Metrics for Migdal et al, Equation (51)

start0.0ms (0%)

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

analyze112.0ms (1.5%)

Memory

20.3MiB live, 112.6MiB allocated; 11ms 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)

sample3.1s (42.9%)

Memory

75.9MiB live, 3 534.2MiB allocated; 711ms collecting garbage

Samples

984.0ms	4 479×	1	invalid
872.0ms	8 256×	0	valid
444.0ms	1 446×	2	invalid
30.0ms	382×	0	invalid
24.0ms	213×	0	exit

Precisions

Click to see histograms. Total time spent on operations: 1.8s

ival-mult: 506.0ms (28.5% of total)

ival-pow: 428.0ms (24.1% of total)

ival-div: 293.0ms (16.5% of total)

adjust: 155.0ms (8.7% of total)

ival-sqrt: 155.0ms (8.7% of total)

ival-sub: 126.0ms (7.1% of total)

ival-pi: 85.0ms (4.8% of total)

exact: 22.0ms (1.2% of total)

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

Bogosity

explain198.0ms (2.7%)

Memory

20.9MiB live, 303.4MiB allocated; 45ms collecting garbage

FPErrors

Click to see full error table

Ground Truth	Overpredictions	Example	Example	Subexpression
3	91	(3.996191282304425e-135 1.320374183204802e-262)	-	`(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	94	26

Confusion

	Predicted +	Predicted -
+	3	0
-	91	162

Precision

0.031914893617021274

Recall

1.0

Confusion?

	Predicted +	Predicted Maybe	Predicted -
+	3	0	0
-	91	26	136

Precision?

0.025

Recall?

1.0

Freqs

test

number	freq
0	162
1	94

Total Confusion?

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

Precision?

1.0

Recall?

1.0

Samples

63.0ms

512×

valid

Compiler

Compiled 128 to 43 computations (66.4% saved)

Precisions

Click to see histograms. Total time spent on operations: 41.0ms

ival-pow: 10.0ms (24.6% of total)

ival-mult: 9.0ms (22.1% of total)

ival-sqrt: 9.0ms (22.1% of total)

ival-div: 7.0ms (17.2% of total)

ival-sub: 3.0ms (7.4% of total)

ival-pi: 2.0ms (4.9% of total)

exact: 1.0ms (2.5% of total)

adjust: 0.0ms (0% of total)

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

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

preprocess234.0ms (3.2%)

Memory

-50.0MiB live, 153.1MiB allocated; 131ms 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 (fma.f64 k #s(literal -1 binary64) #s(literal 1 binary64)) #s(literal 2 binary64))) (/.f64 #s(literal 1 binary64) (sqrt.f64 k)))

Compiler

Compiled 16 to 13 computations (18.8% saved)

eval0.0ms (0%)

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

prune1.0ms (0%)

Memory

1.2MiB live, 1.2MiB allocated; 0ms collecting garbage

Alt Table

Click to see full alt table

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

Compiler

Compiled 16 to 13 computations (18.8% saved)

series91.0ms (1.2%)

Memory

-5.5MiB live, 138.8MiB allocated; 25ms 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
39.0ms	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))
33.0ms	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))
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))
7.0ms	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))

rewrite59.0ms (0.8%)

Memory

2.9MiB live, 93.2MiB allocated; 14ms 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 (pow.f64 k #s(literal -1 binary64)) #s(literal 1/2 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 (pow.f64 k #s(literal -1 binary64)) #s(literal 1/2 binary64)))
(/.f64 (.f64 #s(literal 1 binary64) (pow.f64 (.f64 (*.f64 (PI.f64) #s(literal 2 binary64)) n) (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 2 binary64)))) (pow.f64 k #s(literal 1/2 binary64)))
(pow.f64 (pow.f64 k #s(literal -1 binary64)) #s(literal 1/2 binary64))
(pow.f64 (pow.f64 k #s(literal 1/2 binary64)) #s(literal -1 binary64))
(/.f64 #s(literal -1 binary64) (neg.f64 (pow.f64 k #s(literal 1/2 binary64))))
(/.f64 #s(literal 1 binary64) (pow.f64 k #s(literal 1/2 binary64)))
(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))) (.f64 (pow.f64 #s(literal 2 binary64) #s(literal 1/2 binary64)) (pow.f64 (/.f64 (.f64 (PI.f64) n) k) #s(literal 1/2 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)) (pow.f64 #s(literal 2 binary64) #s(literal 1/2 binary64))) (.f64 (sqrt.f64 (pow.f64 k #s(literal 3 binary64))) (pow.f64 (.f64 (PI.f64) n) #s(literal 1/2 binary64)))) #s(literal -1/2 binary64) (.f64 (pow.f64 (.f64 (*.f64 (PI.f64) n) k) #s(literal 1/2 binary64)) (pow.f64 #s(literal 2 binary64) #s(literal 1/2 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 (sqrt.f64 (pow.f64 k #s(literal 3 binary64))) (pow.f64 (.f64 (PI.f64) n) #s(literal 1/2 binary64)))) (.f64 (.f64 (log.f64 (.f64 (.f64 (PI.f64) #s(literal 2 binary64)) n)) (log.f64 (.f64 (.f64 (PI.f64) #s(literal 2 binary64)) n))) (pow.f64 #s(literal 2 binary64) #s(literal 1/2 binary64))) (.f64 (.f64 #s(literal -1/2 binary64) (pow.f64 (.f64 (.f64 (PI.f64) n) k) #s(literal 1/2 binary64))) (.f64 (log.f64 (.f64 (.f64 (PI.f64) #s(literal 2 binary64)) n)) (pow.f64 #s(literal 2 binary64) #s(literal 1/2 binary64))))) k (.f64 (pow.f64 (.f64 (*.f64 (PI.f64) n) k) #s(literal 1/2 binary64)) (pow.f64 #s(literal 2 binary64) #s(literal 1/2 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) (.f64 (sqrt.f64 (pow.f64 k #s(literal 3 binary64))) (pow.f64 (.f64 (PI.f64) n) #s(literal 1/2 binary64)))) (.f64 (.f64 (.f64 (log.f64 (.f64 (.f64 (PI.f64) #s(literal 2 binary64)) n)) (log.f64 (.f64 (.f64 (PI.f64) #s(literal 2 binary64)) n))) (log.f64 (.f64 (.f64 (PI.f64) #s(literal 2 binary64)) n))) (pow.f64 #s(literal 2 binary64) #s(literal 1/2 binary64))) (.f64 (.f64 #s(literal 1/8 binary64) (pow.f64 (.f64 (.f64 (PI.f64) n) k) #s(literal 1/2 binary64))) (.f64 (.f64 (log.f64 (.f64 (.f64 (PI.f64) #s(literal 2 binary64)) n)) (log.f64 (.f64 (.f64 (PI.f64) #s(literal 2 binary64)) n))) (pow.f64 #s(literal 2 binary64) #s(literal 1/2 binary64))))) k (.f64 (.f64 #s(literal -1/2 binary64) (pow.f64 (.f64 (.f64 (PI.f64) n) k) #s(literal 1/2 binary64))) (.f64 (log.f64 (.f64 (.f64 (PI.f64) #s(literal 2 binary64)) n)) (pow.f64 #s(literal 2 binary64) #s(literal 1/2 binary64))))) k (.f64 (pow.f64 (.f64 (.f64 (PI.f64) n) k) #s(literal 1/2 binary64)) (pow.f64 #s(literal 2 binary64) #s(literal 1/2 binary64)))) k))
#s(approx (/ 1 (sqrt k)) (pow.f64 (pow.f64 k #s(literal -1 binary64)) #s(literal 1/2 binary64)))
#s(approx (sqrt k) (pow.f64 k #s(literal 1/2 binary64)))
#s(approx k k)
#s(approx (pow (* (* 2 (PI)) n) (/ (- 1 k) 2)) (.f64 (pow.f64 (.f64 (PI.f64) n) #s(literal 1/2 binary64)) (pow.f64 #s(literal 2 binary64) #s(literal 1/2 binary64))))
#s(approx (pow (* (* 2 (PI)) n) (/ (- 1 k) 2)) (fma.f64 (.f64 k (.f64 (pow.f64 (.f64 (PI.f64) n) #s(literal 1/2 binary64)) (.f64 (log.f64 (.f64 (.f64 (PI.f64) #s(literal 2 binary64)) n)) (pow.f64 #s(literal 2 binary64) #s(literal 1/2 binary64))))) #s(literal -1/2 binary64) (.f64 (pow.f64 (.f64 (PI.f64) n) #s(literal 1/2 binary64)) (pow.f64 #s(literal 2 binary64) #s(literal 1/2 binary64)))))
#s(approx (pow (* (* 2 (PI)) n) (/ (- 1 k) 2)) (fma.f64 (fma.f64 (.f64 #s(literal 1/8 binary64) (.f64 (.f64 k (.f64 (log.f64 (.f64 (.f64 (PI.f64) #s(literal 2 binary64)) n)) (log.f64 (.f64 (.f64 (PI.f64) #s(literal 2 binary64)) n)))) (pow.f64 #s(literal 2 binary64) #s(literal 1/2 binary64)))) (pow.f64 (.f64 (PI.f64) n) #s(literal 1/2 binary64)) (.f64 (.f64 #s(literal -1/2 binary64) (pow.f64 (.f64 (PI.f64) n) #s(literal 1/2 binary64))) (.f64 (log.f64 (.f64 (.f64 (PI.f64) #s(literal 2 binary64)) n)) (pow.f64 #s(literal 2 binary64) #s(literal 1/2 binary64))))) k (.f64 (pow.f64 (*.f64 (PI.f64) n) #s(literal 1/2 binary64)) (pow.f64 #s(literal 2 binary64) #s(literal 1/2 binary64)))))
#s(approx (pow (* (* 2 (PI)) n) (/ (- 1 k) 2)) (fma.f64 (fma.f64 (fma.f64 (.f64 (.f64 (.f64 k (.f64 (.f64 (log.f64 (.f64 (.f64 (PI.f64) #s(literal 2 binary64)) n)) (log.f64 (.f64 (.f64 (PI.f64) #s(literal 2 binary64)) n))) (log.f64 (.f64 (.f64 (PI.f64) #s(literal 2 binary64)) n)))) (pow.f64 #s(literal 2 binary64) #s(literal 1/2 binary64))) (pow.f64 (.f64 (PI.f64) n) #s(literal 1/2 binary64))) #s(literal -1/48 binary64) (.f64 (.f64 #s(literal 1/8 binary64) (pow.f64 (.f64 (PI.f64) n) #s(literal 1/2 binary64))) (.f64 (.f64 (log.f64 (.f64 (.f64 (PI.f64) #s(literal 2 binary64)) n)) (log.f64 (.f64 (.f64 (PI.f64) #s(literal 2 binary64)) n))) (pow.f64 #s(literal 2 binary64) #s(literal 1/2 binary64))))) k (.f64 (.f64 #s(literal -1/2 binary64) (pow.f64 (.f64 (PI.f64) n) #s(literal 1/2 binary64))) (.f64 (log.f64 (.f64 (.f64 (PI.f64) #s(literal 2 binary64)) n)) (pow.f64 #s(literal 2 binary64) #s(literal 1/2 binary64))))) k (.f64 (pow.f64 (*.f64 (PI.f64) n) #s(literal 1/2 binary64)) (pow.f64 #s(literal 2 binary64) #s(literal 1/2 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 (* (/ 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 (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 (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) (pow.f64 k #s(literal -1 binary64))) #s(literal 1/2 binary64)) k))
#s(approx (- 1 k) (*.f64 #s(literal -1 binary64) 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 (pow.f64 k #s(literal -1 binary64)) #s(literal 1/2 binary64))))
#s(approx (sqrt k) (.f64 (.f64 #s(literal -1 binary64) (pow.f64 k #s(literal 1/2 binary64))) #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 #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 (.f64 (-.f64 #s(literal 1/2 binary64) (*.f64 #s(literal 1/2 binary64) (pow.f64 k #s(literal -1 binary64)))) k) #s(literal -1 binary64)))
#s(approx (- 1 k) (.f64 (.f64 (-.f64 #s(literal 1 binary64) (pow.f64 k #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 (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 (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 (-.f64 #s(literal 0 binary64) (log.f64 n)) #s(literal -1 binary64) (+.f64 (log.f64 #s(literal 2 binary64)) (log.f64 (PI.f64)))) (-.f64 #s(literal 1 binary64) k))) (pow.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 (-.f64 #s(literal 0 binary64) (log.f64 n)) #s(literal -1 binary64) (+.f64 (log.f64 #s(literal 2 binary64)) (log.f64 (PI.f64)))) (-.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 (-.f64 (log.f64 #s(literal -1 binary64)) (log.f64 n)) #s(literal -1 binary64) (+.f64 (log.f64 #s(literal -2 binary64)) (log.f64 (PI.f64)))) (-.f64 #s(literal 1 binary64) k))) (pow.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 (-.f64 (log.f64 #s(literal -1 binary64)) (log.f64 n)) #s(literal -1 binary64) (+.f64 (log.f64 #s(literal -2 binary64)) (log.f64 (PI.f64)))) (-.f64 #s(literal 1 binary64) k))))

eval8.0ms (0.1%)

