Metrics for Migdal et al, Equation (51)

start0.0ms (0%)

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

analyze100.0ms (1.4%)

Memory

-16.0MiB live, 120.4MiB allocated; 46ms 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 (43.1%)

Memory

103.3MiB live, 3 185.3MiB allocated; 1.3s collecting garbage

Samples

1.5s	5 466×	1	invalid
900.0ms	8 256×	0	valid
107.0ms	502×	2	invalid
76.0ms	237×	0	exit
19.0ms	353×	0	invalid

Precisions

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

ival-pow: 754.0ms (42.9% of total)

ival-div!: 263.0ms (15% of total)

ival-mult!: 262.0ms (14.9% of total)

ival-sqrt: 212.0ms (12.1% of total)

adjust: 208.0ms (11.8% of total)

ival-sub!: 59.0ms (3.4% of total)

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

exact: 0.0ms (0% of total)

Bogosity

preprocess68.0ms (0.9%)

Memory

-28.0MiB live, 63.8MiB allocated; 14ms collecting garbage

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	33	101
1	128	87
2	462	87
3	2175	86

Stop Event

1×	node-limit

Alt Table

Click to see full alt table

Status	Accuracy	Program
▶	99.6%	(.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))))

Symmetry

(abs k)

Compiler

Compiled 30 to 26 computations (13.3% saved)

series101.0ms (1.4%)

Memory

8.7MiB live, 201.6MiB allocated; 21ms 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
54.0ms	n	@	0	((* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (/ 1 (sqrt k)) 1 (sqrt k) k (pow (* (* 2 (PI)) n) (/ (- 1 k) 2)) (* (* 2 (PI)) n) (* 2 (PI)) 2 (PI) n (/ (- 1 k) 2) (- 1 k))
31.0ms	n	@	-inf	((* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (/ 1 (sqrt k)) 1 (sqrt k) k (pow (* (* 2 (PI)) n) (/ (- 1 k) 2)) (* (* 2 (PI)) n) (* 2 (PI)) 2 (PI) n (/ (- 1 k) 2) (- 1 k))
9.0ms	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))

rewrite206.0ms (2.8%)

Memory

-11.6MiB live, 227.2MiB allocated; 80ms collecting garbage

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	167	1003
0	181	944
1	950	877
0	8355	841

Stop Event

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

Counts

50 → 262

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

eval72.0ms (1%)

Memory: -6.9MiB live, 88.3MiB allocated; 26ms collecting garbage
Compiler: Compiled 2 220 to 1 020 computations (54.1% saved)

prune16.0ms (0.2%)

Memory

-4.5MiB live, 40.0MiB allocated; 9ms collecting garbage

Pruning

14 alts after pruning (14 fresh and 0 done)

	Pruned	Kept	Total
New	231	14	245
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	232	14	246

Accuracy

100.0%

Counts

246 → 14

Alt Table

Click to see full alt table

Status	Accuracy	Program
	99.6%	(/.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))
	99.5%	(/.f64 #s(literal 1 binary64) (/.f64 (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)))))
	99.5%	(.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) (pow.f64 (.f64 (*.f64 (sqrt.f64 (PI.f64)) (+.f64 (sqrt.f64 (PI.f64)) (sqrt.f64 (PI.f64)))) n) (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 2 binary64))))
	99.4%	(.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) (pow.f64 (.f64 (.f64 (sqrt.f64 #s(literal 2 binary64)) (sqrt.f64 #s(literal 2 binary64))) (.f64 (sqrt.f64 (.f64 (PI.f64) n)) (sqrt.f64 (.f64 (PI.f64) n)))) (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 2 binary64))))
▶	99.7%	(.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))))
	48.8%	(.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) #s(approx (pow ( (* 2 (PI)) n) (/ (- 1 k) 2)) (sqrt.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n))))
	99.5%	(.f64 (/.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))))
	99.6%	(.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) k)) (pow.f64 (.f64 (*.f64 #s(literal 2 binary64) (PI.f64)) n) (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 2 binary64))))
	99.5%	(.f64 #s(approx (/ 1 (sqrt k)) (.f64 (/.f64 #s(literal 1 binary64) 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))))
	46.9%	#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))))
▶	49.1%	#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)))
▶	96.4%	#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 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)))
▶	92.0%	#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (.f64 (/.f64 (exp.f64 (.f64 (log.f64 (sqrt.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n))) (-.f64 #s(literal 1 binary64) k))) k) (sqrt.f64 k)))
▶	39.0%	#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 650 to 526 computations (19.1% saved)

series229.0ms (3.1%)

Memory

-6.8MiB live, 521.9MiB allocated; 144ms collecting garbage

Counts

33 → 120

Calls

Call 1

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

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

Calls

6 calls:

Time	Variable		Point	Expression
68.0ms	k	@	0	((* (/ 1 (sqrt k)) (/ (sqrt (* (+ (PI) (PI)) n)) (pow (* (+ (PI) (PI)) n) (* 1/2 k)))) (/ 1 (sqrt k)) 1 (sqrt k) k (/ (sqrt (* (+ (PI) (PI)) n)) (pow (* (+ (PI) (PI)) n) (* 1/2 k))) (sqrt (* (+ (PI) (PI)) n)) (* (+ (PI) (PI)) n) (+ (PI) (PI)) (PI) n (pow (* (+ (PI) (PI)) n) (* 1/2 k)) (* 1/2 k) 1/2 (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt (/ (* (+ (PI) (PI)) n) k)) (/ (* (+ (PI) (PI)) n) k) (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (/ (exp (* (log (sqrt (* (+ (PI) (PI)) n))) (- 1 k))) (sqrt k)) (exp (* (log (sqrt (* (+ (PI) (PI)) n))) (- 1 k))) (* (log (sqrt (* (+ (PI) (PI)) n))) (- 1 k)) (log (sqrt (* (+ (PI) (PI)) n))) (- 1 k) (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (* (/ (exp (* (log (sqrt (* (+ (PI) (PI)) n))) (- 1 k))) k) (sqrt k)) (/ (exp (* (log (sqrt (* (+ (PI) (PI)) n))) (- 1 k))) k) (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (/ (+ (* (* (* (log (* (+ (PI) (PI)) n)) (sqrt (* (+ (PI) (PI)) n))) k) -1/2) (sqrt (* (+ (PI) (PI)) n))) (sqrt k)) (+ (* (* (* (log (* (+ (PI) (PI)) n)) (sqrt (* (+ (PI) (PI)) n))) k) -1/2) (sqrt (* (+ (PI) (PI)) n))) (* (* (log (* (+ (PI) (PI)) n)) (sqrt (* (+ (PI) (PI)) n))) k) (* (log (* (+ (PI) (PI)) n)) (sqrt (* (+ (PI) (PI)) n))) (log (* (+ (PI) (PI)) n)) -1/2)
48.0ms	n	@	-inf	((* (/ 1 (sqrt k)) (/ (sqrt (* (+ (PI) (PI)) n)) (pow (* (+ (PI) (PI)) n) (* 1/2 k)))) (/ 1 (sqrt k)) 1 (sqrt k) k (/ (sqrt (* (+ (PI) (PI)) n)) (pow (* (+ (PI) (PI)) n) (* 1/2 k))) (sqrt (* (+ (PI) (PI)) n)) (* (+ (PI) (PI)) n) (+ (PI) (PI)) (PI) n (pow (* (+ (PI) (PI)) n) (* 1/2 k)) (* 1/2 k) 1/2 (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt (/ (* (+ (PI) (PI)) n) k)) (/ (* (+ (PI) (PI)) n) k) (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (/ (exp (* (log (sqrt (* (+ (PI) (PI)) n))) (- 1 k))) (sqrt k)) (exp (* (log (sqrt (* (+ (PI) (PI)) n))) (- 1 k))) (* (log (sqrt (* (+ (PI) (PI)) n))) (- 1 k)) (log (sqrt (* (+ (PI) (PI)) n))) (- 1 k) (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (* (/ (exp (* (log (sqrt (* (+ (PI) (PI)) n))) (- 1 k))) k) (sqrt k)) (/ (exp (* (log (sqrt (* (+ (PI) (PI)) n))) (- 1 k))) k) (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (/ (+ (* (* (* (log (* (+ (PI) (PI)) n)) (sqrt (* (+ (PI) (PI)) n))) k) -1/2) (sqrt (* (+ (PI) (PI)) n))) (sqrt k)) (+ (* (* (* (log (* (+ (PI) (PI)) n)) (sqrt (* (+ (PI) (PI)) n))) k) -1/2) (sqrt (* (+ (PI) (PI)) n))) (* (* (log (* (+ (PI) (PI)) n)) (sqrt (* (+ (PI) (PI)) n))) k) (* (log (* (+ (PI) (PI)) n)) (sqrt (* (+ (PI) (PI)) n))) (log (* (+ (PI) (PI)) n)) -1/2)
41.0ms	n	@	0	((* (/ 1 (sqrt k)) (/ (sqrt (* (+ (PI) (PI)) n)) (pow (* (+ (PI) (PI)) n) (* 1/2 k)))) (/ 1 (sqrt k)) 1 (sqrt k) k (/ (sqrt (* (+ (PI) (PI)) n)) (pow (* (+ (PI) (PI)) n) (* 1/2 k))) (sqrt (* (+ (PI) (PI)) n)) (* (+ (PI) (PI)) n) (+ (PI) (PI)) (PI) n (pow (* (+ (PI) (PI)) n) (* 1/2 k)) (* 1/2 k) 1/2 (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt (/ (* (+ (PI) (PI)) n) k)) (/ (* (+ (PI) (PI)) n) k) (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (/ (exp (* (log (sqrt (* (+ (PI) (PI)) n))) (- 1 k))) (sqrt k)) (exp (* (log (sqrt (* (+ (PI) (PI)) n))) (- 1 k))) (* (log (sqrt (* (+ (PI) (PI)) n))) (- 1 k)) (log (sqrt (* (+ (PI) (PI)) n))) (- 1 k) (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (* (/ (exp (* (log (sqrt (* (+ (PI) (PI)) n))) (- 1 k))) k) (sqrt k)) (/ (exp (* (log (sqrt (* (+ (PI) (PI)) n))) (- 1 k))) k) (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (/ (+ (* (* (* (log (* (+ (PI) (PI)) n)) (sqrt (* (+ (PI) (PI)) n))) k) -1/2) (sqrt (* (+ (PI) (PI)) n))) (sqrt k)) (+ (* (* (* (log (* (+ (PI) (PI)) n)) (sqrt (* (+ (PI) (PI)) n))) k) -1/2) (sqrt (* (+ (PI) (PI)) n))) (* (* (log (* (+ (PI) (PI)) n)) (sqrt (* (+ (PI) (PI)) n))) k) (* (log (* (+ (PI) (PI)) n)) (sqrt (* (+ (PI) (PI)) n))) (log (* (+ (PI) (PI)) n)) -1/2)
30.0ms	n	@	inf	((* (/ 1 (sqrt k)) (/ (sqrt (* (+ (PI) (PI)) n)) (pow (* (+ (PI) (PI)) n) (* 1/2 k)))) (/ 1 (sqrt k)) 1 (sqrt k) k (/ (sqrt (* (+ (PI) (PI)) n)) (pow (* (+ (PI) (PI)) n) (* 1/2 k))) (sqrt (* (+ (PI) (PI)) n)) (* (+ (PI) (PI)) n) (+ (PI) (PI)) (PI) n (pow (* (+ (PI) (PI)) n) (* 1/2 k)) (* 1/2 k) 1/2 (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt (/ (* (+ (PI) (PI)) n) k)) (/ (* (+ (PI) (PI)) n) k) (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (/ (exp (* (log (sqrt (* (+ (PI) (PI)) n))) (- 1 k))) (sqrt k)) (exp (* (log (sqrt (* (+ (PI) (PI)) n))) (- 1 k))) (* (log (sqrt (* (+ (PI) (PI)) n))) (- 1 k)) (log (sqrt (* (+ (PI) (PI)) n))) (- 1 k) (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (* (/ (exp (* (log (sqrt (* (+ (PI) (PI)) n))) (- 1 k))) k) (sqrt k)) (/ (exp (* (log (sqrt (* (+ (PI) (PI)) n))) (- 1 k))) k) (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (/ (+ (* (* (* (log (* (+ (PI) (PI)) n)) (sqrt (* (+ (PI) (PI)) n))) k) -1/2) (sqrt (* (+ (PI) (PI)) n))) (sqrt k)) (+ (* (* (* (log (* (+ (PI) (PI)) n)) (sqrt (* (+ (PI) (PI)) n))) k) -1/2) (sqrt (* (+ (PI) (PI)) n))) (* (* (log (* (+ (PI) (PI)) n)) (sqrt (* (+ (PI) (PI)) n))) k) (* (log (* (+ (PI) (PI)) n)) (sqrt (* (+ (PI) (PI)) n))) (log (* (+ (PI) (PI)) n)) -1/2)
20.0ms	k	@	-inf	((* (/ 1 (sqrt k)) (/ (sqrt (* (+ (PI) (PI)) n)) (pow (* (+ (PI) (PI)) n) (* 1/2 k)))) (/ 1 (sqrt k)) 1 (sqrt k) k (/ (sqrt (* (+ (PI) (PI)) n)) (pow (* (+ (PI) (PI)) n) (* 1/2 k))) (sqrt (* (+ (PI) (PI)) n)) (* (+ (PI) (PI)) n) (+ (PI) (PI)) (PI) n (pow (* (+ (PI) (PI)) n) (* 1/2 k)) (* 1/2 k) 1/2 (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt (/ (* (+ (PI) (PI)) n) k)) (/ (* (+ (PI) (PI)) n) k) (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (/ (exp (* (log (sqrt (* (+ (PI) (PI)) n))) (- 1 k))) (sqrt k)) (exp (* (log (sqrt (* (+ (PI) (PI)) n))) (- 1 k))) (* (log (sqrt (* (+ (PI) (PI)) n))) (- 1 k)) (log (sqrt (* (+ (PI) (PI)) n))) (- 1 k) (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (* (/ (exp (* (log (sqrt (* (+ (PI) (PI)) n))) (- 1 k))) k) (sqrt k)) (/ (exp (* (log (sqrt (* (+ (PI) (PI)) n))) (- 1 k))) k) (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (/ (+ (* (* (* (log (* (+ (PI) (PI)) n)) (sqrt (* (+ (PI) (PI)) n))) k) -1/2) (sqrt (* (+ (PI) (PI)) n))) (sqrt k)) (+ (* (* (* (log (* (+ (PI) (PI)) n)) (sqrt (* (+ (PI) (PI)) n))) k) -1/2) (sqrt (* (+ (PI) (PI)) n))) (* (* (log (* (+ (PI) (PI)) n)) (sqrt (* (+ (PI) (PI)) n))) k) (* (log (* (+ (PI) (PI)) n)) (sqrt (* (+ (PI) (PI)) n))) (log (* (+ (PI) (PI)) n)) -1/2)

rewrite233.0ms (3.1%)

Memory

20.8MiB live, 346.1MiB allocated; 23ms collecting garbage

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	542	5098
0	597	4672
1	3348	4479
0	8418	4429

Stop Event

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

Counts

153 → 532

Calls

Call 1

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

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

eval131.0ms (1.8%)

Memory: 4.9MiB live, 322.0MiB allocated; 75ms collecting garbage
Compiler: Compiled 14 930 to 3 338 computations (77.6% saved)

prune57.0ms (0.8%)

Memory

-12.8MiB live, 95.4MiB allocated; 39ms collecting garbage

Pruning

24 alts after pruning (21 fresh and 3 done)

	Pruned	Kept	Total
New	813	19	832
Fresh	7	2	9
Picked	2	3	5
Done	0	0	0
Total	822	24	846

