Details

analyze115.0ms (1.2%)

Algorithm

1×

Search

True	Other	False	Iter
0%	99.9%	0.1%	0
0%	99.9%	0.1%	1
0%	50%	50%	2
0%	50%	50%	3
0%	50%	50%	4
12.5%	37.5%	50%	5
12.5%	34.3%	53.2%	6
15.6%	26.5%	57.9%	7
15.6%	22.6%	61.8%	8
17.2%	17.6%	65.3%	9
17.2%	15%	67.8%	10
18%	12.2%	69.9%	11
18%	10.8%	71.3%	12

Compiler

Compiled 19 to 16 computations (15.8% saved)

sample2.8s (29.8%)

Results

1.4s	8256×	body	256	valid
801.0ms	1371×	body	1024	invalid
366.0ms	2306×	body	256	invalid
245.0ms	704×	body	512	invalid

preprocess46.0ms (0.5%)

Algorithm

2×	egg-herbie

Rules

454×	`neg-mul-1_binary64`
436×	`fma-def_binary64`
428×	`unswap-sqr_binary64`
421×	`div-sub_binary64`
418×	`associate-/l*_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	21	50
1	52	44
2	119	44
3	256	44
4	668	44
5	1836	40
6	4163	40
7	7307	40
0	2	2

Stop Event

1×	saturated
1×	node limit

Calls

Call 1

Inputs
0
1

Outputs
0
1

Call 2

Inputs
(.f64 (/.f64 1 (sqrt.f64 k)) (pow.f64 (.f64 (*.f64 2 (PI.f64)) n) (/.f64 (-.f64 1 k) 2)))
(.f64 (/.f64 1 (sqrt.f64 n)) (pow.f64 (.f64 (*.f64 2 (PI.f64)) k) (/.f64 (-.f64 1 n) 2)))

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

Compiler

Compiled 20 to 17 computations (15% saved)

simplify29.0ms (0.3%)

Algorithm

1×	egg-herbie

Rules

664×	`associate-/l*_binary64`
544×	`associate-/r*_binary64`
456×	`div-sub_binary64`
445×	`distribute-frac-neg_binary64`
416×	`distribute-rgt-in_binary64`

Iterations

Useful iterations: 5 (0.0ms)

Iter	Nodes	Cost
0	14	25
1	32	22
2	68	22
3	140	22
4	354	22
5	958	20
6	2187	20
7	5609	20

Stop Event

1×	node limit

Counts

1 → 2

Calls

Call 1

Inputs
(.f64 (/.f64 1 (sqrt.f64 k)) (pow.f64 (.f64 (*.f64 2 (PI.f64)) n) (/.f64 (-.f64 1 k) 2)))

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

eval1.0ms (0%)

Compiler: Compiled 31 to 23 computations (25.8% saved)

prune2.0ms (0%)

Pruning

3 alts after pruning (3 fresh and 0 done)

	Kept	Total
New	2	2
Fresh	1	1
Picked	0	0
Done	0	0
Total	3	3

Error

0.5b

Counts

3 → 2

Alt Table

Click to see full alt table

Status	Error	Program
▶	0.5b	(/.f64 (pow.f64 (.f64 2 (.f64 (PI.f64) n)) (fma.f64 k -1/2 1/2)) (sqrt.f64 k))
▶	0.6b	(.f64 (/.f64 1 (sqrt.f64 k)) (pow.f64 (.f64 (*.f64 2 (PI.f64)) n) (/.f64 (-.f64 1 k) 2)))

Compiler

Compiled 33 to 27 computations (18.2% saved)

localize28.0ms (0.3%)

Local error

Found 8 expressions with local error:

New	Error	Program
	0.4b	(pow.f64 (.f64 (.f64 2 (PI.f64)) n) (/.f64 (-.f64 1 k) 2))
	0.3b	(/.f64 1 (sqrt.f64 k))
	0.2b	(.f64 (.f64 2 (PI.f64)) n)
	0.2b	(.f64 (/.f64 1 (sqrt.f64 k)) (pow.f64 (.f64 (*.f64 2 (PI.f64)) n) (/.f64 (-.f64 1 k) 2)))
✓	0.2b	(.f64 (/.f64 1 (sqrt.f64 k)) (pow.f64 (.f64 (*.f64 2 (PI.f64)) n) (/.f64 (-.f64 1 k) 2)))
✓	0.2b	(.f64 (.f64 2 (PI.f64)) n)
✓	0.3b	(/.f64 1 (sqrt.f64 k))
✓	0.4b	(pow.f64 (.f64 (.f64 2 (PI.f64)) n) (/.f64 (-.f64 1 k) 2))

Compiler

Compiled 56 to 38 computations (32.1% saved)

series73.0ms (0.8%)

Counts

4 → 48

Calls

18 calls:

Time	Variable		Point	Expression
27.0ms	n	@	0	(pow.f64 (.f64 (.f64 2 (PI.f64)) n) (/.f64 (-.f64 1 k) 2))
19.0ms	n	@	-inf	(pow.f64 (.f64 (.f64 2 (PI.f64)) n) (/.f64 (-.f64 1 k) 2))
10.0ms	n	@	inf	(pow.f64 (.f64 (.f64 2 (PI.f64)) n) (/.f64 (-.f64 1 k) 2))
6.0ms	k	@	0	(/.f64 1 (sqrt.f64 k))
2.0ms	k	@	0	(.f64 (/.f64 1 (sqrt.f64 k)) (pow.f64 (.f64 (*.f64 2 (PI.f64)) n) (/.f64 (-.f64 1 k) 2)))

rewrite68.0ms (0.7%)

Algorithm

1×	batch-egg-rewrite

Rules

751×	`log-prod_binary64`
382×	`pow2_binary64`
265×	`pow1/3_binary64`
260×	`expm1-udef_binary64`
259×	`log1p-udef_binary64`

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	14	53
1	307	51
2	3925	47

Stop Event

1×	node limit

Counts

4 → 108

Calls

Call 1

Inputs
(pow.f64 (.f64 (.f64 2 (PI.f64)) n) (/.f64 (-.f64 1 k) 2))
(/.f64 1 (sqrt.f64 k))
(.f64 (.f64 2 (PI.f64)) n)
(.f64 (/.f64 1 (sqrt.f64 k)) (pow.f64 (.f64 (*.f64 2 (PI.f64)) n) (/.f64 (-.f64 1 k) 2)))

Outputs
((#(struct:change #<rule egg-rr> (2) ((x +.f64 0 (sqrt.f64 (pow.f64 (.f64 2 (.f64 (PI.f64) n)) (-.f64 1 k))))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (log.f64 (pow.f64 (cbrt.f64 (exp.f64 (sqrt.f64 (pow.f64 (.f64 2 (.f64 (PI.f64) n)) (-.f64 1 k))))) 2)) (log.f64 (cbrt.f64 (exp.f64 (sqrt.f64 (pow.f64 (.f64 2 (.f64 (PI.f64) n)) (-.f64 1 k)))))))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (log.f64 (sqrt.f64 (exp.f64 (sqrt.f64 (pow.f64 (.f64 2 (.f64 (PI.f64) n)) (-.f64 1 k)))))) (log.f64 (sqrt.f64 (exp.f64 (sqrt.f64 (pow.f64 (.f64 2 (.f64 (PI.f64) n)) (-.f64 1 k)))))))))) (#(struct:change #<rule egg-rr> (2) ((x -.f64 (exp.f64 (log1p.f64 (sqrt.f64 (pow.f64 (.f64 2 (.f64 (PI.f64) n)) (-.f64 1 k))))) 1)))) (#(struct:change #<rule egg-rr> (2) ((x .f64 1 (sqrt.f64 (pow.f64 (.f64 2 (.f64 (PI.f64) n)) (-.f64 1 k))))))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (sqrt.f64 (pow.f64 (.f64 2 (.f64 (PI.f64) n)) (-.f64 1 k))) 1)))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (cbrt.f64 (sqrt.f64 (pow.f64 (.f64 2 (.f64 (PI.f64) n)) (-.f64 1 k)))) (cbrt.f64 (pow.f64 (.f64 2 (.f64 (PI.f64) n)) (-.f64 1 k))))))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (cbrt.f64 (pow.f64 (.f64 2 (.f64 (PI.f64) n)) (-.f64 1 k))) (cbrt.f64 (sqrt.f64 (pow.f64 (.f64 2 (.f64 (PI.f64) n)) (-.f64 1 k)))))))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (pow.f64 (.f64 2 (PI.f64)) (-.f64 1/2 (/.f64 k 2))) (pow.f64 n (-.f64 1/2 (/.f64 k 2))))))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (pow.f64 n (-.f64 1/2 (/.f64 k 2))) (pow.f64 (.f64 2 (PI.f64)) (-.f64 1/2 (/.f64 k 2))))))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (pow.f64 (.f64 2 (.f64 (PI.f64) n)) (/.f64 (-.f64 1 k) 4)) (pow.f64 (.f64 2 (.f64 (PI.f64) n)) (/.f64 (-.f64 1 k) 4)))))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (pow.f64 2 (-.f64 1/2 (/.f64 k 2))) (pow.f64 (.f64 (PI.f64) n) (-.f64 1/2 (/.f64 k 2))))))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (pow.f64 1 (-.f64 1/2 (/.f64 k 2))) (sqrt.f64 (pow.f64 (.f64 2 (.f64 (PI.f64) n)) (-.f64 1 k))))))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (pow.f64 (pow.f64 (cbrt.f64 (.f64 2 (.f64 (PI.f64) n))) 2) (-.f64 1/2 (/.f64 k 2))) (pow.f64 (cbrt.f64 (.f64 2 (.f64 (PI.f64) n))) (-.f64 1/2 (/.f64 k 2))))))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (pow.f64 (sqrt.f64 (.f64 2 (.f64 (PI.f64) n))) (-.f64 1/2 (/.f64 k 2))) (pow.f64 (sqrt.f64 (.f64 2 (.f64 (PI.f64) n))) (-.f64 1/2 (/.f64 k 2))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (sqrt.f64 (.f64 2 (.f64 (PI.f64) n))) (pow.f64 (.f64 2 (.f64 (PI.f64) n)) (/.f64 k 2)))))) (#(struct:change #<rule egg-rr> (2) ((x sqrt.f64 (pow.f64 (.f64 2 (.f64 (PI.f64) n)) (-.f64 1 k)))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (exp.f64 (sqrt.f64 (pow.f64 (.f64 2 (.f64 (PI.f64) n)) (-.f64 1 k)))))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (+.f64 1 (expm1.f64 (sqrt.f64 (pow.f64 (.f64 2 (.f64 (PI.f64) n)) (-.f64 1 k))))))))) (#(struct:change #<rule egg-rr> (2) ((x cbrt.f64 (pow.f64 (sqrt.f64 (pow.f64 (.f64 2 (.f64 (PI.f64) n)) (-.f64 1 k))) 3))))) (#(struct:change #<rule egg-rr> (2) ((x expm1.f64 (log1p.f64 (sqrt.f64 (pow.f64 (.f64 2 (.f64 (PI.f64) n)) (-.f64 1 k)))))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (log.f64 (sqrt.f64 (pow.f64 (.f64 2 (.f64 (PI.f64) n)) (-.f64 1 k)))))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (.f64 (log.f64 (sqrt.f64 (pow.f64 (.f64 2 (.f64 (PI.f64) n)) (-.f64 1 k)))) 1))))) (#(struct:change #<rule egg-rr> (2) ((x log1p.f64 (expm1.f64 (sqrt.f64 (pow.f64 (.f64 2 (*.f64 (PI.f64) n)) (-.f64 1 k)))))))))
((#(struct:change #<rule egg-rr> (2) ((x +.f64 0 (pow.f64 k -1/2))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (log.f64 (pow.f64 (cbrt.f64 (exp.f64 (pow.f64 k -1/2))) 2)) (log.f64 (cbrt.f64 (exp.f64 (pow.f64 k -1/2)))))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (log.f64 (sqrt.f64 (exp.f64 (pow.f64 k -1/2)))) (log.f64 (sqrt.f64 (exp.f64 (pow.f64 k -1/2)))))))) (#(struct:change #<rule egg-rr> (2) ((x -.f64 (exp.f64 (log1p.f64 (pow.f64 k -1/2))) 1)))) (#(struct:change #<rule egg-rr> (2) ((x .f64 1 (pow.f64 k -1/2))))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (pow.f64 k -1/2) 1)))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (cbrt.f64 (pow.f64 k -1/2)) (cbrt.f64 (/.f64 1 k)))))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (cbrt.f64 (/.f64 1 k)) (cbrt.f64 (pow.f64 k -1/2)))))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (pow.f64 (sqrt.f64 k) -1/2) (pow.f64 (sqrt.f64 k) -1/2))))) (#(struct:change #<rule egg-rr> (2) ((x .f64 -1 (/.f64 1 (neg.f64 (sqrt.f64 k))))))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (/.f64 1 (cbrt.f64 k)) (cbrt.f64 (pow.f64 k -1/2)))))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 k -1/2)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (sqrt.f64 k) -1)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (pow.f64 k -1/2) 1)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (/.f64 1 k) 1/2)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (pow.f64 (pow.f64 k -1/2) 3) 1/3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (cbrt.f64 (pow.f64 k -1/2)) 3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (pow.f64 (sqrt.f64 k) -1/2) 2)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (neg.f64 (neg.f64 (sqrt.f64 k))) -1)))) (#(struct:change #<rule egg-rr> (2) ((x sqrt.f64 (/.f64 1 k))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (exp.f64 (pow.f64 k -1/2)))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (+.f64 1 (expm1.f64 (pow.f64 k -1/2))))))) (#(struct:change #<rule egg-rr> (2) ((x cbrt.f64 (pow.f64 (pow.f64 k -1/2) 3))))) (#(struct:change #<rule egg-rr> (2) ((x expm1.f64 (log1p.f64 (pow.f64 k -1/2)))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (.f64 -1/2 (log.f64 k)))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (.f64 (log.f64 (sqrt.f64 k)) -1))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (.f64 (*.f64 -1/2 (log.f64 k)) 1))))) (#(struct:change #<rule egg-rr> (2) ((x log1p.f64 (expm1.f64 (pow.f64 k -1/2)))))))
((#(struct:change #<rule egg-rr> (2) ((x +.f64 0 (.f64 2 (.f64 (PI.f64) n)))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (log.f64 (pow.f64 (cbrt.f64 (pow.f64 (exp.f64 n) (.f64 2 (PI.f64)))) 2)) (log.f64 (cbrt.f64 (pow.f64 (exp.f64 n) (.f64 2 (PI.f64))))))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (log.f64 (sqrt.f64 (pow.f64 (exp.f64 n) (.f64 2 (PI.f64))))) (log.f64 (sqrt.f64 (pow.f64 (exp.f64 n) (.f64 2 (PI.f64))))))))) (#(struct:change #<rule egg-rr> (2) ((x -.f64 (exp.f64 (log1p.f64 (.f64 2 (.f64 (PI.f64) n)))) 1)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (.f64 2 (.f64 (PI.f64) n)) 1)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (.f64 4 (pow.f64 (.f64 (PI.f64) n) 2)) 1/2)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (pow.f64 (.f64 2 (.f64 (PI.f64) n)) 3) 1/3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (cbrt.f64 (.f64 2 (.f64 (PI.f64) n))) 3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (sqrt.f64 (.f64 2 (.f64 (PI.f64) n))) 2)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (.f64 (pow.f64 (.f64 2 (PI.f64)) 3) (pow.f64 n 3)) 1/3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (.f64 (pow.f64 n 3) (pow.f64 (.f64 2 (PI.f64)) 3)) 1/3)))) (#(struct:change #<rule egg-rr> (2) ((x sqrt.f64 (.f64 4 (pow.f64 (.f64 (PI.f64) n) 2)))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (pow.f64 (exp.f64 n) (.f64 2 (PI.f64))))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (+.f64 1 (expm1.f64 (.f64 2 (.f64 (PI.f64) n)))))))) (#(struct:change #<rule egg-rr> (2) ((x cbrt.f64 (pow.f64 (.f64 2 (.f64 (PI.f64) n)) 3))))) (#(struct:change #<rule egg-rr> (2) ((x cbrt.f64 (.f64 (pow.f64 (.f64 2 (PI.f64)) 3) (pow.f64 n 3)))))) (#(struct:change #<rule egg-rr> (2) ((x cbrt.f64 (.f64 (pow.f64 n 3) (pow.f64 (.f64 2 (PI.f64)) 3)))))) (#(struct:change #<rule egg-rr> (2) ((x expm1.f64 (log1p.f64 (.f64 2 (.f64 (PI.f64) n))))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (log.f64 (.f64 2 (.f64 (PI.f64) n))))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (.f64 (log.f64 (.f64 2 (.f64 (PI.f64) n))) 1))))) (#(struct:change #<rule egg-rr> (2) ((x log1p.f64 (expm1.f64 (.f64 2 (.f64 (PI.f64) n))))))))
((#(struct:change #<rule egg-rr> (2) ((x +.f64 0 (sqrt.f64 (/.f64 (pow.f64 (.f64 2 (.f64 (PI.f64) n)) (-.f64 1 k)) k)))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (log.f64 (pow.f64 (cbrt.f64 (exp.f64 (sqrt.f64 (/.f64 (pow.f64 (.f64 2 (.f64 (PI.f64) n)) (-.f64 1 k)) k)))) 2)) (log.f64 (cbrt.f64 (exp.f64 (sqrt.f64 (/.f64 (pow.f64 (.f64 2 (.f64 (PI.f64) n)) (-.f64 1 k)) k))))))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (log.f64 (sqrt.f64 (exp.f64 (sqrt.f64 (/.f64 (pow.f64 (.f64 2 (.f64 (PI.f64) n)) (-.f64 1 k)) k))))) (log.f64 (sqrt.f64 (exp.f64 (sqrt.f64 (/.f64 (pow.f64 (.f64 2 (.f64 (PI.f64) n)) (-.f64 1 k)) k))))))))) (#(struct:change #<rule egg-rr> (2) ((x -.f64 (exp.f64 (log1p.f64 (sqrt.f64 (/.f64 (pow.f64 (.f64 2 (.f64 (PI.f64) n)) (-.f64 1 k)) k)))) 1)))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 1 (/.f64 (sqrt.f64 k) (sqrt.f64 (pow.f64 (.f64 2 (.f64 (PI.f64) n)) (-.f64 1 k)))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (sqrt.f64 (pow.f64 (.f64 2 (.f64 (PI.f64) n)) (-.f64 1 k))) (sqrt.f64 k))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (cbrt.f64 (pow.f64 (.f64 2 (.f64 (PI.f64) n)) (-.f64 1 k))) (/.f64 (sqrt.f64 k) (cbrt.f64 (sqrt.f64 (pow.f64 (.f64 2 (.f64 (PI.f64) n)) (-.f64 1 k))))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (pow.f64 (.f64 2 (PI.f64)) (-.f64 1/2 (/.f64 k 2))) (/.f64 (sqrt.f64 k) (pow.f64 n (-.f64 1/2 (/.f64 k 2)))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (pow.f64 (.f64 2 (.f64 (PI.f64) n)) (/.f64 (-.f64 1 k) 4)) (/.f64 (sqrt.f64 k) (pow.f64 (.f64 2 (.f64 (PI.f64) n)) (/.f64 (-.f64 1 k) 4))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (neg.f64 (sqrt.f64 (pow.f64 (.f64 2 (.f64 (PI.f64) n)) (-.f64 1 k)))) (neg.f64 (sqrt.f64 k)))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (/.f64 (sqrt.f64 (pow.f64 (.f64 2 (.f64 (PI.f64) n)) (-.f64 1 k))) (pow.f64 k 1/4)) (pow.f64 k 1/4))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (/.f64 (sqrt.f64 (pow.f64 (.f64 2 (.f64 (PI.f64) n)) (-.f64 1 k))) 1) (sqrt.f64 k))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (/.f64 (sqrt.f64 (pow.f64 (.f64 2 (.f64 (PI.f64) n)) (-.f64 1 k))) (cbrt.f64 k)) (cbrt.f64 (sqrt.f64 k)))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (.f64 -1 (sqrt.f64 (pow.f64 (.f64 2 (.f64 (PI.f64) n)) (-.f64 1 k)))) (neg.f64 (sqrt.f64 k)))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (.f64 (sqrt.f64 (pow.f64 (.f64 2 (.f64 (PI.f64) n)) (-.f64 1 k))) -1) (neg.f64 (sqrt.f64 k)))))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (sqrt.f64 (/.f64 (pow.f64 (.f64 2 (.f64 (PI.f64) n)) (-.f64 1 k)) k)) 1)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (/.f64 (pow.f64 (.f64 2 (.f64 (PI.f64) n)) (-.f64 1 k)) k) 1/2)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (pow.f64 (sqrt.f64 (/.f64 (pow.f64 (.f64 2 (.f64 (PI.f64) n)) (-.f64 1 k)) k)) 3) 1/3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (cbrt.f64 (sqrt.f64 (/.f64 (pow.f64 (.f64 2 (.f64 (PI.f64) n)) (-.f64 1 k)) k))) 3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (sqrt.f64 (sqrt.f64 (/.f64 (pow.f64 (.f64 2 (.f64 (PI.f64) n)) (-.f64 1 k)) k))) 2)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (/.f64 (pow.f64 (sqrt.f64 (pow.f64 (.f64 2 (.f64 (PI.f64) n)) (-.f64 1 k))) 3) (pow.f64 k 3/2)) 1/3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (.f64 (pow.f64 (sqrt.f64 (pow.f64 (.f64 2 (.f64 (PI.f64) n)) (-.f64 1 k))) 3) (pow.f64 (pow.f64 k -1/2) 3)) 1/3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (.f64 (pow.f64 (pow.f64 k -1/2) 3) (pow.f64 (sqrt.f64 (pow.f64 (.f64 2 (.f64 (PI.f64) n)) (-.f64 1 k))) 3)) 1/3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (/.f64 (sqrt.f64 k) (sqrt.f64 (pow.f64 (.f64 2 (.f64 (PI.f64) n)) (-.f64 1 k)))) -1)))) (#(struct:change #<rule egg-rr> (2) ((x sqrt.f64 (/.f64 (pow.f64 (.f64 2 (.f64 (PI.f64) n)) (-.f64 1 k)) k))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (exp.f64 (sqrt.f64 (/.f64 (pow.f64 (.f64 2 (.f64 (PI.f64) n)) (-.f64 1 k)) k))))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (+.f64 1 (expm1.f64 (sqrt.f64 (/.f64 (pow.f64 (.f64 2 (.f64 (PI.f64) n)) (-.f64 1 k)) k)))))))) (#(struct:change #<rule egg-rr> (2) ((x cbrt.f64 (pow.f64 (sqrt.f64 (/.f64 (pow.f64 (.f64 2 (.f64 (PI.f64) n)) (-.f64 1 k)) k)) 3))))) (#(struct:change #<rule egg-rr> (2) ((x cbrt.f64 (/.f64 (pow.f64 (sqrt.f64 (pow.f64 (.f64 2 (.f64 (PI.f64) n)) (-.f64 1 k))) 3) (pow.f64 k 3/2)))))) (#(struct:change #<rule egg-rr> (2) ((x cbrt.f64 (.f64 (pow.f64 (sqrt.f64 (pow.f64 (.f64 2 (.f64 (PI.f64) n)) (-.f64 1 k))) 3) (pow.f64 (pow.f64 k -1/2) 3)))))) (#(struct:change #<rule egg-rr> (2) ((x cbrt.f64 (.f64 (pow.f64 (pow.f64 k -1/2) 3) (pow.f64 (sqrt.f64 (pow.f64 (.f64 2 (.f64 (PI.f64) n)) (-.f64 1 k))) 3)))))) (#(struct:change #<rule egg-rr> (2) ((x expm1.f64 (log1p.f64 (sqrt.f64 (/.f64 (pow.f64 (.f64 2 (.f64 (PI.f64) n)) (-.f64 1 k)) k))))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (log.f64 (sqrt.f64 (/.f64 (pow.f64 (.f64 2 (.f64 (PI.f64) n)) (-.f64 1 k)) k))))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (.f64 (log.f64 (sqrt.f64 (/.f64 (pow.f64 (.f64 2 (.f64 (PI.f64) n)) (-.f64 1 k)) k))) 1))))) (#(struct:change #<rule egg-rr> (2) ((x log1p.f64 (expm1.f64 (sqrt.f64 (/.f64 (pow.f64 (.f64 2 (.f64 (PI.f64) n)) (-.f64 1 k)) k))))))))

simplify48.0ms (0.5%)

