Metrics for Migdal et al, Equation (51)

start0.0ms (0%)

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

analyze153.0ms (1.3%)

Memory

-35.0MiB live, 197.5MiB allocated; 99ms 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)

sample3.8s (32.6%)

Memory

34.1MiB live, 4 525.0MiB allocated; 1.3s collecting garbage

Samples

1.3s	8 256×	0	valid
1.1s	4 485×	1	invalid
505.0ms	1 476×	2	invalid
53.0ms	239×	0	exit
32.0ms	371×	0	invalid

Precisions

Click to see histograms. Total time spent on operations: 1.9s

ival-pow: 485.0ms (24.9% of total)

ival-mult: 401.0ms (20.6% of total)

ival-div: 331.0ms (17% of total)

ival-sqrt: 253.0ms (13% of total)

ival-sub: 177.0ms (9.1% of total)

adjust: 160.0ms (8.2% of total)

ival-pi: 109.0ms (5.6% of total)

exact: 24.0ms (1.2% of total)

ival-assert: 6.0ms (0.3% of total)

Bogosity

explain143.0ms (1.2%)

Memory

-35.1MiB live, 203.0MiB allocated; 16ms collecting garbage

FPErrors

Click to see full error table

Ground Truth	Overpredictions	Example	Example	Subexpression
4	87	(1.6060379391112244e-158 2.046659867157457e-215)	-	`(pow.f64 (.f64 (.f64 #s(literal 2 binary64) (PI.f64)) n) (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 2 binary64)))`
0	0	-	-	`k`
0	0	-	-	`n`
0	0	-	-	`(/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 2 binary64))`
0	0	-	-	`#s(literal 1 binary64)`
0	0	-	-	`(.f64 (.f64 #s(literal 2 binary64) (PI.f64)) n)`
0	0	-	-	`(sqrt.f64 k)`
0	0	-	-	`#s(literal 2 binary64)`
0	0	-	-	`(/.f64 #s(literal 1 binary64) (sqrt.f64 k))`
0	0	-	-	`(-.f64 #s(literal 1 binary64) k)`
0	0	-	-	`(*.f64 #s(literal 2 binary64) (PI.f64))`
0	0	-	-	`(.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) (pow.f64 (.f64 (*.f64 #s(literal 2 binary64) (PI.f64)) n) (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 2 binary64))))`
0	0	-	-	`(PI.f64)`

Explanations

Click to see full explanations table

Operator	Subexpression	Explanation	Count
`pow.f64`	`(pow.f64 (.f64 (.f64 #s(literal 2 binary64) (PI.f64)) n) (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 2 binary64)))`	sensitivity	91	25

Confusion

	Predicted +	Predicted -
+	5	0
-	86	165

Precision

0.054945054945054944

Recall

1.0

Confusion?

	Predicted +	Predicted Maybe	Predicted -
+	5	0	0
-	86	25	140

Precision?

0.04310344827586207

Recall?

1.0

Freqs

test

number	freq
0	165
1	91

Total Confusion?

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

Precision?

1.0

Recall?

1.0

Samples

53.0ms

512×

valid

Compiler

Compiled 128 to 43 computations (66.4% saved)

Precisions

Click to see histograms. Total time spent on operations: 34.0ms

ival-pow: 9.0ms (26.8% of total)

ival-mult: 8.0ms (23.8% of total)

ival-div: 7.0ms (20.8% of total)

ival-sqrt: 4.0ms (11.9% of total)

ival-sub: 3.0ms (8.9% of total)

ival-pi: 2.0ms (5.9% of total)

exact: 1.0ms (3% of total)

adjust: 0.0ms (0% of total)

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

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

preprocess143.0ms (1.2%)

Memory

33.6MiB live, 175.8MiB allocated; 12ms collecting garbage

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	33	104
1	76	90
2	162	88
3	382	88
4	1615	88
0	13	16
0	22	16
1	37	14
2	58	14
3	136	14
4	533	14
5	3201	14
0	8098	14

Stop Event

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

Calls

Call 1

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

Outputs

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

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

Compiler

Compiled 16 to 13 computations (18.8% saved)

eval0.0ms (0%)

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

prune0.0ms (0%)

Memory

1.0MiB live, 1.0MiB allocated; 0ms collecting garbage

Alt Table

Click to see full alt table

Status	Accuracy	Program
▶	99.5%	(.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) (pow.f64 (.f64 (*.f64 #s(literal 2 binary64) (PI.f64)) n) (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 2 binary64))))

Compiler

Compiled 16 to 13 computations (18.8% saved)

series75.0ms (0.6%)

Memory

-4.1MiB live, 130.7MiB allocated; 16ms 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
30.0ms	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))
27.0ms	n	@	-inf	((* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (/ 1 (sqrt k)) 1 (sqrt k) k (pow (* (* 2 (PI)) n) (/ (- 1 k) 2)) (* (* 2 (PI)) n) (* 2 (PI)) 2 (PI) n (/ (- 1 k) 2) (- 1 k))
8.0ms	n	@	inf	((* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (/ 1 (sqrt k)) 1 (sqrt k) k (pow (* (* 2 (PI)) n) (/ (- 1 k) 2)) (* (* 2 (PI)) n) (* 2 (PI)) 2 (PI) n (/ (- 1 k) 2) (- 1 k))
5.0ms	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))

rewrite60.0ms (0.5%)

Memory

2.7MiB live, 53.1MiB allocated; 18ms 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))))

eval8.0ms (0.1%)

Memory: 15.1MiB live, 15.1MiB allocated; 0ms collecting garbage
Compiler: Compiled 1 740 to 286 computations (83.6% saved)

prune35.0ms (0.3%)

Memory

-1.9MiB live, 45.6MiB allocated; 3ms collecting garbage

Pruning

8 alts after pruning (8 fresh and 0 done)

	Pruned	Kept	Total
New	64	8	72
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	65	8	73

Accuracy

99.8%

Counts

73 → 8

Alt Table

Click to see full alt table

Status	Accuracy	Program
▶	99.5%	(/.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))
▶	99.5%	(.f64 (pow.f64 (pow.f64 k #s(literal -1 binary64)) #s(literal 1/2 binary64)) (pow.f64 (.f64 (*.f64 #s(literal 2 binary64) (PI.f64)) n) (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 2 binary64))))
	99.3%	(.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) (.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)))))
▶	76.6%	(.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)))))
	61.4%	(.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) #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)))))
▶	96.0%	(.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))))))
	53.0%	#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))
▶	37.8%	#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 630 to 384 computations (39% saved)

series167.0ms (1.4%)

Memory

-11.1MiB live, 221.7MiB allocated; 41ms collecting garbage

Counts

38 → 135

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

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

6 calls:

Time	Variable		Point	Expression
72.0ms	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)) (pow (exp 1/2) (* (+ (* -1 k) 1) (log (* (* (PI) 2) n)))) (exp 1/2) 1/2 (* (+ (* -1 k) 1) (log (* (* (PI) 2) n))) (+ (* -1 k) 1) -1 (log (* (* (PI) 2) n)) (* (/ 1 (sqrt k)) (* (pow (* (PI) 2) (/ (- 1 k) 2)) (pow n (/ (- 1 k) 2)))) (* (pow (* (PI) 2) (/ (- 1 k) 2)) (pow n (/ (- 1 k) 2))) (pow (* (PI) 2) (/ (- 1 k) 2)) (pow n (/ (- 1 k) 2)) (* (pow (pow k -1) 1/2) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (pow (pow k -1) 1/2) (pow k -1) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2)) (* (* 2 (PI)) n) (* 2 (PI)))
37.0ms	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)) (pow (exp 1/2) (* (+ (* -1 k) 1) (log (* (* (PI) 2) n)))) (exp 1/2) 1/2 (* (+ (* -1 k) 1) (log (* (* (PI) 2) n))) (+ (* -1 k) 1) -1 (log (* (* (PI) 2) n)) (* (/ 1 (sqrt k)) (* (pow (* (PI) 2) (/ (- 1 k) 2)) (pow n (/ (- 1 k) 2)))) (* (pow (* (PI) 2) (/ (- 1 k) 2)) (pow n (/ (- 1 k) 2))) (pow (* (PI) 2) (/ (- 1 k) 2)) (pow n (/ (- 1 k) 2)) (* (pow (pow k -1) 1/2) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (pow (pow k -1) 1/2) (pow k -1) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2)) (* (* 2 (PI)) n) (* 2 (PI)))
32.0ms	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)) (pow (exp 1/2) (* (+ (* -1 k) 1) (log (* (* (PI) 2) n)))) (exp 1/2) 1/2 (* (+ (* -1 k) 1) (log (* (* (PI) 2) n))) (+ (* -1 k) 1) -1 (log (* (* (PI) 2) n)) (* (/ 1 (sqrt k)) (* (pow (* (PI) 2) (/ (- 1 k) 2)) (pow n (/ (- 1 k) 2)))) (* (pow (* (PI) 2) (/ (- 1 k) 2)) (pow n (/ (- 1 k) 2))) (pow (* (PI) 2) (/ (- 1 k) 2)) (pow n (/ (- 1 k) 2)) (* (pow (pow k -1) 1/2) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (pow (pow k -1) 1/2) (pow k -1) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2)) (* (* 2 (PI)) n) (* 2 (PI)))
11.0ms	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)) (pow (exp 1/2) (* (+ (* -1 k) 1) (log (* (* (PI) 2) n)))) (exp 1/2) 1/2 (* (+ (* -1 k) 1) (log (* (* (PI) 2) n))) (+ (* -1 k) 1) -1 (log (* (* (PI) 2) n)) (* (/ 1 (sqrt k)) (* (pow (* (PI) 2) (/ (- 1 k) 2)) (pow n (/ (- 1 k) 2)))) (* (pow (* (PI) 2) (/ (- 1 k) 2)) (pow n (/ (- 1 k) 2))) (pow (* (PI) 2) (/ (- 1 k) 2)) (pow n (/ (- 1 k) 2)) (* (pow (pow k -1) 1/2) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (pow (pow k -1) 1/2) (pow k -1) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2)) (* (* 2 (PI)) n) (* 2 (PI)))
7.0ms	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)) (pow (exp 1/2) (* (+ (* -1 k) 1) (log (* (* (PI) 2) n)))) (exp 1/2) 1/2 (* (+ (* -1 k) 1) (log (* (* (PI) 2) n))) (+ (* -1 k) 1) -1 (log (* (* (PI) 2) n)) (* (/ 1 (sqrt k)) (* (pow (* (PI) 2) (/ (- 1 k) 2)) (pow n (/ (- 1 k) 2)))) (* (pow (* (PI) 2) (/ (- 1 k) 2)) (pow n (/ (- 1 k) 2))) (pow (* (PI) 2) (/ (- 1 k) 2)) (pow n (/ (- 1 k) 2)) (* (pow (pow k -1) 1/2) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (pow (pow k -1) 1/2) (pow k -1) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2)) (* (* 2 (PI)) n) (* 2 (PI)))

rewrite95.0ms (0.8%)

Memory

6.6MiB live, 99.5MiB allocated; 12ms collecting garbage

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	502	5153
0	562	4742
0	2334	4646

Stop Event

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

Counts

173 → 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)) #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))))))
(/.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)))))
(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))))
(exp.f64 #s(literal 1/2 binary64))
#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)))
(fma.f64 #s(literal -1 binary64) k #s(literal 1 binary64))
#s(literal -1 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 (PI.f64) #s(literal 2 binary64)) (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 2 binary64))) (pow.f64 n (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 2 binary64)))))
(.f64 (pow.f64 (.f64 (PI.f64) #s(literal 2 binary64)) (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 2 binary64))) (pow.f64 n (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 2 binary64))))
(pow.f64 (*.f64 (PI.f64) #s(literal 2 binary64)) (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 2 binary64)))
(pow.f64 n (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 2 binary64)))
(.f64 (pow.f64 (pow.f64 k #s(literal -1 binary64)) #s(literal 1/2 binary64)) (pow.f64 (.f64 (*.f64 #s(literal 2 binary64) (PI.f64)) n) (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 2 binary64))))
(pow.f64 (pow.f64 k #s(literal -1 binary64)) #s(literal 1/2 binary64))
(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 (.f64 #s(literal 2 binary64) (PI.f64)) n)
(*.f64 #s(literal 2 binary64) (PI.f64))
#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 (pow (exp 1/2) (* (+ (* -1 k) 1) (log (* (* (PI) 2) n)))) #s(hole binary64 (* (sqrt (* n (PI))) (sqrt 2))))
#s(approx (pow (exp 1/2) (* (+ (* -1 k) 1) (log (* (* (PI) 2) n)))) #s(hole binary64 (+ (* -1/2 (* (* k (* (log (* 2 (* n (PI)))) (sqrt 2))) (sqrt (* n (PI))))) (* (sqrt (* n (PI))) (sqrt 2)))))
#s(approx (pow (exp 1/2) (* (+ (* -1 k) 1) (log (* (* (PI) 2) n)))) #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 (exp 1/2) (* (+ (* -1 k) 1) (log (* (* (PI) 2) n)))) #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) 1) (log (* (* (PI) 2) n))) #s(hole binary64 (log (* 2 (* n (PI))))))
#s(approx (* (+ (* -1 k) 1) (log (* (* (PI) 2) n))) #s(hole binary64 (+ (log (* 2 (* n (PI)))) (* -1 (* k (log (* 2 (* n (PI)))))))))
#s(approx (+ (* -1 k) 1) #s(hole binary64 1))
#s(approx (+ (* -1 k) 1) #s(hole binary64 (+ 1 (* -1 k))))
#s(approx (* (/ 1 (sqrt k)) (* (pow (* (PI) 2) (/ (- 1 k) 2)) (pow n (/ (- 1 k) 2)))) #s(hole binary64 (* (sqrt (/ (* n (PI)) k)) (sqrt 2))))
#s(approx (* (/ 1 (sqrt k)) (* (pow (* (PI) 2) (/ (- 1 k) 2)) (pow n (/ (- 1 k) 2)))) #s(hole binary64 (/ (+ (* (sqrt (* k (* n (PI)))) (sqrt 2)) (* (sqrt (pow k 3)) (+ (* -1/2 (* (sqrt (* n (PI))) (* (log n) (sqrt 2)))) (* -1/2 (* (sqrt (* n (PI))) (* (log (* 2 (PI))) (sqrt 2))))))) k)))
#s(approx (* (/ 1 (sqrt k)) (* (pow (* (PI) 2) (/ (- 1 k) 2)) (pow n (/ (- 1 k) 2)))) #s(hole binary64 (/ (+ (* k (+ (* (sqrt k) (+ (* -1/2 (* (sqrt (* n (PI))) (* (log n) (sqrt 2)))) (* -1/2 (* (sqrt (* n (PI))) (* (log (* 2 (PI))) (sqrt 2)))))) (* (sqrt (pow k 3)) (+ (* 1/8 (* (sqrt (* n (PI))) (* (pow (log n) 2) (sqrt 2)))) (+ (* 1/8 (* (sqrt (* n (PI))) (* (pow (log (* 2 (PI))) 2) (sqrt 2)))) (* 1/4 (* (sqrt (* n (PI))) (* (log n) (* (log (* 2 (PI))) (sqrt 2)))))))))) (* (sqrt (* k (* n (PI)))) (sqrt 2))) k)))
#s(approx (* (/ 1 (sqrt k)) (* (pow (* (PI) 2) (/ (- 1 k) 2)) (pow n (/ (- 1 k) 2)))) #s(hole binary64 (/ (+ (* k (+ (* k (+ (* (sqrt k) (+ (* 1/8 (* (sqrt (* n (PI))) (* (pow (log n) 2) (sqrt 2)))) (+ (* 1/8 (* (sqrt (* n (PI))) (* (pow (log (* 2 (PI))) 2) (sqrt 2)))) (* 1/4 (* (sqrt (* n (PI))) (* (log n) (* (log (* 2 (PI))) (sqrt 2)))))))) (* (sqrt (pow k 3)) (+ (* -1/16 (* (sqrt (* n (PI))) (* (log n) (* (pow (log (* 2 (PI))) 2) (sqrt 2))))) (+ (* -1/16 (* (sqrt (* n (PI))) (* (pow (log n) 2) (* (log (* 2 (PI))) (sqrt 2))))) (+ (* -1/48 (* (sqrt (* n (PI))) (* (pow (log n) 3) (sqrt 2)))) (* -1/48 (* (sqrt (* n (PI))) (* (pow (log (* 2 (PI))) 3) (sqrt 2)))))))))) (* (sqrt k) (+ (* -1/2 (* (sqrt (* n (PI))) (* (log n) (sqrt 2)))) (* -1/2 (* (sqrt (* n (PI))) (* (log (* 2 (PI))) (sqrt 2)))))))) (* (sqrt (* k (* n (PI)))) (sqrt 2))) k)))
#s(approx (* (pow (* (PI) 2) (/ (- 1 k) 2)) (pow n (/ (- 1 k) 2))) #s(hole binary64 (* (sqrt (* n (PI))) (sqrt 2))))
#s(approx (* (pow (* (PI) 2) (/ (- 1 k) 2)) (pow n (/ (- 1 k) 2))) #s(hole binary64 (+ (* k (+ (* -1/2 (* (sqrt (* n (PI))) (* (log n) (sqrt 2)))) (* -1/2 (* (sqrt (* n (PI))) (* (log (* 2 (PI))) (sqrt 2)))))) (* (sqrt (* n (PI))) (sqrt 2)))))
#s(approx (* (pow (* (PI) 2) (/ (- 1 k) 2)) (pow n (/ (- 1 k) 2))) #s(hole binary64 (+ (* k (+ (* -1/2 (* (sqrt (* n (PI))) (* (log n) (sqrt 2)))) (+ (* -1/2 (* (sqrt (* n (PI))) (* (log (* 2 (PI))) (sqrt 2)))) (* k (+ (* 1/8 (* (sqrt (* n (PI))) (* (pow (log n) 2) (sqrt 2)))) (+ (* 1/8 (* (sqrt (* n (PI))) (* (pow (log (* 2 (PI))) 2) (sqrt 2)))) (* 1/4 (* (sqrt (* n (PI))) (* (log n) (* (log (* 2 (PI))) (sqrt 2))))))))))) (* (sqrt (* n (PI))) (sqrt 2)))))
#s(approx (* (pow (* (PI) 2) (/ (- 1 k) 2)) (pow n (/ (- 1 k) 2))) #s(hole binary64 (+ (* k (+ (* -1/2 (* (sqrt (* n (PI))) (* (log n) (sqrt 2)))) (+ (* -1/2 (* (sqrt (* n (PI))) (* (log (* 2 (PI))) (sqrt 2)))) (* k (+ (* 1/8 (* (sqrt (* n (PI))) (* (pow (log n) 2) (sqrt 2)))) (+ (* 1/8 (* (sqrt (* n (PI))) (* (pow (log (* 2 (PI))) 2) (sqrt 2)))) (+ (* 1/4 (* (sqrt (* n (PI))) (* (log n) (* (log (* 2 (PI))) (sqrt 2))))) (* k (+ (* -1/16 (* (sqrt (* n (PI))) (* (log n) (* (pow (log (* 2 (PI))) 2) (sqrt 2))))) (+ (* -1/16 (* (sqrt (* n (PI))) (* (pow (log n) 2) (* (log (* 2 (PI))) (sqrt 2))))) (+ (* -1/48 (* (sqrt (* n (PI))) (* (pow (log n) 3) (sqrt 2)))) (* -1/48 (* (sqrt (* n (PI))) (* (pow (log (* 2 (PI))) 3) (sqrt 2))))))))))))))) (* (sqrt (* n (PI))) (sqrt 2)))))
#s(approx (pow (* (PI) 2) (/ (- 1 k) 2)) #s(hole binary64 (* (sqrt (PI)) (sqrt 2))))
#s(approx (pow (* (PI) 2) (/ (- 1 k) 2)) #s(hole binary64 (+ (* -1/2 (* (* k (* (log (* 2 (PI))) (sqrt 2))) (sqrt (PI)))) (* (sqrt (PI)) (sqrt 2)))))
#s(approx (pow (* (PI) 2) (/ (- 1 k) 2)) #s(hole binary64 (+ (* k (+ (* -1/2 (* (sqrt (PI)) (* (log (* 2 (PI))) (sqrt 2)))) (* 1/8 (* (* k (* (pow (log (* 2 (PI))) 2) (sqrt 2))) (sqrt (PI)))))) (* (sqrt (PI)) (sqrt 2)))))
#s(approx (pow (* (PI) 2) (/ (- 1 k) 2)) #s(hole binary64 (+ (* k (+ (* -1/2 (* (sqrt (PI)) (* (log (* 2 (PI))) (sqrt 2)))) (* k (+ (* -1/48 (* (* k (* (pow (log (* 2 (PI))) 3) (sqrt 2))) (sqrt (PI)))) (* 1/8 (* (sqrt (PI)) (* (pow (log (* 2 (PI))) 2) (sqrt 2)))))))) (* (sqrt (PI)) (sqrt 2)))))
#s(approx (pow n (/ (- 1 k) 2)) #s(hole binary64 (sqrt n)))
#s(approx (pow n (/ (- 1 k) 2)) #s(hole binary64 (+ (sqrt n) (* -1/2 (* (* k (log n)) (sqrt n))))))
#s(approx (pow n (/ (- 1 k) 2)) #s(hole binary64 (+ (sqrt n) (* k (+ (* -1/2 (* (sqrt n) (log n))) (* 1/8 (* (* k (pow (log n) 2)) (sqrt n))))))))
#s(approx (pow n (/ (- 1 k) 2)) #s(hole binary64 (+ (sqrt n) (* k (+ (* -1/2 (* (sqrt n) (log n))) (* k (+ (* -1/48 (* (* k (pow (log n) 3)) (sqrt n))) (* 1/8 (* (sqrt n) (pow (log n) 2))))))))))
#s(approx (* (pow (pow k -1) 1/2) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) #s(hole binary64 (* (sqrt (/ (* n (PI)) k)) (sqrt 2))))
#s(approx (* (pow (pow k -1) 1/2) (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 (* (pow (pow k -1) 1/2) (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 (* (pow (pow k -1) 1/2) (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 (pow (pow k -1) 1/2) #s(hole binary64 (sqrt (/ 1 k))))
#s(approx (pow k -1) #s(hole binary64 (/ 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 (* n (PI)))) (- 1 k)))))))
#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))))
#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 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 (exp 1/2) (* (+ (* -1 k) 1) (log (* (* (PI) 2) n)))) #s(hole binary64 (exp (* 1/2 (* (log (* 2 (* n (PI)))) (- 1 k))))))
#s(approx (* (+ (* -1 k) 1) (log (* (* (PI) 2) n))) #s(hole binary64 (* -1 (* k (log (* 2 (* n (PI))))))))
#s(approx (* (+ (* -1 k) 1) (log (* (* (PI) 2) n))) #s(hole binary64 (* k (+ (* -1 (log (* 2 (* n (PI))))) (/ (log (* 2 (* n (PI)))) k)))))
#s(approx (+ (* -1 k) 1) #s(hole binary64 (* -1 k)))
#s(approx (+ (* -1 k) 1) #s(hole binary64 (* k (- (/ 1 k) 1))))
#s(approx (* (/ 1 (sqrt k)) (* (pow (* (PI) 2) (/ (- 1 k) 2)) (pow n (/ (- 1 k) 2)))) #s(hole binary64 (* (sqrt (/ 1 k)) (* (exp (* 1/2 (* (log n) (- 1 k)))) (exp (* 1/2 (* (log (* 2 (PI))) (- 1 k))))))))
#s(approx (* (pow (* (PI) 2) (/ (- 1 k) 2)) (pow n (/ (- 1 k) 2))) #s(hole binary64 (* (exp (* 1/2 (* (log n) (- 1 k)))) (exp (* 1/2 (* (log (* 2 (PI))) (- 1 k)))))))
#s(approx (pow (* (PI) 2) (/ (- 1 k) 2)) #s(hole binary64 (exp (* 1/2 (* (log (* 2 (PI))) (- 1 k))))))
#s(approx (pow n (/ (- 1 k) 2)) #s(hole binary64 (exp (* 1/2 (* (log n) (- 1 k))))))
#s(approx (* (pow (pow k -1) 1/2) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) #s(hole binary64 (* (sqrt (/ 1 k)) (exp (* 1/2 (* (log (* 2 (* n (PI)))) (- 1 k)))))))
#s(approx (/ (* 1 (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)))))))
#s(approx (pow (* (* (PI) 2) n) (/ (- 1 k) 2)) #s(hole binary64 (exp (* 1/2 (* (log (* 2 (* n (PI)))) (+ 1 (* -1 k)))))))
#s(approx (/ (- 1 k) 2) #s(hole binary64 (* -1 (* k (- 1/2 (* 1/2 (/ 1 k)))))))
#s(approx (- 1 k) #s(hole binary64 (* -1 (* k (- 1 (/ 1 k))))))
#s(approx (sqrt 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 (pow (exp 1/2) (* (+ (* -1 k) 1) (log (* (* (PI) 2) n)))) #s(hole binary64 (exp (* 1/2 (* (log (* 2 (* n (PI)))) (+ 1 (* -1 k)))))))
#s(approx (* (+ (* -1 k) 1) (log (* (* (PI) 2) n))) #s(hole binary64 (* -1 (* k (+ (log (* 2 (* n (PI)))) (* -1 (/ (log (* 2 (* n (PI)))) k)))))))
#s(approx (+ (* -1 k) 1) #s(hole binary64 (* -1 (* k (- 1 (/ 1 k))))))
#s(approx (* (/ 1 (sqrt k)) (* (pow (* (PI) 2) (/ (- 1 k) 2)) (pow n (/ (- 1 k) 2)))) #s(hole binary64 (* (sqrt (/ 1 k)) (* (exp (* 1/2 (* (log n) (+ 1 (* -1 k))))) (exp (* 1/2 (* (log (* 2 (PI))) (+ 1 (* -1 k)))))))))
#s(approx (* (pow (* (PI) 2) (/ (- 1 k) 2)) (pow n (/ (- 1 k) 2))) #s(hole binary64 (* (exp (* 1/2 (* (log n) (+ 1 (* -1 k))))) (exp (* 1/2 (* (log (* 2 (PI))) (+ 1 (* -1 k))))))))
#s(approx (pow (* (PI) 2) (/ (- 1 k) 2)) #s(hole binary64 (exp (* 1/2 (* (log (* 2 (PI))) (+ 1 (* -1 k)))))))
#s(approx (pow n (/ (- 1 k) 2)) #s(hole binary64 (exp (* 1/2 (* (log n) (+ 1 (* -1 k)))))))
#s(approx (* (pow (pow k -1) 1/2) (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 (pow (pow k -1) 1/2) #s(hole binary64 (* (sqrt (/ 1 k)) (pow (sqrt -1) 2))))
#s(approx (/ (* 1 (pow (* (* (PI) 2) n) (/ (- 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 (* (* (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)))))))
#s(approx (* (PI) n) #s(hole binary64 (* n (PI))))
#s(approx (pow (* (* 2 (PI)) n) (/ (- 1 k) 2)) #s(hole binary64 (exp (* 1/2 (* (+ (log n) (log (* 2 (PI)))) (- 1 k))))))
#s(approx (pow (exp 1/2) (* (+ (* -1 k) 1) (log (* (* (PI) 2) n)))) #s(hole binary64 (exp (* 1/2 (* (+ 1 (* -1 k)) (+ (log n) (log (* 2 (PI)))))))))
#s(approx (* (+ (* -1 k) 1) (log (* (* (PI) 2) n))) #s(hole binary64 (* (+ 1 (* -1 k)) (+ (log n) (log (* 2 (PI)))))))
#s(approx (log (* (* (PI) 2) n)) #s(hole binary64 (+ (log n) (log (* 2 (PI))))))
#s(approx (* (pow (pow k -1) 1/2) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) #s(hole binary64 (* (sqrt (/ 1 k)) (exp (* 1/2 (* (+ (log n) (log (* 2 (PI)))) (- 1 k)))))))
#s(approx (* (* 2 (PI)) n) #s(hole binary64 (* 2 (* n (PI)))))
#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))))))
#s(approx (pow (* (* (PI) 2) 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))))))
#s(approx (pow (exp 1/2) (* (+ (* -1 k) 1) (log (* (* (PI) 2) n)))) #s(hole binary64 (exp (* 1/2 (* (+ 1 (* -1 k)) (+ (log (* 2 (PI))) (* -1 (log (/ 1 n)))))))))
#s(approx (* (+ (* -1 k) 1) (log (* (* (PI) 2) n))) #s(hole binary64 (* (+ 1 (* -1 k)) (+ (log (* 2 (PI))) (* -1 (log (/ 1 n)))))))
#s(approx (log (* (* (PI) 2) n)) #s(hole binary64 (+ (log (* 2 (PI))) (* -1 (log (/ 1 n))))))
#s(approx (* (/ 1 (sqrt k)) (* (pow (* (PI) 2) (/ (- 1 k) 2)) (pow n (/ (- 1 k) 2)))) #s(hole binary64 (* (sqrt (/ 1 k)) (* (exp (* -1/2 (* (log (/ 1 n)) (- 1 k)))) (exp (* 1/2 (* (log (* 2 (PI))) (- 1 k))))))))
#s(approx (* (pow (* (PI) 2) (/ (- 1 k) 2)) (pow n (/ (- 1 k) 2))) #s(hole binary64 (* (exp (* -1/2 (* (log (/ 1 n)) (- 1 k)))) (exp (* 1/2 (* (log (* 2 (PI))) (- 1 k)))))))
#s(approx (pow n (/ (- 1 k) 2)) #s(hole binary64 (exp (* -1/2 (* (log (/ 1 n)) (- 1 k))))))
#s(approx (* (pow (pow k -1) 1/2) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) #s(hole binary64 (* (sqrt (/ 1 k)) (exp (* 1/2 (* (+ (log (* 2 (PI))) (* -1 (log (/ 1 n)))) (- 1 k)))))))
#s(approx (/ (* 1 (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))))))
#s(approx (pow (* (* (PI) 2) 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 (sqrt (* (/ (* (PI) n) 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 (exp 1/2) (* (+ (* -1 k) 1) (log (* (* (PI) 2) n)))) #s(hole binary64 (exp (* 1/2 (* (+ 1 (* -1 k)) (+ (log (* -2 (PI))) (* -1 (log (/ -1 n)))))))))
#s(approx (* (+ (* -1 k) 1) (log (* (* (PI) 2) n))) #s(hole binary64 (* (+ 1 (* -1 k)) (+ (log (* -2 (PI))) (* -1 (log (/ -1 n)))))))
#s(approx (log (* (* (PI) 2) n)) #s(hole binary64 (+ (log (* -2 (PI))) (* -1 (log (/ -1 n))))))
#s(approx (* (/ 1 (sqrt k)) (* (pow (* (PI) 2) (/ (- 1 k) 2)) (pow n (/ (- 1 k) 2)))) #s(hole binary64 (* (sqrt (/ 1 k)) (* (exp (* 1/2 (* (log (* 2 (PI))) (- 1 k)))) (exp (* 1/2 (* (+ (log -1) (* -1 (log (/ -1 n)))) (- 1 k))))))))
#s(approx (* (pow (* (PI) 2) (/ (- 1 k) 2)) (pow n (/ (- 1 k) 2))) #s(hole binary64 (* (exp (* 1/2 (* (log (* 2 (PI))) (- 1 k)))) (exp (* 1/2 (* (+ (log -1) (* -1 (log (/ -1 n)))) (- 1 k)))))))
#s(approx (pow n (/ (- 1 k) 2)) #s(hole binary64 (exp (* 1/2 (* (+ (log -1) (* -1 (log (/ -1 n)))) (- 1 k))))))
#s(approx (* (pow (pow k -1) 1/2) (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)))))))

