f64 (PI.f64) n) k) #s(literal 2 binary64)))) k))
#s(approx (/ (* 1 (pow (* (* 2 n) (PI)) (/ (- 1 k) 2))) (sqrt k)) (/.f64 (fma.f64 (fma.f64 (fma.f64 (.f64 (.f64 (.f64 (sqrt.f64 (.f64 (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))) #s(literal -1/48 binary64)) (pow.f64 k #s(literal 3/2 binary64)) (.f64 (.f64 #s(literal 1/8 binary64) (sqrt.f64 (.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))))) k (.f64 (.f64 #s(literal -1/2 binary64) (sqrt.f64 (.f64 (.f64 (PI.f64) n) k))) (.f64 (log.f64 (.f64 (.f64 (PI.f64) n) #s(literal 2 binary64))) (sqrt.f64 #s(literal 2 binary64))))) k (sqrt.f64 (.f64 (.f64 (*.f64 (PI.f64) n) k) #s(literal 2 binary64)))) k))
#s(approx (* 1 (pow (* (* 2 n) (PI)) (/ (- 1 k) 2))) (sqrt.f64 (.f64 (.f64 (PI.f64) n) #s(literal 2 binary64))))
#s(approx (* 1 (pow (* (* 2 n) (PI)) (/ (- 1 k) 2))) (fma.f64 (.f64 k (.f64 (.f64 (sqrt.f64 (.f64 (PI.f64) n)) (log.f64 (.f64 (.f64 (PI.f64) n) #s(literal 2 binary64)))) (sqrt.f64 #s(literal 2 binary64)))) #s(literal -1/2 binary64) (sqrt.f64 (.f64 (.f64 (PI.f64) n) #s(literal 2 binary64)))))
#s(approx (* 1 (pow (* (* 2 n) (PI)) (/ (- 1 k) 2))) (fma.f64 (fma.f64 (.f64 #s(literal 1/8 binary64) (.f64 (.f64 (pow.f64 (log.f64 (.f64 (.f64 (PI.f64) n) #s(literal 2 binary64))) #s(literal 2 binary64)) k) (sqrt.f64 #s(literal 2 binary64)))) (sqrt.f64 (.f64 (PI.f64) n)) (.f64 (.f64 #s(literal -1/2 binary64) (sqrt.f64 (.f64 (PI.f64) n))) (.f64 (log.f64 (.f64 (.f64 (PI.f64) n) #s(literal 2 binary64))) (sqrt.f64 #s(literal 2 binary64))))) k (sqrt.f64 (.f64 (.f64 (PI.f64) n) #s(literal 2 binary64)))))
#s(approx (* 1 (pow (* (* 2 n) (PI)) (/ (- 1 k) 2))) (fma.f64 (fma.f64 (fma.f64 (.f64 (.f64 (.f64 (sqrt.f64 (.f64 (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))) #s(literal -1/48 binary64)) k (.f64 (.f64 #s(literal 1/8 binary64) (sqrt.f64 (.f64 (PI.f64) n))) (.f64 (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 (.f64 #s(literal -1/2 binary64) (sqrt.f64 (.f64 (PI.f64) n))) (.f64 (log.f64 (.f64 (.f64 (PI.f64) n) #s(literal 2 binary64))) (sqrt.f64 #s(literal 2 binary64))))) k (sqrt.f64 (.f64 (.f64 (PI.f64) n) #s(literal 2 binary64)))))
#s(approx (pow (* (* (PI) 2) n) (/ (/ (- 1 k) 2) 2)) (pow.f64 (.f64 (.f64 (PI.f64) n) #s(literal 2 binary64)) #s(literal 1/4 binary64)))
#s(approx (pow (* (* (PI) 2) n) (/ (/ (- 1 k) 2) 2)) (fma.f64 (.f64 #s(literal -1/4 binary64) (pow.f64 (.f64 (.f64 (PI.f64) n) #s(literal 2 binary64)) #s(literal 1/4 binary64))) (.f64 (log.f64 (.f64 (.f64 (PI.f64) n) #s(literal 2 binary64))) k) (pow.f64 (.f64 (.f64 (PI.f64) n) #s(literal 2 binary64)) #s(literal 1/4 binary64))))
#s(approx (pow (* (* (PI) 2) n) (/ (/ (- 1 k) 2) 2)) (fma.f64 (fma.f64 (.f64 #s(literal 1/32 binary64) (pow.f64 (.f64 (.f64 (PI.f64) n) #s(literal 2 binary64)) #s(literal 1/4 binary64))) (.f64 (pow.f64 (log.f64 (.f64 (.f64 (PI.f64) n) #s(literal 2 binary64))) #s(literal 2 binary64)) k) (.f64 (.f64 #s(literal -1/4 binary64) (pow.f64 (.f64 (.f64 (PI.f64) n) #s(literal 2 binary64)) #s(literal 1/4 binary64))) (log.f64 (.f64 (.f64 (PI.f64) n) #s(literal 2 binary64))))) k (pow.f64 (.f64 (.f64 (PI.f64) n) #s(literal 2 binary64)) #s(literal 1/4 binary64))))
#s(approx (pow (* (* (PI) 2) n) (/ (/ (- 1 k) 2) 2)) (fma.f64 (fma.f64 (fma.f64 (.f64 #s(literal -1/384 binary64) (pow.f64 (.f64 (.f64 (PI.f64) n) #s(literal 2 binary64)) #s(literal 1/4 binary64))) (.f64 (pow.f64 (log.f64 (.f64 (.f64 (PI.f64) n) #s(literal 2 binary64))) #s(literal 3 binary64)) k) (.f64 (.f64 #s(literal 1/32 binary64) (pow.f64 (.f64 (.f64 (PI.f64) n) #s(literal 2 binary64)) #s(literal 1/4 binary64))) (pow.f64 (log.f64 (.f64 (.f64 (PI.f64) n) #s(literal 2 binary64))) #s(literal 2 binary64)))) k (.f64 (.f64 #s(literal -1/4 binary64) (pow.f64 (.f64 (.f64 (PI.f64) n) #s(literal 2 binary64)) #s(literal 1/4 binary64))) (log.f64 (.f64 (.f64 (PI.f64) n) #s(literal 2 binary64))))) k (pow.f64 (.f64 (.f64 (PI.f64) n) #s(literal 2 binary64)) #s(literal 1/4 binary64))))
#s(approx (/ (/ (- 1 k) 2) 2) #s(literal 1/4 binary64))
#s(approx (/ (/ (- 1 k) 2) 2) (fma.f64 #s(literal -1/4 binary64) k #s(literal 1/4 binary64)))
#s(approx (* (- (/ 1/4 k) 1/4) k) #s(literal 1/4 binary64))
#s(approx (* (- (/ 1/4 k) 1/4) k) (fma.f64 #s(literal -1/4 binary64) k #s(literal 1/4 binary64)))
#s(approx (- (/ 1/4 k) 1/4) (/.f64 #s(literal 1/4 binary64) k))
#s(approx (- (/ 1/4 k) 1/4) (/.f64 (fma.f64 #s(literal -1/4 binary64) k #s(literal 1/4 binary64)) k))
#s(approx (/ 1/4 k) (/.f64 #s(literal 1/4 binary64) k))
#s(approx (/ (* 1 (pow (* (* 2 n) (PI)) (/ (- 1 k) 2))) (sqrt k)) (.f64 (pow.f64 (exp.f64 #s(literal 1/2 binary64)) (.f64 (log.f64 (.f64 (.f64 (PI.f64) n) #s(literal 2 binary64))) (-.f64 #s(literal 1 binary64) k))) (pow.f64 (sqrt.f64 k) #s(literal -1 binary64))))
#s(approx (* 1 (pow (* (* 2 n) (PI)) (/ (- 1 k) 2))) (pow.f64 (exp.f64 #s(literal 1/2 binary64)) (.f64 (log.f64 (.f64 (*.f64 (PI.f64) n) #s(literal 2 binary64))) (-.f64 #s(literal 1 binary64) k))))
#s(approx (* 1 (pow (* (* 2 n) (PI)) (/ (- 1 k) 2))) (pow.f64 (exp.f64 #s(literal 1/2 binary64)) (.f64 (log.f64 (.f64 (*.f64 (PI.f64) n) #s(literal 2 binary64))) (-.f64 #s(literal 1 binary64) k))))
#s(approx (/ (- 1 k) 2) (*.f64 #s(literal -1/2 binary64) k))
#s(approx (/ (- 1 k) 2) (*.f64 (-.f64 (/.f64 #s(literal 1/2 binary64) k) #s(literal 1/2 binary64)) k))
#s(approx (+ (* -1/2 k) 1/2) (*.f64 #s(literal -1/2 binary64) k))
#s(approx (+ (* -1/2 k) 1/2) (*.f64 (-.f64 (/.f64 #s(literal 1/2 binary64) k) #s(literal 1/2 binary64)) k))
#s(approx (/ (* 1 (pow (* (* 2 n) (PI)) (/ (- 1 k) 2))) (sqrt k)) (.f64 (pow.f64 (exp.f64 #s(literal 1/2 binary64)) (.f64 (log.f64 (.f64 (.f64 (PI.f64) n) #s(literal 2 binary64))) (-.f64 #s(literal 1 binary64) k))) (pow.f64 (sqrt.f64 k) #s(literal -1 binary64))))
#s(approx (* 1 (pow (* (* 2 n) (PI)) (/ (- 1 k) 2))) (pow.f64 (exp.f64 #s(literal 1/2 binary64)) (.f64 (log.f64 (.f64 (*.f64 (PI.f64) n) #s(literal 2 binary64))) (-.f64 #s(literal 1 binary64) k))))
#s(approx (/ (* 1 (pow (* (* 2 n) (PI)) (/ (- 1 k) 2))) (sqrt k)) (.f64 (pow.f64 (pow.f64 (exp.f64 #s(literal 1/4 binary64)) (.f64 (log.f64 (.f64 (.f64 (PI.f64) n) #s(literal 2 binary64))) (-.f64 #s(literal 1 binary64) k))) #s(literal 2 binary64)) (pow.f64 (sqrt.f64 k) #s(literal -1 binary64))))
#s(approx (* 1 (pow (* (* 2 n) (PI)) (/ (- 1 k) 2))) (pow.f64 (pow.f64 (exp.f64 #s(literal 1/4 binary64)) (.f64 (log.f64 (.f64 (*.f64 (PI.f64) n) #s(literal 2 binary64))) (-.f64 #s(literal 1 binary64) k))) #s(literal 2 binary64)))
#s(approx (pow (* (* (PI) 2) n) (/ (/ (- 1 k) 2) 2)) (pow.f64 (exp.f64 #s(literal 1/4 binary64)) (.f64 (log.f64 (.f64 (*.f64 (PI.f64) n) #s(literal 2 binary64))) (-.f64 #s(literal 1 binary64) k))))
#s(approx (/ (/ (- 1 k) 2) 2) (*.f64 #s(literal -1/4 binary64) k))
#s(approx (/ (/ (- 1 k) 2) 2) (*.f64 (-.f64 (/.f64 #s(literal 1/4 binary64) k) #s(literal 1/4 binary64)) k))
#s(approx (- 1 k) (neg.f64 k))
#s(approx (- 1 k) (*.f64 (-.f64 (pow.f64 k #s(literal -1 binary64)) #s(literal 1 binary64)) k))
#s(approx (/ (* 1 (pow (* (* 2 n) (PI)) (/ (- 1 k) 2))) (sqrt k)) (.f64 (pow.f64 (pow.f64 (exp.f64 #s(literal 1/4 binary64)) (.f64 (log.f64 (.f64 (.f64 (PI.f64) n) #s(literal 2 binary64))) (-.f64 #s(literal 1 binary64) k))) #s(literal 2 binary64)) (pow.f64 (sqrt.f64 k) #s(literal -1 binary64))))
#s(approx (* 1 (pow (* (* 2 n) (PI)) (/ (- 1 k) 2))) (pow.f64 (pow.f64 (exp.f64 #s(literal 1/4 binary64)) (.f64 (log.f64 (.f64 (*.f64 (PI.f64) n) #s(literal 2 binary64))) (-.f64 #s(literal 1 binary64) k))) #s(literal 2 binary64)))
#s(approx (pow (* (* (PI) 2) n) (/ (/ (- 1 k) 2) 2)) (pow.f64 (exp.f64 #s(literal 1/4 binary64)) (.f64 (log.f64 (.f64 (*.f64 (PI.f64) n) #s(literal 2 binary64))) (-.f64 #s(literal 1 binary64) k))))
#s(approx (/ (/ (- 1 k) 2) 2) (*.f64 #s(literal -1/4 binary64) k))
#s(approx (/ (/ (- 1 k) 2) 2) (*.f64 (-.f64 (/.f64 #s(literal 1/4 binary64) k) #s(literal 1/4 binary64)) k))
#s(approx (* (- (/ 1/4 k) 1/4) k) (*.f64 #s(literal -1/4 binary64) k))
#s(approx (* (- (/ 1/4 k) 1/4) k) (*.f64 (-.f64 (/.f64 #s(literal 1/4 binary64) k) #s(literal 1/4 binary64)) k))
#s(approx (- (/ 1/4 k) 1/4) #s(literal -1/4 binary64))
#s(approx (- (/ 1/4 k) 1/4) (-.f64 (/.f64 #s(literal 1/4 binary64) k) #s(literal 1/4 binary64)))
#s(approx (/ (* 1 (pow (* (* 2 n) (PI)) (/ (- 1 k) 2))) (sqrt k)) (.f64 (pow.f64 (exp.f64 #s(literal 1/2 binary64)) (.f64 (fma.f64 #s(literal -1 binary64) k #s(literal 1 binary64)) (log.f64 (.f64 (.f64 (PI.f64) n) #s(literal 2 binary64))))) (pow.f64 (sqrt.f64 k) #s(literal -1 binary64))))
#s(approx (* 1 (pow (* (* 2 n) (PI)) (/ (- 1 k) 2))) (pow.f64 (exp.f64 #s(literal 1/2 binary64)) (.f64 (fma.f64 #s(literal -1 binary64) k #s(literal 1 binary64)) (log.f64 (.f64 (*.f64 (PI.f64) n) #s(literal 2 binary64))))))
#s(approx (* 1 (pow (* (* 2 n) (PI)) (/ (- 1 k) 2))) (pow.f64 (exp.f64 #s(literal 1/2 binary64)) (.f64 (fma.f64 #s(literal -1 binary64) k #s(literal 1 binary64)) (log.f64 (.f64 (*.f64 (PI.f64) n) #s(literal 2 binary64))))))
#s(approx (/ (- 1 k) 2) (*.f64 (neg.f64 k) (-.f64 #s(literal 1/2 binary64) (/.f64 #s(literal 1/2 binary64) k))))
#s(approx (+ (* -1/2 k) 1/2) (*.f64 (neg.f64 k) (-.f64 #s(literal 1/2 binary64) (/.f64 #s(literal 1/2 binary64) k))))
#s(approx (sqrt k) (neg.f64 (*.f64 #s(literal -1 binary64) (sqrt.f64 k))))
#s(approx (/ (* 1 (pow (* (* 2 n) (PI)) (/ (- 1 k) 2))) (sqrt k)) (.f64 (pow.f64 (exp.f64 #s(literal 1/2 binary64)) (.f64 (fma.f64 #s(literal -1 binary64) k #s(literal 1 binary64)) (log.f64 (.f64 (.f64 (PI.f64) n) #s(literal 2 binary64))))) (pow.f64 (sqrt.f64 k) #s(literal -1 binary64))))
#s(approx (sqrt (* (* n (/ (PI) k)) 2)) (sqrt.f64 (.f64 (/.f64 (.f64 (PI.f64) n) k) #s(literal 2 binary64))))
#s(approx (* 1 (pow (* (* 2 n) (PI)) (/ (- 1 k) 2))) (pow.f64 (exp.f64 #s(literal 1/2 binary64)) (.f64 (fma.f64 #s(literal -1 binary64) k #s(literal 1 binary64)) (log.f64 (.f64 (*.f64 (PI.f64) n) #s(literal 2 binary64))))))
#s(approx (/ (* 1 (pow (* (* 2 n) (PI)) (/ (- 1 k) 2))) (sqrt k)) (.f64 (pow.f64 (pow.f64 (exp.f64 #s(literal 1/4 binary64)) (.f64 (fma.f64 #s(literal -1 binary64) k #s(literal 1 binary64)) (log.f64 (.f64 (.f64 (PI.f64) n) #s(literal 2 binary64))))) #s(literal 2 binary64)) (pow.f64 (sqrt.f64 k) #s(literal -1 binary64))))
#s(approx (* 1 (pow (* (* 2 n) (PI)) (/ (- 1 k) 2))) (pow.f64 (pow.f64 (exp.f64 #s(literal 1/4 binary64)) (.f64 (fma.f64 #s(literal -1 binary64) k #s(literal 1 binary64)) (log.f64 (.f64 (*.f64 (PI.f64) n) #s(literal 2 binary64))))) #s(literal 2 binary64)))
#s(approx (pow (* (* (PI) 2) n) (/ (/ (- 1 k) 2) 2)) (pow.f64 (exp.f64 #s(literal 1/4 binary64)) (.f64 (fma.f64 #s(literal -1 binary64) k #s(literal 1 binary64)) (log.f64 (.f64 (*.f64 (PI.f64) n) #s(literal 2 binary64))))))
#s(approx (/ (/ (- 1 k) 2) 2) (*.f64 (neg.f64 k) (-.f64 #s(literal 1/4 binary64) (/.f64 #s(literal 1/4 binary64) k))))
#s(approx (- 1 k) (*.f64 (neg.f64 k) (-.f64 #s(literal 1 binary64) (pow.f64 k #s(literal -1 binary64)))))
#s(approx (/ (* 1 (pow (* (* 2 n) (PI)) (/ (- 1 k) 2))) (sqrt k)) (.f64 (pow.f64 (pow.f64 (exp.f64 #s(literal 1/4 binary64)) (.f64 (fma.f64 #s(literal -1 binary64) k #s(literal 1 binary64)) (log.f64 (.f64 (.f64 (PI.f64) n) #s(literal 2 binary64))))) #s(literal 2 binary64)) (pow.f64 (sqrt.f64 k) #s(literal -1 binary64))))
#s(approx (* 1 (pow (* (* 2 n) (PI)) (/ (- 1 k) 2))) (pow.f64 (pow.f64 (exp.f64 #s(literal 1/4 binary64)) (.f64 (fma.f64 #s(literal -1 binary64) k #s(literal 1 binary64)) (log.f64 (.f64 (*.f64 (PI.f64) n) #s(literal 2 binary64))))) #s(literal 2 binary64)))
#s(approx (pow (* (* (PI) 2) n) (/ (/ (- 1 k) 2) 2)) (pow.f64 (exp.f64 #s(literal 1/4 binary64)) (.f64 (fma.f64 #s(literal -1 binary64) k #s(literal 1 binary64)) (log.f64 (.f64 (*.f64 (PI.f64) n) #s(literal 2 binary64))))))
#s(approx (/ (/ (- 1 k) 2) 2) (*.f64 (neg.f64 k) (-.f64 #s(literal 1/4 binary64) (/.f64 #s(literal 1/4 binary64) k))))
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#s(approx (/ (* 1 (pow (* (* 2 n) (PI)) (/ (- 1 k) 2))) (sqrt k)) (.f64 (pow.f64 (exp.f64 #s(literal 1/2 binary64)) (.f64 (log.f64 (.f64 (.f64 (PI.f64) n) #s(literal 2 binary64))) (-.f64 #s(literal 1 binary64) k))) (pow.f64 (sqrt.f64 k) #s(literal -1 binary64))))
#s(approx (* 1 (pow (* (* 2 n) (PI)) (/ (- 1 k) 2))) (pow.f64 (exp.f64 #s(literal 1/2 binary64)) (.f64 (log.f64 (.f64 (*.f64 (PI.f64) n) #s(literal 2 binary64))) (-.f64 #s(literal 1 binary64) k))))
#s(approx (* 1 (pow (* (* 2 n) (PI)) (/ (- 1 k) 2))) (pow.f64 (exp.f64 #s(literal 1/2 binary64)) (.f64 (log.f64 (.f64 (*.f64 (PI.f64) n) #s(literal 2 binary64))) (-.f64 #s(literal 1 binary64) k))))
#s(approx (* (* 2 n) (PI)) (.f64 (.f64 (PI.f64) n) #s(literal 2 binary64)))
#s(approx (* 2 n) (*.f64 n #s(literal 2 binary64)))
#s(approx n n)
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#s(approx (* 1 (pow (* (* 2 n) (PI)) (/ (- 1 k) 2))) (pow.f64 (exp.f64 #s(literal 1/2 binary64)) (.f64 (log.f64 (.f64 (*.f64 (PI.f64) n) #s(literal 2 binary64))) (-.f64 #s(literal 1 binary64) k))))
#s(approx (* (* 2 n) (PI)) (.f64 (.f64 (PI.f64) n) #s(literal 2 binary64)))
#s(approx (/ (* 1 (pow (* (* 2 n) (PI)) (/ (- 1 k) 2))) (sqrt k)) (.f64 (pow.f64 (pow.f64 (exp.f64 #s(literal 1/4 binary64)) (.f64 (log.f64 (.f64 (.f64 (PI.f64) n) #s(literal 2 binary64))) (-.f64 #s(literal 1 binary64) k))) #s(literal 2 binary64)) (pow.f64 (sqrt.f64 k) #s(literal -1 binary64))))
#s(approx (* 1 (pow (* (* 2 n) (PI)) (/ (- 1 k) 2))) (pow.f64 (pow.f64 (exp.f64 #s(literal 1/4 binary64)) (.f64 (log.f64 (.f64 (*.f64 (PI.f64) n) #s(literal 2 binary64))) (-.f64 #s(literal 1 binary64) k))) #s(literal 2 binary64)))
#s(approx (pow (* (* (PI) 2) n) (/ (/ (- 1 k) 2) 2)) (pow.f64 (exp.f64 #s(literal 1/4 binary64)) (.f64 (log.f64 (.f64 (*.f64 (PI.f64) n) #s(literal 2 binary64))) (-.f64 #s(literal 1 binary64) k))))
#s(approx (/ (* 1 (pow (* (* 2 n) (PI)) (/ (- 1 k) 2))) (sqrt k)) (.f64 (pow.f64 (pow.f64 (exp.f64 #s(literal 1/4 binary64)) (.f64 (log.f64 (.f64 (.f64 (PI.f64) n) #s(literal 2 binary64))) (-.f64 #s(literal 1 binary64) k))) #s(literal 2 binary64)) (pow.f64 (sqrt.f64 k) #s(literal -1 binary64))))
#s(approx (* 1 (pow (* (* 2 n) (PI)) (/ (- 1 k) 2))) (pow.f64 (pow.f64 (exp.f64 #s(literal 1/4 binary64)) (.f64 (log.f64 (.f64 (*.f64 (PI.f64) n) #s(literal 2 binary64))) (-.f64 #s(literal 1 binary64) k))) #s(literal 2 binary64)))
#s(approx (pow (* (* (PI) 2) n) (/ (/ (- 1 k) 2) 2)) (pow.f64 (exp.f64 #s(literal 1/4 binary64)) (.f64 (log.f64 (.f64 (*.f64 (PI.f64) n) #s(literal 2 binary64))) (-.f64 #s(literal 1 binary64) k))))
#s(approx (* (* 2 n) (PI)) (.f64 (.f64 (PI.f64) n) #s(literal 2 binary64)))
#s(approx (/ (* 1 (pow (* (* 2 n) (PI)) (/ (- 1 k) 2))) (sqrt k)) (.f64 (pow.f64 (exp.f64 #s(literal 1/2 binary64)) (.f64 (fma.f64 (neg.f64 (log.f64 n)) #s(literal -1 binary64) (log.f64 (*.f64 (PI.f64) #s(literal 2 binary64)))) (-.f64 #s(literal 1 binary64) k))) (pow.f64 (sqrt.f64 k) #s(literal -1 binary64))))
#s(approx (* 1 (pow (* (* 2 n) (PI)) (/ (- 1 k) 2))) (pow.f64 (exp.f64 #s(literal 1/2 binary64)) (.f64 (fma.f64 (neg.f64 (log.f64 n)) #s(literal -1 binary64) (log.f64 (.f64 (PI.f64) #s(literal 2 binary64)))) (-.f64 #s(literal 1 binary64) k))))
#s(approx (* 1 (pow (* (* 2 n) (PI)) (/ (- 1 k) 2))) (pow.f64 (exp.f64 #s(literal 1/2 binary64)) (.f64 (fma.f64 (neg.f64 (log.f64 n)) #s(literal -1 binary64) (log.f64 (.f64 (PI.f64) #s(literal 2 binary64)))) (-.f64 #s(literal 1 binary64) k))))
#s(approx (/ (* 1 (pow (* (* 2 n) (PI)) (/ (- 1 k) 2))) (sqrt k)) (.f64 (pow.f64 (exp.f64 #s(literal 1/2 binary64)) (.f64 (fma.f64 (neg.f64 (log.f64 n)) #s(literal -1 binary64) (log.f64 (*.f64 (PI.f64) #s(literal 2 binary64)))) (-.f64 #s(literal 1 binary64) k))) (pow.f64 (sqrt.f64 k) #s(literal -1 binary64))))
#s(approx (* 1 (pow (* (* 2 n) (PI)) (/ (- 1 k) 2))) (pow.f64 (exp.f64 #s(literal 1/2 binary64)) (.f64 (fma.f64 (neg.f64 (log.f64 n)) #s(literal -1 binary64) (log.f64 (.f64 (PI.f64) #s(literal 2 binary64)))) (-.f64 #s(literal 1 binary64) k))))
#s(approx (/ (* 1 (pow (* (* 2 n) (PI)) (/ (- 1 k) 2))) (sqrt k)) (.f64 (pow.f64 (pow.f64 (exp.f64 #s(literal 1/4 binary64)) (.f64 (fma.f64 (neg.f64 (log.f64 n)) #s(literal -1 binary64) (log.f64 (*.f64 (PI.f64) #s(literal 2 binary64)))) (-.f64 #s(literal 1 binary64) k))) #s(literal 2 binary64)) (pow.f64 (sqrt.f64 k) #s(literal -1 binary64))))
#s(approx (* 1 (pow (* (* 2 n) (PI)) (/ (- 1 k) 2))) (pow.f64 (pow.f64 (exp.f64 #s(literal 1/4 binary64)) (.f64 (fma.f64 (neg.f64 (log.f64 n)) #s(literal -1 binary64) (log.f64 (.f64 (PI.f64) #s(literal 2 binary64)))) (-.f64 #s(literal 1 binary64) k))) #s(literal 2 binary64)))
#s(approx (pow (* (* (PI) 2) n) (/ (/ (- 1 k) 2) 2)) (pow.f64 (exp.f64 #s(literal 1/4 binary64)) (.f64 (fma.f64 (neg.f64 (log.f64 n)) #s(literal -1 binary64) (log.f64 (.f64 (PI.f64) #s(literal 2 binary64)))) (-.f64 #s(literal 1 binary64) k))))
#s(approx (/ (* 1 (pow (* (* 2 n) (PI)) (/ (- 1 k) 2))) (sqrt k)) (.f64 (pow.f64 (pow.f64 (exp.f64 #s(literal 1/4 binary64)) (.f64 (fma.f64 (neg.f64 (log.f64 n)) #s(literal -1 binary64) (log.f64 (*.f64 (PI.f64) #s(literal 2 binary64)))) (-.f64 #s(literal 1 binary64) k))) #s(literal 2 binary64)) (pow.f64 (sqrt.f64 k) #s(literal -1 binary64))))
#s(approx (* 1 (pow (* (* 2 n) (PI)) (/ (- 1 k) 2))) (pow.f64 (pow.f64 (exp.f64 #s(literal 1/4 binary64)) (.f64 (fma.f64 (neg.f64 (log.f64 n)) #s(literal -1 binary64) (log.f64 (.f64 (PI.f64) #s(literal 2 binary64)))) (-.f64 #s(literal 1 binary64) k))) #s(literal 2 binary64)))
#s(approx (pow (* (* (PI) 2) n) (/ (/ (- 1 k) 2) 2)) (pow.f64 (exp.f64 #s(literal 1/4 binary64)) (.f64 (fma.f64 (neg.f64 (log.f64 n)) #s(literal -1 binary64) (log.f64 (.f64 (PI.f64) #s(literal 2 binary64)))) (-.f64 #s(literal 1 binary64) k))))
#s(approx (/ (* 1 (pow (* (* 2 n) (PI)) (/ (- 1 k) 2))) (sqrt k)) (.f64 (pow.f64 (exp.f64 #s(literal 1/2 binary64)) (.f64 (fma.f64 (log.f64 (/.f64 #s(literal -1 binary64) n)) #s(literal -1 binary64) (log.f64 (*.f64 #s(literal -2 binary64) (PI.f64)))) (-.f64 #s(literal 1 binary64) k))) (pow.f64 (sqrt.f64 k) #s(literal -1 binary64))))
#s(approx (* 1 (pow (* (* 2 n) (PI)) (/ (- 1 k) 2))) (pow.f64 (exp.f64 #s(literal 1/2 binary64)) (.f64 (fma.f64 (log.f64 (/.f64 #s(literal -1 binary64) n)) #s(literal -1 binary64) (log.f64 (.f64 #s(literal -2 binary64) (PI.f64)))) (-.f64 #s(literal 1 binary64) k))))
#s(approx (* 1 (pow (* (* 2 n) (PI)) (/ (- 1 k) 2))) (pow.f64 (exp.f64 #s(literal 1/2 binary64)) (.f64 (fma.f64 (log.f64 (/.f64 #s(literal -1 binary64) n)) #s(literal -1 binary64) (log.f64 (.f64 #s(literal -2 binary64) (PI.f64)))) (-.f64 #s(literal 1 binary64) k))))
#s(approx (/ (* 1 (pow (* (* 2 n) (PI)) (/ (- 1 k) 2))) (sqrt k)) (.f64 (pow.f64 (exp.f64 #s(literal 1/2 binary64)) (.f64 (fma.f64 (log.f64 (/.f64 #s(literal -1 binary64) n)) #s(literal -1 binary64) (log.f64 (*.f64 #s(literal -2 binary64) (PI.f64)))) (-.f64 #s(literal 1 binary64) k))) (pow.f64 (sqrt.f64 k) #s(literal -1 binary64))))
#s(approx (sqrt (* (* n (/ (PI) k)) 2)) (neg.f64 (sqrt.f64 (.f64 (/.f64 (.f64 (PI.f64) n) k) #s(literal 2 binary64)))))
#s(approx (* 1 (pow (* (* 2 n) (PI)) (/ (- 1 k) 2))) (pow.f64 (exp.f64 #s(literal 1/2 binary64)) (.f64 (fma.f64 (log.f64 (/.f64 #s(literal -1 binary64) n)) #s(literal -1 binary64) (log.f64 (.f64 #s(literal -2 binary64) (PI.f64)))) (-.f64 #s(literal 1 binary64) k))))
#s(approx (/ (* 1 (pow (* (* 2 n) (PI)) (/ (- 1 k) 2))) (sqrt k)) (.f64 (pow.f64 (pow.f64 (exp.f64 #s(literal 1/4 binary64)) (.f64 (fma.f64 (log.f64 (/.f64 #s(literal -1 binary64) n)) #s(literal -1 binary64) (log.f64 (*.f64 #s(literal -2 binary64) (PI.f64)))) (-.f64 #s(literal 1 binary64) k))) #s(literal 2 binary64)) (pow.f64 (sqrt.f64 k) #s(literal -1 binary64))))
#s(approx (* 1 (pow (* (* 2 n) (PI)) (/ (- 1 k) 2))) (pow.f64 (pow.f64 (exp.f64 #s(literal 1/4 binary64)) (.f64 (fma.f64 (log.f64 (/.f64 #s(literal -1 binary64) n)) #s(literal -1 binary64) (log.f64 (.f64 #s(literal -2 binary64) (PI.f64)))) (-.f64 #s(literal 1 binary64) k))) #s(literal 2 binary64)))
#s(approx (pow (* (* (PI) 2) n) (/ (/ (- 1 k) 2) 2)) (pow.f64 (exp.f64 #s(literal 1/4 binary64)) (.f64 (fma.f64 (log.f64 (/.f64 #s(literal -1 binary64) n)) #s(literal -1 binary64) (log.f64 (.f64 #s(literal -2 binary64) (PI.f64)))) (-.f64 #s(literal 1 binary64) k))))
#s(approx (/ (* 1 (pow (* (* 2 n) (PI)) (/ (- 1 k) 2))) (sqrt k)) (.f64 (pow.f64 (pow.f64 (exp.f64 #s(literal 1/4 binary64)) (.f64 (fma.f64 (log.f64 (/.f64 #s(literal -1 binary64) n)) #s(literal -1 binary64) (log.f64 (*.f64 #s(literal -2 binary64) (PI.f64)))) (-.f64 #s(literal 1 binary64) k))) #s(literal 2 binary64)) (pow.f64 (sqrt.f64 k) #s(literal -1 binary64))))
#s(approx (* 1 (pow (* (* 2 n) (PI)) (/ (- 1 k) 2))) (pow.f64 (pow.f64 (exp.f64 #s(literal 1/4 binary64)) (.f64 (fma.f64 (log.f64 (/.f64 #s(literal -1 binary64) n)) #s(literal -1 binary64) (log.f64 (.f64 #s(literal -2 binary64) (PI.f64)))) (-.f64 #s(literal 1 binary64) k))) #s(literal 2 binary64)))
#s(approx (pow (* (* (PI) 2) n) (/ (/ (- 1 k) 2) 2)) (pow.f64 (exp.f64 #s(literal 1/4 binary64)) (.f64 (fma.f64 (log.f64 (/.f64 #s(literal -1 binary64) n)) #s(literal -1 binary64) (log.f64 (.f64 #s(literal -2 binary64) (PI.f64)))) (-.f64 #s(literal 1 binary64) k))))