Algorithm

1×	egg-herbie

Rules

534×	`associate-+r+_binary64`
528×	`associate-+l+_binary64`
423×	`associate-r_binary64`
405×	`associate-l_binary64`
338×	`distribute-rgt-in_binary64`

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	82	1206
1	226	1124
2	739	969
3	4114	958

Stop Event

1×	node limit

Counts

156 → 129

Calls

Call 1

Inputs
(exp.f64 (.f64 1/2 (.f64 (-.f64 1 k) (+.f64 (log.f64 n) (log.f64 (*.f64 2 (PI.f64)))))))
(exp.f64 (.f64 1/2 (.f64 (-.f64 1 k) (+.f64 (log.f64 n) (log.f64 (*.f64 2 (PI.f64)))))))
(exp.f64 (.f64 1/2 (.f64 (-.f64 1 k) (+.f64 (log.f64 n) (log.f64 (*.f64 2 (PI.f64)))))))
(exp.f64 (.f64 1/2 (.f64 (-.f64 1 k) (+.f64 (log.f64 n) (log.f64 (*.f64 2 (PI.f64)))))))
(exp.f64 (.f64 1/2 (.f64 (-.f64 1 k) (+.f64 (.f64 -1 (log.f64 (/.f64 1 n))) (log.f64 (.f64 2 (PI.f64)))))))
(exp.f64 (.f64 1/2 (.f64 (-.f64 1 k) (+.f64 (.f64 -1 (log.f64 (/.f64 1 n))) (log.f64 (.f64 2 (PI.f64)))))))
(exp.f64 (.f64 1/2 (.f64 (-.f64 1 k) (+.f64 (.f64 -1 (log.f64 (/.f64 1 n))) (log.f64 (.f64 2 (PI.f64)))))))
(exp.f64 (.f64 1/2 (.f64 (-.f64 1 k) (+.f64 (.f64 -1 (log.f64 (/.f64 1 n))) (log.f64 (.f64 2 (PI.f64)))))))
(exp.f64 (.f64 1/2 (.f64 (-.f64 1 k) (+.f64 (.f64 -1 (log.f64 (/.f64 -1 n))) (log.f64 (.f64 -2 (PI.f64)))))))
(exp.f64 (.f64 1/2 (.f64 (-.f64 1 k) (+.f64 (.f64 -1 (log.f64 (/.f64 -1 n))) (log.f64 (.f64 -2 (PI.f64)))))))
(exp.f64 (.f64 1/2 (.f64 (-.f64 1 k) (+.f64 (.f64 -1 (log.f64 (/.f64 -1 n))) (log.f64 (.f64 -2 (PI.f64)))))))
(exp.f64 (.f64 1/2 (.f64 (-.f64 1 k) (+.f64 (.f64 -1 (log.f64 (/.f64 -1 n))) (log.f64 (.f64 -2 (PI.f64)))))))
(.f64 (sqrt.f64 2) (sqrt.f64 (.f64 n (PI.f64))))
(+.f64 (.f64 -1/2 (.f64 (.f64 (sqrt.f64 2) (.f64 k (log.f64 (.f64 2 (.f64 n (PI.f64)))))) (sqrt.f64 (.f64 n (PI.f64))))) (.f64 (sqrt.f64 2) (sqrt.f64 (*.f64 n (PI.f64)))))
(+.f64 (.f64 -1/2 (.f64 (.f64 (sqrt.f64 2) (.f64 k (log.f64 (.f64 2 (.f64 n (PI.f64)))))) (sqrt.f64 (.f64 n (PI.f64))))) (+.f64 (.f64 (sqrt.f64 2) (sqrt.f64 (.f64 n (PI.f64)))) (.f64 1/8 (.f64 (.f64 (sqrt.f64 2) (.f64 (pow.f64 k 2) (pow.f64 (log.f64 (.f64 2 (.f64 n (PI.f64)))) 2))) (sqrt.f64 (.f64 n (PI.f64)))))))
(+.f64 (.f64 -1/2 (.f64 (.f64 (sqrt.f64 2) (.f64 k (log.f64 (.f64 2 (.f64 n (PI.f64)))))) (sqrt.f64 (.f64 n (PI.f64))))) (+.f64 (.f64 (sqrt.f64 2) (sqrt.f64 (.f64 n (PI.f64)))) (+.f64 (.f64 1/8 (.f64 (.f64 (sqrt.f64 2) (.f64 (pow.f64 k 2) (pow.f64 (log.f64 (.f64 2 (.f64 n (PI.f64)))) 2))) (sqrt.f64 (.f64 n (PI.f64))))) (.f64 -1/48 (.f64 (.f64 (sqrt.f64 2) (.f64 (pow.f64 k 3) (pow.f64 (log.f64 (.f64 2 (.f64 n (PI.f64)))) 3))) (sqrt.f64 (*.f64 n (PI.f64))))))))
(exp.f64 (.f64 1/2 (.f64 (-.f64 1 k) (log.f64 (.f64 2 (.f64 n (PI.f64)))))))
(exp.f64 (.f64 1/2 (.f64 (-.f64 1 k) (log.f64 (.f64 2 (.f64 n (PI.f64)))))))
(exp.f64 (.f64 1/2 (.f64 (-.f64 1 k) (log.f64 (.f64 2 (.f64 n (PI.f64)))))))
(exp.f64 (.f64 1/2 (.f64 (-.f64 1 k) (log.f64 (.f64 2 (.f64 n (PI.f64)))))))
(exp.f64 (.f64 1/2 (.f64 (+.f64 1 (.f64 -1 k)) (log.f64 (.f64 2 (*.f64 n (PI.f64)))))))
(exp.f64 (.f64 1/2 (.f64 (+.f64 1 (.f64 -1 k)) (log.f64 (.f64 2 (*.f64 n (PI.f64)))))))
(exp.f64 (.f64 1/2 (.f64 (+.f64 1 (.f64 -1 k)) (log.f64 (.f64 2 (*.f64 n (PI.f64)))))))
(exp.f64 (.f64 1/2 (.f64 (+.f64 1 (.f64 -1 k)) (log.f64 (.f64 2 (*.f64 n (PI.f64)))))))
(.f64 2 (.f64 n (PI.f64)))
(.f64 2 (.f64 n (PI.f64)))
(.f64 2 (.f64 n (PI.f64)))
(.f64 2 (.f64 n (PI.f64)))
(.f64 2 (.f64 n (PI.f64)))
(.f64 2 (.f64 n (PI.f64)))
(.f64 2 (.f64 n (PI.f64)))
(.f64 2 (.f64 n (PI.f64)))
(.f64 2 (.f64 n (PI.f64)))
(.f64 2 (.f64 n (PI.f64)))
(.f64 2 (.f64 n (PI.f64)))
(.f64 2 (.f64 n (PI.f64)))
(.f64 (sqrt.f64 (/.f64 1 k)) (exp.f64 (.f64 1/2 (.f64 (-.f64 1 k) (+.f64 (log.f64 (.f64 2 (PI.f64))) (log.f64 n))))))
(.f64 (sqrt.f64 (/.f64 1 k)) (exp.f64 (.f64 1/2 (.f64 (-.f64 1 k) (+.f64 (log.f64 (.f64 2 (PI.f64))) (log.f64 n))))))
(.f64 (sqrt.f64 (/.f64 1 k)) (exp.f64 (.f64 1/2 (.f64 (-.f64 1 k) (+.f64 (log.f64 (.f64 2 (PI.f64))) (log.f64 n))))))
(.f64 (sqrt.f64 (/.f64 1 k)) (exp.f64 (.f64 1/2 (.f64 (-.f64 1 k) (+.f64 (log.f64 (.f64 2 (PI.f64))) (log.f64 n))))))
(.f64 (sqrt.f64 (/.f64 1 k)) (exp.f64 (.f64 1/2 (.f64 (-.f64 1 k) (+.f64 (.f64 -1 (log.f64 (/.f64 1 n))) (log.f64 (*.f64 2 (PI.f64))))))))
(.f64 (sqrt.f64 (/.f64 1 k)) (exp.f64 (.f64 1/2 (.f64 (-.f64 1 k) (+.f64 (.f64 -1 (log.f64 (/.f64 1 n))) (log.f64 (*.f64 2 (PI.f64))))))))
(.f64 (sqrt.f64 (/.f64 1 k)) (exp.f64 (.f64 1/2 (.f64 (-.f64 1 k) (+.f64 (.f64 -1 (log.f64 (/.f64 1 n))) (log.f64 (*.f64 2 (PI.f64))))))))
(.f64 (sqrt.f64 (/.f64 1 k)) (exp.f64 (.f64 1/2 (.f64 (-.f64 1 k) (+.f64 (.f64 -1 (log.f64 (/.f64 1 n))) (log.f64 (*.f64 2 (PI.f64))))))))
(.f64 (sqrt.f64 (/.f64 1 k)) (exp.f64 (.f64 1/2 (.f64 (-.f64 1 k) (+.f64 (.f64 -1 (log.f64 (/.f64 -1 n))) (log.f64 (*.f64 -2 (PI.f64))))))))
(.f64 (sqrt.f64 (/.f64 1 k)) (exp.f64 (.f64 1/2 (.f64 (-.f64 1 k) (+.f64 (.f64 -1 (log.f64 (/.f64 -1 n))) (log.f64 (*.f64 -2 (PI.f64))))))))
(.f64 (sqrt.f64 (/.f64 1 k)) (exp.f64 (.f64 1/2 (.f64 (-.f64 1 k) (+.f64 (.f64 -1 (log.f64 (/.f64 -1 n))) (log.f64 (*.f64 -2 (PI.f64))))))))
(.f64 (sqrt.f64 (/.f64 1 k)) (exp.f64 (.f64 1/2 (.f64 (-.f64 1 k) (+.f64 (.f64 -1 (log.f64 (/.f64 -1 n))) (log.f64 (*.f64 -2 (PI.f64))))))))

Outputs
(exp.f64 (.f64 1/2 (.f64 (-.f64 1 k) (+.f64 (log.f64 n) (log.f64 (*.f64 2 (PI.f64)))))))
(pow.f64 (exp.f64 1/2) (.f64 (-.f64 1 k) (+.f64 (log.f64 n) (log.f64 (.f64 2 (PI.f64))))))
(pow.f64 (exp.f64 1/2) (.f64 (-.f64 1 k) (log.f64 (.f64 n (*.f64 2 (PI.f64))))))
(sqrt.f64 (pow.f64 (.f64 n (.f64 2 (PI.f64))) (-.f64 1 k)))
(exp.f64 (.f64 1/2 (.f64 (-.f64 1 k) (+.f64 (log.f64 n) (log.f64 (*.f64 2 (PI.f64)))))))
(pow.f64 (exp.f64 1/2) (.f64 (-.f64 1 k) (+.f64 (log.f64 n) (log.f64 (.f64 2 (PI.f64))))))
(pow.f64 (exp.f64 1/2) (.f64 (-.f64 1 k) (log.f64 (.f64 n (*.f64 2 (PI.f64))))))
(sqrt.f64 (pow.f64 (.f64 n (.f64 2 (PI.f64))) (-.f64 1 k)))
(exp.f64 (.f64 1/2 (.f64 (-.f64 1 k) (+.f64 (log.f64 n) (log.f64 (*.f64 2 (PI.f64)))))))
(pow.f64 (exp.f64 1/2) (.f64 (-.f64 1 k) (+.f64 (log.f64 n) (log.f64 (.f64 2 (PI.f64))))))
(pow.f64 (exp.f64 1/2) (.f64 (-.f64 1 k) (log.f64 (.f64 n (*.f64 2 (PI.f64))))))
(sqrt.f64 (pow.f64 (.f64 n (.f64 2 (PI.f64))) (-.f64 1 k)))
(exp.f64 (.f64 1/2 (.f64 (-.f64 1 k) (+.f64 (log.f64 n) (log.f64 (*.f64 2 (PI.f64)))))))
(pow.f64 (exp.f64 1/2) (.f64 (-.f64 1 k) (+.f64 (log.f64 n) (log.f64 (.f64 2 (PI.f64))))))
(pow.f64 (exp.f64 1/2) (.f64 (-.f64 1 k) (log.f64 (.f64 n (*.f64 2 (PI.f64))))))
(sqrt.f64 (pow.f64 (.f64 n (.f64 2 (PI.f64))) (-.f64 1 k)))
(exp.f64 (.f64 1/2 (.f64 (-.f64 1 k) (+.f64 (.f64 -1 (log.f64 (/.f64 1 n))) (log.f64 (.f64 2 (PI.f64)))))))
(pow.f64 (exp.f64 1/2) (.f64 (-.f64 1 k) (+.f64 (log.f64 n) (log.f64 (.f64 2 (PI.f64))))))
(pow.f64 (exp.f64 1/2) (.f64 (-.f64 1 k) (log.f64 (.f64 n (*.f64 2 (PI.f64))))))
(sqrt.f64 (pow.f64 (.f64 n (.f64 2 (PI.f64))) (-.f64 1 k)))
(exp.f64 (.f64 1/2 (.f64 (-.f64 1 k) (+.f64 (.f64 -1 (log.f64 (/.f64 1 n))) (log.f64 (.f64 2 (PI.f64)))))))
(pow.f64 (exp.f64 1/2) (.f64 (-.f64 1 k) (+.f64 (log.f64 n) (log.f64 (.f64 2 (PI.f64))))))
(pow.f64 (exp.f64 1/2) (.f64 (-.f64 1 k) (log.f64 (.f64 n (*.f64 2 (PI.f64))))))
(sqrt.f64 (pow.f64 (.f64 n (.f64 2 (PI.f64))) (-.f64 1 k)))
(exp.f64 (.f64 1/2 (.f64 (-.f64 1 k) (+.f64 (.f64 -1 (log.f64 (/.f64 1 n))) (log.f64 (.f64 2 (PI.f64)))))))
(pow.f64 (exp.f64 1/2) (.f64 (-.f64 1 k) (+.f64 (log.f64 n) (log.f64 (.f64 2 (PI.f64))))))
(pow.f64 (exp.f64 1/2) (.f64 (-.f64 1 k) (log.f64 (.f64 n (*.f64 2 (PI.f64))))))
(sqrt.f64 (pow.f64 (.f64 n (.f64 2 (PI.f64))) (-.f64 1 k)))
(exp.f64 (.f64 1/2 (.f64 (-.f64 1 k) (+.f64 (.f64 -1 (log.f64 (/.f64 1 n))) (log.f64 (.f64 2 (PI.f64)))))))
(pow.f64 (exp.f64 1/2) (.f64 (-.f64 1 k) (+.f64 (log.f64 n) (log.f64 (.f64 2 (PI.f64))))))
(pow.f64 (exp.f64 1/2) (.f64 (-.f64 1 k) (log.f64 (.f64 n (*.f64 2 (PI.f64))))))
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(.f64 (pow.f64 (sqrt.f64 (exp.f64 (-.f64 1 k))) (-.f64 (log.f64 (.f64 (PI.f64) -2)) (log.f64 (/.f64 -1 n)))) (sqrt.f64 (/.f64 1 k)))
(.f64 (sqrt.f64 (/.f64 1 k)) (exp.f64 (.f64 1/2 (.f64 (-.f64 1 k) (+.f64 (.f64 -1 (log.f64 (/.f64 -1 n))) (log.f64 (*.f64 -2 (PI.f64))))))))
(.f64 (pow.f64 (exp.f64 1/2) (.f64 (-.f64 1 k) (fma.f64 -1 (log.f64 (/.f64 -1 n)) (log.f64 (*.f64 (PI.f64) -2))))) (sqrt.f64 (/.f64 1 k)))
(.f64 (pow.f64 (exp.f64 1/2) (.f64 (-.f64 1 k) (-.f64 (log.f64 (*.f64 (PI.f64) -2)) (log.f64 (/.f64 -1 n))))) (sqrt.f64 (/.f64 1 k)))
(.f64 (sqrt.f64 (pow.f64 (exp.f64 (-.f64 1 k)) (-.f64 (log.f64 (.f64 (PI.f64) -2)) (log.f64 (/.f64 -1 n))))) (sqrt.f64 (/.f64 1 k)))
(.f64 (pow.f64 (sqrt.f64 (exp.f64 (-.f64 1 k))) (-.f64 (log.f64 (.f64 (PI.f64) -2)) (log.f64 (/.f64 -1 n)))) (sqrt.f64 (/.f64 1 k)))
(.f64 (sqrt.f64 (/.f64 1 k)) (exp.f64 (.f64 1/2 (.f64 (-.f64 1 k) (+.f64 (.f64 -1 (log.f64 (/.f64 -1 n))) (log.f64 (*.f64 -2 (PI.f64))))))))
(.f64 (pow.f64 (exp.f64 1/2) (.f64 (-.f64 1 k) (fma.f64 -1 (log.f64 (/.f64 -1 n)) (log.f64 (*.f64 (PI.f64) -2))))) (sqrt.f64 (/.f64 1 k)))
(.f64 (pow.f64 (exp.f64 1/2) (.f64 (-.f64 1 k) (-.f64 (log.f64 (*.f64 (PI.f64) -2)) (log.f64 (/.f64 -1 n))))) (sqrt.f64 (/.f64 1 k)))
(.f64 (sqrt.f64 (pow.f64 (exp.f64 (-.f64 1 k)) (-.f64 (log.f64 (.f64 (PI.f64) -2)) (log.f64 (/.f64 -1 n))))) (sqrt.f64 (/.f64 1 k)))
(.f64 (pow.f64 (sqrt.f64 (exp.f64 (-.f64 1 k))) (-.f64 (log.f64 (.f64 (PI.f64) -2)) (log.f64 (/.f64 -1 n)))) (sqrt.f64 (/.f64 1 k)))

localize27.0ms (0.3%)

Local error

Found 6 expressions with local error:

New	Error	Program
	0.4b	(pow.f64 (.f64 2 (.f64 (PI.f64) n)) (fma.f64 k -1/2 1/2))
	0.3b	(/.f64 (pow.f64 (.f64 2 (.f64 (PI.f64) n)) (fma.f64 k -1/2 1/2)) (sqrt.f64 k))
	0.2b	(*.f64 (PI.f64) n)
✓	0.2b	(*.f64 (PI.f64) n)
✓	0.3b	(/.f64 (pow.f64 (.f64 2 (.f64 (PI.f64) n)) (fma.f64 k -1/2 1/2)) (sqrt.f64 k))
✓	0.4b	(pow.f64 (.f64 2 (.f64 (PI.f64) n)) (fma.f64 k -1/2 1/2))

Compiler

Compiled 45 to 26 computations (42.2% saved)

series10.0ms (0.1%)

Counts

3 → 48

Calls

15 calls:

Time	Variable		Point	Expression
1.0ms	k	@	-inf	(/.f64 (pow.f64 (.f64 2 (.f64 (PI.f64) n)) (fma.f64 k -1/2 1/2)) (sqrt.f64 k))
1.0ms	n	@	0	(pow.f64 (.f64 2 (.f64 (PI.f64) n)) (fma.f64 k -1/2 1/2))
1.0ms	k	@	inf	(/.f64 (pow.f64 (.f64 2 (.f64 (PI.f64) n)) (fma.f64 k -1/2 1/2)) (sqrt.f64 k))
1.0ms	k	@	0	(/.f64 (pow.f64 (.f64 2 (.f64 (PI.f64) n)) (fma.f64 k -1/2 1/2)) (sqrt.f64 k))
1.0ms	n	@	-inf	(/.f64 (pow.f64 (.f64 2 (.f64 (PI.f64) n)) (fma.f64 k -1/2 1/2)) (sqrt.f64 k))

rewrite63.0ms (0.7%)

Algorithm

1×	batch-egg-rewrite

Rules

655×	`log-prod_binary64`
377×	`pow-prod-down_binary64`
376×	`pow-unpow_binary64`
340×	`pow2_binary64`
258×	`pow-pow_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	13	40
1	274	40
2	3306	40

Stop Event

1×	node limit

Counts

3 → 87

Calls

Call 1

Inputs
(pow.f64 (.f64 2 (.f64 (PI.f64) n)) (fma.f64 k -1/2 1/2))
(/.f64 (pow.f64 (.f64 2 (.f64 (PI.f64) n)) (fma.f64 k -1/2 1/2)) (sqrt.f64 k))
(*.f64 (PI.f64) n)

Outputs
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((#(struct:change #<rule egg-rr> (2) ((x +.f64 0 (/.f64 (pow.f64 (.f64 n (.f64 2 (PI.f64))) (fma.f64 k -1/2 1/2)) (sqrt.f64 k)))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (log.f64 (pow.f64 (cbrt.f64 (exp.f64 (/.f64 (pow.f64 (.f64 n (.f64 2 (PI.f64))) (fma.f64 k -1/2 1/2)) (sqrt.f64 k)))) 2)) (log.f64 (cbrt.f64 (exp.f64 (/.f64 (pow.f64 (.f64 n (.f64 2 (PI.f64))) (fma.f64 k -1/2 1/2)) (sqrt.f64 k))))))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (log.f64 (sqrt.f64 (exp.f64 (/.f64 (pow.f64 (.f64 n (.f64 2 (PI.f64))) (fma.f64 k -1/2 1/2)) (sqrt.f64 k))))) (log.f64 (sqrt.f64 (exp.f64 (/.f64 (pow.f64 (.f64 n (.f64 2 (PI.f64))) (fma.f64 k -1/2 1/2)) (sqrt.f64 k))))))))) (#(struct:change #<rule egg-rr> (2) ((x -.f64 (exp.f64 (log1p.f64 (/.f64 (pow.f64 (.f64 n (.f64 2 (PI.f64))) (fma.f64 k -1/2 1/2)) (sqrt.f64 k)))) 1)))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (pow.f64 (.f64 n (.f64 2 (PI.f64))) (fma.f64 k -1/2 1/2)) (pow.f64 k -1/2))))) (#(struct:change #<rule egg-rr> (2) ((x 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Outputs