Outputs
(.f64 (.f64 (pow.f64 k #s(literal -1/2 binary64)) (pow.f64 (*.f64 (PI.f64) #s(literal 2 binary64)) (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 2 binary64)))) (pow.f64 n (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 2 binary64))))
(.f64 (pow.f64 k #s(literal -1/2 binary64)) (pow.f64 (.f64 n (*.f64 (PI.f64) #s(literal 2 binary64))) (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 2 binary64))))
(.f64 (pow.f64 (.f64 n (*.f64 (PI.f64) #s(literal 2 binary64))) (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 2 binary64))) (pow.f64 k #s(literal -1/2 binary64)))
(.f64 #s(literal 1 binary64) (/.f64 (pow.f64 (.f64 n (*.f64 (PI.f64) #s(literal 2 binary64))) (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 2 binary64))) (sqrt.f64 k)))
(/.f64 (neg.f64 (pow.f64 (.f64 n (.f64 (PI.f64) #s(literal 2 binary64))) (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 2 binary64)))) (neg.f64 (sqrt.f64 k)))
(/.f64 (pow.f64 (.f64 n (.f64 (PI.f64) #s(literal 2 binary64))) (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 2 binary64))) (sqrt.f64 k))
(.f64 (pow.f64 (.f64 n (.f64 (PI.f64) #s(literal 2 binary64))) (/.f64 (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 2 binary64)) #s(literal 2 binary64))) (pow.f64 (.f64 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 (pow.f64 n (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 2 binary64))) (pow.f64 (.f64 (PI.f64) #s(literal 2 binary64)) (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 2 binary64))))
(.f64 (pow.f64 (.f64 (PI.f64) #s(literal 2 binary64)) (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 2 binary64))) (pow.f64 n (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 2 binary64))))
(.f64 (pow.f64 (.f64 n (*.f64 (PI.f64) #s(literal 2 binary64))) (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 2 binary64))) #s(literal 1 binary64))
(.f64 #s(literal 1 binary64) (pow.f64 (.f64 n (*.f64 (PI.f64) #s(literal 2 binary64))) (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 2 binary64))))
(pow.f64 (.f64 n (.f64 (PI.f64) #s(literal 2 binary64))) (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 2 binary64)))
(exp.f64 (.f64 (log.f64 (.f64 n (*.f64 (PI.f64) #s(literal 2 binary64)))) (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 2 binary64))))
#s(literal 1 binary64)
(.f64 (pow.f64 (.f64 n (.f64 (PI.f64) #s(literal 2 binary64))) (/.f64 (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 2 binary64)) #s(literal 2 binary64))) (pow.f64 (.f64 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 (pow.f64 n (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 2 binary64))) (pow.f64 (.f64 (PI.f64) #s(literal 2 binary64)) (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 2 binary64))))
(.f64 (pow.f64 (.f64 (PI.f64) #s(literal 2 binary64)) (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 2 binary64))) (pow.f64 n (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 2 binary64))))
(.f64 (pow.f64 (.f64 n (*.f64 (PI.f64) #s(literal 2 binary64))) (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 2 binary64))) #s(literal 1 binary64))
(.f64 #s(literal 1 binary64) (pow.f64 (.f64 n (*.f64 (PI.f64) #s(literal 2 binary64))) (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 2 binary64))))
(pow.f64 (.f64 n (.f64 (PI.f64) #s(literal 2 binary64))) (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 2 binary64)))
(exp.f64 (.f64 (log.f64 (.f64 n (*.f64 (PI.f64) #s(literal 2 binary64)))) (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 2 binary64))))
(.f64 (.f64 #s(literal 2 binary64) n) (PI.f64))
(.f64 (.f64 (PI.f64) n) #s(literal 2 binary64))
(.f64 (PI.f64) (.f64 #s(literal 2 binary64) n))
(.f64 n (.f64 (PI.f64) #s(literal 2 binary64)))
(.f64 (.f64 (PI.f64) #s(literal 2 binary64)) n)
(.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))
(PI.f64)
#s(literal 2 binary64)
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)
k
(pow.f64 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 (.f64 (PI.f64) n) k) #s(literal 2 binary64))))
(.f64 (.f64 (sqrt.f64 (/.f64 (*.f64 (PI.f64) n) k)) (sqrt.f64 #s(literal -2 binary64))) (sqrt.f64 #s(literal -1 binary64)))
(.f64 (sqrt.f64 #s(literal 2 binary64)) (sqrt.f64 (/.f64 (.f64 (PI.f64) n) k)))
(.f64 (sqrt.f64 (/.f64 (.f64 (PI.f64) n) k)) (sqrt.f64 #s(literal 2 binary64)))
(pow.f64 (.f64 (/.f64 (.f64 (PI.f64) n) k) #s(literal 2 binary64)) #s(literal 1/2 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 #s(literal 2 binary64) (/.f64 (.f64 (PI.f64) n) k))
(/.f64 (.f64 n (.f64 (PI.f64) #s(literal 2 binary64))) k)
(fma.f64 (PI.f64) (/.f64 n k) (/.f64 (*.f64 (PI.f64) n) k))
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#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 n (.f64 (PI.f64) #s(literal 2 binary64)))) #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 n (.f64 (PI.f64) #s(literal 2 binary64)))) (sqrt.f64 #s(literal 2 binary64))))) k (sqrt.f64 (.f64 n (.f64 (PI.f64) #s(literal 2 binary64))))))
#s(approx (pow (* (* 2 (PI)) n) (/ (- 1 k) 2)) (fma.f64 (fma.f64 (fma.f64 (.f64 (.f64 (.f64 k (pow.f64 (log.f64 (.f64 n (.f64 (PI.f64) #s(literal 2 binary64)))) #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 n (.f64 (PI.f64) #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 n (.f64 (PI.f64) #s(literal 2 binary64)))) (sqrt.f64 #s(literal 2 binary64))))) k (sqrt.f64 (.f64 n (.f64 (PI.f64) #s(literal 2 binary64))))))
#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 (* (* 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 n (.f64 (PI.f64) #s(literal 2 binary64)))) (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)) (pow (* (* 2 (PI)) 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 n (.f64 (PI.f64) #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 n (.f64 (PI.f64) #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 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 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 n (.f64 (PI.f64) #s(literal 2 binary64)))) #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 n (.f64 (PI.f64) #s(literal 2 binary64)))) #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 n (.f64 (PI.f64) #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 (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 k #s(literal -1/2 binary64)))
#s(approx (pow (* (* 2 (PI)) n) (/ (- 1 k) 2)) (sqrt.f64 (.f64 n (.f64 (PI.f64) #s(literal 2 binary64)))))
#s(approx (pow (* (* 2 (PI)) n) (/ (- 1 k) 2)) (fma.f64 (.f64 (.f64 (log.f64 (pow.f64 (.f64 n (.f64 (PI.f64) #s(literal 2 binary64))) k)) (sqrt.f64 #s(literal 2 binary64))) (sqrt.f64 (.f64 (PI.f64) n))) #s(literal -1/2 binary64) (sqrt.f64 (.f64 n (*.f64 (PI.f64) #s(literal 2 binary64))))))
#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 n (.f64 (PI.f64) #s(literal 2 binary64)))) #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 n (.f64 (PI.f64) #s(literal 2 binary64)))) (sqrt.f64 #s(literal 2 binary64))))) k (sqrt.f64 (.f64 n (.f64 (PI.f64) #s(literal 2 binary64))))))
#s(approx (pow (* (* 2 (PI)) n) (/ (- 1 k) 2)) (fma.f64 (fma.f64 (fma.f64 (.f64 (.f64 (.f64 k (pow.f64 (log.f64 (.f64 n (.f64 (PI.f64) #s(literal 2 binary64)))) #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 n (.f64 (PI.f64) #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 n (.f64 (PI.f64) #s(literal 2 binary64)))) (sqrt.f64 #s(literal 2 binary64))))) k (sqrt.f64 (.f64 n (.f64 (PI.f64) #s(literal 2 binary64))))))
#s(approx (pow (exp 1/2) (* (+ (* -1 k) 1) (log (* (* (PI) 2) n)))) (sqrt.f64 (.f64 n (.f64 (PI.f64) #s(literal 2 binary64)))))
#s(approx (pow (exp 1/2) (* (+ (* -1 k) 1) (log (* (* (PI) 2) n)))) (fma.f64 (.f64 (.f64 (log.f64 (pow.f64 (.f64 n (.f64 (PI.f64) #s(literal 2 binary64))) k)) (sqrt.f64 #s(literal 2 binary64))) (sqrt.f64 (.f64 (PI.f64) n))) #s(literal -1/2 binary64) (sqrt.f64 (.f64 n (*.f64 (PI.f64) #s(literal 2 binary64))))))
#s(approx (pow (exp 1/2) (* (+ (* -1 k) 1) (log (* (* (PI) 2) n)))) (fma.f64 (fma.f64 (.f64 k (.f64 (.f64 (sqrt.f64 (.f64 (PI.f64) n)) (pow.f64 (log.f64 (.f64 n (.f64 (PI.f64) #s(literal 2 binary64)))) #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 n (.f64 (PI.f64) #s(literal 2 binary64)))) (sqrt.f64 #s(literal 2 binary64))))) k (sqrt.f64 (.f64 n (.f64 (PI.f64) #s(literal 2 binary64))))))
#s(approx (pow (exp 1/2) (* (+ (* -1 k) 1) (log (* (* (PI) 2) n)))) (fma.f64 (fma.f64 (fma.f64 (.f64 (.f64 (.f64 k (pow.f64 (log.f64 (.f64 n (.f64 (PI.f64) #s(literal 2 binary64)))) #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 n (.f64 (PI.f64) #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 n (.f64 (PI.f64) #s(literal 2 binary64)))) (sqrt.f64 #s(literal 2 binary64))))) k (sqrt.f64 (.f64 n (.f64 (PI.f64) #s(literal 2 binary64))))))
#s(approx (* (+ (* -1 k) 1) (log (* (* (PI) 2) n))) (log.f64 (.f64 n (.f64 (PI.f64) #s(literal 2 binary64)))))
#s(approx (* (+ (* -1 k) 1) (log (* (* (PI) 2) n))) (fma.f64 (neg.f64 k) (log.f64 (.f64 n (.f64 (PI.f64) #s(literal 2 binary64)))) (log.f64 (.f64 n (.f64 (PI.f64) #s(literal 2 binary64))))))
#s(approx (+ (* -1 k) 1) #s(literal 1 binary64))
#s(approx (+ (* -1 k) 1) (fma.f64 #s(literal -1 binary64) k #s(literal 1 binary64)))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt.f64 (.f64 (/.f64 (.f64 (PI.f64) n) k) #s(literal 2 binary64))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (/.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 (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (/.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 (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (/.f64 (fma.f64 (fma.f64 (fma.f64 (fma.f64 (.f64 #s(literal -1/16 binary64) (sqrt.f64 (.f64 (PI.f64) n))) (.f64 (.f64 (log.f64 n) (pow.f64 (log.f64 (.f64 (PI.f64) #s(literal 2 binary64))) #s(literal 2 binary64))) (sqrt.f64 #s(literal 2 binary64))) (fma.f64 #s(literal -1/48 binary64) (fma.f64 (.f64 (sqrt.f64 (.f64 (PI.f64) n)) (pow.f64 (log.f64 n) #s(literal 3 binary64))) (sqrt.f64 #s(literal 2 binary64)) (.f64 (.f64 (sqrt.f64 (.f64 (PI.f64) n)) (pow.f64 (log.f64 (.f64 (PI.f64) #s(literal 2 binary64))) #s(literal 3 binary64))) (sqrt.f64 #s(literal 2 binary64)))) (.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))))))) (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 (* (* 2 (PI)) n) (/ (- 1 k) 2)) (sqrt.f64 (.f64 n (.f64 (PI.f64) #s(literal 2 binary64)))))
#s(approx (pow (* (* 2 (PI)) n) (/ (- 1 k) 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 n (*.f64 (PI.f64) #s(literal 2 binary64))))))
#s(approx (pow (* (* 2 (PI)) n) (/ (- 1 k) 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 n (.f64 (PI.f64) #s(literal 2 binary64))))))
#s(approx (pow (* (* 2 (PI)) n) (/ (- 1 k) 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 (log.f64 n) (pow.f64 (log.f64 (.f64 (PI.f64) #s(literal 2 binary64))) #s(literal 2 binary64))) (sqrt.f64 #s(literal 2 binary64))) (fma.f64 #s(literal -1/48 binary64) (fma.f64 (.f64 (sqrt.f64 (.f64 (PI.f64) n)) (pow.f64 (log.f64 n) #s(literal 3 binary64))) (sqrt.f64 #s(literal 2 binary64)) (.f64 (.f64 (sqrt.f64 (.f64 (PI.f64) n)) (pow.f64 (log.f64 (.f64 (PI.f64) #s(literal 2 binary64))) #s(literal 3 binary64))) (sqrt.f64 #s(literal 2 binary64)))) (.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))))))) 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 n (*.f64 (PI.f64) #s(literal 2 binary64))))))
#s(approx (pow (* (PI) 2) (/ (- 1 k) 2)) (sqrt.f64 (*.f64 (PI.f64) #s(literal 2 binary64))))
#s(approx (pow (* (PI) 2) (/ (- 1 k) 2)) (fma.f64 (.f64 k (.f64 (sqrt.f64 (PI.f64)) (.f64 (log.f64 (.f64 (PI.f64) #s(literal 2 binary64))) (sqrt.f64 #s(literal 2 binary64))))) #s(literal -1/2 binary64) (sqrt.f64 (*.f64 (PI.f64) #s(literal 2 binary64)))))
#s(approx (pow (* (PI) 2) (/ (- 1 k) 2)) (fma.f64 (fma.f64 (.f64 #s(literal 1/8 binary64) (.f64 (.f64 k (pow.f64 (log.f64 (.f64 (PI.f64) #s(literal 2 binary64))) #s(literal 2 binary64))) (sqrt.f64 #s(literal 2 binary64)))) (sqrt.f64 (PI.f64)) (.f64 (.f64 #s(literal -1/2 binary64) (sqrt.f64 (PI.f64))) (.f64 (log.f64 (.f64 (PI.f64) #s(literal 2 binary64))) (sqrt.f64 #s(literal 2 binary64))))) k (sqrt.f64 (*.f64 (PI.f64) #s(literal 2 binary64)))))
#s(approx (pow (* (PI) 2) (/ (- 1 k) 2)) (fma.f64 (fma.f64 (fma.f64 (.f64 (.f64 (.f64 k (pow.f64 (log.f64 (.f64 (PI.f64) #s(literal 2 binary64))) #s(literal 3 binary64))) (sqrt.f64 #s(literal 2 binary64))) (sqrt.f64 (PI.f64))) #s(literal -1/48 binary64) (.f64 (.f64 #s(literal 1/8 binary64) (sqrt.f64 (PI.f64))) (.f64 (pow.f64 (log.f64 (.f64 (PI.f64) #s(literal 2 binary64))) #s(literal 2 binary64)) (sqrt.f64 #s(literal 2 binary64))))) k (.f64 (.f64 #s(literal -1/2 binary64) (sqrt.f64 (PI.f64))) (.f64 (log.f64 (.f64 (PI.f64) #s(literal 2 binary64))) (sqrt.f64 #s(literal 2 binary64))))) k (sqrt.f64 (*.f64 (PI.f64) #s(literal 2 binary64)))))
#s(approx (pow n (/ (- 1 k) 2)) (sqrt.f64 n))
#s(approx (pow n (/ (- 1 k) 2)) (fma.f64 (.f64 #s(literal -1/2 binary64) (.f64 (log.f64 n) k)) (sqrt.f64 n) (sqrt.f64 n)))
#s(approx (pow n (/ (- 1 k) 2)) (fma.f64 (fma.f64 (.f64 #s(literal -1/2 binary64) (sqrt.f64 n)) (log.f64 n) (.f64 (.f64 #s(literal 1/8 binary64) (.f64 (pow.f64 (log.f64 n) #s(literal 2 binary64)) k)) (sqrt.f64 n))) k (sqrt.f64 n)))
#s(approx (pow n (/ (- 1 k) 2)) (fma.f64 (fma.f64 (fma.f64 (.f64 #s(literal 1/8 binary64) (sqrt.f64 n)) (pow.f64 (log.f64 n) #s(literal 2 binary64)) (.f64 (.f64 #s(literal -1/48 binary64) (.f64 (pow.f64 (log.f64 n) #s(literal 3 binary64)) k)) (sqrt.f64 n))) k (.f64 (.f64 #s(literal -1/2 binary64) (sqrt.f64 n)) (log.f64 n))) k (sqrt.f64 n)))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt.f64 (.f64 (/.f64 (.f64 (PI.f64) n) k) #s(literal 2 binary64))))
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#s(approx (* (* 2 (PI)) n) (.f64 n (.f64 (PI.f64) #s(literal 2 binary64))))
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eval36.0ms (0.3%)

Memory: 10.2MiB live, 56.0MiB allocated; 3ms collecting garbage
Compiler: Compiled 10 152 to 1 137 computations (88.8% saved)

prune344.0ms (3%)

Memory

-12.6MiB live, 312.8MiB allocated; 30ms collecting garbage

Pruning

12 alts after pruning (9 fresh and 3 done)

	Pruned	Kept	Total
New	327	6	333
Fresh	0	3	3
Picked	2	3	5
Done	0	0	0
Total	329	12	341

Accuracy

99.9%

Counts

341 → 12

Alt Table

Click to see full alt table

Status	Accuracy	Program
▶	99.4%	(/.f64 (.f64 (pow.f64 (.f64 n (.f64 (PI.f64) #s(literal 2 binary64))) (/.f64 (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 2 binary64)) #s(literal 2 binary64))) (pow.f64 (.f64 n (*.f64 (PI.f64) #s(literal 2 binary64))) (/.f64 (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 2 binary64)) #s(literal 2 binary64)))) (sqrt.f64 k))
✓	99.5%	(.f64 (pow.f64 (pow.f64 k #s(literal -1 binary64)) #s(literal 1/2 binary64)) (pow.f64 (.f64 (*.f64 #s(literal 2 binary64) (PI.f64)) n) (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 2 binary64))))
	96.1%	(.f64 (pow.f64 (exp.f64 (.f64 (log.f64 k) #s(literal -1 binary64))) #s(literal 1/2 binary64)) (pow.f64 (.f64 (.f64 #s(literal 2 binary64) (PI.f64)) n) (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 2 binary64))))
▶	99.3%	(.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) (.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)))))
✓	76.6%	(.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)))))
	73.7%	(.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) (.f64 (pow.f64 (.f64 (PI.f64) #s(literal 2 binary64)) (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 2 binary64))) (exp.f64 (.f64 (log.f64 n) (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 2 binary64))))))
▶	76.7%	(.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) (.f64 (*.f64 (pow.f64 (PI.f64) (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 2 binary64))) (pow.f64 #s(literal 2 binary64) (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 2 binary64)))) (pow.f64 n (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 2 binary64)))))
	61.4%	(.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) #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)))))
▶	96.0%	(.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) #s(approx (pow ( (* 2 (PI)) n) (/ (- 1 k) 2)) (.f64 (pow.f64 (exp.f64 #s(literal 1/2 binary64)) (/.f64 (.f64 (fma.f64 #s(literal -1 binary64) k #s(literal 1 binary64)) (log.f64 (.f64 n (.f64 (PI.f64) #s(literal 2 binary64))))) #s(literal 2 binary64))) (pow.f64 (exp.f64 #s(literal 1/2 binary64)) (/.f64 (.f64 (fma.f64 #s(literal -1 binary64) k #s(literal 1 binary64)) (log.f64 (.f64 n (*.f64 (PI.f64) #s(literal 2 binary64))))) #s(literal 2 binary64))))))
	95.5%	(.f64 (exp.f64 (.f64 (log.f64 (pow.f64 k #s(literal -1 binary64))) #s(literal 1/2 binary64))) #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))))))
▶	53.0%	#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))
✓	37.8%	#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 842 to 493 computations (41.4% saved)

series365.0ms (3.1%)

Memory

4.1MiB live, 336.5MiB allocated; 75ms collecting garbage

Counts

66 → 277

Calls

Call 1

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

Outputs
#s(approx (/ (* (pow (* n (* (PI) 2)) (/ (/ (- 1 k) 2) 2)) (pow (* n (* (PI) 2)) (/ (/ (- 1 k) 2) 2))) (sqrt k)) #s(hole binary64 (* (sqrt (/ (* n (PI)) k)) (sqrt 2))))
#s(approx (/ (* (pow (* n (* (PI) 2)) (/ (/ (- 1 k) 2) 2)) (pow (* n (* (PI) 2)) (/ (/ (- 1 k) 2) 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 (* n (* (PI) 2)) (/ (/ (- 1 k) 2) 2)) (pow (* n (* (PI) 2)) (/ (/ (- 1 k) 2) 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 (* n (* (PI) 2)) (/ (/ (- 1 k) 2) 2)) (pow (* n (* (PI) 2)) (/ (/ (- 1 k) 2) 2))) (sqrt k)) #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 (* n (* (PI) 2)) (/ (/ (- 1 k) 2) 2)) (pow (* n (* (PI) 2)) (/ (/ (- 1 k) 2) 2))) #s(hole binary64 (* (sqrt (* n (PI))) (sqrt 2))))
#s(approx (* (pow (* n (* (PI) 2)) (/ (/ (- 1 k) 2) 2)) (pow (* n (* (PI) 2)) (/ (/ (- 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 (* n (* (PI) 2)) (/ (/ (- 1 k) 2) 2)) (pow (* n (* (PI) 2)) (/ (/ (- 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 (* n (* (PI) 2)) (/ (/ (- 1 k) 2) 2)) (pow (* n (* (PI) 2)) (/ (/ (- 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 (* n (* (PI) 2)) (/ (/ (- 1 k) 2) 2)) #s(hole binary64 (pow (* 2 (* n (PI))) 1/4)))
#s(approx (pow (* n (* (PI) 2)) (/ (/ (- 1 k) 2) 2)) #s(hole binary64 (+ (* -1/4 (* (pow (* 2 (* n (PI))) 1/4) (* k (log (* 2 (* n (PI))))))) (pow (* 2 (* n (PI))) 1/4))))
#s(approx (pow (* n (* (PI) 2)) (/ (/ (- 1 k) 2) 2)) #s(hole binary64 (+ (* k (+ (* -1/4 (* (pow (* 2 (* n (PI))) 1/4) (log (* 2 (* n (PI)))))) (* 1/32 (* (pow (* 2 (* n (PI))) 1/4) (* k (pow (log (* 2 (* n (PI)))) 2)))))) (pow (* 2 (* n (PI))) 1/4))))
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Calls

6 calls:

Time	Variable		Point	Expression
166.0ms	n	@	0	((/ (* (pow (* n (* (PI) 2)) (/ (/ (- 1 k) 2) 2)) (pow (* n (* (PI) 2)) (/ (/ (- 1 k) 2) 2))) (sqrt k)) (* (pow (* n (* (PI) 2)) (/ (/ (- 1 k) 2) 2)) (pow (* n (* (PI) 2)) (/ (/ (- 1 k) 2) 2))) (pow (* n (* (PI) 2)) (/ (/ (- 1 k) 2) 2)) (* n (* (PI) 2)) n (* (PI) 2) (PI) 2 (/ (/ (- 1 k) 2) 2) (/ (- 1 k) 2) (- 1 k) 1 k (sqrt k) (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (/ (+ (* (+ (* (+ (* (* -1/48 (sqrt (* (* (pow k 3) n) (PI)))) (* (pow (log (* (* (PI) 2) n)) 3) (sqrt 2))) (* (* 1/8 (sqrt (* (* (PI) n) k))) (* (pow (log (* (* (PI) 2) n)) 2) (sqrt 2)))) k) (* (* -1/2 (sqrt (* (* (PI) n) k))) (* (log (* (* (PI) 2) n)) (sqrt 2)))) k) (sqrt (* (* (* (PI) n) k) 2))) k) (+ (* (+ (* (+ (* (* -1/48 (sqrt (* (* (pow k 3) n) (PI)))) (* (pow (log (* (* (PI) 2) n)) 3) (sqrt 2))) (* (* 1/8 (sqrt (* (* (PI) n) k))) (* (pow (log (* (* (PI) 2) n)) 2) (sqrt 2)))) k) (* (* -1/2 (sqrt (* (* (PI) n) k))) (* (log (* (* (PI) 2) n)) (sqrt 2)))) k) (sqrt (* (* (* (PI) n) k) 2))) (+ (* (+ (* (* -1/48 (sqrt (* (* (pow k 3) n) (PI)))) (* (pow (log (* (* (PI) 2) n)) 3) (sqrt 2))) (* (* 1/8 (sqrt (* (* (PI) n) k))) (* (pow (log (* (* (PI) 2) n)) 2) (sqrt 2)))) k) (* (* -1/2 (sqrt (* (* (PI) n) k))) (* (log (* (* (PI) 2) n)) (sqrt 2)))) (+ (* (* -1/48 (sqrt (* (* (pow k 3) n) (PI)))) (* (pow (log (* (* (PI) 2) n)) 3) (sqrt 2))) (* (* 1/8 (sqrt (* (* (PI) n) k))) (* (pow (log (* (* (PI) 2) n)) 2) (sqrt 2)))) (* -1/48 (sqrt (* (* (pow k 3) n) (PI)))) -1/48 (sqrt (* (* (pow k 3) n) (PI))) (* (* (pow k 3) n) (PI)) (* (pow k 3) n) (pow k 3) 3 (* (pow (log (* (* (PI) 2) n)) 3) (sqrt 2)) (pow (log (* (* (PI) 2) n)) 3) (log (* (* (PI) 2) n)) (* (* (PI) 2) n) (sqrt 2) (* (* 1/8 (sqrt (* (* (PI) n) k))) (* (pow (log (* (* (PI) 2) n)) 2) (sqrt 2))) (* 1/8 (sqrt (* (* (PI) n) k))) 1/8 (sqrt (* (* (PI) n) k)) (* (* (PI) n) k) (* (PI) n) (* (pow (log (* (* (PI) 2) n)) 2) (sqrt 2)) (pow (log (* (* (PI) 2) n)) 2) (* (* -1/2 (sqrt (* (* (PI) n) k))) (* (log (* (* (PI) 2) n)) (sqrt 2))) (* -1/2 (sqrt (* (* (PI) n) k))) -1/2 (* (log (* (* (PI) 2) n)) (sqrt 2)) (sqrt (* (* (* (PI) n) k) 2)) (* (* (* (PI) n) k) 2) (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2)) (* (pow (exp 1/2) (/ (* (+ (* -1 k) 1) (log (* n (* (PI) 2)))) 2)) (pow (exp 1/2) (/ (* (+ (* -1 k) 1) (log (* n (* (PI) 2)))) 2))) (pow (exp 1/2) (/ (* (+ (* -1 k) 1) (log (* n (* (PI) 2)))) 2)) (exp 1/2) 1/2 (/ (* (+ (* -1 k) 1) (log (* n (* (PI) 2)))) 2) (* (+ (* -1 k) 1) (log (* n (* (PI) 2)))) (+ (* -1 k) 1) -1 (log (* n (* (PI) 2))) (* (/ 1 (sqrt k)) (* (* (pow (PI) (/ (- 1 k) 2)) (pow 2 (/ (- 1 k) 2))) (pow n (/ (- 1 k) 2)))) (* (* (pow (PI) (/ (- 1 k) 2)) (pow 2 (/ (- 1 k) 2))) (pow n (/ (- 1 k) 2))) (* (pow (PI) (/ (- 1 k) 2)) (pow 2 (/ (- 1 k) 2))) (pow (PI) (/ (- 1 k) 2)) (pow 2 (/ (- 1 k) 2)) (pow n (/ (- 1 k) 2)) (* (/ 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)))
53.0ms	n	@	-inf	((/ (* (pow (* n (* (PI) 2)) (/ (/ (- 1 k) 2) 2)) (pow (* n (* (PI) 2)) (/ (/ (- 1 k) 2) 2))) (sqrt k)) (* (pow (* n (* (PI) 2)) (/ (/ (- 1 k) 2) 2)) (pow (* n (* (PI) 2)) (/ (/ (- 1 k) 2) 2))) (pow (* n (* (PI) 2)) (/ (/ (- 1 k) 2) 2)) (* n (* (PI) 2)) n (* (PI) 2) (PI) 2 (/ (/ (- 1 k) 2) 2) (/ (- 1 k) 2) (- 1 k) 1 k (sqrt k) (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (/ (+ (* (+ (* (+ (* (* -1/48 (sqrt (* (* (pow k 3) n) (PI)))) (* (pow (log (* (* (PI) 2) n)) 3) (sqrt 2))) (* (* 1/8 (sqrt (* (* (PI) n) k))) (* (pow (log (* (* (PI) 2) n)) 2) (sqrt 2)))) k) (* (* -1/2 (sqrt (* (* (PI) n) k))) (* (log (* (* (PI) 2) n)) (sqrt 2)))) k) (sqrt (* (* (* (PI) n) k) 2))) k) (+ (* (+ (* (+ (* (* -1/48 (sqrt (* (* (pow k 3) n) (PI)))) (* (pow (log (* (* (PI) 2) n)) 3) (sqrt 2))) (* (* 1/8 (sqrt (* (* (PI) n) k))) (* (pow (log (* (* (PI) 2) n)) 2) (sqrt 2)))) k) (* (* -1/2 (sqrt (* (* (PI) n) k))) (* (log (* (* (PI) 2) n)) (sqrt 2)))) k) (sqrt (* (* (* (PI) n) k) 2))) (+ (* (+ (* (* -1/48 (sqrt (* (* (pow k 3) n) (PI)))) (* (pow (log (* (* (PI) 2) n)) 3) (sqrt 2))) (* (* 1/8 (sqrt (* (* (PI) n) k))) (* (pow (log (* (* (PI) 2) n)) 2) (sqrt 2)))) k) (* (* -1/2 (sqrt (* (* (PI) n) k))) (* (log (* (* (PI) 2) n)) (sqrt 2)))) (+ (* (* -1/48 (sqrt (* (* (pow k 3) n) (PI)))) (* (pow (log (* (* (PI) 2) n)) 3) (sqrt 2))) (* (* 1/8 (sqrt (* (* (PI) n) k))) (* (pow (log (* (* (PI) 2) n)) 2) (sqrt 2)))) (* -1/48 (sqrt (* (* (pow k 3) n) (PI)))) -1/48 (sqrt (* (* (pow k 3) n) (PI))) (* (* (pow k 3) n) (PI)) (* (pow k 3) n) (pow k 3) 3 (* (pow (log (* (* (PI) 2) n)) 3) (sqrt 2)) (pow (log (* (* (PI) 2) n)) 3) (log (* (* (PI) 2) n)) (* (* (PI) 2) n) (sqrt 2) (* (* 1/8 (sqrt (* (* (PI) n) k))) (* (pow (log (* (* (PI) 2) n)) 2) (sqrt 2))) (* 1/8 (sqrt (* (* (PI) n) k))) 1/8 (sqrt (* (* (PI) n) k)) (* (* (PI) n) k) (* (PI) n) (* (pow (log (* (* (PI) 2) n)) 2) (sqrt 2)) (pow (log (* (* (PI) 2) n)) 2) (* (* -1/2 (sqrt (* (* (PI) n) k))) (* (log (* (* (PI) 2) n)) (sqrt 2))) (* -1/2 (sqrt (* (* (PI) n) k))) -1/2 (* (log (* (* (PI) 2) n)) (sqrt 2)) (sqrt (* (* (* (PI) n) k) 2)) (* (* (* (PI) n) k) 2) (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2)) (* (pow (exp 1/2) (/ (* (+ (* -1 k) 1) (log (* n (* (PI) 2)))) 2)) (pow (exp 1/2) (/ (* (+ (* -1 k) 1) (log (* n (* (PI) 2)))) 2))) (pow (exp 1/2) (/ (* (+ (* -1 k) 1) (log (* n (* (PI) 2)))) 2)) (exp 1/2) 1/2 (/ (* (+ (* -1 k) 1) (log (* n (* (PI) 2)))) 2) (* (+ (* -1 k) 1) (log (* n (* (PI) 2)))) (+ (* -1 k) 1) -1 (log (* n (* (PI) 2))) (* (/ 1 (sqrt k)) (* (* (pow (PI) (/ (- 1 k) 2)) (pow 2 (/ (- 1 k) 2))) (pow n (/ (- 1 k) 2)))) (* (* (pow (PI) (/ (- 1 k) 2)) (pow 2 (/ (- 1 k) 2))) (pow n (/ (- 1 k) 2))) (* (pow (PI) (/ (- 1 k) 2)) (pow 2 (/ (- 1 k) 2))) (pow (PI) (/ (- 1 k) 2)) (pow 2 (/ (- 1 k) 2)) (pow n (/ (- 1 k) 2)) (* (/ 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)))
49.0ms	n	@	inf	((/ (* (pow (* n (* (PI) 2)) (/ (/ (- 1 k) 2) 2)) (pow (* n (* (PI) 2)) (/ (/ (- 1 k) 2) 2))) (sqrt k)) (* (pow (* n (* (PI) 2)) (/ (/ (- 1 k) 2) 2)) (pow (* n (* (PI) 2)) (/ (/ (- 1 k) 2) 2))) (pow (* n (* (PI) 2)) (/ (/ (- 1 k) 2) 2)) (* n (* (PI) 2)) n (* (PI) 2) (PI) 2 (/ (/ (- 1 k) 2) 2) (/ (- 1 k) 2) (- 1 k) 1 k (sqrt k) (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (/ (+ (* (+ (* (+ (* (* -1/48 (sqrt (* (* (pow k 3) n) (PI)))) (* (pow (log (* (* (PI) 2) n)) 3) (sqrt 2))) (* (* 1/8 (sqrt (* (* (PI) n) k))) (* (pow (log (* (* (PI) 2) n)) 2) (sqrt 2)))) k) (* (* -1/2 (sqrt (* (* (PI) n) k))) (* (log (* (* (PI) 2) n)) (sqrt 2)))) k) (sqrt (* (* (* (PI) n) k) 2))) k) (+ (* (+ (* (+ (* (* -1/48 (sqrt (* (* (pow k 3) n) (PI)))) (* (pow (log (* (* (PI) 2) n)) 3) (sqrt 2))) (* (* 1/8 (sqrt (* (* (PI) n) k))) (* (pow (log (* (* (PI) 2) n)) 2) (sqrt 2)))) k) (* (* -1/2 (sqrt (* (* (PI) n) k))) (* (log (* (* (PI) 2) n)) (sqrt 2)))) k) (sqrt (* (* (* (PI) n) k) 2))) (+ (* (+ (* (* -1/48 (sqrt (* (* (pow k 3) n) (PI)))) (* (pow (log (* (* (PI) 2) n)) 3) (sqrt 2))) (* (* 1/8 (sqrt (* (* (PI) n) k))) (* (pow (log (* (* (PI) 2) n)) 2) (sqrt 2)))) k) (* (* -1/2 (sqrt (* (* (PI) n) k))) (* (log (* (* (PI) 2) n)) (sqrt 2)))) (+ (* (* -1/48 (sqrt (* (* (pow k 3) n) (PI)))) (* (pow (log (* (* (PI) 2) n)) 3) (sqrt 2))) (* (* 1/8 (sqrt (* (* (PI) n) k))) (* (pow (log (* (* (PI) 2) n)) 2) (sqrt 2)))) (* -1/48 (sqrt (* (* (pow k 3) n) (PI)))) -1/48 (sqrt (* (* (pow k 3) n) (PI))) (* (* (pow k 3) n) (PI)) (* (pow k 3) n) (pow k 3) 3 (* (pow (log (* (* (PI) 2) n)) 3) (sqrt 2)) (pow (log (* (* (PI) 2) n)) 3) (log (* (* (PI) 2) n)) (* (* (PI) 2) n) (sqrt 2) (* (* 1/8 (sqrt (* (* (PI) n) k))) (* (pow (log (* (* (PI) 2) n)) 2) (sqrt 2))) (* 1/8 (sqrt (* (* (PI) n) k))) 1/8 (sqrt (* (* (PI) n) k)) (* (* (PI) n) k) (* (PI) n) (* (pow (log (* (* (PI) 2) n)) 2) (sqrt 2)) (pow (log (* (* (PI) 2) n)) 2) (* (* -1/2 (sqrt (* (* (PI) n) k))) (* (log (* (* (PI) 2) n)) (sqrt 2))) (* -1/2 (sqrt (* (* (PI) n) k))) -1/2 (* (log (* (* (PI) 2) n)) (sqrt 2)) (sqrt (* (* (* (PI) n) k) 2)) (* (* (* (PI) n) k) 2) (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2)) (* (pow (exp 1/2) (/ (* (+ (* -1 k) 1) (log (* n (* (PI) 2)))) 2)) (pow (exp 1/2) (/ (* (+ (* -1 k) 1) (log (* n (* (PI) 2)))) 2))) (pow (exp 1/2) (/ (* (+ (* -1 k) 1) (log (* n (* (PI) 2)))) 2)) (exp 1/2) 1/2 (/ (* (+ (* -1 k) 1) (log (* n (* (PI) 2)))) 2) (* (+ (* -1 k) 1) (log (* n (* (PI) 2)))) (+ (* -1 k) 1) -1 (log (* n (* (PI) 2))) (* (/ 1 (sqrt k)) (* (* (pow (PI) (/ (- 1 k) 2)) (pow 2 (/ (- 1 k) 2))) (pow n (/ (- 1 k) 2)))) (* (* (pow (PI) (/ (- 1 k) 2)) (pow 2 (/ (- 1 k) 2))) (pow n (/ (- 1 k) 2))) (* (pow (PI) (/ (- 1 k) 2)) (pow 2 (/ (- 1 k) 2))) (pow (PI) (/ (- 1 k) 2)) (pow 2 (/ (- 1 k) 2)) (pow n (/ (- 1 k) 2)) (* (/ 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)))
36.0ms	k	@	-inf	((/ (* (pow (* n (* (PI) 2)) (/ (/ (- 1 k) 2) 2)) (pow (* n (* (PI) 2)) (/ (/ (- 1 k) 2) 2))) (sqrt k)) (* (pow (* n (* (PI) 2)) (/ (/ (- 1 k) 2) 2)) (pow (* n (* (PI) 2)) (/ (/ (- 1 k) 2) 2))) (pow (* n (* (PI) 2)) (/ (/ (- 1 k) 2) 2)) (* n (* (PI) 2)) n (* (PI) 2) (PI) 2 (/ (/ (- 1 k) 2) 2) (/ (- 1 k) 2) (- 1 k) 1 k (sqrt k) (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (/ (+ (* (+ (* (+ (* (* -1/48 (sqrt (* (* (pow k 3) n) (PI)))) (* (pow (log (* (* (PI) 2) n)) 3) (sqrt 2))) (* (* 1/8 (sqrt (* (* (PI) n) k))) (* (pow (log (* (* (PI) 2) n)) 2) (sqrt 2)))) k) (* (* -1/2 (sqrt (* (* (PI) n) k))) (* (log (* (* (PI) 2) n)) (sqrt 2)))) k) (sqrt (* (* (* (PI) n) k) 2))) k) (+ (* (+ (* (+ (* (* -1/48 (sqrt (* (* (pow k 3) n) (PI)))) (* (pow (log (* (* (PI) 2) n)) 3) (sqrt 2))) (* (* 1/8 (sqrt (* (* (PI) n) k))) (* (pow (log (* (* (PI) 2) n)) 2) (sqrt 2)))) k) (* (* -1/2 (sqrt (* (* (PI) n) k))) (* (log (* (* (PI) 2) n)) (sqrt 2)))) k) (sqrt (* (* (* (PI) n) k) 2))) (+ (* (+ (* (* -1/48 (sqrt (* (* (pow k 3) n) (PI)))) (* (pow (log (* (* (PI) 2) n)) 3) (sqrt 2))) (* (* 1/8 (sqrt (* (* (PI) n) k))) (* (pow (log (* (* (PI) 2) n)) 2) (sqrt 2)))) k) (* (* -1/2 (sqrt (* (* (PI) n) k))) (* (log (* (* (PI) 2) n)) (sqrt 2)))) (+ (* (* -1/48 (sqrt (* (* (pow k 3) n) (PI)))) (* (pow (log (* (* (PI) 2) n)) 3) (sqrt 2))) (* (* 1/8 (sqrt (* (* (PI) n) k))) (* (pow (log (* (* (PI) 2) n)) 2) (sqrt 2)))) (* -1/48 (sqrt (* (* (pow k 3) n) (PI)))) -1/48 (sqrt (* (* (pow k 3) n) (PI))) (* (* (pow k 3) n) (PI)) (* (pow k 3) n) (pow k 3) 3 (* (pow (log (* (* (PI) 2) n)) 3) (sqrt 2)) (pow (log (* (* (PI) 2) n)) 3) (log (* (* (PI) 2) n)) (* (* (PI) 2) n) (sqrt 2) (* (* 1/8 (sqrt (* (* (PI) n) k))) (* (pow (log (* (* (PI) 2) n)) 2) (sqrt 2))) (* 1/8 (sqrt (* (* (PI) n) k))) 1/8 (sqrt (* (* (PI) n) k)) (* (* (PI) n) k) (* (PI) n) (* (pow (log (* (* (PI) 2) n)) 2) (sqrt 2)) (pow (log (* (* (PI) 2) n)) 2) (* (* -1/2 (sqrt (* (* (PI) n) k))) (* (log (* (* (PI) 2) n)) (sqrt 2))) (* -1/2 (sqrt (* (* (PI) n) k))) -1/2 (* (log (* (* (PI) 2) n)) (sqrt 2)) (sqrt (* (* (* (PI) n) k) 2)) (* (* (* (PI) n) k) 2) (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2)) (* (pow (exp 1/2) (/ (* (+ (* -1 k) 1) (log (* n (* (PI) 2)))) 2)) (pow (exp 1/2) (/ (* (+ (* -1 k) 1) (log (* n (* (PI) 2)))) 2))) (pow (exp 1/2) (/ (* (+ (* -1 k) 1) (log (* n (* (PI) 2)))) 2)) (exp 1/2) 1/2 (/ (* (+ (* -1 k) 1) (log (* n (* (PI) 2)))) 2) (* (+ (* -1 k) 1) (log (* n (* (PI) 2)))) (+ (* -1 k) 1) -1 (log (* n (* (PI) 2))) (* (/ 1 (sqrt k)) (* (* (pow (PI) (/ (- 1 k) 2)) (pow 2 (/ (- 1 k) 2))) (pow n (/ (- 1 k) 2)))) (* (* (pow (PI) (/ (- 1 k) 2)) (pow 2 (/ (- 1 k) 2))) (pow n (/ (- 1 k) 2))) (* (pow (PI) (/ (- 1 k) 2)) (pow 2 (/ (- 1 k) 2))) (pow (PI) (/ (- 1 k) 2)) (pow 2 (/ (- 1 k) 2)) (pow n (/ (- 1 k) 2)) (* (/ 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)))
27.0ms	k	@	0	((/ (* (pow (* n (* (PI) 2)) (/ (/ (- 1 k) 2) 2)) (pow (* n (* (PI) 2)) (/ (/ (- 1 k) 2) 2))) (sqrt k)) (* (pow (* n (* (PI) 2)) (/ (/ (- 1 k) 2) 2)) (pow (* n (* (PI) 2)) (/ (/ (- 1 k) 2) 2))) (pow (* n (* (PI) 2)) (/ (/ (- 1 k) 2) 2)) (* n (* (PI) 2)) n (* (PI) 2) (PI) 2 (/ (/ (- 1 k) 2) 2) (/ (- 1 k) 2) (- 1 k) 1 k (sqrt k) (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (/ (+ (* (+ (* (+ (* (* -1/48 (sqrt (* (* (pow k 3) n) (PI)))) (* (pow (log (* (* (PI) 2) n)) 3) (sqrt 2))) (* (* 1/8 (sqrt (* (* (PI) n) k))) (* (pow (log (* (* (PI) 2) n)) 2) (sqrt 2)))) k) (* (* -1/2 (sqrt (* (* (PI) n) k))) (* (log (* (* (PI) 2) n)) (sqrt 2)))) k) (sqrt (* (* (* (PI) n) k) 2))) k) (+ (* (+ (* (+ (* (* -1/48 (sqrt (* (* (pow k 3) n) (PI)))) (* (pow (log (* (* (PI) 2) n)) 3) (sqrt 2))) (* (* 1/8 (sqrt (* (* (PI) n) k))) (* (pow (log (* (* (PI) 2) n)) 2) (sqrt 2)))) k) (* (* -1/2 (sqrt (* (* (PI) n) k))) (* (log (* (* (PI) 2) n)) (sqrt 2)))) k) (sqrt (* (* (* (PI) n) k) 2))) (+ (* (+ (* (* -1/48 (sqrt (* (* (pow k 3) n) (PI)))) (* (pow (log (* (* (PI) 2) n)) 3) (sqrt 2))) (* (* 1/8 (sqrt (* (* (PI) n) k))) (* (pow (log (* (* (PI) 2) n)) 2) (sqrt 2)))) k) (* (* -1/2 (sqrt (* (* (PI) n) k))) (* (log (* (* (PI) 2) n)) (sqrt 2)))) (+ (* (* -1/48 (sqrt (* (* (pow k 3) n) (PI)))) (* (pow (log (* (* (PI) 2) n)) 3) (sqrt 2))) (* (* 1/8 (sqrt (* (* (PI) n) k))) (* (pow (log (* (* (PI) 2) n)) 2) (sqrt 2)))) (* -1/48 (sqrt (* (* (pow k 3) n) (PI)))) -1/48 (sqrt (* (* (pow k 3) n) (PI))) (* (* (pow k 3) n) (PI)) (* (pow k 3) n) (pow k 3) 3 (* (pow (log (* (* (PI) 2) n)) 3) (sqrt 2)) (pow (log (* (* (PI) 2) n)) 3) (log (* (* (PI) 2) n)) (* (* (PI) 2) n) (sqrt 2) (* (* 1/8 (sqrt (* (* (PI) n) k))) (* (pow (log (* (* (PI) 2) n)) 2) (sqrt 2))) (* 1/8 (sqrt (* (* (PI) n) k))) 1/8 (sqrt (* (* (PI) n) k)) (* (* (PI) n) k) (* (PI) n) (* (pow (log (* (* (PI) 2) n)) 2) (sqrt 2)) (pow (log (* (* (PI) 2) n)) 2) (* (* -1/2 (sqrt (* (* (PI) n) k))) (* (log (* (* (PI) 2) n)) (sqrt 2))) (* -1/2 (sqrt (* (* (PI) n) k))) -1/2 (* (log (* (* (PI) 2) n)) (sqrt 2)) (sqrt (* (* (* (PI) n) k) 2)) (* (* (* (PI) n) k) 2) (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2)) (* (pow (exp 1/2) (/ (* (+ (* -1 k) 1) (log (* n (* (PI) 2)))) 2)) (pow (exp 1/2) (/ (* (+ (* -1 k) 1) (log (* n (* (PI) 2)))) 2))) (pow (exp 1/2) (/ (* (+ (* -1 k) 1) (log (* n (* (PI) 2)))) 2)) (exp 1/2) 1/2 (/ (* (+ (* -1 k) 1) (log (* n (* (PI) 2)))) 2) (* (+ (* -1 k) 1) (log (* n (* (PI) 2)))) (+ (* -1 k) 1) -1 (log (* n (* (PI) 2))) (* (/ 1 (sqrt k)) (* (* (pow (PI) (/ (- 1 k) 2)) (pow 2 (/ (- 1 k) 2))) (pow n (/ (- 1 k) 2)))) (* (* (pow (PI) (/ (- 1 k) 2)) (pow 2 (/ (- 1 k) 2))) (pow n (/ (- 1 k) 2))) (* (pow (PI) (/ (- 1 k) 2)) (pow 2 (/ (- 1 k) 2))) (pow (PI) (/ (- 1 k) 2)) (pow 2 (/ (- 1 k) 2)) (pow n (/ (- 1 k) 2)) (* (/ 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)))

rewrite221.0ms (1.9%)

Memory

43.4MiB live, 223.4MiB allocated; 22ms collecting garbage

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	1076	16397
0	1203	14506
1	5385	14356
0	8173	14142

