Metrics for Migdal et al, Equation (51)

start0.0ms (0%)

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

analyze102.0ms (2.3%)

Memory

17.3MiB live, 155.9MiB allocated; 22ms collecting garbage

Algorithm

1×

Search

Probability	Valid	Unknown	Precondition	Infinite	Domain	Can't	Iter
0%	0%	99.9%	0.1%	0%	0%	0%	0
0%	0%	99.9%	0.1%	0%	0%	0%	1
0%	0%	50%	0.1%	0%	50%	0%	2
50%	25%	25%	0.1%	0%	50%	0%	3
50%	25%	25%	0.1%	0%	50%	0%	4
50%	25%	25%	0.1%	0%	50%	0%	5
50%	25%	25%	0.1%	0%	50%	0%	6
51.6%	25%	23.4%	0.1%	0%	51.5%	0%	7
52.5%	25%	22.6%	0.1%	0%	52.3%	0%	8
53.8%	25%	21.5%	0.1%	0%	53.5%	0%	9
54.5%	25%	20.9%	0.1%	0%	54%	0%	10
55.3%	25%	20.2%	0.1%	0%	54.7%	0%	11
55.7%	25%	19.9%	0.1%	0%	55.1%	0%	12

Compiler

Compiled 18 to 15 computations (16.7% saved)

sample3.4s (75.9%)

Memory

-42.4MiB live, 3 476.0MiB allocated; 1.7s collecting garbage

Samples

1.8s	5 377×	1	invalid
858.0ms	8 255×	0	valid
99.0ms	446×	2	invalid
21.0ms	346×	0	invalid
19.0ms	206×	0	exit
0.0ms	1×	1	valid

Precisions

Click to see histograms. Total time spent on operations: 1.5s

ival-pow: 498.0ms (32.3% of total)

ival-mult!: 361.0ms (23.4% of total)

ival-div!: 223.0ms (14.4% of total)

adjust: 207.0ms (13.4% of total)

ival-sqrt: 198.0ms (12.8% of total)

ival-sub!: 57.0ms (3.7% of total)

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

exact: 0.0ms (0% of total)

Bogosity

preprocess35.0ms (0.8%)

Memory

-40.0MiB live, 13.0MiB allocated; 7ms 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
▶	99.4%	(.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)

series70.0ms (1.6%)

Memory

18.7MiB live, 109.9MiB 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
31.0ms	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))
23.0ms	n	@	-inf	((* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (/ 1 (sqrt k)) 1 (sqrt k) k (pow (* (* 2 (PI)) n) (/ (- 1 k) 2)) (* (* 2 (PI)) n) (* 2 (PI)) 2 (PI) n (/ (- 1 k) 2) (- 1 k))
8.0ms	n	@	inf	((* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (/ 1 (sqrt k)) 1 (sqrt k) k (pow (* (* 2 (PI)) n) (/ (- 1 k) 2)) (* (* 2 (PI)) n) (* 2 (PI)) 2 (PI) n (/ (- 1 k) 2) (- 1 k))
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))

rewrite53.0ms (1.2%)

Memory

24.4MiB live, 69.8MiB allocated; 8ms collecting garbage

Iterations

Useful iterations: 0 (0.0ms)

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

Stop Event

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

Counts

47 → 70

Calls

Call 1

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

Outputs
(.f64 (/.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))))

eval17.0ms (0.4%)

Memory: -16.5MiB live, 32.5MiB allocated; 9ms collecting garbage
Compiler: Compiled 783 to 287 computations (63.3% saved)

prune11.0ms (0.2%)

Memory

-8.0MiB live, 39.6MiB allocated; 1ms collecting garbage

Pruning

13 alts after pruning (13 fresh and 0 done)

	Pruned	Kept	Total
New	46	13	59
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	47	13	60

Accuracy

99.9%

Counts

60 → 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))
▶	99.4%	(.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)))))
	52.4%	(.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))))
	74.2%	(.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)))))
	65.0%	(.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)))))
▶	51.1%	(.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)))))
	60.0%	(.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)))))
	50.6%	(.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))))
	96.1%	(.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))))
	54.3%	#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))
▶	40.2%	#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)

series122.0ms (2.7%)

Memory

17.4MiB live, 250.8MiB allocated; 20ms 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))))
#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)))))
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#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)))))
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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 (pow (exp (* 1/4 (* (+ (log n) (log (* 2 (PI)))) (- 1 k)))) 2)))
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#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)))))))
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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))))))
#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))))))
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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 (* (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))))))
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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))))))

Calls

6 calls:

Time	Variable		Point	Expression
29.0ms	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))
29.0ms	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))
18.0ms	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))
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))
13.0ms	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))

rewrite90.0ms (2%)