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1) -1)))) (#(struct:change #<rule egg-rr> (2) ((x neg.f64 (/.f64 (pow.f64 (*.f64 n (*.f64 2 (PI.f64))) (fma.f64 k -1/2 1/2)) (neg.f64 (sqrt.f64 k))))))) (#(struct:change #<rule egg-rr> (2) ((x sqrt.f64 (/.f64 (pow.f64 (pow.f64 (*.f64 n (*.f64 2 (PI.f64))) (fma.f64 k -1/2 1/2)) 2) k))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (exp.f64 (/.f64 (pow.f64 (*.f64 n (*.f64 2 (PI.f64))) (fma.f64 k -1/2 1/2)) (sqrt.f64 k))))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (+.f64 1 (expm1.f64 (/.f64 (pow.f64 (*.f64 n (*.f64 2 (PI.f64))) (fma.f64 k -1/2 1/2)) (sqrt.f64 k)))))))) (#(struct:change #<rule egg-rr> (2) ((x cbrt.f64 (pow.f64 (/.f64 (pow.f64 (*.f64 n (*.f64 2 (PI.f64))) (fma.f64 k -1/2 1/2)) (sqrt.f64 k)) 3))))) (#(struct:change #<rule egg-rr> (2) ((x cbrt.f64 (/.f64 (pow.f64 (*.f64 n (*.f64 2 (PI.f64))) (*.f64 (fma.f64 k -1/2 1/2) 3)) (pow.f64 k 3/2)))))) (#(struct:change #<rule egg-rr> (2) ((x expm1.f64 (log1p.f64 (/.f64 (pow.f64 (*.f64 n (*.f64 2 (PI.f64))) (fma.f64 k -1/2 1/2)) (sqrt.f64 k))))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (log.f64 (/.f64 (pow.f64 (*.f64 n (*.f64 2 (PI.f64))) (fma.f64 k -1/2 1/2)) (sqrt.f64 k))))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (*.f64 (log.f64 (/.f64 (pow.f64 (*.f64 n (*.f64 2 (PI.f64))) (fma.f64 k -1/2 1/2)) (sqrt.f64 k))) 1))))) (#(struct:change #<rule egg-rr> (2) ((x log1p.f64 (expm1.f64 (/.f64 (pow.f64 (*.f64 n (*.f64 2 (PI.f64))) (fma.f64 k -1/2 1/2)) (sqrt.f64 k))))))))

((#(struct:change #<rule egg-rr> (2) ((x +.f64 0 (*.f64 (PI.f64) n))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (log.f64 (pow.f64 (cbrt.f64 (pow.f64 (exp.f64 (PI.f64)) n)) 2)) (log.f64 (cbrt.f64 (pow.f64 (exp.f64 (PI.f64)) n))))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (log.f64 (sqrt.f64 (pow.f64 (exp.f64 (PI.f64)) n))) (log.f64 (sqrt.f64 (pow.f64 (exp.f64 (PI.f64)) n))))))) (#(struct:change #<rule egg-rr> (2) ((x -.f64 (exp.f64 (log1p.f64 (*.f64 (PI.f64) n))) 1)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (*.f64 (PI.f64) n) 1)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (pow.f64 (*.f64 (PI.f64) n) 2) 1/2)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (pow.f64 (*.f64 (PI.f64) n) 3) 1/3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (cbrt.f64 (*.f64 (PI.f64) n)) 3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (sqrt.f64 (*.f64 (PI.f64) n)) 2)))) (#(struct:change #<rule egg-rr> (2) ((x sqrt.f64 (pow.f64 (*.f64 (PI.f64) n) 2))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (pow.f64 (exp.f64 (PI.f64)) n))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (+.f64 1 (expm1.f64 (*.f64 (PI.f64) n))))))) (#(struct:change #<rule egg-rr> (2) ((x cbrt.f64 (pow.f64 (*.f64 (PI.f64) n) 3))))) (#(struct:change #<rule egg-rr> (2) ((x expm1.f64 (log1p.f64 (*.f64 (PI.f64) n)))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (log.f64 (*.f64 (PI.f64) n)))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (*.f64 (log.f64 (*.f64 (PI.f64) n)) 1))))) (#(struct:change #<rule egg-rr> (2) ((x log1p.f64 (expm1.f64 (*.f64 (PI.f64) n)))))))

simplify68.0ms (0.7%)

Algorithm

1×	egg-herbie

Rules

684×	`exp-sum_binary64`
402×	`associate-+r+_binary64`
395×	`associate-+l+_binary64`
393×	`associate-r_binary64`
367×	`associate-l_binary64`

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	73	1106
1	203	1024
2	637	901
3	3614	842
4	6894	842

Stop Event

1×	node limit

Counts

135 → 106

Calls

Call 1

Inputs
(exp.f64 (.f64 (+.f64 1/2 (.f64 -1/2 k)) (+.f64 (log.f64 n) (log.f64 (*.f64 2 (PI.f64))))))
(exp.f64 (.f64 (+.f64 1/2 (.f64 -1/2 k)) (+.f64 (log.f64 n) (log.f64 (*.f64 2 (PI.f64))))))
(exp.f64 (.f64 (+.f64 1/2 (.f64 -1/2 k)) (+.f64 (log.f64 n) (log.f64 (*.f64 2 (PI.f64))))))
(exp.f64 (.f64 (+.f64 1/2 (.f64 -1/2 k)) (+.f64 (log.f64 n) (log.f64 (*.f64 2 (PI.f64))))))
(exp.f64 (.f64 (+.f64 1/2 (.f64 -1/2 k)) (+.f64 (.f64 -1 (log.f64 (/.f64 1 n))) (log.f64 (.f64 2 (PI.f64))))))
(exp.f64 (.f64 (+.f64 1/2 (.f64 -1/2 k)) (+.f64 (.f64 -1 (log.f64 (/.f64 1 n))) (log.f64 (.f64 2 (PI.f64))))))
(exp.f64 (.f64 (+.f64 1/2 (.f64 -1/2 k)) (+.f64 (.f64 -1 (log.f64 (/.f64 1 n))) (log.f64 (.f64 2 (PI.f64))))))
(exp.f64 (.f64 (+.f64 1/2 (.f64 -1/2 k)) (+.f64 (.f64 -1 (log.f64 (/.f64 1 n))) (log.f64 (.f64 2 (PI.f64))))))
(exp.f64 (.f64 (+.f64 1/2 (.f64 -1/2 k)) (+.f64 (.f64 -1 (log.f64 (/.f64 -1 n))) (log.f64 (.f64 -2 (PI.f64))))))
(exp.f64 (.f64 (+.f64 1/2 (.f64 -1/2 k)) (+.f64 (.f64 -1 (log.f64 (/.f64 -1 n))) (log.f64 (.f64 -2 (PI.f64))))))
(exp.f64 (.f64 (+.f64 1/2 (.f64 -1/2 k)) (+.f64 (.f64 -1 (log.f64 (/.f64 -1 n))) (log.f64 (.f64 -2 (PI.f64))))))
(exp.f64 (.f64 (+.f64 1/2 (.f64 -1/2 k)) (+.f64 (.f64 -1 (log.f64 (/.f64 -1 n))) (log.f64 (.f64 -2 (PI.f64))))))
(.f64 (sqrt.f64 2) (sqrt.f64 (.f64 n (PI.f64))))
(+.f64 (.f64 -1/2 (.f64 (.f64 (sqrt.f64 2) (.f64 k (log.f64 (.f64 2 (.f64 n (PI.f64)))))) (sqrt.f64 (.f64 n (PI.f64))))) (.f64 (sqrt.f64 2) (sqrt.f64 (*.f64 n (PI.f64)))))
(+.f64 (.f64 -1/2 (.f64 (.f64 (sqrt.f64 2) (.f64 k (log.f64 (.f64 2 (.f64 n (PI.f64)))))) (sqrt.f64 (.f64 n (PI.f64))))) (+.f64 (.f64 (sqrt.f64 2) (sqrt.f64 (.f64 n (PI.f64)))) (.f64 1/8 (.f64 (.f64 (sqrt.f64 2) (.f64 (pow.f64 k 2) (pow.f64 (log.f64 (.f64 2 (.f64 n (PI.f64)))) 2))) (sqrt.f64 (.f64 n (PI.f64)))))))
(+.f64 (.f64 -1/2 (.f64 (.f64 (sqrt.f64 2) (.f64 k (log.f64 (.f64 2 (.f64 n (PI.f64)))))) (sqrt.f64 (.f64 n (PI.f64))))) (+.f64 (.f64 (sqrt.f64 2) (sqrt.f64 (.f64 n (PI.f64)))) (+.f64 (.f64 1/8 (.f64 (.f64 (sqrt.f64 2) (.f64 (pow.f64 k 2) (pow.f64 (log.f64 (.f64 2 (.f64 n (PI.f64)))) 2))) (sqrt.f64 (.f64 n (PI.f64))))) (.f64 -1/48 (.f64 (.f64 (sqrt.f64 2) (.f64 (pow.f64 k 3) (pow.f64 (log.f64 (.f64 2 (.f64 n (PI.f64)))) 3))) (sqrt.f64 (*.f64 n (PI.f64))))))))
(pow.f64 (.f64 2 (.f64 n (PI.f64))) (fma.f64 k -1/2 1/2))
(pow.f64 (.f64 2 (.f64 n (PI.f64))) (fma.f64 k -1/2 1/2))
(pow.f64 (.f64 2 (.f64 n (PI.f64))) (fma.f64 k -1/2 1/2))
(pow.f64 (.f64 2 (.f64 n (PI.f64))) (fma.f64 k -1/2 1/2))
(pow.f64 (.f64 2 (.f64 n (PI.f64))) (fma.f64 k -1/2 1/2))
(pow.f64 (.f64 2 (.f64 n (PI.f64))) (fma.f64 k -1/2 1/2))
(pow.f64 (.f64 2 (.f64 n (PI.f64))) (fma.f64 k -1/2 1/2))
(pow.f64 (.f64 2 (.f64 n (PI.f64))) (fma.f64 k -1/2 1/2))
(.f64 (exp.f64 (.f64 (+.f64 1/2 (.f64 -1/2 k)) (+.f64 (log.f64 (.f64 2 (PI.f64))) (log.f64 n)))) (sqrt.f64 (/.f64 1 k)))
(.f64 (exp.f64 (.f64 (+.f64 1/2 (.f64 -1/2 k)) (+.f64 (log.f64 (.f64 2 (PI.f64))) (log.f64 n)))) (sqrt.f64 (/.f64 1 k)))
(.f64 (exp.f64 (.f64 (+.f64 1/2 (.f64 -1/2 k)) (+.f64 (log.f64 (.f64 2 (PI.f64))) (log.f64 n)))) (sqrt.f64 (/.f64 1 k)))
(.f64 (exp.f64 (.f64 (+.f64 1/2 (.f64 -1/2 k)) (+.f64 (log.f64 (.f64 2 (PI.f64))) (log.f64 n)))) (sqrt.f64 (/.f64 1 k)))
(.f64 (sqrt.f64 (/.f64 1 k)) (exp.f64 (.f64 (+.f64 1/2 (.f64 -1/2 k)) (+.f64 (.f64 -1 (log.f64 (/.f64 1 n))) (log.f64 (*.f64 2 (PI.f64)))))))
(.f64 (sqrt.f64 (/.f64 1 k)) (exp.f64 (.f64 (+.f64 1/2 (.f64 -1/2 k)) (+.f64 (.f64 -1 (log.f64 (/.f64 1 n))) (log.f64 (*.f64 2 (PI.f64)))))))
(.f64 (sqrt.f64 (/.f64 1 k)) (exp.f64 (.f64 (+.f64 1/2 (.f64 -1/2 k)) (+.f64 (.f64 -1 (log.f64 (/.f64 1 n))) (log.f64 (*.f64 2 (PI.f64)))))))
(.f64 (sqrt.f64 (/.f64 1 k)) (exp.f64 (.f64 (+.f64 1/2 (.f64 -1/2 k)) (+.f64 (.f64 -1 (log.f64 (/.f64 1 n))) (log.f64 (*.f64 2 (PI.f64)))))))
(.f64 (sqrt.f64 (/.f64 1 k)) (exp.f64 (.f64 (+.f64 1/2 (.f64 -1/2 k)) (+.f64 (.f64 -1 (log.f64 (/.f64 -1 n))) (log.f64 (*.f64 -2 (PI.f64)))))))
(.f64 (sqrt.f64 (/.f64 1 k)) (exp.f64 (.f64 (+.f64 1/2 (.f64 -1/2 k)) (+.f64 (.f64 -1 (log.f64 (/.f64 -1 n))) (log.f64 (*.f64 -2 (PI.f64)))))))
(.f64 (sqrt.f64 (/.f64 1 k)) (exp.f64 (.f64 (+.f64 1/2 (.f64 -1/2 k)) (+.f64 (.f64 -1 (log.f64 (/.f64 -1 n))) (log.f64 (*.f64 -2 (PI.f64)))))))
(.f64 (sqrt.f64 (/.f64 1 k)) (exp.f64 (.f64 (+.f64 1/2 (.f64 -1/2 k)) (+.f64 (.f64 -1 (log.f64 (/.f64 -1 n))) (log.f64 (*.f64 -2 (PI.f64)))))))
(*.f64 n (PI.f64))
(*.f64 n (PI.f64))
(*.f64 n (PI.f64))
(*.f64 n (PI.f64))
(*.f64 n (PI.f64))
(*.f64 n (PI.f64))
(*.f64 n (PI.f64))
(*.f64 n (PI.f64))
(*.f64 n (PI.f64))
(*.f64 n (PI.f64))
(*.f64 n (PI.f64))
(*.f64 n (PI.f64))

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

eval109.0ms (1.2%)

Compiler: Compiled 4845 to 3298 computations (31.9% saved)

prune63.0ms (0.7%)

Pruning

24 alts after pruning (22 fresh and 2 done)

	Pruned	Kept	Total
New	213	22	235
Fresh	0	0	0
Picked	0	1	1
Done	0	1	1
Total	213	24	237

Error

0.0b

Counts

237 → 24

Alt Table

Click to see full alt table

Status	Error	Program
	0.5b	(.f64 (sqrt.f64 (/.f64 1 k)) (pow.f64 (.f64 (*.f64 2 (PI.f64)) n) (/.f64 (-.f64 1 k) 2)))
	10.4b	(pow.f64 (cbrt.f64 (sqrt.f64 (/.f64 (pow.f64 (.f64 2 (.f64 (PI.f64) n)) (-.f64 1 k)) k))) 3)
✓	0.5b	(/.f64 (pow.f64 (.f64 2 (.f64 (PI.f64) n)) (fma.f64 k -1/2 1/2)) (sqrt.f64 k))
	19.1b	(pow.f64 (pow.f64 (sqrt.f64 (/.f64 (pow.f64 (.f64 2 (.f64 (PI.f64) n)) (-.f64 1 k)) k)) 3) 1/3)
	0.5b	(.f64 (pow.f64 k -1/2) (pow.f64 (.f64 (*.f64 2 (PI.f64)) n) (/.f64 (-.f64 1 k) 2)))
	23.5b	(/.f64 (.f64 (sqrt.f64 (.f64 n (PI.f64))) (fma.f64 (.f64 (.f64 -1/2 k) (sqrt.f64 2)) (log.f64 (.f64 2 (.f64 n (PI.f64)))) (sqrt.f64 2))) (sqrt.f64 k))
	0.8b	(.f64 (.f64 (/.f64 1 (cbrt.f64 k)) (cbrt.f64 (pow.f64 k -1/2))) (pow.f64 (.f64 (.f64 2 (PI.f64)) n) (/.f64 (-.f64 1 k) 2)))
✓	0.6b	(.f64 (/.f64 1 (sqrt.f64 k)) (pow.f64 (.f64 (*.f64 2 (PI.f64)) n) (/.f64 (-.f64 1 k) 2)))
	0.6b	(.f64 (pow.f64 k -1/4) (/.f64 (pow.f64 (.f64 n (*.f64 2 (PI.f64))) (fma.f64 k -1/2 1/2)) (pow.f64 k 1/4)))
	24.1b	(/.f64 (.f64 (sqrt.f64 2) (sqrt.f64 (.f64 n (PI.f64)))) (sqrt.f64 k))
▶	9.9b	(sqrt.f64 (/.f64 (pow.f64 (.f64 2 (.f64 (PI.f64) n)) (-.f64 1 k)) k))
	3.2b	(.f64 (exp.f64 (.f64 -1/2 (log.f64 k))) (pow.f64 (.f64 (.f64 2 (PI.f64)) n) (/.f64 (-.f64 1 k) 2)))
	24.0b	(.f64 (/.f64 1 (sqrt.f64 k)) (.f64 (sqrt.f64 2) (sqrt.f64 (*.f64 n (PI.f64)))))
	0.7b	(/.f64 (pow.f64 (*.f64 2 (PI.f64)) (-.f64 1/2 (/.f64 k 2))) (/.f64 (sqrt.f64 k) (pow.f64 n (-.f64 1/2 (/.f64 k 2)))))
	3.2b	(.f64 (expm1.f64 (log1p.f64 (pow.f64 k -1/2))) (pow.f64 (.f64 (*.f64 2 (PI.f64)) n) (/.f64 (-.f64 1 k) 2)))
	0.3b	(.f64 (/.f64 1 (sqrt.f64 k)) (/.f64 (sqrt.f64 (.f64 2 (.f64 (PI.f64) n))) (pow.f64 (.f64 2 (*.f64 (PI.f64) n)) (/.f64 k 2))))
	0.5b	(.f64 (sqrt.f64 (/.f64 1 k)) (sqrt.f64 (pow.f64 (.f64 n (*.f64 2 (PI.f64))) (-.f64 1 k))))
	3.2b	(/.f64 (exp.f64 (.f64 (+.f64 1/2 (.f64 -1/2 k)) (+.f64 (log.f64 n) (log.f64 (*.f64 2 (PI.f64)))))) (sqrt.f64 k))
▶	11.7b	(exp.f64 (log.f64 (sqrt.f64 (/.f64 (pow.f64 (.f64 2 (.f64 (PI.f64) n)) (-.f64 1 k)) k))))
▶	0.3b	(/.f64 (.f64 (sqrt.f64 (.f64 n (.f64 2 (PI.f64)))) (pow.f64 (.f64 n (.f64 2 (PI.f64))) (.f64 k -1/2))) (sqrt.f64 k))
	3.1b	(.f64 (/.f64 1 (sqrt.f64 k)) (exp.f64 (.f64 1/2 (.f64 (-.f64 1 k) (log.f64 (.f64 2 (*.f64 n (PI.f64))))))))
	3.1b	(.f64 (/.f64 1 (sqrt.f64 k)) (pow.f64 (exp.f64 (log.f64 (.f64 2 (*.f64 (PI.f64) n)))) (/.f64 (-.f64 1 k) 2)))
▶	13.1b	(.f64 (cbrt.f64 (pow.f64 (pow.f64 k -1/2) 3)) (pow.f64 (.f64 (*.f64 2 (PI.f64)) n) (/.f64 (-.f64 1 k) 2)))
▶	0.6b	(/.f64 1 (/.f64 (sqrt.f64 k) (sqrt.f64 (pow.f64 (.f64 2 (.f64 (PI.f64) n)) (-.f64 1 k)))))

Compiler

Compiled 855 to 699 computations (18.2% saved)

localize31.0ms (0.3%)

Local error

Found 8 expressions with local error:

New	Error	Program
	0.3b	(/.f64 (.f64 (sqrt.f64 (.f64 n (.f64 2 (PI.f64)))) (pow.f64 (.f64 n (.f64 2 (PI.f64))) (.f64 k -1/2))) (sqrt.f64 k))
	0.2b	(.f64 n (.f64 2 (PI.f64)))
	0.1b	(sqrt.f64 (.f64 n (.f64 2 (PI.f64))))
	0.0b	(.f64 (sqrt.f64 (.f64 n (.f64 2 (PI.f64)))) (pow.f64 (.f64 n (.f64 2 (PI.f64))) (.f64 k -1/2)))
✓	0.0b	(.f64 (sqrt.f64 (.f64 n (.f64 2 (PI.f64)))) (pow.f64 (.f64 n (.f64 2 (PI.f64))) (.f64 k -1/2)))
✓	0.1b	(sqrt.f64 (.f64 n (.f64 2 (PI.f64))))
✓	0.2b	(.f64 n (.f64 2 (PI.f64)))
✓	0.3b	(/.f64 (.f64 (sqrt.f64 (.f64 n (.f64 2 (PI.f64)))) (pow.f64 (.f64 n (.f64 2 (PI.f64))) (.f64 k -1/2))) (sqrt.f64 k))

Compiler

Compiled 70 to 46 computations (34.3% saved)

series25.0ms (0.3%)

Counts

4 → 24

Calls

18 calls:

Time	Variable		Point	Expression
5.0ms	k	@	0	(/.f64 (.f64 (sqrt.f64 (.f64 n (.f64 2 (PI.f64)))) (pow.f64 (.f64 n (.f64 2 (PI.f64))) (.f64 k -1/2))) (sqrt.f64 k))
3.0ms	n	@	0	(/.f64 (.f64 (sqrt.f64 (.f64 n (.f64 2 (PI.f64)))) (pow.f64 (.f64 n (.f64 2 (PI.f64))) (.f64 k -1/2))) (sqrt.f64 k))
2.0ms	k	@	inf	(.f64 (sqrt.f64 (.f64 n (.f64 2 (PI.f64)))) (pow.f64 (.f64 n (.f64 2 (PI.f64))) (.f64 k -1/2)))
2.0ms	n	@	inf	(/.f64 (.f64 (sqrt.f64 (.f64 n (.f64 2 (PI.f64)))) (pow.f64 (.f64 n (.f64 2 (PI.f64))) (.f64 k -1/2))) (sqrt.f64 k))
2.0ms	k	@	-inf	(/.f64 (.f64 (sqrt.f64 (.f64 n (.f64 2 (PI.f64)))) (pow.f64 (.f64 n (.f64 2 (PI.f64))) (.f64 k -1/2))) (sqrt.f64 k))

rewrite85.0ms (0.9%)

Algorithm

1×	batch-egg-rewrite

Rules

808×	`log-prod_binary64`
699×	`pow-unpow_binary64`
378×	`pow2_binary64`
260×	`pow1/3_binary64`
256×	`expm1-udef_binary64`

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	14	75
1	298	57
2	3808	53

Stop Event

1×	node limit

Counts

4 → 121

Calls

Call 1

Inputs
(/.f64 (.f64 (sqrt.f64 (.f64 n (.f64 2 (PI.f64)))) (pow.f64 (.f64 n (.f64 2 (PI.f64))) (.f64 k -1/2))) (sqrt.f64 k))
(.f64 n (.f64 2 (PI.f64)))
(sqrt.f64 (.f64 n (.f64 2 (PI.f64))))
(.f64 (sqrt.f64 (.f64 n (.f64 2 (PI.f64)))) (pow.f64 (.f64 n (.f64 2 (PI.f64))) (.f64 k -1/2)))

