Metrics for Migdal et al, Equation (51)

start0.0ms (0%)

Memory: 0.0MiB live, 0.0MiB allocated

analyze142.0ms (1.2%)

Memory

-11.6MiB live, 185.6MiB allocated

Algorithm

1×

Search

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

Compiler

Compiled 18 to 15 computations (16.7% saved)

sample2.8s (24.3%)

Memory

41.0MiB live, 4 233.8MiB allocated

Samples

997.0ms	8 256×	0	valid
697.0ms	3 481×	1	invalid
334.0ms	1 798×	1	exit
108.0ms	407×	2	invalid
36.0ms	463×	0	invalid
27.0ms	221×	0	exit

Precisions

Click to see histograms. Total time spent on operations: 1.6s

ival-pow: 449.0ms (27.6% of total)

ival-mult: 371.0ms (22.8% of total)

ival-div: 238.0ms (14.6% of total)

ival-sub: 174.0ms (10.7% of total)

ival-sqrt: 162.0ms (10% of total)

adjust: 123.0ms (7.6% of total)

ival-pi: 74.0ms (4.6% of total)

exact: 15.0ms (0.9% of total)

ival-true: 12.0ms (0.7% of total)

ival-assert: 6.0ms (0.4% of total)

Bogosity

explain141.0ms (1.2%)

Memory

36.2MiB live, 233.6MiB allocated

FPErrors

Click to see full error table

Ground Truth	Overpredictions	Example	Example	Subexpression
5	86	(7.087918786803694e-162 2.513637579705954e-197)	-	`(pow.f64 (.f64 (.f64 #s(literal 2 binary64) (PI.f64)) n) (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 2 binary64)))`
0	0	-	-	`k`
0	0	-	-	`n`
0	0	-	-	`(/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 2 binary64))`
0	0	-	-	`#s(literal 1 binary64)`
0	0	-	-	`(.f64 (.f64 #s(literal 2 binary64) (PI.f64)) n)`
0	0	-	-	`(sqrt.f64 k)`
0	0	-	-	`#s(literal 2 binary64)`
0	0	-	-	`(/.f64 #s(literal 1 binary64) (sqrt.f64 k))`
0	0	-	-	`(-.f64 #s(literal 1 binary64) k)`
0	0	-	-	`(*.f64 #s(literal 2 binary64) (PI.f64))`
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	-	-	`(PI.f64)`

Explanations

Click to see full explanations table

Operator	Subexpression	Explanation	Count
`pow.f64`	`(pow.f64 (.f64 (.f64 #s(literal 2 binary64) (PI.f64)) n) (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 2 binary64)))`	sensitivity	91	41

Confusion

	Predicted +	Predicted -
+	5	0
-	86	165

Precision

0.054945054945054944

Recall

1.0

Confusion?

	Predicted +	Predicted Maybe	Predicted -
+	5	0	0
-	86	41	124

Precision?

0.03787878787878788

Recall?

1.0

Freqs

test

number	freq
0	165
1	91

Total Confusion?

	Predicted +	Predicted Maybe	Predicted -
+	1	0	0
-	0	0	0

Precision?

1.0

Recall?

1.0

Samples

55.0ms

512×

valid

Compiler

Compiled 130 to 43 computations (66.9% saved)

Precisions

Click to see histograms. Total time spent on operations: 37.0ms

ival-pow: 11.0ms (30% of total)

ival-mult: 8.0ms (21.8% of total)

ival-div: 7.0ms (19.1% of total)

ival-sqrt: 5.0ms (13.7% of total)

ival-sub: 3.0ms (8.2% of total)

ival-pi: 2.0ms (5.5% of total)

exact: 1.0ms (2.7% of total)

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

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

preprocess70.0ms (0.6%)

Memory

-19.5MiB live, 56.6MiB allocated

Algorithm

1×	egg-herbie

Rules

232×	`associate-r`
160×	`sub-neg`
160×	`associate-l`
138×	`distribute-lft-neg-in`
118×	`distribute-lft-in`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	31	88
1	82	74
2	193	74
3	383	74
4	607	74
5	878	74
6	1047	74
7	1230	74
8	1285	74
9	1309	74
10	1327	74
11	1331	74
12	1331	74
0	13	16
0	22	16
1	37	14
2	54	14
3	75	14
4	93	14
5	108	14
6	129	14
7	156	14
8	165	14
9	168	14
0	168	13

Stop Event

1×	iter limit
1×	saturated
1×	iter limit
1×	saturated

Calls

Call 1

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

Outputs

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

Compiler

Compiled 18 to 13 computations (27.8% saved)

eval0.0ms (0%)

Memory: 0.5MiB live, 0.5MiB allocated
Compiler: Compiled 2 to 2 computations (0% saved)

prune1.0ms (0%)

Memory

1.3MiB live, 1.3MiB allocated

Alt Table

Click to see full alt table

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

Compiler

Compiled 18 to 13 computations (27.8% saved)

simplify8.0ms (0.1%)

Memory

10.5MiB live, 10.5MiB allocated

Algorithm

1×	egg-herbie

Localize:

Found 4 expressions of interest:

New	Metric	Score
cost-diff	0	(sqrt.f64 k)
cost-diff	0	(/.f64 #s(literal 1 binary64) (sqrt.f64 k))
cost-diff	320	(.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))))
cost-diff	512	(/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 2 binary64))

Rules

64×	`lower-*.f32`
58×	`lower-*.f64`
48×	`lower-+.f64`
48×	`lower-+.f32`
36×	`lower-fma.f64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	13	54
0	22	54
1	37	52
2	54	52
3	75	52
4	93	52
5	108	52
6	129	52
7	156	52
8	165	52
9	168	52
0	168	49

Stop Event

1×	iter limit
1×	saturated
1×	iter limit

Calls

Call 1

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

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

localize91.0ms (0.8%)

Memory

-21.1MiB live, 59.7MiB allocated

Localize:

Found 4 expressions of interest:

New	Metric	Score
accuracy	0.16796875	(.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	0.2240471803363731	(pow.f64 (.f64 (.f64 #s(literal 2 binary64) (PI.f64)) n) (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 2 binary64)))
accuracy	0.25	(/.f64 #s(literal 1 binary64) (sqrt.f64 k))
accuracy	0.2734375	(.f64 (.f64 #s(literal 2 binary64) (PI.f64)) n)

Samples

79.0ms

256×

valid

Compiler

Compiled 56 to 15 computations (73.2% saved)

Precisions

Click to see histograms. Total time spent on operations: 68.0ms

ival-sub: 37.0ms (54.8% of total)

ival-div: 17.0ms (25.2% of total)

ival-pow: 5.0ms (7.4% of total)

ival-mult: 4.0ms (5.9% of total)

ival-sqrt: 2.0ms (3% of total)

ival-pi: 1.0ms (1.5% of total)

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

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

exact: 0.0ms (0% of total)

series69.0ms (0.6%)

Memory

24.4MiB live, 99.8MiB allocated

Counts

6 → 96

Calls

Call 1

Inputs
#s(alt (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 2 binary64)) (patch (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 2 binary64)) #<representation binary64>) () ())
#s(alt (.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)))) (patch (.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)))) #<representation binary64>) () ())
#s(alt (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) (patch (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) #<representation binary64>) () ())
#s(alt (sqrt.f64 k) (patch (sqrt.f64 k) #<representation binary64>) () ())
#s(alt (.f64 (.f64 #s(literal 2 binary64) (PI.f64)) n) (patch (.f64 (.f64 #s(literal 2 binary64) (PI.f64)) n) #<representation binary64>) () ())
#s(alt (pow.f64 (.f64 (.f64 #s(literal 2 binary64) (PI.f64)) n) (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 2 binary64))) (patch (pow.f64 (.f64 (.f64 #s(literal 2 binary64) (PI.f64)) n) (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 2 binary64))) #<representation binary64>) () ())

Outputs
#s(alt 1/2 (taylor 0 k) (#s(alt (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 2 binary64)) (patch (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 2 binary64)) #<representation binary64>) () ())) ())
#s(alt (+ 1/2 (* -1/2 k)) (taylor 0 k) (#s(alt (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 2 binary64)) (patch (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 2 binary64)) #<representation binary64>) () ())) ())
#s(alt (+ 1/2 (* -1/2 k)) (taylor 0 k) (#s(alt (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 2 binary64)) (patch (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 2 binary64)) #<representation binary64>) () ())) ())
#s(alt (+ 1/2 (* -1/2 k)) (taylor 0 k) (#s(alt (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 2 binary64)) (patch (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 2 binary64)) #<representation binary64>) () ())) ())
#s(alt (* -1/2 k) (taylor inf k) (#s(alt (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 2 binary64)) (patch (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 2 binary64)) #<representation binary64>) () ())) ())
#s(alt (* k (- (* 1/2 (/ 1 k)) 1/2)) (taylor inf k) (#s(alt (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 2 binary64)) (patch (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 2 binary64)) #<representation binary64>) () ())) ())
#s(alt (* k (- (* 1/2 (/ 1 k)) 1/2)) (taylor inf k) (#s(alt (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 2 binary64)) (patch (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 2 binary64)) #<representation binary64>) () ())) ())
#s(alt (* k (- (* 1/2 (/ 1 k)) 1/2)) (taylor inf k) (#s(alt (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 2 binary64)) (patch (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 2 binary64)) #<representation binary64>) () ())) ())
#s(alt (* -1/2 k) (taylor -inf k) (#s(alt (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 2 binary64)) (patch (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 2 binary64)) #<representation binary64>) () ())) ())
#s(alt (* -1 (* k (- 1/2 (* 1/2 (/ 1 k))))) (taylor -inf k) (#s(alt (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 2 binary64)) (patch (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 2 binary64)) #<representation binary64>) () ())) ())
#s(alt (* -1 (* k (- 1/2 (* 1/2 (/ 1 k))))) (taylor -inf k) (#s(alt (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 2 binary64)) (patch (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 2 binary64)) #<representation binary64>) () ())) ())
#s(alt (* -1 (* k (- 1/2 (* 1/2 (/ 1 k))))) (taylor -inf k) (#s(alt (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 2 binary64)) (patch (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 2 binary64)) #<representation binary64>) () ())) ())
#s(alt (* (sqrt (/ (* n (PI)) k)) (sqrt 2)) (taylor 0 k) (#s(alt (.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)))) (patch (.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)))) #<representation binary64>) () ())) ())
#s(alt (/ (+ (* -1/2 (* (sqrt (* (pow k 3) (* n (PI)))) (* (log (* 2 (* n (PI)))) (sqrt 2)))) (* (sqrt (* k (* n (PI)))) (sqrt 2))) k) (taylor 0 k) (#s(alt (.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)))) (patch (.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)))) #<representation binary64>) () ())) ())
#s(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) (taylor 0 k) (#s(alt (.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)))) (patch (.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)))) #<representation binary64>) () ())) ())
#s(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) (taylor 0 k) (#s(alt (.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)))) (patch (.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)))) #<representation binary64>) () ())) ())
#s(alt (* (sqrt (/ 1 k)) (exp (* 1/2 (* (log (* 2 (* n (PI)))) (- 1 k))))) (taylor inf k) (#s(alt (.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)))) (patch (.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)))) #<representation binary64>) () ())) ())
#s(alt (* (sqrt (/ 1 k)) (exp (* 1/2 (* (log (* 2 (* n (PI)))) (- 1 k))))) (taylor inf k) (#s(alt (.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)))) (patch (.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)))) #<representation binary64>) () ())) ())
#s(alt (* (sqrt (/ 1 k)) (exp (* 1/2 (* (log (* 2 (* n (PI)))) (- 1 k))))) (taylor inf k) (#s(alt (.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)))) (patch (.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)))) #<representation binary64>) () ())) ())
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#s(alt (+ (* -1/2 (* (* k (* (log (* 2 (* n (PI)))) (sqrt 2))) (sqrt (* n (PI))))) (* (sqrt (* n (PI))) (sqrt 2))) (taylor 0 k) (#s(alt (pow.f64 (.f64 (.f64 #s(literal 2 binary64) (PI.f64)) n) (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 2 binary64))) (patch (pow.f64 (.f64 (.f64 #s(literal 2 binary64) (PI.f64)) n) (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 2 binary64))) #<representation binary64>) () ())) ())
#s(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))) (taylor 0 k) (#s(alt (pow.f64 (.f64 (.f64 #s(literal 2 binary64) (PI.f64)) n) (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 2 binary64))) (patch (pow.f64 (.f64 (.f64 #s(literal 2 binary64) (PI.f64)) n) (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 2 binary64))) #<representation binary64>) () ())) ())
#s(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))) (taylor 0 k) (#s(alt (pow.f64 (.f64 (.f64 #s(literal 2 binary64) (PI.f64)) n) (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 2 binary64))) (patch (pow.f64 (.f64 (.f64 #s(literal 2 binary64) (PI.f64)) n) (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 2 binary64))) #<representation binary64>) () ())) ())
#s(alt (exp (* 1/2 (* (log (* 2 (* n (PI)))) (- 1 k)))) (taylor inf k) (#s(alt (pow.f64 (.f64 (.f64 #s(literal 2 binary64) (PI.f64)) n) (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 2 binary64))) (patch (pow.f64 (.f64 (.f64 #s(literal 2 binary64) (PI.f64)) n) (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 2 binary64))) #<representation binary64>) () ())) ())
#s(alt (exp (* 1/2 (* (log (* 2 (* n (PI)))) (- 1 k)))) (taylor inf k) (#s(alt (pow.f64 (.f64 (.f64 #s(literal 2 binary64) (PI.f64)) n) (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 2 binary64))) (patch (pow.f64 (.f64 (.f64 #s(literal 2 binary64) (PI.f64)) n) (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 2 binary64))) #<representation binary64>) () ())) ())
#s(alt (exp (* 1/2 (* (log (* 2 (* n (PI)))) (- 1 k)))) (taylor inf k) (#s(alt (pow.f64 (.f64 (.f64 #s(literal 2 binary64) (PI.f64)) n) (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 2 binary64))) (patch (pow.f64 (.f64 (.f64 #s(literal 2 binary64) (PI.f64)) n) (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 2 binary64))) #<representation binary64>) () ())) ())
#s(alt (exp (* 1/2 (* (log (* 2 (* n (PI)))) (- 1 k)))) (taylor inf k) (#s(alt (pow.f64 (.f64 (.f64 #s(literal 2 binary64) (PI.f64)) n) (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 2 binary64))) (patch (pow.f64 (.f64 (.f64 #s(literal 2 binary64) (PI.f64)) n) (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 2 binary64))) #<representation binary64>) () ())) ())
#s(alt (exp (* 1/2 (* (log (* 2 (* n (PI)))) (+ 1 (* -1 k))))) (taylor -inf k) (#s(alt (pow.f64 (.f64 (.f64 #s(literal 2 binary64) (PI.f64)) n) (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 2 binary64))) (patch (pow.f64 (.f64 (.f64 #s(literal 2 binary64) (PI.f64)) n) (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 2 binary64))) #<representation binary64>) () ())) ())
#s(alt (exp (* 1/2 (* (log (* 2 (* n (PI)))) (+ 1 (* -1 k))))) (taylor -inf k) (#s(alt (pow.f64 (.f64 (.f64 #s(literal 2 binary64) (PI.f64)) n) (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 2 binary64))) (patch (pow.f64 (.f64 (.f64 #s(literal 2 binary64) (PI.f64)) n) (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 2 binary64))) #<representation binary64>) () ())) ())
#s(alt (exp (* 1/2 (* (log (* 2 (* n (PI)))) (+ 1 (* -1 k))))) (taylor -inf k) (#s(alt (pow.f64 (.f64 (.f64 #s(literal 2 binary64) (PI.f64)) n) (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 2 binary64))) (patch (pow.f64 (.f64 (.f64 #s(literal 2 binary64) (PI.f64)) n) (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 2 binary64))) #<representation binary64>) () ())) ())
#s(alt (exp (* 1/2 (* (log (* 2 (* n (PI)))) (+ 1 (* -1 k))))) (taylor -inf k) (#s(alt (pow.f64 (.f64 (.f64 #s(literal 2 binary64) (PI.f64)) n) (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 2 binary64))) (patch (pow.f64 (.f64 (.f64 #s(literal 2 binary64) (PI.f64)) n) (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 2 binary64))) #<representation binary64>) () ())) ())

Calls

24 calls:

Time	Variable		Point	Expression
31.0ms	n	@	0	(* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2)))
22.0ms	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	@	-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)))

simplify259.0ms (2.2%)

Memory

-0.2MiB live, 307.3MiB allocated

Algorithm

1×	egg-herbie

Rules

9 974×	`lower-fma.f64`
9 974×	`lower-fma.f32`
5 988×	`lower-*.f64`
5 988×	`lower-*.f32`
1 688×	`lower-+.f64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	128	1174
1	345	1155
2	1011	1065
3	3348	1038
4	5547	966
0	8354	945

Stop Event

1×	iter limit
1×	node limit

Counts

96 → 96

Calls

Call 1

Inputs
1/2
(+ 1/2 (* -1/2 k))
(+ 1/2 (* -1/2 k))
(+ 1/2 (* -1/2 k))
(* -1/2 k)
(* k (- (* 1/2 (/ 1 k)) 1/2))
(* k (- (* 1/2 (/ 1 k)) 1/2))
(* k (- (* 1/2 (/ 1 k)) 1/2))
(* -1/2 k)
(* -1 (* k (- 1/2 (* 1/2 (/ 1 k)))))
(* -1 (* k (- 1/2 (* 1/2 (/ 1 k)))))
(* -1 (* k (- 1/2 (* 1/2 (/ 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))))))
(* (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)))
(* 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)))
(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)))))

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

rewrite610.0ms (5.3%)

Memory

-226.0MiB live, 231.1MiB allocated

Rules

4 378×	`lower-*.f32`
4 372×	`lower-*.f64`
3 286×	`lower-pow.f32`
3 284×	`lower-pow.f64`
2 442×	`lower-/.f32`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	13	43
0	22	43
1	89	40
2	497	38
3	4474	38
0	8599	37

Stop Event

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

Counts

6 → 419

Calls

Call 1

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

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

eval162.0ms (1.4%)

Memory: -5.5MiB live, 120.7MiB allocated
Compiler: Compiled 11 338 to 1 530 computations (86.5% saved)

prune177.0ms (1.5%)

Memory

-5.1MiB live, 156.0MiB allocated

Pruning

12 alts after pruning (12 fresh and 0 done)

	Pruned	Kept	Total
New	503	12	515
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	504	12	516

Accuracy

100.0%

Counts

516 → 12

Alt Table

Click to see full alt table

Status	Accuracy	Program
	53.4%	(/.f64 (pow.f64 (.f64 #s(literal 2 binary64) (.f64 (PI.f64) n)) (fma.f64 k #s(literal 1/2 binary64) #s(literal 1/2 binary64))) (sqrt.f64 k))
▶	99.7%	(/.f64 (sqrt.f64 (.f64 #s(literal 2 binary64) (.f64 (PI.f64) n))) (.f64 (sqrt.f64 k) (pow.f64 (.f64 #s(literal 2 binary64) (.f64 (PI.f64) n)) (.f64 k #s(literal 1/2 binary64)))))
▶	99.4%	(/.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 -1/2 binary64))))))
	52.8%	(.f64 (pow.f64 n (fma.f64 k #s(literal 1/2 binary64) #s(literal 1/2 binary64))) (/.f64 (pow.f64 (.f64 #s(literal 2 binary64) (PI.f64)) (fma.f64 k #s(literal 1/2 binary64) #s(literal 1/2 binary64))) (sqrt.f64 k)))
	52.9%	(.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) (pow.f64 (pow.f64 (.f64 #s(literal 2 binary64) (.f64 (PI.f64) n)) (.f64 (+.f64 #s(literal 1 binary64) k) #s(literal 1/8 binary64))) #s(literal 4 binary64)))
▶	49.2%	(.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) (pow.f64 (.f64 (.f64 #s(literal 2 binary64) (PI.f64)) n) #s(approx (/ (- 1 k) 2) (.f64 #s(literal -1/2 binary64) k))))
▶	53.9%	(.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) (pow.f64 (.f64 (*.f64 #s(literal 2 binary64) (PI.f64)) n) #s(approx (/ (- 1 k) 2) #s(literal 1/2 binary64))))
	99.7%	(.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) (.f64 (pow.f64 (.f64 #s(literal 2 binary64) (.f64 (PI.f64) n)) (.f64 k #s(literal -1/2 binary64))) (sqrt.f64 (.f64 #s(literal 2 binary64) (*.f64 (PI.f64) n)))))
	53.7%	(.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) #s(approx (pow ( (* 2 (PI)) n) (/ (- 1 k) 2)) (.f64 (sqrt.f64 #s(literal 2 binary64)) (sqrt.f64 (.f64 n (PI.f64))))))
▶	41.4%	#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (.f64 (sqrt.f64 (/.f64 (.f64 n (PI.f64)) k)) (sqrt.f64 #s(literal 2 binary64))))
	99.5%	#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) k)) (pow.f64 (/.f64 (.f64 (PI.f64) #s(literal -2 binary64)) (/.f64 #s(literal -1 binary64) n)) (fma.f64 #s(literal -1/2 binary64) k #s(literal 1/2 binary64)))))
	99.5%	#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) k)) (pow.f64 (.f64 n (*.f64 (PI.f64) #s(literal 2 binary64))) (fma.f64 #s(literal -1/2 binary64) k #s(literal 1/2 binary64)))))

Compiler

Compiled 428 to 314 computations (26.6% saved)

simplify58.0ms (0.5%)

Memory

17.9MiB live, 56.4MiB allocated

Algorithm

1×	egg-herbie

Localize:

Found 20 expressions of interest:

New	Metric	Score
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 -1/2 binary64)))))
cost-diff	0	(/.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 -1/2 binary64))))))
cost-diff	128	(-.f64 #s(literal -1/2 binary64) (*.f64 k #s(literal -1/2 binary64)))
cost-diff	0	(pow.f64 (.f64 (.f64 #s(literal 2 binary64) (PI.f64)) n) #s(approx (/ (- 1 k) 2) (*.f64 #s(literal -1/2 binary64) k)))
cost-diff	0	(sqrt.f64 k)
cost-diff	0	(/.f64 #s(literal 1 binary64) (sqrt.f64 k))
cost-diff	320	(.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) (pow.f64 (.f64 (.f64 #s(literal 2 binary64) (PI.f64)) n) #s(approx (/ (- 1 k) 2) (.f64 #s(literal -1/2 binary64) k))))
cost-diff	0	(pow.f64 (.f64 (.f64 #s(literal 2 binary64) (PI.f64)) n) #s(approx (/ (- 1 k) 2) #s(literal 1/2 binary64)))
cost-diff	0	(sqrt.f64 k)
cost-diff	0	(/.f64 #s(literal 1 binary64) (sqrt.f64 k))
cost-diff	320	(.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) (pow.f64 (.f64 (*.f64 #s(literal 2 binary64) (PI.f64)) n) #s(approx (/ (- 1 k) 2) #s(literal 1/2 binary64))))
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	#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (.f64 (sqrt.f64 (/.f64 (.f64 n (PI.f64)) k)) (sqrt.f64 #s(literal 2 binary64))))
cost-diff	0	(*.f64 (PI.f64) n)
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	0	(/.f64 (sqrt.f64 (.f64 #s(literal 2 binary64) (.f64 (PI.f64) n))) (.f64 (sqrt.f64 k) (pow.f64 (.f64 #s(literal 2 binary64) (.f64 (PI.f64) n)) (.f64 k #s(literal 1/2 binary64)))))

Rules

496×	`lower-*.f32`
480×	`lower-fma.f64`
480×	`lower-fma.f32`
470×	`lower-*.f64`
212×	`associate-r`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	45	309
0	72	309
1	112	303
2	151	303
3	187	303
4	216	303
5	292	303
6	373	303
7	434	303
8	511	303
9	667	303
10	849	303
11	1118	303
12	1303	303
13	1328	303
14	1342	303
15	1354	303
16	1354	303
17	1359	303
0	1359	292

Stop Event

1×	iter limit
1×	saturated
1×	iter limit

Calls

Call 1

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

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

localize362.0ms (3.1%)

Memory

-3.7MiB live, 190.1MiB allocated

Localize:

Found 20 expressions of interest:

New	Metric	Score
accuracy	0.1875	(.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 -1/2 binary64)))))
accuracy	0.19053065553371273	(pow.f64 (.f64 #s(literal 2 binary64) (.f64 (PI.f64) n)) (-.f64 #s(literal -1/2 binary64) (*.f64 k #s(literal -1/2 binary64))))
accuracy	0.22265625	(*.f64 (PI.f64) n)
accuracy	14.046533023192913	(PI.f64)
accuracy	0.22265625	(.f64 (.f64 #s(literal 2 binary64) (PI.f64)) n)
accuracy	0.2240471803363731	(pow.f64 (.f64 (.f64 #s(literal 2 binary64) (PI.f64)) n) #s(approx (/ (- 1 k) 2) (*.f64 #s(literal -1/2 binary64) k)))
accuracy	14.046533023192913	(PI.f64)
accuracy	34.904186474779344	#s(approx (/ (- 1 k) 2) (*.f64 #s(literal -1/2 binary64) k))
accuracy	0.22265625	(.f64 (.f64 #s(literal 2 binary64) (PI.f64)) n)
accuracy	0.2240471803363731	(pow.f64 (.f64 (.f64 #s(literal 2 binary64) (PI.f64)) n) #s(approx (/ (- 1 k) 2) #s(literal 1/2 binary64)))
accuracy	14.046533023192913	(PI.f64)
accuracy	15.202179506440986	#s(approx (/ (- 1 k) 2) #s(literal 1/2 binary64))
accuracy	0.38119125976844204	(.f64 (sqrt.f64 (/.f64 (.f64 n (PI.f64)) k)) (sqrt.f64 #s(literal 2 binary64)))
accuracy	8.103760109562641	(sqrt.f64 (/.f64 (*.f64 n (PI.f64)) k))
accuracy	14.046533023192913	(PI.f64)
accuracy	15.11847131460795	#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (.f64 (sqrt.f64 (/.f64 (.f64 n (PI.f64)) k)) (sqrt.f64 #s(literal 2 binary64))))
accuracy	0.11328125	(sqrt.f64 (.f64 #s(literal 2 binary64) (.f64 (PI.f64) n)))
accuracy	0.171875	(/.f64 (sqrt.f64 (.f64 #s(literal 2 binary64) (.f64 (PI.f64) n))) (.f64 (sqrt.f64 k) (pow.f64 (.f64 #s(literal 2 binary64) (.f64 (PI.f64) n)) (.f64 k #s(literal 1/2 binary64)))))
accuracy	0.22265625	(*.f64 (PI.f64) n)
accuracy	14.046533023192913	(PI.f64)

Samples

275.0ms	198×	0	valid
15.0ms	58×	0	exit

Compiler

Compiled 283 to 35 computations (87.6% saved)

Precisions

Click to see histograms. Total time spent on operations: 177.0ms

ival-sqrt: 86.0ms (48.7% of total)

ival-pi: 49.0ms (27.8% of total)

ival-mult: 17.0ms (9.6% of total)

ival-pow: 13.0ms (7.4% of total)

ival-div: 9.0ms (5.1% of total)

ival-sub: 2.0ms (1.1% of total)

exact: 1.0ms (0.6% of total)

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

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

series810.0ms (7%)

