Metrics for Migdal et al, Equation (51)

start0.0ms (0%)

Memory: 0.1MiB live, 0.1MiB allocated

analyze113.0ms (1.3%)

Memory

9.7MiB live, 204.9MiB 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)

sample3.4s (38.7%)

Memory

-99.5MiB live, 4 338.3MiB allocated

Samples

922.0ms	8 256×	0	valid
830.0ms	3 498×	1	invalid
665.0ms	1 838×	1	exit
139.0ms	430×	2	invalid
51.0ms	538×	0	invalid
30.0ms	244×	0	exit

Precisions

Click to see histograms. Total time spent on operations: 2.0s

ival-pow: 493.0ms (24.6% of total)

adjust: 424.0ms (21.1% of total)

ival-mult: 376.0ms (18.7% of total)

ival-div: 307.0ms (15.3% of total)

ival-sqrt: 150.0ms (7.5% of total)

ival-sub: 110.0ms (5.5% of total)

ival-pi: 109.0ms (5.4% of total)

exact: 18.0ms (0.9% of total)

ival-true: 14.0ms (0.7% of total)

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

Bogosity

explain147.0ms (1.7%)

Memory

35.5MiB live, 231.1MiB allocated

FPErrors

Click to see full error table

Ground Truth	Overpredictions	Example	Underpredictions	Example	Subexpression
9	79	(3.030349792691637e-32 3.8700548414994663e-177)	1	(3.060686080845406e-16 2.5286687806400944e+77)	`(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	86	26
`pow.f64`	`(pow.f64 (.f64 (.f64 #s(literal 2 binary64) (PI.f64)) n) (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 2 binary64)))`	oflow-rescue	1	0
↳	`(.f64 (.f64 #s(literal 2 binary64) (PI.f64)) n)`	overflow	2
↳	`(pow.f64 (.f64 (.f64 #s(literal 2 binary64) (PI.f64)) n) (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 2 binary64)))`	overflow	49

Confusion

	Predicted +	Predicted -
+	8	2
-	79	167

Precision

0.09195402298850575

Recall

0.8

Confusion?

	Predicted +	Predicted Maybe	Predicted -
+	8	2	0
-	79	24	143

Precision?

0.08849557522123894

Recall?

1.0

Freqs

test

number	freq
0	169
1	87

Total Confusion?

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

Precision?

1.0

Recall?

1.0

Samples

59.0ms

512×

valid

Compiler

Compiled 182 to 56 computations (69.2% saved)

Precisions

Click to see histograms. Total time spent on operations: 41.0ms

ival-mult: 13.0ms (31.7% of total)

ival-pow: 10.0ms (24.4% of total)

ival-div: 7.0ms (17.1% of total)

ival-sqrt: 4.0ms (9.8% of total)

ival-sub: 3.0ms (7.3% of total)

ival-pi: 2.0ms (4.9% of total)

ival-true: 1.0ms (2.4% of total)

exact: 1.0ms (2.4% of total)

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

preprocess70.0ms (0.8%)

Memory

-27.1MiB live, 65.0MiB allocated

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	31	88
1	82	74
2	193	74
3	383	74
4	630	74
5	922	74
6	1089	74
7	1346	74
8	1405	74
9	1431	74
10	1449	74
11	1455	74
12	1455	74
0	13	16
0	22	16
1	37	14
2	54	14
3	75	14
4	93	14
5	108	14
6	129	14
7	156	14
8	165	14
9	168	14
0	168	13

Stop Event

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

Calls

Call 1

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

Outputs

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

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

Compiler

Compiled 16 to 13 computations (18.8% saved)

eval0.0ms (0%)

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

prune0.0ms (0%)

Memory

1.0MiB live, 1.0MiB allocated

Alt Table

Click to see full alt table

Status	Accuracy	Program
▶	99.1%	(.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) (pow.f64 (.f64 (*.f64 #s(literal 2 binary64) (PI.f64)) n) (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 2 binary64))))

Compiler

Compiled 16 to 13 computations (18.8% saved)

simplify6.0ms (0.1%)

Memory

10.3MiB live, 10.3MiB allocated

Algorithm

1×	egg-herbie

Localize:

Found 4 expressions of interest:

New	Metric	Score
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))

Iterations

Useful iterations: 0 (0.0ms)

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

Stop Event

1×	iter limit
1×	saturated
1×	iter limit

Calls

Call 1

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

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

localize57.0ms (0.6%)

Memory

9.6MiB live, 47.1MiB allocated

Localize:

Found 4 expressions of interest:

New	Metric	Score
accuracy	0.178066259768442	(.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) (pow.f64 (.f64 (*.f64 #s(literal 2 binary64) (PI.f64)) n) (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 2 binary64))))
accuracy	0.22265625	(.f64 (.f64 #s(literal 2 binary64) (PI.f64)) n)
accuracy	0.23046875	(/.f64 #s(literal 1 binary64) (sqrt.f64 k))
accuracy	0.4841279054325469	(pow.f64 (.f64 (.f64 #s(literal 2 binary64) (PI.f64)) n) (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 2 binary64)))

Samples

47.0ms

256×

valid

Compiler

Compiled 110 to 28 computations (74.5% saved)

Precisions

Click to see histograms. Total time spent on operations: 38.0ms

ival-div: 23.0ms (60.8% of total)

ival-mult: 5.0ms (13.2% of total)

ival-pow: 5.0ms (13.2% of total)

ival-sqrt: 2.0ms (5.3% of total)

ival-pi: 1.0ms (2.6% of total)

ival-sub: 1.0ms (2.6% of total)

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

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

exact: 0.0ms (0% of total)

series92.0ms (1%)

Memory

-9.5MiB live, 108.5MiB allocated

Counts

6 → 27

Calls

Call 1

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

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

Calls

6 calls:

Time	Variable		Point	Expression
33.0ms	n	@	0	((/ (- 1 k) 2) (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (/ 1 (sqrt k)) (sqrt k) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2)) (* (* 2 (PI)) n))
23.0ms	n	@	-inf	((/ (- 1 k) 2) (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (/ 1 (sqrt k)) (sqrt k) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2)) (* (* 2 (PI)) n))
22.0ms	k	@	inf	((/ (- 1 k) 2) (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (/ 1 (sqrt k)) (sqrt k) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2)) (* (* 2 (PI)) n))
8.0ms	n	@	inf	((/ (- 1 k) 2) (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (/ 1 (sqrt k)) (sqrt k) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2)) (* (* 2 (PI)) n))
3.0ms	k	@	-inf	((/ (- 1 k) 2) (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (/ 1 (sqrt k)) (sqrt k) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2)) (* (* 2 (PI)) n))

simplify179.0ms (2%)

Memory

16.8MiB live, 168.8MiB allocated

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	128	517
1	345	504
2	1021	460
3	3363	433
4	5589	421
0	8476	406

Stop Event

1×	iter limit
1×	node limit

Counts

27 → 27

Calls

Call 1

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

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

rewrite195.0ms (2.2%)

Memory

-10.9MiB live, 224.4MiB allocated

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	13	43
0	22	43
1	89	40
2	497	38
3	4477	38
0	8503	37

Stop Event

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

Counts

6 → 413

Calls

Call 1

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

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

eval88.0ms (1%)

Memory: -12.1MiB live, 111.9MiB allocated
Compiler: Compiled 9 931 to 1 554 computations (84.4% saved)

prune24.0ms (0.3%)

Memory

11.7MiB live, 49.3MiB allocated

Pruning

19 alts after pruning (19 fresh and 0 done)

	Pruned	Kept	Total
New	412	19	431
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	413	19	432

Accuracy

100.0%

Counts

432 → 19

Alt Table

Click to see full alt table

Status	Accuracy	Program
	47.8%	(/.f64 (pow.f64 (.f64 n (.f64 (PI.f64) #s(literal 2 binary64))) (fma.f64 #s(literal 1/2 binary64) k #s(literal 1/2 binary64))) (sqrt.f64 k))
	99.0%	(/.f64 (sqrt.f64 (.f64 n (.f64 (PI.f64) #s(literal 2 binary64)))) (.f64 (sqrt.f64 k) (pow.f64 (pow.f64 (.f64 n (*.f64 (PI.f64) #s(literal 2 binary64))) k) #s(literal 1/2 binary64))))
	47.7%	(/.f64 #s(literal 1 binary64) (/.f64 (sqrt.f64 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)))))
	47.6%	(.f64 (pow.f64 (.f64 (PI.f64) #s(literal 2 binary64)) (fma.f64 #s(literal 1/2 binary64) k #s(literal 1/2 binary64))) (/.f64 (pow.f64 n (fma.f64 #s(literal 1/2 binary64) k #s(literal 1/2 binary64))) (sqrt.f64 k)))
	47.8%	(.f64 (/.f64 (pow.f64 #s(literal 2 binary64) (fma.f64 #s(literal 1/2 binary64) k #s(literal 1/2 binary64))) (sqrt.f64 k)) (/.f64 (pow.f64 (.f64 n (PI.f64)) (fma.f64 #s(literal 1/2 binary64) k #s(literal 1/2 binary64))) #s(literal 1 binary64)))
	98.9%	(.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) (pow.f64 (.f64 (.f64 (.f64 n #s(literal 2 binary64)) (sqrt.f64 (PI.f64))) (sqrt.f64 (PI.f64))) (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 2 binary64))))
	99.1%	(.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))))
▶	54.3%	(.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) (pow.f64 (.f64 (.f64 #s(literal 2 binary64) (PI.f64)) n) #s(approx (/ (- 1 k) 2) (.f64 #s(literal -1/2 binary64) k))))
	48.4%	(.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) (pow.f64 (.f64 (*.f64 #s(literal 2 binary64) (PI.f64)) n) #s(approx (/ (- 1 k) 2) #s(literal 1/2 binary64))))
	99.1%	(.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) (/.f64 #s(literal 1 binary64) (pow.f64 (.f64 n (.f64 (PI.f64) #s(literal 2 binary64))) (.f64 #s(literal -1/2 binary64) (-.f64 #s(literal 1 binary64) k)))))
	99.0%	(.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) (/.f64 #s(literal 1 binary64) (pow.f64 (sqrt.f64 (.f64 n (*.f64 (PI.f64) #s(literal 2 binary64)))) (-.f64 k #s(literal 1 binary64)))))
	98.9%	(.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) (.f64 (pow.f64 (.f64 n (.f64 (PI.f64) #s(literal 2 binary64))) (.f64 k #s(literal -1/2 binary64))) (sqrt.f64 (.f64 n (*.f64 (PI.f64) #s(literal 2 binary64))))))
▶	99.0%	(.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) #s(approx (pow ( (* 2 (PI)) n) (/ (- 1 k) 2)) (pow.f64 (/.f64 (*.f64 #s(literal -2 binary64) (PI.f64)) (/.f64 #s(literal -1 binary64) n)) (fma.f64 #s(literal -1/2 binary64) k #s(literal 1/2 binary64)))))
▶	49.7%	(.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) #s(approx (pow ( (* 2 (PI)) n) (/ (- 1 k) 2)) (.f64 (fma.f64 (log.f64 (.f64 (.f64 #s(literal 2 binary64) n) (PI.f64))) (.f64 #s(literal -1/2 binary64) k) #s(literal 1 binary64)) (.f64 (sqrt.f64 (.f64 (PI.f64) n)) (sqrt.f64 #s(literal 2 binary64))))))
	48.7%	(.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) #s(approx (pow ( (* 2 (PI)) n) (/ (- 1 k) 2)) (.f64 (sqrt.f64 (.f64 (PI.f64) n)) (sqrt.f64 #s(literal 2 binary64)))))
	50.5%	#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (/.f64 (.f64 (sqrt.f64 #s(literal 2 binary64)) (fma.f64 (.f64 (log.f64 (.f64 (.f64 #s(literal 2 binary64) n) (PI.f64))) (sqrt.f64 (.f64 (.f64 (pow.f64 k #s(literal 3 binary64)) (PI.f64)) n))) #s(literal -1/2 binary64) (sqrt.f64 (.f64 (.f64 (PI.f64) n) k)))) k))
	50.7%	#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (/.f64 (.f64 (sqrt.f64 #s(literal 2 binary64)) (fma.f64 k (.f64 (log.f64 (.f64 (.f64 #s(literal 2 binary64) n) (PI.f64))) (fma.f64 #s(literal 1/8 binary64) (.f64 (log.f64 (.f64 (.f64 #s(literal 2 binary64) n) (PI.f64))) (sqrt.f64 (.f64 (.f64 (pow.f64 k #s(literal 3 binary64)) (PI.f64)) n))) (.f64 (sqrt.f64 (.f64 (.f64 (PI.f64) n) k)) #s(literal -1/2 binary64)))) (sqrt.f64 (.f64 (.f64 (PI.f64) n) k)))) k))
▶	99.1%	#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (.f64 (pow.f64 (.f64 (*.f64 #s(literal 2 binary64) n) (PI.f64)) (fma.f64 #s(literal -1/2 binary64) k #s(literal 1/2 binary64))) (sqrt.f64 (/.f64 #s(literal 1 binary64) k))))
▶	39.6%	#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (.f64 (sqrt.f64 #s(literal 2 binary64)) (sqrt.f64 (/.f64 (.f64 (PI.f64) n) k))))

Compiler

Compiled 936 to 724 computations (22.6% saved)

simplify428.0ms (4.9%)

Memory

13.0MiB live, 92.8MiB allocated

Algorithm

1×	egg-herbie

Localize:

Found 20 expressions of interest:

New	Metric	Score
cost-diff	0	#s(approx (pow (* (* 2 (PI)) n) (/ (- 1 k) 2)) (.f64 (fma.f64 (log.f64 (.f64 (.f64 #s(literal 2 binary64) n) (PI.f64))) (.f64 #s(literal -1/2 binary64) k) #s(literal 1 binary64)) (.f64 (sqrt.f64 (.f64 (PI.f64) n)) (sqrt.f64 #s(literal 2 binary64)))))
cost-diff	0	(sqrt.f64 k)
cost-diff	0	(/.f64 #s(literal 1 binary64) (sqrt.f64 k))
cost-diff	320	(.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) #s(approx (pow ( (* 2 (PI)) n) (/ (- 1 k) 2)) (.f64 (fma.f64 (log.f64 (.f64 (.f64 #s(literal 2 binary64) n) (PI.f64))) (.f64 #s(literal -1/2 binary64) k) #s(literal 1 binary64)) (.f64 (sqrt.f64 (.f64 (PI.f64) n)) (sqrt.f64 #s(literal 2 binary64))))))
cost-diff	0	(sqrt.f64 k)
cost-diff	0	(/.f64 #s(literal 1 binary64) (sqrt.f64 k))
cost-diff	320	(.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) #s(approx (pow ( (* 2 (PI)) n) (/ (- 1 k) 2)) (pow.f64 (/.f64 (*.f64 #s(literal -2 binary64) (PI.f64)) (/.f64 #s(literal -1 binary64) n)) (fma.f64 #s(literal -1/2 binary64) k #s(literal 1/2 binary64)))))
cost-diff	1088	(/.f64 (*.f64 #s(literal -2 binary64) (PI.f64)) (/.f64 #s(literal -1 binary64) n))
cost-diff	0	(pow.f64 (.f64 (.f64 #s(literal 2 binary64) (PI.f64)) n) #s(approx (/ (- 1 k) 2) (*.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) #s(approx (/ (- 1 k) 2) (.f64 #s(literal -1/2 binary64) k))))
cost-diff	0	(sqrt.f64 (/.f64 (*.f64 (PI.f64) n) k))
cost-diff	0	(sqrt.f64 #s(literal 2 binary64))
cost-diff	0	(.f64 (sqrt.f64 #s(literal 2 binary64)) (sqrt.f64 (/.f64 (.f64 (PI.f64) n) k)))
cost-diff	0	#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (.f64 (sqrt.f64 #s(literal 2 binary64)) (sqrt.f64 (/.f64 (.f64 (PI.f64) n) k))))
cost-diff	0	(.f64 (.f64 #s(literal 2 binary64) n) (PI.f64))
cost-diff	0	(pow.f64 (.f64 (.f64 #s(literal 2 binary64) n) (PI.f64)) (fma.f64 #s(literal -1/2 binary64) k #s(literal 1/2 binary64)))
cost-diff	0	(.f64 (pow.f64 (.f64 (*.f64 #s(literal 2 binary64) n) (PI.f64)) (fma.f64 #s(literal -1/2 binary64) k #s(literal 1/2 binary64))) (sqrt.f64 (/.f64 #s(literal 1 binary64) k)))
cost-diff	0	#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (.f64 (pow.f64 (.f64 (*.f64 #s(literal 2 binary64) n) (PI.f64)) (fma.f64 #s(literal -1/2 binary64) k #s(literal 1/2 binary64))) (sqrt.f64 (/.f64 #s(literal 1 binary64) k))))

