Metrics for Migdal et al, Equation (51)

analyze197.0ms (1.5%)

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%	50%	1.6%	7
52.5%	25%	22.6%	0.1%	0%	50%	2.3%	8
53.8%	25%	21.5%	0.1%	0%	50%	3.5%	9
54.5%	25%	20.9%	0.1%	0%	50%	4.1%	10
55.3%	25%	20.2%	0.1%	0%	50%	4.8%	11
55.7%	25%	19.9%	0.1%	0%	50%	5.1%	12

Compiler

Compiled 19 to 14 computations (26.3% saved)

Precisions

Click to see histograms. Total time spent on operations: 143.0ms

ival-div: 58.0ms (40.6% of total)

ival-pow: 47.0ms (32.9% of total)

ival-mult: 19.0ms (13.3% of total)

ival-sqrt: 7.0ms (4.9% of total)

ival-sub: 6.0ms (4.2% of total)

ival-pi: 4.0ms (2.8% of total)

const: 1.0ms (0.7% of total)

backward-pass: 0.0ms (0% of total)

sample4.8s (35.3%)

Results

1.9s	3941×	5	exit
1.3s	8256×	0	valid
519.0ms	1905×	1	invalid
54.0ms	224×	0	unsamplable
38.0ms	436×	0	invalid

Precisions

Click to see histograms. Total time spent on operations: 2.7s

ival-pow: 937.0ms (35.1% of total)

ival-mult: 541.0ms (20.2% of total)

ival-div: 392.0ms (14.7% of total)

backward-pass: 288.0ms (10.8% of total)

ival-sqrt: 239.0ms (8.9% of total)

ival-sub: 123.0ms (4.6% of total)

ival-pi: 111.0ms (4.2% of total)

const: 39.0ms (1.5% of total)

Bogosity

preprocess83.0ms (0.6%)

Algorithm

2×	egg-herbie

Rules

1106×	`fnmadd-define`
930×	`fma-define`
846×	`fmsub-define`
760×	`fnmsub-define`
680×	`sum3-define`

Iterations

Useful iterations: 4 (0.0ms)

Iter	Nodes	Cost
0	33	92
1	93	88
2	208	88
3	414	83
4	742	82
5	1486	82
6	2091	82
7	2661	82
8	3559	82
9	3711	82
10	3770	82
11	3814	82
12	3822	82
0	13	14
1	30	14
2	47	14
3	69	14
4	90	13
5	113	13
6	149	13
7	188	13
8	214	13
9	228	13
10	229	13
0	229	13

Stop Event

1×	iter limit
1×	saturated
1×	saturated

Calls

Call 1

Inputs
(* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2)))

Outputs

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

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

Call 2

Inputs
(* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2)))
(* (/ 1 (sqrt (neg k))) (pow (* (* 2 (PI)) n) (/ (- 1 (neg k)) 2)))
(* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) (neg n)) (/ (- 1 k) 2)))
(neg (* (/ 1 (sqrt (neg k))) (pow (* (* 2 (PI)) n) (/ (- 1 (neg k)) 2))))
(neg (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) (neg n)) (/ (- 1 k) 2))))
(* (/ 1 (sqrt n)) (pow (* (* 2 (PI)) k) (/ (- 1 n) 2)))

Outputs
(* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2)))
(* (rsqrt k) (pow (* 2 (* (PI) n)) (fnmsub k 1/2 -1/2)))
(* (/ 1 (sqrt (neg k))) (pow (* (* 2 (PI)) n) (/ (- 1 (neg k)) 2)))
(* (rsqrt (neg k)) (pow (* 2 (* (PI) n)) (fnmsub k -1/2 -1/2)))
(* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) (neg n)) (/ (- 1 k) 2)))
(* (rsqrt k) (pow (* (PI) (* n -2)) (fnmsub k 1/2 -1/2)))
(neg (* (/ 1 (sqrt (neg k))) (pow (* (* 2 (PI)) n) (/ (- 1 (neg k)) 2))))
(fnmsub (rsqrt (neg k)) (pow (* 2 (* (PI) n)) (fnmsub k -1/2 -1/2)) 0)
(neg (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) (neg n)) (/ (- 1 k) 2))))
(* (pow (* (PI) (* n -2)) (fnmsub k 1/2 -1/2)) (neg (rsqrt k)))
(* (/ 1 (sqrt n)) (pow (* (* 2 (PI)) k) (/ (- 1 n) 2)))
(* (rsqrt n) (pow (* k (* 2 (PI))) (fnmsub n 1/2 -1/2)))

explain144.0ms (1.1%)

FPErrors

Click to see full error table

Ground Truth	Overpredictions	Example	Underpredictions	Example	Subexpression
3	215	(3.310635093299221e+101 9.323487353518214e+271)	1	(3.856288962479538e-12 5.946174112691735e+67)	`(pow.f64 (.f64 (.f64 #s(literal 2 binary64) (PI.f64)) n) (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 2 binary64)))`
0	0	-	0	-	`(.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))))`
0	0	-	0	-	`(PI.f64)`
0	0	-	0	-	`(*.f64 #s(literal 2 binary64) (PI.f64))`
0	0	-	0	-	`(/.f64 #s(literal 1 binary64) (sqrt.f64 k))`
0	0	-	0	-	`(-.f64 #s(literal 1 binary64) k)`
0	0	-	0	-	`#s(literal 2 binary64)`
0	0	-	0	-	`(sqrt.f64 k)`
0	0	-	0	-	`(.f64 (.f64 #s(literal 2 binary64) (PI.f64)) n)`
0	0	-	0	-	`#s(literal 1 binary64)`
0	0	-	0	-	`(/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 2 binary64))`
0	0	-	0	-	`n`
0	0	-	0	-	`k`

Results

84.0ms

512×

valid

Compiler

Compiled 132 to 41 computations (68.9% saved)

Precisions

Click to see histograms. Total time spent on operations: 54.0ms

ival-pow: 17.0ms (31.8% of total)

ival-div: 12.0ms (22.4% of total)

ival-mult: 11.0ms (20.5% of total)

ival-sqrt: 7.0ms (13.1% of total)

ival-sub: 3.0ms (5.6% of total)

ival-pi: 2.0ms (3.7% of total)

const: 1.0ms (1.9% of total)

backward-pass: 0.0ms (0% of total)

eval0.0ms (0%)

Compiler: Compiled 16 to 12 computations (25% saved)

prune1.0ms (0%)

Alt Table

Click to see full alt table

Status	Accuracy	Program
▶	99.3%	(/.f64 (pow.f64 (.f64 #s(literal 2 binary64) (.f64 (PI.f64) n)) (-.f64 #s(literal 1/2 binary64) (/.f64 k #s(literal 2 binary64)))) (sqrt.f64 k))
▶	99.2%	(.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) (pow.f64 (.f64 (*.f64 #s(literal 2 binary64) (PI.f64)) n) (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 2 binary64))))

Status

Accuracy

Program

▶

99.3%

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

▶

99.2%

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

Compiler

Compiled 34 to 25 computations (26.5% saved)

simplify11.0ms (0.1%)

Algorithm

1×	egg-herbie

Localize:

Found 8 expressions of interest:

New	Metric	Score	Program
✓	cost-diff	0	(*.f64 (PI.f64) n)
✓	cost-diff	0	(.f64 #s(literal 2 binary64) (.f64 (PI.f64) n))
✓	cost-diff	0	(pow.f64 (.f64 #s(literal 2 binary64) (.f64 (PI.f64) n)) (-.f64 #s(literal 1/2 binary64) (/.f64 k #s(literal 2 binary64))))
✓	cost-diff	0	(/.f64 (pow.f64 (.f64 #s(literal 2 binary64) (.f64 (PI.f64) n)) (-.f64 #s(literal 1/2 binary64) (/.f64 k #s(literal 2 binary64)))) (sqrt.f64 k))
✓	cost-diff	0	(pow.f64 (.f64 (.f64 #s(literal 2 binary64) (PI.f64)) n) (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 2 binary64)))
✓	cost-diff	0	(sqrt.f64 k)
✓	cost-diff	0	(/.f64 #s(literal 1 binary64) (sqrt.f64 k))
✓	cost-diff	128	(.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))))

Rules

64×	`sum3-define`
64×	`-lowering-.f32`
64×	`-lowering-.f64`
48×	`+-lowering-+.f64`
48×	`+-lowering-+.f32`

Iterations

Useful iterations: 4 (0.0ms)

Iter	Nodes	Cost
0	20	98
1	38	98
2	58	98
3	78	98
4	100	92
5	129	92
6	170	92
7	202	92
8	231	92
9	235	92
0	235	92

Stop Event

1×	iter limit
1×	saturated

Calls

Call 1

Inputs
(* (/ 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)
(/ (pow (* 2 (* (PI) n)) (- 1/2 (/ k 2))) (sqrt k))
(pow (* 2 (* (PI) n)) (- 1/2 (/ k 2)))
(* 2 (* (PI) n))
2
(* (PI) n)
(PI)
n
(- 1/2 (/ k 2))
1/2
(/ k 2)
k
(sqrt k)

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

localize117.0ms (0.9%)

Localize:

Found 8 expressions of interest:

New	Metric	Score	Program
✓	accuracy	100.0%	(PI.f64)
✓	accuracy	99.7%	(/.f64 (pow.f64 (.f64 #s(literal 2 binary64) (.f64 (PI.f64) n)) (-.f64 #s(literal 1/2 binary64) (/.f64 k #s(literal 2 binary64)))) (sqrt.f64 k))
✓	accuracy	99.7%	(*.f64 (PI.f64) n)
✓	accuracy	99.4%	(pow.f64 (.f64 #s(literal 2 binary64) (.f64 (PI.f64) n)) (-.f64 #s(literal 1/2 binary64) (/.f64 k #s(literal 2 binary64))))
✓	accuracy	99.7%	(.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))))
✓	accuracy	99.7%	(.f64 (.f64 #s(literal 2 binary64) (PI.f64)) n)
✓	accuracy	99.5%	(/.f64 #s(literal 1 binary64) (sqrt.f64 k))
✓	accuracy	99.4%	(pow.f64 (.f64 (.f64 #s(literal 2 binary64) (PI.f64)) n) (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 2 binary64)))

Results

83.0ms

256×

valid

Compiler

Compiled 105 to 21 computations (80% saved)

Precisions

Click to see histograms. Total time spent on operations: 57.0ms

ival-mult: 24.0ms (42.4% of total)

ival-pow: 16.0ms (28.2% of total)

ival-div: 9.0ms (15.9% of total)

ival-sub: 3.0ms (5.3% of total)

ival-sqrt: 2.0ms (3.5% of total)

ival-pi: 1.0ms (1.8% of total)

const: 1.0ms (1.8% of total)

backward-pass: 0.0ms (0% of total)

series97.0ms (0.7%)

Counts

10 → 156

Calls

Call 1

Inputs
#<alt (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2)))>
#<alt (/ 1 (sqrt k))>
#<alt (sqrt k)>
#<alt (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))>
#<alt (/ (pow (* 2 (* (PI) n)) (- 1/2 (/ k 2))) (sqrt k))>
#<alt (pow (* 2 (* (PI) n)) (- 1/2 (/ k 2)))>
#<alt (* 2 (* (PI) n))>
#<alt (* (PI) n)>
#<alt (* (* 2 (PI)) n)>
#<alt (PI)>

Outputs
#<alt (* (sqrt (/ (* n (PI)) k)) (sqrt 2))>
#<alt (/ (+ (* -1/2 (* (sqrt (* (pow k 3) (* n (PI)))) (* (log (* 2 (* n (PI)))) (sqrt 2)))) (* (sqrt (* k (* n (PI)))) (sqrt 2))) k)>
#<alt (/ (+ (* 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)>
#<alt (/ (+ (* 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)>
#<alt (* (sqrt (/ 1 k)) (exp (* 1/2 (* (log (* 2 (* n (PI)))) (- 1 k)))))>
#<alt (* (sqrt (/ 1 k)) (exp (* 1/2 (* (log (* 2 (* n (PI)))) (- 1 k)))))>
#<alt (* (sqrt (/ 1 k)) (exp (* 1/2 (* (log (* 2 (* n (PI)))) (- 1 k)))))>
#<alt (* (sqrt (/ 1 k)) (exp (* 1/2 (* (log (* 2 (* n (PI)))) (- 1 k)))))>
#<alt (* (sqrt (/ 1 k)) (exp (* 1/2 (* (log (* 2 (* n (PI)))) (+ 1 (* -1 k))))))>
#<alt (* (sqrt (/ 1 k)) (exp (* 1/2 (* (log (* 2 (* n (PI)))) (+ 1 (* -1 k))))))>
#<alt (* (sqrt (/ 1 k)) (exp (* 1/2 (* (log (* 2 (* n (PI)))) (+ 1 (* -1 k))))))>
#<alt (* (sqrt (/ 1 k)) (exp (* 1/2 (* (log (* 2 (* n (PI)))) (+ 1 (* -1 k))))))>
#<alt (* (sqrt (/ 1 k)) (exp (* 1/2 (* (+ (log n) (log (* 2 (PI)))) (- 1 k)))))>
#<alt (* (sqrt (/ 1 k)) (exp (* 1/2 (* (+ (log n) (log (* 2 (PI)))) (- 1 k)))))>
#<alt (* (sqrt (/ 1 k)) (exp (* 1/2 (* (+ (log n) (log (* 2 (PI)))) (- 1 k)))))>
#<alt (* (sqrt (/ 1 k)) (exp (* 1/2 (* (+ (log n) (log (* 2 (PI)))) (- 1 k)))))>
#<alt (* (sqrt (/ 1 k)) (exp (* 1/2 (* (+ (log (* 2 (PI))) (* -1 (log (/ 1 n)))) (- 1 k)))))>
#<alt (* (sqrt (/ 1 k)) (exp (* 1/2 (* (+ (log (* 2 (PI))) (* -1 (log (/ 1 n)))) (- 1 k)))))>
#<alt (* (sqrt (/ 1 k)) (exp (* 1/2 (* (+ (log (* 2 (PI))) (* -1 (log (/ 1 n)))) (- 1 k)))))>
#<alt (* (sqrt (/ 1 k)) (exp (* 1/2 (* (+ (log (* 2 (PI))) (* -1 (log (/ 1 n)))) (- 1 k)))))>
#<alt (* (sqrt (/ 1 k)) (exp (* 1/2 (* (+ (log (* -2 (PI))) (* -1 (log (/ -1 n)))) (- 1 k)))))>
#<alt (* (sqrt (/ 1 k)) (exp (* 1/2 (* (+ (log (* -2 (PI))) (* -1 (log (/ -1 n)))) (- 1 k)))))>
#<alt (* (sqrt (/ 1 k)) (exp (* 1/2 (* (+ (log (* -2 (PI))) (* -1 (log (/ -1 n)))) (- 1 k)))))>
#<alt (* (sqrt (/ 1 k)) (exp (* 1/2 (* (+ (log (* -2 (PI))) (* -1 (log (/ -1 n)))) (- 1 k)))))>
#<alt (sqrt (/ 1 k))>
#<alt (sqrt (/ 1 k))>
#<alt (sqrt (/ 1 k))>
#<alt (sqrt (/ 1 k))>
#<alt (sqrt (/ 1 k))>
#<alt (sqrt (/ 1 k))>
#<alt (sqrt (/ 1 k))>
#<alt (sqrt (/ 1 k))>
#<alt (sqrt (/ 1 k))>
#<alt (sqrt (/ 1 k))>
#<alt (sqrt (/ 1 k))>
#<alt (sqrt (/ 1 k))>
#<alt (sqrt k)>
#<alt (sqrt k)>
#<alt (sqrt k)>
#<alt (sqrt k)>
#<alt (sqrt k)>
#<alt (sqrt k)>
#<alt (sqrt k)>
#<alt (sqrt k)>
#<alt (* -1 (* (sqrt k) (pow (sqrt -1) 2)))>
#<alt (* -1 (* (sqrt k) (pow (sqrt -1) 2)))>
#<alt (* -1 (* (sqrt k) (pow (sqrt -1) 2)))>
#<alt (* -1 (* (sqrt k) (pow (sqrt -1) 2)))>
#<alt (exp (* 1/2 (* (+ (log n) (log (* 2 (PI)))) (- 1 k))))>
#<alt (exp (* 1/2 (* (+ (log n) (log (* 2 (PI)))) (- 1 k))))>
#<alt (exp (* 1/2 (* (+ (log n) (log (* 2 (PI)))) (- 1 k))))>
#<alt (exp (* 1/2 (* (+ (log n) (log (* 2 (PI)))) (- 1 k))))>
#<alt (exp (* 1/2 (* (+ (log (* 2 (PI))) (* -1 (log (/ 1 n)))) (- 1 k))))>
#<alt (exp (* 1/2 (* (+ (log (* 2 (PI))) (* -1 (log (/ 1 n)))) (- 1 k))))>
#<alt (exp (* 1/2 (* (+ (log (* 2 (PI))) (* -1 (log (/ 1 n)))) (- 1 k))))>
#<alt (exp (* 1/2 (* (+ (log (* 2 (PI))) (* -1 (log (/ 1 n)))) (- 1 k))))>
#<alt (exp (* 1/2 (* (+ (log (* -2 (PI))) (* -1 (log (/ -1 n)))) (- 1 k))))>
#<alt (exp (* 1/2 (* (+ (log (* -2 (PI))) (* -1 (log (/ -1 n)))) (- 1 k))))>
#<alt (exp (* 1/2 (* (+ (log (* -2 (PI))) (* -1 (log (/ -1 n)))) (- 1 k))))>
#<alt (exp (* 1/2 (* (+ (log (* -2 (PI))) (* -1 (log (/ -1 n)))) (- 1 k))))>
#<alt (* (sqrt (* n (PI))) (sqrt 2))>
#<alt (+ (* -1/2 (* (* k (* (log (* 2 (* n (PI)))) (sqrt 2))) (sqrt (* n (PI))))) (* (sqrt (* n (PI))) (sqrt 2)))>
#<alt (+ (* 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)))>
#<alt (+ (* 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)))>
#<alt (exp (* 1/2 (* (log (* 2 (* n (PI)))) (- 1 k))))>
#<alt (exp (* 1/2 (* (log (* 2 (* n (PI)))) (- 1 k))))>
#<alt (exp (* 1/2 (* (log (* 2 (* n (PI)))) (- 1 k))))>
#<alt (exp (* 1/2 (* (log (* 2 (* n (PI)))) (- 1 k))))>
#<alt (exp (* 1/2 (* (log (* 2 (* n (PI)))) (+ 1 (* -1 k)))))>
#<alt (exp (* 1/2 (* (log (* 2 (* n (PI)))) (+ 1 (* -1 k)))))>
#<alt (exp (* 1/2 (* (log (* 2 (* n (PI)))) (+ 1 (* -1 k)))))>
#<alt (exp (* 1/2 (* (log (* 2 (* n (PI)))) (+ 1 (* -1 k)))))>
#<alt (* (sqrt (/ 1 k)) (exp (* (+ (log n) (log (* 2 (PI)))) (- 1/2 (* 1/2 k)))))>
#<alt (* (sqrt (/ 1 k)) (exp (* (+ (log n) (log (* 2 (PI)))) (- 1/2 (* 1/2 k)))))>
#<alt (* (sqrt (/ 1 k)) (exp (* (+ (log n) (log (* 2 (PI)))) (- 1/2 (* 1/2 k)))))>
#<alt (* (sqrt (/ 1 k)) (exp (* (+ (log n) (log (* 2 (PI)))) (- 1/2 (* 1/2 k)))))>
#<alt (* (sqrt (/ 1 k)) (exp (* (+ (log (* 2 (PI))) (* -1 (log (/ 1 n)))) (- 1/2 (* 1/2 k)))))>
#<alt (* (sqrt (/ 1 k)) (exp (* (+ (log (* 2 (PI))) (* -1 (log (/ 1 n)))) (- 1/2 (* 1/2 k)))))>
#<alt (* (sqrt (/ 1 k)) (exp (* (+ (log (* 2 (PI))) (* -1 (log (/ 1 n)))) (- 1/2 (* 1/2 k)))))>
#<alt (* (sqrt (/ 1 k)) (exp (* (+ (log (* 2 (PI))) (* -1 (log (/ 1 n)))) (- 1/2 (* 1/2 k)))))>
#<alt (* (sqrt (/ 1 k)) (exp (* (+ (log (* -2 (PI))) (* -1 (log (/ -1 n)))) (- 1/2 (* 1/2 k)))))>
#<alt (* (sqrt (/ 1 k)) (exp (* (+ (log (* -2 (PI))) (* -1 (log (/ -1 n)))) (- 1/2 (* 1/2 k)))))>
#<alt (* (sqrt (/ 1 k)) (exp (* (+ (log (* -2 (PI))) (* -1 (log (/ -1 n)))) (- 1/2 (* 1/2 k)))))>
#<alt (* (sqrt (/ 1 k)) (exp (* (+ (log (* -2 (PI))) (* -1 (log (/ -1 n)))) (- 1/2 (* 1/2 k)))))>
#<alt (* (sqrt (/ (* n (PI)) k)) (sqrt 2))>
#<alt (/ (+ (* -1/2 (* (sqrt (* (pow k 3) (* n (PI)))) (* (log (* 2 (* n (PI)))) (sqrt 2)))) (* (sqrt (* k (* n (PI)))) (sqrt 2))) k)>
#<alt (/ (+ (* 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)>
#<alt (/ (+ (* 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)>
#<alt (* (sqrt (/ 1 k)) (exp (* (log (* 2 (* n (PI)))) (- 1/2 (* 1/2 k)))))>
#<alt (* (sqrt (/ 1 k)) (exp (* (log (* 2 (* n (PI)))) (- 1/2 (* 1/2 k)))))>
#<alt (* (sqrt (/ 1 k)) (exp (* (log (* 2 (* n (PI)))) (- 1/2 (* 1/2 k)))))>
#<alt (* (sqrt (/ 1 k)) (exp (* (log (* 2 (* n (PI)))) (- 1/2 (* 1/2 k)))))>
#<alt (* (sqrt (/ 1 k)) (exp (* (log (* 2 (* n (PI)))) (+ 1/2 (* -1/2 k)))))>
#<alt (* (sqrt (/ 1 k)) (exp (* (log (* 2 (* n (PI)))) (+ 1/2 (* -1/2 k)))))>
#<alt (* (sqrt (/ 1 k)) (exp (* (log (* 2 (* n (PI)))) (+ 1/2 (* -1/2 k)))))>
#<alt (* (sqrt (/ 1 k)) (exp (* (log (* 2 (* n (PI)))) (+ 1/2 (* -1/2 k)))))>
#<alt (exp (* (+ (log n) (log (* 2 (PI)))) (- 1/2 (* 1/2 k))))>
#<alt (exp (* (+ (log n) (log (* 2 (PI)))) (- 1/2 (* 1/2 k))))>
#<alt (exp (* (+ (log n) (log (* 2 (PI)))) (- 1/2 (* 1/2 k))))>
#<alt (exp (* (+ (log n) (log (* 2 (PI)))) (- 1/2 (* 1/2 k))))>
#<alt (exp (* (+ (log (* 2 (PI))) (* -1 (log (/ 1 n)))) (- 1/2 (* 1/2 k))))>
#<alt (exp (* (+ (log (* 2 (PI))) (* -1 (log (/ 1 n)))) (- 1/2 (* 1/2 k))))>
#<alt (exp (* (+ (log (* 2 (PI))) (* -1 (log (/ 1 n)))) (- 1/2 (* 1/2 k))))>
#<alt (exp (* (+ (log (* 2 (PI))) (* -1 (log (/ 1 n)))) (- 1/2 (* 1/2 k))))>
#<alt (exp (* (+ (log (* -2 (PI))) (* -1 (log (/ -1 n)))) (- 1/2 (* 1/2 k))))>
#<alt (exp (* (+ (log (* -2 (PI))) (* -1 (log (/ -1 n)))) (- 1/2 (* 1/2 k))))>
#<alt (exp (* (+ (log (* -2 (PI))) (* -1 (log (/ -1 n)))) (- 1/2 (* 1/2 k))))>
#<alt (exp (* (+ (log (* -2 (PI))) (* -1 (log (/ -1 n)))) (- 1/2 (* 1/2 k))))>
#<alt (* (sqrt (* n (PI))) (sqrt 2))>
#<alt (+ (* -1/2 (* (* k (* (log (* 2 (* n (PI)))) (sqrt 2))) (sqrt (* n (PI))))) (* (sqrt (* n (PI))) (sqrt 2)))>
#<alt (+ (* 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)))>
#<alt (+ (* 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)))>
#<alt (exp (* (log (* 2 (* n (PI)))) (- 1/2 (* 1/2 k))))>
#<alt (exp (* (log (* 2 (* n (PI)))) (- 1/2 (* 1/2 k))))>
#<alt (exp (* (log (* 2 (* n (PI)))) (- 1/2 (* 1/2 k))))>
#<alt (exp (* (log (* 2 (* n (PI)))) (- 1/2 (* 1/2 k))))>
#<alt (exp (* (log (* 2 (* n (PI)))) (+ 1/2 (* -1/2 k))))>
#<alt (exp (* (log (* 2 (* n (PI)))) (+ 1/2 (* -1/2 k))))>
#<alt (exp (* (log (* 2 (* n (PI)))) (+ 1/2 (* -1/2 k))))>
#<alt (exp (* (log (* 2 (* n (PI)))) (+ 1/2 (* -1/2 k))))>
#<alt (* 2 (* n (PI)))>
#<alt (* 2 (* n (PI)))>
#<alt (* 2 (* n (PI)))>
#<alt (* 2 (* n (PI)))>
#<alt (* 2 (* n (PI)))>
#<alt (* 2 (* n (PI)))>
#<alt (* 2 (* n (PI)))>
#<alt (* 2 (* n (PI)))>
#<alt (* 2 (* n (PI)))>
#<alt (* 2 (* n (PI)))>
#<alt (* 2 (* n (PI)))>
#<alt (* 2 (* n (PI)))>
#<alt (* n (PI))>
#<alt (* n (PI))>
#<alt (* n (PI))>
#<alt (* n (PI))>
#<alt (* n (PI))>
#<alt (* n (PI))>
#<alt (* n (PI))>
#<alt (* n (PI))>
#<alt (* n (PI))>
#<alt (* n (PI))>
#<alt (* n (PI))>
#<alt (* n (PI))>
#<alt (* 2 (* n (PI)))>
#<alt (* 2 (* n (PI)))>
#<alt (* 2 (* n (PI)))>
#<alt (* 2 (* n (PI)))>
#<alt (* 2 (* n (PI)))>
#<alt (* 2 (* n (PI)))>
#<alt (* 2 (* n (PI)))>
#<alt (* 2 (* n (PI)))>
#<alt (* 2 (* n (PI)))>
#<alt (* 2 (* n (PI)))>
#<alt (* 2 (* n (PI)))>
#<alt (* 2 (* n (PI)))>

Calls

39 calls:

Time	Variable		Point	Expression
46.0ms	n	@	0	(* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2)))
25.0ms	n	@	-inf	(* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2)))
12.0ms	n	@	inf	(* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2)))
3.0ms	k	@	-inf	(/ (pow (* 2 (* (PI) n)) (- 1/2 (/ k 2))) (sqrt k))
1.0ms	k	@	0	(* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2)))

rewrite347.0ms (2.6%)

Algorithm

1×	batch-egg-rewrite

Rules

5664×	`-lowering-.f32`
5664×	`-lowering-.f64`
3066×	`/-lowering-/.f32`
3066×	`/-lowering-/.f64`
1334×	`pow-lowering-pow.f64`

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	20	68
1	132	68
2	851	64
0	8618	64

Stop Event

1×	iter limit
1×	node limit

Counts

10 → 740

Calls

Call 1

Inputs
(* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2)))
(/ 1 (sqrt k))
(sqrt k)
(pow (* (* 2 (PI)) n) (/ (- 1 k) 2))
(/ (pow (* 2 (* (PI) n)) (- 1/2 (/ k 2))) (sqrt k))
(pow (* 2 (* (PI) n)) (- 1/2 (/ k 2)))
(* 2 (* (PI) n))
(* (PI) n)
(* (* 2 (PI)) n)
(PI)

Outputs
(exp.f64 (.f64 (log.f64 (/.f64 (sqrt.f64 k) (pow.f64 (.f64 #s(literal 2 binary64) (*.f64 (PI.f64) n)) (+.f64 #s(literal 1/2 binary64) (/.f64 k #s(literal -2 binary64)))))) #s(literal -1 binary64)))
(exp.f64 (+.f64 (.f64 (.f64 #s(literal 1/2 binary64) (log.f64 k)) #s(literal -1 binary64)) (/.f64 (log.f64 (.f64 #s(literal 2 binary64) (.f64 (PI.f64) n))) (/.f64 #s(literal 2 binary64) (-.f64 #s(literal 1 binary64) k)))))
(exp.f64 (+.f64 (/.f64 (log.f64 (.f64 #s(literal 2 binary64) (.f64 (PI.f64) n))) (/.f64 #s(literal 2 binary64) (-.f64 #s(literal 1 binary64) k))) (.f64 (.f64 #s(literal 1/2 binary64) (log.f64 k)) #s(literal -1 binary64))))
(exp.f64 (-.f64 (/.f64 (log.f64 (.f64 #s(literal 2 binary64) (.f64 (PI.f64) n))) (/.f64 #s(literal 2 binary64) (-.f64 #s(literal 1 binary64) k))) (*.f64 #s(literal 1/2 binary64) (log.f64 k))))
(-.f64 #s(literal 0 binary64) (/.f64 (pow.f64 (.f64 #s(literal 2 binary64) (.f64 (PI.f64) n)) (+.f64 #s(literal 1/2 binary64) (/.f64 k #s(literal -2 binary64)))) (-.f64 #s(literal 0 binary64) (sqrt.f64 k))))
(-.f64 (/.f64 #s(literal 0 binary64) (-.f64 #s(literal 0 binary64) (sqrt.f64 k))) (/.f64 (pow.f64 (.f64 #s(literal 2 binary64) (.f64 (PI.f64) n)) (+.f64 #s(literal 1/2 binary64) (/.f64 k #s(literal -2 binary64)))) (-.f64 #s(literal 0 binary64) (sqrt.f64 k))))
(neg.f64 (/.f64 (pow.f64 (.f64 #s(literal 2 binary64) (.f64 (PI.f64) n)) (+.f64 #s(literal 1/2 binary64) (/.f64 k #s(literal -2 binary64)))) (-.f64 #s(literal 0 binary64) (sqrt.f64 k))))
(neg.f64 (.f64 (/.f64 #s(literal -1 binary64) (sqrt.f64 k)) (pow.f64 (.f64 #s(literal 2 binary64) (*.f64 (PI.f64) n)) (+.f64 #s(literal 1/2 binary64) (/.f64 k #s(literal -2 binary64))))))
(neg.f64 (.f64 #s(literal 1 binary64) (/.f64 (pow.f64 (.f64 #s(literal 2 binary64) (*.f64 (PI.f64) n)) (+.f64 #s(literal 1/2 binary64) (/.f64 k #s(literal -2 binary64)))) (-.f64 #s(literal 0 binary64) (sqrt.f64 k)))))
(neg.f64 (/.f64 #s(literal -1 binary64) (/.f64 (sqrt.f64 k) (pow.f64 (.f64 #s(literal 2 binary64) (.f64 (PI.f64) n)) (+.f64 #s(literal 1/2 binary64) (/.f64 k #s(literal -2 binary64)))))))
(/.f64 #s(literal 1 binary64) (/.f64 (sqrt.f64 k) (pow.f64 (.f64 #s(literal 2 binary64) (.f64 (PI.f64) n)) (+.f64 #s(literal 1/2 binary64) (/.f64 k #s(literal -2 binary64))))))
(/.f64 #s(literal 1 binary64) (.f64 (pow.f64 (.f64 #s(literal 2 binary64) (*.f64 (PI.f64) n)) (+.f64 (/.f64 k #s(literal 2 binary64)) #s(literal -1/2 binary64))) (sqrt.f64 k)))
(/.f64 #s(literal 1 binary64) (/.f64 (pow.f64 (.f64 k (pow.f64 (.f64 #s(literal 2 binary64) (.f64 (PI.f64) n)) k)) #s(literal 1/2 binary64)) (sqrt.f64 (.f64 #s(literal 2 binary64) (*.f64 (PI.f64) n)))))
(/.f64 #s(literal 1 binary64) (/.f64 (neg.f64 (pow.f64 (.f64 k (pow.f64 (.f64 #s(literal 2 binary64) (.f64 (PI.f64) n)) k)) #s(literal 1/2 binary64))) (-.f64 #s(literal 0 binary64) (sqrt.f64 (.f64 #s(literal 2 binary64) (*.f64 (PI.f64) n))))))
(/.f64 #s(literal 1 binary64) (/.f64 (pow.f64 (.f64 (pow.f64 (.f64 #s(literal 2 binary64) (.f64 (PI.f64) n)) k) k) #s(literal 1/2 binary64)) (sqrt.f64 (.f64 #s(literal 2 binary64) (*.f64 (PI.f64) n)))))
(/.f64 #s(literal 1 binary64) (/.f64 (neg.f64 (pow.f64 (.f64 (pow.f64 (.f64 #s(literal 2 binary64) (.f64 (PI.f64) n)) k) k) #s(literal 1/2 binary64))) (.f64 (sqrt.f64 (.f64 #s(literal 2 binary64) (.f64 (PI.f64) n))) #s(literal -1 binary64))))
(/.f64 #s(literal 1 binary64) (/.f64 (pow.f64 (.f64 #s(literal 2 binary64) (.f64 (PI.f64) n)) (/.f64 k #s(literal 2 binary64))) (.f64 (pow.f64 k #s(literal -1/2 binary64)) (sqrt.f64 (.f64 #s(literal 2 binary64) (*.f64 (PI.f64) n))))))
(/.f64 #s(literal 1 binary64) (/.f64 (pow.f64 (.f64 #s(literal 2 binary64) (.f64 (PI.f64) n)) (/.f64 k #s(literal 2 binary64))) (/.f64 (sqrt.f64 (.f64 #s(literal 2 binary64) (.f64 (PI.f64) n))) (sqrt.f64 k))))
(/.f64 (pow.f64 k #s(literal -1/2 binary64)) (pow.f64 (.f64 #s(literal 2 binary64) (.f64 (PI.f64) n)) (+.f64 (/.f64 k #s(literal 2 binary64)) #s(literal -1/2 binary64))))
(/.f64 (pow.f64 (.f64 #s(literal 2 binary64) (.f64 (PI.f64) n)) (+.f64 #s(literal 1/2 binary64) (/.f64 k #s(literal -2 binary64)))) (sqrt.f64 k))
(/.f64 #s(literal -1 binary64) (/.f64 #s(literal -1 binary64) (/.f64 (pow.f64 k #s(literal -1/2 binary64)) (pow.f64 (.f64 #s(literal 2 binary64) (.f64 (PI.f64) n)) (+.f64 (/.f64 k #s(literal 2 binary64)) #s(literal -1/2 binary64))))))
(/.f64 #s(literal -1 binary64) (.f64 (pow.f64 (.f64 #s(literal 2 binary64) (*.f64 (PI.f64) n)) (+.f64 (/.f64 k #s(literal 2 binary64)) #s(literal -1/2 binary64))) (-.f64 #s(literal 0 binary64) (sqrt.f64 k))))
(/.f64 (sqrt.f64 (.f64 #s(literal 2 binary64) (.f64 (PI.f64) n))) (pow.f64 (.f64 k (pow.f64 (.f64 #s(literal 2 binary64) (*.f64 (PI.f64) n)) k)) #s(literal 1/2 binary64)))
(/.f64 (sqrt.f64 (.f64 #s(literal 2 binary64) (.f64 (PI.f64) n))) (pow.f64 (.f64 (pow.f64 (.f64 #s(literal 2 binary64) (*.f64 (PI.f64) n)) k) k) #s(literal 1/2 binary64)))
(/.f64 (sqrt.f64 (.f64 #s(literal 2 binary64) (.f64 (PI.f64) n))) (.f64 (-.f64 #s(literal 0 binary64) (pow.f64 (.f64 #s(literal 2 binary64) (*.f64 (PI.f64) n)) (/.f64 k #s(literal 2 binary64)))) (-.f64 #s(literal 0 binary64) (sqrt.f64 k))))
(/.f64 (-.f64 #s(literal 0 binary64) (pow.f64 (.f64 #s(literal 2 binary64) (.f64 (PI.f64) n)) (+.f64 #s(literal 1/2 binary64) (/.f64 k #s(literal -2 binary64))))) (-.f64 #s(literal 0 binary64) (sqrt.f64 k)))
(/.f64 (.f64 (sqrt.f64 (.f64 #s(literal 2 binary64) (.f64 (PI.f64) n))) #s(literal -1 binary64)) (neg.f64 (pow.f64 (.f64 (pow.f64 (.f64 #s(literal 2 binary64) (.f64 (PI.f64) n)) k) k) #s(literal 1/2 binary64))))
(/.f64 (-.f64 #s(literal 0 binary64) (sqrt.f64 (.f64 #s(literal 2 binary64) (.f64 (PI.f64) n)))) (neg.f64 (pow.f64 (.f64 k (pow.f64 (.f64 #s(literal 2 binary64) (*.f64 (PI.f64) n)) k)) #s(literal 1/2 binary64))))
(/.f64 (-.f64 #s(literal 0 binary64) (sqrt.f64 (.f64 #s(literal 2 binary64) (.f64 (PI.f64) n)))) (neg.f64 (pow.f64 (.f64 (pow.f64 (.f64 #s(literal 2 binary64) (*.f64 (PI.f64) n)) k) k) #s(literal 1/2 binary64))))
(/.f64 (.f64 (pow.f64 k #s(literal -1/2 binary64)) (sqrt.f64 (.f64 #s(literal 2 binary64) (.f64 (PI.f64) n)))) (pow.f64 (.f64 #s(literal 2 binary64) (*.f64 (PI.f64) n)) (/.f64 k #s(literal 2 binary64))))
(/.f64 (/.f64 (sqrt.f64 (.f64 #s(literal 2 binary64) (.f64 (PI.f64) n))) (sqrt.f64 k)) (pow.f64 (.f64 #s(literal 2 binary64) (.f64 (PI.f64) n)) (/.f64 k #s(literal 2 binary64))))
(/.f64 (.f64 #s(literal 1 binary64) (-.f64 #s(literal 0 binary64) (sqrt.f64 (.f64 #s(literal 2 binary64) (.f64 (PI.f64) n))))) (.f64 (sqrt.f64 k) (-.f64 #s(literal 0 binary64) (pow.f64 (.f64 #s(literal 2 binary64) (.f64 (PI.f64) n)) (/.f64 k #s(literal 2 binary64))))))
(/.f64 (.f64 #s(literal -1 binary64) (-.f64 #s(literal 0 binary64) (sqrt.f64 (.f64 #s(literal 2 binary64) (.f64 (PI.f64) n))))) (.f64 (-.f64 #s(literal 0 binary64) (sqrt.f64 k)) (-.f64 #s(literal 0 binary64) (pow.f64 (.f64 #s(literal 2 binary64) (.f64 (PI.f64) n)) (/.f64 k #s(literal 2 binary64))))))
(/.f64 (.f64 (-.f64 #s(literal 0 binary64) (sqrt.f64 (.f64 #s(literal 2 binary64) (.f64 (PI.f64) n)))) #s(literal 1 binary64)) (neg.f64 (pow.f64 (.f64 (pow.f64 (.f64 #s(literal 2 binary64) (.f64 (PI.f64) n)) k) k) #s(literal 1/2 binary64))))
(/.f64 (.f64 (-.f64 #s(literal 0 binary64) (sqrt.f64 (.f64 #s(literal 2 binary64) (.f64 (PI.f64) n)))) #s(literal 1 binary64)) (.f64 (-.f64 #s(literal 0 binary64) (pow.f64 (.f64 #s(literal 2 binary64) (.f64 (PI.f64) n)) (/.f64 k #s(literal 2 binary64)))) (sqrt.f64 k)))
(/.f64 (.f64 (-.f64 #s(literal 0 binary64) (sqrt.f64 (.f64 #s(literal 2 binary64) (.f64 (PI.f64) n)))) #s(literal -1 binary64)) (.f64 (-.f64 #s(literal 0 binary64) (pow.f64 (.f64 #s(literal 2 binary64) (.f64 (PI.f64) n)) (/.f64 k #s(literal 2 binary64)))) (-.f64 #s(literal 0 binary64) (sqrt.f64 k))))
(/.f64 (.f64 (sqrt.f64 #s(literal 2 binary64)) (pow.f64 (.f64 (PI.f64) n) (+.f64 #s(literal 1/2 binary64) (/.f64 k #s(literal -2 binary64))))) (*.f64 (pow.f64 #s(literal 2 binary64) (/.f64 k #s(literal 2 binary64))) (sqrt.f64 k)))
(/.f64 (.f64 (pow.f64 (.f64 #s(literal 2 binary64) (PI.f64)) #s(literal 1/2 binary64)) (pow.f64 n (+.f64 #s(literal 1/2 binary64) (/.f64 k #s(literal -2 binary64))))) (.f64 (pow.f64 (.f64 #s(literal 2 binary64) (PI.f64)) (/.f64 k #s(literal 2 binary64))) (sqrt.f64 k)))
(/.f64 (neg.f64 (.f64 (sqrt.f64 (.f64 #s(literal 2 binary64) (.f64 (PI.f64) n))) #s(literal -1 binary64))) (neg.f64 (neg.f64 (pow.f64 (.f64 (pow.f64 (.f64 #s(literal 2 binary64) (.f64 (PI.f64) n)) k) k) #s(literal 1/2 binary64)))))
(/.f64 (neg.f64 (.f64 (pow.f64 k #s(literal -1/2 binary64)) (sqrt.f64 (.f64 #s(literal 2 binary64) (.f64 (PI.f64) n))))) (-.f64 #s(literal 0 binary64) (pow.f64 (.f64 #s(literal 2 binary64) (*.f64 (PI.f64) n)) (/.f64 k #s(literal 2 binary64)))))
(/.f64 (neg.f64 (/.f64 (sqrt.f64 (.f64 #s(literal 2 binary64) (.f64 (PI.f64) n))) (sqrt.f64 k))) (-.f64 #s(literal 0 binary64) (pow.f64 (.f64 #s(literal 2 binary64) (.f64 (PI.f64) n)) (/.f64 k #s(literal 2 binary64)))))
(/.f64 (neg.f64 (-.f64 #s(literal 0 binary64) (sqrt.f64 (.f64 #s(literal 2 binary64) (.f64 (PI.f64) n))))) (neg.f64 (neg.f64 (pow.f64 (.f64 k (pow.f64 (.f64 #s(literal 2 binary64) (*.f64 (PI.f64) n)) k)) #s(literal 1/2 binary64)))))
(pow.f64 (/.f64 (sqrt.f64 k) (pow.f64 (.f64 #s(literal 2 binary64) (.f64 (PI.f64) n)) (+.f64 #s(literal 1/2 binary64) (/.f64 k #s(literal -2 binary64))))) #s(literal -1 binary64))
(.f64 #s(literal 1 binary64) (/.f64 (pow.f64 k #s(literal -1/2 binary64)) (pow.f64 (.f64 #s(literal 2 binary64) (*.f64 (PI.f64) n)) (+.f64 (/.f64 k #s(literal 2 binary64)) #s(literal -1/2 binary64)))))
(.f64 (pow.f64 k #s(literal -1/2 binary64)) (pow.f64 (.f64 #s(literal 2 binary64) (*.f64 (PI.f64) n)) (+.f64 #s(literal 1/2 binary64) (/.f64 k #s(literal -2 binary64)))))
(.f64 (pow.f64 k #s(literal -1/2 binary64)) (/.f64 (pow.f64 (.f64 #s(literal 2 binary64) (*.f64 (PI.f64) n)) (+.f64 #s(literal 1/2 binary64) (/.f64 k #s(literal -2 binary64)))) #s(literal 1 binary64)))
(.f64 (pow.f64 (.f64 #s(literal 2 binary64) (*.f64 (PI.f64) n)) (+.f64 #s(literal 1/2 binary64) (/.f64 k #s(literal -2 binary64)))) (pow.f64 k #s(literal -1/2 binary64)))
(.f64 (/.f64 (pow.f64 k #s(literal -1/2 binary64)) (pow.f64 (.f64 #s(literal 2 binary64) (*.f64 (PI.f64) n)) (+.f64 (/.f64 k #s(literal 2 binary64)) #s(literal -1/2 binary64)))) #s(literal 1 binary64))
(.f64 #s(literal -1 binary64) (/.f64 (pow.f64 (.f64 #s(literal 2 binary64) (*.f64 (PI.f64) n)) (+.f64 #s(literal 1/2 binary64) (/.f64 k #s(literal -2 binary64)))) (-.f64 #s(literal 0 binary64) (sqrt.f64 k))))
(.f64 #s(literal -1 binary64) (.f64 (/.f64 #s(literal -1 binary64) (sqrt.f64 k)) (pow.f64 (.f64 #s(literal 2 binary64) (.f64 (PI.f64) n)) (+.f64 #s(literal 1/2 binary64) (/.f64 k #s(literal -2 binary64))))))
(.f64 (sqrt.f64 (.f64 #s(literal 2 binary64) (.f64 (PI.f64) n))) (/.f64 #s(literal 1 binary64) (pow.f64 (.f64 k (pow.f64 (.f64 #s(literal 2 binary64) (.f64 (PI.f64) n)) k)) #s(literal 1/2 binary64))))
(.f64 (sqrt.f64 (.f64 #s(literal 2 binary64) (.f64 (PI.f64) n))) (/.f64 #s(literal 1 binary64) (pow.f64 (.f64 (pow.f64 (.f64 #s(literal 2 binary64) (.f64 (PI.f64) n)) k) k) #s(literal 1/2 binary64))))
(.f64 (sqrt.f64 (.f64 #s(literal 2 binary64) (.f64 (PI.f64) n))) (.f64 (pow.f64 (.f64 #s(literal 2 binary64) (.f64 (PI.f64) n)) (/.f64 k #s(literal -2 binary64))) (pow.f64 k #s(literal -1/2 binary64))))
(.f64 (pow.f64 #s(literal 2 binary64) (+.f64 #s(literal 1/2 binary64) (/.f64 k #s(literal -2 binary64)))) (/.f64 (pow.f64 (.f64 (PI.f64) n) (+.f64 #s(literal 1/2 binary64) (/.f64 k #s(literal -2 binary64)))) (sqrt.f64 k)))
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(.f64 (cbrt.f64 (PI.f64)) (.f64 (pow.f64 (PI.f64) #s(literal 2/3 binary64)) (*.f64 n #s(literal 2 binary64))))
(.f64 (pow.f64 (PI.f64) #s(literal 2/3 binary64)) (.f64 (cbrt.f64 (PI.f64)) (*.f64 #s(literal 2 binary64) n)))
(.f64 (pow.f64 (PI.f64) #s(literal 2/3 binary64)) (.f64 (cbrt.f64 (PI.f64)) (*.f64 n #s(literal 2 binary64))))
(.f64 (pow.f64 (PI.f64) #s(literal 2/3 binary64)) (.f64 (*.f64 (cbrt.f64 (PI.f64)) #s(literal 2 binary64)) n))
(.f64 (pow.f64 (PI.f64) #s(literal 2/3 binary64)) (.f64 (*.f64 (cbrt.f64 (PI.f64)) n) #s(literal 2 binary64)))
(.f64 (sqrt.f64 (PI.f64)) (.f64 (sqrt.f64 (PI.f64)) (*.f64 #s(literal 2 binary64) n)))
(.f64 (sqrt.f64 (PI.f64)) (.f64 (sqrt.f64 (PI.f64)) (*.f64 n #s(literal 2 binary64))))
(.f64 (sqrt.f64 (PI.f64)) (.f64 (*.f64 (sqrt.f64 (PI.f64)) #s(literal 2 binary64)) n))
(.f64 (sqrt.f64 (PI.f64)) (.f64 (*.f64 (sqrt.f64 (PI.f64)) n) #s(literal 2 binary64)))
(.f64 (.f64 #s(literal 2 binary64) n) (PI.f64))
(.f64 (.f64 n #s(literal 2 binary64)) (PI.f64))
(.f64 (.f64 n (pow.f64 (PI.f64) #s(literal 2/3 binary64))) (*.f64 (cbrt.f64 (PI.f64)) #s(literal 2 binary64)))
(.f64 (.f64 n (sqrt.f64 (PI.f64))) (*.f64 (sqrt.f64 (PI.f64)) #s(literal 2 binary64)))
(.f64 (.f64 #s(literal 2 binary64) (pow.f64 (PI.f64) #s(literal 2/3 binary64))) (*.f64 (cbrt.f64 (PI.f64)) n))
(.f64 (.f64 #s(literal 2 binary64) (sqrt.f64 (PI.f64))) (*.f64 (sqrt.f64 (PI.f64)) n))
(.f64 (exp.f64 (log.f64 (.f64 #s(literal 2 binary64) (PI.f64)))) (exp.f64 (log.f64 n)))
(.f64 (exp.f64 (log.f64 #s(literal 2 binary64))) (exp.f64 (log.f64 (.f64 (PI.f64) n))))
(.f64 (exp.f64 (log.f64 n)) (exp.f64 (log.f64 (.f64 #s(literal 2 binary64) (PI.f64)))))
(.f64 (exp.f64 (log.f64 (.f64 (PI.f64) n))) (exp.f64 (log.f64 #s(literal 2 binary64))))
(.f64 (.f64 #s(literal 2 binary64) (*.f64 n (pow.f64 (PI.f64) #s(literal 2/3 binary64)))) (cbrt.f64 (PI.f64)))
(.f64 (.f64 #s(literal 2 binary64) (*.f64 n (sqrt.f64 (PI.f64)))) (sqrt.f64 (PI.f64)))
(.f64 (.f64 n (*.f64 #s(literal 2 binary64) (pow.f64 (PI.f64) #s(literal 2/3 binary64)))) (cbrt.f64 (PI.f64)))
(.f64 (.f64 n (*.f64 #s(literal 2 binary64) (sqrt.f64 (PI.f64)))) (sqrt.f64 (PI.f64)))
(.f64 (.f64 (*.f64 #s(literal 2 binary64) n) #s(literal 1 binary64)) (PI.f64))
(.f64 (.f64 (*.f64 #s(literal 2 binary64) n) (cbrt.f64 (PI.f64))) (pow.f64 (PI.f64) #s(literal 2/3 binary64)))
(.f64 (.f64 (*.f64 #s(literal 2 binary64) n) (pow.f64 (PI.f64) #s(literal 2/3 binary64))) (cbrt.f64 (PI.f64)))
(.f64 (.f64 (*.f64 #s(literal 2 binary64) n) (sqrt.f64 (PI.f64))) (sqrt.f64 (PI.f64)))
(.f64 (.f64 (*.f64 n #s(literal 2 binary64)) #s(literal 1 binary64)) (PI.f64))
(.f64 (.f64 (*.f64 n #s(literal 2 binary64)) (cbrt.f64 (PI.f64))) (pow.f64 (PI.f64) #s(literal 2/3 binary64)))
(.f64 (.f64 (*.f64 n #s(literal 2 binary64)) (pow.f64 (PI.f64) #s(literal 2/3 binary64))) (cbrt.f64 (PI.f64)))
(.f64 (.f64 (*.f64 n #s(literal 2 binary64)) (sqrt.f64 (PI.f64))) (sqrt.f64 (PI.f64)))
(.f64 #s(literal 1 binary64) (.f64 (PI.f64) n))
(*.f64 (PI.f64) n)
(.f64 (PI.f64) (.f64 #s(literal 1 binary64) n))
(*.f64 n (PI.f64))
(.f64 (.f64 (PI.f64) n) #s(literal 1 binary64))
(.f64 (cbrt.f64 (PI.f64)) (.f64 (pow.f64 (PI.f64) #s(literal 2/3 binary64)) n))
(.f64 (cbrt.f64 (PI.f64)) (.f64 (cbrt.f64 (PI.f64)) (*.f64 (cbrt.f64 (PI.f64)) n)))
(.f64 (cbrt.f64 (PI.f64)) (.f64 (pow.f64 (PI.f64) #s(literal 1/6 binary64)) (*.f64 (sqrt.f64 (PI.f64)) n)))
(.f64 (pow.f64 (PI.f64) #s(literal 2/3 binary64)) (.f64 (cbrt.f64 (PI.f64)) n))
(.f64 (sqrt.f64 (PI.f64)) (.f64 (sqrt.f64 (PI.f64)) n))
(.f64 (pow.f64 (PI.f64) #s(literal 1/4 binary64)) (.f64 (pow.f64 (PI.f64) #s(literal 1/4 binary64)) (*.f64 (sqrt.f64 (PI.f64)) n)))
(.f64 (.f64 n (pow.f64 (PI.f64) #s(literal 2/3 binary64))) (cbrt.f64 (PI.f64)))
(.f64 (.f64 n (sqrt.f64 (PI.f64))) (sqrt.f64 (PI.f64)))
(.f64 (.f64 n (cbrt.f64 (PI.f64))) (pow.f64 (PI.f64) #s(literal 2/3 binary64)))
(.f64 (.f64 #s(literal 1 binary64) n) (PI.f64))
(.f64 (.f64 #s(literal 1 binary64) (*.f64 n (pow.f64 (PI.f64) #s(literal 2/3 binary64)))) (cbrt.f64 (PI.f64)))
(.f64 (.f64 #s(literal 1 binary64) (*.f64 n (sqrt.f64 (PI.f64)))) (sqrt.f64 (PI.f64)))
(.f64 (.f64 (*.f64 n (pow.f64 (PI.f64) #s(literal 2/3 binary64))) #s(literal 1 binary64)) (cbrt.f64 (PI.f64)))
(.f64 (.f64 (*.f64 n (pow.f64 (PI.f64) #s(literal 2/3 binary64))) (pow.f64 (pow.f64 (PI.f64) #s(literal 2/3 binary64)) #s(literal 1/3 binary64))) (pow.f64 (cbrt.f64 (PI.f64)) #s(literal 1/3 binary64)))
(.f64 (.f64 (*.f64 n (pow.f64 (PI.f64) #s(literal 2/3 binary64))) (pow.f64 (sqrt.f64 (PI.f64)) #s(literal 1/3 binary64))) (pow.f64 (sqrt.f64 (PI.f64)) #s(literal 1/3 binary64)))
(.f64 (.f64 (*.f64 n (sqrt.f64 (PI.f64))) #s(literal 1 binary64)) (sqrt.f64 (PI.f64)))
(.f64 (.f64 (*.f64 n (sqrt.f64 (PI.f64))) (cbrt.f64 (PI.f64))) (pow.f64 (PI.f64) #s(literal 1/6 binary64)))
(.f64 (.f64 (*.f64 n (sqrt.f64 (PI.f64))) (pow.f64 (PI.f64) #s(literal 1/4 binary64))) (pow.f64 (PI.f64) #s(literal 1/4 binary64)))
(exp.f64 (log.f64 (.f64 #s(literal 2 binary64) (.f64 (PI.f64) n))))
(.f64 #s(literal 1 binary64) (.f64 #s(literal 2 binary64) (*.f64 (PI.f64) n)))
(.f64 #s(literal 2 binary64) (.f64 (PI.f64) n))
(.f64 (PI.f64) (.f64 #s(literal 2 binary64) n))
(.f64 (PI.f64) (.f64 n #s(literal 2 binary64)))
(.f64 (PI.f64) (.f64 #s(literal 1 binary64) (*.f64 #s(literal 2 binary64) n)))
(.f64 (PI.f64) (.f64 #s(literal 1 binary64) (*.f64 n #s(literal 2 binary64))))
(.f64 (.f64 #s(literal 2 binary64) (PI.f64)) n)
(.f64 n (.f64 #s(literal 2 binary64) (PI.f64)))
(.f64 (.f64 (PI.f64) n) #s(literal 2 binary64))
(.f64 (.f64 #s(literal 2 binary64) (*.f64 (PI.f64) n)) #s(literal 1 binary64))
(.f64 (cbrt.f64 (PI.f64)) (.f64 (pow.f64 (PI.f64) #s(literal 2/3 binary64)) (*.f64 #s(literal 2 binary64) n)))
(.f64 (cbrt.f64 (PI.f64)) (.f64 (pow.f64 (PI.f64) #s(literal 2/3 binary64)) (*.f64 n #s(literal 2 binary64))))
(.f64 (pow.f64 (PI.f64) #s(literal 2/3 binary64)) (.f64 (cbrt.f64 (PI.f64)) (*.f64 #s(literal 2 binary64) n)))
(.f64 (pow.f64 (PI.f64) #s(literal 2/3 binary64)) (.f64 (cbrt.f64 (PI.f64)) (*.f64 n #s(literal 2 binary64))))
(.f64 (pow.f64 (PI.f64) #s(literal 2/3 binary64)) (.f64 (*.f64 (cbrt.f64 (PI.f64)) #s(literal 2 binary64)) n))
(.f64 (pow.f64 (PI.f64) #s(literal 2/3 binary64)) (.f64 (*.f64 (cbrt.f64 (PI.f64)) n) #s(literal 2 binary64)))
(.f64 (sqrt.f64 (PI.f64)) (.f64 (sqrt.f64 (PI.f64)) (*.f64 #s(literal 2 binary64) n)))
(.f64 (sqrt.f64 (PI.f64)) (.f64 (sqrt.f64 (PI.f64)) (*.f64 n #s(literal 2 binary64))))
(.f64 (sqrt.f64 (PI.f64)) (.f64 (*.f64 (sqrt.f64 (PI.f64)) #s(literal 2 binary64)) n))
(.f64 (sqrt.f64 (PI.f64)) (.f64 (*.f64 (sqrt.f64 (PI.f64)) n) #s(literal 2 binary64)))
(.f64 (.f64 #s(literal 2 binary64) n) (PI.f64))
(.f64 (.f64 n #s(literal 2 binary64)) (PI.f64))
(.f64 (.f64 n (pow.f64 (PI.f64) #s(literal 2/3 binary64))) (*.f64 (cbrt.f64 (PI.f64)) #s(literal 2 binary64)))
(.f64 (.f64 n (sqrt.f64 (PI.f64))) (*.f64 (sqrt.f64 (PI.f64)) #s(literal 2 binary64)))
(.f64 (.f64 #s(literal 2 binary64) (pow.f64 (PI.f64) #s(literal 2/3 binary64))) (*.f64 (cbrt.f64 (PI.f64)) n))
(.f64 (.f64 #s(literal 2 binary64) (sqrt.f64 (PI.f64))) (*.f64 (sqrt.f64 (PI.f64)) n))
(.f64 (exp.f64 (log.f64 (.f64 #s(literal 2 binary64) (PI.f64)))) (exp.f64 (log.f64 n)))
(.f64 (exp.f64 (log.f64 #s(literal 2 binary64))) (exp.f64 (log.f64 (.f64 (PI.f64) n))))
(.f64 (exp.f64 (log.f64 n)) (exp.f64 (log.f64 (.f64 #s(literal 2 binary64) (PI.f64)))))
(.f64 (exp.f64 (log.f64 (.f64 (PI.f64) n))) (exp.f64 (log.f64 #s(literal 2 binary64))))
(.f64 (.f64 #s(literal 2 binary64) (*.f64 n (pow.f64 (PI.f64) #s(literal 2/3 binary64)))) (cbrt.f64 (PI.f64)))
(.f64 (.f64 #s(literal 2 binary64) (*.f64 n (sqrt.f64 (PI.f64)))) (sqrt.f64 (PI.f64)))
(.f64 (.f64 n (*.f64 #s(literal 2 binary64) (pow.f64 (PI.f64) #s(literal 2/3 binary64)))) (cbrt.f64 (PI.f64)))
(.f64 (.f64 n (*.f64 #s(literal 2 binary64) (sqrt.f64 (PI.f64)))) (sqrt.f64 (PI.f64)))
(.f64 (.f64 (*.f64 #s(literal 2 binary64) n) #s(literal 1 binary64)) (PI.f64))
(.f64 (.f64 (*.f64 #s(literal 2 binary64) n) (cbrt.f64 (PI.f64))) (pow.f64 (PI.f64) #s(literal 2/3 binary64)))
(.f64 (.f64 (*.f64 #s(literal 2 binary64) n) (pow.f64 (PI.f64) #s(literal 2/3 binary64))) (cbrt.f64 (PI.f64)))
(.f64 (.f64 (*.f64 #s(literal 2 binary64) n) (sqrt.f64 (PI.f64))) (sqrt.f64 (PI.f64)))
(.f64 (.f64 (*.f64 n #s(literal 2 binary64)) #s(literal 1 binary64)) (PI.f64))
(.f64 (.f64 (*.f64 n #s(literal 2 binary64)) (cbrt.f64 (PI.f64))) (pow.f64 (PI.f64) #s(literal 2/3 binary64)))
(.f64 (.f64 (*.f64 n #s(literal 2 binary64)) (pow.f64 (PI.f64) #s(literal 2/3 binary64))) (cbrt.f64 (PI.f64)))
(.f64 (.f64 (*.f64 n #s(literal 2 binary64)) (sqrt.f64 (PI.f64))) (sqrt.f64 (PI.f64)))
(PI.f64)
(log.f64 (exp.f64 (PI.f64)))
(+.f64 (+.f64 #s(literal 1 binary64) (PI.f64)) #s(literal -1 binary64))
(exp.f64 (log.f64 (PI.f64)))
(exp.f64 (.f64 (.f64 #s(literal 1/3 binary64) (log.f64 (PI.f64))) #s(literal 3 binary64)))
(exp.f64 (.f64 (log.f64 (.f64 (PI.f64) (*.f64 (PI.f64) (PI.f64)))) #s(literal 1/3 binary64)))
(exp.f64 (.f64 (.f64 #s(literal 1/2 binary64) (log.f64 (PI.f64))) #s(literal 2 binary64)))
(fabs.f64 (PI.f64))
(-.f64 (+.f64 #s(literal 1 binary64) (PI.f64)) #s(literal 1 binary64))
(sqrt.f64 (*.f64 (PI.f64) (PI.f64)))
(cbrt.f64 (.f64 (PI.f64) (.f64 (PI.f64) (PI.f64))))
(expm1.f64 (log1p.f64 (PI.f64)))
(/.f64 (-.f64 (pow.f64 (+.f64 #s(literal 1 binary64) (PI.f64)) #s(literal 3 binary64)) #s(literal 1 binary64)) (+.f64 (.f64 (+.f64 #s(literal 1 binary64) (PI.f64)) (+.f64 #s(literal 1 binary64) (PI.f64))) (+.f64 #s(literal 1 binary64) (.f64 (+.f64 #s(literal 1 binary64) (PI.f64)) #s(literal 1 binary64)))))
(/.f64 (-.f64 (*.f64 (+.f64 #s(literal 1 binary64) (PI.f64)) (+.f64 #s(literal 1 binary64) (PI.f64))) #s(literal 1 binary64)) (+.f64 (+.f64 #s(literal 1 binary64) (PI.f64)) #s(literal 1 binary64)))
(log1p.f64 (expm1.f64 (PI.f64)))
(pow.f64 (PI.f64) #s(literal 1 binary64))
(pow.f64 (cbrt.f64 (PI.f64)) #s(literal 3 binary64))
(pow.f64 (*.f64 (PI.f64) (PI.f64)) #s(literal 1/2 binary64))
(pow.f64 (.f64 (PI.f64) (.f64 (PI.f64) (PI.f64))) #s(literal 1/3 binary64))
(pow.f64 (sqrt.f64 (PI.f64)) #s(literal 2 binary64))
(pow.f64 (E.f64) (log.f64 (PI.f64)))
(*.f64 #s(literal 1 binary64) (PI.f64))
(*.f64 (PI.f64) #s(literal 1 binary64))
(*.f64 (PI.f64) (log.f64 (E.f64)))
(*.f64 (cbrt.f64 (PI.f64)) (pow.f64 (PI.f64) #s(literal 2/3 binary64)))
(*.f64 (cbrt.f64 (PI.f64)) (log.f64 (exp.f64 (pow.f64 (PI.f64) #s(literal 2/3 binary64)))))
(*.f64 (cbrt.f64 (PI.f64)) (sqrt.f64 (pow.f64 (PI.f64) #s(literal 4/3 binary64))))
(.f64 (cbrt.f64 (PI.f64)) (.f64 (pow.f64 (PI.f64) #s(literal 2/3 binary64)) #s(literal 1 binary64)))
(.f64 (cbrt.f64 (PI.f64)) (.f64 (pow.f64 (PI.f64) #s(literal 1/6 binary64)) (sqrt.f64 (PI.f64))))
(*.f64 (pow.f64 (PI.f64) #s(literal 2/3 binary64)) (cbrt.f64 (PI.f64)))
(*.f64 (pow.f64 (PI.f64) #s(literal 2/3 binary64)) (pow.f64 (pow.f64 (PI.f64) #s(literal 1/6 binary64)) #s(literal 2 binary64)))
(*.f64 (sqrt.f64 (PI.f64)) (sqrt.f64 (PI.f64)))
(*.f64 (sqrt.f64 (PI.f64)) (log.f64 (exp.f64 (sqrt.f64 (PI.f64)))))
(.f64 (pow.f64 (pow.f64 (PI.f64) #s(literal 2/3 binary64)) #s(literal 1/3 binary64)) (.f64 (pow.f64 (cbrt.f64 (PI.f64)) #s(literal 1/3 binary64)) (pow.f64 (PI.f64) #s(literal 2/3 binary64))))
(.f64 (pow.f64 (sqrt.f64 (PI.f64)) #s(literal 1/3 binary64)) (.f64 (pow.f64 (sqrt.f64 (PI.f64)) #s(literal 1/3 binary64)) (pow.f64 (PI.f64) #s(literal 2/3 binary64))))
(*.f64 (pow.f64 (PI.f64) #s(literal 1/4 binary64)) (sqrt.f64 (pow.f64 (PI.f64) #s(literal 3/2 binary64))))
(.f64 (pow.f64 (PI.f64) #s(literal 1/4 binary64)) (.f64 (pow.f64 (PI.f64) #s(literal 1/4 binary64)) (sqrt.f64 (PI.f64))))
(*.f64 (pow.f64 (pow.f64 (pow.f64 (PI.f64) #s(literal 2/3 binary64)) #s(literal 1/3 binary64)) #s(literal 3 binary64)) (pow.f64 (pow.f64 (cbrt.f64 (PI.f64)) #s(literal 1/3 binary64)) #s(literal 3 binary64)))
(*.f64 (pow.f64 (pow.f64 (sqrt.f64 (PI.f64)) #s(literal 1/3 binary64)) #s(literal 3 binary64)) (pow.f64 (pow.f64 (sqrt.f64 (PI.f64)) #s(literal 1/3 binary64)) #s(literal 3 binary64)))
(*.f64 (pow.f64 (pow.f64 (PI.f64) #s(literal 3/2 binary64)) #s(literal 1/3 binary64)) (pow.f64 (pow.f64 (PI.f64) #s(literal 3/2 binary64)) #s(literal 1/3 binary64)))
(.f64 (pow.f64 (.f64 (PI.f64) (*.f64 (PI.f64) (pow.f64 (PI.f64) #s(literal 2/3 binary64)))) #s(literal 1/3 binary64)) (pow.f64 (cbrt.f64 (PI.f64)) #s(literal 1/3 binary64)))
(*.f64 (pow.f64 (pow.f64 (PI.f64) #s(literal 5/2 binary64)) #s(literal 1/3 binary64)) (pow.f64 (sqrt.f64 (PI.f64)) #s(literal 1/3 binary64)))
(.f64 (.f64 (sqrt.f64 (PI.f64)) (cbrt.f64 (PI.f64))) (pow.f64 (PI.f64) #s(literal 1/6 binary64)))
(.f64 (exp.f64 (.f64 #s(literal 2 binary64) (.f64 #s(literal 1/3 binary64) (log.f64 (PI.f64))))) (exp.f64 (.f64 #s(literal 1/3 binary64) (log.f64 (PI.f64)))))
(.f64 (exp.f64 (.f64 #s(literal 1/2 binary64) (log.f64 (PI.f64)))) (exp.f64 (*.f64 #s(literal 1/2 binary64) (log.f64 (PI.f64)))))
(*.f64 (cbrt.f64 (pow.f64 (PI.f64) #s(literal 3/2 binary64))) (cbrt.f64 (pow.f64 (PI.f64) #s(literal 3/2 binary64))))
(.f64 (cbrt.f64 (.f64 (PI.f64) (*.f64 (PI.f64) (pow.f64 (PI.f64) #s(literal 2/3 binary64))))) (pow.f64 (cbrt.f64 (PI.f64)) #s(literal 1/3 binary64)))
(*.f64 (cbrt.f64 (pow.f64 (PI.f64) #s(literal 5/2 binary64))) (pow.f64 (sqrt.f64 (PI.f64)) #s(literal 1/3 binary64)))
(*.f64 (sqrt.f64 (pow.f64 (PI.f64) #s(literal 3/2 binary64))) (pow.f64 (PI.f64) #s(literal 1/4 binary64)))
(*.f64 (sqrt.f64 (pow.f64 (PI.f64) #s(literal 4/3 binary64))) (cbrt.f64 (PI.f64)))
(.f64 (sqrt.f64 (.f64 (PI.f64) (pow.f64 (PI.f64) #s(literal 2/3 binary64)))) (pow.f64 (PI.f64) #s(literal 1/6 binary64)))
(.f64 (.f64 (pow.f64 (sqrt.f64 (PI.f64)) #s(literal 1/3 binary64)) (cbrt.f64 (PI.f64))) (*.f64 (pow.f64 (sqrt.f64 (PI.f64)) #s(literal 1/3 binary64)) (cbrt.f64 (PI.f64))))
(.f64 (.f64 (cbrt.f64 (PI.f64)) (pow.f64 (sqrt.f64 (PI.f64)) #s(literal 1/3 binary64))) (*.f64 (cbrt.f64 (PI.f64)) (pow.f64 (sqrt.f64 (PI.f64)) #s(literal 1/3 binary64))))
(.f64 (.f64 (sqrt.f64 (PI.f64)) (pow.f64 (PI.f64) #s(literal 1/4 binary64))) (pow.f64 (PI.f64) #s(literal 1/4 binary64)))
(.f64 (.f64 (pow.f64 (PI.f64) #s(literal 2/3 binary64)) #s(literal 1 binary64)) (cbrt.f64 (PI.f64)))
(.f64 (.f64 (pow.f64 (PI.f64) #s(literal 2/3 binary64)) (pow.f64 (pow.f64 (PI.f64) #s(literal 2/3 binary64)) #s(literal 1/3 binary64))) (pow.f64 (cbrt.f64 (PI.f64)) #s(literal 1/3 binary64)))
(.f64 (.f64 (pow.f64 (PI.f64) #s(literal 2/3 binary64)) (pow.f64 (sqrt.f64 (PI.f64)) #s(literal 1/3 binary64))) (pow.f64 (sqrt.f64 (PI.f64)) #s(literal 1/3 binary64)))

simplify256.0ms (1.9%)

Algorithm

1×	egg-herbie

Rules

5256×	`-lowering-.f32`
5256×	`-lowering-.f64`
2382×	`+-lowering-+.f64`
2382×	`+-lowering-+.f32`
1472×	`associate-r`

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	139	2132
1	385	2104
2	1189	1816
3	4175	1732
4	7740	1732
0	8111	1732

