Metrics for Migdal et al, Equation (51)

analyze136.0ms (1.2%)

Memory

-16.0MiB live, 84.7MiB allocated

Algorithm

1×

Search

Probability	Valid	Unknown	Precondition	Infinite	Domain	Can't	Iter
0%	0%	99.9%	0.1%	0%	0%	0%	0
0%	0%	99.9%	0.1%	0%	0%	0%	1
0%	0%	50%	0.1%	0%	50%	0%	2
50%	25%	25%	0.1%	0%	50%	0%	3
50%	25%	25%	0.1%	0%	50%	0%	4
50%	25%	25%	0.1%	0%	50%	0%	5
50%	25%	25%	0.1%	0%	50%	0%	6
51.6%	25%	23.4%	0.1%	0%	51.5%	0%	7
52.5%	25%	22.6%	0.1%	0%	52.3%	0%	8
53.8%	25%	21.5%	0.1%	0%	53.5%	0%	9
54.5%	25%	20.9%	0.1%	0%	54%	0%	10
55.3%	25%	20.2%	0.1%	0%	54.7%	0%	11
55.7%	25%	19.9%	0.1%	0%	55.1%	0%	12

Compiler

Compiled 18 to 15 computations (16.7% saved)

sample3.0s (27.2%)

Memory

96.2MiB live, 4 143.0MiB allocated

Samples

920.0ms	8 256×	0	valid
754.0ms	3 593×	1	invalid
434.0ms	1 849×	1	exit
148.0ms	428×	2	invalid
55.0ms	490×	0	invalid
25.0ms	224×	0	exit

Precisions

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

ival-pow: 468.0ms (27% of total)

ival-mult: 370.0ms (21.4% of total)

ival-div: 279.0ms (16.1% of total)

adjust: 172.0ms (9.9% of total)

ival-sqrt: 164.0ms (9.5% of total)

ival-sub: 127.0ms (7.3% of total)

ival-pi: 118.0ms (6.8% of total)

exact: 15.0ms (0.9% of total)

ival-true: 12.0ms (0.7% of total)

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

Bogosity

preprocess62.0ms (0.6%)

Memory

-26.8MiB live, 58.8MiB allocated

Algorithm

1×	egg-herbie

Rules

232×	`associate-r`
160×	`sub-neg`
160×	`associate-l`
138×	`distribute-lft-neg-in`
118×	`distribute-lft-in`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	31	88
1	82	74
2	193	74
3	383	74
4	607	74
5	878	74
6	1047	74
7	1230	74
8	1285	74
9	1309	74
10	1327	74
11	1331	74
12	1331	74
0	13	16
0	22	16
1	37	14
2	54	14
3	75	14
4	93	14
5	108	14
6	129	14
7	156	14
8	165	14
9	168	14
0	168	13

Stop Event

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

Calls

Call 1

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

Outputs

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

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

explain149.0ms (1.3%)

Memory

-13.9MiB live, 274.9MiB allocated

FPErrors

Click to see full error table

Ground Truth	Overpredictions	Example	Underpredictions	Example	Subexpression
7	88	(5.920079365299991e-281 2.51254982423944e-282)	2	(4.748694206738671e-5 2.1552789888743775e+47)	`(pow.f64 (.f64 (.f64 #s(literal 2 binary64) (PI.f64)) n) (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 2 binary64)))`
0	0	-	0	-	`k`
0	0	-	0	-	`n`
0	0	-	0	-	`(/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 2 binary64))`
0	0	-	0	-	`#s(literal 1 binary64)`
0	0	-	0	-	`(.f64 (.f64 #s(literal 2 binary64) (PI.f64)) n)`
0	0	-	0	-	`(sqrt.f64 k)`
0	0	-	0	-	`#s(literal 2 binary64)`
0	0	-	0	-	`(/.f64 #s(literal 1 binary64) (sqrt.f64 k))`
0	0	-	0	-	`(-.f64 #s(literal 1 binary64) k)`
0	0	-	0	-	`(*.f64 #s(literal 2 binary64) (PI.f64))`
0	0	-	0	-	`(.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) (pow.f64 (.f64 (*.f64 #s(literal 2 binary64) (PI.f64)) n) (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 2 binary64))))`
0	0	-	0	-	`(PI.f64)`

Explanations

Click to see full explanations table

Operator	Subexpression	Explanation	Count
`pow.f64`	`(pow.f64 (.f64 (.f64 #s(literal 2 binary64) (PI.f64)) n) (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 2 binary64)))`	sensitivity	93	28

Confusion

	Predicted +	Predicted -
+	5	1
-	88	162

Precision

0.053763440860215055

Recall

0.8333333333333334

Confusion?

	Predicted +	Predicted Maybe	Predicted -
+	5	1	0
-	88	27	135

Precision?

0.049586776859504134

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

53.0ms

512×

valid

Compiler

Compiled 148 to 56 computations (62.2% saved)

Precisions

Click to see histograms. Total time spent on operations: 35.0ms

ival-pow: 10.0ms (28.5% of total)

ival-mult: 8.0ms (22.8% of total)

ival-div: 7.0ms (19.9% of total)

ival-sqrt: 4.0ms (11.4% of total)

ival-sub: 3.0ms (8.5% of total)

ival-pi: 2.0ms (5.7% of total)

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

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

exact: 0.0ms (0% of total)

eval0.0ms (0%)

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

prune1.0ms (0%)

Memory

1.0MiB live, 1.0MiB allocated

Alt Table

Click to see full alt table

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

Compiler

Compiled 18 to 13 computations (27.8% saved)

simplify9.0ms (0.1%)

Memory

13.4MiB live, 13.4MiB allocated

Algorithm

1×	egg-herbie

Localize:

Found 4 expressions of interest:

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

Rules

64×	`lower-*.f32`
58×	`lower-*.f64`
48×	`lower-+.f64`
48×	`lower-+.f32`
36×	`lower-fma.f64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	13	54
0	22	54
1	37	52
2	54	52
3	75	52
4	93	52
5	108	52
6	129	52
7	156	52
8	165	52
9	168	52
0	168	49

Stop Event

1×	iter limit
1×	saturated
1×	iter limit

Calls

Call 1

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

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

localize43.0ms (0.4%)

Memory

-16.8MiB live, 59.3MiB allocated

Localize:

Found 4 expressions of interest:

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

Samples

29.0ms

256×

valid

Compiler

Compiled 56 to 15 computations (73.2% saved)

Precisions

Click to see histograms. Total time spent on operations: 18.0ms

ival-mult: 5.0ms (28.2% of total)

ival-pow: 5.0ms (28.2% of total)

ival-div: 3.0ms (16.9% of total)

ival-sqrt: 2.0ms (11.3% of total)

ival-pi: 1.0ms (5.6% of total)

ival-sub: 1.0ms (5.6% of total)

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

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

exact: 0.0ms (0% of total)

series72.0ms (0.6%)

Memory

21.3MiB live, 100.0MiB allocated

Counts

6 → 96

Calls

Call 1

Inputs
#s(alt (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 2 binary64)) (patch (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 2 binary64)) #<representation binary64>) () ())
#s(alt (.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)))) (patch (.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)))) #<representation binary64>) () ())
#s(alt (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) (patch (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) #<representation binary64>) () ())
#s(alt (sqrt.f64 k) (patch (sqrt.f64 k) #<representation binary64>) () ())
#s(alt (pow.f64 (.f64 (.f64 #s(literal 2 binary64) (PI.f64)) n) (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 2 binary64))) (patch (pow.f64 (.f64 (.f64 #s(literal 2 binary64) (PI.f64)) n) (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 2 binary64))) #<representation binary64>) () ())
#s(alt (.f64 (.f64 #s(literal 2 binary64) (PI.f64)) n) (patch (.f64 (.f64 #s(literal 2 binary64) (PI.f64)) n) #<representation binary64>) () ())

Outputs
#s(alt 1/2 (taylor 0 k) (#s(alt (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 2 binary64)) (patch (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 2 binary64)) #<representation binary64>) () ())) ())
#s(alt (+ 1/2 (* -1/2 k)) (taylor 0 k) (#s(alt (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 2 binary64)) (patch (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 2 binary64)) #<representation binary64>) () ())) ())
#s(alt (+ 1/2 (* -1/2 k)) (taylor 0 k) (#s(alt (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 2 binary64)) (patch (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 2 binary64)) #<representation binary64>) () ())) ())
#s(alt (+ 1/2 (* -1/2 k)) (taylor 0 k) (#s(alt (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 2 binary64)) (patch (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 2 binary64)) #<representation binary64>) () ())) ())
#s(alt (* -1/2 k) (taylor inf k) (#s(alt (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 2 binary64)) (patch (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 2 binary64)) #<representation binary64>) () ())) ())
#s(alt (* k (- (* 1/2 (/ 1 k)) 1/2)) (taylor inf k) (#s(alt (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 2 binary64)) (patch (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 2 binary64)) #<representation binary64>) () ())) ())
#s(alt (* k (- (* 1/2 (/ 1 k)) 1/2)) (taylor inf k) (#s(alt (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 2 binary64)) (patch (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 2 binary64)) #<representation binary64>) () ())) ())
#s(alt (* k (- (* 1/2 (/ 1 k)) 1/2)) (taylor inf k) (#s(alt (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 2 binary64)) (patch (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 2 binary64)) #<representation binary64>) () ())) ())
#s(alt (* -1/2 k) (taylor -inf k) (#s(alt (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 2 binary64)) (patch (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 2 binary64)) #<representation binary64>) () ())) ())
#s(alt (* -1 (* k (- 1/2 (* 1/2 (/ 1 k))))) (taylor -inf k) (#s(alt (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 2 binary64)) (patch (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 2 binary64)) #<representation binary64>) () ())) ())
#s(alt (* -1 (* k (- 1/2 (* 1/2 (/ 1 k))))) (taylor -inf k) (#s(alt (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 2 binary64)) (patch (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 2 binary64)) #<representation binary64>) () ())) ())
#s(alt (* -1 (* k (- 1/2 (* 1/2 (/ 1 k))))) (taylor -inf k) (#s(alt (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 2 binary64)) (patch (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 2 binary64)) #<representation binary64>) () ())) ())
#s(alt (* (sqrt (/ (* n (PI)) k)) (sqrt 2)) (taylor 0 k) (#s(alt (.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)))) (patch (.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)))) #<representation binary64>) () ())) ())
#s(alt (/ (+ (* -1/2 (* (sqrt (* (pow k 3) (* n (PI)))) (* (log (* 2 (* n (PI)))) (sqrt 2)))) (* (sqrt (* k (* n (PI)))) (sqrt 2))) k) (taylor 0 k) (#s(alt (.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)))) (patch (.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)))) #<representation binary64>) () ())) ())
#s(alt (/ (+ (* k (+ (* -1/2 (* (sqrt (* k (* n (PI)))) (* (log (* 2 (* n (PI)))) (sqrt 2)))) (* 1/8 (* (sqrt (* (pow k 3) (* n (PI)))) (* (pow (log (* 2 (* n (PI)))) 2) (sqrt 2)))))) (* (sqrt (* k (* n (PI)))) (sqrt 2))) k) (taylor 0 k) (#s(alt (.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)))) (patch (.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)))) #<representation binary64>) () ())) ())
#s(alt (/ (+ (* k (+ (* -1/2 (* (sqrt (* k (* n (PI)))) (* (log (* 2 (* n (PI)))) (sqrt 2)))) (* k (+ (* -1/48 (* (sqrt (* (pow k 3) (* n (PI)))) (* (pow (log (* 2 (* n (PI)))) 3) (sqrt 2)))) (* 1/8 (* (sqrt (* k (* n (PI)))) (* (pow (log (* 2 (* n (PI)))) 2) (sqrt 2)))))))) (* (sqrt (* k (* n (PI)))) (sqrt 2))) k) (taylor 0 k) (#s(alt (.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)))) (patch (.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)))) #<representation binary64>) () ())) ())
#s(alt (* (sqrt (/ 1 k)) (exp (* 1/2 (* (log (* 2 (* n (PI)))) (- 1 k))))) (taylor inf k) (#s(alt (.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)))) (patch (.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)))) #<representation binary64>) () ())) ())
#s(alt (* (sqrt (/ 1 k)) (exp (* 1/2 (* (log (* 2 (* n (PI)))) (- 1 k))))) (taylor inf k) (#s(alt (.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)))) (patch (.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)))) #<representation binary64>) () ())) ())
#s(alt (* (sqrt (/ 1 k)) (exp (* 1/2 (* (log (* 2 (* n (PI)))) (- 1 k))))) (taylor inf k) (#s(alt (.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)))) (patch (.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)))) #<representation binary64>) () ())) ())
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#s(alt (exp (* 1/2 (* (log (* 2 (* n (PI)))) (- 1 k)))) (taylor inf k) (#s(alt (pow.f64 (.f64 (.f64 #s(literal 2 binary64) (PI.f64)) n) (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 2 binary64))) (patch (pow.f64 (.f64 (.f64 #s(literal 2 binary64) (PI.f64)) n) (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 2 binary64))) #<representation binary64>) () ())) ())
#s(alt (exp (* 1/2 (* (log (* 2 (* n (PI)))) (- 1 k)))) (taylor inf k) (#s(alt (pow.f64 (.f64 (.f64 #s(literal 2 binary64) (PI.f64)) n) (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 2 binary64))) (patch (pow.f64 (.f64 (.f64 #s(literal 2 binary64) (PI.f64)) n) (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 2 binary64))) #<representation binary64>) () ())) ())
#s(alt (exp (* 1/2 (* (log (* 2 (* n (PI)))) (+ 1 (* -1 k))))) (taylor -inf k) (#s(alt (pow.f64 (.f64 (.f64 #s(literal 2 binary64) (PI.f64)) n) (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 2 binary64))) (patch (pow.f64 (.f64 (.f64 #s(literal 2 binary64) (PI.f64)) n) (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 2 binary64))) #<representation binary64>) () ())) ())
#s(alt (exp (* 1/2 (* (log (* 2 (* n (PI)))) (+ 1 (* -1 k))))) (taylor -inf k) (#s(alt (pow.f64 (.f64 (.f64 #s(literal 2 binary64) (PI.f64)) n) (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 2 binary64))) (patch (pow.f64 (.f64 (.f64 #s(literal 2 binary64) (PI.f64)) n) (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 2 binary64))) #<representation binary64>) () ())) ())
#s(alt (exp (* 1/2 (* (log (* 2 (* n (PI)))) (+ 1 (* -1 k))))) (taylor -inf k) (#s(alt (pow.f64 (.f64 (.f64 #s(literal 2 binary64) (PI.f64)) n) (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 2 binary64))) (patch (pow.f64 (.f64 (.f64 #s(literal 2 binary64) (PI.f64)) n) (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 2 binary64))) #<representation binary64>) () ())) ())
#s(alt (exp (* 1/2 (* (log (* 2 (* n (PI)))) (+ 1 (* -1 k))))) (taylor -inf k) (#s(alt (pow.f64 (.f64 (.f64 #s(literal 2 binary64) (PI.f64)) n) (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 2 binary64))) (patch (pow.f64 (.f64 (.f64 #s(literal 2 binary64) (PI.f64)) n) (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 2 binary64))) #<representation binary64>) () ())) ())
#s(alt (* 2 (* n (PI))) (taylor 0 n) (#s(alt (.f64 (.f64 #s(literal 2 binary64) (PI.f64)) n) (patch (.f64 (.f64 #s(literal 2 binary64) (PI.f64)) n) #<representation binary64>) () ())) ())
#s(alt (* 2 (* n (PI))) (taylor 0 n) (#s(alt (.f64 (.f64 #s(literal 2 binary64) (PI.f64)) n) (patch (.f64 (.f64 #s(literal 2 binary64) (PI.f64)) n) #<representation binary64>) () ())) ())
#s(alt (* 2 (* n (PI))) (taylor 0 n) (#s(alt (.f64 (.f64 #s(literal 2 binary64) (PI.f64)) n) (patch (.f64 (.f64 #s(literal 2 binary64) (PI.f64)) n) #<representation binary64>) () ())) ())
#s(alt (* 2 (* n (PI))) (taylor 0 n) (#s(alt (.f64 (.f64 #s(literal 2 binary64) (PI.f64)) n) (patch (.f64 (.f64 #s(literal 2 binary64) (PI.f64)) n) #<representation binary64>) () ())) ())
#s(alt (* 2 (* n (PI))) (taylor inf n) (#s(alt (.f64 (.f64 #s(literal 2 binary64) (PI.f64)) n) (patch (.f64 (.f64 #s(literal 2 binary64) (PI.f64)) n) #<representation binary64>) () ())) ())
#s(alt (* 2 (* n (PI))) (taylor inf n) (#s(alt (.f64 (.f64 #s(literal 2 binary64) (PI.f64)) n) (patch (.f64 (.f64 #s(literal 2 binary64) (PI.f64)) n) #<representation binary64>) () ())) ())
#s(alt (* 2 (* n (PI))) (taylor inf n) (#s(alt (.f64 (.f64 #s(literal 2 binary64) (PI.f64)) n) (patch (.f64 (.f64 #s(literal 2 binary64) (PI.f64)) n) #<representation binary64>) () ())) ())
#s(alt (* 2 (* n (PI))) (taylor inf n) (#s(alt (.f64 (.f64 #s(literal 2 binary64) (PI.f64)) n) (patch (.f64 (.f64 #s(literal 2 binary64) (PI.f64)) n) #<representation binary64>) () ())) ())
#s(alt (* 2 (* n (PI))) (taylor -inf n) (#s(alt (.f64 (.f64 #s(literal 2 binary64) (PI.f64)) n) (patch (.f64 (.f64 #s(literal 2 binary64) (PI.f64)) n) #<representation binary64>) () ())) ())
#s(alt (* 2 (* n (PI))) (taylor -inf n) (#s(alt (.f64 (.f64 #s(literal 2 binary64) (PI.f64)) n) (patch (.f64 (.f64 #s(literal 2 binary64) (PI.f64)) n) #<representation binary64>) () ())) ())
#s(alt (* 2 (* n (PI))) (taylor -inf n) (#s(alt (.f64 (.f64 #s(literal 2 binary64) (PI.f64)) n) (patch (.f64 (.f64 #s(literal 2 binary64) (PI.f64)) n) #<representation binary64>) () ())) ())
#s(alt (* 2 (* n (PI))) (taylor -inf n) (#s(alt (.f64 (.f64 #s(literal 2 binary64) (PI.f64)) n) (patch (.f64 (.f64 #s(literal 2 binary64) (PI.f64)) n) #<representation binary64>) () ())) ())

Calls

24 calls:

Time	Variable		Point	Expression
31.0ms	n	@	0	(* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2)))
25.0ms	n	@	-inf	(* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2)))
7.0ms	n	@	inf	(* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2)))
1.0ms	k	@	-inf	(* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2)))
1.0ms	k	@	0	(* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2)))

simplify278.0ms (2.5%)

Memory

21.2MiB live, 369.5MiB allocated

Algorithm

1×	egg-herbie

Rules

9 974×	`lower-fma.f64`
9 974×	`lower-fma.f32`
5 988×	`lower-*.f64`
5 988×	`lower-*.f32`
1 688×	`lower-+.f64`

Iterations

Useful iterations: 0 (0.0ms)

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

Stop Event

1×	iter limit
1×	node limit

Counts

96 → 96

Calls

Call 1

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

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

rewrite376.0ms (3.4%)

Memory

-16.6MiB live, 279.2MiB allocated

Algorithm

1×	batch-egg-rewrite

Rules

4 378×	`lower-*.f32`
4 372×	`lower-*.f64`
3 286×	`lower-pow.f32`
3 284×	`lower-pow.f64`
2 442×	`lower-/.f32`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	13	43
0	22	43
1	89	40
2	497	38
3	4474	38
0	8599	37

Stop Event

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

Counts

6 → 419

Calls

Call 1

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

eval157.0ms (1.4%)

Memory: -17.1MiB live, 96.3MiB allocated
Compiler: Compiled 11 338 to 1 530 computations (86.5% saved)

prune179.0ms (1.6%)

Memory

0.2MiB live, 122.5MiB allocated

Pruning

15 alts after pruning (15 fresh and 0 done)

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

Accuracy

100.0%

Counts

516 → 15

Alt Table

Click to see full alt table

Status	Accuracy	Program
▶	50.0%	(/.f64 (pow.f64 (.f64 #s(literal 2 binary64) (.f64 (PI.f64) n)) (fma.f64 k #s(literal 1/2 binary64) #s(literal 1/2 binary64))) (sqrt.f64 k))
	99.6%	(/.f64 (.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) (sqrt.f64 (.f64 #s(literal 2 binary64) (.f64 (PI.f64) n)))) (pow.f64 (.f64 #s(literal 2 binary64) (.f64 (PI.f64) n)) (.f64 k #s(literal 1/2 binary64))))
▶	99.7%	(/.f64 (sqrt.f64 (.f64 #s(literal 2 binary64) (.f64 (PI.f64) n))) (.f64 (sqrt.f64 k) (pow.f64 (.f64 #s(literal 2 binary64) (.f64 (PI.f64) n)) (.f64 k #s(literal 1/2 binary64)))))
	99.4%	(/.f64 #s(literal 1 binary64) (.f64 (sqrt.f64 k) (pow.f64 (.f64 #s(literal 2 binary64) (.f64 (PI.f64) n)) (-.f64 #s(literal -1/2 binary64) (.f64 k #s(literal -1/2 binary64))))))
	49.6%	(.f64 (pow.f64 #s(literal 2 binary64) (fma.f64 k #s(literal 1/2 binary64) #s(literal 1/2 binary64))) (/.f64 (pow.f64 (.f64 (PI.f64) n) (fma.f64 k #s(literal 1/2 binary64) #s(literal 1/2 binary64))) (sqrt.f64 k)))
▶	99.4%	(.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) (pow.f64 (.f64 (*.f64 #s(literal 2 binary64) (PI.f64)) n) (fma.f64 k #s(literal -1/2 binary64) #s(literal 1/2 binary64))))
	51.7%	(.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) (pow.f64 (.f64 (.f64 #s(literal 2 binary64) (PI.f64)) n) #s(approx (/ (- 1 k) 2) (.f64 #s(literal -1/2 binary64) k))))
	50.5%	(.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) (pow.f64 (.f64 (*.f64 #s(literal 2 binary64) (PI.f64)) n) #s(approx (/ (- 1 k) 2) #s(literal 1/2 binary64))))
	99.3%	(.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) (/.f64 #s(literal 1 binary64) (pow.f64 (.f64 #s(literal 2 binary64) (.f64 (PI.f64) n)) (-.f64 #s(literal -1/2 binary64) (.f64 k #s(literal -1/2 binary64))))))
▶	99.3%	(.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) (/.f64 #s(literal 1 binary64) (pow.f64 (sqrt.f64 (.f64 #s(literal 2 binary64) (*.f64 (PI.f64) n))) (+.f64 k #s(literal -1 binary64)))))
	99.6%	(.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) (.f64 (pow.f64 (.f64 #s(literal 2 binary64) (.f64 (PI.f64) n)) (.f64 k #s(literal -1/2 binary64))) (sqrt.f64 (.f64 #s(literal 2 binary64) (*.f64 (PI.f64) n)))))
	50.5%	(.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) #s(approx (pow ( (* 2 (PI)) n) (/ (- 1 k) 2)) (.f64 (sqrt.f64 #s(literal 2 binary64)) (sqrt.f64 (.f64 n (PI.f64))))))
	51.0%	#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (/.f64 (.f64 (sqrt.f64 #s(literal 2 binary64)) (fma.f64 #s(literal -1/2 binary64) (.f64 (sqrt.f64 (.f64 k (.f64 k (.f64 (PI.f64) (.f64 k n))))) (log.f64 (.f64 n (.f64 (PI.f64) #s(literal 2 binary64))))) (sqrt.f64 (.f64 (PI.f64) (.f64 k n))))) k))
▶	37.7%	#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (.f64 (sqrt.f64 (/.f64 (.f64 n (PI.f64)) k)) (sqrt.f64 #s(literal 2 binary64))))
	99.1%	#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)))))

Compiler

Compiled 572 to 406 computations (29% saved)

simplify15.0ms (0.1%)

Memory

16.5MiB live, 16.5MiB allocated

Algorithm

1×	egg-herbie

Localize:

Found 20 expressions of interest:

New	Metric	Score	Program
✓	cost-diff	0	(/.f64 #s(literal 1 binary64) (pow.f64 (sqrt.f64 (.f64 #s(literal 2 binary64) (.f64 (PI.f64) n))) (+.f64 k #s(literal -1 binary64))))
✓	cost-diff	0	(sqrt.f64 k)
✓	cost-diff	0	(/.f64 #s(literal 1 binary64) (sqrt.f64 k))
✓	cost-diff	704	(.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) (/.f64 #s(literal 1 binary64) (pow.f64 (sqrt.f64 (.f64 #s(literal 2 binary64) (*.f64 (PI.f64) n))) (+.f64 k #s(literal -1 binary64)))))
✓	cost-diff	0	(pow.f64 (.f64 (.f64 #s(literal 2 binary64) (PI.f64)) n) (fma.f64 k #s(literal -1/2 binary64) #s(literal 1/2 binary64)))
✓	cost-diff	0	(sqrt.f64 k)
✓	cost-diff	0	(/.f64 #s(literal 1 binary64) (sqrt.f64 k))
✓	cost-diff	320	(.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) (pow.f64 (.f64 (*.f64 #s(literal 2 binary64) (PI.f64)) n) (fma.f64 k #s(literal -1/2 binary64) #s(literal 1/2 binary64))))
✓	cost-diff	0	(*.f64 (PI.f64) n)
✓	cost-diff	0	(.f64 #s(literal 2 binary64) (.f64 (PI.f64) n))
✓	cost-diff	0	(pow.f64 (.f64 #s(literal 2 binary64) (.f64 (PI.f64) n)) (fma.f64 k #s(literal 1/2 binary64) #s(literal 1/2 binary64)))
✓	cost-diff	0	(/.f64 (pow.f64 (.f64 #s(literal 2 binary64) (.f64 (PI.f64) n)) (fma.f64 k #s(literal 1/2 binary64) #s(literal 1/2 binary64))) (sqrt.f64 k))
✓	cost-diff	0	(/.f64 (*.f64 n (PI.f64)) k)
✓	cost-diff	0	(sqrt.f64 (/.f64 (*.f64 n (PI.f64)) k))
✓	cost-diff	0	(.f64 (sqrt.f64 (/.f64 (.f64 n (PI.f64)) k)) (sqrt.f64 #s(literal 2 binary64)))
✓	cost-diff	0	#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (.f64 (sqrt.f64 (/.f64 (.f64 n (PI.f64)) k)) (sqrt.f64 #s(literal 2 binary64))))
✓	cost-diff	0	(*.f64 (PI.f64) n)
✓	cost-diff	0	(.f64 #s(literal 2 binary64) (.f64 (PI.f64) n))
✓	cost-diff	0	(sqrt.f64 (.f64 #s(literal 2 binary64) (.f64 (PI.f64) n)))
✓	cost-diff	0	(/.f64 (sqrt.f64 (.f64 #s(literal 2 binary64) (.f64 (PI.f64) n))) (.f64 (sqrt.f64 k) (pow.f64 (.f64 #s(literal 2 binary64) (.f64 (PI.f64) n)) (.f64 k #s(literal 1/2 binary64)))))

Rules

104×	`lower-*.f32`
84×	`lower-*.f64`
68×	`lower-+.f32`
66×	`lower-+.f64`
50×	`*-commutative`

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	44	279
0	72	280
1	111	274
2	145	274
3	167	272
4	184	272
5	198	272
6	218	272
7	251	272
8	263	272
9	267	272
0	267	272

Stop Event

1×	iter limit
1×	saturated
1×	iter limit

Calls

Call 1

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

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

localize222.0ms (2%)

Memory

12.0MiB live, 167.9MiB allocated

Localize:

Found 20 expressions of interest:

New	Metric	Score	Program
✓	accuracy	99.7%	(.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) (/.f64 #s(literal 1 binary64) (pow.f64 (sqrt.f64 (.f64 #s(literal 2 binary64) (*.f64 (PI.f64) n))) (+.f64 k #s(literal -1 binary64)))))
✓	accuracy	99.6%	(/.f64 #s(literal 1 binary64) (sqrt.f64 k))
✓	accuracy	99.6%	(pow.f64 (sqrt.f64 (.f64 #s(literal 2 binary64) (.f64 (PI.f64) n))) (+.f64 k #s(literal -1 binary64)))
✓	accuracy	78.1%	(PI.f64)
✓	accuracy	99.7%	(.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) (pow.f64 (.f64 (*.f64 #s(literal 2 binary64) (PI.f64)) n) (fma.f64 k #s(literal -1/2 binary64) #s(literal 1/2 binary64))))
✓	accuracy	99.7%	(pow.f64 (.f64 (.f64 #s(literal 2 binary64) (PI.f64)) n) (fma.f64 k #s(literal -1/2 binary64) #s(literal 1/2 binary64)))
✓	accuracy	99.6%	(/.f64 #s(literal 1 binary64) (sqrt.f64 k))
✓	accuracy	78.1%	(PI.f64)
✓	accuracy	99.8%	(/.f64 (pow.f64 (.f64 #s(literal 2 binary64) (.f64 (PI.f64) n)) (fma.f64 k #s(literal 1/2 binary64) #s(literal 1/2 binary64))) (sqrt.f64 k))
✓	accuracy	99.8%	(*.f64 (PI.f64) n)
✓	accuracy	99.6%	(pow.f64 (.f64 #s(literal 2 binary64) (.f64 (PI.f64) n)) (fma.f64 k #s(literal 1/2 binary64) #s(literal 1/2 binary64)))
✓	accuracy	78.1%	(PI.f64)
✓	accuracy	99.4%	(.f64 (sqrt.f64 (/.f64 (.f64 n (PI.f64)) k)) (sqrt.f64 #s(literal 2 binary64)))
✓	accuracy	87.0%	(sqrt.f64 (/.f64 (*.f64 n (PI.f64)) k))
✓	accuracy	78.1%	(PI.f64)
✓	accuracy	73.0%	#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (.f64 (sqrt.f64 (/.f64 (.f64 n (PI.f64)) k)) (sqrt.f64 #s(literal 2 binary64))))
✓	accuracy	99.9%	(sqrt.f64 (.f64 #s(literal 2 binary64) (.f64 (PI.f64) n)))
✓	accuracy	99.8%	(/.f64 (sqrt.f64 (.f64 #s(literal 2 binary64) (.f64 (PI.f64) n))) (.f64 (sqrt.f64 k) (pow.f64 (.f64 #s(literal 2 binary64) (.f64 (PI.f64) n)) (.f64 k #s(literal 1/2 binary64)))))
✓	accuracy	99.8%	(*.f64 (PI.f64) n)
✓	accuracy	78.1%	(PI.f64)

Samples

95.0ms	198×	0	valid
46.0ms	58×	0	exit

Compiler

Compiled 277 to 41 computations (85.2% saved)

Precisions

Click to see histograms. Total time spent on operations: 87.0ms

ival-sub: 31.0ms (35.6% of total)

ival-pow: 20.0ms (23% of total)

ival-mult: 16.0ms (18.4% of total)

ival-div: 9.0ms (10.3% of total)

ival-sqrt: 6.0ms (6.9% of total)

ival-add: 3.0ms (3.4% of total)

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

exact: 1.0ms (1.1% of total)

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

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

series247.0ms (2.2%)