Outputs
((#(struct:change #<rule egg-rr> (2) ((x +.f64 0 (/.f64 (pow.f64 (.f64 (PI.f64) (.f64 n 2)) (fma.f64 k -1/2 1/2)) (sqrt.f64 k)))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (log.f64 (pow.f64 (cbrt.f64 (exp.f64 (/.f64 (pow.f64 (.f64 (PI.f64) (.f64 n 2)) (fma.f64 k -1/2 1/2)) (sqrt.f64 k)))) 2)) (log.f64 (cbrt.f64 (exp.f64 (/.f64 (pow.f64 (.f64 (PI.f64) (.f64 n 2)) (fma.f64 k -1/2 1/2)) (sqrt.f64 k))))))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (log.f64 (sqrt.f64 (exp.f64 (/.f64 (pow.f64 (.f64 (PI.f64) (.f64 n 2)) (fma.f64 k -1/2 1/2)) (sqrt.f64 k))))) (log.f64 (sqrt.f64 (exp.f64 (/.f64 (pow.f64 (.f64 (PI.f64) (.f64 n 2)) (fma.f64 k -1/2 1/2)) (sqrt.f64 k))))))))) (#(struct:change #<rule egg-rr> (2) ((x -.f64 (exp.f64 (log1p.f64 (/.f64 (pow.f64 (.f64 (PI.f64) (.f64 n 2)) (fma.f64 k -1/2 1/2)) (sqrt.f64 k)))) 1)))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (sqrt.f64 (.f64 (PI.f64) (.f64 n 2))) (/.f64 1 (/.f64 (sqrt.f64 k) (pow.f64 (.f64 (PI.f64) (.f64 n 2)) (.f64 k -1/2)))))))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (sqrt.f64 (.f64 (PI.f64) (.f64 n 2))) (.f64 (pow.f64 (.f64 (PI.f64) (.f64 n 2)) (.f64 k -1/2)) (pow.f64 k -1/2)))))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (pow.f64 (.f64 (PI.f64) (.f64 n 2)) (.f64 k -1/2)) (.f64 (sqrt.f64 (.f64 (PI.f64) (.f64 n 2))) (pow.f64 k -1/2)))))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (pow.f64 (.f64 (PI.f64) (.f64 n 2)) (fma.f64 k -1/2 1/2)) (pow.f64 k -1/2))))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (/.f64 (pow.f64 (.f64 (PI.f64) (.f64 n 2)) (fma.f64 k -1/2 1/2)) (sqrt.f64 k)) 1)))) (#(struct:change #<rule egg-rr> (2) ((x .f64 1 (/.f64 (pow.f64 (.f64 (PI.f64) (.f64 n 2)) (fma.f64 k -1/2 1/2)) (sqrt.f64 k)))))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (cbrt.f64 (/.f64 (pow.f64 (.f64 (PI.f64) (.f64 n 2)) (fma.f64 k -1/2 1/2)) (sqrt.f64 k))) (cbrt.f64 (/.f64 (pow.f64 (pow.f64 (.f64 (PI.f64) (.f64 n 2)) (fma.f64 k -1/2 1/2)) 2) k)))))) (#(struct:change #<rule egg-rr> (2) ((x .f64 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(#(struct:change #<rule egg-rr> (2) ((x .f64 (pow.f64 k -1/2) (pow.f64 (.f64 (PI.f64) (.f64 n 2)) (fma.f64 k -1/2 1/2)))))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (/.f64 (sqrt.f64 (.f64 (PI.f64) (.f64 n 2))) 1) (/.f64 (pow.f64 (.f64 (PI.f64) (.f64 n 2)) (.f64 k -1/2)) (sqrt.f64 k)))))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (/.f64 (pow.f64 (.f64 (PI.f64) (.f64 n 2)) (.f64 k -1/2)) 1) (/.f64 (sqrt.f64 (.f64 (PI.f64) (.f64 n 2))) (sqrt.f64 k)))))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (/.f64 (sqrt.f64 (.f64 (PI.f64) (.f64 n 2))) (sqrt.f64 k)) (pow.f64 (.f64 (PI.f64) (.f64 n 2)) (.f64 k -1/2)))))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (/.f64 (pow.f64 (cbrt.f64 (pow.f64 (.f64 (PI.f64) (.f64 n 2)) (fma.f64 k -1/2 1/2))) 2) 1) (/.f64 (cbrt.f64 (pow.f64 (.f64 (PI.f64) (.f64 n 2)) (fma.f64 k -1/2 1/2))) (sqrt.f64 k)))))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (/.f64 (sqrt.f64 (pow.f64 (.f64 (PI.f64) (.f64 n 2)) (fma.f64 k -1/2 1/2))) 1) (/.f64 (sqrt.f64 (pow.f64 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(sqrt.f64 k))))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (log.f64 (/.f64 (pow.f64 (.f64 (PI.f64) (.f64 n 2)) (fma.f64 k -1/2 1/2)) (sqrt.f64 k))))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (.f64 (log.f64 (/.f64 (pow.f64 (.f64 (PI.f64) (.f64 n 2)) (fma.f64 k -1/2 1/2)) (sqrt.f64 k))) 1))))) (#(struct:change #<rule egg-rr> (2) ((x log1p.f64 (expm1.f64 (/.f64 (pow.f64 (.f64 (PI.f64) (.f64 n 2)) (fma.f64 k -1/2 1/2)) (sqrt.f64 k))))))))
((#(struct:change #<rule egg-rr> (2) ((x +.f64 0 (.f64 (PI.f64) (.f64 n 2)))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (log.f64 (pow.f64 (cbrt.f64 (pow.f64 (pow.f64 (exp.f64 2) (PI.f64)) n)) 2)) (log.f64 (cbrt.f64 (pow.f64 (pow.f64 (exp.f64 2) (PI.f64)) n))))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (log.f64 (sqrt.f64 (pow.f64 (pow.f64 (exp.f64 2) (PI.f64)) n))) (log.f64 (sqrt.f64 (pow.f64 (pow.f64 (exp.f64 2) (PI.f64)) n))))))) (#(struct:change #<rule egg-rr> (2) ((x -.f64 (exp.f64 (log1p.f64 (.f64 (PI.f64) (.f64 n 2)))) 1)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (.f64 (PI.f64) (.f64 n 2)) 1)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (sqrt.f64 (.f64 (PI.f64) (.f64 n 2))) 2)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (pow.f64 (.f64 (PI.f64) (.f64 n 2)) 2) 1/2)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (pow.f64 (.f64 (PI.f64) (.f64 n 2)) 3) 1/3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (cbrt.f64 (.f64 (PI.f64) (.f64 n 2))) 3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (.f64 (pow.f64 n 3) (pow.f64 (.f64 2 (PI.f64)) 3)) 1/3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (.f64 (pow.f64 (.f64 2 (PI.f64)) 3) (pow.f64 n 3)) 1/3)))) (#(struct:change #<rule egg-rr> (2) ((x sqrt.f64 (pow.f64 (.f64 (PI.f64) (.f64 n 2)) 2))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (pow.f64 (pow.f64 (exp.f64 2) (PI.f64)) n))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (+.f64 1 (expm1.f64 (.f64 (PI.f64) (.f64 n 2)))))))) (#(struct:change #<rule egg-rr> (2) ((x cbrt.f64 (pow.f64 (.f64 (PI.f64) (.f64 n 2)) 3))))) (#(struct:change #<rule egg-rr> (2) ((x cbrt.f64 (.f64 (pow.f64 n 3) (pow.f64 (.f64 2 (PI.f64)) 3)))))) (#(struct:change #<rule egg-rr> (2) ((x cbrt.f64 (.f64 (pow.f64 (.f64 2 (PI.f64)) 3) (pow.f64 n 3)))))) (#(struct:change #<rule egg-rr> (2) ((x expm1.f64 (log1p.f64 (.f64 (PI.f64) (.f64 n 2))))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (log.f64 (.f64 (PI.f64) (.f64 n 2))))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (.f64 (log.f64 (.f64 (PI.f64) (.f64 n 2))) 1))))) (#(struct:change #<rule egg-rr> (2) ((x log1p.f64 (expm1.f64 (.f64 (PI.f64) (*.f64 n 2))))))))
((#(struct:change #<rule egg-rr> (2) ((x +.f64 0 (sqrt.f64 (.f64 (PI.f64) (.f64 n 2))))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (log.f64 (pow.f64 (cbrt.f64 (exp.f64 (sqrt.f64 (.f64 (PI.f64) (.f64 n 2))))) 2)) (log.f64 (cbrt.f64 (exp.f64 (sqrt.f64 (.f64 (PI.f64) (.f64 n 2)))))))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (log.f64 (sqrt.f64 (exp.f64 (sqrt.f64 (.f64 (PI.f64) (.f64 n 2)))))) (log.f64 (sqrt.f64 (exp.f64 (sqrt.f64 (.f64 (PI.f64) (.f64 n 2)))))))))) (#(struct:change #<rule egg-rr> (2) ((x -.f64 (exp.f64 (log1p.f64 (sqrt.f64 (.f64 (PI.f64) (.f64 n 2))))) 1)))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (sqrt.f64 (.f64 (PI.f64) (.f64 n 2))) 1)))) (#(struct:change #<rule egg-rr> (2) ((x .f64 1 (sqrt.f64 (.f64 (PI.f64) (.f64 n 2))))))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (cbrt.f64 (.f64 (PI.f64) (.f64 n 2))) (cbrt.f64 (sqrt.f64 (.f64 (PI.f64) (.f64 n 2)))))))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (cbrt.f64 (sqrt.f64 (.f64 (PI.f64) (.f64 n 2)))) (cbrt.f64 (.f64 (PI.f64) (.f64 n 2))))))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (sqrt.f64 (.f64 2 (PI.f64))) (sqrt.f64 n))))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (sqrt.f64 n) (sqrt.f64 (.f64 2 (PI.f64))))))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (pow.f64 (.f64 (PI.f64) (.f64 n 2)) 1/4) (pow.f64 (.f64 (PI.f64) (.f64 n 2)) 1/4))))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (sqrt.f64 (pow.f64 (cbrt.f64 (.f64 (PI.f64) (.f64 n 2))) 2)) (sqrt.f64 (cbrt.f64 (.f64 (PI.f64) (.f64 n 2)))))))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (sqrt.f64 (.f64 n 2)) (sqrt.f64 (PI.f64)))))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (pow.f64 1 1/2) (sqrt.f64 (.f64 (PI.f64) (.f64 n 2))))))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (.f64 (PI.f64) (.f64 n 2)) 1/2)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (sqrt.f64 (.f64 (PI.f64) (.f64 n 2))) 1)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (pow.f64 (.f64 (PI.f64) (.f64 n 2)) 3/2) 1/3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (cbrt.f64 (sqrt.f64 (.f64 (PI.f64) (.f64 n 2)))) 3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (pow.f64 (.f64 (PI.f64) (.f64 n 2)) 1/4) 2)))) (#(struct:change #<rule egg-rr> (2) ((x fabs.f64 (sqrt.f64 (.f64 (PI.f64) (.f64 n 2))))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (exp.f64 (sqrt.f64 (.f64 (PI.f64) (.f64 n 2)))))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (+.f64 1 (expm1.f64 (sqrt.f64 (.f64 (PI.f64) (.f64 n 2))))))))) (#(struct:change #<rule egg-rr> (2) ((x cbrt.f64 (pow.f64 (.f64 (PI.f64) (.f64 n 2)) 3/2))))) (#(struct:change #<rule egg-rr> (2) ((x expm1.f64 (log1p.f64 (sqrt.f64 (.f64 (PI.f64) (.f64 n 2)))))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (log.f64 (sqrt.f64 (.f64 (PI.f64) (.f64 n 2)))))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (.f64 (log.f64 (.f64 (PI.f64) (.f64 n 2))) 1/2))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (.f64 (log.f64 (sqrt.f64 (.f64 (PI.f64) (.f64 n 2)))) 1))))) (#(struct:change #<rule egg-rr> (2) ((x log1p.f64 (expm1.f64 (sqrt.f64 (.f64 (PI.f64) (*.f64 n 2)))))))))
((#(struct:change #<rule egg-rr> (2) ((x +.f64 0 (pow.f64 (.f64 (PI.f64) (.f64 n 2)) (fma.f64 k -1/2 1/2)))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (log.f64 (pow.f64 (cbrt.f64 (exp.f64 (pow.f64 (.f64 (PI.f64) (.f64 n 2)) (fma.f64 k -1/2 1/2)))) 2)) (log.f64 (cbrt.f64 (exp.f64 (pow.f64 (.f64 (PI.f64) (.f64 n 2)) (fma.f64 k -1/2 1/2))))))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (log.f64 (sqrt.f64 (exp.f64 (pow.f64 (.f64 (PI.f64) (.f64 n 2)) (fma.f64 k -1/2 1/2))))) (log.f64 (sqrt.f64 (exp.f64 (pow.f64 (.f64 (PI.f64) (.f64 n 2)) (fma.f64 k -1/2 1/2))))))))) (#(struct:change #<rule egg-rr> (2) ((x -.f64 (exp.f64 (log1p.f64 (pow.f64 (.f64 (PI.f64) (.f64 n 2)) (fma.f64 k -1/2 1/2)))) 1)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (.f64 (PI.f64) (.f64 n 2)) (+.f64 1/2 (.f64 k -1/2)))))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (.f64 (PI.f64) (.f64 n 2)) (fma.f64 k -1/2 1/2))))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (pow.f64 (.f64 (PI.f64) (.f64 n 2)) (fma.f64 k -1/2 1/2)) 1)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (pow.f64 (pow.f64 (.f64 (PI.f64) (.f64 n 2)) (fma.f64 k -1/2 1/2)) 2) 1/2)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (pow.f64 (pow.f64 (.f64 (PI.f64) (.f64 n 2)) (fma.f64 k -1/2 1/2)) 3) 1/3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (cbrt.f64 (pow.f64 (.f64 (PI.f64) (.f64 n 2)) (fma.f64 k -1/2 1/2))) 3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (sqrt.f64 (pow.f64 (.f64 (PI.f64) (.f64 n 2)) (fma.f64 k -1/2 1/2))) 2)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (.f64 (pow.f64 (.f64 (PI.f64) (.f64 n 2)) 3/2) (pow.f64 (pow.f64 (.f64 (PI.f64) (.f64 n 2)) (.f64 k -1/2)) 3)) 1/3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (.f64 (pow.f64 (pow.f64 (.f64 (PI.f64) (.f64 n 2)) (.f64 k -1/2)) 3) (pow.f64 (.f64 (PI.f64) (.f64 n 2)) 3/2)) 1/3)))) (#(struct:change #<rule egg-rr> (2) ((x sqrt.f64 (pow.f64 (pow.f64 (.f64 (PI.f64) (.f64 n 2)) (fma.f64 k -1/2 1/2)) 2))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (exp.f64 (pow.f64 (.f64 (PI.f64) (.f64 n 2)) (fma.f64 k -1/2 1/2))))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (+.f64 1 (expm1.f64 (pow.f64 (.f64 (PI.f64) (.f64 n 2)) (fma.f64 k -1/2 1/2)))))))) (#(struct:change #<rule egg-rr> (2) ((x cbrt.f64 (pow.f64 (pow.f64 (.f64 (PI.f64) (.f64 n 2)) (fma.f64 k -1/2 1/2)) 3))))) (#(struct:change #<rule egg-rr> (2) ((x cbrt.f64 (.f64 (pow.f64 (.f64 (PI.f64) (.f64 n 2)) 3/2) (pow.f64 (pow.f64 (.f64 (PI.f64) (.f64 n 2)) (.f64 k -1/2)) 3)))))) (#(struct:change #<rule egg-rr> (2) ((x cbrt.f64 (.f64 (pow.f64 (pow.f64 (.f64 (PI.f64) (.f64 n 2)) (.f64 k -1/2)) 3) (pow.f64 (.f64 (PI.f64) (.f64 n 2)) 3/2)))))) (#(struct:change #<rule egg-rr> (2) ((x expm1.f64 (log1p.f64 (pow.f64 (.f64 (PI.f64) (.f64 n 2)) (fma.f64 k -1/2 1/2))))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (.f64 (fma.f64 k -1/2 1/2) (log.f64 (.f64 (PI.f64) (.f64 n 2)))))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (.f64 (.f64 (fma.f64 k -1/2 1/2) (log.f64 (.f64 (PI.f64) (.f64 n 2)))) 1))))) (#(struct:change #<rule egg-rr> (2) ((x log1p.f64 (expm1.f64 (pow.f64 (.f64 (PI.f64) (.f64 n 2)) (fma.f64 k -1/2 1/2))))))))

simplify78.0ms (0.8%)

Algorithm

1×	egg-herbie

Rules

660×	`distribute-lft-out_binary64`
550×	`+-commutative_binary64`
377×	`sqr-pow_binary64`
366×	`associate-r_binary64`
354×	`associate-l_binary64`

Iterations

Useful iterations: 4 (0.0ms)

Iter	Nodes	Cost
0	41	598
1	122	572
2	409	513
3	2665	502
4	4203	495
5	5799	495
6	7247	495

Stop Event

1×	node limit

Counts

145 → 132

Calls

Call 1

Inputs
(.f64 2 (.f64 n (PI.f64)))
(.f64 2 (.f64 n (PI.f64)))
(.f64 2 (.f64 n (PI.f64)))
(.f64 2 (.f64 n (PI.f64)))
(.f64 2 (.f64 n (PI.f64)))
(.f64 2 (.f64 n (PI.f64)))
(.f64 2 (.f64 n (PI.f64)))
(.f64 2 (.f64 n (PI.f64)))
(.f64 2 (.f64 n (PI.f64)))
(.f64 2 (.f64 n (PI.f64)))
(.f64 2 (.f64 n (PI.f64)))
(.f64 2 (.f64 n (PI.f64)))
(.f64 (sqrt.f64 2) (sqrt.f64 (.f64 n (PI.f64))))
(+.f64 (.f64 -1/2 (.f64 (.f64 (sqrt.f64 2) (.f64 k (log.f64 (.f64 2 (.f64 n (PI.f64)))))) (sqrt.f64 (.f64 n (PI.f64))))) (.f64 (sqrt.f64 2) (sqrt.f64 (*.f64 n (PI.f64)))))
(+.f64 (.f64 -1/2 (.f64 (.f64 (sqrt.f64 2) (.f64 k (log.f64 (.f64 2 (.f64 n (PI.f64)))))) (sqrt.f64 (.f64 n (PI.f64))))) (+.f64 (.f64 (sqrt.f64 2) (sqrt.f64 (.f64 n (PI.f64)))) (.f64 1/8 (.f64 (.f64 (sqrt.f64 2) (.f64 (pow.f64 k 2) (pow.f64 (log.f64 (.f64 2 (.f64 n (PI.f64)))) 2))) (sqrt.f64 (.f64 n (PI.f64)))))))
(+.f64 (.f64 -1/2 (.f64 (.f64 (sqrt.f64 2) (.f64 k (log.f64 (.f64 2 (.f64 n (PI.f64)))))) (sqrt.f64 (.f64 n (PI.f64))))) (+.f64 (.f64 (sqrt.f64 2) (sqrt.f64 (.f64 n (PI.f64)))) (+.f64 (.f64 1/8 (.f64 (.f64 (sqrt.f64 2) (.f64 (pow.f64 k 2) (pow.f64 (log.f64 (.f64 2 (.f64 n (PI.f64)))) 2))) (sqrt.f64 (.f64 n (PI.f64))))) (.f64 -1/48 (.f64 (.f64 (sqrt.f64 2) (.f64 (pow.f64 k 3) (pow.f64 (log.f64 (.f64 2 (.f64 n (PI.f64)))) 3))) (sqrt.f64 (*.f64 n (PI.f64))))))))
(.f64 (.f64 (sqrt.f64 2) (exp.f64 (.f64 -1/2 (.f64 k (log.f64 (.f64 2 (.f64 n (PI.f64)))))))) (sqrt.f64 (*.f64 n (PI.f64))))
(.f64 (.f64 (sqrt.f64 2) (exp.f64 (.f64 -1/2 (.f64 k (log.f64 (.f64 2 (.f64 n (PI.f64)))))))) (sqrt.f64 (*.f64 n (PI.f64))))
(.f64 (.f64 (sqrt.f64 2) (exp.f64 (.f64 -1/2 (.f64 k (log.f64 (.f64 2 (.f64 n (PI.f64)))))))) (sqrt.f64 (*.f64 n (PI.f64))))
(.f64 (.f64 (sqrt.f64 2) (exp.f64 (.f64 -1/2 (.f64 k (log.f64 (.f64 2 (.f64 n (PI.f64)))))))) (sqrt.f64 (*.f64 n (PI.f64))))
(.f64 (.f64 (sqrt.f64 2) (exp.f64 (.f64 -1/2 (.f64 k (log.f64 (.f64 2 (.f64 n (PI.f64)))))))) (sqrt.f64 (*.f64 n (PI.f64))))
(.f64 (.f64 (sqrt.f64 2) (exp.f64 (.f64 -1/2 (.f64 k (log.f64 (.f64 2 (.f64 n (PI.f64)))))))) (sqrt.f64 (*.f64 n (PI.f64))))
(.f64 (.f64 (sqrt.f64 2) (exp.f64 (.f64 -1/2 (.f64 k (log.f64 (.f64 2 (.f64 n (PI.f64)))))))) (sqrt.f64 (*.f64 n (PI.f64))))
(.f64 (.f64 (sqrt.f64 2) (exp.f64 (.f64 -1/2 (.f64 k (log.f64 (.f64 2 (.f64 n (PI.f64)))))))) (sqrt.f64 (*.f64 n (PI.f64))))

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

localize21.0ms (0.2%)

Local error

Found 8 expressions with local error:

New	Error	Program
	9.0b	(sqrt.f64 (/.f64 (pow.f64 (.f64 2 (.f64 (PI.f64) n)) (-.f64 1 k)) k))
	0.4b	(pow.f64 (.f64 2 (.f64 (PI.f64) n)) (-.f64 1 k))
	0.2b	(*.f64 (PI.f64) n)
	0.1b	(/.f64 (pow.f64 (.f64 2 (.f64 (PI.f64) n)) (-.f64 1 k)) k)
✓	0.1b	(/.f64 (pow.f64 (.f64 2 (.f64 (PI.f64) n)) (-.f64 1 k)) k)
	0.2b	(*.f64 (PI.f64) n)
✓	0.4b	(pow.f64 (.f64 2 (.f64 (PI.f64) n)) (-.f64 1 k))
✓	9.0b	(sqrt.f64 (/.f64 (pow.f64 (.f64 2 (.f64 (PI.f64) n)) (-.f64 1 k)) k))

Compiler

Compiled 50 to 28 computations (44% saved)

series16.0ms (0.2%)

Counts

3 → 60

Calls

18 calls:

Time	Variable		Point	Expression
3.0ms	k	@	0	(sqrt.f64 (/.f64 (pow.f64 (.f64 2 (.f64 (PI.f64) n)) (-.f64 1 k)) k))
2.0ms	k	@	-inf	(sqrt.f64 (/.f64 (pow.f64 (.f64 2 (.f64 (PI.f64) n)) (-.f64 1 k)) k))
1.0ms	n	@	-inf	(sqrt.f64 (/.f64 (pow.f64 (.f64 2 (.f64 (PI.f64) n)) (-.f64 1 k)) k))
1.0ms	n	@	0	(sqrt.f64 (/.f64 (pow.f64 (.f64 2 (.f64 (PI.f64) n)) (-.f64 1 k)) k))
1.0ms	k	@	inf	(sqrt.f64 (/.f64 (pow.f64 (.f64 2 (.f64 (PI.f64) n)) (-.f64 1 k)) k))

rewrite70.0ms (0.7%)

Algorithm

1×	batch-egg-rewrite

Rules

656×	`log-prod_binary64`
453×	`pow-unpow_binary64`
332×	`pow2_binary64`
226×	`pow1/3_binary64`
222×	`expm1-udef_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	12	50
1	259	50
2	3381	50

Stop Event

1×	node limit

Counts

3 → 119

Calls

Call 1

Inputs
(sqrt.f64 (/.f64 (pow.f64 (.f64 2 (.f64 (PI.f64) n)) (-.f64 1 k)) k))
(pow.f64 (.f64 2 (.f64 (PI.f64) n)) (-.f64 1 k))
(/.f64 (pow.f64 (.f64 2 (.f64 (PI.f64) n)) (-.f64 1 k)) k)

Outputs

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(*.f64 2 (PI.f64))) (-.f64 1 k)) k)) 1)))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (cbrt.f64 (/.f64 (pow.f64 (*.f64 n (*.f64 2 (PI.f64))) (-.f64 1 k)) k)) (cbrt.f64 (sqrt.f64 (/.f64 (pow.f64 (*.f64 n (*.f64 2 (PI.f64))) (-.f64 1 k)) k))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (cbrt.f64 (sqrt.f64 (/.f64 (pow.f64 (*.f64 n (*.f64 2 (PI.f64))) (-.f64 1 k)) k))) (cbrt.f64 (/.f64 (pow.f64 (*.f64 n (*.f64 2 (PI.f64))) (-.f64 1 k)) k)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (pow.f64 (/.f64 (pow.f64 (*.f64 n (*.f64 2 (PI.f64))) (-.f64 1 k)) k) 1/4) (pow.f64 (/.f64 (pow.f64 (*.f64 n (*.f64 2 (PI.f64))) (-.f64 1 k)) k) 1/4))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (sqrt.f64 (pow.f64 (*.f64 n (*.f64 2 (PI.f64))) (-.f64 1 k))) (sqrt.f64 (/.f64 1 k)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (sqrt.f64 (pow.f64 (*.f64 n (*.f64 2 (PI.f64))) (-.f64 1 k))) (pow.f64 (sqrt.f64 k) -1))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (sqrt.f64 (cbrt.f64 (pow.f64 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(#(struct:change #<rule egg-rr> (2) ((x log.f64 (exp.f64 (sqrt.f64 (/.f64 (pow.f64 (*.f64 n (*.f64 2 (PI.f64))) (-.f64 1 k)) k))))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (+.f64 1 (expm1.f64 (sqrt.f64 (/.f64 (pow.f64 (*.f64 n (*.f64 2 (PI.f64))) (-.f64 1 k)) k)))))))) (#(struct:change #<rule egg-rr> (2) ((x cbrt.f64 (pow.f64 (/.f64 (pow.f64 (*.f64 n (*.f64 2 (PI.f64))) (-.f64 1 k)) k) 3/2))))) (#(struct:change #<rule egg-rr> (2) ((x expm1.f64 (log1p.f64 (sqrt.f64 (/.f64 (pow.f64 (*.f64 n (*.f64 2 (PI.f64))) (-.f64 1 k)) k))))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (log.f64 (sqrt.f64 (/.f64 (pow.f64 (*.f64 n (*.f64 2 (PI.f64))) (-.f64 1 k)) k))))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (*.f64 (log.f64 (/.f64 (pow.f64 (*.f64 n (*.f64 2 (PI.f64))) (-.f64 1 k)) k)) 1/2))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (*.f64 (log.f64 (sqrt.f64 (/.f64 (pow.f64 (*.f64 n (*.f64 2 (PI.f64))) (-.f64 1 k)) k))) 1))))) (#(struct:change #<rule egg-rr> (2) ((x log1p.f64 (expm1.f64 (sqrt.f64 (/.f64 (pow.f64 (*.f64 n (*.f64 2 (PI.f64))) (-.f64 1 k)) k))))))))

((#(struct:change #<rule egg-rr> (2) ((x +.f64 0 (pow.f64 (*.f64 n (*.f64 2 (PI.f64))) (-.f64 1 k)))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (log.f64 (pow.f64 (cbrt.f64 (exp.f64 (pow.f64 (*.f64 n (*.f64 2 (PI.f64))) (-.f64 1 k)))) 2)) (log.f64 (cbrt.f64 (exp.f64 (pow.f64 (*.f64 n (*.f64 2 (PI.f64))) (-.f64 1 k))))))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (log.f64 (sqrt.f64 (exp.f64 (pow.f64 (*.f64 n (*.f64 2 (PI.f64))) (-.f64 1 k))))) (log.f64 (sqrt.f64 (exp.f64 (pow.f64 (*.f64 n (*.f64 2 (PI.f64))) (-.f64 1 k))))))))) (#(struct:change #<rule egg-rr> (2) ((x -.f64 (exp.f64 (log1p.f64 (pow.f64 (*.f64 n (*.f64 2 (PI.f64))) (-.f64 1 k)))) 1)))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (*.f64 n (*.f64 2 (PI.f64))) (pow.f64 (*.f64 n (*.f64 2 (PI.f64))) (neg.f64 k)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (*.f64 n (*.f64 2 (PI.f64))) (pow.f64 (*.f64 n (*.f64 2 (PI.f64))) (*.f64 (neg.f64 k) 1)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 1 (pow.f64 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simplify57.0ms (0.6%)

Algorithm

1×	egg-herbie

Rules

580×	`associate-+l+_binary64`
475×	`associate-l_binary64`
439×	`fma-def_binary64`
400×	`associate-r_binary64`
330×	`distribute-lft-out_binary64`

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	84	1569
1	241	1477
2	774	1289
3	4236	1184

Stop Event

1×	node limit

Counts

179 → 154

Calls

Call 1

Inputs
(sqrt.f64 (/.f64 (exp.f64 (.f64 (-.f64 1 k) (+.f64 (log.f64 n) (log.f64 (.f64 2 (PI.f64)))))) k))
(sqrt.f64 (/.f64 (exp.f64 (.f64 (-.f64 1 k) (+.f64 (log.f64 n) (log.f64 (.f64 2 (PI.f64)))))) k))
(sqrt.f64 (/.f64 (exp.f64 (.f64 (-.f64 1 k) (+.f64 (log.f64 n) (log.f64 (.f64 2 (PI.f64)))))) k))
(sqrt.f64 (/.f64 (exp.f64 (.f64 (-.f64 1 k) (+.f64 (log.f64 n) (log.f64 (.f64 2 (PI.f64)))))) k))
(sqrt.f64 (/.f64 (exp.f64 (.f64 (-.f64 1 k) (+.f64 (.f64 -1 (log.f64 (/.f64 1 n))) (log.f64 (*.f64 2 (PI.f64)))))) k))
(sqrt.f64 (/.f64 (exp.f64 (.f64 (-.f64 1 k) (+.f64 (.f64 -1 (log.f64 (/.f64 1 n))) (log.f64 (*.f64 2 (PI.f64)))))) k))
(sqrt.f64 (/.f64 (exp.f64 (.f64 (-.f64 1 k) (+.f64 (.f64 -1 (log.f64 (/.f64 1 n))) (log.f64 (*.f64 2 (PI.f64)))))) k))
(sqrt.f64 (/.f64 (exp.f64 (.f64 (-.f64 1 k) (+.f64 (.f64 -1 (log.f64 (/.f64 1 n))) (log.f64 (*.f64 2 (PI.f64)))))) k))
(sqrt.f64 (/.f64 (exp.f64 (.f64 (-.f64 1 k) (+.f64 (.f64 -1 (log.f64 (/.f64 -1 n))) (log.f64 (*.f64 -2 (PI.f64)))))) k))
(sqrt.f64 (/.f64 (exp.f64 (.f64 (-.f64 1 k) (+.f64 (.f64 -1 (log.f64 (/.f64 -1 n))) (log.f64 (*.f64 -2 (PI.f64)))))) k))
(sqrt.f64 (/.f64 (exp.f64 (.f64 (-.f64 1 k) (+.f64 (.f64 -1 (log.f64 (/.f64 -1 n))) (log.f64 (*.f64 -2 (PI.f64)))))) k))
(sqrt.f64 (/.f64 (exp.f64 (.f64 (-.f64 1 k) (+.f64 (.f64 -1 (log.f64 (/.f64 -1 n))) (log.f64 (*.f64 -2 (PI.f64)))))) k))
(exp.f64 (.f64 (-.f64 1 k) (+.f64 (log.f64 n) (log.f64 (.f64 2 (PI.f64))))))
(exp.f64 (.f64 (-.f64 1 k) (+.f64 (log.f64 n) (log.f64 (.f64 2 (PI.f64))))))
(exp.f64 (.f64 (-.f64 1 k) (+.f64 (log.f64 n) (log.f64 (.f64 2 (PI.f64))))))
(exp.f64 (.f64 (-.f64 1 k) (+.f64 (log.f64 n) (log.f64 (.f64 2 (PI.f64))))))
(exp.f64 (.f64 (-.f64 1 k) (+.f64 (.f64 -1 (log.f64 (/.f64 1 n))) (log.f64 (*.f64 2 (PI.f64))))))
(exp.f64 (.f64 (-.f64 1 k) (+.f64 (.f64 -1 (log.f64 (/.f64 1 n))) (log.f64 (*.f64 2 (PI.f64))))))
(exp.f64 (.f64 (-.f64 1 k) (+.f64 (.f64 -1 (log.f64 (/.f64 1 n))) (log.f64 (*.f64 2 (PI.f64))))))
(exp.f64 (.f64 (-.f64 1 k) (+.f64 (.f64 -1 (log.f64 (/.f64 1 n))) (log.f64 (*.f64 2 (PI.f64))))))
(exp.f64 (.f64 (-.f64 1 k) (+.f64 (.f64 -1 (log.f64 (/.f64 -1 n))) (log.f64 (*.f64 -2 (PI.f64))))))
(exp.f64 (.f64 (-.f64 1 k) (+.f64 (.f64 -1 (log.f64 (/.f64 -1 n))) (log.f64 (*.f64 -2 (PI.f64))))))
(exp.f64 (.f64 (-.f64 1 k) (+.f64 (.f64 -1 (log.f64 (/.f64 -1 n))) (log.f64 (*.f64 -2 (PI.f64))))))
(exp.f64 (.f64 (-.f64 1 k) (+.f64 (.f64 -1 (log.f64 (/.f64 -1 n))) (log.f64 (*.f64 -2 (PI.f64))))))
(.f64 2 (.f64 n (PI.f64)))
(+.f64 (.f64 -2 (.f64 k (.f64 n (.f64 (PI.f64) (log.f64 (.f64 2 (.f64 n (PI.f64)))))))) (.f64 2 (.f64 n (PI.f64))))
(+.f64 (.f64 -2 (.f64 k (.f64 n (.f64 (PI.f64) (log.f64 (.f64 2 (.f64 n (PI.f64)))))))) (+.f64 (.f64 2 (.f64 n (PI.f64))) (.f64 (pow.f64 k 2) (.f64 n (.f64 (pow.f64 (log.f64 (.f64 2 (*.f64 n (PI.f64)))) 2) (PI.f64))))))
(+.f64 (.f64 -2 (.f64 k (.f64 n (.f64 (PI.f64) (log.f64 (.f64 2 (.f64 n (PI.f64)))))))) (+.f64 (.f64 -1/3 (.f64 (pow.f64 k 3) (.f64 n (.f64 (PI.f64) (pow.f64 (log.f64 (.f64 2 (.f64 n (PI.f64)))) 3))))) (+.f64 (.f64 2 (.f64 n (PI.f64))) (.f64 (pow.f64 k 2) (.f64 n (.f64 (pow.f64 (log.f64 (.f64 2 (*.f64 n (PI.f64)))) 2) (PI.f64)))))))
(pow.f64 (.f64 2 (.f64 n (PI.f64))) (-.f64 1 k))
(pow.f64 (.f64 2 (.f64 n (PI.f64))) (-.f64 1 k))
(pow.f64 (.f64 2 (.f64 n (PI.f64))) (-.f64 1 k))
(pow.f64 (.f64 2 (.f64 n (PI.f64))) (-.f64 1 k))
(pow.f64 (.f64 2 (.f64 n (PI.f64))) (+.f64 1 (*.f64 -1 k)))
(pow.f64 (.f64 2 (.f64 n (PI.f64))) (+.f64 1 (*.f64 -1 k)))
(pow.f64 (.f64 2 (.f64 n (PI.f64))) (+.f64 1 (*.f64 -1 k)))
(pow.f64 (.f64 2 (.f64 n (PI.f64))) (+.f64 1 (*.f64 -1 k)))
(/.f64 (exp.f64 (.f64 (-.f64 1 k) (+.f64 (log.f64 (.f64 2 (PI.f64))) (log.f64 n)))) k)
(/.f64 (exp.f64 (.f64 (-.f64 1 k) (+.f64 (log.f64 (.f64 2 (PI.f64))) (log.f64 n)))) k)
(/.f64 (exp.f64 (.f64 (-.f64 1 k) (+.f64 (log.f64 (.f64 2 (PI.f64))) (log.f64 n)))) k)
(/.f64 (exp.f64 (.f64 (-.f64 1 k) (+.f64 (log.f64 (.f64 2 (PI.f64))) (log.f64 n)))) k)
(/.f64 (exp.f64 (.f64 (-.f64 1 k) (+.f64 (.f64 -1 (log.f64 (/.f64 1 n))) (log.f64 (*.f64 2 (PI.f64)))))) k)
(/.f64 (exp.f64 (.f64 (-.f64 1 k) (+.f64 (.f64 -1 (log.f64 (/.f64 1 n))) (log.f64 (*.f64 2 (PI.f64)))))) k)
(/.f64 (exp.f64 (.f64 (-.f64 1 k) (+.f64 (.f64 -1 (log.f64 (/.f64 1 n))) (log.f64 (*.f64 2 (PI.f64)))))) k)
(/.f64 (exp.f64 (.f64 (-.f64 1 k) (+.f64 (.f64 -1 (log.f64 (/.f64 1 n))) (log.f64 (*.f64 2 (PI.f64)))))) k)
(/.f64 (exp.f64 (.f64 (-.f64 1 k) (+.f64 (.f64 -1 (log.f64 (/.f64 -1 n))) (log.f64 (*.f64 -2 (PI.f64)))))) k)
(/.f64 (exp.f64 (.f64 (-.f64 1 k) (+.f64 (.f64 -1 (log.f64 (/.f64 -1 n))) (log.f64 (*.f64 -2 (PI.f64)))))) k)
(/.f64 (exp.f64 (.f64 (-.f64 1 k) (+.f64 (.f64 -1 (log.f64 (/.f64 -1 n))) (log.f64 (*.f64 -2 (PI.f64)))))) k)
(/.f64 (exp.f64 (.f64 (-.f64 1 k) (+.f64 (.f64 -1 (log.f64 (/.f64 -1 n))) (log.f64 (*.f64 -2 (PI.f64)))))) k)
(.f64 2 (/.f64 (.f64 n (PI.f64)) k))
(+.f64 (.f64 2 (/.f64 (.f64 n (PI.f64)) k)) (.f64 -2 (.f64 n (.f64 (log.f64 (.f64 2 (*.f64 n (PI.f64)))) (PI.f64)))))
(+.f64 (.f64 2 (/.f64 (.f64 n (PI.f64)) k)) (+.f64 (.f64 k (.f64 n (.f64 (PI.f64) (pow.f64 (log.f64 (.f64 2 (.f64 n (PI.f64)))) 2)))) (.f64 -2 (.f64 n (.f64 (log.f64 (.f64 2 (.f64 n (PI.f64)))) (PI.f64))))))
(+.f64 (.f64 -1/3 (.f64 (pow.f64 k 2) (.f64 n (.f64 (PI.f64) (pow.f64 (log.f64 (.f64 2 (.f64 n (PI.f64)))) 3))))) (+.f64 (.f64 2 (/.f64 (.f64 n (PI.f64)) k)) (+.f64 (.f64 k (.f64 n (.f64 (PI.f64) (pow.f64 (log.f64 (.f64 2 (.f64 n (PI.f64)))) 2)))) (.f64 -2 (.f64 n (.f64 (log.f64 (.f64 2 (.f64 n (PI.f64)))) (PI.f64)))))))
(/.f64 (pow.f64 (.f64 2 (.f64 n (PI.f64))) (-.f64 1 k)) k)
(/.f64 (pow.f64 (.f64 2 (.f64 n (PI.f64))) (-.f64 1 k)) k)
(/.f64 (pow.f64 (.f64 2 (.f64 n (PI.f64))) (-.f64 1 k)) k)
(/.f64 (pow.f64 (.f64 2 (.f64 n (PI.f64))) (-.f64 1 k)) k)
(/.f64 (pow.f64 (.f64 2 (.f64 n (PI.f64))) (+.f64 1 (*.f64 -1 k))) k)
(/.f64 (pow.f64 (.f64 2 (.f64 n (PI.f64))) (+.f64 1 (*.f64 -1 k))) k)
(/.f64 (pow.f64 (.f64 2 (.f64 n (PI.f64))) (+.f64 1 (*.f64 -1 k))) k)
(/.f64 (pow.f64 (.f64 2 (.f64 n (PI.f64))) (+.f64 1 (*.f64 -1 k))) k)