Stop Event

1×	iter limit
1×	node limit

Counts

156 → 156

Calls

Call 1

Inputs
(* (sqrt (/ (* n (PI)) k)) (sqrt 2))
(/ (+ (* -1/2 (* (sqrt (* (pow k 3) (* n (PI)))) (* (log (* 2 (* n (PI)))) (sqrt 2)))) (* (sqrt (* k (* n (PI)))) (sqrt 2))) k)
(/ (+ (* 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)
(/ (+ (* 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)
(* (sqrt (/ 1 k)) (exp (* 1/2 (* (log (* 2 (* n (PI)))) (- 1 k)))))
(* (sqrt (/ 1 k)) (exp (* 1/2 (* (log (* 2 (* n (PI)))) (- 1 k)))))
(* (sqrt (/ 1 k)) (exp (* 1/2 (* (log (* 2 (* n (PI)))) (- 1 k)))))
(* (sqrt (/ 1 k)) (exp (* 1/2 (* (log (* 2 (* n (PI)))) (- 1 k)))))
(* (sqrt (/ 1 k)) (exp (* 1/2 (* (log (* 2 (* n (PI)))) (+ 1 (* -1 k))))))
(* (sqrt (/ 1 k)) (exp (* 1/2 (* (log (* 2 (* n (PI)))) (+ 1 (* -1 k))))))
(* (sqrt (/ 1 k)) (exp (* 1/2 (* (log (* 2 (* n (PI)))) (+ 1 (* -1 k))))))
(* (sqrt (/ 1 k)) (exp (* 1/2 (* (log (* 2 (* n (PI)))) (+ 1 (* -1 k))))))
(* (sqrt (/ 1 k)) (exp (* 1/2 (* (+ (log n) (log (* 2 (PI)))) (- 1 k)))))
(* (sqrt (/ 1 k)) (exp (* 1/2 (* (+ (log n) (log (* 2 (PI)))) (- 1 k)))))
(* (sqrt (/ 1 k)) (exp (* 1/2 (* (+ (log n) (log (* 2 (PI)))) (- 1 k)))))
(* (sqrt (/ 1 k)) (exp (* 1/2 (* (+ (log n) (log (* 2 (PI)))) (- 1 k)))))
(* (sqrt (/ 1 k)) (exp (* 1/2 (* (+ (log (* 2 (PI))) (* -1 (log (/ 1 n)))) (- 1 k)))))
(* (sqrt (/ 1 k)) (exp (* 1/2 (* (+ (log (* 2 (PI))) (* -1 (log (/ 1 n)))) (- 1 k)))))
(* (sqrt (/ 1 k)) (exp (* 1/2 (* (+ (log (* 2 (PI))) (* -1 (log (/ 1 n)))) (- 1 k)))))
(* (sqrt (/ 1 k)) (exp (* 1/2 (* (+ (log (* 2 (PI))) (* -1 (log (/ 1 n)))) (- 1 k)))))
(* (sqrt (/ 1 k)) (exp (* 1/2 (* (+ (log (* -2 (PI))) (* -1 (log (/ -1 n)))) (- 1 k)))))
(* (sqrt (/ 1 k)) (exp (* 1/2 (* (+ (log (* -2 (PI))) (* -1 (log (/ -1 n)))) (- 1 k)))))
(* (sqrt (/ 1 k)) (exp (* 1/2 (* (+ (log (* -2 (PI))) (* -1 (log (/ -1 n)))) (- 1 k)))))
(* (sqrt (/ 1 k)) (exp (* 1/2 (* (+ (log (* -2 (PI))) (* -1 (log (/ -1 n)))) (- 1 k)))))
(sqrt (/ 1 k))
(sqrt (/ 1 k))
(sqrt (/ 1 k))
(sqrt (/ 1 k))
(sqrt (/ 1 k))
(sqrt (/ 1 k))
(sqrt (/ 1 k))
(sqrt (/ 1 k))
(sqrt (/ 1 k))
(sqrt (/ 1 k))
(sqrt (/ 1 k))
(sqrt (/ 1 k))
(sqrt k)
(sqrt k)
(sqrt k)
(sqrt k)
(sqrt k)
(sqrt k)
(sqrt k)
(sqrt k)
(* -1 (* (sqrt k) (pow (sqrt -1) 2)))
(* -1 (* (sqrt k) (pow (sqrt -1) 2)))
(* -1 (* (sqrt k) (pow (sqrt -1) 2)))
(* -1 (* (sqrt k) (pow (sqrt -1) 2)))
(exp (* 1/2 (* (+ (log n) (log (* 2 (PI)))) (- 1 k))))
(exp (* 1/2 (* (+ (log n) (log (* 2 (PI)))) (- 1 k))))
(exp (* 1/2 (* (+ (log n) (log (* 2 (PI)))) (- 1 k))))
(exp (* 1/2 (* (+ (log n) (log (* 2 (PI)))) (- 1 k))))
(exp (* 1/2 (* (+ (log (* 2 (PI))) (* -1 (log (/ 1 n)))) (- 1 k))))
(exp (* 1/2 (* (+ (log (* 2 (PI))) (* -1 (log (/ 1 n)))) (- 1 k))))
(exp (* 1/2 (* (+ (log (* 2 (PI))) (* -1 (log (/ 1 n)))) (- 1 k))))
(exp (* 1/2 (* (+ (log (* 2 (PI))) (* -1 (log (/ 1 n)))) (- 1 k))))
(exp (* 1/2 (* (+ (log (* -2 (PI))) (* -1 (log (/ -1 n)))) (- 1 k))))
(exp (* 1/2 (* (+ (log (* -2 (PI))) (* -1 (log (/ -1 n)))) (- 1 k))))
(exp (* 1/2 (* (+ (log (* -2 (PI))) (* -1 (log (/ -1 n)))) (- 1 k))))
(exp (* 1/2 (* (+ (log (* -2 (PI))) (* -1 (log (/ -1 n)))) (- 1 k))))
(* (sqrt (* n (PI))) (sqrt 2))
(+ (* -1/2 (* (* k (* (log (* 2 (* n (PI)))) (sqrt 2))) (sqrt (* n (PI))))) (* (sqrt (* n (PI))) (sqrt 2)))
(+ (* 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)))
(+ (* 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)))
(exp (* 1/2 (* (log (* 2 (* n (PI)))) (- 1 k))))
(exp (* 1/2 (* (log (* 2 (* n (PI)))) (- 1 k))))
(exp (* 1/2 (* (log (* 2 (* n (PI)))) (- 1 k))))
(exp (* 1/2 (* (log (* 2 (* n (PI)))) (- 1 k))))
(exp (* 1/2 (* (log (* 2 (* n (PI)))) (+ 1 (* -1 k)))))
(exp (* 1/2 (* (log (* 2 (* n (PI)))) (+ 1 (* -1 k)))))
(exp (* 1/2 (* (log (* 2 (* n (PI)))) (+ 1 (* -1 k)))))
(exp (* 1/2 (* (log (* 2 (* n (PI)))) (+ 1 (* -1 k)))))
(* (sqrt (/ 1 k)) (exp (* (+ (log n) (log (* 2 (PI)))) (- 1/2 (* 1/2 k)))))
(* (sqrt (/ 1 k)) (exp (* (+ (log n) (log (* 2 (PI)))) (- 1/2 (* 1/2 k)))))
(* (sqrt (/ 1 k)) (exp (* (+ (log n) (log (* 2 (PI)))) (- 1/2 (* 1/2 k)))))
(* (sqrt (/ 1 k)) (exp (* (+ (log n) (log (* 2 (PI)))) (- 1/2 (* 1/2 k)))))
(* (sqrt (/ 1 k)) (exp (* (+ (log (* 2 (PI))) (* -1 (log (/ 1 n)))) (- 1/2 (* 1/2 k)))))
(* (sqrt (/ 1 k)) (exp (* (+ (log (* 2 (PI))) (* -1 (log (/ 1 n)))) (- 1/2 (* 1/2 k)))))
(* (sqrt (/ 1 k)) (exp (* (+ (log (* 2 (PI))) (* -1 (log (/ 1 n)))) (- 1/2 (* 1/2 k)))))
(* (sqrt (/ 1 k)) (exp (* (+ (log (* 2 (PI))) (* -1 (log (/ 1 n)))) (- 1/2 (* 1/2 k)))))
(* (sqrt (/ 1 k)) (exp (* (+ (log (* -2 (PI))) (* -1 (log (/ -1 n)))) (- 1/2 (* 1/2 k)))))
(* (sqrt (/ 1 k)) (exp (* (+ (log (* -2 (PI))) (* -1 (log (/ -1 n)))) (- 1/2 (* 1/2 k)))))
(* (sqrt (/ 1 k)) (exp (* (+ (log (* -2 (PI))) (* -1 (log (/ -1 n)))) (- 1/2 (* 1/2 k)))))
(* (sqrt (/ 1 k)) (exp (* (+ (log (* -2 (PI))) (* -1 (log (/ -1 n)))) (- 1/2 (* 1/2 k)))))
(* (sqrt (/ (* n (PI)) k)) (sqrt 2))
(/ (+ (* -1/2 (* (sqrt (* (pow k 3) (* n (PI)))) (* (log (* 2 (* n (PI)))) (sqrt 2)))) (* (sqrt (* k (* n (PI)))) (sqrt 2))) k)
(/ (+ (* 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)
(/ (+ (* 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)
(* (sqrt (/ 1 k)) (exp (* (log (* 2 (* n (PI)))) (- 1/2 (* 1/2 k)))))
(* (sqrt (/ 1 k)) (exp (* (log (* 2 (* n (PI)))) (- 1/2 (* 1/2 k)))))
(* (sqrt (/ 1 k)) (exp (* (log (* 2 (* n (PI)))) (- 1/2 (* 1/2 k)))))
(* (sqrt (/ 1 k)) (exp (* (log (* 2 (* n (PI)))) (- 1/2 (* 1/2 k)))))
(* (sqrt (/ 1 k)) (exp (* (log (* 2 (* n (PI)))) (+ 1/2 (* -1/2 k)))))
(* (sqrt (/ 1 k)) (exp (* (log (* 2 (* n (PI)))) (+ 1/2 (* -1/2 k)))))
(* (sqrt (/ 1 k)) (exp (* (log (* 2 (* n (PI)))) (+ 1/2 (* -1/2 k)))))
(* (sqrt (/ 1 k)) (exp (* (log (* 2 (* n (PI)))) (+ 1/2 (* -1/2 k)))))
(exp (* (+ (log n) (log (* 2 (PI)))) (- 1/2 (* 1/2 k))))
(exp (* (+ (log n) (log (* 2 (PI)))) (- 1/2 (* 1/2 k))))
(exp (* (+ (log n) (log (* 2 (PI)))) (- 1/2 (* 1/2 k))))
(exp (* (+ (log n) (log (* 2 (PI)))) (- 1/2 (* 1/2 k))))
(exp (* (+ (log (* 2 (PI))) (* -1 (log (/ 1 n)))) (- 1/2 (* 1/2 k))))
(exp (* (+ (log (* 2 (PI))) (* -1 (log (/ 1 n)))) (- 1/2 (* 1/2 k))))
(exp (* (+ (log (* 2 (PI))) (* -1 (log (/ 1 n)))) (- 1/2 (* 1/2 k))))
(exp (* (+ (log (* 2 (PI))) (* -1 (log (/ 1 n)))) (- 1/2 (* 1/2 k))))
(exp (* (+ (log (* -2 (PI))) (* -1 (log (/ -1 n)))) (- 1/2 (* 1/2 k))))
(exp (* (+ (log (* -2 (PI))) (* -1 (log (/ -1 n)))) (- 1/2 (* 1/2 k))))
(exp (* (+ (log (* -2 (PI))) (* -1 (log (/ -1 n)))) (- 1/2 (* 1/2 k))))
(exp (* (+ (log (* -2 (PI))) (* -1 (log (/ -1 n)))) (- 1/2 (* 1/2 k))))
(* (sqrt (* n (PI))) (sqrt 2))
(+ (* -1/2 (* (* k (* (log (* 2 (* n (PI)))) (sqrt 2))) (sqrt (* n (PI))))) (* (sqrt (* n (PI))) (sqrt 2)))
(+ (* 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)))
(+ (* 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)))
(exp (* (log (* 2 (* n (PI)))) (- 1/2 (* 1/2 k))))
(exp (* (log (* 2 (* n (PI)))) (- 1/2 (* 1/2 k))))
(exp (* (log (* 2 (* n (PI)))) (- 1/2 (* 1/2 k))))
(exp (* (log (* 2 (* n (PI)))) (- 1/2 (* 1/2 k))))
(exp (* (log (* 2 (* n (PI)))) (+ 1/2 (* -1/2 k))))
(exp (* (log (* 2 (* n (PI)))) (+ 1/2 (* -1/2 k))))
(exp (* (log (* 2 (* n (PI)))) (+ 1/2 (* -1/2 k))))
(exp (* (log (* 2 (* n (PI)))) (+ 1/2 (* -1/2 k))))
(* 2 (* n (PI)))
(* 2 (* n (PI)))
(* 2 (* n (PI)))
(* 2 (* n (PI)))
(* 2 (* n (PI)))
(* 2 (* n (PI)))
(* 2 (* n (PI)))
(* 2 (* n (PI)))
(* 2 (* n (PI)))
(* 2 (* n (PI)))
(* 2 (* n (PI)))
(* 2 (* n (PI)))
(* n (PI))
(* n (PI))
(* n (PI))
(* n (PI))
(* n (PI))
(* n (PI))
(* n (PI))
(* n (PI))
(* n (PI))
(* n (PI))
(* n (PI))
(* n (PI))
(* 2 (* n (PI)))
(* 2 (* n (PI)))
(* 2 (* n (PI)))
(* 2 (* n (PI)))
(* 2 (* n (PI)))
(* 2 (* n (PI)))
(* 2 (* n (PI)))
(* 2 (* n (PI)))
(* 2 (* n (PI)))
(* 2 (* n (PI)))
(* 2 (* n (PI)))
(* 2 (* n (PI)))

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

eval141.0ms (1%)

Compiler: Compiled 21499 to 2036 computations (90.5% saved)

prune115.0ms (0.9%)

Pruning

19 alts after pruning (17 fresh and 2 done)

	Pruned	Kept	Total
New	972	17	989
Fresh	0	0	0
Picked	0	2	2
Done	0	0	0
Total	972	19	991

Accuracy

100.0%

Counts

991 → 19

Alt Table

Click to see full alt table

Status	Accuracy	Program
▶	99.1%	(/.f64 (pow.f64 (pow.f64 (.f64 #s(literal 2 binary64) (.f64 (PI.f64) n)) (-.f64 #s(literal 1/4 binary64) (*.f64 k #s(literal 1/4 binary64)))) #s(literal 2 binary64)) (sqrt.f64 k))
	99.2%	(/.f64 (pow.f64 (.f64 (PI.f64) (/.f64 #s(literal -2 binary64) (/.f64 #s(literal -1 binary64) n))) (+.f64 #s(literal 1/2 binary64) (.f64 k #s(literal -1/2 binary64)))) (sqrt.f64 k))
	80.3%	(/.f64 (pow.f64 (.f64 #s(literal 4 binary64) (.f64 (.f64 (PI.f64) n) (.f64 (PI.f64) n))) (-.f64 #s(literal 1/4 binary64) (*.f64 k #s(literal 1/4 binary64)))) (sqrt.f64 k))
	99.1%	(/.f64 (pow.f64 (.f64 #s(literal 2 binary64) (.f64 (PI.f64) n)) (-.f64 #s(literal 1/2 binary64) (/.f64 k #s(literal 2 binary64)))) (pow.f64 (pow.f64 k #s(literal 1/4 binary64)) #s(literal 2 binary64)))
✓	99.3%	(/.f64 (pow.f64 (.f64 #s(literal 2 binary64) (.f64 (PI.f64) n)) (-.f64 #s(literal 1/2 binary64) (/.f64 k #s(literal 2 binary64)))) (sqrt.f64 k))
▶	99.3%	(/.f64 (pow.f64 k #s(literal -1/2 binary64)) (pow.f64 (.f64 #s(literal 2 binary64) (.f64 (PI.f64) n)) (+.f64 (/.f64 k #s(literal 2 binary64)) #s(literal -1/2 binary64))))
	99.2%	(/.f64 (/.f64 #s(literal 1 binary64) (pow.f64 (.f64 #s(literal 2 binary64) (.f64 (PI.f64) n)) (+.f64 (/.f64 k #s(literal 2 binary64)) #s(literal -1/2 binary64)))) (sqrt.f64 k))
	99.0%	(/.f64 (.f64 (pow.f64 (.f64 #s(literal 2 binary64) (.f64 (PI.f64) n)) (/.f64 k #s(literal -2 binary64))) (sqrt.f64 (.f64 #s(literal 2 binary64) (*.f64 (PI.f64) n)))) (sqrt.f64 k))
	73.6%	(/.f64 (.f64 (pow.f64 (.f64 #s(literal 2 binary64) (PI.f64)) (+.f64 #s(literal 1/2 binary64) (/.f64 k #s(literal -2 binary64)))) (pow.f64 n (+.f64 #s(literal 1/2 binary64) (/.f64 k #s(literal -2 binary64))))) (sqrt.f64 k))
	44.0%	(/.f64 (.f64 (sqrt.f64 #s(literal 2 binary64)) (sqrt.f64 (.f64 n (PI.f64)))) (sqrt.f64 k))
▶	98.6%	(/.f64 (sqrt.f64 (.f64 #s(literal 2 binary64) (.f64 (PI.f64) n))) (pow.f64 (.f64 (pow.f64 (.f64 #s(literal 2 binary64) (*.f64 (PI.f64) n)) k) k) #s(literal 1/2 binary64)))
	96.3%	(/.f64 (exp.f64 (/.f64 (log.f64 (.f64 #s(literal 2 binary64) (.f64 (PI.f64) n))) (/.f64 #s(literal 2 binary64) (-.f64 #s(literal 1 binary64) k)))) (sqrt.f64 k))
	99.1%	(.f64 (pow.f64 (pow.f64 k #s(literal -1/4 binary64)) #s(literal 2 binary64)) (pow.f64 (.f64 (*.f64 #s(literal 2 binary64) (PI.f64)) n) (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 2 binary64))))
	73.7%	(.f64 (pow.f64 n (+.f64 #s(literal 1/2 binary64) (/.f64 k #s(literal -2 binary64)))) (.f64 (pow.f64 (*.f64 #s(literal 2 binary64) (PI.f64)) (+.f64 #s(literal 1/2 binary64) (/.f64 k #s(literal -2 binary64)))) (pow.f64 k #s(literal -1/2 binary64))))
✓	99.2%	(.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) (pow.f64 (.f64 (*.f64 #s(literal 2 binary64) (PI.f64)) n) (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 2 binary64))))
▶	99.2%	(.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) (pow.f64 (.f64 (PI.f64) (/.f64 #s(literal -2 binary64) (/.f64 #s(literal -1 binary64) n))) (+.f64 #s(literal 1/2 binary64) (*.f64 k #s(literal -1/2 binary64)))))
▶	37.1%	(.f64 (sqrt.f64 (/.f64 (.f64 n (PI.f64)) k)) (sqrt.f64 #s(literal 2 binary64)))
	99.2%	(.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))))
	96.2%	(.f64 (exp.f64 (.f64 (log.f64 k) #s(literal -1/2 binary64))) (pow.f64 (.f64 (.f64 #s(literal 2 binary64) (PI.f64)) n) (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 2 binary64))))

Compiler

Compiled 660 to 479 computations (27.4% saved)

simplify54.0ms (0.4%)

Algorithm

1×	egg-herbie

Localize:

Found 20 expressions of interest:

New	Metric	Score	Program
✓	cost-diff	0	(.f64 #s(literal 2 binary64) (.f64 (PI.f64) n))
✓	cost-diff	0	(sqrt.f64 (.f64 #s(literal 2 binary64) (.f64 (PI.f64) n)))
✓	cost-diff	64	(pow.f64 (.f64 (pow.f64 (.f64 #s(literal 2 binary64) (*.f64 (PI.f64) n)) k) k) #s(literal 1/2 binary64))
✓	cost-diff	64	(/.f64 (sqrt.f64 (.f64 #s(literal 2 binary64) (.f64 (PI.f64) n))) (pow.f64 (.f64 (pow.f64 (.f64 #s(literal 2 binary64) (*.f64 (PI.f64) n)) k) k) #s(literal 1/2 binary64)))
✓	cost-diff	0	(.f64 #s(literal 2 binary64) (.f64 (PI.f64) n))
✓	cost-diff	0	(pow.f64 (.f64 #s(literal 2 binary64) (.f64 (PI.f64) n)) (-.f64 #s(literal 1/4 binary64) (*.f64 k #s(literal 1/4 binary64))))
✓	cost-diff	6464	(pow.f64 (pow.f64 (.f64 #s(literal 2 binary64) (.f64 (PI.f64) n)) (-.f64 #s(literal 1/4 binary64) (*.f64 k #s(literal 1/4 binary64)))) #s(literal 2 binary64))
✓	cost-diff	6464	(/.f64 (pow.f64 (pow.f64 (.f64 #s(literal 2 binary64) (.f64 (PI.f64) n)) (-.f64 #s(literal 1/4 binary64) (*.f64 k #s(literal 1/4 binary64)))) #s(literal 2 binary64)) (sqrt.f64 k))
✓	cost-diff	128	(/.f64 #s(literal -2 binary64) (/.f64 #s(literal -1 binary64) n))
✓	cost-diff	128	(*.f64 (PI.f64) (/.f64 #s(literal -2 binary64) (/.f64 #s(literal -1 binary64) n)))
✓	cost-diff	128	(pow.f64 (.f64 (PI.f64) (/.f64 #s(literal -2 binary64) (/.f64 #s(literal -1 binary64) n))) (+.f64 #s(literal 1/2 binary64) (.f64 k #s(literal -1/2 binary64))))
✓	cost-diff	256	(.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) (pow.f64 (.f64 (PI.f64) (/.f64 #s(literal -2 binary64) (/.f64 #s(literal -1 binary64) n))) (+.f64 #s(literal 1/2 binary64) (*.f64 k #s(literal -1/2 binary64)))))
✓	cost-diff	0	(*.f64 n (PI.f64))
✓	cost-diff	0	(/.f64 (*.f64 n (PI.f64)) k)
✓	cost-diff	0	(sqrt.f64 (/.f64 (*.f64 n (PI.f64)) k))
✓	cost-diff	0	(.f64 (sqrt.f64 (/.f64 (.f64 n (PI.f64)) k)) (sqrt.f64 #s(literal 2 binary64)))
✓	cost-diff	0	(.f64 #s(literal 2 binary64) (.f64 (PI.f64) n))
✓	cost-diff	0	(pow.f64 (.f64 #s(literal 2 binary64) (.f64 (PI.f64) n)) (+.f64 (/.f64 k #s(literal 2 binary64)) #s(literal -1/2 binary64)))
✓	cost-diff	0	(pow.f64 k #s(literal -1/2 binary64))
✓	cost-diff	0	(/.f64 (pow.f64 k #s(literal -1/2 binary64)) (pow.f64 (.f64 #s(literal 2 binary64) (.f64 (PI.f64) n)) (+.f64 (/.f64 k #s(literal 2 binary64)) #s(literal -1/2 binary64))))

Rules

274×	`-lowering-.f32`
274×	`-lowering-.f64`
232×	`fma-lowering-fma.f32`
232×	`fma-lowering-fma.f64`
228×	`fmsub-define`

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	41	256
1	72	251
2	108	249
3	155	249
4	233	249
5	372	249
6	528	249
7	662	249
8	790	249
9	869	249
10	877	249
11	878	249
0	878	249

Stop Event

1×	iter limit
1×	saturated

Calls

Call 1

Inputs
(/ (pow k -1/2) (pow (* 2 (* (PI) n)) (+ (/ k 2) -1/2)))
(pow k -1/2)
k
-1/2
(pow (* 2 (* (PI) n)) (+ (/ k 2) -1/2))
(* 2 (* (PI) n))
2
(* (PI) n)
(PI)
n
(+ (/ k 2) -1/2)
(/ k 2)
(* (sqrt (/ (* n (PI)) k)) (sqrt 2))
(sqrt (/ (* n (PI)) k))
(/ (* n (PI)) k)
(* n (PI))
n
(PI)
k
(sqrt 2)
2
(* (/ 1 (sqrt k)) (pow (* (PI) (/ -2 (/ -1 n))) (+ 1/2 (* k -1/2))))
(/ 1 (sqrt k))
1
(sqrt k)
k
(pow (* (PI) (/ -2 (/ -1 n))) (+ 1/2 (* k -1/2)))
(* (PI) (/ -2 (/ -1 n)))
(PI)
(/ -2 (/ -1 n))
-2
(/ -1 n)
-1
n
(+ 1/2 (* k -1/2))
1/2
(* k -1/2)
-1/2
(/ (pow (pow (* 2 (* (PI) n)) (- 1/4 (* k 1/4))) 2) (sqrt k))
(pow (pow (* 2 (* (PI) n)) (- 1/4 (* k 1/4))) 2)
(pow (* 2 (* (PI) n)) (- 1/4 (* k 1/4)))
(* 2 (* (PI) n))
2
(* (PI) n)
(PI)
n
(- 1/4 (* k 1/4))
1/4
(* k 1/4)
k
(sqrt k)
(/ (sqrt (* 2 (* (PI) n))) (pow (* (pow (* 2 (* (PI) n)) k) k) 1/2))
(sqrt (* 2 (* (PI) n)))
(* 2 (* (PI) n))
2
(* (PI) n)
(PI)
n
(pow (* (pow (* 2 (* (PI) n)) k) k) 1/2)
(* (pow (* 2 (* (PI) n)) k) k)
(pow (* 2 (* (PI) n)) k)
k
1/2

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

localize356.0ms (2.6%)

Localize:

Found 20 expressions of interest:

New	Metric	Score	Program
✓	accuracy	99.6%	(pow.f64 (.f64 #s(literal 2 binary64) (.f64 (PI.f64) n)) k)
✓	accuracy	99.5%	(sqrt.f64 (.f64 #s(literal 2 binary64) (.f64 (PI.f64) n)))
✓	accuracy	99.4%	(/.f64 (sqrt.f64 (.f64 #s(literal 2 binary64) (.f64 (PI.f64) n))) (pow.f64 (.f64 (pow.f64 (.f64 #s(literal 2 binary64) (*.f64 (PI.f64) n)) k) k) #s(literal 1/2 binary64)))
✓	accuracy	76.2%	(PI.f64)
✓	accuracy	99.7%	(/.f64 (pow.f64 (pow.f64 (.f64 #s(literal 2 binary64) (.f64 (PI.f64) n)) (-.f64 #s(literal 1/4 binary64) (*.f64 k #s(literal 1/4 binary64)))) #s(literal 2 binary64)) (sqrt.f64 k))
✓	accuracy	99.6%	(pow.f64 (pow.f64 (.f64 #s(literal 2 binary64) (.f64 (PI.f64) n)) (-.f64 #s(literal 1/4 binary64) (*.f64 k #s(literal 1/4 binary64)))) #s(literal 2 binary64))
✓	accuracy	99.5%	(pow.f64 (.f64 #s(literal 2 binary64) (.f64 (PI.f64) n)) (-.f64 #s(literal 1/4 binary64) (*.f64 k #s(literal 1/4 binary64))))
✓	accuracy	76.2%	(PI.f64)
✓	accuracy	99.7%	(.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) (pow.f64 (.f64 (PI.f64) (/.f64 #s(literal -2 binary64) (/.f64 #s(literal -1 binary64) n))) (+.f64 #s(literal 1/2 binary64) (*.f64 k #s(literal -1/2 binary64)))))
✓	accuracy	99.6%	(/.f64 #s(literal 1 binary64) (sqrt.f64 k))
✓	accuracy	99.4%	(pow.f64 (.f64 (PI.f64) (/.f64 #s(literal -2 binary64) (/.f64 #s(literal -1 binary64) n))) (+.f64 #s(literal 1/2 binary64) (.f64 k #s(literal -1/2 binary64))))
✓	accuracy	76.2%	(PI.f64)
✓	accuracy	99.7%	(/.f64 (*.f64 n (PI.f64)) k)
✓	accuracy	99.5%	(.f64 (sqrt.f64 (/.f64 (.f64 n (PI.f64)) k)) (sqrt.f64 #s(literal 2 binary64)))
✓	accuracy	92.6%	(sqrt.f64 (/.f64 (*.f64 n (PI.f64)) k))
✓	accuracy	76.2%	(PI.f64)
✓	accuracy	99.8%	(*.f64 (PI.f64) n)
✓	accuracy	99.7%	(/.f64 (pow.f64 k #s(literal -1/2 binary64)) (pow.f64 (.f64 #s(literal 2 binary64) (.f64 (PI.f64) n)) (+.f64 (/.f64 k #s(literal 2 binary64)) #s(literal -1/2 binary64))))
✓	accuracy	99.5%	(pow.f64 (.f64 #s(literal 2 binary64) (.f64 (PI.f64) n)) (+.f64 (/.f64 k #s(literal 2 binary64)) #s(literal -1/2 binary64)))
✓	accuracy	76.2%	(PI.f64)

Results

163.0ms	63×	5	exit
118.0ms	193×	0	valid

Compiler

Compiled 277 to 42 computations (84.8% saved)

Precisions

Click to see histograms. Total time spent on operations: 155.0ms

ival-pow: 76.0ms (49.1% of total)

backward-pass: 25.0ms (16.2% of total)

ival-mult: 20.0ms (12.9% of total)

ival-div: 16.0ms (10.3% of total)

ival-sqrt: 9.0ms (5.8% of total)

ival-add: 4.0ms (2.6% of total)

const: 2.0ms (1.3% of total)

ival-sub: 2.0ms (1.3% of total)

ival-pi: 1.0ms (0.6% of total)

series81.0ms (0.6%)

Counts

22 → 408

Calls

Call 1

Inputs
#<alt (/ (pow k -1/2) (pow (* 2 (* (PI) n)) (+ (/ k 2) -1/2)))>
#<alt (pow k -1/2)>
#<alt (pow (* 2 (* (PI) n)) (+ (/ k 2) -1/2))>
#<alt (* 2 (* (PI) n))>
#<alt (* (sqrt (/ (* n (PI)) k)) (sqrt 2))>
#<alt (sqrt (/ (* n (PI)) k))>
#<alt (/ (* n (PI)) k)>
#<alt (* n (PI))>
#<alt (* (/ 1 (sqrt k)) (pow (* (PI) (/ -2 (/ -1 n))) (+ 1/2 (* k -1/2))))>
#<alt (pow (* (PI) (/ -2 (/ -1 n))) (+ 1/2 (* k -1/2)))>
#<alt (* (PI) (/ -2 (/ -1 n)))>
#<alt (/ -2 (/ -1 n))>
#<alt (/ (pow (pow (* 2 (* (PI) n)) (- 1/4 (* k 1/4))) 2) (sqrt k))>
#<alt (pow (pow (* 2 (* (PI) n)) (- 1/4 (* k 1/4))) 2)>
#<alt (pow (* 2 (* (PI) n)) (- 1/4 (* k 1/4)))>
#<alt (/ (sqrt (* 2 (* (PI) n))) (pow (* (pow (* 2 (* (PI) n)) k) k) 1/2))>
#<alt (pow (* (pow (* 2 (* (PI) n)) k) k) 1/2)>
#<alt (sqrt (* 2 (* (PI) n)))>
#<alt (PI)>
#<alt (* (PI) n)>
#<alt (/ 1 (sqrt k))>
#<alt (pow (* 2 (* (PI) n)) k)>

Outputs
#<alt (* (sqrt (/ (* n (PI)) k)) (/ 1 (sqrt 1/2)))>
#<alt (/ (+ (* -1/2 (* (sqrt (* (pow k 3) (* n (PI)))) (/ (log (* 2 (* n (PI)))) (sqrt 1/2)))) (* (sqrt (* k (* n (PI)))) (/ 1 (sqrt 1/2)))) k)>
#<alt (/ (+ (* k (+ (* -1 (* (sqrt (pow k 3)) (+ (* -1/4 (* (sqrt (* n (PI))) (/ (pow (log (* 2 (* n (PI)))) 2) (sqrt 1/2)))) (* 1/8 (* (sqrt (* n (PI))) (/ (pow (log (* 2 (* n (PI)))) 2) (sqrt 1/2))))))) (* -1/2 (* (sqrt (* k (* n (PI)))) (/ (log (* 2 (* n (PI)))) (sqrt 1/2)))))) (* (sqrt (* k (* n (PI)))) (/ 1 (sqrt 1/2)))) k)>
#<alt (/ (+ (* k (+ (* -1/2 (* (sqrt (* k (* n (PI)))) (/ (log (* 2 (* n (PI)))) (sqrt 1/2)))) (* k (+ (* -1 (* (sqrt k) (+ (* -1/4 (* (sqrt (* n (PI))) (/ (pow (log (* 2 (* n (PI)))) 2) (sqrt 1/2)))) (* 1/8 (* (sqrt (* n (PI))) (/ (pow (log (* 2 (* n (PI)))) 2) (sqrt 1/2))))))) (* -1 (* (sqrt (pow k 3)) (+ (* -1/2 (* (log (* 2 (* n (PI)))) (+ (* -1/4 (* (sqrt (* n (PI))) (/ (pow (log (* 2 (* n (PI)))) 2) (sqrt 1/2)))) (* 1/8 (* (sqrt (* n (PI))) (/ (pow (log (* 2 (* n (PI)))) 2) (sqrt 1/2))))))) (+ (* -1/16 (* (sqrt (* n (PI))) (/ (pow (log (* 2 (* n (PI)))) 3) (sqrt 1/2)))) (* 1/48 (* (sqrt (* n (PI))) (/ (pow (log (* 2 (* n (PI)))) 3) (sqrt 1/2)))))))))))) (* (sqrt (* k (* n (PI)))) (/ 1 (sqrt 1/2)))) k)>
#<alt (* (sqrt (/ 1 k)) (/ 1 (exp (* (log (* 2 (* n (PI)))) (- (* 1/2 k) 1/2)))))>
#<alt (* (sqrt (/ 1 k)) (/ 1 (exp (* (log (* 2 (* n (PI)))) (- (* 1/2 k) 1/2)))))>
#<alt (* (sqrt (/ 1 k)) (/ 1 (exp (* (log (* 2 (* n (PI)))) (- (* 1/2 k) 1/2)))))>
#<alt (* (sqrt (/ 1 k)) (/ 1 (exp (* (log (* 2 (* n (PI)))) (- (* 1/2 k) 1/2)))))>
#<alt (* (sqrt (/ 1 k)) (/ (pow (sqrt -1) 2) (exp (* -1 (* (log (* 2 (* n (PI)))) (+ 1/2 (* -1/2 k)))))))>
#<alt (* (sqrt (/ 1 k)) (/ (pow (sqrt -1) 2) (exp (* -1 (* (log (* 2 (* n (PI)))) (+ 1/2 (* -1/2 k)))))))>
#<alt (* (sqrt (/ 1 k)) (/ (pow (sqrt -1) 2) (exp (* -1 (* (log (* 2 (* n (PI)))) (+ 1/2 (* -1/2 k)))))))>
#<alt (* (sqrt (/ 1 k)) (/ (pow (sqrt -1) 2) (exp (* -1 (* (log (* 2 (* n (PI)))) (+ 1/2 (* -1/2 k)))))))>
#<alt (* (sqrt (/ 1 k)) (/ 1 (exp (* (+ (log n) (log (* 2 (PI)))) (- (* 1/2 k) 1/2)))))>
#<alt (* (sqrt (/ 1 k)) (/ 1 (exp (* (+ (log n) (log (* 2 (PI)))) (- (* 1/2 k) 1/2)))))>
#<alt (* (sqrt (/ 1 k)) (/ 1 (exp (* (+ (log n) (log (* 2 (PI)))) (- (* 1/2 k) 1/2)))))>
#<alt (* (sqrt (/ 1 k)) (/ 1 (exp (* (+ (log n) (log (* 2 (PI)))) (- (* 1/2 k) 1/2)))))>
#<alt (* (sqrt (/ 1 k)) (/ 1 (exp (* (+ (log (* 2 (PI))) (* -1 (log (/ 1 n)))) (- (* 1/2 k) 1/2)))))>
#<alt (* (sqrt (/ 1 k)) (/ 1 (exp (* (+ (log (* 2 (PI))) (* -1 (log (/ 1 n)))) (- (* 1/2 k) 1/2)))))>
#<alt (* (sqrt (/ 1 k)) (/ 1 (exp (* (+ (log (* 2 (PI))) (* -1 (log (/ 1 n)))) (- (* 1/2 k) 1/2)))))>
#<alt (* (sqrt (/ 1 k)) (/ 1 (exp (* (+ (log (* 2 (PI))) (* -1 (log (/ 1 n)))) (- (* 1/2 k) 1/2)))))>
#<alt (* (sqrt (/ 1 k)) (/ 1 (exp (* (+ (log (* -2 (PI))) (* -1 (log (/ -1 n)))) (- (* 1/2 k) 1/2)))))>
#<alt (* (sqrt (/ 1 k)) (/ 1 (exp (* (+ (log (* -2 (PI))) (* -1 (log (/ -1 n)))) (- (* 1/2 k) 1/2)))))>
#<alt (* (sqrt (/ 1 k)) (/ 1 (exp (* (+ (log (* -2 (PI))) (* -1 (log (/ -1 n)))) (- (* 1/2 k) 1/2)))))>
#<alt (* (sqrt (/ 1 k)) (/ 1 (exp (* (+ (log (* -2 (PI))) (* -1 (log (/ -1 n)))) (- (* 1/2 k) 1/2)))))>
#<alt (sqrt (/ 1 k))>
#<alt (sqrt (/ 1 k))>
#<alt (sqrt (/ 1 k))>
#<alt (sqrt (/ 1 k))>
#<alt (sqrt (/ 1 k))>
#<alt (sqrt (/ 1 k))>
#<alt (sqrt (/ 1 k))>
#<alt (sqrt (/ 1 k))>
#<alt (* (sqrt (/ 1 k)) (pow (sqrt -1) 2))>
#<alt (* (sqrt (/ 1 k)) (pow (sqrt -1) 2))>
#<alt (* (sqrt (/ 1 k)) (pow (sqrt -1) 2))>
#<alt (* (sqrt (/ 1 k)) (pow (sqrt -1) 2))>
#<alt (exp (* (+ (log n) (log (* 2 (PI)))) (- (* 1/2 k) 1/2)))>
#<alt (exp (* (+ (log n) (log (* 2 (PI)))) (- (* 1/2 k) 1/2)))>
#<alt (exp (* (+ (log n) (log (* 2 (PI)))) (- (* 1/2 k) 1/2)))>
#<alt (exp (* (+ (log n) (log (* 2 (PI)))) (- (* 1/2 k) 1/2)))>
#<alt (exp (* (+ (log (* 2 (PI))) (* -1 (log (/ 1 n)))) (- (* 1/2 k) 1/2)))>
#<alt (exp (* (+ (log (* 2 (PI))) (* -1 (log (/ 1 n)))) (- (* 1/2 k) 1/2)))>
#<alt (exp (* (+ (log (* 2 (PI))) (* -1 (log (/ 1 n)))) (- (* 1/2 k) 1/2)))>
#<alt (exp (* (+ (log (* 2 (PI))) (* -1 (log (/ 1 n)))) (- (* 1/2 k) 1/2)))>
#<alt (exp (* (+ (log (* -2 (PI))) (* -1 (log (/ -1 n)))) (- (* 1/2 k) 1/2)))>
#<alt (exp (* (+ (log (* -2 (PI))) (* -1 (log (/ -1 n)))) (- (* 1/2 k) 1/2)))>
#<alt (exp (* (+ (log (* -2 (PI))) (* -1 (log (/ -1 n)))) (- (* 1/2 k) 1/2)))>
#<alt (exp (* (+ (log (* -2 (PI))) (* -1 (log (/ -1 n)))) (- (* 1/2 k) 1/2)))>
#<alt (* (sqrt (/ 1 (* n (PI)))) (sqrt 1/2))>
#<alt (+ (* 1/2 (* (* k (* (log (* 2 (* n (PI)))) (sqrt 1/2))) (sqrt (/ 1 (* n (PI)))))) (* (sqrt (/ 1 (* n (PI)))) (sqrt 1/2)))>
#<alt (+ (* k (+ (* 1/8 (* (* k (* (pow (log (* 2 (* n (PI)))) 2) (sqrt 1/2))) (sqrt (/ 1 (* n (PI)))))) (* 1/2 (* (sqrt (/ 1 (* n (PI)))) (* (log (* 2 (* n (PI)))) (sqrt 1/2)))))) (* (sqrt (/ 1 (* n (PI)))) (sqrt 1/2)))>
#<alt (+ (* k (+ (* 1/2 (* (sqrt (/ 1 (* n (PI)))) (* (log (* 2 (* n (PI)))) (sqrt 1/2)))) (* k (+ (* 1/48 (* (* k (* (pow (log (* 2 (* n (PI)))) 3) (sqrt 1/2))) (sqrt (/ 1 (* n (PI)))))) (* 1/8 (* (sqrt (/ 1 (* n (PI)))) (* (pow (log (* 2 (* n (PI)))) 2) (sqrt 1/2)))))))) (* (sqrt (/ 1 (* n (PI)))) (sqrt 1/2)))>
#<alt (exp (* (log (* 2 (* n (PI)))) (- (* 1/2 k) 1/2)))>
#<alt (exp (* (log (* 2 (* n (PI)))) (- (* 1/2 k) 1/2)))>
#<alt (exp (* (log (* 2 (* n (PI)))) (- (* 1/2 k) 1/2)))>
#<alt (exp (* (log (* 2 (* n (PI)))) (- (* 1/2 k) 1/2)))>
#<alt (exp (* -1 (* (log (* 2 (* n (PI)))) (+ 1/2 (* -1/2 k)))))>
#<alt (exp (* -1 (* (log (* 2 (* n (PI)))) (+ 1/2 (* -1/2 k)))))>
#<alt (exp (* -1 (* (log (* 2 (* n (PI)))) (+ 1/2 (* -1/2 k)))))>
#<alt (exp (* -1 (* (log (* 2 (* n (PI)))) (+ 1/2 (* -1/2 k)))))>
#<alt (* 2 (* n (PI)))>
#<alt (* 2 (* n (PI)))>
#<alt (* 2 (* n (PI)))>
#<alt (* 2 (* n (PI)))>
#<alt (* 2 (* n (PI)))>
#<alt (* 2 (* n (PI)))>
#<alt (* 2 (* n (PI)))>
#<alt (* 2 (* n (PI)))>
#<alt (* 2 (* n (PI)))>
#<alt (* 2 (* n (PI)))>
#<alt (* 2 (* n (PI)))>
#<alt (* 2 (* n (PI)))>
#<alt (* (sqrt (/ (* n (PI)) k)) (sqrt 2))>
#<alt (* (sqrt (/ (* n (PI)) k)) (sqrt 2))>
#<alt (* (sqrt (/ (* n (PI)) k)) (sqrt 2))>
#<alt (* (sqrt (/ (* n (PI)) k)) (sqrt 2))>
#<alt (* (sqrt (/ (* n (PI)) k)) (sqrt 2))>
#<alt (* (sqrt (/ (* n (PI)) k)) (sqrt 2))>
#<alt (* (sqrt (/ (* n (PI)) k)) (sqrt 2))>
#<alt (* (sqrt (/ (* n (PI)) k)) (sqrt 2))>
#<alt (* -1 (* (sqrt (/ (* n (PI)) k)) (* (pow (sqrt -1) 2) (sqrt 2))))>
#<alt (* -1 (* (sqrt (/ (* n (PI)) k)) (* (pow (sqrt -1) 2) (sqrt 2))))>
#<alt (* -1 (* (sqrt (/ (* n (PI)) k)) (* (pow (sqrt -1) 2) (sqrt 2))))>
#<alt (* -1 (* (sqrt (/ (* n (PI)) k)) (* (pow (sqrt -1) 2) (sqrt 2))))>
#<alt (* (sqrt (/ (* n (PI)) k)) (sqrt 2))>
#<alt (* (sqrt (/ (* n (PI)) k)) (sqrt 2))>
#<alt (* (sqrt (/ (* n (PI)) k)) (sqrt 2))>
#<alt (* (sqrt (/ (* n (PI)) k)) (sqrt 2))>
#<alt (* (sqrt (/ (* n (PI)) k)) (sqrt 2))>
#<alt (* (sqrt (/ (* n (PI)) k)) (sqrt 2))>
#<alt (* (sqrt (/ (* n (PI)) k)) (sqrt 2))>
#<alt (* (sqrt (/ (* n (PI)) k)) (sqrt 2))>
#<alt (* (sqrt (/ (* n (PI)) k)) (* (pow (sqrt -1) 2) (sqrt 2)))>
#<alt (* (sqrt (/ (* n (PI)) k)) (* (pow (sqrt -1) 2) (sqrt 2)))>
#<alt (* (sqrt (/ (* n (PI)) k)) (* (pow (sqrt -1) 2) (sqrt 2)))>
#<alt (* (sqrt (/ (* n (PI)) k)) (* (pow (sqrt -1) 2) (sqrt 2)))>
#<alt (sqrt (/ (* n (PI)) k))>
#<alt (sqrt (/ (* n (PI)) k))>
#<alt (sqrt (/ (* n (PI)) k))>
#<alt (sqrt (/ (* n (PI)) k))>
#<alt (sqrt (/ (* n (PI)) k))>
#<alt (sqrt (/ (* n (PI)) k))>
#<alt (sqrt (/ (* n (PI)) k))>
#<alt (sqrt (/ (* n (PI)) k))>
#<alt (* -1 (* (sqrt (/ (* n (PI)) k)) (pow (sqrt -1) 2)))>
#<alt (* -1 (* (sqrt (/ (* n (PI)) k)) (pow (sqrt -1) 2)))>
#<alt (* -1 (* (sqrt (/ (* n (PI)) k)) (pow (sqrt -1) 2)))>
#<alt (* -1 (* (sqrt (/ (* n (PI)) k)) (pow (sqrt -1) 2)))>
#<alt (sqrt (/ (* n (PI)) k))>
#<alt (sqrt (/ (* n (PI)) k))>
#<alt (sqrt (/ (* n (PI)) k))>
#<alt (sqrt (/ (* n (PI)) k))>
#<alt (sqrt (/ (* n (PI)) k))>
#<alt (sqrt (/ (* n (PI)) k))>
#<alt (sqrt (/ (* n (PI)) k))>
#<alt (sqrt (/ (* n (PI)) k))>
#<alt (* (sqrt (/ (* n (PI)) k)) (pow (sqrt -1) 2))>
#<alt (* (sqrt (/ (* n (PI)) k)) (pow (sqrt -1) 2))>
#<alt (* (sqrt (/ (* n (PI)) k)) (pow (sqrt -1) 2))>
#<alt (* (sqrt (/ (* n (PI)) k)) (pow (sqrt -1) 2))>
#<alt (/ (* n (PI)) k)>
#<alt (/ (* n (PI)) k)>
#<alt (/ (* n (PI)) k)>
#<alt (/ (* n (PI)) k)>
#<alt (/ (* n (PI)) k)>
#<alt (/ (* n (PI)) k)>
#<alt (/ (* n (PI)) k)>
#<alt (/ (* n (PI)) k)>
#<alt (/ (* n (PI)) k)>
#<alt (/ (* n (PI)) k)>
#<alt (/ (* n (PI)) k)>
#<alt (/ (* n (PI)) k)>
#<alt (/ (* n (PI)) k)>
#<alt (/ (* n (PI)) k)>
#<alt (/ (* n (PI)) k)>
#<alt (/ (* n (PI)) k)>
#<alt (/ (* n (PI)) k)>
#<alt (/ (* n (PI)) k)>
#<alt (/ (* n (PI)) k)>
#<alt (/ (* n (PI)) k)>
#<alt (/ (* n (PI)) k)>
#<alt (/ (* n (PI)) k)>
#<alt (/ (* n (PI)) k)>
#<alt (/ (* n (PI)) k)>
#<alt (* n (PI))>
#<alt (* n (PI))>
#<alt (* n (PI))>
#<alt (* n (PI))>
#<alt (* n (PI))>
#<alt (* n (PI))>
#<alt (* n (PI))>
#<alt (* n (PI))>
#<alt (* n (PI))>
#<alt (* n (PI))>
#<alt (* n (PI))>
#<alt (* n (PI))>
#<alt (* (sqrt (/ (* n (PI)) k)) (sqrt 2))>
#<alt (/ (+ (* -1/2 (* (sqrt (* (pow k 3) (* n (PI)))) (* (log (* 2 (* n (PI)))) (sqrt 2)))) (* (sqrt (* k (* n (PI)))) (sqrt 2))) k)>
#<alt (/ (+ (* 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)>
#<alt (/ (+ (* 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)>
#<alt (* (sqrt (/ 1 k)) (exp (* (log (* 2 (* n (PI)))) (- 1/2 (* 1/2 k)))))>
#<alt (* (sqrt (/ 1 k)) (exp (* (log (* 2 (* n (PI)))) (- 1/2 (* 1/2 k)))))>
#<alt (* (sqrt (/ 1 k)) (exp (* (log (* 2 (* n (PI)))) (- 1/2 (* 1/2 k)))))>
#<alt (* (sqrt (/ 1 k)) (exp (* (log (* 2 (* n (PI)))) (- 1/2 (* 1/2 k)))))>
#<alt (* (sqrt (/ 1 k)) (exp (* (log (* 2 (* n (PI)))) (+ 1/2 (* -1/2 k)))))>
#<alt (* (sqrt (/ 1 k)) (exp (* (log (* 2 (* n (PI)))) (+ 1/2 (* -1/2 k)))))>
#<alt (* (sqrt (/ 1 k)) (exp (* (log (* 2 (* n (PI)))) (+ 1/2 (* -1/2 k)))))>
#<alt (* (sqrt (/ 1 k)) (exp (* (log (* 2 (* n (PI)))) (+ 1/2 (* -1/2 k)))))>
#<alt (* (sqrt (/ 1 k)) (exp (* (+ 1/2 (* -1/2 k)) (+ (log n) (log (* 2 (PI)))))))>
#<alt (* (sqrt (/ 1 k)) (exp (* (+ 1/2 (* -1/2 k)) (+ (log n) (log (* 2 (PI)))))))>
#<alt (* (sqrt (/ 1 k)) (exp (* (+ 1/2 (* -1/2 k)) (+ (log n) (log (* 2 (PI)))))))>
#<alt (* (sqrt (/ 1 k)) (exp (* (+ 1/2 (* -1/2 k)) (+ (log n) (log (* 2 (PI)))))))>
#<alt (* (sqrt (/ 1 k)) (exp (* (+ 1/2 (* -1/2 k)) (+ (log (* 2 (PI))) (* -1 (log (/ 1 n)))))))>
#<alt (* (sqrt (/ 1 k)) (exp (* (+ 1/2 (* -1/2 k)) (+ (log (* 2 (PI))) (* -1 (log (/ 1 n)))))))>
#<alt (* (sqrt (/ 1 k)) (exp (* (+ 1/2 (* -1/2 k)) (+ (log (* 2 (PI))) (* -1 (log (/ 1 n)))))))>
#<alt (* (sqrt (/ 1 k)) (exp (* (+ 1/2 (* -1/2 k)) (+ (log (* 2 (PI))) (* -1 (log (/ 1 n)))))))>
#<alt (* (sqrt (/ 1 k)) (exp (* (+ 1/2 (* -1/2 k)) (+ (log (* -2 (PI))) (* -1 (log (/ -1 n)))))))>
#<alt (* (sqrt (/ 1 k)) (exp (* (+ 1/2 (* -1/2 k)) (+ (log (* -2 (PI))) (* -1 (log (/ -1 n)))))))>
#<alt (* (sqrt (/ 1 k)) (exp (* (+ 1/2 (* -1/2 k)) (+ (log (* -2 (PI))) (* -1 (log (/ -1 n)))))))>
#<alt (* (sqrt (/ 1 k)) (exp (* (+ 1/2 (* -1/2 k)) (+ (log (* -2 (PI))) (* -1 (log (/ -1 n)))))))>
#<alt (exp (* (+ 1/2 (* -1/2 k)) (+ (log n) (log (* 2 (PI))))))>
#<alt (exp (* (+ 1/2 (* -1/2 k)) (+ (log n) (log (* 2 (PI))))))>
#<alt (exp (* (+ 1/2 (* -1/2 k)) (+ (log n) (log (* 2 (PI))))))>
#<alt (exp (* (+ 1/2 (* -1/2 k)) (+ (log n) (log (* 2 (PI))))))>
#<alt (exp (* (+ 1/2 (* -1/2 k)) (+ (log (* 2 (PI))) (* -1 (log (/ 1 n))))))>
#<alt (exp (* (+ 1/2 (* -1/2 k)) (+ (log (* 2 (PI))) (* -1 (log (/ 1 n))))))>
#<alt (exp (* (+ 1/2 (* -1/2 k)) (+ (log (* 2 (PI))) (* -1 (log (/ 1 n))))))>
#<alt (exp (* (+ 1/2 (* -1/2 k)) (+ (log (* 2 (PI))) (* -1 (log (/ 1 n))))))>
#<alt (exp (* (+ 1/2 (* -1/2 k)) (+ (log (* -2 (PI))) (* -1 (log (/ -1 n))))))>
#<alt (exp (* (+ 1/2 (* -1/2 k)) (+ (log (* -2 (PI))) (* -1 (log (/ -1 n))))))>
#<alt (exp (* (+ 1/2 (* -1/2 k)) (+ (log (* -2 (PI))) (* -1 (log (/ -1 n))))))>
#<alt (exp (* (+ 1/2 (* -1/2 k)) (+ (log (* -2 (PI))) (* -1 (log (/ -1 n))))))>
#<alt (* (sqrt (* n (PI))) (sqrt 2))>
#<alt (+ (* -1/2 (* (* k (* (log (* 2 (* n (PI)))) (sqrt 2))) (sqrt (* n (PI))))) (* (sqrt (* n (PI))) (sqrt 2)))>
#<alt (+ (* 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)))>
#<alt (+ (* 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)))>
#<alt (exp (* (log (* 2 (* n (PI)))) (- 1/2 (* 1/2 k))))>
#<alt (exp (* (log (* 2 (* n (PI)))) (- 1/2 (* 1/2 k))))>
#<alt (exp (* (log (* 2 (* n (PI)))) (- 1/2 (* 1/2 k))))>
#<alt (exp (* (log (* 2 (* n (PI)))) (- 1/2 (* 1/2 k))))>
#<alt (exp (* (log (* 2 (* n (PI)))) (+ 1/2 (* -1/2 k))))>
#<alt (exp (* (log (* 2 (* n (PI)))) (+ 1/2 (* -1/2 k))))>
#<alt (exp (* (log (* 2 (* n (PI)))) (+ 1/2 (* -1/2 k))))>
#<alt (exp (* (log (* 2 (* n (PI)))) (+ 1/2 (* -1/2 k))))>
#<alt (* 2 (* n (PI)))>
#<alt (* 2 (* n (PI)))>
#<alt (* 2 (* n (PI)))>
#<alt (* 2 (* n (PI)))>
#<alt (* 2 (* n (PI)))>
#<alt (* 2 (* n (PI)))>
#<alt (* 2 (* n (PI)))>
#<alt (* 2 (* n (PI)))>
#<alt (* 2 (* n (PI)))>
#<alt (* 2 (* n (PI)))>
#<alt (* 2 (* n (PI)))>
#<alt (* 2 (* n (PI)))>
#<alt (* 2 n)>
#<alt (* 2 n)>
#<alt (* 2 n)>
#<alt (* 2 n)>
#<alt (* 2 n)>
#<alt (* 2 n)>
#<alt (* 2 n)>
#<alt (* 2 n)>
#<alt (* 2 n)>
#<alt (* 2 n)>
#<alt (* 2 n)>
#<alt (* 2 n)>
#<alt (* (sqrt (/ 1 k)) (pow (exp (* (+ (log n) (log (* 2 (PI)))) (- 1/4 (* 1/4 k)))) 2))>
#<alt (* (sqrt (/ 1 k)) (pow (exp (* (+ (log n) (log (* 2 (PI)))) (- 1/4 (* 1/4 k)))) 2))>
#<alt (* (sqrt (/ 1 k)) (pow (exp (* (+ (log n) (log (* 2 (PI)))) (- 1/4 (* 1/4 k)))) 2))>
#<alt (* (sqrt (/ 1 k)) (pow (exp (* (+ (log n) (log (* 2 (PI)))) (- 1/4 (* 1/4 k)))) 2))>
#<alt (* (sqrt (/ 1 k)) (pow (exp (* (+ (log (* 2 (PI))) (* -1 (log (/ 1 n)))) (- 1/4 (* 1/4 k)))) 2))>
#<alt (* (sqrt (/ 1 k)) (pow (exp (* (+ (log (* 2 (PI))) (* -1 (log (/ 1 n)))) (- 1/4 (* 1/4 k)))) 2))>
#<alt (* (sqrt (/ 1 k)) (pow (exp (* (+ (log (* 2 (PI))) (* -1 (log (/ 1 n)))) (- 1/4 (* 1/4 k)))) 2))>
#<alt (* (sqrt (/ 1 k)) (pow (exp (* (+ (log (* 2 (PI))) (* -1 (log (/ 1 n)))) (- 1/4 (* 1/4 k)))) 2))>
#<alt (* (sqrt (/ 1 k)) (pow (exp (* (+ (log (* -2 (PI))) (* -1 (log (/ -1 n)))) (- 1/4 (* 1/4 k)))) 2))>
#<alt (* (sqrt (/ 1 k)) (pow (exp (* (+ (log (* -2 (PI))) (* -1 (log (/ -1 n)))) (- 1/4 (* 1/4 k)))) 2))>
#<alt (* (sqrt (/ 1 k)) (pow (exp (* (+ (log (* -2 (PI))) (* -1 (log (/ -1 n)))) (- 1/4 (* 1/4 k)))) 2))>
#<alt (* (sqrt (/ 1 k)) (pow (exp (* (+ (log (* -2 (PI))) (* -1 (log (/ -1 n)))) (- 1/4 (* 1/4 k)))) 2))>
#<alt (* (sqrt (/ (* n (PI)) k)) (sqrt 2))>
#<alt (/ (+ (* -1/2 (* (sqrt (* (pow k 3) (* n (PI)))) (* (log (* 2 (* n (PI)))) (sqrt 2)))) (* (sqrt (* k (* n (PI)))) (sqrt 2))) k)>
#<alt (/ (+ (* 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)>
#<alt (/ (+ (* k (+ (* -1/2 (* (sqrt (* k (* n (PI)))) (* (log (* 2 (* n (PI)))) (sqrt 2)))) (* k (+ (* 1/8 (* (sqrt (* k (* n (PI)))) (* (pow (log (* 2 (* n (PI)))) 2) (sqrt 2)))) (* (sqrt (pow k 3)) (+ (* -1/64 (* (sqrt (* n (PI))) (* (pow (log (* 2 (* n (PI)))) 3) (sqrt 2)))) (* -1/192 (* (sqrt (* n (PI))) (* (pow (log (* 2 (* n (PI)))) 3) (sqrt 2)))))))))) (* (sqrt (* k (* n (PI)))) (sqrt 2))) k)>
#<alt (* (sqrt (/ 1 k)) (pow (exp (* (log (* 2 (* n (PI)))) (- 1/4 (* 1/4 k)))) 2))>
#<alt (* (sqrt (/ 1 k)) (pow (exp (* (log (* 2 (* n (PI)))) (- 1/4 (* 1/4 k)))) 2))>
#<alt (* (sqrt (/ 1 k)) (pow (exp (* (log (* 2 (* n (PI)))) (- 1/4 (* 1/4 k)))) 2))>
#<alt (* (sqrt (/ 1 k)) (pow (exp (* (log (* 2 (* n (PI)))) (- 1/4 (* 1/4 k)))) 2))>
#<alt (* (sqrt (/ 1 k)) (pow (exp (* (log (* 2 (* n (PI)))) (+ 1/4 (* -1/4 k)))) 2))>
#<alt (* (sqrt (/ 1 k)) (pow (exp (* (log (* 2 (* n (PI)))) (+ 1/4 (* -1/4 k)))) 2))>
#<alt (* (sqrt (/ 1 k)) (pow (exp (* (log (* 2 (* n (PI)))) (+ 1/4 (* -1/4 k)))) 2))>
#<alt (* (sqrt (/ 1 k)) (pow (exp (* (log (* 2 (* n (PI)))) (+ 1/4 (* -1/4 k)))) 2))>
#<alt (pow (exp (* (+ (log n) (log (* 2 (PI)))) (- 1/4 (* 1/4 k)))) 2)>
#<alt (pow (exp (* (+ (log n) (log (* 2 (PI)))) (- 1/4 (* 1/4 k)))) 2)>
#<alt (pow (exp (* (+ (log n) (log (* 2 (PI)))) (- 1/4 (* 1/4 k)))) 2)>
#<alt (pow (exp (* (+ (log n) (log (* 2 (PI)))) (- 1/4 (* 1/4 k)))) 2)>
#<alt (pow (exp (* (+ (log (* 2 (PI))) (* -1 (log (/ 1 n)))) (- 1/4 (* 1/4 k)))) 2)>
#<alt (pow (exp (* (+ (log (* 2 (PI))) (* -1 (log (/ 1 n)))) (- 1/4 (* 1/4 k)))) 2)>
#<alt (pow (exp (* (+ (log (* 2 (PI))) (* -1 (log (/ 1 n)))) (- 1/4 (* 1/4 k)))) 2)>
#<alt (pow (exp (* (+ (log (* 2 (PI))) (* -1 (log (/ 1 n)))) (- 1/4 (* 1/4 k)))) 2)>
#<alt (pow (exp (* (+ (log (* -2 (PI))) (* -1 (log (/ -1 n)))) (- 1/4 (* 1/4 k)))) 2)>
#<alt (pow (exp (* (+ (log (* -2 (PI))) (* -1 (log (/ -1 n)))) (- 1/4 (* 1/4 k)))) 2)>
#<alt (pow (exp (* (+ (log (* -2 (PI))) (* -1 (log (/ -1 n)))) (- 1/4 (* 1/4 k)))) 2)>
#<alt (pow (exp (* (+ (log (* -2 (PI))) (* -1 (log (/ -1 n)))) (- 1/4 (* 1/4 k)))) 2)>
#<alt (* (sqrt (* n (PI))) (sqrt 2))>
#<alt (+ (* -1/2 (* (* k (* (log (* 2 (* n (PI)))) (sqrt 2))) (sqrt (* n (PI))))) (* (sqrt (* n (PI))) (sqrt 2)))>
#<alt (+ (* 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)))>
#<alt (+ (* k (+ (* -1/2 (* (sqrt (* n (PI))) (* (log (* 2 (* n (PI)))) (sqrt 2)))) (* k (+ (* 1/8 (* (sqrt (* n (PI))) (* (pow (log (* 2 (* n (PI)))) 2) (sqrt 2)))) (* k (+ (* -1/64 (* (sqrt (* n (PI))) (* (pow (log (* 2 (* n (PI)))) 3) (sqrt 2)))) (* -1/192 (* (sqrt (* n (PI))) (* (pow (log (* 2 (* n (PI)))) 3) (sqrt 2)))))))))) (* (sqrt (* n (PI))) (sqrt 2)))>
#<alt (pow (exp (* (log (* 2 (* n (PI)))) (- 1/4 (* 1/4 k)))) 2)>
#<alt (pow (exp (* (log (* 2 (* n (PI)))) (- 1/4 (* 1/4 k)))) 2)>
#<alt (pow (exp (* (log (* 2 (* n (PI)))) (- 1/4 (* 1/4 k)))) 2)>
#<alt (pow (exp (* (log (* 2 (* n (PI)))) (- 1/4 (* 1/4 k)))) 2)>
#<alt (pow (exp (* (log (* 2 (* n (PI)))) (+ 1/4 (* -1/4 k)))) 2)>
#<alt (pow (exp (* (log (* 2 (* n (PI)))) (+ 1/4 (* -1/4 k)))) 2)>
#<alt (pow (exp (* (log (* 2 (* n (PI)))) (+ 1/4 (* -1/4 k)))) 2)>
#<alt (pow (exp (* (log (* 2 (* n (PI)))) (+ 1/4 (* -1/4 k)))) 2)>
#<alt (exp (* (+ (log n) (log (* 2 (PI)))) (- 1/4 (* 1/4 k))))>
#<alt (exp (* (+ (log n) (log (* 2 (PI)))) (- 1/4 (* 1/4 k))))>
#<alt (exp (* (+ (log n) (log (* 2 (PI)))) (- 1/4 (* 1/4 k))))>
#<alt (exp (* (+ (log n) (log (* 2 (PI)))) (- 1/4 (* 1/4 k))))>
#<alt (exp (* (+ (log (* 2 (PI))) (* -1 (log (/ 1 n)))) (- 1/4 (* 1/4 k))))>
#<alt (exp (* (+ (log (* 2 (PI))) (* -1 (log (/ 1 n)))) (- 1/4 (* 1/4 k))))>
#<alt (exp (* (+ (log (* 2 (PI))) (* -1 (log (/ 1 n)))) (- 1/4 (* 1/4 k))))>
#<alt (exp (* (+ (log (* 2 (PI))) (* -1 (log (/ 1 n)))) (- 1/4 (* 1/4 k))))>
#<alt (exp (* (+ (log (* -2 (PI))) (* -1 (log (/ -1 n)))) (- 1/4 (* 1/4 k))))>
#<alt (exp (* (+ (log (* -2 (PI))) (* -1 (log (/ -1 n)))) (- 1/4 (* 1/4 k))))>
#<alt (exp (* (+ (log (* -2 (PI))) (* -1 (log (/ -1 n)))) (- 1/4 (* 1/4 k))))>
#<alt (exp (* (+ (log (* -2 (PI))) (* -1 (log (/ -1 n)))) (- 1/4 (* 1/4 k))))>
#<alt (pow (* 2 (* n (PI))) 1/4)>
#<alt (+ (* -1/4 (* (pow (* 2 (* n (PI))) 1/4) (* k (log (* 2 (* n (PI))))))) (pow (* 2 (* n (PI))) 1/4))>
#<alt (+ (* k (+ (* -1/4 (* (pow (* 2 (* n (PI))) 1/4) (log (* 2 (* n (PI)))))) (* 1/32 (* (pow (* 2 (* n (PI))) 1/4) (* k (pow (log (* 2 (* n (PI)))) 2)))))) (pow (* 2 (* n (PI))) 1/4))>
#<alt (+ (* k (+ (* -1/4 (* (pow (* 2 (* n (PI))) 1/4) (log (* 2 (* n (PI)))))) (* k (+ (* -1/384 (* (pow (* 2 (* n (PI))) 1/4) (* k (pow (log (* 2 (* n (PI)))) 3)))) (* 1/32 (* (pow (* 2 (* n (PI))) 1/4) (pow (log (* 2 (* n (PI)))) 2))))))) (pow (* 2 (* n (PI))) 1/4))>
#<alt (exp (* (log (* 2 (* n (PI)))) (- 1/4 (* 1/4 k))))>
#<alt (exp (* (log (* 2 (* n (PI)))) (- 1/4 (* 1/4 k))))>
#<alt (exp (* (log (* 2 (* n (PI)))) (- 1/4 (* 1/4 k))))>
#<alt (exp (* (log (* 2 (* n (PI)))) (- 1/4 (* 1/4 k))))>
#<alt (exp (* (log (* 2 (* n (PI)))) (+ 1/4 (* -1/4 k))))>
#<alt (exp (* (log (* 2 (* n (PI)))) (+ 1/4 (* -1/4 k))))>
#<alt (exp (* (log (* 2 (* n (PI)))) (+ 1/4 (* -1/4 k))))>
#<alt (exp (* (log (* 2 (* n (PI)))) (+ 1/4 (* -1/4 k))))>
#<alt (* (sqrt (/ (* n (PI)) (* k (exp (* k (+ (log n) (log (* 2 (PI))))))))) (sqrt 2))>
#<alt (* (sqrt (/ (* n (PI)) (* k (exp (* k (+ (log n) (log (* 2 (PI))))))))) (sqrt 2))>
#<alt (* (sqrt (/ (* n (PI)) (* k (exp (* k (+ (log n) (log (* 2 (PI))))))))) (sqrt 2))>
#<alt (* (sqrt (/ (* n (PI)) (* k (exp (* k (+ (log n) (log (* 2 (PI))))))))) (sqrt 2))>
#<alt (* (sqrt (/ (* n (PI)) (* k (exp (* k (+ (log (* 2 (PI))) (* -1 (log (/ 1 n))))))))) (sqrt 2))>
#<alt (* (sqrt (/ (* n (PI)) (* k (exp (* k (+ (log (* 2 (PI))) (* -1 (log (/ 1 n))))))))) (sqrt 2))>
#<alt (* (sqrt (/ (* n (PI)) (* k (exp (* k (+ (log (* 2 (PI))) (* -1 (log (/ 1 n))))))))) (sqrt 2))>
#<alt (* (sqrt (/ (* n (PI)) (* k (exp (* k (+ (log (* 2 (PI))) (* -1 (log (/ 1 n))))))))) (sqrt 2))>
#<alt (* -1 (* (sqrt (/ (* n (PI)) (* k (exp (* k (+ (log (* -2 (PI))) (* -1 (log (/ -1 n))))))))) (* (sqrt -2) (sqrt -1))))>
#<alt (* -1 (* (sqrt (/ (* n (PI)) (* k (exp (* k (+ (log (* -2 (PI))) (* -1 (log (/ -1 n))))))))) (* (sqrt -2) (sqrt -1))))>
#<alt (* -1 (* (sqrt (/ (* n (PI)) (* k (exp (* k (+ (log (* -2 (PI))) (* -1 (log (/ -1 n))))))))) (* (sqrt -2) (sqrt -1))))>
#<alt (* -1 (* (sqrt (/ (* n (PI)) (* k (exp (* k (+ (log (* -2 (PI))) (* -1 (log (/ -1 n))))))))) (* (sqrt -2) (sqrt -1))))>
#<alt (* (sqrt (/ (* n (PI)) k)) (sqrt 2))>
#<alt (/ (+ (* -1/2 (* (sqrt (* (pow k 3) (* n (PI)))) (* (log (* 2 (* n (PI)))) (sqrt 2)))) (* (sqrt (* k (* n (PI)))) (sqrt 2))) k)>
#<alt (/ (+ (* (sqrt (* k (* n (PI)))) (sqrt 2)) (* (pow k 2) (+ (* -1/2 (* (sqrt (/ k (* n (PI)))) (* (sqrt 2) (+ (* -1 (* n (* (PI) (pow (log (* 2 (* n (PI)))) 2)))) (* 1/2 (* n (* (PI) (pow (log (* 2 (* n (PI)))) 2)))))))) (* -1/2 (* (sqrt (/ (* n (PI)) k)) (* (log (* 2 (* n (PI)))) (sqrt 2))))))) k)>
#<alt (/ (+ (* (sqrt (* k (* n (PI)))) (sqrt 2)) (* (pow k 2) (+ (* -1/2 (* (sqrt (/ (* n (PI)) k)) (* (log (* 2 (* n (PI)))) (sqrt 2)))) (* k (+ (* -1/2 (* (sqrt (/ 1 (* k (* n (PI))))) (* (sqrt 2) (+ (* -1 (* n (* (PI) (pow (log (* 2 (* n (PI)))) 2)))) (* 1/2 (* n (* (PI) (pow (log (* 2 (* n (PI)))) 2)))))))) (* -1/2 (* (sqrt (/ k (* n (PI)))) (* (sqrt 2) (+ (* -1 (* (log (* 2 (* n (PI)))) (+ (* -1 (* n (* (PI) (pow (log (* 2 (* n (PI)))) 2)))) (* 1/2 (* n (* (PI) (pow (log (* 2 (* n (PI)))) 2))))))) (+ (* -1/2 (* n (* (PI) (pow (log (* 2 (* n (PI)))) 3)))) (+ (* 1/6 (* n (* (PI) (pow (log (* 2 (* n (PI)))) 3)))) (* 1/4 (/ (* n (* (PI) (pow (log (* 2 (* n (PI)))) 2))) k))))))))))))) k)>
#<alt (* (sqrt (/ (* n (PI)) (* k (pow (* 2 (* n (PI))) k)))) (sqrt 2))>
#<alt (* (sqrt (/ (* n (PI)) (* k (pow (* 2 (* n (PI))) k)))) (sqrt 2))>
#<alt (* (sqrt (/ (* n (PI)) (* k (pow (* 2 (* n (PI))) k)))) (sqrt 2))>
#<alt (* (sqrt (/ (* n (PI)) (* k (pow (* 2 (* n (PI))) k)))) (sqrt 2))>
#<alt (* (sqrt (/ (* n (PI)) (* k (pow (* 2 (* n (PI))) k)))) (sqrt 2))>
#<alt (* (sqrt (/ (* n (PI)) (* k (pow (* 2 (* n (PI))) k)))) (sqrt 2))>
#<alt (* (sqrt (/ (* n (PI)) (* k (pow (* 2 (* n (PI))) k)))) (sqrt 2))>
#<alt (* (sqrt (/ (* n (PI)) (* k (pow (* 2 (* n (PI))) k)))) (sqrt 2))>
#<alt (sqrt (* k (exp (* k (+ (log n) (log (* 2 (PI))))))))>
#<alt (sqrt (* k (exp (* k (+ (log n) (log (* 2 (PI))))))))>
#<alt (sqrt (* k (exp (* k (+ (log n) (log (* 2 (PI))))))))>
#<alt (sqrt (* k (exp (* k (+ (log n) (log (* 2 (PI))))))))>
#<alt (sqrt (* k (exp (* k (+ (log (* 2 (PI))) (* -1 (log (/ 1 n))))))))>
#<alt (sqrt (* k (exp (* k (+ (log (* 2 (PI))) (* -1 (log (/ 1 n))))))))>
#<alt (sqrt (* k (exp (* k (+ (log (* 2 (PI))) (* -1 (log (/ 1 n))))))))>
#<alt (sqrt (* k (exp (* k (+ (log (* 2 (PI))) (* -1 (log (/ 1 n))))))))>
#<alt (sqrt (* k (exp (* k (+ (log (* -2 (PI))) (* -1 (log (/ -1 n))))))))>
#<alt (sqrt (* k (exp (* k (+ (log (* -2 (PI))) (* -1 (log (/ -1 n))))))))>
#<alt (sqrt (* k (exp (* k (+ (log (* -2 (PI))) (* -1 (log (/ -1 n))))))))>
#<alt (sqrt (* k (exp (* k (+ (log (* -2 (PI))) (* -1 (log (/ -1 n))))))))>
#<alt (sqrt k)>
#<alt (+ (sqrt k) (* 1/2 (* (sqrt (pow k 3)) (log (* 2 (* n (PI)))))))>
#<alt (+ (sqrt k) (* (pow k 2) (+ (* 1/4 (* (sqrt k) (pow (log (* 2 (* n (PI)))) 2))) (* 1/2 (* (sqrt (/ 1 k)) (log (* 2 (* n (PI)))))))))>
#<alt (+ (sqrt k) (* (pow k 2) (+ (* 1/2 (* (sqrt (/ 1 k)) (log (* 2 (* n (PI)))))) (* k (+ (* 1/4 (* (sqrt (/ 1 k)) (pow (log (* 2 (* n (PI)))) 2))) (* 1/2 (* (sqrt k) (- (* 1/6 (pow (log (* 2 (* n (PI)))) 3)) (* 1/4 (/ (pow (log (* 2 (* n (PI)))) 2) k))))))))))>
#<alt (sqrt (* k (pow (* 2 (* n (PI))) k)))>
#<alt (sqrt (* k (pow (* 2 (* n (PI))) k)))>
#<alt (sqrt (* k (pow (* 2 (* n (PI))) k)))>
#<alt (sqrt (* k (pow (* 2 (* n (PI))) k)))>
#<alt (* -1 (* (sqrt (* k (pow (* 2 (* n (PI))) k))) (pow (sqrt -1) 2)))>
#<alt (* -1 (* (sqrt (* k (pow (* 2 (* n (PI))) k))) (pow (sqrt -1) 2)))>
#<alt (* -1 (* (sqrt (* k (pow (* 2 (* n (PI))) k))) (pow (sqrt -1) 2)))>
#<alt (* -1 (* (sqrt (* k (pow (* 2 (* n (PI))) k))) (pow (sqrt -1) 2)))>
#<alt (* (sqrt (* n (PI))) (sqrt 2))>
#<alt (* (sqrt (* n (PI))) (sqrt 2))>
#<alt (* (sqrt (* n (PI))) (sqrt 2))>
#<alt (* (sqrt (* n (PI))) (sqrt 2))>
#<alt (* (sqrt (* n (PI))) (sqrt 2))>
#<alt (* (sqrt (* n (PI))) (sqrt 2))>
#<alt (* (sqrt (* n (PI))) (sqrt 2))>
#<alt (* (sqrt (* n (PI))) (sqrt 2))>
#<alt (* -1 (* (sqrt (* n (PI))) (* (sqrt -2) (sqrt -1))))>
#<alt (* -1 (* (sqrt (* n (PI))) (* (sqrt -2) (sqrt -1))))>
#<alt (* -1 (* (sqrt (* n (PI))) (* (sqrt -2) (sqrt -1))))>
#<alt (* -1 (* (sqrt (* n (PI))) (* (sqrt -2) (sqrt -1))))>
#<alt (* n (PI))>
#<alt (* n (PI))>
#<alt (* n (PI))>
#<alt (* n (PI))>
#<alt (* n (PI))>
#<alt (* n (PI))>
#<alt (* n (PI))>
#<alt (* n (PI))>
#<alt (* n (PI))>
#<alt (* n (PI))>
#<alt (* n (PI))>
#<alt (* n (PI))>
#<alt (sqrt (/ 1 k))>
#<alt (sqrt (/ 1 k))>
#<alt (sqrt (/ 1 k))>
#<alt (sqrt (/ 1 k))>
#<alt (sqrt (/ 1 k))>
#<alt (sqrt (/ 1 k))>
#<alt (sqrt (/ 1 k))>
#<alt (sqrt (/ 1 k))>
#<alt (sqrt (/ 1 k))>
#<alt (sqrt (/ 1 k))>
#<alt (sqrt (/ 1 k))>
#<alt (sqrt (/ 1 k))>
#<alt (exp (* k (+ (log n) (log (* 2 (PI))))))>
#<alt (exp (* k (+ (log n) (log (* 2 (PI))))))>
#<alt (exp (* k (+ (log n) (log (* 2 (PI))))))>
#<alt (exp (* k (+ (log n) (log (* 2 (PI))))))>
#<alt (exp (* k (+ (log (* 2 (PI))) (* -1 (log (/ 1 n))))))>
#<alt (exp (* k (+ (log (* 2 (PI))) (* -1 (log (/ 1 n))))))>
#<alt (exp (* k (+ (log (* 2 (PI))) (* -1 (log (/ 1 n))))))>
#<alt (exp (* k (+ (log (* 2 (PI))) (* -1 (log (/ 1 n))))))>
#<alt (exp (* k (+ (log (* -2 (PI))) (* -1 (log (/ -1 n))))))>
#<alt (exp (* k (+ (log (* -2 (PI))) (* -1 (log (/ -1 n))))))>
#<alt (exp (* k (+ (log (* -2 (PI))) (* -1 (log (/ -1 n))))))>
#<alt (exp (* k (+ (log (* -2 (PI))) (* -1 (log (/ -1 n))))))>
#<alt 1>
#<alt (+ 1 (* k (log (* 2 (* n (PI))))))>
#<alt (+ 1 (* k (+ (log (* 2 (* n (PI)))) (* 1/2 (* k (pow (log (* 2 (* n (PI)))) 2))))))>
#<alt (+ 1 (* k (+ (log (* 2 (* n (PI)))) (* k (+ (* 1/6 (* k (pow (log (* 2 (* n (PI)))) 3))) (* 1/2 (pow (log (* 2 (* n (PI)))) 2)))))))>
#<alt (pow (* 2 (* n (PI))) k)>
#<alt (pow (* 2 (* n (PI))) k)>
#<alt (pow (* 2 (* n (PI))) k)>
#<alt (pow (* 2 (* n (PI))) k)>
#<alt (pow (* 2 (* n (PI))) k)>
#<alt (pow (* 2 (* n (PI))) k)>
#<alt (pow (* 2 (* n (PI))) k)>
#<alt (pow (* 2 (* n (PI))) k)>