Memory: 19.2MiB live, 19.2MiB allocated; 0ms collecting garbage
Compiler: Compiled 1 864 to 289 computations (84.5% saved)

prune53.0ms (0.7%)

Memory

-44.5MiB live, 53.0MiB allocated; 21ms collecting garbage

Pruning

7 alts after pruning (7 fresh and 0 done)

	Pruned	Kept	Total
New	65	7	72
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	66	7	73

Accuracy

99.9%

Counts

73 → 7

Alt Table

Click to see full alt table

Status	Accuracy	Program
▶	99.6%	(/.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)))) (pow.f64 k #s(literal 1/2 binary64)))
	99.5%	(.f64 (pow.f64 (pow.f64 k #s(literal -1 binary64)) #s(literal 1/2 binary64)) (pow.f64 (.f64 (*.f64 (PI.f64) #s(literal 2 binary64)) n) (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 2 binary64))))
	99.4%	(.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) (.f64 (pow.f64 (.f64 (.f64 (PI.f64) #s(literal 2 binary64)) n) (/.f64 (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 2 binary64)) #s(literal 2 binary64))) (pow.f64 (.f64 (.f64 (PI.f64) #s(literal 2 binary64)) n) (/.f64 (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 2 binary64)) #s(literal 2 binary64)))))
▶	78.6%	(.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)))))
▶	62.7%	(.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 (.f64 (.f64 (log.f64 (.f64 (.f64 (PI.f64) #s(literal 2 binary64)) n)) (log.f64 (.f64 (.f64 (PI.f64) #s(literal 2 binary64)) n))) (log.f64 (.f64 (.f64 (PI.f64) #s(literal 2 binary64)) n)))) (pow.f64 #s(literal 2 binary64) #s(literal 1/2 binary64))) (pow.f64 (.f64 (PI.f64) n) #s(literal 1/2 binary64))) #s(literal -1/48 binary64) (.f64 (.f64 #s(literal 1/8 binary64) (pow.f64 (.f64 (PI.f64) n) #s(literal 1/2 binary64))) (.f64 (.f64 (log.f64 (.f64 (.f64 (PI.f64) #s(literal 2 binary64)) n)) (log.f64 (.f64 (.f64 (PI.f64) #s(literal 2 binary64)) n))) (pow.f64 #s(literal 2 binary64) #s(literal 1/2 binary64))))) k (.f64 (.f64 #s(literal -1/2 binary64) (pow.f64 (.f64 (PI.f64) n) #s(literal 1/2 binary64))) (.f64 (log.f64 (.f64 (.f64 (PI.f64) #s(literal 2 binary64)) n)) (pow.f64 #s(literal 2 binary64) #s(literal 1/2 binary64))))) k (.f64 (pow.f64 (*.f64 (PI.f64) n) #s(literal 1/2 binary64)) (pow.f64 #s(literal 2 binary64) #s(literal 1/2 binary64))))))
▶	51.3%	#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) (.f64 (sqrt.f64 (pow.f64 k #s(literal 3 binary64))) (pow.f64 (.f64 (PI.f64) n) #s(literal 1/2 binary64)))) (.f64 (.f64 (.f64 (log.f64 (.f64 (.f64 (PI.f64) #s(literal 2 binary64)) n)) (log.f64 (.f64 (.f64 (PI.f64) #s(literal 2 binary64)) n))) (log.f64 (.f64 (.f64 (PI.f64) #s(literal 2 binary64)) n))) (pow.f64 #s(literal 2 binary64) #s(literal 1/2 binary64))) (.f64 (.f64 #s(literal 1/8 binary64) (pow.f64 (.f64 (.f64 (PI.f64) n) k) #s(literal 1/2 binary64))) (.f64 (.f64 (log.f64 (.f64 (.f64 (PI.f64) #s(literal 2 binary64)) n)) (log.f64 (.f64 (.f64 (PI.f64) #s(literal 2 binary64)) n))) (pow.f64 #s(literal 2 binary64) #s(literal 1/2 binary64))))) k (.f64 (.f64 #s(literal -1/2 binary64) (pow.f64 (.f64 (.f64 (PI.f64) n) k) #s(literal 1/2 binary64))) (.f64 (log.f64 (.f64 (.f64 (PI.f64) #s(literal 2 binary64)) n)) (pow.f64 #s(literal 2 binary64) #s(literal 1/2 binary64))))) k (.f64 (pow.f64 (.f64 (.f64 (PI.f64) n) k) #s(literal 1/2 binary64)) (pow.f64 #s(literal 2 binary64) #s(literal 1/2 binary64)))) k))
▶	37.5%	#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (.f64 (pow.f64 #s(literal 2 binary64) #s(literal 1/2 binary64)) (pow.f64 (/.f64 (.f64 (PI.f64) n) k) #s(literal 1/2 binary64))))

Compiler

Compiled 682 to 338 computations (50.4% saved)

series336.0ms (4.6%)

Memory

20.3MiB live, 488.6MiB allocated; 86ms collecting garbage

Counts

66 → 256

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

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

Calls

6 calls:

Time	Variable		Point	Expression
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33.0ms	k	@	-inf	((/ (* 1 (pow (* (* (PI) 2) n) (/ (- 1 k) 2))) (pow k 1/2)) (* 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 (pow k 1/2) 1/2 (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (* (pow 2 1/2) (pow (/ (* (PI) n) k) 1/2)) (pow 2 1/2) (pow (/ (* (PI) n) k) 1/2) (/ (* (PI) n) k) (* (PI) n) (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (/ (+ (* (+ (* (+ (* (* -1/48 (* (sqrt (pow k 3)) (pow (* (PI) n) 1/2))) (* (* (* (log (* (* (PI) 2) n)) (log (* (* (PI) 2) n))) (log (* (* (PI) 2) n))) (pow 2 1/2))) (* (* 1/8 (pow (* (* (PI) n) k) 1/2)) (* (* (log (* (* (PI) 2) n)) (log (* (* (PI) 2) n))) (pow 2 1/2)))) k) (* (* -1/2 (pow (* (* (PI) n) k) 1/2)) (* (log (* (* (PI) 2) n)) (pow 2 1/2)))) k) (* (pow (* (* (PI) n) k) 1/2) (pow 2 1/2))) k) (+ (* (+ (* (+ (* (* -1/48 (* (sqrt (pow k 3)) (pow (* (PI) n) 1/2))) (* (* (* (log (* (* (PI) 2) n)) (log (* (* (PI) 2) n))) (log (* (* (PI) 2) n))) (pow 2 1/2))) (* (* 1/8 (pow (* (* (PI) n) k) 1/2)) (* (* (log (* (* (PI) 2) n)) (log (* (* (PI) 2) n))) (pow 2 1/2)))) k) (* (* -1/2 (pow (* (* (PI) n) k) 1/2)) (* (log (* (* (PI) 2) n)) (pow 2 1/2)))) k) (* (pow (* (* (PI) n) k) 1/2) (pow 2 1/2))) (+ (* (+ (* (* -1/48 (* (sqrt (pow k 3)) (pow (* (PI) n) 1/2))) (* (* (* (log (* (* (PI) 2) n)) (log (* (* (PI) 2) n))) (log (* (* (PI) 2) n))) (pow 2 1/2))) (* (* 1/8 (pow (* (* (PI) n) k) 1/2)) (* (* (log (* (* (PI) 2) n)) (log (* (* (PI) 2) n))) (pow 2 1/2)))) k) (* (* -1/2 (pow (* (* (PI) n) k) 1/2)) (* (log (* (* (PI) 2) n)) (pow 2 1/2)))) (+ (* (* -1/48 (* (sqrt (pow k 3)) (pow (* (PI) n) 1/2))) (* (* (* (log (* (* (PI) 2) n)) (log (* (* (PI) 2) n))) (log (* (* (PI) 2) n))) (pow 2 1/2))) (* (* 1/8 (pow (* (* (PI) n) k) 1/2)) (* (* (log (* (* (PI) 2) n)) (log (* (* (PI) 2) n))) (pow 2 1/2)))) (* -1/48 (* (sqrt (pow k 3)) (pow (* (PI) n) 1/2))) -1/48 (* (sqrt (pow k 3)) (pow (* (PI) n) 1/2)) (sqrt (pow k 3)) (pow k 3) 3 (pow (* (PI) n) 1/2) (* (* (* (log (* (* (PI) 2) n)) (log (* (* (PI) 2) n))) (log (* (* (PI) 2) n))) (pow 2 1/2)) (* (* (log (* (* (PI) 2) n)) (log (* (* (PI) 2) n))) (log (* (* (PI) 2) n))) (* (log (* (* (PI) 2) n)) (log (* (* (PI) 2) n))) (log (* (* (PI) 2) n)) (* (* 1/8 (pow (* (* (PI) n) k) 1/2)) (* (* (log (* (* (PI) 2) n)) (log (* (* (PI) 2) n))) (pow 2 1/2))) (* 1/8 (pow (* (* (PI) n) k) 1/2)) 1/8 (pow (* (* (PI) n) k) 1/2) (* (* (PI) n) k) (* (* (log (* (* (PI) 2) n)) (log (* (* (PI) 2) n))) (pow 2 1/2)) (* (* -1/2 (pow (* (* (PI) n) k) 1/2)) (* (log (* (* (PI) 2) n)) (pow 2 1/2))) (* -1/2 (pow (* (* (PI) n) k) 1/2)) -1/2 (* (log (* (* (PI) 2) n)) (pow 2 1/2)) (* (pow (* (* (PI) n) k) 1/2) (pow 2 1/2)) (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (/ 1 (sqrt k)) (sqrt k) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2)) (+ (* (+ (* (+ (* (* (* (* k (* (* (log (* (* (PI) 2) n)) (log (* (* (PI) 2) n))) (log (* (* (PI) 2) n)))) (pow 2 1/2)) (pow (* (PI) n) 1/2)) -1/48) (* (* 1/8 (pow (* (PI) n) 1/2)) (* (* (log (* (* (PI) 2) n)) (log (* (* (PI) 2) n))) (pow 2 1/2)))) k) (* (* -1/2 (pow (* (PI) n) 1/2)) (* (log (* (* (PI) 2) n)) (pow 2 1/2)))) k) (* (pow (* (PI) n) 1/2) (pow 2 1/2))) (+ (* (+ (* (* (* (* k (* (* (log (* (* (PI) 2) n)) (log (* (* (PI) 2) n))) (log (* (* (PI) 2) n)))) (pow 2 1/2)) (pow (* (PI) n) 1/2)) -1/48) (* (* 1/8 (pow (* (PI) n) 1/2)) (* (* (log (* (* (PI) 2) n)) (log (* (* (PI) 2) n))) (pow 2 1/2)))) k) (* (* -1/2 (pow (* (PI) n) 1/2)) (* (log (* (* (PI) 2) n)) (pow 2 1/2)))) (+ (* (* (* (* k (* (* (log (* (* (PI) 2) n)) (log (* (* (PI) 2) n))) (log (* (* (PI) 2) n)))) (pow 2 1/2)) (pow (* (PI) n) 1/2)) -1/48) (* (* 1/8 (pow (* (PI) n) 1/2)) (* (* (log (* (* (PI) 2) n)) (log (* (* (PI) 2) n))) (pow 2 1/2)))) (* (* (* k (* (* (log (* (* (PI) 2) n)) (log (* (* (PI) 2) n))) (log (* (* (PI) 2) n)))) (pow 2 1/2)) (pow (* (PI) n) 1/2)) (* (* k (* (* (log (* (* (PI) 2) n)) (log (* (* (PI) 2) n))) (log (* (* (PI) 2) n)))) (pow 2 1/2)) (* k (* (* (log (* (* (PI) 2) n)) (log (* (* (PI) 2) n))) (log (* (* (PI) 2) n)))) (* (* 1/8 (pow (* (PI) n) 1/2)) (* (* (log (* (* (PI) 2) n)) (log (* (* (PI) 2) n))) (pow 2 1/2))) (* 1/8 (pow (* (PI) n) 1/2)) (* (* -1/2 (pow (* (PI) n) 1/2)) (* (log (* (* (PI) 2) n)) (pow 2 1/2))) (* -1/2 (pow (* (PI) n) 1/2)) (* (pow (* (PI) n) 1/2) (pow 2 1/2)) (* (/ 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)))

