Metrics for Migdal et al, Equation (51)

analyze112.0ms (1%)

Memory

-42.1MiB live, 150.2MiB allocated

Algorithm

1×

Search

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

Compiler

Compiled 18 to 15 computations (16.7% saved)

sample3.2s (27.5%)

Memory

62.4MiB live, 4 557.3MiB allocated

Samples

946.0ms	8 256×	0	valid
732.0ms	3 501×	1	invalid
593.0ms	1 858×	1	exit
137.0ms	458×	2	invalid
58.0ms	442×	0	invalid
57.0ms	259×	0	exit
0.0ms	1×	2	exit

Precisions

Click to see histograms. Total time spent on operations: 1.9s

ival-mult: 660.0ms (34.2% of total)

ival-pow: 520.0ms (26.9% of total)

ival-div: 274.0ms (14.2% of total)

ival-sqrt: 155.0ms (8% of total)

ival-sub: 128.0ms (6.6% of total)

ival-pi: 81.0ms (4.2% of total)

adjust: 78.0ms (4% of total)

exact: 19.0ms (1% of total)

ival-true: 11.0ms (0.6% of total)

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

Bogosity

preprocess56.0ms (0.5%)

Memory

10.3MiB live, 79.1MiB allocated

Algorithm

2×	egg-herbie

Rules

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

Iterations

Useful iterations: 0 (0.0ms)

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

Stop Event

1×	iter limit
1×	saturated
1×	saturated

Calls

Call 1

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

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

Call 2

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

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

explain174.0ms (1.5%)

Memory

-39.0MiB live, 405.1MiB allocated

FPErrors

Click to see full error table

Ground Truth	Overpredictions	Example	Underpredictions	Example	Subexpression
5	84	(4.4660364447346044e-281 4.0246131933440147e-137)	1	(1.635497945397211e-10 1.1415127047921111e-54)	`(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	88	25

Confusion

	Predicted +	Predicted -
+	4	1
-	84	167

Precision

0.045454545454545456

Recall

0.8

Confusion?

	Predicted +	Predicted Maybe	Predicted -
+	4	1	0
-	84	24	143

Precision?

0.04424778761061947

Recall?

1.0

Freqs

test

number	freq
0	168
1	88

Total Confusion?

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

Precision?

1.0

Recall?

1.0

Samples

73.0ms

512×

valid

Compiler

Compiled 148 to 56 computations (62.2% saved)

Precisions

Click to see histograms. Total time spent on operations: 54.0ms

ival-div: 26.0ms (48.4% of total)

ival-pow: 10.0ms (18.6% of total)

ival-mult: 9.0ms (16.7% of total)

ival-sqrt: 4.0ms (7.4% of total)

ival-sub: 3.0ms (5.6% of total)

ival-pi: 2.0ms (3.7% 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: 0.7MiB live, 0.7MiB allocated
Compiler: Compiled 2 to 2 computations (0% saved)

prune1.0ms (0%)

Memory

2.4MiB live, 2.4MiB allocated

Alt Table

Click to see full alt table

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

Compiler

Compiled 18 to 13 computations (27.8% saved)

simplify8.0ms (0.1%)

Memory

22.8MiB live, 22.8MiB allocated

Algorithm

1×	egg-herbie

Localize:

Found 4 expressions of interest:

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

Rules

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

Iterations

Useful iterations: 0 (0.0ms)

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

Stop Event

1×	iter limit
1×	saturated

Calls

Call 1

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

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

localize93.0ms (0.8%)

Memory

-28.6MiB live, 90.3MiB allocated

Localize:

Found 4 expressions of interest:

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

Samples

52.0ms

256×

valid

Compiler

Compiled 56 to 15 computations (73.2% saved)

Precisions

Click to see histograms. Total time spent on operations: 17.0ms

ival-pow: 5.0ms (29% of total)

ival-mult: 4.0ms (23.2% of total)

ival-div: 3.0ms (17.4% of total)

ival-sqrt: 2.0ms (11.6% of total)

ival-pi: 1.0ms (5.8% of total)

ival-sub: 1.0ms (5.8% of total)

exact: 1.0ms (5.8% of total)

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

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

series99.0ms (0.8%)

Memory

12.4MiB live, 124.4MiB allocated

Counts

6 → 96

Calls

Call 1

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

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

Calls

24 calls:

Time	Variable		Point	Expression
41.0ms	n	@	-inf	(* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2)))
30.0ms	n	@	0	(* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2)))
20.0ms	n	@	inf	(* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2)))
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)))

rewrite344.0ms (2.9%)

Memory

11.7MiB live, 558.6MiB allocated

Algorithm

1×	batch-egg-rewrite

Rules

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

Iterations

Useful iterations: 0 (0.0ms)

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

Stop Event

1×	iter limit
1×	node limit

Counts

6 → 419

Calls

Call 1

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

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

simplify343.0ms (2.9%)

Memory

18.6MiB live, 725.3MiB allocated

Algorithm

1×	egg-herbie

Rules

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

Iterations

Useful iterations: 0 (0.0ms)

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

Stop Event

1×	iter limit
1×	node limit

Counts

96 → 96

Calls

Call 1

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

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

eval62.0ms (0.5%)

Memory: 37.7MiB live, 190.9MiB allocated
Compiler: Compiled 11 286 to 1 530 computations (86.4% saved)

prune110.0ms (0.9%)

Memory

-28.1MiB live, 180.1MiB allocated

Pruning

16 alts after pruning (16 fresh and 0 done)

	Pruned	Kept	Total
New	499	16	515
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	500	16	516

Accuracy

100.0%

Counts

516 → 16

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))
▶	99.7%	(/.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))))
	53.3%	(/.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)
▶	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)))))
	99.5%	(/.f64 #s(literal 1 binary64) (.f64 (sqrt.f64 k) (pow.f64 (.f64 #s(literal 2 binary64) (.f64 (PI.f64) n)) (+.f64 #s(literal -1/2 binary64) (.f64 k #s(literal 1/2 binary64))))))
	99.3%	(.f64 (pow.f64 (.f64 #s(literal 2 binary64) (.f64 (PI.f64) n)) (-.f64 #s(literal 1/4 binary64) (.f64 k #s(literal 1/4 binary64)))) (/.f64 (pow.f64 (.f64 #s(literal 2 binary64) (.f64 (PI.f64) n)) (-.f64 #s(literal 1/4 binary64) (*.f64 k #s(literal 1/4 binary64)))) (sqrt.f64 k)))
	99.5%	(.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))))
▶	52.5%	(.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) (pow.f64 (.f64 (.f64 #s(literal 2 binary64) (PI.f64)) n) (.f64 #s(literal -1/2 binary64) k)))
	50.5%	(.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) (pow.f64 (.f64 (*.f64 #s(literal 2 binary64) (PI.f64)) n) #s(literal 1/2 binary64)))
▶	76.1%	(.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) (pow.f64 (.f64 #s(literal 4 binary64) (.f64 (.f64 (PI.f64) n) (.f64 (PI.f64) n))) (-.f64 #s(literal 1/4 binary64) (.f64 k #s(literal 1/4 binary64)))))
	99.5%	(.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))))))
	99.5%	(.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)) (.f64 (sqrt.f64 #s(literal 2 binary64)) (sqrt.f64 (*.f64 n (PI.f64)))))
▶	38.8%	(.f64 (sqrt.f64 (/.f64 (.f64 n (PI.f64)) k)) (sqrt.f64 #s(literal 2 binary64)))
	99.6%	(.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) k)) (pow.f64 (.f64 n (*.f64 (PI.f64) #s(literal 2 binary64))) (fma.f64 #s(literal -1/2 binary64) k #s(literal 1/2 binary64))))

Compiler

Compiled 620 to 442 computations (28.7% saved)

simplify35.0ms (0.3%)

Memory

-7.4MiB live, 28.2MiB allocated

Algorithm

1×	egg-herbie

Localize:

Found 20 expressions of interest:

New	Metric	Score	Program
✓	cost-diff	0	(sqrt.f64 k)
✓	cost-diff	0	(/.f64 #s(literal 1 binary64) (sqrt.f64 k))
✓	cost-diff	320	(.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) (sqrt.f64 (.f64 #s(literal 2 binary64) (*.f64 (PI.f64) n))))
✓	cost-diff	384	(/.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))))
✓	cost-diff	0	(sqrt.f64 k)
✓	cost-diff	0	(/.f64 #s(literal 1 binary64) (sqrt.f64 k))
✓	cost-diff	192	(-.f64 #s(literal 1/4 binary64) (*.f64 k #s(literal 1/4 binary64)))
✓	cost-diff	320	(.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) (pow.f64 (.f64 #s(literal 4 binary64) (.f64 (.f64 (PI.f64) n) (.f64 (PI.f64) n))) (-.f64 #s(literal 1/4 binary64) (.f64 k #s(literal 1/4 binary64)))))
✓	cost-diff	0	(pow.f64 (.f64 (.f64 #s(literal 2 binary64) (PI.f64)) n) (*.f64 #s(literal -1/2 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 (.f64 (.f64 #s(literal 2 binary64) (PI.f64)) n) (.f64 #s(literal -1/2 binary64) k)))
✓	cost-diff	0	(*.f64 n (PI.f64))
✓	cost-diff	0	(/.f64 (*.f64 n (PI.f64)) k)
✓	cost-diff	0	(sqrt.f64 (/.f64 (*.f64 n (PI.f64)) k))
✓	cost-diff	0	(.f64 (sqrt.f64 (/.f64 (.f64 n (PI.f64)) k)) (sqrt.f64 #s(literal 2 binary64)))
✓	cost-diff	0	(*.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

306×	`-lowering-.f32`
306×	`-lowering-.f64`
118×	`associate-r`
98×	`*-commutative`
92×	`associate-l`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	36	281
1	78	275
2	152	275
3	246	275
4	292	275
5	320	275
6	346	275
7	373	275
8	381	275
0	381	272

Stop Event

1×	iter limit
1×	saturated

Calls

Call 1

Inputs
(/ (sqrt (* 2 (* (PI) n))) (* (sqrt k) (pow (* 2 (* (PI) n)) (* k 1/2))))
(sqrt (* 2 (* (PI) n)))
(* 2 (* (PI) n))
2
(* (PI) n)
(PI)
n
(* (sqrt k) (pow (* 2 (* (PI) n)) (* k 1/2)))
(sqrt k)
k
(pow (* 2 (* (PI) n)) (* k 1/2))
(* k 1/2)
1/2
(* (sqrt (/ (* n (PI)) k)) (sqrt 2))
(sqrt (/ (* n (PI)) k))
(/ (* n (PI)) k)
(* n (PI))
n
(PI)
k
(sqrt 2)
2
(* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (* -1/2 k)))
(/ 1 (sqrt k))
1
(sqrt k)
k
(pow (* (* 2 (PI)) n) (* -1/2 k))
(* (* 2 (PI)) n)
(* 2 (PI))
2
(PI)
n
(* -1/2 k)
-1/2
(* (/ 1 (sqrt k)) (pow (* 4 (* (* (PI) n) (* (PI) n))) (- 1/4 (* k 1/4))))
(/ 1 (sqrt k))
1
(sqrt k)
k
(pow (* 4 (* (* (PI) n) (* (PI) n))) (- 1/4 (* k 1/4)))
(* 4 (* (* (PI) n) (* (PI) n)))
4
(* (* (PI) n) (* (PI) n))
(* (PI) n)
(PI)
n
(- 1/4 (* k 1/4))
1/4
(* k 1/4)
(/ (* (/ 1 (sqrt k)) (sqrt (* 2 (* (PI) n)))) (pow (* 2 (* (PI) n)) (* k 1/2)))
(* (/ 1 (sqrt k)) (sqrt (* 2 (* (PI) n))))
(/ 1 (sqrt k))
1
(sqrt k)
k
(sqrt (* 2 (* (PI) n)))
(* 2 (* (PI) n))
2
(* (PI) n)
(PI)
n
(pow (* 2 (* (PI) n)) (* k 1/2))
(* k 1/2)
1/2

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

localize214.0ms (1.8%)

Memory

35.4MiB live, 330.6MiB allocated

Localize:

Found 20 expressions of interest:

New	Metric	Score	Program
✓	accuracy	99.8%	(/.f64 #s(literal 1 binary64) (sqrt.f64 k))
✓	accuracy	99.7%	(*.f64 (PI.f64) n)
✓	accuracy	99.6%	(.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) (sqrt.f64 (.f64 #s(literal 2 binary64) (*.f64 (PI.f64) n))))
✓	accuracy	76.2%	(PI.f64)
✓	accuracy	99.7%	(*.f64 (PI.f64) n)
✓	accuracy	99.7%	(.f64 (.f64 (PI.f64) n) (*.f64 (PI.f64) n))
✓	accuracy	76.2%	(PI.f64)
✓	accuracy	76.2%	(pow.f64 (.f64 #s(literal 4 binary64) (.f64 (.f64 (PI.f64) n) (.f64 (PI.f64) n))) (-.f64 #s(literal 1/4 binary64) (*.f64 k #s(literal 1/4 binary64))))
✓	accuracy	100.0%	(.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) (pow.f64 (.f64 (.f64 #s(literal 2 binary64) (PI.f64)) n) (.f64 #s(literal -1/2 binary64) k)))
✓	accuracy	99.8%	(/.f64 #s(literal 1 binary64) (sqrt.f64 k))
✓	accuracy	99.7%	(.f64 (.f64 #s(literal 2 binary64) (PI.f64)) n)
✓	accuracy	76.2%	(PI.f64)
✓	accuracy	99.7%	(*.f64 n (PI.f64))
✓	accuracy	99.5%	(.f64 (sqrt.f64 (/.f64 (.f64 n (PI.f64)) k)) (sqrt.f64 #s(literal 2 binary64)))
✓	accuracy	88.2%	(sqrt.f64 (/.f64 (*.f64 n (PI.f64)) k))
✓	accuracy	76.2%	(PI.f64)
✓	accuracy	99.9%	(sqrt.f64 (.f64 #s(literal 2 binary64) (.f64 (PI.f64) n)))
✓	accuracy	99.7%	(*.f64 (PI.f64) n)
✓	accuracy	99.7%	(/.f64 (sqrt.f64 (.f64 #s(literal 2 binary64) (.f64 (PI.f64) n))) (.f64 (sqrt.f64 k) (pow.f64 (.f64 #s(literal 2 binary64) (.f64 (PI.f64) n)) (.f64 k #s(literal 1/2 binary64)))))
✓	accuracy	76.2%	(PI.f64)

Samples

52.0ms	193×	0	valid
20.0ms	63×	0	exit

Compiler

Compiled 285 to 38 computations (86.7% saved)

Precisions

Click to see histograms. Total time spent on operations: 49.0ms

ival-mult: 22.0ms (45.1% of total)

ival-pow: 11.0ms (22.5% of total)

ival-sqrt: 7.0ms (14.3% of total)

ival-div: 6.0ms (12.3% of total)

ival-pi: 1.0ms (2% of total)

ival-sub: 1.0ms (2% of total)

exact: 1.0ms (2% of total)

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

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

series81.0ms (0.7%)

Memory

6.8MiB live, 160.0MiB allocated

Counts

20 → 348

Calls

Call 1

Inputs
#<alt (/ (sqrt (* 2 (* (PI) n))) (* (sqrt k) (pow (* 2 (* (PI) n)) (* k 1/2))))>
#<alt (sqrt (* 2 (* (PI) n)))>
#<alt (* 2 (* (PI) n))>
#<alt (* (PI) n)>
#<alt (* (sqrt (/ (* n (PI)) k)) (sqrt 2))>
#<alt (sqrt (/ (* n (PI)) k))>
#<alt (/ (* n (PI)) k)>
#<alt (* n (PI))>
#<alt (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (* -1/2 k)))>
#<alt (/ 1 (sqrt k))>
#<alt (sqrt k)>
#<alt (pow (* (* 2 (PI)) n) (* -1/2 k))>
#<alt (* (/ 1 (sqrt k)) (pow (* 4 (* (* (PI) n) (* (PI) n))) (- 1/4 (* k 1/4))))>
#<alt (- 1/4 (* k 1/4))>
#<alt (/ (* (/ 1 (sqrt k)) (sqrt (* 2 (* (PI) n)))) (pow (* 2 (* (PI) n)) (* k 1/2)))>
#<alt (* (/ 1 (sqrt k)) (sqrt (* 2 (* (PI) n))))>
#<alt (PI)>
#<alt (* (* 2 (PI)) n)>
#<alt (pow (* 4 (* (* (PI) n) (* (PI) n))) (- 1/4 (* k 1/4)))>
#<alt (* (* (PI) n) (* (PI) n))>

