Metrics for Migdal et al, Equation (51)

start0.0ms (0%)

Memory: 0.1MiB live, 0.1MiB allocated

analyze133.0ms (1.3%)

Memory

-9.6MiB live, 180.5MiB 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)

sample3.9s (39.3%)

Memory

16.6MiB live, 4 770.0MiB allocated

Samples

1.2s	8 256×	0	valid
903.0ms	3 484×	1	invalid
836.0ms	1 893×	1	exit
171.0ms	446×	2	invalid
46.0ms	499×	0	invalid
26.0ms	201×	0	exit

Precisions

Click to see histograms. Total time spent on operations: 2.4s

ival-sqrt: 565.0ms (23.4% of total)

ival-pow: 528.0ms (21.8% of total)

ival-mult: 477.0ms (19.7% of total)

ival-div: 335.0ms (13.9% of total)

ival-pi: 166.0ms (6.9% of total)

adjust: 157.0ms (6.5% of total)

ival-sub: 154.0ms (6.4% of total)

exact: 17.0ms (0.7% of total)

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

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

Bogosity

explain148.0ms (1.5%)

Memory

-17.0MiB live, 373.1MiB allocated

FPErrors

Click to see full error table

Ground Truth	Overpredictions	Example	Underpredictions	Example	Subexpression
1	94	(6.747429450425676e-40 1.9117795040633735e+278)	1	(5.3992085673560354e-14 8.311256218367836e+75)	`(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	94	34

Confusion

	Predicted +	Predicted -
+	0	1
-	94	161

Precision

0.0

Recall

0.0

Confusion?

	Predicted +	Predicted Maybe	Predicted -
+	0	1	0
-	94	33	128

Precision?

0.0078125

Recall?

1.0

Freqs

test

number	freq
0	162
1	94

Total Confusion?

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

Precision?

1.0

Recall?

1.0

Samples

55.0ms

512×

valid

Compiler

Compiled 128 to 43 computations (66.4% saved)

Precisions

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

ival-mult: 10.0ms (27.2% of total)

ival-pow: 10.0ms (27.2% of total)

ival-div: 7.0ms (19% of total)

ival-sqrt: 4.0ms (10.9% of total)

ival-sub: 3.0ms (8.1% of total)

ival-pi: 2.0ms (5.4% of total)

exact: 1.0ms (2.7% of total)

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

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

preprocess80.0ms (0.8%)

Memory

-51.1MiB live, 67.2MiB allocated

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 1 (0.0ms)

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

Stop Event

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

Calls

Call 1

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

Outputs

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

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

Compiler

Compiled 16 to 13 computations (18.8% saved)

eval0.0ms (0%)

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

prune0.0ms (0%)

Memory

1.3MiB live, 1.3MiB allocated

Alt Table

Click to see full alt table

Status	Accuracy	Program
▶	99.6%	(.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) (pow.f64 (.f64 (*.f64 #s(literal 2 binary64) (PI.f64)) n) (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 2 binary64))))

Compiler

Compiled 16 to 13 computations (18.8% saved)

simplify8.0ms (0.1%)

Memory

20.1MiB live, 20.1MiB allocated

Algorithm

1×	egg-herbie

Localize:

Found 4 expressions of interest:

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

Iterations

Useful iterations: 1 (0.0ms)

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

Stop Event

1×	iter limit
1×	saturated
1×	iter limit

Calls

Call 1

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

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

localize38.0ms (0.4%)

Memory

-3.4MiB live, 90.0MiB allocated

Localize:

Found 4 expressions of interest:

New	Metric	Score
accuracy	0.10282003162065376	(pow.f64 (.f64 (.f64 #s(literal 2 binary64) (PI.f64)) n) (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 2 binary64)))
accuracy	0.1953125	(.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) (pow.f64 (.f64 (*.f64 #s(literal 2 binary64) (PI.f64)) n) (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 2 binary64))))
accuracy	0.24609375	(/.f64 #s(literal 1 binary64) (sqrt.f64 k))
accuracy	0.2578125	(.f64 (.f64 #s(literal 2 binary64) (PI.f64)) n)

Samples

29.0ms

256×

valid

Compiler

Compiled 56 to 15 computations (73.2% saved)

Precisions

Click to see histograms. Total time spent on operations: 19.0ms

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

ival-div: 4.0ms (20.6% of total)

ival-mult: 4.0ms (20.6% of total)

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

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

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

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

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

exact: 0.0ms (0% of total)

series142.0ms (1.4%)

Memory

0.6MiB live, 139.3MiB allocated

Counts

5 → 22

Calls

Call 1

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

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

Calls

6 calls:

Time	Variable		Point	Expression
86.0ms	n	@	0	((* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (/ 1 (sqrt k)) (sqrt k) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2)) (* (* 2 (PI)) n))
41.0ms	n	@	-inf	((* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (/ 1 (sqrt k)) (sqrt k) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2)) (* (* 2 (PI)) n))
8.0ms	n	@	inf	((* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (/ 1 (sqrt k)) (sqrt k) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2)) (* (* 2 (PI)) n))
3.0ms	k	@	-inf	((* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (/ 1 (sqrt k)) (sqrt k) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2)) (* (* 2 (PI)) n))
2.0ms	k	@	0	((* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (/ 1 (sqrt k)) (sqrt k) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2)) (* (* 2 (PI)) n))

simplify158.0ms (1.6%)

Memory

2.9MiB live, 185.6MiB allocated

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

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

Stop Event

1×	iter limit
1×	node limit

Counts

22 → 22

Calls

Call 1

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

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

rewrite263.0ms (2.6%)

Memory

21.1MiB live, 260.8MiB allocated

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	13	38
0	22	38
1	83	35
2	446	35
3	4007	29
0	8921	29

Stop Event

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

Counts

5 → 321

Calls

Call 1

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

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

eval113.0ms (1.1%)

Memory: -19.4MiB live, 133.6MiB allocated
Compiler: Compiled 7 537 to 1 169 computations (84.5% saved)

prune40.0ms (0.4%)

Memory

-15.7MiB live, 31.5MiB allocated

Pruning

12 alts after pruning (12 fresh and 0 done)

	Pruned	Kept	Total
New	326	12	338
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	327	12	339

Accuracy

100.0%

Counts

339 → 12

Alt Table

Click to see full alt table

Status	Accuracy	Program
▶	29.1%	(/.f64 (pow.f64 (*.f64 #s(literal 0 binary64) n) (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 8 binary64))) (sqrt.f64 k))
	99.5%	(.f64 (pow.f64 (pow.f64 k #s(literal 1/4 binary64)) #s(literal -2 binary64)) (pow.f64 (.f64 (*.f64 #s(literal 2 binary64) (PI.f64)) n) (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 2 binary64))))
▶	99.6%	(.f64 (pow.f64 k #s(literal -1/2 binary64)) (pow.f64 (.f64 (*.f64 #s(literal 2 binary64) (PI.f64)) n) (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 2 binary64))))
	72.6%	(.f64 (pow.f64 #s(literal 2 binary64) (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 2 binary64))) (/.f64 (pow.f64 (.f64 n (PI.f64)) (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 2 binary64))) (sqrt.f64 k)))
	99.5%	(.f64 (/.f64 #s(literal 1 binary64) (pow.f64 (pow.f64 k #s(literal 1/4 binary64)) #s(literal 2 binary64))) (pow.f64 (.f64 (*.f64 #s(literal 2 binary64) (PI.f64)) n) (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 2 binary64))))
	99.5%	(.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) (pow.f64 (.f64 (.f64 (.f64 n #s(literal 2 binary64)) (sqrt.f64 (PI.f64))) (sqrt.f64 (PI.f64))) (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 2 binary64))))
▶	99.6%	(.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) #s(approx (pow ( (* 2 (PI)) n) (/ (- 1 k) 2)) (pow.f64 (.f64 (.f64 #s(literal 2 binary64) n) (PI.f64)) (fma.f64 #s(literal -1/2 binary64) k #s(literal 1/2 binary64)))))
▶	55.5%	(.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) #s(approx (pow ( (* 2 (PI)) n) (/ (- 1 k) 2)) (.f64 (.f64 (fma.f64 (.f64 (log.f64 (.f64 (.f64 #s(literal 2 binary64) n) (PI.f64))) k) #s(literal -1/2 binary64) #s(literal 1 binary64)) (sqrt.f64 #s(literal 2 binary64))) (sqrt.f64 (.f64 (PI.f64) n)))))
	54.9%	(.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)))))
	60.4%	#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (/.f64 (.f64 (sqrt.f64 #s(literal 2 binary64)) (fma.f64 (.f64 (log.f64 (.f64 (.f64 #s(literal 2 binary64) n) (PI.f64))) (sqrt.f64 (.f64 (.f64 (pow.f64 k #s(literal 3 binary64)) (PI.f64)) n))) #s(literal -1/2 binary64) (sqrt.f64 (.f64 (.f64 (PI.f64) n) k)))) k))
	99.6%	#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (.f64 (pow.f64 (.f64 (*.f64 #s(literal 2 binary64) n) (PI.f64)) (fma.f64 #s(literal -1/2 binary64) k #s(literal 1/2 binary64))) (sqrt.f64 (/.f64 #s(literal 1 binary64) k))))
▶	40.0%	#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))))

Compiler

Compiled 586 to 468 computations (20.1% saved)

simplify201.0ms (2%)

Memory

30.8MiB live, 81.5MiB 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 (.f64 (fma.f64 (.f64 (log.f64 (.f64 (.f64 #s(literal 2 binary64) n) (PI.f64))) k) #s(literal -1/2 binary64) #s(literal 1 binary64)) (sqrt.f64 #s(literal 2 binary64))) (sqrt.f64 (.f64 (PI.f64) n))))
cost-diff	0	(sqrt.f64 k)
cost-diff	0	(/.f64 #s(literal 1 binary64) (sqrt.f64 k))
cost-diff	2	(.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) #s(approx (pow ( (* 2 (PI)) n) (/ (- 1 k) 2)) (.f64 (.f64 (fma.f64 (.f64 (log.f64 (.f64 (.f64 #s(literal 2 binary64) n) (PI.f64))) k) #s(literal -1/2 binary64) #s(literal 1 binary64)) (sqrt.f64 #s(literal 2 binary64))) (sqrt.f64 (.f64 (PI.f64) n)))))
cost-diff	0	#s(approx (pow (* (* 2 (PI)) n) (/ (- 1 k) 2)) (pow.f64 (.f64 (.f64 #s(literal 2 binary64) n) (PI.f64)) (fma.f64 #s(literal -1/2 binary64) k #s(literal 1/2 binary64))))
cost-diff	0	(sqrt.f64 k)
cost-diff	0	(/.f64 #s(literal 1 binary64) (sqrt.f64 k))
cost-diff	2	(.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) #s(approx (pow ( (* 2 (PI)) n) (/ (- 1 k) 2)) (pow.f64 (.f64 (.f64 #s(literal 2 binary64) n) (PI.f64)) (fma.f64 #s(literal -1/2 binary64) k #s(literal 1/2 binary64)))))
cost-diff	1	(/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 8 binary64))
cost-diff	2	(*.f64 #s(literal 0 binary64) n)
cost-diff	3	(/.f64 (pow.f64 (*.f64 #s(literal 0 binary64) n) (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 8 binary64))) (sqrt.f64 k))
cost-diff	5	(pow.f64 (*.f64 #s(literal 0 binary64) n) (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 8 binary64)))
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	(pow.f64 (.f64 (.f64 #s(literal 2 binary64) (PI.f64)) n) (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 2 binary64)))
cost-diff	0	(pow.f64 k #s(literal -1/2 binary64))
cost-diff	0	(.f64 (pow.f64 k #s(literal -1/2 binary64)) (pow.f64 (.f64 (*.f64 #s(literal 2 binary64) (PI.f64)) n) (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 2 binary64))))
cost-diff	1	(/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 2 binary64))

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	51	383
0	85	364
1	132	358
2	186	358
3	340	358
4	733	358
5	1634	348
6	2657	348
7	3184	348
8	3592	348
9	3764	348
10	3784	348
11	3810	348
12	3837	348
13	3900	348
14	3929	348
15	3942	348
16	3942	348
17	3942	348
18	3942	348
19	4055	348
20	4263	348
21	4263	348
0	4263	347

Stop Event

1×	iter limit
1×	saturated
1×	iter limit

Calls

Call 1

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

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

localize197.0ms (2%)

Memory

-18.5MiB live, 171.9MiB allocated

Localize:

Found 20 expressions of interest:

New	Metric	Score
accuracy	0.140625	(.f64 (log.f64 (.f64 (*.f64 #s(literal 2 binary64) n) (PI.f64))) k)
accuracy	0.19140625	(.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) #s(approx (pow ( (* 2 (PI)) n) (/ (- 1 k) 2)) (.f64 (.f64 (fma.f64 (.f64 (log.f64 (.f64 (.f64 #s(literal 2 binary64) n) (PI.f64))) k) #s(literal -1/2 binary64) #s(literal 1 binary64)) (sqrt.f64 #s(literal 2 binary64))) (sqrt.f64 (.f64 (PI.f64) n)))))
accuracy	0.265625	(.f64 (.f64 (fma.f64 (.f64 (log.f64 (.f64 (.f64 #s(literal 2 binary64) n) (PI.f64))) k) #s(literal -1/2 binary64) #s(literal 1 binary64)) (sqrt.f64 #s(literal 2 binary64))) (sqrt.f64 (.f64 (PI.f64) n)))
accuracy	28.335247650234145	(PI.f64)
accuracy	0.12109375	(.f64 (.f64 #s(literal 2 binary64) n) (PI.f64))
accuracy	0.140625	(/.f64 #s(literal 1 binary64) (sqrt.f64 k))
accuracy	0.19140625	(.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) #s(approx (pow ( (* 2 (PI)) n) (/ (- 1 k) 2)) (pow.f64 (.f64 (.f64 #s(literal 2 binary64) n) (PI.f64)) (fma.f64 #s(literal -1/2 binary64) k #s(literal 1/2 binary64)))))
accuracy	28.335247650234145	(PI.f64)
accuracy	0.0	(/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 8 binary64))
accuracy	0.0	(-.f64 #s(literal 1 binary64) k)
accuracy	0.0	(*.f64 #s(literal 0 binary64) n)
accuracy	0.0	(sqrt.f64 k)
accuracy	0.12109375	(*.f64 (PI.f64) n)
accuracy	0.232753759768442	(.f64 (sqrt.f64 #s(literal 2 binary64)) (sqrt.f64 (/.f64 (.f64 (PI.f64) n) k)))
accuracy	9.695031462608759	(sqrt.f64 (/.f64 (*.f64 (PI.f64) n) k))
accuracy	28.335247650234145	(PI.f64)
accuracy	0.09891378162065376	(pow.f64 (.f64 (.f64 #s(literal 2 binary64) (PI.f64)) n) (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 2 binary64)))
accuracy	0.12109375	(.f64 (.f64 #s(literal 2 binary64) (PI.f64)) n)
accuracy	0.19140625	(.f64 (pow.f64 k #s(literal -1/2 binary64)) (pow.f64 (.f64 (*.f64 #s(literal 2 binary64) (PI.f64)) n) (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 2 binary64))))
accuracy	28.335247650234145	(PI.f64)

