Metrics for Migdal et al, Equation (51)

start0.0ms (0%)

Memory: 0.0MiB live, 0.0MiB allocated

analyze140.0ms (1.4%)

Memory

42.7MiB live, 197.3MiB 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)

sample3.8s (38.6%)

Memory

-198.8MiB live, 4 089.4MiB allocated

Samples

1.0s	8 256×	0	valid
739.0ms	3 512×	1	invalid
539.0ms	1 833×	1	exit
242.0ms	446×	2	invalid
62.0ms	506×	0	invalid
24.0ms	219×	0	exit

Precisions

Click to see histograms. Total time spent on operations: 1.9s

ival-pow: 499.0ms (26.7% of total)

ival-mult: 489.0ms (26.1% of total)

ival-div: 270.0ms (14.4% of total)

ival-sqrt: 188.0ms (10% of total)

adjust: 184.0ms (9.8% of total)

ival-sub: 109.0ms (5.8% of total)

ival-pi: 99.0ms (5.3% of total)

exact: 16.0ms (0.9% of total)

ival-true: 13.0ms (0.7% of total)

ival-assert: 7.0ms (0.4% of total)

Bogosity

explain149.0ms (1.5%)

Memory

17.4MiB live, 226.7MiB allocated

FPErrors

Click to see full error table

Ground Truth	Overpredictions	Example	Underpredictions	Example	Subexpression
7	85	(5.774068707256294e-304 2.173787307546262e-233)	1	(4.647958045202672e-13 2.8878450828449015e-54)	`(pow.f64 (.f64 (.f64 #s(literal 2 binary64) (PI.f64)) n) (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 2 binary64)))`
0	0	-	0	-	`k`
0	0	-	0	-	`n`
0	0	-	0	-	`(/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 2 binary64))`
0	0	-	0	-	`#s(literal 1 binary64)`
0	0	-	0	-	`(.f64 (.f64 #s(literal 2 binary64) (PI.f64)) n)`
0	0	-	0	-	`(sqrt.f64 k)`
0	0	-	0	-	`#s(literal 2 binary64)`
0	0	-	0	-	`(/.f64 #s(literal 1 binary64) (sqrt.f64 k))`
0	0	-	0	-	`(-.f64 #s(literal 1 binary64) k)`
0	0	-	0	-	`(*.f64 #s(literal 2 binary64) (PI.f64))`
0	0	-	0	-	`(.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) (pow.f64 (.f64 (*.f64 #s(literal 2 binary64) (PI.f64)) n) (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 2 binary64))))`
0	0	-	0	-	`(PI.f64)`

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	31

Confusion

	Predicted +	Predicted -
+	6	2
-	85	163

Precision

0.06593406593406594

Recall

0.75

Confusion?

	Predicted +	Predicted Maybe	Predicted -
+	6	2	0
-	85	29	134

Precision?

0.06557377049180328

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

58.0ms

512×

valid

Compiler

Compiled 182 to 56 computations (69.2% saved)

Precisions

Click to see histograms. Total time spent on operations: 40.0ms

ival-mult: 12.0ms (30.3% of total)

ival-pow: 11.0ms (27.8% of total)

ival-div: 7.0ms (17.7% of total)

ival-sqrt: 4.0ms (10.1% of total)

ival-sub: 3.0ms (7.6% of total)

ival-pi: 2.0ms (5.1% of total)

ival-true: 1.0ms (2.5% of total)

exact: 1.0ms (2.5% of total)

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

preprocess48.0ms (0.5%)

Memory

-9.1MiB live, 28.5MiB allocated

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	31	88
1	82	74
2	193	74
3	383	74
4	630	74
5	922	74
6	1089	74
7	1346	74
8	1405	74
9	1431	74
10	1449	74
11	1455	74
12	1455	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 n (*.f64 (PI.f64) #s(literal 2 binary64))) (fma.f64 #s(literal -1/2 binary64) k #s(literal 1/2 binary64))) (sqrt.f64 k))

Compiler

Compiled 16 to 13 computations (18.8% saved)

eval0.0ms (0%)

Memory: 0.1MiB live, 0.1MiB allocated
Compiler: Compiled 0 to 2 computations (-∞% saved)

prune0.0ms (0%)

Memory

0.7MiB live, 0.7MiB allocated

Alt Table

Click to see full alt table

Status	Accuracy	Program
▶	99.4%	(.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 16 to 13 computations (18.8% saved)

simplify6.0ms (0.1%)

Memory

6.4MiB live, 6.4MiB 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))

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

localize40.0ms (0.4%)

Memory

-7.8MiB live, 66.3MiB allocated

Localize:

Found 4 expressions of interest:

New	Metric	Score
accuracy	0.14681625976844204	(.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	0.234375	(/.f64 #s(literal 1 binary64) (sqrt.f64 k))
accuracy	0.23604328131243874	(pow.f64 (.f64 (.f64 #s(literal 2 binary64) (PI.f64)) n) (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 2 binary64)))
accuracy	0.24609375	(.f64 (.f64 #s(literal 2 binary64) (PI.f64)) n)

Samples

31.0ms

256×

valid

Compiler

Compiled 110 to 28 computations (74.5% saved)

Precisions

Click to see histograms. Total time spent on operations: 20.0ms

ival-mult: 5.0ms (25.3% of total)

ival-pow: 5.0ms (25.3% of total)

ival-sqrt: 4.0ms (20.2% of total)

ival-div: 3.0ms (15.2% of total)

ival-pi: 1.0ms (5.1% of total)

ival-sub: 1.0ms (5.1% of total)

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

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

exact: 0.0ms (0% of total)

series73.0ms (0.8%)

Memory

-7.6MiB live, 111.6MiB allocated

Counts

6 → 27

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

Calls

6 calls:

Time	Variable		Point	Expression
33.0ms	n	@	0	((/ (- 1 k) 2) (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (/ 1 (sqrt k)) (sqrt k) (* (* 2 (PI)) n) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2)))
23.0ms	n	@	-inf	((/ (- 1 k) 2) (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (/ 1 (sqrt k)) (sqrt k) (* (* 2 (PI)) n) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2)))
10.0ms	n	@	inf	((/ (- 1 k) 2) (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (/ 1 (sqrt k)) (sqrt k) (* (* 2 (PI)) n) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2)))
3.0ms	k	@	-inf	((/ (- 1 k) 2) (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (/ 1 (sqrt k)) (sqrt k) (* (* 2 (PI)) n) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2)))
3.0ms	k	@	0	((/ (- 1 k) 2) (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (/ 1 (sqrt k)) (sqrt k) (* (* 2 (PI)) n) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2)))

simplify142.0ms (1.5%)

Memory

38.0MiB live, 194.0MiB allocated

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	128	517
1	345	504
2	1021	460
3	3363	433
4	5589	421
0	8476	406

Stop Event

1×	iter limit
1×	node limit

Counts

27 → 27

Calls

Call 1

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

rewrite167.0ms (1.7%)

Memory

-20.1MiB live, 223.6MiB allocated

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	13	43
0	22	43
1	89	40
2	497	38
3	4477	38
0	8503	37

Stop Event

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

Counts

6 → 413

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

eval55.0ms (0.6%)

Memory: -9.4MiB live, 104.7MiB allocated
Compiler: Compiled 9 931 to 1 554 computations (84.4% saved)

prune23.0ms (0.2%)

Memory

10.0MiB live, 55.0MiB allocated

Pruning

20 alts after pruning (20 fresh and 0 done)

	Pruned	Kept	Total
New	411	20	431
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	412	20	432

Accuracy

100.0%

Counts

432 → 20

Alt Table

Click to see full alt table

Status	Accuracy	Program
	48.1%	(/.f64 (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.f64 k))
▶	99.7%	(/.f64 (sqrt.f64 (.f64 n (.f64 (PI.f64) #s(literal 2 binary64)))) (.f64 (sqrt.f64 k) (pow.f64 (pow.f64 (.f64 n (*.f64 (PI.f64) #s(literal 2 binary64))) k) #s(literal 1/2 binary64))))
	48.0%	(/.f64 #s(literal 1 binary64) (/.f64 (sqrt.f64 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)))))
	47.5%	(.f64 (pow.f64 (.f64 (PI.f64) #s(literal 2 binary64)) (fma.f64 #s(literal 1/2 binary64) k #s(literal 1/2 binary64))) (/.f64 (pow.f64 n (fma.f64 #s(literal 1/2 binary64) k #s(literal 1/2 binary64))) (sqrt.f64 k)))
	98.9%	(.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) (pow.f64 (pow.f64 (.f64 n (.f64 (PI.f64) #s(literal 2 binary64))) (.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 1/8 binary64))) #s(literal 4 binary64)))
	99.3%	(.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) (pow.f64 (.f64 (.f64 (.f64 n #s(literal 2 binary64)) (sqrt.f64 (PI.f64))) (sqrt.f64 (PI.f64))) (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 2 binary64))))
	99.4%	(.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) (pow.f64 (.f64 (*.f64 #s(literal 2 binary64) (PI.f64)) n) (fma.f64 k #s(literal -1/2 binary64) #s(literal 1/2 binary64))))
▶	53.7%	(.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))))
	48.7%	(.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))))
	99.4%	(.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) (pow.f64 (sqrt.f64 (.f64 n (*.f64 (PI.f64) #s(literal 2 binary64)))) (-.f64 #s(literal 1 binary64) k)))
	99.4%	(.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) (/.f64 (pow.f64 (.f64 n (.f64 (PI.f64) #s(literal 2 binary64))) (fma.f64 #s(literal 1/4 binary64) (-.f64 #s(literal 1 binary64) k) #s(literal 1/4 binary64))) (pow.f64 (.f64 n (.f64 (PI.f64) #s(literal 2 binary64))) (.f64 k #s(literal 1/4 binary64)))))
	75.4%	(.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) (/.f64 (sqrt.f64 (.f64 n (.f64 (PI.f64) #s(literal 2 binary64)))) (pow.f64 (pow.f64 (.f64 n (.f64 (PI.f64) #s(literal 2 binary64))) #s(literal 2 binary64)) (.f64 k #s(literal 1/4 binary64)))))
	99.3%	(.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) (/.f64 #s(literal 1 binary64) (pow.f64 (.f64 n (.f64 (PI.f64) #s(literal 2 binary64))) (.f64 #s(literal -1/2 binary64) (-.f64 #s(literal 1 binary64) k)))))
▶	99.7%	(.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) (.f64 (pow.f64 (.f64 n (.f64 (PI.f64) #s(literal 2 binary64))) (.f64 k #s(literal -1/2 binary64))) (sqrt.f64 (.f64 n (*.f64 (PI.f64) #s(literal 2 binary64))))))
▶	99.4%	(.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) (sqrt.f64 (pow.f64 (.f64 n (*.f64 (PI.f64) #s(literal 2 binary64))) (-.f64 #s(literal 1 binary64) k))))
	99.4%	(.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) #s(approx (pow ( (* 2 (PI)) n) (/ (- 1 k) 2)) (pow.f64 (/.f64 (*.f64 #s(literal -2 binary64) (PI.f64)) (/.f64 #s(literal -1 binary64) n)) (fma.f64 #s(literal -1/2 binary64) k #s(literal 1/2 binary64)))))
	48.6%	(.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) #s(approx (pow ( (* 2 (PI)) n) (/ (- 1 k) 2)) (.f64 (sqrt.f64 (.f64 (PI.f64) n)) (sqrt.f64 #s(literal 2 binary64)))))
	56.8%	#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (/.f64 (.f64 (sqrt.f64 #s(literal 2 binary64)) (fma.f64 (.f64 (log.f64 (.f64 (.f64 #s(literal 2 binary64) n) (PI.f64))) (sqrt.f64 (.f64 (.f64 (pow.f64 k #s(literal 3 binary64)) (PI.f64)) n))) #s(literal -1/2 binary64) (sqrt.f64 (.f64 (.f64 (PI.f64) n) k)))) k))
	99.4%	#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (.f64 (pow.f64 (.f64 (*.f64 #s(literal 2 binary64) n) (PI.f64)) (fma.f64 #s(literal -1/2 binary64) k #s(literal 1/2 binary64))) (sqrt.f64 (/.f64 #s(literal 1 binary64) k))))
▶	37.2%	#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (.f64 (sqrt.f64 #s(literal 2 binary64)) (sqrt.f64 (/.f64 (.f64 (PI.f64) n) k))))

Compiler

Compiled 862 to 688 computations (20.2% saved)

simplify13.0ms (0.1%)

Memory

19.1MiB live, 19.1MiB allocated

Algorithm

1×	egg-herbie

Localize:

Found 20 expressions of interest:

New	Metric	Score
cost-diff	0	(.f64 (pow.f64 (.f64 n (.f64 (PI.f64) #s(literal 2 binary64))) (.f64 k #s(literal -1/2 binary64))) (sqrt.f64 (.f64 n (.f64 (PI.f64) #s(literal 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)) (.f64 (pow.f64 (.f64 n (.f64 (PI.f64) #s(literal 2 binary64))) (.f64 k #s(literal -1/2 binary64))) (sqrt.f64 (.f64 n (*.f64 (PI.f64) #s(literal 2 binary64))))))
cost-diff	0	(sqrt.f64 (pow.f64 (.f64 n (.f64 (PI.f64) #s(literal 2 binary64))) (-.f64 #s(literal 1 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)) (sqrt.f64 (pow.f64 (.f64 n (*.f64 (PI.f64) #s(literal 2 binary64))) (-.f64 #s(literal 1 binary64) k))))
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	(sqrt.f64 (/.f64 (*.f64 (PI.f64) n) k))
cost-diff	0	(sqrt.f64 #s(literal 2 binary64))
cost-diff	0	(.f64 (sqrt.f64 #s(literal 2 binary64)) (sqrt.f64 (/.f64 (.f64 (PI.f64) n) k)))
cost-diff	0	#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (.f64 (sqrt.f64 #s(literal 2 binary64)) (sqrt.f64 (/.f64 (.f64 (PI.f64) n) k))))
cost-diff	0	(*.f64 (PI.f64) #s(literal 2 binary64))
cost-diff	0	(.f64 n (.f64 (PI.f64) #s(literal 2 binary64)))
cost-diff	0	(sqrt.f64 (.f64 n (.f64 (PI.f64) #s(literal 2 binary64))))
cost-diff	5824	(pow.f64 (pow.f64 (.f64 n (.f64 (PI.f64) #s(literal 2 binary64))) k) #s(literal 1/2 binary64))

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	45	321
0	73	318
1	112	310
2	157	310
3	206	310
4	239	310
5	277	310
6	305	310
7	332	310
8	341	310
9	344	310
0	344	306

Stop Event

1×	iter limit
1×	saturated
1×	iter limit

Calls

Call 1

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

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

localize110.0ms (1.1%)

Memory

-12.8MiB live, 182.8MiB allocated

Localize:

Found 20 expressions of interest:

New	Metric	Score
accuracy	0.14681625976844204	(.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) (.f64 (pow.f64 (.f64 n (.f64 (PI.f64) #s(literal 2 binary64))) (.f64 k #s(literal -1/2 binary64))) (sqrt.f64 (.f64 n (*.f64 (PI.f64) #s(literal 2 binary64))))))
accuracy	0.1640625	(/.f64 #s(literal 1 binary64) (sqrt.f64 k))
accuracy	0.17578125	(.f64 n (.f64 (PI.f64) #s(literal 2 binary64)))
accuracy	15.499622646281887	(PI.f64)
accuracy	0.1640625	(/.f64 #s(literal 1 binary64) (sqrt.f64 k))
accuracy	0.17578125	(.f64 n (.f64 (PI.f64) #s(literal 2 binary64)))
accuracy	0.25590055190739674	(pow.f64 (.f64 n (.f64 (PI.f64) #s(literal 2 binary64))) (-.f64 #s(literal 1 binary64) k))
accuracy	15.499622646281887	(PI.f64)
accuracy	0.17578125	(.f64 (.f64 #s(literal 2 binary64) (PI.f64)) n)
accuracy	0.23604328131243874	(pow.f64 (.f64 (.f64 #s(literal 2 binary64) (PI.f64)) n) #s(approx (/ (- 1 k) 2) (*.f64 #s(literal -1/2 binary64) k)))
accuracy	15.499622646281887	(PI.f64)
accuracy	31.57174219705135	#s(approx (/ (- 1 k) 2) (*.f64 #s(literal -1/2 binary64) k))
accuracy	0.37337875976844204	(.f64 (sqrt.f64 #s(literal 2 binary64)) (sqrt.f64 (/.f64 (.f64 (PI.f64) n) k)))
accuracy	7.604558117689169	(sqrt.f64 (/.f64 (*.f64 (PI.f64) n) k))
accuracy	15.499622646281887	(PI.f64)
accuracy	17.001606273173245	#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (.f64 (sqrt.f64 #s(literal 2 binary64)) (sqrt.f64 (/.f64 (.f64 (PI.f64) n) k))))
accuracy	0.078125	(sqrt.f64 (.f64 n (.f64 (PI.f64) #s(literal 2 binary64))))
accuracy	0.16796875	(/.f64 (sqrt.f64 (.f64 n (.f64 (PI.f64) #s(literal 2 binary64)))) (.f64 (sqrt.f64 k) (pow.f64 (pow.f64 (.f64 n (*.f64 (PI.f64) #s(literal 2 binary64))) k) #s(literal 1/2 binary64))))
accuracy	0.17578125	(.f64 n (.f64 (PI.f64) #s(literal 2 binary64)))
accuracy	15.499622646281887	(PI.f64)

Samples

58.0ms	192×	0	valid
19.0ms	64×	0	exit

Compiler

Compiled 622 to 84 computations (86.5% saved)

Precisions

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

ival-mult: 20.0ms (37.3% of total)

ival-pow: 15.0ms (28% of total)

ival-sqrt: 10.0ms (18.7% of total)

ival-div: 6.0ms (11.2% of total)

ival-pi: 1.0ms (1.9% of total)

ival-sub: 1.0ms (1.9% of total)

exact: 1.0ms (1.9% of total)

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

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

series78.0ms (0.8%)

Memory

-2.4MiB live, 121.5MiB allocated

Counts

21 → 79

Calls

Call 1

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

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

Calls

6 calls:

Time	Variable		Point	Expression
25.0ms	n	@	-inf	((pow (pow (* n (* (PI) 2)) k) 1/2) (sqrt (* n (* (PI) 2))) (* n (* (PI) 2)) (* (PI) 2) (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (* (sqrt 2) (sqrt (/ (* (PI) n) k))) (sqrt 2) (sqrt (/ (* (PI) n) k)) (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (/ 1 (sqrt k)) (sqrt k) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2)) (* (/ 1 (sqrt k)) (sqrt (pow (* n (* (PI) 2)) (- 1 k)))) (sqrt (pow (* n (* (PI) 2)) (- 1 k))) (* (/ 1 (sqrt k)) (* (pow (* n (* (PI) 2)) (* k -1/2)) (sqrt (* n (* (PI) 2))))) (* (pow (* n (* (PI) 2)) (* k -1/2)) (sqrt (* n (* (PI) 2)))) (PI) (/ (sqrt (* n (* (PI) 2))) (* (sqrt k) (pow (pow (* n (* (PI) 2)) k) 1/2))) (/ (- 1 k) 2) (* (* 2 (PI)) n) (pow (* n (* (PI) 2)) (- 1 k)))
14.0ms	n	@	0	((pow (pow (* n (* (PI) 2)) k) 1/2) (sqrt (* n (* (PI) 2))) (* n (* (PI) 2)) (* (PI) 2) (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (* (sqrt 2) (sqrt (/ (* (PI) n) k))) (sqrt 2) (sqrt (/ (* (PI) n) k)) (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (/ 1 (sqrt k)) (sqrt k) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2)) (* (/ 1 (sqrt k)) (sqrt (pow (* n (* (PI) 2)) (- 1 k)))) (sqrt (pow (* n (* (PI) 2)) (- 1 k))) (* (/ 1 (sqrt k)) (* (pow (* n (* (PI) 2)) (* k -1/2)) (sqrt (* n (* (PI) 2))))) (* (pow (* n (* (PI) 2)) (* k -1/2)) (sqrt (* n (* (PI) 2)))) (PI) (/ (sqrt (* n (* (PI) 2))) (* (sqrt k) (pow (pow (* n (* (PI) 2)) k) 1/2))) (/ (- 1 k) 2) (* (* 2 (PI)) n) (pow (* n (* (PI) 2)) (- 1 k)))
14.0ms	n	@	inf	((pow (pow (* n (* (PI) 2)) k) 1/2) (sqrt (* n (* (PI) 2))) (* n (* (PI) 2)) (* (PI) 2) (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (* (sqrt 2) (sqrt (/ (* (PI) n) k))) (sqrt 2) (sqrt (/ (* (PI) n) k)) (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (/ 1 (sqrt k)) (sqrt k) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2)) (* (/ 1 (sqrt k)) (sqrt (pow (* n (* (PI) 2)) (- 1 k)))) (sqrt (pow (* n (* (PI) 2)) (- 1 k))) (* (/ 1 (sqrt k)) (* (pow (* n (* (PI) 2)) (* k -1/2)) (sqrt (* n (* (PI) 2))))) (* (pow (* n (* (PI) 2)) (* k -1/2)) (sqrt (* n (* (PI) 2)))) (PI) (/ (sqrt (* n (* (PI) 2))) (* (sqrt k) (pow (pow (* n (* (PI) 2)) k) 1/2))) (/ (- 1 k) 2) (* (* 2 (PI)) n) (pow (* n (* (PI) 2)) (- 1 k)))
8.0ms	k	@	inf	((pow (pow (* n (* (PI) 2)) k) 1/2) (sqrt (* n (* (PI) 2))) (* n (* (PI) 2)) (* (PI) 2) (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (* (sqrt 2) (sqrt (/ (* (PI) n) k))) (sqrt 2) (sqrt (/ (* (PI) n) k)) (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (/ 1 (sqrt k)) (sqrt k) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2)) (* (/ 1 (sqrt k)) (sqrt (pow (* n (* (PI) 2)) (- 1 k)))) (sqrt (pow (* n (* (PI) 2)) (- 1 k))) (* (/ 1 (sqrt k)) (* (pow (* n (* (PI) 2)) (* k -1/2)) (sqrt (* n (* (PI) 2))))) (* (pow (* n (* (PI) 2)) (* k -1/2)) (sqrt (* n (* (PI) 2)))) (PI) (/ (sqrt (* n (* (PI) 2))) (* (sqrt k) (pow (pow (* n (* (PI) 2)) k) 1/2))) (/ (- 1 k) 2) (* (* 2 (PI)) n) (pow (* n (* (PI) 2)) (- 1 k)))
7.0ms	k	@	0	((pow (pow (* n (* (PI) 2)) k) 1/2) (sqrt (* n (* (PI) 2))) (* n (* (PI) 2)) (* (PI) 2) (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (* (sqrt 2) (sqrt (/ (* (PI) n) k))) (sqrt 2) (sqrt (/ (* (PI) n) k)) (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (/ 1 (sqrt k)) (sqrt k) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2)) (* (/ 1 (sqrt k)) (sqrt (pow (* n (* (PI) 2)) (- 1 k)))) (sqrt (pow (* n (* (PI) 2)) (- 1 k))) (* (/ 1 (sqrt k)) (* (pow (* n (* (PI) 2)) (* k -1/2)) (sqrt (* n (* (PI) 2))))) (* (pow (* n (* (PI) 2)) (* k -1/2)) (sqrt (* n (* (PI) 2)))) (PI) (/ (sqrt (* n (* (PI) 2))) (* (sqrt k) (pow (pow (* n (* (PI) 2)) k) 1/2))) (/ (- 1 k) 2) (* (* 2 (PI)) n) (pow (* n (* (PI) 2)) (- 1 k)))

simplify157.0ms (1.6%)

Memory

3.5MiB live, 195.6MiB allocated

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	355	1888
1	1073	1764
2	3832	1655
0	8195	1615

Stop Event

1×	iter limit
1×	node limit

Counts

79 → 79

Calls

Call 1

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

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

rewrite252.0ms (2.6%)

Memory

11.1MiB live, 169.8MiB allocated

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	45	212
0	73	192
1	236	181
2	1208	177
0	8225	177

Stop Event

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

Counts

21 → 1 290

Calls

Call 1

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

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

eval334.0ms (3.4%)

Memory: 8.0MiB live, 318.3MiB allocated
Compiler: Compiled 34 607 to 4 383 computations (87.3% saved)

prune201.0ms (2.1%)

Memory

-24.9MiB live, 103.4MiB allocated

Pruning

25 alts after pruning (24 fresh and 1 done)

	Pruned	Kept	Total
New	1 369	22	1 391
Fresh	13	2	15
Picked	4	1	5
Done	0	0	0
Total	1 386	25	1 411

Accuracy

100.0%

Counts

1 411 → 25

Alt Table

Click to see full alt table

Status	Accuracy	Program
▶	99.4%	(/.f64 (pow.f64 (sqrt.f64 (.f64 (.f64 #s(literal 2 binary64) (PI.f64)) n)) (-.f64 #s(literal 1 binary64) k)) (sqrt.f64 k))
	99.7%	(/.f64 (sqrt.f64 (.f64 n (.f64 (PI.f64) #s(literal 2 binary64)))) (.f64 (sqrt.f64 k) (pow.f64 (.f64 (.f64 #s(literal 2 binary64) (PI.f64)) n) (.f64 #s(literal 1/2 binary64) k))))
	89.3%	(/.f64 #s(literal 1 binary64) (sqrt.f64 (/.f64 k (pow.f64 (.f64 (.f64 #s(literal 2 binary64) (PI.f64)) n) (-.f64 #s(literal 1 binary64) k)))))
	99.4%	(.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) (pow.f64 (.f64 (*.f64 #s(literal 2 binary64) (PI.f64)) n) (fma.f64 k #s(literal -1/2 binary64) #s(literal 1/2 binary64))))
	48.7%	(.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) (sqrt.f64 #s(approx (pow ( n (* (PI) 2)) (- 1 k)) (.f64 (.f64 (PI.f64) n) #s(literal 2 binary64)))))
	48.6%	(.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) #s(approx (pow ( (* 2 (PI)) n) (/ (- 1 k) 2)) (.f64 (sqrt.f64 (.f64 (PI.f64) n)) (sqrt.f64 #s(literal 2 binary64)))))
▶	99.7%	(.f64 (sqrt.f64 n) (sqrt.f64 (/.f64 (.f64 #s(literal 2 binary64) (PI.f64)) (.f64 k (pow.f64 (.f64 (*.f64 #s(literal 2 binary64) (PI.f64)) n) k)))))
	87.9%	(sqrt.f64 (/.f64 (pow.f64 (.f64 (.f64 #s(literal 2 binary64) (PI.f64)) n) (-.f64 #s(literal 1 binary64) k)) k))
	75.2%	(sqrt.f64 (/.f64 (.f64 (/.f64 (.f64 (PI.f64) n) k) #s(literal 2 binary64)) (pow.f64 (.f64 (.f64 #s(literal 2 binary64) (PI.f64)) n) k)))
	88.1%	(sqrt.f64 (/.f64 (.f64 (.f64 #s(literal 2 binary64) (PI.f64)) n) (.f64 (pow.f64 (.f64 (*.f64 #s(literal 2 binary64) (PI.f64)) n) k) k)))
	48.8%	#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (/.f64 (sqrt.f64 (.f64 (.f64 #s(literal 2 binary64) (PI.f64)) n)) (sqrt.f64 k)))
▶	38.7%	#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)))))
	38.7%	#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (/.f64 #s(literal 1 binary64) (sqrt.f64 (/.f64 k (.f64 (.f64 #s(literal 2 binary64) (PI.f64)) n)))))
	48.5%	#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (.f64 (/.f64 (sqrt.f64 n) #s(literal -1 binary64)) (/.f64 (neg.f64 (sqrt.f64 (.f64 #s(literal 2 binary64) (PI.f64)))) (sqrt.f64 k))))
▶	48.6%	#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (.f64 (/.f64 (sqrt.f64 #s(literal 2 binary64)) (sqrt.f64 k)) (/.f64 (sqrt.f64 (.f64 (PI.f64) n)) #s(literal 1 binary64))))
	48.8%	#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (.f64 (sqrt.f64 (.f64 (*.f64 #s(literal 2 binary64) (PI.f64)) n)) (pow.f64 k #s(literal -1/2 binary64))))
	37.1%	#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))))
	48.8%	#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))))
	48.6%	#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (.f64 (sqrt.f64 #s(literal 2 binary64)) (/.f64 (sqrt.f64 (.f64 (PI.f64) n)) (sqrt.f64 k))))
	38.6%	#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (.f64 (sqrt.f64 #s(literal 2 binary64)) (/.f64 #s(literal 1 binary64) (sqrt.f64 (/.f64 k (.f64 (PI.f64) n))))))
	48.6%	#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (.f64 (sqrt.f64 #s(literal 2 binary64)) (.f64 (/.f64 (sqrt.f64 (PI.f64)) (sqrt.f64 k)) (/.f64 (sqrt.f64 n) #s(literal 1 binary64)))))
	48.6%	#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (.f64 (sqrt.f64 #s(literal 2 binary64)) (.f64 (sqrt.f64 n) (sqrt.f64 (/.f64 (PI.f64) k)))))
	48.6%	#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (.f64 (sqrt.f64 #s(literal 2 binary64)) (.f64 (neg.f64 (sqrt.f64 (*.f64 (PI.f64) n))) (/.f64 #s(literal -1 binary64) (sqrt.f64 k)))))
✓	37.2%	#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (.f64 (sqrt.f64 #s(literal 2 binary64)) (sqrt.f64 (/.f64 (.f64 (PI.f64) n) k))))
▶	37.3%	#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt.f64 (.f64 (/.f64 (.f64 (PI.f64) n) k) #s(literal 2 binary64))))

Compiler

Compiled 1 128 to 925 computations (18% saved)

simplify13.0ms (0.1%)

Memory

15.9MiB live, 15.9MiB allocated

Algorithm

1×	egg-herbie

Localize:

Found 20 expressions of interest:

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

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	42	296
0	68	290
1	106	284
2	159	284
3	212	284
4	250	284
5	267	284
6	290	284
7	327	284
8	357	284
9	363	284
0	363	281

Stop Event

1×	iter limit
1×	saturated
1×	iter limit

Calls

Call 1

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

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

localize162.0ms (1.7%)

Memory

-8.2MiB live, 149.8MiB allocated

Localize:

Found 20 expressions of interest:

New	Metric	Score
accuracy	0.16796875	(/.f64 (pow.f64 (sqrt.f64 (.f64 (.f64 #s(literal 2 binary64) (PI.f64)) n)) (-.f64 #s(literal 1 binary64) k)) (sqrt.f64 k))
accuracy	0.17578125	(.f64 (.f64 #s(literal 2 binary64) (PI.f64)) n)
accuracy	0.21239241407793455	(pow.f64 (sqrt.f64 (.f64 (.f64 #s(literal 2 binary64) (PI.f64)) n)) (-.f64 #s(literal 1 binary64) k))
accuracy	15.499622646281887	(PI.f64)
accuracy	0.25390625	(.f64 (/.f64 (sqrt.f64 #s(literal 2 binary64)) (sqrt.f64 k)) (/.f64 (sqrt.f64 (.f64 (PI.f64) n)) #s(literal 1 binary64)))
accuracy	0.2858200195368841	(/.f64 (sqrt.f64 #s(literal 2 binary64)) (sqrt.f64 k))
accuracy	15.499622646281887	(PI.f64)
accuracy	17.001606273173245	#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (.f64 (/.f64 (sqrt.f64 #s(literal 2 binary64)) (sqrt.f64 k)) (/.f64 (sqrt.f64 (.f64 (PI.f64) n)) #s(literal 1 binary64))))
accuracy	0.33041000976844204	(/.f64 (sqrt.f64 #s(literal 2 binary64)) (sqrt.f64 (/.f64 k (*.f64 (PI.f64) n))))
accuracy	6.601368888339808	(sqrt.f64 (/.f64 k (*.f64 (PI.f64) n)))
accuracy	15.499622646281887	(PI.f64)
accuracy	17.001606273173245	#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)))))
accuracy	0.19921875	(/.f64 (*.f64 (PI.f64) n) k)
accuracy	7.604149870127605	(sqrt.f64 (.f64 (/.f64 (.f64 (PI.f64) n) k) #s(literal 2 binary64)))
accuracy	15.499622646281887	(PI.f64)
accuracy	17.001606273173245	#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))))
accuracy	0.1328125	(.f64 (sqrt.f64 n) (sqrt.f64 (/.f64 (.f64 #s(literal 2 binary64) (PI.f64)) (.f64 k (pow.f64 (.f64 (*.f64 #s(literal 2 binary64) (PI.f64)) n) k)))))
accuracy	0.140625	(/.f64 (.f64 #s(literal 2 binary64) (PI.f64)) (.f64 k (pow.f64 (.f64 (.f64 #s(literal 2 binary64) (PI.f64)) n) k)))
accuracy	0.17578125	(.f64 (.f64 #s(literal 2 binary64) (PI.f64)) n)
accuracy	15.499622646281887	(PI.f64)

Samples

105.0ms	192×	0	valid
18.0ms	64×	0	exit

Compiler

Compiled 562 to 80 computations (85.8% saved)

Precisions

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

ival-sqrt: 50.0ms (48.9% of total)

ival-div: 19.0ms (18.6% of total)

ival-mult: 18.0ms (17.6% of total)

ival-pow: 12.0ms (11.7% of total)

ival-pi: 1.0ms (1% of total)

ival-sub: 1.0ms (1% of total)

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

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

exact: 0.0ms (0% of total)

series264.0ms (2.7%)

Memory

-3.7MiB live, 153.3MiB allocated

Counts

22 → 64

Calls

Call 1

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

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

Calls

6 calls:

Time	Variable		Point	Expression
80.0ms	n	@	0	((* (sqrt n) (sqrt (/ (* 2 (PI)) (* k (pow (* (* 2 (PI)) n) k))))) (sqrt n) (sqrt (/ (* 2 (PI)) (* k (pow (* (* 2 (PI)) n) k)))) (* 2 (PI)) (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt (* (/ (* (PI) n) k) 2)) (* (/ (* (PI) n) k) 2) (/ (* (PI) n) k) (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (/ (sqrt 2) (sqrt (/ k (* (PI) n)))) (sqrt 2) (sqrt (/ k (* (PI) n))) (/ (sqrt (* (PI) n)) 1) (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (* (/ (sqrt 2) (sqrt k)) (/ (sqrt (* (PI) n)) 1)) (/ (sqrt 2) (sqrt k)) (/ (pow (sqrt (* (* 2 (PI)) n)) (- 1 k)) (sqrt k)) (pow (sqrt (* (* 2 (PI)) n)) (- 1 k)) (sqrt (* (* 2 (PI)) n)) (* (* 2 (PI)) n) (PI) (/ (* 2 (PI)) (* k (pow (* (* 2 (PI)) n) k))))
73.0ms	n	@	-inf	((* (sqrt n) (sqrt (/ (* 2 (PI)) (* k (pow (* (* 2 (PI)) n) k))))) (sqrt n) (sqrt (/ (* 2 (PI)) (* k (pow (* (* 2 (PI)) n) k)))) (* 2 (PI)) (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt (* (/ (* (PI) n) k) 2)) (* (/ (* (PI) n) k) 2) (/ (* (PI) n) k) (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (/ (sqrt 2) (sqrt (/ k (* (PI) n)))) (sqrt 2) (sqrt (/ k (* (PI) n))) (/ (sqrt (* (PI) n)) 1) (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (* (/ (sqrt 2) (sqrt k)) (/ (sqrt (* (PI) n)) 1)) (/ (sqrt 2) (sqrt k)) (/ (pow (sqrt (* (* 2 (PI)) n)) (- 1 k)) (sqrt k)) (pow (sqrt (* (* 2 (PI)) n)) (- 1 k)) (sqrt (* (* 2 (PI)) n)) (* (* 2 (PI)) n) (PI) (/ (* 2 (PI)) (* k (pow (* (* 2 (PI)) n) k))))
60.0ms	n	@	inf	((* (sqrt n) (sqrt (/ (* 2 (PI)) (* k (pow (* (* 2 (PI)) n) k))))) (sqrt n) (sqrt (/ (* 2 (PI)) (* k (pow (* (* 2 (PI)) n) k)))) (* 2 (PI)) (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt (* (/ (* (PI) n) k) 2)) (* (/ (* (PI) n) k) 2) (/ (* (PI) n) k) (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (/ (sqrt 2) (sqrt (/ k (* (PI) n)))) (sqrt 2) (sqrt (/ k (* (PI) n))) (/ (sqrt (* (PI) n)) 1) (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (* (/ (sqrt 2) (sqrt k)) (/ (sqrt (* (PI) n)) 1)) (/ (sqrt 2) (sqrt k)) (/ (pow (sqrt (* (* 2 (PI)) n)) (- 1 k)) (sqrt k)) (pow (sqrt (* (* 2 (PI)) n)) (- 1 k)) (sqrt (* (* 2 (PI)) n)) (* (* 2 (PI)) n) (PI) (/ (* 2 (PI)) (* k (pow (* (* 2 (PI)) n) k))))
6.0ms	k	@	0	((* (sqrt n) (sqrt (/ (* 2 (PI)) (* k (pow (* (* 2 (PI)) n) k))))) (sqrt n) (sqrt (/ (* 2 (PI)) (* k (pow (* (* 2 (PI)) n) k)))) (* 2 (PI)) (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt (* (/ (* (PI) n) k) 2)) (* (/ (* (PI) n) k) 2) (/ (* (PI) n) k) (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (/ (sqrt 2) (sqrt (/ k (* (PI) n)))) (sqrt 2) (sqrt (/ k (* (PI) n))) (/ (sqrt (* (PI) n)) 1) (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (* (/ (sqrt 2) (sqrt k)) (/ (sqrt (* (PI) n)) 1)) (/ (sqrt 2) (sqrt k)) (/ (pow (sqrt (* (* 2 (PI)) n)) (- 1 k)) (sqrt k)) (pow (sqrt (* (* 2 (PI)) n)) (- 1 k)) (sqrt (* (* 2 (PI)) n)) (* (* 2 (PI)) n) (PI) (/ (* 2 (PI)) (* k (pow (* (* 2 (PI)) n) k))))
6.0ms	k	@	-inf	((* (sqrt n) (sqrt (/ (* 2 (PI)) (* k (pow (* (* 2 (PI)) n) k))))) (sqrt n) (sqrt (/ (* 2 (PI)) (* k (pow (* (* 2 (PI)) n) k)))) (* 2 (PI)) (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt (* (/ (* (PI) n) k) 2)) (* (/ (* (PI) n) k) 2) (/ (* (PI) n) k) (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (/ (sqrt 2) (sqrt (/ k (* (PI) n)))) (sqrt 2) (sqrt (/ k (* (PI) n))) (/ (sqrt (* (PI) n)) 1) (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (* (/ (sqrt 2) (sqrt k)) (/ (sqrt (* (PI) n)) 1)) (/ (sqrt 2) (sqrt k)) (/ (pow (sqrt (* (* 2 (PI)) n)) (- 1 k)) (sqrt k)) (pow (sqrt (* (* 2 (PI)) n)) (- 1 k)) (sqrt (* (* 2 (PI)) n)) (* (* 2 (PI)) n) (PI) (/ (* 2 (PI)) (* k (pow (* (* 2 (PI)) n) k))))

simplify198.0ms (2%)

Memory

28.8MiB live, 190.4MiB allocated

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	342	1650
1	1041	1580
2	3767	1471
0	8334	1437

Stop Event

1×	iter limit
1×	node limit

Counts

64 → 64

Calls

Call 1

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

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

rewrite187.0ms (1.9%)

Memory

-21.2MiB live, 250.5MiB allocated

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	42	224
0	68	204
1	233	204
2	1356	198
0	8413	198

Stop Event

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

Counts

22 → 1 046

Calls

Call 1

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

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

eval185.0ms (1.9%)

Memory: 28.6MiB live, 341.8MiB allocated
Compiler: Compiled 27 547 to 4 171 computations (84.9% saved)

prune120.0ms (1.2%)

Memory

-4.9MiB live, 206.2MiB allocated

Pruning

53 alts after pruning (48 fresh and 5 done)

	Pruned	Kept	Total
New	1 046	36	1 082
Fresh	7	12	19
Picked	1	4	5
Done	0	1	1
Total	1 054	53	1 107

Accuracy

100.0%

Counts

1 107 → 53

Alt Table

Click to see full alt table

Status	Accuracy	Program
	99.4%	(/.f64 (pow.f64 (.f64 (.f64 (PI.f64) #s(literal 2 binary64)) n) (-.f64 #s(literal 1/2 binary64) (*.f64 #s(literal 1/2 binary64) k))) (sqrt.f64 k))
✓	99.4%	(/.f64 (pow.f64 (sqrt.f64 (.f64 (.f64 #s(literal 2 binary64) (PI.f64)) n)) (-.f64 #s(literal 1 binary64) k)) (sqrt.f64 k))
▶	99.4%	(/.f64 (sqrt.f64 (pow.f64 (.f64 (.f64 (PI.f64) #s(literal 2 binary64)) n) (-.f64 #s(literal 1 binary64) k))) (sqrt.f64 k))
	48.7%	(/.f64 #s(approx (pow (sqrt (* (* 2 (PI)) n)) (- 1 k)) (.f64 (sqrt.f64 (.f64 (PI.f64) n)) (sqrt.f64 #s(literal 2 binary64)))) (sqrt.f64 k))
	89.3%	(/.f64 #s(literal 1 binary64) (sqrt.f64 (/.f64 k (pow.f64 (.f64 (.f64 #s(literal 2 binary64) (PI.f64)) n) (-.f64 #s(literal 1 binary64) k)))))
	99.4%	(.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) (pow.f64 (.f64 (*.f64 #s(literal 2 binary64) (PI.f64)) n) (fma.f64 k #s(literal -1/2 binary64) #s(literal 1/2 binary64))))
	48.7%	(.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) (sqrt.f64 #s(approx (pow ( n (* (PI) 2)) (- 1 k)) (.f64 (.f64 (PI.f64) n) #s(literal 2 binary64)))))
	48.6%	(.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) #s(approx (pow ( (* 2 (PI)) n) (/ (- 1 k) 2)) (.f64 (sqrt.f64 (.f64 (PI.f64) n)) (sqrt.f64 #s(literal 2 binary64)))))
	75.2%	(.f64 (sqrt.f64 (.f64 (/.f64 (.f64 (PI.f64) n) k) #s(literal 2 binary64))) (pow.f64 (sqrt.f64 (.f64 (*.f64 (PI.f64) #s(literal 2 binary64)) n)) (neg.f64 k)))
✓	99.7%	(.f64 (sqrt.f64 n) (sqrt.f64 (/.f64 (.f64 #s(literal 2 binary64) (PI.f64)) (.f64 k (pow.f64 (.f64 (*.f64 #s(literal 2 binary64) (PI.f64)) n) k)))))
▶	48.8%	(.f64 (sqrt.f64 n) (sqrt.f64 #s(approx (/ ( 2 (PI)) (* k (pow (* (* 2 (PI)) n) k))) (*.f64 (/.f64 (PI.f64) k) #s(literal 2 binary64)))))
	48.7%	(.f64 (sqrt.f64 n) #s(approx (sqrt (/ ( 2 (PI)) (* k (pow (* (* 2 (PI)) n) k)))) (*.f64 (sqrt.f64 (/.f64 (PI.f64) k)) (sqrt.f64 #s(literal 2 binary64)))))
	87.9%	(sqrt.f64 (/.f64 (pow.f64 (.f64 (.f64 #s(literal 2 binary64) (PI.f64)) n) (-.f64 #s(literal 1 binary64) k)) k))
	88.1%	(sqrt.f64 (/.f64 (.f64 (.f64 #s(literal 2 binary64) (PI.f64)) n) (.f64 (pow.f64 (.f64 (*.f64 #s(literal 2 binary64) (PI.f64)) n) k) k)))
	75.2%	(sqrt.f64 (.f64 (.f64 n (/.f64 #s(literal 2 binary64) k)) (/.f64 (PI.f64) (pow.f64 (.f64 (.f64 (PI.f64) #s(literal 2 binary64)) n) k))))
	48.8%	#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (/.f64 (sqrt.f64 (.f64 (.f64 (PI.f64) #s(literal 2 binary64)) n)) (sqrt.f64 k)))
	48.7%	#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)))))
	48.6%	#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (/.f64 (sqrt.f64 #s(literal 2 binary64)) (/.f64 (sqrt.f64 (/.f64 k (PI.f64))) (sqrt.f64 n))))
	38.8%	#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (/.f64 (sqrt.f64 #s(literal 2 binary64)) (/.f64 (sqrt.f64 (/.f64 k n)) (sqrt.f64 (PI.f64)))))
	48.6%	#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (/.f64 (sqrt.f64 #s(literal 2 binary64)) (/.f64 (sqrt.f64 k) (sqrt.f64 (*.f64 (PI.f64) n)))))
	48.6%	#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (/.f64 (sqrt.f64 #s(literal 2 binary64)) (/.f64 #s(literal 1 binary64) (/.f64 (sqrt.f64 n) (sqrt.f64 (/.f64 k (PI.f64)))))))
	48.6%	#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (/.f64 (sqrt.f64 #s(literal 2 binary64)) (.f64 (/.f64 #s(literal -1 binary64) (sqrt.f64 (.f64 (PI.f64) n))) (neg.f64 (sqrt.f64 k)))))
✓	38.7%	#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)))))
	48.7%	#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (/.f64 (neg.f64 (sqrt.f64 (/.f64 #s(literal 2 binary64) k))) (/.f64 #s(literal -1 binary64) (sqrt.f64 (*.f64 (PI.f64) n)))))
▶	48.7%	#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (/.f64 #s(literal 1 binary64) (/.f64 (neg.f64 (sqrt.f64 (.f64 k #s(literal 1/2 binary64)))) (neg.f64 (sqrt.f64 (.f64 (PI.f64) n))))))
	38.7%	#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (/.f64 #s(literal 1 binary64) (sqrt.f64 (/.f64 k (.f64 (.f64 #s(literal 2 binary64) (PI.f64)) n)))))
	48.6%	#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (/.f64 #s(literal -1 binary64) (.f64 (/.f64 #s(literal -1 binary64) (sqrt.f64 (.f64 (PI.f64) n))) (sqrt.f64 (*.f64 k #s(literal 1/2 binary64))))))
	48.5%	#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (.f64 (/.f64 (sqrt.f64 n) #s(literal -1 binary64)) (/.f64 (neg.f64 (sqrt.f64 (.f64 #s(literal 2 binary64) (PI.f64)))) (sqrt.f64 k))))
	48.7%	#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (.f64 (/.f64 (sqrt.f64 #s(literal 2 binary64)) (sqrt.f64 k)) (/.f64 (sqrt.f64 (.f64 (*.f64 (sqrt.f64 (PI.f64)) (sqrt.f64 (PI.f64))) n)) #s(literal 1 binary64))))
▶	48.6%	#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (.f64 (/.f64 (sqrt.f64 #s(literal 2 binary64)) (sqrt.f64 k)) (/.f64 #s(literal -1 binary64) (/.f64 #s(literal -1 binary64) (sqrt.f64 (.f64 (PI.f64) n))))))
	48.6%	#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (.f64 (/.f64 (sqrt.f64 #s(literal 2 binary64)) (sqrt.f64 k)) (sqrt.f64 (.f64 (PI.f64) n))))
	48.6%	#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (.f64 (/.f64 #s(literal 1 binary64) (/.f64 (neg.f64 (sqrt.f64 k)) (.f64 (sqrt.f64 #s(literal 2 binary64)) #s(literal -1 binary64)))) (/.f64 (sqrt.f64 (*.f64 (PI.f64) n)) #s(literal 1 binary64))))
	48.6%	#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (.f64 (.f64 (neg.f64 (sqrt.f64 #s(literal 2 binary64))) (/.f64 #s(literal -1 binary64) (sqrt.f64 k))) (/.f64 (sqrt.f64 (*.f64 (PI.f64) n)) #s(literal 1 binary64))))
	48.7%	#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))))
	37.1%	#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (.f64 (sqrt.f64 (.f64 (PI.f64) #s(literal 2 binary64))) (sqrt.f64 (/.f64 n k))))
	37.1%	#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)))))
	48.6%	#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (.f64 (sqrt.f64 #s(literal 2 binary64)) (/.f64 (sqrt.f64 (.f64 (PI.f64) n)) (sqrt.f64 k))))
	38.6%	#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (.f64 (sqrt.f64 #s(literal 2 binary64)) (/.f64 #s(literal 1 binary64) (sqrt.f64 (/.f64 k (.f64 (PI.f64) n))))))
	48.6%	#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (.f64 (sqrt.f64 #s(literal 2 binary64)) (.f64 (/.f64 (sqrt.f64 (PI.f64)) (sqrt.f64 k)) (/.f64 (sqrt.f64 n) #s(literal 1 binary64)))))
	48.6%	#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (.f64 (sqrt.f64 #s(literal 2 binary64)) (.f64 (sqrt.f64 n) (sqrt.f64 (/.f64 (PI.f64) k)))))
✓	37.2%	#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (.f64 (sqrt.f64 #s(literal 2 binary64)) (sqrt.f64 (/.f64 (.f64 (PI.f64) n) k))))
	48.7%	#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (.f64 (neg.f64 (sqrt.f64 (.f64 (PI.f64) n))) (/.f64 #s(literal 1 binary64) (neg.f64 (sqrt.f64 (*.f64 k #s(literal 1/2 binary64)))))))
	48.6%	#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (.f64 #s(approx (/ (sqrt 2) (sqrt k)) (.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) k)) (sqrt.f64 #s(literal 2 binary64)))) (/.f64 (sqrt.f64 (*.f64 (PI.f64) n)) #s(literal 1 binary64))))
	37.3%	#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt.f64 (/.f64 (*.f64 (PI.f64) #s(literal 2 binary64)) (/.f64 k n))))
	37.3%	#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt.f64 (/.f64 #s(literal 2 binary64) (/.f64 k (*.f64 (PI.f64) n)))))
	37.1%	#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt.f64 (.f64 (/.f64 (.f64 (*.f64 (sqrt.f64 (PI.f64)) (sqrt.f64 (PI.f64))) n) k) #s(literal 2 binary64))))
✓	37.3%	#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))))
	37.3%	#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt.f64 (*.f64 (/.f64 n (/.f64 k (PI.f64))) #s(literal 2 binary64))))
	37.3%	#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt.f64 (.f64 (/.f64 #s(literal 2 binary64) k) (.f64 (PI.f64) n))))
	37.3%	#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt.f64 (.f64 (.f64 (/.f64 (PI.f64) k) n) #s(literal 2 binary64))))
	37.3%	#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt.f64 (.f64 (.f64 (/.f64 n k) (PI.f64)) #s(literal 2 binary64))))
	37.1%	#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt.f64 (.f64 (.f64 (sqrt.f64 (PI.f64)) (*.f64 (sqrt.f64 (PI.f64)) (/.f64 n k))) #s(literal 2 binary64))))
▶	37.2%	#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt.f64 (.f64 (.f64 (PI.f64) (/.f64 #s(literal 2 binary64) k)) n)))

