Metrics for Migdal et al, Equation (51)

start0.0ms (0%)

Memory: 0.1MiB live, 0.1MiB allocated; 0ms collecting garbage

analyze157.0ms (1.4%)

Memory

15.8MiB live, 202.1MiB allocated; 35ms 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)

sample5.1s (44.5%)

Memory

3.7MiB live, 6 213.9MiB allocated; 2.3s collecting garbage

Samples

1.5s	4 437×	1	invalid
1.3s	1 446×	2	invalid
1.2s	8 256×	0	valid
31.0ms	363×	0	invalid
26.0ms	205×	0	exit

Precisions

Click to see histograms. Total time spent on operations: 3.2s

ival-sub: 800.0ms (25% of total)

ival-pow: 724.0ms (22.6% of total)

ival-mult: 565.0ms (17.6% of total)

ival-div: 512.0ms (16% of total)

ival-sqrt: 260.0ms (8.1% of total)

adjust: 163.0ms (5.1% of total)

ival-pi: 137.0ms (4.3% of total)

exact: 21.0ms (0.7% of total)

ival-true: 15.0ms (0.5% of total)

ival-assert: 8.0ms (0.2% of total)

Bogosity

explain166.0ms (1.5%)

Memory

-5.5MiB live, 338.7MiB allocated; 27ms collecting garbage

FPErrors

Click to see full error table

Ground Truth	Overpredictions	Example	Example	Subexpression
4	89	(3.2788665688986984e-100 2.897561222750627e-146)	-	`(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	93	20

Confusion

	Predicted +	Predicted -
+	4	0
-	89	163

Precision

0.043010752688172046

Recall

1.0

Confusion?

	Predicted +	Predicted Maybe	Predicted -
+	4	0	0
-	89	20	143

Precision?

0.035398230088495575

Recall?

1.0

Freqs

test

number	freq
0	163
1	93

Total Confusion?

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

Precision?

1.0

Recall?

1.0

Samples

78.0ms

512×

valid

Compiler

Compiled 128 to 43 computations (66.4% saved)

Precisions

Click to see histograms. Total time spent on operations: 42.0ms

ival-sqrt: 10.0ms (23.7% of total)

ival-pow: 10.0ms (23.7% of total)

ival-mult: 9.0ms (21.3% of total)

ival-div: 7.0ms (16.6% of total)

ival-sub: 3.0ms (7.1% of total)

ival-pi: 2.0ms (4.7% of total)

exact: 1.0ms (2.4% of total)

adjust: 0.0ms (0% of total)

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

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

preprocess33.0ms (0.3%)

Memory

-26.5MiB live, 62.5MiB allocated; 10ms collecting garbage

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 1 (0.0ms)

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

Stop Event

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

Calls

Call 1

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

Outputs

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

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

Compiler

Compiled 16 to 13 computations (18.8% saved)

eval0.0ms (0%)

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

prune0.0ms (0%)

Memory

1.7MiB live, 1.7MiB 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

20.7MiB live, 20.7MiB allocated; 0ms collecting garbage

Algorithm

1×	egg-herbie

Localize:

Found 4 expressions of interest:

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

Iterations

Useful iterations: 1 (0.0ms)

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

Stop Event

1×	iter limit
1×	saturated
1×	iter limit

Calls

Call 1

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

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

localize41.0ms (0.4%)

Memory

-19.3MiB live, 81.5MiB allocated; 7ms collecting garbage

Localize:

Found 4 expressions of interest:

New	Metric	Score
accuracy	0.14987944230411276	(pow.f64 (.f64 (.f64 #s(literal 2 binary64) (PI.f64)) n) (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 2 binary64)))
accuracy	0.171875	(.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	0.22265625	(.f64 (.f64 #s(literal 2 binary64) (PI.f64)) n)
accuracy	0.23828125	(/.f64 #s(literal 1 binary64) (sqrt.f64 k))

Samples

31.0ms

256×

valid

Compiler

Compiled 56 to 15 computations (73.2% saved)

Precisions

Click to see histograms. Total time spent on operations: 22.0ms

ival-pow: 7.0ms (32.3% of total)

ival-div: 4.0ms (18.4% of total)

ival-mult: 4.0ms (18.4% of total)

ival-pi: 2.0ms (9.2% of total)

ival-sqrt: 2.0ms (9.2% of total)

ival-sub: 1.0ms (4.6% 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

0.0MiB live, 137.4MiB allocated; 12ms 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
30.0ms	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))
11.0ms	n	@	inf	((* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (/ 1 (sqrt k)) (sqrt k) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2)) (* (* 2 (PI)) n))
3.0ms	k	@	-inf	((* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (/ 1 (sqrt k)) (sqrt k) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2)) (* (* 2 (PI)) n))
2.0ms	k	@	0	((* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (/ 1 (sqrt k)) (sqrt k) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2)) (* (* 2 (PI)) n))

simplify133.0ms (1.2%)

Memory

21.1MiB live, 201.2MiB allocated; 31ms collecting garbage

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

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

Stop Event

1×	iter limit
1×	node limit

Counts

22 → 22

Calls

Call 1

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

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

rewrite254.0ms (2.2%)

Memory

1.6MiB live, 278.4MiB allocated; 127ms 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))

eval56.0ms (0.5%)

Memory: 6.9MiB live, 95.9MiB allocated; 10ms collecting garbage
Compiler: Compiled 7 537 to 1 169 computations (84.5% saved)

prune28.0ms (0.2%)

Memory

11.7MiB live, 64.8MiB allocated; 16ms collecting garbage

Pruning

17 alts after pruning (17 fresh and 0 done)

	Pruned	Kept	Total
New	321	17	338
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	322	17	339

Accuracy

100.0%

Counts

339 → 17

Alt Table

Click to see full alt table

Status	Accuracy	Program
	29.4%	(/.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 (.f64 (sqrt.f64 k) (sqrt.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))))
	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)))
	99.4%	(.f64 (/.f64 #s(literal 1 binary64) (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))))
▶	99.4%	(.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))))
▶	71.7%	(.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) (.f64 (pow.f64 (*.f64 n #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)))))
	64.0%	(.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) #s(approx (pow ( (* 2 (PI)) n) (/ (- 1 k) 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))))))))))
▶	58.6%	(.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) #s(approx (pow ( (* 2 (PI)) n) (/ (- 1 k) 2)) (fma.f64 (.f64 (sqrt.f64 (.f64 (PI.f64) n)) (fma.f64 (.f64 (.f64 (pow.f64 (log.f64 (.f64 (.f64 #s(literal 2 binary64) n) (PI.f64))) #s(literal 2 binary64)) (sqrt.f64 #s(literal 2 binary64))) #s(literal 1/8 binary64)) k (.f64 (.f64 (log.f64 (.f64 (.f64 #s(literal 2 binary64) n) (PI.f64))) (sqrt.f64 #s(literal 2 binary64))) #s(literal -1/2 binary64)))) k (.f64 (sqrt.f64 (.f64 (PI.f64) n)) (sqrt.f64 #s(literal 2 binary64))))))
	99.5%	(.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) #s(approx (pow ( (* 2 (PI)) n) (/ (- 1 k) 2)) (pow.f64 (.f64 (.f64 #s(literal 2 binary64) n) (PI.f64)) (fma.f64 #s(literal -1/2 binary64) k #s(literal 1/2 binary64)))))
	48.5%	(.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)))))
	47.5%	(.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)))))
	96.4%	(.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))))
	54.8%	#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)))))
	54.6%	#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))))
▶	35.2%	#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (.f64 (sqrt.f64 #s(literal 2 binary64)) (sqrt.f64 (/.f64 (.f64 (PI.f64) n) k))))

Compiler

Compiled 1 094 to 764 computations (30.2% saved)

simplify399.0ms (3.5%)

Memory

-14.2MiB live, 460.9MiB allocated; 84ms collecting garbage

Algorithm

1×	egg-herbie

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	(.f64 (pow.f64 (.f64 n #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))))
cost-diff	0	(sqrt.f64 k)
cost-diff	0	(/.f64 #s(literal 1 binary64) (sqrt.f64 k))
cost-diff	2	(.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) (.f64 (pow.f64 (*.f64 n #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)))))
cost-diff	0	(sqrt.f64 k)
cost-diff	0	(/.f64 #s(literal 1 binary64) (sqrt.f64 k))
cost-diff	2	(.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) (pow.f64 (.f64 (.f64 (.f64 n #s(literal 2 binary64)) (sqrt.f64 (PI.f64))) (sqrt.f64 (PI.f64))) (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 2 binary64))))
cost-diff	4	(.f64 (.f64 (*.f64 n #s(literal 2 binary64)) (sqrt.f64 (PI.f64))) (sqrt.f64 (PI.f64)))
cost-diff	0	(sqrt.f64 (/.f64 (*.f64 (PI.f64) n) k))
cost-diff	0	(sqrt.f64 #s(literal 2 binary64))
cost-diff	0	(.f64 (sqrt.f64 #s(literal 2 binary64)) (sqrt.f64 (/.f64 (.f64 (PI.f64) n) k)))
cost-diff	0	#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (.f64 (sqrt.f64 #s(literal 2 binary64)) (sqrt.f64 (/.f64 (.f64 (PI.f64) n) k))))
cost-diff	0	(.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	58	590
0	100	586
1	175	556
2	363	546
3	1081	536
4	2583	536
5	4557	536
6	5079	536
7	5206	536
8	5448	536
9	6375	536
0	8120	528

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

localize176.0ms (1.5%)

Memory

41.3MiB live, 320.4MiB allocated; 37ms collecting garbage

Localize:

Found 20 expressions of interest:

New	Metric	Score
accuracy	0.38509750976844204	(.f64 (sqrt.f64 (.f64 (PI.f64) n)) (sqrt.f64 #s(literal 2 binary64)))
accuracy	0.418632519536884	(pow.f64 (log.f64 (.f64 (.f64 #s(literal 2 binary64) n) (PI.f64))) #s(literal 2 binary64))
accuracy	16.152822977549047	#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	16.71053066552266	(PI.f64)
accuracy	0.1796875	(/.f64 #s(literal 1 binary64) (sqrt.f64 k))
accuracy	0.453125	(pow.f64 (PI.f64) (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 2 binary64)))
accuracy	0.58984375	(.f64 (pow.f64 (.f64 n #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))))
accuracy	16.71053066552266	(PI.f64)
accuracy	0.23046875	(.f64 (.f64 (*.f64 n #s(literal 2 binary64)) (sqrt.f64 (PI.f64))) (sqrt.f64 (PI.f64)))
accuracy	0.234375	(.f64 (.f64 n #s(literal 2 binary64)) (sqrt.f64 (PI.f64)))
accuracy	0.73046875	(sqrt.f64 (PI.f64))
accuracy	16.71053066552266	(PI.f64)
accuracy	0.3991012695368841	(.f64 (sqrt.f64 #s(literal 2 binary64)) (sqrt.f64 (/.f64 (.f64 (PI.f64) n) k)))
accuracy	8.08343719663338	(sqrt.f64 (/.f64 (*.f64 (PI.f64) n) k))
accuracy	16.463064613501228	#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	16.71053066552266	(PI.f64)
accuracy	0.14987944230411276	(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	0.171875	(.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	0.17578125	(.f64 (.f64 #s(literal 2 binary64) n) (PI.f64))
accuracy	16.71053066552266	(PI.f64)

Samples

84.0ms	187×	0	valid
37.0ms	69×	0	exit

Compiler

Compiled 491 to 54 computations (89% saved)

Precisions

Click to see histograms. Total time spent on operations: 90.0ms

ival-mult: 32.0ms (35.4% of total)

ival-pow: 29.0ms (32.1% of total)

ival-sqrt: 10.0ms (11.1% of total)

ival-div: 7.0ms (7.7% of total)

ival-add: 3.0ms (3.3% of total)

ival-log: 3.0ms (3.3% of total)

ival-pow2: 3.0ms (3.3% of total)

ival-pi: 1.0ms (1.1% of total)

ival-sub: 1.0ms (1.1% of total)

exact: 1.0ms (1.1% of total)

adjust: 0.0ms (0% of total)

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

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

series196.0ms (1.7%)

Memory

-5.4MiB live, 317.0MiB allocated; 104ms collecting garbage

Counts

24 → 79

Calls

Call 1

Inputs
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (.f64 (pow.f64 (.f64 (*.f64 #s(literal 2 binary64) n) (PI.f64)) (fma.f64 #s(literal -1/2 binary64) k #s(literal 1/2 binary64))) (sqrt.f64 (/.f64 #s(literal 1 binary64) k))))
(.f64 (pow.f64 (.f64 (*.f64 #s(literal 2 binary64) n) (PI.f64)) (fma.f64 #s(literal -1/2 binary64) k #s(literal 1/2 binary64))) (sqrt.f64 (/.f64 #s(literal 1 binary64) k)))
(pow.f64 (.f64 (.f64 #s(literal 2 binary64) n) (PI.f64)) (fma.f64 #s(literal -1/2 binary64) k #s(literal 1/2 binary64)))
(.f64 (.f64 #s(literal 2 binary64) n) (PI.f64))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (.f64 (sqrt.f64 #s(literal 2 binary64)) (sqrt.f64 (/.f64 (.f64 (PI.f64) n) k))))
(.f64 (sqrt.f64 #s(literal 2 binary64)) (sqrt.f64 (/.f64 (.f64 (PI.f64) n) k)))
(sqrt.f64 #s(literal 2 binary64))
(sqrt.f64 (/.f64 (*.f64 (PI.f64) n) k))
(.f64 (.f64 (*.f64 n #s(literal 2 binary64)) (sqrt.f64 (PI.f64))) (sqrt.f64 (PI.f64)))
(.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) (pow.f64 (.f64 (.f64 (.f64 n #s(literal 2 binary64)) (sqrt.f64 (PI.f64))) (sqrt.f64 (PI.f64))) (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 2 binary64))))
(/.f64 #s(literal 1 binary64) (sqrt.f64 k))
(sqrt.f64 k)
(.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) (.f64 (pow.f64 (*.f64 n #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 (pow.f64 (.f64 n #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))))
(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))))))
(PI.f64)
(sqrt.f64 (PI.f64))
(.f64 (.f64 n #s(literal 2 binary64)) (sqrt.f64 (PI.f64)))
(pow.f64 (PI.f64) (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 2 binary64)))
#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 (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)) (* (sqrt (pow k 3)) (+ (* -1/2 (* (sqrt (* n (PI))) (* (log (PI)) (sqrt 2)))) (* -1/2 (* (sqrt (* n (PI))) (* (log (* 2 n)) (sqrt 2))))))) k)
(/ (+ (* k (+ (* (sqrt k) (+ (* -1/2 (* (sqrt (* n (PI))) (* (log (PI)) (sqrt 2)))) (* -1/2 (* (sqrt (* n (PI))) (* (log (* 2 n)) (sqrt 2)))))) (* (sqrt (pow k 3)) (+ (* 1/8 (* (sqrt (* n (PI))) (* (pow (log (PI)) 2) (sqrt 2)))) (+ (* 1/8 (* (sqrt (* n (PI))) (* (pow (log (* 2 n)) 2) (sqrt 2)))) (* 1/4 (* (sqrt (* n (PI))) (* (log (PI)) (* (log (* 2 n)) (sqrt 2)))))))))) (* (sqrt (* k (* n (PI)))) (sqrt 2))) k)
(/ (+ (* k (+ (* k (+ (* (sqrt k) (+ (* 1/8 (* (sqrt (* n (PI))) (* (pow (log (PI)) 2) (sqrt 2)))) (+ (* 1/8 (* (sqrt (* n (PI))) (* (pow (log (* 2 n)) 2) (sqrt 2)))) (* 1/4 (* (sqrt (* n (PI))) (* (log (PI)) (* (log (* 2 n)) (sqrt 2)))))))) (* (sqrt (pow k 3)) (+ (* -1/16 (* (sqrt (* n (PI))) (* (log (PI)) (* (pow (log (* 2 n)) 2) (sqrt 2))))) (+ (* -1/16 (* (sqrt (* n (PI))) (* (pow (log (PI)) 2) (* (log (* 2 n)) (sqrt 2))))) (+ (* -1/48 (* (sqrt (* n (PI))) (* (pow (log (PI)) 3) (sqrt 2)))) (* -1/48 (* (sqrt (* n (PI))) (* (pow (log (* 2 n)) 3) (sqrt 2)))))))))) (* (sqrt k) (+ (* -1/2 (* (sqrt (* n (PI))) (* (log (PI)) (sqrt 2)))) (* -1/2 (* (sqrt (* n (PI))) (* (log (* 2 n)) (sqrt 2)))))))) (* (sqrt (* k (* n (PI)))) (sqrt 2))) k)
(+ (* k (+ (* -1/2 (* (sqrt (* n (PI))) (* (log (PI)) (sqrt 2)))) (* -1/2 (* (sqrt (* n (PI))) (* (log (* 2 n)) (sqrt 2)))))) (* (sqrt (* n (PI))) (sqrt 2)))
(+ (* k (+ (* -1/2 (* (sqrt (* n (PI))) (* (log (PI)) (sqrt 2)))) (+ (* -1/2 (* (sqrt (* n (PI))) (* (log (* 2 n)) (sqrt 2)))) (* k (+ (* 1/8 (* (sqrt (* n (PI))) (* (pow (log (PI)) 2) (sqrt 2)))) (+ (* 1/8 (* (sqrt (* n (PI))) (* (pow (log (* 2 n)) 2) (sqrt 2)))) (* 1/4 (* (sqrt (* n (PI))) (* (log (PI)) (* (log (* 2 n)) (sqrt 2))))))))))) (* (sqrt (* n (PI))) (sqrt 2)))
(+ (* k (+ (* -1/2 (* (sqrt (* n (PI))) (* (log (PI)) (sqrt 2)))) (+ (* -1/2 (* (sqrt (* n (PI))) (* (log (* 2 n)) (sqrt 2)))) (* k (+ (* 1/8 (* (sqrt (* n (PI))) (* (pow (log (PI)) 2) (sqrt 2)))) (+ (* 1/8 (* (sqrt (* n (PI))) (* (pow (log (* 2 n)) 2) (sqrt 2)))) (+ (* 1/4 (* (sqrt (* n (PI))) (* (log (PI)) (* (log (* 2 n)) (sqrt 2))))) (* k (+ (* -1/16 (* (sqrt (* n (PI))) (* (log (PI)) (* (pow (log (* 2 n)) 2) (sqrt 2))))) (+ (* -1/16 (* (sqrt (* n (PI))) (* (pow (log (PI)) 2) (* (log (* 2 n)) (sqrt 2))))) (+ (* -1/48 (* (sqrt (* n (PI))) (* (pow (log (PI)) 3) (sqrt 2)))) (* -1/48 (* (sqrt (* n (PI))) (* (pow (log (* 2 n)) 3) (sqrt 2))))))))))))))) (* (sqrt (* 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 (PI))
(+ (sqrt (PI)) (* -1/2 (* (* k (log (PI))) (sqrt (PI)))))
(+ (sqrt (PI)) (* k (+ (* -1/2 (* (sqrt (PI)) (log (PI)))) (* 1/8 (* (* k (pow (log (PI)) 2)) (sqrt (PI)))))))
(+ (sqrt (PI)) (* k (+ (* -1/2 (* (sqrt (PI)) (log (PI)))) (* k (+ (* -1/48 (* (* k (pow (log (PI)) 3)) (sqrt (PI)))) (* 1/8 (* (sqrt (PI)) (pow (log (PI)) 2))))))))
(* (sqrt (/ 1 k)) (exp (* 1/2 (* (log (* 2 (* n (PI)))) (- 1 k)))))
(* (sqrt (/ 1 k)) (exp (* (log (* 2 (* n (PI)))) (- 1/2 (* 1/2 k)))))
(exp (* (log (* 2 (* n (PI)))) (- 1/2 (* 1/2 k))))
(* (sqrt (/ 1 k)) (* (exp (* 1/2 (* (log (PI)) (- 1 k)))) (exp (* 1/2 (* (log (* 2 n)) (- 1 k))))))
(* (exp (* 1/2 (* (log (PI)) (- 1 k)))) (exp (* 1/2 (* (log (* 2 n)) (- 1 k)))))
(* 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 (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))))))
(* (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)))
(* (sqrt (/ 1 k)) (* (exp (* 1/2 (* (log (PI)) (+ 1 (* -1 k))))) (exp (* 1/2 (* (log (* 2 n)) (+ 1 (* -1 k)))))))
(* (exp (* 1/2 (* (log (PI)) (+ 1 (* -1 k))))) (exp (* 1/2 (* (log (* 2 n)) (+ 1 (* -1 k))))))
(* (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)))))
(exp (* 1/2 (* (log (PI)) (+ 1 (* -1 k)))))
(exp (* 1/2 (* (log (* 2 (* n (PI)))) (+ 1 (* -1 k)))))
(* (sqrt (/ 1 k)) (exp (* 1/2 (* (+ (log n) (log (* 2 (PI)))) (- 1 k)))))
(* (sqrt (/ 1 k)) (exp (* (+ 1/2 (* -1/2 k)) (+ (log n) (log (* 2 (PI)))))))
(exp (* (+ 1/2 (* -1/2 k)) (+ (log n) (log (* 2 (PI))))))
(* 2 (* n (PI)))
(* (sqrt (/ 1 k)) (* (exp (* 1/2 (* (log (PI)) (- 1 k)))) (exp (* 1/2 (* (+ (log 2) (log n)) (- 1 k))))))
(* (exp (* 1/2 (* (log (PI)) (- 1 k)))) (exp (* 1/2 (* (+ (log 2) (log n)) (- 1 k)))))
(+ (* (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)))))
(* 2 (* n (sqrt (PI))))
(exp (* 1/2 (* (+ (log n) (log (* 2 (PI)))) (- 1 k))))
(pow (+ (log n) (log (* 2 (PI)))) 2)
(* (sqrt (/ 1 k)) (exp (* 1/2 (* (+ (log (* 2 (PI))) (* -1 (log (/ 1 n)))) (- 1 k)))))
(* (sqrt (/ 1 k)) (exp (* (+ 1/2 (* -1/2 k)) (+ (log (* 2 (PI))) (* -1 (log (/ 1 n)))))))
(exp (* (+ 1/2 (* -1/2 k)) (+ (log (* 2 (PI))) (* -1 (log (/ 1 n))))))
(* (sqrt (/ 1 k)) (* (exp (* 1/2 (* (log (PI)) (- 1 k)))) (exp (* 1/2 (* (+ (log 2) (* -1 (log (/ 1 n)))) (- 1 k))))))
(* (exp (* 1/2 (* (log (PI)) (- 1 k)))) (exp (* 1/2 (* (+ (log 2) (* -1 (log (/ 1 n)))) (- 1 k)))))
(* 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 (/ 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)))
(* (sqrt (/ 1 k)) (* (exp (* 1/2 (* (log (PI)) (- 1 k)))) (exp (* 1/2 (* (+ (log -2) (* -1 (log (/ -1 n)))) (- 1 k))))))
(* (exp (* 1/2 (* (log (PI)) (- 1 k)))) (exp (* 1/2 (* (+ (log -2) (* -1 (log (/ -1 n)))) (- 1 k)))))
(* -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)))))
(exp (* 1/2 (* (+ (log (* -2 (PI))) (* -1 (log (/ -1 n)))) (- 1 k))))
(pow (+ (log (* -2 (PI))) (* -1 (log (/ -1 n)))) 2)
(* -1 (* (sqrt (* n (PI))) (* (pow (sqrt -1) 2) (sqrt 2))))

Calls

6 calls:

Time	Variable		Point	Expression
68.0ms	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)) (* (* (* n 2) (sqrt (PI))) (sqrt (PI))) (* (/ 1 (sqrt k)) (pow (* (* (* n 2) (sqrt (PI))) (sqrt (PI))) (/ (- 1 k) 2))) (/ 1 (sqrt k)) (sqrt k) (* (/ 1 (sqrt k)) (* (pow (* n 2) (/ (- 1 k) 2)) (pow (PI) (/ (- 1 k) 2)))) (* (pow (* n 2) (/ (- 1 k) 2)) (pow (PI) (/ (- 1 k) 2))) (+ (* (* (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))) (PI) (sqrt (PI)) (* (* n 2) (sqrt (PI))) (pow (PI) (/ (- 1 k) 2)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2)) (pow (log (* (* 2 n) (PI))) 2) (* (sqrt (* (PI) n)) (sqrt 2)))
46.0ms	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)) (* (* (* n 2) (sqrt (PI))) (sqrt (PI))) (* (/ 1 (sqrt k)) (pow (* (* (* n 2) (sqrt (PI))) (sqrt (PI))) (/ (- 1 k) 2))) (/ 1 (sqrt k)) (sqrt k) (* (/ 1 (sqrt k)) (* (pow (* n 2) (/ (- 1 k) 2)) (pow (PI) (/ (- 1 k) 2)))) (* (pow (* n 2) (/ (- 1 k) 2)) (pow (PI) (/ (- 1 k) 2))) (+ (* (* (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))) (PI) (sqrt (PI)) (* (* n 2) (sqrt (PI))) (pow (PI) (/ (- 1 k) 2)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2)) (pow (log (* (* 2 n) (PI))) 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)) (* (* (* n 2) (sqrt (PI))) (sqrt (PI))) (* (/ 1 (sqrt k)) (pow (* (* (* n 2) (sqrt (PI))) (sqrt (PI))) (/ (- 1 k) 2))) (/ 1 (sqrt k)) (sqrt k) (* (/ 1 (sqrt k)) (* (pow (* n 2) (/ (- 1 k) 2)) (pow (PI) (/ (- 1 k) 2)))) (* (pow (* n 2) (/ (- 1 k) 2)) (pow (PI) (/ (- 1 k) 2))) (+ (* (* (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))) (PI) (sqrt (PI)) (* (* n 2) (sqrt (PI))) (pow (PI) (/ (- 1 k) 2)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2)) (pow (log (* (* 2 n) (PI))) 2) (* (sqrt (* (PI) n)) (sqrt 2)))
23.0ms	k	@	0	((* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (* (pow (* (* 2 n) (PI)) (+ (* -1/2 k) 1/2)) (sqrt (/ 1 k))) (pow (* (* 2 n) (PI)) (+ (* -1/2 k) 1/2)) (* (* 2 n) (PI)) (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (* (sqrt 2) (sqrt (/ (* (PI) n) k))) (sqrt 2) (sqrt (/ (* (PI) n) k)) (* (* (* n 2) (sqrt (PI))) (sqrt (PI))) (* (/ 1 (sqrt k)) (pow (* (* (* n 2) (sqrt (PI))) (sqrt (PI))) (/ (- 1 k) 2))) (/ 1 (sqrt k)) (sqrt k) (* (/ 1 (sqrt k)) (* (pow (* n 2) (/ (- 1 k) 2)) (pow (PI) (/ (- 1 k) 2)))) (* (pow (* n 2) (/ (- 1 k) 2)) (pow (PI) (/ (- 1 k) 2))) (+ (* (* (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))) (PI) (sqrt (PI)) (* (* n 2) (sqrt (PI))) (pow (PI) (/ (- 1 k) 2)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2)) (pow (log (* (* 2 n) (PI))) 2) (* (sqrt (* (PI) n)) (sqrt 2)))
7.0ms	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)) (* (* (* n 2) (sqrt (PI))) (sqrt (PI))) (* (/ 1 (sqrt k)) (pow (* (* (* n 2) (sqrt (PI))) (sqrt (PI))) (/ (- 1 k) 2))) (/ 1 (sqrt k)) (sqrt k) (* (/ 1 (sqrt k)) (* (pow (* n 2) (/ (- 1 k) 2)) (pow (PI) (/ (- 1 k) 2)))) (* (pow (* n 2) (/ (- 1 k) 2)) (pow (PI) (/ (- 1 k) 2))) (+ (* (* (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))) (PI) (sqrt (PI)) (* (* n 2) (sqrt (PI))) (pow (PI) (/ (- 1 k) 2)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2)) (pow (log (* (* 2 n) (PI))) 2) (* (sqrt (* (PI) n)) (sqrt 2)))

simplify355.0ms (3.1%)