Memory

-33.4MiB live, 125.9MiB allocated

Counts

18 → 348

Calls

Call 1

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

Outputs
#s(alt (* (sqrt (/ (* n (PI)) k)) (/ (sqrt 2) (exp (* 1/2 (* k (+ (log n) (log (* 2 (PI))))))))) (taylor 0 n) (#s(alt (/.f64 (sqrt.f64 (.f64 #s(literal 2 binary64) (.f64 (PI.f64) n))) (.f64 (sqrt.f64 k) (pow.f64 (.f64 #s(literal 2 binary64) (.f64 (PI.f64) n)) (.f64 k #s(literal 1/2 binary64))))) (patch (/.f64 (sqrt.f64 (.f64 #s(literal 2 binary64) (.f64 (PI.f64) n))) (.f64 (sqrt.f64 k) (pow.f64 (.f64 #s(literal 2 binary64) (.f64 (PI.f64) n)) (.f64 k #s(literal 1/2 binary64))))) #<representation binary64>) () ())) ())
#s(alt (* (sqrt (/ (* n (PI)) k)) (/ (sqrt 2) (exp (* 1/2 (* k (+ (log n) (log (* 2 (PI))))))))) (taylor 0 n) (#s(alt (/.f64 (sqrt.f64 (.f64 #s(literal 2 binary64) (.f64 (PI.f64) n))) (.f64 (sqrt.f64 k) (pow.f64 (.f64 #s(literal 2 binary64) (.f64 (PI.f64) n)) (.f64 k #s(literal 1/2 binary64))))) (patch (/.f64 (sqrt.f64 (.f64 #s(literal 2 binary64) (.f64 (PI.f64) n))) (.f64 (sqrt.f64 k) (pow.f64 (.f64 #s(literal 2 binary64) (.f64 (PI.f64) n)) (.f64 k #s(literal 1/2 binary64))))) #<representation binary64>) () ())) ())
#s(alt (* (sqrt (/ (* n (PI)) k)) (/ (sqrt 2) (exp (* 1/2 (* k (+ (log n) (log (* 2 (PI))))))))) (taylor 0 n) (#s(alt (/.f64 (sqrt.f64 (.f64 #s(literal 2 binary64) (.f64 (PI.f64) n))) (.f64 (sqrt.f64 k) (pow.f64 (.f64 #s(literal 2 binary64) (.f64 (PI.f64) n)) (.f64 k #s(literal 1/2 binary64))))) (patch (/.f64 (sqrt.f64 (.f64 #s(literal 2 binary64) (.f64 (PI.f64) n))) (.f64 (sqrt.f64 k) (pow.f64 (.f64 #s(literal 2 binary64) (.f64 (PI.f64) n)) (.f64 k #s(literal 1/2 binary64))))) #<representation binary64>) () ())) ())
#s(alt (* (sqrt (/ (* n (PI)) k)) (/ (sqrt 2) (exp (* 1/2 (* k (+ (log n) (log (* 2 (PI))))))))) (taylor 0 n) (#s(alt (/.f64 (sqrt.f64 (.f64 #s(literal 2 binary64) (.f64 (PI.f64) n))) (.f64 (sqrt.f64 k) (pow.f64 (.f64 #s(literal 2 binary64) (.f64 (PI.f64) n)) (.f64 k #s(literal 1/2 binary64))))) (patch (/.f64 (sqrt.f64 (.f64 #s(literal 2 binary64) (.f64 (PI.f64) n))) (.f64 (sqrt.f64 k) (pow.f64 (.f64 #s(literal 2 binary64) (.f64 (PI.f64) n)) (.f64 k #s(literal 1/2 binary64))))) #<representation binary64>) () ())) ())
#s(alt (* (sqrt (/ (* n (PI)) k)) (/ (sqrt 2) (exp (* 1/2 (* k (+ (log (* 2 (PI))) (* -1 (log (/ 1 n))))))))) (taylor inf n) (#s(alt (/.f64 (sqrt.f64 (.f64 #s(literal 2 binary64) (.f64 (PI.f64) n))) (.f64 (sqrt.f64 k) (pow.f64 (.f64 #s(literal 2 binary64) (.f64 (PI.f64) n)) (.f64 k #s(literal 1/2 binary64))))) (patch (/.f64 (sqrt.f64 (.f64 #s(literal 2 binary64) (.f64 (PI.f64) n))) (.f64 (sqrt.f64 k) (pow.f64 (.f64 #s(literal 2 binary64) (.f64 (PI.f64) n)) (.f64 k #s(literal 1/2 binary64))))) #<representation binary64>) () ())) ())
#s(alt (* (sqrt (/ (* n (PI)) k)) (/ (sqrt 2) (exp (* 1/2 (* k (+ (log (* 2 (PI))) (* -1 (log (/ 1 n))))))))) (taylor inf n) (#s(alt (/.f64 (sqrt.f64 (.f64 #s(literal 2 binary64) (.f64 (PI.f64) n))) (.f64 (sqrt.f64 k) (pow.f64 (.f64 #s(literal 2 binary64) (.f64 (PI.f64) n)) (.f64 k #s(literal 1/2 binary64))))) (patch (/.f64 (sqrt.f64 (.f64 #s(literal 2 binary64) (.f64 (PI.f64) n))) (.f64 (sqrt.f64 k) (pow.f64 (.f64 #s(literal 2 binary64) (.f64 (PI.f64) n)) (.f64 k #s(literal 1/2 binary64))))) #<representation binary64>) () ())) ())
#s(alt (* (sqrt (/ (* n (PI)) k)) (/ (sqrt 2) (exp (* 1/2 (* k (+ (log (* 2 (PI))) (* -1 (log (/ 1 n))))))))) (taylor inf n) (#s(alt (/.f64 (sqrt.f64 (.f64 #s(literal 2 binary64) (.f64 (PI.f64) n))) (.f64 (sqrt.f64 k) (pow.f64 (.f64 #s(literal 2 binary64) (.f64 (PI.f64) n)) (.f64 k #s(literal 1/2 binary64))))) (patch (/.f64 (sqrt.f64 (.f64 #s(literal 2 binary64) (.f64 (PI.f64) n))) (.f64 (sqrt.f64 k) (pow.f64 (.f64 #s(literal 2 binary64) (.f64 (PI.f64) n)) (.f64 k #s(literal 1/2 binary64))))) #<representation binary64>) () ())) ())
#s(alt (* (sqrt (/ (* n (PI)) k)) (/ (sqrt 2) (exp (* 1/2 (* k (+ (log (* 2 (PI))) (* -1 (log (/ 1 n))))))))) (taylor inf n) (#s(alt (/.f64 (sqrt.f64 (.f64 #s(literal 2 binary64) (.f64 (PI.f64) n))) (.f64 (sqrt.f64 k) (pow.f64 (.f64 #s(literal 2 binary64) (.f64 (PI.f64) n)) (.f64 k #s(literal 1/2 binary64))))) (patch (/.f64 (sqrt.f64 (.f64 #s(literal 2 binary64) (.f64 (PI.f64) n))) (.f64 (sqrt.f64 k) (pow.f64 (.f64 #s(literal 2 binary64) (.f64 (PI.f64) n)) (.f64 k #s(literal 1/2 binary64))))) #<representation binary64>) () ())) ())
#s(alt (* -1 (* (sqrt (/ (* n (PI)) k)) (/ (* (sqrt -2) (sqrt -1)) (exp (* 1/2 (* k (+ (log (* -2 (PI))) (* -1 (log (/ -1 n)))))))))) (taylor -inf n) (#s(alt (/.f64 (sqrt.f64 (.f64 #s(literal 2 binary64) (.f64 (PI.f64) n))) (.f64 (sqrt.f64 k) (pow.f64 (.f64 #s(literal 2 binary64) (.f64 (PI.f64) n)) (.f64 k #s(literal 1/2 binary64))))) (patch (/.f64 (sqrt.f64 (.f64 #s(literal 2 binary64) (.f64 (PI.f64) n))) (.f64 (sqrt.f64 k) (pow.f64 (.f64 #s(literal 2 binary64) (.f64 (PI.f64) n)) (.f64 k #s(literal 1/2 binary64))))) #<representation binary64>) () ())) ())
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#s(alt (+ (* k (- (* -1 (* k (+ (* -1 (* (sqrt (* n (PI))) (* (pow (log (* (sqrt (* n (PI))) (sqrt 2))) 2) (sqrt 2)))) (* 1/2 (* (sqrt (* n (PI))) (* (pow (log (* (sqrt (* n (PI))) (sqrt 2))) 2) (sqrt 2))))))) (* (sqrt (* n (PI))) (* (log (* (sqrt (* n (PI))) (sqrt 2))) (sqrt 2))))) (* (sqrt (* n (PI))) (sqrt 2))) (taylor 0 k) (#s(alt (/.f64 #s(literal 1 binary64) (pow.f64 (sqrt.f64 (.f64 #s(literal 2 binary64) (.f64 (PI.f64) n))) (+.f64 k #s(literal -1 binary64)))) (patch (/.f64 #s(literal 1 binary64) (pow.f64 (sqrt.f64 (.f64 #s(literal 2 binary64) (.f64 (PI.f64) n))) (+.f64 k #s(literal -1 binary64)))) #<representation binary64>) () ())) ())
#s(alt (+ (* k (- (* k (- (* -1 (* k (+ (* -1 (* (log (* (sqrt (* n (PI))) (sqrt 2))) (+ (* -1 (* (sqrt (* n (PI))) (* (pow (log (* (sqrt (* n (PI))) (sqrt 2))) 2) (sqrt 2)))) (* 1/2 (* (sqrt (* n (PI))) (* (pow (log (* (sqrt (* n (PI))) (sqrt 2))) 2) (sqrt 2))))))) (+ (* -1/2 (* (sqrt (* n (PI))) (* (pow (log (* (sqrt (* n (PI))) (sqrt 2))) 3) (sqrt 2)))) (* 1/6 (* (sqrt (* n (PI))) (* (pow (log (* (sqrt (* n (PI))) (sqrt 2))) 3) (sqrt 2)))))))) (+ (* -1 (* (sqrt (* n (PI))) (* (pow (log (* (sqrt (* n (PI))) (sqrt 2))) 2) (sqrt 2)))) (* 1/2 (* (sqrt (* n (PI))) (* (pow (log (* (sqrt (* n (PI))) (sqrt 2))) 2) (sqrt 2))))))) (* (sqrt (* n (PI))) (* (log (* (sqrt (* n (PI))) (sqrt 2))) (sqrt 2))))) (* (sqrt (* n (PI))) (sqrt 2))) (taylor 0 k) (#s(alt (/.f64 #s(literal 1 binary64) (pow.f64 (sqrt.f64 (.f64 #s(literal 2 binary64) (.f64 (PI.f64) n))) (+.f64 k #s(literal -1 binary64)))) (patch (/.f64 #s(literal 1 binary64) (pow.f64 (sqrt.f64 (.f64 #s(literal 2 binary64) (.f64 (PI.f64) n))) (+.f64 k #s(literal -1 binary64)))) #<representation binary64>) () ())) ())
#s(alt (/ 1 (exp (* (log (* (sqrt (* n (PI))) (sqrt 2))) (- k 1)))) (taylor inf k) (#s(alt (/.f64 #s(literal 1 binary64) (pow.f64 (sqrt.f64 (.f64 #s(literal 2 binary64) (.f64 (PI.f64) n))) (+.f64 k #s(literal -1 binary64)))) (patch (/.f64 #s(literal 1 binary64) (pow.f64 (sqrt.f64 (.f64 #s(literal 2 binary64) (.f64 (PI.f64) n))) (+.f64 k #s(literal -1 binary64)))) #<representation binary64>) () ())) ())
#s(alt (/ 1 (exp (* (log (* (sqrt (* n (PI))) (sqrt 2))) (- k 1)))) (taylor inf k) (#s(alt (/.f64 #s(literal 1 binary64) (pow.f64 (sqrt.f64 (.f64 #s(literal 2 binary64) (.f64 (PI.f64) n))) (+.f64 k #s(literal -1 binary64)))) (patch (/.f64 #s(literal 1 binary64) (pow.f64 (sqrt.f64 (.f64 #s(literal 2 binary64) (.f64 (PI.f64) n))) (+.f64 k #s(literal -1 binary64)))) #<representation binary64>) () ())) ())
#s(alt (/ 1 (exp (* (log (* (sqrt (* n (PI))) (sqrt 2))) (- k 1)))) (taylor inf k) (#s(alt (/.f64 #s(literal 1 binary64) (pow.f64 (sqrt.f64 (.f64 #s(literal 2 binary64) (.f64 (PI.f64) n))) (+.f64 k #s(literal -1 binary64)))) (patch (/.f64 #s(literal 1 binary64) (pow.f64 (sqrt.f64 (.f64 #s(literal 2 binary64) (.f64 (PI.f64) n))) (+.f64 k #s(literal -1 binary64)))) #<representation binary64>) () ())) ())
#s(alt (/ 1 (exp (* (log (* (sqrt (* n (PI))) (sqrt 2))) (- k 1)))) (taylor inf k) (#s(alt (/.f64 #s(literal 1 binary64) (pow.f64 (sqrt.f64 (.f64 #s(literal 2 binary64) (.f64 (PI.f64) n))) (+.f64 k #s(literal -1 binary64)))) (patch (/.f64 #s(literal 1 binary64) (pow.f64 (sqrt.f64 (.f64 #s(literal 2 binary64) (.f64 (PI.f64) n))) (+.f64 k #s(literal -1 binary64)))) #<representation binary64>) () ())) ())
#s(alt (/ 1 (exp (* -1 (* (log (* (sqrt (* n (PI))) (sqrt 2))) (+ 1 (* -1 k)))))) (taylor -inf k) (#s(alt (/.f64 #s(literal 1 binary64) (pow.f64 (sqrt.f64 (.f64 #s(literal 2 binary64) (.f64 (PI.f64) n))) (+.f64 k #s(literal -1 binary64)))) (patch (/.f64 #s(literal 1 binary64) (pow.f64 (sqrt.f64 (.f64 #s(literal 2 binary64) (.f64 (PI.f64) n))) (+.f64 k #s(literal -1 binary64)))) #<representation binary64>) () ())) ())
#s(alt (/ 1 (exp (* -1 (* (log (* (sqrt (* n (PI))) (sqrt 2))) (+ 1 (* -1 k)))))) (taylor -inf k) (#s(alt (/.f64 #s(literal 1 binary64) (pow.f64 (sqrt.f64 (.f64 #s(literal 2 binary64) (.f64 (PI.f64) n))) (+.f64 k #s(literal -1 binary64)))) (patch (/.f64 #s(literal 1 binary64) (pow.f64 (sqrt.f64 (.f64 #s(literal 2 binary64) (.f64 (PI.f64) n))) (+.f64 k #s(literal -1 binary64)))) #<representation binary64>) () ())) ())
#s(alt (/ 1 (exp (* -1 (* (log (* (sqrt (* n (PI))) (sqrt 2))) (+ 1 (* -1 k)))))) (taylor -inf k) (#s(alt (/.f64 #s(literal 1 binary64) (pow.f64 (sqrt.f64 (.f64 #s(literal 2 binary64) (.f64 (PI.f64) n))) (+.f64 k #s(literal -1 binary64)))) (patch (/.f64 #s(literal 1 binary64) (pow.f64 (sqrt.f64 (.f64 #s(literal 2 binary64) (.f64 (PI.f64) n))) (+.f64 k #s(literal -1 binary64)))) #<representation binary64>) () ())) ())
#s(alt (/ 1 (exp (* -1 (* (log (* (sqrt (* n (PI))) (sqrt 2))) (+ 1 (* -1 k)))))) (taylor -inf k) (#s(alt (/.f64 #s(literal 1 binary64) (pow.f64 (sqrt.f64 (.f64 #s(literal 2 binary64) (.f64 (PI.f64) n))) (+.f64 k #s(literal -1 binary64)))) (patch (/.f64 #s(literal 1 binary64) (pow.f64 (sqrt.f64 (.f64 #s(literal 2 binary64) (.f64 (PI.f64) n))) (+.f64 k #s(literal -1 binary64)))) #<representation binary64>) () ())) ())
#s(alt (exp (* (log (* (sqrt (* n (PI))) (sqrt 2))) (- k 1))) (taylor 0 n) (#s(alt (pow.f64 (sqrt.f64 (.f64 #s(literal 2 binary64) (.f64 (PI.f64) n))) (+.f64 k #s(literal -1 binary64))) (patch (pow.f64 (sqrt.f64 (.f64 #s(literal 2 binary64) (.f64 (PI.f64) n))) (+.f64 k #s(literal -1 binary64))) #<representation binary64>) () ())) ())
#s(alt (exp (* (log (* (sqrt (* n (PI))) (sqrt 2))) (- k 1))) (taylor 0 n) (#s(alt (pow.f64 (sqrt.f64 (.f64 #s(literal 2 binary64) (.f64 (PI.f64) n))) (+.f64 k #s(literal -1 binary64))) (patch (pow.f64 (sqrt.f64 (.f64 #s(literal 2 binary64) (.f64 (PI.f64) n))) (+.f64 k #s(literal -1 binary64))) #<representation binary64>) () ())) ())
#s(alt (exp (* (log (* (sqrt (* n (PI))) (sqrt 2))) (- k 1))) (taylor 0 n) (#s(alt (pow.f64 (sqrt.f64 (.f64 #s(literal 2 binary64) (.f64 (PI.f64) n))) (+.f64 k #s(literal -1 binary64))) (patch (pow.f64 (sqrt.f64 (.f64 #s(literal 2 binary64) (.f64 (PI.f64) n))) (+.f64 k #s(literal -1 binary64))) #<representation binary64>) () ())) ())
#s(alt (exp (* (log (* (sqrt (* n (PI))) (sqrt 2))) (- k 1))) (taylor 0 n) (#s(alt (pow.f64 (sqrt.f64 (.f64 #s(literal 2 binary64) (.f64 (PI.f64) n))) (+.f64 k #s(literal -1 binary64))) (patch (pow.f64 (sqrt.f64 (.f64 #s(literal 2 binary64) (.f64 (PI.f64) n))) (+.f64 k #s(literal -1 binary64))) #<representation binary64>) () ())) ())
#s(alt (exp (* (+ (log (* (sqrt (/ (PI) n)) (sqrt 2))) (* -1 (log (/ 1 n)))) (- k 1))) (taylor inf n) (#s(alt (pow.f64 (sqrt.f64 (.f64 #s(literal 2 binary64) (.f64 (PI.f64) n))) (+.f64 k #s(literal -1 binary64))) (patch (pow.f64 (sqrt.f64 (.f64 #s(literal 2 binary64) (.f64 (PI.f64) n))) (+.f64 k #s(literal -1 binary64))) #<representation binary64>) () ())) ())
#s(alt (exp (* (+ (log (* (sqrt (/ (PI) n)) (sqrt 2))) (* -1 (log (/ 1 n)))) (- k 1))) (taylor inf n) (#s(alt (pow.f64 (sqrt.f64 (.f64 #s(literal 2 binary64) (.f64 (PI.f64) n))) (+.f64 k #s(literal -1 binary64))) (patch (pow.f64 (sqrt.f64 (.f64 #s(literal 2 binary64) (.f64 (PI.f64) n))) (+.f64 k #s(literal -1 binary64))) #<representation binary64>) () ())) ())
#s(alt (exp (* (+ (log (* (sqrt (/ (PI) n)) (sqrt 2))) (* -1 (log (/ 1 n)))) (- k 1))) (taylor inf n) (#s(alt (pow.f64 (sqrt.f64 (.f64 #s(literal 2 binary64) (.f64 (PI.f64) n))) (+.f64 k #s(literal -1 binary64))) (patch (pow.f64 (sqrt.f64 (.f64 #s(literal 2 binary64) (.f64 (PI.f64) n))) (+.f64 k #s(literal -1 binary64))) #<representation binary64>) () ())) ())
#s(alt (exp (* (+ (log (* (sqrt (/ (PI) n)) (sqrt 2))) (* -1 (log (/ 1 n)))) (- k 1))) (taylor inf n) (#s(alt (pow.f64 (sqrt.f64 (.f64 #s(literal 2 binary64) (.f64 (PI.f64) n))) (+.f64 k #s(literal -1 binary64))) (patch (pow.f64 (sqrt.f64 (.f64 #s(literal 2 binary64) (.f64 (PI.f64) n))) (+.f64 k #s(literal -1 binary64))) #<representation binary64>) () ())) ())
#s(alt (exp (* (+ (log (* (sqrt (/ (PI) n)) (* (sqrt -2) (sqrt -1)))) (* -1 (log (/ -1 n)))) (- k 1))) (taylor -inf n) (#s(alt (pow.f64 (sqrt.f64 (.f64 #s(literal 2 binary64) (.f64 (PI.f64) n))) (+.f64 k #s(literal -1 binary64))) (patch (pow.f64 (sqrt.f64 (.f64 #s(literal 2 binary64) (.f64 (PI.f64) n))) (+.f64 k #s(literal -1 binary64))) #<representation binary64>) () ())) ())
#s(alt (exp (* (+ (log (* (sqrt (/ (PI) n)) (* (sqrt -2) (sqrt -1)))) (* -1 (log (/ -1 n)))) (- k 1))) (taylor -inf n) (#s(alt (pow.f64 (sqrt.f64 (.f64 #s(literal 2 binary64) (.f64 (PI.f64) n))) (+.f64 k #s(literal -1 binary64))) (patch (pow.f64 (sqrt.f64 (.f64 #s(literal 2 binary64) (.f64 (PI.f64) n))) (+.f64 k #s(literal -1 binary64))) #<representation binary64>) () ())) ())
#s(alt (exp (* (+ (log (* (sqrt (/ (PI) n)) (* (sqrt -2) (sqrt -1)))) (* -1 (log (/ -1 n)))) (- k 1))) (taylor -inf n) (#s(alt (pow.f64 (sqrt.f64 (.f64 #s(literal 2 binary64) (.f64 (PI.f64) n))) (+.f64 k #s(literal -1 binary64))) (patch (pow.f64 (sqrt.f64 (.f64 #s(literal 2 binary64) (.f64 (PI.f64) n))) (+.f64 k #s(literal -1 binary64))) #<representation binary64>) () ())) ())
#s(alt (exp (* (+ (log (* (sqrt (/ (PI) n)) (* (sqrt -2) (sqrt -1)))) (* -1 (log (/ -1 n)))) (- k 1))) (taylor -inf n) (#s(alt (pow.f64 (sqrt.f64 (.f64 #s(literal 2 binary64) (.f64 (PI.f64) n))) (+.f64 k #s(literal -1 binary64))) (patch (pow.f64 (sqrt.f64 (.f64 #s(literal 2 binary64) (.f64 (PI.f64) n))) (+.f64 k #s(literal -1 binary64))) #<representation binary64>) () ())) ())
#s(alt (* (sqrt (/ 1 (* n (PI)))) (/ 1 (sqrt 2))) (taylor 0 k) (#s(alt (pow.f64 (sqrt.f64 (.f64 #s(literal 2 binary64) (.f64 (PI.f64) n))) (+.f64 k #s(literal -1 binary64))) (patch (pow.f64 (sqrt.f64 (.f64 #s(literal 2 binary64) (.f64 (PI.f64) n))) (+.f64 k #s(literal -1 binary64))) #<representation binary64>) () ())) ())
#s(alt (+ (* (sqrt (/ 1 (* n (PI)))) (/ 1 (sqrt 2))) (* (/ (* k (log (* (sqrt (* n (PI))) (sqrt 2)))) (sqrt 2)) (sqrt (/ 1 (* n (PI)))))) (taylor 0 k) (#s(alt (pow.f64 (sqrt.f64 (.f64 #s(literal 2 binary64) (.f64 (PI.f64) n))) (+.f64 k #s(literal -1 binary64))) (patch (pow.f64 (sqrt.f64 (.f64 #s(literal 2 binary64) (.f64 (PI.f64) n))) (+.f64 k #s(literal -1 binary64))) #<representation binary64>) () ())) ())
#s(alt (+ (* k (+ (* 1/2 (* (/ (* k (pow (log (* (sqrt (* n (PI))) (sqrt 2))) 2)) (sqrt 2)) (sqrt (/ 1 (* n (PI)))))) (* (sqrt (/ 1 (* n (PI)))) (/ (log (* (sqrt (* n (PI))) (sqrt 2))) (sqrt 2))))) (* (sqrt (/ 1 (* n (PI)))) (/ 1 (sqrt 2)))) (taylor 0 k) (#s(alt (pow.f64 (sqrt.f64 (.f64 #s(literal 2 binary64) (.f64 (PI.f64) n))) (+.f64 k #s(literal -1 binary64))) (patch (pow.f64 (sqrt.f64 (.f64 #s(literal 2 binary64) (.f64 (PI.f64) n))) (+.f64 k #s(literal -1 binary64))) #<representation binary64>) () ())) ())
#s(alt (+ (* k (+ (* k (+ (* 1/6 (* (/ (* k (pow (log (* (sqrt (* n (PI))) (sqrt 2))) 3)) (sqrt 2)) (sqrt (/ 1 (* n (PI)))))) (* 1/2 (* (sqrt (/ 1 (* n (PI)))) (/ (pow (log (* (sqrt (* n (PI))) (sqrt 2))) 2) (sqrt 2)))))) (* (sqrt (/ 1 (* n (PI)))) (/ (log (* (sqrt (* n (PI))) (sqrt 2))) (sqrt 2))))) (* (sqrt (/ 1 (* n (PI)))) (/ 1 (sqrt 2)))) (taylor 0 k) (#s(alt (pow.f64 (sqrt.f64 (.f64 #s(literal 2 binary64) (.f64 (PI.f64) n))) (+.f64 k #s(literal -1 binary64))) (patch (pow.f64 (sqrt.f64 (.f64 #s(literal 2 binary64) (.f64 (PI.f64) n))) (+.f64 k #s(literal -1 binary64))) #<representation binary64>) () ())) ())
#s(alt (exp (* (log (* (sqrt (* n (PI))) (sqrt 2))) (- k 1))) (taylor inf k) (#s(alt (pow.f64 (sqrt.f64 (.f64 #s(literal 2 binary64) (.f64 (PI.f64) n))) (+.f64 k #s(literal -1 binary64))) (patch (pow.f64 (sqrt.f64 (.f64 #s(literal 2 binary64) (.f64 (PI.f64) n))) (+.f64 k #s(literal -1 binary64))) #<representation binary64>) () ())) ())
#s(alt (exp (* (log (* (sqrt (* n (PI))) (sqrt 2))) (- k 1))) (taylor inf k) (#s(alt (pow.f64 (sqrt.f64 (.f64 #s(literal 2 binary64) (.f64 (PI.f64) n))) (+.f64 k #s(literal -1 binary64))) (patch (pow.f64 (sqrt.f64 (.f64 #s(literal 2 binary64) (.f64 (PI.f64) n))) (+.f64 k #s(literal -1 binary64))) #<representation binary64>) () ())) ())
#s(alt (exp (* (log (* (sqrt (* n (PI))) (sqrt 2))) (- k 1))) (taylor inf k) (#s(alt (pow.f64 (sqrt.f64 (.f64 #s(literal 2 binary64) (.f64 (PI.f64) n))) (+.f64 k #s(literal -1 binary64))) (patch (pow.f64 (sqrt.f64 (.f64 #s(literal 2 binary64) (.f64 (PI.f64) n))) (+.f64 k #s(literal -1 binary64))) #<representation binary64>) () ())) ())
#s(alt (exp (* (log (* (sqrt (* n (PI))) (sqrt 2))) (- k 1))) (taylor inf k) (#s(alt (pow.f64 (sqrt.f64 (.f64 #s(literal 2 binary64) (.f64 (PI.f64) n))) (+.f64 k #s(literal -1 binary64))) (patch (pow.f64 (sqrt.f64 (.f64 #s(literal 2 binary64) (.f64 (PI.f64) n))) (+.f64 k #s(literal -1 binary64))) #<representation binary64>) () ())) ())
#s(alt (exp (* -1 (* (log (* (sqrt (* n (PI))) (sqrt 2))) (+ 1 (* -1 k))))) (taylor -inf k) (#s(alt (pow.f64 (sqrt.f64 (.f64 #s(literal 2 binary64) (.f64 (PI.f64) n))) (+.f64 k #s(literal -1 binary64))) (patch (pow.f64 (sqrt.f64 (.f64 #s(literal 2 binary64) (.f64 (PI.f64) n))) (+.f64 k #s(literal -1 binary64))) #<representation binary64>) () ())) ())
#s(alt (exp (* -1 (* (log (* (sqrt (* n (PI))) (sqrt 2))) (+ 1 (* -1 k))))) (taylor -inf k) (#s(alt (pow.f64 (sqrt.f64 (.f64 #s(literal 2 binary64) (.f64 (PI.f64) n))) (+.f64 k #s(literal -1 binary64))) (patch (pow.f64 (sqrt.f64 (.f64 #s(literal 2 binary64) (.f64 (PI.f64) n))) (+.f64 k #s(literal -1 binary64))) #<representation binary64>) () ())) ())
#s(alt (exp (* -1 (* (log (* (sqrt (* n (PI))) (sqrt 2))) (+ 1 (* -1 k))))) (taylor -inf k) (#s(alt (pow.f64 (sqrt.f64 (.f64 #s(literal 2 binary64) (.f64 (PI.f64) n))) (+.f64 k #s(literal -1 binary64))) (patch (pow.f64 (sqrt.f64 (.f64 #s(literal 2 binary64) (.f64 (PI.f64) n))) (+.f64 k #s(literal -1 binary64))) #<representation binary64>) () ())) ())
#s(alt (exp (* -1 (* (log (* (sqrt (* n (PI))) (sqrt 2))) (+ 1 (* -1 k))))) (taylor -inf k) (#s(alt (pow.f64 (sqrt.f64 (.f64 #s(literal 2 binary64) (.f64 (PI.f64) n))) (+.f64 k #s(literal -1 binary64))) (patch (pow.f64 (sqrt.f64 (.f64 #s(literal 2 binary64) (.f64 (PI.f64) n))) (+.f64 k #s(literal -1 binary64))) #<representation binary64>) () ())) ())

Calls

87 calls:

Time	Variable		Point	Expression
64.0ms	n	@	0	(* (/ 1 (sqrt k)) (/ 1 (pow (sqrt (* 2 (* (PI) n))) (+ k -1))))
53.0ms	n	@	inf	(* (/ 1 (sqrt k)) (/ 1 (pow (sqrt (* 2 (* (PI) n))) (+ k -1))))
39.0ms	n	@	0	(/ (sqrt (* 2 (* (PI) n))) (* (sqrt k) (pow (* 2 (* (PI) n)) (* k 1/2))))
17.0ms	n	@	-inf	(* (/ 1 (sqrt k)) (/ 1 (pow (sqrt (* 2 (* (PI) n))) (+ k -1))))
2.0ms	k	@	inf	(/ (sqrt (* 2 (* (PI) n))) (* (sqrt k) (pow (* 2 (* (PI) n)) (* k 1/2))))

simplify539.0ms (4.9%)

Memory

37.7MiB live, 631.5MiB allocated

Algorithm

1×	egg-herbie

Rules

14 344×	`lower-fma.f64`
14 344×	`lower-fma.f32`
6 952×	`lower-*.f64`
6 952×	`lower-*.f32`
3 936×	`lower-+.f64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	354	5570
1	1128	5356
2	4031	5027
0	8529	4938

