Metrics for Migdal et al, Equation (51)

start0.0ms (0%)

Memory: 0.0MiB live, 0.0MiB allocated; 0ms collecting garbage

analyze155.0ms (1.3%)

Memory

-18.1MiB live, 134.8MiB allocated; 44ms collecting garbage

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)

sample4.2s (36%)

Memory

175.5MiB live, 6 260.0MiB allocated; 1.4s collecting garbage

Samples

1.3s	4 471×	1	invalid
1.3s	8 255×	0	valid
573.0ms	1 474×	2	invalid
88.0ms	362×	0	invalid
27.0ms	230×	0	exit
0.0ms	1×	1	valid

Precisions

Click to see histograms. Total time spent on operations: 2.5s

ival-pow: 737.0ms (29.8% of total)

ival-mult: 498.0ms (20.1% of total)

ival-div: 453.0ms (18.3% of total)

ival-sqrt: 261.0ms (10.5% of total)

adjust: 199.0ms (8% of total)

ival-pi: 159.0ms (6.4% of total)

ival-sub: 130.0ms (5.2% of total)

exact: 19.0ms (0.8% of total)

ival-true: 13.0ms (0.5% of total)

ival-assert: 7.0ms (0.3% of total)

Bogosity

explain170.0ms (1.4%)

Memory

12.2MiB live, 389.4MiB allocated; 30ms collecting garbage

FPErrors

Click to see full error table

Ground Truth	Overpredictions	Example	Example	Subexpression
2	86	(2.3365515978327255e-176 3.95359494566337e-112)	-	`(pow.f64 (.f64 (.f64 #s(literal 2 binary64) (PI.f64)) n) (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 2 binary64)))`
0	0	-	-	`k`
0	0	-	-	`n`
0	0	-	-	`(/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 2 binary64))`
0	0	-	-	`#s(literal 1 binary64)`
0	0	-	-	`(.f64 (.f64 #s(literal 2 binary64) (PI.f64)) n)`
0	0	-	-	`(sqrt.f64 k)`
0	0	-	-	`#s(literal 2 binary64)`
0	0	-	-	`(/.f64 #s(literal 1 binary64) (sqrt.f64 k))`
0	0	-	-	`(-.f64 #s(literal 1 binary64) k)`
0	0	-	-	`(*.f64 #s(literal 2 binary64) (PI.f64))`
0	0	-	-	`(.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) (pow.f64 (.f64 (*.f64 #s(literal 2 binary64) (PI.f64)) n) (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 2 binary64))))`
0	0	-	-	`(PI.f64)`

Explanations

Click to see full explanations table

Operator	Subexpression	Explanation	Count
`pow.f64`	`(pow.f64 (.f64 (.f64 #s(literal 2 binary64) (PI.f64)) n) (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 2 binary64)))`	sensitivity	88	18

Confusion

	Predicted +	Predicted -
+	2	0
-	86	168

Precision

0.022727272727272728

Recall

1.0

Confusion?

	Predicted +	Predicted Maybe	Predicted -
+	2	0	0
-	86	18	150

Precision?

0.018867924528301886

Recall?

1.0

Freqs

test

number	freq
0	168
1	88

Total Confusion?

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

Precision?

1.0

Recall?

1.0

Samples

68.0ms

512×

valid

Compiler

Compiled 128 to 43 computations (66.4% saved)

Precisions

Click to see histograms. Total time spent on operations: 39.0ms

ival-pow: 10.0ms (25.6% of total)

ival-mult: 9.0ms (23% of total)

ival-div: 7.0ms (17.9% of total)

ival-sqrt: 6.0ms (15.3% of total)

ival-sub: 3.0ms (7.7% of total)

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

exact: 1.0ms (2.6% of total)

adjust: 0.0ms (0% of total)

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

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

preprocess29.0ms (0.2%)

Memory

-7.5MiB live, 38.8MiB allocated; 4ms collecting garbage

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: 0.0MiB live, 0.0MiB allocated; 0ms collecting garbage
Compiler: Compiled 0 to 2 computations (-∞% saved)

prune0.0ms (0%)

Memory

0.7MiB live, 0.7MiB allocated; 0ms collecting garbage

Alt Table

Click to see full alt table

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

Compiler

Compiled 16 to 13 computations (18.8% saved)

simplify8.0ms (0.1%)

Memory

15.7MiB live, 15.7MiB allocated; 0ms collecting garbage

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

-6.9MiB live, 84.6MiB allocated; 7ms collecting garbage

Localize:

Found 4 expressions of interest:

New	Metric	Score
accuracy	0.14182889375630678	(pow.f64 (.f64 (.f64 #s(literal 2 binary64) (PI.f64)) n) (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 2 binary64)))
accuracy	0.15234375	(.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) (pow.f64 (.f64 (*.f64 #s(literal 2 binary64) (PI.f64)) n) (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 2 binary64))))
accuracy	0.24609375	(.f64 (.f64 #s(literal 2 binary64) (PI.f64)) n)
accuracy	0.26953125	(/.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: 19.0ms

ival-pow: 6.0ms (30.9% of total)

ival-mult: 5.0ms (25.8% of total)

ival-div: 3.0ms (15.5% of total)

ival-sqrt: 2.0ms (10.3% of total)

ival-pi: 1.0ms (5.2% of total)

ival-sub: 1.0ms (5.2% 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)

series73.0ms (0.6%)

Memory

1.3MiB live, 145.2MiB allocated; 13ms collecting garbage

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
34.0ms	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))
23.0ms	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))
8.0ms	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))
3.0ms	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))

simplify252.0ms (2.1%)

Memory

-41.9MiB live, 181.2MiB allocated; 145ms collecting garbage

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))))

rewrite232.0ms (2%)

Memory

29.7MiB live, 262.4MiB allocated; 24ms collecting garbage

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))

eval57.0ms (0.5%)

Memory: -6.5MiB live, 132.2MiB allocated; 22ms collecting garbage
Compiler: Compiled 7 537 to 1 169 computations (84.5% saved)

prune22.0ms (0.2%)

Memory

14.5MiB live, 60.5MiB allocated; 5ms collecting garbage

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

100.0%

Counts

339 → 18

Alt Table

Click to see full alt table

Status	Accuracy	Program
	29.8%	(/.f64 (pow.f64 (*.f64 #s(literal 0 binary64) n) (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 8 binary64))) (sqrt.f64 k))
	99.5%	(.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))))
	71.8%	(.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)))))
	71.8%	(.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)))
	71.7%	(.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))))
▶	99.5%	(.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) (pow.f64 (fma.f64 (.f64 (sqrt.f64 (PI.f64)) n) (sqrt.f64 (PI.f64)) (*.f64 n (PI.f64))) (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 2 binary64))))
	99.2%	(.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) (pow.f64 (.f64 (pow.f64 (cbrt.f64 (PI.f64)) #s(literal 2 binary64)) (.f64 (.f64 (cbrt.f64 (PI.f64)) n) #s(literal 2 binary64))) (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 2 binary64))))
	99.5%	(.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))))
	71.8%	(.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)))))
▶	57.0%	(.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))))))
	45.8%	(.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)))))
	45.2%	(.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)))))
	96.6%	(.f64 (/.f64 #s(literal 1 binary64) (exp.f64 (.f64 (.f64 #s(literal 2 binary64) (log.f64 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))))
	96.6%	(.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))))
	52.3%	#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)))))
▶	52.0%	#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (/.f64 (.f64 (sqrt.f64 #s(literal 2 binary64)) (fma.f64 (.f64 (log.f64 (.f64 (.f64 #s(literal 2 binary64) n) (PI.f64))) (sqrt.f64 (.f64 (.f64 (pow.f64 k #s(literal 3 binary64)) (PI.f64)) n))) #s(literal -1/2 binary64) (sqrt.f64 (.f64 (.f64 (PI.f64) n) k)))) k))
▶	99.6%	#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (.f64 (pow.f64 (.f64 (*.f64 #s(literal 2 binary64) n) (PI.f64)) (fma.f64 #s(literal -1/2 binary64) k #s(literal 1/2 binary64))) (sqrt.f64 (/.f64 #s(literal 1 binary64) k))))
▶	35.4%	#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 1 022 to 726 computations (29% saved)

simplify316.0ms (2.7%)

Memory

-20.4MiB live, 309.1MiB allocated; 108ms collecting garbage

Localize:

Found 20 expressions of interest:

New	Metric	Score
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)) (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))))))
cost-diff	5	(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)))
cost-diff	5	(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))))
cost-diff	0	(sqrt.f64 #s(literal 2 binary64))
cost-diff	0	(.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))))
cost-diff	0	(/.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)
cost-diff	0	#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))
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 (fma.f64 (.f64 (sqrt.f64 (PI.f64)) n) (sqrt.f64 (PI.f64)) (*.f64 n (PI.f64))) (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 2 binary64))))
cost-diff	5	(fma.f64 (.f64 (sqrt.f64 (PI.f64)) n) (sqrt.f64 (PI.f64)) (.f64 n (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	(.f64 (.f64 #s(literal 2 binary64) n) (PI.f64))
cost-diff	0	(pow.f64 (.f64 (.f64 #s(literal 2 binary64) n) (PI.f64)) (fma.f64 #s(literal -1/2 binary64) k #s(literal 1/2 binary64)))
cost-diff	0	(.f64 (pow.f64 (.f64 (*.f64 #s(literal 2 binary64) n) (PI.f64)) (fma.f64 #s(literal -1/2 binary64) k #s(literal 1/2 binary64))) (sqrt.f64 (/.f64 #s(literal 1 binary64) k)))
cost-diff	0	#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (.f64 (pow.f64 (.f64 (*.f64 #s(literal 2 binary64) n) (PI.f64)) (fma.f64 #s(literal -1/2 binary64) k #s(literal 1/2 binary64))) (sqrt.f64 (/.f64 #s(literal 1 binary64) k))))

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	66	710
0	116	705
1	210	683
2	447	663
3	1316	653
4	3222	653
5	5973	653
0	8242	645

Stop Event

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

Calls

Call 1

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

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

localize282.0ms (2.4%)

Memory

-10.7MiB live, 380.2MiB allocated; 29ms collecting garbage

Localize:

Found 20 expressions of interest:

New	Metric	Score
accuracy	0.4560737793053261	(.f64 (sqrt.f64 (.f64 (PI.f64) n)) (sqrt.f64 #s(literal 2 binary64)))
accuracy	0.47169877930532605	(.f64 (log.f64 (.f64 (*.f64 #s(literal 2 binary64) n) (PI.f64))) (sqrt.f64 #s(literal 2 binary64)))
accuracy	0.537441259768442	(pow.f64 (log.f64 (.f64 (.f64 #s(literal 2 binary64) n) (PI.f64))) #s(literal 2 binary64))
accuracy	27.19576199004364	#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)))))
accuracy	13.226801376516605	(/.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)
accuracy	16.262801830139225	(sqrt.f64 (.f64 (.f64 (PI.f64) n) k))
accuracy	20.547944470701154	(sqrt.f64 (.f64 (.f64 (pow.f64 k #s(literal 3 binary64)) (PI.f64)) n))
accuracy	34.440854210987645	#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))
accuracy	0.24609375	(*.f64 n (PI.f64))
accuracy	0.26953125	(/.f64 #s(literal 1 binary64) (sqrt.f64 k))
accuracy	0.28125	(*.f64 (sqrt.f64 (PI.f64)) n)
accuracy	1.0	(sqrt.f64 (PI.f64))
accuracy	0.24609375	(*.f64 (PI.f64) n)
accuracy	0.44568256837909415	(.f64 (sqrt.f64 #s(literal 2 binary64)) (sqrt.f64 (/.f64 (.f64 (PI.f64) n) k)))
accuracy	13.860803468935625	(sqrt.f64 (/.f64 (*.f64 (PI.f64) n) k))
accuracy	34.84536208278765	#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	0.1015625	(sqrt.f64 (/.f64 #s(literal 1 binary64) k))
accuracy	0.14182889375630678	(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	0.15234375	(.f64 (pow.f64 (.f64 (*.f64 #s(literal 2 binary64) n) (PI.f64)) (fma.f64 #s(literal -1/2 binary64) k #s(literal 1/2 binary64))) (sqrt.f64 (/.f64 #s(literal 1 binary64) k)))
accuracy	0.24609375	(.f64 (.f64 #s(literal 2 binary64) n) (PI.f64))

Samples

188.0ms

256×

valid

Compiler

Compiled 588 to 63 computations (89.3% saved)

Precisions

Click to see histograms. Total time spent on operations: 150.0ms

ival-mult: 94.0ms (62.5% of total)

ival-pow: 19.0ms (12.6% of total)

ival-sqrt: 14.0ms (9.3% of total)

ival-div: 9.0ms (6% of total)

ival-add: 6.0ms (4% of total)

ival-log: 3.0ms (2% of total)

ival-pow2: 3.0ms (2% of total)

ival-pi: 1.0ms (0.7% of total)

ival-sub: 1.0ms (0.7% of total)

exact: 1.0ms (0.7% of total)

adjust: 0.0ms (0% of total)

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

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

series229.0ms (1.9%)

Memory

37.5MiB live, 271.1MiB allocated; 19ms collecting garbage

Counts

29 → 83

Calls

Call 1

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

Calls

6 calls:

Time	Variable		Point	Expression
57.0ms	n	@	0	((* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (* (pow (* (* 2 n) (PI)) (+ (* -1/2 k) 1/2)) (sqrt (/ 1 k))) (pow (* (* 2 n) (PI)) (+ (* -1/2 k) 1/2)) (* (* 2 n) (PI)) (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (* (sqrt 2) (sqrt (/ (* (PI) n) k))) (sqrt 2) (sqrt (/ (* (PI) n) k)) (+ (* (* (sqrt (PI)) n) (sqrt (PI))) (* n (PI))) (* (/ 1 (sqrt k)) (pow (+ (* (* (sqrt (PI)) n) (sqrt (PI))) (* n (PI))) (/ (- 1 k) 2))) (/ 1 (sqrt k)) (sqrt k) (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (/ (* (sqrt 2) (+ (* (* (log (* (* 2 n) (PI))) (sqrt (* (* (pow k 3) (PI)) n))) -1/2) (sqrt (* (* (PI) n) k)))) k) (* (sqrt 2) (+ (* (* (log (* (* 2 n) (PI))) (sqrt (* (* (pow k 3) (PI)) n))) -1/2) (sqrt (* (* (PI) n) k)))) (+ (* (* (sqrt (* (PI) n)) (+ (* (* (* (pow (log (* (* 2 n) (PI))) 2) (sqrt 2)) 1/8) k) (* (* (log (* (* 2 n) (PI))) (sqrt 2)) -1/2))) k) (* (sqrt (* (PI) n)) (sqrt 2))) (+ (* (* (* (pow (log (* (* 2 n) (PI))) 2) (sqrt 2)) 1/8) k) (* (* (log (* (* 2 n) (PI))) (sqrt 2)) -1/2)) (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt (/ 1 k)) (* (PI) n) (sqrt (PI)) (* (sqrt (PI)) n) (* n (PI)) (sqrt (* (* (pow k 3) (PI)) n)) (sqrt (* (* (PI) n) k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2)) (pow (log (* (* 2 n) (PI))) 2) (* (log (* (* 2 n) (PI))) (sqrt 2)) (* (sqrt (* (PI) n)) (sqrt 2)))
55.0ms	n	@	-inf	((* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (* (pow (* (* 2 n) (PI)) (+ (* -1/2 k) 1/2)) (sqrt (/ 1 k))) (pow (* (* 2 n) (PI)) (+ (* -1/2 k) 1/2)) (* (* 2 n) (PI)) (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (* (sqrt 2) (sqrt (/ (* (PI) n) k))) (sqrt 2) (sqrt (/ (* (PI) n) k)) (+ (* (* (sqrt (PI)) n) (sqrt (PI))) (* n (PI))) (* (/ 1 (sqrt k)) (pow (+ (* (* (sqrt (PI)) n) (sqrt (PI))) (* n (PI))) (/ (- 1 k) 2))) (/ 1 (sqrt k)) (sqrt k) (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (/ (* (sqrt 2) (+ (* (* (log (* (* 2 n) (PI))) (sqrt (* (* (pow k 3) (PI)) n))) -1/2) (sqrt (* (* (PI) n) k)))) k) (* (sqrt 2) (+ (* (* (log (* (* 2 n) (PI))) (sqrt (* (* (pow k 3) (PI)) n))) -1/2) (sqrt (* (* (PI) n) k)))) (+ (* (* (sqrt (* (PI) n)) (+ (* (* (* (pow (log (* (* 2 n) (PI))) 2) (sqrt 2)) 1/8) k) (* (* (log (* (* 2 n) (PI))) (sqrt 2)) -1/2))) k) (* (sqrt (* (PI) n)) (sqrt 2))) (+ (* (* (* (pow (log (* (* 2 n) (PI))) 2) (sqrt 2)) 1/8) k) (* (* (log (* (* 2 n) (PI))) (sqrt 2)) -1/2)) (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt (/ 1 k)) (* (PI) n) (sqrt (PI)) (* (sqrt (PI)) n) (* n (PI)) (sqrt (* (* (pow k 3) (PI)) n)) (sqrt (* (* (PI) n) k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2)) (pow (log (* (* 2 n) (PI))) 2) (* (log (* (* 2 n) (PI))) (sqrt 2)) (* (sqrt (* (PI) n)) (sqrt 2)))
43.0ms	n	@	inf	((* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (* (pow (* (* 2 n) (PI)) (+ (* -1/2 k) 1/2)) (sqrt (/ 1 k))) (pow (* (* 2 n) (PI)) (+ (* -1/2 k) 1/2)) (* (* 2 n) (PI)) (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (* (sqrt 2) (sqrt (/ (* (PI) n) k))) (sqrt 2) (sqrt (/ (* (PI) n) k)) (+ (* (* (sqrt (PI)) n) (sqrt (PI))) (* n (PI))) (* (/ 1 (sqrt k)) (pow (+ (* (* (sqrt (PI)) n) (sqrt (PI))) (* n (PI))) (/ (- 1 k) 2))) (/ 1 (sqrt k)) (sqrt k) (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (/ (* (sqrt 2) (+ (* (* (log (* (* 2 n) (PI))) (sqrt (* (* (pow k 3) (PI)) n))) -1/2) (sqrt (* (* (PI) n) k)))) k) (* (sqrt 2) (+ (* (* (log (* (* 2 n) (PI))) (sqrt (* (* (pow k 3) (PI)) n))) -1/2) (sqrt (* (* (PI) n) k)))) (+ (* (* (sqrt (* (PI) n)) (+ (* (* (* (pow (log (* (* 2 n) (PI))) 2) (sqrt 2)) 1/8) k) (* (* (log (* (* 2 n) (PI))) (sqrt 2)) -1/2))) k) (* (sqrt (* (PI) n)) (sqrt 2))) (+ (* (* (* (pow (log (* (* 2 n) (PI))) 2) (sqrt 2)) 1/8) k) (* (* (log (* (* 2 n) (PI))) (sqrt 2)) -1/2)) (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt (/ 1 k)) (* (PI) n) (sqrt (PI)) (* (sqrt (PI)) n) (* n (PI)) (sqrt (* (* (pow k 3) (PI)) n)) (sqrt (* (* (PI) n) k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2)) (pow (log (* (* 2 n) (PI))) 2) (* (log (* (* 2 n) (PI))) (sqrt 2)) (* (sqrt (* (PI) n)) (sqrt 2)))
35.0ms	k	@	inf	((* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (* (pow (* (* 2 n) (PI)) (+ (* -1/2 k) 1/2)) (sqrt (/ 1 k))) (pow (* (* 2 n) (PI)) (+ (* -1/2 k) 1/2)) (* (* 2 n) (PI)) (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (* (sqrt 2) (sqrt (/ (* (PI) n) k))) (sqrt 2) (sqrt (/ (* (PI) n) k)) (+ (* (* (sqrt (PI)) n) (sqrt (PI))) (* n (PI))) (* (/ 1 (sqrt k)) (pow (+ (* (* (sqrt (PI)) n) (sqrt (PI))) (* n (PI))) (/ (- 1 k) 2))) (/ 1 (sqrt k)) (sqrt k) (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (/ (* (sqrt 2) (+ (* (* (log (* (* 2 n) (PI))) (sqrt (* (* (pow k 3) (PI)) n))) -1/2) (sqrt (* (* (PI) n) k)))) k) (* (sqrt 2) (+ (* (* (log (* (* 2 n) (PI))) (sqrt (* (* (pow k 3) (PI)) n))) -1/2) (sqrt (* (* (PI) n) k)))) (+ (* (* (sqrt (* (PI) n)) (+ (* (* (* (pow (log (* (* 2 n) (PI))) 2) (sqrt 2)) 1/8) k) (* (* (log (* (* 2 n) (PI))) (sqrt 2)) -1/2))) k) (* (sqrt (* (PI) n)) (sqrt 2))) (+ (* (* (* (pow (log (* (* 2 n) (PI))) 2) (sqrt 2)) 1/8) k) (* (* (log (* (* 2 n) (PI))) (sqrt 2)) -1/2)) (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt (/ 1 k)) (* (PI) n) (sqrt (PI)) (* (sqrt (PI)) n) (* n (PI)) (sqrt (* (* (pow k 3) (PI)) n)) (sqrt (* (* (PI) n) k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2)) (pow (log (* (* 2 n) (PI))) 2) (* (log (* (* 2 n) (PI))) (sqrt 2)) (* (sqrt (* (PI) n)) (sqrt 2)))
27.0ms	k	@	-inf	((* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (* (pow (* (* 2 n) (PI)) (+ (* -1/2 k) 1/2)) (sqrt (/ 1 k))) (pow (* (* 2 n) (PI)) (+ (* -1/2 k) 1/2)) (* (* 2 n) (PI)) (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (* (sqrt 2) (sqrt (/ (* (PI) n) k))) (sqrt 2) (sqrt (/ (* (PI) n) k)) (+ (* (* (sqrt (PI)) n) (sqrt (PI))) (* n (PI))) (* (/ 1 (sqrt k)) (pow (+ (* (* (sqrt (PI)) n) (sqrt (PI))) (* n (PI))) (/ (- 1 k) 2))) (/ 1 (sqrt k)) (sqrt k) (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (/ (* (sqrt 2) (+ (* (* (log (* (* 2 n) (PI))) (sqrt (* (* (pow k 3) (PI)) n))) -1/2) (sqrt (* (* (PI) n) k)))) k) (* (sqrt 2) (+ (* (* (log (* (* 2 n) (PI))) (sqrt (* (* (pow k 3) (PI)) n))) -1/2) (sqrt (* (* (PI) n) k)))) (+ (* (* (sqrt (* (PI) n)) (+ (* (* (* (pow (log (* (* 2 n) (PI))) 2) (sqrt 2)) 1/8) k) (* (* (log (* (* 2 n) (PI))) (sqrt 2)) -1/2))) k) (* (sqrt (* (PI) n)) (sqrt 2))) (+ (* (* (* (pow (log (* (* 2 n) (PI))) 2) (sqrt 2)) 1/8) k) (* (* (log (* (* 2 n) (PI))) (sqrt 2)) -1/2)) (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt (/ 1 k)) (* (PI) n) (sqrt (PI)) (* (sqrt (PI)) n) (* n (PI)) (sqrt (* (* (pow k 3) (PI)) n)) (sqrt (* (* (PI) n) k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2)) (pow (log (* (* 2 n) (PI))) 2) (* (log (* (* 2 n) (PI))) (sqrt 2)) (* (sqrt (* (PI) n)) (sqrt 2)))

simplify310.0ms (2.6%)

Memory

-10.1MiB live, 243.3MiB allocated; 30ms collecting garbage

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	278	1898
1	1011	1767
2	4452	1737
0	8231	1688

Stop Event

1×	iter limit
1×	node limit

Counts

83 → 83

Calls

Call 1

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

rewrite331.0ms (2.8%)

Memory

1.3MiB live, 230.7MiB allocated; 52ms collecting garbage

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	66	470
0	116	459
1	377	431
2	2321	431
0	8178	428

Stop Event

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

Counts

29 → 747

Calls

Call 1

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

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

eval264.0ms (2.2%)

Memory: -25.6MiB live, 314.9MiB allocated; 52ms collecting garbage
Compiler: Compiled 61 226 to 5 775 computations (90.6% saved)

prune48.0ms (0.4%)

Memory

26.8MiB live, 73.0MiB allocated; 4ms collecting garbage

Pruning

16 alts after pruning (14 fresh and 2 done)

	Pruned	Kept	Total
New	1 101	12	1 113
Fresh	11	2	13
Picked	3	2	5
Done	0	0	0
Total	1 115	16	1 131

Accuracy

100.0%

Counts

1 131 → 16

Alt Table

Click to see full alt table

Status	Accuracy	Program
	29.8%	(/.f64 (pow.f64 (*.f64 #s(literal 0 binary64) n) (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 8 binary64))) (sqrt.f64 k))
▶	99.7%	(/.f64 (.f64 (sqrt.f64 (.f64 (PI.f64) (.f64 n #s(literal 2 binary64)))) #s(literal 1 binary64)) (.f64 (pow.f64 (.f64 (PI.f64) (.f64 n #s(literal 2 binary64))) (/.f64 k #s(literal 2 binary64))) (sqrt.f64 k)))
	45.2%	(.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)))))
	45.3%	#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (/.f64 (sqrt.f64 (.f64 (PI.f64) (.f64 n #s(literal 2 binary64)))) (sqrt.f64 k)))
▶	34.5%	#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (/.f64 #s(approx (* (sqrt 2) (+ (* (* (log (* (* 2 n) (PI))) (sqrt (* (* (pow k 3) (PI)) n))) -1/2) (sqrt (* (* (PI) n) k)))) (.f64 (sqrt.f64 (.f64 (*.f64 n (PI.f64)) k)) (sqrt.f64 #s(literal 2 binary64)))) k))
✓	99.6%	#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (.f64 (pow.f64 (.f64 (*.f64 #s(literal 2 binary64) n) (PI.f64)) (fma.f64 #s(literal -1/2 binary64) k #s(literal 1/2 binary64))) (sqrt.f64 (/.f64 #s(literal 1 binary64) k))))
	99.7%	#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (.f64 (pow.f64 (.f64 k (pow.f64 (.f64 (PI.f64) (.f64 n #s(literal 2 binary64))) k)) #s(literal -1/2 binary64)) (sqrt.f64 (.f64 (PI.f64) (.f64 n #s(literal 2 binary64))))))
	99.7%	#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (.f64 (/.f64 (sqrt.f64 (.f64 (PI.f64) (.f64 n #s(literal 2 binary64)))) (pow.f64 (.f64 (PI.f64) (.f64 n #s(literal 2 binary64))) (.f64 #s(literal 1/2 binary64) k))) (sqrt.f64 (/.f64 #s(literal 1 binary64) k))))
	35.2%	#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))))
▶	45.3%	#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))))
	35.4%	#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (.f64 (sqrt.f64 #s(literal 2 binary64)) (.f64 (sqrt.f64 (/.f64 n k)) (sqrt.f64 (PI.f64)))))
	45.3%	#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)))))
▶	35.5%	#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)) n) (sqrt.f64 (PI.f64))) k))))
✓	35.4%	#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))))
	45.2%	#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (.f64 #s(approx (pow ( (* 2 n) (PI)) (+ (* -1/2 k) 1/2)) (.f64 (sqrt.f64 (.f64 n (PI.f64))) (sqrt.f64 #s(literal 2 binary64)))) (sqrt.f64 (/.f64 #s(literal 1 binary64) k))))
▶	35.5%	#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt.f64 (.f64 (/.f64 (.f64 (PI.f64) n) k) #s(literal 2 binary64))))