Memory

-29.6MiB live, 341.3MiB allocated; 202ms collecting garbage

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	358	2231
1	1325	2031
2	5956	2002
0	8704	1919

Stop Event

1×	iter limit
1×	node limit

Counts

79 → 79

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)) (* (sqrt (pow k 3)) (+ (* -1/2 (* (sqrt (* n (PI))) (* (log (PI)) (sqrt 2)))) (* -1/2 (* (sqrt (* n (PI))) (* (log (* 2 n)) (sqrt 2))))))) k)
(/ (+ (* k (+ (* (sqrt k) (+ (* -1/2 (* (sqrt (* n (PI))) (* (log (PI)) (sqrt 2)))) (* -1/2 (* (sqrt (* n (PI))) (* (log (* 2 n)) (sqrt 2)))))) (* (sqrt (pow k 3)) (+ (* 1/8 (* (sqrt (* n (PI))) (* (pow (log (PI)) 2) (sqrt 2)))) (+ (* 1/8 (* (sqrt (* n (PI))) (* (pow (log (* 2 n)) 2) (sqrt 2)))) (* 1/4 (* (sqrt (* n (PI))) (* (log (PI)) (* (log (* 2 n)) (sqrt 2)))))))))) (* (sqrt (* k (* n (PI)))) (sqrt 2))) k)
(/ (+ (* k (+ (* k (+ (* (sqrt k) (+ (* 1/8 (* (sqrt (* n (PI))) (* (pow (log (PI)) 2) (sqrt 2)))) (+ (* 1/8 (* (sqrt (* n (PI))) (* (pow (log (* 2 n)) 2) (sqrt 2)))) (* 1/4 (* (sqrt (* n (PI))) (* (log (PI)) (* (log (* 2 n)) (sqrt 2)))))))) (* (sqrt (pow k 3)) (+ (* -1/16 (* (sqrt (* n (PI))) (* (log (PI)) (* (pow (log (* 2 n)) 2) (sqrt 2))))) (+ (* -1/16 (* (sqrt (* n (PI))) (* (pow (log (PI)) 2) (* (log (* 2 n)) (sqrt 2))))) (+ (* -1/48 (* (sqrt (* n (PI))) (* (pow (log (PI)) 3) (sqrt 2)))) (* -1/48 (* (sqrt (* n (PI))) (* (pow (log (* 2 n)) 3) (sqrt 2)))))))))) (* (sqrt k) (+ (* -1/2 (* (sqrt (* n (PI))) (* (log (PI)) (sqrt 2)))) (* -1/2 (* (sqrt (* n (PI))) (* (log (* 2 n)) (sqrt 2)))))))) (* (sqrt (* k (* n (PI)))) (sqrt 2))) k)
(+ (* k (+ (* -1/2 (* (sqrt (* n (PI))) (* (log (PI)) (sqrt 2)))) (* -1/2 (* (sqrt (* n (PI))) (* (log (* 2 n)) (sqrt 2)))))) (* (sqrt (* n (PI))) (sqrt 2)))
(+ (* k (+ (* -1/2 (* (sqrt (* n (PI))) (* (log (PI)) (sqrt 2)))) (+ (* -1/2 (* (sqrt (* n (PI))) (* (log (* 2 n)) (sqrt 2)))) (* k (+ (* 1/8 (* (sqrt (* n (PI))) (* (pow (log (PI)) 2) (sqrt 2)))) (+ (* 1/8 (* (sqrt (* n (PI))) (* (pow (log (* 2 n)) 2) (sqrt 2)))) (* 1/4 (* (sqrt (* n (PI))) (* (log (PI)) (* (log (* 2 n)) (sqrt 2))))))))))) (* (sqrt (* n (PI))) (sqrt 2)))
(+ (* k (+ (* -1/2 (* (sqrt (* n (PI))) (* (log (PI)) (sqrt 2)))) (+ (* -1/2 (* (sqrt (* n (PI))) (* (log (* 2 n)) (sqrt 2)))) (* k (+ (* 1/8 (* (sqrt (* n (PI))) (* (pow (log (PI)) 2) (sqrt 2)))) (+ (* 1/8 (* (sqrt (* n (PI))) (* (pow (log (* 2 n)) 2) (sqrt 2)))) (+ (* 1/4 (* (sqrt (* n (PI))) (* (log (PI)) (* (log (* 2 n)) (sqrt 2))))) (* k (+ (* -1/16 (* (sqrt (* n (PI))) (* (log (PI)) (* (pow (log (* 2 n)) 2) (sqrt 2))))) (+ (* -1/16 (* (sqrt (* n (PI))) (* (pow (log (PI)) 2) (* (log (* 2 n)) (sqrt 2))))) (+ (* -1/48 (* (sqrt (* n (PI))) (* (pow (log (PI)) 3) (sqrt 2)))) (* -1/48 (* (sqrt (* n (PI))) (* (pow (log (* 2 n)) 3) (sqrt 2))))))))))))))) (* (sqrt (* 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 (PI))
(+ (sqrt (PI)) (* -1/2 (* (* k (log (PI))) (sqrt (PI)))))
(+ (sqrt (PI)) (* k (+ (* -1/2 (* (sqrt (PI)) (log (PI)))) (* 1/8 (* (* k (pow (log (PI)) 2)) (sqrt (PI)))))))
(+ (sqrt (PI)) (* k (+ (* -1/2 (* (sqrt (PI)) (log (PI)))) (* k (+ (* -1/48 (* (* k (pow (log (PI)) 3)) (sqrt (PI)))) (* 1/8 (* (sqrt (PI)) (pow (log (PI)) 2))))))))
(* (sqrt (/ 1 k)) (exp (* 1/2 (* (log (* 2 (* n (PI)))) (- 1 k)))))
(* (sqrt (/ 1 k)) (exp (* (log (* 2 (* n (PI)))) (- 1/2 (* 1/2 k)))))
(exp (* (log (* 2 (* n (PI)))) (- 1/2 (* 1/2 k))))
(* (sqrt (/ 1 k)) (* (exp (* 1/2 (* (log (PI)) (- 1 k)))) (exp (* 1/2 (* (log (* 2 n)) (- 1 k))))))
(* (exp (* 1/2 (* (log (PI)) (- 1 k)))) (exp (* 1/2 (* (log (* 2 n)) (- 1 k)))))
(* 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 (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))))))
(* (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)))
(* (sqrt (/ 1 k)) (* (exp (* 1/2 (* (log (PI)) (+ 1 (* -1 k))))) (exp (* 1/2 (* (log (* 2 n)) (+ 1 (* -1 k)))))))
(* (exp (* 1/2 (* (log (PI)) (+ 1 (* -1 k))))) (exp (* 1/2 (* (log (* 2 n)) (+ 1 (* -1 k))))))
(* (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)))))
(exp (* 1/2 (* (log (PI)) (+ 1 (* -1 k)))))
(exp (* 1/2 (* (log (* 2 (* n (PI)))) (+ 1 (* -1 k)))))
(* (sqrt (/ 1 k)) (exp (* 1/2 (* (+ (log n) (log (* 2 (PI)))) (- 1 k)))))
(* (sqrt (/ 1 k)) (exp (* (+ 1/2 (* -1/2 k)) (+ (log n) (log (* 2 (PI)))))))
(exp (* (+ 1/2 (* -1/2 k)) (+ (log n) (log (* 2 (PI))))))
(* 2 (* n (PI)))
(* (sqrt (/ 1 k)) (* (exp (* 1/2 (* (log (PI)) (- 1 k)))) (exp (* 1/2 (* (+ (log 2) (log n)) (- 1 k))))))
(* (exp (* 1/2 (* (log (PI)) (- 1 k)))) (exp (* 1/2 (* (+ (log 2) (log n)) (- 1 k)))))
(+ (* (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)))))
(* 2 (* n (sqrt (PI))))
(exp (* 1/2 (* (+ (log n) (log (* 2 (PI)))) (- 1 k))))
(pow (+ (log n) (log (* 2 (PI)))) 2)
(* (sqrt (/ 1 k)) (exp (* 1/2 (* (+ (log (* 2 (PI))) (* -1 (log (/ 1 n)))) (- 1 k)))))
(* (sqrt (/ 1 k)) (exp (* (+ 1/2 (* -1/2 k)) (+ (log (* 2 (PI))) (* -1 (log (/ 1 n)))))))
(exp (* (+ 1/2 (* -1/2 k)) (+ (log (* 2 (PI))) (* -1 (log (/ 1 n))))))
(* (sqrt (/ 1 k)) (* (exp (* 1/2 (* (log (PI)) (- 1 k)))) (exp (* 1/2 (* (+ (log 2) (* -1 (log (/ 1 n)))) (- 1 k))))))
(* (exp (* 1/2 (* (log (PI)) (- 1 k)))) (exp (* 1/2 (* (+ (log 2) (* -1 (log (/ 1 n)))) (- 1 k)))))
(* 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 (/ 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)))
(* (sqrt (/ 1 k)) (* (exp (* 1/2 (* (log (PI)) (- 1 k)))) (exp (* 1/2 (* (+ (log -2) (* -1 (log (/ -1 n)))) (- 1 k))))))
(* (exp (* 1/2 (* (log (PI)) (- 1 k)))) (exp (* 1/2 (* (+ (log -2) (* -1 (log (/ -1 n)))) (- 1 k)))))
(* -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)))))
(exp (* 1/2 (* (+ (log (* -2 (PI))) (* -1 (log (/ -1 n)))) (- 1 k))))
(pow (+ (log (* -2 (PI))) (* -1 (log (/ -1 n)))) 2)
(* -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)) (PI.f64)) n)) (.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)) (PI.f64)) n))) #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)
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(* (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 (.f64 k k) #s(literal 1/8 binary64)) (.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) k) (.f64 (pow.f64 (log.f64 (.f64 (.f64 n (PI.f64)) #s(literal 2 binary64))) #s(literal 3 binary64)) (.f64 (sqrt.f64 (.f64 n (PI.f64))) (sqrt.f64 #s(literal 2 binary64)))) (.f64 (.f64 (sqrt.f64 (.f64 n (PI.f64))) #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)) (* (sqrt (pow k 3)) (+ (* -1/2 (* (sqrt (* n (PI))) (* (log (PI)) (sqrt 2)))) (* -1/2 (* (sqrt (* n (PI))) (* (log (* 2 n)) (sqrt 2))))))) k)
(/.f64 (fma.f64 (.f64 (sqrt.f64 (pow.f64 k #s(literal 3 binary64))) #s(literal -1/2 binary64)) (.f64 (sqrt.f64 (.f64 n (PI.f64))) (fma.f64 (log.f64 (PI.f64)) (sqrt.f64 #s(literal 2 binary64)) (.f64 (log.f64 (.f64 n #s(literal 2 binary64))) (sqrt.f64 #s(literal 2 binary64))))) (.f64 (sqrt.f64 (.f64 (.f64 n (PI.f64)) k)) (sqrt.f64 #s(literal 2 binary64)))) k)
(/ (+ (* k (+ (* (sqrt k) (+ (* -1/2 (* (sqrt (* n (PI))) (* (log (PI)) (sqrt 2)))) (* -1/2 (* (sqrt (* n (PI))) (* (log (* 2 n)) (sqrt 2)))))) (* (sqrt (pow k 3)) (+ (* 1/8 (* (sqrt (* n (PI))) (* (pow (log (PI)) 2) (sqrt 2)))) (+ (* 1/8 (* (sqrt (* n (PI))) (* (pow (log (* 2 n)) 2) (sqrt 2)))) (* 1/4 (* (sqrt (* n (PI))) (* (log (PI)) (* (log (* 2 n)) (sqrt 2)))))))))) (* (sqrt (* k (* n (PI)))) (sqrt 2))) k)
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(/ (+ (* k (+ (* k (+ (* (sqrt k) (+ (* 1/8 (* (sqrt (* n (PI))) (* (pow (log (PI)) 2) (sqrt 2)))) (+ (* 1/8 (* (sqrt (* n (PI))) (* (pow (log (* 2 n)) 2) (sqrt 2)))) (* 1/4 (* (sqrt (* n (PI))) (* (log (PI)) (* (log (* 2 n)) (sqrt 2)))))))) (* (sqrt (pow k 3)) (+ (* -1/16 (* (sqrt (* n (PI))) (* (log (PI)) (* (pow (log (* 2 n)) 2) (sqrt 2))))) (+ (* -1/16 (* (sqrt (* n (PI))) (* (pow (log (PI)) 2) (* (log (* 2 n)) (sqrt 2))))) (+ (* -1/48 (* (sqrt (* n (PI))) (* (pow (log (PI)) 3) (sqrt 2)))) (* -1/48 (* (sqrt (* n (PI))) (* (pow (log (* 2 n)) 3) (sqrt 2)))))))))) (* (sqrt k) (+ (* -1/2 (* (sqrt (* n (PI))) (* (log (PI)) (sqrt 2)))) (* -1/2 (* (sqrt (* n (PI))) (* (log (* 2 n)) (sqrt 2)))))))) (* (sqrt (* k (* n (PI)))) (sqrt 2))) k)
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(pow.f64 (+.f64 (log.f64 n) (log.f64 (*.f64 (PI.f64) #s(literal 2 binary64)))) #s(literal 2 binary64))
(* (sqrt (/ 1 k)) (exp (* 1/2 (* (+ (log (* -2 (PI))) (* -1 (log (/ -1 n)))) (- 1 k)))))
(.f64 (sqrt.f64 (pow.f64 (exp.f64 (-.f64 #s(literal 1 binary64) k)) (-.f64 (log.f64 (.f64 #s(literal -2 binary64) (PI.f64))) (log.f64 (/.f64 #s(literal -1 binary64) n))))) (sqrt.f64 (/.f64 #s(literal 1 binary64) k)))
(* (sqrt (/ 1 k)) (exp (* (+ 1/2 (* -1/2 k)) (+ (log (* -2 (PI))) (* -1 (log (/ -1 n)))))))
(.f64 (pow.f64 (exp.f64 (fma.f64 #s(literal -1/2 binary64) k #s(literal 1/2 binary64))) (-.f64 (log.f64 (.f64 #s(literal -2 binary64) (PI.f64))) (log.f64 (/.f64 #s(literal -1 binary64) n)))) (sqrt.f64 (/.f64 #s(literal 1 binary64) k)))
(exp (* (+ 1/2 (* -1/2 k)) (+ (log (* -2 (PI))) (* -1 (log (/ -1 n))))))
(pow.f64 (exp.f64 (fma.f64 #s(literal -1/2 binary64) k #s(literal 1/2 binary64))) (-.f64 (log.f64 (*.f64 #s(literal -2 binary64) (PI.f64))) (log.f64 (/.f64 #s(literal -1 binary64) n))))
(* -1 (* (sqrt (/ (* n (PI)) k)) (* (pow (sqrt -1) 2) (sqrt 2))))
(.f64 (neg.f64 (sqrt.f64 (/.f64 (.f64 n (PI.f64)) k))) (neg.f64 (sqrt.f64 #s(literal 2 binary64))))
(* -1 (* (sqrt (/ (* n (PI)) k)) (pow (sqrt -1) 2)))
(.f64 (sqrt.f64 (/.f64 (.f64 n (PI.f64)) k)) #s(literal 1 binary64))
(* (sqrt (/ 1 k)) (* (exp (* 1/2 (* (log (PI)) (- 1 k)))) (exp (* 1/2 (* (+ (log -2) (* -1 (log (/ -1 n)))) (- 1 k))))))
(.f64 (pow.f64 (exp.f64 (-.f64 #s(literal 1 binary64) k)) (fma.f64 #s(literal 1/2 binary64) (log.f64 (PI.f64)) (.f64 (-.f64 (log.f64 #s(literal -2 binary64)) (log.f64 (/.f64 #s(literal -1 binary64) n))) #s(literal 1/2 binary64)))) (sqrt.f64 (/.f64 #s(literal 1 binary64) k)))
(* (exp (* 1/2 (* (log (PI)) (- 1 k)))) (exp (* 1/2 (* (+ (log -2) (* -1 (log (/ -1 n)))) (- 1 k)))))
(pow.f64 (exp.f64 (-.f64 #s(literal 1 binary64) k)) (fma.f64 #s(literal 1/2 binary64) (log.f64 (PI.f64)) (*.f64 (-.f64 (log.f64 #s(literal -2 binary64)) (log.f64 (/.f64 #s(literal -1 binary64) n))) #s(literal 1/2 binary64))))
(* -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 (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 (-.f64 (log.f64 (.f64 #s(literal -2 binary64) (PI.f64))) (log.f64 (/.f64 #s(literal -1 binary64) n))) (sqrt.f64 #s(literal 2 binary64))) #s(literal 1/2 binary64))) k (*.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)))))
(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))
(* -1 (* (sqrt (* n (PI))) (* (pow (sqrt -1) 2) (sqrt 2))))
(.f64 (neg.f64 (sqrt.f64 (.f64 n (PI.f64)))) (neg.f64 (sqrt.f64 #s(literal 2 binary64))))

rewrite205.0ms (1.8%)

Memory

2.3MiB live, 333.4MiB allocated; 36ms collecting garbage

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	58	385
0	100	359
1	320	337
2	1774	337
0	8156	334

Stop Event

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

Counts

24 → 829

Calls

Call 1

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

eval361.0ms (3.2%)

Memory: 24.7MiB live, 434.5MiB allocated; 98ms collecting garbage
Compiler: Compiled 66 063 to 6 250 computations (90.5% saved)

prune70.0ms (0.6%)

Memory

-14.2MiB live, 138.7MiB allocated; 15ms collecting garbage

Pruning

19 alts after pruning (17 fresh and 2 done)

	Pruned	Kept	Total
New	1 322	13	1 335
Fresh	8	4	12
Picked	3	2	5
Done	0	0	0
Total	1 333	19	1 352

Accuracy

100.0%

Counts

1 352 → 19

Alt Table

Click to see full alt table

Status	Accuracy	Program
▶	29.4%	(/.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 n (.f64 (PI.f64) #s(literal 2 binary64)))) #s(literal 1 binary64)) (.f64 (pow.f64 (.f64 n (.f64 (PI.f64) #s(literal 2 binary64))) (/.f64 k #s(literal 2 binary64))) (sqrt.f64 k)))
	98.7%	(.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) (.f64 (pow.f64 (*.f64 n #s(literal 2 binary64)) (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 2 binary64))) #s(approx (pow (PI) (/ (- 1 k) 2)) (sqrt.f64 (PI.f64)))))
	99.5%	(.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) #s(approx (pow ( (* 2 (PI)) n) (/ (- 1 k) 2)) (pow.f64 (.f64 (.f64 #s(literal 2 binary64) n) (PI.f64)) (fma.f64 #s(literal -1/2 binary64) k #s(literal 1/2 binary64)))))
	48.5%	(.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)))))
	47.5%	(.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)))))
	47.6%	#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (/.f64 (sqrt.f64 (.f64 n (.f64 (PI.f64) #s(literal 2 binary64)))) (sqrt.f64 k)))
▶	99.5%	#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (.f64 (pow.f64 (.f64 (.f64 (.f64 (sqrt.f64 (PI.f64)) n) #s(literal 2 binary64)) (sqrt.f64 (PI.f64))) (fma.f64 #s(literal -1/2 binary64) k #s(literal 1/2 binary64))) (sqrt.f64 (/.f64 #s(literal 1 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))))
	99.6%	#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (.f64 (pow.f64 (sqrt.f64 (.f64 n (.f64 (PI.f64) #s(literal 2 binary64)))) (.f64 #s(literal 2 binary64) (fma.f64 #s(literal -1/2 binary64) k #s(literal 1/2 binary64)))) (sqrt.f64 (/.f64 #s(literal 1 binary64) k))))
	47.4%	#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (.f64 (/.f64 (sqrt.f64 (.f64 (PI.f64) #s(literal 2 binary64))) (pow.f64 k #s(literal 1/4 binary64))) (/.f64 (sqrt.f64 n) (pow.f64 k #s(literal 1/4 binary64)))))
▶	99.7%	#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (.f64 (.f64 (pow.f64 (pow.f64 (.f64 n (.f64 (PI.f64) #s(literal 2 binary64))) #s(literal -1/2 binary64)) k) (sqrt.f64 (.f64 n (.f64 (PI.f64) #s(literal 2 binary64))))) (sqrt.f64 (/.f64 #s(literal 1 binary64) k))))
	35.1%	#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (.f64 (sqrt.f64 (.f64 (PI.f64) #s(literal 2 binary64))) (sqrt.f64 (/.f64 n k))))
	47.6%	#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (.f64 (sqrt.f64 #s(literal 2 binary64)) (/.f64 (sqrt.f64 (.f64 (PI.f64) n)) (sqrt.f64 k))))
▶	35.2%	#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)))))
	47.6%	#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (.f64 (sqrt.f64 #s(literal 2 binary64)) (.f64 (sqrt.f64 n) (sqrt.f64 (/.f64 (PI.f64) k)))))
✓	35.2%	#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (.f64 (sqrt.f64 #s(literal 2 binary64)) (sqrt.f64 (/.f64 (.f64 (PI.f64) n) k))))
	47.5%	#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))))
▶	35.3%	#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt.f64 (.f64 (/.f64 (.f64 (PI.f64) n) k) #s(literal 2 binary64))))

Compiler

Compiled 1 028 to 817 computations (20.5% saved)

simplify54.0ms (0.5%)

Memory

11.9MiB live, 58.3MiB allocated; 3ms collecting garbage

Algorithm

1×	egg-herbie

Localize:

Found 20 expressions of interest:

New	Metric	Score
cost-diff	0	(pow.f64 (.f64 (.f64 (*.f64 (sqrt.f64 (PI.f64)) n) #s(literal 2 binary64)) (sqrt.f64 (PI.f64))) (fma.f64 #s(literal -1/2 binary64) k #s(literal 1/2 binary64)))
cost-diff	0	(.f64 (pow.f64 (.f64 (.f64 (.f64 (sqrt.f64 (PI.f64)) n) #s(literal 2 binary64)) (sqrt.f64 (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 (.f64 (sqrt.f64 (PI.f64)) n) #s(literal 2 binary64)) (sqrt.f64 (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	4	(.f64 (.f64 (*.f64 (sqrt.f64 (PI.f64)) n) #s(literal 2 binary64)) (sqrt.f64 (PI.f64)))
cost-diff	0	(/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 8 binary64))
cost-diff	2	(*.f64 #s(literal 0 binary64) n)
cost-diff	3	(/.f64 (pow.f64 (*.f64 #s(literal 0 binary64) n) (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 8 binary64))) (sqrt.f64 k))
cost-diff	6	(pow.f64 (*.f64 #s(literal 0 binary64) n) (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 8 binary64)))
cost-diff	0	(*.f64 (sqrt.f64 (/.f64 n k)) (sqrt.f64 (PI.f64)))
cost-diff	0	(sqrt.f64 #s(literal 2 binary64))
cost-diff	0	(.f64 (sqrt.f64 #s(literal 2 binary64)) (.f64 (sqrt.f64 (/.f64 n k)) (sqrt.f64 (PI.f64))))
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 n k)) (sqrt.f64 (PI.f64)))))
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	(pow.f64 (pow.f64 (.f64 n (.f64 (PI.f64) #s(literal 2 binary64))) #s(literal -1/2 binary64)) k)
cost-diff	0	(.f64 (pow.f64 (pow.f64 (.f64 n (.f64 (PI.f64) #s(literal 2 binary64))) #s(literal -1/2 binary64)) k) (sqrt.f64 (.f64 n (*.f64 (PI.f64) #s(literal 2 binary64)))))
cost-diff	0	(.f64 (.f64 (pow.f64 (pow.f64 (.f64 n (.f64 (PI.f64) #s(literal 2 binary64))) #s(literal -1/2 binary64)) k) (sqrt.f64 (.f64 n (.f64 (PI.f64) #s(literal 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 (.f64 (pow.f64 (pow.f64 (.f64 n (.f64 (PI.f64) #s(literal 2 binary64))) #s(literal -1/2 binary64)) k) (sqrt.f64 (.f64 n (.f64 (PI.f64) #s(literal 2 binary64))))) (sqrt.f64 (/.f64 #s(literal 1 binary64) k))))

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	53	376
0	86	351
1	130	343
2	193	331
3	263	331
4	416	331
5	827	331
6	1474	331
7	1767	331
8	1892	331
9	1975	331
10	1975	331
0	1975	331

Stop Event

1×	iter limit
1×	saturated
1×	iter limit

Calls

Call 1

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

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

localize159.0ms (1.4%)

Memory

23.2MiB live, 208.3MiB allocated; 19ms collecting garbage

Localize:

Found 20 expressions of interest:

New	Metric	Score
accuracy	0.1640625	(*.f64 (sqrt.f64 (PI.f64)) n)
accuracy	0.171875	(.f64 (pow.f64 (.f64 (.f64 (.f64 (sqrt.f64 (PI.f64)) n) #s(literal 2 binary64)) (sqrt.f64 (PI.f64))) (fma.f64 #s(literal -1/2 binary64) k #s(literal 1/2 binary64))) (sqrt.f64 (/.f64 #s(literal 1 binary64) k)))
accuracy	0.4765625	(sqrt.f64 (PI.f64))
accuracy	32.45233491565279	(PI.f64)
accuracy	0.0	(/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 8 binary64))
accuracy	0.0	(-.f64 #s(literal 1 binary64) k)
accuracy	0.0	(*.f64 #s(literal 0 binary64) n)
accuracy	0.0	(sqrt.f64 k)
accuracy	0.4765625	(sqrt.f64 (PI.f64))
accuracy	0.7325497490072508	#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)))))
accuracy	8.033270783320058	(sqrt.f64 (/.f64 n k))
accuracy	32.45233491565279	(PI.f64)
accuracy	0.10546875	(*.f64 (PI.f64) n)
accuracy	0.7325497490072508	#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	8.03228538732968	(sqrt.f64 (.f64 (/.f64 (.f64 (PI.f64) n) k) #s(literal 2 binary64)))
accuracy	32.45233491565279	(PI.f64)
accuracy	0.0703125	(pow.f64 (.f64 n (.f64 (PI.f64) #s(literal 2 binary64))) #s(literal -1/2 binary64))
accuracy	0.10546875	(.f64 n (.f64 (PI.f64) #s(literal 2 binary64)))
accuracy	0.171875	(.f64 (.f64 (pow.f64 (pow.f64 (.f64 n (.f64 (PI.f64) #s(literal 2 binary64))) #s(literal -1/2 binary64)) k) (sqrt.f64 (.f64 n (.f64 (PI.f64) #s(literal 2 binary64))))) (sqrt.f64 (/.f64 #s(literal 1 binary64) k)))
accuracy	32.45233491565279	(PI.f64)

Samples

72.0ms	122×	0	valid
57.0ms	134×	0	invalid

Compiler

Compiled 319 to 49 computations (84.6% saved)

Precisions

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

ival-mult: 46.0ms (44.9% of total)

ival-pow: 28.0ms (27.3% of total)

ival-div: 11.0ms (10.7% of total)

ival-sqrt: 11.0ms (10.7% of total)

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

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

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

exact: 1.0ms (1% of total)

adjust: 0.0ms (0% of total)

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

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

series163.0ms (1.4%)

Memory

-36.4MiB live, 165.5MiB allocated; 32ms collecting garbage

Counts

29 → 108

Calls

Call 1

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

Outputs
(* (sqrt (/ (* n (PI)) k)) (sqrt 2))
(/ (+ (* -1/2 (* (sqrt (* (pow k 3) (* n (PI)))) (* (log (* 2 (* n (PI)))) (sqrt 2)))) (* (sqrt (* k (* n (PI)))) (sqrt 2))) k)
(/ (+ (* k (+ (* -1/2 (* (sqrt (* k (* n (PI)))) (* (log (* 2 (* n (PI)))) (sqrt 2)))) (* 1/8 (* (sqrt (* (pow k 3) (* n (PI)))) (* (pow (log (* 2 (* n (PI)))) 2) (sqrt 2)))))) (* (sqrt (* k (* n (PI)))) (sqrt 2))) k)
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1
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1/8
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0
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Calls

6 calls:

Time	Variable		Point	Expression
85.0ms	n	@	-inf	((* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (* (* (pow (pow (* n (* (PI) 2)) -1/2) k) (sqrt (* n (* (PI) 2)))) (sqrt (/ 1 k))) (* (pow (pow (* n (* (PI) 2)) -1/2) k) (sqrt (* n (* (PI) 2)))) (pow (pow (* n (* (PI) 2)) -1/2) k) (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt (* (/ (* (PI) n) k) 2)) (* (/ (* (PI) n) k) 2) (/ (* (PI) n) k) (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (* (sqrt 2) (* (sqrt (/ n k)) (sqrt (PI)))) (sqrt 2) (* (sqrt (/ n k)) (sqrt (PI))) (pow (* 0 n) (/ (- 1 k) 8)) (/ (pow (* 0 n) (/ (- 1 k) 8)) (sqrt k)) (* 0 n) (/ (- 1 k) 8) (* (* (* (sqrt (PI)) n) 2) (sqrt (PI))) (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (* (pow (* (* (* (sqrt (PI)) n) 2) (sqrt (PI))) (+ (* -1/2 k) 1/2)) (sqrt (/ 1 k))) (pow (* (* (* (sqrt (PI)) n) 2) (sqrt (PI))) (+ (* -1/2 k) 1/2)) (PI) (* n (* (PI) 2)) (pow (* n (* (PI) 2)) -1/2) (* (PI) n) (sqrt (/ n k)) (sqrt (PI)) (sqrt k) (- 1 k) (* (sqrt (PI)) n))
36.0ms	n	@	0	((* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (* (* (pow (pow (* n (* (PI) 2)) -1/2) k) (sqrt (* n (* (PI) 2)))) (sqrt (/ 1 k))) (* (pow (pow (* n (* (PI) 2)) -1/2) k) (sqrt (* n (* (PI) 2)))) (pow (pow (* n (* (PI) 2)) -1/2) k) (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt (* (/ (* (PI) n) k) 2)) (* (/ (* (PI) n) k) 2) (/ (* (PI) n) k) (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (* (sqrt 2) (* (sqrt (/ n k)) (sqrt (PI)))) (sqrt 2) (* (sqrt (/ n k)) (sqrt (PI))) (pow (* 0 n) (/ (- 1 k) 8)) (/ (pow (* 0 n) (/ (- 1 k) 8)) (sqrt k)) (* 0 n) (/ (- 1 k) 8) (* (* (* (sqrt (PI)) n) 2) (sqrt (PI))) (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (* (pow (* (* (* (sqrt (PI)) n) 2) (sqrt (PI))) (+ (* -1/2 k) 1/2)) (sqrt (/ 1 k))) (pow (* (* (* (sqrt (PI)) n) 2) (sqrt (PI))) (+ (* -1/2 k) 1/2)) (PI) (* n (* (PI) 2)) (pow (* n (* (PI) 2)) -1/2) (* (PI) n) (sqrt (/ n k)) (sqrt (PI)) (sqrt k) (- 1 k) (* (sqrt (PI)) n))
20.0ms	n	@	inf	((* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (* (* (pow (pow (* n (* (PI) 2)) -1/2) k) (sqrt (* n (* (PI) 2)))) (sqrt (/ 1 k))) (* (pow (pow (* n (* (PI) 2)) -1/2) k) (sqrt (* n (* (PI) 2)))) (pow (pow (* n (* (PI) 2)) -1/2) k) (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt (* (/ (* (PI) n) k) 2)) (* (/ (* (PI) n) k) 2) (/ (* (PI) n) k) (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (* (sqrt 2) (* (sqrt (/ n k)) (sqrt (PI)))) (sqrt 2) (* (sqrt (/ n k)) (sqrt (PI))) (pow (* 0 n) (/ (- 1 k) 8)) (/ (pow (* 0 n) (/ (- 1 k) 8)) (sqrt k)) (* 0 n) (/ (- 1 k) 8) (* (* (* (sqrt (PI)) n) 2) (sqrt (PI))) (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (* (pow (* (* (* (sqrt (PI)) n) 2) (sqrt (PI))) (+ (* -1/2 k) 1/2)) (sqrt (/ 1 k))) (pow (* (* (* (sqrt (PI)) n) 2) (sqrt (PI))) (+ (* -1/2 k) 1/2)) (PI) (* n (* (PI) 2)) (pow (* n (* (PI) 2)) -1/2) (* (PI) n) (sqrt (/ n k)) (sqrt (PI)) (sqrt k) (- 1 k) (* (sqrt (PI)) n))
9.0ms	k	@	0	((* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (* (* (pow (pow (* n (* (PI) 2)) -1/2) k) (sqrt (* n (* (PI) 2)))) (sqrt (/ 1 k))) (* (pow (pow (* n (* (PI) 2)) -1/2) k) (sqrt (* n (* (PI) 2)))) (pow (pow (* n (* (PI) 2)) -1/2) k) (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt (* (/ (* (PI) n) k) 2)) (* (/ (* (PI) n) k) 2) (/ (* (PI) n) k) (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (* (sqrt 2) (* (sqrt (/ n k)) (sqrt (PI)))) (sqrt 2) (* (sqrt (/ n k)) (sqrt (PI))) (pow (* 0 n) (/ (- 1 k) 8)) (/ (pow (* 0 n) (/ (- 1 k) 8)) (sqrt k)) (* 0 n) (/ (- 1 k) 8) (* (* (* (sqrt (PI)) n) 2) (sqrt (PI))) (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (* (pow (* (* (* (sqrt (PI)) n) 2) (sqrt (PI))) (+ (* -1/2 k) 1/2)) (sqrt (/ 1 k))) (pow (* (* (* (sqrt (PI)) n) 2) (sqrt (PI))) (+ (* -1/2 k) 1/2)) (PI) (* n (* (PI) 2)) (pow (* n (* (PI) 2)) -1/2) (* (PI) n) (sqrt (/ n k)) (sqrt (PI)) (sqrt k) (- 1 k) (* (sqrt (PI)) n))
6.0ms	k	@	-inf	((* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (* (* (pow (pow (* n (* (PI) 2)) -1/2) k) (sqrt (* n (* (PI) 2)))) (sqrt (/ 1 k))) (* (pow (pow (* n (* (PI) 2)) -1/2) k) (sqrt (* n (* (PI) 2)))) (pow (pow (* n (* (PI) 2)) -1/2) k) (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt (* (/ (* (PI) n) k) 2)) (* (/ (* (PI) n) k) 2) (/ (* (PI) n) k) (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (* (sqrt 2) (* (sqrt (/ n k)) (sqrt (PI)))) (sqrt 2) (* (sqrt (/ n k)) (sqrt (PI))) (pow (* 0 n) (/ (- 1 k) 8)) (/ (pow (* 0 n) (/ (- 1 k) 8)) (sqrt k)) (* 0 n) (/ (- 1 k) 8) (* (* (* (sqrt (PI)) n) 2) (sqrt (PI))) (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (* (pow (* (* (* (sqrt (PI)) n) 2) (sqrt (PI))) (+ (* -1/2 k) 1/2)) (sqrt (/ 1 k))) (pow (* (* (* (sqrt (PI)) n) 2) (sqrt (PI))) (+ (* -1/2 k) 1/2)) (PI) (* n (* (PI) 2)) (pow (* n (* (PI) 2)) -1/2) (* (PI) n) (sqrt (/ n k)) (sqrt (PI)) (sqrt k) (- 1 k) (* (sqrt (PI)) n))

simplify152.0ms (1.3%)

Memory

1.1MiB live, 177.9MiB allocated; 63ms collecting garbage

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	485	3834
1	1747	3527
0	8143	3312

Stop Event

1×	iter limit
1×	node limit

Counts

108 → 108

Calls

Call 1

Inputs
(* (sqrt (/ (* n (PI)) k)) (sqrt 2))
(/ (+ (* -1/2 (* (sqrt (* (pow k 3) (* n (PI)))) (* (log (* 2 (* n (PI)))) (sqrt 2)))) (* (sqrt (* k (* n (PI)))) (sqrt 2))) k)
(/ (+ (* k (+ (* -1/2 (* (sqrt (* k (* n (PI)))) (* (log (* 2 (* n (PI)))) (sqrt 2)))) (* 1/8 (* (sqrt (* (pow k 3) (* n (PI)))) (* (pow (log (* 2 (* n (PI)))) 2) (sqrt 2)))))) (* (sqrt (* k (* n (PI)))) (sqrt 2))) k)
(/ (+ (* k (+ (* -1/2 (* (sqrt (* k (* n (PI)))) (* (log (* 2 (* n (PI)))) (sqrt 2)))) (* k (+ (* -1/48 (* (sqrt (* (pow k 3) (* n (PI)))) (* (pow (log (* 2 (* n (PI)))) 3) (sqrt 2)))) (* 1/8 (* (sqrt (* k (* n (PI)))) (* (pow (log (* 2 (* n (PI)))) 2) (sqrt 2)))))))) (* (sqrt (* k (* n (PI)))) (sqrt 2))) k)
(/ (+ (* (sqrt (* k (* n (PI)))) (sqrt 2)) (* (sqrt (* (pow k 3) (* n (PI)))) (* (log (* (sqrt (/ 1 (* n (PI)))) (sqrt 1/2))) (sqrt 2)))) k)
(/ (+ (* k (+ (* 1/2 (* (sqrt (* (pow k 3) (* n (PI)))) (* (pow (log (* (sqrt (/ 1 (* n (PI)))) (sqrt 1/2))) 2) (sqrt 2)))) (* (sqrt (* k (* n (PI)))) (* (log (* (sqrt (/ 1 (* n (PI)))) (sqrt 1/2))) (sqrt 2))))) (* (sqrt (* k (* n (PI)))) (sqrt 2))) k)
(/ (+ (* k (+ (* k (+ (* 1/6 (* (sqrt (* (pow k 3) (* n (PI)))) (* (pow (log (* (sqrt (/ 1 (* n (PI)))) (sqrt 1/2))) 3) (sqrt 2)))) (* 1/2 (* (sqrt (* k (* n (PI)))) (* (pow (log (* (sqrt (/ 1 (* n (PI)))) (sqrt 1/2))) 2) (sqrt 2)))))) (* (sqrt (* k (* n (PI)))) (* (log (* (sqrt (/ 1 (* n (PI)))) (sqrt 1/2))) (sqrt 2))))) (* (sqrt (* k (* n (PI)))) (sqrt 2))) k)
(* (sqrt (* n (PI))) (sqrt 2))
(+ (* (sqrt (* n (PI))) (sqrt 2)) (* (* k (* (log (* (sqrt (/ 1 (* n (PI)))) (sqrt 1/2))) (sqrt 2))) (sqrt (* n (PI)))))
(+ (* k (+ (* 1/2 (* (* k (* (pow (log (* (sqrt (/ 1 (* n (PI)))) (sqrt 1/2))) 2) (sqrt 2))) (sqrt (* n (PI))))) (* (sqrt (* n (PI))) (* (log (* (sqrt (/ 1 (* n (PI)))) (sqrt 1/2))) (sqrt 2))))) (* (sqrt (* n (PI))) (sqrt 2)))
(+ (* k (+ (* k (+ (* 1/6 (* (* k (* (pow (log (* (sqrt (/ 1 (* n (PI)))) (sqrt 1/2))) 3) (sqrt 2))) (sqrt (* n (PI))))) (* 1/2 (* (sqrt (* n (PI))) (* (pow (log (* (sqrt (/ 1 (* n (PI)))) (sqrt 1/2))) 2) (sqrt 2)))))) (* (sqrt (* n (PI))) (* (log (* (sqrt (/ 1 (* n (PI)))) (sqrt 1/2))) (sqrt 2))))) (* (sqrt (* n (PI))) (sqrt 2)))
1
(+ 1 (* k (log (* (sqrt (/ 1 (* n (PI)))) (sqrt 1/2)))))
(+ 1 (* k (+ (log (* (sqrt (/ 1 (* n (PI)))) (sqrt 1/2))) (* 1/2 (* k (pow (log (* (sqrt (/ 1 (* n (PI)))) (sqrt 1/2))) 2))))))
(+ 1 (* k (+ (log (* (sqrt (/ 1 (* n (PI)))) (sqrt 1/2))) (* k (+ (* 1/6 (* k (pow (log (* (sqrt (/ 1 (* n (PI)))) (sqrt 1/2))) 3))) (* 1/2 (pow (log (* (sqrt (/ 1 (* n (PI)))) (sqrt 1/2))) 2)))))))
(* 2 (/ (* n (PI)) k))
(/ (* n (PI)) k)
(sqrt (/ (* n (PI)) k))
(exp (* 1/8 (+ (log 0) (* 20 (log k)))))
(+ (exp (* 1/8 (+ (log 0) (* 20 (log k))))) (* k (* (exp (* 1/8 (+ (log 0) (* 20 (log k))))) (+ (* -1/8 (+ (log 0) (* 20 (log k)))) (* 1/8 (NAN))))))
(+ (exp (* 1/8 (+ (log 0) (* 20 (log k))))) (* k (+ (* k (* (exp (* 1/8 (+ (log 0) (* 20 (log k))))) (+ (* -1/8 (NAN)) (+ (* 1/16 (+ (NAN) (* -1 (NAN)))) (* 1/2 (pow (+ (* -1/8 (+ (log 0) (* 20 (log k)))) (* 1/8 (NAN))) 2)))))) (* (exp (* 1/8 (+ (log 0) (* 20 (log k))))) (+ (* -1/8 (+ (log 0) (* 20 (log k)))) (* 1/8 (NAN)))))))
(+ (exp (* 1/8 (+ (log 0) (* 20 (log k))))) (* k (+ (* k (+ (* k (* (exp (* 1/8 (+ (log 0) (* 20 (log k))))) (+ (* -1/16 (+ (NAN) (* -1 (NAN)))) (+ (* 1/48 (+ (NAN) (+ (* -3 (NAN)) (* 2 (NAN))))) (+ (* 1/6 (pow (+ (* -1/8 (+ (log 0) (* 20 (log k)))) (* 1/8 (NAN))) 3)) (* (+ (* -1/8 (NAN)) (* 1/16 (+ (NAN) (* -1 (NAN))))) (+ (* -1/8 (+ (log 0) (* 20 (log k)))) (* 1/8 (NAN))))))))) (* (exp (* 1/8 (+ (log 0) (* 20 (log k))))) (+ (* -1/8 (NAN)) (+ (* 1/16 (+ (NAN) (* -1 (NAN)))) (* 1/2 (pow (+ (* -1/8 (+ (log 0) (* 20 (log k)))) (* 1/8 (NAN))) 2))))))) (* (exp (* 1/8 (+ (log 0) (* 20 (log k))))) (+ (* -1/8 (+ (log 0) (* 20 (log k)))) (* 1/8 (NAN)))))))
(* (sqrt (/ 1 k)) (exp (* 1/8 (+ (log 0) (* 20 (log k))))))
(/ (+ (* (sqrt k) (exp (* 1/8 (+ (log 0) (* 20 (log k)))))) (* (sqrt (pow k 3)) (* (exp (* 1/8 (+ (log 0) (* 20 (log k))))) (+ (* -1/8 (+ (log 0) (* 20 (log k)))) (* 1/8 (NAN)))))) k)
(/ (+ (* k (+ (* (sqrt k) (* (exp (* 1/8 (+ (log 0) (* 20 (log k))))) (+ (* -1/8 (+ (log 0) (* 20 (log k)))) (* 1/8 (NAN))))) (* (sqrt (pow k 3)) (* (exp (* 1/8 (+ (log 0) (* 20 (log k))))) (+ (* -1/8 (NAN)) (+ (* 1/16 (+ (NAN) (* -1 (NAN)))) (* 1/2 (pow (+ (* -1/8 (+ (log 0) (* 20 (log k)))) (* 1/8 (NAN))) 2)))))))) (* (sqrt k) (exp (* 1/8 (+ (log 0) (* 20 (log k))))))) k)
(/ (+ (* k (+ (* k (+ (* (sqrt k) (* (exp (* 1/8 (+ (log 0) (* 20 (log k))))) (+ (* -1/8 (NAN)) (+ (* 1/16 (+ (NAN) (* -1 (NAN)))) (* 1/2 (pow (+ (* -1/8 (+ (log 0) (* 20 (log k)))) (* 1/8 (NAN))) 2)))))) (* (sqrt (pow k 3)) (* (exp (* 1/8 (+ (log 0) (* 20 (log k))))) (+ (* -1/16 (+ (NAN) (* -1 (NAN)))) (+ (* 1/48 (+ (NAN) (+ (* -3 (NAN)) (* 2 (NAN))))) (+ (* 1/6 (pow (+ (* -1/8 (+ (log 0) (* 20 (log k)))) (* 1/8 (NAN))) 3)) (* (+ (* -1/8 (NAN)) (* 1/16 (+ (NAN) (* -1 (NAN))))) (+ (* -1/8 (+ (log 0) (* 20 (log k)))) (* 1/8 (NAN))))))))))) (* (sqrt k) (* (exp (* 1/8 (+ (log 0) (* 20 (log k))))) (+ (* -1/8 (+ (log 0) (* 20 (log k)))) (* 1/8 (NAN))))))) (* (sqrt k) (exp (* 1/8 (+ (log 0) (* 20 (log k))))))) k)
1/8
(+ 1/8 (* -1/8 k))
(+ (* -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 k))
(sqrt k)
(+ 1 (* -1 k))
(* (sqrt (/ 1 k)) (exp (* 1/2 (* (log (* 2 (* n (PI)))) (- 1 k)))))
(* (sqrt (/ (* n (PI)) k)) (* (sqrt 2) (pow (* (sqrt (/ 1 (* n (PI)))) (sqrt 1/2)) k)))
(* (sqrt (* n (PI))) (* (sqrt 2) (pow (* (sqrt (/ 1 (* n (PI)))) (sqrt 1/2)) k)))
(pow (* (sqrt (/ 1 (* n (PI)))) (sqrt 1/2)) k)
(exp (* 1/8 (* (log 0) (- 1 k))))
(* (sqrt (/ 1 k)) (exp (* 1/8 (* (log 0) (- 1 k)))))
(* -1/8 k)
(* k (- (* 1/8 (/ 1 k)) 1/8))
(* (sqrt (/ 1 k)) (exp (* (log (* 2 (* n (PI)))) (- 1/2 (* 1/2 k)))))
(exp (* (log (* 2 (* n (PI)))) (- 1/2 (* 1/2 k))))
(* -1 k)
(* k (- (/ 1 k) 1))
(* (sqrt (/ 1 k)) (exp (* 1/2 (* (log (* 2 (* n (PI)))) (+ 1 (* -1 k))))))
(* (sqrt (/ (* n (PI)) k)) (* (pow (sqrt -1) 2) (* (sqrt 2) (pow (* (sqrt (/ 1 (* n (PI)))) (sqrt 1/2)) k))))
(* (sqrt (/ (* n (PI)) k)) (* (sqrt -2) (sqrt -1)))
(* (sqrt (/ (* n (PI)) k)) (* (pow (sqrt -1) 2) (sqrt 2)))
(* (sqrt (/ (* n (PI)) k)) (pow (sqrt -1) 2))
(exp (* 1/8 (* (log 0) (+ 1 (* -1 k)))))
(* (sqrt (/ 1 k)) (exp (* 1/8 (* (log 0) (+ 1 (* -1 k))))))
(* -1 (* k (- 1/8 (* 1/8 (/ 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 k)) (pow (sqrt -1) 2))
(* -1 (* (sqrt k) (pow (sqrt -1) 2)))
(* -1 (* k (- 1 (/ 1 k))))
(* (sqrt (/ 1 k)) (exp (* 1/2 (* (+ (log n) (log (* 2 (PI)))) (- 1 k)))))
(* (sqrt (/ (* n (PI)) k)) (* (exp (* k (+ (log (* (sqrt (/ n (PI))) (sqrt 1/2))) (* -1 (log n))))) (sqrt 2)))
(* (sqrt (* n (PI))) (* (exp (* k (+ (log (* (sqrt (/ n (PI))) (sqrt 1/2))) (* -1 (log n))))) (sqrt 2)))
(exp (* k (+ (log (* (sqrt (/ n (PI))) (sqrt 1/2))) (* -1 (log n)))))
(exp (* 1/8 (* (+ (log 0) (* 20 (log n))) (- 1 k))))
(+ (exp (* 1/8 (* (+ (log 0) (* 20 (log n))) (- 1 k)))) (* 1/8 (* n (* (NAN) (* (exp (* 1/8 (* (+ (log 0) (* 20 (log n))) (- 1 k)))) (- 1 k))))))
(+ (exp (* 1/8 (* (+ (log 0) (* 20 (log n))) (- 1 k)))) (* n (+ (* 1/8 (* (NAN) (* (exp (* 1/8 (* (+ (log 0) (* 20 (log n))) (- 1 k)))) (- 1 k)))) (* n (* (exp (* 1/8 (* (+ (log 0) (* 20 (log n))) (- 1 k)))) (+ (* 1/128 (* (pow (NAN) 2) (pow (- 1 k) 2))) (* 1/16 (* (+ (NAN) (* -1 (NAN))) (- 1 k)))))))))
(+ (exp (* 1/8 (* (+ (log 0) (* 20 (log n))) (- 1 k)))) (* n (+ (* 1/8 (* (NAN) (* (exp (* 1/8 (* (+ (log 0) (* 20 (log n))) (- 1 k)))) (- 1 k)))) (* n (+ (* n (* (exp (* 1/8 (* (+ (log 0) (* 20 (log n))) (- 1 k)))) (+ (* 1/3072 (* (pow (NAN) 3) (pow (- 1 k) 3))) (+ (* 1/128 (* (NAN) (* (+ (NAN) (* -1 (NAN))) (pow (- 1 k) 2)))) (* 1/48 (* (+ (NAN) (+ (* -3 (NAN)) (* 2 (NAN)))) (- 1 k))))))) (* (exp (* 1/8 (* (+ (log 0) (* 20 (log n))) (- 1 k)))) (+ (* 1/128 (* (pow (NAN) 2) (pow (- 1 k) 2))) (* 1/16 (* (+ (NAN) (* -1 (NAN))) (- 1 k))))))))))
(* (sqrt (/ 1 k)) (exp (* 1/8 (* (+ (log 0) (* 20 (log n))) (- 1 k)))))
(+ (* 1/8 (* (sqrt (/ 1 k)) (* n (* (NAN) (* (exp (* 1/8 (* (+ (log 0) (* 20 (log n))) (- 1 k)))) (- 1 k)))))) (* (sqrt (/ 1 k)) (exp (* 1/8 (* (+ (log 0) (* 20 (log n))) (- 1 k))))))
(+ (* n (+ (* 1/8 (* (sqrt (/ 1 k)) (* (NAN) (* (exp (* 1/8 (* (+ (log 0) (* 20 (log n))) (- 1 k)))) (- 1 k))))) (* (sqrt (/ 1 k)) (* n (* (exp (* 1/8 (* (+ (log 0) (* 20 (log n))) (- 1 k)))) (+ (* 1/128 (* (pow (NAN) 2) (pow (- 1 k) 2))) (* 1/16 (* (+ (NAN) (* -1 (NAN))) (- 1 k))))))))) (* (sqrt (/ 1 k)) (exp (* 1/8 (* (+ (log 0) (* 20 (log n))) (- 1 k))))))
(+ (* n (+ (* 1/8 (* (sqrt (/ 1 k)) (* (NAN) (* (exp (* 1/8 (* (+ (log 0) (* 20 (log n))) (- 1 k)))) (- 1 k))))) (* n (+ (* (sqrt (/ 1 k)) (* n (* (exp (* 1/8 (* (+ (log 0) (* 20 (log n))) (- 1 k)))) (+ (* 1/3072 (* (pow (NAN) 3) (pow (- 1 k) 3))) (+ (* 1/128 (* (NAN) (* (+ (NAN) (* -1 (NAN))) (pow (- 1 k) 2)))) (* 1/48 (* (+ (NAN) (+ (* -3 (NAN)) (* 2 (NAN)))) (- 1 k)))))))) (* (sqrt (/ 1 k)) (* (exp (* 1/8 (* (+ (log 0) (* 20 (log n))) (- 1 k)))) (+ (* 1/128 (* (pow (NAN) 2) (pow (- 1 k) 2))) (* 1/16 (* (+ (NAN) (* -1 (NAN))) (- 1 k)))))))))) (* (sqrt (/ 1 k)) (exp (* 1/8 (* (+ (log 0) (* 20 (log n))) (- 1 k))))))
0
(* 2 (* n (PI)))
(* (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))))))
(* (sqrt (/ 1 (* n (PI)))) (sqrt 1/2))
(* n (PI))
(* n (sqrt (PI)))
(* (sqrt (/ 1 k)) (exp (* 1/2 (* (+ (log (* 2 (PI))) (* -1 (log (/ 1 n)))) (- 1 k)))))
(exp (* 1/8 (* (+ (log 0) (* 20 (log (/ 1 n)))) (- 1 k))))
(+ (exp (* 1/8 (* (+ (log 0) (* 20 (log (/ 1 n)))) (- 1 k)))) (* 1/8 (/ (* (NAN) (* (exp (* 1/8 (* (+ (log 0) (* 20 (log (/ 1 n)))) (- 1 k)))) (- 1 k))) n)))
(+ (exp (* 1/8 (* (+ (log 0) (* 20 (log (/ 1 n)))) (- 1 k)))) (+ (* 1/8 (/ (* (NAN) (* (exp (* 1/8 (* (+ (log 0) (* 20 (log (/ 1 n)))) (- 1 k)))) (- 1 k))) n)) (/ (* (exp (* 1/8 (* (+ (log 0) (* 20 (log (/ 1 n)))) (- 1 k)))) (+ (* 1/128 (* (pow (NAN) 2) (pow (- 1 k) 2))) (* 1/16 (* (+ (NAN) (* -1 (NAN))) (- 1 k))))) (pow n 2))))
(+ (exp (* 1/8 (* (+ (log 0) (* 20 (log (/ 1 n)))) (- 1 k)))) (+ (* 1/8 (/ (* (NAN) (* (exp (* 1/8 (* (+ (log 0) (* 20 (log (/ 1 n)))) (- 1 k)))) (- 1 k))) n)) (+ (/ (* (exp (* 1/8 (* (+ (log 0) (* 20 (log (/ 1 n)))) (- 1 k)))) (+ (* 1/3072 (* (pow (NAN) 3) (pow (- 1 k) 3))) (+ (* 1/128 (* (NAN) (* (+ (NAN) (* -1 (NAN))) (pow (- 1 k) 2)))) (* 1/48 (* (+ (NAN) (+ (* -3 (NAN)) (* 2 (NAN)))) (- 1 k)))))) (pow n 3)) (/ (* (exp (* 1/8 (* (+ (log 0) (* 20 (log (/ 1 n)))) (- 1 k)))) (+ (* 1/128 (* (pow (NAN) 2) (pow (- 1 k) 2))) (* 1/16 (* (+ (NAN) (* -1 (NAN))) (- 1 k))))) (pow n 2)))))
(* (sqrt (/ 1 k)) (exp (* 1/8 (* (+ (log 0) (* 20 (log (/ 1 n)))) (- 1 k)))))
(+ (* 1/8 (* (sqrt (/ 1 k)) (/ (* (NAN) (* (exp (* 1/8 (* (+ (log 0) (* 20 (log (/ 1 n)))) (- 1 k)))) (- 1 k))) n))) (* (sqrt (/ 1 k)) (exp (* 1/8 (* (+ (log 0) (* 20 (log (/ 1 n)))) (- 1 k))))))
(+ (* 1/8 (* (sqrt (/ 1 k)) (/ (* (NAN) (* (exp (* 1/8 (* (+ (log 0) (* 20 (log (/ 1 n)))) (- 1 k)))) (- 1 k))) n))) (+ (* (sqrt (/ 1 k)) (exp (* 1/8 (* (+ (log 0) (* 20 (log (/ 1 n)))) (- 1 k))))) (* (sqrt (/ 1 k)) (/ (* (exp (* 1/8 (* (+ (log 0) (* 20 (log (/ 1 n)))) (- 1 k)))) (+ (* 1/128 (* (pow (NAN) 2) (pow (- 1 k) 2))) (* 1/16 (* (+ (NAN) (* -1 (NAN))) (- 1 k))))) (pow n 2)))))
(+ (* 1/8 (* (sqrt (/ 1 k)) (/ (* (NAN) (* (exp (* 1/8 (* (+ (log 0) (* 20 (log (/ 1 n)))) (- 1 k)))) (- 1 k))) n))) (+ (* (sqrt (/ 1 k)) (exp (* 1/8 (* (+ (log 0) (* 20 (log (/ 1 n)))) (- 1 k))))) (+ (* (sqrt (/ 1 k)) (/ (* (exp (* 1/8 (* (+ (log 0) (* 20 (log (/ 1 n)))) (- 1 k)))) (+ (* 1/3072 (* (pow (NAN) 3) (pow (- 1 k) 3))) (+ (* 1/128 (* (NAN) (* (+ (NAN) (* -1 (NAN))) (pow (- 1 k) 2)))) (* 1/48 (* (+ (NAN) (+ (* -3 (NAN)) (* 2 (NAN)))) (- 1 k)))))) (pow n 3))) (* (sqrt (/ 1 k)) (/ (* (exp (* 1/8 (* (+ (log 0) (* 20 (log (/ 1 n)))) (- 1 k)))) (+ (* 1/128 (* (pow (NAN) 2) (pow (- 1 k) 2))) (* 1/16 (* (+ (NAN) (* -1 (NAN))) (- 1 k))))) (pow n 2))))))
(* (sqrt (/ 1 k)) (exp (* (+ 1/2 (* -1/2 k)) (+ (log (* 2 (PI))) (* -1 (log (/ 1 n)))))))
(exp (* (+ 1/2 (* -1/2 k)) (+ (log (* 2 (PI))) (* -1 (log (/ 1 n))))))
(* (sqrt (/ 1 k)) (exp (* 1/2 (* (+ (log (* -2 (PI))) (* -1 (log (/ -1 n)))) (- 1 k)))))
(* -1 (* (sqrt (/ (* n (PI)) k)) (* (sqrt -2) (* (sqrt -1) (pow (* (sqrt (/ 1 (* n (PI)))) (* (sqrt -1) (sqrt -1/2))) k)))))
(* -1 (* (sqrt (* n (PI))) (* (sqrt -2) (* (sqrt -1) (pow (* (sqrt (/ 1 (* n (PI)))) (* (sqrt -1) (sqrt -1/2))) k)))))
(pow (* (sqrt (/ 1 (* n (PI)))) (* (sqrt -1) (sqrt -1/2))) k)
(* -1 (* (sqrt (/ (* n (PI)) k)) (* (sqrt -2) (sqrt -1))))
(* -1 (* (sqrt (/ (* n (PI)) k)) (* (pow (sqrt -1) 2) (sqrt 2))))
(* -1 (* (sqrt (/ (* n (PI)) k)) (pow (sqrt -1) 2)))
(exp (* 1/8 (* (+ (log 0) (* 20 (log (/ -1 n)))) (- 1 k))))
(+ (exp (* 1/8 (* (+ (log 0) (* 20 (log (/ -1 n)))) (- 1 k)))) (* -1/8 (/ (* (NAN) (* (exp (* 1/8 (* (+ (log 0) (* 20 (log (/ -1 n)))) (- 1 k)))) (- 1 k))) n)))
(+ (exp (* 1/8 (* (+ (log 0) (* 20 (log (/ -1 n)))) (- 1 k)))) (* -1 (/ (+ (* -1 (/ (* (exp (* 1/8 (* (+ (log 0) (* 20 (log (/ -1 n)))) (- 1 k)))) (+ (* 1/128 (* (pow (NAN) 2) (pow (- 1 k) 2))) (* 1/16 (* (+ (NAN) (* -1 (NAN))) (- 1 k))))) n)) (* 1/8 (* (NAN) (* (exp (* 1/8 (* (+ (log 0) (* 20 (log (/ -1 n)))) (- 1 k)))) (- 1 k))))) n)))
(+ (exp (* 1/8 (* (+ (log 0) (* 20 (log (/ -1 n)))) (- 1 k)))) (* -1 (/ (+ (* -1 (/ (+ (* -1 (/ (* (exp (* 1/8 (* (+ (log 0) (* 20 (log (/ -1 n)))) (- 1 k)))) (+ (* 1/3072 (* (pow (NAN) 3) (pow (- 1 k) 3))) (+ (* 1/128 (* (NAN) (* (+ (NAN) (* -1 (NAN))) (pow (- 1 k) 2)))) (* 1/48 (* (+ (NAN) (+ (* -3 (NAN)) (* 2 (NAN)))) (- 1 k)))))) n)) (* (exp (* 1/8 (* (+ (log 0) (* 20 (log (/ -1 n)))) (- 1 k)))) (+ (* 1/128 (* (pow (NAN) 2) (pow (- 1 k) 2))) (* 1/16 (* (+ (NAN) (* -1 (NAN))) (- 1 k)))))) n)) (* 1/8 (* (NAN) (* (exp (* 1/8 (* (+ (log 0) (* 20 (log (/ -1 n)))) (- 1 k)))) (- 1 k))))) n)))
(* (sqrt (/ 1 k)) (exp (* 1/8 (* (+ (log 0) (* 20 (log (/ -1 n)))) (- 1 k)))))
(+ (* -1/8 (* (sqrt (/ 1 k)) (/ (* (NAN) (* (exp (* 1/8 (* (+ (log 0) (* 20 (log (/ -1 n)))) (- 1 k)))) (- 1 k))) n))) (* (sqrt (/ 1 k)) (exp (* 1/8 (* (+ (log 0) (* 20 (log (/ -1 n)))) (- 1 k))))))
(+ (* -1 (/ (+ (* -1 (* (sqrt (/ 1 k)) (/ (* (exp (* 1/8 (* (+ (log 0) (* 20 (log (/ -1 n)))) (- 1 k)))) (+ (* 1/128 (* (pow (NAN) 2) (pow (- 1 k) 2))) (* 1/16 (* (+ (NAN) (* -1 (NAN))) (- 1 k))))) n))) (* 1/8 (* (sqrt (/ 1 k)) (* (NAN) (* (exp (* 1/8 (* (+ (log 0) (* 20 (log (/ -1 n)))) (- 1 k)))) (- 1 k)))))) n)) (* (sqrt (/ 1 k)) (exp (* 1/8 (* (+ (log 0) (* 20 (log (/ -1 n)))) (- 1 k))))))
(+ (* -1 (/ (+ (* -1 (/ (+ (* -1 (* (sqrt (/ 1 k)) (/ (* (exp (* 1/8 (* (+ (log 0) (* 20 (log (/ -1 n)))) (- 1 k)))) (+ (* 1/3072 (* (pow (NAN) 3) (pow (- 1 k) 3))) (+ (* 1/128 (* (NAN) (* (+ (NAN) (* -1 (NAN))) (pow (- 1 k) 2)))) (* 1/48 (* (+ (NAN) (+ (* -3 (NAN)) (* 2 (NAN)))) (- 1 k)))))) n))) (* (sqrt (/ 1 k)) (* (exp (* 1/8 (* (+ (log 0) (* 20 (log (/ -1 n)))) (- 1 k)))) (+ (* 1/128 (* (pow (NAN) 2) (pow (- 1 k) 2))) (* 1/16 (* (+ (NAN) (* -1 (NAN))) (- 1 k))))))) n)) (* 1/8 (* (sqrt (/ 1 k)) (* (NAN) (* (exp (* 1/8 (* (+ (log 0) (* 20 (log (/ -1 n)))) (- 1 k)))) (- 1 k)))))) n)) (* (sqrt (/ 1 k)) (exp (* 1/8 (* (+ (log 0) (* 20 (log (/ -1 n)))) (- 1 k))))))
(* (sqrt (/ 1 k)) (exp (* (+ 1/2 (* -1/2 k)) (+ (log (* -2 (PI))) (* -1 (log (/ -1 n)))))))
(exp (* (+ 1/2 (* -1/2 k)) (+ (log (* -2 (PI))) (* -1 (log (/ -1 n))))))
(* (sqrt (/ 1 (* n (PI)))) (* (sqrt -1) (sqrt -1/2)))
(* -1 (* (sqrt (/ n k)) (pow (sqrt -1) 2)))