Memory

28.4MiB live, 65.3MiB allocated

Counts

22 → 396

Calls

Call 1

Inputs
#s(alt (/.f64 (sqrt.f64 (.f64 #s(literal 2 binary64) (.f64 (PI.f64) n))) (.f64 (sqrt.f64 k) (pow.f64 (.f64 #s(literal 2 binary64) (.f64 (PI.f64) n)) (.f64 k #s(literal 1/2 binary64))))) (patch (/.f64 (sqrt.f64 (.f64 #s(literal 2 binary64) (.f64 (PI.f64) n))) (.f64 (sqrt.f64 k) (pow.f64 (.f64 #s(literal 2 binary64) (.f64 (PI.f64) n)) (.f64 k #s(literal 1/2 binary64))))) #<representation binary64>) () ())
#s(alt (sqrt.f64 (.f64 #s(literal 2 binary64) (.f64 (PI.f64) n))) (patch (sqrt.f64 (.f64 #s(literal 2 binary64) (.f64 (PI.f64) n))) #<representation binary64>) () ())
#s(alt (.f64 #s(literal 2 binary64) (.f64 (PI.f64) n)) (patch (.f64 #s(literal 2 binary64) (.f64 (PI.f64) n)) #<representation binary64>) () ())
#s(alt (.f64 (PI.f64) n) (patch (.f64 (PI.f64) n) #<representation binary64>) () ())
#s(alt #s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (.f64 (sqrt.f64 (/.f64 (.f64 n (PI.f64)) k)) (sqrt.f64 #s(literal 2 binary64)))) (patch #s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (.f64 (sqrt.f64 (/.f64 (.f64 n (PI.f64)) k)) (sqrt.f64 #s(literal 2 binary64)))) #<representation binary64>) () ())
#s(alt (.f64 (sqrt.f64 (/.f64 (.f64 n (PI.f64)) k)) (sqrt.f64 #s(literal 2 binary64))) (patch (.f64 (sqrt.f64 (/.f64 (.f64 n (PI.f64)) k)) (sqrt.f64 #s(literal 2 binary64))) #<representation binary64>) () ())
#s(alt (sqrt.f64 (/.f64 (.f64 n (PI.f64)) k)) (patch (sqrt.f64 (/.f64 (.f64 n (PI.f64)) k)) #<representation binary64>) () ())
#s(alt (/.f64 (.f64 n (PI.f64)) k) (patch (/.f64 (.f64 n (PI.f64)) k) #<representation binary64>) () ())
#s(alt (.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) (pow.f64 (.f64 (.f64 #s(literal 2 binary64) (PI.f64)) n) #s(approx (/ (- 1 k) 2) #s(literal 1/2 binary64)))) (patch (.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) (pow.f64 (.f64 (.f64 #s(literal 2 binary64) (PI.f64)) n) #s(approx (/ (- 1 k) 2) #s(literal 1/2 binary64)))) #<representation binary64>) () ())
#s(alt (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) (patch (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) #<representation binary64>) () ())
#s(alt (sqrt.f64 k) (patch (sqrt.f64 k) #<representation binary64>) () ())
#s(alt (pow.f64 (.f64 (.f64 #s(literal 2 binary64) (PI.f64)) n) #s(approx (/ (- 1 k) 2) #s(literal 1/2 binary64))) (patch (pow.f64 (.f64 (.f64 #s(literal 2 binary64) (PI.f64)) n) #s(approx (/ (- 1 k) 2) #s(literal 1/2 binary64))) #<representation binary64>) () ())
#s(alt (.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) (pow.f64 (.f64 (.f64 #s(literal 2 binary64) (PI.f64)) n) #s(approx (/ (- 1 k) 2) (.f64 #s(literal -1/2 binary64) k)))) (patch (.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) (pow.f64 (.f64 (.f64 #s(literal 2 binary64) (PI.f64)) n) #s(approx (/ (- 1 k) 2) (.f64 #s(literal -1/2 binary64) k)))) #<representation binary64>) () ())
#s(alt (pow.f64 (.f64 (.f64 #s(literal 2 binary64) (PI.f64)) n) #s(approx (/ (- 1 k) 2) (.f64 #s(literal -1/2 binary64) k))) (patch (pow.f64 (.f64 (.f64 #s(literal 2 binary64) (PI.f64)) n) #s(approx (/ (- 1 k) 2) (.f64 #s(literal -1/2 binary64) k))) #<representation binary64>) () ())
#s(alt (-.f64 #s(literal -1/2 binary64) (.f64 k #s(literal -1/2 binary64))) (patch (-.f64 #s(literal -1/2 binary64) (.f64 k #s(literal -1/2 binary64))) #<representation binary64>) () ())
#s(alt (/.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 -1/2 binary64)))))) (patch (/.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 -1/2 binary64)))))) #<representation binary64>) () ())
#s(alt (.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 -1/2 binary64))))) (patch (.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 -1/2 binary64))))) #<representation binary64>) () ())
#s(alt (PI.f64) (patch (PI.f64) #<representation binary64>) () ())
#s(alt #s(approx (/ (- 1 k) 2) #s(literal 1/2 binary64)) (patch #s(approx (/ (- 1 k) 2) #s(literal 1/2 binary64)) #<representation binary64>) () ())
#s(alt (.f64 (.f64 #s(literal 2 binary64) (PI.f64)) n) (patch (.f64 (.f64 #s(literal 2 binary64) (PI.f64)) n) #<representation binary64>) () ())
#s(alt #s(approx (/ (- 1 k) 2) (.f64 #s(literal -1/2 binary64) k)) (patch #s(approx (/ (- 1 k) 2) (.f64 #s(literal -1/2 binary64) k)) #<representation binary64>) () ())
#s(alt (pow.f64 (.f64 #s(literal 2 binary64) (.f64 (PI.f64) n)) (-.f64 #s(literal -1/2 binary64) (.f64 k #s(literal -1/2 binary64)))) (patch (pow.f64 (.f64 #s(literal 2 binary64) (.f64 (PI.f64) n)) (-.f64 #s(literal -1/2 binary64) (.f64 k #s(literal -1/2 binary64)))) #<representation binary64>) () ())

Outputs
#s(alt (* (sqrt (/ (* n (PI)) k)) (/ (sqrt 2) (exp (* 1/2 (* k (+ (log n) (log (* 2 (PI))))))))) (taylor 0 n) (#s(alt (/.f64 (sqrt.f64 (.f64 #s(literal 2 binary64) (.f64 (PI.f64) n))) (.f64 (sqrt.f64 k) (pow.f64 (.f64 #s(literal 2 binary64) (.f64 (PI.f64) n)) (.f64 k #s(literal 1/2 binary64))))) (patch (/.f64 (sqrt.f64 (.f64 #s(literal 2 binary64) (.f64 (PI.f64) n))) (.f64 (sqrt.f64 k) (pow.f64 (.f64 #s(literal 2 binary64) (.f64 (PI.f64) n)) (.f64 k #s(literal 1/2 binary64))))) #<representation binary64>) () ())) ())
#s(alt (* (sqrt (/ (* n (PI)) k)) (/ (sqrt 2) (exp (* 1/2 (* k (+ (log n) (log (* 2 (PI))))))))) (taylor 0 n) (#s(alt (/.f64 (sqrt.f64 (.f64 #s(literal 2 binary64) (.f64 (PI.f64) n))) (.f64 (sqrt.f64 k) (pow.f64 (.f64 #s(literal 2 binary64) (.f64 (PI.f64) n)) (.f64 k #s(literal 1/2 binary64))))) (patch (/.f64 (sqrt.f64 (.f64 #s(literal 2 binary64) (.f64 (PI.f64) n))) (.f64 (sqrt.f64 k) (pow.f64 (.f64 #s(literal 2 binary64) (.f64 (PI.f64) n)) (.f64 k #s(literal 1/2 binary64))))) #<representation binary64>) () ())) ())
#s(alt (* (sqrt (/ (* n (PI)) k)) (/ (sqrt 2) (exp (* 1/2 (* k (+ (log n) (log (* 2 (PI))))))))) (taylor 0 n) (#s(alt (/.f64 (sqrt.f64 (.f64 #s(literal 2 binary64) (.f64 (PI.f64) n))) (.f64 (sqrt.f64 k) (pow.f64 (.f64 #s(literal 2 binary64) (.f64 (PI.f64) n)) (.f64 k #s(literal 1/2 binary64))))) (patch (/.f64 (sqrt.f64 (.f64 #s(literal 2 binary64) (.f64 (PI.f64) n))) (.f64 (sqrt.f64 k) (pow.f64 (.f64 #s(literal 2 binary64) (.f64 (PI.f64) n)) (.f64 k #s(literal 1/2 binary64))))) #<representation binary64>) () ())) ())
#s(alt (* (sqrt (/ (* n (PI)) k)) (/ (sqrt 2) (exp (* 1/2 (* k (+ (log n) (log (* 2 (PI))))))))) (taylor 0 n) (#s(alt (/.f64 (sqrt.f64 (.f64 #s(literal 2 binary64) (.f64 (PI.f64) n))) (.f64 (sqrt.f64 k) (pow.f64 (.f64 #s(literal 2 binary64) (.f64 (PI.f64) n)) (.f64 k #s(literal 1/2 binary64))))) (patch (/.f64 (sqrt.f64 (.f64 #s(literal 2 binary64) (.f64 (PI.f64) n))) (.f64 (sqrt.f64 k) (pow.f64 (.f64 #s(literal 2 binary64) (.f64 (PI.f64) n)) (.f64 k #s(literal 1/2 binary64))))) #<representation binary64>) () ())) ())
#s(alt (* (sqrt (/ (* n (PI)) k)) (/ (sqrt 2) (exp (* 1/2 (* k (+ (log (* 2 (PI))) (* -1 (log (/ 1 n))))))))) (taylor inf n) (#s(alt (/.f64 (sqrt.f64 (.f64 #s(literal 2 binary64) (.f64 (PI.f64) n))) (.f64 (sqrt.f64 k) (pow.f64 (.f64 #s(literal 2 binary64) (.f64 (PI.f64) n)) (.f64 k #s(literal 1/2 binary64))))) (patch (/.f64 (sqrt.f64 (.f64 #s(literal 2 binary64) (.f64 (PI.f64) n))) (.f64 (sqrt.f64 k) (pow.f64 (.f64 #s(literal 2 binary64) (.f64 (PI.f64) n)) (.f64 k #s(literal 1/2 binary64))))) #<representation binary64>) () ())) ())
#s(alt (* (sqrt (/ (* n (PI)) k)) (/ (sqrt 2) (exp (* 1/2 (* k (+ (log (* 2 (PI))) (* -1 (log (/ 1 n))))))))) (taylor inf n) (#s(alt (/.f64 (sqrt.f64 (.f64 #s(literal 2 binary64) (.f64 (PI.f64) n))) (.f64 (sqrt.f64 k) (pow.f64 (.f64 #s(literal 2 binary64) (.f64 (PI.f64) n)) (.f64 k #s(literal 1/2 binary64))))) (patch (/.f64 (sqrt.f64 (.f64 #s(literal 2 binary64) (.f64 (PI.f64) n))) (.f64 (sqrt.f64 k) (pow.f64 (.f64 #s(literal 2 binary64) (.f64 (PI.f64) n)) (.f64 k #s(literal 1/2 binary64))))) #<representation binary64>) () ())) ())
#s(alt (* (sqrt (/ (* n (PI)) k)) (/ (sqrt 2) (exp (* 1/2 (* k (+ (log (* 2 (PI))) (* -1 (log (/ 1 n))))))))) (taylor inf n) (#s(alt (/.f64 (sqrt.f64 (.f64 #s(literal 2 binary64) (.f64 (PI.f64) n))) (.f64 (sqrt.f64 k) (pow.f64 (.f64 #s(literal 2 binary64) (.f64 (PI.f64) n)) (.f64 k #s(literal 1/2 binary64))))) (patch (/.f64 (sqrt.f64 (.f64 #s(literal 2 binary64) (.f64 (PI.f64) n))) (.f64 (sqrt.f64 k) (pow.f64 (.f64 #s(literal 2 binary64) (.f64 (PI.f64) n)) (.f64 k #s(literal 1/2 binary64))))) #<representation binary64>) () ())) ())
#s(alt (* (sqrt (/ (* n (PI)) k)) (/ (sqrt 2) (exp (* 1/2 (* k (+ (log (* 2 (PI))) (* -1 (log (/ 1 n))))))))) (taylor inf n) (#s(alt (/.f64 (sqrt.f64 (.f64 #s(literal 2 binary64) (.f64 (PI.f64) n))) (.f64 (sqrt.f64 k) (pow.f64 (.f64 #s(literal 2 binary64) (.f64 (PI.f64) n)) (.f64 k #s(literal 1/2 binary64))))) (patch (/.f64 (sqrt.f64 (.f64 #s(literal 2 binary64) (.f64 (PI.f64) n))) (.f64 (sqrt.f64 k) (pow.f64 (.f64 #s(literal 2 binary64) (.f64 (PI.f64) n)) (.f64 k #s(literal 1/2 binary64))))) #<representation binary64>) () ())) ())
#s(alt (* -1 (* (sqrt (/ (* n (PI)) k)) (/ (* (sqrt -2) (sqrt -1)) (exp (* 1/2 (* k (+ (log (* -2 (PI))) (* -1 (log (/ -1 n)))))))))) (taylor -inf n) (#s(alt (/.f64 (sqrt.f64 (.f64 #s(literal 2 binary64) (.f64 (PI.f64) n))) (.f64 (sqrt.f64 k) (pow.f64 (.f64 #s(literal 2 binary64) (.f64 (PI.f64) n)) (.f64 k #s(literal 1/2 binary64))))) (patch (/.f64 (sqrt.f64 (.f64 #s(literal 2 binary64) (.f64 (PI.f64) n))) (.f64 (sqrt.f64 k) (pow.f64 (.f64 #s(literal 2 binary64) (.f64 (PI.f64) n)) (.f64 k #s(literal 1/2 binary64))))) #<representation binary64>) () ())) ())
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#s(alt (exp (* -1 (* (+ 1/2 (* -1/2 k)) (+ (log (* -2 (PI))) (* -1 (log (/ -1 n))))))) (taylor -inf n) (#s(alt (pow.f64 (.f64 #s(literal 2 binary64) (.f64 (PI.f64) n)) (-.f64 #s(literal -1/2 binary64) (.f64 k #s(literal -1/2 binary64)))) (patch (pow.f64 (.f64 #s(literal 2 binary64) (.f64 (PI.f64) n)) (-.f64 #s(literal -1/2 binary64) (.f64 k #s(literal -1/2 binary64)))) #<representation binary64>) () ())) ())
#s(alt (exp (* -1 (* (+ 1/2 (* -1/2 k)) (+ (log (* -2 (PI))) (* -1 (log (/ -1 n))))))) (taylor -inf n) (#s(alt (pow.f64 (.f64 #s(literal 2 binary64) (.f64 (PI.f64) n)) (-.f64 #s(literal -1/2 binary64) (.f64 k #s(literal -1/2 binary64)))) (patch (pow.f64 (.f64 #s(literal 2 binary64) (.f64 (PI.f64) n)) (-.f64 #s(literal -1/2 binary64) (.f64 k #s(literal -1/2 binary64)))) #<representation binary64>) () ())) ())
#s(alt (exp (* -1 (* (+ 1/2 (* -1/2 k)) (+ (log (* -2 (PI))) (* -1 (log (/ -1 n))))))) (taylor -inf n) (#s(alt (pow.f64 (.f64 #s(literal 2 binary64) (.f64 (PI.f64) n)) (-.f64 #s(literal -1/2 binary64) (.f64 k #s(literal -1/2 binary64)))) (patch (pow.f64 (.f64 #s(literal 2 binary64) (.f64 (PI.f64) n)) (-.f64 #s(literal -1/2 binary64) (.f64 k #s(literal -1/2 binary64)))) #<representation binary64>) () ())) ())
#s(alt (exp (* -1 (* (+ 1/2 (* -1/2 k)) (+ (log (* -2 (PI))) (* -1 (log (/ -1 n))))))) (taylor -inf n) (#s(alt (pow.f64 (.f64 #s(literal 2 binary64) (.f64 (PI.f64) n)) (-.f64 #s(literal -1/2 binary64) (.f64 k #s(literal -1/2 binary64)))) (patch (pow.f64 (.f64 #s(literal 2 binary64) (.f64 (PI.f64) n)) (-.f64 #s(literal -1/2 binary64) (.f64 k #s(literal -1/2 binary64)))) #<representation binary64>) () ())) ())
#s(alt (* (sqrt (/ 1 (* n (PI)))) (sqrt 1/2)) (taylor 0 k) (#s(alt (pow.f64 (.f64 #s(literal 2 binary64) (.f64 (PI.f64) n)) (-.f64 #s(literal -1/2 binary64) (.f64 k #s(literal -1/2 binary64)))) (patch (pow.f64 (.f64 #s(literal 2 binary64) (.f64 (PI.f64) n)) (-.f64 #s(literal -1/2 binary64) (.f64 k #s(literal -1/2 binary64)))) #<representation binary64>) () ())) ())
#s(alt (+ (* 1/2 (* (* k (* (log (* 2 (* n (PI)))) (sqrt 1/2))) (sqrt (/ 1 (* n (PI)))))) (* (sqrt (/ 1 (* n (PI)))) (sqrt 1/2))) (taylor 0 k) (#s(alt (pow.f64 (.f64 #s(literal 2 binary64) (.f64 (PI.f64) n)) (-.f64 #s(literal -1/2 binary64) (.f64 k #s(literal -1/2 binary64)))) (patch (pow.f64 (.f64 #s(literal 2 binary64) (.f64 (PI.f64) n)) (-.f64 #s(literal -1/2 binary64) (.f64 k #s(literal -1/2 binary64)))) #<representation binary64>) () ())) ())
#s(alt (+ (* k (+ (* 1/8 (* (* k (* (pow (log (* 2 (* n (PI)))) 2) (sqrt 1/2))) (sqrt (/ 1 (* n (PI)))))) (* 1/2 (* (sqrt (/ 1 (* n (PI)))) (* (log (* 2 (* n (PI)))) (sqrt 1/2)))))) (* (sqrt (/ 1 (* n (PI)))) (sqrt 1/2))) (taylor 0 k) (#s(alt (pow.f64 (.f64 #s(literal 2 binary64) (.f64 (PI.f64) n)) (-.f64 #s(literal -1/2 binary64) (.f64 k #s(literal -1/2 binary64)))) (patch (pow.f64 (.f64 #s(literal 2 binary64) (.f64 (PI.f64) n)) (-.f64 #s(literal -1/2 binary64) (.f64 k #s(literal -1/2 binary64)))) #<representation binary64>) () ())) ())
#s(alt (+ (* k (+ (* 1/2 (* (sqrt (/ 1 (* n (PI)))) (* (log (* 2 (* n (PI)))) (sqrt 1/2)))) (* k (+ (* 1/48 (* (* k (* (pow (log (* 2 (* n (PI)))) 3) (sqrt 1/2))) (sqrt (/ 1 (* n (PI)))))) (* 1/8 (* (sqrt (/ 1 (* n (PI)))) (* (pow (log (* 2 (* n (PI)))) 2) (sqrt 1/2)))))))) (* (sqrt (/ 1 (* n (PI)))) (sqrt 1/2))) (taylor 0 k) (#s(alt (pow.f64 (.f64 #s(literal 2 binary64) (.f64 (PI.f64) n)) (-.f64 #s(literal -1/2 binary64) (.f64 k #s(literal -1/2 binary64)))) (patch (pow.f64 (.f64 #s(literal 2 binary64) (.f64 (PI.f64) n)) (-.f64 #s(literal -1/2 binary64) (.f64 k #s(literal -1/2 binary64)))) #<representation binary64>) () ())) ())
#s(alt (exp (* (log (* 2 (* n (PI)))) (- (* 1/2 k) 1/2))) (taylor inf k) (#s(alt (pow.f64 (.f64 #s(literal 2 binary64) (.f64 (PI.f64) n)) (-.f64 #s(literal -1/2 binary64) (.f64 k #s(literal -1/2 binary64)))) (patch (pow.f64 (.f64 #s(literal 2 binary64) (.f64 (PI.f64) n)) (-.f64 #s(literal -1/2 binary64) (.f64 k #s(literal -1/2 binary64)))) #<representation binary64>) () ())) ())
#s(alt (exp (* (log (* 2 (* n (PI)))) (- (* 1/2 k) 1/2))) (taylor inf k) (#s(alt (pow.f64 (.f64 #s(literal 2 binary64) (.f64 (PI.f64) n)) (-.f64 #s(literal -1/2 binary64) (.f64 k #s(literal -1/2 binary64)))) (patch (pow.f64 (.f64 #s(literal 2 binary64) (.f64 (PI.f64) n)) (-.f64 #s(literal -1/2 binary64) (.f64 k #s(literal -1/2 binary64)))) #<representation binary64>) () ())) ())
#s(alt (exp (* (log (* 2 (* n (PI)))) (- (* 1/2 k) 1/2))) (taylor inf k) (#s(alt (pow.f64 (.f64 #s(literal 2 binary64) (.f64 (PI.f64) n)) (-.f64 #s(literal -1/2 binary64) (.f64 k #s(literal -1/2 binary64)))) (patch (pow.f64 (.f64 #s(literal 2 binary64) (.f64 (PI.f64) n)) (-.f64 #s(literal -1/2 binary64) (.f64 k #s(literal -1/2 binary64)))) #<representation binary64>) () ())) ())
#s(alt (exp (* (log (* 2 (* n (PI)))) (- (* 1/2 k) 1/2))) (taylor inf k) (#s(alt (pow.f64 (.f64 #s(literal 2 binary64) (.f64 (PI.f64) n)) (-.f64 #s(literal -1/2 binary64) (.f64 k #s(literal -1/2 binary64)))) (patch (pow.f64 (.f64 #s(literal 2 binary64) (.f64 (PI.f64) n)) (-.f64 #s(literal -1/2 binary64) (.f64 k #s(literal -1/2 binary64)))) #<representation binary64>) () ())) ())
#s(alt (exp (* -1 (* (log (* 2 (* n (PI)))) (+ 1/2 (* -1/2 k))))) (taylor -inf k) (#s(alt (pow.f64 (.f64 #s(literal 2 binary64) (.f64 (PI.f64) n)) (-.f64 #s(literal -1/2 binary64) (.f64 k #s(literal -1/2 binary64)))) (patch (pow.f64 (.f64 #s(literal 2 binary64) (.f64 (PI.f64) n)) (-.f64 #s(literal -1/2 binary64) (.f64 k #s(literal -1/2 binary64)))) #<representation binary64>) () ())) ())
#s(alt (exp (* -1 (* (log (* 2 (* n (PI)))) (+ 1/2 (* -1/2 k))))) (taylor -inf k) (#s(alt (pow.f64 (.f64 #s(literal 2 binary64) (.f64 (PI.f64) n)) (-.f64 #s(literal -1/2 binary64) (.f64 k #s(literal -1/2 binary64)))) (patch (pow.f64 (.f64 #s(literal 2 binary64) (.f64 (PI.f64) n)) (-.f64 #s(literal -1/2 binary64) (.f64 k #s(literal -1/2 binary64)))) #<representation binary64>) () ())) ())
#s(alt (exp (* -1 (* (log (* 2 (* n (PI)))) (+ 1/2 (* -1/2 k))))) (taylor -inf k) (#s(alt (pow.f64 (.f64 #s(literal 2 binary64) (.f64 (PI.f64) n)) (-.f64 #s(literal -1/2 binary64) (.f64 k #s(literal -1/2 binary64)))) (patch (pow.f64 (.f64 #s(literal 2 binary64) (.f64 (PI.f64) n)) (-.f64 #s(literal -1/2 binary64) (.f64 k #s(literal -1/2 binary64)))) #<representation binary64>) () ())) ())
#s(alt (exp (* -1 (* (log (* 2 (* n (PI)))) (+ 1/2 (* -1/2 k))))) (taylor -inf k) (#s(alt (pow.f64 (.f64 #s(literal 2 binary64) (.f64 (PI.f64) n)) (-.f64 #s(literal -1/2 binary64) (.f64 k #s(literal -1/2 binary64)))) (patch (pow.f64 (.f64 #s(literal 2 binary64) (.f64 (PI.f64) n)) (-.f64 #s(literal -1/2 binary64) (.f64 k #s(literal -1/2 binary64)))) #<representation binary64>) () ())) ())

Calls

99 calls:

Time	Variable		Point	Expression
768.0ms	k	@	-inf	(/ 1 (* (sqrt k) (pow (* 2 (* (PI) n)) (- -1/2 (* k -1/2)))))
2.0ms	n	@	0	(/ (sqrt (* 2 (* (PI) n))) (* (sqrt k) (pow (* 2 (* (PI) n)) (* k 1/2))))
2.0ms	k	@	inf	(/ (sqrt (* 2 (* (PI) n))) (* (sqrt k) (pow (* 2 (* (PI) n)) (* k 1/2))))
2.0ms	n	@	inf	(/ (sqrt (* 2 (* (PI) n))) (* (sqrt k) (pow (* 2 (* (PI) n)) (* k 1/2))))
2.0ms	k	@	0	(/ 1 (* (sqrt k) (pow (* 2 (* (PI) n)) (- -1/2 (* k -1/2)))))

simplify333.0ms (2.9%)

Memory

0.8MiB live, 365.7MiB allocated

Algorithm

1×	egg-herbie

Rules

12 334×	`lower-fma.f64`
12 334×	`lower-fma.f32`
6 902×	`lower-*.f64`
6 902×	`lower-*.f32`
4 090×	`lower-+.f64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	313	5827
1	998	5674
2	3589	5328
0	8150	5221

Stop Event

1×	iter limit
1×	node limit

Counts

396 → 396

Calls

Call 1

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

rewrite282.0ms (2.4%)

Memory

-25.8MiB live, 402.8MiB allocated

Rules

5 258×	`lower-*.f32`
5 232×	`lower-*.f64`
3 676×	`lower-/.f32`
3 668×	`lower-/.f64`
2 376×	`lower-pow.f32`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	45	219
0	72	220
1	253	203
2	1384	199
0	8196	197

Stop Event

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

Counts

22 → 1 175

Calls

Call 1

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

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

eval363.0ms (3.1%)

Memory: 37.2MiB live, 617.8MiB allocated
Compiler: Compiled 42 347 to 4 171 computations (90.2% saved)

prune303.0ms (2.6%)

Memory

13.4MiB live, 569.5MiB allocated

Pruning

31 alts after pruning (30 fresh and 1 done)

	Pruned	Kept	Total
New	1 992	29	2 021
Fresh	6	1	7
Picked	4	1	5
Done	0	0	0
Total	2 002	31	2 033

Accuracy

100.0%

Counts

2 033 → 31

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 1/2 binary64)))) (sqrt.f64 k))
	49.2%	(/.f64 (pow.f64 (.f64 #s(literal 2 binary64) (.f64 (PI.f64) n)) #s(approx (/ (- 1 k) 2) (*.f64 k #s(literal -1/2 binary64)))) (sqrt.f64 k))
	99.4%	(/.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 1/2 binary64))))))
	99.4%	(/.f64 #s(literal 1 binary64) (.f64 (pow.f64 (.f64 #s(literal 2 binary64) (*.f64 (PI.f64) n)) (fma.f64 k #s(literal 1/2 binary64) #s(literal -1/2 binary64))) (sqrt.f64 k)))
▶	53.9%	(/.f64 #s(literal 1 binary64) (.f64 (sqrt.f64 k) (pow.f64 (.f64 #s(literal 2 binary64) (.f64 (PI.f64) n)) #s(approx (- -1/2 ( k -1/2)) #s(literal -1/2 binary64)))))
	53.7%	(/.f64 #s(literal 1 binary64) (.f64 (sqrt.f64 k) #s(approx (pow ( 2 (* (PI) n)) (- -1/2 (* k -1/2))) (.f64 (sqrt.f64 #s(literal 1/2 binary64)) (sqrt.f64 (/.f64 #s(literal 1 binary64) (.f64 n (PI.f64))))))))
▶	42.6%	(/.f64 #s(literal 1 binary64) #s(approx (* (sqrt k) (pow (* 2 (* (PI) n)) (- -1/2 (* k -1/2)))) (.f64 (sqrt.f64 #s(literal 1/2 binary64)) (sqrt.f64 (/.f64 k (.f64 n (PI.f64)))))))
	76.8%	(.f64 (pow.f64 (.f64 #s(literal 2 binary64) (.f64 (PI.f64) n)) (.f64 k #s(literal -1/2 binary64))) (sqrt.f64 (/.f64 (.f64 #s(literal 2 binary64) (.f64 (PI.f64) n)) k)))
	53.7%	(.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) #s(approx (pow ( (* 2 (PI)) n) (/ (- 1 k) 2)) (.f64 (sqrt.f64 #s(literal 2 binary64)) (sqrt.f64 (.f64 n (PI.f64))))))
	76.6%	(.f64 (.f64 (sqrt.f64 #s(literal 2 binary64)) (pow.f64 (.f64 #s(literal 2 binary64) (.f64 (PI.f64) n)) (.f64 k #s(literal -1/2 binary64)))) (sqrt.f64 (/.f64 (.f64 (PI.f64) n) k)))
	76.8%	(sqrt.f64 (/.f64 (/.f64 (.f64 #s(literal 2 binary64) (.f64 (PI.f64) n)) k) (pow.f64 (.f64 #s(literal 2 binary64) (.f64 (PI.f64) n)) k)))
	41.3%	#s(approx (/ 1 (* (sqrt k) (pow (* 2 (* (PI) n)) (- -1/2 (* k -1/2))))) (/.f64 (sqrt.f64 (/.f64 (*.f64 n (PI.f64)) k)) (sqrt.f64 #s(literal 1/2 binary64))))
	99.5%	#s(approx (/ 1 (* (sqrt k) (pow (* 2 (* (PI) n)) (- -1/2 (* k -1/2))))) (.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) k)) (pow.f64 (.f64 (PI.f64) (*.f64 n #s(literal 2 binary64))) (fma.f64 k #s(literal -1/2 binary64) #s(literal 1/2 binary64)))))
	53.9%	#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (/.f64 (sqrt.f64 (.f64 #s(literal 2 binary64) (.f64 (PI.f64) n))) (sqrt.f64 k)))
	42.7%	#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (/.f64 (sqrt.f64 #s(literal 2 binary64)) (sqrt.f64 (/.f64 k (*.f64 (PI.f64) n)))))
	42.6%	#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (/.f64 #s(literal 1 binary64) (sqrt.f64 (/.f64 k (.f64 #s(literal 2 binary64) (.f64 (PI.f64) n))))))
	53.8%	#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (.f64 (/.f64 (sqrt.f64 (.f64 (PI.f64) n)) (sqrt.f64 k)) (sqrt.f64 #s(literal 2 binary64))))
	53.7%	#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (.f64 (/.f64 (sqrt.f64 (.f64 #s(literal 2 binary64) (PI.f64))) (sqrt.f64 k)) (/.f64 (sqrt.f64 n) #s(literal 1 binary64))))
	53.7%	#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (.f64 (/.f64 (sqrt.f64 n) (sqrt.f64 k)) (/.f64 (sqrt.f64 (.f64 #s(literal 2 binary64) (PI.f64))) #s(literal 1 binary64))))
	53.8%	#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (.f64 (.f64 (sqrt.f64 (/.f64 (PI.f64) k)) (sqrt.f64 n)) (sqrt.f64 #s(literal 2 binary64))))
	53.8%	#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (.f64 (.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) k)) (sqrt.f64 (*.f64 (PI.f64) n))) (sqrt.f64 #s(literal 2 binary64))))
	41.4%	#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (.f64 (.f64 (sqrt.f64 (PI.f64)) (sqrt.f64 (/.f64 n k))) (sqrt.f64 #s(literal 2 binary64))))
	41.2%	#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (.f64 (sqrt.f64 (/.f64 (.f64 n (.f64 (sqrt.f64 (.f64 (PI.f64) (sqrt.f64 (PI.f64)))) (sqrt.f64 (sqrt.f64 (PI.f64))))) k)) (sqrt.f64 #s(literal 2 binary64))))
✓	41.4%	#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (.f64 (sqrt.f64 (/.f64 (.f64 n (PI.f64)) k)) (sqrt.f64 #s(literal 2 binary64))))
	41.4%	#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (.f64 (sqrt.f64 (.f64 (/.f64 (PI.f64) k) n)) (sqrt.f64 #s(literal 2 binary64))))
	41.4%	#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (.f64 (sqrt.f64 (.f64 (PI.f64) (/.f64 n k))) (sqrt.f64 #s(literal 2 binary64))))
▶	53.8%	#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (.f64 (sqrt.f64 (.f64 (PI.f64) n)) (sqrt.f64 (*.f64 (/.f64 #s(literal 1 binary64) k) #s(literal 2 binary64)))))
	53.9%	#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (.f64 (sqrt.f64 (.f64 #s(literal 2 binary64) (*.f64 (PI.f64) n))) (sqrt.f64 (/.f64 #s(literal 1 binary64) k))))
	53.9%	#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (.f64 (sqrt.f64 n) (sqrt.f64 (.f64 (/.f64 (PI.f64) k) #s(literal 2 binary64)))))
	53.9%	#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (.f64 (neg.f64 (sqrt.f64 (.f64 #s(literal 2 binary64) (*.f64 (PI.f64) n)))) (/.f64 #s(literal -1 binary64) (sqrt.f64 k))))
▶	41.5%	#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt.f64 (/.f64 (.f64 #s(literal 2 binary64) (.f64 (PI.f64) n)) k)))