Samples

85.0ms	139×	0	valid
57.0ms	117×	0	invalid

Compiler

Compiled 318 to 42 computations (86.8% saved)

Precisions

Click to see histograms. Total time spent on operations: 91.0ms

ival-pow: 49.0ms (53.8% of total)

ival-mult: 18.0ms (19.8% of total)

ival-div: 8.0ms (8.8% of total)

ival-sqrt: 6.0ms (6.6% of total)

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

ival-add: 2.0ms (2.2% 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)

series149.0ms (1.5%)

Memory

6.9MiB live, 144.8MiB allocated

Counts

25 → 92

Calls

Call 1

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

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

Calls

6 calls:

Time	Variable		Point	Expression
35.0ms	k	@	0	((/ (- 1 k) 2) (* (pow k -1/2) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (pow k -1/2) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2)) (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (* (sqrt 2) (sqrt (/ (* (PI) n) k))) (sqrt 2) (sqrt (/ (* (PI) n) k)) (pow (* 0 n) (/ (- 1 k) 8)) (/ (pow (* 0 n) (/ (- 1 k) 8)) (sqrt k)) (* 0 n) (/ (- 1 k) 8) (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (/ 1 (sqrt k)) (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)) (PI) (* (* 2 (PI)) n) (* (PI) n) (- 1 k) (* (* 2 n) (PI)) (* (* (+ (* (* (log (* (* 2 n) (PI))) k) -1/2) 1) (sqrt 2)) (sqrt (* (PI) n))) (* (log (* (* 2 n) (PI))) k))
33.0ms	n	@	-inf	((/ (- 1 k) 2) (* (pow k -1/2) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (pow k -1/2) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2)) (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (* (sqrt 2) (sqrt (/ (* (PI) n) k))) (sqrt 2) (sqrt (/ (* (PI) n) k)) (pow (* 0 n) (/ (- 1 k) 8)) (/ (pow (* 0 n) (/ (- 1 k) 8)) (sqrt k)) (* 0 n) (/ (- 1 k) 8) (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (/ 1 (sqrt k)) (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)) (PI) (* (* 2 (PI)) n) (* (PI) n) (- 1 k) (* (* 2 n) (PI)) (* (* (+ (* (* (log (* (* 2 n) (PI))) k) -1/2) 1) (sqrt 2)) (sqrt (* (PI) n))) (* (log (* (* 2 n) (PI))) k))
28.0ms	k	@	-inf	((/ (- 1 k) 2) (* (pow k -1/2) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (pow k -1/2) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2)) (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (* (sqrt 2) (sqrt (/ (* (PI) n) k))) (sqrt 2) (sqrt (/ (* (PI) n) k)) (pow (* 0 n) (/ (- 1 k) 8)) (/ (pow (* 0 n) (/ (- 1 k) 8)) (sqrt k)) (* 0 n) (/ (- 1 k) 8) (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (/ 1 (sqrt k)) (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)) (PI) (* (* 2 (PI)) n) (* (PI) n) (- 1 k) (* (* 2 n) (PI)) (* (* (+ (* (* (log (* (* 2 n) (PI))) k) -1/2) 1) (sqrt 2)) (sqrt (* (PI) n))) (* (log (* (* 2 n) (PI))) k))
26.0ms	k	@	inf	((/ (- 1 k) 2) (* (pow k -1/2) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (pow k -1/2) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2)) (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (* (sqrt 2) (sqrt (/ (* (PI) n) k))) (sqrt 2) (sqrt (/ (* (PI) n) k)) (pow (* 0 n) (/ (- 1 k) 8)) (/ (pow (* 0 n) (/ (- 1 k) 8)) (sqrt k)) (* 0 n) (/ (- 1 k) 8) (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (/ 1 (sqrt k)) (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)) (PI) (* (* 2 (PI)) n) (* (PI) n) (- 1 k) (* (* 2 n) (PI)) (* (* (+ (* (* (log (* (* 2 n) (PI))) k) -1/2) 1) (sqrt 2)) (sqrt (* (PI) n))) (* (log (* (* 2 n) (PI))) k))
12.0ms	n	@	inf	((/ (- 1 k) 2) (* (pow k -1/2) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (pow k -1/2) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2)) (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (* (sqrt 2) (sqrt (/ (* (PI) n) k))) (sqrt 2) (sqrt (/ (* (PI) n) k)) (pow (* 0 n) (/ (- 1 k) 8)) (/ (pow (* 0 n) (/ (- 1 k) 8)) (sqrt k)) (* 0 n) (/ (- 1 k) 8) (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (/ 1 (sqrt k)) (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)) (PI) (* (* 2 (PI)) n) (* (PI) n) (- 1 k) (* (* 2 n) (PI)) (* (* (+ (* (* (log (* (* 2 n) (PI))) k) -1/2) 1) (sqrt 2)) (sqrt (* (PI) n))) (* (log (* (* 2 n) (PI))) k))

simplify212.0ms (2.1%)

Memory

33.7MiB live, 173.7MiB allocated

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	400	3260
1	1457	2974
2	7175	2791
0	8028	2677

