Metrics for Migdal et al, Equation (51)

start0.0ms (0%)

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

analyze114.0ms (2.4%)

Memory

-19.5MiB live, 170.4MiB allocated; 33ms 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 (66.5%)

Memory

-59.3MiB live, 4 208.5MiB allocated; 1.7s collecting garbage

Samples

1.2s	5 577×	1	invalid
722.0ms	8 256×	0	valid
95.0ms	442×	2	invalid
23.0ms	407×	0	invalid
20.0ms	216×	0	exit

Precisions

Click to see histograms. Total time spent on operations: 1.4s

ival-pow: 521.0ms (36.9% of total)

adjust: 257.0ms (18.2% of total)

ival-mult!: 237.0ms (16.8% of total)

ival-div!: 181.0ms (12.8% of total)

ival-sqrt: 155.0ms (11% of total)

ival-sub!: 63.0ms (4.5% of total)

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

exact: 0.0ms (0% of total)

Bogosity

preprocess41.0ms (0.9%)

Memory

-47.4MiB live, 47.5MiB allocated; 13ms collecting garbage

Iterations

Useful iterations: 2 (0.0ms)

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

Stop Event

1×	node-limit

Alt Table

Click to see full alt table

Status	Accuracy	Program
▶	99.5%	(.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) (pow.f64 (.f64 (*.f64 #s(literal 2 binary64) (PI.f64)) n) (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 2 binary64))))

Compiler

Compiled 30 to 26 computations (13.3% saved)

series79.0ms (1.6%)

Memory

-19.0MiB live, 122.0MiB allocated; 15ms collecting garbage

Counts

13 → 34

Calls

Call 1

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

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

Calls

6 calls:

Time	Variable		Point	Expression
30.0ms	n	@	0	((* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (/ 1 (sqrt k)) 1 (sqrt k) k (pow (* (* 2 (PI)) n) (/ (- 1 k) 2)) (* (* 2 (PI)) n) (* 2 (PI)) 2 (PI) n (/ (- 1 k) 2) (- 1 k))
29.0ms	n	@	-inf	((* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (/ 1 (sqrt k)) 1 (sqrt k) k (pow (* (* 2 (PI)) n) (/ (- 1 k) 2)) (* (* 2 (PI)) n) (* 2 (PI)) 2 (PI) n (/ (- 1 k) 2) (- 1 k))
8.0ms	n	@	inf	((* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (/ 1 (sqrt k)) 1 (sqrt k) k (pow (* (* 2 (PI)) n) (/ (- 1 k) 2)) (* (* 2 (PI)) n) (* 2 (PI)) 2 (PI) n (/ (- 1 k) 2) (- 1 k))
7.0ms	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))
3.0ms	k	@	-inf	((* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (/ 1 (sqrt k)) 1 (sqrt k) k (pow (* (* 2 (PI)) n) (/ (- 1 k) 2)) (* (* 2 (PI)) n) (* 2 (PI)) 2 (PI) n (/ (- 1 k) 2) (- 1 k))

rewrite61.0ms (1.3%)

Memory

3.4MiB live, 48.7MiB allocated; 4ms collecting garbage

Iterations

Useful iterations: 0 (0.0ms)

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

Stop Event

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

Counts

47 → 70

Calls

Call 1

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

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

eval6.0ms (0.1%)

Memory: 11.7MiB live, 11.7MiB allocated; 0ms collecting garbage
Compiler: Compiled 782 to 286 computations (63.4% saved)

prune19.0ms (0.4%)

Memory

-25.6MiB live, 21.3MiB allocated; 2ms collecting garbage

Pruning

14 alts after pruning (14 fresh and 0 done)

	Pruned	Kept	Total
New	44	14	58
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	45	14	59

Accuracy

99.9%

Counts

59 → 14

Alt Table

Click to see full alt table

Status	Accuracy	Program
▶	99.5%	(/.f64 (.f64 #s(literal 1 binary64) (pow.f64 (.f64 (+.f64 (PI.f64) (PI.f64)) n) (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 2 binary64)))) (sqrt.f64 k))
▶	99.5%	(.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) (pow.f64 (.f64 (*.f64 #s(literal 2 binary64) (PI.f64)) n) #s(approx (/ (- 1 k) 2) (fma.f64 #s(literal -1/2 binary64) k #s(literal 1/2 binary64)))))
	56.4%	(.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) (pow.f64 (.f64 (.f64 #s(literal 2 binary64) (PI.f64)) n) #s(approx (/ (- 1 k) 2) (.f64 #s(literal -1/2 binary64) k))))
▶	73.1%	(.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) (.f64 (pow.f64 (+.f64 (PI.f64) (PI.f64)) (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 2 binary64))) (pow.f64 n (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 2 binary64)))))
	99.4%	(.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) (.f64 (pow.f64 (.f64 (+.f64 (PI.f64) (PI.f64)) n) (/.f64 (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 2 binary64)) #s(literal 2 binary64))) (pow.f64 (.f64 (+.f64 (PI.f64) (PI.f64)) n) (/.f64 (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 2 binary64)) #s(literal 2 binary64)))))
	46.4%	(.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) #s(approx (pow ( (* 2 (PI)) n) (/ (- 1 k) 2)) (fma.f64 (.f64 (.f64 (.f64 (log.f64 (.f64 (+.f64 (PI.f64) (PI.f64)) n)) (sqrt.f64 #s(literal 2 binary64))) k) (sqrt.f64 (.f64 (PI.f64) n))) #s(literal -1/2 binary64) (sqrt.f64 (.f64 (+.f64 (PI.f64) (PI.f64)) n)))))
	56.6%	(.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) #s(approx (pow ( (* 2 (PI)) n) (/ (- 1 k) 2)) (fma.f64 k (fma.f64 (.f64 (.f64 (.f64 (.f64 (log.f64 (.f64 (+.f64 (PI.f64) (PI.f64)) n)) (log.f64 (.f64 (+.f64 (PI.f64) (PI.f64)) n))) (sqrt.f64 #s(literal 2 binary64))) k) (sqrt.f64 (.f64 (PI.f64) n))) #s(literal 1/8 binary64) (.f64 (.f64 #s(literal -1/2 binary64) (sqrt.f64 (.f64 (PI.f64) n))) (.f64 (log.f64 (.f64 (+.f64 (PI.f64) (PI.f64)) n)) (sqrt.f64 #s(literal 2 binary64))))) (sqrt.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n)))))
	45.7%	(.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) #s(approx (pow ( (* 2 (PI)) n) (/ (- 1 k) 2)) (sqrt.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n))))
▶	96.2%	(.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) #s(approx (pow ( (* 2 (PI)) n) (/ (- 1 k) 2)) (exp.f64 (.f64 (.f64 (+.f64 (neg.f64 (neg.f64 (log.f64 n))) (log.f64 (+.f64 (PI.f64) (PI.f64)))) (-.f64 #s(literal 1 binary64) k)) #s(literal 1/2 binary64)))))
	96.5%	(.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) #s(approx (pow ( (* 2 (PI)) n) (/ (- 1 k) 2)) (exp.f64 (.f64 (.f64 (log.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n)) (-.f64 #s(literal 1 binary64) k)) #s(literal 1/2 binary64)))))
	99.5%	(.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) k)) (pow.f64 (.f64 (*.f64 #s(literal 2 binary64) (PI.f64)) n) (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 2 binary64))))
	54.0%	#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (/.f64 (fma.f64 (.f64 (.f64 (log.f64 (.f64 (+.f64 (PI.f64) (PI.f64)) n)) (sqrt.f64 #s(literal 2 binary64))) (sqrt.f64 (.f64 (.f64 (.f64 k k) k) (.f64 (PI.f64) n)))) #s(literal -1/2 binary64) (sqrt.f64 (.f64 (.f64 (.f64 (PI.f64) n) k) #s(literal 2 binary64)))) k))
	54.4%	#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (/.f64 (fma.f64 k (fma.f64 (.f64 (.f64 (.f64 (log.f64 (.f64 (+.f64 (PI.f64) (PI.f64)) n)) (log.f64 (.f64 (+.f64 (PI.f64) (PI.f64)) n))) (sqrt.f64 #s(literal 2 binary64))) (sqrt.f64 (.f64 (.f64 (.f64 k k) k) (.f64 (PI.f64) n)))) #s(literal 1/8 binary64) (.f64 (.f64 (sqrt.f64 (.f64 (.f64 (PI.f64) n) k)) (.f64 (log.f64 (.f64 (+.f64 (PI.f64) (PI.f64)) n)) (sqrt.f64 #s(literal 2 binary64)))) #s(literal -1/2 binary64))) (sqrt.f64 (.f64 (.f64 (.f64 (PI.f64) n) k) #s(literal 2 binary64)))) k))
▶	34.8%	#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt.f64 (.f64 (/.f64 (.f64 (PI.f64) n) k) #s(literal 2 binary64))))

Compiler

Compiled 770 to 638 computations (17.1% saved)

series151.0ms (3.1%)

Memory

19.8MiB live, 298.4MiB allocated; 39ms collecting garbage

Counts

41 → 139

Calls

Call 1

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

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

6 calls:

Time	Variable		Point	Expression
55.0ms	n	@	-inf	((/ (* 1 (pow (* (+ (PI) (PI)) n) (/ (- 1 k) 2))) (sqrt k)) (* 1 (pow (* (+ (PI) (PI)) n) (/ (- 1 k) 2))) 1 (pow (* (+ (PI) (PI)) n) (/ (- 1 k) 2)) (* (+ (PI) (PI)) n) (+ (PI) (PI)) (PI) n (/ (- 1 k) 2) (- 1 k) k 2 (sqrt k) (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt (* (/ (* (PI) n) k) 2)) (* (/ (* (PI) n) k) 2) (/ (* (PI) n) k) (* (PI) n) (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2)) (* (* 2 (PI)) n) (* 2 (PI)) (/ (- 1 k) 2) (+ (* -1/2 k) 1/2) -1/2 1/2 (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2)) (exp (* (* (+ (neg (neg (log n))) (log (+ (PI) (PI)))) (- 1 k)) 1/2)) (* (* (+ (neg (neg (log n))) (log (+ (PI) (PI)))) (- 1 k)) 1/2) (* (+ (neg (neg (log n))) (log (+ (PI) (PI)))) (- 1 k)) (+ (neg (neg (log n))) (log (+ (PI) (PI)))) (neg (neg (log n))) (neg (log n)) (log n) (log (+ (PI) (PI))) (* (/ 1 (sqrt k)) (* (pow (+ (PI) (PI)) (/ (- 1 k) 2)) (pow n (/ (- 1 k) 2)))) (* (pow (+ (PI) (PI)) (/ (- 1 k) 2)) (pow n (/ (- 1 k) 2))) (pow (+ (PI) (PI)) (/ (- 1 k) 2)) (pow n (/ (- 1 k) 2)))
36.0ms	n	@	0	((/ (* 1 (pow (* (+ (PI) (PI)) n) (/ (- 1 k) 2))) (sqrt k)) (* 1 (pow (* (+ (PI) (PI)) n) (/ (- 1 k) 2))) 1 (pow (* (+ (PI) (PI)) n) (/ (- 1 k) 2)) (* (+ (PI) (PI)) n) (+ (PI) (PI)) (PI) n (/ (- 1 k) 2) (- 1 k) k 2 (sqrt k) (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt (* (/ (* (PI) n) k) 2)) (* (/ (* (PI) n) k) 2) (/ (* (PI) n) k) (* (PI) n) (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2)) (* (* 2 (PI)) n) (* 2 (PI)) (/ (- 1 k) 2) (+ (* -1/2 k) 1/2) -1/2 1/2 (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2)) (exp (* (* (+ (neg (neg (log n))) (log (+ (PI) (PI)))) (- 1 k)) 1/2)) (* (* (+ (neg (neg (log n))) (log (+ (PI) (PI)))) (- 1 k)) 1/2) (* (+ (neg (neg (log n))) (log (+ (PI) (PI)))) (- 1 k)) (+ (neg (neg (log n))) (log (+ (PI) (PI)))) (neg (neg (log n))) (neg (log n)) (log n) (log (+ (PI) (PI))) (* (/ 1 (sqrt k)) (* (pow (+ (PI) (PI)) (/ (- 1 k) 2)) (pow n (/ (- 1 k) 2)))) (* (pow (+ (PI) (PI)) (/ (- 1 k) 2)) (pow n (/ (- 1 k) 2))) (pow (+ (PI) (PI)) (/ (- 1 k) 2)) (pow n (/ (- 1 k) 2)))
27.0ms	n	@	inf	((/ (* 1 (pow (* (+ (PI) (PI)) n) (/ (- 1 k) 2))) (sqrt k)) (* 1 (pow (* (+ (PI) (PI)) n) (/ (- 1 k) 2))) 1 (pow (* (+ (PI) (PI)) n) (/ (- 1 k) 2)) (* (+ (PI) (PI)) n) (+ (PI) (PI)) (PI) n (/ (- 1 k) 2) (- 1 k) k 2 (sqrt k) (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt (* (/ (* (PI) n) k) 2)) (* (/ (* (PI) n) k) 2) (/ (* (PI) n) k) (* (PI) n) (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2)) (* (* 2 (PI)) n) (* 2 (PI)) (/ (- 1 k) 2) (+ (* -1/2 k) 1/2) -1/2 1/2 (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2)) (exp (* (* (+ (neg (neg (log n))) (log (+ (PI) (PI)))) (- 1 k)) 1/2)) (* (* (+ (neg (neg (log n))) (log (+ (PI) (PI)))) (- 1 k)) 1/2) (* (+ (neg (neg (log n))) (log (+ (PI) (PI)))) (- 1 k)) (+ (neg (neg (log n))) (log (+ (PI) (PI)))) (neg (neg (log n))) (neg (log n)) (log n) (log (+ (PI) (PI))) (* (/ 1 (sqrt k)) (* (pow (+ (PI) (PI)) (/ (- 1 k) 2)) (pow n (/ (- 1 k) 2)))) (* (pow (+ (PI) (PI)) (/ (- 1 k) 2)) (pow n (/ (- 1 k) 2))) (pow (+ (PI) (PI)) (/ (- 1 k) 2)) (pow n (/ (- 1 k) 2)))
11.0ms	k	@	0	((/ (* 1 (pow (* (+ (PI) (PI)) n) (/ (- 1 k) 2))) (sqrt k)) (* 1 (pow (* (+ (PI) (PI)) n) (/ (- 1 k) 2))) 1 (pow (* (+ (PI) (PI)) n) (/ (- 1 k) 2)) (* (+ (PI) (PI)) n) (+ (PI) (PI)) (PI) n (/ (- 1 k) 2) (- 1 k) k 2 (sqrt k) (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt (* (/ (* (PI) n) k) 2)) (* (/ (* (PI) n) k) 2) (/ (* (PI) n) k) (* (PI) n) (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2)) (* (* 2 (PI)) n) (* 2 (PI)) (/ (- 1 k) 2) (+ (* -1/2 k) 1/2) -1/2 1/2 (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2)) (exp (* (* (+ (neg (neg (log n))) (log (+ (PI) (PI)))) (- 1 k)) 1/2)) (* (* (+ (neg (neg (log n))) (log (+ (PI) (PI)))) (- 1 k)) 1/2) (* (+ (neg (neg (log n))) (log (+ (PI) (PI)))) (- 1 k)) (+ (neg (neg (log n))) (log (+ (PI) (PI)))) (neg (neg (log n))) (neg (log n)) (log n) (log (+ (PI) (PI))) (* (/ 1 (sqrt k)) (* (pow (+ (PI) (PI)) (/ (- 1 k) 2)) (pow n (/ (- 1 k) 2)))) (* (pow (+ (PI) (PI)) (/ (- 1 k) 2)) (pow n (/ (- 1 k) 2))) (pow (+ (PI) (PI)) (/ (- 1 k) 2)) (pow n (/ (- 1 k) 2)))
8.0ms	k	@	-inf	((/ (* 1 (pow (* (+ (PI) (PI)) n) (/ (- 1 k) 2))) (sqrt k)) (* 1 (pow (* (+ (PI) (PI)) n) (/ (- 1 k) 2))) 1 (pow (* (+ (PI) (PI)) n) (/ (- 1 k) 2)) (* (+ (PI) (PI)) n) (+ (PI) (PI)) (PI) n (/ (- 1 k) 2) (- 1 k) k 2 (sqrt k) (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt (* (/ (* (PI) n) k) 2)) (* (/ (* (PI) n) k) 2) (/ (* (PI) n) k) (* (PI) n) (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2)) (* (* 2 (PI)) n) (* 2 (PI)) (/ (- 1 k) 2) (+ (* -1/2 k) 1/2) -1/2 1/2 (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2)) (exp (* (* (+ (neg (neg (log n))) (log (+ (PI) (PI)))) (- 1 k)) 1/2)) (* (* (+ (neg (neg (log n))) (log (+ (PI) (PI)))) (- 1 k)) 1/2) (* (+ (neg (neg (log n))) (log (+ (PI) (PI)))) (- 1 k)) (+ (neg (neg (log n))) (log (+ (PI) (PI)))) (neg (neg (log n))) (neg (log n)) (log n) (log (+ (PI) (PI))) (* (/ 1 (sqrt k)) (* (pow (+ (PI) (PI)) (/ (- 1 k) 2)) (pow n (/ (- 1 k) 2)))) (* (pow (+ (PI) (PI)) (/ (- 1 k) 2)) (pow n (/ (- 1 k) 2))) (pow (+ (PI) (PI)) (/ (- 1 k) 2)) (pow n (/ (- 1 k) 2)))

rewrite98.0ms (2%)

Memory

30.6MiB live, 122.6MiB allocated; 7ms collecting garbage

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	546	5142
0	608	4625
0	2698	4534

Stop Event

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

Counts

180 → 301

Calls

Call 1

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

eval43.0ms (0.9%)

Memory: -35.8MiB live, 63.8MiB allocated; 24ms collecting garbage
Compiler: Compiled 4 047 to 1 229 computations (69.6% saved)

prune23.0ms (0.5%)

Memory

5.1MiB live, 52.2MiB allocated; 1ms collecting garbage

Pruning

27 alts after pruning (27 fresh and 0 done)

	Pruned	Kept	Total
New	224	24	248
Fresh	6	3	9
Picked	5	0	5
Done	0	0	0
Total	235	27	262