Stop Event

1×	iter limit
1×	node limit

Counts

348 → 348

Calls

Call 1

Inputs
(* (sqrt (/ (* n (PI)) k)) (/ (sqrt 2) (exp (* 1/2 (* k (+ (log n) (log (* 2 (PI)))))))))
(* (sqrt (/ (* n (PI)) k)) (/ (sqrt 2) (exp (* 1/2 (* k (+ (log n) (log (* 2 (PI)))))))))
(* (sqrt (/ (* n (PI)) k)) (/ (sqrt 2) (exp (* 1/2 (* k (+ (log n) (log (* 2 (PI)))))))))
(* (sqrt (/ (* n (PI)) k)) (/ (sqrt 2) (exp (* 1/2 (* k (+ (log n) (log (* 2 (PI)))))))))
(* (sqrt (/ (* n (PI)) k)) (/ (sqrt 2) (exp (* 1/2 (* k (+ (log (* 2 (PI))) (* -1 (log (/ 1 n)))))))))
(* (sqrt (/ (* n (PI)) k)) (/ (sqrt 2) (exp (* 1/2 (* k (+ (log (* 2 (PI))) (* -1 (log (/ 1 n)))))))))
(* (sqrt (/ (* n (PI)) k)) (/ (sqrt 2) (exp (* 1/2 (* k (+ (log (* 2 (PI))) (* -1 (log (/ 1 n)))))))))
(* (sqrt (/ (* n (PI)) k)) (/ (sqrt 2) (exp (* 1/2 (* k (+ (log (* 2 (PI))) (* -1 (log (/ 1 n)))))))))
(* -1 (* (sqrt (/ (* n (PI)) k)) (/ (* (sqrt -2) (sqrt -1)) (exp (* 1/2 (* k (+ (log (* -2 (PI))) (* -1 (log (/ -1 n))))))))))
(* -1 (* (sqrt (/ (* n (PI)) k)) (/ (* (sqrt -2) (sqrt -1)) (exp (* 1/2 (* k (+ (log (* -2 (PI))) (* -1 (log (/ -1 n))))))))))
(* -1 (* (sqrt (/ (* n (PI)) k)) (/ (* (sqrt -2) (sqrt -1)) (exp (* 1/2 (* k (+ (log (* -2 (PI))) (* -1 (log (/ -1 n))))))))))
(* -1 (* (sqrt (/ (* n (PI)) k)) (/ (* (sqrt -2) (sqrt -1)) (exp (* 1/2 (* k (+ (log (* -2 (PI))) (* -1 (log (/ -1 n))))))))))
(* (sqrt (/ (* n (PI)) k)) (sqrt 2))
(/ (+ (* -1/2 (* (sqrt (* (pow k 3) (* n (PI)))) (* (log (* 2 (* n (PI)))) (sqrt 2)))) (* (sqrt (* k (* n (PI)))) (sqrt 2))) k)
(/ (+ (* k (+ (* -1 (* (sqrt (* (pow k 3) (* n (PI)))) (+ (* -1/4 (* (pow (log (* 2 (* n (PI)))) 2) (sqrt 2))) (* 1/8 (* (pow (log (* 2 (* n (PI)))) 2) (sqrt 2)))))) (* -1/2 (* (sqrt (* k (* n (PI)))) (* (log (* 2 (* n (PI)))) (sqrt 2)))))) (* (sqrt (* k (* n (PI)))) (sqrt 2))) k)
(/ (+ (* k (+ (* -1/2 (* (sqrt (* k (* n (PI)))) (* (log (* 2 (* n (PI)))) (sqrt 2)))) (* k (+ (* -1 (* (sqrt (* k (* n (PI)))) (+ (* -1/4 (* (pow (log (* 2 (* n (PI)))) 2) (sqrt 2))) (* 1/8 (* (pow (log (* 2 (* n (PI)))) 2) (sqrt 2)))))) (* -1 (* (sqrt (* (pow k 3) (* n (PI)))) (+ (* -1/2 (* (log (* 2 (* n (PI)))) (+ (* -1/4 (* (pow (log (* 2 (* n (PI)))) 2) (sqrt 2))) (* 1/8 (* (pow (log (* 2 (* n (PI)))) 2) (sqrt 2)))))) (+ (* -1/16 (* (pow (log (* 2 (* n (PI)))) 3) (sqrt 2))) (* 1/48 (* (pow (log (* 2 (* n (PI)))) 3) (sqrt 2))))))))))) (* (sqrt (* k (* n (PI)))) (sqrt 2))) k)
(* (sqrt (/ (* n (PI)) k)) (/ (sqrt 2) (exp (* 1/2 (* k (log (* 2 (* n (PI)))))))))
(* (sqrt (/ (* n (PI)) k)) (/ (sqrt 2) (exp (* 1/2 (* k (log (* 2 (* n (PI)))))))))
(* (sqrt (/ (* n (PI)) k)) (/ (sqrt 2) (exp (* 1/2 (* k (log (* 2 (* n (PI)))))))))
(* (sqrt (/ (* n (PI)) k)) (/ (sqrt 2) (exp (* 1/2 (* k (log (* 2 (* n (PI)))))))))
(* (sqrt (/ (* n (PI)) k)) (/ (sqrt 2) (exp (* 1/2 (* k (log (* 2 (* n (PI)))))))))
(* (sqrt (/ (* n (PI)) k)) (/ (sqrt 2) (exp (* 1/2 (* k (log (* 2 (* n (PI)))))))))
(* (sqrt (/ (* n (PI)) k)) (/ (sqrt 2) (exp (* 1/2 (* k (log (* 2 (* n (PI)))))))))
(* (sqrt (/ (* n (PI)) k)) (/ (sqrt 2) (exp (* 1/2 (* k (log (* 2 (* n (PI)))))))))
(* (sqrt (* n (PI))) (sqrt 2))
(* (sqrt (* n (PI))) (sqrt 2))
(* (sqrt (* n (PI))) (sqrt 2))
(* (sqrt (* n (PI))) (sqrt 2))
(* (sqrt (* n (PI))) (sqrt 2))
(* (sqrt (* n (PI))) (sqrt 2))
(* (sqrt (* n (PI))) (sqrt 2))
(* (sqrt (* n (PI))) (sqrt 2))
(* -1 (* (sqrt (* n (PI))) (* (sqrt -2) (sqrt -1))))
(* -1 (* (sqrt (* n (PI))) (* (sqrt -2) (sqrt -1))))
(* -1 (* (sqrt (* n (PI))) (* (sqrt -2) (sqrt -1))))
(* -1 (* (sqrt (* n (PI))) (* (sqrt -2) (sqrt -1))))
(* 2 (* n (PI)))
(* 2 (* n (PI)))
(* 2 (* n (PI)))
(* 2 (* n (PI)))
(* 2 (* n (PI)))
(* 2 (* n (PI)))
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(+ (* k (- (* k (- (* -1 (* k (+ (* -1 (* (log (* (sqrt (* n (PI))) (sqrt 2))) (+ (* -1 (* (sqrt (* n (PI))) (* (pow (log (* (sqrt (* n (PI))) (sqrt 2))) 2) (sqrt 2)))) (* 1/2 (* (sqrt (* n (PI))) (* (pow (log (* (sqrt (* n (PI))) (sqrt 2))) 2) (sqrt 2))))))) (+ (* -1/2 (* (sqrt (* n (PI))) (* (pow (log (* (sqrt (* n (PI))) (sqrt 2))) 3) (sqrt 2)))) (* 1/6 (* (sqrt (* n (PI))) (* (pow (log (* (sqrt (* n (PI))) (sqrt 2))) 3) (sqrt 2)))))))) (+ (* -1 (* (sqrt (* n (PI))) (* (pow (log (* (sqrt (* n (PI))) (sqrt 2))) 2) (sqrt 2)))) (* 1/2 (* (sqrt (* n (PI))) (* (pow (log (* (sqrt (* n (PI))) (sqrt 2))) 2) (sqrt 2))))))) (* (sqrt (* n (PI))) (* (log (* (sqrt (* n (PI))) (sqrt 2))) (sqrt 2))))) (* (sqrt (* n (PI))) (sqrt 2)))
(/ 1 (exp (* (log (* (sqrt (* n (PI))) (sqrt 2))) (- k 1))))
(/ 1 (exp (* (log (* (sqrt (* n (PI))) (sqrt 2))) (- k 1))))
(/ 1 (exp (* (log (* (sqrt (* n (PI))) (sqrt 2))) (- k 1))))
(/ 1 (exp (* (log (* (sqrt (* n (PI))) (sqrt 2))) (- k 1))))
(/ 1 (exp (* -1 (* (log (* (sqrt (* n (PI))) (sqrt 2))) (+ 1 (* -1 k))))))
(/ 1 (exp (* -1 (* (log (* (sqrt (* n (PI))) (sqrt 2))) (+ 1 (* -1 k))))))
(/ 1 (exp (* -1 (* (log (* (sqrt (* n (PI))) (sqrt 2))) (+ 1 (* -1 k))))))
(/ 1 (exp (* -1 (* (log (* (sqrt (* n (PI))) (sqrt 2))) (+ 1 (* -1 k))))))
(exp (* (log (* (sqrt (* n (PI))) (sqrt 2))) (- k 1)))
(exp (* (log (* (sqrt (* n (PI))) (sqrt 2))) (- k 1)))
(exp (* (log (* (sqrt (* n (PI))) (sqrt 2))) (- k 1)))
(exp (* (log (* (sqrt (* n (PI))) (sqrt 2))) (- k 1)))
(exp (* (+ (log (* (sqrt (/ (PI) n)) (sqrt 2))) (* -1 (log (/ 1 n)))) (- k 1)))
(exp (* (+ (log (* (sqrt (/ (PI) n)) (sqrt 2))) (* -1 (log (/ 1 n)))) (- k 1)))
(exp (* (+ (log (* (sqrt (/ (PI) n)) (sqrt 2))) (* -1 (log (/ 1 n)))) (- k 1)))
(exp (* (+ (log (* (sqrt (/ (PI) n)) (sqrt 2))) (* -1 (log (/ 1 n)))) (- k 1)))
(exp (* (+ (log (* (sqrt (/ (PI) n)) (* (sqrt -2) (sqrt -1)))) (* -1 (log (/ -1 n)))) (- k 1)))
(exp (* (+ (log (* (sqrt (/ (PI) n)) (* (sqrt -2) (sqrt -1)))) (* -1 (log (/ -1 n)))) (- k 1)))
(exp (* (+ (log (* (sqrt (/ (PI) n)) (* (sqrt -2) (sqrt -1)))) (* -1 (log (/ -1 n)))) (- k 1)))
(exp (* (+ (log (* (sqrt (/ (PI) n)) (* (sqrt -2) (sqrt -1)))) (* -1 (log (/ -1 n)))) (- k 1)))
(* (sqrt (/ 1 (* n (PI)))) (/ 1 (sqrt 2)))
(+ (* (sqrt (/ 1 (* n (PI)))) (/ 1 (sqrt 2))) (* (/ (* k (log (* (sqrt (* n (PI))) (sqrt 2)))) (sqrt 2)) (sqrt (/ 1 (* n (PI))))))
(+ (* k (+ (* 1/2 (* (/ (* k (pow (log (* (sqrt (* n (PI))) (sqrt 2))) 2)) (sqrt 2)) (sqrt (/ 1 (* n (PI)))))) (* (sqrt (/ 1 (* n (PI)))) (/ (log (* (sqrt (* n (PI))) (sqrt 2))) (sqrt 2))))) (* (sqrt (/ 1 (* n (PI)))) (/ 1 (sqrt 2))))
(+ (* k (+ (* k (+ (* 1/6 (* (/ (* k (pow (log (* (sqrt (* n (PI))) (sqrt 2))) 3)) (sqrt 2)) (sqrt (/ 1 (* n (PI)))))) (* 1/2 (* (sqrt (/ 1 (* n (PI)))) (/ (pow (log (* (sqrt (* n (PI))) (sqrt 2))) 2) (sqrt 2)))))) (* (sqrt (/ 1 (* n (PI)))) (/ (log (* (sqrt (* n (PI))) (sqrt 2))) (sqrt 2))))) (* (sqrt (/ 1 (* n (PI)))) (/ 1 (sqrt 2))))
(exp (* (log (* (sqrt (* n (PI))) (sqrt 2))) (- k 1)))
(exp (* (log (* (sqrt (* n (PI))) (sqrt 2))) (- k 1)))
(exp (* (log (* (sqrt (* n (PI))) (sqrt 2))) (- k 1)))
(exp (* (log (* (sqrt (* n (PI))) (sqrt 2))) (- k 1)))
(exp (* -1 (* (log (* (sqrt (* n (PI))) (sqrt 2))) (+ 1 (* -1 k)))))
(exp (* -1 (* (log (* (sqrt (* n (PI))) (sqrt 2))) (+ 1 (* -1 k)))))
(exp (* -1 (* (log (* (sqrt (* n (PI))) (sqrt 2))) (+ 1 (* -1 k)))))
(exp (* -1 (* (log (* (sqrt (* n (PI))) (sqrt 2))) (+ 1 (* -1 k)))))