Stop Event

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

Counts

343 → 753

Calls

Call 1

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

Outputs
(.f64 (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 (*.f64 (PI.f64) #s(literal 2 binary64)) n) (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 4 binary64))) (sqrt.f64 k)))
(/.f64 (neg.f64 (pow.f64 (.f64 (.f64 (PI.f64) #s(literal 2 binary64)) n) (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 2 binary64)))) (neg.f64 (sqrt.f64 k)))
(/.f64 (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 (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 n (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 2 binary64))))
(.f64 (pow.f64 (.f64 #s(literal 2 binary64) n) (.f64 #s(literal 2 binary64) (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 4 binary64)))) (pow.f64 (PI.f64) (.f64 #s(literal 2 binary64) (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 4 binary64)))))
(.f64 (pow.f64 (PI.f64) (.f64 #s(literal 2 binary64) (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 4 binary64)))) (pow.f64 (.f64 #s(literal 2 binary64) n) (.f64 #s(literal 2 binary64) (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 4 binary64)))))
(.f64 (pow.f64 (.f64 (PI.f64) n) (.f64 #s(literal 2 binary64) (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 4 binary64)))) (pow.f64 #s(literal 2 binary64) (.f64 #s(literal 2 binary64) (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 4 binary64)))))
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(pow.f64 (.f64 (.f64 (PI.f64) #s(literal 2 binary64)) n) (*.f64 #s(literal 2 binary64) (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 4 binary64))))
(pow.f64 (.f64 (.f64 (PI.f64) #s(literal 2 binary64)) n) (+.f64 (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 4 binary64)) (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 4 binary64))))
(pow.f64 (.f64 (.f64 (PI.f64) #s(literal 2 binary64)) n) (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 2 binary64)))
(/.f64 (sqrt.f64 (.f64 (.f64 (PI.f64) #s(literal 2 binary64)) n)) (pow.f64 (.f64 (.f64 (PI.f64) #s(literal 2 binary64)) n) (/.f64 k #s(literal 2 binary64))))
(exp.f64 (.f64 (log.f64 (pow.f64 (.f64 (*.f64 (PI.f64) #s(literal 2 binary64)) n) #s(literal 2 binary64))) (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 4 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)))
(exp.f64 (.f64 (log.f64 (.f64 (.f64 (PI.f64) #s(literal 2 binary64)) n)) (.f64 #s(literal 2 binary64) (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 4 binary64)))))
(exp.f64 (.f64 (log.f64 (.f64 (*.f64 (PI.f64) #s(literal 2 binary64)) n)) (+.f64 (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 4 binary64)) (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 4 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 (cosh.f64 (.f64 (log.f64 (.f64 (.f64 (PI.f64) #s(literal 2 binary64)) n)) (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 2 binary64)))) (sinh.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 (pow.f64 (.f64 #s(literal 2 binary64) n) (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 4 binary64))) (pow.f64 (PI.f64) (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 4 binary64))))
(.f64 (pow.f64 (.f64 (PI.f64) n) (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 4 binary64))) (pow.f64 #s(literal 2 binary64) (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 4 binary64))))
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(exp.f64 (.f64 (log.f64 (.f64 (*.f64 (PI.f64) #s(literal 2 binary64)) n)) (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 4 binary64))))
(+.f64 (cosh.f64 (.f64 (log.f64 (.f64 (.f64 (PI.f64) #s(literal 2 binary64)) n)) (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 4 binary64)))) (sinh.f64 (.f64 (log.f64 (.f64 (.f64 (PI.f64) #s(literal 2 binary64)) n)) (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 4 binary64)))))
(.f64 (.f64 #s(literal 2 binary64) n) (PI.f64))
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#s(approx (pow (* (* (PI) 2) n) (/ (/ (- 1 k) 2) 2)) (pow.f64 (.f64 (.f64 (PI.f64) #s(literal 2 binary64)) n) #s(literal 1/4 binary64)))
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#s(approx (+ (* -1 k) 1) (neg.f64 k))
#s(approx (+ (* -1 k) 1) (*.f64 (-.f64 (pow.f64 k #s(literal -1 binary64)) #s(literal 1 binary64)) k))
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#s(approx (pow (PI) (/ (- 1 k) 2)) (exp.f64 (*.f64 (log.f64 (sqrt.f64 (PI.f64))) (-.f64 #s(literal 1 binary64) k))))
#s(approx (pow 2 (/ (- 1 k) 2)) (exp.f64 (*.f64 (log.f64 (sqrt.f64 #s(literal 2 binary64))) (-.f64 #s(literal 1 binary64) k))))
#s(approx (pow n (/ (- 1 k) 2)) (exp.f64 (*.f64 (log.f64 (sqrt.f64 n)) (-.f64 #s(literal 1 binary64) k))))
#s(approx (* (/ 1 (sqrt k)) (* (* (pow (PI) (/ (- 1 k) 2)) (pow 2 (/ (- 1 k) 2))) (pow n (/ (- 1 k) 2)))) (.f64 (pow.f64 (pow.f64 (exp.f64 #s(literal 1/4 binary64)) (.f64 (log.f64 (.f64 (.f64 (PI.f64) #s(literal 2 binary64)) n)) (-.f64 #s(literal 1 binary64) k))) #s(literal 2 binary64)) (pow.f64 k #s(literal -1/2 binary64))))
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#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) #s(literal 2 binary64)) n)) (-.f64 #s(literal 1 binary64) k))))
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#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) 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 (sqrt k) (neg.f64 (*.f64 #s(literal -1 binary64) (sqrt.f64 k))))
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#s(approx (/ (+ (* (+ (* (+ (* (* -1/48 (sqrt (* (* (pow k 3) n) (PI)))) (* (pow (log (* (* (PI) 2) n)) 3) (sqrt 2))) (* (* 1/8 (sqrt (* (* (PI) n) k))) (* (pow (log (* (* (PI) 2) n)) 2) (sqrt 2)))) k) (* (* -1/2 (sqrt (* (* (PI) n) k))) (* (log (* (* (PI) 2) n)) (sqrt 2)))) k) (sqrt (* (* (* (PI) n) k) 2))) k) (.f64 (.f64 #s(literal -1/48 binary64) (sqrt.f64 (.f64 (.f64 (pow.f64 k #s(literal 5 binary64)) n) (PI.f64)))) (.f64 (pow.f64 (neg.f64 (log.f64 (.f64 (*.f64 (PI.f64) #s(literal 2 binary64)) n))) #s(literal 3 binary64)) (sqrt.f64 #s(literal 2 binary64)))))
#s(approx (/ (+ (* (+ (* (+ (* (* -1/48 (sqrt (* (* (pow k 3) n) (PI)))) (* (pow (log (* (* (PI) 2) n)) 3) (sqrt 2))) (* (* 1/8 (sqrt (* (* (PI) n) k))) (* (pow (log (* (* (PI) 2) n)) 2) (sqrt 2)))) k) (* (* -1/2 (sqrt (* (* (PI) n) k))) (* (log (* (* (PI) 2) n)) (sqrt 2)))) k) (sqrt (* (* (* (PI) n) k) 2))) k) (.f64 (pow.f64 (neg.f64 k) #s(literal 3 binary64)) (fma.f64 (.f64 #s(literal 1/48 binary64) (sqrt.f64 (/.f64 (.f64 (PI.f64) n) k))) (.f64 (pow.f64 (neg.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) (/.f64 (sqrt.f64 (.f64 (PI.f64) n)) (pow.f64 k #s(literal 3/2 binary64)))) (.f64 (.f64 (sqrt.f64 #s(literal 2 binary64)) #s(literal -1 binary64)) (pow.f64 (log.f64 (.f64 (*.f64 (PI.f64) #s(literal 2 binary64)) n)) #s(literal 2 binary64)))))))
#s(approx (/ (+ (* (+ (* (+ (* (* -1/48 (sqrt (* (* (pow k 3) n) (PI)))) (* (pow (log (* (* (PI) 2) n)) 3) (sqrt 2))) (* (* 1/8 (sqrt (* (* (PI) n) k))) (* (pow (log (* (* (PI) 2) n)) 2) (sqrt 2)))) k) (* (* -1/2 (sqrt (* (* (PI) n) k))) (* (log (* (* (PI) 2) n)) (sqrt 2)))) k) (sqrt (* (* (* (PI) n) k) 2))) k) (.f64 (pow.f64 (neg.f64 k) #s(literal 3 binary64)) (fma.f64 (.f64 #s(literal 1/48 binary64) (sqrt.f64 (/.f64 (.f64 (PI.f64) n) k))) (.f64 (pow.f64 (neg.f64 (log.f64 (.f64 (.f64 (PI.f64) #s(literal 2 binary64)) n))) #s(literal 3 binary64)) (sqrt.f64 #s(literal 2 binary64))) (neg.f64 (/.f64 (fma.f64 (.f64 #s(literal -1/8 binary64) (sqrt.f64 (/.f64 (.f64 (PI.f64) n) k))) (.f64 (.f64 (sqrt.f64 #s(literal 2 binary64)) #s(literal -1 binary64)) (pow.f64 (log.f64 (.f64 (.f64 (PI.f64) #s(literal 2 binary64)) n)) #s(literal 2 binary64))) (.f64 (.f64 #s(literal 1/2 binary64) (/.f64 (sqrt.f64 (.f64 (PI.f64) n)) (pow.f64 k #s(literal 3/2 binary64)))) (.f64 (neg.f64 (log.f64 (.f64 (.f64 (PI.f64) #s(literal 2 binary64)) n))) (sqrt.f64 #s(literal 2 binary64))))) k)))))
#s(approx (/ (+ (* (+ (* (+ (* (* -1/48 (sqrt (* (* (pow k 3) n) (PI)))) (* (pow (log (* (* (PI) 2) n)) 3) (sqrt 2))) (* (* 1/8 (sqrt (* (* (PI) n) k))) (* (pow (log (* (* (PI) 2) n)) 2) (sqrt 2)))) k) (* (* -1/2 (sqrt (* (* (PI) n) k))) (* (log (* (* (PI) 2) n)) (sqrt 2)))) k) (sqrt (* (* (* (PI) n) k) 2))) k) (.f64 (pow.f64 (neg.f64 k) #s(literal 3 binary64)) (fma.f64 (.f64 #s(literal 1/48 binary64) (sqrt.f64 (/.f64 (.f64 (PI.f64) n) k))) (.f64 (pow.f64 (neg.f64 (log.f64 (.f64 (.f64 (PI.f64) #s(literal 2 binary64)) n))) #s(literal 3 binary64)) (sqrt.f64 #s(literal 2 binary64))) (neg.f64 (/.f64 (fma.f64 (.f64 #s(literal -1/8 binary64) (sqrt.f64 (/.f64 (.f64 (PI.f64) n) k))) (.f64 (.f64 (sqrt.f64 #s(literal 2 binary64)) #s(literal -1 binary64)) (pow.f64 (log.f64 (.f64 (.f64 (PI.f64) #s(literal 2 binary64)) n)) #s(literal 2 binary64))) (neg.f64 (/.f64 (fma.f64 (.f64 #s(literal -1/2 binary64) (sqrt.f64 (/.f64 (.f64 (PI.f64) n) k))) (.f64 (neg.f64 (log.f64 (.f64 (.f64 (PI.f64) #s(literal 2 binary64)) n))) (sqrt.f64 #s(literal 2 binary64))) (.f64 (/.f64 (sqrt.f64 (*.f64 (PI.f64) n)) (pow.f64 k #s(literal 3/2 binary64))) (sqrt.f64 #s(literal 2 binary64)))) k))) k)))))
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#s(approx (+ (* (+ (* (+ (* (* -1/48 (sqrt (* (* (pow k 3) n) (PI)))) (* (pow (log (* (* (PI) 2) n)) 3) (sqrt 2))) (* (* 1/8 (sqrt (* (* (PI) n) k))) (* (pow (log (* (* (PI) 2) n)) 2) (sqrt 2)))) k) (* (* -1/2 (sqrt (* (* (PI) n) k))) (* (log (* (* (PI) 2) n)) (sqrt 2)))) k) (sqrt (* (* (* (PI) n) k) 2))) (.f64 (fma.f64 (.f64 #s(literal -1/8 binary64) (/.f64 (sqrt.f64 (.f64 (PI.f64) n)) (pow.f64 k #s(literal 3/2 binary64)))) (.f64 (.f64 (sqrt.f64 #s(literal 2 binary64)) #s(literal -1 binary64)) (pow.f64 (log.f64 (.f64 (.f64 (PI.f64) #s(literal 2 binary64)) n)) #s(literal 2 binary64))) (.f64 (.f64 #s(literal -1/48 binary64) (sqrt.f64 (/.f64 (.f64 (PI.f64) n) k))) (.f64 (pow.f64 (neg.f64 (log.f64 (.f64 (*.f64 (PI.f64) #s(literal 2 binary64)) n))) #s(literal 3 binary64)) (sqrt.f64 #s(literal 2 binary64))))) (pow.f64 k #s(literal 4 binary64))))
#s(approx (+ (* (+ (* (+ (* (* -1/48 (sqrt (* (* (pow k 3) n) (PI)))) (* (pow (log (* (* (PI) 2) n)) 3) (sqrt 2))) (* (* 1/8 (sqrt (* (* (PI) n) k))) (* (pow (log (* (* (PI) 2) n)) 2) (sqrt 2)))) k) (* (* -1/2 (sqrt (* (* (PI) n) k))) (* (log (* (* (PI) 2) n)) (sqrt 2)))) k) (sqrt (* (* (* (PI) n) k) 2))) (.f64 (fma.f64 (.f64 #s(literal -1/48 binary64) (sqrt.f64 (/.f64 (.f64 (PI.f64) n) k))) (.f64 (pow.f64 (neg.f64 (log.f64 (.f64 (.f64 (PI.f64) #s(literal 2 binary64)) n))) #s(literal 3 binary64)) (sqrt.f64 #s(literal 2 binary64))) (neg.f64 (/.f64 (fma.f64 (.f64 #s(literal 1/8 binary64) (sqrt.f64 (/.f64 (.f64 (PI.f64) n) k))) (.f64 (.f64 (sqrt.f64 #s(literal 2 binary64)) #s(literal -1 binary64)) (pow.f64 (log.f64 (.f64 (.f64 (PI.f64) #s(literal 2 binary64)) n)) #s(literal 2 binary64))) (.f64 (.f64 #s(literal -1/2 binary64) (/.f64 (sqrt.f64 (.f64 (PI.f64) n)) (pow.f64 k #s(literal 3/2 binary64)))) (.f64 (neg.f64 (log.f64 (.f64 (.f64 (PI.f64) #s(literal 2 binary64)) n))) (sqrt.f64 #s(literal 2 binary64))))) k))) (pow.f64 k #s(literal 4 binary64))))
#s(approx (+ (* (+ (* (+ (* (* -1/48 (sqrt (* (* (pow k 3) n) (PI)))) (* (pow (log (* (* (PI) 2) n)) 3) (sqrt 2))) (* (* 1/8 (sqrt (* (* (PI) n) k))) (* (pow (log (* (* (PI) 2) n)) 2) (sqrt 2)))) k) (* (* -1/2 (sqrt (* (* (PI) n) k))) (* (log (* (* (PI) 2) n)) (sqrt 2)))) k) (sqrt (* (* (* (PI) n) k) 2))) (.f64 (fma.f64 (.f64 #s(literal -1/48 binary64) (sqrt.f64 (/.f64 (.f64 (PI.f64) n) k))) (.f64 (pow.f64 (neg.f64 (log.f64 (.f64 (.f64 (PI.f64) #s(literal 2 binary64)) n))) #s(literal 3 binary64)) (sqrt.f64 #s(literal 2 binary64))) (neg.f64 (/.f64 (fma.f64 (.f64 #s(literal 1/8 binary64) (sqrt.f64 (/.f64 (.f64 (PI.f64) n) k))) (.f64 (.f64 (sqrt.f64 #s(literal 2 binary64)) #s(literal -1 binary64)) (pow.f64 (log.f64 (.f64 (.f64 (PI.f64) #s(literal 2 binary64)) n)) #s(literal 2 binary64))) (neg.f64 (/.f64 (fma.f64 (.f64 #s(literal 1/2 binary64) (sqrt.f64 (/.f64 (.f64 (PI.f64) n) k))) (.f64 (neg.f64 (log.f64 (.f64 (.f64 (PI.f64) #s(literal 2 binary64)) n))) (sqrt.f64 #s(literal 2 binary64))) (neg.f64 (.f64 (/.f64 (sqrt.f64 (*.f64 (PI.f64) n)) (pow.f64 k #s(literal 3/2 binary64))) (sqrt.f64 #s(literal 2 binary64))))) k))) k))) (pow.f64 k #s(literal 4 binary64))))
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#s(approx (+ (* (+ (* (* -1/48 (sqrt (* (* (pow k 3) n) (PI)))) (* (pow (log (* (* (PI) 2) n)) 3) (sqrt 2))) (* (* 1/8 (sqrt (* (* (PI) n) k))) (* (pow (log (* (* (PI) 2) n)) 2) (sqrt 2)))) k) (* (* -1/2 (sqrt (* (* (PI) n) k))) (* (log (* (* (PI) 2) n)) (sqrt 2)))) (.f64 (pow.f64 (neg.f64 k) #s(literal 3 binary64)) (fma.f64 (.f64 #s(literal 1/48 binary64) (sqrt.f64 (/.f64 (.f64 (PI.f64) n) k))) (.f64 (pow.f64 (neg.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) (/.f64 (sqrt.f64 (.f64 (PI.f64) n)) (pow.f64 k #s(literal 3/2 binary64)))) (.f64 (.f64 (sqrt.f64 #s(literal 2 binary64)) #s(literal -1 binary64)) (pow.f64 (log.f64 (.f64 (*.f64 (PI.f64) #s(literal 2 binary64)) n)) #s(literal 2 binary64)))))))
#s(approx (+ (* (+ (* (* -1/48 (sqrt (* (* (pow k 3) n) (PI)))) (* (pow (log (* (* (PI) 2) n)) 3) (sqrt 2))) (* (* 1/8 (sqrt (* (* (PI) n) k))) (* (pow (log (* (* (PI) 2) n)) 2) (sqrt 2)))) k) (* (* -1/2 (sqrt (* (* (PI) n) k))) (* (log (* (* (PI) 2) n)) (sqrt 2)))) (.f64 (pow.f64 (neg.f64 k) #s(literal 3 binary64)) (fma.f64 (.f64 #s(literal 1/48 binary64) (sqrt.f64 (/.f64 (.f64 (PI.f64) n) k))) (.f64 (pow.f64 (neg.f64 (log.f64 (.f64 (.f64 (PI.f64) #s(literal 2 binary64)) n))) #s(literal 3 binary64)) (sqrt.f64 #s(literal 2 binary64))) (neg.f64 (/.f64 (fma.f64 (.f64 #s(literal -1/8 binary64) (sqrt.f64 (/.f64 (.f64 (PI.f64) n) k))) (.f64 (.f64 (sqrt.f64 #s(literal 2 binary64)) #s(literal -1 binary64)) (pow.f64 (log.f64 (.f64 (.f64 (PI.f64) #s(literal 2 binary64)) n)) #s(literal 2 binary64))) (.f64 (.f64 #s(literal 1/2 binary64) (/.f64 (sqrt.f64 (.f64 (PI.f64) n)) (pow.f64 k #s(literal 3/2 binary64)))) (.f64 (neg.f64 (log.f64 (.f64 (.f64 (PI.f64) #s(literal 2 binary64)) n))) (sqrt.f64 #s(literal 2 binary64))))) k)))))
#s(approx (+ (* (* -1/48 (sqrt (* (* (pow k 3) n) (PI)))) (* (pow (log (* (* (PI) 2) n)) 3) (sqrt 2))) (* (* 1/8 (sqrt (* (* (PI) n) k))) (* (pow (log (* (* (PI) 2) n)) 2) (sqrt 2)))) (.f64 (.f64 (sqrt.f64 (.f64 (.f64 (pow.f64 k #s(literal 3 binary64)) n) (PI.f64))) #s(literal -1/48 binary64)) (.f64 (pow.f64 (neg.f64 (log.f64 (.f64 (*.f64 (PI.f64) #s(literal 2 binary64)) n))) #s(literal 3 binary64)) (sqrt.f64 #s(literal 2 binary64)))))
#s(approx (+ (* (* -1/48 (sqrt (* (* (pow k 3) n) (PI)))) (* (pow (log (* (* (PI) 2) n)) 3) (sqrt 2))) (* (* 1/8 (sqrt (* (* (PI) n) k))) (* (pow (log (* (* (PI) 2) n)) 2) (sqrt 2)))) (.f64 (fma.f64 (.f64 #s(literal -1/8 binary64) (/.f64 (sqrt.f64 (.f64 (PI.f64) n)) (pow.f64 k #s(literal 3/2 binary64)))) (.f64 (.f64 (sqrt.f64 #s(literal 2 binary64)) #s(literal -1 binary64)) (pow.f64 (log.f64 (.f64 (.f64 (PI.f64) #s(literal 2 binary64)) n)) #s(literal 2 binary64))) (.f64 (.f64 #s(literal -1/48 binary64) (sqrt.f64 (/.f64 (.f64 (PI.f64) n) k))) (.f64 (pow.f64 (neg.f64 (log.f64 (.f64 (.f64 (PI.f64) #s(literal 2 binary64)) n))) #s(literal 3 binary64)) (sqrt.f64 #s(literal 2 binary64))))) (.f64 k k)))
#s(approx (* -1/48 (sqrt (* (* (pow k 3) n) (PI)))) (.f64 (.f64 (sqrt.f64 (.f64 (.f64 (pow.f64 k #s(literal 3 binary64)) n) (PI.f64))) #s(literal -1 binary64)) #s(literal -1/48 binary64)))
#s(approx (sqrt (* (* (pow k 3) n) (PI))) (.f64 (sqrt.f64 (.f64 (*.f64 (pow.f64 k #s(literal 3 binary64)) n) (PI.f64))) #s(literal -1 binary64)))
#s(approx (* (* 1/8 (sqrt (* (* (PI) n) k))) (* (pow (log (* (* (PI) 2) n)) 2) (sqrt 2))) (.f64 (.f64 #s(literal -1/8 binary64) (sqrt.f64 (.f64 (.f64 k n) (PI.f64)))) (.f64 (.f64 (sqrt.f64 #s(literal 2 binary64)) #s(literal -1 binary64)) (pow.f64 (log.f64 (.f64 (.f64 (PI.f64) #s(literal 2 binary64)) n)) #s(literal 2 binary64)))))
#s(approx (* 1/8 (sqrt (* (* (PI) n) k))) (.f64 (.f64 #s(literal -1/8 binary64) (sqrt.f64 (.f64 (.f64 k n) (PI.f64)))) #s(literal -1 binary64)))
#s(approx (sqrt (* (* (PI) n) k)) (neg.f64 (.f64 (sqrt.f64 (.f64 (*.f64 k n) (PI.f64))) #s(literal -1 binary64))))
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#s(approx (* -1/2 (sqrt (* (* (PI) n) k))) (.f64 (.f64 #s(literal 1/2 binary64) (sqrt.f64 (.f64 (.f64 k n) (PI.f64)))) #s(literal -1 binary64)))
#s(approx (sqrt (* (* (* (PI) n) k) 2)) (neg.f64 (sqrt.f64 (.f64 (.f64 #s(literal 2 binary64) k) (*.f64 (PI.f64) n)))))
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#s(approx (* (pow (exp 1/2) (/ (* (+ (* -1 k) 1) (log (* n (* (PI) 2)))) 2)) (pow (exp 1/2) (/ (* (+ (* -1 k) 1) (log (* n (* (PI) 2)))) 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) #s(literal 2 binary64)) n)))) #s(literal 2 binary64)))
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#s(approx (/ (* (+ (* -1 k) 1) (log (* n (* (PI) 2)))) 2) (.f64 (neg.f64 k) (fma.f64 (/.f64 (log.f64 (.f64 (.f64 (PI.f64) #s(literal 2 binary64)) n)) k) #s(literal -1/2 binary64) (log.f64 (sqrt.f64 (.f64 (*.f64 (PI.f64) #s(literal 2 binary64)) n))))))
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#s(approx (* (* -1/2 (sqrt (* (* (PI) n) k))) (* (log (* (* (PI) 2) n)) (sqrt 2))) (.f64 (.f64 (sqrt.f64 (.f64 (.f64 #s(literal 2 binary64) k) (.f64 (PI.f64) n))) (fma.f64 #s(literal 1 binary64) (log.f64 n) (log.f64 (.f64 (PI.f64) #s(literal 2 binary64))))) #s(literal -1/2 binary64)))
#s(approx (* (log (* (* (PI) 2) n)) (sqrt 2)) (.f64 (fma.f64 #s(literal 1 binary64) (log.f64 n) (log.f64 (.f64 (PI.f64) #s(literal 2 binary64)))) (sqrt.f64 #s(literal 2 binary64))))
#s(approx (* (* (pow (PI) (/ (- 1 k) 2)) (pow 2 (/ (- 1 k) 2))) (pow n (/ (- 1 k) 2))) (pow.f64 (exp.f64 #s(literal 1/2 binary64)) (.f64 (fma.f64 #s(literal 1 binary64) (log.f64 n) (log.f64 (.f64 (PI.f64) #s(literal 2 binary64)))) (-.f64 #s(literal 1 binary64) k))))
#s(approx (* (pow (exp 1/2) (/ (* (+ (* -1 k) 1) (log (* n (* (PI) 2)))) 2)) (pow (exp 1/2) (/ (* (+ (* -1 k) 1) (log (* n (* (PI) 2)))) 2))) (pow.f64 (pow.f64 (exp.f64 #s(literal 1/4 binary64)) (.f64 (fma.f64 #s(literal 1 binary64) (log.f64 n) (log.f64 (.f64 (PI.f64) #s(literal 2 binary64)))) (fma.f64 #s(literal -1 binary64) k #s(literal 1 binary64)))) #s(literal 2 binary64)))
#s(approx (pow (exp 1/2) (/ (* (+ (* -1 k) 1) (log (* n (* (PI) 2)))) 2)) (pow.f64 (exp.f64 #s(literal 1/4 binary64)) (.f64 (fma.f64 #s(literal 1 binary64) (log.f64 n) (log.f64 (.f64 (PI.f64) #s(literal 2 binary64)))) (fma.f64 #s(literal -1 binary64) k #s(literal 1 binary64)))))
#s(approx (/ (* (+ (* -1 k) 1) (log (* n (* (PI) 2)))) 2) (.f64 (.f64 #s(literal 1/2 binary64) (fma.f64 #s(literal -1 binary64) k #s(literal 1 binary64))) (fma.f64 #s(literal 1 binary64) (log.f64 n) (log.f64 (*.f64 (PI.f64) #s(literal 2 binary64))))))
#s(approx (* (+ (* -1 k) 1) (log (* n (* (PI) 2)))) (.f64 (fma.f64 #s(literal 1 binary64) (log.f64 n) (log.f64 (.f64 (PI.f64) #s(literal 2 binary64)))) (fma.f64 #s(literal -1 binary64) k #s(literal 1 binary64))))
#s(approx (log (* n (* (PI) 2))) (fma.f64 #s(literal 1 binary64) (log.f64 n) (log.f64 (*.f64 (PI.f64) #s(literal 2 binary64)))))
#s(approx (* (/ 1 (sqrt k)) (* (* (pow (PI) (/ (- 1 k) 2)) (pow 2 (/ (- 1 k) 2))) (pow n (/ (- 1 k) 2)))) (.f64 (.f64 (pow.f64 k #s(literal -1/2 binary64)) (pow.f64 (exp.f64 #s(literal -1/2 binary64)) (.f64 (neg.f64 (log.f64 n)) (-.f64 #s(literal 1 binary64) k)))) (exp.f64 (fma.f64 (log.f64 (sqrt.f64 #s(literal 2 binary64))) (-.f64 #s(literal 1 binary64) k) (.f64 (log.f64 (sqrt.f64 (PI.f64))) (-.f64 #s(literal 1 binary64) k))))))
#s(approx (* (* (pow (PI) (/ (- 1 k) 2)) (pow 2 (/ (- 1 k) 2))) (pow n (/ (- 1 k) 2))) (.f64 (pow.f64 (exp.f64 #s(literal -1/2 binary64)) (.f64 (neg.f64 (log.f64 n)) (-.f64 #s(literal 1 binary64) k))) (exp.f64 (fma.f64 (log.f64 (sqrt.f64 #s(literal 2 binary64))) (-.f64 #s(literal 1 binary64) k) (*.f64 (log.f64 (sqrt.f64 (PI.f64))) (-.f64 #s(literal 1 binary64) k))))))
#s(approx (pow n (/ (- 1 k) 2)) (pow.f64 (exp.f64 #s(literal -1/2 binary64)) (*.f64 (neg.f64 (log.f64 n)) (-.f64 #s(literal 1 binary64) k))))
#s(approx (* (/ 1 (sqrt k)) (* (* (pow (PI) (/ (- 1 k) 2)) (pow 2 (/ (- 1 k) 2))) (pow n (/ (- 1 k) 2)))) (.f64 (pow.f64 (pow.f64 (exp.f64 #s(literal 1/4 binary64)) (.f64 (fma.f64 #s(literal 1 binary64) (log.f64 n) (log.f64 (*.f64 (PI.f64) #s(literal 2 binary64)))) (-.f64 #s(literal 1 binary64) k))) #s(literal 2 binary64)) (pow.f64 k #s(literal -1/2 binary64))))
#s(approx (* (* (pow (PI) (/ (- 1 k) 2)) (pow 2 (/ (- 1 k) 2))) (pow n (/ (- 1 k) 2))) (pow.f64 (pow.f64 (exp.f64 #s(literal 1/4 binary64)) (.f64 (fma.f64 #s(literal 1 binary64) (log.f64 n) (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 #s(literal 1 binary64) (log.f64 n) (log.f64 (.f64 (PI.f64) #s(literal 2 binary64)))) (-.f64 #s(literal 1 binary64) k))))
#s(approx (/ (* (pow (* n (* (PI) 2)) (/ (/ (- 1 k) 2) 2)) (pow (* n (* (PI) 2)) (/ (/ (- 1 k) 2) 2))) (sqrt k)) (.f64 (pow.f64 (pow.f64 (pow.f64 (exp.f64 #s(literal 1/4 binary64)) (-.f64 #s(literal 1 binary64) k)) (fma.f64 (log.f64 (/.f64 #s(literal -1 binary64) n)) #s(literal -1 binary64) (log.f64 (.f64 #s(literal -2 binary64) (PI.f64))))) #s(literal 2 binary64)) (pow.f64 k #s(literal -1/2 binary64))))
#s(approx (* (* (pow (PI) (/ (- 1 k) 2)) (pow 2 (/ (- 1 k) 2))) (pow n (/ (- 1 k) 2))) (pow.f64 (pow.f64 (pow.f64 (exp.f64 #s(literal 1/4 binary64)) (-.f64 #s(literal 1 binary64) k)) (fma.f64 (log.f64 (/.f64 #s(literal -1 binary64) n)) #s(literal -1 binary64) (log.f64 (*.f64 #s(literal -2 binary64) (PI.f64))))) #s(literal 2 binary64)))
#s(approx (pow (* (* (PI) 2) n) (/ (/ (- 1 k) 2) 2)) (pow.f64 (pow.f64 (exp.f64 #s(literal 1/4 binary64)) (-.f64 #s(literal 1 binary64) k)) (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) (/ (- 1 k) 2)) (pow 2 (/ (- 1 k) 2))) (pow n (/ (- 1 k) 2)))) (.f64 (pow.f64 (pow.f64 (exp.f64 #s(literal 1/2 binary64)) (-.f64 #s(literal 1 binary64) k)) (fma.f64 (log.f64 (/.f64 #s(literal -1 binary64) n)) #s(literal -1 binary64) (log.f64 (.f64 #s(literal -2 binary64) (PI.f64))))) (pow.f64 k #s(literal -1/2 binary64))))
#s(approx (/ (+ (* (+ (* (+ (* (* -1/48 (sqrt (* (* (pow k 3) n) (PI)))) (* (pow (log (* (* (PI) 2) n)) 3) (sqrt 2))) (* (* 1/8 (sqrt (* (* (PI) n) k))) (* (pow (log (* (* (PI) 2) n)) 2) (sqrt 2)))) k) (* (* -1/2 (sqrt (* (* (PI) n) k))) (* (log (* (* (PI) 2) n)) (sqrt 2)))) k) (sqrt (* (* (* (PI) n) k) 2))) k) (/.f64 (neg.f64 (.f64 (fma.f64 (fma.f64 (fma.f64 (.f64 #s(literal -1/48 binary64) (sqrt.f64 (/.f64 (.f64 (pow.f64 k #s(literal 3 binary64)) (PI.f64)) n))) (.f64 (.f64 (sqrt.f64 #s(literal 2 binary64)) #s(literal -1 binary64)) (pow.f64 (fma.f64 (log.f64 (/.f64 #s(literal -1 binary64) n)) #s(literal -1 binary64) (log.f64 (.f64 #s(literal -2 binary64) (PI.f64)))) #s(literal 3 binary64))) (.f64 (.f64 #s(literal 1/8 binary64) (sqrt.f64 (/.f64 (.f64 (PI.f64) k) n))) (.f64 (.f64 (sqrt.f64 #s(literal 2 binary64)) #s(literal -1 binary64)) (pow.f64 (fma.f64 (log.f64 (/.f64 #s(literal -1 binary64) n)) #s(literal -1 binary64) (log.f64 (.f64 #s(literal -2 binary64) (PI.f64)))) #s(literal 2 binary64))))) k (.f64 (.f64 (.f64 (sqrt.f64 (/.f64 (.f64 (PI.f64) k) n)) #s(literal -1 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)))) (sqrt.f64 #s(literal 2 binary64)))) #s(literal -1/2 binary64))) k (sqrt.f64 (.f64 (/.f64 (.f64 (PI.f64) k) n) #s(literal 2 binary64)))) n)) k))
#s(approx (+ (* (+ (* (+ (* (* -1/48 (sqrt (* (* (pow k 3) n) (PI)))) (* (pow (log (* (* (PI) 2) n)) 3) (sqrt 2))) (* (* 1/8 (sqrt (* (* (PI) n) k))) (* (pow (log (* (* (PI) 2) n)) 2) (sqrt 2)))) k) (* (* -1/2 (sqrt (* (* (PI) n) k))) (* (log (* (* (PI) 2) n)) (sqrt 2)))) k) (sqrt (* (* (* (PI) n) k) 2))) (neg.f64 (.f64 (fma.f64 (fma.f64 (fma.f64 (.f64 #s(literal -1/48 binary64) (sqrt.f64 (/.f64 (.f64 (pow.f64 k #s(literal 3 binary64)) (PI.f64)) n))) (.f64 (.f64 (sqrt.f64 #s(literal 2 binary64)) #s(literal -1 binary64)) (pow.f64 (fma.f64 (log.f64 (/.f64 #s(literal -1 binary64) n)) #s(literal -1 binary64) (log.f64 (.f64 #s(literal -2 binary64) (PI.f64)))) #s(literal 3 binary64))) (.f64 (.f64 #s(literal 1/8 binary64) (sqrt.f64 (/.f64 (.f64 (PI.f64) k) n))) (.f64 (.f64 (sqrt.f64 #s(literal 2 binary64)) #s(literal -1 binary64)) (pow.f64 (fma.f64 (log.f64 (/.f64 #s(literal -1 binary64) n)) #s(literal -1 binary64) (log.f64 (.f64 #s(literal -2 binary64) (PI.f64)))) #s(literal 2 binary64))))) k (.f64 (.f64 (.f64 (sqrt.f64 (/.f64 (.f64 (PI.f64) k) n)) #s(literal -1 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)))) (sqrt.f64 #s(literal 2 binary64)))) #s(literal -1/2 binary64))) k (sqrt.f64 (.f64 (/.f64 (.f64 (PI.f64) k) n) #s(literal 2 binary64)))) n)))
#s(approx (+ (* (+ (* (* -1/48 (sqrt (* (* (pow k 3) n) (PI)))) (* (pow (log (* (* (PI) 2) n)) 3) (sqrt 2))) (* (* 1/8 (sqrt (* (* (PI) n) k))) (* (pow (log (* (* (PI) 2) n)) 2) (sqrt 2)))) k) (* (* -1/2 (sqrt (* (* (PI) n) k))) (* (log (* (* (PI) 2) n)) (sqrt 2)))) (neg.f64 (.f64 (fma.f64 (fma.f64 (.f64 #s(literal -1/48 binary64) (sqrt.f64 (/.f64 (.f64 (pow.f64 k #s(literal 3 binary64)) (PI.f64)) n))) (.f64 (.f64 (sqrt.f64 #s(literal 2 binary64)) #s(literal -1 binary64)) (pow.f64 (fma.f64 (log.f64 (/.f64 #s(literal -1 binary64) n)) #s(literal -1 binary64) (log.f64 (.f64 #s(literal -2 binary64) (PI.f64)))) #s(literal 3 binary64))) (.f64 (.f64 #s(literal 1/8 binary64) (sqrt.f64 (/.f64 (.f64 (PI.f64) k) n))) (.f64 (.f64 (sqrt.f64 #s(literal 2 binary64)) #s(literal -1 binary64)) (pow.f64 (fma.f64 (log.f64 (/.f64 #s(literal -1 binary64) n)) #s(literal -1 binary64) (log.f64 (.f64 #s(literal -2 binary64) (PI.f64)))) #s(literal 2 binary64))))) k (.f64 (.f64 (.f64 (sqrt.f64 (/.f64 (.f64 (PI.f64) k) n)) #s(literal -1 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)))) (sqrt.f64 #s(literal 2 binary64)))) #s(literal -1/2 binary64))) n)))
#s(approx (+ (* (* -1/48 (sqrt (* (* (pow k 3) n) (PI)))) (* (pow (log (* (* (PI) 2) n)) 3) (sqrt 2))) (* (* 1/8 (sqrt (* (* (PI) n) k))) (* (pow (log (* (* (PI) 2) n)) 2) (sqrt 2)))) (neg.f64 (.f64 (fma.f64 (.f64 #s(literal -1/48 binary64) (sqrt.f64 (/.f64 (.f64 (pow.f64 k #s(literal 3 binary64)) (PI.f64)) n))) (.f64 (.f64 (sqrt.f64 #s(literal 2 binary64)) #s(literal -1 binary64)) (pow.f64 (fma.f64 (log.f64 (/.f64 #s(literal -1 binary64) n)) #s(literal -1 binary64) (log.f64 (.f64 #s(literal -2 binary64) (PI.f64)))) #s(literal 3 binary64))) (.f64 (.f64 #s(literal 1/8 binary64) (sqrt.f64 (/.f64 (.f64 (PI.f64) k) n))) (.f64 (.f64 (sqrt.f64 #s(literal 2 binary64)) #s(literal -1 binary64)) (pow.f64 (fma.f64 (log.f64 (/.f64 #s(literal -1 binary64) n)) #s(literal -1 binary64) (log.f64 (.f64 #s(literal -2 binary64) (PI.f64)))) #s(literal 2 binary64))))) n)))
#s(approx (* -1/48 (sqrt (* (* (pow k 3) n) (PI)))) (.f64 (.f64 #s(literal 1/48 binary64) (sqrt.f64 (.f64 (.f64 (pow.f64 k #s(literal 3 binary64)) n) (PI.f64)))) #s(literal -1 binary64)))
#s(approx (sqrt (* (* (pow k 3) n) (PI))) (neg.f64 (.f64 (sqrt.f64 (.f64 (*.f64 (pow.f64 k #s(literal 3 binary64)) n) (PI.f64))) #s(literal -1 binary64))))
#s(approx (* (pow (log (* (* (PI) 2) n)) 3) (sqrt 2)) (.f64 (pow.f64 (fma.f64 (log.f64 (/.f64 #s(literal -1 binary64) n)) #s(literal -1 binary64) (log.f64 (.f64 #s(literal -2 binary64) (PI.f64)))) #s(literal 3 binary64)) (sqrt.f64 #s(literal 2 binary64))))
#s(approx (pow (log (* (* (PI) 2) n)) 3) (pow.f64 (fma.f64 (log.f64 (/.f64 #s(literal -1 binary64) n)) #s(literal -1 binary64) (log.f64 (*.f64 #s(literal -2 binary64) (PI.f64)))) #s(literal 3 binary64)))
#s(approx (log (* n (* (PI) 2))) (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 (* (* 1/8 (sqrt (* (* (PI) n) k))) (* (pow (log (* (* (PI) 2) n)) 2) (sqrt 2))) (.f64 (.f64 #s(literal -1/8 binary64) (sqrt.f64 (.f64 (.f64 k n) (PI.f64)))) (.f64 (.f64 (sqrt.f64 #s(literal 2 binary64)) #s(literal -1 binary64)) (pow.f64 (fma.f64 (log.f64 (/.f64 #s(literal -1 binary64) n)) #s(literal -1 binary64) (log.f64 (*.f64 #s(literal -2 binary64) (PI.f64)))) #s(literal 2 binary64)))))
#s(approx (* (pow (log (* (* (PI) 2) n)) 2) (sqrt 2)) (.f64 (pow.f64 (fma.f64 (log.f64 (/.f64 #s(literal -1 binary64) n)) #s(literal -1 binary64) (log.f64 (.f64 #s(literal -2 binary64) (PI.f64)))) #s(literal 2 binary64)) (sqrt.f64 #s(literal 2 binary64))))
#s(approx (pow (log (* (* (PI) 2) n)) 2) (pow.f64 (fma.f64 (log.f64 (/.f64 #s(literal -1 binary64) n)) #s(literal -1 binary64) (log.f64 (*.f64 #s(literal -2 binary64) (PI.f64)))) #s(literal 2 binary64)))
#s(approx (* (* -1/2 (sqrt (* (* (PI) n) k))) (* (log (* (* (PI) 2) n)) (sqrt 2))) (.f64 (.f64 #s(literal 1/2 binary64) (sqrt.f64 (.f64 (.f64 k n) (PI.f64)))) (.f64 (.f64 (fma.f64 (log.f64 (/.f64 #s(literal -1 binary64) n)) #s(literal -1 binary64) (log.f64 (*.f64 #s(literal -2 binary64) (PI.f64)))) (sqrt.f64 #s(literal 2 binary64))) #s(literal -1 binary64))))
#s(approx (* (log (* (* (PI) 2) n)) (sqrt 2)) (.f64 (fma.f64 (log.f64 (/.f64 #s(literal -1 binary64) n)) #s(literal -1 binary64) (log.f64 (.f64 #s(literal -2 binary64) (PI.f64)))) (sqrt.f64 #s(literal 2 binary64))))
#s(approx (* (* (pow (PI) (/ (- 1 k) 2)) (pow 2 (/ (- 1 k) 2))) (pow n (/ (- 1 k) 2))) (pow.f64 (pow.f64 (exp.f64 #s(literal 1/2 binary64)) (-.f64 #s(literal 1 binary64) k)) (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 (* (pow (exp 1/2) (/ (* (+ (* -1 k) 1) (log (* n (* (PI) 2)))) 2)) (pow (exp 1/2) (/ (* (+ (* -1 k) 1) (log (* n (* (PI) 2)))) 2))) (pow.f64 (pow.f64 (pow.f64 (exp.f64 #s(literal 1/4 binary64)) (fma.f64 #s(literal -1 binary64) k #s(literal 1 binary64))) (fma.f64 (log.f64 (/.f64 #s(literal -1 binary64) n)) #s(literal -1 binary64) (log.f64 (*.f64 #s(literal -2 binary64) (PI.f64))))) #s(literal 2 binary64)))
#s(approx (pow (exp 1/2) (/ (* (+ (* -1 k) 1) (log (* n (* (PI) 2)))) 2)) (pow.f64 (pow.f64 (exp.f64 #s(literal 1/4 binary64)) (fma.f64 #s(literal -1 binary64) k #s(literal 1 binary64))) (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 k) 1) (log (* n (* (PI) 2)))) 2) (.f64 (.f64 #s(literal 1/2 binary64) (fma.f64 #s(literal -1 binary64) k #s(literal 1 binary64))) (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 k) 1) (log (* n (* (PI) 2)))) (.f64 (fma.f64 (log.f64 (/.f64 #s(literal -1 binary64) n)) #s(literal -1 binary64) (log.f64 (.f64 #s(literal -2 binary64) (PI.f64)))) (fma.f64 #s(literal -1 binary64) k #s(literal 1 binary64))))
#s(approx (log (* n (* (PI) 2))) (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) (/ (- 1 k) 2)) (pow 2 (/ (- 1 k) 2))) (pow n (/ (- 1 k) 2)))) (.f64 (.f64 (pow.f64 k #s(literal -1/2 binary64)) (exp.f64 (.f64 (log.f64 (sqrt.f64 #s(literal 2 binary64))) (-.f64 #s(literal 1 binary64) k)))) (exp.f64 (fma.f64 (log.f64 (sqrt.f64 (PI.f64))) (-.f64 #s(literal 1 binary64) k) (.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 1/2 binary64))))))
#s(approx (* (* (pow (PI) (/ (- 1 k) 2)) (pow 2 (/ (- 1 k) 2))) (pow n (/ (- 1 k) 2))) (.f64 (exp.f64 (fma.f64 (log.f64 (sqrt.f64 (PI.f64))) (-.f64 #s(literal 1 binary64) k) (.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 1/2 binary64)))) (exp.f64 (.f64 (log.f64 (sqrt.f64 #s(literal 2 binary64))) (-.f64 #s(literal 1 binary64) k)))))
#s(approx (pow 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 #s(literal -1 binary64))) (-.f64 #s(literal 1 binary64) k))))
#s(approx (* (/ 1 (sqrt k)) (* (* (pow (PI) (/ (- 1 k) 2)) (pow 2 (/ (- 1 k) 2))) (pow n (/ (- 1 k) 2)))) (.f64 (pow.f64 (pow.f64 (pow.f64 (exp.f64 #s(literal 1/4 binary64)) (-.f64 #s(literal 1 binary64) k)) (fma.f64 (log.f64 (/.f64 #s(literal -1 binary64) n)) #s(literal -1 binary64) (log.f64 (.f64 #s(literal -2 binary64) (PI.f64))))) #s(literal 2 binary64)) (pow.f64 k #s(literal -1/2 binary64))))
#s(approx (* (* (pow (PI) (/ (- 1 k) 2)) (pow 2 (/ (- 1 k) 2))) (pow n (/ (- 1 k) 2))) (pow.f64 (pow.f64 (pow.f64 (exp.f64 #s(literal 1/4 binary64)) (-.f64 #s(literal 1 binary64) k)) (fma.f64 (log.f64 (/.f64 #s(literal -1 binary64) n)) #s(literal -1 binary64) (log.f64 (*.f64 #s(literal -2 binary64) (PI.f64))))) #s(literal 2 binary64)))
#s(approx (pow (* (* (PI) 2) n) (/ (/ (- 1 k) 2) 2)) (pow.f64 (pow.f64 (exp.f64 #s(literal 1/4 binary64)) (-.f64 #s(literal 1 binary64) k)) (fma.f64 (log.f64 (/.f64 #s(literal -1 binary64) n)) #s(literal -1 binary64) (log.f64 (*.f64 #s(literal -2 binary64) (PI.f64))))))