eval32.0ms (0.6%)

Memory: -6.8MiB live, 86.4MiB allocated; 4ms collecting garbage
Compiler: Compiled 8 890 to 999 computations (88.8% saved)

prune37.0ms (0.7%)

Memory

4.1MiB live, 51.0MiB allocated; 3ms collecting garbage

Pruning

27 alts after pruning (25 fresh and 2 done)

	Pruned	Kept	Total
New	290	10	300
Fresh	2	15	17
Picked	4	1	5
Done	0	1	1
Total	296	27	323

Accuracy

100.0%

Counts

323 → 27

Alt Table

Click to see full alt table

Status	Accuracy	Program
	50.8%	(/.f64 (pow.f64 (pow.f64 (.f64 (.f64 #s(literal 2 binary64) n) (PI.f64)) #s(approx (/ (/ (- 1 k) 2) 2) #s(literal 1/4 binary64))) #s(literal 2 binary64)) (sqrt.f64 k))
▶	74.6%	(/.f64 (pow.f64 (.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 4 binary64)))) #s(literal 2 binary64)) (sqrt.f64 k))
▶	99.1%	(/.f64 (pow.f64 (.f64 (.f64 (PI.f64) n) #s(literal 2 binary64)) #s(approx (/ (- 1 k) 2) (fma.f64 #s(literal -1/2 binary64) k #s(literal 1/2 binary64)))) (sqrt.f64 k))
	95.8%	(/.f64 (pow.f64 (exp.f64 (.f64 (log.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)) (sqrt.f64 k))
	95.8%	(/.f64 (pow.f64 (exp.f64 (log.f64 (.f64 (.f64 #s(literal 2 binary64) n) (PI.f64)))) (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 2 binary64))) (sqrt.f64 k))
	93.8%	(/.f64 (pow.f64 #s(approx (pow (* (* (PI) 2) n) (/ (/ (- 1 k) 2) 2)) (pow.f64 (exp.f64 #s(literal 1/4 binary64)) (.f64 (fma.f64 (neg.f64 (log.f64 n)) #s(literal -1 binary64) (log.f64 (.f64 (PI.f64) #s(literal 2 binary64)))) (-.f64 #s(literal 1 binary64) k)))) #s(literal 2 binary64)) (sqrt.f64 k))
	74.6%	(/.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 2 binary64)))) (sqrt.f64 k))
	74.4%	(/.f64 (.f64 (pow.f64 (.f64 n #s(literal 2 binary64)) #s(approx (/ (- 1 k) 2) (fma.f64 #s(literal -1/2 binary64) k #s(literal 1/2 binary64)))) (pow.f64 (PI.f64) #s(approx (/ (- 1 k) 2) (fma.f64 #s(literal -1/2 binary64) k #s(literal 1/2 binary64))))) (sqrt.f64 k))
	95.8%	(/.f64 (exp.f64 (.f64 (log.f64 (.f64 (*.f64 (PI.f64) n) #s(literal 2 binary64))) #s(approx (/ (- 1 k) 2) (fma.f64 #s(literal -1/2 binary64) k #s(literal 1/2 binary64))))) (sqrt.f64 k))
	59.3%	(/.f64 #s(approx (* (pow (* (* (PI) 2) n) (/ (/ (- 1 k) 2) 2)) (pow (* (* (PI) 2) n) (/ (/ (- 1 k) 2) 2))) (fma.f64 (fma.f64 (.f64 #s(literal 1/8 binary64) (.f64 (.f64 (pow.f64 (log.f64 (.f64 (.f64 #s(literal 2 binary64) n) (PI.f64))) #s(literal 2 binary64)) k) (sqrt.f64 #s(literal 2 binary64)))) (sqrt.f64 (.f64 (PI.f64) n)) (.f64 (.f64 #s(literal -1/2 binary64) (sqrt.f64 (.f64 (PI.f64) n))) (.f64 (log.f64 (.f64 (.f64 #s(literal 2 binary64) n) (PI.f64))) (sqrt.f64 #s(literal 2 binary64))))) k (sqrt.f64 (.f64 (.f64 #s(literal 2 binary64) n) (PI.f64))))) (sqrt.f64 k))
	51.5%	(/.f64 #s(approx (* (pow (* (* (PI) 2) n) (/ (/ (- 1 k) 2) 2)) (pow (* (* (PI) 2) n) (/ (/ (- 1 k) 2) 2))) (fma.f64 (.f64 k (.f64 (.f64 (sqrt.f64 (.f64 (PI.f64) n)) (log.f64 (.f64 (.f64 #s(literal 2 binary64) n) (PI.f64)))) (sqrt.f64 #s(literal 2 binary64)))) #s(literal -1/2 binary64) (sqrt.f64 (.f64 (.f64 #s(literal 2 binary64) n) (PI.f64))))) (sqrt.f64 k))
	51.0%	(/.f64 #s(approx (* (pow (* (* (PI) 2) n) (/ (/ (- 1 k) 2) 2)) (pow (* (* (PI) 2) n) (/ (/ (- 1 k) 2) 2))) (sqrt.f64 (.f64 (.f64 #s(literal 2 binary64) n) (PI.f64)))) (sqrt.f64 k))
	98.4%	(.f64 (/.f64 #s(literal 1 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))) (pow.f64 (.f64 (.f64 (PI.f64) n) #s(literal 2 binary64)) #s(approx (/ (/ (- 1 k) 2) 2) (*.f64 (-.f64 (/.f64 #s(literal 1/4 binary64) k) #s(literal 1/4 binary64)) k)))))
	98.4%	(.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) (.f64 (pow.f64 (.f64 (.f64 (PI.f64) #s(literal 2 binary64)) n) (/.f64 (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 2 binary64)) #s(literal 2 binary64))) (.f64 (pow.f64 (.f64 (.f64 (PI.f64) n) #s(literal 2 binary64)) (/.f64 #s(approx (/ (/ (- 1 k) 2) 2) (.f64 (-.f64 (/.f64 #s(literal 1/4 binary64) k) #s(literal 1/4 binary64)) k)) #s(literal 2 binary64))) (pow.f64 (.f64 (.f64 (PI.f64) n) #s(literal 2 binary64)) (/.f64 #s(approx (/ (/ (- 1 k) 2) 2) (*.f64 (-.f64 (/.f64 #s(literal 1/4 binary64) k) #s(literal 1/4 binary64)) k)) #s(literal 2 binary64))))))
	74.4%	(.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) (.f64 (pow.f64 (.f64 (.f64 (PI.f64) #s(literal 2 binary64)) n) (/.f64 (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 2 binary64)) #s(literal 2 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 4 binary64))))))
	96.5%	(.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) (.f64 (pow.f64 (.f64 (.f64 (PI.f64) #s(literal 2 binary64)) n) (/.f64 (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 2 binary64)) #s(literal 2 binary64))) (exp.f64 (.f64 (log.f64 (.f64 (*.f64 #s(literal 2 binary64) n) (PI.f64))) (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 4 binary64))))))
	74.6%	(.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) (.f64 (pow.f64 (*.f64 (PI.f64) #s(literal 2 binary64)) #s(approx (/ (- 1 k) 2) (fma.f64 #s(literal -1/2 binary64) k #s(literal 1/2 binary64)))) (pow.f64 n #s(approx (/ (- 1 k) 2) (fma.f64 #s(literal -1/2 binary64) k #s(literal 1/2 binary64))))))
▶	95.6%	(.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) (exp.f64 (.f64 (log.f64 (.f64 (.f64 (PI.f64) #s(literal 2 binary64)) n)) #s(approx (/ (- 1 k) 2) (*.f64 (-.f64 (/.f64 #s(literal 1/2 binary64) k) #s(literal 1/2 binary64)) k)))))
	95.8%	(.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) (exp.f64 (.f64 (log.f64 (.f64 (.f64 #s(literal 2 binary64) n) (PI.f64))) #s(approx (/ (- 1 k) 2) (fma.f64 #s(literal -1/2 binary64) k #s(literal 1/2 binary64))))))
	51.4%	(.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) #s(approx (pow ( (* 2 (PI)) n) (/ (- 1 k) 2)) (fma.f64 (.f64 (.f64 (.f64 (log.f64 (.f64 (.f64 (PI.f64) #s(literal 2 binary64)) n)) (sqrt.f64 #s(literal 2 binary64))) k) (sqrt.f64 (.f64 (PI.f64) n))) #s(literal -1/2 binary64) (sqrt.f64 (.f64 (.f64 (PI.f64) #s(literal 2 binary64)) n)))))
	50.9%	(.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) #s(approx (pow ( (* 2 (PI)) n) (/ (- 1 k) 2)) (sqrt.f64 (.f64 (.f64 (PI.f64) #s(literal 2 binary64)) n))))
▶	99.1%	(.f64 (sqrt.f64 (pow.f64 k #s(literal -1 binary64))) (pow.f64 (.f64 (*.f64 #s(literal 2 binary64) (PI.f64)) n) #s(approx (/ (- 1 k) 2) (fma.f64 #s(literal -1/2 binary64) k #s(literal 1/2 binary64)))))
	45.5%	#s(approx (/ (* 1 (pow (* (* 2 n) (PI)) (/ (- 1 k) 2))) (sqrt k)) (/.f64 (fma.f64 (.f64 #s(literal -1/2 binary64) (.f64 (pow.f64 k #s(literal 3/2 binary64)) (sqrt.f64 (.f64 (PI.f64) n)))) (.f64 (log.f64 (.f64 (.f64 (PI.f64) n) #s(literal 2 binary64))) (sqrt.f64 #s(literal 2 binary64))) (sqrt.f64 (.f64 (.f64 (*.f64 (PI.f64) n) k) #s(literal 2 binary64)))) k))
	40.7%	#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))))
✓	40.8%	#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))))
▶	40.8%	#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt.f64 (.f64 (.f64 (PI.f64) (/.f64 n k)) #s(literal 2 binary64))))
✓	40.8%	#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt.f64 (.f64 (.f64 n (/.f64 (PI.f64) k)) #s(literal 2 binary64))))