Outputs
(* (sqrt (/ (* n (PI)) k)) (/ (sqrt 2) (exp (* 1/2 (* k (+ (log n) (log (* 2 (PI)))))))))
(/.f64 (.f64 (sqrt.f64 (/.f64 (.f64 n (PI.f64)) k)) (sqrt.f64 #s(literal 2 binary64))) (pow.f64 (.f64 n (exp.f64 (log.f64 (.f64 (PI.f64) #s(literal 2 binary64))))) (*.f64 k #s(literal 1/2 binary64))))
(* (sqrt (/ (* n (PI)) k)) (/ (sqrt 2) (exp (* 1/2 (* k (+ (log n) (log (* 2 (PI)))))))))
(/.f64 (.f64 (sqrt.f64 (/.f64 (.f64 n (PI.f64)) k)) (sqrt.f64 #s(literal 2 binary64))) (pow.f64 (.f64 n (exp.f64 (log.f64 (.f64 (PI.f64) #s(literal 2 binary64))))) (*.f64 k #s(literal 1/2 binary64))))
(* (sqrt (/ (* n (PI)) k)) (/ (sqrt 2) (exp (* 1/2 (* k (+ (log n) (log (* 2 (PI)))))))))
(/.f64 (.f64 (sqrt.f64 (/.f64 (.f64 n (PI.f64)) k)) (sqrt.f64 #s(literal 2 binary64))) (pow.f64 (.f64 n (exp.f64 (log.f64 (.f64 (PI.f64) #s(literal 2 binary64))))) (*.f64 k #s(literal 1/2 binary64))))
(* (sqrt (/ (* n (PI)) k)) (/ (sqrt 2) (exp (* 1/2 (* k (+ (log n) (log (* 2 (PI)))))))))
(/.f64 (.f64 (sqrt.f64 (/.f64 (.f64 n (PI.f64)) k)) (sqrt.f64 #s(literal 2 binary64))) (pow.f64 (.f64 n (exp.f64 (log.f64 (.f64 (PI.f64) #s(literal 2 binary64))))) (*.f64 k #s(literal 1/2 binary64))))
(* (sqrt (/ (* n (PI)) k)) (/ (sqrt 2) (exp (* 1/2 (* k (+ (log (* 2 (PI))) (* -1 (log (/ 1 n)))))))))
(/.f64 (.f64 (sqrt.f64 (/.f64 (.f64 n (PI.f64)) k)) (sqrt.f64 #s(literal 2 binary64))) (pow.f64 (.f64 n (exp.f64 (log.f64 (.f64 (PI.f64) #s(literal 2 binary64))))) (*.f64 k #s(literal 1/2 binary64))))
(* (sqrt (/ (* n (PI)) k)) (/ (sqrt 2) (exp (* 1/2 (* k (+ (log (* 2 (PI))) (* -1 (log (/ 1 n)))))))))
(/.f64 (.f64 (sqrt.f64 (/.f64 (.f64 n (PI.f64)) k)) (sqrt.f64 #s(literal 2 binary64))) (pow.f64 (.f64 n (exp.f64 (log.f64 (.f64 (PI.f64) #s(literal 2 binary64))))) (*.f64 k #s(literal 1/2 binary64))))
(* (sqrt (/ (* n (PI)) k)) (/ (sqrt 2) (exp (* 1/2 (* k (+ (log (* 2 (PI))) (* -1 (log (/ 1 n)))))))))
(/.f64 (.f64 (sqrt.f64 (/.f64 (.f64 n (PI.f64)) k)) (sqrt.f64 #s(literal 2 binary64))) (pow.f64 (.f64 n (exp.f64 (log.f64 (.f64 (PI.f64) #s(literal 2 binary64))))) (*.f64 k #s(literal 1/2 binary64))))
(* (sqrt (/ (* n (PI)) k)) (/ (sqrt 2) (exp (* 1/2 (* k (+ (log (* 2 (PI))) (* -1 (log (/ 1 n)))))))))
(/.f64 (.f64 (sqrt.f64 (/.f64 (.f64 n (PI.f64)) k)) (sqrt.f64 #s(literal 2 binary64))) (pow.f64 (.f64 n (exp.f64 (log.f64 (.f64 (PI.f64) #s(literal 2 binary64))))) (*.f64 k #s(literal 1/2 binary64))))
(* -1 (* (sqrt (/ (* n (PI)) k)) (/ (* (sqrt -2) (sqrt -1)) (exp (* 1/2 (* k (+ (log (* -2 (PI))) (* -1 (log (/ -1 n))))))))))
(/.f64 (.f64 (sqrt.f64 (/.f64 (.f64 n (PI.f64)) k)) (neg.f64 (.f64 (sqrt.f64 #s(literal -2 binary64)) (sqrt.f64 #s(literal -1 binary64))))) (exp.f64 (.f64 #s(literal 1/2 binary64) (.f64 k (-.f64 (log.f64 (.f64 (PI.f64) #s(literal -2 binary64))) (log.f64 (/.f64 #s(literal -1 binary64) n)))))))
(* -1 (* (sqrt (/ (* n (PI)) k)) (/ (* (sqrt -2) (sqrt -1)) (exp (* 1/2 (* k (+ (log (* -2 (PI))) (* -1 (log (/ -1 n))))))))))
(/.f64 (.f64 (sqrt.f64 (/.f64 (.f64 n (PI.f64)) k)) (neg.f64 (.f64 (sqrt.f64 #s(literal -2 binary64)) (sqrt.f64 #s(literal -1 binary64))))) (exp.f64 (.f64 #s(literal 1/2 binary64) (.f64 k (-.f64 (log.f64 (.f64 (PI.f64) #s(literal -2 binary64))) (log.f64 (/.f64 #s(literal -1 binary64) n)))))))
(* -1 (* (sqrt (/ (* n (PI)) k)) (/ (* (sqrt -2) (sqrt -1)) (exp (* 1/2 (* k (+ (log (* -2 (PI))) (* -1 (log (/ -1 n))))))))))
(/.f64 (.f64 (sqrt.f64 (/.f64 (.f64 n (PI.f64)) k)) (neg.f64 (.f64 (sqrt.f64 #s(literal -2 binary64)) (sqrt.f64 #s(literal -1 binary64))))) (exp.f64 (.f64 #s(literal 1/2 binary64) (.f64 k (-.f64 (log.f64 (.f64 (PI.f64) #s(literal -2 binary64))) (log.f64 (/.f64 #s(literal -1 binary64) n)))))))
(* -1 (* (sqrt (/ (* n (PI)) k)) (/ (* (sqrt -2) (sqrt -1)) (exp (* 1/2 (* k (+ (log (* -2 (PI))) (* -1 (log (/ -1 n))))))))))
(/.f64 (.f64 (sqrt.f64 (/.f64 (.f64 n (PI.f64)) k)) (neg.f64 (.f64 (sqrt.f64 #s(literal -2 binary64)) (sqrt.f64 #s(literal -1 binary64))))) (exp.f64 (.f64 #s(literal 1/2 binary64) (.f64 k (-.f64 (log.f64 (.f64 (PI.f64) #s(literal -2 binary64))) (log.f64 (/.f64 #s(literal -1 binary64) n)))))))
(* (sqrt (/ (* n (PI)) k)) (sqrt 2))
(.f64 (sqrt.f64 (/.f64 (.f64 n (PI.f64)) k)) (sqrt.f64 #s(literal 2 binary64)))
(/ (+ (* -1/2 (* (sqrt (* (pow k 3) (* n (PI)))) (* (log (* 2 (* n (PI)))) (sqrt 2)))) (* (sqrt (* k (* n (PI)))) (sqrt 2))) k)
(/.f64 (.f64 (sqrt.f64 #s(literal 2 binary64)) (fma.f64 #s(literal -1/2 binary64) (.f64 (sqrt.f64 (.f64 n (.f64 (PI.f64) (.f64 k (.f64 k k))))) (log.f64 (.f64 (.f64 n (PI.f64)) #s(literal 2 binary64)))) (sqrt.f64 (.f64 n (.f64 (PI.f64) k))))) k)
(/ (+ (* k (+ (* -1 (* (sqrt (* (pow k 3) (* n (PI)))) (+ (* -1/4 (* (pow (log (* 2 (* n (PI)))) 2) (sqrt 2))) (* 1/8 (* (pow (log (* 2 (* n (PI)))) 2) (sqrt 2)))))) (* -1/2 (* (sqrt (* k (* n (PI)))) (* (log (* 2 (* n (PI)))) (sqrt 2)))))) (* (sqrt (* k (* n (PI)))) (sqrt 2))) k)
(/.f64 (fma.f64 k (.f64 (sqrt.f64 #s(literal 2 binary64)) (fma.f64 #s(literal -1/2 binary64) (.f64 (log.f64 (.f64 (.f64 n (PI.f64)) #s(literal 2 binary64))) (sqrt.f64 (.f64 n (.f64 (PI.f64) k)))) (.f64 (sqrt.f64 (.f64 n (.f64 (PI.f64) (.f64 k (.f64 k k))))) (.f64 (pow.f64 (log.f64 (.f64 (.f64 n (PI.f64)) #s(literal 2 binary64))) #s(literal 2 binary64)) #s(literal 1/8 binary64))))) (.f64 (sqrt.f64 #s(literal 2 binary64)) (sqrt.f64 (.f64 n (*.f64 (PI.f64) k))))) 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 k (fma.f64 (neg.f64 k) (fma.f64 (.f64 (pow.f64 (log.f64 (.f64 (.f64 n (PI.f64)) #s(literal 2 binary64))) #s(literal 2 binary64)) (.f64 (sqrt.f64 #s(literal 2 binary64)) #s(literal -1/8 binary64))) (+.f64 (sqrt.f64 (.f64 n (.f64 (PI.f64) k))) (.f64 (sqrt.f64 (.f64 n (.f64 (PI.f64) (.f64 k (.f64 k k))))) (.f64 #s(literal -1/2 binary64) (log.f64 (.f64 (.f64 n (PI.f64)) #s(literal 2 binary64)))))) (.f64 (sqrt.f64 (.f64 n (.f64 (PI.f64) (.f64 k (.f64 k k))))) (.f64 (pow.f64 (log.f64 (.f64 (.f64 n (PI.f64)) #s(literal 2 binary64))) #s(literal 3 binary64)) (.f64 (sqrt.f64 #s(literal 2 binary64)) #s(literal -1/24 binary64))))) (.f64 (.f64 (sqrt.f64 #s(literal 2 binary64)) (log.f64 (.f64 (.f64 n (PI.f64)) #s(literal 2 binary64)))) (.f64 #s(literal -1/2 binary64) (sqrt.f64 (.f64 n (.f64 (PI.f64) k)))))) (.f64 (sqrt.f64 #s(literal 2 binary64)) (sqrt.f64 (.f64 n (*.f64 (PI.f64) k))))) k)
(* (sqrt (/ (* n (PI)) k)) (/ (sqrt 2) (exp (* 1/2 (* k (log (* 2 (* n (PI)))))))))
(/.f64 (.f64 (sqrt.f64 (/.f64 (.f64 n (PI.f64)) k)) (sqrt.f64 #s(literal 2 binary64))) (pow.f64 (.f64 (.f64 n (PI.f64)) #s(literal 2 binary64)) (*.f64 k #s(literal 1/2 binary64))))
(* (sqrt (/ (* n (PI)) k)) (/ (sqrt 2) (exp (* 1/2 (* k (log (* 2 (* n (PI)))))))))
(/.f64 (.f64 (sqrt.f64 (/.f64 (.f64 n (PI.f64)) k)) (sqrt.f64 #s(literal 2 binary64))) (pow.f64 (.f64 (.f64 n (PI.f64)) #s(literal 2 binary64)) (*.f64 k #s(literal 1/2 binary64))))
(* (sqrt (/ (* n (PI)) k)) (/ (sqrt 2) (exp (* 1/2 (* k (log (* 2 (* n (PI)))))))))
(/.f64 (.f64 (sqrt.f64 (/.f64 (.f64 n (PI.f64)) k)) (sqrt.f64 #s(literal 2 binary64))) (pow.f64 (.f64 (.f64 n (PI.f64)) #s(literal 2 binary64)) (*.f64 k #s(literal 1/2 binary64))))
(* (sqrt (/ (* n (PI)) k)) (/ (sqrt 2) (exp (* 1/2 (* k (log (* 2 (* n (PI)))))))))
(/.f64 (.f64 (sqrt.f64 (/.f64 (.f64 n (PI.f64)) k)) (sqrt.f64 #s(literal 2 binary64))) (pow.f64 (.f64 (.f64 n (PI.f64)) #s(literal 2 binary64)) (*.f64 k #s(literal 1/2 binary64))))
(* (sqrt (/ (* n (PI)) k)) (/ (sqrt 2) (exp (* 1/2 (* k (log (* 2 (* n (PI)))))))))
(/.f64 (.f64 (sqrt.f64 (/.f64 (.f64 n (PI.f64)) k)) (sqrt.f64 #s(literal 2 binary64))) (pow.f64 (.f64 (.f64 n (PI.f64)) #s(literal 2 binary64)) (*.f64 k #s(literal 1/2 binary64))))
(* (sqrt (/ (* n (PI)) k)) (/ (sqrt 2) (exp (* 1/2 (* k (log (* 2 (* n (PI)))))))))
(/.f64 (.f64 (sqrt.f64 (/.f64 (.f64 n (PI.f64)) k)) (sqrt.f64 #s(literal 2 binary64))) (pow.f64 (.f64 (.f64 n (PI.f64)) #s(literal 2 binary64)) (*.f64 k #s(literal 1/2 binary64))))
(* (sqrt (/ (* n (PI)) k)) (/ (sqrt 2) (exp (* 1/2 (* k (log (* 2 (* n (PI)))))))))
(/.f64 (.f64 (sqrt.f64 (/.f64 (.f64 n (PI.f64)) k)) (sqrt.f64 #s(literal 2 binary64))) (pow.f64 (.f64 (.f64 n (PI.f64)) #s(literal 2 binary64)) (*.f64 k #s(literal 1/2 binary64))))
(* (sqrt (/ (* n (PI)) k)) (/ (sqrt 2) (exp (* 1/2 (* k (log (* 2 (* n (PI)))))))))
(/.f64 (.f64 (sqrt.f64 (/.f64 (.f64 n (PI.f64)) k)) (sqrt.f64 #s(literal 2 binary64))) (pow.f64 (.f64 (.f64 n (PI.f64)) #s(literal 2 binary64)) (*.f64 k #s(literal 1/2 binary64))))
(* (sqrt (* n (PI))) (sqrt 2))
(.f64 (sqrt.f64 #s(literal 2 binary64)) (sqrt.f64 (.f64 n (PI.f64))))
(* (sqrt (* n (PI))) (sqrt 2))
(.f64 (sqrt.f64 #s(literal 2 binary64)) (sqrt.f64 (.f64 n (PI.f64))))
(* (sqrt (* n (PI))) (sqrt 2))
(.f64 (sqrt.f64 #s(literal 2 binary64)) (sqrt.f64 (.f64 n (PI.f64))))
(* (sqrt (* n (PI))) (sqrt 2))
(.f64 (sqrt.f64 #s(literal 2 binary64)) (sqrt.f64 (.f64 n (PI.f64))))
(* (sqrt (* n (PI))) (sqrt 2))
(.f64 (sqrt.f64 #s(literal 2 binary64)) (sqrt.f64 (.f64 n (PI.f64))))
(* (sqrt (* n (PI))) (sqrt 2))
(.f64 (sqrt.f64 #s(literal 2 binary64)) (sqrt.f64 (.f64 n (PI.f64))))
(* (sqrt (* n (PI))) (sqrt 2))
(.f64 (sqrt.f64 #s(literal 2 binary64)) (sqrt.f64 (.f64 n (PI.f64))))
(* (sqrt (* n (PI))) (sqrt 2))
(.f64 (sqrt.f64 #s(literal 2 binary64)) (sqrt.f64 (.f64 n (PI.f64))))
(* -1 (* (sqrt (* n (PI))) (* (sqrt -2) (sqrt -1))))
(.f64 (.f64 (sqrt.f64 #s(literal -2 binary64)) (sqrt.f64 #s(literal -1 binary64))) (neg.f64 (sqrt.f64 (*.f64 n (PI.f64)))))
(* -1 (* (sqrt (* n (PI))) (* (sqrt -2) (sqrt -1))))
(.f64 (.f64 (sqrt.f64 #s(literal -2 binary64)) (sqrt.f64 #s(literal -1 binary64))) (neg.f64 (sqrt.f64 (*.f64 n (PI.f64)))))
(* -1 (* (sqrt (* n (PI))) (* (sqrt -2) (sqrt -1))))
(.f64 (.f64 (sqrt.f64 #s(literal -2 binary64)) (sqrt.f64 #s(literal -1 binary64))) (neg.f64 (sqrt.f64 (*.f64 n (PI.f64)))))
(* -1 (* (sqrt (* n (PI))) (* (sqrt -2) (sqrt -1))))
(.f64 (.f64 (sqrt.f64 #s(literal -2 binary64)) (sqrt.f64 #s(literal -1 binary64))) (neg.f64 (sqrt.f64 (*.f64 n (PI.f64)))))
(* 2 (* n (PI)))
(.f64 (.f64 n (PI.f64)) #s(literal 2 binary64))
(* 2 (* n (PI)))
(.f64 (.f64 n (PI.f64)) #s(literal 2 binary64))
(* 2 (* n (PI)))
(.f64 (.f64 n (PI.f64)) #s(literal 2 binary64))
(* 2 (* n (PI)))
(.f64 (.f64 n (PI.f64)) #s(literal 2 binary64))
(* 2 (* n (PI)))
(.f64 (.f64 n (PI.f64)) #s(literal 2 binary64))
(* 2 (* n (PI)))
(.f64 (.f64 n (PI.f64)) #s(literal 2 binary64))
(* 2 (* n (PI)))
(.f64 (.f64 n (PI.f64)) #s(literal 2 binary64))
(* 2 (* n (PI)))
(.f64 (.f64 n (PI.f64)) #s(literal 2 binary64))
(* 2 (* n (PI)))
(.f64 (.f64 n (PI.f64)) #s(literal 2 binary64))
(* 2 (* n (PI)))
(.f64 (.f64 n (PI.f64)) #s(literal 2 binary64))
(* 2 (* n (PI)))
(.f64 (.f64 n (PI.f64)) #s(literal 2 binary64))
(* 2 (* n (PI)))
(.f64 (.f64 n (PI.f64)) #s(literal 2 binary64))
(* n (PI))
(*.f64 n (PI.f64))
(* n (PI))
(*.f64 n (PI.f64))
(* n (PI))
(*.f64 n (PI.f64))
(* n (PI))
(*.f64 n (PI.f64))
(* n (PI))
(*.f64 n (PI.f64))
(* n (PI))
(*.f64 n (PI.f64))
(* n (PI))
(*.f64 n (PI.f64))
(* n (PI))
(*.f64 n (PI.f64))
(* n (PI))
(*.f64 n (PI.f64))
(* n (PI))
(*.f64 n (PI.f64))
(* n (PI))
(*.f64 n (PI.f64))
(* n (PI))
(*.f64 n (PI.f64))
(* (sqrt (/ (* n (PI)) k)) (sqrt 2))
(.f64 (sqrt.f64 (/.f64 (.f64 n (PI.f64)) k)) (sqrt.f64 #s(literal 2 binary64)))
(/ (+ (* -1/2 (* (sqrt (* (pow k 3) (* n (PI)))) (* (log (* 2 (* n (PI)))) (sqrt 2)))) (* (sqrt (* k (* n (PI)))) (sqrt 2))) k)
(/.f64 (.f64 (sqrt.f64 #s(literal 2 binary64)) (fma.f64 #s(literal -1/2 binary64) (.f64 (sqrt.f64 (.f64 n (.f64 (PI.f64) (.f64 k (.f64 k k))))) (log.f64 (.f64 (.f64 n (PI.f64)) #s(literal 2 binary64)))) (sqrt.f64 (.f64 n (.f64 (PI.f64) k))))) k)
(/ (+ (* k (+ (* -1/2 (* (sqrt (* k (* n (PI)))) (* (log (* 2 (* n (PI)))) (sqrt 2)))) (* 1/8 (* (sqrt (* (pow k 3) (* n (PI)))) (* (pow (log (* 2 (* n (PI)))) 2) (sqrt 2)))))) (* (sqrt (* k (* n (PI)))) (sqrt 2))) k)
(/.f64 (fma.f64 k (.f64 (sqrt.f64 #s(literal 2 binary64)) (fma.f64 #s(literal -1/2 binary64) (.f64 (log.f64 (.f64 (.f64 n (PI.f64)) #s(literal 2 binary64))) (sqrt.f64 (.f64 n (.f64 (PI.f64) k)))) (.f64 (sqrt.f64 (.f64 n (.f64 (PI.f64) (.f64 k (.f64 k k))))) (.f64 (pow.f64 (log.f64 (.f64 (.f64 n (PI.f64)) #s(literal 2 binary64))) #s(literal 2 binary64)) #s(literal 1/8 binary64))))) (.f64 (sqrt.f64 #s(literal 2 binary64)) (sqrt.f64 (.f64 n (*.f64 (PI.f64) k))))) k)
(/ (+ (* k (+ (* -1/2 (* (sqrt (* k (* n (PI)))) (* (log (* 2 (* n (PI)))) (sqrt 2)))) (* k (+ (* -1/48 (* (sqrt (* (pow k 3) (* n (PI)))) (* (pow (log (* 2 (* n (PI)))) 3) (sqrt 2)))) (* 1/8 (* (sqrt (* k (* n (PI)))) (* (pow (log (* 2 (* n (PI)))) 2) (sqrt 2)))))))) (* (sqrt (* k (* n (PI)))) (sqrt 2))) k)
(/.f64 (fma.f64 k (fma.f64 k (.f64 (sqrt.f64 #s(literal 2 binary64)) (fma.f64 (.f64 (sqrt.f64 (.f64 n (.f64 (PI.f64) (.f64 k (.f64 k k))))) #s(literal -1/48 binary64)) (pow.f64 (log.f64 (.f64 (.f64 n (PI.f64)) #s(literal 2 binary64))) #s(literal 3 binary64)) (.f64 (sqrt.f64 (.f64 n (.f64 (PI.f64) k))) (.f64 (pow.f64 (log.f64 (.f64 (.f64 n (PI.f64)) #s(literal 2 binary64))) #s(literal 2 binary64)) #s(literal 1/8 binary64))))) (.f64 (.f64 (sqrt.f64 #s(literal 2 binary64)) (log.f64 (.f64 (.f64 n (PI.f64)) #s(literal 2 binary64)))) (.f64 #s(literal -1/2 binary64) (sqrt.f64 (.f64 n (.f64 (PI.f64) k)))))) (.f64 (sqrt.f64 #s(literal 2 binary64)) (sqrt.f64 (.f64 n (.f64 (PI.f64) k))))) k)
(* (sqrt (/ 1 k)) (exp (* 1/2 (* (log (* 2 (* n (PI)))) (- 1 k)))))
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(/ 1 (exp (* (log (* (sqrt (* n (PI))) (sqrt 2))) (- k 1))))
(pow.f64 (.f64 (sqrt.f64 #s(literal 2 binary64)) (sqrt.f64 (.f64 n (PI.f64)))) (-.f64 #s(literal 1 binary64) k))
(/ 1 (exp (* (+ (log (* (sqrt (/ (PI) n)) (sqrt 2))) (* -1 (log (/ 1 n)))) (- k 1))))
(pow.f64 (.f64 n (.f64 (sqrt.f64 #s(literal 2 binary64)) (sqrt.f64 (/.f64 (PI.f64) n)))) (-.f64 #s(literal 1 binary64) k))
(/ 1 (exp (* (+ (log (* (sqrt (/ (PI) n)) (sqrt 2))) (* -1 (log (/ 1 n)))) (- k 1))))
(pow.f64 (.f64 n (.f64 (sqrt.f64 #s(literal 2 binary64)) (sqrt.f64 (/.f64 (PI.f64) n)))) (-.f64 #s(literal 1 binary64) k))
(/ 1 (exp (* (+ (log (* (sqrt (/ (PI) n)) (sqrt 2))) (* -1 (log (/ 1 n)))) (- k 1))))
(pow.f64 (.f64 n (.f64 (sqrt.f64 #s(literal 2 binary64)) (sqrt.f64 (/.f64 (PI.f64) n)))) (-.f64 #s(literal 1 binary64) k))
(/ 1 (exp (* (+ (log (* (sqrt (/ (PI) n)) (sqrt 2))) (* -1 (log (/ 1 n)))) (- k 1))))
(pow.f64 (.f64 n (.f64 (sqrt.f64 #s(literal 2 binary64)) (sqrt.f64 (/.f64 (PI.f64) n)))) (-.f64 #s(literal 1 binary64) k))
(/ 1 (exp (* (+ (log (* (sqrt (/ (PI) n)) (* (sqrt -2) (sqrt -1)))) (* -1 (log (/ -1 n)))) (- k 1))))
(pow.f64 (.f64 (pow.f64 (/.f64 #s(literal -1 binary64) n) #s(literal -1 binary64)) (.f64 (*.f64 (sqrt.f64 #s(literal -2 binary64)) (sqrt.f64 #s(literal -1 binary64))) (sqrt.f64 (/.f64 (PI.f64) n)))) (-.f64 #s(literal 1 binary64) k))
(/ 1 (exp (* (+ (log (* (sqrt (/ (PI) n)) (* (sqrt -2) (sqrt -1)))) (* -1 (log (/ -1 n)))) (- k 1))))
(pow.f64 (.f64 (pow.f64 (/.f64 #s(literal -1 binary64) n) #s(literal -1 binary64)) (.f64 (*.f64 (sqrt.f64 #s(literal -2 binary64)) (sqrt.f64 #s(literal -1 binary64))) (sqrt.f64 (/.f64 (PI.f64) n)))) (-.f64 #s(literal 1 binary64) k))
(/ 1 (exp (* (+ (log (* (sqrt (/ (PI) n)) (* (sqrt -2) (sqrt -1)))) (* -1 (log (/ -1 n)))) (- k 1))))
(pow.f64 (.f64 (pow.f64 (/.f64 #s(literal -1 binary64) n) #s(literal -1 binary64)) (.f64 (*.f64 (sqrt.f64 #s(literal -2 binary64)) (sqrt.f64 #s(literal -1 binary64))) (sqrt.f64 (/.f64 (PI.f64) n)))) (-.f64 #s(literal 1 binary64) k))
(/ 1 (exp (* (+ (log (* (sqrt (/ (PI) n)) (* (sqrt -2) (sqrt -1)))) (* -1 (log (/ -1 n)))) (- k 1))))
(pow.f64 (.f64 (pow.f64 (/.f64 #s(literal -1 binary64) n) #s(literal -1 binary64)) (.f64 (*.f64 (sqrt.f64 #s(literal -2 binary64)) (sqrt.f64 #s(literal -1 binary64))) (sqrt.f64 (/.f64 (PI.f64) n)))) (-.f64 #s(literal 1 binary64) k))
(* (sqrt (* n (PI))) (sqrt 2))
(.f64 (sqrt.f64 #s(literal 2 binary64)) (sqrt.f64 (.f64 n (PI.f64))))
(+ (* -1 (* (* k (* (log (* (sqrt (* n (PI))) (sqrt 2))) (sqrt 2))) (sqrt (* n (PI))))) (* (sqrt (* n (PI))) (sqrt 2)))
(.f64 (sqrt.f64 (.f64 n (PI.f64))) (.f64 (fma.f64 (neg.f64 k) (log.f64 (.f64 (sqrt.f64 #s(literal 2 binary64)) (sqrt.f64 (*.f64 n (PI.f64))))) #s(literal 1 binary64)) (sqrt.f64 #s(literal 2 binary64))))
(+ (* k (- (* -1 (* k (+ (* -1 (* (sqrt (* n (PI))) (* (pow (log (* (sqrt (* n (PI))) (sqrt 2))) 2) (sqrt 2)))) (* 1/2 (* (sqrt (* n (PI))) (* (pow (log (* (sqrt (* n (PI))) (sqrt 2))) 2) (sqrt 2))))))) (* (sqrt (* n (PI))) (* (log (* (sqrt (* n (PI))) (sqrt 2))) (sqrt 2))))) (* (sqrt (* n (PI))) (sqrt 2)))
(fma.f64 k (fma.f64 k (.f64 (.f64 (.f64 #s(literal 1/2 binary64) (sqrt.f64 (.f64 n (PI.f64)))) (sqrt.f64 #s(literal 2 binary64))) (pow.f64 (log.f64 (.f64 (sqrt.f64 #s(literal 2 binary64)) (sqrt.f64 (.f64 n (PI.f64))))) #s(literal 2 binary64))) (neg.f64 (.f64 (.f64 (sqrt.f64 #s(literal 2 binary64)) (sqrt.f64 (.f64 n (PI.f64)))) (log.f64 (.f64 (sqrt.f64 #s(literal 2 binary64)) (sqrt.f64 (.f64 n (PI.f64)))))))) (.f64 (sqrt.f64 #s(literal 2 binary64)) (sqrt.f64 (*.f64 n (PI.f64)))))
(+ (* k (- (* k (- (* -1 (* k (+ (* -1 (* (log (* (sqrt (* n (PI))) (sqrt 2))) (+ (* -1 (* (sqrt (* n (PI))) (* (pow (log (* (sqrt (* n (PI))) (sqrt 2))) 2) (sqrt 2)))) (* 1/2 (* (sqrt (* n (PI))) (* (pow (log (* (sqrt (* n (PI))) (sqrt 2))) 2) (sqrt 2))))))) (+ (* -1/2 (* (sqrt (* n (PI))) (* (pow (log (* (sqrt (* n (PI))) (sqrt 2))) 3) (sqrt 2)))) (* 1/6 (* (sqrt (* n (PI))) (* (pow (log (* (sqrt (* n (PI))) (sqrt 2))) 3) (sqrt 2)))))))) (+ (* -1 (* (sqrt (* n (PI))) (* (pow (log (* (sqrt (* n (PI))) (sqrt 2))) 2) (sqrt 2)))) (* 1/2 (* (sqrt (* n (PI))) (* (pow (log (* (sqrt (* n (PI))) (sqrt 2))) 2) (sqrt 2))))))) (* (sqrt (* n (PI))) (* (log (* (sqrt (* n (PI))) (sqrt 2))) (sqrt 2))))) (* (sqrt (* n (PI))) (sqrt 2)))
(fma.f64 k (fma.f64 k (fma.f64 k (neg.f64 (fma.f64 #s(literal 1/2 binary64) (.f64 (.f64 (sqrt.f64 #s(literal 2 binary64)) (sqrt.f64 (.f64 n (PI.f64)))) (pow.f64 (log.f64 (.f64 (sqrt.f64 #s(literal 2 binary64)) (sqrt.f64 (.f64 n (PI.f64))))) #s(literal 3 binary64))) (.f64 (.f64 (sqrt.f64 #s(literal 2 binary64)) (pow.f64 (log.f64 (.f64 (sqrt.f64 #s(literal 2 binary64)) (sqrt.f64 (.f64 n (PI.f64))))) #s(literal 3 binary64))) (.f64 (sqrt.f64 (.f64 n (PI.f64))) #s(literal -1/3 binary64))))) (.f64 (.f64 (.f64 #s(literal 1/2 binary64) (sqrt.f64 (.f64 n (PI.f64)))) (sqrt.f64 #s(literal 2 binary64))) (pow.f64 (log.f64 (.f64 (sqrt.f64 #s(literal 2 binary64)) (sqrt.f64 (.f64 n (PI.f64))))) #s(literal 2 binary64)))) (neg.f64 (.f64 (.f64 (sqrt.f64 #s(literal 2 binary64)) (sqrt.f64 (.f64 n (PI.f64)))) (log.f64 (.f64 (sqrt.f64 #s(literal 2 binary64)) (sqrt.f64 (.f64 n (PI.f64)))))))) (.f64 (sqrt.f64 #s(literal 2 binary64)) (sqrt.f64 (.f64 n (PI.f64)))))
(/ 1 (exp (* (log (* (sqrt (* n (PI))) (sqrt 2))) (- k 1))))
(pow.f64 (.f64 (sqrt.f64 #s(literal 2 binary64)) (sqrt.f64 (.f64 n (PI.f64)))) (-.f64 #s(literal 1 binary64) k))
(/ 1 (exp (* (log (* (sqrt (* n (PI))) (sqrt 2))) (- k 1))))
(pow.f64 (.f64 (sqrt.f64 #s(literal 2 binary64)) (sqrt.f64 (.f64 n (PI.f64)))) (-.f64 #s(literal 1 binary64) k))
(/ 1 (exp (* (log (* (sqrt (* n (PI))) (sqrt 2))) (- k 1))))
(pow.f64 (.f64 (sqrt.f64 #s(literal 2 binary64)) (sqrt.f64 (.f64 n (PI.f64)))) (-.f64 #s(literal 1 binary64) k))
(/ 1 (exp (* (log (* (sqrt (* n (PI))) (sqrt 2))) (- k 1))))
(pow.f64 (.f64 (sqrt.f64 #s(literal 2 binary64)) (sqrt.f64 (.f64 n (PI.f64)))) (-.f64 #s(literal 1 binary64) k))
(/ 1 (exp (* -1 (* (log (* (sqrt (* n (PI))) (sqrt 2))) (+ 1 (* -1 k))))))
(pow.f64 (.f64 (sqrt.f64 #s(literal 2 binary64)) (sqrt.f64 (.f64 n (PI.f64)))) (-.f64 #s(literal 1 binary64) k))
(/ 1 (exp (* -1 (* (log (* (sqrt (* n (PI))) (sqrt 2))) (+ 1 (* -1 k))))))
(pow.f64 (.f64 (sqrt.f64 #s(literal 2 binary64)) (sqrt.f64 (.f64 n (PI.f64)))) (-.f64 #s(literal 1 binary64) k))
(/ 1 (exp (* -1 (* (log (* (sqrt (* n (PI))) (sqrt 2))) (+ 1 (* -1 k))))))
(pow.f64 (.f64 (sqrt.f64 #s(literal 2 binary64)) (sqrt.f64 (.f64 n (PI.f64)))) (-.f64 #s(literal 1 binary64) k))
(/ 1 (exp (* -1 (* (log (* (sqrt (* n (PI))) (sqrt 2))) (+ 1 (* -1 k))))))
(pow.f64 (.f64 (sqrt.f64 #s(literal 2 binary64)) (sqrt.f64 (.f64 n (PI.f64)))) (-.f64 #s(literal 1 binary64) k))
(exp (* (log (* (sqrt (* n (PI))) (sqrt 2))) (- k 1)))
(pow.f64 (.f64 (sqrt.f64 #s(literal 2 binary64)) (sqrt.f64 (.f64 n (PI.f64)))) (+.f64 k #s(literal -1 binary64)))
(exp (* (log (* (sqrt (* n (PI))) (sqrt 2))) (- k 1)))
(pow.f64 (.f64 (sqrt.f64 #s(literal 2 binary64)) (sqrt.f64 (.f64 n (PI.f64)))) (+.f64 k #s(literal -1 binary64)))
(exp (* (log (* (sqrt (* n (PI))) (sqrt 2))) (- k 1)))
(pow.f64 (.f64 (sqrt.f64 #s(literal 2 binary64)) (sqrt.f64 (.f64 n (PI.f64)))) (+.f64 k #s(literal -1 binary64)))
(exp (* (log (* (sqrt (* n (PI))) (sqrt 2))) (- k 1)))
(pow.f64 (.f64 (sqrt.f64 #s(literal 2 binary64)) (sqrt.f64 (.f64 n (PI.f64)))) (+.f64 k #s(literal -1 binary64)))
(exp (* (+ (log (* (sqrt (/ (PI) n)) (sqrt 2))) (* -1 (log (/ 1 n)))) (- k 1)))
(pow.f64 (.f64 n (.f64 (sqrt.f64 #s(literal 2 binary64)) (sqrt.f64 (/.f64 (PI.f64) n)))) (+.f64 k #s(literal -1 binary64)))
(exp (* (+ (log (* (sqrt (/ (PI) n)) (sqrt 2))) (* -1 (log (/ 1 n)))) (- k 1)))
(pow.f64 (.f64 n (.f64 (sqrt.f64 #s(literal 2 binary64)) (sqrt.f64 (/.f64 (PI.f64) n)))) (+.f64 k #s(literal -1 binary64)))
(exp (* (+ (log (* (sqrt (/ (PI) n)) (sqrt 2))) (* -1 (log (/ 1 n)))) (- k 1)))
(pow.f64 (.f64 n (.f64 (sqrt.f64 #s(literal 2 binary64)) (sqrt.f64 (/.f64 (PI.f64) n)))) (+.f64 k #s(literal -1 binary64)))
(exp (* (+ (log (* (sqrt (/ (PI) n)) (sqrt 2))) (* -1 (log (/ 1 n)))) (- k 1)))
(pow.f64 (.f64 n (.f64 (sqrt.f64 #s(literal 2 binary64)) (sqrt.f64 (/.f64 (PI.f64) n)))) (+.f64 k #s(literal -1 binary64)))
(exp (* (+ (log (* (sqrt (/ (PI) n)) (* (sqrt -2) (sqrt -1)))) (* -1 (log (/ -1 n)))) (- k 1)))
(pow.f64 (.f64 (pow.f64 (/.f64 #s(literal -1 binary64) n) #s(literal -1 binary64)) (.f64 (*.f64 (sqrt.f64 #s(literal -2 binary64)) (sqrt.f64 #s(literal -1 binary64))) (sqrt.f64 (/.f64 (PI.f64) n)))) (+.f64 k #s(literal -1 binary64)))
(exp (* (+ (log (* (sqrt (/ (PI) n)) (* (sqrt -2) (sqrt -1)))) (* -1 (log (/ -1 n)))) (- k 1)))
(pow.f64 (.f64 (pow.f64 (/.f64 #s(literal -1 binary64) n) #s(literal -1 binary64)) (.f64 (*.f64 (sqrt.f64 #s(literal -2 binary64)) (sqrt.f64 #s(literal -1 binary64))) (sqrt.f64 (/.f64 (PI.f64) n)))) (+.f64 k #s(literal -1 binary64)))
(exp (* (+ (log (* (sqrt (/ (PI) n)) (* (sqrt -2) (sqrt -1)))) (* -1 (log (/ -1 n)))) (- k 1)))
(pow.f64 (.f64 (pow.f64 (/.f64 #s(literal -1 binary64) n) #s(literal -1 binary64)) (.f64 (*.f64 (sqrt.f64 #s(literal -2 binary64)) (sqrt.f64 #s(literal -1 binary64))) (sqrt.f64 (/.f64 (PI.f64) n)))) (+.f64 k #s(literal -1 binary64)))
(exp (* (+ (log (* (sqrt (/ (PI) n)) (* (sqrt -2) (sqrt -1)))) (* -1 (log (/ -1 n)))) (- k 1)))
(pow.f64 (.f64 (pow.f64 (/.f64 #s(literal -1 binary64) n) #s(literal -1 binary64)) (.f64 (*.f64 (sqrt.f64 #s(literal -2 binary64)) (sqrt.f64 #s(literal -1 binary64))) (sqrt.f64 (/.f64 (PI.f64) n)))) (+.f64 k #s(literal -1 binary64)))
(* (sqrt (/ 1 (* n (PI)))) (/ 1 (sqrt 2)))
(/.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (*.f64 n (PI.f64)))) (sqrt.f64 #s(literal 2 binary64)))
(+ (* (sqrt (/ 1 (* n (PI)))) (/ 1 (sqrt 2))) (* (/ (* k (log (* (sqrt (* n (PI))) (sqrt 2)))) (sqrt 2)) (sqrt (/ 1 (* n (PI))))))
(.f64 (fma.f64 k (log.f64 (.f64 (sqrt.f64 #s(literal 2 binary64)) (sqrt.f64 (.f64 n (PI.f64))))) #s(literal 1 binary64)) (/.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (.f64 n (PI.f64)))) (sqrt.f64 #s(literal 2 binary64))))
(+ (* k (+ (* 1/2 (* (/ (* k (pow (log (* (sqrt (* n (PI))) (sqrt 2))) 2)) (sqrt 2)) (sqrt (/ 1 (* n (PI)))))) (* (sqrt (/ 1 (* n (PI)))) (/ (log (* (sqrt (* n (PI))) (sqrt 2))) (sqrt 2))))) (* (sqrt (/ 1 (* n (PI)))) (/ 1 (sqrt 2))))
(fma.f64 k (.f64 k (/.f64 (.f64 (.f64 #s(literal 1/2 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) (.f64 n (PI.f64))))) (pow.f64 (log.f64 (.f64 (sqrt.f64 #s(literal 2 binary64)) (sqrt.f64 (.f64 n (PI.f64))))) #s(literal 2 binary64))) (sqrt.f64 #s(literal 2 binary64)))) (.f64 (fma.f64 k (log.f64 (.f64 (sqrt.f64 #s(literal 2 binary64)) (sqrt.f64 (.f64 n (PI.f64))))) #s(literal 1 binary64)) (/.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (.f64 n (PI.f64)))) (sqrt.f64 #s(literal 2 binary64)))))
(+ (* k (+ (* k (+ (* 1/6 (* (/ (* k (pow (log (* (sqrt (* n (PI))) (sqrt 2))) 3)) (sqrt 2)) (sqrt (/ 1 (* n (PI)))))) (* 1/2 (* (sqrt (/ 1 (* n (PI)))) (/ (pow (log (* (sqrt (* n (PI))) (sqrt 2))) 2) (sqrt 2)))))) (* (sqrt (/ 1 (* n (PI)))) (/ (log (* (sqrt (* n (PI))) (sqrt 2))) (sqrt 2))))) (* (sqrt (/ 1 (* n (PI)))) (/ 1 (sqrt 2))))
(fma.f64 (.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (.f64 n (PI.f64)))) (fma.f64 #s(literal 1/6 binary64) (.f64 (pow.f64 (log.f64 (.f64 (sqrt.f64 #s(literal 2 binary64)) (sqrt.f64 (.f64 n (PI.f64))))) #s(literal 3 binary64)) (/.f64 k (sqrt.f64 #s(literal 2 binary64)))) (.f64 (/.f64 (pow.f64 (log.f64 (.f64 (sqrt.f64 #s(literal 2 binary64)) (sqrt.f64 (.f64 n (PI.f64))))) #s(literal 2 binary64)) (sqrt.f64 #s(literal 2 binary64))) #s(literal 1/2 binary64)))) (.f64 k k) (.f64 (fma.f64 k (log.f64 (.f64 (sqrt.f64 #s(literal 2 binary64)) (sqrt.f64 (.f64 n (PI.f64))))) #s(literal 1 binary64)) (/.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (*.f64 n (PI.f64)))) (sqrt.f64 #s(literal 2 binary64)))))
(exp (* (log (* (sqrt (* n (PI))) (sqrt 2))) (- k 1)))
(pow.f64 (.f64 (sqrt.f64 #s(literal 2 binary64)) (sqrt.f64 (.f64 n (PI.f64)))) (+.f64 k #s(literal -1 binary64)))
(exp (* (log (* (sqrt (* n (PI))) (sqrt 2))) (- k 1)))
(pow.f64 (.f64 (sqrt.f64 #s(literal 2 binary64)) (sqrt.f64 (.f64 n (PI.f64)))) (+.f64 k #s(literal -1 binary64)))
(exp (* (log (* (sqrt (* n (PI))) (sqrt 2))) (- k 1)))
(pow.f64 (.f64 (sqrt.f64 #s(literal 2 binary64)) (sqrt.f64 (.f64 n (PI.f64)))) (+.f64 k #s(literal -1 binary64)))
(exp (* (log (* (sqrt (* n (PI))) (sqrt 2))) (- k 1)))
(pow.f64 (.f64 (sqrt.f64 #s(literal 2 binary64)) (sqrt.f64 (.f64 n (PI.f64)))) (+.f64 k #s(literal -1 binary64)))
(exp (* -1 (* (log (* (sqrt (* n (PI))) (sqrt 2))) (+ 1 (* -1 k)))))
(pow.f64 (.f64 (sqrt.f64 #s(literal 2 binary64)) (sqrt.f64 (.f64 n (PI.f64)))) (+.f64 k #s(literal -1 binary64)))
(exp (* -1 (* (log (* (sqrt (* n (PI))) (sqrt 2))) (+ 1 (* -1 k)))))
(pow.f64 (.f64 (sqrt.f64 #s(literal 2 binary64)) (sqrt.f64 (.f64 n (PI.f64)))) (+.f64 k #s(literal -1 binary64)))
(exp (* -1 (* (log (* (sqrt (* n (PI))) (sqrt 2))) (+ 1 (* -1 k)))))
(pow.f64 (.f64 (sqrt.f64 #s(literal 2 binary64)) (sqrt.f64 (.f64 n (PI.f64)))) (+.f64 k #s(literal -1 binary64)))
(exp (* -1 (* (log (* (sqrt (* n (PI))) (sqrt 2))) (+ 1 (* -1 k)))))
(pow.f64 (.f64 (sqrt.f64 #s(literal 2 binary64)) (sqrt.f64 (.f64 n (PI.f64)))) (+.f64 k #s(literal -1 binary64)))

rewrite354.0ms (3.2%)

Memory

-16.1MiB live, 698.9MiB allocated

Algorithm

1×	batch-egg-rewrite

Rules

5 570×	`lower-*.f32`
5 552×	`lower-*.f64`
3 662×	`lower-/.f32`
3 652×	`lower-/.f64`
2 668×	`lower-pow.f32`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	44	173
0	72	175
1	284	153
2	1762	153
0	8671	153

Stop Event

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

Counts

18 → 1 672

Calls

Call 1

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

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

eval349.0ms (3.2%)

Memory: -3.8MiB live, 633.3MiB allocated
Compiler: Compiled 54 547 to 4 149 computations (92.4% saved)

prune270.0ms (2.4%)

Memory

27.3MiB live, 504.5MiB allocated

Pruning

29 alts after pruning (27 fresh and 2 done)

	Pruned	Kept	Total
New	2 517	26	2 543
Fresh	9	1	10
Picked	3	2	5
Done	0	0	0
Total	2 529	29	2 558

Accuracy

100.0%

Counts

2 558 → 29

Alt Table

Click to see full alt table

Status	Accuracy	Program
▶	99.5%	(/.f64 (pow.f64 (.f64 #s(literal 2 binary64) (.f64 (PI.f64) n)) (fma.f64 k #s(literal -1/2 binary64) #s(literal 1/2 binary64))) (sqrt.f64 k))
	99.1%	(/.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) k)) (pow.f64 (.f64 #s(literal 2 binary64) (.f64 (PI.f64) n)) (fma.f64 k #s(literal 1/2 binary64) #s(literal -1/2 binary64))))
▶	50.5%	(/.f64 #s(approx (pow (* 2 (* (PI) n)) (+ (* k 1/2) 1/2)) (.f64 (sqrt.f64 #s(literal 2 binary64)) (sqrt.f64 (.f64 n (PI.f64))))) (sqrt.f64 k))
	99.4%	(/.f64 #s(literal 1 binary64) (.f64 (sqrt.f64 k) (pow.f64 (.f64 #s(literal 2 binary64) (*.f64 (PI.f64) n)) (fma.f64 k #s(literal 1/2 binary64) #s(literal -1/2 binary64)))))
	76.0%	(.f64 (pow.f64 (.f64 #s(literal 2 binary64) (.f64 (PI.f64) n)) (.f64 k #s(literal -1/2 binary64))) (sqrt.f64 (.f64 #s(literal 2 binary64) (/.f64 (.f64 (PI.f64) n) k))))
✓	99.4%	(.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) (pow.f64 (.f64 (*.f64 #s(literal 2 binary64) (PI.f64)) n) (fma.f64 k #s(literal -1/2 binary64) #s(literal 1/2 binary64))))
	99.4%	(.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) (pow.f64 (sqrt.f64 (.f64 #s(literal 2 binary64) (*.f64 (PI.f64) n))) (-.f64 #s(literal 1 binary64) k)))
	50.4%	(.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) (/.f64 #s(literal 1 binary64) #s(approx (pow (sqrt ( 2 (* (PI) n))) (+ k -1)) (/.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (*.f64 n (PI.f64)))) (sqrt.f64 #s(literal 2 binary64))))))
	50.5%	(.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) #s(approx (pow ( (* 2 (PI)) n) (/ (- 1 k) 2)) (.f64 (sqrt.f64 #s(literal 2 binary64)) (sqrt.f64 (.f64 n (PI.f64))))))
	76.1%	(sqrt.f64 (/.f64 (.f64 #s(literal 2 binary64) (/.f64 (.f64 (PI.f64) n) k)) (pow.f64 (.f64 #s(literal 2 binary64) (.f64 (PI.f64) n)) k)))
	50.6%	#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (/.f64 (sqrt.f64 (.f64 #s(literal 2 binary64) (.f64 (PI.f64) n))) (sqrt.f64 k)))
	38.4%	#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (/.f64 (sqrt.f64 #s(literal 2 binary64)) (sqrt.f64 (/.f64 k (*.f64 (PI.f64) n)))))
	38.4%	#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (/.f64 #s(literal 1 binary64) (sqrt.f64 (/.f64 k (.f64 #s(literal 2 binary64) (.f64 (PI.f64) n))))))
	50.5%	#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (.f64 (/.f64 (sqrt.f64 (.f64 (PI.f64) n)) (sqrt.f64 k)) (sqrt.f64 #s(literal 2 binary64))))
	50.3%	#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (.f64 (/.f64 (sqrt.f64 (.f64 #s(literal 2 binary64) (PI.f64))) (sqrt.f64 k)) (/.f64 (sqrt.f64 n) #s(literal 1 binary64))))
	50.3%	#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (.f64 (/.f64 (sqrt.f64 n) (sqrt.f64 k)) (/.f64 (sqrt.f64 (.f64 #s(literal 2 binary64) (PI.f64))) #s(literal 1 binary64))))
	38.3%	#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 (/.f64 k (.f64 (PI.f64) n)))) (sqrt.f64 #s(literal 2 binary64))))
▶	50.5%	#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (.f64 (.f64 (/.f64 (sqrt.f64 n) (sqrt.f64 k)) (/.f64 (sqrt.f64 (PI.f64)) #s(literal 1 binary64))) (sqrt.f64 #s(literal 2 binary64))))
	50.2%	#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (.f64 (.f64 (sqrt.f64 (/.f64 (PI.f64) k)) (sqrt.f64 n)) (sqrt.f64 #s(literal 2 binary64))))
	50.1%	#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (.f64 (.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) k)) (sqrt.f64 (*.f64 (PI.f64) n))) (sqrt.f64 #s(literal 2 binary64))))
	37.8%	#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))))
	37.6%	#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (.f64 (sqrt.f64 (/.f64 (.f64 n (.f64 (sqrt.f64 (.f64 (PI.f64) (sqrt.f64 (PI.f64)))) (sqrt.f64 (sqrt.f64 (PI.f64))))) k)) (sqrt.f64 #s(literal 2 binary64))))
✓	37.7%	#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (.f64 (sqrt.f64 (/.f64 (.f64 n (PI.f64)) k)) (sqrt.f64 #s(literal 2 binary64))))
	37.7%	#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (.f64 (sqrt.f64 (.f64 (/.f64 (PI.f64) k) n)) (sqrt.f64 #s(literal 2 binary64))))
	37.7%	#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (.f64 (sqrt.f64 (.f64 (PI.f64) (/.f64 n k))) (sqrt.f64 #s(literal 2 binary64))))
	50.2%	#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (.f64 (sqrt.f64 (.f64 (PI.f64) n)) (sqrt.f64 (*.f64 (/.f64 #s(literal 1 binary64) k) #s(literal 2 binary64)))))
▶	50.2%	#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (.f64 (sqrt.f64 (.f64 #s(literal 2 binary64) (*.f64 (PI.f64) n))) (sqrt.f64 (/.f64 #s(literal 1 binary64) k))))
	50.2%	#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (.f64 (sqrt.f64 n) (sqrt.f64 (.f64 (/.f64 (PI.f64) k) #s(literal 2 binary64)))))
▶	37.8%	#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt.f64 (.f64 #s(literal 2 binary64) (/.f64 (.f64 (PI.f64) n) k))))

Compiler

Compiled 823 to 627 computations (23.8% saved)

simplify22.0ms (0.2%)

Memory

-31.9MiB live, 30.9MiB allocated

Algorithm

1×	egg-herbie

Localize:

Found 20 expressions of interest:

New	Metric	Score	Program
✓	cost-diff	0	(*.f64 (/.f64 (sqrt.f64 n) (sqrt.f64 k)) (/.f64 (sqrt.f64 (PI.f64)) #s(literal 1 binary64)))
✓	cost-diff	0	(.f64 (.f64 (/.f64 (sqrt.f64 n) (sqrt.f64 k)) (/.f64 (sqrt.f64 (PI.f64)) #s(literal 1 binary64))) (sqrt.f64 #s(literal 2 binary64)))
✓	cost-diff	0	#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (.f64 (.f64 (/.f64 (sqrt.f64 n) (sqrt.f64 k)) (/.f64 (sqrt.f64 (PI.f64)) #s(literal 1 binary64))) (sqrt.f64 #s(literal 2 binary64))))
✓	cost-diff	704	(/.f64 (sqrt.f64 (PI.f64)) #s(literal 1 binary64))
✓	cost-diff	0	(sqrt.f64 #s(literal 2 binary64))
✓	cost-diff	0	(.f64 (sqrt.f64 #s(literal 2 binary64)) (sqrt.f64 (.f64 n (PI.f64))))
✓	cost-diff	0	#s(approx (pow (* 2 (* (PI) n)) (+ (* k 1/2) 1/2)) (.f64 (sqrt.f64 #s(literal 2 binary64)) (sqrt.f64 (.f64 n (PI.f64)))))
✓	cost-diff	0	(/.f64 #s(approx (pow (* 2 (* (PI) n)) (+ (* k 1/2) 1/2)) (.f64 (sqrt.f64 #s(literal 2 binary64)) (sqrt.f64 (.f64 n (PI.f64))))) (sqrt.f64 k))
✓	cost-diff	0	(.f64 #s(literal 2 binary64) (.f64 (PI.f64) n))
✓	cost-diff	0	(sqrt.f64 (.f64 #s(literal 2 binary64) (.f64 (PI.f64) n)))
✓	cost-diff	0	(.f64 (sqrt.f64 (.f64 #s(literal 2 binary64) (*.f64 (PI.f64) n))) (sqrt.f64 (/.f64 #s(literal 1 binary64) k)))
✓	cost-diff	0	#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (.f64 (sqrt.f64 (.f64 #s(literal 2 binary64) (*.f64 (PI.f64) n))) (sqrt.f64 (/.f64 #s(literal 1 binary64) k))))
✓	cost-diff	0	(/.f64 (*.f64 (PI.f64) n) k)
✓	cost-diff	0	(.f64 #s(literal 2 binary64) (/.f64 (.f64 (PI.f64) n) k))
✓	cost-diff	0	(sqrt.f64 (.f64 #s(literal 2 binary64) (/.f64 (.f64 (PI.f64) n) k)))
✓	cost-diff	0	#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt.f64 (.f64 #s(literal 2 binary64) (/.f64 (.f64 (PI.f64) n) k))))
✓	cost-diff	0	(*.f64 (PI.f64) n)
✓	cost-diff	0	(.f64 #s(literal 2 binary64) (.f64 (PI.f64) n))
✓	cost-diff	0	(pow.f64 (.f64 #s(literal 2 binary64) (.f64 (PI.f64) n)) (fma.f64 k #s(literal -1/2 binary64) #s(literal 1/2 binary64)))
✓	cost-diff	0	(/.f64 (pow.f64 (.f64 #s(literal 2 binary64) (.f64 (PI.f64) n)) (fma.f64 k #s(literal -1/2 binary64) #s(literal 1/2 binary64))) (sqrt.f64 k))