Outputs
(sqrt.f64 (/.f64 (exp.f64 (.f64 (-.f64 1 k) (+.f64 (log.f64 n) (log.f64 (.f64 2 (PI.f64)))))) k))
(sqrt.f64 (/.f64 (pow.f64 (exp.f64 (-.f64 1 k)) (+.f64 (log.f64 n) (log.f64 (*.f64 2 (PI.f64))))) k))
(sqrt.f64 (/.f64 (pow.f64 (exp.f64 (-.f64 1 k)) (log.f64 (.f64 n (.f64 2 (PI.f64))))) k))
(sqrt.f64 (/.f64 (pow.f64 (.f64 n (.f64 2 (PI.f64))) (-.f64 1 k)) k))
(sqrt.f64 (/.f64 (exp.f64 (.f64 (-.f64 1 k) (+.f64 (log.f64 n) (log.f64 (.f64 2 (PI.f64)))))) k))
(sqrt.f64 (/.f64 (pow.f64 (exp.f64 (-.f64 1 k)) (+.f64 (log.f64 n) (log.f64 (*.f64 2 (PI.f64))))) k))
(sqrt.f64 (/.f64 (pow.f64 (exp.f64 (-.f64 1 k)) (log.f64 (.f64 n (.f64 2 (PI.f64))))) k))
(sqrt.f64 (/.f64 (pow.f64 (.f64 n (.f64 2 (PI.f64))) (-.f64 1 k)) k))
(sqrt.f64 (/.f64 (exp.f64 (.f64 (-.f64 1 k) (+.f64 (log.f64 n) (log.f64 (.f64 2 (PI.f64)))))) k))
(sqrt.f64 (/.f64 (pow.f64 (exp.f64 (-.f64 1 k)) (+.f64 (log.f64 n) (log.f64 (*.f64 2 (PI.f64))))) k))
(sqrt.f64 (/.f64 (pow.f64 (exp.f64 (-.f64 1 k)) (log.f64 (.f64 n (.f64 2 (PI.f64))))) k))
(sqrt.f64 (/.f64 (pow.f64 (.f64 n (.f64 2 (PI.f64))) (-.f64 1 k)) k))
(sqrt.f64 (/.f64 (exp.f64 (.f64 (-.f64 1 k) (+.f64 (log.f64 n) (log.f64 (.f64 2 (PI.f64)))))) k))
(sqrt.f64 (/.f64 (pow.f64 (exp.f64 (-.f64 1 k)) (+.f64 (log.f64 n) (log.f64 (*.f64 2 (PI.f64))))) k))
(sqrt.f64 (/.f64 (pow.f64 (exp.f64 (-.f64 1 k)) (log.f64 (.f64 n (.f64 2 (PI.f64))))) k))
(sqrt.f64 (/.f64 (pow.f64 (.f64 n (.f64 2 (PI.f64))) (-.f64 1 k)) k))
(sqrt.f64 (/.f64 (exp.f64 (.f64 (-.f64 1 k) (+.f64 (.f64 -1 (log.f64 (/.f64 1 n))) (log.f64 (*.f64 2 (PI.f64)))))) k))
(sqrt.f64 (/.f64 (pow.f64 (exp.f64 (-.f64 1 k)) (+.f64 (log.f64 n) (log.f64 (*.f64 2 (PI.f64))))) k))
(sqrt.f64 (/.f64 (pow.f64 (exp.f64 (-.f64 1 k)) (log.f64 (.f64 n (.f64 2 (PI.f64))))) k))
(sqrt.f64 (/.f64 (pow.f64 (.f64 n (.f64 2 (PI.f64))) (-.f64 1 k)) k))
(sqrt.f64 (/.f64 (exp.f64 (.f64 (-.f64 1 k) (+.f64 (.f64 -1 (log.f64 (/.f64 1 n))) (log.f64 (*.f64 2 (PI.f64)))))) k))
(sqrt.f64 (/.f64 (pow.f64 (exp.f64 (-.f64 1 k)) (+.f64 (log.f64 n) (log.f64 (*.f64 2 (PI.f64))))) k))
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(sqrt.f64 (/.f64 (pow.f64 (exp.f64 (-.f64 1 k)) (+.f64 (log.f64 n) (log.f64 (*.f64 2 (PI.f64))))) k))
(sqrt.f64 (/.f64 (pow.f64 (exp.f64 (-.f64 1 k)) (log.f64 (.f64 n (.f64 2 (PI.f64))))) k))
(sqrt.f64 (/.f64 (pow.f64 (.f64 n (.f64 2 (PI.f64))) (-.f64 1 k)) k))
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(sqrt.f64 (/.f64 (pow.f64 (exp.f64 (-.f64 1 k)) (+.f64 (log.f64 n) (log.f64 (*.f64 2 (PI.f64))))) k))
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(sqrt.f64 (/.f64 (pow.f64 (exp.f64 (-.f64 1 k)) (fma.f64 -1 (log.f64 (/.f64 -1 n)) (log.f64 (*.f64 (PI.f64) -2)))) k))
(sqrt.f64 (/.f64 (pow.f64 (exp.f64 (-.f64 1 k)) (-.f64 (log.f64 (*.f64 (PI.f64) -2)) (log.f64 (/.f64 -1 n)))) k))
(sqrt.f64 (/.f64 (pow.f64 (*.f64 -2 (/.f64 (PI.f64) (/.f64 -1 n))) (-.f64 1 k)) k))
(sqrt.f64 (/.f64 (exp.f64 (.f64 (-.f64 1 k) (+.f64 (.f64 -1 (log.f64 (/.f64 -1 n))) (log.f64 (*.f64 -2 (PI.f64)))))) k))
(sqrt.f64 (/.f64 (pow.f64 (exp.f64 (-.f64 1 k)) (fma.f64 -1 (log.f64 (/.f64 -1 n)) (log.f64 (*.f64 (PI.f64) -2)))) k))
(sqrt.f64 (/.f64 (pow.f64 (exp.f64 (-.f64 1 k)) (-.f64 (log.f64 (*.f64 (PI.f64) -2)) (log.f64 (/.f64 -1 n)))) k))
(sqrt.f64 (/.f64 (pow.f64 (*.f64 -2 (/.f64 (PI.f64) (/.f64 -1 n))) (-.f64 1 k)) k))
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(sqrt.f64 (/.f64 (pow.f64 (*.f64 -2 (/.f64 (PI.f64) (/.f64 -1 n))) (-.f64 1 k)) k))
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(pow.f64 (exp.f64 (-.f64 1 k)) (+.f64 (log.f64 n) (log.f64 (*.f64 2 (PI.f64)))))
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(pow.f64 (.f64 n (.f64 2 (PI.f64))) (-.f64 1 k))
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(pow.f64 (exp.f64 (-.f64 1 k)) (+.f64 (log.f64 n) (log.f64 (*.f64 2 (PI.f64)))))
(pow.f64 (exp.f64 (-.f64 1 k)) (log.f64 (.f64 n (.f64 2 (PI.f64)))))
(pow.f64 (.f64 n (.f64 2 (PI.f64))) (-.f64 1 k))
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(pow.f64 (exp.f64 (-.f64 1 k)) (+.f64 (log.f64 n) (log.f64 (*.f64 2 (PI.f64)))))
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(pow.f64 (exp.f64 (-.f64 1 k)) (+.f64 (log.f64 n) (log.f64 (*.f64 2 (PI.f64)))))
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(pow.f64 (.f64 n (.f64 2 (PI.f64))) (-.f64 1 k))
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(pow.f64 (exp.f64 (-.f64 1 k)) (+.f64 (log.f64 n) (log.f64 (*.f64 2 (PI.f64)))))
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(pow.f64 (.f64 n (.f64 2 (PI.f64))) (-.f64 1 k))
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(pow.f64 (exp.f64 (-.f64 1 k)) (+.f64 (log.f64 n) (log.f64 (*.f64 2 (PI.f64)))))
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(pow.f64 (.f64 n (.f64 2 (PI.f64))) (-.f64 1 k))
(exp.f64 (.f64 (-.f64 1 k) (+.f64 (.f64 -1 (log.f64 (/.f64 1 n))) (log.f64 (*.f64 2 (PI.f64))))))
(pow.f64 (exp.f64 (-.f64 1 k)) (+.f64 (log.f64 n) (log.f64 (*.f64 2 (PI.f64)))))
(pow.f64 (exp.f64 (-.f64 1 k)) (log.f64 (.f64 n (.f64 2 (PI.f64)))))
(pow.f64 (.f64 n (.f64 2 (PI.f64))) (-.f64 1 k))
(exp.f64 (.f64 (-.f64 1 k) (+.f64 (.f64 -1 (log.f64 (/.f64 1 n))) (log.f64 (*.f64 2 (PI.f64))))))
(pow.f64 (exp.f64 (-.f64 1 k)) (+.f64 (log.f64 n) (log.f64 (*.f64 2 (PI.f64)))))
(pow.f64 (exp.f64 (-.f64 1 k)) (log.f64 (.f64 n (.f64 2 (PI.f64)))))
(pow.f64 (.f64 n (.f64 2 (PI.f64))) (-.f64 1 k))
(exp.f64 (.f64 (-.f64 1 k) (+.f64 (.f64 -1 (log.f64 (/.f64 -1 n))) (log.f64 (*.f64 -2 (PI.f64))))))
(pow.f64 (exp.f64 (-.f64 1 k)) (fma.f64 -1 (log.f64 (/.f64 -1 n)) (log.f64 (*.f64 (PI.f64) -2))))
(pow.f64 (exp.f64 (-.f64 1 k)) (-.f64 (log.f64 (*.f64 (PI.f64) -2)) (log.f64 (/.f64 -1 n))))
(pow.f64 (*.f64 -2 (/.f64 (PI.f64) (/.f64 -1 n))) (-.f64 1 k))
(exp.f64 (.f64 (-.f64 1 k) (+.f64 (.f64 -1 (log.f64 (/.f64 -1 n))) (log.f64 (*.f64 -2 (PI.f64))))))
(pow.f64 (exp.f64 (-.f64 1 k)) (fma.f64 -1 (log.f64 (/.f64 -1 n)) (log.f64 (*.f64 (PI.f64) -2))))
(pow.f64 (exp.f64 (-.f64 1 k)) (-.f64 (log.f64 (*.f64 (PI.f64) -2)) (log.f64 (/.f64 -1 n))))
(pow.f64 (*.f64 -2 (/.f64 (PI.f64) (/.f64 -1 n))) (-.f64 1 k))
(exp.f64 (.f64 (-.f64 1 k) (+.f64 (.f64 -1 (log.f64 (/.f64 -1 n))) (log.f64 (*.f64 -2 (PI.f64))))))
(pow.f64 (exp.f64 (-.f64 1 k)) (fma.f64 -1 (log.f64 (/.f64 -1 n)) (log.f64 (*.f64 (PI.f64) -2))))
(pow.f64 (exp.f64 (-.f64 1 k)) (-.f64 (log.f64 (*.f64 (PI.f64) -2)) (log.f64 (/.f64 -1 n))))
(pow.f64 (*.f64 -2 (/.f64 (PI.f64) (/.f64 -1 n))) (-.f64 1 k))
(exp.f64 (.f64 (-.f64 1 k) (+.f64 (.f64 -1 (log.f64 (/.f64 -1 n))) (log.f64 (*.f64 -2 (PI.f64))))))
(pow.f64 (exp.f64 (-.f64 1 k)) (fma.f64 -1 (log.f64 (/.f64 -1 n)) (log.f64 (*.f64 (PI.f64) -2))))
(pow.f64 (exp.f64 (-.f64 1 k)) (-.f64 (log.f64 (*.f64 (PI.f64) -2)) (log.f64 (/.f64 -1 n))))
(pow.f64 (*.f64 -2 (/.f64 (PI.f64) (/.f64 -1 n))) (-.f64 1 k))
(.f64 2 (.f64 n (PI.f64)))
(.f64 n (.f64 2 (PI.f64)))
(+.f64 (.f64 -2 (.f64 k (.f64 n (.f64 (PI.f64) (log.f64 (.f64 2 (.f64 n (PI.f64)))))))) (.f64 2 (.f64 n (PI.f64))))
(fma.f64 -2 (.f64 k (.f64 (.f64 n (PI.f64)) (log.f64 (.f64 2 (.f64 n (PI.f64)))))) (.f64 2 (*.f64 n (PI.f64))))
(fma.f64 2 (.f64 n (PI.f64)) (.f64 (.f64 (.f64 k -2) (.f64 n (PI.f64))) (log.f64 (.f64 n (*.f64 2 (PI.f64))))))
(.f64 (PI.f64) (+.f64 (.f64 n 2) (.f64 (.f64 n (log.f64 (.f64 n (.f64 2 (PI.f64))))) (*.f64 k -2))))
(.f64 n (.f64 (PI.f64) (+.f64 (.f64 (.f64 k -2) (log.f64 (.f64 n (.f64 2 (PI.f64))))) 2)))
(+.f64 (.f64 -2 (.f64 k (.f64 n (.f64 (PI.f64) (log.f64 (.f64 2 (.f64 n (PI.f64)))))))) (+.f64 (.f64 2 (.f64 n (PI.f64))) (.f64 (pow.f64 k 2) (.f64 n (.f64 (pow.f64 (log.f64 (.f64 2 (*.f64 n (PI.f64)))) 2) (PI.f64))))))
(fma.f64 -2 (.f64 k (.f64 (.f64 n (PI.f64)) (log.f64 (.f64 2 (.f64 n (PI.f64)))))) (fma.f64 2 (.f64 n (PI.f64)) (.f64 (.f64 k k) (.f64 (.f64 n (PI.f64)) (pow.f64 (log.f64 (.f64 2 (.f64 n (PI.f64)))) 2)))))
(fma.f64 -2 (.f64 k (.f64 (PI.f64) (.f64 n (log.f64 (.f64 n (.f64 2 (PI.f64))))))) (fma.f64 2 (.f64 n (PI.f64)) (.f64 k (.f64 (.f64 n (PI.f64)) (.f64 (pow.f64 (log.f64 (.f64 n (.f64 2 (PI.f64)))) 2) k)))))
(fma.f64 n (.f64 2 (PI.f64)) (.f64 k (.f64 (.f64 n (PI.f64)) (+.f64 (.f64 -2 (log.f64 (.f64 n (.f64 2 (PI.f64))))) (.f64 k (pow.f64 (log.f64 (.f64 n (.f64 2 (PI.f64)))) 2))))))
(.f64 (PI.f64) (+.f64 (.f64 n 2) (.f64 k (.f64 n (.f64 (log.f64 (.f64 n (.f64 2 (PI.f64)))) (+.f64 (.f64 k (log.f64 (.f64 n (.f64 2 (PI.f64))))) -2))))))
(+.f64 (.f64 -2 (.f64 k (.f64 n (.f64 (PI.f64) (log.f64 (.f64 2 (.f64 n (PI.f64)))))))) (+.f64 (.f64 -1/3 (.f64 (pow.f64 k 3) (.f64 n (.f64 (PI.f64) (pow.f64 (log.f64 (.f64 2 (.f64 n (PI.f64)))) 3))))) (+.f64 (.f64 2 (.f64 n (PI.f64))) (.f64 (pow.f64 k 2) (.f64 n (.f64 (pow.f64 (log.f64 (.f64 2 (*.f64 n (PI.f64)))) 2) (PI.f64)))))))
(fma.f64 -2 (.f64 k (.f64 (.f64 n (PI.f64)) (log.f64 (.f64 2 (.f64 n (PI.f64)))))) (fma.f64 -1/3 (.f64 (pow.f64 k 3) (.f64 (.f64 n (PI.f64)) (pow.f64 (log.f64 (.f64 2 (.f64 n (PI.f64)))) 3))) (fma.f64 2 (.f64 n (PI.f64)) (.f64 (.f64 k k) (.f64 (.f64 n (PI.f64)) (pow.f64 (log.f64 (.f64 2 (*.f64 n (PI.f64)))) 2))))))
(fma.f64 -2 (.f64 k (.f64 (PI.f64) (.f64 n (log.f64 (.f64 n (.f64 2 (PI.f64))))))) (fma.f64 -1/3 (.f64 (.f64 n (PI.f64)) (.f64 (pow.f64 (log.f64 (.f64 n (.f64 2 (PI.f64)))) 3) (pow.f64 k 3))) (fma.f64 2 (.f64 n (PI.f64)) (.f64 k (.f64 (.f64 n (PI.f64)) (.f64 (pow.f64 (log.f64 (.f64 n (*.f64 2 (PI.f64)))) 2) k))))))
(fma.f64 -1/3 (.f64 n (.f64 (PI.f64) (.f64 (pow.f64 k 3) (pow.f64 (log.f64 (.f64 n (.f64 2 (PI.f64)))) 3)))) (fma.f64 n (.f64 2 (PI.f64)) (.f64 k (.f64 (.f64 n (PI.f64)) (+.f64 (.f64 -2 (log.f64 (.f64 n (.f64 2 (PI.f64))))) (.f64 k (pow.f64 (log.f64 (.f64 n (*.f64 2 (PI.f64)))) 2)))))))
(.f64 n (+.f64 (.f64 (PI.f64) (+.f64 2 (.f64 (.f64 -1/3 (pow.f64 k 3)) (pow.f64 (log.f64 (.f64 n (.f64 2 (PI.f64)))) 3)))) (.f64 k (.f64 (.f64 (PI.f64) (log.f64 (.f64 n (.f64 2 (PI.f64))))) (+.f64 -2 (.f64 k (log.f64 (.f64 n (.f64 2 (PI.f64))))))))))
(pow.f64 (.f64 2 (.f64 n (PI.f64))) (-.f64 1 k))
(pow.f64 (exp.f64 (-.f64 1 k)) (+.f64 (log.f64 n) (log.f64 (*.f64 2 (PI.f64)))))
(pow.f64 (exp.f64 (-.f64 1 k)) (log.f64 (.f64 n (.f64 2 (PI.f64)))))
(pow.f64 (.f64 n (.f64 2 (PI.f64))) (-.f64 1 k))
(pow.f64 (.f64 2 (.f64 n (PI.f64))) (-.f64 1 k))
(pow.f64 (exp.f64 (-.f64 1 k)) (+.f64 (log.f64 n) (log.f64 (*.f64 2 (PI.f64)))))
(pow.f64 (exp.f64 (-.f64 1 k)) (log.f64 (.f64 n (.f64 2 (PI.f64)))))
(pow.f64 (.f64 n (.f64 2 (PI.f64))) (-.f64 1 k))
(pow.f64 (.f64 2 (.f64 n (PI.f64))) (-.f64 1 k))
(pow.f64 (exp.f64 (-.f64 1 k)) (+.f64 (log.f64 n) (log.f64 (*.f64 2 (PI.f64)))))
(pow.f64 (exp.f64 (-.f64 1 k)) (log.f64 (.f64 n (.f64 2 (PI.f64)))))
(pow.f64 (.f64 n (.f64 2 (PI.f64))) (-.f64 1 k))
(pow.f64 (.f64 2 (.f64 n (PI.f64))) (-.f64 1 k))
(pow.f64 (exp.f64 (-.f64 1 k)) (+.f64 (log.f64 n) (log.f64 (*.f64 2 (PI.f64)))))
(pow.f64 (exp.f64 (-.f64 1 k)) (log.f64 (.f64 n (.f64 2 (PI.f64)))))
(pow.f64 (.f64 n (.f64 2 (PI.f64))) (-.f64 1 k))
(pow.f64 (.f64 2 (.f64 n (PI.f64))) (+.f64 1 (*.f64 -1 k)))
(pow.f64 (exp.f64 (-.f64 1 k)) (+.f64 (log.f64 n) (log.f64 (*.f64 2 (PI.f64)))))
(pow.f64 (exp.f64 (-.f64 1 k)) (log.f64 (.f64 n (.f64 2 (PI.f64)))))
(pow.f64 (.f64 n (.f64 2 (PI.f64))) (-.f64 1 k))
(pow.f64 (.f64 2 (.f64 n (PI.f64))) (+.f64 1 (*.f64 -1 k)))
(pow.f64 (exp.f64 (-.f64 1 k)) (+.f64 (log.f64 n) (log.f64 (*.f64 2 (PI.f64)))))
(pow.f64 (exp.f64 (-.f64 1 k)) (log.f64 (.f64 n (.f64 2 (PI.f64)))))
(pow.f64 (.f64 n (.f64 2 (PI.f64))) (-.f64 1 k))
(pow.f64 (.f64 2 (.f64 n (PI.f64))) (+.f64 1 (*.f64 -1 k)))
(pow.f64 (exp.f64 (-.f64 1 k)) (+.f64 (log.f64 n) (log.f64 (*.f64 2 (PI.f64)))))
(pow.f64 (exp.f64 (-.f64 1 k)) (log.f64 (.f64 n (.f64 2 (PI.f64)))))
(pow.f64 (.f64 n (.f64 2 (PI.f64))) (-.f64 1 k))
(pow.f64 (.f64 2 (.f64 n (PI.f64))) (+.f64 1 (*.f64 -1 k)))
(pow.f64 (exp.f64 (-.f64 1 k)) (+.f64 (log.f64 n) (log.f64 (*.f64 2 (PI.f64)))))
(pow.f64 (exp.f64 (-.f64 1 k)) (log.f64 (.f64 n (.f64 2 (PI.f64)))))
(pow.f64 (.f64 n (.f64 2 (PI.f64))) (-.f64 1 k))
(/.f64 (exp.f64 (.f64 (-.f64 1 k) (+.f64 (log.f64 (.f64 2 (PI.f64))) (log.f64 n)))) k)
(/.f64 (pow.f64 (exp.f64 (-.f64 1 k)) (+.f64 (log.f64 n) (log.f64 (*.f64 2 (PI.f64))))) k)
(/.f64 (pow.f64 (exp.f64 (-.f64 1 k)) (log.f64 (.f64 n (.f64 2 (PI.f64))))) k)
(/.f64 (pow.f64 (.f64 n (.f64 2 (PI.f64))) (-.f64 1 k)) k)
(/.f64 (exp.f64 (.f64 (-.f64 1 k) (+.f64 (log.f64 (.f64 2 (PI.f64))) (log.f64 n)))) k)
(/.f64 (pow.f64 (exp.f64 (-.f64 1 k)) (+.f64 (log.f64 n) (log.f64 (*.f64 2 (PI.f64))))) k)
(/.f64 (pow.f64 (exp.f64 (-.f64 1 k)) (log.f64 (.f64 n (.f64 2 (PI.f64))))) k)
(/.f64 (pow.f64 (.f64 n (.f64 2 (PI.f64))) (-.f64 1 k)) k)
(/.f64 (exp.f64 (.f64 (-.f64 1 k) (+.f64 (log.f64 (.f64 2 (PI.f64))) (log.f64 n)))) k)
(/.f64 (pow.f64 (exp.f64 (-.f64 1 k)) (+.f64 (log.f64 n) (log.f64 (*.f64 2 (PI.f64))))) k)
(/.f64 (pow.f64 (exp.f64 (-.f64 1 k)) (log.f64 (.f64 n (.f64 2 (PI.f64))))) k)
(/.f64 (pow.f64 (.f64 n (.f64 2 (PI.f64))) (-.f64 1 k)) k)
(/.f64 (exp.f64 (.f64 (-.f64 1 k) (+.f64 (log.f64 (.f64 2 (PI.f64))) (log.f64 n)))) k)
(/.f64 (pow.f64 (exp.f64 (-.f64 1 k)) (+.f64 (log.f64 n) (log.f64 (*.f64 2 (PI.f64))))) k)
(/.f64 (pow.f64 (exp.f64 (-.f64 1 k)) (log.f64 (.f64 n (.f64 2 (PI.f64))))) k)
(/.f64 (pow.f64 (.f64 n (.f64 2 (PI.f64))) (-.f64 1 k)) k)
(/.f64 (exp.f64 (.f64 (-.f64 1 k) (+.f64 (.f64 -1 (log.f64 (/.f64 1 n))) (log.f64 (*.f64 2 (PI.f64)))))) k)
(/.f64 (pow.f64 (exp.f64 (-.f64 1 k)) (+.f64 (log.f64 n) (log.f64 (*.f64 2 (PI.f64))))) k)
(/.f64 (pow.f64 (exp.f64 (-.f64 1 k)) (log.f64 (.f64 n (.f64 2 (PI.f64))))) k)
(/.f64 (pow.f64 (.f64 n (.f64 2 (PI.f64))) (-.f64 1 k)) k)
(/.f64 (exp.f64 (.f64 (-.f64 1 k) (+.f64 (.f64 -1 (log.f64 (/.f64 1 n))) (log.f64 (*.f64 2 (PI.f64)))))) k)
(/.f64 (pow.f64 (exp.f64 (-.f64 1 k)) (+.f64 (log.f64 n) (log.f64 (*.f64 2 (PI.f64))))) k)
(/.f64 (pow.f64 (exp.f64 (-.f64 1 k)) (log.f64 (.f64 n (.f64 2 (PI.f64))))) k)
(/.f64 (pow.f64 (.f64 n (.f64 2 (PI.f64))) (-.f64 1 k)) k)
(/.f64 (exp.f64 (.f64 (-.f64 1 k) (+.f64 (.f64 -1 (log.f64 (/.f64 1 n))) (log.f64 (*.f64 2 (PI.f64)))))) k)
(/.f64 (pow.f64 (exp.f64 (-.f64 1 k)) (+.f64 (log.f64 n) (log.f64 (*.f64 2 (PI.f64))))) k)
(/.f64 (pow.f64 (exp.f64 (-.f64 1 k)) (log.f64 (.f64 n (.f64 2 (PI.f64))))) k)
(/.f64 (pow.f64 (.f64 n (.f64 2 (PI.f64))) (-.f64 1 k)) k)
(/.f64 (exp.f64 (.f64 (-.f64 1 k) (+.f64 (.f64 -1 (log.f64 (/.f64 1 n))) (log.f64 (*.f64 2 (PI.f64)))))) k)
(/.f64 (pow.f64 (exp.f64 (-.f64 1 k)) (+.f64 (log.f64 n) (log.f64 (*.f64 2 (PI.f64))))) k)
(/.f64 (pow.f64 (exp.f64 (-.f64 1 k)) (log.f64 (.f64 n (.f64 2 (PI.f64))))) k)
(/.f64 (pow.f64 (.f64 n (.f64 2 (PI.f64))) (-.f64 1 k)) k)
(/.f64 (exp.f64 (.f64 (-.f64 1 k) (+.f64 (.f64 -1 (log.f64 (/.f64 -1 n))) (log.f64 (*.f64 -2 (PI.f64)))))) k)
(/.f64 (pow.f64 (exp.f64 (-.f64 1 k)) (fma.f64 -1 (log.f64 (/.f64 -1 n)) (log.f64 (*.f64 (PI.f64) -2)))) k)
(/.f64 (pow.f64 (exp.f64 (-.f64 1 k)) (-.f64 (log.f64 (*.f64 (PI.f64) -2)) (log.f64 (/.f64 -1 n)))) k)
(/.f64 (pow.f64 (*.f64 -2 (/.f64 (PI.f64) (/.f64 -1 n))) (-.f64 1 k)) k)
(/.f64 (exp.f64 (.f64 (-.f64 1 k) (+.f64 (.f64 -1 (log.f64 (/.f64 -1 n))) (log.f64 (*.f64 -2 (PI.f64)))))) k)
(/.f64 (pow.f64 (exp.f64 (-.f64 1 k)) (fma.f64 -1 (log.f64 (/.f64 -1 n)) (log.f64 (*.f64 (PI.f64) -2)))) k)
(/.f64 (pow.f64 (exp.f64 (-.f64 1 k)) (-.f64 (log.f64 (*.f64 (PI.f64) -2)) (log.f64 (/.f64 -1 n)))) k)
(/.f64 (pow.f64 (*.f64 -2 (/.f64 (PI.f64) (/.f64 -1 n))) (-.f64 1 k)) k)
(/.f64 (exp.f64 (.f64 (-.f64 1 k) (+.f64 (.f64 -1 (log.f64 (/.f64 -1 n))) (log.f64 (*.f64 -2 (PI.f64)))))) k)
(/.f64 (pow.f64 (exp.f64 (-.f64 1 k)) (fma.f64 -1 (log.f64 (/.f64 -1 n)) (log.f64 (*.f64 (PI.f64) -2)))) k)
(/.f64 (pow.f64 (exp.f64 (-.f64 1 k)) (-.f64 (log.f64 (*.f64 (PI.f64) -2)) (log.f64 (/.f64 -1 n)))) k)
(/.f64 (pow.f64 (*.f64 -2 (/.f64 (PI.f64) (/.f64 -1 n))) (-.f64 1 k)) k)
(/.f64 (exp.f64 (.f64 (-.f64 1 k) (+.f64 (.f64 -1 (log.f64 (/.f64 -1 n))) (log.f64 (*.f64 -2 (PI.f64)))))) k)
(/.f64 (pow.f64 (exp.f64 (-.f64 1 k)) (fma.f64 -1 (log.f64 (/.f64 -1 n)) (log.f64 (*.f64 (PI.f64) -2)))) k)
(/.f64 (pow.f64 (exp.f64 (-.f64 1 k)) (-.f64 (log.f64 (*.f64 (PI.f64) -2)) (log.f64 (/.f64 -1 n)))) k)
(/.f64 (pow.f64 (*.f64 -2 (/.f64 (PI.f64) (/.f64 -1 n))) (-.f64 1 k)) k)
(.f64 2 (/.f64 (.f64 n (PI.f64)) k))
(*.f64 2 (/.f64 n (/.f64 k (PI.f64))))
(*.f64 2 (/.f64 (PI.f64) (/.f64 k n)))
(.f64 2 (.f64 (/.f64 (PI.f64) k) n))
(+.f64 (.f64 2 (/.f64 (.f64 n (PI.f64)) k)) (.f64 -2 (.f64 n (.f64 (log.f64 (.f64 2 (*.f64 n (PI.f64)))) (PI.f64)))))
(fma.f64 2 (/.f64 n (/.f64 k (PI.f64))) (.f64 -2 (.f64 (.f64 n (PI.f64)) (log.f64 (.f64 2 (*.f64 n (PI.f64)))))))
(fma.f64 2 (/.f64 (PI.f64) (/.f64 k n)) (.f64 (.f64 -2 (.f64 n (PI.f64))) (log.f64 (.f64 n (*.f64 2 (PI.f64))))))
(fma.f64 (.f64 n (.f64 (PI.f64) -2)) (log.f64 (.f64 n (.f64 2 (PI.f64)))) (.f64 2 (.f64 (/.f64 (PI.f64) k) n)))
(.f64 (.f64 n (PI.f64)) (+.f64 (/.f64 2 k) (.f64 -2 (log.f64 (.f64 n (*.f64 2 (PI.f64)))))))
(+.f64 (.f64 2 (/.f64 (.f64 n (PI.f64)) k)) (+.f64 (.f64 k (.f64 n (.f64 (PI.f64) (pow.f64 (log.f64 (.f64 2 (.f64 n (PI.f64)))) 2)))) (.f64 -2 (.f64 n (.f64 (log.f64 (.f64 2 (.f64 n (PI.f64)))) (PI.f64))))))
(fma.f64 2 (/.f64 n (/.f64 k (PI.f64))) (fma.f64 k (.f64 (.f64 n (PI.f64)) (pow.f64 (log.f64 (.f64 2 (.f64 n (PI.f64)))) 2)) (.f64 -2 (.f64 (.f64 n (PI.f64)) (log.f64 (.f64 2 (*.f64 n (PI.f64))))))))
(fma.f64 2 (/.f64 (PI.f64) (/.f64 k n)) (fma.f64 k (.f64 n (.f64 (PI.f64) (pow.f64 (log.f64 (.f64 n (.f64 2 (PI.f64)))) 2))) (.f64 (.f64 -2 (.f64 n (PI.f64))) (log.f64 (.f64 n (*.f64 2 (PI.f64)))))))
(fma.f64 2 (.f64 (/.f64 (PI.f64) k) n) (.f64 (.f64 n (PI.f64)) (+.f64 (.f64 -2 (log.f64 (.f64 n (.f64 2 (PI.f64))))) (.f64 k (pow.f64 (log.f64 (.f64 n (*.f64 2 (PI.f64)))) 2)))))
(fma.f64 2 (.f64 (/.f64 (PI.f64) k) n) (.f64 n (.f64 (.f64 (PI.f64) (log.f64 (.f64 n (.f64 2 (PI.f64))))) (+.f64 (.f64 k (log.f64 (.f64 n (*.f64 2 (PI.f64))))) -2))))
(+.f64 (.f64 -1/3 (.f64 (pow.f64 k 2) (.f64 n (.f64 (PI.f64) (pow.f64 (log.f64 (.f64 2 (.f64 n (PI.f64)))) 3))))) (+.f64 (.f64 2 (/.f64 (.f64 n (PI.f64)) k)) (+.f64 (.f64 k (.f64 n (.f64 (PI.f64) (pow.f64 (log.f64 (.f64 2 (.f64 n (PI.f64)))) 2)))) (.f64 -2 (.f64 n (.f64 (log.f64 (.f64 2 (.f64 n (PI.f64)))) (PI.f64)))))))
(fma.f64 -1/3 (.f64 (.f64 k k) (.f64 (.f64 n (PI.f64)) (pow.f64 (log.f64 (.f64 2 (.f64 n (PI.f64)))) 3))) (fma.f64 2 (/.f64 n (/.f64 k (PI.f64))) (fma.f64 k (.f64 (.f64 n (PI.f64)) (pow.f64 (log.f64 (.f64 2 (.f64 n (PI.f64)))) 2)) (.f64 -2 (.f64 (.f64 n (PI.f64)) (log.f64 (.f64 2 (*.f64 n (PI.f64)))))))))
(fma.f64 -1/3 (.f64 n (.f64 (.f64 (PI.f64) (pow.f64 (log.f64 (.f64 n (.f64 2 (PI.f64)))) 3)) (.f64 k k))) (fma.f64 2 (/.f64 (PI.f64) (/.f64 k n)) (fma.f64 k (.f64 n (.f64 (PI.f64) (pow.f64 (log.f64 (.f64 n (.f64 2 (PI.f64)))) 2))) (.f64 (.f64 -2 (.f64 n (PI.f64))) (log.f64 (.f64 n (*.f64 2 (PI.f64))))))))
(fma.f64 (.f64 k k) (.f64 n (.f64 -1/3 (.f64 (PI.f64) (pow.f64 (log.f64 (.f64 n (.f64 2 (PI.f64)))) 3)))) (fma.f64 2 (.f64 (/.f64 (PI.f64) k) n) (.f64 (.f64 n (PI.f64)) (+.f64 (.f64 -2 (log.f64 (.f64 n (.f64 2 (PI.f64))))) (.f64 k (pow.f64 (log.f64 (.f64 n (*.f64 2 (PI.f64)))) 2))))))
(fma.f64 2 (.f64 (/.f64 (PI.f64) k) n) (.f64 (.f64 n (PI.f64)) (+.f64 (.f64 (log.f64 (.f64 n (.f64 2 (PI.f64)))) (+.f64 -2 (.f64 k (log.f64 (.f64 n (.f64 2 (PI.f64))))))) (.f64 (pow.f64 (log.f64 (.f64 n (.f64 2 (PI.f64)))) 3) (.f64 (.f64 k k) -1/3)))))
(/.f64 (pow.f64 (.f64 2 (.f64 n (PI.f64))) (-.f64 1 k)) k)
(/.f64 (pow.f64 (exp.f64 (-.f64 1 k)) (+.f64 (log.f64 n) (log.f64 (*.f64 2 (PI.f64))))) k)
(/.f64 (pow.f64 (exp.f64 (-.f64 1 k)) (log.f64 (.f64 n (.f64 2 (PI.f64))))) k)
(/.f64 (pow.f64 (.f64 n (.f64 2 (PI.f64))) (-.f64 1 k)) k)
(/.f64 (pow.f64 (.f64 2 (.f64 n (PI.f64))) (-.f64 1 k)) k)
(/.f64 (pow.f64 (exp.f64 (-.f64 1 k)) (+.f64 (log.f64 n) (log.f64 (*.f64 2 (PI.f64))))) k)
(/.f64 (pow.f64 (exp.f64 (-.f64 1 k)) (log.f64 (.f64 n (.f64 2 (PI.f64))))) k)
(/.f64 (pow.f64 (.f64 n (.f64 2 (PI.f64))) (-.f64 1 k)) k)
(/.f64 (pow.f64 (.f64 2 (.f64 n (PI.f64))) (-.f64 1 k)) k)
(/.f64 (pow.f64 (exp.f64 (-.f64 1 k)) (+.f64 (log.f64 n) (log.f64 (*.f64 2 (PI.f64))))) k)
(/.f64 (pow.f64 (exp.f64 (-.f64 1 k)) (log.f64 (.f64 n (.f64 2 (PI.f64))))) k)
(/.f64 (pow.f64 (.f64 n (.f64 2 (PI.f64))) (-.f64 1 k)) k)
(/.f64 (pow.f64 (.f64 2 (.f64 n (PI.f64))) (-.f64 1 k)) k)
(/.f64 (pow.f64 (exp.f64 (-.f64 1 k)) (+.f64 (log.f64 n) (log.f64 (*.f64 2 (PI.f64))))) k)
(/.f64 (pow.f64 (exp.f64 (-.f64 1 k)) (log.f64 (.f64 n (.f64 2 (PI.f64))))) k)
(/.f64 (pow.f64 (.f64 n (.f64 2 (PI.f64))) (-.f64 1 k)) k)
(/.f64 (pow.f64 (.f64 2 (.f64 n (PI.f64))) (+.f64 1 (*.f64 -1 k))) k)
(/.f64 (pow.f64 (exp.f64 (-.f64 1 k)) (+.f64 (log.f64 n) (log.f64 (*.f64 2 (PI.f64))))) k)
(/.f64 (pow.f64 (exp.f64 (-.f64 1 k)) (log.f64 (.f64 n (.f64 2 (PI.f64))))) k)
(/.f64 (pow.f64 (.f64 n (.f64 2 (PI.f64))) (-.f64 1 k)) k)
(/.f64 (pow.f64 (.f64 2 (.f64 n (PI.f64))) (+.f64 1 (*.f64 -1 k))) k)
(/.f64 (pow.f64 (exp.f64 (-.f64 1 k)) (+.f64 (log.f64 n) (log.f64 (*.f64 2 (PI.f64))))) k)
(/.f64 (pow.f64 (exp.f64 (-.f64 1 k)) (log.f64 (.f64 n (.f64 2 (PI.f64))))) k)
(/.f64 (pow.f64 (.f64 n (.f64 2 (PI.f64))) (-.f64 1 k)) k)
(/.f64 (pow.f64 (.f64 2 (.f64 n (PI.f64))) (+.f64 1 (*.f64 -1 k))) k)
(/.f64 (pow.f64 (exp.f64 (-.f64 1 k)) (+.f64 (log.f64 n) (log.f64 (*.f64 2 (PI.f64))))) k)
(/.f64 (pow.f64 (exp.f64 (-.f64 1 k)) (log.f64 (.f64 n (.f64 2 (PI.f64))))) k)
(/.f64 (pow.f64 (.f64 n (.f64 2 (PI.f64))) (-.f64 1 k)) k)
(/.f64 (pow.f64 (.f64 2 (.f64 n (PI.f64))) (+.f64 1 (*.f64 -1 k))) k)
(/.f64 (pow.f64 (exp.f64 (-.f64 1 k)) (+.f64 (log.f64 n) (log.f64 (*.f64 2 (PI.f64))))) k)
(/.f64 (pow.f64 (exp.f64 (-.f64 1 k)) (log.f64 (.f64 n (.f64 2 (PI.f64))))) k)
(/.f64 (pow.f64 (.f64 n (.f64 2 (PI.f64))) (-.f64 1 k)) k)