rewrite258.0ms (3.5%)

Memory

27.6MiB live, 260.7MiB allocated; 28ms collecting garbage

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	992	19328
0	1129	15397
0	4929	15237

Stop Event

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

Counts

322 → 553

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

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

eval277.0ms (3.8%)

Memory: -13.4MiB live, 353.9MiB allocated; 67ms collecting garbage
Compiler: Compiled 119 672 to 5 433 computations (95.5% saved)

prune363.0ms (5%)

Memory

16.1MiB live, 637.8MiB allocated; 92ms collecting garbage

Pruning

8 alts after pruning (7 fresh and 1 done)

	Pruned	Kept	Total
New	1 087	6	1 093
Fresh	1	1	2
Picked	4	1	5
Done	0	0	0
Total	1 092	8	1 100

Accuracy

100.0%

Counts

1 100 → 8

Alt Table

Click to see full alt table

Status	Accuracy	Program
	99.5%	(/.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)))) (pow.f64 k #s(literal 1/2 binary64)))
✓	99.6%	(/.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)))) (pow.f64 k #s(literal 1/2 binary64)))
▶	99.5%	(.f64 (pow.f64 (pow.f64 k #s(literal -1 binary64)) #s(literal 1/2 binary64)) (pow.f64 (.f64 (*.f64 (PI.f64) #s(literal 2 binary64)) n) (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 2 binary64))))
	75.4%	(.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))))))
▶	24.5%	(.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) #s(approx (pow ( (* 2 (PI)) n) (/ (- 1 k) 2)) #s(approx (+ (* (+ (* (+ (* (* (* (* k (* (* (log (* (* (PI) 2) n)) (log (* (* (PI) 2) n))) (log (* (* (PI) 2) n)))) (pow 2 1/2)) (pow (* (PI) n) 1/2)) -1/48) (* (* 1/8 (pow (* (PI) n) 1/2)) (* (* (log (* (* (PI) 2) n)) (log (* (* (PI) 2) n))) (pow 2 1/2)))) k) (* (* -1/2 (pow (* (PI) n) 1/2)) (* (log (* (* (PI) 2) n)) (pow 2 1/2)))) k) (* (pow (* (PI) n) 1/2) (pow 2 1/2))) (.f64 (.f64 #s(literal -1 binary64) (pow.f64 k #s(literal 3 binary64))) (fma.f64 (.f64 (.f64 (pow.f64 (.f64 (PI.f64) n) #s(literal 1/2 binary64)) (.f64 (.f64 (log.f64 (.f64 n (.f64 (PI.f64) #s(literal 2 binary64)))) (log.f64 (.f64 n (.f64 (PI.f64) #s(literal 2 binary64))))) (log.f64 (.f64 n (.f64 (PI.f64) #s(literal 2 binary64)))))) (pow.f64 #s(literal 2 binary64) #s(literal 1/2 binary64))) #s(literal 1/48 binary64) (.f64 (/.f64 (fma.f64 (/.f64 (fma.f64 (.f64 #s(literal -1 binary64) (/.f64 (pow.f64 #s(literal 2 binary64) #s(literal 1/2 binary64)) k)) (pow.f64 (.f64 (PI.f64) n) #s(literal 1/2 binary64)) (.f64 (.f64 #s(literal 1/2 binary64) (pow.f64 (.f64 (PI.f64) n) #s(literal 1/2 binary64))) (.f64 (pow.f64 #s(literal 2 binary64) #s(literal 1/2 binary64)) (log.f64 (.f64 n (.f64 (PI.f64) #s(literal 2 binary64))))))) k) #s(literal -1 binary64) (.f64 (.f64 (pow.f64 (.f64 (PI.f64) n) #s(literal 1/2 binary64)) #s(literal 1/8 binary64)) (.f64 (log.f64 (.f64 n (.f64 (PI.f64) #s(literal 2 binary64)))) (.f64 (pow.f64 #s(literal 2 binary64) #s(literal 1/2 binary64)) (log.f64 (.f64 n (*.f64 (PI.f64) #s(literal 2 binary64)))))))) k) #s(literal -1 binary64)))))))
▶	51.3%	#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) (.f64 (sqrt.f64 (pow.f64 k #s(literal 3 binary64))) (pow.f64 (.f64 (PI.f64) n) #s(literal 1/2 binary64)))) (.f64 (.f64 (.f64 (log.f64 (.f64 (.f64 (PI.f64) #s(literal 2 binary64)) n)) (log.f64 (.f64 (.f64 (PI.f64) #s(literal 2 binary64)) n))) (log.f64 (.f64 (.f64 (PI.f64) #s(literal 2 binary64)) n))) (pow.f64 #s(literal 2 binary64) #s(literal 1/2 binary64))) (.f64 (.f64 #s(literal 1/8 binary64) (pow.f64 (.f64 (.f64 (PI.f64) n) k) #s(literal 1/2 binary64))) (.f64 (.f64 (log.f64 (.f64 (.f64 (PI.f64) #s(literal 2 binary64)) n)) (log.f64 (.f64 (.f64 (PI.f64) #s(literal 2 binary64)) n))) (pow.f64 #s(literal 2 binary64) #s(literal 1/2 binary64))))) k (.f64 (.f64 #s(literal -1/2 binary64) (pow.f64 (.f64 (.f64 (PI.f64) n) k) #s(literal 1/2 binary64))) (.f64 (log.f64 (.f64 (.f64 (PI.f64) #s(literal 2 binary64)) n)) (pow.f64 #s(literal 2 binary64) #s(literal 1/2 binary64))))) k (pow.f64 (.f64 (.f64 (.f64 k n) (PI.f64)) #s(literal 2 binary64)) #s(literal 1/2 binary64))) k))
▶	63.5%	#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (/.f64 (fma.f64 (pow.f64 #s(literal 2 binary64) #s(literal 1/2 binary64)) (.f64 (pow.f64 (.f64 (PI.f64) n) #s(literal 1/2 binary64)) (pow.f64 k #s(literal 1/2 binary64))) (.f64 (fma.f64 (fma.f64 (.f64 (.f64 (.f64 #s(literal -1/48 binary64) (pow.f64 (pow.f64 k #s(literal 3 binary64)) #s(literal 1/2 binary64))) (pow.f64 (.f64 (PI.f64) n) #s(literal 1/2 binary64))) (.f64 (.f64 (log.f64 (.f64 n (.f64 (PI.f64) #s(literal 2 binary64)))) (log.f64 (.f64 n (.f64 (PI.f64) #s(literal 2 binary64))))) (log.f64 (.f64 n (.f64 (PI.f64) #s(literal 2 binary64)))))) (pow.f64 #s(literal 2 binary64) #s(literal 1/2 binary64)) (.f64 (.f64 (.f64 (pow.f64 (.f64 (PI.f64) n) #s(literal 1/2 binary64)) (pow.f64 k #s(literal 1/2 binary64))) #s(literal 1/8 binary64)) (.f64 (log.f64 (.f64 n (.f64 (PI.f64) #s(literal 2 binary64)))) (.f64 (pow.f64 #s(literal 2 binary64) #s(literal 1/2 binary64)) (log.f64 (.f64 n (.f64 (PI.f64) #s(literal 2 binary64)))))))) k (.f64 (.f64 (.f64 (.f64 (pow.f64 (.f64 (PI.f64) n) #s(literal 1/2 binary64)) (pow.f64 k #s(literal 1/2 binary64))) #s(literal -1/2 binary64)) (log.f64 (.f64 n (.f64 (PI.f64) #s(literal 2 binary64))))) (pow.f64 #s(literal 2 binary64) #s(literal 1/2 binary64)))) k)) k))
▶	50.7%	#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (.f64 (pow.f64 #s(literal 2 binary64) #s(literal 1/2 binary64)) (/.f64 (pow.f64 (.f64 (PI.f64) n) #s(literal 1/2 binary64)) (pow.f64 k #s(literal 1/2 binary64)))))

Compiler

Compiled 1 129 to 504 computations (55.4% saved)

series353.0ms (4.8%)

Memory

9.8MiB live, 480.3MiB allocated; 66ms collecting garbage

Counts

95 → 383

Calls

Call 1

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

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

Calls

6 calls:

Time	Variable		Point	Expression
93.0ms	n	@	-inf	((* (pow (pow k -1) 1/2) (pow (* (* (PI) 2) n) (/ (- 1 k) 2))) (pow (pow k -1) 1/2) (pow k -1) k -1 1/2 (pow (* (* (PI) 2) n) (/ (- 1 k) 2)) (* (* (PI) 2) n) (* (PI) 2) (PI) 2 n (/ (- 1 k) 2) (- 1 k) 1 (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (* (pow 2 1/2) (/ (pow (* (PI) n) 1/2) (pow k 1/2))) (pow 2 1/2) (/ (pow (* (PI) n) 1/2) (pow k 1/2)) (pow (* (PI) n) 1/2) (* (PI) n) (pow k 1/2) (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (/ (+ (* (pow 2 1/2) (* (pow (* (PI) n) 1/2) (pow k 1/2))) (* (+ (* (+ (* (* (* (* -1/48 (pow (pow k 3) 1/2)) (pow (* (PI) n) 1/2)) (* (* (log (* n (* (PI) 2))) (log (* n (* (PI) 2)))) (log (* n (* (PI) 2))))) (pow 2 1/2)) (* (* (* (pow (* (PI) n) 1/2) (pow k 1/2)) 1/8) (* (log (* n (* (PI) 2))) (* (pow 2 1/2) (log (* n (* (PI) 2))))))) k) (* (* (* (* (pow (* (PI) n) 1/2) (pow k 1/2)) -1/2) (log (* n (* (PI) 2)))) (pow 2 1/2))) k)) k) (+ (* (pow 2 1/2) (* (pow (* (PI) n) 1/2) (pow k 1/2))) (* (+ (* (+ (* (* (* (* -1/48 (pow (pow k 3) 1/2)) (pow (* (PI) n) 1/2)) (* (* (log (* n (* (PI) 2))) (log (* n (* (PI) 2)))) (log (* n (* (PI) 2))))) (pow 2 1/2)) (* (* (* (pow (* (PI) n) 1/2) (pow k 1/2)) 1/8) (* (log (* n (* (PI) 2))) (* (pow 2 1/2) (log (* n (* (PI) 2))))))) k) (* (* (* (* (pow (* (PI) n) 1/2) (pow k 1/2)) -1/2) (log (* n (* (PI) 2)))) (pow 2 1/2))) k)) (* (pow (* (PI) n) 1/2) (pow k 1/2)) (* (+ (* (+ (* (* (* (* -1/48 (pow (pow k 3) 1/2)) (pow (* (PI) n) 1/2)) (* (* (log (* n (* (PI) 2))) (log (* n (* (PI) 2)))) (log (* n (* (PI) 2))))) (pow 2 1/2)) (* (* (* (pow (* (PI) n) 1/2) (pow k 1/2)) 1/8) (* (log (* n (* (PI) 2))) (* (pow 2 1/2) (log (* n (* (PI) 2))))))) k) (* (* (* (* (pow (* (PI) n) 1/2) (pow k 1/2)) -1/2) (log (* n (* (PI) 2)))) (pow 2 1/2))) k) (+ (* (+ (* (* (* (* -1/48 (pow (pow k 3) 1/2)) (pow (* (PI) n) 1/2)) (* (* (log (* n (* (PI) 2))) (log (* n (* (PI) 2)))) (log (* n (* (PI) 2))))) (pow 2 1/2)) (* (* (* (pow (* (PI) n) 1/2) (pow k 1/2)) 1/8) (* (log (* n (* (PI) 2))) (* (pow 2 1/2) (log (* n (* (PI) 2))))))) k) (* (* (* (* (pow (* (PI) n) 1/2) (pow k 1/2)) -1/2) (log (* n (* (PI) 2)))) (pow 2 1/2))) (+ (* (* (* (* -1/48 (pow (pow k 3) 1/2)) (pow (* (PI) n) 1/2)) (* (* (log (* n (* (PI) 2))) (log (* n (* (PI) 2)))) (log (* n (* (PI) 2))))) (pow 2 1/2)) (* (* (* (pow (* (PI) n) 1/2) (pow k 1/2)) 1/8) (* (log (* n (* (PI) 2))) (* (pow 2 1/2) (log (* n (* (PI) 2))))))) (* (* (* -1/48 (pow (pow k 3) 1/2)) (pow (* (PI) n) 1/2)) (* (* (log (* n (* (PI) 2))) (log (* n (* (PI) 2)))) (log (* n (* (PI) 2))))) (* (* -1/48 (pow (pow k 3) 1/2)) (pow (* (PI) n) 1/2)) (* -1/48 (pow (pow k 3) 1/2)) -1/48 (pow (pow k 3) 1/2) (pow k 3) 3 (* (* (log (* n (* (PI) 2))) (log (* n (* (PI) 2)))) (log (* n (* (PI) 2)))) (* (log (* n (* (PI) 2))) (log (* n (* (PI) 2)))) (log (* n (* (PI) 2))) (* n (* (PI) 2)) (* (* (* (pow (* (PI) n) 1/2) (pow k 1/2)) 1/8) (* (log (* n (* (PI) 2))) (* (pow 2 1/2) (log (* n (* (PI) 2)))))) (* (* (pow (* (PI) n) 1/2) (pow k 1/2)) 1/8) 1/8 (* (log (* n (* (PI) 2))) (* (pow 2 1/2) (log (* n (* (PI) 2))))) (* (pow 2 1/2) (log (* n (* (PI) 2)))) (* (* (* (* (pow (* (PI) n) 1/2) (pow k 1/2)) -1/2) (log (* n (* (PI) 2)))) (pow 2 1/2)) (* (* (* (pow (* (PI) n) 1/2) (pow k 1/2)) -1/2) (log (* n (* (PI) 2)))) (* (* (pow (* (PI) n) 1/2) (pow k 1/2)) -1/2) -1/2 (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (/ (+ (* (+ (* (+ (* (* -1/48 (* (sqrt (pow k 3)) (pow (* (PI) n) 1/2))) (* (* (* (log (* (* (PI) 2) n)) (log (* (* (PI) 2) n))) (log (* (* (PI) 2) n))) (pow 2 1/2))) (* (* 1/8 (pow (* (* (PI) n) k) 1/2)) (* (* (log (* (* (PI) 2) n)) (log (* (* (PI) 2) n))) (pow 2 1/2)))) k) (* (* -1/2 (pow (* (* (PI) n) k) 1/2)) (* (log (* (* (PI) 2) n)) (pow 2 1/2)))) k) (pow (* (* (* k n) (PI)) 2) 1/2)) k) (+ (* (+ (* (+ (* (* -1/48 (* (sqrt (pow k 3)) (pow (* (PI) n) 1/2))) (* (* (* (log (* (* (PI) 2) n)) (log (* (* (PI) 2) n))) (log (* (* (PI) 2) n))) (pow 2 1/2))) (* (* 1/8 (pow (* (* (PI) n) k) 1/2)) (* (* (log (* (* (PI) 2) n)) (log (* (* (PI) 2) n))) (pow 2 1/2)))) k) (* (* -1/2 (pow (* (* (PI) n) k) 1/2)) (* (log (* (* (PI) 2) n)) (pow 2 1/2)))) k) (pow (* (* (* k n) (PI)) 2) 1/2)) (+ (* (+ (* (* -1/48 (* (sqrt (pow k 3)) (pow (* (PI) n) 1/2))) (* (* (* (log (* (* (PI) 2) n)) (log (* (* (PI) 2) n))) (log (* (* (PI) 2) n))) (pow 2 1/2))) (* (* 1/8 (pow (* (* (PI) n) k) 1/2)) (* (* (log (* (* (PI) 2) n)) (log (* (* (PI) 2) n))) (pow 2 1/2)))) k) (* (* -1/2 (pow (* (* (PI) n) k) 1/2)) (* (log (* (* (PI) 2) n)) (pow 2 1/2)))) (+ (* (* -1/48 (* (sqrt (pow k 3)) (pow (* (PI) n) 1/2))) (* (* (* (log (* (* (PI) 2) n)) (log (* (* (PI) 2) n))) (log (* (* (PI) 2) n))) (pow 2 1/2))) (* (* 1/8 (pow (* (* (PI) n) k) 1/2)) (* (* (log (* (* (PI) 2) n)) (log (* (* (PI) 2) n))) (pow 2 1/2)))) (* -1/48 (* (sqrt (pow k 3)) (pow (* (PI) n) 1/2))) (* (sqrt (pow k 3)) (pow (* (PI) n) 1/2)) (sqrt (pow k 3)) (* (* (* (log (* (* (PI) 2) n)) (log (* (* (PI) 2) n))) (log (* (* (PI) 2) n))) (pow 2 1/2)) (* (* (log (* (* (PI) 2) n)) (log (* (* (PI) 2) n))) (log (* (* (PI) 2) n))) (* (log (* (* (PI) 2) n)) (log (* (* (PI) 2) n))) (log (* (* (PI) 2) n)) (* (* 1/8 (pow (* (* (PI) n) k) 1/2)) (* (* (log (* (* (PI) 2) n)) (log (* (* (PI) 2) n))) (pow 2 1/2))) (* 1/8 (pow (* (* (PI) n) k) 1/2)) (pow (* (* (PI) n) k) 1/2) (* (* (PI) n) k) (* (* (log (* (* (PI) 2) n)) (log (* (* (PI) 2) n))) (pow 2 1/2)) (* (* -1/2 (pow (* (* (PI) n) k) 1/2)) (* (log (* (* (PI) 2) n)) (pow 2 1/2))) (* -1/2 (pow (* (* (PI) n) k) 1/2)) (* (log (* (* (PI) 2) n)) (pow 2 1/2)) (pow (* (* (* k n) (PI)) 2) 1/2) (* (* (* k n) (PI)) 2) (* (* k n) (PI)) (* k n) (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (/ 1 (sqrt k)) (sqrt k) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2)) (+ (* (+ (* (+ (* (* (* (* k (* (* (log (* (* (PI) 2) n)) (log (* (* (PI) 2) n))) (log (* (* (PI) 2) n)))) (pow 2 1/2)) (pow (* (PI) n) 1/2)) -1/48) (* (* 1/8 (pow (* (PI) n) 1/2)) (* (* (log (* (* (PI) 2) n)) (log (* (* (PI) 2) n))) (pow 2 1/2)))) k) (* (* -1/2 (pow (* (PI) n) 1/2)) (* (log (* (* (PI) 2) n)) (pow 2 1/2)))) k) (* (pow (* (PI) n) 1/2) (pow 2 1/2))) (* (* -1 (pow k 3)) (+ (* (* (* (pow (* (PI) n) 1/2) (* (* (log (* n (* (PI) 2))) (log (* n (* (PI) 2)))) (log (* n (* (PI) 2))))) (pow 2 1/2)) 1/48) (* (/ (+ (* (/ (+ (* (* -1 (/ (pow 2 1/2) k)) (pow (* (PI) n) 1/2)) (* (* 1/2 (pow (* (PI) n) 1/2)) (* (pow 2 1/2) (log (* n (* (PI) 2)))))) k) -1) (* (* (pow (* (PI) n) 1/2) 1/8) (* (log (* n (* (PI) 2))) (* (pow 2 1/2) (log (* n (* (PI) 2))))))) k) -1))) (* -1 (pow k 3)) (+ (* (* (* (pow (* (PI) n) 1/2) (* (* (log (* n (* (PI) 2))) (log (* n (* (PI) 2)))) (log (* n (* (PI) 2))))) (pow 2 1/2)) 1/48) (* (/ (+ (* (/ (+ (* (* -1 (/ (pow 2 1/2) k)) (pow (* (PI) n) 1/2)) (* (* 1/2 (pow (* (PI) n) 1/2)) (* (pow 2 1/2) (log (* n (* (PI) 2)))))) k) -1) (* (* (pow (* (PI) n) 1/2) 1/8) (* (log (* n (* (PI) 2))) (* (pow 2 1/2) (log (* n (* (PI) 2))))))) k) -1)) (* (* (pow (* (PI) n) 1/2) (* (* (log (* n (* (PI) 2))) (log (* n (* (PI) 2)))) (log (* n (* (PI) 2))))) (pow 2 1/2)) (* (pow (* (PI) n) 1/2) (* (* (log (* n (* (PI) 2))) (log (* n (* (PI) 2)))) (log (* n (* (PI) 2))))) 1/48 (* (/ (+ (* (/ (+ (* (* -1 (/ (pow 2 1/2) k)) (pow (* (PI) n) 1/2)) (* (* 1/2 (pow (* (PI) n) 1/2)) (* (pow 2 1/2) (log (* n (* (PI) 2)))))) k) -1) (* (* (pow (* (PI) n) 1/2) 1/8) (* (log (* n (* (PI) 2))) (* (pow 2 1/2) (log (* n (* (PI) 2))))))) k) -1) (/ (+ (* (/ (+ (* (* -1 (/ (pow 2 1/2) k)) (pow (* (PI) n) 1/2)) (* (* 1/2 (pow (* (PI) n) 1/2)) (* (pow 2 1/2) (log (* n (* (PI) 2)))))) k) -1) (* (* (pow (* (PI) n) 1/2) 1/8) (* (log (* n (* (PI) 2))) (* (pow 2 1/2) (log (* n (* (PI) 2))))))) k) (+ (* (/ (+ (* (* -1 (/ (pow 2 1/2) k)) (pow (* (PI) n) 1/2)) (* (* 1/2 (pow (* (PI) n) 1/2)) (* (pow 2 1/2) (log (* n (* (PI) 2)))))) k) -1) (* (* (pow (* (PI) n) 1/2) 1/8) (* (log (* n (* (PI) 2))) (* (pow 2 1/2) (log (* n (* (PI) 2))))))) (/ (+ (* (* -1 (/ (pow 2 1/2) k)) (pow (* (PI) n) 1/2)) (* (* 1/2 (pow (* (PI) n) 1/2)) (* (pow 2 1/2) (log (* n (* (PI) 2)))))) k) (+ (* (* -1 (/ (pow 2 1/2) k)) (pow (* (PI) n) 1/2)) (* (* 1/2 (pow (* (PI) n) 1/2)) (* (pow 2 1/2) (log (* n (* (PI) 2)))))) (* -1 (/ (pow 2 1/2) k)) (/ (pow 2 1/2) k) (* (* 1/2 (pow (* (PI) n) 1/2)) (* (pow 2 1/2) (log (* n (* (PI) 2))))) (* 1/2 (pow (* (PI) n) 1/2)) (* (* (pow (* (PI) n) 1/2) 1/8) (* (log (* n (* (PI) 2))) (* (pow 2 1/2) (log (* n (* (PI) 2)))))) (* (pow (* (PI) n) 1/2) 1/8))
53.0ms	n	@	inf	((* (pow (pow k -1) 1/2) (pow (* (* (PI) 2) n) (/ (- 1 k) 2))) (pow (pow k -1) 1/2) (pow k -1) k -1 1/2 (pow (* (* (PI) 2) n) (/ (- 1 k) 2)) (* (* (PI) 2) n) (* (PI) 2) (PI) 2 n (/ (- 1 k) 2) (- 1 k) 1 (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (* (pow 2 1/2) (/ (pow (* (PI) n) 1/2) (pow k 1/2))) (pow 2 1/2) (/ (pow (* (PI) n) 1/2) (pow k 1/2)) (pow (* (PI) n) 1/2) (* (PI) n) (pow k 1/2) (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (/ (+ (* (pow 2 1/2) (* (pow (* (PI) n) 1/2) (pow k 1/2))) (* (+ (* (+ (* (* (* (* -1/48 (pow (pow k 3) 1/2)) (pow (* (PI) n) 1/2)) (* (* (log (* n (* (PI) 2))) (log (* n (* (PI) 2)))) (log (* n (* (PI) 2))))) (pow 2 1/2)) (* (* (* (pow (* (PI) n) 1/2) (pow k 1/2)) 1/8) (* (log (* n (* (PI) 2))) (* (pow 2 1/2) (log (* n (* (PI) 2))))))) k) (* (* (* (* (pow (* (PI) n) 1/2) (pow k 1/2)) -1/2) (log (* n (* (PI) 2)))) (pow 2 1/2))) k)) k) (+ (* (pow 2 1/2) (* (pow (* (PI) n) 1/2) (pow k 1/2))) (* (+ (* (+ (* (* (* (* -1/48 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rewrite308.0ms (4.2%)