Accuracy

100.0%

Counts

846 → 24

Alt Table

Click to see full alt table

Status	Accuracy	Program
	99.6%	(/.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))
	52.7%	(.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) (/.f64 (sqrt.f64 (.f64 (+.f64 (PI.f64) (PI.f64)) n)) #s(approx (pow (* (+ (PI) (PI)) n) (* 1/2 k)) (fma.f64 (.f64 #s(literal 1/2 binary64) k) (log.f64 (.f64 n (+.f64 (PI.f64) (PI.f64)))) #s(literal 1 binary64)))))
	48.8%	(.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))))
▶	99.6%	#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (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)))
	99.7%	#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (/.f64 (/.f64 (sqrt.f64 (.f64 n (+.f64 (PI.f64) (PI.f64)))) (pow.f64 (sqrt.f64 (.f64 n (+.f64 (PI.f64) (PI.f64)))) k)) (sqrt.f64 k)))
	99.6%	#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (/.f64 (.f64 (pow.f64 (sqrt.f64 (.f64 n (+.f64 (PI.f64) (PI.f64)))) (-.f64 #s(literal 1 binary64) k)) (sqrt.f64 k)) k))
▶	99.7%	#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (/.f64 (.f64 (pow.f64 (sqrt.f64 (.f64 n (+.f64 (PI.f64) (PI.f64)))) (neg.f64 k)) (sqrt.f64 (*.f64 n (+.f64 (PI.f64) (PI.f64))))) (sqrt.f64 k)))
	48.8%	#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (/.f64 (sqrt.f64 (*.f64 n (+.f64 (PI.f64) (PI.f64)))) (sqrt.f64 k)))
✓	96.4%	#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 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)))
	45.6%	#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (/.f64 (exp.f64 #s(approx (* (log (sqrt (* (+ (PI) (PI)) n))) (- 1 k)) (log.f64 (sqrt.f64 (*.f64 n (+.f64 (PI.f64) (PI.f64))))))) (sqrt.f64 k)))
✓	92.0%	#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (.f64 (/.f64 (exp.f64 (.f64 (log.f64 (sqrt.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n))) (-.f64 #s(literal 1 binary64) k))) k) (sqrt.f64 k)))
	38.8%	#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))))
	38.8%	#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))))
	44.1%	#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (.f64 #s(approx (/ (exp ( (log (sqrt (* (+ (PI) (PI)) n))) (- 1 k))) k) (/.f64 (sqrt.f64 (*.f64 n (+.f64 (PI.f64) (PI.f64)))) k)) (sqrt.f64 k)))
✓	39.0%	#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt.f64 (/.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n) k)))
	21.6%	#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))))
▶	23.4%	#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt.f64 (/.f64 (sqrt.f64 (.f64 (.f64 n (+.f64 (PI.f64) (PI.f64))) (*.f64 n (+.f64 (PI.f64) (PI.f64))))) k)))
	39.0%	#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))))
▶	39.0%	#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) (/.f64 n k))))
	27.4%	#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt.f64 (sqrt.f64 (.f64 (/.f64 (.f64 n (+.f64 (PI.f64) (PI.f64))) k) (/.f64 (*.f64 n (+.f64 (PI.f64) (PI.f64))) k)))))
	36.4%	#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (exp.f64 (.f64 (log.f64 (/.f64 (.f64 n (+.f64 (PI.f64) (PI.f64))) k)) #s(literal 1/2 binary64))))
	3.0%	#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) #s(approx (/ (+ (* (* (* (log (* (+ (PI) (PI)) n)) (sqrt (* (+ (PI) (PI)) n))) k) -1/2) (sqrt (* (+ (PI) (PI)) n))) (sqrt k)) (.f64 (.f64 (.f64 (log.f64 (.f64 n (+.f64 (PI.f64) (PI.f64)))) (sqrt.f64 (*.f64 n (+.f64 (PI.f64) (PI.f64))))) (sqrt.f64 k)) #s(literal -1/2 binary64))))
	35.5%	#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) #s(approx (* (/ (exp (* (log (sqrt (* (+ (PI) (PI)) n))) (- 1 k))) k) (sqrt k)) (/.f64 (sqrt.f64 (.f64 (.f64 n (+.f64 (PI.f64) (PI.f64))) k)) k)))
▶	46.3%	#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) #s(approx (sqrt (/ (* (+ (PI) (PI)) n) k)) (.f64 (sqrt.f64 (/.f64 (+.f64 (PI.f64) (PI.f64)) (.f64 n k))) n)))

Compiler

Compiled 1 165 to 1 024 computations (12.1% saved)

series90.0ms (1.2%)

Memory

-10.6MiB live, 226.2MiB allocated; 21ms collecting garbage

Counts

32 → 76

Calls

Call 1

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

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

Calls

6 calls:

Time	Variable		Point	Expression
24.0ms	n	@	-inf	((* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (/ (* (pow (sqrt (* n (+ (PI) (PI)))) (neg k)) (sqrt (* n (+ (PI) (PI))))) (sqrt k)) (* (pow (sqrt (* n (+ (PI) (PI)))) (neg k)) (sqrt (* n (+ (PI) (PI))))) (pow (sqrt (* n (+ (PI) (PI)))) (neg k)) (sqrt (* n (+ (PI) (PI)))) (* n (+ (PI) (PI))) n (+ (PI) (PI)) (PI) (neg k) k (sqrt k) (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (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) (PI)) (* n k))) n) (sqrt (/ (+ (PI) (PI)) (* n k))) (/ (+ (PI) (PI)) (* n k)) (* n k) (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt (/ (sqrt (* (* n (+ (PI) (PI))) (* n (+ (PI) (PI))))) k)) (/ (sqrt (* (* n (+ (PI) (PI))) (* n (+ (PI) (PI))))) k) (sqrt (* (* n (+ (PI) (PI))) (* n (+ (PI) (PI))))) (* (* n (+ (PI) (PI))) (* n (+ (PI) (PI)))) (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (/ (pow (sqrt (* n (+ (PI) (PI)))) (- 1 k)) (sqrt k)) (pow (sqrt (* n (+ (PI) (PI)))) (- 1 k)) (- 1 k) 1)
22.0ms	n	@	inf	((* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (/ (* (pow (sqrt (* n (+ (PI) (PI)))) (neg k)) (sqrt (* n (+ (PI) (PI))))) (sqrt k)) (* (pow (sqrt (* n (+ (PI) (PI)))) (neg k)) (sqrt (* n (+ (PI) (PI))))) (pow (sqrt (* n (+ (PI) (PI)))) (neg k)) (sqrt (* n (+ (PI) (PI)))) (* n (+ (PI) (PI))) n (+ (PI) (PI)) (PI) (neg k) k (sqrt k) (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (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) (PI)) (* n k))) n) (sqrt (/ (+ (PI) (PI)) (* n k))) (/ (+ (PI) (PI)) (* n k)) (* n k) (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt (/ (sqrt (* (* n (+ (PI) (PI))) (* n (+ (PI) (PI))))) k)) (/ (sqrt (* (* n (+ (PI) (PI))) (* n (+ (PI) (PI))))) k) (sqrt (* (* n (+ (PI) (PI))) (* n (+ (PI) (PI))))) (* (* n (+ (PI) (PI))) (* n (+ (PI) (PI)))) (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (/ (pow (sqrt (* n (+ (PI) (PI)))) (- 1 k)) (sqrt k)) (pow (sqrt (* n (+ (PI) (PI)))) (- 1 k)) (- 1 k) 1)
22.0ms	n	@	0	((* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (/ (* (pow (sqrt (* n (+ (PI) (PI)))) (neg k)) (sqrt (* n (+ (PI) (PI))))) (sqrt k)) (* (pow (sqrt (* n (+ (PI) (PI)))) (neg k)) (sqrt (* n (+ (PI) (PI))))) (pow (sqrt (* n (+ (PI) (PI)))) (neg k)) (sqrt (* n (+ (PI) (PI)))) (* n (+ (PI) (PI))) n (+ (PI) (PI)) (PI) (neg k) k (sqrt k) (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (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) (PI)) (* n k))) n) (sqrt (/ (+ (PI) (PI)) (* n k))) (/ (+ (PI) (PI)) (* n k)) (* n k) (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt (/ (sqrt (* (* n (+ (PI) (PI))) (* n (+ (PI) (PI))))) k)) (/ (sqrt (* (* n (+ (PI) (PI))) (* n (+ (PI) (PI))))) k) (sqrt (* (* n (+ (PI) (PI))) (* n (+ (PI) (PI))))) (* (* n (+ (PI) (PI))) (* n (+ (PI) (PI)))) (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (/ (pow (sqrt (* n (+ (PI) (PI)))) (- 1 k)) (sqrt k)) (pow (sqrt (* n (+ (PI) (PI)))) (- 1 k)) (- 1 k) 1)
8.0ms	k	@	inf	((* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (/ (* (pow (sqrt (* n (+ (PI) (PI)))) (neg k)) (sqrt (* n (+ (PI) (PI))))) (sqrt k)) (* (pow (sqrt (* n (+ (PI) (PI)))) (neg k)) (sqrt (* n (+ (PI) (PI))))) (pow (sqrt (* n (+ (PI) (PI)))) (neg k)) (sqrt (* n (+ (PI) (PI)))) (* n (+ (PI) (PI))) n (+ (PI) (PI)) (PI) (neg k) k (sqrt k) (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (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) (PI)) (* n k))) n) (sqrt (/ (+ (PI) (PI)) (* n k))) (/ (+ (PI) (PI)) (* n k)) (* n k) (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt (/ (sqrt (* (* n (+ (PI) (PI))) (* n (+ (PI) (PI))))) k)) (/ (sqrt (* (* n (+ (PI) (PI))) (* n (+ (PI) (PI))))) k) (sqrt (* (* n (+ (PI) (PI))) (* n (+ (PI) (PI))))) (* (* n (+ (PI) (PI))) (* n (+ (PI) (PI)))) (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (/ (pow (sqrt (* n (+ (PI) (PI)))) (- 1 k)) (sqrt k)) (pow (sqrt (* n (+ (PI) (PI)))) (- 1 k)) (- 1 k) 1)
6.0ms	k	@	-inf	((* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (/ (* (pow (sqrt (* n (+ (PI) (PI)))) (neg k)) (sqrt (* n (+ (PI) (PI))))) (sqrt k)) (* (pow (sqrt (* n (+ (PI) (PI)))) (neg k)) (sqrt (* n (+ (PI) (PI))))) (pow (sqrt (* n (+ (PI) (PI)))) (neg k)) (sqrt (* n (+ (PI) (PI)))) (* n (+ (PI) (PI))) n (+ (PI) (PI)) (PI) (neg k) k (sqrt k) (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (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) (PI)) (* n k))) n) (sqrt (/ (+ (PI) (PI)) (* n k))) (/ (+ (PI) (PI)) (* n k)) (* n k) (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt (/ (sqrt (* (* n (+ (PI) (PI))) (* n (+ (PI) (PI))))) k)) (/ (sqrt (* (* n (+ (PI) (PI))) (* n (+ (PI) (PI))))) k) (sqrt (* (* n (+ (PI) (PI))) (* n (+ (PI) (PI))))) (* (* n (+ (PI) (PI))) (* n (+ (PI) (PI)))) (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (/ (pow (sqrt (* n (+ (PI) (PI)))) (- 1 k)) (sqrt k)) (pow (sqrt (* n (+ (PI) (PI)))) (- 1 k)) (- 1 k) 1)

