Metrics for Migdal et al, Equation (51)

start0.0ms (0%)

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

analyze133.0ms (2.2%)

Memory

-4.4MiB live, 101.8MiB allocated; 35ms collecting garbage

Algorithm

1×

Search

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

Compiler

Compiled 18 to 15 computations (16.7% saved)

sample2.8s (46%)

Memory

52.8MiB live, 3 868.7MiB allocated; 809ms collecting garbage

Samples

1.4s	5 314×	1	invalid
699.0ms	8 256×	0	valid
130.0ms	447×	2	invalid
60.0ms	233×	0	exit
20.0ms	346×	0	invalid

Precisions

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

ival-pow: 537.0ms (33.7% of total)

adjust: 280.0ms (17.6% of total)

ival-div!: 276.0ms (17.3% of total)

ival-mult!: 229.0ms (14.4% of total)

ival-sqrt: 209.0ms (13.1% of total)

ival-sub!: 60.0ms (3.8% of total)

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

exact: 0.0ms (0% of total)

Bogosity

preprocess45.0ms (0.7%)

Memory

-9.4MiB live, 35.5MiB allocated; 9ms collecting garbage

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	33	104
1	108	90
2	345	88
3	1503	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)

series109.0ms (1.8%)

Memory

40.6MiB live, 138.4MiB allocated; 26ms collecting garbage

Counts

13 → 37

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 (/ (pow (* 2 (* n (PI))) 1/2) (sqrt k))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) #s(hole binary64 (+ (* -1/2 (/ (* k (* (log (* 2 (* n (PI)))) (pow (* 2 (* n (PI))) 1/2))) (sqrt k))) (/ (pow (* 2 (* n (PI))) 1/2) (sqrt k)))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) #s(hole binary64 (+ (* k (+ (* -1/2 (/ (* (log (* 2 (* n (PI)))) (pow (* 2 (* n (PI))) 1/2)) (sqrt k))) (* 1/8 (/ (* k (* (pow (log (* 2 (* n (PI)))) 2) (pow (* 2 (* n (PI))) 1/2))) (sqrt k))))) (/ (pow (* 2 (* n (PI))) 1/2) (sqrt k)))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) #s(hole binary64 (+ (* k (+ (* -1/2 (/ (* (log (* 2 (* n (PI)))) (pow (* 2 (* n (PI))) 1/2)) (sqrt k))) (* k (+ (* -1/48 (/ (* k (* (pow (log (* 2 (* n (PI)))) 3) (pow (* 2 (* n (PI))) 1/2))) (sqrt k))) (* 1/8 (/ (* (pow (log (* 2 (* n (PI)))) 2) (pow (* 2 (* n (PI))) 1/2)) (sqrt k))))))) (/ (pow (* 2 (* n (PI))) 1/2) (sqrt k)))))
#s(approx (/ 1 (sqrt k)) #s(hole binary64 (/ 1 (sqrt 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 (pow (* 2 (* n (PI))) 1/2)))
#s(approx (pow (* (* 2 (PI)) n) (/ (- 1 k) 2)) #s(hole binary64 (+ (* -1/2 (* k (* (log (* 2 (* n (PI)))) (pow (* 2 (* n (PI))) 1/2)))) (pow (* 2 (* n (PI))) 1/2))))
#s(approx (pow (* (* 2 (PI)) n) (/ (- 1 k) 2)) #s(hole binary64 (+ (* k (+ (* -1/2 (* (log (* 2 (* n (PI)))) (pow (* 2 (* n (PI))) 1/2))) (* 1/8 (* k (* (pow (log (* 2 (* n (PI)))) 2) (pow (* 2 (* n (PI))) 1/2)))))) (pow (* 2 (* n (PI))) 1/2))))
#s(approx (pow (* (* 2 (PI)) n) (/ (- 1 k) 2)) #s(hole binary64 (+ (* k (+ (* -1/2 (* (log (* 2 (* n (PI)))) (pow (* 2 (* n (PI))) 1/2))) (* k (+ (* -1/48 (* k (* (pow (log (* 2 (* n (PI)))) 3) (pow (* 2 (* n (PI))) 1/2)))) (* 1/8 (* (pow (log (* 2 (* n (PI)))) 2) (pow (* 2 (* n (PI))) 1/2))))))) (pow (* 2 (* n (PI))) 1/2))))
#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 (/ (exp (* 1/2 (* (log (* 2 (* n (PI)))) (- 1 k)))) (* k (sqrt (/ 1 k))))))
#s(approx (/ 1 (sqrt k)) #s(hole binary64 (/ 1 (* k (sqrt (/ 1 k))))))
#s(approx (sqrt k) #s(hole binary64 (* k (sqrt (/ 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 (* -1 (/ (exp (* 1/2 (* (log (* 2 (* n (PI)))) (+ 1 (* -1 k))))) (* k (sqrt (/ 1 k)))))))
#s(approx (/ 1 (sqrt k)) #s(hole binary64 (/ -1 (* k (sqrt (/ 1 k))))))
#s(approx (sqrt k) #s(hole binary64 (* -1 (* k (sqrt (/ 1 k))))))
#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 (/ (exp (* 1/2 (* (+ (log n) (log (* 2 (PI)))) (- 1 k)))) (sqrt 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 (/ (exp (* 1/2 (* (+ (log (* 2 (PI))) (* -1 (log (/ 1 n)))) (- 1 k)))) (sqrt 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 (/ (exp (* 1/2 (* (+ (log (* -2 (PI))) (* -1 (log (/ -1 n)))) (- 1 k)))) (sqrt 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
62.0ms	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))
31.0ms	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))
2.0ms	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))
2.0ms	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))

rewrite191.0ms (3.1%)

Memory

-11.2MiB live, 282.4MiB allocated; 44ms collecting garbage

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	167	1003
0	181	956
1	765	852
0	6608	834

Stop Event

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

Counts

50 → 216

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

eval23.0ms (0.4%)

Memory: 2.7MiB live, 48.4MiB allocated; 5ms collecting garbage
Compiler: Compiled 2 273 to 825 computations (63.7% saved)

prune48.0ms (0.8%)

Memory

-28.9MiB live, 27.3MiB allocated; 4ms collecting garbage

Pruning

14 alts after pruning (14 fresh and 0 done)

	Pruned	Kept	Total
New	188	14	202
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	189	14	203

Accuracy

100.0%

Counts

203 → 14

Alt Table

Click to see full alt table

Status	Accuracy	Program
	99.5%	(/.f64 (pow.f64 (sqrt.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n)) (-.f64 #s(literal 1 binary64) k)) (sqrt.f64 k))
▶	99.4%	(.f64 (pow.f64 (sqrt.f64 (.f64 (+.f64 (PI.f64) (PI.f64)) n)) (-.f64 #s(literal 1 binary64) k)) (/.f64 #s(literal 1 binary64) (sqrt.f64 k)))
	78.3%	(.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) (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))))
	99.3%	(.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) (pow.f64 (.f64 (*.f64 (+.f64 n n) (sqrt.f64 (PI.f64))) (sqrt.f64 (PI.f64))) (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 2 binary64))))
	99.2%	(.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) (pow.f64 (.f64 (.f64 (sqrt.f64 #s(literal 2 binary64)) (sqrt.f64 #s(literal 2 binary64))) (.f64 (sqrt.f64 (.f64 (PI.f64) n)) (sqrt.f64 (.f64 (PI.f64) n)))) (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 2 binary64))))
▶	99.6%	(.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) (/.f64 (sqrt.f64 (.f64 (+.f64 (PI.f64) (PI.f64)) n)) (pow.f64 (.f64 (+.f64 (PI.f64) (PI.f64)) n) (.f64 #s(literal 1/2 binary64) k))))
	96.5%	(.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) (exp.f64 (.f64 (log.f64 (sqrt.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n))) (-.f64 #s(literal 1 binary64) k))))
	51.6%	(.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))))
▶	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))))
	99.5%	(.f64 #s(approx (/ 1 (sqrt k)) (/.f64 (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))))
	47.6%	#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (fma.f64 (/.f64 (-.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 (.f64 (+.f64 (PI.f64) (PI.f64)) n))) k) #s(literal 1/8 binary64)) (.f64 (log.f64 (sqrt.f64 (.f64 (+.f64 (PI.f64) (PI.f64)) n))) (sqrt.f64 (.f64 (+.f64 (PI.f64) (PI.f64)) n)))) (sqrt.f64 k)) k (sqrt.f64 (/.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n) k))))
▶	52.3%	#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (/.f64 (fma.f64 (.f64 k (neg.f64 (log.f64 (sqrt.f64 (.f64 (+.f64 (PI.f64) (PI.f64)) n))))) (sqrt.f64 (.f64 (+.f64 (PI.f64) (PI.f64)) n)) (sqrt.f64 (.f64 (+.f64 (PI.f64) (PI.f64)) n))) (sqrt.f64 k)))
	99.5%	#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (/.f64 (pow.f64 (sqrt.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n)) (-.f64 #s(literal 1 binary64) k)) (/.f64 k (sqrt.f64 k))))
▶	41.8%	#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt.f64 (/.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n) k)))

Compiler

Compiled 616 to 490 computations (20.5% saved)

series187.0ms (3.1%)

Memory

8.9MiB live, 382.8MiB allocated; 49ms collecting garbage

Counts

34 → 117

Calls

Call 1

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

Outputs
#s(approx (* (/ 1 (sqrt k)) (/ (sqrt (* (+ (PI) (PI)) n)) (pow (* (+ (PI) (PI)) n) (* 1/2 k)))) #s(hole binary64 (/ (sqrt (* 2 (* n (PI)))) (sqrt k))))
#s(approx (* (/ 1 (sqrt k)) (/ (sqrt (* (+ (PI) (PI)) n)) (pow (* (+ (PI) (PI)) n) (* 1/2 k)))) #s(hole binary64 (+ (* -1/2 (/ (* k (* (log (* 2 (* n (PI)))) (sqrt (* 2 (* n (PI)))))) (sqrt k))) (/ (sqrt (* 2 (* n (PI)))) (sqrt k)))))
#s(approx (* (/ 1 (sqrt k)) (/ (sqrt (* (+ (PI) (PI)) n)) (pow (* (+ (PI) (PI)) n) (* 1/2 k)))) #s(hole binary64 (+ (* k (- (* -1 (* k (+ (* -1/4 (/ (* (pow (log (* 2 (* n (PI)))) 2) (sqrt (* 2 (* n (PI))))) (sqrt k))) (* 1/8 (/ (* (pow (log (* 2 (* n (PI)))) 2) (sqrt (* 2 (* n (PI))))) (sqrt k)))))) (* 1/2 (/ (* (log (* 2 (* n (PI)))) (sqrt (* 2 (* n (PI))))) (sqrt k))))) (/ (sqrt (* 2 (* n (PI)))) (sqrt k)))))
#s(approx (* (/ 1 (sqrt k)) (/ (sqrt (* (+ (PI) (PI)) n)) (pow (* (+ (PI) (PI)) n) (* 1/2 k)))) #s(hole binary64 (+ (* k (- (* k (- (* -1 (* k (+ (* -1/2 (* (log (* 2 (* n (PI)))) (+ (* -1/4 (/ (* (pow (log (* 2 (* n (PI)))) 2) (sqrt (* 2 (* n (PI))))) (sqrt k))) (* 1/8 (/ (* (pow (log (* 2 (* n (PI)))) 2) (sqrt (* 2 (* n (PI))))) (sqrt k)))))) (+ (* -1/16 (/ (* (pow (log (* 2 (* n (PI)))) 3) (sqrt (* 2 (* n (PI))))) (sqrt k))) (* 1/48 (/ (* (pow (log (* 2 (* n (PI)))) 3) (sqrt (* 2 (* n (PI))))) (sqrt k))))))) (+ (* -1/4 (/ (* (pow (log (* 2 (* n (PI)))) 2) (sqrt (* 2 (* n (PI))))) (sqrt k))) (* 1/8 (/ (* (pow (log (* 2 (* n (PI)))) 2) (sqrt (* 2 (* n (PI))))) (sqrt k)))))) (* 1/2 (/ (* (log (* 2 (* n (PI)))) (sqrt (* 2 (* n (PI))))) (sqrt k))))) (/ (sqrt (* 2 (* n (PI)))) (sqrt k)))))
#s(approx (/ 1 (sqrt k)) #s(hole binary64 (/ 1 (sqrt k))))
#s(approx (sqrt k) #s(hole binary64 (sqrt k)))
#s(approx k #s(hole binary64 k))
#s(approx (/ (sqrt (* (+ (PI) (PI)) n)) (pow (* (+ (PI) (PI)) n) (* 1/2 k))) #s(hole binary64 (sqrt (* 2 (* n (PI))))))
#s(approx (/ (sqrt (* (+ (PI) (PI)) n)) (pow (* (+ (PI) (PI)) n) (* 1/2 k))) #s(hole binary64 (+ (sqrt (* 2 (* n (PI)))) (* -1/2 (* k (* (log (* 2 (* n (PI)))) (sqrt (* 2 (* n (PI))))))))))
#s(approx (/ (sqrt (* (+ (PI) (PI)) n)) (pow (* (+ (PI) (PI)) n) (* 1/2 k))) #s(hole binary64 (+ (sqrt (* 2 (* n (PI)))) (* k (- (* -1 (* k (+ (* -1/4 (* (pow (log (* 2 (* n (PI)))) 2) (sqrt (* 2 (* n (PI)))))) (* 1/8 (* (pow (log (* 2 (* n (PI)))) 2) (sqrt (* 2 (* n (PI))))))))) (* 1/2 (* (log (* 2 (* n (PI)))) (sqrt (* 2 (* n (PI)))))))))))
#s(approx (/ (sqrt (* (+ (PI) (PI)) n)) (pow (* (+ (PI) (PI)) n) (* 1/2 k))) #s(hole binary64 (+ (sqrt (* 2 (* n (PI)))) (* k (- (* k (- (* -1 (* k (+ (* -1/2 (* (log (* 2 (* n (PI)))) (+ (* -1/4 (* (pow (log (* 2 (* n (PI)))) 2) (sqrt (* 2 (* n (PI)))))) (* 1/8 (* (pow (log (* 2 (* n (PI)))) 2) (sqrt (* 2 (* n (PI))))))))) (+ (* -1/16 (* (pow (log (* 2 (* n (PI)))) 3) (sqrt (* 2 (* n (PI)))))) (* 1/48 (* (pow (log (* 2 (* n (PI)))) 3) (sqrt (* 2 (* n (PI)))))))))) (+ (* -1/4 (* (pow (log (* 2 (* n (PI)))) 2) (sqrt (* 2 (* n (PI)))))) (* 1/8 (* (pow (log (* 2 (* n (PI)))) 2) (sqrt (* 2 (* n (PI))))))))) (* 1/2 (* (log (* 2 (* n (PI)))) (sqrt (* 2 (* n (PI)))))))))))
#s(approx (pow (* (+ (PI) (PI)) n) (* 1/2 k)) #s(hole binary64 1))
#s(approx (pow (* (+ (PI) (PI)) n) (* 1/2 k)) #s(hole binary64 (+ 1 (* 1/2 (* k (log (* 2 (* n (PI)))))))))
#s(approx (pow (* (+ (PI) (PI)) n) (* 1/2 k)) #s(hole binary64 (+ 1 (* k (+ (* 1/8 (* k (pow (log (* 2 (* n (PI)))) 2))) (* 1/2 (log (* 2 (* n (PI))))))))))
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#s(approx (* 1/2 k) #s(hole binary64 (* 1/2 k)))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) #s(hole binary64 (/ (pow (* 2 (* n (PI))) 1/2) (sqrt k))))
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#s(approx (sqrt (/ (* (+ (PI) (PI)) n) k)) #s(hole binary64 (/ (sqrt (* 2 (* k (* n (PI))))) k)))
#s(approx (/ (* (+ (PI) (PI)) n) k) #s(hole binary64 (* 2 (/ (* n (PI)) k))))
#s(approx (* (pow (sqrt (* (+ (PI) (PI)) n)) (- 1 k)) (/ 1 (sqrt k))) #s(hole binary64 (+ (* -1 (/ (* k (* (log (sqrt (* 2 (* n (PI))))) (sqrt (* 2 (* n (PI)))))) (sqrt k))) (/ (sqrt (* 2 (* n (PI)))) (sqrt k)))))
#s(approx (* (pow (sqrt (* (+ (PI) (PI)) n)) (- 1 k)) (/ 1 (sqrt k))) #s(hole binary64 (+ (* k (+ (* -1 (/ (* (log (sqrt (* 2 (* n (PI))))) (sqrt (* 2 (* n (PI))))) (sqrt k))) (* 1/2 (/ (* k (* (pow (log (sqrt (* 2 (* n (PI))))) 2) (sqrt (* 2 (* n (PI)))))) (sqrt k))))) (/ (sqrt (* 2 (* n (PI)))) (sqrt k)))))
#s(approx (* (pow (sqrt (* (+ (PI) (PI)) n)) (- 1 k)) (/ 1 (sqrt k))) #s(hole binary64 (+ (* k (+ (* -1 (/ (* (log (sqrt (* 2 (* n (PI))))) (sqrt (* 2 (* n (PI))))) (sqrt k))) (* k (+ (* -1/6 (/ (* k (* (pow (log (sqrt (* 2 (* n (PI))))) 3) (sqrt (* 2 (* n (PI)))))) (sqrt k))) (* 1/2 (/ (* (pow (log (sqrt (* 2 (* n (PI))))) 2) (sqrt (* 2 (* n (PI))))) (sqrt k))))))) (/ (sqrt (* 2 (* n (PI)))) (sqrt k)))))
#s(approx (pow (sqrt (* (+ (PI) (PI)) n)) (- 1 k)) #s(hole binary64 (+ (sqrt (* 2 (* n (PI)))) (* -1 (* k (* (log (sqrt (* 2 (* n (PI))))) (sqrt (* 2 (* n (PI))))))))))
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#s(approx (- 1 k) #s(hole binary64 (+ 1 (* -1 k))))
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#s(approx (* (sqrt (/ 1 k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) #s(hole binary64 (/ (+ (* k (+ (* -1/2 (* (log (* 2 (* n (PI)))) (* (sqrt k) (pow (* 2 (* n (PI))) 1/2)))) (* 1/8 (* k (* (pow (log (* 2 (* n (PI)))) 2) (* (sqrt k) (pow (* 2 (* n (PI))) 1/2))))))) (* (sqrt k) (pow (* 2 (* n (PI))) 1/2))) k)))
#s(approx (* (sqrt (/ 1 k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) #s(hole binary64 (/ (+ (* k (+ (* -1/2 (* (log (* 2 (* n (PI)))) (* (sqrt k) (pow (* 2 (* n (PI))) 1/2)))) (* k (+ (* -1/48 (* k (* (pow (log (* 2 (* n (PI)))) 3) (* (sqrt k) (pow (* 2 (* n (PI))) 1/2))))) (* 1/8 (* (pow (log (* 2 (* n (PI)))) 2) (* (sqrt k) (pow (* 2 (* n (PI))) 1/2)))))))) (* (sqrt k) (pow (* 2 (* n (PI))) 1/2))) k)))
#s(approx (sqrt (/ 1 k)) #s(hole binary64 (/ (sqrt k) k)))
#s(approx (/ 1 k) #s(hole binary64 (/ 1 k)))
#s(approx (pow (* (* 2 (PI)) n) (/ (- 1 k) 2)) #s(hole binary64 (pow (* 2 (* n (PI))) 1/2)))
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#s(approx (pow (* (* 2 (PI)) n) (/ (- 1 k) 2)) #s(hole binary64 (+ (* k (+ (* -1/2 (* (log (* 2 (* n (PI)))) (pow (* 2 (* n (PI))) 1/2))) (* 1/8 (* k (* (pow (log (* 2 (* n (PI)))) 2) (pow (* 2 (* n (PI))) 1/2)))))) (pow (* 2 (* n (PI))) 1/2))))
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#s(approx (/ (- 1 k) 2) #s(hole binary64 1/2))
#s(approx (/ (- 1 k) 2) #s(hole binary64 (+ 1/2 (* -1/2 k))))
#s(approx (* k (neg (log (sqrt (* (+ (PI) (PI)) n))))) #s(hole binary64 (* -1 (* k (log (sqrt (* 2 (* n (PI)))))))))
#s(approx (* (/ 1 (sqrt k)) (/ (sqrt (* (+ (PI) (PI)) n)) (pow (* (+ (PI) (PI)) n) (* 1/2 k)))) #s(hole binary64 (/ (sqrt (* 2 (* n (PI)))) (* k (* (exp (* 1/2 (* k (log (* 2 (* n (PI))))))) (sqrt (/ 1 k)))))))
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#s(approx (/ (sqrt (* (+ (PI) (PI)) n)) (pow (* (+ (PI) (PI)) n) (* 1/2 k))) #s(hole binary64 (/ (sqrt (* 2 (* n (PI)))) (exp (* 1/2 (* k (log (* 2 (* n (PI))))))))))
#s(approx (pow (* (+ (PI) (PI)) n) (* 1/2 k)) #s(hole binary64 (exp (* 1/2 (* k (log (* 2 (* n (PI)))))))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) #s(hole binary64 (/ (exp (* 1/2 (* (log (* 2 (* n (PI)))) (- 1 k)))) (* k (sqrt (/ 1 k))))))
#s(approx (sqrt (/ (* (+ (PI) (PI)) n) k)) #s(hole binary64 (sqrt (* 2 (/ (* n (PI)) k)))))
#s(approx (* (pow (sqrt (* (+ (PI) (PI)) n)) (- 1 k)) (/ 1 (sqrt k))) #s(hole binary64 (/ (exp (* (log (sqrt (* 2 (* n (PI))))) (- 1 k))) (* k (sqrt (/ 1 k))))))
#s(approx (pow (sqrt (* (+ (PI) (PI)) n)) (- 1 k)) #s(hole binary64 (exp (* (log (sqrt (* 2 (* n (PI))))) (- 1 k)))))
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#s(approx (* (sqrt (/ 1 k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) #s(hole binary64 (* (exp (* 1/2 (* (log (* 2 (* n (PI)))) (- 1 k)))) (sqrt (/ 1 k)))))
#s(approx (sqrt (/ 1 k)) #s(hole binary64 (sqrt (/ 1 k))))
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#s(approx (/ (- 1 k) 2) #s(hole binary64 (* k (- (* 1/2 (/ 1 k)) 1/2))))
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#s(approx (+ (* (* k (neg (log (sqrt (* (+ (PI) (PI)) n))))) (sqrt (* (+ (PI) (PI)) n))) (sqrt (* (+ (PI) (PI)) n))) #s(hole binary64 (* -1 (* k (* (log (sqrt (* 2 (* n (PI))))) (sqrt (* 2 (* n (PI)))))))))
#s(approx (+ (* (* k (neg (log (sqrt (* (+ (PI) (PI)) n))))) (sqrt (* (+ (PI) (PI)) n))) (sqrt (* (+ (PI) (PI)) n))) #s(hole binary64 (* k (+ (* -1 (* (log (sqrt (* 2 (* n (PI))))) (sqrt (* 2 (* n (PI)))))) (/ (sqrt (* 2 (* n (PI)))) k)))))
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#s(approx (/ 1 (sqrt k)) #s(hole binary64 (/ -1 (* k (sqrt (/ 1 k))))))
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#s(approx (pow (sqrt (* (+ (PI) (PI)) n)) (- 1 k)) #s(hole binary64 (exp (* (log (sqrt (* 2 (* n (PI))))) (+ 1 (* -1 k))))))
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#s(approx (* (sqrt (/ 1 k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) #s(hole binary64 (* (exp (* 1/2 (* (log (* 2 (* n (PI)))) (+ 1 (* -1 k))))) (sqrt (/ 1 k)))))
#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 (/ (+ (* (* k (neg (log (sqrt (* (+ (PI) (PI)) n))))) (sqrt (* (+ (PI) (PI)) n))) (sqrt (* (+ (PI) (PI)) n))) (sqrt k)) #s(hole binary64 (/ (* (log (sqrt (* 2 (* n (PI))))) (sqrt (* 2 (* n (PI))))) (sqrt (/ 1 k)))))
#s(approx (/ (+ (* (* k (neg (log (sqrt (* (+ (PI) (PI)) n))))) (sqrt (* (+ (PI) (PI)) n))) (sqrt (* (+ (PI) (PI)) n))) (sqrt k)) #s(hole binary64 (+ (* -1 (/ (sqrt (* 2 (* n (PI)))) (* k (sqrt (/ 1 k))))) (/ (* (log (sqrt (* 2 (* n (PI))))) (sqrt (* 2 (* n (PI))))) (sqrt (/ 1 k))))))
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#s(approx (/ (sqrt (* (+ (PI) (PI)) n)) (pow (* (+ (PI) (PI)) n) (* 1/2 k))) #s(hole binary64 (/ (sqrt (* 2 (* n (PI)))) (exp (* 1/2 (* k (+ (log n) (log (* 2 (PI))))))))))
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#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 (+ (* (* k (neg (log (sqrt (* (+ (PI) (PI)) n))))) (sqrt (* (+ (PI) (PI)) n))) (sqrt (* (+ (PI) (PI)) n))) #s(hole binary64 (* n (+ (sqrt (* 2 (/ (PI) n))) (* -1 (* k (* (sqrt (* 2 (/ (PI) n))) (+ (log (sqrt (* 2 (/ (PI) n)))) (* -1 (log (/ 1 n)))))))))))
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#s(approx (log (sqrt (* (+ (PI) (PI)) n))) #s(hole binary64 (+ (log (sqrt (* 2 (/ (PI) n)))) (* -1 (log (/ -1 n))))))

Calls

6 calls:

Time	Variable		Point	Expression
44.0ms	k	@	0	((* (/ 1 (sqrt k)) (/ (sqrt (* (+ (PI) (PI)) n)) (pow (* (+ (PI) (PI)) n) (* 1/2 k)))) (/ 1 (sqrt k)) 1 (sqrt k) k (/ (sqrt (* (+ (PI) (PI)) n)) (pow (* (+ (PI) (PI)) n) (* 1/2 k))) (sqrt (* (+ (PI) (PI)) n)) (* (+ (PI) (PI)) n) (+ (PI) (PI)) (PI) n (pow (* (+ (PI) (PI)) n) (* 1/2 k)) (* 1/2 k) 1/2 (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt (/ (* (+ (PI) (PI)) n) k)) (/ (* (+ (PI) (PI)) n) k) (* (pow (sqrt (* (+ (PI) (PI)) n)) (- 1 k)) (/ 1 (sqrt k))) (pow (sqrt (* (+ (PI) (PI)) n)) (- 1 k)) (- 1 k) (* (sqrt (/ 1 k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt (/ 1 k)) (/ 1 k) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2)) (* (* 2 (PI)) n) (* 2 (PI)) 2 (/ (- 1 k) 2) (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (/ (+ (* (* k (neg (log (sqrt (* (+ (PI) (PI)) n))))) (sqrt (* (+ (PI) (PI)) n))) (sqrt (* (+ (PI) (PI)) n))) (sqrt k)) (+ (* (* k (neg (log (sqrt (* (+ (PI) (PI)) n))))) (sqrt (* (+ (PI) (PI)) n))) (sqrt (* (+ (PI) (PI)) n))) (* k (neg (log (sqrt (* (+ (PI) (PI)) n))))) (neg (log (sqrt (* (+ (PI) (PI)) n)))) (log (sqrt (* (+ (PI) (PI)) n))))
39.0ms	n	@	-inf	((* (/ 1 (sqrt k)) (/ (sqrt (* (+ (PI) (PI)) n)) (pow (* (+ (PI) (PI)) n) (* 1/2 k)))) (/ 1 (sqrt k)) 1 (sqrt k) k (/ (sqrt (* (+ (PI) (PI)) n)) (pow (* (+ (PI) (PI)) n) (* 1/2 k))) (sqrt (* (+ (PI) (PI)) n)) (* (+ (PI) (PI)) n) (+ (PI) (PI)) (PI) n (pow (* (+ (PI) (PI)) n) (* 1/2 k)) (* 1/2 k) 1/2 (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt (/ (* (+ (PI) (PI)) n) k)) (/ (* (+ (PI) (PI)) n) k) (* (pow (sqrt (* (+ (PI) (PI)) n)) (- 1 k)) (/ 1 (sqrt k))) (pow (sqrt (* (+ (PI) (PI)) n)) (- 1 k)) (- 1 k) (* (sqrt (/ 1 k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt (/ 1 k)) (/ 1 k) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2)) (* (* 2 (PI)) n) (* 2 (PI)) 2 (/ (- 1 k) 2) (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (/ (+ (* (* k (neg (log (sqrt (* (+ (PI) (PI)) n))))) (sqrt (* (+ (PI) (PI)) n))) (sqrt (* (+ (PI) (PI)) n))) (sqrt k)) (+ (* (* k (neg (log (sqrt (* (+ (PI) (PI)) n))))) (sqrt (* (+ (PI) (PI)) n))) (sqrt (* (+ (PI) (PI)) n))) (* k (neg (log (sqrt (* (+ (PI) (PI)) n))))) (neg (log (sqrt (* (+ (PI) (PI)) n)))) (log (sqrt (* (+ (PI) (PI)) n))))
36.0ms	k	@	inf	((* (/ 1 (sqrt k)) (/ (sqrt (* (+ (PI) (PI)) n)) (pow (* (+ (PI) (PI)) n) (* 1/2 k)))) (/ 1 (sqrt k)) 1 (sqrt k) k (/ (sqrt (* (+ (PI) (PI)) n)) (pow (* (+ (PI) (PI)) n) (* 1/2 k))) (sqrt (* (+ (PI) (PI)) n)) (* (+ (PI) (PI)) n) (+ (PI) (PI)) (PI) n (pow (* (+ (PI) (PI)) n) (* 1/2 k)) (* 1/2 k) 1/2 (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt (/ (* (+ (PI) (PI)) n) k)) (/ (* (+ (PI) (PI)) n) k) (* (pow (sqrt (* (+ (PI) (PI)) n)) (- 1 k)) (/ 1 (sqrt k))) (pow (sqrt (* (+ (PI) (PI)) n)) (- 1 k)) (- 1 k) (* (sqrt (/ 1 k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt (/ 1 k)) (/ 1 k) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2)) (* (* 2 (PI)) n) (* 2 (PI)) 2 (/ (- 1 k) 2) (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (/ (+ (* (* k (neg (log (sqrt (* (+ (PI) (PI)) n))))) (sqrt (* (+ (PI) (PI)) n))) (sqrt (* (+ (PI) (PI)) n))) (sqrt k)) (+ (* (* k (neg (log (sqrt (* (+ (PI) (PI)) n))))) (sqrt (* (+ (PI) (PI)) n))) (sqrt (* (+ (PI) (PI)) n))) (* k (neg (log (sqrt (* (+ (PI) (PI)) n))))) (neg (log (sqrt (* (+ (PI) (PI)) n)))) (log (sqrt (* (+ (PI) (PI)) n))))
28.0ms	n	@	0	((* (/ 1 (sqrt k)) (/ (sqrt (* (+ (PI) (PI)) n)) (pow (* (+ (PI) (PI)) n) (* 1/2 k)))) (/ 1 (sqrt k)) 1 (sqrt k) k (/ (sqrt (* (+ (PI) (PI)) n)) (pow (* (+ (PI) (PI)) n) (* 1/2 k))) (sqrt (* (+ (PI) (PI)) n)) (* (+ (PI) (PI)) n) (+ (PI) (PI)) (PI) n (pow (* (+ (PI) (PI)) n) (* 1/2 k)) (* 1/2 k) 1/2 (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt (/ (* (+ (PI) (PI)) n) k)) (/ (* (+ (PI) (PI)) n) k) (* (pow (sqrt (* (+ (PI) (PI)) n)) (- 1 k)) (/ 1 (sqrt k))) (pow (sqrt (* (+ (PI) (PI)) n)) (- 1 k)) (- 1 k) (* (sqrt (/ 1 k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt (/ 1 k)) (/ 1 k) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2)) (* (* 2 (PI)) n) (* 2 (PI)) 2 (/ (- 1 k) 2) (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (/ (+ (* (* k (neg (log (sqrt (* (+ (PI) (PI)) n))))) (sqrt (* (+ (PI) (PI)) n))) (sqrt (* (+ (PI) (PI)) n))) (sqrt k)) (+ (* (* k (neg (log (sqrt (* (+ (PI) (PI)) n))))) (sqrt (* (+ (PI) (PI)) n))) (sqrt (* (+ (PI) (PI)) n))) (* k (neg (log (sqrt (* (+ (PI) (PI)) n))))) (neg (log (sqrt (* (+ (PI) (PI)) n)))) (log (sqrt (* (+ (PI) (PI)) n))))
24.0ms	n	@	inf	((* (/ 1 (sqrt k)) (/ (sqrt (* (+ (PI) (PI)) n)) (pow (* (+ (PI) (PI)) n) (* 1/2 k)))) (/ 1 (sqrt k)) 1 (sqrt k) k (/ (sqrt (* (+ (PI) (PI)) n)) (pow (* (+ (PI) (PI)) n) (* 1/2 k))) (sqrt (* (+ (PI) (PI)) n)) (* (+ (PI) (PI)) n) (+ (PI) (PI)) (PI) n (pow (* (+ (PI) (PI)) n) (* 1/2 k)) (* 1/2 k) 1/2 (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt (/ (* (+ (PI) (PI)) n) k)) (/ (* (+ (PI) (PI)) n) k) (* (pow (sqrt (* (+ (PI) (PI)) n)) (- 1 k)) (/ 1 (sqrt k))) (pow (sqrt (* (+ (PI) (PI)) n)) (- 1 k)) (- 1 k) (* (sqrt (/ 1 k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt (/ 1 k)) (/ 1 k) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2)) (* (* 2 (PI)) n) (* 2 (PI)) 2 (/ (- 1 k) 2) (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (/ (+ (* (* k (neg (log (sqrt (* (+ (PI) (PI)) n))))) (sqrt (* (+ (PI) (PI)) n))) (sqrt (* (+ (PI) (PI)) n))) (sqrt k)) (+ (* (* k (neg (log (sqrt (* (+ (PI) (PI)) n))))) (sqrt (* (+ (PI) (PI)) n))) (sqrt (* (+ (PI) (PI)) n))) (* k (neg (log (sqrt (* (+ (PI) (PI)) n))))) (neg (log (sqrt (* (+ (PI) (PI)) n)))) (log (sqrt (* (+ (PI) (PI)) n))))

rewrite320.0ms (5.2%)