Accuracy

99.9%

Counts

262 → 27

Alt Table

Click to see full alt table

Status	Accuracy	Program
▶	99.5%	(/.f64 (pow.f64 (*.f64 n (+.f64 (PI.f64) (PI.f64))) (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 2 binary64))) (sqrt.f64 k))
	73.1%	(/.f64 (*.f64 (pow.f64 (+.f64 (PI.f64) (PI.f64)) (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 2 binary64))) (pow.f64 n (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 2 binary64)))) (sqrt.f64 k))
	99.4%	(/.f64 (.f64 (pow.f64 (.f64 n (+.f64 (PI.f64) (PI.f64))) (/.f64 (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 2 binary64)) #s(literal 2 binary64))) (pow.f64 (*.f64 n (+.f64 (PI.f64) (PI.f64))) (/.f64 (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 2 binary64)) #s(literal 2 binary64)))) (sqrt.f64 k))
▶	56.4%	(/.f64 (.f64 #s(literal 1 binary64) (pow.f64 (.f64 (+.f64 (PI.f64) (PI.f64)) n) #s(approx (/ (- 1 k) 2) (*.f64 #s(literal -1/2 binary64) k)))) (sqrt.f64 k))
	96.5%	(/.f64 (exp.f64 (.f64 (log.f64 (.f64 n (+.f64 (PI.f64) (PI.f64)))) (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 2 binary64)))) (sqrt.f64 k))
	46.4%	(/.f64 #s(approx (* (pow (+ (PI) (PI)) (/ (- 1 k) 2)) (pow n (/ (- 1 k) 2))) (fma.f64 (.f64 (.f64 (.f64 (log.f64 (.f64 n (+.f64 (PI.f64) (PI.f64)))) (sqrt.f64 #s(literal 2 binary64))) k) (sqrt.f64 (.f64 (PI.f64) n))) #s(literal -1/2 binary64) (sqrt.f64 (.f64 n (+.f64 (PI.f64) (PI.f64)))))) (sqrt.f64 k))
	45.8%	(/.f64 #s(approx (* (pow (+ (PI) (PI)) (/ (- 1 k) 2)) (pow n (/ (- 1 k) 2))) (sqrt.f64 (*.f64 n (+.f64 (PI.f64) (PI.f64))))) (sqrt.f64 k))
	99.5%	(.f64 (pow.f64 (.f64 n (+.f64 (PI.f64) (PI.f64))) #s(approx (/ (- 1 k) 2) (fma.f64 #s(literal -1/2 binary64) k #s(literal 1/2 binary64)))) (/.f64 #s(literal 1 binary64) (sqrt.f64 k)))
	54.3%	(.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) (.f64 (pow.f64 (+.f64 (PI.f64) (PI.f64)) (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 2 binary64))) #s(approx (pow n (/ (- 1 k) 2)) (fma.f64 (fma.f64 (.f64 #s(literal -1/2 binary64) (sqrt.f64 n)) (log.f64 n) (.f64 (.f64 (.f64 (*.f64 (log.f64 n) (log.f64 n)) k) (sqrt.f64 n)) #s(literal 1/8 binary64))) k (sqrt.f64 n)))))
	71.4%	(.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) (.f64 (pow.f64 (+.f64 (PI.f64) (PI.f64)) (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 2 binary64))) #s(approx (pow n (/ (- 1 k) 2)) (sqrt.f64 n))))
	70.4%	(.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) (.f64 (pow.f64 (+.f64 (PI.f64) (PI.f64)) (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 2 binary64))) #s(approx (pow n (/ (- 1 k) 2)) (exp.f64 (.f64 (.f64 #s(literal 1/2 binary64) (log.f64 n)) (-.f64 #s(literal 1 binary64) k))))))
	99.4%	(.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) (.f64 (pow.f64 (.f64 n (+.f64 (PI.f64) (PI.f64))) (/.f64 #s(approx (/ (- 1 k) 2) (fma.f64 #s(literal -1/2 binary64) k #s(literal 1/2 binary64))) #s(literal 2 binary64))) (pow.f64 (.f64 n (+.f64 (PI.f64) (PI.f64))) (/.f64 #s(approx (/ (- 1 k) 2) (fma.f64 #s(literal -1/2 binary64) k #s(literal 1/2 binary64))) #s(literal 2 binary64)))))
	72.1%	(.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) (.f64 #s(approx (pow (+ (PI) (PI)) (/ (- 1 k) 2)) (fma.f64 (.f64 (.f64 (*.f64 (log.f64 (+.f64 (PI.f64) (PI.f64))) (sqrt.f64 #s(literal 2 binary64))) k) (sqrt.f64 (PI.f64))) #s(literal -1/2 binary64) (sqrt.f64 (+.f64 (PI.f64) (PI.f64))))) (pow.f64 n (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 2 binary64)))))
	55.5%	(.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) (.f64 #s(approx (pow (+ (PI) (PI)) (/ (- 1 k) 2)) (fma.f64 k (fma.f64 k (fma.f64 (.f64 (.f64 (.f64 (pow.f64 (log.f64 (+.f64 (PI.f64) (PI.f64))) #s(literal 3 binary64)) (sqrt.f64 #s(literal 2 binary64))) k) (sqrt.f64 (PI.f64))) #s(literal -1/48 binary64) (.f64 (.f64 (.f64 (sqrt.f64 (PI.f64)) (.f64 (log.f64 (+.f64 (PI.f64) (PI.f64))) (log.f64 (+.f64 (PI.f64) (PI.f64))))) (sqrt.f64 #s(literal 2 binary64))) #s(literal 1/8 binary64))) (.f64 (.f64 (sqrt.f64 (PI.f64)) (.f64 (log.f64 (+.f64 (PI.f64) (PI.f64))) (sqrt.f64 #s(literal 2 binary64)))) #s(literal -1/2 binary64))) (sqrt.f64 (+.f64 (PI.f64) (PI.f64))))) (pow.f64 n (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 2 binary64)))))
▶	73.1%	(.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) (.f64 #s(approx (pow (+ (PI) (PI)) (/ (- 1 k) 2)) (exp.f64 (.f64 (.f64 (log.f64 (+.f64 (PI.f64) (PI.f64))) (-.f64 #s(literal 1 binary64) k)) #s(literal 1/2 binary64)))) (pow.f64 n (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 2 binary64)))))
	56.6%	(.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) #s(approx (pow ( (* 2 (PI)) n) (/ (- 1 k) 2)) (fma.f64 k (fma.f64 (.f64 (.f64 (.f64 (.f64 (log.f64 (.f64 (+.f64 (PI.f64) (PI.f64)) n)) (log.f64 (.f64 (+.f64 (PI.f64) (PI.f64)) n))) (sqrt.f64 #s(literal 2 binary64))) k) (sqrt.f64 (.f64 (PI.f64) n))) #s(literal 1/8 binary64) (.f64 (.f64 #s(literal -1/2 binary64) (sqrt.f64 (.f64 (PI.f64) n))) (.f64 (log.f64 (.f64 (+.f64 (PI.f64) (PI.f64)) n)) (sqrt.f64 #s(literal 2 binary64))))) (sqrt.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n)))))
	45.7%	(.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) #s(approx (pow ( (* 2 (PI)) n) (/ (- 1 k) 2)) (sqrt.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n))))
▶	96.2%	(.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) #s(approx (pow ( (* 2 (PI)) n) (/ (- 1 k) 2)) (exp.f64 (.f64 (.f64 (+.f64 (log.f64 (+.f64 (PI.f64) (PI.f64))) (log.f64 n)) (-.f64 #s(literal 1 binary64) k)) #s(literal 1/2 binary64)))))
	42.8%	(.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) #s(approx (pow ( (* 2 (PI)) n) (/ (- 1 k) 2)) (exp.f64 (.f64 #s(approx ( (+ (neg (neg (log n))) (log (+ (PI) (PI)))) (- 1 k)) (log.f64 (*.f64 n (+.f64 (PI.f64) (PI.f64))))) #s(literal 1/2 binary64)))))
	73.0%	(.f64 (.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) (pow.f64 (+.f64 (PI.f64) (PI.f64)) (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 2 binary64)))) (pow.f64 n (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 2 binary64))))
	99.5%	(.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) k)) (pow.f64 (.f64 (*.f64 #s(literal 2 binary64) (PI.f64)) n) #s(approx (/ (- 1 k) 2) (fma.f64 #s(literal -1/2 binary64) k #s(literal 1/2 binary64)))))
	96.2%	(.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) k)) #s(approx (pow ( (* 2 (PI)) n) (/ (- 1 k) 2)) (exp.f64 (.f64 (.f64 (+.f64 (neg.f64 (neg.f64 (log.f64 n))) (log.f64 (+.f64 (PI.f64) (PI.f64)))) (-.f64 #s(literal 1 binary64) k)) #s(literal 1/2 binary64)))))
	54.0%	#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (/.f64 (fma.f64 (.f64 (.f64 (log.f64 (.f64 (+.f64 (PI.f64) (PI.f64)) n)) (sqrt.f64 #s(literal 2 binary64))) (sqrt.f64 (.f64 (.f64 (.f64 k k) k) (.f64 (PI.f64) n)))) #s(literal -1/2 binary64) (sqrt.f64 (.f64 (.f64 (.f64 (PI.f64) n) k) #s(literal 2 binary64)))) k))
	34.7%	#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (.f64 (sqrt.f64 (/.f64 (.f64 (PI.f64) n) k)) (sqrt.f64 #s(literal 2 binary64))))
▶	34.8%	#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt.f64 (/.f64 (*.f64 n (+.f64 (PI.f64) (PI.f64))) k)))
	34.8%	#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt.f64 (.f64 (.f64 (PI.f64) (/.f64 n k)) #s(literal 2 binary64))))
	34.8%	#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt.f64 (.f64 (.f64 n (/.f64 (PI.f64) k)) #s(literal 2 binary64))))

Compiler

Compiled 1 452 to 1 220 computations (16% saved)

series96.0ms (2%)

Memory

17.8MiB live, 207.8MiB allocated; 10ms collecting garbage

Counts

39 → 161

Calls

Call 1

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

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

Calls

6 calls:

Time	Variable		Point	Expression
25.0ms	n	@	inf	((/ (pow (* n (+ (PI) (PI))) (/ (- 1 k) 2)) (sqrt k)) (pow (* n (+ (PI) (PI))) (/ (- 1 k) 2)) (* n (+ (PI) (PI))) n (+ (PI) (PI)) (PI) (/ (- 1 k) 2) (- 1 k) 1 k 2 (sqrt k) (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt (/ (* n (+ (PI) (PI))) k)) (/ (* n (+ (PI) (PI))) k) (/ (* 1 (pow (* (+ (PI) (PI)) n) (/ (- 1 k) 2))) (sqrt k)) (* 1 (pow (* (+ (PI) (PI)) n) (/ (- 1 k) 2))) (pow (* (+ (PI) (PI)) n) (/ (- 1 k) 2)) (* (+ (PI) (PI)) n) (/ (- 1 k) 2) (* -1/2 k) -1/2 (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2)) (exp (* (* (+ (log (+ (PI) (PI))) (log n)) (- 1 k)) 1/2)) (* (* (+ (log (+ (PI) (PI))) (log n)) (- 1 k)) 1/2) (* (+ (log (+ (PI) (PI))) (log n)) (- 1 k)) (+ (log (+ (PI) (PI))) (log n)) (log (+ (PI) (PI))) (log n) 1/2 (* (/ 1 (sqrt k)) (* (pow (+ (PI) (PI)) (/ (- 1 k) 2)) (pow n (/ (- 1 k) 2)))) (* (pow (+ (PI) (PI)) (/ (- 1 k) 2)) (pow n (/ (- 1 k) 2))) (pow (+ (PI) (PI)) (/ (- 1 k) 2)) (exp (* (* (log (+ (PI) (PI))) (- 1 k)) 1/2)) (* (* (log (+ (PI) (PI))) (- 1 k)) 1/2) (* (log (+ (PI) (PI))) (- 1 k)) (pow n (/ (- 1 k) 2)))
24.0ms	n	@	-inf	((/ (pow (* n (+ (PI) (PI))) (/ (- 1 k) 2)) (sqrt k)) (pow (* n (+ (PI) (PI))) (/ (- 1 k) 2)) (* n (+ (PI) (PI))) n (+ (PI) (PI)) (PI) (/ (- 1 k) 2) (- 1 k) 1 k 2 (sqrt k) (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt (/ (* n (+ (PI) (PI))) k)) (/ (* n (+ (PI) (PI))) k) (/ (* 1 (pow (* (+ (PI) (PI)) n) (/ (- 1 k) 2))) (sqrt k)) (* 1 (pow (* (+ (PI) (PI)) n) (/ (- 1 k) 2))) (pow (* (+ (PI) (PI)) n) (/ (- 1 k) 2)) (* (+ (PI) (PI)) n) (/ (- 1 k) 2) (* -1/2 k) -1/2 (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2)) (exp (* (* (+ (log (+ (PI) (PI))) (log n)) (- 1 k)) 1/2)) (* (* (+ (log (+ (PI) (PI))) (log n)) (- 1 k)) 1/2) (* (+ (log (+ (PI) (PI))) (log n)) (- 1 k)) (+ (log (+ (PI) (PI))) (log n)) (log (+ (PI) (PI))) (log n) 1/2 (* (/ 1 (sqrt k)) (* (pow (+ (PI) (PI)) (/ (- 1 k) 2)) (pow n (/ (- 1 k) 2)))) (* (pow (+ (PI) (PI)) (/ (- 1 k) 2)) (pow n (/ (- 1 k) 2))) (pow (+ (PI) (PI)) (/ (- 1 k) 2)) (exp (* (* (log (+ (PI) (PI))) (- 1 k)) 1/2)) (* (* (log (+ (PI) (PI))) (- 1 k)) 1/2) (* (log (+ (PI) (PI))) (- 1 k)) (pow n (/ (- 1 k) 2)))
23.0ms	n	@	0	((/ (pow (* n (+ (PI) (PI))) (/ (- 1 k) 2)) (sqrt k)) (pow (* n (+ (PI) (PI))) (/ (- 1 k) 2)) (* n (+ (PI) (PI))) n (+ (PI) (PI)) (PI) (/ (- 1 k) 2) (- 1 k) 1 k 2 (sqrt k) (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt (/ (* n (+ (PI) (PI))) k)) (/ (* n (+ (PI) (PI))) k) (/ (* 1 (pow (* (+ (PI) (PI)) n) (/ (- 1 k) 2))) (sqrt k)) (* 1 (pow (* (+ (PI) (PI)) n) (/ (- 1 k) 2))) (pow (* (+ (PI) (PI)) n) (/ (- 1 k) 2)) (* (+ (PI) (PI)) n) (/ (- 1 k) 2) (* -1/2 k) -1/2 (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2)) (exp (* (* (+ (log (+ (PI) (PI))) (log n)) (- 1 k)) 1/2)) (* (* (+ (log (+ (PI) (PI))) (log n)) (- 1 k)) 1/2) (* (+ (log (+ (PI) (PI))) (log n)) (- 1 k)) (+ (log (+ (PI) (PI))) (log n)) (log (+ (PI) (PI))) (log n) 1/2 (* (/ 1 (sqrt k)) (* (pow (+ (PI) (PI)) (/ (- 1 k) 2)) (pow n (/ (- 1 k) 2)))) (* (pow (+ (PI) (PI)) (/ (- 1 k) 2)) (pow n (/ (- 1 k) 2))) (pow (+ (PI) (PI)) (/ (- 1 k) 2)) (exp (* (* (log (+ (PI) (PI))) (- 1 k)) 1/2)) (* (* (log (+ (PI) (PI))) (- 1 k)) 1/2) (* (log (+ (PI) (PI))) (- 1 k)) (pow n (/ (- 1 k) 2)))
8.0ms	k	@	-inf	((/ (pow (* n (+ (PI) (PI))) (/ (- 1 k) 2)) (sqrt k)) (pow (* n (+ (PI) (PI))) (/ (- 1 k) 2)) (* n (+ (PI) (PI))) n (+ (PI) (PI)) (PI) (/ (- 1 k) 2) (- 1 k) 1 k 2 (sqrt k) (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt (/ (* n (+ (PI) (PI))) k)) (/ (* n (+ (PI) (PI))) k) (/ (* 1 (pow (* (+ (PI) (PI)) n) (/ (- 1 k) 2))) (sqrt k)) (* 1 (pow (* (+ (PI) (PI)) n) (/ (- 1 k) 2))) (pow (* (+ (PI) (PI)) n) (/ (- 1 k) 2)) (* (+ (PI) (PI)) n) (/ (- 1 k) 2) (* -1/2 k) -1/2 (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2)) (exp (* (* (+ (log (+ (PI) (PI))) (log n)) (- 1 k)) 1/2)) (* (* (+ (log (+ (PI) (PI))) (log n)) (- 1 k)) 1/2) (* (+ (log (+ (PI) (PI))) (log n)) (- 1 k)) (+ (log (+ (PI) (PI))) (log n)) (log (+ (PI) (PI))) (log n) 1/2 (* (/ 1 (sqrt k)) (* (pow (+ (PI) (PI)) (/ (- 1 k) 2)) (pow n (/ (- 1 k) 2)))) (* (pow (+ (PI) (PI)) (/ (- 1 k) 2)) (pow n (/ (- 1 k) 2))) (pow (+ (PI) (PI)) (/ (- 1 k) 2)) (exp (* (* (log (+ (PI) (PI))) (- 1 k)) 1/2)) (* (* (log (+ (PI) (PI))) (- 1 k)) 1/2) (* (log (+ (PI) (PI))) (- 1 k)) (pow n (/ (- 1 k) 2)))
6.0ms	k	@	0	((/ (pow (* n (+ (PI) (PI))) (/ (- 1 k) 2)) (sqrt k)) (pow (* n (+ (PI) (PI))) (/ (- 1 k) 2)) (* n (+ (PI) (PI))) n (+ (PI) (PI)) (PI) (/ (- 1 k) 2) (- 1 k) 1 k 2 (sqrt k) (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt (/ (* n (+ (PI) (PI))) k)) (/ (* n (+ (PI) (PI))) k) (/ (* 1 (pow (* (+ (PI) (PI)) n) (/ (- 1 k) 2))) (sqrt k)) (* 1 (pow (* (+ (PI) (PI)) n) (/ (- 1 k) 2))) (pow (* (+ (PI) (PI)) n) (/ (- 1 k) 2)) (* (+ (PI) (PI)) n) (/ (- 1 k) 2) (* -1/2 k) -1/2 (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2)) (exp (* (* (+ (log (+ (PI) (PI))) (log n)) (- 1 k)) 1/2)) (* (* (+ (log (+ (PI) (PI))) (log n)) (- 1 k)) 1/2) (* (+ (log (+ (PI) (PI))) (log n)) (- 1 k)) (+ (log (+ (PI) (PI))) (log n)) (log (+ (PI) (PI))) (log n) 1/2 (* (/ 1 (sqrt k)) (* (pow (+ (PI) (PI)) (/ (- 1 k) 2)) (pow n (/ (- 1 k) 2)))) (* (pow (+ (PI) (PI)) (/ (- 1 k) 2)) (pow n (/ (- 1 k) 2))) (pow (+ (PI) (PI)) (/ (- 1 k) 2)) (exp (* (* (log (+ (PI) (PI))) (- 1 k)) 1/2)) (* (* (log (+ (PI) (PI))) (- 1 k)) 1/2) (* (log (+ (PI) (PI))) (- 1 k)) (pow n (/ (- 1 k) 2)))

rewrite108.0ms (2.2%)

Memory

-23.4MiB live, 165.6MiB allocated; 8ms collecting garbage

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	586	6173
0	643	5760
0	2852	5646

Stop Event

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

Counts

200 → 292

Calls

Call 1

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

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

eval29.0ms (0.6%)

Memory: 16.9MiB live, 62.4MiB allocated; 3ms collecting garbage
Compiler: Compiled 4 464 to 1 258 computations (71.8% saved)

prune24.0ms (0.5%)

Memory

5.3MiB live, 52.0MiB allocated; 2ms collecting garbage

Pruning

27 alts after pruning (26 fresh and 1 done)

	Pruned	Kept	Total
New	249	11	260
Fresh	7	15	22
Picked	4	1	5
Done	0	0	0
Total	260	27	287

