Metrics for Migdal et al, Equation (51)

analyze150.0ms (1%)

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: 97.0ms

ival-pow: 47.0ms (48.7% of total)

ival-mult: 19.0ms (19.7% of total)

ival-div: 13.0ms (13.5% of total)

ival-sqrt: 7.0ms (7.3% of total)

ival-pi: 5.0ms (5.2% of total)

ival-sub: 4.0ms (4.1% of total)

const: 2.0ms (2.1% of total)

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

sample4.5s (31.1%)

Results

1.6s	3976×	5	exit
1.1s	8256×	0	valid
534.0ms	1942×	1	invalid
46.0ms	425×	0	invalid
37.0ms	242×	0	unsamplable

Precisions

Click to see histograms. Total time spent on operations: 2.4s

ival-pow: 832.0ms (34.4% of total)

ival-mult: 483.0ms (20% of total)

ival-div: 337.0ms (13.9% of total)

backward-pass: 260.0ms (10.7% of total)

ival-sqrt: 209.0ms (8.6% of total)

ival-sub: 170.0ms (7% of total)

ival-pi: 89.0ms (3.7% of total)

const: 39.0ms (1.6% 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)))

explain182.0ms (1.3%)

FPErrors

Click to see full error table

Ground Truth	Overpredictions	Example	Underpredictions	Example	Subexpression
5	215	(7.162405558481969e+214 1.5836850323505494e-71)	1	(5.293926726405799e-16 6.5159187294368155e-77)	`(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

97.0ms

512×

valid

Compiler

Compiled 132 to 41 computations (68.9% saved)

Precisions

Click to see histograms. Total time spent on operations: 48.0ms

ival-pow: 17.0ms (35.4% of total)

ival-mult: 12.0ms (25% of total)

ival-div: 8.0ms (16.6% of total)

ival-sqrt: 4.0ms (8.3% of total)

ival-pi: 3.0ms (6.2% of total)

ival-sub: 3.0ms (6.2% of total)

const: 1.0ms (2.1% 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
▶	99.5%	(/.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))
▶	99.6%	(.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) (pow.f64 (.f64 (*.f64 #s(literal 2 binary64) (PI.f64)) n) (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 2 binary64))))

Status

Accuracy

Program

▶

99.5%

(/.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))

▶

99.6%

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

Compiler

Compiled 34 to 25 computations (26.5% saved)

simplify13.0ms (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)

localize106.0ms (0.7%)

Localize:

Found 8 expressions of interest:

New	Metric	Score	Program
✓	accuracy	100.0%	(PI.f64)
✓	accuracy	99.7%	(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 (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	99.6%	(*.f64 (PI.f64) n)
✓	accuracy	99.8%	(.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%	(pow.f64 (.f64 (.f64 #s(literal 2 binary64) (PI.f64)) n) (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 2 binary64)))
✓	accuracy	99.6%	(.f64 (.f64 #s(literal 2 binary64) (PI.f64)) n)
✓	accuracy	99.6%	(/.f64 #s(literal 1 binary64) (sqrt.f64 k))

Results

76.0ms

256×

valid

Compiler

Compiled 105 to 21 computations (80% saved)

Precisions

Click to see histograms. Total time spent on operations: 42.0ms

ival-pow: 18.0ms (42.7% of total)

ival-div: 9.0ms (21.3% of total)

ival-mult: 8.0ms (19% of total)

ival-sub: 3.0ms (7.1% of total)

ival-sqrt: 2.0ms (4.7% of total)

ival-pi: 1.0ms (2.4% of total)

const: 1.0ms (2.4% of total)

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

series87.0ms (0.6%)

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
33.0ms	n	@	0	(* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2)))
33.0ms	n	@	-inf	(* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2)))
7.0ms	n	@	inf	(* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2)))
1.0ms	k	@	0	(* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2)))
1.0ms	k	@	-inf	(* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2)))

rewrite399.0ms (2.8%)

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)))

simplify280.0ms (2%)

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)))

eval134.0ms (0.9%)

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

prune106.0ms (0.7%)

Pruning

13 alts after pruning (11 fresh and 2 done)

	Pruned	Kept	Total
New	978	11	989
Fresh	0	0	0
Picked	0	2	2
Done	0	0	0
Total	978	13	991

Accuracy

100.0%

Counts

991 → 13

Alt Table

Click to see full alt table

Status	Accuracy	Program
▶	99.6%	(/.f64 (pow.f64 (pow.f64 (.f64 #s(literal 2 binary64) (.f64 (PI.f64) n)) (+.f64 k #s(literal -1 binary64))) #s(literal -1/2 binary64)) (sqrt.f64 k))
	99.5%	(/.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)))
✓	99.5%	(/.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))
▶	96.5%	(/.f64 (pow.f64 (.f64 #s(literal 2 binary64) (.f64 (PI.f64) n)) (-.f64 #s(literal 1/2 binary64) (/.f64 k #s(literal 2 binary64)))) (exp.f64 (*.f64 #s(literal 1/2 binary64) (log.f64 k))))
▶	99.6%	(/.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))))
	99.3%	(/.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)))
	96.7%	(/.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))
	99.6%	(/.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))))))
▶	99.6%	(/.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)))
	99.6%	(.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)))
	73.7%	(.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)))
✓	99.6%	(.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) (pow.f64 (.f64 (*.f64 #s(literal 2 binary64) (PI.f64)) n) (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 2 binary64))))
▶	32.9%	(.f64 (sqrt.f64 (/.f64 (.f64 n (PI.f64)) k)) (sqrt.f64 #s(literal 2 binary64)))

Compiler

Compiled 424 to 315 computations (25.7% saved)

simplify36.0ms (0.3%)

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	(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	6528	(exp.f64 (*.f64 #s(literal 1/2 binary64) (log.f64 k)))
✓	cost-diff	6528	(/.f64 (pow.f64 (.f64 #s(literal 2 binary64) (.f64 (PI.f64) n)) (-.f64 #s(literal 1/2 binary64) (/.f64 k #s(literal 2 binary64)))) (exp.f64 (*.f64 #s(literal 1/2 binary64) (log.f64 k))))
✓	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 k #s(literal -1 binary64)))
✓	cost-diff	0	(pow.f64 (pow.f64 (.f64 #s(literal 2 binary64) (.f64 (PI.f64) n)) (+.f64 k #s(literal -1 binary64))) #s(literal -1/2 binary64))
✓	cost-diff	0	(/.f64 (pow.f64 (pow.f64 (.f64 #s(literal 2 binary64) (.f64 (PI.f64) n)) (+.f64 k #s(literal -1 binary64))) #s(literal -1/2 binary64)) (sqrt.f64 k))
✓	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	(.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))
✓	cost-diff	64	(/.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)))
✓	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

236×	`-lowering-.f32`
236×	`-lowering-.f64`
134×	`fmsub-define`
128×	`fma-lowering-fma.f32`
128×	`fma-lowering-fma.f64`

Iterations

Useful iterations: 12 (0.0ms)

Iter	Nodes	Cost
0	33	253
1	53	251
2	77	250
3	92	250
4	107	250
5	130	244
6	169	244
7	201	244
8	248	244
9	285	244
10	300	244
11	328	244
12	381	237
13	453	237
14	506	237
15	544	237
16	560	237
17	583	237
18	625	237
19	645	237
0	645	237

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

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

localize260.0ms (1.8%)

Localize:

Found 20 expressions of interest:

New	Metric	Score	Program
✓	accuracy	99.7%	(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 (pow.f64 (.f64 #s(literal 2 binary64) (.f64 (PI.f64) n)) (-.f64 #s(literal 1/2 binary64) (/.f64 k #s(literal 2 binary64)))) (exp.f64 (*.f64 #s(literal 1/2 binary64) (log.f64 k))))
✓	accuracy	94.2%	(exp.f64 (*.f64 #s(literal 1/2 binary64) (log.f64 k)))
✓	accuracy	75.0%	(PI.f64)
✓	accuracy	99.7%	(*.f64 (PI.f64) n)
✓	accuracy	99.7%	(/.f64 (pow.f64 (pow.f64 (.f64 #s(literal 2 binary64) (.f64 (PI.f64) n)) (+.f64 k #s(literal -1 binary64))) #s(literal -1/2 binary64)) (sqrt.f64 k))
✓	accuracy	99.6%	(pow.f64 (.f64 #s(literal 2 binary64) (.f64 (PI.f64) n)) (+.f64 k #s(literal -1 binary64)))
✓	accuracy	75.0%	(PI.f64)
✓	accuracy	99.7%	(pow.f64 (.f64 #s(literal 2 binary64) (.f64 (PI.f64) n)) (+.f64 (/.f64 k #s(literal 2 binary64)) #s(literal -1/2 binary64)))
✓	accuracy	99.7%	(*.f64 (PI.f64) n)
✓	accuracy	99.7%	(.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))
✓	accuracy	75.0%	(PI.f64)
✓	accuracy	99.5%	(.f64 (sqrt.f64 (/.f64 (.f64 n (PI.f64)) k)) (sqrt.f64 #s(literal 2 binary64)))
✓	accuracy	99.3%	(/.f64 (*.f64 n (PI.f64)) k)
✓	accuracy	88.9%	(sqrt.f64 (/.f64 (*.f64 n (PI.f64)) k))
✓	accuracy	75.0%	(PI.f64)
✓	accuracy	99.8%	(/.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	99.7%	(pow.f64 (.f64 #s(literal 2 binary64) (.f64 (PI.f64) n)) (+.f64 (/.f64 k #s(literal 2 binary64)) #s(literal -1/2 binary64)))
✓	accuracy	99.7%	(*.f64 (PI.f64) n)
✓	accuracy	75.0%	(PI.f64)