Compiler

Compiled 888 to 687 computations (22.6% saved)

simplify167.0ms (1.4%)

Memory

3.2MiB live, 49.4MiB allocated; 3ms collecting garbage

Localize:

Found 20 expressions of interest:

New	Metric	Score
cost-diff	0	(sqrt.f64 #s(literal 2 binary64))
cost-diff	0	(.f64 (sqrt.f64 #s(literal 2 binary64)) (sqrt.f64 (/.f64 (.f64 (*.f64 (sqrt.f64 (PI.f64)) n) (sqrt.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)) (sqrt.f64 (/.f64 (.f64 (*.f64 (sqrt.f64 (PI.f64)) n) (sqrt.f64 (PI.f64))) k))))
cost-diff	4	(.f64 (.f64 (sqrt.f64 (PI.f64)) n) (sqrt.f64 (PI.f64)))
cost-diff	0	(/.f64 (sqrt.f64 (*.f64 (PI.f64) n)) (sqrt.f64 k))
cost-diff	0	(sqrt.f64 #s(literal 2 binary64))
cost-diff	0	(.f64 (sqrt.f64 #s(literal 2 binary64)) (/.f64 (sqrt.f64 (.f64 (PI.f64) n)) (sqrt.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 (.f64 (PI.f64) n)) (sqrt.f64 k))))
cost-diff	0	(.f64 (sqrt.f64 (.f64 (*.f64 n (PI.f64)) k)) (sqrt.f64 #s(literal 2 binary64)))
cost-diff	0	#s(approx (* (sqrt 2) (+ (* (* (log (* (* 2 n) (PI))) (sqrt (* (* (pow k 3) (PI)) n))) -1/2) (sqrt (* (* (PI) n) k)))) (.f64 (sqrt.f64 (.f64 (*.f64 n (PI.f64)) k)) (sqrt.f64 #s(literal 2 binary64))))
cost-diff	0	(/.f64 #s(approx (* (sqrt 2) (+ (* (* (log (* (* 2 n) (PI))) (sqrt (* (* (pow k 3) (PI)) n))) -1/2) (sqrt (* (* (PI) n) k)))) (.f64 (sqrt.f64 (.f64 (*.f64 n (PI.f64)) k)) (sqrt.f64 #s(literal 2 binary64)))) k)
cost-diff	0	#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (/.f64 #s(approx (* (sqrt 2) (+ (* (* (log (* (* 2 n) (PI))) (sqrt (* (* (pow k 3) (PI)) n))) -1/2) (sqrt (* (* (PI) n) k)))) (.f64 (sqrt.f64 (.f64 (*.f64 n (PI.f64)) k)) (sqrt.f64 #s(literal 2 binary64)))) k))
cost-diff	0	(/.f64 (*.f64 (PI.f64) n) k)
cost-diff	0	(.f64 (/.f64 (.f64 (PI.f64) n) k) #s(literal 2 binary64))
cost-diff	0	(sqrt.f64 (.f64 (/.f64 (.f64 (PI.f64) n) k) #s(literal 2 binary64)))
cost-diff	0	#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt.f64 (.f64 (/.f64 (.f64 (PI.f64) n) k) #s(literal 2 binary64))))
cost-diff	0	(.f64 (PI.f64) (.f64 n #s(literal 2 binary64)))
cost-diff	0	(sqrt.f64 (.f64 (PI.f64) (.f64 n #s(literal 2 binary64))))
cost-diff	0	(/.f64 (.f64 (sqrt.f64 (.f64 (PI.f64) (.f64 n #s(literal 2 binary64)))) #s(literal 1 binary64)) (.f64 (pow.f64 (.f64 (PI.f64) (.f64 n #s(literal 2 binary64))) (/.f64 k #s(literal 2 binary64))) (sqrt.f64 k)))
cost-diff	2	(.f64 (sqrt.f64 (.f64 (PI.f64) (*.f64 n #s(literal 2 binary64)))) #s(literal 1 binary64))

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	64	427
0	96	415
1	166	407
2	280	395
3	533	395
4	1261	395
5	2425	395
6	3003	395
7	3197	395
8	3540	395
9	4490	395
10	6388	395
11	7050	395
12	7222	395
13	7340	395
14	7456	395
15	7540	395
16	7571	395
17	7571	395
18	7571	395
0	8348	392

Stop Event

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

Calls

Call 1

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

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

localize183.0ms (1.5%)

Memory

-19.1MiB live, 215.8MiB allocated; 27ms collecting garbage

Localize:

Found 20 expressions of interest:

New	Metric	Score
accuracy	0.72265625	(sqrt.f64 (PI.f64))
accuracy	6.483641293773012	(sqrt.f64 (/.f64 (.f64 (.f64 (sqrt.f64 (PI.f64)) n) (sqrt.f64 (PI.f64))) k))
accuracy	17.194893873218973	(PI.f64)
accuracy	17.493452446621543	#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)) n) (sqrt.f64 (PI.f64))) k))))
accuracy	0.228847509768442	(/.f64 (sqrt.f64 (*.f64 (PI.f64) n)) (sqrt.f64 k))
accuracy	0.30277255861065216	(.f64 (sqrt.f64 #s(literal 2 binary64)) (/.f64 (sqrt.f64 (.f64 (PI.f64) n)) (sqrt.f64 k)))
accuracy	17.194893873218973	(PI.f64)
accuracy	17.493452446621543	#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))))
accuracy	16.235458080139228	(sqrt.f64 (.f64 (.f64 n (PI.f64)) k))
accuracy	17.194893873218973	(PI.f64)
accuracy	17.25825440316223	#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (/.f64 #s(approx (* (sqrt 2) (+ (* (* (log (* (* 2 n) (PI))) (sqrt (* (* (pow k 3) (PI)) n))) -1/2) (sqrt (* (* (PI) n) k)))) (.f64 (sqrt.f64 (.f64 (*.f64 n (PI.f64)) k)) (sqrt.f64 #s(literal 2 binary64)))) k))
accuracy	17.964722162623872	#s(approx (* (sqrt 2) (+ (* (* (log (* (* 2 n) (PI))) (sqrt (* (* (pow k 3) (PI)) n))) -1/2) (sqrt (* (* (PI) n) k)))) (.f64 (sqrt.f64 (.f64 (*.f64 n (PI.f64)) k)) (sqrt.f64 #s(literal 2 binary64))))
accuracy	0.18359375	(*.f64 (PI.f64) n)
accuracy	6.4482520595467365	(sqrt.f64 (.f64 (/.f64 (.f64 (PI.f64) n) k) #s(literal 2 binary64)))
accuracy	17.194893873218973	(PI.f64)
accuracy	17.493452446621543	#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt.f64 (.f64 (/.f64 (.f64 (PI.f64) n) k) #s(literal 2 binary64))))
accuracy	0.09375	(sqrt.f64 (.f64 (PI.f64) (.f64 n #s(literal 2 binary64))))
accuracy	0.15234375	(/.f64 (.f64 (sqrt.f64 (.f64 (PI.f64) (.f64 n #s(literal 2 binary64)))) #s(literal 1 binary64)) (.f64 (pow.f64 (.f64 (PI.f64) (.f64 n #s(literal 2 binary64))) (/.f64 k #s(literal 2 binary64))) (sqrt.f64 k)))
accuracy	0.18359375	(.f64 (PI.f64) (.f64 n #s(literal 2 binary64)))
accuracy	17.194893873218973	(PI.f64)

Samples

104.0ms	185×	0	valid
37.0ms	71×	0	exit

Compiler

Compiled 335 to 57 computations (83% saved)

Precisions

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

ival-mult: 36.0ms (44.4% of total)

ival-sqrt: 16.0ms (19.7% of total)

ival-div: 11.0ms (13.6% of total)

ival-pow: 11.0ms (13.6% of total)

ival-log: 3.0ms (3.7% 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)

series71.0ms (0.6%)

Memory

12.8MiB live, 153.0MiB allocated; 24ms collecting garbage

Counts

24 → 47

Calls

Call 1

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

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

Calls

6 calls:

Time	Variable		Point	Expression
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 (* (/ (* (PI) n) k) 2)) (* (/ (* (PI) n) k) 2) (/ (* (PI) n) k) (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (/ (* (sqrt 2) (+ (* (* (log (* (* 2 n) (PI))) (sqrt (* (* (pow k 3) (PI)) n))) -1/2) (sqrt (* (* (PI) n) k)))) k) (* (sqrt 2) (+ (* (* (log (* (* 2 n) (PI))) (sqrt (* (* (pow k 3) (PI)) n))) -1/2) (sqrt (* (* (PI) n) k)))) (* (sqrt (* (* n (PI)) k)) (sqrt 2)) (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (* (sqrt 2) (/ (sqrt (* (PI) n)) (sqrt k))) (sqrt 2) (/ (sqrt (* (PI) n)) (sqrt k)) (* (* (sqrt (PI)) n) (sqrt (PI))) (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (* (sqrt 2) (sqrt (/ (* (* (sqrt (PI)) n) (sqrt (PI))) k))) (PI) (* (PI) n) (sqrt (* (* n (PI)) k)) (sqrt (/ (* (* (sqrt (PI)) n) (sqrt (PI))) k)) (sqrt (PI)))
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 (* (/ (* (PI) n) k) 2)) (* (/ (* (PI) n) k) 2) (/ (* (PI) n) k) (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (/ (* (sqrt 2) (+ (* (* (log (* (* 2 n) (PI))) (sqrt (* (* (pow k 3) (PI)) n))) -1/2) (sqrt (* (* (PI) n) k)))) k) (* (sqrt 2) (+ (* (* (log (* (* 2 n) (PI))) (sqrt (* (* (pow k 3) (PI)) n))) -1/2) (sqrt (* (* (PI) n) k)))) (* (sqrt (* (* n (PI)) k)) (sqrt 2)) (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (* (sqrt 2) (/ (sqrt (* (PI) n)) (sqrt k))) (sqrt 2) (/ (sqrt (* (PI) n)) (sqrt k)) (* (* (sqrt (PI)) n) (sqrt (PI))) (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (* (sqrt 2) (sqrt (/ (* (* (sqrt (PI)) n) (sqrt (PI))) k))) (PI) (* (PI) n) (sqrt (* (* n (PI)) k)) (sqrt (/ (* (* (sqrt (PI)) n) (sqrt (PI))) k)) (sqrt (PI)))
14.0ms	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 (* (/ (* (PI) n) k) 2)) (* (/ (* (PI) n) k) 2) (/ (* (PI) n) k) (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (/ (* (sqrt 2) (+ (* (* (log (* (* 2 n) (PI))) (sqrt (* (* (pow k 3) (PI)) n))) -1/2) (sqrt (* (* (PI) n) k)))) k) (* (sqrt 2) (+ (* (* (log (* (* 2 n) (PI))) (sqrt (* (* (pow k 3) (PI)) n))) -1/2) (sqrt (* (* (PI) n) k)))) (* (sqrt (* (* n (PI)) k)) (sqrt 2)) (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (* (sqrt 2) (/ (sqrt (* (PI) n)) (sqrt k))) (sqrt 2) (/ (sqrt (* (PI) n)) (sqrt k)) (* (* (sqrt (PI)) n) (sqrt (PI))) (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (* (sqrt 2) (sqrt (/ (* (* (sqrt (PI)) n) (sqrt (PI))) k))) (PI) (* (PI) n) (sqrt (* (* n (PI)) k)) (sqrt (/ (* (* (sqrt (PI)) n) (sqrt (PI))) k)) (sqrt (PI)))
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 (* (/ (* (PI) n) k) 2)) (* (/ (* (PI) n) k) 2) (/ (* (PI) n) k) (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (/ (* (sqrt 2) (+ (* (* (log (* (* 2 n) (PI))) (sqrt (* (* (pow k 3) (PI)) n))) -1/2) (sqrt (* (* (PI) n) k)))) k) (* (sqrt 2) (+ (* (* (log (* (* 2 n) (PI))) (sqrt (* (* (pow k 3) (PI)) n))) -1/2) (sqrt (* (* (PI) n) k)))) (* (sqrt (* (* n (PI)) k)) (sqrt 2)) (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (* (sqrt 2) (/ (sqrt (* (PI) n)) (sqrt k))) (sqrt 2) (/ (sqrt (* (PI) n)) (sqrt k)) (* (* (sqrt (PI)) n) (sqrt (PI))) (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (* (sqrt 2) (sqrt (/ (* (* (sqrt (PI)) n) (sqrt (PI))) k))) (PI) (* (PI) n) (sqrt (* (* n (PI)) k)) (sqrt (/ (* (* (sqrt (PI)) n) (sqrt (PI))) k)) (sqrt (PI)))
5.0ms	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 (* (/ (* (PI) n) k) 2)) (* (/ (* (PI) n) k) 2) (/ (* (PI) n) k) (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (/ (* (sqrt 2) (+ (* (* (log (* (* 2 n) (PI))) (sqrt (* (* (pow k 3) (PI)) n))) -1/2) (sqrt (* (* (PI) n) k)))) k) (* (sqrt 2) (+ (* (* (log (* (* 2 n) (PI))) (sqrt (* (* (pow k 3) (PI)) n))) -1/2) (sqrt (* (* (PI) n) k)))) (* (sqrt (* (* n (PI)) k)) (sqrt 2)) (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (* (sqrt 2) (/ (sqrt (* (PI) n)) (sqrt k))) (sqrt 2) (/ (sqrt (* (PI) n)) (sqrt k)) (* (* (sqrt (PI)) n) (sqrt (PI))) (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (* (sqrt 2) (sqrt (/ (* (* (sqrt (PI)) n) (sqrt (PI))) k))) (PI) (* (PI) n) (sqrt (* (* n (PI)) k)) (sqrt (/ (* (* (sqrt (PI)) n) (sqrt (PI))) k)) (sqrt (PI)))

simplify156.0ms (1.3%)