Accuracy

99.9%

Counts

287 → 27

Alt Table

Click to see full alt table

Status	Accuracy	Program
	56.4%	(/.f64 (pow.f64 (.f64 (+.f64 (PI.f64) (PI.f64)) n) #s(approx (/ (- 1 k) 2) (.f64 #s(literal -1/2 binary64) k))) (sqrt.f64 k))
▶	99.5%	(/.f64 (pow.f64 (*.f64 n (+.f64 (PI.f64) (PI.f64))) #s(approx (/ (- 1 k) 2) (fma.f64 #s(literal -1/2 binary64) k #s(literal 1/2 binary64)))) (sqrt.f64 k))
	73.1%	(/.f64 (*.f64 (pow.f64 (+.f64 (PI.f64) (PI.f64)) (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 2 binary64))) (pow.f64 n (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 2 binary64)))) (sqrt.f64 k))
	99.4%	(/.f64 (.f64 (pow.f64 (.f64 (+.f64 (PI.f64) (PI.f64)) n) (/.f64 (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 2 binary64)) #s(literal 2 binary64))) (pow.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n) (/.f64 (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 2 binary64)) #s(literal 2 binary64)))) (sqrt.f64 k))
	96.5%	(/.f64 (exp.f64 (.f64 (log.f64 (.f64 (+.f64 (PI.f64) (PI.f64)) n)) (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 2 binary64)))) (sqrt.f64 k))
▶	46.4%	(/.f64 #s(approx (* (pow (+ (PI) (PI)) (/ (- 1 k) 2)) (pow n (/ (- 1 k) 2))) (fma.f64 (.f64 (.f64 (.f64 (log.f64 (.f64 (+.f64 (PI.f64) (PI.f64)) n)) (sqrt.f64 #s(literal 2 binary64))) k) (sqrt.f64 (.f64 (PI.f64) n))) #s(literal -1/2 binary64) (sqrt.f64 (.f64 (+.f64 (PI.f64) (PI.f64)) n)))) (sqrt.f64 k))
	45.8%	(/.f64 #s(approx (* (pow (+ (PI) (PI)) (/ (- 1 k) 2)) (pow n (/ (- 1 k) 2))) (sqrt.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n))) (sqrt.f64 k))
	96.2%	(/.f64 #s(approx (* (pow (+ (PI) (PI)) (/ (- 1 k) 2)) (pow n (/ (- 1 k) 2))) (exp.f64 (.f64 (.f64 (+.f64 (neg.f64 (neg.f64 (log.f64 n))) (log.f64 (+.f64 (PI.f64) (PI.f64)))) (-.f64 #s(literal 1 binary64) k)) #s(literal 1/2 binary64)))) (sqrt.f64 k))
▶	99.5%	(.f64 (pow.f64 (.f64 n (+.f64 (PI.f64) (PI.f64))) #s(approx (/ (- 1 k) 2) (fma.f64 #s(literal -1/2 binary64) k #s(literal 1/2 binary64)))) (/.f64 #s(literal 1 binary64) (sqrt.f64 k)))
	54.3%	(.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) (.f64 (pow.f64 (+.f64 (PI.f64) (PI.f64)) (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 2 binary64))) #s(approx (pow n (/ (- 1 k) 2)) (fma.f64 (fma.f64 (.f64 #s(literal -1/2 binary64) (sqrt.f64 n)) (log.f64 n) (.f64 (.f64 (.f64 (*.f64 (log.f64 n) (log.f64 n)) k) (sqrt.f64 n)) #s(literal 1/8 binary64))) k (sqrt.f64 n)))))
	71.4%	(.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) (.f64 (pow.f64 (+.f64 (PI.f64) (PI.f64)) (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 2 binary64))) #s(approx (pow n (/ (- 1 k) 2)) (sqrt.f64 n))))
	70.4%	(.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) (.f64 (pow.f64 (+.f64 (PI.f64) (PI.f64)) (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 2 binary64))) #s(approx (pow n (/ (- 1 k) 2)) (exp.f64 (.f64 (.f64 #s(literal 1/2 binary64) (log.f64 n)) (-.f64 #s(literal 1 binary64) k))))))
	99.4%	(.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) (.f64 (pow.f64 (.f64 n (+.f64 (PI.f64) (PI.f64))) (/.f64 #s(approx (/ (- 1 k) 2) (fma.f64 #s(literal -1/2 binary64) k #s(literal 1/2 binary64))) #s(literal 2 binary64))) (pow.f64 (.f64 n (+.f64 (PI.f64) (PI.f64))) (/.f64 #s(approx (/ (- 1 k) 2) (fma.f64 #s(literal -1/2 binary64) k #s(literal 1/2 binary64))) #s(literal 2 binary64)))))
	72.1%	(.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) (.f64 #s(approx (pow (+ (PI) (PI)) (/ (- 1 k) 2)) (fma.f64 (.f64 (.f64 (*.f64 (log.f64 (+.f64 (PI.f64) (PI.f64))) (sqrt.f64 #s(literal 2 binary64))) k) (sqrt.f64 (PI.f64))) #s(literal -1/2 binary64) (sqrt.f64 (+.f64 (PI.f64) (PI.f64))))) (pow.f64 n (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 2 binary64)))))
	55.5%	(.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) (.f64 #s(approx (pow (+ (PI) (PI)) (/ (- 1 k) 2)) (fma.f64 k (fma.f64 k (fma.f64 (.f64 (.f64 (.f64 (pow.f64 (log.f64 (+.f64 (PI.f64) (PI.f64))) #s(literal 3 binary64)) (sqrt.f64 #s(literal 2 binary64))) k) (sqrt.f64 (PI.f64))) #s(literal -1/48 binary64) (.f64 (.f64 (.f64 (sqrt.f64 (PI.f64)) (.f64 (log.f64 (+.f64 (PI.f64) (PI.f64))) (log.f64 (+.f64 (PI.f64) (PI.f64))))) (sqrt.f64 #s(literal 2 binary64))) #s(literal 1/8 binary64))) (.f64 (.f64 (sqrt.f64 (PI.f64)) (.f64 (log.f64 (+.f64 (PI.f64) (PI.f64))) (sqrt.f64 #s(literal 2 binary64)))) #s(literal -1/2 binary64))) (sqrt.f64 (+.f64 (PI.f64) (PI.f64))))) (pow.f64 n (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 2 binary64)))))
	73.1%	(.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) (.f64 #s(approx (pow (+ (PI) (PI)) (/ (- 1 k) 2)) (exp.f64 (.f64 (.f64 (log.f64 (+.f64 (PI.f64) (PI.f64))) (-.f64 #s(literal 1 binary64) k)) #s(literal 1/2 binary64)))) (pow.f64 n #s(approx (/ (- 1 k) 2) (fma.f64 #s(literal -1/2 binary64) k #s(literal 1/2 binary64))))))
▶	70.4%	(.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) (.f64 #s(approx (pow (+ (PI) (PI)) (/ (- 1 k) 2)) (exp.f64 (.f64 (.f64 (log.f64 (+.f64 (PI.f64) (PI.f64))) (-.f64 #s(literal 1 binary64) k)) #s(literal 1/2 binary64)))) #s(approx (pow n (/ (- 1 k) 2)) (exp.f64 (.f64 (.f64 #s(literal 1/2 binary64) (log.f64 n)) (-.f64 #s(literal 1 binary64) k))))))
	56.6%	(.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) #s(approx (pow ( (* 2 (PI)) n) (/ (- 1 k) 2)) (fma.f64 k (fma.f64 (.f64 (.f64 (.f64 (.f64 (log.f64 (.f64 (+.f64 (PI.f64) (PI.f64)) n)) (log.f64 (.f64 (+.f64 (PI.f64) (PI.f64)) n))) (sqrt.f64 #s(literal 2 binary64))) k) (sqrt.f64 (.f64 (PI.f64) n))) #s(literal 1/8 binary64) (.f64 (.f64 #s(literal -1/2 binary64) (sqrt.f64 (.f64 (PI.f64) n))) (.f64 (log.f64 (.f64 (+.f64 (PI.f64) (PI.f64)) n)) (sqrt.f64 #s(literal 2 binary64))))) (sqrt.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n)))))
	45.7%	(.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))))
	73.0%	(.f64 (.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) (pow.f64 (+.f64 (PI.f64) (PI.f64)) (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 2 binary64)))) (pow.f64 n (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 2 binary64))))
	99.5%	(.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) k)) (pow.f64 (.f64 (*.f64 #s(literal 2 binary64) (PI.f64)) n) #s(approx (/ (- 1 k) 2) (fma.f64 #s(literal -1/2 binary64) k #s(literal 1/2 binary64)))))
	96.2%	(.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) k)) #s(approx (pow ( (* 2 (PI)) n) (/ (- 1 k) 2)) (exp.f64 (.f64 (.f64 (+.f64 (log.f64 (+.f64 (PI.f64) (PI.f64))) (log.f64 n)) (-.f64 #s(literal 1 binary64) k)) #s(literal 1/2 binary64)))))
	54.0%	#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (/.f64 (fma.f64 (.f64 (.f64 (log.f64 (.f64 (+.f64 (PI.f64) (PI.f64)) n)) (sqrt.f64 #s(literal 2 binary64))) (sqrt.f64 (.f64 (.f64 (.f64 k k) k) (.f64 (PI.f64) n)))) #s(literal -1/2 binary64) (sqrt.f64 (.f64 (.f64 (.f64 (PI.f64) n) k) #s(literal 2 binary64)))) k))
	34.7%	#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (.f64 (sqrt.f64 (/.f64 (.f64 (PI.f64) n) k)) (sqrt.f64 #s(literal 2 binary64))))
✓	34.8%	#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt.f64 (/.f64 (*.f64 n (+.f64 (PI.f64) (PI.f64))) k)))
	34.8%	#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt.f64 (.f64 (.f64 (PI.f64) (/.f64 n k)) #s(literal 2 binary64))))
▶	34.8%	#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt.f64 (*.f64 n (/.f64 (+.f64 (PI.f64) (PI.f64)) k))))

Compiler

Compiled 1 446 to 1 203 computations (16.8% saved)

series168.0ms (3.5%)

Memory

5.4MiB live, 335.4MiB allocated; 44ms collecting garbage

Counts

45 → 166

Calls

Call 1

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

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

Calls

6 calls:

Time	Variable		Point	Expression
39.0ms	n	@	inf	((/ (pow (* n (+ (PI) (PI))) (/ (- 1 k) 2)) (sqrt k)) (pow (* n (+ (PI) (PI))) (/ (- 1 k) 2)) (* n (+ (PI) (PI))) n (+ (PI) (PI)) (PI) (/ (- 1 k) 2) (+ (* -1/2 k) 1/2) -1/2 k 1/2 (sqrt k) (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt (* n (/ (+ (PI) (PI)) k))) (* n (/ (+ (PI) (PI)) k)) (/ (+ (PI) (PI)) k) (* (pow (* n (+ (PI) (PI))) (/ (- 1 k) 2)) (/ 1 (sqrt k))) (/ 1 (sqrt k)) 1 (/ (* (pow (+ (PI) (PI)) (/ (- 1 k) 2)) (pow n (/ (- 1 k) 2))) (sqrt k)) (* (pow (+ (PI) (PI)) (/ (- 1 k) 2)) (pow n (/ (- 1 k) 2))) (+ (* (* (* (* (log (* (+ (PI) (PI)) n)) (sqrt 2)) k) (sqrt (* (PI) n))) -1/2) (sqrt (* (+ (PI) (PI)) n))) (* (* (* (log (* (+ (PI) (PI)) n)) (sqrt 2)) k) (sqrt (* (PI) n))) (* (* (log (* (+ (PI) (PI)) n)) (sqrt 2)) k) (* (log (* (+ (PI) (PI)) n)) (sqrt 2)) (log (* (+ (PI) (PI)) n)) (* (+ (PI) (PI)) n) (sqrt 2) 2 (sqrt (* (PI) n)) (* (PI) n) (sqrt (* (+ (PI) (PI)) n)) (* (/ 1 (sqrt k)) (* (pow (+ (PI) (PI)) (/ (- 1 k) 2)) (pow n (/ (- 1 k) 2)))) (* (pow (+ (PI) (PI)) (/ (- 1 k) 2)) (pow n (/ (- 1 k) 2))) (pow (+ (PI) (PI)) (/ (- 1 k) 2)) (exp (* (* (log (+ (PI) (PI))) (- 1 k)) 1/2)) (* (* (log (+ (PI) (PI))) (- 1 k)) 1/2) (* (log (+ (PI) (PI))) (- 1 k)) (log (+ (PI) (PI))) (- 1 k) (pow n (/ (- 1 k) 2)) (exp (* (* 1/2 (log n)) (- 1 k))) (* (* 1/2 (log n)) (- 1 k)) (* 1/2 (log n)) (log n))
31.0ms	k	@	0	((/ (pow (* n (+ (PI) (PI))) (/ (- 1 k) 2)) (sqrt k)) (pow (* n (+ (PI) (PI))) (/ (- 1 k) 2)) (* n (+ (PI) (PI))) n (+ (PI) (PI)) (PI) (/ (- 1 k) 2) (+ (* -1/2 k) 1/2) -1/2 k 1/2 (sqrt k) (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt (* n (/ (+ (PI) (PI)) k))) (* n (/ (+ (PI) (PI)) k)) (/ (+ (PI) (PI)) k) (* (pow (* n (+ (PI) (PI))) (/ (- 1 k) 2)) (/ 1 (sqrt k))) (/ 1 (sqrt k)) 1 (/ (* (pow (+ (PI) (PI)) (/ (- 1 k) 2)) (pow n (/ (- 1 k) 2))) (sqrt k)) (* (pow (+ (PI) (PI)) (/ (- 1 k) 2)) (pow n (/ (- 1 k) 2))) (+ (* (* (* (* (log (* (+ (PI) (PI)) n)) (sqrt 2)) k) (sqrt (* (PI) n))) -1/2) (sqrt (* (+ (PI) (PI)) n))) (* (* (* (log (* (+ (PI) (PI)) n)) (sqrt 2)) k) (sqrt (* (PI) n))) (* (* (log (* (+ (PI) (PI)) n)) (sqrt 2)) k) (* (log (* (+ (PI) (PI)) n)) (sqrt 2)) (log (* (+ (PI) (PI)) n)) (* (+ (PI) (PI)) n) (sqrt 2) 2 (sqrt (* (PI) n)) (* (PI) n) (sqrt (* (+ (PI) (PI)) n)) (* (/ 1 (sqrt k)) (* (pow (+ (PI) (PI)) (/ (- 1 k) 2)) (pow n (/ (- 1 k) 2)))) (* (pow (+ (PI) (PI)) (/ (- 1 k) 2)) (pow n (/ (- 1 k) 2))) (pow (+ (PI) (PI)) (/ (- 1 k) 2)) (exp (* (* (log (+ (PI) (PI))) (- 1 k)) 1/2)) (* (* (log (+ (PI) (PI))) (- 1 k)) 1/2) (* (log (+ (PI) (PI))) (- 1 k)) (log (+ (PI) (PI))) (- 1 k) (pow n (/ (- 1 k) 2)) (exp (* (* 1/2 (log n)) (- 1 k))) (* (* 1/2 (log n)) (- 1 k)) (* 1/2 (log n)) (log n))
30.0ms	n	@	-inf	((/ (pow (* n (+ (PI) (PI))) (/ (- 1 k) 2)) (sqrt k)) (pow (* n (+ (PI) (PI))) (/ (- 1 k) 2)) (* n (+ (PI) (PI))) n (+ (PI) (PI)) (PI) (/ (- 1 k) 2) (+ (* -1/2 k) 1/2) -1/2 k 1/2 (sqrt k) (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt (* n (/ (+ (PI) (PI)) k))) (* n (/ (+ (PI) (PI)) k)) (/ (+ (PI) (PI)) k) (* (pow (* n (+ (PI) (PI))) (/ (- 1 k) 2)) (/ 1 (sqrt k))) (/ 1 (sqrt k)) 1 (/ (* (pow (+ (PI) (PI)) (/ (- 1 k) 2)) (pow n (/ (- 1 k) 2))) (sqrt k)) (* (pow (+ (PI) (PI)) (/ (- 1 k) 2)) (pow n (/ (- 1 k) 2))) (+ (* (* (* (* (log (* (+ (PI) (PI)) n)) (sqrt 2)) k) (sqrt (* (PI) n))) -1/2) (sqrt (* (+ (PI) (PI)) n))) (* (* (* (log (* (+ (PI) (PI)) n)) (sqrt 2)) k) (sqrt (* (PI) n))) (* (* (log (* (+ (PI) (PI)) n)) (sqrt 2)) k) (* (log (* (+ (PI) (PI)) n)) (sqrt 2)) (log (* (+ (PI) (PI)) n)) (* (+ (PI) (PI)) n) (sqrt 2) 2 (sqrt (* (PI) n)) (* (PI) n) (sqrt (* (+ (PI) (PI)) n)) (* (/ 1 (sqrt k)) (* (pow (+ (PI) (PI)) (/ (- 1 k) 2)) (pow n (/ (- 1 k) 2)))) (* (pow (+ (PI) (PI)) (/ (- 1 k) 2)) (pow n (/ (- 1 k) 2))) (pow (+ (PI) (PI)) (/ (- 1 k) 2)) (exp (* (* (log (+ (PI) (PI))) (- 1 k)) 1/2)) (* (* (log (+ (PI) (PI))) (- 1 k)) 1/2) (* (log (+ (PI) (PI))) (- 1 k)) (log (+ (PI) (PI))) (- 1 k) (pow n (/ (- 1 k) 2)) (exp (* (* 1/2 (log n)) (- 1 k))) (* (* 1/2 (log n)) (- 1 k)) (* 1/2 (log n)) (log n))
28.0ms	n	@	0	((/ (pow (* n (+ (PI) (PI))) (/ (- 1 k) 2)) (sqrt k)) (pow (* n (+ (PI) (PI))) (/ (- 1 k) 2)) (* n (+ (PI) (PI))) n (+ (PI) (PI)) (PI) (/ (- 1 k) 2) (+ (* -1/2 k) 1/2) -1/2 k 1/2 (sqrt k) (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt (* n (/ (+ (PI) (PI)) k))) (* n (/ (+ (PI) (PI)) k)) (/ (+ (PI) (PI)) k) (* (pow (* n (+ (PI) (PI))) (/ (- 1 k) 2)) (/ 1 (sqrt k))) (/ 1 (sqrt k)) 1 (/ (* (pow (+ (PI) (PI)) (/ (- 1 k) 2)) (pow n (/ (- 1 k) 2))) (sqrt k)) (* (pow (+ (PI) (PI)) (/ (- 1 k) 2)) (pow n (/ (- 1 k) 2))) (+ (* (* (* (* (log (* (+ (PI) (PI)) n)) (sqrt 2)) k) (sqrt (* (PI) n))) -1/2) (sqrt (* (+ (PI) (PI)) n))) (* (* (* (log (* (+ (PI) (PI)) n)) (sqrt 2)) k) (sqrt (* (PI) n))) (* (* (log (* (+ (PI) (PI)) n)) (sqrt 2)) k) (* (log (* (+ (PI) (PI)) n)) (sqrt 2)) (log (* (+ (PI) (PI)) n)) (* (+ (PI) (PI)) n) (sqrt 2) 2 (sqrt (* (PI) n)) (* (PI) n) (sqrt (* (+ (PI) (PI)) n)) (* (/ 1 (sqrt k)) (* (pow (+ (PI) (PI)) (/ (- 1 k) 2)) (pow n (/ (- 1 k) 2)))) (* (pow (+ (PI) (PI)) (/ (- 1 k) 2)) (pow n (/ (- 1 k) 2))) (pow (+ (PI) (PI)) (/ (- 1 k) 2)) (exp (* (* (log (+ (PI) (PI))) (- 1 k)) 1/2)) (* (* (log (+ (PI) (PI))) (- 1 k)) 1/2) (* (log (+ (PI) (PI))) (- 1 k)) (log (+ (PI) (PI))) (- 1 k) (pow n (/ (- 1 k) 2)) (exp (* (* 1/2 (log n)) (- 1 k))) (* (* 1/2 (log n)) (- 1 k)) (* 1/2 (log n)) (log n))
18.0ms	k	@	-inf	((/ (pow (* n (+ (PI) (PI))) (/ (- 1 k) 2)) (sqrt k)) (pow (* n (+ (PI) (PI))) (/ (- 1 k) 2)) (* n (+ (PI) (PI))) n (+ (PI) (PI)) (PI) (/ (- 1 k) 2) (+ (* -1/2 k) 1/2) -1/2 k 1/2 (sqrt k) (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt (* n (/ (+ (PI) (PI)) k))) (* n (/ (+ (PI) (PI)) k)) (/ (+ (PI) (PI)) k) (* (pow (* n (+ (PI) (PI))) (/ (- 1 k) 2)) (/ 1 (sqrt k))) (/ 1 (sqrt k)) 1 (/ (* (pow (+ (PI) (PI)) (/ (- 1 k) 2)) (pow n (/ (- 1 k) 2))) (sqrt k)) (* (pow (+ (PI) (PI)) (/ (- 1 k) 2)) (pow n (/ (- 1 k) 2))) (+ (* (* (* (* (log (* (+ (PI) (PI)) n)) (sqrt 2)) k) (sqrt (* (PI) n))) -1/2) (sqrt (* (+ (PI) (PI)) n))) (* (* (* (log (* (+ (PI) (PI)) n)) (sqrt 2)) k) (sqrt (* (PI) n))) (* (* (log (* (+ (PI) (PI)) n)) (sqrt 2)) k) (* (log (* (+ (PI) (PI)) n)) (sqrt 2)) (log (* (+ (PI) (PI)) n)) (* (+ (PI) (PI)) n) (sqrt 2) 2 (sqrt (* (PI) n)) (* (PI) n) (sqrt (* (+ (PI) (PI)) n)) (* (/ 1 (sqrt k)) (* (pow (+ (PI) (PI)) (/ (- 1 k) 2)) (pow n (/ (- 1 k) 2)))) (* (pow (+ (PI) (PI)) (/ (- 1 k) 2)) (pow n (/ (- 1 k) 2))) (pow (+ (PI) (PI)) (/ (- 1 k) 2)) (exp (* (* (log (+ (PI) (PI))) (- 1 k)) 1/2)) (* (* (log (+ (PI) (PI))) (- 1 k)) 1/2) (* (log (+ (PI) (PI))) (- 1 k)) (log (+ (PI) (PI))) (- 1 k) (pow n (/ (- 1 k) 2)) (exp (* (* 1/2 (log n)) (- 1 k))) (* (* 1/2 (log n)) (- 1 k)) (* 1/2 (log n)) (log n))

rewrite134.0ms (2.8%)