Outputs
(* (sqrt (/ (* n (PI)) k)) (sqrt 2))
(.f64 (sqrt.f64 #s(literal 2 binary64)) (sqrt.f64 (/.f64 (.f64 n (PI.f64)) k)))
(/ (+ (* -1/2 (* (sqrt (* (pow k 3) (* n (PI)))) (* (log (* 2 (* n (PI)))) (sqrt 2)))) (* (sqrt (* k (* n (PI)))) (sqrt 2))) k)
(/.f64 (fma.f64 (.f64 (.f64 (log.f64 (.f64 (.f64 n (PI.f64)) #s(literal 2 binary64))) (sqrt.f64 #s(literal 2 binary64))) (sqrt.f64 (.f64 (.f64 (pow.f64 k #s(literal 3 binary64)) (PI.f64)) n))) #s(literal -1/2 binary64) (.f64 (sqrt.f64 (.f64 (*.f64 n (PI.f64)) k)) (sqrt.f64 #s(literal 2 binary64)))) k)
(/ (+ (* k (+ (* -1/2 (* (sqrt (* k (* n (PI)))) (* (log (* 2 (* n (PI)))) (sqrt 2)))) (* 1/8 (* (sqrt (* (pow k 3) (* n (PI)))) (* (pow (log (* 2 (* n (PI)))) 2) (sqrt 2)))))) (* (sqrt (* k (* n (PI)))) (sqrt 2))) k)
(/.f64 (fma.f64 (fma.f64 (.f64 (.f64 #s(literal 1/8 binary64) (sqrt.f64 (.f64 (.f64 (pow.f64 k #s(literal 3 binary64)) (PI.f64)) n))) (pow.f64 (log.f64 (.f64 (.f64 n (PI.f64)) #s(literal 2 binary64))) #s(literal 2 binary64))) (sqrt.f64 #s(literal 2 binary64)) (.f64 (.f64 (.f64 (sqrt.f64 (.f64 (.f64 n (PI.f64)) k)) #s(literal -1/2 binary64)) (log.f64 (.f64 (.f64 n (PI.f64)) #s(literal 2 binary64)))) (sqrt.f64 #s(literal 2 binary64)))) k (.f64 (sqrt.f64 (.f64 (.f64 n (PI.f64)) k)) (sqrt.f64 #s(literal 2 binary64)))) k)
(/ (+ (* k (+ (* -1/2 (* (sqrt (* k (* n (PI)))) (* (log (* 2 (* n (PI)))) (sqrt 2)))) (* k (+ (* -1/48 (* (sqrt (* (pow k 3) (* n (PI)))) (* (pow (log (* 2 (* n (PI)))) 3) (sqrt 2)))) (* 1/8 (* (sqrt (* k (* n (PI)))) (* (pow (log (* 2 (* n (PI)))) 2) (sqrt 2)))))))) (* (sqrt (* k (* n (PI)))) (sqrt 2))) k)
(/.f64 (fma.f64 (fma.f64 (fma.f64 (.f64 (.f64 #s(literal -1/48 binary64) (sqrt.f64 (.f64 (.f64 (pow.f64 k #s(literal 3 binary64)) (PI.f64)) n))) (pow.f64 (log.f64 (.f64 (.f64 n (PI.f64)) #s(literal 2 binary64))) #s(literal 3 binary64))) (sqrt.f64 #s(literal 2 binary64)) (.f64 (.f64 (pow.f64 (log.f64 (.f64 (.f64 n (PI.f64)) #s(literal 2 binary64))) #s(literal 2 binary64)) (sqrt.f64 (.f64 (.f64 n (PI.f64)) k))) (.f64 (sqrt.f64 #s(literal 2 binary64)) #s(literal 1/8 binary64)))) k (.f64 (.f64 (.f64 (sqrt.f64 (.f64 (.f64 n (PI.f64)) k)) #s(literal -1/2 binary64)) (log.f64 (.f64 (.f64 n (PI.f64)) #s(literal 2 binary64)))) (sqrt.f64 #s(literal 2 binary64)))) k (.f64 (sqrt.f64 (.f64 (*.f64 n (PI.f64)) k)) (sqrt.f64 #s(literal 2 binary64)))) k)
(/ (+ (* (sqrt (* k (* n (PI)))) (sqrt 2)) (* (sqrt (* (pow k 3) (* n (PI)))) (* (log (* (sqrt (/ 1 (* n (PI)))) (sqrt 1/2))) (sqrt 2)))) k)
(/.f64 (.f64 (sqrt.f64 #s(literal 2 binary64)) (fma.f64 (log.f64 (.f64 (sqrt.f64 #s(literal 1/2 binary64)) (sqrt.f64 (/.f64 #s(literal 1 binary64) (.f64 n (PI.f64)))))) (sqrt.f64 (.f64 (.f64 (pow.f64 k #s(literal 3 binary64)) (PI.f64)) n)) (sqrt.f64 (.f64 (*.f64 n (PI.f64)) k)))) k)
(/ (+ (* k (+ (* 1/2 (* (sqrt (* (pow k 3) (* n (PI)))) (* (pow (log (* (sqrt (/ 1 (* n (PI)))) (sqrt 1/2))) 2) (sqrt 2)))) (* (sqrt (* k (* n (PI)))) (* (log (* (sqrt (/ 1 (* n (PI)))) (sqrt 1/2))) (sqrt 2))))) (* (sqrt (* k (* n (PI)))) (sqrt 2))) k)
(/.f64 (fma.f64 (fma.f64 (.f64 #s(literal 1/2 binary64) (sqrt.f64 (.f64 (.f64 (pow.f64 k #s(literal 3 binary64)) (PI.f64)) n))) (.f64 (pow.f64 (log.f64 (.f64 (sqrt.f64 #s(literal 1/2 binary64)) (sqrt.f64 (/.f64 #s(literal 1 binary64) (.f64 n (PI.f64)))))) #s(literal 2 binary64)) (sqrt.f64 #s(literal 2 binary64))) (.f64 (log.f64 (.f64 (sqrt.f64 #s(literal 1/2 binary64)) (sqrt.f64 (/.f64 #s(literal 1 binary64) (.f64 n (PI.f64)))))) (.f64 (sqrt.f64 (.f64 (.f64 n (PI.f64)) k)) (sqrt.f64 #s(literal 2 binary64))))) k (.f64 (sqrt.f64 (.f64 (*.f64 n (PI.f64)) k)) (sqrt.f64 #s(literal 2 binary64)))) k)
(/ (+ (* k (+ (* k (+ (* 1/6 (* (sqrt (* (pow k 3) (* n (PI)))) (* (pow (log (* (sqrt (/ 1 (* n (PI)))) (sqrt 1/2))) 3) (sqrt 2)))) (* 1/2 (* (sqrt (* k (* n (PI)))) (* (pow (log (* (sqrt (/ 1 (* n (PI)))) (sqrt 1/2))) 2) (sqrt 2)))))) (* (sqrt (* k (* n (PI)))) (* (log (* (sqrt (/ 1 (* n (PI)))) (sqrt 1/2))) (sqrt 2))))) (* (sqrt (* k (* n (PI)))) (sqrt 2))) k)
(/.f64 (fma.f64 (fma.f64 (fma.f64 (.f64 (.f64 #s(literal 1/2 binary64) (sqrt.f64 (.f64 (.f64 n (PI.f64)) k))) (pow.f64 (log.f64 (.f64 (sqrt.f64 #s(literal 1/2 binary64)) (sqrt.f64 (/.f64 #s(literal 1 binary64) (.f64 n (PI.f64)))))) #s(literal 2 binary64))) (sqrt.f64 #s(literal 2 binary64)) (.f64 (.f64 #s(literal 1/6 binary64) (sqrt.f64 (.f64 (.f64 (pow.f64 k #s(literal 3 binary64)) (PI.f64)) n))) (.f64 (pow.f64 (log.f64 (.f64 (sqrt.f64 #s(literal 1/2 binary64)) (sqrt.f64 (/.f64 #s(literal 1 binary64) (.f64 n (PI.f64)))))) #s(literal 3 binary64)) (sqrt.f64 #s(literal 2 binary64))))) k (.f64 (log.f64 (.f64 (sqrt.f64 #s(literal 1/2 binary64)) (sqrt.f64 (/.f64 #s(literal 1 binary64) (.f64 n (PI.f64)))))) (.f64 (sqrt.f64 (.f64 (.f64 n (PI.f64)) k)) (sqrt.f64 #s(literal 2 binary64))))) k (.f64 (sqrt.f64 (.f64 (.f64 n (PI.f64)) k)) (sqrt.f64 #s(literal 2 binary64)))) k)
(* (sqrt (* n (PI))) (sqrt 2))
(.f64 (sqrt.f64 (.f64 n (PI.f64))) (sqrt.f64 #s(literal 2 binary64)))
(+ (* (sqrt (* n (PI))) (sqrt 2)) (* (* k (* (log (* (sqrt (/ 1 (* n (PI)))) (sqrt 1/2))) (sqrt 2))) (sqrt (* n (PI)))))
(.f64 (sqrt.f64 (.f64 n (PI.f64))) (fma.f64 (.f64 k (sqrt.f64 #s(literal 2 binary64))) (log.f64 (.f64 (sqrt.f64 #s(literal 1/2 binary64)) (sqrt.f64 (/.f64 #s(literal 1 binary64) (*.f64 n (PI.f64)))))) (sqrt.f64 #s(literal 2 binary64))))
(+ (* k (+ (* 1/2 (* (* k (* (pow (log (* (sqrt (/ 1 (* n (PI)))) (sqrt 1/2))) 2) (sqrt 2))) (sqrt (* n (PI))))) (* (sqrt (* n (PI))) (* (log (* (sqrt (/ 1 (* n (PI)))) (sqrt 1/2))) (sqrt 2))))) (* (sqrt (* n (PI))) (sqrt 2)))
(fma.f64 (.f64 (sqrt.f64 (.f64 n (PI.f64))) (fma.f64 (.f64 #s(literal 1/2 binary64) k) (.f64 (pow.f64 (log.f64 (.f64 (sqrt.f64 #s(literal 1/2 binary64)) (sqrt.f64 (/.f64 #s(literal 1 binary64) (.f64 n (PI.f64)))))) #s(literal 2 binary64)) (sqrt.f64 #s(literal 2 binary64))) (.f64 (log.f64 (.f64 (sqrt.f64 #s(literal 1/2 binary64)) (sqrt.f64 (/.f64 #s(literal 1 binary64) (.f64 n (PI.f64)))))) (sqrt.f64 #s(literal 2 binary64))))) k (.f64 (sqrt.f64 (*.f64 n (PI.f64))) (sqrt.f64 #s(literal 2 binary64))))
(+ (* k (+ (* k (+ (* 1/6 (* (* k (* (pow (log (* (sqrt (/ 1 (* n (PI)))) (sqrt 1/2))) 3) (sqrt 2))) (sqrt (* n (PI))))) (* 1/2 (* (sqrt (* n (PI))) (* (pow (log (* (sqrt (/ 1 (* n (PI)))) (sqrt 1/2))) 2) (sqrt 2)))))) (* (sqrt (* n (PI))) (* (log (* (sqrt (/ 1 (* n (PI)))) (sqrt 1/2))) (sqrt 2))))) (* (sqrt (* n (PI))) (sqrt 2)))
(fma.f64 (.f64 k k) (fma.f64 (.f64 (.f64 (sqrt.f64 (.f64 n (PI.f64))) #s(literal 1/2 binary64)) (pow.f64 (log.f64 (.f64 (sqrt.f64 #s(literal 1/2 binary64)) (sqrt.f64 (/.f64 #s(literal 1 binary64) (.f64 n (PI.f64)))))) #s(literal 2 binary64))) (sqrt.f64 #s(literal 2 binary64)) (.f64 (.f64 (.f64 (sqrt.f64 (.f64 n (PI.f64))) k) (.f64 (pow.f64 (log.f64 (.f64 (sqrt.f64 #s(literal 1/2 binary64)) (sqrt.f64 (/.f64 #s(literal 1 binary64) (.f64 n (PI.f64)))))) #s(literal 3 binary64)) (sqrt.f64 #s(literal 2 binary64)))) #s(literal 1/6 binary64))) (.f64 (sqrt.f64 (.f64 n (PI.f64))) (fma.f64 (.f64 k (sqrt.f64 #s(literal 2 binary64))) (log.f64 (.f64 (sqrt.f64 #s(literal 1/2 binary64)) (sqrt.f64 (/.f64 #s(literal 1 binary64) (.f64 n (PI.f64)))))) (sqrt.f64 #s(literal 2 binary64)))))
1
#s(literal 1 binary64)
(+ 1 (* k (log (* (sqrt (/ 1 (* n (PI)))) (sqrt 1/2)))))
(fma.f64 (log.f64 (.f64 (sqrt.f64 #s(literal 1/2 binary64)) (sqrt.f64 (/.f64 #s(literal 1 binary64) (.f64 n (PI.f64)))))) k #s(literal 1 binary64))
(+ 1 (* k (+ (log (* (sqrt (/ 1 (* n (PI)))) (sqrt 1/2))) (* 1/2 (* k (pow (log (* (sqrt (/ 1 (* n (PI)))) (sqrt 1/2))) 2))))))
(fma.f64 (fma.f64 (.f64 #s(literal 1/2 binary64) k) (pow.f64 (log.f64 (.f64 (sqrt.f64 #s(literal 1/2 binary64)) (sqrt.f64 (/.f64 #s(literal 1 binary64) (.f64 n (PI.f64)))))) #s(literal 2 binary64)) (log.f64 (.f64 (sqrt.f64 #s(literal 1/2 binary64)) (sqrt.f64 (/.f64 #s(literal 1 binary64) (*.f64 n (PI.f64))))))) k #s(literal 1 binary64))
(+ 1 (* k (+ (log (* (sqrt (/ 1 (* n (PI)))) (sqrt 1/2))) (* k (+ (* 1/6 (* k (pow (log (* (sqrt (/ 1 (* n (PI)))) (sqrt 1/2))) 3))) (* 1/2 (pow (log (* (sqrt (/ 1 (* n (PI)))) (sqrt 1/2))) 2)))))))
(fma.f64 (fma.f64 (fma.f64 (.f64 #s(literal 1/6 binary64) k) (pow.f64 (log.f64 (.f64 (sqrt.f64 #s(literal 1/2 binary64)) (sqrt.f64 (/.f64 #s(literal 1 binary64) (.f64 n (PI.f64)))))) #s(literal 3 binary64)) (.f64 (pow.f64 (log.f64 (.f64 (sqrt.f64 #s(literal 1/2 binary64)) (sqrt.f64 (/.f64 #s(literal 1 binary64) (.f64 n (PI.f64)))))) #s(literal 2 binary64)) #s(literal 1/2 binary64))) k (log.f64 (.f64 (sqrt.f64 #s(literal 1/2 binary64)) (sqrt.f64 (/.f64 #s(literal 1 binary64) (.f64 n (PI.f64))))))) k #s(literal 1 binary64))
(* 2 (/ (* n (PI)) k))
(.f64 (/.f64 (.f64 n (PI.f64)) k) #s(literal 2 binary64))
(/ (* n (PI)) k)
(/.f64 (*.f64 n (PI.f64)) k)
(sqrt (/ (* n (PI)) k))
(sqrt.f64 (/.f64 (*.f64 n (PI.f64)) k))
(exp (* 1/8 (+ (log 0) (* 20 (log k)))))
(pow.f64 (exp.f64 #s(literal 1/8 binary64)) (fma.f64 (log.f64 k) #s(literal 20 binary64) (log.f64 #s(literal 0 binary64))))
(+ (exp (* 1/8 (+ (log 0) (* 20 (log k))))) (* k (* (exp (* 1/8 (+ (log 0) (* 20 (log k))))) (+ (* -1/8 (+ (log 0) (* 20 (log k)))) (* 1/8 (NAN))))))
(fma.f64 (.f64 k (.f64 #s(literal -1/8 binary64) (-.f64 (fma.f64 (log.f64 k) #s(literal 20 binary64) (log.f64 #s(literal 0 binary64))) (NAN.f64)))) (pow.f64 (exp.f64 #s(literal 1/8 binary64)) (fma.f64 (log.f64 k) #s(literal 20 binary64) (log.f64 #s(literal 0 binary64)))) (pow.f64 (exp.f64 #s(literal 1/8 binary64)) (fma.f64 (log.f64 k) #s(literal 20 binary64) (log.f64 #s(literal 0 binary64)))))
(+ (exp (* 1/8 (+ (log 0) (* 20 (log k))))) (* k (+ (* k (* (exp (* 1/8 (+ (log 0) (* 20 (log k))))) (+ (* -1/8 (NAN)) (+ (* 1/16 (+ (NAN) (* -1 (NAN)))) (* 1/2 (pow (+ (* -1/8 (+ (log 0) (* 20 (log k)))) (* 1/8 (NAN))) 2)))))) (* (exp (* 1/8 (+ (log 0) (* 20 (log k))))) (+ (* -1/8 (+ (log 0) (* 20 (log k)))) (* 1/8 (NAN)))))))
(fma.f64 (fma.f64 (.f64 k (fma.f64 (pow.f64 (.f64 #s(literal -1/8 binary64) (-.f64 (fma.f64 (log.f64 k) #s(literal 20 binary64) (log.f64 #s(literal 0 binary64))) (NAN.f64))) #s(literal 2 binary64)) #s(literal 1/2 binary64) (fma.f64 (NAN.f64) #s(literal -1/8 binary64) #s(literal 0 binary64)))) (pow.f64 (exp.f64 #s(literal 1/8 binary64)) (fma.f64 (log.f64 k) #s(literal 20 binary64) (log.f64 #s(literal 0 binary64)))) (.f64 (.f64 #s(literal -1/8 binary64) (-.f64 (fma.f64 (log.f64 k) #s(literal 20 binary64) (log.f64 #s(literal 0 binary64))) (NAN.f64))) (pow.f64 (exp.f64 #s(literal 1/8 binary64)) (fma.f64 (log.f64 k) #s(literal 20 binary64) (log.f64 #s(literal 0 binary64)))))) k (pow.f64 (exp.f64 #s(literal 1/8 binary64)) (fma.f64 (log.f64 k) #s(literal 20 binary64) (log.f64 #s(literal 0 binary64)))))
(+ (exp (* 1/8 (+ (log 0) (* 20 (log k))))) (* k (+ (* k (+ (* k (* (exp (* 1/8 (+ (log 0) (* 20 (log k))))) (+ (* -1/16 (+ (NAN) (* -1 (NAN)))) (+ (* 1/48 (+ (NAN) (+ (* -3 (NAN)) (* 2 (NAN))))) (+ (* 1/6 (pow (+ (* -1/8 (+ (log 0) (* 20 (log k)))) (* 1/8 (NAN))) 3)) (* (+ (* -1/8 (NAN)) (* 1/16 (+ (NAN) (* -1 (NAN))))) (+ (* -1/8 (+ (log 0) (* 20 (log k)))) (* 1/8 (NAN))))))))) (* (exp (* 1/8 (+ (log 0) (* 20 (log k))))) (+ (* -1/8 (NAN)) (+ (* 1/16 (+ (NAN) (* -1 (NAN)))) (* 1/2 (pow (+ (* -1/8 (+ (log 0) (* 20 (log k)))) (* 1/8 (NAN))) 2))))))) (* (exp (* 1/8 (+ (log 0) (* 20 (log k))))) (+ (* -1/8 (+ (log 0) (* 20 (log k)))) (* 1/8 (NAN)))))))
(fma.f64 (fma.f64 (fma.f64 (.f64 k (fma.f64 (fma.f64 (NAN.f64) #s(literal -1/8 binary64) #s(literal 0 binary64)) (.f64 #s(literal -1/8 binary64) (-.f64 (fma.f64 (log.f64 k) #s(literal 20 binary64) (log.f64 #s(literal 0 binary64))) (NAN.f64))) (fma.f64 (pow.f64 (.f64 #s(literal -1/8 binary64) (-.f64 (fma.f64 (log.f64 k) #s(literal 20 binary64) (log.f64 #s(literal 0 binary64))) (NAN.f64))) #s(literal 3 binary64)) #s(literal 1/6 binary64) #s(literal 0 binary64)))) (pow.f64 (exp.f64 #s(literal 1/8 binary64)) (fma.f64 (log.f64 k) #s(literal 20 binary64) (log.f64 #s(literal 0 binary64)))) (.f64 (fma.f64 (pow.f64 (.f64 #s(literal -1/8 binary64) (-.f64 (fma.f64 (log.f64 k) #s(literal 20 binary64) (log.f64 #s(literal 0 binary64))) (NAN.f64))) #s(literal 2 binary64)) #s(literal 1/2 binary64) (fma.f64 (NAN.f64) #s(literal -1/8 binary64) #s(literal 0 binary64))) (pow.f64 (exp.f64 #s(literal 1/8 binary64)) (fma.f64 (log.f64 k) #s(literal 20 binary64) (log.f64 #s(literal 0 binary64)))))) k (.f64 (*.f64 #s(literal -1/8 binary64) (-.f64 (fma.f64 (log.f64 k) #s(literal 20 binary64) (log.f64 #s(literal 0 binary64))) (NAN.f64))) (pow.f64 (exp.f64 #s(literal 1/8 binary64)) (fma.f64 (log.f64 k) #s(literal 20 binary64) (log.f64 #s(literal 0 binary64)))))) k (pow.f64 (exp.f64 #s(literal 1/8 binary64)) (fma.f64 (log.f64 k) #s(literal 20 binary64) (log.f64 #s(literal 0 binary64)))))
(* (sqrt (/ 1 k)) (exp (* 1/8 (+ (log 0) (* 20 (log k))))))
(*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) k)) (pow.f64 (exp.f64 #s(literal 1/8 binary64)) (fma.f64 (log.f64 k) #s(literal 20 binary64) (log.f64 #s(literal 0 binary64)))))
(/ (+ (* (sqrt k) (exp (* 1/8 (+ (log 0) (* 20 (log k)))))) (* (sqrt (pow k 3)) (* (exp (* 1/8 (+ (log 0) (* 20 (log k))))) (+ (* -1/8 (+ (log 0) (* 20 (log k)))) (* 1/8 (NAN)))))) k)
(/.f64 (fma.f64 (.f64 (sqrt.f64 (pow.f64 k #s(literal 3 binary64))) (.f64 #s(literal -1/8 binary64) (-.f64 (fma.f64 (log.f64 k) #s(literal 20 binary64) (log.f64 #s(literal 0 binary64))) (NAN.f64)))) (pow.f64 (exp.f64 #s(literal 1/8 binary64)) (fma.f64 (log.f64 k) #s(literal 20 binary64) (log.f64 #s(literal 0 binary64)))) (*.f64 (pow.f64 (exp.f64 #s(literal 1/8 binary64)) (fma.f64 (log.f64 k) #s(literal 20 binary64) (log.f64 #s(literal 0 binary64)))) (sqrt.f64 k))) k)
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(-.f64 (pow.f64 (exp.f64 #s(literal 1/8 binary64)) (.f64 (fma.f64 (log.f64 (/.f64 #s(literal -1 binary64) n)) #s(literal 20 binary64) (log.f64 #s(literal 0 binary64))) (-.f64 #s(literal 1 binary64) k))) (/.f64 (fma.f64 (.f64 #s(literal 1/8 binary64) (.f64 (pow.f64 (exp.f64 #s(literal 1/8 binary64)) (.f64 (fma.f64 (log.f64 (/.f64 #s(literal -1 binary64) n)) #s(literal 20 binary64) (log.f64 #s(literal 0 binary64))) (-.f64 #s(literal 1 binary64) k))) (NAN.f64))) (-.f64 #s(literal 1 binary64) k) (/.f64 (fma.f64 (neg.f64 (pow.f64 (exp.f64 #s(literal 1/8 binary64)) (.f64 (fma.f64 (log.f64 (/.f64 #s(literal -1 binary64) n)) #s(literal 20 binary64) (log.f64 #s(literal 0 binary64))) (-.f64 #s(literal 1 binary64) k)))) (/.f64 (fma.f64 (pow.f64 (.f64 (NAN.f64) (-.f64 #s(literal 1 binary64) k)) #s(literal 3 binary64)) #s(literal 1/3072 binary64) (fma.f64 (pow.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 2 binary64)) #s(literal 0 binary64) (.f64 #s(literal 0 binary64) (-.f64 #s(literal 1 binary64) k)))) n) (.f64 (pow.f64 (exp.f64 #s(literal 1/8 binary64)) (.f64 (fma.f64 (log.f64 (/.f64 #s(literal -1 binary64) n)) #s(literal 20 binary64) (log.f64 #s(literal 0 binary64))) (-.f64 #s(literal 1 binary64) k))) (fma.f64 (.f64 #s(literal 1/128 binary64) (pow.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 2 binary64))) (.f64 (NAN.f64) (NAN.f64)) (.f64 #s(literal 0 binary64) (-.f64 #s(literal 1 binary64) k))))) (neg.f64 n))) n))
(* (sqrt (/ 1 k)) (exp (* 1/8 (* (+ (log 0) (* 20 (log (/ -1 n)))) (- 1 k)))))
(.f64 (pow.f64 (exp.f64 #s(literal 1/8 binary64)) (.f64 (fma.f64 (log.f64 (/.f64 #s(literal -1 binary64) n)) #s(literal 20 binary64) (log.f64 #s(literal 0 binary64))) (-.f64 #s(literal 1 binary64) k))) (sqrt.f64 (/.f64 #s(literal 1 binary64) k)))
(+ (* -1/8 (* (sqrt (/ 1 k)) (/ (* (NAN) (* (exp (* 1/8 (* (+ (log 0) (* 20 (log (/ -1 n)))) (- 1 k)))) (- 1 k))) n))) (* (sqrt (/ 1 k)) (exp (* 1/8 (* (+ (log 0) (* 20 (log (/ -1 n)))) (- 1 k))))))
(fma.f64 (.f64 (.f64 (.f64 (pow.f64 (exp.f64 #s(literal 1/8 binary64)) (.f64 (fma.f64 (log.f64 (/.f64 #s(literal -1 binary64) n)) #s(literal 20 binary64) (log.f64 #s(literal 0 binary64))) (-.f64 #s(literal 1 binary64) k))) (-.f64 #s(literal 1 binary64) k)) (/.f64 (NAN.f64) n)) #s(literal -1/8 binary64)) (sqrt.f64 (/.f64 #s(literal 1 binary64) k)) (.f64 (pow.f64 (exp.f64 #s(literal 1/8 binary64)) (.f64 (fma.f64 (log.f64 (/.f64 #s(literal -1 binary64) n)) #s(literal 20 binary64) (log.f64 #s(literal 0 binary64))) (-.f64 #s(literal 1 binary64) k))) (sqrt.f64 (/.f64 #s(literal 1 binary64) k))))
(+ (* -1 (/ (+ (* -1 (* (sqrt (/ 1 k)) (/ (* (exp (* 1/8 (* (+ (log 0) (* 20 (log (/ -1 n)))) (- 1 k)))) (+ (* 1/128 (* (pow (NAN) 2) (pow (- 1 k) 2))) (* 1/16 (* (+ (NAN) (* -1 (NAN))) (- 1 k))))) n))) (* 1/8 (* (sqrt (/ 1 k)) (* (NAN) (* (exp (* 1/8 (* (+ (log 0) (* 20 (log (/ -1 n)))) (- 1 k)))) (- 1 k)))))) n)) (* (sqrt (/ 1 k)) (exp (* 1/8 (* (+ (log 0) (* 20 (log (/ -1 n)))) (- 1 k))))))
(fma.f64 (pow.f64 (exp.f64 #s(literal 1/8 binary64)) (.f64 (fma.f64 (log.f64 (/.f64 #s(literal -1 binary64) n)) #s(literal 20 binary64) (log.f64 #s(literal 0 binary64))) (-.f64 #s(literal 1 binary64) k))) (sqrt.f64 (/.f64 #s(literal 1 binary64) k)) (/.f64 (fma.f64 (.f64 (.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) k)) #s(literal 1/8 binary64)) (.f64 (pow.f64 (exp.f64 #s(literal 1/8 binary64)) (.f64 (fma.f64 (log.f64 (/.f64 #s(literal -1 binary64) n)) #s(literal 20 binary64) (log.f64 #s(literal 0 binary64))) (-.f64 #s(literal 1 binary64) k))) (-.f64 #s(literal 1 binary64) k))) (NAN.f64) (.f64 (.f64 (neg.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) k))) (pow.f64 (exp.f64 #s(literal 1/8 binary64)) (.f64 (fma.f64 (log.f64 (/.f64 #s(literal -1 binary64) n)) #s(literal 20 binary64) (log.f64 #s(literal 0 binary64))) (-.f64 #s(literal 1 binary64) k)))) (/.f64 (fma.f64 (.f64 #s(literal 1/128 binary64) (pow.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 2 binary64))) (.f64 (NAN.f64) (NAN.f64)) (*.f64 #s(literal 0 binary64) (-.f64 #s(literal 1 binary64) k))) n))) (neg.f64 n)))
(+ (* -1 (/ (+ (* -1 (/ (+ (* -1 (* (sqrt (/ 1 k)) (/ (* (exp (* 1/8 (* (+ (log 0) (* 20 (log (/ -1 n)))) (- 1 k)))) (+ (* 1/3072 (* (pow (NAN) 3) (pow (- 1 k) 3))) (+ (* 1/128 (* (NAN) (* (+ (NAN) (* -1 (NAN))) (pow (- 1 k) 2)))) (* 1/48 (* (+ (NAN) (+ (* -3 (NAN)) (* 2 (NAN)))) (- 1 k)))))) n))) (* (sqrt (/ 1 k)) (* (exp (* 1/8 (* (+ (log 0) (* 20 (log (/ -1 n)))) (- 1 k)))) (+ (* 1/128 (* (pow (NAN) 2) (pow (- 1 k) 2))) (* 1/16 (* (+ (NAN) (* -1 (NAN))) (- 1 k))))))) n)) (* 1/8 (* (sqrt (/ 1 k)) (* (NAN) (* (exp (* 1/8 (* (+ (log 0) (* 20 (log (/ -1 n)))) (- 1 k)))) (- 1 k)))))) n)) (* (sqrt (/ 1 k)) (exp (* 1/8 (* (+ (log 0) (* 20 (log (/ -1 n)))) (- 1 k))))))
(fma.f64 (pow.f64 (exp.f64 #s(literal 1/8 binary64)) (.f64 (fma.f64 (log.f64 (/.f64 #s(literal -1 binary64) n)) #s(literal 20 binary64) (log.f64 #s(literal 0 binary64))) (-.f64 #s(literal 1 binary64) k))) (sqrt.f64 (/.f64 #s(literal 1 binary64) k)) (/.f64 (fma.f64 (.f64 (.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) k)) #s(literal 1/8 binary64)) (.f64 (pow.f64 (exp.f64 #s(literal 1/8 binary64)) (.f64 (fma.f64 (log.f64 (/.f64 #s(literal -1 binary64) n)) #s(literal 20 binary64) (log.f64 #s(literal 0 binary64))) (-.f64 #s(literal 1 binary64) k))) (NAN.f64))) (-.f64 #s(literal 1 binary64) k) (/.f64 (fma.f64 (.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) k)) (fma.f64 (.f64 #s(literal 1/128 binary64) (pow.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 2 binary64))) (.f64 (NAN.f64) (NAN.f64)) (.f64 #s(literal 0 binary64) (-.f64 #s(literal 1 binary64) k)))) (pow.f64 (exp.f64 #s(literal 1/8 binary64)) (.f64 (fma.f64 (log.f64 (/.f64 #s(literal -1 binary64) n)) #s(literal 20 binary64) (log.f64 #s(literal 0 binary64))) (-.f64 #s(literal 1 binary64) k))) (.f64 (.f64 (neg.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) k))) (pow.f64 (exp.f64 #s(literal 1/8 binary64)) (.f64 (fma.f64 (log.f64 (/.f64 #s(literal -1 binary64) n)) #s(literal 20 binary64) (log.f64 #s(literal 0 binary64))) (-.f64 #s(literal 1 binary64) k)))) (/.f64 (fma.f64 (pow.f64 (.f64 (NAN.f64) (-.f64 #s(literal 1 binary64) k)) #s(literal 3 binary64)) #s(literal 1/3072 binary64) (fma.f64 (pow.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 2 binary64)) #s(literal 0 binary64) (*.f64 #s(literal 0 binary64) (-.f64 #s(literal 1 binary64) k)))) n))) (neg.f64 n))) (neg.f64 n)))
(* (sqrt (/ 1 k)) (exp (* (+ 1/2 (* -1/2 k)) (+ (log (* -2 (PI))) (* -1 (log (/ -1 n)))))))
(.f64 (pow.f64 (exp.f64 (fma.f64 #s(literal -1/2 binary64) k #s(literal 1/2 binary64))) (-.f64 (log.f64 (.f64 #s(literal -2 binary64) (PI.f64))) (log.f64 (/.f64 #s(literal -1 binary64) n)))) (sqrt.f64 (/.f64 #s(literal 1 binary64) k)))
(exp (* (+ 1/2 (* -1/2 k)) (+ (log (* -2 (PI))) (* -1 (log (/ -1 n))))))
(pow.f64 (exp.f64 (fma.f64 #s(literal -1/2 binary64) k #s(literal 1/2 binary64))) (-.f64 (log.f64 (*.f64 #s(literal -2 binary64) (PI.f64))) (log.f64 (/.f64 #s(literal -1 binary64) n))))
(* (sqrt (/ 1 (* n (PI)))) (* (sqrt -1) (sqrt -1/2)))
(.f64 (.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (*.f64 n (PI.f64)))) (sqrt.f64 #s(literal -1/2 binary64))) (sqrt.f64 #s(literal -1 binary64)))
(* -1 (* (sqrt (/ n k)) (pow (sqrt -1) 2)))
(*.f64 (sqrt.f64 (/.f64 n k)) #s(literal 1 binary64))