Results

145.0ms	190×	0	valid
33.0ms	66×	0	unsamplable

Compiler

Compiled 260 to 34 computations (86.9% saved)

Precisions

Click to see histograms. Total time spent on operations: 121.0ms

ival-pow: 76.0ms (63% of total)

ival-mult: 11.0ms (9.1% of total)

ival-div: 10.0ms (8.3% of total)

ival-add: 10.0ms (8.3% of total)

ival-sqrt: 5.0ms (4.1% of total)

ival-exp: 3.0ms (2.5% of total)

ival-log: 3.0ms (2.5% of total)

ival-pi: 1.0ms (0.8% of total)

ival-sub: 1.0ms (0.8% of total)

const: 1.0ms (0.8% of total)

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

series47.0ms (0.3%)

Counts

18 → 348

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

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)))))))>
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#<alt (+ (* k (+ (* -1 (* (sqrt (* n (PI))) (/ (log (* 2 (* n (PI)))) (sqrt 2)))) (* k (+ (* -1/2 (* (sqrt (/ 1 (* n (PI)))) (/ (+ (* -2 (* n (* (PI) (pow (log (* 2 (* n (PI)))) 2)))) (+ (* n (* (PI) (pow (log (* 2 (* n (PI)))) 2))) (/ (* n (* (PI) (pow (log (* 2 (* n (PI)))) 2))) (pow (sqrt 2) 2)))) (sqrt 2)))) (* -1/2 (* (/ (* k (+ (* -1 (* n (* (PI) (pow (log (* 2 (* n (PI)))) 3)))) (+ (* -1 (* (log (* 2 (* n (PI)))) (+ (* -2 (* n (* (PI) (pow (log (* 2 (* n (PI)))) 2)))) (* n (* (PI) (pow (log (* 2 (* n (PI)))) 2)))))) (+ (* 1/3 (* n (* (PI) (pow (log (* 2 (* n (PI)))) 3)))) (/ (* (log (* 2 (* n (PI)))) (+ (* -2 (* n (* (PI) (pow (log (* 2 (* n (PI)))) 2)))) (+ (* n (* (PI) (pow (log (* 2 (* n (PI)))) 2))) (/ (* n (* (PI) (pow (log (* 2 (* n (PI)))) 2))) (pow (sqrt 2) 2))))) (pow (sqrt 2) 2)))))) (sqrt 2)) (sqrt (/ 1 (* n (PI)))))))))) (* (sqrt (* n (PI))) (sqrt 2)))>
#<alt (sqrt (/ 1 (exp (* (log (* 2 (* n (PI)))) (- k 1)))))>
#<alt (sqrt (/ 1 (exp (* (log (* 2 (* n (PI)))) (- k 1)))))>
#<alt (sqrt (/ 1 (exp (* (log (* 2 (* n (PI)))) (- k 1)))))>
#<alt (sqrt (/ 1 (exp (* (log (* 2 (* n (PI)))) (- k 1)))))>
#<alt (sqrt (/ 1 (exp (* -1 (* (log (* 2 (* n (PI)))) (+ 1 (* -1 k)))))))>
#<alt (sqrt (/ 1 (exp (* -1 (* (log (* 2 (* n (PI)))) (+ 1 (* -1 k)))))))>
#<alt (sqrt (/ 1 (exp (* -1 (* (log (* 2 (* n (PI)))) (+ 1 (* -1 k)))))))>
#<alt (sqrt (/ 1 (exp (* -1 (* (log (* 2 (* n (PI)))) (+ 1 (* -1 k)))))))>
#<alt (exp (* (+ (log n) (log (* 2 (PI)))) (- k 1)))>
#<alt (exp (* (+ (log n) (log (* 2 (PI)))) (- k 1)))>
#<alt (exp (* (+ (log n) (log (* 2 (PI)))) (- k 1)))>
#<alt (exp (* (+ (log n) (log (* 2 (PI)))) (- k 1)))>
#<alt (exp (* (+ (log (* 2 (PI))) (* -1 (log (/ 1 n)))) (- k 1)))>
#<alt (exp (* (+ (log (* 2 (PI))) (* -1 (log (/ 1 n)))) (- k 1)))>
#<alt (exp (* (+ (log (* 2 (PI))) (* -1 (log (/ 1 n)))) (- k 1)))>
#<alt (exp (* (+ (log (* 2 (PI))) (* -1 (log (/ 1 n)))) (- k 1)))>
#<alt (exp (* (+ (log (* -2 (PI))) (* -1 (log (/ -1 n)))) (- k 1)))>
#<alt (exp (* (+ (log (* -2 (PI))) (* -1 (log (/ -1 n)))) (- k 1)))>
#<alt (exp (* (+ (log (* -2 (PI))) (* -1 (log (/ -1 n)))) (- k 1)))>
#<alt (exp (* (+ (log (* -2 (PI))) (* -1 (log (/ -1 n)))) (- k 1)))>
#<alt (/ 1/2 (* n (PI)))>
#<alt (+ (* 1/2 (/ (* k (log (* 2 (* n (PI))))) (* n (PI)))) (* 1/2 (/ 1 (* n (PI)))))>
#<alt (+ (* k (+ (* 1/4 (/ (* k (pow (log (* 2 (* n (PI)))) 2)) (* n (PI)))) (* 1/2 (/ (log (* 2 (* n (PI)))) (* n (PI)))))) (* 1/2 (/ 1 (* n (PI)))))>
#<alt (+ (* k (+ (* 1/2 (/ (log (* 2 (* n (PI)))) (* n (PI)))) (* k (+ (* 1/12 (/ (* k (pow (log (* 2 (* n (PI)))) 3)) (* n (PI)))) (* 1/4 (/ (pow (log (* 2 (* n (PI)))) 2) (* n (PI)))))))) (* 1/2 (/ 1 (* n (PI)))))>
#<alt (exp (* (log (* 2 (* n (PI)))) (- k 1)))>
#<alt (exp (* (log (* 2 (* n (PI)))) (- k 1)))>
#<alt (exp (* (log (* 2 (* n (PI)))) (- k 1)))>
#<alt (exp (* (log (* 2 (* n (PI)))) (- k 1)))>
#<alt (exp (* -1 (* (log (* 2 (* n (PI)))) (+ 1 (* -1 k)))))>
#<alt (exp (* -1 (* (log (* 2 (* n (PI)))) (+ 1 (* -1 k)))))>
#<alt (exp (* -1 (* (log (* 2 (* n (PI)))) (+ 1 (* -1 k)))))>
#<alt (exp (* -1 (* (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 (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 (* (+ (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 (* 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

87 calls:

Time	Variable		Point	Expression
4.0ms	n	@	inf	(* (sqrt (/ (* n (PI)) k)) (sqrt 2))
4.0ms	n	@	inf	(pow (pow (* 2 (* (PI) n)) (+ k -1)) -1/2)
2.0ms	k	@	0	(/ (pow (pow (* 2 (* (PI) n)) (+ k -1)) -1/2) (sqrt k))
2.0ms	k	@	0	(/ (pow k -1/2) (pow (* 2 (* (PI) n)) (+ (/ k 2) -1/2)))
1.0ms	n	@	-inf	(/ (pow (pow (* 2 (* (PI) n)) (+ k -1)) -1/2) (sqrt k))

rewrite400.0ms (2.8%)

Algorithm

1×	batch-egg-rewrite

Rules

5424×	`-lowering-.f32`
5424×	`-lowering-.f64`
4220×	`/-lowering-/.f32`
4220×	`/-lowering-/.f64`
2144×	`pow-lowering-pow.f64`

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	33	153
1	206	143
2	1393	139
0	8551	139

Stop Event

1×	iter limit
1×	node limit

Counts

18 → 1014

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

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

simplify302.0ms (2.1%)

Algorithm

1×	egg-herbie

Rules

6156×	`-lowering-.f32`
6156×	`-lowering-.f64`
1886×	`+-lowering-+.f64`
1886×	`+-lowering-+.f32`
1082×	`distribute-lft-in`

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	391	5169
1	1269	4897
2	4718	4463
0	8466	4463

Stop Event

1×	iter limit
1×	node limit

Counts

348 → 348

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

eval200.0ms (1.4%)

