Metrics for Migdal et al, Equation (51)

start0.0ms (0%)

Memory: 0.1MiB live, 0.1MiB allocated

analyze132.0ms (1.3%)

Memory

33.7MiB live, 127.4MiB 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)

sample4.9s (46.7%)

Memory

-23.3MiB live, 5 747.5MiB allocated

Samples

1.7s	8 256×	0	valid
1.2s	4 540×	1	invalid
654.0ms	1 464×	2	invalid
32.0ms	382×	0	invalid
28.0ms	214×	0	exit

Precisions

Click to see histograms. Total time spent on operations: 2.7s

ival-sub: 712.0ms (26.3% of total)

ival-pow: 627.0ms (23.1% of total)

ival-mult: 435.0ms (16% of total)

ival-div: 352.0ms (13% of total)

adjust: 239.0ms (8.8% of total)

ival-sqrt: 209.0ms (7.7% of total)

ival-pi: 96.0ms (3.5% of total)

exact: 21.0ms (0.8% of total)

ival-true: 14.0ms (0.5% of total)

ival-assert: 8.0ms (0.3% of total)

Bogosity

explain242.0ms (2.3%)

Memory

17.1MiB live, 265.0MiB allocated

FPErrors

Click to see full error table

Ground Truth	Overpredictions	Example	Underpredictions	Example	Subexpression
5	93	(1.741965784241755e-254 4.19414753448018e+297)	1	(1.9826321509275102e-13 1.2804938483659705e-78)	`(pow.f64 (.f64 (.f64 #s(literal 2 binary64) (PI.f64)) n) (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 2 binary64)))`
0	0	-	0	-	`k`
0	0	-	0	-	`n`
0	0	-	0	-	`(/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 2 binary64))`
0	0	-	0	-	`#s(literal 1 binary64)`
0	0	-	0	-	`(.f64 (.f64 #s(literal 2 binary64) (PI.f64)) n)`
0	0	-	0	-	`(sqrt.f64 k)`
0	0	-	0	-	`#s(literal 2 binary64)`
0	0	-	0	-	`(/.f64 #s(literal 1 binary64) (sqrt.f64 k))`
0	0	-	0	-	`(-.f64 #s(literal 1 binary64) k)`
0	0	-	0	-	`(*.f64 #s(literal 2 binary64) (PI.f64))`
0	0	-	0	-	`(.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) (pow.f64 (.f64 (*.f64 #s(literal 2 binary64) (PI.f64)) n) (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 2 binary64))))`
0	0	-	0	-	`(PI.f64)`

Explanations

Click to see full explanations table

Operator	Subexpression	Explanation	Count
`pow.f64`	`(pow.f64 (.f64 (.f64 #s(literal 2 binary64) (PI.f64)) n) (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 2 binary64)))`	sensitivity	97	33

Confusion

	Predicted +	Predicted -
+	6	0
-	91	159

Precision

0.061855670103092786

Recall

1.0

Confusion?

	Predicted +	Predicted Maybe	Predicted -
+	6	0	0
-	91	33	126

Precision?

0.046153846153846156

Recall?

1.0

Freqs

test

number	freq
0	159
1	97

Total Confusion?

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

Precision?

1.0

Recall?

1.0

Samples

73.0ms

512×

valid

Compiler

Compiled 128 to 43 computations (66.4% saved)

Precisions

Click to see histograms. Total time spent on operations: 55.0ms

ival-sub: 22.0ms (40.1% of total)

ival-pow: 10.0ms (18.2% of total)

ival-mult: 9.0ms (16.4% of total)

ival-div: 7.0ms (12.8% of total)

ival-sqrt: 4.0ms (7.3% of total)

ival-pi: 2.0ms (3.6% of total)

exact: 1.0ms (1.8% of total)

adjust: 0.0ms (0% of total)

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

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

preprocess44.0ms (0.4%)

Memory

-3.6MiB live, 43.0MiB allocated

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	31	88
1	71	76
2	145	74
3	227	74
4	296	74
5	363	74
6	428	74
7	501	74
8	528	74
9	541	74
10	547	74
0	13	16
0	22	16
1	37	14
2	50	14
3	67	14
4	80	14
5	98	14
6	132	14
7	202	14
8	227	14
9	247	14
10	257	14
0	257	14

Stop Event

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

Calls

Call 1

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

Outputs

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

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

Compiler

Compiled 16 to 13 computations (18.8% saved)

eval0.0ms (0%)

Memory: 0.2MiB live, 0.2MiB allocated
Compiler: Compiled 0 to 2 computations (-∞% saved)

prune0.0ms (0%)

Memory

0.9MiB live, 0.9MiB allocated

Alt Table

Click to see full alt table

Status	Accuracy	Program
▶	99.4%	(.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) (pow.f64 (.f64 (*.f64 #s(literal 2 binary64) (PI.f64)) n) (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 2 binary64))))

Compiler

Compiled 16 to 13 computations (18.8% saved)

simplify11.0ms (0.1%)

Memory

-34.6MiB live, 12.1MiB allocated

Algorithm

1×	egg-herbie

Localize:

Found 4 expressions of interest:

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

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	13	54
0	22	54
1	37	52
2	50	52
3	67	52
4	80	52
5	98	52
6	132	52
7	202	52
8	227	52
9	247	52
10	257	52
0	257	52

Stop Event

1×	iter limit
1×	saturated
1×	iter limit

Calls

Call 1

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

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

localize43.0ms (0.4%)

Memory

29.0MiB live, 75.1MiB allocated

Localize:

Found 4 expressions of interest:

New	Metric	Score
accuracy	0.19921875	(.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) (pow.f64 (.f64 (*.f64 #s(literal 2 binary64) (PI.f64)) n) (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 2 binary64))))
accuracy	0.2266951500392059	(pow.f64 (.f64 (.f64 #s(literal 2 binary64) (PI.f64)) n) (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 2 binary64)))
accuracy	0.27734375	(.f64 (.f64 #s(literal 2 binary64) (PI.f64)) n)
accuracy	0.30078125	(/.f64 #s(literal 1 binary64) (sqrt.f64 k))

Samples

34.0ms

256×

valid

Compiler

Compiled 56 to 15 computations (73.2% saved)

Precisions

Click to see histograms. Total time spent on operations: 25.0ms

ival-pi: 8.0ms (31.9% of total)

ival-mult: 5.0ms (19.9% of total)

ival-pow: 5.0ms (19.9% of total)

ival-div: 3.0ms (12% of total)

ival-sqrt: 2.0ms (8% of total)

ival-sub: 1.0ms (4% of total)

adjust: 0.0ms (0% of total)

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

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

exact: 0.0ms (0% of total)

series163.0ms (1.6%)

Memory

-4.3MiB live, 135.2MiB allocated

Counts

5 → 22

Calls

Call 1

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

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

Calls

6 calls:

Time	Variable		Point	Expression
107.0ms	n	@	0	((* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (/ 1 (sqrt k)) (sqrt k) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2)) (* (* 2 (PI)) n))
26.0ms	n	@	inf	((* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (/ 1 (sqrt k)) (sqrt k) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2)) (* (* 2 (PI)) n))
24.0ms	n	@	-inf	((* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (/ 1 (sqrt k)) (sqrt k) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2)) (* (* 2 (PI)) n))
3.0ms	k	@	-inf	((* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (/ 1 (sqrt k)) (sqrt k) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2)) (* (* 2 (PI)) n))
2.0ms	k	@	0	((* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (/ 1 (sqrt k)) (sqrt k) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2)) (* (* 2 (PI)) n))

simplify168.0ms (1.6%)

Memory

16.0MiB live, 201.5MiB allocated

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	120	502
1	378	489
2	1377	453
3	4131	453
0	8166	441

Stop Event

1×	iter limit
1×	node limit

Counts

22 → 22

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

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

rewrite204.0ms (2%)

Memory

-18.2MiB live, 361.7MiB allocated

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	13	38
0	22	38
1	83	35
2	446	35
3	4007	29
0	8921	29

Stop Event

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

Counts

5 → 321

Calls

Call 1

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

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

eval87.0ms (0.8%)

Memory: 8.9MiB live, 109.3MiB allocated
Compiler: Compiled 7 537 to 1 169 computations (84.5% saved)

prune23.0ms (0.2%)

Memory

12.2MiB live, 57.4MiB allocated

Pruning

18 alts after pruning (18 fresh and 0 done)

	Pruned	Kept	Total
New	320	18	338
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	321	18	339

Accuracy

99.9%

Counts

339 → 18

Alt Table

Click to see full alt table

Status	Accuracy	Program
	20.7%	(/.f64 (pow.f64 (*.f64 #s(literal 0 binary64) n) (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 8 binary64))) (sqrt.f64 k))
	99.3%	(.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))))
	80.2%	(.f64 (pow.f64 (PI.f64) (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 2 binary64))) (.f64 (pow.f64 #s(literal 2 binary64) (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 2 binary64))) (*.f64 (pow.f64 n (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 2 binary64))) (pow.f64 k #s(literal -1/2 binary64)))))
	80.6%	(.f64 (pow.f64 #s(literal 2 binary64) (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 2 binary64))) (/.f64 (pow.f64 (.f64 n (PI.f64)) (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 2 binary64))) (sqrt.f64 k)))
	66.1%	(.f64 (/.f64 #s(literal 1 binary64) (pow.f64 (.f64 k k) #s(literal 1/4 binary64))) (pow.f64 (.f64 (.f64 #s(literal 2 binary64) (PI.f64)) n) (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 2 binary64))))
▶	99.3%	(.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) (pow.f64 (.f64 (.f64 (.f64 n #s(literal 2 binary64)) (sqrt.f64 (PI.f64))) (sqrt.f64 (PI.f64))) (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 2 binary64))))
▶	80.6%	(.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) (.f64 (pow.f64 (*.f64 n (PI.f64)) (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 2 binary64))) (pow.f64 #s(literal 2 binary64) (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 2 binary64)))))
	60.3%	(.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) #s(approx (pow ( (* 2 (PI)) n) (/ (- 1 k) 2)) (fma.f64 (.f64 (sqrt.f64 (.f64 (PI.f64) n)) (fma.f64 (.f64 (.f64 (pow.f64 (log.f64 (.f64 (.f64 #s(literal 2 binary64) n) (PI.f64))) #s(literal 2 binary64)) (sqrt.f64 #s(literal 2 binary64))) #s(literal 1/8 binary64)) k (.f64 (.f64 (log.f64 (.f64 (.f64 #s(literal 2 binary64) n) (PI.f64))) (sqrt.f64 #s(literal 2 binary64))) #s(literal -1/2 binary64)))) k (.f64 (sqrt.f64 (.f64 (PI.f64) n)) (sqrt.f64 #s(literal 2 binary64))))))
▶	99.4%	(.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) #s(approx (pow ( (* 2 (PI)) n) (/ (- 1 k) 2)) (pow.f64 (.f64 (.f64 #s(literal 2 binary64) n) (PI.f64)) (fma.f64 #s(literal -1/2 binary64) k #s(literal 1/2 binary64)))))
	95.2%	(.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) #s(approx (pow ( (* 2 (PI)) n) (/ (- 1 k) 2)) (pow.f64 (exp.f64 (fma.f64 #s(literal -1/2 binary64) k #s(literal 1/2 binary64))) (+.f64 (log.f64 (*.f64 #s(literal 2 binary64) (PI.f64))) (log.f64 n)))))
	54.3%	(.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) #s(approx (pow ( (* 2 (PI)) n) (/ (- 1 k) 2)) (.f64 (.f64 (fma.f64 (.f64 (log.f64 (.f64 (.f64 #s(literal 2 binary64) n) (PI.f64))) k) #s(literal -1/2 binary64) #s(literal 1 binary64)) (sqrt.f64 #s(literal 2 binary64))) (sqrt.f64 (.f64 (PI.f64) n)))))
	53.8%	(.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) #s(approx (pow ( (* 2 (PI)) n) (/ (- 1 k) 2)) (.f64 (sqrt.f64 (.f64 (PI.f64) n)) (sqrt.f64 #s(literal 2 binary64)))))
▶	80.6%	(.f64 (.f64 (pow.f64 k #s(literal -1/2 binary64)) (pow.f64 #s(literal 2 binary64) (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 2 binary64)))) (pow.f64 (*.f64 n (PI.f64)) (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 2 binary64))))
	95.8%	(.f64 (exp.f64 (.f64 (log.f64 k) #s(literal -1/2 binary64))) (pow.f64 (.f64 (.f64 #s(literal 2 binary64) (PI.f64)) n) (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 2 binary64))))
	52.1%	#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (fma.f64 #s(literal 1 binary64) (.f64 (sqrt.f64 #s(literal 2 binary64)) (fma.f64 (.f64 #s(literal 1/8 binary64) (sqrt.f64 (.f64 (.f64 (pow.f64 k #s(literal 3 binary64)) (PI.f64)) n))) (pow.f64 (log.f64 (.f64 (.f64 #s(literal 2 binary64) n) (PI.f64))) #s(literal 2 binary64)) (.f64 (.f64 (sqrt.f64 (.f64 (.f64 (PI.f64) n) k)) #s(literal -1/2 binary64)) (log.f64 (.f64 (.f64 #s(literal 2 binary64) n) (PI.f64)))))) (.f64 (/.f64 (sqrt.f64 #s(literal 2 binary64)) k) (sqrt.f64 (.f64 (*.f64 (PI.f64) n) k)))))
	51.8%	#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (/.f64 (.f64 (sqrt.f64 #s(literal 2 binary64)) (fma.f64 (.f64 (log.f64 (.f64 (.f64 #s(literal 2 binary64) n) (PI.f64))) (sqrt.f64 (.f64 (.f64 (pow.f64 k #s(literal 3 binary64)) (PI.f64)) n))) #s(literal -1/2 binary64) (sqrt.f64 (.f64 (.f64 (PI.f64) n) k)))) k))
	99.4%	#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (.f64 (pow.f64 (.f64 (*.f64 #s(literal 2 binary64) n) (PI.f64)) (fma.f64 #s(literal -1/2 binary64) k #s(literal 1/2 binary64))) (sqrt.f64 (/.f64 #s(literal 1 binary64) k))))
▶	44.4%	#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (.f64 (sqrt.f64 #s(literal 2 binary64)) (sqrt.f64 (/.f64 (.f64 (PI.f64) n) k))))