Memory

11.1MiB live, 436.0MiB allocated; 34ms collecting garbage

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	1180	36541
0	1391	28588
0	5698	28114

Stop Event

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

Counts

478 → 883

Calls

Call 1

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

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

eval354.0ms (4.8%)

Memory: 14.3MiB live, 501.7MiB allocated; 146ms collecting garbage
Compiler: Compiled 204 424 to 7 552 computations (96.3% saved)

prune499.0ms (6.8%)

Memory

-20.4MiB live, 841.8MiB allocated; 63ms collecting garbage

Pruning

8 alts after pruning (2 fresh and 6 done)

	Pruned	Kept	Total
New	1 302	0	1 302
Fresh	0	2	2
Picked	0	5	5
Done	0	1	1
Total	1 302	8	1 310

Accuracy

100.0%

Counts

1 310 → 8

Alt Table

Click to see full alt table

Status	Accuracy	Program
▶	99.5%	(/.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)))) (pow.f64 k #s(literal 1/2 binary64)))
✓	99.6%	(/.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)))) (pow.f64 k #s(literal 1/2 binary64)))
✓	99.5%	(.f64 (pow.f64 (pow.f64 k #s(literal -1 binary64)) #s(literal 1/2 binary64)) (pow.f64 (.f64 (*.f64 (PI.f64) #s(literal 2 binary64)) n) (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 2 binary64))))
▶	75.4%	(.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))))))
✓	24.5%	(.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) #s(approx (pow ( (* 2 (PI)) n) (/ (- 1 k) 2)) #s(approx (+ (* (+ (* (+ (* (* (* (* k (* (* (log (* (* (PI) 2) n)) (log (* (* (PI) 2) n))) (log (* (* (PI) 2) n)))) (pow 2 1/2)) (pow (* (PI) n) 1/2)) -1/48) (* (* 1/8 (pow (* (PI) n) 1/2)) (* (* (log (* (* (PI) 2) n)) (log (* (* (PI) 2) n))) (pow 2 1/2)))) k) (* (* -1/2 (pow (* (PI) n) 1/2)) (* (log (* (* (PI) 2) n)) (pow 2 1/2)))) k) (* (pow (* (PI) n) 1/2) (pow 2 1/2))) (.f64 (.f64 #s(literal -1 binary64) (pow.f64 k #s(literal 3 binary64))) (fma.f64 (.f64 (.f64 (pow.f64 (.f64 (PI.f64) n) #s(literal 1/2 binary64)) (.f64 (.f64 (log.f64 (.f64 n (.f64 (PI.f64) #s(literal 2 binary64)))) (log.f64 (.f64 n (.f64 (PI.f64) #s(literal 2 binary64))))) (log.f64 (.f64 n (.f64 (PI.f64) #s(literal 2 binary64)))))) (pow.f64 #s(literal 2 binary64) #s(literal 1/2 binary64))) #s(literal 1/48 binary64) (.f64 (/.f64 (fma.f64 (/.f64 (fma.f64 (.f64 #s(literal -1 binary64) (/.f64 (pow.f64 #s(literal 2 binary64) #s(literal 1/2 binary64)) k)) (pow.f64 (.f64 (PI.f64) n) #s(literal 1/2 binary64)) (.f64 (.f64 #s(literal 1/2 binary64) (pow.f64 (.f64 (PI.f64) n) #s(literal 1/2 binary64))) (.f64 (pow.f64 #s(literal 2 binary64) #s(literal 1/2 binary64)) (log.f64 (.f64 n (.f64 (PI.f64) #s(literal 2 binary64))))))) k) #s(literal -1 binary64) (.f64 (.f64 (pow.f64 (.f64 (PI.f64) n) #s(literal 1/2 binary64)) #s(literal 1/8 binary64)) (.f64 (log.f64 (.f64 n (.f64 (PI.f64) #s(literal 2 binary64)))) (.f64 (pow.f64 #s(literal 2 binary64) #s(literal 1/2 binary64)) (log.f64 (.f64 n (*.f64 (PI.f64) #s(literal 2 binary64)))))))) k) #s(literal -1 binary64)))))))
✓	51.3%	#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) (.f64 (sqrt.f64 (pow.f64 k #s(literal 3 binary64))) (pow.f64 (.f64 (PI.f64) n) #s(literal 1/2 binary64)))) (.f64 (.f64 (.f64 (log.f64 (.f64 (.f64 (PI.f64) #s(literal 2 binary64)) n)) (log.f64 (.f64 (.f64 (PI.f64) #s(literal 2 binary64)) n))) (log.f64 (.f64 (.f64 (PI.f64) #s(literal 2 binary64)) n))) (pow.f64 #s(literal 2 binary64) #s(literal 1/2 binary64))) (.f64 (.f64 #s(literal 1/8 binary64) (pow.f64 (.f64 (.f64 (PI.f64) n) k) #s(literal 1/2 binary64))) (.f64 (.f64 (log.f64 (.f64 (.f64 (PI.f64) #s(literal 2 binary64)) n)) (log.f64 (.f64 (.f64 (PI.f64) #s(literal 2 binary64)) n))) (pow.f64 #s(literal 2 binary64) #s(literal 1/2 binary64))))) k (.f64 (.f64 #s(literal -1/2 binary64) (pow.f64 (.f64 (.f64 (PI.f64) n) k) #s(literal 1/2 binary64))) (.f64 (log.f64 (.f64 (.f64 (PI.f64) #s(literal 2 binary64)) n)) (pow.f64 #s(literal 2 binary64) #s(literal 1/2 binary64))))) k (pow.f64 (.f64 (.f64 (.f64 k n) (PI.f64)) #s(literal 2 binary64)) #s(literal 1/2 binary64))) k))
✓	63.5%	#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (/.f64 (fma.f64 (pow.f64 #s(literal 2 binary64) #s(literal 1/2 binary64)) (.f64 (pow.f64 (.f64 (PI.f64) n) #s(literal 1/2 binary64)) (pow.f64 k #s(literal 1/2 binary64))) (.f64 (fma.f64 (fma.f64 (.f64 (.f64 (.f64 #s(literal -1/48 binary64) (pow.f64 (pow.f64 k #s(literal 3 binary64)) #s(literal 1/2 binary64))) (pow.f64 (.f64 (PI.f64) n) #s(literal 1/2 binary64))) (.f64 (.f64 (log.f64 (.f64 n (.f64 (PI.f64) #s(literal 2 binary64)))) (log.f64 (.f64 n (.f64 (PI.f64) #s(literal 2 binary64))))) (log.f64 (.f64 n (.f64 (PI.f64) #s(literal 2 binary64)))))) (pow.f64 #s(literal 2 binary64) #s(literal 1/2 binary64)) (.f64 (.f64 (.f64 (pow.f64 (.f64 (PI.f64) n) #s(literal 1/2 binary64)) (pow.f64 k #s(literal 1/2 binary64))) #s(literal 1/8 binary64)) (.f64 (log.f64 (.f64 n (.f64 (PI.f64) #s(literal 2 binary64)))) (.f64 (pow.f64 #s(literal 2 binary64) #s(literal 1/2 binary64)) (log.f64 (.f64 n (.f64 (PI.f64) #s(literal 2 binary64)))))))) k (.f64 (.f64 (.f64 (.f64 (pow.f64 (.f64 (PI.f64) n) #s(literal 1/2 binary64)) (pow.f64 k #s(literal 1/2 binary64))) #s(literal -1/2 binary64)) (log.f64 (.f64 n (.f64 (PI.f64) #s(literal 2 binary64))))) (pow.f64 #s(literal 2 binary64) #s(literal 1/2 binary64)))) k)) k))
✓	50.7%	#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (.f64 (pow.f64 #s(literal 2 binary64) #s(literal 1/2 binary64)) (/.f64 (pow.f64 (.f64 (PI.f64) n) #s(literal 1/2 binary64)) (pow.f64 k #s(literal 1/2 binary64)))))