Memory

17.4MiB live, 331.5MiB allocated; 107ms collecting garbage

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	535	4688
0	589	4242
1	2738	4038
0	9004	3950

Stop Event

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

Counts

151 → 477

Calls

Call 1

Inputs
(.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) (/.f64 (sqrt.f64 (.f64 (+.f64 (PI.f64) (PI.f64)) n)) (pow.f64 (.f64 (+.f64 (PI.f64) (PI.f64)) n) (.f64 #s(literal 1/2 binary64) k))))
(/.f64 #s(literal 1 binary64) (sqrt.f64 k))
#s(literal 1 binary64)
(sqrt.f64 k)
k
(/.f64 (sqrt.f64 (.f64 (+.f64 (PI.f64) (PI.f64)) n)) (pow.f64 (.f64 (+.f64 (PI.f64) (PI.f64)) n) (*.f64 #s(literal 1/2 binary64) k)))
(sqrt.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n))
(*.f64 (+.f64 (PI.f64) (PI.f64)) n)
(+.f64 (PI.f64) (PI.f64))
(PI.f64)
n
(pow.f64 (.f64 (+.f64 (PI.f64) (PI.f64)) n) (.f64 #s(literal 1/2 binary64) k))
(*.f64 #s(literal 1/2 binary64) k)
#s(literal 1/2 binary64)
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (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 (pow.f64 (sqrt.f64 (.f64 (+.f64 (PI.f64) (PI.f64)) n)) (-.f64 #s(literal 1 binary64) k)) (/.f64 #s(literal 1 binary64) (sqrt.f64 k)))
(pow.f64 (sqrt.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n)) (-.f64 #s(literal 1 binary64) k))
(-.f64 #s(literal 1 binary64) 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))))
(sqrt.f64 (/.f64 #s(literal 1 binary64) k))
(/.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 2 binary64) (PI.f64)) n)
(*.f64 #s(literal 2 binary64) (PI.f64))
#s(literal 2 binary64)
(/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 2 binary64))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (/.f64 (fma.f64 (.f64 k (neg.f64 (log.f64 (sqrt.f64 (.f64 (+.f64 (PI.f64) (PI.f64)) n))))) (sqrt.f64 (.f64 (+.f64 (PI.f64) (PI.f64)) n)) (sqrt.f64 (.f64 (+.f64 (PI.f64) (PI.f64)) n))) (sqrt.f64 k)))
(/.f64 (fma.f64 (.f64 k (neg.f64 (log.f64 (sqrt.f64 (.f64 (+.f64 (PI.f64) (PI.f64)) n))))) (sqrt.f64 (.f64 (+.f64 (PI.f64) (PI.f64)) n)) (sqrt.f64 (.f64 (+.f64 (PI.f64) (PI.f64)) n))) (sqrt.f64 k))
(fma.f64 (.f64 k (neg.f64 (log.f64 (sqrt.f64 (.f64 (+.f64 (PI.f64) (PI.f64)) n))))) (sqrt.f64 (.f64 (+.f64 (PI.f64) (PI.f64)) n)) (sqrt.f64 (.f64 (+.f64 (PI.f64) (PI.f64)) n)))
(.f64 k (neg.f64 (log.f64 (sqrt.f64 (.f64 (+.f64 (PI.f64) (PI.f64)) n)))))
(neg.f64 (log.f64 (sqrt.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n))))
(log.f64 (sqrt.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n)))
#s(approx (* (/ 1 (sqrt k)) (/ (sqrt (* (+ (PI) (PI)) n)) (pow (* (+ (PI) (PI)) n) (* 1/2 k)))) #s(hole binary64 (/ (sqrt (* 2 (* n (PI)))) (sqrt k))))
#s(approx (* (/ 1 (sqrt k)) (/ (sqrt (* (+ (PI) (PI)) n)) (pow (* (+ (PI) (PI)) n) (* 1/2 k)))) #s(hole binary64 (+ (* -1/2 (/ (* k (* (log (* 2 (* n (PI)))) (sqrt (* 2 (* n (PI)))))) (sqrt k))) (/ (sqrt (* 2 (* n (PI)))) (sqrt k)))))
#s(approx (* (/ 1 (sqrt k)) (/ (sqrt (* (+ (PI) (PI)) n)) (pow (* (+ (PI) (PI)) n) (* 1/2 k)))) #s(hole binary64 (+ (* k (- (* -1 (* k (+ (* -1/4 (/ (* (pow (log (* 2 (* n (PI)))) 2) (sqrt (* 2 (* n (PI))))) (sqrt k))) (* 1/8 (/ (* (pow (log (* 2 (* n (PI)))) 2) (sqrt (* 2 (* n (PI))))) (sqrt k)))))) (* 1/2 (/ (* (log (* 2 (* n (PI)))) (sqrt (* 2 (* n (PI))))) (sqrt k))))) (/ (sqrt (* 2 (* n (PI)))) (sqrt k)))))
#s(approx (* (/ 1 (sqrt k)) (/ (sqrt (* (+ (PI) (PI)) n)) (pow (* (+ (PI) (PI)) n) (* 1/2 k)))) #s(hole binary64 (+ (* k (- (* k (- (* -1 (* k (+ (* -1/2 (* (log (* 2 (* n (PI)))) (+ (* -1/4 (/ (* (pow (log (* 2 (* n (PI)))) 2) (sqrt (* 2 (* n (PI))))) (sqrt k))) (* 1/8 (/ (* (pow (log (* 2 (* n (PI)))) 2) (sqrt (* 2 (* n (PI))))) (sqrt k)))))) (+ (* -1/16 (/ (* (pow (log (* 2 (* n (PI)))) 3) (sqrt (* 2 (* n (PI))))) (sqrt k))) (* 1/48 (/ (* (pow (log (* 2 (* n (PI)))) 3) (sqrt (* 2 (* n (PI))))) (sqrt k))))))) (+ (* -1/4 (/ (* (pow (log (* 2 (* n (PI)))) 2) (sqrt (* 2 (* n (PI))))) (sqrt k))) (* 1/8 (/ (* (pow (log (* 2 (* n (PI)))) 2) (sqrt (* 2 (* n (PI))))) (sqrt k)))))) (* 1/2 (/ (* (log (* 2 (* n (PI)))) (sqrt (* 2 (* n (PI))))) (sqrt k))))) (/ (sqrt (* 2 (* n (PI)))) (sqrt k)))))
#s(approx (/ 1 (sqrt k)) #s(hole binary64 (/ 1 (sqrt k))))
#s(approx (sqrt k) #s(hole binary64 (sqrt k)))
#s(approx k #s(hole binary64 k))
#s(approx (/ (sqrt (* (+ (PI) (PI)) n)) (pow (* (+ (PI) (PI)) n) (* 1/2 k))) #s(hole binary64 (sqrt (* 2 (* n (PI))))))
#s(approx (/ (sqrt (* (+ (PI) (PI)) n)) (pow (* (+ (PI) (PI)) n) (* 1/2 k))) #s(hole binary64 (+ (sqrt (* 2 (* n (PI)))) (* -1/2 (* k (* (log (* 2 (* n (PI)))) (sqrt (* 2 (* n (PI))))))))))
#s(approx (/ (sqrt (* (+ (PI) (PI)) n)) (pow (* (+ (PI) (PI)) n) (* 1/2 k))) #s(hole binary64 (+ (sqrt (* 2 (* n (PI)))) (* k (- (* -1 (* k (+ (* -1/4 (* (pow (log (* 2 (* n (PI)))) 2) (sqrt (* 2 (* n (PI)))))) (* 1/8 (* (pow (log (* 2 (* n (PI)))) 2) (sqrt (* 2 (* n (PI))))))))) (* 1/2 (* (log (* 2 (* n (PI)))) (sqrt (* 2 (* n (PI)))))))))))
#s(approx (/ (sqrt (* (+ (PI) (PI)) n)) (pow (* (+ (PI) (PI)) n) (* 1/2 k))) #s(hole binary64 (+ (sqrt (* 2 (* n (PI)))) (* k (- (* k (- (* -1 (* k (+ (* -1/2 (* (log (* 2 (* n (PI)))) (+ (* -1/4 (* (pow (log (* 2 (* n (PI)))) 2) (sqrt (* 2 (* n (PI)))))) (* 1/8 (* (pow (log (* 2 (* n (PI)))) 2) (sqrt (* 2 (* n (PI))))))))) (+ (* -1/16 (* (pow (log (* 2 (* n (PI)))) 3) (sqrt (* 2 (* n (PI)))))) (* 1/48 (* (pow (log (* 2 (* n (PI)))) 3) (sqrt (* 2 (* n (PI)))))))))) (+ (* -1/4 (* (pow (log (* 2 (* n (PI)))) 2) (sqrt (* 2 (* n (PI)))))) (* 1/8 (* (pow (log (* 2 (* n (PI)))) 2) (sqrt (* 2 (* n (PI))))))))) (* 1/2 (* (log (* 2 (* n (PI)))) (sqrt (* 2 (* n (PI)))))))))))
#s(approx (pow (* (+ (PI) (PI)) n) (* 1/2 k)) #s(hole binary64 1))
#s(approx (pow (* (+ (PI) (PI)) n) (* 1/2 k)) #s(hole binary64 (+ 1 (* 1/2 (* k (log (* 2 (* n (PI)))))))))
#s(approx (pow (* (+ (PI) (PI)) n) (* 1/2 k)) #s(hole binary64 (+ 1 (* k (+ (* 1/8 (* k (pow (log (* 2 (* n (PI)))) 2))) (* 1/2 (log (* 2 (* n (PI))))))))))
#s(approx (pow (* (+ (PI) (PI)) n) (* 1/2 k)) #s(hole binary64 (+ 1 (* k (+ (* 1/2 (log (* 2 (* n (PI))))) (* k (+ (* 1/48 (* k (pow (log (* 2 (* n (PI)))) 3))) (* 1/8 (pow (log (* 2 (* n (PI)))) 2)))))))))
#s(approx (* 1/2 k) #s(hole binary64 (* 1/2 k)))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) #s(hole binary64 (/ (pow (* 2 (* n (PI))) 1/2) (sqrt k))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) #s(hole binary64 (+ (* -1/2 (/ (* k (* (log (* 2 (* n (PI)))) (pow (* 2 (* n (PI))) 1/2))) (sqrt k))) (/ (pow (* 2 (* n (PI))) 1/2) (sqrt k)))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) #s(hole binary64 (+ (* k (+ (* -1/2 (/ (* (log (* 2 (* n (PI)))) (pow (* 2 (* n (PI))) 1/2)) (sqrt k))) (* 1/8 (/ (* k (* (pow (log (* 2 (* n (PI)))) 2) (pow (* 2 (* n (PI))) 1/2))) (sqrt k))))) (/ (pow (* 2 (* n (PI))) 1/2) (sqrt k)))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) #s(hole binary64 (+ (* k (+ (* -1/2 (/ (* (log (* 2 (* n (PI)))) (pow (* 2 (* n (PI))) 1/2)) (sqrt k))) (* k (+ (* -1/48 (/ (* k (* (pow (log (* 2 (* n (PI)))) 3) (pow (* 2 (* n (PI))) 1/2))) (sqrt k))) (* 1/8 (/ (* (pow (log (* 2 (* n (PI)))) 2) (pow (* 2 (* n (PI))) 1/2)) (sqrt k))))))) (/ (pow (* 2 (* n (PI))) 1/2) (sqrt k)))))
#s(approx (sqrt (/ (* (+ (PI) (PI)) n) k)) #s(hole binary64 (/ (sqrt (* 2 (* k (* n (PI))))) k)))
#s(approx (/ (* (+ (PI) (PI)) n) k) #s(hole binary64 (* 2 (/ (* n (PI)) k))))
#s(approx (* (pow (sqrt (* (+ (PI) (PI)) n)) (- 1 k)) (/ 1 (sqrt k))) #s(hole binary64 (+ (* -1 (/ (* k (* (log (sqrt (* 2 (* n (PI))))) (sqrt (* 2 (* n (PI)))))) (sqrt k))) (/ (sqrt (* 2 (* n (PI)))) (sqrt k)))))
#s(approx (* (pow (sqrt (* (+ (PI) (PI)) n)) (- 1 k)) (/ 1 (sqrt k))) #s(hole binary64 (+ (* k (+ (* -1 (/ (* (log (sqrt (* 2 (* n (PI))))) (sqrt (* 2 (* n (PI))))) (sqrt k))) (* 1/2 (/ (* k (* (pow (log (sqrt (* 2 (* n (PI))))) 2) (sqrt (* 2 (* n (PI)))))) (sqrt k))))) (/ (sqrt (* 2 (* n (PI)))) (sqrt k)))))
#s(approx (* (pow (sqrt (* (+ (PI) (PI)) n)) (- 1 k)) (/ 1 (sqrt k))) #s(hole binary64 (+ (* k (+ (* -1 (/ (* (log (sqrt (* 2 (* n (PI))))) (sqrt (* 2 (* n (PI))))) (sqrt k))) (* k (+ (* -1/6 (/ (* k (* (pow (log (sqrt (* 2 (* n (PI))))) 3) (sqrt (* 2 (* n (PI)))))) (sqrt k))) (* 1/2 (/ (* (pow (log (sqrt (* 2 (* n (PI))))) 2) (sqrt (* 2 (* n (PI))))) (sqrt k))))))) (/ (sqrt (* 2 (* n (PI)))) (sqrt k)))))
#s(approx (pow (sqrt (* (+ (PI) (PI)) n)) (- 1 k)) #s(hole binary64 (+ (sqrt (* 2 (* n (PI)))) (* -1 (* k (* (log (sqrt (* 2 (* n (PI))))) (sqrt (* 2 (* n (PI))))))))))
#s(approx (pow (sqrt (* (+ (PI) (PI)) n)) (- 1 k)) #s(hole binary64 (+ (sqrt (* 2 (* n (PI)))) (* k (+ (* -1 (* (log (sqrt (* 2 (* n (PI))))) (sqrt (* 2 (* n (PI)))))) (* 1/2 (* k (* (pow (log (sqrt (* 2 (* n (PI))))) 2) (sqrt (* 2 (* n (PI))))))))))))
#s(approx (pow (sqrt (* (+ (PI) (PI)) n)) (- 1 k)) #s(hole binary64 (+ (sqrt (* 2 (* n (PI)))) (* k (+ (* -1 (* (log (sqrt (* 2 (* n (PI))))) (sqrt (* 2 (* n (PI)))))) (* k (+ (* -1/6 (* k (* (pow (log (sqrt (* 2 (* n (PI))))) 3) (sqrt (* 2 (* n (PI))))))) (* 1/2 (* (pow (log (sqrt (* 2 (* n (PI))))) 2) (sqrt (* 2 (* n (PI)))))))))))))
#s(approx (- 1 k) #s(hole binary64 (+ 1 (* -1 k))))
#s(approx (* (sqrt (/ 1 k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) #s(hole binary64 (/ (* (sqrt k) (pow (* 2 (* n (PI))) 1/2)) k)))
#s(approx (* (sqrt (/ 1 k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) #s(hole binary64 (/ (+ (* -1/2 (* k (* (log (* 2 (* n (PI)))) (* (sqrt k) (pow (* 2 (* n (PI))) 1/2))))) (* (sqrt k) (pow (* 2 (* n (PI))) 1/2))) k)))
#s(approx (* (sqrt (/ 1 k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) #s(hole binary64 (/ (+ (* k (+ (* -1/2 (* (log (* 2 (* n (PI)))) (* (sqrt k) (pow (* 2 (* n (PI))) 1/2)))) (* 1/8 (* k (* (pow (log (* 2 (* n (PI)))) 2) (* (sqrt k) (pow (* 2 (* n (PI))) 1/2))))))) (* (sqrt k) (pow (* 2 (* n (PI))) 1/2))) k)))
#s(approx (* (sqrt (/ 1 k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) #s(hole binary64 (/ (+ (* k (+ (* -1/2 (* (log (* 2 (* n (PI)))) (* (sqrt k) (pow (* 2 (* n (PI))) 1/2)))) (* k (+ (* -1/48 (* k (* (pow (log (* 2 (* n (PI)))) 3) (* (sqrt k) (pow (* 2 (* n (PI))) 1/2))))) (* 1/8 (* (pow (log (* 2 (* n (PI)))) 2) (* (sqrt k) (pow (* 2 (* n (PI))) 1/2)))))))) (* (sqrt k) (pow (* 2 (* n (PI))) 1/2))) k)))
#s(approx (sqrt (/ 1 k)) #s(hole binary64 (/ (sqrt k) k)))
#s(approx (/ 1 k) #s(hole binary64 (/ 1 k)))
#s(approx (pow (* (* 2 (PI)) n) (/ (- 1 k) 2)) #s(hole binary64 (pow (* 2 (* n (PI))) 1/2)))
#s(approx (pow (* (* 2 (PI)) n) (/ (- 1 k) 2)) #s(hole binary64 (+ (* -1/2 (* k (* (log (* 2 (* n (PI)))) (pow (* 2 (* n (PI))) 1/2)))) (pow (* 2 (* n (PI))) 1/2))))
#s(approx (pow (* (* 2 (PI)) n) (/ (- 1 k) 2)) #s(hole binary64 (+ (* k (+ (* -1/2 (* (log (* 2 (* n (PI)))) (pow (* 2 (* n (PI))) 1/2))) (* 1/8 (* k (* (pow (log (* 2 (* n (PI)))) 2) (pow (* 2 (* n (PI))) 1/2)))))) (pow (* 2 (* n (PI))) 1/2))))
#s(approx (pow (* (* 2 (PI)) n) (/ (- 1 k) 2)) #s(hole binary64 (+ (* k (+ (* -1/2 (* (log (* 2 (* n (PI)))) (pow (* 2 (* n (PI))) 1/2))) (* k (+ (* -1/48 (* k (* (pow (log (* 2 (* n (PI)))) 3) (pow (* 2 (* n (PI))) 1/2)))) (* 1/8 (* (pow (log (* 2 (* n (PI)))) 2) (pow (* 2 (* n (PI))) 1/2))))))) (pow (* 2 (* n (PI))) 1/2))))
#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 (* k (neg (log (sqrt (* (+ (PI) (PI)) n))))) #s(hole binary64 (* -1 (* k (log (sqrt (* 2 (* n (PI)))))))))
#s(approx (* (/ 1 (sqrt k)) (/ (sqrt (* (+ (PI) (PI)) n)) (pow (* (+ (PI) (PI)) n) (* 1/2 k)))) #s(hole binary64 (/ (sqrt (* 2 (* n (PI)))) (* k (* (exp (* 1/2 (* k (log (* 2 (* n (PI))))))) (sqrt (/ 1 k)))))))
#s(approx (/ 1 (sqrt k)) #s(hole binary64 (/ 1 (* k (sqrt (/ 1 k))))))
#s(approx (sqrt k) #s(hole binary64 (* k (sqrt (/ 1 k)))))
#s(approx (/ (sqrt (* (+ (PI) (PI)) n)) (pow (* (+ (PI) (PI)) n) (* 1/2 k))) #s(hole binary64 (/ (sqrt (* 2 (* n (PI)))) (exp (* 1/2 (* k (log (* 2 (* n (PI))))))))))
#s(approx (pow (* (+ (PI) (PI)) n) (* 1/2 k)) #s(hole binary64 (exp (* 1/2 (* k (log (* 2 (* n (PI)))))))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) #s(hole binary64 (/ (exp (* 1/2 (* (log (* 2 (* n (PI)))) (- 1 k)))) (* k (sqrt (/ 1 k))))))
#s(approx (sqrt (/ (* (+ (PI) (PI)) n) k)) #s(hole binary64 (sqrt (* 2 (/ (* n (PI)) k)))))
#s(approx (* (pow (sqrt (* (+ (PI) (PI)) n)) (- 1 k)) (/ 1 (sqrt k))) #s(hole binary64 (/ (exp (* (log (sqrt (* 2 (* n (PI))))) (- 1 k))) (* k (sqrt (/ 1 k))))))
#s(approx (pow (sqrt (* (+ (PI) (PI)) n)) (- 1 k)) #s(hole binary64 (exp (* (log (sqrt (* 2 (* n (PI))))) (- 1 k)))))
#s(approx (- 1 k) #s(hole binary64 (* -1 k)))
#s(approx (- 1 k) #s(hole binary64 (* k (- (/ 1 k) 1))))
#s(approx (* (sqrt (/ 1 k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) #s(hole binary64 (* (exp (* 1/2 (* (log (* 2 (* n (PI)))) (- 1 k)))) (sqrt (/ 1 k)))))
#s(approx (sqrt (/ 1 k)) #s(hole binary64 (sqrt (/ 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 (/ (+ (* (* k (neg (log (sqrt (* (+ (PI) (PI)) n))))) (sqrt (* (+ (PI) (PI)) n))) (sqrt (* (+ (PI) (PI)) n))) (sqrt k)) #s(hole binary64 (* -1 (/ (* (log (sqrt (* 2 (* n (PI))))) (sqrt (* 2 (* n (PI))))) (sqrt (/ 1 k))))))
#s(approx (/ (+ (* (* k (neg (log (sqrt (* (+ (PI) (PI)) n))))) (sqrt (* (+ (PI) (PI)) n))) (sqrt (* (+ (PI) (PI)) n))) (sqrt k)) #s(hole binary64 (+ (* -1 (/ (* (log (sqrt (* 2 (* n (PI))))) (sqrt (* 2 (* n (PI))))) (sqrt (/ 1 k)))) (/ (sqrt (* 2 (* n (PI)))) (* k (sqrt (/ 1 k)))))))
#s(approx (+ (* (* k (neg (log (sqrt (* (+ (PI) (PI)) n))))) (sqrt (* (+ (PI) (PI)) n))) (sqrt (* (+ (PI) (PI)) n))) #s(hole binary64 (* -1 (* k (* (log (sqrt (* 2 (* n (PI))))) (sqrt (* 2 (* n (PI)))))))))
#s(approx (+ (* (* k (neg (log (sqrt (* (+ (PI) (PI)) n))))) (sqrt (* (+ (PI) (PI)) n))) (sqrt (* (+ (PI) (PI)) n))) #s(hole binary64 (* k (+ (* -1 (* (log (sqrt (* 2 (* n (PI))))) (sqrt (* 2 (* n (PI)))))) (/ (sqrt (* 2 (* n (PI)))) k)))))
#s(approx (* (/ 1 (sqrt k)) (/ (sqrt (* (+ (PI) (PI)) n)) (pow (* (+ (PI) (PI)) n) (* 1/2 k)))) #s(hole binary64 (* -1 (/ (sqrt (* 2 (* n (PI)))) (* k (* (exp (* 1/2 (* k (log (* 2 (* n (PI))))))) (sqrt (/ 1 k))))))))
#s(approx (/ 1 (sqrt k)) #s(hole binary64 (/ -1 (* k (sqrt (/ 1 k))))))
#s(approx (sqrt k) #s(hole binary64 (* -1 (* k (sqrt (/ 1 k))))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) #s(hole binary64 (* -1 (/ (exp (* 1/2 (* (log (* 2 (* n (PI)))) (+ 1 (* -1 k))))) (* k (sqrt (/ 1 k)))))))
#s(approx (* (pow (sqrt (* (+ (PI) (PI)) n)) (- 1 k)) (/ 1 (sqrt k))) #s(hole binary64 (* -1 (/ (exp (* (log (sqrt (* 2 (* n (PI))))) (+ 1 (* -1 k)))) (* k (sqrt (/ 1 k)))))))
#s(approx (pow (sqrt (* (+ (PI) (PI)) n)) (- 1 k)) #s(hole binary64 (exp (* (log (sqrt (* 2 (* n (PI))))) (+ 1 (* -1 k))))))
#s(approx (- 1 k) #s(hole binary64 (* -1 (* k (- 1 (/ 1 k))))))
#s(approx (* (sqrt (/ 1 k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) #s(hole binary64 (* (exp (* 1/2 (* (log (* 2 (* n (PI)))) (+ 1 (* -1 k))))) (sqrt (/ 1 k)))))
#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 (/ (+ (* (* k (neg (log (sqrt (* (+ (PI) (PI)) n))))) (sqrt (* (+ (PI) (PI)) n))) (sqrt (* (+ (PI) (PI)) n))) (sqrt k)) #s(hole binary64 (/ (* (log (sqrt (* 2 (* n (PI))))) (sqrt (* 2 (* n (PI))))) (sqrt (/ 1 k)))))
#s(approx (/ (+ (* (* k (neg (log (sqrt (* (+ (PI) (PI)) n))))) (sqrt (* (+ (PI) (PI)) n))) (sqrt (* (+ (PI) (PI)) n))) (sqrt k)) #s(hole binary64 (+ (* -1 (/ (sqrt (* 2 (* n (PI)))) (* k (sqrt (/ 1 k))))) (/ (* (log (sqrt (* 2 (* n (PI))))) (sqrt (* 2 (* n (PI))))) (sqrt (/ 1 k))))))
#s(approx (+ (* (* k (neg (log (sqrt (* (+ (PI) (PI)) n))))) (sqrt (* (+ (PI) (PI)) n))) (sqrt (* (+ (PI) (PI)) n))) #s(hole binary64 (* -1 (* k (+ (* -1 (/ (sqrt (* 2 (* n (PI)))) k)) (* (log (sqrt (* 2 (* n (PI))))) (sqrt (* 2 (* n (PI))))))))))
#s(approx (* (/ 1 (sqrt k)) (/ (sqrt (* (+ (PI) (PI)) n)) (pow (* (+ (PI) (PI)) n) (* 1/2 k)))) #s(hole binary64 (/ (sqrt (* 2 (* n (PI)))) (* (exp (* 1/2 (* k (+ (log n) (log (* 2 (PI))))))) (sqrt k)))))
#s(approx (/ (sqrt (* (+ (PI) (PI)) n)) (pow (* (+ (PI) (PI)) n) (* 1/2 k))) #s(hole binary64 (/ (sqrt (* 2 (* n (PI)))) (exp (* 1/2 (* k (+ (log n) (log (* 2 (PI))))))))))
#s(approx (* (+ (PI) (PI)) n) #s(hole binary64 (* 2 (* n (PI)))))
#s(approx n #s(hole binary64 n))
#s(approx (pow (* (+ (PI) (PI)) n) (* 1/2 k)) #s(hole binary64 (exp (* 1/2 (* k (+ (log n) (log (* 2 (PI)))))))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) #s(hole binary64 (/ (exp (* 1/2 (* (+ (log n) (log (* 2 (PI)))) (- 1 k)))) (sqrt k))))
#s(approx (* (pow (sqrt (* (+ (PI) (PI)) n)) (- 1 k)) (/ 1 (sqrt k))) #s(hole binary64 (/ (exp (* (log (sqrt (* 2 (* n (PI))))) (- 1 k))) (sqrt k))))
#s(approx (* (sqrt (/ 1 k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) #s(hole binary64 (* (exp (* 1/2 (* (+ (log n) (log (* 2 (PI)))) (- 1 k)))) (sqrt (/ 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 (/ (+ (* (* k (neg (log (sqrt (* (+ (PI) (PI)) n))))) (sqrt (* (+ (PI) (PI)) n))) (sqrt (* (+ (PI) (PI)) n))) (sqrt k)) #s(hole binary64 (/ (+ (sqrt (* 2 (* n (PI)))) (* -1 (* k (* (log (sqrt (* 2 (* n (PI))))) (sqrt (* 2 (* n (PI)))))))) (sqrt k))))
#s(approx (neg (log (sqrt (* (+ (PI) (PI)) n)))) #s(hole binary64 (* -1 (log (sqrt (* 2 (* n (PI))))))))
#s(approx (log (sqrt (* (+ (PI) (PI)) n))) #s(hole binary64 (log (sqrt (* 2 (* n (PI)))))))
#s(approx (* (/ 1 (sqrt k)) (/ (sqrt (* (+ (PI) (PI)) n)) (pow (* (+ (PI) (PI)) n) (* 1/2 k)))) #s(hole binary64 (/ (* n (sqrt (* 2 (/ (PI) n)))) (* (exp (* 1/2 (* k (+ (log (* 2 (PI))) (* -1 (log (/ 1 n))))))) (sqrt k)))))
#s(approx (/ (sqrt (* (+ (PI) (PI)) n)) (pow (* (+ (PI) (PI)) n) (* 1/2 k))) #s(hole binary64 (/ (* n (sqrt (* 2 (/ (PI) n)))) (exp (* 1/2 (* k (+ (log (* 2 (PI))) (* -1 (log (/ 1 n))))))))))
#s(approx (sqrt (* (+ (PI) (PI)) n)) #s(hole binary64 (* n (sqrt (* 2 (/ (PI) n))))))
#s(approx (pow (* (+ (PI) (PI)) n) (* 1/2 k)) #s(hole binary64 (exp (* 1/2 (* k (+ (log (* 2 (PI))) (* -1 (log (/ 1 n)))))))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) #s(hole binary64 (/ (exp (* 1/2 (* (+ (log (* 2 (PI))) (* -1 (log (/ 1 n)))) (- 1 k)))) (sqrt k))))
#s(approx (sqrt (/ (* (+ (PI) (PI)) n) k)) #s(hole binary64 (* n (sqrt (* 2 (/ (PI) (* k n)))))))
#s(approx (* (pow (sqrt (* (+ (PI) (PI)) n)) (- 1 k)) (/ 1 (sqrt k))) #s(hole binary64 (/ (exp (* (+ (log (sqrt (* 2 (/ (PI) n)))) (* -1 (log (/ 1 n)))) (- 1 k))) (sqrt k))))
#s(approx (pow (sqrt (* (+ (PI) (PI)) n)) (- 1 k)) #s(hole binary64 (exp (* (+ (log (sqrt (* 2 (/ (PI) n)))) (* -1 (log (/ 1 n)))) (- 1 k)))))
#s(approx (* (sqrt (/ 1 k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) #s(hole binary64 (* (exp (* 1/2 (* (+ (log (* 2 (PI))) (* -1 (log (/ 1 n)))) (- 1 k)))) (sqrt (/ 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 (/ (+ (* (* k (neg (log (sqrt (* (+ (PI) (PI)) n))))) (sqrt (* (+ (PI) (PI)) n))) (sqrt (* (+ (PI) (PI)) n))) (sqrt k)) #s(hole binary64 (/ (* n (+ (sqrt (* 2 (/ (PI) n))) (* -1 (* k (* (sqrt (* 2 (/ (PI) n))) (+ (log (sqrt (* 2 (/ (PI) n)))) (* -1 (log (/ 1 n))))))))) (sqrt k))))
#s(approx (+ (* (* k (neg (log (sqrt (* (+ (PI) (PI)) n))))) (sqrt (* (+ (PI) (PI)) n))) (sqrt (* (+ (PI) (PI)) n))) #s(hole binary64 (* n (+ (sqrt (* 2 (/ (PI) n))) (* -1 (* k (* (sqrt (* 2 (/ (PI) n))) (+ (log (sqrt (* 2 (/ (PI) n)))) (* -1 (log (/ 1 n)))))))))))
#s(approx (* k (neg (log (sqrt (* (+ (PI) (PI)) n))))) #s(hole binary64 (* -1 (* k (+ (log (sqrt (* 2 (/ (PI) n)))) (* -1 (log (/ 1 n))))))))
#s(approx (neg (log (sqrt (* (+ (PI) (PI)) n)))) #s(hole binary64 (* -1 (+ (log (sqrt (* 2 (/ (PI) n)))) (* -1 (log (/ 1 n)))))))
#s(approx (log (sqrt (* (+ (PI) (PI)) n))) #s(hole binary64 (+ (log (sqrt (* 2 (/ (PI) n)))) (* -1 (log (/ 1 n))))))
#s(approx (* (/ 1 (sqrt k)) (/ (sqrt (* (+ (PI) (PI)) n)) (pow (* (+ (PI) (PI)) n) (* 1/2 k)))) #s(hole binary64 (* -1 (/ (* n (sqrt (* 2 (/ (PI) n)))) (* (exp (* 1/2 (* k (+ (log (* -2 (PI))) (* -1 (log (/ -1 n))))))) (sqrt k))))))
#s(approx (/ (sqrt (* (+ (PI) (PI)) n)) (pow (* (+ (PI) (PI)) n) (* 1/2 k))) #s(hole binary64 (* -1 (/ (* n (sqrt (* 2 (/ (PI) n)))) (exp (* 1/2 (* k (+ (log (* -2 (PI))) (* -1 (log (/ -1 n)))))))))))
#s(approx (sqrt (* (+ (PI) (PI)) n)) #s(hole binary64 (* -1 (* n (sqrt (* 2 (/ (PI) n)))))))
#s(approx (pow (* (+ (PI) (PI)) n) (* 1/2 k)) #s(hole binary64 (exp (* 1/2 (* k (+ (log (* -2 (PI))) (* -1 (log (/ -1 n)))))))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) #s(hole binary64 (/ (exp (* 1/2 (* (+ (log (* -2 (PI))) (* -1 (log (/ -1 n)))) (- 1 k)))) (sqrt k))))
#s(approx (sqrt (/ (* (+ (PI) (PI)) n) k)) #s(hole binary64 (* -1 (* n (sqrt (* 2 (/ (PI) (* k n))))))))
#s(approx (* (pow (sqrt (* (+ (PI) (PI)) n)) (- 1 k)) (/ 1 (sqrt k))) #s(hole binary64 (/ (exp (* (+ (log (sqrt (* 2 (/ (PI) n)))) (* -1 (log (/ -1 n)))) (- 1 k))) (sqrt k))))
#s(approx (pow (sqrt (* (+ (PI) (PI)) n)) (- 1 k)) #s(hole binary64 (exp (* (+ (log (sqrt (* 2 (/ (PI) n)))) (* -1 (log (/ -1 n)))) (- 1 k)))))
#s(approx (* (sqrt (/ 1 k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) #s(hole binary64 (* (exp (* 1/2 (* (+ (log (* -2 (PI))) (* -1 (log (/ -1 n)))) (- 1 k)))) (sqrt (/ 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 (/ (+ (* (* k (neg (log (sqrt (* (+ (PI) (PI)) n))))) (sqrt (* (+ (PI) (PI)) n))) (sqrt (* (+ (PI) (PI)) n))) (sqrt k)) #s(hole binary64 (* -1 (/ (* n (+ (sqrt (* 2 (/ (PI) n))) (* -1 (* k (* (sqrt (* 2 (/ (PI) n))) (+ (log (sqrt (* 2 (/ (PI) n)))) (* -1 (log (/ -1 n))))))))) (sqrt k)))))
#s(approx (+ (* (* k (neg (log (sqrt (* (+ (PI) (PI)) n))))) (sqrt (* (+ (PI) (PI)) n))) (sqrt (* (+ (PI) (PI)) n))) #s(hole binary64 (* -1 (* n (+ (sqrt (* 2 (/ (PI) n))) (* -1 (* k (* (sqrt (* 2 (/ (PI) n))) (+ (log (sqrt (* 2 (/ (PI) n)))) (* -1 (log (/ -1 n))))))))))))
#s(approx (* k (neg (log (sqrt (* (+ (PI) (PI)) n))))) #s(hole binary64 (* -1 (* k (+ (log (sqrt (* 2 (/ (PI) n)))) (* -1 (log (/ -1 n))))))))
#s(approx (neg (log (sqrt (* (+ (PI) (PI)) n)))) #s(hole binary64 (* -1 (+ (log (sqrt (* 2 (/ (PI) n)))) (* -1 (log (/ -1 n)))))))
#s(approx (log (sqrt (* (+ (PI) (PI)) n))) #s(hole binary64 (+ (log (sqrt (* 2 (/ (PI) n)))) (* -1 (log (/ -1 n))))))