Stop Event

1×	iter limit
1×	node limit

Counts

92 → 92

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

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)))
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(/ (+ (* k (+ (* -1/2 (* (sqrt (* k (* n (PI)))) (* (log (* 2 (* n (PI)))) (sqrt 2)))) (* 1/8 (* (sqrt (* (pow k 3) (* n (PI)))) (* (pow (log (* 2 (* n (PI)))) 2) (sqrt 2)))))) (* (sqrt (* k (* n (PI)))) (sqrt 2))) k)
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(/ (+ (* k (+ (* -1/2 (* (sqrt (* k (* n (PI)))) (* (log (* 2 (* n (PI)))) (sqrt 2)))) (* k (+ (* -1/48 (* (sqrt (* (pow k 3) (* n (PI)))) (* (pow (log (* 2 (* n (PI)))) 3) (sqrt 2)))) (* 1/8 (* (sqrt (* k (* n (PI)))) (* (pow (log (* 2 (* n (PI)))) 2) (sqrt 2)))))))) (* (sqrt (* k (* n (PI)))) (sqrt 2))) k)
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(+ (* k (+ (* -1/2 (* (sqrt (* n (PI))) (* (log (* 2 (* n (PI)))) (sqrt 2)))) (* 1/8 (* (* k (* (pow (log (* 2 (* n (PI)))) 2) (sqrt 2))) (sqrt (* n (PI))))))) (* (sqrt (* n (PI))) (sqrt 2)))
(fma.f64 (sqrt.f64 (.f64 (PI.f64) n)) (fma.f64 (.f64 (.f64 k (sqrt.f64 #s(literal 2 binary64))) (log.f64 (.f64 (.f64 (PI.f64) n) #s(literal 2 binary64)))) #s(literal -1/2 binary64) (sqrt.f64 #s(literal 2 binary64))) (.f64 (.f64 (.f64 #s(literal 1/8 binary64) k) (.f64 (pow.f64 (log.f64 (.f64 (.f64 (PI.f64) n) #s(literal 2 binary64))) #s(literal 2 binary64)) (sqrt.f64 #s(literal 2 binary64)))) (.f64 (sqrt.f64 (*.f64 (PI.f64) n)) k)))
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(sqrt (/ (* n (PI)) k))
(sqrt.f64 (/.f64 (*.f64 (PI.f64) n) k))
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(+ (exp (* 1/8 (+ (log 0) (* 20 (log k))))) (* k (* (exp (* 1/8 (+ (log 0) (* 20 (log k))))) (+ (* -1/8 (+ (log 0) (* 20 (log k)))) (* 1/8 (NAN))))))
(fma.f64 (.f64 k (.f64 #s(literal -1/8 binary64) (-.f64 (fma.f64 (log.f64 k) #s(literal 20 binary64) (log.f64 #s(literal 0 binary64))) (NAN.f64)))) (.f64 (pow.f64 k #s(literal 5/2 binary64)) #s(literal 0 binary64)) (.f64 (pow.f64 k #s(literal 5/2 binary64)) #s(literal 0 binary64)))
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(* (sqrt (/ 1 k)) (exp (* 1/8 (+ (log 0) (* 20 (log k))))))
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(/ (+ (* k (+ (* (sqrt k) (* (exp (* 1/8 (+ (log 0) (* 20 (log k))))) (+ (* -1/8 (+ (log 0) (* 20 (log k)))) (* 1/8 (NAN))))) (* (sqrt (pow k 3)) (* (exp (* 1/8 (+ (log 0) (* 20 (log k))))) (+ (* -1/8 (NAN)) (+ (* 1/16 (+ (NAN) (* -1 (NAN)))) (* 1/2 (pow (+ (* -1/8 (+ (log 0) (* 20 (log k)))) (* 1/8 (NAN))) 2)))))))) (* (sqrt k) (exp (* 1/8 (+ (log 0) (* 20 (log k))))))) k)
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(/ (+ (* k (+ (* k (+ (* (sqrt k) (* (exp (* 1/8 (+ (log 0) (* 20 (log k))))) (+ (* -1/8 (NAN)) (+ (* 1/16 (+ (NAN) (* -1 (NAN)))) (* 1/2 (pow (+ (* -1/8 (+ (log 0) (* 20 (log k)))) (* 1/8 (NAN))) 2)))))) (* (sqrt (pow k 3)) (* (exp (* 1/8 (+ (log 0) (* 20 (log k))))) (+ (* -1/16 (+ (NAN) (* -1 (NAN)))) (+ (* 1/48 (+ (NAN) (+ (* -3 (NAN)) (* 2 (NAN))))) (+ (* 1/6 (pow (+ (* -1/8 (+ (log 0) (* 20 (log k)))) (* 1/8 (NAN))) 3)) (* (+ (* -1/8 (NAN)) (* 1/16 (+ (NAN) (* -1 (NAN))))) (+ (* -1/8 (+ (log 0) (* 20 (log k)))) (* 1/8 (NAN))))))))))) (* (sqrt k) (* (exp (* 1/8 (+ (log 0) (* 20 (log k))))) (+ (* -1/8 (+ (log 0) (* 20 (log k)))) (* 1/8 (NAN))))))) (* (sqrt k) (exp (* 1/8 (+ (log 0) (* 20 (log k))))))) k)
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1/8
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1
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(* -1/2 k)
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(+ (* 1/8 (* (sqrt (/ 1 k)) (/ (* (NAN) (* (exp (* 1/8 (* (+ (log 0) (* 20 (log (/ 1 n)))) (- 1 k)))) (- 1 k))) n))) (+ (* (sqrt (/ 1 k)) (exp (* 1/8 (* (+ (log 0) (* 20 (log (/ 1 n)))) (- 1 k))))) (+ (* (sqrt (/ 1 k)) (/ (* (exp (* 1/8 (* (+ (log 0) (* 20 (log (/ 1 n)))) (- 1 k)))) (+ (* 1/3072 (* (pow (NAN) 3) (pow (- 1 k) 3))) (+ (* 1/128 (* (NAN) (* (+ (NAN) (* -1 (NAN))) (pow (- 1 k) 2)))) (* 1/48 (* (+ (NAN) (+ (* -3 (NAN)) (* 2 (NAN)))) (- 1 k)))))) (pow n 3))) (* (sqrt (/ 1 k)) (/ (* (exp (* 1/8 (* (+ (log 0) (* 20 (log (/ 1 n)))) (- 1 k)))) (+ (* 1/128 (* (pow (NAN) 2) (pow (- 1 k) 2))) (* 1/16 (* (+ (NAN) (* -1 (NAN))) (- 1 k))))) (pow n 2))))))
(fma.f64 (.f64 (.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) k)) #s(literal 1/8 binary64)) (NAN.f64)) (.f64 (pow.f64 (exp.f64 #s(literal 1/8 binary64)) (.f64 (fma.f64 (neg.f64 (log.f64 n)) #s(literal 20 binary64) (log.f64 #s(literal 0 binary64))) (-.f64 #s(literal 1 binary64) k))) (/.f64 (-.f64 #s(literal 1 binary64) k) n)) (.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) k)) (fma.f64 (pow.f64 (exp.f64 #s(literal 1/8 binary64)) (.f64 (fma.f64 (neg.f64 (log.f64 n)) #s(literal 20 binary64) (log.f64 #s(literal 0 binary64))) (-.f64 #s(literal 1 binary64) k))) (/.f64 (+.f64 (/.f64 (fma.f64 (pow.f64 (.f64 (NAN.f64) (-.f64 #s(literal 1 binary64) k)) #s(literal 3 binary64)) #s(literal 1/3072 binary64) (fma.f64 (pow.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 2 binary64)) #s(literal 0 binary64) (.f64 #s(literal 0 binary64) (-.f64 #s(literal 1 binary64) k)))) n) (fma.f64 (.f64 #s(literal 1/128 binary64) (pow.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 2 binary64))) (.f64 (NAN.f64) (NAN.f64)) (.f64 #s(literal 0 binary64) (-.f64 #s(literal 1 binary64) k)))) (.f64 n n)) (pow.f64 (exp.f64 #s(literal 1/8 binary64)) (*.f64 (fma.f64 (neg.f64 (log.f64 n)) #s(literal 20 binary64) (log.f64 #s(literal 0 binary64))) (-.f64 #s(literal 1 binary64) k))))))
(* (sqrt (* n (PI))) (* (sqrt 2) (+ 1 (* -1/2 (* k (+ (log (* 2 (PI))) (* -1 (log (/ 1 n)))))))))
(.f64 (.f64 (fma.f64 (+.f64 (log.f64 (.f64 (PI.f64) #s(literal 2 binary64))) (log.f64 n)) (.f64 #s(literal -1/2 binary64) k) #s(literal 1 binary64)) (sqrt.f64 #s(literal 2 binary64))) (sqrt.f64 (*.f64 (PI.f64) n)))
(* k (+ (log (* 2 (PI))) (* -1 (log (/ 1 n)))))
(.f64 (+.f64 (log.f64 (.f64 (PI.f64) #s(literal 2 binary64))) (log.f64 n)) k)
(* (sqrt (/ 1 k)) (exp (* 1/2 (* (+ (log (* -2 (PI))) (* -1 (log (/ -1 n)))) (- 1 k)))))
(.f64 (sqrt.f64 (pow.f64 (exp.f64 (-.f64 #s(literal 1 binary64) k)) (-.f64 (log.f64 (.f64 #s(literal -2 binary64) (PI.f64))) (log.f64 (/.f64 #s(literal -1 binary64) n))))) (sqrt.f64 (/.f64 #s(literal 1 binary64) k)))
(exp (* 1/2 (* (+ (log (* -2 (PI))) (* -1 (log (/ -1 n)))) (- 1 k))))
(sqrt.f64 (pow.f64 (exp.f64 (-.f64 #s(literal 1 binary64) k)) (-.f64 (log.f64 (*.f64 #s(literal -2 binary64) (PI.f64))) (log.f64 (/.f64 #s(literal -1 binary64) n)))))
(* -1 (* (sqrt (/ (* n (PI)) k)) (* (pow (sqrt -1) 2) (sqrt 2))))
(.f64 (neg.f64 (sqrt.f64 (/.f64 (.f64 (PI.f64) n) k))) (neg.f64 (sqrt.f64 #s(literal 2 binary64))))
(* -1 (* (sqrt (/ (* n (PI)) k)) (pow (sqrt -1) 2)))
(.f64 (sqrt.f64 (/.f64 (.f64 (PI.f64) n) k)) #s(literal 1 binary64))
(exp (* 1/8 (* (+ (log 0) (* 20 (log (/ -1 n)))) (- 1 k))))
(pow.f64 (exp.f64 #s(literal 1/8 binary64)) (*.f64 (fma.f64 (log.f64 (/.f64 #s(literal -1 binary64) n)) #s(literal 20 binary64) (log.f64 #s(literal 0 binary64))) (-.f64 #s(literal 1 binary64) k)))
(+ (exp (* 1/8 (* (+ (log 0) (* 20 (log (/ -1 n)))) (- 1 k)))) (* -1/8 (/ (* (NAN) (* (exp (* 1/8 (* (+ (log 0) (* 20 (log (/ -1 n)))) (- 1 k)))) (- 1 k))) n)))
(fma.f64 (.f64 (.f64 (pow.f64 (exp.f64 #s(literal 1/8 binary64)) (.f64 (fma.f64 (log.f64 (/.f64 #s(literal -1 binary64) n)) #s(literal 20 binary64) (log.f64 #s(literal 0 binary64))) (-.f64 #s(literal 1 binary64) k))) (-.f64 #s(literal 1 binary64) k)) (/.f64 (NAN.f64) n)) #s(literal -1/8 binary64) (pow.f64 (exp.f64 #s(literal 1/8 binary64)) (.f64 (fma.f64 (log.f64 (/.f64 #s(literal -1 binary64) n)) #s(literal 20 binary64) (log.f64 #s(literal 0 binary64))) (-.f64 #s(literal 1 binary64) k))))
(+ (exp (* 1/8 (* (+ (log 0) (* 20 (log (/ -1 n)))) (- 1 k)))) (* -1 (/ (+ (* -1 (/ (* (exp (* 1/8 (* (+ (log 0) (* 20 (log (/ -1 n)))) (- 1 k)))) (+ (* 1/128 (* (pow (NAN) 2) (pow (- 1 k) 2))) (* 1/16 (* (+ (NAN) (* -1 (NAN))) (- 1 k))))) n)) (* 1/8 (* (NAN) (* (exp (* 1/8 (* (+ (log 0) (* 20 (log (/ -1 n)))) (- 1 k)))) (- 1 k))))) n)))
(-.f64 (pow.f64 (exp.f64 #s(literal 1/8 binary64)) (.f64 (fma.f64 (log.f64 (/.f64 #s(literal -1 binary64) n)) #s(literal 20 binary64) (log.f64 #s(literal 0 binary64))) (-.f64 #s(literal 1 binary64) k))) (/.f64 (fma.f64 (.f64 #s(literal 1/8 binary64) (.f64 (pow.f64 (exp.f64 #s(literal 1/8 binary64)) (.f64 (fma.f64 (log.f64 (/.f64 #s(literal -1 binary64) n)) #s(literal 20 binary64) (log.f64 #s(literal 0 binary64))) (-.f64 #s(literal 1 binary64) k))) (-.f64 #s(literal 1 binary64) k))) (NAN.f64) (.f64 (neg.f64 (pow.f64 (exp.f64 #s(literal 1/8 binary64)) (.f64 (fma.f64 (log.f64 (/.f64 #s(literal -1 binary64) n)) #s(literal 20 binary64) (log.f64 #s(literal 0 binary64))) (-.f64 #s(literal 1 binary64) k)))) (/.f64 (fma.f64 (.f64 #s(literal 1/128 binary64) (pow.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 2 binary64))) (.f64 (NAN.f64) (NAN.f64)) (*.f64 #s(literal 0 binary64) (-.f64 #s(literal 1 binary64) k))) n))) n))
(+ (exp (* 1/8 (* (+ (log 0) (* 20 (log (/ -1 n)))) (- 1 k)))) (* -1 (/ (+ (* -1 (/ (+ (* -1 (/ (* (exp (* 1/8 (* (+ (log 0) (* 20 (log (/ -1 n)))) (- 1 k)))) (+ (* 1/3072 (* (pow (NAN) 3) (pow (- 1 k) 3))) (+ (* 1/128 (* (NAN) (* (+ (NAN) (* -1 (NAN))) (pow (- 1 k) 2)))) (* 1/48 (* (+ (NAN) (+ (* -3 (NAN)) (* 2 (NAN)))) (- 1 k)))))) n)) (* (exp (* 1/8 (* (+ (log 0) (* 20 (log (/ -1 n)))) (- 1 k)))) (+ (* 1/128 (* (pow (NAN) 2) (pow (- 1 k) 2))) (* 1/16 (* (+ (NAN) (* -1 (NAN))) (- 1 k)))))) n)) (* 1/8 (* (NAN) (* (exp (* 1/8 (* (+ (log 0) (* 20 (log (/ -1 n)))) (- 1 k)))) (- 1 k))))) n)))
(-.f64 (pow.f64 (exp.f64 #s(literal 1/8 binary64)) (.f64 (fma.f64 (log.f64 (/.f64 #s(literal -1 binary64) n)) #s(literal 20 binary64) (log.f64 #s(literal 0 binary64))) (-.f64 #s(literal 1 binary64) k))) (/.f64 (fma.f64 (.f64 #s(literal 1/8 binary64) (.f64 (pow.f64 (exp.f64 #s(literal 1/8 binary64)) (.f64 (fma.f64 (log.f64 (/.f64 #s(literal -1 binary64) n)) #s(literal 20 binary64) (log.f64 #s(literal 0 binary64))) (-.f64 #s(literal 1 binary64) k))) (NAN.f64))) (-.f64 #s(literal 1 binary64) k) (/.f64 (fma.f64 (neg.f64 (pow.f64 (exp.f64 #s(literal 1/8 binary64)) (.f64 (fma.f64 (log.f64 (/.f64 #s(literal -1 binary64) n)) #s(literal 20 binary64) (log.f64 #s(literal 0 binary64))) (-.f64 #s(literal 1 binary64) k)))) (/.f64 (fma.f64 (pow.f64 (.f64 (NAN.f64) (-.f64 #s(literal 1 binary64) k)) #s(literal 3 binary64)) #s(literal 1/3072 binary64) (fma.f64 (pow.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 2 binary64)) #s(literal 0 binary64) (.f64 #s(literal 0 binary64) (-.f64 #s(literal 1 binary64) k)))) n) (.f64 (pow.f64 (exp.f64 #s(literal 1/8 binary64)) (.f64 (fma.f64 (log.f64 (/.f64 #s(literal -1 binary64) n)) #s(literal 20 binary64) (log.f64 #s(literal 0 binary64))) (-.f64 #s(literal 1 binary64) k))) (fma.f64 (.f64 #s(literal 1/128 binary64) (pow.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 2 binary64))) (.f64 (NAN.f64) (NAN.f64)) (.f64 #s(literal 0 binary64) (-.f64 #s(literal 1 binary64) k))))) (neg.f64 n))) n))
(* (sqrt (/ 1 k)) (exp (* 1/8 (* (+ (log 0) (* 20 (log (/ -1 n)))) (- 1 k)))))
(.f64 (pow.f64 (exp.f64 #s(literal 1/8 binary64)) (.f64 (fma.f64 (log.f64 (/.f64 #s(literal -1 binary64) n)) #s(literal 20 binary64) (log.f64 #s(literal 0 binary64))) (-.f64 #s(literal 1 binary64) k))) (sqrt.f64 (/.f64 #s(literal 1 binary64) k)))
(+ (* -1/8 (* (sqrt (/ 1 k)) (/ (* (NAN) (* (exp (* 1/8 (* (+ (log 0) (* 20 (log (/ -1 n)))) (- 1 k)))) (- 1 k))) n))) (* (sqrt (/ 1 k)) (exp (* 1/8 (* (+ (log 0) (* 20 (log (/ -1 n)))) (- 1 k))))))
(fma.f64 (.f64 (.f64 (.f64 (pow.f64 (exp.f64 #s(literal 1/8 binary64)) (.f64 (fma.f64 (log.f64 (/.f64 #s(literal -1 binary64) n)) #s(literal 20 binary64) (log.f64 #s(literal 0 binary64))) (-.f64 #s(literal 1 binary64) k))) (-.f64 #s(literal 1 binary64) k)) (/.f64 (NAN.f64) n)) #s(literal -1/8 binary64)) (sqrt.f64 (/.f64 #s(literal 1 binary64) k)) (.f64 (pow.f64 (exp.f64 #s(literal 1/8 binary64)) (.f64 (fma.f64 (log.f64 (/.f64 #s(literal -1 binary64) n)) #s(literal 20 binary64) (log.f64 #s(literal 0 binary64))) (-.f64 #s(literal 1 binary64) k))) (sqrt.f64 (/.f64 #s(literal 1 binary64) k))))
(+ (* -1 (/ (+ (* -1 (* (sqrt (/ 1 k)) (/ (* (exp (* 1/8 (* (+ (log 0) (* 20 (log (/ -1 n)))) (- 1 k)))) (+ (* 1/128 (* (pow (NAN) 2) (pow (- 1 k) 2))) (* 1/16 (* (+ (NAN) (* -1 (NAN))) (- 1 k))))) n))) (* 1/8 (* (sqrt (/ 1 k)) (* (NAN) (* (exp (* 1/8 (* (+ (log 0) (* 20 (log (/ -1 n)))) (- 1 k)))) (- 1 k)))))) n)) (* (sqrt (/ 1 k)) (exp (* 1/8 (* (+ (log 0) (* 20 (log (/ -1 n)))) (- 1 k))))))
(fma.f64 (pow.f64 (exp.f64 #s(literal 1/8 binary64)) (.f64 (fma.f64 (log.f64 (/.f64 #s(literal -1 binary64) n)) #s(literal 20 binary64) (log.f64 #s(literal 0 binary64))) (-.f64 #s(literal 1 binary64) k))) (sqrt.f64 (/.f64 #s(literal 1 binary64) k)) (/.f64 (fma.f64 (.f64 (.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) k)) #s(literal 1/8 binary64)) (.f64 (pow.f64 (exp.f64 #s(literal 1/8 binary64)) (.f64 (fma.f64 (log.f64 (/.f64 #s(literal -1 binary64) n)) #s(literal 20 binary64) (log.f64 #s(literal 0 binary64))) (-.f64 #s(literal 1 binary64) k))) (-.f64 #s(literal 1 binary64) k))) (NAN.f64) (.f64 (.f64 (neg.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) k))) (pow.f64 (exp.f64 #s(literal 1/8 binary64)) (.f64 (fma.f64 (log.f64 (/.f64 #s(literal -1 binary64) n)) #s(literal 20 binary64) (log.f64 #s(literal 0 binary64))) (-.f64 #s(literal 1 binary64) k)))) (/.f64 (fma.f64 (.f64 #s(literal 1/128 binary64) (pow.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 2 binary64))) (.f64 (NAN.f64) (NAN.f64)) (*.f64 #s(literal 0 binary64) (-.f64 #s(literal 1 binary64) k))) n))) (neg.f64 n)))
(+ (* -1 (/ (+ (* -1 (/ (+ (* -1 (* (sqrt (/ 1 k)) (/ (* (exp (* 1/8 (* (+ (log 0) (* 20 (log (/ -1 n)))) (- 1 k)))) (+ (* 1/3072 (* (pow (NAN) 3) (pow (- 1 k) 3))) (+ (* 1/128 (* (NAN) (* (+ (NAN) (* -1 (NAN))) (pow (- 1 k) 2)))) (* 1/48 (* (+ (NAN) (+ (* -3 (NAN)) (* 2 (NAN)))) (- 1 k)))))) n))) (* (sqrt (/ 1 k)) (* (exp (* 1/8 (* (+ (log 0) (* 20 (log (/ -1 n)))) (- 1 k)))) (+ (* 1/128 (* (pow (NAN) 2) (pow (- 1 k) 2))) (* 1/16 (* (+ (NAN) (* -1 (NAN))) (- 1 k))))))) n)) (* 1/8 (* (sqrt (/ 1 k)) (* (NAN) (* (exp (* 1/8 (* (+ (log 0) (* 20 (log (/ -1 n)))) (- 1 k)))) (- 1 k)))))) n)) (* (sqrt (/ 1 k)) (exp (* 1/8 (* (+ (log 0) (* 20 (log (/ -1 n)))) (- 1 k))))))
(fma.f64 (pow.f64 (exp.f64 #s(literal 1/8 binary64)) (.f64 (fma.f64 (log.f64 (/.f64 #s(literal -1 binary64) n)) #s(literal 20 binary64) (log.f64 #s(literal 0 binary64))) (-.f64 #s(literal 1 binary64) k))) (sqrt.f64 (/.f64 #s(literal 1 binary64) k)) (/.f64 (fma.f64 (.f64 (.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) k)) #s(literal 1/8 binary64)) (.f64 (pow.f64 (exp.f64 #s(literal 1/8 binary64)) (.f64 (fma.f64 (log.f64 (/.f64 #s(literal -1 binary64) n)) #s(literal 20 binary64) (log.f64 #s(literal 0 binary64))) (-.f64 #s(literal 1 binary64) k))) (NAN.f64))) (-.f64 #s(literal 1 binary64) k) (/.f64 (fma.f64 (.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) k)) (fma.f64 (.f64 #s(literal 1/128 binary64) (pow.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 2 binary64))) (.f64 (NAN.f64) (NAN.f64)) (.f64 #s(literal 0 binary64) (-.f64 #s(literal 1 binary64) k)))) (pow.f64 (exp.f64 #s(literal 1/8 binary64)) (.f64 (fma.f64 (log.f64 (/.f64 #s(literal -1 binary64) n)) #s(literal 20 binary64) (log.f64 #s(literal 0 binary64))) (-.f64 #s(literal 1 binary64) k))) (.f64 (.f64 (neg.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) k))) (pow.f64 (exp.f64 #s(literal 1/8 binary64)) (.f64 (fma.f64 (log.f64 (/.f64 #s(literal -1 binary64) n)) #s(literal 20 binary64) (log.f64 #s(literal 0 binary64))) (-.f64 #s(literal 1 binary64) k)))) (/.f64 (fma.f64 (pow.f64 (.f64 (NAN.f64) (-.f64 #s(literal 1 binary64) k)) #s(literal 3 binary64)) #s(literal 1/3072 binary64) (fma.f64 (pow.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 2 binary64)) #s(literal 0 binary64) (*.f64 #s(literal 0 binary64) (-.f64 #s(literal 1 binary64) k)))) n))) (neg.f64 n))) (neg.f64 n)))
(* -1 (* (sqrt (* n (PI))) (* (pow (sqrt -1) 2) (* (sqrt 2) (+ 1 (* -1/2 (* k (+ (log (* -2 (PI))) (* -1 (log (/ -1 n)))))))))))
(.f64 (neg.f64 (neg.f64 (sqrt.f64 (.f64 (PI.f64) n)))) (.f64 (fma.f64 (.f64 (-.f64 (log.f64 (*.f64 #s(literal -2 binary64) (PI.f64))) (log.f64 (/.f64 #s(literal -1 binary64) n))) k) #s(literal -1/2 binary64) #s(literal 1 binary64)) (sqrt.f64 #s(literal 2 binary64))))
(* k (+ (log (* -2 (PI))) (* -1 (log (/ -1 n)))))
(.f64 (-.f64 (log.f64 (.f64 #s(literal -2 binary64) (PI.f64))) (log.f64 (/.f64 #s(literal -1 binary64) n))) k)

rewrite374.0ms (3.7%)