Outputs
#<alt (* (sqrt (/ (* n (PI)) k)) (/ (sqrt 2) (exp (* 1/2 (* k (+ (log n) (log (* 2 (PI)))))))))>
#<alt (* (sqrt (/ (* n (PI)) k)) (/ (sqrt 2) (exp (* 1/2 (* k (+ (log n) (log (* 2 (PI)))))))))>
#<alt (* (sqrt (/ (* n (PI)) k)) (/ (sqrt 2) (exp (* 1/2 (* k (+ (log n) (log (* 2 (PI)))))))))>
#<alt (* (sqrt (/ (* n (PI)) k)) (/ (sqrt 2) (exp (* 1/2 (* k (+ (log n) (log (* 2 (PI)))))))))>
#<alt (* (sqrt (/ (* n (PI)) k)) (/ (sqrt 2) (exp (* 1/2 (* k (+ (log (* 2 (PI))) (* -1 (log (/ 1 n)))))))))>
#<alt (* (sqrt (/ (* n (PI)) k)) (/ (sqrt 2) (exp (* 1/2 (* k (+ (log (* 2 (PI))) (* -1 (log (/ 1 n)))))))))>
#<alt (* (sqrt (/ (* n (PI)) k)) (/ (sqrt 2) (exp (* 1/2 (* k (+ (log (* 2 (PI))) (* -1 (log (/ 1 n)))))))))>
#<alt (* (sqrt (/ (* n (PI)) k)) (/ (sqrt 2) (exp (* 1/2 (* k (+ (log (* 2 (PI))) (* -1 (log (/ 1 n)))))))))>
#<alt (* -1 (* (sqrt (/ (* n (PI)) k)) (/ (* (sqrt -2) (sqrt -1)) (exp (* 1/2 (* k (+ (log (* -2 (PI))) (* -1 (log (/ -1 n))))))))))>
#<alt (* -1 (* (sqrt (/ (* n (PI)) k)) (/ (* (sqrt -2) (sqrt -1)) (exp (* 1/2 (* k (+ (log (* -2 (PI))) (* -1 (log (/ -1 n))))))))))>
#<alt (* -1 (* (sqrt (/ (* n (PI)) k)) (/ (* (sqrt -2) (sqrt -1)) (exp (* 1/2 (* k (+ (log (* -2 (PI))) (* -1 (log (/ -1 n))))))))))>
#<alt (* -1 (* (sqrt (/ (* n (PI)) k)) (/ (* (sqrt -2) (sqrt -1)) (exp (* 1/2 (* k (+ (log (* -2 (PI))) (* -1 (log (/ -1 n))))))))))>
#<alt (* (sqrt (/ (* n (PI)) k)) (sqrt 2))>
#<alt (/ (+ (* -1/2 (* (sqrt (* (pow k 3) (* n (PI)))) (* (log (* 2 (* n (PI)))) (sqrt 2)))) (* (sqrt (* k (* n (PI)))) (sqrt 2))) k)>
#<alt (/ (+ (* k (+ (* -1 (* (sqrt (* (pow k 3) (* n (PI)))) (+ (* -1/4 (* (pow (log (* 2 (* n (PI)))) 2) (sqrt 2))) (* 1/8 (* (pow (log (* 2 (* n (PI)))) 2) (sqrt 2)))))) (* -1/2 (* (sqrt (* k (* n (PI)))) (* (log (* 2 (* n (PI)))) (sqrt 2)))))) (* (sqrt (* k (* n (PI)))) (sqrt 2))) k)>
#<alt (/ (+ (* k (+ (* -1/2 (* (sqrt (* k (* n (PI)))) (* (log (* 2 (* n (PI)))) (sqrt 2)))) (* k (+ (* -1 (* (sqrt (* k (* n (PI)))) (+ (* -1/4 (* (pow (log (* 2 (* n (PI)))) 2) (sqrt 2))) (* 1/8 (* (pow (log (* 2 (* n (PI)))) 2) (sqrt 2)))))) (* -1 (* (sqrt (* (pow k 3) (* n (PI)))) (+ (* -1/2 (* (log (* 2 (* n (PI)))) (+ (* -1/4 (* (pow (log (* 2 (* n (PI)))) 2) (sqrt 2))) (* 1/8 (* (pow (log (* 2 (* n (PI)))) 2) (sqrt 2)))))) (+ (* -1/16 (* (pow (log (* 2 (* n (PI)))) 3) (sqrt 2))) (* 1/48 (* (pow (log (* 2 (* n (PI)))) 3) (sqrt 2))))))))))) (* (sqrt (* k (* n (PI)))) (sqrt 2))) k)>
#<alt (* (sqrt (/ (* n (PI)) k)) (/ (sqrt 2) (exp (* 1/2 (* k (log (* 2 (* n (PI)))))))))>
#<alt (* (sqrt (/ (* n (PI)) k)) (/ (sqrt 2) (exp (* 1/2 (* k (log (* 2 (* n (PI)))))))))>
#<alt (* (sqrt (/ (* n (PI)) k)) (/ (sqrt 2) (exp (* 1/2 (* k (log (* 2 (* n (PI)))))))))>
#<alt (* (sqrt (/ (* n (PI)) k)) (/ (sqrt 2) (exp (* 1/2 (* k (log (* 2 (* n (PI)))))))))>
#<alt (* (sqrt (/ (* n (PI)) k)) (/ (sqrt 2) (exp (* 1/2 (* k (log (* 2 (* n (PI)))))))))>
#<alt (* (sqrt (/ (* n (PI)) k)) (/ (sqrt 2) (exp (* 1/2 (* k (log (* 2 (* n (PI)))))))))>
#<alt (* (sqrt (/ (* n (PI)) k)) (/ (sqrt 2) (exp (* 1/2 (* k (log (* 2 (* n (PI)))))))))>
#<alt (* (sqrt (/ (* n (PI)) k)) (/ (sqrt 2) (exp (* 1/2 (* k (log (* 2 (* n (PI)))))))))>
#<alt (* (sqrt (* n (PI))) (sqrt 2))>
#<alt (* (sqrt (* n (PI))) (sqrt 2))>
#<alt (* (sqrt (* n (PI))) (sqrt 2))>
#<alt (* (sqrt (* n (PI))) (sqrt 2))>
#<alt (* (sqrt (* n (PI))) (sqrt 2))>
#<alt (* (sqrt (* n (PI))) (sqrt 2))>
#<alt (* (sqrt (* n (PI))) (sqrt 2))>
#<alt (* (sqrt (* n (PI))) (sqrt 2))>
#<alt (* -1 (* (sqrt (* n (PI))) (* (sqrt -2) (sqrt -1))))>
#<alt (* -1 (* (sqrt (* n (PI))) (* (sqrt -2) (sqrt -1))))>
#<alt (* -1 (* (sqrt (* n (PI))) (* (sqrt -2) (sqrt -1))))>
#<alt (* -1 (* (sqrt (* n (PI))) (* (sqrt -2) (sqrt -1))))>
#<alt (* 2 (* n (PI)))>
#<alt (* 2 (* n (PI)))>
#<alt (* 2 (* n (PI)))>
#<alt (* 2 (* n (PI)))>
#<alt (* 2 (* n (PI)))>
#<alt (* 2 (* n (PI)))>
#<alt (* 2 (* n (PI)))>
#<alt (* 2 (* n (PI)))>
#<alt (* 2 (* n (PI)))>
#<alt (* 2 (* n (PI)))>
#<alt (* 2 (* n (PI)))>
#<alt (* 2 (* n (PI)))>
#<alt (* n (PI))>
#<alt (* n (PI))>
#<alt (* n (PI))>
#<alt (* n (PI))>
#<alt (* n (PI))>
#<alt (* n (PI))>
#<alt (* n (PI))>
#<alt (* n (PI))>
#<alt (* n (PI))>
#<alt (* n (PI))>
#<alt (* n (PI))>
#<alt (* n (PI))>
#<alt (* (sqrt (/ (* n (PI)) k)) (sqrt 2))>
#<alt (* (sqrt (/ (* n (PI)) k)) (sqrt 2))>
#<alt (* (sqrt (/ (* n (PI)) k)) (sqrt 2))>
#<alt (* (sqrt (/ (* n (PI)) k)) (sqrt 2))>
#<alt (* (sqrt (/ (* n (PI)) k)) (sqrt 2))>
#<alt (* (sqrt (/ (* n (PI)) k)) (sqrt 2))>
#<alt (* (sqrt (/ (* n (PI)) k)) (sqrt 2))>
#<alt (* (sqrt (/ (* n (PI)) k)) (sqrt 2))>
#<alt (* -1 (* (sqrt (/ (* n (PI)) k)) (* (pow (sqrt -1) 2) (sqrt 2))))>
#<alt (* -1 (* (sqrt (/ (* n (PI)) k)) (* (pow (sqrt -1) 2) (sqrt 2))))>
#<alt (* -1 (* (sqrt (/ (* n (PI)) k)) (* (pow (sqrt -1) 2) (sqrt 2))))>
#<alt (* -1 (* (sqrt (/ (* n (PI)) k)) (* (pow (sqrt -1) 2) (sqrt 2))))>
#<alt (* (sqrt (/ (* n (PI)) k)) (sqrt 2))>
#<alt (* (sqrt (/ (* n (PI)) k)) (sqrt 2))>
#<alt (* (sqrt (/ (* n (PI)) k)) (sqrt 2))>
#<alt (* (sqrt (/ (* n (PI)) k)) (sqrt 2))>
#<alt (* (sqrt (/ (* n (PI)) k)) (sqrt 2))>
#<alt (* (sqrt (/ (* n (PI)) k)) (sqrt 2))>
#<alt (* (sqrt (/ (* n (PI)) k)) (sqrt 2))>
#<alt (* (sqrt (/ (* n (PI)) k)) (sqrt 2))>
#<alt (* (sqrt (/ (* n (PI)) k)) (* (pow (sqrt -1) 2) (sqrt 2)))>
#<alt (* (sqrt (/ (* n (PI)) k)) (* (pow (sqrt -1) 2) (sqrt 2)))>
#<alt (* (sqrt (/ (* n (PI)) k)) (* (pow (sqrt -1) 2) (sqrt 2)))>
#<alt (* (sqrt (/ (* n (PI)) k)) (* (pow (sqrt -1) 2) (sqrt 2)))>
#<alt (sqrt (/ (* n (PI)) k))>
#<alt (sqrt (/ (* n (PI)) k))>
#<alt (sqrt (/ (* n (PI)) k))>
#<alt (sqrt (/ (* n (PI)) k))>
#<alt (sqrt (/ (* n (PI)) k))>
#<alt (sqrt (/ (* n (PI)) k))>
#<alt (sqrt (/ (* n (PI)) k))>
#<alt (sqrt (/ (* n (PI)) k))>
#<alt (* -1 (* (sqrt (/ (* n (PI)) k)) (pow (sqrt -1) 2)))>
#<alt (* -1 (* (sqrt (/ (* n (PI)) k)) (pow (sqrt -1) 2)))>
#<alt (* -1 (* (sqrt (/ (* n (PI)) k)) (pow (sqrt -1) 2)))>
#<alt (* -1 (* (sqrt (/ (* n (PI)) k)) (pow (sqrt -1) 2)))>
#<alt (sqrt (/ (* n (PI)) k))>
#<alt (sqrt (/ (* n (PI)) k))>
#<alt (sqrt (/ (* n (PI)) k))>
#<alt (sqrt (/ (* n (PI)) k))>
#<alt (sqrt (/ (* n (PI)) k))>
#<alt (sqrt (/ (* n (PI)) k))>
#<alt (sqrt (/ (* n (PI)) k))>
#<alt (sqrt (/ (* n (PI)) k))>
#<alt (* (sqrt (/ (* n (PI)) k)) (pow (sqrt -1) 2))>
#<alt (* (sqrt (/ (* n (PI)) k)) (pow (sqrt -1) 2))>
#<alt (* (sqrt (/ (* n (PI)) k)) (pow (sqrt -1) 2))>
#<alt (* (sqrt (/ (* n (PI)) k)) (pow (sqrt -1) 2))>
#<alt (/ (* n (PI)) k)>
#<alt (/ (* n (PI)) k)>
#<alt (/ (* n (PI)) k)>
#<alt (/ (* n (PI)) k)>
#<alt (/ (* n (PI)) k)>
#<alt (/ (* n (PI)) k)>
#<alt (/ (* n (PI)) k)>
#<alt (/ (* n (PI)) k)>
#<alt (/ (* n (PI)) k)>
#<alt (/ (* n (PI)) k)>
#<alt (/ (* n (PI)) k)>
#<alt (/ (* n (PI)) k)>
#<alt (/ (* n (PI)) k)>
#<alt (/ (* n (PI)) k)>
#<alt (/ (* n (PI)) k)>
#<alt (/ (* n (PI)) k)>
#<alt (/ (* n (PI)) k)>
#<alt (/ (* n (PI)) k)>
#<alt (/ (* n (PI)) k)>
#<alt (/ (* n (PI)) k)>
#<alt (/ (* n (PI)) k)>
#<alt (/ (* n (PI)) k)>
#<alt (/ (* n (PI)) k)>
#<alt (/ (* n (PI)) k)>
#<alt (* n (PI))>
#<alt (* n (PI))>
#<alt (* n (PI))>
#<alt (* n (PI))>
#<alt (* n (PI))>
#<alt (* n (PI))>
#<alt (* n (PI))>
#<alt (* n (PI))>
#<alt (* n (PI))>
#<alt (* n (PI))>
#<alt (* n (PI))>
#<alt (* n (PI))>
#<alt (sqrt (/ 1 k))>
#<alt (/ (+ (sqrt k) (* -1/2 (* (sqrt (pow k 3)) (log (* 2 (* n (PI))))))) k)>
#<alt (/ (+ (sqrt k) (* k (+ (* -1/2 (* (sqrt k) (log (* 2 (* n (PI)))))) (* 1/8 (* (sqrt (pow k 3)) (pow (log (* 2 (* n (PI)))) 2)))))) k)>
#<alt (/ (+ (sqrt k) (* k (+ (* -1/2 (* (sqrt k) (log (* 2 (* n (PI)))))) (* k (+ (* -1/48 (* (sqrt (pow k 3)) (pow (log (* 2 (* n (PI)))) 3))) (* 1/8 (* (sqrt k) (pow (log (* 2 (* n (PI)))) 2)))))))) k)>
#<alt (* (sqrt (/ 1 k)) (exp (* -1/2 (* k (log (* 2 (* n (PI))))))))>
#<alt (* (sqrt (/ 1 k)) (exp (* -1/2 (* k (log (* 2 (* n (PI))))))))>
#<alt (* (sqrt (/ 1 k)) (exp (* -1/2 (* k (log (* 2 (* n (PI))))))))>
#<alt (* (sqrt (/ 1 k)) (exp (* -1/2 (* k (log (* 2 (* n (PI))))))))>
#<alt (* (sqrt (/ 1 k)) (exp (* -1/2 (* k (log (* 2 (* n (PI))))))))>
#<alt (* (sqrt (/ 1 k)) (exp (* -1/2 (* k (log (* 2 (* n (PI))))))))>
#<alt (* (sqrt (/ 1 k)) (exp (* -1/2 (* k (log (* 2 (* n (PI))))))))>
#<alt (* (sqrt (/ 1 k)) (exp (* -1/2 (* k (log (* 2 (* n (PI))))))))>
#<alt (* (sqrt (/ 1 k)) (exp (* -1/2 (* k (+ (log n) (log (* 2 (PI))))))))>
#<alt (* (sqrt (/ 1 k)) (exp (* -1/2 (* k (+ (log n) (log (* 2 (PI))))))))>
#<alt (* (sqrt (/ 1 k)) (exp (* -1/2 (* k (+ (log n) (log (* 2 (PI))))))))>
#<alt (* (sqrt (/ 1 k)) (exp (* -1/2 (* k (+ (log n) (log (* 2 (PI))))))))>
#<alt (* (sqrt (/ 1 k)) (exp (* -1/2 (* k (+ (log (* 2 (PI))) (* -1 (log (/ 1 n))))))))>
#<alt (* (sqrt (/ 1 k)) (exp (* -1/2 (* k (+ (log (* 2 (PI))) (* -1 (log (/ 1 n))))))))>
#<alt (* (sqrt (/ 1 k)) (exp (* -1/2 (* k (+ (log (* 2 (PI))) (* -1 (log (/ 1 n))))))))>
#<alt (* (sqrt (/ 1 k)) (exp (* -1/2 (* k (+ (log (* 2 (PI))) (* -1 (log (/ 1 n))))))))>
#<alt (* (sqrt (/ 1 k)) (exp (* -1/2 (* k (+ (log (* -2 (PI))) (* -1 (log (/ -1 n))))))))>
#<alt (* (sqrt (/ 1 k)) (exp (* -1/2 (* k (+ (log (* -2 (PI))) (* -1 (log (/ -1 n))))))))>
#<alt (* (sqrt (/ 1 k)) (exp (* -1/2 (* k (+ (log (* -2 (PI))) (* -1 (log (/ -1 n))))))))>
#<alt (* (sqrt (/ 1 k)) (exp (* -1/2 (* k (+ (log (* -2 (PI))) (* -1 (log (/ -1 n))))))))>
#<alt (sqrt (/ 1 k))>
#<alt (sqrt (/ 1 k))>
#<alt (sqrt (/ 1 k))>
#<alt (sqrt (/ 1 k))>
#<alt (sqrt (/ 1 k))>
#<alt (sqrt (/ 1 k))>
#<alt (sqrt (/ 1 k))>
#<alt (sqrt (/ 1 k))>
#<alt (sqrt (/ 1 k))>
#<alt (sqrt (/ 1 k))>
#<alt (sqrt (/ 1 k))>
#<alt (sqrt (/ 1 k))>
#<alt (sqrt k)>
#<alt (sqrt k)>
#<alt (sqrt k)>
#<alt (sqrt k)>
#<alt (sqrt k)>
#<alt (sqrt k)>
#<alt (sqrt k)>
#<alt (sqrt k)>
#<alt (* -1 (* (sqrt k) (pow (sqrt -1) 2)))>
#<alt (* -1 (* (sqrt k) (pow (sqrt -1) 2)))>
#<alt (* -1 (* (sqrt k) (pow (sqrt -1) 2)))>
#<alt (* -1 (* (sqrt k) (pow (sqrt -1) 2)))>
#<alt (exp (* -1/2 (* k (+ (log n) (log (* 2 (PI)))))))>
#<alt (exp (* -1/2 (* k (+ (log n) (log (* 2 (PI)))))))>
#<alt (exp (* -1/2 (* k (+ (log n) (log (* 2 (PI)))))))>
#<alt (exp (* -1/2 (* k (+ (log n) (log (* 2 (PI)))))))>
#<alt (exp (* -1/2 (* k (+ (log (* 2 (PI))) (* -1 (log (/ 1 n)))))))>
#<alt (exp (* -1/2 (* k (+ (log (* 2 (PI))) (* -1 (log (/ 1 n)))))))>
#<alt (exp (* -1/2 (* k (+ (log (* 2 (PI))) (* -1 (log (/ 1 n)))))))>
#<alt (exp (* -1/2 (* k (+ (log (* 2 (PI))) (* -1 (log (/ 1 n)))))))>
#<alt (exp (* -1/2 (* k (+ (log (* -2 (PI))) (* -1 (log (/ -1 n)))))))>
#<alt (exp (* -1/2 (* k (+ (log (* -2 (PI))) (* -1 (log (/ -1 n)))))))>
#<alt (exp (* -1/2 (* k (+ (log (* -2 (PI))) (* -1 (log (/ -1 n)))))))>
#<alt (exp (* -1/2 (* k (+ (log (* -2 (PI))) (* -1 (log (/ -1 n)))))))>
#<alt 1>
#<alt (+ 1 (* -1/2 (* k (log (* 2 (* n (PI)))))))>
#<alt (+ 1 (* k (+ (* -1/2 (log (* 2 (* n (PI))))) (* 1/8 (* k (pow (log (* 2 (* n (PI)))) 2))))))>
#<alt (+ 1 (* k (+ (* -1/2 (log (* 2 (* n (PI))))) (* k (+ (* -1/48 (* k (pow (log (* 2 (* n (PI)))) 3))) (* 1/8 (pow (log (* 2 (* n (PI)))) 2)))))))>