Calls

102 calls:

Time	Variable		Point	Expression
29.0ms	k	@	-inf	(* (sqrt (/ (* n (PI)) k)) (sqrt 2))
4.0ms	k	@	-inf	(pow (* (pow (* 2 (* (PI) n)) k) k) 1/2)
3.0ms	n	@	-inf	(/ (sqrt (* 2 (* (PI) n))) (pow (* (pow (* 2 (* (PI) n)) k) k) 1/2))
2.0ms	n	@	inf	(/ (sqrt (* 2 (* (PI) n))) (pow (* (pow (* 2 (* (PI) n)) k) k) 1/2))
2.0ms	k	@	0	(/ (sqrt (* 2 (* (PI) n))) (pow (* (pow (* 2 (* (PI) n)) k) k) 1/2))

rewrite323.0ms (2.4%)

Algorithm

1×	batch-egg-rewrite

Rules

4896×	`-lowering-.f32`
4896×	`-lowering-.f64`
3004×	`/-lowering-/.f32`
3004×	`/-lowering-/.f64`
1898×	`pow-lowering-pow.f64`

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	41	169
1	262	159
2	1785	158
0	8344	158

Stop Event

1×	iter limit
1×	node limit

Counts

22 → 932

Calls

Call 1

Inputs
(/ (pow k -1/2) (pow (* 2 (* (PI) n)) (+ (/ k 2) -1/2)))
(pow k -1/2)
(pow (* 2 (* (PI) n)) (+ (/ k 2) -1/2))
(* 2 (* (PI) n))
(* (sqrt (/ (* n (PI)) k)) (sqrt 2))
(sqrt (/ (* n (PI)) k))
(/ (* n (PI)) k)
(* n (PI))
(* (/ 1 (sqrt k)) (pow (* (PI) (/ -2 (/ -1 n))) (+ 1/2 (* k -1/2))))
(pow (* (PI) (/ -2 (/ -1 n))) (+ 1/2 (* k -1/2)))
(* (PI) (/ -2 (/ -1 n)))
(/ -2 (/ -1 n))
(/ (pow (pow (* 2 (* (PI) n)) (- 1/4 (* k 1/4))) 2) (sqrt k))
(pow (pow (* 2 (* (PI) n)) (- 1/4 (* k 1/4))) 2)
(pow (* 2 (* (PI) n)) (- 1/4 (* k 1/4)))
(/ (sqrt (* 2 (* (PI) n))) (pow (* (pow (* 2 (* (PI) n)) k) k) 1/2))
(pow (* (pow (* 2 (* (PI) n)) k) k) 1/2)
(sqrt (* 2 (* (PI) n)))
(PI)
(* (PI) n)
(/ 1 (sqrt k))
(pow (* 2 (* (PI) n)) k)

Outputs
(exp.f64 (-.f64 (.f64 #s(literal -1/2 binary64) (log.f64 k)) (.f64 (+.f64 #s(literal -1/2 binary64) (/.f64 k #s(literal 2 binary64))) (log.f64 (.f64 #s(literal 2 binary64) (.f64 (PI.f64) n))))))
(exp.f64 (.f64 (log.f64 (/.f64 (pow.f64 (.f64 #s(literal 2 binary64) (*.f64 (PI.f64) n)) (+.f64 #s(literal -1/2 binary64) (/.f64 k #s(literal 2 binary64)))) (pow.f64 k #s(literal -1/2 binary64)))) #s(literal -1 binary64)))
(exp.f64 (.f64 (-.f64 (.f64 (+.f64 #s(literal -1/2 binary64) (/.f64 k #s(literal 2 binary64))) (log.f64 (.f64 #s(literal 2 binary64) (.f64 (PI.f64) n)))) (*.f64 #s(literal -1/2 binary64) (log.f64 k))) #s(literal -1 binary64)))
(exp.f64 (+.f64 (.f64 #s(literal -1/2 binary64) (log.f64 k)) (neg.f64 (.f64 (+.f64 #s(literal -1/2 binary64) (/.f64 k #s(literal 2 binary64))) (log.f64 (.f64 #s(literal 2 binary64) (.f64 (PI.f64) n)))))))
(exp.f64 (+.f64 (.f64 (.f64 #s(literal 1/2 binary64) (log.f64 k)) #s(literal -1 binary64)) (neg.f64 (.f64 (+.f64 #s(literal -1/2 binary64) (/.f64 k #s(literal 2 binary64))) (log.f64 (.f64 #s(literal 2 binary64) (*.f64 (PI.f64) n)))))))
(exp.f64 (+.f64 (neg.f64 (.f64 (+.f64 #s(literal -1/2 binary64) (/.f64 k #s(literal 2 binary64))) (log.f64 (.f64 #s(literal 2 binary64) (.f64 (PI.f64) n))))) (.f64 #s(literal -1/2 binary64) (log.f64 k))))
(exp.f64 (+.f64 (neg.f64 (.f64 (+.f64 #s(literal -1/2 binary64) (/.f64 k #s(literal 2 binary64))) (log.f64 (.f64 #s(literal 2 binary64) (.f64 (PI.f64) n))))) (.f64 (*.f64 #s(literal 1/2 binary64) (log.f64 k)) #s(literal -1 binary64))))
(exp.f64 (neg.f64 (-.f64 (.f64 (+.f64 #s(literal -1/2 binary64) (/.f64 k #s(literal 2 binary64))) (log.f64 (.f64 #s(literal 2 binary64) (.f64 (PI.f64) n)))) (.f64 #s(literal -1/2 binary64) (log.f64 k)))))
(exp.f64 (-.f64 (.f64 (.f64 #s(literal 1/2 binary64) (log.f64 k)) #s(literal -1 binary64)) (.f64 (+.f64 #s(literal -1/2 binary64) (/.f64 k #s(literal 2 binary64))) (log.f64 (.f64 #s(literal 2 binary64) (*.f64 (PI.f64) n))))))
(neg.f64 (/.f64 (pow.f64 k #s(literal -1/2 binary64)) (-.f64 #s(literal 0 binary64) (pow.f64 (.f64 #s(literal 2 binary64) (.f64 (PI.f64) n)) (+.f64 #s(literal -1/2 binary64) (/.f64 k #s(literal 2 binary64)))))))
(neg.f64 (/.f64 (-.f64 #s(literal 0 binary64) (pow.f64 k #s(literal -1/2 binary64))) (pow.f64 (.f64 #s(literal 2 binary64) (.f64 (PI.f64) n)) (+.f64 #s(literal -1/2 binary64) (/.f64 k #s(literal 2 binary64))))))
(/.f64 #s(literal 1 binary64) (/.f64 (pow.f64 (.f64 #s(literal 2 binary64) (.f64 (PI.f64) n)) (+.f64 #s(literal -1/2 binary64) (/.f64 k #s(literal 2 binary64)))) (pow.f64 k #s(literal -1/2 binary64))))
(/.f64 #s(literal 1 binary64) (/.f64 (/.f64 (pow.f64 (.f64 #s(literal 2 binary64) (.f64 (PI.f64) n)) (+.f64 #s(literal -1/2 binary64) (/.f64 k #s(literal 2 binary64)))) (pow.f64 k #s(literal -1/2 binary64))) #s(literal 1 binary64)))
(/.f64 #s(literal 1 binary64) (.f64 (sqrt.f64 k) (pow.f64 (.f64 #s(literal 2 binary64) (*.f64 (PI.f64) n)) (+.f64 #s(literal -1/2 binary64) (/.f64 k #s(literal 2 binary64))))))
(/.f64 #s(literal 1 binary64) (.f64 (sqrt.f64 k) (/.f64 (pow.f64 (.f64 #s(literal 2 binary64) (*.f64 (PI.f64) n)) (+.f64 #s(literal -1/2 binary64) (/.f64 k #s(literal 2 binary64)))) #s(literal 1 binary64))))
(/.f64 #s(literal 1 binary64) (.f64 (neg.f64 (-.f64 #s(literal 0 binary64) (sqrt.f64 k))) (pow.f64 (.f64 #s(literal 2 binary64) (*.f64 (PI.f64) n)) (+.f64 #s(literal -1/2 binary64) (/.f64 k #s(literal 2 binary64))))))
(/.f64 #s(literal 1 binary64) (.f64 (neg.f64 (-.f64 #s(literal 0 binary64) (sqrt.f64 k))) (/.f64 (pow.f64 (.f64 #s(literal 2 binary64) (*.f64 (PI.f64) n)) (+.f64 #s(literal -1/2 binary64) (/.f64 k #s(literal 2 binary64)))) #s(literal 1 binary64))))
(/.f64 #s(literal 1 binary64) (.f64 (-.f64 #s(literal 0 binary64) (sqrt.f64 k)) (-.f64 #s(literal 0 binary64) (pow.f64 (.f64 #s(literal 2 binary64) (*.f64 (PI.f64) n)) (+.f64 #s(literal -1/2 binary64) (/.f64 k #s(literal 2 binary64)))))))
(/.f64 #s(literal 1 binary64) (.f64 (pow.f64 (.f64 #s(literal 2 binary64) (*.f64 (PI.f64) n)) (+.f64 #s(literal -1/2 binary64) (/.f64 k #s(literal 2 binary64)))) (neg.f64 (-.f64 #s(literal 0 binary64) (sqrt.f64 k)))))
(/.f64 #s(literal 1 binary64) (.f64 (/.f64 (pow.f64 (.f64 #s(literal 2 binary64) (*.f64 (PI.f64) n)) (+.f64 #s(literal -1/2 binary64) (/.f64 k #s(literal 2 binary64)))) #s(literal 1 binary64)) (sqrt.f64 k)))
(/.f64 #s(literal 1 binary64) (.f64 (/.f64 (pow.f64 (.f64 #s(literal 2 binary64) (*.f64 (PI.f64) n)) (+.f64 #s(literal -1/2 binary64) (/.f64 k #s(literal 2 binary64)))) #s(literal 1 binary64)) (neg.f64 (-.f64 #s(literal 0 binary64) (sqrt.f64 k)))))
(/.f64 #s(literal 1 binary64) (.f64 (-.f64 #s(literal 0 binary64) (pow.f64 (.f64 #s(literal 2 binary64) (*.f64 (PI.f64) n)) (+.f64 #s(literal -1/2 binary64) (/.f64 k #s(literal 2 binary64))))) (-.f64 #s(literal 0 binary64) (sqrt.f64 k))))
(/.f64 (pow.f64 k #s(literal -1/2 binary64)) (pow.f64 (.f64 #s(literal 2 binary64) (.f64 (PI.f64) n)) (+.f64 #s(literal -1/2 binary64) (/.f64 k #s(literal 2 binary64)))))
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(.f64 (pow.f64 (.f64 #s(literal 2 binary64) (.f64 (PI.f64) n)) (.f64 k #s(literal 1/4 binary64))) (sqrt.f64 (.f64 (pow.f64 (.f64 #s(literal 2 binary64) (*.f64 (PI.f64) n)) (/.f64 k #s(literal 2 binary64))) k)))
(.f64 (pow.f64 (.f64 #s(literal 2 binary64) (*.f64 (PI.f64) n)) (/.f64 k #s(literal 2 binary64))) (sqrt.f64 k))
(.f64 (pow.f64 (.f64 k (pow.f64 (.f64 #s(literal 2 binary64) (.f64 (PI.f64) n)) k)) #s(literal 1/4 binary64)) (pow.f64 (.f64 k (pow.f64 (.f64 #s(literal 2 binary64) (*.f64 (PI.f64) n)) k)) #s(literal 1/4 binary64)))
(.f64 (pow.f64 #s(literal 2 binary64) (/.f64 k #s(literal 2 binary64))) (sqrt.f64 (.f64 (pow.f64 (*.f64 (PI.f64) n) k) k)))
(.f64 (sqrt.f64 (.f64 k (pow.f64 (.f64 #s(literal 2 binary64) (.f64 (PI.f64) n)) (/.f64 k #s(literal 2 binary64))))) (pow.f64 (.f64 #s(literal 2 binary64) (.f64 (PI.f64) n)) (*.f64 k #s(literal 1/4 binary64))))
(.f64 (sqrt.f64 (.f64 k (pow.f64 #s(literal 2 binary64) k))) (pow.f64 (*.f64 (PI.f64) n) (/.f64 k #s(literal 2 binary64))))
(exp.f64 (.f64 (log.f64 (.f64 #s(literal 2 binary64) (*.f64 (PI.f64) n))) #s(literal 1/2 binary64)))
(exp.f64 (+.f64 (.f64 #s(literal 1/4 binary64) (log.f64 (.f64 #s(literal 2 binary64) (.f64 (PI.f64) n)))) (.f64 #s(literal 1/4 binary64) (log.f64 (.f64 #s(literal 2 binary64) (.f64 (PI.f64) n))))))
(sqrt.f64 (.f64 #s(literal 2 binary64) (.f64 (PI.f64) n)))
(/.f64 #s(literal 1 binary64) (sqrt.f64 (/.f64 (/.f64 #s(literal -1 binary64) n) (*.f64 (PI.f64) #s(literal -2 binary64)))))
(/.f64 (sqrt.f64 (PI.f64)) (sqrt.f64 (/.f64 (/.f64 #s(literal 1 binary64) n) #s(literal 2 binary64))))
(/.f64 (pow.f64 (*.f64 #s(literal 2 binary64) (PI.f64)) #s(literal 1/2 binary64)) (sqrt.f64 (/.f64 #s(literal 1 binary64) n)))
(/.f64 (sqrt.f64 (*.f64 (PI.f64) #s(literal -2 binary64))) (sqrt.f64 (/.f64 #s(literal -1 binary64) n)))
(/.f64 (sqrt.f64 (/.f64 (*.f64 (PI.f64) #s(literal -2 binary64)) #s(literal -1 binary64))) (sqrt.f64 (/.f64 #s(literal 1 binary64) n)))
(/.f64 (sqrt.f64 (neg.f64 (*.f64 (PI.f64) #s(literal -2 binary64)))) (sqrt.f64 (/.f64 #s(literal 1 binary64) n)))
(pow.f64 (.f64 #s(literal 2 binary64) (.f64 (PI.f64) n)) #s(literal 1/2 binary64))
(pow.f64 (pow.f64 (.f64 #s(literal 2 binary64) (.f64 (PI.f64) n)) #s(literal 1/4 binary64)) #s(literal 2 binary64))
(pow.f64 (.f64 (.f64 #s(literal 2 binary64) (.f64 (PI.f64) n)) (.f64 #s(literal 2 binary64) (*.f64 (PI.f64) n))) #s(literal 1/4 binary64))
(.f64 (sqrt.f64 #s(literal 2 binary64)) (pow.f64 (.f64 (PI.f64) n) #s(literal 1/2 binary64)))
(.f64 #s(literal 1 binary64) (sqrt.f64 (.f64 #s(literal 2 binary64) (*.f64 (PI.f64) n))))
(.f64 (pow.f64 (.f64 #s(literal 2 binary64) (.f64 (PI.f64) n)) #s(literal 1/4 binary64)) (pow.f64 (.f64 #s(literal 2 binary64) (*.f64 (PI.f64) n)) #s(literal 1/4 binary64)))
(.f64 (cbrt.f64 (PI.f64)) (sqrt.f64 (.f64 (cbrt.f64 (PI.f64)) (*.f64 #s(literal 2 binary64) n))))
(.f64 (sqrt.f64 (PI.f64)) (pow.f64 (.f64 #s(literal 2 binary64) n) #s(literal 1/2 binary64)))
(.f64 (pow.f64 (.f64 #s(literal 2 binary64) n) #s(literal 1/2 binary64)) (sqrt.f64 (PI.f64)))
(.f64 (sqrt.f64 n) (pow.f64 (.f64 #s(literal 2 binary64) (PI.f64)) #s(literal 1/2 binary64)))
(.f64 (pow.f64 (.f64 (PI.f64) n) #s(literal 1/2 binary64)) (sqrt.f64 #s(literal 2 binary64)))
(.f64 (pow.f64 (.f64 #s(literal 2 binary64) (PI.f64)) #s(literal 1/2 binary64)) (sqrt.f64 n))
(.f64 (pow.f64 (PI.f64) #s(literal 1/4 binary64)) (sqrt.f64 (.f64 (sqrt.f64 (PI.f64)) (*.f64 #s(literal 2 binary64) n))))
(.f64 (sqrt.f64 #s(literal -2 binary64)) (sqrt.f64 (-.f64 #s(literal 0 binary64) (.f64 (PI.f64) n))))
(.f64 (sqrt.f64 (.f64 (PI.f64) #s(literal -2 binary64))) (sqrt.f64 (-.f64 #s(literal 0 binary64) n)))
(*.f64 (sqrt.f64 (/.f64 (PI.f64) #s(literal -1 binary64))) (sqrt.f64 (/.f64 #s(literal -2 binary64) (/.f64 #s(literal 1 binary64) n))))
(.f64 (sqrt.f64 (.f64 (*.f64 #s(literal 2 binary64) n) #s(literal 1 binary64))) (sqrt.f64 (PI.f64)))
(.f64 (sqrt.f64 (.f64 (*.f64 #s(literal 2 binary64) n) (pow.f64 (PI.f64) #s(literal 2/3 binary64)))) (pow.f64 (PI.f64) #s(literal 1/6 binary64)))
(.f64 (sqrt.f64 (.f64 (*.f64 #s(literal 2 binary64) n) (sqrt.f64 (PI.f64)))) (pow.f64 (PI.f64) #s(literal 1/4 binary64)))
(.f64 (sqrt.f64 (/.f64 (.f64 (PI.f64) #s(literal -2 binary64)) #s(literal -1 binary64))) (sqrt.f64 n))
(.f64 (sqrt.f64 (/.f64 (.f64 (PI.f64) #s(literal -2 binary64)) #s(literal 1 binary64))) (sqrt.f64 (-.f64 #s(literal 0 binary64) n)))
(PI.f64)
(log.f64 (exp.f64 (PI.f64)))
(exp.f64 (log.f64 (PI.f64)))
(exp.f64 (.f64 (.f64 #s(literal 1/3 binary64) (log.f64 (PI.f64))) #s(literal 3 binary64)))
(exp.f64 (.f64 (log.f64 (.f64 (PI.f64) (*.f64 (PI.f64) (PI.f64)))) #s(literal 1/3 binary64)))
(exp.f64 (.f64 (.f64 #s(literal 1/2 binary64) (log.f64 (PI.f64))) #s(literal 2 binary64)))
(fabs.f64 (PI.f64))
(-.f64 (+.f64 #s(literal 1 binary64) (PI.f64)) #s(literal 1 binary64))
(sqrt.f64 (*.f64 (PI.f64) (PI.f64)))
(cbrt.f64 (.f64 (PI.f64) (.f64 (PI.f64) (PI.f64))))
(expm1.f64 (log1p.f64 (PI.f64)))
(log1p.f64 (expm1.f64 (PI.f64)))
(pow.f64 (PI.f64) #s(literal 1 binary64))
(pow.f64 (cbrt.f64 (PI.f64)) #s(literal 3 binary64))
(pow.f64 (*.f64 (PI.f64) (PI.f64)) #s(literal 1/2 binary64))
(pow.f64 (.f64 (PI.f64) (.f64 (PI.f64) (PI.f64))) #s(literal 1/3 binary64))
(pow.f64 (sqrt.f64 (PI.f64)) #s(literal 2 binary64))
(pow.f64 (E.f64) (log.f64 (PI.f64)))
(*.f64 (PI.f64) #s(literal 1 binary64))
(*.f64 (PI.f64) (log.f64 (E.f64)))
(*.f64 #s(literal 1 binary64) (PI.f64))
(*.f64 (cbrt.f64 (PI.f64)) (pow.f64 (PI.f64) #s(literal 2/3 binary64)))
(*.f64 (cbrt.f64 (PI.f64)) (log.f64 (exp.f64 (pow.f64 (PI.f64) #s(literal 2/3 binary64)))))
(*.f64 (cbrt.f64 (PI.f64)) (sqrt.f64 (pow.f64 (PI.f64) #s(literal 4/3 binary64))))
(*.f64 (pow.f64 (PI.f64) #s(literal 2/3 binary64)) (cbrt.f64 (PI.f64)))
(*.f64 (sqrt.f64 (PI.f64)) (sqrt.f64 (PI.f64)))
(*.f64 (sqrt.f64 (PI.f64)) (log.f64 (exp.f64 (sqrt.f64 (PI.f64)))))
(*.f64 (pow.f64 (PI.f64) #s(literal 1/4 binary64)) (sqrt.f64 (pow.f64 (PI.f64) #s(literal 3/2 binary64))))
(.f64 (exp.f64 (.f64 #s(literal 2 binary64) (.f64 #s(literal 1/3 binary64) (log.f64 (PI.f64))))) (exp.f64 (.f64 #s(literal 1/3 binary64) (log.f64 (PI.f64)))))
(.f64 (exp.f64 (.f64 #s(literal 1/2 binary64) (log.f64 (PI.f64)))) (exp.f64 (*.f64 #s(literal 1/2 binary64) (log.f64 (PI.f64)))))
(*.f64 (cbrt.f64 (pow.f64 (PI.f64) #s(literal 3/2 binary64))) (cbrt.f64 (pow.f64 (PI.f64) #s(literal 3/2 binary64))))
(.f64 (cbrt.f64 (.f64 (*.f64 (PI.f64) (PI.f64)) #s(literal 1 binary64))) (cbrt.f64 (PI.f64)))
(.f64 (cbrt.f64 (.f64 (*.f64 (PI.f64) (PI.f64)) (pow.f64 (PI.f64) #s(literal 2/3 binary64)))) (pow.f64 (cbrt.f64 (PI.f64)) #s(literal 1/3 binary64)))
(*.f64 (cbrt.f64 (pow.f64 (PI.f64) #s(literal 5/2 binary64))) (pow.f64 (sqrt.f64 (PI.f64)) #s(literal 1/3 binary64)))
(*.f64 (pow.f64 (pow.f64 (pow.f64 (PI.f64) #s(literal 2/3 binary64)) #s(literal 1/3 binary64)) #s(literal 3 binary64)) (pow.f64 (pow.f64 (cbrt.f64 (PI.f64)) #s(literal 1/3 binary64)) #s(literal 3 binary64)))
(*.f64 (pow.f64 (pow.f64 (sqrt.f64 (PI.f64)) #s(literal 1/3 binary64)) #s(literal 3 binary64)) (pow.f64 (pow.f64 (sqrt.f64 (PI.f64)) #s(literal 1/3 binary64)) #s(literal 3 binary64)))
(*.f64 (sqrt.f64 (pow.f64 (PI.f64) #s(literal 3/2 binary64))) (pow.f64 (PI.f64) #s(literal 1/4 binary64)))
(.f64 (sqrt.f64 (cbrt.f64 (.f64 (.f64 (PI.f64) (PI.f64)) (.f64 (PI.f64) (PI.f64))))) (cbrt.f64 (PI.f64)))
(.f64 (sqrt.f64 (.f64 (PI.f64) (pow.f64 (PI.f64) #s(literal 2/3 binary64)))) (pow.f64 (PI.f64) #s(literal 1/6 binary64)))
(*.f64 (PI.f64) n)
(*.f64 n (PI.f64))
(.f64 #s(literal 1 binary64) (.f64 (PI.f64) n))
(.f64 (pow.f64 (PI.f64) #s(literal 2/3 binary64)) (.f64 (cbrt.f64 (PI.f64)) n))
(.f64 (sqrt.f64 (PI.f64)) (.f64 (sqrt.f64 (PI.f64)) n))
(.f64 (.f64 n #s(literal 1 binary64)) (PI.f64))
(.f64 (.f64 n (pow.f64 (PI.f64) #s(literal 2/3 binary64))) (cbrt.f64 (PI.f64)))
(.f64 (.f64 n (sqrt.f64 (PI.f64))) (sqrt.f64 (PI.f64)))
(exp.f64 (*.f64 #s(literal -1/2 binary64) (log.f64 k)))
(exp.f64 (.f64 (.f64 #s(literal 1/2 binary64) (log.f64 k)) #s(literal -1 binary64)))
(exp.f64 (*.f64 (log.f64 (pow.f64 k #s(literal -1/4 binary64))) #s(literal 2 binary64)))
(exp.f64 (.f64 (log.f64 (.f64 k k)) #s(literal -1/4 binary64)))
(exp.f64 (*.f64 (log.f64 (/.f64 #s(literal 1 binary64) k)) #s(literal 1/2 binary64)))
(exp.f64 (.f64 (.f64 (log.f64 k) #s(literal -1/4 binary64)) #s(literal 2 binary64)))
(exp.f64 (+.f64 (.f64 (log.f64 k) #s(literal -1/4 binary64)) (.f64 (log.f64 k) #s(literal -1/4 binary64))))
(exp.f64 (neg.f64 (*.f64 #s(literal 1/2 binary64) (log.f64 k))))
(sqrt.f64 (/.f64 #s(literal 1 binary64) k))
(neg.f64 (/.f64 #s(literal -1 binary64) (sqrt.f64 k)))
(/.f64 #s(literal 1 binary64) (sqrt.f64 k))
(/.f64 #s(literal 1 binary64) (neg.f64 (-.f64 #s(literal 0 binary64) (sqrt.f64 k))))
(/.f64 #s(literal 1 binary64) (sqrt.f64 (/.f64 k #s(literal 1 binary64))))
(/.f64 #s(literal -1 binary64) (-.f64 #s(literal 0 binary64) (sqrt.f64 k)))
(/.f64 (sqrt.f64 #s(literal -1 binary64)) (pow.f64 (-.f64 #s(literal 0 binary64) k) #s(literal 1/2 binary64)))
(pow.f64 k #s(literal -1/2 binary64))
(pow.f64 (sqrt.f64 k) #s(literal -1 binary64))
(pow.f64 (/.f64 #s(literal 1 binary64) k) #s(literal 1/2 binary64))
(pow.f64 (pow.f64 k #s(literal -1/4 binary64)) #s(literal 2 binary64))
(pow.f64 (*.f64 k k) #s(literal -1/4 binary64))
(pow.f64 (neg.f64 (-.f64 #s(literal 0 binary64) (sqrt.f64 k))) #s(literal -1 binary64))
(pow.f64 (*.f64 (sqrt.f64 k) (sqrt.f64 k)) #s(literal -1/2 binary64))
(pow.f64 (exp.f64 #s(literal -1/2 binary64)) (log.f64 k))
(*.f64 #s(literal 1 binary64) (pow.f64 k #s(literal -1/2 binary64)))
(*.f64 (pow.f64 k #s(literal -1/2 binary64)) #s(literal 1 binary64))
(*.f64 #s(literal -1 binary64) (/.f64 #s(literal 1 binary64) (-.f64 #s(literal 0 binary64) (sqrt.f64 k))))
(*.f64 (pow.f64 k #s(literal -1/4 binary64)) (pow.f64 k #s(literal -1/4 binary64)))
(exp.f64 (.f64 k (log.f64 (.f64 #s(literal 2 binary64) (*.f64 (PI.f64) n)))))
(exp.f64 (.f64 (log.f64 (.f64 #s(literal 2 binary64) (*.f64 (PI.f64) n))) (+.f64 (/.f64 k #s(literal 2 binary64)) (/.f64 k #s(literal 2 binary64)))))
(exp.f64 (.f64 (log.f64 (.f64 #s(literal 2 binary64) (.f64 (PI.f64) n))) (.f64 #s(literal 2 binary64) (/.f64 k #s(literal 2 binary64)))))
(exp.f64 (.f64 (log.f64 (pow.f64 (.f64 #s(literal 2 binary64) (*.f64 (PI.f64) n)) (/.f64 k #s(literal 2 binary64)))) #s(literal 2 binary64)))
(exp.f64 (.f64 (log.f64 (.f64 (.f64 #s(literal 2 binary64) (.f64 (PI.f64) n)) (.f64 #s(literal 2 binary64) (.f64 (PI.f64) n)))) (/.f64 k #s(literal 2 binary64))))
(exp.f64 (.f64 (.f64 (.f64 k (log.f64 (.f64 #s(literal 2 binary64) (*.f64 (PI.f64) n)))) #s(literal 1/2 binary64)) #s(literal 2 binary64)))
(exp.f64 (.f64 (.f64 (log.f64 (.f64 #s(literal 2 binary64) (.f64 (PI.f64) n))) (/.f64 k #s(literal 2 binary64))) #s(literal 2 binary64)))
(exp.f64 (+.f64 (.f64 (.f64 k (log.f64 (.f64 #s(literal 2 binary64) (.f64 (PI.f64) n)))) #s(literal 1/2 binary64)) (.f64 (.f64 k (log.f64 (.f64 #s(literal 2 binary64) (.f64 (PI.f64) n)))) #s(literal 1/2 binary64))))
(exp.f64 (+.f64 (.f64 (.f64 k (log.f64 (.f64 #s(literal 2 binary64) (.f64 (PI.f64) n)))) #s(literal 1/2 binary64)) (.f64 (log.f64 (.f64 #s(literal 2 binary64) (*.f64 (PI.f64) n))) (/.f64 k #s(literal 2 binary64)))))
(exp.f64 (+.f64 (.f64 (log.f64 (.f64 #s(literal 2 binary64) (.f64 (PI.f64) n))) (/.f64 k #s(literal 2 binary64))) (.f64 (.f64 k (log.f64 (.f64 #s(literal 2 binary64) (*.f64 (PI.f64) n)))) #s(literal 1/2 binary64))))
(exp.f64 (+.f64 (.f64 (log.f64 (.f64 #s(literal 2 binary64) (.f64 (PI.f64) n))) (/.f64 k #s(literal 2 binary64))) (.f64 (log.f64 (.f64 #s(literal 2 binary64) (.f64 (PI.f64) n))) (/.f64 k #s(literal 2 binary64)))))
(exp.f64 (+.f64 (.f64 (log.f64 #s(literal 2 binary64)) k) (.f64 (log.f64 (*.f64 (PI.f64) n)) k)))
(exp.f64 (+.f64 (.f64 (log.f64 (.f64 (PI.f64) n)) k) (*.f64 (log.f64 #s(literal 2 binary64)) k)))
(sqrt.f64 (.f64 (pow.f64 (.f64 #s(literal 2 binary64) (.f64 (PI.f64) n)) k) (pow.f64 (.f64 #s(literal 2 binary64) (*.f64 (PI.f64) n)) k)))
(/.f64 #s(literal 1 binary64) (pow.f64 (.f64 (.f64 #s(literal 2 binary64) (.f64 (PI.f64) n)) (.f64 #s(literal 2 binary64) (*.f64 (PI.f64) n))) (/.f64 k #s(literal -2 binary64))))
(pow.f64 (.f64 #s(literal 2 binary64) (.f64 (PI.f64) n)) k)
(pow.f64 (.f64 #s(literal 2 binary64) (.f64 (PI.f64) n)) (+.f64 (/.f64 k #s(literal 2 binary64)) (/.f64 k #s(literal 2 binary64))))
(pow.f64 (.f64 #s(literal 2 binary64) (.f64 (PI.f64) n)) (*.f64 #s(literal 2 binary64) (/.f64 k #s(literal 2 binary64))))
(pow.f64 (.f64 #s(literal 2 binary64) (.f64 (PI.f64) n)) (*.f64 (/.f64 k #s(literal 2 binary64)) #s(literal 2 binary64)))
(pow.f64 (pow.f64 (.f64 #s(literal 2 binary64) (.f64 (PI.f64) n)) k) #s(literal 1 binary64))
(pow.f64 (pow.f64 (.f64 #s(literal 2 binary64) (.f64 (PI.f64) n)) (/.f64 k #s(literal 2 binary64))) #s(literal 2 binary64))
(pow.f64 (.f64 (.f64 #s(literal 2 binary64) (.f64 (PI.f64) n)) (.f64 #s(literal 2 binary64) (*.f64 (PI.f64) n))) (/.f64 k #s(literal 2 binary64)))
(pow.f64 (pow.f64 (.f64 (.f64 #s(literal 2 binary64) (.f64 (PI.f64) n)) (.f64 #s(literal 2 binary64) (*.f64 (PI.f64) n))) k) #s(literal 1/2 binary64))
(pow.f64 (pow.f64 (.f64 (.f64 #s(literal 2 binary64) (.f64 (PI.f64) n)) (.f64 #s(literal 2 binary64) (*.f64 (PI.f64) n))) #s(literal 1 binary64)) (/.f64 k #s(literal 2 binary64)))
(pow.f64 (pow.f64 (.f64 (.f64 #s(literal 2 binary64) (.f64 (PI.f64) n)) (.f64 #s(literal 2 binary64) (*.f64 (PI.f64) n))) #s(literal 1/2 binary64)) k)
(pow.f64 (pow.f64 (.f64 (.f64 #s(literal 2 binary64) (.f64 (PI.f64) n)) (.f64 #s(literal 2 binary64) (*.f64 (PI.f64) n))) (-.f64 #s(literal 0 binary64) k)) #s(literal -1/2 binary64))
(pow.f64 (.f64 (pow.f64 (.f64 #s(literal 2 binary64) (.f64 (PI.f64) n)) k) (pow.f64 (.f64 #s(literal 2 binary64) (*.f64 (PI.f64) n)) k)) #s(literal 1/2 binary64))
(pow.f64 (exp.f64 k) (log.f64 (.f64 #s(literal 2 binary64) (.f64 (PI.f64) n))))
(.f64 (pow.f64 (.f64 #s(literal 2 binary64) (.f64 (PI.f64) n)) (/.f64 k #s(literal 2 binary64))) (pow.f64 (.f64 #s(literal 2 binary64) (*.f64 (PI.f64) n)) (/.f64 k #s(literal 2 binary64))))
(.f64 (pow.f64 #s(literal 2 binary64) k) (pow.f64 (.f64 (PI.f64) n) k))
(.f64 (pow.f64 (.f64 (PI.f64) n) k) (pow.f64 #s(literal 2 binary64) k))
(.f64 (pow.f64 (.f64 #s(literal 2 binary64) (PI.f64)) k) (pow.f64 n k))

simplify325.0ms (2.4%)

Algorithm

1×	egg-herbie

Rules

6586×	`-lowering-.f32`
6586×	`-lowering-.f64`
2094×	`+-lowering-+.f64`
2094×	`+-lowering-+.f32`
1354×	`distribute-lft-in`

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	394	5673
1	1286	5389
2	4855	4959
0	8494	4959

Stop Event

1×	iter limit
1×	node limit

Counts

408 → 408

Calls

Call 1

Inputs
(* (sqrt (/ (* n (PI)) k)) (/ 1 (sqrt 1/2)))
(/ (+ (* -1/2 (* (sqrt (* (pow k 3) (* n (PI)))) (/ (log (* 2 (* n (PI)))) (sqrt 1/2)))) (* (sqrt (* k (* n (PI)))) (/ 1 (sqrt 1/2)))) k)
(/ (+ (* k (+ (* -1 (* (sqrt (pow k 3)) (+ (* -1/4 (* (sqrt (* n (PI))) (/ (pow (log (* 2 (* n (PI)))) 2) (sqrt 1/2)))) (* 1/8 (* (sqrt (* n (PI))) (/ (pow (log (* 2 (* n (PI)))) 2) (sqrt 1/2))))))) (* -1/2 (* (sqrt (* k (* n (PI)))) (/ (log (* 2 (* n (PI)))) (sqrt 1/2)))))) (* (sqrt (* k (* n (PI)))) (/ 1 (sqrt 1/2)))) k)
(/ (+ (* k (+ (* -1/2 (* (sqrt (* k (* n (PI)))) (/ (log (* 2 (* n (PI)))) (sqrt 1/2)))) (* k (+ (* -1 (* (sqrt k) (+ (* -1/4 (* (sqrt (* n (PI))) (/ (pow (log (* 2 (* n (PI)))) 2) (sqrt 1/2)))) (* 1/8 (* (sqrt (* n (PI))) (/ (pow (log (* 2 (* n (PI)))) 2) (sqrt 1/2))))))) (* -1 (* (sqrt (pow k 3)) (+ (* -1/2 (* (log (* 2 (* n (PI)))) (+ (* -1/4 (* (sqrt (* n (PI))) (/ (pow (log (* 2 (* n (PI)))) 2) (sqrt 1/2)))) (* 1/8 (* (sqrt (* n (PI))) (/ (pow (log (* 2 (* n (PI)))) 2) (sqrt 1/2))))))) (+ (* -1/16 (* (sqrt (* n (PI))) (/ (pow (log (* 2 (* n (PI)))) 3) (sqrt 1/2)))) (* 1/48 (* (sqrt (* n (PI))) (/ (pow (log (* 2 (* n (PI)))) 3) (sqrt 1/2)))))))))))) (* (sqrt (* k (* n (PI)))) (/ 1 (sqrt 1/2)))) k)
(* (sqrt (/ 1 k)) (/ 1 (exp (* (log (* 2 (* n (PI)))) (- (* 1/2 k) 1/2)))))
(* (sqrt (/ 1 k)) (/ 1 (exp (* (log (* 2 (* n (PI)))) (- (* 1/2 k) 1/2)))))
(* (sqrt (/ 1 k)) (/ 1 (exp (* (log (* 2 (* n (PI)))) (- (* 1/2 k) 1/2)))))
(* (sqrt (/ 1 k)) (/ 1 (exp (* (log (* 2 (* n (PI)))) (- (* 1/2 k) 1/2)))))
(* (sqrt (/ 1 k)) (/ (pow (sqrt -1) 2) (exp (* -1 (* (log (* 2 (* n (PI)))) (+ 1/2 (* -1/2 k)))))))
(* (sqrt (/ 1 k)) (/ (pow (sqrt -1) 2) (exp (* -1 (* (log (* 2 (* n (PI)))) (+ 1/2 (* -1/2 k)))))))
(* (sqrt (/ 1 k)) (/ (pow (sqrt -1) 2) (exp (* -1 (* (log (* 2 (* n (PI)))) (+ 1/2 (* -1/2 k)))))))
(* (sqrt (/ 1 k)) (/ (pow (sqrt -1) 2) (exp (* -1 (* (log (* 2 (* n (PI)))) (+ 1/2 (* -1/2 k)))))))
(* (sqrt (/ 1 k)) (/ 1 (exp (* (+ (log n) (log (* 2 (PI)))) (- (* 1/2 k) 1/2)))))
(* (sqrt (/ 1 k)) (/ 1 (exp (* (+ (log n) (log (* 2 (PI)))) (- (* 1/2 k) 1/2)))))
(* (sqrt (/ 1 k)) (/ 1 (exp (* (+ (log n) (log (* 2 (PI)))) (- (* 1/2 k) 1/2)))))
(* (sqrt (/ 1 k)) (/ 1 (exp (* (+ (log n) (log (* 2 (PI)))) (- (* 1/2 k) 1/2)))))
(* (sqrt (/ 1 k)) (/ 1 (exp (* (+ (log (* 2 (PI))) (* -1 (log (/ 1 n)))) (- (* 1/2 k) 1/2)))))
(* (sqrt (/ 1 k)) (/ 1 (exp (* (+ (log (* 2 (PI))) (* -1 (log (/ 1 n)))) (- (* 1/2 k) 1/2)))))
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(/ (+ (* (sqrt (* k (* n (PI)))) (sqrt 2)) (* (pow k 2) (+ (* -1/2 (* (sqrt (/ k (* n (PI)))) (* (sqrt 2) (+ (* -1 (* n (* (PI) (pow (log (* 2 (* n (PI)))) 2)))) (* 1/2 (* n (* (PI) (pow (log (* 2 (* n (PI)))) 2)))))))) (* -1/2 (* (sqrt (/ (* n (PI)) k)) (* (log (* 2 (* n (PI)))) (sqrt 2))))))) k)
(/ (+ (* (sqrt (* k (* n (PI)))) (sqrt 2)) (* (pow k 2) (+ (* -1/2 (* (sqrt (/ (* n (PI)) k)) (* (log (* 2 (* n (PI)))) (sqrt 2)))) (* k (+ (* -1/2 (* (sqrt (/ 1 (* k (* n (PI))))) (* (sqrt 2) (+ (* -1 (* n (* (PI) (pow (log (* 2 (* n (PI)))) 2)))) (* 1/2 (* n (* (PI) (pow (log (* 2 (* n (PI)))) 2)))))))) (* -1/2 (* (sqrt (/ k (* n (PI)))) (* (sqrt 2) (+ (* -1 (* (log (* 2 (* n (PI)))) (+ (* -1 (* n (* (PI) (pow (log (* 2 (* n (PI)))) 2)))) (* 1/2 (* n (* (PI) (pow (log (* 2 (* n (PI)))) 2))))))) (+ (* -1/2 (* n (* (PI) (pow (log (* 2 (* n (PI)))) 3)))) (+ (* 1/6 (* n (* (PI) (pow (log (* 2 (* n (PI)))) 3)))) (* 1/4 (/ (* n (* (PI) (pow (log (* 2 (* n (PI)))) 2))) k))))))))))))) k)
(* (sqrt (/ (* n (PI)) (* k (pow (* 2 (* n (PI))) k)))) (sqrt 2))
(* (sqrt (/ (* n (PI)) (* k (pow (* 2 (* n (PI))) k)))) (sqrt 2))
(* (sqrt (/ (* n (PI)) (* k (pow (* 2 (* n (PI))) k)))) (sqrt 2))
(* (sqrt (/ (* n (PI)) (* k (pow (* 2 (* n (PI))) k)))) (sqrt 2))
(* (sqrt (/ (* n (PI)) (* k (pow (* 2 (* n (PI))) k)))) (sqrt 2))
(* (sqrt (/ (* n (PI)) (* k (pow (* 2 (* n (PI))) k)))) (sqrt 2))
(* (sqrt (/ (* n (PI)) (* k (pow (* 2 (* n (PI))) k)))) (sqrt 2))
(* (sqrt (/ (* n (PI)) (* k (pow (* 2 (* n (PI))) k)))) (sqrt 2))
(sqrt (* k (exp (* k (+ (log n) (log (* 2 (PI))))))))
(sqrt (* k (exp (* k (+ (log n) (log (* 2 (PI))))))))
(sqrt (* k (exp (* k (+ (log n) (log (* 2 (PI))))))))
(sqrt (* k (exp (* k (+ (log n) (log (* 2 (PI))))))))
(sqrt (* k (exp (* k (+ (log (* 2 (PI))) (* -1 (log (/ 1 n))))))))
(sqrt (* k (exp (* k (+ (log (* 2 (PI))) (* -1 (log (/ 1 n))))))))
(sqrt (* k (exp (* k (+ (log (* 2 (PI))) (* -1 (log (/ 1 n))))))))
(sqrt (* k (exp (* k (+ (log (* 2 (PI))) (* -1 (log (/ 1 n))))))))
(sqrt (* k (exp (* k (+ (log (* -2 (PI))) (* -1 (log (/ -1 n))))))))
(sqrt (* k (exp (* k (+ (log (* -2 (PI))) (* -1 (log (/ -1 n))))))))
(sqrt (* k (exp (* k (+ (log (* -2 (PI))) (* -1 (log (/ -1 n))))))))
(sqrt (* k (exp (* k (+ (log (* -2 (PI))) (* -1 (log (/ -1 n))))))))
(sqrt k)
(+ (sqrt k) (* 1/2 (* (sqrt (pow k 3)) (log (* 2 (* n (PI)))))))
(+ (sqrt k) (* (pow k 2) (+ (* 1/4 (* (sqrt k) (pow (log (* 2 (* n (PI)))) 2))) (* 1/2 (* (sqrt (/ 1 k)) (log (* 2 (* n (PI)))))))))
(+ (sqrt k) (* (pow k 2) (+ (* 1/2 (* (sqrt (/ 1 k)) (log (* 2 (* n (PI)))))) (* k (+ (* 1/4 (* (sqrt (/ 1 k)) (pow (log (* 2 (* n (PI)))) 2))) (* 1/2 (* (sqrt k) (- (* 1/6 (pow (log (* 2 (* n (PI)))) 3)) (* 1/4 (/ (pow (log (* 2 (* n (PI)))) 2) k))))))))))
(sqrt (* k (pow (* 2 (* n (PI))) k)))
(sqrt (* k (pow (* 2 (* n (PI))) k)))
(sqrt (* k (pow (* 2 (* n (PI))) k)))
(sqrt (* k (pow (* 2 (* n (PI))) k)))
(* -1 (* (sqrt (* k (pow (* 2 (* n (PI))) k))) (pow (sqrt -1) 2)))
(* -1 (* (sqrt (* k (pow (* 2 (* n (PI))) k))) (pow (sqrt -1) 2)))
(* -1 (* (sqrt (* k (pow (* 2 (* n (PI))) k))) (pow (sqrt -1) 2)))
(* -1 (* (sqrt (* k (pow (* 2 (* n (PI))) k))) (pow (sqrt -1) 2)))
(* (sqrt (* n (PI))) (sqrt 2))
(* (sqrt (* n (PI))) (sqrt 2))
(* (sqrt (* n (PI))) (sqrt 2))
(* (sqrt (* n (PI))) (sqrt 2))
(* (sqrt (* n (PI))) (sqrt 2))
(* (sqrt (* n (PI))) (sqrt 2))
(* (sqrt (* n (PI))) (sqrt 2))
(* (sqrt (* n (PI))) (sqrt 2))
(* -1 (* (sqrt (* n (PI))) (* (sqrt -2) (sqrt -1))))
(* -1 (* (sqrt (* n (PI))) (* (sqrt -2) (sqrt -1))))
(* -1 (* (sqrt (* n (PI))) (* (sqrt -2) (sqrt -1))))
(* -1 (* (sqrt (* n (PI))) (* (sqrt -2) (sqrt -1))))
(* n (PI))
(* n (PI))
(* n (PI))
(* n (PI))
(* n (PI))
(* n (PI))
(* n (PI))
(* n (PI))
(* n (PI))
(* n (PI))
(* n (PI))
(* n (PI))
(sqrt (/ 1 k))
(sqrt (/ 1 k))
(sqrt (/ 1 k))
(sqrt (/ 1 k))
(sqrt (/ 1 k))
(sqrt (/ 1 k))
(sqrt (/ 1 k))
(sqrt (/ 1 k))
(sqrt (/ 1 k))
(sqrt (/ 1 k))
(sqrt (/ 1 k))
(sqrt (/ 1 k))
(exp (* k (+ (log n) (log (* 2 (PI))))))
(exp (* k (+ (log n) (log (* 2 (PI))))))
(exp (* k (+ (log n) (log (* 2 (PI))))))
(exp (* k (+ (log n) (log (* 2 (PI))))))
(exp (* k (+ (log (* 2 (PI))) (* -1 (log (/ 1 n))))))
(exp (* k (+ (log (* 2 (PI))) (* -1 (log (/ 1 n))))))
(exp (* k (+ (log (* 2 (PI))) (* -1 (log (/ 1 n))))))
(exp (* k (+ (log (* 2 (PI))) (* -1 (log (/ 1 n))))))
(exp (* k (+ (log (* -2 (PI))) (* -1 (log (/ -1 n))))))
(exp (* k (+ (log (* -2 (PI))) (* -1 (log (/ -1 n))))))
(exp (* k (+ (log (* -2 (PI))) (* -1 (log (/ -1 n))))))
(exp (* k (+ (log (* -2 (PI))) (* -1 (log (/ -1 n))))))
1
(+ 1 (* k (log (* 2 (* n (PI))))))
(+ 1 (* k (+ (log (* 2 (* n (PI)))) (* 1/2 (* k (pow (log (* 2 (* n (PI)))) 2))))))
(+ 1 (* k (+ (log (* 2 (* n (PI)))) (* k (+ (* 1/6 (* k (pow (log (* 2 (* n (PI)))) 3))) (* 1/2 (pow (log (* 2 (* n (PI)))) 2)))))))
(pow (* 2 (* n (PI))) k)
(pow (* 2 (* n (PI))) k)
(pow (* 2 (* n (PI))) k)
(pow (* 2 (* n (PI))) k)
(pow (* 2 (* n (PI))) k)
(pow (* 2 (* n (PI))) k)
(pow (* 2 (* n (PI))) k)
(pow (* 2 (* n (PI))) k)

Outputs
(* (sqrt (/ (* n (PI)) k)) (/ 1 (sqrt 1/2)))
(/.f64 (sqrt.f64 (/.f64 (*.f64 n (PI.f64)) k)) (sqrt.f64 #s(literal 1/2 binary64)))
(/ (+ (* -1/2 (* (sqrt (* (pow k 3) (* n (PI)))) (/ (log (* 2 (* n (PI)))) (sqrt 1/2)))) (* (sqrt (* k (* n (PI)))) (/ 1 (sqrt 1/2)))) k)
(/.f64 (+.f64 (.f64 #s(literal -1/2 binary64) (.f64 (sqrt.f64 (.f64 n (.f64 (PI.f64) (.f64 k (.f64 k k))))) (/.f64 (log.f64 (.f64 (.f64 n (PI.f64)) #s(literal 2 binary64))) (sqrt.f64 #s(literal 1/2 binary64))))) (/.f64 (sqrt.f64 (.f64 (PI.f64) (.f64 n k))) (sqrt.f64 #s(literal 1/2 binary64)))) k)
(/ (+ (* k (+ (* -1 (* (sqrt (pow k 3)) (+ (* -1/4 (* (sqrt (* n (PI))) (/ (pow (log (* 2 (* n (PI)))) 2) (sqrt 1/2)))) (* 1/8 (* (sqrt (* n (PI))) (/ (pow (log (* 2 (* n (PI)))) 2) (sqrt 1/2))))))) (* -1/2 (* (sqrt (* k (* n (PI)))) (/ (log (* 2 (* n (PI)))) (sqrt 1/2)))))) (* (sqrt (* k (* n (PI)))) (/ 1 (sqrt 1/2)))) k)
(/.f64 (+.f64 (/.f64 (sqrt.f64 (.f64 (PI.f64) (.f64 n k))) (sqrt.f64 #s(literal 1/2 binary64))) (.f64 k (+.f64 (.f64 (.f64 (sqrt.f64 (.f64 k (.f64 k k))) (.f64 (sqrt.f64 (.f64 n (PI.f64))) #s(literal 1/8 binary64))) (/.f64 (pow.f64 (log.f64 (.f64 (.f64 n (PI.f64)) #s(literal 2 binary64))) #s(literal 2 binary64)) (sqrt.f64 #s(literal 1/2 binary64)))) (.f64 (/.f64 (log.f64 (.f64 (.f64 n (PI.f64)) #s(literal 2 binary64))) (sqrt.f64 #s(literal 1/2 binary64))) (.f64 #s(literal -1/2 binary64) (sqrt.f64 (.f64 (PI.f64) (*.f64 n k)))))))) k)
(/ (+ (* k (+ (* -1/2 (* (sqrt (* k (* n (PI)))) (/ (log (* 2 (* n (PI)))) (sqrt 1/2)))) (* k (+ (* -1 (* (sqrt k) (+ (* -1/4 (* (sqrt (* n (PI))) (/ (pow (log (* 2 (* n (PI)))) 2) (sqrt 1/2)))) (* 1/8 (* (sqrt (* n (PI))) (/ (pow (log (* 2 (* n (PI)))) 2) (sqrt 1/2))))))) (* -1 (* (sqrt (pow k 3)) (+ (* -1/2 (* (log (* 2 (* n (PI)))) (+ (* -1/4 (* (sqrt (* n (PI))) (/ (pow (log (* 2 (* n (PI)))) 2) (sqrt 1/2)))) (* 1/8 (* (sqrt (* n (PI))) (/ (pow (log (* 2 (* n (PI)))) 2) (sqrt 1/2))))))) (+ (* -1/16 (* (sqrt (* n (PI))) (/ (pow (log (* 2 (* n (PI)))) 3) (sqrt 1/2)))) (* 1/48 (* (sqrt (* n (PI))) (/ (pow (log (* 2 (* n (PI)))) 3) (sqrt 1/2)))))))))))) (* (sqrt (* k (* n (PI)))) (/ 1 (sqrt 1/2)))) k)
(/.f64 (+.f64 (/.f64 (sqrt.f64 (.f64 (PI.f64) (.f64 n k))) (sqrt.f64 #s(literal 1/2 binary64))) (.f64 k (+.f64 (.f64 (/.f64 (log.f64 (.f64 (.f64 n (PI.f64)) #s(literal 2 binary64))) (sqrt.f64 #s(literal 1/2 binary64))) (.f64 #s(literal -1/2 binary64) (sqrt.f64 (.f64 (PI.f64) (.f64 n k))))) (.f64 k (-.f64 (.f64 (.f64 (sqrt.f64 k) (.f64 (sqrt.f64 (.f64 n (PI.f64))) #s(literal 1/8 binary64))) (/.f64 (pow.f64 (log.f64 (.f64 (.f64 n (PI.f64)) #s(literal 2 binary64))) #s(literal 2 binary64)) (sqrt.f64 #s(literal 1/2 binary64)))) (.f64 (sqrt.f64 (.f64 k (.f64 k k))) (+.f64 (.f64 (.f64 (sqrt.f64 (.f64 n (PI.f64))) (.f64 (/.f64 (pow.f64 (log.f64 (.f64 (.f64 n (PI.f64)) #s(literal 2 binary64))) #s(literal 2 binary64)) (sqrt.f64 #s(literal 1/2 binary64))) #s(literal -1/8 binary64))) (.f64 #s(literal -1/2 binary64) (log.f64 (.f64 (.f64 n (PI.f64)) #s(literal 2 binary64))))) (/.f64 (.f64 (.f64 (sqrt.f64 (.f64 n (PI.f64))) (pow.f64 (log.f64 (.f64 (*.f64 n (PI.f64)) #s(literal 2 binary64))) #s(literal 3 binary64))) #s(literal -1/24 binary64)) (sqrt.f64 #s(literal 1/2 binary64)))))))))) k)
(* (sqrt (/ 1 k)) (/ 1 (exp (* (log (* 2 (* n (PI)))) (- (* 1/2 k) 1/2)))))
(/.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) k)) (pow.f64 (.f64 (.f64 n (PI.f64)) #s(literal 2 binary64)) (+.f64 #s(literal -1/2 binary64) (*.f64 k #s(literal 1/2 binary64)))))
(* (sqrt (/ 1 k)) (/ 1 (exp (* (log (* 2 (* n (PI)))) (- (* 1/2 k) 1/2)))))
(/.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) k)) (pow.f64 (.f64 (.f64 n (PI.f64)) #s(literal 2 binary64)) (+.f64 #s(literal -1/2 binary64) (*.f64 k #s(literal 1/2 binary64)))))
(* (sqrt (/ 1 k)) (/ 1 (exp (* (log (* 2 (* n (PI)))) (- (* 1/2 k) 1/2)))))
(/.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) k)) (pow.f64 (.f64 (.f64 n (PI.f64)) #s(literal 2 binary64)) (+.f64 #s(literal -1/2 binary64) (*.f64 k #s(literal 1/2 binary64)))))
(* (sqrt (/ 1 k)) (/ 1 (exp (* (log (* 2 (* n (PI)))) (- (* 1/2 k) 1/2)))))
(/.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) k)) (pow.f64 (.f64 (.f64 n (PI.f64)) #s(literal 2 binary64)) (+.f64 #s(literal -1/2 binary64) (*.f64 k #s(literal 1/2 binary64)))))
(* (sqrt (/ 1 k)) (/ (pow (sqrt -1) 2) (exp (* -1 (* (log (* 2 (* n (PI)))) (+ 1/2 (* -1/2 k)))))))
(/.f64 (neg.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) k))) (pow.f64 (.f64 (.f64 n (PI.f64)) #s(literal 2 binary64)) (+.f64 #s(literal -1/2 binary64) (.f64 #s(literal -1 binary64) (.f64 k #s(literal -1/2 binary64))))))
(* (sqrt (/ 1 k)) (/ (pow (sqrt -1) 2) (exp (* -1 (* (log (* 2 (* n (PI)))) (+ 1/2 (* -1/2 k)))))))
(/.f64 (neg.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) k))) (pow.f64 (.f64 (.f64 n (PI.f64)) #s(literal 2 binary64)) (+.f64 #s(literal -1/2 binary64) (.f64 #s(literal -1 binary64) (.f64 k #s(literal -1/2 binary64))))))
(* (sqrt (/ 1 k)) (/ (pow (sqrt -1) 2) (exp (* -1 (* (log (* 2 (* n (PI)))) (+ 1/2 (* -1/2 k)))))))
(/.f64 (neg.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) k))) (pow.f64 (.f64 (.f64 n (PI.f64)) #s(literal 2 binary64)) (+.f64 #s(literal -1/2 binary64) (.f64 #s(literal -1 binary64) (.f64 k #s(literal -1/2 binary64))))))
(* (sqrt (/ 1 k)) (/ (pow (sqrt -1) 2) (exp (* -1 (* (log (* 2 (* n (PI)))) (+ 1/2 (* -1/2 k)))))))
(/.f64 (neg.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) k))) (pow.f64 (.f64 (.f64 n (PI.f64)) #s(literal 2 binary64)) (+.f64 #s(literal -1/2 binary64) (.f64 #s(literal -1 binary64) (.f64 k #s(literal -1/2 binary64))))))
(* (sqrt (/ 1 k)) (/ 1 (exp (* (+ (log n) (log (* 2 (PI)))) (- (* 1/2 k) 1/2)))))
(/.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) k)) (pow.f64 (.f64 (.f64 n (PI.f64)) #s(literal 2 binary64)) (+.f64 #s(literal -1/2 binary64) (*.f64 k #s(literal 1/2 binary64)))))
(* (sqrt (/ 1 k)) (/ 1 (exp (* (+ (log n) (log (* 2 (PI)))) (- (* 1/2 k) 1/2)))))
(/.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) k)) (pow.f64 (.f64 (.f64 n (PI.f64)) #s(literal 2 binary64)) (+.f64 #s(literal -1/2 binary64) (*.f64 k #s(literal 1/2 binary64)))))
(* (sqrt (/ 1 k)) (/ 1 (exp (* (+ (log n) (log (* 2 (PI)))) (- (* 1/2 k) 1/2)))))
(/.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) k)) (pow.f64 (.f64 (.f64 n (PI.f64)) #s(literal 2 binary64)) (+.f64 #s(literal -1/2 binary64) (*.f64 k #s(literal 1/2 binary64)))))
(* (sqrt (/ 1 k)) (/ 1 (exp (* (+ (log n) (log (* 2 (PI)))) (- (* 1/2 k) 1/2)))))
(/.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) k)) (pow.f64 (.f64 (.f64 n (PI.f64)) #s(literal 2 binary64)) (+.f64 #s(literal -1/2 binary64) (*.f64 k #s(literal 1/2 binary64)))))
(* (sqrt (/ 1 k)) (/ 1 (exp (* (+ (log (* 2 (PI))) (* -1 (log (/ 1 n)))) (- (* 1/2 k) 1/2)))))
(/.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) k)) (pow.f64 (.f64 (.f64 n (PI.f64)) #s(literal 2 binary64)) (+.f64 #s(literal -1/2 binary64) (*.f64 k #s(literal 1/2 binary64)))))
(* (sqrt (/ 1 k)) (/ 1 (exp (* (+ (log (* 2 (PI))) (* -1 (log (/ 1 n)))) (- (* 1/2 k) 1/2)))))
(/.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) k)) (pow.f64 (.f64 (.f64 n (PI.f64)) #s(literal 2 binary64)) (+.f64 #s(literal -1/2 binary64) (*.f64 k #s(literal 1/2 binary64)))))
(* (sqrt (/ 1 k)) (/ 1 (exp (* (+ (log (* 2 (PI))) (* -1 (log (/ 1 n)))) (- (* 1/2 k) 1/2)))))
(/.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) k)) (pow.f64 (.f64 (.f64 n (PI.f64)) #s(literal 2 binary64)) (+.f64 #s(literal -1/2 binary64) (*.f64 k #s(literal 1/2 binary64)))))
(* (sqrt (/ 1 k)) (/ 1 (exp (* (+ (log (* 2 (PI))) (* -1 (log (/ 1 n)))) (- (* 1/2 k) 1/2)))))
(/.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) k)) (pow.f64 (.f64 (.f64 n (PI.f64)) #s(literal 2 binary64)) (+.f64 #s(literal -1/2 binary64) (*.f64 k #s(literal 1/2 binary64)))))
(* (sqrt (/ 1 k)) (/ 1 (exp (* (+ (log (* -2 (PI))) (* -1 (log (/ -1 n)))) (- (* 1/2 k) 1/2)))))
(/.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) k)) (pow.f64 (.f64 (.f64 (PI.f64) #s(literal -2 binary64)) (pow.f64 (/.f64 #s(literal -1 binary64) n) #s(literal -1 binary64))) (+.f64 #s(literal -1/2 binary64) (*.f64 k #s(literal 1/2 binary64)))))
(* (sqrt (/ 1 k)) (/ 1 (exp (* (+ (log (* -2 (PI))) (* -1 (log (/ -1 n)))) (- (* 1/2 k) 1/2)))))
(/.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) k)) (pow.f64 (.f64 (.f64 (PI.f64) #s(literal -2 binary64)) (pow.f64 (/.f64 #s(literal -1 binary64) n) #s(literal -1 binary64))) (+.f64 #s(literal -1/2 binary64) (*.f64 k #s(literal 1/2 binary64)))))
(* (sqrt (/ 1 k)) (/ 1 (exp (* (+ (log (* -2 (PI))) (* -1 (log (/ -1 n)))) (- (* 1/2 k) 1/2)))))
(/.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) k)) (pow.f64 (.f64 (.f64 (PI.f64) #s(literal -2 binary64)) (pow.f64 (/.f64 #s(literal -1 binary64) n) #s(literal -1 binary64))) (+.f64 #s(literal -1/2 binary64) (*.f64 k #s(literal 1/2 binary64)))))
(* (sqrt (/ 1 k)) (/ 1 (exp (* (+ (log (* -2 (PI))) (* -1 (log (/ -1 n)))) (- (* 1/2 k) 1/2)))))
(/.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) k)) (pow.f64 (.f64 (.f64 (PI.f64) #s(literal -2 binary64)) (pow.f64 (/.f64 #s(literal -1 binary64) n) #s(literal -1 binary64))) (+.f64 #s(literal -1/2 binary64) (*.f64 k #s(literal 1/2 binary64)))))
(sqrt (/ 1 k))
(sqrt.f64 (/.f64 #s(literal 1 binary64) k))
(sqrt (/ 1 k))
(sqrt.f64 (/.f64 #s(literal 1 binary64) k))
(sqrt (/ 1 k))
(sqrt.f64 (/.f64 #s(literal 1 binary64) k))
(sqrt (/ 1 k))
(sqrt.f64 (/.f64 #s(literal 1 binary64) k))
(sqrt (/ 1 k))
(sqrt.f64 (/.f64 #s(literal 1 binary64) k))
(sqrt (/ 1 k))
(sqrt.f64 (/.f64 #s(literal 1 binary64) k))
(sqrt (/ 1 k))
(sqrt.f64 (/.f64 #s(literal 1 binary64) k))
(sqrt (/ 1 k))
(sqrt.f64 (/.f64 #s(literal 1 binary64) k))
(* (sqrt (/ 1 k)) (pow (sqrt -1) 2))
(neg.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) k)))
(* (sqrt (/ 1 k)) (pow (sqrt -1) 2))
(neg.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) k)))
(* (sqrt (/ 1 k)) (pow (sqrt -1) 2))
(neg.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) k)))
(* (sqrt (/ 1 k)) (pow (sqrt -1) 2))
(neg.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) k)))
(exp (* (+ (log n) (log (* 2 (PI)))) (- (* 1/2 k) 1/2)))
(pow.f64 (.f64 (.f64 n (PI.f64)) #s(literal 2 binary64)) (+.f64 #s(literal -1/2 binary64) (*.f64 k #s(literal 1/2 binary64))))
(exp (* (+ (log n) (log (* 2 (PI)))) (- (* 1/2 k) 1/2)))
(pow.f64 (.f64 (.f64 n (PI.f64)) #s(literal 2 binary64)) (+.f64 #s(literal -1/2 binary64) (*.f64 k #s(literal 1/2 binary64))))
(exp (* (+ (log n) (log (* 2 (PI)))) (- (* 1/2 k) 1/2)))
(pow.f64 (.f64 (.f64 n (PI.f64)) #s(literal 2 binary64)) (+.f64 #s(literal -1/2 binary64) (*.f64 k #s(literal 1/2 binary64))))
(exp (* (+ (log n) (log (* 2 (PI)))) (- (* 1/2 k) 1/2)))
(pow.f64 (.f64 (.f64 n (PI.f64)) #s(literal 2 binary64)) (+.f64 #s(literal -1/2 binary64) (*.f64 k #s(literal 1/2 binary64))))
(exp (* (+ (log (* 2 (PI))) (* -1 (log (/ 1 n)))) (- (* 1/2 k) 1/2)))
(pow.f64 (.f64 (.f64 n (PI.f64)) #s(literal 2 binary64)) (+.f64 #s(literal -1/2 binary64) (*.f64 k #s(literal 1/2 binary64))))
(exp (* (+ (log (* 2 (PI))) (* -1 (log (/ 1 n)))) (- (* 1/2 k) 1/2)))
(pow.f64 (.f64 (.f64 n (PI.f64)) #s(literal 2 binary64)) (+.f64 #s(literal -1/2 binary64) (*.f64 k #s(literal 1/2 binary64))))
(exp (* (+ (log (* 2 (PI))) (* -1 (log (/ 1 n)))) (- (* 1/2 k) 1/2)))
(pow.f64 (.f64 (.f64 n (PI.f64)) #s(literal 2 binary64)) (+.f64 #s(literal -1/2 binary64) (*.f64 k #s(literal 1/2 binary64))))
(exp (* (+ (log (* 2 (PI))) (* -1 (log (/ 1 n)))) (- (* 1/2 k) 1/2)))
(pow.f64 (.f64 (.f64 n (PI.f64)) #s(literal 2 binary64)) (+.f64 #s(literal -1/2 binary64) (*.f64 k #s(literal 1/2 binary64))))
(exp (* (+ (log (* -2 (PI))) (* -1 (log (/ -1 n)))) (- (* 1/2 k) 1/2)))
(pow.f64 (.f64 (.f64 (PI.f64) #s(literal -2 binary64)) (pow.f64 (/.f64 #s(literal -1 binary64) n) #s(literal -1 binary64))) (+.f64 #s(literal -1/2 binary64) (*.f64 k #s(literal 1/2 binary64))))
(exp (* (+ (log (* -2 (PI))) (* -1 (log (/ -1 n)))) (- (* 1/2 k) 1/2)))
(pow.f64 (.f64 (.f64 (PI.f64) #s(literal -2 binary64)) (pow.f64 (/.f64 #s(literal -1 binary64) n) #s(literal -1 binary64))) (+.f64 #s(literal -1/2 binary64) (*.f64 k #s(literal 1/2 binary64))))
(exp (* (+ (log (* -2 (PI))) (* -1 (log (/ -1 n)))) (- (* 1/2 k) 1/2)))
(pow.f64 (.f64 (.f64 (PI.f64) #s(literal -2 binary64)) (pow.f64 (/.f64 #s(literal -1 binary64) n) #s(literal -1 binary64))) (+.f64 #s(literal -1/2 binary64) (*.f64 k #s(literal 1/2 binary64))))
(exp (* (+ (log (* -2 (PI))) (* -1 (log (/ -1 n)))) (- (* 1/2 k) 1/2)))
(pow.f64 (.f64 (.f64 (PI.f64) #s(literal -2 binary64)) (pow.f64 (/.f64 #s(literal -1 binary64) n) #s(literal -1 binary64))) (+.f64 #s(literal -1/2 binary64) (*.f64 k #s(literal 1/2 binary64))))
(* (sqrt (/ 1 (* n (PI)))) (sqrt 1/2))
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(/ (+ (* (sqrt (* k (* n (PI)))) (sqrt 2)) (* (pow k 2) (+ (* -1/2 (* (sqrt (/ (* n (PI)) k)) (* (log (* 2 (* n (PI)))) (sqrt 2)))) (* k (+ (* -1/2 (* (sqrt (/ 1 (* k (* n (PI))))) (* (sqrt 2) (+ (* -1 (* n (* (PI) (pow (log (* 2 (* n (PI)))) 2)))) (* 1/2 (* n (* (PI) (pow (log (* 2 (* n (PI)))) 2)))))))) (* -1/2 (* (sqrt (/ k (* n (PI)))) (* (sqrt 2) (+ (* -1 (* (log (* 2 (* n (PI)))) (+ (* -1 (* n (* (PI) (pow (log (* 2 (* n (PI)))) 2)))) (* 1/2 (* n (* (PI) (pow (log (* 2 (* n (PI)))) 2))))))) (+ (* -1/2 (* n (* (PI) (pow (log (* 2 (* n (PI)))) 3)))) (+ (* 1/6 (* n (* (PI) (pow (log (* 2 (* n (PI)))) 3)))) (* 1/4 (/ (* n (* (PI) (pow (log (* 2 (* n (PI)))) 2))) k))))))))))))) k)
(/.f64 (+.f64 (.f64 (sqrt.f64 (.f64 (PI.f64) (.f64 n k))) (sqrt.f64 #s(literal 2 binary64))) (.f64 (.f64 k k) (+.f64 (.f64 (.f64 (log.f64 (.f64 (.f64 n (PI.f64)) #s(literal 2 binary64))) (sqrt.f64 #s(literal 2 binary64))) (.f64 (sqrt.f64 (/.f64 (.f64 n (PI.f64)) k)) #s(literal -1/2 binary64))) (.f64 k (.f64 #s(literal -1/2 binary64) (+.f64 (.f64 (.f64 (.f64 n (PI.f64)) (.f64 (pow.f64 (log.f64 (.f64 (.f64 n (PI.f64)) #s(literal 2 binary64))) #s(literal 2 binary64)) #s(literal -1/2 binary64))) (.f64 (sqrt.f64 #s(literal 2 binary64)) (sqrt.f64 (/.f64 #s(literal 1 binary64) (.f64 (PI.f64) (.f64 n k)))))) (.f64 (sqrt.f64 #s(literal 2 binary64)) (.f64 (+.f64 (.f64 #s(literal 1/2 binary64) (.f64 (.f64 n (PI.f64)) (pow.f64 (log.f64 (.f64 (.f64 n (PI.f64)) #s(literal 2 binary64))) #s(literal 3 binary64)))) (+.f64 (/.f64 (.f64 #s(literal 1/4 binary64) (.f64 (.f64 n (PI.f64)) (pow.f64 (log.f64 (.f64 (.f64 n (PI.f64)) #s(literal 2 binary64))) #s(literal 2 binary64)))) k) (.f64 (.f64 (.f64 n (PI.f64)) (pow.f64 (log.f64 (.f64 (.f64 n (PI.f64)) #s(literal 2 binary64))) #s(literal 3 binary64))) #s(literal -1/3 binary64)))) (sqrt.f64 (/.f64 k (.f64 n (PI.f64)))))))))))) k)
(* (sqrt (/ (* n (PI)) (* k (pow (* 2 (* n (PI))) k)))) (sqrt 2))
(.f64 (sqrt.f64 #s(literal 2 binary64)) (sqrt.f64 (/.f64 (/.f64 (.f64 n (PI.f64)) k) (pow.f64 (.f64 (.f64 n (PI.f64)) #s(literal 2 binary64)) k))))
(* (sqrt (/ (* n (PI)) (* k (pow (* 2 (* n (PI))) k)))) (sqrt 2))
(.f64 (sqrt.f64 #s(literal 2 binary64)) (sqrt.f64 (/.f64 (/.f64 (.f64 n (PI.f64)) k) (pow.f64 (.f64 (.f64 n (PI.f64)) #s(literal 2 binary64)) k))))
(* (sqrt (/ (* n (PI)) (* k (pow (* 2 (* n (PI))) k)))) (sqrt 2))
(.f64 (sqrt.f64 #s(literal 2 binary64)) (sqrt.f64 (/.f64 (/.f64 (.f64 n (PI.f64)) k) (pow.f64 (.f64 (.f64 n (PI.f64)) #s(literal 2 binary64)) k))))
(* (sqrt (/ (* n (PI)) (* k (pow (* 2 (* n (PI))) k)))) (sqrt 2))
(.f64 (sqrt.f64 #s(literal 2 binary64)) (sqrt.f64 (/.f64 (/.f64 (.f64 n (PI.f64)) k) (pow.f64 (.f64 (.f64 n (PI.f64)) #s(literal 2 binary64)) k))))
(* (sqrt (/ (* n (PI)) (* k (pow (* 2 (* n (PI))) k)))) (sqrt 2))
(.f64 (sqrt.f64 #s(literal 2 binary64)) (sqrt.f64 (/.f64 (/.f64 (.f64 n (PI.f64)) k) (pow.f64 (.f64 (.f64 n (PI.f64)) #s(literal 2 binary64)) k))))
(* (sqrt (/ (* n (PI)) (* k (pow (* 2 (* n (PI))) k)))) (sqrt 2))
(.f64 (sqrt.f64 #s(literal 2 binary64)) (sqrt.f64 (/.f64 (/.f64 (.f64 n (PI.f64)) k) (pow.f64 (.f64 (.f64 n (PI.f64)) #s(literal 2 binary64)) k))))
(* (sqrt (/ (* n (PI)) (* k (pow (* 2 (* n (PI))) k)))) (sqrt 2))
(.f64 (sqrt.f64 #s(literal 2 binary64)) (sqrt.f64 (/.f64 (/.f64 (.f64 n (PI.f64)) k) (pow.f64 (.f64 (.f64 n (PI.f64)) #s(literal 2 binary64)) k))))
(* (sqrt (/ (* n (PI)) (* k (pow (* 2 (* n (PI))) k)))) (sqrt 2))
(.f64 (sqrt.f64 #s(literal 2 binary64)) (sqrt.f64 (/.f64 (/.f64 (.f64 n (PI.f64)) k) (pow.f64 (.f64 (.f64 n (PI.f64)) #s(literal 2 binary64)) k))))
(sqrt (* k (exp (* k (+ (log n) (log (* 2 (PI))))))))
(sqrt.f64 (.f64 k (pow.f64 (.f64 (*.f64 n (PI.f64)) #s(literal 2 binary64)) k)))
(sqrt (* k (exp (* k (+ (log n) (log (* 2 (PI))))))))
(sqrt.f64 (.f64 k (pow.f64 (.f64 (*.f64 n (PI.f64)) #s(literal 2 binary64)) k)))
(sqrt (* k (exp (* k (+ (log n) (log (* 2 (PI))))))))
(sqrt.f64 (.f64 k (pow.f64 (.f64 (*.f64 n (PI.f64)) #s(literal 2 binary64)) k)))
(sqrt (* k (exp (* k (+ (log n) (log (* 2 (PI))))))))
(sqrt.f64 (.f64 k (pow.f64 (.f64 (*.f64 n (PI.f64)) #s(literal 2 binary64)) k)))
(sqrt (* k (exp (* k (+ (log (* 2 (PI))) (* -1 (log (/ 1 n))))))))
(sqrt.f64 (.f64 k (pow.f64 (.f64 (*.f64 n (PI.f64)) #s(literal 2 binary64)) k)))
(sqrt (* k (exp (* k (+ (log (* 2 (PI))) (* -1 (log (/ 1 n))))))))
(sqrt.f64 (.f64 k (pow.f64 (.f64 (*.f64 n (PI.f64)) #s(literal 2 binary64)) k)))
(sqrt (* k (exp (* k (+ (log (* 2 (PI))) (* -1 (log (/ 1 n))))))))
(sqrt.f64 (.f64 k (pow.f64 (.f64 (*.f64 n (PI.f64)) #s(literal 2 binary64)) k)))
(sqrt (* k (exp (* k (+ (log (* 2 (PI))) (* -1 (log (/ 1 n))))))))
(sqrt.f64 (.f64 k (pow.f64 (.f64 (*.f64 n (PI.f64)) #s(literal 2 binary64)) k)))
(sqrt (* k (exp (* k (+ (log (* -2 (PI))) (* -1 (log (/ -1 n))))))))
(sqrt.f64 (.f64 k (pow.f64 (.f64 (*.f64 (PI.f64) #s(literal -2 binary64)) (pow.f64 (/.f64 #s(literal -1 binary64) n) #s(literal -1 binary64))) k)))
(sqrt (* k (exp (* k (+ (log (* -2 (PI))) (* -1 (log (/ -1 n))))))))
(sqrt.f64 (.f64 k (pow.f64 (.f64 (*.f64 (PI.f64) #s(literal -2 binary64)) (pow.f64 (/.f64 #s(literal -1 binary64) n) #s(literal -1 binary64))) k)))
(sqrt (* k (exp (* k (+ (log (* -2 (PI))) (* -1 (log (/ -1 n))))))))
(sqrt.f64 (.f64 k (pow.f64 (.f64 (*.f64 (PI.f64) #s(literal -2 binary64)) (pow.f64 (/.f64 #s(literal -1 binary64) n) #s(literal -1 binary64))) k)))
(sqrt (* k (exp (* k (+ (log (* -2 (PI))) (* -1 (log (/ -1 n))))))))
(sqrt.f64 (.f64 k (pow.f64 (.f64 (*.f64 (PI.f64) #s(literal -2 binary64)) (pow.f64 (/.f64 #s(literal -1 binary64) n) #s(literal -1 binary64))) k)))
(sqrt k)
(sqrt.f64 k)
(+ (sqrt k) (* 1/2 (* (sqrt (pow k 3)) (log (* 2 (* n (PI)))))))
(+.f64 (sqrt.f64 k) (.f64 (sqrt.f64 (.f64 k (.f64 k k))) (.f64 #s(literal 1/2 binary64) (log.f64 (.f64 (.f64 n (PI.f64)) #s(literal 2 binary64))))))
(+ (sqrt k) (* (pow k 2) (+ (* 1/4 (* (sqrt k) (pow (log (* 2 (* n (PI)))) 2))) (* 1/2 (* (sqrt (/ 1 k)) (log (* 2 (* n (PI)))))))))
(+.f64 (sqrt.f64 k) (.f64 k (.f64 k (+.f64 (.f64 (pow.f64 (log.f64 (.f64 (.f64 n (PI.f64)) #s(literal 2 binary64))) #s(literal 2 binary64)) (.f64 (sqrt.f64 k) #s(literal 1/4 binary64))) (.f64 #s(literal 1/2 binary64) (.f64 (log.f64 (.f64 (.f64 n (PI.f64)) #s(literal 2 binary64))) (sqrt.f64 (/.f64 #s(literal 1 binary64) k))))))))
(+ (sqrt k) (* (pow k 2) (+ (* 1/2 (* (sqrt (/ 1 k)) (log (* 2 (* n (PI)))))) (* k (+ (* 1/4 (* (sqrt (/ 1 k)) (pow (log (* 2 (* n (PI)))) 2))) (* 1/2 (* (sqrt k) (- (* 1/6 (pow (log (* 2 (* n (PI)))) 3)) (* 1/4 (/ (pow (log (* 2 (* n (PI)))) 2) k))))))))))
(+.f64 (sqrt.f64 k) (.f64 (.f64 k k) (+.f64 (.f64 #s(literal 1/2 binary64) (.f64 (log.f64 (.f64 (.f64 n (PI.f64)) #s(literal 2 binary64))) (sqrt.f64 (/.f64 #s(literal 1 binary64) k)))) (.f64 k (+.f64 (.f64 (pow.f64 (log.f64 (.f64 (.f64 n (PI.f64)) #s(literal 2 binary64))) #s(literal 2 binary64)) (.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) k)) #s(literal 1/4 binary64))) (.f64 (sqrt.f64 k) (.f64 (+.f64 (.f64 (pow.f64 (log.f64 (.f64 (.f64 n (PI.f64)) #s(literal 2 binary64))) #s(literal 3 binary64)) #s(literal 1/6 binary64)) (/.f64 (.f64 #s(literal -1/4 binary64) (pow.f64 (log.f64 (.f64 (*.f64 n (PI.f64)) #s(literal 2 binary64))) #s(literal 2 binary64))) k)) #s(literal 1/2 binary64))))))))
(sqrt (* k (pow (* 2 (* n (PI))) k)))
(sqrt.f64 (.f64 k (pow.f64 (.f64 (*.f64 n (PI.f64)) #s(literal 2 binary64)) k)))
(sqrt (* k (pow (* 2 (* n (PI))) k)))
(sqrt.f64 (.f64 k (pow.f64 (.f64 (*.f64 n (PI.f64)) #s(literal 2 binary64)) k)))
(sqrt (* k (pow (* 2 (* n (PI))) k)))
(sqrt.f64 (.f64 k (pow.f64 (.f64 (*.f64 n (PI.f64)) #s(literal 2 binary64)) k)))
(sqrt (* k (pow (* 2 (* n (PI))) k)))
(sqrt.f64 (.f64 k (pow.f64 (.f64 (*.f64 n (PI.f64)) #s(literal 2 binary64)) k)))
(* -1 (* (sqrt (* k (pow (* 2 (* n (PI))) k))) (pow (sqrt -1) 2)))
(sqrt.f64 (.f64 k (pow.f64 (.f64 (*.f64 n (PI.f64)) #s(literal 2 binary64)) k)))
(* -1 (* (sqrt (* k (pow (* 2 (* n (PI))) k))) (pow (sqrt -1) 2)))
(sqrt.f64 (.f64 k (pow.f64 (.f64 (*.f64 n (PI.f64)) #s(literal 2 binary64)) k)))
(* -1 (* (sqrt (* k (pow (* 2 (* n (PI))) k))) (pow (sqrt -1) 2)))
(sqrt.f64 (.f64 k (pow.f64 (.f64 (*.f64 n (PI.f64)) #s(literal 2 binary64)) k)))
(* -1 (* (sqrt (* k (pow (* 2 (* n (PI))) k))) (pow (sqrt -1) 2)))
(sqrt.f64 (.f64 k (pow.f64 (.f64 (*.f64 n (PI.f64)) #s(literal 2 binary64)) k)))
(* (sqrt (* n (PI))) (sqrt 2))
(.f64 (sqrt.f64 (.f64 n (PI.f64))) (sqrt.f64 #s(literal 2 binary64)))
(* (sqrt (* n (PI))) (sqrt 2))
(.f64 (sqrt.f64 (.f64 n (PI.f64))) (sqrt.f64 #s(literal 2 binary64)))
(* (sqrt (* n (PI))) (sqrt 2))
(.f64 (sqrt.f64 (.f64 n (PI.f64))) (sqrt.f64 #s(literal 2 binary64)))
(* (sqrt (* n (PI))) (sqrt 2))
(.f64 (sqrt.f64 (.f64 n (PI.f64))) (sqrt.f64 #s(literal 2 binary64)))
(* (sqrt (* n (PI))) (sqrt 2))
(.f64 (sqrt.f64 (.f64 n (PI.f64))) (sqrt.f64 #s(literal 2 binary64)))
(* (sqrt (* n (PI))) (sqrt 2))
(.f64 (sqrt.f64 (.f64 n (PI.f64))) (sqrt.f64 #s(literal 2 binary64)))
(* (sqrt (* n (PI))) (sqrt 2))
(.f64 (sqrt.f64 (.f64 n (PI.f64))) (sqrt.f64 #s(literal 2 binary64)))
(* (sqrt (* n (PI))) (sqrt 2))
(.f64 (sqrt.f64 (.f64 n (PI.f64))) (sqrt.f64 #s(literal 2 binary64)))
(* -1 (* (sqrt (* n (PI))) (* (sqrt -2) (sqrt -1))))
(.f64 (.f64 (sqrt.f64 (*.f64 n (PI.f64))) (sqrt.f64 #s(literal -2 binary64))) (-.f64 #s(literal 0 binary64) (sqrt.f64 #s(literal -1 binary64))))
(* -1 (* (sqrt (* n (PI))) (* (sqrt -2) (sqrt -1))))
(.f64 (.f64 (sqrt.f64 (*.f64 n (PI.f64))) (sqrt.f64 #s(literal -2 binary64))) (-.f64 #s(literal 0 binary64) (sqrt.f64 #s(literal -1 binary64))))
(* -1 (* (sqrt (* n (PI))) (* (sqrt -2) (sqrt -1))))
(.f64 (.f64 (sqrt.f64 (*.f64 n (PI.f64))) (sqrt.f64 #s(literal -2 binary64))) (-.f64 #s(literal 0 binary64) (sqrt.f64 #s(literal -1 binary64))))
(* -1 (* (sqrt (* n (PI))) (* (sqrt -2) (sqrt -1))))
(.f64 (.f64 (sqrt.f64 (*.f64 n (PI.f64))) (sqrt.f64 #s(literal -2 binary64))) (-.f64 #s(literal 0 binary64) (sqrt.f64 #s(literal -1 binary64))))
(* n (PI))
(*.f64 n (PI.f64))
(* n (PI))
(*.f64 n (PI.f64))
(* n (PI))
(*.f64 n (PI.f64))
(* n (PI))
(*.f64 n (PI.f64))
(* n (PI))
(*.f64 n (PI.f64))
(* n (PI))
(*.f64 n (PI.f64))
(* n (PI))
(*.f64 n (PI.f64))
(* n (PI))
(*.f64 n (PI.f64))
(* n (PI))
(*.f64 n (PI.f64))
(* n (PI))
(*.f64 n (PI.f64))
(* n (PI))
(*.f64 n (PI.f64))
(* n (PI))
(*.f64 n (PI.f64))
(sqrt (/ 1 k))
(sqrt.f64 (/.f64 #s(literal 1 binary64) k))
(sqrt (/ 1 k))
(sqrt.f64 (/.f64 #s(literal 1 binary64) k))
(sqrt (/ 1 k))
(sqrt.f64 (/.f64 #s(literal 1 binary64) k))
(sqrt (/ 1 k))
(sqrt.f64 (/.f64 #s(literal 1 binary64) k))
(sqrt (/ 1 k))
(sqrt.f64 (/.f64 #s(literal 1 binary64) k))
(sqrt (/ 1 k))
(sqrt.f64 (/.f64 #s(literal 1 binary64) k))
(sqrt (/ 1 k))
(sqrt.f64 (/.f64 #s(literal 1 binary64) k))
(sqrt (/ 1 k))
(sqrt.f64 (/.f64 #s(literal 1 binary64) k))
(sqrt (/ 1 k))
(sqrt.f64 (/.f64 #s(literal 1 binary64) k))
(sqrt (/ 1 k))
(sqrt.f64 (/.f64 #s(literal 1 binary64) k))
(sqrt (/ 1 k))
(sqrt.f64 (/.f64 #s(literal 1 binary64) k))
(sqrt (/ 1 k))
(sqrt.f64 (/.f64 #s(literal 1 binary64) k))
(exp (* k (+ (log n) (log (* 2 (PI))))))
(pow.f64 (.f64 (.f64 n (PI.f64)) #s(literal 2 binary64)) k)
(exp (* k (+ (log n) (log (* 2 (PI))))))
(pow.f64 (.f64 (.f64 n (PI.f64)) #s(literal 2 binary64)) k)
(exp (* k (+ (log n) (log (* 2 (PI))))))
(pow.f64 (.f64 (.f64 n (PI.f64)) #s(literal 2 binary64)) k)
(exp (* k (+ (log n) (log (* 2 (PI))))))
(pow.f64 (.f64 (.f64 n (PI.f64)) #s(literal 2 binary64)) k)
(exp (* k (+ (log (* 2 (PI))) (* -1 (log (/ 1 n))))))
(pow.f64 (.f64 (.f64 n (PI.f64)) #s(literal 2 binary64)) k)
(exp (* k (+ (log (* 2 (PI))) (* -1 (log (/ 1 n))))))
(pow.f64 (.f64 (.f64 n (PI.f64)) #s(literal 2 binary64)) k)
(exp (* k (+ (log (* 2 (PI))) (* -1 (log (/ 1 n))))))
(pow.f64 (.f64 (.f64 n (PI.f64)) #s(literal 2 binary64)) k)
(exp (* k (+ (log (* 2 (PI))) (* -1 (log (/ 1 n))))))
(pow.f64 (.f64 (.f64 n (PI.f64)) #s(literal 2 binary64)) k)
(exp (* k (+ (log (* -2 (PI))) (* -1 (log (/ -1 n))))))
(pow.f64 (.f64 (.f64 (PI.f64) #s(literal -2 binary64)) (pow.f64 (/.f64 #s(literal -1 binary64) n) #s(literal -1 binary64))) k)
(exp (* k (+ (log (* -2 (PI))) (* -1 (log (/ -1 n))))))
(pow.f64 (.f64 (.f64 (PI.f64) #s(literal -2 binary64)) (pow.f64 (/.f64 #s(literal -1 binary64) n) #s(literal -1 binary64))) k)
(exp (* k (+ (log (* -2 (PI))) (* -1 (log (/ -1 n))))))
(pow.f64 (.f64 (.f64 (PI.f64) #s(literal -2 binary64)) (pow.f64 (/.f64 #s(literal -1 binary64) n) #s(literal -1 binary64))) k)
(exp (* k (+ (log (* -2 (PI))) (* -1 (log (/ -1 n))))))
(pow.f64 (.f64 (.f64 (PI.f64) #s(literal -2 binary64)) (pow.f64 (/.f64 #s(literal -1 binary64) n) #s(literal -1 binary64))) k)
1
#s(literal 1 binary64)
(+ 1 (* k (log (* 2 (* n (PI))))))
(+.f64 #s(literal 1 binary64) (.f64 k (log.f64 (.f64 (*.f64 n (PI.f64)) #s(literal 2 binary64)))))
(+ 1 (* k (+ (log (* 2 (* n (PI)))) (* 1/2 (* k (pow (log (* 2 (* n (PI)))) 2))))))
(+.f64 #s(literal 1 binary64) (.f64 k (+.f64 (log.f64 (.f64 (.f64 n (PI.f64)) #s(literal 2 binary64))) (.f64 #s(literal 1/2 binary64) (.f64 k (pow.f64 (log.f64 (.f64 (*.f64 n (PI.f64)) #s(literal 2 binary64))) #s(literal 2 binary64)))))))
(+ 1 (* k (+ (log (* 2 (* n (PI)))) (* k (+ (* 1/6 (* k (pow (log (* 2 (* n (PI)))) 3))) (* 1/2 (pow (log (* 2 (* n (PI)))) 2)))))))
(+.f64 #s(literal 1 binary64) (.f64 k (+.f64 (log.f64 (.f64 (.f64 n (PI.f64)) #s(literal 2 binary64))) (.f64 k (+.f64 (.f64 (pow.f64 (log.f64 (.f64 (.f64 n (PI.f64)) #s(literal 2 binary64))) #s(literal 3 binary64)) (.f64 k #s(literal 1/6 binary64))) (.f64 #s(literal 1/2 binary64) (pow.f64 (log.f64 (.f64 (*.f64 n (PI.f64)) #s(literal 2 binary64))) #s(literal 2 binary64))))))))
(pow (* 2 (* n (PI))) k)
(pow.f64 (.f64 (.f64 n (PI.f64)) #s(literal 2 binary64)) k)
(pow (* 2 (* n (PI))) k)
(pow.f64 (.f64 (.f64 n (PI.f64)) #s(literal 2 binary64)) k)
(pow (* 2 (* n (PI))) k)
(pow.f64 (.f64 (.f64 n (PI.f64)) #s(literal 2 binary64)) k)
(pow (* 2 (* n (PI))) k)
(pow.f64 (.f64 (.f64 n (PI.f64)) #s(literal 2 binary64)) k)
(pow (* 2 (* n (PI))) k)
(pow.f64 (.f64 (.f64 n (PI.f64)) #s(literal 2 binary64)) k)
(pow (* 2 (* n (PI))) k)
(pow.f64 (.f64 (.f64 n (PI.f64)) #s(literal 2 binary64)) k)
(pow (* 2 (* n (PI))) k)
(pow.f64 (.f64 (.f64 n (PI.f64)) #s(literal 2 binary64)) k)
(pow (* 2 (* n (PI))) k)
(pow.f64 (.f64 (.f64 n (PI.f64)) #s(literal 2 binary64)) k)