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	53	443
0	85	439
1	133	425
2	190	425
3	292	416
4	514	416
5	964	416
6	1485	416
7	2182	416
8	2751	416
9	3021	416
10	3120	416
11	3623	416
12	4024	416
13	4057	416
14	4206	416
15	4364	416
16	4520	416
17	4976	416
18	5288	416
19	5614	416
20	5686	416
21	5690	416
22	5754	416
23	5754	416
24	5774	416
25	5782	416
26	5782	416
27	6298	416
28	6818	416
29	7496	416
30	7496	416
31	7496	416
32	7512	416
33	7512	416
34	7552	416
35	7577	416
36	7577	416
0	7577	416

Stop Event

1×	iter limit
1×	saturated
1×	iter limit

Calls

Call 1

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

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

localize197.0ms (2.2%)

Memory

7.9MiB live, 245.1MiB allocated

Localize:

Found 20 expressions of interest:

New	Metric	Score
accuracy	0.3960267850710212	(.f64 (fma.f64 (log.f64 (.f64 (.f64 #s(literal 2 binary64) n) (PI.f64))) (.f64 #s(literal -1/2 binary64) k) #s(literal 1 binary64)) (.f64 (sqrt.f64 (.f64 (PI.f64) n)) (sqrt.f64 #s(literal 2 binary64))))
accuracy	0.4264450195368841	(.f64 (sqrt.f64 (.f64 (PI.f64) n)) (sqrt.f64 #s(literal 2 binary64)))
accuracy	0.4881774433277768	(log.f64 (.f64 (.f64 #s(literal 2 binary64) n) (PI.f64)))
accuracy	31.841095551842415	#s(approx (pow (* (* 2 (PI)) n) (/ (- 1 k) 2)) (.f64 (fma.f64 (log.f64 (.f64 (.f64 #s(literal 2 binary64) n) (PI.f64))) (.f64 #s(literal -1/2 binary64) k) #s(literal 1 binary64)) (.f64 (sqrt.f64 (.f64 (PI.f64) n)) (sqrt.f64 #s(literal 2 binary64)))))
accuracy	0.178066259768442	(.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) #s(approx (pow ( (* 2 (PI)) n) (/ (- 1 k) 2)) (pow.f64 (/.f64 (*.f64 #s(literal -2 binary64) (PI.f64)) (/.f64 #s(literal -1 binary64) n)) (fma.f64 #s(literal -1/2 binary64) k #s(literal 1/2 binary64)))))
accuracy	0.23046875	(/.f64 #s(literal 1 binary64) (sqrt.f64 k))
accuracy	0.3046875	(/.f64 (*.f64 #s(literal -2 binary64) (PI.f64)) (/.f64 #s(literal -1 binary64) n))
accuracy	0.4841279054325469	(pow.f64 (/.f64 (*.f64 #s(literal -2 binary64) (PI.f64)) (/.f64 #s(literal -1 binary64) n)) (fma.f64 #s(literal -1/2 binary64) k #s(literal 1/2 binary64)))
accuracy	0.22265625	(.f64 (.f64 #s(literal 2 binary64) (PI.f64)) n)
accuracy	0.23046875	(/.f64 #s(literal 1 binary64) (sqrt.f64 k))
accuracy	0.4841279054325469	(pow.f64 (.f64 (.f64 #s(literal 2 binary64) (PI.f64)) n) #s(approx (/ (- 1 k) 2) (*.f64 #s(literal -1/2 binary64) k)))
accuracy	31.73171871616694	#s(approx (/ (- 1 k) 2) (*.f64 #s(literal -1/2 binary64) k))
accuracy	0.42026665918309214	(/.f64 (*.f64 (PI.f64) n) k)
accuracy	0.4388275390737681	(.f64 (sqrt.f64 #s(literal 2 binary64)) (sqrt.f64 (/.f64 (.f64 (PI.f64) n) k)))
accuracy	12.115895492202384	(sqrt.f64 (/.f64 (*.f64 (PI.f64) n) k))
accuracy	32.6099459769306	#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (.f64 (sqrt.f64 #s(literal 2 binary64)) (sqrt.f64 (/.f64 (.f64 (PI.f64) n) k))))
accuracy	0.125	(sqrt.f64 (/.f64 #s(literal 1 binary64) k))
accuracy	0.178066259768442	(.f64 (pow.f64 (.f64 (*.f64 #s(literal 2 binary64) n) (PI.f64)) (fma.f64 #s(literal -1/2 binary64) k #s(literal 1/2 binary64))) (sqrt.f64 (/.f64 #s(literal 1 binary64) k)))
accuracy	0.22265625	(.f64 (.f64 #s(literal 2 binary64) n) (PI.f64))
accuracy	0.4841279054325469	(pow.f64 (.f64 (.f64 #s(literal 2 binary64) n) (PI.f64)) (fma.f64 #s(literal -1/2 binary64) k #s(literal 1/2 binary64)))

Samples

159.0ms

256×

valid

Compiler

Compiled 791 to 97 computations (87.7% saved)

Precisions

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

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

ival-mult: 22.0ms (24.4% of total)

ival-pow: 22.0ms (24.4% of total)

ival-sqrt: 9.0ms (10% of total)

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

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

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

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

exact: 1.0ms (1.1% of total)

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

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

series74.0ms (0.8%)

Memory

-12.2MiB live, 111.0MiB allocated

Counts

24 → 54

Calls

Call 1

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

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

Calls

6 calls:

Time	Variable		Point	Expression
28.0ms	n	@	inf	((* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (* (pow (* (* 2 n) (PI)) (+ (* -1/2 k) 1/2)) (sqrt (/ 1 k))) (pow (* (* 2 n) (PI)) (+ (* -1/2 k) 1/2)) (* (* 2 n) (PI)) (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (* (sqrt 2) (sqrt (/ (* (PI) n) k))) (sqrt 2) (sqrt (/ (* (PI) n) k)) (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (/ 1 (sqrt k)) (sqrt k) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2)) (/ (* -2 (PI)) (/ -1 n)) (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2)) (sqrt (/ 1 k)) (/ (* (PI) n) k) (/ (- 1 k) 2) (* (* 2 (PI)) n) (pow (/ (* -2 (PI)) (/ -1 n)) (+ (* -1/2 k) 1/2)) (log (* (* 2 n) (PI))) (* (sqrt (* (PI) n)) (sqrt 2)) (* (+ (* (log (* (* 2 n) (PI))) (* -1/2 k)) 1) (* (sqrt (* (PI) n)) (sqrt 2))))
13.0ms	n	@	0	((* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (* (pow (* (* 2 n) (PI)) (+ (* -1/2 k) 1/2)) (sqrt (/ 1 k))) (pow (* (* 2 n) (PI)) (+ (* -1/2 k) 1/2)) (* (* 2 n) (PI)) (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (* (sqrt 2) (sqrt (/ (* (PI) n) k))) (sqrt 2) (sqrt (/ (* (PI) n) k)) (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (/ 1 (sqrt k)) (sqrt k) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2)) (/ (* -2 (PI)) (/ -1 n)) (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2)) (sqrt (/ 1 k)) (/ (* (PI) n) k) (/ (- 1 k) 2) (* (* 2 (PI)) n) (pow (/ (* -2 (PI)) (/ -1 n)) (+ (* -1/2 k) 1/2)) (log (* (* 2 n) (PI))) (* (sqrt (* (PI) n)) (sqrt 2)) (* (+ (* (log (* (* 2 n) (PI))) (* -1/2 k)) 1) (* (sqrt (* (PI) n)) (sqrt 2))))
12.0ms	n	@	-inf	((* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (* (pow (* (* 2 n) (PI)) (+ (* -1/2 k) 1/2)) (sqrt (/ 1 k))) (pow (* (* 2 n) (PI)) (+ (* -1/2 k) 1/2)) (* (* 2 n) (PI)) (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (* (sqrt 2) (sqrt (/ (* (PI) n) k))) (sqrt 2) (sqrt (/ (* (PI) n) k)) (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (/ 1 (sqrt k)) (sqrt k) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2)) (/ (* -2 (PI)) (/ -1 n)) (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2)) (sqrt (/ 1 k)) (/ (* (PI) n) k) (/ (- 1 k) 2) (* (* 2 (PI)) n) (pow (/ (* -2 (PI)) (/ -1 n)) (+ (* -1/2 k) 1/2)) (log (* (* 2 n) (PI))) (* (sqrt (* (PI) n)) (sqrt 2)) (* (+ (* (log (* (* 2 n) (PI))) (* -1/2 k)) 1) (* (sqrt (* (PI) n)) (sqrt 2))))
9.0ms	k	@	0	((* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (* (pow (* (* 2 n) (PI)) (+ (* -1/2 k) 1/2)) (sqrt (/ 1 k))) (pow (* (* 2 n) (PI)) (+ (* -1/2 k) 1/2)) (* (* 2 n) (PI)) (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (* (sqrt 2) (sqrt (/ (* (PI) n) k))) (sqrt 2) (sqrt (/ (* (PI) n) k)) (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (/ 1 (sqrt k)) (sqrt k) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2)) (/ (* -2 (PI)) (/ -1 n)) (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2)) (sqrt (/ 1 k)) (/ (* (PI) n) k) (/ (- 1 k) 2) (* (* 2 (PI)) n) (pow (/ (* -2 (PI)) (/ -1 n)) (+ (* -1/2 k) 1/2)) (log (* (* 2 n) (PI))) (* (sqrt (* (PI) n)) (sqrt 2)) (* (+ (* (log (* (* 2 n) (PI))) (* -1/2 k)) 1) (* (sqrt (* (PI) n)) (sqrt 2))))
6.0ms	k	@	-inf	((* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (* (pow (* (* 2 n) (PI)) (+ (* -1/2 k) 1/2)) (sqrt (/ 1 k))) (pow (* (* 2 n) (PI)) (+ (* -1/2 k) 1/2)) (* (* 2 n) (PI)) (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (* (sqrt 2) (sqrt (/ (* (PI) n) k))) (sqrt 2) (sqrt (/ (* (PI) n) k)) (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (/ 1 (sqrt k)) (sqrt k) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2)) (/ (* -2 (PI)) (/ -1 n)) (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2)) (sqrt (/ 1 k)) (/ (* (PI) n) k) (/ (- 1 k) 2) (* (* 2 (PI)) n) (pow (/ (* -2 (PI)) (/ -1 n)) (+ (* -1/2 k) 1/2)) (log (* (* 2 n) (PI))) (* (sqrt (* (PI) n)) (sqrt 2)) (* (+ (* (log (* (* 2 n) (PI))) (* -1/2 k)) 1) (* (sqrt (* (PI) n)) (sqrt 2))))

simplify124.0ms (1.4%)

Memory

2.7MiB live, 161.0MiB allocated

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	180	916
1	545	871
2	1878	797
3	3981	779
0	8242	759

Stop Event

1×	iter limit
1×	node limit

Counts

54 → 54

Calls

Call 1

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

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

rewrite157.0ms (1.8%)

Memory

-19.5MiB live, 226.0MiB allocated

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	53	316
0	85	306
1	278	288
2	1590	283
0	8392	283

Stop Event

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

Counts

24 → 806

Calls

Call 1

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

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

eval125.0ms (1.4%)

Memory: 26.2MiB live, 137.3MiB allocated
Compiler: Compiled 29 921 to 3 069 computations (89.7% saved)

prune80.0ms (0.9%)

Memory

-14.4MiB live, 65.4MiB allocated

Pruning

29 alts after pruning (26 fresh and 3 done)

	Pruned	Kept	Total
New	800	23	823
Fresh	11	3	14
Picked	2	3	5
Done	0	0	0
Total	813	29	842