Memory

6.3MiB live, 105.3MiB allocated; 24ms 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))))

eval36.0ms (0.8%)

Memory: -14.8MiB live, 77.7MiB allocated; 6ms collecting garbage
Compiler: Compiled 4 709 to 1 423 computations (69.8% saved)

prune17.0ms (0.4%)

Memory

-7.6MiB live, 39.6MiB allocated; 2ms collecting garbage

Pruning

16 alts after pruning (15 fresh and 1 done)

	Pruned	Kept	Total
New	318	14	332
Fresh	7	1	8
Picked	4	1	5
Done	0	0	0
Total	329	16	345

Accuracy

100.0%

Counts

345 → 16

Alt Table

Click to see full alt table

Status	Accuracy	Program
▶	99.4%	(/.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))
	52.4%	(/.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))
▶	50.7%	(/.f64 (.f64 #s(literal 1 binary64) (pow.f64 (.f64 (+.f64 (PI.f64) (PI.f64)) n) #s(approx (/ (- 1 k) 2) #s(literal 1/2 binary64)))) (sqrt.f64 k))
	65.1%	(/.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))
	60.1%	(/.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))
▶	50.7%	(/.f64 #s(approx (* 1 (pow (* (+ (PI) (PI)) n) (/ (- 1 k) 2))) (sqrt.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n))) (sqrt.f64 k))
	96.1%	(/.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))
	98.5%	(.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) #s(approx (/ (/ (- 1 k) 2) 2) (*.f64 (-.f64 (/.f64 #s(literal 1/4 binary64) k) #s(literal 1/4 binary64)) k)))))
✓	51.1%	(.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)))))
	51.1%	(.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 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 (.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)))))
	50.6%	(.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))))
▶	40.2%	#s(approx (/ (* 1 (pow (* (+ (PI) (PI)) n) (/ (- 1 k) 2))) (sqrt k)) (sqrt.f64 (/.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n) k)))
	40.1%	#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (.f64 (sqrt.f64 (/.f64 (.f64 (PI.f64) n) k)) (sqrt.f64 #s(literal 2 binary64))))
	40.2%	#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt.f64 (.f64 (.f64 (PI.f64) (/.f64 n k)) #s(literal 2 binary64))))
	40.2%	#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 841 to 689 computations (18.1% saved)

series44.0ms (1%)