Compiler

Compiled 1 658 to 1 128 computations (32% saved)

series217.0ms (4.4%)

Memory

-28.9MiB live, 255.0MiB allocated; 44ms collecting garbage

Counts

45 → 160

Calls

Call 1

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

Outputs
#s(approx (/ (pow (* (* (PI) n) 2) (/ (- 1 k) 2)) (sqrt k)) #s(hole binary64 (* (sqrt (/ (* n (PI)) k)) (sqrt 2))))
#s(approx (/ (pow (* (* (PI) n) 2) (/ (- 1 k) 2)) (sqrt 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 (* (* (PI) n) 2) (/ (- 1 k) 2)) (sqrt 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 (* (* (PI) n) 2) (/ (- 1 k) 2)) (sqrt 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 (* (* (PI) n) 2) (/ (- 1 k) 2)) #s(hole binary64 (* (sqrt (* n (PI))) (sqrt 2))))
#s(approx (pow (* (* (PI) n) 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 (* (* (PI) n) 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 (* (* (PI) n) 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 k) 2) #s(hole binary64 1/2))
#s(approx (/ (- 1 k) 2) #s(hole binary64 (+ 1/2 (* -1/2 k))))
#s(approx (+ (* -1/2 k) 1/2) #s(hole binary64 1/2))
#s(approx (+ (* -1/2 k) 1/2) #s(hole binary64 (+ 1/2 (* -1/2 k))))
#s(approx k #s(hole binary64 k))
#s(approx (sqrt k) #s(hole binary64 (sqrt k)))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) #s(hole binary64 (* (sqrt (/ (* n (PI)) k)) (sqrt 2))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) #s(hole binary64 (/ (+ (* -1/2 (* (sqrt (* (pow k 3) (* n (PI)))) (* (log (* 2 (* n (PI)))) (sqrt 2)))) (* (sqrt (* k (* n (PI)))) (sqrt 2))) k)))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) #s(hole binary64 (/ (+ (* k (+ (* -1/2 (* (sqrt (* k (* n (PI)))) (* (log (* 2 (* n (PI)))) (sqrt 2)))) (* 1/8 (* (sqrt (* (pow k 3) (* n (PI)))) (* (pow (log (* 2 (* n (PI)))) 2) (sqrt 2)))))) (* (sqrt (* k (* n (PI)))) (sqrt 2))) k)))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) #s(hole binary64 (/ (+ (* k (+ (* -1/2 (* (sqrt (* k (* n (PI)))) (* (log (* 2 (* n (PI)))) (sqrt 2)))) (* k (+ (* -1/48 (* (sqrt (* (pow k 3) (* n (PI)))) (* (pow (log (* 2 (* n (PI)))) 3) (sqrt 2)))) (* 1/8 (* (sqrt (* k (* n (PI)))) (* (pow (log (* 2 (* n (PI)))) 2) (sqrt 2)))))))) (* (sqrt (* k (* n (PI)))) (sqrt 2))) k)))
#s(approx (sqrt (* (* (PI) (/ n k)) 2)) #s(hole binary64 (* (sqrt (/ (* n (PI)) k)) (sqrt 2))))
#s(approx (* (* (PI) (/ n k)) 2) #s(hole binary64 (* 2 (/ (* n (PI)) k))))
#s(approx (* (PI) (/ n k)) #s(hole binary64 (/ (* n (PI)) k)))
#s(approx (/ n k) #s(hole binary64 (/ n k)))
#s(approx (* (sqrt (pow k -1)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) #s(hole binary64 (* (sqrt (/ (* n (PI)) k)) (sqrt 2))))
#s(approx (* (sqrt (pow k -1)) (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 (* (sqrt (pow k -1)) (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 (* (sqrt (pow k -1)) (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 (pow k -1)) #s(hole binary64 (sqrt (/ 1 k))))
#s(approx (pow k -1) #s(hole binary64 (/ 1 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)) (exp (* (log (* (* (PI) 2) n)) (/ (- 1 k) 2)))) #s(hole binary64 (* (sqrt (/ (* n (PI)) k)) (sqrt 2))))
#s(approx (* (/ 1 (sqrt k)) (exp (* (log (* (* (PI) 2) 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)) (exp (* (log (* (* (PI) 2) 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)) (exp (* (log (* (* (PI) 2) 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 (exp (* (log (* (* (PI) 2) n)) (/ (- 1 k) 2))) #s(hole binary64 (* (sqrt (* n (PI))) (sqrt 2))))
#s(approx (exp (* (log (* (* (PI) 2) 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 (exp (* (log (* (* (PI) 2) 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 (exp (* (log (* (* (PI) 2) 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 (* (log (* (* (PI) 2) n)) (/ (- 1 k) 2)) #s(hole binary64 (* 1/2 (log (* 2 (* n (PI)))))))
#s(approx (* (log (* (* (PI) 2) n)) (/ (- 1 k) 2)) #s(hole binary64 (+ (* -1/2 (* k (log (* 2 (* n (PI)))))) (* 1/2 (log (* 2 (* n (PI))))))))
#s(approx (* (- (/ 1/2 k) 1/2) k) #s(hole binary64 1/2))
#s(approx (* (- (/ 1/2 k) 1/2) k) #s(hole binary64 (+ 1/2 (* -1/2 k))))
#s(approx (- (/ 1/2 k) 1/2) #s(hole binary64 (/ 1/2 k)))
#s(approx (- (/ 1/2 k) 1/2) #s(hole binary64 (/ (+ 1/2 (* -1/2 k)) k)))
#s(approx (/ 1/2 k) #s(hole binary64 (/ 1/2 k)))
#s(approx (/ (pow (* (pow (* (PI) 2) (/ (- 1 k) 4)) (pow n (/ (- 1 k) 4))) 2) (sqrt k)) #s(hole binary64 (* (sqrt (/ (* n (PI)) k)) (sqrt 2))))
#s(approx (/ (pow (* (pow (* (PI) 2) (/ (- 1 k) 4)) (pow n (/ (- 1 k) 4))) 2) (sqrt k)) #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 (/ (pow (* (pow (* (PI) 2) (/ (- 1 k) 4)) (pow n (/ (- 1 k) 4))) 2) (sqrt k)) #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 (/ (pow (* (pow (* (PI) 2) (/ (- 1 k) 4)) (pow n (/ (- 1 k) 4))) 2) (sqrt k)) #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))))) (+ (* (sqrt n) (+ (* -1/64 (* (sqrt (PI)) (* (pow (log (* 2 (PI))) 3) (sqrt 2)))) (* -1/192 (* (sqrt (PI)) (* (pow (log (* 2 (PI))) 3) (sqrt 2)))))) (* (sqrt (PI)) (* (sqrt 2) (+ (* -1/64 (* (sqrt n) (pow (log n) 3))) (* -1/192 (* (sqrt n) (pow (log n) 3)))))))))))) (* (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 (pow (* (pow (* (PI) 2) (/ (- 1 k) 4)) (pow n (/ (- 1 k) 4))) 2) #s(hole binary64 (* (sqrt (* n (PI))) (sqrt 2))))
#s(approx (pow (* (pow (* (PI) 2) (/ (- 1 k) 4)) (pow n (/ (- 1 k) 4))) 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 (* (pow (* (PI) 2) (/ (- 1 k) 4)) (pow n (/ (- 1 k) 4))) 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 (* (pow (* (PI) 2) (/ (- 1 k) 4)) (pow n (/ (- 1 k) 4))) 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))))) (+ (* (sqrt n) (+ (* -1/64 (* (sqrt (PI)) (* (pow (log (* 2 (PI))) 3) (sqrt 2)))) (* -1/192 (* (sqrt (PI)) (* (pow (log (* 2 (PI))) 3) (sqrt 2)))))) (* (sqrt (PI)) (* (sqrt 2) (+ (* -1/64 (* (sqrt n) (pow (log n) 3))) (* -1/192 (* (sqrt n) (pow (log n) 3))))))))))))))))) (* (sqrt (* n (PI))) (sqrt 2)))))
#s(approx (* (pow (* (PI) 2) (/ (- 1 k) 4)) (pow n (/ (- 1 k) 4))) #s(hole binary64 (pow (* 2 (* n (PI))) 1/4)))
#s(approx (* (pow (* (PI) 2) (/ (- 1 k) 4)) (pow n (/ (- 1 k) 4))) #s(hole binary64 (+ (* k (+ (* -1/4 (* (pow (* 2 (* n (PI))) 1/4) (log n))) (* -1/4 (* (pow (* 2 (* n (PI))) 1/4) (log (* 2 (PI))))))) (pow (* 2 (* n (PI))) 1/4))))
#s(approx (* (pow (* (PI) 2) (/ (- 1 k) 4)) (pow n (/ (- 1 k) 4))) #s(hole binary64 (+ (* k (+ (* -1/4 (* (pow (* 2 (* n (PI))) 1/4) (log n))) (+ (* -1/4 (* (pow (* 2 (* n (PI))) 1/4) (log (* 2 (PI))))) (* k (+ (* 1/32 (* (pow (* 2 (* n (PI))) 1/4) (pow (log n) 2))) (+ (* 1/32 (* (pow (* 2 (* n (PI))) 1/4) (pow (log (* 2 (PI))) 2))) (* 1/16 (* (pow (* 2 (* n (PI))) 1/4) (* (log n) (log (* 2 (PI)))))))))))) (pow (* 2 (* n (PI))) 1/4))))
#s(approx (* (pow (* (PI) 2) (/ (- 1 k) 4)) (pow n (/ (- 1 k) 4))) #s(hole binary64 (+ (* k (+ (* -1/4 (* (pow (* 2 (* n (PI))) 1/4) (log n))) (+ (* -1/4 (* (pow (* 2 (* n (PI))) 1/4) (log (* 2 (PI))))) (* k (+ (* 1/32 (* (pow (* 2 (* n (PI))) 1/4) (pow (log n) 2))) (+ (* 1/32 (* (pow (* 2 (* n (PI))) 1/4) (pow (log (* 2 (PI))) 2))) (+ (* 1/16 (* (pow (* 2 (* n (PI))) 1/4) (* (log n) (log (* 2 (PI)))))) (* k (+ (* -1/128 (* (pow (* 2 (* n (PI))) 1/4) (* (log n) (pow (log (* 2 (PI))) 2)))) (+ (* -1/128 (* (pow (* 2 (* n (PI))) 1/4) (* (pow (log n) 2) (log (* 2 (PI)))))) (+ (* -1/384 (* (pow (* 2 (* n (PI))) 1/4) (pow (log n) 3))) (* -1/384 (* (pow (* 2 (* n (PI))) 1/4) (pow (log (* 2 (PI))) 3)))))))))))))) (pow (* 2 (* n (PI))) 1/4))))
#s(approx (pow (* (PI) 2) (/ (- 1 k) 4)) #s(hole binary64 (pow (* 2 (PI)) 1/4)))
#s(approx (pow (* (PI) 2) (/ (- 1 k) 4)) #s(hole binary64 (+ (* -1/4 (* (pow (* 2 (PI)) 1/4) (* k (log (* 2 (PI)))))) (pow (* 2 (PI)) 1/4))))
#s(approx (pow (* (PI) 2) (/ (- 1 k) 4)) #s(hole binary64 (+ (* k (+ (* -1/4 (* (pow (* 2 (PI)) 1/4) (log (* 2 (PI))))) (* 1/32 (* (pow (* 2 (PI)) 1/4) (* k (pow (log (* 2 (PI))) 2)))))) (pow (* 2 (PI)) 1/4))))
#s(approx (pow (* (PI) 2) (/ (- 1 k) 4)) #s(hole binary64 (+ (* k (+ (* -1/4 (* (pow (* 2 (PI)) 1/4) (log (* 2 (PI))))) (* k (+ (* -1/384 (* (pow (* 2 (PI)) 1/4) (* k (pow (log (* 2 (PI))) 3)))) (* 1/32 (* (pow (* 2 (PI)) 1/4) (pow (log (* 2 (PI))) 2))))))) (pow (* 2 (PI)) 1/4))))
#s(approx (/ (- 1 k) 4) #s(hole binary64 1/4))
#s(approx (/ (- 1 k) 4) #s(hole binary64 (+ 1/4 (* -1/4 k))))
#s(approx (- 1 k) #s(hole binary64 1))
#s(approx (- 1 k) #s(hole binary64 (+ 1 (* -1 k))))
#s(approx (pow n (/ (- 1 k) 4)) #s(hole binary64 (pow (* 1 n) 1/4)))
#s(approx (pow n (/ (- 1 k) 4)) #s(hole binary64 (+ (* -1/4 (* (pow (* 1 n) 1/4) (* k (log n)))) (pow (* 1 n) 1/4))))
#s(approx (pow n (/ (- 1 k) 4)) #s(hole binary64 (+ (* k (+ (* -1/4 (* (pow (* 1 n) 1/4) (log n))) (* 1/32 (* (pow (* 1 n) 1/4) (* k (pow (log n) 2)))))) (pow (* 1 n) 1/4))))
#s(approx (pow n (/ (- 1 k) 4)) #s(hole binary64 (+ (* k (+ (* -1/4 (* (pow (* 1 n) 1/4) (log n))) (* k (+ (* -1/384 (* (pow (* 1 n) 1/4) (* k (pow (log n) 3)))) (* 1/32 (* (pow (* 1 n) 1/4) (pow (log n) 2))))))) (pow (* 1 n) 1/4))))
#s(approx (/ (pow (* (* (PI) n) 2) (/ (- 1 k) 2)) (sqrt k)) #s(hole binary64 (* (sqrt (/ 1 k)) (exp (* 1/2 (* (log (* 2 (* n (PI)))) (- 1 k)))))))
#s(approx (pow (* (* (PI) n) 2) (/ (- 1 k) 2)) #s(hole binary64 (exp (* 1/2 (* (log (* 2 (* n (PI)))) (- 1 k))))))
#s(approx (/ (- 1 k) 2) #s(hole binary64 (* -1/2 k)))
#s(approx (/ (- 1 k) 2) #s(hole binary64 (* k (- (* 1/2 (/ 1 k)) 1/2))))
#s(approx (+ (* -1/2 k) 1/2) #s(hole binary64 (* -1/2 k)))
#s(approx (+ (* -1/2 k) 1/2) #s(hole binary64 (* k (- (* 1/2 (/ 1 k)) 1/2))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) #s(hole binary64 (* (sqrt (/ 1 k)) (exp (* 1/2 (* (log (* 2 (* n (PI)))) (- 1 k)))))))
#s(approx (* (sqrt (pow k -1)) (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)) (exp (* (log (* (* (PI) 2) n)) (/ (- 1 k) 2)))) #s(hole binary64 (* (sqrt (/ 1 k)) (exp (* 1/2 (* (log (* 2 (* n (PI)))) (- 1 k)))))))
#s(approx (exp (* (log (* (* (PI) 2) n)) (/ (- 1 k) 2))) #s(hole binary64 (exp (* 1/2 (* (log (* 2 (* n (PI)))) (- 1 k))))))
#s(approx (* (log (* (* (PI) 2) n)) (/ (- 1 k) 2)) #s(hole binary64 (* -1/2 (* k (log (* 2 (* n (PI))))))))
#s(approx (* (log (* (* (PI) 2) n)) (/ (- 1 k) 2)) #s(hole binary64 (* k (+ (* -1/2 (log (* 2 (* n (PI))))) (* 1/2 (/ (log (* 2 (* n (PI)))) k))))))
#s(approx (* (- (/ 1/2 k) 1/2) k) #s(hole binary64 (* -1/2 k)))
#s(approx (* (- (/ 1/2 k) 1/2) k) #s(hole binary64 (* k (- (* 1/2 (/ 1 k)) 1/2))))
#s(approx (- (/ 1/2 k) 1/2) #s(hole binary64 -1/2))
#s(approx (- (/ 1/2 k) 1/2) #s(hole binary64 (- (* 1/2 (/ 1 k)) 1/2)))
#s(approx (/ (pow (* (pow (* (PI) 2) (/ (- 1 k) 4)) (pow n (/ (- 1 k) 4))) 2) (sqrt k)) #s(hole binary64 (* (sqrt (/ 1 k)) (* (pow (exp (* 1/4 (* (log n) (- 1 k)))) 2) (pow (exp (* 1/4 (* (log (* 2 (PI))) (- 1 k)))) 2)))))
#s(approx (pow (* (pow (* (PI) 2) (/ (- 1 k) 4)) (pow n (/ (- 1 k) 4))) 2) #s(hole binary64 (* (pow (exp (* 1/4 (* (log n) (- 1 k)))) 2) (pow (exp (* 1/4 (* (log (* 2 (PI))) (- 1 k)))) 2))))
#s(approx (* (pow (* (PI) 2) (/ (- 1 k) 4)) (pow n (/ (- 1 k) 4))) #s(hole binary64 (* (exp (* 1/4 (* (log n) (- 1 k)))) (exp (* 1/4 (* (log (* 2 (PI))) (- 1 k)))))))
#s(approx (pow (* (PI) 2) (/ (- 1 k) 4)) #s(hole binary64 (exp (* 1/4 (* (log (* 2 (PI))) (- 1 k))))))
#s(approx (/ (- 1 k) 4) #s(hole binary64 (* -1/4 k)))
#s(approx (/ (- 1 k) 4) #s(hole binary64 (* k (- (* 1/4 (/ 1 k)) 1/4))))
#s(approx (- 1 k) #s(hole binary64 (* -1 k)))
#s(approx (- 1 k) #s(hole binary64 (* k (- (/ 1 k) 1))))
#s(approx (pow n (/ (- 1 k) 4)) #s(hole binary64 (exp (* 1/4 (* (log n) (- 1 k))))))
#s(approx (/ (pow (* (* (PI) n) 2) (/ (- 1 k) 2)) (sqrt k)) #s(hole binary64 (* (sqrt (/ 1 k)) (exp (* 1/2 (* (log (* 2 (* n (PI)))) (+ 1 (* -1 k))))))))
#s(approx (pow (* (* (PI) n) 2) (/ (- 1 k) 2)) #s(hole binary64 (exp (* 1/2 (* (log (* 2 (* n (PI)))) (+ 1 (* -1 k)))))))
#s(approx (/ (- 1 k) 2) #s(hole binary64 (* -1 (* k (- 1/2 (* 1/2 (/ 1 k)))))))
#s(approx (+ (* -1/2 k) 1/2) #s(hole binary64 (* -1 (* k (- 1/2 (* 1/2 (/ 1 k)))))))
#s(approx (sqrt k) #s(hole binary64 (* -1 (* (sqrt k) (pow (sqrt -1) 2)))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) #s(hole binary64 (* (sqrt (/ 1 k)) (exp (* 1/2 (* (log (* 2 (* n (PI)))) (+ 1 (* -1 k))))))))
#s(approx (sqrt (* (* (PI) (/ n k)) 2)) #s(hole binary64 (* (sqrt (/ (* n (PI)) k)) (* (sqrt -2) (sqrt -1)))))
#s(approx (* (sqrt (pow k -1)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) #s(hole binary64 (* (sqrt (/ 1 k)) (* (exp (* 1/2 (* (log (* 2 (* n (PI)))) (+ 1 (* -1 k))))) (pow (sqrt -1) 2)))))
#s(approx (sqrt (pow k -1)) #s(hole binary64 (* (sqrt (/ 1 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)) (exp (* (log (* (* (PI) 2) n)) (/ (- 1 k) 2)))) #s(hole binary64 (* (sqrt (/ 1 k)) (exp (* 1/2 (* (log (* 2 (* n (PI)))) (+ 1 (* -1 k))))))))
#s(approx (exp (* (log (* (* (PI) 2) n)) (/ (- 1 k) 2))) #s(hole binary64 (exp (* 1/2 (* (log (* 2 (* n (PI)))) (+ 1 (* -1 k)))))))
#s(approx (* (log (* (* (PI) 2) n)) (/ (- 1 k) 2)) #s(hole binary64 (* -1 (* k (+ (* -1/2 (/ (log (* 2 (* n (PI)))) k)) (* 1/2 (log (* 2 (* n (PI))))))))))
#s(approx (* (- (/ 1/2 k) 1/2) k) #s(hole binary64 (* -1 (* k (- 1/2 (* 1/2 (/ 1 k)))))))
#s(approx (/ (pow (* (pow (* (PI) 2) (/ (- 1 k) 4)) (pow n (/ (- 1 k) 4))) 2) (sqrt k)) #s(hole binary64 (* (sqrt (/ 1 k)) (* (pow (exp (* 1/4 (* (log n) (+ 1 (* -1 k))))) 2) (pow (exp (* 1/4 (* (log (* 2 (PI))) (+ 1 (* -1 k))))) 2)))))
#s(approx (pow (* (pow (* (PI) 2) (/ (- 1 k) 4)) (pow n (/ (- 1 k) 4))) 2) #s(hole binary64 (* (pow (exp (* 1/4 (* (log n) (+ 1 (* -1 k))))) 2) (pow (exp (* 1/4 (* (log (* 2 (PI))) (+ 1 (* -1 k))))) 2))))
#s(approx (* (pow (* (PI) 2) (/ (- 1 k) 4)) (pow n (/ (- 1 k) 4))) #s(hole binary64 (* (exp (* 1/4 (* (log n) (+ 1 (* -1 k))))) (exp (* 1/4 (* (log (* 2 (PI))) (+ 1 (* -1 k))))))))
#s(approx (pow (* (PI) 2) (/ (- 1 k) 4)) #s(hole binary64 (exp (* 1/4 (* (log (* 2 (PI))) (+ 1 (* -1 k)))))))
#s(approx (/ (- 1 k) 4) #s(hole binary64 (* -1 (* k (- 1/4 (* 1/4 (/ 1 k)))))))
#s(approx (- 1 k) #s(hole binary64 (* -1 (* k (- 1 (/ 1 k))))))
#s(approx (pow n (/ (- 1 k) 4)) #s(hole binary64 (exp (* 1/4 (* (log n) (+ 1 (* -1 k)))))))
#s(approx (/ (pow (* (* (PI) n) 2) (/ (- 1 k) 2)) (sqrt k)) #s(hole binary64 (* (sqrt (/ 1 k)) (exp (* 1/2 (* (+ (log n) (log (* 2 (PI)))) (- 1 k)))))))
#s(approx (pow (* (* (PI) n) 2) (/ (- 1 k) 2)) #s(hole binary64 (exp (* 1/2 (* (+ (log n) (log (* 2 (PI)))) (- 1 k))))))
#s(approx (* (* (PI) n) 2) #s(hole binary64 (* 2 (* n (PI)))))
#s(approx (* (PI) n) #s(hole binary64 (* n (PI))))
#s(approx n #s(hole binary64 n))
#s(approx (* (/ 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 k -1)) (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)) (exp (* (log (* (* (PI) 2) n)) (/ (- 1 k) 2)))) #s(hole binary64 (* (sqrt (/ 1 k)) (exp (* 1/2 (* (+ (log n) (log (* 2 (PI)))) (- 1 k)))))))
#s(approx (exp (* (log (* (* (PI) 2) n)) (/ (- 1 k) 2))) #s(hole binary64 (exp (* 1/2 (* (+ (log n) (log (* 2 (PI)))) (- 1 k))))))
#s(approx (* (log (* (* (PI) 2) n)) (/ (- 1 k) 2)) #s(hole binary64 (* 1/2 (* (+ (log n) (log (* 2 (PI)))) (- 1 k)))))
#s(approx (log (* (* (PI) 2) n)) #s(hole binary64 (+ (log n) (log (* 2 (PI))))))
#s(approx (* (* (PI) 2) n) #s(hole binary64 (* 2 (* n (PI)))))
#s(approx (/ (pow (* (* (PI) n) 2) (/ (- 1 k) 2)) (sqrt k)) #s(hole binary64 (* (sqrt (/ 1 k)) (exp (* 1/2 (* (+ (log (* 2 (PI))) (* -1 (log (/ 1 n)))) (- 1 k)))))))
#s(approx (pow (* (* (PI) n) 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 k -1)) (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)) (exp (* (log (* (* (PI) 2) n)) (/ (- 1 k) 2)))) #s(hole binary64 (* (sqrt (/ 1 k)) (exp (* 1/2 (* (+ (log (* 2 (PI))) (* -1 (log (/ 1 n)))) (- 1 k)))))))
#s(approx (exp (* (log (* (* (PI) 2) n)) (/ (- 1 k) 2))) #s(hole binary64 (exp (* 1/2 (* (+ (log (* 2 (PI))) (* -1 (log (/ 1 n)))) (- 1 k))))))
#s(approx (* (log (* (* (PI) 2) n)) (/ (- 1 k) 2)) #s(hole binary64 (* 1/2 (* (+ (log (* 2 (PI))) (* -1 (log (/ 1 n)))) (- 1 k)))))
#s(approx (log (* (* (PI) 2) n)) #s(hole binary64 (+ (log (* 2 (PI))) (* -1 (log (/ 1 n))))))
#s(approx (/ (pow (* (pow (* (PI) 2) (/ (- 1 k) 4)) (pow n (/ (- 1 k) 4))) 2) (sqrt k)) #s(hole binary64 (* (sqrt (/ 1 k)) (* (pow (exp (* -1/4 (* (log (/ 1 n)) (- 1 k)))) 2) (pow (exp (* 1/4 (* (log (* 2 (PI))) (- 1 k)))) 2)))))
#s(approx (pow (* (pow (* (PI) 2) (/ (- 1 k) 4)) (pow n (/ (- 1 k) 4))) 2) #s(hole binary64 (* (pow (exp (* -1/4 (* (log (/ 1 n)) (- 1 k)))) 2) (pow (exp (* 1/4 (* (log (* 2 (PI))) (- 1 k)))) 2))))
#s(approx (* (pow (* (PI) 2) (/ (- 1 k) 4)) (pow n (/ (- 1 k) 4))) #s(hole binary64 (* (exp (* -1/4 (* (log (/ 1 n)) (- 1 k)))) (exp (* 1/4 (* (log (* 2 (PI))) (- 1 k)))))))
#s(approx (pow n (/ (- 1 k) 4)) #s(hole binary64 (exp (* -1/4 (* (log (/ 1 n)) (- 1 k))))))
#s(approx (/ (pow (* (* (PI) n) 2) (/ (- 1 k) 2)) (sqrt k)) #s(hole binary64 (* (sqrt (/ 1 k)) (exp (* 1/2 (* (+ (log (* -2 (PI))) (* -1 (log (/ -1 n)))) (- 1 k)))))))
#s(approx (pow (* (* (PI) n) 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 (* (* (PI) (/ n k)) 2)) #s(hole binary64 (* -1 (* (sqrt (/ (* n (PI)) k)) (* (sqrt -2) (sqrt -1))))))
#s(approx (* (sqrt (pow k -1)) (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)) (exp (* (log (* (* (PI) 2) n)) (/ (- 1 k) 2)))) #s(hole binary64 (* (sqrt (/ 1 k)) (exp (* 1/2 (* (+ (log (* -2 (PI))) (* -1 (log (/ -1 n)))) (- 1 k)))))))
#s(approx (exp (* (log (* (* (PI) 2) n)) (/ (- 1 k) 2))) #s(hole binary64 (exp (* 1/2 (* (+ (log (* -2 (PI))) (* -1 (log (/ -1 n)))) (- 1 k))))))
#s(approx (* (log (* (* (PI) 2) n)) (/ (- 1 k) 2)) #s(hole binary64 (* 1/2 (* (+ (log (* -2 (PI))) (* -1 (log (/ -1 n)))) (- 1 k)))))
#s(approx (log (* (* (PI) 2) n)) #s(hole binary64 (+ (log (* -2 (PI))) (* -1 (log (/ -1 n))))))
#s(approx (/ (pow (* (pow (* (PI) 2) (/ (- 1 k) 4)) (pow n (/ (- 1 k) 4))) 2) (sqrt k)) #s(hole binary64 (* (sqrt (/ 1 k)) (* (pow (exp (* 1/4 (* (log (* 2 (PI))) (- 1 k)))) 2) (pow (exp (* 1/4 (* (+ (log -1) (* -1 (log (/ -1 n)))) (- 1 k)))) 2)))))
#s(approx (pow (* (pow (* (PI) 2) (/ (- 1 k) 4)) (pow n (/ (- 1 k) 4))) 2) #s(hole binary64 (* (pow (exp (* 1/4 (* (log (* 2 (PI))) (- 1 k)))) 2) (pow (exp (* 1/4 (* (+ (log -1) (* -1 (log (/ -1 n)))) (- 1 k)))) 2))))
#s(approx (* (pow (* (PI) 2) (/ (- 1 k) 4)) (pow n (/ (- 1 k) 4))) #s(hole binary64 (* (exp (* 1/4 (* (log (* 2 (PI))) (- 1 k)))) (exp (* 1/4 (* (+ (log -1) (* -1 (log (/ -1 n)))) (- 1 k)))))))
#s(approx (pow n (/ (- 1 k) 4)) #s(hole binary64 (exp (* 1/4 (* (+ (log -1) (* -1 (log (/ -1 n)))) (- 1 k))))))