#<alt (exp (* -1/2 (* k (log (* 2 (* n (PI)))))))>
#<alt (exp (* -1/2 (* k (log (* 2 (* n (PI)))))))>
#<alt (exp (* -1/2 (* k (log (* 2 (* n (PI)))))))>
#<alt (exp (* -1/2 (* k (log (* 2 (* n (PI)))))))>
#<alt (exp (* -1/2 (* k (log (* 2 (* n (PI)))))))>
#<alt (exp (* -1/2 (* k (log (* 2 (* n (PI)))))))>
#<alt (exp (* -1/2 (* k (log (* 2 (* n (PI)))))))>
#<alt (exp (* -1/2 (* k (log (* 2 (* n (PI)))))))>
#<alt (* (pow 4 1/4) (sqrt (/ (* n (PI)) k)))>
#<alt (/ (+ (* -1/4 (* (pow 4 1/4) (* (sqrt (* (pow k 3) (* n (PI)))) (log (* 4 (* (pow n 2) (pow (PI) 2))))))) (* (pow 4 1/4) (sqrt (* k (* n (PI)))))) k)>
#<alt (/ (+ (* k (+ (* -1/4 (* (pow 4 1/4) (* (sqrt (* k (* n (PI)))) (log (* 4 (* (pow n 2) (pow (PI) 2))))))) (* 1/32 (* (pow 4 1/4) (* (sqrt (* (pow k 3) (* n (PI)))) (pow (log (* 4 (* (pow n 2) (pow (PI) 2)))) 2)))))) (* (pow 4 1/4) (sqrt (* k (* n (PI)))))) k)>
#<alt (/ (+ (* k (+ (* -1/4 (* (pow 4 1/4) (* (sqrt (* k (* n (PI)))) (log (* 4 (* (pow n 2) (pow (PI) 2))))))) (* k (+ (* -1/384 (* (pow 4 1/4) (* (sqrt (* (pow k 3) (* n (PI)))) (pow (log (* 4 (* (pow n 2) (pow (PI) 2)))) 3)))) (* 1/32 (* (pow 4 1/4) (* (sqrt (* k (* n (PI)))) (pow (log (* 4 (* (pow n 2) (pow (PI) 2)))) 2)))))))) (* (pow 4 1/4) (sqrt (* k (* n (PI)))))) k)>
#<alt (* (sqrt (/ 1 k)) (exp (* (log (* 4 (* (pow n 2) (pow (PI) 2)))) (- 1/4 (* 1/4 k)))))>
#<alt (* (sqrt (/ 1 k)) (exp (* (log (* 4 (* (pow n 2) (pow (PI) 2)))) (- 1/4 (* 1/4 k)))))>
#<alt (* (sqrt (/ 1 k)) (exp (* (log (* 4 (* (pow n 2) (pow (PI) 2)))) (- 1/4 (* 1/4 k)))))>
#<alt (* (sqrt (/ 1 k)) (exp (* (log (* 4 (* (pow n 2) (pow (PI) 2)))) (- 1/4 (* 1/4 k)))))>
#<alt (* (sqrt (/ 1 k)) (exp (* (log (* 4 (* (pow n 2) (pow (PI) 2)))) (+ 1/4 (* -1/4 k)))))>
#<alt (* (sqrt (/ 1 k)) (exp (* (log (* 4 (* (pow n 2) (pow (PI) 2)))) (+ 1/4 (* -1/4 k)))))>
#<alt (* (sqrt (/ 1 k)) (exp (* (log (* 4 (* (pow n 2) (pow (PI) 2)))) (+ 1/4 (* -1/4 k)))))>
#<alt (* (sqrt (/ 1 k)) (exp (* (log (* 4 (* (pow n 2) (pow (PI) 2)))) (+ 1/4 (* -1/4 k)))))>
#<alt (* (sqrt (/ 1 k)) (exp (* (+ (log (* 4 (pow (PI) 2))) (* 2 (log n))) (- 1/4 (* 1/4 k)))))>
#<alt (* (sqrt (/ 1 k)) (exp (* (+ (log (* 4 (pow (PI) 2))) (* 2 (log n))) (- 1/4 (* 1/4 k)))))>
#<alt (* (sqrt (/ 1 k)) (exp (* (+ (log (* 4 (pow (PI) 2))) (* 2 (log n))) (- 1/4 (* 1/4 k)))))>
#<alt (* (sqrt (/ 1 k)) (exp (* (+ (log (* 4 (pow (PI) 2))) (* 2 (log n))) (- 1/4 (* 1/4 k)))))>
#<alt (* (sqrt (/ 1 k)) (exp (* (+ (log (* 4 (pow (PI) 2))) (* -2 (log (/ 1 n)))) (- 1/4 (* 1/4 k)))))>
#<alt (* (sqrt (/ 1 k)) (exp (* (+ (log (* 4 (pow (PI) 2))) (* -2 (log (/ 1 n)))) (- 1/4 (* 1/4 k)))))>
#<alt (* (sqrt (/ 1 k)) (exp (* (+ (log (* 4 (pow (PI) 2))) (* -2 (log (/ 1 n)))) (- 1/4 (* 1/4 k)))))>
#<alt (* (sqrt (/ 1 k)) (exp (* (+ (log (* 4 (pow (PI) 2))) (* -2 (log (/ 1 n)))) (- 1/4 (* 1/4 k)))))>
#<alt (* (sqrt (/ 1 k)) (exp (* (+ (log (* 4 (pow (PI) 2))) (* -2 (log (/ -1 n)))) (- 1/4 (* 1/4 k)))))>
#<alt (* (sqrt (/ 1 k)) (exp (* (+ (log (* 4 (pow (PI) 2))) (* -2 (log (/ -1 n)))) (- 1/4 (* 1/4 k)))))>
#<alt (* (sqrt (/ 1 k)) (exp (* (+ (log (* 4 (pow (PI) 2))) (* -2 (log (/ -1 n)))) (- 1/4 (* 1/4 k)))))>
#<alt (* (sqrt (/ 1 k)) (exp (* (+ (log (* 4 (pow (PI) 2))) (* -2 (log (/ -1 n)))) (- 1/4 (* 1/4 k)))))>
#<alt 1/4>
#<alt (+ 1/4 (* -1/4 k))>
#<alt (+ 1/4 (* -1/4 k))>
#<alt (+ 1/4 (* -1/4 k))>
#<alt (* -1/4 k)>
#<alt (* k (- (* 1/4 (/ 1 k)) 1/4))>
#<alt (* k (- (* 1/4 (/ 1 k)) 1/4))>
#<alt (* k (- (* 1/4 (/ 1 k)) 1/4))>
#<alt (* -1/4 k)>
#<alt (* -1 (* k (- 1/4 (* 1/4 (/ 1 k)))))>
#<alt (* -1 (* k (- 1/4 (* 1/4 (/ 1 k)))))>
#<alt (* -1 (* k (- 1/4 (* 1/4 (/ 1 k)))))>
#<alt (* (sqrt (/ (* n (PI)) k)) (sqrt 2))>
#<alt (/ (+ (* -1/2 (* (sqrt (* (pow k 3) (* n (PI)))) (* (log (* 2 (* n (PI)))) (sqrt 2)))) (* (sqrt (* k (* n (PI)))) (sqrt 2))) k)>
#<alt (/ (+ (* k (+ (* -1 (* (sqrt (* (pow k 3) (* n (PI)))) (+ (* -1/4 (* (pow (log (* 2 (* n (PI)))) 2) (sqrt 2))) (* 1/8 (* (pow (log (* 2 (* n (PI)))) 2) (sqrt 2)))))) (* -1/2 (* (sqrt (* k (* n (PI)))) (* (log (* 2 (* n (PI)))) (sqrt 2)))))) (* (sqrt (* k (* n (PI)))) (sqrt 2))) k)>
#<alt (/ (+ (* k (+ (* -1/2 (* (sqrt (* k (* n (PI)))) (* (log (* 2 (* n (PI)))) (sqrt 2)))) (* k (+ (* -1 (* (sqrt (* k (* n (PI)))) (+ (* -1/4 (* (pow (log (* 2 (* n (PI)))) 2) (sqrt 2))) (* 1/8 (* (pow (log (* 2 (* n (PI)))) 2) (sqrt 2)))))) (* -1 (* (sqrt (* (pow k 3) (* n (PI)))) (+ (* -1/2 (* (log (* 2 (* n (PI)))) (+ (* -1/4 (* (pow (log (* 2 (* n (PI)))) 2) (sqrt 2))) (* 1/8 (* (pow (log (* 2 (* n (PI)))) 2) (sqrt 2)))))) (+ (* -1/16 (* (pow (log (* 2 (* n (PI)))) 3) (sqrt 2))) (* 1/48 (* (pow (log (* 2 (* n (PI)))) 3) (sqrt 2))))))))))) (* (sqrt (* k (* n (PI)))) (sqrt 2))) k)>
#<alt (* (sqrt (/ (* n (PI)) k)) (/ (sqrt 2) (exp (* 1/2 (* k (log (* 2 (* n (PI)))))))))>
#<alt (* (sqrt (/ (* n (PI)) k)) (/ (sqrt 2) (exp (* 1/2 (* k (log (* 2 (* n (PI)))))))))>
#<alt (* (sqrt (/ (* n (PI)) k)) (/ (sqrt 2) (exp (* 1/2 (* k (log (* 2 (* n (PI)))))))))>
#<alt (* (sqrt (/ (* n (PI)) k)) (/ (sqrt 2) (exp (* 1/2 (* k (log (* 2 (* n (PI)))))))))>
#<alt (* (sqrt (/ (* n (PI)) k)) (/ (sqrt 2) (exp (* 1/2 (* k (log (* 2 (* n (PI)))))))))>
#<alt (* (sqrt (/ (* n (PI)) k)) (/ (sqrt 2) (exp (* 1/2 (* k (log (* 2 (* n (PI)))))))))>
#<alt (* (sqrt (/ (* n (PI)) k)) (/ (sqrt 2) (exp (* 1/2 (* k (log (* 2 (* n (PI)))))))))>
#<alt (* (sqrt (/ (* n (PI)) k)) (/ (sqrt 2) (exp (* 1/2 (* k (log (* 2 (* n (PI)))))))))>
#<alt (* (sqrt (/ (* n (PI)) k)) (/ (sqrt 2) (exp (* 1/2 (* k (+ (log n) (log (* 2 (PI)))))))))>
#<alt (* (sqrt (/ (* n (PI)) k)) (/ (sqrt 2) (exp (* 1/2 (* k (+ (log n) (log (* 2 (PI)))))))))>
#<alt (* (sqrt (/ (* n (PI)) k)) (/ (sqrt 2) (exp (* 1/2 (* k (+ (log n) (log (* 2 (PI)))))))))>
#<alt (* (sqrt (/ (* n (PI)) k)) (/ (sqrt 2) (exp (* 1/2 (* k (+ (log n) (log (* 2 (PI)))))))))>
#<alt (* (sqrt (/ (* n (PI)) k)) (/ (sqrt 2) (exp (* 1/2 (* k (+ (log (* 2 (PI))) (* -1 (log (/ 1 n)))))))))>
#<alt (* (sqrt (/ (* n (PI)) k)) (/ (sqrt 2) (exp (* 1/2 (* k (+ (log (* 2 (PI))) (* -1 (log (/ 1 n)))))))))>
#<alt (* (sqrt (/ (* n (PI)) k)) (/ (sqrt 2) (exp (* 1/2 (* k (+ (log (* 2 (PI))) (* -1 (log (/ 1 n)))))))))>
#<alt (* (sqrt (/ (* n (PI)) k)) (/ (sqrt 2) (exp (* 1/2 (* k (+ (log (* 2 (PI))) (* -1 (log (/ 1 n)))))))))>
#<alt (* -1 (* (sqrt (/ (* n (PI)) k)) (/ (* (sqrt -2) (sqrt -1)) (exp (* 1/2 (* k (+ (log (* -2 (PI))) (* -1 (log (/ -1 n))))))))))>
#<alt (* -1 (* (sqrt (/ (* n (PI)) k)) (/ (* (sqrt -2) (sqrt -1)) (exp (* 1/2 (* k (+ (log (* -2 (PI))) (* -1 (log (/ -1 n))))))))))>
#<alt (* -1 (* (sqrt (/ (* n (PI)) k)) (/ (* (sqrt -2) (sqrt -1)) (exp (* 1/2 (* k (+ (log (* -2 (PI))) (* -1 (log (/ -1 n))))))))))>
#<alt (* -1 (* (sqrt (/ (* n (PI)) k)) (/ (* (sqrt -2) (sqrt -1)) (exp (* 1/2 (* k (+ (log (* -2 (PI))) (* -1 (log (/ -1 n))))))))))>
#<alt (* (sqrt (/ (* n (PI)) k)) (sqrt 2))>
#<alt (* (sqrt (/ (* n (PI)) k)) (sqrt 2))>
#<alt (* (sqrt (/ (* n (PI)) k)) (sqrt 2))>
#<alt (* (sqrt (/ (* n (PI)) k)) (sqrt 2))>
#<alt (* (sqrt (/ (* n (PI)) k)) (sqrt 2))>
#<alt (* (sqrt (/ (* n (PI)) k)) (sqrt 2))>
#<alt (* (sqrt (/ (* n (PI)) k)) (sqrt 2))>
#<alt (* (sqrt (/ (* n (PI)) k)) (sqrt 2))>
#<alt (* (sqrt (/ (* n (PI)) k)) (sqrt 2))>
#<alt (* (sqrt (/ (* n (PI)) k)) (sqrt 2))>
#<alt (* (sqrt (/ (* n (PI)) k)) (sqrt 2))>
#<alt (* (sqrt (/ (* n (PI)) k)) (sqrt 2))>
#<alt (* (sqrt (/ (* n (PI)) k)) (sqrt 2))>
#<alt (* (sqrt (/ (* n (PI)) k)) (sqrt 2))>
#<alt (* (sqrt (/ (* n (PI)) k)) (sqrt 2))>
#<alt (* (sqrt (/ (* n (PI)) k)) (sqrt 2))>
#<alt (* (sqrt (/ (* n (PI)) k)) (sqrt 2))>
#<alt (* (sqrt (/ (* n (PI)) k)) (sqrt 2))>
#<alt (* (sqrt (/ (* n (PI)) k)) (sqrt 2))>
#<alt (* (sqrt (/ (* n (PI)) k)) (sqrt 2))>
#<alt (* -1 (* (sqrt (/ (* n (PI)) k)) (* (sqrt -2) (sqrt -1))))>
#<alt (* -1 (* (sqrt (/ (* n (PI)) k)) (* (sqrt -2) (sqrt -1))))>
#<alt (* -1 (* (sqrt (/ (* n (PI)) k)) (* (sqrt -2) (sqrt -1))))>
#<alt (* -1 (* (sqrt (/ (* n (PI)) k)) (* (sqrt -2) (sqrt -1))))>
#<alt (* 2 (* n (PI)))>
#<alt (* 2 (* n (PI)))>
#<alt (* 2 (* n (PI)))>
#<alt (* 2 (* n (PI)))>
#<alt (* 2 (* n (PI)))>
#<alt (* 2 (* n (PI)))>
#<alt (* 2 (* n (PI)))>
#<alt (* 2 (* n (PI)))>
#<alt (* 2 (* n (PI)))>
#<alt (* 2 (* n (PI)))>
#<alt (* 2 (* n (PI)))>
#<alt (* 2 (* n (PI)))>
#<alt (exp (* (+ (log (* 4 (pow (PI) 2))) (* 2 (log n))) (- 1/4 (* 1/4 k))))>
#<alt (exp (* (+ (log (* 4 (pow (PI) 2))) (* 2 (log n))) (- 1/4 (* 1/4 k))))>
#<alt (exp (* (+ (log (* 4 (pow (PI) 2))) (* 2 (log n))) (- 1/4 (* 1/4 k))))>
#<alt (exp (* (+ (log (* 4 (pow (PI) 2))) (* 2 (log n))) (- 1/4 (* 1/4 k))))>
#<alt (exp (* (+ (log (* 4 (pow (PI) 2))) (* -2 (log (/ 1 n)))) (- 1/4 (* 1/4 k))))>
#<alt (exp (* (+ (log (* 4 (pow (PI) 2))) (* -2 (log (/ 1 n)))) (- 1/4 (* 1/4 k))))>
#<alt (exp (* (+ (log (* 4 (pow (PI) 2))) (* -2 (log (/ 1 n)))) (- 1/4 (* 1/4 k))))>
#<alt (exp (* (+ (log (* 4 (pow (PI) 2))) (* -2 (log (/ 1 n)))) (- 1/4 (* 1/4 k))))>
#<alt (exp (* (+ (log (* 4 (pow (PI) 2))) (* -2 (log (/ -1 n)))) (- 1/4 (* 1/4 k))))>
#<alt (exp (* (+ (log (* 4 (pow (PI) 2))) (* -2 (log (/ -1 n)))) (- 1/4 (* 1/4 k))))>
#<alt (exp (* (+ (log (* 4 (pow (PI) 2))) (* -2 (log (/ -1 n)))) (- 1/4 (* 1/4 k))))>
#<alt (exp (* (+ (log (* 4 (pow (PI) 2))) (* -2 (log (/ -1 n)))) (- 1/4 (* 1/4 k))))>
#<alt (* (pow 4 1/4) (sqrt (* n (PI))))>
#<alt (+ (* -1/4 (* (pow 4 1/4) (* (* k (log (* 4 (* (pow n 2) (pow (PI) 2))))) (sqrt (* n (PI)))))) (* (pow 4 1/4) (sqrt (* n (PI)))))>
#<alt (+ (* k (+ (* -1/4 (* (pow 4 1/4) (* (sqrt (* n (PI))) (log (* 4 (* (pow n 2) (pow (PI) 2))))))) (* 1/32 (* (pow 4 1/4) (* (* k (pow (log (* 4 (* (pow n 2) (pow (PI) 2)))) 2)) (sqrt (* n (PI)))))))) (* (pow 4 1/4) (sqrt (* n (PI)))))>
#<alt (+ (* k (+ (* -1/4 (* (pow 4 1/4) (* (sqrt (* n (PI))) (log (* 4 (* (pow n 2) (pow (PI) 2))))))) (* k (+ (* -1/384 (* (pow 4 1/4) (* (* k (pow (log (* 4 (* (pow n 2) (pow (PI) 2)))) 3)) (sqrt (* n (PI)))))) (* 1/32 (* (pow 4 1/4) (* (sqrt (* n (PI))) (pow (log (* 4 (* (pow n 2) (pow (PI) 2)))) 2)))))))) (* (pow 4 1/4) (sqrt (* n (PI)))))>
#<alt (exp (* (log (* 4 (* (pow n 2) (pow (PI) 2)))) (- 1/4 (* 1/4 k))))>
#<alt (exp (* (log (* 4 (* (pow n 2) (pow (PI) 2)))) (- 1/4 (* 1/4 k))))>
#<alt (exp (* (log (* 4 (* (pow n 2) (pow (PI) 2)))) (- 1/4 (* 1/4 k))))>
#<alt (exp (* (log (* 4 (* (pow n 2) (pow (PI) 2)))) (- 1/4 (* 1/4 k))))>
#<alt (exp (* (log (* 4 (* (pow n 2) (pow (PI) 2)))) (+ 1/4 (* -1/4 k))))>
#<alt (exp (* (log (* 4 (* (pow n 2) (pow (PI) 2)))) (+ 1/4 (* -1/4 k))))>
#<alt (exp (* (log (* 4 (* (pow n 2) (pow (PI) 2)))) (+ 1/4 (* -1/4 k))))>
#<alt (exp (* (log (* 4 (* (pow n 2) (pow (PI) 2)))) (+ 1/4 (* -1/4 k))))>
#<alt (* (pow n 2) (pow (PI) 2))>
#<alt (* (pow n 2) (pow (PI) 2))>
#<alt (* (pow n 2) (pow (PI) 2))>
#<alt (* (pow n 2) (pow (PI) 2))>
#<alt (* (pow n 2) (pow (PI) 2))>
#<alt (* (pow n 2) (pow (PI) 2))>
#<alt (* (pow n 2) (pow (PI) 2))>
#<alt (* (pow n 2) (pow (PI) 2))>
#<alt (* (pow n 2) (pow (PI) 2))>
#<alt (* (pow n 2) (pow (PI) 2))>
#<alt (* (pow n 2) (pow (PI) 2))>
#<alt (* (pow n 2) (pow (PI) 2))>

