Metrics for Migdal et al, Equation (51)

analyze116.0ms (1%)

Memory

49.8MiB live, 273.8MiB 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)

sample3.2s (28.4%)

Memory

-159.7MiB live, 6 132.7MiB allocated

Samples

968.0ms	8 256×	0	valid
782.0ms	3 509×	1	invalid
310.0ms	1 915×	1	exit
149.0ms	473×	2	invalid
36.0ms	458×	0	invalid
33.0ms	256×	0	exit
0.0ms	1×	2	exit

Precisions

Click to see histograms. Total time spent on operations: 1.7s

ival-pow: 515.0ms (29.9% of total)

ival-mult: 422.0ms (24.5% of total)

ival-div: 307.0ms (17.9% of total)

ival-sqrt: 138.0ms (8% of total)

ival-sub: 130.0ms (7.6% of total)

adjust: 98.0ms (5.7% of total)

ival-pi: 68.0ms (4% of total)

exact: 22.0ms (1.3% of total)

ival-true: 13.0ms (0.8% of total)

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

Bogosity

preprocess53.0ms (0.5%)

Memory

21.2MiB live, 57.7MiB allocated

Algorithm

2×	egg-herbie

Rules

260×	`associate-r`
160×	`sub-neg`
158×	`associate-l`
138×	`distribute-lft-neg-in`
124×	`distribute-lft-in`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	33	104
1	87	88
2	202	88
3	394	88
4	621	88
5	890	88
6	1059	88
7	1264	88
8	1323	88
9	1347	88
10	1365	88
11	1369	88
12	1369	88
0	13	16
1	28	14
2	45	14
3	66	14
4	84	14
5	99	14
6	120	14
7	147	14
8	156	14
9	159	14
0	159	13

Stop Event

1×	iter limit
1×	saturated
1×	saturated

Calls

Call 1

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

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

Call 2

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

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

explain152.0ms (1.3%)

Memory

-8.9MiB live, 265.4MiB allocated

FPErrors

Click to see full error table

Ground Truth	Overpredictions	Example	Example	Subexpression
4	86	(5.795000170166278e-290 1.4317373180146579e+97)	-	`(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	90	28

Confusion

	Predicted +	Predicted -
+	3	0
-	87	166

Precision

0.03333333333333333

Recall

1.0

Confusion?

	Predicted +	Predicted Maybe	Predicted -
+	3	0	0
-	87	28	138

Precision?

0.025423728813559324

Recall?

1.0

Freqs

test

number	freq
0	166
1	90

Total Confusion?

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

Precision?

1.0

Recall?

1.0

Samples

59.0ms

512×

valid

Compiler

Compiled 148 to 56 computations (62.2% saved)

Precisions

Click to see histograms. Total time spent on operations: 41.0ms

ival-pow: 13.0ms (31.4% of total)

ival-div: 9.0ms (21.8% of total)

ival-mult: 9.0ms (21.8% of total)

ival-sqrt: 4.0ms (9.7% of total)

ival-sub: 3.0ms (7.3% of total)

ival-pi: 2.0ms (4.8% of total)

exact: 1.0ms (2.4% of total)

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

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

eval0.0ms (0%)

Memory: 0.3MiB live, 0.3MiB allocated
Compiler: Compiled 2 to 2 computations (0% saved)

prune1.0ms (0%)

Memory

1.5MiB live, 1.5MiB allocated

Alt Table

Click to see full alt table

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

Compiler

Compiled 18 to 13 computations (27.8% saved)

simplify8.0ms (0.1%)

Memory

12.4MiB live, 12.4MiB allocated

Algorithm

1×	egg-herbie

Localize:

Found 4 expressions of interest:

New	Metric	Score	Program
✓	cost-diff	0	(sqrt.f64 k)
✓	cost-diff	0	(/.f64 #s(literal 1 binary64) (sqrt.f64 k))
✓	cost-diff	320	(.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) (pow.f64 (.f64 (*.f64 #s(literal 2 binary64) (PI.f64)) n) (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 2 binary64))))
✓	cost-diff	512	(/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 2 binary64))

Rules

64×	`-lowering-.f32`
64×	`-lowering-.f64`
48×	`+-lowering-+.f64`
48×	`+-lowering-+.f32`
36×	`--lowering--.f32`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	13	54
1	28	52
2	45	52
3	66	52
4	84	52
5	99	52
6	120	52
7	147	52
8	156	52
9	159	52
0	159	49

Stop Event

1×	iter limit
1×	saturated

Calls

Call 1

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

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

localize44.0ms (0.4%)

Memory

-6.2MiB live, 70.5MiB allocated

Localize:

Found 4 expressions of interest:

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

Samples

28.0ms

256×

valid

Compiler

Compiled 56 to 15 computations (73.2% saved)

Precisions

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

ival-mult: 5.0ms (25.5% of total)

ival-pow: 5.0ms (25.5% of total)

ival-div: 3.0ms (15.3% of total)

ival-pi: 2.0ms (10.2% of total)

ival-sqrt: 2.0ms (10.2% of total)

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

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

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

exact: 0.0ms (0% of total)

series68.0ms (0.6%)

Memory

30.7MiB live, 107.9MiB allocated

Counts

6 → 96

Calls

Call 1

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

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

Calls

24 calls:

Time	Variable		Point	Expression
31.0ms	n	@	0	(* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2)))
20.0ms	n	@	-inf	(* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2)))
9.0ms	n	@	inf	(* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2)))
1.0ms	k	@	-inf	(* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2)))
1.0ms	k	@	0	(* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2)))

rewrite303.0ms (2.7%)

Memory

3.7MiB live, 470.5MiB allocated

Algorithm

1×	batch-egg-rewrite

Rules

4 378×	`-lowering-.f32`
4 378×	`-lowering-.f64`
3 286×	`pow-lowering-pow.f64`
3 286×	`pow-lowering-pow.f32`
2 442×	`/-lowering-/.f32`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	13	43
1	80	40
2	488	38
3	4450	38
0	8572	37

Stop Event

1×	iter limit
1×	node limit

Counts

6 → 419

Calls

Call 1

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

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

simplify343.0ms (3%)

Memory

18.6MiB live, 564.5MiB allocated

Algorithm

1×	egg-herbie

Rules

9 974×	`accelerator-lowering-fma.f32`
9 974×	`accelerator-lowering-fma.f64`
5 988×	`-lowering-.f32`
5 988×	`-lowering-.f64`
1 688×	`+-lowering-+.f64`

Iterations

Useful iterations: 0 (0.0ms)

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

Stop Event

1×	iter limit
1×	node limit

Counts

96 → 96

Calls

Call 1

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

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

eval66.0ms (0.6%)

Memory: -0.1MiB live, 117.1MiB allocated
Compiler: Compiled 11 286 to 1 530 computations (86.4% saved)

prune110.0ms (1%)

Memory

-26.9MiB live, 134.9MiB allocated

Pruning

15 alts after pruning (15 fresh and 0 done)

	Pruned	Kept	Total
New	500	15	515
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	501	15	516

Accuracy

100.0%

Counts

516 → 15

Alt Table

Click to see full alt table

Status	Accuracy	Program
▶	50.9%	(/.f64 (pow.f64 (.f64 #s(literal 2 binary64) (.f64 (PI.f64) n)) (fma.f64 k #s(literal 1/2 binary64) #s(literal 1/2 binary64))) (sqrt.f64 k))
	98.9%	(/.f64 (.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) (sqrt.f64 (.f64 #s(literal 2 binary64) (.f64 (PI.f64) n)))) (pow.f64 (.f64 #s(literal 2 binary64) (.f64 (PI.f64) n)) (.f64 k #s(literal 1/2 binary64))))
▶	98.9%	(/.f64 (sqrt.f64 (.f64 #s(literal 2 binary64) (.f64 (PI.f64) n))) (.f64 (sqrt.f64 k) (pow.f64 (.f64 #s(literal 2 binary64) (.f64 (PI.f64) n)) (.f64 k #s(literal 1/2 binary64)))))
	99.5%	(/.f64 #s(literal 1 binary64) (.f64 (sqrt.f64 k) (pow.f64 (.f64 #s(literal 2 binary64) (.f64 (PI.f64) n)) (+.f64 #s(literal -1/2 binary64) (.f64 k #s(literal 1/2 binary64))))))
	99.4%	(.f64 (pow.f64 (pow.f64 k #s(literal 1/4 binary64)) #s(literal -2 binary64)) (pow.f64 (.f64 (*.f64 #s(literal 2 binary64) (PI.f64)) n) (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 2 binary64))))
	50.2%	(.f64 (pow.f64 (.f64 #s(literal 2 binary64) (PI.f64)) (fma.f64 k #s(literal 1/2 binary64) #s(literal 1/2 binary64))) (/.f64 (pow.f64 n (fma.f64 k #s(literal 1/2 binary64) #s(literal 1/2 binary64))) (sqrt.f64 k)))
	99.6%	(.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) (pow.f64 (pow.f64 (.f64 #s(literal 2 binary64) (*.f64 (PI.f64) n)) (+.f64 k #s(literal -1 binary64))) #s(literal -1/2 binary64)))
	50.5%	(.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) (pow.f64 (pow.f64 (.f64 #s(literal 2 binary64) (.f64 (PI.f64) n)) (.f64 (+.f64 #s(literal 1 binary64) k) #s(literal 1/8 binary64))) #s(literal 4 binary64)))
▶	99.3%	(.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) (pow.f64 (.f64 (.f64 (.f64 #s(literal 2 binary64) n) (sqrt.f64 (PI.f64))) (sqrt.f64 (PI.f64))) (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 2 binary64))))
	51.8%	(.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) (pow.f64 (.f64 (.f64 #s(literal 2 binary64) (PI.f64)) n) (.f64 #s(literal -1/2 binary64) k)))
	51.4%	(.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) (pow.f64 (.f64 (*.f64 #s(literal 2 binary64) (PI.f64)) n) #s(literal 1/2 binary64)))
	98.9%	(.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) (/.f64 (sqrt.f64 (.f64 #s(literal 2 binary64) (.f64 (PI.f64) n))) (pow.f64 (.f64 #s(literal 2 binary64) (.f64 (PI.f64) n)) (.f64 k #s(literal 1/2 binary64)))))
	51.4%	(.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) (.f64 (sqrt.f64 #s(literal 2 binary64)) (sqrt.f64 (*.f64 n (PI.f64)))))
▶	39.7%	(.f64 (sqrt.f64 (/.f64 (.f64 n (PI.f64)) k)) (sqrt.f64 #s(literal 2 binary64)))
▶	99.6%	(.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) k)) (pow.f64 (.f64 n (*.f64 (PI.f64) #s(literal 2 binary64))) (fma.f64 #s(literal -1/2 binary64) k #s(literal 1/2 binary64))))

Compiler

Compiled 542 to 404 computations (25.5% saved)

simplify14.0ms (0.1%)

Memory

24.7MiB live, 24.7MiB allocated

Algorithm

1×	egg-herbie

Localize:

Found 20 expressions of interest:

New	Metric	Score	Program
✓	cost-diff	0	(/.f64 #s(literal 1 binary64) (sqrt.f64 k))
✓	cost-diff	320	(.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) (pow.f64 (.f64 (.f64 (.f64 #s(literal 2 binary64) n) (sqrt.f64 (PI.f64))) (sqrt.f64 (PI.f64))) (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 2 binary64))))
✓	cost-diff	512	(/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 2 binary64))
✓	cost-diff	1600	(.f64 (.f64 (*.f64 #s(literal 2 binary64) n) (sqrt.f64 (PI.f64))) (sqrt.f64 (PI.f64)))
✓	cost-diff	0	(*.f64 (PI.f64) n)
✓	cost-diff	0	(.f64 #s(literal 2 binary64) (.f64 (PI.f64) n))
✓	cost-diff	0	(sqrt.f64 (.f64 #s(literal 2 binary64) (.f64 (PI.f64) n)))
✓	cost-diff	0	(/.f64 (sqrt.f64 (.f64 #s(literal 2 binary64) (.f64 (PI.f64) n))) (.f64 (sqrt.f64 k) (pow.f64 (.f64 #s(literal 2 binary64) (.f64 (PI.f64) n)) (.f64 k #s(literal 1/2 binary64)))))
✓	cost-diff	0	(*.f64 (PI.f64) n)
✓	cost-diff	0	(.f64 #s(literal 2 binary64) (.f64 (PI.f64) n))
✓	cost-diff	0	(pow.f64 (.f64 #s(literal 2 binary64) (.f64 (PI.f64) n)) (fma.f64 k #s(literal 1/2 binary64) #s(literal 1/2 binary64)))
✓	cost-diff	0	(/.f64 (pow.f64 (.f64 #s(literal 2 binary64) (.f64 (PI.f64) n)) (fma.f64 k #s(literal 1/2 binary64) #s(literal 1/2 binary64))) (sqrt.f64 k))
✓	cost-diff	0	(*.f64 n (PI.f64))
✓	cost-diff	0	(/.f64 (*.f64 n (PI.f64)) k)
✓	cost-diff	0	(sqrt.f64 (/.f64 (*.f64 n (PI.f64)) k))
✓	cost-diff	0	(.f64 (sqrt.f64 (/.f64 (.f64 n (PI.f64)) k)) (sqrt.f64 #s(literal 2 binary64)))
✓	cost-diff	0	(pow.f64 (.f64 n (.f64 (PI.f64) #s(literal 2 binary64))) (fma.f64 #s(literal -1/2 binary64) k #s(literal 1/2 binary64)))
✓	cost-diff	0	(/.f64 #s(literal 1 binary64) k)
✓	cost-diff	0	(sqrt.f64 (/.f64 #s(literal 1 binary64) k))
✓	cost-diff	0	(.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) k)) (pow.f64 (.f64 n (*.f64 (PI.f64) #s(literal 2 binary64))) (fma.f64 #s(literal -1/2 binary64) k #s(literal 1/2 binary64))))