Calls

6 calls:

Time	Variable		Point	Expression
74.0ms	n	@	0	((/ (pow (* (* (PI) n) 2) (/ (- 1 k) 2)) (sqrt k)) (pow (* (* (PI) n) 2) (/ (- 1 k) 2)) (* (* (PI) n) 2) (* (PI) n) (PI) n 2 (/ (- 1 k) 2) (+ (* -1/2 k) 1/2) -1/2 k 1/2 (sqrt k) (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt (* (* (PI) (/ n k)) 2)) (* (* (PI) (/ n k)) 2) (* (PI) (/ n k)) (/ n k) (* (sqrt (pow k -1)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt (pow k -1)) (pow k -1) -1 (pow (* (* 2 (PI)) n) (/ (- 1 k) 2)) (* (* 2 (PI)) n) (* 2 (PI)) (* (/ 1 (sqrt k)) (exp (* (log (* (* (PI) 2) n)) (/ (- 1 k) 2)))) (/ 1 (sqrt k)) 1 (exp (* (log (* (* (PI) 2) n)) (/ (- 1 k) 2))) (* (log (* (* (PI) 2) n)) (/ (- 1 k) 2)) (log (* (* (PI) 2) n)) (* (* (PI) 2) n) (* (PI) 2) (/ (- 1 k) 2) (* (- (/ 1/2 k) 1/2) k) (- (/ 1/2 k) 1/2) (/ 1/2 k) (/ (pow (* (pow (* (PI) 2) (/ (- 1 k) 4)) (pow n (/ (- 1 k) 4))) 2) (sqrt k)) (pow (* (pow (* (PI) 2) (/ (- 1 k) 4)) (pow n (/ (- 1 k) 4))) 2) (* (pow (* (PI) 2) (/ (- 1 k) 4)) (pow n (/ (- 1 k) 4))) (pow (* (PI) 2) (/ (- 1 k) 4)) (/ (- 1 k) 4) (- 1 k) 4 (pow n (/ (- 1 k) 4)))
49.0ms	n	@	-inf	((/ (pow (* (* (PI) n) 2) (/ (- 1 k) 2)) (sqrt k)) (pow (* (* (PI) n) 2) (/ (- 1 k) 2)) (* (* (PI) n) 2) (* (PI) n) (PI) n 2 (/ (- 1 k) 2) (+ (* -1/2 k) 1/2) -1/2 k 1/2 (sqrt k) (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt (* (* (PI) (/ n k)) 2)) (* (* (PI) (/ n k)) 2) (* (PI) (/ n k)) (/ n k) (* (sqrt (pow k -1)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt (pow k -1)) (pow k -1) -1 (pow (* (* 2 (PI)) n) (/ (- 1 k) 2)) (* (* 2 (PI)) n) (* 2 (PI)) (* (/ 1 (sqrt k)) (exp (* (log (* (* (PI) 2) n)) (/ (- 1 k) 2)))) (/ 1 (sqrt k)) 1 (exp (* (log (* (* (PI) 2) n)) (/ (- 1 k) 2))) (* (log (* (* (PI) 2) n)) (/ (- 1 k) 2)) (log (* (* (PI) 2) n)) (* (* (PI) 2) n) (* (PI) 2) (/ (- 1 k) 2) (* (- (/ 1/2 k) 1/2) k) (- (/ 1/2 k) 1/2) (/ 1/2 k) (/ (pow (* (pow (* (PI) 2) (/ (- 1 k) 4)) (pow n (/ (- 1 k) 4))) 2) (sqrt k)) (pow (* (pow (* (PI) 2) (/ (- 1 k) 4)) (pow n (/ (- 1 k) 4))) 2) (* (pow (* (PI) 2) (/ (- 1 k) 4)) (pow n (/ (- 1 k) 4))) (pow (* (PI) 2) (/ (- 1 k) 4)) (/ (- 1 k) 4) (- 1 k) 4 (pow n (/ (- 1 k) 4)))
32.0ms	n	@	inf	((/ (pow (* (* (PI) n) 2) (/ (- 1 k) 2)) (sqrt k)) (pow (* (* (PI) n) 2) (/ (- 1 k) 2)) (* (* (PI) n) 2) (* (PI) n) (PI) n 2 (/ (- 1 k) 2) (+ (* -1/2 k) 1/2) -1/2 k 1/2 (sqrt k) (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt (* (* (PI) (/ n k)) 2)) (* (* (PI) (/ n k)) 2) (* (PI) (/ n k)) (/ n k) (* (sqrt (pow k -1)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt (pow k -1)) (pow k -1) -1 (pow (* (* 2 (PI)) n) (/ (- 1 k) 2)) (* (* 2 (PI)) n) (* 2 (PI)) (* (/ 1 (sqrt k)) (exp (* (log (* (* (PI) 2) n)) (/ (- 1 k) 2)))) (/ 1 (sqrt k)) 1 (exp (* (log (* (* (PI) 2) n)) (/ (- 1 k) 2))) (* (log (* (* (PI) 2) n)) (/ (- 1 k) 2)) (log (* (* (PI) 2) n)) (* (* (PI) 2) n) (* (PI) 2) (/ (- 1 k) 2) (* (- (/ 1/2 k) 1/2) k) (- (/ 1/2 k) 1/2) (/ 1/2 k) (/ (pow (* (pow (* (PI) 2) (/ (- 1 k) 4)) (pow n (/ (- 1 k) 4))) 2) (sqrt k)) (pow (* (pow (* (PI) 2) (/ (- 1 k) 4)) (pow n (/ (- 1 k) 4))) 2) (* (pow (* (PI) 2) (/ (- 1 k) 4)) (pow n (/ (- 1 k) 4))) (pow (* (PI) 2) (/ (- 1 k) 4)) (/ (- 1 k) 4) (- 1 k) 4 (pow n (/ (- 1 k) 4)))
26.0ms	k	@	0	((/ (pow (* (* (PI) n) 2) (/ (- 1 k) 2)) (sqrt k)) (pow (* (* (PI) n) 2) (/ (- 1 k) 2)) (* (* (PI) n) 2) (* (PI) n) (PI) n 2 (/ (- 1 k) 2) (+ (* -1/2 k) 1/2) -1/2 k 1/2 (sqrt k) (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt (* (* (PI) (/ n k)) 2)) (* (* (PI) (/ n k)) 2) (* (PI) (/ n k)) (/ n k) (* (sqrt (pow k -1)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt (pow k -1)) (pow k -1) -1 (pow (* (* 2 (PI)) n) (/ (- 1 k) 2)) (* (* 2 (PI)) n) (* 2 (PI)) (* (/ 1 (sqrt k)) (exp (* (log (* (* (PI) 2) n)) (/ (- 1 k) 2)))) (/ 1 (sqrt k)) 1 (exp (* (log (* (* (PI) 2) n)) (/ (- 1 k) 2))) (* (log (* (* (PI) 2) n)) (/ (- 1 k) 2)) (log (* (* (PI) 2) n)) (* (* (PI) 2) n) (* (PI) 2) (/ (- 1 k) 2) (* (- (/ 1/2 k) 1/2) k) (- (/ 1/2 k) 1/2) (/ 1/2 k) (/ (pow (* (pow (* (PI) 2) (/ (- 1 k) 4)) (pow n (/ (- 1 k) 4))) 2) (sqrt k)) (pow (* (pow (* (PI) 2) (/ (- 1 k) 4)) (pow n (/ (- 1 k) 4))) 2) (* (pow (* (PI) 2) (/ (- 1 k) 4)) (pow n (/ (- 1 k) 4))) (pow (* (PI) 2) (/ (- 1 k) 4)) (/ (- 1 k) 4) (- 1 k) 4 (pow n (/ (- 1 k) 4)))
10.0ms	k	@	-inf	((/ (pow (* (* (PI) n) 2) (/ (- 1 k) 2)) (sqrt k)) (pow (* (* (PI) n) 2) (/ (- 1 k) 2)) (* (* (PI) n) 2) (* (PI) n) (PI) n 2 (/ (- 1 k) 2) (+ (* -1/2 k) 1/2) -1/2 k 1/2 (sqrt k) (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt (* (* (PI) (/ n k)) 2)) (* (* (PI) (/ n k)) 2) (* (PI) (/ n k)) (/ n k) (* (sqrt (pow k -1)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt (pow k -1)) (pow k -1) -1 (pow (* (* 2 (PI)) n) (/ (- 1 k) 2)) (* (* 2 (PI)) n) (* 2 (PI)) (* (/ 1 (sqrt k)) (exp (* (log (* (* (PI) 2) n)) (/ (- 1 k) 2)))) (/ 1 (sqrt k)) 1 (exp (* (log (* (* (PI) 2) n)) (/ (- 1 k) 2))) (* (log (* (* (PI) 2) n)) (/ (- 1 k) 2)) (log (* (* (PI) 2) n)) (* (* (PI) 2) n) (* (PI) 2) (/ (- 1 k) 2) (* (- (/ 1/2 k) 1/2) k) (- (/ 1/2 k) 1/2) (/ 1/2 k) (/ (pow (* (pow (* (PI) 2) (/ (- 1 k) 4)) (pow n (/ (- 1 k) 4))) 2) (sqrt k)) (pow (* (pow (* (PI) 2) (/ (- 1 k) 4)) (pow n (/ (- 1 k) 4))) 2) (* (pow (* (PI) 2) (/ (- 1 k) 4)) (pow n (/ (- 1 k) 4))) (pow (* (PI) 2) (/ (- 1 k) 4)) (/ (- 1 k) 4) (- 1 k) 4 (pow n (/ (- 1 k) 4)))

rewrite174.0ms (3.5%)