Memory

-17.2MiB live, 173.8MiB allocated; 18ms collecting garbage

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	211	1171
1	749	1096
2	3307	1069
0	8309	1046

Stop Event

1×	iter limit
1×	node limit

Counts

47 → 47

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

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

rewrite228.0ms (1.9%)

Memory

14.8MiB live, 267.7MiB allocated; 51ms collecting garbage

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	64	344
0	96	313
1	282	300
2	1344	300
0	8241	297

Stop Event

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

Counts

24 → 819

Calls

Call 1

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

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

eval231.0ms (2%)

Memory: 7.6MiB live, 473.2MiB allocated; 119ms collecting garbage
Compiler: Compiled 37 889 to 4 750 computations (87.5% saved)

prune149.0ms (1.3%)

Memory

7.6MiB live, 159.0MiB allocated; 39ms collecting garbage

Pruning

41 alts after pruning (35 fresh and 6 done)

	Pruned	Kept	Total
New	1 057	30	1 087
Fresh	4	5	9
Picked	1	4	5
Done	0	2	2
Total	1 062	41	1 103

Accuracy

100.0%

Counts

1 103 → 41

Alt Table

Click to see full alt table

Status	Accuracy	Program
	29.8%	(/.f64 (pow.f64 (*.f64 #s(literal 0 binary64) n) (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 8 binary64))) (sqrt.f64 k))
▶	99.6%	(/.f64 (.f64 (sqrt.f64 (.f64 n (PI.f64))) (sqrt.f64 #s(literal 2 binary64))) (.f64 (pow.f64 (.f64 (PI.f64) (*.f64 n #s(literal 2 binary64))) (/.f64 k #s(literal 2 binary64))) (sqrt.f64 k)))
	78.6%	(/.f64 (sqrt.f64 (/.f64 (.f64 (.f64 #s(literal 2 binary64) n) (PI.f64)) k)) (pow.f64 (.f64 (.f64 #s(literal 2 binary64) n) (PI.f64)) (/.f64 k #s(literal 2 binary64))))
	78.6%	(.f64 (pow.f64 (.f64 (.f64 #s(literal 2 binary64) n) (PI.f64)) (neg.f64 (/.f64 k #s(literal 2 binary64)))) (sqrt.f64 (/.f64 (.f64 (*.f64 #s(literal 2 binary64) n) (PI.f64)) k)))
	45.2%	(.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)))))
	45.2%	#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (/.f64 (.f64 (sqrt.f64 #s(literal 2 binary64)) (neg.f64 (sqrt.f64 (.f64 n (PI.f64))))) (neg.f64 (sqrt.f64 k))))
▶	45.3%	#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (/.f64 (sqrt.f64 (.f64 (.f64 #s(literal 2 binary64) n) (PI.f64))) (sqrt.f64 k)))
	45.2%	#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (/.f64 #s(approx (* (sqrt 2) (+ (* (* (log (* (* 2 n) (PI))) (sqrt (* (* (pow k 3) (PI)) n))) -1/2) (sqrt (* (* (PI) n) k)))) (.f64 (.f64 (sqrt.f64 (*.f64 n (PI.f64))) (sqrt.f64 k)) (sqrt.f64 #s(literal 2 binary64)))) k))
	45.2%	#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (/.f64 #s(approx (* (sqrt 2) (+ (* (* (log (* (* 2 n) (PI))) (sqrt (* (* (pow k 3) (PI)) n))) -1/2) (sqrt (* (* (PI) n) k)))) (.f64 (.f64 (sqrt.f64 (*.f64 k (PI.f64))) (sqrt.f64 n)) (sqrt.f64 #s(literal 2 binary64)))) k))
	22.6%	#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (/.f64 #s(approx (* (sqrt 2) (+ (* (* (log (* (* 2 n) (PI))) (sqrt (* (* (pow k 3) (PI)) n))) -1/2) (sqrt (* (* (PI) n) k)))) (.f64 (.f64 (sqrt.f64 (sqrt.f64 (.f64 (.f64 (.f64 n (PI.f64)) k) (.f64 n (PI.f64))))) (sqrt.f64 (sqrt.f64 k))) (sqrt.f64 #s(literal 2 binary64)))) k))
	34.4%	#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (/.f64 #s(approx (* (sqrt 2) (+ (* (* (log (* (* 2 n) (PI))) (sqrt (* (* (pow k 3) (PI)) n))) -1/2) (sqrt (* (* (PI) n) k)))) (.f64 (.f64 (sqrt.f64 (sqrt.f64 (.f64 (.f64 n (PI.f64)) k))) (sqrt.f64 (sqrt.f64 (.f64 (.f64 n (PI.f64)) k)))) (sqrt.f64 #s(literal 2 binary64)))) k))
	30.3%	#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (/.f64 #s(approx (* (sqrt 2) (+ (* (* (log (* (* 2 n) (PI))) (sqrt (* (* (pow k 3) (PI)) n))) -1/2) (sqrt (* (* (PI) n) k)))) (.f64 (.f64 (sqrt.f64 (sqrt.f64 (.f64 n (PI.f64)))) (sqrt.f64 (sqrt.f64 (.f64 k (.f64 (.f64 n (PI.f64)) k))))) (sqrt.f64 #s(literal 2 binary64)))) k))
✓	34.5%	#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (/.f64 #s(approx (* (sqrt 2) (+ (* (* (log (* (* 2 n) (PI))) (sqrt (* (* (pow k 3) (PI)) n))) -1/2) (sqrt (* (* (PI) n) k)))) (.f64 (sqrt.f64 (.f64 (*.f64 n (PI.f64)) k)) (sqrt.f64 #s(literal 2 binary64)))) k))
	45.3%	#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (/.f64 #s(approx (* (sqrt 2) (+ (* (* (log (* (* 2 n) (PI))) (sqrt (* (* (pow k 3) (PI)) n))) -1/2) (sqrt (* (* (PI) n) k)))) (.f64 (sqrt.f64 (.f64 (*.f64 #s(literal 2 binary64) n) (PI.f64))) (sqrt.f64 k))) k))
	45.3%	#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (/.f64 #s(approx (* (sqrt 2) (+ (* (* (log (* (* 2 n) (PI))) (sqrt (* (* (pow k 3) (PI)) n))) -1/2) (sqrt (* (* (PI) n) k)))) (.f64 (sqrt.f64 (.f64 n (PI.f64))) (sqrt.f64 (*.f64 k #s(literal 2 binary64))))) k))
	45.3%	#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (/.f64 #s(approx (* (sqrt 2) (+ (* (* (log (* (* 2 n) (PI))) (sqrt (* (* (pow k 3) (PI)) n))) -1/2) (sqrt (* (* (PI) n) k)))) (.f64 (sqrt.f64 n) (sqrt.f64 (.f64 (*.f64 k (PI.f64)) #s(literal 2 binary64))))) k))
	34.6%	#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (/.f64 #s(approx (* (sqrt 2) (+ (* (* (log (* (* 2 n) (PI))) (sqrt (* (* (pow k 3) (PI)) n))) -1/2) (sqrt (* (* (PI) n) k)))) (sqrt.f64 (.f64 (.f64 (*.f64 n (PI.f64)) k) #s(literal 2 binary64)))) k))
✓	99.6%	#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (.f64 (pow.f64 (.f64 (*.f64 #s(literal 2 binary64) n) (PI.f64)) (fma.f64 #s(literal -1/2 binary64) k #s(literal 1/2 binary64))) (sqrt.f64 (/.f64 #s(literal 1 binary64) k))))
	35.2%	#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))))
	45.3%	#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (.f64 (sqrt.f64 (.f64 n (PI.f64))) (sqrt.f64 (/.f64 #s(literal 2 binary64) k))))
	45.2%	#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (.f64 (sqrt.f64 (.f64 #s(literal 2 binary64) (*.f64 (sqrt.f64 (PI.f64)) n))) (sqrt.f64 (/.f64 (sqrt.f64 (PI.f64)) k))))
	45.3%	#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (.f64 (sqrt.f64 (.f64 #s(literal 2 binary64) n)) (sqrt.f64 (/.f64 (PI.f64) k))))
	45.3%	#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (.f64 (sqrt.f64 n) (sqrt.f64 (/.f64 (.f64 #s(literal 2 binary64) (PI.f64)) k))))
	45.3%	#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (.f64 (sqrt.f64 #s(literal 2 binary64)) (/.f64 (sqrt.f64 (.f64 (*.f64 (sqrt.f64 (PI.f64)) (sqrt.f64 (PI.f64))) n)) (sqrt.f64 k))))
✓	45.3%	#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))))
	45.3%	#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (.f64 (sqrt.f64 #s(literal 2 binary64)) (.f64 (sqrt.f64 (/.f64 (sqrt.f64 (PI.f64)) k)) (sqrt.f64 (*.f64 (sqrt.f64 (PI.f64)) n)))))
	45.3%	#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)))))
	35.4%	#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 (.f64 (sqrt.f64 (PI.f64)) n)) (sqrt.f64 (*.f64 (sqrt.f64 (PI.f64)) n))) (sqrt.f64 (PI.f64))) k))))
✓	35.5%	#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)) n) (sqrt.f64 (PI.f64))) k))))
✓	35.4%	#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))))
	45.2%	#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (.f64 #s(approx (pow ( (* 2 n) (PI)) (+ (* -1/2 k) 1/2)) (.f64 (sqrt.f64 (.f64 n (PI.f64))) (sqrt.f64 #s(literal 2 binary64)))) (sqrt.f64 (/.f64 #s(literal 1 binary64) k))))
	22.0%	#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt.f64 (/.f64 (fma.f64 (.f64 k n) (PI.f64) (.f64 (.f64 n (PI.f64)) k)) (.f64 k k))))
	35.3%	#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt.f64 (.f64 (/.f64 (.f64 (*.f64 (sqrt.f64 (PI.f64)) (sqrt.f64 (PI.f64))) n) k) #s(literal 2 binary64))))
▶	35.3%	#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt.f64 (.f64 (/.f64 (.f64 (*.f64 #s(literal 2 binary64) n) (sqrt.f64 (PI.f64))) k) (/.f64 (sqrt.f64 (PI.f64)) #s(literal 1 binary64)))))
✓	35.5%	#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt.f64 (.f64 (/.f64 (.f64 (PI.f64) n) k) #s(literal 2 binary64))))
	35.3%	#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt.f64 (.f64 (.f64 (sqrt.f64 (PI.f64)) (*.f64 (sqrt.f64 (PI.f64)) (/.f64 n k))) #s(literal 2 binary64))))
▶	35.3%	#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt.f64 (.f64 (.f64 (sqrt.f64 (PI.f64)) (*.f64 n (/.f64 (sqrt.f64 (PI.f64)) k))) #s(literal 2 binary64))))
	35.5%	#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt.f64 (.f64 (.f64 n (/.f64 (PI.f64) k)) #s(literal 2 binary64))))
	35.3%	#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt.f64 (.f64 (.f64 n (*.f64 (sqrt.f64 (PI.f64)) (/.f64 (sqrt.f64 (PI.f64)) k))) #s(literal 2 binary64))))
	35.4%	#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt.f64 (.f64 (.f64 n (PI.f64)) (/.f64 #s(literal 2 binary64) k))))
▶	35.5%	#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt.f64 (.f64 (.f64 #s(literal 2 binary64) (PI.f64)) (/.f64 n k))))

Compiler

Compiled 2 666 to 1 984 computations (25.6% saved)

simplify57.0ms (0.5%)

Memory

-8.0MiB live, 39.4MiB allocated; 7ms collecting garbage

Localize:

Found 20 expressions of interest:

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

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	48	342
0	79	310
1	136	302
2	233	298
3	417	298
4	682	298
5	1112	298
6	1665	298
7	2024	298
8	2082	298
9	2082	298
10	2091	298
0	2091	294

Stop Event

1×	iter limit
1×	saturated
1×	iter limit

Calls

Call 1

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

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

localize154.0ms (1.3%)

Memory

-25.2MiB live, 210.6MiB allocated; 27ms collecting garbage

Localize:

Found 20 expressions of interest:

New	Metric	Score
accuracy	0.72265625	(sqrt.f64 (PI.f64))
accuracy	6.4482520595467365	(sqrt.f64 (.f64 (/.f64 (.f64 (*.f64 #s(literal 2 binary64) n) (sqrt.f64 (PI.f64))) k) (/.f64 (sqrt.f64 (PI.f64)) #s(literal 1 binary64))))
accuracy	17.194893873218973	(PI.f64)
accuracy	17.493452446621543	#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt.f64 (.f64 (/.f64 (.f64 (*.f64 #s(literal 2 binary64) n) (sqrt.f64 (PI.f64))) k) (/.f64 (sqrt.f64 (PI.f64)) #s(literal 1 binary64)))))
accuracy	0.72265625	(sqrt.f64 (PI.f64))
accuracy	6.4482520595467365	(sqrt.f64 (.f64 (.f64 (sqrt.f64 (PI.f64)) (*.f64 n (/.f64 (sqrt.f64 (PI.f64)) k))) #s(literal 2 binary64)))
accuracy	17.194893873218973	(PI.f64)
accuracy	17.493452446621543	#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt.f64 (.f64 (.f64 (sqrt.f64 (PI.f64)) (*.f64 n (/.f64 (sqrt.f64 (PI.f64)) k))) #s(literal 2 binary64))))
accuracy	0.18359375	(.f64 (.f64 #s(literal 2 binary64) n) (PI.f64))
accuracy	0.25	(/.f64 (sqrt.f64 (.f64 (.f64 #s(literal 2 binary64) n) (PI.f64))) (sqrt.f64 k))
accuracy	17.194893873218973	(PI.f64)
accuracy	17.493452446621543	#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (/.f64 (sqrt.f64 (.f64 (.f64 #s(literal 2 binary64) n) (PI.f64))) (sqrt.f64 k)))
accuracy	0.21484375	(.f64 (.f64 #s(literal 2 binary64) (PI.f64)) (/.f64 n k))
accuracy	6.4482520595467365	(sqrt.f64 (.f64 (.f64 #s(literal 2 binary64) (PI.f64)) (/.f64 n k)))
accuracy	17.194893873218973	(PI.f64)
accuracy	17.493452446621543	#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt.f64 (.f64 (.f64 #s(literal 2 binary64) (PI.f64)) (/.f64 n k))))
accuracy	0.18359375	(.f64 (PI.f64) (.f64 n #s(literal 2 binary64)))
accuracy	0.18359375	(*.f64 n (PI.f64))
accuracy	0.332695019536884	(.f64 (sqrt.f64 (.f64 n (PI.f64))) (sqrt.f64 #s(literal 2 binary64)))
accuracy	17.194893873218973	(PI.f64)

Samples

68.0ms	185×	0	valid
28.0ms	71×	0	exit

Compiler

Compiled 297 to 43 computations (85.5% saved)

Precisions

Click to see histograms. Total time spent on operations: 70.0ms

ival-mult: 26.0ms (37.1% of total)

ival-div: 14.0ms (20% of total)

ival-pow: 14.0ms (20% of total)

ival-sqrt: 13.0ms (18.5% of total)

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

ival-sub: 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)

exact: 0.0ms (0% of total)

series70.0ms (0.6%)

Memory

23.6MiB live, 117.3MiB allocated; 18ms collecting garbage

Counts

23 → 26

Calls

Call 1

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

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

Calls

6 calls:

Time	Variable		Point	Expression
38.0ms	n	@	-inf	((/ (* (sqrt (* n (PI))) (sqrt 2)) (* (pow (* (PI) (* n 2)) (/ k 2)) (sqrt k))) (* (sqrt (* n (PI))) (sqrt 2)) (sqrt (* n (PI))) (* n (PI)) (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt (* (* 2 (PI)) (/ n k))) (* (* 2 (PI)) (/ n k)) (* 2 (PI)) (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (/ (sqrt (* (* 2 n) (PI))) (sqrt k)) (sqrt (* (* 2 n) (PI))) (* (* 2 n) (PI)) (* (sqrt (PI)) (* n (/ (sqrt (PI)) k))) (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt (* (* (sqrt (PI)) (* n (/ (sqrt (PI)) k))) 2)) (* (* (sqrt (PI)) (* n (/ (sqrt (PI)) k))) 2) (* (/ (* (* 2 n) (sqrt (PI))) k) (/ (sqrt (PI)) 1)) (/ (sqrt (PI)) 1) (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt (* (/ (* (* 2 n) (sqrt (PI))) k) (/ (sqrt (PI)) 1))) (PI) (* (PI) (* n 2)) (sqrt (PI)))
15.0ms	n	@	inf	((/ (* (sqrt (* n (PI))) (sqrt 2)) (* (pow (* (PI) (* n 2)) (/ k 2)) (sqrt k))) (* (sqrt (* n (PI))) (sqrt 2)) (sqrt (* n (PI))) (* n (PI)) (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt (* (* 2 (PI)) (/ n k))) (* (* 2 (PI)) (/ n k)) (* 2 (PI)) (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (/ (sqrt (* (* 2 n) (PI))) (sqrt k)) (sqrt (* (* 2 n) (PI))) (* (* 2 n) (PI)) (* (sqrt (PI)) (* n (/ (sqrt (PI)) k))) (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt (* (* (sqrt (PI)) (* n (/ (sqrt (PI)) k))) 2)) (* (* (sqrt (PI)) (* n (/ (sqrt (PI)) k))) 2) (* (/ (* (* 2 n) (sqrt (PI))) k) (/ (sqrt (PI)) 1)) (/ (sqrt (PI)) 1) (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt (* (/ (* (* 2 n) (sqrt (PI))) k) (/ (sqrt (PI)) 1))) (PI) (* (PI) (* n 2)) (sqrt (PI)))
10.0ms	n	@	0	((/ (* (sqrt (* n (PI))) (sqrt 2)) (* (pow (* (PI) (* n 2)) (/ k 2)) (sqrt k))) (* (sqrt (* n (PI))) (sqrt 2)) (sqrt (* n (PI))) (* n (PI)) (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt (* (* 2 (PI)) (/ n k))) (* (* 2 (PI)) (/ n k)) (* 2 (PI)) (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (/ (sqrt (* (* 2 n) (PI))) (sqrt k)) (sqrt (* (* 2 n) (PI))) (* (* 2 n) (PI)) (* (sqrt (PI)) (* n (/ (sqrt (PI)) k))) (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt (* (* (sqrt (PI)) (* n (/ (sqrt (PI)) k))) 2)) (* (* (sqrt (PI)) (* n (/ (sqrt (PI)) k))) 2) (* (/ (* (* 2 n) (sqrt (PI))) k) (/ (sqrt (PI)) 1)) (/ (sqrt (PI)) 1) (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt (* (/ (* (* 2 n) (sqrt (PI))) k) (/ (sqrt (PI)) 1))) (PI) (* (PI) (* n 2)) (sqrt (PI)))
3.0ms	k	@	-inf	((/ (* (sqrt (* n (PI))) (sqrt 2)) (* (pow (* (PI) (* n 2)) (/ k 2)) (sqrt k))) (* (sqrt (* n (PI))) (sqrt 2)) (sqrt (* n (PI))) (* n (PI)) (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt (* (* 2 (PI)) (/ n k))) (* (* 2 (PI)) (/ n k)) (* 2 (PI)) (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (/ (sqrt (* (* 2 n) (PI))) (sqrt k)) (sqrt (* (* 2 n) (PI))) (* (* 2 n) (PI)) (* (sqrt (PI)) (* n (/ (sqrt (PI)) k))) (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt (* (* (sqrt (PI)) (* n (/ (sqrt (PI)) k))) 2)) (* (* (sqrt (PI)) (* n (/ (sqrt (PI)) k))) 2) (* (/ (* (* 2 n) (sqrt (PI))) k) (/ (sqrt (PI)) 1)) (/ (sqrt (PI)) 1) (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt (* (/ (* (* 2 n) (sqrt (PI))) k) (/ (sqrt (PI)) 1))) (PI) (* (PI) (* n 2)) (sqrt (PI)))
2.0ms	k	@	inf	((/ (* (sqrt (* n (PI))) (sqrt 2)) (* (pow (* (PI) (* n 2)) (/ k 2)) (sqrt k))) (* (sqrt (* n (PI))) (sqrt 2)) (sqrt (* n (PI))) (* n (PI)) (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt (* (* 2 (PI)) (/ n k))) (* (* 2 (PI)) (/ n k)) (* 2 (PI)) (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (/ (sqrt (* (* 2 n) (PI))) (sqrt k)) (sqrt (* (* 2 n) (PI))) (* (* 2 n) (PI)) (* (sqrt (PI)) (* n (/ (sqrt (PI)) k))) (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt (* (* (sqrt (PI)) (* n (/ (sqrt (PI)) k))) 2)) (* (* (sqrt (PI)) (* n (/ (sqrt (PI)) k))) 2) (* (/ (* (* 2 n) (sqrt (PI))) k) (/ (sqrt (PI)) 1)) (/ (sqrt (PI)) 1) (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt (* (/ (* (* 2 n) (sqrt (PI))) k) (/ (sqrt (PI)) 1))) (PI) (* (PI) (* n 2)) (sqrt (PI)))

simplify157.0ms (1.3%)

Memory

-9.0MiB live, 221.1MiB allocated; 60ms collecting garbage

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	156	604
1	527	590
2	2160	560
3	7462	557
0	8058	545

Stop Event

1×	iter limit
1×	node limit

Counts

26 → 26

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

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

rewrite232.0ms (2%)

Memory

43.7MiB live, 328.1MiB allocated; 45ms collecting garbage

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	48	254
0	79	220
1	236	203
2	1043	161
0	9239	161

Stop Event

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

Counts

23 → 2 247

Calls

Call 1

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

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

eval209.0ms (1.8%)

Memory: -6.0MiB live, 277.4MiB allocated; 44ms collecting garbage
Compiler: Compiled 45 308 to 5 755 computations (87.3% saved)

prune68.0ms (0.6%)

Memory

-24.4MiB live, 168.4MiB allocated; 18ms collecting garbage

Pruning

24 alts after pruning (18 fresh and 6 done)

	Pruned	Kept	Total
New	1 541	11	1 552
Fresh	23	7	30
Picked	3	2	5
Done	2	4	6
Total	1 569	24	1 593

Accuracy

100.0%

Counts

1 593 → 24

Alt Table

Click to see full alt table

Status	Accuracy	Program
	29.8%	(/.f64 (pow.f64 (*.f64 #s(literal 0 binary64) n) (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 8 binary64))) (sqrt.f64 k))
	52.3%	(/.f64 (pow.f64 (*.f64 #s(literal -2 binary64) n) (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 2 binary64))) (sqrt.f64 k))
✓	99.6%	(/.f64 (.f64 (sqrt.f64 (.f64 n (PI.f64))) (sqrt.f64 #s(literal 2 binary64))) (.f64 (pow.f64 (.f64 (PI.f64) (*.f64 n #s(literal 2 binary64))) (/.f64 k #s(literal 2 binary64))) (sqrt.f64 k)))
	78.6%	(/.f64 (sqrt.f64 (/.f64 (.f64 (.f64 #s(literal 2 binary64) n) (PI.f64)) k)) (pow.f64 (.f64 (.f64 #s(literal 2 binary64) n) (PI.f64)) (/.f64 k #s(literal 2 binary64))))
	78.6%	(.f64 (pow.f64 (.f64 (.f64 #s(literal 2 binary64) n) (PI.f64)) (neg.f64 (/.f64 k #s(literal 2 binary64)))) (sqrt.f64 (/.f64 (.f64 (*.f64 #s(literal 2 binary64) n) (PI.f64)) k)))
	11.1%	#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (pow.f64 (.f64 (.f64 (/.f64 n k) #s(literal 2 binary64)) (*.f64 (/.f64 n k) #s(literal 2 binary64))) #s(literal 1/4 binary64)))
	45.2%	#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (/.f64 (sqrt.f64 (.f64 (.f64 #s(literal 2 binary64) n) (*.f64 (sqrt.f64 (PI.f64)) (sqrt.f64 (PI.f64))))) (sqrt.f64 k)))
✓	45.3%	#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (/.f64 (sqrt.f64 (.f64 (.f64 #s(literal 2 binary64) n) (PI.f64))) (sqrt.f64 k)))
	45.2%	#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (/.f64 #s(approx (* (sqrt 2) (+ (* (* (log (* (* 2 n) (PI))) (sqrt (* (* (pow k 3) (PI)) n))) -1/2) (sqrt (* (* (PI) n) k)))) (.f64 (.f64 (sqrt.f64 (*.f64 n (PI.f64))) (sqrt.f64 k)) (sqrt.f64 #s(literal 2 binary64)))) k))
	22.6%	#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (/.f64 #s(approx (* (sqrt 2) (+ (* (* (log (* (* 2 n) (PI))) (sqrt (* (* (pow k 3) (PI)) n))) -1/2) (sqrt (* (* (PI) n) k)))) (.f64 (.f64 (sqrt.f64 (sqrt.f64 (.f64 (.f64 (.f64 n (PI.f64)) k) (.f64 n (PI.f64))))) (sqrt.f64 (sqrt.f64 k))) (sqrt.f64 #s(literal 2 binary64)))) k))
	30.3%	#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (/.f64 #s(approx (* (sqrt 2) (+ (* (* (log (* (* 2 n) (PI))) (sqrt (* (* (pow k 3) (PI)) n))) -1/2) (sqrt (* (* (PI) n) k)))) (.f64 (.f64 (sqrt.f64 (sqrt.f64 (.f64 n (PI.f64)))) (sqrt.f64 (sqrt.f64 (.f64 k (.f64 (.f64 n (PI.f64)) k))))) (sqrt.f64 #s(literal 2 binary64)))) k))
✓	34.5%	#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (/.f64 #s(approx (* (sqrt 2) (+ (* (* (log (* (* 2 n) (PI))) (sqrt (* (* (pow k 3) (PI)) n))) -1/2) (sqrt (* (* (PI) n) k)))) (.f64 (sqrt.f64 (.f64 (*.f64 n (PI.f64)) k)) (sqrt.f64 #s(literal 2 binary64)))) k))
	34.6%	#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (/.f64 #s(approx (* (sqrt 2) (+ (* (* (log (* (* 2 n) (PI))) (sqrt (* (* (pow k 3) (PI)) n))) -1/2) (sqrt (* (* (PI) n) k)))) (sqrt.f64 (.f64 (.f64 (*.f64 n (PI.f64)) k) #s(literal 2 binary64)))) k))
✓	99.6%	#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (.f64 (pow.f64 (.f64 (*.f64 #s(literal 2 binary64) n) (PI.f64)) (fma.f64 #s(literal -1/2 binary64) k #s(literal 1/2 binary64))) (sqrt.f64 (/.f64 #s(literal 1 binary64) k))))
	45.3%	#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (.f64 (sqrt.f64 (.f64 (PI.f64) n)) (sqrt.f64 (/.f64 #s(literal 2 binary64) k))))
✓	35.4%	#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))))
	22.0%	#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt.f64 (/.f64 (fma.f64 (.f64 (PI.f64) n) k (.f64 k (.f64 (PI.f64) n))) (.f64 k k))))
✓	35.5%	#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt.f64 (.f64 (/.f64 (.f64 (PI.f64) n) k) #s(literal 2 binary64))))
	4.9%	#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt.f64 (.f64 (/.f64 (.f64 #s(literal 2 binary64) (sqrt.f64 (PI.f64))) k) (sqrt.f64 (PI.f64)))))
	4.9%	#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt.f64 (*.f64 (/.f64 (PI.f64) k) #s(literal 2 binary64))))
	8.7%	#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt.f64 (*.f64 (/.f64 n k) #s(literal 2 binary64))))
	4.9%	#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt.f64 (*.f64 (/.f64 #s(literal 2 binary64) k) (PI.f64))))
	35.5%	#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) (/.f64 n k))))
	35.5%	#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt.f64 (.f64 (.f64 (/.f64 (PI.f64) k) n) #s(literal 2 binary64))))