Memory

-3.6MiB live, 94.3MiB allocated; 6ms collecting garbage

Counts

28 → 89

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 #s(approx (* 1 (pow (* (+ (PI) (PI)) n) (/ (- 1 k) 2))) (sqrt.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n))) (sqrt.f64 k))
#s(approx (* 1 (pow (* (+ (PI) (PI)) n) (/ (- 1 k) 2))) (sqrt.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n)))
(sqrt.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n))
(/.f64 (.f64 #s(literal 1 binary64) (pow.f64 (.f64 (+.f64 (PI.f64) (PI.f64)) n) #s(approx (/ (- 1 k) 2) #s(literal 1/2 binary64)))) (sqrt.f64 k))
(.f64 #s(literal 1 binary64) (pow.f64 (.f64 (+.f64 (PI.f64) (PI.f64)) n) #s(approx (/ (- 1 k) 2) #s(literal 1/2 binary64))))
(pow.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n) #s(approx (/ (- 1 k) 2) #s(literal 1/2 binary64)))
#s(approx (/ (- 1 k) 2) #s(literal 1/2 binary64))
#s(literal 1/2 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))
#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 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 (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 (* 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 (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 (/ (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 k) #s(hole binary64 (* -1 k)))
#s(approx (- 1 k) #s(hole binary64 (* k (- (/ 1 k) 1))))
#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 (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 (/ (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 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 (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 (* 1 (pow (* (+ (PI) (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 (/ (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 (* 1 (pow (* (+ (PI) (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 (/ (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 (* 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 (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 (* 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 (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
13.0ms	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 (pow (* (+ (PI) (PI)) n) (/ (- 1 k) 2))) (sqrt k)) (* 1 (pow (* (+ (PI) (PI)) n) (/ (- 1 k) 2))) (sqrt (* (+ (PI) (PI)) n)) (/ (* 1 (pow (* (+ (PI) (PI)) n) (/ (- 1 k) 2))) (sqrt k)) (* 1 (pow (* (+ (PI) (PI)) n) (/ (- 1 k) 2))) (pow (* (+ (PI) (PI)) n) (/ (- 1 k) 2)) (/ (- 1 k) 2) 1/2 (/ (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) 4)
11.0ms	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 (pow (* (+ (PI) (PI)) n) (/ (- 1 k) 2))) (sqrt k)) (* 1 (pow (* (+ (PI) (PI)) n) (/ (- 1 k) 2))) (sqrt (* (+ (PI) (PI)) n)) (/ (* 1 (pow (* (+ (PI) (PI)) n) (/ (- 1 k) 2))) (sqrt k)) (* 1 (pow (* (+ (PI) (PI)) n) (/ (- 1 k) 2))) (pow (* (+ (PI) (PI)) n) (/ (- 1 k) 2)) (/ (- 1 k) 2) 1/2 (/ (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) 4)
10.0ms	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 (pow (* (+ (PI) (PI)) n) (/ (- 1 k) 2))) (sqrt k)) (* 1 (pow (* (+ (PI) (PI)) n) (/ (- 1 k) 2))) (sqrt (* (+ (PI) (PI)) n)) (/ (* 1 (pow (* (+ (PI) (PI)) n) (/ (- 1 k) 2))) (sqrt k)) (* 1 (pow (* (+ (PI) (PI)) n) (/ (- 1 k) 2))) (pow (* (+ (PI) (PI)) n) (/ (- 1 k) 2)) (/ (- 1 k) 2) 1/2 (/ (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) 4)
3.0ms	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 (pow (* (+ (PI) (PI)) n) (/ (- 1 k) 2))) (sqrt k)) (* 1 (pow (* (+ (PI) (PI)) n) (/ (- 1 k) 2))) (sqrt (* (+ (PI) (PI)) n)) (/ (* 1 (pow (* (+ (PI) (PI)) n) (/ (- 1 k) 2))) (sqrt k)) (* 1 (pow (* (+ (PI) (PI)) n) (/ (- 1 k) 2))) (pow (* (+ (PI) (PI)) n) (/ (- 1 k) 2)) (/ (- 1 k) 2) 1/2 (/ (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) 4)