Memory

13.6MiB live, 157.8MiB allocated; 11ms collecting garbage

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	610	6142
0	672	5612
0	2904	5494

Stop Event

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

Counts

205 → 319

Calls

Call 1

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

Outputs
(/.f64 (neg.f64 (pow.f64 (.f64 (.f64 (PI.f64) #s(literal 2 binary64)) n) #s(approx (/ (- 1 k) 2) (fma.f64 #s(literal -1/2 binary64) k #s(literal 1/2 binary64))))) (neg.f64 (sqrt.f64 k)))
(/.f64 (pow.f64 (.f64 (.f64 (PI.f64) #s(literal 2 binary64)) n) #s(approx (/ (- 1 k) 2) (fma.f64 #s(literal -1/2 binary64) k #s(literal 1/2 binary64)))) (sqrt.f64 k))
(.f64 (pow.f64 (.f64 (.f64 (PI.f64) #s(literal 2 binary64)) n) (/.f64 #s(approx (/ (- 1 k) 2) (fma.f64 #s(literal -1/2 binary64) k #s(literal 1/2 binary64))) #s(literal 2 binary64))) (pow.f64 (.f64 (*.f64 (PI.f64) #s(literal 2 binary64)) n) (/.f64 #s(approx (/ (- 1 k) 2) (fma.f64 #s(literal -1/2 binary64) k #s(literal 1/2 binary64))) #s(literal 2 binary64))))
(.f64 (pow.f64 (.f64 (PI.f64) #s(literal 2 binary64)) #s(approx (/ (- 1 k) 2) (fma.f64 #s(literal -1/2 binary64) k #s(literal 1/2 binary64)))) (pow.f64 n #s(approx (/ (- 1 k) 2) (fma.f64 #s(literal -1/2 binary64) k #s(literal 1/2 binary64)))))
(.f64 (pow.f64 (.f64 (PI.f64) n) #s(approx (/ (- 1 k) 2) (fma.f64 #s(literal -1/2 binary64) k #s(literal 1/2 binary64)))) (pow.f64 #s(literal 2 binary64) #s(approx (/ (- 1 k) 2) (fma.f64 #s(literal -1/2 binary64) k #s(literal 1/2 binary64)))))
(pow.f64 (.f64 (.f64 (PI.f64) #s(literal 2 binary64)) n) #s(approx (/ (- 1 k) 2) (fma.f64 #s(literal -1/2 binary64) k #s(literal 1/2 binary64))))
(exp.f64 (.f64 (log.f64 (.f64 (*.f64 (PI.f64) #s(literal 2 binary64)) n)) #s(approx (/ (- 1 k) 2) (fma.f64 #s(literal -1/2 binary64) k #s(literal 1/2 binary64)))))
(.f64 (.f64 #s(literal 2 binary64) n) (PI.f64))
(.f64 (.f64 (PI.f64) n) #s(literal 2 binary64))
(.f64 (.f64 (PI.f64) #s(literal 2 binary64)) n)
(.f64 (PI.f64) (.f64 n #s(literal 2 binary64)))
(.f64 (PI.f64) (.f64 #s(literal 2 binary64) n))
(.f64 #s(literal 2 binary64) (.f64 (PI.f64) n))
(.f64 n (.f64 (PI.f64) #s(literal 2 binary64)))
(fma.f64 (PI.f64) n (*.f64 (PI.f64) n))
(fma.f64 n (PI.f64) (*.f64 (PI.f64) n))
(+.f64 (.f64 (PI.f64) n) (.f64 (PI.f64) n))
(*.f64 (PI.f64) n)
(*.f64 n (PI.f64))
(PI.f64)
n
#s(literal 2 binary64)
#s(approx (/ (- 1 k) 2) (fma.f64 #s(literal -1/2 binary64) k #s(literal 1/2 binary64)))
(/.f64 (-.f64 (.f64 (.f64 #s(literal -1/2 binary64) k) (.f64 #s(literal -1/2 binary64) k)) #s(literal 1/4 binary64)) (-.f64 (.f64 #s(literal -1/2 binary64) k) #s(literal 1/2 binary64)))
(/.f64 (-.f64 #s(literal 1/4 binary64) (.f64 (.f64 #s(literal -1/2 binary64) k) (.f64 #s(literal -1/2 binary64) k))) (-.f64 #s(literal 1/2 binary64) (.f64 #s(literal -1/2 binary64) k)))
(/.f64 (+.f64 (pow.f64 (.f64 #s(literal -1/2 binary64) k) #s(literal 3 binary64)) #s(literal 1/8 binary64)) (fma.f64 (.f64 #s(literal -1/2 binary64) k) (.f64 #s(literal -1/2 binary64) k) (-.f64 #s(literal 1/4 binary64) (.f64 (*.f64 #s(literal -1/2 binary64) k) #s(literal 1/2 binary64)))))
(/.f64 (+.f64 #s(literal 1/8 binary64) (pow.f64 (.f64 #s(literal -1/2 binary64) k) #s(literal 3 binary64))) (+.f64 #s(literal 1/4 binary64) (-.f64 (.f64 (.f64 #s(literal -1/2 binary64) k) (.f64 #s(literal -1/2 binary64) k)) (.f64 #s(literal 1/2 binary64) (.f64 #s(literal -1/2 binary64) k)))))
(fma.f64 #s(literal -1/2 binary64) k #s(literal 1/2 binary64))
(fma.f64 k #s(literal -1/2 binary64) #s(literal 1/2 binary64))
(-.f64 #s(literal 1/2 binary64) (*.f64 #s(literal 1/2 binary64) k))
(+.f64 (*.f64 #s(literal -1/2 binary64) k) #s(literal 1/2 binary64))
(+.f64 #s(literal 1/2 binary64) (*.f64 #s(literal -1/2 binary64) k))
#s(literal -1/2 binary64)
k
#s(literal 1/2 binary64)
(pow.f64 k #s(literal 1/2 binary64))
(sqrt.f64 k)
#s(approx (* (/ 1 (sqrt k)) (exp (* (log (* (* (PI) 2) n)) (/ (- 1 k) 2)))) (sqrt.f64 (.f64 (.f64 (/.f64 n k) (PI.f64)) #s(literal 2 binary64))))
(.f64 (.f64 (sqrt.f64 (*.f64 (/.f64 n k) (PI.f64))) (sqrt.f64 #s(literal -2 binary64))) (sqrt.f64 #s(literal -1 binary64)))
(.f64 (sqrt.f64 #s(literal 2 binary64)) (sqrt.f64 (.f64 (/.f64 n k) (PI.f64))))
(.f64 (sqrt.f64 (.f64 (/.f64 n k) (PI.f64))) (sqrt.f64 #s(literal 2 binary64)))
(pow.f64 (.f64 (.f64 (/.f64 n k) (PI.f64)) #s(literal 2 binary64)) #s(literal 1/2 binary64))
(sqrt.f64 (.f64 (.f64 (/.f64 n k) (PI.f64)) #s(literal 2 binary64)))
(.f64 (.f64 (/.f64 n k) (PI.f64)) #s(literal 2 binary64))
(.f64 (PI.f64) (.f64 (/.f64 n k) #s(literal 2 binary64)))
(.f64 #s(literal 2 binary64) (.f64 (/.f64 n k) (PI.f64)))
(/.f64 (.f64 (.f64 (PI.f64) #s(literal 2 binary64)) n) k)
(fma.f64 (/.f64 n k) (PI.f64) (*.f64 (/.f64 n k) (PI.f64)))
(fma.f64 (PI.f64) (/.f64 n k) (*.f64 (/.f64 n k) (PI.f64)))
(fma.f64 n (/.f64 (PI.f64) k) (*.f64 (/.f64 n k) (PI.f64)))
(+.f64 (.f64 (/.f64 n k) (PI.f64)) (.f64 (/.f64 n k) (PI.f64)))
(*.f64 (/.f64 n k) (PI.f64))
(*.f64 (PI.f64) (/.f64 n k))
(*.f64 n (/.f64 (PI.f64) k))
(/.f64 (neg.f64 (*.f64 (PI.f64) n)) (neg.f64 k))
(/.f64 (*.f64 (PI.f64) n) k)
(/.f64 (neg.f64 n) (neg.f64 k))
(/.f64 n k)
(.f64 (pow.f64 k #s(literal -1/2 binary64)) (pow.f64 (.f64 (*.f64 (PI.f64) #s(literal 2 binary64)) n) #s(approx (/ (- 1 k) 2) (fma.f64 #s(literal -1/2 binary64) k #s(literal 1/2 binary64)))))
(.f64 (pow.f64 (.f64 (*.f64 (PI.f64) #s(literal 2 binary64)) n) #s(approx (/ (- 1 k) 2) (fma.f64 #s(literal -1/2 binary64) k #s(literal 1/2 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 #s(literal -1 binary64) (neg.f64 (sqrt.f64 k)))
(/.f64 #s(literal 1 binary64) (sqrt.f64 k))
(sqrt.f64 (pow.f64 k #s(literal -1 binary64)))
(*.f64 (pow.f64 k #s(literal -1/2 binary64)) (pow.f64 k #s(literal -1/2 binary64)))
(pow.f64 k #s(literal -1 binary64))
(/.f64 #s(literal -1 binary64) (neg.f64 k))
(/.f64 #s(literal 1 binary64) k)
(exp.f64 (*.f64 (log.f64 k) #s(literal -1 binary64)))
#s(literal -1 binary64)
(.f64 (pow.f64 (.f64 (.f64 (PI.f64) #s(literal 2 binary64)) n) (/.f64 #s(approx (/ (- 1 k) 2) (fma.f64 #s(literal -1/2 binary64) k #s(literal 1/2 binary64))) #s(literal 2 binary64))) (pow.f64 (.f64 (*.f64 (PI.f64) #s(literal 2 binary64)) n) (/.f64 #s(approx (/ (- 1 k) 2) (fma.f64 #s(literal -1/2 binary64) k #s(literal 1/2 binary64))) #s(literal 2 binary64))))
(.f64 (pow.f64 (.f64 (PI.f64) #s(literal 2 binary64)) #s(approx (/ (- 1 k) 2) (fma.f64 #s(literal -1/2 binary64) k #s(literal 1/2 binary64)))) (pow.f64 n #s(approx (/ (- 1 k) 2) (fma.f64 #s(literal -1/2 binary64) k #s(literal 1/2 binary64)))))
(.f64 (pow.f64 (.f64 (PI.f64) n) #s(approx (/ (- 1 k) 2) (fma.f64 #s(literal -1/2 binary64) k #s(literal 1/2 binary64)))) (pow.f64 #s(literal 2 binary64) #s(approx (/ (- 1 k) 2) (fma.f64 #s(literal -1/2 binary64) k #s(literal 1/2 binary64)))))
(pow.f64 (.f64 (.f64 (PI.f64) #s(literal 2 binary64)) n) #s(approx (/ (- 1 k) 2) (fma.f64 #s(literal -1/2 binary64) k #s(literal 1/2 binary64))))
(exp.f64 (.f64 (log.f64 (.f64 (*.f64 (PI.f64) #s(literal 2 binary64)) n)) #s(approx (/ (- 1 k) 2) (fma.f64 #s(literal -1/2 binary64) k #s(literal 1/2 binary64)))))
(.f64 (.f64 #s(literal 2 binary64) n) (PI.f64))
(.f64 (.f64 (PI.f64) n) #s(literal 2 binary64))
(.f64 (.f64 (PI.f64) #s(literal 2 binary64)) n)
(.f64 (PI.f64) (.f64 n #s(literal 2 binary64)))
(.f64 (PI.f64) (.f64 #s(literal 2 binary64) n))
(.f64 #s(literal 2 binary64) (.f64 (PI.f64) n))
(.f64 n (.f64 (PI.f64) #s(literal 2 binary64)))
(fma.f64 (PI.f64) n (*.f64 (PI.f64) n))
(fma.f64 n (PI.f64) (*.f64 (PI.f64) n))
(+.f64 (.f64 (PI.f64) n) (.f64 (PI.f64) n))
(*.f64 (PI.f64) #s(literal 2 binary64))
(*.f64 #s(literal 2 binary64) (PI.f64))
(+.f64 (PI.f64) (PI.f64))
(.f64 (pow.f64 k #s(literal -1/2 binary64)) (pow.f64 (.f64 (.f64 (PI.f64) #s(literal 2 binary64)) n) #s(approx (/ (- 1 k) 2) (.f64 (-.f64 (/.f64 #s(literal 1/2 binary64) k) #s(literal 1/2 binary64)) k))))
(.f64 (pow.f64 (.f64 (.f64 (PI.f64) #s(literal 2 binary64)) n) #s(approx (/ (- 1 k) 2) (.f64 (-.f64 (/.f64 #s(literal 1/2 binary64) k) #s(literal 1/2 binary64)) k))) (pow.f64 k #s(literal -1/2 binary64)))
(/.f64 (.f64 #s(literal 1 binary64) (pow.f64 (.f64 (.f64 (PI.f64) #s(literal 2 binary64)) n) #s(approx (/ (- 1 k) 2) (.f64 (-.f64 (/.f64 #s(literal 1/2 binary64) k) #s(literal 1/2 binary64)) k)))) (sqrt.f64 k))
(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 #s(literal -1 binary64) (neg.f64 (sqrt.f64 k)))
(/.f64 #s(literal 1 binary64) (sqrt.f64 k))
(sqrt.f64 (pow.f64 k #s(literal -1 binary64)))
#s(literal 1 binary64)
(pow.f64 (exp.f64 (log.f64 (.f64 (.f64 (PI.f64) #s(literal 2 binary64)) n))) #s(approx (/ (- 1 k) 2) (*.f64 (-.f64 (/.f64 #s(literal 1/2 binary64) k) #s(literal 1/2 binary64)) k)))
(pow.f64 (.f64 (.f64 (PI.f64) #s(literal 2 binary64)) n) #s(approx (/ (- 1 k) 2) (*.f64 (-.f64 (/.f64 #s(literal 1/2 binary64) k) #s(literal 1/2 binary64)) k)))
(exp.f64 (.f64 (log.f64 (.f64 (.f64 (PI.f64) #s(literal 2 binary64)) n)) #s(approx (/ (- 1 k) 2) (.f64 (-.f64 (/.f64 #s(literal 1/2 binary64) k) #s(literal 1/2 binary64)) k))))
(+.f64 (cosh.f64 (.f64 (log.f64 (.f64 (.f64 (PI.f64) #s(literal 2 binary64)) n)) #s(approx (/ (- 1 k) 2) (.f64 (-.f64 (/.f64 #s(literal 1/2 binary64) k) #s(literal 1/2 binary64)) k)))) (sinh.f64 (.f64 (log.f64 (.f64 (.f64 (PI.f64) #s(literal 2 binary64)) n)) #s(approx (/ (- 1 k) 2) (.f64 (-.f64 (/.f64 #s(literal 1/2 binary64) k) #s(literal 1/2 binary64)) k)))))
(.f64 (log.f64 (.f64 (.f64 (PI.f64) #s(literal 2 binary64)) n)) #s(approx (/ (- 1 k) 2) (.f64 (-.f64 (/.f64 #s(literal 1/2 binary64) k) #s(literal 1/2 binary64)) k)))
(.f64 #s(approx (/ (- 1 k) 2) (.f64 (-.f64 (/.f64 #s(literal 1/2 binary64) k) #s(literal 1/2 binary64)) k)) (log.f64 (.f64 (.f64 (PI.f64) #s(literal 2 binary64)) n)))
(/.f64 (-.f64 (pow.f64 (log.f64 n) #s(literal 2 binary64)) (pow.f64 (log.f64 (.f64 (PI.f64) #s(literal 2 binary64))) #s(literal 2 binary64))) (-.f64 (log.f64 n) (log.f64 (.f64 (PI.f64) #s(literal 2 binary64)))))
(/.f64 (+.f64 (pow.f64 (log.f64 n) #s(literal 3 binary64)) (pow.f64 (log.f64 (.f64 (PI.f64) #s(literal 2 binary64))) #s(literal 3 binary64))) (fma.f64 (log.f64 n) (log.f64 n) (-.f64 (pow.f64 (log.f64 (.f64 (PI.f64) #s(literal 2 binary64))) #s(literal 2 binary64)) (.f64 (log.f64 (.f64 (PI.f64) #s(literal 2 binary64))) (log.f64 n)))))
(+.f64 (log.f64 #s(literal 2 binary64)) (log.f64 (*.f64 (PI.f64) n)))
(+.f64 (log.f64 (*.f64 (PI.f64) #s(literal 2 binary64))) (log.f64 n))
(+.f64 (log.f64 n) (log.f64 (*.f64 (PI.f64) #s(literal 2 binary64))))
(log.f64 (.f64 (.f64 (PI.f64) #s(literal 2 binary64)) n))
(.f64 (.f64 #s(literal 2 binary64) n) (PI.f64))
(.f64 (.f64 (PI.f64) n) #s(literal 2 binary64))
(.f64 (.f64 (PI.f64) #s(literal 2 binary64)) n)
(.f64 (PI.f64) (.f64 n #s(literal 2 binary64)))
(.f64 (PI.f64) (.f64 #s(literal 2 binary64) n))
(.f64 #s(literal 2 binary64) (.f64 (PI.f64) n))
(.f64 n (.f64 (PI.f64) #s(literal 2 binary64)))
(fma.f64 (PI.f64) n (*.f64 (PI.f64) n))
(fma.f64 n (PI.f64) (*.f64 (PI.f64) n))
(+.f64 (.f64 (PI.f64) n) (.f64 (PI.f64) n))
(*.f64 (PI.f64) #s(literal 2 binary64))
(*.f64 #s(literal 2 binary64) (PI.f64))
(+.f64 (PI.f64) (PI.f64))
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(*.f64 (-.f64 (/.f64 #s(literal 1/2 binary64) k) #s(literal 1/2 binary64)) k)
(*.f64 k (-.f64 (/.f64 #s(literal 1/2 binary64) k) #s(literal 1/2 binary64)))
(/.f64 (-.f64 (*.f64 (/.f64 #s(literal 1/2 binary64) k) (/.f64 #s(literal 1/2 binary64) k)) #s(literal 1/4 binary64)) (+.f64 (/.f64 #s(literal 1/2 binary64) k) #s(literal 1/2 binary64)))
(/.f64 (-.f64 (pow.f64 (/.f64 #s(literal 1/2 binary64) k) #s(literal 3 binary64)) #s(literal 1/8 binary64)) (fma.f64 (/.f64 #s(literal 1/2 binary64) k) (/.f64 #s(literal 1/2 binary64) k) (+.f64 #s(literal 1/4 binary64) (*.f64 (/.f64 #s(literal 1/2 binary64) k) #s(literal 1/2 binary64)))))
(-.f64 (/.f64 #s(literal 1/2 binary64) k) #s(literal 1/2 binary64))
(*.f64 (pow.f64 k #s(literal -1 binary64)) #s(literal 1/2 binary64))
(*.f64 #s(literal 1/2 binary64) (pow.f64 k #s(literal -1 binary64)))
(/.f64 #s(literal 1/2 binary64) k)
(/.f64 #s(literal -1/2 binary64) (neg.f64 k))
(/.f64 (neg.f64 (pow.f64 (pow.f64 (.f64 (.f64 (PI.f64) #s(literal 2 binary64)) n) (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 4 binary64))) #s(literal 2 binary64))) (neg.f64 (sqrt.f64 k)))
(/.f64 (pow.f64 (pow.f64 (.f64 (.f64 (PI.f64) #s(literal 2 binary64)) n) (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 4 binary64))) #s(literal 2 binary64)) (sqrt.f64 k))
(.f64 (pow.f64 (pow.f64 (.f64 (.f64 (PI.f64) #s(literal 2 binary64)) n) (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 4 binary64))) #s(literal 1 binary64)) (pow.f64 (pow.f64 (.f64 (*.f64 (PI.f64) #s(literal 2 binary64)) n) (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 4 binary64))) #s(literal 1 binary64)))
(.f64 (pow.f64 (pow.f64 (.f64 (PI.f64) #s(literal 2 binary64)) (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 4 binary64))) #s(literal 2 binary64)) (pow.f64 (pow.f64 n (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 4 binary64))) #s(literal 2 binary64)))
(.f64 (pow.f64 (.f64 (.f64 (PI.f64) #s(literal 2 binary64)) n) (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 4 binary64))) (pow.f64 (.f64 (*.f64 (PI.f64) #s(literal 2 binary64)) n) (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 4 binary64))))