Compiler

Compiled 1 038 to 756 computations (27.2% saved)

simplify28.0ms (0.3%)

Memory

-13.8MiB live, 30.7MiB allocated

Algorithm

1×	egg-herbie

Localize:

Found 20 expressions of interest:

New	Metric	Score
cost-diff	0	(pow.f64 #s(literal 2 binary64) (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 2 binary64)))
cost-diff	0	(pow.f64 k #s(literal -1/2 binary64))
cost-diff	0	(*.f64 (pow.f64 k #s(literal -1/2 binary64)) (pow.f64 #s(literal 2 binary64) (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 2 binary64))))
cost-diff	0	(.f64 (.f64 (pow.f64 k #s(literal -1/2 binary64)) (pow.f64 #s(literal 2 binary64) (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 2 binary64)))) (pow.f64 (*.f64 n (PI.f64)) (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 2 binary64))))
cost-diff	0	(.f64 (pow.f64 (.f64 n (PI.f64)) (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 2 binary64))) (pow.f64 #s(literal 2 binary64) (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 2 binary64))))
cost-diff	0	(sqrt.f64 k)
cost-diff	0	(/.f64 #s(literal 1 binary64) (sqrt.f64 k))
cost-diff	2	(.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) (.f64 (pow.f64 (*.f64 n (PI.f64)) (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 2 binary64))) (pow.f64 #s(literal 2 binary64) (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 2 binary64)))))
cost-diff	0	(sqrt.f64 k)
cost-diff	0	(/.f64 #s(literal 1 binary64) (sqrt.f64 k))
cost-diff	2	(.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) (pow.f64 (.f64 (.f64 (.f64 n #s(literal 2 binary64)) (sqrt.f64 (PI.f64))) (sqrt.f64 (PI.f64))) (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 2 binary64))))
cost-diff	4	(.f64 (.f64 (*.f64 n #s(literal 2 binary64)) (sqrt.f64 (PI.f64))) (sqrt.f64 (PI.f64)))
cost-diff	0	(sqrt.f64 (/.f64 (*.f64 (PI.f64) n) k))
cost-diff	0	(sqrt.f64 #s(literal 2 binary64))
cost-diff	0	(.f64 (sqrt.f64 #s(literal 2 binary64)) (sqrt.f64 (/.f64 (.f64 (PI.f64) n) k)))
cost-diff	0	#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (.f64 (sqrt.f64 #s(literal 2 binary64)) (sqrt.f64 (/.f64 (.f64 (PI.f64) n) k))))
cost-diff	0	#s(approx (pow (* (* 2 (PI)) n) (/ (- 1 k) 2)) (pow.f64 (.f64 (.f64 #s(literal 2 binary64) n) (PI.f64)) (fma.f64 #s(literal -1/2 binary64) k #s(literal 1/2 binary64))))
cost-diff	0	(sqrt.f64 k)
cost-diff	0	(/.f64 #s(literal 1 binary64) (sqrt.f64 k))
cost-diff	2	(.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) #s(approx (pow ( (* 2 (PI)) n) (/ (- 1 k) 2)) (pow.f64 (.f64 (.f64 #s(literal 2 binary64) n) (PI.f64)) (fma.f64 #s(literal -1/2 binary64) k #s(literal 1/2 binary64)))))

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	46	358
0	76	354
1	125	338
2	189	338
3	303	338
4	462	338
5	669	338
6	834	338
7	888	338
8	910	338
9	919	338
0	919	338

Stop Event

1×	iter limit
1×	saturated
1×	iter limit

Calls

Call 1

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

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

localize193.0ms (1.9%)

Memory

25.9MiB live, 298.3MiB allocated

Localize:

Found 20 expressions of interest:

New	Metric	Score
accuracy	0.21740134744606632	(pow.f64 (*.f64 n (PI.f64)) (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 2 binary64)))
accuracy	0.22265625	(*.f64 n (PI.f64))
accuracy	0.2578125	(*.f64 (pow.f64 k #s(literal -1/2 binary64)) (pow.f64 #s(literal 2 binary64) (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 2 binary64))))
accuracy	11.624716984711421	(PI.f64)
accuracy	0.22265625	(*.f64 n (PI.f64))
accuracy	0.23503876953688402	(.f64 (pow.f64 (.f64 n (PI.f64)) (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 2 binary64))) (pow.f64 #s(literal 2 binary64) (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 2 binary64))))
accuracy	0.2578125	(/.f64 #s(literal 1 binary64) (sqrt.f64 k))
accuracy	11.624716984711421	(PI.f64)
accuracy	0.2578125	(/.f64 #s(literal 1 binary64) (sqrt.f64 k))
accuracy	0.3203125	(.f64 (.f64 (*.f64 n #s(literal 2 binary64)) (sqrt.f64 (PI.f64))) (sqrt.f64 (PI.f64)))
accuracy	0.8125	(sqrt.f64 (PI.f64))
accuracy	11.624716984711421	(PI.f64)
accuracy	0.37337875976844204	(.f64 (sqrt.f64 #s(literal 2 binary64)) (sqrt.f64 (/.f64 (.f64 (PI.f64) n) k)))
accuracy	6.216111827112914	(sqrt.f64 (/.f64 (*.f64 (PI.f64) n) k))
accuracy	11.624716984711421	(PI.f64)
accuracy	17.574023294913143	#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (.f64 (sqrt.f64 #s(literal 2 binary64)) (sqrt.f64 (/.f64 (.f64 (PI.f64) n) k))))
accuracy	0.22265625	(.f64 (.f64 #s(literal 2 binary64) n) (PI.f64))
accuracy	0.2266951500392059	(pow.f64 (.f64 (.f64 #s(literal 2 binary64) n) (PI.f64)) (fma.f64 #s(literal -1/2 binary64) k #s(literal 1/2 binary64)))
accuracy	0.2578125	(/.f64 #s(literal 1 binary64) (sqrt.f64 k))
accuracy	11.624716984711421	(PI.f64)

Samples

118.0ms	208×	0	valid
17.0ms	48×	0	exit

Compiler

Compiled 330 to 41 computations (87.6% saved)

Precisions

Click to see histograms. Total time spent on operations: 108.0ms

ival-mult: 36.0ms (33.4% of total)

ival-sqrt: 32.0ms (29.7% of total)

ival-pow: 25.0ms (23.2% of total)

ival-sub: 6.0ms (5.6% of total)

ival-div: 5.0ms (4.6% of total)

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

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

exact: 1.0ms (0.9% of total)

adjust: 0.0ms (0% of total)

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

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

series150.0ms (1.4%)

Memory

14.3MiB live, 245.0MiB allocated

Counts

22 → 72

Calls

Call 1

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

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

Calls

6 calls:

Time	Variable		Point	Expression
53.0ms	n	@	0	((* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (/ 1 (sqrt k)) (sqrt k) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2)) (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (* (sqrt 2) (sqrt (/ (* (PI) n) k))) (sqrt 2) (sqrt (/ (* (PI) n) k)) (* (* (* n 2) (sqrt (PI))) (sqrt (PI))) (* (/ 1 (sqrt k)) (pow (* (* (* n 2) (sqrt (PI))) (sqrt (PI))) (/ (- 1 k) 2))) (* (/ 1 (sqrt k)) (* (pow (* n (PI)) (/ (- 1 k) 2)) (pow 2 (/ (- 1 k) 2)))) (* (pow (* n (PI)) (/ (- 1 k) 2)) (pow 2 (/ (- 1 k) 2))) (* (* (pow k -1/2) (pow 2 (/ (- 1 k) 2))) (pow (* n (PI)) (/ (- 1 k) 2))) (* (pow k -1/2) (pow 2 (/ (- 1 k) 2))) (pow k -1/2) (pow 2 (/ (- 1 k) 2)) (PI) (pow (* (* 2 n) (PI)) (+ (* -1/2 k) 1/2)) (* (* 2 n) (PI)) (sqrt (PI)) (* n (PI)) (pow (* n (PI)) (/ (- 1 k) 2)))
47.0ms	n	@	-inf	((* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (/ 1 (sqrt k)) (sqrt k) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2)) (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (* (sqrt 2) (sqrt (/ (* (PI) n) k))) (sqrt 2) (sqrt (/ (* (PI) n) k)) (* (* (* n 2) (sqrt (PI))) (sqrt (PI))) (* (/ 1 (sqrt k)) (pow (* (* (* n 2) (sqrt (PI))) (sqrt (PI))) (/ (- 1 k) 2))) (* (/ 1 (sqrt k)) (* (pow (* n (PI)) (/ (- 1 k) 2)) (pow 2 (/ (- 1 k) 2)))) (* (pow (* n (PI)) (/ (- 1 k) 2)) (pow 2 (/ (- 1 k) 2))) (* (* (pow k -1/2) (pow 2 (/ (- 1 k) 2))) (pow (* n (PI)) (/ (- 1 k) 2))) (* (pow k -1/2) (pow 2 (/ (- 1 k) 2))) (pow k -1/2) (pow 2 (/ (- 1 k) 2)) (PI) (pow (* (* 2 n) (PI)) (+ (* -1/2 k) 1/2)) (* (* 2 n) (PI)) (sqrt (PI)) (* n (PI)) (pow (* n (PI)) (/ (- 1 k) 2)))
26.0ms	n	@	inf	((* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (/ 1 (sqrt k)) (sqrt k) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2)) (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (* (sqrt 2) (sqrt (/ (* (PI) n) k))) (sqrt 2) (sqrt (/ (* (PI) n) k)) (* (* (* n 2) (sqrt (PI))) (sqrt (PI))) (* (/ 1 (sqrt k)) (pow (* (* (* n 2) (sqrt (PI))) (sqrt (PI))) (/ (- 1 k) 2))) (* (/ 1 (sqrt k)) (* (pow (* n (PI)) (/ (- 1 k) 2)) (pow 2 (/ (- 1 k) 2)))) (* (pow (* n (PI)) (/ (- 1 k) 2)) (pow 2 (/ (- 1 k) 2))) (* (* (pow k -1/2) (pow 2 (/ (- 1 k) 2))) (pow (* n (PI)) (/ (- 1 k) 2))) (* (pow k -1/2) (pow 2 (/ (- 1 k) 2))) (pow k -1/2) (pow 2 (/ (- 1 k) 2)) (PI) (pow (* (* 2 n) (PI)) (+ (* -1/2 k) 1/2)) (* (* 2 n) (PI)) (sqrt (PI)) (* n (PI)) (pow (* n (PI)) (/ (- 1 k) 2)))
13.0ms	k	@	-inf	((* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (/ 1 (sqrt k)) (sqrt k) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2)) (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (* (sqrt 2) (sqrt (/ (* (PI) n) k))) (sqrt 2) (sqrt (/ (* (PI) n) k)) (* (* (* n 2) (sqrt (PI))) (sqrt (PI))) (* (/ 1 (sqrt k)) (pow (* (* (* n 2) (sqrt (PI))) (sqrt (PI))) (/ (- 1 k) 2))) (* (/ 1 (sqrt k)) (* (pow (* n (PI)) (/ (- 1 k) 2)) (pow 2 (/ (- 1 k) 2)))) (* (pow (* n (PI)) (/ (- 1 k) 2)) (pow 2 (/ (- 1 k) 2))) (* (* (pow k -1/2) (pow 2 (/ (- 1 k) 2))) (pow (* n (PI)) (/ (- 1 k) 2))) (* (pow k -1/2) (pow 2 (/ (- 1 k) 2))) (pow k -1/2) (pow 2 (/ (- 1 k) 2)) (PI) (pow (* (* 2 n) (PI)) (+ (* -1/2 k) 1/2)) (* (* 2 n) (PI)) (sqrt (PI)) (* n (PI)) (pow (* n (PI)) (/ (- 1 k) 2)))
6.0ms	k	@	0	((* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (/ 1 (sqrt k)) (sqrt k) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2)) (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (* (sqrt 2) (sqrt (/ (* (PI) n) k))) (sqrt 2) (sqrt (/ (* (PI) n) k)) (* (* (* n 2) (sqrt (PI))) (sqrt (PI))) (* (/ 1 (sqrt k)) (pow (* (* (* n 2) (sqrt (PI))) (sqrt (PI))) (/ (- 1 k) 2))) (* (/ 1 (sqrt k)) (* (pow (* n (PI)) (/ (- 1 k) 2)) (pow 2 (/ (- 1 k) 2)))) (* (pow (* n (PI)) (/ (- 1 k) 2)) (pow 2 (/ (- 1 k) 2))) (* (* (pow k -1/2) (pow 2 (/ (- 1 k) 2))) (pow (* n (PI)) (/ (- 1 k) 2))) (* (pow k -1/2) (pow 2 (/ (- 1 k) 2))) (pow k -1/2) (pow 2 (/ (- 1 k) 2)) (PI) (pow (* (* 2 n) (PI)) (+ (* -1/2 k) 1/2)) (* (* 2 n) (PI)) (sqrt (PI)) (* n (PI)) (pow (* n (PI)) (/ (- 1 k) 2)))

simplify220.0ms (2.1%)

Memory

2.4MiB live, 287.6MiB allocated

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	321	1914
1	1184	1734
2	5202	1690
0	8330	1617

Stop Event

1×	iter limit
1×	node limit

Counts

72 → 72

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

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

rewrite217.0ms (2.1%)

Memory

22.3MiB live, 305.8MiB allocated

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	46	238
0	76	212
1	240	200
2	1121	200
0	8962	200

Stop Event

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

Counts

22 → 1 161

Calls

Call 1

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

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

eval299.0ms (2.9%)

Memory: 3.5MiB live, 425.6MiB allocated
Compiler: Compiled 42 838 to 4 551 computations (89.4% saved)

prune88.0ms (0.8%)

Memory

-30.5MiB live, 160.6MiB allocated

Pruning

20 alts after pruning (18 fresh and 2 done)

	Pruned	Kept	Total
New	1 371	17	1 388
Fresh	12	1	13
Picked	3	2	5
Done	0	0	0
Total	1 386	20	1 406

Accuracy

100.0%

Counts

1 406 → 20

Alt Table

Click to see full alt table

Status	Accuracy	Program
▶	99.6%	(/.f64 (.f64 (sqrt.f64 (.f64 (.f64 (PI.f64) n) #s(literal 2 binary64))) #s(literal 1 binary64)) (.f64 (pow.f64 (.f64 (.f64 (PI.f64) n) #s(literal 2 binary64)) (/.f64 k #s(literal 2 binary64))) (sqrt.f64 k)))
▶	99.4%	(/.f64 #s(approx (pow (* (* 2 (PI)) n) (/ (- 1 k) 2)) (pow.f64 (.f64 (.f64 (PI.f64) n) #s(literal 2 binary64)) (fma.f64 #s(literal -1/2 binary64) k #s(literal 1/2 binary64)))) (sqrt.f64 k))
	80.6%	(.f64 (pow.f64 (.f64 (.f64 n (sqrt.f64 (PI.f64))) #s(literal 2 binary64)) (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 2 binary64))) (.f64 (pow.f64 (PI.f64) (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 4 binary64))) (pow.f64 k #s(literal -1/2 binary64))))
	99.2%	(.f64 (/.f64 #s(approx (pow ( (* 2 (PI)) n) (/ (- 1 k) 2)) (pow.f64 (.f64 (.f64 (PI.f64) n) #s(literal 2 binary64)) (fma.f64 #s(literal -1/2 binary64) k #s(literal 1/2 binary64)))) (pow.f64 k #s(literal 1/4 binary64))) (/.f64 #s(literal 1 binary64) (pow.f64 k #s(literal 1/4 binary64))))
	80.8%	(.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) (.f64 (/.f64 (sqrt.f64 (.f64 (PI.f64) n)) (pow.f64 (.f64 (PI.f64) n) (/.f64 k #s(literal 2 binary64)))) (pow.f64 #s(literal 2 binary64) (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 2 binary64)))))
✓	99.4%	(.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) #s(approx (pow ( (* 2 (PI)) n) (/ (- 1 k) 2)) (pow.f64 (.f64 (.f64 #s(literal 2 binary64) n) (PI.f64)) (fma.f64 #s(literal -1/2 binary64) k #s(literal 1/2 binary64)))))
	99.6%	(.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) #s(approx (pow ( (* 2 (PI)) n) (/ (- 1 k) 2)) (.f64 (pow.f64 (.f64 (.f64 (PI.f64) n) #s(literal 2 binary64)) (.f64 #s(literal -1/2 binary64) k)) (sqrt.f64 (.f64 (.f64 (PI.f64) n) #s(literal 2 binary64))))))
▶	99.3%	(.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) #s(approx (pow ( (* 2 (PI)) n) (/ (- 1 k) 2)) (.f64 (.f64 (pow.f64 (.f64 (.f64 (PI.f64) n) #s(literal 2 binary64)) (.f64 #s(literal -1/2 binary64) k)) (sqrt.f64 (.f64 (PI.f64) #s(literal 2 binary64)))) (sqrt.f64 n))))
	80.9%	(.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) #s(approx (pow ( (* 2 (PI)) n) (/ (- 1 k) 2)) (.f64 (.f64 (sqrt.f64 (.f64 (.f64 (PI.f64) n) #s(literal 2 binary64))) (pow.f64 (.f64 (.f64 n (sqrt.f64 (PI.f64))) #s(literal 2 binary64)) (.f64 #s(literal -1/2 binary64) k))) (pow.f64 (PI.f64) (.f64 #s(literal -1/4 binary64) k)))))
	53.8%	(.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) #s(approx (pow ( (* 2 (PI)) n) (/ (- 1 k) 2)) (.f64 (sqrt.f64 (.f64 (PI.f64) n)) (sqrt.f64 #s(literal 2 binary64)))))
	99.4%	(.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) #s(approx (pow ( (* 2 (PI)) n) (/ (- 1 k) 2)) (sqrt.f64 (pow.f64 (.f64 (.f64 n (PI.f64)) #s(literal 2 binary64)) (-.f64 #s(literal 1 binary64) k)))))
	99.4%	(.f64 #s(approx (/ 1 (sqrt k)) (sqrt.f64 (/.f64 #s(literal 1 binary64) k))) #s(approx (pow ( (* 2 (PI)) n) (/ (- 1 k) 2)) (pow.f64 (.f64 (.f64 #s(literal 2 binary64) n) (PI.f64)) (fma.f64 #s(literal -1/2 binary64) k #s(literal 1/2 binary64)))))
	53.9%	#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (/.f64 (sqrt.f64 (.f64 (.f64 (PI.f64) n) #s(literal 2 binary64))) (sqrt.f64 k)))
	44.4%	#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (.f64 (sqrt.f64 (.f64 (/.f64 n k) (PI.f64))) (sqrt.f64 #s(literal 2 binary64))))
	44.2%	#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (.f64 (sqrt.f64 (.f64 (PI.f64) #s(literal 2 binary64))) (sqrt.f64 (/.f64 n k))))
	53.8%	#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (.f64 (sqrt.f64 #s(literal 2 binary64)) (/.f64 (sqrt.f64 (.f64 (PI.f64) n)) (sqrt.f64 k))))
▶	53.8%	#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (.f64 (sqrt.f64 #s(literal 2 binary64)) (.f64 (sqrt.f64 n) (sqrt.f64 (/.f64 (PI.f64) k)))))
	44.4%	#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (.f64 (sqrt.f64 #s(literal 2 binary64)) (sqrt.f64 (/.f64 (.f64 (*.f64 (sqrt.f64 (PI.f64)) (sqrt.f64 (PI.f64))) n) k))))
✓	44.4%	#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (.f64 (sqrt.f64 #s(literal 2 binary64)) (sqrt.f64 (/.f64 (.f64 (PI.f64) n) k))))
▶	44.5%	#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt.f64 (.f64 (.f64 #s(literal 2 binary64) (/.f64 n k)) (PI.f64))))

Compiler

Compiled 1 061 to 836 computations (21.2% saved)

simplify28.0ms (0.3%)

Memory

16.9MiB live, 58.9MiB allocated

Algorithm

1×	egg-herbie

Localize:

Found 20 expressions of interest:

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

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	50	397
0	81	393
1	126	387
2	189	387
3	254	387
4	317	387
5	390	387
6	571	387
7	723	387
8	772	387
9	822	387
10	852	387
0	852	387

Stop Event

1×	iter limit
1×	saturated
1×	iter limit

Calls

Call 1

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

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

localize152.0ms (1.5%)

Memory

3.3MiB live, 294.0MiB allocated

Localize:

Found 20 expressions of interest:

New	Metric	Score
accuracy	0.23275375976844204	(.f64 (.f64 (pow.f64 (.f64 (.f64 (PI.f64) n) #s(literal 2 binary64)) (.f64 #s(literal -1/2 binary64) k)) (sqrt.f64 (.f64 (PI.f64) #s(literal 2 binary64)))) (sqrt.f64 n))
accuracy	0.2578125	(/.f64 #s(literal 1 binary64) (sqrt.f64 k))
accuracy	0.8125	(sqrt.f64 (*.f64 (PI.f64) #s(literal 2 binary64)))
accuracy	11.624716984711421	(PI.f64)
accuracy	0.1875	(/.f64 #s(approx (pow (* (* 2 (PI)) n) (/ (- 1 k) 2)) (pow.f64 (.f64 (.f64 (PI.f64) n) #s(literal 2 binary64)) (fma.f64 #s(literal -1/2 binary64) k #s(literal 1/2 binary64)))) (sqrt.f64 k))
accuracy	0.22265625	(*.f64 (PI.f64) n)
accuracy	0.2266951500392059	(pow.f64 (.f64 (.f64 (PI.f64) n) #s(literal 2 binary64)) (fma.f64 #s(literal -1/2 binary64) k #s(literal 1/2 binary64)))
accuracy	11.624716984711421	(PI.f64)
accuracy	0.3203125	(*.f64 (sqrt.f64 n) (sqrt.f64 (/.f64 (PI.f64) k)))
accuracy	0.37337875976844204	(.f64 (sqrt.f64 #s(literal 2 binary64)) (.f64 (sqrt.f64 n) (sqrt.f64 (/.f64 (PI.f64) k))))
accuracy	11.624716984711421	(PI.f64)
accuracy	17.574023294913143	#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (.f64 (sqrt.f64 #s(literal 2 binary64)) (.f64 (sqrt.f64 n) (sqrt.f64 (/.f64 (PI.f64) k)))))
accuracy	0.25228500976844204	(.f64 (.f64 #s(literal 2 binary64) (/.f64 n k)) (PI.f64))
accuracy	6.215802432375007	(sqrt.f64 (.f64 (.f64 #s(literal 2 binary64) (/.f64 n k)) (PI.f64)))
accuracy	11.624716984711421	(PI.f64)
accuracy	17.574023294913143	#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt.f64 (.f64 (.f64 #s(literal 2 binary64) (/.f64 n k)) (PI.f64))))
accuracy	0.109375	(sqrt.f64 (.f64 (.f64 (PI.f64) n) #s(literal 2 binary64)))
accuracy	0.20703125	(/.f64 (.f64 (sqrt.f64 (.f64 (.f64 (PI.f64) n) #s(literal 2 binary64))) #s(literal 1 binary64)) (.f64 (pow.f64 (.f64 (.f64 (PI.f64) n) #s(literal 2 binary64)) (/.f64 k #s(literal 2 binary64))) (sqrt.f64 k)))
accuracy	0.22265625	(*.f64 (PI.f64) n)
accuracy	11.624716984711421	(PI.f64)

Samples

85.0ms	208×	0	valid
31.0ms	48×	0	exit

Compiler

Compiled 323 to 44 computations (86.4% saved)

Precisions

Click to see histograms. Total time spent on operations: 81.0ms

ival-mult: 27.0ms (33.5% of total)

ival-pow: 19.0ms (23.6% of total)

ival-div: 15.0ms (18.6% of total)

ival-sqrt: 14.0ms (17.4% of total)

ival-pi: 1.0ms (1.2% of total)

ival-add: 1.0ms (1.2% of total)

ival-sub: 1.0ms (1.2% of total)

exact: 1.0ms (1.2% of total)

adjust: 0.0ms (0% of total)

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

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

series70.0ms (0.7%)

Memory

-31.8MiB live, 126.3MiB allocated

Counts

23 → 48

Calls

Call 1

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

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

Calls

6 calls:

Time	Variable		Point	Expression
19.0ms	n	@	-inf	((* (sqrt (* (* (PI) n) 2)) 1) (/ (* (sqrt (* (* (PI) n) 2)) 1) (* (pow (* (* (PI) n) 2) (/ k 2)) (sqrt k))) (sqrt (* (* (PI) n) 2)) (* (* (PI) n) 2) (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt (* (* 2 (/ n k)) (PI))) (* (* 2 (/ n k)) (PI)) (* 2 (/ n k)) (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (* (sqrt 2) (* (sqrt n) (sqrt (/ (PI) k)))) (sqrt 2) (* (sqrt n) (sqrt (/ (PI) k))) (/ (pow (* (* 2 (PI)) n) (/ (- 1 k) 2)) (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2)) (pow (* (* (PI) n) 2) (+ (* -1/2 k) 1/2)) (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (/ 1 (sqrt k)) (sqrt k) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2)) (PI) (* (PI) n) (sqrt (* (PI) 2)) (* (* (pow (* (* (PI) n) 2) (* -1/2 k)) (sqrt (* (PI) 2))) (sqrt n)))
16.0ms	n	@	inf	((* (sqrt (* (* (PI) n) 2)) 1) (/ (* (sqrt (* (* (PI) n) 2)) 1) (* (pow (* (* (PI) n) 2) (/ k 2)) (sqrt k))) (sqrt (* (* (PI) n) 2)) (* (* (PI) n) 2) (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt (* (* 2 (/ n k)) (PI))) (* (* 2 (/ n k)) (PI)) (* 2 (/ n k)) (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (* (sqrt 2) (* (sqrt n) (sqrt (/ (PI) k)))) (sqrt 2) (* (sqrt n) (sqrt (/ (PI) k))) (/ (pow (* (* 2 (PI)) n) (/ (- 1 k) 2)) (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2)) (pow (* (* (PI) n) 2) (+ (* -1/2 k) 1/2)) (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (/ 1 (sqrt k)) (sqrt k) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2)) (PI) (* (PI) n) (sqrt (* (PI) 2)) (* (* (pow (* (* (PI) n) 2) (* -1/2 k)) (sqrt (* (PI) 2))) (sqrt n)))
12.0ms	k	@	-inf	((* (sqrt (* (* (PI) n) 2)) 1) (/ (* (sqrt (* (* (PI) n) 2)) 1) (* (pow (* (* (PI) n) 2) (/ k 2)) (sqrt k))) (sqrt (* (* (PI) n) 2)) (* (* (PI) n) 2) (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt (* (* 2 (/ n k)) (PI))) (* (* 2 (/ n k)) (PI)) (* 2 (/ n k)) (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (* (sqrt 2) (* (sqrt n) (sqrt (/ (PI) k)))) (sqrt 2) (* (sqrt n) (sqrt (/ (PI) k))) (/ (pow (* (* 2 (PI)) n) (/ (- 1 k) 2)) (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2)) (pow (* (* (PI) n) 2) (+ (* -1/2 k) 1/2)) (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (/ 1 (sqrt k)) (sqrt k) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2)) (PI) (* (PI) n) (sqrt (* (PI) 2)) (* (* (pow (* (* (PI) n) 2) (* -1/2 k)) (sqrt (* (PI) 2))) (sqrt n)))
12.0ms	n	@	0	((* (sqrt (* (* (PI) n) 2)) 1) (/ (* (sqrt (* (* (PI) n) 2)) 1) (* (pow (* (* (PI) n) 2) (/ k 2)) (sqrt k))) (sqrt (* (* (PI) n) 2)) (* (* (PI) n) 2) (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt (* (* 2 (/ n k)) (PI))) (* (* 2 (/ n k)) (PI)) (* 2 (/ n k)) (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (* (sqrt 2) (* (sqrt n) (sqrt (/ (PI) k)))) (sqrt 2) (* (sqrt n) (sqrt (/ (PI) k))) (/ (pow (* (* 2 (PI)) n) (/ (- 1 k) 2)) (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2)) (pow (* (* (PI) n) 2) (+ (* -1/2 k) 1/2)) (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (/ 1 (sqrt k)) (sqrt k) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2)) (PI) (* (PI) n) (sqrt (* (PI) 2)) (* (* (pow (* (* (PI) n) 2) (* -1/2 k)) (sqrt (* (PI) 2))) (sqrt n)))
5.0ms	k	@	0	((* (sqrt (* (* (PI) n) 2)) 1) (/ (* (sqrt (* (* (PI) n) 2)) 1) (* (pow (* (* (PI) n) 2) (/ k 2)) (sqrt k))) (sqrt (* (* (PI) n) 2)) (* (* (PI) n) 2) (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt (* (* 2 (/ n k)) (PI))) (* (* 2 (/ n k)) (PI)) (* 2 (/ n k)) (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (* (sqrt 2) (* (sqrt n) (sqrt (/ (PI) k)))) (sqrt 2) (* (sqrt n) (sqrt (/ (PI) k))) (/ (pow (* (* 2 (PI)) n) (/ (- 1 k) 2)) (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2)) (pow (* (* (PI) n) 2) (+ (* -1/2 k) 1/2)) (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (/ 1 (sqrt k)) (sqrt k) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2)) (PI) (* (PI) n) (sqrt (* (PI) 2)) (* (* (pow (* (* (PI) n) 2) (* -1/2 k)) (sqrt (* (PI) 2))) (sqrt n)))

simplify128.0ms (1.2%)

Memory

35.0MiB live, 166.2MiB allocated

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	214	1030
1	766	983
2	3134	944
0	8431	926

Stop Event

1×	iter limit
1×	node limit

Counts

48 → 48

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

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

rewrite237.0ms (2.3%)

Memory

6.3MiB live, 289.2MiB allocated

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	50	282
0	81	250
1	244	240
2	1225	240
0	8204	240

Stop Event

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

Counts

23 → 922

Calls

Call 1

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

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

eval212.0ms (2%)

Memory: 5.1MiB live, 345.7MiB allocated
Compiler: Compiled 42 124 to 5 262 computations (87.5% saved)

prune88.0ms (0.8%)

Memory

-11.3MiB live, 122.5MiB allocated

Pruning

22 alts after pruning (17 fresh and 5 done)

	Pruned	Kept	Total
New	1 271	12	1 283
Fresh	8	5	13
Picked	2	3	5
Done	0	2	2
Total	1 281	22	1 303