2.0ms	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 (pow (* (+ (PI) (PI)) n) (/ (- 1 k) 2))) (sqrt k)) (* 1 (pow (* (+ (PI) (PI)) n) (/ (- 1 k) 2))) (sqrt (* (+ (PI) (PI)) n)) (/ (* 1 (pow (* (+ (PI) (PI)) n) (/ (- 1 k) 2))) (sqrt k)) (* 1 (pow (* (+ (PI) (PI)) n) (/ (- 1 k) 2))) (pow (* (+ (PI) (PI)) n) (/ (- 1 k) 2)) (/ (- 1 k) 2) 1/2 (/ (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) 4)

rewrite67.0ms (1.5%)

Memory

13.4MiB live, 107.3MiB allocated; 4ms collecting garbage

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	340	3247
0	373	3070
0	1496	3026

Stop Event

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

Counts

117 → 163

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

eval23.0ms (0.5%)

Memory: -3.3MiB live, 44.6MiB allocated; 4ms collecting garbage
Compiler: Compiled 2 499 to 659 computations (73.6% saved)

prune15.0ms (0.3%)

Memory

35.3MiB live, 35.3MiB allocated; 0ms collecting garbage

Pruning

18 alts after pruning (16 fresh and 2 done)

	Pruned	Kept	Total
New	164	9	173
Fresh	3	7	10
Picked	3	2	5
Done	1	0	1
Total	171	18	189

Accuracy

100.0%

Counts

189 → 18

Alt Table

Click to see full alt table

Status	Accuracy	Program
	50.5%	(/.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))
▶	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))
	52.4%	(/.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))
	50.7%	(/.f64 (pow.f64 (*.f64 n (+.f64 (PI.f64) (PI.f64))) #s(approx (/ (- 1 k) 2) #s(literal 1/2 binary64))) (sqrt.f64 k))
	47.4%	(/.f64 (exp.f64 (.f64 (log.f64 (.f64 n (+.f64 (PI.f64) (PI.f64)))) #s(approx (/ (- 1 k) 2) #s(literal 1/2 binary64)))) (sqrt.f64 k))
	51.2%	(/.f64 #s(approx (pow (pow (* (+ (PI) (PI)) n) (/ (- 1 k) 4)) 2) (fma.f64 (.f64 (.f64 (.f64 (log.f64 (.f64 (.f64 (PI.f64) n) #s(literal 2 binary64))) (sqrt.f64 #s(literal 2 binary64))) k) (sqrt.f64 (.f64 (PI.f64) n))) #s(literal -1/2 binary64) (sqrt.f64 (.f64 (.f64 (PI.f64) n) #s(literal 2 binary64))))) (sqrt.f64 k))
	65.1%	(/.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))
	60.1%	(/.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))
	50.5%	(/.f64 #s(approx (* 1 (pow (* (+ (PI) (PI)) n) (/ (- 1 k) 2))) (*.f64 (sqrt.f64 (+.f64 (PI.f64) (PI.f64))) (sqrt.f64 n))) (sqrt.f64 k))
✓	50.7%	(/.f64 #s(approx (* 1 (pow (* (+ (PI) (PI)) n) (/ (- 1 k) 2))) (sqrt.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n))) (sqrt.f64 k))
▶	96.1%	(/.f64 #s(approx (* 1 (pow (* (+ (PI) (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))
▶	98.5%	(.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) #s(approx (/ (/ (- 1 k) 2) 2) (*.f64 (-.f64 (/.f64 #s(literal 1/4 binary64) k) #s(literal 1/4 binary64)) k)))))
	51.1%	(.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 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 (.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)))))
▶	50.6%	(.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))))
✓	40.2%	#s(approx (/ (* 1 (pow (* (+ (PI) (PI)) n) (/ (- 1 k) 2))) (sqrt k)) (sqrt.f64 (/.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n) k)))
▶	40.2%	#s(approx (/ (* 1 (pow (* (+ (PI) (PI)) n) (/ (- 1 k) 2))) (sqrt k)) (sqrt.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) (/.f64 n k))))
	40.1%	#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (.f64 (sqrt.f64 (/.f64 (.f64 (PI.f64) n) k)) (sqrt.f64 #s(literal 2 binary64))))
	40.2%	#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 915 to 751 computations (17.9% saved)