Memory

0.7MiB live, 317.5MiB allocated

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	51	272
0	85	257
1	251	241
2	1233	241
0	8250	241

Stop Event

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

Counts

25 → 557

Calls

Call 1

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

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

eval231.0ms (2.3%)

Memory: 27.2MiB live, 400.9MiB allocated
Compiler: Compiled 28 004 to 3 619 computations (87.1% saved)

prune28.0ms (0.3%)

Memory

-0.2MiB live, 89.9MiB allocated

Pruning

15 alts after pruning (14 fresh and 1 done)

	Pruned	Kept	Total
New	842	11	853
Fresh	4	3	7
Picked	4	1	5
Done	0	0	0
Total	850	15	865

Accuracy

100.0%

Counts

865 → 15

Alt Table

Click to see full alt table

Status	Accuracy	Program
▶	99.6%	(/.f64 #s(approx (pow (* (* 2 (PI)) n) (/ (- 1 k) 2)) (pow.f64 (.f64 (.f64 n #s(literal 2 binary64)) (PI.f64)) (fma.f64 #s(literal -1/2 binary64) k #s(literal 1/2 binary64)))) (sqrt.f64 k))
	55.7%	(/.f64 #s(approx (pow (* (* 2 (PI)) n) (/ (- 1 k) 2)) (.f64 (sqrt.f64 (.f64 (.f64 n #s(literal 2 binary64)) (PI.f64))) (fma.f64 (.f64 #s(literal -1/2 binary64) k) (log.f64 (.f64 (.f64 n #s(literal 2 binary64)) (PI.f64))) #s(literal 1 binary64)))) (sqrt.f64 k))
	29.1%	(/.f64 #s(approx (pow (* 0 n) (/ (- 1 k) 8)) (pow.f64 #s(literal 0 binary64) (-.f64 #s(literal 1 binary64) k))) (sqrt.f64 k))
▶	19.5%	(/.f64 #s(literal 0 binary64) (sqrt.f64 k))
	55.0%	(.f64 (pow.f64 k #s(literal -1/2 binary64)) #s(approx (pow ( (* 2 (PI)) n) (/ (- 1 k) 2)) (.f64 (sqrt.f64 (.f64 (PI.f64) n)) (sqrt.f64 #s(literal 2 binary64)))))
	99.4%	(.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) #s(approx (pow ( (* 2 (PI)) n) (/ (- 1 k) 2)) (pow.f64 (.f64 (.f64 #s(literal 2 binary64) n) (*.f64 (sqrt.f64 (PI.f64)) (sqrt.f64 (PI.f64)))) (fma.f64 #s(literal -1/2 binary64) k #s(literal 1/2 binary64)))))
▶	54.9%	(.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)))))
	60.4%	#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))
▶	55.1%	#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)))
▶	99.6%	#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (.f64 (pow.f64 (.f64 (*.f64 #s(literal 2 binary64) n) (PI.f64)) (fma.f64 #s(literal -1/2 binary64) k #s(literal 1/2 binary64))) (sqrt.f64 (/.f64 #s(literal 1 binary64) k))))
	39.9%	#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))))
	55.0%	#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (.f64 (sqrt.f64 #s(literal 2 binary64)) (/.f64 (sqrt.f64 (.f64 n (PI.f64))) (sqrt.f64 k))))
	55.0%	#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)))))
✓	40.0%	#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))))
	40.1%	#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt.f64 (.f64 (/.f64 (.f64 n (PI.f64)) k) #s(literal 2 binary64))))

Compiler

Compiled 758 to 615 computations (18.9% saved)

simplify57.0ms (0.6%)

Memory

-41.9MiB live, 17.9MiB allocated

Algorithm

1×	egg-herbie

Localize:

Found 18 expressions of interest:

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

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	42	293
0	65	290
1	90	284
2	106	284
3	130	284
4	152	284
5	176	284
6	220	284
7	302	284
8	326	284
9	346	284
10	356	284
0	356	284

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

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

localize111.0ms (1.1%)

Memory

24.6MiB live, 216.6MiB allocated

Localize:

Found 18 expressions of interest:

New	Metric	Score
accuracy	0.10282003162065376	(pow.f64 (.f64 (.f64 #s(literal 2 binary64) n) (PI.f64)) (fma.f64 #s(literal -1/2 binary64) k #s(literal 1/2 binary64)))
accuracy	0.14453125	(sqrt.f64 (/.f64 #s(literal 1 binary64) k))
accuracy	0.1953125	(.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	0.2578125	(.f64 (.f64 #s(literal 2 binary64) n) (PI.f64))
accuracy	0.2578125	(*.f64 (PI.f64) n)
accuracy	0.3515576177835908	(sqrt.f64 (*.f64 (PI.f64) n))
accuracy	0.47951127930532605	(.f64 (sqrt.f64 (.f64 (PI.f64) n)) (sqrt.f64 #s(literal 2 binary64)))
accuracy	28.51009728160764	#s(approx (pow (* (* 2 (PI)) n) (/ (- 1 k) 2)) (.f64 (sqrt.f64 (.f64 (PI.f64) n)) (sqrt.f64 #s(literal 2 binary64))))
accuracy	0.2578125	(.f64 (.f64 n #s(literal 2 binary64)) (PI.f64))
accuracy	0.36556625976844204	(/.f64 (sqrt.f64 (.f64 (.f64 n #s(literal 2 binary64)) (PI.f64))) (sqrt.f64 k))
accuracy	0.38670750498874384	(sqrt.f64 (.f64 (.f64 n #s(literal 2 binary64)) (PI.f64)))
accuracy	28.536650363278138	#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)))
accuracy	0.0	(/.f64 #s(literal 0 binary64) (sqrt.f64 k))
accuracy	0.0	(sqrt.f64 k)
accuracy	0.0	#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))))
accuracy	0.10282003162065376	(pow.f64 (.f64 (.f64 n #s(literal 2 binary64)) (PI.f64)) (fma.f64 #s(literal -1/2 binary64) k #s(literal 1/2 binary64)))
accuracy	0.20150375976844204	(/.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))
accuracy	0.2578125	(.f64 (.f64 n #s(literal 2 binary64)) (PI.f64))

Samples

77.0ms

256×

valid

Compiler

Compiled 236 to 37 computations (84.3% saved)

Precisions

Click to see histograms. Total time spent on operations: 55.0ms

ival-mult: 16.0ms (29.4% of total)

ival-pow: 15.0ms (27.5% of total)

ival-div: 10.0ms (18.3% of total)

ival-sqrt: 8.0ms (14.7% of total)

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

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

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

exact: 1.0ms (1.8% of total)

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

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

series45.0ms (0.4%)

Memory

10.7MiB live, 104.2MiB allocated

Counts

20 → 40

Calls

Call 1

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

Calls

6 calls:

Time	Variable		Point	Expression
11.0ms	n	@	-inf	((/ (pow (* (* 2 (PI)) n) (/ (- 1 k) 2)) (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2)) (pow (* (* n 2) (PI)) (+ (* -1/2 k) 1/2)) (* (* n 2) (PI)) (/ 0 (sqrt k)) (sqrt k) (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (/ (sqrt (* (* n 2) (PI))) (sqrt k)) (sqrt (* (* n 2) (PI))) (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2)) (* (/ 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)) (* (sqrt (* (PI) n)) (sqrt 2)) (sqrt (* (PI) n)) (* (PI) n) (sqrt (/ 1 k)))
11.0ms	n	@	inf	((/ (pow (* (* 2 (PI)) n) (/ (- 1 k) 2)) (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2)) (pow (* (* n 2) (PI)) (+ (* -1/2 k) 1/2)) (* (* n 2) (PI)) (/ 0 (sqrt k)) (sqrt k) (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (/ (sqrt (* (* n 2) (PI))) (sqrt k)) (sqrt (* (* n 2) (PI))) (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2)) (* (/ 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)) (* (sqrt (* (PI) n)) (sqrt 2)) (sqrt (* (PI) n)) (* (PI) n) (sqrt (/ 1 k)))
10.0ms	n	@	0	((/ (pow (* (* 2 (PI)) n) (/ (- 1 k) 2)) (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2)) (pow (* (* n 2) (PI)) (+ (* -1/2 k) 1/2)) (* (* n 2) (PI)) (/ 0 (sqrt k)) (sqrt k) (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (/ (sqrt (* (* n 2) (PI))) (sqrt k)) (sqrt (* (* n 2) (PI))) (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2)) (* (/ 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)) (* (sqrt (* (PI) n)) (sqrt 2)) (sqrt (* (PI) n)) (* (PI) n) (sqrt (/ 1 k)))
7.0ms	k	@	-inf	((/ (pow (* (* 2 (PI)) n) (/ (- 1 k) 2)) (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2)) (pow (* (* n 2) (PI)) (+ (* -1/2 k) 1/2)) (* (* n 2) (PI)) (/ 0 (sqrt k)) (sqrt k) (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (/ (sqrt (* (* n 2) (PI))) (sqrt k)) (sqrt (* (* n 2) (PI))) (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2)) (* (/ 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)) (* (sqrt (* (PI) n)) (sqrt 2)) (sqrt (* (PI) n)) (* (PI) n) (sqrt (/ 1 k)))
2.0ms	k	@	inf	((/ (pow (* (* 2 (PI)) n) (/ (- 1 k) 2)) (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2)) (pow (* (* n 2) (PI)) (+ (* -1/2 k) 1/2)) (* (* n 2) (PI)) (/ 0 (sqrt k)) (sqrt k) (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (/ (sqrt (* (* n 2) (PI))) (sqrt k)) (sqrt (* (* n 2) (PI))) (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2)) (* (/ 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)) (* (sqrt (* (PI) n)) (sqrt 2)) (sqrt (* (PI) n)) (* (PI) n) (sqrt (/ 1 k)))

simplify169.0ms (1.7%)

Memory

-34.6MiB live, 251.2MiB allocated

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	153	716
1	500	695
2	1855	625
3	5611	613
0	8462	601

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)))
0
(sqrt k)
(sqrt (/ 1 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))))
(* (sqrt (/ 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))))
(* -1 (* (sqrt k) (pow (sqrt -1) 2)))
(* (sqrt (/ 1 k)) (* (exp (* (log (* 2 (* n (PI)))) (+ 1/2 (* -1/2 k)))) (pow (sqrt -1) 2)))
(* (sqrt (/ 1 k)) (pow (sqrt -1) 2))
(* (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 (/ 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 (* -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))) (* (sqrt -2) (sqrt -1))))
(* (sqrt (/ 1 k)) (exp (* (+ 1/2 (* -1/2 k)) (+ (log (* -2 (PI))) (* -1 (log (/ -1 n)))))))
(* -1 (* (sqrt (* n (PI))) (* (pow (sqrt -1) 2) (sqrt 2))))
(* -1 (* (sqrt (* n (PI))) (pow (sqrt -1) 2)))

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)
(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)))))) #s(literal 1 binary64) (.f64 (/.f64 (sqrt.f64 #s(literal 2 binary64)) k) (sqrt.f64 (.f64 (*.f64 n (PI.f64)) k))))
(/ (+ (* k (+ (* -1/2 (* (sqrt (* k (* n (PI)))) (* (log (* 2 (* n (PI)))) (sqrt 2)))) (* k (+ (* -1/48 (* (sqrt (* (pow k 3) (* n (PI)))) (* (pow (log (* 2 (* n (PI)))) 3) (sqrt 2)))) (* 1/8 (* (sqrt (* k (* n (PI)))) (* (pow (log (* 2 (* n (PI)))) 2) (sqrt 2)))))))) (* (sqrt (* k (* n (PI)))) (sqrt 2))) k)
(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 (pow.f64 (log.f64 (.f64 (.f64 n (PI.f64)) #s(literal 2 binary64))) #s(literal 2 binary64)) (sqrt.f64 (.f64 (.f64 n (PI.f64)) k))) #s(literal 1/8 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)))))) #s(literal 1 binary64) (.f64 (/.f64 (sqrt.f64 #s(literal 2 binary64)) k) (sqrt.f64 (.f64 (.f64 n (PI.f64)) 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)))
(fma.f64 (.f64 (sqrt.f64 (.f64 n (PI.f64))) (fma.f64 (.f64 (.f64 (pow.f64 (log.f64 (.f64 (.f64 n (PI.f64)) #s(literal 2 binary64))) #s(literal 2 binary64)) (sqrt.f64 #s(literal 2 binary64))) #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)))) k (.f64 (sqrt.f64 (.f64 n (PI.f64))) (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 k k) (.f64 (sqrt.f64 (.f64 n (PI.f64))) (fma.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 #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 (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)))))
0
#s(literal 0 binary64)
(sqrt k)
(sqrt.f64 k)
(sqrt (/ 1 k))
(sqrt.f64 (/.f64 #s(literal 1 binary64) k))
(* (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)))
(* (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)))
(* (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)))
(* -1 (* (sqrt k) (pow (sqrt -1) 2)))
(sqrt.f64 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)))
(* (sqrt (/ 1 k)) (pow (sqrt -1) 2))
(neg.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) k)))
(* (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 (/ 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)))
(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 (* -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)))
(* (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))) (* (sqrt -2) (sqrt -1))))
(.f64 (neg.f64 (sqrt.f64 #s(literal -2 binary64))) (.f64 (sqrt.f64 #s(literal -1 binary64)) (sqrt.f64 (*.f64 n (PI.f64)))))
(* (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)))
(* -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.f64 (*.f64 n (PI.f64)))

rewrite292.0ms (2.9%)

Memory

15.3MiB live, 346.4MiB allocated

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	42	236
0	65	228
1	200	218
2	904	170
0	9162	170

Stop Event

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

Counts

20 → 1 411

Calls

Call 1

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

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

eval150.0ms (1.5%)

Memory: 3.7MiB live, 376.3MiB allocated
Compiler: Compiled 34 660 to 3 941 computations (88.6% saved)

prune38.0ms (0.4%)

Memory

27.0MiB live, 127.8MiB allocated

Pruning

20 alts after pruning (16 fresh and 4 done)

	Pruned	Kept	Total
New	1 094	12	1 106
Fresh	5	4	9
Picked	2	3	5
Done	0	1	1
Total	1 101	20	1 121