rewrite203.0ms (1.8%)

Memory

4.4MiB live, 239.6MiB allocated; 32ms collecting garbage

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	53	313
0	86	285
1	259	239
2	1224	137
0	9264	137

Stop Event

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

Counts

29 → 1 377

Calls

Call 1

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

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

eval281.0ms (2.5%)

Memory: 13.0MiB live, 349.2MiB allocated; 57ms collecting garbage
Compiler: Compiled 47 147 to 5 799 computations (87.7% saved)

prune77.0ms (0.7%)

Memory

3.4MiB live, 114.5MiB allocated; 10ms collecting garbage

Pruning

23 alts after pruning (19 fresh and 4 done)

	Pruned	Kept	Total
New	1 217	9	1 226
Fresh	2	10	12
Picked	3	2	5
Done	0	2	2
Total	1 222	23	1 245

Accuracy

100.0%

Counts

1 245 → 23

Alt Table

Click to see full alt table

Status	Accuracy	Program
▶	99.7%	(/.f64 (.f64 (sqrt.f64 (.f64 n (.f64 (PI.f64) #s(literal 2 binary64)))) #s(literal 1 binary64)) (.f64 (pow.f64 (.f64 n (.f64 (PI.f64) #s(literal 2 binary64))) (/.f64 k #s(literal 2 binary64))) (sqrt.f64 k)))
	98.7%	(.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) (.f64 (pow.f64 (*.f64 n #s(literal 2 binary64)) (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 2 binary64))) #s(approx (pow (PI) (/ (- 1 k) 2)) (sqrt.f64 (PI.f64)))))
▶	99.5%	(.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) #s(approx (pow ( (* 2 (PI)) n) (/ (- 1 k) 2)) (pow.f64 (.f64 (.f64 #s(literal 2 binary64) n) (PI.f64)) (fma.f64 #s(literal -1/2 binary64) k #s(literal 1/2 binary64)))))
	48.5%	(.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)))))
	47.5%	(.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)))))
	29.4%	#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (pow.f64 #s(literal 0 binary64) (fma.f64 #s(literal -1/2 binary64) k #s(literal 1/2 binary64))))
	47.6%	#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (/.f64 (sqrt.f64 (.f64 n (.f64 (PI.f64) #s(literal 2 binary64)))) (sqrt.f64 k)))
✓	99.5%	#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (.f64 (pow.f64 (.f64 (.f64 (.f64 (sqrt.f64 (PI.f64)) n) #s(literal 2 binary64)) (sqrt.f64 (PI.f64))) (fma.f64 #s(literal -1/2 binary64) k #s(literal 1/2 binary64))) (sqrt.f64 (/.f64 #s(literal 1 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))))
	99.6%	#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (.f64 (pow.f64 (sqrt.f64 (.f64 n (.f64 (PI.f64) #s(literal 2 binary64)))) (.f64 #s(literal 2 binary64) (fma.f64 #s(literal -1/2 binary64) k #s(literal 1/2 binary64)))) (sqrt.f64 (/.f64 #s(literal 1 binary64) k))))
	47.4%	#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (.f64 (/.f64 (sqrt.f64 (.f64 (PI.f64) #s(literal 2 binary64))) (pow.f64 k #s(literal 1/4 binary64))) (/.f64 (sqrt.f64 n) (pow.f64 k #s(literal 1/4 binary64)))))
▶	47.7%	#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (.f64 (.f64 #s(approx (pow (pow (* n (* (PI) 2)) -1/2) k) #s(literal 1 binary64)) (sqrt.f64 (.f64 n (.f64 (PI.f64) #s(literal 2 binary64))))) (sqrt.f64 (/.f64 #s(literal 1 binary64) k))))
	47.6%	#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (.f64 (sqrt.f64 #s(literal 2 binary64)) (/.f64 (sqrt.f64 (.f64 (PI.f64) n)) (sqrt.f64 k))))
	47.6%	#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (.f64 (sqrt.f64 #s(literal 2 binary64)) (.f64 (sqrt.f64 n) (sqrt.f64 (/.f64 (PI.f64) k)))))
✓	35.2%	#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (.f64 (sqrt.f64 #s(literal 2 binary64)) (sqrt.f64 (/.f64 (.f64 (PI.f64) n) k))))
	35.1%	#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt.f64 (.f64 (/.f64 (.f64 (*.f64 (sqrt.f64 (PI.f64)) (sqrt.f64 (PI.f64))) n) k) #s(literal 2 binary64))))
✓	35.3%	#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt.f64 (.f64 (/.f64 (.f64 (PI.f64) n) k) #s(literal 2 binary64))))
	35.3%	#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt.f64 (.f64 (/.f64 (PI.f64) k) (.f64 n #s(literal 2 binary64)))))
	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))))
▶	4.9%	#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt.f64 (*.f64 (/.f64 (PI.f64) #s(literal 1 binary64)) (/.f64 #s(literal 2 binary64) k))))
	35.3%	#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt.f64 (.f64 (.f64 (/.f64 n k) (PI.f64)) #s(literal 2 binary64))))
	74.8%	#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) #s(approx (* (* (pow (pow (* n (* (PI) 2)) -1/2) k) (sqrt (* n (* (PI) 2)))) (sqrt (/ 1 k))) (.f64 (pow.f64 (.f64 (sqrt.f64 #s(literal 1/2 binary64)) (sqrt.f64 (/.f64 #s(literal 1 binary64) (.f64 n (PI.f64))))) k) (.f64 (sqrt.f64 #s(literal 2 binary64)) (sqrt.f64 (/.f64 (*.f64 n (PI.f64)) k))))))
▶	26.3%	#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) #s(literal 0 binary64))

Compiler

Compiled 1 215 to 955 computations (21.4% saved)

simplify24.0ms (0.2%)

Memory

-18.8MiB live, 25.9MiB allocated; 5ms collecting garbage

Algorithm

1×	egg-herbie

Localize:

Found 17 expressions of interest:

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

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	49	345
0	75	333
1	117	325
2	182	325
3	259	320
4	328	320
5	392	320
6	498	320
7	582	320
8	614	320
9	644	320
0	644	320

Stop Event

1×	iter limit
1×	saturated
1×	iter limit

Calls

Call 1

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

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

localize115.0ms (1%)

Memory

12.9MiB live, 203.4MiB allocated; 14ms collecting garbage

Localize:

Found 17 expressions of interest:

New	Metric	Score
accuracy	0.171875	(.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) #s(approx (pow ( (* 2 (PI)) n) (/ (- 1 k) 2)) (pow.f64 (.f64 (.f64 #s(literal 2 binary64) n) (PI.f64)) (fma.f64 #s(literal -1/2 binary64) k #s(literal 1/2 binary64)))))
accuracy	0.17578125	(.f64 (.f64 #s(literal 2 binary64) n) (PI.f64))
accuracy	0.1796875	(/.f64 #s(literal 1 binary64) (sqrt.f64 k))
accuracy	16.952712269370817	(PI.f64)
accuracy	0.171875	(.f64 (.f64 #s(approx (pow (pow (* n (* (PI) 2)) -1/2) k) #s(literal 1 binary64)) (sqrt.f64 (.f64 n (.f64 (PI.f64) #s(literal 2 binary64))))) (sqrt.f64 (/.f64 #s(literal 1 binary64) k)))
accuracy	0.17578125	(.f64 n (.f64 (PI.f64) #s(literal 2 binary64)))
accuracy	16.23387786927176	#s(approx (pow (pow (* n (* (PI) 2)) -1/2) k) #s(literal 1 binary64))
accuracy	16.952712269370817	(PI.f64)
accuracy	0.09375	(sqrt.f64 (*.f64 (/.f64 (PI.f64) #s(literal 1 binary64)) (/.f64 #s(literal 2 binary64) k)))
accuracy	0.23828125	(*.f64 (/.f64 (PI.f64) #s(literal 1 binary64)) (/.f64 #s(literal 2 binary64) k))
accuracy	16.952712269370817	(PI.f64)
accuracy	43.826347104420314	#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt.f64 (*.f64 (/.f64 (PI.f64) #s(literal 1 binary64)) (/.f64 #s(literal 2 binary64) k))))
accuracy	29.911167320086086	#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) #s(literal 0 binary64))
accuracy	0.07421875	(sqrt.f64 (.f64 n (.f64 (PI.f64) #s(literal 2 binary64))))
accuracy	0.17578125	(.f64 n (.f64 (PI.f64) #s(literal 2 binary64)))
accuracy	0.18359375	(/.f64 (.f64 (sqrt.f64 (.f64 n (.f64 (PI.f64) #s(literal 2 binary64)))) #s(literal 1 binary64)) (.f64 (pow.f64 (.f64 n (.f64 (PI.f64) #s(literal 2 binary64))) (/.f64 k #s(literal 2 binary64))) (sqrt.f64 k)))
accuracy	16.952712269370817	(PI.f64)

Samples

63.0ms	186×	0	valid
25.0ms	70×	0	exit

Compiler

Compiled 286 to 41 computations (85.7% saved)

Precisions

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

ival-pow: 24.0ms (36% of total)

ival-mult: 20.0ms (30% of total)

ival-div: 10.0ms (15% of total)

ival-sqrt: 7.0ms (10.5% of total)

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

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

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

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

exact: 1.0ms (1.5% of total)

adjust: 0.0ms (0% of total)

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

series80.0ms (0.7%)

Memory

13.9MiB live, 104.6MiB allocated; 7ms collecting garbage

Counts

19 → 52

Calls

Call 1

Inputs
(.f64 (sqrt.f64 (.f64 n (*.f64 (PI.f64) #s(literal 2 binary64)))) #s(literal 1 binary64))
(/.f64 (.f64 (sqrt.f64 (.f64 n (.f64 (PI.f64) #s(literal 2 binary64)))) #s(literal 1 binary64)) (.f64 (pow.f64 (.f64 n (.f64 (PI.f64) #s(literal 2 binary64))) (/.f64 k #s(literal 2 binary64))) (sqrt.f64 k)))
(sqrt.f64 (.f64 n (.f64 (PI.f64) #s(literal 2 binary64))))
(.f64 n (.f64 (PI.f64) #s(literal 2 binary64)))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) #s(literal 0 binary64))
(/.f64 (PI.f64) #s(literal 1 binary64))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt.f64 (*.f64 (/.f64 (PI.f64) #s(literal 1 binary64)) (/.f64 #s(literal 2 binary64) k))))
(sqrt.f64 (*.f64 (/.f64 (PI.f64) #s(literal 1 binary64)) (/.f64 #s(literal 2 binary64) k)))
(*.f64 (/.f64 (PI.f64) #s(literal 1 binary64)) (/.f64 #s(literal 2 binary64) k))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (.f64 (.f64 #s(approx (pow (pow (* n (* (PI) 2)) -1/2) k) #s(literal 1 binary64)) (sqrt.f64 (.f64 n (.f64 (PI.f64) #s(literal 2 binary64))))) (sqrt.f64 (/.f64 #s(literal 1 binary64) k))))
(.f64 (.f64 #s(approx (pow (pow (* n (* (PI) 2)) -1/2) k) #s(literal 1 binary64)) (sqrt.f64 (.f64 n (.f64 (PI.f64) #s(literal 2 binary64))))) (sqrt.f64 (/.f64 #s(literal 1 binary64) k)))
(.f64 #s(approx (pow (pow ( n (* (PI) 2)) -1/2) k) #s(literal 1 binary64)) (sqrt.f64 (.f64 n (.f64 (PI.f64) #s(literal 2 binary64)))))
#s(approx (pow (pow (* n (* (PI) 2)) -1/2) k) #s(literal 1 binary64))
(.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) #s(approx (pow ( (* 2 (PI)) n) (/ (- 1 k) 2)) (pow.f64 (.f64 (.f64 #s(literal 2 binary64) n) (PI.f64)) (fma.f64 #s(literal -1/2 binary64) k #s(literal 1/2 binary64)))))
(/.f64 #s(literal 1 binary64) (sqrt.f64 k))
(sqrt.f64 k)
#s(approx (pow (* (* 2 (PI)) n) (/ (- 1 k) 2)) (pow.f64 (.f64 (.f64 #s(literal 2 binary64) n) (PI.f64)) (fma.f64 #s(literal -1/2 binary64) k #s(literal 1/2 binary64))))
(PI.f64)
(.f64 (.f64 #s(literal 2 binary64) n) (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)
(* (sqrt (/ (PI) k)) (sqrt 2))
(* 2 (/ (PI) k))
(/ (+ (* (sqrt (* k (* n (PI)))) (sqrt 2)) (* (sqrt (* (pow k 3) (* n (PI)))) (* (log (* (sqrt (/ 1 (* n (PI)))) (sqrt 1/2))) (sqrt 2)))) k)
(/ (+ (* k (+ (* 1/2 (* (sqrt (* (pow k 3) (* n (PI)))) (* (pow (log (* (sqrt (/ 1 (* n (PI)))) (sqrt 1/2))) 2) (sqrt 2)))) (* (sqrt (* k (* n (PI)))) (* (log (* (sqrt (/ 1 (* n (PI)))) (sqrt 1/2))) (sqrt 2))))) (* (sqrt (* k (* n (PI)))) (sqrt 2))) k)
(/ (+ (* k (+ (* k (+ (* 1/6 (* (sqrt (* (pow k 3) (* n (PI)))) (* (pow (log (* (sqrt (/ 1 (* n (PI)))) (sqrt 1/2))) 3) (sqrt 2)))) (* 1/2 (* (sqrt (* k (* n (PI)))) (* (pow (log (* (sqrt (/ 1 (* n (PI)))) (sqrt 1/2))) 2) (sqrt 2)))))) (* (sqrt (* k (* n (PI)))) (* (log (* (sqrt (/ 1 (* n (PI)))) (sqrt 1/2))) (sqrt 2))))) (* (sqrt (* k (* n (PI)))) (sqrt 2))) k)
(* (sqrt (* n (PI))) (sqrt 2))
(+ (* (sqrt (* n (PI))) (sqrt 2)) (* (* k (* (log (* (sqrt (/ 1 (* n (PI)))) (sqrt 1/2))) (sqrt 2))) (sqrt (* n (PI)))))
(+ (* k (+ (* 1/2 (* (* k (* (pow (log (* (sqrt (/ 1 (* n (PI)))) (sqrt 1/2))) 2) (sqrt 2))) (sqrt (* n (PI))))) (* (sqrt (* n (PI))) (* (log (* (sqrt (/ 1 (* n (PI)))) (sqrt 1/2))) (sqrt 2))))) (* (sqrt (* n (PI))) (sqrt 2)))
(+ (* k (+ (* k (+ (* 1/6 (* (* k (* (pow (log (* (sqrt (/ 1 (* n (PI)))) (sqrt 1/2))) 3) (sqrt 2))) (sqrt (* n (PI))))) (* 1/2 (* (sqrt (* n (PI))) (* (pow (log (* (sqrt (/ 1 (* n (PI)))) (sqrt 1/2))) 2) (sqrt 2)))))) (* (sqrt (* n (PI))) (* (log (* (sqrt (/ 1 (* n (PI)))) (sqrt 1/2))) (sqrt 2))))) (* (sqrt (* n (PI))) (sqrt 2)))
1
(+ 1 (* k (log (* (sqrt (/ 1 (* n (PI)))) (sqrt 1/2)))))
(+ 1 (* k (+ (log (* (sqrt (/ 1 (* n (PI)))) (sqrt 1/2))) (* 1/2 (* k (pow (log (* (sqrt (/ 1 (* n (PI)))) (sqrt 1/2))) 2))))))
(+ 1 (* k (+ (log (* (sqrt (/ 1 (* n (PI)))) (sqrt 1/2))) (* k (+ (* 1/6 (* k (pow (log (* (sqrt (/ 1 (* n (PI)))) (sqrt 1/2))) 3))) (* 1/2 (pow (log (* (sqrt (/ 1 (* n (PI)))) (sqrt 1/2))) 2)))))))
(sqrt (/ 1 k))
(sqrt k)
(+ (* -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 2) (exp (* 1/2 (* k (log (* 2 (* n (PI)))))))))
(* (sqrt (/ 1 k)) (exp (* 1/2 (* (log (* 2 (* n (PI)))) (- 1 k)))))
(* (sqrt (/ (* n (PI)) k)) (* (sqrt 2) (pow (* (sqrt (/ 1 (* n (PI)))) (sqrt 1/2)) k)))
(* (sqrt (* n (PI))) (* (sqrt 2) (pow (* (sqrt (/ 1 (* n (PI)))) (sqrt 1/2)) k)))
(pow (* (sqrt (/ 1 (* n (PI)))) (sqrt 1/2)) k)
(exp (* 1/2 (* (log (* 2 (* n (PI)))) (- 1 k))))
(* (sqrt (/ 1 k)) (exp (* 1/2 (* (log (* 2 (* n (PI)))) (+ 1 (* -1 k))))))
(* (sqrt (/ (PI) k)) (* (sqrt -2) (sqrt -1)))
(* (sqrt (/ (* n (PI)) k)) (* (pow (sqrt -1) 2) (* (sqrt 2) (pow (* (sqrt (/ 1 (* n (PI)))) (sqrt 1/2)) k))))
(* -1 (* (sqrt k) (pow (sqrt -1) 2)))
(exp (* 1/2 (* (log (* 2 (* n (PI)))) (+ 1 (* -1 k)))))
(* (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 (/ (* n (PI)) k)) (* (exp (* k (+ (log (* (sqrt (/ n (PI))) (sqrt 1/2))) (* -1 (log n))))) (sqrt 2)))
(* (sqrt (* n (PI))) (* (exp (* k (+ (log (* (sqrt (/ n (PI))) (sqrt 1/2))) (* -1 (log n))))) (sqrt 2)))
(exp (* k (+ (log (* (sqrt (/ n (PI))) (sqrt 1/2))) (* -1 (log n)))))
(exp (* 1/2 (* (+ (log n) (log (* 2 (PI)))) (- 1 k))))
(* (sqrt (/ (* n (PI)) k)) (/ (sqrt 2) (exp (* 1/2 (* k (+ (log (* 2 (PI))) (* -1 (log (/ 1 n)))))))))
(* (sqrt (/ 1 k)) (exp (* 1/2 (* (+ (log (* 2 (PI))) (* -1 (log (/ 1 n)))) (- 1 k)))))
(exp (* 1/2 (* (+ (log (* 2 (PI))) (* -1 (log (/ 1 n)))) (- 1 k))))
(* -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) (pow (* (sqrt (/ 1 (* n (PI)))) (* (sqrt -1) (sqrt -1/2))) k)))))
(* -1 (* (sqrt (* n (PI))) (* (sqrt -2) (* (sqrt -1) (pow (* (sqrt (/ 1 (* n (PI)))) (* (sqrt -1) (sqrt -1/2))) k)))))
(pow (* (sqrt (/ 1 (* n (PI)))) (* (sqrt -1) (sqrt -1/2))) k)
(exp (* 1/2 (* (+ (log (* -2 (PI))) (* -1 (log (/ -1 n)))) (- 1 k))))

Calls

6 calls:

Time	Variable		Point	Expression
30.0ms	n	@	inf	((* (sqrt (* n (* (PI) 2))) 1) (/ (* (sqrt (* n (* (PI) 2))) 1) (* (pow (* n (* (PI) 2)) (/ k 2)) (sqrt k))) (sqrt (* n (* (PI) 2))) (* n (* (PI) 2)) (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (/ (PI) 1) (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt (* (/ (PI) 1) (/ 2 k))) (* (/ (PI) 1) (/ 2 k)) (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (* (* (pow (pow (* n (* (PI) 2)) -1/2) k) (sqrt (* n (* (PI) 2)))) (sqrt (/ 1 k))) (* (pow (pow (* n (* (PI) 2)) -1/2) k) (sqrt (* n (* (PI) 2)))) (pow (pow (* n (* (PI) 2)) -1/2) k) (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (/ 1 (sqrt k)) (sqrt k) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2)) (PI) (* (* 2 n) (PI)))
20.0ms	n	@	0	((* (sqrt (* n (* (PI) 2))) 1) (/ (* (sqrt (* n (* (PI) 2))) 1) (* (pow (* n (* (PI) 2)) (/ k 2)) (sqrt k))) (sqrt (* n (* (PI) 2))) (* n (* (PI) 2)) (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (/ (PI) 1) (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt (* (/ (PI) 1) (/ 2 k))) (* (/ (PI) 1) (/ 2 k)) (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (* (* (pow (pow (* n (* (PI) 2)) -1/2) k) (sqrt (* n (* (PI) 2)))) (sqrt (/ 1 k))) (* (pow (pow (* n (* (PI) 2)) -1/2) k) (sqrt (* n (* (PI) 2)))) (pow (pow (* n (* (PI) 2)) -1/2) k) (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (/ 1 (sqrt k)) (sqrt k) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2)) (PI) (* (* 2 n) (PI)))
18.0ms	n	@	-inf	((* (sqrt (* n (* (PI) 2))) 1) (/ (* (sqrt (* n (* (PI) 2))) 1) (* (pow (* n (* (PI) 2)) (/ k 2)) (sqrt k))) (sqrt (* n (* (PI) 2))) (* n (* (PI) 2)) (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (/ (PI) 1) (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt (* (/ (PI) 1) (/ 2 k))) (* (/ (PI) 1) (/ 2 k)) (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (* (* (pow (pow (* n (* (PI) 2)) -1/2) k) (sqrt (* n (* (PI) 2)))) (sqrt (/ 1 k))) (* (pow (pow (* n (* (PI) 2)) -1/2) k) (sqrt (* n (* (PI) 2)))) (pow (pow (* n (* (PI) 2)) -1/2) k) (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (/ 1 (sqrt k)) (sqrt k) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2)) (PI) (* (* 2 n) (PI)))
5.0ms	k	@	-inf	((* (sqrt (* n (* (PI) 2))) 1) (/ (* (sqrt (* n (* (PI) 2))) 1) (* (pow (* n (* (PI) 2)) (/ k 2)) (sqrt k))) (sqrt (* n (* (PI) 2))) (* n (* (PI) 2)) (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (/ (PI) 1) (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt (* (/ (PI) 1) (/ 2 k))) (* (/ (PI) 1) (/ 2 k)) (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (* (* (pow (pow (* n (* (PI) 2)) -1/2) k) (sqrt (* n (* (PI) 2)))) (sqrt (/ 1 k))) (* (pow (pow (* n (* (PI) 2)) -1/2) k) (sqrt (* n (* (PI) 2)))) (pow (pow (* n (* (PI) 2)) -1/2) k) (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (/ 1 (sqrt k)) (sqrt k) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2)) (PI) (* (* 2 n) (PI)))
3.0ms	k	@	inf	((* (sqrt (* n (* (PI) 2))) 1) (/ (* (sqrt (* n (* (PI) 2))) 1) (* (pow (* n (* (PI) 2)) (/ k 2)) (sqrt k))) (sqrt (* n (* (PI) 2))) (* n (* (PI) 2)) (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (/ (PI) 1) (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt (* (/ (PI) 1) (/ 2 k))) (* (/ (PI) 1) (/ 2 k)) (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (* (* (pow (pow (* n (* (PI) 2)) -1/2) k) (sqrt (* n (* (PI) 2)))) (sqrt (/ 1 k))) (* (pow (pow (* n (* (PI) 2)) -1/2) k) (sqrt (* n (* (PI) 2)))) (pow (pow (* n (* (PI) 2)) -1/2) k) (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (/ 1 (sqrt k)) (sqrt k) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2)) (PI) (* (* 2 n) (PI)))

simplify153.0ms (1.3%)

Memory

18.0MiB live, 197.7MiB allocated; 26ms collecting garbage

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	271	1439
1	951	1390
2	3825	1363
0	8322	1327