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

eval89.0ms (1.5%)

Memory: -2.0MiB live, 102.0MiB allocated; 22ms collecting garbage
Compiler: Compiled 10 037 to 2 164 computations (78.4% saved)

prune40.0ms (0.7%)

Memory

1.3MiB live, 48.7MiB allocated; 2ms collecting garbage

Pruning

26 alts after pruning (24 fresh and 2 done)

	Pruned	Kept	Total
New	521	19	540
Fresh	4	5	9
Picked	3	2	5
Done	0	0	0
Total	528	26	554

Accuracy

100.0%

Counts

554 → 26

Alt Table

Click to see full alt table

Status	Accuracy	Program
▶	99.5%	(/.f64 (pow.f64 (sqrt.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n)) (-.f64 #s(literal 1 binary64) k)) (sqrt.f64 k))
	99.7%	(/.f64 (.f64 (sqrt.f64 (.f64 (+.f64 (PI.f64) (PI.f64)) n)) #s(literal 1 binary64)) (.f64 (pow.f64 (sqrt.f64 (.f64 (+.f64 (PI.f64) (PI.f64)) n)) k) (sqrt.f64 k)))
	99.5%	(/.f64 (.f64 #s(literal 1 binary64) (pow.f64 (.f64 (+.f64 (PI.f64) (PI.f64)) n) (fma.f64 #s(literal -1/2 binary64) k #s(literal 1/2 binary64)))) (sqrt.f64 k))
	78.2%	(/.f64 (sqrt.f64 (.f64 (/.f64 #s(literal 1 binary64) k) (.f64 (+.f64 (PI.f64) (PI.f64)) n))) (pow.f64 (.f64 (+.f64 (PI.f64) (PI.f64)) n) (.f64 #s(literal 1/2 binary64) k)))
✓	99.4%	(.f64 (pow.f64 (sqrt.f64 (.f64 (+.f64 (PI.f64) (PI.f64)) n)) (-.f64 #s(literal 1 binary64) k)) (/.f64 #s(literal 1 binary64) (sqrt.f64 k)))
	99.5%	(.f64 (pow.f64 (sqrt.f64 (.f64 (+.f64 (PI.f64) (PI.f64)) n)) (-.f64 #s(literal 1 binary64) k)) (sqrt.f64 (/.f64 #s(literal 1 binary64) k)))
	55.5%	(.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) (/.f64 (sqrt.f64 (.f64 (+.f64 (PI.f64) (PI.f64)) n)) #s(approx (pow (* (+ (PI) (PI)) n) (* 1/2 k)) (fma.f64 (.f64 (log.f64 (.f64 (+.f64 (PI.f64) (PI.f64)) n)) k) #s(literal 1/2 binary64) #s(literal 1 binary64)))))
▶	96.5%	(.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) (exp.f64 (.f64 (log.f64 (sqrt.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n))) (-.f64 #s(literal 1 binary64) k))))
	51.6%	(.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))))
▶	99.7%	(.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) k)) (/.f64 (sqrt.f64 (.f64 (+.f64 (PI.f64) (PI.f64)) n)) (pow.f64 (.f64 (+.f64 (PI.f64) (PI.f64)) n) (.f64 #s(literal 1/2 binary64) k))))
▶	51.7%	(.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))))
	99.5%	(.f64 #s(approx (/ 1 (sqrt k)) (/.f64 (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))))
	99.5%	#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (/.f64 (pow.f64 (sqrt.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n)) (-.f64 #s(literal 1 binary64) k)) (/.f64 k (sqrt.f64 k))))
	52.3%	#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (/.f64 (.f64 (fma.f64 (neg.f64 k) (log.f64 (sqrt.f64 (.f64 (+.f64 (PI.f64) (PI.f64)) n))) #s(literal 1 binary64)) (sqrt.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n))) (sqrt.f64 k)))
	51.7%	#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (/.f64 (sqrt.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n)) (sqrt.f64 k)))
	41.7%	#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (.f64 (sqrt.f64 (/.f64 (.f64 (PI.f64) n) k)) (sqrt.f64 #s(literal 2 binary64))))
	41.5%	#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (*.f64 (sqrt.f64 (+.f64 (PI.f64) (PI.f64))) (sqrt.f64 (/.f64 n k))))
✓	41.8%	#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt.f64 (/.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n) k)))
	24.0%	#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt.f64 (/.f64 (.f64 (.f64 (.f64 (PI.f64) n) k) #s(literal 2 binary64)) (.f64 k k))))
	41.8%	#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt.f64 (/.f64 (.f64 (sqrt.f64 (.f64 (+.f64 (PI.f64) (PI.f64)) n)) (sqrt.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n))) k)))
	27.0%	#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt.f64 (/.f64 (sqrt.f64 (.f64 (.f64 (+.f64 (PI.f64) (PI.f64)) n) (*.f64 (+.f64 (PI.f64) (PI.f64)) n))) k)))
▶	41.8%	#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) (/.f64 n k))))
	39.3%	#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (exp.f64 (.f64 (log.f64 (.f64 (+.f64 (PI.f64) (PI.f64)) (/.f64 n k))) #s(literal 1/2 binary64))))
	47.2%	#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) #s(approx (/ (+ (* (* k (neg (log (sqrt (* (+ (PI) (PI)) n))))) (sqrt (* (+ (PI) (PI)) n))) (sqrt (* (+ (PI) (PI)) n))) (sqrt k)) (/.f64 (fma.f64 (neg.f64 (log.f64 (sqrt.f64 (.f64 (+.f64 (PI.f64) (PI.f64)) n)))) (sqrt.f64 (.f64 (+.f64 (PI.f64) (PI.f64)) n)) (/.f64 (sqrt.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n)) k)) (/.f64 #s(literal 1 binary64) (sqrt.f64 k)))))
	50.6%	#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) #s(approx (sqrt (/ (* (+ (PI) (PI)) n) k)) (.f64 (sqrt.f64 (/.f64 (+.f64 (PI.f64) (PI.f64)) (.f64 n k))) n)))
	39.9%	#s(approx (* (sqrt (/ 1 k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (/.f64 (sqrt.f64 (.f64 (.f64 (+.f64 (PI.f64) (PI.f64)) n) k)) k))

Compiler

Compiled 1 115 to 955 computations (14.3% saved)

series95.0ms (1.6%)

Memory

-6.3MiB live, 93.6MiB allocated; 10ms collecting garbage

Counts

29 → 102

Calls

Call 1

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

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

Calls

6 calls:

Time	Variable		Point	Expression
31.0ms	n	@	0	((* (sqrt (/ 1 k)) (/ (sqrt (* (+ (PI) (PI)) n)) (pow (* (+ (PI) (PI)) n) (* 1/2 k)))) (sqrt (/ 1 k)) (/ 1 k) 1 k (/ (sqrt (* (+ (PI) (PI)) n)) (pow (* (+ (PI) (PI)) n) (* 1/2 k))) (sqrt (* (+ (PI) (PI)) n)) (* (+ (PI) (PI)) n) (+ (PI) (PI)) (PI) n (pow (* (+ (PI) (PI)) n) (* 1/2 k)) (* 1/2 k) 1/2 (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt (* (+ (PI) (PI)) (/ n k))) (* (+ (PI) (PI)) (/ n k)) (/ n k) (* (sqrt (/ 1 k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2)) (/ (pow (sqrt (* (+ (PI) (PI)) n)) (- 1 k)) (sqrt k)) (pow (sqrt (* (+ (PI) (PI)) n)) (- 1 k)) (- 1 k) (sqrt k) (* (/ 1 (sqrt k)) (exp (* (log (sqrt (* (+ (PI) (PI)) n))) (- 1 k)))) (/ 1 (sqrt k)) (exp (* (log (sqrt (* (+ (PI) (PI)) n))) (- 1 k))) (* (log (sqrt (* (+ (PI) (PI)) n))) (- 1 k)) (log (sqrt (* (+ (PI) (PI)) n))))
26.0ms	n	@	-inf	((* (sqrt (/ 1 k)) (/ (sqrt (* (+ (PI) (PI)) n)) (pow (* (+ (PI) (PI)) n) (* 1/2 k)))) (sqrt (/ 1 k)) (/ 1 k) 1 k (/ (sqrt (* (+ (PI) (PI)) n)) (pow (* (+ (PI) (PI)) n) (* 1/2 k))) (sqrt (* (+ (PI) (PI)) n)) (* (+ (PI) (PI)) n) (+ (PI) (PI)) (PI) n (pow (* (+ (PI) (PI)) n) (* 1/2 k)) (* 1/2 k) 1/2 (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt (* (+ (PI) (PI)) (/ n k))) (* (+ (PI) (PI)) (/ n k)) (/ n k) (* (sqrt (/ 1 k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2)) (/ (pow (sqrt (* (+ (PI) (PI)) n)) (- 1 k)) (sqrt k)) (pow (sqrt (* (+ (PI) (PI)) n)) (- 1 k)) (- 1 k) (sqrt k) (* (/ 1 (sqrt k)) (exp (* (log (sqrt (* (+ (PI) (PI)) n))) (- 1 k)))) (/ 1 (sqrt k)) (exp (* (log (sqrt (* (+ (PI) (PI)) n))) (- 1 k))) (* (log (sqrt (* (+ (PI) (PI)) n))) (- 1 k)) (log (sqrt (* (+ (PI) (PI)) n))))
18.0ms	n	@	inf	((* (sqrt (/ 1 k)) (/ (sqrt (* (+ (PI) (PI)) n)) (pow (* (+ (PI) (PI)) n) (* 1/2 k)))) (sqrt (/ 1 k)) (/ 1 k) 1 k (/ (sqrt (* (+ (PI) (PI)) n)) (pow (* (+ (PI) (PI)) n) (* 1/2 k))) (sqrt (* (+ (PI) (PI)) n)) (* (+ (PI) (PI)) n) (+ (PI) (PI)) (PI) n (pow (* (+ (PI) (PI)) n) (* 1/2 k)) (* 1/2 k) 1/2 (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt (* (+ (PI) (PI)) (/ n k))) (* (+ (PI) (PI)) (/ n k)) (/ n k) (* (sqrt (/ 1 k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2)) (/ (pow (sqrt (* (+ (PI) (PI)) n)) (- 1 k)) (sqrt k)) (pow (sqrt (* (+ (PI) (PI)) n)) (- 1 k)) (- 1 k) (sqrt k) (* (/ 1 (sqrt k)) (exp (* (log (sqrt (* (+ (PI) (PI)) n))) (- 1 k)))) (/ 1 (sqrt k)) (exp (* (log (sqrt (* (+ (PI) (PI)) n))) (- 1 k))) (* (log (sqrt (* (+ (PI) (PI)) n))) (- 1 k)) (log (sqrt (* (+ (PI) (PI)) n))))
6.0ms	k	@	-inf	((* (sqrt (/ 1 k)) (/ (sqrt (* (+ (PI) (PI)) n)) (pow (* (+ (PI) (PI)) n) (* 1/2 k)))) (sqrt (/ 1 k)) (/ 1 k) 1 k (/ (sqrt (* (+ (PI) (PI)) n)) (pow (* (+ (PI) (PI)) n) (* 1/2 k))) (sqrt (* (+ (PI) (PI)) n)) (* (+ (PI) (PI)) n) (+ (PI) (PI)) (PI) n (pow (* (+ (PI) (PI)) n) (* 1/2 k)) (* 1/2 k) 1/2 (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt (* (+ (PI) (PI)) (/ n k))) (* (+ (PI) (PI)) (/ n k)) (/ n k) (* (sqrt (/ 1 k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2)) (/ (pow (sqrt (* (+ (PI) (PI)) n)) (- 1 k)) (sqrt k)) (pow (sqrt (* (+ (PI) (PI)) n)) (- 1 k)) (- 1 k) (sqrt k) (* (/ 1 (sqrt k)) (exp (* (log (sqrt (* (+ (PI) (PI)) n))) (- 1 k)))) (/ 1 (sqrt k)) (exp (* (log (sqrt (* (+ (PI) (PI)) n))) (- 1 k))) (* (log (sqrt (* (+ (PI) (PI)) n))) (- 1 k)) (log (sqrt (* (+ (PI) (PI)) n))))
5.0ms	k	@	inf	((* (sqrt (/ 1 k)) (/ (sqrt (* (+ (PI) (PI)) n)) (pow (* (+ (PI) (PI)) n) (* 1/2 k)))) (sqrt (/ 1 k)) (/ 1 k) 1 k (/ (sqrt (* (+ (PI) (PI)) n)) (pow (* (+ (PI) (PI)) n) (* 1/2 k))) (sqrt (* (+ (PI) (PI)) n)) (* (+ (PI) (PI)) n) (+ (PI) (PI)) (PI) n (pow (* (+ (PI) (PI)) n) (* 1/2 k)) (* 1/2 k) 1/2 (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt (* (+ (PI) (PI)) (/ n k))) (* (+ (PI) (PI)) (/ n k)) (/ n k) (* (sqrt (/ 1 k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2)) (/ (pow (sqrt (* (+ (PI) (PI)) n)) (- 1 k)) (sqrt k)) (pow (sqrt (* (+ (PI) (PI)) n)) (- 1 k)) (- 1 k) (sqrt k) (* (/ 1 (sqrt k)) (exp (* (log (sqrt (* (+ (PI) (PI)) n))) (- 1 k)))) (/ 1 (sqrt k)) (exp (* (log (sqrt (* (+ (PI) (PI)) n))) (- 1 k))) (* (log (sqrt (* (+ (PI) (PI)) n))) (- 1 k)) (log (sqrt (* (+ (PI) (PI)) n))))

rewrite232.0ms (3.8%)

Memory

-4.5MiB live, 183.9MiB allocated; 28ms collecting garbage

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	481	3931
0	525	3550
1	2476	3388
0	10205	3343