Compiler

Compiled 906 to 679 computations (25.1% saved)

simplify97.0ms (0.8%)

Memory

-0.0MiB live, 71.1MiB allocated

Algorithm

1×	egg-herbie

Localize:

Found 20 expressions of interest:

New	Metric	Score
cost-diff	0	(pow.f64 (.f64 #s(literal 2 binary64) (.f64 (PI.f64) n)) #s(approx (- -1/2 (* k -1/2)) #s(literal -1/2 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)) #s(approx (- -1/2 ( k -1/2)) #s(literal -1/2 binary64))))
cost-diff	0	(/.f64 #s(literal 1 binary64) (.f64 (sqrt.f64 k) (pow.f64 (.f64 #s(literal 2 binary64) (.f64 (PI.f64) n)) #s(approx (- -1/2 ( k -1/2)) #s(literal -1/2 binary64)))))
cost-diff	0	(sqrt.f64 #s(literal 1/2 binary64))
cost-diff	0	(.f64 (sqrt.f64 #s(literal 1/2 binary64)) (sqrt.f64 (/.f64 k (.f64 n (PI.f64)))))
cost-diff	0	#s(approx (* (sqrt k) (pow (* 2 (* (PI) n)) (- -1/2 (* k -1/2)))) (.f64 (sqrt.f64 #s(literal 1/2 binary64)) (sqrt.f64 (/.f64 k (.f64 n (PI.f64))))))
cost-diff	0	(/.f64 #s(literal 1 binary64) #s(approx (* (sqrt k) (pow (* 2 (* (PI) n)) (- -1/2 (* k -1/2)))) (.f64 (sqrt.f64 #s(literal 1/2 binary64)) (sqrt.f64 (/.f64 k (.f64 n (PI.f64)))))))
cost-diff	0	(sqrt.f64 (*.f64 (PI.f64) n))
cost-diff	0	(.f64 (sqrt.f64 (.f64 (PI.f64) n)) (sqrt.f64 (*.f64 (/.f64 #s(literal 1 binary64) k) #s(literal 2 binary64))))
cost-diff	0	#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (.f64 (sqrt.f64 (.f64 (PI.f64) n)) (sqrt.f64 (*.f64 (/.f64 #s(literal 1 binary64) k) #s(literal 2 binary64)))))
cost-diff	320	(*.f64 (/.f64 #s(literal 1 binary64) k) #s(literal 2 binary64))
cost-diff	0	(.f64 #s(literal 2 binary64) (.f64 (PI.f64) n))
cost-diff	0	(/.f64 (.f64 #s(literal 2 binary64) (.f64 (PI.f64) n)) k)
cost-diff	0	(sqrt.f64 (/.f64 (.f64 #s(literal 2 binary64) (.f64 (PI.f64) n)) k))
cost-diff	0	#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt.f64 (/.f64 (.f64 #s(literal 2 binary64) (.f64 (PI.f64) n)) 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 #s(literal 1/2 binary64) (*.f64 k #s(literal 1/2 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 1/2 binary64)))) (sqrt.f64 k))
cost-diff	128	(-.f64 #s(literal 1/2 binary64) (*.f64 k #s(literal 1/2 binary64)))

Rules

960×	`lower-fma.f64`
960×	`lower-fma.f32`
956×	`lower-*.f32`
940×	`lower-*.f64`
770×	`times-frac`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	49	315
0	75	307
1	113	303
2	158	303
3	241	303
4	318	303
5	568	303
6	1324	303
7	2330	303
8	2598	303
9	2838	303
10	2982	303
11	3040	303
12	3040	303
13	3044	303
14	3048	303
0	3048	292

Stop Event

1×	iter limit
1×	saturated
1×	iter limit

Calls

Call 1

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

localize161.0ms (1.4%)

Memory

-38.3MiB live, 268.8MiB allocated

Localize:

Found 20 expressions of interest:

New	Metric	Score
accuracy	0.19053065553371273	(pow.f64 (.f64 #s(literal 2 binary64) (.f64 (PI.f64) n)) #s(approx (- -1/2 (* k -1/2)) #s(literal -1/2 binary64)))
accuracy	0.22265625	(*.f64 (PI.f64) n)
accuracy	14.046533023192913	(PI.f64)
accuracy	15.202179506440986	#s(approx (- -1/2 (* k -1/2)) #s(literal -1/2 binary64))
accuracy	0.3287887695368841	(.f64 (sqrt.f64 #s(literal 1/2 binary64)) (sqrt.f64 (/.f64 k (.f64 n (PI.f64)))))
accuracy	7.2769331177730585	(sqrt.f64 (/.f64 k (*.f64 n (PI.f64))))
accuracy	14.046533023192913	(PI.f64)
accuracy	15.114254451666671	#s(approx (* (sqrt k) (pow (* 2 (* (PI) n)) (- -1/2 (* k -1/2)))) (.f64 (sqrt.f64 #s(literal 1/2 binary64)) (sqrt.f64 (/.f64 k (.f64 n (PI.f64))))))
accuracy	0.22265625	(*.f64 (PI.f64) n)
accuracy	0.28353500976844204	(.f64 (sqrt.f64 (.f64 (PI.f64) n)) (sqrt.f64 (*.f64 (/.f64 #s(literal 1 binary64) k) #s(literal 2 binary64))))
accuracy	14.046533023192913	(PI.f64)
accuracy	15.11847131460795	#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (.f64 (sqrt.f64 (.f64 (PI.f64) n)) (sqrt.f64 (*.f64 (/.f64 #s(literal 1 binary64) k) #s(literal 2 binary64)))))
accuracy	0.22265625	(*.f64 (PI.f64) n)
accuracy	8.107365991328408	(sqrt.f64 (/.f64 (.f64 #s(literal 2 binary64) (.f64 (PI.f64) n)) k))
accuracy	14.046533023192913	(PI.f64)
accuracy	15.11847131460795	#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt.f64 (/.f64 (.f64 #s(literal 2 binary64) (.f64 (PI.f64) n)) k)))
accuracy	0.171875	(/.f64 (pow.f64 (.f64 #s(literal 2 binary64) (.f64 (PI.f64) n)) (-.f64 #s(literal 1/2 binary64) (*.f64 k #s(literal 1/2 binary64)))) (sqrt.f64 k))
accuracy	0.22265625	(*.f64 (PI.f64) n)
accuracy	0.2240471803363731	(pow.f64 (.f64 #s(literal 2 binary64) (.f64 (PI.f64) n)) (-.f64 #s(literal 1/2 binary64) (*.f64 k #s(literal 1/2 binary64))))
accuracy	14.046533023192913	(PI.f64)

Samples

65.0ms	198×	0	valid
20.0ms	58×	0	exit

Compiler

Compiled 268 to 40 computations (85.1% saved)

Precisions

Click to see histograms. Total time spent on operations: 62.0ms

ival-mult: 17.0ms (27.5% of total)

ival-pow: 16.0ms (25.9% of total)

ival-div: 13.0ms (21% of total)

ival-sqrt: 10.0ms (16.2% of total)

ival-sub: 4.0ms (6.5% of total)

ival-pi: 1.0ms (1.6% of total)

exact: 1.0ms (1.6% of total)

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

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

series86.0ms (0.7%)

Memory

16.3MiB live, 89.8MiB allocated

Counts

23 → 420

Calls

Call 1

Inputs
#s(alt (-.f64 #s(literal 1/2 binary64) (.f64 k #s(literal 1/2 binary64))) (patch (-.f64 #s(literal 1/2 binary64) (.f64 k #s(literal 1/2 binary64))) #<representation binary64>) () ())
#s(alt (/.f64 (pow.f64 (.f64 #s(literal 2 binary64) (.f64 (PI.f64) n)) (-.f64 #s(literal 1/2 binary64) (.f64 k #s(literal 1/2 binary64)))) (sqrt.f64 k)) (patch (/.f64 (pow.f64 (.f64 #s(literal 2 binary64) (.f64 (PI.f64) n)) (-.f64 #s(literal 1/2 binary64) (.f64 k #s(literal 1/2 binary64)))) (sqrt.f64 k)) #<representation binary64>) () ())
#s(alt (pow.f64 (.f64 #s(literal 2 binary64) (.f64 (PI.f64) n)) (-.f64 #s(literal 1/2 binary64) (.f64 k #s(literal 1/2 binary64)))) (patch (pow.f64 (.f64 #s(literal 2 binary64) (.f64 (PI.f64) n)) (-.f64 #s(literal 1/2 binary64) (.f64 k #s(literal 1/2 binary64)))) #<representation binary64>) () ())
#s(alt (.f64 #s(literal 2 binary64) (.f64 (PI.f64) n)) (patch (.f64 #s(literal 2 binary64) (.f64 (PI.f64) n)) #<representation binary64>) () ())
#s(alt #s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt.f64 (/.f64 (.f64 #s(literal 2 binary64) (.f64 (PI.f64) n)) k))) (patch #s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt.f64 (/.f64 (.f64 #s(literal 2 binary64) (.f64 (PI.f64) n)) k))) #<representation binary64>) () ())
#s(alt (sqrt.f64 (/.f64 (.f64 #s(literal 2 binary64) (.f64 (PI.f64) n)) k)) (patch (sqrt.f64 (/.f64 (.f64 #s(literal 2 binary64) (.f64 (PI.f64) n)) k)) #<representation binary64>) () ())
#s(alt (/.f64 (.f64 #s(literal 2 binary64) (.f64 (PI.f64) n)) k) (patch (/.f64 (.f64 #s(literal 2 binary64) (.f64 (PI.f64) n)) k) #<representation binary64>) () ())
#s(alt (.f64 (/.f64 #s(literal 1 binary64) k) #s(literal 2 binary64)) (patch (.f64 (/.f64 #s(literal 1 binary64) k) #s(literal 2 binary64)) #<representation binary64>) () ())
#s(alt #s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (.f64 (sqrt.f64 (.f64 (PI.f64) n)) (sqrt.f64 (.f64 (/.f64 #s(literal 1 binary64) k) #s(literal 2 binary64))))) (patch #s(approx ( (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (.f64 (sqrt.f64 (.f64 (PI.f64) n)) (sqrt.f64 (*.f64 (/.f64 #s(literal 1 binary64) k) #s(literal 2 binary64))))) #<representation binary64>) () ())
#s(alt (.f64 (sqrt.f64 (.f64 (PI.f64) n)) (sqrt.f64 (.f64 (/.f64 #s(literal 1 binary64) k) #s(literal 2 binary64)))) (patch (.f64 (sqrt.f64 (.f64 (PI.f64) n)) (sqrt.f64 (.f64 (/.f64 #s(literal 1 binary64) k) #s(literal 2 binary64)))) #<representation binary64>) () ())
#s(alt (sqrt.f64 (.f64 (PI.f64) n)) (patch (sqrt.f64 (.f64 (PI.f64) n)) #<representation binary64>) () ())
#s(alt (/.f64 #s(literal 1 binary64) #s(approx (* (sqrt k) (pow (* 2 (* (PI) n)) (- -1/2 (* k -1/2)))) (.f64 (sqrt.f64 #s(literal 1/2 binary64)) (sqrt.f64 (/.f64 k (.f64 n (PI.f64))))))) (patch (/.f64 #s(literal 1 binary64) #s(approx (* (sqrt k) (pow (* 2 (* (PI) n)) (- -1/2 (* k -1/2)))) (.f64 (sqrt.f64 #s(literal 1/2 binary64)) (sqrt.f64 (/.f64 k (.f64 n (PI.f64))))))) #<representation binary64>) () ())
#s(alt #s(approx (* (sqrt k) (pow (* 2 (* (PI) n)) (- -1/2 (* k -1/2)))) (.f64 (sqrt.f64 #s(literal 1/2 binary64)) (sqrt.f64 (/.f64 k (.f64 n (PI.f64)))))) (patch #s(approx (* (sqrt k) (pow (* 2 (* (PI) n)) (- -1/2 (* k -1/2)))) (.f64 (sqrt.f64 #s(literal 1/2 binary64)) (sqrt.f64 (/.f64 k (.f64 n (PI.f64)))))) #<representation binary64>) () ())
#s(alt (.f64 (sqrt.f64 #s(literal 1/2 binary64)) (sqrt.f64 (/.f64 k (.f64 n (PI.f64))))) (patch (.f64 (sqrt.f64 #s(literal 1/2 binary64)) (sqrt.f64 (/.f64 k (.f64 n (PI.f64))))) #<representation binary64>) () ())
#s(alt (sqrt.f64 #s(literal 1/2 binary64)) (patch (sqrt.f64 #s(literal 1/2 binary64)) #<representation binary64>) () ())
#s(alt (/.f64 #s(literal 1 binary64) (.f64 (sqrt.f64 k) (pow.f64 (.f64 #s(literal 2 binary64) (.f64 (PI.f64) n)) #s(approx (- -1/2 ( k -1/2)) #s(literal -1/2 binary64))))) (patch (/.f64 #s(literal 1 binary64) (.f64 (sqrt.f64 k) (pow.f64 (.f64 #s(literal 2 binary64) (.f64 (PI.f64) n)) #s(approx (- -1/2 ( k -1/2)) #s(literal -1/2 binary64))))) #<representation binary64>) () ())
#s(alt (.f64 (sqrt.f64 k) (pow.f64 (.f64 #s(literal 2 binary64) (.f64 (PI.f64) n)) #s(approx (- -1/2 ( k -1/2)) #s(literal -1/2 binary64)))) (patch (.f64 (sqrt.f64 k) (pow.f64 (.f64 #s(literal 2 binary64) (.f64 (PI.f64) n)) #s(approx (- -1/2 ( k -1/2)) #s(literal -1/2 binary64)))) #<representation binary64>) () ())
#s(alt (sqrt.f64 k) (patch (sqrt.f64 k) #<representation binary64>) () ())
#s(alt (pow.f64 (.f64 #s(literal 2 binary64) (.f64 (PI.f64) n)) #s(approx (- -1/2 (* k -1/2)) #s(literal -1/2 binary64))) (patch (pow.f64 (.f64 #s(literal 2 binary64) (.f64 (PI.f64) n)) #s(approx (- -1/2 (* k -1/2)) #s(literal -1/2 binary64))) #<representation binary64>) () ())
#s(alt (PI.f64) (patch (PI.f64) #<representation binary64>) () ())
#s(alt (.f64 (PI.f64) n) (patch (.f64 (PI.f64) n) #<representation binary64>) () ())
#s(alt (sqrt.f64 (/.f64 k (.f64 n (PI.f64)))) (patch (sqrt.f64 (/.f64 k (.f64 n (PI.f64)))) #<representation binary64>) () ())
#s(alt #s(approx (- -1/2 (* k -1/2)) #s(literal -1/2 binary64)) (patch #s(approx (- -1/2 (* k -1/2)) #s(literal -1/2 binary64)) #<representation binary64>) () ())