localize27.0ms (0.3%)

Local error

Found 8 expressions with local error:

New	Error	Program
	0.2b	(*.f64 (PI.f64) n)
	0.2b	(/.f64 (sqrt.f64 k) (sqrt.f64 (pow.f64 (.f64 2 (.f64 (PI.f64) n)) (-.f64 1 k))))
	0.2b	(/.f64 1 (/.f64 (sqrt.f64 k) (sqrt.f64 (pow.f64 (.f64 2 (.f64 (PI.f64) n)) (-.f64 1 k)))))
	0.1b	(sqrt.f64 (pow.f64 (.f64 2 (.f64 (PI.f64) n)) (-.f64 1 k)))
✓	0.2b	(/.f64 1 (/.f64 (sqrt.f64 k) (sqrt.f64 (pow.f64 (.f64 2 (.f64 (PI.f64) n)) (-.f64 1 k)))))
✓	0.2b	(/.f64 (sqrt.f64 k) (sqrt.f64 (pow.f64 (.f64 2 (.f64 (PI.f64) n)) (-.f64 1 k))))
	0.2b	(*.f64 (PI.f64) n)
	0.4b	(pow.f64 (.f64 2 (.f64 (PI.f64) n)) (-.f64 1 k))

Compiler

Compiled 67 to 38 computations (43.3% saved)

series15.0ms (0.2%)

Counts

2 → 24

Calls

12 calls:

Time	Variable		Point	Expression
4.0ms	k	@	-inf	(/.f64 (sqrt.f64 k) (sqrt.f64 (pow.f64 (.f64 2 (.f64 (PI.f64) n)) (-.f64 1 k))))
3.0ms	k	@	0	(/.f64 (sqrt.f64 k) (sqrt.f64 (pow.f64 (.f64 2 (.f64 (PI.f64) n)) (-.f64 1 k))))
2.0ms	n	@	0	(/.f64 (sqrt.f64 k) (sqrt.f64 (pow.f64 (.f64 2 (.f64 (PI.f64) n)) (-.f64 1 k))))
1.0ms	k	@	inf	(/.f64 (sqrt.f64 k) (sqrt.f64 (pow.f64 (.f64 2 (.f64 (PI.f64) n)) (-.f64 1 k))))
1.0ms	k	@	-inf	(/.f64 1 (/.f64 (sqrt.f64 k) (sqrt.f64 (pow.f64 (.f64 2 (.f64 (PI.f64) n)) (-.f64 1 k)))))

rewrite71.0ms (0.8%)

Algorithm

1×	batch-egg-rewrite

Rules

770×	`log-prod_binary64`
379×	`pow2_binary64`
261×	`pow1/3_binary64`
257×	`expm1-udef_binary64`
256×	`log1p-udef_binary64`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	14	41
1	307	38
2	4013	38

Stop Event

1×	node limit

Counts

2 → 85

Calls

Call 1

Inputs
(/.f64 (sqrt.f64 k) (sqrt.f64 (pow.f64 (.f64 2 (.f64 (PI.f64) n)) (-.f64 1 k))))
(/.f64 1 (/.f64 (sqrt.f64 k) (sqrt.f64 (pow.f64 (.f64 2 (.f64 (PI.f64) n)) (-.f64 1 k)))))

Outputs

((#(struct:change #<rule egg-rr> (2) ((x +.f64 0 (sqrt.f64 (/.f64 k (pow.f64 (*.f64 2 (*.f64 (PI.f64) n)) (-.f64 1 k)))))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (log.f64 (pow.f64 (cbrt.f64 (exp.f64 (sqrt.f64 (/.f64 k (pow.f64 (*.f64 2 (*.f64 (PI.f64) n)) (-.f64 1 k)))))) 2)) (log.f64 (cbrt.f64 (exp.f64 (sqrt.f64 (/.f64 k (pow.f64 (*.f64 2 (*.f64 (PI.f64) n)) (-.f64 1 k))))))))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (log.f64 (sqrt.f64 (exp.f64 (sqrt.f64 (/.f64 k (pow.f64 (*.f64 2 (*.f64 (PI.f64) n)) (-.f64 1 k))))))) (log.f64 (sqrt.f64 (exp.f64 (sqrt.f64 (/.f64 k (pow.f64 (*.f64 2 (*.f64 (PI.f64) n)) (-.f64 1 k))))))))))) (#(struct:change #<rule egg-rr> (2) ((x -.f64 (exp.f64 (log1p.f64 (sqrt.f64 (/.f64 k (pow.f64 (*.f64 2 (*.f64 (PI.f64) n)) (-.f64 1 k)))))) 1)))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (sqrt.f64 k) (pow.f64 (pow.f64 (*.f64 2 (*.f64 (PI.f64) n)) (-.f64 1 k)) -1/2))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 1 (sqrt.f64 (/.f64 k (pow.f64 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((x pow.f64 (sqrt.f64 (/.f64 (pow.f64 (*.f64 2 (*.f64 (PI.f64) n)) (-.f64 1 k)) k)) -1)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (/.f64 k (pow.f64 (*.f64 2 (*.f64 (PI.f64) n)) (-.f64 1 k))) 1/2)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (pow.f64 (sqrt.f64 (/.f64 k (pow.f64 (*.f64 2 (*.f64 (PI.f64) n)) (-.f64 1 k)))) 3) 1/3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (cbrt.f64 (sqrt.f64 (/.f64 k (pow.f64 (*.f64 2 (*.f64 (PI.f64) n)) (-.f64 1 k))))) 3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (sqrt.f64 (sqrt.f64 (/.f64 k (pow.f64 (*.f64 2 (*.f64 (PI.f64) n)) (-.f64 1 k))))) 2)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (/.f64 (pow.f64 k 3/2) (pow.f64 (pow.f64 (*.f64 2 (*.f64 (PI.f64) n)) (-.f64 1 k)) 3/2)) 1/3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (/.f64 (sqrt.f64 (/.f64 (pow.f64 (*.f64 2 (*.f64 (PI.f64) n)) (-.f64 1 k)) k)) 1) -1)))) (#(struct:change #<rule egg-rr> (2) ((x neg.f64 (/.f64 (sqrt.f64 k) (neg.f64 (sqrt.f64 (pow.f64 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((#(struct:change #<rule egg-rr> (2) ((x +.f64 0 (sqrt.f64 (/.f64 (pow.f64 (*.f64 2 (*.f64 (PI.f64) n)) (-.f64 1 k)) k)))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (log.f64 (pow.f64 (cbrt.f64 (exp.f64 (sqrt.f64 (/.f64 (pow.f64 (*.f64 2 (*.f64 (PI.f64) n)) (-.f64 1 k)) k)))) 2)) (log.f64 (cbrt.f64 (exp.f64 (sqrt.f64 (/.f64 (pow.f64 (*.f64 2 (*.f64 (PI.f64) n)) (-.f64 1 k)) k))))))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (log.f64 (sqrt.f64 (exp.f64 (sqrt.f64 (/.f64 (pow.f64 (*.f64 2 (*.f64 (PI.f64) n)) (-.f64 1 k)) k))))) (log.f64 (sqrt.f64 (exp.f64 (sqrt.f64 (/.f64 (pow.f64 (*.f64 2 (*.f64 (PI.f64) n)) (-.f64 1 k)) k))))))))) (#(struct:change #<rule egg-rr> (2) ((x -.f64 (exp.f64 (log1p.f64 (sqrt.f64 (/.f64 (pow.f64 (*.f64 2 (*.f64 (PI.f64) n)) (-.f64 1 k)) k)))) 1)))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 1 (sqrt.f64 (/.f64 (pow.f64 (*.f64 2 (*.f64 (PI.f64) n)) (-.f64 1 k)) k)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (sqrt.f64 (pow.f64 (*.f64 2 (*.f64 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((x *.f64 (pow.f64 k -1/2) (sqrt.f64 (pow.f64 (*.f64 2 (*.f64 (PI.f64) n)) (-.f64 1 k))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (pow.f64 k -1/2) (/.f64 1 (pow.f64 (pow.f64 (*.f64 2 (*.f64 (PI.f64) n)) (-.f64 1 k)) -1/2)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (/.f64 1 (cbrt.f64 (/.f64 k (pow.f64 (*.f64 2 (*.f64 (PI.f64) n)) (-.f64 1 k))))) (cbrt.f64 (sqrt.f64 (/.f64 (pow.f64 (*.f64 2 (*.f64 (PI.f64) n)) (-.f64 1 k)) k))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (/.f64 (cbrt.f64 (pow.f64 (*.f64 2 (*.f64 (PI.f64) n)) (-.f64 1 k))) 1) (/.f64 (cbrt.f64 (sqrt.f64 (pow.f64 (*.f64 2 (*.f64 (PI.f64) n)) (-.f64 1 k)))) (sqrt.f64 k)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (/.f64 (pow.f64 (pow.f64 (*.f64 2 (*.f64 (PI.f64) n)) (-.f64 1 k)) 1/4) 1) (/.f64 (pow.f64 (pow.f64 (*.f64 2 (*.f64 (PI.f64) n)) (-.f64 1 k)) 1/4) (sqrt.f64 k)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (/.f64 1 (cbrt.f64 k)) (/.f64 (sqrt.f64 (pow.f64 (*.f64 2 (*.f64 (PI.f64) 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k))))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (log.f64 (sqrt.f64 (/.f64 (pow.f64 (*.f64 2 (*.f64 (PI.f64) n)) (-.f64 1 k)) k))))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (*.f64 (log.f64 (sqrt.f64 (/.f64 k (pow.f64 (*.f64 2 (*.f64 (PI.f64) n)) (-.f64 1 k))))) -1))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (*.f64 (log.f64 (sqrt.f64 (/.f64 (pow.f64 (*.f64 2 (*.f64 (PI.f64) n)) (-.f64 1 k)) k))) 1))))) (#(struct:change #<rule egg-rr> (2) ((x log1p.f64 (expm1.f64 (sqrt.f64 (/.f64 (pow.f64 (*.f64 2 (*.f64 (PI.f64) n)) (-.f64 1 k)) k))))))))

simplify42.0ms (0.4%)

Algorithm

1×	egg-herbie

Rules

543×	`exp-sum_binary64`
410×	`unsub-neg_binary64`
308×	`associate--r+_binary64`
308×	`fma-neg_binary64`
305×	`fma-def_binary64`

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	41	600
1	89	600
2	235	600
3	821	456
4	3350	456