Compiler

Compiled 3 039 to 960 computations (68.4% saved)

regimes113.0ms (1%)

Memory

32.9MiB live, 124.9MiB allocated; 5ms collecting garbage

Counts

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

Calls

4 calls:

55.0ms	(.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))))
19.0ms	n
18.0ms	(.f64 (.f64 #s(literal 2 binary64) (PI.f64)) n)
17.0ms	k

Results

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

Compiler

Compiled 23 to 23 computations (0% saved)

regimes80.0ms (0.7%)

Memory

-2.4MiB live, 96.4MiB allocated; 22ms collecting garbage

Counts

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

Outputs

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

Calls

4 calls:

34.0ms	n
15.0ms	(.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) (pow.f64 (.f64 (*.f64 #s(literal 2 binary64) (PI.f64)) n) (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 2 binary64))))
14.0ms	k
14.0ms	(.f64 (.f64 #s(literal 2 binary64) (PI.f64)) n)

Results

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

Compiler

Compiled 23 to 23 computations (0% saved)

regimes60.0ms (0.5%)

Memory

-9.9MiB live, 83.0MiB allocated; 3ms collecting garbage

Counts

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

Outputs

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

Calls

4 calls:

17.0ms	k
14.0ms	n
14.0ms	(.f64 (.f64 #s(literal 2 binary64) (PI.f64)) n)
12.0ms	(.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) (pow.f64 (.f64 (*.f64 #s(literal 2 binary64) (PI.f64)) n) (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 2 binary64))))

Results

Accuracy	Segments	Branch
99.6%	1	`k`
99.6%	1	`(.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	`n`

Compiler

Compiled 23 to 23 computations (0% saved)

regimes60.0ms (0.5%)

Memory

-17.1MiB live, 82.8MiB allocated; 8ms collecting garbage

Counts

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

Outputs

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

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

Calls

4 calls:

17.0ms	k
16.0ms	(.f64 (.f64 #s(literal 2 binary64) (PI.f64)) n)
13.0ms	n
11.0ms	(.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
62.9%	5	`(.f64 (.f64 #s(literal 2 binary64) (PI.f64)) n)`
97.7%	3	`(.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) (pow.f64 (.f64 (*.f64 #s(literal 2 binary64) (PI.f64)) n) (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 2 binary64))))`
96.2%	2	`k`
62.9%	5	`n`

Compiler

Compiled 23 to 23 computations (0% saved)

regimes55.0ms (0.5%)

Memory

11.1MiB live, 99.8MiB allocated; 6ms collecting garbage

Counts

48 → 3

Calls

Call 1

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

Outputs

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

#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (/.f64 (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))) (/.f64 #s(approx (* (sqrt 2) (+ (* (* (log (* (* 2 n) (PI))) (sqrt (* (* (pow k 3) (PI)) n))) -1/2) (sqrt (* (* (PI) n) k)))) (*.f64 (*.f64 (sqrt.f64 (sqrt.f64 (*.f64 n (PI.f64)))) (sqrt.f64 (sqrt.f64 (*.f64 k (*.f64 (*.f64 n (PI.f64)) k))))) (sqrt.f64 #s(literal 2 binary64)))) k))

Calls

4 calls:

14.0ms	(.f64 (.f64 #s(literal 2 binary64) (PI.f64)) n)
13.0ms	(.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))))
12.0ms	n
12.0ms	k

Results

Accuracy	Segments	Branch
45.3%	1	`(.f64 (.f64 #s(literal 2 binary64) (PI.f64)) n)`
45.3%	1	`n`
56.3%	3	`(.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) (pow.f64 (.f64 (*.f64 #s(literal 2 binary64) (PI.f64)) n) (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 2 binary64))))`
51.5%	2	`k`

Compiler

Compiled 23 to 23 computations (0% saved)

regimes13.0ms (0.1%)

Memory

30.0MiB live, 30.0MiB allocated; 0ms collecting garbage

Counts

47 → 3

Calls

Call 1

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

Outputs

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

#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (/.f64 (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))) (/.f64 #s(approx (* (sqrt 2) (+ (* (* (log (* (* 2 n) (PI))) (sqrt (* (* (pow k 3) (PI)) n))) -1/2) (sqrt (* (* (PI) n) k)))) (*.f64 (*.f64 (sqrt.f64 (sqrt.f64 (*.f64 n (PI.f64)))) (sqrt.f64 (sqrt.f64 (*.f64 k (*.f64 (*.f64 n (PI.f64)) k))))) (sqrt.f64 #s(literal 2 binary64)))) k))

Calls

1 calls:

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
53.6%	3	`(.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) (pow.f64 (.f64 (*.f64 #s(literal 2 binary64) (PI.f64)) n) (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 2 binary64))))`

Compiler

Compiled 16 to 13 computations (18.8% saved)

regimes27.0ms (0.2%)

Memory

-13.9MiB live, 41.5MiB allocated; 6ms collecting garbage

Counts

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

Outputs

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

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

Calls

2 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))))
11.0ms	k

Results

Accuracy	Segments	Branch
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 17 to 15 computations (11.8% saved)

regimes28.0ms (0.2%)

Memory

-33.4MiB live, 59.7MiB allocated; 4ms collecting garbage

Counts

22 → 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) k) (PI.f64))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt.f64 (*.f64 (/.f64 n k) #s(literal 2 binary64))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt.f64 (*.f64 (/.f64 (PI.f64) k) #s(literal 2 binary64))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) (/.f64 n k))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt.f64 (.f64 (.f64 #s(literal 2 binary64) (PI.f64)) (/.f64 n k))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt.f64 (.f64 (.f64 n (PI.f64)) (/.f64 #s(literal 2 binary64) k))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt.f64 (.f64 (.f64 n (/.f64 (PI.f64) k)) #s(literal 2 binary64))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt.f64 (.f64 (.f64 (/.f64 (PI.f64) k) n) #s(literal 2 binary64))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt.f64 (.f64 (/.f64 (.f64 (PI.f64) n) k) #s(literal 2 binary64))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (/.f64 #s(approx (* (sqrt 2) (+ (* (* (log (* (* 2 n) (PI))) (sqrt (* (* (pow k 3) (PI)) n))) -1/2) (sqrt (* (* (PI) n) k)))) (sqrt.f64 (.f64 (.f64 (*.f64 n (PI.f64)) k) #s(literal 2 binary64)))) k))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (.f64 (sqrt.f64 #s(literal 2 binary64)) (sqrt.f64 (/.f64 (.f64 (PI.f64) n) k))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (.f64 (sqrt.f64 n) (sqrt.f64 (/.f64 (.f64 #s(literal 2 binary64) (PI.f64)) k))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (.f64 (sqrt.f64 (.f64 #s(literal 2 binary64) n)) (sqrt.f64 (/.f64 (PI.f64) k))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (.f64 (sqrt.f64 (.f64 n (PI.f64))) (sqrt.f64 (/.f64 #s(literal 2 binary64) k))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (.f64 (sqrt.f64 (.f64 (PI.f64) #s(literal 2 binary64))) (sqrt.f64 (/.f64 n k))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (.f64 (sqrt.f64 (.f64 (PI.f64) n)) (sqrt.f64 (/.f64 #s(literal 2 binary64) k))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (/.f64 (sqrt.f64 (.f64 (PI.f64) (.f64 n #s(literal 2 binary64)))) (sqrt.f64 k)))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (/.f64 (sqrt.f64 (.f64 (.f64 #s(literal 2 binary64) n) (PI.f64))) (sqrt.f64 k)))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (/.f64 #s(approx (* (sqrt 2) (+ (* (* (log (* (* 2 n) (PI))) (sqrt (* (* (pow k 3) (PI)) n))) -1/2) (sqrt (* (* (PI) n) k)))) (.f64 (sqrt.f64 n) (sqrt.f64 (.f64 (*.f64 k (PI.f64)) #s(literal 2 binary64))))) k))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (/.f64 #s(approx (* (sqrt 2) (+ (* (* (log (* (* 2 n) (PI))) (sqrt (* (* (pow k 3) (PI)) n))) -1/2) (sqrt (* (* (PI) n) k)))) (.f64 (sqrt.f64 (.f64 n (PI.f64))) (sqrt.f64 (*.f64 k #s(literal 2 binary64))))) k))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (/.f64 #s(approx (* (sqrt 2) (+ (* (* (log (* (* 2 n) (PI))) (sqrt (* (* (pow k 3) (PI)) n))) -1/2) (sqrt (* (* (PI) n) k)))) (.f64 (sqrt.f64 (.f64 (*.f64 #s(literal 2 binary64) n) (PI.f64))) (sqrt.f64 k))) k))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (/.f64 #s(approx (* (sqrt 2) (+ (* (* (log (* (* 2 n) (PI))) (sqrt (* (* (pow k 3) (PI)) n))) -1/2) (sqrt (* (* (PI) n) k)))) (.f64 (sqrt.f64 (.f64 (*.f64 n (PI.f64)) k)) (sqrt.f64 #s(literal 2 binary64)))) k))

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

Calls

4 calls:

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

Results

Accuracy	Segments	Branch
45.3%	1	`(.f64 (.f64 #s(literal 2 binary64) (PI.f64)) n)`
45.3%	1	`n`
45.3%	1	`k`
45.3%	1	`(.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) (pow.f64 (.f64 (*.f64 #s(literal 2 binary64) (PI.f64)) n) (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 2 binary64))))`

Compiler

Compiled 23 to 23 computations (0% saved)

regimes20.0ms (0.2%)

Memory

38.9MiB live, 38.9MiB allocated; 0ms collecting garbage

Counts

16 → 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) k) (PI.f64))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt.f64 (*.f64 (/.f64 n k) #s(literal 2 binary64))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt.f64 (*.f64 (/.f64 (PI.f64) k) #s(literal 2 binary64))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) (/.f64 n k))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt.f64 (.f64 (.f64 #s(literal 2 binary64) (PI.f64)) (/.f64 n k))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt.f64 (.f64 (.f64 n (PI.f64)) (/.f64 #s(literal 2 binary64) k))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt.f64 (.f64 (.f64 n (/.f64 (PI.f64) k)) #s(literal 2 binary64))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt.f64 (.f64 (.f64 (/.f64 (PI.f64) k) n) #s(literal 2 binary64))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt.f64 (.f64 (/.f64 (.f64 (PI.f64) n) k) #s(literal 2 binary64))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (/.f64 #s(approx (* (sqrt 2) (+ (* (* (log (* (* 2 n) (PI))) (sqrt (* (* (pow k 3) (PI)) n))) -1/2) (sqrt (* (* (PI) n) k)))) (sqrt.f64 (.f64 (.f64 (*.f64 n (PI.f64)) k) #s(literal 2 binary64)))) k))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (.f64 (sqrt.f64 #s(literal 2 binary64)) (sqrt.f64 (/.f64 (.f64 (PI.f64) n) k))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (.f64 (sqrt.f64 n) (sqrt.f64 (/.f64 (.f64 #s(literal 2 binary64) (PI.f64)) k))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (.f64 (sqrt.f64 (.f64 #s(literal 2 binary64) n)) (sqrt.f64 (/.f64 (PI.f64) k))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (.f64 (sqrt.f64 (.f64 n (PI.f64))) (sqrt.f64 (/.f64 #s(literal 2 binary64) k))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (.f64 (sqrt.f64 (.f64 (PI.f64) #s(literal 2 binary64))) (sqrt.f64 (/.f64 n k))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (.f64 (sqrt.f64 (.f64 (PI.f64) n)) (sqrt.f64 (/.f64 #s(literal 2 binary64) k))))