Outputs
#s(alt 1/2 (taylor 0 k) (#s(alt (-.f64 #s(literal 1/2 binary64) (.f64 k #s(literal 1/2 binary64))) (patch (-.f64 #s(literal 1/2 binary64) (.f64 k #s(literal 1/2 binary64))) #<representation binary64>) () ())) ())
#s(alt (+ 1/2 (* -1/2 k)) (taylor 0 k) (#s(alt (-.f64 #s(literal 1/2 binary64) (.f64 k #s(literal 1/2 binary64))) (patch (-.f64 #s(literal 1/2 binary64) (.f64 k #s(literal 1/2 binary64))) #<representation binary64>) () ())) ())
#s(alt (+ 1/2 (* -1/2 k)) (taylor 0 k) (#s(alt (-.f64 #s(literal 1/2 binary64) (.f64 k #s(literal 1/2 binary64))) (patch (-.f64 #s(literal 1/2 binary64) (.f64 k #s(literal 1/2 binary64))) #<representation binary64>) () ())) ())
#s(alt (+ 1/2 (* -1/2 k)) (taylor 0 k) (#s(alt (-.f64 #s(literal 1/2 binary64) (.f64 k #s(literal 1/2 binary64))) (patch (-.f64 #s(literal 1/2 binary64) (.f64 k #s(literal 1/2 binary64))) #<representation binary64>) () ())) ())
#s(alt (* -1/2 k) (taylor inf k) (#s(alt (-.f64 #s(literal 1/2 binary64) (.f64 k #s(literal 1/2 binary64))) (patch (-.f64 #s(literal 1/2 binary64) (.f64 k #s(literal 1/2 binary64))) #<representation binary64>) () ())) ())
#s(alt (* k (- (* 1/2 (/ 1 k)) 1/2)) (taylor inf k) (#s(alt (-.f64 #s(literal 1/2 binary64) (.f64 k #s(literal 1/2 binary64))) (patch (-.f64 #s(literal 1/2 binary64) (.f64 k #s(literal 1/2 binary64))) #<representation binary64>) () ())) ())
#s(alt (* k (- (* 1/2 (/ 1 k)) 1/2)) (taylor inf k) (#s(alt (-.f64 #s(literal 1/2 binary64) (.f64 k #s(literal 1/2 binary64))) (patch (-.f64 #s(literal 1/2 binary64) (.f64 k #s(literal 1/2 binary64))) #<representation binary64>) () ())) ())
#s(alt (* k (- (* 1/2 (/ 1 k)) 1/2)) (taylor inf k) (#s(alt (-.f64 #s(literal 1/2 binary64) (.f64 k #s(literal 1/2 binary64))) (patch (-.f64 #s(literal 1/2 binary64) (.f64 k #s(literal 1/2 binary64))) #<representation binary64>) () ())) ())
#s(alt (* -1/2 k) (taylor -inf k) (#s(alt (-.f64 #s(literal 1/2 binary64) (.f64 k #s(literal 1/2 binary64))) (patch (-.f64 #s(literal 1/2 binary64) (.f64 k #s(literal 1/2 binary64))) #<representation binary64>) () ())) ())
#s(alt (* -1 (* k (- 1/2 (* 1/2 (/ 1 k))))) (taylor -inf k) (#s(alt (-.f64 #s(literal 1/2 binary64) (.f64 k #s(literal 1/2 binary64))) (patch (-.f64 #s(literal 1/2 binary64) (.f64 k #s(literal 1/2 binary64))) #<representation binary64>) () ())) ())
#s(alt (* -1 (* k (- 1/2 (* 1/2 (/ 1 k))))) (taylor -inf k) (#s(alt (-.f64 #s(literal 1/2 binary64) (.f64 k #s(literal 1/2 binary64))) (patch (-.f64 #s(literal 1/2 binary64) (.f64 k #s(literal 1/2 binary64))) #<representation binary64>) () ())) ())
#s(alt (* -1 (* k (- 1/2 (* 1/2 (/ 1 k))))) (taylor -inf k) (#s(alt (-.f64 #s(literal 1/2 binary64) (.f64 k #s(literal 1/2 binary64))) (patch (-.f64 #s(literal 1/2 binary64) (.f64 k #s(literal 1/2 binary64))) #<representation binary64>) () ())) ())
#s(alt (* (sqrt (/ 1 k)) (exp (* (+ (log n) (log (* 2 (PI)))) (- 1/2 (* 1/2 k))))) (taylor 0 n) (#s(alt (/.f64 (pow.f64 (.f64 #s(literal 2 binary64) (.f64 (PI.f64) n)) (-.f64 #s(literal 1/2 binary64) (.f64 k #s(literal 1/2 binary64)))) (sqrt.f64 k)) (patch (/.f64 (pow.f64 (.f64 #s(literal 2 binary64) (.f64 (PI.f64) n)) (-.f64 #s(literal 1/2 binary64) (.f64 k #s(literal 1/2 binary64)))) (sqrt.f64 k)) #<representation binary64>) () ())) ())
#s(alt (* (sqrt (/ 1 k)) (exp (* (+ (log n) (log (* 2 (PI)))) (- 1/2 (* 1/2 k))))) (taylor 0 n) (#s(alt (/.f64 (pow.f64 (.f64 #s(literal 2 binary64) (.f64 (PI.f64) n)) (-.f64 #s(literal 1/2 binary64) (.f64 k #s(literal 1/2 binary64)))) (sqrt.f64 k)) (patch (/.f64 (pow.f64 (.f64 #s(literal 2 binary64) (.f64 (PI.f64) n)) (-.f64 #s(literal 1/2 binary64) (.f64 k #s(literal 1/2 binary64)))) (sqrt.f64 k)) #<representation binary64>) () ())) ())
#s(alt (* (sqrt (/ 1 k)) (exp (* (+ (log n) (log (* 2 (PI)))) (- 1/2 (* 1/2 k))))) (taylor 0 n) (#s(alt (/.f64 (pow.f64 (.f64 #s(literal 2 binary64) (.f64 (PI.f64) n)) (-.f64 #s(literal 1/2 binary64) (.f64 k #s(literal 1/2 binary64)))) (sqrt.f64 k)) (patch (/.f64 (pow.f64 (.f64 #s(literal 2 binary64) (.f64 (PI.f64) n)) (-.f64 #s(literal 1/2 binary64) (.f64 k #s(literal 1/2 binary64)))) (sqrt.f64 k)) #<representation binary64>) () ())) ())
#s(alt (* (sqrt (/ 1 k)) (exp (* (+ (log n) (log (* 2 (PI)))) (- 1/2 (* 1/2 k))))) (taylor 0 n) (#s(alt (/.f64 (pow.f64 (.f64 #s(literal 2 binary64) (.f64 (PI.f64) n)) (-.f64 #s(literal 1/2 binary64) (.f64 k #s(literal 1/2 binary64)))) (sqrt.f64 k)) (patch (/.f64 (pow.f64 (.f64 #s(literal 2 binary64) (.f64 (PI.f64) n)) (-.f64 #s(literal 1/2 binary64) (.f64 k #s(literal 1/2 binary64)))) (sqrt.f64 k)) #<representation binary64>) () ())) ())
#s(alt (* (sqrt (/ 1 k)) (exp (* (+ (log (* 2 (PI))) (* -1 (log (/ 1 n)))) (- 1/2 (* 1/2 k))))) (taylor inf n) (#s(alt (/.f64 (pow.f64 (.f64 #s(literal 2 binary64) (.f64 (PI.f64) n)) (-.f64 #s(literal 1/2 binary64) (.f64 k #s(literal 1/2 binary64)))) (sqrt.f64 k)) (patch (/.f64 (pow.f64 (.f64 #s(literal 2 binary64) (.f64 (PI.f64) n)) (-.f64 #s(literal 1/2 binary64) (.f64 k #s(literal 1/2 binary64)))) (sqrt.f64 k)) #<representation binary64>) () ())) ())
#s(alt (* (sqrt (/ 1 k)) (exp (* (+ (log (* 2 (PI))) (* -1 (log (/ 1 n)))) (- 1/2 (* 1/2 k))))) (taylor inf n) (#s(alt (/.f64 (pow.f64 (.f64 #s(literal 2 binary64) (.f64 (PI.f64) n)) (-.f64 #s(literal 1/2 binary64) (.f64 k #s(literal 1/2 binary64)))) (sqrt.f64 k)) (patch (/.f64 (pow.f64 (.f64 #s(literal 2 binary64) (.f64 (PI.f64) n)) (-.f64 #s(literal 1/2 binary64) (.f64 k #s(literal 1/2 binary64)))) (sqrt.f64 k)) #<representation binary64>) () ())) ())
#s(alt (* (sqrt (/ 1 k)) (exp (* (+ (log (* 2 (PI))) (* -1 (log (/ 1 n)))) (- 1/2 (* 1/2 k))))) (taylor inf n) (#s(alt (/.f64 (pow.f64 (.f64 #s(literal 2 binary64) (.f64 (PI.f64) n)) (-.f64 #s(literal 1/2 binary64) (.f64 k #s(literal 1/2 binary64)))) (sqrt.f64 k)) (patch (/.f64 (pow.f64 (.f64 #s(literal 2 binary64) (.f64 (PI.f64) n)) (-.f64 #s(literal 1/2 binary64) (.f64 k #s(literal 1/2 binary64)))) (sqrt.f64 k)) #<representation binary64>) () ())) ())
#s(alt (* (sqrt (/ 1 k)) (exp (* (+ (log (* 2 (PI))) (* -1 (log (/ 1 n)))) (- 1/2 (* 1/2 k))))) (taylor inf n) (#s(alt (/.f64 (pow.f64 (.f64 #s(literal 2 binary64) (.f64 (PI.f64) n)) (-.f64 #s(literal 1/2 binary64) (.f64 k #s(literal 1/2 binary64)))) (sqrt.f64 k)) (patch (/.f64 (pow.f64 (.f64 #s(literal 2 binary64) (.f64 (PI.f64) n)) (-.f64 #s(literal 1/2 binary64) (.f64 k #s(literal 1/2 binary64)))) (sqrt.f64 k)) #<representation binary64>) () ())) ())
#s(alt (* (sqrt (/ 1 k)) (exp (* (+ (log (* -2 (PI))) (* -1 (log (/ -1 n)))) (- 1/2 (* 1/2 k))))) (taylor -inf n) (#s(alt (/.f64 (pow.f64 (.f64 #s(literal 2 binary64) (.f64 (PI.f64) n)) (-.f64 #s(literal 1/2 binary64) (.f64 k #s(literal 1/2 binary64)))) (sqrt.f64 k)) (patch (/.f64 (pow.f64 (.f64 #s(literal 2 binary64) (.f64 (PI.f64) n)) (-.f64 #s(literal 1/2 binary64) (.f64 k #s(literal 1/2 binary64)))) (sqrt.f64 k)) #<representation binary64>) () ())) ())
#s(alt (* (sqrt (/ 1 k)) (exp (* (+ (log (* -2 (PI))) (* -1 (log (/ -1 n)))) (- 1/2 (* 1/2 k))))) (taylor -inf n) (#s(alt (/.f64 (pow.f64 (.f64 #s(literal 2 binary64) (.f64 (PI.f64) n)) (-.f64 #s(literal 1/2 binary64) (.f64 k #s(literal 1/2 binary64)))) (sqrt.f64 k)) (patch (/.f64 (pow.f64 (.f64 #s(literal 2 binary64) (.f64 (PI.f64) n)) (-.f64 #s(literal 1/2 binary64) (.f64 k #s(literal 1/2 binary64)))) (sqrt.f64 k)) #<representation binary64>) () ())) ())
#s(alt (* (sqrt (/ 1 k)) (exp (* (+ (log (* -2 (PI))) (* -1 (log (/ -1 n)))) (- 1/2 (* 1/2 k))))) (taylor -inf n) (#s(alt (/.f64 (pow.f64 (.f64 #s(literal 2 binary64) (.f64 (PI.f64) n)) (-.f64 #s(literal 1/2 binary64) (.f64 k #s(literal 1/2 binary64)))) (sqrt.f64 k)) (patch (/.f64 (pow.f64 (.f64 #s(literal 2 binary64) (.f64 (PI.f64) n)) (-.f64 #s(literal 1/2 binary64) (.f64 k #s(literal 1/2 binary64)))) (sqrt.f64 k)) #<representation binary64>) () ())) ())
#s(alt (* (sqrt (/ 1 k)) (exp (* (+ (log (* -2 (PI))) (* -1 (log (/ -1 n)))) (- 1/2 (* 1/2 k))))) (taylor -inf n) (#s(alt (/.f64 (pow.f64 (.f64 #s(literal 2 binary64) (.f64 (PI.f64) n)) (-.f64 #s(literal 1/2 binary64) (.f64 k #s(literal 1/2 binary64)))) (sqrt.f64 k)) (patch (/.f64 (pow.f64 (.f64 #s(literal 2 binary64) (.f64 (PI.f64) n)) (-.f64 #s(literal 1/2 binary64) (.f64 k #s(literal 1/2 binary64)))) (sqrt.f64 k)) #<representation binary64>) () ())) ())
#s(alt (* (sqrt (/ (* n (PI)) k)) (sqrt 2)) (taylor 0 k) (#s(alt (/.f64 (pow.f64 (.f64 #s(literal 2 binary64) (.f64 (PI.f64) n)) (-.f64 #s(literal 1/2 binary64) (.f64 k #s(literal 1/2 binary64)))) (sqrt.f64 k)) (patch (/.f64 (pow.f64 (.f64 #s(literal 2 binary64) (.f64 (PI.f64) n)) (-.f64 #s(literal 1/2 binary64) (.f64 k #s(literal 1/2 binary64)))) (sqrt.f64 k)) #<representation binary64>) () ())) ())
#s(alt (/ (+ (* -1/2 (* (sqrt (* (pow k 3) (* n (PI)))) (* (log (* 2 (* n (PI)))) (sqrt 2)))) (* (sqrt (* k (* n (PI)))) (sqrt 2))) k) (taylor 0 k) (#s(alt (/.f64 (pow.f64 (.f64 #s(literal 2 binary64) (.f64 (PI.f64) n)) (-.f64 #s(literal 1/2 binary64) (.f64 k #s(literal 1/2 binary64)))) (sqrt.f64 k)) (patch (/.f64 (pow.f64 (.f64 #s(literal 2 binary64) (.f64 (PI.f64) n)) (-.f64 #s(literal 1/2 binary64) (.f64 k #s(literal 1/2 binary64)))) (sqrt.f64 k)) #<representation binary64>) () ())) ())
#s(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) (taylor 0 k) (#s(alt (/.f64 (pow.f64 (.f64 #s(literal 2 binary64) (.f64 (PI.f64) n)) (-.f64 #s(literal 1/2 binary64) (.f64 k #s(literal 1/2 binary64)))) (sqrt.f64 k)) (patch (/.f64 (pow.f64 (.f64 #s(literal 2 binary64) (.f64 (PI.f64) n)) (-.f64 #s(literal 1/2 binary64) (.f64 k #s(literal 1/2 binary64)))) (sqrt.f64 k)) #<representation binary64>) () ())) ())
#s(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) (taylor 0 k) (#s(alt (/.f64 (pow.f64 (.f64 #s(literal 2 binary64) (.f64 (PI.f64) n)) (-.f64 #s(literal 1/2 binary64) (.f64 k #s(literal 1/2 binary64)))) (sqrt.f64 k)) (patch (/.f64 (pow.f64 (.f64 #s(literal 2 binary64) (.f64 (PI.f64) n)) (-.f64 #s(literal 1/2 binary64) (.f64 k #s(literal 1/2 binary64)))) (sqrt.f64 k)) #<representation binary64>) () ())) ())
#s(alt (* (sqrt (/ 1 k)) (exp (* (log (* 2 (* n (PI)))) (- 1/2 (* 1/2 k))))) (taylor inf k) (#s(alt (/.f64 (pow.f64 (.f64 #s(literal 2 binary64) (.f64 (PI.f64) n)) (-.f64 #s(literal 1/2 binary64) (.f64 k #s(literal 1/2 binary64)))) (sqrt.f64 k)) (patch (/.f64 (pow.f64 (.f64 #s(literal 2 binary64) (.f64 (PI.f64) n)) (-.f64 #s(literal 1/2 binary64) (.f64 k #s(literal 1/2 binary64)))) (sqrt.f64 k)) #<representation binary64>) () ())) ())
#s(alt (* (sqrt (/ 1 k)) (exp (* (log (* 2 (* n (PI)))) (- 1/2 (* 1/2 k))))) (taylor inf k) (#s(alt (/.f64 (pow.f64 (.f64 #s(literal 2 binary64) (.f64 (PI.f64) n)) (-.f64 #s(literal 1/2 binary64) (.f64 k #s(literal 1/2 binary64)))) (sqrt.f64 k)) (patch (/.f64 (pow.f64 (.f64 #s(literal 2 binary64) (.f64 (PI.f64) n)) (-.f64 #s(literal 1/2 binary64) (.f64 k #s(literal 1/2 binary64)))) (sqrt.f64 k)) #<representation binary64>) () ())) ())
#s(alt (* (sqrt (/ 1 k)) (exp (* (log (* 2 (* n (PI)))) (- 1/2 (* 1/2 k))))) (taylor inf k) (#s(alt (/.f64 (pow.f64 (.f64 #s(literal 2 binary64) (.f64 (PI.f64) n)) (-.f64 #s(literal 1/2 binary64) (.f64 k #s(literal 1/2 binary64)))) (sqrt.f64 k)) (patch (/.f64 (pow.f64 (.f64 #s(literal 2 binary64) (.f64 (PI.f64) n)) (-.f64 #s(literal 1/2 binary64) (.f64 k #s(literal 1/2 binary64)))) (sqrt.f64 k)) #<representation binary64>) () ())) ())
#s(alt (* (sqrt (/ 1 k)) (exp (* (log (* 2 (* n (PI)))) (- 1/2 (* 1/2 k))))) (taylor inf k) (#s(alt (/.f64 (pow.f64 (.f64 #s(literal 2 binary64) (.f64 (PI.f64) n)) (-.f64 #s(literal 1/2 binary64) (.f64 k #s(literal 1/2 binary64)))) (sqrt.f64 k)) (patch (/.f64 (pow.f64 (.f64 #s(literal 2 binary64) (.f64 (PI.f64) n)) (-.f64 #s(literal 1/2 binary64) (.f64 k #s(literal 1/2 binary64)))) (sqrt.f64 k)) #<representation binary64>) () ())) ())
#s(alt (* (sqrt (/ 1 k)) (exp (* (log (* 2 (* n (PI)))) (+ 1/2 (* -1/2 k))))) (taylor -inf k) (#s(alt (/.f64 (pow.f64 (.f64 #s(literal 2 binary64) (.f64 (PI.f64) n)) (-.f64 #s(literal 1/2 binary64) (.f64 k #s(literal 1/2 binary64)))) (sqrt.f64 k)) (patch (/.f64 (pow.f64 (.f64 #s(literal 2 binary64) (.f64 (PI.f64) n)) (-.f64 #s(literal 1/2 binary64) (.f64 k #s(literal 1/2 binary64)))) (sqrt.f64 k)) #<representation binary64>) () ())) ())
#s(alt (* (sqrt (/ 1 k)) (exp (* (log (* 2 (* n (PI)))) (+ 1/2 (* -1/2 k))))) (taylor -inf k) (#s(alt (/.f64 (pow.f64 (.f64 #s(literal 2 binary64) (.f64 (PI.f64) n)) (-.f64 #s(literal 1/2 binary64) (.f64 k #s(literal 1/2 binary64)))) (sqrt.f64 k)) (patch (/.f64 (pow.f64 (.f64 #s(literal 2 binary64) (.f64 (PI.f64) n)) (-.f64 #s(literal 1/2 binary64) (.f64 k #s(literal 1/2 binary64)))) (sqrt.f64 k)) #<representation binary64>) () ())) ())
#s(alt (* (sqrt (/ 1 k)) (exp (* (log (* 2 (* n (PI)))) (+ 1/2 (* -1/2 k))))) (taylor -inf k) (#s(alt (/.f64 (pow.f64 (.f64 #s(literal 2 binary64) (.f64 (PI.f64) n)) (-.f64 #s(literal 1/2 binary64) (.f64 k #s(literal 1/2 binary64)))) (sqrt.f64 k)) (patch (/.f64 (pow.f64 (.f64 #s(literal 2 binary64) (.f64 (PI.f64) n)) (-.f64 #s(literal 1/2 binary64) (.f64 k #s(literal 1/2 binary64)))) (sqrt.f64 k)) #<representation binary64>) () ())) ())
#s(alt (* (sqrt (/ 1 k)) (exp (* (log (* 2 (* n (PI)))) (+ 1/2 (* -1/2 k))))) (taylor -inf k) (#s(alt (/.f64 (pow.f64 (.f64 #s(literal 2 binary64) (.f64 (PI.f64) n)) (-.f64 #s(literal 1/2 binary64) (.f64 k #s(literal 1/2 binary64)))) (sqrt.f64 k)) (patch (/.f64 (pow.f64 (.f64 #s(literal 2 binary64) (.f64 (PI.f64) n)) (-.f64 #s(literal 1/2 binary64) (.f64 k #s(literal 1/2 binary64)))) (sqrt.f64 k)) #<representation binary64>) () ())) ())
#s(alt (exp (* (+ (log n) (log (* 2 (PI)))) (- 1/2 (* 1/2 k)))) (taylor 0 n) (#s(alt (pow.f64 (.f64 #s(literal 2 binary64) (.f64 (PI.f64) n)) (-.f64 #s(literal 1/2 binary64) (.f64 k #s(literal 1/2 binary64)))) (patch (pow.f64 (.f64 #s(literal 2 binary64) (.f64 (PI.f64) n)) (-.f64 #s(literal 1/2 binary64) (.f64 k #s(literal 1/2 binary64)))) #<representation binary64>) () ())) ())
#s(alt (exp (* (+ (log n) (log (* 2 (PI)))) (- 1/2 (* 1/2 k)))) (taylor 0 n) (#s(alt (pow.f64 (.f64 #s(literal 2 binary64) (.f64 (PI.f64) n)) (-.f64 #s(literal 1/2 binary64) (.f64 k #s(literal 1/2 binary64)))) (patch (pow.f64 (.f64 #s(literal 2 binary64) (.f64 (PI.f64) n)) (-.f64 #s(literal 1/2 binary64) (.f64 k #s(literal 1/2 binary64)))) #<representation binary64>) () ())) ())
#s(alt (exp (* (+ (log n) (log (* 2 (PI)))) (- 1/2 (* 1/2 k)))) (taylor 0 n) (#s(alt (pow.f64 (.f64 #s(literal 2 binary64) (.f64 (PI.f64) n)) (-.f64 #s(literal 1/2 binary64) (.f64 k #s(literal 1/2 binary64)))) (patch (pow.f64 (.f64 #s(literal 2 binary64) (.f64 (PI.f64) n)) (-.f64 #s(literal 1/2 binary64) (.f64 k #s(literal 1/2 binary64)))) #<representation binary64>) () ())) ())
#s(alt (exp (* (+ (log n) (log (* 2 (PI)))) (- 1/2 (* 1/2 k)))) (taylor 0 n) (#s(alt (pow.f64 (.f64 #s(literal 2 binary64) (.f64 (PI.f64) n)) (-.f64 #s(literal 1/2 binary64) (.f64 k #s(literal 1/2 binary64)))) (patch (pow.f64 (.f64 #s(literal 2 binary64) (.f64 (PI.f64) n)) (-.f64 #s(literal 1/2 binary64) (.f64 k #s(literal 1/2 binary64)))) #<representation binary64>) () ())) ())
#s(alt (exp (* (+ (log (* 2 (PI))) (* -1 (log (/ 1 n)))) (- 1/2 (* 1/2 k)))) (taylor inf n) (#s(alt (pow.f64 (.f64 #s(literal 2 binary64) (.f64 (PI.f64) n)) (-.f64 #s(literal 1/2 binary64) (.f64 k #s(literal 1/2 binary64)))) (patch (pow.f64 (.f64 #s(literal 2 binary64) (.f64 (PI.f64) n)) (-.f64 #s(literal 1/2 binary64) (.f64 k #s(literal 1/2 binary64)))) #<representation binary64>) () ())) ())
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#s(alt (* n (PI)) (taylor inf n) (#s(alt (.f64 (PI.f64) n) (patch (.f64 (PI.f64) n) #<representation binary64>) () ())) ())
#s(alt (* n (PI)) (taylor -inf n) (#s(alt (.f64 (PI.f64) n) (patch (.f64 (PI.f64) n) #<representation binary64>) () ())) ())
#s(alt (* n (PI)) (taylor -inf n) (#s(alt (.f64 (PI.f64) n) (patch (.f64 (PI.f64) n) #<representation binary64>) () ())) ())
#s(alt (* n (PI)) (taylor -inf n) (#s(alt (.f64 (PI.f64) n) (patch (.f64 (PI.f64) n) #<representation binary64>) () ())) ())
#s(alt (* n (PI)) (taylor -inf n) (#s(alt (.f64 (PI.f64) n) (patch (.f64 (PI.f64) n) #<representation binary64>) () ())) ())
#s(alt (sqrt (/ k (* n (PI)))) (taylor 0 k) (#s(alt (sqrt.f64 (/.f64 k (.f64 n (PI.f64)))) (patch (sqrt.f64 (/.f64 k (.f64 n (PI.f64)))) #<representation binary64>) () ())) ())
#s(alt (sqrt (/ k (* n (PI)))) (taylor 0 k) (#s(alt (sqrt.f64 (/.f64 k (.f64 n (PI.f64)))) (patch (sqrt.f64 (/.f64 k (.f64 n (PI.f64)))) #<representation binary64>) () ())) ())
#s(alt (sqrt (/ k (* n (PI)))) (taylor 0 k) (#s(alt (sqrt.f64 (/.f64 k (.f64 n (PI.f64)))) (patch (sqrt.f64 (/.f64 k (.f64 n (PI.f64)))) #<representation binary64>) () ())) ())
#s(alt (sqrt (/ k (* n (PI)))) (taylor 0 k) (#s(alt (sqrt.f64 (/.f64 k (.f64 n (PI.f64)))) (patch (sqrt.f64 (/.f64 k (.f64 n (PI.f64)))) #<representation binary64>) () ())) ())
#s(alt (sqrt (/ k (* n (PI)))) (taylor inf k) (#s(alt (sqrt.f64 (/.f64 k (.f64 n (PI.f64)))) (patch (sqrt.f64 (/.f64 k (.f64 n (PI.f64)))) #<representation binary64>) () ())) ())
#s(alt (sqrt (/ k (* n (PI)))) (taylor inf k) (#s(alt (sqrt.f64 (/.f64 k (.f64 n (PI.f64)))) (patch (sqrt.f64 (/.f64 k (.f64 n (PI.f64)))) #<representation binary64>) () ())) ())
#s(alt (sqrt (/ k (* n (PI)))) (taylor inf k) (#s(alt (sqrt.f64 (/.f64 k (.f64 n (PI.f64)))) (patch (sqrt.f64 (/.f64 k (.f64 n (PI.f64)))) #<representation binary64>) () ())) ())
#s(alt (sqrt (/ k (* n (PI)))) (taylor inf k) (#s(alt (sqrt.f64 (/.f64 k (.f64 n (PI.f64)))) (patch (sqrt.f64 (/.f64 k (.f64 n (PI.f64)))) #<representation binary64>) () ())) ())
#s(alt (* -1 (* (sqrt (/ k (* n (PI)))) (pow (sqrt -1) 2))) (taylor -inf k) (#s(alt (sqrt.f64 (/.f64 k (.f64 n (PI.f64)))) (patch (sqrt.f64 (/.f64 k (.f64 n (PI.f64)))) #<representation binary64>) () ())) ())
#s(alt (* -1 (* (sqrt (/ k (* n (PI)))) (pow (sqrt -1) 2))) (taylor -inf k) (#s(alt (sqrt.f64 (/.f64 k (.f64 n (PI.f64)))) (patch (sqrt.f64 (/.f64 k (.f64 n (PI.f64)))) #<representation binary64>) () ())) ())
#s(alt (* -1 (* (sqrt (/ k (* n (PI)))) (pow (sqrt -1) 2))) (taylor -inf k) (#s(alt (sqrt.f64 (/.f64 k (.f64 n (PI.f64)))) (patch (sqrt.f64 (/.f64 k (.f64 n (PI.f64)))) #<representation binary64>) () ())) ())
#s(alt (* -1 (* (sqrt (/ k (* n (PI)))) (pow (sqrt -1) 2))) (taylor -inf k) (#s(alt (sqrt.f64 (/.f64 k (.f64 n (PI.f64)))) (patch (sqrt.f64 (/.f64 k (.f64 n (PI.f64)))) #<representation binary64>) () ())) ())
#s(alt (sqrt (/ k (* n (PI)))) (taylor 0 n) (#s(alt (sqrt.f64 (/.f64 k (.f64 n (PI.f64)))) (patch (sqrt.f64 (/.f64 k (.f64 n (PI.f64)))) #<representation binary64>) () ())) ())
#s(alt (sqrt (/ k (* n (PI)))) (taylor 0 n) (#s(alt (sqrt.f64 (/.f64 k (.f64 n (PI.f64)))) (patch (sqrt.f64 (/.f64 k (.f64 n (PI.f64)))) #<representation binary64>) () ())) ())
#s(alt (sqrt (/ k (* n (PI)))) (taylor 0 n) (#s(alt (sqrt.f64 (/.f64 k (.f64 n (PI.f64)))) (patch (sqrt.f64 (/.f64 k (.f64 n (PI.f64)))) #<representation binary64>) () ())) ())
#s(alt (sqrt (/ k (* n (PI)))) (taylor 0 n) (#s(alt (sqrt.f64 (/.f64 k (.f64 n (PI.f64)))) (patch (sqrt.f64 (/.f64 k (.f64 n (PI.f64)))) #<representation binary64>) () ())) ())
#s(alt (sqrt (/ k (* n (PI)))) (taylor inf n) (#s(alt (sqrt.f64 (/.f64 k (.f64 n (PI.f64)))) (patch (sqrt.f64 (/.f64 k (.f64 n (PI.f64)))) #<representation binary64>) () ())) ())
#s(alt (sqrt (/ k (* n (PI)))) (taylor inf n) (#s(alt (sqrt.f64 (/.f64 k (.f64 n (PI.f64)))) (patch (sqrt.f64 (/.f64 k (.f64 n (PI.f64)))) #<representation binary64>) () ())) ())
#s(alt (sqrt (/ k (* n (PI)))) (taylor inf n) (#s(alt (sqrt.f64 (/.f64 k (.f64 n (PI.f64)))) (patch (sqrt.f64 (/.f64 k (.f64 n (PI.f64)))) #<representation binary64>) () ())) ())
#s(alt (sqrt (/ k (* n (PI)))) (taylor inf n) (#s(alt (sqrt.f64 (/.f64 k (.f64 n (PI.f64)))) (patch (sqrt.f64 (/.f64 k (.f64 n (PI.f64)))) #<representation binary64>) () ())) ())
#s(alt (* (sqrt (/ k (* n (PI)))) (pow (sqrt -1) 2)) (taylor -inf n) (#s(alt (sqrt.f64 (/.f64 k (.f64 n (PI.f64)))) (patch (sqrt.f64 (/.f64 k (.f64 n (PI.f64)))) #<representation binary64>) () ())) ())
#s(alt (* (sqrt (/ k (* n (PI)))) (pow (sqrt -1) 2)) (taylor -inf n) (#s(alt (sqrt.f64 (/.f64 k (.f64 n (PI.f64)))) (patch (sqrt.f64 (/.f64 k (.f64 n (PI.f64)))) #<representation binary64>) () ())) ())
#s(alt (* (sqrt (/ k (* n (PI)))) (pow (sqrt -1) 2)) (taylor -inf n) (#s(alt (sqrt.f64 (/.f64 k (.f64 n (PI.f64)))) (patch (sqrt.f64 (/.f64 k (.f64 n (PI.f64)))) #<representation binary64>) () ())) ())
#s(alt (* (sqrt (/ k (* n (PI)))) (pow (sqrt -1) 2)) (taylor -inf n) (#s(alt (sqrt.f64 (/.f64 k (.f64 n (PI.f64)))) (patch (sqrt.f64 (/.f64 k (.f64 n (PI.f64)))) #<representation binary64>) () ())) ())
#s(alt -1/2 (taylor 0 k) (#s(alt #s(approx (- -1/2 (* k -1/2)) #s(literal -1/2 binary64)) (patch #s(approx (- -1/2 (* k -1/2)) #s(literal -1/2 binary64)) #<representation binary64>) () ())) ())
#s(alt (- (* 1/2 k) 1/2) (taylor 0 k) (#s(alt #s(approx (- -1/2 (* k -1/2)) #s(literal -1/2 binary64)) (patch #s(approx (- -1/2 (* k -1/2)) #s(literal -1/2 binary64)) #<representation binary64>) () ())) ())
#s(alt (- (* 1/2 k) 1/2) (taylor 0 k) (#s(alt #s(approx (- -1/2 (* k -1/2)) #s(literal -1/2 binary64)) (patch #s(approx (- -1/2 (* k -1/2)) #s(literal -1/2 binary64)) #<representation binary64>) () ())) ())
#s(alt (- (* 1/2 k) 1/2) (taylor 0 k) (#s(alt #s(approx (- -1/2 (* k -1/2)) #s(literal -1/2 binary64)) (patch #s(approx (- -1/2 (* k -1/2)) #s(literal -1/2 binary64)) #<representation binary64>) () ())) ())
#s(alt (* 1/2 k) (taylor inf k) (#s(alt #s(approx (- -1/2 (* k -1/2)) #s(literal -1/2 binary64)) (patch #s(approx (- -1/2 (* k -1/2)) #s(literal -1/2 binary64)) #<representation binary64>) () ())) ())
#s(alt (* k (- 1/2 (* 1/2 (/ 1 k)))) (taylor inf k) (#s(alt #s(approx (- -1/2 (* k -1/2)) #s(literal -1/2 binary64)) (patch #s(approx (- -1/2 (* k -1/2)) #s(literal -1/2 binary64)) #<representation binary64>) () ())) ())
#s(alt (* k (- 1/2 (* 1/2 (/ 1 k)))) (taylor inf k) (#s(alt #s(approx (- -1/2 (* k -1/2)) #s(literal -1/2 binary64)) (patch #s(approx (- -1/2 (* k -1/2)) #s(literal -1/2 binary64)) #<representation binary64>) () ())) ())
#s(alt (* k (- 1/2 (* 1/2 (/ 1 k)))) (taylor inf k) (#s(alt #s(approx (- -1/2 (* k -1/2)) #s(literal -1/2 binary64)) (patch #s(approx (- -1/2 (* k -1/2)) #s(literal -1/2 binary64)) #<representation binary64>) () ())) ())
#s(alt (* 1/2 k) (taylor -inf k) (#s(alt #s(approx (- -1/2 (* k -1/2)) #s(literal -1/2 binary64)) (patch #s(approx (- -1/2 (* k -1/2)) #s(literal -1/2 binary64)) #<representation binary64>) () ())) ())
#s(alt (* -1 (* k (- (* 1/2 (/ 1 k)) 1/2))) (taylor -inf k) (#s(alt #s(approx (- -1/2 (* k -1/2)) #s(literal -1/2 binary64)) (patch #s(approx (- -1/2 (* k -1/2)) #s(literal -1/2 binary64)) #<representation binary64>) () ())) ())
#s(alt (* -1 (* k (- (* 1/2 (/ 1 k)) 1/2))) (taylor -inf k) (#s(alt #s(approx (- -1/2 (* k -1/2)) #s(literal -1/2 binary64)) (patch #s(approx (- -1/2 (* k -1/2)) #s(literal -1/2 binary64)) #<representation binary64>) () ())) ())
#s(alt (* -1 (* k (- (* 1/2 (/ 1 k)) 1/2))) (taylor -inf k) (#s(alt #s(approx (- -1/2 (* k -1/2)) #s(literal -1/2 binary64)) (patch #s(approx (- -1/2 (* k -1/2)) #s(literal -1/2 binary64)) #<representation binary64>) () ())) ())

Calls

105 calls:

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

simplify296.0ms (2.5%)

Memory

-21.5MiB live, 388.6MiB allocated

Algorithm

1×	egg-herbie

Rules

8 114×	`lower-fma.f64`
8 114×	`lower-fma.f32`
6 658×	`lower-*.f64`
6 658×	`lower-*.f32`
2 870×	`lower-+.f64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	289	6361
1	886	6125
2	3032	5416
3	6523	5344
0	8252	5256

Stop Event

1×	iter limit
1×	node limit

Counts

420 → 420

Calls

Call 1

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

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

rewrite213.0ms (1.8%)

Memory

13.4MiB live, 329.9MiB allocated

Rules

4 998×	`lower-*.f32`
4 982×	`lower-*.f64`
3 946×	`lower-/.f32`
3 934×	`lower-/.f64`
2 244×	`lower-pow.f32`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	49	250
0	75	239
1	280	234
2	1649	228
0	8194	223