Accuracy

100.0%

Counts

1 303 → 22

Alt Table

Click to see full alt table

Status	Accuracy	Program
✓	99.4%	(/.f64 #s(approx (pow (* (* 2 (PI)) n) (/ (- 1 k) 2)) (pow.f64 (.f64 (.f64 (PI.f64) n) #s(literal 2 binary64)) (fma.f64 #s(literal -1/2 binary64) k #s(literal 1/2 binary64)))) (sqrt.f64 k))
	53.9%	(/.f64 #s(approx (pow (* (* 2 (PI)) n) (/ (- 1 k) 2)) (.f64 (sqrt.f64 (.f64 (PI.f64) n)) (sqrt.f64 #s(literal 2 binary64)))) (sqrt.f64 k))
	82.1%	(.f64 (pow.f64 (.f64 #s(literal 2 binary64) (.f64 n (PI.f64))) (/.f64 k #s(literal -2 binary64))) (sqrt.f64 (.f64 (*.f64 (/.f64 n k) #s(literal 2 binary64)) (PI.f64))))
	80.7%	(.f64 (/.f64 (sqrt.f64 (PI.f64)) (pow.f64 (.f64 n (PI.f64)) (/.f64 k #s(literal 2 binary64)))) (/.f64 (sqrt.f64 (.f64 #s(literal 2 binary64) n)) (.f64 (pow.f64 #s(literal 2 binary64) (/.f64 k #s(literal 2 binary64))) (sqrt.f64 k))))
✓	99.4%	(.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) #s(approx (pow ( (* 2 (PI)) n) (/ (- 1 k) 2)) (pow.f64 (.f64 (.f64 #s(literal 2 binary64) n) (PI.f64)) (fma.f64 #s(literal -1/2 binary64) k #s(literal 1/2 binary64)))))
▶	53.8%	(.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) #s(approx (pow ( (* 2 (PI)) n) (/ (- 1 k) 2)) (.f64 (sqrt.f64 (.f64 (PI.f64) n)) (sqrt.f64 #s(literal 2 binary64)))))
	99.4%	(.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) #s(approx (pow ( (* 2 (PI)) n) (/ (- 1 k) 2)) (sqrt.f64 (pow.f64 (.f64 (.f64 n (PI.f64)) #s(literal 2 binary64)) (-.f64 #s(literal 1 binary64) k)))))
▶	99.4%	(.f64 #s(approx (/ 1 (sqrt k)) (sqrt.f64 (/.f64 #s(literal 1 binary64) k))) #s(approx (pow ( (* 2 (PI)) n) (/ (- 1 k) 2)) (pow.f64 (.f64 (.f64 #s(literal 2 binary64) n) (PI.f64)) (fma.f64 #s(literal -1/2 binary64) k #s(literal 1/2 binary64)))))
	53.9%	#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (/.f64 (sqrt.f64 (.f64 (.f64 (PI.f64) n) #s(literal 2 binary64))) (sqrt.f64 k)))
	53.9%	#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (.f64 (sqrt.f64 (/.f64 (PI.f64) k)) (sqrt.f64 (.f64 #s(literal 2 binary64) n))))
	44.2%	#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (.f64 (sqrt.f64 (/.f64 n k)) (sqrt.f64 (.f64 #s(literal 2 binary64) (PI.f64)))))
▶	44.4%	#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (.f64 (sqrt.f64 (.f64 (/.f64 (PI.f64) k) n)) (sqrt.f64 #s(literal 2 binary64))))
	44.3%	#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (.f64 (sqrt.f64 (.f64 (/.f64 n k) #s(literal 2 binary64))) (sqrt.f64 (PI.f64))))
	53.9%	#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (.f64 (sqrt.f64 (.f64 #s(literal 2 binary64) (/.f64 (PI.f64) k))) (sqrt.f64 n)))
	53.8%	#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (.f64 (sqrt.f64 #s(literal 2 binary64)) (/.f64 (sqrt.f64 (.f64 (PI.f64) n)) (sqrt.f64 k))))
✓	53.8%	#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (.f64 (sqrt.f64 #s(literal 2 binary64)) (.f64 (sqrt.f64 n) (sqrt.f64 (/.f64 (PI.f64) k)))))
✓	44.4%	#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (.f64 (sqrt.f64 #s(literal 2 binary64)) (sqrt.f64 (/.f64 (.f64 (PI.f64) n) k))))
	44.4%	#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt.f64 (/.f64 (.f64 #s(literal 2 binary64) (.f64 n (PI.f64))) k)))
▶	24.4%	#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt.f64 (.f64 (/.f64 (fma.f64 n k (.f64 k n)) (*.f64 k k)) (PI.f64))))
▶	44.5%	#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt.f64 (.f64 (/.f64 (PI.f64) k) (.f64 #s(literal 2 binary64) n))))
	44.3%	#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt.f64 (.f64 (.f64 (*.f64 (/.f64 n k) #s(literal 2 binary64)) (sqrt.f64 (PI.f64))) (sqrt.f64 (PI.f64)))))
✓	44.5%	#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt.f64 (.f64 (.f64 #s(literal 2 binary64) (/.f64 n k)) (PI.f64))))

Compiler

Compiled 1 008 to 805 computations (20.1% saved)

simplify145.0ms (1.4%)

Memory

15.6MiB live, 115.9MiB allocated

Algorithm

1×	egg-herbie

Localize:

Found 20 expressions of interest:

New	Metric	Score
cost-diff	0	#s(approx (pow (* (* 2 (PI)) n) (/ (- 1 k) 2)) (.f64 (sqrt.f64 (.f64 (PI.f64) n)) (sqrt.f64 #s(literal 2 binary64))))
cost-diff	0	(sqrt.f64 k)
cost-diff	0	(/.f64 #s(literal 1 binary64) (sqrt.f64 k))
cost-diff	2	(.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) #s(approx (pow ( (* 2 (PI)) n) (/ (- 1 k) 2)) (.f64 (sqrt.f64 (.f64 (PI.f64) n)) (sqrt.f64 #s(literal 2 binary64)))))
cost-diff	0	(sqrt.f64 (.f64 (/.f64 (fma.f64 n k (.f64 k n)) (*.f64 k k)) (PI.f64)))
cost-diff	0	#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt.f64 (.f64 (/.f64 (fma.f64 n k (.f64 k n)) (*.f64 k k)) (PI.f64))))
cost-diff	1	(fma.f64 n k (*.f64 k n))
cost-diff	4	(/.f64 (fma.f64 n k (.f64 k n)) (.f64 k k))
cost-diff	0	(*.f64 (/.f64 (PI.f64) k) n)
cost-diff	0	(sqrt.f64 (*.f64 (/.f64 (PI.f64) k) n))
cost-diff	0	(.f64 (sqrt.f64 (.f64 (/.f64 (PI.f64) k) n)) (sqrt.f64 #s(literal 2 binary64)))
cost-diff	0	#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (.f64 (sqrt.f64 (.f64 (/.f64 (PI.f64) k) n)) (sqrt.f64 #s(literal 2 binary64))))
cost-diff	0	(/.f64 (PI.f64) k)
cost-diff	0	(.f64 (/.f64 (PI.f64) k) (.f64 #s(literal 2 binary64) n))
cost-diff	0	(sqrt.f64 (.f64 (/.f64 (PI.f64) k) (.f64 #s(literal 2 binary64) n)))
cost-diff	0	#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt.f64 (.f64 (/.f64 (PI.f64) k) (.f64 #s(literal 2 binary64) n))))
cost-diff	0	(/.f64 #s(literal 1 binary64) k)
cost-diff	0	(sqrt.f64 (/.f64 #s(literal 1 binary64) k))
cost-diff	0	#s(approx (/ 1 (sqrt k)) (sqrt.f64 (/.f64 #s(literal 1 binary64) k)))
cost-diff	0	(.f64 #s(approx (/ 1 (sqrt k)) (sqrt.f64 (/.f64 #s(literal 1 binary64) k))) #s(approx (pow ( (* 2 (PI)) n) (/ (- 1 k) 2)) (pow.f64 (.f64 (.f64 #s(literal 2 binary64) n) (PI.f64)) (fma.f64 #s(literal -1/2 binary64) k #s(literal 1/2 binary64)))))

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	48	354
0	78	339
1	130	329
2	237	325
3	693	325
4	2587	325
5	6082	325
0	8499	325

Stop Event

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

Calls

Call 1

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

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

localize179.0ms (1.7%)

Memory

-14.1MiB live, 206.0MiB allocated

Localize:

Found 20 expressions of interest:

New	Metric	Score
accuracy	0.27734375	(*.f64 (PI.f64) n)
accuracy	0.30078125	(/.f64 #s(literal 1 binary64) (sqrt.f64 k))
accuracy	0.4576950195368841	(.f64 (sqrt.f64 (.f64 (PI.f64) n)) (sqrt.f64 #s(literal 2 binary64)))
accuracy	29.33593649995235	#s(approx (pow (* (* 2 (PI)) n) (/ (- 1 k) 2)) (.f64 (sqrt.f64 (.f64 (PI.f64) n)) (sqrt.f64 #s(literal 2 binary64))))
accuracy	0.27181625976844204	(.f64 (/.f64 (fma.f64 n k (.f64 k n)) (*.f64 k k)) (PI.f64))
accuracy	11.176777877028591	(sqrt.f64 (.f64 (/.f64 (fma.f64 n k (.f64 k n)) (*.f64 k k)) (PI.f64)))
accuracy	25.524076236424126	(/.f64 (fma.f64 n k (.f64 k n)) (.f64 k k))
accuracy	29.30514975746795	#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt.f64 (.f64 (/.f64 (fma.f64 n k (.f64 k n)) (*.f64 k k)) (PI.f64))))
accuracy	0.2734375	(/.f64 (PI.f64) k)
accuracy	0.4811325195368841	(.f64 (sqrt.f64 (.f64 (/.f64 (PI.f64) k) n)) (sqrt.f64 #s(literal 2 binary64)))
accuracy	11.180798009109315	(sqrt.f64 (*.f64 (/.f64 (PI.f64) k) n))
accuracy	29.30514975746795	#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (.f64 (sqrt.f64 (.f64 (/.f64 (PI.f64) k) n)) (sqrt.f64 #s(literal 2 binary64))))
accuracy	0.203125	(.f64 (/.f64 (PI.f64) k) (.f64 #s(literal 2 binary64) n))
accuracy	0.2734375	(/.f64 (PI.f64) k)
accuracy	11.176777877028591	(sqrt.f64 (.f64 (/.f64 (PI.f64) k) (.f64 #s(literal 2 binary64) n)))
accuracy	29.30514975746795	#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt.f64 (.f64 (/.f64 (PI.f64) k) (.f64 #s(literal 2 binary64) n))))
accuracy	0.16796875	(sqrt.f64 (/.f64 #s(literal 1 binary64) k))
accuracy	0.19921875	(.f64 #s(approx (/ 1 (sqrt k)) (sqrt.f64 (/.f64 #s(literal 1 binary64) k))) #s(approx (pow ( (* 2 (PI)) n) (/ (- 1 k) 2)) (pow.f64 (.f64 (.f64 #s(literal 2 binary64) n) (PI.f64)) (fma.f64 #s(literal -1/2 binary64) k #s(literal 1/2 binary64)))))
accuracy	0.2266951500392059	(pow.f64 (.f64 (.f64 #s(literal 2 binary64) n) (PI.f64)) (fma.f64 #s(literal -1/2 binary64) k #s(literal 1/2 binary64)))
accuracy	0.27734375	(.f64 (.f64 #s(literal 2 binary64) n) (PI.f64))

Samples

132.0ms

256×

valid

Compiler

Compiled 281 to 41 computations (85.4% saved)

Precisions

Click to see histograms. Total time spent on operations: 72.0ms

ival-mult: 26.0ms (36.2% of total)

ival-sqrt: 16.0ms (22.3% of total)

ival-sub: 9.0ms (12.5% of total)

ival-pow: 9.0ms (12.5% of total)

ival-div: 8.0ms (11.1% of total)

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

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

exact: 1.0ms (1.4% of total)

adjust: 0.0ms (0% of total)

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

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

series46.0ms (0.4%)

Memory

39.2MiB live, 85.3MiB allocated

Counts

25 → 43

Calls

Call 1

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

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

Calls

6 calls:

Time	Variable		Point	Expression
14.0ms	n	@	0	((* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (/ 1 (sqrt k)) (sqrt (/ 1 k)) (/ 1 k) (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt (* (/ (PI) k) (* 2 n))) (* (/ (PI) k) (* 2 n)) (/ (PI) k) (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (* (sqrt (* (/ (PI) k) n)) (sqrt 2)) (sqrt (* (/ (PI) k) n)) (* (/ (PI) k) n) (/ (+ (* n k) (* k n)) (* k k)) (+ (* n k) (* k n)) (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt (* (/ (+ (* n k) (* k n)) (* k k)) (PI))) (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (/ 1 (sqrt k)) (sqrt k) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2)) (* (* 2 n) (PI)) (pow (* (* 2 n) (PI)) (+ (* -1/2 k) 1/2)) (* (/ (+ (* n k) (* k n)) (* k k)) (PI)) (* (sqrt (* (PI) n)) (sqrt 2)) (* (PI) n))
11.0ms	n	@	-inf	((* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (/ 1 (sqrt k)) (sqrt (/ 1 k)) (/ 1 k) (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt (* (/ (PI) k) (* 2 n))) (* (/ (PI) k) (* 2 n)) (/ (PI) k) (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (* (sqrt (* (/ (PI) k) n)) (sqrt 2)) (sqrt (* (/ (PI) k) n)) (* (/ (PI) k) n) (/ (+ (* n k) (* k n)) (* k k)) (+ (* n k) (* k n)) (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt (* (/ (+ (* n k) (* k n)) (* k k)) (PI))) (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (/ 1 (sqrt k)) (sqrt k) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2)) (* (* 2 n) (PI)) (pow (* (* 2 n) (PI)) (+ (* -1/2 k) 1/2)) (* (/ (+ (* n k) (* k n)) (* k k)) (PI)) (* (sqrt (* (PI) n)) (sqrt 2)) (* (PI) n))
10.0ms	n	@	inf	((* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (/ 1 (sqrt k)) (sqrt (/ 1 k)) (/ 1 k) (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt (* (/ (PI) k) (* 2 n))) (* (/ (PI) k) (* 2 n)) (/ (PI) k) (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (* (sqrt (* (/ (PI) k) n)) (sqrt 2)) (sqrt (* (/ (PI) k) n)) (* (/ (PI) k) n) (/ (+ (* n k) (* k n)) (* k k)) (+ (* n k) (* k n)) (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt (* (/ (+ (* n k) (* k n)) (* k k)) (PI))) (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (/ 1 (sqrt k)) (sqrt k) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2)) (* (* 2 n) (PI)) (pow (* (* 2 n) (PI)) (+ (* -1/2 k) 1/2)) (* (/ (+ (* n k) (* k n)) (* k k)) (PI)) (* (sqrt (* (PI) n)) (sqrt 2)) (* (PI) n))
5.0ms	k	@	-inf	((* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (/ 1 (sqrt k)) (sqrt (/ 1 k)) (/ 1 k) (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt (* (/ (PI) k) (* 2 n))) (* (/ (PI) k) (* 2 n)) (/ (PI) k) (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (* (sqrt (* (/ (PI) k) n)) (sqrt 2)) (sqrt (* (/ (PI) k) n)) (* (/ (PI) k) n) (/ (+ (* n k) (* k n)) (* k k)) (+ (* n k) (* k n)) (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt (* (/ (+ (* n k) (* k n)) (* k k)) (PI))) (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (/ 1 (sqrt k)) (sqrt k) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2)) (* (* 2 n) (PI)) (pow (* (* 2 n) (PI)) (+ (* -1/2 k) 1/2)) (* (/ (+ (* n k) (* k n)) (* k k)) (PI)) (* (sqrt (* (PI) n)) (sqrt 2)) (* (PI) n))
3.0ms	k	@	0	((* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (/ 1 (sqrt k)) (sqrt (/ 1 k)) (/ 1 k) (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt (* (/ (PI) k) (* 2 n))) (* (/ (PI) k) (* 2 n)) (/ (PI) k) (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (* (sqrt (* (/ (PI) k) n)) (sqrt 2)) (sqrt (* (/ (PI) k) n)) (* (/ (PI) k) n) (/ (+ (* n k) (* k n)) (* k k)) (+ (* n k) (* k n)) (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt (* (/ (+ (* n k) (* k n)) (* k k)) (PI))) (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (/ 1 (sqrt k)) (sqrt k) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2)) (* (* 2 n) (PI)) (pow (* (* 2 n) (PI)) (+ (* -1/2 k) 1/2)) (* (/ (+ (* n k) (* k n)) (* k k)) (PI)) (* (sqrt (* (PI) n)) (sqrt 2)) (* (PI) n))

simplify212.0ms (2%)

Memory

-4.0MiB live, 184.9MiB allocated

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	152	685
1	500	660
2	1840	602
3	5509	593
0	8397	581

Stop Event

1×	iter limit
1×	node limit

Counts

43 → 43

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

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

rewrite213.0ms (2%)

Memory

-59.1MiB live, 207.4MiB allocated

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	48	282
0	78	275
1	248	244
2	1247	238
0	8353	238

Stop Event

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

Counts

25 → 913

Calls

Call 1

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

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

eval115.0ms (1.1%)

Memory: 33.6MiB live, 164.7MiB allocated
Compiler: Compiled 26 208 to 3 306 computations (87.4% saved)

prune54.0ms (0.5%)

Memory

15.9MiB live, 119.2MiB allocated

Pruning

30 alts after pruning (22 fresh and 8 done)

	Pruned	Kept	Total
New	721	15	736
Fresh	5	7	12
Picked	2	3	5
Done	0	5	5
Total	728	30	758

Accuracy

100.0%

Counts

758 → 30

Alt Table

Click to see full alt table

Status	Accuracy	Program
✓	99.4%	(/.f64 #s(approx (pow (* (* 2 (PI)) n) (/ (- 1 k) 2)) (pow.f64 (.f64 (.f64 (PI.f64) n) #s(literal 2 binary64)) (fma.f64 #s(literal -1/2 binary64) k #s(literal 1/2 binary64)))) (sqrt.f64 k))
	53.9%	(/.f64 #s(approx (pow (* (* 2 (PI)) n) (/ (- 1 k) 2)) (.f64 (sqrt.f64 (.f64 (PI.f64) n)) (sqrt.f64 #s(literal 2 binary64)))) (sqrt.f64 k))
	53.9%	(/.f64 #s(approx (pow (* (* 2 (PI)) n) (/ (- 1 k) 2)) (sqrt.f64 (.f64 (PI.f64) (.f64 n #s(literal 2 binary64))))) (sqrt.f64 k))
	82.1%	(.f64 (pow.f64 (.f64 #s(literal 2 binary64) (.f64 n (PI.f64))) (/.f64 k #s(literal -2 binary64))) (sqrt.f64 (.f64 (*.f64 (/.f64 n k) #s(literal 2 binary64)) (PI.f64))))
	53.9%	(.f64 (pow.f64 k #s(literal -1/2 binary64)) #s(approx (pow ( (* 2 (PI)) n) (/ (- 1 k) 2)) (sqrt.f64 (.f64 (PI.f64) (.f64 n #s(literal 2 binary64))))))
	80.7%	(.f64 (/.f64 (sqrt.f64 (PI.f64)) (pow.f64 (.f64 n (PI.f64)) (/.f64 k #s(literal 2 binary64)))) (/.f64 (sqrt.f64 (.f64 #s(literal 2 binary64) n)) (.f64 (pow.f64 #s(literal 2 binary64) (/.f64 k #s(literal 2 binary64))) (sqrt.f64 k))))
✓	99.4%	(.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) #s(approx (pow ( (* 2 (PI)) n) (/ (- 1 k) 2)) (pow.f64 (.f64 (.f64 #s(literal 2 binary64) n) (PI.f64)) (fma.f64 #s(literal -1/2 binary64) k #s(literal 1/2 binary64)))))
✓	53.8%	(.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) #s(approx (pow ( (* 2 (PI)) n) (/ (- 1 k) 2)) (.f64 (sqrt.f64 (.f64 (PI.f64) n)) (sqrt.f64 #s(literal 2 binary64)))))
	99.4%	(.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) #s(approx (pow ( (* 2 (PI)) n) (/ (- 1 k) 2)) (sqrt.f64 (pow.f64 (.f64 (.f64 n (PI.f64)) #s(literal 2 binary64)) (-.f64 #s(literal 1 binary64) k)))))
	53.9%	(.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) #s(approx (pow ( (* 2 (PI)) n) (/ (- 1 k) 2)) (sqrt.f64 (.f64 (PI.f64) (.f64 n #s(literal 2 binary64))))))
	5.5%	#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (/.f64 (sqrt.f64 (fma.f64 (.f64 n k) (.f64 k k) (.f64 (.f64 k k) (.f64 n k)))) (.f64 k k)))
	53.8%	#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (.f64 (/.f64 (sqrt.f64 (.f64 (PI.f64) n)) (sqrt.f64 k)) (sqrt.f64 #s(literal 2 binary64))))
	53.9%	#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (.f64 (sqrt.f64 (/.f64 (PI.f64) k)) (sqrt.f64 (.f64 n #s(literal 2 binary64)))))
	44.2%	#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (.f64 (sqrt.f64 (/.f64 n k)) (sqrt.f64 (.f64 #s(literal 2 binary64) (PI.f64)))))
✓	44.4%	#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (.f64 (sqrt.f64 (.f64 (/.f64 (PI.f64) k) n)) (sqrt.f64 #s(literal 2 binary64))))
	53.9%	#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (.f64 (sqrt.f64 (.f64 (/.f64 (PI.f64) k) #s(literal 2 binary64))) (sqrt.f64 n)))
	44.3%	#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (.f64 (sqrt.f64 (.f64 (/.f64 n k) #s(literal 2 binary64))) (sqrt.f64 (PI.f64))))
✓	53.8%	#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (.f64 (sqrt.f64 #s(literal 2 binary64)) (.f64 (sqrt.f64 n) (sqrt.f64 (/.f64 (PI.f64) k)))))
✓	44.4%	#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (.f64 (sqrt.f64 #s(literal 2 binary64)) (sqrt.f64 (/.f64 (.f64 (PI.f64) n) k))))
	10.5%	#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (.f64 (sqrt.f64 #s(literal 2 binary64)) (sqrt.f64 (.f64 (/.f64 n k) (/.f64 k k)))))
	44.4%	#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt.f64 (/.f64 (.f64 (PI.f64) (.f64 n #s(literal 2 binary64))) k)))
	10.4%	#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt.f64 (.f64 (fma.f64 (.f64 (/.f64 n k) (/.f64 k k)) (PI.f64) (.f64 (.f64 (/.f64 n k) (/.f64 k k)) (PI.f64))) (PI.f64))))
	13.8%	#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt.f64 (.f64 (/.f64 (fma.f64 (/.f64 (.f64 (neg.f64 k) n) k) (.f64 k k) (.f64 (neg.f64 k) (.f64 n k))) (.f64 (neg.f64 k) (*.f64 k k))) (PI.f64))))
	9.8%	#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt.f64 (.f64 (/.f64 (fma.f64 (.f64 (neg.f64 k) n) (.f64 k k) (.f64 (.f64 (neg.f64 k) k) (.f64 n k))) (.f64 (.f64 (neg.f64 k) k) (*.f64 k k))) (PI.f64))))
	9.3%	#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt.f64 (.f64 (/.f64 (fma.f64 (PI.f64) (.f64 n k) (.f64 (PI.f64) (.f64 n k))) (*.f64 k k)) (PI.f64))))
	24.4%	#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt.f64 (.f64 (/.f64 (.f64 n (+.f64 k k)) (*.f64 k k)) (PI.f64))))
✓	44.5%	#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt.f64 (.f64 (/.f64 (PI.f64) k) (.f64 #s(literal 2 binary64) n))))
	44.3%	#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt.f64 (.f64 (.f64 (*.f64 (/.f64 n k) #s(literal 2 binary64)) (sqrt.f64 (PI.f64))) (sqrt.f64 (PI.f64)))))
✓	44.5%	#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt.f64 (.f64 (.f64 #s(literal 2 binary64) (/.f64 n k)) (PI.f64))))
	38.9%	#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt.f64 (.f64 (sqrt.f64 (/.f64 (.f64 (PI.f64) (PI.f64)) (.f64 k k))) (.f64 #s(literal 2 binary64) n))))

Compiler

Compiled 2 601 to 956 computations (63.2% saved)

regimes116.0ms (1.1%)

Memory

-7.6MiB live, 82.0MiB allocated

Counts

63 → 1

Calls

Call 1

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

Outputs

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

Calls

4 calls:

42.0ms	(.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))))
40.0ms	n
15.0ms	k
15.0ms	(.f64 (.f64 #s(literal 2 binary64) (PI.f64)) n)

Results

Accuracy	Segments	Branch
99.6%	1	`(.f64 (.f64 #s(literal 2 binary64) (PI.f64)) 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	`k`
99.6%	1	`n`

Compiler

Compiled 23 to 23 computations (0% saved)

regimes62.0ms (0.6%)

Memory

-17.9MiB live, 81.9MiB allocated

Counts

43 → 1

Calls

Call 1

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

Outputs

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

Calls

4 calls:

24.0ms	k
15.0ms	(.f64 (.f64 #s(literal 2 binary64) (PI.f64)) n)
11.0ms	n
10.0ms	(.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	`(.f64 (.f64 #s(literal 2 binary64) (PI.f64)) 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	`k`
99.6%	1	`n`