Rules

158×	`-lowering-.f32`
158×	`-lowering-.f64`
68×	`+-lowering-+.f64`
68×	`+-lowering-+.f32`
58×	`*-commutative`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	40	258
1	76	252
2	106	252
3	144	252
4	170	252
5	194	252
6	215	252
7	248	252
8	260	252
9	264	252
0	264	243

Stop Event

1×	iter limit
1×	saturated

Calls

Call 1

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

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

localize159.0ms (1.4%)

Memory

-29.5MiB live, 240.0MiB allocated

Localize:

Found 20 expressions of interest:

New	Metric	Score	Program
✓	accuracy	99.7%	(.f64 (.f64 #s(literal 2 binary64) n) (sqrt.f64 (PI.f64)))
✓	accuracy	99.5%	(.f64 (.f64 (*.f64 #s(literal 2 binary64) n) (sqrt.f64 (PI.f64))) (sqrt.f64 (PI.f64)))
✓	accuracy	98.8%	(sqrt.f64 (PI.f64))
✓	accuracy	76.9%	(PI.f64)
✓	accuracy	99.7%	(/.f64 (sqrt.f64 (.f64 #s(literal 2 binary64) (.f64 (PI.f64) n))) (.f64 (sqrt.f64 k) (pow.f64 (.f64 #s(literal 2 binary64) (.f64 (PI.f64) n)) (.f64 k #s(literal 1/2 binary64)))))
✓	accuracy	99.7%	(*.f64 (PI.f64) n)
✓	accuracy	99.1%	(sqrt.f64 (.f64 #s(literal 2 binary64) (.f64 (PI.f64) n)))
✓	accuracy	76.9%	(PI.f64)
✓	accuracy	99.8%	(/.f64 (pow.f64 (.f64 #s(literal 2 binary64) (.f64 (PI.f64) n)) (fma.f64 k #s(literal 1/2 binary64) #s(literal 1/2 binary64))) (sqrt.f64 k))
✓	accuracy	99.7%	(*.f64 (PI.f64) n)
✓	accuracy	99.7%	(pow.f64 (.f64 #s(literal 2 binary64) (.f64 (PI.f64) n)) (fma.f64 k #s(literal 1/2 binary64) #s(literal 1/2 binary64)))
✓	accuracy	76.9%	(PI.f64)
✓	accuracy	99.4%	(.f64 (sqrt.f64 (/.f64 (.f64 n (PI.f64)) k)) (sqrt.f64 #s(literal 2 binary64)))
✓	accuracy	99.4%	(/.f64 (*.f64 n (PI.f64)) k)
✓	accuracy	88.1%	(sqrt.f64 (/.f64 (*.f64 n (PI.f64)) k))
✓	accuracy	76.9%	(PI.f64)
✓	accuracy	99.8%	(.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) k)) (pow.f64 (.f64 n (*.f64 (PI.f64) #s(literal 2 binary64))) (fma.f64 #s(literal -1/2 binary64) k #s(literal 1/2 binary64))))
✓	accuracy	99.7%	(pow.f64 (.f64 n (.f64 (PI.f64) #s(literal 2 binary64))) (fma.f64 #s(literal -1/2 binary64) k #s(literal 1/2 binary64)))
✓	accuracy	99.7%	(.f64 n (.f64 (PI.f64) #s(literal 2 binary64)))
✓	accuracy	76.9%	(PI.f64)

Samples

79.0ms	195×	0	valid
21.0ms	61×	0	exit

Compiler

Compiled 262 to 42 computations (84% saved)

Precisions

Click to see histograms. Total time spent on operations: 77.0ms

ival-div: 23.0ms (29.9% of total)

ival-mult: 21.0ms (27.3% of total)

ival-pow: 17.0ms (22.1% of total)

ival-sqrt: 10.0ms (13% of total)

ival-add: 2.0ms (2.6% of total)

ival-pi: 1.0ms (1.3% of total)

ival-sub: 1.0ms (1.3% of total)

exact: 1.0ms (1.3% of total)

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

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

series32.0ms (0.3%)

Memory

7.6MiB live, 45.3MiB allocated

Counts

22 → 348

Calls

Call 1

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

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

Calls

87 calls:

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

rewrite421.0ms (3.7%)

Memory

-5.3MiB live, 512.7MiB allocated

Algorithm

1×	batch-egg-rewrite

Rules

5 370×	`-lowering-.f32`
5 370×	`-lowering-.f64`
3 320×	`/-lowering-/.f32`
3 320×	`/-lowering-/.f64`
2 608×	`pow-lowering-pow.f64`

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	40	155
1	225	147
2	1446	141
0	8239	141

Stop Event

1×	iter limit
1×	node limit

Counts

22 → 1 230

Calls

Call 1

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

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

simplify511.0ms (4.5%)

Memory

-14.4MiB live, 860.1MiB allocated

Algorithm

1×	egg-herbie

Rules

13 928×	`accelerator-lowering-fma.f32`
13 928×	`accelerator-lowering-fma.f64`
6 092×	`-lowering-.f32`
6 092×	`-lowering-.f64`
2 800×	`+-lowering-+.f64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	249	4329
1	765	4219
2	2536	4079
3	5126	3775
0	8433	3735

Stop Event

1×	iter limit
1×	node limit

Counts

348 → 348

Calls

Call 1

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

Outputs
(* (sqrt (/ (* n (PI)) k)) (sqrt 2))
(.f64 (sqrt.f64 (/.f64 (.f64 n (PI.f64)) k)) (sqrt.f64 #s(literal 2 binary64)))
(/ (+ (* -1/2 (* (sqrt (* (pow k 3) (* n (PI)))) (* (log (* 2 (* n (PI)))) (sqrt 2)))) (* (sqrt (* k (* n (PI)))) (sqrt 2))) k)
(/.f64 (.f64 (sqrt.f64 #s(literal 2 binary64)) (fma.f64 #s(literal -1/2 binary64) (.f64 (sqrt.f64 (.f64 (PI.f64) (.f64 n (.f64 k (.f64 k k))))) (log.f64 (.f64 (PI.f64) (.f64 n #s(literal 2 binary64))))) (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 k (.f64 (sqrt.f64 #s(literal 2 binary64)) (fma.f64 #s(literal -1/2 binary64) (.f64 (log.f64 (.f64 (PI.f64) (.f64 n #s(literal 2 binary64)))) (sqrt.f64 (.f64 (.f64 n (PI.f64)) k))) (.f64 #s(literal 1/8 binary64) (.f64 (sqrt.f64 (.f64 (PI.f64) (.f64 n (.f64 k (.f64 k k))))) (pow.f64 (log.f64 (.f64 (PI.f64) (.f64 n #s(literal 2 binary64)))) #s(literal 2 binary64)))))) (.f64 (sqrt.f64 #s(literal 2 binary64)) (sqrt.f64 (.f64 (*.f64 n (PI.f64)) 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 k (fma.f64 k (.f64 (sqrt.f64 #s(literal 2 binary64)) (fma.f64 #s(literal -1/48 binary64) (.f64 (sqrt.f64 (.f64 (PI.f64) (.f64 n (.f64 k (.f64 k k))))) (pow.f64 (log.f64 (.f64 (PI.f64) (.f64 n #s(literal 2 binary64)))) #s(literal 3 binary64))) (.f64 #s(literal 1/8 binary64) (.f64 (sqrt.f64 (.f64 (.f64 n (PI.f64)) k)) (pow.f64 (log.f64 (.f64 (PI.f64) (.f64 n #s(literal 2 binary64)))) #s(literal 2 binary64)))))) (fma.f64 #s(literal -1/2 binary64) (.f64 (log.f64 (.f64 (PI.f64) (.f64 n #s(literal 2 binary64)))) (.f64 (sqrt.f64 #s(literal 2 binary64)) (sqrt.f64 (.f64 (.f64 n (PI.f64)) k)))) #s(literal 0 binary64))) (.f64 (sqrt.f64 #s(literal 2 binary64)) (sqrt.f64 (.f64 (*.f64 n (PI.f64)) k)))) k)
(* (sqrt (/ 1 k)) (exp (* (log (* 2 (* n (PI)))) (- 1/2 (* 1/2 k)))))
(.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) k)) (pow.f64 (.f64 (PI.f64) (*.f64 n #s(literal 2 binary64))) (fma.f64 k #s(literal -1/2 binary64) #s(literal 1/2 binary64))))
(* (sqrt (/ 1 k)) (exp (* (log (* 2 (* n (PI)))) (- 1/2 (* 1/2 k)))))
(.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) k)) (pow.f64 (.f64 (PI.f64) (*.f64 n #s(literal 2 binary64))) (fma.f64 k #s(literal -1/2 binary64) #s(literal 1/2 binary64))))
(* (sqrt (/ 1 k)) (exp (* (log (* 2 (* n (PI)))) (- 1/2 (* 1/2 k)))))
(.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) k)) (pow.f64 (.f64 (PI.f64) (*.f64 n #s(literal 2 binary64))) (fma.f64 k #s(literal -1/2 binary64) #s(literal 1/2 binary64))))
(* (sqrt (/ 1 k)) (exp (* (log (* 2 (* n (PI)))) (- 1/2 (* 1/2 k)))))
(.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) k)) (pow.f64 (.f64 (PI.f64) (*.f64 n #s(literal 2 binary64))) (fma.f64 k #s(literal -1/2 binary64) #s(literal 1/2 binary64))))
(* (sqrt (/ 1 k)) (* (exp (* (log (* 2 (* n (PI)))) (+ 1/2 (* -1/2 k)))) (pow (sqrt -1) 2)))
(.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) k)) (-.f64 #s(literal 0 binary64) (pow.f64 (.f64 (PI.f64) (*.f64 n #s(literal 2 binary64))) (fma.f64 k #s(literal -1/2 binary64) #s(literal 1/2 binary64)))))
(* (sqrt (/ 1 k)) (* (exp (* (log (* 2 (* n (PI)))) (+ 1/2 (* -1/2 k)))) (pow (sqrt -1) 2)))
(.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) k)) (-.f64 #s(literal 0 binary64) (pow.f64 (.f64 (PI.f64) (*.f64 n #s(literal 2 binary64))) (fma.f64 k #s(literal -1/2 binary64) #s(literal 1/2 binary64)))))
(* (sqrt (/ 1 k)) (* (exp (* (log (* 2 (* n (PI)))) (+ 1/2 (* -1/2 k)))) (pow (sqrt -1) 2)))
(.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) k)) (-.f64 #s(literal 0 binary64) (pow.f64 (.f64 (PI.f64) (*.f64 n #s(literal 2 binary64))) (fma.f64 k #s(literal -1/2 binary64) #s(literal 1/2 binary64)))))
(* (sqrt (/ 1 k)) (* (exp (* (log (* 2 (* n (PI)))) (+ 1/2 (* -1/2 k)))) (pow (sqrt -1) 2)))
(.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) k)) (-.f64 #s(literal 0 binary64) (pow.f64 (.f64 (PI.f64) (*.f64 n #s(literal 2 binary64))) (fma.f64 k #s(literal -1/2 binary64) #s(literal 1/2 binary64)))))
(* (sqrt (/ 1 k)) (exp (* (+ 1/2 (* -1/2 k)) (+ (log n) (log (* 2 (PI)))))))
(.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) k)) (pow.f64 (.f64 (PI.f64) (*.f64 n #s(literal 2 binary64))) (fma.f64 k #s(literal -1/2 binary64) #s(literal 1/2 binary64))))
(* (sqrt (/ 1 k)) (exp (* (+ 1/2 (* -1/2 k)) (+ (log n) (log (* 2 (PI)))))))
(.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) k)) (pow.f64 (.f64 (PI.f64) (*.f64 n #s(literal 2 binary64))) (fma.f64 k #s(literal -1/2 binary64) #s(literal 1/2 binary64))))
(* (sqrt (/ 1 k)) (exp (* (+ 1/2 (* -1/2 k)) (+ (log n) (log (* 2 (PI)))))))
(.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) k)) (pow.f64 (.f64 (PI.f64) (*.f64 n #s(literal 2 binary64))) (fma.f64 k #s(literal -1/2 binary64) #s(literal 1/2 binary64))))
(* (sqrt (/ 1 k)) (exp (* (+ 1/2 (* -1/2 k)) (+ (log n) (log (* 2 (PI)))))))
(.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) k)) (pow.f64 (.f64 (PI.f64) (*.f64 n #s(literal 2 binary64))) (fma.f64 k #s(literal -1/2 binary64) #s(literal 1/2 binary64))))
(* (sqrt (/ 1 k)) (exp (* (+ 1/2 (* -1/2 k)) (+ (log (* 2 (PI))) (* -1 (log (/ 1 n)))))))
(.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) k)) (pow.f64 (.f64 (PI.f64) (*.f64 n #s(literal 2 binary64))) (fma.f64 k #s(literal -1/2 binary64) #s(literal 1/2 binary64))))
(* (sqrt (/ 1 k)) (exp (* (+ 1/2 (* -1/2 k)) (+ (log (* 2 (PI))) (* -1 (log (/ 1 n)))))))
(.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) k)) (pow.f64 (.f64 (PI.f64) (*.f64 n #s(literal 2 binary64))) (fma.f64 k #s(literal -1/2 binary64) #s(literal 1/2 binary64))))
(* (sqrt (/ 1 k)) (exp (* (+ 1/2 (* -1/2 k)) (+ (log (* 2 (PI))) (* -1 (log (/ 1 n)))))))
(.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) k)) (pow.f64 (.f64 (PI.f64) (*.f64 n #s(literal 2 binary64))) (fma.f64 k #s(literal -1/2 binary64) #s(literal 1/2 binary64))))
(* (sqrt (/ 1 k)) (exp (* (+ 1/2 (* -1/2 k)) (+ (log (* 2 (PI))) (* -1 (log (/ 1 n)))))))
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eval453.0ms (4%)

