Metrics for Migdal et al, Equation (51)

start0.0ms (0%)

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

analyze100.0ms (2.3%)

Memory

21.4MiB live, 116.1MiB allocated; 47ms 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)

sample2.7s (61.6%)

Memory

91.8MiB live, 2 919.8MiB allocated; 1.2s collecting garbage

Samples

1.3s	5 234×	1	invalid
710.0ms	8 255×	0	valid
122.0ms	428×	2	invalid
25.0ms	220×	0	exit
22.0ms	382×	0	invalid
0.0ms	1×	1	valid

Precisions

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

ival-div!: 517.0ms (33.3% of total)

ival-pow: 411.0ms (26.5% of total)

ival-mult!: 202.0ms (13% of total)

adjust: 194.0ms (12.5% of total)

ival-sqrt: 173.0ms (11.2% of total)

ival-sub!: 55.0ms (3.5% of total)

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

exact: 0.0ms (0% of total)

Bogosity

preprocess70.0ms (1.6%)

Memory

-12.2MiB live, 33.2MiB allocated; 5ms collecting garbage

Iterations

Useful iterations: 2 (0.0ms)

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

Stop Event

1×	node-limit

Alt Table

Click to see full alt table

Status	Accuracy	Program
▶	99.5%	(.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 30 to 26 computations (13.3% saved)

series84.0ms (1.9%)

Memory

32.5MiB live, 84.3MiB allocated; 10ms 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
28.0ms	n	@	0	((* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (/ 1 (sqrt k)) 1 (sqrt k) k (pow (* (* 2 (PI)) n) (/ (- 1 k) 2)) (* (* 2 (PI)) n) (* 2 (PI)) 2 (PI) n (/ (- 1 k) 2) (- 1 k))
28.0ms	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))
20.0ms	n	@	-inf	((* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (/ 1 (sqrt k)) 1 (sqrt k) k (pow (* (* 2 (PI)) n) (/ (- 1 k) 2)) (* (* 2 (PI)) n) (* 2 (PI)) 2 (PI) n (/ (- 1 k) 2) (- 1 k))
3.0ms	k	@	-inf	((* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (/ 1 (sqrt k)) 1 (sqrt k) k (pow (* (* 2 (PI)) n) (/ (- 1 k) 2)) (* (* 2 (PI)) n) (* 2 (PI)) 2 (PI) n (/ (- 1 k) 2) (- 1 k))
3.0ms	k	@	0	((* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (/ 1 (sqrt k)) 1 (sqrt k) k (pow (* (* 2 (PI)) n) (/ (- 1 k) 2)) (* (* 2 (PI)) n) (* 2 (PI)) 2 (PI) n (/ (- 1 k) 2) (- 1 k))

rewrite61.0ms (1.4%)

Memory

7.2MiB live, 91.4MiB 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 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) (pow.f64 (.f64 (+.f64 (PI.f64) (PI.f64)) n) (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 2 binary64))))
(.f64 (pow.f64 (.f64 (+.f64 (PI.f64) (PI.f64)) n) (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 2 binary64))) (/.f64 #s(literal 1 binary64) (sqrt.f64 k)))
(/.f64 (.f64 #s(literal 1 binary64) (pow.f64 (.f64 (+.f64 (PI.f64) (PI.f64)) n) (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 2 binary64)))) (sqrt.f64 k))
(pow.f64 (/.f64 #s(literal 1 binary64) k) #s(literal 1/2 binary64))
(pow.f64 (sqrt.f64 k) #s(literal -1 binary64))
(/.f64 #s(literal -1 binary64) (neg.f64 (sqrt.f64 k)))
(/.f64 #s(literal 1 binary64) (sqrt.f64 k))
(sqrt.f64 (/.f64 #s(literal 1 binary64) k))
#s(literal 1 binary64)
(pow.f64 k #s(literal 1/2 binary64))
(sqrt.f64 k)
k
(.f64 (pow.f64 (.f64 (+.f64 (PI.f64) (PI.f64)) n) (/.f64 (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 2 binary64)) #s(literal 2 binary64))) (pow.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n) (/.f64 (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 2 binary64)) #s(literal 2 binary64))))
(*.f64 (pow.f64 (+.f64 (PI.f64) (PI.f64)) (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 2 binary64))) (pow.f64 n (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 2 binary64))))
(pow.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n) (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 2 binary64)))
(exp.f64 (.f64 (log.f64 (.f64 (+.f64 (PI.f64) (PI.f64)) 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) (PI.f64)) n)
(*.f64 n (+.f64 (PI.f64) (PI.f64)))
(.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) (.f64 (.f64 k k) k)) (+.f64 #s(literal 1 binary64) (fma.f64 k k (*.f64 #s(literal 1 binary64) k))))
(-.f64 #s(literal 1 binary64) k)
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt.f64 (.f64 (/.f64 (.f64 (PI.f64) n) k) #s(literal 2 binary64))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (/.f64 (fma.f64 (.f64 (.f64 (log.f64 (.f64 (+.f64 (PI.f64) (PI.f64)) n)) (sqrt.f64 #s(literal 2 binary64))) (sqrt.f64 (.f64 (.f64 (.f64 k k) k) (.f64 (PI.f64) n)))) #s(literal -1/2 binary64) (sqrt.f64 (.f64 (.f64 (.f64 (PI.f64) n) k) #s(literal 2 binary64)))) k))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (/.f64 (fma.f64 k (fma.f64 (.f64 (.f64 (.f64 (log.f64 (.f64 (+.f64 (PI.f64) (PI.f64)) n)) (log.f64 (.f64 (+.f64 (PI.f64) (PI.f64)) n))) (sqrt.f64 #s(literal 2 binary64))) (sqrt.f64 (.f64 (.f64 (.f64 k k) k) (.f64 (PI.f64) n)))) #s(literal 1/8 binary64) (.f64 (.f64 (sqrt.f64 (.f64 (.f64 (PI.f64) n) k)) (.f64 (log.f64 (.f64 (+.f64 (PI.f64) (PI.f64)) n)) (sqrt.f64 #s(literal 2 binary64)))) #s(literal -1/2 binary64))) (sqrt.f64 (.f64 (.f64 (.f64 (PI.f64) n) k) #s(literal 2 binary64)))) k))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (/.f64 (fma.f64 (fma.f64 k (fma.f64 (.f64 (.f64 (sqrt.f64 (.f64 (.f64 (PI.f64) n) k)) (.f64 (log.f64 (.f64 (+.f64 (PI.f64) (PI.f64)) n)) (log.f64 (.f64 (+.f64 (PI.f64) (PI.f64)) n)))) (sqrt.f64 #s(literal 2 binary64))) #s(literal 1/8 binary64) (.f64 (.f64 (.f64 (pow.f64 (log.f64 (.f64 (+.f64 (PI.f64) (PI.f64)) n)) #s(literal 3 binary64)) (sqrt.f64 #s(literal 2 binary64))) (sqrt.f64 (.f64 (.f64 (.f64 k k) k) (.f64 (PI.f64) n)))) #s(literal -1/48 binary64))) (.f64 (.f64 (sqrt.f64 (.f64 (.f64 (PI.f64) n) k)) (.f64 (log.f64 (.f64 (+.f64 (PI.f64) (PI.f64)) n)) (sqrt.f64 #s(literal 2 binary64)))) #s(literal -1/2 binary64))) k (sqrt.f64 (.f64 (.f64 (.f64 (PI.f64) n) k) #s(literal 2 binary64)))) k))
#s(approx (/ 1 (sqrt k)) (/.f64 #s(literal 1 binary64) (sqrt.f64 k)))
#s(approx (sqrt k) (sqrt.f64 k))
#s(approx k k)
#s(approx (pow (* (* 2 (PI)) n) (/ (- 1 k) 2)) (sqrt.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n)))
#s(approx (pow (* (* 2 (PI)) n) (/ (- 1 k) 2)) (fma.f64 (.f64 (.f64 (.f64 (log.f64 (.f64 (+.f64 (PI.f64) (PI.f64)) n)) (sqrt.f64 #s(literal 2 binary64))) k) (sqrt.f64 (.f64 (PI.f64) n))) #s(literal -1/2 binary64) (sqrt.f64 (.f64 (+.f64 (PI.f64) (PI.f64)) n))))
#s(approx (pow (* (* 2 (PI)) n) (/ (- 1 k) 2)) (fma.f64 k (fma.f64 (.f64 (.f64 (.f64 (.f64 (log.f64 (.f64 (+.f64 (PI.f64) (PI.f64)) n)) (log.f64 (.f64 (+.f64 (PI.f64) (PI.f64)) n))) (sqrt.f64 #s(literal 2 binary64))) k) (sqrt.f64 (.f64 (PI.f64) n))) #s(literal 1/8 binary64) (.f64 (.f64 #s(literal -1/2 binary64) (sqrt.f64 (.f64 (PI.f64) n))) (.f64 (log.f64 (.f64 (+.f64 (PI.f64) (PI.f64)) n)) (sqrt.f64 #s(literal 2 binary64))))) (sqrt.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n))))
#s(approx (pow (* (* 2 (PI)) n) (/ (- 1 k) 2)) (fma.f64 (fma.f64 k (fma.f64 (.f64 (.f64 (.f64 (pow.f64 (log.f64 (.f64 (+.f64 (PI.f64) (PI.f64)) n)) #s(literal 3 binary64)) (sqrt.f64 #s(literal 2 binary64))) k) (sqrt.f64 (.f64 (PI.f64) n))) #s(literal -1/48 binary64) (.f64 (.f64 #s(literal 1/8 binary64) (sqrt.f64 (.f64 (PI.f64) n))) (.f64 (.f64 (log.f64 (.f64 (+.f64 (PI.f64) (PI.f64)) n)) (log.f64 (.f64 (+.f64 (PI.f64) (PI.f64)) n))) (sqrt.f64 #s(literal 2 binary64))))) (.f64 (.f64 #s(literal -1/2 binary64) (sqrt.f64 (.f64 (PI.f64) n))) (.f64 (log.f64 (.f64 (+.f64 (PI.f64) (PI.f64)) n)) (sqrt.f64 #s(literal 2 binary64))))) k (sqrt.f64 (.f64 (+.f64 (PI.f64) (PI.f64)) n))))
#s(approx (/ (- 1 k) 2) #s(literal 1/2 binary64))
#s(approx (/ (- 1 k) 2) (fma.f64 #s(literal -1/2 binary64) k #s(literal 1/2 binary64)))
#s(approx (- 1 k) #s(literal 1 binary64))
#s(approx (- 1 k) (+.f64 (neg.f64 k) #s(literal 1 binary64)))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (.f64 (exp.f64 (.f64 (.f64 (log.f64 (.f64 (+.f64 (PI.f64) (PI.f64)) n)) (-.f64 #s(literal 1 binary64) k)) #s(literal 1/2 binary64))) (/.f64 #s(literal 1 binary64) (sqrt.f64 k))))
#s(approx (pow (* (* 2 (PI)) n) (/ (- 1 k) 2)) (exp.f64 (.f64 (.f64 (log.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n)) (-.f64 #s(literal 1 binary64) k)) #s(literal 1/2 binary64))))
#s(approx (/ (- 1 k) 2) (*.f64 #s(literal -1/2 binary64) k))
#s(approx (/ (- 1 k) 2) (*.f64 (-.f64 (/.f64 #s(literal 1/2 binary64) k) #s(literal 1/2 binary64)) k))
#s(approx (- 1 k) (neg.f64 k))
#s(approx (- 1 k) (*.f64 (-.f64 (/.f64 #s(literal 1 binary64) k) #s(literal 1 binary64)) k))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (.f64 (exp.f64 (.f64 (.f64 (+.f64 (neg.f64 k) #s(literal 1 binary64)) (log.f64 (.f64 (+.f64 (PI.f64) (PI.f64)) n))) #s(literal 1/2 binary64))) (/.f64 #s(literal 1 binary64) (sqrt.f64 k))))
#s(approx (sqrt k) (neg.f64 (*.f64 #s(literal -1 binary64) (sqrt.f64 k))))
#s(approx (pow (* (* 2 (PI)) n) (/ (- 1 k) 2)) (exp.f64 (.f64 (.f64 (+.f64 (neg.f64 k) #s(literal 1 binary64)) (log.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n))) #s(literal 1/2 binary64))))
#s(approx (/ (- 1 k) 2) (*.f64 (neg.f64 k) (-.f64 #s(literal 1/2 binary64) (/.f64 #s(literal 1/2 binary64) k))))
#s(approx (- 1 k) (*.f64 (neg.f64 k) (-.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) k))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (.f64 (exp.f64 (.f64 (.f64 (log.f64 (.f64 (+.f64 (PI.f64) (PI.f64)) n)) (-.f64 #s(literal 1 binary64) k)) #s(literal 1/2 binary64))) (/.f64 #s(literal 1 binary64) (sqrt.f64 k))))
#s(approx (pow (* (* 2 (PI)) n) (/ (- 1 k) 2)) (exp.f64 (.f64 (.f64 (log.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n)) (-.f64 #s(literal 1 binary64) k)) #s(literal 1/2 binary64))))
#s(approx (* (* 2 (PI)) n) (*.f64 (+.f64 (PI.f64) (PI.f64)) n))
#s(approx n n)
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (.f64 (exp.f64 (.f64 (*.f64 (+.f64 (neg.f64 (neg.f64 (log.f64 n))) (log.f64 (+.f64 (PI.f64) (PI.f64)))) (-.f64 #s(literal 1 binary64) k)) #s(literal 1/2 binary64))) (/.f64 #s(literal 1 binary64) (sqrt.f64 k))))
#s(approx (pow (* (* 2 (PI)) n) (/ (- 1 k) 2)) (exp.f64 (.f64 (.f64 (+.f64 (neg.f64 (neg.f64 (log.f64 n))) (log.f64 (+.f64 (PI.f64) (PI.f64)))) (-.f64 #s(literal 1 binary64) k)) #s(literal 1/2 binary64))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (.f64 (exp.f64 (.f64 (.f64 #s(literal 1/2 binary64) (+.f64 (neg.f64 (log.f64 (/.f64 #s(literal -1 binary64) n))) (log.f64 (.f64 #s(literal -2 binary64) (PI.f64))))) (-.f64 #s(literal 1 binary64) k))) (/.f64 #s(literal 1 binary64) (sqrt.f64 k))))
#s(approx (pow (* (* 2 (PI)) n) (/ (- 1 k) 2)) (exp.f64 (.f64 (.f64 #s(literal 1/2 binary64) (+.f64 (neg.f64 (log.f64 (/.f64 #s(literal -1 binary64) n))) (log.f64 (*.f64 #s(literal -2 binary64) (PI.f64))))) (-.f64 #s(literal 1 binary64) k))))