eval185.0ms (1.6%)

Memory: -26.2MiB live, 207.4MiB allocated; 39ms collecting garbage
Compiler: Compiled 70 644 to 4 595 computations (93.5% saved)

prune4.2s (36.3%)

Memory

7.3MiB live, 5 004.4MiB allocated; 405ms collecting garbage

Pruning

8 alts after pruning (3 fresh and 5 done)

	Pruned	Kept	Total
New	1 093	3	1 096
Fresh	4	0	4
Picked	3	2	5
Done	0	3	3
Total	1 100	8	1 108

Accuracy

100.0%

Counts

1 108 → 8

Alt Table

Click to see full alt table

Status	Accuracy	Program
▶	99.7%	(/.f64 (/.f64 (sqrt.f64 (.f64 (.f64 (PI.f64) #s(literal 2 binary64)) n)) (pow.f64 (.f64 (.f64 (PI.f64) #s(literal 2 binary64)) n) (/.f64 k #s(literal 2 binary64)))) (sqrt.f64 k))
✓	99.4%	(/.f64 (.f64 (pow.f64 (.f64 n (.f64 (PI.f64) #s(literal 2 binary64))) (/.f64 (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 2 binary64)) #s(literal 2 binary64))) (pow.f64 (.f64 n (*.f64 (PI.f64) #s(literal 2 binary64))) (/.f64 (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 2 binary64)) #s(literal 2 binary64)))) (sqrt.f64 k))
✓	99.5%	(.f64 (pow.f64 (pow.f64 k #s(literal -1 binary64)) #s(literal 1/2 binary64)) (pow.f64 (.f64 (*.f64 #s(literal 2 binary64) (PI.f64)) n) (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 2 binary64))))
✓	76.6%	(.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)))))
▶	76.9%	(.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) (.f64 (*.f64 (pow.f64 (PI.f64) (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 2 binary64))) (pow.f64 #s(literal 2 binary64) (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 2 binary64)))) (/.f64 (sqrt.f64 n) (pow.f64 n (/.f64 k #s(literal 2 binary64))))))
▶	95.5%	(.f64 (exp.f64 (.f64 (log.f64 (pow.f64 k #s(literal -1 binary64))) #s(literal 1/2 binary64))) #s(approx (pow (* (* 2 (PI)) n) (/ (- 1 k) 2)) (.f64 (pow.f64 (exp.f64 #s(literal 1/2 binary64)) (/.f64 (.f64 (fma.f64 #s(literal -1 binary64) k #s(literal 1 binary64)) (log.f64 (.f64 n (.f64 (PI.f64) #s(literal 2 binary64))))) #s(literal 2 binary64))) (pow.f64 (exp.f64 #s(literal 1/2 binary64)) (/.f64 (.f64 (fma.f64 #s(literal -1 binary64) k #s(literal 1 binary64)) (log.f64 (.f64 n (*.f64 (PI.f64) #s(literal 2 binary64))))) #s(literal 2 binary64))))))
✓	53.0%	#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))
✓	37.8%	#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 286 to 170 computations (40.6% saved)

series177.0ms (1.5%)

Memory

11.8MiB live, 248.5MiB allocated; 11ms collecting garbage

Counts

40 → 163

Calls

Call 1

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

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

Calls

6 calls:

Time	Variable		Point	Expression
42.0ms	n	@	inf	((* (exp (* (log (pow k -1)) 1/2)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (exp (* (log (pow k -1)) 1/2)) (* (log (pow k -1)) 1/2) (log (pow k -1)) (pow k -1) k -1 1/2 (pow (* (* 2 (PI)) n) (/ (- 1 k) 2)) (* (pow (exp 1/2) (/ (* (+ (* -1 k) 1) (log (* n (* (PI) 2)))) 2)) (pow (exp 1/2) (/ (* (+ (* -1 k) 1) (log (* n (* (PI) 2)))) 2))) (pow (exp 1/2) (/ (* (+ (* -1 k) 1) (log (* n (* (PI) 2)))) 2)) (exp 1/2) (/ (* (+ (* -1 k) 1) (log (* n (* (PI) 2)))) 2) (* (+ (* -1 k) 1) (log (* n (* (PI) 2)))) (+ (* -1 k) 1) 1 (log (* n (* (PI) 2))) (* n (* (PI) 2)) n (* (PI) 2) (PI) 2 (* (/ 1 (sqrt k)) (* (* (pow (PI) (/ (- 1 k) 2)) (pow 2 (/ (- 1 k) 2))) (/ (sqrt n) (pow n (/ k 2))))) (/ 1 (sqrt k)) (sqrt k) (* (* (pow (PI) (/ (- 1 k) 2)) (pow 2 (/ (- 1 k) 2))) (/ (sqrt n) (pow n (/ k 2)))) (* (pow (PI) (/ (- 1 k) 2)) (pow 2 (/ (- 1 k) 2))) (pow (PI) (/ (- 1 k) 2)) (/ (- 1 k) 2) (- 1 k) (pow 2 (/ (- 1 k) 2)) (/ (sqrt n) (pow n (/ k 2))) (sqrt n) (pow n (/ k 2)) (/ k 2) (/ (/ (sqrt (* (* (PI) 2) n)) (pow (* (* (PI) 2) n) (/ k 2))) (sqrt k)) (/ (sqrt (* (* (PI) 2) n)) (pow (* (* (PI) 2) n) (/ k 2))) (sqrt (* (* (PI) 2) n)) (* (* (PI) 2) n) (pow (* (* (PI) 2) n) (/ k 2)))
42.0ms	n	@	-inf	((* (exp (* (log (pow k -1)) 1/2)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (exp (* (log (pow k -1)) 1/2)) (* (log (pow k -1)) 1/2) (log (pow k -1)) (pow k -1) k -1 1/2 (pow (* (* 2 (PI)) n) (/ (- 1 k) 2)) (* (pow (exp 1/2) (/ (* (+ (* -1 k) 1) (log (* n (* (PI) 2)))) 2)) (pow (exp 1/2) (/ (* (+ (* -1 k) 1) (log (* n (* (PI) 2)))) 2))) (pow (exp 1/2) (/ (* (+ (* -1 k) 1) (log (* n (* (PI) 2)))) 2)) (exp 1/2) (/ (* (+ (* -1 k) 1) (log (* n (* (PI) 2)))) 2) (* (+ (* -1 k) 1) (log (* n (* (PI) 2)))) (+ (* -1 k) 1) 1 (log (* n (* (PI) 2))) (* n (* (PI) 2)) n (* (PI) 2) (PI) 2 (* (/ 1 (sqrt k)) (* (* (pow (PI) (/ (- 1 k) 2)) (pow 2 (/ (- 1 k) 2))) (/ (sqrt n) (pow n (/ k 2))))) (/ 1 (sqrt k)) (sqrt k) (* (* (pow (PI) (/ (- 1 k) 2)) (pow 2 (/ (- 1 k) 2))) (/ (sqrt n) (pow n (/ k 2)))) (* (pow (PI) (/ (- 1 k) 2)) (pow 2 (/ (- 1 k) 2))) (pow (PI) (/ (- 1 k) 2)) (/ (- 1 k) 2) (- 1 k) (pow 2 (/ (- 1 k) 2)) (/ (sqrt n) (pow n (/ k 2))) (sqrt n) (pow n (/ k 2)) (/ k 2) (/ (/ (sqrt (* (* (PI) 2) n)) (pow (* (* (PI) 2) n) (/ k 2))) (sqrt k)) (/ (sqrt (* (* (PI) 2) n)) (pow (* (* (PI) 2) n) (/ k 2))) (sqrt (* (* (PI) 2) n)) (* (* (PI) 2) n) (pow (* (* (PI) 2) n) (/ k 2)))
39.0ms	n	@	0	((* (exp (* (log (pow k -1)) 1/2)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (exp (* (log (pow k -1)) 1/2)) (* (log (pow k -1)) 1/2) (log (pow k -1)) (pow k -1) k -1 1/2 (pow (* (* 2 (PI)) n) (/ (- 1 k) 2)) (* (pow (exp 1/2) (/ (* (+ (* -1 k) 1) (log (* n (* (PI) 2)))) 2)) (pow (exp 1/2) (/ (* (+ (* -1 k) 1) (log (* n (* (PI) 2)))) 2))) (pow (exp 1/2) (/ (* (+ (* -1 k) 1) (log (* n (* (PI) 2)))) 2)) (exp 1/2) (/ (* (+ (* -1 k) 1) (log (* n (* (PI) 2)))) 2) (* (+ (* -1 k) 1) (log (* n (* (PI) 2)))) (+ (* -1 k) 1) 1 (log (* n (* (PI) 2))) (* n (* (PI) 2)) n (* (PI) 2) (PI) 2 (* (/ 1 (sqrt k)) (* (* (pow (PI) (/ (- 1 k) 2)) (pow 2 (/ (- 1 k) 2))) (/ (sqrt n) (pow n (/ k 2))))) (/ 1 (sqrt k)) (sqrt k) (* (* (pow (PI) (/ (- 1 k) 2)) (pow 2 (/ (- 1 k) 2))) (/ (sqrt n) (pow n (/ k 2)))) (* (pow (PI) (/ (- 1 k) 2)) (pow 2 (/ (- 1 k) 2))) (pow (PI) (/ (- 1 k) 2)) (/ (- 1 k) 2) (- 1 k) (pow 2 (/ (- 1 k) 2)) (/ (sqrt n) (pow n (/ k 2))) (sqrt n) (pow n (/ k 2)) (/ k 2) (/ (/ (sqrt (* (* (PI) 2) n)) (pow (* (* (PI) 2) n) (/ k 2))) (sqrt k)) (/ (sqrt (* (* (PI) 2) n)) (pow (* (* (PI) 2) n) (/ k 2))) (sqrt (* (* (PI) 2) n)) (* (* (PI) 2) n) (pow (* (* (PI) 2) n) (/ k 2)))
17.0ms	k	@	-inf	((* (exp (* (log (pow k -1)) 1/2)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (exp (* (log (pow k -1)) 1/2)) (* (log (pow k -1)) 1/2) (log (pow k -1)) (pow k -1) k -1 1/2 (pow (* (* 2 (PI)) n) (/ (- 1 k) 2)) (* (pow (exp 1/2) (/ (* (+ (* -1 k) 1) (log (* n (* (PI) 2)))) 2)) (pow (exp 1/2) (/ (* (+ (* -1 k) 1) (log (* n (* (PI) 2)))) 2))) (pow (exp 1/2) (/ (* (+ (* -1 k) 1) (log (* n (* (PI) 2)))) 2)) (exp 1/2) (/ (* (+ (* -1 k) 1) (log (* n (* (PI) 2)))) 2) (* (+ (* -1 k) 1) (log (* n (* (PI) 2)))) (+ (* -1 k) 1) 1 (log (* n (* (PI) 2))) (* n (* (PI) 2)) n (* (PI) 2) (PI) 2 (* (/ 1 (sqrt k)) (* (* (pow (PI) (/ (- 1 k) 2)) (pow 2 (/ (- 1 k) 2))) (/ (sqrt n) (pow n (/ k 2))))) (/ 1 (sqrt k)) (sqrt k) (* (* (pow (PI) (/ (- 1 k) 2)) (pow 2 (/ (- 1 k) 2))) (/ (sqrt n) (pow n (/ k 2)))) (* (pow (PI) (/ (- 1 k) 2)) (pow 2 (/ (- 1 k) 2))) (pow (PI) (/ (- 1 k) 2)) (/ (- 1 k) 2) (- 1 k) (pow 2 (/ (- 1 k) 2)) (/ (sqrt n) (pow n (/ k 2))) (sqrt n) (pow n (/ k 2)) (/ k 2) (/ (/ (sqrt (* (* (PI) 2) n)) (pow (* (* (PI) 2) n) (/ k 2))) (sqrt k)) (/ (sqrt (* (* (PI) 2) n)) (pow (* (* (PI) 2) n) (/ k 2))) (sqrt (* (* (PI) 2) n)) (* (* (PI) 2) n) (pow (* (* (PI) 2) n) (/ k 2)))
16.0ms	k	@	inf	((* (exp (* (log (pow k -1)) 1/2)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (exp (* (log (pow k -1)) 1/2)) (* (log (pow k -1)) 1/2) (log (pow k -1)) (pow k -1) k -1 1/2 (pow (* (* 2 (PI)) n) (/ (- 1 k) 2)) (* (pow (exp 1/2) (/ (* (+ (* -1 k) 1) (log (* n (* (PI) 2)))) 2)) (pow (exp 1/2) (/ (* (+ (* -1 k) 1) (log (* n (* (PI) 2)))) 2))) (pow (exp 1/2) (/ (* (+ (* -1 k) 1) (log (* n (* (PI) 2)))) 2)) (exp 1/2) (/ (* (+ (* -1 k) 1) (log (* n (* (PI) 2)))) 2) (* (+ (* -1 k) 1) (log (* n (* (PI) 2)))) (+ (* -1 k) 1) 1 (log (* n (* (PI) 2))) (* n (* (PI) 2)) n (* (PI) 2) (PI) 2 (* (/ 1 (sqrt k)) (* (* (pow (PI) (/ (- 1 k) 2)) (pow 2 (/ (- 1 k) 2))) (/ (sqrt n) (pow n (/ k 2))))) (/ 1 (sqrt k)) (sqrt k) (* (* (pow (PI) (/ (- 1 k) 2)) (pow 2 (/ (- 1 k) 2))) (/ (sqrt n) (pow n (/ k 2)))) (* (pow (PI) (/ (- 1 k) 2)) (pow 2 (/ (- 1 k) 2))) (pow (PI) (/ (- 1 k) 2)) (/ (- 1 k) 2) (- 1 k) (pow 2 (/ (- 1 k) 2)) (/ (sqrt n) (pow n (/ k 2))) (sqrt n) (pow n (/ k 2)) (/ k 2) (/ (/ (sqrt (* (* (PI) 2) n)) (pow (* (* (PI) 2) n) (/ k 2))) (sqrt k)) (/ (sqrt (* (* (PI) 2) n)) (pow (* (* (PI) 2) n) (/ k 2))) (sqrt (* (* (PI) 2) n)) (* (* (PI) 2) n) (pow (* (* (PI) 2) n) (/ k 2)))