Memory: 18.3MiB live, 364.6MiB allocated
Compiler: Compiled 40 496 to 3 937 computations (90.3% saved)

prune485.0ms (4.3%)

Memory

0.4MiB live, 401.6MiB allocated

Pruning

27 alts after pruning (25 fresh and 2 done)

	Pruned	Kept	Total
New	1 938	25	1 963
Fresh	10	0	10
Picked	3	2	5
Done	0	0	0
Total	1 951	27	1 978

Accuracy

100.0%

Counts

1 978 → 27

Alt Table

Click to see full alt table

Status	Accuracy	Program
▶	99.6%	(/.f64 (pow.f64 (.f64 n (.f64 (PI.f64) #s(literal 2 binary64))) (fma.f64 k #s(literal -1/2 binary64) #s(literal 1/2 binary64))) (sqrt.f64 k))
	51.4%	(/.f64 (.f64 (sqrt.f64 #s(literal 2 binary64)) (sqrt.f64 (.f64 n (PI.f64)))) (sqrt.f64 k))
	51.5%	(/.f64 (sqrt.f64 (.f64 n (.f64 (PI.f64) #s(literal 2 binary64)))) (sqrt.f64 k))
	40.3%	(/.f64 (sqrt.f64 #s(literal 2 binary64)) (sqrt.f64 (/.f64 k (*.f64 n (PI.f64)))))
▶	40.3%	(/.f64 #s(literal 1 binary64) (sqrt.f64 (/.f64 k (.f64 n (.f64 (PI.f64) #s(literal 2 binary64))))))
	77.1%	(.f64 (pow.f64 (.f64 n (.f64 (PI.f64) #s(literal 2 binary64))) (.f64 k #s(literal -1/2 binary64))) (sqrt.f64 (/.f64 (.f64 n (.f64 (PI.f64) #s(literal 2 binary64))) k)))
	51.2%	(.f64 (/.f64 (sqrt.f64 (.f64 (PI.f64) #s(literal 2 binary64))) (sqrt.f64 k)) (/.f64 (sqrt.f64 n) #s(literal 1 binary64)))
	51.4%	(.f64 (/.f64 (sqrt.f64 (.f64 n (PI.f64))) (sqrt.f64 k)) (sqrt.f64 #s(literal 2 binary64)))
	51.2%	(.f64 (/.f64 (sqrt.f64 n) (sqrt.f64 k)) (/.f64 (sqrt.f64 (.f64 (PI.f64) #s(literal 2 binary64))) #s(literal 1 binary64)))
	40.3%	(.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 (/.f64 k (.f64 n (PI.f64))))) (sqrt.f64 #s(literal 2 binary64)))
▶	51.4%	(.f64 (.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) (sqrt.f64 (*.f64 n (PI.f64)))) (sqrt.f64 #s(literal 2 binary64)))
▶	51.4%	(.f64 (.f64 (sqrt.f64 (/.f64 (PI.f64) k)) (sqrt.f64 n)) (sqrt.f64 #s(literal 2 binary64)))
	39.7%	(.f64 (.f64 (sqrt.f64 (PI.f64)) (sqrt.f64 (/.f64 n k))) (sqrt.f64 #s(literal 2 binary64)))
	39.7%	(.f64 (.f64 (sqrt.f64 (PI.f64)) (sqrt.f64 (*.f64 n (/.f64 #s(literal 1 binary64) k)))) (sqrt.f64 #s(literal 2 binary64)))
	39.5%	(.f64 (sqrt.f64 (/.f64 (.f64 n (.f64 (sqrt.f64 (.f64 (PI.f64) (sqrt.f64 (PI.f64)))) (sqrt.f64 (sqrt.f64 (PI.f64))))) k)) (sqrt.f64 #s(literal 2 binary64)))
✓	39.7%	(.f64 (sqrt.f64 (/.f64 (.f64 n (PI.f64)) k)) (sqrt.f64 #s(literal 2 binary64)))
✓	99.6%	(.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) k)) (pow.f64 (.f64 n (*.f64 (PI.f64) #s(literal 2 binary64))) (fma.f64 #s(literal -1/2 binary64) k #s(literal 1/2 binary64))))
	51.4%	(.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) k)) (.f64 (sqrt.f64 #s(literal 2 binary64)) (sqrt.f64 (*.f64 n (PI.f64)))))
	39.7%	(.f64 (sqrt.f64 (.f64 (/.f64 (PI.f64) k) n)) (sqrt.f64 #s(literal 2 binary64)))
	39.7%	(.f64 (sqrt.f64 (.f64 (PI.f64) (/.f64 n k))) (sqrt.f64 #s(literal 2 binary64)))
	39.7%	(.f64 (sqrt.f64 (.f64 (PI.f64) (*.f64 n (/.f64 #s(literal 1 binary64) k)))) (sqrt.f64 #s(literal 2 binary64)))
	51.4%	(.f64 (sqrt.f64 (.f64 n (*.f64 (PI.f64) #s(literal 2 binary64)))) (/.f64 #s(literal 1 binary64) (sqrt.f64 k)))
	51.4%	(.f64 (sqrt.f64 (.f64 n (PI.f64))) (sqrt.f64 (*.f64 (/.f64 #s(literal 1 binary64) k) #s(literal 2 binary64))))
	51.5%	(.f64 (sqrt.f64 n) (sqrt.f64 (.f64 (/.f64 (PI.f64) k) #s(literal 2 binary64))))
	77.1%	(sqrt.f64 (/.f64 (/.f64 (.f64 n (.f64 (PI.f64) #s(literal 2 binary64))) k) (pow.f64 (.f64 n (.f64 (PI.f64) #s(literal 2 binary64))) k)))
▶	39.8%	(sqrt.f64 (/.f64 (.f64 n (.f64 (PI.f64) #s(literal 2 binary64))) k))
	39.8%	(sqrt.f64 (.f64 (.f64 n (*.f64 (PI.f64) #s(literal 2 binary64))) (/.f64 #s(literal 1 binary64) k)))

Compiler

Compiled 690 to 553 computations (19.9% saved)

simplify10.0ms (0.1%)

Memory

11.7MiB live, 11.7MiB allocated

Algorithm

1×	egg-herbie

Localize:

Found 20 expressions of interest:

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

Rules

176×	`-lowering-.f32`
176×	`-lowering-.f64`
64×	`/-lowering-/.f32`
64×	`/-lowering-/.f64`
60×	`associate-r`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	30	184
1	52	180
2	97	180
3	159	180
4	178	180
5	196	180
6	196	180
0	196	177

Stop Event

1×	iter limit
1×	saturated

Calls

Call 1

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

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

localize167.0ms (1.5%)

Memory

-10.3MiB live, 144.1MiB allocated

Localize:

Found 20 expressions of interest:

New	Metric	Score	Program
✓	accuracy	99.6%	(/.f64 #s(literal 1 binary64) (sqrt.f64 k))
✓	accuracy	99.4%	(sqrt.f64 (*.f64 n (PI.f64)))
✓	accuracy	99.3%	(.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) (sqrt.f64 (.f64 n (PI.f64))))
✓	accuracy	99.3%	(.f64 (.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) (sqrt.f64 (*.f64 n (PI.f64)))) (sqrt.f64 #s(literal 2 binary64)))
✓	accuracy	99.8%	(sqrt.f64 (/.f64 (PI.f64) k))
✓	accuracy	99.6%	(/.f64 (PI.f64) k)
✓	accuracy	99.4%	(*.f64 (sqrt.f64 (/.f64 (PI.f64) k)) (sqrt.f64 n))
✓	accuracy	99.3%	(.f64 (.f64 (sqrt.f64 (/.f64 (PI.f64) k)) (sqrt.f64 n)) (sqrt.f64 #s(literal 2 binary64)))
✓	accuracy	99.6%	(.f64 n (.f64 (PI.f64) #s(literal 2 binary64)))
✓	accuracy	99.6%	(/.f64 #s(literal 1 binary64) (sqrt.f64 (/.f64 k (.f64 n (.f64 (PI.f64) #s(literal 2 binary64))))))
✓	accuracy	99.0%	(/.f64 k (.f64 n (.f64 (PI.f64) #s(literal 2 binary64))))
✓	accuracy	78.7%	(sqrt.f64 (/.f64 k (.f64 n (.f64 (PI.f64) #s(literal 2 binary64)))))
✓	accuracy	100.0%	(PI.f64)
✓	accuracy	99.6%	(.f64 n (.f64 (PI.f64) #s(literal 2 binary64)))
✓	accuracy	99.0%	(/.f64 (.f64 n (.f64 (PI.f64) #s(literal 2 binary64))) k)
✓	accuracy	78.5%	(sqrt.f64 (/.f64 (.f64 n (.f64 (PI.f64) #s(literal 2 binary64))) k))
✓	accuracy	100.0%	(PI.f64)
✓	accuracy	99.8%	(/.f64 (pow.f64 (.f64 n (.f64 (PI.f64) #s(literal 2 binary64))) (fma.f64 k #s(literal -1/2 binary64) #s(literal 1/2 binary64))) (sqrt.f64 k))
✓	accuracy	99.7%	(pow.f64 (.f64 n (.f64 (PI.f64) #s(literal 2 binary64))) (fma.f64 k #s(literal -1/2 binary64) #s(literal 1/2 binary64)))
✓	accuracy	99.6%	(.f64 n (.f64 (PI.f64) #s(literal 2 binary64)))

Samples

99.0ms

256×

valid

Compiler

Compiled 183 to 32 computations (82.5% saved)

Precisions

Click to see histograms. Total time spent on operations: 69.0ms

ival-div: 24.0ms (34.6% of total)

ival-pow: 20.0ms (28.8% of total)

ival-mult: 11.0ms (15.8% of total)

ival-sqrt: 11.0ms (15.8% of total)

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

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

exact: 1.0ms (1.4% of total)

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

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

series19.0ms (0.2%)

Memory

29.9MiB live, 29.9MiB allocated

Counts

19 → 336

Calls

Call 1

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

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

Calls

84 calls:

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

rewrite537.0ms (4.7%)

Memory

-25.6MiB live, 584.9MiB allocated

Algorithm

1×	batch-egg-rewrite

Rules

5 894×	`-lowering-.f32`
5 894×	`-lowering-.f64`
2 934×	`/-lowering-/.f32`
2 934×	`/-lowering-/.f64`
2 538×	`+-lowering-+.f64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	30	117
1	141	116
2	847	116
3	7467	116
0	9021	114

Stop Event

1×	iter limit
1×	node limit

Counts

19 → 1 493

Calls

Call 1

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

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

simplify407.0ms (3.6%)

Memory

9.8MiB live, 605.0MiB allocated

Algorithm

1×	egg-herbie

Rules

6 346×	`accelerator-lowering-fma.f32`
6 346×	`accelerator-lowering-fma.f64`
4 580×	`-lowering-.f32`
4 580×	`-lowering-.f64`
2 216×	`+-lowering-+.f64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	145	3150
1	399	3055
2	1192	3033
3	2056	2907
4	3565	2907
5	7646	2907
0	8201	2855

Stop Event

1×	iter limit
1×	node limit

Counts

336 → 336

Calls

Call 1

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

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

eval297.0ms (2.6%)

Memory: -4.2MiB live, 746.9MiB allocated
Compiler: Compiled 33 323 to 4 449 computations (86.6% saved)

prune315.0ms (2.8%)

Memory

-20.8MiB live, 833.5MiB allocated

Pruning

66 alts after pruning (62 fresh and 4 done)