Stop Event

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

Counts

23 → 883

Calls

Call 1

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

Outputs
(+.f64 #s(literal 1/2 binary64) (*.f64 k #s(literal -1/2 binary64)))
(+.f64 (*.f64 k #s(literal -1/2 binary64)) #s(literal 1/2 binary64))
(exp.f64 (*.f64 (log.f64 (/.f64 #s(literal 2 binary64) (-.f64 #s(literal 1 binary64) k))) #s(literal -1 binary64)))
(-.f64 #s(literal 1/2 binary64) (*.f64 #s(literal 1/2 binary64) k))
(-.f64 #s(literal 0 binary64) (-.f64 #s(literal -1/2 binary64) (/.f64 k #s(literal -2 binary64))))
(-.f64 (/.f64 #s(literal 1/8 binary64) (fma.f64 (.f64 #s(literal 1/2 binary64) k) (fma.f64 #s(literal 1/2 binary64) k #s(literal 1/2 binary64)) #s(literal 1/4 binary64))) (/.f64 (.f64 #s(literal -1/8 binary64) (.f64 k (.f64 k k))) (fma.f64 (*.f64 #s(literal 1/2 binary64) k) (fma.f64 #s(literal 1/2 binary64) k #s(literal 1/2 binary64)) #s(literal 1/4 binary64))))
(-.f64 (/.f64 #s(literal 1/4 binary64) (fma.f64 #s(literal 1/2 binary64) k #s(literal 1/2 binary64))) (.f64 (/.f64 (.f64 k k) (+.f64 k #s(literal 1 binary64))) #s(literal 1/2 binary64)))
(-.f64 (/.f64 (/.f64 #s(literal 1 binary64) (fma.f64 k (+.f64 k #s(literal 1 binary64)) #s(literal 1 binary64))) #s(literal 2 binary64)) (/.f64 (/.f64 (.f64 k (.f64 k k)) (fma.f64 k (+.f64 k #s(literal 1 binary64)) #s(literal 1 binary64))) #s(literal 2 binary64)))
(-.f64 (/.f64 (/.f64 #s(literal 1 binary64) (+.f64 k #s(literal 1 binary64))) #s(literal 2 binary64)) (/.f64 (/.f64 (*.f64 k k) (+.f64 k #s(literal 1 binary64))) #s(literal 2 binary64)))
(-.f64 (/.f64 #s(literal 1 binary64) (.f64 #s(literal 2 binary64) (fma.f64 k (+.f64 k #s(literal 1 binary64)) #s(literal 1 binary64)))) (/.f64 (.f64 k (.f64 k k)) (.f64 #s(literal 2 binary64) (fma.f64 k (+.f64 k #s(literal 1 binary64)) #s(literal 1 binary64)))))
(-.f64 (/.f64 #s(literal 1 binary64) (.f64 #s(literal 2 binary64) (+.f64 k #s(literal 1 binary64)))) (/.f64 (.f64 k k) (*.f64 #s(literal 2 binary64) (+.f64 k #s(literal 1 binary64)))))
(-.f64 (/.f64 #s(literal 1/4 binary64) (-.f64 #s(literal 1/2 binary64) (.f64 k #s(literal -1/2 binary64)))) (/.f64 (.f64 #s(literal 1/4 binary64) (.f64 k k)) (-.f64 #s(literal 1/2 binary64) (.f64 k #s(literal -1/2 binary64)))))
(fma.f64 #s(literal 1/2 binary64) (neg.f64 k) #s(literal 1/2 binary64))
(fma.f64 k #s(literal -1/2 binary64) #s(literal 1/2 binary64))
(fma.f64 #s(literal -1/2 binary64) k #s(literal 1/2 binary64))
(fma.f64 #s(literal -1 binary64) (*.f64 #s(literal 1/2 binary64) k) #s(literal 1/2 binary64))
(fma.f64 (neg.f64 k) #s(literal 1/2 binary64) #s(literal 1/2 binary64))
(neg.f64 (-.f64 #s(literal -1/2 binary64) (/.f64 k #s(literal -2 binary64))))
(/.f64 #s(literal 1 binary64) (/.f64 #s(literal 2 binary64) (-.f64 #s(literal 1 binary64) k)))
(/.f64 #s(literal 1 binary64) (neg.f64 (neg.f64 (/.f64 #s(literal 2 binary64) (-.f64 #s(literal 1 binary64) k)))))
(/.f64 #s(literal 1 binary64) (/.f64 (.f64 #s(literal 2 binary64) (fma.f64 k (+.f64 k #s(literal 1 binary64)) #s(literal 1 binary64))) (-.f64 #s(literal 1 binary64) (.f64 k (*.f64 k k)))))
(/.f64 #s(literal 1 binary64) (/.f64 (.f64 #s(literal 2 binary64) (+.f64 k #s(literal 1 binary64))) (-.f64 #s(literal 1 binary64) (.f64 k k))))
(/.f64 #s(literal 1 binary64) (/.f64 (-.f64 #s(literal 1/2 binary64) (.f64 k #s(literal -1/2 binary64))) (-.f64 #s(literal 1/4 binary64) (.f64 #s(literal 1/4 binary64) (*.f64 k k)))))
(/.f64 #s(literal 1 binary64) (/.f64 (+.f64 #s(literal 1/4 binary64) (-.f64 (.f64 #s(literal 1/4 binary64) (.f64 k k)) (.f64 #s(literal 1/2 binary64) (.f64 k #s(literal -1/2 binary64))))) (+.f64 #s(literal 1/8 binary64) (.f64 #s(literal -1/8 binary64) (.f64 k (*.f64 k k))))))
(/.f64 #s(literal 1 binary64) (/.f64 (fma.f64 k (+.f64 k #s(literal 1 binary64)) #s(literal 1 binary64)) (.f64 (-.f64 #s(literal 1 binary64) (.f64 k (*.f64 k k))) #s(literal 1/2 binary64))))
(/.f64 #s(literal 1 binary64) (/.f64 (+.f64 k #s(literal 1 binary64)) (.f64 (-.f64 #s(literal 1 binary64) (.f64 k k)) #s(literal 1/2 binary64))))
(/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 2 binary64))
(/.f64 #s(literal -1 binary64) (neg.f64 (/.f64 #s(literal 2 binary64) (-.f64 #s(literal 1 binary64) k))))
(/.f64 (neg.f64 (-.f64 #s(literal 1 binary64) k)) #s(literal -2 binary64))
(/.f64 (-.f64 #s(literal 1 binary64) (.f64 k (.f64 k k))) (*.f64 #s(literal 2 binary64) (fma.f64 k (+.f64 k #s(literal 1 binary64)) #s(literal 1 binary64))))
(/.f64 (+.f64 #s(literal 1/8 binary64) (.f64 #s(literal -1/8 binary64) (.f64 k (.f64 k k)))) (fma.f64 (.f64 #s(literal 1/2 binary64) k) (fma.f64 #s(literal 1/2 binary64) k #s(literal 1/2 binary64)) #s(literal 1/4 binary64)))
(/.f64 (+.f64 #s(literal 1/8 binary64) (.f64 #s(literal -1/8 binary64) (.f64 k (.f64 k k)))) (+.f64 #s(literal 1/4 binary64) (-.f64 (.f64 #s(literal 1/4 binary64) (.f64 k k)) (.f64 #s(literal 1/2 binary64) (*.f64 k #s(literal -1/2 binary64))))))
(/.f64 (-.f64 #s(literal 1 binary64) (.f64 k k)) (.f64 #s(literal 2 binary64) (+.f64 k #s(literal 1 binary64))))
(/.f64 (-.f64 #s(literal 1/4 binary64) (.f64 #s(literal 1/4 binary64) (.f64 k k))) (fma.f64 #s(literal 1/2 binary64) k #s(literal 1/2 binary64)))
(/.f64 (-.f64 #s(literal 1/4 binary64) (.f64 #s(literal 1/4 binary64) (.f64 k k))) (-.f64 #s(literal 1/2 binary64) (*.f64 k #s(literal -1/2 binary64))))
(/.f64 (neg.f64 (neg.f64 (-.f64 #s(literal 1 binary64) k))) #s(literal 2 binary64))
(/.f64 (neg.f64 (-.f64 #s(literal 1 binary64) (.f64 k (.f64 k k)))) (neg.f64 (*.f64 #s(literal 2 binary64) (fma.f64 k (+.f64 k #s(literal 1 binary64)) #s(literal 1 binary64)))))
(/.f64 (neg.f64 (-.f64 #s(literal 1 binary64) (.f64 k k))) (neg.f64 (.f64 #s(literal 2 binary64) (+.f64 k #s(literal 1 binary64)))))
(/.f64 (neg.f64 (+.f64 #s(literal 1/8 binary64) (.f64 #s(literal -1/8 binary64) (.f64 k (.f64 k k))))) (neg.f64 (fma.f64 (.f64 #s(literal 1/2 binary64) k) (fma.f64 #s(literal 1/2 binary64) k #s(literal 1/2 binary64)) #s(literal 1/4 binary64))))
(/.f64 (neg.f64 (+.f64 #s(literal 1/8 binary64) (.f64 #s(literal -1/8 binary64) (.f64 k (.f64 k k))))) (neg.f64 (+.f64 #s(literal 1/4 binary64) (-.f64 (.f64 #s(literal 1/4 binary64) (.f64 k k)) (.f64 #s(literal 1/2 binary64) (*.f64 k #s(literal -1/2 binary64)))))))
(/.f64 (neg.f64 (-.f64 #s(literal 1/4 binary64) (.f64 #s(literal 1/4 binary64) (.f64 k k)))) (neg.f64 (fma.f64 #s(literal 1/2 binary64) k #s(literal 1/2 binary64))))
(/.f64 (neg.f64 (-.f64 #s(literal 1/4 binary64) (.f64 #s(literal 1/4 binary64) (.f64 k k)))) (neg.f64 (-.f64 #s(literal 1/2 binary64) (*.f64 k #s(literal -1/2 binary64)))))
(/.f64 (.f64 (-.f64 #s(literal 1 binary64) (.f64 k (*.f64 k k))) #s(literal 1/2 binary64)) (fma.f64 k (+.f64 k #s(literal 1 binary64)) #s(literal 1 binary64)))
(/.f64 (.f64 (-.f64 #s(literal 1 binary64) (.f64 k k)) #s(literal 1/2 binary64)) (+.f64 k #s(literal 1 binary64)))
(/.f64 (-.f64 (.f64 #s(literal 1/8 binary64) (fma.f64 (.f64 #s(literal 1/2 binary64) k) (fma.f64 #s(literal 1/2 binary64) k #s(literal 1/2 binary64)) #s(literal 1/4 binary64))) (.f64 (fma.f64 (.f64 #s(literal 1/2 binary64) k) (fma.f64 #s(literal 1/2 binary64) k #s(literal 1/2 binary64)) #s(literal 1/4 binary64)) (.f64 #s(literal -1/8 binary64) (.f64 k (.f64 k k))))) (.f64 (fma.f64 (.f64 #s(literal 1/2 binary64) k) (fma.f64 #s(literal 1/2 binary64) k #s(literal 1/2 binary64)) #s(literal 1/4 binary64)) (fma.f64 (.f64 #s(literal 1/2 binary64) k) (fma.f64 #s(literal 1/2 binary64) k #s(literal 1/2 binary64)) #s(literal 1/4 binary64))))
(/.f64 (-.f64 (.f64 #s(literal 1/4 binary64) (fma.f64 #s(literal 1/2 binary64) k #s(literal 1/2 binary64))) (.f64 (fma.f64 #s(literal 1/2 binary64) k #s(literal 1/2 binary64)) (.f64 #s(literal 1/4 binary64) (.f64 k k)))) (*.f64 (fma.f64 #s(literal 1/2 binary64) k #s(literal 1/2 binary64)) (fma.f64 #s(literal 1/2 binary64) k #s(literal 1/2 binary64))))
(/.f64 (.f64 (-.f64 #s(literal 1/512 binary64) (.f64 #s(literal -1/512 binary64) (.f64 (.f64 k (.f64 k k)) (.f64 (.f64 k (.f64 k k)) (.f64 k (.f64 k k)))))) #s(literal 1 binary64)) (.f64 (+.f64 #s(literal 1/64 binary64) (fma.f64 (.f64 k (.f64 k k)) (.f64 #s(literal 1/64 binary64) (.f64 k (.f64 k k))) (.f64 #s(literal 1/64 binary64) (.f64 k (.f64 k k))))) (fma.f64 (.f64 #s(literal 1/2 binary64) k) (fma.f64 #s(literal 1/2 binary64) k #s(literal 1/2 binary64)) #s(literal 1/4 binary64))))
(/.f64 (.f64 (-.f64 #s(literal 1/64 binary64) (.f64 (.f64 k (.f64 k k)) (.f64 #s(literal 1/64 binary64) (.f64 k (.f64 k k))))) #s(literal 1 binary64)) (.f64 (+.f64 #s(literal 1/8 binary64) (.f64 #s(literal -1/8 binary64) (.f64 k (.f64 k k)))) (fma.f64 (.f64 #s(literal 1/2 binary64) k) (fma.f64 #s(literal 1/2 binary64) k #s(literal 1/2 binary64)) #s(literal 1/4 binary64))))
(/.f64 (.f64 (-.f64 #s(literal 1/64 binary64) (.f64 (.f64 k (.f64 k k)) (.f64 #s(literal 1/64 binary64) (.f64 k (.f64 k k))))) #s(literal 1 binary64)) (.f64 (+.f64 #s(literal 1/16 binary64) (fma.f64 (.f64 #s(literal 1/4 binary64) (.f64 k k)) (.f64 #s(literal 1/4 binary64) (.f64 k k)) (.f64 #s(literal 1/4 binary64) (.f64 #s(literal 1/4 binary64) (*.f64 k k))))) (fma.f64 #s(literal 1/2 binary64) k #s(literal 1/2 binary64))))
(/.f64 (.f64 (-.f64 #s(literal 1/16 binary64) (.f64 (.f64 #s(literal 1/4 binary64) (.f64 k k)) (.f64 #s(literal 1/4 binary64) (.f64 k k)))) #s(literal 1 binary64)) (.f64 (+.f64 #s(literal 1/4 binary64) (.f64 #s(literal 1/4 binary64) (*.f64 k k))) (fma.f64 #s(literal 1/2 binary64) k #s(literal 1/2 binary64))))
(/.f64 (neg.f64 (neg.f64 (neg.f64 (-.f64 #s(literal 1 binary64) k)))) #s(literal -2 binary64))
(/.f64 (neg.f64 (neg.f64 (+.f64 #s(literal 1/8 binary64) (.f64 #s(literal -1/8 binary64) (.f64 k (.f64 k k)))))) (neg.f64 (neg.f64 (fma.f64 (.f64 #s(literal 1/2 binary64) k) (fma.f64 #s(literal 1/2 binary64) k #s(literal 1/2 binary64)) #s(literal 1/4 binary64)))))
(/.f64 (neg.f64 (neg.f64 (-.f64 #s(literal 1/4 binary64) (.f64 #s(literal 1/4 binary64) (.f64 k k))))) (neg.f64 (neg.f64 (fma.f64 #s(literal 1/2 binary64) k #s(literal 1/2 binary64)))))
(/.f64 (neg.f64 (.f64 (-.f64 #s(literal 1 binary64) (.f64 k (*.f64 k k))) #s(literal 1/2 binary64))) (neg.f64 (fma.f64 k (+.f64 k #s(literal 1 binary64)) #s(literal 1 binary64))))
(/.f64 (neg.f64 (.f64 (-.f64 #s(literal 1 binary64) (.f64 k k)) #s(literal 1/2 binary64))) (neg.f64 (+.f64 k #s(literal 1 binary64))))
(/.f64 (fma.f64 #s(literal -1/8 binary64) (.f64 k (.f64 k k)) #s(literal 1/8 binary64)) (fma.f64 k (.f64 #s(literal 1/4 binary64) k) (-.f64 #s(literal 1/4 binary64) (.f64 (*.f64 k #s(literal -1/2 binary64)) #s(literal 1/2 binary64)))))
(/.f64 (-.f64 (pow.f64 (/.f64 #s(literal 1/8 binary64) (fma.f64 (.f64 #s(literal 1/2 binary64) k) (fma.f64 #s(literal 1/2 binary64) k #s(literal 1/2 binary64)) #s(literal 1/4 binary64))) #s(literal 3 binary64)) (pow.f64 (/.f64 (.f64 #s(literal -1/8 binary64) (.f64 k (.f64 k k))) (fma.f64 (.f64 #s(literal 1/2 binary64) k) (fma.f64 #s(literal 1/2 binary64) k #s(literal 1/2 binary64)) #s(literal 1/4 binary64))) #s(literal 3 binary64))) (fma.f64 (/.f64 #s(literal 1/8 binary64) (fma.f64 (.f64 #s(literal 1/2 binary64) k) (fma.f64 #s(literal 1/2 binary64) k #s(literal 1/2 binary64)) #s(literal 1/4 binary64))) (/.f64 #s(literal 1/8 binary64) (fma.f64 (.f64 #s(literal 1/2 binary64) k) (fma.f64 #s(literal 1/2 binary64) k #s(literal 1/2 binary64)) #s(literal 1/4 binary64))) (fma.f64 (/.f64 (.f64 #s(literal -1/8 binary64) (.f64 k (.f64 k k))) (fma.f64 (.f64 #s(literal 1/2 binary64) k) (fma.f64 #s(literal 1/2 binary64) k #s(literal 1/2 binary64)) #s(literal 1/4 binary64))) (/.f64 (.f64 #s(literal -1/8 binary64) (.f64 k (.f64 k k))) (fma.f64 (.f64 #s(literal 1/2 binary64) k) (fma.f64 #s(literal 1/2 binary64) k #s(literal 1/2 binary64)) #s(literal 1/4 binary64))) (.f64 (/.f64 #s(literal 1/8 binary64) (fma.f64 (.f64 #s(literal 1/2 binary64) k) (fma.f64 #s(literal 1/2 binary64) k #s(literal 1/2 binary64)) #s(literal 1/4 binary64))) (/.f64 (.f64 #s(literal -1/8 binary64) (.f64 k (.f64 k k))) (fma.f64 (*.f64 #s(literal 1/2 binary64) k) (fma.f64 #s(literal 1/2 binary64) k #s(literal 1/2 binary64)) #s(literal 1/4 binary64)))))))
(/.f64 (-.f64 (pow.f64 (/.f64 #s(literal 1/4 binary64) (fma.f64 #s(literal 1/2 binary64) k #s(literal 1/2 binary64))) #s(literal 3 binary64)) (pow.f64 (.f64 (/.f64 (.f64 k k) (+.f64 k #s(literal 1 binary64))) #s(literal 1/2 binary64)) #s(literal 3 binary64))) (fma.f64 (/.f64 #s(literal 1/4 binary64) (fma.f64 #s(literal 1/2 binary64) k #s(literal 1/2 binary64))) (/.f64 #s(literal 1/4 binary64) (fma.f64 #s(literal 1/2 binary64) k #s(literal 1/2 binary64))) (fma.f64 (.f64 (/.f64 (.f64 k k) (+.f64 k #s(literal 1 binary64))) #s(literal 1/2 binary64)) (.f64 (/.f64 (.f64 k k) (+.f64 k #s(literal 1 binary64))) #s(literal 1/2 binary64)) (.f64 (/.f64 #s(literal 1/4 binary64) (fma.f64 #s(literal 1/2 binary64) k #s(literal 1/2 binary64))) (.f64 (/.f64 (*.f64 k k) (+.f64 k #s(literal 1 binary64))) #s(literal 1/2 binary64))))))
(pow.f64 (/.f64 #s(literal 2 binary64) (-.f64 #s(literal 1 binary64) k)) #s(literal -1 binary64))
(*.f64 #s(literal 1/2 binary64) (-.f64 #s(literal 1 binary64) k))
(*.f64 #s(literal 1 binary64) (fma.f64 k #s(literal -1/2 binary64) #s(literal 1/2 binary64)))
(*.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 1/2 binary64))
(*.f64 (neg.f64 (-.f64 #s(literal 1 binary64) k)) #s(literal -1/2 binary64))
(.f64 (+.f64 #s(literal 1/8 binary64) (.f64 #s(literal -1/8 binary64) (.f64 k (.f64 k k)))) (/.f64 #s(literal 1 binary64) (fma.f64 (*.f64 #s(literal 1/2 binary64) k) (fma.f64 #s(literal 1/2 binary64) k #s(literal 1/2 binary64)) #s(literal 1/4 binary64))))
(.f64 (-.f64 #s(literal 1/4 binary64) (.f64 #s(literal 1/4 binary64) (*.f64 k k))) (/.f64 #s(literal 1 binary64) (fma.f64 #s(literal 1/2 binary64) k #s(literal 1/2 binary64))))
(.f64 (pow.f64 (/.f64 #s(literal 2 binary64) (-.f64 #s(literal 1 binary64) (.f64 k (*.f64 k k)))) #s(literal -1 binary64)) (/.f64 #s(literal 1 binary64) (fma.f64 k (+.f64 k #s(literal 1 binary64)) #s(literal 1 binary64))))
(.f64 (pow.f64 (/.f64 #s(literal 2 binary64) (-.f64 #s(literal 1 binary64) (.f64 k k))) #s(literal -1 binary64)) (/.f64 #s(literal 1 binary64) (+.f64 k #s(literal 1 binary64))))
(exp.f64 (.f64 (log.f64 (.f64 (sqrt.f64 k) (pow.f64 (.f64 #s(literal 2 binary64) (.f64 (PI.f64) n)) (fma.f64 #s(literal 1/2 binary64) k #s(literal -1/2 binary64))))) #s(literal -1 binary64)))
(exp.f64 (fma.f64 (.f64 #s(literal 1/2 binary64) (log.f64 k)) #s(literal -1 binary64) (.f64 (fma.f64 k #s(literal -1/2 binary64) #s(literal 1/2 binary64)) (log.f64 (.f64 #s(literal 2 binary64) (.f64 (PI.f64) n))))))
(exp.f64 (fma.f64 (fma.f64 k #s(literal -1/2 binary64) #s(literal 1/2 binary64)) (log.f64 (.f64 #s(literal 2 binary64) (.f64 (PI.f64) n))) (.f64 (.f64 #s(literal 1/2 binary64) (log.f64 k)) #s(literal -1 binary64))))
(exp.f64 (-.f64 (.f64 (fma.f64 k #s(literal -1/2 binary64) #s(literal 1/2 binary64)) (log.f64 (.f64 #s(literal 2 binary64) (.f64 (PI.f64) n)))) (.f64 #s(literal 1/2 binary64) (log.f64 k))))
(exp.f64 (-.f64 (.f64 (log.f64 (.f64 (PI.f64) (.f64 n (/.f64 #s(literal 2 binary64) k)))) #s(literal 1/2 binary64)) (.f64 (log.f64 (.f64 #s(literal 2 binary64) (.f64 (PI.f64) n))) (*.f64 #s(literal 1/2 binary64) k))))
(-.f64 (/.f64 #s(literal 0 binary64) (neg.f64 (sqrt.f64 k))) (/.f64 (pow.f64 (.f64 #s(literal 2 binary64) (.f64 (PI.f64) n)) (fma.f64 k #s(literal -1/2 binary64) #s(literal 1/2 binary64))) (neg.f64 (sqrt.f64 k))))
(neg.f64 (/.f64 (pow.f64 (.f64 #s(literal 2 binary64) (.f64 (PI.f64) n)) (fma.f64 k #s(literal -1/2 binary64) #s(literal 1/2 binary64))) (neg.f64 (sqrt.f64 k))))
(neg.f64 (/.f64 (neg.f64 (pow.f64 (.f64 #s(literal 2 binary64) (.f64 (PI.f64) n)) (fma.f64 k #s(literal -1/2 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)) (fma.f64 #s(literal 1/2 binary64) k #s(literal -1/2 binary64)))))
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(/.f64 (sqrt.f64 (/.f64 k (PI.f64))) (sqrt.f64 n))
(/.f64 (sqrt.f64 (neg.f64 (neg.f64 k))) (sqrt.f64 (neg.f64 (*.f64 n (neg.f64 (PI.f64))))))
(/.f64 (sqrt.f64 (neg.f64 (/.f64 k n))) (sqrt.f64 (neg.f64 (PI.f64))))
(/.f64 (sqrt.f64 (/.f64 (/.f64 k n) (pow.f64 (PI.f64) #s(literal 2/3 binary64)))) (pow.f64 (PI.f64) #s(literal 1/6 binary64)))
(/.f64 (sqrt.f64 (/.f64 (/.f64 k n) (sqrt.f64 (PI.f64)))) (sqrt.f64 (sqrt.f64 (PI.f64))))
(/.f64 (.f64 (neg.f64 (sqrt.f64 k)) #s(literal 1 binary64)) (.f64 #s(literal -1 binary64) (sqrt.f64 (*.f64 (PI.f64) n))))
(/.f64 (neg.f64 (sqrt.f64 (neg.f64 k))) (neg.f64 (sqrt.f64 (*.f64 n (neg.f64 (PI.f64))))))
(/.f64 (neg.f64 (sqrt.f64 (/.f64 k n))) (neg.f64 (sqrt.f64 (PI.f64))))
(/.f64 (neg.f64 (sqrt.f64 (/.f64 k (PI.f64)))) (neg.f64 (sqrt.f64 n)))
(pow.f64 (/.f64 k (*.f64 (PI.f64) n)) #s(literal 1/2 binary64))
(pow.f64 (/.f64 (*.f64 (PI.f64) n) k) #s(literal -1/2 binary64))
(pow.f64 (sqrt.f64 (/.f64 (*.f64 (PI.f64) n) k)) #s(literal -1 binary64))
(pow.f64 (pow.f64 (/.f64 k (*.f64 (PI.f64) n)) #s(literal 1/4 binary64)) #s(literal 2 binary64))
(pow.f64 (.f64 (/.f64 k (.f64 (PI.f64) n)) (/.f64 k (*.f64 (PI.f64) n))) #s(literal 1/4 binary64))
(pow.f64 (exp.f64 (log.f64 (/.f64 k (*.f64 (PI.f64) n)))) #s(literal 1/2 binary64))
(.f64 (sqrt.f64 k) (sqrt.f64 (/.f64 #s(literal 1 binary64) (.f64 (PI.f64) n))))
(.f64 #s(literal 1 binary64) (sqrt.f64 (/.f64 k (.f64 (PI.f64) n))))
(.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (.f64 (PI.f64) n))) (sqrt.f64 k))
(.f64 (sqrt.f64 (neg.f64 k)) (pow.f64 (/.f64 #s(literal 1 binary64) (.f64 n (neg.f64 (PI.f64)))) #s(literal 1/2 binary64)))
(.f64 (sqrt.f64 (neg.f64 k)) (sqrt.f64 (/.f64 #s(literal 1 binary64) (.f64 n (neg.f64 (PI.f64))))))
(*.f64 (sqrt.f64 (/.f64 k n)) (pow.f64 (/.f64 #s(literal 1 binary64) (PI.f64)) #s(literal 1/2 binary64)))
(*.f64 (sqrt.f64 (/.f64 k n)) (sqrt.f64 (/.f64 #s(literal 1 binary64) (PI.f64))))
(*.f64 (sqrt.f64 (/.f64 k n)) (/.f64 #s(literal 1 binary64) (sqrt.f64 (PI.f64))))
(.f64 (pow.f64 (/.f64 k (.f64 (PI.f64) n)) #s(literal 1/4 binary64)) (pow.f64 (/.f64 k (*.f64 (PI.f64) n)) #s(literal 1/4 binary64)))
(*.f64 (sqrt.f64 (/.f64 k (PI.f64))) (/.f64 #s(literal 1 binary64) (sqrt.f64 n)))
(.f64 (pow.f64 #s(literal 1 binary64) #s(literal 1/2 binary64)) (sqrt.f64 (/.f64 k (.f64 (PI.f64) n))))
(*.f64 (/.f64 (pow.f64 k #s(literal 1/4 binary64)) (sqrt.f64 n)) (/.f64 (pow.f64 k #s(literal 1/4 binary64)) (sqrt.f64 (PI.f64))))
(*.f64 (/.f64 (pow.f64 k #s(literal 1/4 binary64)) (sqrt.f64 (PI.f64))) (/.f64 (pow.f64 k #s(literal 1/4 binary64)) (sqrt.f64 n)))
(.f64 (/.f64 (sqrt.f64 k) (pow.f64 (.f64 (PI.f64) n) #s(literal 1/4 binary64))) (/.f64 #s(literal 1 binary64) (pow.f64 (*.f64 (PI.f64) n) #s(literal 1/4 binary64))))
(.f64 (/.f64 (pow.f64 k #s(literal 1/4 binary64)) (pow.f64 (.f64 (PI.f64) n) #s(literal 1/4 binary64))) (/.f64 (pow.f64 k #s(literal 1/4 binary64)) (pow.f64 (*.f64 (PI.f64) n) #s(literal 1/4 binary64))))
#s(approx (- -1/2 (* k -1/2)) #s(literal -1/2 binary64))

eval256.0ms (2.2%)

Memory: 35.4MiB live, 374.2MiB allocated
Compiler: Compiled 28 429 to 3 339 computations (88.3% saved)

prune346.0ms (3%)

Memory

6.1MiB live, 503.9MiB allocated

Pruning

58 alts after pruning (56 fresh and 2 done)

	Pruned	Kept	Total
New	1 567	37	1 604
Fresh	6	19	25
Picked	4	1	5
Done	0	1	1
Total	1 577	58	1 635