rewrite174.0ms (2.3%)

Memory

18.5MiB live, 295.2MiB allocated; 19ms collecting garbage

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	374	2723
0	419	2335
1	2069	2227
0	8896	2203

Stop Event

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

Counts

108 → 656

Calls

Call 1

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

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

eval100.0ms (1.4%)

Memory: 29.6MiB live, 199.4MiB allocated; 45ms collecting garbage
Compiler: Compiled 10 063 to 3 031 computations (69.9% saved)

prune92.0ms (1.2%)

Memory

-27.7MiB live, 125.5MiB allocated; 61ms collecting garbage

Pruning

41 alts after pruning (33 fresh and 8 done)

	Pruned	Kept	Total
New	601	23	624
Fresh	6	10	16
Picked	0	5	5
Done	0	3	3
Total	607	41	648

Accuracy

100.0%

Counts

648 → 41

Alt Table

Click to see full alt table

Status	Accuracy	Program
	99.6%	(/.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))
	48.8%	(.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))))
✓	99.6%	#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (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)))
▶	99.7%	#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (/.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)))
	99.6%	#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (/.f64 (.f64 (pow.f64 (sqrt.f64 (.f64 n (+.f64 (PI.f64) (PI.f64)))) (-.f64 #s(literal 1 binary64) k)) (sqrt.f64 k)) k))
✓	99.7%	#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (/.f64 (.f64 (pow.f64 (sqrt.f64 (.f64 n (+.f64 (PI.f64) (PI.f64)))) (neg.f64 k)) (sqrt.f64 (*.f64 n (+.f64 (PI.f64) (PI.f64))))) (sqrt.f64 k)))
	49.4%	#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (/.f64 (.f64 #s(approx (pow (sqrt ( n (+ (PI) (PI)))) (neg k)) (fma.f64 (neg.f64 k) (log.f64 (sqrt.f64 (.f64 (+.f64 (PI.f64) (PI.f64)) n))) #s(literal 1 binary64))) (sqrt.f64 (.f64 n (+.f64 (PI.f64) (PI.f64))))) (sqrt.f64 k)))
	48.8%	#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (/.f64 (sqrt.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n)) (sqrt.f64 k)))
✓	96.4%	#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 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)))
▶	45.6%	#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (/.f64 (exp.f64 #s(approx (* (log (sqrt (* (+ (PI) (PI)) n))) (- 1 k)) (log.f64 (sqrt.f64 (*.f64 n (+.f64 (PI.f64) (PI.f64))))))) (sqrt.f64 k)))
	79.0%	#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (.f64 (pow.f64 (sqrt.f64 (.f64 (+.f64 (PI.f64) (PI.f64)) n)) (neg.f64 k)) (sqrt.f64 (/.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n) k))))
✓	92.0%	#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (.f64 (/.f64 (exp.f64 (.f64 (log.f64 (sqrt.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n))) (-.f64 #s(literal 1 binary64) k))) k) (sqrt.f64 k)))
	38.8%	#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))))
	38.8%	#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (*.f64 (sqrt.f64 (/.f64 n k)) (sqrt.f64 (+.f64 (PI.f64) (PI.f64)))))
	48.8%	#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (*.f64 (sqrt.f64 n) (sqrt.f64 (/.f64 (+.f64 (PI.f64) (PI.f64)) k))))
	44.1%	#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (.f64 #s(approx (/ (exp ( (log (sqrt (* (+ (PI) (PI)) n))) (- 1 k))) k) (/.f64 (sqrt.f64 (*.f64 n (+.f64 (PI.f64) (PI.f64)))) k)) (sqrt.f64 k)))
✓	39.0%	#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt.f64 (/.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n) k)))
▶	21.6%	#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))))
✓	23.4%	#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt.f64 (/.f64 (sqrt.f64 (.f64 (.f64 n (+.f64 (PI.f64) (PI.f64))) (*.f64 n (+.f64 (PI.f64) (PI.f64))))) k)))
	39.0%	#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt.f64 (/.f64 #s(literal 2 binary64) (/.f64 k (*.f64 n (PI.f64))))))
	39.0%	#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))))
✓	39.0%	#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) (/.f64 n k))))
▶	39.0%	#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt.f64 (*.f64 n (/.f64 (+.f64 (PI.f64) (PI.f64)) k))))
	27.4%	#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt.f64 (sqrt.f64 (.f64 (/.f64 (.f64 (+.f64 (PI.f64) (PI.f64)) n) k) (/.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n) k)))))
	36.4%	#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (exp.f64 (.f64 (log.f64 (/.f64 (.f64 (+.f64 (PI.f64) (PI.f64)) n) k)) #s(literal 1/2 binary64))))
	3.0%	#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) #s(approx (/ (+ (* (* (* (log (* (+ (PI) (PI)) n)) (sqrt (* (+ (PI) (PI)) n))) k) -1/2) (sqrt (* (+ (PI) (PI)) n))) (sqrt k)) (.f64 (.f64 (.f64 (log.f64 (.f64 n (+.f64 (PI.f64) (PI.f64)))) (sqrt.f64 (*.f64 n (+.f64 (PI.f64) (PI.f64))))) (sqrt.f64 k)) #s(literal -1/2 binary64))))
	35.5%	#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) #s(approx (* (/ (exp (* (log (sqrt (* (+ (PI) (PI)) n))) (- 1 k))) k) (sqrt k)) (/.f64 (sqrt.f64 (.f64 (.f64 n (+.f64 (PI.f64) (PI.f64))) k)) k)))
	49.1%	#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 (PI.f64) (PI.f64)) n)) (sqrt.f64 k)) n)))
	48.7%	#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 (PI.f64) (PI.f64)) k)) (sqrt.f64 n)) n)))
	46.8%	#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) #s(approx (sqrt (/ (* (+ (PI) (PI)) n) k)) (.f64 (/.f64 (sqrt.f64 (+.f64 (PI.f64) (PI.f64))) (sqrt.f64 (.f64 n k))) n)))
	46.9%	#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) #s(approx (sqrt (/ (* (+ (PI) (PI)) n) k)) (.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 (/.f64 (.f64 n k) (+.f64 (PI.f64) (PI.f64))))) n)))
	46.2%	#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) #s(approx (sqrt (/ (* (+ (PI) (PI)) n) k)) (.f64 (.f64 (sqrt.f64 (/.f64 (PI.f64) (*.f64 n k))) (sqrt.f64 #s(literal 2 binary64))) n)))
	33.3%	#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) #s(approx (sqrt (/ (* (+ (PI) (PI)) n) k)) (.f64 (sqrt.f64 (/.f64 (fma.f64 (/.f64 (PI.f64) k) (.f64 n k) (.f64 n (PI.f64))) (.f64 n (*.f64 n k)))) n)))
	37.7%	#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) #s(approx (sqrt (/ (* (+ (PI) (PI)) n) k)) (.f64 (sqrt.f64 (/.f64 (fma.f64 (/.f64 (PI.f64) k) n (/.f64 (.f64 n (PI.f64)) k)) (*.f64 n n))) n)))
	31.6%	#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) #s(approx (sqrt (/ (* (+ (PI) (PI)) n) k)) (.f64 (sqrt.f64 (/.f64 (fma.f64 (PI.f64) (.f64 n k) (.f64 (.f64 n (PI.f64)) k)) (.f64 (.f64 n k) (*.f64 n k)))) n)))
▶	44.4%	#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) (PI.f64)) n) k)) n)))
✓	46.3%	#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) #s(approx (sqrt (/ (* (+ (PI) (PI)) n) k)) (.f64 (sqrt.f64 (/.f64 (+.f64 (PI.f64) (PI.f64)) (.f64 n k))) n)))
	44.4%	#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) n) (/.f64 #s(literal 2 binary64) k))) n)))
	44.2%	#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 (PI.f64) (PI.f64)) (*.f64 n k))) #s(literal 1/2 binary64))) n)))
	50.3%	#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) #s(approx (sqrt (/ (* (+ (PI) (PI)) n) k)) (.f64 #s(approx (sqrt (/ (+ (PI) (PI)) ( n k))) (/.f64 (sqrt.f64 (.f64 (/.f64 (.f64 (PI.f64) k) n) #s(literal 2 binary64))) k)) n)))
	50.4%	#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) #s(approx (sqrt (/ (* (+ (PI) (PI)) n) k)) #s(approx (* (sqrt (/ (+ (PI) (PI)) (* n k))) n) (/.f64 (.f64 (sqrt.f64 (.f64 (/.f64 (*.f64 (PI.f64) k) n) #s(literal 2 binary64))) n) k))))