Accuracy

100.0%

Counts

1 121 → 20

Alt Table

Click to see full alt table

Status	Accuracy	Program
	55.5%	(/.f64 #s(approx (pow (* (* 2 (PI)) n) (/ (- 1 k) 2)) (pow.f64 (+.f64 n n) (fma.f64 #s(literal -1/2 binary64) k #s(literal 1/2 binary64)))) (sqrt.f64 k))
▶	99.5%	(/.f64 #s(approx (pow (* (* 2 (PI)) n) (/ (- 1 k) 2)) (pow.f64 (.f64 (.f64 (sqrt.f64 (PI.f64)) n) (*.f64 #s(literal 2 binary64) (sqrt.f64 (PI.f64)))) (fma.f64 #s(literal -1/2 binary64) k #s(literal 1/2 binary64)))) (sqrt.f64 k))
✓	99.6%	(/.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))
	55.7%	(/.f64 #s(approx (pow (* (* 2 (PI)) n) (/ (- 1 k) 2)) (.f64 (sqrt.f64 (.f64 (.f64 n #s(literal 2 binary64)) (PI.f64))) (fma.f64 (.f64 #s(literal -1/2 binary64) k) (log.f64 (.f64 (.f64 n #s(literal 2 binary64)) (PI.f64))) #s(literal 1 binary64)))) (sqrt.f64 k))
▶	29.1%	(/.f64 #s(approx (pow (* 0 n) (/ (- 1 k) 8)) (pow.f64 #s(literal 0 binary64) (-.f64 #s(literal 1 binary64) k))) (sqrt.f64 k))
✓	54.9%	(.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)))))
▶	19.5%	#s(approx (/ 0 (sqrt k)) #s(literal 0 binary64))
	54.9%	#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 n)) (sqrt.f64 k)))
▶	5.2%	#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (/.f64 (sqrt.f64 (+.f64 (PI.f64) (PI.f64))) (sqrt.f64 k)))
	11.6%	#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (/.f64 (sqrt.f64 (+.f64 n n)) (sqrt.f64 k)))
	5.2%	#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (/.f64 (sqrt.f64 (.f64 (.f64 (PI.f64) #s(literal 2 binary64)) (PI.f64))) (sqrt.f64 k)))
✓	55.1%	#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)))
	54.9%	#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (.f64 (sqrt.f64 (.f64 (PI.f64) n)) (/.f64 (sqrt.f64 #s(literal 2 binary64)) (sqrt.f64 k))))
	54.9%	#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (.f64 (sqrt.f64 (.f64 (PI.f64) #s(literal 2 binary64))) (/.f64 (sqrt.f64 n) (sqrt.f64 k))))
	5.2%	#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (.f64 (sqrt.f64 (.f64 (PI.f64) #s(literal 2 binary64))) (sqrt.f64 (/.f64 (PI.f64) k))))
	39.9%	#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))))
▶	55.0%	#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (.f64 (sqrt.f64 n) (.f64 (sqrt.f64 #s(literal 2 binary64)) (sqrt.f64 (/.f64 (PI.f64) k)))))
✓	40.0%	#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))))
	40.1%	#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt.f64 (.f64 (/.f64 (.f64 n (PI.f64)) k) #s(literal 2 binary64))))
	9.4%	#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt.f64 (*.f64 (/.f64 n k) #s(literal 2 binary64))))

Compiler

Compiled 883 to 712 computations (19.4% saved)

simplify37.0ms (0.4%)

Memory

-23.5MiB live, 22.4MiB allocated

Algorithm

1×	egg-herbie

Localize:

Found 17 expressions of interest:

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

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	47	254
0	70	229
1	105	219
2	149	219
3	199	203
4	253	203
5	346	203
6	498	203
7	666	203
8	720	203
9	763	203
0	763	203

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

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

localize155.0ms (1.5%)

Memory

15.9MiB live, 240.1MiB allocated

Localize:

Found 17 expressions of interest:

New	Metric	Score
accuracy	0.0	(/.f64 #s(approx (pow (* 0 n) (/ (- 1 k) 8)) (pow.f64 #s(literal 0 binary64) (-.f64 #s(literal 1 binary64) k))) (sqrt.f64 k))
accuracy	0.0	(-.f64 #s(literal 1 binary64) k)
accuracy	0.0	(sqrt.f64 k)
accuracy	0.0	#s(approx (pow (* 0 n) (/ (- 1 k) 8)) (pow.f64 #s(literal 0 binary64) (-.f64 #s(literal 1 binary64) k)))
accuracy	0.11328125	(/.f64 (PI.f64) k)
accuracy	0.170253759768442	(.f64 (sqrt.f64 n) (.f64 (sqrt.f64 #s(literal 2 binary64)) (sqrt.f64 (/.f64 (PI.f64) k))))
accuracy	0.25	(*.f64 (sqrt.f64 #s(literal 2 binary64)) (sqrt.f64 (/.f64 (PI.f64) k)))
accuracy	28.335247650234145	(PI.f64)
accuracy	0.27572250976844204	(/.f64 (sqrt.f64 (+.f64 (PI.f64) (PI.f64))) (sqrt.f64 k))
accuracy	0.54296875	(sqrt.f64 (+.f64 (PI.f64) (PI.f64)))
accuracy	28.335247650234145	(PI.f64)
accuracy	32.30420145647867	#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (/.f64 (sqrt.f64 (+.f64 (PI.f64) (PI.f64))) (sqrt.f64 k)))
accuracy	0.0	#s(approx (/ 0 (sqrt k)) #s(literal 0 binary64))
accuracy	0.185878759768442	(.f64 (.f64 (sqrt.f64 (PI.f64)) n) (*.f64 #s(literal 2 binary64) (sqrt.f64 (PI.f64))))
accuracy	0.19759750976844204	(/.f64 #s(approx (pow (* (* 2 (PI)) n) (/ (- 1 k) 2)) (pow.f64 (.f64 (.f64 (sqrt.f64 (PI.f64)) n) (*.f64 #s(literal 2 binary64) (sqrt.f64 (PI.f64)))) (fma.f64 #s(literal -1/2 binary64) k #s(literal 1/2 binary64)))) (sqrt.f64 k))
accuracy	0.54296875	(sqrt.f64 (PI.f64))
accuracy	28.335247650234145	(PI.f64)

Samples

72.0ms	139×	0	valid
36.0ms	117×	0	invalid

Compiler

Compiled 195 to 42 computations (78.5% saved)

Precisions

Click to see histograms. Total time spent on operations: 84.0ms

ival-pow: 29.0ms (34.4% of total)

ival-mult: 23.0ms (27.3% of total)

ival-div: 16.0ms (19% of total)

ival-sqrt: 10.0ms (11.9% of total)

ival-add: 3.0ms (3.6% 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-assert: 0.0ms (0% of total)

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

series148.0ms (1.5%)

Memory

48.0MiB live, 162.8MiB allocated

Counts

21 → 81

Calls

Call 1

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

Calls

6 calls:

Time	Variable		Point	Expression
100.0ms	n	@	-inf	((* (* (sqrt (PI)) n) (* 2 (sqrt (PI)))) (/ (pow (* (* 2 (PI)) n) (/ (- 1 k) 2)) (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2)) (pow (* (* (sqrt (PI)) n) (* 2 (sqrt (PI)))) (+ (* -1/2 k) 1/2)) (/ 0 (sqrt k)) (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (/ (sqrt (+ (PI) (PI))) (sqrt k)) (sqrt (+ (PI) (PI))) (+ (PI) (PI)) (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (* (sqrt n) (* (sqrt 2) (sqrt (/ (PI) k)))) (sqrt n) (* (sqrt 2) (sqrt (/ (PI) k))) (pow 0 (- 1 k)) (/ (pow (* 0 n) (/ (- 1 k) 8)) (sqrt k)) (pow (* 0 n) (/ (- 1 k) 8)) (- 1 k) (PI) (sqrt (PI)) (/ (PI) k) (sqrt k))
26.0ms	n	@	0	((* (* (sqrt (PI)) n) (* 2 (sqrt (PI)))) (/ (pow (* (* 2 (PI)) n) (/ (- 1 k) 2)) (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2)) (pow (* (* (sqrt (PI)) n) (* 2 (sqrt (PI)))) (+ (* -1/2 k) 1/2)) (/ 0 (sqrt k)) (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (/ (sqrt (+ (PI) (PI))) (sqrt k)) (sqrt (+ (PI) (PI))) (+ (PI) (PI)) (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (* (sqrt n) (* (sqrt 2) (sqrt (/ (PI) k)))) (sqrt n) (* (sqrt 2) (sqrt (/ (PI) k))) (pow 0 (- 1 k)) (/ (pow (* 0 n) (/ (- 1 k) 8)) (sqrt k)) (pow (* 0 n) (/ (- 1 k) 8)) (- 1 k) (PI) (sqrt (PI)) (/ (PI) k) (sqrt k))
10.0ms	n	@	inf	((* (* (sqrt (PI)) n) (* 2 (sqrt (PI)))) (/ (pow (* (* 2 (PI)) n) (/ (- 1 k) 2)) (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2)) (pow (* (* (sqrt (PI)) n) (* 2 (sqrt (PI)))) (+ (* -1/2 k) 1/2)) (/ 0 (sqrt k)) (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (/ (sqrt (+ (PI) (PI))) (sqrt k)) (sqrt (+ (PI) (PI))) (+ (PI) (PI)) (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (* (sqrt n) (* (sqrt 2) (sqrt (/ (PI) k)))) (sqrt n) (* (sqrt 2) (sqrt (/ (PI) k))) (pow 0 (- 1 k)) (/ (pow (* 0 n) (/ (- 1 k) 8)) (sqrt k)) (pow (* 0 n) (/ (- 1 k) 8)) (- 1 k) (PI) (sqrt (PI)) (/ (PI) k) (sqrt k))
4.0ms	k	@	-inf	((* (* (sqrt (PI)) n) (* 2 (sqrt (PI)))) (/ (pow (* (* 2 (PI)) n) (/ (- 1 k) 2)) (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2)) (pow (* (* (sqrt (PI)) n) (* 2 (sqrt (PI)))) (+ (* -1/2 k) 1/2)) (/ 0 (sqrt k)) (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (/ (sqrt (+ (PI) (PI))) (sqrt k)) (sqrt (+ (PI) (PI))) (+ (PI) (PI)) (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (* (sqrt n) (* (sqrt 2) (sqrt (/ (PI) k)))) (sqrt n) (* (sqrt 2) (sqrt (/ (PI) k))) (pow 0 (- 1 k)) (/ (pow (* 0 n) (/ (- 1 k) 8)) (sqrt k)) (pow (* 0 n) (/ (- 1 k) 8)) (- 1 k) (PI) (sqrt (PI)) (/ (PI) k) (sqrt k))
3.0ms	k	@	0	((* (* (sqrt (PI)) n) (* 2 (sqrt (PI)))) (/ (pow (* (* 2 (PI)) n) (/ (- 1 k) 2)) (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2)) (pow (* (* (sqrt (PI)) n) (* 2 (sqrt (PI)))) (+ (* -1/2 k) 1/2)) (/ 0 (sqrt k)) (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (/ (sqrt (+ (PI) (PI))) (sqrt k)) (sqrt (+ (PI) (PI))) (+ (PI) (PI)) (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (* (sqrt n) (* (sqrt 2) (sqrt (/ (PI) k)))) (sqrt n) (* (sqrt 2) (sqrt (/ (PI) k))) (pow 0 (- 1 k)) (/ (pow (* 0 n) (/ (- 1 k) 8)) (sqrt k)) (pow (* 0 n) (/ (- 1 k) 8)) (- 1 k) (PI) (sqrt (PI)) (/ (PI) k) (sqrt k))

simplify189.0ms (1.9%)

Memory

-5.7MiB live, 228.4MiB allocated

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	407	3264
1	1542	2859
0	8202	2689

Stop Event

1×	iter limit
1×	node limit

Counts

81 → 81

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

rewrite249.0ms (2.5%)

Memory

-8.5MiB live, 286.0MiB allocated

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	47	217
0	70	273
1	226	76
2	1180	48
0	8272	48