Compiler: Compiled 35675 to 3184 computations (91.1% saved)

prune170.0ms (1.2%)

Pruning

20 alts after pruning (16 fresh and 4 done)

	Pruned	Kept	Total
New	1710	12	1722
Fresh	2	4	6
Picked	3	2	5
Done	0	2	2
Total	1715	20	1735

Accuracy

100.0%

Counts

1735 → 20

Alt Table

Click to see full alt table

Status	Accuracy	Program
	43.9%	(/.f64 (pow.f64 (/.f64 #s(literal 1/2 binary64) (*.f64 n (PI.f64))) #s(literal -1/2 binary64)) (sqrt.f64 k))
	99.5%	(/.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)))
✓	99.5%	(/.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))
✓	96.5%	(/.f64 (pow.f64 (.f64 #s(literal 2 binary64) (.f64 (PI.f64) n)) (-.f64 #s(literal 1/2 binary64) (/.f64 k #s(literal 2 binary64)))) (exp.f64 (*.f64 #s(literal 1/2 binary64) (log.f64 k))))
✓	99.6%	(/.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))))
▶	32.8%	(/.f64 (sqrt.f64 (/.f64 (*.f64 n (PI.f64)) k)) (sqrt.f64 #s(literal 1/2 binary64)))
	99.3%	(/.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)))
	43.8%	(/.f64 (sqrt.f64 (.f64 #s(literal 2 binary64) (.f64 (PI.f64) n))) (sqrt.f64 k))
	32.9%	(/.f64 (sqrt.f64 #s(literal 2 binary64)) (pow.f64 (/.f64 k (*.f64 (PI.f64) n)) #s(literal 1/2 binary64)))
▶	96.7%	(/.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))
	96.7%	(/.f64 (exp.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))))) (sqrt.f64 k))
▶	99.6%	(/.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))))))
	32.8%	(/.f64 #s(literal 1 binary64) (.f64 (sqrt.f64 #s(literal 1/2 binary64)) (sqrt.f64 (/.f64 k (.f64 n (PI.f64))))))
	32.9%	(.f64 (pow.f64 (/.f64 k (.f64 (PI.f64) n)) #s(literal -1/2 binary64)) (sqrt.f64 #s(literal 2 binary64)))
✓	99.6%	(.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) (pow.f64 (.f64 (*.f64 #s(literal 2 binary64) (PI.f64)) n) (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 2 binary64))))
	32.9%	(.f64 (sqrt.f64 (.f64 (PI.f64) (/.f64 n k))) (sqrt.f64 #s(literal 2 binary64)))
	43.5%	(.f64 (sqrt.f64 n) (sqrt.f64 (.f64 (/.f64 (PI.f64) k) #s(literal 2 binary64))))
	88.7%	(sqrt.f64 (/.f64 (pow.f64 (.f64 (.f64 n (PI.f64)) #s(literal 2 binary64)) (-.f64 #s(literal 1 binary64) k)) k))
▶	33.0%	(sqrt.f64 (/.f64 #s(literal 2 binary64) (/.f64 k (*.f64 (PI.f64) n))))
▶	30.9%	(exp.f64 (.f64 (log.f64 (/.f64 #s(literal 2 binary64) (/.f64 k (.f64 (PI.f64) n)))) #s(literal 1/2 binary64)))

Compiler

Compiled 516 to 405 computations (21.5% saved)

simplify194.0ms (1.4%)

Algorithm

1×	egg-herbie

Localize:

Found 20 expressions of interest:

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

Rules

1438×	`sum3-define`
1376×	`fma-define`
1346×	`-lowering-.f32`
1346×	`-lowering-.f64`
1240×	`sum5-define`

Iterations

Useful iterations: 5 (0.0ms)

Iter	Nodes	Cost
0	32	234
1	56	232
2	99	232
3	172	232
4	331	232
5	606	225
6	1132	225
7	1789	225
8	4362	225
9	5343	225
10	6601	225
11	6990	225
12	7541	225
0	8034	225

Stop Event

1×	iter limit
1×	node limit

Calls

Call 1

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

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

localize305.0ms (2.1%)

Localize:

Found 20 expressions of interest:

New	Metric	Score	Program
✓	accuracy	99.8%	(*.f64 (PI.f64) n)
✓	accuracy	99.7%	(/.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))
✓	accuracy	96.7%	(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))))
✓	accuracy	45.9%	(PI.f64)
✓	accuracy	99.8%	(*.f64 (PI.f64) n)
✓	accuracy	96.4%	(exp.f64 (.f64 (log.f64 (/.f64 #s(literal 2 binary64) (/.f64 k (.f64 (PI.f64) n)))) #s(literal 1/2 binary64)))
✓	accuracy	88.7%	(log.f64 (/.f64 #s(literal 2 binary64) (/.f64 k (*.f64 (PI.f64) n))))
✓	accuracy	45.9%	(PI.f64)
✓	accuracy	99.8%	(*.f64 n (PI.f64))
✓	accuracy	99.7%	(/.f64 (sqrt.f64 (/.f64 (*.f64 n (PI.f64)) k)) (sqrt.f64 #s(literal 1/2 binary64)))
✓	accuracy	88.9%	(sqrt.f64 (/.f64 (*.f64 n (PI.f64)) k))
✓	accuracy	45.9%	(PI.f64)
✓	accuracy	99.8%	(/.f64 #s(literal 2 binary64) (/.f64 k (*.f64 (PI.f64) n)))
✓	accuracy	99.8%	(*.f64 (PI.f64) n)
✓	accuracy	88.9%	(sqrt.f64 (/.f64 #s(literal 2 binary64) (/.f64 k (*.f64 (PI.f64) n))))
✓	accuracy	45.9%	(PI.f64)
✓	accuracy	99.8%	(*.f64 (PI.f64) n)
✓	accuracy	99.8%	(/.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)))))
✓	accuracy	99.7%	(pow.f64 (.f64 #s(literal 2 binary64) (.f64 (PI.f64) n)) (+.f64 #s(literal 1/2 binary64) (/.f64 k #s(literal -2 binary64))))
✓	accuracy	45.9%	(PI.f64)

Results

148.0ms	77×	5	exit
72.0ms	113×	0	valid
26.0ms	66×	0	unsamplable

Compiler

Compiled 244 to 33 computations (86.5% saved)

Precisions

Click to see histograms. Total time spent on operations: 117.0ms

ival-pow: 28.0ms (23.8% of total)

backward-pass: 26.0ms (22.1% of total)

ival-div: 21.0ms (17.9% of total)

ival-mult: 12.0ms (10.2% of total)

ival-sqrt: 10.0ms (8.5% of total)

ival-log: 9.0ms (7.7% of total)

ival-exp: 6.0ms (5.1% of total)

ival-sub: 2.0ms (1.7% of total)

ival-add: 2.0ms (1.7% of total)

const: 1.0ms (0.9% of total)

ival-pi: 1.0ms (0.9% of total)

series161.0ms (1.1%)

Counts

20 → 408

Calls

Call 1

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

Calls

102 calls:

Time	Variable		Point	Expression
41.0ms	k	@	0	(* (log (/ 2 (/ k (* (PI) n)))) 1/2)
24.0ms	n	@	-inf	(* (log (/ 2 (/ k (* (PI) n)))) 1/2)
17.0ms	n	@	0	(* (log (/ 2 (/ k (* (PI) n)))) 1/2)
16.0ms	k	@	-inf	(* (log (/ 2 (/ k (* (PI) n)))) 1/2)
14.0ms	k	@	inf	(/ 1 (/ (sqrt k) (pow (* 2 (* (PI) n)) (+ 1/2 (/ k -2)))))

rewrite375.0ms (2.6%)

Algorithm

1×	batch-egg-rewrite

Rules

4682×	`-lowering-.f32`
4682×	`-lowering-.f64`
4490×	`/-lowering-/.f32`
4490×	`/-lowering-/.f64`
1490×	`pow-lowering-pow.f64`

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	32	158
1	197	151
2	1275	150
0	8269	150

Stop Event

1×	iter limit
1×	node limit

Counts

20 → 1218

Calls

Call 1

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

simplify376.0ms (2.6%)

Algorithm

1×	egg-herbie

Rules

4292×	`-lowering-.f32`
4292×	`-lowering-.f64`
2698×	`fma-lowering-fma.f32`
2698×	`fma-lowering-fma.f64`
2248×	`+-lowering-+.f64`

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	244	4796
1	756	4555
2	2524	4466
3	6900	4466
0	8320	4466

Stop Event

1×	iter limit
1×	node limit

Counts

408 → 408

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

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

eval305.0ms (2.1%)

Compiler: Compiled 36296 to 4597 computations (87.3% saved)

prune326.0ms (2.3%)

Pruning

42 alts after pruning (37 fresh and 5 done)

	Pruned	Kept	Total
New	2040	31	2071
Fresh	5	6	11
Picked	2	3	5
Done	2	2	4
Total	2049	42	2091