eval210.0ms (1.6%)

Compiler: Compiled 35691 to 3535 computations (90.1% saved)

prune229.0ms (1.7%)

Pruning

16 alts after pruning (13 fresh and 3 done)

	Pruned	Kept	Total
New	1727	12	1739
Fresh	11	1	12
Picked	4	1	5
Done	0	2	2
Total	1742	16	1758

Accuracy

100.0%

Counts

1758 → 16

Alt Table

Click to see full alt table

Status	Accuracy	Program
	93.2%	(pow.f64 (/.f64 (.f64 k (pow.f64 (.f64 #s(literal 2 binary64) (.f64 (PI.f64) n)) k)) (.f64 #s(literal 2 binary64) (*.f64 (PI.f64) n))) #s(literal -1/2 binary64))
	80.3%	(/.f64 (pow.f64 (.f64 #s(literal 4 binary64) (.f64 (.f64 (PI.f64) n) (.f64 (PI.f64) n))) (-.f64 #s(literal 1/4 binary64) (*.f64 k #s(literal 1/4 binary64)))) (sqrt.f64 k))
✓	99.3%	(/.f64 (pow.f64 (.f64 #s(literal 2 binary64) (.f64 (PI.f64) n)) (-.f64 #s(literal 1/2 binary64) (/.f64 k #s(literal 2 binary64)))) (sqrt.f64 k))
✓	99.3%	(/.f64 (pow.f64 k #s(literal -1/2 binary64)) (pow.f64 (.f64 #s(literal 2 binary64) (.f64 (PI.f64) n)) (+.f64 (/.f64 k #s(literal 2 binary64)) #s(literal -1/2 binary64))))
▶	37.0%	(/.f64 (sqrt.f64 (/.f64 (*.f64 n (PI.f64)) k)) (sqrt.f64 #s(literal 1/2 binary64)))
▶	98.6%	(/.f64 (sqrt.f64 (/.f64 (.f64 #s(literal 2 binary64) (.f64 (PI.f64) n)) (pow.f64 (.f64 #s(literal 2 binary64) (.f64 (PI.f64) n)) k))) (sqrt.f64 k))
	44.1%	(/.f64 (sqrt.f64 (.f64 #s(literal 2 binary64) (.f64 (PI.f64) n))) (sqrt.f64 k))
	38.5%	(/.f64 (sqrt.f64 #s(literal 2 binary64)) (sqrt.f64 (/.f64 k (*.f64 (PI.f64) n))))
	44.1%	(.f64 (pow.f64 (.f64 (PI.f64) n) #s(literal 1/2 binary64)) (sqrt.f64 (*.f64 (/.f64 #s(literal 1 binary64) k) #s(literal 2 binary64))))
✓	99.2%	(.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) (pow.f64 (.f64 (*.f64 #s(literal 2 binary64) (PI.f64)) n) (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 2 binary64))))
▶	37.1%	(.f64 (sqrt.f64 (.f64 (/.f64 (PI.f64) k) n)) (sqrt.f64 #s(literal 2 binary64)))
	37.1%	(.f64 (sqrt.f64 (.f64 (PI.f64) (/.f64 n k))) (sqrt.f64 #s(literal 2 binary64)))
	44.4%	(.f64 (sqrt.f64 n) (sqrt.f64 (.f64 (/.f64 (PI.f64) k) #s(literal 2 binary64))))
▶	91.8%	(sqrt.f64 (/.f64 (.f64 #s(literal 2 binary64) (.f64 (PI.f64) n)) (.f64 k (pow.f64 (.f64 #s(literal 2 binary64) (*.f64 (PI.f64) n)) k))))
▶	37.2%	(sqrt.f64 (/.f64 #s(literal 2 binary64) (/.f64 k (*.f64 (PI.f64) n))))
	34.9%	(exp.f64 (.f64 (log.f64 (/.f64 #s(literal 2 binary64) (/.f64 k (.f64 (PI.f64) n)))) #s(literal 1/2 binary64)))

Compiler

Compiled 409 to 297 computations (27.4% saved)

simplify16.0ms (0.1%)

Algorithm

1×	egg-herbie

Localize:

Found 20 expressions of interest:

New	Metric	Program
✓	cost-diff	(*.f64 (PI.f64) n)
✓	cost-diff	(.f64 #s(literal 2 binary64) (.f64 (PI.f64) n))
✓	cost-diff	(/.f64 (.f64 #s(literal 2 binary64) (.f64 (PI.f64) n)) (.f64 k (pow.f64 (.f64 #s(literal 2 binary64) (*.f64 (PI.f64) n)) k)))
✓	cost-diff	(sqrt.f64 (/.f64 (.f64 #s(literal 2 binary64) (.f64 (PI.f64) n)) (.f64 k (pow.f64 (.f64 #s(literal 2 binary64) (*.f64 (PI.f64) n)) k))))
✓	cost-diff	(*.f64 n (PI.f64))
✓	cost-diff	(/.f64 (*.f64 n (PI.f64)) k)
✓	cost-diff	(sqrt.f64 (/.f64 (*.f64 n (PI.f64)) k))
✓	cost-diff	(/.f64 (sqrt.f64 (/.f64 (*.f64 n (PI.f64)) k)) (sqrt.f64 #s(literal 1/2 binary64)))
✓	cost-diff	(/.f64 (PI.f64) k)
✓	cost-diff	(*.f64 (/.f64 (PI.f64) k) n)
✓	cost-diff	(sqrt.f64 (*.f64 (/.f64 (PI.f64) k) n))
✓	cost-diff	(.f64 (sqrt.f64 (.f64 (/.f64 (PI.f64) k) n)) (sqrt.f64 #s(literal 2 binary64)))
✓	cost-diff	(*.f64 (PI.f64) n)
✓	cost-diff	(/.f64 k (*.f64 (PI.f64) n))
✓	cost-diff	(/.f64 #s(literal 2 binary64) (/.f64 k (*.f64 (PI.f64) n)))
✓	cost-diff	(sqrt.f64 (/.f64 #s(literal 2 binary64) (/.f64 k (*.f64 (PI.f64) n))))
✓	cost-diff	(.f64 #s(literal 2 binary64) (.f64 (PI.f64) n))
✓	cost-diff	(/.f64 (.f64 #s(literal 2 binary64) (.f64 (PI.f64) n)) (pow.f64 (.f64 #s(literal 2 binary64) (.f64 (PI.f64) n)) k))
✓	cost-diff	(sqrt.f64 (/.f64 (.f64 #s(literal 2 binary64) (.f64 (PI.f64) n)) (pow.f64 (.f64 #s(literal 2 binary64) (.f64 (PI.f64) n)) k)))
✓	cost-diff	(/.f64 (sqrt.f64 (/.f64 (.f64 #s(literal 2 binary64) (.f64 (PI.f64) n)) (pow.f64 (.f64 #s(literal 2 binary64) (.f64 (PI.f64) n)) k))) (sqrt.f64 k))

Rules

256×	`-lowering-.f32`
256×	`-lowering-.f64`
174×	`/-lowering-/.f32`
174×	`/-lowering-/.f64`
74×	`times-frac`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	28	209
1	47	209
2	98	209
3	212	209
4	266	209
5	299	209
6	324	209
7	336	209
8	346	209
0	346	209

Stop Event

1×	iter limit
1×	saturated

Calls

Call 1

Inputs
(/ (sqrt (/ (* 2 (* (PI) n)) (pow (* 2 (* (PI) n)) k))) (sqrt k))
(sqrt (/ (* 2 (* (PI) n)) (pow (* 2 (* (PI) n)) k)))
(/ (* 2 (* (PI) n)) (pow (* 2 (* (PI) n)) k))
(* 2 (* (PI) n))
2
(* (PI) n)
(PI)
n
(pow (* 2 (* (PI) n)) k)
k
(sqrt k)
(sqrt (/ 2 (/ k (* (PI) n))))
(/ 2 (/ k (* (PI) n)))
2
(/ k (* (PI) n))
k
(* (PI) n)
(PI)
n
(* (sqrt (* (/ (PI) k) n)) (sqrt 2))
(sqrt (* (/ (PI) k) n))
(* (/ (PI) k) n)
(/ (PI) k)
(PI)
k
n
(sqrt 2)
2
(/ (sqrt (/ (* n (PI)) k)) (sqrt 1/2))
(sqrt (/ (* n (PI)) k))
(/ (* n (PI)) k)
(* n (PI))
n
(PI)
k
(sqrt 1/2)
1/2
(sqrt (/ (* 2 (* (PI) n)) (* k (pow (* 2 (* (PI) n)) k))))
(/ (* 2 (* (PI) n)) (* k (pow (* 2 (* (PI) n)) k)))
(* 2 (* (PI) n))
2
(* (PI) n)
(PI)
n
(* k (pow (* 2 (* (PI) n)) k))
k
(pow (* 2 (* (PI) n)) k)

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

localize240.0ms (1.8%)

Localize:

Found 20 expressions of interest:

New	Metric	Score	Program
✓	accuracy	99.8%	(*.f64 (PI.f64) n)
✓	accuracy	99.6%	(pow.f64 (.f64 #s(literal 2 binary64) (.f64 (PI.f64) n)) k)
✓	accuracy	91.9%	(sqrt.f64 (/.f64 (.f64 #s(literal 2 binary64) (.f64 (PI.f64) n)) (.f64 k (pow.f64 (.f64 #s(literal 2 binary64) (*.f64 (PI.f64) n)) k))))
✓	accuracy	76.2%	(PI.f64)
✓	accuracy	99.7%	(/.f64 (*.f64 n (PI.f64)) k)
✓	accuracy	99.5%	(/.f64 (sqrt.f64 (/.f64 (*.f64 n (PI.f64)) k)) (sqrt.f64 #s(literal 1/2 binary64)))
✓	accuracy	92.6%	(sqrt.f64 (/.f64 (*.f64 n (PI.f64)) k))
✓	accuracy	76.2%	(PI.f64)
✓	accuracy	99.7%	(*.f64 (/.f64 (PI.f64) k) n)
✓	accuracy	99.5%	(.f64 (sqrt.f64 (.f64 (/.f64 (PI.f64) k) n)) (sqrt.f64 #s(literal 2 binary64)))
✓	accuracy	92.6%	(sqrt.f64 (*.f64 (/.f64 (PI.f64) k) n))
✓	accuracy	76.2%	(PI.f64)
✓	accuracy	99.7%	(/.f64 k (*.f64 (PI.f64) n))
✓	accuracy	99.7%	(/.f64 #s(literal 2 binary64) (/.f64 k (*.f64 (PI.f64) n)))
✓	accuracy	92.6%	(sqrt.f64 (/.f64 #s(literal 2 binary64) (/.f64 k (*.f64 (PI.f64) n))))
✓	accuracy	76.2%	(PI.f64)
✓	accuracy	99.7%	(/.f64 (sqrt.f64 (/.f64 (.f64 #s(literal 2 binary64) (.f64 (PI.f64) n)) (pow.f64 (.f64 #s(literal 2 binary64) (.f64 (PI.f64) n)) k))) (sqrt.f64 k))
✓	accuracy	99.6%	(pow.f64 (.f64 #s(literal 2 binary64) (.f64 (PI.f64) n)) k)
✓	accuracy	98.8%	(sqrt.f64 (/.f64 (.f64 #s(literal 2 binary64) (.f64 (PI.f64) n)) (pow.f64 (.f64 #s(literal 2 binary64) (.f64 (PI.f64) n)) k)))
✓	accuracy	76.2%	(PI.f64)

Results

97.0ms	63×	5	exit
82.0ms	193×	0	valid

Compiler

Compiled 212 to 29 computations (86.3% saved)

Precisions

Click to see histograms. Total time spent on operations: 102.0ms

ival-div: 29.0ms (28.5% of total)

ival-pow: 25.0ms (24.5% of total)

ival-sqrt: 18.0ms (17.7% of total)

backward-pass: 14.0ms (13.7% of total)

ival-mult: 13.0ms (12.8% of total)

ival-pi: 2.0ms (2% of total)

const: 1.0ms (1% of total)

series73.0ms (0.5%)

Counts

20 → 408

Calls

Call 1

Inputs
#<alt (/ (sqrt (/ (* 2 (* (PI) n)) (pow (* 2 (* (PI) n)) k))) (sqrt k))>
#<alt (sqrt (/ (* 2 (* (PI) n)) (pow (* 2 (* (PI) n)) k)))>
#<alt (/ (* 2 (* (PI) n)) (pow (* 2 (* (PI) n)) k))>
#<alt (* 2 (* (PI) n))>
#<alt (sqrt (/ 2 (/ k (* (PI) n))))>
#<alt (/ 2 (/ k (* (PI) n)))>
#<alt (/ k (* (PI) n))>
#<alt (* (PI) n)>
#<alt (* (sqrt (* (/ (PI) k) n)) (sqrt 2))>
#<alt (sqrt (* (/ (PI) k) n))>
#<alt (* (/ (PI) k) n)>
#<alt (/ (PI) k)>
#<alt (/ (sqrt (/ (* n (PI)) k)) (sqrt 1/2))>
#<alt (sqrt (/ (* n (PI)) k))>
#<alt (/ (* n (PI)) k)>
#<alt (* n (PI))>
#<alt (sqrt (/ (* 2 (* (PI) n)) (* k (pow (* 2 (* (PI) n)) k))))>
#<alt (/ (* 2 (* (PI) n)) (* k (pow (* 2 (* (PI) n)) k)))>
#<alt (PI)>
#<alt (pow (* 2 (* (PI) n)) k)>

Outputs
#<alt (* (sqrt (/ (* n (PI)) (* k (exp (* k (+ (log n) (log (* 2 (PI))))))))) (sqrt 2))>
#<alt (* (sqrt (/ (* n (PI)) (* k (exp (* k (+ (log n) (log (* 2 (PI))))))))) (sqrt 2))>
#<alt (* (sqrt (/ (* n (PI)) (* k (exp (* k (+ (log n) (log (* 2 (PI))))))))) (sqrt 2))>
#<alt (* (sqrt (/ (* n (PI)) (* k (exp (* k (+ (log n) (log (* 2 (PI))))))))) (sqrt 2))>
#<alt (* (sqrt (/ (* n (PI)) (* k (exp (* k (+ (log (* 2 (PI))) (* -1 (log (/ 1 n))))))))) (sqrt 2))>
#<alt (* (sqrt (/ (* n (PI)) (* k (exp (* k (+ (log (* 2 (PI))) (* -1 (log (/ 1 n))))))))) (sqrt 2))>
#<alt (* (sqrt (/ (* n (PI)) (* k (exp (* k (+ (log (* 2 (PI))) (* -1 (log (/ 1 n))))))))) (sqrt 2))>
#<alt (* (sqrt (/ (* n (PI)) (* k (exp (* k (+ (log (* 2 (PI))) (* -1 (log (/ 1 n))))))))) (sqrt 2))>
#<alt (* -1 (* (sqrt (/ (* n (PI)) (* k (exp (* k (+ (log (* -2 (PI))) (* -1 (log (/ -1 n))))))))) (* (sqrt -2) (sqrt -1))))>
#<alt (* -1 (* (sqrt (/ (* n (PI)) (* k (exp (* k (+ (log (* -2 (PI))) (* -1 (log (/ -1 n))))))))) (* (sqrt -2) (sqrt -1))))>
#<alt (* -1 (* (sqrt (/ (* n (PI)) (* k (exp (* k (+ (log (* -2 (PI))) (* -1 (log (/ -1 n))))))))) (* (sqrt -2) (sqrt -1))))>
#<alt (* -1 (* (sqrt (/ (* n (PI)) (* k (exp (* k (+ (log (* -2 (PI))) (* -1 (log (/ -1 n))))))))) (* (sqrt -2) (sqrt -1))))>
#<alt (* (sqrt (/ (* n (PI)) k)) (sqrt 2))>
#<alt (/ (+ (* -1/2 (* (sqrt (* (pow k 3) (* n (PI)))) (* (log (* 2 (* n (PI)))) (sqrt 2)))) (* (sqrt (* k (* n (PI)))) (sqrt 2))) k)>
#<alt (/ (+ (* (sqrt (* k (* n (PI)))) (sqrt 2)) (* (pow k 2) (+ (* -1/2 (* (sqrt (/ k (* n (PI)))) (* (sqrt 2) (+ (* -1 (* n (* (PI) (pow (log (* 2 (* n (PI)))) 2)))) (* 1/2 (* n (* (PI) (pow (log (* 2 (* n (PI)))) 2)))))))) (* -1/2 (* (sqrt (/ (* n (PI)) k)) (* (log (* 2 (* n (PI)))) (sqrt 2))))))) k)>
#<alt (/ (+ (* (sqrt (* k (* n (PI)))) (sqrt 2)) (* (pow k 2) (+ (* -1/2 (* (sqrt (/ (* n (PI)) k)) (* (log (* 2 (* n (PI)))) (sqrt 2)))) (* k (+ (* -1/2 (* (sqrt (/ 1 (* k (* n (PI))))) (* (sqrt 2) (+ (* -1 (* n (* (PI) (pow (log (* 2 (* n (PI)))) 2)))) (* 1/2 (* n (* (PI) (pow (log (* 2 (* n (PI)))) 2)))))))) (* -1/2 (* (sqrt (/ k (* n (PI)))) (* (sqrt 2) (+ (* -1 (* (log (* 2 (* n (PI)))) (+ (* -1 (* n (* (PI) (pow (log (* 2 (* n (PI)))) 2)))) (* 1/2 (* n (* (PI) (pow (log (* 2 (* n (PI)))) 2))))))) (+ (* -1/2 (* n (* (PI) (pow (log (* 2 (* n (PI)))) 3)))) (+ (* 1/6 (* n (* (PI) (pow (log (* 2 (* n (PI)))) 3)))) (* 1/4 (/ (* n (* (PI) (pow (log (* 2 (* n (PI)))) 2))) k))))))))))))) k)>
#<alt (* (sqrt (/ (* n (PI)) (* k (pow (* 2 (* n (PI))) k)))) (sqrt 2))>
#<alt (* (sqrt (/ (* n (PI)) (* k (pow (* 2 (* n (PI))) k)))) (sqrt 2))>
#<alt (* (sqrt (/ (* n (PI)) (* k (pow (* 2 (* n (PI))) k)))) (sqrt 2))>
#<alt (* (sqrt (/ (* n (PI)) (* k (pow (* 2 (* n (PI))) k)))) (sqrt 2))>
#<alt (* (sqrt (/ (* n (PI)) (* k (pow (* 2 (* n (PI))) k)))) (sqrt 2))>
#<alt (* (sqrt (/ (* n (PI)) (* k (pow (* 2 (* n (PI))) k)))) (sqrt 2))>
#<alt (* (sqrt (/ (* n (PI)) (* k (pow (* 2 (* n (PI))) k)))) (sqrt 2))>
#<alt (* (sqrt (/ (* n (PI)) (* k (pow (* 2 (* n (PI))) k)))) (sqrt 2))>
#<alt (* (sqrt (/ (* n (PI)) (exp (* k (+ (log n) (log (* 2 (PI)))))))) (sqrt 2))>
#<alt (* (sqrt (/ (* n (PI)) (exp (* k (+ (log n) (log (* 2 (PI)))))))) (sqrt 2))>
#<alt (* (sqrt (/ (* n (PI)) (exp (* k (+ (log n) (log (* 2 (PI)))))))) (sqrt 2))>
#<alt (* (sqrt (/ (* n (PI)) (exp (* k (+ (log n) (log (* 2 (PI)))))))) (sqrt 2))>
#<alt (* (sqrt (/ (* n (PI)) (exp (* k (+ (log (* 2 (PI))) (* -1 (log (/ 1 n)))))))) (sqrt 2))>
#<alt (* (sqrt (/ (* n (PI)) (exp (* k (+ (log (* 2 (PI))) (* -1 (log (/ 1 n)))))))) (sqrt 2))>
#<alt (* (sqrt (/ (* n (PI)) (exp (* k (+ (log (* 2 (PI))) (* -1 (log (/ 1 n)))))))) (sqrt 2))>
#<alt (* (sqrt (/ (* n (PI)) (exp (* k (+ (log (* 2 (PI))) (* -1 (log (/ 1 n)))))))) (sqrt 2))>
#<alt (* -1 (* (sqrt (/ (* n (PI)) (exp (* k (+ (log (* -2 (PI))) (* -1 (log (/ -1 n)))))))) (* (sqrt -2) (sqrt -1))))>
#<alt (* -1 (* (sqrt (/ (* n (PI)) (exp (* k (+ (log (* -2 (PI))) (* -1 (log (/ -1 n)))))))) (* (sqrt -2) (sqrt -1))))>
#<alt (* -1 (* (sqrt (/ (* n (PI)) (exp (* k (+ (log (* -2 (PI))) (* -1 (log (/ -1 n)))))))) (* (sqrt -2) (sqrt -1))))>
#<alt (* -1 (* (sqrt (/ (* n (PI)) (exp (* k (+ (log (* -2 (PI))) (* -1 (log (/ -1 n)))))))) (* (sqrt -2) (sqrt -1))))>
#<alt (* (sqrt (* n (PI))) (sqrt 2))>
#<alt (+ (* -1/2 (* (* k (* (log (* 2 (* n (PI)))) (sqrt 2))) (sqrt (* n (PI))))) (* (sqrt (* n (PI))) (sqrt 2)))>
#<alt (+ (* k (+ (* -1/2 (* (sqrt (* n (PI))) (* (log (* 2 (* n (PI)))) (sqrt 2)))) (* -1/2 (* (* k (* (sqrt 2) (+ (* -1 (* n (* (PI) (pow (log (* 2 (* n (PI)))) 2)))) (+ (* 1/4 (* n (* (PI) (pow (log (* 2 (* n (PI)))) 2)))) (* 1/2 (* n (* (PI) (pow (log (* 2 (* n (PI)))) 2)))))))) (sqrt (/ 1 (* n (PI)))))))) (* (sqrt (* n (PI))) (sqrt 2)))>
#<alt (+ (* k (+ (* -1/2 (* (sqrt (* n (PI))) (* (log (* 2 (* n (PI)))) (sqrt 2)))) (* k (+ (* -1/2 (* (sqrt (/ 1 (* n (PI)))) (* (sqrt 2) (+ (* -1 (* n (* (PI) (pow (log (* 2 (* n (PI)))) 2)))) (+ (* 1/4 (* n (* (PI) (pow (log (* 2 (* n (PI)))) 2)))) (* 1/2 (* n (* (PI) (pow (log (* 2 (* n (PI)))) 2))))))))) (* -1/2 (* (* k (* (sqrt 2) (+ (* -1 (* (log (* 2 (* n (PI)))) (+ (* -1 (* n (* (PI) (pow (log (* 2 (* n (PI)))) 2)))) (* 1/2 (* n (* (PI) (pow (log (* 2 (* n (PI)))) 2))))))) (+ (* -1/2 (* n (* (PI) (pow (log (* 2 (* n (PI)))) 3)))) (+ (* 1/6 (* n (* (PI) (pow (log (* 2 (* n (PI)))) 3)))) (* 1/2 (* (log (* 2 (* n (PI)))) (+ (* -1 (* n (* (PI) (pow (log (* 2 (* n (PI)))) 2)))) (+ (* 1/4 (* n (* (PI) (pow (log (* 2 (* n (PI)))) 2)))) (* 1/2 (* n (* (PI) (pow (log (* 2 (* n (PI)))) 2))))))))))))) (sqrt (/ 1 (* n (PI)))))))))) (* (sqrt (* n (PI))) (sqrt 2)))>
#<alt (* (sqrt (/ (* n (PI)) (pow (* 2 (* n (PI))) k))) (sqrt 2))>
#<alt (* (sqrt (/ (* n (PI)) (pow (* 2 (* n (PI))) k))) (sqrt 2))>
#<alt (* (sqrt (/ (* n (PI)) (pow (* 2 (* n (PI))) k))) (sqrt 2))>
#<alt (* (sqrt (/ (* n (PI)) (pow (* 2 (* n (PI))) k))) (sqrt 2))>
#<alt (* (sqrt (/ (* n (PI)) (pow (* 2 (* n (PI))) k))) (sqrt 2))>
#<alt (* (sqrt (/ (* n (PI)) (pow (* 2 (* n (PI))) k))) (sqrt 2))>
#<alt (* (sqrt (/ (* n (PI)) (pow (* 2 (* n (PI))) k))) (sqrt 2))>
#<alt (* (sqrt (/ (* n (PI)) (pow (* 2 (* n (PI))) k))) (sqrt 2))>
#<alt (* 2 (/ (* n (PI)) (exp (* k (+ (log n) (log (* 2 (PI))))))))>
#<alt (* 2 (/ (* n (PI)) (exp (* k (+ (log n) (log (* 2 (PI))))))))>
#<alt (* 2 (/ (* n (PI)) (exp (* k (+ (log n) (log (* 2 (PI))))))))>
#<alt (* 2 (/ (* n (PI)) (exp (* k (+ (log n) (log (* 2 (PI))))))))>
#<alt (* 2 (/ (* n (PI)) (exp (* k (+ (log (* 2 (PI))) (* -1 (log (/ 1 n))))))))>
#<alt (* 2 (/ (* n (PI)) (exp (* k (+ (log (* 2 (PI))) (* -1 (log (/ 1 n))))))))>
#<alt (* 2 (/ (* n (PI)) (exp (* k (+ (log (* 2 (PI))) (* -1 (log (/ 1 n))))))))>
#<alt (* 2 (/ (* n (PI)) (exp (* k (+ (log (* 2 (PI))) (* -1 (log (/ 1 n))))))))>
#<alt (* 2 (/ (* n (PI)) (exp (* k (+ (log (* -2 (PI))) (* -1 (log (/ -1 n))))))))>
#<alt (* 2 (/ (* n (PI)) (exp (* k (+ (log (* -2 (PI))) (* -1 (log (/ -1 n))))))))>
#<alt (* 2 (/ (* n (PI)) (exp (* k (+ (log (* -2 (PI))) (* -1 (log (/ -1 n))))))))>
#<alt (* 2 (/ (* n (PI)) (exp (* k (+ (log (* -2 (PI))) (* -1 (log (/ -1 n))))))))>
#<alt (* 2 (* n (PI)))>
#<alt (+ (* -2 (* k (* n (* (PI) (log (* 2 (* n (PI)))))))) (* 2 (* n (PI))))>
#<alt (+ (* 2 (* n (PI))) (* k (+ (* -2 (* k (+ (* -1 (* n (* (PI) (pow (log (* 2 (* n (PI)))) 2)))) (* 1/2 (* n (* (PI) (pow (log (* 2 (* n (PI)))) 2))))))) (* -2 (* n (* (PI) (log (* 2 (* n (PI))))))))))>
#<alt (+ (* 2 (* n (PI))) (* k (+ (* -2 (* n (* (PI) (log (* 2 (* n (PI))))))) (* k (+ (* -2 (* k (+ (* -1 (* (log (* 2 (* n (PI)))) (+ (* -1 (* n (* (PI) (pow (log (* 2 (* n (PI)))) 2)))) (* 1/2 (* n (* (PI) (pow (log (* 2 (* n (PI)))) 2))))))) (+ (* -1/2 (* n (* (PI) (pow (log (* 2 (* n (PI)))) 3)))) (* 1/6 (* n (* (PI) (pow (log (* 2 (* n (PI)))) 3)))))))) (* -2 (+ (* -1 (* n (* (PI) (pow (log (* 2 (* n (PI)))) 2)))) (* 1/2 (* n (* (PI) (pow (log (* 2 (* n (PI)))) 2)))))))))))>
#<alt (* 2 (/ (* n (PI)) (pow (* 2 (* n (PI))) k)))>
#<alt (* 2 (/ (* n (PI)) (pow (* 2 (* n (PI))) k)))>
#<alt (* 2 (/ (* n (PI)) (pow (* 2 (* n (PI))) k)))>
#<alt (* 2 (/ (* n (PI)) (pow (* 2 (* n (PI))) k)))>
#<alt (* 2 (/ (* n (PI)) (pow (* 2 (* n (PI))) k)))>
#<alt (* 2 (/ (* n (PI)) (pow (* 2 (* n (PI))) k)))>
#<alt (* 2 (/ (* n (PI)) (pow (* 2 (* n (PI))) k)))>
#<alt (* 2 (/ (* n (PI)) (pow (* 2 (* n (PI))) k)))>
#<alt (* 2 (* n (PI)))>
#<alt (* 2 (* n (PI)))>
#<alt (* 2 (* n (PI)))>
#<alt (* 2 (* n (PI)))>
#<alt (* 2 (* n (PI)))>
#<alt (* 2 (* n (PI)))>
#<alt (* 2 (* n (PI)))>
#<alt (* 2 (* n (PI)))>
#<alt (* 2 (* n (PI)))>
#<alt (* 2 (* n (PI)))>
#<alt (* 2 (* n (PI)))>
#<alt (* 2 (* n (PI)))>
#<alt (* (sqrt (/ (* n (PI)) k)) (sqrt 2))>
#<alt (* (sqrt (/ (* n (PI)) k)) (sqrt 2))>
#<alt (* (sqrt (/ (* n (PI)) k)) (sqrt 2))>
#<alt (* (sqrt (/ (* n (PI)) k)) (sqrt 2))>
#<alt (* (sqrt (/ (* n (PI)) k)) (sqrt 2))>
#<alt (* (sqrt (/ (* n (PI)) k)) (sqrt 2))>
#<alt (* (sqrt (/ (* n (PI)) k)) (sqrt 2))>
#<alt (* (sqrt (/ (* n (PI)) k)) (sqrt 2))>
#<alt (* (sqrt (/ (* n (PI)) k)) (* (sqrt -2) (sqrt -1)))>
#<alt (* (sqrt (/ (* n (PI)) k)) (* (sqrt -2) (sqrt -1)))>
#<alt (* (sqrt (/ (* n (PI)) k)) (* (sqrt -2) (sqrt -1)))>
#<alt (* (sqrt (/ (* n (PI)) k)) (* (sqrt -2) (sqrt -1)))>
#<alt (* (sqrt (/ (* n (PI)) k)) (sqrt 2))>
#<alt (* (sqrt (/ (* n (PI)) k)) (sqrt 2))>
#<alt (* (sqrt (/ (* n (PI)) k)) (sqrt 2))>
#<alt (* (sqrt (/ (* n (PI)) k)) (sqrt 2))>
#<alt (* (sqrt (/ (* n (PI)) k)) (sqrt 2))>
#<alt (* (sqrt (/ (* n (PI)) k)) (sqrt 2))>
#<alt (* (sqrt (/ (* n (PI)) k)) (sqrt 2))>
#<alt (* (sqrt (/ (* n (PI)) k)) (sqrt 2))>
#<alt (* -1 (* (sqrt (/ (* n (PI)) k)) (* (sqrt -2) (sqrt -1))))>
#<alt (* -1 (* (sqrt (/ (* n (PI)) k)) (* (sqrt -2) (sqrt -1))))>
#<alt (* -1 (* (sqrt (/ (* n (PI)) k)) (* (sqrt -2) (sqrt -1))))>
#<alt (* -1 (* (sqrt (/ (* n (PI)) k)) (* (sqrt -2) (sqrt -1))))>
#<alt (* 2 (/ (* n (PI)) k))>
#<alt (* 2 (/ (* n (PI)) k))>
#<alt (* 2 (/ (* n (PI)) k))>
#<alt (* 2 (/ (* n (PI)) k))>
#<alt (* 2 (/ (* n (PI)) k))>
#<alt (* 2 (/ (* n (PI)) k))>
#<alt (* 2 (/ (* n (PI)) k))>
#<alt (* 2 (/ (* n (PI)) k))>
#<alt (* 2 (/ (* n (PI)) k))>
#<alt (* 2 (/ (* n (PI)) k))>
#<alt (* 2 (/ (* n (PI)) k))>
#<alt (* 2 (/ (* n (PI)) k))>
#<alt (* 2 (/ (* n (PI)) k))>
#<alt (* 2 (/ (* n (PI)) k))>
#<alt (* 2 (/ (* n (PI)) k))>
#<alt (* 2 (/ (* n (PI)) k))>
#<alt (* 2 (/ (* n (PI)) k))>
#<alt (* 2 (/ (* n (PI)) k))>
#<alt (* 2 (/ (* n (PI)) k))>
#<alt (* 2 (/ (* n (PI)) k))>
#<alt (* 2 (/ (* n (PI)) k))>
#<alt (* 2 (/ (* n (PI)) k))>
#<alt (* 2 (/ (* n (PI)) k))>
#<alt (* 2 (/ (* n (PI)) k))>
#<alt (/ k (* n (PI)))>
#<alt (/ k (* n (PI)))>
#<alt (/ k (* n (PI)))>
#<alt (/ k (* n (PI)))>
#<alt (/ k (* n (PI)))>
#<alt (/ k (* n (PI)))>
#<alt (/ k (* n (PI)))>
#<alt (/ k (* n (PI)))>
#<alt (/ k (* n (PI)))>
#<alt (/ k (* n (PI)))>
#<alt (/ k (* n (PI)))>
#<alt (/ k (* n (PI)))>
#<alt (/ k (* n (PI)))>
#<alt (/ k (* n (PI)))>
#<alt (/ k (* n (PI)))>
#<alt (/ k (* n (PI)))>
#<alt (/ k (* n (PI)))>
#<alt (/ k (* n (PI)))>
#<alt (/ k (* n (PI)))>
#<alt (/ k (* n (PI)))>
#<alt (/ k (* n (PI)))>
#<alt (/ k (* n (PI)))>
#<alt (/ k (* n (PI)))>
#<alt (/ k (* n (PI)))>
#<alt (* n (PI))>
#<alt (* n (PI))>
#<alt (* n (PI))>
#<alt (* n (PI))>
#<alt (* n (PI))>
#<alt (* n (PI))>
#<alt (* n (PI))>
#<alt (* n (PI))>
#<alt (* n (PI))>
#<alt (* n (PI))>
#<alt (* n (PI))>
#<alt (* n (PI))>
#<alt (* (sqrt (/ (* n (PI)) k)) (sqrt 2))>
#<alt (* (sqrt (/ (* n (PI)) k)) (sqrt 2))>
#<alt (* (sqrt (/ (* n (PI)) k)) (sqrt 2))>
#<alt (* (sqrt (/ (* n (PI)) k)) (sqrt 2))>
#<alt (* (sqrt (/ (* n (PI)) k)) (sqrt 2))>
#<alt (* (sqrt (/ (* n (PI)) k)) (sqrt 2))>
#<alt (* (sqrt (/ (* n (PI)) k)) (sqrt 2))>
#<alt (* (sqrt (/ (* n (PI)) k)) (sqrt 2))>
#<alt (* (sqrt (/ (* n (PI)) k)) (* (pow (sqrt -1) 2) (sqrt 2)))>
#<alt (* (sqrt (/ (* n (PI)) k)) (* (pow (sqrt -1) 2) (sqrt 2)))>
#<alt (* (sqrt (/ (* n (PI)) k)) (* (pow (sqrt -1) 2) (sqrt 2)))>
#<alt (* (sqrt (/ (* n (PI)) k)) (* (pow (sqrt -1) 2) (sqrt 2)))>
#<alt (* (sqrt (/ (* n (PI)) k)) (sqrt 2))>
#<alt (* (sqrt (/ (* n (PI)) k)) (sqrt 2))>
#<alt (* (sqrt (/ (* n (PI)) k)) (sqrt 2))>
#<alt (* (sqrt (/ (* n (PI)) k)) (sqrt 2))>
#<alt (* (sqrt (/ (* n (PI)) k)) (sqrt 2))>
#<alt (* (sqrt (/ (* n (PI)) k)) (sqrt 2))>
#<alt (* (sqrt (/ (* n (PI)) k)) (sqrt 2))>
#<alt (* (sqrt (/ (* n (PI)) k)) (sqrt 2))>
#<alt (* -1 (* (sqrt (/ (* n (PI)) k)) (* (pow (sqrt -1) 2) (sqrt 2))))>
#<alt (* -1 (* (sqrt (/ (* n (PI)) k)) (* (pow (sqrt -1) 2) (sqrt 2))))>
#<alt (* -1 (* (sqrt (/ (* n (PI)) k)) (* (pow (sqrt -1) 2) (sqrt 2))))>
#<alt (* -1 (* (sqrt (/ (* n (PI)) k)) (* (pow (sqrt -1) 2) (sqrt 2))))>
#<alt (sqrt (/ (* n (PI)) k))>
#<alt (sqrt (/ (* n (PI)) k))>
#<alt (sqrt (/ (* n (PI)) k))>
#<alt (sqrt (/ (* n (PI)) k))>
#<alt (sqrt (/ (* n (PI)) k))>
#<alt (sqrt (/ (* n (PI)) k))>
#<alt (sqrt (/ (* n (PI)) k))>
#<alt (sqrt (/ (* n (PI)) k))>
#<alt (* (sqrt (/ (* n (PI)) k)) (pow (sqrt -1) 2))>
#<alt (* (sqrt (/ (* n (PI)) k)) (pow (sqrt -1) 2))>
#<alt (* (sqrt (/ (* n (PI)) k)) (pow (sqrt -1) 2))>
#<alt (* (sqrt (/ (* n (PI)) k)) (pow (sqrt -1) 2))>
#<alt (sqrt (/ (* n (PI)) k))>
#<alt (sqrt (/ (* n (PI)) k))>
#<alt (sqrt (/ (* n (PI)) k))>
#<alt (sqrt (/ (* n (PI)) k))>
#<alt (sqrt (/ (* n (PI)) k))>
#<alt (sqrt (/ (* n (PI)) k))>
#<alt (sqrt (/ (* n (PI)) k))>
#<alt (sqrt (/ (* n (PI)) k))>
#<alt (* -1 (* (sqrt (/ (* n (PI)) k)) (pow (sqrt -1) 2)))>
#<alt (* -1 (* (sqrt (/ (* n (PI)) k)) (pow (sqrt -1) 2)))>
#<alt (* -1 (* (sqrt (/ (* n (PI)) k)) (pow (sqrt -1) 2)))>
#<alt (* -1 (* (sqrt (/ (* n (PI)) k)) (pow (sqrt -1) 2)))>
#<alt (/ (* n (PI)) k)>
#<alt (/ (* n (PI)) k)>
#<alt (/ (* n (PI)) k)>
#<alt (/ (* n (PI)) k)>
#<alt (/ (* n (PI)) k)>
#<alt (/ (* n (PI)) k)>
#<alt (/ (* n (PI)) k)>
#<alt (/ (* n (PI)) k)>
#<alt (/ (* n (PI)) k)>
#<alt (/ (* n (PI)) k)>
#<alt (/ (* n (PI)) k)>
#<alt (/ (* n (PI)) k)>
#<alt (/ (* n (PI)) k)>
#<alt (/ (* n (PI)) k)>
#<alt (/ (* n (PI)) k)>
#<alt (/ (* n (PI)) k)>
#<alt (/ (* n (PI)) k)>
#<alt (/ (* n (PI)) k)>
#<alt (/ (* n (PI)) k)>
#<alt (/ (* n (PI)) k)>
#<alt (/ (* n (PI)) k)>
#<alt (/ (* n (PI)) k)>
#<alt (/ (* n (PI)) k)>
#<alt (/ (* n (PI)) k)>
#<alt (/ (PI) k)>
#<alt (/ (PI) k)>
#<alt (/ (PI) k)>
#<alt (/ (PI) k)>
#<alt (/ (PI) k)>
#<alt (/ (PI) k)>
#<alt (/ (PI) k)>
#<alt (/ (PI) k)>
#<alt (/ (PI) k)>
#<alt (/ (PI) k)>
#<alt (/ (PI) k)>
#<alt (/ (PI) k)>
#<alt (* (sqrt (/ (* n (PI)) k)) (/ 1 (sqrt 1/2)))>
#<alt (* (sqrt (/ (* n (PI)) k)) (/ 1 (sqrt 1/2)))>
#<alt (* (sqrt (/ (* n (PI)) k)) (/ 1 (sqrt 1/2)))>
#<alt (* (sqrt (/ (* n (PI)) k)) (/ 1 (sqrt 1/2)))>
#<alt (* (sqrt (/ (* n (PI)) k)) (/ 1 (sqrt 1/2)))>
#<alt (* (sqrt (/ (* n (PI)) k)) (/ 1 (sqrt 1/2)))>
#<alt (* (sqrt (/ (* n (PI)) k)) (/ 1 (sqrt 1/2)))>
#<alt (* (sqrt (/ (* n (PI)) k)) (/ 1 (sqrt 1/2)))>
#<alt (* -1 (* (sqrt (/ (* n (PI)) k)) (/ (pow (sqrt -1) 2) (sqrt 1/2))))>
#<alt (* -1 (* (sqrt (/ (* n (PI)) k)) (/ (pow (sqrt -1) 2) (sqrt 1/2))))>
#<alt (* -1 (* (sqrt (/ (* n (PI)) k)) (/ (pow (sqrt -1) 2) (sqrt 1/2))))>
#<alt (* -1 (* (sqrt (/ (* n (PI)) k)) (/ (pow (sqrt -1) 2) (sqrt 1/2))))>
#<alt (* (sqrt (/ (* n (PI)) k)) (/ 1 (sqrt 1/2)))>
#<alt (* (sqrt (/ (* n (PI)) k)) (/ 1 (sqrt 1/2)))>
#<alt (* (sqrt (/ (* n (PI)) k)) (/ 1 (sqrt 1/2)))>
#<alt (* (sqrt (/ (* n (PI)) k)) (/ 1 (sqrt 1/2)))>
#<alt (* (sqrt (/ (* n (PI)) k)) (/ 1 (sqrt 1/2)))>
#<alt (* (sqrt (/ (* n (PI)) k)) (/ 1 (sqrt 1/2)))>
#<alt (* (sqrt (/ (* n (PI)) k)) (/ 1 (sqrt 1/2)))>
#<alt (* (sqrt (/ (* n (PI)) k)) (/ 1 (sqrt 1/2)))>
#<alt (* (sqrt (/ (* n (PI)) k)) (/ (pow (sqrt -1) 2) (sqrt 1/2)))>
#<alt (* (sqrt (/ (* n (PI)) k)) (/ (pow (sqrt -1) 2) (sqrt 1/2)))>
#<alt (* (sqrt (/ (* n (PI)) k)) (/ (pow (sqrt -1) 2) (sqrt 1/2)))>
#<alt (* (sqrt (/ (* n (PI)) k)) (/ (pow (sqrt -1) 2) (sqrt 1/2)))>
#<alt (sqrt (/ (* n (PI)) k))>
#<alt (sqrt (/ (* n (PI)) k))>
#<alt (sqrt (/ (* n (PI)) k))>
#<alt (sqrt (/ (* n (PI)) k))>
#<alt (sqrt (/ (* n (PI)) k))>
#<alt (sqrt (/ (* n (PI)) k))>
#<alt (sqrt (/ (* n (PI)) k))>
#<alt (sqrt (/ (* n (PI)) k))>
#<alt (* -1 (* (sqrt (/ (* n (PI)) k)) (pow (sqrt -1) 2)))>
#<alt (* -1 (* (sqrt (/ (* n (PI)) k)) (pow (sqrt -1) 2)))>
#<alt (* -1 (* (sqrt (/ (* n (PI)) k)) (pow (sqrt -1) 2)))>
#<alt (* -1 (* (sqrt (/ (* n (PI)) k)) (pow (sqrt -1) 2)))>
#<alt (sqrt (/ (* n (PI)) k))>
#<alt (sqrt (/ (* n (PI)) k))>
#<alt (sqrt (/ (* n (PI)) k))>
#<alt (sqrt (/ (* n (PI)) k))>
#<alt (sqrt (/ (* n (PI)) k))>
#<alt (sqrt (/ (* n (PI)) k))>
#<alt (sqrt (/ (* n (PI)) k))>
#<alt (sqrt (/ (* n (PI)) k))>
#<alt (* (sqrt (/ (* n (PI)) k)) (pow (sqrt -1) 2))>
#<alt (* (sqrt (/ (* n (PI)) k)) (pow (sqrt -1) 2))>
#<alt (* (sqrt (/ (* n (PI)) k)) (pow (sqrt -1) 2))>
#<alt (* (sqrt (/ (* n (PI)) k)) (pow (sqrt -1) 2))>
#<alt (/ (* n (PI)) k)>
#<alt (/ (* n (PI)) k)>
#<alt (/ (* n (PI)) k)>
#<alt (/ (* n (PI)) k)>
#<alt (/ (* n (PI)) k)>
#<alt (/ (* n (PI)) k)>
#<alt (/ (* n (PI)) k)>
#<alt (/ (* n (PI)) k)>
#<alt (/ (* n (PI)) k)>
#<alt (/ (* n (PI)) k)>
#<alt (/ (* n (PI)) k)>
#<alt (/ (* n (PI)) k)>
#<alt (/ (* n (PI)) k)>
#<alt (/ (* n (PI)) k)>
#<alt (/ (* n (PI)) k)>
#<alt (/ (* n (PI)) k)>
#<alt (/ (* n (PI)) k)>
#<alt (/ (* n (PI)) k)>
#<alt (/ (* n (PI)) k)>
#<alt (/ (* n (PI)) k)>
#<alt (/ (* n (PI)) k)>
#<alt (/ (* n (PI)) k)>
#<alt (/ (* n (PI)) k)>
#<alt (/ (* n (PI)) k)>
#<alt (* n (PI))>
#<alt (* n (PI))>
#<alt (* n (PI))>
#<alt (* n (PI))>
#<alt (* n (PI))>
#<alt (* n (PI))>
#<alt (* n (PI))>
#<alt (* n (PI))>
#<alt (* n (PI))>
#<alt (* n (PI))>
#<alt (* n (PI))>
#<alt (* n (PI))>
#<alt (* (sqrt (/ (* n (PI)) (* k (exp (* k (+ (log n) (log (* 2 (PI))))))))) (sqrt 2))>
#<alt (* (sqrt (/ (* n (PI)) (* k (exp (* k (+ (log n) (log (* 2 (PI))))))))) (sqrt 2))>
#<alt (* (sqrt (/ (* n (PI)) (* k (exp (* k (+ (log n) (log (* 2 (PI))))))))) (sqrt 2))>
#<alt (* (sqrt (/ (* n (PI)) (* k (exp (* k (+ (log n) (log (* 2 (PI))))))))) (sqrt 2))>
#<alt (* (sqrt (/ (* n (PI)) (* k (exp (* k (+ (log (* 2 (PI))) (* -1 (log (/ 1 n))))))))) (sqrt 2))>
#<alt (* (sqrt (/ (* n (PI)) (* k (exp (* k (+ (log (* 2 (PI))) (* -1 (log (/ 1 n))))))))) (sqrt 2))>
#<alt (* (sqrt (/ (* n (PI)) (* k (exp (* k (+ (log (* 2 (PI))) (* -1 (log (/ 1 n))))))))) (sqrt 2))>
#<alt (* (sqrt (/ (* n (PI)) (* k (exp (* k (+ (log (* 2 (PI))) (* -1 (log (/ 1 n))))))))) (sqrt 2))>
#<alt (* -1 (* (sqrt (/ (* n (PI)) (* k (exp (* k (+ (log (* -2 (PI))) (* -1 (log (/ -1 n))))))))) (* (sqrt -2) (sqrt -1))))>
#<alt (* -1 (* (sqrt (/ (* n (PI)) (* k (exp (* k (+ (log (* -2 (PI))) (* -1 (log (/ -1 n))))))))) (* (sqrt -2) (sqrt -1))))>
#<alt (* -1 (* (sqrt (/ (* n (PI)) (* k (exp (* k (+ (log (* -2 (PI))) (* -1 (log (/ -1 n))))))))) (* (sqrt -2) (sqrt -1))))>
#<alt (* -1 (* (sqrt (/ (* n (PI)) (* k (exp (* k (+ (log (* -2 (PI))) (* -1 (log (/ -1 n))))))))) (* (sqrt -2) (sqrt -1))))>
#<alt (* (sqrt (/ (* n (PI)) k)) (sqrt 2))>
#<alt (/ (+ (* -1/2 (* (sqrt (* (pow k 3) (* n (PI)))) (* (log (* 2 (* n (PI)))) (sqrt 2)))) (* (sqrt (* k (* n (PI)))) (sqrt 2))) k)>
#<alt (/ (+ (* (sqrt (* k (* n (PI)))) (sqrt 2)) (* (pow k 2) (+ (* -1/2 (* (sqrt (/ k (* n (PI)))) (* (sqrt 2) (+ (* -1 (* n (* (PI) (pow (log (* 2 (* n (PI)))) 2)))) (* 1/2 (* n (* (PI) (pow (log (* 2 (* n (PI)))) 2)))))))) (* -1/2 (* (sqrt (/ (* n (PI)) k)) (* (log (* 2 (* n (PI)))) (sqrt 2))))))) k)>
#<alt (/ (+ (* (sqrt (* k (* n (PI)))) (sqrt 2)) (* (pow k 2) (+ (* -1/2 (* (sqrt (/ (* n (PI)) k)) (* (log (* 2 (* n (PI)))) (sqrt 2)))) (* k (+ (* -1/2 (* (sqrt (/ 1 (* k (* n (PI))))) (* (sqrt 2) (+ (* -1 (* n (* (PI) (pow (log (* 2 (* n (PI)))) 2)))) (* 1/2 (* n (* (PI) (pow (log (* 2 (* n (PI)))) 2)))))))) (* -1/2 (* (sqrt (/ k (* n (PI)))) (* (sqrt 2) (+ (* -1 (* (log (* 2 (* n (PI)))) (+ (* -1 (* n (* (PI) (pow (log (* 2 (* n (PI)))) 2)))) (* 1/2 (* n (* (PI) (pow (log (* 2 (* n (PI)))) 2))))))) (+ (* -1/2 (* n (* (PI) (pow (log (* 2 (* n (PI)))) 3)))) (+ (* 1/6 (* n (* (PI) (pow (log (* 2 (* n (PI)))) 3)))) (* 1/4 (/ (* n (* (PI) (pow (log (* 2 (* n (PI)))) 2))) k))))))))))))) k)>
#<alt (* (sqrt (/ (* n (PI)) (* k (pow (* 2 (* n (PI))) k)))) (sqrt 2))>
#<alt (* (sqrt (/ (* n (PI)) (* k (pow (* 2 (* n (PI))) k)))) (sqrt 2))>
#<alt (* (sqrt (/ (* n (PI)) (* k (pow (* 2 (* n (PI))) k)))) (sqrt 2))>
#<alt (* (sqrt (/ (* n (PI)) (* k (pow (* 2 (* n (PI))) k)))) (sqrt 2))>
#<alt (* (sqrt (/ (* n (PI)) (* k (pow (* 2 (* n (PI))) k)))) (* (sqrt -2) (sqrt -1)))>
#<alt (* (sqrt (/ (* n (PI)) (* k (pow (* 2 (* n (PI))) k)))) (* (sqrt -2) (sqrt -1)))>
#<alt (* (sqrt (/ (* n (PI)) (* k (pow (* 2 (* n (PI))) k)))) (* (sqrt -2) (sqrt -1)))>
#<alt (* (sqrt (/ (* n (PI)) (* k (pow (* 2 (* n (PI))) k)))) (* (sqrt -2) (sqrt -1)))>
#<alt (* 2 (/ (* n (PI)) (* k (exp (* k (+ (log n) (log (* 2 (PI)))))))))>
#<alt (* 2 (/ (* n (PI)) (* k (exp (* k (+ (log n) (log (* 2 (PI)))))))))>
#<alt (* 2 (/ (* n (PI)) (* k (exp (* k (+ (log n) (log (* 2 (PI)))))))))>
#<alt (* 2 (/ (* n (PI)) (* k (exp (* k (+ (log n) (log (* 2 (PI)))))))))>
#<alt (* 2 (/ (* n (PI)) (* k (exp (* k (+ (log (* 2 (PI))) (* -1 (log (/ 1 n)))))))))>
#<alt (* 2 (/ (* n (PI)) (* k (exp (* k (+ (log (* 2 (PI))) (* -1 (log (/ 1 n)))))))))>
#<alt (* 2 (/ (* n (PI)) (* k (exp (* k (+ (log (* 2 (PI))) (* -1 (log (/ 1 n)))))))))>
#<alt (* 2 (/ (* n (PI)) (* k (exp (* k (+ (log (* 2 (PI))) (* -1 (log (/ 1 n)))))))))>
#<alt (* 2 (/ (* n (PI)) (* k (exp (* k (+ (log (* -2 (PI))) (* -1 (log (/ -1 n)))))))))>
#<alt (* 2 (/ (* n (PI)) (* k (exp (* k (+ (log (* -2 (PI))) (* -1 (log (/ -1 n)))))))))>
#<alt (* 2 (/ (* n (PI)) (* k (exp (* k (+ (log (* -2 (PI))) (* -1 (log (/ -1 n)))))))))>
#<alt (* 2 (/ (* n (PI)) (* k (exp (* k (+ (log (* -2 (PI))) (* -1 (log (/ -1 n)))))))))>
#<alt (* 2 (/ (* n (PI)) k))>
#<alt (/ (+ (* -2 (* k (* n (* (PI) (log (* 2 (* n (PI)))))))) (* 2 (* n (PI)))) k)>
#<alt (/ (+ (* 2 (* n (PI))) (* k (+ (* -2 (* k (+ (* -1 (* n (* (PI) (pow (log (* 2 (* n (PI)))) 2)))) (* 1/2 (* n (* (PI) (pow (log (* 2 (* n (PI)))) 2))))))) (* -2 (* n (* (PI) (log (* 2 (* n (PI)))))))))) k)>
#<alt (/ (+ (* 2 (* n (PI))) (* k (+ (* -2 (* n (* (PI) (log (* 2 (* n (PI))))))) (* k (+ (* -2 (* k (+ (* -1 (* (log (* 2 (* n (PI)))) (+ (* -1 (* n (* (PI) (pow (log (* 2 (* n (PI)))) 2)))) (* 1/2 (* n (* (PI) (pow (log (* 2 (* n (PI)))) 2))))))) (+ (* -1/2 (* n (* (PI) (pow (log (* 2 (* n (PI)))) 3)))) (* 1/6 (* n (* (PI) (pow (log (* 2 (* n (PI)))) 3)))))))) (* -2 (+ (* -1 (* n (* (PI) (pow (log (* 2 (* n (PI)))) 2)))) (* 1/2 (* n (* (PI) (pow (log (* 2 (* n (PI)))) 2))))))))))) k)>
#<alt (* 2 (/ (* n (PI)) (* k (pow (* 2 (* n (PI))) k))))>
#<alt (* 2 (/ (* n (PI)) (* k (pow (* 2 (* n (PI))) k))))>
#<alt (* 2 (/ (* n (PI)) (* k (pow (* 2 (* n (PI))) k))))>
#<alt (* 2 (/ (* n (PI)) (* k (pow (* 2 (* n (PI))) k))))>
#<alt (* 2 (/ (* n (PI)) (* k (pow (* 2 (* n (PI))) k))))>
#<alt (* 2 (/ (* n (PI)) (* k (pow (* 2 (* n (PI))) k))))>
#<alt (* 2 (/ (* n (PI)) (* k (pow (* 2 (* n (PI))) k))))>
#<alt (* 2 (/ (* n (PI)) (* k (pow (* 2 (* n (PI))) k))))>
#<alt (exp (* k (+ (log n) (log (* 2 (PI))))))>
#<alt (exp (* k (+ (log n) (log (* 2 (PI))))))>
#<alt (exp (* k (+ (log n) (log (* 2 (PI))))))>
#<alt (exp (* k (+ (log n) (log (* 2 (PI))))))>
#<alt (exp (* k (+ (log (* 2 (PI))) (* -1 (log (/ 1 n))))))>
#<alt (exp (* k (+ (log (* 2 (PI))) (* -1 (log (/ 1 n))))))>
#<alt (exp (* k (+ (log (* 2 (PI))) (* -1 (log (/ 1 n))))))>
#<alt (exp (* k (+ (log (* 2 (PI))) (* -1 (log (/ 1 n))))))>
#<alt (exp (* k (+ (log (* -2 (PI))) (* -1 (log (/ -1 n))))))>
#<alt (exp (* k (+ (log (* -2 (PI))) (* -1 (log (/ -1 n))))))>
#<alt (exp (* k (+ (log (* -2 (PI))) (* -1 (log (/ -1 n))))))>
#<alt (exp (* k (+ (log (* -2 (PI))) (* -1 (log (/ -1 n))))))>
#<alt 1>
#<alt (+ 1 (* k (log (* 2 (* n (PI))))))>
#<alt (+ 1 (* k (+ (log (* 2 (* n (PI)))) (* 1/2 (* k (pow (log (* 2 (* n (PI)))) 2))))))>
#<alt (+ 1 (* k (+ (log (* 2 (* n (PI)))) (* k (+ (* 1/6 (* k (pow (log (* 2 (* n (PI)))) 3))) (* 1/2 (pow (log (* 2 (* n (PI)))) 2)))))))>
#<alt (pow (* 2 (* n (PI))) k)>
#<alt (pow (* 2 (* n (PI))) k)>
#<alt (pow (* 2 (* n (PI))) k)>
#<alt (pow (* 2 (* n (PI))) k)>
#<alt (pow (* 2 (* n (PI))) k)>
#<alt (pow (* 2 (* n (PI))) k)>
#<alt (pow (* 2 (* n (PI))) k)>
#<alt (pow (* 2 (* n (PI))) k)>