Rules

204×	`lower-*.f32`
188×	`lower-*.f64`
90×	`lower-/.f32`
78×	`lower-/.f64`
74×	`*-commutative`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	49	298
0	76	290
1	114	284
2	167	284
3	240	281
4	316	281
5	333	281
6	356	281
7	389	281
8	401	281
9	405	281
0	405	279

Stop Event

1×	iter limit
1×	saturated
1×	iter limit

Calls

Call 1

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

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

localize198.0ms (1.8%)

Memory

7.9MiB live, 200.9MiB allocated

Localize:

Found 20 expressions of interest:

New	Metric	Score	Program
✓	accuracy	99.4%	(*.f64 (/.f64 (sqrt.f64 n) (sqrt.f64 k)) (/.f64 (sqrt.f64 (PI.f64)) #s(literal 1 binary64)))
✓	accuracy	99.2%	(.f64 (.f64 (/.f64 (sqrt.f64 n) (sqrt.f64 k)) (/.f64 (sqrt.f64 (PI.f64)) #s(literal 1 binary64))) (sqrt.f64 #s(literal 2 binary64)))
✓	accuracy	98.4%	(sqrt.f64 (PI.f64))
✓	accuracy	50.9%	#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (.f64 (.f64 (/.f64 (sqrt.f64 n) (sqrt.f64 k)) (/.f64 (sqrt.f64 (PI.f64)) #s(literal 1 binary64))) (sqrt.f64 #s(literal 2 binary64))))
✓	accuracy	99.8%	(/.f64 #s(approx (pow (* 2 (* (PI) n)) (+ (* k 1/2) 1/2)) (.f64 (sqrt.f64 #s(literal 2 binary64)) (sqrt.f64 (.f64 n (PI.f64))))) (sqrt.f64 k))
✓	accuracy	99.7%	(*.f64 n (PI.f64))
✓	accuracy	99.3%	(.f64 (sqrt.f64 #s(literal 2 binary64)) (sqrt.f64 (.f64 n (PI.f64))))
✓	accuracy	51.4%	#s(approx (pow (* 2 (* (PI) n)) (+ (* k 1/2) 1/2)) (.f64 (sqrt.f64 #s(literal 2 binary64)) (sqrt.f64 (.f64 n (PI.f64)))))
✓	accuracy	99.7%	(*.f64 (PI.f64) n)
✓	accuracy	99.5%	(.f64 (sqrt.f64 (.f64 #s(literal 2 binary64) (*.f64 (PI.f64) n))) (sqrt.f64 (/.f64 #s(literal 1 binary64) k)))
✓	accuracy	99.4%	(sqrt.f64 (/.f64 #s(literal 1 binary64) k))
✓	accuracy	50.9%	#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (.f64 (sqrt.f64 (.f64 #s(literal 2 binary64) (*.f64 (PI.f64) n))) (sqrt.f64 (/.f64 #s(literal 1 binary64) k))))
✓	accuracy	99.7%	(/.f64 (*.f64 (PI.f64) n) k)
✓	accuracy	99.7%	(*.f64 (PI.f64) n)
✓	accuracy	76.3%	(sqrt.f64 (.f64 #s(literal 2 binary64) (/.f64 (.f64 (PI.f64) n) k)))
✓	accuracy	50.9%	#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt.f64 (.f64 #s(literal 2 binary64) (/.f64 (.f64 (PI.f64) n) k))))
✓	accuracy	100.0%	(PI.f64)
✓	accuracy	99.8%	(/.f64 (pow.f64 (.f64 #s(literal 2 binary64) (.f64 (PI.f64) n)) (fma.f64 k #s(literal -1/2 binary64) #s(literal 1/2 binary64))) (sqrt.f64 k))
✓	accuracy	99.7%	(*.f64 (PI.f64) n)
✓	accuracy	99.7%	(pow.f64 (.f64 #s(literal 2 binary64) (.f64 (PI.f64) n)) (fma.f64 k #s(literal -1/2 binary64) #s(literal 1/2 binary64)))

Samples

115.0ms

256×

valid

Compiler

Compiled 252 to 44 computations (82.5% saved)

Precisions

Click to see histograms. Total time spent on operations: 71.0ms

ival-mult: 17.0ms (24% of total)

ival-pow: 14.0ms (19.8% of total)

ival-add: 13.0ms (18.4% of total)

ival-div: 12.0ms (17% of total)

ival-sqrt: 12.0ms (17% of total)

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

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

exact: 1.0ms (1.4% of total)

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

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

series45.0ms (0.4%)

Memory

-5.9MiB live, 31.6MiB allocated

Counts

23 → 384

Calls

Call 1

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

Outputs
#s(alt (* (sqrt (/ 1 k)) (exp (* (+ 1/2 (* -1/2 k)) (+ (log n) (log (* 2 (PI))))))) (taylor 0 n) (#s(alt (/.f64 (pow.f64 (.f64 #s(literal 2 binary64) (.f64 (PI.f64) n)) (fma.f64 k #s(literal -1/2 binary64) #s(literal 1/2 binary64))) (sqrt.f64 k)) (patch (/.f64 (pow.f64 (.f64 #s(literal 2 binary64) (.f64 (PI.f64) n)) (fma.f64 k #s(literal -1/2 binary64) #s(literal 1/2 binary64))) (sqrt.f64 k)) #<representation binary64>) () ())) ())
#s(alt (* (sqrt (/ 1 k)) (exp (* (+ 1/2 (* -1/2 k)) (+ (log n) (log (* 2 (PI))))))) (taylor 0 n) (#s(alt (/.f64 (pow.f64 (.f64 #s(literal 2 binary64) (.f64 (PI.f64) n)) (fma.f64 k #s(literal -1/2 binary64) #s(literal 1/2 binary64))) (sqrt.f64 k)) (patch (/.f64 (pow.f64 (.f64 #s(literal 2 binary64) (.f64 (PI.f64) n)) (fma.f64 k #s(literal -1/2 binary64) #s(literal 1/2 binary64))) (sqrt.f64 k)) #<representation binary64>) () ())) ())
#s(alt (* (sqrt (/ 1 k)) (exp (* (+ 1/2 (* -1/2 k)) (+ (log n) (log (* 2 (PI))))))) (taylor 0 n) (#s(alt (/.f64 (pow.f64 (.f64 #s(literal 2 binary64) (.f64 (PI.f64) n)) (fma.f64 k #s(literal -1/2 binary64) #s(literal 1/2 binary64))) (sqrt.f64 k)) (patch (/.f64 (pow.f64 (.f64 #s(literal 2 binary64) (.f64 (PI.f64) n)) (fma.f64 k #s(literal -1/2 binary64) #s(literal 1/2 binary64))) (sqrt.f64 k)) #<representation binary64>) () ())) ())
#s(alt (* (sqrt (/ 1 k)) (exp (* (+ 1/2 (* -1/2 k)) (+ (log n) (log (* 2 (PI))))))) (taylor 0 n) (#s(alt (/.f64 (pow.f64 (.f64 #s(literal 2 binary64) (.f64 (PI.f64) n)) (fma.f64 k #s(literal -1/2 binary64) #s(literal 1/2 binary64))) (sqrt.f64 k)) (patch (/.f64 (pow.f64 (.f64 #s(literal 2 binary64) (.f64 (PI.f64) n)) (fma.f64 k #s(literal -1/2 binary64) #s(literal 1/2 binary64))) (sqrt.f64 k)) #<representation binary64>) () ())) ())
#s(alt (* (sqrt (/ 1 k)) (exp (* (+ 1/2 (* -1/2 k)) (+ (log (* 2 (PI))) (* -1 (log (/ 1 n))))))) (taylor inf n) (#s(alt (/.f64 (pow.f64 (.f64 #s(literal 2 binary64) (.f64 (PI.f64) n)) (fma.f64 k #s(literal -1/2 binary64) #s(literal 1/2 binary64))) (sqrt.f64 k)) (patch (/.f64 (pow.f64 (.f64 #s(literal 2 binary64) (.f64 (PI.f64) n)) (fma.f64 k #s(literal -1/2 binary64) #s(literal 1/2 binary64))) (sqrt.f64 k)) #<representation binary64>) () ())) ())
#s(alt (* (sqrt (/ 1 k)) (exp (* (+ 1/2 (* -1/2 k)) (+ (log (* 2 (PI))) (* -1 (log (/ 1 n))))))) (taylor inf n) (#s(alt (/.f64 (pow.f64 (.f64 #s(literal 2 binary64) (.f64 (PI.f64) n)) (fma.f64 k #s(literal -1/2 binary64) #s(literal 1/2 binary64))) (sqrt.f64 k)) (patch (/.f64 (pow.f64 (.f64 #s(literal 2 binary64) (.f64 (PI.f64) n)) (fma.f64 k #s(literal -1/2 binary64) #s(literal 1/2 binary64))) (sqrt.f64 k)) #<representation binary64>) () ())) ())
#s(alt (* (sqrt (/ 1 k)) (exp (* (+ 1/2 (* -1/2 k)) (+ (log (* 2 (PI))) (* -1 (log (/ 1 n))))))) (taylor inf n) (#s(alt (/.f64 (pow.f64 (.f64 #s(literal 2 binary64) (.f64 (PI.f64) n)) (fma.f64 k #s(literal -1/2 binary64) #s(literal 1/2 binary64))) (sqrt.f64 k)) (patch (/.f64 (pow.f64 (.f64 #s(literal 2 binary64) (.f64 (PI.f64) n)) (fma.f64 k #s(literal -1/2 binary64) #s(literal 1/2 binary64))) (sqrt.f64 k)) #<representation binary64>) () ())) ())
#s(alt (* (sqrt (/ 1 k)) (exp (* (+ 1/2 (* -1/2 k)) (+ (log (* 2 (PI))) (* -1 (log (/ 1 n))))))) (taylor inf n) (#s(alt (/.f64 (pow.f64 (.f64 #s(literal 2 binary64) (.f64 (PI.f64) n)) (fma.f64 k #s(literal -1/2 binary64) #s(literal 1/2 binary64))) (sqrt.f64 k)) (patch (/.f64 (pow.f64 (.f64 #s(literal 2 binary64) (.f64 (PI.f64) n)) (fma.f64 k #s(literal -1/2 binary64) #s(literal 1/2 binary64))) (sqrt.f64 k)) #<representation binary64>) () ())) ())
#s(alt (* (sqrt (/ 1 k)) (exp (* (+ 1/2 (* -1/2 k)) (+ (log (* -2 (PI))) (* -1 (log (/ -1 n))))))) (taylor -inf n) (#s(alt (/.f64 (pow.f64 (.f64 #s(literal 2 binary64) (.f64 (PI.f64) n)) (fma.f64 k #s(literal -1/2 binary64) #s(literal 1/2 binary64))) (sqrt.f64 k)) (patch (/.f64 (pow.f64 (.f64 #s(literal 2 binary64) (.f64 (PI.f64) n)) (fma.f64 k #s(literal -1/2 binary64) #s(literal 1/2 binary64))) (sqrt.f64 k)) #<representation binary64>) () ())) ())
#s(alt (* (sqrt (/ 1 k)) (exp (* (+ 1/2 (* -1/2 k)) (+ (log (* -2 (PI))) (* -1 (log (/ -1 n))))))) (taylor -inf n) (#s(alt (/.f64 (pow.f64 (.f64 #s(literal 2 binary64) (.f64 (PI.f64) n)) (fma.f64 k #s(literal -1/2 binary64) #s(literal 1/2 binary64))) (sqrt.f64 k)) (patch (/.f64 (pow.f64 (.f64 #s(literal 2 binary64) (.f64 (PI.f64) n)) (fma.f64 k #s(literal -1/2 binary64) #s(literal 1/2 binary64))) (sqrt.f64 k)) #<representation binary64>) () ())) ())
#s(alt (* (sqrt (/ 1 k)) (exp (* (+ 1/2 (* -1/2 k)) (+ (log (* -2 (PI))) (* -1 (log (/ -1 n))))))) (taylor -inf n) (#s(alt (/.f64 (pow.f64 (.f64 #s(literal 2 binary64) (.f64 (PI.f64) n)) (fma.f64 k #s(literal -1/2 binary64) #s(literal 1/2 binary64))) (sqrt.f64 k)) (patch (/.f64 (pow.f64 (.f64 #s(literal 2 binary64) (.f64 (PI.f64) n)) (fma.f64 k #s(literal -1/2 binary64) #s(literal 1/2 binary64))) (sqrt.f64 k)) #<representation binary64>) () ())) ())
#s(alt (* (sqrt (/ 1 k)) (exp (* (+ 1/2 (* -1/2 k)) (+ (log (* -2 (PI))) (* -1 (log (/ -1 n))))))) (taylor -inf n) (#s(alt (/.f64 (pow.f64 (.f64 #s(literal 2 binary64) (.f64 (PI.f64) n)) (fma.f64 k #s(literal -1/2 binary64) #s(literal 1/2 binary64))) (sqrt.f64 k)) (patch (/.f64 (pow.f64 (.f64 #s(literal 2 binary64) (.f64 (PI.f64) n)) (fma.f64 k #s(literal -1/2 binary64) #s(literal 1/2 binary64))) (sqrt.f64 k)) #<representation binary64>) () ())) ())
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#s(alt (* -1 (* (sqrt (/ (* n (PI)) k)) (* (pow (sqrt -1) 2) (sqrt 2)))) (taylor -inf n) (#s(alt (.f64 (.f64 (/.f64 (sqrt.f64 n) (sqrt.f64 k)) (/.f64 (sqrt.f64 (PI.f64)) #s(literal 1 binary64))) (sqrt.f64 #s(literal 2 binary64))) (patch (.f64 (.f64 (/.f64 (sqrt.f64 n) (sqrt.f64 k)) (/.f64 (sqrt.f64 (PI.f64)) #s(literal 1 binary64))) (sqrt.f64 #s(literal 2 binary64))) #<representation binary64>) () ())) ())
#s(alt (* -1 (* (sqrt (/ (* n (PI)) k)) (* (pow (sqrt -1) 2) (sqrt 2)))) (taylor -inf n) (#s(alt (.f64 (.f64 (/.f64 (sqrt.f64 n) (sqrt.f64 k)) (/.f64 (sqrt.f64 (PI.f64)) #s(literal 1 binary64))) (sqrt.f64 #s(literal 2 binary64))) (patch (.f64 (.f64 (/.f64 (sqrt.f64 n) (sqrt.f64 k)) (/.f64 (sqrt.f64 (PI.f64)) #s(literal 1 binary64))) (sqrt.f64 #s(literal 2 binary64))) #<representation binary64>) () ())) ())
#s(alt (* -1 (* (sqrt (/ (* n (PI)) k)) (* (pow (sqrt -1) 2) (sqrt 2)))) (taylor -inf n) (#s(alt (.f64 (.f64 (/.f64 (sqrt.f64 n) (sqrt.f64 k)) (/.f64 (sqrt.f64 (PI.f64)) #s(literal 1 binary64))) (sqrt.f64 #s(literal 2 binary64))) (patch (.f64 (.f64 (/.f64 (sqrt.f64 n) (sqrt.f64 k)) (/.f64 (sqrt.f64 (PI.f64)) #s(literal 1 binary64))) (sqrt.f64 #s(literal 2 binary64))) #<representation binary64>) () ())) ())
#s(alt (* -1 (* (sqrt (/ (* n (PI)) k)) (* (pow (sqrt -1) 2) (sqrt 2)))) (taylor -inf n) (#s(alt (.f64 (.f64 (/.f64 (sqrt.f64 n) (sqrt.f64 k)) (/.f64 (sqrt.f64 (PI.f64)) #s(literal 1 binary64))) (sqrt.f64 #s(literal 2 binary64))) (patch (.f64 (.f64 (/.f64 (sqrt.f64 n) (sqrt.f64 k)) (/.f64 (sqrt.f64 (PI.f64)) #s(literal 1 binary64))) (sqrt.f64 #s(literal 2 binary64))) #<representation binary64>) () ())) ())
#s(alt (* (sqrt (/ (* n (PI)) k)) (sqrt 2)) (taylor 0 k) (#s(alt (.f64 (.f64 (/.f64 (sqrt.f64 n) (sqrt.f64 k)) (/.f64 (sqrt.f64 (PI.f64)) #s(literal 1 binary64))) (sqrt.f64 #s(literal 2 binary64))) (patch (.f64 (.f64 (/.f64 (sqrt.f64 n) (sqrt.f64 k)) (/.f64 (sqrt.f64 (PI.f64)) #s(literal 1 binary64))) (sqrt.f64 #s(literal 2 binary64))) #<representation binary64>) () ())) ())
#s(alt (* (sqrt (/ (* n (PI)) k)) (sqrt 2)) (taylor 0 k) (#s(alt (.f64 (.f64 (/.f64 (sqrt.f64 n) (sqrt.f64 k)) (/.f64 (sqrt.f64 (PI.f64)) #s(literal 1 binary64))) (sqrt.f64 #s(literal 2 binary64))) (patch (.f64 (.f64 (/.f64 (sqrt.f64 n) (sqrt.f64 k)) (/.f64 (sqrt.f64 (PI.f64)) #s(literal 1 binary64))) (sqrt.f64 #s(literal 2 binary64))) #<representation binary64>) () ())) ())
#s(alt (* (sqrt (/ (* n (PI)) k)) (sqrt 2)) (taylor 0 k) (#s(alt (.f64 (.f64 (/.f64 (sqrt.f64 n) (sqrt.f64 k)) (/.f64 (sqrt.f64 (PI.f64)) #s(literal 1 binary64))) (sqrt.f64 #s(literal 2 binary64))) (patch (.f64 (.f64 (/.f64 (sqrt.f64 n) (sqrt.f64 k)) (/.f64 (sqrt.f64 (PI.f64)) #s(literal 1 binary64))) (sqrt.f64 #s(literal 2 binary64))) #<representation binary64>) () ())) ())
#s(alt (* (sqrt (/ (* n (PI)) k)) (sqrt 2)) (taylor 0 k) (#s(alt (.f64 (.f64 (/.f64 (sqrt.f64 n) (sqrt.f64 k)) (/.f64 (sqrt.f64 (PI.f64)) #s(literal 1 binary64))) (sqrt.f64 #s(literal 2 binary64))) (patch (.f64 (.f64 (/.f64 (sqrt.f64 n) (sqrt.f64 k)) (/.f64 (sqrt.f64 (PI.f64)) #s(literal 1 binary64))) (sqrt.f64 #s(literal 2 binary64))) #<representation binary64>) () ())) ())
#s(alt (* (sqrt (/ (* n (PI)) k)) (sqrt 2)) (taylor inf k) (#s(alt (.f64 (.f64 (/.f64 (sqrt.f64 n) (sqrt.f64 k)) (/.f64 (sqrt.f64 (PI.f64)) #s(literal 1 binary64))) (sqrt.f64 #s(literal 2 binary64))) (patch (.f64 (.f64 (/.f64 (sqrt.f64 n) (sqrt.f64 k)) (/.f64 (sqrt.f64 (PI.f64)) #s(literal 1 binary64))) (sqrt.f64 #s(literal 2 binary64))) #<representation binary64>) () ())) ())
#s(alt (* (sqrt (/ (* n (PI)) k)) (sqrt 2)) (taylor inf k) (#s(alt (.f64 (.f64 (/.f64 (sqrt.f64 n) (sqrt.f64 k)) (/.f64 (sqrt.f64 (PI.f64)) #s(literal 1 binary64))) (sqrt.f64 #s(literal 2 binary64))) (patch (.f64 (.f64 (/.f64 (sqrt.f64 n) (sqrt.f64 k)) (/.f64 (sqrt.f64 (PI.f64)) #s(literal 1 binary64))) (sqrt.f64 #s(literal 2 binary64))) #<representation binary64>) () ())) ())
#s(alt (* (sqrt (/ (* n (PI)) k)) (sqrt 2)) (taylor inf k) (#s(alt (.f64 (.f64 (/.f64 (sqrt.f64 n) (sqrt.f64 k)) (/.f64 (sqrt.f64 (PI.f64)) #s(literal 1 binary64))) (sqrt.f64 #s(literal 2 binary64))) (patch (.f64 (.f64 (/.f64 (sqrt.f64 n) (sqrt.f64 k)) (/.f64 (sqrt.f64 (PI.f64)) #s(literal 1 binary64))) (sqrt.f64 #s(literal 2 binary64))) #<representation binary64>) () ())) ())
#s(alt (* (sqrt (/ (* n (PI)) k)) (sqrt 2)) (taylor inf k) (#s(alt (.f64 (.f64 (/.f64 (sqrt.f64 n) (sqrt.f64 k)) (/.f64 (sqrt.f64 (PI.f64)) #s(literal 1 binary64))) (sqrt.f64 #s(literal 2 binary64))) (patch (.f64 (.f64 (/.f64 (sqrt.f64 n) (sqrt.f64 k)) (/.f64 (sqrt.f64 (PI.f64)) #s(literal 1 binary64))) (sqrt.f64 #s(literal 2 binary64))) #<representation binary64>) () ())) ())
#s(alt (* (sqrt (/ (* n (PI)) k)) (sqrt 2)) (taylor -inf k) (#s(alt (.f64 (.f64 (/.f64 (sqrt.f64 n) (sqrt.f64 k)) (/.f64 (sqrt.f64 (PI.f64)) #s(literal 1 binary64))) (sqrt.f64 #s(literal 2 binary64))) (patch (.f64 (.f64 (/.f64 (sqrt.f64 n) (sqrt.f64 k)) (/.f64 (sqrt.f64 (PI.f64)) #s(literal 1 binary64))) (sqrt.f64 #s(literal 2 binary64))) #<representation binary64>) () ())) ())
#s(alt (* (sqrt (/ (* n (PI)) k)) (sqrt 2)) (taylor -inf k) (#s(alt (.f64 (.f64 (/.f64 (sqrt.f64 n) (sqrt.f64 k)) (/.f64 (sqrt.f64 (PI.f64)) #s(literal 1 binary64))) (sqrt.f64 #s(literal 2 binary64))) (patch (.f64 (.f64 (/.f64 (sqrt.f64 n) (sqrt.f64 k)) (/.f64 (sqrt.f64 (PI.f64)) #s(literal 1 binary64))) (sqrt.f64 #s(literal 2 binary64))) #<representation binary64>) () ())) ())
#s(alt (* (sqrt (/ (* n (PI)) k)) (sqrt 2)) (taylor -inf k) (#s(alt (.f64 (.f64 (/.f64 (sqrt.f64 n) (sqrt.f64 k)) (/.f64 (sqrt.f64 (PI.f64)) #s(literal 1 binary64))) (sqrt.f64 #s(literal 2 binary64))) (patch (.f64 (.f64 (/.f64 (sqrt.f64 n) (sqrt.f64 k)) (/.f64 (sqrt.f64 (PI.f64)) #s(literal 1 binary64))) (sqrt.f64 #s(literal 2 binary64))) #<representation binary64>) () ())) ())
#s(alt (* (sqrt (/ (* n (PI)) k)) (sqrt 2)) (taylor -inf k) (#s(alt (.f64 (.f64 (/.f64 (sqrt.f64 n) (sqrt.f64 k)) (/.f64 (sqrt.f64 (PI.f64)) #s(literal 1 binary64))) (sqrt.f64 #s(literal 2 binary64))) (patch (.f64 (.f64 (/.f64 (sqrt.f64 n) (sqrt.f64 k)) (/.f64 (sqrt.f64 (PI.f64)) #s(literal 1 binary64))) (sqrt.f64 #s(literal 2 binary64))) #<representation binary64>) () ())) ())
#s(alt (sqrt (/ (* n (PI)) k)) (taylor 0 n) (#s(alt (.f64 (/.f64 (sqrt.f64 n) (sqrt.f64 k)) (/.f64 (sqrt.f64 (PI.f64)) #s(literal 1 binary64))) (patch (.f64 (/.f64 (sqrt.f64 n) (sqrt.f64 k)) (/.f64 (sqrt.f64 (PI.f64)) #s(literal 1 binary64))) #<representation binary64>) () ())) ())
#s(alt (sqrt (/ (* n (PI)) k)) (taylor 0 n) (#s(alt (.f64 (/.f64 (sqrt.f64 n) (sqrt.f64 k)) (/.f64 (sqrt.f64 (PI.f64)) #s(literal 1 binary64))) (patch (.f64 (/.f64 (sqrt.f64 n) (sqrt.f64 k)) (/.f64 (sqrt.f64 (PI.f64)) #s(literal 1 binary64))) #<representation binary64>) () ())) ())
#s(alt (sqrt (/ (* n (PI)) k)) (taylor 0 n) (#s(alt (.f64 (/.f64 (sqrt.f64 n) (sqrt.f64 k)) (/.f64 (sqrt.f64 (PI.f64)) #s(literal 1 binary64))) (patch (.f64 (/.f64 (sqrt.f64 n) (sqrt.f64 k)) (/.f64 (sqrt.f64 (PI.f64)) #s(literal 1 binary64))) #<representation binary64>) () ())) ())
#s(alt (sqrt (/ (* n (PI)) k)) (taylor 0 n) (#s(alt (.f64 (/.f64 (sqrt.f64 n) (sqrt.f64 k)) (/.f64 (sqrt.f64 (PI.f64)) #s(literal 1 binary64))) (patch (.f64 (/.f64 (sqrt.f64 n) (sqrt.f64 k)) (/.f64 (sqrt.f64 (PI.f64)) #s(literal 1 binary64))) #<representation binary64>) () ())) ())
#s(alt (sqrt (/ (* n (PI)) k)) (taylor inf n) (#s(alt (.f64 (/.f64 (sqrt.f64 n) (sqrt.f64 k)) (/.f64 (sqrt.f64 (PI.f64)) #s(literal 1 binary64))) (patch (.f64 (/.f64 (sqrt.f64 n) (sqrt.f64 k)) (/.f64 (sqrt.f64 (PI.f64)) #s(literal 1 binary64))) #<representation binary64>) () ())) ())
#s(alt (sqrt (/ (* n (PI)) k)) (taylor inf n) (#s(alt (.f64 (/.f64 (sqrt.f64 n) (sqrt.f64 k)) (/.f64 (sqrt.f64 (PI.f64)) #s(literal 1 binary64))) (patch (.f64 (/.f64 (sqrt.f64 n) (sqrt.f64 k)) (/.f64 (sqrt.f64 (PI.f64)) #s(literal 1 binary64))) #<representation binary64>) () ())) ())
#s(alt (sqrt (/ (* n (PI)) k)) (taylor inf n) (#s(alt (.f64 (/.f64 (sqrt.f64 n) (sqrt.f64 k)) (/.f64 (sqrt.f64 (PI.f64)) #s(literal 1 binary64))) (patch (.f64 (/.f64 (sqrt.f64 n) (sqrt.f64 k)) (/.f64 (sqrt.f64 (PI.f64)) #s(literal 1 binary64))) #<representation binary64>) () ())) ())
#s(alt (sqrt (/ (* n (PI)) k)) (taylor inf n) (#s(alt (.f64 (/.f64 (sqrt.f64 n) (sqrt.f64 k)) (/.f64 (sqrt.f64 (PI.f64)) #s(literal 1 binary64))) (patch (.f64 (/.f64 (sqrt.f64 n) (sqrt.f64 k)) (/.f64 (sqrt.f64 (PI.f64)) #s(literal 1 binary64))) #<representation binary64>) () ())) ())
#s(alt (* -1 (* (sqrt (/ (* n (PI)) k)) (pow (sqrt -1) 2))) (taylor -inf n) (#s(alt (.f64 (/.f64 (sqrt.f64 n) (sqrt.f64 k)) (/.f64 (sqrt.f64 (PI.f64)) #s(literal 1 binary64))) (patch (.f64 (/.f64 (sqrt.f64 n) (sqrt.f64 k)) (/.f64 (sqrt.f64 (PI.f64)) #s(literal 1 binary64))) #<representation binary64>) () ())) ())
#s(alt (* -1 (* (sqrt (/ (* n (PI)) k)) (pow (sqrt -1) 2))) (taylor -inf n) (#s(alt (.f64 (/.f64 (sqrt.f64 n) (sqrt.f64 k)) (/.f64 (sqrt.f64 (PI.f64)) #s(literal 1 binary64))) (patch (.f64 (/.f64 (sqrt.f64 n) (sqrt.f64 k)) (/.f64 (sqrt.f64 (PI.f64)) #s(literal 1 binary64))) #<representation binary64>) () ())) ())
#s(alt (* -1 (* (sqrt (/ (* n (PI)) k)) (pow (sqrt -1) 2))) (taylor -inf n) (#s(alt (.f64 (/.f64 (sqrt.f64 n) (sqrt.f64 k)) (/.f64 (sqrt.f64 (PI.f64)) #s(literal 1 binary64))) (patch (.f64 (/.f64 (sqrt.f64 n) (sqrt.f64 k)) (/.f64 (sqrt.f64 (PI.f64)) #s(literal 1 binary64))) #<representation binary64>) () ())) ())
#s(alt (* -1 (* (sqrt (/ (* n (PI)) k)) (pow (sqrt -1) 2))) (taylor -inf n) (#s(alt (.f64 (/.f64 (sqrt.f64 n) (sqrt.f64 k)) (/.f64 (sqrt.f64 (PI.f64)) #s(literal 1 binary64))) (patch (.f64 (/.f64 (sqrt.f64 n) (sqrt.f64 k)) (/.f64 (sqrt.f64 (PI.f64)) #s(literal 1 binary64))) #<representation binary64>) () ())) ())
#s(alt (sqrt (/ (* n (PI)) k)) (taylor 0 k) (#s(alt (.f64 (/.f64 (sqrt.f64 n) (sqrt.f64 k)) (/.f64 (sqrt.f64 (PI.f64)) #s(literal 1 binary64))) (patch (.f64 (/.f64 (sqrt.f64 n) (sqrt.f64 k)) (/.f64 (sqrt.f64 (PI.f64)) #s(literal 1 binary64))) #<representation binary64>) () ())) ())
#s(alt (sqrt (/ (* n (PI)) k)) (taylor 0 k) (#s(alt (.f64 (/.f64 (sqrt.f64 n) (sqrt.f64 k)) (/.f64 (sqrt.f64 (PI.f64)) #s(literal 1 binary64))) (patch (.f64 (/.f64 (sqrt.f64 n) (sqrt.f64 k)) (/.f64 (sqrt.f64 (PI.f64)) #s(literal 1 binary64))) #<representation binary64>) () ())) ())
#s(alt (sqrt (/ (* n (PI)) k)) (taylor 0 k) (#s(alt (.f64 (/.f64 (sqrt.f64 n) (sqrt.f64 k)) (/.f64 (sqrt.f64 (PI.f64)) #s(literal 1 binary64))) (patch (.f64 (/.f64 (sqrt.f64 n) (sqrt.f64 k)) (/.f64 (sqrt.f64 (PI.f64)) #s(literal 1 binary64))) #<representation binary64>) () ())) ())
#s(alt (sqrt (/ (* n (PI)) k)) (taylor 0 k) (#s(alt (.f64 (/.f64 (sqrt.f64 n) (sqrt.f64 k)) (/.f64 (sqrt.f64 (PI.f64)) #s(literal 1 binary64))) (patch (.f64 (/.f64 (sqrt.f64 n) (sqrt.f64 k)) (/.f64 (sqrt.f64 (PI.f64)) #s(literal 1 binary64))) #<representation binary64>) () ())) ())
#s(alt (sqrt (/ (* n (PI)) k)) (taylor inf k) (#s(alt (.f64 (/.f64 (sqrt.f64 n) (sqrt.f64 k)) (/.f64 (sqrt.f64 (PI.f64)) #s(literal 1 binary64))) (patch (.f64 (/.f64 (sqrt.f64 n) (sqrt.f64 k)) (/.f64 (sqrt.f64 (PI.f64)) #s(literal 1 binary64))) #<representation binary64>) () ())) ())
#s(alt (sqrt (/ (* n (PI)) k)) (taylor inf k) (#s(alt (.f64 (/.f64 (sqrt.f64 n) (sqrt.f64 k)) (/.f64 (sqrt.f64 (PI.f64)) #s(literal 1 binary64))) (patch (.f64 (/.f64 (sqrt.f64 n) (sqrt.f64 k)) (/.f64 (sqrt.f64 (PI.f64)) #s(literal 1 binary64))) #<representation binary64>) () ())) ())
#s(alt (sqrt (/ (* n (PI)) k)) (taylor inf k) (#s(alt (.f64 (/.f64 (sqrt.f64 n) (sqrt.f64 k)) (/.f64 (sqrt.f64 (PI.f64)) #s(literal 1 binary64))) (patch (.f64 (/.f64 (sqrt.f64 n) (sqrt.f64 k)) (/.f64 (sqrt.f64 (PI.f64)) #s(literal 1 binary64))) #<representation binary64>) () ())) ())
#s(alt (sqrt (/ (* n (PI)) k)) (taylor inf k) (#s(alt (.f64 (/.f64 (sqrt.f64 n) (sqrt.f64 k)) (/.f64 (sqrt.f64 (PI.f64)) #s(literal 1 binary64))) (patch (.f64 (/.f64 (sqrt.f64 n) (sqrt.f64 k)) (/.f64 (sqrt.f64 (PI.f64)) #s(literal 1 binary64))) #<representation binary64>) () ())) ())
#s(alt (sqrt (/ (* n (PI)) k)) (taylor -inf k) (#s(alt (.f64 (/.f64 (sqrt.f64 n) (sqrt.f64 k)) (/.f64 (sqrt.f64 (PI.f64)) #s(literal 1 binary64))) (patch (.f64 (/.f64 (sqrt.f64 n) (sqrt.f64 k)) (/.f64 (sqrt.f64 (PI.f64)) #s(literal 1 binary64))) #<representation binary64>) () ())) ())
#s(alt (sqrt (/ (* n (PI)) k)) (taylor -inf k) (#s(alt (.f64 (/.f64 (sqrt.f64 n) (sqrt.f64 k)) (/.f64 (sqrt.f64 (PI.f64)) #s(literal 1 binary64))) (patch (.f64 (/.f64 (sqrt.f64 n) (sqrt.f64 k)) (/.f64 (sqrt.f64 (PI.f64)) #s(literal 1 binary64))) #<representation binary64>) () ())) ())
#s(alt (sqrt (/ (* n (PI)) k)) (taylor -inf k) (#s(alt (.f64 (/.f64 (sqrt.f64 n) (sqrt.f64 k)) (/.f64 (sqrt.f64 (PI.f64)) #s(literal 1 binary64))) (patch (.f64 (/.f64 (sqrt.f64 n) (sqrt.f64 k)) (/.f64 (sqrt.f64 (PI.f64)) #s(literal 1 binary64))) #<representation binary64>) () ())) ())
#s(alt (sqrt (/ (* n (PI)) k)) (taylor -inf k) (#s(alt (.f64 (/.f64 (sqrt.f64 n) (sqrt.f64 k)) (/.f64 (sqrt.f64 (PI.f64)) #s(literal 1 binary64))) (patch (.f64 (/.f64 (sqrt.f64 n) (sqrt.f64 k)) (/.f64 (sqrt.f64 (PI.f64)) #s(literal 1 binary64))) #<representation binary64>) () ())) ())
#s(alt (sqrt (/ 1 k)) (taylor 0 k) (#s(alt (sqrt.f64 (/.f64 #s(literal 1 binary64) k)) (patch (sqrt.f64 (/.f64 #s(literal 1 binary64) k)) #<representation binary64>) () ())) ())
#s(alt (sqrt (/ 1 k)) (taylor 0 k) (#s(alt (sqrt.f64 (/.f64 #s(literal 1 binary64) k)) (patch (sqrt.f64 (/.f64 #s(literal 1 binary64) k)) #<representation binary64>) () ())) ())
#s(alt (sqrt (/ 1 k)) (taylor 0 k) (#s(alt (sqrt.f64 (/.f64 #s(literal 1 binary64) k)) (patch (sqrt.f64 (/.f64 #s(literal 1 binary64) k)) #<representation binary64>) () ())) ())
#s(alt (sqrt (/ 1 k)) (taylor 0 k) (#s(alt (sqrt.f64 (/.f64 #s(literal 1 binary64) k)) (patch (sqrt.f64 (/.f64 #s(literal 1 binary64) k)) #<representation binary64>) () ())) ())
#s(alt (sqrt (/ 1 k)) (taylor inf k) (#s(alt (sqrt.f64 (/.f64 #s(literal 1 binary64) k)) (patch (sqrt.f64 (/.f64 #s(literal 1 binary64) k)) #<representation binary64>) () ())) ())
#s(alt (sqrt (/ 1 k)) (taylor inf k) (#s(alt (sqrt.f64 (/.f64 #s(literal 1 binary64) k)) (patch (sqrt.f64 (/.f64 #s(literal 1 binary64) k)) #<representation binary64>) () ())) ())
#s(alt (sqrt (/ 1 k)) (taylor inf k) (#s(alt (sqrt.f64 (/.f64 #s(literal 1 binary64) k)) (patch (sqrt.f64 (/.f64 #s(literal 1 binary64) k)) #<representation binary64>) () ())) ())
#s(alt (sqrt (/ 1 k)) (taylor inf k) (#s(alt (sqrt.f64 (/.f64 #s(literal 1 binary64) k)) (patch (sqrt.f64 (/.f64 #s(literal 1 binary64) k)) #<representation binary64>) () ())) ())
#s(alt (* (sqrt (/ 1 k)) (pow (sqrt -1) 2)) (taylor -inf k) (#s(alt (sqrt.f64 (/.f64 #s(literal 1 binary64) k)) (patch (sqrt.f64 (/.f64 #s(literal 1 binary64) k)) #<representation binary64>) () ())) ())
#s(alt (* (sqrt (/ 1 k)) (pow (sqrt -1) 2)) (taylor -inf k) (#s(alt (sqrt.f64 (/.f64 #s(literal 1 binary64) k)) (patch (sqrt.f64 (/.f64 #s(literal 1 binary64) k)) #<representation binary64>) () ())) ())
#s(alt (* (sqrt (/ 1 k)) (pow (sqrt -1) 2)) (taylor -inf k) (#s(alt (sqrt.f64 (/.f64 #s(literal 1 binary64) k)) (patch (sqrt.f64 (/.f64 #s(literal 1 binary64) k)) #<representation binary64>) () ())) ())
#s(alt (* (sqrt (/ 1 k)) (pow (sqrt -1) 2)) (taylor -inf k) (#s(alt (sqrt.f64 (/.f64 #s(literal 1 binary64) k)) (patch (sqrt.f64 (/.f64 #s(literal 1 binary64) k)) #<representation binary64>) () ())) ())
#s(alt (* n (PI)) (taylor 0 n) (#s(alt (.f64 n (PI.f64)) (patch (.f64 n (PI.f64)) #<representation binary64>) () ())) ())
#s(alt (* n (PI)) (taylor 0 n) (#s(alt (.f64 n (PI.f64)) (patch (.f64 n (PI.f64)) #<representation binary64>) () ())) ())
#s(alt (* n (PI)) (taylor 0 n) (#s(alt (.f64 n (PI.f64)) (patch (.f64 n (PI.f64)) #<representation binary64>) () ())) ())
#s(alt (* n (PI)) (taylor 0 n) (#s(alt (.f64 n (PI.f64)) (patch (.f64 n (PI.f64)) #<representation binary64>) () ())) ())
#s(alt (* n (PI)) (taylor inf n) (#s(alt (.f64 n (PI.f64)) (patch (.f64 n (PI.f64)) #<representation binary64>) () ())) ())
#s(alt (* n (PI)) (taylor inf n) (#s(alt (.f64 n (PI.f64)) (patch (.f64 n (PI.f64)) #<representation binary64>) () ())) ())
#s(alt (* n (PI)) (taylor inf n) (#s(alt (.f64 n (PI.f64)) (patch (.f64 n (PI.f64)) #<representation binary64>) () ())) ())
#s(alt (* n (PI)) (taylor inf n) (#s(alt (.f64 n (PI.f64)) (patch (.f64 n (PI.f64)) #<representation binary64>) () ())) ())
#s(alt (* n (PI)) (taylor -inf n) (#s(alt (.f64 n (PI.f64)) (patch (.f64 n (PI.f64)) #<representation binary64>) () ())) ())
#s(alt (* n (PI)) (taylor -inf n) (#s(alt (.f64 n (PI.f64)) (patch (.f64 n (PI.f64)) #<representation binary64>) () ())) ())
#s(alt (* n (PI)) (taylor -inf n) (#s(alt (.f64 n (PI.f64)) (patch (.f64 n (PI.f64)) #<representation binary64>) () ())) ())
#s(alt (* n (PI)) (taylor -inf n) (#s(alt (.f64 n (PI.f64)) (patch (.f64 n (PI.f64)) #<representation binary64>) () ())) ())