Stop Event

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

Counts

131 → 385

Calls

Call 1

Inputs
(.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) k)) (/.f64 (sqrt.f64 (.f64 (+.f64 (PI.f64) (PI.f64)) n)) (pow.f64 (.f64 (+.f64 (PI.f64) (PI.f64)) n) (.f64 #s(literal 1/2 binary64) k))))
(sqrt.f64 (/.f64 #s(literal 1 binary64) k))
(/.f64 #s(literal 1 binary64) k)
#s(literal 1 binary64)
k
(/.f64 (sqrt.f64 (.f64 (+.f64 (PI.f64) (PI.f64)) n)) (pow.f64 (.f64 (+.f64 (PI.f64) (PI.f64)) n) (*.f64 #s(literal 1/2 binary64) k)))
(sqrt.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n))
(*.f64 (+.f64 (PI.f64) (PI.f64)) n)
(+.f64 (PI.f64) (PI.f64))
(PI.f64)
n
(pow.f64 (.f64 (+.f64 (PI.f64) (PI.f64)) n) (.f64 #s(literal 1/2 binary64) k))
(*.f64 #s(literal 1/2 binary64) k)
#s(literal 1/2 binary64)
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) (/.f64 n k))))
(sqrt.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) (/.f64 n k)))
(*.f64 (+.f64 (PI.f64) (PI.f64)) (/.f64 n k))
(/.f64 n k)
(.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) k)) #s(approx (pow ( (* 2 (PI)) n) (/ (- 1 k) 2)) (sqrt.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n))))
#s(approx (pow (* (* 2 (PI)) n) (/ (- 1 k) 2)) (sqrt.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n)))
(/.f64 (pow.f64 (sqrt.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n)) (-.f64 #s(literal 1 binary64) k)) (sqrt.f64 k))
(pow.f64 (sqrt.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n)) (-.f64 #s(literal 1 binary64) k))
(-.f64 #s(literal 1 binary64) k)
(sqrt.f64 k)
(.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) (exp.f64 (.f64 (log.f64 (sqrt.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n))) (-.f64 #s(literal 1 binary64) k))))
(/.f64 #s(literal 1 binary64) (sqrt.f64 k))
(exp.f64 (.f64 (log.f64 (sqrt.f64 (.f64 (+.f64 (PI.f64) (PI.f64)) n))) (-.f64 #s(literal 1 binary64) k)))
(.f64 (log.f64 (sqrt.f64 (.f64 (+.f64 (PI.f64) (PI.f64)) n))) (-.f64 #s(literal 1 binary64) k))
(log.f64 (sqrt.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n)))
#s(approx (* (sqrt (/ 1 k)) (/ (sqrt (* (+ (PI) (PI)) n)) (pow (* (+ (PI) (PI)) n) (* 1/2 k)))) #s(hole binary64 (/ (* (sqrt k) (sqrt (* 2 (* n (PI))))) k)))
#s(approx (* (sqrt (/ 1 k)) (/ (sqrt (* (+ (PI) (PI)) n)) (pow (* (+ (PI) (PI)) n) (* 1/2 k)))) #s(hole binary64 (/ (+ (* -1/2 (* k (* (log (* 2 (* n (PI)))) (* (sqrt k) (sqrt (* 2 (* n (PI)))))))) (* (sqrt k) (sqrt (* 2 (* n (PI)))))) k)))
#s(approx (* (sqrt (/ 1 k)) (/ (sqrt (* (+ (PI) (PI)) n)) (pow (* (+ (PI) (PI)) n) (* 1/2 k)))) #s(hole binary64 (/ (+ (* k (- (* -1 (* k (+ (* -1/4 (* (pow (log (* 2 (* n (PI)))) 2) (* (sqrt k) (sqrt (* 2 (* n (PI))))))) (* 1/8 (* (pow (log (* 2 (* n (PI)))) 2) (* (sqrt k) (sqrt (* 2 (* n (PI)))))))))) (* 1/2 (* (log (* 2 (* n (PI)))) (* (sqrt k) (sqrt (* 2 (* n (PI))))))))) (* (sqrt k) (sqrt (* 2 (* n (PI)))))) k)))
#s(approx (* (sqrt (/ 1 k)) (/ (sqrt (* (+ (PI) (PI)) n)) (pow (* (+ (PI) (PI)) n) (* 1/2 k)))) #s(hole binary64 (/ (+ (* k (- (* k (- (* -1 (* k (+ (* -1/2 (* (log (* 2 (* n (PI)))) (+ (* -1/4 (* (pow (log (* 2 (* n (PI)))) 2) (* (sqrt k) (sqrt (* 2 (* n (PI))))))) (* 1/8 (* (pow (log (* 2 (* n (PI)))) 2) (* (sqrt k) (sqrt (* 2 (* n (PI)))))))))) (+ (* -1/16 (* (pow (log (* 2 (* n (PI)))) 3) (* (sqrt k) (sqrt (* 2 (* n (PI))))))) (* 1/48 (* (pow (log (* 2 (* n (PI)))) 3) (* (sqrt k) (sqrt (* 2 (* n (PI))))))))))) (+ (* -1/4 (* (pow (log (* 2 (* n (PI)))) 2) (* (sqrt k) (sqrt (* 2 (* n (PI))))))) (* 1/8 (* (pow (log (* 2 (* n (PI)))) 2) (* (sqrt k) (sqrt (* 2 (* n (PI)))))))))) (* 1/2 (* (log (* 2 (* n (PI)))) (* (sqrt k) (sqrt (* 2 (* n (PI))))))))) (* (sqrt k) (sqrt (* 2 (* n (PI)))))) k)))
#s(approx (sqrt (/ 1 k)) #s(hole binary64 (/ (sqrt k) k)))
#s(approx (/ 1 k) #s(hole binary64 (/ 1 k)))
#s(approx k #s(hole binary64 k))
#s(approx (/ (sqrt (* (+ (PI) (PI)) n)) (pow (* (+ (PI) (PI)) n) (* 1/2 k))) #s(hole binary64 (sqrt (* 2 (* n (PI))))))
#s(approx (/ (sqrt (* (+ (PI) (PI)) n)) (pow (* (+ (PI) (PI)) n) (* 1/2 k))) #s(hole binary64 (+ (sqrt (* 2 (* n (PI)))) (* -1/2 (* k (* (log (* 2 (* n (PI)))) (sqrt (* 2 (* n (PI))))))))))
#s(approx (/ (sqrt (* (+ (PI) (PI)) n)) (pow (* (+ (PI) (PI)) n) (* 1/2 k))) #s(hole binary64 (+ (sqrt (* 2 (* n (PI)))) (* k (- (* -1 (* k (+ (* -1/4 (* (pow (log (* 2 (* n (PI)))) 2) (sqrt (* 2 (* n (PI)))))) (* 1/8 (* (pow (log (* 2 (* n (PI)))) 2) (sqrt (* 2 (* n (PI))))))))) (* 1/2 (* (log (* 2 (* n (PI)))) (sqrt (* 2 (* n (PI)))))))))))
#s(approx (/ (sqrt (* (+ (PI) (PI)) n)) (pow (* (+ (PI) (PI)) n) (* 1/2 k))) #s(hole binary64 (+ (sqrt (* 2 (* n (PI)))) (* k (- (* k (- (* -1 (* k (+ (* -1/2 (* (log (* 2 (* n (PI)))) (+ (* -1/4 (* (pow (log (* 2 (* n (PI)))) 2) (sqrt (* 2 (* n (PI)))))) (* 1/8 (* (pow (log (* 2 (* n (PI)))) 2) (sqrt (* 2 (* n (PI))))))))) (+ (* -1/16 (* (pow (log (* 2 (* n (PI)))) 3) (sqrt (* 2 (* n (PI)))))) (* 1/48 (* (pow (log (* 2 (* n (PI)))) 3) (sqrt (* 2 (* n (PI)))))))))) (+ (* -1/4 (* (pow (log (* 2 (* n (PI)))) 2) (sqrt (* 2 (* n (PI)))))) (* 1/8 (* (pow (log (* 2 (* n (PI)))) 2) (sqrt (* 2 (* n (PI))))))))) (* 1/2 (* (log (* 2 (* n (PI)))) (sqrt (* 2 (* n (PI)))))))))))
#s(approx (pow (* (+ (PI) (PI)) n) (* 1/2 k)) #s(hole binary64 1))
#s(approx (pow (* (+ (PI) (PI)) n) (* 1/2 k)) #s(hole binary64 (+ 1 (* 1/2 (* k (log (* 2 (* n (PI)))))))))
#s(approx (pow (* (+ (PI) (PI)) n) (* 1/2 k)) #s(hole binary64 (+ 1 (* k (+ (* 1/8 (* k (pow (log (* 2 (* n (PI)))) 2))) (* 1/2 (log (* 2 (* n (PI))))))))))
#s(approx (pow (* (+ (PI) (PI)) n) (* 1/2 k)) #s(hole binary64 (+ 1 (* k (+ (* 1/2 (log (* 2 (* n (PI))))) (* k (+ (* 1/48 (* k (pow (log (* 2 (* n (PI)))) 3))) (* 1/8 (pow (log (* 2 (* n (PI)))) 2)))))))))
#s(approx (* 1/2 k) #s(hole binary64 (* 1/2 k)))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) #s(hole binary64 (/ (pow (* 2 (* n (PI))) 1/2) (sqrt k))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) #s(hole binary64 (+ (* -1/2 (/ (* k (* (log (* 2 (* n (PI)))) (pow (* 2 (* n (PI))) 1/2))) (sqrt k))) (/ (pow (* 2 (* n (PI))) 1/2) (sqrt k)))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) #s(hole binary64 (+ (* k (+ (* -1/2 (/ (* (log (* 2 (* n (PI)))) (pow (* 2 (* n (PI))) 1/2)) (sqrt k))) (* 1/8 (/ (* k (* (pow (log (* 2 (* n (PI)))) 2) (pow (* 2 (* n (PI))) 1/2))) (sqrt k))))) (/ (pow (* 2 (* n (PI))) 1/2) (sqrt k)))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) #s(hole binary64 (+ (* k (+ (* -1/2 (/ (* (log (* 2 (* n (PI)))) (pow (* 2 (* n (PI))) 1/2)) (sqrt k))) (* k (+ (* -1/48 (/ (* k (* (pow (log (* 2 (* n (PI)))) 3) (pow (* 2 (* n (PI))) 1/2))) (sqrt k))) (* 1/8 (/ (* (pow (log (* 2 (* n (PI)))) 2) (pow (* 2 (* n (PI))) 1/2)) (sqrt k))))))) (/ (pow (* 2 (* n (PI))) 1/2) (sqrt k)))))
#s(approx (sqrt (* (+ (PI) (PI)) (/ n k))) #s(hole binary64 (/ (sqrt (* 2 (* k (* n (PI))))) k)))
#s(approx (* (+ (PI) (PI)) (/ n k)) #s(hole binary64 (* 2 (/ (* n (PI)) k))))
#s(approx (/ n k) #s(hole binary64 (/ n k)))
#s(approx (* (sqrt (/ 1 k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) #s(hole binary64 (/ (* (sqrt k) (pow (* 2 (* n (PI))) 1/2)) k)))
#s(approx (* (sqrt (/ 1 k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) #s(hole binary64 (/ (+ (* -1/2 (* k (* (log (* 2 (* n (PI)))) (* (sqrt k) (pow (* 2 (* n (PI))) 1/2))))) (* (sqrt k) (pow (* 2 (* n (PI))) 1/2))) k)))
#s(approx (* (sqrt (/ 1 k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) #s(hole binary64 (/ (+ (* k (+ (* -1/2 (* (log (* 2 (* n (PI)))) (* (sqrt k) (pow (* 2 (* n (PI))) 1/2)))) (* 1/8 (* k (* (pow (log (* 2 (* n (PI)))) 2) (* (sqrt k) (pow (* 2 (* n (PI))) 1/2))))))) (* (sqrt k) (pow (* 2 (* n (PI))) 1/2))) k)))
#s(approx (* (sqrt (/ 1 k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) #s(hole binary64 (/ (+ (* k (+ (* -1/2 (* (log (* 2 (* n (PI)))) (* (sqrt k) (pow (* 2 (* n (PI))) 1/2)))) (* k (+ (* -1/48 (* k (* (pow (log (* 2 (* n (PI)))) 3) (* (sqrt k) (pow (* 2 (* n (PI))) 1/2))))) (* 1/8 (* (pow (log (* 2 (* n (PI)))) 2) (* (sqrt k) (pow (* 2 (* n (PI))) 1/2)))))))) (* (sqrt k) (pow (* 2 (* n (PI))) 1/2))) k)))
#s(approx (pow (* (* 2 (PI)) n) (/ (- 1 k) 2)) #s(hole binary64 (pow (* 2 (* n (PI))) 1/2)))
#s(approx (pow (* (* 2 (PI)) n) (/ (- 1 k) 2)) #s(hole binary64 (+ (* -1/2 (* k (* (log (* 2 (* n (PI)))) (pow (* 2 (* n (PI))) 1/2)))) (pow (* 2 (* n (PI))) 1/2))))
#s(approx (pow (* (* 2 (PI)) n) (/ (- 1 k) 2)) #s(hole binary64 (+ (* k (+ (* -1/2 (* (log (* 2 (* n (PI)))) (pow (* 2 (* n (PI))) 1/2))) (* 1/8 (* k (* (pow (log (* 2 (* n (PI)))) 2) (pow (* 2 (* n (PI))) 1/2)))))) (pow (* 2 (* n (PI))) 1/2))))
#s(approx (pow (* (* 2 (PI)) n) (/ (- 1 k) 2)) #s(hole binary64 (+ (* k (+ (* -1/2 (* (log (* 2 (* n (PI)))) (pow (* 2 (* n (PI))) 1/2))) (* k (+ (* -1/48 (* k (* (pow (log (* 2 (* n (PI)))) 3) (pow (* 2 (* n (PI))) 1/2)))) (* 1/8 (* (pow (log (* 2 (* n (PI)))) 2) (pow (* 2 (* n (PI))) 1/2))))))) (pow (* 2 (* n (PI))) 1/2))))
#s(approx (/ (pow (sqrt (* (+ (PI) (PI)) n)) (- 1 k)) (sqrt k)) #s(hole binary64 (/ (sqrt (* 2 (* n (PI)))) (sqrt k))))
#s(approx (/ (pow (sqrt (* (+ (PI) (PI)) n)) (- 1 k)) (sqrt k)) #s(hole binary64 (+ (* -1 (/ (* k (* (log (sqrt (* 2 (* n (PI))))) (sqrt (* 2 (* n (PI)))))) (sqrt k))) (/ (sqrt (* 2 (* n (PI)))) (sqrt k)))))
#s(approx (/ (pow (sqrt (* (+ (PI) (PI)) n)) (- 1 k)) (sqrt k)) #s(hole binary64 (+ (* k (+ (* -1 (/ (* (log (sqrt (* 2 (* n (PI))))) (sqrt (* 2 (* n (PI))))) (sqrt k))) (* 1/2 (/ (* k (* (pow (log (sqrt (* 2 (* n (PI))))) 2) (sqrt (* 2 (* n (PI)))))) (sqrt k))))) (/ (sqrt (* 2 (* n (PI)))) (sqrt k)))))
#s(approx (/ (pow (sqrt (* (+ (PI) (PI)) n)) (- 1 k)) (sqrt k)) #s(hole binary64 (+ (* k (+ (* -1 (/ (* (log (sqrt (* 2 (* n (PI))))) (sqrt (* 2 (* n (PI))))) (sqrt k))) (* k (+ (* -1/6 (/ (* k (* (pow (log (sqrt (* 2 (* n (PI))))) 3) (sqrt (* 2 (* n (PI)))))) (sqrt k))) (* 1/2 (/ (* (pow (log (sqrt (* 2 (* n (PI))))) 2) (sqrt (* 2 (* n (PI))))) (sqrt k))))))) (/ (sqrt (* 2 (* n (PI)))) (sqrt k)))))
#s(approx (pow (sqrt (* (+ (PI) (PI)) n)) (- 1 k)) #s(hole binary64 (+ (sqrt (* 2 (* n (PI)))) (* -1 (* k (* (log (sqrt (* 2 (* n (PI))))) (sqrt (* 2 (* n (PI))))))))))
#s(approx (pow (sqrt (* (+ (PI) (PI)) n)) (- 1 k)) #s(hole binary64 (+ (sqrt (* 2 (* n (PI)))) (* k (+ (* -1 (* (log (sqrt (* 2 (* n (PI))))) (sqrt (* 2 (* n (PI)))))) (* 1/2 (* k (* (pow (log (sqrt (* 2 (* n (PI))))) 2) (sqrt (* 2 (* n (PI))))))))))))
#s(approx (pow (sqrt (* (+ (PI) (PI)) n)) (- 1 k)) #s(hole binary64 (+ (sqrt (* 2 (* n (PI)))) (* k (+ (* -1 (* (log (sqrt (* 2 (* n (PI))))) (sqrt (* 2 (* n (PI)))))) (* k (+ (* -1/6 (* k (* (pow (log (sqrt (* 2 (* n (PI))))) 3) (sqrt (* 2 (* n (PI))))))) (* 1/2 (* (pow (log (sqrt (* 2 (* n (PI))))) 2) (sqrt (* 2 (* n (PI)))))))))))))
#s(approx (- 1 k) #s(hole binary64 (+ 1 (* -1 k))))
#s(approx (sqrt k) #s(hole binary64 (sqrt k)))
#s(approx (/ 1 (sqrt k)) #s(hole binary64 (/ 1 (sqrt k))))
#s(approx (* (log (sqrt (* (+ (PI) (PI)) n))) (- 1 k)) #s(hole binary64 (log (sqrt (* 2 (* n (PI)))))))
#s(approx (* (log (sqrt (* (+ (PI) (PI)) n))) (- 1 k)) #s(hole binary64 (+ (log (sqrt (* 2 (* n (PI))))) (* -1 (* k (log (sqrt (* 2 (* n (PI))))))))))
#s(approx (* (sqrt (/ 1 k)) (/ (sqrt (* (+ (PI) (PI)) n)) (pow (* (+ (PI) (PI)) n) (* 1/2 k)))) #s(hole binary64 (/ (* (sqrt (* 2 (* n (PI)))) (sqrt (/ 1 k))) (exp (* 1/2 (* k (log (* 2 (* n (PI))))))))))
#s(approx (sqrt (/ 1 k)) #s(hole binary64 (sqrt (/ 1 k))))
#s(approx (/ (sqrt (* (+ (PI) (PI)) n)) (pow (* (+ (PI) (PI)) n) (* 1/2 k))) #s(hole binary64 (/ (sqrt (* 2 (* n (PI)))) (exp (* 1/2 (* k (log (* 2 (* n (PI))))))))))
#s(approx (pow (* (+ (PI) (PI)) n) (* 1/2 k)) #s(hole binary64 (exp (* 1/2 (* k (log (* 2 (* n (PI)))))))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) #s(hole binary64 (/ (exp (* 1/2 (* (log (* 2 (* n (PI)))) (- 1 k)))) (* k (sqrt (/ 1 k))))))
#s(approx (sqrt (* (+ (PI) (PI)) (/ n k))) #s(hole binary64 (sqrt (* 2 (/ (* n (PI)) k)))))
#s(approx (* (sqrt (/ 1 k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) #s(hole binary64 (* (exp (* 1/2 (* (log (* 2 (* n (PI)))) (- 1 k)))) (sqrt (/ 1 k)))))
#s(approx (pow (* (* 2 (PI)) n) (/ (- 1 k) 2)) #s(hole binary64 (exp (* 1/2 (* (log (* 2 (* n (PI)))) (- 1 k))))))
#s(approx (/ (pow (sqrt (* (+ (PI) (PI)) n)) (- 1 k)) (sqrt k)) #s(hole binary64 (/ (exp (* (log (sqrt (* 2 (* n (PI))))) (- 1 k))) (* k (sqrt (/ 1 k))))))
#s(approx (pow (sqrt (* (+ (PI) (PI)) n)) (- 1 k)) #s(hole binary64 (exp (* (log (sqrt (* 2 (* n (PI))))) (- 1 k)))))
#s(approx (- 1 k) #s(hole binary64 (* -1 k)))
#s(approx (- 1 k) #s(hole binary64 (* k (- (/ 1 k) 1))))
#s(approx (sqrt k) #s(hole binary64 (* k (sqrt (/ 1 k)))))
#s(approx (/ 1 (sqrt k)) #s(hole binary64 (/ 1 (* k (sqrt (/ 1 k))))))
#s(approx (* (log (sqrt (* (+ (PI) (PI)) n))) (- 1 k)) #s(hole binary64 (* -1 (* k (log (sqrt (* 2 (* n (PI)))))))))
#s(approx (* (log (sqrt (* (+ (PI) (PI)) n))) (- 1 k)) #s(hole binary64 (* k (+ (* -1 (log (sqrt (* 2 (* n (PI)))))) (/ (log (sqrt (* 2 (* n (PI))))) k)))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) #s(hole binary64 (* -1 (/ (exp (* 1/2 (* (log (* 2 (* n (PI)))) (+ 1 (* -1 k))))) (* k (sqrt (/ 1 k)))))))
#s(approx (* (sqrt (/ 1 k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) #s(hole binary64 (* (exp (* 1/2 (* (log (* 2 (* n (PI)))) (+ 1 (* -1 k))))) (sqrt (/ 1 k)))))
#s(approx (pow (* (* 2 (PI)) n) (/ (- 1 k) 2)) #s(hole binary64 (exp (* 1/2 (* (log (* 2 (* n (PI)))) (+ 1 (* -1 k)))))))
#s(approx (/ (pow (sqrt (* (+ (PI) (PI)) n)) (- 1 k)) (sqrt k)) #s(hole binary64 (* -1 (/ (exp (* (log (sqrt (* 2 (* n (PI))))) (+ 1 (* -1 k)))) (* k (sqrt (/ 1 k)))))))
#s(approx (pow (sqrt (* (+ (PI) (PI)) n)) (- 1 k)) #s(hole binary64 (exp (* (log (sqrt (* 2 (* n (PI))))) (+ 1 (* -1 k))))))
#s(approx (- 1 k) #s(hole binary64 (* -1 (* k (- 1 (/ 1 k))))))
#s(approx (sqrt k) #s(hole binary64 (* -1 (* k (sqrt (/ 1 k))))))
#s(approx (/ 1 (sqrt k)) #s(hole binary64 (/ -1 (* k (sqrt (/ 1 k))))))
#s(approx (* (log (sqrt (* (+ (PI) (PI)) n))) (- 1 k)) #s(hole binary64 (* -1 (* k (+ (log (sqrt (* 2 (* n (PI))))) (* -1 (/ (log (sqrt (* 2 (* n (PI))))) k)))))))
#s(approx (* (sqrt (/ 1 k)) (/ (sqrt (* (+ (PI) (PI)) n)) (pow (* (+ (PI) (PI)) n) (* 1/2 k)))) #s(hole binary64 (/ (* (sqrt (* 2 (* n (PI)))) (sqrt (/ 1 k))) (exp (* 1/2 (* k (+ (log n) (log (* 2 (PI))))))))))
#s(approx (/ (sqrt (* (+ (PI) (PI)) n)) (pow (* (+ (PI) (PI)) n) (* 1/2 k))) #s(hole binary64 (/ (sqrt (* 2 (* n (PI)))) (exp (* 1/2 (* k (+ (log n) (log (* 2 (PI))))))))))
#s(approx (* (+ (PI) (PI)) n) #s(hole binary64 (* 2 (* n (PI)))))
#s(approx n #s(hole binary64 n))
#s(approx (pow (* (+ (PI) (PI)) n) (* 1/2 k)) #s(hole binary64 (exp (* 1/2 (* k (+ (log n) (log (* 2 (PI)))))))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) #s(hole binary64 (/ (exp (* 1/2 (* (+ (log n) (log (* 2 (PI)))) (- 1 k)))) (sqrt k))))
#s(approx (* (sqrt (/ 1 k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) #s(hole binary64 (* (exp (* 1/2 (* (+ (log n) (log (* 2 (PI)))) (- 1 k)))) (sqrt (/ 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 (/ (pow (sqrt (* (+ (PI) (PI)) n)) (- 1 k)) (sqrt k)) #s(hole binary64 (/ (exp (* (log (sqrt (* 2 (* n (PI))))) (- 1 k))) (sqrt k))))
#s(approx (* (log (sqrt (* (+ (PI) (PI)) n))) (- 1 k)) #s(hole binary64 (* (log (sqrt (* 2 (* n (PI))))) (- 1 k))))
#s(approx (* (sqrt (/ 1 k)) (/ (sqrt (* (+ (PI) (PI)) n)) (pow (* (+ (PI) (PI)) n) (* 1/2 k)))) #s(hole binary64 (/ (* n (* (sqrt (* 2 (/ (PI) n))) (sqrt (/ 1 k)))) (exp (* 1/2 (* k (+ (log (* 2 (PI))) (* -1 (log (/ 1 n))))))))))
#s(approx (/ (sqrt (* (+ (PI) (PI)) n)) (pow (* (+ (PI) (PI)) n) (* 1/2 k))) #s(hole binary64 (/ (* n (sqrt (* 2 (/ (PI) n)))) (exp (* 1/2 (* k (+ (log (* 2 (PI))) (* -1 (log (/ 1 n))))))))))
#s(approx (sqrt (* (+ (PI) (PI)) n)) #s(hole binary64 (* n (sqrt (* 2 (/ (PI) n))))))
#s(approx (pow (* (+ (PI) (PI)) n) (* 1/2 k)) #s(hole binary64 (exp (* 1/2 (* k (+ (log (* 2 (PI))) (* -1 (log (/ 1 n)))))))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) #s(hole binary64 (/ (exp (* 1/2 (* (+ (log (* 2 (PI))) (* -1 (log (/ 1 n)))) (- 1 k)))) (sqrt k))))
#s(approx (sqrt (* (+ (PI) (PI)) (/ n k))) #s(hole binary64 (* n (sqrt (* 2 (/ (PI) (* k n)))))))
#s(approx (* (sqrt (/ 1 k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) #s(hole binary64 (* (exp (* 1/2 (* (+ (log (* 2 (PI))) (* -1 (log (/ 1 n)))) (- 1 k)))) (sqrt (/ 1 k)))))
#s(approx (pow (* (* 2 (PI)) n) (/ (- 1 k) 2)) #s(hole binary64 (exp (* 1/2 (* (+ (log (* 2 (PI))) (* -1 (log (/ 1 n)))) (- 1 k))))))
#s(approx (/ (pow (sqrt (* (+ (PI) (PI)) n)) (- 1 k)) (sqrt k)) #s(hole binary64 (/ (exp (* (+ (log (sqrt (* 2 (/ (PI) n)))) (* -1 (log (/ 1 n)))) (- 1 k))) (sqrt k))))
#s(approx (pow (sqrt (* (+ (PI) (PI)) n)) (- 1 k)) #s(hole binary64 (exp (* (+ (log (sqrt (* 2 (/ (PI) n)))) (* -1 (log (/ 1 n)))) (- 1 k)))))
#s(approx (* (log (sqrt (* (+ (PI) (PI)) n))) (- 1 k)) #s(hole binary64 (* (+ (log (sqrt (* 2 (/ (PI) n)))) (* -1 (log (/ 1 n)))) (- 1 k))))
#s(approx (log (sqrt (* (+ (PI) (PI)) n))) #s(hole binary64 (+ (log (sqrt (* 2 (/ (PI) n)))) (* -1 (log (/ 1 n))))))
#s(approx (* (sqrt (/ 1 k)) (/ (sqrt (* (+ (PI) (PI)) n)) (pow (* (+ (PI) (PI)) n) (* 1/2 k)))) #s(hole binary64 (* -1 (/ (* n (* (sqrt (* 2 (/ (PI) n))) (sqrt (/ 1 k)))) (exp (* 1/2 (* k (+ (log (* -2 (PI))) (* -1 (log (/ -1 n)))))))))))
#s(approx (/ (sqrt (* (+ (PI) (PI)) n)) (pow (* (+ (PI) (PI)) n) (* 1/2 k))) #s(hole binary64 (* -1 (/ (* n (sqrt (* 2 (/ (PI) n)))) (exp (* 1/2 (* k (+ (log (* -2 (PI))) (* -1 (log (/ -1 n)))))))))))
#s(approx (sqrt (* (+ (PI) (PI)) n)) #s(hole binary64 (* -1 (* n (sqrt (* 2 (/ (PI) n)))))))
#s(approx (pow (* (+ (PI) (PI)) n) (* 1/2 k)) #s(hole binary64 (exp (* 1/2 (* k (+ (log (* -2 (PI))) (* -1 (log (/ -1 n)))))))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) #s(hole binary64 (/ (exp (* 1/2 (* (+ (log (* -2 (PI))) (* -1 (log (/ -1 n)))) (- 1 k)))) (sqrt k))))
#s(approx (sqrt (* (+ (PI) (PI)) (/ n k))) #s(hole binary64 (* -1 (* n (sqrt (* 2 (/ (PI) (* k n))))))))
#s(approx (* (sqrt (/ 1 k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) #s(hole binary64 (* (exp (* 1/2 (* (+ (log (* -2 (PI))) (* -1 (log (/ -1 n)))) (- 1 k)))) (sqrt (/ 1 k)))))
#s(approx (pow (* (* 2 (PI)) n) (/ (- 1 k) 2)) #s(hole binary64 (exp (* 1/2 (* (+ (log (* -2 (PI))) (* -1 (log (/ -1 n)))) (- 1 k))))))
#s(approx (/ (pow (sqrt (* (+ (PI) (PI)) n)) (- 1 k)) (sqrt k)) #s(hole binary64 (/ (exp (* (+ (log (sqrt (* 2 (/ (PI) n)))) (* -1 (log (/ -1 n)))) (- 1 k))) (sqrt k))))
#s(approx (pow (sqrt (* (+ (PI) (PI)) n)) (- 1 k)) #s(hole binary64 (exp (* (+ (log (sqrt (* 2 (/ (PI) n)))) (* -1 (log (/ -1 n)))) (- 1 k)))))
#s(approx (* (log (sqrt (* (+ (PI) (PI)) n))) (- 1 k)) #s(hole binary64 (* (+ (log (sqrt (* 2 (/ (PI) n)))) (* -1 (log (/ -1 n)))) (- 1 k))))
#s(approx (log (sqrt (* (+ (PI) (PI)) n))) #s(hole binary64 (+ (log (sqrt (* 2 (/ (PI) n)))) (* -1 (log (/ -1 n))))))

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

eval78.0ms (1.3%)

Memory: 0.9MiB live, 91.7MiB allocated; 10ms collecting garbage
Compiler: Compiled 8 021 to 1 859 computations (76.8% saved)

prune26.0ms (0.4%)

Memory

42.3MiB live, 42.3MiB allocated; 0ms collecting garbage

Pruning

31 alts after pruning (27 fresh and 4 done)

	Pruned	Kept	Total
New	515	15	530
Fresh	7	12	19
Picked	2	3	5
Done	1	1	2
Total	525	31	556

Accuracy

100.0%

Counts

556 → 31

Alt Table

Click to see full alt table

Status	Accuracy	Program
▶	99.3%	(/.f64 (pow.f64 (*.f64 (sqrt.f64 (+.f64 (PI.f64) (PI.f64))) (sqrt.f64 n)) (-.f64 #s(literal 1 binary64) k)) (sqrt.f64 k))
	99.4%	(/.f64 (pow.f64 (.f64 (sqrt.f64 (.f64 (PI.f64) n)) (sqrt.f64 #s(literal 2 binary64))) (-.f64 #s(literal 1 binary64) k)) (sqrt.f64 k))
	99.5%	(/.f64 (pow.f64 (*.f64 n (+.f64 (PI.f64) (PI.f64))) (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 2 binary64))) (sqrt.f64 k))
✓	99.5%	(/.f64 (pow.f64 (sqrt.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n)) (-.f64 #s(literal 1 binary64) k)) (sqrt.f64 k))
	51.8%	(/.f64 (pow.f64 (sqrt.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n)) #s(approx (- 1 k) (neg.f64 k))) (sqrt.f64 k))
▶	99.7%	(/.f64 (/.f64 (sqrt.f64 (.f64 n (+.f64 (PI.f64) (PI.f64)))) (pow.f64 (sqrt.f64 (.f64 n (+.f64 (PI.f64) (PI.f64)))) k)) (sqrt.f64 k))
	78.2%	(/.f64 (sqrt.f64 (.f64 (/.f64 #s(literal 1 binary64) k) (.f64 (+.f64 (PI.f64) (PI.f64)) n))) (pow.f64 (.f64 (+.f64 (PI.f64) (PI.f64)) n) (.f64 #s(literal 1/2 binary64) k)))
	96.5%	(/.f64 (exp.f64 (.f64 (log.f64 (sqrt.f64 (.f64 n (+.f64 (PI.f64) (PI.f64))))) (-.f64 #s(literal 1 binary64) k))) (sqrt.f64 k))
	99.5%	(.f64 (pow.f64 (sqrt.f64 (.f64 (+.f64 (PI.f64) (PI.f64)) n)) (-.f64 #s(literal 1 binary64) k)) (sqrt.f64 (/.f64 #s(literal 1 binary64) k)))
	55.5%	(.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) (/.f64 (sqrt.f64 (.f64 (+.f64 (PI.f64) (PI.f64)) n)) #s(approx (pow (* (+ (PI) (PI)) n) (* 1/2 k)) (fma.f64 (.f64 (log.f64 (.f64 (+.f64 (PI.f64) (PI.f64)) n)) k) #s(literal 1/2 binary64) #s(literal 1 binary64)))))
▶	51.6%	(.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))))
✓	99.7%	(.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) k)) (/.f64 (sqrt.f64 (.f64 (+.f64 (PI.f64) (PI.f64)) n)) (pow.f64 (.f64 (+.f64 (PI.f64) (PI.f64)) n) (.f64 #s(literal 1/2 binary64) k))))
▶	51.6%	(.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) k)) #s(approx (pow ( (* 2 (PI)) n) (/ (- 1 k) 2)) (/.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (sqrt.f64 (*.f64 n (+.f64 (PI.f64) (PI.f64))))))))
	51.4%	(.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) k)) #s(approx (pow ( (* 2 (PI)) n) (/ (- 1 k) 2)) (*.f64 (sqrt.f64 (+.f64 (PI.f64) (PI.f64))) (sqrt.f64 n))))
	51.5%	(.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) k)) #s(approx (pow ( (* 2 (PI)) n) (/ (- 1 k) 2)) (.f64 (sqrt.f64 (.f64 (PI.f64) n)) (sqrt.f64 #s(literal 2 binary64)))))
	51.4%	(.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) k)) #s(approx (pow ( (* 2 (PI)) n) (/ (- 1 k) 2)) (.f64 (sqrt.f64 (.f64 #s(literal 2 binary64) n)) (sqrt.f64 (PI.f64)))))
	51.6%	(.f64 #s(approx (/ 1 (sqrt k)) (/.f64 (sqrt.f64 k) k)) #s(approx (pow ( (* 2 (PI)) n) (/ (- 1 k) 2)) (sqrt.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n))))
	52.3%	#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (/.f64 (.f64 (fma.f64 (neg.f64 k) (log.f64 (sqrt.f64 (.f64 (+.f64 (PI.f64) (PI.f64)) n))) #s(literal 1 binary64)) (sqrt.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n))) (sqrt.f64 k)))
	51.7%	#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (/.f64 (sqrt.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n)) (sqrt.f64 k)))
	39.9%	#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (/.f64 (sqrt.f64 (.f64 (.f64 n (+.f64 (PI.f64) (PI.f64))) k)) k))
	41.8%	#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (/.f64 #s(literal 1 binary64) (pow.f64 (/.f64 (*.f64 n (+.f64 (PI.f64) (PI.f64))) k) #s(literal -1/2 binary64))))
	41.7%	#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (.f64 (sqrt.f64 (/.f64 (.f64 (PI.f64) n) k)) (sqrt.f64 #s(literal 2 binary64))))
▶	41.5%	#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (*.f64 (sqrt.f64 (/.f64 n k)) (sqrt.f64 (+.f64 (PI.f64) (PI.f64)))))
✓	41.8%	#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt.f64 (/.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n) k)))
	24.0%	#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt.f64 (/.f64 (.f64 (.f64 (.f64 (PI.f64) n) k) #s(literal 2 binary64)) (.f64 k k))))
	41.8%	#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt.f64 (/.f64 (.f64 (sqrt.f64 (.f64 (+.f64 (PI.f64) (PI.f64)) n)) (sqrt.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n))) k)))
	27.0%	#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt.f64 (/.f64 (sqrt.f64 (.f64 (.f64 (+.f64 (PI.f64) (PI.f64)) n) (*.f64 (+.f64 (PI.f64) (PI.f64)) n))) k)))
✓	41.8%	#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) (/.f64 n k))))
	39.3%	#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (exp.f64 (.f64 (log.f64 (/.f64 (.f64 n (+.f64 (PI.f64) (PI.f64))) k)) #s(literal 1/2 binary64))))
	47.2%	#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) #s(approx (/ (+ (* (* k (neg (log (sqrt (* (+ (PI) (PI)) n))))) (sqrt (* (+ (PI) (PI)) n))) (sqrt (* (+ (PI) (PI)) n))) (sqrt k)) (/.f64 (fma.f64 (neg.f64 (log.f64 (sqrt.f64 (.f64 (+.f64 (PI.f64) (PI.f64)) n)))) (sqrt.f64 (.f64 (+.f64 (PI.f64) (PI.f64)) n)) (/.f64 (sqrt.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n)) k)) (/.f64 #s(literal 1 binary64) (sqrt.f64 k)))))
	50.6%	#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) #s(approx (sqrt (/ (* (+ (PI) (PI)) n) k)) (.f64 (sqrt.f64 (/.f64 (+.f64 (PI.f64) (PI.f64)) (.f64 n k))) n)))

Compiler

Compiled 1 257 to 1 099 computations (12.6% saved)

series175.0ms (2.9%)