Calls

102 calls:

Time	Variable		Point	Expression
32.0ms	n	@	inf	(/ (* 2 (* (PI) n)) (pow (* 2 (* (PI) n)) k))
11.0ms	n	@	-inf	(/ (* 2 (* (PI) n)) (pow (* 2 (* (PI) n)) k))
4.0ms	n	@	-inf	(/ (* 2 (* (PI) n)) (* k (pow (* 2 (* (PI) n)) k)))
3.0ms	n	@	0	(sqrt (/ (* 2 (* (PI) n)) (pow (* 2 (* (PI) n)) k)))
1.0ms	k	@	0	(sqrt (/ (* 2 (* (PI) n)) (pow (* 2 (* (PI) n)) k)))

rewrite376.0ms (2.8%)

Algorithm

1×	batch-egg-rewrite

Rules

5716×	`-lowering-.f32`
5716×	`-lowering-.f64`
4126×	`/-lowering-/.f32`
4126×	`/-lowering-/.f64`
1076×	`associate-/r*`

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	28	154
1	159	154
2	1002	139
0	8191	139

Stop Event

1×	iter limit
1×	node limit

Counts

20 → 1744

Calls

Call 1

Inputs
(/ (sqrt (/ (* 2 (* (PI) n)) (pow (* 2 (* (PI) n)) k))) (sqrt k))
(sqrt (/ (* 2 (* (PI) n)) (pow (* 2 (* (PI) n)) k)))
(/ (* 2 (* (PI) n)) (pow (* 2 (* (PI) n)) k))
(* 2 (* (PI) n))
(sqrt (/ 2 (/ k (* (PI) n))))
(/ 2 (/ k (* (PI) n)))
(/ k (* (PI) n))
(* (PI) n)
(* (sqrt (* (/ (PI) k) n)) (sqrt 2))
(sqrt (* (/ (PI) k) n))
(* (/ (PI) k) n)
(/ (PI) k)
(/ (sqrt (/ (* n (PI)) k)) (sqrt 1/2))
(sqrt (/ (* n (PI)) k))
(/ (* n (PI)) k)
(* n (PI))
(sqrt (/ (* 2 (* (PI) n)) (* k (pow (* 2 (* (PI) n)) k))))
(/ (* 2 (* (PI) n)) (* k (pow (* 2 (* (PI) n)) k)))
(PI)
(pow (* 2 (* (PI) n)) k)

Outputs
(exp.f64 (.f64 (log.f64 (/.f64 (pow.f64 (.f64 #s(literal 2 binary64) (*.f64 (PI.f64) n)) (+.f64 (-.f64 #s(literal 0 binary64) k) #s(literal 1 binary64))) k)) #s(literal 1/2 binary64)))
(exp.f64 (.f64 (log.f64 (/.f64 (sqrt.f64 k) (pow.f64 (.f64 #s(literal 2 binary64) (*.f64 (PI.f64) n)) (-.f64 #s(literal 1/2 binary64) (/.f64 k #s(literal 2 binary64)))))) #s(literal -1 binary64)))
(exp.f64 (-.f64 (.f64 (log.f64 (pow.f64 (.f64 #s(literal 2 binary64) (.f64 (PI.f64) n)) (+.f64 (-.f64 #s(literal 0 binary64) k) #s(literal 1 binary64)))) #s(literal 1/2 binary64)) (.f64 (log.f64 k) #s(literal 1/2 binary64))))
(exp.f64 (-.f64 (.f64 (log.f64 (/.f64 #s(literal 2 binary64) (/.f64 k (.f64 (PI.f64) n)))) #s(literal 1/2 binary64)) (/.f64 (log.f64 (.f64 #s(literal 2 binary64) (.f64 (PI.f64) n))) (/.f64 #s(literal 2 binary64) k))))
(-.f64 #s(literal 0 binary64) (neg.f64 (/.f64 (pow.f64 k #s(literal -1/2 binary64)) (pow.f64 (.f64 #s(literal 2 binary64) (.f64 (PI.f64) n)) (-.f64 (/.f64 k #s(literal 2 binary64)) #s(literal 1/2 binary64))))))
(-.f64 (/.f64 #s(literal 0 binary64) (-.f64 #s(literal 0 binary64) (sqrt.f64 k))) (neg.f64 (/.f64 (pow.f64 k #s(literal -1/2 binary64)) (pow.f64 (.f64 #s(literal 2 binary64) (.f64 (PI.f64) n)) (-.f64 (/.f64 k #s(literal 2 binary64)) #s(literal 1/2 binary64))))))
(sqrt.f64 (/.f64 (pow.f64 (.f64 #s(literal 2 binary64) (.f64 (PI.f64) n)) (+.f64 (-.f64 #s(literal 0 binary64) k) #s(literal 1 binary64))) k))
(neg.f64 (neg.f64 (/.f64 (pow.f64 k #s(literal -1/2 binary64)) (pow.f64 (.f64 #s(literal 2 binary64) (.f64 (PI.f64) n)) (-.f64 (/.f64 k #s(literal 2 binary64)) #s(literal 1/2 binary64))))))
(neg.f64 (.f64 #s(literal 1 binary64) (neg.f64 (/.f64 (pow.f64 k #s(literal -1/2 binary64)) (pow.f64 (.f64 #s(literal 2 binary64) (*.f64 (PI.f64) n)) (-.f64 (/.f64 k #s(literal 2 binary64)) #s(literal 1/2 binary64)))))))
(neg.f64 (/.f64 (neg.f64 (sqrt.f64 (/.f64 #s(literal 2 binary64) (/.f64 k (.f64 (PI.f64) n))))) (pow.f64 (.f64 #s(literal 2 binary64) (*.f64 (PI.f64) n)) (/.f64 k #s(literal 2 binary64)))))
(neg.f64 (/.f64 (sqrt.f64 (.f64 #s(literal 2 binary64) (.f64 (PI.f64) n))) (-.f64 #s(literal 0 binary64) (sqrt.f64 (.f64 k (pow.f64 (.f64 #s(literal 2 binary64) (*.f64 (PI.f64) n)) k))))))
(neg.f64 (/.f64 #s(literal -1 binary64) (/.f64 (sqrt.f64 k) (pow.f64 (.f64 #s(literal 2 binary64) (.f64 (PI.f64) n)) (-.f64 #s(literal 1/2 binary64) (/.f64 k #s(literal 2 binary64)))))))
(neg.f64 (/.f64 (-.f64 #s(literal 0 binary64) (sqrt.f64 (.f64 #s(literal 2 binary64) (.f64 (PI.f64) n)))) (sqrt.f64 (.f64 k (pow.f64 (.f64 #s(literal 2 binary64) (*.f64 (PI.f64) n)) k)))))
(/.f64 (pow.f64 (.f64 #s(literal 2 binary64) (.f64 (PI.f64) n)) (-.f64 #s(literal 1/2 binary64) (/.f64 k #s(literal 2 binary64)))) (sqrt.f64 k))
(/.f64 (sqrt.f64 (/.f64 #s(literal 2 binary64) (/.f64 k (.f64 (PI.f64) n)))) (pow.f64 (.f64 #s(literal 2 binary64) (*.f64 (PI.f64) n)) (/.f64 k #s(literal 2 binary64))))
(/.f64 #s(literal 1 binary64) (/.f64 (sqrt.f64 k) (pow.f64 (.f64 #s(literal 2 binary64) (.f64 (PI.f64) n)) (-.f64 #s(literal 1/2 binary64) (/.f64 k #s(literal 2 binary64))))))
(/.f64 #s(literal 1 binary64) (.f64 (pow.f64 (.f64 #s(literal 2 binary64) (*.f64 (PI.f64) n)) (-.f64 (/.f64 k #s(literal 2 binary64)) #s(literal 1/2 binary64))) (sqrt.f64 k)))
(/.f64 #s(literal 1 binary64) (/.f64 (pow.f64 (.f64 #s(literal 2 binary64) (.f64 (PI.f64) n)) (/.f64 k #s(literal 2 binary64))) (sqrt.f64 (/.f64 #s(literal 2 binary64) (/.f64 k (*.f64 (PI.f64) n))))))
(/.f64 (sqrt.f64 (.f64 #s(literal 2 binary64) (.f64 (PI.f64) n))) (sqrt.f64 (.f64 k (pow.f64 (.f64 #s(literal 2 binary64) (*.f64 (PI.f64) n)) k))))
(/.f64 (sqrt.f64 (.f64 #s(literal 2 binary64) (.f64 (PI.f64) n))) (.f64 (-.f64 #s(literal 0 binary64) (pow.f64 (.f64 #s(literal 2 binary64) (*.f64 (PI.f64) n)) (/.f64 k #s(literal 2 binary64)))) (-.f64 #s(literal 0 binary64) (sqrt.f64 k))))
(/.f64 (-.f64 #s(literal 0 binary64) (pow.f64 (.f64 #s(literal 2 binary64) (.f64 (PI.f64) n)) (-.f64 #s(literal 1/2 binary64) (/.f64 k #s(literal 2 binary64))))) (-.f64 #s(literal 0 binary64) (sqrt.f64 k)))
(/.f64 (pow.f64 k #s(literal -1/2 binary64)) (pow.f64 (.f64 #s(literal 2 binary64) (.f64 (PI.f64) n)) (-.f64 (/.f64 k #s(literal 2 binary64)) #s(literal 1/2 binary64))))
(/.f64 #s(literal -1 binary64) (-.f64 #s(literal 0 binary64) (/.f64 (sqrt.f64 k) (pow.f64 (.f64 #s(literal 2 binary64) (.f64 (PI.f64) n)) (-.f64 #s(literal 1/2 binary64) (/.f64 k #s(literal 2 binary64)))))))
(/.f64 #s(literal -1 binary64) (.f64 (pow.f64 (.f64 #s(literal 2 binary64) (*.f64 (PI.f64) n)) (-.f64 (/.f64 k #s(literal 2 binary64)) #s(literal 1/2 binary64))) (-.f64 #s(literal 0 binary64) (sqrt.f64 k))))
(/.f64 (sqrt.f64 (.f64 (.f64 (PI.f64) n) #s(literal -2 binary64))) (sqrt.f64 (.f64 (pow.f64 (.f64 #s(literal 2 binary64) (*.f64 (PI.f64) n)) k) (-.f64 #s(literal 0 binary64) k))))
(/.f64 (-.f64 #s(literal 0 binary64) (sqrt.f64 (.f64 #s(literal 2 binary64) (.f64 (PI.f64) n)))) (-.f64 #s(literal 0 binary64) (sqrt.f64 (.f64 k (pow.f64 (.f64 #s(literal 2 binary64) (*.f64 (PI.f64) n)) k)))))
(/.f64 (neg.f64 (sqrt.f64 (/.f64 #s(literal 2 binary64) (/.f64 k (.f64 (PI.f64) n))))) (-.f64 #s(literal 0 binary64) (pow.f64 (.f64 #s(literal 2 binary64) (*.f64 (PI.f64) n)) (/.f64 k #s(literal 2 binary64)))))
(/.f64 (sqrt.f64 #s(literal -1 binary64)) (sqrt.f64 (-.f64 #s(literal 0 binary64) (/.f64 k (pow.f64 (.f64 #s(literal 2 binary64) (.f64 (PI.f64) n)) (+.f64 (-.f64 #s(literal 0 binary64) k) #s(literal 1 binary64)))))))
(/.f64 (sqrt.f64 (-.f64 #s(literal 0 binary64) (pow.f64 (.f64 #s(literal 2 binary64) (.f64 (PI.f64) n)) (+.f64 (-.f64 #s(literal 0 binary64) k) #s(literal 1 binary64))))) (sqrt.f64 (-.f64 #s(literal 0 binary64) k)))
(/.f64 (sqrt.f64 (/.f64 (/.f64 (.f64 (PI.f64) n) k) #s(literal -1/2 binary64))) (sqrt.f64 (-.f64 #s(literal 0 binary64) (pow.f64 (.f64 #s(literal 2 binary64) (*.f64 (PI.f64) n)) k))))
(/.f64 (sqrt.f64 (/.f64 (/.f64 #s(literal 2 binary64) (/.f64 k (.f64 (PI.f64) n))) (pow.f64 #s(literal 2 binary64) k))) (pow.f64 (.f64 (PI.f64) n) (/.f64 k #s(literal 2 binary64))))
(/.f64 (sqrt.f64 (/.f64 (/.f64 #s(literal 2 binary64) (/.f64 k (.f64 (PI.f64) n))) (pow.f64 (.f64 #s(literal 2 binary64) (.f64 (PI.f64) n)) (/.f64 k #s(literal 2 binary64))))) (pow.f64 (.f64 #s(literal 2 binary64) (*.f64 (PI.f64) n)) (/.f64 (/.f64 k #s(literal 2 binary64)) #s(literal 2 binary64))))
(/.f64 (.f64 (sqrt.f64 (.f64 #s(literal 2 binary64) (.f64 (PI.f64) n))) #s(literal -1 binary64)) (-.f64 #s(literal 0 binary64) (sqrt.f64 (.f64 k (pow.f64 (.f64 #s(literal 2 binary64) (.f64 (PI.f64) n)) k)))))
(/.f64 (.f64 (sqrt.f64 (.f64 (.f64 (PI.f64) n) #s(literal -2 binary64))) #s(literal 1 binary64)) (sqrt.f64 (.f64 (pow.f64 (.f64 #s(literal 2 binary64) (.f64 (PI.f64) n)) k) (-.f64 #s(literal 0 binary64) k))))
(/.f64 (.f64 (sqrt.f64 (.f64 (.f64 (PI.f64) n) #s(literal -2 binary64))) #s(literal -1 binary64)) (.f64 (sqrt.f64 (-.f64 #s(literal 0 binary64) (pow.f64 (.f64 #s(literal 2 binary64) (.f64 (PI.f64) n)) k))) (-.f64 #s(literal 0 binary64) (sqrt.f64 k))))
(/.f64 (.f64 (-.f64 #s(literal 0 binary64) (sqrt.f64 (.f64 #s(literal 2 binary64) (.f64 (PI.f64) n)))) #s(literal 1 binary64)) (-.f64 #s(literal 0 binary64) (sqrt.f64 (.f64 k (pow.f64 (.f64 #s(literal 2 binary64) (.f64 (PI.f64) n)) k)))))
(/.f64 (.f64 (-.f64 #s(literal 0 binary64) (sqrt.f64 (.f64 #s(literal 2 binary64) (.f64 (PI.f64) n)))) #s(literal -1 binary64)) (.f64 (-.f64 #s(literal 0 binary64) (pow.f64 (.f64 #s(literal 2 binary64) (.f64 (PI.f64) n)) (/.f64 k #s(literal 2 binary64)))) (-.f64 #s(literal 0 binary64) (sqrt.f64 k))))
(/.f64 (.f64 #s(literal 1 binary64) (sqrt.f64 (.f64 #s(literal 2 binary64) (.f64 (PI.f64) n)))) (sqrt.f64 (.f64 k (pow.f64 (.f64 #s(literal 2 binary64) (.f64 (PI.f64) n)) k))))
(/.f64 (.f64 #s(literal 1 binary64) (sqrt.f64 (.f64 (.f64 (PI.f64) n) #s(literal -2 binary64)))) (sqrt.f64 (.f64 (pow.f64 (.f64 #s(literal 2 binary64) (.f64 (PI.f64) n)) k) (-.f64 #s(literal 0 binary64) k))))
(/.f64 (.f64 #s(literal 1 binary64) (-.f64 #s(literal 0 binary64) (sqrt.f64 (.f64 #s(literal 2 binary64) (.f64 (PI.f64) n))))) (-.f64 #s(literal 0 binary64) (sqrt.f64 (.f64 k (pow.f64 (.f64 #s(literal 2 binary64) (.f64 (PI.f64) n)) k)))))
(/.f64 (.f64 #s(literal -1 binary64) (sqrt.f64 (.f64 (.f64 (PI.f64) n) #s(literal -2 binary64)))) (.f64 (-.f64 #s(literal 0 binary64) (sqrt.f64 k)) (sqrt.f64 (-.f64 #s(literal 0 binary64) (pow.f64 (.f64 #s(literal 2 binary64) (.f64 (PI.f64) n)) k)))))
(/.f64 (.f64 #s(literal -1 binary64) (-.f64 #s(literal 0 binary64) (sqrt.f64 (.f64 #s(literal 2 binary64) (.f64 (PI.f64) n))))) (.f64 (-.f64 #s(literal 0 binary64) (sqrt.f64 k)) (-.f64 #s(literal 0 binary64) (pow.f64 (.f64 #s(literal 2 binary64) (.f64 (PI.f64) n)) (/.f64 k #s(literal 2 binary64))))))
(/.f64 (neg.f64 (-.f64 #s(literal 0 binary64) (sqrt.f64 (.f64 #s(literal 2 binary64) (.f64 (PI.f64) n))))) (neg.f64 (-.f64 #s(literal 0 binary64) (sqrt.f64 (.f64 k (pow.f64 (.f64 #s(literal 2 binary64) (*.f64 (PI.f64) n)) k))))))
(/.f64 (neg.f64 (sqrt.f64 (.f64 (.f64 (PI.f64) n) #s(literal -2 binary64)))) (neg.f64 (sqrt.f64 (.f64 (pow.f64 (.f64 #s(literal 2 binary64) (*.f64 (PI.f64) n)) k) (-.f64 #s(literal 0 binary64) k)))))
(/.f64 (.f64 #s(literal 1 binary64) (-.f64 #s(literal 0 binary64) (pow.f64 (.f64 #s(literal 2 binary64) (*.f64 (PI.f64) n)) (-.f64 #s(literal 1/2 binary64) (/.f64 k #s(literal 2 binary64)))))) (-.f64 #s(literal 0 binary64) (sqrt.f64 k)))
(/.f64 (.f64 (pow.f64 k #s(literal -1/2 binary64)) (sqrt.f64 (.f64 #s(literal 2 binary64) (.f64 (PI.f64) n)))) (pow.f64 (.f64 #s(literal 2 binary64) (*.f64 (PI.f64) n)) (/.f64 k #s(literal 2 binary64))))
(/.f64 (.f64 (pow.f64 k #s(literal -1/2 binary64)) #s(literal 1 binary64)) (pow.f64 (.f64 #s(literal 2 binary64) (*.f64 (PI.f64) n)) (-.f64 (/.f64 k #s(literal 2 binary64)) #s(literal 1/2 binary64))))
(/.f64 (.f64 (pow.f64 (.f64 #s(literal 2 binary64) (*.f64 (PI.f64) n)) (-.f64 #s(literal 1/2 binary64) (/.f64 k #s(literal 2 binary64)))) #s(literal -1 binary64)) (-.f64 #s(literal 0 binary64) (sqrt.f64 k)))
(/.f64 (.f64 (-.f64 #s(literal 0 binary64) (pow.f64 (.f64 #s(literal 2 binary64) (*.f64 (PI.f64) n)) (-.f64 #s(literal 1/2 binary64) (/.f64 k #s(literal 2 binary64))))) #s(literal 1 binary64)) (-.f64 #s(literal 0 binary64) (sqrt.f64 k)))
(/.f64 (.f64 (pow.f64 k #s(literal -1/2 binary64)) (sqrt.f64 (.f64 (.f64 (PI.f64) n) #s(literal -2 binary64)))) (sqrt.f64 (-.f64 #s(literal 0 binary64) (pow.f64 (.f64 #s(literal 2 binary64) (*.f64 (PI.f64) n)) k))))
(/.f64 (.f64 (pow.f64 k #s(literal -1/2 binary64)) (-.f64 #s(literal 0 binary64) (sqrt.f64 (.f64 #s(literal 2 binary64) (.f64 (PI.f64) n))))) (-.f64 #s(literal 0 binary64) (pow.f64 (.f64 #s(literal 2 binary64) (*.f64 (PI.f64) n)) (/.f64 k #s(literal 2 binary64)))))
(/.f64 (.f64 (sqrt.f64 (.f64 (.f64 (PI.f64) n) #s(literal -2 binary64))) (pow.f64 k #s(literal -1/2 binary64))) (sqrt.f64 (-.f64 #s(literal 0 binary64) (pow.f64 (.f64 #s(literal 2 binary64) (*.f64 (PI.f64) n)) k))))
(/.f64 (.f64 (-.f64 #s(literal 0 binary64) (sqrt.f64 (.f64 #s(literal 2 binary64) (.f64 (PI.f64) n)))) (pow.f64 k #s(literal -1/2 binary64))) (-.f64 #s(literal 0 binary64) (pow.f64 (.f64 #s(literal 2 binary64) (*.f64 (PI.f64) n)) (/.f64 k #s(literal 2 binary64)))))
(/.f64 (.f64 (sqrt.f64 (.f64 #s(literal 2 binary64) (.f64 (PI.f64) n))) (/.f64 #s(literal -1 binary64) (sqrt.f64 k))) (-.f64 #s(literal 0 binary64) (pow.f64 (.f64 #s(literal 2 binary64) (*.f64 (PI.f64) n)) (/.f64 k #s(literal 2 binary64)))))
(/.f64 (.f64 (-.f64 #s(literal 0 binary64) (sqrt.f64 (.f64 #s(literal 2 binary64) (.f64 (PI.f64) n)))) (/.f64 #s(literal -1 binary64) (sqrt.f64 k))) (pow.f64 (.f64 #s(literal 2 binary64) (*.f64 (PI.f64) n)) (/.f64 k #s(literal 2 binary64))))
(/.f64 (/.f64 (pow.f64 (.f64 #s(literal 2 binary64) (.f64 (PI.f64) n)) (-.f64 #s(literal 1/2 binary64) (/.f64 k #s(literal 2 binary64)))) (pow.f64 k #s(literal 1/4 binary64))) (pow.f64 k #s(literal 1/4 binary64)))
(/.f64 (/.f64 (sqrt.f64 (/.f64 #s(literal 2 binary64) (/.f64 k (.f64 (PI.f64) n)))) (pow.f64 #s(literal 2 binary64) (/.f64 k #s(literal 2 binary64)))) (pow.f64 (.f64 (PI.f64) n) (/.f64 k #s(literal 2 binary64))))
(/.f64 (/.f64 (sqrt.f64 (/.f64 #s(literal 2 binary64) (/.f64 k (.f64 (PI.f64) n)))) (pow.f64 (.f64 (PI.f64) n) (/.f64 k #s(literal 2 binary64)))) (pow.f64 #s(literal 2 binary64) (/.f64 k #s(literal 2 binary64))))
(/.f64 (/.f64 (sqrt.f64 (/.f64 #s(literal 2 binary64) (/.f64 k (.f64 (PI.f64) n)))) (pow.f64 (.f64 #s(literal 2 binary64) (PI.f64)) (/.f64 k #s(literal 2 binary64)))) (pow.f64 n (/.f64 k #s(literal 2 binary64))))
(/.f64 (/.f64 (sqrt.f64 (/.f64 #s(literal 2 binary64) (/.f64 k (.f64 (PI.f64) n)))) (pow.f64 (.f64 #s(literal 2 binary64) (.f64 (PI.f64) n)) (/.f64 (/.f64 k #s(literal 2 binary64)) #s(literal 2 binary64)))) (pow.f64 (.f64 #s(literal 2 binary64) (*.f64 (PI.f64) n)) (/.f64 (/.f64 k #s(literal 2 binary64)) #s(literal 2 binary64))))
(/.f64 (/.f64 (-.f64 #s(literal 0 binary64) (pow.f64 (.f64 #s(literal 2 binary64) (.f64 (PI.f64) n)) (-.f64 #s(literal 1/2 binary64) (/.f64 k #s(literal 2 binary64))))) #s(literal -1 binary64)) (sqrt.f64 k))
(pow.f64 (/.f64 (pow.f64 (.f64 #s(literal 2 binary64) (.f64 (PI.f64) n)) (+.f64 (-.f64 #s(literal 0 binary64) k) #s(literal 1 binary64))) k) #s(literal 1/2 binary64))
(pow.f64 (/.f64 k (pow.f64 (.f64 #s(literal 2 binary64) (.f64 (PI.f64) n)) (+.f64 (-.f64 #s(literal 0 binary64) k) #s(literal 1 binary64)))) #s(literal -1/2 binary64))
(pow.f64 (/.f64 (sqrt.f64 k) (pow.f64 (.f64 #s(literal 2 binary64) (.f64 (PI.f64) n)) (-.f64 #s(literal 1/2 binary64) (/.f64 k #s(literal 2 binary64))))) #s(literal -1 binary64))
(pow.f64 (pow.f64 (/.f64 (pow.f64 (.f64 #s(literal 2 binary64) (.f64 (PI.f64) n)) (+.f64 (-.f64 #s(literal 0 binary64) k) #s(literal 1 binary64))) k) #s(literal 1/4 binary64)) #s(literal 2 binary64))
(pow.f64 (.f64 (/.f64 (pow.f64 (.f64 #s(literal 2 binary64) (.f64 (PI.f64) n)) (+.f64 (-.f64 #s(literal 0 binary64) k) #s(literal 1 binary64))) k) (/.f64 (pow.f64 (.f64 #s(literal 2 binary64) (*.f64 (PI.f64) n)) (+.f64 (-.f64 #s(literal 0 binary64) k) #s(literal 1 binary64))) k)) #s(literal 1/4 binary64))
(pow.f64 (exp.f64 (log.f64 (/.f64 (pow.f64 (.f64 #s(literal 2 binary64) (.f64 (PI.f64) n)) (+.f64 (-.f64 #s(literal 0 binary64) k) #s(literal 1 binary64))) k))) #s(literal 1/2 binary64))
(.f64 (pow.f64 (.f64 #s(literal 2 binary64) (*.f64 (PI.f64) n)) (-.f64 #s(literal 1/2 binary64) (/.f64 k #s(literal 2 binary64)))) (pow.f64 k #s(literal -1/2 binary64)))
(.f64 (sqrt.f64 #s(literal 2 binary64)) (sqrt.f64 (/.f64 (.f64 n (pow.f64 (/.f64 #s(literal 1/2 binary64) (*.f64 (PI.f64) n)) k)) (/.f64 k (PI.f64)))))
(.f64 (sqrt.f64 #s(literal 2 binary64)) (.f64 (sqrt.f64 (.f64 (PI.f64) (.f64 n (pow.f64 (/.f64 #s(literal 1/2 binary64) (*.f64 (PI.f64) n)) k)))) (pow.f64 k #s(literal -1/2 binary64))))
(.f64 (pow.f64 (/.f64 k (.f64 (PI.f64) n)) #s(literal -1/2 binary64)) (pow.f64 (.f64 #s(literal 2 binary64) (pow.f64 (/.f64 #s(literal 1/2 binary64) (.f64 (PI.f64) n)) k)) #s(literal 1/2 binary64)))
(.f64 (pow.f64 (/.f64 k (.f64 (PI.f64) n)) #s(literal -1/2 binary64)) (sqrt.f64 (.f64 #s(literal 2 binary64) (pow.f64 (/.f64 #s(literal 1/2 binary64) (.f64 (PI.f64) n)) k))))
(.f64 (sqrt.f64 (/.f64 #s(literal 2 binary64) (/.f64 k (.f64 (PI.f64) n)))) (/.f64 #s(literal 1 binary64) (pow.f64 (.f64 #s(literal 2 binary64) (.f64 (PI.f64) n)) (/.f64 k #s(literal 2 binary64)))))
(.f64 #s(literal 1 binary64) (/.f64 (pow.f64 k #s(literal -1/2 binary64)) (pow.f64 (.f64 #s(literal 2 binary64) (*.f64 (PI.f64) n)) (-.f64 (/.f64 k #s(literal 2 binary64)) #s(literal 1/2 binary64)))))
(.f64 (sqrt.f64 (.f64 #s(literal 2 binary64) (.f64 (PI.f64) n))) (sqrt.f64 (/.f64 (pow.f64 (/.f64 #s(literal 1/2 binary64) (.f64 (PI.f64) n)) k) k)))
(.f64 (sqrt.f64 (.f64 #s(literal 2 binary64) (.f64 (PI.f64) n))) (.f64 (/.f64 #s(literal 1 binary64) (pow.f64 (.f64 #s(literal 2 binary64) (.f64 (PI.f64) n)) (/.f64 k #s(literal 2 binary64)))) (pow.f64 k #s(literal -1/2 binary64))))
(.f64 (-.f64 #s(literal 0 binary64) (pow.f64 (.f64 #s(literal 2 binary64) (*.f64 (PI.f64) n)) (-.f64 #s(literal 1/2 binary64) (/.f64 k #s(literal 2 binary64))))) (/.f64 #s(literal -1 binary64) (sqrt.f64 k)))
(.f64 (pow.f64 k #s(literal -1/2 binary64)) (pow.f64 (.f64 #s(literal 2 binary64) (*.f64 (PI.f64) n)) (-.f64 #s(literal 1/2 binary64) (/.f64 k #s(literal 2 binary64)))))
(.f64 #s(literal -1 binary64) (neg.f64 (/.f64 (pow.f64 k #s(literal -1/2 binary64)) (pow.f64 (.f64 #s(literal 2 binary64) (*.f64 (PI.f64) n)) (-.f64 (/.f64 k #s(literal 2 binary64)) #s(literal 1/2 binary64))))))
(.f64 (sqrt.f64 (/.f64 #s(literal 2 binary64) k)) (sqrt.f64 (.f64 (PI.f64) (.f64 n (pow.f64 (/.f64 #s(literal 1/2 binary64) (.f64 (PI.f64) n)) k)))))
(.f64 (pow.f64 (.f64 (PI.f64) n) #s(literal 1/2 binary64)) (pow.f64 (.f64 #s(literal 2 binary64) (/.f64 (pow.f64 (/.f64 #s(literal 1/2 binary64) (.f64 (PI.f64) n)) k) k)) #s(literal 1/2 binary64)))
(.f64 (pow.f64 (.f64 (PI.f64) n) #s(literal 1/2 binary64)) (sqrt.f64 (.f64 #s(literal 2 binary64) (/.f64 (pow.f64 (/.f64 #s(literal 1/2 binary64) (.f64 (PI.f64) n)) k) k))))
(.f64 (pow.f64 (.f64 (PI.f64) n) #s(literal 1/2 binary64)) (.f64 (sqrt.f64 #s(literal 2 binary64)) (sqrt.f64 (/.f64 (pow.f64 (/.f64 #s(literal 1/2 binary64) (.f64 (PI.f64) n)) k) k))))
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(.f64 (pow.f64 (pow.f64 (.f64 #s(literal 2 binary64) (PI.f64)) (/.f64 k #s(literal 2 binary64))) #s(literal 2 binary64)) (pow.f64 (pow.f64 n (/.f64 k #s(literal 2 binary64))) #s(literal 2 binary64)))
(.f64 (neg.f64 (-.f64 #s(literal 0 binary64) (pow.f64 (.f64 #s(literal 2 binary64) (.f64 (PI.f64) n)) (/.f64 k #s(literal 2 binary64))))) (pow.f64 (.f64 #s(literal 2 binary64) (*.f64 (PI.f64) n)) (/.f64 k #s(literal 2 binary64))))
(.f64 (neg.f64 (-.f64 #s(literal 0 binary64) (pow.f64 #s(literal 2 binary64) k))) (pow.f64 (.f64 (PI.f64) n) k))
(.f64 (.f64 (pow.f64 #s(literal 2 binary64) k) (pow.f64 n k)) (pow.f64 (PI.f64) k))
(.f64 (.f64 (pow.f64 #s(literal 2 binary64) k) (pow.f64 (.f64 (PI.f64) n) (/.f64 k #s(literal 2 binary64)))) (pow.f64 (.f64 (PI.f64) n) (/.f64 k #s(literal 2 binary64))))
(.f64 (.f64 (pow.f64 (*.f64 (PI.f64) n) k) (pow.f64 #s(literal 2 binary64) (/.f64 k #s(literal 2 binary64)))) (pow.f64 #s(literal 2 binary64) (/.f64 k #s(literal 2 binary64))))
(.f64 (.f64 (pow.f64 (.f64 #s(literal 2 binary64) (.f64 (PI.f64) n)) (/.f64 k #s(literal 2 binary64))) (pow.f64 #s(literal 2 binary64) (/.f64 k #s(literal 2 binary64)))) (pow.f64 (*.f64 (PI.f64) n) (/.f64 k #s(literal 2 binary64))))
(.f64 (.f64 (pow.f64 (.f64 #s(literal 2 binary64) (.f64 (PI.f64) n)) (/.f64 k #s(literal 2 binary64))) (pow.f64 (*.f64 (PI.f64) n) (/.f64 k #s(literal 2 binary64)))) (pow.f64 #s(literal 2 binary64) (/.f64 k #s(literal 2 binary64))))
(.f64 (.f64 (pow.f64 (.f64 #s(literal 2 binary64) (.f64 (PI.f64) n)) (/.f64 k #s(literal 2 binary64))) (pow.f64 (*.f64 #s(literal 2 binary64) (PI.f64)) (/.f64 k #s(literal 2 binary64)))) (pow.f64 n (/.f64 k #s(literal 2 binary64))))
(.f64 (.f64 (pow.f64 (.f64 #s(literal 2 binary64) (.f64 (PI.f64) n)) (/.f64 k #s(literal 2 binary64))) (pow.f64 (.f64 #s(literal 2 binary64) (.f64 (PI.f64) n)) (/.f64 (/.f64 k #s(literal 2 binary64)) #s(literal 2 binary64)))) (pow.f64 (.f64 #s(literal 2 binary64) (.f64 (PI.f64) n)) (/.f64 (/.f64 k #s(literal 2 binary64)) #s(literal 2 binary64))))

simplify354.0ms (2.6%)

Algorithm

1×	egg-herbie

Rules

6574×	`-lowering-.f32`
6574×	`-lowering-.f64`
3710×	`+-lowering-+.f64`
3710×	`+-lowering-+.f32`
1540×	`distribute-rgt-in`

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	227	4819
1	739	4624
2	3009	4531
0	8947	4531

Stop Event

1×	iter limit
1×	node limit

Counts

408 → 408

Calls

Call 1

Inputs
(* (sqrt (/ (* n (PI)) (* k (exp (* k (+ (log n) (log (* 2 (PI))))))))) (sqrt 2))
(* (sqrt (/ (* n (PI)) (* k (exp (* k (+ (log n) (log (* 2 (PI))))))))) (sqrt 2))
(* (sqrt (/ (* n (PI)) (* k (exp (* k (+ (log n) (log (* 2 (PI))))))))) (sqrt 2))
(* (sqrt (/ (* n (PI)) (* k (exp (* k (+ (log n) (log (* 2 (PI))))))))) (sqrt 2))
(* (sqrt (/ (* n (PI)) (* k (exp (* k (+ (log (* 2 (PI))) (* -1 (log (/ 1 n))))))))) (sqrt 2))
(* (sqrt (/ (* n (PI)) (* k (exp (* k (+ (log (* 2 (PI))) (* -1 (log (/ 1 n))))))))) (sqrt 2))
(* (sqrt (/ (* n (PI)) (* k (exp (* k (+ (log (* 2 (PI))) (* -1 (log (/ 1 n))))))))) (sqrt 2))
(* (sqrt (/ (* n (PI)) (* k (exp (* k (+ (log (* 2 (PI))) (* -1 (log (/ 1 n))))))))) (sqrt 2))
(* -1 (* (sqrt (/ (* n (PI)) (* k (exp (* k (+ (log (* -2 (PI))) (* -1 (log (/ -1 n))))))))) (* (sqrt -2) (sqrt -1))))
(* -1 (* (sqrt (/ (* n (PI)) (* k (exp (* k (+ (log (* -2 (PI))) (* -1 (log (/ -1 n))))))))) (* (sqrt -2) (sqrt -1))))
(* -1 (* (sqrt (/ (* n (PI)) (* k (exp (* k (+ (log (* -2 (PI))) (* -1 (log (/ -1 n))))))))) (* (sqrt -2) (sqrt -1))))
(* -1 (* (sqrt (/ (* n (PI)) (* k (exp (* k (+ (log (* -2 (PI))) (* -1 (log (/ -1 n))))))))) (* (sqrt -2) (sqrt -1))))
(* (sqrt (/ (* n (PI)) k)) (sqrt 2))
(/ (+ (* -1/2 (* (sqrt (* (pow k 3) (* n (PI)))) (* (log (* 2 (* n (PI)))) (sqrt 2)))) (* (sqrt (* k (* n (PI)))) (sqrt 2))) k)
(/ (+ (* (sqrt (* k (* n (PI)))) (sqrt 2)) (* (pow k 2) (+ (* -1/2 (* (sqrt (/ k (* n (PI)))) (* (sqrt 2) (+ (* -1 (* n (* (PI) (pow (log (* 2 (* n (PI)))) 2)))) (* 1/2 (* n (* (PI) (pow (log (* 2 (* n (PI)))) 2)))))))) (* -1/2 (* (sqrt (/ (* n (PI)) k)) (* (log (* 2 (* n (PI)))) (sqrt 2))))))) k)
(/ (+ (* (sqrt (* k (* n (PI)))) (sqrt 2)) (* (pow k 2) (+ (* -1/2 (* (sqrt (/ (* n (PI)) k)) (* (log (* 2 (* n (PI)))) (sqrt 2)))) (* k (+ (* -1/2 (* (sqrt (/ 1 (* k (* n (PI))))) (* (sqrt 2) (+ (* -1 (* n (* (PI) (pow (log (* 2 (* n (PI)))) 2)))) (* 1/2 (* n (* (PI) (pow (log (* 2 (* n (PI)))) 2)))))))) (* -1/2 (* (sqrt (/ k (* n (PI)))) (* (sqrt 2) (+ (* -1 (* (log (* 2 (* n (PI)))) (+ (* -1 (* n (* (PI) (pow (log (* 2 (* n (PI)))) 2)))) (* 1/2 (* n (* (PI) (pow (log (* 2 (* n (PI)))) 2))))))) (+ (* -1/2 (* n (* (PI) (pow (log (* 2 (* n (PI)))) 3)))) (+ (* 1/6 (* n (* (PI) (pow (log (* 2 (* n (PI)))) 3)))) (* 1/4 (/ (* n (* (PI) (pow (log (* 2 (* n (PI)))) 2))) k))))))))))))) k)
(* (sqrt (/ (* n (PI)) (* k (pow (* 2 (* n (PI))) k)))) (sqrt 2))
(* (sqrt (/ (* n (PI)) (* k (pow (* 2 (* n (PI))) k)))) (sqrt 2))
(* (sqrt (/ (* n (PI)) (* k (pow (* 2 (* n (PI))) k)))) (sqrt 2))
(* (sqrt (/ (* n (PI)) (* k (pow (* 2 (* n (PI))) k)))) (sqrt 2))
(* (sqrt (/ (* n (PI)) (* k (pow (* 2 (* n (PI))) k)))) (sqrt 2))
(* (sqrt (/ (* n (PI)) (* k (pow (* 2 (* n (PI))) k)))) (sqrt 2))
(* (sqrt (/ (* n (PI)) (* k (pow (* 2 (* n (PI))) k)))) (sqrt 2))
(* (sqrt (/ (* n (PI)) (* k (pow (* 2 (* n (PI))) k)))) (sqrt 2))
(* (sqrt (/ (* n (PI)) (exp (* k (+ (log n) (log (* 2 (PI)))))))) (sqrt 2))
(* (sqrt (/ (* n (PI)) (exp (* k (+ (log n) (log (* 2 (PI)))))))) (sqrt 2))
(* (sqrt (/ (* n (PI)) (exp (* k (+ (log n) (log (* 2 (PI)))))))) (sqrt 2))
(* (sqrt (/ (* n (PI)) (exp (* k (+ (log n) (log (* 2 (PI)))))))) (sqrt 2))
(* (sqrt (/ (* n (PI)) (exp (* k (+ (log (* 2 (PI))) (* -1 (log (/ 1 n)))))))) (sqrt 2))
(* (sqrt (/ (* n (PI)) (exp (* k (+ (log (* 2 (PI))) (* -1 (log (/ 1 n)))))))) (sqrt 2))
(* (sqrt (/ (* n (PI)) (exp (* k (+ (log (* 2 (PI))) (* -1 (log (/ 1 n)))))))) (sqrt 2))
(* (sqrt (/ (* n (PI)) (exp (* k (+ (log (* 2 (PI))) (* -1 (log (/ 1 n)))))))) (sqrt 2))
(* -1 (* (sqrt (/ (* n (PI)) (exp (* k (+ (log (* -2 (PI))) (* -1 (log (/ -1 n)))))))) (* (sqrt -2) (sqrt -1))))
(* -1 (* (sqrt (/ (* n (PI)) (exp (* k (+ (log (* -2 (PI))) (* -1 (log (/ -1 n)))))))) (* (sqrt -2) (sqrt -1))))
(* -1 (* (sqrt (/ (* n (PI)) (exp (* k (+ (log (* -2 (PI))) (* -1 (log (/ -1 n)))))))) (* (sqrt -2) (sqrt -1))))
(* -1 (* (sqrt (/ (* n (PI)) (exp (* k (+ (log (* -2 (PI))) (* -1 (log (/ -1 n)))))))) (* (sqrt -2) (sqrt -1))))
(* (sqrt (* n (PI))) (sqrt 2))
(+ (* -1/2 (* (* k (* (log (* 2 (* n (PI)))) (sqrt 2))) (sqrt (* n (PI))))) (* (sqrt (* n (PI))) (sqrt 2)))
(+ (* k (+ (* -1/2 (* (sqrt (* n (PI))) (* (log (* 2 (* n (PI)))) (sqrt 2)))) (* -1/2 (* (* k (* (sqrt 2) (+ (* -1 (* n (* (PI) (pow (log (* 2 (* n (PI)))) 2)))) (+ (* 1/4 (* n (* (PI) (pow (log (* 2 (* n (PI)))) 2)))) (* 1/2 (* n (* (PI) (pow (log (* 2 (* n (PI)))) 2)))))))) (sqrt (/ 1 (* n (PI)))))))) (* (sqrt (* n (PI))) (sqrt 2)))
(+ (* k (+ (* -1/2 (* (sqrt (* n (PI))) (* (log (* 2 (* n (PI)))) (sqrt 2)))) (* k (+ (* -1/2 (* (sqrt (/ 1 (* n (PI)))) (* (sqrt 2) (+ (* -1 (* n (* (PI) (pow (log (* 2 (* n (PI)))) 2)))) (+ (* 1/4 (* n (* (PI) (pow (log (* 2 (* n (PI)))) 2)))) (* 1/2 (* n (* (PI) (pow (log (* 2 (* n (PI)))) 2))))))))) (* -1/2 (* (* k (* (sqrt 2) (+ (* -1 (* (log (* 2 (* n (PI)))) (+ (* -1 (* n (* (PI) (pow (log (* 2 (* n (PI)))) 2)))) (* 1/2 (* n (* (PI) (pow (log (* 2 (* n (PI)))) 2))))))) (+ (* -1/2 (* n (* (PI) (pow (log (* 2 (* n (PI)))) 3)))) (+ (* 1/6 (* n (* (PI) (pow (log (* 2 (* n (PI)))) 3)))) (* 1/2 (* (log (* 2 (* n (PI)))) (+ (* -1 (* n (* (PI) (pow (log (* 2 (* n (PI)))) 2)))) (+ (* 1/4 (* n (* (PI) (pow (log (* 2 (* n (PI)))) 2)))) (* 1/2 (* n (* (PI) (pow (log (* 2 (* n (PI)))) 2))))))))))))) (sqrt (/ 1 (* n (PI)))))))))) (* (sqrt (* n (PI))) (sqrt 2)))
(* (sqrt (/ (* n (PI)) (pow (* 2 (* n (PI))) k))) (sqrt 2))
(* (sqrt (/ (* n (PI)) (pow (* 2 (* n (PI))) k))) (sqrt 2))
(* (sqrt (/ (* n (PI)) (pow (* 2 (* n (PI))) k))) (sqrt 2))
(* (sqrt (/ (* n (PI)) (pow (* 2 (* n (PI))) k))) (sqrt 2))
(* (sqrt (/ (* n (PI)) (pow (* 2 (* n (PI))) k))) (sqrt 2))
(* (sqrt (/ (* n (PI)) (pow (* 2 (* n (PI))) k))) (sqrt 2))
(* (sqrt (/ (* n (PI)) (pow (* 2 (* n (PI))) k))) (sqrt 2))
(* (sqrt (/ (* n (PI)) (pow (* 2 (* n (PI))) k))) (sqrt 2))
(* 2 (/ (* n (PI)) (exp (* k (+ (log n) (log (* 2 (PI))))))))
(* 2 (/ (* n (PI)) (exp (* k (+ (log n) (log (* 2 (PI))))))))
(* 2 (/ (* n (PI)) (exp (* k (+ (log n) (log (* 2 (PI))))))))
(* 2 (/ (* n (PI)) (exp (* k (+ (log n) (log (* 2 (PI))))))))
(* 2 (/ (* n (PI)) (exp (* k (+ (log (* 2 (PI))) (* -1 (log (/ 1 n))))))))
(* 2 (/ (* n (PI)) (exp (* k (+ (log (* 2 (PI))) (* -1 (log (/ 1 n))))))))
(* 2 (/ (* n (PI)) (exp (* k (+ (log (* 2 (PI))) (* -1 (log (/ 1 n))))))))
(* 2 (/ (* n (PI)) (exp (* k (+ (log (* 2 (PI))) (* -1 (log (/ 1 n))))))))
(* 2 (/ (* n (PI)) (exp (* k (+ (log (* -2 (PI))) (* -1 (log (/ -1 n))))))))
(* 2 (/ (* n (PI)) (exp (* k (+ (log (* -2 (PI))) (* -1 (log (/ -1 n))))))))
(* 2 (/ (* n (PI)) (exp (* k (+ (log (* -2 (PI))) (* -1 (log (/ -1 n))))))))
(* 2 (/ (* n (PI)) (exp (* k (+ (log (* -2 (PI))) (* -1 (log (/ -1 n))))))))
(* 2 (* n (PI)))
(+ (* -2 (* k (* n (* (PI) (log (* 2 (* n (PI)))))))) (* 2 (* n (PI))))
(+ (* 2 (* n (PI))) (* k (+ (* -2 (* k (+ (* -1 (* n (* (PI) (pow (log (* 2 (* n (PI)))) 2)))) (* 1/2 (* n (* (PI) (pow (log (* 2 (* n (PI)))) 2))))))) (* -2 (* n (* (PI) (log (* 2 (* n (PI))))))))))
(+ (* 2 (* n (PI))) (* k (+ (* -2 (* n (* (PI) (log (* 2 (* n (PI))))))) (* k (+ (* -2 (* k (+ (* -1 (* (log (* 2 (* n (PI)))) (+ (* -1 (* n (* (PI) (pow (log (* 2 (* n (PI)))) 2)))) (* 1/2 (* n (* (PI) (pow (log (* 2 (* n (PI)))) 2))))))) (+ (* -1/2 (* n (* (PI) (pow (log (* 2 (* n (PI)))) 3)))) (* 1/6 (* n (* (PI) (pow (log (* 2 (* n (PI)))) 3)))))))) (* -2 (+ (* -1 (* n (* (PI) (pow (log (* 2 (* n (PI)))) 2)))) (* 1/2 (* n (* (PI) (pow (log (* 2 (* n (PI)))) 2)))))))))))
(* 2 (/ (* n (PI)) (pow (* 2 (* n (PI))) k)))
(* 2 (/ (* n (PI)) (pow (* 2 (* n (PI))) k)))
(* 2 (/ (* n (PI)) (pow (* 2 (* n (PI))) k)))
(* 2 (/ (* n (PI)) (pow (* 2 (* n (PI))) k)))
(* 2 (/ (* n (PI)) (pow (* 2 (* n (PI))) k)))
(* 2 (/ (* n (PI)) (pow (* 2 (* n (PI))) k)))
(* 2 (/ (* n (PI)) (pow (* 2 (* n (PI))) k)))
(* 2 (/ (* n (PI)) (pow (* 2 (* n (PI))) k)))
(* 2 (* n (PI)))
(* 2 (* n (PI)))
(* 2 (* n (PI)))
(* 2 (* n (PI)))
(* 2 (* n (PI)))
(* 2 (* n (PI)))
(* 2 (* n (PI)))
(* 2 (* n (PI)))
(* 2 (* n (PI)))
(* 2 (* n (PI)))
(* 2 (* n (PI)))
(* 2 (* n (PI)))
(* (sqrt (/ (* n (PI)) k)) (sqrt 2))
(* (sqrt (/ (* n (PI)) k)) (sqrt 2))
(* (sqrt (/ (* n (PI)) k)) (sqrt 2))
(* (sqrt (/ (* n (PI)) k)) (sqrt 2))
(* (sqrt (/ (* n (PI)) k)) (sqrt 2))
(* (sqrt (/ (* n (PI)) k)) (sqrt 2))
(* (sqrt (/ (* n (PI)) k)) (sqrt 2))
(* (sqrt (/ (* n (PI)) k)) (sqrt 2))
(* (sqrt (/ (* n (PI)) k)) (* (sqrt -2) (sqrt -1)))
(* (sqrt (/ (* n (PI)) k)) (* (sqrt -2) (sqrt -1)))
(* (sqrt (/ (* n (PI)) k)) (* (sqrt -2) (sqrt -1)))
(* (sqrt (/ (* n (PI)) k)) (* (sqrt -2) (sqrt -1)))
(* (sqrt (/ (* n (PI)) k)) (sqrt 2))
(* (sqrt (/ (* n (PI)) k)) (sqrt 2))
(* (sqrt (/ (* n (PI)) k)) (sqrt 2))
(* (sqrt (/ (* n (PI)) k)) (sqrt 2))
(* (sqrt (/ (* n (PI)) k)) (sqrt 2))
(* (sqrt (/ (* n (PI)) k)) (sqrt 2))
(* (sqrt (/ (* n (PI)) k)) (sqrt 2))
(* (sqrt (/ (* n (PI)) k)) (sqrt 2))
(* -1 (* (sqrt (/ (* n (PI)) k)) (* (sqrt -2) (sqrt -1))))
(* -1 (* (sqrt (/ (* n (PI)) k)) (* (sqrt -2) (sqrt -1))))
(* -1 (* (sqrt (/ (* n (PI)) k)) (* (sqrt -2) (sqrt -1))))
(* -1 (* (sqrt (/ (* n (PI)) k)) (* (sqrt -2) (sqrt -1))))
(* 2 (/ (* n (PI)) k))
(* 2 (/ (* n (PI)) k))
(* 2 (/ (* n (PI)) k))
(* 2 (/ (* n (PI)) k))
(* 2 (/ (* n (PI)) k))
(* 2 (/ (* n (PI)) k))
(* 2 (/ (* n (PI)) k))
(* 2 (/ (* n (PI)) k))
(* 2 (/ (* n (PI)) k))
(* 2 (/ (* n (PI)) k))
(* 2 (/ (* n (PI)) k))
(* 2 (/ (* n (PI)) k))
(* 2 (/ (* n (PI)) k))
(* 2 (/ (* n (PI)) k))
(* 2 (/ (* n (PI)) k))
(* 2 (/ (* n (PI)) k))
(* 2 (/ (* n (PI)) k))
(* 2 (/ (* n (PI)) k))
(* 2 (/ (* n (PI)) k))
(* 2 (/ (* n (PI)) k))
(* 2 (/ (* n (PI)) k))
(* 2 (/ (* n (PI)) k))
(* 2 (/ (* n (PI)) k))
(* 2 (/ (* n (PI)) k))
(/ k (* n (PI)))
(/ k (* n (PI)))
(/ k (* n (PI)))
(/ k (* n (PI)))
(/ k (* n (PI)))
(/ k (* n (PI)))
(/ k (* n (PI)))
(/ k (* n (PI)))
(/ k (* n (PI)))
(/ k (* n (PI)))
(/ k (* n (PI)))
(/ k (* n (PI)))
(/ k (* n (PI)))
(/ k (* n (PI)))
(/ k (* n (PI)))
(/ k (* n (PI)))
(/ k (* n (PI)))
(/ k (* n (PI)))
(/ k (* n (PI)))
(/ k (* n (PI)))
(/ k (* n (PI)))
(/ k (* n (PI)))
(/ k (* n (PI)))
(/ k (* n (PI)))
(* n (PI))
(* n (PI))
(* n (PI))
(* n (PI))
(* n (PI))
(* n (PI))
(* n (PI))
(* n (PI))
(* n (PI))
(* n (PI))
(* n (PI))
(* n (PI))
(* (sqrt (/ (* n (PI)) k)) (sqrt 2))
(* (sqrt (/ (* n (PI)) k)) (sqrt 2))
(* (sqrt (/ (* n (PI)) k)) (sqrt 2))
(* (sqrt (/ (* n (PI)) k)) (sqrt 2))
(* (sqrt (/ (* n (PI)) k)) (sqrt 2))
(* (sqrt (/ (* n (PI)) k)) (sqrt 2))
(* (sqrt (/ (* n (PI)) k)) (sqrt 2))
(* (sqrt (/ (* n (PI)) k)) (sqrt 2))
(* (sqrt (/ (* n (PI)) k)) (* (pow (sqrt -1) 2) (sqrt 2)))
(* (sqrt (/ (* n (PI)) k)) (* (pow (sqrt -1) 2) (sqrt 2)))
(* (sqrt (/ (* n (PI)) k)) (* (pow (sqrt -1) 2) (sqrt 2)))
(* (sqrt (/ (* n (PI)) k)) (* (pow (sqrt -1) 2) (sqrt 2)))
(* (sqrt (/ (* n (PI)) k)) (sqrt 2))
(* (sqrt (/ (* n (PI)) k)) (sqrt 2))
(* (sqrt (/ (* n (PI)) k)) (sqrt 2))
(* (sqrt (/ (* n (PI)) k)) (sqrt 2))
(* (sqrt (/ (* n (PI)) k)) (sqrt 2))
(* (sqrt (/ (* n (PI)) k)) (sqrt 2))
(* (sqrt (/ (* n (PI)) k)) (sqrt 2))
(* (sqrt (/ (* n (PI)) k)) (sqrt 2))
(* -1 (* (sqrt (/ (* n (PI)) k)) (* (pow (sqrt -1) 2) (sqrt 2))))
(* -1 (* (sqrt (/ (* n (PI)) k)) (* (pow (sqrt -1) 2) (sqrt 2))))
(* -1 (* (sqrt (/ (* n (PI)) k)) (* (pow (sqrt -1) 2) (sqrt 2))))
(* -1 (* (sqrt (/ (* n (PI)) k)) (* (pow (sqrt -1) 2) (sqrt 2))))
(sqrt (/ (* n (PI)) k))
(sqrt (/ (* n (PI)) k))
(sqrt (/ (* n (PI)) k))
(sqrt (/ (* n (PI)) k))
(sqrt (/ (* n (PI)) k))
(sqrt (/ (* n (PI)) k))
(sqrt (/ (* n (PI)) k))
(sqrt (/ (* n (PI)) k))
(* (sqrt (/ (* n (PI)) k)) (pow (sqrt -1) 2))
(* (sqrt (/ (* n (PI)) k)) (pow (sqrt -1) 2))
(* (sqrt (/ (* n (PI)) k)) (pow (sqrt -1) 2))
(* (sqrt (/ (* n (PI)) k)) (pow (sqrt -1) 2))
(sqrt (/ (* n (PI)) k))
(sqrt (/ (* n (PI)) k))
(sqrt (/ (* n (PI)) k))
(sqrt (/ (* n (PI)) k))
(sqrt (/ (* n (PI)) k))
(sqrt (/ (* n (PI)) k))
(sqrt (/ (* n (PI)) k))
(sqrt (/ (* n (PI)) k))
(* -1 (* (sqrt (/ (* n (PI)) k)) (pow (sqrt -1) 2)))
(* -1 (* (sqrt (/ (* n (PI)) k)) (pow (sqrt -1) 2)))
(* -1 (* (sqrt (/ (* n (PI)) k)) (pow (sqrt -1) 2)))
(* -1 (* (sqrt (/ (* n (PI)) k)) (pow (sqrt -1) 2)))
(/ (* n (PI)) k)
(/ (* n (PI)) k)
(/ (* n (PI)) k)
(/ (* n (PI)) k)
(/ (* n (PI)) k)
(/ (* n (PI)) k)
(/ (* n (PI)) k)
(/ (* n (PI)) k)
(/ (* n (PI)) k)
(/ (* n (PI)) k)
(/ (* n (PI)) k)
(/ (* n (PI)) k)
(/ (* n (PI)) k)
(/ (* n (PI)) k)
(/ (* n (PI)) k)
(/ (* n (PI)) k)
(/ (* n (PI)) k)
(/ (* n (PI)) k)
(/ (* n (PI)) k)
(/ (* n (PI)) k)
(/ (* n (PI)) k)
(/ (* n (PI)) k)
(/ (* n (PI)) k)
(/ (* n (PI)) k)
(/ (PI) k)
(/ (PI) k)
(/ (PI) k)
(/ (PI) k)
(/ (PI) k)
(/ (PI) k)
(/ (PI) k)
(/ (PI) k)
(/ (PI) k)
(/ (PI) k)
(/ (PI) k)
(/ (PI) k)
(* (sqrt (/ (* n (PI)) k)) (/ 1 (sqrt 1/2)))
(* (sqrt (/ (* n (PI)) k)) (/ 1 (sqrt 1/2)))
(* (sqrt (/ (* n (PI)) k)) (/ 1 (sqrt 1/2)))
(* (sqrt (/ (* n (PI)) k)) (/ 1 (sqrt 1/2)))
(* (sqrt (/ (* n (PI)) k)) (/ 1 (sqrt 1/2)))
(* (sqrt (/ (* n (PI)) k)) (/ 1 (sqrt 1/2)))
(* (sqrt (/ (* n (PI)) k)) (/ 1 (sqrt 1/2)))
(* (sqrt (/ (* n (PI)) k)) (/ 1 (sqrt 1/2)))
(* -1 (* (sqrt (/ (* n (PI)) k)) (/ (pow (sqrt -1) 2) (sqrt 1/2))))
(* -1 (* (sqrt (/ (* n (PI)) k)) (/ (pow (sqrt -1) 2) (sqrt 1/2))))
(* -1 (* (sqrt (/ (* n (PI)) k)) (/ (pow (sqrt -1) 2) (sqrt 1/2))))
(* -1 (* (sqrt (/ (* n (PI)) k)) (/ (pow (sqrt -1) 2) (sqrt 1/2))))
(* (sqrt (/ (* n (PI)) k)) (/ 1 (sqrt 1/2)))
(* (sqrt (/ (* n (PI)) k)) (/ 1 (sqrt 1/2)))
(* (sqrt (/ (* n (PI)) k)) (/ 1 (sqrt 1/2)))
(* (sqrt (/ (* n (PI)) k)) (/ 1 (sqrt 1/2)))
(* (sqrt (/ (* n (PI)) k)) (/ 1 (sqrt 1/2)))
(* (sqrt (/ (* n (PI)) k)) (/ 1 (sqrt 1/2)))
(* (sqrt (/ (* n (PI)) k)) (/ 1 (sqrt 1/2)))
(* (sqrt (/ (* n (PI)) k)) (/ 1 (sqrt 1/2)))
(* (sqrt (/ (* n (PI)) k)) (/ (pow (sqrt -1) 2) (sqrt 1/2)))
(* (sqrt (/ (* n (PI)) k)) (/ (pow (sqrt -1) 2) (sqrt 1/2)))
(* (sqrt (/ (* n (PI)) k)) (/ (pow (sqrt -1) 2) (sqrt 1/2)))
(* (sqrt (/ (* n (PI)) k)) (/ (pow (sqrt -1) 2) (sqrt 1/2)))
(sqrt (/ (* n (PI)) k))
(sqrt (/ (* n (PI)) k))
(sqrt (/ (* n (PI)) k))
(sqrt (/ (* n (PI)) k))
(sqrt (/ (* n (PI)) k))
(sqrt (/ (* n (PI)) k))
(sqrt (/ (* n (PI)) k))
(sqrt (/ (* n (PI)) k))
(* -1 (* (sqrt (/ (* n (PI)) k)) (pow (sqrt -1) 2)))
(* -1 (* (sqrt (/ (* n (PI)) k)) (pow (sqrt -1) 2)))
(* -1 (* (sqrt (/ (* n (PI)) k)) (pow (sqrt -1) 2)))
(* -1 (* (sqrt (/ (* n (PI)) k)) (pow (sqrt -1) 2)))
(sqrt (/ (* n (PI)) k))
(sqrt (/ (* n (PI)) k))
(sqrt (/ (* n (PI)) k))
(sqrt (/ (* n (PI)) k))
(sqrt (/ (* n (PI)) k))
(sqrt (/ (* n (PI)) k))
(sqrt (/ (* n (PI)) k))
(sqrt (/ (* n (PI)) k))
(* (sqrt (/ (* n (PI)) k)) (pow (sqrt -1) 2))
(* (sqrt (/ (* n (PI)) k)) (pow (sqrt -1) 2))
(* (sqrt (/ (* n (PI)) k)) (pow (sqrt -1) 2))
(* (sqrt (/ (* n (PI)) k)) (pow (sqrt -1) 2))
(/ (* n (PI)) k)
(/ (* n (PI)) k)
(/ (* n (PI)) k)
(/ (* n (PI)) k)
(/ (* n (PI)) k)
(/ (* n (PI)) k)
(/ (* n (PI)) k)
(/ (* n (PI)) k)
(/ (* n (PI)) k)
(/ (* n (PI)) k)
(/ (* n (PI)) k)
(/ (* n (PI)) k)
(/ (* n (PI)) k)
(/ (* n (PI)) k)
(/ (* n (PI)) k)
(/ (* n (PI)) k)
(/ (* n (PI)) k)
(/ (* n (PI)) k)
(/ (* n (PI)) k)
(/ (* n (PI)) k)
(/ (* n (PI)) k)
(/ (* n (PI)) k)
(/ (* n (PI)) k)
(/ (* n (PI)) k)
(* n (PI))
(* n (PI))
(* n (PI))
(* n (PI))
(* n (PI))
(* n (PI))
(* n (PI))
(* n (PI))
(* n (PI))
(* n (PI))
(* n (PI))
(* n (PI))
(* (sqrt (/ (* n (PI)) (* k (exp (* k (+ (log n) (log (* 2 (PI))))))))) (sqrt 2))
(* (sqrt (/ (* n (PI)) (* k (exp (* k (+ (log n) (log (* 2 (PI))))))))) (sqrt 2))
(* (sqrt (/ (* n (PI)) (* k (exp (* k (+ (log n) (log (* 2 (PI))))))))) (sqrt 2))
(* (sqrt (/ (* n (PI)) (* k (exp (* k (+ (log n) (log (* 2 (PI))))))))) (sqrt 2))
(* (sqrt (/ (* n (PI)) (* k (exp (* k (+ (log (* 2 (PI))) (* -1 (log (/ 1 n))))))))) (sqrt 2))
(* (sqrt (/ (* n (PI)) (* k (exp (* k (+ (log (* 2 (PI))) (* -1 (log (/ 1 n))))))))) (sqrt 2))
(* (sqrt (/ (* n (PI)) (* k (exp (* k (+ (log (* 2 (PI))) (* -1 (log (/ 1 n))))))))) (sqrt 2))
(* (sqrt (/ (* n (PI)) (* k (exp (* k (+ (log (* 2 (PI))) (* -1 (log (/ 1 n))))))))) (sqrt 2))
(* -1 (* (sqrt (/ (* n (PI)) (* k (exp (* k (+ (log (* -2 (PI))) (* -1 (log (/ -1 n))))))))) (* (sqrt -2) (sqrt -1))))
(* -1 (* (sqrt (/ (* n (PI)) (* k (exp (* k (+ (log (* -2 (PI))) (* -1 (log (/ -1 n))))))))) (* (sqrt -2) (sqrt -1))))
(* -1 (* (sqrt (/ (* n (PI)) (* k (exp (* k (+ (log (* -2 (PI))) (* -1 (log (/ -1 n))))))))) (* (sqrt -2) (sqrt -1))))
(* -1 (* (sqrt (/ (* n (PI)) (* k (exp (* k (+ (log (* -2 (PI))) (* -1 (log (/ -1 n))))))))) (* (sqrt -2) (sqrt -1))))
(* (sqrt (/ (* n (PI)) k)) (sqrt 2))
(/ (+ (* -1/2 (* (sqrt (* (pow k 3) (* n (PI)))) (* (log (* 2 (* n (PI)))) (sqrt 2)))) (* (sqrt (* k (* n (PI)))) (sqrt 2))) k)
(/ (+ (* (sqrt (* k (* n (PI)))) (sqrt 2)) (* (pow k 2) (+ (* -1/2 (* (sqrt (/ k (* n (PI)))) (* (sqrt 2) (+ (* -1 (* n (* (PI) (pow (log (* 2 (* n (PI)))) 2)))) (* 1/2 (* n (* (PI) (pow (log (* 2 (* n (PI)))) 2)))))))) (* -1/2 (* (sqrt (/ (* n (PI)) k)) (* (log (* 2 (* n (PI)))) (sqrt 2))))))) k)
(/ (+ (* (sqrt (* k (* n (PI)))) (sqrt 2)) (* (pow k 2) (+ (* -1/2 (* (sqrt (/ (* n (PI)) k)) (* (log (* 2 (* n (PI)))) (sqrt 2)))) (* k (+ (* -1/2 (* (sqrt (/ 1 (* k (* n (PI))))) (* (sqrt 2) (+ (* -1 (* n (* (PI) (pow (log (* 2 (* n (PI)))) 2)))) (* 1/2 (* n (* (PI) (pow (log (* 2 (* n (PI)))) 2)))))))) (* -1/2 (* (sqrt (/ k (* n (PI)))) (* (sqrt 2) (+ (* -1 (* (log (* 2 (* n (PI)))) (+ (* -1 (* n (* (PI) (pow (log (* 2 (* n (PI)))) 2)))) (* 1/2 (* n (* (PI) (pow (log (* 2 (* n (PI)))) 2))))))) (+ (* -1/2 (* n (* (PI) (pow (log (* 2 (* n (PI)))) 3)))) (+ (* 1/6 (* n (* (PI) (pow (log (* 2 (* n (PI)))) 3)))) (* 1/4 (/ (* n (* (PI) (pow (log (* 2 (* n (PI)))) 2))) k))))))))))))) k)
(* (sqrt (/ (* n (PI)) (* k (pow (* 2 (* n (PI))) k)))) (sqrt 2))
(* (sqrt (/ (* n (PI)) (* k (pow (* 2 (* n (PI))) k)))) (sqrt 2))
(* (sqrt (/ (* n (PI)) (* k (pow (* 2 (* n (PI))) k)))) (sqrt 2))
(* (sqrt (/ (* n (PI)) (* k (pow (* 2 (* n (PI))) k)))) (sqrt 2))
(* (sqrt (/ (* n (PI)) (* k (pow (* 2 (* n (PI))) k)))) (* (sqrt -2) (sqrt -1)))
(* (sqrt (/ (* n (PI)) (* k (pow (* 2 (* n (PI))) k)))) (* (sqrt -2) (sqrt -1)))
(* (sqrt (/ (* n (PI)) (* k (pow (* 2 (* n (PI))) k)))) (* (sqrt -2) (sqrt -1)))
(* (sqrt (/ (* n (PI)) (* k (pow (* 2 (* n (PI))) k)))) (* (sqrt -2) (sqrt -1)))
(* 2 (/ (* n (PI)) (* k (exp (* k (+ (log n) (log (* 2 (PI)))))))))
(* 2 (/ (* n (PI)) (* k (exp (* k (+ (log n) (log (* 2 (PI)))))))))
(* 2 (/ (* n (PI)) (* k (exp (* k (+ (log n) (log (* 2 (PI)))))))))
(* 2 (/ (* n (PI)) (* k (exp (* k (+ (log n) (log (* 2 (PI)))))))))
(* 2 (/ (* n (PI)) (* k (exp (* k (+ (log (* 2 (PI))) (* -1 (log (/ 1 n)))))))))
(* 2 (/ (* n (PI)) (* k (exp (* k (+ (log (* 2 (PI))) (* -1 (log (/ 1 n)))))))))
(* 2 (/ (* n (PI)) (* k (exp (* k (+ (log (* 2 (PI))) (* -1 (log (/ 1 n)))))))))
(* 2 (/ (* n (PI)) (* k (exp (* k (+ (log (* 2 (PI))) (* -1 (log (/ 1 n)))))))))
(* 2 (/ (* n (PI)) (* k (exp (* k (+ (log (* -2 (PI))) (* -1 (log (/ -1 n)))))))))
(* 2 (/ (* n (PI)) (* k (exp (* k (+ (log (* -2 (PI))) (* -1 (log (/ -1 n)))))))))
(* 2 (/ (* n (PI)) (* k (exp (* k (+ (log (* -2 (PI))) (* -1 (log (/ -1 n)))))))))
(* 2 (/ (* n (PI)) (* k (exp (* k (+ (log (* -2 (PI))) (* -1 (log (/ -1 n)))))))))
(* 2 (/ (* n (PI)) k))
(/ (+ (* -2 (* k (* n (* (PI) (log (* 2 (* n (PI)))))))) (* 2 (* n (PI)))) k)
(/ (+ (* 2 (* n (PI))) (* k (+ (* -2 (* k (+ (* -1 (* n (* (PI) (pow (log (* 2 (* n (PI)))) 2)))) (* 1/2 (* n (* (PI) (pow (log (* 2 (* n (PI)))) 2))))))) (* -2 (* n (* (PI) (log (* 2 (* n (PI)))))))))) k)
(/ (+ (* 2 (* n (PI))) (* k (+ (* -2 (* n (* (PI) (log (* 2 (* n (PI))))))) (* k (+ (* -2 (* k (+ (* -1 (* (log (* 2 (* n (PI)))) (+ (* -1 (* n (* (PI) (pow (log (* 2 (* n (PI)))) 2)))) (* 1/2 (* n (* (PI) (pow (log (* 2 (* n (PI)))) 2))))))) (+ (* -1/2 (* n (* (PI) (pow (log (* 2 (* n (PI)))) 3)))) (* 1/6 (* n (* (PI) (pow (log (* 2 (* n (PI)))) 3)))))))) (* -2 (+ (* -1 (* n (* (PI) (pow (log (* 2 (* n (PI)))) 2)))) (* 1/2 (* n (* (PI) (pow (log (* 2 (* n (PI)))) 2))))))))))) k)
(* 2 (/ (* n (PI)) (* k (pow (* 2 (* n (PI))) k))))
(* 2 (/ (* n (PI)) (* k (pow (* 2 (* n (PI))) k))))
(* 2 (/ (* n (PI)) (* k (pow (* 2 (* n (PI))) k))))
(* 2 (/ (* n (PI)) (* k (pow (* 2 (* n (PI))) k))))
(* 2 (/ (* n (PI)) (* k (pow (* 2 (* n (PI))) k))))
(* 2 (/ (* n (PI)) (* k (pow (* 2 (* n (PI))) k))))
(* 2 (/ (* n (PI)) (* k (pow (* 2 (* n (PI))) k))))
(* 2 (/ (* n (PI)) (* k (pow (* 2 (* n (PI))) k))))
(exp (* k (+ (log n) (log (* 2 (PI))))))
(exp (* k (+ (log n) (log (* 2 (PI))))))
(exp (* k (+ (log n) (log (* 2 (PI))))))
(exp (* k (+ (log n) (log (* 2 (PI))))))
(exp (* k (+ (log (* 2 (PI))) (* -1 (log (/ 1 n))))))
(exp (* k (+ (log (* 2 (PI))) (* -1 (log (/ 1 n))))))
(exp (* k (+ (log (* 2 (PI))) (* -1 (log (/ 1 n))))))
(exp (* k (+ (log (* 2 (PI))) (* -1 (log (/ 1 n))))))
(exp (* k (+ (log (* -2 (PI))) (* -1 (log (/ -1 n))))))
(exp (* k (+ (log (* -2 (PI))) (* -1 (log (/ -1 n))))))
(exp (* k (+ (log (* -2 (PI))) (* -1 (log (/ -1 n))))))
(exp (* k (+ (log (* -2 (PI))) (* -1 (log (/ -1 n))))))
1
(+ 1 (* k (log (* 2 (* n (PI))))))
(+ 1 (* k (+ (log (* 2 (* n (PI)))) (* 1/2 (* k (pow (log (* 2 (* n (PI)))) 2))))))
(+ 1 (* k (+ (log (* 2 (* n (PI)))) (* k (+ (* 1/6 (* k (pow (log (* 2 (* n (PI)))) 3))) (* 1/2 (pow (log (* 2 (* n (PI)))) 2)))))))
(pow (* 2 (* n (PI))) k)
(pow (* 2 (* n (PI))) k)
(pow (* 2 (* n (PI))) k)
(pow (* 2 (* n (PI))) k)
(pow (* 2 (* n (PI))) k)
(pow (* 2 (* n (PI))) k)
(pow (* 2 (* n (PI))) k)
(pow (* 2 (* n (PI))) k)