Accuracy

100.0%

Counts

1 635 → 58

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)) (fma.f64 k #s(literal -1/2 binary64) #s(literal 1/2 binary64))) (sqrt.f64 k))
	49.2%	(/.f64 (pow.f64 (.f64 #s(literal 2 binary64) (.f64 (PI.f64) n)) #s(approx (/ (- 1 k) 2) (*.f64 k #s(literal -1/2 binary64)))) (sqrt.f64 k))
	53.8%	(/.f64 #s(approx (pow (* 2 (* (PI) n)) (- 1/2 (* k 1/2))) (.f64 (sqrt.f64 #s(literal 2 binary64)) (sqrt.f64 (.f64 n (PI.f64))))) (sqrt.f64 k))
	99.4%	(/.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 1/2 binary64))))))
	99.4%	(/.f64 #s(literal 1 binary64) (.f64 (pow.f64 (.f64 #s(literal 2 binary64) (*.f64 (PI.f64) n)) (fma.f64 k #s(literal 1/2 binary64) #s(literal -1/2 binary64))) (sqrt.f64 k)))
	53.7%	(/.f64 #s(literal 1 binary64) (.f64 (sqrt.f64 k) #s(approx (pow ( 2 (* (PI) n)) (- -1/2 (* k -1/2))) (.f64 (sqrt.f64 #s(literal 1/2 binary64)) (sqrt.f64 (/.f64 #s(literal 1 binary64) (.f64 n (PI.f64))))))))
	53.8%	(/.f64 #s(literal 1 binary64) #s(approx (* (sqrt k) (pow (* 2 (* (PI) n)) (- -1/2 (* k -1/2)))) (/.f64 (sqrt.f64 (/.f64 k (*.f64 #s(literal 2 binary64) (PI.f64)))) (sqrt.f64 n))))
	42.5%	(/.f64 #s(literal 1 binary64) #s(approx (* (sqrt k) (pow (* 2 (* (PI) n)) (- -1/2 (* k -1/2)))) (/.f64 (sqrt.f64 (/.f64 k n)) (sqrt.f64 (*.f64 #s(literal 2 binary64) (PI.f64))))))
	42.5%	(/.f64 #s(literal 1 binary64) #s(approx (* (sqrt k) (pow (* 2 (* (PI) n)) (- -1/2 (* k -1/2)))) (/.f64 (sqrt.f64 (*.f64 #s(literal 1/2 binary64) (/.f64 k n))) (sqrt.f64 (PI.f64)))))
	53.9%	(/.f64 #s(literal 1 binary64) #s(approx (* (sqrt k) (pow (* 2 (* (PI) n)) (- -1/2 (* k -1/2)))) (/.f64 (sqrt.f64 (.f64 #s(literal 1/2 binary64) k)) (sqrt.f64 (.f64 (PI.f64) n)))))
	53.8%	(/.f64 #s(literal 1 binary64) #s(approx (* (sqrt k) (pow (* 2 (* (PI) n)) (- -1/2 (* k -1/2)))) (/.f64 (sqrt.f64 k) (sqrt.f64 (.f64 #s(literal 2 binary64) (.f64 (PI.f64) n))))))
	41.3%	(/.f64 #s(literal 1 binary64) #s(approx (* (sqrt k) (pow (* 2 (* (PI) n)) (- -1/2 (* k -1/2)))) (/.f64 (sqrt.f64 #s(literal 1/2 binary64)) (sqrt.f64 (/.f64 (*.f64 (PI.f64) n) k)))))
	53.8%	(/.f64 #s(literal 1 binary64) #s(approx (* (sqrt k) (pow (* 2 (* (PI) n)) (- -1/2 (* k -1/2)))) (/.f64 #s(literal 1 binary64) (/.f64 (sqrt.f64 (.f64 (PI.f64) n)) (sqrt.f64 (.f64 #s(literal 1/2 binary64) k))))))
	41.4%	(/.f64 #s(literal 1 binary64) #s(approx (* (sqrt k) (pow (* 2 (* (PI) n)) (- -1/2 (* k -1/2)))) (/.f64 #s(literal 1 binary64) (sqrt.f64 (.f64 (PI.f64) (.f64 n (/.f64 #s(literal 2 binary64) k)))))))
	53.8%	(/.f64 #s(literal 1 binary64) #s(approx (* (sqrt k) (pow (* 2 (* (PI) n)) (- -1/2 (* k -1/2)))) (.f64 (/.f64 (sqrt.f64 k) (sqrt.f64 #s(literal 2 binary64))) (sqrt.f64 (/.f64 #s(literal 1 binary64) (.f64 (PI.f64) n))))))
	42.3%	(/.f64 #s(literal 1 binary64) #s(approx (* (sqrt k) (pow (* 2 (* (PI) n)) (- -1/2 (* k -1/2)))) (*.f64 (/.f64 (sqrt.f64 #s(literal 1/2 binary64)) (sqrt.f64 (PI.f64))) (sqrt.f64 (/.f64 k n)))))
	53.6%	(/.f64 #s(literal 1 binary64) #s(approx (* (sqrt k) (pow (* 2 (* (PI) n)) (- -1/2 (* k -1/2)))) (*.f64 (/.f64 (sqrt.f64 #s(literal 1/2 binary64)) (sqrt.f64 n)) (sqrt.f64 (/.f64 k (PI.f64))))))
	42.6%	(/.f64 #s(literal 1 binary64) #s(approx (* (sqrt k) (pow (* 2 (* (PI) n)) (- -1/2 (* k -1/2)))) (.f64 (sqrt.f64 (/.f64 k (.f64 (PI.f64) n))) (/.f64 #s(literal 1 binary64) (sqrt.f64 #s(literal 2 binary64))))))
▶	53.8%	(/.f64 #s(literal 1 binary64) #s(approx (* (sqrt k) (pow (* 2 (* (PI) n)) (- -1/2 (* k -1/2)))) (.f64 (sqrt.f64 (.f64 #s(literal 1/2 binary64) k)) (sqrt.f64 (/.f64 #s(literal 1 binary64) (*.f64 (PI.f64) n))))))
	53.6%	(/.f64 #s(literal 1 binary64) #s(approx (* (sqrt k) (pow (* 2 (* (PI) n)) (- -1/2 (* k -1/2)))) (.f64 (sqrt.f64 #s(literal 1/2 binary64)) (/.f64 (sqrt.f64 k) (sqrt.f64 (.f64 (PI.f64) n))))))
	42.4%	(/.f64 #s(literal 1 binary64) #s(approx (* (sqrt k) (pow (* 2 (* (PI) n)) (- -1/2 (* k -1/2)))) (*.f64 (sqrt.f64 #s(literal 1/2 binary64)) (/.f64 #s(literal 1 binary64) (/.f64 (sqrt.f64 (PI.f64)) (sqrt.f64 (/.f64 k n)))))))
▶	53.6%	(/.f64 #s(literal 1 binary64) #s(approx (* (sqrt k) (pow (* 2 (* (PI) n)) (- -1/2 (* k -1/2)))) (.f64 (sqrt.f64 #s(literal 1/2 binary64)) (/.f64 #s(literal 1 binary64) (.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) (sqrt.f64 (*.f64 (PI.f64) n)))))))
	42.4%	(/.f64 #s(literal 1 binary64) #s(approx (* (sqrt k) (pow (* 2 (* (PI) n)) (- -1/2 (* k -1/2)))) (.f64 (sqrt.f64 #s(literal 1/2 binary64)) (sqrt.f64 (/.f64 k (.f64 n (*.f64 (sqrt.f64 (PI.f64)) (sqrt.f64 (PI.f64)))))))))
✓	42.6%	(/.f64 #s(literal 1 binary64) #s(approx (* (sqrt k) (pow (* 2 (* (PI) n)) (- -1/2 (* k -1/2)))) (.f64 (sqrt.f64 #s(literal 1/2 binary64)) (sqrt.f64 (/.f64 k (.f64 n (PI.f64)))))))
	76.8%	(.f64 (pow.f64 (.f64 #s(literal 2 binary64) (.f64 (PI.f64) n)) (.f64 k #s(literal -1/2 binary64))) (sqrt.f64 (/.f64 (.f64 #s(literal 2 binary64) (.f64 (PI.f64) n)) k)))
	53.7%	(.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) #s(approx (pow ( (* 2 (PI)) n) (/ (- 1 k) 2)) (.f64 (sqrt.f64 #s(literal 2 binary64)) (sqrt.f64 (.f64 n (PI.f64))))))
	76.6%	(.f64 (.f64 (sqrt.f64 #s(literal 2 binary64)) (pow.f64 (.f64 #s(literal 2 binary64) (.f64 (PI.f64) n)) (.f64 k #s(literal -1/2 binary64)))) (sqrt.f64 (/.f64 (.f64 (PI.f64) n) k)))
	76.7%	(.f64 (sqrt.f64 (.f64 (PI.f64) (.f64 n (/.f64 #s(literal 2 binary64) k)))) (pow.f64 (.f64 #s(literal 2 binary64) (.f64 (PI.f64) n)) (.f64 k #s(literal -1/2 binary64))))
	76.8%	(sqrt.f64 (/.f64 (/.f64 (.f64 #s(literal 2 binary64) (.f64 (PI.f64) n)) k) (pow.f64 (.f64 #s(literal 2 binary64) (.f64 (PI.f64) n)) k)))
	99.5%	#s(approx (/ (pow (* 2 (* (PI) n)) (- 1/2 (* k 1/2))) (sqrt k)) (.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) k)) (pow.f64 (.f64 n (*.f64 #s(literal 2 binary64) (PI.f64))) (fma.f64 #s(literal -1/2 binary64) k #s(literal 1/2 binary64)))))
	41.3%	#s(approx (/ 1 (* (sqrt k) (pow (* 2 (* (PI) n)) (- -1/2 (* k -1/2))))) (/.f64 (sqrt.f64 (/.f64 (*.f64 n (PI.f64)) k)) (sqrt.f64 #s(literal 1/2 binary64))))
	53.9%	#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (/.f64 (sqrt.f64 (.f64 #s(literal 2 binary64) (.f64 (PI.f64) n))) (sqrt.f64 k)))
	42.7%	#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (/.f64 (sqrt.f64 #s(literal 2 binary64)) (sqrt.f64 (/.f64 k (*.f64 (PI.f64) n)))))
	53.8%	#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (.f64 (/.f64 (sqrt.f64 (.f64 (PI.f64) n)) (sqrt.f64 k)) (sqrt.f64 #s(literal 2 binary64))))
	53.7%	#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (.f64 (/.f64 (sqrt.f64 (.f64 #s(literal 2 binary64) (PI.f64))) (sqrt.f64 k)) (/.f64 (sqrt.f64 n) #s(literal 1 binary64))))
▶	53.9%	#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) (sqrt.f64 (.f64 #s(literal 2 binary64) (*.f64 (PI.f64) n)))))
	53.8%	#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (.f64 (.f64 (sqrt.f64 (/.f64 (PI.f64) k)) (sqrt.f64 n)) (sqrt.f64 #s(literal 2 binary64))))
	53.8%	#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (.f64 (.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) k)) (sqrt.f64 (*.f64 (PI.f64) n))) (sqrt.f64 #s(literal 2 binary64))))
	53.8%	#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (.f64 (.f64 (sqrt.f64 (.f64 n (sqrt.f64 (PI.f64)))) (sqrt.f64 (sqrt.f64 (PI.f64)))) (sqrt.f64 (.f64 (/.f64 #s(literal 1 binary64) k) #s(literal 2 binary64)))))
	41.4%	#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (.f64 (.f64 (sqrt.f64 (PI.f64)) (sqrt.f64 (/.f64 n k))) (sqrt.f64 #s(literal 2 binary64))))
	53.7%	#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (.f64 (.f64 (sqrt.f64 (PI.f64)) (sqrt.f64 n)) (sqrt.f64 (*.f64 (/.f64 #s(literal 1 binary64) k) #s(literal 2 binary64)))))
	41.2%	#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (.f64 (sqrt.f64 (/.f64 (.f64 n (.f64 (sqrt.f64 (.f64 (PI.f64) (sqrt.f64 (PI.f64)))) (sqrt.f64 (sqrt.f64 (PI.f64))))) k)) (sqrt.f64 #s(literal 2 binary64))))
✓	41.4%	#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (.f64 (sqrt.f64 (/.f64 (.f64 n (PI.f64)) k)) (sqrt.f64 #s(literal 2 binary64))))
	53.8%	#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (.f64 (sqrt.f64 (/.f64 #s(literal 2 binary64) k)) (sqrt.f64 (.f64 (PI.f64) n))))
	53.9%	#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (.f64 (sqrt.f64 (.f64 (/.f64 #s(literal 2 binary64) k) (PI.f64))) (sqrt.f64 n)))
	53.8%	#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (.f64 (sqrt.f64 (.f64 (.f64 (sqrt.f64 (.f64 (PI.f64) (sqrt.f64 (PI.f64)))) (sqrt.f64 (sqrt.f64 (PI.f64)))) n)) (sqrt.f64 (*.f64 (/.f64 #s(literal 1 binary64) k) #s(literal 2 binary64)))))
	41.4%	#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (.f64 (sqrt.f64 (.f64 (PI.f64) (/.f64 n k))) (sqrt.f64 #s(literal 2 binary64))))
	53.9%	#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (.f64 (sqrt.f64 (.f64 #s(literal 2 binary64) (*.f64 (PI.f64) n))) (sqrt.f64 (/.f64 #s(literal 1 binary64) k))))
	41.3%	#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (.f64 (sqrt.f64 (.f64 #s(literal 2 binary64) (PI.f64))) (sqrt.f64 (/.f64 n k))))
	41.2%	#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (.f64 (sqrt.f64 (.f64 #s(literal 2 binary64) (PI.f64))) (sqrt.f64 (*.f64 n (/.f64 #s(literal 1 binary64) k)))))
	41.3%	#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (.f64 (sqrt.f64 (PI.f64)) (sqrt.f64 (.f64 n (/.f64 #s(literal 2 binary64) k)))))
	53.9%	#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (.f64 (sqrt.f64 n) (sqrt.f64 (/.f64 (.f64 #s(literal 2 binary64) (PI.f64)) k))))
	41.3%	#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt.f64 (/.f64 (.f64 #s(literal 2 binary64) (.f64 (*.f64 n (sqrt.f64 (PI.f64))) (sqrt.f64 (PI.f64)))) k)))
	41.5%	#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt.f64 (.f64 (/.f64 (.f64 (PI.f64) n) k) #s(literal 2 binary64))))
	41.5%	#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt.f64 (.f64 (.f64 #s(literal 2 binary64) (PI.f64)) (/.f64 n k))))
	41.5%	#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt.f64 (.f64 (PI.f64) (.f64 n (/.f64 #s(literal 2 binary64) k)))))
	41.5%	#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt.f64 (.f64 n (/.f64 (.f64 #s(literal 2 binary64) (PI.f64)) k))))
▶	41.5%	#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt.f64 (.f64 n (.f64 (PI.f64) (/.f64 #s(literal 2 binary64) k)))))

Compiler

Compiled 1 696 to 1 272 computations (25% saved)

simplify115.0ms (1%)

Memory

-21.7MiB live, 48.3MiB allocated

Algorithm

1×	egg-herbie

Localize:

Found 20 expressions of interest:

New	Metric	Score
cost-diff	0	#s(approx (* (sqrt k) (pow (* 2 (* (PI) n)) (- -1/2 (* k -1/2)))) (.f64 (sqrt.f64 #s(literal 1/2 binary64)) (/.f64 #s(literal 1 binary64) (.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) (sqrt.f64 (*.f64 (PI.f64) n))))))
cost-diff	0	(/.f64 #s(literal 1 binary64) #s(approx (* (sqrt k) (pow (* 2 (* (PI) n)) (- -1/2 (* k -1/2)))) (.f64 (sqrt.f64 #s(literal 1/2 binary64)) (/.f64 #s(literal 1 binary64) (.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) (sqrt.f64 (*.f64 (PI.f64) n)))))))
cost-diff	320	(.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) (sqrt.f64 (.f64 (PI.f64) n)))
cost-diff	704	(/.f64 #s(literal 1 binary64) (.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) (sqrt.f64 (.f64 (PI.f64) n))))
cost-diff	0	(sqrt.f64 (*.f64 #s(literal 1/2 binary64) k))
cost-diff	0	(.f64 (sqrt.f64 (.f64 #s(literal 1/2 binary64) k)) (sqrt.f64 (/.f64 #s(literal 1 binary64) (*.f64 (PI.f64) n))))
cost-diff	0	#s(approx (* (sqrt k) (pow (* 2 (* (PI) n)) (- -1/2 (* k -1/2)))) (.f64 (sqrt.f64 (.f64 #s(literal 1/2 binary64) k)) (sqrt.f64 (/.f64 #s(literal 1 binary64) (*.f64 (PI.f64) n)))))
cost-diff	0	(/.f64 #s(literal 1 binary64) #s(approx (* (sqrt k) (pow (* 2 (* (PI) n)) (- -1/2 (* k -1/2)))) (.f64 (sqrt.f64 (.f64 #s(literal 1/2 binary64) k)) (sqrt.f64 (/.f64 #s(literal 1 binary64) (*.f64 (PI.f64) n))))))
cost-diff	0	(sqrt.f64 k)
cost-diff	0	(/.f64 #s(literal 1 binary64) (sqrt.f64 k))
cost-diff	0	#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) (sqrt.f64 (.f64 #s(literal 2 binary64) (*.f64 (PI.f64) n)))))
cost-diff	320	(.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) (sqrt.f64 (.f64 #s(literal 2 binary64) (*.f64 (PI.f64) n))))
cost-diff	0	(*.f64 (PI.f64) (/.f64 #s(literal 2 binary64) k))
cost-diff	0	(.f64 n (.f64 (PI.f64) (/.f64 #s(literal 2 binary64) k)))
cost-diff	0	(sqrt.f64 (.f64 n (.f64 (PI.f64) (/.f64 #s(literal 2 binary64) k))))
cost-diff	0	#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt.f64 (.f64 n (.f64 (PI.f64) (/.f64 #s(literal 2 binary64) k)))))
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)) (fma.f64 k #s(literal -1/2 binary64) #s(literal 1/2 binary64)))
cost-diff	0	(/.f64 (pow.f64 (.f64 #s(literal 2 binary64) (.f64 (PI.f64) n)) (fma.f64 k #s(literal -1/2 binary64) #s(literal 1/2 binary64))) (sqrt.f64 k))

Rules

892×	`lower-*.f32`
874×	`lower-*.f64`
832×	`lower-fma.f32`
830×	`lower-fma.f64`
646×	`associate-r`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	51	364
0	79	364
1	122	338
2	187	338
3	298	336
4	384	336
5	466	336
6	542	336
7	664	336
8	944	336
9	1498	336
10	1896	336
11	2301	336
12	2414	336
13	2446	336
14	2524	336
15	2564	336
16	2564	336
17	2564	336
18	2668	336
19	3329	336
0	3329	332

Stop Event

1×	iter limit
1×	saturated
1×	iter limit

Calls

Call 1

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

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

localize166.0ms (1.4%)

Memory

-1.4MiB live, 264.4MiB allocated

Localize:

Found 20 expressions of interest:

New	Metric	Score
accuracy	0.30697250976844204	(.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) (sqrt.f64 (.f64 (PI.f64) n)))
accuracy	0.3287887695368841	(.f64 (sqrt.f64 #s(literal 1/2 binary64)) (/.f64 #s(literal 1 binary64) (.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) (sqrt.f64 (*.f64 (PI.f64) n)))))
accuracy	14.046533023192913	(PI.f64)
accuracy	15.114254451666671	#s(approx (* (sqrt k) (pow (* 2 (* (PI) n)) (- -1/2 (* k -1/2)))) (.f64 (sqrt.f64 #s(literal 1/2 binary64)) (/.f64 #s(literal 1 binary64) (.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) (sqrt.f64 (*.f64 (PI.f64) n))))))
accuracy	0.2421875	(/.f64 #s(literal 1 binary64) (*.f64 (PI.f64) n))
accuracy	0.32259750976844204	(.f64 (sqrt.f64 (.f64 #s(literal 1/2 binary64) k)) (sqrt.f64 (/.f64 #s(literal 1 binary64) (*.f64 (PI.f64) n))))
accuracy	14.046533023192913	(PI.f64)
accuracy	15.114254451666671	#s(approx (* (sqrt k) (pow (* 2 (* (PI) n)) (- -1/2 (* k -1/2)))) (.f64 (sqrt.f64 (.f64 #s(literal 1/2 binary64) k)) (sqrt.f64 (/.f64 #s(literal 1 binary64) (*.f64 (PI.f64) n)))))
accuracy	0.22265625	(*.f64 (PI.f64) n)
accuracy	0.2421875	(.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) (sqrt.f64 (.f64 #s(literal 2 binary64) (*.f64 (PI.f64) n))))
accuracy	14.046533023192913	(PI.f64)
accuracy	15.11847131460795	#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) (sqrt.f64 (.f64 #s(literal 2 binary64) (*.f64 (PI.f64) n)))))
accuracy	0.29296875	(*.f64 (PI.f64) (/.f64 #s(literal 2 binary64) k))
accuracy	8.107365991328408	(sqrt.f64 (.f64 n (.f64 (PI.f64) (/.f64 #s(literal 2 binary64) k))))
accuracy	14.046533023192913	(PI.f64)
accuracy	15.11847131460795	#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt.f64 (.f64 n (.f64 (PI.f64) (/.f64 #s(literal 2 binary64) k)))))
accuracy	0.171875	(/.f64 (pow.f64 (.f64 #s(literal 2 binary64) (.f64 (PI.f64) n)) (fma.f64 k #s(literal -1/2 binary64) #s(literal 1/2 binary64))) (sqrt.f64 k))
accuracy	0.22265625	(*.f64 (PI.f64) n)
accuracy	0.2240471803363731	(pow.f64 (.f64 #s(literal 2 binary64) (.f64 (PI.f64) n)) (fma.f64 k #s(literal -1/2 binary64) #s(literal 1/2 binary64)))
accuracy	14.046533023192913	(PI.f64)

Samples

72.0ms	198×	0	valid
38.0ms	58×	0	exit

Compiler

Compiled 294 to 43 computations (85.4% saved)

Precisions

Click to see histograms. Total time spent on operations: 68.0ms

ival-mult: 22.0ms (32.2% of total)

ival-div: 15.0ms (22% of total)

ival-pow: 14.0ms (20.5% of total)

ival-sqrt: 11.0ms (16.1% of total)

ival-sub: 2.0ms (2.9% of total)

ival-pi: 1.0ms (1.5% of total)

ival-add: 1.0ms (1.5% of total)

exact: 1.0ms (1.5% of total)

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

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

series35.0ms (0.3%)

Memory

21.6MiB live, 60.1MiB allocated

Counts

23 → 444

Calls

Call 1

Inputs
#s(alt (/.f64 (pow.f64 (.f64 #s(literal 2 binary64) (.f64 (PI.f64) n)) (fma.f64 k #s(literal -1/2 binary64) #s(literal 1/2 binary64))) (sqrt.f64 k)) (patch (/.f64 (pow.f64 (.f64 #s(literal 2 binary64) (.f64 (PI.f64) n)) (fma.f64 k #s(literal -1/2 binary64) #s(literal 1/2 binary64))) (sqrt.f64 k)) #<representation binary64>) () ())
#s(alt (pow.f64 (.f64 #s(literal 2 binary64) (.f64 (PI.f64) n)) (fma.f64 k #s(literal -1/2 binary64) #s(literal 1/2 binary64))) (patch (pow.f64 (.f64 #s(literal 2 binary64) (.f64 (PI.f64) n)) (fma.f64 k #s(literal -1/2 binary64) #s(literal 1/2 binary64))) #<representation binary64>) () ())
#s(alt (.f64 #s(literal 2 binary64) (.f64 (PI.f64) n)) (patch (.f64 #s(literal 2 binary64) (.f64 (PI.f64) n)) #<representation binary64>) () ())
#s(alt (.f64 (PI.f64) n) (patch (.f64 (PI.f64) n) #<representation binary64>) () ())
#s(alt #s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt.f64 (.f64 n (.f64 (PI.f64) (/.f64 #s(literal 2 binary64) k))))) (patch #s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt.f64 (.f64 n (.f64 (PI.f64) (/.f64 #s(literal 2 binary64) k))))) #<representation binary64>) () ())
#s(alt (sqrt.f64 (.f64 n (.f64 (PI.f64) (/.f64 #s(literal 2 binary64) k)))) (patch (sqrt.f64 (.f64 n (.f64 (PI.f64) (/.f64 #s(literal 2 binary64) k)))) #<representation binary64>) () ())
#s(alt (.f64 n (.f64 (PI.f64) (/.f64 #s(literal 2 binary64) k))) (patch (.f64 n (.f64 (PI.f64) (/.f64 #s(literal 2 binary64) k))) #<representation binary64>) () ())
#s(alt (.f64 (PI.f64) (/.f64 #s(literal 2 binary64) k)) (patch (.f64 (PI.f64) (/.f64 #s(literal 2 binary64) k)) #<representation binary64>) () ())
#s(alt (.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) (sqrt.f64 (.f64 #s(literal 2 binary64) (.f64 (PI.f64) n)))) (patch (.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) (sqrt.f64 (.f64 #s(literal 2 binary64) (.f64 (PI.f64) n)))) #<representation binary64>) () ())
#s(alt #s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) (sqrt.f64 (.f64 #s(literal 2 binary64) (.f64 (PI.f64) n))))) (patch #s(approx ( (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) (sqrt.f64 (.f64 #s(literal 2 binary64) (*.f64 (PI.f64) n))))) #<representation binary64>) () ())
#s(alt (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) (patch (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) #<representation binary64>) () ())
#s(alt (sqrt.f64 k) (patch (sqrt.f64 k) #<representation binary64>) () ())
#s(alt (/.f64 #s(literal 1 binary64) #s(approx (* (sqrt k) (pow (* 2 (* (PI) n)) (- -1/2 (* k -1/2)))) (.f64 (sqrt.f64 (.f64 #s(literal 1/2 binary64) k)) (sqrt.f64 (/.f64 #s(literal 1 binary64) (.f64 (PI.f64) n)))))) (patch (/.f64 #s(literal 1 binary64) #s(approx ( (sqrt k) (pow (* 2 (* (PI) n)) (- -1/2 (* k -1/2)))) (.f64 (sqrt.f64 (.f64 #s(literal 1/2 binary64) k)) (sqrt.f64 (/.f64 #s(literal 1 binary64) (*.f64 (PI.f64) n)))))) #<representation binary64>) () ())
#s(alt #s(approx (* (sqrt k) (pow (* 2 (* (PI) n)) (- -1/2 (* k -1/2)))) (.f64 (sqrt.f64 (.f64 #s(literal 1/2 binary64) k)) (sqrt.f64 (/.f64 #s(literal 1 binary64) (.f64 (PI.f64) n))))) (patch #s(approx ( (sqrt k) (pow (* 2 (* (PI) n)) (- -1/2 (* k -1/2)))) (.f64 (sqrt.f64 (.f64 #s(literal 1/2 binary64) k)) (sqrt.f64 (/.f64 #s(literal 1 binary64) (*.f64 (PI.f64) n))))) #<representation binary64>) () ())
#s(alt (.f64 (sqrt.f64 (.f64 #s(literal 1/2 binary64) k)) (sqrt.f64 (/.f64 #s(literal 1 binary64) (.f64 (PI.f64) n)))) (patch (.f64 (sqrt.f64 (.f64 #s(literal 1/2 binary64) k)) (sqrt.f64 (/.f64 #s(literal 1 binary64) (.f64 (PI.f64) n)))) #<representation binary64>) () ())
#s(alt (sqrt.f64 (.f64 #s(literal 1/2 binary64) k)) (patch (sqrt.f64 (.f64 #s(literal 1/2 binary64) k)) #<representation binary64>) () ())
#s(alt (/.f64 #s(literal 1 binary64) (.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) (sqrt.f64 (.f64 (PI.f64) n)))) (patch (/.f64 #s(literal 1 binary64) (.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) (sqrt.f64 (.f64 (PI.f64) n)))) #<representation binary64>) () ())
#s(alt (.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) (sqrt.f64 (.f64 (PI.f64) n))) (patch (.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) (sqrt.f64 (.f64 (PI.f64) n))) #<representation binary64>) () ())
#s(alt (/.f64 #s(literal 1 binary64) #s(approx (* (sqrt k) (pow (* 2 (* (PI) n)) (- -1/2 (* k -1/2)))) (.f64 (sqrt.f64 #s(literal 1/2 binary64)) (/.f64 #s(literal 1 binary64) (.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) (sqrt.f64 (.f64 (PI.f64) n))))))) (patch (/.f64 #s(literal 1 binary64) #s(approx ( (sqrt k) (pow (* 2 (* (PI) n)) (- -1/2 (* k -1/2)))) (.f64 (sqrt.f64 #s(literal 1/2 binary64)) (/.f64 #s(literal 1 binary64) (.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) (sqrt.f64 (*.f64 (PI.f64) n))))))) #<representation binary64>) () ())
#s(alt #s(approx (* (sqrt k) (pow (* 2 (* (PI) n)) (- -1/2 (* k -1/2)))) (.f64 (sqrt.f64 #s(literal 1/2 binary64)) (/.f64 #s(literal 1 binary64) (.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) (sqrt.f64 (.f64 (PI.f64) n)))))) (patch #s(approx ( (sqrt k) (pow (* 2 (* (PI) n)) (- -1/2 (* k -1/2)))) (.f64 (sqrt.f64 #s(literal 1/2 binary64)) (/.f64 #s(literal 1 binary64) (.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) (sqrt.f64 (*.f64 (PI.f64) n)))))) #<representation binary64>) () ())
#s(alt (PI.f64) (patch (PI.f64) #<representation binary64>) () ())
#s(alt (/.f64 #s(literal 1 binary64) (.f64 (PI.f64) n)) (patch (/.f64 #s(literal 1 binary64) (.f64 (PI.f64) n)) #<representation binary64>) () ())
#s(alt (.f64 (sqrt.f64 #s(literal 1/2 binary64)) (/.f64 #s(literal 1 binary64) (.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) (sqrt.f64 (.f64 (PI.f64) n))))) (patch (.f64 (sqrt.f64 #s(literal 1/2 binary64)) (/.f64 #s(literal 1 binary64) (.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) (sqrt.f64 (.f64 (PI.f64) n))))) #<representation binary64>) () ())