Compiler

Compiled 2 042 to 1 813 computations (11.2% saved)

series100.0ms (1.3%)

Memory

9.1MiB live, 151.0MiB allocated; 24ms collecting garbage

Counts

36 → 79

Calls

Call 1

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

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

Calls

6 calls:

Time	Variable		Point	Expression
36.0ms	n	@	inf	((* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (/ (/ (sqrt (* (+ (PI) (PI)) n)) (pow (sqrt (* (+ (PI) (PI)) n)) k)) (sqrt k)) (/ (sqrt (* (+ (PI) (PI)) n)) (pow (sqrt (* (+ (PI) (PI)) n)) k)) (sqrt (* (+ (PI) (PI)) n)) (* (+ (PI) (PI)) n) (+ (PI) (PI)) (PI) n (pow (sqrt (* (+ (PI) (PI)) n)) k) k (sqrt k) (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt (* n (/ (+ (PI) (PI)) k))) (* n (/ (+ (PI) (PI)) k)) (/ (+ (PI) (PI)) k) (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt (/ (* (+ (PI) (PI)) n) k)) (* (sqrt (/ (/ (+ (PI) (PI)) n) k)) n) (sqrt (/ (/ (+ (PI) (PI)) n) k)) (/ (/ (+ (PI) (PI)) n) k) (/ (+ (PI) (PI)) n) (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt (/ (* (* (* (PI) n) k) 2) (* k k))) (/ (* (* (* (PI) n) k) 2) (* k k)) (* (* (* (PI) n) k) 2) (* (* (PI) n) k) (* (PI) n) 2 (* k k) (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (/ (exp (* (log (sqrt (* (+ (PI) (PI)) n))) (- 1 k))) (sqrt k)) (exp (* (log (sqrt (* (+ (PI) (PI)) n))) (- 1 k))) (* (log (sqrt (* (+ (PI) (PI)) n))) (- 1 k)) (log (sqrt (* n (+ (PI) (PI))))) (sqrt (* n (+ (PI) (PI)))) (* n (+ (PI) (PI))))
22.0ms	n	@	-inf	((* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (/ (/ (sqrt (* (+ (PI) (PI)) n)) (pow (sqrt (* (+ (PI) (PI)) n)) k)) (sqrt k)) (/ (sqrt (* (+ (PI) (PI)) n)) (pow (sqrt (* (+ (PI) (PI)) n)) k)) (sqrt (* (+ (PI) (PI)) n)) (* (+ (PI) (PI)) n) (+ (PI) (PI)) (PI) n (pow (sqrt (* (+ (PI) (PI)) n)) k) k (sqrt k) (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt (* n (/ (+ (PI) (PI)) k))) (* n (/ (+ (PI) (PI)) k)) (/ (+ (PI) (PI)) k) (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt (/ (* (+ (PI) (PI)) n) k)) (* (sqrt (/ (/ (+ (PI) (PI)) n) k)) n) (sqrt (/ (/ (+ (PI) (PI)) n) k)) (/ (/ (+ (PI) (PI)) n) k) (/ (+ (PI) (PI)) n) (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt (/ (* (* (* (PI) n) k) 2) (* k k))) (/ (* (* (* (PI) n) k) 2) (* k k)) (* (* (* (PI) n) k) 2) (* (* (PI) n) k) (* (PI) n) 2 (* k k) (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (/ (exp (* (log (sqrt (* (+ (PI) (PI)) n))) (- 1 k))) (sqrt k)) (exp (* (log (sqrt (* (+ (PI) (PI)) n))) (- 1 k))) (* (log (sqrt (* (+ (PI) (PI)) n))) (- 1 k)) (log (sqrt (* n (+ (PI) (PI))))) (sqrt (* n (+ (PI) (PI)))) (* n (+ (PI) (PI))))
20.0ms	n	@	0	((* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (/ (/ (sqrt (* (+ (PI) (PI)) n)) (pow (sqrt (* (+ (PI) (PI)) n)) k)) (sqrt k)) (/ (sqrt (* (+ (PI) (PI)) n)) (pow (sqrt (* (+ (PI) (PI)) n)) k)) (sqrt (* (+ (PI) (PI)) n)) (* (+ (PI) (PI)) n) (+ (PI) (PI)) (PI) n (pow (sqrt (* (+ (PI) (PI)) n)) k) k (sqrt k) (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt (* n (/ (+ (PI) (PI)) k))) (* n (/ (+ (PI) (PI)) k)) (/ (+ (PI) (PI)) k) (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt (/ (* (+ (PI) (PI)) n) k)) (* (sqrt (/ (/ (+ (PI) (PI)) n) k)) n) (sqrt (/ (/ (+ (PI) (PI)) n) k)) (/ (/ (+ (PI) (PI)) n) k) (/ (+ (PI) (PI)) n) (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt (/ (* (* (* (PI) n) k) 2) (* k k))) (/ (* (* (* (PI) n) k) 2) (* k k)) (* (* (* (PI) n) k) 2) (* (* (PI) n) k) (* (PI) n) 2 (* k k) (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (/ (exp (* (log (sqrt (* (+ (PI) (PI)) n))) (- 1 k))) (sqrt k)) (exp (* (log (sqrt (* (+ (PI) (PI)) n))) (- 1 k))) (* (log (sqrt (* (+ (PI) (PI)) n))) (- 1 k)) (log (sqrt (* n (+ (PI) (PI))))) (sqrt (* n (+ (PI) (PI)))) (* n (+ (PI) (PI))))
7.0ms	k	@	-inf	((* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (/ (/ (sqrt (* (+ (PI) (PI)) n)) (pow (sqrt (* (+ (PI) (PI)) n)) k)) (sqrt k)) (/ (sqrt (* (+ (PI) (PI)) n)) (pow (sqrt (* (+ (PI) (PI)) n)) k)) (sqrt (* (+ (PI) (PI)) n)) (* (+ (PI) (PI)) n) (+ (PI) (PI)) (PI) n (pow (sqrt (* (+ (PI) (PI)) n)) k) k (sqrt k) (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt (* n (/ (+ (PI) (PI)) k))) (* n (/ (+ (PI) (PI)) k)) (/ (+ (PI) (PI)) k) (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt (/ (* (+ (PI) (PI)) n) k)) (* (sqrt (/ (/ (+ (PI) (PI)) n) k)) n) (sqrt (/ (/ (+ (PI) (PI)) n) k)) (/ (/ (+ (PI) (PI)) n) k) (/ (+ (PI) (PI)) n) (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt (/ (* (* (* (PI) n) k) 2) (* k k))) (/ (* (* (* (PI) n) k) 2) (* k k)) (* (* (* (PI) n) k) 2) (* (* (PI) n) k) (* (PI) n) 2 (* k k) (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (/ (exp (* (log (sqrt (* (+ (PI) (PI)) n))) (- 1 k))) (sqrt k)) (exp (* (log (sqrt (* (+ (PI) (PI)) n))) (- 1 k))) (* (log (sqrt (* (+ (PI) (PI)) n))) (- 1 k)) (log (sqrt (* n (+ (PI) (PI))))) (sqrt (* n (+ (PI) (PI)))) (* n (+ (PI) (PI))))
7.0ms	k	@	0	((* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (/ (/ (sqrt (* (+ (PI) (PI)) n)) (pow (sqrt (* (+ (PI) (PI)) n)) k)) (sqrt k)) (/ (sqrt (* (+ (PI) (PI)) n)) (pow (sqrt (* (+ (PI) (PI)) n)) k)) (sqrt (* (+ (PI) (PI)) n)) (* (+ (PI) (PI)) n) (+ (PI) (PI)) (PI) n (pow (sqrt (* (+ (PI) (PI)) n)) k) k (sqrt k) (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt (* n (/ (+ (PI) (PI)) k))) (* n (/ (+ (PI) (PI)) k)) (/ (+ (PI) (PI)) k) (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt (/ (* (+ (PI) (PI)) n) k)) (* (sqrt (/ (/ (+ (PI) (PI)) n) k)) n) (sqrt (/ (/ (+ (PI) (PI)) n) k)) (/ (/ (+ (PI) (PI)) n) k) (/ (+ (PI) (PI)) n) (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt (/ (* (* (* (PI) n) k) 2) (* k k))) (/ (* (* (* (PI) n) k) 2) (* k k)) (* (* (* (PI) n) k) 2) (* (* (PI) n) k) (* (PI) n) 2 (* k k) (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (/ (exp (* (log (sqrt (* (+ (PI) (PI)) n))) (- 1 k))) (sqrt k)) (exp (* (log (sqrt (* (+ (PI) (PI)) n))) (- 1 k))) (* (log (sqrt (* (+ (PI) (PI)) n))) (- 1 k)) (log (sqrt (* n (+ (PI) (PI))))) (sqrt (* n (+ (PI) (PI)))) (* n (+ (PI) (PI))))