Accuracy

100.0%

Counts

842 → 29

Alt Table

Click to see full alt table

Status	Accuracy	Program
▶	54.3%	(/.f64 (pow.f64 (.f64 (PI.f64) (.f64 n #s(literal 2 binary64))) #s(approx (/ (- 1 k) 2) (*.f64 #s(literal -1/2 binary64) k))) (sqrt.f64 k))
▶	99.1%	(/.f64 #s(approx (pow (* (* 2 (PI)) n) (/ (- 1 k) 2)) (pow.f64 (.f64 (PI.f64) (.f64 n #s(literal 2 binary64))) (fma.f64 #s(literal -1/2 binary64) k #s(literal 1/2 binary64)))) (sqrt.f64 k))
	49.9%	(/.f64 #s(approx (pow (* (* 2 (PI)) n) (/ (- 1 k) 2)) (.f64 (sqrt.f64 (.f64 (PI.f64) (.f64 n #s(literal 2 binary64)))) (fma.f64 (log.f64 (.f64 (PI.f64) (.f64 n #s(literal 2 binary64)))) (.f64 #s(literal -1/2 binary64) k) #s(literal 1 binary64)))) (sqrt.f64 k))
	99.0%	(/.f64 #s(literal 1 binary64) (/.f64 (sqrt.f64 k) #s(approx (pow (* (* 2 (PI)) n) (/ (- 1 k) 2)) (pow.f64 (.f64 (PI.f64) (.f64 n #s(literal 2 binary64))) (fma.f64 #s(literal -1/2 binary64) k #s(literal 1/2 binary64))))))
	99.0%	(.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) (/.f64 #s(literal 1 binary64) (pow.f64 (sqrt.f64 (.f64 n (*.f64 (PI.f64) #s(literal 2 binary64)))) (-.f64 k #s(literal 1 binary64)))))
	98.9%	(.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) (.f64 (pow.f64 (.f64 n (.f64 (PI.f64) #s(literal 2 binary64))) (.f64 k #s(literal -1/2 binary64))) (sqrt.f64 (.f64 n (*.f64 (PI.f64) #s(literal 2 binary64))))))
✓	99.0%	(.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) #s(approx (pow ( (* 2 (PI)) n) (/ (- 1 k) 2)) (pow.f64 (/.f64 (*.f64 #s(literal -2 binary64) (PI.f64)) (/.f64 #s(literal -1 binary64) n)) (fma.f64 #s(literal -1/2 binary64) k #s(literal 1/2 binary64)))))
	48.7%	(.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) #s(approx (pow ( (* 2 (PI)) n) (/ (- 1 k) 2)) (.f64 (sqrt.f64 (.f64 (PI.f64) n)) (sqrt.f64 #s(literal 2 binary64)))))
	50.5%	#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (/.f64 (.f64 (sqrt.f64 #s(literal 2 binary64)) (fma.f64 (.f64 (log.f64 (.f64 (.f64 n (PI.f64)) #s(literal 2 binary64))) (sqrt.f64 (.f64 (.f64 (pow.f64 k #s(literal 3 binary64)) (PI.f64)) n))) #s(literal -1/2 binary64) (sqrt.f64 (.f64 (.f64 n (PI.f64)) k)))) k))
	48.5%	#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (/.f64 (sqrt.f64 (.f64 (PI.f64) (.f64 n #s(literal 2 binary64)))) (sqrt.f64 k)))
	40.1%	#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (/.f64 (sqrt.f64 #s(literal 2 binary64)) (sqrt.f64 (/.f64 k (*.f64 (PI.f64) n)))))
	48.4%	#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (/.f64 #s(literal 1 binary64) (/.f64 (sqrt.f64 k) (sqrt.f64 (.f64 (PI.f64) (.f64 n #s(literal 2 binary64)))))))
✓	99.1%	#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (.f64 (pow.f64 (.f64 (*.f64 #s(literal 2 binary64) n) (PI.f64)) (fma.f64 #s(literal -1/2 binary64) k #s(literal 1/2 binary64))) (sqrt.f64 (/.f64 #s(literal 1 binary64) k))))
	98.9%	#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (.f64 (pow.f64 (.f64 k (pow.f64 (.f64 (PI.f64) (.f64 n #s(literal 2 binary64))) k)) #s(literal -1/2 binary64)) (sqrt.f64 (.f64 (PI.f64) (.f64 n #s(literal 2 binary64))))))
	48.6%	#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (.f64 (/.f64 (sqrt.f64 (.f64 (PI.f64) #s(literal 2 binary64))) (sqrt.f64 k)) (/.f64 (sqrt.f64 n) #s(literal 1 binary64))))
	48.6%	#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (.f64 (/.f64 (sqrt.f64 (.f64 n #s(literal 2 binary64))) (sqrt.f64 k)) (/.f64 (sqrt.f64 (PI.f64)) #s(literal 1 binary64))))
	48.6%	#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (.f64 (/.f64 (sqrt.f64 (PI.f64)) (sqrt.f64 k)) (/.f64 (sqrt.f64 (.f64 n #s(literal 2 binary64))) #s(literal 1 binary64))))
▶	48.7%	#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (.f64 (/.f64 (sqrt.f64 #s(literal 2 binary64)) (sqrt.f64 k)) (/.f64 (sqrt.f64 (.f64 (PI.f64) n)) #s(literal 1 binary64))))
	48.4%	#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (.f64 (sqrt.f64 (.f64 (PI.f64) (*.f64 n #s(literal 2 binary64)))) (pow.f64 k #s(literal -1/2 binary64))))
	39.5%	#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (.f64 (sqrt.f64 (.f64 (PI.f64) #s(literal 2 binary64))) (sqrt.f64 (/.f64 n k))))
▶	48.7%	#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (.f64 (sqrt.f64 #s(literal 2 binary64)) (/.f64 (sqrt.f64 (.f64 (PI.f64) n)) (sqrt.f64 k))))
	40.1%	#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (.f64 (sqrt.f64 #s(literal 2 binary64)) (/.f64 #s(literal 1 binary64) (sqrt.f64 (/.f64 k (.f64 (PI.f64) n))))))
	48.7%	#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (.f64 (sqrt.f64 #s(literal 2 binary64)) (.f64 (pow.f64 k #s(literal -1/2 binary64)) (sqrt.f64 (*.f64 (PI.f64) n)))))
	48.7%	#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (.f64 (sqrt.f64 #s(literal 2 binary64)) (.f64 (sqrt.f64 n) (sqrt.f64 (/.f64 (PI.f64) k)))))
✓	39.6%	#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (.f64 (sqrt.f64 #s(literal 2 binary64)) (sqrt.f64 (/.f64 (.f64 (PI.f64) n) k))))
	39.6%	#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (.f64 (sqrt.f64 #s(literal 2 binary64)) (sqrt.f64 (/.f64 #s(literal 1 binary64) (/.f64 k (.f64 (PI.f64) n))))))
	39.6%	#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (.f64 (sqrt.f64 #s(literal 2 binary64)) (sqrt.f64 (.f64 (/.f64 n k) (PI.f64)))))
	48.7%	#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (.f64 #s(approx (pow ( (* 2 n) (PI)) (+ (* -1/2 k) 1/2)) (.f64 (sqrt.f64 (.f64 n (PI.f64))) (sqrt.f64 #s(literal 2 binary64)))) (sqrt.f64 (/.f64 #s(literal 1 binary64) k))))
▶	39.7%	#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt.f64 (.f64 (/.f64 (.f64 (PI.f64) n) k) #s(literal 2 binary64))))

Compiler

Compiled 1 535 to 1 232 computations (19.7% saved)

simplify11.0ms (0.1%)

Memory

2.0MiB live, 2.0MiB allocated

Algorithm

1×	egg-herbie

Localize:

Found 20 expressions of interest:

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

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	41	316
0	62	310
1	93	304
2	129	304
3	166	296
4	205	296
5	219	296
6	240	296
7	267	296
8	276	296
9	279	296
0	279	296

Stop Event

1×	iter limit
1×	saturated
1×	iter limit

Calls

Call 1

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

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

localize192.0ms (2.2%)

Memory

-22.3MiB live, 102.7MiB allocated

Localize:

Found 20 expressions of interest:

New	Metric	Score
accuracy	0.16015625	(/.f64 (pow.f64 (.f64 (PI.f64) (.f64 n #s(literal 2 binary64))) #s(approx (/ (- 1 k) 2) (*.f64 #s(literal -1/2 binary64) k))) (sqrt.f64 k))
accuracy	0.22265625	(.f64 (PI.f64) (.f64 n #s(literal 2 binary64)))
accuracy	0.4841279054325469	(pow.f64 (.f64 (PI.f64) (.f64 n #s(literal 2 binary64))) #s(approx (/ (- 1 k) 2) (*.f64 #s(literal -1/2 binary64) k)))
accuracy	31.73171871616694	#s(approx (/ (- 1 k) 2) (*.f64 #s(literal -1/2 binary64) k))
accuracy	0.3388862793053261	(.f64 (/.f64 (sqrt.f64 #s(literal 2 binary64)) (sqrt.f64 k)) (/.f64 (sqrt.f64 (.f64 (PI.f64) n)) #s(literal 1 binary64)))
accuracy	0.3671875	(/.f64 (sqrt.f64 #s(literal 2 binary64)) (sqrt.f64 k))
accuracy	0.38671601768998964	(sqrt.f64 (*.f64 (PI.f64) n))
accuracy	32.6099459769306	#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (.f64 (/.f64 (sqrt.f64 #s(literal 2 binary64)) (sqrt.f64 k)) (/.f64 (sqrt.f64 (.f64 (PI.f64) n)) #s(literal 1 binary64))))
accuracy	0.359375	(/.f64 (sqrt.f64 (*.f64 (PI.f64) n)) (sqrt.f64 k))
accuracy	0.38671601768998964	(sqrt.f64 (*.f64 (PI.f64) n))
accuracy	0.4388275390737681	(.f64 (sqrt.f64 #s(literal 2 binary64)) (/.f64 (sqrt.f64 (.f64 (PI.f64) n)) (sqrt.f64 k)))
accuracy	32.6099459769306	#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (.f64 (sqrt.f64 #s(literal 2 binary64)) (/.f64 (sqrt.f64 (.f64 (PI.f64) n)) (sqrt.f64 k))))
accuracy	0.22265625	(*.f64 (PI.f64) n)
accuracy	0.42026665918309214	(/.f64 (*.f64 (PI.f64) n) k)
accuracy	12.072893065940132	(sqrt.f64 (.f64 (/.f64 (.f64 (PI.f64) n) k) #s(literal 2 binary64)))
accuracy	32.6099459769306	#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt.f64 (.f64 (/.f64 (.f64 (PI.f64) n) k) #s(literal 2 binary64))))
accuracy	0.0	#s(approx (pow (* (* 2 (PI)) n) (/ (- 1 k) 2)) (pow.f64 (.f64 (PI.f64) (.f64 n #s(literal 2 binary64))) (fma.f64 #s(literal -1/2 binary64) k #s(literal 1/2 binary64))))
accuracy	0.16015625	(/.f64 #s(approx (pow (* (* 2 (PI)) n) (/ (- 1 k) 2)) (pow.f64 (.f64 (PI.f64) (.f64 n #s(literal 2 binary64))) (fma.f64 #s(literal -1/2 binary64) k #s(literal 1/2 binary64)))) (sqrt.f64 k))
accuracy	0.22265625	(.f64 (PI.f64) (.f64 n #s(literal 2 binary64)))
accuracy	0.4841279054325469	(pow.f64 (.f64 (PI.f64) (.f64 n #s(literal 2 binary64))) (fma.f64 #s(literal -1/2 binary64) k #s(literal 1/2 binary64)))

Samples

138.0ms

256×

valid

Compiler

Compiled 569 to 79 computations (86.1% saved)

Precisions

Click to see histograms. Total time spent on operations: 118.0ms

ival-mult: 53.0ms (44.9% of total)

ival-pow: 41.0ms (34.7% of total)

ival-div: 13.0ms (11% of total)

ival-sqrt: 7.0ms (5.9% of total)

ival-pi: 1.0ms (0.8% of total)

ival-add: 1.0ms (0.8% of total)

ival-sub: 1.0ms (0.8% of total)

exact: 1.0ms (0.8% of total)

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

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

series70.0ms (0.8%)

Memory

7.0MiB live, 43.3MiB allocated

Counts

22 → 40

Calls

Call 1

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

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

Calls

6 calls:

Time	Variable		Point	Expression
41.0ms	n	@	-inf	((/ (pow (* (* 2 (PI)) n) (/ (- 1 k) 2)) (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2)) (pow (* (PI) (* n 2)) (+ (* -1/2 k) 1/2)) (* (PI) (* n 2)) (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt (* (/ (* (PI) n) k) 2)) (* (/ (* (PI) n) k) 2) (/ (* (PI) n) k) (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (* (sqrt 2) (/ (sqrt (* (PI) n)) (sqrt k))) (sqrt 2) (/ (sqrt (* (PI) n)) (sqrt k)) (/ (sqrt (* (PI) n)) 1) (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (* (/ (sqrt 2) (sqrt k)) (/ (sqrt (* (PI) n)) 1)) (/ (sqrt 2) (sqrt k)) (/ (pow (* (PI) (* n 2)) (/ (- 1 k) 2)) (sqrt k)) (pow (* (PI) (* n 2)) (/ (- 1 k) 2)) (PI) (* (PI) n) (sqrt (* (PI) n)) (/ (- 1 k) 2))
10.0ms	n	@	0	((/ (pow (* (* 2 (PI)) n) (/ (- 1 k) 2)) (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2)) (pow (* (PI) (* n 2)) (+ (* -1/2 k) 1/2)) (* (PI) (* n 2)) (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt (* (/ (* (PI) n) k) 2)) (* (/ (* (PI) n) k) 2) (/ (* (PI) n) k) (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (* (sqrt 2) (/ (sqrt (* (PI) n)) (sqrt k))) (sqrt 2) (/ (sqrt (* (PI) n)) (sqrt k)) (/ (sqrt (* (PI) n)) 1) (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (* (/ (sqrt 2) (sqrt k)) (/ (sqrt (* (PI) n)) 1)) (/ (sqrt 2) (sqrt k)) (/ (pow (* (PI) (* n 2)) (/ (- 1 k) 2)) (sqrt k)) (pow (* (PI) (* n 2)) (/ (- 1 k) 2)) (PI) (* (PI) n) (sqrt (* (PI) n)) (/ (- 1 k) 2))
10.0ms	n	@	inf	((/ (pow (* (* 2 (PI)) n) (/ (- 1 k) 2)) (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2)) (pow (* (PI) (* n 2)) (+ (* -1/2 k) 1/2)) (* (PI) (* n 2)) (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt (* (/ (* (PI) n) k) 2)) (* (/ (* (PI) n) k) 2) (/ (* (PI) n) k) (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (* (sqrt 2) (/ (sqrt (* (PI) n)) (sqrt k))) (sqrt 2) (/ (sqrt (* (PI) n)) (sqrt k)) (/ (sqrt (* (PI) n)) 1) (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (* (/ (sqrt 2) (sqrt k)) (/ (sqrt (* (PI) n)) 1)) (/ (sqrt 2) (sqrt k)) (/ (pow (* (PI) (* n 2)) (/ (- 1 k) 2)) (sqrt k)) (pow (* (PI) (* n 2)) (/ (- 1 k) 2)) (PI) (* (PI) n) (sqrt (* (PI) n)) (/ (- 1 k) 2))
4.0ms	k	@	-inf	((/ (pow (* (* 2 (PI)) n) (/ (- 1 k) 2)) (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2)) (pow (* (PI) (* n 2)) (+ (* -1/2 k) 1/2)) (* (PI) (* n 2)) (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt (* (/ (* (PI) n) k) 2)) (* (/ (* (PI) n) k) 2) (/ (* (PI) n) k) (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (* (sqrt 2) (/ (sqrt (* (PI) n)) (sqrt k))) (sqrt 2) (/ (sqrt (* (PI) n)) (sqrt k)) (/ (sqrt (* (PI) n)) 1) (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (* (/ (sqrt 2) (sqrt k)) (/ (sqrt (* (PI) n)) 1)) (/ (sqrt 2) (sqrt k)) (/ (pow (* (PI) (* n 2)) (/ (- 1 k) 2)) (sqrt k)) (pow (* (PI) (* n 2)) (/ (- 1 k) 2)) (PI) (* (PI) n) (sqrt (* (PI) n)) (/ (- 1 k) 2))
2.0ms	k	@	0	((/ (pow (* (* 2 (PI)) n) (/ (- 1 k) 2)) (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2)) (pow (* (PI) (* n 2)) (+ (* -1/2 k) 1/2)) (* (PI) (* n 2)) (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt (* (/ (* (PI) n) k) 2)) (* (/ (* (PI) n) k) 2) (/ (* (PI) n) k) (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (* (sqrt 2) (/ (sqrt (* (PI) n)) (sqrt k))) (sqrt 2) (/ (sqrt (* (PI) n)) (sqrt k)) (/ (sqrt (* (PI) n)) 1) (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (* (/ (sqrt 2) (sqrt k)) (/ (sqrt (* (PI) n)) 1)) (/ (sqrt 2) (sqrt k)) (/ (pow (* (PI) (* n 2)) (/ (- 1 k) 2)) (sqrt k)) (pow (* (PI) (* n 2)) (/ (- 1 k) 2)) (PI) (* (PI) n) (sqrt (* (PI) n)) (/ (- 1 k) 2))

simplify152.0ms (1.7%)

Memory

33.9MiB live, 106.7MiB allocated

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	150	654
1	425	640
2	1361	583
3	2701	568
4	5034	568
0	8450	553

Stop Event

1×	iter limit
1×	node limit

Counts

40 → 40

Calls

Call 1

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

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

rewrite220.0ms (2.5%)

Memory

6.7MiB live, 163.1MiB allocated

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	41	255
0	62	239
1	221	233
2	1297	225
0	8629	225