(pow.f64 (pow.f64 (.f64 (.f64 (PI.f64) #s(literal 2 binary64)) n) (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 4 binary64))) #s(literal 2 binary64))
(exp.f64 (.f64 (log.f64 (pow.f64 (.f64 (*.f64 (PI.f64) #s(literal 2 binary64)) n) (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 4 binary64)))) #s(literal 2 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 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 4 binary64))))
(pow.f64 (.f64 (.f64 (PI.f64) #s(literal 2 binary64)) n) (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 4 binary64)))
(.f64 (pow.f64 (.f64 (PI.f64) #s(literal 2 binary64)) (/.f64 (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 4 binary64)) #s(literal 2 binary64))) (pow.f64 (*.f64 (PI.f64) #s(literal 2 binary64)) (/.f64 (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 4 binary64)) #s(literal 2 binary64))))
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(pow.f64 (*.f64 (PI.f64) #s(literal 2 binary64)) (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 4 binary64)))
(exp.f64 (.f64 (log.f64 (.f64 (PI.f64) #s(literal 2 binary64))) (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 4 binary64))))
(/.f64 (neg.f64 (-.f64 #s(literal 1 binary64) k)) #s(literal -4 binary64))
(/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 4 binary64))
(-.f64 #s(literal 1/4 binary64) (/.f64 k #s(literal 4 binary64)))
(/.f64 (-.f64 #s(literal 1 binary64) (*.f64 k k)) (+.f64 #s(literal 1 binary64) k))
(/.f64 (-.f64 #s(literal 1 binary64) (pow.f64 k #s(literal 3 binary64))) (+.f64 #s(literal 1 binary64) (fma.f64 k k (*.f64 #s(literal 1 binary64) k))))
(-.f64 #s(literal 1 binary64) k)
#s(literal 4 binary64)
(*.f64 (pow.f64 n (/.f64 (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 4 binary64)) #s(literal 2 binary64))) (pow.f64 n (/.f64 (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 4 binary64)) #s(literal 2 binary64))))
(pow.f64 n (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 4 binary64)))
(exp.f64 (*.f64 (log.f64 n) (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 4 binary64))))
#s(approx (/ (pow (* (* (PI) n) 2) (/ (- 1 k) 2)) (sqrt k)) (sqrt.f64 (.f64 (.f64 (/.f64 n k) (PI.f64)) #s(literal 2 binary64))))
#s(approx (/ (pow (* (* (PI) n) 2) (/ (- 1 k) 2)) (sqrt k)) (/.f64 (fma.f64 (.f64 (.f64 (log.f64 (.f64 (.f64 (PI.f64) #s(literal 2 binary64)) n)) (sqrt.f64 #s(literal 2 binary64))) (.f64 (pow.f64 k #s(literal 3/2 binary64)) (sqrt.f64 (.f64 (PI.f64) n)))) #s(literal -1/2 binary64) (sqrt.f64 (.f64 (.f64 (*.f64 (PI.f64) n) k) #s(literal 2 binary64)))) k))
#s(approx (/ (pow (* (* (PI) n) 2) (/ (- 1 k) 2)) (sqrt k)) (/.f64 (fma.f64 (fma.f64 (.f64 #s(literal 1/8 binary64) (.f64 (pow.f64 k #s(literal 3/2 binary64)) (sqrt.f64 (.f64 (PI.f64) n)))) (.f64 (pow.f64 (log.f64 (.f64 (.f64 (PI.f64) #s(literal 2 binary64)) n)) #s(literal 2 binary64)) (sqrt.f64 #s(literal 2 binary64))) (.f64 (.f64 #s(literal -1/2 binary64) (sqrt.f64 (.f64 (.f64 (PI.f64) n) k))) (.f64 (log.f64 (.f64 (.f64 (PI.f64) #s(literal 2 binary64)) n)) (sqrt.f64 #s(literal 2 binary64))))) k (sqrt.f64 (.f64 (.f64 (.f64 (PI.f64) n) k) #s(literal 2 binary64)))) k))
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#s(approx (pow (* (* (PI) n) 2) (/ (- 1 k) 2)) (sqrt.f64 (.f64 (.f64 (PI.f64) #s(literal 2 binary64)) n)))
#s(approx (pow (* (* (PI) n) 2) (/ (- 1 k) 2)) (fma.f64 (.f64 (.f64 (log.f64 (pow.f64 (.f64 (.f64 (PI.f64) #s(literal 2 binary64)) n) k)) (sqrt.f64 #s(literal 2 binary64))) (sqrt.f64 (.f64 (PI.f64) n))) #s(literal -1/2 binary64) (sqrt.f64 (.f64 (*.f64 (PI.f64) #s(literal 2 binary64)) n))))
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#s(approx (pow (* (* (PI) n) 2) (/ (- 1 k) 2)) (fma.f64 (fma.f64 (fma.f64 (.f64 (.f64 (.f64 k (pow.f64 (log.f64 (.f64 (.f64 (PI.f64) #s(literal 2 binary64)) n)) #s(literal 3 binary64))) (sqrt.f64 #s(literal 2 binary64))) (sqrt.f64 (.f64 (PI.f64) n))) #s(literal -1/48 binary64) (.f64 (.f64 #s(literal 1/8 binary64) (sqrt.f64 (.f64 (PI.f64) n))) (.f64 (pow.f64 (log.f64 (.f64 (.f64 (PI.f64) #s(literal 2 binary64)) n)) #s(literal 2 binary64)) (sqrt.f64 #s(literal 2 binary64))))) k (.f64 (.f64 #s(literal -1/2 binary64) (sqrt.f64 (.f64 (PI.f64) n))) (.f64 (log.f64 (.f64 (.f64 (PI.f64) #s(literal 2 binary64)) n)) (sqrt.f64 #s(literal 2 binary64))))) k (sqrt.f64 (.f64 (.f64 (PI.f64) #s(literal 2 binary64)) n))))
#s(approx (/ (- 1 k) 2) #s(literal 1/2 binary64))
#s(approx (/ (- 1 k) 2) (fma.f64 #s(literal -1/2 binary64) k #s(literal 1/2 binary64)))
#s(approx (+ (* -1/2 k) 1/2) #s(literal 1/2 binary64))
#s(approx (+ (* -1/2 k) 1/2) (fma.f64 #s(literal -1/2 binary64) k #s(literal 1/2 binary64)))
#s(approx k k)
#s(approx (sqrt k) (sqrt.f64 k))
#s(approx (* (/ 1 (sqrt k)) (exp (* (log (* (* (PI) 2) n)) (/ (- 1 k) 2)))) (sqrt.f64 (.f64 (.f64 (/.f64 n k) (PI.f64)) #s(literal 2 binary64))))
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#s(approx (sqrt (* (* (PI) (/ n k)) 2)) (sqrt.f64 (.f64 (.f64 (/.f64 n k) (PI.f64)) #s(literal 2 binary64))))
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#s(approx (* (PI) (/ n k)) (*.f64 (/.f64 n k) (PI.f64)))
#s(approx (/ n k) (/.f64 n k))
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#s(approx (sqrt (pow k -1)) (pow.f64 k #s(literal -1/2 binary64)))
#s(approx (pow k -1) (pow.f64 k #s(literal -1 binary64)))
#s(approx (pow (* (* (PI) n) 2) (/ (- 1 k) 2)) (sqrt.f64 (.f64 (.f64 (PI.f64) #s(literal 2 binary64)) n)))
#s(approx (pow (* (* (PI) n) 2) (/ (- 1 k) 2)) (fma.f64 (.f64 (.f64 (log.f64 (pow.f64 (.f64 (.f64 (PI.f64) #s(literal 2 binary64)) n) k)) (sqrt.f64 #s(literal 2 binary64))) (sqrt.f64 (.f64 (PI.f64) n))) #s(literal -1/2 binary64) (sqrt.f64 (.f64 (*.f64 (PI.f64) #s(literal 2 binary64)) n))))
#s(approx (pow (* (* (PI) n) 2) (/ (- 1 k) 2)) (fma.f64 (fma.f64 (.f64 k (.f64 (.f64 (sqrt.f64 (.f64 (PI.f64) n)) (pow.f64 (log.f64 (.f64 (.f64 (PI.f64) #s(literal 2 binary64)) n)) #s(literal 2 binary64))) (sqrt.f64 #s(literal 2 binary64)))) #s(literal 1/8 binary64) (.f64 (.f64 #s(literal -1/2 binary64) (sqrt.f64 (.f64 (PI.f64) n))) (.f64 (log.f64 (.f64 (.f64 (PI.f64) #s(literal 2 binary64)) n)) (sqrt.f64 #s(literal 2 binary64))))) k (sqrt.f64 (.f64 (.f64 (PI.f64) #s(literal 2 binary64)) n))))
#s(approx (pow (* (* (PI) n) 2) (/ (- 1 k) 2)) (fma.f64 (fma.f64 (fma.f64 (.f64 (.f64 (.f64 k (pow.f64 (log.f64 (.f64 (.f64 (PI.f64) #s(literal 2 binary64)) n)) #s(literal 3 binary64))) (sqrt.f64 #s(literal 2 binary64))) (sqrt.f64 (.f64 (PI.f64) n))) #s(literal -1/48 binary64) (.f64 (.f64 #s(literal 1/8 binary64) (sqrt.f64 (.f64 (PI.f64) n))) (.f64 (pow.f64 (log.f64 (.f64 (.f64 (PI.f64) #s(literal 2 binary64)) n)) #s(literal 2 binary64)) (sqrt.f64 #s(literal 2 binary64))))) k (.f64 (.f64 #s(literal -1/2 binary64) (sqrt.f64 (.f64 (PI.f64) n))) (.f64 (log.f64 (.f64 (.f64 (PI.f64) #s(literal 2 binary64)) n)) (sqrt.f64 #s(literal 2 binary64))))) k (sqrt.f64 (.f64 (.f64 (PI.f64) #s(literal 2 binary64)) n))))
#s(approx (* (/ 1 (sqrt k)) (exp (* (log (* (* (PI) 2) n)) (/ (- 1 k) 2)))) (sqrt.f64 (.f64 (.f64 (/.f64 n k) (PI.f64)) #s(literal 2 binary64))))
#s(approx (* (/ 1 (sqrt k)) (exp (* (log (* (* (PI) 2) n)) (/ (- 1 k) 2)))) (/.f64 (fma.f64 (.f64 (.f64 (log.f64 (.f64 (.f64 (PI.f64) #s(literal 2 binary64)) n)) (sqrt.f64 #s(literal 2 binary64))) (.f64 (pow.f64 k #s(literal 3/2 binary64)) (sqrt.f64 (.f64 (PI.f64) n)))) #s(literal -1/2 binary64) (sqrt.f64 (.f64 (.f64 (*.f64 (PI.f64) n) k) #s(literal 2 binary64)))) k))
#s(approx (* (/ 1 (sqrt k)) (exp (* (log (* (* (PI) 2) n)) (/ (- 1 k) 2)))) (/.f64 (fma.f64 (fma.f64 (.f64 #s(literal 1/8 binary64) (.f64 (pow.f64 k #s(literal 3/2 binary64)) (sqrt.f64 (.f64 (PI.f64) n)))) (.f64 (pow.f64 (log.f64 (.f64 (.f64 (PI.f64) #s(literal 2 binary64)) n)) #s(literal 2 binary64)) (sqrt.f64 #s(literal 2 binary64))) (.f64 (.f64 #s(literal -1/2 binary64) (sqrt.f64 (.f64 (.f64 (PI.f64) n) k))) (.f64 (log.f64 (.f64 (.f64 (PI.f64) #s(literal 2 binary64)) n)) (sqrt.f64 #s(literal 2 binary64))))) k (sqrt.f64 (.f64 (.f64 (.f64 (PI.f64) n) k) #s(literal 2 binary64)))) k))
#s(approx (* (/ 1 (sqrt k)) (exp (* (log (* (* (PI) 2) n)) (/ (- 1 k) 2)))) (/.f64 (fma.f64 (fma.f64 (fma.f64 (.f64 #s(literal -1/48 binary64) (.f64 (pow.f64 k #s(literal 3/2 binary64)) (sqrt.f64 (.f64 (PI.f64) n)))) (.f64 (pow.f64 (log.f64 (.f64 (.f64 (PI.f64) #s(literal 2 binary64)) n)) #s(literal 3 binary64)) (sqrt.f64 #s(literal 2 binary64))) (.f64 (.f64 #s(literal 1/8 binary64) (sqrt.f64 (.f64 (.f64 (PI.f64) n) k))) (.f64 (pow.f64 (log.f64 (.f64 (.f64 (PI.f64) #s(literal 2 binary64)) n)) #s(literal 2 binary64)) (sqrt.f64 #s(literal 2 binary64))))) k (.f64 (.f64 #s(literal -1/2 binary64) (sqrt.f64 (.f64 (.f64 (PI.f64) n) k))) (.f64 (log.f64 (.f64 (.f64 (PI.f64) #s(literal 2 binary64)) n)) (sqrt.f64 #s(literal 2 binary64))))) k (sqrt.f64 (.f64 (.f64 (*.f64 (PI.f64) n) k) #s(literal 2 binary64)))) k))
#s(approx (sqrt (pow k -1)) (pow.f64 k #s(literal -1/2 binary64)))
#s(approx (pow (* (* (PI) n) 2) (/ (- 1 k) 2)) (sqrt.f64 (.f64 (.f64 (PI.f64) #s(literal 2 binary64)) n)))
#s(approx (pow (* (* (PI) n) 2) (/ (- 1 k) 2)) (fma.f64 (.f64 (.f64 (log.f64 (pow.f64 (.f64 (.f64 (PI.f64) #s(literal 2 binary64)) n) k)) (sqrt.f64 #s(literal 2 binary64))) (sqrt.f64 (.f64 (PI.f64) n))) #s(literal -1/2 binary64) (sqrt.f64 (.f64 (*.f64 (PI.f64) #s(literal 2 binary64)) n))))
#s(approx (pow (* (* (PI) n) 2) (/ (- 1 k) 2)) (fma.f64 (fma.f64 (.f64 k (.f64 (.f64 (sqrt.f64 (.f64 (PI.f64) n)) (pow.f64 (log.f64 (.f64 (.f64 (PI.f64) #s(literal 2 binary64)) n)) #s(literal 2 binary64))) (sqrt.f64 #s(literal 2 binary64)))) #s(literal 1/8 binary64) (.f64 (.f64 #s(literal -1/2 binary64) (sqrt.f64 (.f64 (PI.f64) n))) (.f64 (log.f64 (.f64 (.f64 (PI.f64) #s(literal 2 binary64)) n)) (sqrt.f64 #s(literal 2 binary64))))) k (sqrt.f64 (.f64 (.f64 (PI.f64) #s(literal 2 binary64)) n))))
#s(approx (pow (* (* (PI) n) 2) (/ (- 1 k) 2)) (fma.f64 (fma.f64 (fma.f64 (.f64 (.f64 (.f64 k (pow.f64 (log.f64 (.f64 (.f64 (PI.f64) #s(literal 2 binary64)) n)) #s(literal 3 binary64))) (sqrt.f64 #s(literal 2 binary64))) (sqrt.f64 (.f64 (PI.f64) n))) #s(literal -1/48 binary64) (.f64 (.f64 #s(literal 1/8 binary64) (sqrt.f64 (.f64 (PI.f64) n))) (.f64 (pow.f64 (log.f64 (.f64 (.f64 (PI.f64) #s(literal 2 binary64)) n)) #s(literal 2 binary64)) (sqrt.f64 #s(literal 2 binary64))))) k (.f64 (.f64 #s(literal -1/2 binary64) (sqrt.f64 (.f64 (PI.f64) n))) (.f64 (log.f64 (.f64 (.f64 (PI.f64) #s(literal 2 binary64)) n)) (sqrt.f64 #s(literal 2 binary64))))) k (sqrt.f64 (.f64 (.f64 (PI.f64) #s(literal 2 binary64)) n))))
#s(approx (* (log (* (* (PI) 2) n)) (/ (- 1 k) 2)) (log.f64 (pow.f64 (.f64 (.f64 (PI.f64) #s(literal 2 binary64)) n) #s(literal 1/2 binary64))))
#s(approx (* (log (* (* (PI) 2) n)) (/ (- 1 k) 2)) (fma.f64 (.f64 #s(literal -1/2 binary64) k) (log.f64 (.f64 (.f64 (PI.f64) #s(literal 2 binary64)) n)) (log.f64 (pow.f64 (.f64 (*.f64 (PI.f64) #s(literal 2 binary64)) n) #s(literal 1/2 binary64)))))
#s(approx (* (- (/ 1/2 k) 1/2) k) #s(literal 1/2 binary64))
#s(approx (* (- (/ 1/2 k) 1/2) k) (fma.f64 #s(literal -1/2 binary64) k #s(literal 1/2 binary64)))
#s(approx (- (/ 1/2 k) 1/2) (/.f64 #s(literal 1/2 binary64) k))
#s(approx (- (/ 1/2 k) 1/2) (/.f64 (fma.f64 #s(literal -1/2 binary64) k #s(literal 1/2 binary64)) k))
#s(approx (/ 1/2 k) (/.f64 #s(literal 1/2 binary64) k))
#s(approx (/ (pow (* (pow (* (PI) 2) (/ (- 1 k) 4)) (pow n (/ (- 1 k) 4))) 2) (sqrt k)) (sqrt.f64 (.f64 (.f64 (/.f64 n k) (PI.f64)) #s(literal 2 binary64))))
#s(approx (/ (pow (* (pow (* (PI) 2) (/ (- 1 k) 4)) (pow n (/ (- 1 k) 4))) 2) (sqrt k)) (/.f64 (fma.f64 (.f64 #s(literal -1/2 binary64) (fma.f64 (.f64 (log.f64 n) (sqrt.f64 #s(literal 2 binary64))) (sqrt.f64 (.f64 (PI.f64) n)) (.f64 (.f64 (log.f64 (.f64 (PI.f64) #s(literal 2 binary64))) (sqrt.f64 #s(literal 2 binary64))) (sqrt.f64 (.f64 (PI.f64) n))))) (pow.f64 k #s(literal 3/2 binary64)) (sqrt.f64 (.f64 (.f64 (.f64 (PI.f64) n) k) #s(literal 2 binary64)))) k))
#s(approx (/ (pow (* (pow (* (PI) 2) (/ (- 1 k) 4)) (pow n (/ (- 1 k) 4))) 2) (sqrt k)) (/.f64 (fma.f64 (fma.f64 (fma.f64 (.f64 #s(literal 1/8 binary64) (sqrt.f64 (.f64 (PI.f64) n))) (.f64 (pow.f64 (log.f64 n) #s(literal 2 binary64)) (sqrt.f64 #s(literal 2 binary64))) (fma.f64 (.f64 #s(literal 1/8 binary64) (sqrt.f64 (.f64 (PI.f64) n))) (.f64 (pow.f64 (log.f64 (.f64 (PI.f64) #s(literal 2 binary64))) #s(literal 2 binary64)) (sqrt.f64 #s(literal 2 binary64))) (.f64 (.f64 #s(literal 1/4 binary64) (sqrt.f64 (.f64 (PI.f64) n))) (.f64 (.f64 (log.f64 (.f64 (PI.f64) #s(literal 2 binary64))) (sqrt.f64 #s(literal 2 binary64))) (log.f64 n))))) (pow.f64 k #s(literal 3/2 binary64)) (.f64 (.f64 #s(literal -1/2 binary64) (fma.f64 (.f64 (log.f64 n) (sqrt.f64 #s(literal 2 binary64))) (sqrt.f64 (.f64 (PI.f64) n)) (.f64 (.f64 (log.f64 (.f64 (PI.f64) #s(literal 2 binary64))) (sqrt.f64 #s(literal 2 binary64))) (sqrt.f64 (.f64 (PI.f64) n))))) (sqrt.f64 k))) k (sqrt.f64 (.f64 (.f64 (.f64 (PI.f64) n) k) #s(literal 2 binary64)))) k))
