Metrics for Migdal et al, Equation (51)

start0.0ms (0%)

Memory: 0.1MiB live, 0.1MiB allocated

analyze174.0ms (1.9%)

Memory

18.6MiB live, 175.7MiB 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 (40.4%)

Memory

-85.9MiB live, 4 498.7MiB allocated

Samples

1.5s	8 256×	0	valid
921.0ms	3 492×	1	invalid
375.0ms	1 807×	1	exit
133.0ms	450×	2	invalid
56.0ms	523×	0	invalid
30.0ms	258×	0	exit

Precisions

Click to see histograms. Total time spent on operations: 2.3s

ival-mult: 746.0ms (32.9% of total)

ival-pow: 614.0ms (27.1% of total)

ival-div: 358.0ms (15.8% of total)

ival-sqrt: 176.0ms (7.8% of total)

adjust: 142.0ms (6.3% of total)

ival-sub: 113.0ms (5% of total)

ival-pi: 79.0ms (3.5% of total)

exact: 17.0ms (0.8% of total)

ival-true: 13.0ms (0.6% of total)

ival-assert: 6.0ms (0.3% of total)

Bogosity

explain147.0ms (1.6%)

Memory

18.2MiB live, 256.0MiB allocated

FPErrors

Click to see full error table

Ground Truth	Overpredictions	Example	Example	Subexpression
5	75	(2.4267141748333313e-252 7.362351854224066e-179)	-	`(pow.f64 (.f64 (.f64 #s(literal 2 binary64) (PI.f64)) n) (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 2 binary64)))`
0	0	-	-	`k`
0	0	-	-	`n`
0	0	-	-	`(/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 2 binary64))`
0	0	-	-	`#s(literal 1 binary64)`
0	0	-	-	`(.f64 (.f64 #s(literal 2 binary64) (PI.f64)) n)`
0	0	-	-	`(sqrt.f64 k)`
0	0	-	-	`#s(literal 2 binary64)`
0	0	-	-	`(/.f64 #s(literal 1 binary64) (sqrt.f64 k))`
0	0	-	-	`(-.f64 #s(literal 1 binary64) k)`
0	0	-	-	`(*.f64 #s(literal 2 binary64) (PI.f64))`
0	0	-	-	`(.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) (pow.f64 (.f64 (*.f64 #s(literal 2 binary64) (PI.f64)) n) (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 2 binary64))))`
0	0	-	-	`(PI.f64)`

Explanations

Click to see full explanations table

Operator	Subexpression	Explanation	Count
`pow.f64`	`(pow.f64 (.f64 (.f64 #s(literal 2 binary64) (PI.f64)) n) (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 2 binary64)))`	sensitivity	80	18

Confusion

	Predicted +	Predicted -
+	4	0
-	76	176

Precision

0.05

Recall

1.0

Confusion?

	Predicted +	Predicted Maybe	Predicted -
+	4	0	0
-	76	18	158

Precision?

0.04081632653061224

Recall?

1.0

Freqs

test

number	freq
0	176
1	80

Total Confusion?

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

Precision?

1.0

Recall?

1.0

Samples

57.0ms

512×

valid

Compiler

Compiled 128 to 43 computations (66.4% saved)

Precisions

Click to see histograms. Total time spent on operations: 36.0ms

ival-pow: 10.0ms (27.7% of total)

ival-mult: 9.0ms (24.9% of total)

ival-div: 7.0ms (19.4% of total)

ival-sqrt: 4.0ms (11.1% of total)

ival-sub: 3.0ms (8.3% of total)

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

ival-true: 1.0ms (2.8% of total)

exact: 1.0ms (2.8% of total)

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

preprocess49.0ms (0.5%)

Memory

-19.3MiB live, 27.5MiB 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

1.7MiB live, 1.7MiB allocated

Alt Table

Click to see full alt table

Status	Accuracy	Program
▶	99.6%	(.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) (pow.f64 (.f64 (*.f64 #s(literal 2 binary64) (PI.f64)) n) (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 2 binary64))))

Compiler

Compiled 16 to 13 computations (18.8% saved)

simplify6.0ms (0.1%)

Memory

9.7MiB live, 9.7MiB 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	1	(/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 2 binary64))
cost-diff	2	(.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) (pow.f64 (.f64 (*.f64 #s(literal 2 binary64) (PI.f64)) n) (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 2 binary64))))

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)

localize39.0ms (0.4%)

Memory

-14.4MiB live, 63.4MiB allocated

Localize:

Found 4 expressions of interest:

New	Metric	Score
accuracy	0.15234375	(.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	0.1526850729236806	(pow.f64 (.f64 (.f64 #s(literal 2 binary64) (PI.f64)) n) (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 2 binary64)))
accuracy	0.20703125	(.f64 (.f64 #s(literal 2 binary64) (PI.f64)) n)
accuracy	0.30078125	(/.f64 #s(literal 1 binary64) (sqrt.f64 k))

Samples

29.0ms

256×

valid

Compiler

Compiled 56 to 15 computations (73.2% saved)

Precisions

Click to see histograms. Total time spent on operations: 19.0ms

ival-pow: 5.0ms (26.9% of total)

ival-div: 4.0ms (21.5% of total)

ival-mult: 4.0ms (21.5% of total)

ival-sqrt: 2.0ms (10.8% of total)

ival-pi: 1.0ms (5.4% of total)

ival-sub: 1.0ms (5.4% of total)

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

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

exact: 0.0ms (0% of total)

series72.0ms (0.8%)

Memory

31.1MiB live, 110.1MiB allocated

Counts

6 → 27

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 (-.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
(* (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)
1/2
(+ 1/2 (* -1/2 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)))
(* (sqrt (/ 1 k)) (exp (* 1/2 (* (log (* 2 (* n (PI)))) (- 1 k)))))
(* -1/2 k)
(* k (- (* 1/2 (/ 1 k)) 1/2))
(exp (* 1/2 (* (log (* 2 (* n (PI)))) (- 1 k))))
(* (sqrt (/ 1 k)) (exp (* 1/2 (* (log (* 2 (* n (PI)))) (+ 1 (* -1 k))))))
(* -1 (* k (- 1/2 (* 1/2 (/ 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
30.0ms	n	@	0	((* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (/ (- 1 k) 2) (/ 1 (sqrt k)) (sqrt k) (* (* 2 (PI)) n) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2)))
20.0ms	n	@	-inf	((* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (/ (- 1 k) 2) (/ 1 (sqrt k)) (sqrt k) (* (* 2 (PI)) n) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2)))
14.0ms	n	@	inf	((* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (/ (- 1 k) 2) (/ 1 (sqrt k)) (sqrt k) (* (* 2 (PI)) n) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2)))
3.0ms	k	@	-inf	((* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (/ (- 1 k) 2) (/ 1 (sqrt k)) (sqrt k) (* (* 2 (PI)) n) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2)))
3.0ms	k	@	0	((* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (/ (- 1 k) 2) (/ 1 (sqrt k)) (sqrt k) (* (* 2 (PI)) n) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2)))

simplify145.0ms (1.6%)

Memory

6.4MiB live, 198.5MiB allocated

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	128	517
1	345	504
2	1022	460
3	3355	433
4	5591	421
0	8473	406

Stop Event

1×	iter limit
1×	node limit

Counts

27 → 27

Calls

Call 1

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

rewrite293.0ms (3.1%)