Accuracy

100.0%

Counts

2091 → 42

Alt Table

Click to see full alt table

Status	Accuracy	Program
	32.8%	(pow.f64 (pow.f64 (/.f64 (.f64 #s(literal 2 binary64) (.f64 (PI.f64) n)) k) #s(literal 1/4 binary64)) #s(literal 2 binary64))
	33.0%	(pow.f64 (/.f64 k (.f64 #s(literal 2 binary64) (.f64 (PI.f64) n))) #s(literal -1/2 binary64))
	23.4%	(pow.f64 (.f64 (/.f64 (.f64 #s(literal 2 binary64) (.f64 (PI.f64) n)) k) (/.f64 (.f64 #s(literal 2 binary64) (*.f64 (PI.f64) n)) k)) #s(literal 1/4 binary64))
	32.8%	(/.f64 (pow.f64 (/.f64 k (*.f64 (PI.f64) n)) #s(literal -1/2 binary64)) (sqrt.f64 #s(literal 1/2 binary64)))
	43.5%	(/.f64 (pow.f64 (/.f64 #s(literal 2 binary64) k) #s(literal 1/2 binary64)) (pow.f64 (*.f64 (PI.f64) n) #s(literal -1/2 binary64)))
	43.9%	(/.f64 (pow.f64 (.f64 (PI.f64) n) #s(literal 1/2 binary64)) (pow.f64 (.f64 #s(literal 1/2 binary64) k) #s(literal 1/2 binary64)))
✓	99.5%	(/.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))
✓	99.6%	(/.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))))
✓	32.8%	(/.f64 (sqrt.f64 (/.f64 (*.f64 n (PI.f64)) k)) (sqrt.f64 #s(literal 1/2 binary64)))
	32.8%	(/.f64 (sqrt.f64 (/.f64 n (/.f64 k (PI.f64)))) (sqrt.f64 #s(literal 1/2 binary64)))
	32.8%	(/.f64 (sqrt.f64 (*.f64 (/.f64 (PI.f64) k) n)) (sqrt.f64 #s(literal 1/2 binary64)))
▶	99.3%	(/.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)))
	43.8%	(/.f64 (sqrt.f64 (.f64 #s(literal 2 binary64) (.f64 (PI.f64) n))) (sqrt.f64 k))
	32.9%	(/.f64 (sqrt.f64 #s(literal 2 binary64)) (sqrt.f64 (/.f64 k (*.f64 (PI.f64) n))))
	33.0%	(/.f64 #s(literal 1 binary64) (pow.f64 (/.f64 (.f64 #s(literal 2 binary64) (.f64 (PI.f64) n)) k) #s(literal -1/2 binary64)))
	77.9%	(/.f64 #s(literal 1 binary64) (/.f64 (pow.f64 (/.f64 (.f64 #s(literal 2 binary64) (.f64 (PI.f64) n)) k) #s(literal -1/2 binary64)) (pow.f64 (.f64 #s(literal 2 binary64) (.f64 (PI.f64) n)) (/.f64 k #s(literal -2 binary64)))))
✓	99.6%	(/.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))))))
	77.9%	(/.f64 #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))) (pow.f64 (/.f64 (.f64 #s(literal 2 binary64) (.f64 (PI.f64) n)) k) #s(literal -1/2 binary64)))))
	32.8%	(/.f64 #s(literal 1 binary64) (.f64 (sqrt.f64 #s(literal 1/2 binary64)) (sqrt.f64 (/.f64 k (.f64 n (PI.f64))))))
	32.9%	(.f64 (pow.f64 (/.f64 k (.f64 (PI.f64) n)) #s(literal -1/2 binary64)) (sqrt.f64 #s(literal 2 binary64)))
▶	32.9%	(*.f64 (sqrt.f64 (/.f64 n (/.f64 k (PI.f64)))) (sqrt.f64 #s(literal 2 binary64)))
	43.5%	(*.f64 (sqrt.f64 (/.f64 #s(literal 2 binary64) (/.f64 k (PI.f64)))) (sqrt.f64 n))
	43.5%	(.f64 (sqrt.f64 (.f64 (/.f64 #s(literal 2 binary64) k) (PI.f64))) (sqrt.f64 n))
	32.8%	(.f64 (sqrt.f64 (.f64 (/.f64 #s(literal 2 binary64) k) n)) (sqrt.f64 (PI.f64)))
	32.9%	(.f64 (sqrt.f64 (.f64 (PI.f64) (/.f64 n k))) (sqrt.f64 #s(literal 2 binary64)))
	43.9%	(.f64 (sqrt.f64 (.f64 #s(literal 2 binary64) (*.f64 (PI.f64) n))) (pow.f64 k #s(literal -1/2 binary64)))
	43.5%	(.f64 (sqrt.f64 (.f64 #s(literal 2 binary64) n)) (pow.f64 (/.f64 (PI.f64) k) #s(literal 1/2 binary64)))
	43.5%	(*.f64 (sqrt.f64 n) (sqrt.f64 (/.f64 (/.f64 (PI.f64) k) #s(literal 1/2 binary64))))
	88.7%	(sqrt.f64 (/.f64 (pow.f64 (.f64 (.f64 n (PI.f64)) #s(literal 2 binary64)) (-.f64 #s(literal 1 binary64) k)) k))
	32.9%	(sqrt.f64 (/.f64 #s(literal 2 binary64) (/.f64 (/.f64 k n) (PI.f64))))
▶	32.9%	(sqrt.f64 (/.f64 #s(literal 2 binary64) (/.f64 (/.f64 #s(literal 1 binary64) n) (/.f64 (PI.f64) k))))
✓	33.0%	(sqrt.f64 (/.f64 #s(literal 2 binary64) (/.f64 k (*.f64 (PI.f64) n))))
	33.0%	(sqrt.f64 (/.f64 #s(literal 2 binary64) (/.f64 #s(literal 1 binary64) (/.f64 (/.f64 (PI.f64) k) (/.f64 #s(literal 1 binary64) n)))))
	33.0%	(sqrt.f64 (/.f64 #s(literal 2 binary64) (/.f64 #s(literal 1 binary64) (/.f64 (PI.f64) (/.f64 k n)))))
	33.0%	(sqrt.f64 (/.f64 #s(literal 2 binary64) (*.f64 (/.f64 k (PI.f64)) (/.f64 #s(literal 1 binary64) n))))
	33.0%	(sqrt.f64 (*.f64 (/.f64 (PI.f64) #s(literal 1/2 binary64)) (/.f64 n k)))
	32.9%	(sqrt.f64 (*.f64 (/.f64 #s(literal 2 binary64) (/.f64 k (PI.f64))) n))
	33.0%	(sqrt.f64 (.f64 (/.f64 #s(literal 2 binary64) k) (.f64 (PI.f64) n)))
	33.0%	(sqrt.f64 (.f64 (.f64 (/.f64 #s(literal 2 binary64) k) (PI.f64)) n))
▶	33.0%	(sqrt.f64 (.f64 (.f64 (/.f64 #s(literal 2 binary64) k) n) (PI.f64)))
	30.9%	(exp.f64 (.f64 (log.f64 (.f64 (/.f64 (PI.f64) #s(literal 1/2 binary64)) (/.f64 n k))) #s(literal 1/2 binary64)))
▶	30.9%	(exp.f64 (.f64 (log.f64 (.f64 (*.f64 (/.f64 #s(literal 2 binary64) k) (PI.f64)) n)) #s(literal 1/2 binary64)))

Compiler

Compiled 1014 to 786 computations (22.5% saved)

simplify19.0ms (0.1%)

Algorithm

1×	egg-herbie

Localize:

Found 20 expressions of interest:

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

Rules

144×	`-lowering-.f32`
144×	`-lowering-.f64`
114×	`/-lowering-/.f32`
114×	`/-lowering-/.f64`
82×	`times-frac`

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	32	195
1	64	195
2	103	195
3	142	194
4	189	194
5	280	194
6	320	194
0	320	194

Stop Event

1×	iter limit
1×	saturated

Calls

Call 1

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

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

localize276.0ms (1.9%)

Localize:

Found 20 expressions of interest:

New	Metric	Score	Program
✓	accuracy	99.6%	(*.f64 (/.f64 #s(literal 2 binary64) k) (PI.f64))
✓	accuracy	94.4%	(exp.f64 (.f64 (log.f64 (.f64 (*.f64 (/.f64 #s(literal 2 binary64) k) (PI.f64)) n)) #s(literal 1/2 binary64)))
✓	accuracy	88.7%	(log.f64 (.f64 (.f64 (/.f64 #s(literal 2 binary64) k) (PI.f64)) n))
✓	accuracy	75.0%	(PI.f64)
✓	accuracy	99.7%	(/.f64 k (PI.f64))
✓	accuracy	99.5%	(*.f64 (sqrt.f64 (/.f64 n (/.f64 k (PI.f64)))) (sqrt.f64 #s(literal 2 binary64)))
✓	accuracy	88.9%	(sqrt.f64 (/.f64 n (/.f64 k (PI.f64))))
✓	accuracy	75.0%	(PI.f64)
✓	accuracy	99.7%	(/.f64 #s(literal 2 binary64) (/.f64 (/.f64 #s(literal 1 binary64) n) (/.f64 (PI.f64) k)))
✓	accuracy	99.7%	(/.f64 (PI.f64) k)
✓	accuracy	88.9%	(sqrt.f64 (/.f64 #s(literal 2 binary64) (/.f64 (/.f64 #s(literal 1 binary64) n) (/.f64 (PI.f64) k))))
✓	accuracy	75.0%	(PI.f64)
✓	accuracy	99.7%	(*.f64 (/.f64 #s(literal 2 binary64) k) n)
✓	accuracy	99.7%	(.f64 (.f64 (/.f64 #s(literal 2 binary64) k) n) (PI.f64))
✓	accuracy	88.9%	(sqrt.f64 (.f64 (.f64 (/.f64 #s(literal 2 binary64) k) n) (PI.f64)))
✓	accuracy	75.0%	(PI.f64)
✓	accuracy	99.7%	(*.f64 (PI.f64) n)
✓	accuracy	99.7%	(/.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	99.4%	(sqrt.f64 (.f64 #s(literal 2 binary64) (.f64 (PI.f64) n)))
✓	accuracy	75.0%	(PI.f64)

Results

119.0ms	66×	5	exit
76.0ms	190×	0	valid

Compiler

Compiled 209 to 33 computations (84.2% saved)

Precisions

Click to see histograms. Total time spent on operations: 99.0ms

ival-pow: 25.0ms (25.2% of total)

ival-mult: 20.0ms (20.1% of total)

backward-pass: 18.0ms (18.1% of total)

ival-div: 16.0ms (16.1% of total)

ival-sqrt: 11.0ms (11.1% of total)

ival-log: 4.0ms (4% of total)

ival-exp: 3.0ms (3% of total)

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

const: 1.0ms (1% of total)

series41.0ms (0.3%)

Counts

24 → 456

Calls

Call 1

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

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 (* 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 (* 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 (* 2 (/ n k))>
#<alt (* 2 (/ n k))>
#<alt (* 2 (/ n k))>
#<alt (* 2 (/ n k))>
#<alt (* 2 (/ n k))>
#<alt (* 2 (/ n k))>
#<alt (* 2 (/ n k))>
#<alt (* 2 (/ n k))>
#<alt (* 2 (/ n k))>
#<alt (* 2 (/ n k))>
#<alt (* 2 (/ n k))>
#<alt (* 2 (/ n k))>
#<alt (* 2 (/ n k))>
#<alt (* 2 (/ n k))>
#<alt (* 2 (/ n k))>
#<alt (* 2 (/ n k))>
#<alt (* 2 (/ n k))>
#<alt (* 2 (/ n k))>
#<alt (* 2 (/ n k))>
#<alt (* 2 (/ n k))>
#<alt (* 2 (/ n k))>
#<alt (* 2 (/ n k))>
#<alt (* 2 (/ n k))>
#<alt (* 2 (/ n k))>
#<alt (/ 2 k)>
#<alt (/ 2 k)>
#<alt (/ 2 k)>
#<alt (/ 2 k)>
#<alt (/ 2 k)>
#<alt (/ 2 k)>
#<alt (/ 2 k)>
#<alt (/ 2 k)>
#<alt (/ 2 k)>
#<alt (/ 2 k)>
#<alt (/ 2 k)>
#<alt (/ 2 k)>
#<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 (* (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 (* 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 (/ 1 n)>
#<alt (/ 1 n)>
#<alt (/ 1 n)>
#<alt (/ 1 n)>
#<alt (/ 1 n)>
#<alt (/ 1 n)>
#<alt (/ 1 n)>
#<alt (/ 1 n)>
#<alt (/ 1 n)>
#<alt (/ 1 n)>
#<alt (/ 1 n)>
#<alt (/ 1 n)>
#<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 (/ k (PI))>
#<alt (/ k (PI))>
#<alt (/ k (PI))>
#<alt (/ k (PI))>
#<alt (/ k (PI))>
#<alt (/ k (PI))>
#<alt (/ k (PI))>
#<alt (/ k (PI))>
#<alt (/ k (PI))>
#<alt (/ k (PI))>
#<alt (/ k (PI))>
#<alt (/ k (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 (* 1/2 (+ (log (* 2 (* n (PI)))) (* -1 (log k))))>
#<alt (* 1/2 (+ (log (* 2 (* n (PI)))) (* -1 (log k))))>
#<alt (* 1/2 (+ (log (* 2 (* n (PI)))) (* -1 (log k))))>
#<alt (* 1/2 (+ (log (* 2 (* n (PI)))) (* -1 (log k))))>
#<alt (* 1/2 (+ (log (* 2 (* n (PI)))) (log (/ 1 k))))>
#<alt (* 1/2 (+ (log (* 2 (* n (PI)))) (log (/ 1 k))))>
#<alt (* 1/2 (+ (log (* 2 (* n (PI)))) (log (/ 1 k))))>
#<alt (* 1/2 (+ (log (* 2 (* n (PI)))) (log (/ 1 k))))>
#<alt (* 1/2 (+ (log (* -2 (* n (PI)))) (log (/ -1 k))))>
#<alt (* 1/2 (+ (log (* -2 (* n (PI)))) (log (/ -1 k))))>
#<alt (* 1/2 (+ (log (* -2 (* n (PI)))) (log (/ -1 k))))>
#<alt (* 1/2 (+ (log (* -2 (* n (PI)))) (log (/ -1 k))))>
#<alt (* 1/2 (+ (log n) (log (* 2 (/ (PI) k)))))>
#<alt (* 1/2 (+ (log n) (log (* 2 (/ (PI) k)))))>
#<alt (* 1/2 (+ (log n) (log (* 2 (/ (PI) k)))))>
#<alt (* 1/2 (+ (log n) (log (* 2 (/ (PI) k)))))>
#<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 (* 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 (* 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 (/ (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 (* 2 (/ (PI) k))>
#<alt (* 2 (/ (PI) k))>
#<alt (* 2 (/ (PI) k))>
#<alt (* 2 (/ (PI) k))>
#<alt (* 2 (/ (PI) k))>
#<alt (* 2 (/ (PI) k))>
#<alt (* 2 (/ (PI) k))>
#<alt (* 2 (/ (PI) k))>
#<alt (* 2 (/ (PI) k))>
#<alt (* 2 (/ (PI) k))>
#<alt (* 2 (/ (PI) k))>
#<alt (* 2 (/ (PI) k))>

Calls

114 calls:

Time	Variable		Point	Expression
12.0ms	n	@	-inf	(sqrt (* 2 (* (PI) n)))
2.0ms	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))
2.0ms	n	@	0	(/ (sqrt (* 2 (* (PI) n))) (pow (* (pow (* 2 (* (PI) n)) k) k) 1/2))

rewrite409.0ms (2.9%)

Algorithm

1×	batch-egg-rewrite

Rules

5736×	`-lowering-.f32`
5736×	`-lowering-.f64`
3696×	`/-lowering-/.f32`
3696×	`/-lowering-/.f64`
1278×	`times-frac`

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	32	151
1	167	149
2	1039	147
0	8698	147

Stop Event

1×	iter limit
1×	node limit

Counts

24 → 1997

Calls

Call 1

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

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

simplify328.0ms (2.3%)

Algorithm

1×	egg-herbie

Rules

4762×	`-lowering-.f32`
4762×	`-lowering-.f64`
2096×	`+-lowering-+.f64`
2096×	`+-lowering-+.f32`
1770×	`fma-lowering-fma.f32`

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	188	3970
1	553	3880
2	1933	3838
3	5523	3735
0	8295	3735

Stop Event

1×	iter limit
1×	node limit

Counts

456 → 456

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 (* 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))))
(* 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))
(* 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))
(/ 2 k)
(/ 2 k)
(/ 2 k)
(/ 2 k)
(/ 2 k)
(/ 2 k)
(/ 2 k)
(/ 2 k)
(/ 2 k)
(/ 2 k)
(/ 2 k)
(/ 2 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)
(/ k (PI))
(/ k (PI))
(/ k (PI))
(/ k (PI))
(/ k (PI))
(/ k (PI))
(/ k (PI))
(/ k (PI))
(/ k (PI))
(/ k (PI))
(/ k (PI))
(/ k (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))))
(* 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))
(* n (PI))
(* n (PI))
(* n (PI))
(* n (PI))
(* n (PI))
(* n (PI))
(* n (PI))
(* n (PI))
(* n (PI))
(* n (PI))
(* n (PI))
(* 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)
(* 2 (/ (PI) k))
(* 2 (/ (PI) k))
(* 2 (/ (PI) k))
(* 2 (/ (PI) k))
(* 2 (/ (PI) k))
(* 2 (/ (PI) k))
(* 2 (/ (PI) k))
(* 2 (/ (PI) k))
(* 2 (/ (PI) k))
(* 2 (/ (PI) k))
(* 2 (/ (PI) k))
(* 2 (/ (PI) k))