series58.0ms (1.3%)

Memory

-15.2MiB live, 125.6MiB allocated; 7ms collecting garbage

Counts

41 → 153

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

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

Calls

6 calls:

Time	Variable		Point	Expression
13.0ms	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) (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (/ 1 (sqrt k)) 1 (pow (* (* 2 (PI)) n) (/ (- 1 k) 2)) (sqrt (* (+ (PI) (PI)) n)) (/ (* 1 (pow (* (+ (PI) (PI)) n) (/ (- 1 k) 2))) (sqrt k)) (* 1 (pow (* (+ (PI) (PI)) n) (/ (- 1 k) 2))) (exp (* (* (log (* n (+ (PI) (PI)))) (- 1 k)) 1/2)) (* (* (log (* n (+ (PI) (PI)))) (- 1 k)) 1/2) (* (log (* n (+ (PI) (PI)))) (- 1 k)) (log (* n (+ (PI) (PI)))) (* n (+ (PI) (PI))) (- 1 k) (* (/ 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) (/ (- 1 k) 2) 2 (pow (* (+ (PI) (PI)) n) (/ (/ (- 1 k) 2) 2)) (/ (/ (- 1 k) 2) 2) (* (- (/ 1/4 k) 1/4) k) (- (/ 1/4 k) 1/4) (/ 1/4 k) 1/4)
12.0ms	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) (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (/ 1 (sqrt k)) 1 (pow (* (* 2 (PI)) n) (/ (- 1 k) 2)) (sqrt (* (+ (PI) (PI)) n)) (/ (* 1 (pow (* (+ (PI) (PI)) n) (/ (- 1 k) 2))) (sqrt k)) (* 1 (pow (* (+ (PI) (PI)) n) (/ (- 1 k) 2))) (exp (* (* (log (* n (+ (PI) (PI)))) (- 1 k)) 1/2)) (* (* (log (* n (+ (PI) (PI)))) (- 1 k)) 1/2) (* (log (* n (+ (PI) (PI)))) (- 1 k)) (log (* n (+ (PI) (PI)))) (* n (+ (PI) (PI))) (- 1 k) (* (/ 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) (/ (- 1 k) 2) 2 (pow (* (+ (PI) (PI)) n) (/ (/ (- 1 k) 2) 2)) (/ (/ (- 1 k) 2) 2) (* (- (/ 1/4 k) 1/4) k) (- (/ 1/4 k) 1/4) (/ 1/4 k) 1/4)
11.0ms	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) (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (/ 1 (sqrt k)) 1 (pow (* (* 2 (PI)) n) (/ (- 1 k) 2)) (sqrt (* (+ (PI) (PI)) n)) (/ (* 1 (pow (* (+ (PI) (PI)) n) (/ (- 1 k) 2))) (sqrt k)) (* 1 (pow (* (+ (PI) (PI)) n) (/ (- 1 k) 2))) (exp (* (* (log (* n (+ (PI) (PI)))) (- 1 k)) 1/2)) (* (* (log (* n (+ (PI) (PI)))) (- 1 k)) 1/2) (* (log (* n (+ (PI) (PI)))) (- 1 k)) (log (* n (+ (PI) (PI)))) (* n (+ (PI) (PI))) (- 1 k) (* (/ 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) (/ (- 1 k) 2) 2 (pow (* (+ (PI) (PI)) n) (/ (/ (- 1 k) 2) 2)) (/ (/ (- 1 k) 2) 2) (* (- (/ 1/4 k) 1/4) k) (- (/ 1/4 k) 1/4) (/ 1/4 k) 1/4)
7.0ms	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) (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (/ 1 (sqrt k)) 1 (pow (* (* 2 (PI)) n) (/ (- 1 k) 2)) (sqrt (* (+ (PI) (PI)) n)) (/ (* 1 (pow (* (+ (PI) (PI)) n) (/ (- 1 k) 2))) (sqrt k)) (* 1 (pow (* (+ (PI) (PI)) n) (/ (- 1 k) 2))) (exp (* (* (log (* n (+ (PI) (PI)))) (- 1 k)) 1/2)) (* (* (log (* n (+ (PI) (PI)))) (- 1 k)) 1/2) (* (log (* n (+ (PI) (PI)))) (- 1 k)) (log (* n (+ (PI) (PI)))) (* n (+ (PI) (PI))) (- 1 k) (* (/ 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) (/ (- 1 k) 2) 2 (pow (* (+ (PI) (PI)) n) (/ (/ (- 1 k) 2) 2)) (/ (/ (- 1 k) 2) 2) (* (- (/ 1/4 k) 1/4) k) (- (/ 1/4 k) 1/4) (/ 1/4 k) 1/4)
5.0ms	k	@	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) (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (/ 1 (sqrt k)) 1 (pow (* (* 2 (PI)) n) (/ (- 1 k) 2)) (sqrt (* (+ (PI) (PI)) n)) (/ (* 1 (pow (* (+ (PI) (PI)) n) (/ (- 1 k) 2))) (sqrt k)) (* 1 (pow (* (+ (PI) (PI)) n) (/ (- 1 k) 2))) (exp (* (* (log (* n (+ (PI) (PI)))) (- 1 k)) 1/2)) (* (* (log (* n (+ (PI) (PI)))) (- 1 k)) 1/2) (* (log (* n (+ (PI) (PI)))) (- 1 k)) (log (* n (+ (PI) (PI)))) (* n (+ (PI) (PI))) (- 1 k) (* (/ 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) (/ (- 1 k) 2) 2 (pow (* (+ (PI) (PI)) n) (/ (/ (- 1 k) 2) 2)) (/ (/ (- 1 k) 2) 2) (* (- (/ 1/4 k) 1/4) k) (- (/ 1/4 k) 1/4) (/ 1/4 k) 1/4)