Memory

-28.8MiB live, 208.5MiB allocated

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	13	43
0	22	43
1	89	40
2	497	38
3	4478	38
0	8506	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) (sqrt.f64 k)) (pow.f64 (.f64 (*.f64 #s(literal 2 binary64) (PI.f64)) n) (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 2 binary64))))
(/.f64 (-.f64 #s(literal 1 binary64) 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 (pow.f64 (.f64 n (.f64 (PI.f64) #s(literal 2 binary64))) (.f64 #s(literal 1/4 binary64) (-.f64 #s(literal 1 binary64) k))) (sqrt.f64 k)) (pow.f64 (.f64 n (.f64 (PI.f64) #s(literal 2 binary64))) (.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 1/8 binary64)))) (pow.f64 (.f64 n (.f64 (PI.f64) #s(literal 2 binary64))) (*.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 1/8 binary64))))
(.f64 (.f64 (/.f64 (pow.f64 (.f64 n (.f64 (PI.f64) #s(literal 2 binary64))) (.f64 #s(literal 1/4 binary64) (-.f64 #s(literal 1 binary64) k))) (sqrt.f64 k)) (pow.f64 (pow.f64 n (-.f64 #s(literal 1 binary64) k)) #s(literal 1/4 binary64))) (pow.f64 (sqrt.f64 (.f64 (PI.f64) #s(literal 2 binary64))) (fma.f64 #s(literal 1/2 binary64) k #s(literal 1/2 binary64))))
(.f64 (.f64 (/.f64 (pow.f64 (.f64 n (.f64 (PI.f64) #s(literal 2 binary64))) (.f64 #s(literal 1/4 binary64) (-.f64 #s(literal 1 binary64) k))) (sqrt.f64 k)) (pow.f64 (sqrt.f64 (.f64 (PI.f64) #s(literal 2 binary64))) (fma.f64 #s(literal 1/2 binary64) k #s(literal 1/2 binary64)))) (pow.f64 (pow.f64 n (-.f64 #s(literal 1 binary64) k)) #s(literal 1/4 binary64)))
(.f64 (.f64 (/.f64 (pow.f64 (.f64 n (.f64 (PI.f64) #s(literal 2 binary64))) (.f64 #s(literal 1/4 binary64) (-.f64 #s(literal 1 binary64) k))) (sqrt.f64 k)) (pow.f64 #s(literal 2 binary64) (.f64 #s(literal 1/4 binary64) (-.f64 #s(literal 1 binary64) k)))) (pow.f64 (.f64 n (PI.f64)) (.f64 #s(literal 1/4 binary64) (-.f64 #s(literal 1 binary64) k))))
(.f64 (.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 k)) (pow.f64 (pow.f64 n (-.f64 #s(literal 1 binary64) k)) #s(literal 1/4 binary64))) (pow.f64 (pow.f64 n (-.f64 #s(literal 1 binary64) k)) #s(literal 1/4 binary64)))
(.f64 (.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))) (pow.f64 k #s(literal -1/4 binary64))) (pow.f64 k #s(literal -1/4 binary64)))
(.f64 (.f64 (pow.f64 k #s(literal -1/2 binary64)) (pow.f64 #s(literal 2 binary64) (fma.f64 #s(literal 1/2 binary64) k #s(literal 1/2 binary64)))) (pow.f64 (*.f64 n (PI.f64)) (fma.f64 #s(literal 1/2 binary64) k #s(literal 1/2 binary64))))
(.f64 (/.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))) (neg.f64 (sqrt.f64 k))) #s(literal -1 binary64))
(.f64 (.f64 (pow.f64 (.f64 n (.f64 (PI.f64) #s(literal 2 binary64))) (.f64 #s(literal 1/4 binary64) (-.f64 #s(literal 1 binary64) k))) (pow.f64 k #s(literal -1/4 binary64))) (.f64 (pow.f64 (.f64 n (.f64 (PI.f64) #s(literal 2 binary64))) (*.f64 #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 (.f64 n (.f64 (PI.f64) #s(literal 2 binary64))) (.f64 #s(literal 1/4 binary64) (-.f64 #s(literal 1 binary64) k)))) (.f64 (pow.f64 k #s(literal -1/4 binary64)) (pow.f64 (.f64 n (.f64 (PI.f64) #s(literal 2 binary64))) (*.f64 #s(literal 1/4 binary64) (-.f64 #s(literal 1 binary64) k)))))
(.f64 (/.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))) #s(literal -1 binary64)) (/.f64 #s(literal -1 binary64) (sqrt.f64 k)))
(.f64 (/.f64 (pow.f64 #s(literal 2 binary64) (fma.f64 #s(literal 1/2 binary64) k #s(literal 1/2 binary64))) (pow.f64 k #s(literal 1/4 binary64))) (/.f64 (pow.f64 (.f64 n (PI.f64)) (fma.f64 #s(literal 1/2 binary64) k #s(literal 1/2 binary64))) (pow.f64 k #s(literal 1/4 binary64))))
(.f64 (/.f64 (pow.f64 #s(literal 2 binary64) (fma.f64 #s(literal 1/2 binary64) k #s(literal 1/2 binary64))) (sqrt.f64 k)) (/.f64 (pow.f64 (.f64 n (PI.f64)) (fma.f64 #s(literal 1/2 binary64) k #s(literal 1/2 binary64))) #s(literal 1 binary64)))
(.f64 (/.f64 (pow.f64 (.f64 n (.f64 (PI.f64) #s(literal 2 binary64))) (.f64 #s(literal 1/4 binary64) (-.f64 #s(literal 1 binary64) k))) (pow.f64 k #s(literal 1/4 binary64))) (/.f64 (pow.f64 (.f64 n (.f64 (PI.f64) #s(literal 2 binary64))) (*.f64 #s(literal 1/4 binary64) (-.f64 #s(literal 1 binary64) k))) (pow.f64 k #s(literal 1/4 binary64))))
(.f64 (/.f64 (pow.f64 n (fma.f64 #s(literal 1/2 binary64) k #s(literal 1/2 binary64))) (pow.f64 k #s(literal 1/4 binary64))) (/.f64 (pow.f64 (.f64 (PI.f64) #s(literal 2 binary64)) (fma.f64 #s(literal 1/2 binary64) k #s(literal 1/2 binary64))) (pow.f64 k #s(literal 1/4 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))) (pow.f64 k #s(literal 1/4 binary64))) (/.f64 (pow.f64 n (fma.f64 #s(literal 1/2 binary64) k #s(literal 1/2 binary64))) (pow.f64 k #s(literal 1/4 binary64))))
(.f64 (/.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))) (pow.f64 k #s(literal 1/4 binary64))) (/.f64 #s(literal 1 binary64) (pow.f64 k #s(literal 1/4 binary64))))
(.f64 (/.f64 #s(literal 1 binary64) (pow.f64 k #s(literal 1/4 binary64))) (/.f64 (pow.f64 (.f64 n (*.f64 (PI.f64) #s(literal 2 binary64))) (fma.f64 #s(literal 1/2 binary64) k #s(literal 1/2 binary64))) (pow.f64 k #s(literal 1/4 binary64))))
(.f64 (/.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))) #s(literal 1 binary64)) (pow.f64 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 k)) (/.f64 (pow.f64 (.f64 (PI.f64) #s(literal 2 binary64)) (fma.f64 #s(literal 1/2 binary64) k #s(literal 1/2 binary64))) #s(literal 1 binary64)))
(.f64 (/.f64 (pow.f64 n (fma.f64 #s(literal 1/2 binary64) k #s(literal 1/2 binary64))) (sqrt.f64 k)) (pow.f64 (.f64 (PI.f64) #s(literal 2 binary64)) (fma.f64 #s(literal 1/2 binary64) k #s(literal 1/2 binary64))))
(.f64 (/.f64 (pow.f64 (.f64 n (.f64 (PI.f64) #s(literal 2 binary64))) (.f64 #s(literal 1/4 binary64) (-.f64 #s(literal 1 binary64) k))) (sqrt.f64 k)) (/.f64 (pow.f64 (.f64 n (.f64 (PI.f64) #s(literal 2 binary64))) (*.f64 #s(literal 1/4 binary64) (-.f64 #s(literal 1 binary64) k))) #s(literal 1 binary64)))
(.f64 (/.f64 (pow.f64 (.f64 n (.f64 (PI.f64) #s(literal 2 binary64))) (.f64 #s(literal 1/4 binary64) (-.f64 #s(literal 1 binary64) k))) (sqrt.f64 k)) (pow.f64 (.f64 n (.f64 (PI.f64) #s(literal 2 binary64))) (*.f64 #s(literal 1/4 binary64) (-.f64 #s(literal 1 binary64) k))))
(.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 k)) (/.f64 (pow.f64 n (fma.f64 #s(literal 1/2 binary64) k #s(literal 1/2 binary64))) #s(literal 1 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 k)) (pow.f64 n (fma.f64 #s(literal 1/2 binary64) k #s(literal 1/2 binary64))))
(.f64 (pow.f64 k #s(literal -1/4 binary64)) (.f64 (pow.f64 k #s(literal -1/4 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 (pow.f64 (.f64 n (.f64 (PI.f64) #s(literal 2 binary64))) (.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 1/8 binary64))) (.f64 (pow.f64 (.f64 n (.f64 (PI.f64) #s(literal 2 binary64))) (.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 1/8 binary64))) (/.f64 (pow.f64 (.f64 n (.f64 (PI.f64) #s(literal 2 binary64))) (*.f64 #s(literal 1/4 binary64) (-.f64 #s(literal 1 binary64) k))) (sqrt.f64 k))))
(.f64 (neg.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)))) (/.f64 #s(literal -1 binary64) (sqrt.f64 k)))
(.f64 (pow.f64 (pow.f64 n (-.f64 #s(literal 1 binary64) k)) #s(literal 1/4 binary64)) (.f64 (pow.f64 (sqrt.f64 (.f64 (PI.f64) #s(literal 2 binary64))) (fma.f64 #s(literal 1/2 binary64) k #s(literal 1/2 binary64))) (/.f64 (pow.f64 (.f64 n (.f64 (PI.f64) #s(literal 2 binary64))) (.f64 #s(literal 1/4 binary64) (-.f64 #s(literal 1 binary64) k))) (sqrt.f64 k))))
(.f64 (pow.f64 (sqrt.f64 (.f64 (PI.f64) #s(literal 2 binary64))) (fma.f64 #s(literal 1/2 binary64) k #s(literal 1/2 binary64))) (.f64 (pow.f64 (pow.f64 n (-.f64 #s(literal 1 binary64) k)) #s(literal 1/4 binary64)) (/.f64 (pow.f64 (.f64 n (.f64 (PI.f64) #s(literal 2 binary64))) (.f64 #s(literal 1/4 binary64) (-.f64 #s(literal 1 binary64) k))) (sqrt.f64 k))))
(.f64 (pow.f64 (sqrt.f64 (.f64 (PI.f64) #s(literal 2 binary64))) (fma.f64 #s(literal 1/2 binary64) k #s(literal 1/2 binary64))) (.f64 (pow.f64 (sqrt.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 (pow.f64 #s(literal 2 binary64) (.f64 #s(literal 1/4 binary64) (-.f64 #s(literal 1 binary64) k))) (.f64 (pow.f64 (.f64 n (PI.f64)) (.f64 #s(literal 1/4 binary64) (-.f64 #s(literal 1 binary64) k))) (/.f64 (pow.f64 (.f64 n (.f64 (PI.f64) #s(literal 2 binary64))) (.f64 #s(literal 1/4 binary64) (-.f64 #s(literal 1 binary64) k))) (sqrt.f64 k))))
(.f64 (pow.f64 (PI.f64) (fma.f64 #s(literal 1/2 binary64) k #s(literal 1/2 binary64))) (.f64 (pow.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 (pow.f64 #s(literal 2 binary64) (fma.f64 #s(literal 1/2 binary64) k #s(literal 1/2 binary64))) (/.f64 (pow.f64 (.f64 n (PI.f64)) (fma.f64 #s(literal 1/2 binary64) k #s(literal 1/2 binary64))) (sqrt.f64 k)))
(.f64 (pow.f64 #s(literal 2 binary64) (fma.f64 #s(literal 1/2 binary64) k #s(literal 1/2 binary64))) (.f64 (pow.f64 (PI.f64) (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 (pow.f64 #s(literal 2 binary64) (fma.f64 #s(literal 1/2 binary64) k #s(literal 1/2 binary64))) (.f64 (pow.f64 (*.f64 n (PI.f64)) (fma.f64 #s(literal 1/2 binary64) k #s(literal 1/2 binary64))) (pow.f64 k #s(literal -1/2 binary64))))
(.f64 (pow.f64 (.f64 n (.f64 (PI.f64) #s(literal 2 binary64))) (.f64 #s(literal 1/4 binary64) (-.f64 #s(literal 1 binary64) k))) (/.f64 (pow.f64 (.f64 n (.f64 (PI.f64) #s(literal 2 binary64))) (*.f64 #s(literal 1/4 binary64) (-.f64 #s(literal 1 binary64) k))) (sqrt.f64 k)))
(.f64 #s(literal -1 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))) (neg.f64 (sqrt.f64 k))))
(.f64 #s(literal -1 binary64) (.f64 (/.f64 #s(literal -1 binary64) (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 (pow.f64 n (fma.f64 #s(literal 1/2 binary64) k #s(literal 1/2 binary64))) (/.f64 (pow.f64 (.f64 (PI.f64) #s(literal 2 binary64)) (fma.f64 #s(literal 1/2 binary64) k #s(literal 1/2 binary64))) (sqrt.f64 k)))
(.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 (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)) #s(literal 1 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))) (pow.f64 k #s(literal -1/2 binary64)))
(.f64 (pow.f64 k #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))) #s(literal 1 binary64)))
(.f64 (pow.f64 k #s(literal -1/2 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 #s(literal 1 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)))
(pow.f64 (/.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)))) #s(literal -1 binary64))
(/.f64 (/.f64 (neg.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)))) #s(literal -1 binary64)) (sqrt.f64 k))
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(/.f64 (pow.f64 (.f64 n (.f64 (PI.f64) #s(literal 2 binary64))) (/.f64 #s(literal 1 binary64) (fma.f64 #s(literal 2 binary64) k #s(literal 2 binary64)))) (pow.f64 (.f64 n (.f64 (PI.f64) #s(literal 2 binary64))) (/.f64 (*.f64 k k) (fma.f64 #s(literal 2 binary64) k #s(literal 2 binary64)))))
(/.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))))

eval121.0ms (1.3%)

Memory: 21.0MiB live, 105.0MiB allocated
Compiler: Compiled 9 931 to 1 555 computations (84.3% saved)

prune50.0ms (0.5%)

Memory

7.3MiB live, 46.0MiB allocated

Pruning

22 alts after pruning (22 fresh and 0 done)