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

eval478.0ms (3.3%)

Compiler: Compiled 45391 to 7226 computations (84.1% saved)

prune378.0ms (2.6%)

Pruning

48 alts after pruning (42 fresh and 6 done)

	Pruned	Kept	Total
New	2942	22	2964
Fresh	12	20	32
Picked	2	3	5
Done	2	3	5
Total	2958	48	3006

Accuracy

100.0%

Counts

3006 → 48

Alt Table

Click to see full alt table

Status	Accuracy	Program
	33.0%	(pow.f64 (/.f64 k (.f64 n (.f64 #s(literal 2 binary64) (PI.f64)))) #s(literal -1/2 binary64))
	23.4%	(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))
	43.5%	(/.f64 (pow.f64 (/.f64 (*.f64 #s(literal 2 binary64) (PI.f64)) k) #s(literal 1/2 binary64)) (pow.f64 n #s(literal -1/2 binary64)))
	32.8%	(/.f64 (pow.f64 (/.f64 k (*.f64 (PI.f64) n)) #s(literal -1/2 binary64)) (sqrt.f64 #s(literal 1/2 binary64)))
	76.0%	(/.f64 (pow.f64 (.f64 n (.f64 #s(literal 2 binary64) (PI.f64))) (/.f64 k #s(literal -2 binary64))) (pow.f64 (/.f64 k (.f64 n (.f64 #s(literal 2 binary64) (PI.f64)))) #s(literal 1/2 binary64)))
✓	99.5%	(/.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))
	32.7%	(/.f64 (pow.f64 (*.f64 #s(literal 2 binary64) (PI.f64)) #s(literal 1/2 binary64)) (sqrt.f64 (/.f64 k n)))
	43.9%	(/.f64 (pow.f64 (*.f64 #s(literal 2 binary64) n) #s(literal 1/2 binary64)) (sqrt.f64 (/.f64 k (PI.f64))))
✓	99.6%	(/.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))))
	32.8%	(/.f64 (sqrt.f64 (/.f64 n (/.f64 k (PI.f64)))) (sqrt.f64 #s(literal 1/2 binary64)))
	32.8%	(/.f64 (sqrt.f64 (*.f64 (/.f64 (PI.f64) k) n)) (sqrt.f64 #s(literal 1/2 binary64)))
	43.9%	(/.f64 (sqrt.f64 (*.f64 (PI.f64) n)) (sqrt.f64 (/.f64 k #s(literal 2 binary64))))
	43.8%	(/.f64 (sqrt.f64 (.f64 #s(literal 2 binary64) (.f64 (PI.f64) n))) (sqrt.f64 k))
	32.9%	(/.f64 (sqrt.f64 #s(literal 2 binary64)) (sqrt.f64 (/.f64 k (*.f64 (PI.f64) n))))
	33.0%	(/.f64 #s(literal 1 binary64) (pow.f64 (/.f64 (.f64 #s(literal 2 binary64) (.f64 (PI.f64) n)) k) #s(literal -1/2 binary64)))
	32.8%	(/.f64 #s(literal 1 binary64) (.f64 (sqrt.f64 #s(literal 1/2 binary64)) (sqrt.f64 (/.f64 k (.f64 n (PI.f64))))))
	32.8%	(.f64 (pow.f64 (/.f64 n k) #s(literal 1/2 binary64)) (pow.f64 (.f64 #s(literal 2 binary64) (PI.f64)) #s(literal 1/2 binary64)))
	32.9%	(.f64 (pow.f64 (/.f64 k (.f64 (PI.f64) n)) #s(literal -1/2 binary64)) (sqrt.f64 #s(literal 2 binary64)))
	43.5%	(.f64 (pow.f64 (/.f64 #s(literal 2 binary64) k) #s(literal 1/2 binary64)) (sqrt.f64 (.f64 (PI.f64) n)))
	43.5%	(*.f64 (sqrt.f64 (/.f64 #s(literal 2 binary64) (/.f64 k (PI.f64)))) (sqrt.f64 n))
	32.9%	(.f64 (sqrt.f64 (.f64 (/.f64 n k) (PI.f64))) (sqrt.f64 #s(literal 2 binary64)))
	32.8%	(.f64 (sqrt.f64 (.f64 (/.f64 #s(literal 2 binary64) k) n)) (sqrt.f64 (PI.f64)))
	43.9%	(.f64 (sqrt.f64 (.f64 #s(literal 2 binary64) (*.f64 (PI.f64) n))) (pow.f64 k #s(literal -1/2 binary64)))
	43.5%	(.f64 (sqrt.f64 (.f64 #s(literal 2 binary64) n)) (pow.f64 (/.f64 (PI.f64) k) #s(literal 1/2 binary64)))
	43.5%	(*.f64 (sqrt.f64 n) (sqrt.f64 (/.f64 (/.f64 (PI.f64) k) #s(literal 1/2 binary64))))
	88.7%	(sqrt.f64 (/.f64 (pow.f64 (.f64 (.f64 n (PI.f64)) #s(literal 2 binary64)) (-.f64 #s(literal 1 binary64) k)) k))
	76.0%	(sqrt.f64 (/.f64 (/.f64 #s(literal 2 binary64) (/.f64 k (.f64 (PI.f64) n))) (pow.f64 (.f64 n (*.f64 #s(literal 2 binary64) (PI.f64))) k)))
	32.9%	(sqrt.f64 (/.f64 (/.f64 #s(literal 2 binary64) (/.f64 k n)) (/.f64 #s(literal 1 binary64) (PI.f64))))
	32.9%	(sqrt.f64 (/.f64 (/.f64 #s(literal 1 binary64) k) (*.f64 (/.f64 (/.f64 #s(literal -1 binary64) n) #s(literal -2 binary64)) (/.f64 #s(literal 1 binary64) (PI.f64)))))
	33.0%	(sqrt.f64 (/.f64 (/.f64 #s(literal -2 binary64) (/.f64 k (PI.f64))) (/.f64 #s(literal -1 binary64) n)))
	32.9%	(sqrt.f64 (/.f64 #s(literal 2 binary64) (/.f64 (/.f64 (/.f64 #s(literal 1 binary64) n) (PI.f64)) (/.f64 #s(literal 1 binary64) k))))
	32.9%	(sqrt.f64 (/.f64 #s(literal 2 binary64) (/.f64 (/.f64 k n) (PI.f64))))
✓	32.9%	(sqrt.f64 (/.f64 #s(literal 2 binary64) (/.f64 (/.f64 #s(literal 1 binary64) n) (/.f64 (PI.f64) k))))
	32.9%	(sqrt.f64 (/.f64 #s(literal 2 binary64) (/.f64 (/.f64 #s(literal 1 binary64) n) (-.f64 (/.f64 (+.f64 #s(literal 1 binary64) (PI.f64)) k) (/.f64 #s(literal 1 binary64) k)))))
	32.9%	(sqrt.f64 (/.f64 #s(literal 2 binary64) (/.f64 (*.f64 (/.f64 #s(literal -1 binary64) n) (-.f64 #s(literal 0 binary64) k)) (PI.f64))))
✓	33.0%	(sqrt.f64 (/.f64 #s(literal 2 binary64) (/.f64 k (*.f64 (PI.f64) n))))
	32.9%	(sqrt.f64 (/.f64 #s(literal 2 binary64) (*.f64 (/.f64 (/.f64 #s(literal 1 binary64) n) (/.f64 #s(literal -1 binary64) k)) (/.f64 #s(literal -1 binary64) (PI.f64)))))
	33.0%	(sqrt.f64 (/.f64 #s(literal 2 binary64) (*.f64 (/.f64 (/.f64 #s(literal 1 binary64) n) (PI.f64)) k)))
	33.0%	(sqrt.f64 (/.f64 #s(literal 2 binary64) (*.f64 (/.f64 k (PI.f64)) (/.f64 #s(literal 1 binary64) n))))
	32.9%	(sqrt.f64 (/.f64 #s(literal 2 binary64) (.f64 (/.f64 #s(literal -1 binary64) (PI.f64)) (.f64 (-.f64 #s(literal 0 binary64) k) (/.f64 #s(literal 1 binary64) n)))))
	33.0%	(sqrt.f64 (*.f64 (/.f64 (/.f64 n k) #s(literal 1/2 binary64)) (PI.f64)))
	32.9%	(sqrt.f64 (*.f64 (/.f64 #s(literal 2 binary64) (/.f64 k (PI.f64))) n))
	33.0%	(sqrt.f64 (*.f64 (/.f64 #s(literal 2 binary64) (/.f64 k n)) (PI.f64)))
	33.0%	(sqrt.f64 (.f64 (/.f64 #s(literal 2 binary64) k) (.f64 (PI.f64) n)))
	33.0%	(sqrt.f64 (.f64 (.f64 (/.f64 #s(literal 2 binary64) k) (PI.f64)) n))
✓	33.0%	(sqrt.f64 (.f64 (.f64 (/.f64 #s(literal 2 binary64) k) n) (PI.f64)))
	30.9%	(exp.f64 (.f64 (log.f64 (.f64 (/.f64 (PI.f64) #s(literal 1/2 binary64)) (/.f64 n k))) #s(literal 1/2 binary64)))
✓	30.9%	(exp.f64 (.f64 (log.f64 (.f64 (*.f64 (/.f64 #s(literal 2 binary64) k) (PI.f64)) n)) #s(literal 1/2 binary64)))