Calls

87 calls:

Time	Variable		Point	Expression
20.0ms	n	@	0	(pow (* 4 (* (* (PI) n) (* (PI) n))) (- 1/4 (* k 1/4)))
18.0ms	n	@	0	(* (/ 1 (sqrt k)) (pow (* 4 (* (* (PI) n) (* (PI) n))) (- 1/4 (* k 1/4))))
12.0ms	n	@	inf	(* (/ 1 (sqrt k)) (pow (* 4 (* (* (PI) n) (* (PI) n))) (- 1/4 (* k 1/4))))
4.0ms	k	@	inf	(/ (sqrt (* 2 (* (PI) n))) (* (sqrt k) (pow (* 2 (* (PI) n)) (* k 1/2))))
2.0ms	n	@	0	(/ (sqrt (* 2 (* (PI) n))) (* (sqrt k) (pow (* 2 (* (PI) n)) (* k 1/2))))

rewrite404.0ms (3.4%)

Memory

-35.3MiB live, 669.0MiB allocated

Algorithm

1×	batch-egg-rewrite

Rules

6 020×	`-lowering-.f32`
6 020×	`-lowering-.f64`
2 112×	`pow-lowering-pow.f64`
2 112×	`pow-lowering-pow.f32`
2 110×	`accelerator-lowering-fma.f32`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	36	159
1	186	141
2	1201	138
0	8497	133

Stop Event

1×	iter limit
1×	node limit

Counts

20 → 1 154

Calls

Call 1

Inputs
(/ (sqrt (* 2 (* (PI) n))) (* (sqrt k) (pow (* 2 (* (PI) n)) (* k 1/2))))
(sqrt (* 2 (* (PI) n)))
(* 2 (* (PI) n))
(* (PI) n)
(* (sqrt (/ (* n (PI)) k)) (sqrt 2))
(sqrt (/ (* n (PI)) k))
(/ (* n (PI)) k)
(* n (PI))
(* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (* -1/2 k)))
(/ 1 (sqrt k))
(sqrt k)
(pow (* (* 2 (PI)) n) (* -1/2 k))
(* (/ 1 (sqrt k)) (pow (* 4 (* (* (PI) n) (* (PI) n))) (- 1/4 (* k 1/4))))
(- 1/4 (* k 1/4))
(/ (* (/ 1 (sqrt k)) (sqrt (* 2 (* (PI) n)))) (pow (* 2 (* (PI) n)) (* k 1/2)))
(* (/ 1 (sqrt k)) (sqrt (* 2 (* (PI) n))))
(PI)
(* (* 2 (PI)) n)
(pow (* 4 (* (* (PI) n) (* (PI) n))) (- 1/4 (* k 1/4)))
(* (* (PI) n) (* (PI) n))

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

simplify533.0ms (4.5%)

Memory

18.2MiB live, 852.3MiB allocated

Algorithm

1×	egg-herbie

Rules

12 638×	`accelerator-lowering-fma.f32`
12 638×	`accelerator-lowering-fma.f64`
6 086×	`-lowering-.f32`
6 086×	`-lowering-.f64`
2 394×	`--lowering--.f32`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	271	4532
1	766	4466
2	2492	4244
3	4396	4190
0	8768	4109