Memory

-7.9MiB live, 137.1MiB allocated; 15ms collecting garbage

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	604	6260
0	671	5847
0	2823	5729

Stop Event

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

Counts

211 → 326

Calls

Call 1

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

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

eval38.0ms (0.8%)

Memory: -12.5MiB live, 78.8MiB allocated; 9ms collecting garbage
Compiler: Compiled 6 087 to 1 541 computations (74.7% saved)

prune36.0ms (0.7%)

Memory

24.0MiB live, 78.2MiB allocated; 4ms collecting garbage

Pruning

29 alts after pruning (24 fresh and 5 done)

	Pruned	Kept	Total
New	323	11	334
Fresh	8	13	21
Picked	1	4	5
Done	0	1	1
Total	332	29	361

Accuracy

99.9%

Counts

361 → 29

Alt Table

Click to see full alt table

Status	Accuracy	Program
	56.4%	(/.f64 (pow.f64 (.f64 (+.f64 (PI.f64) (PI.f64)) n) #s(approx (/ (- 1 k) 2) (.f64 #s(literal -1/2 binary64) k))) (sqrt.f64 k))
✓	99.5%	(/.f64 (pow.f64 (*.f64 n (+.f64 (PI.f64) (PI.f64))) #s(approx (/ (- 1 k) 2) (fma.f64 #s(literal -1/2 binary64) k #s(literal 1/2 binary64)))) (sqrt.f64 k))
	73.1%	(/.f64 (*.f64 (pow.f64 n #s(approx (/ (- 1 k) 2) (fma.f64 #s(literal -1/2 binary64) k #s(literal 1/2 binary64)))) (pow.f64 (+.f64 (PI.f64) (PI.f64)) #s(approx (/ (- 1 k) 2) (fma.f64 #s(literal -1/2 binary64) k #s(literal 1/2 binary64))))) (sqrt.f64 k))
	70.4%	(/.f64 (.f64 #s(literal 1 binary64) (.f64 #s(approx (pow n (/ (- 1 k) 2)) (exp.f64 (.f64 (log.f64 (sqrt.f64 n)) (-.f64 #s(literal 1 binary64) k)))) #s(approx (pow (+ (PI) (PI)) (/ (- 1 k) 2)) (exp.f64 (.f64 (*.f64 (log.f64 (+.f64 (PI.f64) (PI.f64))) (-.f64 #s(literal 1 binary64) k)) #s(literal 1/2 binary64)))))) (sqrt.f64 k))
	96.5%	(/.f64 (exp.f64 (.f64 (log.f64 (.f64 (+.f64 (PI.f64) (PI.f64)) n)) #s(approx (/ (- 1 k) 2) (fma.f64 #s(literal -1/2 binary64) k #s(literal 1/2 binary64))))) (sqrt.f64 k))
	45.8%	(/.f64 #s(approx (pow (* n (+ (PI) (PI))) (/ (- 1 k) 2)) (sqrt.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n))) (sqrt.f64 k))
	96.2%	(/.f64 #s(approx (pow (* n (+ (PI) (PI))) (/ (- 1 k) 2)) (exp.f64 (.f64 (.f64 (+.f64 (neg.f64 (neg.f64 (log.f64 n))) (log.f64 (+.f64 (PI.f64) (PI.f64)))) (-.f64 #s(literal 1 binary64) k)) #s(literal 1/2 binary64)))) (sqrt.f64 k))
	46.3%	(/.f64 #s(approx (* (pow (+ (PI) (PI)) (/ (- 1 k) 2)) (pow n (/ (- 1 k) 2))) (fma.f64 (.f64 (.f64 (.f64 (log.f64 (.f64 (+.f64 (PI.f64) (PI.f64)) n)) (sqrt.f64 #s(literal 2 binary64))) k) (sqrt.f64 (.f64 (PI.f64) n))) #s(literal -1/2 binary64) (.f64 (sqrt.f64 (*.f64 (PI.f64) n)) (sqrt.f64 #s(literal 2 binary64))))) (sqrt.f64 k))
✓	46.4%	(/.f64 #s(approx (* (pow (+ (PI) (PI)) (/ (- 1 k) 2)) (pow n (/ (- 1 k) 2))) (fma.f64 (.f64 (.f64 (.f64 (log.f64 (.f64 (+.f64 (PI.f64) (PI.f64)) n)) (sqrt.f64 #s(literal 2 binary64))) k) (sqrt.f64 (.f64 (PI.f64) n))) #s(literal -1/2 binary64) (sqrt.f64 (.f64 (+.f64 (PI.f64) (PI.f64)) n)))) (sqrt.f64 k))
✓	99.5%	(.f64 (pow.f64 (.f64 n (+.f64 (PI.f64) (PI.f64))) #s(approx (/ (- 1 k) 2) (fma.f64 #s(literal -1/2 binary64) k #s(literal 1/2 binary64)))) (/.f64 #s(literal 1 binary64) (sqrt.f64 k)))
	54.3%	(.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) (.f64 (pow.f64 (+.f64 (PI.f64) (PI.f64)) (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 2 binary64))) #s(approx (pow n (/ (- 1 k) 2)) (fma.f64 (fma.f64 (.f64 #s(literal -1/2 binary64) (sqrt.f64 n)) (log.f64 n) (.f64 (.f64 (.f64 (*.f64 (log.f64 n) (log.f64 n)) k) (sqrt.f64 n)) #s(literal 1/8 binary64))) k (sqrt.f64 n)))))
	71.4%	(.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) (.f64 (pow.f64 (+.f64 (PI.f64) (PI.f64)) (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 2 binary64))) #s(approx (pow n (/ (- 1 k) 2)) (sqrt.f64 n))))
	70.4%	(.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) (.f64 (pow.f64 (+.f64 (PI.f64) (PI.f64)) (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 2 binary64))) #s(approx (pow n (/ (- 1 k) 2)) (exp.f64 (.f64 (.f64 #s(literal 1/2 binary64) (log.f64 n)) (-.f64 #s(literal 1 binary64) k))))))
	72.1%	(.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) (.f64 #s(approx (pow (+ (PI) (PI)) (/ (- 1 k) 2)) (fma.f64 (.f64 (.f64 (*.f64 (log.f64 (+.f64 (PI.f64) (PI.f64))) (sqrt.f64 #s(literal 2 binary64))) k) (sqrt.f64 (PI.f64))) #s(literal -1/2 binary64) (sqrt.f64 (+.f64 (PI.f64) (PI.f64))))) (pow.f64 n (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 2 binary64)))))
	55.5%	(.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) (.f64 #s(approx (pow (+ (PI) (PI)) (/ (- 1 k) 2)) (fma.f64 k (fma.f64 k (fma.f64 (.f64 (.f64 (.f64 (pow.f64 (log.f64 (+.f64 (PI.f64) (PI.f64))) #s(literal 3 binary64)) (sqrt.f64 #s(literal 2 binary64))) k) (sqrt.f64 (PI.f64))) #s(literal -1/48 binary64) (.f64 (.f64 (.f64 (sqrt.f64 (PI.f64)) (.f64 (log.f64 (+.f64 (PI.f64) (PI.f64))) (log.f64 (+.f64 (PI.f64) (PI.f64))))) (sqrt.f64 #s(literal 2 binary64))) #s(literal 1/8 binary64))) (.f64 (.f64 (sqrt.f64 (PI.f64)) (.f64 (log.f64 (+.f64 (PI.f64) (PI.f64))) (sqrt.f64 #s(literal 2 binary64)))) #s(literal -1/2 binary64))) (sqrt.f64 (+.f64 (PI.f64) (PI.f64))))) (pow.f64 n (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 2 binary64)))))
	52.9%	(.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) (.f64 #s(approx (pow (+ (PI) (PI)) (/ (- 1 k) 2)) (fma.f64 k (fma.f64 k (fma.f64 (.f64 (.f64 (.f64 (pow.f64 (log.f64 (+.f64 (PI.f64) (PI.f64))) #s(literal 3 binary64)) (sqrt.f64 #s(literal 2 binary64))) k) (sqrt.f64 (PI.f64))) #s(literal -1/48 binary64) (.f64 (.f64 (.f64 (sqrt.f64 (PI.f64)) (.f64 (log.f64 (+.f64 (PI.f64) (PI.f64))) (log.f64 (+.f64 (PI.f64) (PI.f64))))) (sqrt.f64 #s(literal 2 binary64))) #s(literal 1/8 binary64))) (.f64 (.f64 (sqrt.f64 (PI.f64)) (.f64 (log.f64 (+.f64 (PI.f64) (PI.f64))) (sqrt.f64 #s(literal 2 binary64)))) #s(literal -1/2 binary64))) (sqrt.f64 (+.f64 (PI.f64) (PI.f64))))) #s(approx (pow n (/ (- 1 k) 2)) (exp.f64 (.f64 (.f64 #s(literal 1/2 binary64) (log.f64 n)) (-.f64 #s(literal 1 binary64) k))))))
	73.1%	(.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) (.f64 #s(approx (pow (+ (PI) (PI)) (/ (- 1 k) 2)) (exp.f64 (.f64 (.f64 (log.f64 (+.f64 (PI.f64) (PI.f64))) (-.f64 #s(literal 1 binary64) k)) #s(literal 1/2 binary64)))) (pow.f64 n #s(approx (/ (- 1 k) 2) (fma.f64 #s(literal -1/2 binary64) k #s(literal 1/2 binary64))))))
	70.4%	(.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) (.f64 #s(approx (pow (+ (PI) (PI)) (/ (- 1 k) 2)) (exp.f64 (.f64 (.f64 (log.f64 (+.f64 (PI.f64) (PI.f64))) (-.f64 #s(literal 1 binary64) k)) #s(literal 1/2 binary64)))) #s(approx (pow n (/ (- 1 k) 2)) (pow.f64 (exp.f64 (log.f64 (sqrt.f64 n))) (-.f64 #s(literal 1 binary64) k)))))
	70.4%	(.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) (.f64 #s(approx (pow n (/ (- 1 k) 2)) (exp.f64 (.f64 (log.f64 (sqrt.f64 n)) (-.f64 #s(literal 1 binary64) k)))) #s(approx (pow (+ (PI) (PI)) (/ (- 1 k) 2)) (exp.f64 (.f64 (*.f64 (log.f64 (+.f64 (PI.f64) (PI.f64))) (-.f64 #s(literal 1 binary64) k)) #s(literal 1/2 binary64))))))
	56.6%	(.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) #s(approx (pow ( (* 2 (PI)) n) (/ (- 1 k) 2)) (fma.f64 k (fma.f64 (.f64 (.f64 (.f64 (.f64 (log.f64 (.f64 (+.f64 (PI.f64) (PI.f64)) n)) (log.f64 (.f64 (+.f64 (PI.f64) (PI.f64)) n))) (sqrt.f64 #s(literal 2 binary64))) k) (sqrt.f64 (.f64 (PI.f64) n))) #s(literal 1/8 binary64) (.f64 (.f64 #s(literal -1/2 binary64) (sqrt.f64 (.f64 (PI.f64) n))) (.f64 (log.f64 (.f64 (+.f64 (PI.f64) (PI.f64)) n)) (sqrt.f64 #s(literal 2 binary64))))) (sqrt.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) n)))))
	45.7%	(.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))))
	73.0%	(.f64 (.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) (pow.f64 (+.f64 (PI.f64) (PI.f64)) (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 2 binary64)))) (pow.f64 n (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 2 binary64))))
	96.2%	(.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) k)) #s(approx (pow ( (* 2 (PI)) n) (/ (- 1 k) 2)) (exp.f64 (.f64 (.f64 (+.f64 (log.f64 (+.f64 (PI.f64) (PI.f64))) (log.f64 n)) (-.f64 #s(literal 1 binary64) k)) #s(literal 1/2 binary64)))))
	54.0%	#s(approx (/ (pow (* n (+ (PI) (PI))) (/ (- 1 k) 2)) (sqrt k)) (/.f64 (fma.f64 (.f64 (.f64 (log.f64 (.f64 (+.f64 (PI.f64) (PI.f64)) n)) (sqrt.f64 #s(literal 2 binary64))) (sqrt.f64 (.f64 (.f64 (.f64 k k) k) (.f64 (PI.f64) n)))) #s(literal -1/2 binary64) (sqrt.f64 (.f64 (.f64 (.f64 (PI.f64) n) k) #s(literal 2 binary64)))) k))
	34.7%	#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (.f64 (sqrt.f64 (/.f64 (.f64 (PI.f64) n) k)) (sqrt.f64 #s(literal 2 binary64))))
	45.7%	#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))))
✓	34.8%	#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt.f64 (/.f64 (*.f64 n (+.f64 (PI.f64) (PI.f64))) k)))
	34.8%	#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt.f64 (.f64 (.f64 (PI.f64) (/.f64 n k)) #s(literal 2 binary64))))
✓	34.8%	#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt.f64 (*.f64 n (/.f64 (+.f64 (PI.f64) (PI.f64)) k))))