Memory

-15.6MiB live, 229.4MiB allocated; 46ms collecting garbage

Counts

32 → 102

Calls

Call 1

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

Outputs
#s(approx (/ (/ (sqrt (* n (+ (PI) (PI)))) (pow (sqrt (* n (+ (PI) (PI)))) k)) (sqrt k)) #s(hole binary64 (/ (sqrt (* 2 (* n (PI)))) (sqrt k))))
#s(approx (/ (/ (sqrt (* n (+ (PI) (PI)))) (pow (sqrt (* n (+ (PI) (PI)))) k)) (sqrt k)) #s(hole binary64 (+ (* -1 (/ (* k (* (log (sqrt (* 2 (* n (PI))))) (sqrt (* 2 (* n (PI)))))) (sqrt k))) (/ (sqrt (* 2 (* n (PI)))) (sqrt k)))))
#s(approx (/ (/ (sqrt (* n (+ (PI) (PI)))) (pow (sqrt (* n (+ (PI) (PI)))) k)) (sqrt k)) #s(hole binary64 (+ (* k (- (* -1 (* k (+ (* -1 (/ (* (pow (log (sqrt (* 2 (* n (PI))))) 2) (sqrt (* 2 (* n (PI))))) (sqrt k))) (* 1/2 (/ (* (pow (log (sqrt (* 2 (* n (PI))))) 2) (sqrt (* 2 (* n (PI))))) (sqrt k)))))) (/ (* (log (sqrt (* 2 (* n (PI))))) (sqrt (* 2 (* n (PI))))) (sqrt k)))) (/ (sqrt (* 2 (* n (PI)))) (sqrt k)))))
#s(approx (/ (/ (sqrt (* n (+ (PI) (PI)))) (pow (sqrt (* n (+ (PI) (PI)))) k)) (sqrt k)) #s(hole binary64 (+ (* k (- (* k (- (* -1 (* k (+ (* -1 (* (log (sqrt (* 2 (* n (PI))))) (+ (* -1 (/ (* (pow (log (sqrt (* 2 (* n (PI))))) 2) (sqrt (* 2 (* n (PI))))) (sqrt k))) (* 1/2 (/ (* (pow (log (sqrt (* 2 (* n (PI))))) 2) (sqrt (* 2 (* n (PI))))) (sqrt k)))))) (+ (* -1/2 (/ (* (pow (log (sqrt (* 2 (* n (PI))))) 3) (sqrt (* 2 (* n (PI))))) (sqrt k))) (* 1/6 (/ (* (pow (log (sqrt (* 2 (* n (PI))))) 3) (sqrt (* 2 (* n (PI))))) (sqrt k))))))) (+ (* -1 (/ (* (pow (log (sqrt (* 2 (* n (PI))))) 2) (sqrt (* 2 (* n (PI))))) (sqrt k))) (* 1/2 (/ (* (pow (log (sqrt (* 2 (* n (PI))))) 2) (sqrt (* 2 (* n (PI))))) (sqrt k)))))) (/ (* (log (sqrt (* 2 (* n (PI))))) (sqrt (* 2 (* n (PI))))) (sqrt k)))) (/ (sqrt (* 2 (* n (PI)))) (sqrt k)))))
#s(approx (/ (sqrt (* n (+ (PI) (PI)))) (pow (sqrt (* n (+ (PI) (PI)))) k)) #s(hole binary64 (sqrt (* 2 (* n (PI))))))
#s(approx (/ (sqrt (* n (+ (PI) (PI)))) (pow (sqrt (* n (+ (PI) (PI)))) k)) #s(hole binary64 (+ (sqrt (* 2 (* n (PI)))) (* -1 (* k (* (log (sqrt (* 2 (* n (PI))))) (sqrt (* 2 (* n (PI))))))))))
#s(approx (/ (sqrt (* n (+ (PI) (PI)))) (pow (sqrt (* n (+ (PI) (PI)))) k)) #s(hole binary64 (+ (sqrt (* 2 (* n (PI)))) (* k (- (* -1 (* k (+ (* -1 (* (pow (log (sqrt (* 2 (* n (PI))))) 2) (sqrt (* 2 (* n (PI)))))) (* 1/2 (* (pow (log (sqrt (* 2 (* n (PI))))) 2) (sqrt (* 2 (* n (PI))))))))) (* (log (sqrt (* 2 (* n (PI))))) (sqrt (* 2 (* n (PI))))))))))
#s(approx (/ (sqrt (* n (+ (PI) (PI)))) (pow (sqrt (* n (+ (PI) (PI)))) k)) #s(hole binary64 (+ (sqrt (* 2 (* n (PI)))) (* k (- (* k (- (* -1 (* k (+ (* -1 (* (log (sqrt (* 2 (* n (PI))))) (+ (* -1 (* (pow (log (sqrt (* 2 (* n (PI))))) 2) (sqrt (* 2 (* n (PI)))))) (* 1/2 (* (pow (log (sqrt (* 2 (* n (PI))))) 2) (sqrt (* 2 (* n (PI))))))))) (+ (* -1/2 (* (pow (log (sqrt (* 2 (* n (PI))))) 3) (sqrt (* 2 (* n (PI)))))) (* 1/6 (* (pow (log (sqrt (* 2 (* n (PI))))) 3) (sqrt (* 2 (* n (PI)))))))))) (+ (* -1 (* (pow (log (sqrt (* 2 (* n (PI))))) 2) (sqrt (* 2 (* n (PI)))))) (* 1/2 (* (pow (log (sqrt (* 2 (* n (PI))))) 2) (sqrt (* 2 (* n (PI))))))))) (* (log (sqrt (* 2 (* n (PI))))) (sqrt (* 2 (* n (PI))))))))))
#s(approx (pow (sqrt (* n (+ (PI) (PI)))) k) #s(hole binary64 1))
#s(approx (pow (sqrt (* n (+ (PI) (PI)))) k) #s(hole binary64 (+ 1 (* k (log (sqrt (* 2 (* n (PI)))))))))
#s(approx (pow (sqrt (* n (+ (PI) (PI)))) k) #s(hole binary64 (+ 1 (* k (+ (log (sqrt (* 2 (* n (PI))))) (* 1/2 (* k (pow (log (sqrt (* 2 (* n (PI))))) 2))))))))
#s(approx (pow (sqrt (* n (+ (PI) (PI)))) k) #s(hole binary64 (+ 1 (* k (+ (log (sqrt (* 2 (* n (PI))))) (* k (+ (* 1/6 (* k (pow (log (sqrt (* 2 (* n (PI))))) 3))) (* 1/2 (pow (log (sqrt (* 2 (* n (PI))))) 2)))))))))
#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 (/ (pow (* 2 (* n (PI))) 1/2) (sqrt k))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) #s(hole binary64 (+ (* -1/2 (/ (* k (* (log (* 2 (* n (PI)))) (pow (* 2 (* n (PI))) 1/2))) (sqrt k))) (/ (pow (* 2 (* n (PI))) 1/2) (sqrt k)))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) #s(hole binary64 (+ (* k (+ (* -1/2 (/ (* (log (* 2 (* n (PI)))) (pow (* 2 (* n (PI))) 1/2)) (sqrt k))) (* 1/8 (/ (* k (* (pow (log (* 2 (* n (PI)))) 2) (pow (* 2 (* n (PI))) 1/2))) (sqrt k))))) (/ (pow (* 2 (* n (PI))) 1/2) (sqrt k)))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) #s(hole binary64 (+ (* k (+ (* -1/2 (/ (* (log (* 2 (* n (PI)))) (pow (* 2 (* n (PI))) 1/2)) (sqrt k))) (* k (+ (* -1/48 (/ (* k (* (pow (log (* 2 (* n (PI)))) 3) (pow (* 2 (* n (PI))) 1/2))) (sqrt k))) (* 1/8 (/ (* (pow (log (* 2 (* n (PI)))) 2) (pow (* 2 (* n (PI))) 1/2)) (sqrt k))))))) (/ (pow (* 2 (* n (PI))) 1/2) (sqrt k)))))
#s(approx (* (sqrt (/ n k)) (sqrt (+ (PI) (PI)))) #s(hole binary64 (/ (* (sqrt (* 2 (PI))) (sqrt (* k n))) k)))
#s(approx (sqrt (/ n k)) #s(hole binary64 (/ (sqrt (* k n)) k)))
#s(approx (/ n k) #s(hole binary64 (/ n k)))
#s(approx (/ 1 (sqrt k)) #s(hole binary64 (/ 1 (sqrt k))))
#s(approx (pow (* (* 2 (PI)) n) (/ (- 1 k) 2)) #s(hole binary64 (pow (* 2 (* n (PI))) 1/2)))
#s(approx (pow (* (* 2 (PI)) n) (/ (- 1 k) 2)) #s(hole binary64 (+ (* -1/2 (* k (* (log (* 2 (* n (PI)))) (pow (* 2 (* n (PI))) 1/2)))) (pow (* 2 (* n (PI))) 1/2))))
#s(approx (pow (* (* 2 (PI)) n) (/ (- 1 k) 2)) #s(hole binary64 (+ (* k (+ (* -1/2 (* (log (* 2 (* n (PI)))) (pow (* 2 (* n (PI))) 1/2))) (* 1/8 (* k (* (pow (log (* 2 (* n (PI)))) 2) (pow (* 2 (* n (PI))) 1/2)))))) (pow (* 2 (* n (PI))) 1/2))))
#s(approx (pow (* (* 2 (PI)) n) (/ (- 1 k) 2)) #s(hole binary64 (+ (* k (+ (* -1/2 (* (log (* 2 (* n (PI)))) (pow (* 2 (* n (PI))) 1/2))) (* k (+ (* -1/48 (* k (* (pow (log (* 2 (* n (PI)))) 3) (pow (* 2 (* n (PI))) 1/2)))) (* 1/8 (* (pow (log (* 2 (* n (PI)))) 2) (pow (* 2 (* n (PI))) 1/2))))))) (pow (* 2 (* n (PI))) 1/2))))
#s(approx (* (sqrt (/ 1 k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) #s(hole binary64 (/ (* (sqrt k) (pow (* 2 (* n (PI))) 1/2)) k)))
#s(approx (* (sqrt (/ 1 k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) #s(hole binary64 (/ (+ (* -1/2 (* k (* (log (* 2 (* n (PI)))) (* (sqrt k) (pow (* 2 (* n (PI))) 1/2))))) (* (sqrt k) (pow (* 2 (* n (PI))) 1/2))) k)))
#s(approx (* (sqrt (/ 1 k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) #s(hole binary64 (/ (+ (* k (+ (* -1/2 (* (log (* 2 (* n (PI)))) (* (sqrt k) (pow (* 2 (* n (PI))) 1/2)))) (* 1/8 (* k (* (pow (log (* 2 (* n (PI)))) 2) (* (sqrt k) (pow (* 2 (* n (PI))) 1/2))))))) (* (sqrt k) (pow (* 2 (* n (PI))) 1/2))) k)))
#s(approx (* (sqrt (/ 1 k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) #s(hole binary64 (/ (+ (* k (+ (* -1/2 (* (log (* 2 (* n (PI)))) (* (sqrt k) (pow (* 2 (* n (PI))) 1/2)))) (* k (+ (* -1/48 (* k (* (pow (log (* 2 (* n (PI)))) 3) (* (sqrt k) (pow (* 2 (* n (PI))) 1/2))))) (* 1/8 (* (pow (log (* 2 (* n (PI)))) 2) (* (sqrt k) (pow (* 2 (* n (PI))) 1/2)))))))) (* (sqrt k) (pow (* 2 (* n (PI))) 1/2))) k)))
#s(approx (sqrt (/ 1 k)) #s(hole binary64 (/ (sqrt k) k)))
#s(approx (/ 1 k) #s(hole binary64 (/ 1 k)))
#s(approx (/ (pow (* (sqrt (+ (PI) (PI))) (sqrt n)) (- 1 k)) (sqrt k)) #s(hole binary64 (/ (* (sqrt n) (sqrt (* 2 (PI)))) (sqrt k))))
#s(approx (/ (pow (* (sqrt (+ (PI) (PI))) (sqrt n)) (- 1 k)) (sqrt k)) #s(hole binary64 (+ (* -1 (/ (* k (* (log (* (sqrt n) (sqrt (* 2 (PI))))) (* (sqrt n) (sqrt (* 2 (PI)))))) (sqrt k))) (/ (* (sqrt n) (sqrt (* 2 (PI)))) (sqrt k)))))
#s(approx (/ (pow (* (sqrt (+ (PI) (PI))) (sqrt n)) (- 1 k)) (sqrt k)) #s(hole binary64 (+ (* k (+ (* -1 (/ (* (log (* (sqrt n) (sqrt (* 2 (PI))))) (* (sqrt n) (sqrt (* 2 (PI))))) (sqrt k))) (* 1/2 (/ (* k (* (pow (log (* (sqrt n) (sqrt (* 2 (PI))))) 2) (* (sqrt n) (sqrt (* 2 (PI)))))) (sqrt k))))) (/ (* (sqrt n) (sqrt (* 2 (PI)))) (sqrt k)))))
#s(approx (/ (pow (* (sqrt (+ (PI) (PI))) (sqrt n)) (- 1 k)) (sqrt k)) #s(hole binary64 (+ (* k (+ (* -1 (/ (* (log (* (sqrt n) (sqrt (* 2 (PI))))) (* (sqrt n) (sqrt (* 2 (PI))))) (sqrt k))) (* k (+ (* -1/6 (/ (* k (* (pow (log (* (sqrt n) (sqrt (* 2 (PI))))) 3) (* (sqrt n) (sqrt (* 2 (PI)))))) (sqrt k))) (* 1/2 (/ (* (pow (log (* (sqrt n) (sqrt (* 2 (PI))))) 2) (* (sqrt n) (sqrt (* 2 (PI))))) (sqrt k))))))) (/ (* (sqrt n) (sqrt (* 2 (PI)))) (sqrt k)))))
#s(approx (pow (* (sqrt (+ (PI) (PI))) (sqrt n)) (- 1 k)) #s(hole binary64 (* (sqrt n) (sqrt (* 2 (PI))))))
#s(approx (pow (* (sqrt (+ (PI) (PI))) (sqrt n)) (- 1 k)) #s(hole binary64 (+ (* -1 (* k (* (log (* (sqrt n) (sqrt (* 2 (PI))))) (* (sqrt n) (sqrt (* 2 (PI))))))) (* (sqrt n) (sqrt (* 2 (PI)))))))
#s(approx (pow (* (sqrt (+ (PI) (PI))) (sqrt n)) (- 1 k)) #s(hole binary64 (+ (* k (+ (* -1 (* (log (* (sqrt n) (sqrt (* 2 (PI))))) (* (sqrt n) (sqrt (* 2 (PI)))))) (* 1/2 (* k (* (pow (log (* (sqrt n) (sqrt (* 2 (PI))))) 2) (* (sqrt n) (sqrt (* 2 (PI))))))))) (* (sqrt n) (sqrt (* 2 (PI)))))))
#s(approx (pow (* (sqrt (+ (PI) (PI))) (sqrt n)) (- 1 k)) #s(hole binary64 (+ (* k (+ (* -1 (* (log (* (sqrt n) (sqrt (* 2 (PI))))) (* (sqrt n) (sqrt (* 2 (PI)))))) (* k (+ (* -1/6 (* k (* (pow (log (* (sqrt n) (sqrt (* 2 (PI))))) 3) (* (sqrt n) (sqrt (* 2 (PI))))))) (* 1/2 (* (pow (log (* (sqrt n) (sqrt (* 2 (PI))))) 2) (* (sqrt n) (sqrt (* 2 (PI)))))))))) (* (sqrt n) (sqrt (* 2 (PI)))))))
#s(approx (- 1 k) #s(hole binary64 (+ 1 (* -1 k))))
#s(approx (/ (/ (sqrt (* n (+ (PI) (PI)))) (pow (sqrt (* n (+ (PI) (PI)))) k)) (sqrt k)) #s(hole binary64 (/ (sqrt (* 2 (* n (PI)))) (* k (* (sqrt (/ 1 k)) (pow (sqrt (* 2 (* n (PI)))) k))))))
#s(approx (/ (sqrt (* n (+ (PI) (PI)))) (pow (sqrt (* n (+ (PI) (PI)))) k)) #s(hole binary64 (/ (sqrt (* 2 (* n (PI)))) (pow (sqrt (* 2 (* n (PI)))) k))))
#s(approx (pow (sqrt (* n (+ (PI) (PI)))) k) #s(hole binary64 (pow (sqrt (* 2 (* n (PI)))) k)))
#s(approx (sqrt k) #s(hole binary64 (* k (sqrt (/ 1 k)))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) #s(hole binary64 (/ (exp (* 1/2 (* (log (* 2 (* n (PI)))) (- 1 k)))) (* k (sqrt (/ 1 k))))))
#s(approx (* (sqrt (/ n k)) (sqrt (+ (PI) (PI)))) #s(hole binary64 (* (sqrt (* 2 (PI))) (sqrt (/ n k)))))
#s(approx (sqrt (/ n k)) #s(hole binary64 (sqrt (/ n k))))
#s(approx (/ 1 (sqrt k)) #s(hole binary64 (/ 1 (* k (sqrt (/ 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 (* (sqrt (/ 1 k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) #s(hole binary64 (* (exp (* 1/2 (* (log (* 2 (* n (PI)))) (- 1 k)))) (sqrt (/ 1 k)))))
#s(approx (sqrt (/ 1 k)) #s(hole binary64 (sqrt (/ 1 k))))
#s(approx (/ (pow (* (sqrt (+ (PI) (PI))) (sqrt n)) (- 1 k)) (sqrt k)) #s(hole binary64 (/ (exp (* (log (* (sqrt n) (sqrt (* 2 (PI))))) (- 1 k))) (* k (sqrt (/ 1 k))))))
#s(approx (pow (* (sqrt (+ (PI) (PI))) (sqrt n)) (- 1 k)) #s(hole binary64 (exp (* (log (* (sqrt n) (sqrt (* 2 (PI))))) (- 1 k)))))
#s(approx (- 1 k) #s(hole binary64 (* -1 k)))
#s(approx (- 1 k) #s(hole binary64 (* k (- (/ 1 k) 1))))
#s(approx (/ (/ (sqrt (* n (+ (PI) (PI)))) (pow (sqrt (* n (+ (PI) (PI)))) k)) (sqrt k)) #s(hole binary64 (* -1 (/ (sqrt (* 2 (* n (PI)))) (* k (* (sqrt (/ 1 k)) (pow (sqrt (* 2 (* n (PI)))) k)))))))
#s(approx (sqrt k) #s(hole binary64 (* -1 (* k (sqrt (/ 1 k))))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) #s(hole binary64 (* -1 (/ (exp (* 1/2 (* (log (* 2 (* n (PI)))) (+ 1 (* -1 k))))) (* k (sqrt (/ 1 k)))))))
#s(approx (/ 1 (sqrt k)) #s(hole binary64 (/ -1 (* k (sqrt (/ 1 k))))))
#s(approx (pow (* (* 2 (PI)) n) (/ (- 1 k) 2)) #s(hole binary64 (exp (* 1/2 (* (log (* 2 (* n (PI)))) (+ 1 (* -1 k)))))))
#s(approx (* (sqrt (/ 1 k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) #s(hole binary64 (* (exp (* 1/2 (* (log (* 2 (* n (PI)))) (+ 1 (* -1 k))))) (sqrt (/ 1 k)))))
#s(approx (/ (pow (* (sqrt (+ (PI) (PI))) (sqrt n)) (- 1 k)) (sqrt k)) #s(hole binary64 (* -1 (/ (exp (* (log (* (sqrt n) (sqrt (* 2 (PI))))) (+ 1 (* -1 k)))) (* k (sqrt (/ 1 k)))))))
#s(approx (pow (* (sqrt (+ (PI) (PI))) (sqrt n)) (- 1 k)) #s(hole binary64 (exp (* (log (* (sqrt n) (sqrt (* 2 (PI))))) (+ 1 (* -1 k))))))
#s(approx (- 1 k) #s(hole binary64 (* -1 (* k (- 1 (/ 1 k))))))
#s(approx (/ (/ (sqrt (* n (+ (PI) (PI)))) (pow (sqrt (* n (+ (PI) (PI)))) k)) (sqrt k)) #s(hole binary64 (/ (sqrt (* 2 (* n (PI)))) (* (sqrt k) (pow (sqrt (* 2 (* n (PI)))) k)))))
#s(approx (* n (+ (PI) (PI))) #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 (/ (exp (* 1/2 (* (+ (log n) (log (* 2 (PI)))) (- 1 k)))) (sqrt k))))
#s(approx (pow (* (* 2 (PI)) n) (/ (- 1 k) 2)) #s(hole binary64 (exp (* 1/2 (* (+ (log n) (log (* 2 (PI)))) (- 1 k))))))
#s(approx (* (sqrt (/ 1 k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) #s(hole binary64 (* (exp (* 1/2 (* (+ (log n) (log (* 2 (PI)))) (- 1 k)))) (sqrt (/ 1 k)))))
#s(approx (/ 1 (sqrt (* n (+ (PI) (PI))))) #s(hole binary64 (/ 1 (sqrt (* 2 (* n (PI)))))))
#s(approx (/ (pow (* (sqrt (+ (PI) (PI))) (sqrt n)) (- 1 k)) (sqrt k)) #s(hole binary64 (/ (exp (* (log (* (sqrt n) (sqrt (* 2 (PI))))) (- 1 k))) (sqrt k))))
#s(approx (sqrt n) #s(hole binary64 (sqrt n)))
#s(approx (/ (/ (sqrt (* n (+ (PI) (PI)))) (pow (sqrt (* n (+ (PI) (PI)))) k)) (sqrt k)) #s(hole binary64 (/ (* n (sqrt (* 2 (/ (PI) n)))) (* (exp (* k (+ (log (sqrt (* 2 (/ (PI) n)))) (* -1 (log (/ 1 n)))))) (sqrt k)))))
#s(approx (/ (sqrt (* n (+ (PI) (PI)))) (pow (sqrt (* n (+ (PI) (PI)))) k)) #s(hole binary64 (/ (* n (sqrt (* 2 (/ (PI) n)))) (exp (* k (+ (log (sqrt (* 2 (/ (PI) n)))) (* -1 (log (/ 1 n)))))))))
#s(approx (sqrt (* n (+ (PI) (PI)))) #s(hole binary64 (* n (sqrt (* 2 (/ (PI) n))))))
#s(approx (pow (sqrt (* n (+ (PI) (PI)))) k) #s(hole binary64 (exp (* k (+ (log (sqrt (* 2 (/ (PI) n)))) (* -1 (log (/ 1 n))))))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) #s(hole binary64 (/ (exp (* 1/2 (* (+ (log (* 2 (PI))) (* -1 (log (/ 1 n)))) (- 1 k)))) (sqrt k))))
#s(approx (* (sqrt (/ n k)) (sqrt (+ (PI) (PI)))) #s(hole binary64 (* n (* (sqrt (* 2 (PI))) (sqrt (/ 1 (* k n)))))))
#s(approx (sqrt (/ n k)) #s(hole binary64 (* n (sqrt (/ 1 (* k n))))))
#s(approx (pow (* (* 2 (PI)) n) (/ (- 1 k) 2)) #s(hole binary64 (exp (* 1/2 (* (+ (log (* 2 (PI))) (* -1 (log (/ 1 n)))) (- 1 k))))))
#s(approx (* (sqrt (/ 1 k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) #s(hole binary64 (* (exp (* 1/2 (* (+ (log (* 2 (PI))) (* -1 (log (/ 1 n)))) (- 1 k)))) (sqrt (/ 1 k)))))
#s(approx (/ 1 (sqrt (* n (+ (PI) (PI))))) #s(hole binary64 (/ 1 (* n (sqrt (* 2 (/ (PI) n)))))))
#s(approx (/ (pow (* (sqrt (+ (PI) (PI))) (sqrt n)) (- 1 k)) (sqrt k)) #s(hole binary64 (/ (exp (* (+ (log (* (sqrt (* 2 (PI))) (sqrt (/ 1 n)))) (* -1 (log (/ 1 n)))) (- 1 k))) (sqrt k))))
#s(approx (pow (* (sqrt (+ (PI) (PI))) (sqrt n)) (- 1 k)) #s(hole binary64 (exp (* (+ (log (* (sqrt (* 2 (PI))) (sqrt (/ 1 n)))) (* -1 (log (/ 1 n)))) (- 1 k)))))
#s(approx (* (sqrt (+ (PI) (PI))) (sqrt n)) #s(hole binary64 (* n (* (sqrt (* 2 (PI))) (sqrt (/ 1 n))))))
#s(approx (sqrt n) #s(hole binary64 (* n (sqrt (/ 1 n)))))
#s(approx (/ (/ (sqrt (* n (+ (PI) (PI)))) (pow (sqrt (* n (+ (PI) (PI)))) k)) (sqrt k)) #s(hole binary64 (* -1 (/ (* n (sqrt (* 2 (/ (PI) n)))) (* (exp (* k (+ (log (sqrt (* 2 (/ (PI) n)))) (* -1 (log (/ -1 n)))))) (sqrt k))))))
#s(approx (/ (sqrt (* n (+ (PI) (PI)))) (pow (sqrt (* n (+ (PI) (PI)))) k)) #s(hole binary64 (* -1 (/ (* n (sqrt (* 2 (/ (PI) n)))) (exp (* k (+ (log (sqrt (* 2 (/ (PI) n)))) (* -1 (log (/ -1 n))))))))))
#s(approx (sqrt (* n (+ (PI) (PI)))) #s(hole binary64 (* -1 (* n (sqrt (* 2 (/ (PI) n)))))))
#s(approx (pow (sqrt (* n (+ (PI) (PI)))) k) #s(hole binary64 (exp (* k (+ (log (sqrt (* 2 (/ (PI) n)))) (* -1 (log (/ -1 n))))))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) #s(hole binary64 (/ (exp (* 1/2 (* (+ (log (* -2 (PI))) (* -1 (log (/ -1 n)))) (- 1 k)))) (sqrt k))))
#s(approx (* (sqrt (/ n k)) (sqrt (+ (PI) (PI)))) #s(hole binary64 (* -1 (* n (* (sqrt (* 2 (PI))) (sqrt (/ 1 (* k n))))))))
#s(approx (sqrt (/ n k)) #s(hole binary64 (* -1 (* n (sqrt (/ 1 (* k n)))))))
#s(approx (pow (* (* 2 (PI)) n) (/ (- 1 k) 2)) #s(hole binary64 (exp (* 1/2 (* (+ (log (* -2 (PI))) (* -1 (log (/ -1 n)))) (- 1 k))))))
#s(approx (* (sqrt (/ 1 k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) #s(hole binary64 (* (exp (* 1/2 (* (+ (log (* -2 (PI))) (* -1 (log (/ -1 n)))) (- 1 k)))) (sqrt (/ 1 k)))))
#s(approx (/ 1 (sqrt (* n (+ (PI) (PI))))) #s(hole binary64 (/ -1 (* n (sqrt (* 2 (/ (PI) n)))))))
#s(approx (/ (pow (* (sqrt (+ (PI) (PI))) (sqrt n)) (- 1 k)) (sqrt k)) #s(hole binary64 (/ (exp (* (+ (log (* (sqrt (* 2 (PI))) (sqrt (/ 1 n)))) (* -1 (log (/ -1 n)))) (- 1 k))) (sqrt k))))
#s(approx (pow (* (sqrt (+ (PI) (PI))) (sqrt n)) (- 1 k)) #s(hole binary64 (exp (* (+ (log (* (sqrt (* 2 (PI))) (sqrt (/ 1 n)))) (* -1 (log (/ -1 n)))) (- 1 k)))))
#s(approx (* (sqrt (+ (PI) (PI))) (sqrt n)) #s(hole binary64 (* -1 (* n (* (sqrt (* 2 (PI))) (sqrt (/ 1 n)))))))
#s(approx (sqrt n) #s(hole binary64 (* -1 (* n (sqrt (/ 1 n))))))

Calls

6 calls:

Time	Variable		Point	Expression
62.0ms	n	@	0	((/ (/ (sqrt (* n (+ (PI) (PI)))) (pow (sqrt (* n (+ (PI) (PI)))) k)) (sqrt k)) (/ (sqrt (* n (+ (PI) (PI)))) (pow (sqrt (* n (+ (PI) (PI)))) k)) (sqrt (* n (+ (PI) (PI)))) (* n (+ (PI) (PI))) n (+ (PI) (PI)) (PI) (pow (sqrt (* n (+ (PI) (PI)))) k) k (sqrt k) (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (* (sqrt (/ n k)) (sqrt (+ (PI) (PI)))) (sqrt (/ n k)) (/ n k) (sqrt (+ (PI) (PI))) (* (/ 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)) (* (+ (PI) (PI)) n) (* (sqrt (/ 1 k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt (/ 1 k)) (/ 1 k) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2)) (/ 1 (/ 1 (sqrt (* n (+ (PI) (PI)))))) (/ 1 (sqrt (* n (+ (PI) (PI))))) (/ (pow (* (sqrt (+ (PI) (PI))) (sqrt n)) (- 1 k)) (sqrt k)) (pow (* (sqrt (+ (PI) (PI))) (sqrt n)) (- 1 k)) (* (sqrt (+ (PI) (PI))) (sqrt n)) (sqrt n) (- 1 k))
55.0ms	n	@	-inf	((/ (/ (sqrt (* n (+ (PI) (PI)))) (pow (sqrt (* n (+ (PI) (PI)))) k)) (sqrt k)) (/ (sqrt (* n (+ (PI) (PI)))) (pow (sqrt (* n (+ (PI) (PI)))) k)) (sqrt (* n (+ (PI) (PI)))) (* n (+ (PI) (PI))) n (+ (PI) (PI)) (PI) (pow (sqrt (* n (+ (PI) (PI)))) k) k (sqrt k) (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (* (sqrt (/ n k)) (sqrt (+ (PI) (PI)))) (sqrt (/ n k)) (/ n k) (sqrt (+ (PI) (PI))) (* (/ 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)) (* (+ (PI) (PI)) n) (* (sqrt (/ 1 k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt (/ 1 k)) (/ 1 k) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2)) (/ 1 (/ 1 (sqrt (* n (+ (PI) (PI)))))) (/ 1 (sqrt (* n (+ (PI) (PI))))) (/ (pow (* (sqrt (+ (PI) (PI))) (sqrt n)) (- 1 k)) (sqrt k)) (pow (* (sqrt (+ (PI) (PI))) (sqrt n)) (- 1 k)) (* (sqrt (+ (PI) (PI))) (sqrt n)) (sqrt n) (- 1 k))
30.0ms	n	@	inf	((/ (/ (sqrt (* n (+ (PI) (PI)))) (pow (sqrt (* n (+ (PI) (PI)))) k)) (sqrt k)) (/ (sqrt (* n (+ (PI) (PI)))) (pow (sqrt (* n (+ (PI) (PI)))) k)) (sqrt (* n (+ (PI) (PI)))) (* n (+ (PI) (PI))) n (+ (PI) (PI)) (PI) (pow (sqrt (* n (+ (PI) (PI)))) k) k (sqrt k) (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (* (sqrt (/ n k)) (sqrt (+ (PI) (PI)))) (sqrt (/ n k)) (/ n k) (sqrt (+ (PI) (PI))) (* (/ 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)) (* (+ (PI) (PI)) n) (* (sqrt (/ 1 k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt (/ 1 k)) (/ 1 k) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2)) (/ 1 (/ 1 (sqrt (* n (+ (PI) (PI)))))) (/ 1 (sqrt (* n (+ (PI) (PI))))) (/ (pow (* (sqrt (+ (PI) (PI))) (sqrt n)) (- 1 k)) (sqrt k)) (pow (* (sqrt (+ (PI) (PI))) (sqrt n)) (- 1 k)) (* (sqrt (+ (PI) (PI))) (sqrt n)) (sqrt n) (- 1 k))
16.0ms	k	@	0	((/ (/ (sqrt (* n (+ (PI) (PI)))) (pow (sqrt (* n (+ (PI) (PI)))) k)) (sqrt k)) (/ (sqrt (* n (+ (PI) (PI)))) (pow (sqrt (* n (+ (PI) (PI)))) k)) (sqrt (* n (+ (PI) (PI)))) (* n (+ (PI) (PI))) n (+ (PI) (PI)) (PI) (pow (sqrt (* n (+ (PI) (PI)))) k) k (sqrt k) (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (* (sqrt (/ n k)) (sqrt (+ (PI) (PI)))) (sqrt (/ n k)) (/ n k) (sqrt (+ (PI) (PI))) (* (/ 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)) (* (+ (PI) (PI)) n) (* (sqrt (/ 1 k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt (/ 1 k)) (/ 1 k) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2)) (/ 1 (/ 1 (sqrt (* n (+ (PI) (PI)))))) (/ 1 (sqrt (* n (+ (PI) (PI))))) (/ (pow (* (sqrt (+ (PI) (PI))) (sqrt n)) (- 1 k)) (sqrt k)) (pow (* (sqrt (+ (PI) (PI))) (sqrt n)) (- 1 k)) (* (sqrt (+ (PI) (PI))) (sqrt n)) (sqrt n) (- 1 k))
5.0ms	k	@	-inf	((/ (/ (sqrt (* n (+ (PI) (PI)))) (pow (sqrt (* n (+ (PI) (PI)))) k)) (sqrt k)) (/ (sqrt (* n (+ (PI) (PI)))) (pow (sqrt (* n (+ (PI) (PI)))) k)) (sqrt (* n (+ (PI) (PI)))) (* n (+ (PI) (PI))) n (+ (PI) (PI)) (PI) (pow (sqrt (* n (+ (PI) (PI)))) k) k (sqrt k) (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (* (sqrt (/ n k)) (sqrt (+ (PI) (PI)))) (sqrt (/ n k)) (/ n k) (sqrt (+ (PI) (PI))) (* (/ 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)) (* (+ (PI) (PI)) n) (* (sqrt (/ 1 k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt (/ 1 k)) (/ 1 k) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2)) (/ 1 (/ 1 (sqrt (* n (+ (PI) (PI)))))) (/ 1 (sqrt (* n (+ (PI) (PI))))) (/ (pow (* (sqrt (+ (PI) (PI))) (sqrt n)) (- 1 k)) (sqrt k)) (pow (* (sqrt (+ (PI) (PI))) (sqrt n)) (- 1 k)) (* (sqrt (+ (PI) (PI))) (sqrt n)) (sqrt n) (- 1 k))

rewrite163.0ms (2.7%)