	Pruned	Kept	Total
New	409	22	431
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	410	22	432

Accuracy

100.0%

Counts

432 → 22

Alt Table

Click to see full alt table

Status	Accuracy	Program
	40.8%	(/.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))
	99.4%	(/.f64 (.f64 (pow.f64 k #s(literal -1/2 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)))
▶	99.4%	(/.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))))
	40.7%	(/.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)))))
	40.1%	(.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)))
	40.8%	(.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))) (pow.f64 k #s(literal -1/2 binary64)))
	40.3%	(.f64 (pow.f64 (sqrt.f64 (.f64 (PI.f64) #s(literal 2 binary64))) (fma.f64 #s(literal 1/2 binary64) k #s(literal 1/2 binary64))) (.f64 (pow.f64 (sqrt.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))))
	40.2%	(.f64 (pow.f64 #s(literal 2 binary64) (fma.f64 #s(literal 1/2 binary64) k #s(literal 1/2 binary64))) (/.f64 (pow.f64 (.f64 n (PI.f64)) (fma.f64 #s(literal 1/2 binary64) k #s(literal 1/2 binary64))) (sqrt.f64 k)))
	99.3%	(.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)))
▶	99.6%	(.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))))
	99.6%	(.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) (pow.f64 (.f64 (*.f64 #s(literal 2 binary64) (PI.f64)) n) (/.f64 (fma.f64 (neg.f64 k) k #s(literal 1 binary64)) (fma.f64 #s(literal 2 binary64) k #s(literal 2 binary64)))))
	61.1%	(.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))))
	41.5%	(.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) (pow.f64 (.f64 (*.f64 #s(literal 2 binary64) (PI.f64)) n) #s(approx (/ (- 1 k) 2) #s(literal 1/2 binary64))))
	99.6%	(.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)))))
	99.3%	(.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) (/.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)))))))
	99.3%	(.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))))))
▶	42.4%	(.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) #s(approx (pow ( (* 2 (PI)) n) (/ (- 1 k) 2)) (.f64 (fma.f64 (.f64 #s(literal -1/2 binary64) k) (log.f64 (.f64 (.f64 #s(literal 2 binary64) n) (PI.f64))) #s(literal 1 binary64)) (.f64 (sqrt.f64 (.f64 (PI.f64) n)) (sqrt.f64 #s(literal 2 binary64))))))
	41.4%	(.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)))))
	99.3%	(.f64 (.f64 (pow.f64 (.f64 n (.f64 (PI.f64) #s(literal 2 binary64))) (.f64 #s(literal 1/4 binary64) (-.f64 #s(literal 1 binary64) k))) (pow.f64 k #s(literal -1/4 binary64))) (.f64 (pow.f64 (.f64 n (.f64 (PI.f64) #s(literal 2 binary64))) (*.f64 #s(literal 1/4 binary64) (-.f64 #s(literal 1 binary64) k))) (pow.f64 k #s(literal -1/4 binary64))))
	48.4%	#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))
▶	99.6%	#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))))
▶	28.6%	#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 988 to 742 computations (24.9% saved)

simplify275.0ms (2.9%)

Memory

-24.2MiB live, 57.5MiB allocated

Algorithm

1×	egg-herbie

Localize:

Found 20 expressions of interest:

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

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	52	398
0	88	395
1	141	387
2	186	387
3	278	383
4	480	383
5	900	383
6	1421	383
7	2120	383
8	2679	383
9	2936	383
10	3036	383
11	3539	383
12	3940	383
13	3976	383
14	4129	383
15	4279	383
16	4376	383
17	4616	383
18	4727	383
19	4760	383
20	4769	383
21	4769	383
22	4769	383
23	4791	383
24	4799	383
25	4799	383
26	4799	383
27	4807	383
0	4807	383

Stop Event

1×	iter limit
1×	saturated
1×	iter limit

Calls

Call 1

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

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

localize289.0ms (3.1%)

Memory

10.4MiB live, 167.7MiB allocated

Localize:

Found 20 expressions of interest:

New	Metric	Score
accuracy	0.125	(/.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	0.15625	(.f64 n (.f64 (PI.f64) #s(literal 2 binary64)))
accuracy	0.32811858260009796	(sqrt.f64 (.f64 n (.f64 (PI.f64) #s(literal 2 binary64))))
accuracy	16.71053066552266	(PI.f64)
accuracy	0.32421743848645357	(sqrt.f64 (*.f64 (PI.f64) n))
accuracy	0.33984375	(.f64 (sqrt.f64 (.f64 (PI.f64) n)) (sqrt.f64 #s(literal 2 binary64)))
accuracy	16.71053066552266	(PI.f64)
accuracy	20.25258798941464	#s(approx (pow (* (* 2 (PI)) n) (/ (- 1 k) 2)) (.f64 (fma.f64 (.f64 #s(literal -1/2 binary64) k) (log.f64 (.f64 (.f64 #s(literal 2 binary64) n) (PI.f64))) #s(literal 1 binary64)) (.f64 (sqrt.f64 (.f64 (PI.f64) n)) (sqrt.f64 #s(literal 2 binary64)))))
accuracy	0.1526850729236806	(pow.f64 (.f64 (.f64 #s(literal 2 binary64) (PI.f64)) n) (fma.f64 k #s(literal -1/2 binary64) #s(literal 1/2 binary64)))
accuracy	0.15625	(.f64 (.f64 #s(literal 2 binary64) (PI.f64)) n)
accuracy	0.2265625	(/.f64 #s(literal 1 binary64) (sqrt.f64 k))
accuracy	16.71053066552266	(PI.f64)
accuracy	0.4034230627183166	(/.f64 (*.f64 (PI.f64) n) k)
accuracy	8.34882710348366	(sqrt.f64 (/.f64 (*.f64 (PI.f64) n) k))
accuracy	16.71053066552266	(PI.f64)
accuracy	20.442540493736956	#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	0.15234375	(.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)))
accuracy	0.1526850729236806	(pow.f64 (.f64 (.f64 #s(literal 2 binary64) n) (PI.f64)) (fma.f64 #s(literal -1/2 binary64) k #s(literal 1/2 binary64)))
accuracy	0.15625	(.f64 (.f64 #s(literal 2 binary64) n) (PI.f64))
accuracy	16.71053066552266	(PI.f64)

Samples

101.0ms	187×	0	valid
26.0ms	69×	0	exit

Compiler

Compiled 342 to 47 computations (86.3% saved)

Precisions

Click to see histograms. Total time spent on operations: 103.0ms

ival-mult: 56.0ms (54.6% of total)

ival-pow: 17.0ms (16.6% of total)

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

ival-div: 8.0ms (7.8% of total)

ival-add: 4.0ms (3.9% of total)

ival-log: 3.0ms (2.9% of total)

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

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

exact: 1.0ms (1% of total)

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

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

series202.0ms (2.2%)

Memory

17.5MiB live, 134.0MiB allocated

Counts

23 → 57

Calls

Call 1

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

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

Calls

6 calls:

Time	Variable		Point	Expression
93.0ms	k	@	-inf	((* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (* (pow (* (* 2 n) (PI)) (+ (* -1/2 k) 1/2)) (sqrt (/ 1 k))) (pow (* (* 2 n) (PI)) (+ (* -1/2 k) 1/2)) (* (* 2 n) (PI)) (* (/ 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) (+ (* k -1/2) 1/2))) (/ 1 (sqrt k)) (sqrt k) (pow (* (* 2 (PI)) n) (+ (* k -1/2) 1/2)) (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2)) (pow (pow (* n (* (PI) 2)) k) 1/2) (/ (sqrt (* n (* (PI) 2))) (* (sqrt k) (pow (pow (* n (* (PI) 2)) k) 1/2))) (sqrt (* n (* (PI) 2))) (* n (* (PI) 2)) (PI) (/ (* (PI) n) k) (* (* 2 (PI)) n) (* (sqrt (* (PI) n)) (sqrt 2)) (sqrt (* (PI) n)))
52.0ms	n	@	-inf	((* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (* (pow (* (* 2 n) (PI)) (+ (* -1/2 k) 1/2)) (sqrt (/ 1 k))) (pow (* (* 2 n) (PI)) (+ (* -1/2 k) 1/2)) (* (* 2 n) (PI)) (* (/ 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) (+ (* k -1/2) 1/2))) (/ 1 (sqrt k)) (sqrt k) (pow (* (* 2 (PI)) n) (+ (* k -1/2) 1/2)) (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2)) (pow (pow (* n (* (PI) 2)) k) 1/2) (/ (sqrt (* n (* (PI) 2))) (* (sqrt k) (pow (pow (* n (* (PI) 2)) k) 1/2))) (sqrt (* n (* (PI) 2))) (* n (* (PI) 2)) (PI) (/ (* (PI) n) k) (* (* 2 (PI)) n) (* (sqrt (* (PI) n)) (sqrt 2)) (sqrt (* (PI) n)))
34.0ms	n	@	inf	((* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (* (pow (* (* 2 n) (PI)) (+ (* -1/2 k) 1/2)) (sqrt (/ 1 k))) (pow (* (* 2 n) (PI)) (+ (* -1/2 k) 1/2)) (* (* 2 n) (PI)) (* (/ 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) (+ (* k -1/2) 1/2))) (/ 1 (sqrt k)) (sqrt k) (pow (* (* 2 (PI)) n) (+ (* k -1/2) 1/2)) (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2)) (pow (pow (* n (* (PI) 2)) k) 1/2) (/ (sqrt (* n (* (PI) 2))) (* (sqrt k) (pow (pow (* n (* (PI) 2)) k) 1/2))) (sqrt (* n (* (PI) 2))) (* n (* (PI) 2)) (PI) (/ (* (PI) n) k) (* (* 2 (PI)) n) (* (sqrt (* (PI) n)) (sqrt 2)) (sqrt (* (PI) n)))
12.0ms	n	@	0	((* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (* (pow (* (* 2 n) (PI)) (+ (* -1/2 k) 1/2)) (sqrt (/ 1 k))) (pow (* (* 2 n) (PI)) (+ (* -1/2 k) 1/2)) (* (* 2 n) (PI)) (* (/ 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) (+ (* k -1/2) 1/2))) (/ 1 (sqrt k)) (sqrt k) (pow (* (* 2 (PI)) n) (+ (* k -1/2) 1/2)) (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2)) (pow (pow (* n (* (PI) 2)) k) 1/2) (/ (sqrt (* n (* (PI) 2))) (* (sqrt k) (pow (pow (* n (* (PI) 2)) k) 1/2))) (sqrt (* n (* (PI) 2))) (* n (* (PI) 2)) (PI) (/ (* (PI) n) k) (* (* 2 (PI)) n) (* (sqrt (* (PI) n)) (sqrt 2)) (sqrt (* (PI) n)))
5.0ms	k	@	0	((* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (* (pow (* (* 2 n) (PI)) (+ (* -1/2 k) 1/2)) (sqrt (/ 1 k))) (pow (* (* 2 n) (PI)) (+ (* -1/2 k) 1/2)) (* (* 2 n) (PI)) (* (/ 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) (+ (* k -1/2) 1/2))) (/ 1 (sqrt k)) (sqrt k) (pow (* (* 2 (PI)) n) (+ (* k -1/2) 1/2)) (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2)) (pow (pow (* n (* (PI) 2)) k) 1/2) (/ (sqrt (* n (* (PI) 2))) (* (sqrt k) (pow (pow (* n (* (PI) 2)) k) 1/2))) (sqrt (* n (* (PI) 2))) (* n (* (PI) 2)) (PI) (/ (* (PI) n) k) (* (* 2 (PI)) n) (* (sqrt (* (PI) n)) (sqrt 2)) (sqrt (* (PI) n)))

simplify261.0ms (2.8%)