Stop Event

1×	iter limit
1×	node limit

Counts

52 → 52

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)
(* (sqrt (/ (PI) k)) (sqrt 2))
(* 2 (/ (PI) k))
(/ (+ (* (sqrt (* k (* n (PI)))) (sqrt 2)) (* (sqrt (* (pow k 3) (* n (PI)))) (* (log (* (sqrt (/ 1 (* n (PI)))) (sqrt 1/2))) (sqrt 2)))) k)
(/ (+ (* k (+ (* 1/2 (* (sqrt (* (pow k 3) (* n (PI)))) (* (pow (log (* (sqrt (/ 1 (* n (PI)))) (sqrt 1/2))) 2) (sqrt 2)))) (* (sqrt (* k (* n (PI)))) (* (log (* (sqrt (/ 1 (* n (PI)))) (sqrt 1/2))) (sqrt 2))))) (* (sqrt (* k (* n (PI)))) (sqrt 2))) k)
(/ (+ (* k (+ (* k (+ (* 1/6 (* (sqrt (* (pow k 3) (* n (PI)))) (* (pow (log (* (sqrt (/ 1 (* n (PI)))) (sqrt 1/2))) 3) (sqrt 2)))) (* 1/2 (* (sqrt (* k (* n (PI)))) (* (pow (log (* (sqrt (/ 1 (* n (PI)))) (sqrt 1/2))) 2) (sqrt 2)))))) (* (sqrt (* k (* n (PI)))) (* (log (* (sqrt (/ 1 (* n (PI)))) (sqrt 1/2))) (sqrt 2))))) (* (sqrt (* k (* n (PI)))) (sqrt 2))) k)
(* (sqrt (* n (PI))) (sqrt 2))
(+ (* (sqrt (* n (PI))) (sqrt 2)) (* (* k (* (log (* (sqrt (/ 1 (* n (PI)))) (sqrt 1/2))) (sqrt 2))) (sqrt (* n (PI)))))
(+ (* k (+ (* 1/2 (* (* k (* (pow (log (* (sqrt (/ 1 (* n (PI)))) (sqrt 1/2))) 2) (sqrt 2))) (sqrt (* n (PI))))) (* (sqrt (* n (PI))) (* (log (* (sqrt (/ 1 (* n (PI)))) (sqrt 1/2))) (sqrt 2))))) (* (sqrt (* n (PI))) (sqrt 2)))
(+ (* k (+ (* k (+ (* 1/6 (* (* k (* (pow (log (* (sqrt (/ 1 (* n (PI)))) (sqrt 1/2))) 3) (sqrt 2))) (sqrt (* n (PI))))) (* 1/2 (* (sqrt (* n (PI))) (* (pow (log (* (sqrt (/ 1 (* n (PI)))) (sqrt 1/2))) 2) (sqrt 2)))))) (* (sqrt (* n (PI))) (* (log (* (sqrt (/ 1 (* n (PI)))) (sqrt 1/2))) (sqrt 2))))) (* (sqrt (* n (PI))) (sqrt 2)))
1
(+ 1 (* k (log (* (sqrt (/ 1 (* n (PI)))) (sqrt 1/2)))))
(+ 1 (* k (+ (log (* (sqrt (/ 1 (* n (PI)))) (sqrt 1/2))) (* 1/2 (* k (pow (log (* (sqrt (/ 1 (* n (PI)))) (sqrt 1/2))) 2))))))
(+ 1 (* k (+ (log (* (sqrt (/ 1 (* n (PI)))) (sqrt 1/2))) (* k (+ (* 1/6 (* k (pow (log (* (sqrt (/ 1 (* n (PI)))) (sqrt 1/2))) 3))) (* 1/2 (pow (log (* (sqrt (/ 1 (* n (PI)))) (sqrt 1/2))) 2)))))))
(sqrt (/ 1 k))
(sqrt k)
(+ (* -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 2) (exp (* 1/2 (* k (log (* 2 (* n (PI)))))))))
(* (sqrt (/ 1 k)) (exp (* 1/2 (* (log (* 2 (* n (PI)))) (- 1 k)))))
(* (sqrt (/ (* n (PI)) k)) (* (sqrt 2) (pow (* (sqrt (/ 1 (* n (PI)))) (sqrt 1/2)) k)))
(* (sqrt (* n (PI))) (* (sqrt 2) (pow (* (sqrt (/ 1 (* n (PI)))) (sqrt 1/2)) k)))
(pow (* (sqrt (/ 1 (* n (PI)))) (sqrt 1/2)) k)
(exp (* 1/2 (* (log (* 2 (* n (PI)))) (- 1 k))))
(* (sqrt (/ 1 k)) (exp (* 1/2 (* (log (* 2 (* n (PI)))) (+ 1 (* -1 k))))))
(* (sqrt (/ (PI) k)) (* (sqrt -2) (sqrt -1)))
(* (sqrt (/ (* n (PI)) k)) (* (pow (sqrt -1) 2) (* (sqrt 2) (pow (* (sqrt (/ 1 (* n (PI)))) (sqrt 1/2)) k))))
(* -1 (* (sqrt k) (pow (sqrt -1) 2)))
(exp (* 1/2 (* (log (* 2 (* n (PI)))) (+ 1 (* -1 k)))))
(* (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 (/ (* n (PI)) k)) (* (exp (* k (+ (log (* (sqrt (/ n (PI))) (sqrt 1/2))) (* -1 (log n))))) (sqrt 2)))
(* (sqrt (* n (PI))) (* (exp (* k (+ (log (* (sqrt (/ n (PI))) (sqrt 1/2))) (* -1 (log n))))) (sqrt 2)))
(exp (* k (+ (log (* (sqrt (/ n (PI))) (sqrt 1/2))) (* -1 (log n)))))
(exp (* 1/2 (* (+ (log n) (log (* 2 (PI)))) (- 1 k))))
(* (sqrt (/ (* n (PI)) k)) (/ (sqrt 2) (exp (* 1/2 (* k (+ (log (* 2 (PI))) (* -1 (log (/ 1 n)))))))))
(* (sqrt (/ 1 k)) (exp (* 1/2 (* (+ (log (* 2 (PI))) (* -1 (log (/ 1 n)))) (- 1 k)))))
(exp (* 1/2 (* (+ (log (* 2 (PI))) (* -1 (log (/ 1 n)))) (- 1 k))))
(* -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) (pow (* (sqrt (/ 1 (* n (PI)))) (* (sqrt -1) (sqrt -1/2))) k)))))
(* -1 (* (sqrt (* n (PI))) (* (sqrt -2) (* (sqrt -1) (pow (* (sqrt (/ 1 (* n (PI)))) (* (sqrt -1) (sqrt -1/2))) k)))))
(pow (* (sqrt (/ 1 (* n (PI)))) (* (sqrt -1) (sqrt -1/2))) 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 (fma.f64 (.f64 (.f64 (log.f64 (.f64 (.f64 (PI.f64) n) #s(literal 2 binary64))) (sqrt.f64 #s(literal 2 binary64))) (sqrt.f64 (.f64 (.f64 (pow.f64 k #s(literal 3 binary64)) (PI.f64)) n))) #s(literal -1/2 binary64) (.f64 (sqrt.f64 (.f64 (*.f64 (PI.f64) n) k)) (sqrt.f64 #s(literal 2 binary64)))) k)
(/ (+ (* k (+ (* -1 (* (sqrt (* (pow k 3) (* n (PI)))) (+ (* -1/4 (* (pow (log (* 2 (* n (PI)))) 2) (sqrt 2))) (* 1/8 (* (pow (log (* 2 (* n (PI)))) 2) (sqrt 2)))))) (* -1/2 (* (sqrt (* k (* n (PI)))) (* (log (* 2 (* n (PI)))) (sqrt 2)))))) (* (sqrt (* k (* n (PI)))) (sqrt 2))) k)
(/.f64 (fma.f64 (fma.f64 (.f64 (.f64 (sqrt.f64 (.f64 (.f64 (PI.f64) n) k)) #s(literal -1/2 binary64)) (log.f64 (.f64 (.f64 (PI.f64) n) #s(literal 2 binary64)))) (sqrt.f64 #s(literal 2 binary64)) (.f64 (.f64 (.f64 #s(literal 1/8 binary64) (sqrt.f64 #s(literal 2 binary64))) (pow.f64 (log.f64 (.f64 (.f64 (PI.f64) n) #s(literal 2 binary64))) #s(literal 2 binary64))) (sqrt.f64 (.f64 (.f64 (pow.f64 k #s(literal 3 binary64)) (PI.f64)) n)))) k (.f64 (sqrt.f64 (.f64 (.f64 (PI.f64) n) k)) (sqrt.f64 #s(literal 2 binary64)))) k)
(/ (+ (* k (+ (* -1/2 (* (sqrt (* k (* n (PI)))) (* (log (* 2 (* n (PI)))) (sqrt 2)))) (* k (+ (* -1 (* (sqrt (* k (* n (PI)))) (+ (* -1/4 (* (pow (log (* 2 (* n (PI)))) 2) (sqrt 2))) (* 1/8 (* (pow (log (* 2 (* n (PI)))) 2) (sqrt 2)))))) (* -1 (* (sqrt (* (pow k 3) (* n (PI)))) (+ (* -1/2 (* (log (* 2 (* n (PI)))) (+ (* -1/4 (* (pow (log (* 2 (* n (PI)))) 2) (sqrt 2))) (* 1/8 (* (pow (log (* 2 (* n (PI)))) 2) (sqrt 2)))))) (+ (* -1/16 (* (pow (log (* 2 (* n (PI)))) 3) (sqrt 2))) (* 1/48 (* (pow (log (* 2 (* n (PI)))) 3) (sqrt 2))))))))))) (* (sqrt (* k (* n (PI)))) (sqrt 2))) k)
(/.f64 (fma.f64 (fma.f64 (.f64 (.f64 (sqrt.f64 (.f64 (.f64 (PI.f64) n) k)) #s(literal -1/2 binary64)) (sqrt.f64 #s(literal 2 binary64))) (log.f64 (.f64 (.f64 (PI.f64) n) #s(literal 2 binary64))) (.f64 (fma.f64 (.f64 (.f64 #s(literal 1/8 binary64) (sqrt.f64 (.f64 (.f64 (PI.f64) n) k))) (pow.f64 (log.f64 (.f64 (.f64 (PI.f64) n) #s(literal 2 binary64))) #s(literal 2 binary64))) (sqrt.f64 #s(literal 2 binary64)) (.f64 (fma.f64 (.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 (fma.f64 (.f64 (.f64 (sqrt.f64 (.f64 (.f64 (PI.f64) n) k)) #s(literal -1/2 binary64)) (log.f64 (.f64 (.f64 (PI.f64) n) #s(literal 2 binary64)))) (sqrt.f64 #s(literal 2 binary64)) (.f64 (.f64 (.f64 #s(literal 1/8 binary64) (sqrt.f64 #s(literal 2 binary64))) (pow.f64 (log.f64 (.f64 (.f64 (PI.f64) n) #s(literal 2 binary64))) #s(literal 2 binary64))) (sqrt.f64 (.f64 (.f64 (pow.f64 k #s(literal 3 binary64)) (PI.f64)) n)))) k (.f64 (sqrt.f64 (.f64 (.f64 (PI.f64) n) k)) (sqrt.f64 #s(literal 2 binary64)))) k)
(/ (+ (* k (+ (* -1/2 (* (sqrt (* k (* n (PI)))) (* (log (* 2 (* n (PI)))) (sqrt 2)))) (* k (+ (* -1/48 (* (sqrt (* (pow k 3) (* n (PI)))) (* (pow (log (* 2 (* n (PI)))) 3) (sqrt 2)))) (* 1/8 (* (sqrt (* k (* n (PI)))) (* (pow (log (* 2 (* n (PI)))) 2) (sqrt 2)))))))) (* (sqrt (* k (* n (PI)))) (sqrt 2))) k)
(/.f64 (fma.f64 (fma.f64 (.f64 (.f64 (sqrt.f64 (.f64 (.f64 (PI.f64) n) k)) #s(literal -1/2 binary64)) (sqrt.f64 #s(literal 2 binary64))) (log.f64 (.f64 (.f64 (PI.f64) n) #s(literal 2 binary64))) (.f64 (fma.f64 (.f64 (.f64 (pow.f64 (log.f64 (.f64 (.f64 (PI.f64) n) #s(literal 2 binary64))) #s(literal 3 binary64)) (sqrt.f64 #s(literal 2 binary64))) (sqrt.f64 (.f64 (.f64 (pow.f64 k #s(literal 3 binary64)) (PI.f64)) n))) #s(literal -1/48 binary64) (.f64 (.f64 (pow.f64 (log.f64 (.f64 (.f64 (PI.f64) n) #s(literal 2 binary64))) #s(literal 2 binary64)) (sqrt.f64 (.f64 (.f64 (PI.f64) n) k))) (.f64 (sqrt.f64 #s(literal 2 binary64)) #s(literal 1/8 binary64)))) k)) k (.f64 (sqrt.f64 (.f64 (*.f64 (PI.f64) n) k)) (sqrt.f64 #s(literal 2 binary64)))) k)
(* (sqrt (/ (PI) k)) (sqrt 2))
(*.f64 (sqrt.f64 (/.f64 (PI.f64) k)) (sqrt.f64 #s(literal 2 binary64)))
(* 2 (/ (PI) k))
(*.f64 (/.f64 (PI.f64) k) #s(literal 2 binary64))
(/ (+ (* (sqrt (* k (* n (PI)))) (sqrt 2)) (* (sqrt (* (pow k 3) (* n (PI)))) (* (log (* (sqrt (/ 1 (* n (PI)))) (sqrt 1/2))) (sqrt 2)))) k)
(/.f64 (.f64 (sqrt.f64 #s(literal 2 binary64)) (fma.f64 (log.f64 (.f64 (sqrt.f64 #s(literal 1/2 binary64)) (sqrt.f64 (/.f64 #s(literal 1 binary64) (.f64 (PI.f64) n))))) (sqrt.f64 (.f64 (.f64 (pow.f64 k #s(literal 3 binary64)) (PI.f64)) n)) (sqrt.f64 (.f64 (*.f64 (PI.f64) n) k)))) k)
(/ (+ (* k (+ (* 1/2 (* (sqrt (* (pow k 3) (* n (PI)))) (* (pow (log (* (sqrt (/ 1 (* n (PI)))) (sqrt 1/2))) 2) (sqrt 2)))) (* (sqrt (* k (* n (PI)))) (* (log (* (sqrt (/ 1 (* n (PI)))) (sqrt 1/2))) (sqrt 2))))) (* (sqrt (* k (* n (PI)))) (sqrt 2))) k)
(/.f64 (fma.f64 (fma.f64 (.f64 (pow.f64 (log.f64 (.f64 (sqrt.f64 #s(literal 1/2 binary64)) (sqrt.f64 (/.f64 #s(literal 1 binary64) (.f64 (PI.f64) n))))) #s(literal 2 binary64)) (sqrt.f64 (.f64 (.f64 (pow.f64 k #s(literal 3 binary64)) (PI.f64)) n))) (.f64 (sqrt.f64 #s(literal 2 binary64)) #s(literal 1/2 binary64)) (.f64 (log.f64 (.f64 (sqrt.f64 #s(literal 1/2 binary64)) (sqrt.f64 (/.f64 #s(literal 1 binary64) (.f64 (PI.f64) n))))) (.f64 (sqrt.f64 (.f64 (.f64 (PI.f64) n) k)) (sqrt.f64 #s(literal 2 binary64))))) k (.f64 (sqrt.f64 (.f64 (*.f64 (PI.f64) n) k)) (sqrt.f64 #s(literal 2 binary64)))) k)
(/ (+ (* k (+ (* k (+ (* 1/6 (* (sqrt (* (pow k 3) (* n (PI)))) (* (pow (log (* (sqrt (/ 1 (* n (PI)))) (sqrt 1/2))) 3) (sqrt 2)))) (* 1/2 (* (sqrt (* k (* n (PI)))) (* (pow (log (* (sqrt (/ 1 (* n (PI)))) (sqrt 1/2))) 2) (sqrt 2)))))) (* (sqrt (* k (* n (PI)))) (* (log (* (sqrt (/ 1 (* n (PI)))) (sqrt 1/2))) (sqrt 2))))) (* (sqrt (* k (* n (PI)))) (sqrt 2))) k)
(/.f64 (fma.f64 (fma.f64 (fma.f64 (.f64 (.f64 #s(literal 1/2 binary64) (sqrt.f64 (.f64 (.f64 (PI.f64) n) k))) (pow.f64 (log.f64 (.f64 (sqrt.f64 #s(literal 1/2 binary64)) (sqrt.f64 (/.f64 #s(literal 1 binary64) (.f64 (PI.f64) n))))) #s(literal 2 binary64))) (sqrt.f64 #s(literal 2 binary64)) (.f64 (.f64 #s(literal 1/6 binary64) (sqrt.f64 (.f64 (.f64 (pow.f64 k #s(literal 3 binary64)) (PI.f64)) n))) (.f64 (pow.f64 (log.f64 (.f64 (sqrt.f64 #s(literal 1/2 binary64)) (sqrt.f64 (/.f64 #s(literal 1 binary64) (.f64 (PI.f64) n))))) #s(literal 3 binary64)) (sqrt.f64 #s(literal 2 binary64))))) k (.f64 (log.f64 (.f64 (sqrt.f64 #s(literal 1/2 binary64)) (sqrt.f64 (/.f64 #s(literal 1 binary64) (.f64 (PI.f64) n))))) (.f64 (sqrt.f64 (.f64 (.f64 (PI.f64) n) k)) (sqrt.f64 #s(literal 2 binary64))))) k (.f64 (sqrt.f64 (.f64 (.f64 (PI.f64) n) k)) (sqrt.f64 #s(literal 2 binary64)))) k)
(* (sqrt (* n (PI))) (sqrt 2))
(.f64 (sqrt.f64 (.f64 (PI.f64) n)) (sqrt.f64 #s(literal 2 binary64)))
(+ (* (sqrt (* n (PI))) (sqrt 2)) (* (* k (* (log (* (sqrt (/ 1 (* n (PI)))) (sqrt 1/2))) (sqrt 2))) (sqrt (* n (PI)))))
(.f64 (sqrt.f64 (.f64 (PI.f64) n)) (fma.f64 (.f64 k (sqrt.f64 #s(literal 2 binary64))) (log.f64 (.f64 (sqrt.f64 #s(literal 1/2 binary64)) (sqrt.f64 (/.f64 #s(literal 1 binary64) (*.f64 (PI.f64) n))))) (sqrt.f64 #s(literal 2 binary64))))
(+ (* k (+ (* 1/2 (* (* k (* (pow (log (* (sqrt (/ 1 (* n (PI)))) (sqrt 1/2))) 2) (sqrt 2))) (sqrt (* n (PI))))) (* (sqrt (* n (PI))) (* (log (* (sqrt (/ 1 (* n (PI)))) (sqrt 1/2))) (sqrt 2))))) (* (sqrt (* n (PI))) (sqrt 2)))
(fma.f64 (.f64 (sqrt.f64 (.f64 (PI.f64) n)) (fma.f64 (.f64 #s(literal 1/2 binary64) k) (.f64 (pow.f64 (log.f64 (.f64 (sqrt.f64 #s(literal 1/2 binary64)) (sqrt.f64 (/.f64 #s(literal 1 binary64) (.f64 (PI.f64) n))))) #s(literal 2 binary64)) (sqrt.f64 #s(literal 2 binary64))) (.f64 (log.f64 (.f64 (sqrt.f64 #s(literal 1/2 binary64)) (sqrt.f64 (/.f64 #s(literal 1 binary64) (.f64 (PI.f64) n))))) (sqrt.f64 #s(literal 2 binary64))))) k (.f64 (sqrt.f64 (*.f64 (PI.f64) n)) (sqrt.f64 #s(literal 2 binary64))))
(+ (* k (+ (* k (+ (* 1/6 (* (* k (* (pow (log (* (sqrt (/ 1 (* n (PI)))) (sqrt 1/2))) 3) (sqrt 2))) (sqrt (* n (PI))))) (* 1/2 (* (sqrt (* n (PI))) (* (pow (log (* (sqrt (/ 1 (* n (PI)))) (sqrt 1/2))) 2) (sqrt 2)))))) (* (sqrt (* n (PI))) (* (log (* (sqrt (/ 1 (* n (PI)))) (sqrt 1/2))) (sqrt 2))))) (* (sqrt (* n (PI))) (sqrt 2)))
(fma.f64 (.f64 k k) (fma.f64 (.f64 (.f64 (sqrt.f64 (.f64 (PI.f64) n)) #s(literal 1/2 binary64)) (pow.f64 (log.f64 (.f64 (sqrt.f64 #s(literal 1/2 binary64)) (sqrt.f64 (/.f64 #s(literal 1 binary64) (.f64 (PI.f64) n))))) #s(literal 2 binary64))) (sqrt.f64 #s(literal 2 binary64)) (.f64 (.f64 (.f64 (sqrt.f64 (.f64 (PI.f64) n)) k) (.f64 (pow.f64 (log.f64 (.f64 (sqrt.f64 #s(literal 1/2 binary64)) (sqrt.f64 (/.f64 #s(literal 1 binary64) (.f64 (PI.f64) n))))) #s(literal 3 binary64)) (sqrt.f64 #s(literal 2 binary64)))) #s(literal 1/6 binary64))) (.f64 (sqrt.f64 (.f64 (PI.f64) n)) (fma.f64 (.f64 k (sqrt.f64 #s(literal 2 binary64))) (log.f64 (.f64 (sqrt.f64 #s(literal 1/2 binary64)) (sqrt.f64 (/.f64 #s(literal 1 binary64) (.f64 (PI.f64) n))))) (sqrt.f64 #s(literal 2 binary64)))))
1
#s(literal 1 binary64)
(+ 1 (* k (log (* (sqrt (/ 1 (* n (PI)))) (sqrt 1/2)))))
(fma.f64 (log.f64 (.f64 (sqrt.f64 #s(literal 1/2 binary64)) (sqrt.f64 (/.f64 #s(literal 1 binary64) (.f64 (PI.f64) n))))) k #s(literal 1 binary64))
(+ 1 (* k (+ (log (* (sqrt (/ 1 (* n (PI)))) (sqrt 1/2))) (* 1/2 (* k (pow (log (* (sqrt (/ 1 (* n (PI)))) (sqrt 1/2))) 2))))))
(fma.f64 (fma.f64 (.f64 #s(literal 1/2 binary64) k) (pow.f64 (log.f64 (.f64 (sqrt.f64 #s(literal 1/2 binary64)) (sqrt.f64 (/.f64 #s(literal 1 binary64) (.f64 (PI.f64) n))))) #s(literal 2 binary64)) (log.f64 (.f64 (sqrt.f64 #s(literal 1/2 binary64)) (sqrt.f64 (/.f64 #s(literal 1 binary64) (*.f64 (PI.f64) n)))))) k #s(literal 1 binary64))
(+ 1 (* k (+ (log (* (sqrt (/ 1 (* n (PI)))) (sqrt 1/2))) (* k (+ (* 1/6 (* k (pow (log (* (sqrt (/ 1 (* n (PI)))) (sqrt 1/2))) 3))) (* 1/2 (pow (log (* (sqrt (/ 1 (* n (PI)))) (sqrt 1/2))) 2)))))))
(fma.f64 (fma.f64 (fma.f64 (.f64 #s(literal 1/6 binary64) k) (pow.f64 (log.f64 (.f64 (sqrt.f64 #s(literal 1/2 binary64)) (sqrt.f64 (/.f64 #s(literal 1 binary64) (.f64 (PI.f64) n))))) #s(literal 3 binary64)) (.f64 (pow.f64 (log.f64 (.f64 (sqrt.f64 #s(literal 1/2 binary64)) (sqrt.f64 (/.f64 #s(literal 1 binary64) (.f64 (PI.f64) n))))) #s(literal 2 binary64)) #s(literal 1/2 binary64))) k (log.f64 (.f64 (sqrt.f64 #s(literal 1/2 binary64)) (sqrt.f64 (/.f64 #s(literal 1 binary64) (.f64 (PI.f64) n)))))) k #s(literal 1 binary64))
(sqrt (/ 1 k))
(sqrt.f64 (/.f64 #s(literal 1 binary64) k))
(sqrt k)
(sqrt.f64 k)
(+ (* -1/2 (* (* k (* (log (* 2 (* n (PI)))) (sqrt 2))) (sqrt (* n (PI))))) (* (sqrt (* n (PI))) (sqrt 2)))
(.f64 (sqrt.f64 (.f64 (PI.f64) n)) (fma.f64 (.f64 #s(literal -1/2 binary64) k) (.f64 (log.f64 (.f64 (.f64 (PI.f64) n) #s(literal 2 binary64))) (sqrt.f64 #s(literal 2 binary64))) (sqrt.f64 #s(literal 2 binary64))))
(+ (* k (+ (* -1/2 (* (sqrt (* n (PI))) (* (log (* 2 (* n (PI)))) (sqrt 2)))) (* 1/8 (* (* k (* (pow (log (* 2 (* n (PI)))) 2) (sqrt 2))) (sqrt (* n (PI))))))) (* (sqrt (* n (PI))) (sqrt 2)))
(fma.f64 (sqrt.f64 (.f64 (PI.f64) n)) (fma.f64 (.f64 #s(literal -1/2 binary64) k) (.f64 (log.f64 (.f64 (.f64 (PI.f64) n) #s(literal 2 binary64))) (sqrt.f64 #s(literal 2 binary64))) (sqrt.f64 #s(literal 2 binary64))) (.f64 (.f64 k #s(literal 1/8 binary64)) (.f64 (.f64 k (sqrt.f64 (.f64 (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 (+ (* -1/2 (* (sqrt (* n (PI))) (* (log (* 2 (* n (PI)))) (sqrt 2)))) (* k (+ (* -1/48 (* (* k (* (pow (log (* 2 (* n (PI)))) 3) (sqrt 2))) (sqrt (* n (PI))))) (* 1/8 (* (sqrt (* n (PI))) (* (pow (log (* 2 (* n (PI)))) 2) (sqrt 2)))))))) (* (sqrt (* n (PI))) (sqrt 2)))
(fma.f64 (sqrt.f64 (.f64 (PI.f64) n)) (fma.f64 (.f64 #s(literal -1/2 binary64) k) (.f64 (log.f64 (.f64 (.f64 (PI.f64) n) #s(literal 2 binary64))) (sqrt.f64 #s(literal 2 binary64))) (sqrt.f64 #s(literal 2 binary64))) (.f64 (.f64 k k) (fma.f64 (.f64 #s(literal -1/48 binary64) (sqrt.f64 (.f64 (PI.f64) n))) (.f64 (.f64 k (sqrt.f64 #s(literal 2 binary64))) (pow.f64 (log.f64 (.f64 (.f64 (PI.f64) n) #s(literal 2 binary64))) #s(literal 3 binary64))) (.f64 (.f64 (sqrt.f64 (.f64 (PI.f64) n)) (pow.f64 (log.f64 (.f64 (.f64 (PI.f64) n) #s(literal 2 binary64))) #s(literal 2 binary64))) (*.f64 (sqrt.f64 #s(literal 2 binary64)) #s(literal 1/8 binary64))))))
(* (sqrt (/ (* 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)))
(* (sqrt (/ (* n (PI)) k)) (* (sqrt 2) (pow (* (sqrt (/ 1 (* n (PI)))) (sqrt 1/2)) k)))
(.f64 (pow.f64 (.f64 (sqrt.f64 #s(literal 1/2 binary64)) (sqrt.f64 (/.f64 #s(literal 1 binary64) (.f64 (PI.f64) n)))) k) (.f64 (sqrt.f64 #s(literal 2 binary64)) (sqrt.f64 (/.f64 (*.f64 (PI.f64) n) k))))
(* (sqrt (* n (PI))) (* (sqrt 2) (pow (* (sqrt (/ 1 (* n (PI)))) (sqrt 1/2)) k)))
(.f64 (pow.f64 (.f64 (sqrt.f64 #s(literal 1/2 binary64)) (sqrt.f64 (/.f64 #s(literal 1 binary64) (.f64 (PI.f64) n)))) k) (.f64 (sqrt.f64 (*.f64 (PI.f64) n)) (sqrt.f64 #s(literal 2 binary64))))
(pow (* (sqrt (/ 1 (* n (PI)))) (sqrt 1/2)) k)
(pow.f64 (.f64 (sqrt.f64 #s(literal 1/2 binary64)) (sqrt.f64 (/.f64 #s(literal 1 binary64) (.f64 (PI.f64) n)))) k)
(exp (* 1/2 (* (log (* 2 (* n (PI)))) (- 1 k))))
(sqrt.f64 (pow.f64 (.f64 (.f64 (PI.f64) n) #s(literal 2 binary64)) (-.f64 #s(literal 1 binary64) k)))
(* (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 (/ (PI) k)) (* (sqrt -2) (sqrt -1)))
(.f64 (.f64 (sqrt.f64 (/.f64 (PI.f64) k)) (sqrt.f64 #s(literal -1 binary64))) (sqrt.f64 #s(literal -2 binary64)))
(* (sqrt (/ (* n (PI)) k)) (* (pow (sqrt -1) 2) (* (sqrt 2) (pow (* (sqrt (/ 1 (* n (PI)))) (sqrt 1/2)) k))))
(.f64 (neg.f64 (.f64 (sqrt.f64 #s(literal 2 binary64)) (sqrt.f64 (/.f64 (.f64 (PI.f64) n) k)))) (pow.f64 (.f64 (sqrt.f64 #s(literal 1/2 binary64)) (sqrt.f64 (/.f64 #s(literal 1 binary64) (*.f64 (PI.f64) n)))) k))
(* -1 (* (sqrt k) (pow (sqrt -1) 2)))
(*.f64 (sqrt.f64 k) #s(literal 1 binary64))
(exp (* 1/2 (* (log (* 2 (* n (PI)))) (+ 1 (* -1 k)))))
(sqrt.f64 (pow.f64 (.f64 (.f64 (PI.f64) n) #s(literal 2 binary64)) (-.f64 #s(literal 1 binary64) k)))
(* (sqrt (/ (* n (PI)) k)) (/ (sqrt 2) (exp (* 1/2 (* k (+ (log n) (log (* 2 (PI)))))))))
(.f64 (/.f64 (sqrt.f64 #s(literal 2 binary64)) (sqrt.f64 (pow.f64 (exp.f64 k) (+.f64 (log.f64 n) (log.f64 (.f64 (PI.f64) #s(literal 2 binary64))))))) (sqrt.f64 (/.f64 (*.f64 (PI.f64) n) k)))
(* 2 (* n (PI)))
(.f64 (.f64 (PI.f64) n) #s(literal 2 binary64))
(* (sqrt (/ 1 k)) (exp (* 1/2 (* (+ (log n) (log (* 2 (PI)))) (- 1 k)))))
(.f64 (pow.f64 (exp.f64 (fma.f64 #s(literal -1/2 binary64) k #s(literal 1/2 binary64))) (+.f64 (log.f64 n) (log.f64 (.f64 (PI.f64) #s(literal 2 binary64))))) (sqrt.f64 (/.f64 #s(literal 1 binary64) k)))
(* (sqrt (/ (* n (PI)) k)) (* (exp (* k (+ (log (* (sqrt (/ n (PI))) (sqrt 1/2))) (* -1 (log n))))) (sqrt 2)))
(.f64 (.f64 (pow.f64 (.f64 (sqrt.f64 (/.f64 n (PI.f64))) (sqrt.f64 #s(literal 1/2 binary64))) k) (pow.f64 n (neg.f64 k))) (.f64 (sqrt.f64 #s(literal 2 binary64)) (sqrt.f64 (/.f64 (*.f64 (PI.f64) n) k))))
(* (sqrt (* n (PI))) (* (exp (* k (+ (log (* (sqrt (/ n (PI))) (sqrt 1/2))) (* -1 (log n))))) (sqrt 2)))
(.f64 (.f64 (pow.f64 (.f64 (sqrt.f64 (/.f64 n (PI.f64))) (sqrt.f64 #s(literal 1/2 binary64))) k) (pow.f64 n (neg.f64 k))) (.f64 (sqrt.f64 (*.f64 (PI.f64) n)) (sqrt.f64 #s(literal 2 binary64))))
(exp (* k (+ (log (* (sqrt (/ n (PI))) (sqrt 1/2))) (* -1 (log n)))))
(.f64 (pow.f64 (.f64 (sqrt.f64 (/.f64 n (PI.f64))) (sqrt.f64 #s(literal 1/2 binary64))) k) (pow.f64 n (neg.f64 k)))
(exp (* 1/2 (* (+ (log n) (log (* 2 (PI)))) (- 1 k))))
(pow.f64 (exp.f64 (fma.f64 #s(literal -1/2 binary64) k #s(literal 1/2 binary64))) (+.f64 (log.f64 n) (log.f64 (*.f64 (PI.f64) #s(literal 2 binary64)))))
(* (sqrt (/ (* n (PI)) k)) (/ (sqrt 2) (exp (* 1/2 (* k (+ (log (* 2 (PI))) (* -1 (log (/ 1 n)))))))))
(.f64 (/.f64 (sqrt.f64 #s(literal 2 binary64)) (sqrt.f64 (pow.f64 (exp.f64 k) (+.f64 (log.f64 n) (log.f64 (.f64 (PI.f64) #s(literal 2 binary64))))))) (sqrt.f64 (/.f64 (*.f64 (PI.f64) n) k)))
(* (sqrt (/ 1 k)) (exp (* 1/2 (* (+ (log (* 2 (PI))) (* -1 (log (/ 1 n)))) (- 1 k)))))
(.f64 (pow.f64 (exp.f64 (fma.f64 #s(literal -1/2 binary64) k #s(literal 1/2 binary64))) (+.f64 (log.f64 n) (log.f64 (.f64 (PI.f64) #s(literal 2 binary64))))) (sqrt.f64 (/.f64 #s(literal 1 binary64) k)))
(exp (* 1/2 (* (+ (log (* 2 (PI))) (* -1 (log (/ 1 n)))) (- 1 k))))
(pow.f64 (exp.f64 (fma.f64 #s(literal -1/2 binary64) k #s(literal 1/2 binary64))) (+.f64 (log.f64 n) (log.f64 (*.f64 (PI.f64) #s(literal 2 binary64)))))
(* -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 (.f64 (sqrt.f64 (/.f64 (.f64 (PI.f64) n) k)) (sqrt.f64 #s(literal -1 binary64))) (neg.f64 (sqrt.f64 #s(literal -2 binary64)))) (sqrt.f64 (pow.f64 (exp.f64 k) (-.f64 (log.f64 (.f64 #s(literal -2 binary64) (PI.f64))) (log.f64 (/.f64 #s(literal -1 binary64) n))))))
(* (sqrt (/ 1 k)) (exp (* 1/2 (* (+ (log (* -2 (PI))) (* -1 (log (/ -1 n)))) (- 1 k)))))
(.f64 (pow.f64 (exp.f64 (fma.f64 #s(literal -1/2 binary64) k #s(literal 1/2 binary64))) (-.f64 (log.f64 (.f64 #s(literal -2 binary64) (PI.f64))) (log.f64 (/.f64 #s(literal -1 binary64) n)))) (sqrt.f64 (/.f64 #s(literal 1 binary64) k)))
(* -1 (* (sqrt (/ (* n (PI)) k)) (* (sqrt -2) (* (sqrt -1) (pow (* (sqrt (/ 1 (* n (PI)))) (* (sqrt -1) (sqrt -1/2))) k)))))
(.f64 (.f64 (.f64 (sqrt.f64 (/.f64 (.f64 (PI.f64) n) k)) (sqrt.f64 #s(literal -1 binary64))) (neg.f64 (sqrt.f64 #s(literal -2 binary64)))) (pow.f64 (.f64 (.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (*.f64 (PI.f64) n))) (sqrt.f64 #s(literal -1/2 binary64))) (sqrt.f64 #s(literal -1 binary64))) k))
(* -1 (* (sqrt (* n (PI))) (* (sqrt -2) (* (sqrt -1) (pow (* (sqrt (/ 1 (* n (PI)))) (* (sqrt -1) (sqrt -1/2))) k)))))
(.f64 (.f64 (neg.f64 (sqrt.f64 #s(literal -2 binary64))) (.f64 (sqrt.f64 #s(literal -1 binary64)) (sqrt.f64 (.f64 (PI.f64) n)))) (pow.f64 (.f64 (.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (*.f64 (PI.f64) n))) (sqrt.f64 #s(literal -1/2 binary64))) (sqrt.f64 #s(literal -1 binary64))) k))
(pow (* (sqrt (/ 1 (* n (PI)))) (* (sqrt -1) (sqrt -1/2))) k)
(pow.f64 (.f64 (.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (*.f64 (PI.f64) n))) (sqrt.f64 #s(literal -1/2 binary64))) (sqrt.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))))

rewrite263.0ms (2.3%)