Memory

18.6MiB live, 199.2MiB allocated; 22ms collecting garbage

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	479	3884
0	525	3560
1	2487	3242
0	8207	3198

Stop Event

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

Counts

134 → 527

Calls

Call 1

Inputs
(/.f64 (/.f64 (sqrt.f64 (.f64 n (+.f64 (PI.f64) (PI.f64)))) (pow.f64 (sqrt.f64 (.f64 n (+.f64 (PI.f64) (PI.f64)))) k)) (sqrt.f64 k))
(/.f64 (sqrt.f64 (.f64 n (+.f64 (PI.f64) (PI.f64)))) (pow.f64 (sqrt.f64 (.f64 n (+.f64 (PI.f64) (PI.f64)))) k))
(sqrt.f64 (*.f64 n (+.f64 (PI.f64) (PI.f64))))
(*.f64 n (+.f64 (PI.f64) (PI.f64)))
n
(+.f64 (PI.f64) (PI.f64))
(PI.f64)
(pow.f64 (sqrt.f64 (*.f64 n (+.f64 (PI.f64) (PI.f64)))) k)
k
(sqrt.f64 k)
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (*.f64 (sqrt.f64 (/.f64 n k)) (sqrt.f64 (+.f64 (PI.f64) (PI.f64)))))
(*.f64 (sqrt.f64 (/.f64 n k)) (sqrt.f64 (+.f64 (PI.f64) (PI.f64))))
(sqrt.f64 (/.f64 n k))
(/.f64 n k)
(sqrt.f64 (+.f64 (PI.f64) (PI.f64)))
(.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 (+.f64 (PI.f64) (PI.f64)) n)
(.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) k)) #s(approx (pow ( (* 2 (PI)) n) (/ (- 1 k) 2)) (/.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (sqrt.f64 (*.f64 n (+.f64 (PI.f64) (PI.f64))))))))
(sqrt.f64 (/.f64 #s(literal 1 binary64) k))
(/.f64 #s(literal 1 binary64) k)
#s(approx (pow (* (* 2 (PI)) n) (/ (- 1 k) 2)) (/.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (sqrt.f64 (*.f64 n (+.f64 (PI.f64) (PI.f64)))))))
(/.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (sqrt.f64 (*.f64 n (+.f64 (PI.f64) (PI.f64))))))
(/.f64 #s(literal 1 binary64) (sqrt.f64 (*.f64 n (+.f64 (PI.f64) (PI.f64)))))
(/.f64 (pow.f64 (*.f64 (sqrt.f64 (+.f64 (PI.f64) (PI.f64))) (sqrt.f64 n)) (-.f64 #s(literal 1 binary64) k)) (sqrt.f64 k))
(pow.f64 (*.f64 (sqrt.f64 (+.f64 (PI.f64) (PI.f64))) (sqrt.f64 n)) (-.f64 #s(literal 1 binary64) k))
(*.f64 (sqrt.f64 (+.f64 (PI.f64) (PI.f64))) (sqrt.f64 n))
(sqrt.f64 n)
(-.f64 #s(literal 1 binary64) k)
#s(approx (/ (/ (sqrt (* n (+ (PI) (PI)))) (pow (sqrt (* n (+ (PI) (PI)))) k)) (sqrt k)) #s(hole binary64 (/ (sqrt (* 2 (* n (PI)))) (sqrt k))))
#s(approx (/ (/ (sqrt (* n (+ (PI) (PI)))) (pow (sqrt (* n (+ (PI) (PI)))) k)) (sqrt k)) #s(hole binary64 (+ (* -1 (/ (* k (* (log (sqrt (* 2 (* n (PI))))) (sqrt (* 2 (* n (PI)))))) (sqrt k))) (/ (sqrt (* 2 (* n (PI)))) (sqrt k)))))
#s(approx (/ (/ (sqrt (* n (+ (PI) (PI)))) (pow (sqrt (* n (+ (PI) (PI)))) k)) (sqrt k)) #s(hole binary64 (+ (* k (- (* -1 (* k (+ (* -1 (/ (* (pow (log (sqrt (* 2 (* n (PI))))) 2) (sqrt (* 2 (* n (PI))))) (sqrt k))) (* 1/2 (/ (* (pow (log (sqrt (* 2 (* n (PI))))) 2) (sqrt (* 2 (* n (PI))))) (sqrt k)))))) (/ (* (log (sqrt (* 2 (* n (PI))))) (sqrt (* 2 (* n (PI))))) (sqrt k)))) (/ (sqrt (* 2 (* n (PI)))) (sqrt k)))))
#s(approx (/ (/ (sqrt (* n (+ (PI) (PI)))) (pow (sqrt (* n (+ (PI) (PI)))) k)) (sqrt k)) #s(hole binary64 (+ (* k (- (* k (- (* -1 (* k (+ (* -1 (* (log (sqrt (* 2 (* n (PI))))) (+ (* -1 (/ (* (pow (log (sqrt (* 2 (* n (PI))))) 2) (sqrt (* 2 (* n (PI))))) (sqrt k))) (* 1/2 (/ (* (pow (log (sqrt (* 2 (* n (PI))))) 2) (sqrt (* 2 (* n (PI))))) (sqrt k)))))) (+ (* -1/2 (/ (* (pow (log (sqrt (* 2 (* n (PI))))) 3) (sqrt (* 2 (* n (PI))))) (sqrt k))) (* 1/6 (/ (* (pow (log (sqrt (* 2 (* n (PI))))) 3) (sqrt (* 2 (* n (PI))))) (sqrt k))))))) (+ (* -1 (/ (* (pow (log (sqrt (* 2 (* n (PI))))) 2) (sqrt (* 2 (* n (PI))))) (sqrt k))) (* 1/2 (/ (* (pow (log (sqrt (* 2 (* n (PI))))) 2) (sqrt (* 2 (* n (PI))))) (sqrt k)))))) (/ (* (log (sqrt (* 2 (* n (PI))))) (sqrt (* 2 (* n (PI))))) (sqrt k)))) (/ (sqrt (* 2 (* n (PI)))) (sqrt k)))))
#s(approx (/ (sqrt (* n (+ (PI) (PI)))) (pow (sqrt (* n (+ (PI) (PI)))) k)) #s(hole binary64 (sqrt (* 2 (* n (PI))))))
#s(approx (/ (sqrt (* n (+ (PI) (PI)))) (pow (sqrt (* n (+ (PI) (PI)))) k)) #s(hole binary64 (+ (sqrt (* 2 (* n (PI)))) (* -1 (* k (* (log (sqrt (* 2 (* n (PI))))) (sqrt (* 2 (* n (PI))))))))))
#s(approx (/ (sqrt (* n (+ (PI) (PI)))) (pow (sqrt (* n (+ (PI) (PI)))) k)) #s(hole binary64 (+ (sqrt (* 2 (* n (PI)))) (* k (- (* -1 (* k (+ (* -1 (* (pow (log (sqrt (* 2 (* n (PI))))) 2) (sqrt (* 2 (* n (PI)))))) (* 1/2 (* (pow (log (sqrt (* 2 (* n (PI))))) 2) (sqrt (* 2 (* n (PI))))))))) (* (log (sqrt (* 2 (* n (PI))))) (sqrt (* 2 (* n (PI))))))))))
#s(approx (/ (sqrt (* n (+ (PI) (PI)))) (pow (sqrt (* n (+ (PI) (PI)))) k)) #s(hole binary64 (+ (sqrt (* 2 (* n (PI)))) (* k (- (* k (- (* -1 (* k (+ (* -1 (* (log (sqrt (* 2 (* n (PI))))) (+ (* -1 (* (pow (log (sqrt (* 2 (* n (PI))))) 2) (sqrt (* 2 (* n (PI)))))) (* 1/2 (* (pow (log (sqrt (* 2 (* n (PI))))) 2) (sqrt (* 2 (* n (PI))))))))) (+ (* -1/2 (* (pow (log (sqrt (* 2 (* n (PI))))) 3) (sqrt (* 2 (* n (PI)))))) (* 1/6 (* (pow (log (sqrt (* 2 (* n (PI))))) 3) (sqrt (* 2 (* n (PI)))))))))) (+ (* -1 (* (pow (log (sqrt (* 2 (* n (PI))))) 2) (sqrt (* 2 (* n (PI)))))) (* 1/2 (* (pow (log (sqrt (* 2 (* n (PI))))) 2) (sqrt (* 2 (* n (PI))))))))) (* (log (sqrt (* 2 (* n (PI))))) (sqrt (* 2 (* n (PI))))))))))
#s(approx (pow (sqrt (* n (+ (PI) (PI)))) k) #s(hole binary64 1))
#s(approx (pow (sqrt (* n (+ (PI) (PI)))) k) #s(hole binary64 (+ 1 (* k (log (sqrt (* 2 (* n (PI)))))))))
#s(approx (pow (sqrt (* n (+ (PI) (PI)))) k) #s(hole binary64 (+ 1 (* k (+ (log (sqrt (* 2 (* n (PI))))) (* 1/2 (* k (pow (log (sqrt (* 2 (* n (PI))))) 2))))))))
#s(approx (pow (sqrt (* n (+ (PI) (PI)))) k) #s(hole binary64 (+ 1 (* k (+ (log (sqrt (* 2 (* n (PI))))) (* k (+ (* 1/6 (* k (pow (log (sqrt (* 2 (* n (PI))))) 3))) (* 1/2 (pow (log (sqrt (* 2 (* n (PI))))) 2)))))))))
#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 (/ (pow (* 2 (* n (PI))) 1/2) (sqrt k))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) #s(hole binary64 (+ (* -1/2 (/ (* k (* (log (* 2 (* n (PI)))) (pow (* 2 (* n (PI))) 1/2))) (sqrt k))) (/ (pow (* 2 (* n (PI))) 1/2) (sqrt k)))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) #s(hole binary64 (+ (* k (+ (* -1/2 (/ (* (log (* 2 (* n (PI)))) (pow (* 2 (* n (PI))) 1/2)) (sqrt k))) (* 1/8 (/ (* k (* (pow (log (* 2 (* n (PI)))) 2) (pow (* 2 (* n (PI))) 1/2))) (sqrt k))))) (/ (pow (* 2 (* n (PI))) 1/2) (sqrt k)))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) #s(hole binary64 (+ (* k (+ (* -1/2 (/ (* (log (* 2 (* n (PI)))) (pow (* 2 (* n (PI))) 1/2)) (sqrt k))) (* k (+ (* -1/48 (/ (* k (* (pow (log (* 2 (* n (PI)))) 3) (pow (* 2 (* n (PI))) 1/2))) (sqrt k))) (* 1/8 (/ (* (pow (log (* 2 (* n (PI)))) 2) (pow (* 2 (* n (PI))) 1/2)) (sqrt k))))))) (/ (pow (* 2 (* n (PI))) 1/2) (sqrt k)))))
#s(approx (* (sqrt (/ n k)) (sqrt (+ (PI) (PI)))) #s(hole binary64 (/ (* (sqrt (* 2 (PI))) (sqrt (* k n))) k)))
#s(approx (sqrt (/ n k)) #s(hole binary64 (/ (sqrt (* k n)) k)))
#s(approx (/ n k) #s(hole binary64 (/ n k)))
#s(approx (/ 1 (sqrt k)) #s(hole binary64 (/ 1 (sqrt k))))
#s(approx (pow (* (* 2 (PI)) n) (/ (- 1 k) 2)) #s(hole binary64 (pow (* 2 (* n (PI))) 1/2)))
#s(approx (pow (* (* 2 (PI)) n) (/ (- 1 k) 2)) #s(hole binary64 (+ (* -1/2 (* k (* (log (* 2 (* n (PI)))) (pow (* 2 (* n (PI))) 1/2)))) (pow (* 2 (* n (PI))) 1/2))))
#s(approx (pow (* (* 2 (PI)) n) (/ (- 1 k) 2)) #s(hole binary64 (+ (* k (+ (* -1/2 (* (log (* 2 (* n (PI)))) (pow (* 2 (* n (PI))) 1/2))) (* 1/8 (* k (* (pow (log (* 2 (* n (PI)))) 2) (pow (* 2 (* n (PI))) 1/2)))))) (pow (* 2 (* n (PI))) 1/2))))
#s(approx (pow (* (* 2 (PI)) n) (/ (- 1 k) 2)) #s(hole binary64 (+ (* k (+ (* -1/2 (* (log (* 2 (* n (PI)))) (pow (* 2 (* n (PI))) 1/2))) (* k (+ (* -1/48 (* k (* (pow (log (* 2 (* n (PI)))) 3) (pow (* 2 (* n (PI))) 1/2)))) (* 1/8 (* (pow (log (* 2 (* n (PI)))) 2) (pow (* 2 (* n (PI))) 1/2))))))) (pow (* 2 (* n (PI))) 1/2))))
#s(approx (* (sqrt (/ 1 k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) #s(hole binary64 (/ (* (sqrt k) (pow (* 2 (* n (PI))) 1/2)) k)))
#s(approx (* (sqrt (/ 1 k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) #s(hole binary64 (/ (+ (* -1/2 (* k (* (log (* 2 (* n (PI)))) (* (sqrt k) (pow (* 2 (* n (PI))) 1/2))))) (* (sqrt k) (pow (* 2 (* n (PI))) 1/2))) k)))
#s(approx (* (sqrt (/ 1 k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) #s(hole binary64 (/ (+ (* k (+ (* -1/2 (* (log (* 2 (* n (PI)))) (* (sqrt k) (pow (* 2 (* n (PI))) 1/2)))) (* 1/8 (* k (* (pow (log (* 2 (* n (PI)))) 2) (* (sqrt k) (pow (* 2 (* n (PI))) 1/2))))))) (* (sqrt k) (pow (* 2 (* n (PI))) 1/2))) k)))
#s(approx (* (sqrt (/ 1 k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) #s(hole binary64 (/ (+ (* k (+ (* -1/2 (* (log (* 2 (* n (PI)))) (* (sqrt k) (pow (* 2 (* n (PI))) 1/2)))) (* k (+ (* -1/48 (* k (* (pow (log (* 2 (* n (PI)))) 3) (* (sqrt k) (pow (* 2 (* n (PI))) 1/2))))) (* 1/8 (* (pow (log (* 2 (* n (PI)))) 2) (* (sqrt k) (pow (* 2 (* n (PI))) 1/2)))))))) (* (sqrt k) (pow (* 2 (* n (PI))) 1/2))) k)))
#s(approx (sqrt (/ 1 k)) #s(hole binary64 (/ (sqrt k) k)))
#s(approx (/ 1 k) #s(hole binary64 (/ 1 k)))
#s(approx (/ (pow (* (sqrt (+ (PI) (PI))) (sqrt n)) (- 1 k)) (sqrt k)) #s(hole binary64 (/ (* (sqrt n) (sqrt (* 2 (PI)))) (sqrt k))))
#s(approx (/ (pow (* (sqrt (+ (PI) (PI))) (sqrt n)) (- 1 k)) (sqrt k)) #s(hole binary64 (+ (* -1 (/ (* k (* (log (* (sqrt n) (sqrt (* 2 (PI))))) (* (sqrt n) (sqrt (* 2 (PI)))))) (sqrt k))) (/ (* (sqrt n) (sqrt (* 2 (PI)))) (sqrt k)))))
#s(approx (/ (pow (* (sqrt (+ (PI) (PI))) (sqrt n)) (- 1 k)) (sqrt k)) #s(hole binary64 (+ (* k (+ (* -1 (/ (* (log (* (sqrt n) (sqrt (* 2 (PI))))) (* (sqrt n) (sqrt (* 2 (PI))))) (sqrt k))) (* 1/2 (/ (* k (* (pow (log (* (sqrt n) (sqrt (* 2 (PI))))) 2) (* (sqrt n) (sqrt (* 2 (PI)))))) (sqrt k))))) (/ (* (sqrt n) (sqrt (* 2 (PI)))) (sqrt k)))))
#s(approx (/ (pow (* (sqrt (+ (PI) (PI))) (sqrt n)) (- 1 k)) (sqrt k)) #s(hole binary64 (+ (* k (+ (* -1 (/ (* (log (* (sqrt n) (sqrt (* 2 (PI))))) (* (sqrt n) (sqrt (* 2 (PI))))) (sqrt k))) (* k (+ (* -1/6 (/ (* k (* (pow (log (* (sqrt n) (sqrt (* 2 (PI))))) 3) (* (sqrt n) (sqrt (* 2 (PI)))))) (sqrt k))) (* 1/2 (/ (* (pow (log (* (sqrt n) (sqrt (* 2 (PI))))) 2) (* (sqrt n) (sqrt (* 2 (PI))))) (sqrt k))))))) (/ (* (sqrt n) (sqrt (* 2 (PI)))) (sqrt k)))))
#s(approx (pow (* (sqrt (+ (PI) (PI))) (sqrt n)) (- 1 k)) #s(hole binary64 (* (sqrt n) (sqrt (* 2 (PI))))))
#s(approx (pow (* (sqrt (+ (PI) (PI))) (sqrt n)) (- 1 k)) #s(hole binary64 (+ (* -1 (* k (* (log (* (sqrt n) (sqrt (* 2 (PI))))) (* (sqrt n) (sqrt (* 2 (PI))))))) (* (sqrt n) (sqrt (* 2 (PI)))))))
#s(approx (pow (* (sqrt (+ (PI) (PI))) (sqrt n)) (- 1 k)) #s(hole binary64 (+ (* k (+ (* -1 (* (log (* (sqrt n) (sqrt (* 2 (PI))))) (* (sqrt n) (sqrt (* 2 (PI)))))) (* 1/2 (* k (* (pow (log (* (sqrt n) (sqrt (* 2 (PI))))) 2) (* (sqrt n) (sqrt (* 2 (PI))))))))) (* (sqrt n) (sqrt (* 2 (PI)))))))
#s(approx (pow (* (sqrt (+ (PI) (PI))) (sqrt n)) (- 1 k)) #s(hole binary64 (+ (* k (+ (* -1 (* (log (* (sqrt n) (sqrt (* 2 (PI))))) (* (sqrt n) (sqrt (* 2 (PI)))))) (* k (+ (* -1/6 (* k (* (pow (log (* (sqrt n) (sqrt (* 2 (PI))))) 3) (* (sqrt n) (sqrt (* 2 (PI))))))) (* 1/2 (* (pow (log (* (sqrt n) (sqrt (* 2 (PI))))) 2) (* (sqrt n) (sqrt (* 2 (PI)))))))))) (* (sqrt n) (sqrt (* 2 (PI)))))))
#s(approx (- 1 k) #s(hole binary64 (+ 1 (* -1 k))))
#s(approx (/ (/ (sqrt (* n (+ (PI) (PI)))) (pow (sqrt (* n (+ (PI) (PI)))) k)) (sqrt k)) #s(hole binary64 (/ (sqrt (* 2 (* n (PI)))) (* k (* (sqrt (/ 1 k)) (pow (sqrt (* 2 (* n (PI)))) k))))))
#s(approx (/ (sqrt (* n (+ (PI) (PI)))) (pow (sqrt (* n (+ (PI) (PI)))) k)) #s(hole binary64 (/ (sqrt (* 2 (* n (PI)))) (pow (sqrt (* 2 (* n (PI)))) k))))
#s(approx (pow (sqrt (* n (+ (PI) (PI)))) k) #s(hole binary64 (pow (sqrt (* 2 (* n (PI)))) k)))
#s(approx (sqrt k) #s(hole binary64 (* k (sqrt (/ 1 k)))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) #s(hole binary64 (/ (exp (* 1/2 (* (log (* 2 (* n (PI)))) (- 1 k)))) (* k (sqrt (/ 1 k))))))
#s(approx (* (sqrt (/ n k)) (sqrt (+ (PI) (PI)))) #s(hole binary64 (* (sqrt (* 2 (PI))) (sqrt (/ n k)))))
#s(approx (sqrt (/ n k)) #s(hole binary64 (sqrt (/ n k))))
#s(approx (/ 1 (sqrt k)) #s(hole binary64 (/ 1 (* k (sqrt (/ 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 (* (sqrt (/ 1 k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) #s(hole binary64 (* (exp (* 1/2 (* (log (* 2 (* n (PI)))) (- 1 k)))) (sqrt (/ 1 k)))))
#s(approx (sqrt (/ 1 k)) #s(hole binary64 (sqrt (/ 1 k))))
#s(approx (/ (pow (* (sqrt (+ (PI) (PI))) (sqrt n)) (- 1 k)) (sqrt k)) #s(hole binary64 (/ (exp (* (log (* (sqrt n) (sqrt (* 2 (PI))))) (- 1 k))) (* k (sqrt (/ 1 k))))))
#s(approx (pow (* (sqrt (+ (PI) (PI))) (sqrt n)) (- 1 k)) #s(hole binary64 (exp (* (log (* (sqrt n) (sqrt (* 2 (PI))))) (- 1 k)))))
#s(approx (- 1 k) #s(hole binary64 (* -1 k)))
#s(approx (- 1 k) #s(hole binary64 (* k (- (/ 1 k) 1))))
#s(approx (/ (/ (sqrt (* n (+ (PI) (PI)))) (pow (sqrt (* n (+ (PI) (PI)))) k)) (sqrt k)) #s(hole binary64 (* -1 (/ (sqrt (* 2 (* n (PI)))) (* k (* (sqrt (/ 1 k)) (pow (sqrt (* 2 (* n (PI)))) k)))))))
#s(approx (sqrt k) #s(hole binary64 (* -1 (* k (sqrt (/ 1 k))))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) #s(hole binary64 (* -1 (/ (exp (* 1/2 (* (log (* 2 (* n (PI)))) (+ 1 (* -1 k))))) (* k (sqrt (/ 1 k)))))))
#s(approx (/ 1 (sqrt k)) #s(hole binary64 (/ -1 (* k (sqrt (/ 1 k))))))
#s(approx (pow (* (* 2 (PI)) n) (/ (- 1 k) 2)) #s(hole binary64 (exp (* 1/2 (* (log (* 2 (* n (PI)))) (+ 1 (* -1 k)))))))
#s(approx (* (sqrt (/ 1 k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) #s(hole binary64 (* (exp (* 1/2 (* (log (* 2 (* n (PI)))) (+ 1 (* -1 k))))) (sqrt (/ 1 k)))))
#s(approx (/ (pow (* (sqrt (+ (PI) (PI))) (sqrt n)) (- 1 k)) (sqrt k)) #s(hole binary64 (* -1 (/ (exp (* (log (* (sqrt n) (sqrt (* 2 (PI))))) (+ 1 (* -1 k)))) (* k (sqrt (/ 1 k)))))))
#s(approx (pow (* (sqrt (+ (PI) (PI))) (sqrt n)) (- 1 k)) #s(hole binary64 (exp (* (log (* (sqrt n) (sqrt (* 2 (PI))))) (+ 1 (* -1 k))))))
#s(approx (- 1 k) #s(hole binary64 (* -1 (* k (- 1 (/ 1 k))))))
#s(approx (/ (/ (sqrt (* n (+ (PI) (PI)))) (pow (sqrt (* n (+ (PI) (PI)))) k)) (sqrt k)) #s(hole binary64 (/ (sqrt (* 2 (* n (PI)))) (* (sqrt k) (pow (sqrt (* 2 (* n (PI)))) k)))))
#s(approx (* n (+ (PI) (PI))) #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 (/ (exp (* 1/2 (* (+ (log n) (log (* 2 (PI)))) (- 1 k)))) (sqrt k))))
#s(approx (pow (* (* 2 (PI)) n) (/ (- 1 k) 2)) #s(hole binary64 (exp (* 1/2 (* (+ (log n) (log (* 2 (PI)))) (- 1 k))))))
#s(approx (* (sqrt (/ 1 k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) #s(hole binary64 (* (exp (* 1/2 (* (+ (log n) (log (* 2 (PI)))) (- 1 k)))) (sqrt (/ 1 k)))))
#s(approx (/ 1 (sqrt (* n (+ (PI) (PI))))) #s(hole binary64 (/ 1 (sqrt (* 2 (* n (PI)))))))
#s(approx (/ (pow (* (sqrt (+ (PI) (PI))) (sqrt n)) (- 1 k)) (sqrt k)) #s(hole binary64 (/ (exp (* (log (* (sqrt n) (sqrt (* 2 (PI))))) (- 1 k))) (sqrt k))))
#s(approx (sqrt n) #s(hole binary64 (sqrt n)))
#s(approx (/ (/ (sqrt (* n (+ (PI) (PI)))) (pow (sqrt (* n (+ (PI) (PI)))) k)) (sqrt k)) #s(hole binary64 (/ (* n (sqrt (* 2 (/ (PI) n)))) (* (exp (* k (+ (log (sqrt (* 2 (/ (PI) n)))) (* -1 (log (/ 1 n)))))) (sqrt k)))))
#s(approx (/ (sqrt (* n (+ (PI) (PI)))) (pow (sqrt (* n (+ (PI) (PI)))) k)) #s(hole binary64 (/ (* n (sqrt (* 2 (/ (PI) n)))) (exp (* k (+ (log (sqrt (* 2 (/ (PI) n)))) (* -1 (log (/ 1 n)))))))))
#s(approx (sqrt (* n (+ (PI) (PI)))) #s(hole binary64 (* n (sqrt (* 2 (/ (PI) n))))))
#s(approx (pow (sqrt (* n (+ (PI) (PI)))) k) #s(hole binary64 (exp (* k (+ (log (sqrt (* 2 (/ (PI) n)))) (* -1 (log (/ 1 n))))))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) #s(hole binary64 (/ (exp (* 1/2 (* (+ (log (* 2 (PI))) (* -1 (log (/ 1 n)))) (- 1 k)))) (sqrt k))))
#s(approx (* (sqrt (/ n k)) (sqrt (+ (PI) (PI)))) #s(hole binary64 (* n (* (sqrt (* 2 (PI))) (sqrt (/ 1 (* k n)))))))
#s(approx (sqrt (/ n k)) #s(hole binary64 (* n (sqrt (/ 1 (* k n))))))
#s(approx (pow (* (* 2 (PI)) n) (/ (- 1 k) 2)) #s(hole binary64 (exp (* 1/2 (* (+ (log (* 2 (PI))) (* -1 (log (/ 1 n)))) (- 1 k))))))
#s(approx (* (sqrt (/ 1 k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) #s(hole binary64 (* (exp (* 1/2 (* (+ (log (* 2 (PI))) (* -1 (log (/ 1 n)))) (- 1 k)))) (sqrt (/ 1 k)))))
#s(approx (/ 1 (sqrt (* n (+ (PI) (PI))))) #s(hole binary64 (/ 1 (* n (sqrt (* 2 (/ (PI) n)))))))
#s(approx (/ (pow (* (sqrt (+ (PI) (PI))) (sqrt n)) (- 1 k)) (sqrt k)) #s(hole binary64 (/ (exp (* (+ (log (* (sqrt (* 2 (PI))) (sqrt (/ 1 n)))) (* -1 (log (/ 1 n)))) (- 1 k))) (sqrt k))))
#s(approx (pow (* (sqrt (+ (PI) (PI))) (sqrt n)) (- 1 k)) #s(hole binary64 (exp (* (+ (log (* (sqrt (* 2 (PI))) (sqrt (/ 1 n)))) (* -1 (log (/ 1 n)))) (- 1 k)))))
#s(approx (* (sqrt (+ (PI) (PI))) (sqrt n)) #s(hole binary64 (* n (* (sqrt (* 2 (PI))) (sqrt (/ 1 n))))))
#s(approx (sqrt n) #s(hole binary64 (* n (sqrt (/ 1 n)))))
#s(approx (/ (/ (sqrt (* n (+ (PI) (PI)))) (pow (sqrt (* n (+ (PI) (PI)))) k)) (sqrt k)) #s(hole binary64 (* -1 (/ (* n (sqrt (* 2 (/ (PI) n)))) (* (exp (* k (+ (log (sqrt (* 2 (/ (PI) n)))) (* -1 (log (/ -1 n)))))) (sqrt k))))))
#s(approx (/ (sqrt (* n (+ (PI) (PI)))) (pow (sqrt (* n (+ (PI) (PI)))) k)) #s(hole binary64 (* -1 (/ (* n (sqrt (* 2 (/ (PI) n)))) (exp (* k (+ (log (sqrt (* 2 (/ (PI) n)))) (* -1 (log (/ -1 n))))))))))
#s(approx (sqrt (* n (+ (PI) (PI)))) #s(hole binary64 (* -1 (* n (sqrt (* 2 (/ (PI) n)))))))
#s(approx (pow (sqrt (* n (+ (PI) (PI)))) k) #s(hole binary64 (exp (* k (+ (log (sqrt (* 2 (/ (PI) n)))) (* -1 (log (/ -1 n))))))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) #s(hole binary64 (/ (exp (* 1/2 (* (+ (log (* -2 (PI))) (* -1 (log (/ -1 n)))) (- 1 k)))) (sqrt k))))
#s(approx (* (sqrt (/ n k)) (sqrt (+ (PI) (PI)))) #s(hole binary64 (* -1 (* n (* (sqrt (* 2 (PI))) (sqrt (/ 1 (* k n))))))))
#s(approx (sqrt (/ n k)) #s(hole binary64 (* -1 (* n (sqrt (/ 1 (* k n)))))))
#s(approx (pow (* (* 2 (PI)) n) (/ (- 1 k) 2)) #s(hole binary64 (exp (* 1/2 (* (+ (log (* -2 (PI))) (* -1 (log (/ -1 n)))) (- 1 k))))))
#s(approx (* (sqrt (/ 1 k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) #s(hole binary64 (* (exp (* 1/2 (* (+ (log (* -2 (PI))) (* -1 (log (/ -1 n)))) (- 1 k)))) (sqrt (/ 1 k)))))
#s(approx (/ 1 (sqrt (* n (+ (PI) (PI))))) #s(hole binary64 (/ -1 (* n (sqrt (* 2 (/ (PI) n)))))))
#s(approx (/ (pow (* (sqrt (+ (PI) (PI))) (sqrt n)) (- 1 k)) (sqrt k)) #s(hole binary64 (/ (exp (* (+ (log (* (sqrt (* 2 (PI))) (sqrt (/ 1 n)))) (* -1 (log (/ -1 n)))) (- 1 k))) (sqrt k))))
#s(approx (pow (* (sqrt (+ (PI) (PI))) (sqrt n)) (- 1 k)) #s(hole binary64 (exp (* (+ (log (* (sqrt (* 2 (PI))) (sqrt (/ 1 n)))) (* -1 (log (/ -1 n)))) (- 1 k)))))
#s(approx (* (sqrt (+ (PI) (PI))) (sqrt n)) #s(hole binary64 (* -1 (* n (* (sqrt (* 2 (PI))) (sqrt (/ 1 n)))))))
#s(approx (sqrt n) #s(hole binary64 (* -1 (* n (sqrt (/ 1 n))))))