Compiler

Compiled 573 to 259 computations (54.8% saved)

series97.0ms (1.3%)

Memory

25.9MiB live, 214.1MiB allocated; 18ms collecting garbage

Counts

23 → 91

Calls

Call 1

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

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

Calls

6 calls:

Time	Variable		Point	Expression
26.0ms	n	@	-inf	((* (/ 1 (sqrt k)) (* (pow (* (PI) 2) (/ (- 1 k) 2)) (exp (* (log n) (/ (- 1 k) 2))))) (/ 1 (sqrt k)) 1 (sqrt k) k (* (pow (* (PI) 2) (/ (- 1 k) 2)) (exp (* (log n) (/ (- 1 k) 2)))) (pow (* (PI) 2) (/ (- 1 k) 2)) (* (PI) 2) (PI) 2 (/ (- 1 k) 2) (- 1 k) (exp (* (log n) (/ (- 1 k) 2))) (* (log n) (/ (- 1 k) 2)) (log n) n (/ (* (pow (* n (* (PI) 2)) (/ (/ (- 1 k) 2) 2)) (pow (* n (* (PI) 2)) (/ (/ (- 1 k) 2) 2))) (pow k 1/2)) (* (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)) (/ (/ (- 1 k) 2) 2) (pow k 1/2) 1/2)
25.0ms	n	@	0	((* (/ 1 (sqrt k)) (* (pow (* (PI) 2) (/ (- 1 k) 2)) (exp (* (log n) (/ (- 1 k) 2))))) (/ 1 (sqrt k)) 1 (sqrt k) k (* (pow (* (PI) 2) (/ (- 1 k) 2)) (exp (* (log n) (/ (- 1 k) 2)))) (pow (* (PI) 2) (/ (- 1 k) 2)) (* (PI) 2) (PI) 2 (/ (- 1 k) 2) (- 1 k) (exp (* (log n) (/ (- 1 k) 2))) (* (log n) (/ (- 1 k) 2)) (log n) n (/ (* (pow (* n (* (PI) 2)) (/ (/ (- 1 k) 2) 2)) (pow (* n (* (PI) 2)) (/ (/ (- 1 k) 2) 2))) (pow k 1/2)) (* (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)) (/ (/ (- 1 k) 2) 2) (pow k 1/2) 1/2)
24.0ms	n	@	inf	((* (/ 1 (sqrt k)) (* (pow (* (PI) 2) (/ (- 1 k) 2)) (exp (* (log n) (/ (- 1 k) 2))))) (/ 1 (sqrt k)) 1 (sqrt k) k (* (pow (* (PI) 2) (/ (- 1 k) 2)) (exp (* (log n) (/ (- 1 k) 2)))) (pow (* (PI) 2) (/ (- 1 k) 2)) (* (PI) 2) (PI) 2 (/ (- 1 k) 2) (- 1 k) (exp (* (log n) (/ (- 1 k) 2))) (* (log n) (/ (- 1 k) 2)) (log n) n (/ (* (pow (* n (* (PI) 2)) (/ (/ (- 1 k) 2) 2)) (pow (* n (* (PI) 2)) (/ (/ (- 1 k) 2) 2))) (pow k 1/2)) (* (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)) (/ (/ (- 1 k) 2) 2) (pow k 1/2) 1/2)
9.0ms	k	@	-inf	((* (/ 1 (sqrt k)) (* (pow (* (PI) 2) (/ (- 1 k) 2)) (exp (* (log n) (/ (- 1 k) 2))))) (/ 1 (sqrt k)) 1 (sqrt k) k (* (pow (* (PI) 2) (/ (- 1 k) 2)) (exp (* (log n) (/ (- 1 k) 2)))) (pow (* (PI) 2) (/ (- 1 k) 2)) (* (PI) 2) (PI) 2 (/ (- 1 k) 2) (- 1 k) (exp (* (log n) (/ (- 1 k) 2))) (* (log n) (/ (- 1 k) 2)) (log n) n (/ (* (pow (* n (* (PI) 2)) (/ (/ (- 1 k) 2) 2)) (pow (* n (* (PI) 2)) (/ (/ (- 1 k) 2) 2))) (pow k 1/2)) (* (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)) (/ (/ (- 1 k) 2) 2) (pow k 1/2) 1/2)
6.0ms	k	@	0	((* (/ 1 (sqrt k)) (* (pow (* (PI) 2) (/ (- 1 k) 2)) (exp (* (log n) (/ (- 1 k) 2))))) (/ 1 (sqrt k)) 1 (sqrt k) k (* (pow (* (PI) 2) (/ (- 1 k) 2)) (exp (* (log n) (/ (- 1 k) 2)))) (pow (* (PI) 2) (/ (- 1 k) 2)) (* (PI) 2) (PI) 2 (/ (- 1 k) 2) (- 1 k) (exp (* (log n) (/ (- 1 k) 2))) (* (log n) (/ (- 1 k) 2)) (log n) n (/ (* (pow (* n (* (PI) 2)) (/ (/ (- 1 k) 2) 2)) (pow (* n (* (PI) 2)) (/ (/ (- 1 k) 2) 2))) (pow k 1/2)) (* (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)) (/ (/ (- 1 k) 2) 2) (pow k 1/2) 1/2)

rewrite123.0ms (1.7%)

Memory

-31.6MiB live, 151.1MiB allocated; 38ms collecting garbage

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	458	3648
0	492	3118
0	2353	3043

Stop Event

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

Counts

114 → 162

Calls

Call 1

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

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

eval49.0ms (0.7%)

Memory: 25.8MiB live, 74.3MiB allocated; 25ms collecting garbage
Compiler: Compiled 10 611 to 955 computations (91% saved)

prune75.0ms (1%)

Memory

0.8MiB live, 140.7MiB allocated; 12ms collecting garbage

Pruning

8 alts after pruning (2 fresh and 6 done)

	Pruned	Kept	Total
New	262	2	264
Fresh	0	0	0
Picked	2	0	2
Done	0	6	6
Total	264	8	272

Accuracy

100.0%

Counts

272 → 8

Alt Table

Click to see full alt table

Status	Accuracy	Program
	99.5%	(/.f64 (.f64 (pow.f64 (.f64 n (.f64 (PI.f64) #s(literal 2 binary64))) (/.f64 (/.f64 (/.f64 (-.f64 #s(literal 1 binary64) (.f64 k k)) (+.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 k #s(literal 1/2 binary64)))
✓	99.6%	(/.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)))) (pow.f64 k #s(literal 1/2 binary64)))
✓	99.5%	(.f64 (pow.f64 (pow.f64 k #s(literal -1 binary64)) #s(literal 1/2 binary64)) (pow.f64 (.f64 (*.f64 (PI.f64) #s(literal 2 binary64)) n) (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 2 binary64))))
	75.4%	(.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) (.f64 (pow.f64 (.f64 (PI.f64) #s(literal 2 binary64)) (/.f64 #s(approx (- 1 k) (.f64 (-.f64 (pow.f64 k #s(literal -1 binary64)) #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))))))
✓	24.5%	(.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) #s(approx (pow ( (* 2 (PI)) n) (/ (- 1 k) 2)) #s(approx (+ (* (+ (* (+ (* (* (* (* k (* (* (log (* (* (PI) 2) n)) (log (* (* (PI) 2) n))) (log (* (* (PI) 2) n)))) (pow 2 1/2)) (pow (* (PI) n) 1/2)) -1/48) (* (* 1/8 (pow (* (PI) n) 1/2)) (* (* (log (* (* (PI) 2) n)) (log (* (* (PI) 2) n))) (pow 2 1/2)))) k) (* (* -1/2 (pow (* (PI) n) 1/2)) (* (log (* (* (PI) 2) n)) (pow 2 1/2)))) k) (* (pow (* (PI) n) 1/2) (pow 2 1/2))) (.f64 (.f64 #s(literal -1 binary64) (pow.f64 k #s(literal 3 binary64))) (fma.f64 (.f64 (.f64 (pow.f64 (.f64 (PI.f64) n) #s(literal 1/2 binary64)) (.f64 (.f64 (log.f64 (.f64 n (.f64 (PI.f64) #s(literal 2 binary64)))) (log.f64 (.f64 n (.f64 (PI.f64) #s(literal 2 binary64))))) (log.f64 (.f64 n (.f64 (PI.f64) #s(literal 2 binary64)))))) (pow.f64 #s(literal 2 binary64) #s(literal 1/2 binary64))) #s(literal 1/48 binary64) (.f64 (/.f64 (fma.f64 (/.f64 (fma.f64 (.f64 #s(literal -1 binary64) (/.f64 (pow.f64 #s(literal 2 binary64) #s(literal 1/2 binary64)) k)) (pow.f64 (.f64 (PI.f64) n) #s(literal 1/2 binary64)) (.f64 (.f64 #s(literal 1/2 binary64) (pow.f64 (.f64 (PI.f64) n) #s(literal 1/2 binary64))) (.f64 (pow.f64 #s(literal 2 binary64) #s(literal 1/2 binary64)) (log.f64 (.f64 n (.f64 (PI.f64) #s(literal 2 binary64))))))) k) #s(literal -1 binary64) (.f64 (.f64 (pow.f64 (.f64 (PI.f64) n) #s(literal 1/2 binary64)) #s(literal 1/8 binary64)) (.f64 (log.f64 (.f64 n (.f64 (PI.f64) #s(literal 2 binary64)))) (.f64 (pow.f64 #s(literal 2 binary64) #s(literal 1/2 binary64)) (log.f64 (.f64 n (*.f64 (PI.f64) #s(literal 2 binary64)))))))) k) #s(literal -1 binary64)))))))
✓	51.3%	#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) (.f64 (sqrt.f64 (pow.f64 k #s(literal 3 binary64))) (pow.f64 (.f64 (PI.f64) n) #s(literal 1/2 binary64)))) (.f64 (.f64 (.f64 (log.f64 (.f64 (.f64 (PI.f64) #s(literal 2 binary64)) n)) (log.f64 (.f64 (.f64 (PI.f64) #s(literal 2 binary64)) n))) (log.f64 (.f64 (.f64 (PI.f64) #s(literal 2 binary64)) n))) (pow.f64 #s(literal 2 binary64) #s(literal 1/2 binary64))) (.f64 (.f64 #s(literal 1/8 binary64) (pow.f64 (.f64 (.f64 (PI.f64) n) k) #s(literal 1/2 binary64))) (.f64 (.f64 (log.f64 (.f64 (.f64 (PI.f64) #s(literal 2 binary64)) n)) (log.f64 (.f64 (.f64 (PI.f64) #s(literal 2 binary64)) n))) (pow.f64 #s(literal 2 binary64) #s(literal 1/2 binary64))))) k (.f64 (.f64 #s(literal -1/2 binary64) (pow.f64 (.f64 (.f64 (PI.f64) n) k) #s(literal 1/2 binary64))) (.f64 (log.f64 (.f64 (.f64 (PI.f64) #s(literal 2 binary64)) n)) (pow.f64 #s(literal 2 binary64) #s(literal 1/2 binary64))))) k (pow.f64 (.f64 (.f64 (.f64 k n) (PI.f64)) #s(literal 2 binary64)) #s(literal 1/2 binary64))) k))
✓	63.5%	#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (/.f64 (fma.f64 (pow.f64 #s(literal 2 binary64) #s(literal 1/2 binary64)) (.f64 (pow.f64 (.f64 (PI.f64) n) #s(literal 1/2 binary64)) (pow.f64 k #s(literal 1/2 binary64))) (.f64 (fma.f64 (fma.f64 (.f64 (.f64 (.f64 #s(literal -1/48 binary64) (pow.f64 (pow.f64 k #s(literal 3 binary64)) #s(literal 1/2 binary64))) (pow.f64 (.f64 (PI.f64) n) #s(literal 1/2 binary64))) (.f64 (.f64 (log.f64 (.f64 n (.f64 (PI.f64) #s(literal 2 binary64)))) (log.f64 (.f64 n (.f64 (PI.f64) #s(literal 2 binary64))))) (log.f64 (.f64 n (.f64 (PI.f64) #s(literal 2 binary64)))))) (pow.f64 #s(literal 2 binary64) #s(literal 1/2 binary64)) (.f64 (.f64 (.f64 (pow.f64 (.f64 (PI.f64) n) #s(literal 1/2 binary64)) (pow.f64 k #s(literal 1/2 binary64))) #s(literal 1/8 binary64)) (.f64 (log.f64 (.f64 n (.f64 (PI.f64) #s(literal 2 binary64)))) (.f64 (pow.f64 #s(literal 2 binary64) #s(literal 1/2 binary64)) (log.f64 (.f64 n (.f64 (PI.f64) #s(literal 2 binary64)))))))) k (.f64 (.f64 (.f64 (.f64 (pow.f64 (.f64 (PI.f64) n) #s(literal 1/2 binary64)) (pow.f64 k #s(literal 1/2 binary64))) #s(literal -1/2 binary64)) (log.f64 (.f64 n (.f64 (PI.f64) #s(literal 2 binary64))))) (pow.f64 #s(literal 2 binary64) #s(literal 1/2 binary64)))) k)) k))
✓	50.7%	#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (.f64 (pow.f64 #s(literal 2 binary64) #s(literal 1/2 binary64)) (/.f64 (pow.f64 (.f64 (PI.f64) n) #s(literal 1/2 binary64)) (pow.f64 k #s(literal 1/2 binary64)))))