Stop Event

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

Counts

21 → 254

Calls

Call 1

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

Outputs
#s(literal 0 binary64)
(/.f64 (/.f64 #s(approx (pow (* (* 2 (PI)) n) (/ (- 1 k) 2)) #s(literal 0 binary64)) (pow.f64 k #s(literal 1/4 binary64))) (pow.f64 k #s(literal 1/4 binary64)))
(/.f64 (neg.f64 #s(approx (pow (* (* 2 (PI)) n) (/ (- 1 k) 2)) #s(literal 0 binary64))) (neg.f64 (sqrt.f64 k)))
(/.f64 #s(approx (pow (* (* 2 (PI)) n) (/ (- 1 k) 2)) #s(literal 0 binary64)) (sqrt.f64 k))
(neg.f64 (/.f64 (neg.f64 #s(approx (pow (* (* 2 (PI)) n) (/ (- 1 k) 2)) #s(literal 0 binary64))) (sqrt.f64 k)))
#s(approx (pow (* (* 2 (PI)) n) (/ (- 1 k) 2)) #s(literal 0 binary64))
(neg.f64 (neg.f64 #s(approx (pow (* (* 2 (PI)) n) (/ (- 1 k) 2)) #s(literal 0 binary64))))
#s(literal 0 binary64)
#s(approx (pow (* (* 2 (PI)) n) (/ (- 1 k) 2)) #s(literal 0 binary64))
(neg.f64 (neg.f64 #s(approx (pow (* (* 2 (PI)) n) (/ (- 1 k) 2)) #s(literal 0 binary64))))
#s(approx (pow (* (* 2 (PI)) n) (/ (- 1 k) 2)) #s(literal 0 binary64))
(neg.f64 (neg.f64 #s(approx (pow (* (* 2 (PI)) n) (/ (- 1 k) 2)) #s(literal 0 binary64))))
#s(literal 0 binary64)
#s(literal 0 binary64)
#s(literal 0 binary64)
#s(approx (pow (* (* 2 (PI)) n) (/ (- 1 k) 2)) #s(literal 0 binary64))
(neg.f64 (neg.f64 #s(approx (pow (* (* 2 (PI)) n) (/ (- 1 k) 2)) #s(literal 0 binary64))))
#s(literal 0 binary64)
(*.f64 (neg.f64 (pow.f64 n #s(literal 1/4 binary64))) (neg.f64 (pow.f64 n #s(literal 1/4 binary64))))
(*.f64 (fabs.f64 (pow.f64 n #s(literal 1/4 binary64))) (fabs.f64 (pow.f64 n #s(literal 1/4 binary64))))
(*.f64 (pow.f64 n #s(literal 1/4 binary64)) (pow.f64 n #s(literal 1/4 binary64)))
(pow.f64 (exp.f64 (log.f64 n)) #s(literal 1/2 binary64))
(pow.f64 (*.f64 n n) #s(literal 1/4 binary64))
(pow.f64 (pow.f64 n #s(literal 1/4 binary64)) #s(literal 2 binary64))
(pow.f64 n #s(literal 1/2 binary64))
(sqrt.f64 n)
(exp.f64 (*.f64 (log.f64 n) #s(literal 1/2 binary64)))
(+.f64 (cosh.f64 (.f64 (log.f64 n) #s(literal 1/2 binary64))) (sinh.f64 (.f64 (log.f64 n) #s(literal 1/2 binary64))))
#s(literal 0 binary64)
#s(literal 0 binary64)
(/.f64 (/.f64 #s(approx (pow (* (* 2 (PI)) n) (/ (- 1 k) 2)) #s(literal 0 binary64)) (pow.f64 k #s(literal 1/4 binary64))) (pow.f64 k #s(literal 1/4 binary64)))
(/.f64 (neg.f64 #s(approx (pow (* (* 2 (PI)) n) (/ (- 1 k) 2)) #s(literal 0 binary64))) (neg.f64 (sqrt.f64 k)))
(/.f64 #s(approx (pow (* (* 2 (PI)) n) (/ (- 1 k) 2)) #s(literal 0 binary64)) (sqrt.f64 k))
(neg.f64 (/.f64 (neg.f64 #s(approx (pow (* (* 2 (PI)) n) (/ (- 1 k) 2)) #s(literal 0 binary64))) (sqrt.f64 k)))
#s(approx (pow (* (* 2 (PI)) n) (/ (- 1 k) 2)) #s(literal 0 binary64))
(neg.f64 (neg.f64 #s(approx (pow (* (* 2 (PI)) n) (/ (- 1 k) 2)) #s(literal 0 binary64))))
(*.f64 (/.f64 (fma.f64 (neg.f64 k) k #s(literal 1 binary64)) (+.f64 (pow.f64 k #s(literal 3 binary64)) #s(literal 1 binary64))) (fma.f64 k (-.f64 k #s(literal 1 binary64)) #s(literal 1 binary64)))
(*.f64 (/.f64 (-.f64 #s(literal 1 binary64) (pow.f64 k #s(literal 3 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 #s(literal 1 binary64) (pow.f64 k #s(literal 3 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 (fma.f64 (neg.f64 k) k #s(literal 1 binary64)) (fma.f64 (neg.f64 k) k #s(literal 1 binary64))) (-.f64 #s(literal 1 binary64) k))
(/.f64 (-.f64 (.f64 (pow.f64 (+.f64 k #s(literal 1 binary64)) #s(literal -1 binary64)) (pow.f64 (+.f64 k #s(literal 1 binary64)) #s(literal -1 binary64))) (.f64 (.f64 k (/.f64 k (+.f64 k #s(literal 1 binary64)))) (.f64 k (/.f64 k (+.f64 k #s(literal 1 binary64)))))) (+.f64 (pow.f64 (+.f64 k #s(literal 1 binary64)) #s(literal -1 binary64)) (*.f64 k (/.f64 k (+.f64 k #s(literal 1 binary64))))))
(/.f64 (-.f64 (.f64 (pow.f64 (+.f64 (fma.f64 k k k) #s(literal 1 binary64)) #s(literal -1 binary64)) (pow.f64 (+.f64 (fma.f64 k k k) #s(literal 1 binary64)) #s(literal -1 binary64))) (.f64 (/.f64 (pow.f64 k #s(literal 3 binary64)) (+.f64 (fma.f64 k k k) #s(literal 1 binary64))) (/.f64 (pow.f64 k #s(literal 3 binary64)) (+.f64 (fma.f64 k k k) #s(literal 1 binary64))))) (+.f64 (pow.f64 (+.f64 (fma.f64 k k k) #s(literal 1 binary64)) #s(literal -1 binary64)) (/.f64 (pow.f64 k #s(literal 3 binary64)) (+.f64 (fma.f64 k k k) #s(literal 1 binary64)))))
(/.f64 (-.f64 (pow.f64 (pow.f64 (+.f64 k #s(literal 1 binary64)) #s(literal -1 binary64)) #s(literal 3 binary64)) (pow.f64 (.f64 k (/.f64 k (+.f64 k #s(literal 1 binary64)))) #s(literal 3 binary64))) (fma.f64 (pow.f64 (+.f64 k #s(literal 1 binary64)) #s(literal -1 binary64)) (pow.f64 (+.f64 k #s(literal 1 binary64)) #s(literal -1 binary64)) (fma.f64 (.f64 k (/.f64 k (+.f64 k #s(literal 1 binary64)))) (.f64 k (/.f64 k (+.f64 k #s(literal 1 binary64)))) (.f64 (pow.f64 (+.f64 k #s(literal 1 binary64)) #s(literal -1 binary64)) (*.f64 k (/.f64 k (+.f64 k #s(literal 1 binary64))))))))
(/.f64 (-.f64 (pow.f64 (pow.f64 (+.f64 (fma.f64 k k k) #s(literal 1 binary64)) #s(literal -1 binary64)) #s(literal 3 binary64)) (pow.f64 (/.f64 (pow.f64 k #s(literal 3 binary64)) (+.f64 (fma.f64 k k k) #s(literal 1 binary64))) #s(literal 3 binary64))) (fma.f64 (pow.f64 (+.f64 (fma.f64 k k k) #s(literal 1 binary64)) #s(literal -1 binary64)) (pow.f64 (+.f64 (fma.f64 k k k) #s(literal 1 binary64)) #s(literal -1 binary64)) (fma.f64 (/.f64 (pow.f64 k #s(literal 3 binary64)) (+.f64 (fma.f64 k k k) #s(literal 1 binary64))) (/.f64 (pow.f64 k #s(literal 3 binary64)) (+.f64 (fma.f64 k k k) #s(literal 1 binary64))) (*.f64 (pow.f64 (+.f64 (fma.f64 k k k) #s(literal 1 binary64)) #s(literal -1 binary64)) (/.f64 (pow.f64 k #s(literal 3 binary64)) (+.f64 (fma.f64 k k k) #s(literal 1 binary64)))))))
(/.f64 (neg.f64 (+.f64 #s(literal -1 binary64) (*.f64 k k))) (neg.f64 (fma.f64 #s(literal -1 binary64) k #s(literal -1 binary64))))
(/.f64 (neg.f64 (+.f64 #s(literal -1 binary64) (*.f64 k k))) (+.f64 k #s(literal 1 binary64)))
(/.f64 (neg.f64 (neg.f64 (-.f64 #s(literal 1 binary64) (pow.f64 k #s(literal 3 binary64))))) (neg.f64 (neg.f64 (+.f64 (fma.f64 k k k) #s(literal 1 binary64)))))
(/.f64 (neg.f64 (neg.f64 (-.f64 #s(literal 1 binary64) (pow.f64 k #s(literal 3 binary64))))) (+.f64 (fma.f64 k k k) #s(literal 1 binary64)))
(/.f64 (-.f64 (.f64 #s(literal 1 binary64) (+.f64 k #s(literal 1 binary64))) (.f64 (+.f64 k #s(literal 1 binary64)) (.f64 k k))) (.f64 (+.f64 k #s(literal 1 binary64)) (+.f64 k #s(literal 1 binary64))))
(/.f64 (-.f64 (.f64 #s(literal 1 binary64) (+.f64 (fma.f64 k k k) #s(literal 1 binary64))) (.f64 (+.f64 (fma.f64 k k k) #s(literal 1 binary64)) (pow.f64 k #s(literal 3 binary64)))) (*.f64 (+.f64 (fma.f64 k k k) #s(literal 1 binary64)) (+.f64 (fma.f64 k k k) #s(literal 1 binary64))))
(/.f64 (-.f64 #s(literal 1 binary64) (pow.f64 k #s(literal 4 binary64))) (*.f64 (fma.f64 k k #s(literal 1 binary64)) (+.f64 k #s(literal 1 binary64))))
(/.f64 (-.f64 #s(literal 1 binary64) (pow.f64 k #s(literal 9 binary64))) (*.f64 (+.f64 (+.f64 #s(literal 1 binary64) (pow.f64 k #s(literal 6 binary64))) (pow.f64 k #s(literal 3 binary64))) (+.f64 (fma.f64 k k k) #s(literal 1 binary64))))
(/.f64 (-.f64 #s(literal 1 binary64) (pow.f64 k #s(literal 6 binary64))) (*.f64 (+.f64 (fma.f64 k k (pow.f64 k #s(literal 4 binary64))) #s(literal 1 binary64)) (+.f64 k #s(literal 1 binary64))))
(/.f64 (-.f64 #s(literal 1 binary64) (pow.f64 k #s(literal 6 binary64))) (*.f64 (+.f64 (pow.f64 k #s(literal 3 binary64)) #s(literal 1 binary64)) (+.f64 (fma.f64 k k k) #s(literal 1 binary64))))
(/.f64 (+.f64 #s(literal -1 binary64) (*.f64 k k)) (fma.f64 #s(literal -1 binary64) k #s(literal -1 binary64)))
(/.f64 (neg.f64 (-.f64 #s(literal 1 binary64) (pow.f64 k #s(literal 3 binary64)))) (neg.f64 (+.f64 (fma.f64 k k k) #s(literal 1 binary64))))
(/.f64 (fma.f64 (neg.f64 k) k #s(literal 1 binary64)) (neg.f64 (fma.f64 #s(literal -1 binary64) k #s(literal -1 binary64))))
(/.f64 (fma.f64 (neg.f64 k) k #s(literal 1 binary64)) (+.f64 k #s(literal 1 binary64)))
(/.f64 (-.f64 #s(literal 1 binary64) (pow.f64 k #s(literal 3 binary64))) (neg.f64 (neg.f64 (+.f64 (fma.f64 k k k) #s(literal 1 binary64)))))
(/.f64 (-.f64 #s(literal 1 binary64) (pow.f64 k #s(literal 3 binary64))) (+.f64 (fma.f64 k k k) #s(literal 1 binary64)))
(neg.f64 (neg.f64 (-.f64 #s(literal 1 binary64) k)))
(fma.f64 (/.f64 #s(literal 1 binary64) (fma.f64 (neg.f64 k) k #s(literal 1 binary64))) (-.f64 #s(literal 1 binary64) k) (/.f64 (*.f64 (neg.f64 k) k) (+.f64 k #s(literal 1 binary64))))
(fma.f64 (/.f64 #s(literal 1 binary64) (+.f64 (pow.f64 k #s(literal 3 binary64)) #s(literal 1 binary64))) (fma.f64 k (-.f64 k #s(literal 1 binary64)) #s(literal 1 binary64)) (/.f64 (*.f64 (neg.f64 k) k) (+.f64 k #s(literal 1 binary64))))
(-.f64 (pow.f64 (+.f64 k #s(literal 1 binary64)) #s(literal -1 binary64)) (*.f64 k (/.f64 k (+.f64 k #s(literal 1 binary64)))))
(-.f64 (pow.f64 (+.f64 (fma.f64 k k k) #s(literal 1 binary64)) #s(literal -1 binary64)) (/.f64 (pow.f64 k #s(literal 3 binary64)) (+.f64 (fma.f64 k k k) #s(literal 1 binary64))))
(-.f64 #s(literal 1 binary64) k)
(+.f64 (pow.f64 (+.f64 k #s(literal 1 binary64)) #s(literal -1 binary64)) (/.f64 (*.f64 (neg.f64 k) k) (+.f64 k #s(literal 1 binary64))))
(+.f64 #s(literal 1 binary64) (neg.f64 k))
(.f64 (.f64 (pow.f64 (cbrt.f64 (PI.f64)) #s(literal 2 binary64)) (cbrt.f64 (pow.f64 (cbrt.f64 (PI.f64)) #s(literal 2 binary64)))) (cbrt.f64 (cbrt.f64 (PI.f64))))
(.f64 (.f64 (pow.f64 (cbrt.f64 (PI.f64)) #s(literal 2 binary64)) (cbrt.f64 (sqrt.f64 (PI.f64)))) (cbrt.f64 (sqrt.f64 (PI.f64))))
(.f64 (.f64 (sqrt.f64 (PI.f64)) (pow.f64 (PI.f64) #s(literal 1/4 binary64))) (pow.f64 (PI.f64) #s(literal 1/4 binary64)))
(.f64 (.f64 (neg.f64 (cbrt.f64 (PI.f64))) (cbrt.f64 (sqrt.f64 (PI.f64)))) (*.f64 (neg.f64 (cbrt.f64 (PI.f64))) (cbrt.f64 (sqrt.f64 (PI.f64)))))
(.f64 (.f64 (cbrt.f64 (PI.f64)) (cbrt.f64 (sqrt.f64 (PI.f64)))) (*.f64 (cbrt.f64 (PI.f64)) (cbrt.f64 (sqrt.f64 (PI.f64)))))
(.f64 (.f64 (cbrt.f64 (sqrt.f64 (PI.f64))) (neg.f64 (cbrt.f64 (PI.f64)))) (*.f64 (cbrt.f64 (sqrt.f64 (PI.f64))) (neg.f64 (cbrt.f64 (PI.f64)))))
(.f64 (.f64 (cbrt.f64 (sqrt.f64 (PI.f64))) (cbrt.f64 (PI.f64))) (*.f64 (cbrt.f64 (sqrt.f64 (PI.f64))) (cbrt.f64 (PI.f64))))
(*.f64 (neg.f64 (neg.f64 (sqrt.f64 (PI.f64)))) (neg.f64 (neg.f64 (sqrt.f64 (PI.f64)))))
(*.f64 (neg.f64 (neg.f64 (sqrt.f64 (PI.f64)))) (sqrt.f64 (PI.f64)))
(*.f64 (sqrt.f64 (pow.f64 (cbrt.f64 (PI.f64)) #s(literal 5 binary64))) (pow.f64 (PI.f64) #s(literal 1/6 binary64)))
(.f64 (sqrt.f64 (.f64 (cbrt.f64 (PI.f64)) (PI.f64))) (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 (.f64 (pow.f64 (cbrt.f64 (PI.f64)) #s(literal 5 binary64)) (PI.f64))) (cbrt.f64 (cbrt.f64 (PI.f64))))
(*.f64 (cbrt.f64 (pow.f64 (PI.f64) #s(literal 5/2 binary64))) (cbrt.f64 (sqrt.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 (.f64 (sqrt.f64 (PI.f64)) (cbrt.f64 (PI.f64))) (pow.f64 (PI.f64) #s(literal 1/6 binary64)))
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(neg.f64 (/.f64 (neg.f64 (PI.f64)) k))
(+.f64 (/.f64 (cosh.f64 (log.f64 (PI.f64))) k) (/.f64 (sinh.f64 (log.f64 (PI.f64))) k))
(*.f64 (neg.f64 (pow.f64 k #s(literal 1/4 binary64))) (neg.f64 (pow.f64 k #s(literal 1/4 binary64))))
(*.f64 (fabs.f64 (pow.f64 k #s(literal 1/4 binary64))) (fabs.f64 (pow.f64 k #s(literal 1/4 binary64))))
(*.f64 (pow.f64 #s(literal 1 binary64) #s(literal 1/2 binary64)) (sqrt.f64 k))
(*.f64 (pow.f64 k #s(literal 1/4 binary64)) (pow.f64 k #s(literal 1/4 binary64)))
(*.f64 (sqrt.f64 k) (pow.f64 #s(literal 1 binary64) #s(literal 1/2 binary64)))
(*.f64 (sqrt.f64 k) #s(literal 1 binary64))
(*.f64 #s(literal 1 binary64) (sqrt.f64 k))
(pow.f64 (exp.f64 (log.f64 k)) #s(literal 1/2 binary64))
(pow.f64 (pow.f64 k #s(literal 1/4 binary64)) #s(literal 2 binary64))
(pow.f64 (*.f64 k k) #s(literal 1/4 binary64))
(pow.f64 k #s(literal 1/2 binary64))
(neg.f64 (neg.f64 (sqrt.f64 k)))
(sqrt.f64 k)
(exp.f64 (log.f64 (sqrt.f64 k)))
(+.f64 (cosh.f64 (log.f64 (sqrt.f64 k))) (sinh.f64 (log.f64 (sqrt.f64 k))))

eval158.0ms (1.6%)

Memory: 14.7MiB live, 244.5MiB allocated
Compiler: Compiled 30 562 to 4 383 computations (85.7% saved)

prune38.0ms (0.4%)