Outputs
(.f64 (/.f64 (sqrt.f64 n) (pow.f64 (sqrt.f64 (.f64 (+.f64 (PI.f64) (PI.f64)) n)) (/.f64 k #s(literal 2 binary64)))) (/.f64 (sqrt.f64 (/.f64 (+.f64 (PI.f64) (PI.f64)) k)) (pow.f64 (sqrt.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n)) (/.f64 k #s(literal 2 binary64)))))
(.f64 (/.f64 (pow.f64 (.f64 (+.f64 (PI.f64) (PI.f64)) n) #s(literal 1/4 binary64)) (pow.f64 (sqrt.f64 (.f64 (+.f64 (PI.f64) (PI.f64)) n)) k)) (/.f64 (pow.f64 (.f64 (+.f64 (PI.f64) (PI.f64)) n) #s(literal 1/4 binary64)) (sqrt.f64 k)))
(.f64 (/.f64 (pow.f64 (.f64 (+.f64 (PI.f64) (PI.f64)) n) #s(literal 1/4 binary64)) (sqrt.f64 k)) (/.f64 (pow.f64 (.f64 (+.f64 (PI.f64) (PI.f64)) n) #s(literal 1/4 binary64)) (pow.f64 (sqrt.f64 (.f64 (+.f64 (PI.f64) (PI.f64)) n)) k)))
(.f64 (/.f64 (sqrt.f64 #s(literal 2 binary64)) (pow.f64 (sqrt.f64 (.f64 (+.f64 (PI.f64) (PI.f64)) n)) k)) (/.f64 (sqrt.f64 (*.f64 (PI.f64) n)) (sqrt.f64 k)))
(.f64 (/.f64 (sqrt.f64 #s(literal 2 binary64)) (sqrt.f64 k)) (/.f64 (sqrt.f64 (.f64 (PI.f64) n)) (pow.f64 (sqrt.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n)) k)))
(.f64 (/.f64 (sqrt.f64 (+.f64 (PI.f64) (PI.f64))) (pow.f64 (sqrt.f64 (.f64 (+.f64 (PI.f64) (PI.f64)) n)) k)) (sqrt.f64 (/.f64 n k)))
(.f64 (/.f64 (sqrt.f64 n) (pow.f64 (sqrt.f64 (.f64 (+.f64 (PI.f64) (PI.f64)) n)) k)) (sqrt.f64 (/.f64 (+.f64 (PI.f64) (PI.f64)) k)))
(.f64 (/.f64 #s(literal 1 binary64) (pow.f64 (sqrt.f64 (.f64 (+.f64 (PI.f64) (PI.f64)) n)) k)) (sqrt.f64 (/.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n) k)))
(.f64 (sqrt.f64 (/.f64 (+.f64 (PI.f64) (PI.f64)) k)) (/.f64 (sqrt.f64 n) (pow.f64 (sqrt.f64 (.f64 (+.f64 (PI.f64) (PI.f64)) n)) k)))
(.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) (pow.f64 (sqrt.f64 (.f64 (+.f64 (PI.f64) (PI.f64)) n)) (-.f64 #s(literal 1 binary64) k)))
(.f64 (sqrt.f64 (/.f64 n k)) (/.f64 (sqrt.f64 (+.f64 (PI.f64) (PI.f64))) (pow.f64 (sqrt.f64 (.f64 (+.f64 (PI.f64) (PI.f64)) n)) k)))
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(/.f64 #s(literal -1 binary64) (.f64 #s(literal 1 binary64) (neg.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 (.f64 (+.f64 (PI.f64) (PI.f64)) n))))))
(/.f64 #s(literal -1 binary64) (neg.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n)))))
(/.f64 #s(literal 2 binary64) (.f64 #s(literal 2 binary64) (/.f64 #s(literal 1 binary64) (sqrt.f64 (.f64 (+.f64 (PI.f64) (PI.f64)) n)))))
(/.f64 #s(literal 1 binary64) (neg.f64 (neg.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n))))))
(/.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (sqrt.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n))))
(sqrt.f64 (.f64 #s(literal 1 binary64) (.f64 (+.f64 (PI.f64) (PI.f64)) n)))
(sqrt.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n))
(exp.f64 (.f64 (neg.f64 (log.f64 (sqrt.f64 (.f64 (+.f64 (PI.f64) (PI.f64)) n)))) #s(literal -1 binary64)))
(exp.f64 (.f64 (log.f64 (sqrt.f64 (.f64 (+.f64 (PI.f64) (PI.f64)) n))) #s(literal 1 binary64)))
(exp.f64 (log.f64 (sqrt.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n))))
(+.f64 (cosh.f64 (log.f64 (sqrt.f64 (.f64 (+.f64 (PI.f64) (PI.f64)) n)))) (sinh.f64 (log.f64 (sqrt.f64 (.f64 (+.f64 (PI.f64) (PI.f64)) n)))))
(pow.f64 n #s(literal 1/2 binary64))
(sqrt.f64 n)
(exp.f64 (*.f64 (log.f64 n) #s(literal 1/2 binary64)))
(/.f64 (neg.f64 (-.f64 #s(literal 1 binary64) (*.f64 k k))) (neg.f64 (+.f64 #s(literal 1 binary64) k)))
(/.f64 (neg.f64 (-.f64 #s(literal 1 binary64) (.f64 (.f64 k k) k))) (neg.f64 (+.f64 #s(literal 1 binary64) (fma.f64 k k (*.f64 #s(literal 1 binary64) k)))))
(/.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 (/.f64 #s(literal 1 binary64) (+.f64 #s(literal 1 binary64) k)) (/.f64 (*.f64 k k) (+.f64 #s(literal 1 binary64) k)))
(-.f64 (/.f64 #s(literal 1 binary64) (+.f64 #s(literal 1 binary64) (fma.f64 k k (.f64 #s(literal 1 binary64) k)))) (/.f64 (.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 (/ (pow (* (sqrt (+ (PI) (PI))) (sqrt n)) (- 1 k)) (sqrt k)) (sqrt.f64 (/.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n) k)))
#s(approx (/ (pow (* (sqrt (+ (PI) (PI))) (sqrt n)) (- 1 k)) (sqrt k)) (/.f64 (fma.f64 (neg.f64 k) (.f64 (log.f64 (sqrt.f64 (.f64 (+.f64 (PI.f64) (PI.f64)) n))) (sqrt.f64 (.f64 (+.f64 (PI.f64) (PI.f64)) n))) (sqrt.f64 (.f64 (+.f64 (PI.f64) (PI.f64)) n))) (sqrt.f64 k)))
#s(approx (/ (pow (* (sqrt (+ (PI) (PI))) (sqrt n)) (- 1 k)) (sqrt k)) (fma.f64 k (-.f64 (.f64 (neg.f64 k) (.f64 (.f64 (pow.f64 (log.f64 (sqrt.f64 (.f64 (+.f64 (PI.f64) (PI.f64)) n))) #s(literal 2 binary64)) (sqrt.f64 (/.f64 (.f64 (+.f64 (PI.f64) (PI.f64)) n) k))) #s(literal -1/2 binary64))) (.f64 (log.f64 (sqrt.f64 (.f64 (+.f64 (PI.f64) (PI.f64)) n))) (sqrt.f64 (/.f64 (.f64 (+.f64 (PI.f64) (PI.f64)) n) k)))) (sqrt.f64 (/.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n) k))))
#s(approx (/ (pow (* (sqrt (+ (PI) (PI))) (sqrt n)) (- 1 k)) (sqrt k)) (fma.f64 (-.f64 (.f64 (-.f64 (.f64 (neg.f64 k) (fma.f64 (neg.f64 (log.f64 (sqrt.f64 (.f64 (+.f64 (PI.f64) (PI.f64)) n)))) (.f64 (.f64 (pow.f64 (log.f64 (sqrt.f64 (.f64 (+.f64 (PI.f64) (PI.f64)) n))) #s(literal 2 binary64)) (sqrt.f64 (/.f64 (.f64 (+.f64 (PI.f64) (PI.f64)) n) k))) #s(literal -1/2 binary64)) (.f64 (.f64 (pow.f64 (log.f64 (sqrt.f64 (.f64 (+.f64 (PI.f64) (PI.f64)) n))) #s(literal 3 binary64)) (sqrt.f64 (/.f64 (.f64 (+.f64 (PI.f64) (PI.f64)) n) k))) #s(literal -1/3 binary64)))) (.f64 (.f64 (pow.f64 (log.f64 (sqrt.f64 (.f64 (+.f64 (PI.f64) (PI.f64)) n))) #s(literal 2 binary64)) (sqrt.f64 (/.f64 (.f64 (+.f64 (PI.f64) (PI.f64)) n) k))) #s(literal -1/2 binary64))) k) (.f64 (log.f64 (sqrt.f64 (.f64 (+.f64 (PI.f64) (PI.f64)) n))) (sqrt.f64 (/.f64 (.f64 (+.f64 (PI.f64) (PI.f64)) n) k)))) k (sqrt.f64 (/.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n) k))))
#s(approx (pow (* (sqrt (+ (PI) (PI))) (sqrt n)) (- 1 k)) (sqrt.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n)))
#s(approx (pow (* (sqrt (+ (PI) (PI))) (sqrt n)) (- 1 k)) (fma.f64 (neg.f64 k) (.f64 (log.f64 (sqrt.f64 (.f64 (+.f64 (PI.f64) (PI.f64)) n))) (sqrt.f64 (.f64 (+.f64 (PI.f64) (PI.f64)) n))) (sqrt.f64 (.f64 (+.f64 (PI.f64) (PI.f64)) n))))
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#s(approx (pow (sqrt (* n (+ (PI) (PI)))) k) #s(literal 1 binary64))
#s(approx (pow (sqrt (* n (+ (PI) (PI)))) k) (fma.f64 (log.f64 (sqrt.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n))) k #s(literal 1 binary64)))
#s(approx (pow (sqrt (* n (+ (PI) (PI)))) k) (fma.f64 (fma.f64 (.f64 (pow.f64 (log.f64 (sqrt.f64 (.f64 (+.f64 (PI.f64) (PI.f64)) n))) #s(literal 2 binary64)) k) #s(literal 1/2 binary64) (log.f64 (sqrt.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n)))) k #s(literal 1 binary64)))
#s(approx (pow (sqrt (* n (+ (PI) (PI)))) k) (fma.f64 k (fma.f64 k (fma.f64 (.f64 (pow.f64 (log.f64 (sqrt.f64 (.f64 (+.f64 (PI.f64) (PI.f64)) n))) #s(literal 3 binary64)) k) #s(literal 1/6 binary64) (.f64 (pow.f64 (log.f64 (sqrt.f64 (.f64 (+.f64 (PI.f64) (PI.f64)) n))) #s(literal 2 binary64)) #s(literal 1/2 binary64))) (log.f64 (sqrt.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n)))) #s(literal 1 binary64)))
#s(approx k k)
#s(approx (sqrt k) (sqrt.f64 k))
#s(approx (/ (pow (* (sqrt (+ (PI) (PI))) (sqrt n)) (- 1 k)) (sqrt k)) (sqrt.f64 (/.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n) k)))
#s(approx (/ (pow (* (sqrt (+ (PI) (PI))) (sqrt n)) (- 1 k)) (sqrt k)) (/.f64 (fma.f64 (.f64 (.f64 (log.f64 (.f64 (+.f64 (PI.f64) (PI.f64)) n)) (sqrt.f64 (.f64 (+.f64 (PI.f64) (PI.f64)) n))) k) #s(literal -1/2 binary64) (sqrt.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n))) (sqrt.f64 k)))
#s(approx (/ (pow (* (sqrt (+ (PI) (PI))) (sqrt n)) (- 1 k)) (sqrt k)) (fma.f64 (/.f64 (fma.f64 (.f64 #s(literal 1/8 binary64) k) (.f64 (.f64 (log.f64 (.f64 (+.f64 (PI.f64) (PI.f64)) n)) (log.f64 (.f64 (+.f64 (PI.f64) (PI.f64)) n))) (sqrt.f64 (.f64 (+.f64 (PI.f64) (PI.f64)) n))) (neg.f64 (.f64 (log.f64 (sqrt.f64 (.f64 (+.f64 (PI.f64) (PI.f64)) n))) (sqrt.f64 (.f64 (+.f64 (PI.f64) (PI.f64)) n))))) (sqrt.f64 k)) k (sqrt.f64 (/.f64 (.f64 (+.f64 (PI.f64) (PI.f64)) n) k))))
#s(approx (/ (pow (* (sqrt (+ (PI) (PI))) (sqrt n)) (- 1 k)) (sqrt k)) (fma.f64 (fma.f64 k (/.f64 (fma.f64 (.f64 #s(literal -1/48 binary64) k) (.f64 (pow.f64 (log.f64 (.f64 (+.f64 (PI.f64) (PI.f64)) n)) #s(literal 3 binary64)) (sqrt.f64 (.f64 (+.f64 (PI.f64) (PI.f64)) n))) (.f64 (.f64 (.f64 (log.f64 (.f64 (+.f64 (PI.f64) (PI.f64)) n)) (log.f64 (.f64 (+.f64 (PI.f64) (PI.f64)) n))) (sqrt.f64 (.f64 (+.f64 (PI.f64) (PI.f64)) n))) #s(literal 1/8 binary64))) (sqrt.f64 k)) (neg.f64 (.f64 (log.f64 (sqrt.f64 (.f64 (+.f64 (PI.f64) (PI.f64)) n))) (sqrt.f64 (/.f64 (.f64 (+.f64 (PI.f64) (PI.f64)) n) k))))) k (sqrt.f64 (/.f64 (.f64 (+.f64 (PI.f64) (PI.f64)) n) k))))
#s(approx (* (sqrt (/ n k)) (sqrt (+ (PI) (PI)))) (/.f64 (sqrt.f64 (.f64 (.f64 k n) (+.f64 (PI.f64) (PI.f64)))) k))
#s(approx (sqrt (/ n k)) (/.f64 (sqrt.f64 (*.f64 k n)) k))
#s(approx (/ n k) (/.f64 n k))
#s(approx (sqrt (/ 1 k)) (/.f64 #s(literal 1 binary64) (sqrt.f64 k)))
#s(approx (pow (* (sqrt (+ (PI) (PI))) (sqrt n)) (- 1 k)) (sqrt.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n)))
#s(approx (pow (* (sqrt (+ (PI) (PI))) (sqrt n)) (- 1 k)) (fma.f64 (.f64 (.f64 (log.f64 (.f64 (+.f64 (PI.f64) (PI.f64)) n)) (sqrt.f64 (.f64 (+.f64 (PI.f64) (PI.f64)) n))) k) #s(literal -1/2 binary64) (sqrt.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n))))
#s(approx (pow (* (sqrt (+ (PI) (PI))) (sqrt n)) (- 1 k)) (fma.f64 k (fma.f64 (.f64 #s(literal 1/8 binary64) k) (.f64 (.f64 (log.f64 (.f64 (+.f64 (PI.f64) (PI.f64)) n)) (log.f64 (.f64 (+.f64 (PI.f64) (PI.f64)) n))) (sqrt.f64 (.f64 (+.f64 (PI.f64) (PI.f64)) n))) (neg.f64 (.f64 (log.f64 (sqrt.f64 (.f64 (+.f64 (PI.f64) (PI.f64)) n))) (sqrt.f64 (.f64 (+.f64 (PI.f64) (PI.f64)) n))))) (sqrt.f64 (.f64 (+.f64 (PI.f64) (PI.f64)) n))))
#s(approx (pow (* (sqrt (+ (PI) (PI))) (sqrt n)) (- 1 k)) (fma.f64 k (fma.f64 k (fma.f64 (.f64 #s(literal -1/48 binary64) k) (.f64 (pow.f64 (log.f64 (.f64 (+.f64 (PI.f64) (PI.f64)) n)) #s(literal 3 binary64)) (sqrt.f64 (.f64 (+.f64 (PI.f64) (PI.f64)) n))) (.f64 (.f64 (.f64 (log.f64 (.f64 (+.f64 (PI.f64) (PI.f64)) n)) (log.f64 (.f64 (+.f64 (PI.f64) (PI.f64)) n))) (sqrt.f64 (.f64 (+.f64 (PI.f64) (PI.f64)) n))) #s(literal 1/8 binary64))) (neg.f64 (.f64 (log.f64 (sqrt.f64 (.f64 (+.f64 (PI.f64) (PI.f64)) n))) (sqrt.f64 (.f64 (+.f64 (PI.f64) (PI.f64)) n))))) (sqrt.f64 (.f64 (+.f64 (PI.f64) (PI.f64)) n))))
#s(approx (/ (pow (* (sqrt (+ (PI) (PI))) (sqrt n)) (- 1 k)) (sqrt k)) (/.f64 (sqrt.f64 (.f64 (.f64 (+.f64 (PI.f64) (PI.f64)) n) k)) k))
#s(approx (/ (pow (* (sqrt (+ (PI) (PI))) (sqrt n)) (- 1 k)) (sqrt k)) (/.f64 (fma.f64 (.f64 #s(literal -1/2 binary64) k) (.f64 (sqrt.f64 (.f64 (.f64 (+.f64 (PI.f64) (PI.f64)) n) k)) (log.f64 (.f64 (+.f64 (PI.f64) (PI.f64)) n))) (sqrt.f64 (.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n) k))) k))
#s(approx (/ (pow (* (sqrt (+ (PI) (PI))) (sqrt n)) (- 1 k)) (sqrt k)) (/.f64 (fma.f64 k (fma.f64 (.f64 (.f64 (sqrt.f64 (.f64 (.f64 (+.f64 (PI.f64) (PI.f64)) n) k)) (.f64 (log.f64 (.f64 (+.f64 (PI.f64) (PI.f64)) n)) (log.f64 (.f64 (+.f64 (PI.f64) (PI.f64)) n)))) k) #s(literal 1/8 binary64) (.f64 (neg.f64 (log.f64 (sqrt.f64 (.f64 (+.f64 (PI.f64) (PI.f64)) n)))) (sqrt.f64 (.f64 (.f64 (+.f64 (PI.f64) (PI.f64)) n) k)))) (sqrt.f64 (.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n) k))) k))
#s(approx (/ (pow (* (sqrt (+ (PI) (PI))) (sqrt n)) (- 1 k)) (sqrt k)) (/.f64 (fma.f64 (fma.f64 k (fma.f64 (.f64 #s(literal -1/48 binary64) k) (.f64 (sqrt.f64 (.f64 (.f64 (+.f64 (PI.f64) (PI.f64)) n) k)) (pow.f64 (log.f64 (.f64 (+.f64 (PI.f64) (PI.f64)) n)) #s(literal 3 binary64))) (.f64 (.f64 (sqrt.f64 (.f64 (.f64 (+.f64 (PI.f64) (PI.f64)) n) k)) (.f64 (log.f64 (.f64 (+.f64 (PI.f64) (PI.f64)) n)) (log.f64 (.f64 (+.f64 (PI.f64) (PI.f64)) n)))) #s(literal 1/8 binary64))) (.f64 (neg.f64 (log.f64 (sqrt.f64 (.f64 (+.f64 (PI.f64) (PI.f64)) n)))) (sqrt.f64 (.f64 (.f64 (+.f64 (PI.f64) (PI.f64)) n) k)))) k (sqrt.f64 (.f64 (.f64 (+.f64 (PI.f64) (PI.f64)) n) k))) k))
#s(approx (sqrt (/ 1 k)) (/.f64 (sqrt.f64 k) k))
#s(approx (/ 1 k) (/.f64 #s(literal 1 binary64) k))
#s(approx (/ (pow (* (sqrt (+ (PI) (PI))) (sqrt n)) (- 1 k)) (sqrt k)) (sqrt.f64 (/.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n) k)))
#s(approx (/ (pow (* (sqrt (+ (PI) (PI))) (sqrt n)) (- 1 k)) (sqrt k)) (/.f64 (fma.f64 (neg.f64 k) (.f64 (log.f64 (sqrt.f64 (.f64 (+.f64 (PI.f64) (PI.f64)) n))) (sqrt.f64 (.f64 (+.f64 (PI.f64) (PI.f64)) n))) (sqrt.f64 (.f64 (+.f64 (PI.f64) (PI.f64)) n))) (sqrt.f64 k)))
#s(approx (/ (pow (* (sqrt (+ (PI) (PI))) (sqrt n)) (- 1 k)) (sqrt k)) (fma.f64 (/.f64 (fma.f64 (.f64 #s(literal 1/2 binary64) k) (.f64 (pow.f64 (log.f64 (sqrt.f64 (.f64 (+.f64 (PI.f64) (PI.f64)) n))) #s(literal 2 binary64)) (sqrt.f64 (.f64 (+.f64 (PI.f64) (PI.f64)) n))) (neg.f64 (.f64 (log.f64 (sqrt.f64 (.f64 (+.f64 (PI.f64) (PI.f64)) n))) (sqrt.f64 (.f64 (+.f64 (PI.f64) (PI.f64)) n))))) (sqrt.f64 k)) k (sqrt.f64 (/.f64 (.f64 (+.f64 (PI.f64) (PI.f64)) n) k))))
#s(approx (/ (pow (* (sqrt (+ (PI) (PI))) (sqrt n)) (- 1 k)) (sqrt k)) (fma.f64 (fma.f64 k (/.f64 (fma.f64 (.f64 (.f64 (pow.f64 (log.f64 (sqrt.f64 (.f64 (+.f64 (PI.f64) (PI.f64)) n))) #s(literal 3 binary64)) (sqrt.f64 (.f64 (+.f64 (PI.f64) (PI.f64)) n))) k) #s(literal -1/6 binary64) (.f64 (.f64 (pow.f64 (log.f64 (sqrt.f64 (.f64 (+.f64 (PI.f64) (PI.f64)) n))) #s(literal 2 binary64)) (sqrt.f64 (.f64 (+.f64 (PI.f64) (PI.f64)) n))) #s(literal 1/2 binary64))) (sqrt.f64 k)) (neg.f64 (.f64 (log.f64 (sqrt.f64 (.f64 (+.f64 (PI.f64) (PI.f64)) n))) (sqrt.f64 (/.f64 (.f64 (+.f64 (PI.f64) (PI.f64)) n) k))))) k (sqrt.f64 (/.f64 (.f64 (+.f64 (PI.f64) (PI.f64)) n) k))))
#s(approx (pow (* (sqrt (+ (PI) (PI))) (sqrt n)) (- 1 k)) (sqrt.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n)))
#s(approx (pow (* (sqrt (+ (PI) (PI))) (sqrt n)) (- 1 k)) (fma.f64 (neg.f64 k) (.f64 (log.f64 (sqrt.f64 (.f64 (+.f64 (PI.f64) (PI.f64)) n))) (sqrt.f64 (.f64 (+.f64 (PI.f64) (PI.f64)) n))) (sqrt.f64 (.f64 (+.f64 (PI.f64) (PI.f64)) n))))
#s(approx (pow (* (sqrt (+ (PI) (PI))) (sqrt n)) (- 1 k)) (fma.f64 k (fma.f64 (.f64 #s(literal 1/2 binary64) k) (.f64 (pow.f64 (log.f64 (sqrt.f64 (.f64 (+.f64 (PI.f64) (PI.f64)) n))) #s(literal 2 binary64)) (sqrt.f64 (.f64 (+.f64 (PI.f64) (PI.f64)) n))) (neg.f64 (.f64 (log.f64 (sqrt.f64 (.f64 (+.f64 (PI.f64) (PI.f64)) n))) (sqrt.f64 (.f64 (+.f64 (PI.f64) (PI.f64)) n))))) (sqrt.f64 (.f64 (+.f64 (PI.f64) (PI.f64)) n))))
#s(approx (pow (* (sqrt (+ (PI) (PI))) (sqrt n)) (- 1 k)) (fma.f64 k (fma.f64 k (fma.f64 (.f64 (.f64 (pow.f64 (log.f64 (sqrt.f64 (.f64 (+.f64 (PI.f64) (PI.f64)) n))) #s(literal 3 binary64)) (sqrt.f64 (.f64 (+.f64 (PI.f64) (PI.f64)) n))) k) #s(literal -1/6 binary64) (.f64 (.f64 (pow.f64 (log.f64 (sqrt.f64 (.f64 (+.f64 (PI.f64) (PI.f64)) n))) #s(literal 2 binary64)) (sqrt.f64 (.f64 (+.f64 (PI.f64) (PI.f64)) n))) #s(literal 1/2 binary64))) (neg.f64 (.f64 (log.f64 (sqrt.f64 (.f64 (+.f64 (PI.f64) (PI.f64)) n))) (sqrt.f64 (.f64 (+.f64 (PI.f64) (PI.f64)) n))))) (sqrt.f64 (.f64 (+.f64 (PI.f64) (PI.f64)) n))))
#s(approx (- 1 k) (+.f64 (neg.f64 k) #s(literal 1 binary64)))
#s(approx (/ (pow (* (sqrt (+ (PI) (PI))) (sqrt n)) (- 1 k)) (sqrt k)) (.f64 (/.f64 #s(literal 1 binary64) (.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) k)) (pow.f64 (sqrt.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n)) (-.f64 #s(literal 1 binary64) k))))
#s(approx (pow (* (sqrt (+ (PI) (PI))) (sqrt n)) (- 1 k)) (pow.f64 (sqrt.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n)) (-.f64 #s(literal 1 binary64) k)))
#s(approx (pow (sqrt (* n (+ (PI) (PI)))) k) (pow.f64 (sqrt.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n)) k))
#s(approx (sqrt k) (*.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) k))
#s(approx (/ (pow (* (sqrt (+ (PI) (PI))) (sqrt n)) (- 1 k)) (sqrt k)) (/.f64 (pow.f64 (sqrt.f64 (.f64 (+.f64 (PI.f64) (PI.f64)) n)) (-.f64 #s(literal 1 binary64) k)) (.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) k)))
#s(approx (* (sqrt (/ n k)) (sqrt (+ (PI) (PI)))) (sqrt.f64 (*.f64 (/.f64 n k) (+.f64 (PI.f64) (PI.f64)))))
#s(approx (sqrt (/ n k)) (sqrt.f64 (/.f64 n k)))
#s(approx (sqrt (/ 1 k)) (/.f64 #s(literal 1 binary64) (*.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) k)))
#s(approx (pow (* (sqrt (+ (PI) (PI))) (sqrt n)) (- 1 k)) (pow.f64 (sqrt.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n)) (-.f64 #s(literal 1 binary64) k)))
#s(approx (/ (pow (* (sqrt (+ (PI) (PI))) (sqrt n)) (- 1 k)) (sqrt k)) (/.f64 (pow.f64 (sqrt.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n)) (-.f64 #s(literal 1 binary64) k)) (sqrt.f64 k)))
#s(approx (sqrt (/ 1 k)) (/.f64 #s(literal 1 binary64) (sqrt.f64 k)))
#s(approx (/ (pow (* (sqrt (+ (PI) (PI))) (sqrt n)) (- 1 k)) (sqrt k)) (/.f64 (pow.f64 (sqrt.f64 (.f64 (+.f64 (PI.f64) (PI.f64)) n)) (-.f64 #s(literal 1 binary64) k)) (.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) k)))
#s(approx (pow (* (sqrt (+ (PI) (PI))) (sqrt n)) (- 1 k)) (pow.f64 (sqrt.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n)) (-.f64 #s(literal 1 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 (/ (pow (* (sqrt (+ (PI) (PI))) (sqrt n)) (- 1 k)) (sqrt k)) (.f64 (/.f64 #s(literal -1 binary64) (.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) k)) (pow.f64 (sqrt.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n)) (-.f64 #s(literal 1 binary64) k))))
#s(approx (sqrt k) (*.f64 (neg.f64 k) (/.f64 #s(literal 1 binary64) (sqrt.f64 k))))
#s(approx (/ (pow (* (sqrt (+ (PI) (PI))) (sqrt n)) (- 1 k)) (sqrt k)) (neg.f64 (/.f64 (pow.f64 (sqrt.f64 (.f64 (+.f64 (PI.f64) (PI.f64)) n)) (+.f64 (neg.f64 k) #s(literal 1 binary64))) (.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) k))))
#s(approx (sqrt (/ 1 k)) (/.f64 #s(literal -1 binary64) (*.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) k)))
#s(approx (pow (* (sqrt (+ (PI) (PI))) (sqrt n)) (- 1 k)) (pow.f64 (sqrt.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n)) (+.f64 (neg.f64 k) #s(literal 1 binary64))))
#s(approx (/ (pow (* (sqrt (+ (PI) (PI))) (sqrt n)) (- 1 k)) (sqrt k)) (.f64 (pow.f64 (sqrt.f64 (.f64 (+.f64 (PI.f64) (PI.f64)) n)) (+.f64 (neg.f64 k) #s(literal 1 binary64))) (/.f64 #s(literal 1 binary64) (sqrt.f64 k))))
#s(approx (/ (pow (* (sqrt (+ (PI) (PI))) (sqrt n)) (- 1 k)) (sqrt k)) (neg.f64 (/.f64 (pow.f64 (sqrt.f64 (.f64 (+.f64 (PI.f64) (PI.f64)) n)) (+.f64 (neg.f64 k) #s(literal 1 binary64))) (.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) k))))
#s(approx (pow (* (sqrt (+ (PI) (PI))) (sqrt n)) (- 1 k)) (pow.f64 (sqrt.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n)) (+.f64 (neg.f64 k) #s(literal 1 binary64))))
#s(approx (- 1 k) (*.f64 (neg.f64 k) (-.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) k))))
#s(approx (/ (pow (* (sqrt (+ (PI) (PI))) (sqrt n)) (- 1 k)) (sqrt k)) (/.f64 (pow.f64 (sqrt.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n)) (-.f64 #s(literal 1 binary64) k)) (sqrt.f64 k)))
#s(approx (* n (+ (PI) (PI))) (*.f64 (+.f64 (PI.f64) (PI.f64)) n))
#s(approx n n)
#s(approx (/ (pow (* (sqrt (+ (PI) (PI))) (sqrt n)) (- 1 k)) (sqrt k)) (/.f64 (pow.f64 (sqrt.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n)) (-.f64 #s(literal 1 binary64) k)) (sqrt.f64 k)))
#s(approx (pow (* (sqrt (+ (PI) (PI))) (sqrt n)) (- 1 k)) (pow.f64 (sqrt.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n)) (-.f64 #s(literal 1 binary64) k)))
#s(approx (/ (pow (* (sqrt (+ (PI) (PI))) (sqrt n)) (- 1 k)) (sqrt k)) (/.f64 (pow.f64 (sqrt.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n)) (-.f64 #s(literal 1 binary64) k)) (sqrt.f64 k)))
#s(approx (/ 1 (sqrt (* n (+ (PI) (PI))))) (/.f64 #s(literal 1 binary64) (sqrt.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n))))
#s(approx (/ (pow (* (sqrt (+ (PI) (PI))) (sqrt n)) (- 1 k)) (sqrt k)) (/.f64 (pow.f64 (sqrt.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n)) (-.f64 #s(literal 1 binary64) k)) (sqrt.f64 k)))
#s(approx (sqrt n) (sqrt.f64 n))
#s(approx (/ (pow (* (sqrt (+ (PI) (PI))) (sqrt n)) (- 1 k)) (sqrt k)) (.f64 (sqrt.f64 (/.f64 (/.f64 (+.f64 (PI.f64) (PI.f64)) n) k)) (/.f64 n (exp.f64 (.f64 (log.f64 (*.f64 (/.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) n)) (sqrt.f64 (/.f64 (+.f64 (PI.f64) (PI.f64)) n)))) k)))))
#s(approx (pow (* (sqrt (+ (PI) (PI))) (sqrt n)) (- 1 k)) (.f64 n (/.f64 (sqrt.f64 (/.f64 (+.f64 (PI.f64) (PI.f64)) n)) (exp.f64 (.f64 (log.f64 (*.f64 (/.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) n)) (sqrt.f64 (/.f64 (+.f64 (PI.f64) (PI.f64)) n)))) k)))))
#s(approx (* (sqrt (+ (PI) (PI))) (sqrt n)) (*.f64 (sqrt.f64 (/.f64 (+.f64 (PI.f64) (PI.f64)) n)) n))
#s(approx (pow (sqrt (* n (+ (PI) (PI)))) k) (exp.f64 (.f64 (log.f64 (.f64 (/.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) n)) (sqrt.f64 (/.f64 (+.f64 (PI.f64) (PI.f64)) n)))) k)))
#s(approx (/ (pow (* (sqrt (+ (PI) (PI))) (sqrt n)) (- 1 k)) (sqrt k)) (/.f64 (exp.f64 (.f64 (.f64 (log.f64 (*.f64 (/.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) n)) (+.f64 (PI.f64) (PI.f64)))) (-.f64 #s(literal 1 binary64) k)) #s(literal 1/2 binary64))) (sqrt.f64 k)))
#s(approx (* (sqrt (/ n k)) (sqrt (+ (PI) (PI)))) (.f64 (sqrt.f64 (.f64 (/.f64 #s(literal 1 binary64) (*.f64 k n)) (+.f64 (PI.f64) (PI.f64)))) n))
#s(approx (sqrt (/ n k)) (.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 (.f64 k n))) n))
#s(approx (pow (* (sqrt (+ (PI) (PI))) (sqrt n)) (- 1 k)) (exp.f64 (.f64 (.f64 (log.f64 (*.f64 (/.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) n)) (+.f64 (PI.f64) (PI.f64)))) (-.f64 #s(literal 1 binary64) k)) #s(literal 1/2 binary64))))
#s(approx (/ (pow (* (sqrt (+ (PI) (PI))) (sqrt n)) (- 1 k)) (sqrt k)) (.f64 (exp.f64 (.f64 (.f64 (log.f64 (.f64 (/.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) 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 (sqrt (* n (+ (PI) (PI))))) (/.f64 #s(literal 1 binary64) (*.f64 (sqrt.f64 (/.f64 (+.f64 (PI.f64) (PI.f64)) n)) n)))
#s(approx (/ (pow (* (sqrt (+ (PI) (PI))) (sqrt n)) (- 1 k)) (sqrt k)) (/.f64 (exp.f64 (.f64 (log.f64 (.f64 (sqrt.f64 (*.f64 (/.f64 #s(literal 1 binary64) n) (+.f64 (PI.f64) (PI.f64)))) (/.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) n)))) (-.f64 #s(literal 1 binary64) k))) (sqrt.f64 k)))
#s(approx (pow (* (sqrt (+ (PI) (PI))) (sqrt n)) (- 1 k)) (exp.f64 (.f64 (log.f64 (.f64 (sqrt.f64 (*.f64 (/.f64 #s(literal 1 binary64) n) (+.f64 (PI.f64) (PI.f64)))) (/.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) n)))) (-.f64 #s(literal 1 binary64) k))))
#s(approx (* (sqrt (+ (PI) (PI))) (sqrt n)) (.f64 (sqrt.f64 (.f64 (/.f64 #s(literal 1 binary64) n) (+.f64 (PI.f64) (PI.f64)))) n))
#s(approx (sqrt n) (*.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 n)) n))
#s(approx (/ (pow (* (sqrt (+ (PI) (PI))) (sqrt n)) (- 1 k)) (sqrt k)) (neg.f64 (.f64 (/.f64 n (exp.f64 (.f64 (log.f64 (*.f64 (/.f64 #s(literal 1 binary64) (/.f64 #s(literal -1 binary64) n)) (sqrt.f64 (/.f64 (+.f64 (PI.f64) (PI.f64)) n)))) k))) (sqrt.f64 (/.f64 (/.f64 (+.f64 (PI.f64) (PI.f64)) n) k)))))
#s(approx (pow (* (sqrt (+ (PI) (PI))) (sqrt n)) (- 1 k)) (neg.f64 (.f64 n (/.f64 (sqrt.f64 (/.f64 (+.f64 (PI.f64) (PI.f64)) n)) (exp.f64 (.f64 (log.f64 (*.f64 (/.f64 #s(literal 1 binary64) (/.f64 #s(literal -1 binary64) n)) (sqrt.f64 (/.f64 (+.f64 (PI.f64) (PI.f64)) n)))) k))))))
#s(approx (* (sqrt (+ (PI) (PI))) (sqrt n)) (neg.f64 (*.f64 (sqrt.f64 (/.f64 (+.f64 (PI.f64) (PI.f64)) n)) n)))
#s(approx (pow (sqrt (* n (+ (PI) (PI)))) k) (exp.f64 (.f64 (log.f64 (.f64 (/.f64 #s(literal 1 binary64) (/.f64 #s(literal -1 binary64) n)) (sqrt.f64 (/.f64 (+.f64 (PI.f64) (PI.f64)) n)))) k)))
#s(approx (/ (pow (* (sqrt (+ (PI) (PI))) (sqrt n)) (- 1 k)) (sqrt k)) (/.f64 (exp.f64 (.f64 (.f64 (log.f64 (.f64 (.f64 #s(literal -2 binary64) (PI.f64)) (/.f64 #s(literal 1 binary64) (/.f64 #s(literal -1 binary64) n)))) (-.f64 #s(literal 1 binary64) k)) #s(literal 1/2 binary64))) (sqrt.f64 k)))
#s(approx (* (sqrt (/ n k)) (sqrt (+ (PI) (PI)))) (neg.f64 (.f64 (sqrt.f64 (.f64 (/.f64 #s(literal 1 binary64) (*.f64 k n)) (+.f64 (PI.f64) (PI.f64)))) n)))
#s(approx (sqrt (/ n k)) (neg.f64 (.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 (.f64 k n))) n)))
#s(approx (pow (* (sqrt (+ (PI) (PI))) (sqrt n)) (- 1 k)) (exp.f64 (.f64 (.f64 (log.f64 (.f64 (.f64 #s(literal -2 binary64) (PI.f64)) (/.f64 #s(literal 1 binary64) (/.f64 #s(literal -1 binary64) n)))) (-.f64 #s(literal 1 binary64) k)) #s(literal 1/2 binary64))))
#s(approx (/ (pow (* (sqrt (+ (PI) (PI))) (sqrt n)) (- 1 k)) (sqrt k)) (.f64 (exp.f64 (.f64 (.f64 (log.f64 (.f64 (*.f64 #s(literal -2 binary64) (PI.f64)) (/.f64 #s(literal 1 binary64) (/.f64 #s(literal -1 binary64) n)))) (-.f64 #s(literal 1 binary64) k)) #s(literal 1/2 binary64))) (/.f64 #s(literal 1 binary64) (sqrt.f64 k))))
#s(approx (/ 1 (sqrt (* n (+ (PI) (PI))))) (/.f64 #s(literal -1 binary64) (*.f64 (sqrt.f64 (/.f64 (+.f64 (PI.f64) (PI.f64)) n)) n)))
#s(approx (/ (pow (* (sqrt (+ (PI) (PI))) (sqrt n)) (- 1 k)) (sqrt k)) (/.f64 (exp.f64 (.f64 (log.f64 (.f64 (/.f64 #s(literal 1 binary64) (/.f64 #s(literal -1 binary64) n)) (sqrt.f64 (*.f64 (/.f64 #s(literal 1 binary64) n) (+.f64 (PI.f64) (PI.f64)))))) (-.f64 #s(literal 1 binary64) k))) (sqrt.f64 k)))
#s(approx (pow (* (sqrt (+ (PI) (PI))) (sqrt n)) (- 1 k)) (exp.f64 (.f64 (log.f64 (.f64 (/.f64 #s(literal 1 binary64) (/.f64 #s(literal -1 binary64) n)) (sqrt.f64 (*.f64 (/.f64 #s(literal 1 binary64) n) (+.f64 (PI.f64) (PI.f64)))))) (-.f64 #s(literal 1 binary64) k))))
#s(approx (* (sqrt (+ (PI) (PI))) (sqrt n)) (neg.f64 (.f64 (sqrt.f64 (.f64 (/.f64 #s(literal 1 binary64) n) (+.f64 (PI.f64) (PI.f64)))) n)))
#s(approx (sqrt n) (neg.f64 (*.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 n)) n)))