Stop Event

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

Counts

22 → 1 017

Calls

Call 1

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

Outputs
(.f64 (pow.f64 (/.f64 (sqrt.f64 k) #s(approx (pow ( (* 2 (PI)) n) (/ (- 1 k) 2)) (pow.f64 (.f64 (.f64 n #s(literal 2 binary64)) (PI.f64)) (fma.f64 #s(literal -1/2 binary64) k #s(literal 1/2 binary64))))) #s(literal -1/2 binary64)) (pow.f64 (/.f64 (sqrt.f64 k) #s(approx (pow (* (* 2 (PI)) n) (/ (- 1 k) 2)) (pow.f64 (.f64 (.f64 n #s(literal 2 binary64)) (PI.f64)) (fma.f64 #s(literal -1/2 binary64) k #s(literal 1/2 binary64))))) #s(literal -1/2 binary64)))
(.f64 (/.f64 #s(approx (pow ( (* 2 (PI)) n) (/ (- 1 k) 2)) (pow.f64 (.f64 (.f64 n #s(literal 2 binary64)) (PI.f64)) (fma.f64 #s(literal -1/2 binary64) k #s(literal 1/2 binary64)))) #s(literal -1 binary64)) (/.f64 #s(literal -1 binary64) (sqrt.f64 k)))
(.f64 (/.f64 #s(approx (pow ( (* 2 (PI)) n) (/ (- 1 k) 2)) (pow.f64 (.f64 (.f64 n #s(literal 2 binary64)) (PI.f64)) (fma.f64 #s(literal -1/2 binary64) k #s(literal 1/2 binary64)))) (pow.f64 k #s(literal 1/4 binary64))) (/.f64 #s(literal 1 binary64) (pow.f64 k #s(literal 1/4 binary64))))
(.f64 (/.f64 #s(approx (pow ( (* 2 (PI)) n) (/ (- 1 k) 2)) (pow.f64 (.f64 (.f64 n #s(literal 2 binary64)) (PI.f64)) (fma.f64 #s(literal -1/2 binary64) k #s(literal 1/2 binary64)))) #s(literal 1 binary64)) (pow.f64 k #s(literal -1/2 binary64)))
(.f64 (.f64 #s(approx (pow (* (* 2 (PI)) n) (/ (- 1 k) 2)) (pow.f64 (.f64 (.f64 n #s(literal 2 binary64)) (PI.f64)) (fma.f64 #s(literal -1/2 binary64) k #s(literal 1/2 binary64)))) #s(literal -1 binary64)) (/.f64 #s(literal -1 binary64) (sqrt.f64 k)))
(.f64 (neg.f64 #s(approx (pow ( (* 2 (PI)) n) (/ (- 1 k) 2)) (pow.f64 (.f64 (.f64 n #s(literal 2 binary64)) (PI.f64)) (fma.f64 #s(literal -1/2 binary64) k #s(literal 1/2 binary64))))) (/.f64 #s(literal -1 binary64) (sqrt.f64 k)))
(.f64 #s(literal -1 binary64) (/.f64 #s(literal 1 binary64) (neg.f64 (/.f64 (sqrt.f64 k) #s(approx (pow ( (* 2 (PI)) n) (/ (- 1 k) 2)) (pow.f64 (.f64 (.f64 n #s(literal 2 binary64)) (PI.f64)) (fma.f64 #s(literal -1/2 binary64) k #s(literal 1/2 binary64))))))))
(.f64 #s(literal -1 binary64) (/.f64 #s(approx (pow ( (* 2 (PI)) n) (/ (- 1 k) 2)) (pow.f64 (.f64 (.f64 n #s(literal 2 binary64)) (PI.f64)) (fma.f64 #s(literal -1/2 binary64) k #s(literal 1/2 binary64)))) (neg.f64 (sqrt.f64 k))))
(.f64 (pow.f64 k #s(literal -1/2 binary64)) (pow.f64 (pow.f64 #s(approx (pow ( (* 2 (PI)) n) (/ (- 1 k) 2)) (pow.f64 (.f64 (.f64 n #s(literal 2 binary64)) (PI.f64)) (fma.f64 #s(literal -1/2 binary64) k #s(literal 1/2 binary64)))) #s(literal -1 binary64)) #s(literal -1 binary64)))
(.f64 (pow.f64 k #s(literal -1/2 binary64)) #s(approx (pow ( (* 2 (PI)) n) (/ (- 1 k) 2)) (pow.f64 (.f64 (.f64 n #s(literal 2 binary64)) (PI.f64)) (fma.f64 #s(literal -1/2 binary64) k #s(literal 1/2 binary64)))))
(.f64 (/.f64 #s(approx (pow ( (* 2 (PI)) n) (/ (- 1 k) 2)) (pow.f64 (.f64 (.f64 n #s(literal 2 binary64)) (PI.f64)) (fma.f64 #s(literal -1/2 binary64) k #s(literal 1/2 binary64)))) (sqrt.f64 k)) #s(literal 1 binary64))
(.f64 #s(approx (pow ( (* 2 (PI)) n) (/ (- 1 k) 2)) (pow.f64 (.f64 (.f64 n #s(literal 2 binary64)) (PI.f64)) (fma.f64 #s(literal -1/2 binary64) k #s(literal 1/2 binary64)))) (pow.f64 k #s(literal -1/2 binary64)))
(.f64 #s(literal 1 binary64) (/.f64 #s(approx (pow ( (* 2 (PI)) n) (/ (- 1 k) 2)) (pow.f64 (.f64 (.f64 n #s(literal 2 binary64)) (PI.f64)) (fma.f64 #s(literal -1/2 binary64) k #s(literal 1/2 binary64)))) (sqrt.f64 k)))
(pow.f64 (/.f64 (sqrt.f64 k) #s(approx (pow (* (* 2 (PI)) n) (/ (- 1 k) 2)) (pow.f64 (.f64 (.f64 n #s(literal 2 binary64)) (PI.f64)) (fma.f64 #s(literal -1/2 binary64) k #s(literal 1/2 binary64))))) #s(literal -1 binary64))
(/.f64 (neg.f64 (.f64 #s(approx (pow ( (* 2 (PI)) n) (/ (- 1 k) 2)) (pow.f64 (.f64 (.f64 n #s(literal 2 binary64)) (PI.f64)) (fma.f64 #s(literal -1/2 binary64) k #s(literal 1/2 binary64)))) #s(literal -1 binary64))) (sqrt.f64 k))
(/.f64 (.f64 #s(approx (pow ( (* 2 (PI)) n) (/ (- 1 k) 2)) (pow.f64 (.f64 (.f64 n #s(literal 2 binary64)) (PI.f64)) (fma.f64 #s(literal -1/2 binary64) k #s(literal 1/2 binary64)))) #s(literal -1 binary64)) (neg.f64 (sqrt.f64 k)))
(/.f64 (neg.f64 #s(approx (pow (* (* 2 (PI)) n) (/ (- 1 k) 2)) (pow.f64 (.f64 (.f64 n #s(literal 2 binary64)) (PI.f64)) (fma.f64 #s(literal -1/2 binary64) k #s(literal 1/2 binary64))))) (neg.f64 (sqrt.f64 k)))
(/.f64 #s(literal -1 binary64) (neg.f64 (/.f64 (sqrt.f64 k) #s(approx (pow (* (* 2 (PI)) n) (/ (- 1 k) 2)) (pow.f64 (.f64 (.f64 n #s(literal 2 binary64)) (PI.f64)) (fma.f64 #s(literal -1/2 binary64) k #s(literal 1/2 binary64)))))))
(/.f64 #s(approx (pow (* (* 2 (PI)) n) (/ (- 1 k) 2)) (pow.f64 (.f64 (.f64 n #s(literal 2 binary64)) (PI.f64)) (fma.f64 #s(literal -1/2 binary64) k #s(literal 1/2 binary64)))) (sqrt.f64 k))
(/.f64 #s(literal 1 binary64) (/.f64 (neg.f64 (sqrt.f64 k)) (.f64 #s(approx (pow ( (* 2 (PI)) n) (/ (- 1 k) 2)) (pow.f64 (.f64 (.f64 n #s(literal 2 binary64)) (PI.f64)) (fma.f64 #s(literal -1/2 binary64) k #s(literal 1/2 binary64)))) #s(literal -1 binary64))))
(/.f64 #s(literal 1 binary64) (neg.f64 (neg.f64 (/.f64 (sqrt.f64 k) #s(approx (pow (* (* 2 (PI)) n) (/ (- 1 k) 2)) (pow.f64 (.f64 (.f64 n #s(literal 2 binary64)) (PI.f64)) (fma.f64 #s(literal -1/2 binary64) k #s(literal 1/2 binary64))))))))
(/.f64 #s(literal 1 binary64) (/.f64 (sqrt.f64 k) #s(approx (pow (* (* 2 (PI)) n) (/ (- 1 k) 2)) (pow.f64 (.f64 (.f64 n #s(literal 2 binary64)) (PI.f64)) (fma.f64 #s(literal -1/2 binary64) k #s(literal 1/2 binary64))))))
(neg.f64 (/.f64 #s(approx (pow (* (* 2 (PI)) n) (/ (- 1 k) 2)) (pow.f64 (.f64 (.f64 n #s(literal 2 binary64)) (PI.f64)) (fma.f64 #s(literal -1/2 binary64) k #s(literal 1/2 binary64)))) (neg.f64 (sqrt.f64 k))))
(-.f64 (/.f64 #s(literal 0 binary64) (neg.f64 (sqrt.f64 k))) (/.f64 #s(approx (pow (* (* 2 (PI)) n) (/ (- 1 k) 2)) (pow.f64 (.f64 (.f64 n #s(literal 2 binary64)) (PI.f64)) (fma.f64 #s(literal -1/2 binary64) k #s(literal 1/2 binary64)))) (neg.f64 (sqrt.f64 k))))
(-.f64 #s(literal 0 binary64) (/.f64 #s(approx (pow (* (* 2 (PI)) n) (/ (- 1 k) 2)) (pow.f64 (.f64 (.f64 n #s(literal 2 binary64)) (PI.f64)) (fma.f64 #s(literal -1/2 binary64) k #s(literal 1/2 binary64)))) (neg.f64 (sqrt.f64 k))))
(exp.f64 (.f64 (log.f64 (/.f64 (sqrt.f64 k) #s(approx (pow ( (* 2 (PI)) n) (/ (- 1 k) 2)) (pow.f64 (.f64 (.f64 n #s(literal 2 binary64)) (PI.f64)) (fma.f64 #s(literal -1/2 binary64) k #s(literal 1/2 binary64)))))) #s(literal -1 binary64)))
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(.f64 (pow.f64 (sqrt.f64 (PI.f64)) #s(approx (/ (- 1 k) 2) (.f64 #s(literal -1/2 binary64) k))) (pow.f64 (.f64 (sqrt.f64 (PI.f64)) (.f64 n #s(literal 2 binary64))) #s(approx (/ (- 1 k) 2) (*.f64 #s(literal -1/2 binary64) k))))
(.f64 (pow.f64 (pow.f64 (cbrt.f64 (PI.f64)) #s(literal 2 binary64)) #s(approx (/ (- 1 k) 2) (.f64 #s(literal -1/2 binary64) k))) (pow.f64 (.f64 (cbrt.f64 (PI.f64)) (.f64 n #s(literal 2 binary64))) #s(approx (/ (- 1 k) 2) (*.f64 #s(literal -1/2 binary64) k))))
(.f64 (pow.f64 (pow.f64 (.f64 (.f64 n #s(literal 2 binary64)) (PI.f64)) #s(approx (/ (- 1 k) 2) (.f64 #s(literal -1/2 binary64) k))) #s(literal 1/2 binary64)) (pow.f64 (pow.f64 (.f64 (.f64 n #s(literal 2 binary64)) (PI.f64)) #s(approx (/ (- 1 k) 2) (*.f64 #s(literal -1/2 binary64) k))) #s(literal 1/2 binary64)))
(.f64 #s(literal -1 binary64) (neg.f64 (pow.f64 (.f64 (.f64 n #s(literal 2 binary64)) (PI.f64)) #s(approx (/ (- 1 k) 2) (.f64 #s(literal -1/2 binary64) k)))))
(.f64 (pow.f64 (.f64 n #s(literal 2 binary64)) #s(approx (/ (- 1 k) 2) (.f64 #s(literal -1/2 binary64) k))) (pow.f64 (PI.f64) #s(approx (/ (- 1 k) 2) (.f64 #s(literal -1/2 binary64) k))))
(.f64 (pow.f64 (PI.f64) #s(approx (/ (- 1 k) 2) (.f64 #s(literal -1/2 binary64) k))) (pow.f64 (.f64 n #s(literal 2 binary64)) #s(approx (/ (- 1 k) 2) (.f64 #s(literal -1/2 binary64) k))))
(.f64 (pow.f64 (.f64 (.f64 n #s(literal 2 binary64)) (PI.f64)) #s(approx (/ (- 1 k) 2) (.f64 #s(literal -1/2 binary64) k))) #s(literal 1 binary64))
(.f64 #s(literal 1 binary64) (pow.f64 (.f64 (.f64 n #s(literal 2 binary64)) (PI.f64)) #s(approx (/ (- 1 k) 2) (.f64 #s(literal -1/2 binary64) k))))
(pow.f64 (exp.f64 #s(approx (/ (- 1 k) 2) (.f64 #s(literal -1/2 binary64) k))) (log.f64 (.f64 (*.f64 n #s(literal 2 binary64)) (PI.f64))))
(pow.f64 (pow.f64 (pow.f64 (.f64 (.f64 n #s(literal 2 binary64)) (PI.f64)) #s(literal 2 binary64)) #s(approx (/ (- 1 k) 2) (*.f64 #s(literal -1/2 binary64) k))) #s(literal 1/2 binary64))
(pow.f64 (pow.f64 (.f64 (.f64 n #s(literal 2 binary64)) (PI.f64)) #s(literal 2 binary64)) (.f64 #s(approx (/ (- 1 k) 2) (.f64 #s(literal -1/2 binary64) k)) #s(literal 1/2 binary64)))
(pow.f64 (pow.f64 (pow.f64 (.f64 (.f64 n #s(literal 2 binary64)) (PI.f64)) #s(approx (/ (- 1 k) 2) (*.f64 #s(literal -1/2 binary64) k))) #s(literal 1/2 binary64)) #s(literal 2 binary64))
(pow.f64 (.f64 (.f64 n #s(literal 2 binary64)) (PI.f64)) (.f64 (.f64 #s(approx (/ (- 1 k) 2) (*.f64 #s(literal -1/2 binary64) k)) #s(literal 1/2 binary64)) #s(literal 2 binary64)))
(pow.f64 (.f64 (.f64 n #s(literal 2 binary64)) (PI.f64)) (.f64 #s(literal 2 binary64) (.f64 #s(approx (/ (- 1 k) 2) (*.f64 #s(literal -1/2 binary64) k)) #s(literal 1/2 binary64))))