Compiler

Compiled 23 to 23 computations (0% saved)

regimes51.0ms (0.5%)

Memory

34.5MiB live, 78.0MiB allocated

Counts

42 → 1

Calls

Call 1

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

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

Calls

4 calls:

14.0ms	(.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))))
13.0ms	k
11.0ms	n
10.0ms	(.f64 (.f64 #s(literal 2 binary64) (PI.f64)) n)

Results

Accuracy	Segments	Branch
99.4%	1	`(.f64 (.f64 #s(literal 2 binary64) (PI.f64)) n)`
99.4%	1	`(.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) (pow.f64 (.f64 (*.f64 #s(literal 2 binary64) (PI.f64)) n) (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 2 binary64))))`
99.4%	1	`k`
99.4%	1	`n`

Compiler

Compiled 23 to 23 computations (0% saved)

regimes76.0ms (0.7%)

Memory

-14.4MiB live, 31.6MiB allocated

Counts

34 → 2

Calls

Call 1

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

Outputs

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

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

Calls

4 calls:

49.0ms	k
9.0ms	n
9.0ms	(.f64 (.f64 #s(literal 2 binary64) (PI.f64)) n)
8.0ms	(.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
57.1%	3	`(.f64 (.f64 #s(literal 2 binary64) (PI.f64)) n)`
66.4%	2	`(.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) (pow.f64 (.f64 (*.f64 #s(literal 2 binary64) (PI.f64)) n) (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 2 binary64))))`
57.1%	3	`n`
66.3%	2	`k`

Compiler

Compiled 23 to 23 computations (0% saved)

regimes11.0ms (0.1%)

Memory

13.3MiB live, 13.3MiB allocated

Counts

19 → 2

Calls

Call 1

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

Outputs

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

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

Calls

2 calls:

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

Results

Accuracy	Segments	Branch
56.5%	2	`k`
56.6%	2	`(.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) (pow.f64 (.f64 (*.f64 #s(literal 2 binary64) (PI.f64)) n) (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 2 binary64))))`

Compiler

Compiled 17 to 15 computations (11.8% saved)

regimes53.0ms (0.5%)

Memory

-79.0MiB live, 7.1MiB allocated

Counts

15 → 2

Calls

Call 1

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

Outputs

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

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

Calls

1 calls:

52.0ms

(*.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
56.5%	2	`(.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) (pow.f64 (.f64 (*.f64 #s(literal 2 binary64) (PI.f64)) n) (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 2 binary64))))`

Compiler

Compiled 16 to 13 computations (18.8% saved)

regimes9.0ms (0.1%)

Memory

5.6MiB live, 5.6MiB allocated

Counts

13 → 2

Calls

Call 1

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

Outputs

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

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

Calls

2 calls:

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

Results

Accuracy	Segments	Branch
56.5%	2	`k`
56.5%	2	`(.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) (pow.f64 (.f64 (*.f64 #s(literal 2 binary64) (PI.f64)) n) (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 2 binary64))))`

Compiler

Compiled 17 to 15 computations (11.8% saved)

regimes10.0ms (0.1%)

Memory

13.1MiB live, 13.1MiB allocated

Counts

6 → 2

Calls

Call 1

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

Outputs

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

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

Calls

4 calls:

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

Results

Accuracy	Segments	Branch
44.5%	1	`(.f64 (.f64 #s(literal 2 binary64) (PI.f64)) n)`
44.5%	1	`n`
47.1%	2	`k`
47.1%	2	`(.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) (pow.f64 (.f64 (*.f64 #s(literal 2 binary64) (PI.f64)) n) (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 2 binary64))))`

Compiler

Compiled 23 to 23 computations (0% saved)

regimes8.0ms (0.1%)

Memory

14.1MiB live, 14.1MiB allocated

Accuracy

Total -0.1b remaining (-0.2%)

Threshold costs -0.1b (-0.2%)

Counts

4 → 1

Calls

Call 1

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

Outputs
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt.f64 (.f64 (.f64 #s(literal 2 binary64) (/.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
44.5%	1	`(.f64 (.f64 #s(literal 2 binary64) (PI.f64)) n)`
44.5%	1	`n`
44.5%	1	`k`
44.5%	1	`(.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) (pow.f64 (.f64 (*.f64 #s(literal 2 binary64) (PI.f64)) n) (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 2 binary64))))`

Compiler

Compiled 23 to 23 computations (0% saved)

bsearch1.0ms (0%)

Memory

0.9MiB live, 0.9MiB allocated

Algorithm

1×	left-value

Steps

Time	Left	Right
0.0ms	1.2922943846369765e-62	2.075795724381046e-62

Compiler

Compiled 19 to 18 computations (5.3% saved)

bsearch0.0ms (0%)

Memory

0.6MiB live, 0.6MiB allocated

Algorithm

1×	left-value

Steps

Time	Left	Right
0.0ms	0.0	1.0935999357109921e-125

Compiler

Compiled 19 to 18 computations (5.3% saved)

bsearch0.0ms (0%)

Memory

0.5MiB live, 0.5MiB allocated

Algorithm

1×	left-value

Steps

Time	Left	Right
0.0ms	0.0	1.0935999357109921e-125

Compiler

Compiled 19 to 18 computations (5.3% saved)

bsearch0.0ms (0%)

Memory

0.5MiB live, 0.5MiB allocated

Algorithm

1×	left-value

Steps

Time	Left	Right
0.0ms	0.0	1.0935999357109921e-125

Compiler

Compiled 19 to 18 computations (5.3% saved)

bsearch0.0ms (0%)

Memory

0.5MiB live, 0.5MiB allocated

Algorithm

1×	left-value

Steps

Time	Left	Right
0.0ms	0.0	1.0935999357109921e-125

Compiler

Compiled 19 to 18 computations (5.3% saved)

simplify32.0ms (0.3%)

Memory

-11.2MiB live, 33.2MiB allocated

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	81	472
1	99	450
2	115	450
3	136	450
4	153	450
5	172	450
6	206	450
7	271	450
8	302	450
9	335	450
10	345	450

Stop Event

1×

saturated

Calls

Call 1

Inputs
(/.f64 (.f64 (sqrt.f64 (.f64 (.f64 (PI.f64) n) #s(literal 2 binary64))) #s(literal 1 binary64)) (.f64 (pow.f64 (.f64 (.f64 (PI.f64) n) #s(literal 2 binary64)) (/.f64 k #s(literal 2 binary64))) (sqrt.f64 k)))
(.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) #s(approx (pow ( (* 2 (PI)) n) (/ (- 1 k) 2)) (.f64 (pow.f64 (.f64 (.f64 (PI.f64) n) #s(literal 2 binary64)) (.f64 #s(literal -1/2 binary64) k)) (sqrt.f64 (.f64 (.f64 (PI.f64) n) #s(literal 2 binary64))))))
(/.f64 #s(approx (pow (* (* 2 (PI)) n) (/ (- 1 k) 2)) (pow.f64 (.f64 (.f64 (PI.f64) n) #s(literal 2 binary64)) (fma.f64 #s(literal -1/2 binary64) k #s(literal 1/2 binary64)))) (sqrt.f64 k))
(if (<=.f64 (.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) (pow.f64 (.f64 (.f64 #s(literal 2 binary64) (PI.f64)) n) (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 2 binary64)))) #s(literal 578960446186581/28948022309329048855892746252171976963317496166410141009864396001978282409984 binary64)) #s(approx ( (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt.f64 (.f64 (sqrt.f64 (/.f64 (.f64 (PI.f64) (PI.f64)) (.f64 k k))) (.f64 #s(literal 2 binary64) n)))) #s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (/.f64 (sqrt.f64 (.f64 (.f64 (PI.f64) n) #s(literal 2 binary64))) (sqrt.f64 k))))
(if (<=.f64 (.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) (pow.f64 (.f64 (.f64 #s(literal 2 binary64) (PI.f64)) n) (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 2 binary64)))) #s(literal 0 binary64)) #s(approx ( (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt.f64 (.f64 (/.f64 (.f64 n (+.f64 k k)) (.f64 k k)) (PI.f64)))) #s(approx ( (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (/.f64 (sqrt.f64 (.f64 (.f64 (PI.f64) n) #s(literal 2 binary64))) (sqrt.f64 k))))
(if (<=.f64 (.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) (pow.f64 (.f64 (.f64 #s(literal 2 binary64) (PI.f64)) n) (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 2 binary64)))) #s(literal 0 binary64)) #s(approx ( (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt.f64 (.f64 (/.f64 (.f64 n (+.f64 k k)) (.f64 k k)) (PI.f64)))) #s(approx ( (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (.f64 (sqrt.f64 (/.f64 (PI.f64) k)) (sqrt.f64 (.f64 #s(literal 2 binary64) n)))))
(if (<=.f64 (.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) (pow.f64 (.f64 (.f64 #s(literal 2 binary64) (PI.f64)) n) (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 2 binary64)))) #s(literal 0 binary64)) #s(approx ( (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt.f64 (.f64 (/.f64 (.f64 n (+.f64 k k)) (.f64 k k)) (PI.f64)))) #s(approx ( (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (.f64 (sqrt.f64 (.f64 #s(literal 2 binary64) (/.f64 (PI.f64) k))) (sqrt.f64 n))))
(if (<=.f64 (.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) (pow.f64 (.f64 (.f64 #s(literal 2 binary64) (PI.f64)) n) (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 2 binary64)))) #s(literal 0 binary64)) #s(approx ( (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt.f64 (.f64 (/.f64 (.f64 n (+.f64 k k)) (.f64 k k)) (PI.f64)))) #s(approx ( (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt.f64 (.f64 (.f64 #s(literal 2 binary64) (/.f64 n k)) (PI.f64)))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt.f64 (.f64 (.f64 #s(literal 2 binary64) (/.f64 n k)) (PI.f64))))