Compiler

Compiled 2 541 to 2 064 computations (18.8% saved)

simplify74.0ms (0.8%)

Memory

-3.4MiB live, 72.7MiB allocated

Algorithm

1×	egg-herbie

Localize:

Found 20 expressions of interest:

New	Metric	Score
cost-diff	0	(/.f64 (sqrt.f64 #s(literal 2 binary64)) (sqrt.f64 k))
cost-diff	0	(.f64 (/.f64 (sqrt.f64 #s(literal 2 binary64)) (sqrt.f64 k)) (/.f64 #s(literal -1 binary64) (/.f64 #s(literal -1 binary64) (sqrt.f64 (.f64 (PI.f64) n)))))
cost-diff	0	#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (.f64 (/.f64 (sqrt.f64 #s(literal 2 binary64)) (sqrt.f64 k)) (/.f64 #s(literal -1 binary64) (/.f64 #s(literal -1 binary64) (sqrt.f64 (.f64 (PI.f64) n))))))
cost-diff	1408	(/.f64 #s(literal -1 binary64) (/.f64 #s(literal -1 binary64) (sqrt.f64 (*.f64 (PI.f64) n))))
cost-diff	0	(neg.f64 (sqrt.f64 (*.f64 k #s(literal 1/2 binary64))))
cost-diff	0	#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (/.f64 #s(literal 1 binary64) (/.f64 (neg.f64 (sqrt.f64 (.f64 k #s(literal 1/2 binary64)))) (neg.f64 (sqrt.f64 (.f64 (PI.f64) n))))))
cost-diff	256	(/.f64 (neg.f64 (sqrt.f64 (.f64 k #s(literal 1/2 binary64)))) (neg.f64 (sqrt.f64 (.f64 (PI.f64) n))))
cost-diff	704	(/.f64 #s(literal 1 binary64) (/.f64 (neg.f64 (sqrt.f64 (.f64 k #s(literal 1/2 binary64)))) (neg.f64 (sqrt.f64 (.f64 (PI.f64) n)))))
cost-diff	0	#s(approx (/ (* 2 (PI)) (* k (pow (* (* 2 (PI)) n) k))) (*.f64 (/.f64 (PI.f64) k) #s(literal 2 binary64)))
cost-diff	0	(sqrt.f64 #s(approx (/ (* 2 (PI)) (* k (pow (* (* 2 (PI)) n) k))) (*.f64 (/.f64 (PI.f64) k) #s(literal 2 binary64))))
cost-diff	0	(sqrt.f64 n)
cost-diff	0	(.f64 (sqrt.f64 n) (sqrt.f64 #s(approx (/ ( 2 (PI)) (* k (pow (* (* 2 (PI)) n) k))) (*.f64 (/.f64 (PI.f64) k) #s(literal 2 binary64)))))
cost-diff	0	(*.f64 (PI.f64) (/.f64 #s(literal 2 binary64) k))
cost-diff	0	(.f64 (.f64 (PI.f64) (/.f64 #s(literal 2 binary64) k)) n)
cost-diff	0	(sqrt.f64 (.f64 (.f64 (PI.f64) (/.f64 #s(literal 2 binary64) k)) n))
cost-diff	0	#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt.f64 (.f64 (.f64 (PI.f64) (/.f64 #s(literal 2 binary64) k)) n)))
cost-diff	0	(.f64 (.f64 (PI.f64) #s(literal 2 binary64)) n)
cost-diff	0	(pow.f64 (.f64 (.f64 (PI.f64) #s(literal 2 binary64)) n) (-.f64 #s(literal 1 binary64) k))
cost-diff	0	(sqrt.f64 (pow.f64 (.f64 (.f64 (PI.f64) #s(literal 2 binary64)) n) (-.f64 #s(literal 1 binary64) k)))
cost-diff	0	(/.f64 (sqrt.f64 (pow.f64 (.f64 (.f64 (PI.f64) #s(literal 2 binary64)) n) (-.f64 #s(literal 1 binary64) k))) (sqrt.f64 k))

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	52	341
0	82	333
1	135	321
2	239	313
3	446	313
4	856	313
5	1390	313
6	1832	313
7	2018	313
8	2160	313
9	2230	313
10	2273	313
11	2288	313
12	2290	313
13	2290	313
0	2290	310

Stop Event

1×	iter limit
1×	saturated
1×	iter limit

Calls

Call 1

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

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

localize131.0ms (1.3%)

Memory

-8.1MiB live, 270.8MiB allocated

Localize:

Found 20 expressions of interest:

New	Metric	Score
accuracy	0.25390625	(.f64 (/.f64 (sqrt.f64 #s(literal 2 binary64)) (sqrt.f64 k)) (/.f64 #s(literal -1 binary64) (/.f64 #s(literal -1 binary64) (sqrt.f64 (.f64 (PI.f64) n)))))
accuracy	0.2858200195368841	(/.f64 (sqrt.f64 #s(literal 2 binary64)) (sqrt.f64 k))
accuracy	15.499622646281887	(PI.f64)
accuracy	17.001606273173245	#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (.f64 (/.f64 (sqrt.f64 #s(literal 2 binary64)) (sqrt.f64 k)) (/.f64 #s(literal -1 binary64) (/.f64 #s(literal -1 binary64) (sqrt.f64 (.f64 (PI.f64) n))))))
accuracy	0.1875	(/.f64 #s(literal 1 binary64) (/.f64 (neg.f64 (sqrt.f64 (.f64 k #s(literal 1/2 binary64)))) (neg.f64 (sqrt.f64 (.f64 (PI.f64) n)))))
accuracy	0.27572250976844204	(/.f64 (neg.f64 (sqrt.f64 (.f64 k #s(literal 1/2 binary64)))) (neg.f64 (sqrt.f64 (.f64 (PI.f64) n))))
accuracy	15.499622646281887	(PI.f64)
accuracy	17.001606273173245	#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (/.f64 #s(literal 1 binary64) (/.f64 (neg.f64 (sqrt.f64 (.f64 k #s(literal 1/2 binary64)))) (neg.f64 (sqrt.f64 (.f64 (PI.f64) n))))))
accuracy	0.1328125	(.f64 (sqrt.f64 n) (sqrt.f64 #s(approx (/ ( 2 (PI)) (* k (pow (* (* 2 (PI)) n) k))) (*.f64 (/.f64 (PI.f64) k) #s(literal 2 binary64)))))
accuracy	0.1875	(/.f64 (PI.f64) k)
accuracy	15.499622646281887	(PI.f64)
accuracy	16.64980705545134	#s(approx (/ (* 2 (PI)) (* k (pow (* (* 2 (PI)) n) k))) (*.f64 (/.f64 (PI.f64) k) #s(literal 2 binary64)))
accuracy	0.2421875	(*.f64 (PI.f64) (/.f64 #s(literal 2 binary64) k))
accuracy	7.604149870127605	(sqrt.f64 (.f64 (.f64 (PI.f64) (/.f64 #s(literal 2 binary64) k)) n))
accuracy	15.499622646281887	(PI.f64)
accuracy	17.001606273173245	#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt.f64 (.f64 (.f64 (PI.f64) (/.f64 #s(literal 2 binary64) k)) n)))
accuracy	0.16796875	(/.f64 (sqrt.f64 (pow.f64 (.f64 (.f64 (PI.f64) #s(literal 2 binary64)) n) (-.f64 #s(literal 1 binary64) k))) (sqrt.f64 k))
accuracy	0.17578125	(.f64 (.f64 (PI.f64) #s(literal 2 binary64)) n)
accuracy	0.25590055190739674	(pow.f64 (.f64 (.f64 (PI.f64) #s(literal 2 binary64)) n) (-.f64 #s(literal 1 binary64) k))
accuracy	15.499622646281887	(PI.f64)

Samples

74.0ms	192×	0	valid
22.0ms	64×	0	exit

Compiler

Compiled 628 to 101 computations (83.9% saved)

Precisions

Click to see histograms. Total time spent on operations: 71.0ms

ival-div: 20.0ms (28.1% of total)

ival-mult: 19.0ms (26.7% of total)

ival-sqrt: 15.0ms (21.1% of total)

ival-pow: 13.0ms (18.3% of total)

ival-neg: 2.0ms (2.8% of total)

ival-pi: 1.0ms (1.4% of total)

ival-sub: 1.0ms (1.4% of total)

exact: 1.0ms (1.4% of total)

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

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

series75.0ms (0.8%)

Memory

-16.3MiB live, 115.1MiB allocated

Counts

22 → 76

Calls

Call 1

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

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

Calls

6 calls:

Time	Variable		Point	Expression
30.0ms	n	@	-inf	((/ (sqrt (pow (* (* (PI) 2) n) (- 1 k))) (sqrt k)) (sqrt (pow (* (* (PI) 2) n) (- 1 k))) (pow (* (* (PI) 2) n) (- 1 k)) (* (* (PI) 2) n) (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt (* (* (PI) (/ 2 k)) n)) (* (* (PI) (/ 2 k)) n) (* (PI) (/ 2 k)) (* (sqrt n) (sqrt (/ (* 2 (PI)) (* k (pow (* (* 2 (PI)) n) k))))) (sqrt n) (sqrt (/ (* 2 (PI)) (* k (pow (* (* 2 (PI)) n) k)))) (/ (* 2 (PI)) (* k (pow (* (* 2 (PI)) n) k))) (/ 1 (/ (neg (sqrt (* k 1/2))) (neg (sqrt (* (PI) n))))) (/ (neg (sqrt (* k 1/2))) (neg (sqrt (* (PI) n)))) (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (neg (sqrt (* k 1/2))) (/ -1 (/ -1 (sqrt (* (PI) n)))) (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (* (/ (sqrt 2) (sqrt k)) (/ -1 (/ -1 (sqrt (* (PI) n))))) (/ (sqrt 2) (sqrt k)) (PI) (/ (PI) k))
14.0ms	n	@	inf	((/ (sqrt (pow (* (* (PI) 2) n) (- 1 k))) (sqrt k)) (sqrt (pow (* (* (PI) 2) n) (- 1 k))) (pow (* (* (PI) 2) n) (- 1 k)) (* (* (PI) 2) n) (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt (* (* (PI) (/ 2 k)) n)) (* (* (PI) (/ 2 k)) n) (* (PI) (/ 2 k)) (* (sqrt n) (sqrt (/ (* 2 (PI)) (* k (pow (* (* 2 (PI)) n) k))))) (sqrt n) (sqrt (/ (* 2 (PI)) (* k (pow (* (* 2 (PI)) n) k)))) (/ (* 2 (PI)) (* k (pow (* (* 2 (PI)) n) k))) (/ 1 (/ (neg (sqrt (* k 1/2))) (neg (sqrt (* (PI) n))))) (/ (neg (sqrt (* k 1/2))) (neg (sqrt (* (PI) n)))) (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (neg (sqrt (* k 1/2))) (/ -1 (/ -1 (sqrt (* (PI) n)))) (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (* (/ (sqrt 2) (sqrt k)) (/ -1 (/ -1 (sqrt (* (PI) n))))) (/ (sqrt 2) (sqrt k)) (PI) (/ (PI) k))
11.0ms	n	@	0	((/ (sqrt (pow (* (* (PI) 2) n) (- 1 k))) (sqrt k)) (sqrt (pow (* (* (PI) 2) n) (- 1 k))) (pow (* (* (PI) 2) n) (- 1 k)) (* (* (PI) 2) n) (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt (* (* (PI) (/ 2 k)) n)) (* (* (PI) (/ 2 k)) n) (* (PI) (/ 2 k)) (* (sqrt n) (sqrt (/ (* 2 (PI)) (* k (pow (* (* 2 (PI)) n) k))))) (sqrt n) (sqrt (/ (* 2 (PI)) (* k (pow (* (* 2 (PI)) n) k)))) (/ (* 2 (PI)) (* k (pow (* (* 2 (PI)) n) k))) (/ 1 (/ (neg (sqrt (* k 1/2))) (neg (sqrt (* (PI) n))))) (/ (neg (sqrt (* k 1/2))) (neg (sqrt (* (PI) n)))) (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (neg (sqrt (* k 1/2))) (/ -1 (/ -1 (sqrt (* (PI) n)))) (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (* (/ (sqrt 2) (sqrt k)) (/ -1 (/ -1 (sqrt (* (PI) n))))) (/ (sqrt 2) (sqrt k)) (PI) (/ (PI) k))
9.0ms	k	@	-inf	((/ (sqrt (pow (* (* (PI) 2) n) (- 1 k))) (sqrt k)) (sqrt (pow (* (* (PI) 2) n) (- 1 k))) (pow (* (* (PI) 2) n) (- 1 k)) (* (* (PI) 2) n) (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt (* (* (PI) (/ 2 k)) n)) (* (* (PI) (/ 2 k)) n) (* (PI) (/ 2 k)) (* (sqrt n) (sqrt (/ (* 2 (PI)) (* k (pow (* (* 2 (PI)) n) k))))) (sqrt n) (sqrt (/ (* 2 (PI)) (* k (pow (* (* 2 (PI)) n) k)))) (/ (* 2 (PI)) (* k (pow (* (* 2 (PI)) n) k))) (/ 1 (/ (neg (sqrt (* k 1/2))) (neg (sqrt (* (PI) n))))) (/ (neg (sqrt (* k 1/2))) (neg (sqrt (* (PI) n)))) (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (neg (sqrt (* k 1/2))) (/ -1 (/ -1 (sqrt (* (PI) n)))) (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (* (/ (sqrt 2) (sqrt k)) (/ -1 (/ -1 (sqrt (* (PI) n))))) (/ (sqrt 2) (sqrt k)) (PI) (/ (PI) k))
4.0ms	k	@	0	((/ (sqrt (pow (* (* (PI) 2) n) (- 1 k))) (sqrt k)) (sqrt (pow (* (* (PI) 2) n) (- 1 k))) (pow (* (* (PI) 2) n) (- 1 k)) (* (* (PI) 2) n) (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt (* (* (PI) (/ 2 k)) n)) (* (* (PI) (/ 2 k)) n) (* (PI) (/ 2 k)) (* (sqrt n) (sqrt (/ (* 2 (PI)) (* k (pow (* (* 2 (PI)) n) k))))) (sqrt n) (sqrt (/ (* 2 (PI)) (* k (pow (* (* 2 (PI)) n) k)))) (/ (* 2 (PI)) (* k (pow (* (* 2 (PI)) n) k))) (/ 1 (/ (neg (sqrt (* k 1/2))) (neg (sqrt (* (PI) n))))) (/ (neg (sqrt (* k 1/2))) (neg (sqrt (* (PI) n)))) (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (neg (sqrt (* k 1/2))) (/ -1 (/ -1 (sqrt (* (PI) n)))) (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (* (/ (sqrt 2) (sqrt k)) (/ -1 (/ -1 (sqrt (* (PI) n))))) (/ (sqrt 2) (sqrt k)) (PI) (/ (PI) k))

simplify151.0ms (1.5%)

Memory

5.7MiB live, 194.1MiB allocated

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	384	1888
1	1144	1784
2	4216	1762
0	8099	1723

Stop Event

1×	iter limit
1×	node limit

Counts

76 → 76

Calls

Call 1

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

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

rewrite198.0ms (2%)

Memory

34.0MiB live, 182.7MiB allocated

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	52	267
0	82	228
1	279	224
2	1566	223
0	8237	223

Stop Event

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

Counts

22 → 1 034

Calls

Call 1

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

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

eval200.0ms (2.1%)

Memory: -32.4MiB live, 298.9MiB allocated
Compiler: Compiled 27 555 to 3 972 computations (85.6% saved)

prune104.0ms (1.1%)

Memory

11.4MiB live, 246.2MiB allocated

Pruning

74 alts after pruning (65 fresh and 9 done)

	Pruned	Kept	Total
New	912	31	943
Fresh	9	34	43
Picked	1	4	5
Done	0	5	5
Total	922	74	996

Accuracy

100.0%

Counts

996 → 74

Alt Table

Click to see full alt table

Status	Accuracy	Program
	99.4%	(/.f64 (pow.f64 (.f64 (.f64 (PI.f64) #s(literal 2 binary64)) n) (-.f64 #s(literal 1/2 binary64) (*.f64 #s(literal 1/2 binary64) k))) (sqrt.f64 k))
✓	99.4%	(/.f64 (pow.f64 (sqrt.f64 (.f64 (.f64 #s(literal 2 binary64) (PI.f64)) n)) (-.f64 #s(literal 1 binary64) k)) (sqrt.f64 k))
✓	99.4%	(/.f64 (sqrt.f64 (pow.f64 (.f64 (.f64 (PI.f64) #s(literal 2 binary64)) n) (-.f64 #s(literal 1 binary64) k))) (sqrt.f64 k))
	99.7%	(/.f64 (sqrt.f64 (.f64 (pow.f64 (.f64 (.f64 n #s(literal 2 binary64)) (PI.f64)) (neg.f64 k)) (.f64 (*.f64 n #s(literal 2 binary64)) (PI.f64)))) (sqrt.f64 k))
	48.8%	(/.f64 (sqrt.f64 #s(approx (pow (* (* (PI) 2) n) (- 1 k)) (.f64 (.f64 (PI.f64) n) #s(literal 2 binary64)))) (sqrt.f64 k))
	48.7%	(/.f64 #s(approx (pow (sqrt (* (* 2 (PI)) n)) (- 1 k)) (.f64 (sqrt.f64 (.f64 (PI.f64) n)) (sqrt.f64 #s(literal 2 binary64)))) (sqrt.f64 k))
	89.4%	(/.f64 #s(literal 1 binary64) (sqrt.f64 (.f64 k (pow.f64 (.f64 (*.f64 n #s(literal 2 binary64)) (PI.f64)) (-.f64 k #s(literal 1 binary64))))))
	99.4%	(.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) (pow.f64 (.f64 (*.f64 #s(literal 2 binary64) (PI.f64)) n) (fma.f64 k #s(literal -1/2 binary64) #s(literal 1/2 binary64))))
	48.7%	(.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) (sqrt.f64 #s(approx (pow ( n (* (PI) 2)) (- 1 k)) (.f64 (.f64 (PI.f64) n) #s(literal 2 binary64)))))
	48.6%	(.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) #s(approx (pow ( (* 2 (PI)) n) (/ (- 1 k) 2)) (.f64 (sqrt.f64 (.f64 (PI.f64) n)) (sqrt.f64 #s(literal 2 binary64)))))
✓	99.7%	(.f64 (sqrt.f64 n) (sqrt.f64 (/.f64 (.f64 #s(literal 2 binary64) (PI.f64)) (.f64 k (pow.f64 (.f64 (*.f64 #s(literal 2 binary64) (PI.f64)) n) k)))))
✓	48.8%	(.f64 (sqrt.f64 n) (sqrt.f64 #s(approx (/ ( 2 (PI)) (* k (pow (* (* 2 (PI)) n) k))) (*.f64 (/.f64 (PI.f64) k) #s(literal 2 binary64)))))
	48.6%	(.f64 (sqrt.f64 n) (sqrt.f64 #s(approx (/ ( 2 (PI)) (* k (pow (* (* 2 (PI)) n) k))) (.f64 (.f64 (sqrt.f64 (PI.f64)) (/.f64 (sqrt.f64 (PI.f64)) k)) #s(literal 2 binary64)))))
	48.7%	(.f64 (sqrt.f64 n) #s(approx (sqrt (/ ( 2 (PI)) (* k (pow (* (* 2 (PI)) n) k)))) (*.f64 (sqrt.f64 (/.f64 (PI.f64) k)) (sqrt.f64 #s(literal 2 binary64)))))
	87.9%	(sqrt.f64 (/.f64 (pow.f64 (.f64 (.f64 n #s(literal 2 binary64)) (PI.f64)) (-.f64 #s(literal 1 binary64) k)) k))
	88.1%	(sqrt.f64 (/.f64 (.f64 (.f64 #s(literal 2 binary64) (PI.f64)) n) (.f64 (pow.f64 (.f64 (*.f64 #s(literal 2 binary64) (PI.f64)) n) k) k)))
	75.2%	(sqrt.f64 (.f64 (.f64 n (/.f64 #s(literal 2 binary64) k)) (/.f64 (PI.f64) (pow.f64 (.f64 (.f64 (PI.f64) #s(literal 2 binary64)) n) k))))
	48.7%	#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (/.f64 (.f64 (-.f64 #s(literal 0 binary64) (.f64 n (PI.f64))) (neg.f64 (sqrt.f64 #s(literal 2 binary64)))) (.f64 (+.f64 #s(literal 0 binary64) (sqrt.f64 (.f64 n (PI.f64)))) (sqrt.f64 k))))
	48.7%	#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (/.f64 (.f64 (-.f64 #s(literal 0 binary64) (.f64 n (PI.f64))) #s(literal -1 binary64)) (.f64 (+.f64 #s(literal 0 binary64) (sqrt.f64 (.f64 n (PI.f64)))) (sqrt.f64 (*.f64 #s(literal 1/2 binary64) k)))))
	42.4%	#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (/.f64 (.f64 (sqrt.f64 (/.f64 #s(literal 2 binary64) k)) (-.f64 #s(literal 0 binary64) (.f64 n (PI.f64)))) (.f64 #s(literal -1 binary64) (+.f64 #s(literal 0 binary64) (sqrt.f64 (.f64 n (PI.f64)))))))
	48.7%	#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)))))
	48.6%	#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (/.f64 (sqrt.f64 #s(literal 2 binary64)) (/.f64 (sqrt.f64 (/.f64 k (PI.f64))) (sqrt.f64 n))))
	38.8%	#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (/.f64 (sqrt.f64 #s(literal 2 binary64)) (/.f64 (sqrt.f64 (/.f64 k n)) (sqrt.f64 (PI.f64)))))
	48.6%	#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (/.f64 (sqrt.f64 #s(literal 2 binary64)) (/.f64 (sqrt.f64 k) (sqrt.f64 (*.f64 (PI.f64) n)))))
	48.6%	#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (/.f64 (sqrt.f64 #s(literal 2 binary64)) (/.f64 #s(literal 1 binary64) (/.f64 (sqrt.f64 n) (sqrt.f64 (/.f64 k (PI.f64)))))))