#s(approx (/ (pow (* (pow (* (PI) 2) (/ (- 1 k) 4)) (pow n (/ (- 1 k) 4))) 2) (sqrt k)) (/.f64 (fma.f64 (fma.f64 (fma.f64 (fma.f64 (.f64 #s(literal -1/16 binary64) (sqrt.f64 (.f64 (PI.f64) n))) (.f64 (.f64 (pow.f64 (log.f64 (.f64 (PI.f64) #s(literal 2 binary64))) #s(literal 2 binary64)) (log.f64 n)) (sqrt.f64 #s(literal 2 binary64))) (fma.f64 (.f64 #s(literal -1/16 binary64) (sqrt.f64 (.f64 (PI.f64) n))) (.f64 (pow.f64 (log.f64 n) #s(literal 2 binary64)) (.f64 (log.f64 (.f64 (PI.f64) #s(literal 2 binary64))) (sqrt.f64 #s(literal 2 binary64)))) (fma.f64 (.f64 (.f64 (.f64 (sqrt.f64 (PI.f64)) (pow.f64 (log.f64 (.f64 (PI.f64) #s(literal 2 binary64))) #s(literal 3 binary64))) (sqrt.f64 #s(literal 2 binary64))) #s(literal -1/48 binary64)) (sqrt.f64 n) (.f64 (.f64 (sqrt.f64 (PI.f64)) (sqrt.f64 #s(literal 2 binary64))) (.f64 (.f64 (pow.f64 (log.f64 n) #s(literal 3 binary64)) (sqrt.f64 n)) #s(literal -1/48 binary64)))))) (pow.f64 k #s(literal 3/2 binary64)) (.f64 (fma.f64 (.f64 #s(literal 1/8 binary64) (sqrt.f64 (.f64 (PI.f64) n))) (.f64 (pow.f64 (log.f64 n) #s(literal 2 binary64)) (sqrt.f64 #s(literal 2 binary64))) (fma.f64 (.f64 #s(literal 1/8 binary64) (sqrt.f64 (.f64 (PI.f64) n))) (.f64 (pow.f64 (log.f64 (.f64 (PI.f64) #s(literal 2 binary64))) #s(literal 2 binary64)) (sqrt.f64 #s(literal 2 binary64))) (.f64 (.f64 #s(literal 1/4 binary64) (sqrt.f64 (.f64 (PI.f64) n))) (.f64 (.f64 (log.f64 (.f64 (PI.f64) #s(literal 2 binary64))) (sqrt.f64 #s(literal 2 binary64))) (log.f64 n))))) (sqrt.f64 k))) k (.f64 (.f64 #s(literal -1/2 binary64) (fma.f64 (.f64 (log.f64 n) (sqrt.f64 #s(literal 2 binary64))) (sqrt.f64 (.f64 (PI.f64) n)) (.f64 (.f64 (log.f64 (.f64 (PI.f64) #s(literal 2 binary64))) (sqrt.f64 #s(literal 2 binary64))) (sqrt.f64 (.f64 (PI.f64) n))))) (sqrt.f64 k))) k (sqrt.f64 (.f64 (.f64 (*.f64 (PI.f64) n) k) #s(literal 2 binary64)))) k))
#s(approx (pow (* (pow (* (PI) 2) (/ (- 1 k) 4)) (pow n (/ (- 1 k) 4))) 2) (sqrt.f64 (.f64 (.f64 (PI.f64) #s(literal 2 binary64)) n)))
#s(approx (pow (* (pow (* (PI) 2) (/ (- 1 k) 4)) (pow n (/ (- 1 k) 4))) 2) (fma.f64 (.f64 #s(literal -1/2 binary64) (fma.f64 (.f64 (log.f64 n) (sqrt.f64 #s(literal 2 binary64))) (sqrt.f64 (.f64 (PI.f64) n)) (.f64 (.f64 (log.f64 (.f64 (PI.f64) #s(literal 2 binary64))) (sqrt.f64 #s(literal 2 binary64))) (sqrt.f64 (.f64 (PI.f64) n))))) k (sqrt.f64 (.f64 (*.f64 (PI.f64) #s(literal 2 binary64)) n))))
#s(approx (pow (* (pow (* (PI) 2) (/ (- 1 k) 4)) (pow n (/ (- 1 k) 4))) 2) (fma.f64 (fma.f64 #s(literal -1/2 binary64) (fma.f64 (.f64 (log.f64 n) (sqrt.f64 #s(literal 2 binary64))) (sqrt.f64 (.f64 (PI.f64) n)) (.f64 (.f64 (log.f64 (.f64 (PI.f64) #s(literal 2 binary64))) (sqrt.f64 #s(literal 2 binary64))) (sqrt.f64 (.f64 (PI.f64) n)))) (.f64 (fma.f64 (.f64 #s(literal 1/8 binary64) (sqrt.f64 (.f64 (PI.f64) n))) (.f64 (pow.f64 (log.f64 n) #s(literal 2 binary64)) (sqrt.f64 #s(literal 2 binary64))) (fma.f64 (.f64 #s(literal 1/8 binary64) (sqrt.f64 (.f64 (PI.f64) n))) (.f64 (pow.f64 (log.f64 (.f64 (PI.f64) #s(literal 2 binary64))) #s(literal 2 binary64)) (sqrt.f64 #s(literal 2 binary64))) (.f64 (.f64 #s(literal 1/4 binary64) (sqrt.f64 (.f64 (PI.f64) n))) (.f64 (.f64 (log.f64 (.f64 (PI.f64) #s(literal 2 binary64))) (sqrt.f64 #s(literal 2 binary64))) (log.f64 n))))) k)) k (sqrt.f64 (.f64 (.f64 (PI.f64) #s(literal 2 binary64)) n))))
#s(approx (pow (* (pow (* (PI) 2) (/ (- 1 k) 4)) (pow n (/ (- 1 k) 4))) 2) (fma.f64 (fma.f64 #s(literal -1/2 binary64) (fma.f64 (.f64 (log.f64 n) (sqrt.f64 #s(literal 2 binary64))) (sqrt.f64 (.f64 (PI.f64) n)) (.f64 (.f64 (log.f64 (.f64 (PI.f64) #s(literal 2 binary64))) (sqrt.f64 #s(literal 2 binary64))) (sqrt.f64 (.f64 (PI.f64) n)))) (.f64 (fma.f64 (.f64 #s(literal 1/8 binary64) (sqrt.f64 (.f64 (PI.f64) n))) (.f64 (pow.f64 (log.f64 n) #s(literal 2 binary64)) (sqrt.f64 #s(literal 2 binary64))) (fma.f64 (.f64 #s(literal 1/8 binary64) (sqrt.f64 (.f64 (PI.f64) n))) (.f64 (pow.f64 (log.f64 (.f64 (PI.f64) #s(literal 2 binary64))) #s(literal 2 binary64)) (sqrt.f64 #s(literal 2 binary64))) (fma.f64 (fma.f64 (.f64 #s(literal -1/16 binary64) (sqrt.f64 (.f64 (PI.f64) n))) (.f64 (.f64 (pow.f64 (log.f64 (.f64 (PI.f64) #s(literal 2 binary64))) #s(literal 2 binary64)) (log.f64 n)) (sqrt.f64 #s(literal 2 binary64))) (fma.f64 (.f64 #s(literal -1/16 binary64) (sqrt.f64 (.f64 (PI.f64) n))) (.f64 (pow.f64 (log.f64 n) #s(literal 2 binary64)) (.f64 (log.f64 (.f64 (PI.f64) #s(literal 2 binary64))) (sqrt.f64 #s(literal 2 binary64)))) (fma.f64 (.f64 (.f64 (.f64 (sqrt.f64 (PI.f64)) (pow.f64 (log.f64 (.f64 (PI.f64) #s(literal 2 binary64))) #s(literal 3 binary64))) (sqrt.f64 #s(literal 2 binary64))) #s(literal -1/48 binary64)) (sqrt.f64 n) (.f64 (.f64 (sqrt.f64 (PI.f64)) (sqrt.f64 #s(literal 2 binary64))) (.f64 (.f64 (pow.f64 (log.f64 n) #s(literal 3 binary64)) (sqrt.f64 n)) #s(literal -1/48 binary64)))))) k (.f64 (.f64 #s(literal 1/4 binary64) (sqrt.f64 (.f64 (PI.f64) n))) (.f64 (.f64 (log.f64 (.f64 (PI.f64) #s(literal 2 binary64))) (sqrt.f64 #s(literal 2 binary64))) (log.f64 n)))))) k)) k (sqrt.f64 (.f64 (.f64 (PI.f64) #s(literal 2 binary64)) n))))
#s(approx (* (pow (* (PI) 2) (/ (- 1 k) 4)) (pow n (/ (- 1 k) 4))) (pow.f64 (.f64 (.f64 (PI.f64) #s(literal 2 binary64)) n) #s(literal 1/4 binary64)))
#s(approx (* (pow (* (PI) 2) (/ (- 1 k) 4)) (pow n (/ (- 1 k) 4))) (fma.f64 (.f64 #s(literal -1/4 binary64) (fma.f64 (pow.f64 (.f64 (.f64 (PI.f64) #s(literal 2 binary64)) n) #s(literal 1/4 binary64)) (log.f64 n) (.f64 (pow.f64 (.f64 (.f64 (PI.f64) #s(literal 2 binary64)) n) #s(literal 1/4 binary64)) (log.f64 (.f64 (PI.f64) #s(literal 2 binary64)))))) k (pow.f64 (.f64 (*.f64 (PI.f64) #s(literal 2 binary64)) n) #s(literal 1/4 binary64))))
#s(approx (* (pow (* (PI) 2) (/ (- 1 k) 4)) (pow n (/ (- 1 k) 4))) (fma.f64 (fma.f64 #s(literal -1/4 binary64) (fma.f64 (pow.f64 (.f64 (.f64 (PI.f64) #s(literal 2 binary64)) n) #s(literal 1/4 binary64)) (log.f64 n) (.f64 (pow.f64 (.f64 (.f64 (PI.f64) #s(literal 2 binary64)) n) #s(literal 1/4 binary64)) (log.f64 (.f64 (PI.f64) #s(literal 2 binary64))))) (.f64 (fma.f64 (.f64 (pow.f64 (.f64 (.f64 (PI.f64) #s(literal 2 binary64)) n) #s(literal 1/4 binary64)) (pow.f64 (log.f64 n) #s(literal 2 binary64))) #s(literal 1/32 binary64) (fma.f64 (.f64 #s(literal 1/32 binary64) (pow.f64 (.f64 (.f64 (PI.f64) #s(literal 2 binary64)) n) #s(literal 1/4 binary64))) (pow.f64 (log.f64 (.f64 (PI.f64) #s(literal 2 binary64))) #s(literal 2 binary64)) (.f64 (.f64 #s(literal 1/16 binary64) (pow.f64 (.f64 (.f64 (PI.f64) #s(literal 2 binary64)) n) #s(literal 1/4 binary64))) (.f64 (log.f64 (.f64 (PI.f64) #s(literal 2 binary64))) (log.f64 n))))) k)) k (pow.f64 (.f64 (.f64 (PI.f64) #s(literal 2 binary64)) n) #s(literal 1/4 binary64))))
#s(approx (* (pow (* (PI) 2) (/ (- 1 k) 4)) (pow n (/ (- 1 k) 4))) (fma.f64 (fma.f64 #s(literal -1/4 binary64) (fma.f64 (pow.f64 (.f64 (.f64 (PI.f64) #s(literal 2 binary64)) n) #s(literal 1/4 binary64)) (log.f64 n) (.f64 (pow.f64 (.f64 (.f64 (PI.f64) #s(literal 2 binary64)) n) #s(literal 1/4 binary64)) (log.f64 (.f64 (PI.f64) #s(literal 2 binary64))))) (.f64 (fma.f64 (.f64 #s(literal 1/32 binary64) (pow.f64 (.f64 (.f64 (PI.f64) #s(literal 2 binary64)) n) #s(literal 1/4 binary64))) (pow.f64 (log.f64 n) #s(literal 2 binary64)) (fma.f64 (.f64 #s(literal 1/32 binary64) (pow.f64 (.f64 (.f64 (PI.f64) #s(literal 2 binary64)) n) #s(literal 1/4 binary64))) (pow.f64 (log.f64 (.f64 (PI.f64) #s(literal 2 binary64))) #s(literal 2 binary64)) (fma.f64 (fma.f64 (.f64 #s(literal -1/128 binary64) (pow.f64 (.f64 (.f64 (PI.f64) #s(literal 2 binary64)) n) #s(literal 1/4 binary64))) (.f64 (pow.f64 (log.f64 (.f64 (PI.f64) #s(literal 2 binary64))) #s(literal 2 binary64)) (log.f64 n)) (fma.f64 #s(literal -1/384 binary64) (fma.f64 (pow.f64 (.f64 (.f64 (PI.f64) #s(literal 2 binary64)) n) #s(literal 1/4 binary64)) (pow.f64 (log.f64 n) #s(literal 3 binary64)) (.f64 (pow.f64 (.f64 (.f64 (PI.f64) #s(literal 2 binary64)) n) #s(literal 1/4 binary64)) (pow.f64 (log.f64 (.f64 (PI.f64) #s(literal 2 binary64))) #s(literal 3 binary64)))) (.f64 (.f64 #s(literal -1/128 binary64) (pow.f64 (.f64 (.f64 (PI.f64) #s(literal 2 binary64)) n) #s(literal 1/4 binary64))) (.f64 (pow.f64 (log.f64 n) #s(literal 2 binary64)) (log.f64 (.f64 (PI.f64) #s(literal 2 binary64))))))) k (.f64 (.f64 #s(literal 1/16 binary64) (pow.f64 (.f64 (.f64 (PI.f64) #s(literal 2 binary64)) n) #s(literal 1/4 binary64))) (.f64 (log.f64 (.f64 (PI.f64) #s(literal 2 binary64))) (log.f64 n)))))) k)) k (pow.f64 (.f64 (*.f64 (PI.f64) #s(literal 2 binary64)) n) #s(literal 1/4 binary64))))
#s(approx (pow (* (PI) 2) (/ (- 1 k) 4)) (pow.f64 (*.f64 (PI.f64) #s(literal 2 binary64)) #s(literal 1/4 binary64)))
#s(approx (pow (* (PI) 2) (/ (- 1 k) 4)) (fma.f64 (.f64 #s(literal -1/4 binary64) (pow.f64 (.f64 (PI.f64) #s(literal 2 binary64)) #s(literal 1/4 binary64))) (log.f64 (pow.f64 (.f64 (PI.f64) #s(literal 2 binary64)) k)) (pow.f64 (.f64 (PI.f64) #s(literal 2 binary64)) #s(literal 1/4 binary64))))
#s(approx (pow (* (PI) 2) (/ (- 1 k) 4)) (fma.f64 (fma.f64 (.f64 #s(literal 1/32 binary64) (pow.f64 (.f64 (PI.f64) #s(literal 2 binary64)) #s(literal 1/4 binary64))) (.f64 (pow.f64 (log.f64 (.f64 (PI.f64) #s(literal 2 binary64))) #s(literal 2 binary64)) k) (.f64 (.f64 #s(literal -1/4 binary64) (pow.f64 (.f64 (PI.f64) #s(literal 2 binary64)) #s(literal 1/4 binary64))) (log.f64 (.f64 (PI.f64) #s(literal 2 binary64))))) k (pow.f64 (*.f64 (PI.f64) #s(literal 2 binary64)) #s(literal 1/4 binary64))))
#s(approx (pow (* (PI) 2) (/ (- 1 k) 4)) (fma.f64 (fma.f64 (fma.f64 (.f64 #s(literal -1/384 binary64) (pow.f64 (.f64 (PI.f64) #s(literal 2 binary64)) #s(literal 1/4 binary64))) (.f64 (pow.f64 (log.f64 (.f64 (PI.f64) #s(literal 2 binary64))) #s(literal 3 binary64)) k) (.f64 (.f64 #s(literal 1/32 binary64) (pow.f64 (.f64 (PI.f64) #s(literal 2 binary64)) #s(literal 1/4 binary64))) (pow.f64 (log.f64 (.f64 (PI.f64) #s(literal 2 binary64))) #s(literal 2 binary64)))) k (.f64 (.f64 #s(literal -1/4 binary64) (pow.f64 (.f64 (PI.f64) #s(literal 2 binary64)) #s(literal 1/4 binary64))) (log.f64 (.f64 (PI.f64) #s(literal 2 binary64))))) k (pow.f64 (*.f64 (PI.f64) #s(literal 2 binary64)) #s(literal 1/4 binary64))))
#s(approx (/ (- 1 k) 4) #s(literal 1/4 binary64))
#s(approx (/ (- 1 k) 4) (fma.f64 #s(literal -1/4 binary64) k #s(literal 1/4 binary64)))
#s(approx (- 1 k) #s(literal 1 binary64))
#s(approx (- 1 k) (fma.f64 #s(literal -1 binary64) k #s(literal 1 binary64)))
#s(approx (pow n (/ (- 1 k) 4)) (pow.f64 n #s(literal 1/4 binary64)))
#s(approx (pow n (/ (- 1 k) 4)) (fma.f64 (.f64 #s(literal -1/4 binary64) (pow.f64 n #s(literal 1/4 binary64))) (.f64 (log.f64 n) k) (pow.f64 n #s(literal 1/4 binary64))))
#s(approx (pow n (/ (- 1 k) 4)) (fma.f64 (fma.f64 (.f64 #s(literal 1/32 binary64) (pow.f64 n #s(literal 1/4 binary64))) (.f64 (pow.f64 (log.f64 n) #s(literal 2 binary64)) k) (.f64 (.f64 #s(literal -1/4 binary64) (pow.f64 n #s(literal 1/4 binary64))) (log.f64 n))) k (pow.f64 n #s(literal 1/4 binary64))))
#s(approx (pow n (/ (- 1 k) 4)) (fma.f64 (fma.f64 (fma.f64 (.f64 #s(literal -1/384 binary64) (pow.f64 n #s(literal 1/4 binary64))) (.f64 (pow.f64 (log.f64 n) #s(literal 3 binary64)) k) (.f64 (.f64 #s(literal 1/32 binary64) (pow.f64 n #s(literal 1/4 binary64))) (pow.f64 (log.f64 n) #s(literal 2 binary64)))) k (.f64 (.f64 #s(literal -1/4 binary64) (pow.f64 n #s(literal 1/4 binary64))) (log.f64 n))) k (pow.f64 n #s(literal 1/4 binary64))))
#s(approx (/ (pow (* (* (PI) n) 2) (/ (- 1 k) 2)) (sqrt k)) (.f64 (pow.f64 (exp.f64 #s(literal 1/2 binary64)) (.f64 (log.f64 (.f64 (.f64 (PI.f64) #s(literal 2 binary64)) n)) (-.f64 #s(literal 1 binary64) k))) (pow.f64 k #s(literal -1/2 binary64))))
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#s(approx (/ (- 1 k) 2) (*.f64 #s(literal -1/2 binary64) k))
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#s(approx (/ (pow (* (pow (* (PI) 2) (/ (- 1 k) 4)) (pow n (/ (- 1 k) 4))) 2) (sqrt k)) (.f64 (pow.f64 (exp.f64 (fma.f64 (.f64 (log.f64 (.f64 (PI.f64) #s(literal 2 binary64))) (-.f64 #s(literal 1 binary64) k)) #s(literal 1/4 binary64) (.f64 (*.f64 (fma.f64 (log.f64 (/.f64 #s(literal -1 binary64) n)) #s(literal -1 binary64) (log.f64 #s(literal -1 binary64))) (-.f64 #s(literal 1 binary64) k)) #s(literal 1/4 binary64)))) #s(literal 2 binary64)) (pow.f64 k #s(literal -1/2 binary64))))
#s(approx (pow (* (pow (* (PI) 2) (/ (- 1 k) 4)) (pow n (/ (- 1 k) 4))) 2) (pow.f64 (exp.f64 (fma.f64 (.f64 (log.f64 (.f64 (PI.f64) #s(literal 2 binary64))) (-.f64 #s(literal 1 binary64) k)) #s(literal 1/4 binary64) (.f64 (.f64 (fma.f64 (log.f64 (/.f64 #s(literal -1 binary64) n)) #s(literal -1 binary64) (log.f64 #s(literal -1 binary64))) (-.f64 #s(literal 1 binary64) k)) #s(literal 1/4 binary64)))) #s(literal 2 binary64)))
#s(approx (* (pow (* (PI) 2) (/ (- 1 k) 4)) (pow n (/ (- 1 k) 4))) (exp.f64 (fma.f64 (.f64 (log.f64 (.f64 (PI.f64) #s(literal 2 binary64))) (-.f64 #s(literal 1 binary64) k)) #s(literal 1/4 binary64) (.f64 (.f64 (fma.f64 (log.f64 (/.f64 #s(literal -1 binary64) n)) #s(literal -1 binary64) (log.f64 #s(literal -1 binary64))) (-.f64 #s(literal 1 binary64) k)) #s(literal 1/4 binary64)))))
#s(approx (pow n (/ (- 1 k) 4)) (pow.f64 (exp.f64 #s(literal 1/4 binary64)) (*.f64 (fma.f64 (log.f64 (/.f64 #s(literal -1 binary64) n)) #s(literal -1 binary64) (log.f64 #s(literal -1 binary64))) (-.f64 #s(literal 1 binary64) k))))