Compiler

Compiled 1 869 to 1 009 computations (46% saved)

regimes65.0ms (1.4%)

Memory

-7.7MiB live, 131.3MiB allocated; 7ms collecting garbage

Counts

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

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

Calls

4 calls:

17.0ms	n
16.0ms	k
16.0ms	(.f64 (.f64 #s(literal 2 binary64) (PI.f64)) n)
13.0ms	(.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) (pow.f64 (.f64 (*.f64 #s(literal 2 binary64) (PI.f64)) n) (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 2 binary64))))

Results

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

Compiler

Compiled 22 to 23 computations (-4.5% saved)

regimes40.0ms (0.8%)

Memory

-10.6MiB live, 40.5MiB allocated; 4ms collecting garbage

Counts

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

Outputs

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

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

Calls

4 calls:

29.0ms	(.f64 (.f64 #s(literal 2 binary64) (PI.f64)) n)
4.0ms	n
4.0ms	k
3.0ms	(.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) (pow.f64 (.f64 (*.f64 #s(literal 2 binary64) (PI.f64)) n) (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 2 binary64))))

Results

Accuracy	Segments	Branch
60.0%	3	`(.f64 (.f64 #s(literal 2 binary64) (PI.f64)) n)`
97.5%	3	`(.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) (pow.f64 (.f64 (*.f64 #s(literal 2 binary64) (PI.f64)) n) (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 2 binary64))))`
97.5%	2	`k`
60.0%	3	`n`

Compiler

Compiled 22 to 23 computations (-4.5% saved)

regimes15.0ms (0.3%)

Memory

32.5MiB live, 32.5MiB allocated; 0ms collecting garbage

Counts

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

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

Calls

4 calls:

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

Results

Accuracy	Segments	Branch
45.8%	1	`(.f64 (.f64 #s(literal 2 binary64) (PI.f64)) n)`
45.8%	1	`n`
45.8%	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))))`
45.8%	1	`k`

Compiler

Compiled 22 to 23 computations (-4.5% saved)

regimes28.0ms (0.6%)

Memory

-28.5MiB live, 19.2MiB allocated; 1ms collecting garbage

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

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:

21.0ms	(.f64 (.f64 #s(literal 2 binary64) (PI.f64)) n)
2.0ms	k
2.0ms	n
2.0ms	(.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) (pow.f64 (.f64 (*.f64 #s(literal 2 binary64) (PI.f64)) n) (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 2 binary64))))

Results

Accuracy	Segments	Branch
45.7%	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))))`
45.7%	1	`k`
45.7%	1	`(.f64 (.f64 #s(literal 2 binary64) (PI.f64)) n)`
45.7%	1	`n`

Compiler

Compiled 22 to 23 computations (-4.5% saved)

regimes8.0ms (0.2%)

Memory

18.4MiB live, 18.4MiB allocated; 0ms collecting garbage

Counts

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

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

Calls

4 calls:

2.0ms	(.f64 (.f64 #s(literal 2 binary64) (PI.f64)) n)
2.0ms	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
34.8%	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))))`
34.8%	1	`k`
34.8%	1	`(.f64 (.f64 #s(literal 2 binary64) (PI.f64)) n)`
34.8%	1	`n`

Compiler

Compiled 22 to 23 computations (-4.5% saved)

regimes6.0ms (0.1%)

Memory

14.5MiB live, 14.5MiB allocated; 0ms collecting garbage

Counts

3 → 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 n (+.f64 (PI.f64) (PI.f64))) k)))

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

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

Calls

4 calls:

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

Results

Accuracy	Segments	Branch
34.8%	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))))`
34.8%	1	`k`
34.8%	1	`(.f64 (.f64 #s(literal 2 binary64) (PI.f64)) n)`
34.8%	1	`n`

Compiler

Compiled 22 to 23 computations (-4.5% saved)

regimes14.0ms (0.3%)

Memory

-34.2MiB live, 11.0MiB allocated; 3ms collecting garbage

Accuracy

Total -0.0b remaining (-0%)

Threshold costs -0b (-0%)

Counts

1 → 1

Calls

Call 1

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

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:

10.0ms	n
1.0ms	(.f64 (.f64 #s(literal 2 binary64) (PI.f64)) n)
1.0ms	k
1.0ms	(.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) (pow.f64 (.f64 (*.f64 #s(literal 2 binary64) (PI.f64)) n) (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 2 binary64))))

Results

Accuracy	Segments	Branch
34.8%	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))))`
34.8%	1	`k`
34.8%	1	`(.f64 (.f64 #s(literal 2 binary64) (PI.f64)) n)`
34.8%	1	`n`

Compiler

Compiled 22 to 23 computations (-4.5% saved)

bsearch15.0ms (0.3%)

Memory

26.7MiB live, 26.7MiB allocated; 0ms collecting garbage

Algorithm

1×	binary-search

Stop Event

1×	narrow-enough

Steps

Time	Left	Right
13.0ms	0.002652239545751857	1.1448665318608207

Samples

9.0ms

128×

valid

Compiler

Compiled 323 to 298 computations (7.7% saved)

Precisions

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

ival-pow: 2.0ms (34.7% of total)

ival-sqrt: 1.0ms (17.4% of total)

ival-div!: 1.0ms (17.4% of total)

ival-mult!: 1.0ms (17.4% of total)

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

adjust: 0.0ms (0% of total)

derivations70.0ms (1.4%)

Memory

-18.3MiB live, 84.0MiB allocated; 12ms collecting garbage

Stop Event

1×

fuel

Compiler

Compiled 86 to 55 computations (36% saved)

preprocess83.0ms (1.7%)

Memory: -17.6MiB live, 170.5MiB allocated; 15ms collecting garbage
Compiler: Compiled 101 to 68 computations (32.7% saved)

end0.0ms (0%)

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

start0.0ms (0%)

analyze114.0ms (2.4%)

sample3.2s (66.5%)

preprocess41.0ms (0.9%)

series79.0ms (1.6%)

rewrite61.0ms (1.3%)

eval6.0ms (0.1%)

prune19.0ms (0.4%)

series151.0ms (3.1%)

rewrite98.0ms (2%)

eval43.0ms (0.9%)

prune23.0ms (0.5%)

series96.0ms (2%)

rewrite108.0ms (2.2%)

eval29.0ms (0.6%)

prune24.0ms (0.5%)

series168.0ms (3.5%)

rewrite134.0ms (2.8%)

eval38.0ms (0.8%)

prune36.0ms (0.7%)

regimes65.0ms (1.4%)

regimes40.0ms (0.8%)

regimes15.0ms (0.3%)

regimes28.0ms (0.6%)

regimes8.0ms (0.2%)

regimes6.0ms (0.1%)

regimes14.0ms (0.3%)

bsearch15.0ms (0.3%)

derivations70.0ms (1.4%)

preprocess83.0ms (1.7%)

end0.0ms (0%)

Profiling