Compiler

Compiled 1 552 to 467 computations (69.9% saved)

regimes24.0ms (0.3%)

Memory

-7.5MiB live, 42.9MiB allocated; 6ms collecting garbage

Counts

16 → 1

Calls

Call 1

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

Outputs
(/.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)))) (pow.f64 k #s(literal 1/2 binary64)))

Calls

4 calls:

7.0ms	(.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) (pow.f64 (.f64 (*.f64 #s(literal 2 binary64) (PI.f64)) n) (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 2 binary64))))
5.0ms	(.f64 (.f64 #s(literal 2 binary64) (PI.f64)) n)
5.0ms	n
5.0ms	k

Results

Accuracy	Segments	Branch
99.6%	1	`(.f64 (.f64 #s(literal 2 binary64) (PI.f64)) n)`
99.6%	1	`(.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) (pow.f64 (.f64 (*.f64 #s(literal 2 binary64) (PI.f64)) n) (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 2 binary64))))`
99.6%	1	`k`
99.6%	1	`n`

Compiler

Compiled 23 to 23 computations (0% saved)

regimes18.0ms (0.2%)

Memory

-8.5MiB live, 38.5MiB allocated; 2ms collecting garbage

Counts

13 → 1

Calls

Call 1

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

Calls

4 calls:

5.0ms	(.f64 (.f64 #s(literal 2 binary64) (PI.f64)) n)
4.0ms	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
99.5%	1	`(.f64 (.f64 #s(literal 2 binary64) (PI.f64)) n)`
99.5%	1	`k`
99.5%	1	`n`
99.5%	1	`(.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) (pow.f64 (.f64 (*.f64 #s(literal 2 binary64) (PI.f64)) n) (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 2 binary64))))`

Compiler

Compiled 23 to 23 computations (0% saved)

regimes16.0ms (0.2%)

Memory

31.8MiB live, 31.8MiB allocated; 0ms collecting garbage

Counts

12 → 1

Calls

Call 1

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

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	(.f64 (.f64 #s(literal 2 binary64) (PI.f64)) n)
4.0ms	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
99.5%	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 (0.2%)

Memory

-14.4MiB live, 32.4MiB allocated; 2ms collecting garbage

Counts

11 → 1

Calls

Call 1

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

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

Results

Accuracy	Segments	Branch
99.4%	1	`(.f64 (.f64 #s(literal 2 binary64) (PI.f64)) n)`
99.4%	1	`n`
99.4%	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))))`
99.4%	1	`k`

Compiler

Compiled 23 to 23 computations (0% saved)

regimes15.0ms (0.2%)

Memory

-15.6MiB live, 31.4MiB allocated; 1ms collecting garbage

Counts

10 → 2

Calls

Call 1

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

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

Calls

4 calls:

4.0ms	(.f64 (.f64 #s(literal 2 binary64) (PI.f64)) n)
3.0ms	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
91.6%	2	`(.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) (pow.f64 (.f64 (*.f64 #s(literal 2 binary64) (PI.f64)) n) (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 2 binary64))))`
90.6%	2	`(.f64 (.f64 #s(literal 2 binary64) (PI.f64)) n)`
78.6%	1	`k`
90.6%	2	`n`

Compiler

Compiled 23 to 23 computations (0% saved)

regimes4.0ms (0.1%)

Memory

9.1MiB live, 9.1MiB allocated; 0ms collecting garbage

Counts

9 → 2

Calls

Call 1

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

Outputs

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

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

Calls

1 calls:

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
91.2%	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))))`

Compiler

Compiled 16 to 13 computations (18.8% saved)

regimes11.0ms (0.2%)

Memory

26.5MiB live, 26.5MiB allocated; 0ms collecting garbage

Counts

7 → 1

Calls

Call 1

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

Outputs

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

Calls

4 calls:

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

Results

Accuracy	Segments	Branch
63.5%	1	`k`
63.5%	1	`(.f64 (.f64 #s(literal 2 binary64) (PI.f64)) n)`
63.5%	1	`n`
63.5%	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))))`

Compiler

Compiled 23 to 23 computations (0% saved)

regimes8.0ms (0.1%)

Memory

-35.4MiB live, 13.9MiB allocated; 3ms collecting garbage

Accuracy

Total -8.5b remaining (-26.8%)

Threshold costs -8.5b (-26.8%)

Counts

2 → 1

Calls

Call 1

Inputs

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

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

Outputs

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

Calls

4 calls:

3.0ms	(.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
50.7%	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))))`
50.7%	1	`k`
50.7%	1	`(.f64 (.f64 #s(literal 2 binary64) (PI.f64)) n)`
50.7%	1	`n`

Compiler

Compiled 23 to 23 computations (0% saved)

bsearch1.0ms (0%)

Memory

0.9MiB live, 0.9MiB allocated; 0ms collecting garbage

Algorithm

1×	left-value

Steps

Time	Left	Right
0.0ms	4.632314852630527e-41	6.093527699425342e-41

Compiler

Compiled 19 to 18 computations (5.3% saved)

bsearch0.0ms (0%)

Memory

0.8MiB live, 0.8MiB allocated; 0ms collecting garbage

Algorithm

1×	left-value

Steps

Time	Left	Right
0.0ms	4.646148883718438e-65	3.190842068171933e-64

Compiler

Compiled 19 to 18 computations (5.3% saved)

simplify48.0ms (0.7%)

Memory

12.2MiB live, 58.8MiB allocated; 3ms collecting garbage

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	90	577
1	109	569
2	136	569
3	236	569
4	895	569
5	3710	569

Stop Event

1×	node limit

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)))) (pow.f64 k #s(literal 1/2 binary64)))
(.f64 (pow.f64 (pow.f64 k #s(literal -1 binary64)) #s(literal 1/2 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 #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 (.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 1225996432692711/24519928653854221733733552434404946937899825954937634816 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))))) #s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (/.f64 (fma.f64 (pow.f64 #s(literal 2 binary64) #s(literal 1/2 binary64)) (.f64 (pow.f64 (.f64 (PI.f64) n) #s(literal 1/2 binary64)) (pow.f64 k #s(literal 1/2 binary64))) (.f64 (fma.f64 (fma.f64 (.f64 (.f64 (.f64 #s(literal -1/48 binary64) (pow.f64 (pow.f64 k #s(literal 3 binary64)) #s(literal 1/2 binary64))) (pow.f64 (.f64 (PI.f64) n) #s(literal 1/2 binary64))) (.f64 (.f64 (log.f64 (.f64 n (.f64 (PI.f64) #s(literal 2 binary64)))) (log.f64 (.f64 n (.f64 (PI.f64) #s(literal 2 binary64))))) (log.f64 (.f64 n (.f64 (PI.f64) #s(literal 2 binary64)))))) (pow.f64 #s(literal 2 binary64) #s(literal 1/2 binary64)) (.f64 (.f64 (.f64 (pow.f64 (.f64 (PI.f64) n) #s(literal 1/2 binary64)) (pow.f64 k #s(literal 1/2 binary64))) #s(literal 1/8 binary64)) (.f64 (log.f64 (.f64 n (.f64 (PI.f64) #s(literal 2 binary64)))) (.f64 (pow.f64 #s(literal 2 binary64) #s(literal 1/2 binary64)) (log.f64 (.f64 n (.f64 (PI.f64) #s(literal 2 binary64)))))))) k (.f64 (.f64 (.f64 (.f64 (pow.f64 (.f64 (PI.f64) n) #s(literal 1/2 binary64)) (pow.f64 k #s(literal 1/2 binary64))) #s(literal -1/2 binary64)) (log.f64 (.f64 n (.f64 (PI.f64) #s(literal 2 binary64))))) (pow.f64 #s(literal 2 binary64) #s(literal 1/2 binary64)))) k)) k)))
(if (<=.f64 (.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) (pow.f64 (.f64 (.f64 #s(literal 2 binary64) (PI.f64)) n) (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 2 binary64)))) #s(literal 5928554968950589/118571099379011784113736688648896417641748464297615937576404566024103044751294464 binary64)) (.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) (.f64 (pow.f64 (.f64 (PI.f64) #s(literal 2 binary64)) (/.f64 #s(approx (- 1 k) (.f64 (-.f64 (pow.f64 k #s(literal -1 binary64)) #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)))))) #s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (/.f64 (fma.f64 (pow.f64 #s(literal 2 binary64) #s(literal 1/2 binary64)) (.f64 (pow.f64 (.f64 (PI.f64) n) #s(literal 1/2 binary64)) (pow.f64 k #s(literal 1/2 binary64))) (.f64 (fma.f64 (fma.f64 (.f64 (.f64 (.f64 #s(literal -1/48 binary64) (pow.f64 (pow.f64 k #s(literal 3 binary64)) #s(literal 1/2 binary64))) (pow.f64 (.f64 (PI.f64) n) #s(literal 1/2 binary64))) (.f64 (.f64 (log.f64 (.f64 n (.f64 (PI.f64) #s(literal 2 binary64)))) (log.f64 (.f64 n (.f64 (PI.f64) #s(literal 2 binary64))))) (log.f64 (.f64 n (.f64 (PI.f64) #s(literal 2 binary64)))))) (pow.f64 #s(literal 2 binary64) #s(literal 1/2 binary64)) (.f64 (.f64 (.f64 (pow.f64 (.f64 (PI.f64) n) #s(literal 1/2 binary64)) (pow.f64 k #s(literal 1/2 binary64))) #s(literal 1/8 binary64)) (.f64 (log.f64 (.f64 n (.f64 (PI.f64) #s(literal 2 binary64)))) (.f64 (pow.f64 #s(literal 2 binary64) #s(literal 1/2 binary64)) (log.f64 (.f64 n (.f64 (PI.f64) #s(literal 2 binary64)))))))) k (.f64 (.f64 (.f64 (.f64 (pow.f64 (.f64 (PI.f64) n) #s(literal 1/2 binary64)) (pow.f64 k #s(literal 1/2 binary64))) #s(literal -1/2 binary64)) (log.f64 (.f64 n (.f64 (PI.f64) #s(literal 2 binary64))))) (pow.f64 #s(literal 2 binary64) #s(literal 1/2 binary64)))) k)) k)))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (/.f64 (fma.f64 (pow.f64 #s(literal 2 binary64) #s(literal 1/2 binary64)) (.f64 (pow.f64 (.f64 (PI.f64) n) #s(literal 1/2 binary64)) (pow.f64 k #s(literal 1/2 binary64))) (.f64 (fma.f64 (fma.f64 (.f64 (.f64 (.f64 #s(literal -1/48 binary64) (pow.f64 (pow.f64 k #s(literal 3 binary64)) #s(literal 1/2 binary64))) (pow.f64 (.f64 (PI.f64) n) #s(literal 1/2 binary64))) (.f64 (.f64 (log.f64 (.f64 n (.f64 (PI.f64) #s(literal 2 binary64)))) (log.f64 (.f64 n (.f64 (PI.f64) #s(literal 2 binary64))))) (log.f64 (.f64 n (.f64 (PI.f64) #s(literal 2 binary64)))))) (pow.f64 #s(literal 2 binary64) #s(literal 1/2 binary64)) (.f64 (.f64 (.f64 (pow.f64 (.f64 (PI.f64) n) #s(literal 1/2 binary64)) (pow.f64 k #s(literal 1/2 binary64))) #s(literal 1/8 binary64)) (.f64 (log.f64 (.f64 n (.f64 (PI.f64) #s(literal 2 binary64)))) (.f64 (pow.f64 #s(literal 2 binary64) #s(literal 1/2 binary64)) (log.f64 (.f64 n (.f64 (PI.f64) #s(literal 2 binary64)))))))) k (.f64 (.f64 (.f64 (.f64 (pow.f64 (.f64 (PI.f64) n) #s(literal 1/2 binary64)) (pow.f64 k #s(literal 1/2 binary64))) #s(literal -1/2 binary64)) (log.f64 (.f64 n (.f64 (PI.f64) #s(literal 2 binary64))))) (pow.f64 #s(literal 2 binary64) #s(literal 1/2 binary64)))) k)) k))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (.f64 (pow.f64 #s(literal 2 binary64) #s(literal 1/2 binary64)) (/.f64 (pow.f64 (.f64 (PI.f64) n) #s(literal 1/2 binary64)) (pow.f64 k #s(literal 1/2 binary64)))))

