Metrics for Migdal et al, Equation (51)

start0.0ms (0%)

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

analyze151.0ms (2.2%)

Memory

-27.4MiB live, 221.2MiB allocated; 148ms collecting garbage

Algorithm

1×

Search

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

Compiler

Compiled 18 to 15 computations (16.7% saved)

sample3.2s (46.5%)

Memory

188.7MiB live, 4 437.4MiB allocated; 967ms collecting garbage

Samples

1.2s	8 255×	0	valid
1.2s	5 586×	1	invalid
110.0ms	488×	2	invalid
24.0ms	255×	0	exit
19.0ms	351×	0	invalid
0.0ms	1×	1	valid

Precisions

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

ival-pow: 760.0ms (41% of total)

ival-mult!: 286.0ms (15.4% of total)

ival-div!: 263.0ms (14.2% of total)

adjust: 221.0ms (11.9% of total)

ival-sqrt: 177.0ms (9.5% of total)

ival-sub!: 147.0ms (7.9% of total)

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

exact: 0.0ms (0% of total)

Bogosity

preprocess127.0ms (1.8%)

Memory

-44.9MiB live, 74.7MiB allocated; 122ms 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
▶	99.5%	(.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) (pow.f64 (.f64 (*.f64 #s(literal 2 binary64) (PI.f64)) n) (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 2 binary64))))

Compiler

Compiled 30 to 26 computations (13.3% saved)

series77.0ms (1.1%)

Memory

15.6MiB live, 157.3MiB allocated; 16ms 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
31.0ms	n	@	0	((* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (/ 1 (sqrt k)) 1 (sqrt k) k (pow (* (* 2 (PI)) n) (/ (- 1 k) 2)) (* (* 2 (PI)) n) (* 2 (PI)) 2 (PI) n (/ (- 1 k) 2) (- 1 k))
29.0ms	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))
10.0ms	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))

rewrite164.0ms (2.4%)

Memory

38.5MiB live, 176.4MiB allocated; 8ms 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)))))))

eval32.0ms (0.5%)

Memory: -40.9MiB live, 56.9MiB allocated; 10ms collecting garbage
Compiler: Compiled 2 273 to 825 computations (63.7% saved)

prune12.0ms (0.2%)

Memory

32.0MiB live, 32.0MiB allocated; 0ms collecting garbage

Pruning

15 alts after pruning (15 fresh and 0 done)

	Pruned	Kept	Total
New	187	15	202
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	188	15	203

Accuracy

100.0%

Counts

203 → 15

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))
	99.3%	(.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) (pow.f64 (pow.f64 (.f64 (+.f64 (PI.f64) (PI.f64)) n) (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 4 binary64))) #s(literal 2 binary64)))
▶	99.5%	(.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))))
▶	99.4%	(.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) (pow.f64 (.f64 (.f64 (sqrt.f64 (.f64 (+.f64 (PI.f64) (PI.f64)) n)) (sqrt.f64 #s(literal 2 binary64))) (sqrt.f64 (*.f64 (PI.f64) n))) (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 2 binary64))))
	99.3%	(.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) (/.f64 (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))))
	96.2%	(.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))))
	63.6%	(.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) #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)))))
	47.9%	(.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))))
▶	99.3%	(.f64 (/.f64 #s(literal 1 binary64) #s(approx (sqrt k) (/.f64 k (sqrt.f64 k)))) (pow.f64 (.f64 (*.f64 #s(literal 2 binary64) (PI.f64)) n) (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 2 binary64))))
	96.3%	(.f64 (exp.f64 (.f64 (log.f64 (sqrt.f64 k)) #s(literal -1 binary64))) (pow.f64 (.f64 (.f64 #s(literal 2 binary64) (PI.f64)) n) (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 2 binary64))))
	99.4%	(.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))))
	43.4%	#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))))
	48.7%	#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)))
	99.4%	#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))))
▶	37.7%	#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 756 to 576 computations (23.8% saved)

series189.0ms (2.7%)

Memory

-9.2MiB live, 409.1MiB allocated; 69ms collecting garbage

Counts

36 → 100

Calls

Call 1

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

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

Calls

6 calls:

Time	Variable		Point	Expression
76.0ms	n	@	0	((/ (pow (sqrt (* (+ (PI) (PI)) n)) (- 1 k)) (sqrt k)) (pow (sqrt (* (+ (PI) (PI)) n)) (- 1 k)) (sqrt (* (+ (PI) (PI)) n)) (* (+ (PI) (PI)) n) (+ (PI) (PI)) (PI) n (- 1 k) 1 k (sqrt k) (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt (/ (* (+ (PI) (PI)) n) k)) (/ (* (+ (PI) (PI)) n) k) (* (/ 1 (sqrt k)) (pow (* (+ (PI) (PI)) n) (+ (* -1/2 k) 1/2))) (/ 1 (sqrt k)) (pow (* (+ (PI) (PI)) n) (+ (* -1/2 k) 1/2)) (+ (* -1/2 k) 1/2) -1/2 1/2 (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (/ 1 (sqrt k)) (sqrt k) (/ k (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2)) (* (* 2 (PI)) n) (* 2 (PI)) 2 (/ (- 1 k) 2) (* (/ 1 (sqrt k)) (pow (* (* (sqrt (* (+ (PI) (PI)) n)) (sqrt 2)) (sqrt (* (PI) n))) (/ (- 1 k) 2))) (pow (* (* (sqrt (* (+ (PI) (PI)) n)) (sqrt 2)) (sqrt (* (PI) n))) (/ (- 1 k) 2)) (* (* (sqrt (* (+ (PI) (PI)) n)) (sqrt 2)) (sqrt (* (PI) n))) (* (sqrt (* (+ (PI) (PI)) n)) (sqrt 2)) (sqrt 2) (sqrt (* (PI) n)) (* (PI) n))
65.0ms	n	@	-inf	((/ (pow (sqrt (* (+ (PI) (PI)) n)) (- 1 k)) (sqrt k)) (pow (sqrt (* (+ (PI) (PI)) n)) (- 1 k)) (sqrt (* (+ (PI) (PI)) n)) (* (+ (PI) (PI)) n) (+ (PI) (PI)) (PI) n (- 1 k) 1 k (sqrt k) (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt (/ (* (+ (PI) (PI)) n) k)) (/ (* (+ (PI) (PI)) n) k) (* (/ 1 (sqrt k)) (pow (* (+ (PI) (PI)) n) (+ (* -1/2 k) 1/2))) (/ 1 (sqrt k)) (pow (* (+ (PI) (PI)) n) (+ (* -1/2 k) 1/2)) (+ (* -1/2 k) 1/2) -1/2 1/2 (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (/ 1 (sqrt k)) (sqrt k) (/ k (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2)) (* (* 2 (PI)) n) (* 2 (PI)) 2 (/ (- 1 k) 2) (* (/ 1 (sqrt k)) (pow (* (* (sqrt (* (+ (PI) (PI)) n)) (sqrt 2)) (sqrt (* (PI) n))) (/ (- 1 k) 2))) (pow (* (* (sqrt (* (+ (PI) (PI)) n)) (sqrt 2)) (sqrt (* (PI) n))) (/ (- 1 k) 2)) (* (* (sqrt (* (+ (PI) (PI)) n)) (sqrt 2)) (sqrt (* (PI) n))) (* (sqrt (* (+ (PI) (PI)) n)) (sqrt 2)) (sqrt 2) (sqrt (* (PI) n)) (* (PI) n))
28.0ms	n	@	inf	((/ (pow (sqrt (* (+ (PI) (PI)) n)) (- 1 k)) (sqrt k)) (pow (sqrt (* (+ (PI) (PI)) n)) (- 1 k)) (sqrt (* (+ (PI) (PI)) n)) (* (+ (PI) (PI)) n) (+ (PI) (PI)) (PI) n (- 1 k) 1 k (sqrt k) (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt (/ (* (+ (PI) (PI)) n) k)) (/ (* (+ (PI) (PI)) n) k) (* (/ 1 (sqrt k)) (pow (* (+ (PI) (PI)) n) (+ (* -1/2 k) 1/2))) (/ 1 (sqrt k)) (pow (* (+ (PI) (PI)) n) (+ (* -1/2 k) 1/2)) (+ (* -1/2 k) 1/2) -1/2 1/2 (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (/ 1 (sqrt k)) (sqrt k) (/ k (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2)) (* (* 2 (PI)) n) (* 2 (PI)) 2 (/ (- 1 k) 2) (* (/ 1 (sqrt k)) (pow (* (* (sqrt (* (+ (PI) (PI)) n)) (sqrt 2)) (sqrt (* (PI) n))) (/ (- 1 k) 2))) (pow (* (* (sqrt (* (+ (PI) (PI)) n)) (sqrt 2)) (sqrt (* (PI) n))) (/ (- 1 k) 2)) (* (* (sqrt (* (+ (PI) (PI)) n)) (sqrt 2)) (sqrt (* (PI) n))) (* (sqrt (* (+ (PI) (PI)) n)) (sqrt 2)) (sqrt 2) (sqrt (* (PI) n)) (* (PI) n))
8.0ms	k	@	0	((/ (pow (sqrt (* (+ (PI) (PI)) n)) (- 1 k)) (sqrt k)) (pow (sqrt (* (+ (PI) (PI)) n)) (- 1 k)) (sqrt (* (+ (PI) (PI)) n)) (* (+ (PI) (PI)) n) (+ (PI) (PI)) (PI) n (- 1 k) 1 k (sqrt k) (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt (/ (* (+ (PI) (PI)) n) k)) (/ (* (+ (PI) (PI)) n) k) (* (/ 1 (sqrt k)) (pow (* (+ (PI) (PI)) n) (+ (* -1/2 k) 1/2))) (/ 1 (sqrt k)) (pow (* (+ (PI) (PI)) n) (+ (* -1/2 k) 1/2)) (+ (* -1/2 k) 1/2) -1/2 1/2 (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (/ 1 (sqrt k)) (sqrt k) (/ k (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2)) (* (* 2 (PI)) n) (* 2 (PI)) 2 (/ (- 1 k) 2) (* (/ 1 (sqrt k)) (pow (* (* (sqrt (* (+ (PI) (PI)) n)) (sqrt 2)) (sqrt (* (PI) n))) (/ (- 1 k) 2))) (pow (* (* (sqrt (* (+ (PI) (PI)) n)) (sqrt 2)) (sqrt (* (PI) n))) (/ (- 1 k) 2)) (* (* (sqrt (* (+ (PI) (PI)) n)) (sqrt 2)) (sqrt (* (PI) n))) (* (sqrt (* (+ (PI) (PI)) n)) (sqrt 2)) (sqrt 2) (sqrt (* (PI) n)) (* (PI) n))
5.0ms	k	@	-inf	((/ (pow (sqrt (* (+ (PI) (PI)) n)) (- 1 k)) (sqrt k)) (pow (sqrt (* (+ (PI) (PI)) n)) (- 1 k)) (sqrt (* (+ (PI) (PI)) n)) (* (+ (PI) (PI)) n) (+ (PI) (PI)) (PI) n (- 1 k) 1 k (sqrt k) (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt (/ (* (+ (PI) (PI)) n) k)) (/ (* (+ (PI) (PI)) n) k) (* (/ 1 (sqrt k)) (pow (* (+ (PI) (PI)) n) (+ (* -1/2 k) 1/2))) (/ 1 (sqrt k)) (pow (* (+ (PI) (PI)) n) (+ (* -1/2 k) 1/2)) (+ (* -1/2 k) 1/2) -1/2 1/2 (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (/ 1 (sqrt k)) (sqrt k) (/ k (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2)) (* (* 2 (PI)) n) (* 2 (PI)) 2 (/ (- 1 k) 2) (* (/ 1 (sqrt k)) (pow (* (* (sqrt (* (+ (PI) (PI)) n)) (sqrt 2)) (sqrt (* (PI) n))) (/ (- 1 k) 2))) (pow (* (* (sqrt (* (+ (PI) (PI)) n)) (sqrt 2)) (sqrt (* (PI) n))) (/ (- 1 k) 2)) (* (* (sqrt (* (+ (PI) (PI)) n)) (sqrt 2)) (sqrt (* (PI) n))) (* (sqrt (* (+ (PI) (PI)) n)) (sqrt 2)) (sqrt 2) (sqrt (* (PI) n)) (* (PI) n))