Memory

-45.6MiB live, 233.8MiB allocated; 64ms collecting garbage

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	49	254
0	75	242
1	242	224
2	1295	222
0	8131	222

Stop Event

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

Counts

19 → 682

Calls

Call 1

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

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

eval135.0ms (1.2%)

Memory: -3.4MiB live, 180.8MiB allocated; 22ms collecting garbage
Compiler: Compiled 21 895 to 2 534 computations (88.4% saved)

prune39.0ms (0.3%)

Memory

18.3MiB live, 105.4MiB allocated; 10ms collecting garbage

Pruning

23 alts after pruning (18 fresh and 5 done)

	Pruned	Kept	Total
New	702	9	711
Fresh	5	9	14
Picked	3	2	5
Done	1	3	4
Total	711	23	734

Accuracy

100.0%

Counts

734 → 23

Alt Table

Click to see full alt table

Status	Accuracy	Program
	99.6%	(/.f64 #s(approx (pow (* (* 2 (PI)) n) (/ (- 1 k) 2)) (pow.f64 (.f64 (.f64 #s(literal 2 binary64) (PI.f64)) n) (fma.f64 #s(literal -1/2 binary64) k #s(literal 1/2 binary64)))) (sqrt.f64 k))
	74.9%	(.f64 (pow.f64 (.f64 (.f64 #s(literal 2 binary64) (PI.f64)) n) (neg.f64 (/.f64 k #s(literal 2 binary64)))) (sqrt.f64 (/.f64 (.f64 (*.f64 #s(literal 2 binary64) (PI.f64)) n) k)))
	99.7%	(.f64 (/.f64 (sqrt.f64 (.f64 (PI.f64) n)) (sqrt.f64 (pow.f64 (.f64 (.f64 #s(literal 2 binary64) (PI.f64)) n) k))) (sqrt.f64 (/.f64 #s(literal 2 binary64) k)))
	99.5%	(.f64 (/.f64 (sqrt.f64 n) (neg.f64 (sqrt.f64 k))) (/.f64 (neg.f64 (sqrt.f64 (.f64 #s(literal 2 binary64) (PI.f64)))) (sqrt.f64 (pow.f64 (.f64 (.f64 #s(literal 2 binary64) (PI.f64)) n) k))))
	47.5%	(.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)))))
	29.4%	#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (pow.f64 #s(literal 0 binary64) (fma.f64 #s(literal -1/2 binary64) k #s(literal 1/2 binary64))))
	47.6%	#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (/.f64 (sqrt.f64 (.f64 n (.f64 (PI.f64) #s(literal 2 binary64)))) (sqrt.f64 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))))
	99.6%	#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (.f64 (pow.f64 (sqrt.f64 (.f64 n (.f64 (PI.f64) #s(literal 2 binary64)))) (.f64 #s(literal 2 binary64) (fma.f64 #s(literal -1/2 binary64) k #s(literal 1/2 binary64)))) (sqrt.f64 (/.f64 #s(literal 1 binary64) k))))
	47.5%	#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (.f64 (.f64 (.f64 #s(approx (pow (pow ( n (* (PI) 2)) -1/2) k) #s(literal 1 binary64)) (sqrt.f64 n)) (sqrt.f64 (*.f64 #s(literal 2 binary64) (PI.f64)))) (sqrt.f64 (/.f64 #s(literal 1 binary64) k))))
✓	47.7%	#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (.f64 (.f64 #s(approx (pow (pow (* n (* (PI) 2)) -1/2) k) #s(literal 1 binary64)) (sqrt.f64 (.f64 n (.f64 (PI.f64) #s(literal 2 binary64))))) (sqrt.f64 (/.f64 #s(literal 1 binary64) k))))
	4.9%	#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (*.f64 (sqrt.f64 (/.f64 #s(literal 2 binary64) k)) (sqrt.f64 (PI.f64))))
	47.6%	#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (.f64 (sqrt.f64 #s(literal 2 binary64)) (/.f64 (sqrt.f64 (.f64 (PI.f64) n)) (sqrt.f64 k))))
	47.6%	#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (.f64 (sqrt.f64 #s(literal 2 binary64)) (.f64 (sqrt.f64 n) (sqrt.f64 (/.f64 (PI.f64) k)))))
✓	35.2%	#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (.f64 (sqrt.f64 #s(literal 2 binary64)) (sqrt.f64 (/.f64 (.f64 (PI.f64) n) k))))
	4.9%	#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (*.f64 (sqrt.f64 #s(literal 2 binary64)) (sqrt.f64 (/.f64 (PI.f64) k))))
	4.9%	#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt.f64 (/.f64 (*.f64 #s(literal 2 binary64) (PI.f64)) k)))
	35.1%	#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt.f64 (.f64 (/.f64 (.f64 (*.f64 (sqrt.f64 (PI.f64)) (sqrt.f64 (PI.f64))) n) k) #s(literal 2 binary64))))
✓	35.3%	#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt.f64 (.f64 (/.f64 (.f64 (PI.f64) n) k) #s(literal 2 binary64))))
	35.3%	#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt.f64 (.f64 (/.f64 (PI.f64) k) (.f64 n #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))))
	35.3%	#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt.f64 (.f64 (.f64 (/.f64 n k) (PI.f64)) #s(literal 2 binary64))))
✓	26.3%	#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) #s(literal 0 binary64))

Compiler

Compiled 2 035 to 762 computations (62.6% saved)

regimes56.0ms (0.5%)

Memory

-3.8MiB live, 100.0MiB allocated; 9ms collecting garbage

Counts

49 → 1

Calls

Call 1

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

Outputs

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

Calls

4 calls:

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

regimes46.0ms (0.4%)

Memory

-15.7MiB live, 74.9MiB allocated; 6ms collecting garbage

Counts

40 → 1

Calls

Call 1

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

Outputs

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

Calls

4 calls:

12.0ms	k
12.0ms	(.f64 (.f64 #s(literal 2 binary64) (PI.f64)) n)
10.0ms	n
9.0ms	(.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
99.7%	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)

regimes44.0ms (0.4%)

Memory

-14.5MiB live, 90.7MiB allocated; 15ms collecting garbage

Counts

32 → 1

Calls

Call 1

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

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

Calls

4 calls:

14.0ms	(.f64 (.f64 #s(literal 2 binary64) (PI.f64)) n)
12.0ms	k
8.0ms	n
7.0ms	(.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
99.7%	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)

regimes36.0ms (0.3%)

Memory

20.9MiB live, 67.4MiB allocated; 2ms collecting garbage

Counts

31 → 1

Calls

Call 1

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

Outputs

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

Calls

4 calls:

10.0ms	(.f64 (.f64 #s(literal 2 binary64) (PI.f64)) n)
8.0ms	n
8.0ms	k
7.0ms	(.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)

regimes34.0ms (0.3%)

Memory

-5.2MiB live, 41.3MiB allocated; 3ms collecting garbage

Counts

27 → 1

Calls

Call 1

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

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))))
7.0ms	n
7.0ms	(.f64 (.f64 #s(literal 2 binary64) (PI.f64)) n)
7.0ms	k

Results

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

Compiler

Compiled 23 to 23 computations (0% saved)

regimes39.0ms (0.3%)

Memory

1.4MiB live, 47.9MiB allocated; 2ms collecting garbage

Counts

24 → 1

Calls

Call 1

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

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

Calls

4 calls:

18.0ms	(.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))))
7.0ms	(.f64 (.f64 #s(literal 2 binary64) (PI.f64)) n)
7.0ms	n
6.0ms	k

Results

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

Compiler

Compiled 23 to 23 computations (0% saved)

regimes73.0ms (0.6%)

Memory

-10.1MiB live, 37.8MiB allocated; 6ms collecting garbage

Counts

22 → 3

Calls

Call 1

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

Outputs

#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) #s(literal 0 binary64))

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

Calls

4 calls:

54.0ms	(.f64 (.f64 #s(literal 2 binary64) (PI.f64)) n)
6.0ms	n
6.0ms	k
5.0ms	(.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) (pow.f64 (.f64 (*.f64 #s(literal 2 binary64) (PI.f64)) n) (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 2 binary64))))

Results

Accuracy	Segments	Branch
63.7%	7	`(.f64 (.f64 #s(literal 2 binary64) (PI.f64)) n)`
98.6%	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))))`
77.1%	3	`k`
63.7%	7	`n`

Compiler

Compiled 23 to 23 computations (0% saved)

regimes12.0ms (0.1%)

Memory

28.5MiB live, 28.5MiB allocated; 0ms collecting garbage

Counts

21 → 2

Calls

Call 1

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

Outputs

#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) #s(literal 0 binary64))

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

Calls

2 calls:

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

Results

Accuracy	Segments	Branch
71.3%	2	`k`
71.5%	2	`(.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) (pow.f64 (.f64 (*.f64 #s(literal 2 binary64) (PI.f64)) n) (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 2 binary64))))`

Compiler

Compiled 17 to 15 computations (11.8% saved)

regimes9.0ms (0.1%)

Memory

-28.5MiB live, 14.1MiB allocated; 6ms collecting garbage

Counts

16 → 2

Calls

Call 1

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

Outputs

#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) #s(literal 0 binary64))

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

Calls

1 calls:

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
71.5%	2	`(.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) (pow.f64 (.f64 (*.f64 #s(literal 2 binary64) (PI.f64)) n) (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 2 binary64))))`

Compiler

Compiled 16 to 13 computations (18.8% saved)

regimes8.0ms (0.1%)

Memory

20.0MiB live, 20.0MiB allocated; 0ms collecting garbage

Counts

12 → 2

Calls

Call 1

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

Outputs

#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) #s(literal 0 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))))

Calls

2 calls:

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
59.0%	2	`k`
59.1%	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)

regimes7.0ms (0.1%)

Memory

13.8MiB live, 13.8MiB allocated; 0ms collecting garbage

Counts

4 → 2

Calls

Call 1

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

Outputs

#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) #s(literal 0 binary64))

#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:

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
26.3%	1	`(.f64 (.f64 #s(literal 2 binary64) (PI.f64)) n)`
26.3%	1	`n`
28.3%	2	`k`
28.6%	2	`(.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) (pow.f64 (.f64 (*.f64 #s(literal 2 binary64) (PI.f64)) n) (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 2 binary64))))`

Compiler

Compiled 23 to 23 computations (0% saved)

regimes6.0ms (0.1%)

Memory

-31.2MiB live, 14.4MiB allocated; 3ms 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))) #s(literal 0 binary64))

Outputs
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) #s(literal 0 binary64))

Calls

4 calls:

3.0ms	(.f64 (.f64 #s(literal 2 binary64) (PI.f64)) n)
1.0ms	k
1.0ms	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))))

Results

Accuracy	Segments	Branch
26.3%	1	`(.f64 (.f64 #s(literal 2 binary64) (PI.f64)) n)`
26.3%	1	`n`
26.3%	1	`k`
26.3%	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)

bsearch1.0ms (0%)

Memory

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

Algorithm

2×	left-value

Steps

Time	Left	Right
0.0ms	1.8459407281513985e+284	+inf
0.0ms	0.0	2.5285926685443254e-129

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	2.5285926685443254e-129

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	0.0	2.5285926685443254e-129

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	0.0	2.5285926685443254e-129

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	0.0	2.5285926685443254e-129

Compiler

Compiled 19 to 18 computations (5.3% saved)

simplify22.0ms (0.2%)

Memory

35.5MiB live, 35.5MiB allocated; 0ms collecting garbage

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	91	566
1	113	536
2	127	536
3	148	536
4	165	536
5	184	536
6	218	536
7	283	536
8	314	536
9	347	536
10	357	536

Stop Event

1×

saturated

Calls

Call 1

Inputs
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (.f64 (.f64 (pow.f64 (pow.f64 (.f64 n (.f64 (PI.f64) #s(literal 2 binary64))) #s(literal -1/2 binary64)) k) (sqrt.f64 (.f64 n (.f64 (PI.f64) #s(literal 2 binary64))))) (sqrt.f64 (/.f64 #s(literal 1 binary64) k))))
(/.f64 (.f64 (sqrt.f64 (.f64 n (.f64 (PI.f64) #s(literal 2 binary64)))) #s(literal 1 binary64)) (.f64 (pow.f64 (.f64 n (.f64 (PI.f64) #s(literal 2 binary64))) (/.f64 k #s(literal 2 binary64))) (sqrt.f64 k)))
(.f64 (/.f64 (sqrt.f64 (.f64 (PI.f64) n)) (sqrt.f64 (pow.f64 (.f64 (.f64 #s(literal 2 binary64) (PI.f64)) n) k))) (sqrt.f64 (/.f64 #s(literal 2 binary64) k)))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (.f64 (pow.f64 (sqrt.f64 (.f64 n (.f64 (PI.f64) #s(literal 2 binary64)))) (.f64 #s(literal 2 binary64) (fma.f64 #s(literal -1/2 binary64) k #s(literal 1/2 binary64)))) (sqrt.f64 (/.f64 #s(literal 1 binary64) k))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (.f64 (pow.f64 (.f64 (*.f64 #s(literal 2 binary64) n) (PI.f64)) (fma.f64 #s(literal -1/2 binary64) k #s(literal 1/2 binary64))) (sqrt.f64 (/.f64 #s(literal 1 binary64) k))))
(/.f64 #s(approx (pow (* (* 2 (PI)) n) (/ (- 1 k) 2)) (pow.f64 (.f64 (.f64 #s(literal 2 binary64) (PI.f64)) n) (fma.f64 #s(literal -1/2 binary64) k #s(literal 1/2 binary64)))) (sqrt.f64 k))
(if (<=.f64 (.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) (pow.f64 (.f64 (.f64 #s(literal 2 binary64) (PI.f64)) n) (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 2 binary64)))) #s(literal 0 binary64)) #s(approx ( (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) #s(literal 0 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 200000000000000015842876501691535308251363838339942186816779868466887151795034205545089069114411529059504325666588836124813676426230104197677563914641752713707086241642983763505789334141041164451549418938435594261010114368138763297090749546488747114934452621501484084432923307385290752 binary64)) #s(approx ( (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (.f64 (.f64 #s(approx (pow (pow (* n (* (PI) 2)) -1/2) k) #s(literal 1 binary64)) (sqrt.f64 (.f64 n (.f64 (PI.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))) (pow.f64 #s(literal 0 binary64) (fma.f64 #s(literal -1/2 binary64) k #s(literal 1/2 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 0 binary64)) #s(approx ( (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) #s(literal 0 binary64)) #s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (.f64 (.f64 #s(approx (pow (pow (* n (* (PI) 2)) -1/2) k) #s(literal 1 binary64)) (sqrt.f64 (.f64 n (.f64 (PI.f64) #s(literal 2 binary64))))) (sqrt.f64 (/.f64 #s(literal 1 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))) #s(literal 0 binary64)) #s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (/.f64 (sqrt.f64 (.f64 n (.f64 (PI.f64) #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))) #s(literal 0 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)))))
(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))) #s(literal 0 binary64)) #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))) #s(literal 0 binary64))

Outputs
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (.f64 (.f64 (pow.f64 (pow.f64 (.f64 n (.f64 (PI.f64) #s(literal 2 binary64))) #s(literal -1/2 binary64)) k) (sqrt.f64 (.f64 n (.f64 (PI.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 (.f64 (pow.f64 (pow.f64 (.f64 n (.f64 (PI.f64) #s(literal 2 binary64))) #s(literal -1/2 binary64)) k) (sqrt.f64 (.f64 n (.f64 (PI.f64) #s(literal 2 binary64))))) (sqrt.f64 (pow.f64 k #s(literal -1 binary64)))))
(/.f64 (.f64 (sqrt.f64 (.f64 n (.f64 (PI.f64) #s(literal 2 binary64)))) #s(literal 1 binary64)) (.f64 (pow.f64 (.f64 n (.f64 (PI.f64) #s(literal 2 binary64))) (/.f64 k #s(literal 2 binary64))) (sqrt.f64 k)))
(/.f64 (sqrt.f64 (.f64 n (.f64 (PI.f64) #s(literal 2 binary64)))) (.f64 (pow.f64 (.f64 n (*.f64 (PI.f64) #s(literal 2 binary64))) (/.f64 k #s(literal 2 binary64))) (sqrt.f64 k)))
(.f64 (/.f64 (sqrt.f64 (.f64 (PI.f64) n)) (sqrt.f64 (pow.f64 (.f64 (.f64 #s(literal 2 binary64) (PI.f64)) n) k))) (sqrt.f64 (/.f64 #s(literal 2 binary64) k)))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (.f64 (pow.f64 (sqrt.f64 (.f64 n (.f64 (PI.f64) #s(literal 2 binary64)))) (.f64 #s(literal 2 binary64) (fma.f64 #s(literal -1/2 binary64) k #s(literal 1/2 binary64)))) (sqrt.f64 (/.f64 #s(literal 1 binary64) k))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (.f64 (pow.f64 (sqrt.f64 (.f64 n (.f64 (PI.f64) #s(literal 2 binary64)))) (.f64 #s(literal 2 binary64) (fma.f64 #s(literal -1/2 binary64) k #s(literal 1/2 binary64)))) (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)))))
(/.f64 #s(approx (pow (* (* 2 (PI)) n) (/ (- 1 k) 2)) (pow.f64 (.f64 (.f64 #s(literal 2 binary64) (PI.f64)) n) (fma.f64 #s(literal -1/2 binary64) k #s(literal 1/2 binary64)))) (sqrt.f64 k))
(if (<=.f64 (.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) (pow.f64 (.f64 (.f64 #s(literal 2 binary64) (PI.f64)) n) (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 2 binary64)))) #s(literal 0 binary64)) #s(approx ( (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) #s(literal 0 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 200000000000000015842876501691535308251363838339942186816779868466887151795034205545089069114411529059504325666588836124813676426230104197677563914641752713707086241642983763505789334141041164451549418938435594261010114368138763297090749546488747114934452621501484084432923307385290752 binary64)) #s(approx ( (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (.f64 (.f64 #s(approx (pow (pow (* n (* (PI) 2)) -1/2) k) #s(literal 1 binary64)) (sqrt.f64 (.f64 n (.f64 (PI.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))) (pow.f64 #s(literal 0 binary64) (fma.f64 #s(literal -1/2 binary64) k #s(literal 1/2 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 0 binary64)) #s(approx ( (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) #s(literal 0 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 200000000000000015842876501691535308251363838339942186816779868466887151795034205545089069114411529059504325666588836124813676426230104197677563914641752713707086241642983763505789334141041164451549418938435594261010114368138763297090749546488747114934452621501484084432923307385290752 binary64)) #s(approx ( (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (.f64 (.f64 #s(approx (pow (pow (* n (* (PI) 2)) -1/2) k) #s(literal 1 binary64)) (sqrt.f64 (.f64 n (.f64 (PI.f64) #s(literal 2 binary64))))) (sqrt.f64 (pow.f64 k #s(literal -1 binary64))))) #s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (pow.f64 #s(literal 0 binary64) (fma.f64 #s(literal -1/2 binary64) k #s(literal 1/2 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 0 binary64)) #s(approx ( (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) #s(literal 0 binary64)) #s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (.f64 (.f64 #s(approx (pow (pow (* n (* (PI) 2)) -1/2) k) #s(literal 1 binary64)) (sqrt.f64 (.f64 n (.f64 (PI.f64) #s(literal 2 binary64))))) (sqrt.f64 (/.f64 #s(literal 1 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))) #s(literal 0 binary64)) #s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (.f64 (.f64 #s(approx (pow (pow (* n (* (PI) 2)) -1/2) k) #s(literal 1 binary64)) (sqrt.f64 (.f64 n (.f64 (PI.f64) #s(literal 2 binary64))))) (sqrt.f64 (pow.f64 k #s(literal -1 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 0 binary64)) #s(approx ( (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) #s(literal 0 binary64)) #s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (/.f64 (sqrt.f64 (.f64 n (.f64 (PI.f64) #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))) #s(literal 0 binary64)) #s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (/.f64 (sqrt.f64 (.f64 n (.f64 (PI.f64) #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))) #s(literal 0 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)))))
(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))) #s(literal 0 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)))))
(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))) #s(literal 0 binary64)) #s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt.f64 (*.f64 (/.f64 #s(literal 2 binary64) k) (PI.f64)))))
(if (<=.f64 (.f64 (pow.f64 (sqrt.f64 k) #s(literal -1 binary64)) (pow.f64 (.f64 (.f64 #s(literal 2 binary64) (PI.f64)) n) (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 2 binary64)))) #s(literal 0 binary64)) #s(approx ( (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) #s(literal 0 binary64)) #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))) #s(literal 0 binary64))

derivations1.2s (10.3%)

Memory

-26.7MiB live, 979.8MiB allocated; 88ms collecting garbage

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	53	313
0	86	285
1	259	239
2	1224	137
0	9264	137
0	13	38
0	22	38
1	83	35
2	446	35
3	4007	29
0	8921	29
0	485	3834
1	1747	3527
0	8143	3312
0	58	385
0	100	359
1	320	337
2	1774	337
0	8156	334
0	49	254
0	75	242
1	242	224
2	1295	222
0	8131	222
0	120	502
1	378	489
2	1377	453
3	4131	453
0	8166	441

Stop Event

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

Compiler

Compiled 566 to 94 computations (83.4% saved)

preprocess139.0ms (1.2%)

Memory: -2.9MiB live, 138.4MiB allocated; 13ms collecting garbage
Compiler: Compiled 1 164 to 214 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	49	345
0	75	333
1	117	325
2	182	325
3	259	320
4	328	320
5	392	320
6	498	320
7	582	320
8	614	320
9	644	320
0	644	320

Iter	Nodes	Cost
0	91	566
1	113	536
2	127	536
3	148	536
4	165	536
5	184	536
6	218	536
7	283	536
8	314	536
9	347	536
10	357	536

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	49	345
0	75	333
1	117	325
2	182	325
3	259	320
4	328	320
5	392	320
6	498	320
7	582	320
8	614	320
9	644	320
0	644	320

Iter	Nodes	Cost
0	91	566
1	113	536
2	127	536
3	148	536
4	165	536
5	184	536
6	218	536
7	283	536
8	314	536
9	347	536
10	357	536

start0.0ms (0%)

analyze157.0ms (1.4%)

sample5.1s (44.5%)

explain166.0ms (1.5%)

preprocess33.0ms (0.3%)

eval0.0ms (0%)

prune0.0ms (0%)

simplify8.0ms (0.1%)

localize41.0ms (0.4%)

series70.0ms (0.6%)

simplify133.0ms (1.2%)

rewrite254.0ms (2.2%)

eval56.0ms (0.5%)

prune28.0ms (0.2%)

simplify399.0ms (3.5%)

localize176.0ms (1.5%)

series196.0ms (1.7%)

simplify355.0ms (3.1%)

rewrite205.0ms (1.8%)

eval361.0ms (3.2%)

prune70.0ms (0.6%)

simplify54.0ms (0.5%)

localize159.0ms (1.4%)

series163.0ms (1.4%)

simplify152.0ms (1.3%)

rewrite203.0ms (1.8%)

eval281.0ms (2.5%)

prune77.0ms (0.7%)

simplify24.0ms (0.2%)

localize115.0ms (1%)

series80.0ms (0.7%)

simplify153.0ms (1.3%)

rewrite263.0ms (2.3%)

eval135.0ms (1.2%)

prune39.0ms (0.3%)

regimes56.0ms (0.5%)

regimes46.0ms (0.4%)

regimes44.0ms (0.4%)

regimes36.0ms (0.3%)

regimes34.0ms (0.3%)

regimes39.0ms (0.3%)

regimes73.0ms (0.6%)

regimes12.0ms (0.1%)

regimes9.0ms (0.1%)

regimes8.0ms (0.1%)

regimes7.0ms (0.1%)

regimes6.0ms (0.1%)

bsearch1.0ms (0%)

bsearch0.0ms (0%)

bsearch0.0ms (0%)

bsearch0.0ms (0%)

bsearch0.0ms (0%)

simplify22.0ms (0.2%)

derivations1.2s (10.3%)

preprocess139.0ms (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

Iter	Nodes	Cost
0	49	345
0	75	333
1	117	325
2	182	325
3	259	320
4	328	320
5	392	320
6	498	320
7	582	320
8	614	320
9	644	320
0	644	320

Iter	Nodes	Cost
0	91	566
1	113	536
2	127	536
3	148	536
4	165	536
5	184	536
6	218	536
7	283	536
8	314	536
9	347	536
10	357	536