Compiler

Compiled 1527 to 751 computations (50.8% saved)

regimes107.0ms (0.7%)

Counts

78 → 1

Calls

Call 1

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

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:

24.0ms	(.f64 (.f64 #s(literal 2 binary64) (PI.f64)) n)
23.0ms	n
23.0ms	k
23.0ms	(.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) (pow.f64 (.f64 (*.f64 #s(literal 2 binary64) (PI.f64)) n) (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 2 binary64))))

Results

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

Compiler

Compiled 31 to 23 computations (25.8% saved)

regimes44.0ms (0.3%)

Counts

63 → 1

Calls

Call 1

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

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

Calls

2 calls:

19.0ms	n
19.0ms	k

Results

Accuracy	Segments	Branch
99.6%	1	`k`
99.6%	1	`n`

Compiler

Compiled 6 to 4 computations (33.3% saved)

regimes46.0ms (0.3%)

Counts

62 → 1

Calls

Call 1

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

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:

20.0ms	n
19.0ms	k

Results

Accuracy	Segments	Branch
99.5%	1	`k`
99.5%	1	`n`

Compiler

Compiled 6 to 4 computations (33.3% saved)

regimes47.0ms (0.3%)

Counts

61 → 2

Calls

Call 1

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

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

Calls

2 calls:

20.0ms	k
19.0ms	n

Results

Accuracy	Segments	Branch
99.6%	2	`k`
88.7%	1	`n`

Compiler

Compiled 6 to 4 computations (33.3% saved)

regimes42.0ms (0.3%)

Counts

60 → 2

Calls

Call 1

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

Outputs

(/.f64 (sqrt.f64 (*.f64 (PI.f64) n)) (sqrt.f64 (/.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:

19.0ms	n
19.0ms	k

Results

Accuracy	Segments	Branch
43.9%	1	`n`
45.8%	2	`k`

Compiler

Compiled 6 to 4 computations (33.3% saved)

regimes21.0ms (0.1%)

Counts

38 → 2

Calls

Call 1

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

Outputs

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

Calls

1 calls:

11.0ms

Results

Accuracy	Segments	Branch
45.7%	2	`k`

Compiler

Compiled 3 to 2 computations (33.3% saved)

regimes33.0ms (0.2%)

Counts

37 → 2

Calls

Call 1

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

Outputs

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

Calls

2 calls:

13.0ms	k
12.0ms	n

Results

Accuracy	Segments	Branch
43.5%	1	`n`
45.4%	2	`k`

Compiler

Compiled 6 to 4 computations (33.3% saved)

regimes21.0ms (0.1%)

Counts

33 → 2

Calls

Call 1

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

1 calls:

10.0ms

Results

Accuracy	Segments	Branch
45.4%	2	`k`

Compiler

Compiled 3 to 2 computations (33.3% saved)

regimes19.0ms (0.1%)

Counts

27 → 2

Calls

Call 1

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

Outputs

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

(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:

9.0ms	n
8.0ms	k

Results

Accuracy	Segments	Branch
33.0%	1	`n`
34.9%	2	`k`

Compiler

Compiled 6 to 4 computations (33.3% saved)

regimes17.0ms (0.1%)

Accuracy

Total -0.2b remaining (-0.4%)

Threshold costs -0.2b (-0.4%)

Counts

25 → 1

Calls

Call 1

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

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

Calls

2 calls:

8.0ms	n
8.0ms	k

Results

Accuracy	Segments	Branch
33.0%	1	`n`
33.0%	1	`k`

Compiler

Compiled 6 to 4 computations (33.3% saved)

bsearch19.0ms (0.1%)

Algorithm

1×	binary-search

Stop Event

1×	narrow-enough

Steps

Time	Left	Right
17.0ms	5.771376227367736e-29	2.5792058822941473e-27

Results

13.0ms

112×

valid

Compiler

Compiled 212 to 171 computations (19.3% saved)

Precisions

Click to see histograms. Total time spent on operations: 9.0ms

ival-pow: 3.0ms (32.2% of total)

ival-div: 2.0ms (21.5% of total)

ival-mult: 2.0ms (21.5% of total)

ival-sub: 1.0ms (10.7% of total)

ival-sqrt: 1.0ms (10.7% of total)

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

const: 0.0ms (0% of total)

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

bsearch24.0ms (0.2%)

Algorithm

1×	binary-search

Stop Event

1×	narrow-enough

Steps

Time	Left	Right
22.0ms	1.081567992309339e+242	5.4547269783613945e+244

Results

16.0ms

128×

valid

Compiler

Compiled 279 to 185 computations (33.7% saved)

Precisions

Click to see histograms. Total time spent on operations: 12.0ms

ival-pow: 5.0ms (41.8% of total)

ival-mult: 3.0ms (25.1% of total)

ival-div: 2.0ms (16.7% of total)

ival-pi: 1.0ms (8.4% of total)

ival-sub: 1.0ms (8.4% of total)

ival-sqrt: 1.0ms (8.4% of total)

const: 0.0ms (0% of total)

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

bsearch15.0ms (0.1%)

Algorithm

1×	binary-search

Stop Event

1×	narrow-enough

Steps

Time	Left	Right
13.0ms	4.428334950567642e+241	1.081567992309339e+242

Results

11.0ms

80×

valid

Compiler

Compiled 183 to 122 computations (33.3% saved)

Precisions

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

ival-pow: 4.0ms (48.6% of total)

ival-mult: 2.0ms (24.3% of total)

ival-div: 1.0ms (12.1% of total)

ival-sqrt: 1.0ms (12.1% of total)

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

ival-sub: 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	1.081567992309339e+242	5.4547269783613945e+244

Results

16.0ms

128×

valid

Compiler

Compiled 279 to 185 computations (33.7% saved)

Precisions

Click to see histograms. Total time spent on operations: 12.0ms

ival-pow: 5.0ms (42.7% of total)

ival-mult: 3.0ms (25.6% of total)

ival-div: 2.0ms (17.1% of total)

ival-pi: 1.0ms (8.5% of total)

ival-sub: 1.0ms (8.5% of total)

ival-sqrt: 1.0ms (8.5% of total)

const: 0.0ms (0% of total)

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

bsearch24.0ms (0.2%)

Algorithm

1×	binary-search

Stop Event

1×	narrow-enough

Steps

Time	Left	Right
22.0ms	1.081567992309339e+242	5.4547269783613945e+244

Results

17.0ms

128×

valid

Compiler

Compiled 279 to 185 computations (33.7% saved)

Precisions

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

ival-pow: 5.0ms (37.2% of total)

ival-mult: 4.0ms (29.8% of total)

ival-div: 2.0ms (14.9% of total)

ival-sub: 1.0ms (7.4% of total)

ival-sqrt: 1.0ms (7.4% of total)

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

const: 0.0ms (0% of total)

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

bsearch18.0ms (0.1%)

Algorithm

1×	binary-search

Stop Event

1×	narrow-enough

Steps

Time	Left	Right
16.0ms	6.559769737145305e+229	3.8384071347167438e+230

Results

12.0ms

96×

valid

Compiler

Compiled 209 to 137 computations (34.4% saved)

Precisions

Click to see histograms. Total time spent on operations: 9.0ms

ival-pow: 4.0ms (44.8% of total)

ival-mult: 2.0ms (22.4% of total)

ival-sub: 1.0ms (11.2% of total)

ival-div: 1.0ms (11.2% of total)

ival-sqrt: 1.0ms (11.2% of total)

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

const: 0.0ms (0% of total)

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

simplify13.0ms (0.1%)

Algorithm

1×	egg-herbie

Rules

24×	`*-commutative_binary64`
14×	`+-commutative_binary64`
10×	`sub-neg_binary64`
6×	`neg-sub0_binary64`
6×	`neg-mul-1_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	70	226
1	88	226
2	98	226
3	104	226
4	108	226
5	109	226