rewrite156.0ms (2.2%)

Memory

23.3MiB live, 309.5MiB allocated; 23ms collecting garbage

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	450	3803
0	504	3228
1	2158	2932
0	10032	2894

Stop Event

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

Counts

136 → 531

Calls

Call 1

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

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

eval986.0ms (14.2%)

Memory: -236.0MiB live, 252.2MiB allocated; 1.4s collecting garbage
Compiler: Compiled 7 387 to 2 131 computations (71.2% saved)

prune26.0ms (0.4%)

Memory

13.8MiB live, 61.0MiB allocated; 2ms collecting garbage

Pruning

27 alts after pruning (25 fresh and 2 done)

	Pruned	Kept	Total
New	566	24	590
Fresh	9	1	10
Picked	3	2	5
Done	0	0	0
Total	578	27	605

Accuracy

100.0%

Counts

605 → 27

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 (sqrt.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n)) (-.f64 #s(literal 1 binary64) k)) (sqrt.f64 k))
	54.6%	(/.f64 (pow.f64 (sqrt.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n)) #s(approx (- 1 k) (neg.f64 k))) (sqrt.f64 k))
	99.4%	(/.f64 (/.f64 (sqrt.f64 (.f64 (+.f64 (PI.f64) (PI.f64)) n)) (pow.f64 (sqrt.f64 (.f64 (+.f64 (PI.f64) (PI.f64)) n)) k)) (sqrt.f64 k))
	99.4%	(/.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)))
	99.3%	(/.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) #s(approx (sqrt k) (/.f64 k (sqrt.f64 k)))))
	96.2%	(/.f64 (exp.f64 (.f64 (log.f64 (sqrt.f64 (.f64 (+.f64 (PI.f64) (PI.f64)) n))) (-.f64 #s(literal 1 binary64) k))) (sqrt.f64 k))
	48.7%	(/.f64 #s(approx (pow (* (* 2 (PI)) n) (/ (- 1 k) 2)) (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))
	47.9%	(/.f64 #s(approx (pow (* (* 2 (PI)) n) (/ (- 1 k) 2)) (sqrt.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n))) (sqrt.f64 k))
	99.3%	(.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) (.f64 (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))))
	47.9%	(.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) #s(approx (pow ( (+ (PI) (PI)) n) (+ (* -1/2 k) 1/2)) (sqrt.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n))))
▶	99.4%	(.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))))
▶	37.7%	#s(approx (/ (pow (sqrt (* (+ (PI) (PI)) n)) (- 1 k)) (sqrt k)) (sqrt.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) (/.f64 n k))))
▶	99.5%	#s(approx (* (/ 1 (sqrt k)) (pow (* (+ (PI) (PI)) n) (+ (* -1/2 k) 1/2))) (/.f64 (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)))
	37.6%	#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))))
	37.5%	#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))))
✓	37.7%	#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt.f64 (/.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 (.f64 (.f64 (.f64 (PI.f64) n) k) #s(literal 2 binary64)) (.f64 k k))))
	37.6%	#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)))
	23.6%	#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt.f64 (/.f64 (.f64 (sqrt.f64 (.f64 (.f64 (PI.f64) n) (.f64 (+.f64 (PI.f64) (PI.f64)) n))) (sqrt.f64 #s(literal 2 binary64))) k)))
	37.6%	#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt.f64 (/.f64 (.f64 (sqrt.f64 (.f64 (PI.f64) n)) (sqrt.f64 (.f64 #s(literal 2 binary64) (.f64 (+.f64 (PI.f64) (PI.f64)) n)))) k)))
▶	35.5%	#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt.f64 (/.f64 (exp.f64 (log.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n))) k)))
	37.7%	#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt.f64 (.f64 (/.f64 (.f64 (PI.f64) n) k) #s(literal 2 binary64))))
	35.3%	#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))))
▶	38.2%	#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) #s(approx (sqrt (/ (* (+ (PI) (PI)) n) k)) (/.f64 (sqrt.f64 (.f64 (.f64 (*.f64 (PI.f64) n) k) #s(literal 2 binary64))) 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 k n))) n)))

Compiler

Compiled 1 088 to 960 computations (11.8% saved)

series87.0ms (1.3%)

Memory

23.5MiB live, 168.4MiB allocated; 32ms collecting garbage

Counts

38 → 79

Calls

Call 1

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

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

Calls

6 calls:

Time	Variable		Point	Expression
33.0ms	n	@	0	((* (/ 1 (sqrt k)) (pow (* (+ (PI) (PI)) n) (+ (* -1/2 k) 1/2))) (/ (pow (* (+ (PI) (PI)) n) (+ (* -1/2 k) 1/2)) (sqrt k)) (pow (* (+ (PI) (PI)) n) (+ (* -1/2 k) 1/2)) (* (+ (PI) (PI)) n) (+ (PI) (PI)) (PI) n (+ (* -1/2 k) 1/2) -1/2 k 1/2 (sqrt k) (/ (pow (sqrt (* (+ (PI) (PI)) n)) (- 1 k)) (sqrt k)) (sqrt (* (+ (PI) (PI)) (/ n k))) (* (+ (PI) (PI)) (/ n k)) (/ n k) (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt (/ (* (+ (PI) (PI)) n) k)) (/ (sqrt (* (* (* (PI) n) k) 2)) k) (sqrt (* (* (* (PI) n) k) 2)) (* (* (* (PI) n) k) 2) (* (* (PI) n) k) (* (PI) n) 2 (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt (/ (exp (log (* (+ (PI) (PI)) n))) k)) (/ (exp (log (* (+ (PI) (PI)) n))) k) (exp (log (* (+ (PI) (PI)) n))) (log (* (+ (PI) (PI)) n)) (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (/ 1 (sqrt k)) (/ (sqrt k) k) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2)) (* (* 2 (PI)) n) (* 2 (PI)) (/ (- 1 k) 2) (- 1 k) 1)
21.0ms	n	@	inf	((* (/ 1 (sqrt k)) (pow (* (+ (PI) (PI)) n) (+ (* -1/2 k) 1/2))) (/ (pow (* (+ (PI) (PI)) n) (+ (* -1/2 k) 1/2)) (sqrt k)) (pow (* (+ (PI) (PI)) n) (+ (* -1/2 k) 1/2)) (* (+ (PI) (PI)) n) (+ (PI) (PI)) (PI) n (+ (* -1/2 k) 1/2) -1/2 k 1/2 (sqrt k) (/ (pow (sqrt (* (+ (PI) (PI)) n)) (- 1 k)) (sqrt k)) (sqrt (* (+ (PI) (PI)) (/ n k))) (* (+ (PI) (PI)) (/ n k)) (/ n k) (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt (/ (* (+ (PI) (PI)) n) k)) (/ (sqrt (* (* (* (PI) n) k) 2)) k) (sqrt (* (* (* (PI) n) k) 2)) (* (* (* (PI) n) k) 2) (* (* (PI) n) k) (* (PI) n) 2 (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt (/ (exp (log (* (+ (PI) (PI)) n))) k)) (/ (exp (log (* (+ (PI) (PI)) n))) k) (exp (log (* (+ (PI) (PI)) n))) (log (* (+ (PI) (PI)) n)) (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (/ 1 (sqrt k)) (/ (sqrt k) k) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2)) (* (* 2 (PI)) n) (* 2 (PI)) (/ (- 1 k) 2) (- 1 k) 1)
19.0ms	n	@	-inf	((* (/ 1 (sqrt k)) (pow (* (+ (PI) (PI)) n) (+ (* -1/2 k) 1/2))) (/ (pow (* (+ (PI) (PI)) n) (+ (* -1/2 k) 1/2)) (sqrt k)) (pow (* (+ (PI) (PI)) n) (+ (* -1/2 k) 1/2)) (* (+ (PI) (PI)) n) (+ (PI) (PI)) (PI) n (+ (* -1/2 k) 1/2) -1/2 k 1/2 (sqrt k) (/ (pow (sqrt (* (+ (PI) (PI)) n)) (- 1 k)) (sqrt k)) (sqrt (* (+ (PI) (PI)) (/ n k))) (* (+ (PI) (PI)) (/ n k)) (/ n k) (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt (/ (* (+ (PI) (PI)) n) k)) (/ (sqrt (* (* (* (PI) n) k) 2)) k) (sqrt (* (* (* (PI) n) k) 2)) (* (* (* (PI) n) k) 2) (* (* (PI) n) k) (* (PI) n) 2 (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt (/ (exp (log (* (+ (PI) (PI)) n))) k)) (/ (exp (log (* (+ (PI) (PI)) n))) k) (exp (log (* (+ (PI) (PI)) n))) (log (* (+ (PI) (PI)) n)) (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (/ 1 (sqrt k)) (/ (sqrt k) k) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2)) (* (* 2 (PI)) n) (* 2 (PI)) (/ (- 1 k) 2) (- 1 k) 1)
5.0ms	k	@	-inf	((* (/ 1 (sqrt k)) (pow (* (+ (PI) (PI)) n) (+ (* -1/2 k) 1/2))) (/ (pow (* (+ (PI) (PI)) n) (+ (* -1/2 k) 1/2)) (sqrt k)) (pow (* (+ (PI) (PI)) n) (+ (* -1/2 k) 1/2)) (* (+ (PI) (PI)) n) (+ (PI) (PI)) (PI) n (+ (* -1/2 k) 1/2) -1/2 k 1/2 (sqrt k) (/ (pow (sqrt (* (+ (PI) (PI)) n)) (- 1 k)) (sqrt k)) (sqrt (* (+ (PI) (PI)) (/ n k))) (* (+ (PI) (PI)) (/ n k)) (/ n k) (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt (/ (* (+ (PI) (PI)) n) k)) (/ (sqrt (* (* (* (PI) n) k) 2)) k) (sqrt (* (* (* (PI) n) k) 2)) (* (* (* (PI) n) k) 2) (* (* (PI) n) k) (* (PI) n) 2 (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt (/ (exp (log (* (+ (PI) (PI)) n))) k)) (/ (exp (log (* (+ (PI) (PI)) n))) k) (exp (log (* (+ (PI) (PI)) n))) (log (* (+ (PI) (PI)) n)) (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (/ 1 (sqrt k)) (/ (sqrt k) k) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2)) (* (* 2 (PI)) n) (* 2 (PI)) (/ (- 1 k) 2) (- 1 k) 1)
4.0ms	k	@	inf	((* (/ 1 (sqrt k)) (pow (* (+ (PI) (PI)) n) (+ (* -1/2 k) 1/2))) (/ (pow (* (+ (PI) (PI)) n) (+ (* -1/2 k) 1/2)) (sqrt k)) (pow (* (+ (PI) (PI)) n) (+ (* -1/2 k) 1/2)) (* (+ (PI) (PI)) n) (+ (PI) (PI)) (PI) n (+ (* -1/2 k) 1/2) -1/2 k 1/2 (sqrt k) (/ (pow (sqrt (* (+ (PI) (PI)) n)) (- 1 k)) (sqrt k)) (sqrt (* (+ (PI) (PI)) (/ n k))) (* (+ (PI) (PI)) (/ n k)) (/ n k) (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt (/ (* (+ (PI) (PI)) n) k)) (/ (sqrt (* (* (* (PI) n) k) 2)) k) (sqrt (* (* (* (PI) n) k) 2)) (* (* (* (PI) n) k) 2) (* (* (PI) n) k) (* (PI) n) 2 (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt (/ (exp (log (* (+ (PI) (PI)) n))) k)) (/ (exp (log (* (+ (PI) (PI)) n))) k) (exp (log (* (+ (PI) (PI)) n))) (log (* (+ (PI) (PI)) n)) (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (/ 1 (sqrt k)) (/ (sqrt k) k) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2)) (* (* 2 (PI)) n) (* 2 (PI)) (/ (- 1 k) 2) (- 1 k) 1)

rewrite215.0ms (3.1%)

Memory

16.6MiB live, 364.8MiB allocated; 89ms collecting garbage

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	346	2346
0	392	2210
1	1540	2149
0	8183	2131

Stop Event

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

Counts

117 → 505

Calls

Call 1

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

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

eval57.0ms (0.8%)

Memory: 14.6MiB live, 162.0MiB allocated; 19ms collecting garbage
Compiler: Compiled 6 152 to 2 008 computations (67.4% saved)

prune30.0ms (0.4%)

Memory

0.5MiB live, 92.2MiB allocated; 5ms collecting garbage

Pruning

34 alts after pruning (28 fresh and 6 done)

	Pruned	Kept	Total
New	401	15	416
Fresh	7	13	20
Picked	1	4	5
Done	0	2	2
Total	409	34	443