eval8.0ms (0.2%)

Memory: -29.1MiB live, 16.8MiB allocated; 3ms collecting garbage
Compiler: Compiled 782 to 286 computations (63.4% saved)

prune10.0ms (0.2%)

Memory

24.7MiB live, 24.7MiB allocated; 0ms collecting garbage

Pruning

13 alts after pruning (13 fresh and 0 done)

	Pruned	Kept	Total
New	45	13	58
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	46	13	59

Accuracy

99.8%

Counts

59 → 13

Alt Table

Click to see full alt table

Status	Accuracy	Program
▶	99.5%	(/.f64 (.f64 #s(literal 1 binary64) (pow.f64 (.f64 (+.f64 (PI.f64) (PI.f64)) n) (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 2 binary64)))) (sqrt.f64 k))
▶	99.5%	(.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) (pow.f64 (.f64 (*.f64 #s(literal 2 binary64) (PI.f64)) n) #s(approx (/ (- 1 k) 2) (fma.f64 #s(literal -1/2 binary64) k #s(literal 1/2 binary64)))))
	53.8%	(.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) (pow.f64 (.f64 (.f64 #s(literal 2 binary64) (PI.f64)) n) #s(approx (/ (- 1 k) 2) (.f64 #s(literal -1/2 binary64) k))))
	75.0%	(.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) (.f64 (pow.f64 (+.f64 (PI.f64) (PI.f64)) (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 2 binary64))) (pow.f64 n (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 2 binary64)))))
▶	99.3%	(.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) (.f64 (pow.f64 (.f64 (+.f64 (PI.f64) (PI.f64)) n) (/.f64 (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 2 binary64)) #s(literal 2 binary64))) (pow.f64 (.f64 (+.f64 (PI.f64) (PI.f64)) n) (/.f64 (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 2 binary64)) #s(literal 2 binary64)))))
	61.0%	(.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) #s(approx (pow ( (* 2 (PI)) n) (/ (- 1 k) 2)) (fma.f64 (fma.f64 k (fma.f64 (.f64 (.f64 (.f64 (pow.f64 (log.f64 (.f64 (+.f64 (PI.f64) (PI.f64)) n)) #s(literal 3 binary64)) (sqrt.f64 #s(literal 2 binary64))) k) (sqrt.f64 (.f64 (PI.f64) n))) #s(literal -1/48 binary64) (.f64 (.f64 #s(literal 1/8 binary64) (sqrt.f64 (.f64 (PI.f64) n))) (.f64 (.f64 (log.f64 (.f64 (+.f64 (PI.f64) (PI.f64)) n)) (log.f64 (.f64 (+.f64 (PI.f64) (PI.f64)) n))) (sqrt.f64 #s(literal 2 binary64))))) (.f64 (.f64 #s(literal -1/2 binary64) (sqrt.f64 (.f64 (PI.f64) n))) (.f64 (log.f64 (.f64 (+.f64 (PI.f64) (PI.f64)) n)) (sqrt.f64 #s(literal 2 binary64))))) k (sqrt.f64 (.f64 (+.f64 (PI.f64) (PI.f64)) n)))))
▶	48.5%	(.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) #s(approx (pow ( (* 2 (PI)) n) (/ (- 1 k) 2)) (fma.f64 (.f64 (.f64 (.f64 (log.f64 (.f64 (+.f64 (PI.f64) (PI.f64)) n)) (sqrt.f64 #s(literal 2 binary64))) k) (sqrt.f64 (.f64 (PI.f64) n))) #s(literal -1/2 binary64) (sqrt.f64 (.f64 (+.f64 (PI.f64) (PI.f64)) n)))))
	56.9%	(.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) #s(approx (pow ( (* 2 (PI)) n) (/ (- 1 k) 2)) (fma.f64 k (fma.f64 (.f64 (.f64 (.f64 (.f64 (log.f64 (.f64 (+.f64 (PI.f64) (PI.f64)) n)) (log.f64 (.f64 (+.f64 (PI.f64) (PI.f64)) n))) (sqrt.f64 #s(literal 2 binary64))) k) (sqrt.f64 (.f64 (PI.f64) n))) #s(literal 1/8 binary64) (.f64 (.f64 #s(literal -1/2 binary64) (sqrt.f64 (.f64 (PI.f64) n))) (.f64 (log.f64 (.f64 (+.f64 (PI.f64) (PI.f64)) n)) (sqrt.f64 #s(literal 2 binary64))))) (sqrt.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n)))))
	47.4%	(.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) #s(approx (pow ( (* 2 (PI)) n) (/ (- 1 k) 2)) (sqrt.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n))))
	96.0%	(.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) #s(approx (pow ( (* 2 (PI)) n) (/ (- 1 k) 2)) (exp.f64 (.f64 (.f64 (log.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n)) (-.f64 #s(literal 1 binary64) k)) #s(literal 1/2 binary64)))))
	99.5%	(.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) k)) (pow.f64 (.f64 (*.f64 #s(literal 2 binary64) (PI.f64)) n) (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 2 binary64))))
	51.3%	#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (/.f64 (fma.f64 (.f64 (.f64 (log.f64 (.f64 (+.f64 (PI.f64) (PI.f64)) n)) (sqrt.f64 #s(literal 2 binary64))) (sqrt.f64 (.f64 (.f64 (.f64 k k) k) (.f64 (PI.f64) n)))) #s(literal -1/2 binary64) (sqrt.f64 (.f64 (.f64 (.f64 (PI.f64) n) k) #s(literal 2 binary64)))) k))
▶	33.6%	#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt.f64 (.f64 (/.f64 (.f64 (PI.f64) n) k) #s(literal 2 binary64))))

Compiler

Compiled 740 to 588 computations (20.5% saved)

series142.0ms (3.3%)

Memory

-16.7MiB live, 216.1MiB allocated; 58ms collecting garbage

Counts

41 → 131

Calls

Call 1

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

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

Calls

6 calls:

Time	Variable		Point	Expression
35.0ms	k	@	0	((/ (* 1 (pow (* (+ (PI) (PI)) n) (/ (- 1 k) 2))) (sqrt k)) (* 1 (pow (* (+ (PI) (PI)) n) (/ (- 1 k) 2))) 1 (pow (* (+ (PI) (PI)) n) (/ (- 1 k) 2)) (* (+ (PI) (PI)) n) (+ (PI) (PI)) (PI) n (/ (- 1 k) 2) (- 1 k) k 2 (sqrt k) (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt (* (/ (* (PI) n) k) 2)) (* (/ (* (PI) n) k) 2) (/ (* (PI) n) k) (* (PI) n) (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2)) (* (* 2 (PI)) n) (* 2 (PI)) (/ (- 1 k) 2) (+ (* -1/2 k) 1/2) -1/2 1/2 (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2)) (+ (* (* (* (* (log (* (+ (PI) (PI)) n)) (sqrt 2)) k) (sqrt (* (PI) n))) -1/2) (sqrt (* (+ (PI) (PI)) n))) (* (* (* (log (* (+ (PI) (PI)) n)) (sqrt 2)) k) (sqrt (* (PI) n))) (* (* (log (* (+ (PI) (PI)) n)) (sqrt 2)) k) (* (log (* (+ (PI) (PI)) n)) (sqrt 2)) (log (* (+ (PI) (PI)) n)) (sqrt 2) (sqrt (* (PI) n)) (sqrt (* (+ (PI) (PI)) n)) (* (/ 1 (sqrt k)) (* (pow (* (+ (PI) (PI)) n) (/ (/ (- 1 k) 2) 2)) (pow (* (+ (PI) (PI)) n) (/ (/ (- 1 k) 2) 2)))) (* (pow (* (+ (PI) (PI)) n) (/ (/ (- 1 k) 2) 2)) (pow (* (+ (PI) (PI)) n) (/ (/ (- 1 k) 2) 2))) (pow (* (+ (PI) (PI)) n) (/ (/ (- 1 k) 2) 2)) (/ (/ (- 1 k) 2) 2))
32.0ms	k	@	inf	((/ (* 1 (pow (* (+ (PI) (PI)) n) (/ (- 1 k) 2))) (sqrt k)) (* 1 (pow (* (+ (PI) (PI)) n) (/ (- 1 k) 2))) 1 (pow (* (+ (PI) (PI)) n) (/ (- 1 k) 2)) (* (+ (PI) (PI)) n) (+ (PI) (PI)) (PI) n (/ (- 1 k) 2) (- 1 k) k 2 (sqrt k) (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt (* (/ (* (PI) n) k) 2)) (* (/ (* (PI) n) k) 2) (/ (* (PI) n) k) (* (PI) n) (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2)) (* (* 2 (PI)) n) (* 2 (PI)) (/ (- 1 k) 2) (+ (* -1/2 k) 1/2) -1/2 1/2 (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2)) (+ (* (* (* (* (log (* (+ (PI) (PI)) n)) (sqrt 2)) k) (sqrt (* (PI) n))) -1/2) (sqrt (* (+ (PI) (PI)) n))) (* (* (* (log (* (+ (PI) (PI)) n)) (sqrt 2)) k) (sqrt (* (PI) n))) (* (* (log (* (+ (PI) (PI)) n)) (sqrt 2)) k) (* (log (* (+ (PI) (PI)) n)) (sqrt 2)) (log (* (+ (PI) (PI)) n)) (sqrt 2) (sqrt (* (PI) n)) (sqrt (* (+ (PI) (PI)) n)) (* (/ 1 (sqrt k)) (* (pow (* (+ (PI) (PI)) n) (/ (/ (- 1 k) 2) 2)) (pow (* (+ (PI) (PI)) n) (/ (/ (- 1 k) 2) 2)))) (* (pow (* (+ (PI) (PI)) n) (/ (/ (- 1 k) 2) 2)) (pow (* (+ (PI) (PI)) n) (/ (/ (- 1 k) 2) 2))) (pow (* (+ (PI) (PI)) n) (/ (/ (- 1 k) 2) 2)) (/ (/ (- 1 k) 2) 2))
17.0ms	n	@	0	((/ (* 1 (pow (* (+ (PI) (PI)) n) (/ (- 1 k) 2))) (sqrt k)) (* 1 (pow (* (+ (PI) (PI)) n) (/ (- 1 k) 2))) 1 (pow (* (+ (PI) (PI)) n) (/ (- 1 k) 2)) (* (+ (PI) (PI)) n) (+ (PI) (PI)) (PI) n (/ (- 1 k) 2) (- 1 k) k 2 (sqrt k) (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt (* (/ (* (PI) n) k) 2)) (* (/ (* (PI) n) k) 2) (/ (* (PI) n) k) (* (PI) n) (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2)) (* (* 2 (PI)) n) (* 2 (PI)) (/ (- 1 k) 2) (+ (* -1/2 k) 1/2) -1/2 1/2 (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2)) (+ (* (* (* (* (log (* (+ (PI) (PI)) n)) (sqrt 2)) k) (sqrt (* (PI) n))) -1/2) (sqrt (* (+ (PI) (PI)) n))) (* (* (* (log (* (+ (PI) (PI)) n)) (sqrt 2)) k) (sqrt (* (PI) n))) (* (* (log (* (+ (PI) (PI)) n)) (sqrt 2)) k) (* (log (* (+ (PI) (PI)) n)) (sqrt 2)) (log (* (+ (PI) (PI)) n)) (sqrt 2) (sqrt (* (PI) n)) (sqrt (* (+ (PI) (PI)) n)) (* (/ 1 (sqrt k)) (* (pow (* (+ (PI) (PI)) n) (/ (/ (- 1 k) 2) 2)) (pow (* (+ (PI) (PI)) n) (/ (/ (- 1 k) 2) 2)))) (* (pow (* (+ (PI) (PI)) n) (/ (/ (- 1 k) 2) 2)) (pow (* (+ (PI) (PI)) n) (/ (/ (- 1 k) 2) 2))) (pow (* (+ (PI) (PI)) n) (/ (/ (- 1 k) 2) 2)) (/ (/ (- 1 k) 2) 2))
16.0ms	n	@	inf	((/ (* 1 (pow (* (+ (PI) (PI)) n) (/ (- 1 k) 2))) (sqrt k)) (* 1 (pow (* (+ (PI) (PI)) n) (/ (- 1 k) 2))) 1 (pow (* (+ (PI) (PI)) n) (/ (- 1 k) 2)) (* (+ (PI) (PI)) n) (+ (PI) (PI)) (PI) n (/ (- 1 k) 2) (- 1 k) k 2 (sqrt k) (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt (* (/ (* (PI) n) k) 2)) (* (/ (* (PI) n) k) 2) (/ (* (PI) n) k) (* (PI) n) (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2)) (* (* 2 (PI)) n) (* 2 (PI)) (/ (- 1 k) 2) (+ (* -1/2 k) 1/2) -1/2 1/2 (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2)) (+ (* (* (* (* (log (* (+ (PI) (PI)) n)) (sqrt 2)) k) (sqrt (* (PI) n))) -1/2) (sqrt (* (+ (PI) (PI)) n))) (* (* (* (log (* (+ (PI) (PI)) n)) (sqrt 2)) k) (sqrt (* (PI) n))) (* (* (log (* (+ (PI) (PI)) n)) (sqrt 2)) k) (* (log (* (+ (PI) (PI)) n)) (sqrt 2)) (log (* (+ (PI) (PI)) n)) (sqrt 2) (sqrt (* (PI) n)) (sqrt (* (+ (PI) (PI)) n)) (* (/ 1 (sqrt k)) (* (pow (* (+ (PI) (PI)) n) (/ (/ (- 1 k) 2) 2)) (pow (* (+ (PI) (PI)) n) (/ (/ (- 1 k) 2) 2)))) (* (pow (* (+ (PI) (PI)) n) (/ (/ (- 1 k) 2) 2)) (pow (* (+ (PI) (PI)) n) (/ (/ (- 1 k) 2) 2))) (pow (* (+ (PI) (PI)) n) (/ (/ (- 1 k) 2) 2)) (/ (/ (- 1 k) 2) 2))
14.0ms	n	@	-inf	((/ (* 1 (pow (* (+ (PI) (PI)) n) (/ (- 1 k) 2))) (sqrt k)) (* 1 (pow (* (+ (PI) (PI)) n) (/ (- 1 k) 2))) 1 (pow (* (+ (PI) (PI)) n) (/ (- 1 k) 2)) (* (+ (PI) (PI)) n) (+ (PI) (PI)) (PI) n (/ (- 1 k) 2) (- 1 k) k 2 (sqrt k) (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt (* (/ (* (PI) n) k) 2)) (* (/ (* (PI) n) k) 2) (/ (* (PI) n) k) (* (PI) n) (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2)) (* (* 2 (PI)) n) (* 2 (PI)) (/ (- 1 k) 2) (+ (* -1/2 k) 1/2) -1/2 1/2 (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2)) (+ (* (* (* (* (log (* (+ (PI) (PI)) n)) (sqrt 2)) k) (sqrt (* (PI) n))) -1/2) (sqrt (* (+ (PI) (PI)) n))) (* (* (* (log (* (+ (PI) (PI)) n)) (sqrt 2)) k) (sqrt (* (PI) n))) (* (* (log (* (+ (PI) (PI)) n)) (sqrt 2)) k) (* (log (* (+ (PI) (PI)) n)) (sqrt 2)) (log (* (+ (PI) (PI)) n)) (sqrt 2) (sqrt (* (PI) n)) (sqrt (* (+ (PI) (PI)) n)) (* (/ 1 (sqrt k)) (* (pow (* (+ (PI) (PI)) n) (/ (/ (- 1 k) 2) 2)) (pow (* (+ (PI) (PI)) n) (/ (/ (- 1 k) 2) 2)))) (* (pow (* (+ (PI) (PI)) n) (/ (/ (- 1 k) 2) 2)) (pow (* (+ (PI) (PI)) n) (/ (/ (- 1 k) 2) 2))) (pow (* (+ (PI) (PI)) n) (/ (/ (- 1 k) 2) 2)) (/ (/ (- 1 k) 2) 2))

rewrite86.0ms (2%)

Memory

38.7MiB live, 129.0MiB allocated; 15ms collecting garbage

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	446	4972
0	509	4341
0	1967	4292

Stop Event

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

Counts

172 → 319

Calls

Call 1

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

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

eval61.0ms (1.4%)

Memory: 12.8MiB live, 59.2MiB allocated; 3ms collecting garbage
Compiler: Compiled 4 570 to 1 285 computations (71.9% saved)

prune65.0ms (1.5%)

Memory

-61.4MiB live, 40.0MiB allocated; 88ms collecting garbage

Pruning

22 alts after pruning (22 fresh and 0 done)

	Pruned	Kept	Total
New	248	20	268
Fresh	6	2	8
Picked	5	0	5
Done	0	0	0
Total	259	22	281