Calls

96 calls:

Time	Variable		Point	Expression
1.0ms	k	@	-inf	(* (* (/ (sqrt n) (sqrt k)) (/ (sqrt (PI)) 1)) (sqrt 2))
0.0ms	k	@	-inf	(sqrt (* 2 (/ (* (PI) n) k)))
0.0ms	n	@	-inf	(sqrt (* 2 (/ (* (PI) n) k)))
0.0ms	n	@	-inf	(* (sqrt 2) (sqrt (* n (PI))))
0.0ms	k	@	-inf	(* (/ (sqrt n) (sqrt k)) (/ (sqrt (PI)) 1))

simplify373.0ms (3.4%)

Memory

25.0MiB live, 535.7MiB allocated

Algorithm

1×	egg-herbie

Rules

10 910×	`lower-fma.f64`
10 910×	`lower-fma.f32`
4 890×	`lower-*.f64`
4 890×	`lower-*.f32`
3 010×	`lower-+.f64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	196	5238
1	572	5160
2	1811	4993
3	3603	4529
4	6501	4529
0	8251	4479

Stop Event

1×	iter limit
1×	node limit

Counts

384 → 384

Calls

Call 1

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

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

rewrite288.0ms (2.6%)

Memory

-10.8MiB live, 503.3MiB allocated

Algorithm

1×	batch-egg-rewrite

Rules

4 954×	`lower-*.f32`
4 938×	`lower-*.f64`
4 268×	`lower-/.f32`
4 256×	`lower-/.f64`
2 118×	`lower-pow.f32`

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	49	238
0	76	214
1	267	206
2	1520	201
0	8282	201

Stop Event

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

Counts

23 → 1 122

Calls

Call 1

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

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

eval367.0ms (3.3%)

Memory: -177.1MiB live, 535.8MiB allocated
Compiler: Compiled 30 591 to 3 844 computations (87.4% saved)

prune393.0ms (3.5%)

Memory

-14.5MiB live, 669.2MiB allocated

Pruning

57 alts after pruning (51 fresh and 6 done)

	Pruned	Kept	Total
New	1 862	40	1 902
Fresh	11	11	22
Picked	1	4	5
Done	0	2	2
Total	1 874	57	1 931

Accuracy

100.0%

Counts

1 931 → 57

Alt Table

Click to see full alt table

Status	Accuracy	Program
✓	99.5%	(/.f64 (pow.f64 (.f64 #s(literal 2 binary64) (.f64 (PI.f64) n)) (fma.f64 k #s(literal -1/2 binary64) #s(literal 1/2 binary64))) (sqrt.f64 k))
	99.1%	(/.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) k)) (pow.f64 (.f64 #s(literal 2 binary64) (.f64 (PI.f64) n)) (fma.f64 k #s(literal 1/2 binary64) #s(literal -1/2 binary64))))
	50.4%	(/.f64 #s(approx (pow (* 2 (* (PI) n)) (+ (* k 1/2) 1/2)) (.f64 (sqrt.f64 (.f64 n #s(literal 2 binary64))) (sqrt.f64 (PI.f64)))) (sqrt.f64 k))
	50.3%	(/.f64 #s(approx (pow (* 2 (* (PI) n)) (+ (* k 1/2) 1/2)) (.f64 (sqrt.f64 (.f64 #s(literal 2 binary64) (PI.f64))) (sqrt.f64 n))) (sqrt.f64 k))
	50.4%	(/.f64 #s(approx (pow (* 2 (* (PI) n)) (+ (* k 1/2) 1/2)) (.f64 (sqrt.f64 #s(literal 2 binary64)) (sqrt.f64 (.f64 n (.f64 (sqrt.f64 (.f64 (PI.f64) (sqrt.f64 (PI.f64)))) (sqrt.f64 (sqrt.f64 (PI.f64)))))))) (sqrt.f64 k))
✓	50.5%	(/.f64 #s(approx (pow (* 2 (* (PI) n)) (+ (* k 1/2) 1/2)) (.f64 (sqrt.f64 #s(literal 2 binary64)) (sqrt.f64 (.f64 n (PI.f64))))) (sqrt.f64 k))
	50.6%	(/.f64 #s(approx (pow (* 2 (* (PI) n)) (+ (* k 1/2) 1/2)) (sqrt.f64 (.f64 (PI.f64) (.f64 n #s(literal 2 binary64))))) (sqrt.f64 k))
	50.5%	(/.f64 #s(literal 1 binary64) (/.f64 (sqrt.f64 k) #s(approx (pow (* 2 (* (PI) n)) (+ (* k 1/2) 1/2)) (sqrt.f64 (.f64 (PI.f64) (.f64 n #s(literal 2 binary64)))))))
	99.4%	(/.f64 #s(literal 1 binary64) (.f64 (sqrt.f64 k) (pow.f64 (.f64 #s(literal 2 binary64) (*.f64 (PI.f64) n)) (fma.f64 k #s(literal 1/2 binary64) #s(literal -1/2 binary64)))))
	76.0%	(.f64 (pow.f64 (.f64 (PI.f64) (.f64 n #s(literal 2 binary64))) (.f64 k #s(literal -1/2 binary64))) (sqrt.f64 (/.f64 (.f64 (PI.f64) (.f64 n #s(literal 2 binary64))) k)))
✓	99.4%	(.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) (pow.f64 (.f64 (*.f64 #s(literal 2 binary64) (PI.f64)) n) (fma.f64 k #s(literal -1/2 binary64) #s(literal 1/2 binary64))))
▶	99.4%	(.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) (pow.f64 (sqrt.f64 (.f64 #s(literal 2 binary64) (*.f64 (PI.f64) n))) (-.f64 #s(literal 1 binary64) k)))
	50.5%	(.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) #s(approx (pow ( (* 2 (PI)) n) (/ (- 1 k) 2)) (.f64 (sqrt.f64 #s(literal 2 binary64)) (sqrt.f64 (.f64 n (PI.f64))))))
	50.5%	(.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) #s(approx (pow ( 2 (* (PI) n)) (+ (* k 1/2) 1/2)) (sqrt.f64 (.f64 (PI.f64) (.f64 n #s(literal 2 binary64))))))
	76.1%	(sqrt.f64 (/.f64 (.f64 #s(literal 2 binary64) (/.f64 (.f64 (PI.f64) n) k)) (pow.f64 (.f64 #s(literal 2 binary64) (.f64 (PI.f64) n)) k)))
	50.5%	#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (/.f64 (.f64 (.f64 (neg.f64 (sqrt.f64 (PI.f64))) (sqrt.f64 #s(literal 2 binary64))) (sqrt.f64 n)) (neg.f64 (sqrt.f64 k))))
	50.5%	#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (/.f64 (.f64 (.f64 #s(literal 1 binary64) (sqrt.f64 #s(literal 2 binary64))) (neg.f64 (sqrt.f64 n))) (*.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 (PI.f64))) (neg.f64 (sqrt.f64 k)))))
	38.3%	#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (/.f64 (.f64 (.f64 #s(literal 1 binary64) (sqrt.f64 #s(literal 2 binary64))) #s(literal -1 binary64)) (*.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 (PI.f64))) (neg.f64 (sqrt.f64 (/.f64 k n))))))
	38.3%	#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (/.f64 (sqrt.f64 (*.f64 #s(literal 2 binary64) (PI.f64))) (sqrt.f64 (/.f64 k n))))
	38.3%	#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (/.f64 #s(literal 1 binary64) (/.f64 (sqrt.f64 (/.f64 k n)) (sqrt.f64 (*.f64 #s(literal 2 binary64) (PI.f64))))))
	50.3%	#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (/.f64 #s(literal 1 binary64) (/.f64 (neg.f64 (sqrt.f64 k)) (.f64 (neg.f64 (sqrt.f64 n)) (sqrt.f64 (.f64 #s(literal 2 binary64) (PI.f64)))))))
	50.3%	#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (.f64 (/.f64 (sqrt.f64 (.f64 #s(literal 2 binary64) (PI.f64))) (sqrt.f64 k)) (/.f64 (sqrt.f64 n) #s(literal 1 binary64))))
	50.4%	#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (.f64 (/.f64 (sqrt.f64 (.f64 #s(literal 2 binary64) n)) (sqrt.f64 k)) (sqrt.f64 (PI.f64))))
	50.3%	#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (.f64 (/.f64 (sqrt.f64 n) (sqrt.f64 k)) (/.f64 (sqrt.f64 (.f64 #s(literal 2 binary64) (PI.f64))) #s(literal 1 binary64))))
	50.5%	#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (.f64 (/.f64 (sqrt.f64 #s(literal 2 binary64)) (sqrt.f64 k)) (sqrt.f64 (.f64 (PI.f64) n))))
▶	50.4%	#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (.f64 (/.f64 (neg.f64 (sqrt.f64 n)) (.f64 (neg.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 (PI.f64)))) (sqrt.f64 k))) (sqrt.f64 #s(literal 2 binary64))))
	50.3%	#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) (/.f64 (sqrt.f64 (.f64 #s(literal 2 binary64) (PI.f64))) (/.f64 #s(literal 1 binary64) (sqrt.f64 n)))))
	38.3%	#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (.f64 (/.f64 #s(literal -1 binary64) (.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 (PI.f64))) (neg.f64 (sqrt.f64 (/.f64 k n))))) (sqrt.f64 #s(literal 2 binary64))))
	38.2%	#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (.f64 (.f64 (/.f64 (sqrt.f64 (sqrt.f64 (PI.f64))) (sqrt.f64 (/.f64 k n))) (sqrt.f64 (sqrt.f64 (PI.f64)))) (sqrt.f64 #s(literal 2 binary64))))
	50.3%	#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (.f64 (.f64 (/.f64 (sqrt.f64 (sqrt.f64 (PI.f64))) (sqrt.f64 k)) (/.f64 (sqrt.f64 (sqrt.f64 (PI.f64))) (/.f64 #s(literal 1 binary64) (sqrt.f64 n)))) (sqrt.f64 #s(literal 2 binary64))))
	50.4%	#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (.f64 (.f64 (/.f64 (sqrt.f64 n) (/.f64 #s(literal -1 binary64) (sqrt.f64 (PI.f64)))) (/.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) #s(literal -1 binary64))) (sqrt.f64 #s(literal 2 binary64))))
	50.4%	#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (.f64 (.f64 (/.f64 (sqrt.f64 n) (sqrt.f64 k)) (/.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (sqrt.f64 (PI.f64))))) (sqrt.f64 #s(literal 2 binary64))))
	50.5%	#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (.f64 (.f64 (/.f64 (sqrt.f64 n) (sqrt.f64 k)) (sqrt.f64 (PI.f64))) (sqrt.f64 #s(literal 2 binary64))))
	50.2%	#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (.f64 (.f64 (sqrt.f64 (/.f64 (PI.f64) k)) (sqrt.f64 n)) (sqrt.f64 #s(literal 2 binary64))))
▶	50.1%	#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (.f64 (.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) k)) (sqrt.f64 (*.f64 (PI.f64) n))) (sqrt.f64 #s(literal 2 binary64))))
	50.1%	#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (.f64 (.f64 (sqrt.f64 (*.f64 (PI.f64) n)) (sqrt.f64 #s(literal 2 binary64))) (sqrt.f64 (/.f64 #s(literal 1 binary64) k))))
	50.0%	#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (.f64 (.f64 (sqrt.f64 (*.f64 n #s(literal 2 binary64))) (sqrt.f64 (PI.f64))) (sqrt.f64 (/.f64 #s(literal 1 binary64) k))))
	50.0%	#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (.f64 (.f64 (sqrt.f64 (*.f64 #s(literal 2 binary64) (PI.f64))) (sqrt.f64 n)) (sqrt.f64 (/.f64 #s(literal 1 binary64) k))))
	37.7%	#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (.f64 (.f64 (sqrt.f64 (sqrt.f64 (PI.f64))) (sqrt.f64 (/.f64 (*.f64 (sqrt.f64 (PI.f64)) n) k))) (sqrt.f64 #s(literal 2 binary64))))
	37.6%	#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (.f64 (sqrt.f64 (/.f64 (.f64 n (.f64 (sqrt.f64 (.f64 (PI.f64) (sqrt.f64 (PI.f64)))) (sqrt.f64 (sqrt.f64 (PI.f64))))) k)) (sqrt.f64 #s(literal 2 binary64))))
✓	37.7%	#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (.f64 (sqrt.f64 (/.f64 (.f64 n (PI.f64)) k)) (sqrt.f64 #s(literal 2 binary64))))
▶	37.7%	#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (*.f64 (sqrt.f64 (/.f64 (PI.f64) (/.f64 k n))) (sqrt.f64 #s(literal 2 binary64))))
	37.6%	#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (.f64 (sqrt.f64 (/.f64 n k)) (sqrt.f64 (.f64 #s(literal 2 binary64) (PI.f64)))))
	37.7%	#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (.f64 (sqrt.f64 (.f64 (/.f64 (PI.f64) k) n)) (sqrt.f64 #s(literal 2 binary64))))
	50.2%	#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (.f64 (sqrt.f64 (.f64 (PI.f64) n)) (sqrt.f64 (/.f64 #s(literal 2 binary64) k))))
	37.7%	#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (.f64 (sqrt.f64 (.f64 #s(literal 2 binary64) (/.f64 n k))) (sqrt.f64 (PI.f64))))
	50.1%	#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (.f64 (sqrt.f64 (.f64 #s(literal 2 binary64) (.f64 (.f64 (sqrt.f64 (PI.f64)) (sqrt.f64 (PI.f64))) n))) (sqrt.f64 (/.f64 #s(literal 1 binary64) k))))
	50.4%	#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (.f64 (sqrt.f64 (.f64 #s(literal 2 binary64) (.f64 (PI.f64) n))) (.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k))) (sqrt.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k))))))
✓	50.2%	#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (.f64 (sqrt.f64 (.f64 #s(literal 2 binary64) (*.f64 (PI.f64) n))) (sqrt.f64 (/.f64 #s(literal 1 binary64) k))))
	50.2%	#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (.f64 (sqrt.f64 n) (sqrt.f64 (/.f64 (.f64 #s(literal 2 binary64) (PI.f64)) k))))
	37.8%	#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt.f64 (/.f64 #s(literal 2 binary64) (/.f64 k (*.f64 (PI.f64) n)))))
	37.8%	#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt.f64 (.f64 (.f64 (PI.f64) n) (/.f64 #s(literal 2 binary64) k))))
	37.8%	#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt.f64 (.f64 n (.f64 (*.f64 #s(literal 2 binary64) (PI.f64)) (/.f64 #s(literal 1 binary64) k)))))
	37.7%	#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt.f64 (.f64 #s(literal 2 binary64) (/.f64 (.f64 (*.f64 (sqrt.f64 (PI.f64)) (sqrt.f64 (PI.f64))) n) k))))
✓	37.8%	#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt.f64 (.f64 #s(literal 2 binary64) (/.f64 (.f64 (PI.f64) n) k))))
	37.8%	#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt.f64 (.f64 #s(literal 2 binary64) (.f64 (/.f64 n k) (PI.f64)))))
▶	37.9%	#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt.f64 (.f64 #s(literal 2 binary64) (.f64 n (/.f64 (PI.f64) k)))))

Compiler

Compiled 1 648 to 1 248 computations (24.3% saved)

simplify139.0ms (1.3%)

Memory

-11.2MiB live, 80.9MiB allocated

Algorithm

1×	egg-herbie

Localize:

Found 20 expressions of interest:

New	Metric	Score	Program
✓	cost-diff	0	#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (.f64 (/.f64 (neg.f64 (sqrt.f64 n)) (.f64 (neg.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 (PI.f64)))) (sqrt.f64 k))) (sqrt.f64 #s(literal 2 binary64))))
✓	cost-diff	128	(neg.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 (PI.f64))))
✓	cost-diff	192	(*.f64 (neg.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 (PI.f64)))) (sqrt.f64 k))
✓	cost-diff	640	(/.f64 (neg.f64 (sqrt.f64 n)) (*.f64 (neg.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 (PI.f64)))) (sqrt.f64 k)))
✓	cost-diff	0	(sqrt.f64 (/.f64 #s(literal 1 binary64) k))
✓	cost-diff	0	(.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) k)) (sqrt.f64 (.f64 (PI.f64) n)))
✓	cost-diff	0	(.f64 (.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) k)) (sqrt.f64 (*.f64 (PI.f64) n))) (sqrt.f64 #s(literal 2 binary64)))
✓	cost-diff	0	#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (.f64 (.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) k)) (sqrt.f64 (*.f64 (PI.f64) n))) (sqrt.f64 #s(literal 2 binary64))))
✓	cost-diff	0	(sqrt.f64 (/.f64 (PI.f64) (/.f64 k n)))
✓	cost-diff	0	(*.f64 (sqrt.f64 (/.f64 (PI.f64) (/.f64 k n))) (sqrt.f64 #s(literal 2 binary64)))
✓	cost-diff	0	#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (*.f64 (sqrt.f64 (/.f64 (PI.f64) (/.f64 k n))) (sqrt.f64 #s(literal 2 binary64))))
✓	cost-diff	384	(/.f64 (PI.f64) (/.f64 k n))
✓	cost-diff	0	(*.f64 n (/.f64 (PI.f64) k))
✓	cost-diff	0	(.f64 #s(literal 2 binary64) (.f64 n (/.f64 (PI.f64) k)))
✓	cost-diff	0	(sqrt.f64 (.f64 #s(literal 2 binary64) (.f64 n (/.f64 (PI.f64) k))))
✓	cost-diff	0	#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt.f64 (.f64 #s(literal 2 binary64) (.f64 n (/.f64 (PI.f64) k)))))
✓	cost-diff	0	(pow.f64 (sqrt.f64 (.f64 #s(literal 2 binary64) (.f64 (PI.f64) n))) (-.f64 #s(literal 1 binary64) k))
✓	cost-diff	0	(sqrt.f64 k)
✓	cost-diff	0	(/.f64 #s(literal 1 binary64) (sqrt.f64 k))
✓	cost-diff	320	(.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) (pow.f64 (sqrt.f64 (.f64 #s(literal 2 binary64) (*.f64 (PI.f64) n))) (-.f64 #s(literal 1 binary64) k)))

Rules

1 136×	`lower-*.f32`
1 116×	`lower-*.f64`
1 076×	`lower-fma.f64`
1 076×	`lower-fma.f32`
810×	`times-frac`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	48	323
0	79	318
1	130	308
2	247	298
3	707	298
4	2500	298
5	3253	298
6	3517	298
7	3756	298
8	3977	298
9	4051	298
10	4127	298
11	4222	298
12	4349	298
13	4349	298
0	4349	294

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

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

localize145.0ms (1.3%)

Memory

24.2MiB live, 213.9MiB allocated

Localize:

Found 20 expressions of interest:

New	Metric	Score	Program
✓	accuracy	99.4%	(/.f64 (neg.f64 (sqrt.f64 n)) (*.f64 (neg.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 (PI.f64)))) (sqrt.f64 k)))
✓	accuracy	99.2%	(.f64 (/.f64 (neg.f64 (sqrt.f64 n)) (.f64 (neg.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 (PI.f64)))) (sqrt.f64 k))) (sqrt.f64 #s(literal 2 binary64)))
✓	accuracy	98.4%	(sqrt.f64 (PI.f64))
✓	accuracy	50.9%	#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (.f64 (/.f64 (neg.f64 (sqrt.f64 n)) (.f64 (neg.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 (PI.f64)))) (sqrt.f64 k))) (sqrt.f64 #s(literal 2 binary64))))
✓	accuracy	99.4%	(.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) k)) (sqrt.f64 (.f64 (PI.f64) n)))
✓	accuracy	99.4%	(sqrt.f64 (/.f64 #s(literal 1 binary64) k))
✓	accuracy	99.2%	(.f64 (.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) k)) (sqrt.f64 (*.f64 (PI.f64) n))) (sqrt.f64 #s(literal 2 binary64)))
✓	accuracy	50.9%	#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (.f64 (.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) k)) (sqrt.f64 (*.f64 (PI.f64) n))) (sqrt.f64 #s(literal 2 binary64))))
✓	accuracy	99.2%	(*.f64 (sqrt.f64 (/.f64 (PI.f64) (/.f64 k n))) (sqrt.f64 #s(literal 2 binary64)))
✓	accuracy	99.1%	(/.f64 (PI.f64) (/.f64 k n))
✓	accuracy	76.3%	(sqrt.f64 (/.f64 (PI.f64) (/.f64 k n)))
✓	accuracy	50.9%	#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (*.f64 (sqrt.f64 (/.f64 (PI.f64) (/.f64 k n))) (sqrt.f64 #s(literal 2 binary64))))
✓	accuracy	99.8%	(*.f64 n (/.f64 (PI.f64) k))
✓	accuracy	99.5%	(/.f64 (PI.f64) k)
✓	accuracy	76.3%	(sqrt.f64 (.f64 #s(literal 2 binary64) (.f64 n (/.f64 (PI.f64) k))))
✓	accuracy	50.9%	#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt.f64 (.f64 #s(literal 2 binary64) (.f64 n (/.f64 (PI.f64) k)))))
✓	accuracy	99.7%	(pow.f64 (sqrt.f64 (.f64 #s(literal 2 binary64) (.f64 (PI.f64) n))) (-.f64 #s(literal 1 binary64) k))
✓	accuracy	99.7%	(.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) (pow.f64 (sqrt.f64 (.f64 #s(literal 2 binary64) (*.f64 (PI.f64) n))) (-.f64 #s(literal 1 binary64) k)))
✓	accuracy	99.7%	(*.f64 (PI.f64) n)
✓	accuracy	99.6%	(/.f64 #s(literal 1 binary64) (sqrt.f64 k))

Samples

78.0ms

256×

valid

Compiler

Compiled 277 to 42 computations (84.8% saved)

Precisions

Click to see histograms. Total time spent on operations: 57.0ms

ival-mult: 18.0ms (31.6% of total)

ival-sqrt: 13.0ms (22.8% of total)

ival-div: 12.0ms (21.1% of total)

ival-pow: 9.0ms (15.8% of total)

ival-neg: 2.0ms (3.5% of total)

ival-pi: 1.0ms (1.8% of total)

ival-sub: 1.0ms (1.8% of total)

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

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

exact: 0.0ms (0% of total)

series32.0ms (0.3%)