eval35.0ms (0.7%)

Memory: 25.2MiB live, 71.2MiB allocated; 5ms collecting garbage
Compiler: Compiled 10 086 to 1 221 computations (87.9% saved)

prune46.0ms (0.9%)

Memory

-4.4MiB live, 88.9MiB allocated; 8ms collecting garbage

Pruning

29 alts after pruning (24 fresh and 5 done)

	Pruned	Kept	Total
New	316	10	326
Fresh	6	14	20
Picked	2	3	5
Done	0	2	2
Total	324	29	353

Accuracy

100.0%

Counts

353 → 29

Alt Table

Click to see full alt table

Status	Accuracy	Program
	50.8%	(/.f64 (pow.f64 (pow.f64 (.f64 (.f64 #s(literal 2 binary64) n) (PI.f64)) #s(approx (/ (/ (- 1 k) 2) 2) #s(literal 1/4 binary64))) #s(literal 2 binary64)) (sqrt.f64 k))
	72.9%	(/.f64 (pow.f64 (.f64 (pow.f64 (.f64 (PI.f64) #s(literal 2 binary64)) (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 4 binary64))) (pow.f64 n #s(approx (/ (- 1 k) 4) #s(literal 1/4 binary64)))) #s(literal 2 binary64)) (sqrt.f64 k))
✓	99.1%	(/.f64 (pow.f64 (.f64 (.f64 (PI.f64) n) #s(literal 2 binary64)) #s(approx (/ (- 1 k) 2) (fma.f64 #s(literal -1/2 binary64) k #s(literal 1/2 binary64)))) (sqrt.f64 k))
	51.8%	(/.f64 (pow.f64 (.f64 (.f64 (PI.f64) n) #s(literal 2 binary64)) #s(approx (/ (- 1 k) 2) (*.f64 #s(literal -1/2 binary64) k))) (sqrt.f64 k))
	95.8%	(/.f64 (pow.f64 (exp.f64 (.f64 (log.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)) (sqrt.f64 k))
	95.8%	(/.f64 (pow.f64 (exp.f64 (log.f64 (.f64 (.f64 #s(literal 2 binary64) n) (PI.f64)))) (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 2 binary64))) (sqrt.f64 k))
	93.8%	(/.f64 (pow.f64 #s(approx (pow (* (* (PI) 2) n) (/ (/ (- 1 k) 2) 2)) (pow.f64 (exp.f64 #s(literal 1/4 binary64)) (.f64 (fma.f64 (neg.f64 (log.f64 n)) #s(literal -1 binary64) (log.f64 (.f64 (PI.f64) #s(literal 2 binary64)))) (-.f64 #s(literal 1 binary64) k)))) #s(literal 2 binary64)) (sqrt.f64 k))
	74.6%	(/.f64 (.f64 (pow.f64 (.f64 (PI.f64) #s(literal 2 binary64)) #s(approx (/ (- 1 k) 2) (fma.f64 #s(literal -1/2 binary64) k #s(literal 1/2 binary64)))) (pow.f64 n #s(approx (/ (- 1 k) 2) (fma.f64 #s(literal -1/2 binary64) k #s(literal 1/2 binary64))))) (sqrt.f64 k))
	74.4%	(/.f64 (.f64 (pow.f64 (.f64 n #s(literal 2 binary64)) #s(approx (/ (- 1 k) 2) (fma.f64 #s(literal -1/2 binary64) k #s(literal 1/2 binary64)))) (pow.f64 (PI.f64) #s(approx (/ (- 1 k) 2) (fma.f64 #s(literal -1/2 binary64) k #s(literal 1/2 binary64))))) (sqrt.f64 k))
	95.8%	(/.f64 (exp.f64 (.f64 (log.f64 (.f64 (*.f64 (PI.f64) n) #s(literal 2 binary64))) #s(approx (/ (- 1 k) 2) (fma.f64 #s(literal -1/2 binary64) k #s(literal 1/2 binary64))))) (sqrt.f64 k))
	51.0%	(/.f64 #s(approx (pow (* (pow (* (PI) 2) (/ (- 1 k) 4)) (pow n (/ (- 1 k) 4))) 2) (sqrt.f64 (.f64 (.f64 (PI.f64) #s(literal 2 binary64)) n))) (sqrt.f64 k))
	59.3%	(/.f64 #s(approx (pow (* (* (PI) n) 2) (/ (- 1 k) 2)) (fma.f64 (fma.f64 (.f64 k (.f64 (.f64 (sqrt.f64 (.f64 (PI.f64) n)) (pow.f64 (log.f64 (.f64 (.f64 (PI.f64) #s(literal 2 binary64)) n)) #s(literal 2 binary64))) (sqrt.f64 #s(literal 2 binary64)))) #s(literal 1/8 binary64) (.f64 (.f64 #s(literal -1/2 binary64) (sqrt.f64 (.f64 (PI.f64) n))) (.f64 (log.f64 (.f64 (.f64 (PI.f64) #s(literal 2 binary64)) n)) (sqrt.f64 #s(literal 2 binary64))))) k (sqrt.f64 (.f64 (.f64 (PI.f64) #s(literal 2 binary64)) n)))) (sqrt.f64 k))
	51.5%	(/.f64 #s(approx (* (pow (* (* (PI) 2) n) (/ (/ (- 1 k) 2) 2)) (pow (* (* (PI) 2) n) (/ (/ (- 1 k) 2) 2))) (fma.f64 (.f64 k (.f64 (.f64 (sqrt.f64 (.f64 (PI.f64) n)) (log.f64 (.f64 (.f64 #s(literal 2 binary64) n) (PI.f64)))) (sqrt.f64 #s(literal 2 binary64)))) #s(literal -1/2 binary64) (sqrt.f64 (.f64 (.f64 #s(literal 2 binary64) n) (PI.f64))))) (sqrt.f64 k))
	99.1%	(.f64 (pow.f64 (.f64 (*.f64 (PI.f64) #s(literal 2 binary64)) n) #s(approx (/ (- 1 k) 2) (fma.f64 #s(literal -1/2 binary64) k #s(literal 1/2 binary64)))) (pow.f64 k #s(literal -1/2 binary64)))
	98.4%	(.f64 (/.f64 #s(literal 1 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))) (pow.f64 (.f64 (.f64 (PI.f64) n) #s(literal 2 binary64)) #s(approx (/ (/ (- 1 k) 2) 2) (*.f64 (-.f64 (/.f64 #s(literal 1/4 binary64) k) #s(literal 1/4 binary64)) k)))))
	98.4%	(.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) (.f64 (pow.f64 (.f64 (.f64 (PI.f64) #s(literal 2 binary64)) n) (/.f64 (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 2 binary64)) #s(literal 2 binary64))) (.f64 (pow.f64 (.f64 (.f64 (PI.f64) n) #s(literal 2 binary64)) (/.f64 #s(approx (/ (/ (- 1 k) 2) 2) (.f64 (-.f64 (/.f64 #s(literal 1/4 binary64) k) #s(literal 1/4 binary64)) k)) #s(literal 2 binary64))) (pow.f64 (.f64 (.f64 (PI.f64) n) #s(literal 2 binary64)) (/.f64 #s(approx (/ (/ (- 1 k) 2) 2) (*.f64 (-.f64 (/.f64 #s(literal 1/4 binary64) k) #s(literal 1/4 binary64)) k)) #s(literal 2 binary64))))))
	74.4%	(.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) (.f64 (pow.f64 (.f64 (.f64 (PI.f64) #s(literal 2 binary64)) n) (/.f64 (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 2 binary64)) #s(literal 2 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 4 binary64))))))
	96.5%	(.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) (.f64 (pow.f64 (.f64 (.f64 (PI.f64) #s(literal 2 binary64)) n) (/.f64 (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 2 binary64)) #s(literal 2 binary64))) (exp.f64 (.f64 (log.f64 (.f64 (*.f64 #s(literal 2 binary64) n) (PI.f64))) (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 4 binary64))))))
✓	95.6%	(.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) (exp.f64 (.f64 (log.f64 (.f64 (.f64 (PI.f64) #s(literal 2 binary64)) n)) #s(approx (/ (- 1 k) 2) (*.f64 (-.f64 (/.f64 #s(literal 1/2 binary64) k) #s(literal 1/2 binary64)) k)))))
	95.8%	(.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) (exp.f64 (.f64 (log.f64 (.f64 (.f64 (PI.f64) #s(literal 2 binary64)) n)) #s(approx (/ (- 1 k) 2) #s(approx (* (- (/ 1/2 k) 1/2) k) (fma.f64 #s(literal -1/2 binary64) k #s(literal 1/2 binary64)))))))
	51.4%	(.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) #s(approx (pow ( (* 2 (PI)) n) (/ (- 1 k) 2)) (fma.f64 (.f64 (.f64 (.f64 (log.f64 (.f64 (.f64 (PI.f64) #s(literal 2 binary64)) n)) (sqrt.f64 #s(literal 2 binary64))) k) (sqrt.f64 (.f64 (PI.f64) n))) #s(literal -1/2 binary64) (sqrt.f64 (.f64 (.f64 (PI.f64) #s(literal 2 binary64)) n)))))
	50.9%	(.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) #s(approx (pow ( (* 2 (PI)) n) (/ (- 1 k) 2)) (sqrt.f64 (.f64 (.f64 (PI.f64) #s(literal 2 binary64)) n))))
	99.1%	(.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) k)) (pow.f64 (.f64 (*.f64 #s(literal 2 binary64) (PI.f64)) n) #s(approx (/ (- 1 k) 2) (fma.f64 #s(literal -1/2 binary64) k #s(literal 1/2 binary64)))))
	45.5%	#s(approx (/ (pow (* (* (PI) n) 2) (/ (- 1 k) 2)) (sqrt k)) (/.f64 (fma.f64 (.f64 (.f64 (log.f64 (.f64 (.f64 (PI.f64) #s(literal 2 binary64)) n)) (sqrt.f64 #s(literal 2 binary64))) (.f64 (pow.f64 k #s(literal 3/2 binary64)) (sqrt.f64 (.f64 (PI.f64) n)))) #s(literal -1/2 binary64) (sqrt.f64 (.f64 (.f64 (*.f64 (PI.f64) n) k) #s(literal 2 binary64)))) k))
	40.7%	#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))))
	40.7%	#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))))
✓	40.8%	#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))))
✓	40.8%	#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt.f64 (.f64 (.f64 (PI.f64) (/.f64 n k)) #s(literal 2 binary64))))
✓	40.8%	#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt.f64 (.f64 (.f64 n (/.f64 (PI.f64) k)) #s(literal 2 binary64))))

Compiler

Compiled 2 464 to 918 computations (62.7% saved)

regimes78.0ms (1.6%)

Memory

2.1MiB live, 99.5MiB allocated; 9ms collecting garbage

Counts

52 → 1

Calls

Call 1

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

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

Calls

4 calls:

33.0ms	(.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) (pow.f64 (.f64 (*.f64 #s(literal 2 binary64) (PI.f64)) n) (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 2 binary64))))
16.0ms	n
13.0ms	(.f64 (.f64 #s(literal 2 binary64) (PI.f64)) n)
13.0ms	k

Results

Accuracy	Segments	Branch
99.1%	1	`(.f64 (.f64 #s(literal 2 binary64) (PI.f64)) n)`
99.1%	1	`(.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) (pow.f64 (.f64 (*.f64 #s(literal 2 binary64) (PI.f64)) n) (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 2 binary64))))`
99.1%	1	`k`
99.1%	1	`n`

Compiler

Compiled 23 to 23 computations (0% saved)

regimes14.0ms (0.3%)

Memory

-14.6MiB live, 32.0MiB allocated; 2ms collecting garbage

Counts

9 → 2

Calls

Call 1

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

Outputs

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

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

Calls

4 calls:

5.0ms	k
3.0ms	n
3.0ms	(.f64 (.f64 #s(literal 2 binary64) (PI.f64)) 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
55.6%	2	`(.f64 (.f64 #s(literal 2 binary64) (PI.f64)) n)`
97.7%	3	`(.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) (pow.f64 (.f64 (*.f64 #s(literal 2 binary64) (PI.f64)) n) (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 2 binary64))))`
97.7%	2	`k`
55.6%	2	`n`

Compiler

Compiled 23 to 23 computations (0% saved)

regimes13.0ms (0.3%)

Memory

-15.5MiB live, 31.2MiB allocated; 2ms collecting garbage

Counts

8 → 1

Calls

Call 1

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

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

Calls

4 calls:

4.0ms	(.f64 (.f64 #s(literal 2 binary64) (PI.f64)) n)
3.0ms	k
3.0ms	n
2.0ms	(.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) (pow.f64 (.f64 (*.f64 #s(literal 2 binary64) (PI.f64)) n) (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 2 binary64))))

Results

Accuracy	Segments	Branch
51.0%	1	`(.f64 (.f64 #s(literal 2 binary64) (PI.f64)) n)`
51.0%	1	`n`
51.0%	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))))`
51.0%	1	`k`

Compiler

Compiled 23 to 23 computations (0% saved)

regimes8.0ms (0.2%)

Memory

25.2MiB live, 25.2MiB allocated; 0ms collecting garbage

Accuracy

Total -0.2b remaining (-0.4%)

Threshold costs -0.2b (-0.4%)

Counts

5 → 1

Calls

Call 1

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

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

Calls

4 calls:

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

Results

Accuracy	Segments	Branch
40.8%	1	`(.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) (pow.f64 (.f64 (*.f64 #s(literal 2 binary64) (PI.f64)) n) (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 2 binary64))))`
40.8%	1	`(.f64 (.f64 #s(literal 2 binary64) (PI.f64)) n)`
40.8%	1	`k`
40.8%	1	`n`

Compiler

Compiled 23 to 23 computations (0% saved)

bsearch20.0ms (0.4%)

Memory

-26.5MiB live, 27.2MiB allocated; 10ms collecting garbage

Algorithm

1×	binary-search

Stop Event

1×	narrow-enough

Steps

Time	Left	Right
19.0ms	0.01276731369293365	1.709898347262241

Samples

8.0ms

112×

valid

Compiler

Compiled 404 to 284 computations (29.7% saved)

Precisions

Click to see histograms. Total time spent on operations: 5.0ms

ival-pow: 2.0ms (38.4% of total)

ival-sqrt: 1.0ms (19.2% of total)

ival-div!: 1.0ms (19.2% of total)

ival-mult!: 1.0ms (19.2% of total)

ival-sub!: 0.0ms (0% of total)

adjust: 0.0ms (0% of total)

derivations27.0ms (0.5%)

Memory

38.7MiB live, 38.7MiB allocated; 0ms collecting garbage

Stop Event

1×

fuel

Compiler

Compiled 140 to 46 computations (67.1% saved)

preprocess34.0ms (0.7%)

Memory: -3.3MiB live, 43.6MiB allocated; 4ms collecting garbage
Compiler: Compiled 312 to 118 computations (62.2% saved)

end0.0ms (0%)

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

start0.0ms (0%)

analyze144.0ms (2.9%)

sample3.2s (64.9%)

explain236.0ms (4.7%)

preprocess46.0ms (0.9%)

series108.0ms (2.2%)

rewrite72.0ms (1.4%)

eval7.0ms (0.2%)

prune12.0ms (0.2%)

series111.0ms (2.2%)

rewrite78.0ms (1.6%)

eval37.0ms (0.7%)

prune27.0ms (0.5%)

series50.0ms (1%)

rewrite79.0ms (1.6%)

eval32.0ms (0.6%)

prune37.0ms (0.7%)

series217.0ms (4.4%)

rewrite174.0ms (3.5%)

eval35.0ms (0.7%)

prune46.0ms (0.9%)

regimes78.0ms (1.6%)

regimes14.0ms (0.3%)

regimes13.0ms (0.3%)

regimes8.0ms (0.2%)

bsearch20.0ms (0.4%)

derivations27.0ms (0.5%)

preprocess34.0ms (0.7%)

end0.0ms (0%)

Profiling