Outputs
(* (sqrt (/ (* n (PI)) (* k (exp (* k (+ (log n) (log (* 2 (PI))))))))) (sqrt 2))
(.f64 (sqrt.f64 (/.f64 (/.f64 (.f64 n (PI.f64)) k) (.f64 (pow.f64 n k) (pow.f64 (.f64 (PI.f64) #s(literal 2 binary64)) k)))) (sqrt.f64 #s(literal 2 binary64)))
(* (sqrt (/ (* n (PI)) (* k (exp (* k (+ (log n) (log (* 2 (PI))))))))) (sqrt 2))
(.f64 (sqrt.f64 (/.f64 (/.f64 (.f64 n (PI.f64)) k) (.f64 (pow.f64 n k) (pow.f64 (.f64 (PI.f64) #s(literal 2 binary64)) k)))) (sqrt.f64 #s(literal 2 binary64)))
(* (sqrt (/ (* n (PI)) (* k (exp (* k (+ (log n) (log (* 2 (PI))))))))) (sqrt 2))
(.f64 (sqrt.f64 (/.f64 (/.f64 (.f64 n (PI.f64)) k) (.f64 (pow.f64 n k) (pow.f64 (.f64 (PI.f64) #s(literal 2 binary64)) k)))) (sqrt.f64 #s(literal 2 binary64)))
(* (sqrt (/ (* n (PI)) (* k (exp (* k (+ (log n) (log (* 2 (PI))))))))) (sqrt 2))
(.f64 (sqrt.f64 (/.f64 (/.f64 (.f64 n (PI.f64)) k) (.f64 (pow.f64 n k) (pow.f64 (.f64 (PI.f64) #s(literal 2 binary64)) k)))) (sqrt.f64 #s(literal 2 binary64)))
(* (sqrt (/ (* n (PI)) (* k (exp (* k (+ (log (* 2 (PI))) (* -1 (log (/ 1 n))))))))) (sqrt 2))
(.f64 (sqrt.f64 (/.f64 (/.f64 (.f64 n (PI.f64)) k) (.f64 (pow.f64 n k) (pow.f64 (.f64 (PI.f64) #s(literal 2 binary64)) k)))) (sqrt.f64 #s(literal 2 binary64)))
(* (sqrt (/ (* n (PI)) (* k (exp (* k (+ (log (* 2 (PI))) (* -1 (log (/ 1 n))))))))) (sqrt 2))
(.f64 (sqrt.f64 (/.f64 (/.f64 (.f64 n (PI.f64)) k) (.f64 (pow.f64 n k) (pow.f64 (.f64 (PI.f64) #s(literal 2 binary64)) k)))) (sqrt.f64 #s(literal 2 binary64)))
(* (sqrt (/ (* n (PI)) (* k (exp (* k (+ (log (* 2 (PI))) (* -1 (log (/ 1 n))))))))) (sqrt 2))
(.f64 (sqrt.f64 (/.f64 (/.f64 (.f64 n (PI.f64)) k) (.f64 (pow.f64 n k) (pow.f64 (.f64 (PI.f64) #s(literal 2 binary64)) k)))) (sqrt.f64 #s(literal 2 binary64)))
(* (sqrt (/ (* n (PI)) (* k (exp (* k (+ (log (* 2 (PI))) (* -1 (log (/ 1 n))))))))) (sqrt 2))
(.f64 (sqrt.f64 (/.f64 (/.f64 (.f64 n (PI.f64)) k) (.f64 (pow.f64 n k) (pow.f64 (.f64 (PI.f64) #s(literal 2 binary64)) k)))) (sqrt.f64 #s(literal 2 binary64)))
(* -1 (* (sqrt (/ (* n (PI)) (* k (exp (* k (+ (log (* -2 (PI))) (* -1 (log (/ -1 n))))))))) (* (sqrt -2) (sqrt -1))))
(.f64 (sqrt.f64 (.f64 (/.f64 n (pow.f64 (.f64 (PI.f64) #s(literal -2 binary64)) k)) (/.f64 (/.f64 (PI.f64) k) (pow.f64 (/.f64 #s(literal -1 binary64) n) (neg.f64 k))))) (.f64 (sqrt.f64 #s(literal -2 binary64)) (-.f64 #s(literal 0 binary64) (sqrt.f64 #s(literal -1 binary64)))))
(* -1 (* (sqrt (/ (* n (PI)) (* k (exp (* k (+ (log (* -2 (PI))) (* -1 (log (/ -1 n))))))))) (* (sqrt -2) (sqrt -1))))
(.f64 (sqrt.f64 (.f64 (/.f64 n (pow.f64 (.f64 (PI.f64) #s(literal -2 binary64)) k)) (/.f64 (/.f64 (PI.f64) k) (pow.f64 (/.f64 #s(literal -1 binary64) n) (neg.f64 k))))) (.f64 (sqrt.f64 #s(literal -2 binary64)) (-.f64 #s(literal 0 binary64) (sqrt.f64 #s(literal -1 binary64)))))
(* -1 (* (sqrt (/ (* n (PI)) (* k (exp (* k (+ (log (* -2 (PI))) (* -1 (log (/ -1 n))))))))) (* (sqrt -2) (sqrt -1))))
(.f64 (sqrt.f64 (.f64 (/.f64 n (pow.f64 (.f64 (PI.f64) #s(literal -2 binary64)) k)) (/.f64 (/.f64 (PI.f64) k) (pow.f64 (/.f64 #s(literal -1 binary64) n) (neg.f64 k))))) (.f64 (sqrt.f64 #s(literal -2 binary64)) (-.f64 #s(literal 0 binary64) (sqrt.f64 #s(literal -1 binary64)))))
(* -1 (* (sqrt (/ (* n (PI)) (* k (exp (* k (+ (log (* -2 (PI))) (* -1 (log (/ -1 n))))))))) (* (sqrt -2) (sqrt -1))))
(.f64 (sqrt.f64 (.f64 (/.f64 n (pow.f64 (.f64 (PI.f64) #s(literal -2 binary64)) k)) (/.f64 (/.f64 (PI.f64) k) (pow.f64 (/.f64 #s(literal -1 binary64) n) (neg.f64 k))))) (.f64 (sqrt.f64 #s(literal -2 binary64)) (-.f64 #s(literal 0 binary64) (sqrt.f64 #s(literal -1 binary64)))))
(* (sqrt (/ (* n (PI)) k)) (sqrt 2))
(.f64 (sqrt.f64 #s(literal 2 binary64)) (sqrt.f64 (/.f64 (.f64 n (PI.f64)) k)))
(/ (+ (* -1/2 (* (sqrt (* (pow k 3) (* n (PI)))) (* (log (* 2 (* n (PI)))) (sqrt 2)))) (* (sqrt (* k (* n (PI)))) (sqrt 2))) k)
(/.f64 (.f64 (sqrt.f64 #s(literal 2 binary64)) (+.f64 (.f64 #s(literal -1/2 binary64) (.f64 (sqrt.f64 (.f64 n (.f64 (PI.f64) (.f64 k (.f64 k k))))) (log.f64 (.f64 (.f64 n (PI.f64)) #s(literal 2 binary64))))) (sqrt.f64 (.f64 (*.f64 n (PI.f64)) k)))) k)
(/ (+ (* (sqrt (* k (* n (PI)))) (sqrt 2)) (* (pow k 2) (+ (* -1/2 (* (sqrt (/ k (* n (PI)))) (* (sqrt 2) (+ (* -1 (* n (* (PI) (pow (log (* 2 (* n (PI)))) 2)))) (* 1/2 (* n (* (PI) (pow (log (* 2 (* n (PI)))) 2)))))))) (* -1/2 (* (sqrt (/ (* n (PI)) k)) (* (log (* 2 (* n (PI)))) (sqrt 2))))))) k)
(/.f64 (+.f64 (.f64 (sqrt.f64 #s(literal 2 binary64)) (sqrt.f64 (.f64 (.f64 n (PI.f64)) k))) (.f64 (.f64 (.f64 k k) #s(literal -1/2 binary64)) (.f64 (sqrt.f64 #s(literal 2 binary64)) (+.f64 (.f64 (.f64 (.f64 n (PI.f64)) (.f64 (pow.f64 (log.f64 (.f64 (.f64 n (PI.f64)) #s(literal 2 binary64))) #s(literal 2 binary64)) #s(literal -1/2 binary64))) (sqrt.f64 (/.f64 k (.f64 n (PI.f64))))) (.f64 (sqrt.f64 (/.f64 (.f64 n (PI.f64)) k)) (log.f64 (.f64 (.f64 n (PI.f64)) #s(literal 2 binary64)))))))) k)
(/ (+ (* (sqrt (* k (* n (PI)))) (sqrt 2)) (* (pow k 2) (+ (* -1/2 (* (sqrt (/ (* n (PI)) k)) (* (log (* 2 (* n (PI)))) (sqrt 2)))) (* k (+ (* -1/2 (* (sqrt (/ 1 (* k (* n (PI))))) (* (sqrt 2) (+ (* -1 (* n (* (PI) (pow (log (* 2 (* n (PI)))) 2)))) (* 1/2 (* n (* (PI) (pow (log (* 2 (* n (PI)))) 2)))))))) (* -1/2 (* (sqrt (/ k (* n (PI)))) (* (sqrt 2) (+ (* -1 (* (log (* 2 (* n (PI)))) (+ (* -1 (* n (* (PI) (pow (log (* 2 (* n (PI)))) 2)))) (* 1/2 (* n (* (PI) (pow (log (* 2 (* n (PI)))) 2))))))) (+ (* -1/2 (* n (* (PI) (pow (log (* 2 (* n (PI)))) 3)))) (+ (* 1/6 (* n (* (PI) (pow (log (* 2 (* n (PI)))) 3)))) (* 1/4 (/ (* n (* (PI) (pow (log (* 2 (* n (PI)))) 2))) k))))))))))))) k)
(/.f64 (+.f64 (.f64 (sqrt.f64 #s(literal 2 binary64)) (sqrt.f64 (.f64 (.f64 n (PI.f64)) k))) (.f64 (.f64 k k) (.f64 #s(literal -1/2 binary64) (+.f64 (.f64 (sqrt.f64 (/.f64 (.f64 n (PI.f64)) k)) (.f64 (sqrt.f64 #s(literal 2 binary64)) (log.f64 (.f64 (.f64 n (PI.f64)) #s(literal 2 binary64))))) (.f64 (.f64 (sqrt.f64 #s(literal 2 binary64)) (+.f64 (.f64 (.f64 (.f64 n (PI.f64)) (.f64 (pow.f64 (log.f64 (.f64 (.f64 n (PI.f64)) #s(literal 2 binary64))) #s(literal 2 binary64)) #s(literal -1/2 binary64))) (sqrt.f64 (/.f64 #s(literal 1 binary64) (.f64 (.f64 n (PI.f64)) k)))) (.f64 (+.f64 (.f64 #s(literal 1/2 binary64) (.f64 (.f64 n (PI.f64)) (pow.f64 (log.f64 (.f64 (.f64 n (PI.f64)) #s(literal 2 binary64))) #s(literal 3 binary64)))) (.f64 n (+.f64 (.f64 (.f64 (pow.f64 (log.f64 (.f64 (.f64 n (PI.f64)) #s(literal 2 binary64))) #s(literal 2 binary64)) (/.f64 (PI.f64) k)) #s(literal 1/4 binary64)) (.f64 (.f64 (PI.f64) (pow.f64 (log.f64 (.f64 (.f64 n (PI.f64)) #s(literal 2 binary64))) #s(literal 3 binary64))) #s(literal -1/3 binary64))))) (sqrt.f64 (/.f64 k (*.f64 n (PI.f64))))))) k))))) k)
(* (sqrt (/ (* n (PI)) (* k (pow (* 2 (* n (PI))) k)))) (sqrt 2))
(.f64 (sqrt.f64 #s(literal 2 binary64)) (sqrt.f64 (/.f64 (.f64 n (PI.f64)) (.f64 k (pow.f64 (.f64 (*.f64 n (PI.f64)) #s(literal 2 binary64)) k)))))
(* (sqrt (/ (* n (PI)) (* k (pow (* 2 (* n (PI))) k)))) (sqrt 2))
(.f64 (sqrt.f64 #s(literal 2 binary64)) (sqrt.f64 (/.f64 (.f64 n (PI.f64)) (.f64 k (pow.f64 (.f64 (*.f64 n (PI.f64)) #s(literal 2 binary64)) k)))))
(* (sqrt (/ (* n (PI)) (* k (pow (* 2 (* n (PI))) k)))) (sqrt 2))
(.f64 (sqrt.f64 #s(literal 2 binary64)) (sqrt.f64 (/.f64 (.f64 n (PI.f64)) (.f64 k (pow.f64 (.f64 (*.f64 n (PI.f64)) #s(literal 2 binary64)) k)))))
(* (sqrt (/ (* n (PI)) (* k (pow (* 2 (* n (PI))) k)))) (sqrt 2))
(.f64 (sqrt.f64 #s(literal 2 binary64)) (sqrt.f64 (/.f64 (.f64 n (PI.f64)) (.f64 k (pow.f64 (.f64 (*.f64 n (PI.f64)) #s(literal 2 binary64)) k)))))
(* (sqrt (/ (* n (PI)) (* k (pow (* 2 (* n (PI))) k)))) (sqrt 2))
(.f64 (sqrt.f64 #s(literal 2 binary64)) (sqrt.f64 (/.f64 (.f64 n (PI.f64)) (.f64 k (pow.f64 (.f64 (*.f64 n (PI.f64)) #s(literal 2 binary64)) k)))))
(* (sqrt (/ (* n (PI)) (* k (pow (* 2 (* n (PI))) k)))) (sqrt 2))
(.f64 (sqrt.f64 #s(literal 2 binary64)) (sqrt.f64 (/.f64 (.f64 n (PI.f64)) (.f64 k (pow.f64 (.f64 (*.f64 n (PI.f64)) #s(literal 2 binary64)) k)))))
(* (sqrt (/ (* n (PI)) (* k (pow (* 2 (* n (PI))) k)))) (sqrt 2))
(.f64 (sqrt.f64 #s(literal 2 binary64)) (sqrt.f64 (/.f64 (.f64 n (PI.f64)) (.f64 k (pow.f64 (.f64 (*.f64 n (PI.f64)) #s(literal 2 binary64)) k)))))
(* (sqrt (/ (* n (PI)) (* k (pow (* 2 (* n (PI))) k)))) (sqrt 2))
(.f64 (sqrt.f64 #s(literal 2 binary64)) (sqrt.f64 (/.f64 (.f64 n (PI.f64)) (.f64 k (pow.f64 (.f64 (*.f64 n (PI.f64)) #s(literal 2 binary64)) k)))))
(* (sqrt (/ (* n (PI)) (exp (* k (+ (log n) (log (* 2 (PI)))))))) (sqrt 2))
(.f64 (sqrt.f64 #s(literal 2 binary64)) (sqrt.f64 (.f64 (/.f64 n (pow.f64 n k)) (/.f64 (PI.f64) (pow.f64 (*.f64 (PI.f64) #s(literal 2 binary64)) k)))))
(* (sqrt (/ (* n (PI)) (exp (* k (+ (log n) (log (* 2 (PI)))))))) (sqrt 2))
(.f64 (sqrt.f64 #s(literal 2 binary64)) (sqrt.f64 (.f64 (/.f64 n (pow.f64 n k)) (/.f64 (PI.f64) (pow.f64 (*.f64 (PI.f64) #s(literal 2 binary64)) k)))))
(* (sqrt (/ (* n (PI)) (exp (* k (+ (log n) (log (* 2 (PI)))))))) (sqrt 2))
(.f64 (sqrt.f64 #s(literal 2 binary64)) (sqrt.f64 (.f64 (/.f64 n (pow.f64 n k)) (/.f64 (PI.f64) (pow.f64 (*.f64 (PI.f64) #s(literal 2 binary64)) k)))))
(* (sqrt (/ (* n (PI)) (exp (* k (+ (log n) (log (* 2 (PI)))))))) (sqrt 2))
(.f64 (sqrt.f64 #s(literal 2 binary64)) (sqrt.f64 (.f64 (/.f64 n (pow.f64 n k)) (/.f64 (PI.f64) (pow.f64 (*.f64 (PI.f64) #s(literal 2 binary64)) k)))))
(* (sqrt (/ (* n (PI)) (exp (* k (+ (log (* 2 (PI))) (* -1 (log (/ 1 n)))))))) (sqrt 2))
(.f64 (sqrt.f64 #s(literal 2 binary64)) (sqrt.f64 (.f64 (/.f64 n (pow.f64 n k)) (/.f64 (PI.f64) (pow.f64 (*.f64 (PI.f64) #s(literal 2 binary64)) k)))))
(* (sqrt (/ (* n (PI)) (exp (* k (+ (log (* 2 (PI))) (* -1 (log (/ 1 n)))))))) (sqrt 2))
(.f64 (sqrt.f64 #s(literal 2 binary64)) (sqrt.f64 (.f64 (/.f64 n (pow.f64 n k)) (/.f64 (PI.f64) (pow.f64 (*.f64 (PI.f64) #s(literal 2 binary64)) k)))))
(* (sqrt (/ (* n (PI)) (exp (* k (+ (log (* 2 (PI))) (* -1 (log (/ 1 n)))))))) (sqrt 2))
(.f64 (sqrt.f64 #s(literal 2 binary64)) (sqrt.f64 (.f64 (/.f64 n (pow.f64 n k)) (/.f64 (PI.f64) (pow.f64 (*.f64 (PI.f64) #s(literal 2 binary64)) k)))))
(* (sqrt (/ (* n (PI)) (exp (* k (+ (log (* 2 (PI))) (* -1 (log (/ 1 n)))))))) (sqrt 2))
(.f64 (sqrt.f64 #s(literal 2 binary64)) (sqrt.f64 (.f64 (/.f64 n (pow.f64 n k)) (/.f64 (PI.f64) (pow.f64 (*.f64 (PI.f64) #s(literal 2 binary64)) k)))))
(* -1 (* (sqrt (/ (* n (PI)) (exp (* k (+ (log (* -2 (PI))) (* -1 (log (/ -1 n)))))))) (* (sqrt -2) (sqrt -1))))
(.f64 (sqrt.f64 (/.f64 (.f64 n (PI.f64)) (.f64 (pow.f64 (/.f64 #s(literal -1 binary64) n) (neg.f64 k)) (pow.f64 (.f64 (PI.f64) #s(literal -2 binary64)) k)))) (*.f64 (sqrt.f64 #s(literal -2 binary64)) (-.f64 #s(literal 0 binary64) (sqrt.f64 #s(literal -1 binary64)))))
(* -1 (* (sqrt (/ (* n (PI)) (exp (* k (+ (log (* -2 (PI))) (* -1 (log (/ -1 n)))))))) (* (sqrt -2) (sqrt -1))))
(.f64 (sqrt.f64 (/.f64 (.f64 n (PI.f64)) (.f64 (pow.f64 (/.f64 #s(literal -1 binary64) n) (neg.f64 k)) (pow.f64 (.f64 (PI.f64) #s(literal -2 binary64)) k)))) (*.f64 (sqrt.f64 #s(literal -2 binary64)) (-.f64 #s(literal 0 binary64) (sqrt.f64 #s(literal -1 binary64)))))
(* -1 (* (sqrt (/ (* n (PI)) (exp (* k (+ (log (* -2 (PI))) (* -1 (log (/ -1 n)))))))) (* (sqrt -2) (sqrt -1))))
(.f64 (sqrt.f64 (/.f64 (.f64 n (PI.f64)) (.f64 (pow.f64 (/.f64 #s(literal -1 binary64) n) (neg.f64 k)) (pow.f64 (.f64 (PI.f64) #s(literal -2 binary64)) k)))) (*.f64 (sqrt.f64 #s(literal -2 binary64)) (-.f64 #s(literal 0 binary64) (sqrt.f64 #s(literal -1 binary64)))))
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(/ (+ (* (sqrt (* k (* n (PI)))) (sqrt 2)) (* (pow k 2) (+ (* -1/2 (* (sqrt (/ (* n (PI)) k)) (* (log (* 2 (* n (PI)))) (sqrt 2)))) (* k (+ (* -1/2 (* (sqrt (/ 1 (* k (* n (PI))))) (* (sqrt 2) (+ (* -1 (* n (* (PI) (pow (log (* 2 (* n (PI)))) 2)))) (* 1/2 (* n (* (PI) (pow (log (* 2 (* n (PI)))) 2)))))))) (* -1/2 (* (sqrt (/ k (* n (PI)))) (* (sqrt 2) (+ (* -1 (* (log (* 2 (* n (PI)))) (+ (* -1 (* n (* (PI) (pow (log (* 2 (* n (PI)))) 2)))) (* 1/2 (* n (* (PI) (pow (log (* 2 (* n (PI)))) 2))))))) (+ (* -1/2 (* n (* (PI) (pow (log (* 2 (* n (PI)))) 3)))) (+ (* 1/6 (* n (* (PI) (pow (log (* 2 (* n (PI)))) 3)))) (* 1/4 (/ (* n (* (PI) (pow (log (* 2 (* n (PI)))) 2))) k))))))))))))) k)
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(/.f64 (/.f64 (.f64 (.f64 n (PI.f64)) #s(literal 2 binary64)) k) (.f64 (pow.f64 n k) (pow.f64 (.f64 (PI.f64) #s(literal 2 binary64)) k)))
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(exp (* k (+ (log n) (log (* 2 (PI))))))
(.f64 (pow.f64 n k) (pow.f64 (.f64 (PI.f64) #s(literal 2 binary64)) k))
(exp (* k (+ (log n) (log (* 2 (PI))))))
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(exp (* k (+ (log n) (log (* 2 (PI))))))
(.f64 (pow.f64 n k) (pow.f64 (.f64 (PI.f64) #s(literal 2 binary64)) k))
(exp (* k (+ (log n) (log (* 2 (PI))))))
(.f64 (pow.f64 n k) (pow.f64 (.f64 (PI.f64) #s(literal 2 binary64)) k))
(exp (* k (+ (log (* 2 (PI))) (* -1 (log (/ 1 n))))))
(.f64 (pow.f64 n k) (pow.f64 (.f64 (PI.f64) #s(literal 2 binary64)) k))
(exp (* k (+ (log (* 2 (PI))) (* -1 (log (/ 1 n))))))
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(.f64 (pow.f64 n k) (pow.f64 (.f64 (PI.f64) #s(literal 2 binary64)) k))
(exp (* k (+ (log (* 2 (PI))) (* -1 (log (/ 1 n))))))
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1
#s(literal 1 binary64)
(+ 1 (* k (log (* 2 (* n (PI))))))
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(+.f64 #s(literal 1 binary64) (.f64 k (+.f64 (log.f64 (.f64 (.f64 n (PI.f64)) #s(literal 2 binary64))) (.f64 (pow.f64 (log.f64 (.f64 (.f64 n (PI.f64)) #s(literal 2 binary64))) #s(literal 2 binary64)) (*.f64 k #s(literal 1/2 binary64))))))
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(pow (* 2 (* n (PI))) k)
(pow.f64 (.f64 (.f64 n (PI.f64)) #s(literal 2 binary64)) k)
(pow (* 2 (* n (PI))) k)
(pow.f64 (.f64 (.f64 n (PI.f64)) #s(literal 2 binary64)) k)
(pow (* 2 (* n (PI))) k)
(pow.f64 (.f64 (.f64 n (PI.f64)) #s(literal 2 binary64)) k)
(pow (* 2 (* n (PI))) k)
(pow.f64 (.f64 (.f64 n (PI.f64)) #s(literal 2 binary64)) k)
(pow (* 2 (* n (PI))) k)
(pow.f64 (.f64 (.f64 n (PI.f64)) #s(literal 2 binary64)) k)
(pow (* 2 (* n (PI))) k)
(pow.f64 (.f64 (.f64 n (PI.f64)) #s(literal 2 binary64)) k)
(pow (* 2 (* n (PI))) k)
(pow.f64 (.f64 (.f64 n (PI.f64)) #s(literal 2 binary64)) k)
(pow (* 2 (* n (PI))) k)
(pow.f64 (.f64 (.f64 n (PI.f64)) #s(literal 2 binary64)) k)

eval422.0ms (3.1%)

Compiler: Compiled 51358 to 6732 computations (86.9% saved)

prune428.0ms (3.2%)

Pruning

44 alts after pruning (40 fresh and 4 done)

	Pruned	Kept	Total
New	2932	36	2968
Fresh	4	4	8
Picked	2	3	5
Done	2	1	3
Total	2940	44	2984

Accuracy

100.0%

Counts

2984 → 44

Alt Table

Click to see full alt table

Status	Accuracy	Program
	38.6%	(pow.f64 (/.f64 (/.f64 k (*.f64 (PI.f64) n)) #s(literal 2 binary64)) #s(literal -1/2 binary64))
	25.7%	(pow.f64 (.f64 (/.f64 #s(literal 2 binary64) (/.f64 k (.f64 (PI.f64) n))) (/.f64 #s(literal 2 binary64) (/.f64 k (*.f64 (PI.f64) n)))) #s(literal 1/4 binary64))
	44.1%	(/.f64 (pow.f64 (*.f64 (PI.f64) n) #s(literal 1/2 binary64)) (sqrt.f64 (/.f64 k #s(literal 2 binary64))))
	80.3%	(/.f64 (pow.f64 (.f64 #s(literal 4 binary64) (.f64 (.f64 (PI.f64) n) (.f64 (PI.f64) n))) (-.f64 #s(literal 1/4 binary64) (*.f64 k #s(literal 1/4 binary64)))) (sqrt.f64 k))
✓	99.3%	(/.f64 (pow.f64 (.f64 #s(literal 2 binary64) (.f64 (PI.f64) n)) (-.f64 #s(literal 1/2 binary64) (/.f64 k #s(literal 2 binary64)))) (sqrt.f64 k))
	38.4%	(/.f64 (/.f64 #s(literal 1 binary64) (pow.f64 (/.f64 k (*.f64 (PI.f64) n)) #s(literal 1/2 binary64))) (sqrt.f64 #s(literal 1/2 binary64)))
	44.0%	(/.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 (/.f64 #s(literal 1/2 binary64) (*.f64 (PI.f64) n)))) (sqrt.f64 k))
	44.1%	(/.f64 (*.f64 #s(literal 1 binary64) (pow.f64 (/.f64 n #s(literal 1/2 binary64)) #s(literal 1/2 binary64))) (pow.f64 (/.f64 k (PI.f64)) #s(literal 1/2 binary64)))
	37.0%	(/.f64 (sqrt.f64 (/.f64 (/.f64 n k) (/.f64 #s(literal 1 binary64) (PI.f64)))) (sqrt.f64 #s(literal 1/2 binary64)))
	37.0%	(/.f64 (sqrt.f64 (/.f64 (/.f64 #s(literal 1 binary64) (/.f64 (/.f64 #s(literal 1 binary64) n) (PI.f64))) k)) (sqrt.f64 #s(literal 1/2 binary64)))
✓	37.0%	(/.f64 (sqrt.f64 (/.f64 (*.f64 n (PI.f64)) k)) (sqrt.f64 #s(literal 1/2 binary64)))
	37.1%	(/.f64 (sqrt.f64 (*.f64 (/.f64 (PI.f64) k) n)) (sqrt.f64 #s(literal 1/2 binary64)))
	44.1%	(/.f64 (sqrt.f64 (.f64 (.f64 n (PI.f64)) #s(literal 2 binary64))) (sqrt.f64 k))
	38.5%	(/.f64 (sqrt.f64 #s(literal 2 binary64)) (sqrt.f64 (/.f64 k (*.f64 (PI.f64) n))))
	37.1%	(/.f64 #s(literal 1 binary64) (pow.f64 (/.f64 #s(literal 2 binary64) (/.f64 k (*.f64 (PI.f64) n))) #s(literal -1/2 binary64)))
	44.0%	(/.f64 #s(literal 1 binary64) (/.f64 (sqrt.f64 (/.f64 k #s(literal 2 binary64))) (pow.f64 (*.f64 (PI.f64) n) #s(literal 1/2 binary64))))
	44.1%	(.f64 (pow.f64 (.f64 (PI.f64) n) #s(literal 1/2 binary64)) (sqrt.f64 (/.f64 #s(literal 2 binary64) k)))
	37.4%	(.f64 (pow.f64 (.f64 #s(literal 2 binary64) (PI.f64)) #s(literal 1/2 binary64)) (sqrt.f64 (/.f64 n k)))
	1.8%	(.f64 (sqrt.f64 (/.f64 (.f64 n (PI.f64)) k)) (/.f64 #s(literal -1 binary64) (sqrt.f64 #s(literal 1/2 binary64))))
	37.1%	(*.f64 (sqrt.f64 (/.f64 n (/.f64 k #s(literal 2 binary64)))) (sqrt.f64 (PI.f64)))
✓	37.1%	(.f64 (sqrt.f64 (.f64 (/.f64 (PI.f64) k) n)) (sqrt.f64 #s(literal 2 binary64)))
▶	37.1%	(.f64 (sqrt.f64 (.f64 (/.f64 n k) (PI.f64))) (sqrt.f64 #s(literal 2 binary64)))
	44.1%	(.f64 (sqrt.f64 (.f64 #s(literal 2 binary64) (*.f64 (PI.f64) n))) (pow.f64 k #s(literal -1/2 binary64)))
	44.0%	(.f64 (sqrt.f64 (.f64 #s(literal 2 binary64) n)) (pow.f64 (/.f64 (PI.f64) k) #s(literal 1/2 binary64)))
	44.4%	(.f64 (sqrt.f64 n) (sqrt.f64 (.f64 (/.f64 (PI.f64) k) #s(literal 2 binary64))))
	37.2%	(sqrt.f64 (/.f64 (/.f64 (*.f64 (PI.f64) n) #s(literal 1/2 binary64)) k))
	37.2%	(sqrt.f64 (/.f64 (/.f64 n #s(literal 1/2 binary64)) (/.f64 k (PI.f64))))
	37.2%	(sqrt.f64 (/.f64 (/.f64 #s(literal 2 binary64) (/.f64 (/.f64 #s(literal 1 binary64) n) (PI.f64))) k))
	37.2%	(sqrt.f64 (/.f64 (/.f64 #s(literal 1 binary64) k) (/.f64 #s(literal 1/2 binary64) (*.f64 (PI.f64) n))))
	37.1%	(sqrt.f64 (/.f64 #s(literal 2 binary64) (/.f64 (/.f64 (/.f64 #s(literal 1 binary64) n) (PI.f64)) (/.f64 #s(literal 1 binary64) k))))
	37.2%	(sqrt.f64 (/.f64 #s(literal 2 binary64) (/.f64 (/.f64 k (PI.f64)) n)))
	37.2%	(sqrt.f64 (/.f64 #s(literal 2 binary64) (/.f64 (/.f64 k n) (PI.f64))))
	37.2%	(sqrt.f64 (/.f64 #s(literal 2 binary64) (/.f64 (/.f64 #s(literal 1 binary64) (/.f64 #s(literal -1 binary64) k)) (-.f64 #s(literal 0 binary64) (*.f64 (PI.f64) n)))))
	37.2%	(sqrt.f64 (/.f64 #s(literal 2 binary64) (/.f64 (/.f64 #s(literal 1 binary64) (PI.f64)) (/.f64 n k))))
▶	37.1%	(sqrt.f64 (/.f64 #s(literal 2 binary64) (/.f64 (/.f64 #s(literal 1 binary64) n) (/.f64 (PI.f64) k))))
	37.2%	(sqrt.f64 (/.f64 #s(literal 2 binary64) (/.f64 (/.f64 #s(literal -1 binary64) (*.f64 (PI.f64) n)) (/.f64 #s(literal -1 binary64) k))))
✓	37.2%	(sqrt.f64 (/.f64 #s(literal 2 binary64) (/.f64 k (*.f64 (PI.f64) n))))
	37.2%	(sqrt.f64 (*.f64 (/.f64 (PI.f64) k) (/.f64 n #s(literal 1/2 binary64))))
	37.1%	(sqrt.f64 (*.f64 (/.f64 #s(literal 2 binary64) (/.f64 k (PI.f64))) n))
	37.2%	(sqrt.f64 (.f64 (/.f64 #s(literal 2 binary64) k) (.f64 (PI.f64) n)))
▶	91.8%	(sqrt.f64 (.f64 (.f64 (.f64 #s(literal 2 binary64) (pow.f64 (/.f64 #s(literal 1/2 binary64) (.f64 (PI.f64) n)) k)) (/.f64 (PI.f64) k)) n))
	37.2%	(sqrt.f64 (.f64 (.f64 #s(literal 2 binary64) (PI.f64)) (/.f64 n k)))
▶	37.2%	(sqrt.f64 (.f64 (PI.f64) (.f64 n (/.f64 #s(literal 2 binary64) k))))
▶	34.9%	(exp.f64 (.f64 (log.f64 (/.f64 #s(literal 2 binary64) (/.f64 k (.f64 (PI.f64) n)))) #s(literal 1/2 binary64)))

Compiler

Compiled 1046 to 834 computations (20.3% saved)

simplify29.0ms (0.2%)

Algorithm

1×	egg-herbie

Localize:

Found 20 expressions of interest:

New	Metric	Score	Program
✓	cost-diff	0	(/.f64 #s(literal 2 binary64) (/.f64 k (*.f64 (PI.f64) n)))
✓	cost-diff	0	(log.f64 (/.f64 #s(literal 2 binary64) (/.f64 k (*.f64 (PI.f64) n))))
✓	cost-diff	0	(.f64 (log.f64 (/.f64 #s(literal 2 binary64) (/.f64 k (.f64 (PI.f64) n)))) #s(literal 1/2 binary64))
✓	cost-diff	6528	(exp.f64 (.f64 (log.f64 (/.f64 #s(literal 2 binary64) (/.f64 k (.f64 (PI.f64) n)))) #s(literal 1/2 binary64)))
✓	cost-diff	0	(/.f64 n k)
✓	cost-diff	0	(*.f64 (/.f64 n k) (PI.f64))
✓	cost-diff	0	(sqrt.f64 (*.f64 (/.f64 n k) (PI.f64)))
✓	cost-diff	0	(.f64 (sqrt.f64 (.f64 (/.f64 n k) (PI.f64))) (sqrt.f64 #s(literal 2 binary64)))
✓	cost-diff	0	(/.f64 #s(literal 1 binary64) n)
✓	cost-diff	128	(/.f64 (/.f64 #s(literal 1 binary64) n) (/.f64 (PI.f64) k))
✓	cost-diff	128	(/.f64 #s(literal 2 binary64) (/.f64 (/.f64 #s(literal 1 binary64) n) (/.f64 (PI.f64) k)))
✓	cost-diff	128	(sqrt.f64 (/.f64 #s(literal 2 binary64) (/.f64 (/.f64 #s(literal 1 binary64) n) (/.f64 (PI.f64) k))))
✓	cost-diff	0	(*.f64 n (/.f64 #s(literal 2 binary64) k))
✓	cost-diff	0	(PI.f64)
✓	cost-diff	0	(.f64 (PI.f64) (.f64 n (/.f64 #s(literal 2 binary64) k)))
✓	cost-diff	0	(sqrt.f64 (.f64 (PI.f64) (.f64 n (/.f64 #s(literal 2 binary64) k))))
✓	cost-diff	0	(.f64 #s(literal 2 binary64) (pow.f64 (/.f64 #s(literal 1/2 binary64) (.f64 (PI.f64) n)) k))
✓	cost-diff	0	(.f64 (.f64 #s(literal 2 binary64) (pow.f64 (/.f64 #s(literal 1/2 binary64) (*.f64 (PI.f64) n)) k)) (/.f64 (PI.f64) k))
✓	cost-diff	0	(.f64 (.f64 (.f64 #s(literal 2 binary64) (pow.f64 (/.f64 #s(literal 1/2 binary64) (.f64 (PI.f64) n)) k)) (/.f64 (PI.f64) k)) n)
✓	cost-diff	0	(sqrt.f64 (.f64 (.f64 (.f64 #s(literal 2 binary64) (pow.f64 (/.f64 #s(literal 1/2 binary64) (.f64 (PI.f64) n)) k)) (/.f64 (PI.f64) k)) n))

Rules

558×	`times-frac`
392×	`-lowering-.f32`
392×	`-lowering-.f64`
282×	`associate-r`
230×	`/-lowering-/.f32`

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	32	210
1	68	210
2	144	210
3	269	208
4	432	208
5	754	208
6	1025	208
7	1034	208
8	1047	208
9	1054	208
0	1054	208

Stop Event

1×	iter limit
1×	saturated

Calls

Call 1

Inputs
(sqrt (* (* (* 2 (pow (/ 1/2 (* (PI) n)) k)) (/ (PI) k)) n))
(* (* (* 2 (pow (/ 1/2 (* (PI) n)) k)) (/ (PI) k)) n)
(* (* 2 (pow (/ 1/2 (* (PI) n)) k)) (/ (PI) k))
(* 2 (pow (/ 1/2 (* (PI) n)) k))
2
(pow (/ 1/2 (* (PI) n)) k)
(/ 1/2 (* (PI) n))
1/2
(* (PI) n)
(PI)
n
k
(/ (PI) k)
(sqrt (* (PI) (* n (/ 2 k))))
(* (PI) (* n (/ 2 k)))
(PI)
(* n (/ 2 k))
n
(/ 2 k)
2
k
(sqrt (/ 2 (/ (/ 1 n) (/ (PI) k))))
(/ 2 (/ (/ 1 n) (/ (PI) k)))
2
(/ (/ 1 n) (/ (PI) k))
(/ 1 n)
1
n
(/ (PI) k)
(PI)
k
(* (sqrt (* (/ n k) (PI))) (sqrt 2))
(sqrt (* (/ n k) (PI)))
(* (/ n k) (PI))
(/ n k)
n
k
(PI)
(sqrt 2)
2
(exp (* (log (/ 2 (/ k (* (PI) n)))) 1/2))
(* (log (/ 2 (/ k (* (PI) n)))) 1/2)
(log (/ 2 (/ k (* (PI) n))))
(/ 2 (/ k (* (PI) n)))
2
(/ k (* (PI) n))
k
(* (PI) n)
(PI)
n
1/2

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

localize179.0ms (1.3%)

Localize:

Found 20 expressions of interest:

New	Metric	Score	Program
✓	accuracy	99.7%	(*.f64 (PI.f64) n)
✓	accuracy	98.8%	(/.f64 #s(literal 2 binary64) (/.f64 k (*.f64 (PI.f64) n)))
✓	accuracy	92.5%	(exp.f64 (.f64 (log.f64 (/.f64 #s(literal 2 binary64) (/.f64 k (.f64 (PI.f64) n)))) #s(literal 1/2 binary64)))
✓	accuracy	82.7%	(log.f64 (/.f64 #s(literal 2 binary64) (/.f64 k (*.f64 (PI.f64) n))))
✓	accuracy	100.0%	(PI.f64)
✓	accuracy	99.6%	(*.f64 (/.f64 n k) (PI.f64))
✓	accuracy	99.4%	(.f64 (sqrt.f64 (.f64 (/.f64 n k) (PI.f64))) (sqrt.f64 #s(literal 2 binary64)))
✓	accuracy	82.7%	(sqrt.f64 (*.f64 (/.f64 n k) (PI.f64)))
✓	accuracy	99.7%	(/.f64 (PI.f64) k)
✓	accuracy	99.6%	(/.f64 (/.f64 #s(literal 1 binary64) n) (/.f64 (PI.f64) k))
✓	accuracy	98.8%	(/.f64 #s(literal 2 binary64) (/.f64 (/.f64 #s(literal 1 binary64) n) (/.f64 (PI.f64) k)))
✓	accuracy	82.8%	(sqrt.f64 (/.f64 #s(literal 2 binary64) (/.f64 (/.f64 #s(literal 1 binary64) n) (/.f64 (PI.f64) k))))
✓	accuracy	100.0%	(PI.f64)
✓	accuracy	99.7%	(*.f64 n (/.f64 #s(literal 2 binary64) k))
✓	accuracy	99.6%	(.f64 (PI.f64) (.f64 n (/.f64 #s(literal 2 binary64) k)))
✓	accuracy	82.8%	(sqrt.f64 (.f64 (PI.f64) (.f64 n (/.f64 #s(literal 2 binary64) k))))
✓	accuracy	99.7%	(*.f64 (PI.f64) n)
✓	accuracy	99.7%	(/.f64 (PI.f64) k)
✓	accuracy	99.3%	(/.f64 #s(literal 1/2 binary64) (*.f64 (PI.f64) n))
✓	accuracy	91.9%	(sqrt.f64 (.f64 (.f64 (.f64 #s(literal 2 binary64) (pow.f64 (/.f64 #s(literal 1/2 binary64) (.f64 (PI.f64) n)) k)) (/.f64 (PI.f64) k)) n))

Results

128.0ms

256×

valid

Compiler

Compiled 221 to 33 computations (85.1% saved)

Precisions

Click to see histograms. Total time spent on operations: 85.0ms

ival-sqrt: 33.0ms (38.9% of total)

ival-div: 17.0ms (20% of total)

ival-mult: 16.0ms (18.9% of total)

ival-pow: 9.0ms (10.6% of total)

ival-log: 4.0ms (4.7% of total)

ival-exp: 3.0ms (3.5% of total)

ival-pi: 1.0ms (1.2% of total)

const: 1.0ms (1.2% of total)

backward-pass: 0.0ms (0% of total)

series311.0ms (2.3%)

Counts

23 → 480

Calls

Call 1

Inputs
#<alt (sqrt (* (* (* 2 (pow (/ 1/2 (* (PI) n)) k)) (/ (PI) k)) n))>
#<alt (* (* (* 2 (pow (/ 1/2 (* (PI) n)) k)) (/ (PI) k)) n)>
#<alt (* (* 2 (pow (/ 1/2 (* (PI) n)) k)) (/ (PI) k))>
#<alt (* 2 (pow (/ 1/2 (* (PI) n)) k))>
#<alt (sqrt (* (PI) (* n (/ 2 k))))>
#<alt (* (PI) (* n (/ 2 k)))>
#<alt (PI)>
#<alt (* n (/ 2 k))>
#<alt (sqrt (/ 2 (/ (/ 1 n) (/ (PI) k))))>
#<alt (/ 2 (/ (/ 1 n) (/ (PI) k)))>
#<alt (/ (/ 1 n) (/ (PI) k))>
#<alt (/ 1 n)>
#<alt (* (sqrt (* (/ n k) (PI))) (sqrt 2))>
#<alt (sqrt (* (/ n k) (PI)))>
#<alt (* (/ n k) (PI))>
#<alt (/ n k)>
#<alt (exp (* (log (/ 2 (/ k (* (PI) n)))) 1/2))>
#<alt (* (log (/ 2 (/ k (* (PI) n)))) 1/2)>
#<alt (log (/ 2 (/ k (* (PI) n))))>
#<alt (/ 2 (/ k (* (PI) n)))>
#<alt (/ 1/2 (* (PI) n))>
#<alt (/ (PI) k)>
#<alt (* (PI) n)>

Outputs
#<alt (* (sqrt (/ (* n (* (PI) (exp (* k (+ (log (/ 1/2 (PI))) (* -1 (log n))))))) k)) (sqrt 2))>
#<alt (* (sqrt (/ (* n (* (PI) (exp (* k (+ (log (/ 1/2 (PI))) (* -1 (log n))))))) k)) (sqrt 2))>
#<alt (* (sqrt (/ (* n (* (PI) (exp (* k (+ (log (/ 1/2 (PI))) (* -1 (log n))))))) k)) (sqrt 2))>
#<alt (* (sqrt (/ (* n (* (PI) (exp (* k (+ (log (/ 1/2 (PI))) (* -1 (log n))))))) k)) (sqrt 2))>
#<alt (* (sqrt (/ (* n (* (PI) (exp (* k (+ (log (/ 1/2 (PI))) (log (/ 1 n))))))) k)) (sqrt 2))>
#<alt (* (sqrt (/ (* n (* (PI) (exp (* k (+ (log (/ 1/2 (PI))) (log (/ 1 n))))))) k)) (sqrt 2))>
#<alt (* (sqrt (/ (* n (* (PI) (exp (* k (+ (log (/ 1/2 (PI))) (log (/ 1 n))))))) k)) (sqrt 2))>
#<alt (* (sqrt (/ (* n (* (PI) (exp (* k (+ (log (/ 1/2 (PI))) (log (/ 1 n))))))) k)) (sqrt 2))>
#<alt (* -1 (* (sqrt (/ (* n (* (PI) (exp (* k (+ (log (/ -1 n)) (log (/ -1/2 (PI)))))))) k)) (* (sqrt -2) (sqrt -1))))>
#<alt (* -1 (* (sqrt (/ (* n (* (PI) (exp (* k (+ (log (/ -1 n)) (log (/ -1/2 (PI)))))))) k)) (* (sqrt -2) (sqrt -1))))>
#<alt (* -1 (* (sqrt (/ (* n (* (PI) (exp (* k (+ (log (/ -1 n)) (log (/ -1/2 (PI)))))))) k)) (* (sqrt -2) (sqrt -1))))>
#<alt (* -1 (* (sqrt (/ (* n (* (PI) (exp (* k (+ (log (/ -1 n)) (log (/ -1/2 (PI)))))))) k)) (* (sqrt -2) (sqrt -1))))>
#<alt (* (sqrt (/ (* n (PI)) k)) (sqrt 2))>
#<alt (/ (+ (* 1/2 (* (sqrt (* (pow k 3) (* n (PI)))) (* (log (/ 1/2 (* n (PI)))) (sqrt 2)))) (* (sqrt (* k (* n (PI)))) (sqrt 2))) k)>
#<alt (/ (+ (* (sqrt (* k (* n (PI)))) (sqrt 2)) (* (pow k 2) (+ (* 1/4 (* (sqrt (* k (* n (PI)))) (* (pow (log (/ 1/2 (* n (PI)))) 2) (sqrt 2)))) (* 1/2 (* (sqrt (/ (* n (PI)) k)) (* (log (/ 1/2 (* n (PI)))) (sqrt 2))))))) k)>
#<alt (/ (+ (* (sqrt (* k (* n (PI)))) (sqrt 2)) (* (pow k 2) (+ (* 1/2 (* (sqrt (/ (* n (PI)) k)) (* (log (/ 1/2 (* n (PI)))) (sqrt 2)))) (* k (+ (* 1/4 (* (sqrt (/ (* n (PI)) k)) (* (pow (log (/ 1/2 (* n (PI)))) 2) (sqrt 2)))) (* 1/2 (* (sqrt (/ k (* n (PI)))) (* (sqrt 2) (- (* 1/6 (* n (* (PI) (pow (log (/ 1/2 (* n (PI)))) 3)))) (* 1/4 (/ (* n (* (PI) (pow (log (/ 1/2 (* n (PI)))) 2))) k))))))))))) k)>
#<alt (* (sqrt (/ (* n (* (PI) (pow (/ 1/2 (* n (PI))) k))) k)) (sqrt 2))>
#<alt (* (sqrt (/ (* n (* (PI) (pow (/ 1/2 (* n (PI))) k))) k)) (sqrt 2))>
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#<alt (* 1/2 (+ (log (* -2 (/ (PI) k))) (* -1 (log (/ -1 n)))))>
#<alt (* 1/2 (+ (log (* -2 (/ (PI) k))) (* -1 (log (/ -1 n)))))>
#<alt (* 1/2 (+ (log (* -2 (/ (PI) k))) (* -1 (log (/ -1 n)))))>
#<alt (* 1/2 (+ (log (* -2 (/ (PI) k))) (* -1 (log (/ -1 n)))))>
#<alt (+ (log (* 2 (* n (PI)))) (* -1 (log k)))>
#<alt (+ (log (* 2 (* n (PI)))) (* -1 (log k)))>
#<alt (+ (log (* 2 (* n (PI)))) (* -1 (log k)))>
#<alt (+ (log (* 2 (* n (PI)))) (* -1 (log k)))>
#<alt (+ (log (* 2 (* n (PI)))) (log (/ 1 k)))>
#<alt (+ (log (* 2 (* n (PI)))) (log (/ 1 k)))>
#<alt (+ (log (* 2 (* n (PI)))) (log (/ 1 k)))>
#<alt (+ (log (* 2 (* n (PI)))) (log (/ 1 k)))>
#<alt (+ (log (* -2 (* n (PI)))) (log (/ -1 k)))>
#<alt (+ (log (* -2 (* n (PI)))) (log (/ -1 k)))>
#<alt (+ (log (* -2 (* n (PI)))) (log (/ -1 k)))>
#<alt (+ (log (* -2 (* n (PI)))) (log (/ -1 k)))>
#<alt (+ (log n) (log (* 2 (/ (PI) k))))>
#<alt (+ (log n) (log (* 2 (/ (PI) k))))>
#<alt (+ (log n) (log (* 2 (/ (PI) k))))>
#<alt (+ (log n) (log (* 2 (/ (PI) k))))>
#<alt (+ (log (* 2 (/ (PI) k))) (* -1 (log (/ 1 n))))>
#<alt (+ (log (* 2 (/ (PI) k))) (* -1 (log (/ 1 n))))>
#<alt (+ (log (* 2 (/ (PI) k))) (* -1 (log (/ 1 n))))>
#<alt (+ (log (* 2 (/ (PI) k))) (* -1 (log (/ 1 n))))>
#<alt (+ (log (* -2 (/ (PI) k))) (* -1 (log (/ -1 n))))>
#<alt (+ (log (* -2 (/ (PI) k))) (* -1 (log (/ -1 n))))>
#<alt (+ (log (* -2 (/ (PI) k))) (* -1 (log (/ -1 n))))>
#<alt (+ (log (* -2 (/ (PI) k))) (* -1 (log (/ -1 n))))>
#<alt (* 2 (/ (* n (PI)) k))>
#<alt (* 2 (/ (* n (PI)) k))>
#<alt (* 2 (/ (* n (PI)) k))>
#<alt (* 2 (/ (* n (PI)) k))>
#<alt (* 2 (/ (* n (PI)) k))>
#<alt (* 2 (/ (* n (PI)) k))>
#<alt (* 2 (/ (* n (PI)) k))>
#<alt (* 2 (/ (* n (PI)) k))>
#<alt (* 2 (/ (* n (PI)) k))>
#<alt (* 2 (/ (* n (PI)) k))>
#<alt (* 2 (/ (* n (PI)) k))>
#<alt (* 2 (/ (* n (PI)) k))>
#<alt (* 2 (/ (* n (PI)) k))>
#<alt (* 2 (/ (* n (PI)) k))>
#<alt (* 2 (/ (* n (PI)) k))>
#<alt (* 2 (/ (* n (PI)) k))>
#<alt (* 2 (/ (* n (PI)) k))>
#<alt (* 2 (/ (* n (PI)) k))>
#<alt (* 2 (/ (* n (PI)) k))>
#<alt (* 2 (/ (* n (PI)) k))>
#<alt (* 2 (/ (* n (PI)) k))>
#<alt (* 2 (/ (* n (PI)) k))>
#<alt (* 2 (/ (* n (PI)) k))>
#<alt (* 2 (/ (* n (PI)) k))>
#<alt (/ 1/2 (* n (PI)))>
#<alt (/ 1/2 (* n (PI)))>
#<alt (/ 1/2 (* n (PI)))>
#<alt (/ 1/2 (* n (PI)))>
#<alt (/ 1/2 (* n (PI)))>
#<alt (/ 1/2 (* n (PI)))>
#<alt (/ 1/2 (* n (PI)))>
#<alt (/ 1/2 (* n (PI)))>
#<alt (/ 1/2 (* n (PI)))>
#<alt (/ 1/2 (* n (PI)))>
#<alt (/ 1/2 (* n (PI)))>
#<alt (/ 1/2 (* n (PI)))>
#<alt (/ (PI) k)>
#<alt (/ (PI) k)>
#<alt (/ (PI) k)>
#<alt (/ (PI) k)>
#<alt (/ (PI) k)>
#<alt (/ (PI) k)>
#<alt (/ (PI) k)>
#<alt (/ (PI) k)>
#<alt (/ (PI) k)>
#<alt (/ (PI) k)>
#<alt (/ (PI) k)>
#<alt (/ (PI) k)>
#<alt (* n (PI))>
#<alt (* n (PI))>
#<alt (* n (PI))>
#<alt (* n (PI))>
#<alt (* n (PI))>
#<alt (* n (PI))>
#<alt (* n (PI))>
#<alt (* n (PI))>
#<alt (* n (PI))>
#<alt (* n (PI))>
#<alt (* n (PI))>
#<alt (* n (PI))>

Calls

120 calls:

Time	Variable		Point	Expression
105.0ms	k	@	-inf	(* (log (/ 2 (/ k (* (PI) n)))) 1/2)
41.0ms	n	@	-inf	(* (* (* 2 (pow (/ 1/2 (* (PI) n)) k)) (/ (PI) k)) n)
36.0ms	k	@	0	(* (log (/ 2 (/ k (* (PI) n)))) 1/2)
22.0ms	n	@	0	(* (log (/ 2 (/ k (* (PI) n)))) 1/2)
22.0ms	n	@	0	(sqrt (* (* (* 2 (pow (/ 1/2 (* (PI) n)) k)) (/ (PI) k)) n))

rewrite374.0ms (2.8%)

Algorithm

1×	batch-egg-rewrite

Rules

5532×	`-lowering-.f32`
5532×	`-lowering-.f64`
3226×	`/-lowering-/.f32`
3226×	`/-lowering-/.f64`
906×	`associate-r`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	32	163
1	165	162
2	1024	162
0	8460	162

Stop Event

1×	iter limit
1×	node limit

Counts

23 → 1905

Calls

Call 1

Inputs
(sqrt (* (* (* 2 (pow (/ 1/2 (* (PI) n)) k)) (/ (PI) k)) n))
(* (* (* 2 (pow (/ 1/2 (* (PI) n)) k)) (/ (PI) k)) n)
(* (* 2 (pow (/ 1/2 (* (PI) n)) k)) (/ (PI) k))
(* 2 (pow (/ 1/2 (* (PI) n)) k))
(sqrt (* (PI) (* n (/ 2 k))))
(* (PI) (* n (/ 2 k)))
(PI)
(* n (/ 2 k))
(sqrt (/ 2 (/ (/ 1 n) (/ (PI) k))))
(/ 2 (/ (/ 1 n) (/ (PI) k)))
(/ (/ 1 n) (/ (PI) k))
(/ 1 n)
(* (sqrt (* (/ n k) (PI))) (sqrt 2))
(sqrt (* (/ n k) (PI)))
(* (/ n k) (PI))
(/ n k)
(exp (* (log (/ 2 (/ k (* (PI) n)))) 1/2))
(* (log (/ 2 (/ k (* (PI) n)))) 1/2)
(log (/ 2 (/ k (* (PI) n))))
(/ 2 (/ k (* (PI) n)))
(/ 1/2 (* (PI) n))
(/ (PI) k)
(* (PI) n)

Outputs
(exp.f64 (.f64 (log.f64 (.f64 n (/.f64 (.f64 #s(literal 2 binary64) (.f64 (pow.f64 (/.f64 #s(literal 1/2 binary64) (*.f64 (PI.f64) n)) k) (PI.f64))) k))) #s(literal 1/2 binary64)))
(sqrt.f64 (.f64 n (/.f64 (.f64 #s(literal 2 binary64) (.f64 (pow.f64 (/.f64 #s(literal 1/2 binary64) (.f64 (PI.f64) n)) k) (PI.f64))) k)))
(/.f64 (sqrt.f64 (.f64 #s(literal 2 binary64) (.f64 (.f64 (pow.f64 (/.f64 #s(literal 1/2 binary64) (.f64 (PI.f64) n)) k) (PI.f64)) n))) (sqrt.f64 k))
(/.f64 (.f64 (sqrt.f64 n) (pow.f64 (.f64 #s(literal 2 binary64) (.f64 (pow.f64 (/.f64 #s(literal 1/2 binary64) (.f64 (PI.f64) n)) k) (PI.f64))) #s(literal 1/2 binary64))) (sqrt.f64 k))
(/.f64 (.f64 (sqrt.f64 (.f64 #s(literal 2 binary64) (pow.f64 (/.f64 #s(literal 1/2 binary64) (.f64 (PI.f64) n)) k))) (pow.f64 (.f64 (PI.f64) n) #s(literal 1/2 binary64))) (sqrt.f64 k))
(/.f64 (.f64 (pow.f64 (.f64 #s(literal 2 binary64) (.f64 (pow.f64 (/.f64 #s(literal 1/2 binary64) (.f64 (PI.f64) n)) k) (PI.f64))) #s(literal 1/2 binary64)) (sqrt.f64 n)) (sqrt.f64 k))
(pow.f64 (.f64 n (/.f64 (.f64 #s(literal 2 binary64) (.f64 (pow.f64 (/.f64 #s(literal 1/2 binary64) (.f64 (PI.f64) n)) k) (PI.f64))) k)) #s(literal 1/2 binary64))
(pow.f64 (pow.f64 (.f64 n (/.f64 (.f64 #s(literal 2 binary64) (.f64 (pow.f64 (/.f64 #s(literal 1/2 binary64) (.f64 (PI.f64) n)) k) (PI.f64))) k)) #s(literal 1/4 binary64)) #s(literal 2 binary64))
(pow.f64 (.f64 (.f64 n (/.f64 (.f64 #s(literal 2 binary64) (.f64 (pow.f64 (/.f64 #s(literal 1/2 binary64) (.f64 (PI.f64) n)) k) (PI.f64))) k)) (.f64 n (/.f64 (.f64 #s(literal 2 binary64) (.f64 (pow.f64 (/.f64 #s(literal 1/2 binary64) (*.f64 (PI.f64) n)) k) (PI.f64))) k))) #s(literal 1/4 binary64))
(pow.f64 (exp.f64 (log.f64 (.f64 n (/.f64 (.f64 #s(literal 2 binary64) (.f64 (pow.f64 (/.f64 #s(literal 1/2 binary64) (.f64 (PI.f64) n)) k) (PI.f64))) k)))) #s(literal 1/2 binary64))
(.f64 (sqrt.f64 (/.f64 (.f64 (PI.f64) n) k)) (sqrt.f64 (.f64 #s(literal 2 binary64) (pow.f64 (/.f64 #s(literal 1/2 binary64) (.f64 (PI.f64) n)) k))))
(.f64 (sqrt.f64 #s(literal 2 binary64)) (pow.f64 (/.f64 (.f64 (.f64 (pow.f64 (/.f64 #s(literal 1/2 binary64) (.f64 (PI.f64) n)) k) (PI.f64)) n) k) #s(literal 1/2 binary64)))
(.f64 (sqrt.f64 #s(literal 2 binary64)) (sqrt.f64 (/.f64 (.f64 (.f64 (pow.f64 (/.f64 #s(literal 1/2 binary64) (.f64 (PI.f64) n)) k) (PI.f64)) n) k)))
(.f64 (sqrt.f64 #s(literal 2 binary64)) (.f64 (sqrt.f64 (/.f64 (.f64 (pow.f64 (/.f64 #s(literal 1/2 binary64) (.f64 (PI.f64) n)) k) (PI.f64)) k)) (sqrt.f64 n)))
(.f64 (pow.f64 (/.f64 #s(literal 1/2 binary64) (.f64 (PI.f64) n)) (/.f64 k #s(literal 2 binary64))) (pow.f64 (/.f64 #s(literal 2 binary64) (/.f64 k (*.f64 (PI.f64) n))) #s(literal 1/2 binary64)))
(.f64 (pow.f64 (/.f64 n #s(literal 1/2 binary64)) #s(literal 1/2 binary64)) (sqrt.f64 (/.f64 (.f64 (pow.f64 (/.f64 #s(literal 1/2 binary64) (*.f64 (PI.f64) n)) k) (PI.f64)) k)))
(.f64 (sqrt.f64 (/.f64 (PI.f64) k)) (pow.f64 (.f64 #s(literal 2 binary64) (.f64 (pow.f64 (/.f64 #s(literal 1/2 binary64) (.f64 (PI.f64) n)) k) n)) #s(literal 1/2 binary64)))
(.f64 (sqrt.f64 (/.f64 (PI.f64) k)) (sqrt.f64 (.f64 #s(literal 2 binary64) (.f64 (pow.f64 (/.f64 #s(literal 1/2 binary64) (.f64 (PI.f64) n)) k) n))))
(.f64 (sqrt.f64 (/.f64 (PI.f64) k)) (.f64 (sqrt.f64 (.f64 #s(literal 2 binary64) (pow.f64 (/.f64 #s(literal 1/2 binary64) (.f64 (PI.f64) n)) k))) (sqrt.f64 n)))
(.f64 (sqrt.f64 n) (pow.f64 (/.f64 (.f64 #s(literal 2 binary64) (.f64 (pow.f64 (/.f64 #s(literal 1/2 binary64) (.f64 (PI.f64) n)) k) (PI.f64))) k) #s(literal 1/2 binary64)))
(.f64 (pow.f64 (/.f64 (.f64 #s(literal 2 binary64) (.f64 (pow.f64 (/.f64 #s(literal 1/2 binary64) (.f64 (PI.f64) n)) k) (PI.f64))) k) #s(literal 1/2 binary64)) (sqrt.f64 n))
(.f64 (sqrt.f64 (.f64 #s(literal 2 binary64) (pow.f64 (/.f64 #s(literal 1/2 binary64) (.f64 (PI.f64) n)) k))) (sqrt.f64 (/.f64 (.f64 (PI.f64) n) k)))
(.f64 (pow.f64 (.f64 #s(literal 2 binary64) (.f64 (pow.f64 (/.f64 #s(literal 1/2 binary64) (.f64 (PI.f64) n)) k) (PI.f64))) #s(literal 1/2 binary64)) (pow.f64 (/.f64 n k) #s(literal 1/2 binary64)))
(.f64 (pow.f64 (.f64 n (/.f64 (.f64 #s(literal 2 binary64) (.f64 (pow.f64 (/.f64 #s(literal 1/2 binary64) (.f64 (PI.f64) n)) k) (PI.f64))) k)) #s(literal 1/4 binary64)) (pow.f64 (.f64 n (/.f64 (.f64 #s(literal 2 binary64) (.f64 (pow.f64 (/.f64 #s(literal 1/2 binary64) (*.f64 (PI.f64) n)) k) (PI.f64))) k)) #s(literal 1/4 binary64)))
(.f64 (pow.f64 (.f64 #s(literal 2 binary64) (.f64 (pow.f64 (/.f64 #s(literal 1/2 binary64) (.f64 (PI.f64) n)) k) n)) #s(literal 1/2 binary64)) (sqrt.f64 (/.f64 (PI.f64) k)))
(.f64 (sqrt.f64 (pow.f64 (/.f64 #s(literal 1/2 binary64) (.f64 (PI.f64) n)) k)) (pow.f64 (/.f64 #s(literal 2 binary64) (/.f64 k (*.f64 (PI.f64) n))) #s(literal 1/2 binary64)))
(.f64 (sqrt.f64 (.f64 #s(literal 2 binary64) (.f64 (pow.f64 (/.f64 #s(literal 1/2 binary64) (.f64 (PI.f64) n)) k) n))) (sqrt.f64 (/.f64 (PI.f64) k)))
(.f64 (.f64 (sqrt.f64 n) (sqrt.f64 (.f64 #s(literal 2 binary64) (pow.f64 (/.f64 #s(literal 1/2 binary64) (.f64 (PI.f64) n)) k)))) (sqrt.f64 (/.f64 (PI.f64) k)))
(.f64 (.f64 (sqrt.f64 (.f64 #s(literal 2 binary64) (pow.f64 (/.f64 #s(literal 1/2 binary64) (.f64 (PI.f64) n)) k))) (pow.f64 (/.f64 n k) #s(literal 1/2 binary64))) (sqrt.f64 (PI.f64)))
(.f64 (.f64 (sqrt.f64 (.f64 #s(literal 2 binary64) (pow.f64 (/.f64 #s(literal 1/2 binary64) (.f64 (PI.f64) n)) k))) (pow.f64 (/.f64 k (.f64 (PI.f64) n)) #s(literal -1/4 binary64))) (pow.f64 (/.f64 k (.f64 (PI.f64) n)) #s(literal -1/4 binary64)))
(exp.f64 (+.f64 (.f64 k (log.f64 (/.f64 #s(literal 1/2 binary64) (.f64 (PI.f64) n)))) (log.f64 (/.f64 #s(literal 2 binary64) (/.f64 k (*.f64 (PI.f64) n))))))
(neg.f64 (.f64 (/.f64 (PI.f64) (-.f64 #s(literal 0 binary64) k)) (.f64 #s(literal 2 binary64) (.f64 (pow.f64 (/.f64 #s(literal 1/2 binary64) (.f64 (PI.f64) n)) k) n))))
(neg.f64 (.f64 (pow.f64 (/.f64 #s(literal 1/2 binary64) (.f64 (PI.f64) n)) k) (/.f64 #s(literal -2 binary64) (/.f64 k (*.f64 (PI.f64) n)))))
(neg.f64 (.f64 (.f64 #s(literal 2 binary64) (.f64 (pow.f64 (/.f64 #s(literal 1/2 binary64) (.f64 (PI.f64) n)) k) n)) (/.f64 (PI.f64) (-.f64 #s(literal 0 binary64) k))))
(/.f64 n (/.f64 k (.f64 #s(literal 2 binary64) (.f64 (pow.f64 (/.f64 #s(literal 1/2 binary64) (*.f64 (PI.f64) n)) k) (PI.f64)))))
(/.f64 n (.f64 #s(literal 1 binary64) (/.f64 k (.f64 #s(literal 2 binary64) (.f64 (pow.f64 (/.f64 #s(literal 1/2 binary64) (.f64 (PI.f64) n)) k) (PI.f64))))))
(/.f64 n (.f64 (/.f64 k (.f64 #s(literal 2 binary64) (.f64 (pow.f64 (/.f64 #s(literal 1/2 binary64) (.f64 (PI.f64) n)) k) (PI.f64)))) #s(literal 1 binary64)))
(/.f64 (pow.f64 (/.f64 #s(literal 1/2 binary64) (.f64 (PI.f64) n)) k) (/.f64 #s(literal 1/2 binary64) (/.f64 (.f64 (PI.f64) n) k)))
(/.f64 (.f64 #s(literal 2 binary64) (pow.f64 (/.f64 #s(literal 1/2 binary64) (.f64 (PI.f64) n)) k)) (/.f64 k (*.f64 (PI.f64) n)))
(/.f64 (/.f64 (.f64 #s(literal 2 binary64) (.f64 (pow.f64 (/.f64 #s(literal 1/2 binary64) (*.f64 (PI.f64) n)) k) (PI.f64))) k) (/.f64 #s(literal 1 binary64) n))
(/.f64 (.f64 n (/.f64 (.f64 #s(literal 2 binary64) (.f64 (pow.f64 (/.f64 #s(literal 1/2 binary64) (.f64 (PI.f64) n)) k) (PI.f64))) k)) #s(literal 1 binary64))
(/.f64 #s(literal 1 binary64) (.f64 (/.f64 #s(literal 1 binary64) n) (/.f64 k (.f64 #s(literal 2 binary64) (.f64 (pow.f64 (/.f64 #s(literal 1/2 binary64) (.f64 (PI.f64) n)) k) (PI.f64))))))
(/.f64 #s(literal 1 binary64) (.f64 (/.f64 k (.f64 #s(literal 2 binary64) (.f64 (pow.f64 (/.f64 #s(literal 1/2 binary64) (.f64 (PI.f64) n)) k) (PI.f64)))) (/.f64 #s(literal 1 binary64) n)))
(/.f64 #s(literal 1 binary64) (/.f64 k (.f64 #s(literal 2 binary64) (.f64 (.f64 (pow.f64 (/.f64 #s(literal 1/2 binary64) (.f64 (PI.f64) n)) k) (PI.f64)) n))))
(/.f64 (-.f64 #s(literal 0 binary64) n) (.f64 #s(literal -1 binary64) (/.f64 k (.f64 #s(literal 2 binary64) (.f64 (pow.f64 (/.f64 #s(literal 1/2 binary64) (.f64 (PI.f64) n)) k) (PI.f64))))))
(/.f64 (-.f64 #s(literal 0 binary64) n) (.f64 (/.f64 k (.f64 #s(literal 2 binary64) (.f64 (pow.f64 (/.f64 #s(literal 1/2 binary64) (.f64 (PI.f64) n)) k) (PI.f64)))) #s(literal -1 binary64)))
(/.f64 (/.f64 (.f64 (pow.f64 (/.f64 #s(literal 1/2 binary64) (.f64 (PI.f64) n)) k) (PI.f64)) k) (/.f64 #s(literal 1/2 binary64) n))
(/.f64 (.f64 #s(literal 2 binary64) (.f64 (pow.f64 (/.f64 #s(literal 1/2 binary64) (*.f64 (PI.f64) n)) k) (PI.f64))) (/.f64 k n))
(/.f64 (.f64 #s(literal -2 binary64) (.f64 (pow.f64 (/.f64 #s(literal 1/2 binary64) (*.f64 (PI.f64) n)) k) (PI.f64))) (-.f64 #s(literal 0 binary64) (/.f64 k n)))
(/.f64 (.f64 (/.f64 #s(literal 2 binary64) k) (pow.f64 (/.f64 #s(literal 1/2 binary64) (.f64 (PI.f64) n)) k)) (/.f64 (/.f64 #s(literal 1 binary64) (PI.f64)) n))
(/.f64 (.f64 #s(literal 2 binary64) (.f64 (pow.f64 (/.f64 #s(literal 1/2 binary64) (*.f64 (PI.f64) n)) k) n)) (/.f64 k (PI.f64)))
(/.f64 (.f64 #s(literal 2 binary64) (.f64 (.f64 (pow.f64 (/.f64 #s(literal 1/2 binary64) (.f64 (PI.f64) n)) k) (PI.f64)) n)) k)
(/.f64 (.f64 n (.f64 #s(literal -2 binary64) (.f64 (pow.f64 (/.f64 #s(literal 1/2 binary64) (.f64 (PI.f64) n)) k) (PI.f64)))) (-.f64 #s(literal 0 binary64) k))
(/.f64 (.f64 n (.f64 #s(literal -2 binary64) (.f64 (pow.f64 (/.f64 #s(literal 1/2 binary64) (.f64 (PI.f64) n)) k) (PI.f64)))) (*.f64 #s(literal 1 binary64) (-.f64 #s(literal 0 binary64) k)))
(/.f64 (.f64 (-.f64 #s(literal 0 binary64) n) (.f64 #s(literal 2 binary64) (pow.f64 (/.f64 #s(literal 1/2 binary64) (*.f64 (PI.f64) n)) k))) (/.f64 k (-.f64 #s(literal 0 binary64) (PI.f64))))
(/.f64 (.f64 (-.f64 #s(literal 0 binary64) n) (.f64 #s(literal 2 binary64) (.f64 (pow.f64 (/.f64 #s(literal 1/2 binary64) (.f64 (PI.f64) n)) k) (PI.f64)))) (-.f64 #s(literal 0 binary64) k))
(/.f64 (.f64 (-.f64 #s(literal 0 binary64) n) (.f64 #s(literal -2 binary64) (.f64 (pow.f64 (/.f64 #s(literal 1/2 binary64) (.f64 (PI.f64) n)) k) (PI.f64)))) k)
(/.f64 (.f64 (.f64 #s(literal 2 binary64) (pow.f64 (/.f64 #s(literal 1/2 binary64) (.f64 (PI.f64) n)) k)) (-.f64 #s(literal 0 binary64) n)) (.f64 (/.f64 k (PI.f64)) #s(literal -1 binary64)))
(/.f64 (.f64 (.f64 #s(literal 2 binary64) (.f64 (pow.f64 (/.f64 #s(literal 1/2 binary64) (.f64 (PI.f64) n)) k) (PI.f64))) (-.f64 #s(literal 0 binary64) n)) (*.f64 k #s(literal -1 binary64)))
(/.f64 (.f64 (.f64 #s(literal -2 binary64) (.f64 (pow.f64 (/.f64 #s(literal 1/2 binary64) (.f64 (PI.f64) n)) k) (PI.f64))) n) (-.f64 #s(literal 0 binary64) k))
(/.f64 (.f64 (.f64 #s(literal -2 binary64) (.f64 (pow.f64 (/.f64 #s(literal 1/2 binary64) (.f64 (PI.f64) n)) k) (PI.f64))) n) (*.f64 (-.f64 #s(literal 0 binary64) k) #s(literal 1 binary64)))
(/.f64 (.f64 (.f64 #s(literal -2 binary64) (.f64 (pow.f64 (/.f64 #s(literal 1/2 binary64) (.f64 (PI.f64) n)) k) (PI.f64))) #s(literal 1 binary64)) (-.f64 #s(literal 0 binary64) (/.f64 k n)))
(/.f64 (.f64 (.f64 #s(literal -2 binary64) (.f64 (pow.f64 (/.f64 #s(literal 1/2 binary64) (.f64 (PI.f64) n)) k) (PI.f64))) (-.f64 #s(literal 0 binary64) n)) (*.f64 (-.f64 #s(literal 0 binary64) k) #s(literal -1 binary64)))
(/.f64 (.f64 #s(literal 1 binary64) (pow.f64 (/.f64 #s(literal 1/2 binary64) (.f64 (PI.f64) n)) k)) (/.f64 #s(literal 1/2 binary64) (/.f64 (*.f64 (PI.f64) n) k)))
(/.f64 (.f64 #s(literal 1 binary64) (.f64 (pow.f64 (/.f64 #s(literal 1/2 binary64) (.f64 (PI.f64) n)) k) (PI.f64))) (.f64 (/.f64 #s(literal 1/2 binary64) n) k))
(/.f64 (.f64 #s(literal 1 binary64) (neg.f64 (.f64 (pow.f64 (/.f64 #s(literal 1/2 binary64) (.f64 (PI.f64) n)) k) (PI.f64)))) (.f64 (/.f64 #s(literal 1/2 binary64) n) (-.f64 #s(literal 0 binary64) k)))
(/.f64 (.f64 #s(literal -2 binary64) (pow.f64 (/.f64 #s(literal 1/2 binary64) (.f64 (PI.f64) n)) k)) (-.f64 #s(literal 0 binary64) (/.f64 k (*.f64 (PI.f64) n))))
(/.f64 (.f64 #s(literal -2 binary64) (neg.f64 (.f64 (pow.f64 (/.f64 #s(literal 1/2 binary64) (*.f64 (PI.f64) n)) k) (PI.f64)))) (/.f64 k n))
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(.f64 (sqrt.f64 (PI.f64)) (.f64 n (sqrt.f64 (PI.f64))))
(*.f64 (-.f64 #s(literal 0 binary64) n) (-.f64 #s(literal 0 binary64) (PI.f64)))
(*.f64 (-.f64 #s(literal 0 binary64) (PI.f64)) (-.f64 #s(literal 0 binary64) n))
(*.f64 (sqrt.f64 n) (/.f64 (PI.f64) (pow.f64 n #s(literal -1/2 binary64))))
(.f64 (.f64 n (pow.f64 (PI.f64) #s(literal 2/3 binary64))) (cbrt.f64 (PI.f64)))
(.f64 (.f64 n (pow.f64 (PI.f64) #s(literal 2/3 binary64))) (/.f64 (cbrt.f64 (PI.f64)) #s(literal 1 binary64)))
(.f64 (.f64 (cbrt.f64 (PI.f64)) n) (/.f64 (pow.f64 (PI.f64) #s(literal 2/3 binary64)) #s(literal 1 binary64)))
(.f64 (.f64 n (sqrt.f64 (PI.f64))) (sqrt.f64 (PI.f64)))
(.f64 (.f64 n (sqrt.f64 (PI.f64))) (/.f64 (sqrt.f64 (PI.f64)) #s(literal 1 binary64)))
(.f64 (pow.f64 (PI.f64) #s(literal 1/4 binary64)) (.f64 (pow.f64 (PI.f64) #s(literal 1/4 binary64)) (*.f64 n (sqrt.f64 (PI.f64)))))
(.f64 (.f64 n (cbrt.f64 (PI.f64))) (pow.f64 (PI.f64) #s(literal 2/3 binary64)))
(*.f64 (/.f64 (PI.f64) #s(literal -1 binary64)) (-.f64 #s(literal 0 binary64) n))
(*.f64 (/.f64 (PI.f64) (pow.f64 n #s(literal -1/2 binary64))) (sqrt.f64 n))
(.f64 (/.f64 (cbrt.f64 (PI.f64)) #s(literal 1 binary64)) (.f64 n (pow.f64 (PI.f64) #s(literal 2/3 binary64))))
(.f64 (/.f64 (pow.f64 (PI.f64) #s(literal 2/3 binary64)) #s(literal 1 binary64)) (.f64 (cbrt.f64 (PI.f64)) n))
(*.f64 (/.f64 (cbrt.f64 (PI.f64)) #s(literal -1 binary64)) (/.f64 (pow.f64 (PI.f64) #s(literal 2/3 binary64)) (/.f64 #s(literal -1 binary64) n)))
(*.f64 (/.f64 (cbrt.f64 (PI.f64)) (pow.f64 n #s(literal -1/2 binary64))) (/.f64 (pow.f64 (PI.f64) #s(literal 2/3 binary64)) (pow.f64 n #s(literal -1/2 binary64))))
(*.f64 (/.f64 (pow.f64 (PI.f64) #s(literal 2/3 binary64)) (pow.f64 n #s(literal -1/2 binary64))) (/.f64 (cbrt.f64 (PI.f64)) (pow.f64 n #s(literal -1/2 binary64))))
(*.f64 (/.f64 (pow.f64 (PI.f64) #s(literal 2/3 binary64)) #s(literal -1 binary64)) (/.f64 (cbrt.f64 (PI.f64)) (/.f64 #s(literal -1 binary64) n)))
(.f64 (/.f64 (sqrt.f64 (PI.f64)) #s(literal 1 binary64)) (.f64 n (sqrt.f64 (PI.f64))))
(*.f64 (/.f64 (sqrt.f64 (PI.f64)) #s(literal -1 binary64)) (/.f64 (sqrt.f64 (PI.f64)) (/.f64 #s(literal -1 binary64) n)))
(*.f64 (/.f64 (sqrt.f64 (PI.f64)) (pow.f64 n #s(literal -1/2 binary64))) (/.f64 (sqrt.f64 (PI.f64)) (pow.f64 n #s(literal -1/2 binary64))))
(.f64 (.f64 #s(literal 1 binary64) (*.f64 n (pow.f64 (PI.f64) #s(literal 2/3 binary64)))) (cbrt.f64 (PI.f64)))
(.f64 (.f64 (*.f64 n (pow.f64 (PI.f64) #s(literal 2/3 binary64))) #s(literal 1 binary64)) (cbrt.f64 (PI.f64)))
(.f64 (.f64 (*.f64 n (pow.f64 (PI.f64) #s(literal 2/3 binary64))) (pow.f64 (pow.f64 (PI.f64) #s(literal 2/3 binary64)) #s(literal 1/3 binary64))) (pow.f64 (cbrt.f64 (PI.f64)) #s(literal 1/3 binary64)))
(.f64 (.f64 (*.f64 n (pow.f64 (PI.f64) #s(literal 2/3 binary64))) (pow.f64 (sqrt.f64 (PI.f64)) #s(literal 1/3 binary64))) (pow.f64 (sqrt.f64 (PI.f64)) #s(literal 1/3 binary64)))
(.f64 (.f64 (*.f64 n (sqrt.f64 (PI.f64))) (cbrt.f64 (PI.f64))) (pow.f64 (PI.f64) #s(literal 1/6 binary64)))
(.f64 (.f64 (*.f64 n (sqrt.f64 (PI.f64))) (pow.f64 (PI.f64) #s(literal 1/4 binary64))) (pow.f64 (PI.f64) #s(literal 1/4 binary64)))
(.f64 (/.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (.f64 n (sqrt.f64 (PI.f64))))) (sqrt.f64 (PI.f64)))
(.f64 (/.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (.f64 n (pow.f64 (PI.f64) #s(literal 2/3 binary64))))) (cbrt.f64 (PI.f64)))

simplify335.0ms (2.5%)