Accuracy

100.0%

Counts

443 → 34

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 (sqrt.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n)) (-.f64 #s(literal 1 binary64) k)) (sqrt.f64 k))
	54.6%	(/.f64 (pow.f64 (sqrt.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n)) #s(approx (- 1 k) (neg.f64 k))) (sqrt.f64 k))
	99.4%	(/.f64 (/.f64 (sqrt.f64 (.f64 (+.f64 (PI.f64) (PI.f64)) n)) (pow.f64 (sqrt.f64 (.f64 (+.f64 (PI.f64) (PI.f64)) n)) k)) (sqrt.f64 k))
	99.4%	(/.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)))
	99.3%	(/.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) #s(approx (sqrt k) (/.f64 k (sqrt.f64 k)))))
	96.2%	(/.f64 (exp.f64 (.f64 (log.f64 (sqrt.f64 (.f64 (+.f64 (PI.f64) (PI.f64)) n))) (-.f64 #s(literal 1 binary64) k))) (sqrt.f64 k))
	47.9%	(/.f64 #s(approx (pow (* (* 2 (PI)) n) (/ (- 1 k) 2)) (sqrt.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n))) (sqrt.f64 k))
	99.3%	(.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) (.f64 (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))))
▶	47.9%	(.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) #s(approx (pow ( (+ (PI) (PI)) n) (+ (* -1/2 k) 1/2)) (sqrt.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n))))
▶	99.4%	(.f64 #s(approx (/ 1 (sqrt k)) (/.f64 (sqrt.f64 k) k)) (pow.f64 (.f64 (+.f64 (PI.f64) (PI.f64)) n) (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 2 binary64))))
	96.2%	(.f64 #s(approx (/ 1 (sqrt k)) (/.f64 (sqrt.f64 k) k)) (exp.f64 (.f64 (log.f64 (sqrt.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n))) (-.f64 #s(literal 1 binary64) k))))
	37.6%	#s(approx (/ (pow (sqrt (* (+ (PI) (PI)) n)) (- 1 k)) (sqrt k)) (.f64 (sqrt.f64 (/.f64 (.f64 n (PI.f64)) k)) (sqrt.f64 #s(literal 2 binary64))))
	37.5%	#s(approx (/ (pow (sqrt (* (+ (PI) (PI)) n)) (- 1 k)) (sqrt k)) (*.f64 (sqrt.f64 (/.f64 n k)) (sqrt.f64 (+.f64 (PI.f64) (PI.f64)))))
	27.0%	#s(approx (/ (pow (sqrt (* (+ (PI) (PI)) n)) (- 1 k)) (sqrt k)) (sqrt.f64 (/.f64 (.f64 (.f64 (.f64 n (PI.f64)) k) #s(literal 2 binary64)) (.f64 k k))))
▶	37.7%	#s(approx (/ (pow (sqrt (* (+ (PI) (PI)) n)) (- 1 k)) (sqrt k)) (sqrt.f64 (.f64 (/.f64 (.f64 n (PI.f64)) k) #s(literal 2 binary64))))
✓	37.7%	#s(approx (/ (pow (sqrt (* (+ (PI) (PI)) n)) (- 1 k)) (sqrt k)) (sqrt.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) (/.f64 n k))))
	37.5%	#s(approx (/ (pow (sqrt (* (+ (PI) (PI)) n)) (- 1 k)) (sqrt k)) (sqrt.f64 (.f64 (.f64 (sqrt.f64 #s(literal 2 binary64)) (sqrt.f64 #s(literal 2 binary64))) (.f64 (sqrt.f64 (/.f64 (.f64 n (PI.f64)) k)) (sqrt.f64 (/.f64 (*.f64 n (PI.f64)) k))))))
	35.3%	#s(approx (/ (pow (sqrt (* (+ (PI) (PI)) n)) (- 1 k)) (sqrt k)) (exp.f64 (.f64 (log.f64 (/.f64 (.f64 (+.f64 (PI.f64) (PI.f64)) n) k)) #s(literal 1/2 binary64))))
	50.6%	#s(approx (/ (pow (sqrt (* (+ (PI) (PI)) n)) (- 1 k)) (sqrt k)) #s(approx (sqrt (* (+ (PI) (PI)) (/ n k))) (.f64 (sqrt.f64 (/.f64 (+.f64 (PI.f64) (PI.f64)) (.f64 n k))) n)))
✓	99.5%	#s(approx (* (/ 1 (sqrt k)) (pow (* (+ (PI) (PI)) n) (+ (* -1/2 k) 1/2))) (/.f64 (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)))
	99.4%	#s(approx (* (/ 1 (sqrt k)) (pow (* (+ (PI) (PI)) n) (+ (* -1/2 k) 1/2))) (/.f64 (.f64 (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))) (sqrt.f64 k)))
✓	37.7%	#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt.f64 (/.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n) k)))
	37.6%	#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)))
	23.6%	#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt.f64 (/.f64 (.f64 (sqrt.f64 (.f64 (.f64 (PI.f64) n) (.f64 (+.f64 (PI.f64) (PI.f64)) n))) (sqrt.f64 #s(literal 2 binary64))) k)))
▶	37.6%	#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt.f64 (/.f64 (.f64 (sqrt.f64 (.f64 (PI.f64) n)) (sqrt.f64 (.f64 #s(literal 2 binary64) (.f64 (+.f64 (PI.f64) (PI.f64)) n)))) k)))
✓	35.5%	#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt.f64 (/.f64 (exp.f64 (log.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n))) k)))
	38.1%	#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) #s(approx (sqrt (/ (* (+ (PI) (PI)) n) k)) (/.f64 (.f64 (sqrt.f64 (.f64 (*.f64 n (PI.f64)) k)) (sqrt.f64 #s(literal 2 binary64))) k)))
	47.8%	#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) #s(approx (sqrt (/ (* (+ (PI) (PI)) n) k)) (/.f64 (.f64 (sqrt.f64 (.f64 n (PI.f64))) (sqrt.f64 (*.f64 k #s(literal 2 binary64)))) k)))
✓	38.2%	#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) #s(approx (sqrt (/ (* (+ (PI) (PI)) n) k)) (/.f64 (sqrt.f64 (.f64 (.f64 (*.f64 (PI.f64) n) k) #s(literal 2 binary64))) k)))
	38.1%	#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) #s(approx (sqrt (/ (* (+ (PI) (PI)) n) k)) (/.f64 (sqrt.f64 (.f64 (.f64 (*.f64 n k) (PI.f64)) #s(literal 2 binary64))) k)))
	35.9%	#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) #s(approx (sqrt (/ (* (+ (PI) (PI)) n) k)) (/.f64 (exp.f64 (.f64 (log.f64 (.f64 (.f64 (.f64 n (PI.f64)) k) #s(literal 2 binary64))) #s(literal 1/2 binary64))) k)))
	51.1%	#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) #s(approx (sqrt (/ (* (+ (PI) (PI)) n) k)) (/.f64 #s(approx (sqrt (* (* (* (PI) n) k) 2)) (.f64 (sqrt.f64 (.f64 (*.f64 k (/.f64 (PI.f64) n)) #s(literal 2 binary64))) n)) k)))

Compiler

Compiled 1 377 to 1 216 computations (11.7% saved)

series222.0ms (3.2%)