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

Calls

4 calls:

5.0ms	n
5.0ms	(.f64 (.f64 #s(literal 2 binary64) (PI.f64)) n)
5.0ms	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
45.3%	1	`(.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) (pow.f64 (.f64 (*.f64 #s(literal 2 binary64) (PI.f64)) n) (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 2 binary64))))`
45.3%	1	`(.f64 (.f64 #s(literal 2 binary64) (PI.f64)) n)`
45.3%	1	`k`
45.3%	1	`n`

Compiler

Compiled 23 to 23 computations (0% saved)

regimes22.0ms (0.2%)

Memory

-24.5MiB live, 22.0MiB allocated; 2ms collecting garbage

Counts

13 → 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) k) (PI.f64))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt.f64 (*.f64 (/.f64 n k) #s(literal 2 binary64))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt.f64 (*.f64 (/.f64 (PI.f64) k) #s(literal 2 binary64))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) (/.f64 n k))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt.f64 (.f64 (.f64 #s(literal 2 binary64) (PI.f64)) (/.f64 n k))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt.f64 (.f64 (.f64 n (PI.f64)) (/.f64 #s(literal 2 binary64) k))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt.f64 (.f64 (.f64 n (/.f64 (PI.f64) k)) #s(literal 2 binary64))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt.f64 (.f64 (.f64 (/.f64 (PI.f64) k) n) #s(literal 2 binary64))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt.f64 (.f64 (/.f64 (.f64 (PI.f64) n) k) #s(literal 2 binary64))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (/.f64 #s(approx (* (sqrt 2) (+ (* (* (log (* (* 2 n) (PI))) (sqrt (* (* (pow k 3) (PI)) n))) -1/2) (sqrt (* (* (PI) n) k)))) (sqrt.f64 (.f64 (.f64 (*.f64 n (PI.f64)) k) #s(literal 2 binary64)))) k))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (.f64 (sqrt.f64 #s(literal 2 binary64)) (sqrt.f64 (/.f64 (.f64 (PI.f64) n) k))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (.f64 (sqrt.f64 n) (sqrt.f64 (/.f64 (.f64 #s(literal 2 binary64) (PI.f64)) k))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (.f64 (sqrt.f64 (.f64 #s(literal 2 binary64) n)) (sqrt.f64 (/.f64 (PI.f64) k))))

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

Calls

4 calls:

9.0ms	k
4.0ms	(.f64 (.f64 #s(literal 2 binary64) (PI.f64)) n)
4.0ms	n
4.0ms	(.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) (pow.f64 (.f64 (*.f64 #s(literal 2 binary64) (PI.f64)) n) (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 2 binary64))))

Results

Accuracy	Segments	Branch
45.3%	1	`(.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) (pow.f64 (.f64 (*.f64 #s(literal 2 binary64) (PI.f64)) n) (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 2 binary64))))`
45.3%	1	`(.f64 (.f64 #s(literal 2 binary64) (PI.f64)) n)`
45.3%	1	`k`
45.3%	1	`n`

Compiler

Compiled 23 to 23 computations (0% saved)

regimes15.0ms (0.1%)

Memory

20.3MiB live, 20.3MiB allocated; 0ms collecting garbage

Counts

11 → 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) k) (PI.f64))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt.f64 (*.f64 (/.f64 n k) #s(literal 2 binary64))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt.f64 (*.f64 (/.f64 (PI.f64) k) #s(literal 2 binary64))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) (/.f64 n k))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt.f64 (.f64 (.f64 #s(literal 2 binary64) (PI.f64)) (/.f64 n k))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt.f64 (.f64 (.f64 n (PI.f64)) (/.f64 #s(literal 2 binary64) k))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt.f64 (.f64 (.f64 n (/.f64 (PI.f64) k)) #s(literal 2 binary64))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt.f64 (.f64 (.f64 (/.f64 (PI.f64) k) n) #s(literal 2 binary64))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt.f64 (.f64 (/.f64 (.f64 (PI.f64) n) k) #s(literal 2 binary64))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (/.f64 #s(approx (* (sqrt 2) (+ (* (* (log (* (* 2 n) (PI))) (sqrt (* (* (pow k 3) (PI)) n))) -1/2) (sqrt (* (* (PI) n) k)))) (sqrt.f64 (.f64 (.f64 (*.f64 n (PI.f64)) k) #s(literal 2 binary64)))) k))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (.f64 (sqrt.f64 #s(literal 2 binary64)) (sqrt.f64 (/.f64 (.f64 (PI.f64) n) k))))

Outputs

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

#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (/.f64 #s(approx (* (sqrt 2) (+ (* (* (log (* (* 2 n) (PI))) (sqrt (* (* (pow k 3) (PI)) n))) -1/2) (sqrt (* (* (PI) n) k)))) (sqrt.f64 (*.f64 (*.f64 (*.f64 n (PI.f64)) k) #s(literal 2 binary64)))) k))

Calls

4 calls:

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

Results

Accuracy	Segments	Branch
45.4%	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))))`
45.2%	2	`(.f64 (.f64 #s(literal 2 binary64) (PI.f64)) n)`
35.5%	1	`k`
45.2%	2	`n`

Compiler

Compiled 23 to 23 computations (0% saved)

regimes14.0ms (0.1%)

Memory

-35.2MiB live, 16.3MiB allocated; 3ms collecting garbage

Counts

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

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

Calls

3 calls:

7.0ms

(*.f64 (*.f64 #s(literal 2 binary64) (PI.f64)) n)

3.0ms

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

Results

Accuracy	Segments	Branch
35.5%	1	`(.f64 (.f64 #s(literal 2 binary64) (PI.f64)) n)`
35.5%	1	`n`
35.5%	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 22 to 21 computations (4.5% saved)

regimes12.0ms (0.1%)

Memory

25.2MiB live, 25.2MiB allocated; 0ms collecting garbage

Counts

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

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

Calls

4 calls:

3.0ms	(.f64 (.f64 #s(literal 2 binary64) (PI.f64)) n)
3.0ms	n
3.0ms	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
35.5%	1	`k`
35.5%	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))))`
35.5%	1	`(.f64 (.f64 #s(literal 2 binary64) (PI.f64)) n)`
35.5%	1	`n`

Compiler

Compiled 23 to 23 computations (0% saved)

regimes13.0ms (0.1%)

Memory

-24.4MiB live, 19.9MiB allocated; 4ms collecting garbage

Counts

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

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

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
35.5%	1	`k`
35.5%	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))))`
35.5%	1	`(.f64 (.f64 #s(literal 2 binary64) (PI.f64)) n)`
35.5%	1	`n`

Compiler

Compiled 23 to 23 computations (0% saved)

regimes7.0ms (0.1%)

Memory

14.3MiB live, 14.3MiB allocated; 0ms collecting garbage

Counts

3 → 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) k) (PI.f64))))

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

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

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

Calls

4 calls:

2.0ms	n
2.0ms	(.f64 (.f64 #s(literal 2 binary64) (PI.f64)) n)
1.0ms	k
1.0ms	(.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) (pow.f64 (.f64 (*.f64 #s(literal 2 binary64) (PI.f64)) n) (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 2 binary64))))

Results

Accuracy	Segments	Branch
8.7%	1	`k`
8.7%	1	`(.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) (pow.f64 (.f64 (*.f64 #s(literal 2 binary64) (PI.f64)) n) (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 2 binary64))))`
8.7%	1	`(.f64 (.f64 #s(literal 2 binary64) (PI.f64)) n)`
8.7%	1	`n`

Compiler

Compiled 23 to 23 computations (0% saved)

regimes5.0ms (0%)

Memory

14.1MiB live, 14.1MiB allocated; 0ms collecting garbage

Accuracy

Total -0.0b remaining (-0%)

Threshold costs -0b (-0%)

Counts

1 → 1

Calls

Call 1

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

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

Calls

4 calls:

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

Results

Accuracy	Segments	Branch
4.9%	1	`(.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) (pow.f64 (.f64 (*.f64 #s(literal 2 binary64) (PI.f64)) n) (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 2 binary64))))`
4.9%	1	`k`
4.9%	1	`(.f64 (.f64 #s(literal 2 binary64) (PI.f64)) n)`
4.9%	1	`n`

Compiler

Compiled 23 to 23 computations (0% saved)

bsearch25.0ms (0.2%)

Memory

-6.2MiB live, 38.9MiB allocated; 3ms collecting garbage

Algorithm

1×	binary-search

Stop Event

1×	narrow-enough

Steps

Time	Left	Right
22.0ms	66074768936.3803	27223907735161640.0

Samples

16.0ms

144×

valid

Compiler

Compiled 361 to 324 computations (10.2% saved)

Precisions

Click to see histograms. Total time spent on operations: 11.0ms

ival-pow: 4.0ms (36.7% of total)

ival-div: 2.0ms (18.4% of total)

ival-mult: 2.0ms (18.4% of total)

ival-pi: 1.0ms (9.2% of total)

ival-sub: 1.0ms (9.2% of total)

ival-sqrt: 1.0ms (9.2% 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)

bsearch1.0ms (0%)

Memory

0.8MiB live, 0.8MiB allocated; 0ms collecting garbage

Algorithm

2×	left-value

Steps

Time	Left	Right
0.0ms	5.794038048803666e+272	+inf
0.0ms	0.0	7.45464056481539e-109

Compiler

Compiled 19 to 18 computations (5.3% saved)

bsearch1.0ms (0%)

Memory

0.9MiB live, 0.9MiB allocated; 0ms collecting garbage

Algorithm

2×	left-value

Steps

Time	Left	Right
0.0ms	5.794038048803666e+272	+inf
0.0ms	0.0	7.45464056481539e-109

Compiler

Compiled 19 to 18 computations (5.3% saved)

bsearch0.0ms (0%)

Memory

0.5MiB live, 0.5MiB allocated; 0ms collecting garbage

Algorithm

1×	left-value

Steps

Time	Left	Right
0.0ms	0.0	7.45464056481539e-109

Compiler

Compiled 19 to 18 computations (5.3% saved)

bsearch0.0ms (0%)

Memory

0.4MiB live, 0.4MiB allocated; 0ms collecting garbage

Algorithm

1×	left-value

Steps

Time	Left	Right
0.0ms	4.7415183117730326e+142	2.8539674460733873e+145

Compiler

Compiled 19 to 18 computations (5.3% saved)

simplify58.0ms (0.5%)

Memory

-12.9MiB live, 32.9MiB allocated; 3ms collecting garbage

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	139	826
1	184	784
2	255	784
3	455	784
4	912	784
5	1519	784
6	1822	784
7	1906	784
8	1949	784
9	1974	784
10	1989	784
11	1989	784

Stop Event

1×

saturated

Calls

Call 1

Inputs
(/.f64 (.f64 (sqrt.f64 (.f64 (PI.f64) (.f64 n #s(literal 2 binary64)))) #s(literal 1 binary64)) (.f64 (pow.f64 (.f64 (PI.f64) (.f64 n #s(literal 2 binary64))) (/.f64 k #s(literal 2 binary64))) (sqrt.f64 k)))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (.f64 (/.f64 (sqrt.f64 (.f64 (PI.f64) (.f64 n #s(literal 2 binary64)))) (pow.f64 (.f64 (PI.f64) (.f64 n #s(literal 2 binary64))) (.f64 #s(literal 1/2 binary64) k))) (sqrt.f64 (/.f64 #s(literal 1 binary64) k))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (.f64 (pow.f64 (.f64 (*.f64 #s(literal 2 binary64) n) (PI.f64)) (fma.f64 #s(literal -1/2 binary64) k #s(literal 1/2 binary64))) (sqrt.f64 (/.f64 #s(literal 1 binary64) k))))
(if (<=.f64 k #s(literal 2300000000000000 binary64)) #s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (/.f64 (sqrt.f64 (.f64 (PI.f64) (.f64 n #s(literal 2 binary64)))) (sqrt.f64 k))) (/.f64 (pow.f64 (*.f64 #s(literal -2 binary64) n) (/.f64 (-.f64 #s(literal 1 binary64) k) #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))) (pow.f64 (.f64 (.f64 (/.f64 n k) #s(literal 2 binary64)) (.f64 (/.f64 n k) #s(literal 2 binary64))) #s(literal 1/4 binary64))) (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 999999999999999945402341696592674884578976541955442659132610359825718694242914119314842162820675279649039207299571308833846909191138684972507989282336695782607667040225918275050684065261167516978177354790265605065466066369376850351293060923539046438669680406904714953752576 binary64)) #s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (/.f64 (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))) (/.f64 #s(approx (* (sqrt 2) (+ (* (* (log (* (* 2 n) (PI))) (sqrt (* (* (pow k 3) (PI)) n))) -1/2) (sqrt (* (* (PI) n) k)))) (.f64 (.f64 (sqrt.f64 (sqrt.f64 (.f64 n (PI.f64)))) (sqrt.f64 (sqrt.f64 (.f64 k (.f64 (.f64 n (PI.f64)) k))))) (sqrt.f64 #s(literal 2 binary64)))) 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 (fma.f64 (.f64 k n) (PI.f64) (.f64 (.f64 n (PI.f64)) k)) (.f64 k 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 999999999999999945402341696592674884578976541955442659132610359825718694242914119314842162820675279649039207299571308833846909191138684972507989282336695782607667040225918275050684065261167516978177354790265605065466066369376850351293060923539046438669680406904714953752576 binary64)) #s(approx ( (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (/.f64 (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))) (/.f64 #s(approx (* (sqrt 2) (+ (* (* (log (* (* 2 n) (PI))) (sqrt (* (* (pow k 3) (PI)) n))) -1/2) (sqrt (* (* (PI) n) k)))) (.f64 (.f64 (sqrt.f64 (sqrt.f64 (.f64 n (PI.f64)))) (sqrt.f64 (sqrt.f64 (.f64 k (.f64 (.f64 n (PI.f64)) k))))) (sqrt.f64 #s(literal 2 binary64)))) 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 (fma.f64 (.f64 k n) (PI.f64) (.f64 (.f64 n (PI.f64)) k)) (.f64 k k)))) #s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (/.f64 (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))) (/.f64 (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))) (.f64 (sqrt.f64 (.f64 n (PI.f64))) (sqrt.f64 (/.f64 #s(literal 2 binary64) k))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (.f64 (sqrt.f64 n) (sqrt.f64 (/.f64 (.f64 #s(literal 2 binary64) (PI.f64)) k))))
(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 50000000000000001187271617932555267870432896391434109373673249433511871477101028628408881410804164706467298456692005803789670658494504078671872 binary64)) #s(approx ( (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt.f64 (.f64 (/.f64 (.f64 (PI.f64) n) k) #s(literal 2 binary64)))) #s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (/.f64 #s(approx (* (sqrt 2) (+ (* (* (log (* (* 2 n) (PI))) (sqrt (* (* (pow k 3) (PI)) n))) -1/2) (sqrt (* (* (PI) n) k)))) (sqrt.f64 (.f64 (.f64 (*.f64 n (PI.f64)) k) #s(literal 2 binary64)))) k)))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt.f64 (.f64 (/.f64 (.f64 (PI.f64) n) k) #s(literal 2 binary64))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt.f64 (.f64 (.f64 n (/.f64 (PI.f64) k)) #s(literal 2 binary64))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) (/.f64 n k))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt.f64 (*.f64 (/.f64 n k) #s(literal 2 binary64))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt.f64 (*.f64 (/.f64 #s(literal 2 binary64) k) (PI.f64))))