Outputs
(/.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)))) (pow.f64 k #s(literal 1/2 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 k #s(literal 1/2 binary64)))
(.f64 (pow.f64 (pow.f64 k #s(literal -1 binary64)) #s(literal 1/2 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 #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 (.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 1225996432692711/24519928653854221733733552434404946937899825954937634816 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))))) #s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (/.f64 (fma.f64 (pow.f64 #s(literal 2 binary64) #s(literal 1/2 binary64)) (.f64 (pow.f64 (.f64 (PI.f64) n) #s(literal 1/2 binary64)) (pow.f64 k #s(literal 1/2 binary64))) (.f64 (fma.f64 (fma.f64 (.f64 (.f64 (.f64 #s(literal -1/48 binary64) (pow.f64 (pow.f64 k #s(literal 3 binary64)) #s(literal 1/2 binary64))) (pow.f64 (.f64 (PI.f64) n) #s(literal 1/2 binary64))) (.f64 (.f64 (log.f64 (.f64 n (.f64 (PI.f64) #s(literal 2 binary64)))) (log.f64 (.f64 n (.f64 (PI.f64) #s(literal 2 binary64))))) (log.f64 (.f64 n (.f64 (PI.f64) #s(literal 2 binary64)))))) (pow.f64 #s(literal 2 binary64) #s(literal 1/2 binary64)) (.f64 (.f64 (.f64 (pow.f64 (.f64 (PI.f64) n) #s(literal 1/2 binary64)) (pow.f64 k #s(literal 1/2 binary64))) #s(literal 1/8 binary64)) (.f64 (log.f64 (.f64 n (.f64 (PI.f64) #s(literal 2 binary64)))) (.f64 (pow.f64 #s(literal 2 binary64) #s(literal 1/2 binary64)) (log.f64 (.f64 n (.f64 (PI.f64) #s(literal 2 binary64)))))))) k (.f64 (.f64 (.f64 (.f64 (pow.f64 (.f64 (PI.f64) n) #s(literal 1/2 binary64)) (pow.f64 k #s(literal 1/2 binary64))) #s(literal -1/2 binary64)) (log.f64 (.f64 n (.f64 (PI.f64) #s(literal 2 binary64))))) (pow.f64 #s(literal 2 binary64) #s(literal 1/2 binary64)))) k)) k)))
(if (<=.f64 (.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) (pow.f64 (.f64 (.f64 #s(literal 2 binary64) (PI.f64)) n) (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 2 binary64)))) #s(literal 5928554968950589/118571099379011784113736688648896417641748464297615937576404566024103044751294464 binary64)) (.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) (.f64 (pow.f64 (.f64 (PI.f64) #s(literal 2 binary64)) (/.f64 #s(approx (- 1 k) (.f64 (-.f64 (pow.f64 k #s(literal -1 binary64)) #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)))))) #s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (/.f64 (fma.f64 (pow.f64 #s(literal 2 binary64) #s(literal 1/2 binary64)) (.f64 (pow.f64 (.f64 (PI.f64) n) #s(literal 1/2 binary64)) (pow.f64 k #s(literal 1/2 binary64))) (.f64 (fma.f64 (fma.f64 (.f64 (.f64 (.f64 #s(literal -1/48 binary64) (pow.f64 (pow.f64 k #s(literal 3 binary64)) #s(literal 1/2 binary64))) (pow.f64 (.f64 (PI.f64) n) #s(literal 1/2 binary64))) (.f64 (.f64 (log.f64 (.f64 n (.f64 (PI.f64) #s(literal 2 binary64)))) (log.f64 (.f64 n (.f64 (PI.f64) #s(literal 2 binary64))))) (log.f64 (.f64 n (.f64 (PI.f64) #s(literal 2 binary64)))))) (pow.f64 #s(literal 2 binary64) #s(literal 1/2 binary64)) (.f64 (.f64 (.f64 (pow.f64 (.f64 (PI.f64) n) #s(literal 1/2 binary64)) (pow.f64 k #s(literal 1/2 binary64))) #s(literal 1/8 binary64)) (.f64 (log.f64 (.f64 n (.f64 (PI.f64) #s(literal 2 binary64)))) (.f64 (pow.f64 #s(literal 2 binary64) #s(literal 1/2 binary64)) (log.f64 (.f64 n (.f64 (PI.f64) #s(literal 2 binary64)))))))) k (.f64 (.f64 (.f64 (.f64 (pow.f64 (.f64 (PI.f64) n) #s(literal 1/2 binary64)) (pow.f64 k #s(literal 1/2 binary64))) #s(literal -1/2 binary64)) (log.f64 (.f64 n (.f64 (PI.f64) #s(literal 2 binary64))))) (pow.f64 #s(literal 2 binary64) #s(literal 1/2 binary64)))) k)) k)))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (/.f64 (fma.f64 (pow.f64 #s(literal 2 binary64) #s(literal 1/2 binary64)) (.f64 (pow.f64 (.f64 (PI.f64) n) #s(literal 1/2 binary64)) (pow.f64 k #s(literal 1/2 binary64))) (.f64 (fma.f64 (fma.f64 (.f64 (.f64 (.f64 #s(literal -1/48 binary64) (pow.f64 (pow.f64 k #s(literal 3 binary64)) #s(literal 1/2 binary64))) (pow.f64 (.f64 (PI.f64) n) #s(literal 1/2 binary64))) (.f64 (.f64 (log.f64 (.f64 n (.f64 (PI.f64) #s(literal 2 binary64)))) (log.f64 (.f64 n (.f64 (PI.f64) #s(literal 2 binary64))))) (log.f64 (.f64 n (.f64 (PI.f64) #s(literal 2 binary64)))))) (pow.f64 #s(literal 2 binary64) #s(literal 1/2 binary64)) (.f64 (.f64 (.f64 (pow.f64 (.f64 (PI.f64) n) #s(literal 1/2 binary64)) (pow.f64 k #s(literal 1/2 binary64))) #s(literal 1/8 binary64)) (.f64 (log.f64 (.f64 n (.f64 (PI.f64) #s(literal 2 binary64)))) (.f64 (pow.f64 #s(literal 2 binary64) #s(literal 1/2 binary64)) (log.f64 (.f64 n (.f64 (PI.f64) #s(literal 2 binary64)))))))) k (.f64 (.f64 (.f64 (.f64 (pow.f64 (.f64 (PI.f64) n) #s(literal 1/2 binary64)) (pow.f64 k #s(literal 1/2 binary64))) #s(literal -1/2 binary64)) (log.f64 (.f64 n (.f64 (PI.f64) #s(literal 2 binary64))))) (pow.f64 #s(literal 2 binary64) #s(literal 1/2 binary64)))) k)) k))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (.f64 (pow.f64 #s(literal 2 binary64) #s(literal 1/2 binary64)) (/.f64 (pow.f64 (.f64 (PI.f64) n) #s(literal 1/2 binary64)) (pow.f64 k #s(literal 1/2 binary64)))))

derivations89.0ms (1.2%)

Memory

20.7MiB live, 67.2MiB allocated; 2ms collecting garbage

Stop Event

1×

fuel

Compiler

Compiled 577 to 91 computations (84.2% saved)

preprocess86.0ms (1.2%)

Memory: -3.5MiB live, 140.8MiB allocated; 36ms collecting garbage
Compiler: Compiled 1 186 to 208 computations (82.5% saved)

end0.0ms (0%)

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

start0.0ms (0%)

analyze112.0ms (1.5%)

sample3.1s (42.9%)

explain198.0ms (2.7%)

preprocess234.0ms (3.2%)

eval0.0ms (0%)

prune1.0ms (0%)

series91.0ms (1.2%)

rewrite59.0ms (0.8%)

eval8.0ms (0.1%)

prune53.0ms (0.7%)

series336.0ms (4.6%)

rewrite258.0ms (3.5%)

eval277.0ms (3.8%)

prune363.0ms (5%)

series353.0ms (4.8%)

rewrite308.0ms (4.2%)

eval354.0ms (4.8%)

prune499.0ms (6.8%)

series97.0ms (1.3%)

rewrite123.0ms (1.7%)

eval49.0ms (0.7%)

prune75.0ms (1%)

regimes24.0ms (0.3%)

regimes18.0ms (0.2%)

regimes16.0ms (0.2%)

regimes16.0ms (0.2%)

regimes15.0ms (0.2%)

regimes4.0ms (0.1%)

regimes11.0ms (0.2%)

regimes8.0ms (0.1%)

bsearch1.0ms (0%)

bsearch0.0ms (0%)

simplify48.0ms (0.7%)

derivations89.0ms (1.2%)

preprocess86.0ms (1.2%)

end0.0ms (0%)

Profiling