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)))
(* 2 (* n (PI)))
(* 2 (* n (PI)))
(* 2 (* n (PI)))
(* 2 (* n (PI)))
(* 2 (* n (PI)))
(* 2 (* n (PI)))
(* n (PI))
(* n (PI))
(* n (PI))
(* n (PI))
(* n (PI))
(* n (PI))
(* n (PI))
(* n (PI))
(* n (PI))
(* n (PI))
(* n (PI))
(* n (PI))
(* (sqrt (/ (* n (PI)) k)) (sqrt 2))
(* (sqrt (/ (* n (PI)) k)) (sqrt 2))
(* (sqrt (/ (* n (PI)) k)) (sqrt 2))
(* (sqrt (/ (* n (PI)) k)) (sqrt 2))
(* (sqrt (/ (* n (PI)) k)) (sqrt 2))
(* (sqrt (/ (* n (PI)) k)) (sqrt 2))
(* (sqrt (/ (* n (PI)) k)) (sqrt 2))
(* (sqrt (/ (* n (PI)) k)) (sqrt 2))
(* -1 (* (sqrt (/ (* n (PI)) k)) (* (pow (sqrt -1) 2) (sqrt 2))))
(* -1 (* (sqrt (/ (* n (PI)) k)) (* (pow (sqrt -1) 2) (sqrt 2))))
(* -1 (* (sqrt (/ (* n (PI)) k)) (* (pow (sqrt -1) 2) (sqrt 2))))
(* -1 (* (sqrt (/ (* n (PI)) k)) (* (pow (sqrt -1) 2) (sqrt 2))))
(* (sqrt (/ (* n (PI)) k)) (sqrt 2))
(* (sqrt (/ (* n (PI)) k)) (sqrt 2))
(* (sqrt (/ (* n (PI)) k)) (sqrt 2))
(* (sqrt (/ (* n (PI)) k)) (sqrt 2))
(* (sqrt (/ (* n (PI)) k)) (sqrt 2))
(* (sqrt (/ (* n (PI)) k)) (sqrt 2))
(* (sqrt (/ (* n (PI)) k)) (sqrt 2))
(* (sqrt (/ (* n (PI)) k)) (sqrt 2))
(* (sqrt (/ (* n (PI)) k)) (* (pow (sqrt -1) 2) (sqrt 2)))
(* (sqrt (/ (* n (PI)) k)) (* (pow (sqrt -1) 2) (sqrt 2)))
(* (sqrt (/ (* n (PI)) k)) (* (pow (sqrt -1) 2) (sqrt 2)))
(* (sqrt (/ (* n (PI)) k)) (* (pow (sqrt -1) 2) (sqrt 2)))
(sqrt (/ (* n (PI)) k))
(sqrt (/ (* n (PI)) k))
(sqrt (/ (* n (PI)) k))
(sqrt (/ (* n (PI)) k))
(sqrt (/ (* n (PI)) k))
(sqrt (/ (* n (PI)) k))
(sqrt (/ (* n (PI)) k))
(sqrt (/ (* n (PI)) k))
(* -1 (* (sqrt (/ (* n (PI)) k)) (pow (sqrt -1) 2)))
(* -1 (* (sqrt (/ (* n (PI)) k)) (pow (sqrt -1) 2)))
(* -1 (* (sqrt (/ (* n (PI)) k)) (pow (sqrt -1) 2)))
(* -1 (* (sqrt (/ (* n (PI)) k)) (pow (sqrt -1) 2)))
(sqrt (/ (* n (PI)) k))
(sqrt (/ (* n (PI)) k))
(sqrt (/ (* n (PI)) k))
(sqrt (/ (* n (PI)) k))
(sqrt (/ (* n (PI)) k))
(sqrt (/ (* n (PI)) k))
(sqrt (/ (* n (PI)) k))
(sqrt (/ (* n (PI)) k))
(* (sqrt (/ (* n (PI)) k)) (pow (sqrt -1) 2))
(* (sqrt (/ (* n (PI)) k)) (pow (sqrt -1) 2))
(* (sqrt (/ (* n (PI)) k)) (pow (sqrt -1) 2))
(* (sqrt (/ (* n (PI)) k)) (pow (sqrt -1) 2))
(/ (* n (PI)) k)
(/ (* n (PI)) k)
(/ (* n (PI)) k)
(/ (* n (PI)) k)
(/ (* n (PI)) k)
(/ (* n (PI)) k)
(/ (* n (PI)) k)
(/ (* n (PI)) k)
(/ (* n (PI)) k)
(/ (* n (PI)) k)
(/ (* n (PI)) k)
(/ (* n (PI)) k)
(/ (* n (PI)) k)
(/ (* n (PI)) k)
(/ (* n (PI)) k)
(/ (* n (PI)) k)
(/ (* n (PI)) k)
(/ (* n (PI)) k)
(/ (* n (PI)) k)
(/ (* n (PI)) k)
(/ (* n (PI)) k)
(/ (* n (PI)) k)
(/ (* n (PI)) k)
(/ (* n (PI)) k)
(* n (PI))
(* n (PI))
(* n (PI))
(* n (PI))
(* n (PI))
(* n (PI))
(* n (PI))
(* n (PI))
(* n (PI))
(* n (PI))
(* n (PI))
(* n (PI))
(sqrt (/ 1 k))
(/ (+ (sqrt k) (* -1/2 (* (sqrt (pow k 3)) (log (* 2 (* n (PI))))))) k)
(/ (+ (sqrt k) (* k (+ (* -1/2 (* (sqrt k) (log (* 2 (* n (PI)))))) (* 1/8 (* (sqrt (pow k 3)) (pow (log (* 2 (* n (PI)))) 2)))))) k)
(/ (+ (sqrt k) (* k (+ (* -1/2 (* (sqrt k) (log (* 2 (* n (PI)))))) (* k (+ (* -1/48 (* (sqrt (pow k 3)) (pow (log (* 2 (* n (PI)))) 3))) (* 1/8 (* (sqrt k) (pow (log (* 2 (* n (PI)))) 2)))))))) k)
(* (sqrt (/ 1 k)) (exp (* -1/2 (* k (log (* 2 (* n (PI))))))))
(* (sqrt (/ 1 k)) (exp (* -1/2 (* k (log (* 2 (* n (PI))))))))
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(sqrt (/ 1 k))
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(sqrt (/ 1 k))
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(sqrt (/ 1 k))
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(sqrt k)
(sqrt k)
(sqrt k)
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(sqrt k)
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(* -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 (* k (+ (log n) (log (* 2 (PI)))))))
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(exp (* -1/2 (* k (+ (log (* -2 (PI))) (* -1 (log (/ -1 n)))))))
(exp (* -1/2 (* k (+ (log (* -2 (PI))) (* -1 (log (/ -1 n)))))))
1
(+ 1 (* -1/2 (* k (log (* 2 (* n (PI)))))))
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(exp (* -1/2 (* k (log (* 2 (* n (PI)))))))
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(* (pow 4 1/4) (sqrt (/ (* n (PI)) k)))
(/ (+ (* -1/4 (* (pow 4 1/4) (* (sqrt (* (pow k 3) (* n (PI)))) (log (* 4 (* (pow n 2) (pow (PI) 2))))))) (* (pow 4 1/4) (sqrt (* k (* n (PI)))))) k)
(/ (+ (* k (+ (* -1/4 (* (pow 4 1/4) (* (sqrt (* k (* n (PI)))) (log (* 4 (* (pow n 2) (pow (PI) 2))))))) (* 1/32 (* (pow 4 1/4) (* (sqrt (* (pow k 3) (* n (PI)))) (pow (log (* 4 (* (pow n 2) (pow (PI) 2)))) 2)))))) (* (pow 4 1/4) (sqrt (* k (* n (PI)))))) k)
(/ (+ (* k (+ (* -1/4 (* (pow 4 1/4) (* (sqrt (* k (* n (PI)))) (log (* 4 (* (pow n 2) (pow (PI) 2))))))) (* k (+ (* -1/384 (* (pow 4 1/4) (* (sqrt (* (pow k 3) (* n (PI)))) (pow (log (* 4 (* (pow n 2) (pow (PI) 2)))) 3)))) (* 1/32 (* (pow 4 1/4) (* (sqrt (* k (* n (PI)))) (pow (log (* 4 (* (pow n 2) (pow (PI) 2)))) 2)))))))) (* (pow 4 1/4) (sqrt (* k (* n (PI)))))) k)
(* (sqrt (/ 1 k)) (exp (* (log (* 4 (* (pow n 2) (pow (PI) 2)))) (- 1/4 (* 1/4 k)))))
(* (sqrt (/ 1 k)) (exp (* (log (* 4 (* (pow n 2) (pow (PI) 2)))) (- 1/4 (* 1/4 k)))))
(* (sqrt (/ 1 k)) (exp (* (log (* 4 (* (pow n 2) (pow (PI) 2)))) (- 1/4 (* 1/4 k)))))
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(* (sqrt (/ 1 k)) (exp (* (+ (log (* 4 (pow (PI) 2))) (* 2 (log n))) (- 1/4 (* 1/4 k)))))
(* (sqrt (/ 1 k)) (exp (* (+ (log (* 4 (pow (PI) 2))) (* 2 (log n))) (- 1/4 (* 1/4 k)))))
(* (sqrt (/ 1 k)) (exp (* (+ (log (* 4 (pow (PI) 2))) (* -2 (log (/ 1 n)))) (- 1/4 (* 1/4 k)))))
(* (sqrt (/ 1 k)) (exp (* (+ (log (* 4 (pow (PI) 2))) (* -2 (log (/ 1 n)))) (- 1/4 (* 1/4 k)))))
(* (sqrt (/ 1 k)) (exp (* (+ (log (* 4 (pow (PI) 2))) (* -2 (log (/ 1 n)))) (- 1/4 (* 1/4 k)))))
(* (sqrt (/ 1 k)) (exp (* (+ (log (* 4 (pow (PI) 2))) (* -2 (log (/ 1 n)))) (- 1/4 (* 1/4 k)))))
(* (sqrt (/ 1 k)) (exp (* (+ (log (* 4 (pow (PI) 2))) (* -2 (log (/ -1 n)))) (- 1/4 (* 1/4 k)))))
(* (sqrt (/ 1 k)) (exp (* (+ (log (* 4 (pow (PI) 2))) (* -2 (log (/ -1 n)))) (- 1/4 (* 1/4 k)))))
(* (sqrt (/ 1 k)) (exp (* (+ (log (* 4 (pow (PI) 2))) (* -2 (log (/ -1 n)))) (- 1/4 (* 1/4 k)))))
(* (sqrt (/ 1 k)) (exp (* (+ (log (* 4 (pow (PI) 2))) (* -2 (log (/ -1 n)))) (- 1/4 (* 1/4 k)))))
1/4
(+ 1/4 (* -1/4 k))
(+ 1/4 (* -1/4 k))
(+ 1/4 (* -1/4 k))
(* -1/4 k)
(* k (- (* 1/4 (/ 1 k)) 1/4))
(* k (- (* 1/4 (/ 1 k)) 1/4))
(* k (- (* 1/4 (/ 1 k)) 1/4))
(* -1/4 k)
(* -1 (* k (- 1/4 (* 1/4 (/ 1 k)))))
(* -1 (* k (- 1/4 (* 1/4 (/ 1 k)))))
(* -1 (* k (- 1/4 (* 1/4 (/ 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 (* (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)
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(* (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))
(* (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))
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(* 2 (* n (PI)))
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(* 2 (* n (PI)))
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(* (pow 4 1/4) (sqrt (* n (PI))))
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(+ (* k (+ (* -1/4 (* (pow 4 1/4) (* (sqrt (* n (PI))) (log (* 4 (* (pow n 2) (pow (PI) 2))))))) (* k (+ (* -1/384 (* (pow 4 1/4) (* (* k (pow (log (* 4 (* (pow n 2) (pow (PI) 2)))) 3)) (sqrt (* n (PI)))))) (* 1/32 (* (pow 4 1/4) (* (sqrt (* n (PI))) (pow (log (* 4 (* (pow n 2) (pow (PI) 2)))) 2)))))))) (* (pow 4 1/4) (sqrt (* n (PI)))))
(exp (* (log (* 4 (* (pow n 2) (pow (PI) 2)))) (- 1/4 (* 1/4 k))))
(exp (* (log (* 4 (* (pow n 2) (pow (PI) 2)))) (- 1/4 (* 1/4 k))))
(exp (* (log (* 4 (* (pow n 2) (pow (PI) 2)))) (- 1/4 (* 1/4 k))))
(exp (* (log (* 4 (* (pow n 2) (pow (PI) 2)))) (- 1/4 (* 1/4 k))))
(exp (* (log (* 4 (* (pow n 2) (pow (PI) 2)))) (+ 1/4 (* -1/4 k))))
(exp (* (log (* 4 (* (pow n 2) (pow (PI) 2)))) (+ 1/4 (* -1/4 k))))
(exp (* (log (* 4 (* (pow n 2) (pow (PI) 2)))) (+ 1/4 (* -1/4 k))))
(exp (* (log (* 4 (* (pow n 2) (pow (PI) 2)))) (+ 1/4 (* -1/4 k))))
(* (pow n 2) (pow (PI) 2))
(* (pow n 2) (pow (PI) 2))
(* (pow n 2) (pow (PI) 2))
(* (pow n 2) (pow (PI) 2))
(* (pow n 2) (pow (PI) 2))
(* (pow n 2) (pow (PI) 2))
(* (pow n 2) (pow (PI) 2))
(* (pow n 2) (pow (PI) 2))
(* (pow n 2) (pow (PI) 2))
(* (pow n 2) (pow (PI) 2))
(* (pow n 2) (pow (PI) 2))
(* (pow n 2) (pow (PI) 2))

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))) (.f64 (pow.f64 n (.f64 k #s(literal 1/2 binary64))) (pow.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))) (.f64 (pow.f64 n (.f64 k #s(literal 1/2 binary64))) (pow.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))) (.f64 (pow.f64 n (.f64 k #s(literal 1/2 binary64))) (pow.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)))))))))
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(* (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))) (.f64 (pow.f64 n (.f64 k #s(literal 1/2 binary64))) (pow.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)))))))))
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(* (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))) (.f64 (pow.f64 n (.f64 k #s(literal 1/2 binary64))) (pow.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))) (.f64 (pow.f64 n (.f64 k #s(literal 1/2 binary64))) (pow.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))))))))))
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(* -1 (* (sqrt (/ (* n (PI)) k)) (/ (* (sqrt -2) (sqrt -1)) (exp (* 1/2 (* k (+ (log (* -2 (PI))) (* -1 (log (/ -1 n))))))))))
(/.f64 (.f64 (sqrt.f64 #s(literal -1 binary64)) (.f64 (sqrt.f64 (/.f64 (.f64 n (PI.f64)) k)) (-.f64 #s(literal 0 binary64) (sqrt.f64 #s(literal -2 binary64))))) (sqrt.f64 (.f64 (pow.f64 (/.f64 #s(literal -1 binary64) n) (-.f64 #s(literal 0 binary64) k)) (pow.f64 (*.f64 (PI.f64) #s(literal -2 binary64)) k))))
(* -1 (* (sqrt (/ (* n (PI)) k)) (/ (* (sqrt -2) (sqrt -1)) (exp (* 1/2 (* k (+ (log (* -2 (PI))) (* -1 (log (/ -1 n))))))))))
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(* -1 (* (sqrt (/ (* n (PI)) k)) (/ (* (sqrt -2) (sqrt -1)) (exp (* 1/2 (* k (+ (log (* -2 (PI))) (* -1 (log (/ -1 n))))))))))
(/.f64 (.f64 (sqrt.f64 #s(literal -1 binary64)) (.f64 (sqrt.f64 (/.f64 (.f64 n (PI.f64)) k)) (-.f64 #s(literal 0 binary64) (sqrt.f64 #s(literal -2 binary64))))) (sqrt.f64 (.f64 (pow.f64 (/.f64 #s(literal -1 binary64) n) (-.f64 #s(literal 0 binary64) k)) (pow.f64 (*.f64 (PI.f64) #s(literal -2 binary64)) k))))
(* (sqrt (/ (* n (PI)) k)) (sqrt 2))
(.f64 (sqrt.f64 (/.f64 (.f64 n (PI.f64)) k)) (sqrt.f64 #s(literal 2 binary64)))
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(exp (* (+ (log (* 4 (pow (PI) 2))) (* -2 (log (/ -1 n)))) (- 1/4 (* 1/4 k))))
(pow.f64 (.f64 (.f64 (PI.f64) (*.f64 (PI.f64) #s(literal 4 binary64))) (pow.f64 (/.f64 #s(literal -1 binary64) n) #s(literal -2 binary64))) (fma.f64 k #s(literal -1/4 binary64) #s(literal 1/4 binary64)))
(exp (* (+ (log (* 4 (pow (PI) 2))) (* -2 (log (/ -1 n)))) (- 1/4 (* 1/4 k))))
(pow.f64 (.f64 (.f64 (PI.f64) (*.f64 (PI.f64) #s(literal 4 binary64))) (pow.f64 (/.f64 #s(literal -1 binary64) n) #s(literal -2 binary64))) (fma.f64 k #s(literal -1/4 binary64) #s(literal 1/4 binary64)))
(exp (* (+ (log (* 4 (pow (PI) 2))) (* -2 (log (/ -1 n)))) (- 1/4 (* 1/4 k))))
(pow.f64 (.f64 (.f64 (PI.f64) (*.f64 (PI.f64) #s(literal 4 binary64))) (pow.f64 (/.f64 #s(literal -1 binary64) n) #s(literal -2 binary64))) (fma.f64 k #s(literal -1/4 binary64) #s(literal 1/4 binary64)))
(exp (* (+ (log (* 4 (pow (PI) 2))) (* -2 (log (/ -1 n)))) (- 1/4 (* 1/4 k))))
(pow.f64 (.f64 (.f64 (PI.f64) (*.f64 (PI.f64) #s(literal 4 binary64))) (pow.f64 (/.f64 #s(literal -1 binary64) n) #s(literal -2 binary64))) (fma.f64 k #s(literal -1/4 binary64) #s(literal 1/4 binary64)))
(* (pow 4 1/4) (sqrt (* n (PI))))
(.f64 (sqrt.f64 (.f64 n (PI.f64))) (pow.f64 #s(literal 4 binary64) #s(literal 1/4 binary64)))
(+ (* -1/4 (* (pow 4 1/4) (* (* k (log (* 4 (* (pow n 2) (pow (PI) 2))))) (sqrt (* n (PI)))))) (* (pow 4 1/4) (sqrt (* n (PI)))))
(.f64 (pow.f64 #s(literal 4 binary64) #s(literal 1/4 binary64)) (fma.f64 (.f64 (log.f64 (.f64 (.f64 n n) (.f64 (PI.f64) (.f64 (PI.f64) #s(literal 4 binary64))))) (.f64 k (sqrt.f64 (.f64 n (PI.f64))))) #s(literal -1/4 binary64) (sqrt.f64 (*.f64 n (PI.f64)))))
(+ (* k (+ (* -1/4 (* (pow 4 1/4) (* (sqrt (* n (PI))) (log (* 4 (* (pow n 2) (pow (PI) 2))))))) (* 1/32 (* (pow 4 1/4) (* (* k (pow (log (* 4 (* (pow n 2) (pow (PI) 2)))) 2)) (sqrt (* n (PI)))))))) (* (pow 4 1/4) (sqrt (* n (PI)))))
(fma.f64 k (.f64 (pow.f64 #s(literal 4 binary64) #s(literal 1/4 binary64)) (fma.f64 (.f64 (sqrt.f64 (.f64 n (PI.f64))) (log.f64 (.f64 (.f64 n n) (.f64 (PI.f64) (.f64 (PI.f64) #s(literal 4 binary64)))))) #s(literal -1/4 binary64) (.f64 (.f64 (pow.f64 (log.f64 (.f64 (.f64 n n) (.f64 (PI.f64) (.f64 (PI.f64) #s(literal 4 binary64))))) #s(literal 2 binary64)) (.f64 k (sqrt.f64 (.f64 n (PI.f64))))) #s(literal 1/32 binary64)))) (.f64 (sqrt.f64 (*.f64 n (PI.f64))) (pow.f64 #s(literal 4 binary64) #s(literal 1/4 binary64))))
(+ (* k (+ (* -1/4 (* (pow 4 1/4) (* (sqrt (* n (PI))) (log (* 4 (* (pow n 2) (pow (PI) 2))))))) (* k (+ (* -1/384 (* (pow 4 1/4) (* (* k (pow (log (* 4 (* (pow n 2) (pow (PI) 2)))) 3)) (sqrt (* n (PI)))))) (* 1/32 (* (pow 4 1/4) (* (sqrt (* n (PI))) (pow (log (* 4 (* (pow n 2) (pow (PI) 2)))) 2)))))))) (* (pow 4 1/4) (sqrt (* n (PI)))))
(fma.f64 k (.f64 k (.f64 (pow.f64 #s(literal 4 binary64) #s(literal 1/4 binary64)) (fma.f64 (.f64 (pow.f64 (log.f64 (.f64 (.f64 n n) (.f64 (PI.f64) (.f64 (PI.f64) #s(literal 4 binary64))))) #s(literal 3 binary64)) (.f64 k (sqrt.f64 (.f64 n (PI.f64))))) #s(literal -1/384 binary64) (.f64 (.f64 (sqrt.f64 (.f64 n (PI.f64))) (pow.f64 (log.f64 (.f64 (.f64 n n) (.f64 (PI.f64) (.f64 (PI.f64) #s(literal 4 binary64))))) #s(literal 2 binary64))) #s(literal 1/32 binary64))))) (.f64 (pow.f64 #s(literal 4 binary64) #s(literal 1/4 binary64)) (fma.f64 (.f64 (log.f64 (.f64 (.f64 n n) (.f64 (PI.f64) (.f64 (PI.f64) #s(literal 4 binary64))))) (.f64 k (sqrt.f64 (.f64 n (PI.f64))))) #s(literal -1/4 binary64) (sqrt.f64 (*.f64 n (PI.f64))))))
(exp (* (log (* 4 (* (pow n 2) (pow (PI) 2)))) (- 1/4 (* 1/4 k))))
(pow.f64 (.f64 (.f64 n n) (.f64 (PI.f64) (.f64 (PI.f64) #s(literal 4 binary64)))) (fma.f64 k #s(literal -1/4 binary64) #s(literal 1/4 binary64)))
(exp (* (log (* 4 (* (pow n 2) (pow (PI) 2)))) (- 1/4 (* 1/4 k))))
(pow.f64 (.f64 (.f64 n n) (.f64 (PI.f64) (.f64 (PI.f64) #s(literal 4 binary64)))) (fma.f64 k #s(literal -1/4 binary64) #s(literal 1/4 binary64)))
(exp (* (log (* 4 (* (pow n 2) (pow (PI) 2)))) (- 1/4 (* 1/4 k))))
(pow.f64 (.f64 (.f64 n n) (.f64 (PI.f64) (.f64 (PI.f64) #s(literal 4 binary64)))) (fma.f64 k #s(literal -1/4 binary64) #s(literal 1/4 binary64)))
(exp (* (log (* 4 (* (pow n 2) (pow (PI) 2)))) (- 1/4 (* 1/4 k))))
(pow.f64 (.f64 (.f64 n n) (.f64 (PI.f64) (.f64 (PI.f64) #s(literal 4 binary64)))) (fma.f64 k #s(literal -1/4 binary64) #s(literal 1/4 binary64)))
(exp (* (log (* 4 (* (pow n 2) (pow (PI) 2)))) (+ 1/4 (* -1/4 k))))
(pow.f64 (.f64 (.f64 n n) (.f64 (PI.f64) (.f64 (PI.f64) #s(literal 4 binary64)))) (fma.f64 k #s(literal -1/4 binary64) #s(literal 1/4 binary64)))
(exp (* (log (* 4 (* (pow n 2) (pow (PI) 2)))) (+ 1/4 (* -1/4 k))))
(pow.f64 (.f64 (.f64 n n) (.f64 (PI.f64) (.f64 (PI.f64) #s(literal 4 binary64)))) (fma.f64 k #s(literal -1/4 binary64) #s(literal 1/4 binary64)))
(exp (* (log (* 4 (* (pow n 2) (pow (PI) 2)))) (+ 1/4 (* -1/4 k))))
(pow.f64 (.f64 (.f64 n n) (.f64 (PI.f64) (.f64 (PI.f64) #s(literal 4 binary64)))) (fma.f64 k #s(literal -1/4 binary64) #s(literal 1/4 binary64)))
(exp (* (log (* 4 (* (pow n 2) (pow (PI) 2)))) (+ 1/4 (* -1/4 k))))
(pow.f64 (.f64 (.f64 n n) (.f64 (PI.f64) (.f64 (PI.f64) #s(literal 4 binary64)))) (fma.f64 k #s(literal -1/4 binary64) #s(literal 1/4 binary64)))
(* (pow n 2) (pow (PI) 2))
(.f64 n (.f64 n (*.f64 (PI.f64) (PI.f64))))
(* (pow n 2) (pow (PI) 2))
(.f64 n (.f64 n (*.f64 (PI.f64) (PI.f64))))
(* (pow n 2) (pow (PI) 2))
(.f64 n (.f64 n (*.f64 (PI.f64) (PI.f64))))
(* (pow n 2) (pow (PI) 2))
(.f64 n (.f64 n (*.f64 (PI.f64) (PI.f64))))
(* (pow n 2) (pow (PI) 2))
(.f64 n (.f64 n (*.f64 (PI.f64) (PI.f64))))
(* (pow n 2) (pow (PI) 2))
(.f64 n (.f64 n (*.f64 (PI.f64) (PI.f64))))
(* (pow n 2) (pow (PI) 2))
(.f64 n (.f64 n (*.f64 (PI.f64) (PI.f64))))
(* (pow n 2) (pow (PI) 2))
(.f64 n (.f64 n (*.f64 (PI.f64) (PI.f64))))
(* (pow n 2) (pow (PI) 2))
(.f64 n (.f64 n (*.f64 (PI.f64) (PI.f64))))
(* (pow n 2) (pow (PI) 2))
(.f64 n (.f64 n (*.f64 (PI.f64) (PI.f64))))
(* (pow n 2) (pow (PI) 2))
(.f64 n (.f64 n (*.f64 (PI.f64) (PI.f64))))
(* (pow n 2) (pow (PI) 2))
(.f64 n (.f64 n (*.f64 (PI.f64) (PI.f64))))