Accuracy

99.9%

Counts

281 → 22

Alt Table

Click to see full alt table

Status	Accuracy	Program
	99.3%	(/.f64 (pow.f64 (pow.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n) (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 4 binary64))) #s(literal 2 binary64)) (sqrt.f64 k))
▶	99.5%	(/.f64 (pow.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n) (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 2 binary64))) (sqrt.f64 k))
	74.5%	(/.f64 (pow.f64 (.f64 (.f64 (+.f64 (PI.f64) (PI.f64)) n) (*.f64 (+.f64 (PI.f64) (PI.f64)) n)) (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 4 binary64))) (sqrt.f64 k))
	53.8%	(/.f64 (.f64 #s(literal 1 binary64) (pow.f64 (.f64 (+.f64 (PI.f64) (PI.f64)) n) #s(approx (/ (- 1 k) 2) (*.f64 #s(literal -1/2 binary64) k)))) (sqrt.f64 k))
	61.0%	(/.f64 #s(approx (* 1 (pow (* (+ (PI) (PI)) n) (/ (- 1 k) 2))) (fma.f64 (fma.f64 k (fma.f64 (.f64 (.f64 (.f64 (pow.f64 (log.f64 (.f64 (+.f64 (PI.f64) (PI.f64)) n)) #s(literal 3 binary64)) k) (sqrt.f64 #s(literal 2 binary64))) (sqrt.f64 (.f64 (PI.f64) n))) #s(literal -1/48 binary64) (.f64 (.f64 #s(literal 1/8 binary64) (sqrt.f64 (.f64 (PI.f64) n))) (.f64 (.f64 (log.f64 (.f64 (+.f64 (PI.f64) (PI.f64)) n)) (log.f64 (.f64 (+.f64 (PI.f64) (PI.f64)) n))) (sqrt.f64 #s(literal 2 binary64))))) (.f64 (.f64 #s(literal -1/2 binary64) (sqrt.f64 (.f64 (PI.f64) n))) (.f64 (log.f64 (.f64 (+.f64 (PI.f64) (PI.f64)) n)) (sqrt.f64 #s(literal 2 binary64))))) k (sqrt.f64 (.f64 (+.f64 (PI.f64) (PI.f64)) n)))) (sqrt.f64 k))
	57.0%	(/.f64 #s(approx (* 1 (pow (* (+ (PI) (PI)) n) (/ (- 1 k) 2))) (fma.f64 k (fma.f64 (.f64 (.f64 (.f64 (.f64 (log.f64 (.f64 (+.f64 (PI.f64) (PI.f64)) n)) (log.f64 (.f64 (+.f64 (PI.f64) (PI.f64)) n))) k) (sqrt.f64 #s(literal 2 binary64))) (sqrt.f64 (.f64 (PI.f64) n))) #s(literal 1/8 binary64) (.f64 (.f64 #s(literal -1/2 binary64) (sqrt.f64 (.f64 (PI.f64) n))) (.f64 (log.f64 (.f64 (+.f64 (PI.f64) (PI.f64)) n)) (sqrt.f64 #s(literal 2 binary64))))) (sqrt.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n)))) (sqrt.f64 k))
	47.5%	(/.f64 #s(approx (* 1 (pow (* (+ (PI) (PI)) n) (/ (- 1 k) 2))) (sqrt.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n))) (sqrt.f64 k))
	96.0%	(/.f64 #s(approx (* 1 (pow (* (+ (PI) (PI)) n) (/ (- 1 k) 2))) (exp.f64 (.f64 (.f64 #s(literal 1/2 binary64) (log.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n))) (-.f64 #s(literal 1 binary64) k)))) (sqrt.f64 k))
	75.0%	(.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) (.f64 (.f64 (pow.f64 (+.f64 (PI.f64) (PI.f64)) (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 4 binary64))) (pow.f64 n (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 4 binary64)))) (.f64 (pow.f64 (+.f64 (PI.f64) (PI.f64)) (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 4 binary64))) (pow.f64 n (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 4 binary64))))))
	64.0%	(.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) (.f64 #s(approx (pow (* (+ (PI) (PI)) n) (/ (/ (- 1 k) 2) 2)) (fma.f64 (fma.f64 (.f64 (.f64 (pow.f64 (.f64 (+.f64 (PI.f64) (PI.f64)) n) #s(literal 1/4 binary64)) k) (.f64 (log.f64 (.f64 (+.f64 (PI.f64) (PI.f64)) n)) (log.f64 (.f64 (+.f64 (PI.f64) (PI.f64)) n)))) #s(literal 1/32 binary64) (.f64 (.f64 (pow.f64 (.f64 (+.f64 (PI.f64) (PI.f64)) n) #s(literal 1/4 binary64)) (log.f64 (.f64 (+.f64 (PI.f64) (PI.f64)) n))) #s(literal -1/4 binary64))) k (pow.f64 (.f64 (+.f64 (PI.f64) (PI.f64)) n) #s(literal 1/4 binary64)))) #s(approx (pow ( (+ (PI) (PI)) n) (/ (/ (- 1 k) 2) 2)) (fma.f64 (fma.f64 (.f64 (.f64 (pow.f64 (.f64 (+.f64 (PI.f64) (PI.f64)) n) #s(literal 1/4 binary64)) k) (.f64 (log.f64 (.f64 (+.f64 (PI.f64) (PI.f64)) n)) (log.f64 (.f64 (+.f64 (PI.f64) (PI.f64)) n)))) #s(literal 1/32 binary64) (.f64 (.f64 (pow.f64 (.f64 (+.f64 (PI.f64) (PI.f64)) n) #s(literal 1/4 binary64)) (log.f64 (.f64 (+.f64 (PI.f64) (PI.f64)) n))) #s(literal -1/4 binary64))) k (pow.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n) #s(literal 1/4 binary64))))))
	48.3%	(.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) #s(approx (pow ( (* 2 (PI)) n) (/ (- 1 k) 2)) (fma.f64 (.f64 (.f64 (.f64 (log.f64 (.f64 (+.f64 (PI.f64) (PI.f64)) n)) (sqrt.f64 #s(literal 2 binary64))) k) (sqrt.f64 (.f64 (PI.f64) n))) #s(literal -1/2 binary64) (.f64 (sqrt.f64 (+.f64 (PI.f64) (PI.f64))) (sqrt.f64 n)))))
	48.3%	(.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) #s(approx (pow ( (* 2 (PI)) n) (/ (- 1 k) 2)) (fma.f64 (.f64 (.f64 (.f64 (log.f64 (.f64 (+.f64 (PI.f64) (PI.f64)) n)) (sqrt.f64 #s(literal 2 binary64))) k) (sqrt.f64 (.f64 (PI.f64) n))) #s(literal -1/2 binary64) (.f64 (sqrt.f64 (*.f64 (PI.f64) n)) (sqrt.f64 #s(literal 2 binary64))))))
	56.9%	(.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) #s(approx (pow ( (* 2 (PI)) n) (/ (- 1 k) 2)) (fma.f64 k (fma.f64 (.f64 (.f64 (.f64 (.f64 (log.f64 (.f64 (+.f64 (PI.f64) (PI.f64)) n)) (log.f64 (.f64 (+.f64 (PI.f64) (PI.f64)) n))) (sqrt.f64 #s(literal 2 binary64))) k) (sqrt.f64 (.f64 (PI.f64) n))) #s(literal 1/8 binary64) (.f64 (.f64 #s(literal -1/2 binary64) (sqrt.f64 (.f64 (PI.f64) n))) (.f64 (log.f64 (.f64 (+.f64 (PI.f64) (PI.f64)) n)) (sqrt.f64 #s(literal 2 binary64))))) (sqrt.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n)))))
▶	47.4%	(.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) #s(approx (pow ( (* 2 (PI)) n) (/ (- 1 k) 2)) (sqrt.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n))))
▶	52.9%	(.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) #s(approx (pow ( (* 2 (PI)) n) (/ (- 1 k) 2)) #s(approx (+ (* (* (* (* (log (* (+ (PI) (PI)) n)) (sqrt 2)) k) (sqrt (* (PI) n))) -1/2) (sqrt (* (+ (PI) (PI)) n))) (.f64 (fma.f64 (.f64 (sqrt.f64 (/.f64 (PI.f64) n)) (.f64 (.f64 (+.f64 (neg.f64 (neg.f64 (log.f64 n))) (log.f64 (+.f64 (PI.f64) (PI.f64)))) (sqrt.f64 #s(literal 2 binary64))) k)) #s(literal -1/2 binary64) (sqrt.f64 (*.f64 (/.f64 (PI.f64) n) #s(literal 2 binary64)))) n))))
	99.5%	(.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) k)) (pow.f64 (.f64 (*.f64 #s(literal 2 binary64) (PI.f64)) n) #s(approx (/ (- 1 k) 2) (fma.f64 #s(literal -1/2 binary64) k #s(literal 1/2 binary64)))))
▶	48.5%	(.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) k)) #s(approx (pow ( (* 2 (PI)) n) (/ (- 1 k) 2)) (fma.f64 (.f64 (.f64 (.f64 (log.f64 (.f64 (+.f64 (PI.f64) (PI.f64)) n)) (sqrt.f64 #s(literal 2 binary64))) k) (sqrt.f64 (.f64 (PI.f64) n))) #s(literal -1/2 binary64) (sqrt.f64 (.f64 (+.f64 (PI.f64) (PI.f64)) n)))))
	51.3%	#s(approx (/ (* 1 (pow (* (+ (PI) (PI)) n) (/ (- 1 k) 2))) (sqrt k)) (/.f64 (fma.f64 (.f64 (.f64 (sqrt.f64 (.f64 (.f64 (.f64 k k) k) (.f64 (PI.f64) n))) (log.f64 (.f64 (+.f64 (PI.f64) (PI.f64)) n))) (sqrt.f64 #s(literal 2 binary64))) #s(literal -1/2 binary64) (sqrt.f64 (.f64 (.f64 (.f64 (PI.f64) n) k) #s(literal 2 binary64)))) k))
▶	33.6%	#s(approx (/ (* 1 (pow (* (+ (PI) (PI)) n) (/ (- 1 k) 2))) (sqrt k)) (sqrt.f64 (/.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n) k)))
	33.5%	#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (.f64 (sqrt.f64 (/.f64 (.f64 (PI.f64) n) k)) (sqrt.f64 #s(literal 2 binary64))))
	33.6%	#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt.f64 (.f64 (.f64 (PI.f64) (/.f64 n k)) #s(literal 2 binary64))))
	33.6%	#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt.f64 (.f64 (.f64 n (/.f64 (PI.f64) k)) #s(literal 2 binary64))))

Compiler

Compiled 1 494 to 1 086 computations (27.3% saved)

series260.0ms (6%)

Memory

3.1MiB live, 374.0MiB allocated; 83ms collecting garbage

Counts

49 → 146

Calls

Call 1

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

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

Calls

6 calls:

Time	Variable		Point	Expression
63.0ms	k	@	0	((/ (pow (* (+ (PI) (PI)) n) (/ (- 1 k) 2)) (sqrt k)) (pow (* (+ (PI) (PI)) n) (/ (- 1 k) 2)) (* (+ (PI) (PI)) n) (+ (PI) (PI)) (PI) n (/ (- 1 k) 2) (- 1 k) 1 k 2 (sqrt k) (/ (* 1 (pow (* (+ (PI) (PI)) n) (/ (- 1 k) 2))) (sqrt k)) (sqrt (/ (* (+ (PI) (PI)) n) k)) (/ (* (+ (PI) (PI)) n) k) (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2)) (sqrt (* (+ (PI) (PI)) n)) (* (sqrt (/ 1 k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt (/ 1 k)) (/ 1 k) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2)) (+ (* (* (* (* (log (* (+ (PI) (PI)) n)) (sqrt 2)) k) (sqrt (* (PI) n))) -1/2) (sqrt (* (+ (PI) (PI)) n))) (* (* (* (log (* (+ (PI) (PI)) n)) (sqrt 2)) k) (sqrt (* (PI) n))) (* (* (log (* (+ (PI) (PI)) n)) (sqrt 2)) k) (* (log (* (+ (PI) (PI)) n)) (sqrt 2)) (log (* (+ (PI) (PI)) n)) (sqrt 2) (sqrt (* (PI) n)) (* (PI) n) -1/2 (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2)) (+ (* (* (* (* (log (* (+ (PI) (PI)) n)) (sqrt 2)) k) (sqrt (* (PI) n))) -1/2) (sqrt (* (+ (PI) (PI)) n))) (* (+ (* (* (sqrt (/ (PI) n)) (* (* (+ (neg (neg (log n))) (log (+ (PI) (PI)))) (sqrt 2)) k)) -1/2) (sqrt (* (/ (PI) n) 2))) n) (+ (* (* (sqrt (/ (PI) n)) (* (* (+ (neg (neg (log n))) (log (+ (PI) (PI)))) (sqrt 2)) k)) -1/2) (sqrt (* (/ (PI) n) 2))) (* (sqrt (/ (PI) n)) (* (* (+ (neg (neg (log n))) (log (+ (PI) (PI)))) (sqrt 2)) k)) (sqrt (/ (PI) n)) (/ (PI) n) (* (* (+ (neg (neg (log n))) (log (+ (PI) (PI)))) (sqrt 2)) k) (* (+ (neg (neg (log n))) (log (+ (PI) (PI)))) (sqrt 2)) (+ (neg (neg (log n))) (log (+ (PI) (PI)))) (neg (neg (log n))) (neg (log n)) (log n) (log (+ (PI) (PI))) (sqrt (* (/ (PI) n) 2)) (* (/ (PI) n) 2))
52.0ms	n	@	0	((/ (pow (* (+ (PI) (PI)) n) (/ (- 1 k) 2)) (sqrt k)) (pow (* (+ (PI) (PI)) n) (/ (- 1 k) 2)) (* (+ (PI) (PI)) n) (+ (PI) (PI)) (PI) n (/ (- 1 k) 2) (- 1 k) 1 k 2 (sqrt k) (/ (* 1 (pow (* (+ (PI) (PI)) n) (/ (- 1 k) 2))) (sqrt k)) (sqrt (/ (* (+ (PI) (PI)) n) k)) (/ (* (+ (PI) (PI)) n) k) (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2)) (sqrt (* (+ (PI) (PI)) n)) (* (sqrt (/ 1 k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt (/ 1 k)) (/ 1 k) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2)) (+ (* (* (* (* (log (* (+ (PI) (PI)) n)) (sqrt 2)) k) (sqrt (* (PI) n))) -1/2) (sqrt (* (+ (PI) (PI)) n))) (* (* (* (log (* (+ (PI) (PI)) n)) (sqrt 2)) k) (sqrt (* (PI) n))) (* (* (log (* (+ (PI) (PI)) n)) (sqrt 2)) k) (* (log (* (+ (PI) (PI)) n)) (sqrt 2)) (log (* (+ (PI) (PI)) n)) (sqrt 2) (sqrt (* (PI) n)) (* (PI) n) -1/2 (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2)) (+ (* (* (* (* (log (* (+ (PI) (PI)) n)) (sqrt 2)) k) (sqrt (* (PI) n))) -1/2) (sqrt (* (+ (PI) (PI)) n))) (* (+ (* (* (sqrt (/ (PI) n)) (* (* (+ (neg (neg (log n))) (log (+ (PI) (PI)))) (sqrt 2)) k)) -1/2) (sqrt (* (/ (PI) n) 2))) n) (+ (* (* (sqrt (/ (PI) n)) (* (* (+ (neg (neg (log n))) (log (+ (PI) (PI)))) (sqrt 2)) k)) -1/2) (sqrt (* (/ (PI) n) 2))) (* (sqrt (/ (PI) n)) (* (* (+ (neg (neg (log n))) (log (+ (PI) (PI)))) (sqrt 2)) k)) (sqrt (/ (PI) n)) (/ (PI) n) (* (* (+ (neg (neg (log n))) (log (+ (PI) (PI)))) (sqrt 2)) k) (* (+ (neg (neg (log n))) (log (+ (PI) (PI)))) (sqrt 2)) (+ (neg (neg (log n))) (log (+ (PI) (PI)))) (neg (neg (log n))) (neg (log n)) (log n) (log (+ (PI) (PI))) (sqrt (* (/ (PI) n) 2)) (* (/ (PI) n) 2))
45.0ms	n	@	-inf	((/ (pow (* (+ (PI) (PI)) n) (/ (- 1 k) 2)) (sqrt k)) (pow (* (+ (PI) (PI)) n) (/ (- 1 k) 2)) (* (+ (PI) (PI)) n) (+ (PI) (PI)) (PI) n (/ (- 1 k) 2) (- 1 k) 1 k 2 (sqrt k) (/ (* 1 (pow (* (+ (PI) (PI)) n) (/ (- 1 k) 2))) (sqrt k)) (sqrt (/ (* (+ (PI) (PI)) n) k)) (/ (* (+ (PI) (PI)) n) k) (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2)) (sqrt (* (+ (PI) (PI)) n)) (* (sqrt (/ 1 k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt (/ 1 k)) (/ 1 k) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2)) (+ (* (* (* (* (log (* (+ (PI) (PI)) n)) (sqrt 2)) k) (sqrt (* (PI) n))) -1/2) (sqrt (* (+ (PI) (PI)) n))) (* (* (* (log (* (+ (PI) (PI)) n)) (sqrt 2)) k) (sqrt (* (PI) n))) (* (* (log (* (+ (PI) (PI)) n)) (sqrt 2)) k) (* (log (* (+ (PI) (PI)) n)) (sqrt 2)) (log (* (+ (PI) (PI)) n)) (sqrt 2) (sqrt (* (PI) n)) (* (PI) n) -1/2 (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2)) (+ (* (* (* (* (log (* (+ (PI) (PI)) n)) (sqrt 2)) k) (sqrt (* (PI) n))) -1/2) (sqrt (* (+ (PI) (PI)) n))) (* (+ (* (* (sqrt (/ (PI) n)) (* (* (+ (neg (neg (log n))) (log (+ (PI) (PI)))) (sqrt 2)) k)) -1/2) (sqrt (* (/ (PI) n) 2))) n) (+ (* (* (sqrt (/ (PI) n)) (* (* (+ (neg (neg (log n))) (log (+ (PI) (PI)))) (sqrt 2)) k)) -1/2) (sqrt (* (/ (PI) n) 2))) (* (sqrt (/ (PI) n)) (* (* (+ (neg (neg (log n))) (log (+ (PI) (PI)))) (sqrt 2)) k)) (sqrt (/ (PI) n)) (/ (PI) n) (* (* (+ (neg (neg (log n))) (log (+ (PI) (PI)))) (sqrt 2)) k) (* (+ (neg (neg (log n))) (log (+ (PI) (PI)))) (sqrt 2)) (+ (neg (neg (log n))) (log (+ (PI) (PI)))) (neg (neg (log n))) (neg (log n)) (log n) (log (+ (PI) (PI))) (sqrt (* (/ (PI) n) 2)) (* (/ (PI) n) 2))
36.0ms	k	@	-inf	((/ (pow (* (+ (PI) (PI)) n) (/ (- 1 k) 2)) (sqrt k)) (pow (* (+ (PI) (PI)) n) (/ (- 1 k) 2)) (* (+ (PI) (PI)) n) (+ (PI) (PI)) (PI) n (/ (- 1 k) 2) (- 1 k) 1 k 2 (sqrt k) (/ (* 1 (pow (* (+ (PI) (PI)) n) (/ (- 1 k) 2))) (sqrt k)) (sqrt (/ (* (+ (PI) (PI)) n) k)) (/ (* (+ (PI) (PI)) n) k) (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2)) (sqrt (* (+ (PI) (PI)) n)) (* (sqrt (/ 1 k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt (/ 1 k)) (/ 1 k) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2)) (+ (* (* (* (* (log (* (+ (PI) (PI)) n)) (sqrt 2)) k) (sqrt (* (PI) n))) -1/2) (sqrt (* (+ (PI) (PI)) n))) (* (* (* (log (* (+ (PI) (PI)) n)) (sqrt 2)) k) (sqrt (* (PI) n))) (* (* (log (* (+ (PI) (PI)) n)) (sqrt 2)) k) (* (log (* (+ (PI) (PI)) n)) (sqrt 2)) (log (* (+ (PI) (PI)) n)) (sqrt 2) (sqrt (* (PI) n)) (* (PI) n) -1/2 (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2)) (+ (* (* (* (* (log (* (+ (PI) (PI)) n)) (sqrt 2)) k) (sqrt (* (PI) n))) -1/2) (sqrt (* (+ (PI) (PI)) n))) (* (+ (* (* (sqrt (/ (PI) n)) (* (* (+ (neg (neg (log n))) (log (+ (PI) (PI)))) (sqrt 2)) k)) -1/2) (sqrt (* (/ (PI) n) 2))) n) (+ (* (* (sqrt (/ (PI) n)) (* (* (+ (neg (neg (log n))) (log (+ (PI) (PI)))) (sqrt 2)) k)) -1/2) (sqrt (* (/ (PI) n) 2))) (* (sqrt (/ (PI) n)) (* (* (+ (neg (neg (log n))) (log (+ (PI) (PI)))) (sqrt 2)) k)) (sqrt (/ (PI) n)) (/ (PI) n) (* (* (+ (neg (neg (log n))) (log (+ (PI) (PI)))) (sqrt 2)) k) (* (+ (neg (neg (log n))) (log (+ (PI) (PI)))) (sqrt 2)) (+ (neg (neg (log n))) (log (+ (PI) (PI)))) (neg (neg (log n))) (neg (log n)) (log n) (log (+ (PI) (PI))) (sqrt (* (/ (PI) n) 2)) (* (/ (PI) n) 2))
30.0ms	n	@	inf	((/ (pow (* (+ (PI) (PI)) n) (/ (- 1 k) 2)) (sqrt k)) (pow (* (+ (PI) (PI)) n) (/ (- 1 k) 2)) (* (+ (PI) (PI)) n) (+ (PI) (PI)) (PI) n (/ (- 1 k) 2) (- 1 k) 1 k 2 (sqrt k) (/ (* 1 (pow (* (+ (PI) (PI)) n) (/ (- 1 k) 2))) (sqrt k)) (sqrt (/ (* (+ (PI) (PI)) n) k)) (/ (* (+ (PI) (PI)) n) k) (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2)) (sqrt (* (+ (PI) (PI)) n)) (* (sqrt (/ 1 k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt (/ 1 k)) (/ 1 k) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2)) (+ (* (* (* (* (log (* (+ (PI) (PI)) n)) (sqrt 2)) k) (sqrt (* (PI) n))) -1/2) (sqrt (* (+ (PI) (PI)) n))) (* (* (* (log (* (+ (PI) (PI)) n)) (sqrt 2)) k) (sqrt (* (PI) n))) (* (* (log (* (+ (PI) (PI)) n)) (sqrt 2)) k) (* (log (* (+ (PI) (PI)) n)) (sqrt 2)) (log (* (+ (PI) (PI)) n)) (sqrt 2) (sqrt (* (PI) n)) (* (PI) n) -1/2 (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2)) (+ (* (* (* (* (log (* (+ (PI) (PI)) n)) (sqrt 2)) k) (sqrt (* (PI) n))) -1/2) (sqrt (* (+ (PI) (PI)) n))) (* (+ (* (* (sqrt (/ (PI) n)) (* (* (+ (neg (neg (log n))) (log (+ (PI) (PI)))) (sqrt 2)) k)) -1/2) (sqrt (* (/ (PI) n) 2))) n) (+ (* (* (sqrt (/ (PI) n)) (* (* (+ (neg (neg (log n))) (log (+ (PI) (PI)))) (sqrt 2)) k)) -1/2) (sqrt (* (/ (PI) n) 2))) (* (sqrt (/ (PI) n)) (* (* (+ (neg (neg (log n))) (log (+ (PI) (PI)))) (sqrt 2)) k)) (sqrt (/ (PI) n)) (/ (PI) n) (* (* (+ (neg (neg (log n))) (log (+ (PI) (PI)))) (sqrt 2)) k) (* (+ (neg (neg (log n))) (log (+ (PI) (PI)))) (sqrt 2)) (+ (neg (neg (log n))) (log (+ (PI) (PI)))) (neg (neg (log n))) (neg (log n)) (log n) (log (+ (PI) (PI))) (sqrt (* (/ (PI) n) 2)) (* (/ (PI) n) 2))

rewrite79.0ms (1.8%)

Memory

7.2MiB live, 95.8MiB allocated; 15ms collecting garbage

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	444	5475
0	523	4949
0	1849	4905

Stop Event

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

Counts

195 → 361

Calls

Call 1

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

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

eval59.0ms (1.4%)

Memory: 23.5MiB live, 68.1MiB allocated; 7ms collecting garbage
Compiler: Compiled 5 276 to 1 600 computations (69.7% saved)

prune40.0ms (0.9%)

Memory

-30.9MiB live, 67.2MiB allocated; 18ms collecting garbage

Pruning

25 alts after pruning (23 fresh and 2 done)

	Pruned	Kept	Total
New	294	13	307
Fresh	7	10	17
Picked	3	2	5
Done	0	0	0
Total	304	25	329