rewrite139.0ms (1.2%)

Memory

-18.0MiB live, 126.6MiB allocated; 7ms collecting garbage

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	792	7070
0	855	6276
0	4113	6106

Stop Event

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

Counts

203 → 312

Calls

Call 1

Inputs
(.f64 (exp.f64 (.f64 (log.f64 (pow.f64 k #s(literal -1 binary64))) #s(literal 1/2 binary64))) #s(approx (pow (* (* 2 (PI)) n) (/ (- 1 k) 2)) (.f64 (pow.f64 (exp.f64 #s(literal 1/2 binary64)) (/.f64 (.f64 (fma.f64 #s(literal -1 binary64) k #s(literal 1 binary64)) (log.f64 (.f64 n (.f64 (PI.f64) #s(literal 2 binary64))))) #s(literal 2 binary64))) (pow.f64 (exp.f64 #s(literal 1/2 binary64)) (/.f64 (.f64 (fma.f64 #s(literal -1 binary64) k #s(literal 1 binary64)) (log.f64 (.f64 n (*.f64 (PI.f64) #s(literal 2 binary64))))) #s(literal 2 binary64))))))
(exp.f64 (*.f64 (log.f64 (pow.f64 k #s(literal -1 binary64))) #s(literal 1/2 binary64)))
(*.f64 (log.f64 (pow.f64 k #s(literal -1 binary64))) #s(literal 1/2 binary64))
(log.f64 (pow.f64 k #s(literal -1 binary64)))
(pow.f64 k #s(literal -1 binary64))
k
#s(literal -1 binary64)
#s(literal 1/2 binary64)
#s(approx (pow (* (* 2 (PI)) n) (/ (- 1 k) 2)) (.f64 (pow.f64 (exp.f64 #s(literal 1/2 binary64)) (/.f64 (.f64 (fma.f64 #s(literal -1 binary64) k #s(literal 1 binary64)) (log.f64 (.f64 n (.f64 (PI.f64) #s(literal 2 binary64))))) #s(literal 2 binary64))) (pow.f64 (exp.f64 #s(literal 1/2 binary64)) (/.f64 (.f64 (fma.f64 #s(literal -1 binary64) k #s(literal 1 binary64)) (log.f64 (.f64 n (*.f64 (PI.f64) #s(literal 2 binary64))))) #s(literal 2 binary64)))))
(.f64 (pow.f64 (exp.f64 #s(literal 1/2 binary64)) (/.f64 (.f64 (fma.f64 #s(literal -1 binary64) k #s(literal 1 binary64)) (log.f64 (.f64 n (.f64 (PI.f64) #s(literal 2 binary64))))) #s(literal 2 binary64))) (pow.f64 (exp.f64 #s(literal 1/2 binary64)) (/.f64 (.f64 (fma.f64 #s(literal -1 binary64) k #s(literal 1 binary64)) (log.f64 (.f64 n (*.f64 (PI.f64) #s(literal 2 binary64))))) #s(literal 2 binary64))))
(pow.f64 (exp.f64 #s(literal 1/2 binary64)) (/.f64 (.f64 (fma.f64 #s(literal -1 binary64) k #s(literal 1 binary64)) (log.f64 (.f64 n (*.f64 (PI.f64) #s(literal 2 binary64))))) #s(literal 2 binary64)))
(exp.f64 #s(literal 1/2 binary64))
(/.f64 (.f64 (fma.f64 #s(literal -1 binary64) k #s(literal 1 binary64)) (log.f64 (.f64 n (*.f64 (PI.f64) #s(literal 2 binary64))))) #s(literal 2 binary64))
(.f64 (fma.f64 #s(literal -1 binary64) k #s(literal 1 binary64)) (log.f64 (.f64 n (*.f64 (PI.f64) #s(literal 2 binary64)))))
(fma.f64 #s(literal -1 binary64) k #s(literal 1 binary64))
#s(literal 1 binary64)
(log.f64 (.f64 n (.f64 (PI.f64) #s(literal 2 binary64))))
(.f64 n (.f64 (PI.f64) #s(literal 2 binary64)))
n
(*.f64 (PI.f64) #s(literal 2 binary64))
(PI.f64)
#s(literal 2 binary64)
(.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) (.f64 (*.f64 (pow.f64 (PI.f64) (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 2 binary64))) (pow.f64 #s(literal 2 binary64) (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 2 binary64)))) (/.f64 (sqrt.f64 n) (pow.f64 n (/.f64 k #s(literal 2 binary64))))))
(/.f64 #s(literal 1 binary64) (sqrt.f64 k))
(sqrt.f64 k)
(.f64 (.f64 (pow.f64 (PI.f64) (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 2 binary64))) (pow.f64 #s(literal 2 binary64) (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 2 binary64)))) (/.f64 (sqrt.f64 n) (pow.f64 n (/.f64 k #s(literal 2 binary64)))))
(*.f64 (pow.f64 (PI.f64) (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 2 binary64))) (pow.f64 #s(literal 2 binary64) (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 2 binary64))))
(pow.f64 (PI.f64) (/.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 binary64) k)
(pow.f64 #s(literal 2 binary64) (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 2 binary64)))
(/.f64 (sqrt.f64 n) (pow.f64 n (/.f64 k #s(literal 2 binary64))))
(sqrt.f64 n)
(pow.f64 n (/.f64 k #s(literal 2 binary64)))
(/.f64 k #s(literal 2 binary64))
(/.f64 (/.f64 (sqrt.f64 (.f64 (.f64 (PI.f64) #s(literal 2 binary64)) n)) (pow.f64 (.f64 (.f64 (PI.f64) #s(literal 2 binary64)) n) (/.f64 k #s(literal 2 binary64)))) (sqrt.f64 k))
(/.f64 (sqrt.f64 (.f64 (.f64 (PI.f64) #s(literal 2 binary64)) n)) (pow.f64 (.f64 (.f64 (PI.f64) #s(literal 2 binary64)) n) (/.f64 k #s(literal 2 binary64))))
(sqrt.f64 (.f64 (.f64 (PI.f64) #s(literal 2 binary64)) n))
(.f64 (.f64 (PI.f64) #s(literal 2 binary64)) n)
(pow.f64 (.f64 (.f64 (PI.f64) #s(literal 2 binary64)) n) (/.f64 k #s(literal 2 binary64)))
#s(approx (* (exp (* (log (pow k -1)) 1/2)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) #s(hole binary64 (* (sqrt (/ (* n (PI)) k)) (sqrt 2))))
#s(approx (* (exp (* (log (pow k -1)) 1/2)) (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 (* (exp (* (log (pow k -1)) 1/2)) (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 (* (exp (* (log (pow k -1)) 1/2)) (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 (exp (* (log (pow k -1)) 1/2)) #s(hole binary64 (sqrt (/ 1 k))))
#s(approx (* (log (pow k -1)) 1/2) #s(hole binary64 (* -1/2 (log k))))
#s(approx (log (pow k -1)) #s(hole binary64 (* -1 (log k))))
#s(approx (pow k -1) #s(hole binary64 (/ 1 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 (* (pow (exp 1/2) (/ (* (+ (* -1 k) 1) (log (* n (* (PI) 2)))) 2)) (pow (exp 1/2) (/ (* (+ (* -1 k) 1) (log (* n (* (PI) 2)))) 2))) #s(hole binary64 (* (sqrt (* n (PI))) (sqrt 2))))
#s(approx (* (pow (exp 1/2) (/ (* (+ (* -1 k) 1) (log (* n (* (PI) 2)))) 2)) (pow (exp 1/2) (/ (* (+ (* -1 k) 1) (log (* n (* (PI) 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 (exp 1/2) (/ (* (+ (* -1 k) 1) (log (* n (* (PI) 2)))) 2)) (pow (exp 1/2) (/ (* (+ (* -1 k) 1) (log (* n (* (PI) 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 (exp 1/2) (/ (* (+ (* -1 k) 1) (log (* n (* (PI) 2)))) 2)) (pow (exp 1/2) (/ (* (+ (* -1 k) 1) (log (* n (* (PI) 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 (exp 1/2) (/ (* (+ (* -1 k) 1) (log (* n (* (PI) 2)))) 2)) #s(hole binary64 (pow (* 2 (* n (PI))) 1/4)))
#s(approx (pow (exp 1/2) (/ (* (+ (* -1 k) 1) (log (* n (* (PI) 2)))) 2)) #s(hole binary64 (+ (* -1/4 (* (pow (* 2 (* n (PI))) 1/4) (* k (log (* 2 (* n (PI))))))) (pow (* 2 (* n (PI))) 1/4))))
#s(approx (pow (exp 1/2) (/ (* (+ (* -1 k) 1) (log (* n (* (PI) 2)))) 2)) #s(hole binary64 (+ (* k (+ (* -1/4 (* (pow (* 2 (* n (PI))) 1/4) (log (* 2 (* n (PI)))))) (* 1/32 (* (pow (* 2 (* n (PI))) 1/4) (* k (pow (log (* 2 (* n (PI)))) 2)))))) (pow (* 2 (* n (PI))) 1/4))))
#s(approx (pow (exp 1/2) (/ (* (+ (* -1 k) 1) (log (* n (* (PI) 2)))) 2)) #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) 1) (log (* n (* (PI) 2)))) 2) #s(hole binary64 (* 1/2 (log (* 2 (* n (PI)))))))
#s(approx (/ (* (+ (* -1 k) 1) (log (* n (* (PI) 2)))) 2) #s(hole binary64 (+ (* -1/2 (* k (log (* 2 (* n (PI)))))) (* 1/2 (log (* 2 (* n (PI))))))))
#s(approx (* (+ (* -1 k) 1) (log (* n (* (PI) 2)))) #s(hole binary64 (log (* 2 (* n (PI))))))
#s(approx (* (+ (* -1 k) 1) (log (* n (* (PI) 2)))) #s(hole binary64 (+ (log (* 2 (* n (PI)))) (* -1 (* k (log (* 2 (* n (PI)))))))))
#s(approx (+ (* -1 k) 1) #s(hole binary64 1))
#s(approx (+ (* -1 k) 1) #s(hole binary64 (+ 1 (* -1 k))))
#s(approx (* (/ 1 (sqrt k)) (* (* (pow (PI) (/ (- 1 k) 2)) (pow 2 (/ (- 1 k) 2))) (/ (sqrt n) (pow n (/ k 2))))) #s(hole binary64 (* (sqrt (/ (* n (PI)) k)) (sqrt 2))))
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#s(approx (* (pow (exp 1/2) (/ (* (+ (* -1 k) 1) (log (* n (* (PI) 2)))) 2)) (pow (exp 1/2) (/ (* (+ (* -1 k) 1) (log (* n (* (PI) 2)))) 2))) #s(hole binary64 (pow (exp (* 1/4 (* (+ 1 (* -1 k)) (+ (log n) (log (* 2 (PI))))))) 2)))
#s(approx (pow (exp 1/2) (/ (* (+ (* -1 k) 1) (log (* n (* (PI) 2)))) 2)) #s(hole binary64 (exp (* 1/4 (* (+ 1 (* -1 k)) (+ (log n) (log (* 2 (PI)))))))))
#s(approx (/ (* (+ (* -1 k) 1) (log (* n (* (PI) 2)))) 2) #s(hole binary64 (* 1/2 (* (+ 1 (* -1 k)) (+ (log n) (log (* 2 (PI))))))))
#s(approx (* (+ (* -1 k) 1) (log (* n (* (PI) 2)))) #s(hole binary64 (* (+ 1 (* -1 k)) (+ (log n) (log (* 2 (PI)))))))
#s(approx (log (* n (* (PI) 2))) #s(hole binary64 (+ (log n) (log (* 2 (PI))))))
#s(approx (* n (* (PI) 2)) #s(hole binary64 (* 2 (* n (PI)))))
#s(approx n #s(hole binary64 n))
#s(approx (sqrt n) #s(hole binary64 (sqrt n)))
#s(approx (/ (/ (sqrt (* (* (PI) 2) n)) (pow (* (* (PI) 2) n) (/ k 2))) (sqrt k)) #s(hole binary64 (* (sqrt (/ (* n (PI)) k)) (/ (sqrt 2) (exp (* 1/2 (* k (+ (log n) (log (* 2 (PI)))))))))))
#s(approx (/ (sqrt (* (* (PI) 2) n)) (pow (* (* (PI) 2) n) (/ k 2))) #s(hole binary64 (* (sqrt (* n (PI))) (/ (sqrt 2) (exp (* 1/2 (* k (+ (log n) (log (* 2 (PI)))))))))))
#s(approx (sqrt (* (* (PI) 2) n)) #s(hole binary64 (* (sqrt (* n (PI))) (sqrt 2))))
#s(approx (* (* (PI) 2) n) #s(hole binary64 (* 2 (* n (PI)))))
#s(approx (pow (* (* (PI) 2) n) (/ k 2)) #s(hole binary64 (exp (* 1/2 (* k (+ (log n) (log (* 2 (PI)))))))))
#s(approx (* (exp (* (log (pow k -1)) 1/2)) (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 (* (pow (exp 1/2) (/ (* (+ (* -1 k) 1) (log (* n (* (PI) 2)))) 2)) (pow (exp 1/2) (/ (* (+ (* -1 k) 1) (log (* n (* (PI) 2)))) 2))) #s(hole binary64 (pow (exp (* 1/4 (* (+ 1 (* -1 k)) (+ (log (* 2 (PI))) (* -1 (log (/ 1 n))))))) 2)))
#s(approx (pow (exp 1/2) (/ (* (+ (* -1 k) 1) (log (* n (* (PI) 2)))) 2)) #s(hole binary64 (exp (* 1/4 (* (+ 1 (* -1 k)) (+ (log (* 2 (PI))) (* -1 (log (/ 1 n)))))))))
#s(approx (/ (* (+ (* -1 k) 1) (log (* n (* (PI) 2)))) 2) #s(hole binary64 (* 1/2 (* (+ 1 (* -1 k)) (+ (log (* 2 (PI))) (* -1 (log (/ 1 n))))))))
#s(approx (* (+ (* -1 k) 1) (log (* n (* (PI) 2)))) #s(hole binary64 (* (+ 1 (* -1 k)) (+ (log (* 2 (PI))) (* -1 (log (/ 1 n)))))))
#s(approx (log (* n (* (PI) 2))) #s(hole binary64 (+ (log (* 2 (PI))) (* -1 (log (/ 1 n))))))
#s(approx (* (/ 1 (sqrt k)) (* (* (pow (PI) (/ (- 1 k) 2)) (pow 2 (/ (- 1 k) 2))) (/ (sqrt n) (pow n (/ k 2))))) #s(hole binary64 (* (sqrt (/ n k)) (/ (* (exp (* 1/2 (* (log 2) (- 1 k)))) (exp (* 1/2 (* (log (PI)) (- 1 k))))) (exp (* -1/2 (* k (log (/ 1 n)))))))))
#s(approx (* (* (pow (PI) (/ (- 1 k) 2)) (pow 2 (/ (- 1 k) 2))) (/ (sqrt n) (pow n (/ k 2)))) #s(hole binary64 (* (sqrt n) (/ (* (exp (* 1/2 (* (log 2) (- 1 k)))) (exp (* 1/2 (* (log (PI)) (- 1 k))))) (exp (* -1/2 (* k (log (/ 1 n)))))))))
#s(approx (/ (sqrt n) (pow n (/ k 2))) #s(hole binary64 (* (sqrt n) (/ 1 (exp (* -1/2 (* k (log (/ 1 n)))))))))
#s(approx (pow n (/ k 2)) #s(hole binary64 (exp (* -1/2 (* k (log (/ 1 n)))))))
#s(approx (/ (/ (sqrt (* (* (PI) 2) n)) (pow (* (* (PI) 2) n) (/ k 2))) (sqrt k)) #s(hole binary64 (* (sqrt (/ (* n (PI)) k)) (/ (sqrt 2) (exp (* 1/2 (* k (+ (log (* 2 (PI))) (* -1 (log (/ 1 n)))))))))))
#s(approx (/ (sqrt (* (* (PI) 2) n)) (pow (* (* (PI) 2) n) (/ k 2))) #s(hole binary64 (* (sqrt (* n (PI))) (/ (sqrt 2) (exp (* 1/2 (* k (+ (log (* 2 (PI))) (* -1 (log (/ 1 n)))))))))))
#s(approx (pow (* (* (PI) 2) n) (/ k 2)) #s(hole binary64 (exp (* 1/2 (* k (+ (log (* 2 (PI))) (* -1 (log (/ 1 n)))))))))
#s(approx (* (exp (* (log (pow k -1)) 1/2)) (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 (* (pow (exp 1/2) (/ (* (+ (* -1 k) 1) (log (* n (* (PI) 2)))) 2)) (pow (exp 1/2) (/ (* (+ (* -1 k) 1) (log (* n (* (PI) 2)))) 2))) #s(hole binary64 (pow (exp (* 1/4 (* (+ 1 (* -1 k)) (+ (log (* -2 (PI))) (* -1 (log (/ -1 n))))))) 2)))
#s(approx (pow (exp 1/2) (/ (* (+ (* -1 k) 1) (log (* n (* (PI) 2)))) 2)) #s(hole binary64 (exp (* 1/4 (* (+ 1 (* -1 k)) (+ (log (* -2 (PI))) (* -1 (log (/ -1 n)))))))))
#s(approx (/ (* (+ (* -1 k) 1) (log (* n (* (PI) 2)))) 2) #s(hole binary64 (* 1/2 (* (+ 1 (* -1 k)) (+ (log (* -2 (PI))) (* -1 (log (/ -1 n))))))))
#s(approx (* (+ (* -1 k) 1) (log (* n (* (PI) 2)))) #s(hole binary64 (* (+ 1 (* -1 k)) (+ (log (* -2 (PI))) (* -1 (log (/ -1 n)))))))
#s(approx (log (* n (* (PI) 2))) #s(hole binary64 (+ (log (* -2 (PI))) (* -1 (log (/ -1 n))))))
#s(approx (* (/ 1 (sqrt k)) (* (* (pow (PI) (/ (- 1 k) 2)) (pow 2 (/ (- 1 k) 2))) (/ (sqrt n) (pow n (/ k 2))))) #s(hole binary64 (* -1 (* (sqrt (/ n k)) (/ (* (exp (* 1/2 (* (log 2) (- 1 k)))) (* (exp (* 1/2 (* (log (PI)) (- 1 k)))) (pow (sqrt -1) 2))) (exp (* 1/2 (* k (+ (log -1) (* -1 (log (/ -1 n))))))))))))
#s(approx (* (* (pow (PI) (/ (- 1 k) 2)) (pow 2 (/ (- 1 k) 2))) (/ (sqrt n) (pow n (/ k 2)))) #s(hole binary64 (* -1 (* (sqrt n) (/ (* (exp (* 1/2 (* (log 2) (- 1 k)))) (* (exp (* 1/2 (* (log (PI)) (- 1 k)))) (pow (sqrt -1) 2))) (exp (* 1/2 (* k (+ (log -1) (* -1 (log (/ -1 n))))))))))))
#s(approx (/ (sqrt n) (pow n (/ k 2))) #s(hole binary64 (* -1 (* (sqrt n) (/ (pow (sqrt -1) 2) (exp (* 1/2 (* k (+ (log -1) (* -1 (log (/ -1 n))))))))))))
#s(approx (sqrt n) #s(hole binary64 (* -1 (* (sqrt n) (pow (sqrt -1) 2)))))
#s(approx (pow n (/ k 2)) #s(hole binary64 (exp (* 1/2 (* k (+ (log -1) (* -1 (log (/ -1 n)))))))))
#s(approx (/ (/ (sqrt (* (* (PI) 2) n)) (pow (* (* (PI) 2) n) (/ k 2))) (sqrt k)) #s(hole binary64 (* -1 (* (sqrt (/ (* n (PI)) k)) (/ (* (sqrt -2) (sqrt -1)) (exp (* 1/2 (* k (+ (log (* -2 (PI))) (* -1 (log (/ -1 n))))))))))))
#s(approx (/ (sqrt (* (* (PI) 2) n)) (pow (* (* (PI) 2) n) (/ k 2))) #s(hole binary64 (* -1 (* (sqrt (* n (PI))) (/ (* (sqrt -2) (sqrt -1)) (exp (* 1/2 (* k (+ (log (* -2 (PI))) (* -1 (log (/ -1 n))))))))))))
#s(approx (sqrt (* (* (PI) 2) n)) #s(hole binary64 (* -1 (* (sqrt (* n (PI))) (* (sqrt -2) (sqrt -1))))))
#s(approx (pow (* (* (PI) 2) n) (/ k 2)) #s(hole binary64 (exp (* 1/2 (* k (+ (log (* -2 (PI))) (* -1 (log (/ -1 n)))))))))