(pow.f64 (.f64 (.f64 n #s(literal 2 binary64)) (PI.f64)) (.f64 #s(approx (/ (- 1 k) 2) (.f64 #s(literal -1/2 binary64) k)) #s(literal 1 binary64)))
(pow.f64 (.f64 (.f64 n #s(literal 2 binary64)) (PI.f64)) #s(approx (/ (- 1 k) 2) (*.f64 #s(literal -1/2 binary64) k)))
(neg.f64 (neg.f64 (pow.f64 (.f64 (.f64 n #s(literal 2 binary64)) (PI.f64)) #s(approx (/ (- 1 k) 2) (*.f64 #s(literal -1/2 binary64) k)))))
(-.f64 #s(literal 0 binary64) (neg.f64 (pow.f64 (.f64 (.f64 n #s(literal 2 binary64)) (PI.f64)) #s(approx (/ (- 1 k) 2) (*.f64 #s(literal -1/2 binary64) k)))))
(exp.f64 (fma.f64 (log.f64 (.f64 (.f64 n #s(literal 2 binary64)) (PI.f64))) (.f64 #s(approx (/ (- 1 k) 2) (.f64 #s(literal -1/2 binary64) k)) #s(literal 1/2 binary64)) (.f64 (log.f64 (.f64 (.f64 n #s(literal 2 binary64)) (PI.f64))) (.f64 #s(approx (/ (- 1 k) 2) (*.f64 #s(literal -1/2 binary64) k)) #s(literal 1/2 binary64)))))
(exp.f64 (.f64 (.f64 (log.f64 (.f64 (.f64 n #s(literal 2 binary64)) (PI.f64))) (.f64 #s(approx (/ (- 1 k) 2) (.f64 #s(literal -1/2 binary64) k)) #s(literal 1/2 binary64))) #s(literal 2 binary64)))
(exp.f64 (.f64 (log.f64 (pow.f64 (.f64 (.f64 n #s(literal 2 binary64)) (PI.f64)) #s(literal 2 binary64))) (.f64 #s(approx (/ (- 1 k) 2) (*.f64 #s(literal -1/2 binary64) k)) #s(literal 1/2 binary64))))
(exp.f64 (.f64 (log.f64 (pow.f64 (pow.f64 (.f64 (.f64 n #s(literal 2 binary64)) (PI.f64)) #s(approx (/ (- 1 k) 2) (.f64 #s(literal -1/2 binary64) k))) #s(literal 1/2 binary64))) #s(literal 2 binary64)))
(exp.f64 (.f64 (log.f64 (.f64 (.f64 n #s(literal 2 binary64)) (PI.f64))) (.f64 #s(literal 2 binary64) (.f64 #s(approx (/ (- 1 k) 2) (.f64 #s(literal -1/2 binary64) k)) #s(literal 1/2 binary64)))))
(exp.f64 (.f64 (log.f64 (.f64 (.f64 n #s(literal 2 binary64)) (PI.f64))) (.f64 #s(approx (/ (- 1 k) 2) (*.f64 #s(literal -1/2 binary64) k)) #s(literal 1 binary64))))
(exp.f64 (.f64 (log.f64 (.f64 (.f64 n #s(literal 2 binary64)) (PI.f64))) #s(approx (/ (- 1 k) 2) (.f64 #s(literal -1/2 binary64) k))))
(.f64 (.f64 (cbrt.f64 (PI.f64)) (cbrt.f64 (sqrt.f64 (PI.f64)))) (*.f64 (cbrt.f64 (PI.f64)) (cbrt.f64 (sqrt.f64 (PI.f64)))))
(.f64 (.f64 (cbrt.f64 (sqrt.f64 (PI.f64))) (cbrt.f64 (PI.f64))) (*.f64 (cbrt.f64 (sqrt.f64 (PI.f64))) (cbrt.f64 (PI.f64))))
(*.f64 (sqrt.f64 (pow.f64 (cbrt.f64 (PI.f64)) #s(literal 5 binary64))) (pow.f64 (PI.f64) #s(literal 1/6 binary64)))
(*.f64 (sqrt.f64 (pow.f64 (cbrt.f64 (PI.f64)) #s(literal 4 binary64))) (cbrt.f64 (PI.f64)))
(*.f64 (sqrt.f64 (pow.f64 (PI.f64) #s(literal 3/2 binary64))) (pow.f64 (PI.f64) #s(literal 1/4 binary64)))
(*.f64 (cbrt.f64 (pow.f64 (PI.f64) #s(literal 5/2 binary64))) (cbrt.f64 (sqrt.f64 (PI.f64))))
(.f64 (cbrt.f64 (pow.f64 (.f64 (PI.f64) (cbrt.f64 (PI.f64))) #s(literal 2 binary64))) (cbrt.f64 (cbrt.f64 (PI.f64))))
(*.f64 (cbrt.f64 (pow.f64 (PI.f64) #s(literal 3/2 binary64))) (cbrt.f64 (pow.f64 (PI.f64) #s(literal 3/2 binary64))))
(*.f64 (exp.f64 (log.f64 (sqrt.f64 (PI.f64)))) (exp.f64 (log.f64 (sqrt.f64 (PI.f64)))))
(*.f64 (exp.f64 (log.f64 (pow.f64 (cbrt.f64 (PI.f64)) #s(literal 2 binary64)))) (exp.f64 (log.f64 (cbrt.f64 (PI.f64)))))
(*.f64 (pow.f64 (pow.f64 (PI.f64) #s(literal 5/2 binary64)) #s(literal 1/3 binary64)) (cbrt.f64 (sqrt.f64 (PI.f64))))
(.f64 (pow.f64 (pow.f64 (.f64 (PI.f64) (cbrt.f64 (PI.f64))) #s(literal 2 binary64)) #s(literal 1/3 binary64)) (cbrt.f64 (cbrt.f64 (PI.f64))))
(*.f64 (pow.f64 (pow.f64 (PI.f64) #s(literal 3/2 binary64)) #s(literal 1/3 binary64)) (pow.f64 (pow.f64 (PI.f64) #s(literal 3/2 binary64)) #s(literal 1/3 binary64)))
(*.f64 (pow.f64 (cbrt.f64 (sqrt.f64 (PI.f64))) #s(literal 3 binary64)) (pow.f64 (cbrt.f64 (sqrt.f64 (PI.f64))) #s(literal 3 binary64)))
(*.f64 (pow.f64 (cbrt.f64 (pow.f64 (cbrt.f64 (PI.f64)) #s(literal 2 binary64))) #s(literal 3 binary64)) (pow.f64 (cbrt.f64 (cbrt.f64 (PI.f64))) #s(literal 3 binary64)))
(*.f64 (pow.f64 (PI.f64) #s(literal 1/4 binary64)) (sqrt.f64 (pow.f64 (PI.f64) #s(literal 3/2 binary64))))
(*.f64 (sqrt.f64 (PI.f64)) (log.f64 (exp.f64 (sqrt.f64 (PI.f64)))))
(*.f64 (sqrt.f64 (PI.f64)) (sqrt.f64 (PI.f64)))
(*.f64 (pow.f64 (cbrt.f64 (PI.f64)) #s(literal 2 binary64)) (pow.f64 (pow.f64 (PI.f64) #s(literal 1/6 binary64)) #s(literal 2 binary64)))
(*.f64 (pow.f64 (cbrt.f64 (PI.f64)) #s(literal 2 binary64)) (cbrt.f64 (PI.f64)))
(.f64 (cbrt.f64 (PI.f64)) (sqrt.f64 (.f64 (cbrt.f64 (PI.f64)) (PI.f64))))
(*.f64 (cbrt.f64 (PI.f64)) (log.f64 (exp.f64 (pow.f64 (cbrt.f64 (PI.f64)) #s(literal 2 binary64)))))
(*.f64 (cbrt.f64 (PI.f64)) (pow.f64 (cbrt.f64 (PI.f64)) #s(literal 2 binary64)))
(*.f64 (PI.f64) (log.f64 (E.f64)))
(*.f64 (PI.f64) #s(literal 1 binary64))
(*.f64 #s(literal 1 binary64) (PI.f64))
(pow.f64 (E.f64) (log.f64 (PI.f64)))
(pow.f64 (sqrt.f64 (PI.f64)) #s(literal 2 binary64))
(pow.f64 (pow.f64 (PI.f64) #s(literal 3 binary64)) #s(literal 1/3 binary64))
(pow.f64 (*.f64 (PI.f64) (PI.f64)) #s(literal 1/2 binary64))
(pow.f64 (cbrt.f64 (PI.f64)) #s(literal 3 binary64))
(pow.f64 (PI.f64) #s(literal 1 binary64))
(cbrt.f64 (pow.f64 (PI.f64) #s(literal 3 binary64)))
(sqrt.f64 (*.f64 (PI.f64) (PI.f64)))
(fabs.f64 (PI.f64))
(exp.f64 (*.f64 (log.f64 (sqrt.f64 (PI.f64))) #s(literal 2 binary64)))
(exp.f64 (*.f64 (log.f64 (pow.f64 (PI.f64) #s(literal 3 binary64))) #s(literal 1/3 binary64)))
(exp.f64 (*.f64 (log.f64 (cbrt.f64 (PI.f64))) #s(literal 3 binary64)))
(exp.f64 (log.f64 (PI.f64)))
(log.f64 (exp.f64 (PI.f64)))
(PI.f64)
(*.f64 (neg.f64 (neg.f64 (PI.f64))) n)
(*.f64 (neg.f64 (neg.f64 n)) (PI.f64))
(.f64 (.f64 n (sqrt.f64 (PI.f64))) (sqrt.f64 (PI.f64)))
(.f64 (.f64 n (pow.f64 (cbrt.f64 (PI.f64)) #s(literal 2 binary64))) (cbrt.f64 (PI.f64)))
(*.f64 (neg.f64 (PI.f64)) (neg.f64 n))
(*.f64 (neg.f64 n) (neg.f64 (PI.f64)))
(.f64 (sqrt.f64 (PI.f64)) (.f64 (sqrt.f64 (PI.f64)) n))
(.f64 (pow.f64 (cbrt.f64 (PI.f64)) #s(literal 2 binary64)) (.f64 (cbrt.f64 (PI.f64)) n))
(.f64 #s(literal -1 binary64) (.f64 (neg.f64 (PI.f64)) n))
(.f64 (.f64 (PI.f64) n) #s(literal 1 binary64))
(*.f64 (PI.f64) n)
(.f64 #s(literal 1 binary64) (.f64 (PI.f64) n))
(*.f64 n (PI.f64))
(neg.f64 (*.f64 (neg.f64 (PI.f64)) n))
(-.f64 #s(literal 0 binary64) (*.f64 (neg.f64 (PI.f64)) n))
(*.f64 (neg.f64 (neg.f64 (sqrt.f64 (PI.f64)))) (sqrt.f64 n))
(.f64 (pow.f64 (pow.f64 (.f64 (PI.f64) n) #s(literal -1/2 binary64)) #s(literal -1/2 binary64)) (pow.f64 (pow.f64 (*.f64 (PI.f64) n) #s(literal -1/2 binary64)) #s(literal -1/2 binary64)))
(.f64 (sqrt.f64 (.f64 n (sqrt.f64 (PI.f64)))) (pow.f64 (PI.f64) #s(literal 1/4 binary64)))
(.f64 (sqrt.f64 (.f64 n (pow.f64 (cbrt.f64 (PI.f64)) #s(literal 2 binary64)))) (pow.f64 (PI.f64) #s(literal 1/6 binary64)))
(.f64 (pow.f64 (.f64 n (sqrt.f64 (PI.f64))) #s(literal 1/2 binary64)) (pow.f64 (PI.f64) #s(literal 1/4 binary64)))
(.f64 (pow.f64 (.f64 n (pow.f64 (cbrt.f64 (PI.f64)) #s(literal 2 binary64))) #s(literal 1/2 binary64)) (pow.f64 (PI.f64) #s(literal 1/6 binary64)))
(.f64 (pow.f64 (PI.f64) #s(literal 1/4 binary64)) (sqrt.f64 (.f64 (sqrt.f64 (PI.f64)) n)))
(.f64 (pow.f64 (PI.f64) #s(literal 1/4 binary64)) (pow.f64 (.f64 (sqrt.f64 (PI.f64)) n) #s(literal 1/2 binary64)))
(.f64 (pow.f64 #s(literal 1 binary64) #s(literal 1/2 binary64)) (sqrt.f64 (.f64 (PI.f64) n)))
(*.f64 (neg.f64 (sqrt.f64 (PI.f64))) (neg.f64 (sqrt.f64 n)))
(.f64 (pow.f64 (.f64 (PI.f64) n) #s(literal 1/4 binary64)) (pow.f64 (*.f64 (PI.f64) n) #s(literal 1/4 binary64)))
(*.f64 (sqrt.f64 n) (sqrt.f64 (PI.f64)))
(.f64 (neg.f64 (sqrt.f64 (.f64 (PI.f64) n))) #s(literal -1 binary64))
(*.f64 (sqrt.f64 (PI.f64)) (sqrt.f64 n))
(.f64 (cbrt.f64 (PI.f64)) (sqrt.f64 (.f64 (cbrt.f64 (PI.f64)) n)))
(.f64 (cbrt.f64 (PI.f64)) (pow.f64 (.f64 (cbrt.f64 (PI.f64)) n) #s(literal 1/2 binary64)))
(.f64 #s(literal -1 binary64) (neg.f64 (sqrt.f64 (.f64 (PI.f64) n))))
(.f64 (sqrt.f64 (.f64 (PI.f64) n)) #s(literal 1 binary64))
(.f64 #s(literal 1 binary64) (sqrt.f64 (.f64 (PI.f64) n)))
(pow.f64 (exp.f64 (log.f64 (*.f64 (PI.f64) n))) #s(literal 1/2 binary64))
(pow.f64 (.f64 (.f64 (PI.f64) n) (*.f64 (PI.f64) n)) #s(literal 1/4 binary64))
(pow.f64 (pow.f64 (*.f64 (PI.f64) n) #s(literal 1/4 binary64)) #s(literal 2 binary64))
(pow.f64 (pow.f64 (*.f64 (PI.f64) n) #s(literal -1/2 binary64)) #s(literal -1 binary64))
(pow.f64 (sqrt.f64 (*.f64 (PI.f64) n)) #s(literal 1 binary64))
(pow.f64 (*.f64 (PI.f64) n) #s(literal 1/2 binary64))
(/.f64 (neg.f64 (sqrt.f64 (*.f64 (PI.f64) n))) #s(literal -1 binary64))
(/.f64 #s(literal -1 binary64) (/.f64 #s(literal -1 binary64) (sqrt.f64 (*.f64 (PI.f64) n))))
(/.f64 (sqrt.f64 (*.f64 (PI.f64) n)) #s(literal 1 binary64))
(/.f64 #s(literal 1 binary64) (neg.f64 (/.f64 #s(literal -1 binary64) (sqrt.f64 (*.f64 (PI.f64) n)))))
(/.f64 #s(literal 1 binary64) (pow.f64 (*.f64 (PI.f64) n) #s(literal -1/2 binary64)))
(neg.f64 (neg.f64 (sqrt.f64 (*.f64 (PI.f64) n))))
(sqrt.f64 (*.f64 (PI.f64) n))
(-.f64 #s(literal 0 binary64) (neg.f64 (sqrt.f64 (*.f64 (PI.f64) n))))
(exp.f64 (.f64 (log.f64 (pow.f64 (.f64 (PI.f64) n) #s(literal -1/2 binary64))) #s(literal -1 binary64)))
(exp.f64 (.f64 (log.f64 (.f64 (PI.f64) n)) #s(literal 1/2 binary64)))
(.f64 #s(literal 1 binary64) #s(approx (/ (- 1 k) 2) (.f64 #s(literal -1/2 binary64) k)))
#s(approx (/ (- 1 k) 2) (*.f64 #s(literal -1/2 binary64) k))