Memory

-17.4MiB live, 80.9MiB allocated

Pruning

21 alts after pruning (13 fresh and 8 done)

	Pruned	Kept	Total
New	856	2	858
Fresh	0	11	11
Picked	1	4	5
Done	0	4	4
Total	857	21	878

Accuracy

100.0%

Counts

878 → 21

Alt Table

Click to see full alt table

Status	Accuracy	Program
	55.5%	(/.f64 #s(approx (pow (* (* 2 (PI)) n) (/ (- 1 k) 2)) (pow.f64 (+.f64 n n) (fma.f64 #s(literal -1/2 binary64) k #s(literal 1/2 binary64)))) (sqrt.f64 k))
✓	99.5%	(/.f64 #s(approx (pow (* (* 2 (PI)) n) (/ (- 1 k) 2)) (pow.f64 (.f64 (.f64 (sqrt.f64 (PI.f64)) n) (*.f64 #s(literal 2 binary64) (sqrt.f64 (PI.f64)))) (fma.f64 #s(literal -1/2 binary64) k #s(literal 1/2 binary64)))) (sqrt.f64 k))
✓	99.6%	(/.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))
	55.7%	(/.f64 #s(approx (pow (* (* 2 (PI)) n) (/ (- 1 k) 2)) (.f64 (sqrt.f64 (.f64 (.f64 n #s(literal 2 binary64)) (PI.f64))) (fma.f64 (.f64 #s(literal -1/2 binary64) k) (log.f64 (.f64 (.f64 n #s(literal 2 binary64)) (PI.f64))) #s(literal 1 binary64)))) (sqrt.f64 k))
	29.9%	(/.f64 #s(approx (pow (* 0 n) (/ (- 1 k) 8)) (pow.f64 #s(literal 0 binary64) #s(approx (- 1 k) (neg.f64 k)))) (sqrt.f64 k))
✓	54.9%	(.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)))))
✓	19.5%	#s(approx (/ 0 (sqrt k)) #s(literal 0 binary64))
	54.9%	#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 n)) (sqrt.f64 k)))
✓	5.2%	#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (/.f64 (sqrt.f64 (+.f64 (PI.f64) (PI.f64))) (sqrt.f64 k)))
	11.6%	#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (/.f64 (sqrt.f64 (+.f64 n n)) (sqrt.f64 k)))
	5.2%	#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (/.f64 (sqrt.f64 (.f64 (.f64 (PI.f64) #s(literal 2 binary64)) (PI.f64))) (sqrt.f64 k)))
✓	55.1%	#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)))
	54.9%	#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (.f64 (sqrt.f64 (.f64 (PI.f64) n)) (/.f64 (sqrt.f64 #s(literal 2 binary64)) (sqrt.f64 k))))
	54.9%	#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (.f64 (sqrt.f64 (.f64 (PI.f64) #s(literal 2 binary64))) (/.f64 (sqrt.f64 n) (sqrt.f64 k))))
	5.2%	#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (.f64 (sqrt.f64 (.f64 (PI.f64) #s(literal 2 binary64))) (sqrt.f64 (/.f64 (PI.f64) k))))
	39.9%	#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))))
✓	55.0%	#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (.f64 (sqrt.f64 n) (.f64 (sqrt.f64 #s(literal 2 binary64)) (sqrt.f64 (/.f64 (PI.f64) k)))))
✓	40.0%	#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))))
	40.1%	#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt.f64 (.f64 (/.f64 (.f64 n (PI.f64)) k) #s(literal 2 binary64))))
	9.4%	#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt.f64 (*.f64 (/.f64 n k) #s(literal 2 binary64))))
	5.2%	#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) #s(approx (/ (sqrt (+ (PI) (PI))) (sqrt k)) (*.f64 (sqrt.f64 (/.f64 (PI.f64) k)) (sqrt.f64 #s(literal 2 binary64)))))

Compiler

Compiled 1 443 to 613 computations (57.5% saved)

regimes45.0ms (0.5%)

Memory

44.3MiB live, 87.0MiB allocated

Counts

38 → 1

Calls

Call 1

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

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

Calls

4 calls:

13.0ms	(.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) (pow.f64 (.f64 (*.f64 #s(literal 2 binary64) (PI.f64)) n) (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 2 binary64))))
10.0ms	(.f64 (.f64 #s(literal 2 binary64) (PI.f64)) n)
10.0ms	n
10.0ms	k

Results

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

Compiler

Compiled 23 to 23 computations (0% saved)

regimes42.0ms (0.4%)

Memory

-14.2MiB live, 75.3MiB allocated

Counts

33 → 1

Calls

Call 1

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

Outputs
(/.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))

Calls

4 calls:

11.0ms	n
11.0ms	(.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) (pow.f64 (.f64 (*.f64 #s(literal 2 binary64) (PI.f64)) n) (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 2 binary64))))
9.0ms	(.f64 (.f64 #s(literal 2 binary64) (PI.f64)) n)
9.0ms	k

Results

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

Compiler

Compiled 23 to 23 computations (0% saved)

regimes34.0ms (0.3%)

Memory

-24.1MiB live, 75.7MiB allocated

Counts

23 → 2

Calls

Call 1

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

Calls

4 calls:

12.0ms	k
7.0ms	(.f64 (.f64 #s(literal 2 binary64) (PI.f64)) n)
7.0ms	n
6.0ms	(.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
61.1%	2	`(.f64 (.f64 #s(literal 2 binary64) (PI.f64)) n)`
98.9%	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))))`
98.9%	2	`k`
61.1%	2	`n`

Compiler

Compiled 23 to 23 computations (0% saved)

regimes13.0ms (0.1%)

Memory

40.5MiB live, 40.5MiB allocated

Counts

21 → 3

Calls

Call 1

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

Outputs

#s(approx (/ 0 (sqrt k)) #s(literal 0 binary64))

#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)))

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

Calls

2 calls:

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

Results

Accuracy	Segments	Branch
98.8%	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))))`
84.2%	3	`k`

Compiler

Compiled 17 to 15 computations (11.8% saved)

regimes12.0ms (0.1%)

Memory

-12.6MiB live, 34.1MiB allocated

Counts

19 → 2

Calls

Call 1

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

Outputs
#s(approx (/ 0 (sqrt k)) #s(literal 0 binary64))
#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)))

Calls

2 calls:

6.0ms	(.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))))
5.0ms	k

Results

Accuracy	Segments	Branch
71.9%	2	`k`
72.1%	2	`(.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) (pow.f64 (.f64 (*.f64 #s(literal 2 binary64) (PI.f64)) n) (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 2 binary64))))`

Compiler

Compiled 17 to 15 computations (11.8% saved)

regimes33.0ms (0.3%)

Memory

-8.4MiB live, 38.9MiB allocated

Counts

10 → 3

Calls

Call 1

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

Outputs

#s(approx (/ 0 (sqrt k)) #s(literal 0 binary64))

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

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

Calls

4 calls:

22.0ms	n
3.0ms	k
3.0ms	(.f64 (.f64 #s(literal 2 binary64) (PI.f64)) n)
3.0ms	(.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) (pow.f64 (.f64 (*.f64 #s(literal 2 binary64) (PI.f64)) n) (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 2 binary64))))

Results

Accuracy	Segments	Branch
47.9%	2	`(.f64 (.f64 #s(literal 2 binary64) (PI.f64)) n)`
47.9%	2	`n`
57.1%	2	`k`
59.4%	3	`(.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) (pow.f64 (.f64 (*.f64 #s(literal 2 binary64) (PI.f64)) n) (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 2 binary64))))`

Compiler

Compiled 23 to 23 computations (0% saved)

regimes2.0ms (0%)

Memory

7.3MiB live, 7.3MiB allocated

Counts

4 → 2

Calls

Call 1

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

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

Calls

1 calls:

2.0ms

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

Results

Accuracy	Segments	Branch
57.2%	2	`(.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) (pow.f64 (.f64 (*.f64 #s(literal 2 binary64) (PI.f64)) n) (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 2 binary64))))`

Compiler

Compiled 16 to 13 computations (18.8% saved)

regimes7.0ms (0.1%)

Memory

23.8MiB live, 23.8MiB allocated

Counts

3 → 2

Calls

Call 1

Inputs

#s(approx (/ 0 (sqrt k)) #s(literal 0 binary64))

(/.f64 #s(literal 0 binary64) (sqrt.f64 k))

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

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

Calls

4 calls:

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

Results

Accuracy	Segments	Branch
24.2%	2	`(.f64 (.f64 #s(literal 2 binary64) (PI.f64)) n)`
24.2%	2	`n`
26.3%	2	`k`
26.4%	2	`(.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) (pow.f64 (.f64 (*.f64 #s(literal 2 binary64) (PI.f64)) n) (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 2 binary64))))`

Compiler

Compiled 23 to 23 computations (0% saved)

regimes44.0ms (0.4%)

Memory

-32.0MiB live, 26.2MiB allocated

Accuracy

Total -0.0b remaining (-0%)

Threshold costs -0b (-0%)

Counts

2 → 1

Calls

Call 1

Inputs
#s(approx (/ 0 (sqrt k)) #s(literal 0 binary64))
(/.f64 #s(literal 0 binary64) (sqrt.f64 k))

Outputs
#s(approx (/ 0 (sqrt k)) #s(literal 0 binary64))

Calls

4 calls:

40.0ms	(.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	(.f64 (.f64 #s(literal 2 binary64) (PI.f64)) n)
1.0ms	k
1.0ms	n

Results

Accuracy	Segments	Branch
19.5%	1	`(.f64 (.f64 #s(literal 2 binary64) (PI.f64)) n)`
19.5%	1	`n`
19.5%	1	`k`
19.5%	1	`(.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) (pow.f64 (.f64 (*.f64 #s(literal 2 binary64) (PI.f64)) n) (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 2 binary64))))`

Compiler

Compiled 23 to 23 computations (0% saved)

bsearch34.0ms (0.3%)

Memory

4.1MiB live, 94.0MiB allocated

Algorithm

1×	binary-search

Stop Event

1×	narrow-enough

Steps

Time	Left	Right
31.0ms	5.3992085673560354e-14	2.3005238183322123

Samples

24.0ms

160×

valid

Compiler

Compiled 509 to 428 computations (15.9% saved)

Precisions

Click to see histograms. Total time spent on operations: 19.0ms

ival-pow: 9.0ms (46.3% of total)

ival-mult: 3.0ms (15.4% of total)

ival-sub: 3.0ms (15.4% of total)

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

ival-pi: 1.0ms (5.1% of total)

ival-sqrt: 1.0ms (5.1% of total)

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

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

exact: 0.0ms (0% of total)

bsearch1.0ms (0%)

Memory

2.3MiB live, 2.3MiB allocated

Algorithm

2×	left-value

Steps

Time	Left	Right
0.0ms	3.987243498737837e+284	+inf
0.0ms	4.325395907374826e-227	9.80229732164679e-126

Compiler

Compiled 19 to 18 computations (5.3% saved)

bsearch0.0ms (0%)

Memory

1.4MiB live, 1.4MiB allocated

Algorithm

1×	left-value

Steps

Time	Left	Right
0.0ms	4.325395907374826e-227	9.80229732164679e-126

Compiler

Compiled 19 to 18 computations (5.3% saved)

bsearch1.0ms (0%)

Memory

1.6MiB live, 1.6MiB allocated

Algorithm

2×	left-value

Steps

Time	Left	Right
0.0ms	1.5173560213464794e+153	1.3342575182450216e+159
0.0ms	4.325395907374826e-227	9.80229732164679e-126

Compiler

Compiled 19 to 18 computations (5.3% saved)

bsearch0.0ms (0%)

Memory

1.1MiB live, 1.1MiB allocated

Algorithm

1×	left-value

Steps

Time	Left	Right
0.0ms	4.325395907374826e-227	9.80229732164679e-126

Compiler

Compiled 19 to 18 computations (5.3% saved)

bsearch0.0ms (0%)

Memory

1.3MiB live, 1.3MiB allocated

Algorithm

1×	left-value

Steps

Time	Left	Right
0.0ms	4.325395907374826e-227	9.80229732164679e-126

Compiler

Compiled 19 to 18 computations (5.3% saved)

simplify31.0ms (0.3%)

Memory

-24.6MiB live, 72.8MiB allocated

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	79	412
1	104	392
2	119	392
3	139	392
4	156	392
5	175	392
6	209	392
7	276	392
8	307	392
9	340	392
10	350	392

Stop Event

1×

saturated

Calls

Call 1

Inputs
(.f64 (pow.f64 k #s(literal -1/2 binary64)) (pow.f64 (.f64 (*.f64 #s(literal 2 binary64) (PI.f64)) n) (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 2 binary64))))
(/.f64 #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))
(if (<=.f64 k #s(literal 3170534137668829/576460752303423488 binary64)) #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))) (/.f64 #s(approx (pow (* (* 2 (PI)) n) (/ (- 1 k) 2)) (pow.f64 (+.f64 n n) (fma.f64 #s(literal -1/2 binary64) k #s(literal 1/2 binary64)))) (sqrt.f64 k)))
(if (<=.f64 (.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) (pow.f64 (.f64 (.f64 #s(literal 2 binary64) (PI.f64)) n) (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 2 binary64)))) #s(literal 5334411546303883/106688230926077668385277628651540124754316133157054530566340124988224595805082113144342915213944868651886878569494931847134220826465909841285813696837293280737522521272224232935409252574589024395663440258174185631707051968599623380658622038016 binary64)) #s(approx (/ 0 (sqrt k)) #s(literal 0 binary64)) (if (<=.f64 (.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) (pow.f64 (.f64 (.f64 #s(literal 2 binary64) (PI.f64)) n) (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 2 binary64)))) #s(literal 499999999999999990079578960260221425096554759926423605900012855280825179991269042612044308093073246922143074698610725186309660447719446848973826083227612667029686373206874073603221710445876270310293765181110136931503450775547995353849221420762954771236422294344040540188066309300289536 binary64)) #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))) (/.f64 #s(approx (pow (* 0 n) (/ (- 1 k) 8)) (pow.f64 #s(literal 0 binary64) #s(approx (- 1 k) (neg.f64 k)))) (sqrt.f64 k))))
(if (<=.f64 (.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) (pow.f64 (.f64 (.f64 #s(literal 2 binary64) (PI.f64)) n) (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 2 binary64)))) #s(literal 5334411546303883/106688230926077668385277628651540124754316133157054530566340124988224595805082113144342915213944868651886878569494931847134220826465909841285813696837293280737522521272224232935409252574589024395663440258174185631707051968599623380658622038016 binary64)) #s(approx (/ 0 (sqrt k)) #s(literal 0 binary64)) #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))))
(if (<=.f64 (.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) (pow.f64 (.f64 (.f64 #s(literal 2 binary64) (PI.f64)) n) (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 2 binary64)))) #s(literal 5334411546303883/106688230926077668385277628651540124754316133157054530566340124988224595805082113144342915213944868651886878569494931847134220826465909841285813696837293280737522521272224232935409252574589024395663440258174185631707051968599623380658622038016 binary64)) #s(approx (/ 0 (sqrt k)) #s(literal 0 binary64)) (if (<=.f64 (.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) (pow.f64 (.f64 (.f64 #s(literal 2 binary64) (PI.f64)) n) (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 2 binary64)))) #s(literal 1999999999999999999466806008246307489711078038236873372571680376048739359044847523345839519129134316887338757648057420040785188188258060440266031719514112 binary64)) #s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt.f64 (.f64 (/.f64 (.f64 n (PI.f64)) k) #s(literal 2 binary64)))) #s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (/.f64 (sqrt.f64 (+.f64 n n)) (sqrt.f64 k)))))
(if (<=.f64 (.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) (pow.f64 (.f64 (.f64 #s(literal 2 binary64) (PI.f64)) n) (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 2 binary64)))) #s(literal 5334411546303883/106688230926077668385277628651540124754316133157054530566340124988224595805082113144342915213944868651886878569494931847134220826465909841285813696837293280737522521272224232935409252574589024395663440258174185631707051968599623380658622038016 binary64)) #s(approx (/ 0 (sqrt k)) #s(literal 0 binary64)) #s(approx ( (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt.f64 (.f64 (/.f64 (.f64 n (PI.f64)) k) #s(literal 2 binary64)))))
(if (<=.f64 (.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) (pow.f64 (.f64 (.f64 #s(literal 2 binary64) (PI.f64)) n) (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 2 binary64)))) #s(literal 5334411546303883/106688230926077668385277628651540124754316133157054530566340124988224595805082113144342915213944868651886878569494931847134220826465909841285813696837293280737522521272224232935409252574589024395663440258174185631707051968599623380658622038016 binary64)) #s(approx (/ 0 (sqrt k)) #s(literal 0 binary64)) #s(approx ( (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt.f64 (*.f64 (/.f64 n k) #s(literal 2 binary64)))))
#s(approx (/ 0 (sqrt k)) #s(literal 0 binary64))