Outputs
#s(alt (* (sqrt (/ 1 k)) (exp (* (+ 1/2 (* -1/2 k)) (+ (log n) (log (* 2 (PI))))))) (taylor 0 n) (#s(alt (/.f64 (pow.f64 (.f64 #s(literal 2 binary64) (.f64 (PI.f64) n)) (fma.f64 k #s(literal -1/2 binary64) #s(literal 1/2 binary64))) (sqrt.f64 k)) (patch (/.f64 (pow.f64 (.f64 #s(literal 2 binary64) (.f64 (PI.f64) n)) (fma.f64 k #s(literal -1/2 binary64) #s(literal 1/2 binary64))) (sqrt.f64 k)) #<representation binary64>) () ())) ())
#s(alt (* (sqrt (/ 1 k)) (exp (* (+ 1/2 (* -1/2 k)) (+ (log n) (log (* 2 (PI))))))) (taylor 0 n) (#s(alt (/.f64 (pow.f64 (.f64 #s(literal 2 binary64) (.f64 (PI.f64) n)) (fma.f64 k #s(literal -1/2 binary64) #s(literal 1/2 binary64))) (sqrt.f64 k)) (patch (/.f64 (pow.f64 (.f64 #s(literal 2 binary64) (.f64 (PI.f64) n)) (fma.f64 k #s(literal -1/2 binary64) #s(literal 1/2 binary64))) (sqrt.f64 k)) #<representation binary64>) () ())) ())
#s(alt (* (sqrt (/ 1 k)) (exp (* (+ 1/2 (* -1/2 k)) (+ (log n) (log (* 2 (PI))))))) (taylor 0 n) (#s(alt (/.f64 (pow.f64 (.f64 #s(literal 2 binary64) (.f64 (PI.f64) n)) (fma.f64 k #s(literal -1/2 binary64) #s(literal 1/2 binary64))) (sqrt.f64 k)) (patch (/.f64 (pow.f64 (.f64 #s(literal 2 binary64) (.f64 (PI.f64) n)) (fma.f64 k #s(literal -1/2 binary64) #s(literal 1/2 binary64))) (sqrt.f64 k)) #<representation binary64>) () ())) ())
#s(alt (* (sqrt (/ 1 k)) (exp (* (+ 1/2 (* -1/2 k)) (+ (log n) (log (* 2 (PI))))))) (taylor 0 n) (#s(alt (/.f64 (pow.f64 (.f64 #s(literal 2 binary64) (.f64 (PI.f64) n)) (fma.f64 k #s(literal -1/2 binary64) #s(literal 1/2 binary64))) (sqrt.f64 k)) (patch (/.f64 (pow.f64 (.f64 #s(literal 2 binary64) (.f64 (PI.f64) n)) (fma.f64 k #s(literal -1/2 binary64) #s(literal 1/2 binary64))) (sqrt.f64 k)) #<representation binary64>) () ())) ())
#s(alt (* (sqrt (/ 1 k)) (exp (* (+ 1/2 (* -1/2 k)) (+ (log (* 2 (PI))) (* -1 (log (/ 1 n))))))) (taylor inf n) (#s(alt (/.f64 (pow.f64 (.f64 #s(literal 2 binary64) (.f64 (PI.f64) n)) (fma.f64 k #s(literal -1/2 binary64) #s(literal 1/2 binary64))) (sqrt.f64 k)) (patch (/.f64 (pow.f64 (.f64 #s(literal 2 binary64) (.f64 (PI.f64) n)) (fma.f64 k #s(literal -1/2 binary64) #s(literal 1/2 binary64))) (sqrt.f64 k)) #<representation binary64>) () ())) ())
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#s(alt (* (sqrt (/ 1 k)) (exp (* (+ 1/2 (* -1/2 k)) (+ (log (* 2 (PI))) (* -1 (log (/ 1 n))))))) (taylor inf n) (#s(alt (/.f64 (pow.f64 (.f64 #s(literal 2 binary64) (.f64 (PI.f64) n)) (fma.f64 k #s(literal -1/2 binary64) #s(literal 1/2 binary64))) (sqrt.f64 k)) (patch (/.f64 (pow.f64 (.f64 #s(literal 2 binary64) (.f64 (PI.f64) n)) (fma.f64 k #s(literal -1/2 binary64) #s(literal 1/2 binary64))) (sqrt.f64 k)) #<representation binary64>) () ())) ())
#s(alt (* (sqrt (/ 1 k)) (exp (* (+ 1/2 (* -1/2 k)) (+ (log (* 2 (PI))) (* -1 (log (/ 1 n))))))) (taylor inf n) (#s(alt (/.f64 (pow.f64 (.f64 #s(literal 2 binary64) (.f64 (PI.f64) n)) (fma.f64 k #s(literal -1/2 binary64) #s(literal 1/2 binary64))) (sqrt.f64 k)) (patch (/.f64 (pow.f64 (.f64 #s(literal 2 binary64) (.f64 (PI.f64) n)) (fma.f64 k #s(literal -1/2 binary64) #s(literal 1/2 binary64))) (sqrt.f64 k)) #<representation binary64>) () ())) ())
#s(alt (* (sqrt (/ 1 k)) (exp (* (+ 1/2 (* -1/2 k)) (+ (log (* -2 (PI))) (* -1 (log (/ -1 n))))))) (taylor -inf n) (#s(alt (/.f64 (pow.f64 (.f64 #s(literal 2 binary64) (.f64 (PI.f64) n)) (fma.f64 k #s(literal -1/2 binary64) #s(literal 1/2 binary64))) (sqrt.f64 k)) (patch (/.f64 (pow.f64 (.f64 #s(literal 2 binary64) (.f64 (PI.f64) n)) (fma.f64 k #s(literal -1/2 binary64) #s(literal 1/2 binary64))) (sqrt.f64 k)) #<representation binary64>) () ())) ())
#s(alt (* (sqrt (/ 1 k)) (exp (* (+ 1/2 (* -1/2 k)) (+ (log (* -2 (PI))) (* -1 (log (/ -1 n))))))) (taylor -inf n) (#s(alt (/.f64 (pow.f64 (.f64 #s(literal 2 binary64) (.f64 (PI.f64) n)) (fma.f64 k #s(literal -1/2 binary64) #s(literal 1/2 binary64))) (sqrt.f64 k)) (patch (/.f64 (pow.f64 (.f64 #s(literal 2 binary64) (.f64 (PI.f64) n)) (fma.f64 k #s(literal -1/2 binary64) #s(literal 1/2 binary64))) (sqrt.f64 k)) #<representation binary64>) () ())) ())
#s(alt (* (sqrt (/ 1 k)) (exp (* (+ 1/2 (* -1/2 k)) (+ (log (* -2 (PI))) (* -1 (log (/ -1 n))))))) (taylor -inf n) (#s(alt (/.f64 (pow.f64 (.f64 #s(literal 2 binary64) (.f64 (PI.f64) n)) (fma.f64 k #s(literal -1/2 binary64) #s(literal 1/2 binary64))) (sqrt.f64 k)) (patch (/.f64 (pow.f64 (.f64 #s(literal 2 binary64) (.f64 (PI.f64) n)) (fma.f64 k #s(literal -1/2 binary64) #s(literal 1/2 binary64))) (sqrt.f64 k)) #<representation binary64>) () ())) ())
#s(alt (* (sqrt (/ 1 k)) (exp (* (+ 1/2 (* -1/2 k)) (+ (log (* -2 (PI))) (* -1 (log (/ -1 n))))))) (taylor -inf n) (#s(alt (/.f64 (pow.f64 (.f64 #s(literal 2 binary64) (.f64 (PI.f64) n)) (fma.f64 k #s(literal -1/2 binary64) #s(literal 1/2 binary64))) (sqrt.f64 k)) (patch (/.f64 (pow.f64 (.f64 #s(literal 2 binary64) (.f64 (PI.f64) n)) (fma.f64 k #s(literal -1/2 binary64) #s(literal 1/2 binary64))) (sqrt.f64 k)) #<representation binary64>) () ())) ())
#s(alt (* (sqrt (/ (* n (PI)) k)) (sqrt 2)) (taylor 0 k) (#s(alt (/.f64 (pow.f64 (.f64 #s(literal 2 binary64) (.f64 (PI.f64) n)) (fma.f64 k #s(literal -1/2 binary64) #s(literal 1/2 binary64))) (sqrt.f64 k)) (patch (/.f64 (pow.f64 (.f64 #s(literal 2 binary64) (.f64 (PI.f64) n)) (fma.f64 k #s(literal -1/2 binary64) #s(literal 1/2 binary64))) (sqrt.f64 k)) #<representation binary64>) () ())) ())
#s(alt (/ (+ (* -1/2 (* (sqrt (* (pow k 3) (* n (PI)))) (* (log (* 2 (* n (PI)))) (sqrt 2)))) (* (sqrt (* k (* n (PI)))) (sqrt 2))) k) (taylor 0 k) (#s(alt (/.f64 (pow.f64 (.f64 #s(literal 2 binary64) (.f64 (PI.f64) n)) (fma.f64 k #s(literal -1/2 binary64) #s(literal 1/2 binary64))) (sqrt.f64 k)) (patch (/.f64 (pow.f64 (.f64 #s(literal 2 binary64) (.f64 (PI.f64) n)) (fma.f64 k #s(literal -1/2 binary64) #s(literal 1/2 binary64))) (sqrt.f64 k)) #<representation binary64>) () ())) ())
#s(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) (taylor 0 k) (#s(alt (/.f64 (pow.f64 (.f64 #s(literal 2 binary64) (.f64 (PI.f64) n)) (fma.f64 k #s(literal -1/2 binary64) #s(literal 1/2 binary64))) (sqrt.f64 k)) (patch (/.f64 (pow.f64 (.f64 #s(literal 2 binary64) (.f64 (PI.f64) n)) (fma.f64 k #s(literal -1/2 binary64) #s(literal 1/2 binary64))) (sqrt.f64 k)) #<representation binary64>) () ())) ())
#s(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) (taylor 0 k) (#s(alt (/.f64 (pow.f64 (.f64 #s(literal 2 binary64) (.f64 (PI.f64) n)) (fma.f64 k #s(literal -1/2 binary64) #s(literal 1/2 binary64))) (sqrt.f64 k)) (patch (/.f64 (pow.f64 (.f64 #s(literal 2 binary64) (.f64 (PI.f64) n)) (fma.f64 k #s(literal -1/2 binary64) #s(literal 1/2 binary64))) (sqrt.f64 k)) #<representation binary64>) () ())) ())
#s(alt (* (sqrt (/ 1 k)) (exp (* (log (* 2 (* n (PI)))) (- 1/2 (* 1/2 k))))) (taylor inf k) (#s(alt (/.f64 (pow.f64 (.f64 #s(literal 2 binary64) (.f64 (PI.f64) n)) (fma.f64 k #s(literal -1/2 binary64) #s(literal 1/2 binary64))) (sqrt.f64 k)) (patch (/.f64 (pow.f64 (.f64 #s(literal 2 binary64) (.f64 (PI.f64) n)) (fma.f64 k #s(literal -1/2 binary64) #s(literal 1/2 binary64))) (sqrt.f64 k)) #<representation binary64>) () ())) ())
#s(alt (* (sqrt (/ 1 k)) (exp (* (log (* 2 (* n (PI)))) (- 1/2 (* 1/2 k))))) (taylor inf k) (#s(alt (/.f64 (pow.f64 (.f64 #s(literal 2 binary64) (.f64 (PI.f64) n)) (fma.f64 k #s(literal -1/2 binary64) #s(literal 1/2 binary64))) (sqrt.f64 k)) (patch (/.f64 (pow.f64 (.f64 #s(literal 2 binary64) (.f64 (PI.f64) n)) (fma.f64 k #s(literal -1/2 binary64) #s(literal 1/2 binary64))) (sqrt.f64 k)) #<representation binary64>) () ())) ())
#s(alt (* (sqrt (/ 1 k)) (exp (* (log (* 2 (* n (PI)))) (- 1/2 (* 1/2 k))))) (taylor inf k) (#s(alt (/.f64 (pow.f64 (.f64 #s(literal 2 binary64) (.f64 (PI.f64) n)) (fma.f64 k #s(literal -1/2 binary64) #s(literal 1/2 binary64))) (sqrt.f64 k)) (patch (/.f64 (pow.f64 (.f64 #s(literal 2 binary64) (.f64 (PI.f64) n)) (fma.f64 k #s(literal -1/2 binary64) #s(literal 1/2 binary64))) (sqrt.f64 k)) #<representation binary64>) () ())) ())
#s(alt (* (sqrt (/ 1 k)) (exp (* (log (* 2 (* n (PI)))) (- 1/2 (* 1/2 k))))) (taylor inf k) (#s(alt (/.f64 (pow.f64 (.f64 #s(literal 2 binary64) (.f64 (PI.f64) n)) (fma.f64 k #s(literal -1/2 binary64) #s(literal 1/2 binary64))) (sqrt.f64 k)) (patch (/.f64 (pow.f64 (.f64 #s(literal 2 binary64) (.f64 (PI.f64) n)) (fma.f64 k #s(literal -1/2 binary64) #s(literal 1/2 binary64))) (sqrt.f64 k)) #<representation binary64>) () ())) ())
#s(alt (* (sqrt (/ 1 k)) (exp (* (log (* 2 (* n (PI)))) (+ 1/2 (* -1/2 k))))) (taylor -inf k) (#s(alt (/.f64 (pow.f64 (.f64 #s(literal 2 binary64) (.f64 (PI.f64) n)) (fma.f64 k #s(literal -1/2 binary64) #s(literal 1/2 binary64))) (sqrt.f64 k)) (patch (/.f64 (pow.f64 (.f64 #s(literal 2 binary64) (.f64 (PI.f64) n)) (fma.f64 k #s(literal -1/2 binary64) #s(literal 1/2 binary64))) (sqrt.f64 k)) #<representation binary64>) () ())) ())
#s(alt (* (sqrt (/ 1 k)) (exp (* (log (* 2 (* n (PI)))) (+ 1/2 (* -1/2 k))))) (taylor -inf k) (#s(alt (/.f64 (pow.f64 (.f64 #s(literal 2 binary64) (.f64 (PI.f64) n)) (fma.f64 k #s(literal -1/2 binary64) #s(literal 1/2 binary64))) (sqrt.f64 k)) (patch (/.f64 (pow.f64 (.f64 #s(literal 2 binary64) (.f64 (PI.f64) n)) (fma.f64 k #s(literal -1/2 binary64) #s(literal 1/2 binary64))) (sqrt.f64 k)) #<representation binary64>) () ())) ())
#s(alt (* (sqrt (/ 1 k)) (exp (* (log (* 2 (* n (PI)))) (+ 1/2 (* -1/2 k))))) (taylor -inf k) (#s(alt (/.f64 (pow.f64 (.f64 #s(literal 2 binary64) (.f64 (PI.f64) n)) (fma.f64 k #s(literal -1/2 binary64) #s(literal 1/2 binary64))) (sqrt.f64 k)) (patch (/.f64 (pow.f64 (.f64 #s(literal 2 binary64) (.f64 (PI.f64) n)) (fma.f64 k #s(literal -1/2 binary64) #s(literal 1/2 binary64))) (sqrt.f64 k)) #<representation binary64>) () ())) ())
#s(alt (* (sqrt (/ 1 k)) (exp (* (log (* 2 (* n (PI)))) (+ 1/2 (* -1/2 k))))) (taylor -inf k) (#s(alt (/.f64 (pow.f64 (.f64 #s(literal 2 binary64) (.f64 (PI.f64) n)) (fma.f64 k #s(literal -1/2 binary64) #s(literal 1/2 binary64))) (sqrt.f64 k)) (patch (/.f64 (pow.f64 (.f64 #s(literal 2 binary64) (.f64 (PI.f64) n)) (fma.f64 k #s(literal -1/2 binary64) #s(literal 1/2 binary64))) (sqrt.f64 k)) #<representation binary64>) () ())) ())
#s(alt (exp (* (+ 1/2 (* -1/2 k)) (+ (log n) (log (* 2 (PI)))))) (taylor 0 n) (#s(alt (pow.f64 (.f64 #s(literal 2 binary64) (.f64 (PI.f64) n)) (fma.f64 k #s(literal -1/2 binary64) #s(literal 1/2 binary64))) (patch (pow.f64 (.f64 #s(literal 2 binary64) (.f64 (PI.f64) n)) (fma.f64 k #s(literal -1/2 binary64) #s(literal 1/2 binary64))) #<representation binary64>) () ())) ())
#s(alt (exp (* (+ 1/2 (* -1/2 k)) (+ (log n) (log (* 2 (PI)))))) (taylor 0 n) (#s(alt (pow.f64 (.f64 #s(literal 2 binary64) (.f64 (PI.f64) n)) (fma.f64 k #s(literal -1/2 binary64) #s(literal 1/2 binary64))) (patch (pow.f64 (.f64 #s(literal 2 binary64) (.f64 (PI.f64) n)) (fma.f64 k #s(literal -1/2 binary64) #s(literal 1/2 binary64))) #<representation binary64>) () ())) ())
#s(alt (exp (* (+ 1/2 (* -1/2 k)) (+ (log n) (log (* 2 (PI)))))) (taylor 0 n) (#s(alt (pow.f64 (.f64 #s(literal 2 binary64) (.f64 (PI.f64) n)) (fma.f64 k #s(literal -1/2 binary64) #s(literal 1/2 binary64))) (patch (pow.f64 (.f64 #s(literal 2 binary64) (.f64 (PI.f64) n)) (fma.f64 k #s(literal -1/2 binary64) #s(literal 1/2 binary64))) #<representation binary64>) () ())) ())
#s(alt (exp (* (+ 1/2 (* -1/2 k)) (+ (log n) (log (* 2 (PI)))))) (taylor 0 n) (#s(alt (pow.f64 (.f64 #s(literal 2 binary64) (.f64 (PI.f64) n)) (fma.f64 k #s(literal -1/2 binary64) #s(literal 1/2 binary64))) (patch (pow.f64 (.f64 #s(literal 2 binary64) (.f64 (PI.f64) n)) (fma.f64 k #s(literal -1/2 binary64) #s(literal 1/2 binary64))) #<representation binary64>) () ())) ())
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#s(alt (* (sqrt (/ k (* n (PI)))) (sqrt 1/2)) (taylor 0 k) (#s(alt (.f64 (sqrt.f64 #s(literal 1/2 binary64)) (/.f64 #s(literal 1 binary64) (.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) (sqrt.f64 (.f64 (PI.f64) n))))) (patch (.f64 (sqrt.f64 #s(literal 1/2 binary64)) (/.f64 #s(literal 1 binary64) (.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) (sqrt.f64 (.f64 (PI.f64) n))))) #<representation binary64>) () ())) ())
#s(alt (* (sqrt (/ k (* n (PI)))) (sqrt 1/2)) (taylor 0 k) (#s(alt (.f64 (sqrt.f64 #s(literal 1/2 binary64)) (/.f64 #s(literal 1 binary64) (.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) (sqrt.f64 (.f64 (PI.f64) n))))) (patch (.f64 (sqrt.f64 #s(literal 1/2 binary64)) (/.f64 #s(literal 1 binary64) (.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) (sqrt.f64 (.f64 (PI.f64) n))))) #<representation binary64>) () ())) ())
#s(alt (* (sqrt (/ k (* n (PI)))) (sqrt 1/2)) (taylor 0 k) (#s(alt (.f64 (sqrt.f64 #s(literal 1/2 binary64)) (/.f64 #s(literal 1 binary64) (.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) (sqrt.f64 (.f64 (PI.f64) n))))) (patch (.f64 (sqrt.f64 #s(literal 1/2 binary64)) (/.f64 #s(literal 1 binary64) (.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) (sqrt.f64 (.f64 (PI.f64) n))))) #<representation binary64>) () ())) ())
#s(alt (* (sqrt (/ k (* n (PI)))) (sqrt 1/2)) (taylor inf k) (#s(alt (.f64 (sqrt.f64 #s(literal 1/2 binary64)) (/.f64 #s(literal 1 binary64) (.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) (sqrt.f64 (.f64 (PI.f64) n))))) (patch (.f64 (sqrt.f64 #s(literal 1/2 binary64)) (/.f64 #s(literal 1 binary64) (.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) (sqrt.f64 (.f64 (PI.f64) n))))) #<representation binary64>) () ())) ())
#s(alt (* (sqrt (/ k (* n (PI)))) (sqrt 1/2)) (taylor inf k) (#s(alt (.f64 (sqrt.f64 #s(literal 1/2 binary64)) (/.f64 #s(literal 1 binary64) (.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) (sqrt.f64 (.f64 (PI.f64) n))))) (patch (.f64 (sqrt.f64 #s(literal 1/2 binary64)) (/.f64 #s(literal 1 binary64) (.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) (sqrt.f64 (.f64 (PI.f64) n))))) #<representation binary64>) () ())) ())
#s(alt (* (sqrt (/ k (* n (PI)))) (sqrt 1/2)) (taylor inf k) (#s(alt (.f64 (sqrt.f64 #s(literal 1/2 binary64)) (/.f64 #s(literal 1 binary64) (.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) (sqrt.f64 (.f64 (PI.f64) n))))) (patch (.f64 (sqrt.f64 #s(literal 1/2 binary64)) (/.f64 #s(literal 1 binary64) (.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) (sqrt.f64 (.f64 (PI.f64) n))))) #<representation binary64>) () ())) ())
#s(alt (* (sqrt (/ k (* n (PI)))) (sqrt 1/2)) (taylor inf k) (#s(alt (.f64 (sqrt.f64 #s(literal 1/2 binary64)) (/.f64 #s(literal 1 binary64) (.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) (sqrt.f64 (.f64 (PI.f64) n))))) (patch (.f64 (sqrt.f64 #s(literal 1/2 binary64)) (/.f64 #s(literal 1 binary64) (.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) (sqrt.f64 (.f64 (PI.f64) n))))) #<representation binary64>) () ())) ())
#s(alt (* -1 (* (sqrt (/ k (* n (PI)))) (* (pow (sqrt -1) 2) (sqrt 1/2)))) (taylor -inf k) (#s(alt (.f64 (sqrt.f64 #s(literal 1/2 binary64)) (/.f64 #s(literal 1 binary64) (.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) (sqrt.f64 (.f64 (PI.f64) n))))) (patch (.f64 (sqrt.f64 #s(literal 1/2 binary64)) (/.f64 #s(literal 1 binary64) (.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) (sqrt.f64 (.f64 (PI.f64) n))))) #<representation binary64>) () ())) ())
#s(alt (* -1 (* (sqrt (/ k (* n (PI)))) (* (pow (sqrt -1) 2) (sqrt 1/2)))) (taylor -inf k) (#s(alt (.f64 (sqrt.f64 #s(literal 1/2 binary64)) (/.f64 #s(literal 1 binary64) (.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) (sqrt.f64 (.f64 (PI.f64) n))))) (patch (.f64 (sqrt.f64 #s(literal 1/2 binary64)) (/.f64 #s(literal 1 binary64) (.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) (sqrt.f64 (.f64 (PI.f64) n))))) #<representation binary64>) () ())) ())
#s(alt (* -1 (* (sqrt (/ k (* n (PI)))) (* (pow (sqrt -1) 2) (sqrt 1/2)))) (taylor -inf k) (#s(alt (.f64 (sqrt.f64 #s(literal 1/2 binary64)) (/.f64 #s(literal 1 binary64) (.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) (sqrt.f64 (.f64 (PI.f64) n))))) (patch (.f64 (sqrt.f64 #s(literal 1/2 binary64)) (/.f64 #s(literal 1 binary64) (.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) (sqrt.f64 (.f64 (PI.f64) n))))) #<representation binary64>) () ())) ())
#s(alt (* -1 (* (sqrt (/ k (* n (PI)))) (* (pow (sqrt -1) 2) (sqrt 1/2)))) (taylor -inf k) (#s(alt (.f64 (sqrt.f64 #s(literal 1/2 binary64)) (/.f64 #s(literal 1 binary64) (.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) (sqrt.f64 (.f64 (PI.f64) n))))) (patch (.f64 (sqrt.f64 #s(literal 1/2 binary64)) (/.f64 #s(literal 1 binary64) (.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) (sqrt.f64 (.f64 (PI.f64) n))))) #<representation binary64>) () ())) ())
#s(alt (* (sqrt (/ k (* n (PI)))) (sqrt 1/2)) (taylor 0 n) (#s(alt (.f64 (sqrt.f64 #s(literal 1/2 binary64)) (/.f64 #s(literal 1 binary64) (.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) (sqrt.f64 (.f64 (PI.f64) n))))) (patch (.f64 (sqrt.f64 #s(literal 1/2 binary64)) (/.f64 #s(literal 1 binary64) (.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) (sqrt.f64 (.f64 (PI.f64) n))))) #<representation binary64>) () ())) ())
#s(alt (* (sqrt (/ k (* n (PI)))) (sqrt 1/2)) (taylor 0 n) (#s(alt (.f64 (sqrt.f64 #s(literal 1/2 binary64)) (/.f64 #s(literal 1 binary64) (.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) (sqrt.f64 (.f64 (PI.f64) n))))) (patch (.f64 (sqrt.f64 #s(literal 1/2 binary64)) (/.f64 #s(literal 1 binary64) (.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) (sqrt.f64 (.f64 (PI.f64) n))))) #<representation binary64>) () ())) ())
#s(alt (* (sqrt (/ k (* n (PI)))) (sqrt 1/2)) (taylor 0 n) (#s(alt (.f64 (sqrt.f64 #s(literal 1/2 binary64)) (/.f64 #s(literal 1 binary64) (.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) (sqrt.f64 (.f64 (PI.f64) n))))) (patch (.f64 (sqrt.f64 #s(literal 1/2 binary64)) (/.f64 #s(literal 1 binary64) (.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) (sqrt.f64 (.f64 (PI.f64) n))))) #<representation binary64>) () ())) ())
#s(alt (* (sqrt (/ k (* n (PI)))) (sqrt 1/2)) (taylor 0 n) (#s(alt (.f64 (sqrt.f64 #s(literal 1/2 binary64)) (/.f64 #s(literal 1 binary64) (.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) (sqrt.f64 (.f64 (PI.f64) n))))) (patch (.f64 (sqrt.f64 #s(literal 1/2 binary64)) (/.f64 #s(literal 1 binary64) (.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) (sqrt.f64 (.f64 (PI.f64) n))))) #<representation binary64>) () ())) ())
#s(alt (* (sqrt (/ k (* n (PI)))) (sqrt 1/2)) (taylor inf n) (#s(alt (.f64 (sqrt.f64 #s(literal 1/2 binary64)) (/.f64 #s(literal 1 binary64) (.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) (sqrt.f64 (.f64 (PI.f64) n))))) (patch (.f64 (sqrt.f64 #s(literal 1/2 binary64)) (/.f64 #s(literal 1 binary64) (.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) (sqrt.f64 (.f64 (PI.f64) n))))) #<representation binary64>) () ())) ())
#s(alt (* (sqrt (/ k (* n (PI)))) (sqrt 1/2)) (taylor inf n) (#s(alt (.f64 (sqrt.f64 #s(literal 1/2 binary64)) (/.f64 #s(literal 1 binary64) (.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) (sqrt.f64 (.f64 (PI.f64) n))))) (patch (.f64 (sqrt.f64 #s(literal 1/2 binary64)) (/.f64 #s(literal 1 binary64) (.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) (sqrt.f64 (.f64 (PI.f64) n))))) #<representation binary64>) () ())) ())
#s(alt (* (sqrt (/ k (* n (PI)))) (sqrt 1/2)) (taylor inf n) (#s(alt (.f64 (sqrt.f64 #s(literal 1/2 binary64)) (/.f64 #s(literal 1 binary64) (.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) (sqrt.f64 (.f64 (PI.f64) n))))) (patch (.f64 (sqrt.f64 #s(literal 1/2 binary64)) (/.f64 #s(literal 1 binary64) (.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) (sqrt.f64 (.f64 (PI.f64) n))))) #<representation binary64>) () ())) ())
#s(alt (* (sqrt (/ k (* n (PI)))) (sqrt 1/2)) (taylor inf n) (#s(alt (.f64 (sqrt.f64 #s(literal 1/2 binary64)) (/.f64 #s(literal 1 binary64) (.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) (sqrt.f64 (.f64 (PI.f64) n))))) (patch (.f64 (sqrt.f64 #s(literal 1/2 binary64)) (/.f64 #s(literal 1 binary64) (.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) (sqrt.f64 (.f64 (PI.f64) n))))) #<representation binary64>) () ())) ())
#s(alt (* (sqrt (/ k (* n (PI)))) (sqrt 1/2)) (taylor -inf n) (#s(alt (.f64 (sqrt.f64 #s(literal 1/2 binary64)) (/.f64 #s(literal 1 binary64) (.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) (sqrt.f64 (.f64 (PI.f64) n))))) (patch (.f64 (sqrt.f64 #s(literal 1/2 binary64)) (/.f64 #s(literal 1 binary64) (.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) (sqrt.f64 (.f64 (PI.f64) n))))) #<representation binary64>) () ())) ())
#s(alt (* (sqrt (/ k (* n (PI)))) (sqrt 1/2)) (taylor -inf n) (#s(alt (.f64 (sqrt.f64 #s(literal 1/2 binary64)) (/.f64 #s(literal 1 binary64) (.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) (sqrt.f64 (.f64 (PI.f64) n))))) (patch (.f64 (sqrt.f64 #s(literal 1/2 binary64)) (/.f64 #s(literal 1 binary64) (.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) (sqrt.f64 (.f64 (PI.f64) n))))) #<representation binary64>) () ())) ())
#s(alt (* (sqrt (/ k (* n (PI)))) (sqrt 1/2)) (taylor -inf n) (#s(alt (.f64 (sqrt.f64 #s(literal 1/2 binary64)) (/.f64 #s(literal 1 binary64) (.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) (sqrt.f64 (.f64 (PI.f64) n))))) (patch (.f64 (sqrt.f64 #s(literal 1/2 binary64)) (/.f64 #s(literal 1 binary64) (.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) (sqrt.f64 (.f64 (PI.f64) n))))) #<representation binary64>) () ())) ())
#s(alt (* (sqrt (/ k (* n (PI)))) (sqrt 1/2)) (taylor -inf n) (#s(alt (.f64 (sqrt.f64 #s(literal 1/2 binary64)) (/.f64 #s(literal 1 binary64) (.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) (sqrt.f64 (.f64 (PI.f64) n))))) (patch (.f64 (sqrt.f64 #s(literal 1/2 binary64)) (/.f64 #s(literal 1 binary64) (.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) (sqrt.f64 (.f64 (PI.f64) n))))) #<representation binary64>) () ())) ())

Calls

111 calls:

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

simplify288.0ms (2.5%)

Memory

-20.3MiB live, 460.7MiB allocated

Algorithm

1×	egg-herbie

Rules

7 428×	`lower-fma.f64`
7 428×	`lower-fma.f32`
6 500×	`lower-*.f64`
6 500×	`lower-*.f32`
2 968×	`lower-+.f64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	260	6286
1	774	6087
2	2654	5749
3	6000	5363
0	8195	5309

Stop Event

1×	iter limit
1×	node limit

Counts

444 → 444

Calls

Call 1

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

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

rewrite266.0ms (2.3%)

Memory

56.5MiB live, 458.2MiB allocated

Rules

5 306×	`lower-*.f32`
5 288×	`lower-*.f64`
4 138×	`lower-/.f32`
4 126×	`lower-/.f64`
2 160×	`lower-pow.f32`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	51	290
0	79	269
1	274	246
2	1517	242
0	8284	238

Stop Event

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

Counts

23 → 1 106

Calls

Call 1

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

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

eval278.0ms (2.4%)

Memory: 5.7MiB live, 524.8MiB allocated
Compiler: Compiled 32 288 to 4 053 computations (87.4% saved)

prune537.0ms (4.6%)

Memory

-6.4MiB live, 677.8MiB allocated

Pruning

79 alts after pruning (72 fresh and 7 done)

	Pruned	Kept	Total
New	1 918	31	1 949
Fresh	10	41	51
Picked	0	5	5
Done	0	2	2
Total	1 928	79	2 007