rewrite80.0ms (1.8%)

Memory

-0.4MiB live, 96.0MiB allocated; 5ms collecting garbage

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	452	5525
0	506	4866
0	1883	4799

Stop Event

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

Counts

194 → 284

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

eval27.0ms (0.6%)

Memory: 19.9MiB live, 66.4MiB allocated; 3ms collecting garbage
Compiler: Compiled 3 771 to 1 216 computations (67.8% saved)

prune35.0ms (0.8%)

Memory

-30.3MiB live, 67.0MiB allocated; 12ms collecting garbage

Pruning

22 alts after pruning (17 fresh and 5 done)

	Pruned	Kept	Total
New	261	12	273
Fresh	6	5	11
Picked	2	3	5
Done	0	2	2
Total	269	22	291

Accuracy

100.0%

Counts

291 → 22

Alt Table

Click to see full alt table

Status	Accuracy	Program
	50.5%	(/.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))
✓	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))
	52.4%	(/.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))
	65.1%	(/.f64 #s(approx (pow (* (* 2 (PI)) n) (/ (- 1 k) 2)) (fma.f64 (fma.f64 k (fma.f64 (.f64 (.f64 (.f64 (pow.f64 (log.f64 (.f64 n (+.f64 (PI.f64) (PI.f64)))) #s(literal 3 binary64)) k) (sqrt.f64 #s(literal 2 binary64))) (sqrt.f64 (.f64 (PI.f64) n))) #s(literal -1/48 binary64) (.f64 (.f64 #s(literal 1/8 binary64) (sqrt.f64 (.f64 (PI.f64) n))) (.f64 (.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)))))) (sqrt.f64 k))
	51.2%	(/.f64 #s(approx (pow (* (* 2 (PI)) n) (/ (- 1 k) 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))
	60.1%	(/.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))))) 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)))))) (sqrt.f64 k))
	96.2%	(/.f64 #s(approx (pow (* (* 2 (PI)) n) (/ (- 1 k) 2)) (exp.f64 (.f64 (log.f64 (sqrt.f64 (.f64 n (+.f64 (PI.f64) (PI.f64))))) (-.f64 #s(literal 1 binary64) k)))) (sqrt.f64 k))
	50.5%	(/.f64 #s(approx (* 1 (pow (* (+ (PI) (PI)) n) (/ (- 1 k) 2))) (*.f64 (sqrt.f64 (+.f64 (PI.f64) (PI.f64))) (sqrt.f64 n))) (sqrt.f64 k))
✓	50.7%	(/.f64 #s(approx (* 1 (pow (* (+ (PI) (PI)) n) (/ (- 1 k) 2))) (sqrt.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n))) (sqrt.f64 k))
	47.4%	(/.f64 #s(approx (* 1 (pow (* (+ (PI) (PI)) n) (/ (- 1 k) 2))) (exp.f64 #s(approx (* (* (log (* n (+ (PI) (PI)))) (- 1 k)) 1/2) (log.f64 (sqrt.f64 (*.f64 n (+.f64 (PI.f64) (PI.f64)))))))) (sqrt.f64 k))
	98.5%	(.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) (.f64 (pow.f64 (.f64 (+.f64 (PI.f64) (PI.f64)) n) #s(approx (/ (/ (- 1 k) 2) 2) (fma.f64 #s(literal -1/4 binary64) k #s(literal 1/4 binary64)))) (pow.f64 (.f64 (+.f64 (PI.f64) (PI.f64)) n) #s(approx (/ (/ (- 1 k) 2) 2) (*.f64 (-.f64 (/.f64 #s(literal 1/4 binary64) k) #s(literal 1/4 binary64)) k)))))
	96.6%	(.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) (.f64 #s(approx (pow (* (+ (PI) (PI)) n) (/ (/ (- 1 k) 2) 2)) (exp.f64 (.f64 (.f64 (log.f64 (.f64 n (+.f64 (PI.f64) (PI.f64)))) (-.f64 #s(literal 1 binary64) k)) #s(literal 1/4 binary64)))) (pow.f64 (.f64 (+.f64 (PI.f64) (PI.f64)) n) #s(approx (/ (/ (- 1 k) 2) 2) (*.f64 (-.f64 (/.f64 #s(literal 1/4 binary64) k) #s(literal 1/4 binary64)) k)))))
	51.1%	(.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 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 (.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)))))
	50.4%	(.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))))
	50.6%	(.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)))))
✓	50.6%	(.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))))
	50.6%	(.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))))
	40.1%	#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))))
	39.9%	#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))))
✓	40.2%	#s(approx (/ (* 1 (pow (* (+ (PI) (PI)) n) (/ (- 1 k) 2))) (sqrt k)) (sqrt.f64 (/.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n) k)))
✓	40.2%	#s(approx (/ (* 1 (pow (* (+ (PI) (PI)) n) (/ (- 1 k) 2))) (sqrt k)) (sqrt.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) (/.f64 n k))))
	40.2%	#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 1 455 to 775 computations (46.7% saved)

regimes52.0ms (1.2%)