eval213.0ms (2.4%)

Memory: 6.5MiB live, 243.9MiB allocated
Compiler: Compiled 28 426 to 3 359 computations (88.2% saved)

prune107.0ms (1.2%)

Memory

-27.4MiB live, 163.0MiB allocated

Pruning

52 alts after pruning (48 fresh and 4 done)

	Pruned	Kept	Total
New	907	37	944
Fresh	10	11	21
Picked	2	3	5
Done	2	1	3
Total	921	52	973

Accuracy

100.0%

Counts

973 → 52

Alt Table

Click to see full alt table

Status	Accuracy	Program
✓	54.3%	(/.f64 (pow.f64 (.f64 (PI.f64) (.f64 n #s(literal 2 binary64))) #s(approx (/ (- 1 k) 2) (*.f64 #s(literal -1/2 binary64) k))) (sqrt.f64 k))
▶	99.1%	(/.f64 #s(approx (pow (* (* 2 (PI)) n) (/ (- 1 k) 2)) (pow.f64 (/.f64 (*.f64 #s(literal -2 binary64) (PI.f64)) (/.f64 #s(literal -1 binary64) n)) (fma.f64 #s(literal -1/2 binary64) k #s(literal 1/2 binary64)))) (sqrt.f64 k))
	99.0%	(/.f64 #s(approx (pow (* (* 2 (PI)) n) (/ (- 1 k) 2)) (pow.f64 (.f64 (.f64 (*.f64 n #s(literal 2 binary64)) (sqrt.f64 (PI.f64))) (sqrt.f64 (PI.f64))) (fma.f64 #s(literal -1/2 binary64) k #s(literal 1/2 binary64)))) (sqrt.f64 k))
✓	99.1%	(/.f64 #s(approx (pow (* (* 2 (PI)) n) (/ (- 1 k) 2)) (pow.f64 (.f64 (PI.f64) (.f64 n #s(literal 2 binary64))) (fma.f64 #s(literal -1/2 binary64) k #s(literal 1/2 binary64)))) (sqrt.f64 k))
	99.0%	(/.f64 #s(approx (pow (* (* 2 (PI)) n) (/ (- 1 k) 2)) (.f64 (sqrt.f64 (.f64 (.f64 n #s(literal 2 binary64)) (PI.f64))) (pow.f64 (.f64 (.f64 n #s(literal 2 binary64)) (PI.f64)) (.f64 (neg.f64 k) #s(literal 1/2 binary64))))) (sqrt.f64 k))
	99.0%	(/.f64 #s(literal 1 binary64) (/.f64 (sqrt.f64 k) #s(approx (pow (* (* 2 (PI)) n) (/ (- 1 k) 2)) (pow.f64 (.f64 (.f64 n #s(literal 2 binary64)) (PI.f64)) (fma.f64 #s(literal -1/2 binary64) k #s(literal 1/2 binary64))))))
	99.0%	(.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) (/.f64 #s(literal 1 binary64) (pow.f64 (sqrt.f64 (.f64 n (*.f64 (PI.f64) #s(literal 2 binary64)))) (-.f64 k #s(literal 1 binary64)))))
	98.9%	(.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) (.f64 (pow.f64 (.f64 n (.f64 (PI.f64) #s(literal 2 binary64))) (.f64 k #s(literal -1/2 binary64))) (sqrt.f64 (.f64 n (*.f64 (PI.f64) #s(literal 2 binary64))))))
	50.5%	#s(approx (/ (pow (* (* 2 (PI)) n) (/ (- 1 k) 2)) (sqrt k)) (/.f64 (.f64 (sqrt.f64 #s(literal 2 binary64)) (fma.f64 (.f64 (log.f64 (.f64 (.f64 n (PI.f64)) #s(literal 2 binary64))) (sqrt.f64 (.f64 (.f64 (pow.f64 k #s(literal 3 binary64)) (PI.f64)) n))) #s(literal -1/2 binary64) (sqrt.f64 (.f64 (.f64 n (PI.f64)) k)))) k))
	48.5%	#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (/.f64 (sqrt.f64 (.f64 (.f64 n #s(literal 2 binary64)) (PI.f64))) (sqrt.f64 k)))
▶	48.8%	#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (/.f64 (sqrt.f64 (.f64 (PI.f64) n)) (sqrt.f64 (.f64 #s(literal 1/2 binary64) k))))
	48.7%	#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (/.f64 (sqrt.f64 #s(literal 2 binary64)) (.f64 (/.f64 #s(literal -1 binary64) (sqrt.f64 (.f64 (PI.f64) n))) (neg.f64 (sqrt.f64 k)))))
	40.1%	#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (/.f64 (sqrt.f64 #s(literal 2 binary64)) (sqrt.f64 (/.f64 k (*.f64 (PI.f64) n)))))
	48.7%	#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (/.f64 (neg.f64 (sqrt.f64 (/.f64 #s(literal 2 binary64) k))) (/.f64 #s(literal -1 binary64) (sqrt.f64 (*.f64 (PI.f64) n)))))
	48.7%	#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (/.f64 #s(literal 1 binary64) (/.f64 (neg.f64 (sqrt.f64 (.f64 #s(literal 1/2 binary64) k))) (neg.f64 (sqrt.f64 (.f64 (PI.f64) n))))))
	48.7%	#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (/.f64 #s(literal 1 binary64) (/.f64 (neg.f64 (sqrt.f64 k)) (.f64 (sqrt.f64 #s(literal 2 binary64)) (neg.f64 (sqrt.f64 (.f64 (PI.f64) n)))))))
	40.1%	#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (/.f64 #s(literal 1 binary64) (sqrt.f64 (.f64 (/.f64 k (.f64 (PI.f64) n)) #s(literal 1/2 binary64)))))
✓	99.1%	#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (.f64 (pow.f64 (.f64 (*.f64 #s(literal 2 binary64) n) (PI.f64)) (fma.f64 #s(literal -1/2 binary64) k #s(literal 1/2 binary64))) (sqrt.f64 (/.f64 #s(literal 1 binary64) k))))
	98.9%	#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (.f64 (pow.f64 (.f64 k (pow.f64 (.f64 (PI.f64) (.f64 n #s(literal 2 binary64))) k)) #s(literal -1/2 binary64)) (sqrt.f64 (.f64 (PI.f64) (.f64 n #s(literal 2 binary64))))))
	48.4%	#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (.f64 (pow.f64 k #s(literal -1/2 binary64)) (sqrt.f64 (.f64 (*.f64 n #s(literal 2 binary64)) (PI.f64)))))
	48.6%	#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (.f64 (/.f64 (sqrt.f64 (.f64 (PI.f64) #s(literal 2 binary64))) (sqrt.f64 k)) (sqrt.f64 n)))
	48.6%	#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (.f64 (/.f64 (sqrt.f64 (.f64 n #s(literal 2 binary64))) (sqrt.f64 k)) (/.f64 (sqrt.f64 (PI.f64)) #s(literal 1 binary64))))
	48.7%	#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (.f64 (/.f64 (sqrt.f64 (PI.f64)) (sqrt.f64 (.f64 #s(literal 1/2 binary64) k))) (sqrt.f64 n)))
	48.6%	#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (.f64 (/.f64 (sqrt.f64 (PI.f64)) #s(literal -1 binary64)) (/.f64 (neg.f64 (sqrt.f64 n)) (sqrt.f64 (.f64 #s(literal 1/2 binary64) k)))))
	48.8%	#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (.f64 (/.f64 (sqrt.f64 #s(literal 2 binary64)) (sqrt.f64 k)) (/.f64 (sqrt.f64 (.f64 (*.f64 (sqrt.f64 (PI.f64)) (sqrt.f64 (PI.f64))) n)) #s(literal 1 binary64))))
	48.7%	#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (.f64 (/.f64 (sqrt.f64 #s(literal 2 binary64)) (sqrt.f64 k)) (/.f64 #s(literal -1 binary64) (/.f64 #s(literal -1 binary64) (sqrt.f64 (.f64 (PI.f64) n))))))
	48.7%	#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (.f64 (/.f64 (sqrt.f64 #s(literal 2 binary64)) (sqrt.f64 k)) (.f64 (sqrt.f64 (PI.f64)) (sqrt.f64 n))))
	48.7%	#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (.f64 (/.f64 (sqrt.f64 #s(literal 2 binary64)) (sqrt.f64 k)) (sqrt.f64 (.f64 (PI.f64) n))))
▶	48.7%	#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (.f64 (.f64 (neg.f64 (sqrt.f64 #s(literal 2 binary64))) (/.f64 #s(literal -1 binary64) (sqrt.f64 k))) (/.f64 (sqrt.f64 (*.f64 (PI.f64) n)) #s(literal 1 binary64))))
	48.8%	#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (.f64 (sqrt.f64 (/.f64 #s(literal 2 binary64) k)) (sqrt.f64 (.f64 (PI.f64) n))))
	48.8%	#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (.f64 (sqrt.f64 (.f64 (/.f64 #s(literal 2 binary64) k) (PI.f64))) (sqrt.f64 n)))
	39.5%	#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (.f64 (sqrt.f64 (.f64 (PI.f64) #s(literal 2 binary64))) (sqrt.f64 (/.f64 n k))))
	48.8%	#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (.f64 (sqrt.f64 (.f64 n #s(literal 2 binary64))) (sqrt.f64 (/.f64 (PI.f64) k))))
	39.5%	#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (.f64 (sqrt.f64 (PI.f64)) (sqrt.f64 (.f64 (/.f64 n k) #s(literal 2 binary64)))))
	39.5%	#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (.f64 (sqrt.f64 (PI.f64)) (sqrt.f64 (.f64 n (/.f64 #s(literal 2 binary64) k)))))
	48.7%	#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (.f64 (sqrt.f64 #s(literal 2 binary64)) (/.f64 #s(literal 1 binary64) (.f64 (/.f64 #s(literal -1 binary64) (sqrt.f64 (*.f64 (PI.f64) n))) (neg.f64 (sqrt.f64 k))))))
	40.1%	#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (.f64 (sqrt.f64 #s(literal 2 binary64)) (/.f64 #s(literal 1 binary64) (sqrt.f64 (/.f64 k (.f64 (PI.f64) n))))))
	48.7%	#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (.f64 (sqrt.f64 #s(literal 2 binary64)) (.f64 (sqrt.f64 n) (sqrt.f64 (/.f64 (PI.f64) k)))))
	39.6%	#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (.f64 (sqrt.f64 #s(literal 2 binary64)) (sqrt.f64 (/.f64 #s(literal 1 binary64) (/.f64 k (.f64 (PI.f64) n))))))
	39.6%	#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (.f64 (sqrt.f64 #s(literal 2 binary64)) (sqrt.f64 (.f64 (/.f64 n k) (PI.f64)))))
	48.4%	#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (.f64 (neg.f64 (sqrt.f64 (.f64 (*.f64 n #s(literal 2 binary64)) (PI.f64)))) (/.f64 #s(literal -1 binary64) (sqrt.f64 k))))
	48.7%	#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (.f64 (neg.f64 (sqrt.f64 (.f64 (PI.f64) n))) (/.f64 #s(literal -1 binary64) (sqrt.f64 (*.f64 #s(literal 1/2 binary64) k)))))
	48.7%	#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (.f64 #s(approx (pow ( (* 2 n) (PI)) (+ (* -1/2 k) 1/2)) (.f64 (sqrt.f64 (.f64 n (PI.f64))) (sqrt.f64 #s(literal 2 binary64)))) (sqrt.f64 (/.f64 #s(literal 1 binary64) k))))
	48.7%	#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (.f64 #s(approx (/ (sqrt 2) (sqrt k)) (.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) k)) (sqrt.f64 #s(literal 2 binary64)))) (/.f64 (sqrt.f64 (*.f64 (PI.f64) n)) #s(literal 1 binary64))))
	39.7%	#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt.f64 (/.f64 (*.f64 (PI.f64) #s(literal 2 binary64)) (/.f64 k n))))
	39.7%	#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt.f64 (/.f64 #s(literal 2 binary64) (/.f64 k (*.f64 (PI.f64) n)))))
	39.5%	#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt.f64 (.f64 (/.f64 (.f64 (*.f64 n #s(literal 2 binary64)) (sqrt.f64 (PI.f64))) k) (/.f64 (sqrt.f64 (PI.f64)) #s(literal 1 binary64)))))
✓	39.7%	#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt.f64 (.f64 (/.f64 (.f64 (PI.f64) n) k) #s(literal 2 binary64))))
	39.7%	#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt.f64 (.f64 (/.f64 #s(literal 2 binary64) k) (.f64 (PI.f64) n))))
	39.7%	#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt.f64 (.f64 (.f64 (/.f64 n k) (PI.f64)) #s(literal 2 binary64))))
▶	39.5%	#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt.f64 (.f64 (.f64 (sqrt.f64 (PI.f64)) (*.f64 (sqrt.f64 (PI.f64)) (/.f64 n k))) #s(literal 2 binary64))))
▶	39.7%	#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt.f64 (.f64 (.f64 n (/.f64 (PI.f64) k)) #s(literal 2 binary64))))

Compiler

Compiled 2 830 to 2 273 computations (19.7% saved)

simplify240.0ms (2.7%)

Memory

-13.4MiB live, 108.5MiB allocated

Algorithm

1×	egg-herbie

Localize:

Found 20 expressions of interest:

New	Metric	Score
cost-diff	0	(.f64 (.f64 (neg.f64 (sqrt.f64 #s(literal 2 binary64))) (/.f64 #s(literal -1 binary64) (sqrt.f64 k))) (/.f64 (sqrt.f64 (*.f64 (PI.f64) n)) #s(literal 1 binary64)))
cost-diff	0	#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (.f64 (.f64 (neg.f64 (sqrt.f64 #s(literal 2 binary64))) (/.f64 #s(literal -1 binary64) (sqrt.f64 k))) (/.f64 (sqrt.f64 (*.f64 (PI.f64) n)) #s(literal 1 binary64))))
cost-diff	448	(*.f64 (neg.f64 (sqrt.f64 #s(literal 2 binary64))) (/.f64 #s(literal -1 binary64) (sqrt.f64 k)))
cost-diff	704	(/.f64 (sqrt.f64 (*.f64 (PI.f64) n)) #s(literal 1 binary64))
cost-diff	0	(.f64 (.f64 (sqrt.f64 (PI.f64)) (*.f64 (sqrt.f64 (PI.f64)) (/.f64 n k))) #s(literal 2 binary64))
cost-diff	0	(sqrt.f64 (.f64 (.f64 (sqrt.f64 (PI.f64)) (*.f64 (sqrt.f64 (PI.f64)) (/.f64 n k))) #s(literal 2 binary64)))
cost-diff	0	#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt.f64 (.f64 (.f64 (sqrt.f64 (PI.f64)) (*.f64 (sqrt.f64 (PI.f64)) (/.f64 n k))) #s(literal 2 binary64))))
cost-diff	1600	(.f64 (sqrt.f64 (PI.f64)) (.f64 (sqrt.f64 (PI.f64)) (/.f64 n k)))
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 1/2 binary64) k)))
cost-diff	0	#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (/.f64 (sqrt.f64 (.f64 (PI.f64) n)) (sqrt.f64 (.f64 #s(literal 1/2 binary64) k))))
cost-diff	0	(*.f64 n (/.f64 (PI.f64) k))
cost-diff	0	(.f64 (.f64 n (/.f64 (PI.f64) k)) #s(literal 2 binary64))
cost-diff	0	(sqrt.f64 (.f64 (.f64 n (/.f64 (PI.f64) k)) #s(literal 2 binary64)))
cost-diff	0	#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt.f64 (.f64 (.f64 n (/.f64 (PI.f64) k)) #s(literal 2 binary64))))
cost-diff	0	(pow.f64 (/.f64 (*.f64 #s(literal -2 binary64) (PI.f64)) (/.f64 #s(literal -1 binary64) n)) (fma.f64 #s(literal -1/2 binary64) k #s(literal 1/2 binary64)))
cost-diff	0	#s(approx (pow (* (* 2 (PI)) n) (/ (- 1 k) 2)) (pow.f64 (/.f64 (*.f64 #s(literal -2 binary64) (PI.f64)) (/.f64 #s(literal -1 binary64) n)) (fma.f64 #s(literal -1/2 binary64) k #s(literal 1/2 binary64))))
cost-diff	0	(/.f64 #s(approx (pow (* (* 2 (PI)) n) (/ (- 1 k) 2)) (pow.f64 (/.f64 (*.f64 #s(literal -2 binary64) (PI.f64)) (/.f64 #s(literal -1 binary64) n)) (fma.f64 #s(literal -1/2 binary64) k #s(literal 1/2 binary64)))) (sqrt.f64 k))
cost-diff	1088	(/.f64 (*.f64 #s(literal -2 binary64) (PI.f64)) (/.f64 #s(literal -1 binary64) n))

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	51	355
0	81	333
1	132	314
2	230	308
3	479	302
4	928	302
5	1585	302
6	1929	302
7	2200	302
8	2515	302
9	2820	302
10	2949	302
11	3276	302
12	3334	302
13	3410	302
14	3647	302
15	4336	302
16	5094	302
17	5327	302
18	5440	302
19	5474	302
20	5490	302
21	5500	302
22	5500	302
23	5507	302
24	5511	302
25	5511	302
0	5511	302

Stop Event

1×	iter limit
1×	saturated
1×	iter limit

Calls

Call 1

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

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

localize159.0ms (1.8%)

Memory

-12.5MiB live, 219.3MiB allocated

Localize:

Found 20 expressions of interest:

New	Metric	Score
accuracy	0.3388862793053261	(.f64 (.f64 (neg.f64 (sqrt.f64 #s(literal 2 binary64))) (/.f64 #s(literal -1 binary64) (sqrt.f64 k))) (/.f64 (sqrt.f64 (*.f64 (PI.f64) n)) #s(literal 1 binary64)))
accuracy	0.38671601768998964	(sqrt.f64 (*.f64 (PI.f64) n))
accuracy	0.4209175293053261	(*.f64 (neg.f64 (sqrt.f64 #s(literal 2 binary64))) (/.f64 #s(literal -1 binary64) (sqrt.f64 k)))
accuracy	32.6099459769306	#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (.f64 (.f64 (neg.f64 (sqrt.f64 #s(literal 2 binary64))) (/.f64 #s(literal -1 binary64) (sqrt.f64 k))) (/.f64 (sqrt.f64 (*.f64 (PI.f64) n)) #s(literal 1 binary64))))
accuracy	0.328125	(*.f64 (sqrt.f64 (PI.f64)) (/.f64 n k))
accuracy	1.0	(sqrt.f64 (PI.f64))
accuracy	12.072893065940132	(sqrt.f64 (.f64 (.f64 (sqrt.f64 (PI.f64)) (*.f64 (sqrt.f64 (PI.f64)) (/.f64 n k))) #s(literal 2 binary64)))
accuracy	32.6099459769306	#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt.f64 (.f64 (.f64 (sqrt.f64 (PI.f64)) (*.f64 (sqrt.f64 (PI.f64)) (/.f64 n k))) #s(literal 2 binary64))))
accuracy	0.22265625	(*.f64 (PI.f64) n)
accuracy	0.301445019536884	(/.f64 (sqrt.f64 (.f64 (PI.f64) n)) (sqrt.f64 (.f64 #s(literal 1/2 binary64) k)))
accuracy	0.38671601768998964	(sqrt.f64 (*.f64 (PI.f64) n))
accuracy	32.6099459769306	#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (/.f64 (sqrt.f64 (.f64 (PI.f64) n)) (sqrt.f64 (.f64 #s(literal 1/2 binary64) k))))
accuracy	0.1640625	(*.f64 n (/.f64 (PI.f64) k))
accuracy	0.2578125	(/.f64 (PI.f64) k)
accuracy	12.072893065940132	(sqrt.f64 (.f64 (.f64 n (/.f64 (PI.f64) k)) #s(literal 2 binary64)))
accuracy	32.6099459769306	#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt.f64 (.f64 (.f64 n (/.f64 (PI.f64) k)) #s(literal 2 binary64))))
accuracy	0.0	#s(approx (pow (* (* 2 (PI)) n) (/ (- 1 k) 2)) (pow.f64 (/.f64 (*.f64 #s(literal -2 binary64) (PI.f64)) (/.f64 #s(literal -1 binary64) n)) (fma.f64 #s(literal -1/2 binary64) k #s(literal 1/2 binary64))))
accuracy	0.16015625	(/.f64 #s(approx (pow (* (* 2 (PI)) n) (/ (- 1 k) 2)) (pow.f64 (/.f64 (*.f64 #s(literal -2 binary64) (PI.f64)) (/.f64 #s(literal -1 binary64) n)) (fma.f64 #s(literal -1/2 binary64) k #s(literal 1/2 binary64)))) (sqrt.f64 k))
accuracy	0.3046875	(/.f64 (*.f64 #s(literal -2 binary64) (PI.f64)) (/.f64 #s(literal -1 binary64) n))
accuracy	0.4841279054325469	(pow.f64 (/.f64 (*.f64 #s(literal -2 binary64) (PI.f64)) (/.f64 #s(literal -1 binary64) n)) (fma.f64 #s(literal -1/2 binary64) k #s(literal 1/2 binary64)))

Samples

114.0ms

256×

valid

Compiler

Compiled 640 to 100 computations (84.4% saved)

Precisions

Click to see histograms. Total time spent on operations: 86.0ms

ival-mult: 20.0ms (23.3% of total)

ival-add: 18.0ms (20.9% of total)

ival-div: 16.0ms (18.6% of total)

ival-pow: 16.0ms (18.6% of total)

ival-sqrt: 11.0ms (12.8% of total)

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

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

exact: 1.0ms (1.2% of total)

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

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

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

series51.0ms (0.6%)

Memory

19.8MiB live, 102.4MiB allocated

Counts

23 → 38

Calls

Call 1

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

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

Calls

6 calls:

Time	Variable		Point	Expression
14.0ms	n	@	inf	((/ (* -2 (PI)) (/ -1 n)) (/ (pow (* (* 2 (PI)) n) (/ (- 1 k) 2)) (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2)) (pow (/ (* -2 (PI)) (/ -1 n)) (+ (* -1/2 k) 1/2)) (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt (* (* n (/ (PI) k)) 2)) (* (* n (/ (PI) k)) 2) (* n (/ (PI) k)) (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (/ (sqrt (* (PI) n)) (sqrt (* 1/2 k))) (sqrt (* (PI) n)) (* (PI) n) (* (sqrt (PI)) (* (sqrt (PI)) (/ n k))) (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt (* (* (sqrt (PI)) (* (sqrt (PI)) (/ n k))) 2)) (* (* (sqrt (PI)) (* (sqrt (PI)) (/ n k))) 2) (/ (sqrt (* (PI) n)) 1) (* (neg (sqrt 2)) (/ -1 (sqrt k))) (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (* (* (neg (sqrt 2)) (/ -1 (sqrt k))) (/ (sqrt (* (PI) n)) 1)) (/ (PI) k) (sqrt (PI)) (* (sqrt (PI)) (/ n k)))
13.0ms	n	@	0	((/ (* -2 (PI)) (/ -1 n)) (/ (pow (* (* 2 (PI)) n) (/ (- 1 k) 2)) (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2)) (pow (/ (* -2 (PI)) (/ -1 n)) (+ (* -1/2 k) 1/2)) (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt (* (* n (/ (PI) k)) 2)) (* (* n (/ (PI) k)) 2) (* n (/ (PI) k)) (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (/ (sqrt (* (PI) n)) (sqrt (* 1/2 k))) (sqrt (* (PI) n)) (* (PI) n) (* (sqrt (PI)) (* (sqrt (PI)) (/ n k))) (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt (* (* (sqrt (PI)) (* (sqrt (PI)) (/ n k))) 2)) (* (* (sqrt (PI)) (* (sqrt (PI)) (/ n k))) 2) (/ (sqrt (* (PI) n)) 1) (* (neg (sqrt 2)) (/ -1 (sqrt k))) (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (* (* (neg (sqrt 2)) (/ -1 (sqrt k))) (/ (sqrt (* (PI) n)) 1)) (/ (PI) k) (sqrt (PI)) (* (sqrt (PI)) (/ n k)))
12.0ms	n	@	-inf	((/ (* -2 (PI)) (/ -1 n)) (/ (pow (* (* 2 (PI)) n) (/ (- 1 k) 2)) (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2)) (pow (/ (* -2 (PI)) (/ -1 n)) (+ (* -1/2 k) 1/2)) (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt (* (* n (/ (PI) k)) 2)) (* (* n (/ (PI) k)) 2) (* n (/ (PI) k)) (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (/ (sqrt (* (PI) n)) (sqrt (* 1/2 k))) (sqrt (* (PI) n)) (* (PI) n) (* (sqrt (PI)) (* (sqrt (PI)) (/ n k))) (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt (* (* (sqrt (PI)) (* (sqrt (PI)) (/ n k))) 2)) (* (* (sqrt (PI)) (* (sqrt (PI)) (/ n k))) 2) (/ (sqrt (* (PI) n)) 1) (* (neg (sqrt 2)) (/ -1 (sqrt k))) (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (* (* (neg (sqrt 2)) (/ -1 (sqrt k))) (/ (sqrt (* (PI) n)) 1)) (/ (PI) k) (sqrt (PI)) (* (sqrt (PI)) (/ n k)))
4.0ms	k	@	-inf	((/ (* -2 (PI)) (/ -1 n)) (/ (pow (* (* 2 (PI)) n) (/ (- 1 k) 2)) (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2)) (pow (/ (* -2 (PI)) (/ -1 n)) (+ (* -1/2 k) 1/2)) (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt (* (* n (/ (PI) k)) 2)) (* (* n (/ (PI) k)) 2) (* n (/ (PI) k)) (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (/ (sqrt (* (PI) n)) (sqrt (* 1/2 k))) (sqrt (* (PI) n)) (* (PI) n) (* (sqrt (PI)) (* (sqrt (PI)) (/ n k))) (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt (* (* (sqrt (PI)) (* (sqrt (PI)) (/ n k))) 2)) (* (* (sqrt (PI)) (* (sqrt (PI)) (/ n k))) 2) (/ (sqrt (* (PI) n)) 1) (* (neg (sqrt 2)) (/ -1 (sqrt k))) (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (* (* (neg (sqrt 2)) (/ -1 (sqrt k))) (/ (sqrt (* (PI) n)) 1)) (/ (PI) k) (sqrt (PI)) (* (sqrt (PI)) (/ n k)))
4.0ms	k	@	0	((/ (* -2 (PI)) (/ -1 n)) (/ (pow (* (* 2 (PI)) n) (/ (- 1 k) 2)) (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2)) (pow (/ (* -2 (PI)) (/ -1 n)) (+ (* -1/2 k) 1/2)) (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt (* (* n (/ (PI) k)) 2)) (* (* n (/ (PI) k)) 2) (* n (/ (PI) k)) (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (/ (sqrt (* (PI) n)) (sqrt (* 1/2 k))) (sqrt (* (PI) n)) (* (PI) n) (* (sqrt (PI)) (* (sqrt (PI)) (/ n k))) (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt (* (* (sqrt (PI)) (* (sqrt (PI)) (/ n k))) 2)) (* (* (sqrt (PI)) (* (sqrt (PI)) (/ n k))) 2) (/ (sqrt (* (PI) n)) 1) (* (neg (sqrt 2)) (/ -1 (sqrt k))) (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (* (* (neg (sqrt 2)) (/ -1 (sqrt k))) (/ (sqrt (* (PI) n)) 1)) (/ (PI) k) (sqrt (PI)) (* (sqrt (PI)) (/ n k)))

simplify116.0ms (1.3%)

Memory

10.9MiB live, 126.1MiB allocated

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	155	666
1	427	648
2	1343	591
3	2632	576
4	4886	576
0	8268	564

Stop Event

1×	iter limit
1×	node limit

Counts

38 → 38

Calls

Call 1

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

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

rewrite227.0ms (2.6%)

Memory

-8.4MiB live, 270.6MiB allocated

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	51	290
0	81	266
1	264	244
2	1552	238
0	8261	238

Stop Event

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

Counts

23 → 1 352

Calls

Call 1

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

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

eval154.0ms (1.7%)

Memory: 7.5MiB live, 240.7MiB allocated
Compiler: Compiled 29 538 to 3 693 computations (87.5% saved)

prune150.0ms (1.7%)

Memory

-16.7MiB live, 223.5MiB allocated

Pruning

57 alts after pruning (49 fresh and 8 done)

	Pruned	Kept	Total
New	915	21	936
Fresh	15	28	43
Picked	1	4	5
Done	0	4	4
Total	931	57	988