Memory

-20.1MiB live, 506.8MiB allocated; 88ms collecting garbage

Counts

36 → 106

Calls

Call 1

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

Outputs
#s(approx (* (/ 1 (sqrt k)) (pow (* (+ (PI) (PI)) n) (/ (- 1 k) 2))) #s(hole binary64 (/ (pow (* 2 (* n (PI))) 1/2) (sqrt k))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (+ (PI) (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 (* (+ (PI) (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 (* (+ (PI) (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) k) #s(hole binary64 (/ (sqrt k) k)))
#s(approx (sqrt k) #s(hole binary64 (sqrt k)))
#s(approx k #s(hole binary64 k))
#s(approx (pow (* (+ (PI) (PI)) n) (/ (- 1 k) 2)) #s(hole binary64 (pow (* 2 (* n (PI))) 1/2)))
#s(approx (pow (* (+ (PI) (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 (* (+ (PI) (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 (* (+ (PI) (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 (/ (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 (sqrt (* (/ (* n (PI)) k) 2)) #s(hole binary64 (/ (sqrt (* 2 (* k (* n (PI))))) k)))
#s(approx (* (/ (* n (PI)) k) 2) #s(hole binary64 (* 2 (/ (* n (PI)) k))))
#s(approx (/ (* n (PI)) k) #s(hole binary64 (/ (* n (PI)) k)))
#s(approx (sqrt (/ (* (sqrt (* (PI) n)) (sqrt (* 2 (* (+ (PI) (PI)) n)))) k)) #s(hole binary64 (/ (sqrt (* k (* (sqrt (* 4 (* n (PI)))) (sqrt (* n (PI)))))) k)))
#s(approx (/ (* (sqrt (* (PI) n)) (sqrt (* 2 (* (+ (PI) (PI)) n)))) k) #s(hole binary64 (/ (* (sqrt (* 4 (* n (PI)))) (sqrt (* n (PI)))) 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 (sqrt k)) (pow (* (+ (PI) (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) k) #s(hole binary64 (sqrt (/ 1 k))))
#s(approx (sqrt k) #s(hole binary64 (* k (sqrt (/ 1 k)))))
#s(approx (pow (* (+ (PI) (PI)) n) (/ (- 1 k) 2)) #s(hole binary64 (exp (* 1/2 (* (log (* 2 (* n (PI)))) (- 1 k))))))
#s(approx (/ (- 1 k) 2) #s(hole binary64 (* -1/2 k)))
#s(approx (/ (- 1 k) 2) #s(hole binary64 (* k (- (* 1/2 (/ 1 k)) 1/2))))
#s(approx (- 1 k) #s(hole binary64 (* -1 k)))
#s(approx (- 1 k) #s(hole binary64 (* k (- (/ 1 k) 1))))
#s(approx (/ (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 (sqrt (* (/ (* n (PI)) k) 2)) #s(hole binary64 (sqrt (* 2 (/ (* n (PI)) k)))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (+ (PI) (PI)) n) (+ (* -1/2 k) 1/2))) #s(hole binary64 (/ (exp (* (log (* 2 (* n (PI)))) (- 1/2 (* 1/2 k)))) (* k (sqrt (/ 1 k))))))
#s(approx (pow (* (+ (PI) (PI)) n) (+ (* -1/2 k) 1/2)) #s(hole binary64 (exp (* (log (* 2 (* n (PI)))) (- 1/2 (* 1/2 k))))))
#s(approx (sqrt (/ (* (sqrt (* (PI) n)) (sqrt (* 2 (* (+ (PI) (PI)) n)))) k)) #s(hole binary64 (sqrt (/ (* (sqrt (* 4 (* n (PI)))) (sqrt (* n (PI)))) 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 (sqrt k)) (pow (* (+ (PI) (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) k) #s(hole binary64 (* -1 (sqrt (/ 1 k)))))
#s(approx (sqrt k) #s(hole binary64 (* -1 (* k (sqrt (/ 1 k))))))
#s(approx (pow (* (+ (PI) (PI)) n) (/ (- 1 k) 2)) #s(hole binary64 (exp (* 1/2 (* (log (* 2 (* n (PI)))) (+ 1 (* -1 k)))))))
#s(approx (/ (- 1 k) 2) #s(hole binary64 (* -1 (* k (- 1/2 (* 1/2 (/ 1 k)))))))
#s(approx (- 1 k) #s(hole binary64 (* -1 (* k (- 1 (/ 1 k))))))
#s(approx (/ (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 (* (/ 1 (sqrt k)) (pow (* (+ (PI) (PI)) n) (+ (* -1/2 k) 1/2))) #s(hole binary64 (* -1 (/ (exp (* (log (* 2 (* n (PI)))) (+ 1/2 (* -1/2 k)))) (* k (sqrt (/ 1 k)))))))
#s(approx (pow (* (+ (PI) (PI)) n) (+ (* -1/2 k) 1/2)) #s(hole binary64 (exp (* (log (* 2 (* n (PI)))) (+ 1/2 (* -1/2 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 (sqrt k)) (pow (* (+ (PI) (PI)) n) (/ (- 1 k) 2))) #s(hole binary64 (/ (exp (* 1/2 (* (+ (log n) (log (* 2 (PI)))) (- 1 k)))) (sqrt k))))
#s(approx (pow (* (+ (PI) (PI)) n) (/ (- 1 k) 2)) #s(hole binary64 (exp (* 1/2 (* (+ (log n) (log (* 2 (PI)))) (- 1 k))))))
#s(approx (* (+ (PI) (PI)) n) #s(hole binary64 (* 2 (* n (PI)))))
#s(approx n #s(hole binary64 n))
#s(approx (/ (pow (sqrt (* (+ (PI) (PI)) n)) (- 1 k)) (sqrt k)) #s(hole binary64 (/ (exp (* (log (sqrt (* 2 (* n (PI))))) (- 1 k))) (sqrt k))))
#s(approx (* n (PI)) #s(hole binary64 (* n (PI))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (+ (PI) (PI)) n) (+ (* -1/2 k) 1/2))) #s(hole binary64 (/ (exp (* (+ 1/2 (* -1/2 k)) (+ (log n) (log (* 2 (PI)))))) (sqrt k))))
#s(approx (pow (* (+ (PI) (PI)) n) (+ (* -1/2 k) 1/2)) #s(hole binary64 (exp (* (+ 1/2 (* -1/2 k)) (+ (log n) (log (* 2 (PI))))))))
#s(approx (sqrt (* (+ (PI) (PI)) n)) #s(hole binary64 (sqrt (* 2 (* n (PI))))))
#s(approx (* (sqrt (* (PI) n)) (sqrt (* 2 (* (+ (PI) (PI)) n)))) #s(hole binary64 (* (sqrt (* 4 (* n (PI)))) (sqrt (* n (PI))))))
#s(approx (sqrt (* (PI) n)) #s(hole binary64 (sqrt (* n (PI)))))
#s(approx (sqrt (* 2 (* (+ (PI) (PI)) n))) #s(hole binary64 (sqrt (* 4 (* n (PI))))))
#s(approx (* 2 (* (+ (PI) (PI)) n)) #s(hole binary64 (* 4 (* 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 (* (/ 1 (sqrt k)) (pow (* (+ (PI) (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 (* (+ (PI) (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 (sqrt (* (/ (* n (PI)) k) 2)) #s(hole binary64 (* n (sqrt (* 2 (/ (PI) (* k n)))))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (+ (PI) (PI)) n) (+ (* -1/2 k) 1/2))) #s(hole binary64 (/ (exp (* (+ 1/2 (* -1/2 k)) (+ (log (* 2 (PI))) (* -1 (log (/ 1 n)))))) (sqrt k))))
#s(approx (pow (* (+ (PI) (PI)) n) (+ (* -1/2 k) 1/2)) #s(hole binary64 (exp (* (+ 1/2 (* -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 (sqrt (/ (* (sqrt (* (PI) n)) (sqrt (* 2 (* (+ (PI) (PI)) n)))) k)) #s(hole binary64 (* n (sqrt (/ (* (sqrt (* 4 (/ (PI) n))) (sqrt (/ (PI) n))) k)))))
#s(approx (/ (* (sqrt (* (PI) n)) (sqrt (* 2 (* (+ (PI) (PI)) n)))) k) #s(hole binary64 (/ (* (pow n 2) (* (sqrt (* 4 (/ (PI) n))) (sqrt (/ (PI) n)))) k)))
#s(approx (* (sqrt (* (PI) n)) (sqrt (* 2 (* (+ (PI) (PI)) n)))) #s(hole binary64 (* (pow n 2) (* (sqrt (* 4 (/ (PI) n))) (sqrt (/ (PI) n))))))
#s(approx (sqrt (* (PI) n)) #s(hole binary64 (* n (sqrt (/ (PI) n)))))