Outputs
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(pow.f64 (sqrt.f64 k) #s(literal -1 binary64))
(pow.f64 (pow.f64 k #s(literal -1 binary64)) #s(literal 1/2 binary64))
(/.f64 #s(literal 1 binary64) (sqrt.f64 k))
(/.f64 #s(literal -1 binary64) (neg.f64 (sqrt.f64 k)))
(sqrt.f64 (pow.f64 k #s(literal -1 binary64)))
(exp.f64 (*.f64 (neg.f64 (log.f64 k)) #s(literal 1/2 binary64)))
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(*.f64 (neg.f64 (log.f64 k)) #s(literal 1/2 binary64))
(*.f64 #s(literal 1/2 binary64) (neg.f64 (log.f64 k)))
(log.f64 (pow.f64 (sqrt.f64 k) #s(literal -1 binary64)))
(*.f64 (log.f64 k) #s(literal -1 binary64))
(*.f64 #s(literal -1 binary64) (log.f64 k))
(neg.f64 (log.f64 k))
(-.f64 #s(literal 0 binary64) (log.f64 k))
(log.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) k)
(/.f64 #s(literal -1 binary64) (neg.f64 k))
(exp.f64 (neg.f64 (log.f64 k)))
k
#s(literal -1 binary64)
#s(literal 1/2 binary64)
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(.f64 (pow.f64 (exp.f64 #s(literal 1/2 binary64)) (/.f64 (/.f64 (.f64 (fma.f64 #s(literal -1 binary64) k #s(literal 1 binary64)) (log.f64 (.f64 (.f64 n (PI.f64)) #s(literal 2 binary64)))) #s(literal 2 binary64)) #s(literal 2 binary64))) (pow.f64 (exp.f64 #s(literal 1/2 binary64)) (/.f64 (/.f64 (.f64 (fma.f64 #s(literal -1 binary64) k #s(literal 1 binary64)) (log.f64 (.f64 (*.f64 n (PI.f64)) #s(literal 2 binary64)))) #s(literal 2 binary64)) #s(literal 2 binary64))))
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(exp.f64 #s(literal 1/2 binary64))
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(fma.f64 (log.f64 n) (fma.f64 #s(literal -1 binary64) k #s(literal 1 binary64)) (.f64 (log.f64 (.f64 (PI.f64) #s(literal 2 binary64))) (fma.f64 #s(literal -1 binary64) k #s(literal 1 binary64))))
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(/.f64 (-.f64 (pow.f64 (log.f64 n) #s(literal 2 binary64)) (.f64 (log.f64 (.f64 (PI.f64) #s(literal 2 binary64))) (log.f64 (.f64 (PI.f64) #s(literal 2 binary64))))) (-.f64 (log.f64 n) (log.f64 (.f64 (PI.f64) #s(literal 2 binary64)))))
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(log.f64 (.f64 (.f64 n (PI.f64)) #s(literal 2 binary64)))
(.f64 (.f64 #s(literal 2 binary64) n) (PI.f64))
(.f64 (.f64 n (PI.f64)) #s(literal 2 binary64))
(.f64 (.f64 (PI.f64) #s(literal 2 binary64)) n)
(.f64 n (.f64 (PI.f64) #s(literal 2 binary64)))
(.f64 (PI.f64) (.f64 #s(literal 2 binary64) n))
(.f64 #s(literal 2 binary64) (.f64 n (PI.f64)))
(fma.f64 n (PI.f64) (*.f64 n (PI.f64)))
(fma.f64 (PI.f64) n (*.f64 n (PI.f64)))
(+.f64 (.f64 n (PI.f64)) (.f64 n (PI.f64)))
n
(*.f64 (PI.f64) #s(literal 2 binary64))
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(+.f64 (PI.f64) (PI.f64))
(PI.f64)
#s(literal 2 binary64)
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(.f64 (.f64 #s(literal 2 binary64) n) (PI.f64))
(.f64 (.f64 n (PI.f64)) #s(literal 2 binary64))
(.f64 (.f64 (PI.f64) #s(literal 2 binary64)) n)
(.f64 n (.f64 (PI.f64) #s(literal 2 binary64)))
(.f64 (PI.f64) (.f64 #s(literal 2 binary64) n))
(.f64 #s(literal 2 binary64) (.f64 n (PI.f64)))
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(+.f64 (.f64 n (PI.f64)) (.f64 n (PI.f64)))
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#s(approx (pow n (/ k 2)) #s(literal 1 binary64))
#s(approx (pow n (/ k 2)) (fma.f64 (*.f64 (log.f64 n) k) #s(literal 1/2 binary64) #s(literal 1 binary64)))
#s(approx (pow n (/ k 2)) (fma.f64 (fma.f64 (*.f64 #s(literal 1/8 binary64) k) (pow.f64 (log.f64 n) #s(literal 2 binary64)) (log.f64 (sqrt.f64 n))) k #s(literal 1 binary64)))
#s(approx (pow n (/ k 2)) (fma.f64 (fma.f64 (fma.f64 (.f64 (pow.f64 (log.f64 n) #s(literal 3 binary64)) k) #s(literal 1/48 binary64) (.f64 (pow.f64 (log.f64 n) #s(literal 2 binary64)) #s(literal 1/8 binary64))) k (log.f64 (sqrt.f64 n))) k #s(literal 1 binary64)))
#s(approx (/ k 2) (*.f64 #s(literal 1/2 binary64) k))
#s(approx (/ (/ (sqrt (* (* (PI) 2) n)) (pow (* (* (PI) 2) n) (/ k 2))) (sqrt k)) (sqrt.f64 (.f64 (/.f64 (.f64 n (PI.f64)) k) #s(literal 2 binary64))))
#s(approx (/ (/ (sqrt (* (* (PI) 2) n)) (pow (* (* (PI) 2) n) (/ k 2))) (sqrt k)) (/.f64 (fma.f64 (.f64 (.f64 (log.f64 (.f64 (.f64 n (PI.f64)) #s(literal 2 binary64))) (sqrt.f64 #s(literal 2 binary64))) (sqrt.f64 (.f64 (.f64 (pow.f64 k #s(literal 3 binary64)) n) (PI.f64)))) #s(literal -1/2 binary64) (sqrt.f64 (.f64 (.f64 (*.f64 n (PI.f64)) k) #s(literal 2 binary64)))) k))
#s(approx (/ (/ (sqrt (* (* (PI) 2) n)) (pow (* (* (PI) 2) n) (/ k 2))) (sqrt k)) (/.f64 (fma.f64 (fma.f64 (.f64 #s(literal -1/2 binary64) (sqrt.f64 (.f64 (.f64 n (PI.f64)) k))) (.f64 (log.f64 (.f64 (.f64 n (PI.f64)) #s(literal 2 binary64))) (sqrt.f64 #s(literal 2 binary64))) (neg.f64 (.f64 (.f64 (.f64 (pow.f64 (log.f64 (.f64 (.f64 n (PI.f64)) #s(literal 2 binary64))) #s(literal 2 binary64)) (sqrt.f64 #s(literal 2 binary64))) #s(literal -1/8 binary64)) (sqrt.f64 (.f64 (.f64 (pow.f64 k #s(literal 3 binary64)) n) (PI.f64)))))) k (sqrt.f64 (.f64 (.f64 (.f64 n (PI.f64)) k) #s(literal 2 binary64)))) k))
#s(approx (/ (/ (sqrt (* (* (PI) 2) n)) (pow (* (* (PI) 2) n) (/ k 2))) (sqrt k)) (/.f64 (fma.f64 (fma.f64 (.f64 #s(literal -1 binary64) (fma.f64 (.f64 (.f64 (pow.f64 (log.f64 (.f64 (.f64 n (PI.f64)) #s(literal 2 binary64))) #s(literal 2 binary64)) (sqrt.f64 #s(literal 2 binary64))) #s(literal -1/8 binary64)) (sqrt.f64 (.f64 (.f64 n (PI.f64)) k)) (.f64 (fma.f64 (log.f64 (pow.f64 (.f64 (.f64 n (PI.f64)) #s(literal 2 binary64)) #s(literal -1/2 binary64))) (.f64 (.f64 (pow.f64 (log.f64 (.f64 (.f64 n (PI.f64)) #s(literal 2 binary64))) #s(literal 2 binary64)) (sqrt.f64 #s(literal 2 binary64))) #s(literal -1/8 binary64)) (.f64 (.f64 (pow.f64 (log.f64 (.f64 (.f64 n (PI.f64)) #s(literal 2 binary64))) #s(literal 3 binary64)) (sqrt.f64 #s(literal 2 binary64))) #s(literal -1/24 binary64))) (sqrt.f64 (.f64 (.f64 (pow.f64 k #s(literal 3 binary64)) n) (PI.f64)))))) k (.f64 (.f64 #s(literal -1/2 binary64) (sqrt.f64 (.f64 (.f64 n (PI.f64)) k))) (.f64 (log.f64 (.f64 (.f64 n (PI.f64)) #s(literal 2 binary64))) (sqrt.f64 #s(literal 2 binary64))))) k (sqrt.f64 (.f64 (.f64 (.f64 n (PI.f64)) k) #s(literal 2 binary64)))) k))
#s(approx (/ (sqrt (* (* (PI) 2) n)) (pow (* (* (PI) 2) n) (/ k 2))) (sqrt.f64 (.f64 (.f64 n (PI.f64)) #s(literal 2 binary64))))
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#s(approx (/ (sqrt (* (* (PI) 2) n)) (pow (* (* (PI) 2) n) (/ k 2))) (fma.f64 (fma.f64 (.f64 #s(literal -1/2 binary64) (sqrt.f64 (.f64 n (PI.f64)))) (.f64 (log.f64 (.f64 (.f64 n (PI.f64)) #s(literal 2 binary64))) (sqrt.f64 #s(literal 2 binary64))) (neg.f64 (.f64 (.f64 (.f64 (.f64 (pow.f64 (log.f64 (.f64 (.f64 n (PI.f64)) #s(literal 2 binary64))) #s(literal 2 binary64)) (sqrt.f64 #s(literal 2 binary64))) #s(literal -1/8 binary64)) k) (sqrt.f64 (.f64 n (PI.f64)))))) k (sqrt.f64 (.f64 (.f64 n (PI.f64)) #s(literal 2 binary64)))))
#s(approx (/ (sqrt (* (* (PI) 2) n)) (pow (* (* (PI) 2) n) (/ k 2))) (fma.f64 (fma.f64 (.f64 #s(literal -1 binary64) (fma.f64 (.f64 (.f64 (pow.f64 (log.f64 (.f64 (.f64 n (PI.f64)) #s(literal 2 binary64))) #s(literal 2 binary64)) (sqrt.f64 #s(literal 2 binary64))) #s(literal -1/8 binary64)) (sqrt.f64 (.f64 n (PI.f64))) (.f64 (.f64 (fma.f64 (log.f64 (pow.f64 (.f64 (.f64 n (PI.f64)) #s(literal 2 binary64)) #s(literal -1/2 binary64))) (.f64 (.f64 (pow.f64 (log.f64 (.f64 (.f64 n (PI.f64)) #s(literal 2 binary64))) #s(literal 2 binary64)) (sqrt.f64 #s(literal 2 binary64))) #s(literal -1/8 binary64)) (.f64 (.f64 (pow.f64 (log.f64 (.f64 (.f64 n (PI.f64)) #s(literal 2 binary64))) #s(literal 3 binary64)) (sqrt.f64 #s(literal 2 binary64))) #s(literal -1/24 binary64))) k) (sqrt.f64 (.f64 n (PI.f64)))))) k (.f64 (.f64 #s(literal -1/2 binary64) (sqrt.f64 (.f64 n (PI.f64)))) (.f64 (log.f64 (.f64 (.f64 n (PI.f64)) #s(literal 2 binary64))) (sqrt.f64 #s(literal 2 binary64))))) k (sqrt.f64 (.f64 (*.f64 n (PI.f64)) #s(literal 2 binary64)))))
#s(approx (pow (* (* (PI) 2) n) (/ k 2)) #s(literal 1 binary64))
#s(approx (pow (* (* (PI) 2) n) (/ k 2)) (fma.f64 (.f64 #s(literal 1/2 binary64) k) (log.f64 (.f64 (*.f64 n (PI.f64)) #s(literal 2 binary64))) #s(literal 1 binary64)))
#s(approx (pow (* (* (PI) 2) n) (/ k 2)) (fma.f64 (fma.f64 (.f64 #s(literal 1/8 binary64) k) (pow.f64 (log.f64 (.f64 (.f64 n (PI.f64)) #s(literal 2 binary64))) #s(literal 2 binary64)) (log.f64 (sqrt.f64 (.f64 (*.f64 n (PI.f64)) #s(literal 2 binary64))))) k #s(literal 1 binary64)))
#s(approx (pow (* (* (PI) 2) n) (/ k 2)) (fma.f64 (fma.f64 (fma.f64 (.f64 #s(literal 1/48 binary64) k) (pow.f64 (log.f64 (.f64 (.f64 n (PI.f64)) #s(literal 2 binary64))) #s(literal 3 binary64)) (.f64 (pow.f64 (log.f64 (.f64 (.f64 n (PI.f64)) #s(literal 2 binary64))) #s(literal 2 binary64)) #s(literal 1/8 binary64))) k (log.f64 (sqrt.f64 (.f64 (.f64 n (PI.f64)) #s(literal 2 binary64))))) k #s(literal 1 binary64)))
#s(approx (* (exp (* (log (pow k -1)) 1/2)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (.f64 (exp.f64 (.f64 (log.f64 (sqrt.f64 (.f64 (.f64 n (PI.f64)) #s(literal 2 binary64)))) (-.f64 #s(literal 1 binary64) k))) (pow.f64 (sqrt.f64 k) #s(literal -1 binary64))))
#s(approx (* (log (pow k -1)) 1/2) (*.f64 (neg.f64 (log.f64 k)) #s(literal 1/2 binary64)))
#s(approx (log (pow k -1)) (neg.f64 (log.f64 k)))
#s(approx (pow (* (* 2 (PI)) n) (/ (- 1 k) 2)) (exp.f64 (.f64 (log.f64 (sqrt.f64 (.f64 (*.f64 n (PI.f64)) #s(literal 2 binary64)))) (-.f64 #s(literal 1 binary64) k))))
#s(approx (* (pow (exp 1/2) (/ (* (+ (* -1 k) 1) (log (* n (* (PI) 2)))) 2)) (pow (exp 1/2) (/ (* (+ (* -1 k) 1) (log (* n (* (PI) 2)))) 2))) (pow.f64 (pow.f64 (exp.f64 #s(literal 1/4 binary64)) (.f64 (log.f64 (.f64 (*.f64 n (PI.f64)) #s(literal 2 binary64))) (-.f64 #s(literal 1 binary64) k))) #s(literal 2 binary64)))
#s(approx (pow (exp 1/2) (/ (* (+ (* -1 k) 1) (log (* n (* (PI) 2)))) 2)) (pow.f64 (exp.f64 #s(literal 1/4 binary64)) (.f64 (log.f64 (.f64 (*.f64 n (PI.f64)) #s(literal 2 binary64))) (-.f64 #s(literal 1 binary64) k))))
#s(approx (/ (* (+ (* -1 k) 1) (log (* n (* (PI) 2)))) 2) (.f64 (.f64 #s(literal -1/2 binary64) k) (log.f64 (.f64 (.f64 n (PI.f64)) #s(literal 2 binary64)))))
#s(approx (/ (* (+ (* -1 k) 1) (log (* n (* (PI) 2)))) 2) (.f64 (fma.f64 (log.f64 (.f64 (.f64 n (PI.f64)) #s(literal 2 binary64))) #s(literal -1/2 binary64) (/.f64 (log.f64 (sqrt.f64 (.f64 (*.f64 n (PI.f64)) #s(literal 2 binary64)))) k)) k))
#s(approx (* (+ (* -1 k) 1) (log (* n (* (PI) 2)))) (.f64 (neg.f64 k) (log.f64 (.f64 (*.f64 n (PI.f64)) #s(literal 2 binary64)))))
#s(approx (* (+ (* -1 k) 1) (log (* n (* (PI) 2)))) (.f64 (fma.f64 (log.f64 (.f64 (.f64 n (PI.f64)) #s(literal 2 binary64))) #s(literal -1 binary64) (/.f64 (log.f64 (.f64 (*.f64 n (PI.f64)) #s(literal 2 binary64))) k)) k))
#s(approx (+ (* -1 k) 1) (neg.f64 k))
#s(approx (+ (* -1 k) 1) (*.f64 (expm1.f64 (neg.f64 (log.f64 k))) k))
#s(approx (* (/ 1 (sqrt k)) (* (* (pow (PI) (/ (- 1 k) 2)) (pow 2 (/ (- 1 k) 2))) (/ (sqrt n) (pow n (/ k 2))))) (.f64 (/.f64 (exp.f64 (fma.f64 (.f64 #s(literal 1/2 binary64) (log.f64 #s(literal 2 binary64))) (-.f64 #s(literal 1 binary64) k) (.f64 (.f64 #s(literal 1/2 binary64) (log.f64 (PI.f64))) (-.f64 #s(literal 1 binary64) k)))) (pow.f64 (exp.f64 #s(literal 1/2 binary64)) (*.f64 (log.f64 n) k))) (sqrt.f64 (/.f64 n k))))
#s(approx (* (* (pow (PI) (/ (- 1 k) 2)) (pow 2 (/ (- 1 k) 2))) (/ (sqrt n) (pow n (/ k 2)))) (.f64 (/.f64 (exp.f64 (fma.f64 (.f64 #s(literal 1/2 binary64) (log.f64 #s(literal 2 binary64))) (-.f64 #s(literal 1 binary64) k) (.f64 (.f64 #s(literal 1/2 binary64) (log.f64 (PI.f64))) (-.f64 #s(literal 1 binary64) k)))) (pow.f64 (exp.f64 #s(literal 1/2 binary64)) (*.f64 (log.f64 n) k))) (sqrt.f64 n)))
#s(approx (* (pow (PI) (/ (- 1 k) 2)) (pow 2 (/ (- 1 k) 2))) (exp.f64 (fma.f64 (.f64 #s(literal 1/2 binary64) (log.f64 #s(literal 2 binary64))) (-.f64 #s(literal 1 binary64) k) (.f64 (*.f64 #s(literal 1/2 binary64) (log.f64 (PI.f64))) (-.f64 #s(literal 1 binary64) k)))))
#s(approx (pow (PI) (/ (- 1 k) 2)) (pow.f64 (exp.f64 #s(literal 1/2 binary64)) (*.f64 (log.f64 (PI.f64)) (-.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 (expm1.f64 (neg.f64 (log.f64 k))) k))
#s(approx (pow 2 (/ (- 1 k) 2)) (pow.f64 (exp.f64 #s(literal 1/2 binary64)) (*.f64 (log.f64 #s(literal 2 binary64)) (-.f64 #s(literal 1 binary64) k))))
#s(approx (/ (sqrt n) (pow n (/ k 2))) (.f64 (exp.f64 (neg.f64 (.f64 (*.f64 (log.f64 n) k) #s(literal 1/2 binary64)))) (sqrt.f64 n)))
#s(approx (pow n (/ k 2)) (pow.f64 (exp.f64 #s(literal 1/2 binary64)) (*.f64 (log.f64 n) k)))
#s(approx (/ (/ (sqrt (* (* (PI) 2) n)) (pow (* (* (PI) 2) n) (/ k 2))) (sqrt k)) (/.f64 (sqrt.f64 (.f64 (/.f64 (.f64 n (PI.f64)) k) #s(literal 2 binary64))) (pow.f64 (exp.f64 #s(literal 1/2 binary64)) (log.f64 (pow.f64 (.f64 (.f64 n (PI.f64)) #s(literal 2 binary64)) k)))))
#s(approx (/ (sqrt (* (* (PI) 2) n)) (pow (* (* (PI) 2) n) (/ k 2))) (/.f64 (sqrt.f64 (.f64 (.f64 n (PI.f64)) #s(literal 2 binary64))) (pow.f64 (exp.f64 #s(literal 1/2 binary64)) (log.f64 (pow.f64 (.f64 (.f64 n (PI.f64)) #s(literal 2 binary64)) k)))))
#s(approx (pow (* (* (PI) 2) n) (/ k 2)) (pow.f64 (exp.f64 #s(literal 1/2 binary64)) (log.f64 (pow.f64 (.f64 (.f64 n (PI.f64)) #s(literal 2 binary64)) k))))
#s(approx (* (exp (* (log (pow k -1)) 1/2)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (.f64 (.f64 (exp.f64 (.f64 (log.f64 (sqrt.f64 (.f64 (*.f64 n (PI.f64)) #s(literal 2 binary64)))) (fma.f64 #s(literal -1 binary64) k #s(literal 1 binary64)))) #s(literal -1 binary64)) (pow.f64 (sqrt.f64 k) #s(literal -1 binary64))))
#s(approx (exp (* (log (pow k -1)) 1/2)) (*.f64 (pow.f64 (sqrt.f64 k) #s(literal -1 binary64)) #s(literal -1 binary64)))
#s(approx (* (log (pow k -1)) 1/2) (.f64 (log.f64 (.f64 #s(literal -1 binary64) (/.f64 #s(literal -1 binary64) k))) #s(literal 1/2 binary64)))
#s(approx (log (pow k -1)) (log.f64 (*.f64 #s(literal -1 binary64) (/.f64 #s(literal -1 binary64) k))))
#s(approx (pow (* (* 2 (PI)) n) (/ (- 1 k) 2)) (exp.f64 (.f64 (log.f64 (sqrt.f64 (.f64 (*.f64 n (PI.f64)) #s(literal 2 binary64)))) (fma.f64 #s(literal -1 binary64) k #s(literal 1 binary64)))))
#s(approx (* (pow (exp 1/2) (/ (* (+ (* -1 k) 1) (log (* n (* (PI) 2)))) 2)) (pow (exp 1/2) (/ (* (+ (* -1 k) 1) (log (* n (* (PI) 2)))) 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 n (PI.f64)) #s(literal 2 binary64))))) #s(literal 2 binary64)))
#s(approx (pow (exp 1/2) (/ (* (+ (* -1 k) 1) (log (* n (* (PI) 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 n (PI.f64)) #s(literal 2 binary64))))))
#s(approx (/ (* (+ (* -1 k) 1) (log (* n (* (PI) 2)))) 2) (.f64 (neg.f64 k) (fma.f64 (/.f64 (log.f64 (.f64 (.f64 n (PI.f64)) #s(literal 2 binary64))) k) #s(literal -1/2 binary64) (log.f64 (sqrt.f64 (.f64 (*.f64 n (PI.f64)) #s(literal 2 binary64)))))))
#s(approx (* (+ (* -1 k) 1) (log (* n (* (PI) 2)))) (.f64 (neg.f64 k) (fma.f64 (/.f64 (log.f64 (.f64 (.f64 n (PI.f64)) #s(literal 2 binary64))) k) #s(literal -1 binary64) (log.f64 (.f64 (*.f64 n (PI.f64)) #s(literal 2 binary64))))))
#s(approx (+ (* -1 k) 1) (*.f64 (neg.f64 k) (-.f64 #s(literal 1 binary64) (pow.f64 k #s(literal -1 binary64)))))
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#s(approx (sqrt k) (neg.f64 (*.f64 (sqrt.f64 k) #s(literal -1 binary64))))
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#s(approx (* (pow (PI) (/ (- 1 k) 2)) (pow 2 (/ (- 1 k) 2))) (exp.f64 (fma.f64 (.f64 #s(literal 1/2 binary64) (log.f64 #s(literal 2 binary64))) (fma.f64 #s(literal -1 binary64) k #s(literal 1 binary64)) (.f64 (*.f64 #s(literal 1/2 binary64) (log.f64 (PI.f64))) (fma.f64 #s(literal -1 binary64) k #s(literal 1 binary64))))))
#s(approx (pow (PI) (/ (- 1 k) 2)) (pow.f64 (exp.f64 #s(literal 1/2 binary64)) (*.f64 (log.f64 (PI.f64)) (fma.f64 #s(literal -1 binary64) k #s(literal 1 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 k) (*.f64 (neg.f64 k) (-.f64 #s(literal 1 binary64) (pow.f64 k #s(literal -1 binary64)))))
#s(approx (pow 2 (/ (- 1 k) 2)) (pow.f64 (exp.f64 #s(literal 1/2 binary64)) (*.f64 (log.f64 #s(literal 2 binary64)) (fma.f64 #s(literal -1 binary64) k #s(literal 1 binary64)))))
#s(approx (* (exp (* (log (pow k -1)) 1/2)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (.f64 (exp.f64 (.f64 (log.f64 (sqrt.f64 (.f64 (.f64 n (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)) (exp.f64 (.f64 (log.f64 (sqrt.f64 (.f64 (*.f64 n (PI.f64)) #s(literal 2 binary64)))) (-.f64 #s(literal 1 binary64) k))))
#s(approx (* (pow (exp 1/2) (/ (* (+ (* -1 k) 1) (log (* n (* (PI) 2)))) 2)) (pow (exp 1/2) (/ (* (+ (* -1 k) 1) (log (* n (* (PI) 2)))) 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 n (PI.f64)) #s(literal 2 binary64))))) #s(literal 2 binary64)))
#s(approx (pow (exp 1/2) (/ (* (+ (* -1 k) 1) (log (* n (* (PI) 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 n (PI.f64)) #s(literal 2 binary64))))))
#s(approx (/ (* (+ (* -1 k) 1) (log (* n (* (PI) 2)))) 2) (.f64 (log.f64 (sqrt.f64 (.f64 (*.f64 n (PI.f64)) #s(literal 2 binary64)))) (fma.f64 #s(literal -1 binary64) k #s(literal 1 binary64))))
#s(approx (* (+ (* -1 k) 1) (log (* n (* (PI) 2)))) (.f64 (fma.f64 #s(literal -1 binary64) k #s(literal 1 binary64)) (log.f64 (.f64 (*.f64 n (PI.f64)) #s(literal 2 binary64)))))
#s(approx (log (* n (* (PI) 2))) (log.f64 (.f64 (.f64 n (PI.f64)) #s(literal 2 binary64))))
#s(approx (* n (* (PI) 2)) (.f64 (.f64 n (PI.f64)) #s(literal 2 binary64)))
#s(approx n n)
#s(approx (sqrt n) (sqrt.f64 n))
#s(approx (/ (/ (sqrt (* (* (PI) 2) n)) (pow (* (* (PI) 2) n) (/ k 2))) (sqrt k)) (/.f64 (sqrt.f64 (.f64 (/.f64 (.f64 n (PI.f64)) k) #s(literal 2 binary64))) (pow.f64 (exp.f64 #s(literal 1/2 binary64)) (log.f64 (pow.f64 (.f64 (.f64 n (PI.f64)) #s(literal 2 binary64)) k)))))
#s(approx (/ (sqrt (* (* (PI) 2) n)) (pow (* (* (PI) 2) n) (/ k 2))) (/.f64 (sqrt.f64 (.f64 (.f64 n (PI.f64)) #s(literal 2 binary64))) (pow.f64 (exp.f64 #s(literal 1/2 binary64)) (log.f64 (pow.f64 (.f64 (.f64 n (PI.f64)) #s(literal 2 binary64)) k)))))
#s(approx (sqrt (* (* (PI) 2) n)) (sqrt.f64 (.f64 (.f64 n (PI.f64)) #s(literal 2 binary64))))
#s(approx (* n (* (PI) 2)) (.f64 (.f64 n (PI.f64)) #s(literal 2 binary64)))
#s(approx (pow (* (* (PI) 2) n) (/ k 2)) (pow.f64 (exp.f64 #s(literal 1/2 binary64)) (log.f64 (pow.f64 (.f64 (.f64 n (PI.f64)) #s(literal 2 binary64)) k))))
#s(approx (* (exp (* (log (pow k -1)) 1/2)) (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 (* (pow (exp 1/2) (/ (* (+ (* -1 k) 1) (log (* n (* (PI) 2)))) 2)) (pow (exp 1/2) (/ (* (+ (* -1 k) 1) (log (* n (* (PI) 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)))) (fma.f64 #s(literal -1 binary64) k #s(literal 1 binary64)))) #s(literal 2 binary64)))
#s(approx (pow (exp 1/2) (/ (* (+ (* -1 k) 1) (log (* n (* (PI) 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)))) (fma.f64 #s(literal -1 binary64) k #s(literal 1 binary64)))))
#s(approx (/ (* (+ (* -1 k) 1) (log (* n (* (PI) 2)))) 2) (.f64 (.f64 #s(literal 1/2 binary64) (fma.f64 #s(literal -1 binary64) k #s(literal 1 binary64))) (fma.f64 (neg.f64 (log.f64 n)) #s(literal -1 binary64) (log.f64 (*.f64 (PI.f64) #s(literal 2 binary64))))))
#s(approx (* (+ (* -1 k) 1) (log (* n (* (PI) 2)))) (.f64 (fma.f64 (neg.f64 (log.f64 n)) #s(literal -1 binary64) (log.f64 (.f64 (PI.f64) #s(literal 2 binary64)))) (fma.f64 #s(literal -1 binary64) k #s(literal 1 binary64))))
#s(approx (log (* n (* (PI) 2))) (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) (/ (- 1 k) 2)) (pow 2 (/ (- 1 k) 2))) (/ (sqrt n) (pow n (/ k 2))))) (.f64 (/.f64 (exp.f64 (fma.f64 (.f64 #s(literal 1/2 binary64) (log.f64 #s(literal 2 binary64))) (-.f64 #s(literal 1 binary64) k) (.f64 (.f64 #s(literal 1/2 binary64) (log.f64 (PI.f64))) (-.f64 #s(literal 1 binary64) k)))) (pow.f64 (exp.f64 #s(literal -1/2 binary64)) (*.f64 (neg.f64 (log.f64 n)) k))) (sqrt.f64 (/.f64 n k))))
#s(approx (* (* (pow (PI) (/ (- 1 k) 2)) (pow 2 (/ (- 1 k) 2))) (/ (sqrt n) (pow n (/ k 2)))) (.f64 (/.f64 (exp.f64 (fma.f64 (.f64 #s(literal 1/2 binary64) (log.f64 #s(literal 2 binary64))) (-.f64 #s(literal 1 binary64) k) (.f64 (.f64 #s(literal 1/2 binary64) (log.f64 (PI.f64))) (-.f64 #s(literal 1 binary64) k)))) (pow.f64 (exp.f64 #s(literal -1/2 binary64)) (*.f64 (neg.f64 (log.f64 n)) k))) (sqrt.f64 n)))
#s(approx (/ (sqrt n) (pow n (/ k 2))) (.f64 (exp.f64 (neg.f64 (.f64 (*.f64 (neg.f64 (log.f64 n)) k) #s(literal -1/2 binary64)))) (sqrt.f64 n)))
#s(approx (pow n (/ k 2)) (pow.f64 (exp.f64 #s(literal -1/2 binary64)) (*.f64 (neg.f64 (log.f64 n)) k)))
#s(approx (/ (/ (sqrt (* (* (PI) 2) n)) (pow (* (* (PI) 2) n) (/ k 2))) (sqrt k)) (/.f64 (sqrt.f64 (.f64 (/.f64 (.f64 n (PI.f64)) k) #s(literal 2 binary64))) (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)))) k))))
#s(approx (/ (sqrt (* (* (PI) 2) n)) (pow (* (* (PI) 2) n) (/ k 2))) (/.f64 (sqrt.f64 (.f64 (.f64 n (PI.f64)) #s(literal 2 binary64))) (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)))) k))))
#s(approx (pow (* (* (PI) 2) n) (/ 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)))) k)))
#s(approx (* (exp (* (log (pow k -1)) 1/2)) (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))))
#s(approx (* (pow (exp 1/2) (/ (* (+ (* -1 k) 1) (log (* n (* (PI) 2)))) 2)) (pow (exp 1/2) (/ (* (+ (* -1 k) 1) (log (* n (* (PI) 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)))) (fma.f64 #s(literal -1 binary64) k #s(literal 1 binary64)))) #s(literal 2 binary64)))
#s(approx (pow (exp 1/2) (/ (* (+ (* -1 k) 1) (log (* n (* (PI) 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)))) (fma.f64 #s(literal -1 binary64) k #s(literal 1 binary64)))))
#s(approx (/ (* (+ (* -1 k) 1) (log (* n (* (PI) 2)))) 2) (.f64 (.f64 #s(literal 1/2 binary64) (fma.f64 #s(literal -1 binary64) k #s(literal 1 binary64))) (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 k) 1) (log (* n (* (PI) 2)))) (.f64 (fma.f64 (log.f64 (/.f64 #s(literal -1 binary64) n)) #s(literal -1 binary64) (log.f64 (.f64 #s(literal -2 binary64) (PI.f64)))) (fma.f64 #s(literal -1 binary64) k #s(literal 1 binary64))))
#s(approx (log (* n (* (PI) 2))) (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) (/ (- 1 k) 2)) (pow 2 (/ (- 1 k) 2))) (/ (sqrt n) (pow n (/ k 2))))) (neg.f64 (.f64 (/.f64 (.f64 (exp.f64 (fma.f64 (.f64 #s(literal 1/2 binary64) (log.f64 #s(literal 2 binary64))) (-.f64 #s(literal 1 binary64) k) (.f64 (.f64 #s(literal 1/2 binary64) (log.f64 (PI.f64))) (-.f64 #s(literal 1 binary64) k)))) #s(literal -1 binary64)) (exp.f64 (.f64 (*.f64 #s(literal 1/2 binary64) k) (fma.f64 (log.f64 (/.f64 #s(literal -1 binary64) n)) #s(literal -1 binary64) (log.f64 #s(literal -1 binary64)))))) (sqrt.f64 (/.f64 n k)))))
#s(approx (* (* (pow (PI) (/ (- 1 k) 2)) (pow 2 (/ (- 1 k) 2))) (/ (sqrt n) (pow n (/ k 2)))) (neg.f64 (.f64 (/.f64 (.f64 (exp.f64 (fma.f64 (.f64 #s(literal 1/2 binary64) (log.f64 #s(literal 2 binary64))) (-.f64 #s(literal 1 binary64) k) (.f64 (.f64 #s(literal 1/2 binary64) (log.f64 (PI.f64))) (-.f64 #s(literal 1 binary64) k)))) #s(literal -1 binary64)) (exp.f64 (.f64 (*.f64 #s(literal 1/2 binary64) k) (fma.f64 (log.f64 (/.f64 #s(literal -1 binary64) n)) #s(literal -1 binary64) (log.f64 #s(literal -1 binary64)))))) (sqrt.f64 n))))
#s(approx (/ (sqrt n) (pow n (/ k 2))) (neg.f64 (/.f64 (.f64 (sqrt.f64 n) #s(literal -1 binary64)) (exp.f64 (.f64 (*.f64 #s(literal 1/2 binary64) k) (fma.f64 (log.f64 (/.f64 #s(literal -1 binary64) n)) #s(literal -1 binary64) (log.f64 #s(literal -1 binary64))))))))
#s(approx (sqrt n) (neg.f64 (*.f64 (sqrt.f64 n) #s(literal -1 binary64))))
#s(approx (pow n (/ k 2)) (exp.f64 (.f64 (.f64 #s(literal 1/2 binary64) k) (fma.f64 (log.f64 (/.f64 #s(literal -1 binary64) n)) #s(literal -1 binary64) (log.f64 #s(literal -1 binary64))))))
#s(approx (/ (/ (sqrt (* (* (PI) 2) n)) (pow (* (* (PI) 2) n) (/ k 2))) (sqrt k)) (neg.f64 (/.f64 (sqrt.f64 (.f64 (/.f64 (.f64 n (PI.f64)) k) #s(literal 2 binary64))) (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)))) k)))))
#s(approx (/ (sqrt (* (* (PI) 2) n)) (pow (* (* (PI) 2) n) (/ k 2))) (neg.f64 (/.f64 (sqrt.f64 (.f64 (.f64 n (PI.f64)) #s(literal 2 binary64))) (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)))) k)))))
#s(approx (sqrt (* (* (PI) 2) n)) (neg.f64 (sqrt.f64 (.f64 (.f64 n (PI.f64)) #s(literal 2 binary64)))))
#s(approx (pow (* (* (PI) 2) n) (/ 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)))) k)))