	Pruned	Kept	Total
New	2 228	52	2 280
Fresh	10	10	20
Picked	2	3	5
Done	1	1	2
Total	2 241	66	2 307

Accuracy

100.0%

Counts

2 307 → 66

Alt Table

Click to see full alt table

Status	Accuracy	Program
✓	99.6%	(/.f64 (pow.f64 (.f64 n (.f64 (PI.f64) #s(literal 2 binary64))) (fma.f64 k #s(literal -1/2 binary64) #s(literal 1/2 binary64))) (sqrt.f64 k))
	51.4%	(/.f64 (.f64 (sqrt.f64 #s(literal 2 binary64)) (sqrt.f64 (.f64 n (PI.f64)))) (sqrt.f64 k))
	39.6%	(/.f64 (sqrt.f64 (/.f64 (*.f64 n (PI.f64)) k)) (sqrt.f64 #s(literal 1/2 binary64)))
	51.5%	(/.f64 (sqrt.f64 (.f64 n (.f64 (PI.f64) #s(literal 2 binary64)))) (sqrt.f64 k))
	51.5%	(/.f64 (sqrt.f64 (*.f64 n #s(literal 2 binary64))) (sqrt.f64 (/.f64 k (PI.f64))))
	51.2%	(/.f64 #s(literal 1 binary64) (/.f64 (/.f64 (sqrt.f64 k) (sqrt.f64 (*.f64 (PI.f64) #s(literal 2 binary64)))) (sqrt.f64 n)))
	51.3%	(/.f64 #s(literal 1 binary64) (/.f64 (/.f64 #s(literal 1 binary64) (/.f64 (sqrt.f64 #s(literal 2 binary64)) (sqrt.f64 k))) (sqrt.f64 (*.f64 n (PI.f64)))))
	51.3%	(/.f64 #s(literal 1 binary64) (/.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 (*.f64 n (PI.f64)))) (/.f64 (sqrt.f64 #s(literal 2 binary64)) (sqrt.f64 k))))
	51.4%	(/.f64 #s(literal 1 binary64) (/.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 (*.f64 n #s(literal 2 binary64)))) (sqrt.f64 (/.f64 (PI.f64) k))))
▶	51.5%	(/.f64 #s(literal 1 binary64) (/.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 n)) (sqrt.f64 (/.f64 (*.f64 (PI.f64) #s(literal 2 binary64)) k))))
	39.6%	(/.f64 #s(literal 1 binary64) (/.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 #s(literal 2 binary64))) (sqrt.f64 (/.f64 (*.f64 n (PI.f64)) k))))
	40.3%	(/.f64 #s(literal 1 binary64) (/.f64 (sqrt.f64 (/.f64 k (*.f64 n (PI.f64)))) (sqrt.f64 #s(literal 2 binary64))))
	40.2%	(/.f64 #s(literal 1 binary64) (/.f64 (sqrt.f64 (/.f64 k (*.f64 n #s(literal 2 binary64)))) (sqrt.f64 (PI.f64))))
	51.4%	(/.f64 #s(literal 1 binary64) (/.f64 (sqrt.f64 (/.f64 k (PI.f64))) (sqrt.f64 (*.f64 n #s(literal 2 binary64)))))
	51.4%	(/.f64 #s(literal 1 binary64) (/.f64 (sqrt.f64 k) (sqrt.f64 (.f64 n (.f64 (PI.f64) #s(literal 2 binary64))))))
	51.2%	(/.f64 #s(literal 1 binary64) (.f64 (/.f64 (sqrt.f64 k) (sqrt.f64 (.f64 (PI.f64) #s(literal 2 binary64)))) (/.f64 #s(literal 1 binary64) (sqrt.f64 n))))
	51.3%	(/.f64 #s(literal 1 binary64) (.f64 (/.f64 (sqrt.f64 k) (sqrt.f64 #s(literal 2 binary64))) (/.f64 #s(literal 1 binary64) (sqrt.f64 (.f64 n (PI.f64))))))
	40.3%	(/.f64 #s(literal 1 binary64) (.f64 (sqrt.f64 (/.f64 k (.f64 n (PI.f64)))) (/.f64 #s(literal 1 binary64) (sqrt.f64 #s(literal 2 binary64)))))
	51.4%	(/.f64 #s(literal 1 binary64) (.f64 (sqrt.f64 (/.f64 #s(literal 1/2 binary64) (.f64 n (PI.f64)))) (sqrt.f64 k)))
	40.1%	(/.f64 #s(literal 1 binary64) (.f64 (sqrt.f64 #s(literal 1/2 binary64)) (sqrt.f64 (/.f64 k (.f64 n (PI.f64))))))
	40.3%	(/.f64 #s(literal 1 binary64) (sqrt.f64 (.f64 (/.f64 k (.f64 (PI.f64) #s(literal 2 binary64))) (/.f64 #s(literal 1 binary64) n))))
	40.1%	(/.f64 #s(literal 1 binary64) (sqrt.f64 (.f64 (/.f64 k (sqrt.f64 (PI.f64))) (/.f64 (/.f64 #s(literal 1 binary64) n) (.f64 #s(literal 2 binary64) (sqrt.f64 (PI.f64)))))))
	40.3%	(/.f64 #s(literal 1 binary64) (sqrt.f64 (.f64 (/.f64 #s(literal 1/2 binary64) (.f64 n (PI.f64))) k)))
	77.1%	(.f64 (pow.f64 (.f64 n (.f64 (PI.f64) #s(literal 2 binary64))) (.f64 k #s(literal -1/2 binary64))) (sqrt.f64 (/.f64 (.f64 n (.f64 (PI.f64) #s(literal 2 binary64))) k)))
	51.4%	(.f64 (/.f64 (sqrt.f64 (.f64 n (PI.f64))) (sqrt.f64 k)) (sqrt.f64 #s(literal 2 binary64)))
	51.4%	(*.f64 (/.f64 (sqrt.f64 n) (sqrt.f64 (/.f64 k (PI.f64)))) (sqrt.f64 #s(literal 2 binary64)))
	51.4%	(.f64 (/.f64 (sqrt.f64 #s(literal 2 binary64)) (sqrt.f64 k)) (sqrt.f64 (.f64 n (PI.f64))))
	40.3%	(.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 (/.f64 k (.f64 n (PI.f64))))) (sqrt.f64 #s(literal 2 binary64)))
	40.2%	(.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 (/.f64 k n))) (sqrt.f64 (.f64 (PI.f64) #s(literal 2 binary64))))
▶	51.4%	(.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) (sqrt.f64 (.f64 n (*.f64 (PI.f64) #s(literal 2 binary64)))))
	51.4%	(.f64 (.f64 (/.f64 (sqrt.f64 #s(literal 2 binary64)) (sqrt.f64 k)) (sqrt.f64 (PI.f64))) (sqrt.f64 n))
	51.4%	(.f64 (.f64 (/.f64 (sqrt.f64 #s(literal 2 binary64)) (sqrt.f64 k)) (sqrt.f64 n)) (sqrt.f64 (PI.f64)))
	51.4%	(.f64 (.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 (/.f64 k (PI.f64)))) (sqrt.f64 n)) (sqrt.f64 #s(literal 2 binary64)))
	51.1%	(.f64 (.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) (.f64 (.f64 (sqrt.f64 n) (sqrt.f64 (sqrt.f64 (PI.f64)))) (sqrt.f64 (sqrt.f64 (PI.f64))))) (sqrt.f64 #s(literal 2 binary64)))
	51.3%	(.f64 (.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) (.f64 (sqrt.f64 (.f64 n (sqrt.f64 (PI.f64)))) (sqrt.f64 (sqrt.f64 (PI.f64))))) (sqrt.f64 #s(literal 2 binary64)))
	51.4%	(.f64 (.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) (*.f64 (sqrt.f64 (PI.f64)) (sqrt.f64 n))) (sqrt.f64 #s(literal 2 binary64)))
	51.2%	(.f64 (.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) (sqrt.f64 (*.f64 (PI.f64) #s(literal 2 binary64)))) (sqrt.f64 n))
	51.2%	(.f64 (.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) (sqrt.f64 (.f64 n (.f64 (sqrt.f64 (*.f64 (PI.f64) (sqrt.f64 (PI.f64)))) (sqrt.f64 (sqrt.f64 (PI.f64))))))) (sqrt.f64 #s(literal 2 binary64)))
✓	51.4%	(.f64 (.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) (sqrt.f64 (*.f64 n (PI.f64)))) (sqrt.f64 #s(literal 2 binary64)))
	51.2%	(.f64 (.f64 (*.f64 (/.f64 (sqrt.f64 n) (sqrt.f64 k)) (sqrt.f64 (sqrt.f64 (PI.f64)))) (sqrt.f64 (sqrt.f64 (PI.f64)))) (sqrt.f64 #s(literal 2 binary64)))
	51.1%	(.f64 (.f64 (*.f64 (sqrt.f64 (sqrt.f64 (PI.f64))) (/.f64 (sqrt.f64 (sqrt.f64 (PI.f64))) (sqrt.f64 k))) (sqrt.f64 n)) (sqrt.f64 #s(literal 2 binary64)))
	51.2%	(.f64 (.f64 (.f64 (sqrt.f64 (sqrt.f64 (PI.f64))) (.f64 (sqrt.f64 (sqrt.f64 (PI.f64))) (/.f64 #s(literal 1 binary64) (sqrt.f64 k)))) (sqrt.f64 n)) (sqrt.f64 #s(literal 2 binary64)))
	51.3%	(.f64 (.f64 (*.f64 (sqrt.f64 (sqrt.f64 (PI.f64))) (sqrt.f64 (/.f64 (sqrt.f64 (PI.f64)) k))) (sqrt.f64 n)) (sqrt.f64 #s(literal 2 binary64)))
✓	51.4%	(.f64 (.f64 (sqrt.f64 (/.f64 (PI.f64) k)) (sqrt.f64 n)) (sqrt.f64 #s(literal 2 binary64)))
	51.4%	(.f64 (.f64 (sqrt.f64 #s(literal 2 binary64)) (/.f64 (sqrt.f64 n) (sqrt.f64 k))) (sqrt.f64 (PI.f64)))
	51.5%	(.f64 (sqrt.f64 (/.f64 (.f64 (PI.f64) #s(literal 2 binary64)) k)) (sqrt.f64 n))
	39.5%	(.f64 (sqrt.f64 (/.f64 (.f64 n (.f64 (sqrt.f64 (.f64 (PI.f64) (sqrt.f64 (PI.f64)))) (sqrt.f64 (sqrt.f64 (PI.f64))))) k)) (sqrt.f64 #s(literal 2 binary64)))
	51.5%	(.f64 (sqrt.f64 (/.f64 (PI.f64) k)) (sqrt.f64 (.f64 n #s(literal 2 binary64))))
	39.6%	(.f64 (sqrt.f64 (/.f64 n k)) (sqrt.f64 (.f64 (PI.f64) #s(literal 2 binary64))))
✓	99.6%	(.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) k)) (pow.f64 (.f64 n (*.f64 (PI.f64) #s(literal 2 binary64))) (fma.f64 #s(literal -1/2 binary64) k #s(literal 1/2 binary64))))
	51.4%	(.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) k)) (.f64 (sqrt.f64 #s(literal 2 binary64)) (sqrt.f64 (*.f64 n (PI.f64)))))
	39.7%	(.f64 (sqrt.f64 (.f64 (PI.f64) (/.f64 n k))) (sqrt.f64 #s(literal 2 binary64)))
	39.7%	(.f64 (sqrt.f64 (.f64 (PI.f64) (*.f64 n (/.f64 #s(literal 1 binary64) k)))) (sqrt.f64 #s(literal 2 binary64)))
	51.4%	(.f64 (sqrt.f64 (.f64 n (PI.f64))) (sqrt.f64 (/.f64 #s(literal 2 binary64) k)))
	51.3%	(.f64 (sqrt.f64 (PI.f64)) (/.f64 (sqrt.f64 (.f64 n #s(literal 2 binary64))) (sqrt.f64 k)))
	39.8%	(sqrt.f64 (/.f64 (/.f64 (*.f64 (PI.f64) #s(literal 2 binary64)) k) (/.f64 #s(literal 1 binary64) n)))
▶	77.1%	(sqrt.f64 (/.f64 (/.f64 (.f64 n (.f64 (PI.f64) #s(literal 2 binary64))) k) (pow.f64 (.f64 n (.f64 (PI.f64) #s(literal 2 binary64))) k)))
	39.9%	(sqrt.f64 (/.f64 (*.f64 (PI.f64) #s(literal 2 binary64)) (/.f64 k n)))
	39.9%	(sqrt.f64 (/.f64 (*.f64 n #s(literal 2 binary64)) (/.f64 k (PI.f64))))
	39.9%	(sqrt.f64 (.f64 (/.f64 (.f64 (PI.f64) #s(literal 2 binary64)) k) n))
	39.8%	(sqrt.f64 (.f64 (/.f64 n k) (.f64 (PI.f64) #s(literal 2 binary64))))
	39.8%	(sqrt.f64 (*.f64 (/.f64 #s(literal 2 binary64) k) (/.f64 (PI.f64) (/.f64 #s(literal 1 binary64) n))))
	39.8%	(sqrt.f64 (.f64 (/.f64 #s(literal 2 binary64) k) (.f64 n (PI.f64))))
	39.8%	(sqrt.f64 (.f64 (.f64 (/.f64 #s(literal -1 binary64) k) (*.f64 (PI.f64) #s(literal -2 binary64))) n))
▶	39.6%	(sqrt.f64 (.f64 (.f64 n (sqrt.f64 (PI.f64))) (*.f64 (sqrt.f64 (PI.f64)) (/.f64 #s(literal 2 binary64) k))))
▶	39.8%	(sqrt.f64 (.f64 (PI.f64) (.f64 (/.f64 #s(literal 2 binary64) k) n)))