Accuracy

100.0%

Counts

988 → 57

Alt Table

Click to see full alt table

Status	Accuracy	Program
✓	54.3%	(/.f64 (pow.f64 (.f64 (PI.f64) (.f64 n #s(literal 2 binary64))) #s(approx (/ (- 1 k) 2) (*.f64 #s(literal -1/2 binary64) k))) (sqrt.f64 k))
✓	99.1%	(/.f64 #s(approx (pow (* (* 2 (PI)) n) (/ (- 1 k) 2)) (pow.f64 (/.f64 (*.f64 #s(literal -2 binary64) (PI.f64)) (/.f64 #s(literal -1 binary64) n)) (fma.f64 #s(literal -1/2 binary64) k #s(literal 1/2 binary64)))) (sqrt.f64 k))
✓	99.1%	(/.f64 #s(approx (pow (* (* 2 (PI)) n) (/ (- 1 k) 2)) (pow.f64 (.f64 (PI.f64) (.f64 n #s(literal 2 binary64))) (fma.f64 #s(literal -1/2 binary64) k #s(literal 1/2 binary64)))) (sqrt.f64 k))
	99.0%	(/.f64 #s(approx (pow (* (* 2 (PI)) n) (/ (- 1 k) 2)) (.f64 (pow.f64 (.f64 (.f64 n #s(literal 2 binary64)) (PI.f64)) (.f64 #s(literal -1/2 binary64) k)) (sqrt.f64 (.f64 (.f64 n #s(literal 2 binary64)) (PI.f64))))) (sqrt.f64 k))
	99.0%	(/.f64 #s(literal 1 binary64) (/.f64 (sqrt.f64 k) #s(approx (pow (* (* 2 (PI)) n) (/ (- 1 k) 2)) (pow.f64 (.f64 (.f64 n #s(literal 2 binary64)) (PI.f64)) (fma.f64 #s(literal -1/2 binary64) k #s(literal 1/2 binary64))))))
	99.0%	(.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) (/.f64 #s(literal 1 binary64) (pow.f64 (sqrt.f64 (.f64 n (*.f64 (PI.f64) #s(literal 2 binary64)))) (-.f64 k #s(literal 1 binary64)))))
	98.9%	(.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) (.f64 (pow.f64 (.f64 n (.f64 (PI.f64) #s(literal 2 binary64))) (.f64 k #s(literal -1/2 binary64))) (sqrt.f64 (.f64 n (*.f64 (PI.f64) #s(literal 2 binary64))))))
	50.5%	#s(approx (/ (pow (* (* 2 (PI)) n) (/ (- 1 k) 2)) (sqrt k)) (/.f64 (.f64 (sqrt.f64 #s(literal 2 binary64)) (fma.f64 (.f64 (log.f64 (.f64 (.f64 (PI.f64) n) #s(literal 2 binary64))) (sqrt.f64 (.f64 (.f64 (pow.f64 k #s(literal 3 binary64)) (PI.f64)) n))) #s(literal -1/2 binary64) (sqrt.f64 (.f64 (.f64 (PI.f64) n) k)))) k))
	48.7%	#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (/.f64 (.f64 (sqrt.f64 (PI.f64)) (sqrt.f64 n)) (sqrt.f64 (.f64 #s(literal 1/2 binary64) k))))
	39.5%	#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (/.f64 (sqrt.f64 (*.f64 (/.f64 n k) (PI.f64))) (sqrt.f64 #s(literal 1/2 binary64))))
	48.7%	#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (/.f64 (sqrt.f64 (.f64 (.f64 (sqrt.f64 (PI.f64)) n) (sqrt.f64 (PI.f64)))) (sqrt.f64 (*.f64 #s(literal 1/2 binary64) k))))
	48.5%	#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (/.f64 (sqrt.f64 (.f64 (.f64 n #s(literal 2 binary64)) (PI.f64))) (sqrt.f64 k)))
✓	48.8%	#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (/.f64 (sqrt.f64 (.f64 (PI.f64) n)) (sqrt.f64 (.f64 #s(literal 1/2 binary64) k))))
	48.6%	#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (/.f64 (sqrt.f64 (.f64 n (PI.f64))) (.f64 (sqrt.f64 #s(literal 1/2 binary64)) (neg.f64 (neg.f64 (sqrt.f64 k))))))
	48.7%	#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (/.f64 (sqrt.f64 #s(literal 2 binary64)) (.f64 (/.f64 #s(literal -1 binary64) (sqrt.f64 (.f64 (PI.f64) n))) (neg.f64 (sqrt.f64 k)))))
	40.1%	#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (/.f64 (sqrt.f64 #s(literal 2 binary64)) (sqrt.f64 (/.f64 k (*.f64 (PI.f64) n)))))
	48.7%	#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (/.f64 (neg.f64 (sqrt.f64 (/.f64 #s(literal 2 binary64) k))) (/.f64 #s(literal -1 binary64) (sqrt.f64 (*.f64 (PI.f64) n)))))
	40.0%	#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (/.f64 #s(literal 2 binary64) (.f64 (+.f64 #s(literal 0 binary64) (sqrt.f64 #s(literal 2 binary64))) (sqrt.f64 (/.f64 k (.f64 n (PI.f64)))))))
	48.7%	#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (/.f64 #s(literal 1 binary64) (/.f64 (neg.f64 (sqrt.f64 k)) (.f64 (sqrt.f64 #s(literal 2 binary64)) (neg.f64 (sqrt.f64 (.f64 (PI.f64) n)))))))
	40.1%	#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (/.f64 #s(literal 1 binary64) (sqrt.f64 (.f64 (/.f64 k (.f64 (PI.f64) n)) #s(literal 1/2 binary64)))))
	40.1%	#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (/.f64 #s(literal 1 binary64) (sqrt.f64 (*.f64 (/.f64 #s(literal 1/2 binary64) n) (/.f64 k (PI.f64))))))
✓	99.1%	#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (.f64 (pow.f64 (.f64 (*.f64 #s(literal 2 binary64) n) (PI.f64)) (fma.f64 #s(literal -1/2 binary64) k #s(literal 1/2 binary64))) (sqrt.f64 (/.f64 #s(literal 1 binary64) k))))
	98.9%	#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (.f64 (pow.f64 (.f64 k (pow.f64 (.f64 (PI.f64) (.f64 n #s(literal 2 binary64))) k)) #s(literal -1/2 binary64)) (sqrt.f64 (.f64 (PI.f64) (.f64 n #s(literal 2 binary64))))))
	48.6%	#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (.f64 (/.f64 (sqrt.f64 (.f64 (PI.f64) #s(literal 2 binary64))) (sqrt.f64 k)) (sqrt.f64 n)))
	48.6%	#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (.f64 (/.f64 (sqrt.f64 (.f64 n #s(literal 2 binary64))) (sqrt.f64 k)) (/.f64 (sqrt.f64 (PI.f64)) #s(literal 1 binary64))))
	48.6%	#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (.f64 (/.f64 (sqrt.f64 (PI.f64)) #s(literal -1 binary64)) (/.f64 (neg.f64 (sqrt.f64 n)) (sqrt.f64 (.f64 #s(literal 1/2 binary64) k)))))
	48.6%	#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (*.f64 (/.f64 (sqrt.f64 n) (sqrt.f64 #s(literal 1/2 binary64))) (sqrt.f64 (/.f64 (PI.f64) k))))
	48.7%	#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (.f64 (/.f64 (sqrt.f64 #s(literal 2 binary64)) (sqrt.f64 k)) (/.f64 #s(literal -1 binary64) (/.f64 #s(literal -1 binary64) (sqrt.f64 (.f64 (PI.f64) n))))))
	48.7%	#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (.f64 (/.f64 (sqrt.f64 #s(literal 2 binary64)) (sqrt.f64 k)) (sqrt.f64 (.f64 (PI.f64) n))))
	48.7%	#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (.f64 (/.f64 #s(literal -1 binary64) (sqrt.f64 (.f64 #s(literal 1/2 binary64) k))) (neg.f64 (sqrt.f64 (*.f64 n (PI.f64))))))
	48.7%	#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (.f64 (.f64 (sqrt.f64 #s(literal 2 binary64)) (pow.f64 k #s(literal -1/2 binary64))) (sqrt.f64 (*.f64 n (PI.f64)))))
✓	48.7%	#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (.f64 (.f64 (neg.f64 (sqrt.f64 #s(literal 2 binary64))) (/.f64 #s(literal -1 binary64) (sqrt.f64 k))) (/.f64 (sqrt.f64 (*.f64 (PI.f64) n)) #s(literal 1 binary64))))
	48.8%	#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (.f64 (sqrt.f64 (/.f64 (PI.f64) k)) (sqrt.f64 (.f64 n #s(literal 2 binary64)))))
	48.6%	#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (.f64 (sqrt.f64 (/.f64 (PI.f64) #s(literal 1/2 binary64))) (/.f64 (.f64 (sqrt.f64 n) #s(literal 1 binary64)) (sqrt.f64 k))))
	48.8%	#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (.f64 (sqrt.f64 (/.f64 #s(literal 2 binary64) k)) (sqrt.f64 (.f64 (PI.f64) n))))
	48.8%	#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (.f64 (sqrt.f64 (.f64 (/.f64 (PI.f64) k) #s(literal 2 binary64))) (sqrt.f64 n)))
	39.6%	#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (.f64 (sqrt.f64 (.f64 (/.f64 n k) (PI.f64))) (sqrt.f64 #s(literal 2 binary64))))
	48.8%	#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (.f64 (sqrt.f64 (.f64 (/.f64 #s(literal 2 binary64) k) (PI.f64))) (sqrt.f64 n)))
	39.5%	#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (.f64 (sqrt.f64 (.f64 (PI.f64) #s(literal 2 binary64))) (sqrt.f64 (/.f64 n k))))
	39.5%	#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (.f64 (sqrt.f64 (PI.f64)) (sqrt.f64 (/.f64 n (.f64 #s(literal 1/2 binary64) k)))))
	39.5%	#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (.f64 (sqrt.f64 (PI.f64)) (sqrt.f64 (.f64 n (/.f64 #s(literal 2 binary64) k)))))
	48.7%	#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (.f64 (sqrt.f64 #s(literal 2 binary64)) (/.f64 #s(literal 1 binary64) (.f64 (/.f64 #s(literal -1 binary64) (sqrt.f64 (*.f64 (PI.f64) n))) (neg.f64 (sqrt.f64 k))))))
	40.1%	#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (.f64 (sqrt.f64 #s(literal 2 binary64)) (/.f64 #s(literal 1 binary64) (sqrt.f64 (/.f64 k (.f64 (PI.f64) n))))))
	48.7%	#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (.f64 (sqrt.f64 #s(literal 2 binary64)) (.f64 (sqrt.f64 n) (sqrt.f64 (/.f64 (PI.f64) k)))))
	39.6%	#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (.f64 (sqrt.f64 #s(literal 2 binary64)) (sqrt.f64 (/.f64 #s(literal 1 binary64) (/.f64 k (.f64 (PI.f64) n))))))
	48.7%	#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (.f64 #s(approx (pow ( (* 2 n) (PI)) (+ (* -1/2 k) 1/2)) (.f64 (sqrt.f64 (.f64 n (PI.f64))) (sqrt.f64 #s(literal 2 binary64)))) (sqrt.f64 (/.f64 #s(literal 1 binary64) k))))
	48.7%	#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (.f64 #s(approx (/ (sqrt 2) (sqrt k)) (.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) k)) (sqrt.f64 #s(literal 2 binary64)))) (/.f64 (sqrt.f64 (*.f64 (PI.f64) n)) #s(literal 1 binary64))))
	39.7%	#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt.f64 (/.f64 (*.f64 (PI.f64) #s(literal 2 binary64)) (/.f64 k n))))
	39.7%	#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt.f64 (/.f64 #s(literal 2 binary64) (/.f64 k (*.f64 (PI.f64) n)))))
✓	39.7%	#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt.f64 (.f64 (/.f64 (.f64 (PI.f64) n) k) #s(literal 2 binary64))))
	39.7%	#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt.f64 (*.f64 (/.f64 n (/.f64 k (PI.f64))) #s(literal 2 binary64))))
	39.7%	#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt.f64 (.f64 (/.f64 n k) (.f64 #s(literal 2 binary64) (PI.f64)))))
	39.7%	#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt.f64 (.f64 (/.f64 #s(literal 2 binary64) k) (.f64 (PI.f64) n))))
	39.5%	#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt.f64 (.f64 (.f64 (sqrt.f64 (PI.f64)) #s(approx (* (sqrt (PI)) (/ n k)) (*.f64 (/.f64 (sqrt.f64 (PI.f64)) k) n))) #s(literal 2 binary64))))
✓	39.7%	#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt.f64 (.f64 (.f64 n (/.f64 (PI.f64) k)) #s(literal 2 binary64))))
	39.5%	#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt.f64 (.f64 (.f64 n (*.f64 (sqrt.f64 (PI.f64)) (/.f64 (sqrt.f64 (PI.f64)) k))) #s(literal 2 binary64))))
	39.5%	#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) #s(approx (/ (sqrt (* (PI) n)) (sqrt (* 1/2 k))) (/.f64 (sqrt.f64 (/.f64 (*.f64 (PI.f64) n) k)) (sqrt.f64 #s(literal 1/2 binary64)))))

Compiler

Compiled 4 424 to 1 745 computations (60.6% saved)

regimes170.0ms (1.9%)

Memory

-3.5MiB live, 112.9MiB allocated

Counts

101 → 1

Calls

Call 1

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

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

Calls

4 calls:

36.0ms	k
25.0ms	(.f64 (.f64 #s(literal 2 binary64) (PI.f64)) n)
25.0ms	n
22.0ms	(.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
99.1%	1	`k`
99.1%	1	`n`
99.1%	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))))`
99.1%	1	`(.f64 (.f64 #s(literal 2 binary64) (PI.f64)) n)`

Compiler

Compiled 23 to 23 computations (0% saved)

regimes87.0ms (1%)

Memory

30.6MiB live, 193.3MiB allocated

Counts

72 → 2

Calls

Call 1

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

Outputs

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

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

Calls

4 calls:

24.0ms	n
21.0ms	(.f64 (.f64 #s(literal 2 binary64) (PI.f64)) n)
20.0ms	k
18.0ms	(.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) (pow.f64 (.f64 (*.f64 #s(literal 2 binary64) (PI.f64)) n) (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 2 binary64))))

Results

Accuracy	Segments	Branch
98.2%	2	`k`
64.7%	4	`n`
97.8%	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))))`
64.7%	4	`(.f64 (.f64 #s(literal 2 binary64) (PI.f64)) n)`

Compiler

Compiled 23 to 23 computations (0% saved)

regimes81.0ms (0.9%)

Memory

-22.0MiB live, 134.3MiB allocated

Counts

71 → 1

Calls

Call 1

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

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

Calls

4 calls:

21.0ms	(.f64 (.f64 #s(literal 2 binary64) (PI.f64)) n)
20.0ms	n
19.0ms	k
18.0ms	(.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) (pow.f64 (.f64 (*.f64 #s(literal 2 binary64) (PI.f64)) n) (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 2 binary64))))

Results

Accuracy	Segments	Branch
48.8%	1	`n`
48.8%	1	`(.f64 (.f64 #s(literal 2 binary64) (PI.f64)) n)`
48.8%	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))))`
48.8%	1	`k`

Compiler

Compiled 23 to 23 computations (0% saved)

regimes24.0ms (0.3%)

Memory

4.1MiB live, 42.1MiB allocated

Counts

18 → 1

Calls

Call 1

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

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

Calls

4 calls:

7.0ms	(.f64 (.f64 #s(literal 2 binary64) (PI.f64)) n)
5.0ms	n
5.0ms	k
5.0ms	(.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) (pow.f64 (.f64 (*.f64 #s(literal 2 binary64) (PI.f64)) n) (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 2 binary64))))

Results

Accuracy	Segments	Branch
48.8%	1	`n`
48.8%	1	`(.f64 (.f64 #s(literal 2 binary64) (PI.f64)) n)`
48.8%	1	`k`
48.8%	1	`(.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) (pow.f64 (.f64 (*.f64 #s(literal 2 binary64) (PI.f64)) n) (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 2 binary64))))`

Compiler

Compiled 23 to 23 computations (0% saved)

regimes20.0ms (0.2%)

Memory

-1.1MiB live, 36.9MiB allocated

Counts

15 → 1

Calls

Call 1

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

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

Calls

4 calls:

6.0ms	n
5.0ms	(.f64 (.f64 #s(literal 2 binary64) (PI.f64)) n)
4.0ms	k
4.0ms	(.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) (pow.f64 (.f64 (*.f64 #s(literal 2 binary64) (PI.f64)) n) (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 2 binary64))))

Results

Accuracy	Segments	Branch
48.8%	1	`n`
48.8%	1	`(.f64 (.f64 #s(literal 2 binary64) (PI.f64)) n)`
48.8%	1	`k`
48.8%	1	`(.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) (pow.f64 (.f64 (*.f64 #s(literal 2 binary64) (PI.f64)) n) (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 2 binary64))))`

Compiler

Compiled 23 to 23 computations (0% saved)

regimes25.0ms (0.3%)

Memory

-14.2MiB live, 35.4MiB allocated

Counts

13 → 1

Calls

Call 1

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

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

Calls

4 calls:

12.0ms	n
4.0ms	(.f64 (.f64 #s(literal 2 binary64) (PI.f64)) n)
4.0ms	k
4.0ms	(.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) (pow.f64 (.f64 (*.f64 #s(literal 2 binary64) (PI.f64)) n) (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 2 binary64))))

Results

Accuracy	Segments	Branch
39.7%	1	`n`
39.7%	1	`(.f64 (.f64 #s(literal 2 binary64) (PI.f64)) n)`
39.7%	1	`k`
39.7%	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))))`

Compiler

Compiled 23 to 23 computations (0% saved)

regimes5.0ms (0.1%)

Memory

9.1MiB live, 9.1MiB allocated

Accuracy

Total -0.0b remaining (-0%)

Threshold costs -0b (-0%)

Counts

1 → 1

Calls

Call 1

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

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

Calls

4 calls:

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

Results

Accuracy	Segments	Branch
39.7%	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))))`
39.7%	1	`k`
39.7%	1	`n`
39.7%	1	`(.f64 (.f64 #s(literal 2 binary64) (PI.f64)) n)`

Compiler

Compiled 23 to 23 computations (0% saved)

bsearch23.0ms (0.3%)

Memory

21.4MiB live, 21.4MiB allocated

Algorithm

1×	binary-search

Stop Event

1×	narrow-enough

Steps

Time	Left	Right
20.0ms	0.00010344248431844784	6984.716989541763

Samples

14.0ms

144×

valid

Compiler

Compiled 415 to 369 computations (11.1% saved)

Precisions

Click to see histograms. Total time spent on operations: 10.0ms

ival-mult: 3.0ms (28.6% of total)

ival-pow: 3.0ms (28.6% of total)

ival-div: 2.0ms (19.1% of total)

ival-pi: 1.0ms (9.5% of total)

ival-sub: 1.0ms (9.5% of total)

ival-sqrt: 1.0ms (9.5% of total)

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

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

exact: 0.0ms (0% of total)

simplify72.0ms (0.8%)

Memory

-7.2MiB live, 69.4MiB allocated

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	54	201
1	68	189
2	85	189
3	109	189
4	136	189
5	165	189
6	238	189
7	533	189
8	4977	189

Stop Event

1×	node limit

Calls

Call 1

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

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

soundness627.0ms (7.1%)

Memory

15.0MiB live, 406.5MiB allocated

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	41	255
0	62	239
1	221	233
2	1297	225
0	8629	225
0	53	316
0	85	306
1	278	288
2	1590	283
0	8392	283
0	128	517
1	345	504
2	1021	460
3	3363	433
4	5589	421
0	8476	406

Stop Event

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

Compiler

Compiled 705 to 424 computations (39.9% saved)

preprocess44.0ms (0.5%)

Memory: 15.9MiB live, 88.9MiB allocated
Compiler: Compiled 434 to 138 computations (68.2% saved)

end0.0ms (0%)

Memory: 0.0MiB live, 0.0MiB allocated

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

Iter	Nodes	Cost
0	41	316
0	62	310
1	93	304
2	129	304
3	166	296
4	205	296
5	219	296
6	240	296
7	267	296
8	276	296
9	279	296
0	279	296

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

Iter	Nodes	Cost
0	41	316
0	62	310
1	93	304
2	129	304
3	166	296
4	205	296
5	219	296
6	240	296
7	267	296
8	276	296
9	279	296
0	279	296

start0.0ms (0%)

analyze113.0ms (1.3%)

sample3.4s (38.7%)

explain147.0ms (1.7%)

preprocess70.0ms (0.8%)

eval0.0ms (0%)

prune0.0ms (0%)

simplify6.0ms (0.1%)

localize57.0ms (0.6%)

series92.0ms (1%)

simplify179.0ms (2%)

rewrite195.0ms (2.2%)

eval88.0ms (1%)

prune24.0ms (0.3%)

simplify428.0ms (4.9%)

localize197.0ms (2.2%)

series74.0ms (0.8%)

simplify124.0ms (1.4%)

rewrite157.0ms (1.8%)

eval125.0ms (1.4%)

prune80.0ms (0.9%)

simplify11.0ms (0.1%)

localize192.0ms (2.2%)

series70.0ms (0.8%)

simplify152.0ms (1.7%)

rewrite220.0ms (2.5%)

eval213.0ms (2.4%)

prune107.0ms (1.2%)

simplify240.0ms (2.7%)

localize159.0ms (1.8%)

series51.0ms (0.6%)

simplify116.0ms (1.3%)

rewrite227.0ms (2.6%)

eval154.0ms (1.7%)

prune150.0ms (1.7%)

regimes170.0ms (1.9%)

regimes87.0ms (1%)

regimes81.0ms (0.9%)

regimes24.0ms (0.3%)

regimes20.0ms (0.2%)

regimes25.0ms (0.3%)

regimes5.0ms (0.1%)

bsearch23.0ms (0.3%)

simplify72.0ms (0.8%)

soundness627.0ms (7.1%)

preprocess44.0ms (0.5%)

end0.0ms (0%)

Profiling

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

Iter	Nodes	Cost
0	41	316
0	62	310
1	93	304
2	129	304
3	166	296
4	205	296
5	219	296
6	240	296
7	267	296
8	276	296
9	279	296
0	279	296