eval56.0ms (0.5%)

Memory: -2.8MiB live, 90.3MiB allocated; 6ms collecting garbage
Compiler: Compiled 22 415 to 1 894 computations (91.6% saved)

prune888.0ms (7.6%)

Memory

13.9MiB live, 834.1MiB allocated; 49ms collecting garbage

Pruning

8 alts after pruning (2 fresh and 6 done)

	Pruned	Kept	Total
New	441	2	443
Fresh	0	0	0
Picked	2	1	3
Done	0	5	5
Total	443	8	451

Accuracy

100.0%

Counts

451 → 8

Alt Table

Click to see full alt table

Status	Accuracy	Program
	99.7%	(/.f64 (/.f64 (sqrt.f64 (.f64 (.f64 (PI.f64) #s(literal 2 binary64)) n)) (exp.f64 (.f64 (log.f64 (.f64 (*.f64 n (PI.f64)) #s(literal 2 binary64))) (/.f64 k #s(literal 2 binary64))))) (sqrt.f64 k))
✓	99.4%	(/.f64 (.f64 (pow.f64 (.f64 n (.f64 (PI.f64) #s(literal 2 binary64))) (/.f64 (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 2 binary64)) #s(literal 2 binary64))) (pow.f64 (.f64 n (*.f64 (PI.f64) #s(literal 2 binary64))) (/.f64 (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 2 binary64)) #s(literal 2 binary64)))) (sqrt.f64 k))
	99.7%	(/.f64 (sqrt.f64 (.f64 (.f64 n (PI.f64)) #s(literal 2 binary64))) (.f64 (pow.f64 (.f64 (*.f64 n (PI.f64)) #s(literal 2 binary64)) (/.f64 k #s(literal 2 binary64))) (sqrt.f64 k)))
✓	99.5%	(.f64 (pow.f64 (pow.f64 k #s(literal -1 binary64)) #s(literal 1/2 binary64)) (pow.f64 (.f64 (*.f64 #s(literal 2 binary64) (PI.f64)) n) (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 2 binary64))))
✓	76.6%	(.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)))))
✓	76.9%	(.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) (.f64 (*.f64 (pow.f64 (PI.f64) (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 2 binary64))) (pow.f64 #s(literal 2 binary64) (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 2 binary64)))) (/.f64 (sqrt.f64 n) (pow.f64 n (/.f64 k #s(literal 2 binary64))))))
✓	53.0%	#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))
✓	37.8%	#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 911 to 303 computations (66.7% saved)

regimes26.0ms (0.2%)

Memory

-23.0MiB live, 29.2MiB allocated; 4ms collecting garbage

Counts

20 → 1

Calls

Call 1

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

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

Calls

4 calls:

8.0ms	(.f64 (.f64 #s(literal 2 binary64) (PI.f64)) n)
6.0ms	n
6.0ms	k
5.0ms	(.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) (pow.f64 (.f64 (*.f64 #s(literal 2 binary64) (PI.f64)) n) (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 2 binary64))))

Results

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

Compiler

Compiled 23 to 23 computations (0% saved)

regimes18.0ms (0.2%)

Memory

22.6MiB live, 22.6MiB allocated; 0ms collecting garbage

Counts

15 → 1

Calls

Call 1

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

Outputs

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

Calls

4 calls:

5.0ms	n
5.0ms	(.f64 (.f64 #s(literal 2 binary64) (PI.f64)) n)
4.0ms	k
4.0ms	(.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) (pow.f64 (.f64 (*.f64 #s(literal 2 binary64) (PI.f64)) n) (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 2 binary64))))

Results

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

Compiler

Compiled 23 to 23 computations (0% saved)

regimes17.0ms (0.1%)

Memory

21.6MiB live, 21.6MiB allocated; 0ms collecting garbage

Counts

14 → 1

Calls

Call 1

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

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

Calls

4 calls:

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

Results

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

Compiler

Compiled 23 to 23 computations (0% saved)

regimes16.0ms (0.1%)

Memory

-30.3MiB live, 17.4MiB allocated; 1ms collecting garbage

Counts

12 → 1

Calls

Call 1

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

Outputs

(*.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)))))

Calls

4 calls:

5.0ms	n
4.0ms	(.f64 (.f64 #s(literal 2 binary64) (PI.f64)) n)
4.0ms	k
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
99.3%	1	`(.f64 (.f64 #s(literal 2 binary64) (PI.f64)) n)`
99.3%	1	`(.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) (pow.f64 (.f64 (*.f64 #s(literal 2 binary64) (PI.f64)) n) (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 2 binary64))))`
99.3%	1	`k`
99.3%	1	`n`

Compiler

Compiled 23 to 23 computations (0% saved)

regimes15.0ms (0.1%)

Memory

16.9MiB live, 16.9MiB allocated; 0ms collecting garbage

Counts

11 → 2

Calls

Call 1

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

Outputs

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

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

Calls

4 calls:

4.0ms	(.f64 (.f64 #s(literal 2 binary64) (PI.f64)) n)
4.0ms	n
3.0ms	k
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
96.0%	1	`(.f64 (.f64 #s(literal 2 binary64) (PI.f64)) n)`
99.5%	2	`(.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) (pow.f64 (.f64 (*.f64 #s(literal 2 binary64) (PI.f64)) n) (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 2 binary64))))`
99.5%	2	`k`
96.0%	1	`n`

Compiler

Compiled 23 to 23 computations (0% saved)

regimes10.0ms (0.1%)

Memory

12.3MiB live, 12.3MiB allocated; 0ms collecting garbage

Counts

6 → 1

Calls

Call 1

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

Outputs

(*.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))))))

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
96.0%	1	`(.f64 (.f64 #s(literal 2 binary64) (PI.f64)) n)`
96.0%	1	`n`
96.0%	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))))`
96.0%	1	`k`

Compiler

Compiled 23 to 23 computations (0% saved)

regimes9.0ms (0.1%)

Memory

-36.4MiB live, 11.3MiB allocated; 1ms collecting garbage

Counts

5 → 1

Calls

Call 1

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

Outputs

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

Calls

4 calls:

3.0ms	n
2.0ms	(.f64 (.f64 #s(literal 2 binary64) (PI.f64)) 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
96.0%	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))))`
96.0%	1	`k`
96.0%	1	`(.f64 (.f64 #s(literal 2 binary64) (PI.f64)) n)`
96.0%	1	`n`

Compiler

Compiled 23 to 23 computations (0% saved)

regimes8.0ms (0.1%)

Memory

10.3MiB live, 10.3MiB allocated; 0ms collecting garbage

Counts

4 → 1

Calls

Call 1

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

Outputs

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

Calls

4 calls:

2.0ms	n
2.0ms	(.f64 (.f64 #s(literal 2 binary64) (PI.f64)) 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
95.5%	1	`(.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) (pow.f64 (.f64 (*.f64 #s(literal 2 binary64) (PI.f64)) n) (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 2 binary64))))`
95.5%	1	`k`
95.5%	1	`(.f64 (.f64 #s(literal 2 binary64) (PI.f64)) n)`
95.5%	1	`n`

Compiler

Compiled 23 to 23 computations (0% saved)

regimes6.0ms (0%)

Memory

8.6MiB live, 8.6MiB allocated; 0ms collecting garbage

Counts

2 → 2

Calls

Call 1

Inputs

#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 (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))

Outputs

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

#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))

Calls

4 calls:

1.0ms	(.f64 (.f64 #s(literal 2 binary64) (PI.f64)) n)
1.0ms	k
1.0ms	n
1.0ms	(.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) (pow.f64 (.f64 (*.f64 #s(literal 2 binary64) (PI.f64)) n) (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 2 binary64))))

Results

Accuracy	Segments	Branch
63.5%	2	`(.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) (pow.f64 (.f64 (*.f64 #s(literal 2 binary64) (PI.f64)) n) (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 2 binary64))))`
53.0%	1	`(.f64 (.f64 #s(literal 2 binary64) (PI.f64)) n)`
53.0%	1	`n`
54.8%	2	`k`

Compiler

Compiled 23 to 23 computations (0% saved)

regimes5.0ms (0%)

Memory

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

Accuracy

Total 0.0b remaining (0%)

Threshold costs 0b (0%)

Counts

1 → 1

Calls

Call 1

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

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

Calls

4 calls:

1.0ms	k
1.0ms	(.f64 (.f64 #s(literal 2 binary64) (PI.f64)) n)
1.0ms	n
1.0ms	(.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) (pow.f64 (.f64 (*.f64 #s(literal 2 binary64) (PI.f64)) n) (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 2 binary64))))

Results

Accuracy	Segments	Branch
37.8%	1	`(.f64 (.f64 #s(literal 2 binary64) (PI.f64)) n)`
37.8%	1	`n`
37.8%	1	`k`
37.8%	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))))`

Compiler

Compiled 23 to 23 computations (0% saved)

bsearch21.0ms (0.2%)

Memory

-31.5MiB live, 16.0MiB allocated; 1ms collecting garbage

Algorithm

1×	binary-search

Stop Event

1×	narrow-enough

Steps

Time	Left	Right
19.0ms	3.686540422154319e-9	1.3988182534088641e-5

Samples

12.0ms

128×

valid

Compiler

Compiled 1 091 to 610 computations (44.1% saved)

Precisions

Click to see histograms. Total time spent on operations: 8.0ms

ival-mult: 2.0ms (24.3% of total)

ival-pow: 2.0ms (24.3% of total)

ival-div: 1.0ms (12.1% of total)

ival-sub: 1.0ms (12.1% of total)

ival-sqrt: 1.0ms (12.1% of total)

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

adjust: 0.0ms (0% of total)

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

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

exact: 0.0ms (0% of total)

bsearch0.0ms (0%)

Memory

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

Algorithm

1×	left-value

Steps

Time	Left	Right
0.0ms	2.0220207550736855e+149	6.204227563148402e+152

Compiler

Compiled 19 to 18 computations (5.3% saved)

simplify43.0ms (0.4%)

Memory

-4.5MiB live, 44.4MiB allocated; 2ms collecting garbage

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	112	516
1	128	510
2	152	510
3	246	510
4	901	510
5	3658	510

Stop Event

1×	node limit

Calls

Call 1

Inputs
(/.f64 (sqrt.f64 (.f64 (.f64 n (PI.f64)) #s(literal 2 binary64))) (.f64 (pow.f64 (.f64 (*.f64 n (PI.f64)) #s(literal 2 binary64)) (/.f64 k #s(literal 2 binary64))) (sqrt.f64 k)))
(.f64 (pow.f64 (pow.f64 k #s(literal -1 binary64)) #s(literal 1/2 binary64)) (pow.f64 (.f64 (*.f64 #s(literal 2 binary64) (PI.f64)) n) (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 2 binary64))))
(.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) (pow.f64 (.f64 (*.f64 #s(literal 2 binary64) (PI.f64)) n) (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 2 binary64))))
(.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) (.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)))))
(if (<=.f64 k #s(literal 2184094498327211/590295810358705651712 binary64)) (.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) #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))))) (.f64 (exp.f64 (.f64 (log.f64 (pow.f64 k #s(literal -1 binary64))) #s(literal 1/2 binary64))) #s(approx (pow (* (* 2 (PI)) n) (/ (- 1 k) 2)) (.f64 (pow.f64 (exp.f64 #s(literal 1/2 binary64)) (/.f64 (.f64 (fma.f64 #s(literal -1 binary64) k #s(literal 1 binary64)) (log.f64 (.f64 n (.f64 (PI.f64) #s(literal 2 binary64))))) #s(literal 2 binary64))) (pow.f64 (exp.f64 #s(literal 1/2 binary64)) (/.f64 (.f64 (fma.f64 #s(literal -1 binary64) k #s(literal 1 binary64)) (log.f64 (.f64 n (*.f64 (PI.f64) #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 (fma.f64 #s(literal -1 binary64) k #s(literal 1 binary64)) (log.f64 (.f64 (*.f64 (PI.f64) #s(literal 2 binary64)) n))))))
(.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) #s(approx (pow ( (* 2 (PI)) n) (/ (- 1 k) 2)) (.f64 (pow.f64 (exp.f64 #s(literal 1/2 binary64)) (/.f64 (.f64 (fma.f64 #s(literal -1 binary64) k #s(literal 1 binary64)) (log.f64 (.f64 n (.f64 (PI.f64) #s(literal 2 binary64))))) #s(literal 2 binary64))) (pow.f64 (exp.f64 #s(literal 1/2 binary64)) (/.f64 (.f64 (fma.f64 #s(literal -1 binary64) k #s(literal 1 binary64)) (log.f64 (.f64 n (*.f64 (PI.f64) #s(literal 2 binary64))))) #s(literal 2 binary64))))))
(.f64 (exp.f64 (.f64 (log.f64 (pow.f64 k #s(literal -1 binary64))) #s(literal 1/2 binary64))) #s(approx (pow (* (* 2 (PI)) n) (/ (- 1 k) 2)) (.f64 (pow.f64 (exp.f64 #s(literal 1/2 binary64)) (/.f64 (.f64 (fma.f64 #s(literal -1 binary64) k #s(literal 1 binary64)) (log.f64 (.f64 n (.f64 (PI.f64) #s(literal 2 binary64))))) #s(literal 2 binary64))) (pow.f64 (exp.f64 #s(literal 1/2 binary64)) (/.f64 (.f64 (fma.f64 #s(literal -1 binary64) k #s(literal 1 binary64)) (log.f64 (.f64 n (*.f64 (PI.f64) #s(literal 2 binary64))))) #s(literal 2 binary64))))))
(if (<=.f64 (.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) (pow.f64 (.f64 (.f64 #s(literal 2 binary64) (PI.f64)) n) (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 2 binary64)))) #s(literal 400000000000000019590690630060208231828890801412297555498016949836067305437353902464492611698910585517245225872604110704821373167465034086840910479360 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 (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 (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt.f64 (.f64 (/.f64 (.f64 (PI.f64) n) k) #s(literal 2 binary64))))

Outputs
(/.f64 (sqrt.f64 (.f64 (.f64 n (PI.f64)) #s(literal 2 binary64))) (.f64 (pow.f64 (.f64 (*.f64 n (PI.f64)) #s(literal 2 binary64)) (/.f64 k #s(literal 2 binary64))) (sqrt.f64 k)))
(.f64 (pow.f64 (pow.f64 k #s(literal -1 binary64)) #s(literal 1/2 binary64)) (pow.f64 (.f64 (*.f64 #s(literal 2 binary64) (PI.f64)) n) (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 2 binary64))))
(.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) (pow.f64 (.f64 (*.f64 #s(literal 2 binary64) (PI.f64)) n) (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 2 binary64))))
(.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) (.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)))))
(if (<=.f64 k #s(literal 2184094498327211/590295810358705651712 binary64)) (.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) #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))))) (.f64 (exp.f64 (.f64 (log.f64 (pow.f64 k #s(literal -1 binary64))) #s(literal 1/2 binary64))) #s(approx (pow (* (* 2 (PI)) n) (/ (- 1 k) 2)) (.f64 (pow.f64 (exp.f64 #s(literal 1/2 binary64)) (/.f64 (.f64 (fma.f64 #s(literal -1 binary64) k #s(literal 1 binary64)) (log.f64 (.f64 n (.f64 (PI.f64) #s(literal 2 binary64))))) #s(literal 2 binary64))) (pow.f64 (exp.f64 #s(literal 1/2 binary64)) (/.f64 (.f64 (fma.f64 #s(literal -1 binary64) k #s(literal 1 binary64)) (log.f64 (.f64 n (*.f64 (PI.f64) #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 (fma.f64 #s(literal -1 binary64) k #s(literal 1 binary64)) (log.f64 (.f64 (*.f64 (PI.f64) #s(literal 2 binary64)) n))))))
(.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) #s(approx (pow ( (* 2 (PI)) n) (/ (- 1 k) 2)) (.f64 (pow.f64 (exp.f64 #s(literal 1/2 binary64)) (/.f64 (.f64 (fma.f64 #s(literal -1 binary64) k #s(literal 1 binary64)) (log.f64 (.f64 n (.f64 (PI.f64) #s(literal 2 binary64))))) #s(literal 2 binary64))) (pow.f64 (exp.f64 #s(literal 1/2 binary64)) (/.f64 (.f64 (fma.f64 #s(literal -1 binary64) k #s(literal 1 binary64)) (log.f64 (.f64 n (*.f64 (PI.f64) #s(literal 2 binary64))))) #s(literal 2 binary64))))))
(.f64 (exp.f64 (.f64 (log.f64 (pow.f64 k #s(literal -1 binary64))) #s(literal 1/2 binary64))) #s(approx (pow (* (* 2 (PI)) n) (/ (- 1 k) 2)) (.f64 (pow.f64 (exp.f64 #s(literal 1/2 binary64)) (/.f64 (.f64 (fma.f64 #s(literal -1 binary64) k #s(literal 1 binary64)) (log.f64 (.f64 n (.f64 (PI.f64) #s(literal 2 binary64))))) #s(literal 2 binary64))) (pow.f64 (exp.f64 #s(literal 1/2 binary64)) (/.f64 (.f64 (fma.f64 #s(literal -1 binary64) k #s(literal 1 binary64)) (log.f64 (.f64 n (*.f64 (PI.f64) #s(literal 2 binary64))))) #s(literal 2 binary64))))))
(if (<=.f64 (.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) (pow.f64 (.f64 (.f64 #s(literal 2 binary64) (PI.f64)) n) (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 2 binary64)))) #s(literal 400000000000000019590690630060208231828890801412297555498016949836067305437353902464492611698910585517245225872604110704821373167465034086840910479360 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 (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 (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt.f64 (.f64 (/.f64 (.f64 (PI.f64) n) k) #s(literal 2 binary64))))

derivations83.0ms (0.7%)

Memory

24.4MiB live, 72.1MiB allocated; 1ms collecting garbage

Stop Event

1×

fuel

Compiler

Compiled 516 to 114 computations (77.9% saved)

preprocess57.0ms (0.5%)

Memory: 18.2MiB live, 65.5MiB allocated; 2ms collecting garbage
Compiler: Compiled 1 064 to 254 computations (76.1% saved)

end0.0ms (0%)

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

start0.0ms (0%)

analyze153.0ms (1.3%)

sample3.8s (32.6%)

explain143.0ms (1.2%)

preprocess143.0ms (1.2%)

eval0.0ms (0%)

prune0.0ms (0%)

series75.0ms (0.6%)

rewrite60.0ms (0.5%)

eval8.0ms (0.1%)

prune35.0ms (0.3%)

series167.0ms (1.4%)

rewrite95.0ms (0.8%)

eval36.0ms (0.3%)

prune344.0ms (3%)

series365.0ms (3.1%)

rewrite221.0ms (1.9%)

eval185.0ms (1.6%)

prune4.2s (36.3%)

series177.0ms (1.5%)

rewrite139.0ms (1.2%)

eval56.0ms (0.5%)

prune888.0ms (7.6%)

regimes26.0ms (0.2%)

regimes18.0ms (0.2%)

regimes17.0ms (0.1%)

regimes16.0ms (0.1%)

regimes15.0ms (0.1%)

regimes10.0ms (0.1%)

regimes9.0ms (0.1%)

regimes8.0ms (0.1%)

regimes6.0ms (0%)

regimes5.0ms (0%)

bsearch21.0ms (0.2%)

bsearch0.0ms (0%)

simplify43.0ms (0.4%)

derivations83.0ms (0.7%)

preprocess57.0ms (0.5%)

end0.0ms (0%)

Profiling