Memory

4.8MiB live, 42.3MiB allocated

Counts

24 → 456

Calls

Call 1

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

Outputs
#s(alt (* (sqrt (/ (* n (PI)) k)) (sqrt 2)) (taylor 0 k) (#s(alt (.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) (pow.f64 (sqrt.f64 (.f64 #s(literal 2 binary64) (.f64 (PI.f64) n))) (-.f64 #s(literal 1 binary64) k))) (patch (.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) (pow.f64 (sqrt.f64 (.f64 #s(literal 2 binary64) (.f64 (PI.f64) n))) (-.f64 #s(literal 1 binary64) k))) #<representation binary64>) () ())) ())
#s(alt (/ (+ (* -1 (* (sqrt (* (pow k 3) (* n (PI)))) (* (log (* (sqrt (* n (PI))) (sqrt 2))) (sqrt 2)))) (* (sqrt (* k (* n (PI)))) (sqrt 2))) k) (taylor 0 k) (#s(alt (.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) (pow.f64 (sqrt.f64 (.f64 #s(literal 2 binary64) (.f64 (PI.f64) n))) (-.f64 #s(literal 1 binary64) k))) (patch (.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) (pow.f64 (sqrt.f64 (.f64 #s(literal 2 binary64) (.f64 (PI.f64) n))) (-.f64 #s(literal 1 binary64) k))) #<representation binary64>) () ())) ())
#s(alt (/ (+ (* k (+ (* -1 (* (sqrt (* k (* n (PI)))) (* (log (* (sqrt (* n (PI))) (sqrt 2))) (sqrt 2)))) (* 1/2 (* (sqrt (* (pow k 3) (* n (PI)))) (* (pow (log (* (sqrt (* n (PI))) (sqrt 2))) 2) (sqrt 2)))))) (* (sqrt (* k (* n (PI)))) (sqrt 2))) k) (taylor 0 k) (#s(alt (.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) (pow.f64 (sqrt.f64 (.f64 #s(literal 2 binary64) (.f64 (PI.f64) n))) (-.f64 #s(literal 1 binary64) k))) (patch (.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) (pow.f64 (sqrt.f64 (.f64 #s(literal 2 binary64) (.f64 (PI.f64) n))) (-.f64 #s(literal 1 binary64) k))) #<representation binary64>) () ())) ())
#s(alt (/ (+ (* k (+ (* -1 (* (sqrt (* k (* n (PI)))) (* (log (* (sqrt (* n (PI))) (sqrt 2))) (sqrt 2)))) (* k (+ (* -1/6 (* (sqrt (* (pow k 3) (* n (PI)))) (* (pow (log (* (sqrt (* n (PI))) (sqrt 2))) 3) (sqrt 2)))) (* 1/2 (* (sqrt (* k (* n (PI)))) (* (pow (log (* (sqrt (* n (PI))) (sqrt 2))) 2) (sqrt 2)))))))) (* (sqrt (* k (* n (PI)))) (sqrt 2))) k) (taylor 0 k) (#s(alt (.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) (pow.f64 (sqrt.f64 (.f64 #s(literal 2 binary64) (.f64 (PI.f64) n))) (-.f64 #s(literal 1 binary64) k))) (patch (.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) (pow.f64 (sqrt.f64 (.f64 #s(literal 2 binary64) (.f64 (PI.f64) n))) (-.f64 #s(literal 1 binary64) k))) #<representation binary64>) () ())) ())
#s(alt (* (sqrt (/ 1 k)) (exp (* (log (* (sqrt (* n (PI))) (sqrt 2))) (- 1 k)))) (taylor inf k) (#s(alt (.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) (pow.f64 (sqrt.f64 (.f64 #s(literal 2 binary64) (.f64 (PI.f64) n))) (-.f64 #s(literal 1 binary64) k))) (patch (.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) (pow.f64 (sqrt.f64 (.f64 #s(literal 2 binary64) (.f64 (PI.f64) n))) (-.f64 #s(literal 1 binary64) k))) #<representation binary64>) () ())) ())
#s(alt (* (sqrt (/ 1 k)) (exp (* (log (* (sqrt (* n (PI))) (sqrt 2))) (- 1 k)))) (taylor inf k) (#s(alt (.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) (pow.f64 (sqrt.f64 (.f64 #s(literal 2 binary64) (.f64 (PI.f64) n))) (-.f64 #s(literal 1 binary64) k))) (patch (.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) (pow.f64 (sqrt.f64 (.f64 #s(literal 2 binary64) (.f64 (PI.f64) n))) (-.f64 #s(literal 1 binary64) k))) #<representation binary64>) () ())) ())
#s(alt (* (sqrt (/ 1 k)) (exp (* (log (* (sqrt (* n (PI))) (sqrt 2))) (- 1 k)))) (taylor inf k) (#s(alt (.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) (pow.f64 (sqrt.f64 (.f64 #s(literal 2 binary64) (.f64 (PI.f64) n))) (-.f64 #s(literal 1 binary64) k))) (patch (.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) (pow.f64 (sqrt.f64 (.f64 #s(literal 2 binary64) (.f64 (PI.f64) n))) (-.f64 #s(literal 1 binary64) k))) #<representation binary64>) () ())) ())
#s(alt (* (sqrt (/ 1 k)) (exp (* (log (* (sqrt (* n (PI))) (sqrt 2))) (- 1 k)))) (taylor inf k) (#s(alt (.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) (pow.f64 (sqrt.f64 (.f64 #s(literal 2 binary64) (.f64 (PI.f64) n))) (-.f64 #s(literal 1 binary64) k))) (patch (.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) (pow.f64 (sqrt.f64 (.f64 #s(literal 2 binary64) (.f64 (PI.f64) n))) (-.f64 #s(literal 1 binary64) k))) #<representation binary64>) () ())) ())
#s(alt (* (sqrt (/ 1 k)) (exp (* (log (* (sqrt (* n (PI))) (sqrt 2))) (+ 1 (* -1 k))))) (taylor -inf k) (#s(alt (.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) (pow.f64 (sqrt.f64 (.f64 #s(literal 2 binary64) (.f64 (PI.f64) n))) (-.f64 #s(literal 1 binary64) k))) (patch (.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) (pow.f64 (sqrt.f64 (.f64 #s(literal 2 binary64) (.f64 (PI.f64) n))) (-.f64 #s(literal 1 binary64) k))) #<representation binary64>) () ())) ())
#s(alt (* (sqrt (/ 1 k)) (exp (* (log (* (sqrt (* n (PI))) (sqrt 2))) (+ 1 (* -1 k))))) (taylor -inf k) (#s(alt (.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) (pow.f64 (sqrt.f64 (.f64 #s(literal 2 binary64) (.f64 (PI.f64) n))) (-.f64 #s(literal 1 binary64) k))) (patch (.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) (pow.f64 (sqrt.f64 (.f64 #s(literal 2 binary64) (.f64 (PI.f64) n))) (-.f64 #s(literal 1 binary64) k))) #<representation binary64>) () ())) ())
#s(alt (* (sqrt (/ 1 k)) (exp (* (log (* (sqrt (* n (PI))) (sqrt 2))) (+ 1 (* -1 k))))) (taylor -inf k) (#s(alt (.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) (pow.f64 (sqrt.f64 (.f64 #s(literal 2 binary64) (.f64 (PI.f64) n))) (-.f64 #s(literal 1 binary64) k))) (patch (.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) (pow.f64 (sqrt.f64 (.f64 #s(literal 2 binary64) (.f64 (PI.f64) n))) (-.f64 #s(literal 1 binary64) k))) #<representation binary64>) () ())) ())
#s(alt (* (sqrt (/ 1 k)) (exp (* (log (* (sqrt (* n (PI))) (sqrt 2))) (+ 1 (* -1 k))))) (taylor -inf k) (#s(alt (.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) (pow.f64 (sqrt.f64 (.f64 #s(literal 2 binary64) (.f64 (PI.f64) n))) (-.f64 #s(literal 1 binary64) k))) (patch (.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) (pow.f64 (sqrt.f64 (.f64 #s(literal 2 binary64) (.f64 (PI.f64) n))) (-.f64 #s(literal 1 binary64) k))) #<representation binary64>) () ())) ())
#s(alt (* (sqrt (/ 1 k)) (exp (* (log (* (sqrt (* n (PI))) (sqrt 2))) (- 1 k)))) (taylor 0 n) (#s(alt (.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) (pow.f64 (sqrt.f64 (.f64 #s(literal 2 binary64) (.f64 (PI.f64) n))) (-.f64 #s(literal 1 binary64) k))) (patch (.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) (pow.f64 (sqrt.f64 (.f64 #s(literal 2 binary64) (.f64 (PI.f64) n))) (-.f64 #s(literal 1 binary64) k))) #<representation binary64>) () ())) ())
#s(alt (* (sqrt (/ 1 k)) (exp (* (log (* (sqrt (* n (PI))) (sqrt 2))) (- 1 k)))) (taylor 0 n) (#s(alt (.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) (pow.f64 (sqrt.f64 (.f64 #s(literal 2 binary64) (.f64 (PI.f64) n))) (-.f64 #s(literal 1 binary64) k))) (patch (.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) (pow.f64 (sqrt.f64 (.f64 #s(literal 2 binary64) (.f64 (PI.f64) n))) (-.f64 #s(literal 1 binary64) k))) #<representation binary64>) () ())) ())
#s(alt (* (sqrt (/ 1 k)) (exp (* (log (* (sqrt (* n (PI))) (sqrt 2))) (- 1 k)))) (taylor 0 n) (#s(alt (.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) (pow.f64 (sqrt.f64 (.f64 #s(literal 2 binary64) (.f64 (PI.f64) n))) (-.f64 #s(literal 1 binary64) k))) (patch (.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) (pow.f64 (sqrt.f64 (.f64 #s(literal 2 binary64) (.f64 (PI.f64) n))) (-.f64 #s(literal 1 binary64) k))) #<representation binary64>) () ())) ())
#s(alt (* (sqrt (/ 1 k)) (exp (* (log (* (sqrt (* n (PI))) (sqrt 2))) (- 1 k)))) (taylor 0 n) (#s(alt (.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) (pow.f64 (sqrt.f64 (.f64 #s(literal 2 binary64) (.f64 (PI.f64) n))) (-.f64 #s(literal 1 binary64) k))) (patch (.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) (pow.f64 (sqrt.f64 (.f64 #s(literal 2 binary64) (.f64 (PI.f64) n))) (-.f64 #s(literal 1 binary64) k))) #<representation binary64>) () ())) ())
#s(alt (* (sqrt (/ 1 k)) (exp (* (+ (log (* (sqrt (/ (PI) n)) (sqrt 2))) (* -1 (log (/ 1 n)))) (- 1 k)))) (taylor inf n) (#s(alt (.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) (pow.f64 (sqrt.f64 (.f64 #s(literal 2 binary64) (.f64 (PI.f64) n))) (-.f64 #s(literal 1 binary64) k))) (patch (.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) (pow.f64 (sqrt.f64 (.f64 #s(literal 2 binary64) (.f64 (PI.f64) n))) (-.f64 #s(literal 1 binary64) k))) #<representation binary64>) () ())) ())
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#s(alt (/ (PI) k) (taylor inf k) (#s(alt (/.f64 (PI.f64) k) (patch (/.f64 (PI.f64) k) #<representation binary64>) () ())) ())
#s(alt (/ (PI) k) (taylor inf k) (#s(alt (/.f64 (PI.f64) k) (patch (/.f64 (PI.f64) k) #<representation binary64>) () ())) ())
#s(alt (/ (PI) k) (taylor inf k) (#s(alt (/.f64 (PI.f64) k) (patch (/.f64 (PI.f64) k) #<representation binary64>) () ())) ())
#s(alt (/ (PI) k) (taylor -inf k) (#s(alt (/.f64 (PI.f64) k) (patch (/.f64 (PI.f64) k) #<representation binary64>) () ())) ())
#s(alt (/ (PI) k) (taylor -inf k) (#s(alt (/.f64 (PI.f64) k) (patch (/.f64 (PI.f64) k) #<representation binary64>) () ())) ())
#s(alt (/ (PI) k) (taylor -inf k) (#s(alt (/.f64 (PI.f64) k) (patch (/.f64 (PI.f64) k) #<representation binary64>) () ())) ())
#s(alt (/ (PI) k) (taylor -inf k) (#s(alt (/.f64 (PI.f64) k) (patch (/.f64 (PI.f64) k) #<representation binary64>) () ())) ())
#s(alt (* (sqrt (/ (* n (PI)) k)) (sqrt 2)) (taylor 0 n) (#s(alt (.f64 (/.f64 (neg.f64 (sqrt.f64 n)) (.f64 (neg.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 (PI.f64)))) (sqrt.f64 k))) (sqrt.f64 #s(literal 2 binary64))) (patch (.f64 (/.f64 (neg.f64 (sqrt.f64 n)) (.f64 (neg.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 (PI.f64)))) (sqrt.f64 k))) (sqrt.f64 #s(literal 2 binary64))) #<representation binary64>) () ())) ())
#s(alt (* (sqrt (/ (* n (PI)) k)) (sqrt 2)) (taylor 0 n) (#s(alt (.f64 (/.f64 (neg.f64 (sqrt.f64 n)) (.f64 (neg.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 (PI.f64)))) (sqrt.f64 k))) (sqrt.f64 #s(literal 2 binary64))) (patch (.f64 (/.f64 (neg.f64 (sqrt.f64 n)) (.f64 (neg.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 (PI.f64)))) (sqrt.f64 k))) (sqrt.f64 #s(literal 2 binary64))) #<representation binary64>) () ())) ())
#s(alt (* (sqrt (/ (* n (PI)) k)) (sqrt 2)) (taylor 0 n) (#s(alt (.f64 (/.f64 (neg.f64 (sqrt.f64 n)) (.f64 (neg.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 (PI.f64)))) (sqrt.f64 k))) (sqrt.f64 #s(literal 2 binary64))) (patch (.f64 (/.f64 (neg.f64 (sqrt.f64 n)) (.f64 (neg.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 (PI.f64)))) (sqrt.f64 k))) (sqrt.f64 #s(literal 2 binary64))) #<representation binary64>) () ())) ())
#s(alt (* (sqrt (/ (* n (PI)) k)) (sqrt 2)) (taylor 0 n) (#s(alt (.f64 (/.f64 (neg.f64 (sqrt.f64 n)) (.f64 (neg.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 (PI.f64)))) (sqrt.f64 k))) (sqrt.f64 #s(literal 2 binary64))) (patch (.f64 (/.f64 (neg.f64 (sqrt.f64 n)) (.f64 (neg.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 (PI.f64)))) (sqrt.f64 k))) (sqrt.f64 #s(literal 2 binary64))) #<representation binary64>) () ())) ())
#s(alt (* (sqrt (/ (* n (PI)) k)) (sqrt 2)) (taylor inf n) (#s(alt (.f64 (/.f64 (neg.f64 (sqrt.f64 n)) (.f64 (neg.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 (PI.f64)))) (sqrt.f64 k))) (sqrt.f64 #s(literal 2 binary64))) (patch (.f64 (/.f64 (neg.f64 (sqrt.f64 n)) (.f64 (neg.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 (PI.f64)))) (sqrt.f64 k))) (sqrt.f64 #s(literal 2 binary64))) #<representation binary64>) () ())) ())
#s(alt (* (sqrt (/ (* n (PI)) k)) (sqrt 2)) (taylor inf n) (#s(alt (.f64 (/.f64 (neg.f64 (sqrt.f64 n)) (.f64 (neg.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 (PI.f64)))) (sqrt.f64 k))) (sqrt.f64 #s(literal 2 binary64))) (patch (.f64 (/.f64 (neg.f64 (sqrt.f64 n)) (.f64 (neg.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 (PI.f64)))) (sqrt.f64 k))) (sqrt.f64 #s(literal 2 binary64))) #<representation binary64>) () ())) ())
#s(alt (* (sqrt (/ (* n (PI)) k)) (sqrt 2)) (taylor inf n) (#s(alt (.f64 (/.f64 (neg.f64 (sqrt.f64 n)) (.f64 (neg.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 (PI.f64)))) (sqrt.f64 k))) (sqrt.f64 #s(literal 2 binary64))) (patch (.f64 (/.f64 (neg.f64 (sqrt.f64 n)) (.f64 (neg.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 (PI.f64)))) (sqrt.f64 k))) (sqrt.f64 #s(literal 2 binary64))) #<representation binary64>) () ())) ())
#s(alt (* (sqrt (/ (* n (PI)) k)) (sqrt 2)) (taylor inf n) (#s(alt (.f64 (/.f64 (neg.f64 (sqrt.f64 n)) (.f64 (neg.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 (PI.f64)))) (sqrt.f64 k))) (sqrt.f64 #s(literal 2 binary64))) (patch (.f64 (/.f64 (neg.f64 (sqrt.f64 n)) (.f64 (neg.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 (PI.f64)))) (sqrt.f64 k))) (sqrt.f64 #s(literal 2 binary64))) #<representation binary64>) () ())) ())
#s(alt (* -1 (* (sqrt (/ (* n (PI)) k)) (* (pow (sqrt -1) 2) (sqrt 2)))) (taylor -inf n) (#s(alt (.f64 (/.f64 (neg.f64 (sqrt.f64 n)) (.f64 (neg.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 (PI.f64)))) (sqrt.f64 k))) (sqrt.f64 #s(literal 2 binary64))) (patch (.f64 (/.f64 (neg.f64 (sqrt.f64 n)) (.f64 (neg.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 (PI.f64)))) (sqrt.f64 k))) (sqrt.f64 #s(literal 2 binary64))) #<representation binary64>) () ())) ())
#s(alt (* -1 (* (sqrt (/ (* n (PI)) k)) (* (pow (sqrt -1) 2) (sqrt 2)))) (taylor -inf n) (#s(alt (.f64 (/.f64 (neg.f64 (sqrt.f64 n)) (.f64 (neg.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 (PI.f64)))) (sqrt.f64 k))) (sqrt.f64 #s(literal 2 binary64))) (patch (.f64 (/.f64 (neg.f64 (sqrt.f64 n)) (.f64 (neg.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 (PI.f64)))) (sqrt.f64 k))) (sqrt.f64 #s(literal 2 binary64))) #<representation binary64>) () ())) ())
#s(alt (* -1 (* (sqrt (/ (* n (PI)) k)) (* (pow (sqrt -1) 2) (sqrt 2)))) (taylor -inf n) (#s(alt (.f64 (/.f64 (neg.f64 (sqrt.f64 n)) (.f64 (neg.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 (PI.f64)))) (sqrt.f64 k))) (sqrt.f64 #s(literal 2 binary64))) (patch (.f64 (/.f64 (neg.f64 (sqrt.f64 n)) (.f64 (neg.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 (PI.f64)))) (sqrt.f64 k))) (sqrt.f64 #s(literal 2 binary64))) #<representation binary64>) () ())) ())
#s(alt (* -1 (* (sqrt (/ (* n (PI)) k)) (* (pow (sqrt -1) 2) (sqrt 2)))) (taylor -inf n) (#s(alt (.f64 (/.f64 (neg.f64 (sqrt.f64 n)) (.f64 (neg.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 (PI.f64)))) (sqrt.f64 k))) (sqrt.f64 #s(literal 2 binary64))) (patch (.f64 (/.f64 (neg.f64 (sqrt.f64 n)) (.f64 (neg.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 (PI.f64)))) (sqrt.f64 k))) (sqrt.f64 #s(literal 2 binary64))) #<representation binary64>) () ())) ())
#s(alt (* (sqrt (/ (* n (PI)) k)) (sqrt 2)) (taylor 0 k) (#s(alt (.f64 (/.f64 (neg.f64 (sqrt.f64 n)) (.f64 (neg.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 (PI.f64)))) (sqrt.f64 k))) (sqrt.f64 #s(literal 2 binary64))) (patch (.f64 (/.f64 (neg.f64 (sqrt.f64 n)) (.f64 (neg.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 (PI.f64)))) (sqrt.f64 k))) (sqrt.f64 #s(literal 2 binary64))) #<representation binary64>) () ())) ())
#s(alt (* (sqrt (/ (* n (PI)) k)) (sqrt 2)) (taylor 0 k) (#s(alt (.f64 (/.f64 (neg.f64 (sqrt.f64 n)) (.f64 (neg.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 (PI.f64)))) (sqrt.f64 k))) (sqrt.f64 #s(literal 2 binary64))) (patch (.f64 (/.f64 (neg.f64 (sqrt.f64 n)) (.f64 (neg.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 (PI.f64)))) (sqrt.f64 k))) (sqrt.f64 #s(literal 2 binary64))) #<representation binary64>) () ())) ())
#s(alt (* (sqrt (/ (* n (PI)) k)) (sqrt 2)) (taylor 0 k) (#s(alt (.f64 (/.f64 (neg.f64 (sqrt.f64 n)) (.f64 (neg.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 (PI.f64)))) (sqrt.f64 k))) (sqrt.f64 #s(literal 2 binary64))) (patch (.f64 (/.f64 (neg.f64 (sqrt.f64 n)) (.f64 (neg.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 (PI.f64)))) (sqrt.f64 k))) (sqrt.f64 #s(literal 2 binary64))) #<representation binary64>) () ())) ())
#s(alt (* (sqrt (/ (* n (PI)) k)) (sqrt 2)) (taylor 0 k) (#s(alt (.f64 (/.f64 (neg.f64 (sqrt.f64 n)) (.f64 (neg.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 (PI.f64)))) (sqrt.f64 k))) (sqrt.f64 #s(literal 2 binary64))) (patch (.f64 (/.f64 (neg.f64 (sqrt.f64 n)) (.f64 (neg.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 (PI.f64)))) (sqrt.f64 k))) (sqrt.f64 #s(literal 2 binary64))) #<representation binary64>) () ())) ())
#s(alt (* (sqrt (/ (* n (PI)) k)) (sqrt 2)) (taylor inf k) (#s(alt (.f64 (/.f64 (neg.f64 (sqrt.f64 n)) (.f64 (neg.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 (PI.f64)))) (sqrt.f64 k))) (sqrt.f64 #s(literal 2 binary64))) (patch (.f64 (/.f64 (neg.f64 (sqrt.f64 n)) (.f64 (neg.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 (PI.f64)))) (sqrt.f64 k))) (sqrt.f64 #s(literal 2 binary64))) #<representation binary64>) () ())) ())
#s(alt (* (sqrt (/ (* n (PI)) k)) (sqrt 2)) (taylor inf k) (#s(alt (.f64 (/.f64 (neg.f64 (sqrt.f64 n)) (.f64 (neg.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 (PI.f64)))) (sqrt.f64 k))) (sqrt.f64 #s(literal 2 binary64))) (patch (.f64 (/.f64 (neg.f64 (sqrt.f64 n)) (.f64 (neg.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 (PI.f64)))) (sqrt.f64 k))) (sqrt.f64 #s(literal 2 binary64))) #<representation binary64>) () ())) ())
#s(alt (* (sqrt (/ (* n (PI)) k)) (sqrt 2)) (taylor inf k) (#s(alt (.f64 (/.f64 (neg.f64 (sqrt.f64 n)) (.f64 (neg.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 (PI.f64)))) (sqrt.f64 k))) (sqrt.f64 #s(literal 2 binary64))) (patch (.f64 (/.f64 (neg.f64 (sqrt.f64 n)) (.f64 (neg.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 (PI.f64)))) (sqrt.f64 k))) (sqrt.f64 #s(literal 2 binary64))) #<representation binary64>) () ())) ())
#s(alt (* (sqrt (/ (* n (PI)) k)) (sqrt 2)) (taylor inf k) (#s(alt (.f64 (/.f64 (neg.f64 (sqrt.f64 n)) (.f64 (neg.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 (PI.f64)))) (sqrt.f64 k))) (sqrt.f64 #s(literal 2 binary64))) (patch (.f64 (/.f64 (neg.f64 (sqrt.f64 n)) (.f64 (neg.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 (PI.f64)))) (sqrt.f64 k))) (sqrt.f64 #s(literal 2 binary64))) #<representation binary64>) () ())) ())
#s(alt (* (sqrt (/ (* n (PI)) k)) (sqrt 2)) (taylor -inf k) (#s(alt (.f64 (/.f64 (neg.f64 (sqrt.f64 n)) (.f64 (neg.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 (PI.f64)))) (sqrt.f64 k))) (sqrt.f64 #s(literal 2 binary64))) (patch (.f64 (/.f64 (neg.f64 (sqrt.f64 n)) (.f64 (neg.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 (PI.f64)))) (sqrt.f64 k))) (sqrt.f64 #s(literal 2 binary64))) #<representation binary64>) () ())) ())
#s(alt (* (sqrt (/ (* n (PI)) k)) (sqrt 2)) (taylor -inf k) (#s(alt (.f64 (/.f64 (neg.f64 (sqrt.f64 n)) (.f64 (neg.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 (PI.f64)))) (sqrt.f64 k))) (sqrt.f64 #s(literal 2 binary64))) (patch (.f64 (/.f64 (neg.f64 (sqrt.f64 n)) (.f64 (neg.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 (PI.f64)))) (sqrt.f64 k))) (sqrt.f64 #s(literal 2 binary64))) #<representation binary64>) () ())) ())
#s(alt (* (sqrt (/ (* n (PI)) k)) (sqrt 2)) (taylor -inf k) (#s(alt (.f64 (/.f64 (neg.f64 (sqrt.f64 n)) (.f64 (neg.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 (PI.f64)))) (sqrt.f64 k))) (sqrt.f64 #s(literal 2 binary64))) (patch (.f64 (/.f64 (neg.f64 (sqrt.f64 n)) (.f64 (neg.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 (PI.f64)))) (sqrt.f64 k))) (sqrt.f64 #s(literal 2 binary64))) #<representation binary64>) () ())) ())
#s(alt (* (sqrt (/ (* n (PI)) k)) (sqrt 2)) (taylor -inf k) (#s(alt (.f64 (/.f64 (neg.f64 (sqrt.f64 n)) (.f64 (neg.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 (PI.f64)))) (sqrt.f64 k))) (sqrt.f64 #s(literal 2 binary64))) (patch (.f64 (/.f64 (neg.f64 (sqrt.f64 n)) (.f64 (neg.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 (PI.f64)))) (sqrt.f64 k))) (sqrt.f64 #s(literal 2 binary64))) #<representation binary64>) () ())) ())

Calls

114 calls:

Time	Variable		Point	Expression
7.0ms	k	@	0	(/ (neg (sqrt n)) (* (neg (/ 1 (sqrt (PI)))) (sqrt k)))
1.0ms	k	@	-inf	(* (/ 1 (sqrt k)) (pow (sqrt (* 2 (* (PI) n))) (- 1 k)))
1.0ms	n	@	inf	(* (/ 1 (sqrt k)) (pow (sqrt (* 2 (* (PI) n))) (- 1 k)))
1.0ms	k	@	0	(* (/ 1 (sqrt k)) (pow (sqrt (* 2 (* (PI) n))) (- 1 k)))
1.0ms	k	@	0	(* (neg (/ 1 (sqrt (PI)))) (sqrt k))

simplify322.0ms (2.9%)

Memory

3.1MiB live, 444.4MiB allocated

Algorithm

1×	egg-herbie

Rules

8 336×	`lower-fma.f64`
8 336×	`lower-fma.f32`
4 914×	`lower-*.f64`
4 914×	`lower-*.f32`
2 422×	`lower-+.f64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	185	5308
1	503	5178
2	1548	4879
3	2963	4836
4	5348	4803
0	8457	4773

Stop Event

1×	iter limit
1×	node limit

Counts

456 → 456

Calls

Call 1

Inputs
(* (sqrt (/ (* n (PI)) k)) (sqrt 2))
(/ (+ (* -1 (* (sqrt (* (pow k 3) (* n (PI)))) (* (log (* (sqrt (* n (PI))) (sqrt 2))) (sqrt 2)))) (* (sqrt (* k (* n (PI)))) (sqrt 2))) k)
(/ (+ (* k (+ (* -1 (* (sqrt (* k (* n (PI)))) (* (log (* (sqrt (* n (PI))) (sqrt 2))) (sqrt 2)))) (* 1/2 (* (sqrt (* (pow k 3) (* n (PI)))) (* (pow (log (* (sqrt (* n (PI))) (sqrt 2))) 2) (sqrt 2)))))) (* (sqrt (* k (* n (PI)))) (sqrt 2))) k)
(/ (+ (* k (+ (* -1 (* (sqrt (* k (* n (PI)))) (* (log (* (sqrt (* n (PI))) (sqrt 2))) (sqrt 2)))) (* k (+ (* -1/6 (* (sqrt (* (pow k 3) (* n (PI)))) (* (pow (log (* (sqrt (* n (PI))) (sqrt 2))) 3) (sqrt 2)))) (* 1/2 (* (sqrt (* k (* n (PI)))) (* (pow (log (* (sqrt (* n (PI))) (sqrt 2))) 2) (sqrt 2)))))))) (* (sqrt (* k (* n (PI)))) (sqrt 2))) k)
(* (sqrt (/ 1 k)) (exp (* (log (* (sqrt (* n (PI))) (sqrt 2))) (- 1 k))))
(* (sqrt (/ 1 k)) (exp (* (log (* (sqrt (* n (PI))) (sqrt 2))) (- 1 k))))
(* (sqrt (/ 1 k)) (exp (* (log (* (sqrt (* n (PI))) (sqrt 2))) (- 1 k))))
(* (sqrt (/ 1 k)) (exp (* (log (* (sqrt (* n (PI))) (sqrt 2))) (- 1 k))))
(* (sqrt (/ 1 k)) (exp (* (log (* (sqrt (* n (PI))) (sqrt 2))) (+ 1 (* -1 k)))))
(* (sqrt (/ 1 k)) (exp (* (log (* (sqrt (* n (PI))) (sqrt 2))) (+ 1 (* -1 k)))))
(* (sqrt (/ 1 k)) (exp (* (log (* (sqrt (* n (PI))) (sqrt 2))) (+ 1 (* -1 k)))))
(* (sqrt (/ 1 k)) (exp (* (log (* (sqrt (* n (PI))) (sqrt 2))) (+ 1 (* -1 k)))))
(* (sqrt (/ 1 k)) (exp (* (log (* (sqrt (* n (PI))) (sqrt 2))) (- 1 k))))
(* (sqrt (/ 1 k)) (exp (* (log (* (sqrt (* n (PI))) (sqrt 2))) (- 1 k))))
(* (sqrt (/ 1 k)) (exp (* (log (* (sqrt (* n (PI))) (sqrt 2))) (- 1 k))))
(* (sqrt (/ 1 k)) (exp (* (log (* (sqrt (* n (PI))) (sqrt 2))) (- 1 k))))
(* (sqrt (/ 1 k)) (exp (* (+ (log (* (sqrt (/ (PI) n)) (sqrt 2))) (* -1 (log (/ 1 n)))) (- 1 k))))
(* (sqrt (/ 1 k)) (exp (* (+ (log (* (sqrt (/ (PI) n)) (sqrt 2))) (* -1 (log (/ 1 n)))) (- 1 k))))
(* (sqrt (/ 1 k)) (exp (* (+ (log (* (sqrt (/ (PI) n)) (sqrt 2))) (* -1 (log (/ 1 n)))) (- 1 k))))
(* (sqrt (/ 1 k)) (exp (* (+ (log (* (sqrt (/ (PI) n)) (sqrt 2))) (* -1 (log (/ 1 n)))) (- 1 k))))
(* (sqrt (/ 1 k)) (exp (* (+ (log (* (sqrt (/ (PI) n)) (* (sqrt -2) (sqrt -1)))) (* -1 (log (/ -1 n)))) (- 1 k))))
(* (sqrt (/ 1 k)) (exp (* (+ (log (* (sqrt (/ (PI) n)) (* (sqrt -2) (sqrt -1)))) (* -1 (log (/ -1 n)))) (- 1 k))))
(* (sqrt (/ 1 k)) (exp (* (+ (log (* (sqrt (/ (PI) n)) (* (sqrt -2) (sqrt -1)))) (* -1 (log (/ -1 n)))) (- 1 k))))
(* (sqrt (/ 1 k)) (exp (* (+ (log (* (sqrt (/ (PI) n)) (* (sqrt -2) (sqrt -1)))) (* -1 (log (/ -1 n)))) (- 1 k))))
(sqrt (/ 1 k))
(sqrt (/ 1 k))
(sqrt (/ 1 k))
(sqrt (/ 1 k))
(sqrt (/ 1 k))
(sqrt (/ 1 k))
(sqrt (/ 1 k))
(sqrt (/ 1 k))
(sqrt (/ 1 k))
(sqrt (/ 1 k))
(sqrt (/ 1 k))
(sqrt (/ 1 k))
(sqrt k)
(sqrt k)
(sqrt k)
(sqrt k)
(sqrt k)
(sqrt k)
(sqrt k)
(sqrt k)
(* -1 (* (sqrt k) (pow (sqrt -1) 2)))
(* -1 (* (sqrt k) (pow (sqrt -1) 2)))
(* -1 (* (sqrt k) (pow (sqrt -1) 2)))
(* -1 (* (sqrt k) (pow (sqrt -1) 2)))
(exp (* (log (* (sqrt (* n (PI))) (sqrt 2))) (- 1 k)))
(exp (* (log (* (sqrt (* n (PI))) (sqrt 2))) (- 1 k)))
(exp (* (log (* (sqrt (* n (PI))) (sqrt 2))) (- 1 k)))
(exp (* (log (* (sqrt (* n (PI))) (sqrt 2))) (- 1 k)))
(exp (* (+ (log (* (sqrt (/ (PI) n)) (sqrt 2))) (* -1 (log (/ 1 n)))) (- 1 k)))
(exp (* (+ (log (* (sqrt (/ (PI) n)) (sqrt 2))) (* -1 (log (/ 1 n)))) (- 1 k)))
(exp (* (+ (log (* (sqrt (/ (PI) n)) (sqrt 2))) (* -1 (log (/ 1 n)))) (- 1 k)))
(exp (* (+ (log (* (sqrt (/ (PI) n)) (sqrt 2))) (* -1 (log (/ 1 n)))) (- 1 k)))
(exp (* (+ (log (* (sqrt (/ (PI) n)) (* (sqrt -2) (sqrt -1)))) (* -1 (log (/ -1 n)))) (- 1 k)))
(exp (* (+ (log (* (sqrt (/ (PI) n)) (* (sqrt -2) (sqrt -1)))) (* -1 (log (/ -1 n)))) (- 1 k)))
(exp (* (+ (log (* (sqrt (/ (PI) n)) (* (sqrt -2) (sqrt -1)))) (* -1 (log (/ -1 n)))) (- 1 k)))
(exp (* (+ (log (* (sqrt (/ (PI) n)) (* (sqrt -2) (sqrt -1)))) (* -1 (log (/ -1 n)))) (- 1 k)))
(* (sqrt (* n (PI))) (sqrt 2))
(+ (* -1 (* (* k (* (log (* (sqrt (* n (PI))) (sqrt 2))) (sqrt 2))) (sqrt (* n (PI))))) (* (sqrt (* n (PI))) (sqrt 2)))
(+ (* k (+ (* -1 (* (sqrt (* n (PI))) (* (log (* (sqrt (* n (PI))) (sqrt 2))) (sqrt 2)))) (* 1/2 (* (* k (* (pow (log (* (sqrt (* n (PI))) (sqrt 2))) 2) (sqrt 2))) (sqrt (* n (PI))))))) (* (sqrt (* n (PI))) (sqrt 2)))
(+ (* k (+ (* -1 (* (sqrt (* n (PI))) (* (log (* (sqrt (* n (PI))) (sqrt 2))) (sqrt 2)))) (* k (+ (* -1/6 (* (* k (* (pow (log (* (sqrt (* n (PI))) (sqrt 2))) 3) (sqrt 2))) (sqrt (* n (PI))))) (* 1/2 (* (sqrt (* n (PI))) (* (pow (log (* (sqrt (* n (PI))) (sqrt 2))) 2) (sqrt 2)))))))) (* (sqrt (* n (PI))) (sqrt 2)))
(exp (* (log (* (sqrt (* n (PI))) (sqrt 2))) (- 1 k)))
(exp (* (log (* (sqrt (* n (PI))) (sqrt 2))) (- 1 k)))
(exp (* (log (* (sqrt (* n (PI))) (sqrt 2))) (- 1 k)))
(exp (* (log (* (sqrt (* n (PI))) (sqrt 2))) (- 1 k)))
(exp (* (log (* (sqrt (* n (PI))) (sqrt 2))) (+ 1 (* -1 k))))
(exp (* (log (* (sqrt (* n (PI))) (sqrt 2))) (+ 1 (* -1 k))))
(exp (* (log (* (sqrt (* n (PI))) (sqrt 2))) (+ 1 (* -1 k))))
(exp (* (log (* (sqrt (* n (PI))) (sqrt 2))) (+ 1 (* -1 k))))
(* (sqrt (/ (* n (PI)) k)) (sqrt 2))
(/ (+ (* -1/2 (* (sqrt (* (pow k 3) (* n (PI)))) (* (log (* 2 (* n (PI)))) (sqrt 2)))) (* (sqrt (* k (* n (PI)))) (sqrt 2))) k)
(/ (+ (* k (+ (* -1/2 (* (sqrt (* k (* n (PI)))) (* (log (* 2 (* n (PI)))) (sqrt 2)))) (* 1/8 (* (sqrt (* (pow k 3) (* n (PI)))) (* (pow (log (* 2 (* n (PI)))) 2) (sqrt 2)))))) (* (sqrt (* k (* n (PI)))) (sqrt 2))) k)
(/ (+ (* k (+ (* -1/2 (* (sqrt (* k (* n (PI)))) (* (log (* 2 (* n (PI)))) (sqrt 2)))) (* k (+ (* -1/48 (* (sqrt (* (pow k 3) (* n (PI)))) (* (pow (log (* 2 (* n (PI)))) 3) (sqrt 2)))) (* 1/8 (* (sqrt (* k (* n (PI)))) (* (pow (log (* 2 (* n (PI)))) 2) (sqrt 2)))))))) (* (sqrt (* k (* n (PI)))) (sqrt 2))) k)
(* (sqrt (/ 1 k)) (exp (* 1/2 (* (log (* 2 (* n (PI)))) (- 1 k)))))
(* (sqrt (/ 1 k)) (exp (* 1/2 (* (log (* 2 (* n (PI)))) (- 1 k)))))
(* (sqrt (/ 1 k)) (exp (* 1/2 (* (log (* 2 (* n (PI)))) (- 1 k)))))
(* (sqrt (/ 1 k)) (exp (* 1/2 (* (log (* 2 (* n (PI)))) (- 1 k)))))
(* (sqrt (/ 1 k)) (exp (* 1/2 (* (log (* 2 (* n (PI)))) (+ 1 (* -1 k))))))
(* (sqrt (/ 1 k)) (exp (* 1/2 (* (log (* 2 (* n (PI)))) (+ 1 (* -1 k))))))
(* (sqrt (/ 1 k)) (exp (* 1/2 (* (log (* 2 (* n (PI)))) (+ 1 (* -1 k))))))
(* (sqrt (/ 1 k)) (exp (* 1/2 (* (log (* 2 (* n (PI)))) (+ 1 (* -1 k))))))
(* (sqrt (/ 1 k)) (exp (* 1/2 (* (+ (log n) (log (* 2 (PI)))) (- 1 k)))))
(* (sqrt (/ 1 k)) (exp (* 1/2 (* (+ (log n) (log (* 2 (PI)))) (- 1 k)))))
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(* (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)
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(* (sqrt (/ 1 k)) (exp (* 1/2 (* (log (* 2 (* n (PI)))) (+ 1 (* -1 k))))))
(* (sqrt (/ 1 k)) (exp (* 1/2 (* (log (* 2 (* n (PI)))) (+ 1 (* -1 k))))))
(* (sqrt (/ 1 k)) (exp (* 1/2 (* (log (* 2 (* n (PI)))) (+ 1 (* -1 k))))))
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(* (sqrt (/ 1 k)) (exp (* 1/2 (* (+ (log n) (log (* 2 (PI)))) (- 1 k)))))
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(* (sqrt (/ 1 k)) (exp (* 1/2 (* (+ (log (* -2 (PI))) (* -1 (log (/ -1 n)))) (- 1 k)))))
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(/ (+ (* -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)
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(* n (PI))
(* n (PI))
(* n (PI))
(* n (PI))
(* n (PI))
(* n (PI))
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(* n (PI))
(* n (PI))
(* n (PI))
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(/ (PI) k)
(/ (PI) k)
(/ (PI) k)
(/ (PI) k)
(/ (PI) k)
(/ (PI) k)
(/ (PI) k)
(/ (PI) k)
(/ (PI) k)
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(* (sqrt (/ (* n (PI)) k)) (sqrt 2))
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Outputs
(* (sqrt (/ (* n (PI)) k)) (sqrt 2))
(.f64 (sqrt.f64 (/.f64 (.f64 n (PI.f64)) k)) (sqrt.f64 #s(literal 2 binary64)))
(/ (+ (* -1 (* (sqrt (* (pow k 3) (* n (PI)))) (* (log (* (sqrt (* n (PI))) (sqrt 2))) (sqrt 2)))) (* (sqrt (* k (* n (PI)))) (sqrt 2))) k)
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rewrite309.0ms (2.8%)