Accuracy

99.9%

Counts

329 → 25

Alt Table

Click to see full alt table

Status	Accuracy	Program
▶	99.3%	(/.f64 (pow.f64 (pow.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n) (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 4 binary64))) #s(literal 2 binary64)) (sqrt.f64 k))
▶	99.5%	(/.f64 (pow.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n) #s(approx (/ (- 1 k) 2) (fma.f64 #s(literal -1/2 binary64) k #s(literal 1/2 binary64)))) (sqrt.f64 k))
	53.8%	(/.f64 (pow.f64 (.f64 (+.f64 (PI.f64) (PI.f64)) n) #s(approx (/ (- 1 k) 2) (.f64 #s(literal -1/2 binary64) k))) (sqrt.f64 k))
	74.5%	(/.f64 (pow.f64 (.f64 (.f64 (+.f64 (PI.f64) (PI.f64)) n) (*.f64 (+.f64 (PI.f64) (PI.f64)) n)) (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 4 binary64))) (sqrt.f64 k))
	57.0%	(/.f64 #s(approx (pow (* (* 2 (PI)) n) (/ (- 1 k) 2)) (fma.f64 k (fma.f64 (.f64 (.f64 (.f64 (.f64 (log.f64 (.f64 n (+.f64 (PI.f64) (PI.f64)))) (log.f64 (.f64 n (+.f64 (PI.f64) (PI.f64))))) (sqrt.f64 #s(literal 2 binary64))) k) (sqrt.f64 (.f64 (PI.f64) n))) #s(literal 1/8 binary64) (.f64 (.f64 (sqrt.f64 (.f64 n (+.f64 (PI.f64) (PI.f64)))) (log.f64 (.f64 n (+.f64 (PI.f64) (PI.f64))))) #s(literal -1/2 binary64))) (sqrt.f64 (.f64 n (+.f64 (PI.f64) (PI.f64)))))) (sqrt.f64 k))
	61.0%	(/.f64 #s(approx (pow (* (* 2 (PI)) n) (/ (- 1 k) 2)) (fma.f64 k (fma.f64 k (fma.f64 (.f64 (.f64 (.f64 (pow.f64 (log.f64 (.f64 n (+.f64 (PI.f64) (PI.f64)))) #s(literal 3 binary64)) (sqrt.f64 #s(literal 2 binary64))) k) (sqrt.f64 (.f64 (PI.f64) n))) #s(literal -1/48 binary64) (.f64 (.f64 #s(literal 1/8 binary64) (sqrt.f64 (.f64 (PI.f64) n))) (.f64 (.f64 (log.f64 (.f64 n (+.f64 (PI.f64) (PI.f64)))) (log.f64 (.f64 n (+.f64 (PI.f64) (PI.f64))))) (sqrt.f64 #s(literal 2 binary64))))) (.f64 (.f64 (sqrt.f64 (.f64 n (+.f64 (PI.f64) (PI.f64)))) (log.f64 (.f64 n (+.f64 (PI.f64) (PI.f64))))) #s(literal -1/2 binary64))) (sqrt.f64 (*.f64 n (+.f64 (PI.f64) (PI.f64)))))) (sqrt.f64 k))
	96.0%	(/.f64 #s(approx (pow (* (* 2 (PI)) n) (/ (- 1 k) 2)) (exp.f64 (.f64 (.f64 (log.f64 (*.f64 n (+.f64 (PI.f64) (PI.f64)))) (-.f64 #s(literal 1 binary64) k)) #s(literal 1/2 binary64)))) (sqrt.f64 k))
	47.5%	(/.f64 #s(approx (* 1 (pow (* (+ (PI) (PI)) n) (/ (- 1 k) 2))) (sqrt.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n))) (sqrt.f64 k))
	75.0%	(.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) (.f64 (.f64 (pow.f64 (+.f64 (PI.f64) (PI.f64)) (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 4 binary64))) (pow.f64 n (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 4 binary64)))) (.f64 (pow.f64 (+.f64 (PI.f64) (PI.f64)) (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 4 binary64))) (pow.f64 n (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 4 binary64))))))
	64.0%	(.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) (.f64 #s(approx (pow (* (+ (PI) (PI)) n) (/ (/ (- 1 k) 2) 2)) (fma.f64 (fma.f64 (.f64 (.f64 (pow.f64 (.f64 (+.f64 (PI.f64) (PI.f64)) n) #s(literal 1/4 binary64)) k) (.f64 (log.f64 (.f64 (+.f64 (PI.f64) (PI.f64)) n)) (log.f64 (.f64 (+.f64 (PI.f64) (PI.f64)) n)))) #s(literal 1/32 binary64) (.f64 (.f64 (pow.f64 (.f64 (+.f64 (PI.f64) (PI.f64)) n) #s(literal 1/4 binary64)) (log.f64 (.f64 (+.f64 (PI.f64) (PI.f64)) n))) #s(literal -1/4 binary64))) k (pow.f64 (.f64 (+.f64 (PI.f64) (PI.f64)) n) #s(literal 1/4 binary64)))) #s(approx (pow ( (+ (PI) (PI)) n) (/ (/ (- 1 k) 2) 2)) (fma.f64 (fma.f64 (.f64 (.f64 (pow.f64 (.f64 (+.f64 (PI.f64) (PI.f64)) n) #s(literal 1/4 binary64)) k) (.f64 (log.f64 (.f64 (+.f64 (PI.f64) (PI.f64)) n)) (log.f64 (.f64 (+.f64 (PI.f64) (PI.f64)) n)))) #s(literal 1/32 binary64) (.f64 (.f64 (pow.f64 (.f64 (+.f64 (PI.f64) (PI.f64)) n) #s(literal 1/4 binary64)) (log.f64 (.f64 (+.f64 (PI.f64) (PI.f64)) n))) #s(literal -1/4 binary64))) k (pow.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n) #s(literal 1/4 binary64))))))
	56.9%	(.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) #s(approx (pow ( (* 2 (PI)) n) (/ (- 1 k) 2)) (fma.f64 k (fma.f64 (.f64 (.f64 (.f64 (.f64 (log.f64 (.f64 (+.f64 (PI.f64) (PI.f64)) n)) (log.f64 (.f64 (+.f64 (PI.f64) (PI.f64)) n))) (sqrt.f64 #s(literal 2 binary64))) k) (sqrt.f64 (.f64 (PI.f64) n))) #s(literal 1/8 binary64) (.f64 (.f64 #s(literal -1/2 binary64) (sqrt.f64 (.f64 (PI.f64) n))) (.f64 (log.f64 (.f64 (+.f64 (PI.f64) (PI.f64)) n)) (sqrt.f64 #s(literal 2 binary64))))) (sqrt.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n)))))
	47.2%	(.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) #s(approx (pow ( (* 2 (PI)) n) (/ (- 1 k) 2)) (*.f64 (sqrt.f64 (+.f64 (PI.f64) (PI.f64))) (sqrt.f64 n))))
	47.3%	(.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) #s(approx (pow ( (* 2 (PI)) n) (/ (- 1 k) 2)) (.f64 (sqrt.f64 (.f64 (PI.f64) n)) (sqrt.f64 #s(literal 2 binary64)))))
✓	47.4%	(.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) #s(approx (pow ( (* 2 (PI)) n) (/ (- 1 k) 2)) (sqrt.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n))))
	47.4%	(.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) #s(approx (pow ( (* 2 (PI)) n) (/ (- 1 k) 2)) #s(approx (+ (* (* (* (* (log (* (+ (PI) (PI)) n)) (sqrt 2)) k) (sqrt (* (PI) n))) -1/2) (sqrt (* (+ (PI) (PI)) n))) (.f64 #s(approx (+ ( (* (sqrt (/ (PI) n)) (* (* (+ (neg (neg (log n))) (log (+ (PI) (PI)))) (sqrt 2)) k)) -1/2) (sqrt (* (/ (PI) n) 2))) (sqrt.f64 (/.f64 (+.f64 (PI.f64) (PI.f64)) n))) n))))
▶	99.5%	(.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) k)) (pow.f64 (.f64 (*.f64 #s(literal 2 binary64) (PI.f64)) n) #s(approx (/ (- 1 k) 2) (fma.f64 #s(literal -1/2 binary64) k #s(literal 1/2 binary64)))))
	48.1%	(.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) k)) #s(approx (pow ( (* 2 (PI)) n) (/ (- 1 k) 2)) (fma.f64 (.f64 k (.f64 (sqrt.f64 (.f64 n (+.f64 (PI.f64) (PI.f64)))) (log.f64 (.f64 n (+.f64 (PI.f64) (PI.f64)))))) #s(literal -1/2 binary64) (sqrt.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n)))))
	48.0%	(.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) k)) #s(approx (pow ( (* 2 (PI)) n) (/ (- 1 k) 2)) (fma.f64 (sqrt.f64 (.f64 (PI.f64) n)) (sqrt.f64 #s(literal 2 binary64)) (.f64 (.f64 k (.f64 (sqrt.f64 (.f64 n (+.f64 (PI.f64) (PI.f64)))) (log.f64 (.f64 n (+.f64 (PI.f64) (PI.f64)))))) #s(literal -1/2 binary64)))))
▶	47.4%	(.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) k)) #s(approx (pow ( (* 2 (PI)) n) (/ (- 1 k) 2)) (sqrt.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n))))
	51.3%	#s(approx (/ (* 1 (pow (* (+ (PI) (PI)) n) (/ (- 1 k) 2))) (sqrt k)) (/.f64 (fma.f64 (.f64 (.f64 (sqrt.f64 (.f64 (.f64 (.f64 k k) k) (.f64 (PI.f64) n))) (log.f64 (.f64 (+.f64 (PI.f64) (PI.f64)) n))) (sqrt.f64 #s(literal 2 binary64))) #s(literal -1/2 binary64) (sqrt.f64 (.f64 (.f64 (.f64 (PI.f64) n) k) #s(literal 2 binary64)))) k))
	33.5%	#s(approx (/ (* 1 (pow (* (+ (PI) (PI)) n) (/ (- 1 k) 2))) (sqrt k)) (.f64 (sqrt.f64 (/.f64 (.f64 (PI.f64) n) k)) (sqrt.f64 #s(literal 2 binary64))))
✓	33.6%	#s(approx (/ (* 1 (pow (* (+ (PI) (PI)) n) (/ (- 1 k) 2))) (sqrt k)) (sqrt.f64 (/.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n) k)))
▶	33.6%	#s(approx (/ (* 1 (pow (* (+ (PI) (PI)) n) (/ (- 1 k) 2))) (sqrt k)) (sqrt.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) (/.f64 n k))))
	33.6%	#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt.f64 (.f64 (.f64 (PI.f64) (/.f64 n k)) #s(literal 2 binary64))))
	33.6%	#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt.f64 (.f64 (.f64 n (/.f64 (PI.f64) k)) #s(literal 2 binary64))))

Compiler

Compiled 1 549 to 1 134 computations (26.8% saved)

series66.0ms (1.5%)

Memory

-1.0MiB live, 91.7MiB allocated; 6ms collecting garbage

Counts

33 → 108

Calls

Call 1

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

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

Calls

6 calls:

Time	Variable		Point	Expression
32.0ms	n	@	-inf	((/ (pow (* (+ (PI) (PI)) n) (/ (- 1 k) 2)) (sqrt k)) (pow (* (+ (PI) (PI)) n) (/ (- 1 k) 2)) (* (+ (PI) (PI)) n) (+ (PI) (PI)) (PI) n (/ (- 1 k) 2) (+ (* -1/2 k) 1/2) -1/2 k 1/2 (sqrt k) (/ (* 1 (pow (* (+ (PI) (PI)) n) (/ (- 1 k) 2))) (sqrt k)) (sqrt (* (+ (PI) (PI)) (/ n k))) (* (+ (PI) (PI)) (/ n k)) (/ n k) (* (sqrt (/ 1 k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt (/ 1 k)) (/ 1 k) 1 (pow (* (* 2 (PI)) n) (/ (- 1 k) 2)) (sqrt (* (+ (PI) (PI)) n)) (* (sqrt (/ 1 k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2)) (* (* 2 (PI)) n) (* 2 (PI)) 2 (/ (pow (pow (* (+ (PI) (PI)) n) (/ (- 1 k) 4)) 2) (sqrt k)) (pow (pow (* (+ (PI) (PI)) n) (/ (- 1 k) 4)) 2) (pow (* (+ (PI) (PI)) n) (/ (- 1 k) 4)) (/ (- 1 k) 4) (- 1 k) 4)
11.0ms	n	@	0	((/ (pow (* (+ (PI) (PI)) n) (/ (- 1 k) 2)) (sqrt k)) (pow (* (+ (PI) (PI)) n) (/ (- 1 k) 2)) (* (+ (PI) (PI)) n) (+ (PI) (PI)) (PI) n (/ (- 1 k) 2) (+ (* -1/2 k) 1/2) -1/2 k 1/2 (sqrt k) (/ (* 1 (pow (* (+ (PI) (PI)) n) (/ (- 1 k) 2))) (sqrt k)) (sqrt (* (+ (PI) (PI)) (/ n k))) (* (+ (PI) (PI)) (/ n k)) (/ n k) (* (sqrt (/ 1 k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt (/ 1 k)) (/ 1 k) 1 (pow (* (* 2 (PI)) n) (/ (- 1 k) 2)) (sqrt (* (+ (PI) (PI)) n)) (* (sqrt (/ 1 k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2)) (* (* 2 (PI)) n) (* 2 (PI)) 2 (/ (pow (pow (* (+ (PI) (PI)) n) (/ (- 1 k) 4)) 2) (sqrt k)) (pow (pow (* (+ (PI) (PI)) n) (/ (- 1 k) 4)) 2) (pow (* (+ (PI) (PI)) n) (/ (- 1 k) 4)) (/ (- 1 k) 4) (- 1 k) 4)
10.0ms	n	@	inf	((/ (pow (* (+ (PI) (PI)) n) (/ (- 1 k) 2)) (sqrt k)) (pow (* (+ (PI) (PI)) n) (/ (- 1 k) 2)) (* (+ (PI) (PI)) n) (+ (PI) (PI)) (PI) n (/ (- 1 k) 2) (+ (* -1/2 k) 1/2) -1/2 k 1/2 (sqrt k) (/ (* 1 (pow (* (+ (PI) (PI)) n) (/ (- 1 k) 2))) (sqrt k)) (sqrt (* (+ (PI) (PI)) (/ n k))) (* (+ (PI) (PI)) (/ n k)) (/ n k) (* (sqrt (/ 1 k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt (/ 1 k)) (/ 1 k) 1 (pow (* (* 2 (PI)) n) (/ (- 1 k) 2)) (sqrt (* (+ (PI) (PI)) n)) (* (sqrt (/ 1 k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2)) (* (* 2 (PI)) n) (* 2 (PI)) 2 (/ (pow (pow (* (+ (PI) (PI)) n) (/ (- 1 k) 4)) 2) (sqrt k)) (pow (pow (* (+ (PI) (PI)) n) (/ (- 1 k) 4)) 2) (pow (* (+ (PI) (PI)) n) (/ (- 1 k) 4)) (/ (- 1 k) 4) (- 1 k) 4)
4.0ms	k	@	-inf	((/ (pow (* (+ (PI) (PI)) n) (/ (- 1 k) 2)) (sqrt k)) (pow (* (+ (PI) (PI)) n) (/ (- 1 k) 2)) (* (+ (PI) (PI)) n) (+ (PI) (PI)) (PI) n (/ (- 1 k) 2) (+ (* -1/2 k) 1/2) -1/2 k 1/2 (sqrt k) (/ (* 1 (pow (* (+ (PI) (PI)) n) (/ (- 1 k) 2))) (sqrt k)) (sqrt (* (+ (PI) (PI)) (/ n k))) (* (+ (PI) (PI)) (/ n k)) (/ n k) (* (sqrt (/ 1 k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt (/ 1 k)) (/ 1 k) 1 (pow (* (* 2 (PI)) n) (/ (- 1 k) 2)) (sqrt (* (+ (PI) (PI)) n)) (* (sqrt (/ 1 k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2)) (* (* 2 (PI)) n) (* 2 (PI)) 2 (/ (pow (pow (* (+ (PI) (PI)) n) (/ (- 1 k) 4)) 2) (sqrt k)) (pow (pow (* (+ (PI) (PI)) n) (/ (- 1 k) 4)) 2) (pow (* (+ (PI) (PI)) n) (/ (- 1 k) 4)) (/ (- 1 k) 4) (- 1 k) 4)
3.0ms	k	@	0	((/ (pow (* (+ (PI) (PI)) n) (/ (- 1 k) 2)) (sqrt k)) (pow (* (+ (PI) (PI)) n) (/ (- 1 k) 2)) (* (+ (PI) (PI)) n) (+ (PI) (PI)) (PI) n (/ (- 1 k) 2) (+ (* -1/2 k) 1/2) -1/2 k 1/2 (sqrt k) (/ (* 1 (pow (* (+ (PI) (PI)) n) (/ (- 1 k) 2))) (sqrt k)) (sqrt (* (+ (PI) (PI)) (/ n k))) (* (+ (PI) (PI)) (/ n k)) (/ n k) (* (sqrt (/ 1 k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt (/ 1 k)) (/ 1 k) 1 (pow (* (* 2 (PI)) n) (/ (- 1 k) 2)) (sqrt (* (+ (PI) (PI)) n)) (* (sqrt (/ 1 k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2)) (* (* 2 (PI)) n) (* 2 (PI)) 2 (/ (pow (pow (* (+ (PI) (PI)) n) (/ (- 1 k) 4)) 2) (sqrt k)) (pow (pow (* (+ (PI) (PI)) n) (/ (- 1 k) 4)) 2) (pow (* (+ (PI) (PI)) n) (/ (- 1 k) 4)) (/ (- 1 k) 4) (- 1 k) 4)

rewrite97.0ms (2.3%)

Memory

-21.6MiB live, 86.2MiB allocated; 25ms collecting garbage

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	372	3786
0	412	3613
0	1587	3564

Stop Event

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

Counts

141 → 214

Calls

Call 1

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

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

eval21.0ms (0.5%)

Memory: 42.3MiB live, 42.3MiB allocated; 0ms collecting garbage
Compiler: Compiled 2 879 to 793 computations (72.5% saved)

prune44.0ms (1%)

Memory

-18.9MiB live, 71.6MiB allocated; 7ms collecting garbage

Pruning

31 alts after pruning (25 fresh and 6 done)

	Pruned	Kept	Total
New	197	11	208
Fresh	4	14	18
Picked	1	4	5
Done	0	2	2
Total	202	31	233

Accuracy

99.9%

Counts

233 → 31

Alt Table

Click to see full alt table

Status	Accuracy	Program
	99.3%	(/.f64 (pow.f64 (pow.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n) #s(approx (/ (- 1 k) 4) (fma.f64 #s(literal -1/4 binary64) k #s(literal 1/4 binary64)))) #s(literal 2 binary64)) (sqrt.f64 k))
	47.3%	(/.f64 (pow.f64 (pow.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n) #s(approx (/ (- 1 k) 4) #s(literal 1/4 binary64))) #s(literal 2 binary64)) (sqrt.f64 k))
	75.0%	(/.f64 (pow.f64 (*.f64 (pow.f64 (+.f64 (PI.f64) (PI.f64)) (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 4 binary64))) (pow.f64 n (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 4 binary64)))) #s(literal 2 binary64)) (sqrt.f64 k))
✓	99.5%	(/.f64 (pow.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n) #s(approx (/ (- 1 k) 2) (fma.f64 #s(literal -1/2 binary64) k #s(literal 1/2 binary64)))) (sqrt.f64 k))
	53.8%	(/.f64 (pow.f64 (.f64 (+.f64 (PI.f64) (PI.f64)) n) #s(approx (/ (- 1 k) 2) (.f64 #s(literal -1/2 binary64) k))) (sqrt.f64 k))
	74.5%	(/.f64 (pow.f64 (.f64 (.f64 (+.f64 (PI.f64) (PI.f64)) n) (*.f64 (+.f64 (PI.f64) (PI.f64)) n)) (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 4 binary64))) (sqrt.f64 k))
	64.0%	(/.f64 (pow.f64 #s(approx (pow (* (+ (PI) (PI)) n) (/ (- 1 k) 4)) (fma.f64 (fma.f64 (.f64 (.f64 (pow.f64 (.f64 n (+.f64 (PI.f64) (PI.f64))) #s(literal 1/4 binary64)) k) (.f64 (log.f64 (.f64 n (+.f64 (PI.f64) (PI.f64)))) (log.f64 (.f64 n (+.f64 (PI.f64) (PI.f64)))))) #s(literal 1/32 binary64) (.f64 (.f64 (pow.f64 (.f64 n (+.f64 (PI.f64) (PI.f64))) #s(literal 1/4 binary64)) (log.f64 (.f64 n (+.f64 (PI.f64) (PI.f64))))) #s(literal -1/4 binary64))) k (pow.f64 (*.f64 n (+.f64 (PI.f64) (PI.f64))) #s(literal 1/4 binary64)))) #s(literal 2 binary64)) (sqrt.f64 k))
	96.0%	(/.f64 (exp.f64 (.f64 (log.f64 (pow.f64 (.f64 n (+.f64 (PI.f64) (PI.f64))) (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 4 binary64)))) #s(literal 2 binary64))) (sqrt.f64 k))
	96.0%	(/.f64 (exp.f64 (.f64 (log.f64 (.f64 n (+.f64 (PI.f64) (PI.f64)))) #s(approx (/ (- 1 k) 2) (fma.f64 #s(literal -1/2 binary64) k #s(literal 1/2 binary64))))) (sqrt.f64 k))
	48.5%	(/.f64 #s(approx (pow (pow (* (+ (PI) (PI)) n) (/ (- 1 k) 4)) 2) (fma.f64 (.f64 (.f64 (.f64 (log.f64 (.f64 n (+.f64 (PI.f64) (PI.f64)))) (sqrt.f64 #s(literal 2 binary64))) k) (sqrt.f64 (.f64 (PI.f64) n))) #s(literal -1/2 binary64) (sqrt.f64 (.f64 n (+.f64 (PI.f64) (PI.f64)))))) (sqrt.f64 k))
	47.5%	(/.f64 #s(approx (pow (pow (* (+ (PI) (PI)) n) (/ (- 1 k) 4)) 2) (sqrt.f64 (*.f64 n (+.f64 (PI.f64) (PI.f64))))) (sqrt.f64 k))
	57.0%	(/.f64 #s(approx (pow (* (* 2 (PI)) n) (/ (- 1 k) 2)) (fma.f64 k (fma.f64 (.f64 (.f64 (.f64 (.f64 (log.f64 (.f64 n (+.f64 (PI.f64) (PI.f64)))) (log.f64 (.f64 n (+.f64 (PI.f64) (PI.f64))))) (sqrt.f64 #s(literal 2 binary64))) k) (sqrt.f64 (.f64 (PI.f64) n))) #s(literal 1/8 binary64) (.f64 (.f64 (sqrt.f64 (.f64 n (+.f64 (PI.f64) (PI.f64)))) (log.f64 (.f64 n (+.f64 (PI.f64) (PI.f64))))) #s(literal -1/2 binary64))) (sqrt.f64 (.f64 n (+.f64 (PI.f64) (PI.f64)))))) (sqrt.f64 k))
	61.0%	(/.f64 #s(approx (pow (* (* 2 (PI)) n) (/ (- 1 k) 2)) (fma.f64 k (fma.f64 k (fma.f64 (.f64 (.f64 (.f64 (pow.f64 (log.f64 (.f64 n (+.f64 (PI.f64) (PI.f64)))) #s(literal 3 binary64)) (sqrt.f64 #s(literal 2 binary64))) k) (sqrt.f64 (.f64 (PI.f64) n))) #s(literal -1/48 binary64) (.f64 (.f64 #s(literal 1/8 binary64) (sqrt.f64 (.f64 (PI.f64) n))) (.f64 (.f64 (log.f64 (.f64 n (+.f64 (PI.f64) (PI.f64)))) (log.f64 (.f64 n (+.f64 (PI.f64) (PI.f64))))) (sqrt.f64 #s(literal 2 binary64))))) (.f64 (.f64 (sqrt.f64 (.f64 n (+.f64 (PI.f64) (PI.f64)))) (log.f64 (.f64 n (+.f64 (PI.f64) (PI.f64))))) #s(literal -1/2 binary64))) (sqrt.f64 (*.f64 n (+.f64 (PI.f64) (PI.f64)))))) (sqrt.f64 k))
	75.0%	(.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) (.f64 (.f64 (pow.f64 (+.f64 (PI.f64) (PI.f64)) (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 4 binary64))) (pow.f64 n (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 4 binary64)))) (.f64 (pow.f64 (+.f64 (PI.f64) (PI.f64)) (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 4 binary64))) (pow.f64 n (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 4 binary64))))))
	56.9%	(.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) #s(approx (pow ( (* 2 (PI)) n) (/ (- 1 k) 2)) (fma.f64 k (fma.f64 (.f64 (.f64 (.f64 (.f64 (log.f64 (.f64 (+.f64 (PI.f64) (PI.f64)) n)) (log.f64 (.f64 (+.f64 (PI.f64) (PI.f64)) n))) (sqrt.f64 #s(literal 2 binary64))) k) (sqrt.f64 (.f64 (PI.f64) n))) #s(literal 1/8 binary64) (.f64 (.f64 #s(literal -1/2 binary64) (sqrt.f64 (.f64 (PI.f64) n))) (.f64 (log.f64 (.f64 (+.f64 (PI.f64) (PI.f64)) n)) (sqrt.f64 #s(literal 2 binary64))))) (sqrt.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n)))))
	47.2%	(.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) #s(approx (pow ( (* 2 (PI)) n) (/ (- 1 k) 2)) (*.f64 (sqrt.f64 (+.f64 (PI.f64) (PI.f64))) (sqrt.f64 n))))
	47.3%	(.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) #s(approx (pow ( (* 2 (PI)) n) (/ (- 1 k) 2)) (.f64 (sqrt.f64 (.f64 (PI.f64) n)) (sqrt.f64 #s(literal 2 binary64)))))
✓	47.4%	(.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) #s(approx (pow ( (* 2 (PI)) n) (/ (- 1 k) 2)) (sqrt.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n))))
	47.4%	(.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) #s(approx (pow ( (* 2 (PI)) n) (/ (- 1 k) 2)) #s(approx (+ (* (* (* (* (log (* (+ (PI) (PI)) n)) (sqrt 2)) k) (sqrt (* (PI) n))) -1/2) (sqrt (* (+ (PI) (PI)) n))) (.f64 #s(approx (+ ( (* (sqrt (/ (PI) n)) (* (* (+ (neg (neg (log n))) (log (+ (PI) (PI)))) (sqrt 2)) k)) -1/2) (sqrt (* (/ (PI) n) 2))) (sqrt.f64 (/.f64 (+.f64 (PI.f64) (PI.f64)) n))) n))))
✓	99.5%	(.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) k)) (pow.f64 (.f64 (*.f64 #s(literal 2 binary64) (PI.f64)) n) #s(approx (/ (- 1 k) 2) (fma.f64 #s(literal -1/2 binary64) k #s(literal 1/2 binary64)))))
	48.1%	(.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) k)) #s(approx (pow ( (* 2 (PI)) n) (/ (- 1 k) 2)) (fma.f64 (.f64 k (.f64 (sqrt.f64 (.f64 n (+.f64 (PI.f64) (PI.f64)))) (log.f64 (.f64 n (+.f64 (PI.f64) (PI.f64)))))) #s(literal -1/2 binary64) (sqrt.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n)))))
	48.0%	(.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) k)) #s(approx (pow ( (* 2 (PI)) n) (/ (- 1 k) 2)) (fma.f64 (sqrt.f64 (.f64 (PI.f64) n)) (sqrt.f64 #s(literal 2 binary64)) (.f64 (.f64 k (.f64 (sqrt.f64 (.f64 n (+.f64 (PI.f64) (PI.f64)))) (log.f64 (.f64 n (+.f64 (PI.f64) (PI.f64)))))) #s(literal -1/2 binary64)))))
	47.3%	(.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) k)) #s(approx (pow ( (* 2 (PI)) n) (/ (- 1 k) 2)) (.f64 (sqrt.f64 (.f64 (PI.f64) n)) (sqrt.f64 #s(literal 2 binary64)))))
✓	47.4%	(.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) k)) #s(approx (pow ( (* 2 (PI)) n) (/ (- 1 k) 2)) (sqrt.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n))))
	51.3%	#s(approx (/ (pow (pow (* (+ (PI) (PI)) n) (/ (- 1 k) 4)) 2) (sqrt k)) (/.f64 (fma.f64 (.f64 (.f64 (log.f64 (.f64 n (+.f64 (PI.f64) (PI.f64)))) (sqrt.f64 #s(literal 2 binary64))) (sqrt.f64 (.f64 (.f64 (.f64 k k) k) (.f64 (PI.f64) n)))) #s(literal -1/2 binary64) (sqrt.f64 (.f64 (.f64 (.f64 (PI.f64) n) k) #s(literal 2 binary64)))) k))
	33.5%	#s(approx (/ (* 1 (pow (* (+ (PI) (PI)) n) (/ (- 1 k) 2))) (sqrt k)) (.f64 (sqrt.f64 (/.f64 (.f64 (PI.f64) n) k)) (sqrt.f64 #s(literal 2 binary64))))
	33.4%	#s(approx (/ (* 1 (pow (* (+ (PI) (PI)) n) (/ (- 1 k) 2))) (sqrt k)) (*.f64 (sqrt.f64 (+.f64 (PI.f64) (PI.f64))) (sqrt.f64 (/.f64 n k))))
✓	33.6%	#s(approx (/ (* 1 (pow (* (+ (PI) (PI)) n) (/ (- 1 k) 2))) (sqrt k)) (sqrt.f64 (/.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n) k)))
✓	33.6%	#s(approx (/ (* 1 (pow (* (+ (PI) (PI)) n) (/ (- 1 k) 2))) (sqrt k)) (sqrt.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) (/.f64 n k))))
	33.6%	#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt.f64 (.f64 (.f64 (PI.f64) (/.f64 n k)) #s(literal 2 binary64))))
	33.6%	#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt.f64 (.f64 (.f64 n (/.f64 (PI.f64) k)) #s(literal 2 binary64))))