Outputs
(/.f64 (.f64 (sqrt.f64 (.f64 (.f64 (PI.f64) n) #s(literal 2 binary64))) #s(literal 1 binary64)) (.f64 (pow.f64 (.f64 (.f64 (PI.f64) n) #s(literal 2 binary64)) (/.f64 k #s(literal 2 binary64))) (sqrt.f64 k)))
(/.f64 (sqrt.f64 (.f64 (.f64 (PI.f64) n) #s(literal 2 binary64))) (.f64 (pow.f64 (.f64 (*.f64 (PI.f64) n) #s(literal 2 binary64)) (/.f64 k #s(literal 2 binary64))) (sqrt.f64 k)))
(.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) #s(approx (pow ( (* 2 (PI)) n) (/ (- 1 k) 2)) (.f64 (pow.f64 (.f64 (.f64 (PI.f64) n) #s(literal 2 binary64)) (.f64 #s(literal -1/2 binary64) k)) (sqrt.f64 (.f64 (.f64 (PI.f64) n) #s(literal 2 binary64))))))
(.f64 (pow.f64 (sqrt.f64 k) #s(literal -1 binary64)) #s(approx (pow ( (* 2 (PI)) n) (/ (- 1 k) 2)) (.f64 (pow.f64 (.f64 (.f64 (PI.f64) n) #s(literal 2 binary64)) (.f64 #s(literal -1/2 binary64) k)) (sqrt.f64 (.f64 (.f64 (PI.f64) n) #s(literal 2 binary64))))))
(/.f64 #s(approx (pow (* (* 2 (PI)) n) (/ (- 1 k) 2)) (pow.f64 (.f64 (.f64 (PI.f64) n) #s(literal 2 binary64)) (fma.f64 #s(literal -1/2 binary64) k #s(literal 1/2 binary64)))) (sqrt.f64 k))
(if (<=.f64 (.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) (pow.f64 (.f64 (.f64 #s(literal 2 binary64) (PI.f64)) n) (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 2 binary64)))) #s(literal 578960446186581/28948022309329048855892746252171976963317496166410141009864396001978282409984 binary64)) #s(approx ( (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt.f64 (.f64 (sqrt.f64 (/.f64 (.f64 (PI.f64) (PI.f64)) (.f64 k k))) (.f64 #s(literal 2 binary64) n)))) #s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (/.f64 (sqrt.f64 (.f64 (.f64 (PI.f64) n) #s(literal 2 binary64))) (sqrt.f64 k))))
(if (<=.f64 (.f64 (pow.f64 (sqrt.f64 k) #s(literal -1 binary64)) (pow.f64 (.f64 (.f64 #s(literal 2 binary64) (PI.f64)) n) (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 2 binary64)))) #s(literal 578960446186581/28948022309329048855892746252171976963317496166410141009864396001978282409984 binary64)) #s(approx ( (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt.f64 (.f64 (sqrt.f64 (/.f64 (.f64 (PI.f64) (PI.f64)) (.f64 k k))) (.f64 #s(literal 2 binary64) n)))) #s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (/.f64 (sqrt.f64 (.f64 (.f64 (PI.f64) n) #s(literal 2 binary64))) (sqrt.f64 k))))
(if (<=.f64 (.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) (pow.f64 (.f64 (.f64 #s(literal 2 binary64) (PI.f64)) n) (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 2 binary64)))) #s(literal 0 binary64)) #s(approx ( (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt.f64 (.f64 (/.f64 (.f64 n (+.f64 k k)) (.f64 k k)) (PI.f64)))) #s(approx ( (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (/.f64 (sqrt.f64 (.f64 (.f64 (PI.f64) n) #s(literal 2 binary64))) (sqrt.f64 k))))
(if (<=.f64 (.f64 (pow.f64 (sqrt.f64 k) #s(literal -1 binary64)) (pow.f64 (.f64 (.f64 #s(literal 2 binary64) (PI.f64)) n) (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 2 binary64)))) #s(literal 0 binary64)) #s(approx ( (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt.f64 (.f64 (/.f64 (.f64 n (+.f64 k k)) (.f64 k k)) (PI.f64)))) #s(approx ( (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (/.f64 (sqrt.f64 (.f64 (.f64 (PI.f64) n) #s(literal 2 binary64))) (sqrt.f64 k))))
(if (<=.f64 (.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) (pow.f64 (.f64 (.f64 #s(literal 2 binary64) (PI.f64)) n) (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 2 binary64)))) #s(literal 0 binary64)) #s(approx ( (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt.f64 (.f64 (/.f64 (.f64 n (+.f64 k k)) (.f64 k k)) (PI.f64)))) #s(approx ( (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (.f64 (sqrt.f64 (/.f64 (PI.f64) k)) (sqrt.f64 (.f64 #s(literal 2 binary64) n)))))
(if (<=.f64 (.f64 (pow.f64 (sqrt.f64 k) #s(literal -1 binary64)) (pow.f64 (.f64 (.f64 #s(literal 2 binary64) (PI.f64)) n) (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 2 binary64)))) #s(literal 0 binary64)) #s(approx ( (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt.f64 (.f64 (/.f64 (.f64 n (+.f64 k k)) (.f64 k k)) (PI.f64)))) #s(approx ( (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (.f64 (sqrt.f64 (/.f64 (PI.f64) k)) (sqrt.f64 (.f64 #s(literal 2 binary64) n)))))
(if (<=.f64 (.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) (pow.f64 (.f64 (.f64 #s(literal 2 binary64) (PI.f64)) n) (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 2 binary64)))) #s(literal 0 binary64)) #s(approx ( (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt.f64 (.f64 (/.f64 (.f64 n (+.f64 k k)) (.f64 k k)) (PI.f64)))) #s(approx ( (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (.f64 (sqrt.f64 (.f64 #s(literal 2 binary64) (/.f64 (PI.f64) k))) (sqrt.f64 n))))
(if (<=.f64 (.f64 (pow.f64 (sqrt.f64 k) #s(literal -1 binary64)) (pow.f64 (.f64 (.f64 #s(literal 2 binary64) (PI.f64)) n) (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 2 binary64)))) #s(literal 0 binary64)) #s(approx ( (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt.f64 (.f64 (/.f64 (.f64 n (+.f64 k k)) (.f64 k k)) (PI.f64)))) #s(approx ( (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (.f64 (sqrt.f64 (.f64 #s(literal 2 binary64) (/.f64 (PI.f64) k))) (sqrt.f64 n))))
(if (<=.f64 (.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) (pow.f64 (.f64 (.f64 #s(literal 2 binary64) (PI.f64)) n) (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 2 binary64)))) #s(literal 0 binary64)) #s(approx ( (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt.f64 (.f64 (/.f64 (.f64 n (+.f64 k k)) (.f64 k k)) (PI.f64)))) #s(approx ( (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt.f64 (.f64 (.f64 #s(literal 2 binary64) (/.f64 n k)) (PI.f64)))))
(if (<=.f64 (.f64 (pow.f64 (sqrt.f64 k) #s(literal -1 binary64)) (pow.f64 (.f64 (.f64 #s(literal 2 binary64) (PI.f64)) n) (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 2 binary64)))) #s(literal 0 binary64)) #s(approx ( (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt.f64 (.f64 (/.f64 (.f64 n (+.f64 k k)) (.f64 k k)) (PI.f64)))) #s(approx ( (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt.f64 (.f64 (.f64 #s(literal 2 binary64) (/.f64 n k)) (PI.f64)))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt.f64 (.f64 (.f64 #s(literal 2 binary64) (/.f64 n k)) (PI.f64))))

derivations854.0ms (8.2%)

Memory

-13.5MiB live, 794.0MiB allocated

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	13	38
0	22	38
1	83	35
2	446	35
3	4007	29
0	8921	29
0	48	282
0	78	275
1	248	244
2	1247	238
0	8353	238
0	120	502
1	378	489
2	1377	453
3	4131	453
0	8166	441
0	46	238
0	76	212
1	240	200
2	1121	200
0	8962	200
0	50	282
0	81	250
1	244	240
2	1225	240
0	8204	240

Stop Event

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

Compiler

Compiled 472 to 83 computations (82.4% saved)

preprocess90.0ms (0.9%)

Memory: 24.1MiB live, 122.8MiB allocated
Compiler: Compiled 976 to 192 computations (80.3% saved)

end0.0ms (0%)

Memory: 0.0MiB live, 0.0MiB allocated

Iter	Nodes	Cost
0	31	88
1	71	76
2	145	74
3	227	74
4	296	74
5	363	74
6	428	74
7	501	74
8	528	74
9	541	74
10	547	74
0	13	16
0	22	16
1	37	14
2	50	14
3	67	14
4	80	14
5	98	14
6	132	14
7	202	14
8	227	14
9	247	14
10	257	14
0	257	14

Iter	Nodes	Cost
0	13	54
0	22	54
1	37	52
2	50	52
3	67	52
4	80	52
5	98	52
6	132	52
7	202	52
8	227	52
9	247	52
10	257	52
0	257	52

Iter	Nodes	Cost
0	46	358
0	76	354
1	125	338
2	189	338
3	303	338
4	462	338
5	669	338
6	834	338
7	888	338
8	910	338
9	919	338
0	919	338

Iter	Nodes	Cost
0	50	397
0	81	393
1	126	387
2	189	387
3	254	387
4	317	387
5	390	387
6	571	387
7	723	387
8	772	387
9	822	387
10	852	387
0	852	387

Iter	Nodes	Cost
0	81	472
1	99	450
2	115	450
3	136	450
4	153	450
5	172	450
6	206	450
7	271	450
8	302	450
9	335	450
10	345	450

Iter	Nodes	Cost
0	31	88
1	71	76
2	145	74
3	227	74
4	296	74
5	363	74
6	428	74
7	501	74
8	528	74
9	541	74
10	547	74
0	13	16
0	22	16
1	37	14
2	50	14
3	67	14
4	80	14
5	98	14
6	132	14
7	202	14
8	227	14
9	247	14
10	257	14
0	257	14

Iter	Nodes	Cost
0	13	54
0	22	54
1	37	52
2	50	52
3	67	52
4	80	52
5	98	52
6	132	52
7	202	52
8	227	52
9	247	52
10	257	52
0	257	52

Iter	Nodes	Cost
0	46	358
0	76	354
1	125	338
2	189	338
3	303	338
4	462	338
5	669	338
6	834	338
7	888	338
8	910	338
9	919	338
0	919	338

Iter	Nodes	Cost
0	50	397
0	81	393
1	126	387
2	189	387
3	254	387
4	317	387
5	390	387
6	571	387
7	723	387
8	772	387
9	822	387
10	852	387
0	852	387

Iter	Nodes	Cost
0	81	472
1	99	450
2	115	450
3	136	450
4	153	450
5	172	450
6	206	450
7	271	450
8	302	450
9	335	450
10	345	450

start0.0ms (0%)

analyze132.0ms (1.3%)

sample4.9s (46.7%)

explain242.0ms (2.3%)

preprocess44.0ms (0.4%)

eval0.0ms (0%)

prune0.0ms (0%)

simplify11.0ms (0.1%)

localize43.0ms (0.4%)

series163.0ms (1.6%)

simplify168.0ms (1.6%)

rewrite204.0ms (2%)

eval87.0ms (0.8%)

prune23.0ms (0.2%)

simplify28.0ms (0.3%)

localize193.0ms (1.9%)

series150.0ms (1.4%)

simplify220.0ms (2.1%)

rewrite217.0ms (2.1%)

eval299.0ms (2.9%)

prune88.0ms (0.8%)

simplify28.0ms (0.3%)

localize152.0ms (1.5%)

series70.0ms (0.7%)

simplify128.0ms (1.2%)

rewrite237.0ms (2.3%)

eval212.0ms (2%)

prune88.0ms (0.8%)

simplify145.0ms (1.4%)

localize179.0ms (1.7%)

series46.0ms (0.4%)

simplify212.0ms (2%)

rewrite213.0ms (2%)

eval115.0ms (1.1%)

prune54.0ms (0.5%)

regimes116.0ms (1.1%)

regimes62.0ms (0.6%)

regimes51.0ms (0.5%)

regimes76.0ms (0.7%)

regimes11.0ms (0.1%)

regimes53.0ms (0.5%)

regimes9.0ms (0.1%)

regimes10.0ms (0.1%)

regimes8.0ms (0.1%)

bsearch1.0ms (0%)

bsearch0.0ms (0%)

bsearch0.0ms (0%)

bsearch0.0ms (0%)

bsearch0.0ms (0%)

simplify32.0ms (0.3%)

derivations854.0ms (8.2%)

preprocess90.0ms (0.9%)

end0.0ms (0%)

Profiling

Iter	Nodes	Cost
0	31	88
1	71	76
2	145	74
3	227	74
4	296	74
5	363	74
6	428	74
7	501	74
8	528	74
9	541	74
10	547	74
0	13	16
0	22	16
1	37	14
2	50	14
3	67	14
4	80	14
5	98	14
6	132	14
7	202	14
8	227	14
9	247	14
10	257	14
0	257	14

Iter	Nodes	Cost
0	13	54
0	22	54
1	37	52
2	50	52
3	67	52
4	80	52
5	98	52
6	132	52
7	202	52
8	227	52
9	247	52
10	257	52
0	257	52

Iter	Nodes	Cost
0	46	358
0	76	354
1	125	338
2	189	338
3	303	338
4	462	338
5	669	338
6	834	338
7	888	338
8	910	338
9	919	338
0	919	338

Iter	Nodes	Cost
0	50	397
0	81	393
1	126	387
2	189	387
3	254	387
4	317	387
5	390	387
6	571	387
7	723	387
8	772	387
9	822	387
10	852	387
0	852	387

Iter	Nodes	Cost
0	81	472
1	99	450
2	115	450
3	136	450
4	153	450
5	172	450
6	206	450
7	271	450
8	302	450
9	335	450
10	345	450