Memory

-3.1MiB live, 151.4MiB allocated

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	249	1177
1	753	1120
2	2683	1037
3	6302	999
0	8318	974

Stop Event

1×	iter limit
1×	node limit

Counts

57 → 57

Calls

Call 1

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

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

rewrite280.0ms (3%)

Memory

-11.6MiB live, 192.9MiB allocated

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	52	264
0	88	254
1	318	239
2	1576	235
0	8268	235

Stop Event

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

Counts

23 → 891

Calls

Call 1

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

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

eval232.0ms (2.5%)

Memory: -4.9MiB live, 185.5MiB allocated
Compiler: Compiled 29 805 to 3 588 computations (88% saved)

prune34.0ms (0.4%)

Memory

17.6MiB live, 96.3MiB allocated

Pruning

25 alts after pruning (22 fresh and 3 done)

	Pruned	Kept	Total
New	888	21	909
Fresh	16	1	17
Picked	2	3	5
Done	0	0	0
Total	906	25	931

Accuracy

100.0%

Counts

931 → 25

Alt Table

Click to see full alt table

Status	Accuracy	Program
✓	99.6%	(.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))))
▶	41.4%	(.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%	#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (/.f64 (pow.f64 (.f64 (.f64 (PI.f64) #s(literal 2 binary64)) n) (fma.f64 #s(literal -1/2 binary64) k #s(literal 1/2 binary64))) (sqrt.f64 k)))
▶	41.5%	#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)))
	29.3%	#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)))))
	29.3%	#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (/.f64 #s(literal 1 binary64) (sqrt.f64 (/.f64 k (.f64 (.f64 (PI.f64) #s(literal 2 binary64)) n)))))
✓	99.6%	#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))))
	41.5%	#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (.f64 (sqrt.f64 (.f64 (*.f64 (PI.f64) #s(literal 2 binary64)) n)) (pow.f64 k #s(literal -1/2 binary64))))
	41.5%	#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (.f64 (sqrt.f64 (.f64 (PI.f64) n)) (sqrt.f64 (/.f64 #s(literal 2 binary64) k))))
	28.5%	#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))))
▶	99.8%	#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (.f64 (sqrt.f64 n) (sqrt.f64 (/.f64 (.f64 (PI.f64) #s(literal 2 binary64)) (.f64 (pow.f64 (.f64 (*.f64 (PI.f64) #s(literal 2 binary64)) n) k) k)))))
	41.5%	#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (.f64 (sqrt.f64 n) (sqrt.f64 (/.f64 (.f64 (PI.f64) #s(literal 2 binary64)) k))))
	41.4%	#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))))
	29.3%	#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))))))
▶	41.4%	#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)))))
	41.4%	#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)))))
	86.6%	#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) (.f64 (pow.f64 (.f64 (*.f64 (PI.f64) #s(literal 2 binary64)) n) k) k)))))
✓	28.6%	#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))))
	28.6%	#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (.f64 (sqrt.f64 #s(literal 2 binary64)) (sqrt.f64 (/.f64 #s(literal 1 binary64) (/.f64 k (.f64 (PI.f64) n))))))
	28.6%	#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (.f64 (sqrt.f64 #s(literal 2 binary64)) (sqrt.f64 (.f64 (*.f64 (neg.f64 (PI.f64)) n) (/.f64 #s(literal -1 binary64) k)))))
	28.6%	#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (.f64 (sqrt.f64 #s(literal 2 binary64)) (sqrt.f64 (.f64 n (/.f64 (PI.f64) k)))))
	41.5%	#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (.f64 (neg.f64 (sqrt.f64 (.f64 (*.f64 (PI.f64) #s(literal 2 binary64)) n))) (/.f64 #s(literal -1 binary64) (sqrt.f64 k))))
	41.4%	#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (.f64 #s(approx (pow ( (* 2 n) (PI)) (+ (* -1/2 k) 1/2)) (.f64 (sqrt.f64 (.f64 n (PI.f64))) (sqrt.f64 #s(literal 2 binary64)))) (sqrt.f64 (/.f64 #s(literal 1 binary64) k))))
	86.6%	#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt.f64 (/.f64 (.f64 (.f64 (PI.f64) #s(literal 2 binary64)) n) (.f64 (pow.f64 (.f64 (*.f64 (PI.f64) #s(literal 2 binary64)) n) k) k))))
▶	28.7%	#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 1 331 to 1 063 computations (20.1% saved)

simplify15.0ms (0.2%)

Memory

-21.8MiB live, 22.6MiB allocated

Algorithm

1×	egg-herbie

Localize:

Found 20 expressions of interest:

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

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	43	344
0	68	344
1	107	334
2	156	334
3	205	334
4	228	334
5	243	334
6	264	334
7	295	334
8	306	334
9	309	334
0	309	328

Stop Event

1×	iter limit
1×	saturated
1×	iter limit

Calls

Call 1

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

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

localize127.0ms (1.4%)

Memory

-3.9MiB live, 196.6MiB allocated

Localize:

Found 20 expressions of interest:

New	Metric	Score
accuracy	0.32421743848645357	(sqrt.f64 (*.f64 (PI.f64) n))
accuracy	0.33984375	(.f64 (sqrt.f64 (.f64 (PI.f64) n)) (sqrt.f64 #s(literal 2 binary64)))
accuracy	16.71053066552266	(PI.f64)
accuracy	20.553316912866627	#s(approx (pow (* (* 2 (PI)) n) (/ (- 1 k) 2)) (.f64 (sqrt.f64 (.f64 (PI.f64) n)) (sqrt.f64 #s(literal 2 binary64))))
accuracy	0.26791000976844204	(*.f64 (sqrt.f64 n) (sqrt.f64 (/.f64 (PI.f64) k)))
accuracy	0.332695019536884	(.f64 (sqrt.f64 #s(literal 2 binary64)) (.f64 (sqrt.f64 n) (sqrt.f64 (/.f64 (PI.f64) k))))
accuracy	16.71053066552266	(PI.f64)
accuracy	20.442540493736956	#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)))))
accuracy	0.22265625	(/.f64 (sqrt.f64 (.f64 (.f64 (PI.f64) #s(literal 2 binary64)) n)) (sqrt.f64 k))
accuracy	0.32811858260009796	(sqrt.f64 (.f64 (.f64 (PI.f64) #s(literal 2 binary64)) n))
accuracy	16.71053066552266	(PI.f64)
accuracy	20.442540493736956	#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)))
accuracy	0.4034230627183166	(/.f64 (*.f64 (PI.f64) n) k)
accuracy	8.336756415667018	(sqrt.f64 (.f64 (/.f64 (.f64 (PI.f64) n) k) #s(literal 2 binary64)))
accuracy	16.71053066552266	(PI.f64)
accuracy	20.442540493736956	#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	0.1171875	(/.f64 (.f64 (PI.f64) #s(literal 2 binary64)) (.f64 (pow.f64 (.f64 (.f64 (PI.f64) #s(literal 2 binary64)) n) k) k))
accuracy	0.13671875	(.f64 (sqrt.f64 n) (sqrt.f64 (/.f64 (.f64 (PI.f64) #s(literal 2 binary64)) (.f64 (pow.f64 (.f64 (*.f64 (PI.f64) #s(literal 2 binary64)) n) k) k))))
accuracy	0.15625	(.f64 (.f64 (PI.f64) #s(literal 2 binary64)) n)
accuracy	16.71053066552266	(PI.f64)

Samples

58.0ms	187×	0	valid
38.0ms	69×	0	exit

Compiler

Compiled 282 to 36 computations (87.2% saved)

Precisions

Click to see histograms. Total time spent on operations: 73.0ms

ival-div: 28.0ms (38.5% of total)

ival-mult: 19.0ms (26.1% of total)

ival-sqrt: 15.0ms (20.6% of total)

ival-pow: 9.0ms (12.4% of total)

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

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

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

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

exact: 0.0ms (0% of total)

series62.0ms (0.7%)

Memory

-0.5MiB live, 121.8MiB allocated

Counts

24 → 61

Calls

Call 1

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

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

Calls

6 calls:

Time	Variable		Point	Expression
16.0ms	n	@	-inf	((* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (* (sqrt n) (sqrt (/ (* (PI) 2) (* (pow (* (* (PI) 2) n) k) k)))) (sqrt n) (sqrt (/ (* (PI) 2) (* (pow (* (* (PI) 2) n) k) k))) (* (/ 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 (* (* (PI) 2) n)) (sqrt k)) (sqrt (* (* (PI) 2) n)) (* (* (PI) 2) n) (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (* (sqrt 2) (* (sqrt n) (sqrt (/ (PI) k)))) (sqrt 2) (* (sqrt n) (sqrt (/ (PI) k))) (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (/ 1 (sqrt k)) (sqrt k) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2)) (PI) (/ (* (PI) 2) (* (pow (* (* (PI) 2) n) k) k)) (* (sqrt (* (PI) n)) (sqrt 2)) (sqrt (* (PI) n)))
15.0ms	n	@	inf	((* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (* (sqrt n) (sqrt (/ (* (PI) 2) (* (pow (* (* (PI) 2) n) k) k)))) (sqrt n) (sqrt (/ (* (PI) 2) (* (pow (* (* (PI) 2) n) k) k))) (* (/ 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 (* (* (PI) 2) n)) (sqrt k)) (sqrt (* (* (PI) 2) n)) (* (* (PI) 2) n) (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (* (sqrt 2) (* (sqrt n) (sqrt (/ (PI) k)))) (sqrt 2) (* (sqrt n) (sqrt (/ (PI) k))) (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (/ 1 (sqrt k)) (sqrt k) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2)) (PI) (/ (* (PI) 2) (* (pow (* (* (PI) 2) n) k) k)) (* (sqrt (* (PI) n)) (sqrt 2)) (sqrt (* (PI) n)))
14.0ms	n	@	0	((* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (* (sqrt n) (sqrt (/ (* (PI) 2) (* (pow (* (* (PI) 2) n) k) k)))) (sqrt n) (sqrt (/ (* (PI) 2) (* (pow (* (* (PI) 2) n) k) k))) (* (/ 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 (* (* (PI) 2) n)) (sqrt k)) (sqrt (* (* (PI) 2) n)) (* (* (PI) 2) n) (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (* (sqrt 2) (* (sqrt n) (sqrt (/ (PI) k)))) (sqrt 2) (* (sqrt n) (sqrt (/ (PI) k))) (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (/ 1 (sqrt k)) (sqrt k) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2)) (PI) (/ (* (PI) 2) (* (pow (* (* (PI) 2) n) k) k)) (* (sqrt (* (PI) n)) (sqrt 2)) (sqrt (* (PI) n)))
7.0ms	k	@	-inf	((* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (* (sqrt n) (sqrt (/ (* (PI) 2) (* (pow (* (* (PI) 2) n) k) k)))) (sqrt n) (sqrt (/ (* (PI) 2) (* (pow (* (* (PI) 2) n) k) k))) (* (/ 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 (* (* (PI) 2) n)) (sqrt k)) (sqrt (* (* (PI) 2) n)) (* (* (PI) 2) n) (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (* (sqrt 2) (* (sqrt n) (sqrt (/ (PI) k)))) (sqrt 2) (* (sqrt n) (sqrt (/ (PI) k))) (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (/ 1 (sqrt k)) (sqrt k) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2)) (PI) (/ (* (PI) 2) (* (pow (* (* (PI) 2) n) k) k)) (* (sqrt (* (PI) n)) (sqrt 2)) (sqrt (* (PI) n)))
4.0ms	k	@	0	((* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (* (sqrt n) (sqrt (/ (* (PI) 2) (* (pow (* (* (PI) 2) n) k) k)))) (sqrt n) (sqrt (/ (* (PI) 2) (* (pow (* (* (PI) 2) n) k) k))) (* (/ 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 (* (* (PI) 2) n)) (sqrt k)) (sqrt (* (* (PI) 2) n)) (* (* (PI) 2) n) (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (* (sqrt 2) (* (sqrt n) (sqrt (/ (PI) k)))) (sqrt 2) (* (sqrt n) (sqrt (/ (PI) k))) (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (/ 1 (sqrt k)) (sqrt k) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2)) (PI) (/ (* (PI) 2) (* (pow (* (* (PI) 2) n) k) k)) (* (sqrt (* (PI) n)) (sqrt 2)) (sqrt (* (PI) n)))