Memory

-0.9MiB live, 382.1MiB allocated

Algorithm

1×	batch-egg-rewrite

Rules

4 636×	`lower-*.f32`
4 620×	`lower-*.f64`
3 352×	`lower-/.f32`
3 338×	`lower-/.f64`
1 592×	`lower-pow.f32`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	48	256
0	79	217
1	244	204
2	1283	204
0	8502	204

Stop Event

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

Counts

24 → 1 459

Calls

Call 1

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

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

eval322.0ms (2.9%)

Memory: 31.8MiB live, 531.5MiB allocated
Compiler: Compiled 31 389 to 3 012 computations (90.4% saved)

prune386.0ms (3.5%)

Memory

-18.0MiB live, 597.8MiB allocated

Pruning

73 alts after pruning (63 fresh and 10 done)

	Pruned	Kept	Total
New	1 947	29	1 976
Fresh	12	34	46
Picked	1	4	5
Done	0	6	6
Total	1 960	73	2 033

Accuracy

100.0%

Counts

2 033 → 73

Alt Table

Click to see full alt table

Status	Accuracy	Program
✓	99.5%	(/.f64 (pow.f64 (.f64 #s(literal 2 binary64) (.f64 (PI.f64) n)) (fma.f64 k #s(literal -1/2 binary64) #s(literal 1/2 binary64))) (sqrt.f64 k))
	99.1%	(/.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) k)) (pow.f64 (.f64 #s(literal 2 binary64) (.f64 (PI.f64) n)) (fma.f64 k #s(literal 1/2 binary64) #s(literal -1/2 binary64))))
	50.4%	(/.f64 #s(approx (pow (* 2 (* (PI) n)) (+ (* k 1/2) 1/2)) (.f64 (sqrt.f64 (.f64 n #s(literal 2 binary64))) (sqrt.f64 (PI.f64)))) (sqrt.f64 k))
	50.3%	(/.f64 #s(approx (pow (* 2 (* (PI) n)) (+ (* k 1/2) 1/2)) (.f64 (sqrt.f64 (.f64 #s(literal 2 binary64) (PI.f64))) (sqrt.f64 n))) (sqrt.f64 k))
✓	50.5%	(/.f64 #s(approx (pow (* 2 (* (PI) n)) (+ (* k 1/2) 1/2)) (.f64 (sqrt.f64 #s(literal 2 binary64)) (sqrt.f64 (.f64 n (PI.f64))))) (sqrt.f64 k))
	50.6%	(/.f64 #s(approx (pow (* 2 (* (PI) n)) (+ (* k 1/2) 1/2)) (sqrt.f64 (.f64 (PI.f64) (.f64 n #s(literal 2 binary64))))) (sqrt.f64 k))
	50.5%	(/.f64 #s(literal 1 binary64) (/.f64 (sqrt.f64 k) #s(approx (pow (* 2 (* (PI) n)) (+ (* k 1/2) 1/2)) (sqrt.f64 (.f64 (PI.f64) (.f64 n #s(literal 2 binary64)))))))
	99.4%	(/.f64 #s(literal 1 binary64) (.f64 (sqrt.f64 k) (pow.f64 (.f64 #s(literal 2 binary64) (*.f64 (PI.f64) n)) (fma.f64 k #s(literal 1/2 binary64) #s(literal -1/2 binary64)))))
	76.0%	(.f64 (pow.f64 (.f64 (PI.f64) (.f64 n #s(literal 2 binary64))) (.f64 k #s(literal -1/2 binary64))) (sqrt.f64 (/.f64 (.f64 (PI.f64) (.f64 n #s(literal 2 binary64))) k)))
✓	99.4%	(.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) (pow.f64 (.f64 (*.f64 #s(literal 2 binary64) (PI.f64)) n) (fma.f64 k #s(literal -1/2 binary64) #s(literal 1/2 binary64))))
✓	99.4%	(.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) (pow.f64 (sqrt.f64 (.f64 #s(literal 2 binary64) (*.f64 (PI.f64) n))) (-.f64 #s(literal 1 binary64) k)))
	50.5%	(.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) #s(approx (pow ( (* 2 (PI)) n) (/ (- 1 k) 2)) (.f64 (sqrt.f64 #s(literal 2 binary64)) (sqrt.f64 (.f64 n (PI.f64))))))
	50.5%	(.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) #s(approx (pow ( 2 (* (PI) n)) (+ (* k 1/2) 1/2)) (sqrt.f64 (.f64 (PI.f64) (.f64 n #s(literal 2 binary64))))))
	76.1%	(sqrt.f64 (/.f64 (.f64 #s(literal 2 binary64) (/.f64 (.f64 (PI.f64) n) k)) (pow.f64 (.f64 #s(literal 2 binary64) (.f64 (PI.f64) n)) k)))
	50.5%	#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (/.f64 (.f64 (.f64 (neg.f64 (sqrt.f64 (PI.f64))) (sqrt.f64 #s(literal 2 binary64))) (sqrt.f64 n)) (neg.f64 (sqrt.f64 k))))
	38.3%	#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (/.f64 (.f64 (.f64 #s(literal 1 binary64) (sqrt.f64 #s(literal 2 binary64))) #s(literal -1 binary64)) (*.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 (PI.f64))) (neg.f64 (sqrt.f64 (/.f64 k n))))))
	37.3%	#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (/.f64 (.f64 (neg.f64 (.f64 n (sqrt.f64 n))) (sqrt.f64 #s(literal 2 binary64))) (*.f64 (+.f64 n #s(literal 0 binary64)) (/.f64 #s(literal -1 binary64) (sqrt.f64 (/.f64 (PI.f64) k))))))
	50.1%	#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (/.f64 (.f64 (neg.f64 n) (sqrt.f64 #s(literal 2 binary64))) (.f64 (sqrt.f64 n) (/.f64 #s(literal -1 binary64) (sqrt.f64 (/.f64 (PI.f64) k))))))
	38.3%	#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (/.f64 (sqrt.f64 (*.f64 #s(literal 2 binary64) (PI.f64))) (sqrt.f64 (/.f64 k n))))
	50.4%	#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (/.f64 (sqrt.f64 (*.f64 #s(literal 2 binary64) n)) (/.f64 (sqrt.f64 k) (sqrt.f64 (PI.f64)))))
	50.5%	#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (/.f64 (sqrt.f64 (*.f64 #s(literal 2 binary64) n)) (sqrt.f64 (/.f64 k (PI.f64)))))
	38.3%	#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (/.f64 #s(literal 1 binary64) (/.f64 (sqrt.f64 (/.f64 k n)) (sqrt.f64 (*.f64 #s(literal 2 binary64) (PI.f64))))))
	50.3%	#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (/.f64 #s(literal 1 binary64) (/.f64 (neg.f64 (sqrt.f64 k)) (.f64 (neg.f64 (sqrt.f64 n)) (sqrt.f64 (.f64 #s(literal 2 binary64) (PI.f64)))))))
	45.3%	#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (.f64 (/.f64 (.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) (neg.f64 n)) (*.f64 (/.f64 #s(literal -1 binary64) (sqrt.f64 (PI.f64))) (sqrt.f64 n))) (sqrt.f64 #s(literal 2 binary64))))
	37.2%	#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (.f64 (/.f64 (.f64 (neg.f64 (.f64 n (sqrt.f64 n))) (neg.f64 (sqrt.f64 (PI.f64)))) (.f64 (+.f64 n #s(literal 0 binary64)) (sqrt.f64 k))) (sqrt.f64 #s(literal 2 binary64))))
	37.2%	#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (.f64 (/.f64 (.f64 (neg.f64 (.f64 n (sqrt.f64 n))) #s(literal 1 binary64)) (.f64 (+.f64 n #s(literal 0 binary64)) (/.f64 #s(literal -1 binary64) (sqrt.f64 (/.f64 (PI.f64) k))))) (sqrt.f64 #s(literal 2 binary64))))
	50.1%	#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (*.f64 (/.f64 (sqrt.f64 (/.f64 (PI.f64) k)) (sqrt.f64 (/.f64 #s(literal 1 binary64) n))) (sqrt.f64 #s(literal 2 binary64))))
	50.3%	#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (.f64 (/.f64 (sqrt.f64 (.f64 #s(literal 2 binary64) (PI.f64))) (sqrt.f64 k)) (/.f64 (sqrt.f64 n) #s(literal 1 binary64))))
	50.4%	#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (.f64 (/.f64 (sqrt.f64 (.f64 #s(literal 2 binary64) n)) (sqrt.f64 k)) (sqrt.f64 (PI.f64))))
	50.5%	#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (*.f64 (/.f64 (sqrt.f64 n) (sqrt.f64 (/.f64 k (PI.f64)))) (sqrt.f64 #s(literal 2 binary64))))
	50.5%	#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (.f64 (/.f64 (sqrt.f64 #s(literal 2 binary64)) (sqrt.f64 k)) (sqrt.f64 (.f64 (PI.f64) n))))
	50.4%	#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (*.f64 (/.f64 (neg.f64 (sqrt.f64 n)) (/.f64 (/.f64 #s(literal -1 binary64) (sqrt.f64 (PI.f64))) (/.f64 #s(literal 1 binary64) (sqrt.f64 k)))) (sqrt.f64 #s(literal 2 binary64))))
	50.4%	#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (.f64 (/.f64 (neg.f64 (sqrt.f64 n)) (.f64 (/.f64 #s(literal -1 binary64) (sqrt.f64 (PI.f64))) (sqrt.f64 k))) (sqrt.f64 #s(literal 2 binary64))))
	50.3%	#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (.f64 (/.f64 (neg.f64 (sqrt.f64 n)) (.f64 (.f64 (neg.f64 (/.f64 #s(literal 1 binary64) (.f64 (PI.f64) (sqrt.f64 (PI.f64))))) (/.f64 #s(literal 1 binary64) (+.f64 (/.f64 #s(literal 1 binary64) (PI.f64)) #s(literal 0 binary64)))) (sqrt.f64 k))) (sqrt.f64 #s(literal 2 binary64))))
	50.3%	#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (.f64 (/.f64 (neg.f64 (sqrt.f64 n)) (.f64 (sqrt.f64 k) #s(literal -1 binary64))) (sqrt.f64 (*.f64 #s(literal 2 binary64) (PI.f64)))))
	50.5%	#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (.f64 (/.f64 n (.f64 (/.f64 (sqrt.f64 k) (sqrt.f64 (PI.f64))) (sqrt.f64 n))) (sqrt.f64 #s(literal 2 binary64))))
	50.3%	#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) (/.f64 (sqrt.f64 (.f64 #s(literal 2 binary64) (PI.f64))) (/.f64 #s(literal 1 binary64) (sqrt.f64 n)))))
	50.4%	#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (.f64 (/.f64 #s(literal -1 binary64) (.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 (*.f64 (PI.f64) n))) (neg.f64 (sqrt.f64 k)))) (sqrt.f64 #s(literal 2 binary64))))
	38.3%	#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (.f64 (/.f64 #s(literal -1 binary64) (.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 (PI.f64))) (neg.f64 (sqrt.f64 (/.f64 k n))))) (sqrt.f64 #s(literal 2 binary64))))
	50.4%	#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (.f64 (/.f64 #s(literal -1 binary64) (sqrt.f64 k)) (/.f64 (sqrt.f64 #s(literal 2 binary64)) (/.f64 #s(literal 1 binary64) (neg.f64 (sqrt.f64 (.f64 (PI.f64) n)))))))
	50.3%	#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (.f64 (.f64 (/.f64 (sqrt.f64 (sqrt.f64 (PI.f64))) (sqrt.f64 k)) (/.f64 (sqrt.f64 (sqrt.f64 (PI.f64))) (/.f64 #s(literal 1 binary64) (sqrt.f64 n)))) (sqrt.f64 #s(literal 2 binary64))))
	50.4%	#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (.f64 (.f64 (/.f64 (sqrt.f64 n) (sqrt.f64 k)) (/.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (sqrt.f64 (PI.f64))))) (sqrt.f64 #s(literal 2 binary64))))
	50.3%	#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (.f64 (.f64 (.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k))) (sqrt.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)))) (sqrt.f64 (.f64 (PI.f64) n))) (sqrt.f64 #s(literal 2 binary64))))
	50.2%	#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (.f64 (.f64 (sqrt.f64 (/.f64 (PI.f64) k)) (sqrt.f64 n)) (sqrt.f64 #s(literal 2 binary64))))
	50.2%	#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (.f64 (.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) k)) (sqrt.f64 (/.f64 (PI.f64) (/.f64 #s(literal 1 binary64) n)))) (sqrt.f64 #s(literal 2 binary64))))
✓	50.1%	#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (.f64 (.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) k)) (sqrt.f64 (*.f64 (PI.f64) n))) (sqrt.f64 #s(literal 2 binary64))))
	50.0%	#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (.f64 (.f64 (sqrt.f64 (*.f64 n #s(literal 2 binary64))) (sqrt.f64 (PI.f64))) (sqrt.f64 (/.f64 #s(literal 1 binary64) k))))
	50.0%	#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (.f64 (.f64 (sqrt.f64 (*.f64 #s(literal 2 binary64) (PI.f64))) (sqrt.f64 n)) (sqrt.f64 (/.f64 #s(literal 1 binary64) k))))
	50.2%	#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (.f64 (.f64 (sqrt.f64 #s(literal 2 binary64)) (neg.f64 (sqrt.f64 (/.f64 (PI.f64) k)))) (neg.f64 (sqrt.f64 n))))
✓	37.7%	#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (.f64 (sqrt.f64 (/.f64 (.f64 n (PI.f64)) k)) (sqrt.f64 #s(literal 2 binary64))))
✓	37.7%	#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (*.f64 (sqrt.f64 (/.f64 (PI.f64) (/.f64 k n))) (sqrt.f64 #s(literal 2 binary64))))
	50.2%	#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (*.f64 (sqrt.f64 (/.f64 (PI.f64) k)) (/.f64 (sqrt.f64 #s(literal 2 binary64)) (sqrt.f64 (/.f64 #s(literal 1 binary64) n)))))
	50.2%	#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (.f64 (sqrt.f64 (/.f64 (PI.f64) k)) (sqrt.f64 (.f64 #s(literal 2 binary64) n))))
	37.6%	#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (.f64 (sqrt.f64 (/.f64 n k)) (sqrt.f64 (.f64 #s(literal 2 binary64) (PI.f64)))))
	50.0%	#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (*.f64 (sqrt.f64 (/.f64 #s(literal 2 binary64) k)) (/.f64 (sqrt.f64 (PI.f64)) (sqrt.f64 (/.f64 #s(literal 1 binary64) n)))))
	50.2%	#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (.f64 (sqrt.f64 (/.f64 #s(literal 2 binary64) k)) (sqrt.f64 (.f64 (PI.f64) n))))
	37.7%	#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (.f64 (sqrt.f64 (.f64 (/.f64 (PI.f64) k) n)) (sqrt.f64 #s(literal 2 binary64))))
	50.2%	#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (.f64 (sqrt.f64 (.f64 #s(literal 2 binary64) (/.f64 (PI.f64) k))) (sqrt.f64 n)))
	37.7%	#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (.f64 (sqrt.f64 (.f64 #s(literal 2 binary64) (/.f64 n k))) (sqrt.f64 (PI.f64))))
	50.1%	#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (.f64 (sqrt.f64 (.f64 #s(literal 2 binary64) (.f64 (.f64 (sqrt.f64 (PI.f64)) (sqrt.f64 (PI.f64))) n))) (sqrt.f64 (/.f64 #s(literal 1 binary64) k))))
	50.4%	#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (.f64 (sqrt.f64 (.f64 #s(literal 2 binary64) (.f64 (PI.f64) n))) (.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k))) (sqrt.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k))))))
✓	50.2%	#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (.f64 (sqrt.f64 (.f64 #s(literal 2 binary64) (*.f64 (PI.f64) n))) (sqrt.f64 (/.f64 #s(literal 1 binary64) k))))
	37.9%	#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt.f64 (/.f64 (*.f64 #s(literal 2 binary64) n) (/.f64 k (PI.f64)))))
	37.8%	#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt.f64 (/.f64 #s(literal 2 binary64) (/.f64 k (*.f64 (PI.f64) n)))))
	37.7%	#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt.f64 (.f64 (/.f64 (.f64 #s(literal 2 binary64) (sqrt.f64 (PI.f64))) #s(literal 1 binary64)) (/.f64 (*.f64 (sqrt.f64 (PI.f64)) n) k))))
	37.8%	#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt.f64 (.f64 (/.f64 #s(literal 2 binary64) k) (.f64 (PI.f64) n))))
	37.8%	#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt.f64 (*.f64 (PI.f64) (/.f64 #s(literal 2 binary64) (/.f64 k n)))))
	37.8%	#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt.f64 (.f64 n (.f64 (*.f64 #s(literal 2 binary64) (PI.f64)) (/.f64 #s(literal 1 binary64) k)))))
	37.7%	#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt.f64 (.f64 #s(literal 2 binary64) (/.f64 (.f64 (*.f64 (sqrt.f64 (PI.f64)) (sqrt.f64 (PI.f64))) n) k))))
✓	37.8%	#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt.f64 (.f64 #s(literal 2 binary64) (/.f64 (.f64 (PI.f64) n) k))))
	37.8%	#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt.f64 (.f64 #s(literal 2 binary64) (.f64 (/.f64 n k) (PI.f64)))))
✓	37.9%	#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt.f64 (.f64 #s(literal 2 binary64) (.f64 n (/.f64 (PI.f64) k)))))
	37.8%	#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt.f64 (.f64 #s(literal 2 binary64) (.f64 n (/.f64 #s(literal 1 binary64) (/.f64 k (PI.f64)))))))

Compiler

Compiled 2 677 to 1 236 computations (53.8% saved)

regimes142.0ms (1.3%)

Memory

13.8MiB live, 315.3MiB allocated

Counts

111 → 1

Calls

Call 1

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

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

Calls

4 calls:

37.0ms	n
35.0ms	(.f64 (.f64 #s(literal 2 binary64) (PI.f64)) n)
33.0ms	k
31.0ms	(.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	`k`
99.7%	1	`n`
99.7%	1	`(.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) (pow.f64 (.f64 (*.f64 #s(literal 2 binary64) (PI.f64)) n) (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 2 binary64))))`
99.7%	1	`(.f64 (.f64 #s(literal 2 binary64) (PI.f64)) n)`

Compiler

Compiled 31 to 23 computations (25.8% saved)

regimes157.0ms (1.4%)

Memory

0.7MiB live, 350.7MiB allocated

Counts

106 → 1

Calls

Call 1

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

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

Calls

4 calls:

43.0ms	(.f64 (.f64 #s(literal 2 binary64) (PI.f64)) n)
40.0ms	n
31.0ms	k
30.0ms	(.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) (pow.f64 (.f64 (*.f64 #s(literal 2 binary64) (PI.f64)) n) (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 2 binary64))))

Results

Accuracy	Segments	Branch
99.5%	1	`k`
99.5%	1	`n`
99.5%	1	`(.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) (pow.f64 (.f64 (*.f64 #s(literal 2 binary64) (PI.f64)) n) (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 2 binary64))))`
99.5%	1	`(.f64 (.f64 #s(literal 2 binary64) (PI.f64)) n)`

Compiler

Compiled 31 to 23 computations (25.8% saved)

regimes139.0ms (1.3%)

Memory

28.5MiB live, 220.1MiB allocated

Counts

91 → 1

Calls

Call 1

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

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

Calls

4 calls:

41.0ms	(.f64 (.f64 #s(literal 2 binary64) (PI.f64)) n)
34.0ms	n
33.0ms	(.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))))
26.0ms	k

Results

Accuracy	Segments	Branch
50.6%	1	`k`
50.6%	1	`n`
50.6%	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))))`
50.6%	1	`(.f64 (.f64 #s(literal 2 binary64) (PI.f64)) n)`

Compiler

Compiled 31 to 23 computations (25.8% saved)

regimes28.0ms (0.3%)

Memory

-3.2MiB live, 74.3MiB allocated

Counts

20 → 1

Calls

Call 1

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

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

Calls

4 calls:

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

Results

Accuracy	Segments	Branch
50.2%	1	`k`
50.2%	1	`n`
50.2%	1	`(.f64 (.f64 #s(literal 2 binary64) (PI.f64)) n)`
50.2%	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 31 to 23 computations (25.8% saved)

regimes20.0ms (0.2%)

Memory

-34.2MiB live, 36.4MiB allocated

Counts

9 → 1

Calls

Call 1

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

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

Calls

4 calls:

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

Results

Accuracy	Segments	Branch
37.9%	1	`k`
37.9%	1	`n`
37.9%	1	`(.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) (pow.f64 (.f64 (*.f64 #s(literal 2 binary64) (PI.f64)) n) (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 2 binary64))))`
37.9%	1	`(.f64 (.f64 #s(literal 2 binary64) (PI.f64)) n)`

Compiler

Compiled 31 to 23 computations (25.8% saved)

regimes14.0ms (0.1%)

Memory

-1.1MiB live, 38.5MiB allocated

Accuracy

Total -0.1b remaining (-0.3%)

Threshold costs -0.1b (-0.3%)

Counts

8 → 1

Calls

Call 1

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

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

Calls

4 calls:

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

Results

Accuracy	Segments	Branch
37.9%	1	`k`
37.9%	1	`(.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) (pow.f64 (.f64 (*.f64 #s(literal 2 binary64) (PI.f64)) n) (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 2 binary64))))`
37.9%	1	`n`
37.9%	1	`(.f64 (.f64 #s(literal 2 binary64) (PI.f64)) n)`

Compiler

Compiled 31 to 23 computations (25.8% saved)

simplify6.0ms (0.1%)

Memory

13.3MiB live, 13.3MiB allocated

Algorithm

1×	egg-herbie

Rules

18×	`*-commutative_binary64`
2×	`1-exp_binary64`
2×	`1-exp_binary32`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	44	134
1	56	134

Stop Event

1×

saturated

Calls

Call 1

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

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

soundness705.0ms (6.4%)

Memory

-7.6MiB live, 661.5MiB allocated

Rules

9 974×	`lower-fma.f64`
9 974×	`lower-fma.f32`
5 988×	`lower-*.f64`
5 988×	`lower-*.f32`
5 570×	`lower-*.f32`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	13	43
0	22	43
1	89	40
2	497	38
3	4474	38
0	8599	37
0	44	173
0	72	175
1	284	153
2	1762	153
0	8671	153
0	49	238
0	76	214
1	267	206
2	1520	201
0	8282	201
0	128	1174
1	345	1155
2	1011	1065
3	3348	1038
4	5547	966
0	8354	945
0	48	256
0	79	217
1	244	204
2	1283	204
0	8502	204

Stop Event

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

Compiler

Compiled 233 to 152 computations (34.8% saved)

preprocess48.0ms (0.4%)

Memory: 23.1MiB live, 105.0MiB allocated
Compiler: Compiled 180 to 86 computations (52.2% saved)

end0.0ms (0%)

Memory: 0.0MiB live, 0.0MiB allocated

Iter	Nodes	Cost
0	13	54
0	22	54
1	37	52
2	54	52
3	75	52
4	93	52
5	108	52
6	129	52
7	156	52
8	165	52
9	168	52
0	168	49

Iter	Nodes	Cost
0	44	279
0	72	280
1	111	274
2	145	274
3	167	272
4	184	272
5	198	272
6	218	272
7	251	272
8	263	272
9	267	272
0	267	272

Iter	Nodes	Cost
0	49	298
0	76	290
1	114	284
2	167	284
3	240	281
4	316	281
5	333	281
6	356	281
7	389	281
8	401	281
9	405	281
0	405	279

Iter	Nodes	Cost
0	13	54
0	22	54
1	37	52
2	54	52
3	75	52
4	93	52
5	108	52
6	129	52
7	156	52
8	165	52
9	168	52
0	168	49

Iter	Nodes	Cost
0	44	279
0	72	280
1	111	274
2	145	274
3	167	272
4	184	272
5	198	272
6	218	272
7	251	272
8	263	272
9	267	272
0	267	272

Iter	Nodes	Cost
0	49	298
0	76	290
1	114	284
2	167	284
3	240	281
4	316	281
5	333	281
6	356	281
7	389	281
8	401	281
9	405	281
0	405	279

analyze136.0ms (1.2%)

sample3.0s (27.2%)

preprocess62.0ms (0.6%)

explain149.0ms (1.3%)

eval0.0ms (0%)

prune1.0ms (0%)

simplify9.0ms (0.1%)

localize43.0ms (0.4%)

series72.0ms (0.6%)

simplify278.0ms (2.5%)

rewrite376.0ms (3.4%)

eval157.0ms (1.4%)

prune179.0ms (1.6%)

simplify15.0ms (0.1%)

localize222.0ms (2%)

series247.0ms (2.2%)

simplify539.0ms (4.9%)

rewrite354.0ms (3.2%)

eval349.0ms (3.2%)

prune270.0ms (2.4%)

simplify22.0ms (0.2%)

localize198.0ms (1.8%)

series45.0ms (0.4%)

simplify373.0ms (3.4%)

rewrite288.0ms (2.6%)

eval367.0ms (3.3%)

prune393.0ms (3.5%)

simplify139.0ms (1.3%)

localize145.0ms (1.3%)

series32.0ms (0.3%)

simplify322.0ms (2.9%)

rewrite309.0ms (2.8%)

eval322.0ms (2.9%)

prune386.0ms (3.5%)

regimes142.0ms (1.3%)

regimes157.0ms (1.4%)

regimes139.0ms (1.3%)

regimes28.0ms (0.3%)

regimes20.0ms (0.2%)

regimes14.0ms (0.1%)

simplify6.0ms (0.1%)

soundness705.0ms (6.4%)

preprocess48.0ms (0.4%)

end0.0ms (0%)

Profiling

Iter	Nodes	Cost
0	13	54
0	22	54
1	37	52
2	54	52
3	75	52
4	93	52
5	108	52
6	129	52
7	156	52
8	165	52
9	168	52
0	168	49

Iter	Nodes	Cost
0	44	279
0	72	280
1	111	274
2	145	274
3	167	272
4	184	272
5	198	272
6	218	272
7	251	272
8	263	272
9	267	272
0	267	272

Iter	Nodes	Cost
0	49	298
0	76	290
1	114	284
2	167	284
3	240	281
4	316	281
5	333	281
6	356	281
7	389	281
8	401	281
9	405	281
0	405	279