Outputs
(/.f64 (.f64 (sqrt.f64 (.f64 (PI.f64) (.f64 n #s(literal 2 binary64)))) #s(literal 1 binary64)) (.f64 (pow.f64 (.f64 (PI.f64) (.f64 n #s(literal 2 binary64))) (/.f64 k #s(literal 2 binary64))) (sqrt.f64 k)))
(/.f64 (sqrt.f64 (.f64 (PI.f64) (.f64 n #s(literal 2 binary64)))) (.f64 (pow.f64 (.f64 (PI.f64) (*.f64 n #s(literal 2 binary64))) (/.f64 k #s(literal 2 binary64))) (sqrt.f64 k)))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (.f64 (/.f64 (sqrt.f64 (.f64 (PI.f64) (.f64 n #s(literal 2 binary64)))) (pow.f64 (.f64 (PI.f64) (.f64 n #s(literal 2 binary64))) (.f64 #s(literal 1/2 binary64) k))) (sqrt.f64 (/.f64 #s(literal 1 binary64) k))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (.f64 (/.f64 (sqrt.f64 (.f64 (PI.f64) (.f64 n #s(literal 2 binary64)))) (pow.f64 (.f64 (PI.f64) (.f64 n #s(literal 2 binary64))) (.f64 #s(literal 1/2 binary64) k))) (sqrt.f64 (pow.f64 k #s(literal -1 binary64)))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (.f64 (pow.f64 (.f64 (*.f64 #s(literal 2 binary64) n) (PI.f64)) (fma.f64 #s(literal -1/2 binary64) k #s(literal 1/2 binary64))) (sqrt.f64 (/.f64 #s(literal 1 binary64) k))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (.f64 (pow.f64 (.f64 (*.f64 #s(literal 2 binary64) n) (PI.f64)) (fma.f64 #s(literal -1/2 binary64) k #s(literal 1/2 binary64))) (sqrt.f64 (pow.f64 k #s(literal -1 binary64)))))
(if (<=.f64 k #s(literal 2300000000000000 binary64)) #s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (/.f64 (sqrt.f64 (.f64 (PI.f64) (.f64 n #s(literal 2 binary64)))) (sqrt.f64 k))) (/.f64 (pow.f64 (*.f64 #s(literal -2 binary64) n) (/.f64 (-.f64 #s(literal 1 binary64) k) #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))) (pow.f64 (.f64 (.f64 (/.f64 n k) #s(literal 2 binary64)) (.f64 (/.f64 n k) #s(literal 2 binary64))) #s(literal 1/4 binary64))) (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 999999999999999945402341696592674884578976541955442659132610359825718694242914119314842162820675279649039207299571308833846909191138684972507989282336695782607667040225918275050684065261167516978177354790265605065466066369376850351293060923539046438669680406904714953752576 binary64)) #s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (/.f64 (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))) (/.f64 #s(approx (* (sqrt 2) (+ (* (* (log (* (* 2 n) (PI))) (sqrt (* (* (pow k 3) (PI)) n))) -1/2) (sqrt (* (* (PI) n) k)))) (.f64 (.f64 (sqrt.f64 (sqrt.f64 (.f64 n (PI.f64)))) (sqrt.f64 (sqrt.f64 (.f64 k (.f64 (.f64 n (PI.f64)) k))))) (sqrt.f64 #s(literal 2 binary64)))) 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))) (pow.f64 (.f64 (.f64 (/.f64 n k) #s(literal 2 binary64)) (.f64 (/.f64 n k) #s(literal 2 binary64))) #s(literal 1/4 binary64))) (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 999999999999999945402341696592674884578976541955442659132610359825718694242914119314842162820675279649039207299571308833846909191138684972507989282336695782607667040225918275050684065261167516978177354790265605065466066369376850351293060923539046438669680406904714953752576 binary64)) #s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (/.f64 (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))) (/.f64 #s(approx (* (sqrt 2) (+ (* (* (log (* (* 2 n) (PI))) (sqrt (* (* (pow k 3) (PI)) n))) -1/2) (sqrt (* (* (PI) n) k)))) (.f64 (.f64 (sqrt.f64 (sqrt.f64 (.f64 n (PI.f64)))) (sqrt.f64 (sqrt.f64 (.f64 k (.f64 (.f64 n (PI.f64)) k))))) (sqrt.f64 #s(literal 2 binary64)))) 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 (fma.f64 (.f64 k n) (PI.f64) (.f64 (.f64 n (PI.f64)) k)) (.f64 k 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 999999999999999945402341696592674884578976541955442659132610359825718694242914119314842162820675279649039207299571308833846909191138684972507989282336695782607667040225918275050684065261167516978177354790265605065466066369376850351293060923539046438669680406904714953752576 binary64)) #s(approx ( (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (/.f64 (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))) (/.f64 #s(approx (* (sqrt 2) (+ (* (* (log (* (* 2 n) (PI))) (sqrt (* (* (pow k 3) (PI)) n))) -1/2) (sqrt (* (* (PI) n) k)))) (.f64 (.f64 (sqrt.f64 (sqrt.f64 (.f64 n (PI.f64)))) (sqrt.f64 (sqrt.f64 (.f64 k (.f64 (.f64 n (PI.f64)) k))))) (sqrt.f64 #s(literal 2 binary64)))) 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 (fma.f64 (.f64 k n) (PI.f64) (.f64 (.f64 n (PI.f64)) k)) (.f64 k 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 999999999999999945402341696592674884578976541955442659132610359825718694242914119314842162820675279649039207299571308833846909191138684972507989282336695782607667040225918275050684065261167516978177354790265605065466066369376850351293060923539046438669680406904714953752576 binary64)) #s(approx ( (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (/.f64 (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))) (/.f64 #s(approx (* (sqrt 2) (+ (* (* (log (* (* 2 n) (PI))) (sqrt (* (* (pow k 3) (PI)) n))) -1/2) (sqrt (* (* (PI) n) k)))) (.f64 (.f64 (sqrt.f64 (sqrt.f64 (.f64 n (PI.f64)))) (sqrt.f64 (sqrt.f64 (.f64 k (.f64 (.f64 n (PI.f64)) k))))) (sqrt.f64 #s(literal 2 binary64)))) 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 (fma.f64 (.f64 k n) (PI.f64) (.f64 (.f64 n (PI.f64)) k)) (.f64 k k)))) #s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (/.f64 (sqrt.f64 (.f64 (PI.f64) (.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 (fma.f64 (.f64 k n) (PI.f64) (.f64 (.f64 n (PI.f64)) k)) (.f64 k k)))) #s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (/.f64 (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))) (/.f64 (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))) (.f64 (sqrt.f64 (.f64 n (PI.f64))) (sqrt.f64 (/.f64 #s(literal 2 binary64) k))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (.f64 (sqrt.f64 n) (sqrt.f64 (/.f64 (.f64 #s(literal 2 binary64) (PI.f64)) k))))
(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 50000000000000001187271617932555267870432896391434109373673249433511871477101028628408881410804164706467298456692005803789670658494504078671872 binary64)) #s(approx ( (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt.f64 (.f64 (/.f64 (.f64 (PI.f64) n) k) #s(literal 2 binary64)))) #s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (/.f64 #s(approx (* (sqrt 2) (+ (* (* (log (* (* 2 n) (PI))) (sqrt (* (* (pow k 3) (PI)) n))) -1/2) (sqrt (* (* (PI) n) k)))) (sqrt.f64 (.f64 (.f64 (*.f64 n (PI.f64)) k) #s(literal 2 binary64)))) 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 50000000000000001187271617932555267870432896391434109373673249433511871477101028628408881410804164706467298456692005803789670658494504078671872 binary64)) #s(approx ( (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt.f64 (.f64 (/.f64 (.f64 (PI.f64) n) k) #s(literal 2 binary64)))) #s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (/.f64 #s(approx (* (sqrt 2) (+ (* (* (log (* (* 2 n) (PI))) (sqrt (* (* (pow k 3) (PI)) n))) -1/2) (sqrt (* (* (PI) n) k)))) (sqrt.f64 (.f64 (.f64 (*.f64 n (PI.f64)) k) #s(literal 2 binary64)))) k)))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt.f64 (.f64 (/.f64 (.f64 (PI.f64) n) k) #s(literal 2 binary64))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt.f64 (.f64 (.f64 n (/.f64 (PI.f64) k)) #s(literal 2 binary64))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) (/.f64 n k))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt.f64 (*.f64 (/.f64 n k) #s(literal 2 binary64))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt.f64 (*.f64 (/.f64 #s(literal 2 binary64) k) (PI.f64))))

derivations1.8s (15.5%)

Memory

-102.3MiB live, 1 087.8MiB allocated; 1.2s collecting garbage

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	120	502
1	378	489
2	1377	453
3	4131	453
0	8166	441
0	48	254
0	79	220
1	236	203
2	1043	161
0	9239	161
0	64	344
0	96	313
1	282	300
2	1344	300
0	8241	297
0	66	470
0	116	459
1	377	431
2	2321	431
0	8178	428
0	278	1898
1	1011	1767
2	4452	1737
0	8231	1688
0	13	38
0	22	38
1	83	35
2	446	35
3	4007	29
0	8921	29

Stop Event

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

Compiler

Compiled 826 to 142 computations (82.8% saved)

preprocess144.0ms (1.2%)

Memory: -21.2MiB live, 119.5MiB allocated; 23ms collecting garbage
Compiler: Compiled 1 684 to 310 computations (81.6% saved)

end0.0ms (0%)

Memory: 0.0MiB live, 0.0MiB allocated; 0ms collecting garbage

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	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

start0.0ms (0%)

analyze155.0ms (1.3%)

sample4.2s (36%)

explain170.0ms (1.4%)

preprocess29.0ms (0.2%)

eval0.0ms (0%)

prune0.0ms (0%)

simplify8.0ms (0.1%)

localize43.0ms (0.4%)

series73.0ms (0.6%)

simplify252.0ms (2.1%)

rewrite232.0ms (2%)

eval57.0ms (0.5%)

prune22.0ms (0.2%)

simplify316.0ms (2.7%)

localize282.0ms (2.4%)

series229.0ms (1.9%)

simplify310.0ms (2.6%)

rewrite331.0ms (2.8%)

eval264.0ms (2.2%)

prune48.0ms (0.4%)

simplify167.0ms (1.4%)

localize183.0ms (1.5%)

series71.0ms (0.6%)

simplify156.0ms (1.3%)

rewrite228.0ms (1.9%)

eval231.0ms (2%)

prune149.0ms (1.3%)

simplify57.0ms (0.5%)

localize154.0ms (1.3%)

series70.0ms (0.6%)

simplify157.0ms (1.3%)

rewrite232.0ms (2%)

eval209.0ms (1.8%)

prune68.0ms (0.6%)

regimes113.0ms (1%)

regimes80.0ms (0.7%)

regimes60.0ms (0.5%)

regimes60.0ms (0.5%)

regimes55.0ms (0.5%)

regimes13.0ms (0.1%)

regimes27.0ms (0.2%)

regimes28.0ms (0.2%)

regimes20.0ms (0.2%)

regimes22.0ms (0.2%)

regimes15.0ms (0.1%)

regimes14.0ms (0.1%)

regimes12.0ms (0.1%)

regimes13.0ms (0.1%)

regimes7.0ms (0.1%)

regimes5.0ms (0%)

bsearch25.0ms (0.2%)

bsearch1.0ms (0%)

bsearch1.0ms (0%)

bsearch0.0ms (0%)

bsearch0.0ms (0%)

simplify58.0ms (0.5%)

derivations1.8s (15.5%)

preprocess144.0ms (1.2%)

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