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)))) (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)))) (sqrt.f64 k))
(if (<=.f64 k #s(literal 5463682573640003/5575186299632655785383929568162090376495104 binary64)) (/.f64 (sqrt.f64 (.f64 (PI.f64) n)) (sqrt.f64 (/.f64 k #s(literal 2 binary64)))) (sqrt.f64 (/.f64 (pow.f64 (.f64 (*.f64 n (PI.f64)) #s(literal 2 binary64)) (-.f64 #s(literal 1 binary64) k)) k)))
(if (<=.f64 k #s(literal 109999999999999999683326730474174269376590273441305299896387059129015007260360070390049907773131580764763934010510740446243578599144694302698579389312061868337020420080133630465262157970962565688711382084349119577252340199599017350108041707520 binary64)) (/.f64 (sqrt.f64 (.f64 (PI.f64) n)) (sqrt.f64 (/.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 44999999999999999332053069600084406548439883985341283331883927921200729420615871876605863022676723360621308898573613945507609388244894942758107180275789006810879166157638666918192984184015497082551338480668440865882030632039889549993135046656 binary64)) (/.f64 (sqrt.f64 (.f64 #s(literal 2 binary64) (.f64 (PI.f64) n))) (sqrt.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 115000000000000002899325139059103503527426653132520849646051139424348148887565015105539499069900192512945915645345907888806868767537060402896384780937482498314296473334635705119259647794275997415181806411211273325091006906357223425419335696384 binary64)) (.f64 (sqrt.f64 (/.f64 #s(literal 2 binary64) (/.f64 k (PI.f64)))) (sqrt.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)))
(if (<=.f64 k #s(literal 275000000000000011053089869251147153765110696897502715507004765717256536240591628200244952892125264861116445352254008330633747348776295740355305011021353336036393175453486078150269164617728569604051447395309176088997238390511129426393508610048 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 105999999999999998057643439966102448050559598308265606531597313090629388490738531841271394056172516760906673156614009371170209468282933382064192200628894947217774315055072348099460423482058536050433407516101593067770681409415413760 binary64)) (sqrt.f64 (.f64 (.f64 (/.f64 #s(literal 2 binary64) k) n) (PI.f64))) (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)))
(sqrt.f64 (.f64 (.f64 (/.f64 #s(literal 2 binary64) k) n) (PI.f64)))

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)))) (pow.f64 k #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 5463682573640003/5575186299632655785383929568162090376495104 binary64)) (/.f64 (sqrt.f64 (.f64 (PI.f64) n)) (sqrt.f64 (/.f64 k #s(literal 2 binary64)))) (sqrt.f64 (/.f64 (pow.f64 (.f64 (*.f64 n (PI.f64)) #s(literal 2 binary64)) (-.f64 #s(literal 1 binary64) k)) k)))
(if (<=.f64 k #s(literal 5463682573640003/5575186299632655785383929568162090376495104 binary64)) (/.f64 (sqrt.f64 (.f64 (PI.f64) n)) (sqrt.f64 (/.f64 k #s(literal 2 binary64)))) (sqrt.f64 (/.f64 (pow.f64 (.f64 #s(literal 2 binary64) (*.f64 (PI.f64) n)) (-.f64 #s(literal 1 binary64) k)) k)))
(if (<=.f64 k #s(literal 109999999999999999683326730474174269376590273441305299896387059129015007260360070390049907773131580764763934010510740446243578599144694302698579389312061868337020420080133630465262157970962565688711382084349119577252340199599017350108041707520 binary64)) (/.f64 (sqrt.f64 (.f64 (PI.f64) n)) (sqrt.f64 (/.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 44999999999999999332053069600084406548439883985341283331883927921200729420615871876605863022676723360621308898573613945507609388244894942758107180275789006810879166157638666918192984184015497082551338480668440865882030632039889549993135046656 binary64)) (/.f64 (sqrt.f64 (.f64 #s(literal 2 binary64) (.f64 (PI.f64) n))) (sqrt.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 115000000000000002899325139059103503527426653132520849646051139424348148887565015105539499069900192512945915645345907888806868767537060402896384780937482498314296473334635705119259647794275997415181806411211273325091006906357223425419335696384 binary64)) (.f64 (sqrt.f64 (/.f64 #s(literal 2 binary64) (/.f64 k (PI.f64)))) (sqrt.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)))
(if (<=.f64 k #s(literal 275000000000000011053089869251147153765110696897502715507004765717256536240591628200244952892125264861116445352254008330633747348776295740355305011021353336036393175453486078150269164617728569604051447395309176088997238390511129426393508610048 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 275000000000000011053089869251147153765110696897502715507004765717256536240591628200244952892125264861116445352254008330633747348776295740355305011021353336036393175453486078150269164617728569604051447395309176088997238390511129426393508610048 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 105999999999999998057643439966102448050559598308265606531597313090629388490738531841271394056172516760906673156614009371170209468282933382064192200628894947217774315055072348099460423482058536050433407516101593067770681409415413760 binary64)) (sqrt.f64 (.f64 (.f64 (/.f64 #s(literal 2 binary64) k) n) (PI.f64))) (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 105999999999999998057643439966102448050559598308265606531597313090629388490738531841271394056172516760906673156614009371170209468282933382064192200628894947217774315055072348099460423482058536050433407516101593067770681409415413760 binary64)) (sqrt.f64 (.f64 (PI.f64) (.f64 n (/.f64 #s(literal 2 binary64) 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)))
(sqrt.f64 (.f64 (.f64 (/.f64 #s(literal 2 binary64) k) n) (PI.f64)))
(sqrt.f64 (.f64 (PI.f64) (.f64 n (/.f64 #s(literal 2 binary64) k))))

soundness2.3s (16%)

Rules

6156×	`-lowering-.f32`
6156×	`-lowering-.f64`
5736×	`-lowering-.f32`
5736×	`-lowering-.f64`
5664×	`-lowering-.f32`

Iterations

Useful iterations: 4 (0.0ms)

Iter	Nodes	Cost
0	32	158
1	197	151
2	1275	150
0	8269	150
0	20	68
1	132	68
2	851	64
0	8618	64
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	33	153
1	206	143
2	1393	139
0	8551	139
0	391	5169
1	1269	4897
2	4718	4463
0	8466	4463
0	139	2132
1	385	2104
2	1189	1816
3	4175	1732
4	7740	1732
0	8111	1732
0	32	151
1	167	149
2	1039	147
0	8698	147

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

Compiler

Compiled 667 to 424 computations (36.4% saved)

preprocess108.0ms (0.8%)

Compiler: Compiled 492 to 162 computations (67.1% 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	33	253
1	53	251
2	77	250
3	92	250
4	107	250
5	130	244
6	169	244
7	201	244
8	248	244
9	285	244
10	300	244
11	328	244
12	381	237
13	453	237
14	506	237
15	544	237
16	560	237
17	583	237
18	625	237
19	645	237
0	645	237

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	33	253
1	53	251
2	77	250
3	92	250
4	107	250
5	130	244
6	169	244
7	201	244
8	248	244
9	285	244
10	300	244
11	328	244
12	381	237
13	453	237
14	506	237
15	544	237
16	560	237
17	583	237
18	625	237
19	645	237
0	645	237

analyze150.0ms (1%)

sample4.5s (31.1%)

preprocess83.0ms (0.6%)

explain182.0ms (1.3%)

eval0.0ms (0%)

prune1.0ms (0%)

simplify13.0ms (0.1%)

localize106.0ms (0.7%)

series87.0ms (0.6%)

rewrite399.0ms (2.8%)

simplify280.0ms (2%)

eval134.0ms (0.9%)

prune106.0ms (0.7%)

simplify36.0ms (0.3%)

localize260.0ms (1.8%)

series47.0ms (0.3%)

rewrite400.0ms (2.8%)

simplify302.0ms (2.1%)

eval200.0ms (1.4%)

prune170.0ms (1.2%)

simplify194.0ms (1.4%)

localize305.0ms (2.1%)

series161.0ms (1.1%)

rewrite375.0ms (2.6%)

simplify376.0ms (2.6%)

eval305.0ms (2.1%)

prune326.0ms (2.3%)

simplify19.0ms (0.1%)

localize276.0ms (1.9%)

series41.0ms (0.3%)

rewrite409.0ms (2.9%)

simplify328.0ms (2.3%)

eval478.0ms (3.3%)

prune378.0ms (2.6%)

regimes107.0ms (0.7%)

regimes44.0ms (0.3%)

regimes46.0ms (0.3%)

regimes47.0ms (0.3%)

regimes42.0ms (0.3%)

regimes21.0ms (0.1%)

regimes33.0ms (0.2%)

regimes21.0ms (0.1%)

regimes19.0ms (0.1%)

regimes17.0ms (0.1%)

bsearch19.0ms (0.1%)

bsearch24.0ms (0.2%)

bsearch15.0ms (0.1%)

bsearch23.0ms (0.2%)

bsearch24.0ms (0.2%)

bsearch18.0ms (0.1%)

simplify13.0ms (0.1%)

soundness2.3s (16%)

preprocess108.0ms (0.8%)

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	33	253
1	53	251
2	77	250
3	92	250
4	107	250
5	130	244
6	169	244
7	201	244
8	248	244
9	285	244
10	300	244
11	328	244
12	381	237
13	453	237
14	506	237
15	544	237
16	560	237
17	583	237
18	625	237
19	645	237
0	645	237