#s(approx (sqrt (* 2 (* (+ (PI) (PI)) n))) #s(hole binary64 (* n (sqrt (* 4 (/ (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 (* (/ 1 (sqrt k)) (pow (* (+ (PI) (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 (* (+ (PI) (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 (sqrt (* (/ (* n (PI)) k) 2)) #s(hole binary64 (* -1 (* n (sqrt (* 2 (/ (PI) (* k n))))))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (+ (PI) (PI)) n) (+ (* -1/2 k) 1/2))) #s(hole binary64 (/ (exp (* (+ 1/2 (* -1/2 k)) (+ (log (* -2 (PI))) (* -1 (log (/ -1 n)))))) (sqrt k))))
#s(approx (pow (* (+ (PI) (PI)) n) (+ (* -1/2 k) 1/2)) #s(hole binary64 (exp (* (+ 1/2 (* -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 (sqrt (/ (* (sqrt (* (PI) n)) (sqrt (* 2 (* (+ (PI) (PI)) n)))) k)) #s(hole binary64 (* -1 (* n (sqrt (/ (* (sqrt (* 4 (/ (PI) n))) (sqrt (/ (PI) n))) k))))))
#s(approx (sqrt (* (PI) n)) #s(hole binary64 (* -1 (* n (sqrt (/ (PI) n))))))
#s(approx (sqrt (* 2 (* (+ (PI) (PI)) n))) #s(hole binary64 (* -1 (* n (sqrt (* 4 (/ (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
98.0ms	n	@	-inf	((* (/ 1 (sqrt k)) (pow (* (+ (PI) (PI)) n) (/ (- 1 k) 2))) (/ 1 (sqrt k)) (/ (sqrt k) k) (sqrt k) k (pow (* (+ (PI) (PI)) n) (/ (- 1 k) 2)) (* (+ (PI) (PI)) n) (+ (PI) (PI)) (PI) n (/ (- 1 k) 2) (- 1 k) 1 2 (/ (pow (sqrt (* (+ (PI) (PI)) n)) (- 1 k)) (sqrt k)) (sqrt (* (/ (* n (PI)) k) 2)) (* (/ (* n (PI)) k) 2) (/ (* n (PI)) k) (* n (PI)) (* (/ 1 (sqrt k)) (pow (* (+ (PI) (PI)) n) (+ (* -1/2 k) 1/2))) (/ 1 (sqrt k)) (pow (* (+ (PI) (PI)) n) (+ (* -1/2 k) 1/2)) (sqrt (* (+ (PI) (PI)) n)) (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt (/ (* (sqrt (* (PI) n)) (sqrt (* 2 (* (+ (PI) (PI)) n)))) k)) (/ (* (sqrt (* (PI) n)) (sqrt (* 2 (* (+ (PI) (PI)) n)))) k) (* (sqrt (* (PI) n)) (sqrt (* 2 (* (+ (PI) (PI)) n)))) (sqrt (* (PI) n)) (* (PI) n) (sqrt (* 2 (* (+ (PI) (PI)) n))) (* 2 (* (+ (PI) (PI)) n)) (/ (pow (* (sqrt (+ (PI) (PI))) (sqrt n)) (- 1 k)) (sqrt k)) (pow (* (sqrt (+ (PI) (PI))) (sqrt n)) (- 1 k)) (* (sqrt (+ (PI) (PI))) (sqrt n)) (sqrt (+ (PI) (PI))) (sqrt n))
44.0ms	n	@	0	((* (/ 1 (sqrt k)) (pow (* (+ (PI) (PI)) n) (/ (- 1 k) 2))) (/ 1 (sqrt k)) (/ (sqrt k) k) (sqrt k) k (pow (* (+ (PI) (PI)) n) (/ (- 1 k) 2)) (* (+ (PI) (PI)) n) (+ (PI) (PI)) (PI) n (/ (- 1 k) 2) (- 1 k) 1 2 (/ (pow (sqrt (* (+ (PI) (PI)) n)) (- 1 k)) (sqrt k)) (sqrt (* (/ (* n (PI)) k) 2)) (* (/ (* n (PI)) k) 2) (/ (* n (PI)) k) (* n (PI)) (* (/ 1 (sqrt k)) (pow (* (+ (PI) (PI)) n) (+ (* -1/2 k) 1/2))) (/ 1 (sqrt k)) (pow (* (+ (PI) (PI)) n) (+ (* -1/2 k) 1/2)) (sqrt (* (+ (PI) (PI)) n)) (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt (/ (* (sqrt (* (PI) n)) (sqrt (* 2 (* (+ (PI) (PI)) n)))) k)) (/ (* (sqrt (* (PI) n)) (sqrt (* 2 (* (+ (PI) (PI)) n)))) k) (* (sqrt (* (PI) n)) (sqrt (* 2 (* (+ (PI) (PI)) n)))) (sqrt (* (PI) n)) (* (PI) n) (sqrt (* 2 (* (+ (PI) (PI)) n))) (* 2 (* (+ (PI) (PI)) n)) (/ (pow (* (sqrt (+ (PI) (PI))) (sqrt n)) (- 1 k)) (sqrt k)) (pow (* (sqrt (+ (PI) (PI))) (sqrt n)) (- 1 k)) (* (sqrt (+ (PI) (PI))) (sqrt n)) (sqrt (+ (PI) (PI))) (sqrt n))
39.0ms	k	@	0	((* (/ 1 (sqrt k)) (pow (* (+ (PI) (PI)) n) (/ (- 1 k) 2))) (/ 1 (sqrt k)) (/ (sqrt k) k) (sqrt k) k (pow (* (+ (PI) (PI)) n) (/ (- 1 k) 2)) (* (+ (PI) (PI)) n) (+ (PI) (PI)) (PI) n (/ (- 1 k) 2) (- 1 k) 1 2 (/ (pow (sqrt (* (+ (PI) (PI)) n)) (- 1 k)) (sqrt k)) (sqrt (* (/ (* n (PI)) k) 2)) (* (/ (* n (PI)) k) 2) (/ (* n (PI)) k) (* n (PI)) (* (/ 1 (sqrt k)) (pow (* (+ (PI) (PI)) n) (+ (* -1/2 k) 1/2))) (/ 1 (sqrt k)) (pow (* (+ (PI) (PI)) n) (+ (* -1/2 k) 1/2)) (sqrt (* (+ (PI) (PI)) n)) (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt (/ (* (sqrt (* (PI) n)) (sqrt (* 2 (* (+ (PI) (PI)) n)))) k)) (/ (* (sqrt (* (PI) n)) (sqrt (* 2 (* (+ (PI) (PI)) n)))) k) (* (sqrt (* (PI) n)) (sqrt (* 2 (* (+ (PI) (PI)) n)))) (sqrt (* (PI) n)) (* (PI) n) (sqrt (* 2 (* (+ (PI) (PI)) n))) (* 2 (* (+ (PI) (PI)) n)) (/ (pow (* (sqrt (+ (PI) (PI))) (sqrt n)) (- 1 k)) (sqrt k)) (pow (* (sqrt (+ (PI) (PI))) (sqrt n)) (- 1 k)) (* (sqrt (+ (PI) (PI))) (sqrt n)) (sqrt (+ (PI) (PI))) (sqrt n))
30.0ms	n	@	inf	((* (/ 1 (sqrt k)) (pow (* (+ (PI) (PI)) n) (/ (- 1 k) 2))) (/ 1 (sqrt k)) (/ (sqrt k) k) (sqrt k) k (pow (* (+ (PI) (PI)) n) (/ (- 1 k) 2)) (* (+ (PI) (PI)) n) (+ (PI) (PI)) (PI) n (/ (- 1 k) 2) (- 1 k) 1 2 (/ (pow (sqrt (* (+ (PI) (PI)) n)) (- 1 k)) (sqrt k)) (sqrt (* (/ (* n (PI)) k) 2)) (* (/ (* n (PI)) k) 2) (/ (* n (PI)) k) (* n (PI)) (* (/ 1 (sqrt k)) (pow (* (+ (PI) (PI)) n) (+ (* -1/2 k) 1/2))) (/ 1 (sqrt k)) (pow (* (+ (PI) (PI)) n) (+ (* -1/2 k) 1/2)) (sqrt (* (+ (PI) (PI)) n)) (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt (/ (* (sqrt (* (PI) n)) (sqrt (* 2 (* (+ (PI) (PI)) n)))) k)) (/ (* (sqrt (* (PI) n)) (sqrt (* 2 (* (+ (PI) (PI)) n)))) k) (* (sqrt (* (PI) n)) (sqrt (* 2 (* (+ (PI) (PI)) n)))) (sqrt (* (PI) n)) (* (PI) n) (sqrt (* 2 (* (+ (PI) (PI)) n))) (* 2 (* (+ (PI) (PI)) n)) (/ (pow (* (sqrt (+ (PI) (PI))) (sqrt n)) (- 1 k)) (sqrt k)) (pow (* (sqrt (+ (PI) (PI))) (sqrt n)) (- 1 k)) (* (sqrt (+ (PI) (PI))) (sqrt n)) (sqrt (+ (PI) (PI))) (sqrt n))
5.0ms	k	@	-inf	((* (/ 1 (sqrt k)) (pow (* (+ (PI) (PI)) n) (/ (- 1 k) 2))) (/ 1 (sqrt k)) (/ (sqrt k) k) (sqrt k) k (pow (* (+ (PI) (PI)) n) (/ (- 1 k) 2)) (* (+ (PI) (PI)) n) (+ (PI) (PI)) (PI) n (/ (- 1 k) 2) (- 1 k) 1 2 (/ (pow (sqrt (* (+ (PI) (PI)) n)) (- 1 k)) (sqrt k)) (sqrt (* (/ (* n (PI)) k) 2)) (* (/ (* n (PI)) k) 2) (/ (* n (PI)) k) (* n (PI)) (* (/ 1 (sqrt k)) (pow (* (+ (PI) (PI)) n) (+ (* -1/2 k) 1/2))) (/ 1 (sqrt k)) (pow (* (+ (PI) (PI)) n) (+ (* -1/2 k) 1/2)) (sqrt (* (+ (PI) (PI)) n)) (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt (/ (* (sqrt (* (PI) n)) (sqrt (* 2 (* (+ (PI) (PI)) n)))) k)) (/ (* (sqrt (* (PI) n)) (sqrt (* 2 (* (+ (PI) (PI)) n)))) k) (* (sqrt (* (PI) n)) (sqrt (* 2 (* (+ (PI) (PI)) n)))) (sqrt (* (PI) n)) (* (PI) n) (sqrt (* 2 (* (+ (PI) (PI)) n))) (* 2 (* (+ (PI) (PI)) n)) (/ (pow (* (sqrt (+ (PI) (PI))) (sqrt n)) (- 1 k)) (sqrt k)) (pow (* (sqrt (+ (PI) (PI))) (sqrt n)) (- 1 k)) (* (sqrt (+ (PI) (PI))) (sqrt n)) (sqrt (+ (PI) (PI))) (sqrt n))