simplify180.0ms (1.9%)

Memory

23.1MiB live, 250.6MiB allocated

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	296	1406
1	906	1340
2	3392	1242
0	8620	1210

Stop Event

1×	iter limit
1×	node limit

Counts

61 → 61

Calls

Call 1

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

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

rewrite164.0ms (1.8%)

Memory

17.6MiB live, 212.2MiB allocated

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	43	278
0	68	266
1	215	255
2	1119	243
0	8347	243

Stop Event

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

Counts

24 → 1 034

Calls

Call 1

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

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

eval293.0ms (3.1%)

Memory: -25.9MiB live, 377.9MiB allocated
Compiler: Compiled 41 729 to 5 384 computations (87.1% saved)

prune99.0ms (1.1%)

Memory

16.2MiB live, 213.4MiB allocated

Pruning

50 alts after pruning (43 fresh and 7 done)

	Pruned	Kept	Total
New	1 201	33	1 234
Fresh	7	10	17
Picked	1	4	5
Done	0	3	3
Total	1 209	50	1 259

Accuracy

100.0%

Counts

1 259 → 50

Alt Table

Click to see full alt table

Status	Accuracy	Program
	41.5%	(.f64 (pow.f64 k #s(literal -1/2 binary64)) #s(approx (pow ( (* 2 (PI)) n) (/ (- 1 k) 2)) (sqrt.f64 (.f64 (.f64 (PI.f64) #s(literal 2 binary64)) n))))
✓	99.6%	(.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))))
	41.4%	(.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) #s(approx (pow ( (* 2 (PI)) n) (/ (- 1 k) 2)) (.f64 (.f64 (sqrt.f64 (PI.f64)) (sqrt.f64 n)) (sqrt.f64 #s(literal 2 binary64)))))
	41.5%	(.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) #s(approx (pow ( (* 2 (PI)) n) (/ (- 1 k) 2)) (.f64 (sqrt.f64 (.f64 (*.f64 (sqrt.f64 (PI.f64)) (sqrt.f64 (PI.f64))) n)) (sqrt.f64 #s(literal 2 binary64)))))
	41.5%	(.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) #s(approx (pow ( (* 2 (PI)) n) (/ (- 1 k) 2)) (sqrt.f64 (.f64 (.f64 (PI.f64) #s(literal 2 binary64)) n))))
	41.4%	(.f64 #s(approx (/ 1 (sqrt k)) (sqrt.f64 (/.f64 #s(literal 1 binary64) 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%	#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (/.f64 (pow.f64 (.f64 (.f64 (PI.f64) #s(literal 2 binary64)) n) (fma.f64 k #s(literal -1/2 binary64) #s(literal 1/2 binary64))) (sqrt.f64 k)))
	41.4%	#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (/.f64 (.f64 (sqrt.f64 (.f64 (PI.f64) n)) (sqrt.f64 #s(literal 2 binary64))) (sqrt.f64 k)))
	41.3%	#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (/.f64 (.f64 (sqrt.f64 (.f64 (PI.f64) #s(literal 2 binary64))) (sqrt.f64 n)) (sqrt.f64 k)))
	41.4%	#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (/.f64 (.f64 (sqrt.f64 (.f64 n #s(literal 2 binary64))) (sqrt.f64 (PI.f64))) (sqrt.f64 k)))
	35.8%	#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (/.f64 (sqrt.f64 (.f64 (.f64 (PI.f64) #s(literal 2 binary64)) n)) (pow.f64 (*.f64 k k) #s(literal 1/4 binary64))))
✓	41.5%	#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)))
	41.5%	#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (/.f64 (sqrt.f64 (*.f64 n #s(literal 2 binary64))) (sqrt.f64 (/.f64 k (PI.f64)))))
	29.3%	#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)))))
	29.3%	#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (/.f64 #s(literal 1 binary64) (sqrt.f64 (/.f64 k (.f64 (.f64 (PI.f64) #s(literal 2 binary64)) n)))))
✓	99.6%	#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))))
	41.3%	#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (.f64 (.f64 (pow.f64 k #s(literal -1/2 binary64)) (sqrt.f64 (*.f64 (PI.f64) #s(literal 2 binary64)))) (sqrt.f64 n)))
	41.4%	#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (.f64 (.f64 (pow.f64 k #s(literal -1/2 binary64)) (sqrt.f64 #s(literal 2 binary64))) (sqrt.f64 (*.f64 (PI.f64) n))))
	41.5%	#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)))))
	41.5%	#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (.f64 (sqrt.f64 (.f64 (/.f64 (PI.f64) k) #s(literal 2 binary64))) (sqrt.f64 n)))
	99.3%	#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (.f64 (sqrt.f64 (.f64 (PI.f64) n)) (sqrt.f64 (/.f64 #s(literal 2 binary64) (.f64 (pow.f64 (.f64 (*.f64 (PI.f64) #s(literal 2 binary64)) n) k) k)))))
	41.5%	#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (.f64 (sqrt.f64 (.f64 (PI.f64) n)) (sqrt.f64 (/.f64 #s(literal 2 binary64) k))))
▶	41.3%	#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (.f64 (sqrt.f64 (.f64 (PI.f64) #s(literal 2 binary64))) (*.f64 (neg.f64 (sqrt.f64 n)) (/.f64 #s(literal -1 binary64) (sqrt.f64 k)))))
▶	28.5%	#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))))
	41.3%	#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (.f64 (sqrt.f64 (PI.f64)) (.f64 (pow.f64 k #s(literal -1/2 binary64)) (sqrt.f64 (*.f64 n #s(literal 2 binary64))))))
	28.5%	#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (.f64 (sqrt.f64 (PI.f64)) (sqrt.f64 (.f64 (/.f64 n k) #s(literal 2 binary64)))))
✓	99.8%	#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (.f64 (sqrt.f64 n) (sqrt.f64 (/.f64 (.f64 (PI.f64) #s(literal 2 binary64)) (.f64 (pow.f64 (.f64 (*.f64 (PI.f64) #s(literal 2 binary64)) n) k) k)))))
▶	41.5%	#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (.f64 (sqrt.f64 n) #s(approx (sqrt (/ ( (PI) 2) (* (pow (* (* (PI) 2) n) k) k))) (*.f64 (sqrt.f64 (/.f64 (PI.f64) k)) (sqrt.f64 #s(literal 2 binary64))))))
	41.5%	#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (.f64 (sqrt.f64 #s(literal 2 binary64)) (/.f64 (.f64 (sqrt.f64 n) (neg.f64 (sqrt.f64 (PI.f64)))) (neg.f64 (sqrt.f64 k)))))
	41.4%	#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))))
	41.4%	#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 k (PI.f64))))))
	29.3%	#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))))))
✓	41.4%	#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)))))
✓	28.6%	#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))))
	28.6%	#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (.f64 (sqrt.f64 #s(literal 2 binary64)) (sqrt.f64 (/.f64 #s(literal 1 binary64) (/.f64 k (.f64 (PI.f64) n))))))
	28.6%	#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (.f64 (sqrt.f64 #s(literal 2 binary64)) (sqrt.f64 (.f64 (*.f64 (neg.f64 (PI.f64)) n) (/.f64 #s(literal -1 binary64) k)))))
	28.6%	#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (.f64 (sqrt.f64 #s(literal 2 binary64)) (sqrt.f64 (.f64 n (/.f64 (PI.f64) k)))))
	86.6%	#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt.f64 (/.f64 (.f64 (.f64 (PI.f64) #s(literal 2 binary64)) n) (.f64 (pow.f64 (.f64 (*.f64 (PI.f64) #s(literal 2 binary64)) n) k) k))))
	28.7%	#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))))
	28.7%	#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt.f64 (/.f64 (*.f64 n #s(literal 2 binary64)) (/.f64 k (PI.f64)))))
	28.7%	#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)))))
	28.5%	#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))))
✓	28.7%	#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))))
	28.7%	#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))))
	28.7%	#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))))
	28.7%	#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))))
	28.7%	#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt.f64 (.f64 (.f64 (neg.f64 (PI.f64)) (*.f64 (/.f64 #s(literal -1 binary64) k) n)) #s(literal 2 binary64))))
	87.0%	#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt.f64 (.f64 (.f64 n (/.f64 #s(literal 2 binary64) (pow.f64 (.f64 (.f64 (PI.f64) #s(literal 2 binary64)) n) k))) (/.f64 (PI.f64) k))))
	28.6%	#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt.f64 (.f64 (sqrt.f64 (PI.f64)) (.f64 (*.f64 (sqrt.f64 (PI.f64)) n) (/.f64 #s(literal 2 binary64) k)))))
▶	28.7%	#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt.f64 (.f64 n (.f64 (PI.f64) (/.f64 #s(literal 2 binary64) k)))))

Compiler

Compiled 2 561 to 2 050 computations (20% saved)

simplify48.0ms (0.5%)

Memory

-2.4MiB live, 36.6MiB allocated

Algorithm

1×	egg-herbie

Localize:

Found 20 expressions of interest:

New	Metric	Score
cost-diff	0	(sqrt.f64 (*.f64 (PI.f64) #s(literal 2 binary64)))
cost-diff	0	(.f64 (sqrt.f64 (.f64 (PI.f64) #s(literal 2 binary64))) (*.f64 (neg.f64 (sqrt.f64 n)) (/.f64 #s(literal -1 binary64) (sqrt.f64 k))))
cost-diff	0	#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (.f64 (sqrt.f64 (.f64 (PI.f64) #s(literal 2 binary64))) (*.f64 (neg.f64 (sqrt.f64 n)) (/.f64 #s(literal -1 binary64) (sqrt.f64 k)))))
cost-diff	3	(*.f64 (neg.f64 (sqrt.f64 n)) (/.f64 #s(literal -1 binary64) (sqrt.f64 k)))
cost-diff	0	#s(approx (sqrt (/ (* (PI) 2) (* (pow (* (* (PI) 2) n) k) k))) (*.f64 (sqrt.f64 (/.f64 (PI.f64) k)) (sqrt.f64 #s(literal 2 binary64))))
cost-diff	0	(sqrt.f64 n)
cost-diff	0	(.f64 (sqrt.f64 n) #s(approx (sqrt (/ ( (PI) 2) (* (pow (* (* (PI) 2) n) k) k))) (*.f64 (sqrt.f64 (/.f64 (PI.f64) k)) (sqrt.f64 #s(literal 2 binary64)))))
cost-diff	0	#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (.f64 (sqrt.f64 n) #s(approx (sqrt (/ ( (PI) 2) (* (pow (* (* (PI) 2) n) k) k))) (*.f64 (sqrt.f64 (/.f64 (PI.f64) k)) (sqrt.f64 #s(literal 2 binary64))))))
cost-diff	0	(*.f64 (PI.f64) #s(literal 2 binary64))
cost-diff	0	(sqrt.f64 (*.f64 (PI.f64) #s(literal 2 binary64)))
cost-diff	0	(.f64 (sqrt.f64 (.f64 (PI.f64) #s(literal 2 binary64))) (sqrt.f64 (/.f64 n k)))
cost-diff	0	#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))))
cost-diff	0	(*.f64 (PI.f64) (/.f64 #s(literal 2 binary64) k))
cost-diff	0	(.f64 n (.f64 (PI.f64) (/.f64 #s(literal 2 binary64) k)))
cost-diff	0	(sqrt.f64 (.f64 n (.f64 (PI.f64) (/.f64 #s(literal 2 binary64) k))))
cost-diff	0	#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt.f64 (.f64 n (.f64 (PI.f64) (/.f64 #s(literal 2 binary64) k)))))
cost-diff	0	(.f64 (.f64 (PI.f64) #s(literal 2 binary64)) n)
cost-diff	0	(pow.f64 (.f64 (.f64 (PI.f64) #s(literal 2 binary64)) n) (fma.f64 k #s(literal -1/2 binary64) #s(literal 1/2 binary64)))
cost-diff	0	(/.f64 (pow.f64 (.f64 (.f64 (PI.f64) #s(literal 2 binary64)) n) (fma.f64 k #s(literal -1/2 binary64) #s(literal 1/2 binary64))) (sqrt.f64 k))
cost-diff	0	#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (/.f64 (pow.f64 (.f64 (.f64 (PI.f64) #s(literal 2 binary64)) n) (fma.f64 k #s(literal -1/2 binary64) #s(literal 1/2 binary64))) (sqrt.f64 k)))

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	53	363
0	81	363
1	124	350
2	198	344
3	336	339
4	597	339
5	923	339
6	1454	339
7	1618	339
8	1702	339
9	1808	339
10	1817	339
11	1820	339
12	1821	339
0	1821	339

Stop Event

1×	iter limit
1×	saturated
1×	iter limit

Calls

Call 1

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

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

localize130.0ms (1.4%)

Memory

20.7MiB live, 183.3MiB allocated

Localize:

Found 20 expressions of interest:

New	Metric	Score
accuracy	0.3639450195368841	(.f64 (sqrt.f64 (.f64 (PI.f64) #s(literal 2 binary64))) (*.f64 (neg.f64 (sqrt.f64 n)) (/.f64 #s(literal -1 binary64) (sqrt.f64 k))))
accuracy	0.73046875	(sqrt.f64 (*.f64 (PI.f64) #s(literal 2 binary64)))
accuracy	16.71053066552266	(PI.f64)
accuracy	20.442540493736956	#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (.f64 (sqrt.f64 (.f64 (PI.f64) #s(literal 2 binary64))) (*.f64 (neg.f64 (sqrt.f64 n)) (/.f64 #s(literal -1 binary64) (sqrt.f64 k)))))
accuracy	0.203125	(/.f64 (PI.f64) k)
accuracy	0.3450775390737681	(*.f64 (sqrt.f64 (/.f64 (PI.f64) k)) (sqrt.f64 #s(literal 2 binary64)))
accuracy	16.71053066552266	(PI.f64)
accuracy	20.299868177063235	#s(approx (sqrt (/ (* (PI) 2) (* (pow (* (* (PI) 2) n) k) k))) (*.f64 (sqrt.f64 (/.f64 (PI.f64) k)) (sqrt.f64 #s(literal 2 binary64))))
accuracy	0.73046875	(sqrt.f64 (*.f64 (PI.f64) #s(literal 2 binary64)))
accuracy	8.333765336521225	(sqrt.f64 (/.f64 n k))
accuracy	16.71053066552266	(PI.f64)
accuracy	20.442540493736956	#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))))
accuracy	0.25228500976844204	(*.f64 (PI.f64) (/.f64 #s(literal 2 binary64) k))
accuracy	8.336756415667018	(sqrt.f64 (.f64 n (.f64 (PI.f64) (/.f64 #s(literal 2 binary64) k))))
accuracy	16.71053066552266	(PI.f64)
accuracy	20.442540493736956	#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt.f64 (.f64 n (.f64 (PI.f64) (/.f64 #s(literal 2 binary64) k)))))
accuracy	0.1171875	(/.f64 (pow.f64 (.f64 (.f64 (PI.f64) #s(literal 2 binary64)) n) (fma.f64 k #s(literal -1/2 binary64) #s(literal 1/2 binary64))) (sqrt.f64 k))
accuracy	0.1526850729236806	(pow.f64 (.f64 (.f64 (PI.f64) #s(literal 2 binary64)) n) (fma.f64 k #s(literal -1/2 binary64) #s(literal 1/2 binary64)))
accuracy	0.15625	(.f64 (.f64 (PI.f64) #s(literal 2 binary64)) n)
accuracy	16.71053066552266	(PI.f64)

Samples

62.0ms	187×	0	valid
38.0ms	69×	0	exit

Compiler

Compiled 279 to 46 computations (83.5% saved)

Precisions

Click to see histograms. Total time spent on operations: 67.0ms

ival-mult: 22.0ms (33% of total)

ival-div: 13.0ms (19.5% of total)

ival-sqrt: 13.0ms (19.5% of total)

ival-pow: 13.0ms (19.5% of total)

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

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

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

exact: 1.0ms (1.5% of total)

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

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

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

series76.0ms (0.8%)

Memory

-4.7MiB live, 77.8MiB allocated

Counts

23 → 53

Calls

Call 1

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

Calls

6 calls:

Time	Variable		Point	Expression
12.0ms	n	@	-inf	((* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (/ (pow (* (* (PI) 2) n) (+ (* k -1/2) 1/2)) (sqrt k)) (pow (* (* (PI) 2) n) (+ (* k -1/2) 1/2)) (* (* (PI) 2) n) (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt (* n (* (PI) (/ 2 k)))) (* n (* (PI) (/ 2 k))) (* (PI) (/ 2 k)) (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (* (sqrt (* (PI) 2)) (sqrt (/ n k))) (sqrt (* (PI) 2)) (* (PI) 2) (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (* (sqrt n) (sqrt (/ (* (PI) 2) (* (pow (* (* (PI) 2) n) k) k)))) (sqrt n) (sqrt (/ (* (PI) 2) (* (pow (* (* (PI) 2) n) k) k))) (* (neg (sqrt n)) (/ -1 (sqrt k))) (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (* (sqrt (* (PI) 2)) (* (neg (sqrt n)) (/ -1 (sqrt k)))) (PI) (sqrt (/ n k)) (* (sqrt (/ (PI) k)) (sqrt 2)) (/ (PI) k))
11.0ms	n	@	inf	((* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (/ (pow (* (* (PI) 2) n) (+ (* k -1/2) 1/2)) (sqrt k)) (pow (* (* (PI) 2) n) (+ (* k -1/2) 1/2)) (* (* (PI) 2) n) (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt (* n (* (PI) (/ 2 k)))) (* n (* (PI) (/ 2 k))) (* (PI) (/ 2 k)) (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (* (sqrt (* (PI) 2)) (sqrt (/ n k))) (sqrt (* (PI) 2)) (* (PI) 2) (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (* (sqrt n) (sqrt (/ (* (PI) 2) (* (pow (* (* (PI) 2) n) k) k)))) (sqrt n) (sqrt (/ (* (PI) 2) (* (pow (* (* (PI) 2) n) k) k))) (* (neg (sqrt n)) (/ -1 (sqrt k))) (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (* (sqrt (* (PI) 2)) (* (neg (sqrt n)) (/ -1 (sqrt k)))) (PI) (sqrt (/ n k)) (* (sqrt (/ (PI) k)) (sqrt 2)) (/ (PI) k))
10.0ms	n	@	0	((* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (/ (pow (* (* (PI) 2) n) (+ (* k -1/2) 1/2)) (sqrt k)) (pow (* (* (PI) 2) n) (+ (* k -1/2) 1/2)) (* (* (PI) 2) n) (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt (* n (* (PI) (/ 2 k)))) (* n (* (PI) (/ 2 k))) (* (PI) (/ 2 k)) (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (* (sqrt (* (PI) 2)) (sqrt (/ n k))) (sqrt (* (PI) 2)) (* (PI) 2) (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (* (sqrt n) (sqrt (/ (* (PI) 2) (* (pow (* (* (PI) 2) n) k) k)))) (sqrt n) (sqrt (/ (* (PI) 2) (* (pow (* (* (PI) 2) n) k) k))) (* (neg (sqrt n)) (/ -1 (sqrt k))) (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (* (sqrt (* (PI) 2)) (* (neg (sqrt n)) (/ -1 (sqrt k)))) (PI) (sqrt (/ n k)) (* (sqrt (/ (PI) k)) (sqrt 2)) (/ (PI) k))
8.0ms	k	@	0	((* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (/ (pow (* (* (PI) 2) n) (+ (* k -1/2) 1/2)) (sqrt k)) (pow (* (* (PI) 2) n) (+ (* k -1/2) 1/2)) (* (* (PI) 2) n) (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt (* n (* (PI) (/ 2 k)))) (* n (* (PI) (/ 2 k))) (* (PI) (/ 2 k)) (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (* (sqrt (* (PI) 2)) (sqrt (/ n k))) (sqrt (* (PI) 2)) (* (PI) 2) (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (* (sqrt n) (sqrt (/ (* (PI) 2) (* (pow (* (* (PI) 2) n) k) k)))) (sqrt n) (sqrt (/ (* (PI) 2) (* (pow (* (* (PI) 2) n) k) k))) (* (neg (sqrt n)) (/ -1 (sqrt k))) (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (* (sqrt (* (PI) 2)) (* (neg (sqrt n)) (/ -1 (sqrt k)))) (PI) (sqrt (/ n k)) (* (sqrt (/ (PI) k)) (sqrt 2)) (/ (PI) k))
6.0ms	k	@	-inf	((* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (/ (pow (* (* (PI) 2) n) (+ (* k -1/2) 1/2)) (sqrt k)) (pow (* (* (PI) 2) n) (+ (* k -1/2) 1/2)) (* (* (PI) 2) n) (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt (* n (* (PI) (/ 2 k)))) (* n (* (PI) (/ 2 k))) (* (PI) (/ 2 k)) (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (* (sqrt (* (PI) 2)) (sqrt (/ n k))) (sqrt (* (PI) 2)) (* (PI) 2) (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (* (sqrt n) (sqrt (/ (* (PI) 2) (* (pow (* (* (PI) 2) n) k) k)))) (sqrt n) (sqrt (/ (* (PI) 2) (* (pow (* (* (PI) 2) n) k) k))) (* (neg (sqrt n)) (/ -1 (sqrt k))) (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (* (sqrt (* (PI) 2)) (* (neg (sqrt n)) (/ -1 (sqrt k)))) (PI) (sqrt (/ n k)) (* (sqrt (/ (PI) k)) (sqrt 2)) (/ (PI) k))

simplify174.0ms (1.9%)