	48.6%	#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (/.f64 (sqrt.f64 #s(literal 2 binary64)) (.f64 (/.f64 #s(literal -1 binary64) (sqrt.f64 (.f64 (PI.f64) n))) (neg.f64 (sqrt.f64 k)))))
✓	38.7%	#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)))))
	48.6%	#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (/.f64 #s(literal 1 binary64) (/.f64 (/.f64 (sqrt.f64 k) (neg.f64 (sqrt.f64 (*.f64 n (PI.f64))))) (neg.f64 (sqrt.f64 #s(literal 2 binary64))))))
	48.6%	#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (/.f64 #s(literal 1 binary64) (/.f64 (/.f64 #s(literal 1 binary64) (/.f64 (+.f64 #s(literal 0 binary64) (sqrt.f64 (.f64 #s(literal 1/2 binary64) k))) (-.f64 #s(literal 0 binary64) (.f64 #s(literal 1/2 binary64) k)))) (neg.f64 (sqrt.f64 (*.f64 (PI.f64) n))))))
	36.4%	#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (/.f64 #s(literal 1 binary64) (/.f64 (-.f64 (.f64 #s(literal 0 binary64) (sqrt.f64 (.f64 (.f64 (/.f64 #s(literal 2 binary64) k) (PI.f64)) n))) (sqrt.f64 (.f64 n (PI.f64)))) (.f64 (neg.f64 (sqrt.f64 (.f64 n (PI.f64)))) (sqrt.f64 (.f64 (.f64 (/.f64 #s(literal 2 binary64) k) (PI.f64)) n))))))
	48.6%	#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (/.f64 #s(literal 1 binary64) (/.f64 (-.f64 (.f64 #s(literal 0 binary64) (sqrt.f64 (.f64 n (PI.f64)))) (.f64 (neg.f64 (sqrt.f64 (.f64 n (PI.f64)))) (neg.f64 (sqrt.f64 (.f64 #s(literal 1/2 binary64) k))))) (.f64 (neg.f64 (sqrt.f64 (.f64 n (PI.f64)))) (sqrt.f64 (.f64 n (PI.f64)))))))
	48.5%	#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (/.f64 #s(literal 1 binary64) (/.f64 (-.f64 (.f64 #s(literal 0 binary64) (sqrt.f64 n)) (.f64 (neg.f64 (sqrt.f64 (.f64 n (PI.f64)))) (/.f64 (neg.f64 (sqrt.f64 (.f64 #s(literal 1/2 binary64) k))) (sqrt.f64 (PI.f64))))) (.f64 (neg.f64 (sqrt.f64 (.f64 n (PI.f64)))) (sqrt.f64 n)))))
	42.8%	#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (/.f64 #s(literal 1 binary64) (/.f64 (.f64 (-.f64 #s(literal 0 binary64) (.f64 #s(literal 1/2 binary64) k)) (/.f64 #s(literal -1 binary64) (sqrt.f64 (.f64 n (PI.f64))))) (.f64 (+.f64 #s(literal 0 binary64) (sqrt.f64 (*.f64 #s(literal 1/2 binary64) k))) #s(literal 1 binary64)))))
	48.6%	#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (/.f64 #s(literal 1 binary64) (/.f64 (.f64 (sqrt.f64 k) (neg.f64 (sqrt.f64 #s(literal 1/2 binary64)))) (neg.f64 (sqrt.f64 (.f64 (PI.f64) n))))))
	48.7%	#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (/.f64 #s(literal 1 binary64) (/.f64 (sqrt.f64 (.f64 #s(literal 1/2 binary64) k)) (sqrt.f64 (.f64 n (PI.f64))))))
	48.7%	#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (/.f64 #s(literal 1 binary64) (/.f64 (sqrt.f64 k) (sqrt.f64 (.f64 (.f64 n #s(literal 2 binary64)) (PI.f64))))))
	48.5%	#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (/.f64 #s(literal 1 binary64) (/.f64 (neg.f64 (sqrt.f64 (.f64 k #s(literal 1/2 binary64)))) (neg.f64 (sqrt.f64 (.f64 (*.f64 (sqrt.f64 (PI.f64)) (sqrt.f64 (PI.f64))) n))))))
	48.6%	#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (/.f64 #s(literal 1 binary64) (/.f64 (neg.f64 (sqrt.f64 k)) (.f64 (sqrt.f64 (.f64 n (PI.f64))) (neg.f64 (sqrt.f64 #s(literal 2 binary64)))))))
	48.7%	#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (/.f64 #s(literal 1 binary64) (/.f64 #s(literal -1 binary64) (.f64 (sqrt.f64 (/.f64 #s(literal 2 binary64) k)) (neg.f64 (sqrt.f64 (.f64 n (PI.f64))))))))
	48.6%	#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (/.f64 #s(literal 1 binary64) (.f64 (/.f64 (sqrt.f64 k) (neg.f64 (sqrt.f64 (.f64 n (PI.f64))))) (/.f64 #s(literal 1 binary64) (neg.f64 (sqrt.f64 #s(literal 2 binary64)))))))
	38.7%	#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (/.f64 #s(literal 1 binary64) (sqrt.f64 (/.f64 (.f64 #s(literal 1/2 binary64) k) (.f64 n (PI.f64))))))
	38.5%	#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (/.f64 #s(literal 1 binary64) #s(approx (/ (neg (sqrt (* k 1/2))) (neg (sqrt (* (PI) n)))) (.f64 (sqrt.f64 #s(literal 1/2 binary64)) (sqrt.f64 (/.f64 k (.f64 (PI.f64) n)))))))
	48.6%	#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (/.f64 #s(literal -1 binary64) (.f64 (/.f64 #s(literal -1 binary64) (sqrt.f64 (.f64 (PI.f64) n))) (sqrt.f64 (*.f64 k #s(literal 1/2 binary64))))))
	48.5%	#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (.f64 (/.f64 (sqrt.f64 n) #s(literal -1 binary64)) (/.f64 (neg.f64 (sqrt.f64 (.f64 #s(literal 2 binary64) (PI.f64)))) (sqrt.f64 k))))
	48.7%	#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (.f64 (/.f64 (sqrt.f64 #s(literal 2 binary64)) (sqrt.f64 k)) (/.f64 (sqrt.f64 (.f64 (*.f64 (sqrt.f64 (PI.f64)) (sqrt.f64 (PI.f64))) n)) #s(literal 1 binary64))))
✓	48.6%	#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (.f64 (/.f64 (sqrt.f64 #s(literal 2 binary64)) (sqrt.f64 k)) (/.f64 #s(literal -1 binary64) (/.f64 #s(literal -1 binary64) (sqrt.f64 (.f64 (PI.f64) n))))))
	48.6%	#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (.f64 (/.f64 (sqrt.f64 #s(literal 2 binary64)) (sqrt.f64 k)) (sqrt.f64 (.f64 (PI.f64) n))))
	48.6%	#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (.f64 (/.f64 #s(literal 1 binary64) (/.f64 (neg.f64 (sqrt.f64 k)) (.f64 (sqrt.f64 #s(literal 2 binary64)) #s(literal -1 binary64)))) (/.f64 (sqrt.f64 (*.f64 (PI.f64) n)) #s(literal 1 binary64))))
	48.6%	#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 (.f64 #s(literal 1/2 binary64) k))) (/.f64 #s(literal -1 binary64) (/.f64 #s(literal -1 binary64) (sqrt.f64 (*.f64 (PI.f64) n))))))
	48.6%	#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (.f64 (.f64 (neg.f64 (sqrt.f64 #s(literal 2 binary64))) (/.f64 #s(literal -1 binary64) (sqrt.f64 k))) (/.f64 (sqrt.f64 (*.f64 (PI.f64) n)) #s(literal 1 binary64))))
	48.8%	#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (.f64 (sqrt.f64 (/.f64 (PI.f64) k)) (sqrt.f64 (.f64 n #s(literal 2 binary64)))))
	48.7%	#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (.f64 (sqrt.f64 (/.f64 #s(literal 2 binary64) k)) (/.f64 #s(literal -1 binary64) (/.f64 #s(literal -1 binary64) (sqrt.f64 (.f64 (PI.f64) n))))))
	48.7%	#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))))
	37.1%	#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (.f64 (sqrt.f64 (.f64 (/.f64 #s(literal 2 binary64) k) n)) (sqrt.f64 (PI.f64))))
	37.1%	#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (.f64 (sqrt.f64 (.f64 (PI.f64) #s(literal 2 binary64))) (sqrt.f64 (/.f64 n k))))
	48.6%	#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (.f64 (sqrt.f64 #s(literal 2 binary64)) (/.f64 (sqrt.f64 (.f64 (PI.f64) n)) (sqrt.f64 k))))
	38.6%	#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (.f64 (sqrt.f64 #s(literal 2 binary64)) (/.f64 #s(literal 1 binary64) (sqrt.f64 (/.f64 k (.f64 (PI.f64) n))))))
	48.6%	#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (.f64 (sqrt.f64 #s(literal 2 binary64)) (.f64 (/.f64 (sqrt.f64 (PI.f64)) (sqrt.f64 k)) (/.f64 (sqrt.f64 n) #s(literal 1 binary64)))))
	48.6%	#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (.f64 (sqrt.f64 #s(literal 2 binary64)) (.f64 (sqrt.f64 n) (sqrt.f64 (/.f64 (PI.f64) k)))))
✓	37.2%	#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (.f64 (sqrt.f64 #s(literal 2 binary64)) (sqrt.f64 (/.f64 (.f64 (PI.f64) n) k))))
	48.7%	#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (.f64 (neg.f64 (sqrt.f64 (.f64 (PI.f64) n))) (/.f64 #s(literal 1 binary64) (neg.f64 (sqrt.f64 (*.f64 k #s(literal 1/2 binary64)))))))
	48.6%	#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (.f64 #s(approx (/ (sqrt 2) (sqrt k)) (.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) k)) (sqrt.f64 #s(literal 2 binary64)))) (/.f64 (sqrt.f64 (*.f64 (PI.f64) n)) #s(literal 1 binary64))))
	37.3%	#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt.f64 (/.f64 (*.f64 (PI.f64) #s(literal 2 binary64)) (/.f64 k n))))
	37.3%	#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt.f64 (/.f64 #s(literal 2 binary64) (/.f64 k (*.f64 (PI.f64) n)))))
✓	37.3%	#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))))
	37.3%	#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt.f64 (.f64 (/.f64 (.f64 #s(literal 2 binary64) (PI.f64)) k) n)))
	37.3%	#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt.f64 (*.f64 (/.f64 n (/.f64 k (PI.f64))) #s(literal 2 binary64))))
	37.3%	#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt.f64 (.f64 (/.f64 #s(literal 2 binary64) k) (.f64 (PI.f64) n))))
	37.3%	#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt.f64 (.f64 (.f64 (/.f64 n k) (PI.f64)) #s(literal 2 binary64))))
	37.2%	#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt.f64 (.f64 (.f64 (/.f64 #s(literal 2 binary64) k) n) (PI.f64))))
	37.1%	#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt.f64 (.f64 (.f64 (*.f64 (/.f64 #s(literal 2 binary64) k) (sqrt.f64 (PI.f64))) (sqrt.f64 (PI.f64))) n)))
	37.1%	#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt.f64 (.f64 (.f64 (sqrt.f64 (PI.f64)) (*.f64 (sqrt.f64 (PI.f64)) (/.f64 n k))) #s(literal 2 binary64))))
✓	37.2%	#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt.f64 (.f64 (.f64 (PI.f64) (/.f64 #s(literal 2 binary64) k)) n)))
	37.1%	#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) #s(approx (/ 1 (/ (neg (sqrt (* k 1/2))) (neg (sqrt (* (PI) n))))) (/.f64 (sqrt.f64 (/.f64 (*.f64 (PI.f64) n) k)) (sqrt.f64 #s(literal 1/2 binary64)))))