Compiler

Compiled 1 772 to 1 418 computations (20% saved)

simplify21.0ms (0.2%)

Memory

17.6MiB live, 57.0MiB allocated

Algorithm

1×	egg-herbie

Localize:

Found 20 expressions of interest:

New	Metric	Score	Program
✓	cost-diff	0	(sqrt.f64 n)
✓	cost-diff	0	(/.f64 #s(literal 1 binary64) (sqrt.f64 n))
✓	cost-diff	384	(/.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 n)) (sqrt.f64 (/.f64 (*.f64 (PI.f64) #s(literal 2 binary64)) k)))
✓	cost-diff	1408	(/.f64 #s(literal 1 binary64) (/.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 n)) (sqrt.f64 (/.f64 (*.f64 (PI.f64) #s(literal 2 binary64)) k))))
✓	cost-diff	0	(sqrt.f64 (PI.f64))
✓	cost-diff	0	(*.f64 n (sqrt.f64 (PI.f64)))
✓	cost-diff	0	(sqrt.f64 (.f64 (.f64 n (sqrt.f64 (PI.f64))) (*.f64 (sqrt.f64 (PI.f64)) (/.f64 #s(literal 2 binary64) k))))
✓	cost-diff	1600	(.f64 (.f64 n (sqrt.f64 (PI.f64))) (*.f64 (sqrt.f64 (PI.f64)) (/.f64 #s(literal 2 binary64) k)))
✓	cost-diff	0	(sqrt.f64 (.f64 n (.f64 (PI.f64) #s(literal 2 binary64))))
✓	cost-diff	0	(sqrt.f64 k)
✓	cost-diff	0	(/.f64 #s(literal 1 binary64) (sqrt.f64 k))
✓	cost-diff	320	(.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) (sqrt.f64 (.f64 n (*.f64 (PI.f64) #s(literal 2 binary64)))))
✓	cost-diff	0	(*.f64 (/.f64 #s(literal 2 binary64) k) n)
✓	cost-diff	0	(PI.f64)
✓	cost-diff	0	(.f64 (PI.f64) (.f64 (/.f64 #s(literal 2 binary64) k) n))
✓	cost-diff	0	(sqrt.f64 (.f64 (PI.f64) (.f64 (/.f64 #s(literal 2 binary64) k) n)))
✓	cost-diff	0	(.f64 n (.f64 (PI.f64) #s(literal 2 binary64)))
✓	cost-diff	0	(/.f64 (.f64 n (.f64 (PI.f64) #s(literal 2 binary64))) k)
✓	cost-diff	0	(sqrt.f64 (/.f64 (/.f64 (.f64 n (.f64 (PI.f64) #s(literal 2 binary64))) k) (pow.f64 (.f64 n (.f64 (PI.f64) #s(literal 2 binary64))) k)))
✓	cost-diff	384	(/.f64 (/.f64 (.f64 n (.f64 (PI.f64) #s(literal 2 binary64))) k) (pow.f64 (.f64 n (.f64 (PI.f64) #s(literal 2 binary64))) k))

Rules

610×	`-lowering-.f32`
610×	`-lowering-.f64`
360×	`associate-r`
316×	`associate-l`
148×	`associate-/l*`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	30	203
1	62	197
2	138	197
3	263	197
4	495	197
5	729	197
6	769	197
0	769	197

Stop Event

1×	iter limit
1×	saturated

Calls

Call 1

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

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

localize193.0ms (1.7%)

Memory

17.2MiB live, 254.6MiB allocated

Localize:

Found 20 expressions of interest:

New	Metric	Score	Program
✓	accuracy	99.7%	(/.f64 #s(literal 1 binary64) (sqrt.f64 n))
✓	accuracy	99.7%	(/.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 n)) (sqrt.f64 (/.f64 (*.f64 (PI.f64) #s(literal 2 binary64)) k)))
✓	accuracy	99.7%	(/.f64 (*.f64 (PI.f64) #s(literal 2 binary64)) k)
✓	accuracy	76.9%	(PI.f64)
✓	accuracy	99.6%	(*.f64 (sqrt.f64 (PI.f64)) (/.f64 #s(literal 2 binary64) k))
✓	accuracy	98.8%	(sqrt.f64 (PI.f64))
✓	accuracy	88.1%	(sqrt.f64 (.f64 (.f64 n (sqrt.f64 (PI.f64))) (*.f64 (sqrt.f64 (PI.f64)) (/.f64 #s(literal 2 binary64) k))))
✓	accuracy	76.9%	(PI.f64)
✓	accuracy	99.7%	(/.f64 #s(literal 1 binary64) (sqrt.f64 k))
✓	accuracy	99.6%	(.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) (sqrt.f64 (.f64 n (*.f64 (PI.f64) #s(literal 2 binary64)))))
✓	accuracy	99.1%	(sqrt.f64 (.f64 n (.f64 (PI.f64) #s(literal 2 binary64))))
✓	accuracy	76.9%	(PI.f64)
✓	accuracy	99.7%	(*.f64 (/.f64 #s(literal 2 binary64) k) n)
✓	accuracy	99.7%	(.f64 (PI.f64) (.f64 (/.f64 #s(literal 2 binary64) k) n))
✓	accuracy	88.1%	(sqrt.f64 (.f64 (PI.f64) (.f64 (/.f64 #s(literal 2 binary64) k) n)))
✓	accuracy	76.9%	(PI.f64)
✓	accuracy	99.7%	(.f64 n (.f64 (PI.f64) #s(literal 2 binary64)))
✓	accuracy	99.0%	(/.f64 (.f64 n (.f64 (PI.f64) #s(literal 2 binary64))) k)
✓	accuracy	88.1%	(sqrt.f64 (/.f64 (/.f64 (.f64 n (.f64 (PI.f64) #s(literal 2 binary64))) k) (pow.f64 (.f64 n (.f64 (PI.f64) #s(literal 2 binary64))) k)))
✓	accuracy	76.9%	(PI.f64)

Samples

132.0ms	195×	0	valid
15.0ms	61×	0	exit

Compiler

Compiled 213 to 32 computations (85% saved)

Precisions

Click to see histograms. Total time spent on operations: 98.0ms

ival-div: 65.0ms (66.5% of total)

ival-mult: 15.0ms (15.3% of total)

ival-sqrt: 13.0ms (13.3% of total)

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

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

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

exact: 0.0ms (0% of total)

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

series72.0ms (0.6%)

Memory

-5.8MiB live, 155.8MiB allocated

Counts

22 → 372

Calls

Call 1

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

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

Calls

93 calls:

Time	Variable		Point	Expression
28.0ms	n	@	-inf	(/ (/ (* n (* (PI) 2)) k) (pow (* n (* (PI) 2)) k))
10.0ms	n	@	inf	(/ (/ (* n (* (PI) 2)) k) (pow (* n (* (PI) 2)) k))
8.0ms	n	@	0	(/ (/ (* n (* (PI) 2)) k) (pow (* n (* (PI) 2)) k))
5.0ms	n	@	-inf	(* (/ 2 k) n)
1.0ms	k	@	0	(sqrt (/ (/ (* n (* (PI) 2)) k) (pow (* n (* (PI) 2)) k)))

rewrite334.0ms (2.9%)

Memory

4.1MiB live, 674.9MiB allocated

Algorithm

1×	batch-egg-rewrite

Rules

5 740×	`-lowering-.f32`
5 740×	`-lowering-.f64`
3 508×	`/-lowering-/.f32`
3 508×	`/-lowering-/.f64`
966×	`pow-lowering-pow.f64`

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	30	141
1	155	138
2	950	136
0	8031	136

Stop Event

1×	iter limit
1×	node limit

Counts

22 → 1 701

Calls

Call 1

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

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

simplify601.0ms (5.3%)

Memory

8.5MiB live, 870.9MiB allocated

Algorithm

1×	egg-herbie

Rules

17 698×	`accelerator-lowering-fma.f32`
17 698×	`accelerator-lowering-fma.f64`
5 832×	`-lowering-.f32`
5 832×	`-lowering-.f64`
2 938×	`+-lowering-+.f64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	176	3531
1	522	3445
2	1956	3396
3	5046	3286
0	8386	3273