Memory

9.1MiB live, 160.2MiB allocated

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	282	1295
1	845	1221
2	3054	1153
3	7753	1153
0	8213	1126

Stop Event

1×	iter limit
1×	node limit

Counts

53 → 53

Calls

Call 1

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

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

rewrite118.0ms (1.3%)

Memory

2.5MiB live, 163.6MiB allocated

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	53	302
0	81	282
1	260	272
2	1453	267
0	8636	267

Stop Event

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

Counts

23 → 596

Calls

Call 1

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

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

eval116.0ms (1.2%)

Memory: 0.8MiB live, 161.9MiB allocated
Compiler: Compiled 26 728 to 3 111 computations (88.4% saved)

prune88.0ms (0.9%)

Memory

-25.0MiB live, 134.0MiB allocated

Pruning

55 alts after pruning (43 fresh and 12 done)

	Pruned	Kept	Total
New	726	15	741
Fresh	10	28	38
Picked	0	5	5
Done	0	7	7
Total	736	55	791

Accuracy

100.0%

Counts

791 → 55

Alt Table

Click to see full alt table

Status	Accuracy	Program
✓	99.6%	(.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))))
	41.4%	(.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) #s(approx (pow ( (* 2 (PI)) n) (/ (- 1 k) 2)) (.f64 (.f64 (sqrt.f64 (PI.f64)) (sqrt.f64 n)) (sqrt.f64 #s(literal 2 binary64)))))
	41.5%	(.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) #s(approx (pow ( (* 2 (PI)) n) (/ (- 1 k) 2)) (sqrt.f64 (.f64 (.f64 (PI.f64) #s(literal 2 binary64)) n))))
	41.4%	(.f64 #s(approx (/ 1 (sqrt k)) (sqrt.f64 (/.f64 #s(literal 1 binary64) 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%	#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (/.f64 (pow.f64 (.f64 (.f64 (PI.f64) #s(literal 2 binary64)) n) (fma.f64 k #s(literal -1/2 binary64) #s(literal 1/2 binary64))) (sqrt.f64 k)))
	41.4%	#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (/.f64 (.f64 (sqrt.f64 (.f64 (PI.f64) n)) (sqrt.f64 #s(literal 2 binary64))) (sqrt.f64 k)))
	41.3%	#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (/.f64 (.f64 (sqrt.f64 (.f64 (PI.f64) #s(literal 2 binary64))) (sqrt.f64 n)) (sqrt.f64 k)))
	41.4%	#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (/.f64 (.f64 (sqrt.f64 (.f64 n #s(literal 2 binary64))) (sqrt.f64 (PI.f64))) (sqrt.f64 k)))
	35.8%	#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (/.f64 (sqrt.f64 (.f64 (.f64 (PI.f64) #s(literal 2 binary64)) n)) (pow.f64 (*.f64 k k) #s(literal 1/4 binary64))))
✓	41.5%	#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)))
	41.4%	#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (/.f64 (sqrt.f64 (.f64 (PI.f64) n)) (sqrt.f64 (.f64 #s(literal 1/2 binary64) k))))
	29.2%	#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 k n))))
	41.5%	#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (/.f64 (sqrt.f64 (*.f64 n #s(literal 2 binary64))) (sqrt.f64 (/.f64 k (PI.f64)))))
	29.3%	#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)))))
	29.3%	#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (/.f64 #s(literal 1 binary64) (sqrt.f64 (/.f64 k (.f64 (.f64 (PI.f64) #s(literal 2 binary64)) n)))))
✓	99.6%	#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))))
	41.4%	#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (.f64 (/.f64 (neg.f64 n) (neg.f64 (sqrt.f64 n))) #s(approx (sqrt (/ ( (PI) 2) (* (pow (* (* (PI) 2) n) k) k))) (*.f64 (sqrt.f64 (/.f64 (PI.f64) k)) (sqrt.f64 #s(literal 2 binary64))))))
	41.4%	#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (.f64 (.f64 (pow.f64 k #s(literal -1/2 binary64)) (sqrt.f64 #s(literal 2 binary64))) (sqrt.f64 (*.f64 (PI.f64) n))))
	41.3%	#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (.f64 (.f64 (sqrt.f64 (PI.f64)) (sqrt.f64 #s(literal 2 binary64))) (*.f64 (neg.f64 (sqrt.f64 n)) (/.f64 #s(literal -1 binary64) (sqrt.f64 k)))))
	28.6%	#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (.f64 (.f64 (sqrt.f64 (PI.f64)) (sqrt.f64 #s(literal 2 binary64))) (sqrt.f64 (/.f64 n k))))
	41.5%	#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)))))
	41.5%	#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (.f64 (sqrt.f64 (.f64 (/.f64 (PI.f64) k) #s(literal 2 binary64))) (sqrt.f64 n)))
	99.3%	#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (.f64 (sqrt.f64 (.f64 (PI.f64) n)) (sqrt.f64 (/.f64 #s(literal 2 binary64) (.f64 (pow.f64 (.f64 (*.f64 (PI.f64) #s(literal 2 binary64)) n) k) k)))))
	41.3%	#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (.f64 (sqrt.f64 (.f64 (PI.f64) #s(literal 2 binary64))) (/.f64 (sqrt.f64 n) (sqrt.f64 k))))
	41.3%	#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (.f64 (sqrt.f64 (.f64 (PI.f64) #s(literal 2 binary64))) (/.f64 n (*.f64 (sqrt.f64 k) (sqrt.f64 n)))))
	29.2%	#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (.f64 (sqrt.f64 (.f64 (PI.f64) #s(literal 2 binary64))) (/.f64 #s(literal 1 binary64) (sqrt.f64 (/.f64 k n)))))
	41.2%	#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (.f64 (sqrt.f64 (.f64 (PI.f64) #s(literal 2 binary64))) (*.f64 (neg.f64 (/.f64 (neg.f64 n) (neg.f64 (sqrt.f64 n)))) (/.f64 #s(literal -1 binary64) (sqrt.f64 k)))))
✓	41.3%	#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (.f64 (sqrt.f64 (.f64 (PI.f64) #s(literal 2 binary64))) (*.f64 (neg.f64 (sqrt.f64 n)) (/.f64 #s(literal -1 binary64) (sqrt.f64 k)))))
✓	28.5%	#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))))
	41.3%	#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (.f64 (sqrt.f64 (PI.f64)) (.f64 (pow.f64 k #s(literal -1/2 binary64)) (sqrt.f64 (*.f64 n #s(literal 2 binary64))))))
	28.5%	#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (.f64 (sqrt.f64 (PI.f64)) (sqrt.f64 (.f64 (/.f64 n k) #s(literal 2 binary64)))))
✓	99.8%	#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (.f64 (sqrt.f64 n) (sqrt.f64 (/.f64 (.f64 (PI.f64) #s(literal 2 binary64)) (.f64 (pow.f64 (.f64 (*.f64 (PI.f64) #s(literal 2 binary64)) n) k) k)))))
	41.4%	#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (.f64 (sqrt.f64 n) #s(approx (sqrt (/ ( (PI) 2) (* (pow (* (* (PI) 2) n) k) k))) (/.f64 (sqrt.f64 (PI.f64)) (sqrt.f64 (*.f64 #s(literal 1/2 binary64) k))))))
	41.4%	#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (.f64 (sqrt.f64 n) #s(approx (sqrt (/ ( (PI) 2) (* (pow (* (* (PI) 2) n) k) k))) (/.f64 (sqrt.f64 #s(literal 2 binary64)) (sqrt.f64 (/.f64 k (PI.f64)))))))
✓	41.5%	#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (.f64 (sqrt.f64 n) #s(approx (sqrt (/ ( (PI) 2) (* (pow (* (* (PI) 2) n) k) k))) (*.f64 (sqrt.f64 (/.f64 (PI.f64) k)) (sqrt.f64 #s(literal 2 binary64))))))
	41.3%	#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (.f64 (sqrt.f64 n) #s(approx (sqrt (/ ( (PI) 2) (* (pow (* (* (PI) 2) n) k) k))) (*.f64 (sqrt.f64 (/.f64 #s(literal 2 binary64) k)) (sqrt.f64 (PI.f64))))))
	41.5%	#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (.f64 (sqrt.f64 #s(literal 2 binary64)) (/.f64 (.f64 (sqrt.f64 n) (neg.f64 (sqrt.f64 (PI.f64)))) (neg.f64 (sqrt.f64 k)))))
	41.4%	#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))))
	41.4%	#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 k (PI.f64))))))
✓	41.4%	#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)))))
✓	28.6%	#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))))
	28.6%	#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (.f64 (sqrt.f64 #s(literal 2 binary64)) (sqrt.f64 (.f64 (*.f64 (neg.f64 (PI.f64)) n) (/.f64 #s(literal -1 binary64) k)))))
	28.6%	#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (.f64 (sqrt.f64 #s(literal 2 binary64)) (sqrt.f64 (.f64 n (/.f64 (PI.f64) k)))))
	41.3%	#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (.f64 (neg.f64 (sqrt.f64 n)) (.f64 (/.f64 #s(literal -1 binary64) (sqrt.f64 k)) (sqrt.f64 (*.f64 (PI.f64) #s(literal 2 binary64))))))
	86.6%	#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt.f64 (/.f64 (.f64 (.f64 (PI.f64) #s(literal 2 binary64)) n) (.f64 (pow.f64 (.f64 (*.f64 (PI.f64) #s(literal 2 binary64)) n) k) k))))
	28.7%	#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))))
	28.7%	#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)))))
✓	28.7%	#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))))
	28.7%	#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))))
	28.7%	#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))))
	87.0%	#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt.f64 (.f64 (.f64 n (/.f64 #s(literal 2 binary64) (pow.f64 (.f64 (.f64 (PI.f64) #s(literal 2 binary64)) n) k))) (/.f64 (PI.f64) k))))
	28.7%	#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt.f64 (.f64 (.f64 n (/.f64 #s(literal 2 binary64) k)) (PI.f64))))
	28.6%	#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt.f64 (.f64 (sqrt.f64 (PI.f64)) (.f64 (*.f64 (sqrt.f64 (PI.f64)) n) (/.f64 #s(literal 2 binary64) k)))))
	28.7%	#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt.f64 (*.f64 n (/.f64 #s(literal 2 binary64) (/.f64 k (PI.f64))))))
✓	28.7%	#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt.f64 (.f64 n (.f64 (PI.f64) (/.f64 #s(literal 2 binary64) k)))))