eval87.0ms (1.4%)

Memory: -1.8MiB live, 97.3MiB allocated; 16ms collecting garbage
Compiler: Compiled 6 875 to 1 720 computations (75% saved)

prune43.0ms (0.7%)

Memory

-3.8MiB live, 90.4MiB allocated; 3ms collecting garbage

Pruning

41 alts after pruning (35 fresh and 6 done)

	Pruned	Kept	Total
New	396	21	417
Fresh	8	14	22
Picked	2	3	5
Done	1	3	4
Total	407	41	448

Accuracy

100.0%

Counts

448 → 41

Alt Table

Click to see full alt table

Status	Accuracy	Program
	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))
✓	99.3%	(/.f64 (pow.f64 (*.f64 (sqrt.f64 (+.f64 (PI.f64) (PI.f64))) (sqrt.f64 n)) (-.f64 #s(literal 1 binary64) k)) (sqrt.f64 k))
	99.4%	(/.f64 (pow.f64 (.f64 (sqrt.f64 (.f64 (PI.f64) n)) (sqrt.f64 #s(literal 2 binary64))) (-.f64 #s(literal 1 binary64) k)) (sqrt.f64 k))
✓	99.5%	(/.f64 (pow.f64 (sqrt.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n)) (-.f64 #s(literal 1 binary64) k)) (sqrt.f64 k))
	51.8%	(/.f64 (pow.f64 (sqrt.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n)) #s(approx (- 1 k) (neg.f64 k))) (sqrt.f64 k))
	55.6%	(/.f64 (/.f64 (sqrt.f64 (.f64 n (+.f64 (PI.f64) (PI.f64)))) #s(approx (pow (sqrt ( n (+ (PI) (PI)))) k) (fma.f64 (log.f64 (sqrt.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n))) k #s(literal 1 binary64)))) (sqrt.f64 k))
	78.2%	(/.f64 (sqrt.f64 (/.f64 (.f64 (+.f64 (PI.f64) (PI.f64)) n) k)) (pow.f64 (sqrt.f64 (.f64 (+.f64 (PI.f64) (PI.f64)) n)) k))
	99.7%	(/.f64 (sqrt.f64 (.f64 (+.f64 (PI.f64) (PI.f64)) n)) (.f64 (pow.f64 (sqrt.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n)) k) (sqrt.f64 k)))
	96.5%	(/.f64 (exp.f64 (.f64 (log.f64 (sqrt.f64 (.f64 (+.f64 (PI.f64) (PI.f64)) n))) (-.f64 #s(literal 1 binary64) k))) (sqrt.f64 k))
	99.5%	(.f64 (pow.f64 (sqrt.f64 (.f64 (+.f64 (PI.f64) (PI.f64)) n)) (-.f64 #s(literal 1 binary64) k)) (sqrt.f64 (/.f64 #s(literal 1 binary64) k)))
	99.6%	(.f64 (/.f64 (sqrt.f64 #s(literal 2 binary64)) (sqrt.f64 k)) (/.f64 (sqrt.f64 (.f64 (PI.f64) n)) (pow.f64 (sqrt.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n)) k)))
	78.2%	(.f64 (/.f64 #s(literal 1 binary64) (pow.f64 (sqrt.f64 (.f64 (+.f64 (PI.f64) (PI.f64)) n)) k)) (sqrt.f64 (/.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n) k)))
	55.5%	(.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) (/.f64 (sqrt.f64 (.f64 (+.f64 (PI.f64) (PI.f64)) n)) #s(approx (pow (* (+ (PI) (PI)) n) (* 1/2 k)) (fma.f64 (.f64 (log.f64 (.f64 (+.f64 (PI.f64) (PI.f64)) n)) k) #s(literal 1/2 binary64) #s(literal 1 binary64)))))
✓	51.6%	(.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))))
	51.5%	(.f64 (/.f64 #s(literal 1 binary64) #s(approx (sqrt k) (.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) k))) #s(approx (pow (* (* 2 (PI)) n) (/ (- 1 k) 2)) (sqrt.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n))))
	51.5%	(.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) k)) #s(approx (pow ( (* 2 (PI)) n) (/ (- 1 k) 2)) (/.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (.f64 (sqrt.f64 (.f64 (PI.f64) n)) (sqrt.f64 #s(literal 2 binary64)))))))
	51.5%	(.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) k)) #s(approx (pow ( (* 2 (PI)) n) (/ (- 1 k) 2)) (/.f64 #s(literal 1 binary64) (*.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 (+.f64 (PI.f64) (PI.f64)))) (/.f64 #s(literal 1 binary64) (sqrt.f64 n))))))
	51.5%	(.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) k)) #s(approx (pow ( (* 2 (PI)) n) (/ (- 1 k) 2)) (/.f64 #s(literal 1 binary64) (.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 #s(literal 2 binary64))) (/.f64 #s(literal 1 binary64) (sqrt.f64 (.f64 (PI.f64) n)))))))
	51.6%	(.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) k)) #s(approx (pow ( (* 2 (PI)) n) (/ (- 1 k) 2)) (/.f64 #s(literal 1 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) (*.f64 (+.f64 (PI.f64) (PI.f64)) n))))))
	51.4%	(.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) k)) #s(approx (pow ( (* 2 (PI)) n) (/ (- 1 k) 2)) (*.f64 (sqrt.f64 (+.f64 (PI.f64) (PI.f64))) (sqrt.f64 n))))
	51.5%	(.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) k)) #s(approx (pow ( (* 2 (PI)) n) (/ (- 1 k) 2)) (.f64 (sqrt.f64 (.f64 (PI.f64) n)) (sqrt.f64 #s(literal 2 binary64)))))
	51.6%	(.f64 #s(approx (/ 1 (sqrt k)) (/.f64 (sqrt.f64 k) k)) #s(approx (pow ( (* 2 (PI)) n) (/ (- 1 k) 2)) (sqrt.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n))))
	51.6%	(.f64 #s(approx (sqrt (/ 1 k)) (/.f64 (sqrt.f64 k) k)) #s(approx (pow ( (* 2 (PI)) n) (/ (- 1 k) 2)) (/.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (sqrt.f64 (*.f64 n (+.f64 (PI.f64) (PI.f64))))))))
	39.9%	#s(approx (/ (pow (* (sqrt (+ (PI) (PI))) (sqrt n)) (- 1 k)) (sqrt k)) (/.f64 (sqrt.f64 (.f64 (.f64 (+.f64 (PI.f64) (PI.f64)) n) k)) k))
	52.3%	#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (/.f64 (.f64 (fma.f64 (neg.f64 k) (log.f64 (sqrt.f64 (.f64 (+.f64 (PI.f64) (PI.f64)) n))) #s(literal 1 binary64)) (sqrt.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n))) (sqrt.f64 k)))
	51.7%	#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (/.f64 (sqrt.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n)) (sqrt.f64 k)))
	51.4%	#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (*.f64 (/.f64 (sqrt.f64 n) (sqrt.f64 k)) (sqrt.f64 (+.f64 (PI.f64) (PI.f64)))))
	41.7%	#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (.f64 (sqrt.f64 (/.f64 (.f64 (PI.f64) n) k)) (sqrt.f64 #s(literal 2 binary64))))
	41.7%	#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (.f64 (sqrt.f64 (/.f64 n k)) (.f64 (sqrt.f64 (PI.f64)) (sqrt.f64 #s(literal 2 binary64)))))
✓	41.5%	#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (*.f64 (sqrt.f64 (/.f64 n k)) (sqrt.f64 (+.f64 (PI.f64) (PI.f64)))))
	39.1%	#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (.f64 (exp.f64 (.f64 (log.f64 (/.f64 n k)) #s(literal 1/2 binary64))) (sqrt.f64 (+.f64 (PI.f64) (PI.f64)))))
	39.6%	#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (.f64 #s(approx (sqrt (/ n k)) (/.f64 (sqrt.f64 (.f64 k n)) k)) (sqrt.f64 (+.f64 (PI.f64) (PI.f64)))))
	50.4%	#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (.f64 #s(approx (sqrt (/ n k)) (.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 (*.f64 k n))) n)) (sqrt.f64 (+.f64 (PI.f64) (PI.f64)))))
✓	41.8%	#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt.f64 (/.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n) k)))
	24.0%	#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt.f64 (/.f64 (.f64 (.f64 (.f64 (PI.f64) n) k) #s(literal 2 binary64)) (.f64 k k))))
	27.0%	#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt.f64 (/.f64 (sqrt.f64 (.f64 (.f64 (+.f64 (PI.f64) (PI.f64)) n) (*.f64 (+.f64 (PI.f64) (PI.f64)) n))) k)))
✓	41.8%	#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) (/.f64 n k))))
	39.3%	#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (exp.f64 (.f64 (log.f64 (/.f64 (.f64 n (+.f64 (PI.f64) (PI.f64))) k)) #s(literal 1/2 binary64))))
	39.9%	#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) #s(approx (* (sqrt (/ n k)) (sqrt (+ (PI) (PI)))) (/.f64 (sqrt.f64 (.f64 (.f64 k n) (+.f64 (PI.f64) (PI.f64)))) k)))
	50.6%	#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) #s(approx (* (sqrt (/ n k)) (sqrt (+ (PI) (PI)))) (.f64 (sqrt.f64 (.f64 (/.f64 #s(literal 1 binary64) (*.f64 k n)) (+.f64 (PI.f64) (PI.f64)))) n)))
	50.6%	#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) #s(approx (sqrt (/ (* (+ (PI) (PI)) n) k)) (.f64 (sqrt.f64 (/.f64 (+.f64 (PI.f64) (PI.f64)) (.f64 n k))) n)))

Compiler

Compiled 1 710 to 1 109 computations (35.1% saved)

regimes104.0ms (1.7%)

Memory

-1.8MiB live, 140.3MiB allocated; 11ms collecting garbage

Counts

70 → 1

Calls

Call 1

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

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

Calls

4 calls:

34.0ms	(.f64 (.f64 #s(literal 2 binary64) (PI.f64)) n)
30.0ms	n
20.0ms	k
15.0ms	(.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) (pow.f64 (.f64 (*.f64 #s(literal 2 binary64) (PI.f64)) n) (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 2 binary64))))

Results

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

Compiler

Compiled 22 to 23 computations (-4.5% saved)

regimes146.0ms (2.4%)

Memory

-43.0MiB live, 114.2MiB allocated; 94ms collecting garbage

Counts

64 → 1

Calls

Call 1

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

Outputs
(/.f64 (sqrt.f64 (.f64 (+.f64 (PI.f64) (PI.f64)) n)) (.f64 (pow.f64 (sqrt.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n)) k) (sqrt.f64 k)))

Calls

4 calls:

62.0ms	(.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))))
34.0ms	n
16.0ms	k
16.0ms	(.f64 (.f64 #s(literal 2 binary64) (PI.f64)) n)

Results

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

Compiler

Compiled 22 to 23 computations (-4.5% saved)

regimes64.0ms (1%)

Memory

26.5MiB live, 71.3MiB allocated; 5ms collecting garbage

Counts

56 → 1

Calls

Call 1

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

Outputs
(.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))))

Calls

4 calls:

20.0ms	(.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))))
14.0ms	k
14.0ms	n
14.0ms	(.f64 (.f64 #s(literal 2 binary64) (PI.f64)) n)

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	`n`
99.5%	1	`k`

Compiler

Compiled 22 to 23 computations (-4.5% saved)

regimes76.0ms (1.2%)

Memory

10.6MiB live, 102.4MiB allocated; 26ms collecting garbage

Counts

51 → 1

Calls

Call 1

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

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

Calls

4 calls:

28.0ms	(.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))))
20.0ms	n
13.0ms	k
13.0ms	(.f64 (.f64 #s(literal 2 binary64) (PI.f64)) n)

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)

regimes55.0ms (0.9%)

Memory

9.9MiB live, 145.8MiB allocated; 15ms collecting garbage

Counts

42 → 1

Calls

Call 1

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

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

Calls

4 calls:

14.0ms	n
14.0ms	(.f64 (.f64 #s(literal 2 binary64) (PI.f64)) n)
13.0ms	(.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))))
11.0ms	k

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)

regimes58.0ms (0.9%)

Memory

-21.7MiB live, 116.0MiB allocated; 25ms collecting garbage

Counts

38 → 1

Calls

Call 1

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

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

Calls

4 calls:

19.0ms	n
14.0ms	(.f64 (.f64 #s(literal 2 binary64) (PI.f64)) n)
13.0ms	(.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))))
10.0ms	k

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)

regimes59.0ms (1%)

Memory

18.7MiB live, 108.8MiB allocated; 33ms collecting garbage

Counts

37 → 2

Calls

Call 1

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

Outputs

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

Calls

4 calls:

24.0ms	(.f64 (.f64 #s(literal 2 binary64) (PI.f64)) n)
13.0ms	(.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))))
10.0ms	n
10.0ms	k

Results

Accuracy	Segments	Branch
66.9%	3	`(.f64 (.f64 #s(literal 2 binary64) (PI.f64)) n)`
66.9%	3	`n`
98.5%	3	`(.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) (pow.f64 (.f64 (*.f64 #s(literal 2 binary64) (PI.f64)) n) (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 2 binary64))))`
98.5%	2	`k`

Compiler

Compiled 22 to 23 computations (-4.5% saved)

regimes44.0ms (0.7%)

Memory

9.0MiB live, 97.7MiB allocated; 14ms collecting garbage

Counts

35 → 2

Calls

Call 1

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

Outputs

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

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

Calls

4 calls:

13.0ms	(.f64 (.f64 #s(literal 2 binary64) (PI.f64)) n)
12.0ms	(.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) (pow.f64 (.f64 (*.f64 #s(literal 2 binary64) (PI.f64)) n) (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 2 binary64))))
9.0ms	n
9.0ms	k

Results

Accuracy	Segments	Branch
62.3%	2	`(.f64 (.f64 #s(literal 2 binary64) (PI.f64)) n)`
62.3%	2	`n`
62.3%	2	`(.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) (pow.f64 (.f64 (*.f64 #s(literal 2 binary64) (PI.f64)) n) (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 2 binary64))))`
62.3%	2	`k`

Compiler

Compiled 22 to 23 computations (-4.5% saved)

regimes11.0ms (0.2%)

Memory

26.0MiB live, 26.0MiB allocated; 0ms collecting garbage

Counts

7 → 1

Calls

Call 1

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

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

Calls

4 calls:

3.0ms	n
3.0ms	(.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
51.7%	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))))`
51.7%	1	`k`
51.7%	1	`(.f64 (.f64 #s(literal 2 binary64) (PI.f64)) n)`
51.7%	1	`n`

Compiler

Compiled 22 to 23 computations (-4.5% saved)

regimes12.0ms (0.2%)

Memory

-25.2MiB live, 19.6MiB allocated; 6ms collecting garbage

Counts

4 → 1

Calls

Call 1

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

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

Calls

4 calls:

6.0ms	k
2.0ms	(.f64 (.f64 #s(literal 2 binary64) (PI.f64)) n)
2.0ms	n
2.0ms	(.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) (pow.f64 (.f64 (*.f64 #s(literal 2 binary64) (PI.f64)) n) (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 2 binary64))))

Results

Accuracy	Segments	Branch
41.8%	1	`(.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) (pow.f64 (.f64 (*.f64 #s(literal 2 binary64) (PI.f64)) n) (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 2 binary64))))`
41.8%	1	`(.f64 (.f64 #s(literal 2 binary64) (PI.f64)) n)`
41.8%	1	`n`
41.8%	1	`k`

Compiler

Compiled 22 to 23 computations (-4.5% saved)

regimes4.0ms (0.1%)

Memory

13.0MiB live, 13.0MiB allocated; 0ms collecting garbage

Accuracy

Total 0.0b remaining (0%)

Threshold costs 0b (0%)

Counts

1 → 1

Calls

Call 1

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

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

Calls

4 calls:

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

Results

Accuracy	Segments	Branch
41.8%	1	`k`
41.8%	1	`(.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) (pow.f64 (.f64 (*.f64 #s(literal 2 binary64) (PI.f64)) n) (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 2 binary64))))`
41.8%	1	`(.f64 (.f64 #s(literal 2 binary64) (PI.f64)) n)`
41.8%	1	`n`

Compiler

Compiled 22 to 23 computations (-4.5% saved)

bsearch73.0ms (1.2%)

Memory

-17.6MiB live, 29.5MiB allocated; 72ms collecting garbage

Algorithm

1×	binary-search

Stop Event

1×	narrow-enough

Steps

Time	Left	Right
71.0ms	0.0009527922051224008	7.787706343404761

Samples

9.0ms

128×

valid

Compiler

Compiled 291 to 290 computations (0.3% saved)

Precisions

Click to see histograms. Total time spent on operations: 6.0ms

ival-pow: 2.0ms (34.9% of total)

ival-sqrt: 1.0ms (17.5% of total)

ival-div!: 1.0ms (17.5% of total)

ival-mult!: 1.0ms (17.5% of total)

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

adjust: 0.0ms (0% of total)

bsearch6.0ms (0.1%)

Memory

11.4MiB live, 11.4MiB allocated; 0ms collecting garbage

Algorithm

1×	binary-search

Stop Event

1×	narrow-enough

Steps

Time	Left	Right
5.0ms	1.445810246036586e-14	1.9549878791455743e-14

Samples

3.0ms

48×

valid

Compiler

Compiled 163 to 156 computations (4.3% saved)

Precisions

Click to see histograms. Total time spent on operations: 2.0ms

ival-pow: 1.0ms (47.2% of total)

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

adjust: 0.0ms (0% of total)

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

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

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

derivations422.0ms (6.9%)

Memory

10.5MiB live, 607.2MiB allocated; 108ms collecting garbage

Stop Event

1×

fuel

Compiler

Compiled 145 to 73 computations (49.7% saved)

preprocess85.0ms (1.4%)

Memory: -17.7MiB live, 245.9MiB allocated; 31ms collecting garbage
Compiler: Compiled 160 to 86 computations (46.3% saved)

end0.0ms (0%)

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

start0.0ms (0%)

analyze133.0ms (2.2%)

sample2.8s (46%)

preprocess45.0ms (0.7%)

series109.0ms (1.8%)

rewrite191.0ms (3.1%)

eval23.0ms (0.4%)

prune48.0ms (0.8%)

series187.0ms (3.1%)

rewrite320.0ms (5.2%)

eval89.0ms (1.5%)

prune40.0ms (0.7%)

series95.0ms (1.6%)

rewrite232.0ms (3.8%)

eval78.0ms (1.3%)

prune26.0ms (0.4%)

series175.0ms (2.9%)

rewrite163.0ms (2.7%)

eval87.0ms (1.4%)

prune43.0ms (0.7%)

regimes104.0ms (1.7%)

regimes146.0ms (2.4%)

regimes64.0ms (1%)

regimes76.0ms (1.2%)

regimes55.0ms (0.9%)

regimes58.0ms (0.9%)

regimes59.0ms (1%)

regimes44.0ms (0.7%)

regimes11.0ms (0.2%)

regimes12.0ms (0.2%)

regimes4.0ms (0.1%)

bsearch73.0ms (1.2%)

bsearch6.0ms (0.1%)

derivations422.0ms (6.9%)

preprocess85.0ms (1.4%)

end0.0ms (0%)

Profiling