Compiler

Compiled 2 023 to 1 048 computations (48.2% saved)

regimes90.0ms (2.1%)

Memory

9.3MiB live, 105.8MiB allocated; 11ms collecting garbage

Counts

58 → 1

Calls

Call 1

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

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

Calls

4 calls:

35.0ms	(.f64 (.f64 #s(literal 2 binary64) (PI.f64)) n)
24.0ms	k
14.0ms	n
12.0ms	(.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) (pow.f64 (.f64 (*.f64 #s(literal 2 binary64) (PI.f64)) n) (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 2 binary64))))

Results

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

Compiler

Compiled 22 to 23 computations (-4.5% saved)

regimes23.0ms (0.5%)

Memory

-2.2MiB live, 42.1MiB allocated; 3ms collecting garbage

Counts

17 → 2

Calls

Call 1

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

Outputs

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

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

Calls

4 calls:

8.0ms	k
5.0ms	n
5.0ms	(.f64 (.f64 #s(literal 2 binary64) (PI.f64)) n)
4.0ms	(.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) (pow.f64 (.f64 (*.f64 #s(literal 2 binary64) (PI.f64)) n) (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 2 binary64))))

Results

Accuracy	Segments	Branch
57.4%	2	`(.f64 (.f64 #s(literal 2 binary64) (PI.f64)) n)`
96.5%	3	`(.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) (pow.f64 (.f64 (*.f64 #s(literal 2 binary64) (PI.f64)) n) (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 2 binary64))))`
96.5%	2	`k`
57.4%	2	`n`

Compiler

Compiled 22 to 23 computations (-4.5% saved)

regimes34.0ms (0.8%)

Memory

-2.7MiB live, 43.0MiB allocated; 2ms collecting garbage

Counts

16 → 1

Calls

Call 1

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

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

Calls

4 calls:

19.0ms	n
5.0ms	k
5.0ms	(.f64 (.f64 #s(literal 2 binary64) (PI.f64)) n)
4.0ms	(.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) (pow.f64 (.f64 (*.f64 #s(literal 2 binary64) (PI.f64)) n) (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 2 binary64))))

Results

Accuracy	Segments	Branch
47.5%	1	`(.f64 (.f64 #s(literal 2 binary64) (PI.f64)) n)`
47.5%	1	`n`
47.5%	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))))`
47.5%	1	`k`

Compiler

Compiled 22 to 23 computations (-4.5% saved)

regimes10.0ms (0.2%)

Memory

18.0MiB live, 18.0MiB allocated; 0ms collecting garbage

Counts

6 → 1

Calls

Call 1

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

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

Calls

4 calls:

2.0ms	(.f64 (.f64 #s(literal 2 binary64) (PI.f64)) n)
2.0ms	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
33.6%	1	`(.f64 (.f64 #s(literal 2 binary64) (PI.f64)) n)`
33.6%	1	`n`
33.6%	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))))`
33.6%	1	`k`

Compiler

Compiled 22 to 23 computations (-4.5% saved)

regimes34.0ms (0.8%)

Memory

-36.7MiB live, 15.1MiB allocated; 8ms collecting garbage

Accuracy

Total -0.0b remaining (-0.1%)

Threshold costs -0b (-0.1%)

Counts

3 → 1

Calls

Call 1

Inputs

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

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

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

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

Calls

4 calls:

29.0ms	k
2.0ms	(.f64 (.f64 #s(literal 2 binary64) (PI.f64)) n)
1.0ms	n
1.0ms	(.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) (pow.f64 (.f64 (*.f64 #s(literal 2 binary64) (PI.f64)) n) (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 2 binary64))))

Results

Accuracy	Segments	Branch
33.6%	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))))`
33.6%	1	`k`
33.6%	1	`(.f64 (.f64 #s(literal 2 binary64) (PI.f64)) n)`
33.6%	1	`n`

Compiler

Compiled 22 to 23 computations (-4.5% saved)

bsearch13.0ms (0.3%)

Memory

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

Algorithm

1×	binary-search

Stop Event

1×	narrow-enough

Steps

Time	Left	Right
12.0ms	0.030316526567739695	3.5238903302563545

Samples

7.0ms

112×

valid

Compiler

Compiled 271 to 263 computations (3% saved)

Precisions

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

ival-pow: 2.0ms (40% of total)

ival-sqrt: 1.0ms (20% of total)

ival-div!: 1.0ms (20% of total)

ival-mult!: 1.0ms (20% of total)

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

adjust: 0.0ms (0% of total)

derivations37.0ms (0.9%)

Memory

-1.1MiB live, 42.5MiB allocated; 5ms collecting garbage

Stop Event

1×

fuel

Compiler

Compiled 75 to 47 computations (37.3% saved)

preprocess61.0ms (1.4%)

Memory: -11.8MiB live, 177.0MiB allocated; 28ms collecting garbage
Compiler: Compiled 90 to 60 computations (33.3% saved)

end0.0ms (0%)

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

start0.0ms (0%)

analyze100.0ms (2.3%)

sample2.7s (61.6%)

preprocess70.0ms (1.6%)

series84.0ms (1.9%)

rewrite61.0ms (1.4%)

eval8.0ms (0.2%)

prune10.0ms (0.2%)

series142.0ms (3.3%)

rewrite86.0ms (2%)

eval61.0ms (1.4%)

prune65.0ms (1.5%)

series260.0ms (6%)

rewrite79.0ms (1.8%)

eval59.0ms (1.4%)

prune40.0ms (0.9%)

series66.0ms (1.5%)

rewrite97.0ms (2.3%)

eval21.0ms (0.5%)

prune44.0ms (1%)

regimes90.0ms (2.1%)

regimes23.0ms (0.5%)

regimes34.0ms (0.8%)

regimes10.0ms (0.2%)

regimes34.0ms (0.8%)

bsearch13.0ms (0.3%)

derivations37.0ms (0.9%)

preprocess61.0ms (1.4%)

end0.0ms (0%)

Profiling