Compiler

Compiled 4 929 to 2 142 computations (56.5% saved)

regimes146.0ms (1.5%)

Memory

-17.3MiB live, 184.7MiB allocated

Counts

110 → 1

Calls

Call 1

Inputs
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt.f64 (.f64 (.f64 (PI.f64) (/.f64 #s(literal 2 binary64) k)) n)))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt.f64 (.f64 (.f64 (/.f64 #s(literal 2 binary64) k) n) (PI.f64))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt.f64 (.f64 (.f64 (/.f64 n k) (PI.f64)) #s(literal 2 binary64))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt.f64 (.f64 (.f64 (/.f64 (PI.f64) k) n) #s(literal 2 binary64))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt.f64 (.f64 (/.f64 #s(literal 2 binary64) k) (.f64 (PI.f64) n))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt.f64 (.f64 (/.f64 (.f64 #s(literal 2 binary64) (PI.f64)) k) 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 n (/.f64 k (PI.f64))) #s(literal 2 binary64))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt.f64 (/.f64 #s(literal 2 binary64) (/.f64 k (*.f64 (PI.f64) n)))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt.f64 (/.f64 (*.f64 (PI.f64) #s(literal 2 binary64)) (/.f64 k n))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (.f64 (sqrt.f64 #s(literal 2 binary64)) (sqrt.f64 (/.f64 (.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 #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 (PI.f64) #s(literal 2 binary64))) (sqrt.f64 (/.f64 n k))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (.f64 (sqrt.f64 (.f64 (/.f64 #s(literal 2 binary64) k) n)) (sqrt.f64 (PI.f64))))
#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) k)) (sqrt.f64 (.f64 n #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 k #s(literal 1/2 binary64)))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (/.f64 (sqrt.f64 (.f64 (.f64 #s(literal 2 binary64) (PI.f64)) n)) (sqrt.f64 k)))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (/.f64 (sqrt.f64 (.f64 (.f64 (PI.f64) #s(literal 2 binary64)) n)) (sqrt.f64 k)))
(.f64 (sqrt.f64 n) (sqrt.f64 #s(approx (/ ( 2 (PI)) (* k (pow (* (* 2 (PI)) n) k))) (*.f64 (/.f64 (PI.f64) k) #s(literal 2 binary64)))))
(/.f64 (sqrt.f64 #s(approx (pow (* (* (PI) 2) n) (- 1 k)) (.f64 (.f64 (PI.f64) n) #s(literal 2 binary64)))) (sqrt.f64 k))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (/.f64 #s(literal 1 binary64) (sqrt.f64 (/.f64 k (.f64 (.f64 #s(literal 2 binary64) (PI.f64)) n)))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (/.f64 #s(literal 1 binary64) (sqrt.f64 (/.f64 (.f64 #s(literal 1/2 binary64) k) (.f64 n (PI.f64))))))
(.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) (sqrt.f64 #s(approx (pow ( n (* (PI) 2)) (- 1 k)) (.f64 (.f64 (PI.f64) n) #s(literal 2 binary64)))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) #s(approx (/ 1 (/ (neg (sqrt (* k 1/2))) (neg (sqrt (* (PI) n))))) (/.f64 (sqrt.f64 (/.f64 (*.f64 (PI.f64) n) k)) (sqrt.f64 #s(literal 1/2 binary64)))))
#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 k) 2))) (.f64 (neg.f64 (sqrt.f64 (.f64 (PI.f64) n))) (/.f64 #s(literal 1 binary64) (neg.f64 (sqrt.f64 (*.f64 k #s(literal 1/2 binary64)))))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (.f64 (sqrt.f64 #s(literal 2 binary64)) (.f64 (sqrt.f64 n) (sqrt.f64 (/.f64 (PI.f64) k)))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (.f64 (sqrt.f64 #s(literal 2 binary64)) (/.f64 (sqrt.f64 (.f64 (PI.f64) n)) (sqrt.f64 k))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (.f64 (/.f64 (sqrt.f64 #s(literal 2 binary64)) (sqrt.f64 k)) (sqrt.f64 (.f64 (PI.f64) n))))
(.f64 (sqrt.f64 n) #s(approx (sqrt (/ ( 2 (PI)) (* k (pow (* (* 2 (PI)) n) k)))) (*.f64 (sqrt.f64 (/.f64 (PI.f64) k)) (sqrt.f64 #s(literal 2 binary64)))))
(/.f64 #s(approx (pow (sqrt (* (* 2 (PI)) n)) (- 1 k)) (.f64 (sqrt.f64 (.f64 (PI.f64) n)) (sqrt.f64 #s(literal 2 binary64)))) (sqrt.f64 k))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (.f64 (sqrt.f64 #s(literal 2 binary64)) (/.f64 #s(literal 1 binary64) (sqrt.f64 (/.f64 k (.f64 (PI.f64) n))))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (/.f64 #s(literal 1 binary64) #s(approx (/ (neg (sqrt (* k 1/2))) (neg (sqrt (* (PI) n)))) (.f64 (sqrt.f64 #s(literal 1/2 binary64)) (sqrt.f64 (/.f64 k (.f64 (PI.f64) n)))))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (/.f64 #s(literal 1 binary64) (/.f64 (sqrt.f64 k) (sqrt.f64 (.f64 (.f64 n #s(literal 2 binary64)) (PI.f64))))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (/.f64 #s(literal 1 binary64) (/.f64 (sqrt.f64 (.f64 #s(literal 1/2 binary64) k)) (sqrt.f64 (.f64 n (PI.f64))))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt.f64 (.f64 (.f64 (sqrt.f64 (PI.f64)) (*.f64 (sqrt.f64 (PI.f64)) (/.f64 n k))) #s(literal 2 binary64))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt.f64 (.f64 (.f64 (*.f64 (/.f64 #s(literal 2 binary64) k) (sqrt.f64 (PI.f64))) (sqrt.f64 (PI.f64))) n)))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt.f64 (.f64 (/.f64 (.f64 (*.f64 (sqrt.f64 (PI.f64)) (sqrt.f64 (PI.f64))) n) k) #s(literal 2 binary64))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (/.f64 #s(literal 1 binary64) (/.f64 (neg.f64 (sqrt.f64 (.f64 k #s(literal 1/2 binary64)))) (neg.f64 (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 (.f64 (PI.f64) n)) (sqrt.f64 #s(literal 2 binary64)))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (/.f64 #s(literal -1 binary64) (.f64 (/.f64 #s(literal -1 binary64) (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))) (/.f64 (sqrt.f64 #s(literal 2 binary64)) (/.f64 (sqrt.f64 k) (sqrt.f64 (*.f64 (PI.f64) n)))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (.f64 (sqrt.f64 #s(literal 2 binary64)) (.f64 (neg.f64 (sqrt.f64 (*.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 (neg.f64 (sqrt.f64 (/.f64 #s(literal 2 binary64) k))) (/.f64 #s(literal -1 binary64) (sqrt.f64 (*.f64 (PI.f64) n)))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (.f64 (/.f64 (sqrt.f64 #s(literal 2 binary64)) (sqrt.f64 k)) (/.f64 (sqrt.f64 (.f64 (PI.f64) n)) #s(literal 1 binary64))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (/.f64 (.f64 (-.f64 #s(literal 0 binary64) (.f64 n (PI.f64))) #s(literal -1 binary64)) (.f64 (+.f64 #s(literal 0 binary64) (sqrt.f64 (.f64 n (PI.f64)))) (sqrt.f64 (*.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 2 binary64) k)) (/.f64 #s(literal -1 binary64) (/.f64 #s(literal -1 binary64) (sqrt.f64 (.f64 (PI.f64) n))))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (/.f64 (sqrt.f64 #s(literal 2 binary64)) (/.f64 (sqrt.f64 (/.f64 k n)) (sqrt.f64 (PI.f64)))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (/.f64 (sqrt.f64 #s(literal 2 binary64)) (/.f64 (sqrt.f64 (/.f64 k (PI.f64))) (sqrt.f64 n))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (.f64 (/.f64 (sqrt.f64 n) #s(literal -1 binary64)) (/.f64 (neg.f64 (sqrt.f64 (.f64 #s(literal 2 binary64) (PI.f64)))) (sqrt.f64 k))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (/.f64 (sqrt.f64 #s(literal 2 binary64)) (.f64 (/.f64 #s(literal -1 binary64) (sqrt.f64 (.f64 (PI.f64) n))) (neg.f64 (sqrt.f64 k)))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (/.f64 #s(literal 1 binary64) (/.f64 #s(literal -1 binary64) (.f64 (sqrt.f64 (/.f64 #s(literal 2 binary64) k)) (neg.f64 (sqrt.f64 (.f64 n (PI.f64))))))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (/.f64 #s(literal 1 binary64) (/.f64 (neg.f64 (sqrt.f64 k)) (.f64 (sqrt.f64 (.f64 n (PI.f64))) (neg.f64 (sqrt.f64 #s(literal 2 binary64)))))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (/.f64 #s(literal 1 binary64) (/.f64 (.f64 (sqrt.f64 k) (neg.f64 (sqrt.f64 #s(literal 1/2 binary64)))) (neg.f64 (sqrt.f64 (.f64 (PI.f64) n))))))
(.f64 (sqrt.f64 n) (sqrt.f64 #s(approx (/ ( 2 (PI)) (* k (pow (* (* 2 (PI)) n) k))) (.f64 (.f64 (sqrt.f64 (PI.f64)) (/.f64 (sqrt.f64 (PI.f64)) k)) #s(literal 2 binary64)))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (.f64 #s(approx (/ (sqrt 2) (sqrt k)) (.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) k)) (sqrt.f64 #s(literal 2 binary64)))) (/.f64 (sqrt.f64 (*.f64 (PI.f64) n)) #s(literal 1 binary64))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 (.f64 #s(literal 1/2 binary64) k))) (/.f64 #s(literal -1 binary64) (/.f64 #s(literal -1 binary64) (sqrt.f64 (*.f64 (PI.f64) n))))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (/.f64 (.f64 (sqrt.f64 (/.f64 #s(literal 2 binary64) k)) (-.f64 #s(literal 0 binary64) (.f64 n (PI.f64)))) (.f64 #s(literal -1 binary64) (+.f64 #s(literal 0 binary64) (sqrt.f64 (.f64 n (PI.f64)))))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (.f64 (.f64 (neg.f64 (sqrt.f64 #s(literal 2 binary64))) (/.f64 #s(literal -1 binary64) (sqrt.f64 k))) (/.f64 (sqrt.f64 (*.f64 (PI.f64) n)) #s(literal 1 binary64))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (/.f64 (.f64 (-.f64 #s(literal 0 binary64) (.f64 n (PI.f64))) (neg.f64 (sqrt.f64 #s(literal 2 binary64)))) (.f64 (+.f64 #s(literal 0 binary64) (sqrt.f64 (.f64 n (PI.f64)))) (sqrt.f64 k))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (.f64 (sqrt.f64 #s(literal 2 binary64)) (.f64 (/.f64 (sqrt.f64 (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 #s(literal 1 binary64) (/.f64 (/.f64 (sqrt.f64 k) (neg.f64 (sqrt.f64 (*.f64 n (PI.f64))))) (neg.f64 (sqrt.f64 #s(literal 2 binary64))))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (.f64 (/.f64 (sqrt.f64 #s(literal 2 binary64)) (sqrt.f64 k)) (/.f64 #s(literal -1 binary64) (/.f64 #s(literal -1 binary64) (sqrt.f64 (.f64 (PI.f64) n))))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (/.f64 (sqrt.f64 #s(literal 2 binary64)) (/.f64 #s(literal 1 binary64) (/.f64 (sqrt.f64 n) (sqrt.f64 (/.f64 k (PI.f64)))))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (/.f64 #s(literal 1 binary64) (.f64 (/.f64 (sqrt.f64 k) (neg.f64 (sqrt.f64 (.f64 n (PI.f64))))) (/.f64 #s(literal 1 binary64) (neg.f64 (sqrt.f64 #s(literal 2 binary64)))))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (.f64 (/.f64 #s(literal 1 binary64) (/.f64 (neg.f64 (sqrt.f64 k)) (.f64 (sqrt.f64 #s(literal 2 binary64)) #s(literal -1 binary64)))) (/.f64 (sqrt.f64 (*.f64 (PI.f64) n)) #s(literal 1 binary64))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (/.f64 #s(literal 1 binary64) (/.f64 (neg.f64 (sqrt.f64 (.f64 k #s(literal 1/2 binary64)))) (neg.f64 (sqrt.f64 (.f64 (*.f64 (sqrt.f64 (PI.f64)) (sqrt.f64 (PI.f64))) n))))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (/.f64 #s(literal 1 binary64) (/.f64 (.f64 (-.f64 #s(literal 0 binary64) (.f64 #s(literal 1/2 binary64) k)) (/.f64 #s(literal -1 binary64) (sqrt.f64 (.f64 n (PI.f64))))) (.f64 (+.f64 #s(literal 0 binary64) (sqrt.f64 (*.f64 #s(literal 1/2 binary64) k))) #s(literal 1 binary64)))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (.f64 (/.f64 (sqrt.f64 #s(literal 2 binary64)) (sqrt.f64 k)) (/.f64 (sqrt.f64 (.f64 (*.f64 (sqrt.f64 (PI.f64)) (sqrt.f64 (PI.f64))) n)) #s(literal 1 binary64))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (/.f64 #s(literal 1 binary64) (/.f64 (/.f64 #s(literal 1 binary64) (/.f64 (+.f64 #s(literal 0 binary64) (sqrt.f64 (.f64 #s(literal 1/2 binary64) k))) (-.f64 #s(literal 0 binary64) (.f64 #s(literal 1/2 binary64) k)))) (neg.f64 (sqrt.f64 (*.f64 (PI.f64) n))))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (/.f64 #s(literal 1 binary64) (/.f64 (-.f64 (.f64 #s(literal 0 binary64) (sqrt.f64 (.f64 n (PI.f64)))) (.f64 (neg.f64 (sqrt.f64 (.f64 n (PI.f64)))) (neg.f64 (sqrt.f64 (.f64 #s(literal 1/2 binary64) k))))) (.f64 (neg.f64 (sqrt.f64 (.f64 n (PI.f64)))) (sqrt.f64 (.f64 n (PI.f64)))))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (.f64 (sqrt.f64 (.f64 (*.f64 #s(literal 2 binary64) (PI.f64)) n)) (pow.f64 k #s(literal -1/2 binary64))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (/.f64 #s(literal 1 binary64) (/.f64 (-.f64 (.f64 #s(literal 0 binary64) (sqrt.f64 (.f64 (.f64 (/.f64 #s(literal 2 binary64) k) (PI.f64)) n))) (sqrt.f64 (.f64 n (PI.f64)))) (.f64 (neg.f64 (sqrt.f64 (.f64 n (PI.f64)))) (sqrt.f64 (.f64 (.f64 (/.f64 #s(literal 2 binary64) k) (PI.f64)) n))))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (/.f64 #s(literal 1 binary64) (/.f64 (-.f64 (.f64 #s(literal 0 binary64) (sqrt.f64 n)) (.f64 (neg.f64 (sqrt.f64 (.f64 n (PI.f64)))) (/.f64 (neg.f64 (sqrt.f64 (.f64 #s(literal 1/2 binary64) k))) (sqrt.f64 (PI.f64))))) (.f64 (neg.f64 (sqrt.f64 (.f64 n (PI.f64)))) (sqrt.f64 n)))))
(sqrt.f64 (/.f64 (pow.f64 (.f64 (.f64 #s(literal 2 binary64) (PI.f64)) n) (-.f64 #s(literal 1 binary64) k)) k))
(sqrt.f64 (/.f64 (pow.f64 (.f64 (.f64 n #s(literal 2 binary64)) (PI.f64)) (-.f64 #s(literal 1 binary64) k)) 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 (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.f64 k))
(/.f64 #s(literal 1 binary64) (sqrt.f64 (.f64 k (pow.f64 (.f64 (*.f64 n #s(literal 2 binary64)) (PI.f64)) (-.f64 k #s(literal 1 binary64))))))
(/.f64 (pow.f64 (.f64 (.f64 (PI.f64) #s(literal 2 binary64)) n) (-.f64 #s(literal 1/2 binary64) (*.f64 #s(literal 1/2 binary64) k))) (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 (pow.f64 (.f64 (*.f64 #s(literal 2 binary64) n) (PI.f64)) (fma.f64 #s(literal -1/2 binary64) k #s(literal 1/2 binary64))) (sqrt.f64 (/.f64 #s(literal 1 binary64) k))))
(.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) (pow.f64 (.f64 (*.f64 #s(literal 2 binary64) (PI.f64)) n) (fma.f64 k #s(literal -1/2 binary64) #s(literal 1/2 binary64))))
(/.f64 (sqrt.f64 (pow.f64 (.f64 (.f64 (PI.f64) #s(literal 2 binary64)) n) (-.f64 #s(literal 1 binary64) k))) (sqrt.f64 k))
(/.f64 (pow.f64 (sqrt.f64 (.f64 (.f64 #s(literal 2 binary64) (PI.f64)) n)) (-.f64 #s(literal 1 binary64) k)) (sqrt.f64 k))
(/.f64 #s(literal 1 binary64) (sqrt.f64 (/.f64 k (pow.f64 (.f64 (.f64 #s(literal 2 binary64) (PI.f64)) n) (-.f64 #s(literal 1 binary64) k)))))
(sqrt.f64 (/.f64 (.f64 (.f64 #s(literal 2 binary64) (PI.f64)) n) (.f64 (pow.f64 (.f64 (*.f64 #s(literal 2 binary64) (PI.f64)) n) k) k)))
(/.f64 #s(literal 1 binary64) (/.f64 (sqrt.f64 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)))))
(.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) (sqrt.f64 (pow.f64 (.f64 n (*.f64 (PI.f64) #s(literal 2 binary64))) (-.f64 #s(literal 1 binary64) k))))
(.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) (pow.f64 (sqrt.f64 (.f64 n (*.f64 (PI.f64) #s(literal 2 binary64)))) (-.f64 #s(literal 1 binary64) k)))
(.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) (pow.f64 (.f64 (*.f64 #s(literal 2 binary64) (PI.f64)) n) (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 2 binary64))))
(sqrt.f64 (.f64 (.f64 n (/.f64 #s(literal 2 binary64) k)) (/.f64 (PI.f64) (pow.f64 (.f64 (.f64 (PI.f64) #s(literal 2 binary64)) n) k))))
(sqrt.f64 (/.f64 (.f64 (/.f64 (.f64 (PI.f64) n) k) #s(literal 2 binary64)) (pow.f64 (.f64 (.f64 #s(literal 2 binary64) (PI.f64)) n) k)))
(.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) (/.f64 #s(literal 1 binary64) (pow.f64 (.f64 n (.f64 (PI.f64) #s(literal 2 binary64))) (.f64 #s(literal -1/2 binary64) (-.f64 #s(literal 1 binary64) k)))))
(.f64 (sqrt.f64 n) (sqrt.f64 (/.f64 (.f64 #s(literal 2 binary64) (PI.f64)) (.f64 k (pow.f64 (.f64 (*.f64 #s(literal 2 binary64) (PI.f64)) n) k)))))
(.f64 (sqrt.f64 (.f64 (/.f64 (.f64 (PI.f64) n) k) #s(literal 2 binary64))) (pow.f64 (sqrt.f64 (.f64 (*.f64 (PI.f64) #s(literal 2 binary64)) n)) (neg.f64 k)))
(/.f64 (sqrt.f64 (.f64 (pow.f64 (.f64 (.f64 n #s(literal 2 binary64)) (PI.f64)) (neg.f64 k)) (.f64 (*.f64 n #s(literal 2 binary64)) (PI.f64)))) (sqrt.f64 k))
(.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) #s(approx (pow ( (* 2 (PI)) n) (/ (- 1 k) 2)) (pow.f64 (/.f64 (*.f64 #s(literal -2 binary64) (PI.f64)) (/.f64 #s(literal -1 binary64) n)) (fma.f64 #s(literal -1/2 binary64) k #s(literal 1/2 binary64)))))
(/.f64 (sqrt.f64 (.f64 n (.f64 (PI.f64) #s(literal 2 binary64)))) (.f64 (sqrt.f64 k) (pow.f64 (.f64 (.f64 #s(literal 2 binary64) (PI.f64)) n) (.f64 #s(literal 1/2 binary64) k))))
(.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) (.f64 (pow.f64 (.f64 n (.f64 (PI.f64) #s(literal 2 binary64))) (.f64 k #s(literal -1/2 binary64))) (sqrt.f64 (.f64 n (*.f64 (PI.f64) #s(literal 2 binary64))))))
(.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) (pow.f64 (.f64 (.f64 (.f64 n #s(literal 2 binary64)) (sqrt.f64 (PI.f64))) (sqrt.f64 (PI.f64))) (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 2 binary64))))
(.f64 (pow.f64 (.f64 (PI.f64) #s(literal 2 binary64)) (fma.f64 #s(literal 1/2 binary64) k #s(literal 1/2 binary64))) (/.f64 (pow.f64 n (fma.f64 #s(literal 1/2 binary64) k #s(literal 1/2 binary64))) (sqrt.f64 k)))
(.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) (pow.f64 (pow.f64 (.f64 n (.f64 (PI.f64) #s(literal 2 binary64))) (.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 1/8 binary64))) #s(literal 4 binary64)))
(/.f64 (sqrt.f64 (.f64 n (.f64 (PI.f64) #s(literal 2 binary64)))) (.f64 (sqrt.f64 k) (pow.f64 (pow.f64 (.f64 n (*.f64 (PI.f64) #s(literal 2 binary64))) k) #s(literal 1/2 binary64))))
(.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) (/.f64 (pow.f64 (.f64 n (.f64 (PI.f64) #s(literal 2 binary64))) (fma.f64 #s(literal 1/4 binary64) (-.f64 #s(literal 1 binary64) k) #s(literal 1/4 binary64))) (pow.f64 (.f64 n (.f64 (PI.f64) #s(literal 2 binary64))) (.f64 k #s(literal 1/4 binary64)))))
(.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) (/.f64 (sqrt.f64 (.f64 n (.f64 (PI.f64) #s(literal 2 binary64)))) (pow.f64 (pow.f64 (.f64 n (.f64 (PI.f64) #s(literal 2 binary64))) #s(literal 2 binary64)) (.f64 k #s(literal 1/4 binary64)))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (/.f64 (.f64 (sqrt.f64 #s(literal 2 binary64)) (fma.f64 (.f64 (log.f64 (.f64 (.f64 #s(literal 2 binary64) n) (PI.f64))) (sqrt.f64 (.f64 (.f64 (pow.f64 k #s(literal 3 binary64)) (PI.f64)) n))) #s(literal -1/2 binary64) (sqrt.f64 (.f64 (.f64 (PI.f64) n) k)))) k))

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

Calls

4 calls:

41.0ms	(.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))))
33.0ms	(.f64 (.f64 #s(literal 2 binary64) (PI.f64)) n)
33.0ms	k
31.0ms	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 23 to 23 computations (0% saved)

regimes111.0ms (1.1%)

Memory

38.3MiB live, 150.7MiB allocated

Counts

97 → 1

Calls

Call 1

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

Outputs

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

Calls

4 calls:

28.0ms	n
28.0ms	k
26.0ms	(.f64 (.f64 #s(literal 2 binary64) (PI.f64)) n)
25.0ms	(.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
99.4%	1	`k`
99.4%	1	`n`
99.4%	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))))`
99.4%	1	`(.f64 (.f64 #s(literal 2 binary64) (PI.f64)) n)`

Compiler

Compiled 23 to 23 computations (0% saved)

regimes103.0ms (1.1%)

Memory

-21.5MiB live, 138.0MiB allocated

Counts

84 → 1

Calls

Call 1

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

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

Calls

4 calls:

28.0ms	(.f64 (.f64 #s(literal 2 binary64) (PI.f64)) n)
25.0ms	k
24.0ms	n
22.0ms	(.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
99.4%	1	`k`
99.4%	1	`n`
99.4%	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))))`
99.4%	1	`(.f64 (.f64 #s(literal 2 binary64) (PI.f64)) n)`

Compiler

Compiled 23 to 23 computations (0% saved)

regimes109.0ms (1.1%)

Memory

12.2MiB live, 130.8MiB allocated

Counts

82 → 2

Calls

Call 1

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

Outputs

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

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

Calls

4 calls:

35.0ms	k
25.0ms	(.f64 (.f64 #s(literal 2 binary64) (PI.f64)) n)
22.0ms	n
22.0ms	(.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
99.4%	2	`k`
89.4%	1	`n`
99.4%	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))))`
89.4%	1	`(.f64 (.f64 #s(literal 2 binary64) (PI.f64)) n)`