Stop Event

1×	iter limit
1×	node limit

Counts

372 → 372

Calls

Call 1

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

Outputs
(* 2 (/ (* n (PI)) (* k (exp (* k (+ (log n) (log (* 2 (PI)))))))))
(/.f64 (.f64 #s(literal 2 binary64) (.f64 n (PI.f64))) (.f64 k (pow.f64 (.f64 #s(literal 2 binary64) (*.f64 n (PI.f64))) k)))
(* 2 (/ (* n (PI)) (* k (exp (* k (+ (log n) (log (* 2 (PI)))))))))
(/.f64 (.f64 #s(literal 2 binary64) (.f64 n (PI.f64))) (.f64 k (pow.f64 (.f64 #s(literal 2 binary64) (*.f64 n (PI.f64))) k)))
(* 2 (/ (* n (PI)) (* k (exp (* k (+ (log n) (log (* 2 (PI)))))))))
(/.f64 (.f64 #s(literal 2 binary64) (.f64 n (PI.f64))) (.f64 k (pow.f64 (.f64 #s(literal 2 binary64) (*.f64 n (PI.f64))) k)))
(* 2 (/ (* n (PI)) (* k (exp (* k (+ (log n) (log (* 2 (PI)))))))))
(/.f64 (.f64 #s(literal 2 binary64) (.f64 n (PI.f64))) (.f64 k (pow.f64 (.f64 #s(literal 2 binary64) (*.f64 n (PI.f64))) k)))
(* 2 (/ (* n (PI)) (* k (exp (* k (+ (log (* 2 (PI))) (* -1 (log (/ 1 n)))))))))
(/.f64 (.f64 #s(literal 2 binary64) (.f64 n (PI.f64))) (.f64 k (pow.f64 (.f64 #s(literal 2 binary64) (*.f64 n (PI.f64))) k)))
(* 2 (/ (* n (PI)) (* k (exp (* k (+ (log (* 2 (PI))) (* -1 (log (/ 1 n)))))))))
(/.f64 (.f64 #s(literal 2 binary64) (.f64 n (PI.f64))) (.f64 k (pow.f64 (.f64 #s(literal 2 binary64) (*.f64 n (PI.f64))) k)))
(* 2 (/ (* n (PI)) (* k (exp (* k (+ (log (* 2 (PI))) (* -1 (log (/ 1 n)))))))))
(/.f64 (.f64 #s(literal 2 binary64) (.f64 n (PI.f64))) (.f64 k (pow.f64 (.f64 #s(literal 2 binary64) (*.f64 n (PI.f64))) k)))
(* 2 (/ (* n (PI)) (* k (exp (* k (+ (log (* 2 (PI))) (* -1 (log (/ 1 n)))))))))
(/.f64 (.f64 #s(literal 2 binary64) (.f64 n (PI.f64))) (.f64 k (pow.f64 (.f64 #s(literal 2 binary64) (*.f64 n (PI.f64))) k)))
(* 2 (/ (* n (PI)) (* k (exp (* k (+ (log (* -2 (PI))) (* -1 (log (/ -1 n)))))))))
(/.f64 (.f64 #s(literal 2 binary64) (.f64 n (PI.f64))) (.f64 k (pow.f64 (/.f64 (.f64 (PI.f64) #s(literal -2 binary64)) (/.f64 #s(literal -1 binary64) n)) k)))
(* 2 (/ (* n (PI)) (* k (exp (* k (+ (log (* -2 (PI))) (* -1 (log (/ -1 n)))))))))
(/.f64 (.f64 #s(literal 2 binary64) (.f64 n (PI.f64))) (.f64 k (pow.f64 (/.f64 (.f64 (PI.f64) #s(literal -2 binary64)) (/.f64 #s(literal -1 binary64) n)) k)))
(* 2 (/ (* n (PI)) (* k (exp (* k (+ (log (* -2 (PI))) (* -1 (log (/ -1 n)))))))))
(/.f64 (.f64 #s(literal 2 binary64) (.f64 n (PI.f64))) (.f64 k (pow.f64 (/.f64 (.f64 (PI.f64) #s(literal -2 binary64)) (/.f64 #s(literal -1 binary64) n)) k)))
(* 2 (/ (* n (PI)) (* k (exp (* k (+ (log (* -2 (PI))) (* -1 (log (/ -1 n)))))))))
(/.f64 (.f64 #s(literal 2 binary64) (.f64 n (PI.f64))) (.f64 k (pow.f64 (/.f64 (.f64 (PI.f64) #s(literal -2 binary64)) (/.f64 #s(literal -1 binary64) n)) k)))
(* 2 (/ (* n (PI)) k))
(/.f64 (.f64 #s(literal 2 binary64) (.f64 n (PI.f64))) k)
(/ (+ (* -2 (* k (* n (* (PI) (log (* 2 (* n (PI)))))))) (* 2 (* n (PI)))) k)
(/.f64 (.f64 n (fma.f64 (.f64 k #s(literal -2 binary64)) (.f64 (PI.f64) (log.f64 (.f64 #s(literal 2 binary64) (.f64 n (PI.f64))))) (.f64 #s(literal 2 binary64) (PI.f64)))) k)
(/ (+ (* 2 (* n (PI))) (* k (+ (* -2 (* k (+ (* -1 (* n (* (PI) (pow (log (* 2 (* n (PI)))) 2)))) (* 1/2 (* n (* (PI) (pow (log (* 2 (* n (PI)))) 2))))))) (* -2 (* n (* (PI) (log (* 2 (* n (PI)))))))))) k)
(/.f64 (fma.f64 k (fma.f64 (.f64 n (PI.f64)) (.f64 (log.f64 (.f64 #s(literal 2 binary64) (.f64 n (PI.f64)))) #s(literal -2 binary64)) (.f64 k (.f64 (.f64 n (PI.f64)) (pow.f64 (log.f64 (.f64 #s(literal 2 binary64) (.f64 n (PI.f64)))) #s(literal 2 binary64))))) (.f64 #s(literal 2 binary64) (*.f64 n (PI.f64)))) k)
(/ (+ (* 2 (* n (PI))) (* k (+ (* -2 (* n (* (PI) (log (* 2 (* n (PI))))))) (* k (+ (* -2 (* k (+ (* -1 (* (log (* 2 (* n (PI)))) (+ (* -1 (* n (* (PI) (pow (log (* 2 (* n (PI)))) 2)))) (* 1/2 (* n (* (PI) (pow (log (* 2 (* n (PI)))) 2))))))) (+ (* -1/2 (* n (* (PI) (pow (log (* 2 (* n (PI)))) 3)))) (* 1/6 (* n (* (PI) (pow (log (* 2 (* n (PI)))) 3)))))))) (* -2 (+ (* -1 (* n (* (PI) (pow (log (* 2 (* n (PI)))) 2)))) (* 1/2 (* n (* (PI) (pow (log (* 2 (* n (PI)))) 2))))))))))) k)
(/.f64 (fma.f64 n (fma.f64 (.f64 k #s(literal -2 binary64)) (.f64 (PI.f64) (log.f64 (.f64 #s(literal 2 binary64) (.f64 n (PI.f64))))) (.f64 #s(literal 2 binary64) (PI.f64))) (.f64 (fma.f64 #s(literal -2 binary64) (fma.f64 k (fma.f64 (.f64 #s(literal 1/6 binary64) (.f64 n (PI.f64))) (pow.f64 (log.f64 (.f64 #s(literal 2 binary64) (.f64 n (PI.f64)))) #s(literal 3 binary64)) #s(literal 0 binary64)) #s(literal 0 binary64)) (.f64 (.f64 n (PI.f64)) (pow.f64 (log.f64 (.f64 #s(literal 2 binary64) (.f64 n (PI.f64)))) #s(literal 2 binary64)))) (*.f64 k k))) k)
(* 2 (/ (* n (PI)) (* k (pow (* 2 (* n (PI))) k))))
(/.f64 (.f64 #s(literal 2 binary64) (.f64 n (PI.f64))) (.f64 k (pow.f64 (.f64 #s(literal 2 binary64) (*.f64 n (PI.f64))) k)))
(* 2 (/ (* n (PI)) (* k (pow (* 2 (* n (PI))) k))))
(/.f64 (.f64 #s(literal 2 binary64) (.f64 n (PI.f64))) (.f64 k (pow.f64 (.f64 #s(literal 2 binary64) (*.f64 n (PI.f64))) k)))
(* 2 (/ (* n (PI)) (* k (pow (* 2 (* n (PI))) k))))
(/.f64 (.f64 #s(literal 2 binary64) (.f64 n (PI.f64))) (.f64 k (pow.f64 (.f64 #s(literal 2 binary64) (*.f64 n (PI.f64))) k)))
(* 2 (/ (* n (PI)) (* k (pow (* 2 (* n (PI))) k))))
(/.f64 (.f64 #s(literal 2 binary64) (.f64 n (PI.f64))) (.f64 k (pow.f64 (.f64 #s(literal 2 binary64) (*.f64 n (PI.f64))) k)))
(* 2 (/ (* n (PI)) (* k (pow (* 2 (* n (PI))) k))))
(/.f64 (.f64 #s(literal 2 binary64) (.f64 n (PI.f64))) (.f64 k (pow.f64 (.f64 #s(literal 2 binary64) (*.f64 n (PI.f64))) k)))
(* 2 (/ (* n (PI)) (* k (pow (* 2 (* n (PI))) k))))
(/.f64 (.f64 #s(literal 2 binary64) (.f64 n (PI.f64))) (.f64 k (pow.f64 (.f64 #s(literal 2 binary64) (*.f64 n (PI.f64))) k)))
(* 2 (/ (* n (PI)) (* k (pow (* 2 (* n (PI))) k))))
(/.f64 (.f64 #s(literal 2 binary64) (.f64 n (PI.f64))) (.f64 k (pow.f64 (.f64 #s(literal 2 binary64) (*.f64 n (PI.f64))) k)))
(* 2 (/ (* n (PI)) (* k (pow (* 2 (* n (PI))) k))))
(/.f64 (.f64 #s(literal 2 binary64) (.f64 n (PI.f64))) (.f64 k (pow.f64 (.f64 #s(literal 2 binary64) (*.f64 n (PI.f64))) k)))
(* (sqrt (/ (* n (PI)) (* k (exp (* k (+ (log n) (log (* 2 (PI))))))))) (sqrt 2))
(.f64 (sqrt.f64 #s(literal 2 binary64)) (sqrt.f64 (/.f64 (.f64 n (PI.f64)) (.f64 k (pow.f64 (.f64 #s(literal 2 binary64) (*.f64 n (PI.f64))) k)))))
(* (sqrt (/ (* n (PI)) (* k (exp (* k (+ (log n) (log (* 2 (PI))))))))) (sqrt 2))
(.f64 (sqrt.f64 #s(literal 2 binary64)) (sqrt.f64 (/.f64 (.f64 n (PI.f64)) (.f64 k (pow.f64 (.f64 #s(literal 2 binary64) (*.f64 n (PI.f64))) k)))))
(* (sqrt (/ (* n (PI)) (* k (exp (* k (+ (log n) (log (* 2 (PI))))))))) (sqrt 2))
(.f64 (sqrt.f64 #s(literal 2 binary64)) (sqrt.f64 (/.f64 (.f64 n (PI.f64)) (.f64 k (pow.f64 (.f64 #s(literal 2 binary64) (*.f64 n (PI.f64))) k)))))
(* (sqrt (/ (* n (PI)) (* k (exp (* k (+ (log n) (log (* 2 (PI))))))))) (sqrt 2))
(.f64 (sqrt.f64 #s(literal 2 binary64)) (sqrt.f64 (/.f64 (.f64 n (PI.f64)) (.f64 k (pow.f64 (.f64 #s(literal 2 binary64) (*.f64 n (PI.f64))) k)))))
(* (sqrt (/ (* n (PI)) (* k (exp (* k (+ (log (* 2 (PI))) (* -1 (log (/ 1 n))))))))) (sqrt 2))
(.f64 (sqrt.f64 #s(literal 2 binary64)) (sqrt.f64 (/.f64 (.f64 n (PI.f64)) (.f64 k (pow.f64 (.f64 #s(literal 2 binary64) (*.f64 n (PI.f64))) k)))))
(* (sqrt (/ (* n (PI)) (* k (exp (* k (+ (log (* 2 (PI))) (* -1 (log (/ 1 n))))))))) (sqrt 2))
(.f64 (sqrt.f64 #s(literal 2 binary64)) (sqrt.f64 (/.f64 (.f64 n (PI.f64)) (.f64 k (pow.f64 (.f64 #s(literal 2 binary64) (*.f64 n (PI.f64))) k)))))
(* (sqrt (/ (* n (PI)) (* k (exp (* k (+ (log (* 2 (PI))) (* -1 (log (/ 1 n))))))))) (sqrt 2))
(.f64 (sqrt.f64 #s(literal 2 binary64)) (sqrt.f64 (/.f64 (.f64 n (PI.f64)) (.f64 k (pow.f64 (.f64 #s(literal 2 binary64) (*.f64 n (PI.f64))) k)))))
(* (sqrt (/ (* n (PI)) (* k (exp (* k (+ (log (* 2 (PI))) (* -1 (log (/ 1 n))))))))) (sqrt 2))
(.f64 (sqrt.f64 #s(literal 2 binary64)) (sqrt.f64 (/.f64 (.f64 n (PI.f64)) (.f64 k (pow.f64 (.f64 #s(literal 2 binary64) (*.f64 n (PI.f64))) k)))))
(* -1 (* (sqrt (/ (* n (PI)) (* k (exp (* k (+ (log (* -2 (PI))) (* -1 (log (/ -1 n))))))))) (* (sqrt -2) (sqrt -1))))
(.f64 (sqrt.f64 (/.f64 (.f64 n (PI.f64)) (.f64 k (pow.f64 (/.f64 (.f64 (PI.f64) #s(literal -2 binary64)) (/.f64 #s(literal -1 binary64) n)) k)))) (*.f64 (sqrt.f64 #s(literal -2 binary64)) (-.f64 #s(literal 0 binary64) (sqrt.f64 #s(literal -1 binary64)))))
(* -1 (* (sqrt (/ (* n (PI)) (* k (exp (* k (+ (log (* -2 (PI))) (* -1 (log (/ -1 n))))))))) (* (sqrt -2) (sqrt -1))))
(.f64 (sqrt.f64 (/.f64 (.f64 n (PI.f64)) (.f64 k (pow.f64 (/.f64 (.f64 (PI.f64) #s(literal -2 binary64)) (/.f64 #s(literal -1 binary64) n)) k)))) (*.f64 (sqrt.f64 #s(literal -2 binary64)) (-.f64 #s(literal 0 binary64) (sqrt.f64 #s(literal -1 binary64)))))
(* -1 (* (sqrt (/ (* n (PI)) (* k (exp (* k (+ (log (* -2 (PI))) (* -1 (log (/ -1 n))))))))) (* (sqrt -2) (sqrt -1))))
(.f64 (sqrt.f64 (/.f64 (.f64 n (PI.f64)) (.f64 k (pow.f64 (/.f64 (.f64 (PI.f64) #s(literal -2 binary64)) (/.f64 #s(literal -1 binary64) n)) k)))) (*.f64 (sqrt.f64 #s(literal -2 binary64)) (-.f64 #s(literal 0 binary64) (sqrt.f64 #s(literal -1 binary64)))))
(* -1 (* (sqrt (/ (* n (PI)) (* k (exp (* k (+ (log (* -2 (PI))) (* -1 (log (/ -1 n))))))))) (* (sqrt -2) (sqrt -1))))
(.f64 (sqrt.f64 (/.f64 (.f64 n (PI.f64)) (.f64 k (pow.f64 (/.f64 (.f64 (PI.f64) #s(literal -2 binary64)) (/.f64 #s(literal -1 binary64) n)) k)))) (*.f64 (sqrt.f64 #s(literal -2 binary64)) (-.f64 #s(literal 0 binary64) (sqrt.f64 #s(literal -1 binary64)))))
(* (sqrt (/ (* n (PI)) k)) (sqrt 2))
(.f64 (sqrt.f64 #s(literal 2 binary64)) (sqrt.f64 (/.f64 (.f64 n (PI.f64)) k)))
(/ (+ (* -1/2 (* (sqrt (* (pow k 3) (* n (PI)))) (* (log (* 2 (* n (PI)))) (sqrt 2)))) (* (sqrt (* k (* n (PI)))) (sqrt 2))) k)
(/.f64 (.f64 (sqrt.f64 #s(literal 2 binary64)) (fma.f64 #s(literal -1/2 binary64) (.f64 (log.f64 (.f64 #s(literal 2 binary64) (.f64 n (PI.f64)))) (sqrt.f64 (.f64 (PI.f64) (.f64 n (.f64 k (.f64 k k)))))) (sqrt.f64 (.f64 (PI.f64) (.f64 n k))))) k)
(/ (+ (* (sqrt (* k (* n (PI)))) (sqrt 2)) (* (pow k 2) (+ (* -1/2 (* (sqrt (/ k (* n (PI)))) (* (sqrt 2) (+ (* -1 (* n (* (PI) (pow (log (* 2 (* n (PI)))) 2)))) (* 1/2 (* n (* (PI) (pow (log (* 2 (* n (PI)))) 2)))))))) (* -1/2 (* (sqrt (/ (* n (PI)) k)) (* (log (* 2 (* n (PI)))) (sqrt 2))))))) k)
(/.f64 (fma.f64 #s(literal -1/2 binary64) (.f64 (.f64 (sqrt.f64 #s(literal 2 binary64)) (fma.f64 (.f64 (pow.f64 (log.f64 (.f64 #s(literal 2 binary64) (.f64 n (PI.f64)))) #s(literal 2 binary64)) (.f64 (.f64 n (PI.f64)) #s(literal -1/2 binary64))) (sqrt.f64 (/.f64 k (.f64 n (PI.f64)))) (.f64 (log.f64 (.f64 #s(literal 2 binary64) (.f64 n (PI.f64)))) (sqrt.f64 (/.f64 (.f64 n (PI.f64)) k))))) (.f64 k k)) (.f64 (sqrt.f64 #s(literal 2 binary64)) (sqrt.f64 (.f64 (PI.f64) (.f64 n k))))) k)
(/ (+ (* (sqrt (* k (* n (PI)))) (sqrt 2)) (* (pow k 2) (+ (* -1/2 (* (sqrt (/ (* 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 k (.f64 k (.f64 #s(literal -1/2 binary64) (fma.f64 (log.f64 (.f64 #s(literal 2 binary64) (.f64 n (PI.f64)))) (.f64 (sqrt.f64 #s(literal 2 binary64)) (sqrt.f64 (/.f64 (.f64 n (PI.f64)) k))) (.f64 (.f64 (sqrt.f64 #s(literal 2 binary64)) (fma.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (.f64 (PI.f64) (.f64 n k)))) (.f64 (pow.f64 (log.f64 (.f64 #s(literal 2 binary64) (.f64 n (PI.f64)))) #s(literal 2 binary64)) (.f64 (.f64 n (PI.f64)) #s(literal -1/2 binary64))) (.f64 (sqrt.f64 (/.f64 k (.f64 n (PI.f64)))) (fma.f64 n (fma.f64 (.f64 (PI.f64) (pow.f64 (log.f64 (.f64 #s(literal 2 binary64) (.f64 n (PI.f64)))) #s(literal 3 binary64))) #s(literal 1/6 binary64) (.f64 (.f64 (pow.f64 (log.f64 (.f64 #s(literal 2 binary64) (.f64 n (PI.f64)))) #s(literal 2 binary64)) (/.f64 (PI.f64) k)) #s(literal 1/4 binary64))) #s(literal 0 binary64))))) k)))) (.f64 (sqrt.f64 #s(literal 2 binary64)) (sqrt.f64 (.f64 (PI.f64) (*.f64 n k))))) k)
(* (sqrt (/ (* n (PI)) (* k (pow (* 2 (* n (PI))) k)))) (sqrt 2))
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eval355.0ms (3.1%)