eval343.0ms (2.9%)

Memory: 61.4MiB live, 774.3MiB allocated
Compiler: Compiled 53 180 to 4 795 computations (91% saved)

prune539.0ms (4.6%)

Memory

-123.2MiB live, 781.4MiB allocated

Pruning

20 alts after pruning (20 fresh and 0 done)

	Pruned	Kept	Total
New	2 389	18	2 407
Fresh	9	2	11
Picked	5	0	5
Done	0	0	0
Total	2 403	20	2 423

Accuracy

100.0%

Counts

2 423 → 20

Alt Table

Click to see full alt table

Status	Accuracy	Program
	99.5%	(/.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))
	52.5%	(/.f64 (pow.f64 (.f64 (PI.f64) (.f64 n #s(literal 2 binary64))) (*.f64 k #s(literal -1/2 binary64))) (sqrt.f64 k))
▶	99.7%	(/.f64 (sqrt.f64 (.f64 (PI.f64) (.f64 n #s(literal 2 binary64)))) (sqrt.f64 (.f64 k (pow.f64 (.f64 (PI.f64) (*.f64 n #s(literal 2 binary64))) k))))
	50.5%	(/.f64 (sqrt.f64 (.f64 (PI.f64) (.f64 n #s(literal 2 binary64)))) (sqrt.f64 k))
▶	39.1%	(/.f64 (sqrt.f64 #s(literal 2 binary64)) (sqrt.f64 (/.f64 k (*.f64 (PI.f64) n))))
	99.5%	(/.f64 #s(literal 1 binary64) (.f64 (sqrt.f64 k) (pow.f64 (.f64 (PI.f64) (.f64 n #s(literal 2 binary64))) (-.f64 (.f64 k #s(literal 1/2 binary64)) #s(literal 1/2 binary64)))))
	74.5%	(.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)))
	50.5%	(.f64 (/.f64 (sqrt.f64 (.f64 (PI.f64) n)) (sqrt.f64 k)) (sqrt.f64 #s(literal 2 binary64)))
	99.5%	(.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))))
▶	50.5%	(.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) (.f64 (sqrt.f64 #s(literal 2 binary64)) (sqrt.f64 (*.f64 n (PI.f64)))))
	5.2%	(*.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) #s(literal 1 binary64))
	50.5%	(.f64 (.f64 (sqrt.f64 (/.f64 (PI.f64) k)) (sqrt.f64 n)) (sqrt.f64 #s(literal 2 binary64)))
	50.6%	(.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) k)) (sqrt.f64 (.f64 (PI.f64) (*.f64 n #s(literal 2 binary64)))))
	38.8%	(.f64 (sqrt.f64 (.f64 (/.f64 #s(literal 1 binary64) k) (*.f64 (PI.f64) n))) (sqrt.f64 #s(literal 2 binary64)))
▶	50.6%	(.f64 (sqrt.f64 (.f64 (PI.f64) n)) (sqrt.f64 (/.f64 #s(literal 2 binary64) k)))
	50.3%	(.f64 (sqrt.f64 (.f64 #s(literal 2 binary64) (PI.f64))) (*.f64 (sqrt.f64 n) (sqrt.f64 (/.f64 #s(literal 1 binary64) k))))
	50.6%	(.f64 (sqrt.f64 n) (sqrt.f64 (.f64 (/.f64 (PI.f64) k) #s(literal 2 binary64))))
	74.5%	(sqrt.f64 (/.f64 (/.f64 (.f64 (PI.f64) (.f64 n #s(literal 2 binary64))) k) (pow.f64 (.f64 (PI.f64) (.f64 n #s(literal 2 binary64))) k)))
	38.6%	(sqrt.f64 (/.f64 (.f64 (PI.f64) (.f64 n #s(literal 2 binary64))) k))
▶	5.2%	(sqrt.f64 (/.f64 #s(literal 1 binary64) k))

Compiler

Compiled 534 to 410 computations (23.2% saved)

simplify8.0ms (0.1%)

Memory

19.9MiB live, 19.9MiB allocated

Algorithm

1×	egg-herbie

Localize:

Found 18 expressions of interest:

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

Rules

104×	`-lowering-.f32`
104×	`-lowering-.f64`
38×	`associate-r`
34×	`*-commutative`
28×	`/-lowering-/.f32`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	29	165
1	46	163
2	70	163
3	95	163
4	107	163
5	111	163
6	114	163
0	114	163

Stop Event

1×	iter limit
1×	saturated

Calls

Call 1

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

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

localize164.0ms (1.4%)

Memory

-10.4MiB live, 242.7MiB allocated

Localize:

Found 18 expressions of interest:

New	Metric	Score	Program
✓	accuracy	99.7%	(*.f64 n (PI.f64))
✓	accuracy	99.6%	(.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) (.f64 (sqrt.f64 #s(literal 2 binary64)) (sqrt.f64 (*.f64 n (PI.f64)))))
✓	accuracy	99.5%	(.f64 (sqrt.f64 #s(literal 2 binary64)) (sqrt.f64 (.f64 n (PI.f64))))
✓	accuracy	76.2%	(PI.f64)
✓	accuracy	99.7%	(*.f64 (PI.f64) n)
✓	accuracy	99.4%	(/.f64 (sqrt.f64 #s(literal 2 binary64)) (sqrt.f64 (/.f64 k (*.f64 (PI.f64) n))))
✓	accuracy	88.5%	(sqrt.f64 (/.f64 k (*.f64 (PI.f64) n)))
✓	accuracy	76.2%	(PI.f64)
✓	accuracy	99.9%	(sqrt.f64 (*.f64 (PI.f64) n))
✓	accuracy	99.7%	(*.f64 (PI.f64) n)
✓	accuracy	99.6%	(.f64 (sqrt.f64 (.f64 (PI.f64) n)) (sqrt.f64 (/.f64 #s(literal 2 binary64) k)))
✓	accuracy	76.2%	(PI.f64)
✓	accuracy	100.0%	(/.f64 #s(literal 1 binary64) k)
✓	accuracy	99.8%	(sqrt.f64 (/.f64 #s(literal 1 binary64) k))
✓	accuracy	99.9%	(sqrt.f64 (.f64 (PI.f64) (.f64 n #s(literal 2 binary64))))
✓	accuracy	99.7%	(.f64 (PI.f64) (.f64 n #s(literal 2 binary64)))
✓	accuracy	99.7%	(/.f64 (sqrt.f64 (.f64 (PI.f64) (.f64 n #s(literal 2 binary64)))) (sqrt.f64 (.f64 k (pow.f64 (.f64 (PI.f64) (*.f64 n #s(literal 2 binary64))) k))))
✓	accuracy	76.2%	(PI.f64)

Samples

77.0ms	193×	0	valid
14.0ms	63×	0	exit

Compiler

Compiled 167 to 31 computations (81.4% saved)

Precisions

Click to see histograms. Total time spent on operations: 73.0ms

ival-mult: 44.0ms (60.1% of total)

ival-sqrt: 14.0ms (19.1% of total)

ival-div: 9.0ms (12.3% of total)

ival-pow: 4.0ms (5.5% of total)

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

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

exact: 0.0ms (0% of total)

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

series23.0ms (0.2%)

Memory

-18.2MiB live, 59.8MiB allocated

Counts

18 → 264

Calls

Call 1

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

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

Calls

66 calls:

Time	Variable		Point	Expression
4.0ms	n	@	inf	(/ (sqrt (* (PI) (* n 2))) (sqrt (* k (pow (* (PI) (* n 2)) k))))
3.0ms	n	@	-inf	(/ (sqrt (* (PI) (* n 2))) (sqrt (* k (pow (* (PI) (* n 2)) k))))
2.0ms	k	@	0	(/ (sqrt (* (PI) (* n 2))) (sqrt (* k (pow (* (PI) (* n 2)) k))))
2.0ms	n	@	inf	(sqrt (/ k (* (PI) n)))
2.0ms	n	@	0	(/ (sqrt (* (PI) (* n 2))) (sqrt (* k (pow (* (PI) (* n 2)) k))))

rewrite429.0ms (3.7%)

Memory

9.5MiB live, 602.3MiB allocated

Algorithm

1×	batch-egg-rewrite

Rules

5 726×	`-lowering-.f32`
5 726×	`-lowering-.f64`
3 220×	`/-lowering-/.f32`
3 220×	`/-lowering-/.f64`
2 058×	`+-lowering-+.f64`

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	29	94
1	138	92
2	724	91
3	7241	91
0	8790	91

Stop Event

1×	iter limit
1×	node limit

Counts

18 → 1 128

Calls

Call 1

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

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

simplify702.0ms (6%)

Memory

-28.8MiB live, 1 265.8MiB allocated

Algorithm

1×	egg-herbie

Rules

26 056×	`accelerator-lowering-fma.f32`
26 056×	`accelerator-lowering-fma.f64`
6 424×	`+-lowering-+.f64`
6 424×	`+-lowering-+.f32`
4 168×	`-lowering-.f32`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	136	2161
1	390	2107
2	1382	2075
3	3757	2014
0	8913	2007

Stop Event

1×	iter limit
1×	node limit

Counts

264 → 264

Calls

Call 1

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

eval236.0ms (2%)

Memory: 29.8MiB live, 443.2MiB allocated
Compiler: Compiled 26 760 to 3 261 computations (87.8% saved)

prune246.0ms (2.1%)

Memory

11.5MiB live, 449.1MiB allocated

Pruning

28 alts after pruning (23 fresh and 5 done)

	Pruned	Kept	Total
New	1 694	16	1 710
Fresh	8	7	15
Picked	0	5	5
Done	0	0	0
Total	1 702	28	1 730