rewrite154.0ms (2.2%)

Memory

13.5MiB live, 242.3MiB allocated; 28ms collecting garbage

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	462	3329
0	517	3078
1	2223	2986
0	8408	2933

Stop Event

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

Counts

142 → 408

Calls

Call 1

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

eval96.0ms (1.4%)

Memory: -2.5MiB live, 60.4MiB allocated; 14ms collecting garbage
Compiler: Compiled 5 795 to 1 793 computations (69.1% saved)

prune43.0ms (0.6%)

Memory

-0.3MiB live, 46.4MiB allocated; 3ms collecting garbage

Pruning

43 alts after pruning (36 fresh and 7 done)

	Pruned	Kept	Total
New	411	17	428
Fresh	4	19	23
Picked	4	1	5
Done	0	6	6
Total	419	43	462

Accuracy

100.0%

Counts

462 → 43

Alt Table

Click to see full alt table

Status	Accuracy	Program
	99.3%	(/.f64 (pow.f64 (.f64 (.f64 (sqrt.f64 (PI.f64)) (sqrt.f64 #s(literal 2 binary64))) (sqrt.f64 n)) (-.f64 #s(literal 1 binary64) k)) (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))
	54.6%	(/.f64 (pow.f64 (sqrt.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n)) #s(approx (- 1 k) (neg.f64 k))) (sqrt.f64 k))
	99.4%	(/.f64 (/.f64 (sqrt.f64 (.f64 (+.f64 (PI.f64) (PI.f64)) n)) (pow.f64 (sqrt.f64 (.f64 (+.f64 (PI.f64) (PI.f64)) n)) k)) (sqrt.f64 k))
	99.4%	(/.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)))
	99.3%	(/.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) #s(approx (sqrt k) (/.f64 k (sqrt.f64 k)))))
	96.2%	(/.f64 (exp.f64 (.f64 (log.f64 (sqrt.f64 (.f64 (+.f64 (PI.f64) (PI.f64)) n))) (-.f64 #s(literal 1 binary64) k))) (sqrt.f64 k))
	47.9%	(/.f64 #s(approx (pow (* (* 2 (PI)) n) (/ (- 1 k) 2)) (sqrt.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n))) (sqrt.f64 k))
	99.3%	(.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) (.f64 (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))))
	47.7%	(.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) #s(approx (pow ( (+ (PI) (PI)) n) (+ (* -1/2 k) 1/2)) (*.f64 (sqrt.f64 (+.f64 (PI.f64) (PI.f64))) (sqrt.f64 n))))
	47.7%	(.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) #s(approx (pow ( (+ (PI) (PI)) n) (+ (* -1/2 k) 1/2)) (.f64 (sqrt.f64 (.f64 #s(literal 2 binary64) n)) (sqrt.f64 (PI.f64)))))
	44.8%	(.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) #s(approx (pow ( (+ (PI) (PI)) n) (+ (* -1/2 k) 1/2)) (sqrt.f64 (exp.f64 (log.f64 (*.f64 n (+.f64 (PI.f64) (PI.f64))))))))
	44.7%	(.f64 (/.f64 #s(literal 1 binary64) (exp.f64 (.f64 (log.f64 k) #s(literal 1/2 binary64)))) #s(approx (pow (* (+ (PI) (PI)) n) (+ (* -1/2 k) 1/2)) (sqrt.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n))))
	47.7%	(.f64 (/.f64 #s(literal 1 binary64) #s(approx (sqrt k) (.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) k))) #s(approx (pow (* (+ (PI) (PI)) n) (+ (* -1/2 k) 1/2)) (sqrt.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n))))
	47.9%	(.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) k)) #s(approx (pow ( (+ (PI) (PI)) n) (+ (* -1/2 k) 1/2)) (sqrt.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n))))
	44.7%	(.f64 (exp.f64 (.f64 (log.f64 (sqrt.f64 k)) #s(literal -1 binary64))) #s(approx (pow (* (+ (PI) (PI)) n) (+ (* -1/2 k) 1/2)) (sqrt.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n))))
	99.4%	(.f64 #s(approx (/ 1 (sqrt k)) (/.f64 (sqrt.f64 k) k)) (pow.f64 (.f64 (+.f64 (PI.f64) (PI.f64)) n) #s(approx (/ (- 1 k) 2) (fma.f64 #s(literal -1/2 binary64) k #s(literal 1/2 binary64)))))
	96.2%	(.f64 #s(approx (/ 1 (sqrt k)) (/.f64 (sqrt.f64 k) k)) (exp.f64 (.f64 (log.f64 (sqrt.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n))) (-.f64 #s(literal 1 binary64) k))))
	47.8%	(.f64 #s(approx (/ 1 (sqrt k)) (/.f64 (sqrt.f64 k) k)) #s(approx (pow ( (+ (PI) (PI)) n) (/ (- 1 k) 2)) (sqrt.f64 (*.f64 n (+.f64 (PI.f64) (PI.f64))))))
	37.6%	#s(approx (/ (pow (sqrt (* (+ (PI) (PI)) n)) (- 1 k)) (sqrt k)) (.f64 (sqrt.f64 (/.f64 (.f64 (PI.f64) n) k)) (sqrt.f64 #s(literal 2 binary64))))
	37.5%	#s(approx (/ (pow (sqrt (* (+ (PI) (PI)) n)) (- 1 k)) (sqrt k)) (*.f64 (sqrt.f64 (/.f64 n k)) (sqrt.f64 (+.f64 (PI.f64) (PI.f64)))))
	47.8%	#s(approx (/ (pow (sqrt (* (+ (PI) (PI)) n)) (- 1 k)) (sqrt k)) (*.f64 (sqrt.f64 n) (sqrt.f64 (/.f64 (+.f64 (PI.f64) (PI.f64)) k))))
	27.0%	#s(approx (/ (pow (sqrt (* (+ (PI) (PI)) n)) (- 1 k)) (sqrt k)) (sqrt.f64 (/.f64 (.f64 (.f64 (.f64 (PI.f64) n) k) #s(literal 2 binary64)) (.f64 k k))))
✓	37.7%	#s(approx (/ (pow (sqrt (* (+ (PI) (PI)) n)) (- 1 k)) (sqrt k)) (sqrt.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) (/.f64 n k))))
	37.5%	#s(approx (/ (pow (sqrt (* (+ (PI) (PI)) n)) (- 1 k)) (sqrt k)) (sqrt.f64 (.f64 (.f64 (sqrt.f64 #s(literal 2 binary64)) (sqrt.f64 #s(literal 2 binary64))) (.f64 (sqrt.f64 (/.f64 (.f64 n (PI.f64)) k)) (sqrt.f64 (/.f64 (*.f64 n (PI.f64)) k))))))
	37.7%	#s(approx (/ (pow (sqrt (* (+ (PI) (PI)) n)) (- 1 k)) (sqrt k)) (sqrt.f64 (.f64 (.f64 n (/.f64 (PI.f64) k)) #s(literal 2 binary64))))
	35.3%	#s(approx (/ (pow (sqrt (* (+ (PI) (PI)) n)) (- 1 k)) (sqrt k)) (exp.f64 (.f64 (log.f64 (/.f64 (.f64 (+.f64 (PI.f64) (PI.f64)) n) k)) #s(literal 1/2 binary64))))
	50.6%	#s(approx (/ (pow (sqrt (* (+ (PI) (PI)) n)) (- 1 k)) (sqrt k)) #s(approx (sqrt (* (/ (* n (PI)) k) 2)) (.f64 (sqrt.f64 (/.f64 (+.f64 (PI.f64) (PI.f64)) (.f64 n k))) n)))
✓	99.5%	#s(approx (* (/ 1 (sqrt k)) (pow (* (+ (PI) (PI)) n) (+ (* -1/2 k) 1/2))) (/.f64 (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)))
	99.4%	#s(approx (* (/ 1 (sqrt k)) (pow (* (+ (PI) (PI)) n) (+ (* -1/2 k) 1/2))) (/.f64 (.f64 (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))) (sqrt.f64 k)))
	41.7%	#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (.f64 (sqrt.f64 (sqrt.f64 (.f64 (PI.f64) n))) (sqrt.f64 (/.f64 (sqrt.f64 (.f64 #s(literal 2 binary64) (.f64 n (+.f64 (PI.f64) (PI.f64))))) k))))
✓	37.7%	#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt.f64 (/.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n) k)))
	23.6%	#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt.f64 (/.f64 (.f64 (sqrt.f64 (.f64 (.f64 (PI.f64) n) (.f64 (+.f64 (PI.f64) (PI.f64)) n))) (sqrt.f64 #s(literal 2 binary64))) k)))
✓	35.5%	#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt.f64 (/.f64 (exp.f64 (log.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n))) k)))
	38.1%	#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) #s(approx (sqrt (/ (* (+ (PI) (PI)) n) k)) (/.f64 (.f64 (sqrt.f64 (.f64 (*.f64 n (PI.f64)) k)) (sqrt.f64 #s(literal 2 binary64))) k)))
	47.8%	#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) #s(approx (sqrt (/ (* (+ (PI) (PI)) n) k)) (/.f64 (.f64 (sqrt.f64 (.f64 n (PI.f64))) (sqrt.f64 (*.f64 k #s(literal 2 binary64)))) k)))
✓	38.2%	#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) #s(approx (sqrt (/ (* (+ (PI) (PI)) n) k)) (/.f64 (sqrt.f64 (.f64 (.f64 (*.f64 (PI.f64) n) k) #s(literal 2 binary64))) k)))
	38.1%	#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) #s(approx (sqrt (/ (* (+ (PI) (PI)) n) k)) (/.f64 (sqrt.f64 (.f64 (.f64 (*.f64 n k) (PI.f64)) #s(literal 2 binary64))) k)))
	35.9%	#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) #s(approx (sqrt (/ (* (+ (PI) (PI)) n) k)) (/.f64 (exp.f64 (.f64 (log.f64 (.f64 (.f64 (.f64 n (PI.f64)) k) #s(literal 2 binary64))) #s(literal 1/2 binary64))) k)))
	51.1%	#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) #s(approx (sqrt (/ (* (+ (PI) (PI)) n) k)) (/.f64 #s(approx (sqrt (* (* (* (PI) n) k) 2)) (.f64 (sqrt.f64 (.f64 (*.f64 k (/.f64 (PI.f64) n)) #s(literal 2 binary64))) n)) k)))
	51.5%	#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) #s(approx (sqrt (/ (* (sqrt (* (PI) n)) (sqrt (* 2 (* (+ (PI) (PI)) n)))) k)) (.f64 (sqrt.f64 (/.f64 (sqrt.f64 (/.f64 (.f64 (.f64 #s(literal 4 binary64) (PI.f64)) (PI.f64)) (.f64 n n))) k)) n)))

Compiler

Compiled 1 860 to 1 222 computations (34.3% saved)

regimes76.0ms (1.1%)

Memory

-12.5MiB live, 79.8MiB allocated; 5ms collecting garbage

Counts

72 → 1

Calls

Call 1

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

Outputs

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

Calls

4 calls:

20.0ms	n
19.0ms	(.f64 (.f64 #s(literal 2 binary64) (PI.f64)) n)
18.0ms	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
99.5%	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)

regimes49.0ms (0.7%)

Memory

25.8MiB live, 75.6MiB allocated; 6ms collecting garbage

Counts

44 → 1

Calls

Call 1

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

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:

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

regimes49.0ms (0.7%)

Memory

4.8MiB live, 49.1MiB allocated; 5ms collecting garbage

Counts

42 → 2

Calls

Call 1

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

Outputs

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

(/.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:

15.0ms	n
11.0ms	(.f64 (.f64 #s(literal 2 binary64) (PI.f64)) n)
11.0ms	k
9.0ms	(.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
97.7%	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))))`
97.7%	2	`k`
78.1%	3	`(.f64 (.f64 #s(literal 2 binary64) (PI.f64)) n)`
78.1%	3	`n`