Outputs
(.f64 (pow.f64 k #s(literal -1/2 binary64)) (pow.f64 (.f64 (*.f64 #s(literal 2 binary64) (PI.f64)) n) (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 2 binary64))))
(/.f64 #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))
(if (<=.f64 k #s(literal 3170534137668829/576460752303423488 binary64)) #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))) (/.f64 #s(approx (pow (* (* 2 (PI)) n) (/ (- 1 k) 2)) (pow.f64 (+.f64 n n) (fma.f64 #s(literal -1/2 binary64) k #s(literal 1/2 binary64)))) (sqrt.f64 k)))
(if (<=.f64 (.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) (pow.f64 (.f64 (.f64 #s(literal 2 binary64) (PI.f64)) n) (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 2 binary64)))) #s(literal 5334411546303883/106688230926077668385277628651540124754316133157054530566340124988224595805082113144342915213944868651886878569494931847134220826465909841285813696837293280737522521272224232935409252574589024395663440258174185631707051968599623380658622038016 binary64)) #s(approx (/ 0 (sqrt k)) #s(literal 0 binary64)) (if (<=.f64 (.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) (pow.f64 (.f64 (.f64 #s(literal 2 binary64) (PI.f64)) n) (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 2 binary64)))) #s(literal 499999999999999990079578960260221425096554759926423605900012855280825179991269042612044308093073246922143074698610725186309660447719446848973826083227612667029686373206874073603221710445876270310293765181110136931503450775547995353849221420762954771236422294344040540188066309300289536 binary64)) #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))) (/.f64 #s(approx (pow (* 0 n) (/ (- 1 k) 8)) (pow.f64 #s(literal 0 binary64) #s(approx (- 1 k) (neg.f64 k)))) (sqrt.f64 k))))
(if (<=.f64 (.f64 (pow.f64 (sqrt.f64 k) #s(literal -1 binary64)) (pow.f64 (.f64 (.f64 #s(literal 2 binary64) (PI.f64)) n) (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 2 binary64)))) #s(literal 5334411546303883/106688230926077668385277628651540124754316133157054530566340124988224595805082113144342915213944868651886878569494931847134220826465909841285813696837293280737522521272224232935409252574589024395663440258174185631707051968599623380658622038016 binary64)) #s(approx (/ 0 (sqrt k)) #s(literal 0 binary64)) (if (<=.f64 (.f64 (pow.f64 (sqrt.f64 k) #s(literal -1 binary64)) (pow.f64 (.f64 (.f64 #s(literal 2 binary64) (PI.f64)) n) (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 2 binary64)))) #s(literal 499999999999999990079578960260221425096554759926423605900012855280825179991269042612044308093073246922143074698610725186309660447719446848973826083227612667029686373206874073603221710445876270310293765181110136931503450775547995353849221420762954771236422294344040540188066309300289536 binary64)) #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))) (/.f64 #s(approx (/ 0 (sqrt k)) (pow.f64 #s(literal 0 binary64) #s(approx (- 1 k) (neg.f64 k)))) (sqrt.f64 k))))
(if (<=.f64 (.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) (pow.f64 (.f64 (.f64 #s(literal 2 binary64) (PI.f64)) n) (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 2 binary64)))) #s(literal 5334411546303883/106688230926077668385277628651540124754316133157054530566340124988224595805082113144342915213944868651886878569494931847134220826465909841285813696837293280737522521272224232935409252574589024395663440258174185631707051968599623380658622038016 binary64)) #s(approx (/ 0 (sqrt k)) #s(literal 0 binary64)) #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))))
(if (<=.f64 (.f64 (pow.f64 (sqrt.f64 k) #s(literal -1 binary64)) (pow.f64 (.f64 (.f64 #s(literal 2 binary64) (PI.f64)) n) (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 2 binary64)))) #s(literal 5334411546303883/106688230926077668385277628651540124754316133157054530566340124988224595805082113144342915213944868651886878569494931847134220826465909841285813696837293280737522521272224232935409252574589024395663440258174185631707051968599623380658622038016 binary64)) #s(approx (/ 0 (sqrt k)) #s(literal 0 binary64)) #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))))
(if (<=.f64 (.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) (pow.f64 (.f64 (.f64 #s(literal 2 binary64) (PI.f64)) n) (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 2 binary64)))) #s(literal 5334411546303883/106688230926077668385277628651540124754316133157054530566340124988224595805082113144342915213944868651886878569494931847134220826465909841285813696837293280737522521272224232935409252574589024395663440258174185631707051968599623380658622038016 binary64)) #s(approx (/ 0 (sqrt k)) #s(literal 0 binary64)) (if (<=.f64 (.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) (pow.f64 (.f64 (.f64 #s(literal 2 binary64) (PI.f64)) n) (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 2 binary64)))) #s(literal 1999999999999999999466806008246307489711078038236873372571680376048739359044847523345839519129134316887338757648057420040785188188258060440266031719514112 binary64)) #s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt.f64 (.f64 (/.f64 (.f64 n (PI.f64)) k) #s(literal 2 binary64)))) #s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (/.f64 (sqrt.f64 (+.f64 n n)) (sqrt.f64 k)))))
(if (<=.f64 (.f64 (pow.f64 (sqrt.f64 k) #s(literal -1 binary64)) (pow.f64 (.f64 (.f64 #s(literal 2 binary64) (PI.f64)) n) (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 2 binary64)))) #s(literal 5334411546303883/106688230926077668385277628651540124754316133157054530566340124988224595805082113144342915213944868651886878569494931847134220826465909841285813696837293280737522521272224232935409252574589024395663440258174185631707051968599623380658622038016 binary64)) #s(approx (/ 0 (sqrt k)) #s(literal 0 binary64)) (if (<=.f64 (.f64 (pow.f64 (sqrt.f64 k) #s(literal -1 binary64)) (pow.f64 (.f64 (.f64 #s(literal 2 binary64) (PI.f64)) n) (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 2 binary64)))) #s(literal 1999999999999999999466806008246307489711078038236873372571680376048739359044847523345839519129134316887338757648057420040785188188258060440266031719514112 binary64)) #s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt.f64 (.f64 (/.f64 (.f64 n (PI.f64)) k) #s(literal 2 binary64)))) #s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (/.f64 (sqrt.f64 (+.f64 n n)) (sqrt.f64 k)))))
(if (<=.f64 (.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) (pow.f64 (.f64 (.f64 #s(literal 2 binary64) (PI.f64)) n) (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 2 binary64)))) #s(literal 5334411546303883/106688230926077668385277628651540124754316133157054530566340124988224595805082113144342915213944868651886878569494931847134220826465909841285813696837293280737522521272224232935409252574589024395663440258174185631707051968599623380658622038016 binary64)) #s(approx (/ 0 (sqrt k)) #s(literal 0 binary64)) #s(approx ( (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt.f64 (.f64 (/.f64 (.f64 n (PI.f64)) k) #s(literal 2 binary64)))))
(if (<=.f64 (.f64 (pow.f64 (sqrt.f64 k) #s(literal -1 binary64)) (pow.f64 (.f64 (.f64 #s(literal 2 binary64) (PI.f64)) n) (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 2 binary64)))) #s(literal 5334411546303883/106688230926077668385277628651540124754316133157054530566340124988224595805082113144342915213944868651886878569494931847134220826465909841285813696837293280737522521272224232935409252574589024395663440258174185631707051968599623380658622038016 binary64)) #s(approx (/ 0 (sqrt k)) #s(literal 0 binary64)) #s(approx ( (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt.f64 (.f64 (/.f64 (.f64 n (PI.f64)) k) #s(literal 2 binary64)))))
(if (<=.f64 (.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) (pow.f64 (.f64 (.f64 #s(literal 2 binary64) (PI.f64)) n) (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 2 binary64)))) #s(literal 5334411546303883/106688230926077668385277628651540124754316133157054530566340124988224595805082113144342915213944868651886878569494931847134220826465909841285813696837293280737522521272224232935409252574589024395663440258174185631707051968599623380658622038016 binary64)) #s(approx (/ 0 (sqrt k)) #s(literal 0 binary64)) #s(approx ( (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt.f64 (*.f64 (/.f64 n k) #s(literal 2 binary64)))))
(if (<=.f64 (.f64 (pow.f64 (sqrt.f64 k) #s(literal -1 binary64)) (pow.f64 (.f64 (.f64 #s(literal 2 binary64) (PI.f64)) n) (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 2 binary64)))) #s(literal 5334411546303883/106688230926077668385277628651540124754316133157054530566340124988224595805082113144342915213944868651886878569494931847134220826465909841285813696837293280737522521272224232935409252574589024395663440258174185631707051968599623380658622038016 binary64)) #s(approx (/ 0 (sqrt k)) #s(literal 0 binary64)) #s(approx ( (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt.f64 (*.f64 (/.f64 n k) #s(literal 2 binary64)))))
#s(approx (/ 0 (sqrt k)) #s(literal 0 binary64))

soundness1.4s (13.6%)

Memory

21.7MiB live, 1 178.8MiB allocated

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	51	272
0	85	257
1	251	241
2	1233	241
0	8250	241
0	13	38
0	22	38
1	83	35
2	446	35
3	4007	29
0	8921	29
0	407	3264
1	1542	2859
0	8202	2689
0	153	716
1	500	695
2	1855	625
3	5611	613
0	8462	601
0	400	3260
1	1457	2974
2	7175	2791
0	8028	2677
0	42	236
0	65	228
1	200	218
2	904	170
0	9162	170
0	120	502
1	378	489
2	1377	453
3	4131	453
0	8166	441

Stop Event

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

Compiler

Compiled 986 to 514 computations (47.9% saved)

preprocess49.0ms (0.5%)

Memory: 8.8MiB live, 96.8MiB allocated
Compiler: Compiled 886 to 184 computations (79.2% saved)

end0.0ms (0%)

Memory: 0.0MiB live, 0.0MiB allocated

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

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

Iter	Nodes	Cost
0	42	293
0	65	290
1	90	284
2	106	284
3	130	284
4	152	284
5	176	284
6	220	284
7	302	284
8	326	284
9	346	284
10	356	284
0	356	284

Iter	Nodes	Cost
0	47	254
0	70	229
1	105	219
2	149	219
3	199	203
4	253	203
5	346	203
6	498	203
7	666	203
8	720	203
9	763	203
0	763	203

Iter	Nodes	Cost
0	79	412
1	104	392
2	119	392
3	139	392
4	156	392
5	175	392
6	209	392
7	276	392
8	307	392
9	340	392
10	350	392

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

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

Iter	Nodes	Cost
0	42	293
0	65	290
1	90	284
2	106	284
3	130	284
4	152	284
5	176	284
6	220	284
7	302	284
8	326	284
9	346	284
10	356	284
0	356	284

Iter	Nodes	Cost
0	47	254
0	70	229
1	105	219
2	149	219
3	199	203
4	253	203
5	346	203
6	498	203
7	666	203
8	720	203
9	763	203
0	763	203

Iter	Nodes	Cost
0	79	412
1	104	392
2	119	392
3	139	392
4	156	392
5	175	392
6	209	392
7	276	392
8	307	392
9	340	392
10	350	392

start0.0ms (0%)

analyze133.0ms (1.3%)

sample3.9s (39.3%)

explain148.0ms (1.5%)

preprocess80.0ms (0.8%)

eval0.0ms (0%)

prune0.0ms (0%)

simplify8.0ms (0.1%)

localize38.0ms (0.4%)

series142.0ms (1.4%)

simplify158.0ms (1.6%)

rewrite263.0ms (2.6%)

eval113.0ms (1.1%)

prune40.0ms (0.4%)

simplify201.0ms (2%)

localize197.0ms (2%)

series149.0ms (1.5%)

simplify212.0ms (2.1%)

rewrite374.0ms (3.7%)

eval231.0ms (2.3%)

prune28.0ms (0.3%)

simplify57.0ms (0.6%)

localize111.0ms (1.1%)

series45.0ms (0.4%)

simplify169.0ms (1.7%)

rewrite292.0ms (2.9%)

eval150.0ms (1.5%)

prune38.0ms (0.4%)

simplify37.0ms (0.4%)

localize155.0ms (1.5%)

series148.0ms (1.5%)

simplify189.0ms (1.9%)

rewrite249.0ms (2.5%)

eval158.0ms (1.6%)

prune38.0ms (0.4%)

regimes45.0ms (0.5%)

regimes42.0ms (0.4%)

regimes34.0ms (0.3%)

regimes13.0ms (0.1%)

regimes12.0ms (0.1%)

regimes33.0ms (0.3%)

regimes2.0ms (0%)

regimes7.0ms (0.1%)

regimes44.0ms (0.4%)

bsearch34.0ms (0.3%)

bsearch1.0ms (0%)

bsearch0.0ms (0%)

bsearch1.0ms (0%)

bsearch0.0ms (0%)

bsearch0.0ms (0%)

simplify31.0ms (0.3%)

soundness1.4s (13.6%)

preprocess49.0ms (0.5%)

end0.0ms (0%)

Profiling

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

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

Iter	Nodes	Cost
0	42	293
0	65	290
1	90	284
2	106	284
3	130	284
4	152	284
5	176	284
6	220	284
7	302	284
8	326	284
9	346	284
10	356	284
0	356	284

Iter	Nodes	Cost
0	47	254
0	70	229
1	105	219
2	149	219
3	199	203
4	253	203
5	346	203
6	498	203
7	666	203
8	720	203
9	763	203
0	763	203

Iter	Nodes	Cost
0	79	412
1	104	392
2	119	392
3	139	392
4	156	392
5	175	392
6	209	392
7	276	392
8	307	392
9	340	392
10	350	392