Memory

9.3MiB live, 103.0MiB allocated; 4ms collecting garbage

Counts

49 → 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))
#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 #s(approx (* 1 (pow (* (+ (PI) (PI)) n) (/ (- 1 k) 2))) (*.f64 (sqrt.f64 (+.f64 (PI.f64) (PI.f64))) (sqrt.f64 n))) (sqrt.f64 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))))
(.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 (/.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 (pow.f64 (*.f64 n (+.f64 (PI.f64) (PI.f64))) #s(approx (/ (- 1 k) 2) #s(literal 1/2 binary64))) (sqrt.f64 k))
(/.f64 #s(approx (* 1 (pow (* (+ (PI) (PI)) n) (/ (- 1 k) 2))) (exp.f64 #s(approx (* (* (log (* n (+ (PI) (PI)))) (- 1 k)) 1/2) (log.f64 (sqrt.f64 (*.f64 n (+.f64 (PI.f64) (PI.f64)))))))) (sqrt.f64 k))
(/.f64 (.f64 #s(literal 1 binary64) (pow.f64 (.f64 (+.f64 (PI.f64) (PI.f64)) n) #s(approx (/ (- 1 k) 2) #s(literal 1/2 binary64)))) (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))
(/.f64 (exp.f64 (.f64 (log.f64 (.f64 n (+.f64 (PI.f64) (PI.f64)))) #s(approx (/ (- 1 k) 2) #s(literal 1/2 binary64)))) (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 #s(approx (pow (* (* 2 (PI)) n) (/ (- 1 k) 2)) (exp.f64 (.f64 (log.f64 (sqrt.f64 (.f64 n (+.f64 (PI.f64) (PI.f64))))) (-.f64 #s(literal 1 binary64) k)))) (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) (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 (* 1 (pow (* (+ (PI) (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 (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 (* (* 2 (PI)) n) (/ (- 1 k) 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 #s(approx (pow (pow (* (+ (PI) (PI)) n) (/ (- 1 k) 4)) 2) (fma.f64 (.f64 (.f64 (.f64 (log.f64 (.f64 (.f64 (PI.f64) n) #s(literal 2 binary64))) (sqrt.f64 #s(literal 2 binary64))) k) (sqrt.f64 (.f64 (PI.f64) n))) #s(literal -1/2 binary64) (sqrt.f64 (.f64 (.f64 (PI.f64) n) #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) (sqrt.f64 (.f64 (+.f64 (PI.f64) (PI.f64)) n)))))
(/.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 (sqrt.f64 (.f64 (PI.f64) n)) (sqrt.f64 #s(literal 2 binary64)) (.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)))))
#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))
(.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)) (.f64 (pow.f64 (.f64 (+.f64 (PI.f64) (PI.f64)) n) #s(approx (/ (/ (- 1 k) 2) 2) (fma.f64 #s(literal -1/4 binary64) k #s(literal 1/4 binary64)))) (pow.f64 (.f64 (+.f64 (PI.f64) (PI.f64)) n) #s(approx (/ (/ (- 1 k) 2) 2) (*.f64 (-.f64 (/.f64 #s(literal 1/4 binary64) k) #s(literal 1/4 binary64)) k)))))
(.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) (.f64 #s(approx (pow (* (+ (PI) (PI)) n) (/ (/ (- 1 k) 2) 2)) (exp.f64 (.f64 (.f64 (log.f64 (.f64 n (+.f64 (PI.f64) (PI.f64)))) (-.f64 #s(literal 1 binary64) k)) #s(literal 1/4 binary64)))) (pow.f64 (.f64 (+.f64 (PI.f64) (PI.f64)) n) #s(approx (/ (/ (- 1 k) 2) 2) (*.f64 (-.f64 (/.f64 #s(literal 1/4 binary64) k) #s(literal 1/4 binary64)) k)))))
(.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) (.f64 (pow.f64 (.f64 (+.f64 (PI.f64) (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) #s(approx (/ (/ (- 1 k) 2) 2) (*.f64 (-.f64 (/.f64 #s(literal 1/4 binary64) k) #s(literal 1/4 binary64)) k)))))
(.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) (.f64 (pow.f64 (.f64 (+.f64 (PI.f64) (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 (* 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 #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))))) 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)))))) (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 #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 #s(approx (pow (* (* 2 (PI)) n) (/ (- 1 k) 2)) (fma.f64 (fma.f64 k (fma.f64 (.f64 (.f64 (.f64 (pow.f64 (log.f64 (.f64 n (+.f64 (PI.f64) (PI.f64)))) #s(literal 3 binary64)) k) (sqrt.f64 #s(literal 2 binary64))) (sqrt.f64 (.f64 (PI.f64) n))) #s(literal -1/48 binary64) (.f64 (.f64 #s(literal 1/8 binary64) (sqrt.f64 (.f64 (PI.f64) n))) (.f64 (.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)))))) (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)))))

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:

13.0ms	(.f64 (.f64 #s(literal 2 binary64) (PI.f64)) n)
12.0ms	n
12.0ms	k
10.0ms	(.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

2.1MiB live, 49.1MiB allocated; 2ms collecting garbage

Counts

19 → 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))
#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 #s(approx (* 1 (pow (* (+ (PI) (PI)) n) (/ (- 1 k) 2))) (*.f64 (sqrt.f64 (+.f64 (PI.f64) (PI.f64))) (sqrt.f64 n))) (sqrt.f64 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))))
(.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 (/.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 (pow.f64 (*.f64 n (+.f64 (PI.f64) (PI.f64))) #s(approx (/ (- 1 k) 2) #s(literal 1/2 binary64))) (sqrt.f64 k))
(/.f64 #s(approx (* 1 (pow (* (+ (PI) (PI)) n) (/ (- 1 k) 2))) (exp.f64 #s(approx (* (* (log (* n (+ (PI) (PI)))) (- 1 k)) 1/2) (log.f64 (sqrt.f64 (*.f64 n (+.f64 (PI.f64) (PI.f64)))))))) (sqrt.f64 k))
(/.f64 (.f64 #s(literal 1 binary64) (pow.f64 (.f64 (+.f64 (PI.f64) (PI.f64)) n) #s(approx (/ (- 1 k) 2) #s(literal 1/2 binary64)))) (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))
(/.f64 (exp.f64 (.f64 (log.f64 (.f64 n (+.f64 (PI.f64) (PI.f64)))) #s(approx (/ (- 1 k) 2) #s(literal 1/2 binary64)))) (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:

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

Results

Accuracy	Segments	Branch
58.4%	3	`(.f64 (.f64 #s(literal 2 binary64) (PI.f64)) n)`
98.2%	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))))`
98.2%	2	`k`
58.4%	3	`n`