Accuracy

100.0%

Counts

1 730 → 28

Alt Table

Click to see full alt table

Status	Accuracy	Program
	15.4%	(pow.f64 (*.f64 (/.f64 #s(literal 1 binary64) k) (/.f64 #s(literal 1 binary64) k)) #s(literal 1/4 binary64))
	5.2%	(pow.f64 (*.f64 (sqrt.f64 k) (sqrt.f64 k)) #s(literal -1/2 binary64))
▶	99.5%	(/.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))
	52.5%	(/.f64 (pow.f64 (.f64 (PI.f64) (.f64 n #s(literal 2 binary64))) (*.f64 k #s(literal -1/2 binary64))) (sqrt.f64 k))
✓	99.7%	(/.f64 (sqrt.f64 (.f64 (PI.f64) (.f64 n #s(literal 2 binary64)))) (sqrt.f64 (.f64 k (pow.f64 (.f64 (PI.f64) (*.f64 n #s(literal 2 binary64))) k))))
	50.6%	(/.f64 (sqrt.f64 (.f64 (PI.f64) n)) (sqrt.f64 (.f64 k #s(literal 1/2 binary64))))
✓	39.1%	(/.f64 (sqrt.f64 #s(literal 2 binary64)) (sqrt.f64 (/.f64 k (*.f64 (PI.f64) n))))
▶	39.1%	(/.f64 (sqrt.f64 #s(literal 2 binary64)) (sqrt.f64 (.f64 (/.f64 #s(literal 1 binary64) (.f64 (PI.f64) n)) k)))
	99.5%	(/.f64 #s(literal 1 binary64) (.f64 (sqrt.f64 k) (pow.f64 (.f64 (PI.f64) (.f64 n #s(literal 2 binary64))) (-.f64 (.f64 k #s(literal 1/2 binary64)) #s(literal 1/2 binary64)))))
▶	5.2%	(/.f64 #s(literal 1 binary64) (sqrt.f64 k))
	99.5%	(.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))))
✓	50.5%	(.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) (.f64 (sqrt.f64 #s(literal 2 binary64)) (sqrt.f64 (*.f64 n (PI.f64)))))
	50.5%	(.f64 (.f64 (sqrt.f64 (/.f64 (PI.f64) k)) (sqrt.f64 n)) (sqrt.f64 #s(literal 2 binary64)))
	50.3%	(.f64 (.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) k)) (sqrt.f64 n)) (sqrt.f64 (*.f64 (PI.f64) #s(literal 2 binary64))))
	50.6%	(.f64 (sqrt.f64 (/.f64 (PI.f64) (.f64 k #s(literal 1/2 binary64)))) (sqrt.f64 n))
	39.1%	(.f64 (sqrt.f64 (/.f64 n (.f64 k #s(literal 1/2 binary64)))) (sqrt.f64 (PI.f64)))
	38.8%	(.f64 (sqrt.f64 (.f64 (/.f64 #s(literal 1 binary64) k) (*.f64 (PI.f64) n))) (sqrt.f64 #s(literal 2 binary64)))
	50.4%	(.f64 (sqrt.f64 (.f64 (*.f64 (sqrt.f64 (PI.f64)) (sqrt.f64 (PI.f64))) n)) (sqrt.f64 (/.f64 #s(literal 2 binary64) k)))
✓	50.6%	(.f64 (sqrt.f64 (.f64 (PI.f64) n)) (sqrt.f64 (/.f64 #s(literal 2 binary64) k)))
	50.3%	(.f64 (sqrt.f64 (.f64 (PI.f64) #s(literal 2 binary64))) (/.f64 (sqrt.f64 n) (sqrt.f64 k)))
	5.2%	(*.f64 (sqrt.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) k))) (sqrt.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) k))))
	15.8%	(sqrt.f64 (pow.f64 (*.f64 k k) #s(literal -1/2 binary64)))
▶	5.2%	(sqrt.f64 (pow.f64 (sqrt.f64 k) #s(literal -2 binary64)))
	87.8%	(sqrt.f64 (/.f64 (.f64 (PI.f64) (.f64 n #s(literal 2 binary64))) (.f64 k (pow.f64 (.f64 (PI.f64) (*.f64 n #s(literal 2 binary64))) k))))
	38.6%	(sqrt.f64 (/.f64 (.f64 (PI.f64) (.f64 n #s(literal 2 binary64))) k))
▶	5.2%	(sqrt.f64 (/.f64 #s(literal 1 binary64) (*.f64 (sqrt.f64 k) (sqrt.f64 k))))
✓	5.2%	(sqrt.f64 (/.f64 #s(literal 1 binary64) k))
	15.4%	(sqrt.f64 (sqrt.f64 (*.f64 (/.f64 #s(literal 1 binary64) k) (/.f64 #s(literal 1 binary64) k))))

Compiler

Compiled 619 to 470 computations (24.1% saved)

simplify9.0ms (0.1%)

Memory

21.5MiB live, 21.6MiB allocated

Algorithm

1×	egg-herbie

Localize:

Found 17 expressions of interest:

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

Rules

150×	`-lowering-.f32`
150×	`-lowering-.f64`
82×	`associate-r`
66×	`associate-l`
54×	`associate-*r/`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	27	120
1	42	114
2	75	114
3	139	114
4	222	114
5	233	114
0	233	111

Stop Event

1×	iter limit
1×	saturated

Calls

Call 1

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

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

localize90.0ms (0.8%)

Memory

-1.2MiB live, 196.5MiB allocated

Localize:

Found 17 expressions of interest:

New	Metric	Score	Program
✓	accuracy	100.0%	(sqrt.f64 k)
✓	accuracy	99.8%	(sqrt.f64 (pow.f64 (sqrt.f64 k) #s(literal -2 binary64)))
✓	accuracy	99.1%	(pow.f64 (sqrt.f64 k) #s(literal -2 binary64))
✓	accuracy	99.6%	(*.f64 (PI.f64) n)
✓	accuracy	99.5%	(/.f64 #s(literal 1 binary64) (*.f64 (PI.f64) n))
✓	accuracy	99.3%	(/.f64 (sqrt.f64 #s(literal 2 binary64)) (sqrt.f64 (.f64 (/.f64 #s(literal 1 binary64) (.f64 (PI.f64) n)) k)))
✓	accuracy	73.4%	(sqrt.f64 (.f64 (/.f64 #s(literal 1 binary64) (.f64 (PI.f64) n)) k))
✓	accuracy	100.0%	(/.f64 #s(literal 1 binary64) (*.f64 (sqrt.f64 k) (sqrt.f64 k)))
✓	accuracy	100.0%	(sqrt.f64 k)
✓	accuracy	99.8%	(sqrt.f64 (/.f64 #s(literal 1 binary64) (*.f64 (sqrt.f64 k) (sqrt.f64 k))))
✓	accuracy	99.2%	(*.f64 (sqrt.f64 k) (sqrt.f64 k))
✓	accuracy	100.0%	(sqrt.f64 k)
✓	accuracy	99.7%	(/.f64 #s(literal 1 binary64) (sqrt.f64 k))
✓	accuracy	100.0%	(PI.f64)
✓	accuracy	99.7%	(pow.f64 (.f64 (PI.f64) (.f64 n #s(literal 2 binary64))) (fma.f64 k #s(literal -1/2 binary64) #s(literal 1/2 binary64)))
✓	accuracy	99.7%	(/.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))
✓	accuracy	99.6%	(.f64 (PI.f64) (.f64 n #s(literal 2 binary64)))

Samples

55.0ms

256×

valid

Compiler

Compiled 131 to 29 computations (77.9% saved)

Precisions

Click to see histograms. Total time spent on operations: 37.0ms

ival-sqrt: 9.0ms (24% of total)

ival-pow: 9.0ms (24% of total)

ival-mult: 8.0ms (21.3% of total)

ival-div: 7.0ms (18.7% of total)

ival-pi: 1.0ms (2.7% of total)

ival-add: 1.0ms (2.7% of total)

exact: 1.0ms (2.7% of total)

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

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

series23.0ms (0.2%)

Memory

-23.9MiB live, 14.2MiB allocated

Counts

17 → 240

Calls

Call 1

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

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

Calls

60 calls:

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

rewrite308.0ms (2.6%)

Memory

27.7MiB live, 544.2MiB allocated

Algorithm

1×	batch-egg-rewrite

Rules

5 722×	`-lowering-.f32`
5 722×	`-lowering-.f64`
3 004×	`/-lowering-/.f32`
3 004×	`/-lowering-/.f64`
2 540×	`accelerator-lowering-fma.f32`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	27	87
1	137	78
2	832	78
0	8009	76

Stop Event

1×	iter limit
1×	node limit

Counts

17 → 982

Calls

Call 1

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

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

simplify516.0ms (4.4%)

Memory

14.8MiB live, 973.2MiB allocated

Algorithm

1×	egg-herbie

Rules

10 846×	`accelerator-lowering-fma.f32`
10 846×	`accelerator-lowering-fma.f64`
7 066×	`-lowering-.f32`
7 066×	`-lowering-.f64`
2 072×	`+-lowering-+.f64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	125	1918
1	351	1883
2	1027	1865
3	3178	1718
4	6347	1718
0	8042	1666

Stop Event

1×	iter limit
1×	node limit

Counts

240 → 240

Calls

Call 1

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

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

eval186.0ms (1.6%)

Memory: 11.8MiB live, 466.5MiB allocated
Compiler: Compiled 19 981 to 3 348 computations (83.2% saved)

prune222.0ms (1.9%)

Memory

-25.8MiB live, 425.5MiB allocated

Pruning

34 alts after pruning (24 fresh and 10 done)

	Pruned	Kept	Total
New	1 451	10	1 461
Fresh	4	14	18
Picked	0	5	5
Done	0	5	5
Total	1 455	34	1 489

Accuracy

100.0%

Counts

1 489 → 34

Alt Table

Click to see full alt table

Status	Accuracy	Program
	15.4%	(pow.f64 (*.f64 (/.f64 #s(literal 1 binary64) k) (/.f64 #s(literal 1 binary64) k)) #s(literal 1/4 binary64))
	5.2%	(pow.f64 (*.f64 (sqrt.f64 k) (sqrt.f64 k)) #s(literal -1/2 binary64))
✓	99.5%	(/.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))
	52.5%	(/.f64 (pow.f64 (.f64 (PI.f64) (.f64 n #s(literal 2 binary64))) (*.f64 k #s(literal -1/2 binary64))) (sqrt.f64 k))
	50.5%	(/.f64 (.f64 (sqrt.f64 #s(literal 2 binary64)) (sqrt.f64 (.f64 n (PI.f64)))) (sqrt.f64 k))
	5.2%	(/.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k))) (sqrt.f64 (sqrt.f64 k)))
✓	99.7%	(/.f64 (sqrt.f64 (.f64 (PI.f64) (.f64 n #s(literal 2 binary64)))) (sqrt.f64 (.f64 k (pow.f64 (.f64 (PI.f64) (*.f64 n #s(literal 2 binary64))) k))))
	50.6%	(/.f64 (sqrt.f64 (.f64 (PI.f64) n)) (sqrt.f64 (.f64 k #s(literal 1/2 binary64))))
✓	39.1%	(/.f64 (sqrt.f64 #s(literal 2 binary64)) (sqrt.f64 (/.f64 k (*.f64 (PI.f64) n))))
✓	39.1%	(/.f64 (sqrt.f64 #s(literal 2 binary64)) (sqrt.f64 (.f64 (/.f64 #s(literal 1 binary64) (.f64 (PI.f64) n)) k)))
	5.2%	(/.f64 #s(literal 1 binary64) (*.f64 (sqrt.f64 (sqrt.f64 k)) (sqrt.f64 (sqrt.f64 k))))
	99.5%	(/.f64 #s(literal 1 binary64) (.f64 (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)))))
✓	5.2%	(/.f64 #s(literal 1 binary64) (sqrt.f64 k))
✓	50.5%	(.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) (.f64 (sqrt.f64 #s(literal 2 binary64)) (sqrt.f64 (*.f64 n (PI.f64)))))
	50.3%	(.f64 (.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) k)) (sqrt.f64 n)) (sqrt.f64 (*.f64 (PI.f64) #s(literal 2 binary64))))
	50.6%	(.f64 (sqrt.f64 (/.f64 (PI.f64) (.f64 k #s(literal 1/2 binary64)))) (sqrt.f64 n))
	39.1%	(.f64 (sqrt.f64 (/.f64 n (.f64 k #s(literal 1/2 binary64)))) (sqrt.f64 (PI.f64)))
	38.8%	(.f64 (sqrt.f64 (.f64 (/.f64 #s(literal 1 binary64) k) (*.f64 (PI.f64) n))) (sqrt.f64 #s(literal 2 binary64)))
	50.4%	(.f64 (sqrt.f64 (.f64 (*.f64 (sqrt.f64 (PI.f64)) (sqrt.f64 (PI.f64))) n)) (sqrt.f64 (/.f64 #s(literal 2 binary64) k)))
✓	50.6%	(.f64 (sqrt.f64 (.f64 (PI.f64) n)) (sqrt.f64 (/.f64 #s(literal 2 binary64) k)))
	50.3%	(.f64 (sqrt.f64 (.f64 (PI.f64) #s(literal 2 binary64))) (/.f64 (sqrt.f64 n) (sqrt.f64 k)))
	5.2%	(*.f64 (sqrt.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) k))) (sqrt.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) k))))
	22.0%	(sqrt.f64 (pow.f64 (.f64 k (.f64 k (*.f64 k k))) #s(literal -1/4 binary64)))
✓	5.2%	(sqrt.f64 (pow.f64 (sqrt.f64 k) #s(literal -2 binary64)))
	5.2%	(sqrt.f64 (/.f64 (/.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) (sqrt.f64 (sqrt.f64 k))) (sqrt.f64 (sqrt.f64 k))))
	87.8%	(sqrt.f64 (/.f64 (.f64 (PI.f64) (.f64 n #s(literal 2 binary64))) (.f64 k (pow.f64 (.f64 (PI.f64) (*.f64 n #s(literal 2 binary64))) k))))
	38.6%	(sqrt.f64 (/.f64 (.f64 (PI.f64) (.f64 n #s(literal 2 binary64))) k))
	5.2%	(sqrt.f64 (/.f64 #s(literal 1 binary64) (/.f64 (/.f64 (sqrt.f64 k) (sqrt.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)))) (sqrt.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k))))))
	5.2%	(sqrt.f64 (/.f64 #s(literal 1 binary64) (.f64 (.f64 (sqrt.f64 k) (sqrt.f64 (sqrt.f64 k))) (sqrt.f64 (sqrt.f64 k)))))
✓	5.2%	(sqrt.f64 (/.f64 #s(literal 1 binary64) (*.f64 (sqrt.f64 k) (sqrt.f64 k))))
✓	5.2%	(sqrt.f64 (/.f64 #s(literal 1 binary64) k))
	5.2%	(sqrt.f64 (*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k))) (/.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k))) (sqrt.f64 k))))
	15.7%	(sqrt.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (*.f64 k k))))
	15.4%	(sqrt.f64 (sqrt.f64 (*.f64 (/.f64 #s(literal 1 binary64) k) (/.f64 #s(literal 1 binary64) k))))

Compiler

Compiled 1 185 to 510 computations (57% saved)

regimes73.0ms (0.6%)

Memory

19.7MiB live, 173.3MiB allocated

Counts

61 → 1

Calls

Call 1

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

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

Calls

4 calls:

18.0ms	n
18.0ms	k
17.0ms	(.f64 (.f64 #s(literal 2 binary64) (PI.f64)) n)
16.0ms	(.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)

regimes74.0ms (0.6%)

Memory

1.4MiB live, 127.5MiB allocated

Counts

54 → 1

Calls

Call 1

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

Outputs
(.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))))

Calls

4 calls:

24.0ms	k
17.0ms	(.f64 (.f64 #s(literal 2 binary64) (PI.f64)) n)
16.0ms	(.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) (pow.f64 (.f64 (*.f64 #s(literal 2 binary64) (PI.f64)) n) (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 2 binary64))))
14.0ms	n

Results

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

Compiler

Compiled 31 to 23 computations (25.8% saved)

regimes57.0ms (0.5%)

Memory

7.6MiB live, 117.5MiB allocated

Counts

43 → 1

Calls

Call 1

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

Outputs
(/.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))

Calls

4 calls:

15.0ms	(.f64 (.f64 #s(literal 2 binary64) (PI.f64)) n)
15.0ms	k
13.0ms	(.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) (pow.f64 (.f64 (*.f64 #s(literal 2 binary64) (PI.f64)) n) (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 2 binary64))))
12.0ms	n

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)

regimes57.0ms (0.5%)

Memory

-7.1MiB live, 108.6MiB allocated

Counts

41 → 2

Calls

Call 1

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

Outputs

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

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

Calls

4 calls:

20.0ms	(.f64 (.f64 #s(literal 2 binary64) (PI.f64)) n)
12.0ms	k
12.0ms	(.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) (pow.f64 (.f64 (*.f64 #s(literal 2 binary64) (PI.f64)) n) (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 2 binary64))))
11.0ms	n