Compiler

Compiled 4 093 to 1 655 computations (59.6% saved)

regimes106.0ms (1.1%)

Memory

16.1MiB live, 131.8MiB allocated

Counts

92 → 1

Calls

Call 1

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

Outputs

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

Calls

4 calls:

27.0ms	(.f64 (.f64 #s(literal 2 binary64) (PI.f64)) n)
27.0ms	k
26.0ms	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
99.8%	1	`k`
99.8%	1	`n`
99.8%	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))))`
99.8%	1	`(.f64 (.f64 #s(literal 2 binary64) (PI.f64)) n)`

Compiler

Compiled 23 to 23 computations (0% saved)

regimes92.0ms (1%)

Memory

19.3MiB live, 131.9MiB allocated

Counts

77 → 1

Calls

Call 1

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

Outputs

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

Calls

4 calls:

24.0ms	n
22.0ms	(.f64 (.f64 #s(literal 2 binary64) (PI.f64)) n)
21.0ms	(.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	k

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)

regimes93.0ms (1%)

Memory

-28.7MiB live, 89.9MiB allocated

Counts

65 → 2

Calls

Call 1

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

Outputs

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

#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)))

Calls

4 calls:

26.0ms	k
24.0ms	(.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	(.f64 (.f64 #s(literal 2 binary64) (PI.f64)) n)
18.0ms	n

Results

Accuracy	Segments	Branch
56.2%	2	`k`
44.6%	2	`n`
56.2%	2	`(.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) (pow.f64 (.f64 (*.f64 #s(literal 2 binary64) (PI.f64)) n) (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 2 binary64))))`
44.6%	2	`(.f64 (.f64 #s(literal 2 binary64) (PI.f64)) n)`

Compiler

Compiled 23 to 23 computations (0% saved)

regimes93.0ms (1%)

Memory

-7.9MiB live, 118.0MiB allocated

Counts

63 → 1

Calls

Call 1

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

Outputs
#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)))

Calls

4 calls:

34.0ms	(.f64 (.f64 #s(literal 2 binary64) (PI.f64)) n)
21.0ms	k
17.0ms	n
15.0ms	(.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) (pow.f64 (.f64 (*.f64 #s(literal 2 binary64) (PI.f64)) n) (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 2 binary64))))

Results

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

Compiler

Compiled 23 to 23 computations (0% saved)

regimes26.0ms (0.3%)

Memory

32.8MiB live, 32.8MiB allocated

Counts

20 → 1

Calls

Call 1

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

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

Calls

4 calls:

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

Results

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

Compiler

Compiled 23 to 23 computations (0% saved)

regimes21.0ms (0.2%)

Memory

-16.4MiB live, 22.1MiB allocated

Counts

13 → 1

Calls

Call 1

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

Calls

4 calls:

7.0ms	k
4.0ms	(.f64 (.f64 #s(literal 2 binary64) (PI.f64)) n)
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
28.7%	1	`n`
28.7%	1	`(.f64 (.f64 #s(literal 2 binary64) (PI.f64)) n)`
28.7%	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))))`
28.7%	1	`k`

Compiler

Compiled 23 to 23 computations (0% saved)

regimes5.0ms (0.1%)

Memory

9.1MiB live, 9.1MiB allocated

Accuracy

Total -0.0b remaining (-0%)

Threshold costs -0b (-0%)

Counts

1 → 1

Calls

Call 1

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

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

Calls

4 calls:

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	(.f64 (.f64 #s(literal 2 binary64) (PI.f64)) n)
1.0ms	n
1.0ms	k

Results

Accuracy	Segments	Branch
28.7%	1	`k`
28.7%	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))))`
28.7%	1	`n`
28.7%	1	`(.f64 (.f64 #s(literal 2 binary64) (PI.f64)) n)`

Compiler

Compiled 23 to 23 computations (0% saved)

bsearch1.0ms (0%)

Memory

0.7MiB live, 0.7MiB allocated

Algorithm

1×	left-value

Steps

Time	Left	Right
0.0ms	2.0933783783267708e-107	3.6135912532294255e-104

Compiler

Compiled 19 to 18 computations (5.3% saved)

simplify69.0ms (0.7%)

Memory

-15.8MiB live, 22.8MiB allocated

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	61	240
1	79	224
2	98	224
3	123	224
4	150	224
5	179	224
6	252	224
7	541	224
8	5004	224

Stop Event

1×	node limit

Calls

Call 1

Inputs
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (.f64 (sqrt.f64 n) (sqrt.f64 (/.f64 (.f64 (PI.f64) #s(literal 2 binary64)) (.f64 (pow.f64 (.f64 (*.f64 (PI.f64) #s(literal 2 binary64)) n) k) k)))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (/.f64 (pow.f64 (.f64 (.f64 (PI.f64) #s(literal 2 binary64)) n) (fma.f64 #s(literal -1/2 binary64) k #s(literal 1/2 binary64))) (sqrt.f64 k)))
(if (<=.f64 (.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)))) #s(literal 3305279843951243/82631996098781074868989413504096379978550585370535152410581099409300723904538918228148651304964410605948901503127919788032 binary64)) #s(approx ( (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (/.f64 (sqrt.f64 (.f64 (.f64 (PI.f64) #s(literal 2 binary64)) n)) (pow.f64 (.f64 k k) #s(literal 1/4 binary64)))) #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))))
#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)))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (.f64 (sqrt.f64 n) (sqrt.f64 (/.f64 (.f64 (PI.f64) #s(literal 2 binary64)) k))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt.f64 (.f64 (.f64 n (/.f64 #s(literal 2 binary64) k)) (PI.f64))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt.f64 (.f64 n (.f64 (PI.f64) (/.f64 #s(literal 2 binary64) k)))))

Outputs
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (.f64 (sqrt.f64 n) (sqrt.f64 (/.f64 (.f64 (PI.f64) #s(literal 2 binary64)) (.f64 (pow.f64 (.f64 (*.f64 (PI.f64) #s(literal 2 binary64)) n) k) k)))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (/.f64 (pow.f64 (.f64 (.f64 (PI.f64) #s(literal 2 binary64)) n) (fma.f64 #s(literal -1/2 binary64) k #s(literal 1/2 binary64))) (sqrt.f64 k)))
(if (<=.f64 (.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)))) #s(literal 3305279843951243/82631996098781074868989413504096379978550585370535152410581099409300723904538918228148651304964410605948901503127919788032 binary64)) #s(approx ( (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (/.f64 (sqrt.f64 (.f64 (.f64 (PI.f64) #s(literal 2 binary64)) n)) (pow.f64 (.f64 k k) #s(literal 1/4 binary64)))) #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))))
(if (<=.f64 (.f64 (pow.f64 (sqrt.f64 k) #s(literal -1 binary64)) (pow.f64 (.f64 (.f64 #s(literal 2 binary64) (PI.f64)) n) (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 2 binary64)))) #s(literal 3305279843951243/82631996098781074868989413504096379978550585370535152410581099409300723904538918228148651304964410605948901503127919788032 binary64)) #s(approx ( (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (/.f64 (sqrt.f64 (.f64 (.f64 (PI.f64) #s(literal 2 binary64)) n)) (pow.f64 (.f64 k k) #s(literal 1/4 binary64)))) #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))))
#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)))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (.f64 (sqrt.f64 n) (sqrt.f64 (/.f64 (.f64 (PI.f64) #s(literal 2 binary64)) k))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt.f64 (.f64 (.f64 n (/.f64 #s(literal 2 binary64) k)) (PI.f64))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt.f64 (.f64 n (.f64 (PI.f64) (/.f64 #s(literal 2 binary64) k)))))

soundness607.0ms (6.5%)

Memory

39.9MiB live, 504.4MiB allocated

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	43	278
0	68	266
1	215	255
2	1119	243
0	8347	243
0	52	264
0	88	254
1	318	239
2	1576	235
0	8268	235
0	128	517
1	345	504
2	1022	460
3	3355	433
4	5591	421
0	8473	406
0	53	302
0	81	282
1	260	272
2	1453	267
0	8636	267

Stop Event

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

Compiler

Compiled 583 to 355 computations (39.1% saved)

preprocess89.0ms (1%)

Memory: -41.2MiB live, 92.5MiB allocated
Compiler: Compiled 512 to 154 computations (69.9% 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	43	344
0	68	344
1	107	334
2	156	334
3	205	334
4	228	334
5	243	334
6	264	334
7	295	334
8	306	334
9	309	334
0	309	328

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	43	344
0	68	344
1	107	334
2	156	334
3	205	334
4	228	334
5	243	334
6	264	334
7	295	334
8	306	334
9	309	334
0	309	328

start0.0ms (0%)

analyze174.0ms (1.9%)

sample3.8s (40.4%)

explain147.0ms (1.6%)

preprocess49.0ms (0.5%)

eval0.0ms (0%)

prune0.0ms (0%)

simplify6.0ms (0.1%)

localize39.0ms (0.4%)

series72.0ms (0.8%)

simplify145.0ms (1.6%)

rewrite293.0ms (3.1%)

eval121.0ms (1.3%)

prune50.0ms (0.5%)

simplify275.0ms (2.9%)

localize289.0ms (3.1%)

series202.0ms (2.2%)

simplify261.0ms (2.8%)

rewrite280.0ms (3%)

eval232.0ms (2.5%)

prune34.0ms (0.4%)

simplify15.0ms (0.2%)

localize127.0ms (1.4%)

series62.0ms (0.7%)

simplify180.0ms (1.9%)

rewrite164.0ms (1.8%)

eval293.0ms (3.1%)

prune99.0ms (1.1%)

simplify48.0ms (0.5%)

localize130.0ms (1.4%)

series76.0ms (0.8%)

simplify174.0ms (1.9%)

rewrite118.0ms (1.3%)

eval116.0ms (1.2%)

prune88.0ms (0.9%)

regimes106.0ms (1.1%)

regimes92.0ms (1%)

regimes93.0ms (1%)

regimes93.0ms (1%)

regimes26.0ms (0.3%)

regimes21.0ms (0.2%)

regimes5.0ms (0.1%)

bsearch1.0ms (0%)

simplify69.0ms (0.7%)

soundness607.0ms (6.5%)

preprocess89.0ms (1%)

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	43	344
0	68	344
1	107	334
2	156	334
3	205	334
4	228	334
5	243	334
6	264	334
7	295	334
8	306	334
9	309	334
0	309	328