Compiler

Compiled 22 to 23 computations (-4.5% saved)

regimes22.0ms (0.5%)

Memory

-5.6MiB live, 44.2MiB allocated; 3ms collecting garbage

Counts

17 → 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))
#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 #s(approx (* 1 (pow (* (+ (PI) (PI)) n) (/ (- 1 k) 2))) (*.f64 (sqrt.f64 (+.f64 (PI.f64) (PI.f64))) (sqrt.f64 n))) (sqrt.f64 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))))
(.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 (/.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 (pow.f64 (*.f64 n (+.f64 (PI.f64) (PI.f64))) #s(approx (/ (- 1 k) 2) #s(literal 1/2 binary64))) (sqrt.f64 k))
(/.f64 #s(approx (* 1 (pow (* (+ (PI) (PI)) n) (/ (- 1 k) 2))) (exp.f64 #s(approx (* (* (log (* n (+ (PI) (PI)))) (- 1 k)) 1/2) (log.f64 (sqrt.f64 (*.f64 n (+.f64 (PI.f64) (PI.f64)))))))) (sqrt.f64 k))
(/.f64 (.f64 #s(literal 1 binary64) (pow.f64 (.f64 (+.f64 (PI.f64) (PI.f64)) n) #s(approx (/ (- 1 k) 2) #s(literal 1/2 binary64)))) (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))

Calls

4 calls:

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

Results

Accuracy	Segments	Branch
50.7%	1	`(.f64 (.f64 #s(literal 2 binary64) (PI.f64)) n)`
50.7%	1	`n`
50.7%	1	`(.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) (pow.f64 (.f64 (*.f64 #s(literal 2 binary64) (PI.f64)) n) (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 2 binary64))))`
50.7%	1	`k`

Compiler

Compiled 22 to 23 computations (-4.5% saved)

regimes9.0ms (0.2%)

Memory

21.8MiB live, 21.8MiB allocated; 0ms collecting garbage

Accuracy

Total -0.2b remaining (-0.6%)

Threshold costs -0.2b (-0.6%)

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

Calls

4 calls:

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

Results

Accuracy	Segments	Branch
40.2%	1	`(.f64 (.f64 #s(literal 2 binary64) (PI.f64)) n)`
40.2%	1	`n`
40.2%	1	`k`
40.2%	1	`(.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) (pow.f64 (.f64 (*.f64 #s(literal 2 binary64) (PI.f64)) n) (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 2 binary64))))`

Compiler

Compiled 22 to 23 computations (-4.5% saved)

bsearch17.0ms (0.4%)

Memory

-16.2MiB live, 30.9MiB allocated; 1ms collecting garbage

Algorithm

1×	binary-search

Stop Event

1×	narrow-enough

Steps

Time	Left	Right
15.0ms	0.009598667634539352	3.7662634907996826

Samples

10.0ms

128×

valid

Compiler

Compiled 307 to 298 computations (2.9% saved)

Precisions

Click to see histograms. Total time spent on operations: 7.0ms

ival-pow: 3.0ms (42.9% of total)

ival-sqrt: 1.0ms (14.3% of total)

ival-div!: 1.0ms (14.3% of total)

ival-mult!: 1.0ms (14.3% of total)

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

adjust: 0.0ms (0% of total)

derivations29.0ms (0.6%)

Memory

-3.6MiB live, 43.6MiB allocated; 3ms collecting garbage

Stop Event

1×

fuel

Compiler

Compiled 58 to 37 computations (36.2% saved)

preprocess29.0ms (0.6%)

Memory: 25.0MiB live, 71.9MiB allocated; 3ms collecting garbage
Compiler: Compiled 73 to 50 computations (31.5% saved)

end0.0ms (0%)

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

start0.0ms (0%)

analyze102.0ms (2.3%)

sample3.4s (75.9%)

preprocess35.0ms (0.8%)

series70.0ms (1.6%)

rewrite53.0ms (1.2%)

eval17.0ms (0.4%)

prune11.0ms (0.2%)

series122.0ms (2.7%)

rewrite90.0ms (2%)

eval36.0ms (0.8%)

prune17.0ms (0.4%)

series44.0ms (1%)

rewrite67.0ms (1.5%)

eval23.0ms (0.5%)

prune15.0ms (0.3%)

series58.0ms (1.3%)

rewrite80.0ms (1.8%)

eval27.0ms (0.6%)

prune35.0ms (0.8%)

regimes52.0ms (1.2%)

regimes23.0ms (0.5%)

regimes22.0ms (0.5%)

regimes9.0ms (0.2%)

bsearch17.0ms (0.4%)

derivations29.0ms (0.6%)

preprocess29.0ms (0.6%)

end0.0ms (0%)

Profiling