Compiler

Compiled 23 to 23 computations (0% saved)

regimes34.0ms (0.3%)

Memory

-1.4MiB live, 36.2MiB allocated

Counts

81 → 2

Calls

Call 1

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

Outputs

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

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

Calls

1 calls:

30.0ms

Results

Accuracy	Segments	Branch
99.1%	2	`k`

Compiler

Compiled 1 to 2 computations (-100% saved)

regimes94.0ms (1%)

Memory

17.1MiB live, 131.8MiB allocated

Counts

77 → 1

Calls

Call 1

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

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

Calls

4 calls:

26.0ms	k
22.0ms	(.f64 (.f64 #s(literal 2 binary64) (PI.f64)) n)
22.0ms	(.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))))
21.0ms	n

Results

Accuracy	Segments	Branch
48.8%	1	`n`
48.8%	1	`(.f64 (.f64 #s(literal 2 binary64) (PI.f64)) n)`
48.8%	1	`(.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) (pow.f64 (.f64 (*.f64 #s(literal 2 binary64) (PI.f64)) n) (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 2 binary64))))`
48.8%	1	`k`

Compiler

Compiled 23 to 23 computations (0% saved)

regimes132.0ms (1.4%)

Memory

-17.0MiB live, 138.0MiB allocated

Counts

74 → 1

Calls

Call 1

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

Outputs
#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))))

Calls

4 calls:

61.0ms	(.f64 (.f64 #s(literal 2 binary64) (PI.f64)) n)
25.0ms	n
20.0ms	(.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))))
20.0ms	k

Results

Accuracy	Segments	Branch
48.8%	1	`k`
48.8%	1	`(.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) (pow.f64 (.f64 (*.f64 #s(literal 2 binary64) (PI.f64)) n) (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 2 binary64))))`
48.8%	1	`n`
48.8%	1	`(.f64 (.f64 #s(literal 2 binary64) (PI.f64)) n)`

Compiler

Compiled 23 to 23 computations (0% saved)

regimes16.0ms (0.2%)

Memory

32.5MiB live, 32.5MiB allocated

Counts

11 → 1

Calls

Call 1

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

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

Calls

4 calls:

4.0ms	(.f64 (.f64 #s(literal 2 binary64) (PI.f64)) n)
4.0ms	k
4.0ms	n
4.0ms	(.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
37.3%	1	`k`
37.3%	1	`(.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) (pow.f64 (.f64 (*.f64 #s(literal 2 binary64) (PI.f64)) n) (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 2 binary64))))`
37.3%	1	`n`
37.3%	1	`(.f64 (.f64 #s(literal 2 binary64) (PI.f64)) n)`

Compiler

Compiled 23 to 23 computations (0% saved)

regimes13.0ms (0.1%)

Memory

-12.2MiB live, 26.1MiB allocated

Counts

7 → 1

Calls

Call 1

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

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

Calls

4 calls:

4.0ms	(.f64 (.f64 #s(literal 2 binary64) (PI.f64)) n)
3.0ms	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
37.3%	1	`(.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) (pow.f64 (.f64 (*.f64 #s(literal 2 binary64) (PI.f64)) n) (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 2 binary64))))`
37.3%	1	`k`
37.3%	1	`n`
37.3%	1	`(.f64 (.f64 #s(literal 2 binary64) (PI.f64)) n)`

Compiler

Compiled 23 to 23 computations (0% saved)

regimes17.0ms (0.2%)

Memory

-28.1MiB live, 20.5MiB allocated

Counts

6 → 1

Calls

Call 1

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

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

Calls

4 calls:

9.0ms	k
3.0ms	(.f64 (.f64 #s(literal 2 binary64) (PI.f64)) n)
2.0ms	n
2.0ms	(.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) (pow.f64 (.f64 (*.f64 #s(literal 2 binary64) (PI.f64)) n) (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 2 binary64))))

Results

Accuracy	Segments	Branch
37.3%	1	`(.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) (pow.f64 (.f64 (*.f64 #s(literal 2 binary64) (PI.f64)) n) (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 2 binary64))))`
37.3%	1	`k`
37.3%	1	`n`
37.3%	1	`(.f64 (.f64 #s(literal 2 binary64) (PI.f64)) n)`

Compiler

Compiled 23 to 23 computations (0% saved)

regimes6.0ms (0.1%)

Memory

10.4MiB live, 10.4MiB allocated

Accuracy

Total -0.0b remaining (-0.1%)

Threshold costs -0b (-0.1%)

Counts

2 → 1

Calls

Call 1

Inputs

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

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

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

Calls

4 calls:

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

Results

Accuracy	Segments	Branch
37.2%	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))))`
37.2%	1	`k`
37.2%	1	`n`
37.2%	1	`(.f64 (.f64 #s(literal 2 binary64) (PI.f64)) n)`

Compiler

Compiled 23 to 23 computations (0% saved)

bsearch15.0ms (0.2%)

Memory

14.3MiB live, 14.3MiB allocated

Algorithm

1×	binary-search

Stop Event

1×	narrow-enough

Steps

Time	Left	Right
13.0ms	1.1464766518134056e-30	9.9468470496016e-30

Samples

9.0ms

96×

valid

Compiler

Compiled 265 to 234 computations (11.7% saved)

Precisions

Click to see histograms. Total time spent on operations: 7.0ms

ival-mult: 2.0ms (29.2% of total)

ival-pow: 2.0ms (29.2% of total)

ival-div: 1.0ms (14.6% of total)

ival-sqrt: 1.0ms (14.6% 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)

bsearch18.0ms (0.2%)

Memory

-12.7MiB live, 25.4MiB allocated

Algorithm

1×	binary-search

Stop Event

1×	narrow-enough

Steps

Time	Left	Right
16.0ms	5.938707897198817e-33	5.014426473036351e-31

Samples

11.0ms

112×

valid

Compiler

Compiled 292 to 263 computations (9.9% saved)

Precisions

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

ival-mult: 2.0ms (23.3% of total)

ival-pow: 2.0ms (23.3% of total)

ival-pi: 1.0ms (11.6% of total)

ival-div: 1.0ms (11.6% of total)

ival-sub: 1.0ms (11.6% of total)

ival-sqrt: 1.0ms (11.6% of total)

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

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

exact: 0.0ms (0% of total)

simplify79.0ms (0.8%)

Memory

8.8MiB live, 46.2MiB allocated

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	84	304
1	110	286
2	139	286
3	175	286
4	230	286
5	352	286
6	510	286
7	1878	286
8	5199	286

Stop Event

1×	node limit

Calls

Call 1

Inputs
(.f64 (sqrt.f64 n) (sqrt.f64 (/.f64 (.f64 #s(literal 2 binary64) (PI.f64)) (.f64 k (pow.f64 (.f64 (*.f64 #s(literal 2 binary64) (PI.f64)) n) k)))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (.f64 (pow.f64 (.f64 (*.f64 #s(literal 2 binary64) n) (PI.f64)) (fma.f64 #s(literal -1/2 binary64) k #s(literal 1/2 binary64))) (sqrt.f64 (/.f64 #s(literal 1 binary64) k))))
(/.f64 (pow.f64 (.f64 (.f64 (PI.f64) #s(literal 2 binary64)) n) (-.f64 #s(literal 1/2 binary64) (*.f64 #s(literal 1/2 binary64) k))) (sqrt.f64 k))
(if (<=.f64 k #s(literal 35681192317649/11150372599265311570767859136324180752990208 binary64)) #s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (.f64 (sqrt.f64 (.f64 (.f64 #s(literal 2 binary64) (PI.f64)) n)) (pow.f64 k #s(literal -1/2 binary64)))) (/.f64 #s(literal 1 binary64) (sqrt.f64 (.f64 k (pow.f64 (.f64 (.f64 n #s(literal 2 binary64)) (PI.f64)) (-.f64 k #s(literal 1 binary64)))))))
(if (<=.f64 k #s(literal 5023911878324979/22835963083295358096932575511191922182123945984 binary64)) #s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (.f64 (sqrt.f64 (.f64 (.f64 #s(literal 2 binary64) (PI.f64)) n)) (pow.f64 k #s(literal -1/2 binary64)))) (sqrt.f64 (/.f64 (pow.f64 (.f64 (*.f64 #s(literal 2 binary64) (PI.f64)) n) (-.f64 #s(literal 1 binary64) k)) k)))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (.f64 (sqrt.f64 (.f64 (*.f64 #s(literal 2 binary64) (PI.f64)) n)) (pow.f64 k #s(literal -1/2 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))) (sqrt.f64 (*.f64 (/.f64 n (/.f64 k (PI.f64))) #s(literal 2 binary64))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt.f64 (.f64 (/.f64 (.f64 (PI.f64) n) k) #s(literal 2 binary64))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt.f64 (.f64 (.f64 (/.f64 n k) (PI.f64)) #s(literal 2 binary64))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt.f64 (.f64 (.f64 (PI.f64) (/.f64 #s(literal 2 binary64) k)) n)))

Outputs
(.f64 (sqrt.f64 n) (sqrt.f64 (/.f64 (.f64 #s(literal 2 binary64) (PI.f64)) (.f64 k (pow.f64 (.f64 (*.f64 #s(literal 2 binary64) (PI.f64)) n) k)))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (.f64 (pow.f64 (.f64 (*.f64 #s(literal 2 binary64) n) (PI.f64)) (fma.f64 #s(literal -1/2 binary64) k #s(literal 1/2 binary64))) (sqrt.f64 (/.f64 #s(literal 1 binary64) k))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (.f64 (pow.f64 (.f64 (*.f64 #s(literal 2 binary64) n) (PI.f64)) (fma.f64 #s(literal -1/2 binary64) k #s(literal 1/2 binary64))) (sqrt.f64 (pow.f64 k #s(literal -1 binary64)))))
(/.f64 (pow.f64 (.f64 (.f64 (PI.f64) #s(literal 2 binary64)) n) (-.f64 #s(literal 1/2 binary64) (*.f64 #s(literal 1/2 binary64) k))) (sqrt.f64 k))
(if (<=.f64 k #s(literal 35681192317649/11150372599265311570767859136324180752990208 binary64)) #s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (.f64 (sqrt.f64 (.f64 (.f64 #s(literal 2 binary64) (PI.f64)) n)) (pow.f64 k #s(literal -1/2 binary64)))) (/.f64 #s(literal 1 binary64) (sqrt.f64 (.f64 k (pow.f64 (.f64 (.f64 n #s(literal 2 binary64)) (PI.f64)) (-.f64 k #s(literal 1 binary64)))))))
(if (<=.f64 k #s(literal 35681192317649/11150372599265311570767859136324180752990208 binary64)) #s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (.f64 (sqrt.f64 (.f64 (.f64 #s(literal 2 binary64) (PI.f64)) n)) (pow.f64 k #s(literal -1/2 binary64)))) (pow.f64 (sqrt.f64 (.f64 k (pow.f64 (.f64 (.f64 n #s(literal 2 binary64)) (PI.f64)) (-.f64 k #s(literal 1 binary64))))) #s(literal -1 binary64)))
(if (<=.f64 k #s(literal 5023911878324979/22835963083295358096932575511191922182123945984 binary64)) #s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (.f64 (sqrt.f64 (.f64 (.f64 #s(literal 2 binary64) (PI.f64)) n)) (pow.f64 k #s(literal -1/2 binary64)))) (sqrt.f64 (/.f64 (pow.f64 (.f64 (*.f64 #s(literal 2 binary64) (PI.f64)) n) (-.f64 #s(literal 1 binary64) k)) k)))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (.f64 (sqrt.f64 (.f64 (*.f64 #s(literal 2 binary64) (PI.f64)) n)) (pow.f64 k #s(literal -1/2 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))) (sqrt.f64 (*.f64 (/.f64 n (/.f64 k (PI.f64))) #s(literal 2 binary64))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt.f64 (.f64 (/.f64 (.f64 (PI.f64) n) k) #s(literal 2 binary64))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt.f64 (.f64 (.f64 (/.f64 n k) (PI.f64)) #s(literal 2 binary64))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt.f64 (.f64 (.f64 (PI.f64) (/.f64 #s(literal 2 binary64) k)) n)))

soundness966.0ms (9.9%)

Memory

20.7MiB live, 729.2MiB allocated

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	13	43
0	22	43
1	89	40
2	497	38
3	4477	38
0	8503	37
0	128	517
1	345	504
2	1021	460
3	3363	433
4	5589	421
0	8476	406
0	52	267
0	82	228
1	279	224
2	1566	223
0	8237	223
0	45	212
0	73	192
1	236	181
2	1208	177
0	8225	177
0	42	224
0	68	204
1	233	204
2	1356	198
0	8413	198

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

Compiler

Compiled 1 104 to 605 computations (45.2% saved)

preprocess67.0ms (0.7%)

Memory: 17.9MiB live, 128.8MiB allocated
Compiler: Compiled 640 to 200 computations (68.8% 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	45	321
0	73	318
1	112	310
2	157	310
3	206	310
4	239	310
5	277	310
6	305	310
7	332	310
8	341	310
9	344	310
0	344	306

Iter	Nodes	Cost
0	42	296
0	68	290
1	106	284
2	159	284
3	212	284
4	250	284
5	267	284
6	290	284
7	327	284
8	357	284
9	363	284
0	363	281

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	45	321
0	73	318
1	112	310
2	157	310
3	206	310
4	239	310
5	277	310
6	305	310
7	332	310
8	341	310
9	344	310
0	344	306

Iter	Nodes	Cost
0	42	296
0	68	290
1	106	284
2	159	284
3	212	284
4	250	284
5	267	284
6	290	284
7	327	284
8	357	284
9	363	284
0	363	281

start0.0ms (0%)

analyze140.0ms (1.4%)

sample3.8s (38.6%)

explain149.0ms (1.5%)

preprocess48.0ms (0.5%)

eval0.0ms (0%)

prune0.0ms (0%)

simplify6.0ms (0.1%)

localize40.0ms (0.4%)

series73.0ms (0.8%)

simplify142.0ms (1.5%)

rewrite167.0ms (1.7%)

eval55.0ms (0.6%)

prune23.0ms (0.2%)

simplify13.0ms (0.1%)

localize110.0ms (1.1%)

series78.0ms (0.8%)

simplify157.0ms (1.6%)

rewrite252.0ms (2.6%)

eval334.0ms (3.4%)

prune201.0ms (2.1%)

simplify13.0ms (0.1%)

localize162.0ms (1.7%)

series264.0ms (2.7%)

simplify198.0ms (2%)

rewrite187.0ms (1.9%)

eval185.0ms (1.9%)

prune120.0ms (1.2%)

simplify74.0ms (0.8%)

localize131.0ms (1.3%)

series75.0ms (0.8%)

simplify151.0ms (1.5%)

rewrite198.0ms (2%)

eval200.0ms (2.1%)

prune104.0ms (1.1%)

regimes146.0ms (1.5%)

regimes111.0ms (1.1%)

regimes103.0ms (1.1%)

regimes109.0ms (1.1%)

regimes34.0ms (0.3%)

regimes94.0ms (1%)

regimes132.0ms (1.4%)

regimes16.0ms (0.2%)

regimes13.0ms (0.1%)

regimes17.0ms (0.2%)

regimes6.0ms (0.1%)

bsearch15.0ms (0.2%)

bsearch18.0ms (0.2%)

simplify79.0ms (0.8%)

soundness966.0ms (9.9%)

preprocess67.0ms (0.7%)

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

Iter	Nodes	Cost
0	45	321
0	73	318
1	112	310
2	157	310
3	206	310
4	239	310
5	277	310
6	305	310
7	332	310
8	341	310
9	344	310
0	344	306

Iter	Nodes	Cost
0	42	296
0	68	290
1	106	284
2	159	284
3	212	284
4	250	284
5	267	284
6	290	284
7	327	284
8	357	284
9	363	284
0	363	281