rewrite195.0ms (2.6%)

Memory

23.6MiB live, 251.8MiB allocated; 21ms collecting garbage

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	408	3242
0	452	2961
1	2486	2759
0	9444	2728

Stop Event

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

Counts

115 → 671

Calls

Call 1

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

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

eval65.0ms (0.9%)

Memory: 24.6MiB live, 123.7MiB allocated; 11ms collecting garbage
Compiler: Compiled 8 675 to 2 768 computations (68.1% saved)

prune51.0ms (0.7%)

Memory

-31.2MiB live, 105.8MiB allocated; 10ms collecting garbage

Pruning

44 alts after pruning (33 fresh and 11 done)

	Pruned	Kept	Total
New	533	13	546
Fresh	8	20	28
Picked	1	4	5
Done	1	7	8
Total	543	44	587

Accuracy

100.0%

Counts

587 → 44

Alt Table

Click to see full alt table

Status	Accuracy	Program
	99.6%	(/.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))
	48.8%	(.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))))
✓	99.6%	#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (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)))
	52.7%	#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (/.f64 (/.f64 (sqrt.f64 (.f64 (+.f64 (PI.f64) (PI.f64)) n)) #s(approx (pow (sqrt ( (+ (PI) (PI)) n)) k) (fma.f64 (log.f64 (sqrt.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n))) k #s(literal 1 binary64)))) (sqrt.f64 k)))
	99.6%	#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (/.f64 (.f64 (pow.f64 (sqrt.f64 (.f64 n (+.f64 (PI.f64) (PI.f64)))) (-.f64 #s(literal 1 binary64) k)) (sqrt.f64 k)) k))
✓	99.7%	#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (/.f64 (.f64 (pow.f64 (sqrt.f64 (.f64 n (+.f64 (PI.f64) (PI.f64)))) (neg.f64 k)) (sqrt.f64 (*.f64 n (+.f64 (PI.f64) (PI.f64))))) (sqrt.f64 k)))
	79.0%	#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (/.f64 (sqrt.f64 (.f64 (/.f64 (+.f64 (PI.f64) (PI.f64)) k) n)) (pow.f64 (sqrt.f64 (.f64 (+.f64 (PI.f64) (PI.f64)) n)) k)))
	48.8%	#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (/.f64 (sqrt.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n)) (sqrt.f64 k)))
✓	96.4%	#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 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)))
	45.6%	#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (/.f64 (exp.f64 #s(approx (* (log (sqrt (* (+ (PI) (PI)) n))) (- 1 k)) (.f64 (log.f64 (.f64 (+.f64 (PI.f64) (PI.f64)) n)) #s(literal 1/2 binary64)))) (sqrt.f64 k)))
✓	45.6%	#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (/.f64 (exp.f64 #s(approx (* (log (sqrt (* (+ (PI) (PI)) n))) (- 1 k)) (log.f64 (sqrt.f64 (*.f64 n (+.f64 (PI.f64) (PI.f64))))))) (sqrt.f64 k)))
✓	92.0%	#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (.f64 (/.f64 (exp.f64 (.f64 (log.f64 (sqrt.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n))) (-.f64 #s(literal 1 binary64) k))) k) (sqrt.f64 k)))
	48.8%	#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (*.f64 (sqrt.f64 (/.f64 (+.f64 (PI.f64) (PI.f64)) k)) (sqrt.f64 n)))
	35.4%	#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (.f64 (sqrt.f64 (/.f64 (.f64 (*.f64 n k) (PI.f64)) k)) (sqrt.f64 (/.f64 #s(literal 2 binary64) k))))
	38.8%	#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))))
	38.8%	#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (*.f64 (sqrt.f64 (/.f64 n k)) (sqrt.f64 (+.f64 (PI.f64) (PI.f64)))))
	44.1%	#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (.f64 #s(approx (/ (exp ( (log (sqrt (* (+ (PI) (PI)) n))) (- 1 k))) k) (/.f64 (sqrt.f64 (*.f64 n (+.f64 (PI.f64) (PI.f64)))) k)) (sqrt.f64 k)))
✓	39.0%	#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt.f64 (/.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n) k)))
✓	21.6%	#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))))
	39.0%	#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt.f64 (/.f64 #s(literal 2 binary64) (/.f64 k (*.f64 n (PI.f64))))))
	39.0%	#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))))
✓	39.0%	#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) (/.f64 n k))))
	33.2%	#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt.f64 (.f64 n (/.f64 (fma.f64 (PI.f64) (/.f64 k (PI.f64)) (.f64 k #s(literal 1 binary64))) (*.f64 k (/.f64 k (PI.f64)))))))
✓	39.0%	#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt.f64 (*.f64 n (/.f64 (+.f64 (PI.f64) (PI.f64)) k))))
	39.0%	#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt.f64 (*.f64 n (/.f64 #s(literal 2 binary64) (/.f64 k (PI.f64))))))
	27.4%	#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt.f64 (sqrt.f64 (.f64 (/.f64 (.f64 (+.f64 (PI.f64) (PI.f64)) n) k) (/.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n) k)))))
	36.4%	#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (exp.f64 (.f64 (log.f64 (/.f64 (.f64 (+.f64 (PI.f64) (PI.f64)) n) k)) #s(literal 1/2 binary64))))
	3.0%	#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) #s(approx (/ (+ (* (* (* (log (* (+ (PI) (PI)) n)) (sqrt (* (+ (PI) (PI)) n))) k) -1/2) (sqrt (* (+ (PI) (PI)) n))) (sqrt k)) (.f64 (.f64 (.f64 (log.f64 (.f64 n (+.f64 (PI.f64) (PI.f64)))) (sqrt.f64 (*.f64 n (+.f64 (PI.f64) (PI.f64))))) (sqrt.f64 k)) #s(literal -1/2 binary64))))
	35.5%	#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) #s(approx (* (/ (exp (* (log (sqrt (* (+ (PI) (PI)) n))) (- 1 k))) k) (sqrt k)) (/.f64 (sqrt.f64 (.f64 (.f64 n (+.f64 (PI.f64) (PI.f64))) k)) k)))
	35.9%	#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) #s(approx (sqrt (/ (* (+ (PI) (PI)) n) k)) (/.f64 (sqrt.f64 (.f64 (.f64 #s(literal 2 binary64) k) (*.f64 n (PI.f64)))) k)))
	49.1%	#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 (PI.f64) (PI.f64)) n)) (sqrt.f64 k)) n)))
	48.7%	#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 (PI.f64) (PI.f64)) k)) (sqrt.f64 n)) n)))
	46.8%	#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) #s(approx (sqrt (/ (* (+ (PI) (PI)) n) k)) (.f64 (/.f64 (sqrt.f64 (+.f64 (PI.f64) (PI.f64))) (sqrt.f64 (.f64 n k))) n)))
	46.9%	#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) #s(approx (sqrt (/ (* (+ (PI) (PI)) n) k)) (.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 (/.f64 (.f64 n k) (+.f64 (PI.f64) (PI.f64))))) n)))
	46.2%	#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) #s(approx (sqrt (/ (* (+ (PI) (PI)) n) k)) (.f64 (.f64 (sqrt.f64 (/.f64 (PI.f64) (*.f64 n k))) (sqrt.f64 #s(literal 2 binary64))) n)))
	44.9%	#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) #s(approx (sqrt (/ (* (+ (PI) (PI)) n) k)) (.f64 (sqrt.f64 (/.f64 (/.f64 (fma.f64 (PI.f64) (/.f64 n (PI.f64)) (.f64 n #s(literal 1 binary64))) (*.f64 n (/.f64 n (PI.f64)))) k)) n)))
✓	44.4%	#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) (PI.f64)) n) k)) n)))
	44.9%	#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 (+.f64 (PI.f64) (PI.f64)) n) (*.f64 n n)) k)) n)))
✓	46.3%	#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) #s(approx (sqrt (/ (* (+ (PI) (PI)) n) k)) (.f64 (sqrt.f64 (/.f64 (+.f64 (PI.f64) (PI.f64)) (.f64 n k))) n)))
	31.6%	#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) #s(approx (sqrt (/ (* (+ (PI) (PI)) n) k)) (.f64 (sqrt.f64 (/.f64 (.f64 (.f64 #s(literal 2 binary64) k) (.f64 n (PI.f64))) (.f64 (.f64 n k) (*.f64 n k)))) n)))
	44.4%	#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) n) (/.f64 #s(literal 2 binary64) k))) n)))
	44.2%	#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 (PI.f64) (PI.f64)) (*.f64 n k))) #s(literal 1/2 binary64))) n)))
	50.3%	#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) #s(approx (sqrt (/ (* (+ (PI) (PI)) n) k)) (.f64 #s(approx (sqrt (/ (/ (+ (PI) (PI)) n) k)) (/.f64 (sqrt.f64 (.f64 (/.f64 (*.f64 (PI.f64) k) n) #s(literal 2 binary64))) k)) n)))
	50.4%	#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) #s(approx (sqrt (/ (* (+ (PI) (PI)) n) k)) #s(approx (* (sqrt (/ (/ (+ (PI) (PI)) n) k)) n) (/.f64 (.f64 (sqrt.f64 (.f64 (/.f64 (*.f64 (PI.f64) k) n) #s(literal 2 binary64))) n) k))))