Accuracy

100.0%

Counts

2 007 → 79

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)) (fma.f64 k #s(literal -1/2 binary64) #s(literal 1/2 binary64))) (sqrt.f64 k))
	49.2%	(/.f64 (pow.f64 (.f64 #s(literal 2 binary64) (.f64 (PI.f64) n)) #s(approx (/ (- 1 k) 2) (*.f64 k #s(literal -1/2 binary64)))) (sqrt.f64 k))
	53.8%	(/.f64 #s(approx (pow (* 2 (* (PI) n)) (- 1/2 (* k 1/2))) (.f64 (sqrt.f64 #s(literal 2 binary64)) (sqrt.f64 (.f64 n (PI.f64))))) (sqrt.f64 k))
	99.4%	(/.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 1/2 binary64))))))
	99.4%	(/.f64 #s(literal 1 binary64) (.f64 (pow.f64 (.f64 #s(literal 2 binary64) (*.f64 (PI.f64) n)) (fma.f64 k #s(literal 1/2 binary64) #s(literal -1/2 binary64))) (sqrt.f64 k)))
	53.8%	(/.f64 #s(literal 1 binary64) #s(approx (* (sqrt k) (pow (* 2 (* (PI) n)) (- -1/2 (* k -1/2)))) (/.f64 (sqrt.f64 (/.f64 k (*.f64 #s(literal 2 binary64) (PI.f64)))) (sqrt.f64 n))))
	42.5%	(/.f64 #s(literal 1 binary64) #s(approx (* (sqrt k) (pow (* 2 (* (PI) n)) (- -1/2 (* k -1/2)))) (/.f64 (sqrt.f64 (/.f64 k n)) (sqrt.f64 (*.f64 #s(literal 2 binary64) (PI.f64))))))
	53.9%	(/.f64 #s(literal 1 binary64) #s(approx (* (sqrt k) (pow (* 2 (* (PI) n)) (- -1/2 (* k -1/2)))) (/.f64 (sqrt.f64 (.f64 k #s(literal 1/2 binary64))) (sqrt.f64 (.f64 (PI.f64) n)))))
	42.5%	(/.f64 #s(literal 1 binary64) #s(approx (* (sqrt k) (pow (* 2 (* (PI) n)) (- -1/2 (* k -1/2)))) (/.f64 (sqrt.f64 (*.f64 #s(literal 1/2 binary64) (/.f64 k n))) (sqrt.f64 (PI.f64)))))
	53.8%	(/.f64 #s(literal 1 binary64) #s(approx (* (sqrt k) (pow (* 2 (* (PI) n)) (- -1/2 (* k -1/2)))) (/.f64 (sqrt.f64 k) (sqrt.f64 (.f64 #s(literal 2 binary64) (.f64 (PI.f64) n))))))
	41.3%	(/.f64 #s(literal 1 binary64) #s(approx (* (sqrt k) (pow (* 2 (* (PI) n)) (- -1/2 (* k -1/2)))) (/.f64 (sqrt.f64 #s(literal 1/2 binary64)) (sqrt.f64 (/.f64 (*.f64 (PI.f64) n) k)))))
	53.8%	(/.f64 #s(literal 1 binary64) #s(approx (* (sqrt k) (pow (* 2 (* (PI) n)) (- -1/2 (* k -1/2)))) (/.f64 #s(literal 1 binary64) (/.f64 (sqrt.f64 (.f64 (PI.f64) n)) (sqrt.f64 (.f64 #s(literal 1/2 binary64) k))))))
	41.4%	(/.f64 #s(literal 1 binary64) #s(approx (* (sqrt k) (pow (* 2 (* (PI) n)) (- -1/2 (* k -1/2)))) (/.f64 #s(literal 1 binary64) (sqrt.f64 (/.f64 (.f64 (PI.f64) n) (.f64 k #s(literal 1/2 binary64)))))))
	53.8%	(/.f64 #s(literal 1 binary64) #s(approx (* (sqrt k) (pow (* 2 (* (PI) n)) (- -1/2 (* k -1/2)))) (.f64 (/.f64 (sqrt.f64 (.f64 k #s(literal 1/2 binary64))) (sqrt.f64 n)) (/.f64 #s(literal 1 binary64) (sqrt.f64 (PI.f64))))))
	53.3%	(/.f64 #s(literal 1 binary64) #s(approx (* (sqrt k) (pow (* 2 (* (PI) n)) (- -1/2 (* k -1/2)))) (*.f64 (/.f64 (sqrt.f64 k) (sqrt.f64 n)) (/.f64 (sqrt.f64 #s(literal 1/2 binary64)) (sqrt.f64 (PI.f64))))))
	53.8%	(/.f64 #s(literal 1 binary64) #s(approx (* (sqrt k) (pow (* 2 (* (PI) n)) (- -1/2 (* k -1/2)))) (.f64 (/.f64 (sqrt.f64 k) (sqrt.f64 #s(literal 2 binary64))) (sqrt.f64 (/.f64 #s(literal 1 binary64) (.f64 (PI.f64) n))))))
	53.5%	(/.f64 #s(literal 1 binary64) #s(approx (* (sqrt k) (pow (* 2 (* (PI) n)) (- -1/2 (* k -1/2)))) (.f64 (/.f64 (sqrt.f64 #s(literal 1/2 binary64)) (.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) (sqrt.f64 (PI.f64)))) (/.f64 #s(literal 1 binary64) (sqrt.f64 n)))))
	53.3%	(/.f64 #s(literal 1 binary64) #s(approx (* (sqrt k) (pow (* 2 (* (PI) n)) (- -1/2 (* k -1/2)))) (.f64 (/.f64 (sqrt.f64 #s(literal 1/2 binary64)) (sqrt.f64 (PI.f64))) (/.f64 #s(literal 1 binary64) (.f64 (sqrt.f64 n) (/.f64 #s(literal 1 binary64) (sqrt.f64 k)))))))
	42.3%	(/.f64 #s(literal 1 binary64) #s(approx (* (sqrt k) (pow (* 2 (* (PI) n)) (- -1/2 (* k -1/2)))) (*.f64 (/.f64 (sqrt.f64 #s(literal 1/2 binary64)) (sqrt.f64 (PI.f64))) (sqrt.f64 (/.f64 k n)))))
	53.6%	(/.f64 #s(literal 1 binary64) #s(approx (* (sqrt k) (pow (* 2 (* (PI) n)) (- -1/2 (* k -1/2)))) (*.f64 (/.f64 (sqrt.f64 #s(literal 1/2 binary64)) (sqrt.f64 n)) (sqrt.f64 (/.f64 k (PI.f64))))))
	53.7%	(/.f64 #s(literal 1 binary64) #s(approx (* (sqrt k) (pow (* 2 (* (PI) n)) (- -1/2 (* k -1/2)))) (.f64 (/.f64 #s(literal -1 binary64) (sqrt.f64 (.f64 (PI.f64) n))) (/.f64 (neg.f64 (sqrt.f64 k)) (sqrt.f64 #s(literal 2 binary64))))))
	53.8%	(/.f64 #s(literal 1 binary64) #s(approx (* (sqrt k) (pow (* 2 (* (PI) n)) (- -1/2 (* k -1/2)))) (.f64 (sqrt.f64 (.f64 #s(literal 1/2 binary64) k)) (sqrt.f64 (/.f64 (/.f64 #s(literal 1 binary64) n) (PI.f64))))))
	53.7%	(/.f64 #s(literal 1 binary64) #s(approx (* (sqrt k) (pow (* 2 (* (PI) n)) (- -1/2 (* k -1/2)))) (.f64 (sqrt.f64 (.f64 #s(literal 1/2 binary64) k)) (sqrt.f64 (/.f64 #s(literal 1 binary64) (.f64 (.f64 (sqrt.f64 (*.f64 (PI.f64) (sqrt.f64 (PI.f64)))) (sqrt.f64 (sqrt.f64 (PI.f64)))) n))))))
✓	53.8%	(/.f64 #s(literal 1 binary64) #s(approx (* (sqrt k) (pow (* 2 (* (PI) n)) (- -1/2 (* k -1/2)))) (.f64 (sqrt.f64 (.f64 #s(literal 1/2 binary64) k)) (sqrt.f64 (/.f64 #s(literal 1 binary64) (*.f64 (PI.f64) n))))))
	53.6%	(/.f64 #s(literal 1 binary64) #s(approx (* (sqrt k) (pow (* 2 (* (PI) n)) (- -1/2 (* k -1/2)))) (.f64 (sqrt.f64 #s(literal 1/2 binary64)) (/.f64 (sqrt.f64 k) (sqrt.f64 (.f64 (PI.f64) n))))))
	53.7%	(/.f64 #s(literal 1 binary64) #s(approx (* (sqrt k) (pow (* 2 (* (PI) n)) (- -1/2 (* k -1/2)))) (.f64 (sqrt.f64 #s(literal 1/2 binary64)) (/.f64 #s(literal 1 binary64) (/.f64 (sqrt.f64 (.f64 (PI.f64) n)) (sqrt.f64 k))))))
	42.4%	(/.f64 #s(literal 1 binary64) #s(approx (* (sqrt k) (pow (* 2 (* (PI) n)) (- -1/2 (* k -1/2)))) (*.f64 (sqrt.f64 #s(literal 1/2 binary64)) (/.f64 #s(literal 1 binary64) (/.f64 (sqrt.f64 (PI.f64)) (sqrt.f64 (/.f64 k n)))))))
	53.6%	(/.f64 #s(literal 1 binary64) #s(approx (* (sqrt k) (pow (* 2 (* (PI) n)) (- -1/2 (* k -1/2)))) (.f64 (sqrt.f64 #s(literal 1/2 binary64)) (/.f64 #s(literal 1 binary64) (.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) (sqrt.f64 (/.f64 n (/.f64 #s(literal 1 binary64) (PI.f64)))))))))
	53.4%	(/.f64 #s(literal 1 binary64) #s(approx (* (sqrt k) (pow (* 2 (* (PI) n)) (- -1/2 (* k -1/2)))) (.f64 (sqrt.f64 #s(literal 1/2 binary64)) (/.f64 #s(literal 1 binary64) (.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) (sqrt.f64 (.f64 (.f64 (sqrt.f64 (PI.f64)) (sqrt.f64 (PI.f64))) n)))))))
✓	53.6%	(/.f64 #s(literal 1 binary64) #s(approx (* (sqrt k) (pow (* 2 (* (PI) n)) (- -1/2 (* k -1/2)))) (.f64 (sqrt.f64 #s(literal 1/2 binary64)) (/.f64 #s(literal 1 binary64) (.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) (sqrt.f64 (*.f64 (PI.f64) n)))))))
	53.5%	(/.f64 #s(literal 1 binary64) #s(approx (* (sqrt k) (pow (* 2 (* (PI) n)) (- -1/2 (* k -1/2)))) (.f64 (sqrt.f64 #s(literal 1/2 binary64)) (/.f64 #s(literal 1 binary64) (.f64 (*.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) (sqrt.f64 (PI.f64))) (sqrt.f64 n))))))
	53.6%	(/.f64 #s(literal 1 binary64) #s(approx (* (sqrt k) (pow (* 2 (* (PI) n)) (- -1/2 (* k -1/2)))) (.f64 (sqrt.f64 #s(literal 1/2 binary64)) (/.f64 #s(literal 1 binary64) (.f64 #s(approx (/ 1 (sqrt k)) (sqrt.f64 (/.f64 #s(literal 1 binary64) k))) (sqrt.f64 (*.f64 (PI.f64) n)))))))
	53.6%	(/.f64 #s(literal 1 binary64) #s(approx (* (sqrt k) (pow (* 2 (* (PI) n)) (- -1/2 (* k -1/2)))) (.f64 (sqrt.f64 #s(literal 1/2 binary64)) (.f64 (/.f64 #s(literal -1 binary64) (sqrt.f64 (*.f64 (PI.f64) n))) (/.f64 (neg.f64 (sqrt.f64 k)) #s(literal 1 binary64))))))
	53.5%	(/.f64 #s(literal 1 binary64) #s(approx (* (sqrt k) (pow (* 2 (* (PI) n)) (- -1/2 (* k -1/2)))) (.f64 (sqrt.f64 #s(literal 1/2 binary64)) (.f64 (/.f64 #s(literal -1 binary64) (sqrt.f64 n)) (/.f64 (neg.f64 (sqrt.f64 k)) (sqrt.f64 (PI.f64)))))))
✓	42.6%	(/.f64 #s(literal 1 binary64) #s(approx (* (sqrt k) (pow (* 2 (* (PI) n)) (- -1/2 (* k -1/2)))) (.f64 (sqrt.f64 #s(literal 1/2 binary64)) (sqrt.f64 (/.f64 k (.f64 n (PI.f64)))))))
	76.8%	(.f64 (pow.f64 (.f64 #s(literal 2 binary64) (.f64 (PI.f64) n)) (.f64 k #s(literal -1/2 binary64))) (sqrt.f64 (/.f64 (.f64 (PI.f64) n) (.f64 k #s(literal 1/2 binary64)))))
	53.7%	(.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) #s(approx (pow ( (* 2 (PI)) n) (/ (- 1 k) 2)) (.f64 (sqrt.f64 #s(literal 2 binary64)) (sqrt.f64 (.f64 n (PI.f64))))))
	76.6%	(.f64 (.f64 (sqrt.f64 #s(literal 2 binary64)) (pow.f64 (.f64 #s(literal 2 binary64) (.f64 (PI.f64) n)) (.f64 k #s(literal -1/2 binary64)))) (sqrt.f64 (/.f64 (.f64 (PI.f64) n) k)))
	76.7%	(.f64 (sqrt.f64 (.f64 (PI.f64) (.f64 n (/.f64 #s(literal 2 binary64) k)))) (pow.f64 (.f64 #s(literal 2 binary64) (.f64 (PI.f64) n)) (.f64 k #s(literal -1/2 binary64))))
	76.8%	(sqrt.f64 (/.f64 (/.f64 (.f64 #s(literal 2 binary64) (.f64 (PI.f64) n)) k) (pow.f64 (.f64 #s(literal 2 binary64) (.f64 (PI.f64) n)) k)))
	99.5%	#s(approx (/ (pow (* 2 (* (PI) n)) (- 1/2 (* k 1/2))) (sqrt k)) (.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) k)) (pow.f64 (.f64 n (*.f64 #s(literal 2 binary64) (PI.f64))) (fma.f64 #s(literal -1/2 binary64) k #s(literal 1/2 binary64)))))
	41.3%	#s(approx (/ 1 (* (sqrt k) (pow (* 2 (* (PI) n)) (- -1/2 (* k -1/2))))) (/.f64 (sqrt.f64 (/.f64 (*.f64 n (PI.f64)) k)) (sqrt.f64 #s(literal 1/2 binary64))))
	53.9%	#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (/.f64 (sqrt.f64 (.f64 (PI.f64) n)) (sqrt.f64 (.f64 k #s(literal 1/2 binary64)))))
	53.9%	#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (/.f64 (sqrt.f64 (.f64 #s(literal 2 binary64) (.f64 (PI.f64) n))) (sqrt.f64 k)))
	42.7%	#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (/.f64 (sqrt.f64 #s(literal 2 binary64)) (sqrt.f64 (/.f64 k (*.f64 (PI.f64) n)))))
	53.6%	#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (.f64 (/.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) (sqrt.f64 #s(literal 1/2 binary64))) (sqrt.f64 (.f64 (PI.f64) n))))
	53.5%	#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (.f64 (/.f64 (.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) (sqrt.f64 (PI.f64))) (sqrt.f64 #s(literal 1/2 binary64))) (/.f64 (sqrt.f64 n) #s(literal 1 binary64))))
	53.5%	#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (.f64 (/.f64 (.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) (sqrt.f64 (PI.f64))) #s(literal 1 binary64)) (/.f64 (sqrt.f64 n) (sqrt.f64 #s(literal 1/2 binary64)))))
	53.7%	#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (.f64 (/.f64 (.f64 #s(literal 1 binary64) (sqrt.f64 #s(literal 2 binary64))) (sqrt.f64 k)) (sqrt.f64 (*.f64 (PI.f64) n))))
	53.8%	#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (.f64 (/.f64 (sqrt.f64 (.f64 (PI.f64) n)) (sqrt.f64 k)) (sqrt.f64 #s(literal 2 binary64))))
	53.7%	#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (.f64 (/.f64 (sqrt.f64 (.f64 (PI.f64) n)) (sqrt.f64 #s(literal 1/2 binary64))) (/.f64 #s(literal 1 binary64) (sqrt.f64 k))))
	53.7%	#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (.f64 (/.f64 (sqrt.f64 (.f64 #s(literal 2 binary64) (PI.f64))) (sqrt.f64 k)) (/.f64 (sqrt.f64 n) #s(literal 1 binary64))))
	53.5%	#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (.f64 (/.f64 (sqrt.f64 (PI.f64)) #s(literal 1 binary64)) (/.f64 (.f64 (sqrt.f64 n) (/.f64 #s(literal 1 binary64) (sqrt.f64 k))) (sqrt.f64 #s(literal 1/2 binary64)))))
✓	53.9%	#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) (sqrt.f64 (.f64 #s(literal 2 binary64) (*.f64 (PI.f64) n)))))
	53.7%	#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (.f64 (.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) (sqrt.f64 #s(literal 2 binary64))) (sqrt.f64 (*.f64 (PI.f64) n))))
	53.8%	#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (.f64 (.f64 (sqrt.f64 (/.f64 (PI.f64) k)) (sqrt.f64 n)) (sqrt.f64 #s(literal 2 binary64))))
	53.8%	#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (.f64 (.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) k)) (sqrt.f64 (*.f64 (PI.f64) n))) (sqrt.f64 #s(literal 2 binary64))))
	53.8%	#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (.f64 (.f64 (sqrt.f64 (.f64 n (sqrt.f64 (PI.f64)))) (sqrt.f64 (sqrt.f64 (PI.f64)))) (sqrt.f64 (.f64 (/.f64 #s(literal 1 binary64) k) #s(literal 2 binary64)))))
	41.4%	#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (.f64 (.f64 (sqrt.f64 (PI.f64)) (sqrt.f64 (/.f64 n k))) (sqrt.f64 #s(literal 2 binary64))))
	53.7%	#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (.f64 (.f64 (sqrt.f64 (PI.f64)) (sqrt.f64 n)) (sqrt.f64 (*.f64 (/.f64 #s(literal 1 binary64) k) #s(literal 2 binary64)))))
	41.2%	#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (.f64 (sqrt.f64 (/.f64 (.f64 n (.f64 (sqrt.f64 (.f64 (PI.f64) (sqrt.f64 (PI.f64)))) (sqrt.f64 (sqrt.f64 (PI.f64))))) k)) (sqrt.f64 #s(literal 2 binary64))))
✓	41.4%	#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (.f64 (sqrt.f64 (/.f64 (.f64 n (PI.f64)) k)) (sqrt.f64 #s(literal 2 binary64))))
	53.9%	#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (.f64 (sqrt.f64 (/.f64 (PI.f64) (.f64 k #s(literal 1/2 binary64)))) (sqrt.f64 n)))
	53.8%	#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (.f64 (sqrt.f64 (/.f64 #s(literal 2 binary64) k)) (sqrt.f64 (.f64 (PI.f64) n))))
	53.9%	#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (.f64 (sqrt.f64 (.f64 (/.f64 #s(literal 2 binary64) k) (PI.f64))) (sqrt.f64 n)))
	53.8%	#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (.f64 (sqrt.f64 (.f64 (.f64 (sqrt.f64 (.f64 (PI.f64) (sqrt.f64 (PI.f64)))) (sqrt.f64 (sqrt.f64 (PI.f64)))) n)) (sqrt.f64 (*.f64 (/.f64 #s(literal 1 binary64) k) #s(literal 2 binary64)))))
	41.4%	#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (.f64 (sqrt.f64 (.f64 (PI.f64) (/.f64 n k))) (sqrt.f64 #s(literal 2 binary64))))
	41.3%	#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (.f64 (sqrt.f64 (.f64 n (/.f64 #s(literal 2 binary64) k))) (sqrt.f64 (PI.f64))))
	53.9%	#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (.f64 (sqrt.f64 (.f64 #s(literal 2 binary64) (*.f64 (PI.f64) n))) (sqrt.f64 (/.f64 #s(literal 1 binary64) k))))
	41.3%	#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (.f64 (sqrt.f64 (.f64 #s(literal 2 binary64) (PI.f64))) (sqrt.f64 (/.f64 n k))))
	41.2%	#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (.f64 (sqrt.f64 (.f64 #s(literal 2 binary64) (PI.f64))) (sqrt.f64 (*.f64 n (/.f64 #s(literal 1 binary64) k)))))
	41.3%	#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt.f64 (/.f64 (.f64 #s(literal 2 binary64) (.f64 (*.f64 n (sqrt.f64 (PI.f64))) (sqrt.f64 (PI.f64)))) k)))
	41.5%	#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt.f64 (.f64 (/.f64 (.f64 (PI.f64) n) k) #s(literal 2 binary64))))
	41.5%	#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt.f64 (.f64 (/.f64 (PI.f64) (.f64 k #s(literal 1/2 binary64))) n)))
	41.5%	#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt.f64 (.f64 (.f64 n (/.f64 #s(literal 2 binary64) k)) (PI.f64))))
	41.5%	#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt.f64 (.f64 (.f64 #s(literal 2 binary64) (PI.f64)) (/.f64 n k))))
	41.5%	#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt.f64 (.f64 n (/.f64 #s(literal 1 binary64) (/.f64 (.f64 k #s(literal 1/2 binary64)) (PI.f64))))))
	41.3%	#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt.f64 (.f64 n (.f64 (/.f64 (sqrt.f64 (PI.f64)) k) (/.f64 (sqrt.f64 (PI.f64)) #s(literal 1/2 binary64))))))
✓	41.5%	#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt.f64 (.f64 n (.f64 (PI.f64) (/.f64 #s(literal 2 binary64) k)))))

Compiler

Compiled 2 744 to 1 310 computations (52.3% saved)

regimes174.0ms (1.5%)

Memory

8.6MiB live, 204.7MiB allocated

Counts

110 → 1

Calls

Call 1

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

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

Calls

4 calls:

70.0ms	(.f64 (.f64 #s(literal 2 binary64) (PI.f64)) n)
38.0ms	(.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))))
30.0ms	k
28.0ms	n

Results

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

Compiler

Compiled 31 to 23 computations (25.8% saved)

regimes136.0ms (1.2%)

Memory

20.2MiB live, 250.8MiB allocated

Counts

106 → 1

Calls

Call 1

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

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

Calls

4 calls:

37.0ms	(.f64 (.f64 #s(literal 2 binary64) (PI.f64)) n)
33.0ms	k
31.0ms	n
28.0ms	(.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) (pow.f64 (.f64 (*.f64 #s(literal 2 binary64) (PI.f64)) n) (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 2 binary64))))

Results

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

Compiler

Compiled 31 to 23 computations (25.8% saved)

regimes138.0ms (1.2%)

Memory

-3.1MiB live, 191.5MiB allocated

Counts

89 → 2

Calls

Call 1

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

Outputs

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

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

Calls

4 calls:

40.0ms	(.f64 (.f64 #s(literal 2 binary64) (PI.f64)) n)
26.0ms	n
25.0ms	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
98.0%	2	`k`
60.9%	3	`n`
98.0%	3	`(.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) (pow.f64 (.f64 (*.f64 #s(literal 2 binary64) (PI.f64)) n) (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 2 binary64))))`
60.9%	3	`(.f64 (.f64 #s(literal 2 binary64) (PI.f64)) n)`

Compiler

Compiled 31 to 23 computations (25.8% saved)

regimes122.0ms (1%)

Memory

-60.5MiB live, 190.9MiB allocated

Counts

88 → 1

Calls

Call 1

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

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

Calls

4 calls:

34.0ms	(.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))))
29.0ms	k
28.0ms	(.f64 (.f64 #s(literal 2 binary64) (PI.f64)) n)
24.0ms	n

Results

Accuracy	Segments	Branch
53.9%	1	`n`
53.9%	1	`(.f64 (.f64 #s(literal 2 binary64) (PI.f64)) n)`
53.9%	1	`(.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) (pow.f64 (.f64 (*.f64 #s(literal 2 binary64) (PI.f64)) n) (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 2 binary64))))`
53.9%	1	`k`

Compiler

Compiled 31 to 23 computations (25.8% saved)

regimes26.0ms (0.2%)

Memory

10.4MiB live, 47.7MiB allocated

Counts

19 → 1

Calls

Call 1

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

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

Calls

4 calls:

8.0ms	n
6.0ms	(.f64 (.f64 #s(literal 2 binary64) (PI.f64)) n)
6.0ms	k
5.0ms	(.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) (pow.f64 (.f64 (*.f64 #s(literal 2 binary64) (PI.f64)) n) (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 2 binary64))))

Results

Accuracy	Segments	Branch
53.9%	1	`(.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) (pow.f64 (.f64 (*.f64 #s(literal 2 binary64) (PI.f64)) n) (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 2 binary64))))`
53.9%	1	`k`
53.9%	1	`n`
53.9%	1	`(.f64 (.f64 #s(literal 2 binary64) (PI.f64)) n)`

Compiler

Compiled 31 to 23 computations (25.8% saved)

regimes18.0ms (0.2%)

Memory

-9.7MiB live, 33.3MiB allocated

Counts

8 → 1

Calls

Call 1

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

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

Calls

4 calls:

8.0ms	n
3.0ms	(.f64 (.f64 #s(literal 2 binary64) (PI.f64)) n)
3.0ms	k
3.0ms	(.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) (pow.f64 (.f64 (*.f64 #s(literal 2 binary64) (PI.f64)) n) (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 2 binary64))))

Results

Accuracy	Segments	Branch
41.5%	1	`(.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) (pow.f64 (.f64 (*.f64 #s(literal 2 binary64) (PI.f64)) n) (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 2 binary64))))`
41.5%	1	`k`
41.5%	1	`n`
41.5%	1	`(.f64 (.f64 #s(literal 2 binary64) (PI.f64)) n)`

Compiler

Compiled 31 to 23 computations (25.8% saved)

regimes8.0ms (0.1%)

Memory

16.7MiB live, 16.7MiB allocated

Accuracy

Total -0.1b remaining (-0.2%)

Threshold costs -0.1b (-0.2%)

Counts

3 → 1

Calls

Call 1

Inputs

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

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

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

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

Calls

4 calls:

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

Results

Accuracy	Segments	Branch
41.5%	1	`k`
41.5%	1	`(.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) (pow.f64 (.f64 (*.f64 #s(literal 2 binary64) (PI.f64)) n) (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 2 binary64))))`
41.5%	1	`n`
41.5%	1	`(.f64 (.f64 #s(literal 2 binary64) (PI.f64)) n)`

Compiler

Compiled 31 to 23 computations (25.8% saved)

bsearch18.0ms (0.2%)

Memory

-6.6MiB live, 31.3MiB allocated

Algorithm

1×	binary-search

Stop Event

1×	narrow-enough

Steps

Time	Left	Right
16.0ms	0.32468835323202694	27.594480005639646

Samples

12.0ms

112×

valid

Compiler

Compiled 224 to 172 computations (23.2% saved)

Precisions

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

ival-pow: 4.0ms (43.3% of total)

ival-mult: 2.0ms (21.7% of total)

ival-div: 1.0ms (10.8% of total)

ival-sqrt: 1.0ms (10.8% of total)

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

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

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

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

exact: 0.0ms (0% of total)

simplify8.0ms (0.1%)

Memory

-21.8MiB live, 16.8MiB allocated

Algorithm

1×	egg-herbie

Rules

22×	`*-commutative_binary64`
2×	`1-exp_binary64`
2×	`1-exp_binary32`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	51	182
1	65	182

Stop Event

1×

saturated

Calls

Call 1

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

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

soundness697.0ms (6%)

Memory

30.4MiB live, 659.9MiB allocated

Rules

9 974×	`lower-fma.f64`
9 974×	`lower-fma.f32`
5 988×	`lower-*.f64`
5 988×	`lower-*.f32`
5 258×	`lower-*.f32`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	45	219
0	72	220
1	253	203
2	1384	199
0	8196	197
0	128	1174
1	345	1155
2	1011	1065
3	3348	1038
4	5547	966
0	8354	945
0	49	250
0	75	239
1	280	234
2	1649	228
0	8194	223
0	13	43
0	22	43
1	89	40
2	497	38
3	4474	38
0	8599	37

Stop Event

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

Compiler

Compiled 381 to 229 computations (39.9% saved)

preprocess70.0ms (0.6%)

Memory: -3.1MiB live, 75.3MiB allocated
Compiler: Compiled 234 to 100 computations (57.3% saved)

end0.0ms (0%)

Memory: 0.0MiB live, 0.0MiB allocated

Iter	Nodes	Cost
0	13	54
0	22	54
1	37	52
2	54	52
3	75	52
4	93	52
5	108	52
6	129	52
7	156	52
8	165	52
9	168	52
0	168	49

Iter	Nodes	Cost
0	13	54
0	22	54
1	37	52
2	54	52
3	75	52
4	93	52
5	108	52
6	129	52
7	156	52
8	165	52
9	168	52
0	168	49

start0.0ms (0%)

analyze142.0ms (1.2%)

sample2.8s (24.3%)

explain141.0ms (1.2%)

preprocess70.0ms (0.6%)

eval0.0ms (0%)

prune1.0ms (0%)

simplify8.0ms (0.1%)

localize91.0ms (0.8%)

series69.0ms (0.6%)

simplify259.0ms (2.2%)

rewrite610.0ms (5.3%)

eval162.0ms (1.4%)

prune177.0ms (1.5%)

simplify58.0ms (0.5%)

localize362.0ms (3.1%)

series810.0ms (7%)

simplify333.0ms (2.9%)

rewrite282.0ms (2.4%)

eval363.0ms (3.1%)

prune303.0ms (2.6%)

simplify97.0ms (0.8%)

localize161.0ms (1.4%)

series86.0ms (0.7%)

simplify296.0ms (2.5%)

rewrite213.0ms (1.8%)

eval256.0ms (2.2%)

prune346.0ms (3%)

simplify115.0ms (1%)

localize166.0ms (1.4%)

series35.0ms (0.3%)

simplify288.0ms (2.5%)

rewrite266.0ms (2.3%)

eval278.0ms (2.4%)

prune537.0ms (4.6%)

regimes174.0ms (1.5%)

regimes136.0ms (1.2%)

regimes138.0ms (1.2%)

regimes122.0ms (1%)

regimes26.0ms (0.2%)

regimes18.0ms (0.2%)

regimes8.0ms (0.1%)

bsearch18.0ms (0.2%)

simplify8.0ms (0.1%)

soundness697.0ms (6%)

preprocess70.0ms (0.6%)

end0.0ms (0%)

Profiling

Iter	Nodes	Cost
0	13	54
0	22	54
1	37	52
2	54	52
3	75	52
4	93	52
5	108	52
6	129	52
7	156	52
8	165	52
9	168	52
0	168	49