Algorithm

1×	egg-herbie

Rules

5158×	`-lowering-.f32`
5158×	`-lowering-.f64`
2024×	`+-lowering-+.f64`
2024×	`+-lowering-+.f32`
1560×	`fma-lowering-fma.f32`

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	219	4653
1	626	4533
2	1757	4490
3	3483	4277
4	5642	4277
0	8320	4277

Stop Event

1×	iter limit
1×	node limit

Counts

480 → 480

Calls

Call 1

Inputs
(* (sqrt (/ (* n (* (PI) (exp (* k (+ (log (/ 1/2 (PI))) (* -1 (log n))))))) k)) (sqrt 2))
(* (sqrt (/ (* n (* (PI) (exp (* k (+ (log (/ 1/2 (PI))) (* -1 (log n))))))) k)) (sqrt 2))
(* (sqrt (/ (* n (* (PI) (exp (* k (+ (log (/ 1/2 (PI))) (* -1 (log n))))))) k)) (sqrt 2))
(* (sqrt (/ (* n (* (PI) (exp (* k (+ (log (/ 1/2 (PI))) (* -1 (log n))))))) k)) (sqrt 2))
(* (sqrt (/ (* n (* (PI) (exp (* k (+ (log (/ 1/2 (PI))) (log (/ 1 n))))))) k)) (sqrt 2))
(* (sqrt (/ (* n (* (PI) (exp (* k (+ (log (/ 1/2 (PI))) (log (/ 1 n))))))) k)) (sqrt 2))
(* (sqrt (/ (* n (* (PI) (exp (* k (+ (log (/ 1/2 (PI))) (log (/ 1 n))))))) k)) (sqrt 2))
(* (sqrt (/ (* n (* (PI) (exp (* k (+ (log (/ 1/2 (PI))) (log (/ 1 n))))))) k)) (sqrt 2))
(* -1 (* (sqrt (/ (* n (* (PI) (exp (* k (+ (log (/ -1 n)) (log (/ -1/2 (PI)))))))) k)) (* (sqrt -2) (sqrt -1))))
(* -1 (* (sqrt (/ (* n (* (PI) (exp (* k (+ (log (/ -1 n)) (log (/ -1/2 (PI)))))))) k)) (* (sqrt -2) (sqrt -1))))
(* -1 (* (sqrt (/ (* n (* (PI) (exp (* k (+ (log (/ -1 n)) (log (/ -1/2 (PI)))))))) k)) (* (sqrt -2) (sqrt -1))))
(* -1 (* (sqrt (/ (* n (* (PI) (exp (* k (+ (log (/ -1 n)) (log (/ -1/2 (PI)))))))) k)) (* (sqrt -2) (sqrt -1))))
(* (sqrt (/ (* n (PI)) k)) (sqrt 2))
(/ (+ (* 1/2 (* (sqrt (* (pow k 3) (* n (PI)))) (* (log (/ 1/2 (* n (PI)))) (sqrt 2)))) (* (sqrt (* k (* n (PI)))) (sqrt 2))) k)
(/ (+ (* (sqrt (* k (* n (PI)))) (sqrt 2)) (* (pow k 2) (+ (* 1/4 (* (sqrt (* k (* n (PI)))) (* (pow (log (/ 1/2 (* n (PI)))) 2) (sqrt 2)))) (* 1/2 (* (sqrt (/ (* n (PI)) k)) (* (log (/ 1/2 (* n (PI)))) (sqrt 2))))))) k)
(/ (+ (* (sqrt (* k (* n (PI)))) (sqrt 2)) (* (pow k 2) (+ (* 1/2 (* (sqrt (/ (* n (PI)) k)) (* (log (/ 1/2 (* n (PI)))) (sqrt 2)))) (* k (+ (* 1/4 (* (sqrt (/ (* n (PI)) k)) (* (pow (log (/ 1/2 (* n (PI)))) 2) (sqrt 2)))) (* 1/2 (* (sqrt (/ k (* n (PI)))) (* (sqrt 2) (- (* 1/6 (* n (* (PI) (pow (log (/ 1/2 (* n (PI)))) 3)))) (* 1/4 (/ (* n (* (PI) (pow (log (/ 1/2 (* n (PI)))) 2))) k))))))))))) k)
(* (sqrt (/ (* n (* (PI) (pow (/ 1/2 (* n (PI))) k))) k)) (sqrt 2))
(* (sqrt (/ (* n (* (PI) (pow (/ 1/2 (* n (PI))) k))) k)) (sqrt 2))
(* (sqrt (/ (* n (* (PI) (pow (/ 1/2 (* n (PI))) k))) k)) (sqrt 2))
(* (sqrt (/ (* n (* (PI) (pow (/ 1/2 (* n (PI))) k))) k)) (sqrt 2))
(* (sqrt (/ (* n (* (PI) (pow (/ 1/2 (* n (PI))) k))) k)) (* (sqrt -2) (sqrt -1)))
(* (sqrt (/ (* n (* (PI) (pow (/ 1/2 (* n (PI))) k))) k)) (* (sqrt -2) (sqrt -1)))
(* (sqrt (/ (* n (* (PI) (pow (/ 1/2 (* n (PI))) k))) k)) (* (sqrt -2) (sqrt -1)))
(* (sqrt (/ (* n (* (PI) (pow (/ 1/2 (* n (PI))) k))) k)) (* (sqrt -2) (sqrt -1)))
(* 2 (/ (* n (* (PI) (exp (* k (+ (log (/ 1/2 (PI))) (* -1 (log n))))))) k))
(* 2 (/ (* n (* (PI) (exp (* k (+ (log (/ 1/2 (PI))) (* -1 (log n))))))) k))
(* 2 (/ (* n (* (PI) (exp (* k (+ (log (/ 1/2 (PI))) (* -1 (log n))))))) k))
(* 2 (/ (* n (* (PI) (exp (* k (+ (log (/ 1/2 (PI))) (* -1 (log n))))))) k))
(* 2 (/ (* n (* (PI) (exp (* k (+ (log (/ 1/2 (PI))) (log (/ 1 n))))))) k))
(* 2 (/ (* n (* (PI) (exp (* k (+ (log (/ 1/2 (PI))) (log (/ 1 n))))))) k))
(* 2 (/ (* n (* (PI) (exp (* k (+ (log (/ 1/2 (PI))) (log (/ 1 n))))))) k))
(* 2 (/ (* n (* (PI) (exp (* k (+ (log (/ 1/2 (PI))) (log (/ 1 n))))))) k))
(* 2 (/ (* n (* (PI) (exp (* k (+ (log (/ -1 n)) (log (/ -1/2 (PI)))))))) k))
(* 2 (/ (* n (* (PI) (exp (* k (+ (log (/ -1 n)) (log (/ -1/2 (PI)))))))) k))
(* 2 (/ (* n (* (PI) (exp (* k (+ (log (/ -1 n)) (log (/ -1/2 (PI)))))))) k))
(* 2 (/ (* n (* (PI) (exp (* k (+ (log (/ -1 n)) (log (/ -1/2 (PI)))))))) k))
(* 2 (/ (* n (PI)) k))
(/ (+ (* 2 (* k (* n (* (PI) (log (/ 1/2 (* n (PI)))))))) (* 2 (* n (PI)))) k)
(/ (+ (* 2 (* n (PI))) (* k (+ (* 2 (* n (* (PI) (log (/ 1/2 (* n (PI))))))) (* k (* n (* (PI) (pow (log (/ 1/2 (* n (PI)))) 2))))))) k)
(/ (+ (* 2 (* n (PI))) (* k (+ (* 2 (* n (* (PI) (log (/ 1/2 (* n (PI))))))) (* k (+ (* 1/3 (* k (* n (* (PI) (pow (log (/ 1/2 (* n (PI)))) 3))))) (* n (* (PI) (pow (log (/ 1/2 (* n (PI)))) 2)))))))) k)
(* 2 (/ (* n (* (PI) (pow (/ 1/2 (* n (PI))) k))) k))
(* 2 (/ (* n (* (PI) (pow (/ 1/2 (* n (PI))) k))) k))
(* 2 (/ (* n (* (PI) (pow (/ 1/2 (* n (PI))) k))) k))
(* 2 (/ (* n (* (PI) (pow (/ 1/2 (* n (PI))) k))) k))
(* 2 (/ (* n (* (PI) (pow (/ 1/2 (* n (PI))) k))) k))
(* 2 (/ (* n (* (PI) (pow (/ 1/2 (* n (PI))) k))) k))
(* 2 (/ (* n (* (PI) (pow (/ 1/2 (* n (PI))) k))) k))
(* 2 (/ (* n (* (PI) (pow (/ 1/2 (* n (PI))) k))) k))
(* 2 (/ (* (PI) (exp (* k (+ (log (/ 1/2 (PI))) (* -1 (log n)))))) k))
(* 2 (/ (* (PI) (exp (* k (+ (log (/ 1/2 (PI))) (* -1 (log n)))))) k))
(* 2 (/ (* (PI) (exp (* k (+ (log (/ 1/2 (PI))) (* -1 (log n)))))) k))
(* 2 (/ (* (PI) (exp (* k (+ (log (/ 1/2 (PI))) (* -1 (log n)))))) k))
(* 2 (/ (* (PI) (exp (* k (+ (log (/ 1/2 (PI))) (log (/ 1 n)))))) k))
(* 2 (/ (* (PI) (exp (* k (+ (log (/ 1/2 (PI))) (log (/ 1 n)))))) k))
(* 2 (/ (* (PI) (exp (* k (+ (log (/ 1/2 (PI))) (log (/ 1 n)))))) k))
(* 2 (/ (* (PI) (exp (* k (+ (log (/ 1/2 (PI))) (log (/ 1 n)))))) k))
(* 2 (/ (* (PI) (exp (* k (+ (log (/ -1 n)) (log (/ -1/2 (PI))))))) k))
(* 2 (/ (* (PI) (exp (* k (+ (log (/ -1 n)) (log (/ -1/2 (PI))))))) k))
(* 2 (/ (* (PI) (exp (* k (+ (log (/ -1 n)) (log (/ -1/2 (PI))))))) k))
(* 2 (/ (* (PI) (exp (* k (+ (log (/ -1 n)) (log (/ -1/2 (PI))))))) k))
(* 2 (/ (PI) k))
(/ (+ (* 2 (PI)) (* 2 (* k (* (PI) (log (/ 1/2 (* n (PI)))))))) k)
(/ (+ (* 2 (PI)) (* k (+ (* 2 (* (PI) (log (/ 1/2 (* n (PI)))))) (* k (* (PI) (pow (log (/ 1/2 (* n (PI)))) 2)))))) k)
(/ (+ (* 2 (PI)) (* k (+ (* 2 (* (PI) (log (/ 1/2 (* n (PI)))))) (* k (+ (* 1/3 (* k (* (PI) (pow (log (/ 1/2 (* n (PI)))) 3)))) (* (PI) (pow (log (/ 1/2 (* n (PI)))) 2))))))) k)
(* 2 (/ (* (PI) (pow (/ 1/2 (* n (PI))) k)) k))
(* 2 (/ (* (PI) (pow (/ 1/2 (* n (PI))) k)) k))
(* 2 (/ (* (PI) (pow (/ 1/2 (* n (PI))) k)) k))
(* 2 (/ (* (PI) (pow (/ 1/2 (* n (PI))) k)) k))
(* 2 (/ (* (PI) (pow (/ 1/2 (* n (PI))) k)) k))
(* 2 (/ (* (PI) (pow (/ 1/2 (* n (PI))) k)) k))
(* 2 (/ (* (PI) (pow (/ 1/2 (* n (PI))) k)) k))
(* 2 (/ (* (PI) (pow (/ 1/2 (* n (PI))) k)) k))
(* 2 (exp (* k (+ (log (/ 1/2 (PI))) (* -1 (log n))))))
(* 2 (exp (* k (+ (log (/ 1/2 (PI))) (* -1 (log n))))))
(* 2 (exp (* k (+ (log (/ 1/2 (PI))) (* -1 (log n))))))
(* 2 (exp (* k (+ (log (/ 1/2 (PI))) (* -1 (log n))))))
(* 2 (exp (* k (+ (log (/ 1/2 (PI))) (log (/ 1 n))))))
(* 2 (exp (* k (+ (log (/ 1/2 (PI))) (log (/ 1 n))))))
(* 2 (exp (* k (+ (log (/ 1/2 (PI))) (log (/ 1 n))))))
(* 2 (exp (* k (+ (log (/ 1/2 (PI))) (log (/ 1 n))))))
(* 2 (exp (* k (+ (log (/ -1 n)) (log (/ -1/2 (PI)))))))
(* 2 (exp (* k (+ (log (/ -1 n)) (log (/ -1/2 (PI)))))))
(* 2 (exp (* k (+ (log (/ -1 n)) (log (/ -1/2 (PI)))))))
(* 2 (exp (* k (+ (log (/ -1 n)) (log (/ -1/2 (PI)))))))
2
(+ 2 (* 2 (* k (log (/ 1/2 (* n (PI)))))))
(+ 2 (* k (+ (* 2 (log (/ 1/2 (* n (PI))))) (* k (pow (log (/ 1/2 (* n (PI)))) 2)))))
(+ 2 (* k (+ (* 2 (log (/ 1/2 (* n (PI))))) (* k (+ (* 1/3 (* k (pow (log (/ 1/2 (* n (PI)))) 3))) (pow (log (/ 1/2 (* n (PI)))) 2))))))
(* 2 (pow (/ 1/2 (* n (PI))) k))
(* 2 (pow (/ 1/2 (* n (PI))) k))
(* 2 (pow (/ 1/2 (* n (PI))) k))
(* 2 (pow (/ 1/2 (* n (PI))) k))
(* 2 (pow (/ 1/2 (* n (PI))) k))
(* 2 (pow (/ 1/2 (* n (PI))) k))
(* 2 (pow (/ 1/2 (* n (PI))) k))
(* 2 (pow (/ 1/2 (* n (PI))) k))
(* (sqrt (/ (* n (PI)) k)) (sqrt 2))
(* (sqrt (/ (* n (PI)) k)) (sqrt 2))
(* (sqrt (/ (* n (PI)) k)) (sqrt 2))
(* (sqrt (/ (* n (PI)) k)) (sqrt 2))
(* (sqrt (/ (* n (PI)) k)) (sqrt 2))
(* (sqrt (/ (* n (PI)) k)) (sqrt 2))
(* (sqrt (/ (* n (PI)) k)) (sqrt 2))
(* (sqrt (/ (* n (PI)) k)) (sqrt 2))
(* -1 (* (sqrt (/ (* n (PI)) k)) (* (sqrt -2) (sqrt -1))))
(* -1 (* (sqrt (/ (* n (PI)) k)) (* (sqrt -2) (sqrt -1))))
(* -1 (* (sqrt (/ (* n (PI)) k)) (* (sqrt -2) (sqrt -1))))
(* -1 (* (sqrt (/ (* n (PI)) k)) (* (sqrt -2) (sqrt -1))))
(* (sqrt (/ (* n (PI)) k)) (sqrt 2))
(* (sqrt (/ (* n (PI)) k)) (sqrt 2))
(* (sqrt (/ (* n (PI)) k)) (sqrt 2))
(* (sqrt (/ (* n (PI)) k)) (sqrt 2))
(* (sqrt (/ (* n (PI)) k)) (sqrt 2))
(* (sqrt (/ (* n (PI)) k)) (sqrt 2))
(* (sqrt (/ (* n (PI)) k)) (sqrt 2))
(* (sqrt (/ (* n (PI)) k)) (sqrt 2))
(* (sqrt (/ (* n (PI)) k)) (* (sqrt -2) (sqrt -1)))
(* (sqrt (/ (* n (PI)) k)) (* (sqrt -2) (sqrt -1)))
(* (sqrt (/ (* n (PI)) k)) (* (sqrt -2) (sqrt -1)))
(* (sqrt (/ (* n (PI)) k)) (* (sqrt -2) (sqrt -1)))
(* 2 (/ (* n (PI)) k))
(* 2 (/ (* n (PI)) k))
(* 2 (/ (* n (PI)) k))
(* 2 (/ (* n (PI)) k))
(* 2 (/ (* n (PI)) k))
(* 2 (/ (* n (PI)) k))
(* 2 (/ (* n (PI)) k))
(* 2 (/ (* n (PI)) k))
(* 2 (/ (* n (PI)) k))
(* 2 (/ (* n (PI)) k))
(* 2 (/ (* n (PI)) k))
(* 2 (/ (* n (PI)) k))
(* 2 (/ (* n (PI)) k))
(* 2 (/ (* n (PI)) k))
(* 2 (/ (* n (PI)) k))
(* 2 (/ (* n (PI)) k))
(* 2 (/ (* n (PI)) k))
(* 2 (/ (* n (PI)) k))
(* 2 (/ (* n (PI)) k))
(* 2 (/ (* n (PI)) k))
(* 2 (/ (* n (PI)) k))
(* 2 (/ (* n (PI)) k))
(* 2 (/ (* n (PI)) k))
(* 2 (/ (* n (PI)) k))
(* 2 (/ n k))
(* 2 (/ n k))
(* 2 (/ n k))
(* 2 (/ n k))
(* 2 (/ n k))
(* 2 (/ n k))
(* 2 (/ n k))
(* 2 (/ n k))
(* 2 (/ n k))
(* 2 (/ n k))
(* 2 (/ n k))
(* 2 (/ n k))
(* 2 (/ n k))
(* 2 (/ n k))
(* 2 (/ n k))
(* 2 (/ n k))
(* 2 (/ n k))
(* 2 (/ n k))
(* 2 (/ n k))
(* 2 (/ n k))
(* 2 (/ n k))
(* 2 (/ n k))
(* 2 (/ n k))
(* 2 (/ n k))
(* (sqrt (/ (* n (PI)) k)) (sqrt 2))
(* (sqrt (/ (* n (PI)) k)) (sqrt 2))
(* (sqrt (/ (* n (PI)) k)) (sqrt 2))
(* (sqrt (/ (* n (PI)) k)) (sqrt 2))
(* (sqrt (/ (* n (PI)) k)) (sqrt 2))
(* (sqrt (/ (* n (PI)) k)) (sqrt 2))
(* (sqrt (/ (* n (PI)) k)) (sqrt 2))
(* (sqrt (/ (* n (PI)) k)) (sqrt 2))
(* -1 (* (sqrt (/ (* n (PI)) k)) (* (sqrt -2) (sqrt -1))))
(* -1 (* (sqrt (/ (* n (PI)) k)) (* (sqrt -2) (sqrt -1))))
(* -1 (* (sqrt (/ (* n (PI)) k)) (* (sqrt -2) (sqrt -1))))
(* -1 (* (sqrt (/ (* n (PI)) k)) (* (sqrt -2) (sqrt -1))))
(* (sqrt (/ (* n (PI)) k)) (sqrt 2))
(* (sqrt (/ (* n (PI)) k)) (sqrt 2))
(* (sqrt (/ (* n (PI)) k)) (sqrt 2))
(* (sqrt (/ (* n (PI)) k)) (sqrt 2))
(* (sqrt (/ (* n (PI)) k)) (sqrt 2))
(* (sqrt (/ (* n (PI)) k)) (sqrt 2))
(* (sqrt (/ (* n (PI)) k)) (sqrt 2))
(* (sqrt (/ (* n (PI)) k)) (sqrt 2))
(* (sqrt (/ (* n (PI)) k)) (* (sqrt -2) (sqrt -1)))
(* (sqrt (/ (* n (PI)) k)) (* (sqrt -2) (sqrt -1)))
(* (sqrt (/ (* n (PI)) k)) (* (sqrt -2) (sqrt -1)))
(* (sqrt (/ (* n (PI)) k)) (* (sqrt -2) (sqrt -1)))
(* 2 (/ (* n (PI)) k))
(* 2 (/ (* n (PI)) k))
(* 2 (/ (* n (PI)) k))
(* 2 (/ (* n (PI)) k))
(* 2 (/ (* n (PI)) k))
(* 2 (/ (* n (PI)) k))
(* 2 (/ (* n (PI)) k))
(* 2 (/ (* n (PI)) k))
(* 2 (/ (* n (PI)) k))
(* 2 (/ (* n (PI)) k))
(* 2 (/ (* n (PI)) k))
(* 2 (/ (* n (PI)) k))
(* 2 (/ (* n (PI)) k))
(* 2 (/ (* n (PI)) k))
(* 2 (/ (* n (PI)) k))
(* 2 (/ (* n (PI)) k))
(* 2 (/ (* n (PI)) k))
(* 2 (/ (* n (PI)) k))
(* 2 (/ (* n (PI)) k))
(* 2 (/ (* n (PI)) k))
(* 2 (/ (* n (PI)) k))
(* 2 (/ (* n (PI)) k))
(* 2 (/ (* n (PI)) k))
(* 2 (/ (* n (PI)) k))
(/ k (* n (PI)))
(/ k (* n (PI)))
(/ k (* n (PI)))
(/ k (* n (PI)))
(/ k (* n (PI)))
(/ k (* n (PI)))
(/ k (* n (PI)))
(/ k (* n (PI)))
(/ k (* n (PI)))
(/ k (* n (PI)))
(/ k (* n (PI)))
(/ k (* n (PI)))
(/ k (* n (PI)))
(/ k (* n (PI)))
(/ k (* n (PI)))
(/ k (* n (PI)))
(/ k (* n (PI)))
(/ k (* n (PI)))
(/ k (* n (PI)))
(/ k (* n (PI)))
(/ k (* n (PI)))
(/ k (* n (PI)))
(/ k (* n (PI)))
(/ k (* n (PI)))
(/ 1 n)
(/ 1 n)
(/ 1 n)
(/ 1 n)
(/ 1 n)
(/ 1 n)
(/ 1 n)
(/ 1 n)
(/ 1 n)
(/ 1 n)
(/ 1 n)
(/ 1 n)
(* (sqrt (/ (* n (PI)) k)) (sqrt 2))
(* (sqrt (/ (* n (PI)) k)) (sqrt 2))
(* (sqrt (/ (* n (PI)) k)) (sqrt 2))
(* (sqrt (/ (* n (PI)) k)) (sqrt 2))
(* (sqrt (/ (* n (PI)) k)) (sqrt 2))
(* (sqrt (/ (* n (PI)) k)) (sqrt 2))
(* (sqrt (/ (* n (PI)) k)) (sqrt 2))
(* (sqrt (/ (* n (PI)) k)) (sqrt 2))
(* -1 (* (sqrt (/ (* n (PI)) k)) (* (pow (sqrt -1) 2) (sqrt 2))))
(* -1 (* (sqrt (/ (* n (PI)) k)) (* (pow (sqrt -1) 2) (sqrt 2))))
(* -1 (* (sqrt (/ (* n (PI)) k)) (* (pow (sqrt -1) 2) (sqrt 2))))
(* -1 (* (sqrt (/ (* n (PI)) k)) (* (pow (sqrt -1) 2) (sqrt 2))))
(* (sqrt (/ (* n (PI)) k)) (sqrt 2))
(* (sqrt (/ (* n (PI)) k)) (sqrt 2))
(* (sqrt (/ (* n (PI)) k)) (sqrt 2))
(* (sqrt (/ (* n (PI)) k)) (sqrt 2))
(* (sqrt (/ (* n (PI)) k)) (sqrt 2))
(* (sqrt (/ (* n (PI)) k)) (sqrt 2))
(* (sqrt (/ (* n (PI)) k)) (sqrt 2))
(* (sqrt (/ (* n (PI)) k)) (sqrt 2))
(* (sqrt (/ (* n (PI)) k)) (* (pow (sqrt -1) 2) (sqrt 2)))
(* (sqrt (/ (* n (PI)) k)) (* (pow (sqrt -1) 2) (sqrt 2)))
(* (sqrt (/ (* n (PI)) k)) (* (pow (sqrt -1) 2) (sqrt 2)))
(* (sqrt (/ (* n (PI)) k)) (* (pow (sqrt -1) 2) (sqrt 2)))
(sqrt (/ (* n (PI)) k))
(sqrt (/ (* n (PI)) k))
(sqrt (/ (* n (PI)) k))
(sqrt (/ (* n (PI)) k))
(sqrt (/ (* n (PI)) k))
(sqrt (/ (* n (PI)) k))
(sqrt (/ (* n (PI)) k))
(sqrt (/ (* n (PI)) k))
(* -1 (* (sqrt (/ (* n (PI)) k)) (pow (sqrt -1) 2)))
(* -1 (* (sqrt (/ (* n (PI)) k)) (pow (sqrt -1) 2)))
(* -1 (* (sqrt (/ (* n (PI)) k)) (pow (sqrt -1) 2)))
(* -1 (* (sqrt (/ (* n (PI)) k)) (pow (sqrt -1) 2)))
(sqrt (/ (* n (PI)) k))
(sqrt (/ (* n (PI)) k))
(sqrt (/ (* n (PI)) k))
(sqrt (/ (* n (PI)) k))
(sqrt (/ (* n (PI)) k))
(sqrt (/ (* n (PI)) k))
(sqrt (/ (* n (PI)) k))
(sqrt (/ (* n (PI)) k))
(* (sqrt (/ (* n (PI)) k)) (pow (sqrt -1) 2))
(* (sqrt (/ (* n (PI)) k)) (pow (sqrt -1) 2))
(* (sqrt (/ (* n (PI)) k)) (pow (sqrt -1) 2))
(* (sqrt (/ (* n (PI)) k)) (pow (sqrt -1) 2))
(/ (* n (PI)) k)
(/ (* n (PI)) k)
(/ (* n (PI)) k)
(/ (* n (PI)) k)
(/ (* n (PI)) k)
(/ (* n (PI)) k)
(/ (* n (PI)) k)
(/ (* n (PI)) k)
(/ (* n (PI)) k)
(/ (* n (PI)) k)
(/ (* n (PI)) k)
(/ (* n (PI)) k)
(/ (* n (PI)) k)
(/ (* n (PI)) k)
(/ (* n (PI)) k)
(/ (* n (PI)) k)
(/ (* n (PI)) k)
(/ (* n (PI)) k)
(/ (* n (PI)) k)
(/ (* n (PI)) k)
(/ (* n (PI)) k)
(/ (* n (PI)) k)
(/ (* n (PI)) k)
(/ (* n (PI)) k)
(/ n k)
(/ n k)
(/ n k)
(/ n k)
(/ n k)
(/ n k)
(/ n k)
(/ n k)
(/ n k)
(/ n k)
(/ n k)
(/ n k)
(/ n k)
(/ n k)
(/ n k)
(/ n k)
(/ n k)
(/ n k)
(/ n k)
(/ n k)
(/ n k)
(/ n k)
(/ n k)
(/ n k)
(* (sqrt (/ (* n (PI)) k)) (sqrt 2))
(* (sqrt (/ (* n (PI)) k)) (sqrt 2))
(* (sqrt (/ (* n (PI)) k)) (sqrt 2))
(* (sqrt (/ (* n (PI)) k)) (sqrt 2))
(* (sqrt (/ (* n (PI)) k)) (sqrt 2))
(* (sqrt (/ (* n (PI)) k)) (sqrt 2))
(* (sqrt (/ (* n (PI)) k)) (sqrt 2))
(* (sqrt (/ (* n (PI)) k)) (sqrt 2))
(* (sqrt (/ (* n (PI)) k)) (* (sqrt -2) (sqrt -1)))
(* (sqrt (/ (* n (PI)) k)) (* (sqrt -2) (sqrt -1)))
(* (sqrt (/ (* n (PI)) k)) (* (sqrt -2) (sqrt -1)))
(* (sqrt (/ (* n (PI)) k)) (* (sqrt -2) (sqrt -1)))
(* (sqrt (/ (* n (PI)) k)) (sqrt 2))
(* (sqrt (/ (* n (PI)) k)) (sqrt 2))
(* (sqrt (/ (* n (PI)) k)) (sqrt 2))
(* (sqrt (/ (* n (PI)) k)) (sqrt 2))
(* (sqrt (/ (* n (PI)) k)) (sqrt 2))
(* (sqrt (/ (* n (PI)) k)) (sqrt 2))
(* (sqrt (/ (* n (PI)) k)) (sqrt 2))
(* (sqrt (/ (* n (PI)) k)) (sqrt 2))
(* -1 (* (sqrt (/ (* n (PI)) k)) (* (sqrt -2) (sqrt -1))))
(* -1 (* (sqrt (/ (* n (PI)) k)) (* (sqrt -2) (sqrt -1))))
(* -1 (* (sqrt (/ (* n (PI)) k)) (* (sqrt -2) (sqrt -1))))
(* -1 (* (sqrt (/ (* n (PI)) k)) (* (sqrt -2) (sqrt -1))))
(* 1/2 (+ (log (* 2 (* n (PI)))) (* -1 (log k))))
(* 1/2 (+ (log (* 2 (* n (PI)))) (* -1 (log k))))
(* 1/2 (+ (log (* 2 (* n (PI)))) (* -1 (log k))))
(* 1/2 (+ (log (* 2 (* n (PI)))) (* -1 (log k))))
(* 1/2 (+ (log (* 2 (* n (PI)))) (log (/ 1 k))))
(* 1/2 (+ (log (* 2 (* n (PI)))) (log (/ 1 k))))
(* 1/2 (+ (log (* 2 (* n (PI)))) (log (/ 1 k))))
(* 1/2 (+ (log (* 2 (* n (PI)))) (log (/ 1 k))))
(* 1/2 (+ (log (* -2 (* n (PI)))) (log (/ -1 k))))
(* 1/2 (+ (log (* -2 (* n (PI)))) (log (/ -1 k))))
(* 1/2 (+ (log (* -2 (* n (PI)))) (log (/ -1 k))))
(* 1/2 (+ (log (* -2 (* n (PI)))) (log (/ -1 k))))
(* 1/2 (+ (log n) (log (* 2 (/ (PI) k)))))
(* 1/2 (+ (log n) (log (* 2 (/ (PI) k)))))
(* 1/2 (+ (log n) (log (* 2 (/ (PI) k)))))
(* 1/2 (+ (log n) (log (* 2 (/ (PI) k)))))
(* 1/2 (+ (log (* 2 (/ (PI) k))) (* -1 (log (/ 1 n)))))
(* 1/2 (+ (log (* 2 (/ (PI) k))) (* -1 (log (/ 1 n)))))
(* 1/2 (+ (log (* 2 (/ (PI) k))) (* -1 (log (/ 1 n)))))
(* 1/2 (+ (log (* 2 (/ (PI) k))) (* -1 (log (/ 1 n)))))
(* 1/2 (+ (log (* -2 (/ (PI) k))) (* -1 (log (/ -1 n)))))
(* 1/2 (+ (log (* -2 (/ (PI) k))) (* -1 (log (/ -1 n)))))
(* 1/2 (+ (log (* -2 (/ (PI) k))) (* -1 (log (/ -1 n)))))
(* 1/2 (+ (log (* -2 (/ (PI) k))) (* -1 (log (/ -1 n)))))
(+ (log (* 2 (* n (PI)))) (* -1 (log k)))
(+ (log (* 2 (* n (PI)))) (* -1 (log k)))
(+ (log (* 2 (* n (PI)))) (* -1 (log k)))
(+ (log (* 2 (* n (PI)))) (* -1 (log k)))
(+ (log (* 2 (* n (PI)))) (log (/ 1 k)))
(+ (log (* 2 (* n (PI)))) (log (/ 1 k)))
(+ (log (* 2 (* n (PI)))) (log (/ 1 k)))
(+ (log (* 2 (* n (PI)))) (log (/ 1 k)))
(+ (log (* -2 (* n (PI)))) (log (/ -1 k)))
(+ (log (* -2 (* n (PI)))) (log (/ -1 k)))
(+ (log (* -2 (* n (PI)))) (log (/ -1 k)))
(+ (log (* -2 (* n (PI)))) (log (/ -1 k)))
(+ (log n) (log (* 2 (/ (PI) k))))
(+ (log n) (log (* 2 (/ (PI) k))))
(+ (log n) (log (* 2 (/ (PI) k))))
(+ (log n) (log (* 2 (/ (PI) k))))
(+ (log (* 2 (/ (PI) k))) (* -1 (log (/ 1 n))))
(+ (log (* 2 (/ (PI) k))) (* -1 (log (/ 1 n))))
(+ (log (* 2 (/ (PI) k))) (* -1 (log (/ 1 n))))
(+ (log (* 2 (/ (PI) k))) (* -1 (log (/ 1 n))))
(+ (log (* -2 (/ (PI) k))) (* -1 (log (/ -1 n))))
(+ (log (* -2 (/ (PI) k))) (* -1 (log (/ -1 n))))
(+ (log (* -2 (/ (PI) k))) (* -1 (log (/ -1 n))))
(+ (log (* -2 (/ (PI) k))) (* -1 (log (/ -1 n))))
(* 2 (/ (* n (PI)) k))
(* 2 (/ (* n (PI)) k))
(* 2 (/ (* n (PI)) k))
(* 2 (/ (* n (PI)) k))
(* 2 (/ (* n (PI)) k))
(* 2 (/ (* n (PI)) k))
(* 2 (/ (* n (PI)) k))
(* 2 (/ (* n (PI)) k))
(* 2 (/ (* n (PI)) k))
(* 2 (/ (* n (PI)) k))
(* 2 (/ (* n (PI)) k))
(* 2 (/ (* n (PI)) k))
(* 2 (/ (* n (PI)) k))
(* 2 (/ (* n (PI)) k))
(* 2 (/ (* n (PI)) k))
(* 2 (/ (* n (PI)) k))
(* 2 (/ (* n (PI)) k))
(* 2 (/ (* n (PI)) k))
(* 2 (/ (* n (PI)) k))
(* 2 (/ (* n (PI)) k))
(* 2 (/ (* n (PI)) k))
(* 2 (/ (* n (PI)) k))
(* 2 (/ (* n (PI)) k))
(* 2 (/ (* n (PI)) k))
(/ 1/2 (* n (PI)))
(/ 1/2 (* n (PI)))
(/ 1/2 (* n (PI)))
(/ 1/2 (* n (PI)))
(/ 1/2 (* n (PI)))
(/ 1/2 (* n (PI)))
(/ 1/2 (* n (PI)))
(/ 1/2 (* n (PI)))
(/ 1/2 (* n (PI)))
(/ 1/2 (* n (PI)))
(/ 1/2 (* n (PI)))
(/ 1/2 (* n (PI)))
(/ (PI) k)
(/ (PI) k)
(/ (PI) k)
(/ (PI) k)
(/ (PI) k)
(/ (PI) k)
(/ (PI) k)
(/ (PI) k)
(/ (PI) k)
(/ (PI) k)
(/ (PI) k)
(/ (PI) k)
(* n (PI))
(* n (PI))
(* n (PI))
(* n (PI))
(* n (PI))
(* n (PI))
(* n (PI))
(* n (PI))
(* n (PI))
(* n (PI))
(* n (PI))
(* n (PI))

Outputs
(* (sqrt (/ (* n (* (PI) (exp (* k (+ (log (/ 1/2 (PI))) (* -1 (log n))))))) k)) (sqrt 2))
(.f64 (sqrt.f64 #s(literal 2 binary64)) (sqrt.f64 (/.f64 (.f64 n (.f64 (PI.f64) (pow.f64 (/.f64 #s(literal 1/2 binary64) (.f64 n (PI.f64))) k))) k)))
(* (sqrt (/ (* n (* (PI) (exp (* k (+ (log (/ 1/2 (PI))) (* -1 (log n))))))) k)) (sqrt 2))
(.f64 (sqrt.f64 #s(literal 2 binary64)) (sqrt.f64 (/.f64 (.f64 n (.f64 (PI.f64) (pow.f64 (/.f64 #s(literal 1/2 binary64) (.f64 n (PI.f64))) k))) k)))
(* (sqrt (/ (* n (* (PI) (exp (* k (+ (log (/ 1/2 (PI))) (* -1 (log n))))))) k)) (sqrt 2))
(.f64 (sqrt.f64 #s(literal 2 binary64)) (sqrt.f64 (/.f64 (.f64 n (.f64 (PI.f64) (pow.f64 (/.f64 #s(literal 1/2 binary64) (.f64 n (PI.f64))) k))) k)))
(* (sqrt (/ (* n (* (PI) (exp (* k (+ (log (/ 1/2 (PI))) (* -1 (log n))))))) k)) (sqrt 2))
(.f64 (sqrt.f64 #s(literal 2 binary64)) (sqrt.f64 (/.f64 (.f64 n (.f64 (PI.f64) (pow.f64 (/.f64 #s(literal 1/2 binary64) (.f64 n (PI.f64))) k))) k)))
(* (sqrt (/ (* n (* (PI) (exp (* k (+ (log (/ 1/2 (PI))) (log (/ 1 n))))))) k)) (sqrt 2))
(.f64 (sqrt.f64 #s(literal 2 binary64)) (sqrt.f64 (/.f64 (.f64 n (.f64 (PI.f64) (pow.f64 (/.f64 #s(literal 1/2 binary64) (.f64 n (PI.f64))) k))) k)))
(* (sqrt (/ (* n (* (PI) (exp (* k (+ (log (/ 1/2 (PI))) (log (/ 1 n))))))) k)) (sqrt 2))
(.f64 (sqrt.f64 #s(literal 2 binary64)) (sqrt.f64 (/.f64 (.f64 n (.f64 (PI.f64) (pow.f64 (/.f64 #s(literal 1/2 binary64) (.f64 n (PI.f64))) k))) k)))
(* (sqrt (/ (* n (* (PI) (exp (* k (+ (log (/ 1/2 (PI))) (log (/ 1 n))))))) k)) (sqrt 2))
(.f64 (sqrt.f64 #s(literal 2 binary64)) (sqrt.f64 (/.f64 (.f64 n (.f64 (PI.f64) (pow.f64 (/.f64 #s(literal 1/2 binary64) (.f64 n (PI.f64))) k))) k)))
(* (sqrt (/ (* n (* (PI) (exp (* k (+ (log (/ 1/2 (PI))) (log (/ 1 n))))))) k)) (sqrt 2))
(.f64 (sqrt.f64 #s(literal 2 binary64)) (sqrt.f64 (/.f64 (.f64 n (.f64 (PI.f64) (pow.f64 (/.f64 #s(literal 1/2 binary64) (.f64 n (PI.f64))) k))) k)))
(* -1 (* (sqrt (/ (* n (* (PI) (exp (* k (+ (log (/ -1 n)) (log (/ -1/2 (PI)))))))) k)) (* (sqrt -2) (sqrt -1))))
(.f64 (sqrt.f64 (/.f64 (.f64 (pow.f64 (.f64 (/.f64 #s(literal -1/2 binary64) (PI.f64)) (/.f64 #s(literal -1 binary64) n)) k) (.f64 n (PI.f64))) k)) (*.f64 (sqrt.f64 #s(literal -2 binary64)) (-.f64 #s(literal 0 binary64) (sqrt.f64 #s(literal -1 binary64)))))
(* -1 (* (sqrt (/ (* n (* (PI) (exp (* k (+ (log (/ -1 n)) (log (/ -1/2 (PI)))))))) k)) (* (sqrt -2) (sqrt -1))))
(.f64 (sqrt.f64 (/.f64 (.f64 (pow.f64 (.f64 (/.f64 #s(literal -1/2 binary64) (PI.f64)) (/.f64 #s(literal -1 binary64) n)) k) (.f64 n (PI.f64))) k)) (*.f64 (sqrt.f64 #s(literal -2 binary64)) (-.f64 #s(literal 0 binary64) (sqrt.f64 #s(literal -1 binary64)))))
(* -1 (* (sqrt (/ (* n (* (PI) (exp (* k (+ (log (/ -1 n)) (log (/ -1/2 (PI)))))))) k)) (* (sqrt -2) (sqrt -1))))
(.f64 (sqrt.f64 (/.f64 (.f64 (pow.f64 (.f64 (/.f64 #s(literal -1/2 binary64) (PI.f64)) (/.f64 #s(literal -1 binary64) n)) k) (.f64 n (PI.f64))) k)) (*.f64 (sqrt.f64 #s(literal -2 binary64)) (-.f64 #s(literal 0 binary64) (sqrt.f64 #s(literal -1 binary64)))))
(* -1 (* (sqrt (/ (* n (* (PI) (exp (* k (+ (log (/ -1 n)) (log (/ -1/2 (PI)))))))) k)) (* (sqrt -2) (sqrt -1))))
(.f64 (sqrt.f64 (/.f64 (.f64 (pow.f64 (.f64 (/.f64 #s(literal -1/2 binary64) (PI.f64)) (/.f64 #s(literal -1 binary64) n)) k) (.f64 n (PI.f64))) k)) (*.f64 (sqrt.f64 #s(literal -2 binary64)) (-.f64 #s(literal 0 binary64) (sqrt.f64 #s(literal -1 binary64)))))
(* (sqrt (/ (* n (PI)) k)) (sqrt 2))
(.f64 (sqrt.f64 #s(literal 2 binary64)) (sqrt.f64 (/.f64 (.f64 n (PI.f64)) k)))
(/ (+ (* 1/2 (* (sqrt (* (pow k 3) (* n (PI)))) (* (log (/ 1/2 (* n (PI)))) (sqrt 2)))) (* (sqrt (* k (* n (PI)))) (sqrt 2))) k)
(/.f64 (.f64 (sqrt.f64 #s(literal 2 binary64)) (+.f64 (sqrt.f64 (.f64 n (.f64 (PI.f64) k))) (.f64 (log.f64 (/.f64 #s(literal 1/2 binary64) (.f64 n (PI.f64)))) (.f64 #s(literal 1/2 binary64) (sqrt.f64 (.f64 (.f64 n (PI.f64)) (.f64 k (.f64 k k)))))))) k)
(/ (+ (* (sqrt (* k (* n (PI)))) (sqrt 2)) (* (pow k 2) (+ (* 1/4 (* (sqrt (* k (* n (PI)))) (* (pow (log (/ 1/2 (* n (PI)))) 2) (sqrt 2)))) (* 1/2 (* (sqrt (/ (* n (PI)) k)) (* (log (/ 1/2 (* n (PI)))) (sqrt 2))))))) k)
(/.f64 (+.f64 (.f64 (sqrt.f64 #s(literal 2 binary64)) (sqrt.f64 (.f64 n (.f64 (PI.f64) k)))) (.f64 (.f64 k k) (.f64 (sqrt.f64 #s(literal 2 binary64)) (+.f64 (.f64 #s(literal 1/4 binary64) (.f64 (sqrt.f64 (.f64 n (.f64 (PI.f64) k))) (pow.f64 (log.f64 (/.f64 #s(literal 1/2 binary64) (.f64 n (PI.f64)))) #s(literal 2 binary64)))) (.f64 (log.f64 (/.f64 #s(literal 1/2 binary64) (.f64 n (PI.f64)))) (.f64 #s(literal 1/2 binary64) (sqrt.f64 (/.f64 (*.f64 n (PI.f64)) k)))))))) k)
(/ (+ (* (sqrt (* k (* n (PI)))) (sqrt 2)) (* (pow k 2) (+ (* 1/2 (* (sqrt (/ (* n (PI)) k)) (* (log (/ 1/2 (* n (PI)))) (sqrt 2)))) (* k (+ (* 1/4 (* (sqrt (/ (* n (PI)) k)) (* (pow (log (/ 1/2 (* n (PI)))) 2) (sqrt 2)))) (* 1/2 (* (sqrt (/ k (* n (PI)))) (* (sqrt 2) (- (* 1/6 (* n (* (PI) (pow (log (/ 1/2 (* n (PI)))) 3)))) (* 1/4 (/ (* n (* (PI) (pow (log (/ 1/2 (* n (PI)))) 2))) k))))))))))) k)
(/.f64 (+.f64 (.f64 (sqrt.f64 #s(literal 2 binary64)) (sqrt.f64 (.f64 n (.f64 (PI.f64) k)))) (.f64 (.f64 k k) (+.f64 (.f64 #s(literal 1/2 binary64) (.f64 (sqrt.f64 (/.f64 (.f64 n (PI.f64)) k)) (.f64 (sqrt.f64 #s(literal 2 binary64)) (log.f64 (/.f64 #s(literal 1/2 binary64) (.f64 n (PI.f64))))))) (.f64 k (.f64 (sqrt.f64 #s(literal 2 binary64)) (+.f64 (.f64 (.f64 n (+.f64 (.f64 #s(literal 1/6 binary64) (.f64 (PI.f64) (pow.f64 (log.f64 (/.f64 #s(literal 1/2 binary64) (.f64 n (PI.f64)))) #s(literal 3 binary64)))) (.f64 #s(literal -1/4 binary64) (.f64 (pow.f64 (log.f64 (/.f64 #s(literal 1/2 binary64) (.f64 n (PI.f64)))) #s(literal 2 binary64)) (/.f64 (PI.f64) k))))) (.f64 #s(literal 1/2 binary64) (sqrt.f64 (/.f64 k (.f64 n (PI.f64)))))) (.f64 (pow.f64 (log.f64 (/.f64 #s(literal 1/2 binary64) (.f64 n (PI.f64)))) #s(literal 2 binary64)) (.f64 (sqrt.f64 (/.f64 (.f64 n (PI.f64)) k)) #s(literal 1/4 binary64))))))))) k)
(* (sqrt (/ (* n (* (PI) (pow (/ 1/2 (* n (PI))) k))) k)) (sqrt 2))
(.f64 (sqrt.f64 #s(literal 2 binary64)) (sqrt.f64 (/.f64 (.f64 n (.f64 (PI.f64) (pow.f64 (/.f64 #s(literal 1/2 binary64) (.f64 n (PI.f64))) k))) k)))
(* (sqrt (/ (* n (* (PI) (pow (/ 1/2 (* n (PI))) k))) k)) (sqrt 2))
(.f64 (sqrt.f64 #s(literal 2 binary64)) (sqrt.f64 (/.f64 (.f64 n (.f64 (PI.f64) (pow.f64 (/.f64 #s(literal 1/2 binary64) (.f64 n (PI.f64))) k))) k)))
(* (sqrt (/ (* n (* (PI) (pow (/ 1/2 (* n (PI))) k))) k)) (sqrt 2))
(.f64 (sqrt.f64 #s(literal 2 binary64)) (sqrt.f64 (/.f64 (.f64 n (.f64 (PI.f64) (pow.f64 (/.f64 #s(literal 1/2 binary64) (.f64 n (PI.f64))) k))) k)))
(* (sqrt (/ (* n (* (PI) (pow (/ 1/2 (* n (PI))) k))) k)) (sqrt 2))
(.f64 (sqrt.f64 #s(literal 2 binary64)) (sqrt.f64 (/.f64 (.f64 n (.f64 (PI.f64) (pow.f64 (/.f64 #s(literal 1/2 binary64) (.f64 n (PI.f64))) k))) k)))
(* (sqrt (/ (* n (* (PI) (pow (/ 1/2 (* n (PI))) k))) k)) (* (sqrt -2) (sqrt -1)))
(.f64 (.f64 (sqrt.f64 #s(literal -2 binary64)) (sqrt.f64 #s(literal -1 binary64))) (sqrt.f64 (/.f64 (.f64 n (.f64 (PI.f64) (pow.f64 (/.f64 #s(literal 1/2 binary64) (*.f64 n (PI.f64))) k))) k)))
(* (sqrt (/ (* n (* (PI) (pow (/ 1/2 (* n (PI))) k))) k)) (* (sqrt -2) (sqrt -1)))
(.f64 (.f64 (sqrt.f64 #s(literal -2 binary64)) (sqrt.f64 #s(literal -1 binary64))) (sqrt.f64 (/.f64 (.f64 n (.f64 (PI.f64) (pow.f64 (/.f64 #s(literal 1/2 binary64) (*.f64 n (PI.f64))) k))) k)))
(* (sqrt (/ (* n (* (PI) (pow (/ 1/2 (* n (PI))) k))) k)) (* (sqrt -2) (sqrt -1)))
(.f64 (.f64 (sqrt.f64 #s(literal -2 binary64)) (sqrt.f64 #s(literal -1 binary64))) (sqrt.f64 (/.f64 (.f64 n (.f64 (PI.f64) (pow.f64 (/.f64 #s(literal 1/2 binary64) (*.f64 n (PI.f64))) k))) k)))
(* (sqrt (/ (* n (* (PI) (pow (/ 1/2 (* n (PI))) k))) k)) (* (sqrt -2) (sqrt -1)))
(.f64 (.f64 (sqrt.f64 #s(literal -2 binary64)) (sqrt.f64 #s(literal -1 binary64))) (sqrt.f64 (/.f64 (.f64 n (.f64 (PI.f64) (pow.f64 (/.f64 #s(literal 1/2 binary64) (*.f64 n (PI.f64))) k))) k)))
(* 2 (/ (* n (* (PI) (exp (* k (+ (log (/ 1/2 (PI))) (* -1 (log n))))))) k))
(/.f64 (.f64 n (.f64 #s(literal 2 binary64) (.f64 (PI.f64) (pow.f64 (/.f64 #s(literal 1/2 binary64) (.f64 n (PI.f64))) k)))) k)
(* 2 (/ (* n (* (PI) (exp (* k (+ (log (/ 1/2 (PI))) (* -1 (log n))))))) k))
(/.f64 (.f64 n (.f64 #s(literal 2 binary64) (.f64 (PI.f64) (pow.f64 (/.f64 #s(literal 1/2 binary64) (.f64 n (PI.f64))) k)))) k)
(* 2 (/ (* n (* (PI) (exp (* k (+ (log (/ 1/2 (PI))) (* -1 (log n))))))) k))
(/.f64 (.f64 n (.f64 #s(literal 2 binary64) (.f64 (PI.f64) (pow.f64 (/.f64 #s(literal 1/2 binary64) (.f64 n (PI.f64))) k)))) k)
(* 2 (/ (* n (* (PI) (exp (* k (+ (log (/ 1/2 (PI))) (* -1 (log n))))))) k))
(/.f64 (.f64 n (.f64 #s(literal 2 binary64) (.f64 (PI.f64) (pow.f64 (/.f64 #s(literal 1/2 binary64) (.f64 n (PI.f64))) k)))) k)
(* 2 (/ (* n (* (PI) (exp (* k (+ (log (/ 1/2 (PI))) (log (/ 1 n))))))) k))
(/.f64 (.f64 n (.f64 #s(literal 2 binary64) (.f64 (PI.f64) (pow.f64 (/.f64 #s(literal 1/2 binary64) (.f64 n (PI.f64))) k)))) k)
(* 2 (/ (* n (* (PI) (exp (* k (+ (log (/ 1/2 (PI))) (log (/ 1 n))))))) k))
(/.f64 (.f64 n (.f64 #s(literal 2 binary64) (.f64 (PI.f64) (pow.f64 (/.f64 #s(literal 1/2 binary64) (.f64 n (PI.f64))) k)))) k)
(* 2 (/ (* n (* (PI) (exp (* k (+ (log (/ 1/2 (PI))) (log (/ 1 n))))))) k))
(/.f64 (.f64 n (.f64 #s(literal 2 binary64) (.f64 (PI.f64) (pow.f64 (/.f64 #s(literal 1/2 binary64) (.f64 n (PI.f64))) k)))) k)
(* 2 (/ (* n (* (PI) (exp (* k (+ (log (/ 1/2 (PI))) (log (/ 1 n))))))) k))
(/.f64 (.f64 n (.f64 #s(literal 2 binary64) (.f64 (PI.f64) (pow.f64 (/.f64 #s(literal 1/2 binary64) (.f64 n (PI.f64))) k)))) k)
(* 2 (/ (* n (* (PI) (exp (* k (+ (log (/ -1 n)) (log (/ -1/2 (PI)))))))) k))
(.f64 n (.f64 (PI.f64) (.f64 (pow.f64 (.f64 (/.f64 #s(literal -1/2 binary64) (PI.f64)) (/.f64 #s(literal -1 binary64) n)) k) (/.f64 #s(literal 2 binary64) k))))
(* 2 (/ (* n (* (PI) (exp (* k (+ (log (/ -1 n)) (log (/ -1/2 (PI)))))))) k))
(.f64 n (.f64 (PI.f64) (.f64 (pow.f64 (.f64 (/.f64 #s(literal -1/2 binary64) (PI.f64)) (/.f64 #s(literal -1 binary64) n)) k) (/.f64 #s(literal 2 binary64) k))))
(* 2 (/ (* n (* (PI) (exp (* k (+ (log (/ -1 n)) (log (/ -1/2 (PI)))))))) k))
(.f64 n (.f64 (PI.f64) (.f64 (pow.f64 (.f64 (/.f64 #s(literal -1/2 binary64) (PI.f64)) (/.f64 #s(literal -1 binary64) n)) k) (/.f64 #s(literal 2 binary64) k))))
(* 2 (/ (* n (* (PI) (exp (* k (+ (log (/ -1 n)) (log (/ -1/2 (PI)))))))) k))
(.f64 n (.f64 (PI.f64) (.f64 (pow.f64 (.f64 (/.f64 #s(literal -1/2 binary64) (PI.f64)) (/.f64 #s(literal -1 binary64) n)) k) (/.f64 #s(literal 2 binary64) k))))
(* 2 (/ (* n (PI)) k))
(/.f64 (.f64 (PI.f64) (.f64 n #s(literal 2 binary64))) k)
(/ (+ (* 2 (* k (* n (* (PI) (log (/ 1/2 (* n (PI)))))))) (* 2 (* n (PI)))) k)
(.f64 n (.f64 (PI.f64) (/.f64 (+.f64 #s(literal 2 binary64) (.f64 (log.f64 (/.f64 #s(literal 1/2 binary64) (.f64 n (PI.f64)))) (*.f64 k #s(literal 2 binary64)))) k)))
(/ (+ (* 2 (* n (PI))) (* k (+ (* 2 (* n (* (PI) (log (/ 1/2 (* n (PI))))))) (* k (* n (* (PI) (pow (log (/ 1/2 (* n (PI)))) 2))))))) k)
(/.f64 (+.f64 (.f64 (PI.f64) (.f64 n #s(literal 2 binary64))) (.f64 k (.f64 (.f64 n (PI.f64)) (.f64 (log.f64 (/.f64 #s(literal 1/2 binary64) (.f64 n (PI.f64)))) (+.f64 #s(literal 2 binary64) (.f64 k (log.f64 (/.f64 #s(literal 1/2 binary64) (*.f64 n (PI.f64)))))))))) k)
(/ (+ (* 2 (* n (PI))) (* k (+ (* 2 (* n (* (PI) (log (/ 1/2 (* n (PI))))))) (* k (+ (* 1/3 (* k (* n (* (PI) (pow (log (/ 1/2 (* n (PI)))) 3))))) (* n (* (PI) (pow (log (/ 1/2 (* n (PI)))) 2)))))))) k)
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(.f64 (sqrt.f64 #s(literal -2 binary64)) (.f64 (sqrt.f64 #s(literal -1 binary64)) (sqrt.f64 (/.f64 (*.f64 n (PI.f64)) k))))
(* (sqrt (/ (* n (PI)) k)) (sqrt 2))
(.f64 (sqrt.f64 #s(literal 2 binary64)) (sqrt.f64 (/.f64 (.f64 n (PI.f64)) k)))
(* (sqrt (/ (* n (PI)) k)) (sqrt 2))
(.f64 (sqrt.f64 #s(literal 2 binary64)) (sqrt.f64 (/.f64 (.f64 n (PI.f64)) k)))
(* (sqrt (/ (* n (PI)) k)) (sqrt 2))
(.f64 (sqrt.f64 #s(literal 2 binary64)) (sqrt.f64 (/.f64 (.f64 n (PI.f64)) k)))
(* (sqrt (/ (* n (PI)) k)) (sqrt 2))
(.f64 (sqrt.f64 #s(literal 2 binary64)) (sqrt.f64 (/.f64 (.f64 n (PI.f64)) k)))
(* (sqrt (/ (* n (PI)) k)) (sqrt 2))
(.f64 (sqrt.f64 #s(literal 2 binary64)) (sqrt.f64 (/.f64 (.f64 n (PI.f64)) k)))
(* (sqrt (/ (* n (PI)) k)) (sqrt 2))
(.f64 (sqrt.f64 #s(literal 2 binary64)) (sqrt.f64 (/.f64 (.f64 n (PI.f64)) k)))
(* (sqrt (/ (* n (PI)) k)) (sqrt 2))
(.f64 (sqrt.f64 #s(literal 2 binary64)) (sqrt.f64 (/.f64 (.f64 n (PI.f64)) k)))
(* (sqrt (/ (* n (PI)) k)) (sqrt 2))
(.f64 (sqrt.f64 #s(literal 2 binary64)) (sqrt.f64 (/.f64 (.f64 n (PI.f64)) k)))
(* -1 (* (sqrt (/ (* n (PI)) k)) (* (sqrt -2) (sqrt -1))))
(.f64 (sqrt.f64 #s(literal -2 binary64)) (.f64 (sqrt.f64 (/.f64 (*.f64 n (PI.f64)) k)) (-.f64 #s(literal 0 binary64) (sqrt.f64 #s(literal -1 binary64)))))
(* -1 (* (sqrt (/ (* n (PI)) k)) (* (sqrt -2) (sqrt -1))))
(.f64 (sqrt.f64 #s(literal -2 binary64)) (.f64 (sqrt.f64 (/.f64 (*.f64 n (PI.f64)) k)) (-.f64 #s(literal 0 binary64) (sqrt.f64 #s(literal -1 binary64)))))
(* -1 (* (sqrt (/ (* n (PI)) k)) (* (sqrt -2) (sqrt -1))))
(.f64 (sqrt.f64 #s(literal -2 binary64)) (.f64 (sqrt.f64 (/.f64 (*.f64 n (PI.f64)) k)) (-.f64 #s(literal 0 binary64) (sqrt.f64 #s(literal -1 binary64)))))
(* -1 (* (sqrt (/ (* n (PI)) k)) (* (sqrt -2) (sqrt -1))))
(.f64 (sqrt.f64 #s(literal -2 binary64)) (.f64 (sqrt.f64 (/.f64 (*.f64 n (PI.f64)) k)) (-.f64 #s(literal 0 binary64) (sqrt.f64 #s(literal -1 binary64)))))
(* 1/2 (+ (log (* 2 (* n (PI)))) (* -1 (log k))))
(.f64 #s(literal 1/2 binary64) (-.f64 (log.f64 (.f64 (PI.f64) (*.f64 n #s(literal 2 binary64)))) (log.f64 k)))
(* 1/2 (+ (log (* 2 (* n (PI)))) (* -1 (log k))))
(.f64 #s(literal 1/2 binary64) (-.f64 (log.f64 (.f64 (PI.f64) (*.f64 n #s(literal 2 binary64)))) (log.f64 k)))
(* 1/2 (+ (log (* 2 (* n (PI)))) (* -1 (log k))))
(.f64 #s(literal 1/2 binary64) (-.f64 (log.f64 (.f64 (PI.f64) (*.f64 n #s(literal 2 binary64)))) (log.f64 k)))
(* 1/2 (+ (log (* 2 (* n (PI)))) (* -1 (log k))))
(.f64 #s(literal 1/2 binary64) (-.f64 (log.f64 (.f64 (PI.f64) (*.f64 n #s(literal 2 binary64)))) (log.f64 k)))
(* 1/2 (+ (log (* 2 (* n (PI)))) (log (/ 1 k))))
(.f64 #s(literal 1/2 binary64) (-.f64 (log.f64 (.f64 (PI.f64) (*.f64 n #s(literal 2 binary64)))) (log.f64 k)))
(* 1/2 (+ (log (* 2 (* n (PI)))) (log (/ 1 k))))
(.f64 #s(literal 1/2 binary64) (-.f64 (log.f64 (.f64 (PI.f64) (*.f64 n #s(literal 2 binary64)))) (log.f64 k)))
(* 1/2 (+ (log (* 2 (* n (PI)))) (log (/ 1 k))))
(.f64 #s(literal 1/2 binary64) (-.f64 (log.f64 (.f64 (PI.f64) (*.f64 n #s(literal 2 binary64)))) (log.f64 k)))
(* 1/2 (+ (log (* 2 (* n (PI)))) (log (/ 1 k))))
(.f64 #s(literal 1/2 binary64) (-.f64 (log.f64 (.f64 (PI.f64) (*.f64 n #s(literal 2 binary64)))) (log.f64 k)))
(* 1/2 (+ (log (* -2 (* n (PI)))) (log (/ -1 k))))
(.f64 #s(literal 1/2 binary64) (+.f64 (log.f64 (.f64 #s(literal -2 binary64) (*.f64 n (PI.f64)))) (log.f64 (/.f64 #s(literal -1 binary64) k))))
(* 1/2 (+ (log (* -2 (* n (PI)))) (log (/ -1 k))))
(.f64 #s(literal 1/2 binary64) (+.f64 (log.f64 (.f64 #s(literal -2 binary64) (*.f64 n (PI.f64)))) (log.f64 (/.f64 #s(literal -1 binary64) k))))
(* 1/2 (+ (log (* -2 (* n (PI)))) (log (/ -1 k))))
(.f64 #s(literal 1/2 binary64) (+.f64 (log.f64 (.f64 #s(literal -2 binary64) (*.f64 n (PI.f64)))) (log.f64 (/.f64 #s(literal -1 binary64) k))))
(* 1/2 (+ (log (* -2 (* n (PI)))) (log (/ -1 k))))
(.f64 #s(literal 1/2 binary64) (+.f64 (log.f64 (.f64 #s(literal -2 binary64) (*.f64 n (PI.f64)))) (log.f64 (/.f64 #s(literal -1 binary64) k))))
(* 1/2 (+ (log n) (log (* 2 (/ (PI) k)))))
(.f64 #s(literal 1/2 binary64) (+.f64 (log.f64 n) (log.f64 (/.f64 (.f64 (PI.f64) #s(literal 2 binary64)) k))))
(* 1/2 (+ (log n) (log (* 2 (/ (PI) k)))))
(.f64 #s(literal 1/2 binary64) (+.f64 (log.f64 n) (log.f64 (/.f64 (.f64 (PI.f64) #s(literal 2 binary64)) k))))
(* 1/2 (+ (log n) (log (* 2 (/ (PI) k)))))
(.f64 #s(literal 1/2 binary64) (+.f64 (log.f64 n) (log.f64 (/.f64 (.f64 (PI.f64) #s(literal 2 binary64)) k))))
(* 1/2 (+ (log n) (log (* 2 (/ (PI) k)))))
(.f64 #s(literal 1/2 binary64) (+.f64 (log.f64 n) (log.f64 (/.f64 (.f64 (PI.f64) #s(literal 2 binary64)) k))))
(* 1/2 (+ (log (* 2 (/ (PI) k))) (* -1 (log (/ 1 n)))))
(.f64 #s(literal 1/2 binary64) (+.f64 (log.f64 n) (log.f64 (/.f64 (.f64 (PI.f64) #s(literal 2 binary64)) k))))
(* 1/2 (+ (log (* 2 (/ (PI) k))) (* -1 (log (/ 1 n)))))
(.f64 #s(literal 1/2 binary64) (+.f64 (log.f64 n) (log.f64 (/.f64 (.f64 (PI.f64) #s(literal 2 binary64)) k))))
(* 1/2 (+ (log (* 2 (/ (PI) k))) (* -1 (log (/ 1 n)))))
(.f64 #s(literal 1/2 binary64) (+.f64 (log.f64 n) (log.f64 (/.f64 (.f64 (PI.f64) #s(literal 2 binary64)) k))))
(* 1/2 (+ (log (* 2 (/ (PI) k))) (* -1 (log (/ 1 n)))))
(.f64 #s(literal 1/2 binary64) (+.f64 (log.f64 n) (log.f64 (/.f64 (.f64 (PI.f64) #s(literal 2 binary64)) k))))
(* 1/2 (+ (log (* -2 (/ (PI) k))) (* -1 (log (/ -1 n)))))
(.f64 #s(literal 1/2 binary64) (-.f64 (log.f64 (.f64 #s(literal -2 binary64) (/.f64 (PI.f64) k))) (log.f64 (/.f64 #s(literal -1 binary64) n))))
(* 1/2 (+ (log (* -2 (/ (PI) k))) (* -1 (log (/ -1 n)))))
(.f64 #s(literal 1/2 binary64) (-.f64 (log.f64 (.f64 #s(literal -2 binary64) (/.f64 (PI.f64) k))) (log.f64 (/.f64 #s(literal -1 binary64) n))))
(* 1/2 (+ (log (* -2 (/ (PI) k))) (* -1 (log (/ -1 n)))))
(.f64 #s(literal 1/2 binary64) (-.f64 (log.f64 (.f64 #s(literal -2 binary64) (/.f64 (PI.f64) k))) (log.f64 (/.f64 #s(literal -1 binary64) n))))
(* 1/2 (+ (log (* -2 (/ (PI) k))) (* -1 (log (/ -1 n)))))
(.f64 #s(literal 1/2 binary64) (-.f64 (log.f64 (.f64 #s(literal -2 binary64) (/.f64 (PI.f64) k))) (log.f64 (/.f64 #s(literal -1 binary64) n))))
(+ (log (* 2 (* n (PI)))) (* -1 (log k)))
(-.f64 (log.f64 (.f64 (PI.f64) (.f64 n #s(literal 2 binary64)))) (log.f64 k))
(+ (log (* 2 (* n (PI)))) (* -1 (log k)))
(-.f64 (log.f64 (.f64 (PI.f64) (.f64 n #s(literal 2 binary64)))) (log.f64 k))
(+ (log (* 2 (* n (PI)))) (* -1 (log k)))
(-.f64 (log.f64 (.f64 (PI.f64) (.f64 n #s(literal 2 binary64)))) (log.f64 k))
(+ (log (* 2 (* n (PI)))) (* -1 (log k)))
(-.f64 (log.f64 (.f64 (PI.f64) (.f64 n #s(literal 2 binary64)))) (log.f64 k))
(+ (log (* 2 (* n (PI)))) (log (/ 1 k)))
(-.f64 (log.f64 (.f64 (PI.f64) (.f64 n #s(literal 2 binary64)))) (log.f64 k))
(+ (log (* 2 (* n (PI)))) (log (/ 1 k)))
(-.f64 (log.f64 (.f64 (PI.f64) (.f64 n #s(literal 2 binary64)))) (log.f64 k))
(+ (log (* 2 (* n (PI)))) (log (/ 1 k)))
(-.f64 (log.f64 (.f64 (PI.f64) (.f64 n #s(literal 2 binary64)))) (log.f64 k))
(+ (log (* 2 (* n (PI)))) (log (/ 1 k)))
(-.f64 (log.f64 (.f64 (PI.f64) (.f64 n #s(literal 2 binary64)))) (log.f64 k))
(+ (log (* -2 (* n (PI)))) (log (/ -1 k)))
(+.f64 (log.f64 (.f64 #s(literal -2 binary64) (.f64 n (PI.f64)))) (log.f64 (/.f64 #s(literal -1 binary64) k)))
(+ (log (* -2 (* n (PI)))) (log (/ -1 k)))
(+.f64 (log.f64 (.f64 #s(literal -2 binary64) (.f64 n (PI.f64)))) (log.f64 (/.f64 #s(literal -1 binary64) k)))
(+ (log (* -2 (* n (PI)))) (log (/ -1 k)))
(+.f64 (log.f64 (.f64 #s(literal -2 binary64) (.f64 n (PI.f64)))) (log.f64 (/.f64 #s(literal -1 binary64) k)))
(+ (log (* -2 (* n (PI)))) (log (/ -1 k)))
(+.f64 (log.f64 (.f64 #s(literal -2 binary64) (.f64 n (PI.f64)))) (log.f64 (/.f64 #s(literal -1 binary64) k)))
(+ (log n) (log (* 2 (/ (PI) k))))
(+.f64 (log.f64 n) (log.f64 (/.f64 (*.f64 (PI.f64) #s(literal 2 binary64)) k)))
(+ (log n) (log (* 2 (/ (PI) k))))
(+.f64 (log.f64 n) (log.f64 (/.f64 (*.f64 (PI.f64) #s(literal 2 binary64)) k)))
(+ (log n) (log (* 2 (/ (PI) k))))
(+.f64 (log.f64 n) (log.f64 (/.f64 (*.f64 (PI.f64) #s(literal 2 binary64)) k)))
(+ (log n) (log (* 2 (/ (PI) k))))
(+.f64 (log.f64 n) (log.f64 (/.f64 (*.f64 (PI.f64) #s(literal 2 binary64)) k)))
(+ (log (* 2 (/ (PI) k))) (* -1 (log (/ 1 n))))
(+.f64 (log.f64 n) (log.f64 (/.f64 (*.f64 (PI.f64) #s(literal 2 binary64)) k)))
(+ (log (* 2 (/ (PI) k))) (* -1 (log (/ 1 n))))
(+.f64 (log.f64 n) (log.f64 (/.f64 (*.f64 (PI.f64) #s(literal 2 binary64)) k)))
(+ (log (* 2 (/ (PI) k))) (* -1 (log (/ 1 n))))
(+.f64 (log.f64 n) (log.f64 (/.f64 (*.f64 (PI.f64) #s(literal 2 binary64)) k)))
(+ (log (* 2 (/ (PI) k))) (* -1 (log (/ 1 n))))
(+.f64 (log.f64 n) (log.f64 (/.f64 (*.f64 (PI.f64) #s(literal 2 binary64)) k)))
(+ (log (* -2 (/ (PI) k))) (* -1 (log (/ -1 n))))
(-.f64 (log.f64 (*.f64 #s(literal -2 binary64) (/.f64 (PI.f64) k))) (log.f64 (/.f64 #s(literal -1 binary64) n)))
(+ (log (* -2 (/ (PI) k))) (* -1 (log (/ -1 n))))
(-.f64 (log.f64 (*.f64 #s(literal -2 binary64) (/.f64 (PI.f64) k))) (log.f64 (/.f64 #s(literal -1 binary64) n)))
(+ (log (* -2 (/ (PI) k))) (* -1 (log (/ -1 n))))
(-.f64 (log.f64 (*.f64 #s(literal -2 binary64) (/.f64 (PI.f64) k))) (log.f64 (/.f64 #s(literal -1 binary64) n)))
(+ (log (* -2 (/ (PI) k))) (* -1 (log (/ -1 n))))
(-.f64 (log.f64 (*.f64 #s(literal -2 binary64) (/.f64 (PI.f64) k))) (log.f64 (/.f64 #s(literal -1 binary64) n)))
(* 2 (/ (* n (PI)) k))
(/.f64 (.f64 (PI.f64) (.f64 n #s(literal 2 binary64))) k)
(* 2 (/ (* n (PI)) k))
(/.f64 (.f64 (PI.f64) (.f64 n #s(literal 2 binary64))) k)
(* 2 (/ (* n (PI)) k))
(/.f64 (.f64 (PI.f64) (.f64 n #s(literal 2 binary64))) k)
(* 2 (/ (* n (PI)) k))
(/.f64 (.f64 (PI.f64) (.f64 n #s(literal 2 binary64))) k)
(* 2 (/ (* n (PI)) k))
(/.f64 (.f64 (PI.f64) (.f64 n #s(literal 2 binary64))) k)
(* 2 (/ (* n (PI)) k))
(/.f64 (.f64 (PI.f64) (.f64 n #s(literal 2 binary64))) k)
(* 2 (/ (* n (PI)) k))
(/.f64 (.f64 (PI.f64) (.f64 n #s(literal 2 binary64))) k)
(* 2 (/ (* n (PI)) k))
(/.f64 (.f64 (PI.f64) (.f64 n #s(literal 2 binary64))) k)
(* 2 (/ (* n (PI)) k))
(/.f64 (.f64 (PI.f64) (.f64 n #s(literal 2 binary64))) k)
(* 2 (/ (* n (PI)) k))
(/.f64 (.f64 (PI.f64) (.f64 n #s(literal 2 binary64))) k)
(* 2 (/ (* n (PI)) k))
(/.f64 (.f64 (PI.f64) (.f64 n #s(literal 2 binary64))) k)
(* 2 (/ (* n (PI)) k))
(/.f64 (.f64 (PI.f64) (.f64 n #s(literal 2 binary64))) k)
(* 2 (/ (* n (PI)) k))
(/.f64 (.f64 (PI.f64) (.f64 n #s(literal 2 binary64))) k)
(* 2 (/ (* n (PI)) k))
(/.f64 (.f64 (PI.f64) (.f64 n #s(literal 2 binary64))) k)
(* 2 (/ (* n (PI)) k))
(/.f64 (.f64 (PI.f64) (.f64 n #s(literal 2 binary64))) k)
(* 2 (/ (* n (PI)) k))
(/.f64 (.f64 (PI.f64) (.f64 n #s(literal 2 binary64))) k)
(* 2 (/ (* n (PI)) k))
(/.f64 (.f64 (PI.f64) (.f64 n #s(literal 2 binary64))) k)
(* 2 (/ (* n (PI)) k))
(/.f64 (.f64 (PI.f64) (.f64 n #s(literal 2 binary64))) k)
(* 2 (/ (* n (PI)) k))
(/.f64 (.f64 (PI.f64) (.f64 n #s(literal 2 binary64))) k)
(* 2 (/ (* n (PI)) k))
(/.f64 (.f64 (PI.f64) (.f64 n #s(literal 2 binary64))) k)
(* 2 (/ (* n (PI)) k))
(/.f64 (.f64 (PI.f64) (.f64 n #s(literal 2 binary64))) k)
(* 2 (/ (* n (PI)) k))
(/.f64 (.f64 (PI.f64) (.f64 n #s(literal 2 binary64))) k)
(* 2 (/ (* n (PI)) k))
(/.f64 (.f64 (PI.f64) (.f64 n #s(literal 2 binary64))) k)
(* 2 (/ (* n (PI)) k))
(/.f64 (.f64 (PI.f64) (.f64 n #s(literal 2 binary64))) k)
(/ 1/2 (* n (PI)))
(/.f64 #s(literal 1/2 binary64) (*.f64 n (PI.f64)))
(/ 1/2 (* n (PI)))
(/.f64 #s(literal 1/2 binary64) (*.f64 n (PI.f64)))
(/ 1/2 (* n (PI)))
(/.f64 #s(literal 1/2 binary64) (*.f64 n (PI.f64)))
(/ 1/2 (* n (PI)))
(/.f64 #s(literal 1/2 binary64) (*.f64 n (PI.f64)))
(/ 1/2 (* n (PI)))
(/.f64 #s(literal 1/2 binary64) (*.f64 n (PI.f64)))
(/ 1/2 (* n (PI)))
(/.f64 #s(literal 1/2 binary64) (*.f64 n (PI.f64)))
(/ 1/2 (* n (PI)))
(/.f64 #s(literal 1/2 binary64) (*.f64 n (PI.f64)))
(/ 1/2 (* n (PI)))
(/.f64 #s(literal 1/2 binary64) (*.f64 n (PI.f64)))
(/ 1/2 (* n (PI)))
(/.f64 #s(literal 1/2 binary64) (*.f64 n (PI.f64)))
(/ 1/2 (* n (PI)))
(/.f64 #s(literal 1/2 binary64) (*.f64 n (PI.f64)))
(/ 1/2 (* n (PI)))
(/.f64 #s(literal 1/2 binary64) (*.f64 n (PI.f64)))
(/ 1/2 (* n (PI)))
(/.f64 #s(literal 1/2 binary64) (*.f64 n (PI.f64)))
(/ (PI) k)
(/.f64 (PI.f64) k)
(/ (PI) k)
(/.f64 (PI.f64) k)
(/ (PI) k)
(/.f64 (PI.f64) k)
(/ (PI) k)
(/.f64 (PI.f64) k)
(/ (PI) k)
(/.f64 (PI.f64) k)
(/ (PI) k)
(/.f64 (PI.f64) k)
(/ (PI) k)
(/.f64 (PI.f64) k)
(/ (PI) k)
(/.f64 (PI.f64) k)
(/ (PI) k)
(/.f64 (PI.f64) k)
(/ (PI) k)
(/.f64 (PI.f64) k)
(/ (PI) k)
(/.f64 (PI.f64) k)
(/ (PI) k)
(/.f64 (PI.f64) k)
(* n (PI))
(*.f64 n (PI.f64))
(* n (PI))
(*.f64 n (PI.f64))
(* n (PI))
(*.f64 n (PI.f64))
(* n (PI))
(*.f64 n (PI.f64))
(* n (PI))
(*.f64 n (PI.f64))
(* n (PI))
(*.f64 n (PI.f64))
(* n (PI))
(*.f64 n (PI.f64))
(* n (PI))
(*.f64 n (PI.f64))
(* n (PI))
(*.f64 n (PI.f64))
(* n (PI))
(*.f64 n (PI.f64))
(* n (PI))
(*.f64 n (PI.f64))
(* n (PI))
(*.f64 n (PI.f64))

eval400.0ms (3%)