Compiler

Compiled 2 126 to 1 468 computations (31% saved)

regimes139.0ms (1.9%)

Memory

-9.7MiB live, 143.6MiB allocated; 126ms collecting garbage

Counts

70 → 1

Calls

Call 1

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

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

Outputs

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

Calls

4 calls:

20.0ms	(.f64 (.f64 #s(literal 2 binary64) (PI.f64)) n)
19.0ms	(.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))))
16.0ms	k
16.0ms	n

Results

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

Compiler

Compiled 22 to 23 computations (-4.5% saved)

regimes118.0ms (1.6%)

Memory

1.8MiB live, 100.0MiB allocated; 15ms collecting garbage

Counts

62 → 1

Calls

Call 1

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

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

Calls

4 calls:

68.0ms	(.f64 (.f64 #s(literal 2 binary64) (PI.f64)) n)
19.0ms	k
14.0ms	n
13.0ms	(.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) (pow.f64 (.f64 (*.f64 #s(literal 2 binary64) (PI.f64)) n) (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 2 binary64))))

Results

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

Compiler

Compiled 22 to 23 computations (-4.5% saved)

regimes87.0ms (1.2%)

Memory

27.7MiB live, 73.4MiB allocated; 5ms collecting garbage

Counts

54 → 1

Calls

Call 1

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

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

Calls

4 calls:

47.0ms	k
13.0ms	(.f64 (.f64 #s(literal 2 binary64) (PI.f64)) n)
13.0ms	n
11.0ms	(.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
99.6%	1	`(.f64 (.f64 #s(literal 2 binary64) (PI.f64)) n)`
99.6%	1	`(.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) (pow.f64 (.f64 (*.f64 #s(literal 2 binary64) (PI.f64)) n) (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 2 binary64))))`
99.6%	1	`k`
99.6%	1	`n`

Compiler

Compiled 22 to 23 computations (-4.5% saved)

regimes64.0ms (0.9%)

Memory

-9.0MiB live, 80.8MiB allocated; 10ms collecting garbage

Counts

49 → 1

Calls

Call 1

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

Outputs
(/.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:

24.0ms	n
16.0ms	(.f64 (.f64 #s(literal 2 binary64) (PI.f64)) n)
12.0ms	k
10.0ms	(.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) (pow.f64 (.f64 (*.f64 #s(literal 2 binary64) (PI.f64)) n) (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 2 binary64))))

Results

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

Compiler

Compiled 22 to 23 computations (-4.5% saved)

regimes55.0ms (0.7%)

Memory

-10.8MiB live, 87.4MiB allocated; 12ms collecting garbage

Counts

48 → 1

Calls

Call 1

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

Outputs
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (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)))

Calls

4 calls:

16.0ms	k
14.0ms	(.f64 (.f64 #s(literal 2 binary64) (PI.f64)) n)
12.0ms	n
10.0ms	(.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) (pow.f64 (.f64 (*.f64 #s(literal 2 binary64) (PI.f64)) n) (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 2 binary64))))

Results

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

Compiler

Compiled 22 to 23 computations (-4.5% saved)

regimes48.0ms (0.6%)

Memory

24.5MiB live, 71.4MiB allocated; 2ms collecting garbage

Counts

47 → 3

Calls

Call 1

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

Outputs

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

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

Calls

4 calls:

13.0ms	k
11.0ms	(.f64 (.f64 #s(literal 2 binary64) (PI.f64)) n)
11.0ms	n
10.0ms	(.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) (pow.f64 (.f64 (*.f64 #s(literal 2 binary64) (PI.f64)) n) (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 2 binary64))))

Results

Accuracy	Segments	Branch
75.4%	3	`(.f64 (.f64 #s(literal 2 binary64) (PI.f64)) n)`
73.9%	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))))`
72.4%	2	`k`
75.4%	3	`n`

Compiler

Compiled 22 to 23 computations (-4.5% saved)

regimes33.0ms (0.4%)

Memory

-11.9MiB live, 34.1MiB allocated; 3ms collecting garbage

Counts

45 → 3

Calls

Call 1

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

Outputs

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

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

Calls

2 calls:

19.0ms	n
11.0ms	(.f64 (.f64 #s(literal 2 binary64) (PI.f64)) n)

Results

Accuracy	Segments	Branch
75.4%	3	`(.f64 (.f64 #s(literal 2 binary64) (PI.f64)) n)`
75.4%	3	`n`

Compiler

Compiled 6 to 8 computations (-33.3% saved)

regimes91.0ms (1.2%)

Memory

-19.8MiB live, 32.6MiB allocated; 6ms collecting garbage

Counts

37 → 2

Calls

Call 1

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

Outputs

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

Calls

3 calls:

70.0ms	k
9.0ms	n
9.0ms	(.f64 (.f64 #s(literal 2 binary64) (PI.f64)) n)

Results

Accuracy	Segments	Branch
72.4%	2	`k`
72.1%	2	`(.f64 (.f64 #s(literal 2 binary64) (PI.f64)) n)`
72.1%	2	`n`

Compiler

Compiled 7 to 10 computations (-42.9% saved)

regimes32.0ms (0.4%)

Memory

27.8MiB live, 27.8MiB allocated; 0ms collecting garbage

Counts

31 → 2

Calls

Call 1

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

Outputs

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

Calls

4 calls:

8.0ms	k
8.0ms	(.f64 (.f64 #s(literal 2 binary64) (PI.f64)) n)
8.0ms	n
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
72.1%	2	`(.f64 (.f64 #s(literal 2 binary64) (PI.f64)) n)`
72.1%	2	`n`
72.0%	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))))`
63.3%	3	`k`

Compiler

Compiled 22 to 23 computations (-4.5% saved)

regimes36.0ms (0.5%)

Memory

-9.2MiB live, 36.7MiB allocated; 3ms collecting garbage

Counts

26 → 2

Calls

Call 1

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

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

Calls

4 calls:

15.0ms	(.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
60.2%	2	`k`
60.5%	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))))`
60.5%	2	`(.f64 (.f64 #s(literal 2 binary64) (PI.f64)) n)`
60.5%	2	`n`

Compiler

Compiled 22 to 23 computations (-4.5% saved)

regimes14.0ms (0.2%)

Memory

19.6MiB live, 19.6MiB allocated; 0ms collecting garbage

Counts

25 → 2

Calls

Call 1

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

Outputs

#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 (PI.f64) (PI.f64)) n)) (sqrt.f64 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 (PI.f64) (PI.f64)) (*.f64 n k))) n)))

Calls

2 calls:

6.0ms	(.f64 (.f64 #s(literal 2 binary64) (PI.f64)) n)
6.0ms	n

Results

Accuracy	Segments	Branch
60.5%	2	`(.f64 (.f64 #s(literal 2 binary64) (PI.f64)) n)`
60.5%	2	`n`

Compiler

Compiled 6 to 8 computations (-33.3% saved)

regimes29.0ms (0.4%)

Memory

-16.8MiB live, 28.3MiB allocated; 4ms collecting garbage

Counts

23 → 2

Calls

Call 1

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

Calls

3 calls:

16.0ms

6.0ms

(*.f64 (*.f64 #s(literal 2 binary64) (PI.f64)) n)

5.0ms

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

Results

Accuracy	Segments	Branch
60.1%	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))))`
60.2%	2	`(.f64 (.f64 #s(literal 2 binary64) (PI.f64)) n)`
60.2%	2	`n`

Compiler

Compiled 21 to 21 computations (0% saved)

regimes20.0ms (0.3%)

Memory

-12.6MiB live, 31.8MiB allocated; 4ms collecting garbage

Counts

13 → 1

Calls

Call 1

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

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

Calls

4 calls:

8.0ms	(.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))))
4.0ms	(.f64 (.f64 #s(literal 2 binary64) (PI.f64)) n)
4.0ms	n
4.0ms	k

Results

Accuracy	Segments	Branch
48.8%	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))))`
48.8%	1	`k`
48.8%	1	`(.f64 (.f64 #s(literal 2 binary64) (PI.f64)) n)`
48.8%	1	`n`

Compiler

Compiled 22 to 23 computations (-4.5% saved)

regimes9.0ms (0.1%)

Memory

17.1MiB live, 17.0MiB allocated; 0ms collecting garbage

Accuracy

Total -0.1b remaining (-0.2%)

Threshold costs -0.1b (-0.2%)

Counts

6 → 1

Calls

Call 1

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

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

Calls

4 calls:

2.0ms	(.f64 (.f64 #s(literal 2 binary64) (PI.f64)) n)
2.0ms	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
39.0%	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))))`
39.0%	1	`(.f64 (.f64 #s(literal 2 binary64) (PI.f64)) n)`
39.0%	1	`k`
39.0%	1	`n`

Compiler

Compiled 22 to 23 computations (-4.5% saved)

bsearch32.0ms (0.4%)

Memory

-25.5MiB live, 30.7MiB allocated; 18ms collecting garbage

Algorithm

2×	binary-search

Stop Event

1×	narrow-enough
1×	narrow-enough

Steps

Time	Left	Right
21.0ms	1.9457841877154848e+180	3.725795613329981e+182
9.0ms	8328423664.908538	17801540602.988052

Samples

22.0ms

192×

valid

Compiler

Compiled 810 to 727 computations (10.2% saved)

Precisions

Click to see histograms. Total time spent on operations: 8.0ms

ival-pow: 3.0ms (35.6% of total)

ival-sqrt: 2.0ms (23.7% of total)

ival-div!: 2.0ms (23.7% of total)

ival-mult!: 2.0ms (23.7% of total)

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

adjust: 0.0ms (0% of total)

bsearch2.0ms (0%)

Memory

5.2MiB live, 5.2MiB allocated; 0ms collecting garbage

Algorithm

2×	binary-search

Stop Event

1×	narrow-enough
1×	narrow-enough

Steps

Time	Left	Right
1.0ms	1.9457841877154848e+180	3.725795613329981e+182
1.0ms	8328423664.908538	17801540602.988052

Compiler

Compiled 798 to 739 computations (7.4% saved)

bsearch12.0ms (0.2%)

Memory

24.4MiB live, 24.4MiB allocated; 0ms collecting garbage

Algorithm

1×	binary-search

Stop Event

1×	narrow-enough

Steps

Time	Left	Right
10.0ms	5.8861398062767926e-5	0.0002368966863633644

Samples

7.0ms

96×

valid

Compiler

Compiled 325 to 312 computations (4% saved)

Precisions

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

ival-pow: 2.0ms (44.9% of total)

ival-sqrt: 1.0ms (22.5% of total)

ival-div!: 1.0ms (22.5% of total)

ival-mult!: 1.0ms (22.5% of total)

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

adjust: 0.0ms (0% of total)

bsearch20.0ms (0.3%)

Memory

-6.6MiB live, 39.6MiB allocated; 3ms collecting garbage

Algorithm

1×	binary-search

Stop Event

1×	narrow-enough

Steps

Time	Left	Right
18.0ms	2.8442696328925037e-27	2.97002709366971e-22

Samples

12.0ms

144×

valid

Compiler

Compiled 622 to 567 computations (8.8% saved)

Precisions

Click to see histograms. Total time spent on operations: 8.0ms

ival-pow: 4.0ms (47.6% of total)

ival-sqrt: 1.0ms (11.9% of total)

ival-div!: 1.0ms (11.9% of total)

ival-mult!: 1.0ms (11.9% of total)

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

adjust: 0.0ms (0% of total)

bsearch13.0ms (0.2%)

Memory

-22.7MiB live, 22.1MiB allocated; 6ms collecting garbage

Algorithm

1×	binary-search

Stop Event

1×	predicate-same

Steps

Time	Left	Right
12.0ms	2.4957966469852626e-15	1.9018303164958382e-14

Samples

9.0ms

80×

valid

Compiler

Compiled 314 to 293 computations (6.7% saved)

Precisions

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

ival-sqrt: 1.0ms (27.5% of total)

ival-div!: 1.0ms (27.5% of total)

ival-pow: 1.0ms (27.5% of total)

ival-mult!: 1.0ms (27.5% of total)

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

adjust: 0.0ms (0% of total)

bsearch14.0ms (0.2%)

Memory

31.1MiB live, 31.1MiB allocated; 0ms collecting garbage

Algorithm

1×	binary-search

Stop Event

1×	narrow-enough

Steps

Time	Left	Right
12.0ms	6.262099263329901e-53	1.8491101173156478e-51

Samples

8.0ms

112×

valid

Compiler

Compiled 418 to 389 computations (6.9% saved)

Precisions

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

ival-pow: 2.0ms (38.7% of total)

ival-sqrt: 1.0ms (19.3% of total)

ival-div!: 1.0ms (19.3% of total)

ival-mult!: 1.0ms (19.3% of total)

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

adjust: 0.0ms (0% of total)

bsearch1.0ms (0%)

Memory

3.2MiB live, 3.2MiB allocated; 0ms collecting garbage

Algorithm

1×	binary-search

Stop Event

1×	predicate-same

Steps

Time	Left	Right
1.0ms	2.8442696328925037e-27	2.97002709366971e-22

Compiler

Compiled 355 to 347 computations (2.3% saved)

derivations690.0ms (9.3%)

Memory

-9.2MiB live, 695.7MiB allocated; 138ms collecting garbage

Stop Event

1×

fuel

Compiler

Compiled 238 to 138 computations (42% saved)

preprocess569.0ms (7.7%)

Memory: -4.0MiB live, 369.2MiB allocated; 769ms collecting garbage
Remove: (abs k)
Compiler: Compiled 1 241 to 1 009 computations (18.7% saved)

end0.0ms (0%)

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

start0.0ms (0%)

analyze100.0ms (1.4%)

sample3.2s (43.1%)

preprocess68.0ms (0.9%)

series101.0ms (1.4%)

rewrite206.0ms (2.8%)

eval72.0ms (1%)

prune16.0ms (0.2%)

series229.0ms (3.1%)

rewrite233.0ms (3.1%)

eval131.0ms (1.8%)

prune57.0ms (0.8%)

series90.0ms (1.2%)

rewrite174.0ms (2.3%)

eval100.0ms (1.4%)

prune92.0ms (1.2%)

series100.0ms (1.3%)

rewrite195.0ms (2.6%)

eval65.0ms (0.9%)

prune51.0ms (0.7%)

regimes139.0ms (1.9%)

regimes118.0ms (1.6%)

regimes87.0ms (1.2%)

regimes64.0ms (0.9%)

regimes55.0ms (0.7%)

regimes48.0ms (0.6%)

regimes33.0ms (0.4%)

regimes91.0ms (1.2%)

regimes32.0ms (0.4%)

regimes36.0ms (0.5%)

regimes14.0ms (0.2%)

regimes29.0ms (0.4%)

regimes20.0ms (0.3%)

regimes9.0ms (0.1%)

bsearch32.0ms (0.4%)

bsearch2.0ms (0%)

bsearch12.0ms (0.2%)

bsearch20.0ms (0.3%)

bsearch13.0ms (0.2%)

bsearch14.0ms (0.2%)

bsearch1.0ms (0%)

derivations690.0ms (9.3%)

preprocess569.0ms (7.7%)

end0.0ms (0%)

Profiling