Memory: 5.6MiB live, 704.0MiB allocated
Compiler: Compiled 40 254 to 4 913 computations (87.8% saved)

prune365.0ms (3.2%)

Memory

27.2MiB live, 742.9MiB allocated

Pruning

74 alts after pruning (66 fresh and 8 done)

	Pruned	Kept	Total
New	2 515	17	2 532
Fresh	8	49	57
Picked	1	4	5
Done	0	4	4
Total	2 524	74	2 598

Accuracy

100.0%

Counts

2 598 → 74

Alt Table

Click to see full alt table

Status	Accuracy	Program
✓	99.6%	(/.f64 (pow.f64 (.f64 n (.f64 (PI.f64) #s(literal 2 binary64))) (fma.f64 k #s(literal -1/2 binary64) #s(literal 1/2 binary64))) (sqrt.f64 k))
	51.4%	(/.f64 (.f64 (sqrt.f64 #s(literal 2 binary64)) (sqrt.f64 (.f64 n (PI.f64)))) (sqrt.f64 k))
	39.6%	(/.f64 (sqrt.f64 (/.f64 (*.f64 n (PI.f64)) k)) (sqrt.f64 #s(literal 1/2 binary64)))
	51.5%	(/.f64 (sqrt.f64 (.f64 n (.f64 (PI.f64) #s(literal 2 binary64)))) (sqrt.f64 k))
	51.5%	(/.f64 (sqrt.f64 (.f64 n (PI.f64))) (sqrt.f64 (.f64 k #s(literal 1/2 binary64))))
	51.5%	(/.f64 (sqrt.f64 (*.f64 n #s(literal 2 binary64))) (sqrt.f64 (/.f64 k (PI.f64))))
	51.2%	(/.f64 #s(literal 1 binary64) (/.f64 (/.f64 (sqrt.f64 k) (sqrt.f64 (*.f64 (PI.f64) #s(literal 2 binary64)))) (sqrt.f64 n)))
	51.4%	(/.f64 #s(literal 1 binary64) (/.f64 (/.f64 (sqrt.f64 k) (sqrt.f64 (*.f64 n (PI.f64)))) (sqrt.f64 #s(literal 2 binary64))))
	51.3%	(/.f64 #s(literal 1 binary64) (/.f64 (/.f64 #s(literal 1 binary64) (/.f64 (sqrt.f64 #s(literal 2 binary64)) (sqrt.f64 k))) (sqrt.f64 (*.f64 n (PI.f64)))))
	51.4%	(/.f64 #s(literal 1 binary64) (/.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 (.f64 n (.f64 (PI.f64) #s(literal 2 binary64))))) (sqrt.f64 (/.f64 #s(literal 1 binary64) k))))
	51.3%	(/.f64 #s(literal 1 binary64) (/.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 (.f64 n (sqrt.f64 (PI.f64))))) (sqrt.f64 (/.f64 (sqrt.f64 (PI.f64)) (.f64 k #s(literal 1/2 binary64))))))
	51.3%	(/.f64 #s(literal 1 binary64) (/.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 (*.f64 n (PI.f64)))) (/.f64 (sqrt.f64 #s(literal 2 binary64)) (sqrt.f64 k))))
	51.4%	(/.f64 #s(literal 1 binary64) (/.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 (*.f64 n #s(literal 2 binary64)))) (sqrt.f64 (/.f64 (PI.f64) k))))
✓	51.5%	(/.f64 #s(literal 1 binary64) (/.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 n)) (sqrt.f64 (/.f64 (*.f64 (PI.f64) #s(literal 2 binary64)) k))))
	51.3%	(/.f64 #s(literal 1 binary64) (/.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 n)) (sqrt.f64 (.f64 (/.f64 (sqrt.f64 (PI.f64)) (.f64 k #s(literal 1/2 binary64))) (sqrt.f64 (PI.f64))))))
	39.6%	(/.f64 #s(literal 1 binary64) (/.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 #s(literal 2 binary64))) (sqrt.f64 (/.f64 (*.f64 n (PI.f64)) k))))
	40.3%	(/.f64 #s(literal 1 binary64) (/.f64 (sqrt.f64 (/.f64 k (*.f64 n (PI.f64)))) (sqrt.f64 #s(literal 2 binary64))))
	40.2%	(/.f64 #s(literal 1 binary64) (/.f64 (sqrt.f64 (/.f64 k (*.f64 n #s(literal 2 binary64)))) (sqrt.f64 (PI.f64))))
	51.4%	(/.f64 #s(literal 1 binary64) (/.f64 (sqrt.f64 (/.f64 k (PI.f64))) (sqrt.f64 (*.f64 n #s(literal 2 binary64)))))
	51.4%	(/.f64 #s(literal 1 binary64) (/.f64 (sqrt.f64 k) (sqrt.f64 (.f64 n (.f64 (PI.f64) #s(literal 2 binary64))))))
	51.2%	(/.f64 #s(literal 1 binary64) (.f64 (/.f64 (/.f64 #s(literal -1 binary64) (sqrt.f64 n)) (sqrt.f64 (.f64 (PI.f64) #s(literal 2 binary64)))) (-.f64 #s(literal 0 binary64) (sqrt.f64 k))))
	51.4%	(/.f64 #s(literal 1 binary64) (.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 n)) (sqrt.f64 (/.f64 k (.f64 (PI.f64) #s(literal 2 binary64))))))
	40.3%	(/.f64 #s(literal 1 binary64) (.f64 (sqrt.f64 (/.f64 k (.f64 n (PI.f64)))) (/.f64 #s(literal 1 binary64) (sqrt.f64 #s(literal 2 binary64)))))
	51.4%	(/.f64 #s(literal 1 binary64) (.f64 (sqrt.f64 (/.f64 #s(literal 1/2 binary64) (.f64 n (PI.f64)))) (sqrt.f64 k)))
	40.1%	(/.f64 #s(literal 1 binary64) (.f64 (sqrt.f64 #s(literal 1/2 binary64)) (sqrt.f64 (/.f64 k (.f64 n (PI.f64))))))
	40.3%	(/.f64 #s(literal 1 binary64) (sqrt.f64 (.f64 (/.f64 k (.f64 (PI.f64) #s(literal 2 binary64))) (/.f64 #s(literal 1 binary64) n))))
	40.3%	(/.f64 #s(literal 1 binary64) (sqrt.f64 (.f64 (/.f64 #s(literal 1/2 binary64) (.f64 n (PI.f64))) k)))
	51.4%	(.f64 (/.f64 (sqrt.f64 (.f64 n (PI.f64))) (sqrt.f64 k)) (sqrt.f64 #s(literal 2 binary64)))
	51.4%	(*.f64 (/.f64 (sqrt.f64 n) (sqrt.f64 (/.f64 k (PI.f64)))) (sqrt.f64 #s(literal 2 binary64)))
	51.4%	(.f64 (/.f64 (sqrt.f64 #s(literal 2 binary64)) (sqrt.f64 k)) (sqrt.f64 (.f64 n (PI.f64))))
	51.5%	(.f64 (/.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) k)))) (sqrt.f64 (.f64 n (*.f64 (PI.f64) #s(literal 2 binary64)))))
	40.3%	(.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 (/.f64 k (.f64 n (PI.f64))))) (sqrt.f64 #s(literal 2 binary64)))
	40.2%	(.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 (/.f64 k n))) (sqrt.f64 (.f64 (PI.f64) #s(literal 2 binary64))))
	51.3%	(.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) (.f64 (sqrt.f64 (*.f64 (PI.f64) #s(literal 2 binary64))) (sqrt.f64 n)))
	51.4%	(.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) (.f64 (sqrt.f64 (*.f64 n (PI.f64))) (sqrt.f64 #s(literal 2 binary64))))
✓	51.4%	(.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) (sqrt.f64 (.f64 n (*.f64 (PI.f64) #s(literal 2 binary64)))))
	51.4%	(.f64 (.f64 (/.f64 (sqrt.f64 n) (sqrt.f64 k)) (sqrt.f64 #s(literal 2 binary64))) (sqrt.f64 (PI.f64)))
	51.4%	(.f64 (.f64 (/.f64 (sqrt.f64 #s(literal 2 binary64)) (sqrt.f64 k)) (sqrt.f64 (PI.f64))) (sqrt.f64 n))
	51.4%	(.f64 (.f64 (/.f64 (sqrt.f64 #s(literal 2 binary64)) (sqrt.f64 k)) (sqrt.f64 n)) (sqrt.f64 (PI.f64)))
	51.4%	(.f64 (.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 (/.f64 k (PI.f64)))) (sqrt.f64 n)) (sqrt.f64 #s(literal 2 binary64)))
	51.1%	(.f64 (.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) (.f64 (.f64 (sqrt.f64 n) (sqrt.f64 (sqrt.f64 (PI.f64)))) (sqrt.f64 (sqrt.f64 (PI.f64))))) (sqrt.f64 #s(literal 2 binary64)))
	51.3%	(.f64 (.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) (.f64 (sqrt.f64 (.f64 n (sqrt.f64 (PI.f64)))) (sqrt.f64 (sqrt.f64 (PI.f64))))) (sqrt.f64 #s(literal 2 binary64)))
	51.4%	(.f64 (.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) (*.f64 (sqrt.f64 (PI.f64)) (sqrt.f64 n))) (sqrt.f64 #s(literal 2 binary64)))
	51.2%	(.f64 (.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) (sqrt.f64 (*.f64 (PI.f64) #s(literal 2 binary64)))) (sqrt.f64 n))
	51.2%	(.f64 (.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) (sqrt.f64 (.f64 n (.f64 (sqrt.f64 (*.f64 (PI.f64) (sqrt.f64 (PI.f64)))) (sqrt.f64 (sqrt.f64 (PI.f64))))))) (sqrt.f64 #s(literal 2 binary64)))
✓	51.4%	(.f64 (.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) (sqrt.f64 (*.f64 n (PI.f64)))) (sqrt.f64 #s(literal 2 binary64)))
	51.2%	(.f64 (.f64 (*.f64 (/.f64 (sqrt.f64 n) (sqrt.f64 k)) (sqrt.f64 (sqrt.f64 (PI.f64)))) (sqrt.f64 (sqrt.f64 (PI.f64)))) (sqrt.f64 #s(literal 2 binary64)))
	51.1%	(.f64 (.f64 (*.f64 (sqrt.f64 (sqrt.f64 (PI.f64))) (/.f64 (sqrt.f64 (sqrt.f64 (PI.f64))) (sqrt.f64 k))) (sqrt.f64 n)) (sqrt.f64 #s(literal 2 binary64)))
	51.2%	(.f64 (.f64 (.f64 (sqrt.f64 (sqrt.f64 (PI.f64))) (.f64 (sqrt.f64 (sqrt.f64 (PI.f64))) (/.f64 #s(literal 1 binary64) (sqrt.f64 k)))) (sqrt.f64 n)) (sqrt.f64 #s(literal 2 binary64)))
	51.3%	(.f64 (.f64 (*.f64 (sqrt.f64 (sqrt.f64 (PI.f64))) (sqrt.f64 (/.f64 (sqrt.f64 (PI.f64)) k))) (sqrt.f64 n)) (sqrt.f64 #s(literal 2 binary64)))
✓	51.4%	(.f64 (.f64 (sqrt.f64 (/.f64 (PI.f64) k)) (sqrt.f64 n)) (sqrt.f64 #s(literal 2 binary64)))
	51.4%	(.f64 (.f64 (sqrt.f64 (*.f64 n (sqrt.f64 (PI.f64)))) (sqrt.f64 (/.f64 #s(literal 2 binary64) k))) (sqrt.f64 (sqrt.f64 (PI.f64))))
	51.5%	(.f64 (sqrt.f64 (/.f64 (.f64 (PI.f64) #s(literal 2 binary64)) k)) (sqrt.f64 n))
	39.5%	(.f64 (sqrt.f64 (/.f64 (.f64 n (.f64 (sqrt.f64 (.f64 (PI.f64) (sqrt.f64 (PI.f64)))) (sqrt.f64 (sqrt.f64 (PI.f64))))) k)) (sqrt.f64 #s(literal 2 binary64)))
	51.3%	(.f64 (sqrt.f64 (/.f64 (sqrt.f64 (PI.f64)) (.f64 k #s(literal 1/2 binary64)))) (sqrt.f64 (*.f64 n (sqrt.f64 (PI.f64)))))
	51.5%	(.f64 (sqrt.f64 (/.f64 (PI.f64) k)) (sqrt.f64 (.f64 n #s(literal 2 binary64))))
	39.6%	(.f64 (sqrt.f64 (/.f64 n (.f64 k #s(literal 1/2 binary64)))) (sqrt.f64 (PI.f64)))
	39.6%	(.f64 (sqrt.f64 (/.f64 n k)) (sqrt.f64 (.f64 (PI.f64) #s(literal 2 binary64))))
	51.4%	(.f64 (sqrt.f64 (/.f64 #s(literal 2 binary64) k)) (sqrt.f64 (.f64 n (PI.f64))))
✓	99.6%	(.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) k)) (pow.f64 (.f64 n (*.f64 (PI.f64) #s(literal 2 binary64))) (fma.f64 #s(literal -1/2 binary64) k #s(literal 1/2 binary64))))
	39.7%	(.f64 (sqrt.f64 (.f64 (PI.f64) (/.f64 n k))) (sqrt.f64 #s(literal 2 binary64)))
	39.7%	(.f64 (sqrt.f64 (.f64 (PI.f64) (*.f64 n (/.f64 #s(literal 1 binary64) k)))) (sqrt.f64 #s(literal 2 binary64)))
	51.3%	(.f64 (sqrt.f64 (PI.f64)) (/.f64 (sqrt.f64 (.f64 n #s(literal 2 binary64))) (sqrt.f64 k)))
	39.8%	(sqrt.f64 (/.f64 (/.f64 (*.f64 (PI.f64) #s(literal 2 binary64)) k) (/.f64 #s(literal 1 binary64) n)))
	39.9%	(sqrt.f64 (/.f64 (*.f64 (PI.f64) #s(literal 2 binary64)) (/.f64 k n)))
	39.9%	(sqrt.f64 (/.f64 (*.f64 n #s(literal 2 binary64)) (/.f64 k (PI.f64))))
	88.1%	(sqrt.f64 (.f64 (/.f64 (.f64 (PI.f64) #s(literal 2 binary64)) (.f64 k (pow.f64 (.f64 n (*.f64 (PI.f64) #s(literal 2 binary64))) k))) n))
	39.9%	(sqrt.f64 (.f64 (/.f64 (.f64 (PI.f64) #s(literal 2 binary64)) k) n))
	39.8%	(sqrt.f64 (*.f64 (/.f64 #s(literal 2 binary64) k) (/.f64 (PI.f64) (/.f64 #s(literal 1 binary64) n))))
	39.8%	(sqrt.f64 (.f64 (/.f64 #s(literal 2 binary64) k) (.f64 n (PI.f64))))
	39.8%	(sqrt.f64 (.f64 (.f64 (/.f64 #s(literal -1 binary64) k) (*.f64 (PI.f64) #s(literal -2 binary64))) n))
✓	39.6%	(sqrt.f64 (.f64 (.f64 n (sqrt.f64 (PI.f64))) (*.f64 (sqrt.f64 (PI.f64)) (/.f64 #s(literal 2 binary64) k))))
✓	39.8%	(sqrt.f64 (.f64 (PI.f64) (.f64 (/.f64 #s(literal 2 binary64) k) n)))
	39.8%	(sqrt.f64 (.f64 #s(literal 2 binary64) (.f64 (/.f64 n k) (PI.f64))))