Compiler

Compiled 22 to 23 computations (-4.5% saved)

regimes26.0ms (0.4%)

Memory

-11.7MiB live, 33.1MiB allocated; 7ms collecting garbage

Counts

38 → 2

Calls

Call 1

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

Outputs

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

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

Calls

2 calls:

16.0ms	k
9.0ms	(.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
77.6%	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))))`
77.6%	2	`k`

Compiler

Compiled 16 to 15 computations (6.3% saved)

regimes36.0ms (0.5%)

Memory

17.4MiB live, 63.5MiB allocated; 4ms collecting garbage

Counts

30 → 2

Calls

Call 1

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

Outputs

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

Calls

4 calls:

12.0ms	n
8.0ms	(.f64 (.f64 #s(literal 2 binary64) (PI.f64)) n)
8.0ms	k
7.0ms	(.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) (pow.f64 (.f64 (*.f64 #s(literal 2 binary64) (PI.f64)) n) (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 2 binary64))))

Results

Accuracy	Segments	Branch
74.5%	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))))`
74.5%	2	`(.f64 (.f64 #s(literal 2 binary64) (PI.f64)) n)`
74.5%	2	`n`
61.7%	2	`k`

Compiler

Compiled 22 to 23 computations (-4.5% saved)

regimes35.0ms (0.5%)

Memory

-19.9MiB live, 35.5MiB allocated; 6ms collecting garbage

Counts

27 → 2

Calls

Call 1

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

Outputs

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

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

Calls

4 calls:

12.0ms	(.f64 (.f64 #s(literal 2 binary64) (PI.f64)) n)
7.0ms	n
7.0ms	k
6.0ms	(.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) (pow.f64 (.f64 (*.f64 #s(literal 2 binary64) (PI.f64)) n) (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 2 binary64))))

Results

Accuracy	Segments	Branch
60.8%	2	`k`
60.7%	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))))`
60.8%	2	`(.f64 (.f64 #s(literal 2 binary64) (PI.f64)) n)`
60.8%	2	`n`

Compiler

Compiled 22 to 23 computations (-4.5% saved)

regimes15.0ms (0.2%)

Memory

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

Counts

12 → 1

Calls

Call 1

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

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

Calls

4 calls:

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

Results

Accuracy	Segments	Branch
47.9%	1	`(.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) (pow.f64 (.f64 (*.f64 #s(literal 2 binary64) (PI.f64)) n) (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 2 binary64))))`
47.9%	1	`k`
47.9%	1	`(.f64 (.f64 #s(literal 2 binary64) (PI.f64)) n)`
47.9%	1	`n`

Compiler

Compiled 22 to 23 computations (-4.5% saved)

regimes15.0ms (0.2%)

Memory

-7.4MiB live, 39.6MiB allocated; 4ms collecting garbage

Counts

8 → 1

Calls

Call 1

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

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

Calls

4 calls:

6.0ms	(.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) (pow.f64 (.f64 (*.f64 #s(literal 2 binary64) (PI.f64)) n) (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 2 binary64))))
3.0ms	k
3.0ms	n
3.0ms	(.f64 (.f64 #s(literal 2 binary64) (PI.f64)) n)

Results

Accuracy	Segments	Branch
47.8%	1	`(.f64 (.f64 #s(literal 2 binary64) (PI.f64)) n)`
47.8%	1	`n`
47.8%	1	`k`
47.8%	1	`(.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) (pow.f64 (.f64 (*.f64 #s(literal 2 binary64) (PI.f64)) n) (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 2 binary64))))`

Compiler

Compiled 22 to 23 computations (-4.5% saved)

regimes10.0ms (0.2%)

Memory

-27.1MiB live, 19.9MiB allocated; 2ms collecting garbage

Counts

6 → 1

Calls

Call 1

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

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

Calls

4 calls:

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

Results

Accuracy	Segments	Branch
37.7%	1	`(.f64 (.f64 #s(literal 2 binary64) (PI.f64)) n)`
37.7%	1	`n`
37.7%	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))))`
37.7%	1	`k`

Compiler

Compiled 22 to 23 computations (-4.5% saved)

regimes5.0ms (0.1%)

Memory

13.7MiB live, 13.7MiB allocated; 0ms collecting garbage

Accuracy

Total -0.0b remaining (-0.1%)

Threshold costs -0b (-0.1%)

Counts

2 → 1

Calls

Call 1

Inputs

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

Calls

4 calls:

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

Results

Accuracy	Segments	Branch
37.7%	1	`k`
37.7%	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))))`
37.7%	1	`(.f64 (.f64 #s(literal 2 binary64) (PI.f64)) n)`
37.7%	1	`n`

Compiler

Compiled 22 to 23 computations (-4.5% saved)

bsearch15.0ms (0.2%)

Memory

25.3MiB live, 25.3MiB allocated; 0ms collecting garbage

Algorithm

1×	binary-search

Stop Event

1×	narrow-enough

Steps

Time	Left	Right
14.0ms	0.06093871596461519	1779.3193967400596

Samples

9.0ms

128×

valid

Compiler

Compiled 275 to 274 computations (0.4% saved)

Precisions

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

ival-pow: 3.0ms (49.5% of total)

ival-sqrt: 1.0ms (16.5% of total)

ival-div!: 1.0ms (16.5% of total)

ival-mult!: 1.0ms (16.5% of total)

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

adjust: 0.0ms (0% of total)

bsearch22.0ms (0.3%)

Memory

-17.5MiB live, 28.2MiB allocated; 5ms collecting garbage

Algorithm

1×	binary-search

Stop Event

1×	narrow-enough

Steps

Time	Left	Right
15.0ms	1779.3193967400596	747576.0388682971

Samples

10.0ms

128×

valid

Compiler

Compiled 467 to 442 computations (5.4% saved)

Precisions

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

ival-pow: 4.0ms (54.4% of total)

ival-sqrt: 1.0ms (13.6% of total)

ival-div!: 1.0ms (13.6% of total)

ival-mult!: 1.0ms (13.6% of total)

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

adjust: 0.0ms (0% of total)

bsearch23.0ms (0.3%)

Memory

-14.2MiB live, 35.6MiB allocated; 8ms collecting garbage

Algorithm

1×	binary-search

Stop Event

1×	narrow-enough

Steps

Time	Left	Right
21.0ms	1.2810573408693087e-52	8.207773198539498e-43

Samples

15.0ms

160×

valid

Compiler

Compiled 649 to 608 computations (6.3% saved)

Precisions

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

ival-pow: 3.0ms (40.2% of total)

ival-div!: 2.0ms (26.8% of total)

ival-sqrt: 1.0ms (13.4% of total)

ival-mult!: 1.0ms (13.4% of total)

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

adjust: 0.0ms (0% of total)

bsearch11.0ms (0.2%)

Memory

21.0MiB live, 21.0MiB allocated; 0ms collecting garbage

Algorithm

1×	binary-search

Stop Event

1×	predicate-same

Steps

Time	Left	Right
10.0ms	251.19404411456574	52197.29897641039

Samples

6.0ms

96×

valid

Compiler

Compiled 307 to 300 computations (2.3% saved)

Precisions

Click to see histograms. Total time spent on operations: 4.0ms

ival-sqrt: 1.0ms (24.3% of total)

ival-div!: 1.0ms (24.3% of total)

ival-pow: 1.0ms (24.3% of total)

ival-mult!: 1.0ms (24.3% of total)

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

adjust: 0.0ms (0% of total)

derivations399.0ms (5.7%)

Memory

-7.9MiB live, 228.1MiB allocated; 56ms collecting garbage

Stop Event

1×

fuel

Compiler

Compiled 168 to 108 computations (35.7% saved)

preprocess107.0ms (1.5%)

Memory: 14.3MiB live, 155.0MiB allocated; 14ms collecting garbage
Compiler: Compiled 183 to 121 computations (33.9% saved)

end0.0ms (0%)

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

start0.0ms (0%)

analyze151.0ms (2.2%)

sample3.2s (46.5%)

preprocess127.0ms (1.8%)

series77.0ms (1.1%)

rewrite164.0ms (2.4%)

eval32.0ms (0.5%)

prune12.0ms (0.2%)

series189.0ms (2.7%)

rewrite156.0ms (2.2%)

eval986.0ms (14.2%)

prune26.0ms (0.4%)

series87.0ms (1.3%)

rewrite215.0ms (3.1%)

eval57.0ms (0.8%)

prune30.0ms (0.4%)

series222.0ms (3.2%)

rewrite154.0ms (2.2%)

eval96.0ms (1.4%)

prune43.0ms (0.6%)

regimes76.0ms (1.1%)

regimes49.0ms (0.7%)

regimes49.0ms (0.7%)

regimes26.0ms (0.4%)

regimes36.0ms (0.5%)

regimes35.0ms (0.5%)

regimes15.0ms (0.2%)

regimes15.0ms (0.2%)

regimes10.0ms (0.2%)

regimes5.0ms (0.1%)

bsearch15.0ms (0.2%)

bsearch22.0ms (0.3%)

bsearch23.0ms (0.3%)

bsearch11.0ms (0.2%)

derivations399.0ms (5.7%)

preprocess107.0ms (1.5%)

end0.0ms (0%)

Profiling