Compiler: Compiled 42835 to 7306 computations (82.9% saved)

prune330.0ms (2.4%)

Pruning

48 alts after pruning (40 fresh and 8 done)

	Pruned	Kept	Total
New	2851	16	2867
Fresh	11	24	35
Picked	1	4	5
Done	0	4	4
Total	2863	48	2911

Accuracy

100.0%

Counts

2911 → 48

Alt Table

Click to see full alt table

Status	Accuracy	Program
	38.6%	(pow.f64 (/.f64 (/.f64 k (*.f64 (PI.f64) n)) #s(literal 2 binary64)) #s(literal -1/2 binary64))
	37.2%	(pow.f64 (/.f64 #s(literal 1/2 binary64) (/.f64 (*.f64 (PI.f64) n) k)) #s(literal -1/2 binary64))
	25.7%	(pow.f64 (.f64 (/.f64 #s(literal 2 binary64) (/.f64 k (.f64 (PI.f64) n))) (/.f64 #s(literal 2 binary64) (/.f64 k (*.f64 (PI.f64) n)))) #s(literal 1/4 binary64))
	44.1%	(/.f64 (pow.f64 (/.f64 n #s(literal 1/2 binary64)) #s(literal 1/2 binary64)) (sqrt.f64 (/.f64 k (PI.f64))))
	44.1%	(/.f64 (pow.f64 (*.f64 (PI.f64) n) #s(literal 1/2 binary64)) (sqrt.f64 (/.f64 k #s(literal 2 binary64))))
	80.3%	(/.f64 (pow.f64 (.f64 #s(literal 4 binary64) (.f64 (.f64 (PI.f64) n) (.f64 (PI.f64) n))) (-.f64 #s(literal 1/4 binary64) (*.f64 k #s(literal 1/4 binary64)))) (sqrt.f64 k))
✓	99.3%	(/.f64 (pow.f64 (.f64 #s(literal 2 binary64) (.f64 (PI.f64) n)) (-.f64 #s(literal 1/2 binary64) (/.f64 k #s(literal 2 binary64)))) (sqrt.f64 k))
	38.4%	(/.f64 (/.f64 #s(literal 1 binary64) (pow.f64 (/.f64 k (*.f64 (PI.f64) n)) #s(literal 1/2 binary64))) (sqrt.f64 #s(literal 1/2 binary64)))
	44.0%	(/.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 (/.f64 #s(literal 1/2 binary64) (*.f64 (PI.f64) n)))) (sqrt.f64 k))
	37.0%	(/.f64 (sqrt.f64 (/.f64 (/.f64 n k) (/.f64 #s(literal 1 binary64) (PI.f64)))) (sqrt.f64 #s(literal 1/2 binary64)))
✓	37.0%	(/.f64 (sqrt.f64 (/.f64 (*.f64 n (PI.f64)) k)) (sqrt.f64 #s(literal 1/2 binary64)))
	44.1%	(/.f64 (sqrt.f64 (/.f64 n (/.f64 #s(literal 1/2 binary64) (PI.f64)))) (sqrt.f64 k))
	37.1%	(/.f64 (sqrt.f64 (*.f64 (/.f64 (PI.f64) k) n)) (sqrt.f64 #s(literal 1/2 binary64)))
	44.1%	(/.f64 (sqrt.f64 (.f64 (.f64 n (PI.f64)) #s(literal 2 binary64))) (sqrt.f64 k))
	38.5%	(/.f64 (sqrt.f64 (*.f64 #s(literal 2 binary64) (PI.f64))) (pow.f64 (/.f64 k n) #s(literal 1/2 binary64)))
	38.5%	(/.f64 (sqrt.f64 #s(literal 2 binary64)) (sqrt.f64 (/.f64 k (*.f64 (PI.f64) n))))
	37.1%	(/.f64 #s(literal 1 binary64) (pow.f64 (/.f64 #s(literal 1/2 binary64) (/.f64 (*.f64 (PI.f64) n) k)) #s(literal 1/2 binary64)))
	44.0%	(/.f64 #s(literal 1 binary64) (/.f64 (sqrt.f64 (/.f64 k #s(literal 2 binary64))) (pow.f64 (*.f64 (PI.f64) n) #s(literal 1/2 binary64))))
	44.0%	(*.f64 (pow.f64 (/.f64 n #s(literal 1/2 binary64)) #s(literal 1/2 binary64)) (sqrt.f64 (/.f64 (PI.f64) k)))
	37.1%	(*.f64 (pow.f64 (/.f64 #s(literal 2 binary64) (/.f64 k n)) #s(literal 1/2 binary64)) (sqrt.f64 (PI.f64)))
	44.1%	(.f64 (pow.f64 (.f64 (PI.f64) n) #s(literal 1/2 binary64)) (sqrt.f64 (/.f64 #s(literal 2 binary64) k)))
	37.4%	(.f64 (pow.f64 (.f64 #s(literal 2 binary64) (PI.f64)) #s(literal 1/2 binary64)) (sqrt.f64 (/.f64 n k)))
	1.8%	(.f64 (sqrt.f64 (/.f64 (.f64 n (PI.f64)) k)) (/.f64 #s(literal -1 binary64) (sqrt.f64 #s(literal 1/2 binary64))))
	37.1%	(*.f64 (sqrt.f64 (/.f64 n (/.f64 k #s(literal 2 binary64)))) (sqrt.f64 (PI.f64)))
✓	37.1%	(.f64 (sqrt.f64 (.f64 (/.f64 (PI.f64) k) n)) (sqrt.f64 #s(literal 2 binary64)))
✓	37.1%	(.f64 (sqrt.f64 (.f64 (/.f64 n k) (PI.f64))) (sqrt.f64 #s(literal 2 binary64)))
	44.1%	(.f64 (sqrt.f64 (.f64 #s(literal 2 binary64) (*.f64 (PI.f64) n))) (pow.f64 k #s(literal -1/2 binary64)))
	44.4%	(.f64 (sqrt.f64 n) (sqrt.f64 (.f64 (/.f64 (PI.f64) k) #s(literal 2 binary64))))
	37.1%	(sqrt.f64 (/.f64 (/.f64 (PI.f64) k) (/.f64 #s(literal 1/2 binary64) n)))
	37.2%	(sqrt.f64 (/.f64 (/.f64 (PI.f64) #s(literal 1/2 binary64)) (/.f64 k n)))
	37.2%	(sqrt.f64 (/.f64 (/.f64 #s(literal 2 binary64) (/.f64 (/.f64 #s(literal 1 binary64) n) (PI.f64))) k))
	37.2%	(sqrt.f64 (/.f64 (/.f64 #s(literal 2 binary64) k) (/.f64 (/.f64 #s(literal 1 binary64) (PI.f64)) n)))
	37.2%	(sqrt.f64 (/.f64 #s(literal 2 binary64) (/.f64 (/.f64 (/.f64 #s(literal 1 binary64) (PI.f64)) n) (/.f64 #s(literal 1 binary64) k))))
	37.1%	(sqrt.f64 (/.f64 #s(literal 2 binary64) (/.f64 (/.f64 (/.f64 #s(literal 1 binary64) n) (PI.f64)) (/.f64 #s(literal 1 binary64) k))))
	37.2%	(sqrt.f64 (/.f64 #s(literal 2 binary64) (/.f64 (/.f64 k (PI.f64)) n)))
	37.2%	(sqrt.f64 (/.f64 #s(literal 2 binary64) (/.f64 (/.f64 #s(literal 1 binary64) (/.f64 #s(literal -1 binary64) k)) (-.f64 #s(literal 0 binary64) (*.f64 (PI.f64) n)))))
	37.2%	(sqrt.f64 (/.f64 #s(literal 2 binary64) (/.f64 (/.f64 #s(literal 1 binary64) (PI.f64)) (/.f64 n k))))
	37.2%	(sqrt.f64 (/.f64 #s(literal 2 binary64) (/.f64 (/.f64 #s(literal 1 binary64) n) (/.f64 (/.f64 #s(literal 1 binary64) k) (/.f64 #s(literal 1 binary64) (PI.f64))))))
✓	37.1%	(sqrt.f64 (/.f64 #s(literal 2 binary64) (/.f64 (/.f64 #s(literal 1 binary64) n) (/.f64 (PI.f64) k))))
✓	37.2%	(sqrt.f64 (/.f64 #s(literal 2 binary64) (/.f64 k (*.f64 (PI.f64) n))))
	37.2%	(sqrt.f64 (*.f64 (/.f64 (PI.f64) #s(literal 1/2 binary64)) (/.f64 n k)))
	37.1%	(sqrt.f64 (*.f64 (/.f64 #s(literal 2 binary64) (/.f64 k (PI.f64))) n))
	37.2%	(sqrt.f64 (*.f64 (/.f64 #s(literal 2 binary64) (/.f64 k n)) (PI.f64)))
	37.2%	(sqrt.f64 (.f64 (/.f64 #s(literal 2 binary64) k) (.f64 (PI.f64) n)))
✓	91.8%	(sqrt.f64 (.f64 (.f64 (.f64 #s(literal 2 binary64) (pow.f64 (/.f64 #s(literal 1/2 binary64) (.f64 (PI.f64) n)) k)) (/.f64 (PI.f64) k)) n))
	37.2%	(sqrt.f64 (*.f64 (PI.f64) (/.f64 (/.f64 #s(literal 2 binary64) k) (/.f64 #s(literal 1 binary64) n))))
✓	37.2%	(sqrt.f64 (.f64 (PI.f64) (.f64 n (/.f64 #s(literal 2 binary64) k))))
	34.9%	(exp.f64 (*.f64 (log.f64 (/.f64 (/.f64 (PI.f64) k) (/.f64 #s(literal 1/2 binary64) n))) #s(literal 1/2 binary64)))

Compiler

Compiled 1569 to 753 computations (52% saved)

regimes112.0ms (0.8%)

Counts

83 → 1

Calls

Call 1

Inputs
(sqrt.f64 (.f64 (PI.f64) (.f64 n (/.f64 #s(literal 2 binary64) k))))
(sqrt.f64 (.f64 (.f64 #s(literal 2 binary64) (PI.f64)) (/.f64 n k)))
(sqrt.f64 (.f64 (/.f64 #s(literal 2 binary64) k) (.f64 (PI.f64) n)))
(sqrt.f64 (*.f64 (/.f64 #s(literal 2 binary64) (/.f64 k n)) (PI.f64)))
(sqrt.f64 (*.f64 (/.f64 #s(literal 2 binary64) (/.f64 k (PI.f64))) n))
(sqrt.f64 (*.f64 (/.f64 (PI.f64) #s(literal 1/2 binary64)) (/.f64 n k)))
(sqrt.f64 (*.f64 (/.f64 (PI.f64) k) (/.f64 n #s(literal 1/2 binary64))))
(sqrt.f64 (/.f64 #s(literal 2 binary64) (/.f64 k (*.f64 (PI.f64) n))))
(sqrt.f64 (/.f64 #s(literal 2 binary64) (/.f64 (/.f64 k n) (PI.f64))))
(sqrt.f64 (/.f64 #s(literal 2 binary64) (/.f64 (/.f64 k (PI.f64)) n)))
(sqrt.f64 (/.f64 (/.f64 n #s(literal 1/2 binary64)) (/.f64 k (PI.f64))))
(sqrt.f64 (/.f64 (/.f64 (PI.f64) #s(literal 1/2 binary64)) (/.f64 k n)))
(sqrt.f64 (/.f64 (/.f64 (PI.f64) k) (/.f64 #s(literal 1/2 binary64) n)))
(sqrt.f64 (/.f64 (/.f64 (*.f64 (PI.f64) n) #s(literal 1/2 binary64)) k))
(pow.f64 (/.f64 #s(literal 1/2 binary64) (/.f64 (*.f64 (PI.f64) n) k)) #s(literal -1/2 binary64))
(pow.f64 (/.f64 (/.f64 k (*.f64 (PI.f64) n)) #s(literal 2 binary64)) #s(literal -1/2 binary64))
(sqrt.f64 (*.f64 (PI.f64) (/.f64 (/.f64 #s(literal 2 binary64) k) (/.f64 #s(literal 1 binary64) n))))
(sqrt.f64 (/.f64 #s(literal 2 binary64) (/.f64 (/.f64 #s(literal 1 binary64) n) (/.f64 (PI.f64) k))))
(sqrt.f64 (/.f64 #s(literal 2 binary64) (/.f64 (/.f64 #s(literal 1 binary64) (PI.f64)) (/.f64 n k))))
(sqrt.f64 (/.f64 (/.f64 #s(literal 1 binary64) k) (/.f64 #s(literal 1/2 binary64) (*.f64 (PI.f64) n))))
(sqrt.f64 (/.f64 (/.f64 #s(literal 2 binary64) k) (/.f64 (/.f64 #s(literal 1 binary64) (PI.f64)) n)))
(sqrt.f64 (/.f64 (/.f64 #s(literal 2 binary64) (/.f64 (/.f64 #s(literal 1 binary64) n) (PI.f64))) k))
(/.f64 #s(literal 1 binary64) (pow.f64 (/.f64 #s(literal 1/2 binary64) (/.f64 (*.f64 (PI.f64) n) k)) #s(literal 1/2 binary64)))
(/.f64 #s(literal 1 binary64) (pow.f64 (/.f64 #s(literal 2 binary64) (/.f64 k (*.f64 (PI.f64) n))) #s(literal -1/2 binary64)))
(sqrt.f64 (/.f64 #s(literal 2 binary64) (/.f64 (/.f64 #s(literal -1 binary64) (*.f64 (PI.f64) n)) (/.f64 #s(literal -1 binary64) k))))
(sqrt.f64 (/.f64 #s(literal 2 binary64) (/.f64 (/.f64 (/.f64 #s(literal 1 binary64) n) (PI.f64)) (/.f64 #s(literal 1 binary64) k))))
(sqrt.f64 (/.f64 #s(literal 2 binary64) (/.f64 (/.f64 (/.f64 #s(literal 1 binary64) (PI.f64)) n) (/.f64 #s(literal 1 binary64) k))))
(sqrt.f64 (/.f64 #s(literal 2 binary64) (/.f64 (/.f64 #s(literal 1 binary64) n) (/.f64 (/.f64 #s(literal 1 binary64) k) (/.f64 #s(literal 1 binary64) (PI.f64))))))
(sqrt.f64 (/.f64 #s(literal 2 binary64) (/.f64 (/.f64 #s(literal 1 binary64) (/.f64 #s(literal -1 binary64) k)) (-.f64 #s(literal 0 binary64) (*.f64 (PI.f64) n)))))
(pow.f64 (.f64 (/.f64 #s(literal 2 binary64) (/.f64 k (.f64 (PI.f64) n))) (/.f64 #s(literal 2 binary64) (/.f64 k (*.f64 (PI.f64) n)))) #s(literal 1/4 binary64))
(.f64 (sqrt.f64 n) (sqrt.f64 (.f64 (/.f64 (PI.f64) k) #s(literal 2 binary64))))
(.f64 (sqrt.f64 (.f64 (PI.f64) (/.f64 n k))) (sqrt.f64 #s(literal 2 binary64)))
(.f64 (sqrt.f64 (.f64 (/.f64 n k) (PI.f64))) (sqrt.f64 #s(literal 2 binary64)))
(.f64 (sqrt.f64 (.f64 (/.f64 (PI.f64) k) n)) (sqrt.f64 #s(literal 2 binary64)))
(*.f64 (sqrt.f64 (/.f64 n (/.f64 k #s(literal 2 binary64)))) (sqrt.f64 (PI.f64)))
(.f64 (sqrt.f64 (/.f64 (.f64 n (PI.f64)) k)) (sqrt.f64 #s(literal 2 binary64)))
(/.f64 (sqrt.f64 #s(literal 2 binary64)) (sqrt.f64 (/.f64 k (*.f64 (PI.f64) n))))
(/.f64 (sqrt.f64 (.f64 #s(literal 2 binary64) (.f64 (PI.f64) n))) (sqrt.f64 k))
(/.f64 (sqrt.f64 (.f64 (.f64 n (PI.f64)) #s(literal 2 binary64))) (sqrt.f64 k))
(/.f64 (sqrt.f64 (*.f64 (/.f64 (PI.f64) k) n)) (sqrt.f64 #s(literal 1/2 binary64)))
(/.f64 (sqrt.f64 (/.f64 n (/.f64 #s(literal 1/2 binary64) (PI.f64)))) (sqrt.f64 k))
(/.f64 (sqrt.f64 (/.f64 (*.f64 n (PI.f64)) k)) (sqrt.f64 #s(literal 1/2 binary64)))
(.f64 (sqrt.f64 (.f64 #s(literal 2 binary64) n)) (pow.f64 (/.f64 (PI.f64) k) #s(literal 1/2 binary64)))
(.f64 (sqrt.f64 (.f64 #s(literal 2 binary64) (*.f64 (PI.f64) n))) (pow.f64 k #s(literal -1/2 binary64)))
(.f64 (pow.f64 (.f64 #s(literal 2 binary64) (PI.f64)) #s(literal 1/2 binary64)) (sqrt.f64 (/.f64 n k)))
(.f64 (pow.f64 (.f64 (PI.f64) n) #s(literal 1/2 binary64)) (sqrt.f64 (/.f64 #s(literal 2 binary64) k)))
(*.f64 (pow.f64 (/.f64 #s(literal 2 binary64) (/.f64 k n)) #s(literal 1/2 binary64)) (sqrt.f64 (PI.f64)))
(*.f64 (pow.f64 (/.f64 n #s(literal 1/2 binary64)) #s(literal 1/2 binary64)) (sqrt.f64 (/.f64 (PI.f64) k)))
(/.f64 (sqrt.f64 (*.f64 #s(literal 2 binary64) (PI.f64))) (pow.f64 (/.f64 k n) #s(literal 1/2 binary64)))
(/.f64 (pow.f64 (*.f64 (PI.f64) n) #s(literal 1/2 binary64)) (sqrt.f64 (/.f64 k #s(literal 2 binary64))))
(/.f64 (pow.f64 (/.f64 n #s(literal 1/2 binary64)) #s(literal 1/2 binary64)) (sqrt.f64 (/.f64 k (PI.f64))))
(exp.f64 (.f64 (log.f64 (/.f64 #s(literal 2 binary64) (/.f64 k (.f64 (PI.f64) n)))) #s(literal 1/2 binary64)))
(exp.f64 (*.f64 (log.f64 (/.f64 (/.f64 (PI.f64) k) (/.f64 #s(literal 1/2 binary64) n))) #s(literal 1/2 binary64)))
(.f64 (sqrt.f64 (/.f64 (.f64 n (PI.f64)) k)) (/.f64 #s(literal -1 binary64) (sqrt.f64 #s(literal 1/2 binary64))))
(/.f64 (sqrt.f64 (/.f64 (/.f64 n k) (/.f64 #s(literal 1 binary64) (PI.f64)))) (sqrt.f64 #s(literal 1/2 binary64)))
(/.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 (/.f64 #s(literal 1/2 binary64) (*.f64 (PI.f64) n)))) (sqrt.f64 k))
(.f64 (pow.f64 (.f64 (PI.f64) n) #s(literal 1/2 binary64)) (sqrt.f64 (*.f64 (/.f64 #s(literal 1 binary64) k) #s(literal 2 binary64))))
(/.f64 #s(literal 1 binary64) (/.f64 (sqrt.f64 (/.f64 k #s(literal 2 binary64))) (pow.f64 (*.f64 (PI.f64) n) #s(literal 1/2 binary64))))
(/.f64 (/.f64 #s(literal 1 binary64) (pow.f64 (/.f64 k (*.f64 (PI.f64) n)) #s(literal 1/2 binary64))) (sqrt.f64 #s(literal 1/2 binary64)))
(/.f64 (sqrt.f64 (/.f64 (/.f64 #s(literal 1 binary64) (/.f64 (/.f64 #s(literal 1 binary64) n) (PI.f64))) k)) (sqrt.f64 #s(literal 1/2 binary64)))
(/.f64 (*.f64 #s(literal 1 binary64) (pow.f64 (/.f64 n #s(literal 1/2 binary64)) #s(literal 1/2 binary64))) (pow.f64 (/.f64 k (PI.f64)) #s(literal 1/2 binary64)))
(/.f64 (pow.f64 (.f64 #s(literal 2 binary64) (.f64 (PI.f64) n)) (-.f64 #s(literal 1/2 binary64) (/.f64 k #s(literal 2 binary64)))) (sqrt.f64 k))
(/.f64 (pow.f64 k #s(literal -1/2 binary64)) (pow.f64 (.f64 #s(literal 2 binary64) (.f64 (PI.f64) n)) (+.f64 (/.f64 k #s(literal 2 binary64)) #s(literal -1/2 binary64))))
(sqrt.f64 (.f64 (.f64 (.f64 #s(literal 2 binary64) (pow.f64 (/.f64 #s(literal 1/2 binary64) (.f64 (PI.f64) n)) k)) (/.f64 (PI.f64) k)) n))
(sqrt.f64 (/.f64 (.f64 #s(literal 2 binary64) (.f64 (PI.f64) n)) (.f64 k (pow.f64 (.f64 #s(literal 2 binary64) (*.f64 (PI.f64) n)) 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) (pow.f64 (.f64 #s(literal 2 binary64) (.f64 (PI.f64) n)) (+.f64 (/.f64 k #s(literal 2 binary64)) #s(literal -1/2 binary64)))) (sqrt.f64 k))
(/.f64 (pow.f64 (.f64 (PI.f64) (/.f64 #s(literal -2 binary64) (/.f64 #s(literal -1 binary64) n))) (+.f64 #s(literal 1/2 binary64) (.f64 k #s(literal -1/2 binary64)))) (sqrt.f64 k))
(pow.f64 (/.f64 (.f64 k (pow.f64 (.f64 #s(literal 2 binary64) (.f64 (PI.f64) n)) k)) (.f64 #s(literal 2 binary64) (*.f64 (PI.f64) n))) #s(literal -1/2 binary64))
(.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) (pow.f64 (.f64 (PI.f64) (/.f64 #s(literal -2 binary64) (/.f64 #s(literal -1 binary64) n))) (+.f64 #s(literal 1/2 binary64) (*.f64 k #s(literal -1/2 binary64)))))
(/.f64 (pow.f64 (.f64 #s(literal 4 binary64) (.f64 (.f64 (PI.f64) n) (.f64 (PI.f64) n))) (-.f64 #s(literal 1/4 binary64) (*.f64 k #s(literal 1/4 binary64)))) (sqrt.f64 k))
(/.f64 (.f64 (sqrt.f64 #s(literal 2 binary64)) (sqrt.f64 (.f64 n (PI.f64)))) (sqrt.f64 k))
(/.f64 (exp.f64 (/.f64 (log.f64 (.f64 #s(literal 2 binary64) (.f64 (PI.f64) n))) (/.f64 #s(literal 2 binary64) (-.f64 #s(literal 1 binary64) k)))) (sqrt.f64 k))
(/.f64 (pow.f64 (pow.f64 (.f64 #s(literal 2 binary64) (.f64 (PI.f64) n)) (-.f64 #s(literal 1/4 binary64) (*.f64 k #s(literal 1/4 binary64)))) #s(literal 2 binary64)) (sqrt.f64 k))
(.f64 (exp.f64 (.f64 (log.f64 k) #s(literal -1/2 binary64))) (pow.f64 (.f64 (.f64 #s(literal 2 binary64) (PI.f64)) n) (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 2 binary64))))
(.f64 (pow.f64 (pow.f64 k #s(literal -1/4 binary64)) #s(literal 2 binary64)) (pow.f64 (.f64 (*.f64 #s(literal 2 binary64) (PI.f64)) n) (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 2 binary64))))
(/.f64 (sqrt.f64 (/.f64 (.f64 #s(literal 2 binary64) (.f64 (PI.f64) n)) (pow.f64 (.f64 #s(literal 2 binary64) (.f64 (PI.f64) n)) k))) (sqrt.f64 k))
(/.f64 (pow.f64 (.f64 #s(literal 2 binary64) (.f64 (PI.f64) n)) (-.f64 #s(literal 1/2 binary64) (/.f64 k #s(literal 2 binary64)))) (pow.f64 (pow.f64 k #s(literal 1/4 binary64)) #s(literal 2 binary64)))
(/.f64 (sqrt.f64 (.f64 #s(literal 2 binary64) (.f64 (PI.f64) n))) (pow.f64 (.f64 (pow.f64 (.f64 #s(literal 2 binary64) (*.f64 (PI.f64) n)) k) k) #s(literal 1/2 binary64)))
(/.f64 (.f64 (pow.f64 (.f64 #s(literal 2 binary64) (.f64 (PI.f64) n)) (/.f64 k #s(literal -2 binary64))) (sqrt.f64 (.f64 #s(literal 2 binary64) (*.f64 (PI.f64) n)))) (sqrt.f64 k))
(/.f64 (.f64 (pow.f64 (.f64 #s(literal 2 binary64) (PI.f64)) (+.f64 #s(literal 1/2 binary64) (/.f64 k #s(literal -2 binary64)))) (pow.f64 n (+.f64 #s(literal 1/2 binary64) (/.f64 k #s(literal -2 binary64))))) (sqrt.f64 k))
(.f64 (pow.f64 n (+.f64 #s(literal 1/2 binary64) (/.f64 k #s(literal -2 binary64)))) (.f64 (pow.f64 (*.f64 #s(literal 2 binary64) (PI.f64)) (+.f64 #s(literal 1/2 binary64) (/.f64 k #s(literal -2 binary64)))) (pow.f64 k #s(literal -1/2 binary64))))

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

Calls

4 calls:

28.0ms	k
26.0ms	n
26.0ms	(.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))))
25.0ms	(.f64 (.f64 #s(literal 2 binary64) (PI.f64)) n)

Results

Accuracy	Segments	Branch
99.3%	1	`k`
99.3%	1	`n`
99.3%	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))))`
99.3%	1	`(.f64 (.f64 #s(literal 2 binary64) (PI.f64)) n)`

Compiler

Compiled 31 to 23 computations (25.8% saved)

regimes72.0ms (0.5%)

Counts

62 → 1

Calls

Call 1

Inputs
(sqrt.f64 (.f64 (PI.f64) (.f64 n (/.f64 #s(literal 2 binary64) k))))
(sqrt.f64 (.f64 (.f64 #s(literal 2 binary64) (PI.f64)) (/.f64 n k)))
(sqrt.f64 (.f64 (/.f64 #s(literal 2 binary64) k) (.f64 (PI.f64) n)))
(sqrt.f64 (*.f64 (/.f64 #s(literal 2 binary64) (/.f64 k n)) (PI.f64)))
(sqrt.f64 (*.f64 (/.f64 #s(literal 2 binary64) (/.f64 k (PI.f64))) n))
(sqrt.f64 (*.f64 (/.f64 (PI.f64) #s(literal 1/2 binary64)) (/.f64 n k)))
(sqrt.f64 (*.f64 (/.f64 (PI.f64) k) (/.f64 n #s(literal 1/2 binary64))))
(sqrt.f64 (/.f64 #s(literal 2 binary64) (/.f64 k (*.f64 (PI.f64) n))))
(sqrt.f64 (/.f64 #s(literal 2 binary64) (/.f64 (/.f64 k n) (PI.f64))))
(sqrt.f64 (/.f64 #s(literal 2 binary64) (/.f64 (/.f64 k (PI.f64)) n)))
(sqrt.f64 (/.f64 (/.f64 n #s(literal 1/2 binary64)) (/.f64 k (PI.f64))))
(sqrt.f64 (/.f64 (/.f64 (PI.f64) #s(literal 1/2 binary64)) (/.f64 k n)))
(sqrt.f64 (/.f64 (/.f64 (PI.f64) k) (/.f64 #s(literal 1/2 binary64) n)))
(sqrt.f64 (/.f64 (/.f64 (*.f64 (PI.f64) n) #s(literal 1/2 binary64)) k))
(pow.f64 (/.f64 #s(literal 1/2 binary64) (/.f64 (*.f64 (PI.f64) n) k)) #s(literal -1/2 binary64))
(pow.f64 (/.f64 (/.f64 k (*.f64 (PI.f64) n)) #s(literal 2 binary64)) #s(literal -1/2 binary64))
(sqrt.f64 (*.f64 (PI.f64) (/.f64 (/.f64 #s(literal 2 binary64) k) (/.f64 #s(literal 1 binary64) n))))
(sqrt.f64 (/.f64 #s(literal 2 binary64) (/.f64 (/.f64 #s(literal 1 binary64) n) (/.f64 (PI.f64) k))))
(sqrt.f64 (/.f64 #s(literal 2 binary64) (/.f64 (/.f64 #s(literal 1 binary64) (PI.f64)) (/.f64 n k))))
(sqrt.f64 (/.f64 (/.f64 #s(literal 1 binary64) k) (/.f64 #s(literal 1/2 binary64) (*.f64 (PI.f64) n))))
(sqrt.f64 (/.f64 (/.f64 #s(literal 2 binary64) k) (/.f64 (/.f64 #s(literal 1 binary64) (PI.f64)) n)))
(sqrt.f64 (/.f64 (/.f64 #s(literal 2 binary64) (/.f64 (/.f64 #s(literal 1 binary64) n) (PI.f64))) k))
(/.f64 #s(literal 1 binary64) (pow.f64 (/.f64 #s(literal 1/2 binary64) (/.f64 (*.f64 (PI.f64) n) k)) #s(literal 1/2 binary64)))
(/.f64 #s(literal 1 binary64) (pow.f64 (/.f64 #s(literal 2 binary64) (/.f64 k (*.f64 (PI.f64) n))) #s(literal -1/2 binary64)))
(sqrt.f64 (/.f64 #s(literal 2 binary64) (/.f64 (/.f64 #s(literal -1 binary64) (*.f64 (PI.f64) n)) (/.f64 #s(literal -1 binary64) k))))
(sqrt.f64 (/.f64 #s(literal 2 binary64) (/.f64 (/.f64 (/.f64 #s(literal 1 binary64) n) (PI.f64)) (/.f64 #s(literal 1 binary64) k))))
(sqrt.f64 (/.f64 #s(literal 2 binary64) (/.f64 (/.f64 (/.f64 #s(literal 1 binary64) (PI.f64)) n) (/.f64 #s(literal 1 binary64) k))))
(sqrt.f64 (/.f64 #s(literal 2 binary64) (/.f64 (/.f64 #s(literal 1 binary64) n) (/.f64 (/.f64 #s(literal 1 binary64) k) (/.f64 #s(literal 1 binary64) (PI.f64))))))
(sqrt.f64 (/.f64 #s(literal 2 binary64) (/.f64 (/.f64 #s(literal 1 binary64) (/.f64 #s(literal -1 binary64) k)) (-.f64 #s(literal 0 binary64) (*.f64 (PI.f64) n)))))
(pow.f64 (.f64 (/.f64 #s(literal 2 binary64) (/.f64 k (.f64 (PI.f64) n))) (/.f64 #s(literal 2 binary64) (/.f64 k (*.f64 (PI.f64) n)))) #s(literal 1/4 binary64))
(.f64 (sqrt.f64 n) (sqrt.f64 (.f64 (/.f64 (PI.f64) k) #s(literal 2 binary64))))
(.f64 (sqrt.f64 (.f64 (PI.f64) (/.f64 n k))) (sqrt.f64 #s(literal 2 binary64)))
(.f64 (sqrt.f64 (.f64 (/.f64 n k) (PI.f64))) (sqrt.f64 #s(literal 2 binary64)))
(.f64 (sqrt.f64 (.f64 (/.f64 (PI.f64) k) n)) (sqrt.f64 #s(literal 2 binary64)))
(*.f64 (sqrt.f64 (/.f64 n (/.f64 k #s(literal 2 binary64)))) (sqrt.f64 (PI.f64)))
(.f64 (sqrt.f64 (/.f64 (.f64 n (PI.f64)) k)) (sqrt.f64 #s(literal 2 binary64)))
(/.f64 (sqrt.f64 #s(literal 2 binary64)) (sqrt.f64 (/.f64 k (*.f64 (PI.f64) n))))
(/.f64 (sqrt.f64 (.f64 #s(literal 2 binary64) (.f64 (PI.f64) n))) (sqrt.f64 k))
(/.f64 (sqrt.f64 (.f64 (.f64 n (PI.f64)) #s(literal 2 binary64))) (sqrt.f64 k))
(/.f64 (sqrt.f64 (*.f64 (/.f64 (PI.f64) k) n)) (sqrt.f64 #s(literal 1/2 binary64)))
(/.f64 (sqrt.f64 (/.f64 n (/.f64 #s(literal 1/2 binary64) (PI.f64)))) (sqrt.f64 k))
(/.f64 (sqrt.f64 (/.f64 (*.f64 n (PI.f64)) k)) (sqrt.f64 #s(literal 1/2 binary64)))
(.f64 (sqrt.f64 (.f64 #s(literal 2 binary64) n)) (pow.f64 (/.f64 (PI.f64) k) #s(literal 1/2 binary64)))
(.f64 (sqrt.f64 (.f64 #s(literal 2 binary64) (*.f64 (PI.f64) n))) (pow.f64 k #s(literal -1/2 binary64)))
(.f64 (pow.f64 (.f64 #s(literal 2 binary64) (PI.f64)) #s(literal 1/2 binary64)) (sqrt.f64 (/.f64 n k)))
(.f64 (pow.f64 (.f64 (PI.f64) n) #s(literal 1/2 binary64)) (sqrt.f64 (/.f64 #s(literal 2 binary64) k)))
(*.f64 (pow.f64 (/.f64 #s(literal 2 binary64) (/.f64 k n)) #s(literal 1/2 binary64)) (sqrt.f64 (PI.f64)))
(*.f64 (pow.f64 (/.f64 n #s(literal 1/2 binary64)) #s(literal 1/2 binary64)) (sqrt.f64 (/.f64 (PI.f64) k)))
(/.f64 (sqrt.f64 (*.f64 #s(literal 2 binary64) (PI.f64))) (pow.f64 (/.f64 k n) #s(literal 1/2 binary64)))
(/.f64 (pow.f64 (*.f64 (PI.f64) n) #s(literal 1/2 binary64)) (sqrt.f64 (/.f64 k #s(literal 2 binary64))))
(/.f64 (pow.f64 (/.f64 n #s(literal 1/2 binary64)) #s(literal 1/2 binary64)) (sqrt.f64 (/.f64 k (PI.f64))))
(exp.f64 (.f64 (log.f64 (/.f64 #s(literal 2 binary64) (/.f64 k (.f64 (PI.f64) n)))) #s(literal 1/2 binary64)))
(exp.f64 (*.f64 (log.f64 (/.f64 (/.f64 (PI.f64) k) (/.f64 #s(literal 1/2 binary64) n))) #s(literal 1/2 binary64)))
(.f64 (sqrt.f64 (/.f64 (.f64 n (PI.f64)) k)) (/.f64 #s(literal -1 binary64) (sqrt.f64 #s(literal 1/2 binary64))))
(/.f64 (sqrt.f64 (/.f64 (/.f64 n k) (/.f64 #s(literal 1 binary64) (PI.f64)))) (sqrt.f64 #s(literal 1/2 binary64)))
(/.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 (/.f64 #s(literal 1/2 binary64) (*.f64 (PI.f64) n)))) (sqrt.f64 k))
(.f64 (pow.f64 (.f64 (PI.f64) n) #s(literal 1/2 binary64)) (sqrt.f64 (*.f64 (/.f64 #s(literal 1 binary64) k) #s(literal 2 binary64))))
(/.f64 #s(literal 1 binary64) (/.f64 (sqrt.f64 (/.f64 k #s(literal 2 binary64))) (pow.f64 (*.f64 (PI.f64) n) #s(literal 1/2 binary64))))
(/.f64 (/.f64 #s(literal 1 binary64) (pow.f64 (/.f64 k (*.f64 (PI.f64) n)) #s(literal 1/2 binary64))) (sqrt.f64 #s(literal 1/2 binary64)))
(/.f64 (sqrt.f64 (/.f64 (/.f64 #s(literal 1 binary64) (/.f64 (/.f64 #s(literal 1 binary64) n) (PI.f64))) k)) (sqrt.f64 #s(literal 1/2 binary64)))
(/.f64 (*.f64 #s(literal 1 binary64) (pow.f64 (/.f64 n #s(literal 1/2 binary64)) #s(literal 1/2 binary64))) (pow.f64 (/.f64 k (PI.f64)) #s(literal 1/2 binary64)))
(/.f64 (pow.f64 (.f64 #s(literal 2 binary64) (.f64 (PI.f64) n)) (-.f64 #s(literal 1/2 binary64) (/.f64 k #s(literal 2 binary64)))) (sqrt.f64 k))

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

Calls

2 calls:

45.0ms	k
21.0ms	n

Results

Accuracy	Segments	Branch
99.3%	1	`k`
99.3%	1	`n`

Compiler

Compiled 6 to 4 computations (33.3% saved)

regimes56.0ms (0.4%)

Counts

61 → 2

Calls

Call 1

Inputs
(sqrt.f64 (.f64 (PI.f64) (.f64 n (/.f64 #s(literal 2 binary64) k))))
(sqrt.f64 (.f64 (.f64 #s(literal 2 binary64) (PI.f64)) (/.f64 n k)))
(sqrt.f64 (.f64 (/.f64 #s(literal 2 binary64) k) (.f64 (PI.f64) n)))
(sqrt.f64 (*.f64 (/.f64 #s(literal 2 binary64) (/.f64 k n)) (PI.f64)))
(sqrt.f64 (*.f64 (/.f64 #s(literal 2 binary64) (/.f64 k (PI.f64))) n))
(sqrt.f64 (*.f64 (/.f64 (PI.f64) #s(literal 1/2 binary64)) (/.f64 n k)))
(sqrt.f64 (*.f64 (/.f64 (PI.f64) k) (/.f64 n #s(literal 1/2 binary64))))
(sqrt.f64 (/.f64 #s(literal 2 binary64) (/.f64 k (*.f64 (PI.f64) n))))
(sqrt.f64 (/.f64 #s(literal 2 binary64) (/.f64 (/.f64 k n) (PI.f64))))
(sqrt.f64 (/.f64 #s(literal 2 binary64) (/.f64 (/.f64 k (PI.f64)) n)))
(sqrt.f64 (/.f64 (/.f64 n #s(literal 1/2 binary64)) (/.f64 k (PI.f64))))
(sqrt.f64 (/.f64 (/.f64 (PI.f64) #s(literal 1/2 binary64)) (/.f64 k n)))
(sqrt.f64 (/.f64 (/.f64 (PI.f64) k) (/.f64 #s(literal 1/2 binary64) n)))
(sqrt.f64 (/.f64 (/.f64 (*.f64 (PI.f64) n) #s(literal 1/2 binary64)) k))
(pow.f64 (/.f64 #s(literal 1/2 binary64) (/.f64 (*.f64 (PI.f64) n) k)) #s(literal -1/2 binary64))
(pow.f64 (/.f64 (/.f64 k (*.f64 (PI.f64) n)) #s(literal 2 binary64)) #s(literal -1/2 binary64))
(sqrt.f64 (*.f64 (PI.f64) (/.f64 (/.f64 #s(literal 2 binary64) k) (/.f64 #s(literal 1 binary64) n))))
(sqrt.f64 (/.f64 #s(literal 2 binary64) (/.f64 (/.f64 #s(literal 1 binary64) n) (/.f64 (PI.f64) k))))
(sqrt.f64 (/.f64 #s(literal 2 binary64) (/.f64 (/.f64 #s(literal 1 binary64) (PI.f64)) (/.f64 n k))))
(sqrt.f64 (/.f64 (/.f64 #s(literal 1 binary64) k) (/.f64 #s(literal 1/2 binary64) (*.f64 (PI.f64) n))))
(sqrt.f64 (/.f64 (/.f64 #s(literal 2 binary64) k) (/.f64 (/.f64 #s(literal 1 binary64) (PI.f64)) n)))
(sqrt.f64 (/.f64 (/.f64 #s(literal 2 binary64) (/.f64 (/.f64 #s(literal 1 binary64) n) (PI.f64))) k))
(/.f64 #s(literal 1 binary64) (pow.f64 (/.f64 #s(literal 1/2 binary64) (/.f64 (*.f64 (PI.f64) n) k)) #s(literal 1/2 binary64)))
(/.f64 #s(literal 1 binary64) (pow.f64 (/.f64 #s(literal 2 binary64) (/.f64 k (*.f64 (PI.f64) n))) #s(literal -1/2 binary64)))
(sqrt.f64 (/.f64 #s(literal 2 binary64) (/.f64 (/.f64 #s(literal -1 binary64) (*.f64 (PI.f64) n)) (/.f64 #s(literal -1 binary64) k))))
(sqrt.f64 (/.f64 #s(literal 2 binary64) (/.f64 (/.f64 (/.f64 #s(literal 1 binary64) n) (PI.f64)) (/.f64 #s(literal 1 binary64) k))))
(sqrt.f64 (/.f64 #s(literal 2 binary64) (/.f64 (/.f64 (/.f64 #s(literal 1 binary64) (PI.f64)) n) (/.f64 #s(literal 1 binary64) k))))
(sqrt.f64 (/.f64 #s(literal 2 binary64) (/.f64 (/.f64 #s(literal 1 binary64) n) (/.f64 (/.f64 #s(literal 1 binary64) k) (/.f64 #s(literal 1 binary64) (PI.f64))))))
(sqrt.f64 (/.f64 #s(literal 2 binary64) (/.f64 (/.f64 #s(literal 1 binary64) (/.f64 #s(literal -1 binary64) k)) (-.f64 #s(literal 0 binary64) (*.f64 (PI.f64) n)))))
(pow.f64 (.f64 (/.f64 #s(literal 2 binary64) (/.f64 k (.f64 (PI.f64) n))) (/.f64 #s(literal 2 binary64) (/.f64 k (*.f64 (PI.f64) n)))) #s(literal 1/4 binary64))
(.f64 (sqrt.f64 n) (sqrt.f64 (.f64 (/.f64 (PI.f64) k) #s(literal 2 binary64))))
(.f64 (sqrt.f64 (.f64 (PI.f64) (/.f64 n k))) (sqrt.f64 #s(literal 2 binary64)))
(.f64 (sqrt.f64 (.f64 (/.f64 n k) (PI.f64))) (sqrt.f64 #s(literal 2 binary64)))
(.f64 (sqrt.f64 (.f64 (/.f64 (PI.f64) k) n)) (sqrt.f64 #s(literal 2 binary64)))
(*.f64 (sqrt.f64 (/.f64 n (/.f64 k #s(literal 2 binary64)))) (sqrt.f64 (PI.f64)))
(.f64 (sqrt.f64 (/.f64 (.f64 n (PI.f64)) k)) (sqrt.f64 #s(literal 2 binary64)))
(/.f64 (sqrt.f64 #s(literal 2 binary64)) (sqrt.f64 (/.f64 k (*.f64 (PI.f64) n))))
(/.f64 (sqrt.f64 (.f64 #s(literal 2 binary64) (.f64 (PI.f64) n))) (sqrt.f64 k))
(/.f64 (sqrt.f64 (.f64 (.f64 n (PI.f64)) #s(literal 2 binary64))) (sqrt.f64 k))
(/.f64 (sqrt.f64 (*.f64 (/.f64 (PI.f64) k) n)) (sqrt.f64 #s(literal 1/2 binary64)))
(/.f64 (sqrt.f64 (/.f64 n (/.f64 #s(literal 1/2 binary64) (PI.f64)))) (sqrt.f64 k))
(/.f64 (sqrt.f64 (/.f64 (*.f64 n (PI.f64)) k)) (sqrt.f64 #s(literal 1/2 binary64)))
(.f64 (sqrt.f64 (.f64 #s(literal 2 binary64) n)) (pow.f64 (/.f64 (PI.f64) k) #s(literal 1/2 binary64)))
(.f64 (sqrt.f64 (.f64 #s(literal 2 binary64) (*.f64 (PI.f64) n))) (pow.f64 k #s(literal -1/2 binary64)))
(.f64 (pow.f64 (.f64 #s(literal 2 binary64) (PI.f64)) #s(literal 1/2 binary64)) (sqrt.f64 (/.f64 n k)))
(.f64 (pow.f64 (.f64 (PI.f64) n) #s(literal 1/2 binary64)) (sqrt.f64 (/.f64 #s(literal 2 binary64) k)))
(*.f64 (pow.f64 (/.f64 #s(literal 2 binary64) (/.f64 k n)) #s(literal 1/2 binary64)) (sqrt.f64 (PI.f64)))
(*.f64 (pow.f64 (/.f64 n #s(literal 1/2 binary64)) #s(literal 1/2 binary64)) (sqrt.f64 (/.f64 (PI.f64) k)))
(/.f64 (sqrt.f64 (*.f64 #s(literal 2 binary64) (PI.f64))) (pow.f64 (/.f64 k n) #s(literal 1/2 binary64)))
(/.f64 (pow.f64 (*.f64 (PI.f64) n) #s(literal 1/2 binary64)) (sqrt.f64 (/.f64 k #s(literal 2 binary64))))
(/.f64 (pow.f64 (/.f64 n #s(literal 1/2 binary64)) #s(literal 1/2 binary64)) (sqrt.f64 (/.f64 k (PI.f64))))
(exp.f64 (.f64 (log.f64 (/.f64 #s(literal 2 binary64) (/.f64 k (.f64 (PI.f64) n)))) #s(literal 1/2 binary64)))
(exp.f64 (*.f64 (log.f64 (/.f64 (/.f64 (PI.f64) k) (/.f64 #s(literal 1/2 binary64) n))) #s(literal 1/2 binary64)))
(.f64 (sqrt.f64 (/.f64 (.f64 n (PI.f64)) k)) (/.f64 #s(literal -1 binary64) (sqrt.f64 #s(literal 1/2 binary64))))
(/.f64 (sqrt.f64 (/.f64 (/.f64 n k) (/.f64 #s(literal 1 binary64) (PI.f64)))) (sqrt.f64 #s(literal 1/2 binary64)))
(/.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 (/.f64 #s(literal 1/2 binary64) (*.f64 (PI.f64) n)))) (sqrt.f64 k))
(.f64 (pow.f64 (.f64 (PI.f64) n) #s(literal 1/2 binary64)) (sqrt.f64 (*.f64 (/.f64 #s(literal 1 binary64) k) #s(literal 2 binary64))))
(/.f64 #s(literal 1 binary64) (/.f64 (sqrt.f64 (/.f64 k #s(literal 2 binary64))) (pow.f64 (*.f64 (PI.f64) n) #s(literal 1/2 binary64))))
(/.f64 (/.f64 #s(literal 1 binary64) (pow.f64 (/.f64 k (*.f64 (PI.f64) n)) #s(literal 1/2 binary64))) (sqrt.f64 #s(literal 1/2 binary64)))
(/.f64 (sqrt.f64 (/.f64 (/.f64 #s(literal 1 binary64) (/.f64 (/.f64 #s(literal 1 binary64) n) (PI.f64))) k)) (sqrt.f64 #s(literal 1/2 binary64)))
(/.f64 (*.f64 #s(literal 1 binary64) (pow.f64 (/.f64 n #s(literal 1/2 binary64)) #s(literal 1/2 binary64))) (pow.f64 (/.f64 k (PI.f64)) #s(literal 1/2 binary64)))

Outputs

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

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

Calls

2 calls:

29.0ms	n
23.0ms	k

Results

Accuracy	Segments	Branch
48.1%	2	`k`
44.4%	1	`n`

Compiler

Compiled 6 to 4 computations (33.3% saved)

regimes26.0ms (0.2%)

Counts

30 → 2

Calls

Call 1

Inputs
(sqrt.f64 (.f64 (PI.f64) (.f64 n (/.f64 #s(literal 2 binary64) k))))
(sqrt.f64 (.f64 (.f64 #s(literal 2 binary64) (PI.f64)) (/.f64 n k)))
(sqrt.f64 (.f64 (/.f64 #s(literal 2 binary64) k) (.f64 (PI.f64) n)))
(sqrt.f64 (*.f64 (/.f64 #s(literal 2 binary64) (/.f64 k n)) (PI.f64)))
(sqrt.f64 (*.f64 (/.f64 #s(literal 2 binary64) (/.f64 k (PI.f64))) n))
(sqrt.f64 (*.f64 (/.f64 (PI.f64) #s(literal 1/2 binary64)) (/.f64 n k)))
(sqrt.f64 (*.f64 (/.f64 (PI.f64) k) (/.f64 n #s(literal 1/2 binary64))))
(sqrt.f64 (/.f64 #s(literal 2 binary64) (/.f64 k (*.f64 (PI.f64) n))))
(sqrt.f64 (/.f64 #s(literal 2 binary64) (/.f64 (/.f64 k n) (PI.f64))))
(sqrt.f64 (/.f64 #s(literal 2 binary64) (/.f64 (/.f64 k (PI.f64)) n)))
(sqrt.f64 (/.f64 (/.f64 n #s(literal 1/2 binary64)) (/.f64 k (PI.f64))))
(sqrt.f64 (/.f64 (/.f64 (PI.f64) #s(literal 1/2 binary64)) (/.f64 k n)))
(sqrt.f64 (/.f64 (/.f64 (PI.f64) k) (/.f64 #s(literal 1/2 binary64) n)))
(sqrt.f64 (/.f64 (/.f64 (*.f64 (PI.f64) n) #s(literal 1/2 binary64)) k))
(pow.f64 (/.f64 #s(literal 1/2 binary64) (/.f64 (*.f64 (PI.f64) n) k)) #s(literal -1/2 binary64))
(pow.f64 (/.f64 (/.f64 k (*.f64 (PI.f64) n)) #s(literal 2 binary64)) #s(literal -1/2 binary64))
(sqrt.f64 (*.f64 (PI.f64) (/.f64 (/.f64 #s(literal 2 binary64) k) (/.f64 #s(literal 1 binary64) n))))
(sqrt.f64 (/.f64 #s(literal 2 binary64) (/.f64 (/.f64 #s(literal 1 binary64) n) (/.f64 (PI.f64) k))))
(sqrt.f64 (/.f64 #s(literal 2 binary64) (/.f64 (/.f64 #s(literal 1 binary64) (PI.f64)) (/.f64 n k))))
(sqrt.f64 (/.f64 (/.f64 #s(literal 1 binary64) k) (/.f64 #s(literal 1/2 binary64) (*.f64 (PI.f64) n))))
(sqrt.f64 (/.f64 (/.f64 #s(literal 2 binary64) k) (/.f64 (/.f64 #s(literal 1 binary64) (PI.f64)) n)))
(sqrt.f64 (/.f64 (/.f64 #s(literal 2 binary64) (/.f64 (/.f64 #s(literal 1 binary64) n) (PI.f64))) k))
(/.f64 #s(literal 1 binary64) (pow.f64 (/.f64 #s(literal 1/2 binary64) (/.f64 (*.f64 (PI.f64) n) k)) #s(literal 1/2 binary64)))
(/.f64 #s(literal 1 binary64) (pow.f64 (/.f64 #s(literal 2 binary64) (/.f64 k (*.f64 (PI.f64) n))) #s(literal -1/2 binary64)))
(sqrt.f64 (/.f64 #s(literal 2 binary64) (/.f64 (/.f64 #s(literal -1 binary64) (*.f64 (PI.f64) n)) (/.f64 #s(literal -1 binary64) k))))
(sqrt.f64 (/.f64 #s(literal 2 binary64) (/.f64 (/.f64 (/.f64 #s(literal 1 binary64) n) (PI.f64)) (/.f64 #s(literal 1 binary64) k))))
(sqrt.f64 (/.f64 #s(literal 2 binary64) (/.f64 (/.f64 (/.f64 #s(literal 1 binary64) (PI.f64)) n) (/.f64 #s(literal 1 binary64) k))))
(sqrt.f64 (/.f64 #s(literal 2 binary64) (/.f64 (/.f64 #s(literal 1 binary64) n) (/.f64 (/.f64 #s(literal 1 binary64) k) (/.f64 #s(literal 1 binary64) (PI.f64))))))
(sqrt.f64 (/.f64 #s(literal 2 binary64) (/.f64 (/.f64 #s(literal 1 binary64) (/.f64 #s(literal -1 binary64) k)) (-.f64 #s(literal 0 binary64) (*.f64 (PI.f64) n)))))
(pow.f64 (.f64 (/.f64 #s(literal 2 binary64) (/.f64 k (.f64 (PI.f64) n))) (/.f64 #s(literal 2 binary64) (/.f64 k (*.f64 (PI.f64) n)))) #s(literal 1/4 binary64))

Outputs

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

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

Calls

2 calls:

14.0ms	n
9.0ms	k

Results

Accuracy	Segments	Branch
38.6%	1	`n`
42.4%	2	`k`

Compiler

Compiled 6 to 4 computations (33.3% saved)

regimes22.0ms (0.2%)

Counts

29 → 1

Calls

Call 1

Inputs
(sqrt.f64 (.f64 (PI.f64) (.f64 n (/.f64 #s(literal 2 binary64) k))))
(sqrt.f64 (.f64 (.f64 #s(literal 2 binary64) (PI.f64)) (/.f64 n k)))
(sqrt.f64 (.f64 (/.f64 #s(literal 2 binary64) k) (.f64 (PI.f64) n)))
(sqrt.f64 (*.f64 (/.f64 #s(literal 2 binary64) (/.f64 k n)) (PI.f64)))
(sqrt.f64 (*.f64 (/.f64 #s(literal 2 binary64) (/.f64 k (PI.f64))) n))
(sqrt.f64 (*.f64 (/.f64 (PI.f64) #s(literal 1/2 binary64)) (/.f64 n k)))
(sqrt.f64 (*.f64 (/.f64 (PI.f64) k) (/.f64 n #s(literal 1/2 binary64))))
(sqrt.f64 (/.f64 #s(literal 2 binary64) (/.f64 k (*.f64 (PI.f64) n))))
(sqrt.f64 (/.f64 #s(literal 2 binary64) (/.f64 (/.f64 k n) (PI.f64))))
(sqrt.f64 (/.f64 #s(literal 2 binary64) (/.f64 (/.f64 k (PI.f64)) n)))
(sqrt.f64 (/.f64 (/.f64 n #s(literal 1/2 binary64)) (/.f64 k (PI.f64))))
(sqrt.f64 (/.f64 (/.f64 (PI.f64) #s(literal 1/2 binary64)) (/.f64 k n)))
(sqrt.f64 (/.f64 (/.f64 (PI.f64) k) (/.f64 #s(literal 1/2 binary64) n)))
(sqrt.f64 (/.f64 (/.f64 (*.f64 (PI.f64) n) #s(literal 1/2 binary64)) k))
(pow.f64 (/.f64 #s(literal 1/2 binary64) (/.f64 (*.f64 (PI.f64) n) k)) #s(literal -1/2 binary64))
(pow.f64 (/.f64 (/.f64 k (*.f64 (PI.f64) n)) #s(literal 2 binary64)) #s(literal -1/2 binary64))
(sqrt.f64 (*.f64 (PI.f64) (/.f64 (/.f64 #s(literal 2 binary64) k) (/.f64 #s(literal 1 binary64) n))))
(sqrt.f64 (/.f64 #s(literal 2 binary64) (/.f64 (/.f64 #s(literal 1 binary64) n) (/.f64 (PI.f64) k))))
(sqrt.f64 (/.f64 #s(literal 2 binary64) (/.f64 (/.f64 #s(literal 1 binary64) (PI.f64)) (/.f64 n k))))
(sqrt.f64 (/.f64 (/.f64 #s(literal 1 binary64) k) (/.f64 #s(literal 1/2 binary64) (*.f64 (PI.f64) n))))
(sqrt.f64 (/.f64 (/.f64 #s(literal 2 binary64) k) (/.f64 (/.f64 #s(literal 1 binary64) (PI.f64)) n)))
(sqrt.f64 (/.f64 (/.f64 #s(literal 2 binary64) (/.f64 (/.f64 #s(literal 1 binary64) n) (PI.f64))) k))
(/.f64 #s(literal 1 binary64) (pow.f64 (/.f64 #s(literal 1/2 binary64) (/.f64 (*.f64 (PI.f64) n) k)) #s(literal 1/2 binary64)))
(/.f64 #s(literal 1 binary64) (pow.f64 (/.f64 #s(literal 2 binary64) (/.f64 k (*.f64 (PI.f64) n))) #s(literal -1/2 binary64)))
(sqrt.f64 (/.f64 #s(literal 2 binary64) (/.f64 (/.f64 #s(literal -1 binary64) (*.f64 (PI.f64) n)) (/.f64 #s(literal -1 binary64) k))))
(sqrt.f64 (/.f64 #s(literal 2 binary64) (/.f64 (/.f64 (/.f64 #s(literal 1 binary64) n) (PI.f64)) (/.f64 #s(literal 1 binary64) k))))
(sqrt.f64 (/.f64 #s(literal 2 binary64) (/.f64 (/.f64 (/.f64 #s(literal 1 binary64) (PI.f64)) n) (/.f64 #s(literal 1 binary64) k))))
(sqrt.f64 (/.f64 #s(literal 2 binary64) (/.f64 (/.f64 #s(literal 1 binary64) n) (/.f64 (/.f64 #s(literal 1 binary64) k) (/.f64 #s(literal 1 binary64) (PI.f64))))))
(sqrt.f64 (/.f64 #s(literal 2 binary64) (/.f64 (/.f64 #s(literal 1 binary64) (/.f64 #s(literal -1 binary64) k)) (-.f64 #s(literal 0 binary64) (*.f64 (PI.f64) n)))))

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

Calls

2 calls:

9.0ms	k
9.0ms	n

Results

Accuracy	Segments	Branch
38.6%	1	`n`
38.6%	1	`k`

Compiler

Compiled 6 to 4 computations (33.3% saved)

regimes11.0ms (0.1%)

Accuracy

Total -0.2b remaining (-0.4%)

Threshold costs -0.2b (-0.4%)

Counts

15 → 1

Calls

Call 1

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

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

Calls

2 calls:

5.0ms	n
5.0ms	k

Results

Accuracy	Segments	Branch
37.2%	1	`k`
37.2%	1	`n`

Compiler

Compiled 6 to 4 computations (33.3% saved)

bsearch22.0ms (0.2%)

Algorithm

1×	binary-search

Stop Event

1×	narrow-enough

Steps

Time	Left	Right
20.0ms	6.663585521336365e+161	3.012957748234626e+163

Results

16.0ms

112×

valid

Compiler

Compiled 247 to 164 computations (33.6% saved)

Precisions

Click to see histograms. Total time spent on operations: 13.0ms

ival-pow: 7.0ms (54.6% of total)

ival-div: 2.0ms (15.6% of total)

ival-mult: 2.0ms (15.6% of total)

ival-sub: 1.0ms (7.8% of total)

ival-sqrt: 1.0ms (7.8% of total)

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

const: 0.0ms (0% of total)

backward-pass: 0.0ms (0% of total)

bsearch23.0ms (0.2%)

Algorithm

1×	binary-search

Stop Event

1×	narrow-enough

Steps

Time	Left	Right
21.0ms	3.633676824740339e+160	6.663585521336365e+161

Results

14.0ms

112×

valid

Compiler

Compiled 247 to 164 computations (33.6% saved)

Precisions

Click to see histograms. Total time spent on operations: 10.0ms

ival-pow: 4.0ms (38.4% of total)

ival-div: 2.0ms (19.2% of total)

ival-mult: 2.0ms (19.2% of total)

ival-sub: 1.0ms (9.6% of total)

ival-sqrt: 1.0ms (9.6% of total)

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

const: 0.0ms (0% of total)

backward-pass: 0.0ms (0% of total)

simplify9.0ms (0.1%)

Algorithm

1×	egg-herbie

Rules

18×	`*-commutative_binary64`
10×	`+-commutative_binary64`
8×	`sub-neg_binary64`
6×	`neg-sub0_binary64`
6×	`neg-mul-1_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	39	106
1	48	106
2	57	106
3	63	106
4	68	106
5	70	106

Stop Event

1×

saturated

Calls

Call 1

Inputs
(/.f64 (pow.f64 k #s(literal -1/2 binary64)) (pow.f64 (.f64 #s(literal 2 binary64) (.f64 (PI.f64) n)) (+.f64 (/.f64 k #s(literal 2 binary64)) #s(literal -1/2 binary64))))
(/.f64 (pow.f64 (.f64 #s(literal 2 binary64) (.f64 (PI.f64) n)) (-.f64 #s(literal 1/2 binary64) (/.f64 k #s(literal 2 binary64)))) (sqrt.f64 k))
(if (<=.f64 k #s(literal 30000000000000001332168704667067968928271318091371336647836257566611034246247676731166325460361286831240448925672604857758253281137641325011616793212250695678296064 binary64)) (.f64 (sqrt.f64 n) (sqrt.f64 (.f64 (/.f64 (PI.f64) k) #s(literal 2 binary64)))) (pow.f64 (.f64 (/.f64 #s(literal 2 binary64) (/.f64 k (.f64 (PI.f64) n))) (/.f64 #s(literal 2 binary64) (/.f64 k (*.f64 (PI.f64) n)))) #s(literal 1/4 binary64)))
(if (<=.f64 k #s(literal 659999999999999994943503460797052833373346692446994712571829312009440324759849076529567059199968364002960293841877688343306714400584004317164253173064070653280256 binary64)) (pow.f64 (/.f64 (/.f64 k (.f64 (PI.f64) n)) #s(literal 2 binary64)) #s(literal -1/2 binary64)) (pow.f64 (.f64 (/.f64 #s(literal 2 binary64) (/.f64 k (.f64 (PI.f64) n))) (/.f64 #s(literal 2 binary64) (/.f64 k (.f64 (PI.f64) n)))) #s(literal 1/4 binary64)))
(pow.f64 (/.f64 (/.f64 k (*.f64 (PI.f64) n)) #s(literal 2 binary64)) #s(literal -1/2 binary64))
(sqrt.f64 (.f64 (PI.f64) (.f64 n (/.f64 #s(literal 2 binary64) k))))

Outputs
(/.f64 (pow.f64 k #s(literal -1/2 binary64)) (pow.f64 (.f64 #s(literal 2 binary64) (.f64 (PI.f64) n)) (+.f64 (/.f64 k #s(literal 2 binary64)) #s(literal -1/2 binary64))))
(/.f64 (pow.f64 k #s(literal -1/2 binary64)) (pow.f64 (.f64 #s(literal 2 binary64) (.f64 (PI.f64) n)) (+.f64 #s(literal -1/2 binary64) (/.f64 k #s(literal 2 binary64)))))
(/.f64 (pow.f64 (.f64 #s(literal 2 binary64) (.f64 (PI.f64) n)) (-.f64 #s(literal 1/2 binary64) (/.f64 k #s(literal 2 binary64)))) (sqrt.f64 k))
(if (<=.f64 k #s(literal 30000000000000001332168704667067968928271318091371336647836257566611034246247676731166325460361286831240448925672604857758253281137641325011616793212250695678296064 binary64)) (.f64 (sqrt.f64 n) (sqrt.f64 (.f64 (/.f64 (PI.f64) k) #s(literal 2 binary64)))) (pow.f64 (.f64 (/.f64 #s(literal 2 binary64) (/.f64 k (.f64 (PI.f64) n))) (/.f64 #s(literal 2 binary64) (/.f64 k (*.f64 (PI.f64) n)))) #s(literal 1/4 binary64)))
(if (<=.f64 k #s(literal 30000000000000001332168704667067968928271318091371336647836257566611034246247676731166325460361286831240448925672604857758253281137641325011616793212250695678296064 binary64)) (.f64 (sqrt.f64 n) (sqrt.f64 (.f64 #s(literal 2 binary64) (/.f64 (PI.f64) k)))) (pow.f64 (.f64 (/.f64 #s(literal 2 binary64) (/.f64 k (.f64 (PI.f64) n))) (/.f64 #s(literal 2 binary64) (/.f64 k (*.f64 (PI.f64) n)))) #s(literal 1/4 binary64)))
(if (<=.f64 k #s(literal 659999999999999994943503460797052833373346692446994712571829312009440324759849076529567059199968364002960293841877688343306714400584004317164253173064070653280256 binary64)) (pow.f64 (/.f64 (/.f64 k (.f64 (PI.f64) n)) #s(literal 2 binary64)) #s(literal -1/2 binary64)) (pow.f64 (.f64 (/.f64 #s(literal 2 binary64) (/.f64 k (.f64 (PI.f64) n))) (/.f64 #s(literal 2 binary64) (/.f64 k (.f64 (PI.f64) n)))) #s(literal 1/4 binary64)))
(pow.f64 (/.f64 (/.f64 k (*.f64 (PI.f64) n)) #s(literal 2 binary64)) #s(literal -1/2 binary64))
(sqrt.f64 (.f64 (PI.f64) (.f64 n (/.f64 #s(literal 2 binary64) k))))

soundness1.4s (10.2%)

Rules

5716×	`-lowering-.f32`
5716×	`-lowering-.f64`
5664×	`-lowering-.f32`
5664×	`-lowering-.f64`
5256×	`-lowering-.f32`

Iterations

Useful iterations: 4 (0.0ms)

Iter	Nodes	Cost
0	13	14
1	30	14
2	47	14
3	69	14
4	90	13
5	113	13
6	149	13
7	188	13
8	214	13
9	228	13
10	229	13
0	229	13
0	41	169
1	262	159
2	1785	158
0	8344	158
0	139	2132
1	385	2104
2	1189	1816
3	4175	1732
4	7740	1732
0	8111	1732
0	20	68
1	132	68
2	851	64
0	8618	64
0	28	154
1	159	154
2	1002	139
0	8191	139

Stop Event

1×	fuel
1×	iter limit
1×	node limit
1×	iter limit
1×	node limit
1×	iter limit
1×	node limit
1×	iter limit
1×	node limit
1×	iter limit
1×	saturated

Compiler

Compiled 323 to 202 computations (37.5% saved)

preprocess44.0ms (0.3%)

Compiler: Compiled 252 to 104 computations (58.7% saved)

Iter	Nodes	Cost
0	20	98
1	38	98
2	58	98
3	78	98
4	100	92
5	129	92
6	170	92
7	202	92
8	231	92
9	235	92
0	235	92

Iter	Nodes	Cost
0	41	256
1	72	251
2	108	249
3	155	249
4	233	249
5	372	249
6	528	249
7	662	249
8	790	249
9	869	249
10	877	249
11	878	249
0	878	249

Iter	Nodes	Cost
0	28	209
1	47	209
2	98	209
3	212	209
4	266	209
5	299	209
6	324	209
7	336	209
8	346	209
0	346	209

Iter	Nodes	Cost
0	20	98
1	38	98
2	58	98
3	78	98
4	100	92
5	129	92
6	170	92
7	202	92
8	231	92
9	235	92
0	235	92

Iter	Nodes	Cost
0	41	256
1	72	251
2	108	249
3	155	249
4	233	249
5	372	249
6	528	249
7	662	249
8	790	249
9	869	249
10	877	249
11	878	249
0	878	249

Iter	Nodes	Cost
0	28	209
1	47	209
2	98	209
3	212	209
4	266	209
5	299	209
6	324	209
7	336	209
8	346	209
0	346	209

analyze197.0ms (1.5%)

sample4.8s (35.3%)

preprocess83.0ms (0.6%)

explain144.0ms (1.1%)

eval0.0ms (0%)

prune1.0ms (0%)

simplify11.0ms (0.1%)

localize117.0ms (0.9%)

series97.0ms (0.7%)

rewrite347.0ms (2.6%)

simplify256.0ms (1.9%)

eval141.0ms (1%)

prune115.0ms (0.9%)

simplify54.0ms (0.4%)

localize356.0ms (2.6%)

series81.0ms (0.6%)

rewrite323.0ms (2.4%)

simplify325.0ms (2.4%)

eval210.0ms (1.6%)

prune229.0ms (1.7%)

simplify16.0ms (0.1%)

localize240.0ms (1.8%)

series73.0ms (0.5%)

rewrite376.0ms (2.8%)

simplify354.0ms (2.6%)

eval422.0ms (3.1%)

prune428.0ms (3.2%)

simplify29.0ms (0.2%)

localize179.0ms (1.3%)

series311.0ms (2.3%)

rewrite374.0ms (2.8%)

simplify335.0ms (2.5%)

eval400.0ms (3%)

prune330.0ms (2.4%)

regimes112.0ms (0.8%)

regimes72.0ms (0.5%)

regimes56.0ms (0.4%)

regimes26.0ms (0.2%)

regimes22.0ms (0.2%)

regimes11.0ms (0.1%)

bsearch22.0ms (0.2%)

bsearch23.0ms (0.2%)

simplify9.0ms (0.1%)

soundness1.4s (10.2%)

preprocess44.0ms (0.3%)

end0.0ms (0%)

Profiling

Iter	Nodes	Cost
0	20	98
1	38	98
2	58	98
3	78	98
4	100	92
5	129	92
6	170	92
7	202	92
8	231	92
9	235	92
0	235	92

Iter	Nodes	Cost
0	41	256
1	72	251
2	108	249
3	155	249
4	233	249
5	372	249
6	528	249
7	662	249
8	790	249
9	869	249
10	877	249
11	878	249
0	878	249

Iter	Nodes	Cost
0	28	209
1	47	209
2	98	209
3	212	209
4	266	209
5	299	209
6	324	209
7	336	209
8	346	209
0	346	209