Compiler

Compiled 2 399 to 1 181 computations (50.8% saved)

regimes156.0ms (1.4%)

Memory

1.2MiB live, 205.3MiB allocated

Counts

110 → 1

Calls

Call 1

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

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

Calls

4 calls:

54.0ms	(.f64 (.f64 #s(literal 2 binary64) (PI.f64)) n)
35.0ms	k
31.0ms	n
30.0ms	(.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) (pow.f64 (.f64 (*.f64 #s(literal 2 binary64) (PI.f64)) n) (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 2 binary64))))

Results

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

Compiler

Compiled 31 to 23 computations (25.8% saved)

regimes108.0ms (1%)

Memory

8.7MiB live, 241.8MiB allocated

Counts

94 → 1

Calls

Call 1

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

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

Calls

4 calls:

28.0ms	n
27.0ms	(.f64 (.f64 #s(literal 2 binary64) (PI.f64)) n)
25.0ms	k
23.0ms	(.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) (pow.f64 (.f64 (*.f64 #s(literal 2 binary64) (PI.f64)) n) (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 2 binary64))))

Results

Accuracy	Segments	Branch
51.5%	1	`k`
51.5%	1	`n`
51.5%	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))))`
51.5%	1	`(.f64 (.f64 #s(literal 2 binary64) (PI.f64)) n)`

Compiler

Compiled 31 to 23 computations (25.8% saved)

regimes33.0ms (0.3%)

Memory

-22.6MiB live, 55.0MiB allocated

Counts

21 → 1

Calls

Call 1

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

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

Calls

4 calls:

11.0ms	k
8.0ms	(.f64 (.f64 #s(literal 2 binary64) (PI.f64)) n)
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
51.5%	1	`k`
51.5%	1	`n`
51.5%	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))))`
51.5%	1	`(.f64 (.f64 #s(literal 2 binary64) (PI.f64)) n)`

Compiler

Compiled 31 to 23 computations (25.8% saved)

regimes24.0ms (0.2%)

Memory

6.8MiB live, 44.4MiB allocated

Counts

17 → 1

Calls

Call 1

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

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

Calls

4 calls:

7.0ms	k
5.0ms	(.f64 (.f64 #s(literal 2 binary64) (PI.f64)) n)
5.0ms	n
5.0ms	(.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) (pow.f64 (.f64 (*.f64 #s(literal 2 binary64) (PI.f64)) n) (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 2 binary64))))

Results

Accuracy	Segments	Branch
51.5%	1	`k`
51.5%	1	`n`
51.5%	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))))`
51.5%	1	`(.f64 (.f64 #s(literal 2 binary64) (PI.f64)) n)`

Compiler

Compiled 31 to 23 computations (25.8% saved)

regimes17.0ms (0.2%)

Memory

-6.2MiB live, 31.5MiB allocated

Counts

10 → 1

Calls

Call 1

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

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

Calls

4 calls:

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

Results

Accuracy	Segments	Branch
39.9%	1	`(.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) (pow.f64 (.f64 (*.f64 #s(literal 2 binary64) (PI.f64)) n) (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 2 binary64))))`
39.9%	1	`k`
39.9%	1	`n`
39.9%	1	`(.f64 (.f64 #s(literal 2 binary64) (PI.f64)) n)`

Compiler

Compiled 31 to 23 computations (25.8% saved)

regimes9.0ms (0.1%)

Memory

19.7MiB live, 19.7MiB allocated

Accuracy

Total -0.0b remaining (-0.1%)

Threshold costs -0b (-0.1%)

Counts

4 → 1

Calls

Call 1

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

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

Calls

4 calls:

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

Results

Accuracy	Segments	Branch
39.8%	1	`k`
39.8%	1	`n`
39.8%	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))))`
39.8%	1	`(.f64 (.f64 #s(literal 2 binary64) (PI.f64)) n)`

Compiler

Compiled 31 to 23 computations (25.8% saved)

simplify7.0ms (0.1%)

Memory

15.0MiB live, 15.0MiB allocated

Algorithm

1×	egg-herbie

Rules

18×	`*-commutative_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	30	56
1	39	56

Stop Event

1×

saturated

Calls

Call 1

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

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

soundness690.0ms (6.1%)

Memory

3.9MiB live, 666.3MiB allocated

Rules

9 974×	`accelerator-lowering-fma.f32`
9 974×	`accelerator-lowering-fma.f64`
5 988×	`-lowering-.f32`
5 988×	`-lowering-.f64`
5 894×	`-lowering-.f32`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	40	155
1	225	147
2	1446	141
0	8239	141
0	128	1174
1	345	1155
2	1011	1065
3	3348	1038
4	5547	966
0	8354	945
0	30	141
1	155	138
2	950	136
0	8031	136
0	30	117
1	141	116
2	847	116
3	7467	116
0	9021	114

Stop Event

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

Compiler

Compiled 208 to 152 computations (26.9% saved)

preprocess55.0ms (0.5%)

Memory: 14.7MiB live, 136.2MiB allocated
Compiler: Compiled 152 to 86 computations (43.4% saved)

end0.0ms (0%)

Memory: 0.0MiB live, 0.0MiB allocated

Iter	Nodes	Cost
0	13	54
1	28	52
2	45	52
3	66	52
4	84	52
5	99	52
6	120	52
7	147	52
8	156	52
9	159	52
0	159	49

Iter	Nodes	Cost
0	40	258
1	76	252
2	106	252
3	144	252
4	170	252
5	194	252
6	215	252
7	248	252
8	260	252
9	264	252
0	264	243

Iter	Nodes	Cost
0	13	54
1	28	52
2	45	52
3	66	52
4	84	52
5	99	52
6	120	52
7	147	52
8	156	52
9	159	52
0	159	49

Iter	Nodes	Cost
0	40	258
1	76	252
2	106	252
3	144	252
4	170	252
5	194	252
6	215	252
7	248	252
8	260	252
9	264	252
0	264	243

analyze116.0ms (1%)

sample3.2s (28.4%)

preprocess53.0ms (0.5%)

explain152.0ms (1.3%)

eval0.0ms (0%)

prune1.0ms (0%)

simplify8.0ms (0.1%)

localize44.0ms (0.4%)

series68.0ms (0.6%)

rewrite303.0ms (2.7%)

simplify343.0ms (3%)

eval66.0ms (0.6%)

prune110.0ms (1%)

simplify14.0ms (0.1%)

localize159.0ms (1.4%)

series32.0ms (0.3%)

rewrite421.0ms (3.7%)

simplify511.0ms (4.5%)

eval453.0ms (4%)

prune485.0ms (4.3%)

simplify10.0ms (0.1%)

localize167.0ms (1.5%)

series19.0ms (0.2%)

rewrite537.0ms (4.7%)

simplify407.0ms (3.6%)

eval297.0ms (2.6%)

prune315.0ms (2.8%)

simplify21.0ms (0.2%)

localize193.0ms (1.7%)

series72.0ms (0.6%)

rewrite334.0ms (2.9%)

simplify601.0ms (5.3%)

eval355.0ms (3.1%)

prune365.0ms (3.2%)

regimes156.0ms (1.4%)

regimes108.0ms (1%)

regimes33.0ms (0.3%)

regimes24.0ms (0.2%)

regimes17.0ms (0.2%)

regimes9.0ms (0.1%)

simplify7.0ms (0.1%)

soundness690.0ms (6.1%)

preprocess55.0ms (0.5%)

end0.0ms (0%)

Profiling

Iter	Nodes	Cost
0	13	54
1	28	52
2	45	52
3	66	52
4	84	52
5	99	52
6	120	52
7	147	52
8	156	52
9	159	52
0	159	49

Iter	Nodes	Cost
0	40	258
1	76	252
2	106	252
3	144	252
4	170	252
5	194	252
6	215	252
7	248	252
8	260	252
9	264	252
0	264	243