Results

Accuracy	Segments	Branch
98.1%	2	`k`
62.3%	4	`n`
98.1%	3	`(.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) (pow.f64 (.f64 (*.f64 #s(literal 2 binary64) (PI.f64)) n) (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 2 binary64))))`
62.3%	4	`(.f64 (.f64 #s(literal 2 binary64) (PI.f64)) n)`

Compiler

Compiled 31 to 23 computations (25.8% saved)

regimes24.0ms (0.2%)

Memory

5.8MiB live, 44.3MiB allocated

Counts

39 → 2

Calls

Call 1

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

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

Calls

2 calls:

11.0ms	k
11.0ms	(.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) (pow.f64 (.f64 (*.f64 #s(literal 2 binary64) (PI.f64)) n) (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 2 binary64))))

Results

Accuracy	Segments	Branch
68.8%	2	`(.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) (pow.f64 (.f64 (*.f64 #s(literal 2 binary64) (PI.f64)) n) (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 2 binary64))))`
68.7%	2	`k`

Compiler

Compiled 21 to 15 computations (28.6% saved)

regimes26.0ms (0.2%)

Memory

-2.9MiB live, 41.1MiB allocated

Counts

35 → 2

Calls

Call 1

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

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

Calls

2 calls:

16.0ms	k
9.0ms	(.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) (pow.f64 (.f64 (*.f64 #s(literal 2 binary64) (PI.f64)) n) (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 2 binary64))))

Results

Accuracy	Segments	Branch
62.0%	2	`k`
62.0%	2	`(.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) (pow.f64 (.f64 (*.f64 #s(literal 2 binary64) (PI.f64)) n) (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 2 binary64))))`

Compiler

Compiled 21 to 15 computations (28.6% saved)

regimes5.0ms (0%)

Memory

9.3MiB live, 9.3MiB allocated

Counts

14 → 2

Calls

Call 1

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

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

Calls

1 calls:

4.0ms

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

Results

Accuracy	Segments	Branch
62.0%	2	`(.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) (pow.f64 (.f64 (*.f64 #s(literal 2 binary64) (PI.f64)) n) (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 2 binary64))))`

Compiler

Compiled 18 to 13 computations (27.8% saved)

regimes5.0ms (0%)

Memory

-28.6MiB live, 10.9MiB allocated

Counts

10 → 2

Calls

Call 1

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

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

Calls

1 calls:

4.0ms

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

Results

Accuracy	Segments	Branch
62.0%	2	`(.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) (pow.f64 (.f64 (*.f64 #s(literal 2 binary64) (PI.f64)) n) (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 2 binary64))))`

Compiler

Compiled 18 to 13 computations (27.8% saved)

regimes10.0ms (0.1%)

Memory

25.7MiB live, 25.6MiB allocated

Counts

5 → 2

Calls

Call 1

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

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

Calls

4 calls:

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

Results

Accuracy	Segments	Branch
42.5%	2	`n`
42.5%	2	`(.f64 (.f64 #s(literal 2 binary64) (PI.f64)) n)`
50.0%	2	`k`
50.0%	2	`(.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) (pow.f64 (.f64 (*.f64 #s(literal 2 binary64) (PI.f64)) n) (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 2 binary64))))`

Compiler

Compiled 31 to 23 computations (25.8% saved)

regimes10.0ms (0.1%)

Memory

-10.7MiB live, 27.5MiB allocated

Counts

4 → 1

Calls

Call 1

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

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

Calls

4 calls:

3.0ms	(.f64 (.f64 #s(literal 2 binary64) (PI.f64)) n)
2.0ms	n
2.0ms	k
2.0ms	(.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) (pow.f64 (.f64 (*.f64 #s(literal 2 binary64) (PI.f64)) n) (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 2 binary64))))

Results

Accuracy	Segments	Branch
38.6%	1	`n`
38.6%	1	`(.f64 (.f64 #s(literal 2 binary64) (PI.f64)) n)`
38.6%	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))))`
38.6%	1	`k`

Compiler

Compiled 31 to 23 computations (25.8% saved)

regimes8.0ms (0.1%)

Memory

20.5MiB live, 20.5MiB allocated

Accuracy

Total -0.0b remaining (-0%)

Threshold costs -0b (-0%)

Counts

3 → 1

Calls

Call 1

Inputs
(sqrt.f64 (/.f64 #s(literal 1 binary64) k))
(/.f64 #s(literal 1 binary64) (sqrt.f64 k))
(*.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) #s(literal 1 binary64))

Outputs
(sqrt.f64 (/.f64 #s(literal 1 binary64) k))

Calls

4 calls:

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

Results

Accuracy	Segments	Branch
5.2%	1	`k`
5.2%	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))))`
5.2%	1	`n`
5.2%	1	`(.f64 (.f64 #s(literal 2 binary64) (PI.f64)) n)`

Compiler

Compiled 31 to 23 computations (25.8% saved)

bsearch20.0ms (0.2%)

Memory

-6.1MiB live, 32.5MiB allocated

Algorithm

1×	binary-search

Stop Event

1×	narrow-enough

Steps

Time	Left	Right
17.0ms	0.012278353135199392	326.51452571147394

Samples

13.0ms

128×

valid

Compiler

Compiled 253 to 210 computations (17% saved)

Precisions

Click to see histograms. Total time spent on operations: 8.0ms

ival-div: 2.0ms (25.2% of total)

ival-mult: 2.0ms (25.2% of total)

ival-pow: 2.0ms (25.2% of total)

ival-sub: 1.0ms (12.6% of total)

ival-sqrt: 1.0ms (12.6% of total)

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

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

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

exact: 0.0ms (0% of total)

bsearch0.0ms (0%)

Memory

0.7MiB live, 0.7MiB allocated

Algorithm

1×	left-value

Steps

Time	Left	Right
0.0ms	0.0	9.408623207613693e-140

Compiler

Compiled 21 to 18 computations (14.3% saved)

bsearch0.0ms (0%)

Memory

0.6MiB live, 0.6MiB allocated

Algorithm

1×	left-value

Steps

Time	Left	Right
0.0ms	0.0	9.408623207613693e-140

Compiler

Compiled 21 to 18 computations (14.3% saved)

bsearch0.0ms (0%)

Memory

0.3MiB live, 0.3MiB allocated

Algorithm

1×	left-value

Steps

Time	Left	Right
0.0ms	0.0	9.408623207613693e-140

Compiler

Compiled 21 to 18 computations (14.3% saved)

bsearch0.0ms (0%)

Memory

0.3MiB live, 0.3MiB allocated

Algorithm

1×	left-value

Steps

Time	Left	Right
0.0ms	0.0	9.408623207613693e-140

Compiler

Compiled 21 to 18 computations (14.3% saved)

bsearch20.0ms (0.2%)

Memory

-10.9MiB live, 31.1MiB allocated

Algorithm

1×	binary-search

Stop Event

1×	narrow-enough

Steps

Time	Left	Right
18.0ms	0.012278353135199392	326.51452571147394

Samples

14.0ms

128×

valid

Compiler

Compiled 189 to 154 computations (18.5% saved)

Precisions

Click to see histograms. Total time spent on operations: 8.0ms

ival-div: 2.0ms (25.1% of total)

ival-mult: 2.0ms (25.1% of total)

ival-pow: 2.0ms (25.1% of total)

ival-sub: 1.0ms (12.5% of total)

ival-sqrt: 1.0ms (12.5% of total)

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

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

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

exact: 0.0ms (0% of total)

simplify12.0ms (0.1%)

Memory

-16.6MiB live, 21.8MiB allocated

Algorithm

1×	egg-herbie

Rules

32×	`*-commutative_binary64`
4×	`+-commutative_binary64`
4×	`sub-neg_binary64`
2×	`1-exp_binary64`
2×	`neg-sub0_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	67	250
1	86	250
2	90	250
3	92	250
4	93	250

Stop Event

1×

saturated

Calls

Call 1

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

Outputs
(/.f64 (sqrt.f64 (.f64 (PI.f64) (.f64 n #s(literal 2 binary64)))) (sqrt.f64 (.f64 k (pow.f64 (.f64 (PI.f64) (*.f64 n #s(literal 2 binary64))) k))))
(.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) k)) (pow.f64 (.f64 n (*.f64 (PI.f64) #s(literal 2 binary64))) (fma.f64 #s(literal -1/2 binary64) k #s(literal 1/2 binary64))))
(/.f64 (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))
(if (<=.f64 k #s(literal 1 binary64)) (.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) k)) (sqrt.f64 (.f64 (PI.f64) (.f64 n #s(literal 2 binary64))))) (/.f64 (pow.f64 (.f64 (PI.f64) (.f64 n #s(literal 2 binary64))) (.f64 k #s(literal -1/2 binary64))) (sqrt.f64 k)))
(if (<=.f64 k #s(literal 1 binary64)) (.f64 (sqrt.f64 (.f64 (PI.f64) (.f64 n #s(literal 2 binary64)))) (sqrt.f64 (/.f64 #s(literal 1 binary64) k))) (/.f64 (pow.f64 (.f64 (PI.f64) (.f64 n #s(literal 2 binary64))) (.f64 k #s(literal -1/2 binary64))) (sqrt.f64 k)))
(if (<=.f64 (.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) (pow.f64 (.f64 (.f64 #s(literal 2 binary64) (PI.f64)) n) (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 2 binary64)))) #s(literal 0 binary64)) (sqrt.f64 (pow.f64 (.f64 k (.f64 k (.f64 k k))) #s(literal -1/4 binary64))) (.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) k)) (sqrt.f64 (.f64 (PI.f64) (*.f64 n #s(literal 2 binary64))))))
(if (<=.f64 (.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) (pow.f64 (.f64 n (.f64 (PI.f64) #s(literal 2 binary64))) (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 2 binary64)))) #s(literal 0 binary64)) (sqrt.f64 (pow.f64 (.f64 k (.f64 k (.f64 k k))) #s(literal -1/4 binary64))) (.f64 (sqrt.f64 (.f64 (PI.f64) (*.f64 n #s(literal 2 binary64)))) (sqrt.f64 (/.f64 #s(literal 1 binary64) k))))
(if (<=.f64 (.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) (pow.f64 (.f64 (.f64 #s(literal 2 binary64) (PI.f64)) n) (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 2 binary64)))) #s(literal 0 binary64)) (sqrt.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (.f64 k k)))) (.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) k)) (sqrt.f64 (.f64 (PI.f64) (*.f64 n #s(literal 2 binary64))))))
(if (<=.f64 (.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) (pow.f64 (.f64 n (.f64 (PI.f64) #s(literal 2 binary64))) (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 2 binary64)))) #s(literal 0 binary64)) (sqrt.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (.f64 k k)))) (.f64 (sqrt.f64 (.f64 (PI.f64) (*.f64 n #s(literal 2 binary64)))) (sqrt.f64 (/.f64 #s(literal 1 binary64) k))))
(if (<=.f64 (.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) (pow.f64 (.f64 (.f64 #s(literal 2 binary64) (PI.f64)) n) (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 2 binary64)))) #s(literal 0 binary64)) (sqrt.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (.f64 k k)))) (/.f64 (sqrt.f64 (.f64 (PI.f64) n)) (sqrt.f64 (.f64 k #s(literal 1/2 binary64)))))
(if (<=.f64 (.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) (pow.f64 (.f64 n (.f64 (PI.f64) #s(literal 2 binary64))) (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 2 binary64)))) #s(literal 0 binary64)) (sqrt.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (.f64 k k)))) (/.f64 (sqrt.f64 (.f64 (PI.f64) n)) (sqrt.f64 (.f64 k #s(literal 1/2 binary64)))))
(if (<=.f64 (.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) (pow.f64 (.f64 (.f64 #s(literal 2 binary64) (PI.f64)) n) (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 2 binary64)))) #s(literal 0 binary64)) (sqrt.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (.f64 k k)))) (.f64 (sqrt.f64 n) (sqrt.f64 (.f64 (/.f64 (PI.f64) k) #s(literal 2 binary64)))))
(if (<=.f64 (.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) (pow.f64 (.f64 n (.f64 (PI.f64) #s(literal 2 binary64))) (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 2 binary64)))) #s(literal 0 binary64)) (sqrt.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (.f64 k k)))) (.f64 (sqrt.f64 n) (sqrt.f64 (.f64 #s(literal 2 binary64) (/.f64 (PI.f64) k)))))
(if (<=.f64 k #s(literal 1/2 binary64)) (sqrt.f64 (/.f64 (.f64 (PI.f64) (.f64 n #s(literal 2 binary64))) k)) (sqrt.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (*.f64 k k)))))
(sqrt.f64 (/.f64 (.f64 (PI.f64) (.f64 n #s(literal 2 binary64))) k))
(sqrt.f64 (/.f64 #s(literal 1 binary64) k))

soundness1.3s (10.7%)

Memory

-3.0MiB live, 955.6MiB allocated

Rules

12 638×	`accelerator-lowering-fma.f32`
12 638×	`accelerator-lowering-fma.f64`
9 974×	`accelerator-lowering-fma.f32`
9 974×	`accelerator-lowering-fma.f64`
6 086×	`-lowering-.f32`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	13	43
1	80	40
2	488	38
3	4450	38
0	8572	37
0	29	94
1	138	92
2	724	91
3	7241	91
0	8790	91
0	271	4532
1	766	4466
2	2492	4244
3	4396	4190
0	8768	4109
0	128	1174
1	345	1155
2	1011	1065
3	3348	1038
4	5547	966
0	8354	945
0	36	159
1	186	141
2	1201	138
0	8497	133
0	27	87
1	137	78
2	832	78
0	8009	76

Stop Event

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

Compiler

Compiled 706 to 424 computations (39.9% saved)

preprocess149.0ms (1.3%)

Memory: -6.1MiB live, 109.0MiB allocated
Compiler: Compiled 540 to 156 computations (71.1% saved)

end0.0ms (0%)

Memory: 0.0MiB live, 0.0MiB allocated

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

Iter	Nodes	Cost
0	36	281
1	78	275
2	152	275
3	246	275
4	292	275
5	320	275
6	346	275
7	373	275
8	381	275
0	381	272

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

Iter	Nodes	Cost
0	36	281
1	78	275
2	152	275
3	246	275
4	292	275
5	320	275
6	346	275
7	373	275
8	381	275
0	381	272

analyze112.0ms (1%)

sample3.2s (27.5%)

preprocess56.0ms (0.5%)

explain174.0ms (1.5%)

eval0.0ms (0%)

prune1.0ms (0%)

simplify8.0ms (0.1%)

localize93.0ms (0.8%)

series99.0ms (0.8%)

rewrite344.0ms (2.9%)

simplify343.0ms (2.9%)

eval62.0ms (0.5%)

prune110.0ms (0.9%)

simplify35.0ms (0.3%)

localize214.0ms (1.8%)

series81.0ms (0.7%)

rewrite404.0ms (3.4%)

simplify533.0ms (4.5%)

eval343.0ms (2.9%)

prune539.0ms (4.6%)

simplify8.0ms (0.1%)

localize164.0ms (1.4%)

series23.0ms (0.2%)

rewrite429.0ms (3.7%)

simplify702.0ms (6%)

eval236.0ms (2%)

prune246.0ms (2.1%)

simplify9.0ms (0.1%)

localize90.0ms (0.8%)

series23.0ms (0.2%)

rewrite308.0ms (2.6%)

simplify516.0ms (4.4%)

eval186.0ms (1.6%)

prune222.0ms (1.9%)

regimes73.0ms (0.6%)

regimes74.0ms (0.6%)

regimes57.0ms (0.5%)

regimes57.0ms (0.5%)

regimes24.0ms (0.2%)

regimes26.0ms (0.2%)

regimes5.0ms (0%)

regimes5.0ms (0%)

regimes10.0ms (0.1%)

regimes10.0ms (0.1%)

regimes8.0ms (0.1%)

bsearch20.0ms (0.2%)

bsearch0.0ms (0%)

bsearch0.0ms (0%)

bsearch0.0ms (0%)

bsearch0.0ms (0%)

bsearch20.0ms (0.2%)

simplify12.0ms (0.1%)

soundness1.3s (10.7%)

preprocess149.0ms (1.3%)

end0.0ms (0%)

Profiling

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

Iter	Nodes	Cost
0	36	281
1	78	275
2	152	275
3	246	275
4	292	275
5	320	275
6	346	275
7	373	275
8	381	275
0	381	272