Stop Event

1×	node limit

Counts

109 → 93

Calls

Call 1

Inputs
(sqrt.f64 (/.f64 k (exp.f64 (.f64 (-.f64 1 k) (+.f64 (log.f64 n) (log.f64 (.f64 2 (PI.f64))))))))
(sqrt.f64 (/.f64 k (exp.f64 (.f64 (-.f64 1 k) (+.f64 (log.f64 n) (log.f64 (.f64 2 (PI.f64))))))))
(sqrt.f64 (/.f64 k (exp.f64 (.f64 (-.f64 1 k) (+.f64 (log.f64 n) (log.f64 (.f64 2 (PI.f64))))))))
(sqrt.f64 (/.f64 k (exp.f64 (.f64 (-.f64 1 k) (+.f64 (log.f64 n) (log.f64 (.f64 2 (PI.f64))))))))
(sqrt.f64 (/.f64 k (exp.f64 (.f64 (-.f64 1 k) (+.f64 (.f64 -1 (log.f64 (/.f64 1 n))) (log.f64 (*.f64 2 (PI.f64))))))))
(sqrt.f64 (/.f64 k (exp.f64 (.f64 (-.f64 1 k) (+.f64 (.f64 -1 (log.f64 (/.f64 1 n))) (log.f64 (*.f64 2 (PI.f64))))))))
(sqrt.f64 (/.f64 k (exp.f64 (.f64 (-.f64 1 k) (+.f64 (.f64 -1 (log.f64 (/.f64 1 n))) (log.f64 (*.f64 2 (PI.f64))))))))
(sqrt.f64 (/.f64 k (exp.f64 (.f64 (-.f64 1 k) (+.f64 (.f64 -1 (log.f64 (/.f64 1 n))) (log.f64 (*.f64 2 (PI.f64))))))))
(sqrt.f64 (/.f64 k (exp.f64 (.f64 (-.f64 1 k) (+.f64 (.f64 -1 (log.f64 (/.f64 -1 n))) (log.f64 (*.f64 -2 (PI.f64))))))))
(sqrt.f64 (/.f64 k (exp.f64 (.f64 (-.f64 1 k) (+.f64 (.f64 -1 (log.f64 (/.f64 -1 n))) (log.f64 (*.f64 -2 (PI.f64))))))))
(sqrt.f64 (/.f64 k (exp.f64 (.f64 (-.f64 1 k) (+.f64 (.f64 -1 (log.f64 (/.f64 -1 n))) (log.f64 (*.f64 -2 (PI.f64))))))))
(sqrt.f64 (/.f64 k (exp.f64 (.f64 (-.f64 1 k) (+.f64 (.f64 -1 (log.f64 (/.f64 -1 n))) (log.f64 (*.f64 -2 (PI.f64))))))))
(sqrt.f64 (/.f64 (exp.f64 (.f64 (-.f64 1 k) (+.f64 (log.f64 n) (log.f64 (.f64 2 (PI.f64)))))) k))
(sqrt.f64 (/.f64 (exp.f64 (.f64 (-.f64 1 k) (+.f64 (log.f64 n) (log.f64 (.f64 2 (PI.f64)))))) k))
(sqrt.f64 (/.f64 (exp.f64 (.f64 (-.f64 1 k) (+.f64 (log.f64 n) (log.f64 (.f64 2 (PI.f64)))))) k))
(sqrt.f64 (/.f64 (exp.f64 (.f64 (-.f64 1 k) (+.f64 (log.f64 n) (log.f64 (.f64 2 (PI.f64)))))) k))
(sqrt.f64 (/.f64 (exp.f64 (.f64 (-.f64 1 k) (+.f64 (.f64 -1 (log.f64 (/.f64 1 n))) (log.f64 (*.f64 2 (PI.f64)))))) k))
(sqrt.f64 (/.f64 (exp.f64 (.f64 (-.f64 1 k) (+.f64 (.f64 -1 (log.f64 (/.f64 1 n))) (log.f64 (*.f64 2 (PI.f64)))))) k))
(sqrt.f64 (/.f64 (exp.f64 (.f64 (-.f64 1 k) (+.f64 (.f64 -1 (log.f64 (/.f64 1 n))) (log.f64 (*.f64 2 (PI.f64)))))) k))
(sqrt.f64 (/.f64 (exp.f64 (.f64 (-.f64 1 k) (+.f64 (.f64 -1 (log.f64 (/.f64 1 n))) (log.f64 (*.f64 2 (PI.f64)))))) k))
(sqrt.f64 (/.f64 (exp.f64 (.f64 (-.f64 1 k) (+.f64 (.f64 -1 (log.f64 (/.f64 -1 n))) (log.f64 (*.f64 -2 (PI.f64)))))) k))
(sqrt.f64 (/.f64 (exp.f64 (.f64 (-.f64 1 k) (+.f64 (.f64 -1 (log.f64 (/.f64 -1 n))) (log.f64 (*.f64 -2 (PI.f64)))))) k))
(sqrt.f64 (/.f64 (exp.f64 (.f64 (-.f64 1 k) (+.f64 (.f64 -1 (log.f64 (/.f64 -1 n))) (log.f64 (*.f64 -2 (PI.f64)))))) k))
(sqrt.f64 (/.f64 (exp.f64 (.f64 (-.f64 1 k) (+.f64 (.f64 -1 (log.f64 (/.f64 -1 n))) (log.f64 (*.f64 -2 (PI.f64)))))) k))

Outputs
(sqrt.f64 (/.f64 k (exp.f64 (.f64 (-.f64 1 k) (+.f64 (log.f64 n) (log.f64 (.f64 2 (PI.f64))))))))
(sqrt.f64 (/.f64 k (pow.f64 (exp.f64 (-.f64 1 k)) (+.f64 (log.f64 n) (log.f64 (*.f64 2 (PI.f64)))))))
(sqrt.f64 (/.f64 k (.f64 (pow.f64 (.f64 2 (PI.f64)) (-.f64 1 k)) (pow.f64 n (-.f64 1 k)))))
(sqrt.f64 (/.f64 k (pow.f64 (.f64 2 (.f64 n (PI.f64))) (-.f64 1 k))))
(sqrt.f64 (/.f64 k (exp.f64 (.f64 (-.f64 1 k) (+.f64 (log.f64 n) (log.f64 (.f64 2 (PI.f64))))))))
(sqrt.f64 (/.f64 k (pow.f64 (exp.f64 (-.f64 1 k)) (+.f64 (log.f64 n) (log.f64 (*.f64 2 (PI.f64)))))))
(sqrt.f64 (/.f64 k (.f64 (pow.f64 (.f64 2 (PI.f64)) (-.f64 1 k)) (pow.f64 n (-.f64 1 k)))))
(sqrt.f64 (/.f64 k (pow.f64 (.f64 2 (.f64 n (PI.f64))) (-.f64 1 k))))
(sqrt.f64 (/.f64 k (exp.f64 (.f64 (-.f64 1 k) (+.f64 (log.f64 n) (log.f64 (.f64 2 (PI.f64))))))))
(sqrt.f64 (/.f64 k (pow.f64 (exp.f64 (-.f64 1 k)) (+.f64 (log.f64 n) (log.f64 (*.f64 2 (PI.f64)))))))
(sqrt.f64 (/.f64 k (.f64 (pow.f64 (.f64 2 (PI.f64)) (-.f64 1 k)) (pow.f64 n (-.f64 1 k)))))
(sqrt.f64 (/.f64 k (pow.f64 (.f64 2 (.f64 n (PI.f64))) (-.f64 1 k))))
(sqrt.f64 (/.f64 k (exp.f64 (.f64 (-.f64 1 k) (+.f64 (log.f64 n) (log.f64 (.f64 2 (PI.f64))))))))
(sqrt.f64 (/.f64 k (pow.f64 (exp.f64 (-.f64 1 k)) (+.f64 (log.f64 n) (log.f64 (*.f64 2 (PI.f64)))))))
(sqrt.f64 (/.f64 k (.f64 (pow.f64 (.f64 2 (PI.f64)) (-.f64 1 k)) (pow.f64 n (-.f64 1 k)))))
(sqrt.f64 (/.f64 k (pow.f64 (.f64 2 (.f64 n (PI.f64))) (-.f64 1 k))))
(sqrt.f64 (/.f64 k (exp.f64 (.f64 (-.f64 1 k) (+.f64 (.f64 -1 (log.f64 (/.f64 1 n))) (log.f64 (*.f64 2 (PI.f64))))))))
(sqrt.f64 (/.f64 k (pow.f64 (exp.f64 (-.f64 1 k)) (+.f64 (log.f64 n) (log.f64 (*.f64 2 (PI.f64)))))))
(sqrt.f64 (/.f64 k (.f64 (pow.f64 (.f64 2 (PI.f64)) (-.f64 1 k)) (pow.f64 n (-.f64 1 k)))))
(sqrt.f64 (/.f64 k (pow.f64 (.f64 2 (.f64 n (PI.f64))) (-.f64 1 k))))
(sqrt.f64 (/.f64 k (exp.f64 (.f64 (-.f64 1 k) (+.f64 (.f64 -1 (log.f64 (/.f64 1 n))) (log.f64 (*.f64 2 (PI.f64))))))))
(sqrt.f64 (/.f64 k (pow.f64 (exp.f64 (-.f64 1 k)) (+.f64 (log.f64 n) (log.f64 (*.f64 2 (PI.f64)))))))
(sqrt.f64 (/.f64 k (.f64 (pow.f64 (.f64 2 (PI.f64)) (-.f64 1 k)) (pow.f64 n (-.f64 1 k)))))
(sqrt.f64 (/.f64 k (pow.f64 (.f64 2 (.f64 n (PI.f64))) (-.f64 1 k))))
(sqrt.f64 (/.f64 k (exp.f64 (.f64 (-.f64 1 k) (+.f64 (.f64 -1 (log.f64 (/.f64 1 n))) (log.f64 (*.f64 2 (PI.f64))))))))
(sqrt.f64 (/.f64 k (pow.f64 (exp.f64 (-.f64 1 k)) (+.f64 (log.f64 n) (log.f64 (*.f64 2 (PI.f64)))))))
(sqrt.f64 (/.f64 k (.f64 (pow.f64 (.f64 2 (PI.f64)) (-.f64 1 k)) (pow.f64 n (-.f64 1 k)))))
(sqrt.f64 (/.f64 k (pow.f64 (.f64 2 (.f64 n (PI.f64))) (-.f64 1 k))))
(sqrt.f64 (/.f64 k (exp.f64 (.f64 (-.f64 1 k) (+.f64 (.f64 -1 (log.f64 (/.f64 1 n))) (log.f64 (*.f64 2 (PI.f64))))))))
(sqrt.f64 (/.f64 k (pow.f64 (exp.f64 (-.f64 1 k)) (+.f64 (log.f64 n) (log.f64 (*.f64 2 (PI.f64)))))))
(sqrt.f64 (/.f64 k (.f64 (pow.f64 (.f64 2 (PI.f64)) (-.f64 1 k)) (pow.f64 n (-.f64 1 k)))))
(sqrt.f64 (/.f64 k (pow.f64 (.f64 2 (.f64 n (PI.f64))) (-.f64 1 k))))
(sqrt.f64 (/.f64 k (exp.f64 (.f64 (-.f64 1 k) (+.f64 (.f64 -1 (log.f64 (/.f64 -1 n))) (log.f64 (*.f64 -2 (PI.f64))))))))
(sqrt.f64 (/.f64 k (pow.f64 (exp.f64 (-.f64 1 k)) (+.f64 (log.f64 n) (log.f64 (*.f64 2 (PI.f64)))))))
(sqrt.f64 (/.f64 k (.f64 (pow.f64 (.f64 2 (PI.f64)) (-.f64 1 k)) (pow.f64 n (-.f64 1 k)))))
(sqrt.f64 (/.f64 k (pow.f64 (.f64 2 (.f64 n (PI.f64))) (-.f64 1 k))))
(sqrt.f64 (/.f64 k (exp.f64 (.f64 (-.f64 1 k) (+.f64 (.f64 -1 (log.f64 (/.f64 -1 n))) (log.f64 (*.f64 -2 (PI.f64))))))))
(sqrt.f64 (/.f64 k (pow.f64 (exp.f64 (-.f64 1 k)) (+.f64 (log.f64 n) (log.f64 (*.f64 2 (PI.f64)))))))
(sqrt.f64 (/.f64 k (.f64 (pow.f64 (.f64 2 (PI.f64)) (-.f64 1 k)) (pow.f64 n (-.f64 1 k)))))
(sqrt.f64 (/.f64 k (pow.f64 (.f64 2 (.f64 n (PI.f64))) (-.f64 1 k))))
(sqrt.f64 (/.f64 k (exp.f64 (.f64 (-.f64 1 k) (+.f64 (.f64 -1 (log.f64 (/.f64 -1 n))) (log.f64 (*.f64 -2 (PI.f64))))))))
(sqrt.f64 (/.f64 k (pow.f64 (exp.f64 (-.f64 1 k)) (+.f64 (log.f64 n) (log.f64 (*.f64 2 (PI.f64)))))))
(sqrt.f64 (/.f64 k (.f64 (pow.f64 (.f64 2 (PI.f64)) (-.f64 1 k)) (pow.f64 n (-.f64 1 k)))))
(sqrt.f64 (/.f64 k (pow.f64 (.f64 2 (.f64 n (PI.f64))) (-.f64 1 k))))
(sqrt.f64 (/.f64 k (exp.f64 (.f64 (-.f64 1 k) (+.f64 (.f64 -1 (log.f64 (/.f64 -1 n))) (log.f64 (*.f64 -2 (PI.f64))))))))
(sqrt.f64 (/.f64 k (pow.f64 (exp.f64 (-.f64 1 k)) (+.f64 (log.f64 n) (log.f64 (*.f64 2 (PI.f64)))))))
(sqrt.f64 (/.f64 k (.f64 (pow.f64 (.f64 2 (PI.f64)) (-.f64 1 k)) (pow.f64 n (-.f64 1 k)))))
(sqrt.f64 (/.f64 k (pow.f64 (.f64 2 (.f64 n (PI.f64))) (-.f64 1 k))))
(sqrt.f64 (/.f64 (exp.f64 (.f64 (-.f64 1 k) (+.f64 (log.f64 n) (log.f64 (.f64 2 (PI.f64)))))) k))
(sqrt.f64 (/.f64 (pow.f64 (exp.f64 (-.f64 1 k)) (+.f64 (log.f64 n) (log.f64 (*.f64 2 (PI.f64))))) k))
(sqrt.f64 (/.f64 (.f64 (pow.f64 (.f64 2 (PI.f64)) (-.f64 1 k)) (pow.f64 n (-.f64 1 k))) k))
(sqrt.f64 (/.f64 (pow.f64 (.f64 2 (.f64 n (PI.f64))) (-.f64 1 k)) k))
(sqrt.f64 (/.f64 (exp.f64 (.f64 (-.f64 1 k) (+.f64 (log.f64 n) (log.f64 (.f64 2 (PI.f64)))))) k))
(sqrt.f64 (/.f64 (pow.f64 (exp.f64 (-.f64 1 k)) (+.f64 (log.f64 n) (log.f64 (*.f64 2 (PI.f64))))) k))
(sqrt.f64 (/.f64 (.f64 (pow.f64 (.f64 2 (PI.f64)) (-.f64 1 k)) (pow.f64 n (-.f64 1 k))) k))
(sqrt.f64 (/.f64 (pow.f64 (.f64 2 (.f64 n (PI.f64))) (-.f64 1 k)) k))
(sqrt.f64 (/.f64 (exp.f64 (.f64 (-.f64 1 k) (+.f64 (log.f64 n) (log.f64 (.f64 2 (PI.f64)))))) k))
(sqrt.f64 (/.f64 (pow.f64 (exp.f64 (-.f64 1 k)) (+.f64 (log.f64 n) (log.f64 (*.f64 2 (PI.f64))))) k))
(sqrt.f64 (/.f64 (.f64 (pow.f64 (.f64 2 (PI.f64)) (-.f64 1 k)) (pow.f64 n (-.f64 1 k))) k))
(sqrt.f64 (/.f64 (pow.f64 (.f64 2 (.f64 n (PI.f64))) (-.f64 1 k)) k))
(sqrt.f64 (/.f64 (exp.f64 (.f64 (-.f64 1 k) (+.f64 (log.f64 n) (log.f64 (.f64 2 (PI.f64)))))) k))
(sqrt.f64 (/.f64 (pow.f64 (exp.f64 (-.f64 1 k)) (+.f64 (log.f64 n) (log.f64 (*.f64 2 (PI.f64))))) k))
(sqrt.f64 (/.f64 (.f64 (pow.f64 (.f64 2 (PI.f64)) (-.f64 1 k)) (pow.f64 n (-.f64 1 k))) k))
(sqrt.f64 (/.f64 (pow.f64 (.f64 2 (.f64 n (PI.f64))) (-.f64 1 k)) k))
(sqrt.f64 (/.f64 (exp.f64 (.f64 (-.f64 1 k) (+.f64 (.f64 -1 (log.f64 (/.f64 1 n))) (log.f64 (*.f64 2 (PI.f64)))))) k))
(sqrt.f64 (/.f64 (pow.f64 (exp.f64 (-.f64 1 k)) (+.f64 (log.f64 n) (log.f64 (*.f64 2 (PI.f64))))) k))
(sqrt.f64 (/.f64 (.f64 (pow.f64 (.f64 2 (PI.f64)) (-.f64 1 k)) (pow.f64 n (-.f64 1 k))) k))
(sqrt.f64 (/.f64 (pow.f64 (.f64 2 (.f64 n (PI.f64))) (-.f64 1 k)) k))
(sqrt.f64 (/.f64 (exp.f64 (.f64 (-.f64 1 k) (+.f64 (.f64 -1 (log.f64 (/.f64 1 n))) (log.f64 (*.f64 2 (PI.f64)))))) k))
(sqrt.f64 (/.f64 (pow.f64 (exp.f64 (-.f64 1 k)) (+.f64 (log.f64 n) (log.f64 (*.f64 2 (PI.f64))))) k))
(sqrt.f64 (/.f64 (.f64 (pow.f64 (.f64 2 (PI.f64)) (-.f64 1 k)) (pow.f64 n (-.f64 1 k))) k))
(sqrt.f64 (/.f64 (pow.f64 (.f64 2 (.f64 n (PI.f64))) (-.f64 1 k)) k))
(sqrt.f64 (/.f64 (exp.f64 (.f64 (-.f64 1 k) (+.f64 (.f64 -1 (log.f64 (/.f64 1 n))) (log.f64 (*.f64 2 (PI.f64)))))) k))
(sqrt.f64 (/.f64 (pow.f64 (exp.f64 (-.f64 1 k)) (+.f64 (log.f64 n) (log.f64 (*.f64 2 (PI.f64))))) k))
(sqrt.f64 (/.f64 (.f64 (pow.f64 (.f64 2 (PI.f64)) (-.f64 1 k)) (pow.f64 n (-.f64 1 k))) k))
(sqrt.f64 (/.f64 (pow.f64 (.f64 2 (.f64 n (PI.f64))) (-.f64 1 k)) k))
(sqrt.f64 (/.f64 (exp.f64 (.f64 (-.f64 1 k) (+.f64 (.f64 -1 (log.f64 (/.f64 1 n))) (log.f64 (*.f64 2 (PI.f64)))))) k))
(sqrt.f64 (/.f64 (pow.f64 (exp.f64 (-.f64 1 k)) (+.f64 (log.f64 n) (log.f64 (*.f64 2 (PI.f64))))) k))
(sqrt.f64 (/.f64 (.f64 (pow.f64 (.f64 2 (PI.f64)) (-.f64 1 k)) (pow.f64 n (-.f64 1 k))) k))
(sqrt.f64 (/.f64 (pow.f64 (.f64 2 (.f64 n (PI.f64))) (-.f64 1 k)) k))
(sqrt.f64 (/.f64 (exp.f64 (.f64 (-.f64 1 k) (+.f64 (.f64 -1 (log.f64 (/.f64 -1 n))) (log.f64 (*.f64 -2 (PI.f64)))))) k))
(sqrt.f64 (/.f64 (pow.f64 (exp.f64 (-.f64 1 k)) (+.f64 (log.f64 n) (log.f64 (*.f64 2 (PI.f64))))) k))
(sqrt.f64 (/.f64 (.f64 (pow.f64 (.f64 2 (PI.f64)) (-.f64 1 k)) (pow.f64 n (-.f64 1 k))) k))
(sqrt.f64 (/.f64 (pow.f64 (.f64 2 (.f64 n (PI.f64))) (-.f64 1 k)) k))
(sqrt.f64 (/.f64 (exp.f64 (.f64 (-.f64 1 k) (+.f64 (.f64 -1 (log.f64 (/.f64 -1 n))) (log.f64 (*.f64 -2 (PI.f64)))))) k))
(sqrt.f64 (/.f64 (pow.f64 (exp.f64 (-.f64 1 k)) (+.f64 (log.f64 n) (log.f64 (*.f64 2 (PI.f64))))) k))
(sqrt.f64 (/.f64 (.f64 (pow.f64 (.f64 2 (PI.f64)) (-.f64 1 k)) (pow.f64 n (-.f64 1 k))) k))
(sqrt.f64 (/.f64 (pow.f64 (.f64 2 (.f64 n (PI.f64))) (-.f64 1 k)) k))
(sqrt.f64 (/.f64 (exp.f64 (.f64 (-.f64 1 k) (+.f64 (.f64 -1 (log.f64 (/.f64 -1 n))) (log.f64 (*.f64 -2 (PI.f64)))))) k))
(sqrt.f64 (/.f64 (pow.f64 (exp.f64 (-.f64 1 k)) (+.f64 (log.f64 n) (log.f64 (*.f64 2 (PI.f64))))) k))
(sqrt.f64 (/.f64 (.f64 (pow.f64 (.f64 2 (PI.f64)) (-.f64 1 k)) (pow.f64 n (-.f64 1 k))) k))
(sqrt.f64 (/.f64 (pow.f64 (.f64 2 (.f64 n (PI.f64))) (-.f64 1 k)) k))
(sqrt.f64 (/.f64 (exp.f64 (.f64 (-.f64 1 k) (+.f64 (.f64 -1 (log.f64 (/.f64 -1 n))) (log.f64 (*.f64 -2 (PI.f64)))))) k))
(sqrt.f64 (/.f64 (pow.f64 (exp.f64 (-.f64 1 k)) (+.f64 (log.f64 n) (log.f64 (*.f64 2 (PI.f64))))) k))
(sqrt.f64 (/.f64 (.f64 (pow.f64 (.f64 2 (PI.f64)) (-.f64 1 k)) (pow.f64 n (-.f64 1 k))) k))
(sqrt.f64 (/.f64 (pow.f64 (.f64 2 (.f64 n (PI.f64))) (-.f64 1 k)) k))

localize35.0ms (0.4%)

Local error

Found 8 expressions with local error:

New	Error	Program
	0.4b	(pow.f64 (.f64 2 (.f64 (PI.f64) n)) (-.f64 1 k))
	0.2b	(*.f64 (PI.f64) n)
	0.2b	(log.f64 (sqrt.f64 (/.f64 (pow.f64 (.f64 2 (.f64 (PI.f64) n)) (-.f64 1 k)) k)))
	0.1b	(/.f64 (pow.f64 (.f64 2 (.f64 (PI.f64) n)) (-.f64 1 k)) k)
	0.2b	(*.f64 (PI.f64) n)
	0.4b	(pow.f64 (.f64 2 (.f64 (PI.f64) n)) (-.f64 1 k))
✓	3.2b	(exp.f64 (log.f64 (sqrt.f64 (/.f64 (pow.f64 (.f64 2 (.f64 (PI.f64) n)) (-.f64 1 k)) k))))
	9.0b	(sqrt.f64 (/.f64 (pow.f64 (.f64 2 (.f64 (PI.f64) n)) (-.f64 1 k)) k))

Compiler

Compiled 77 to 45 computations (41.6% saved)

series5.0ms (0.1%)

Counts

1 → 12

Calls

6 calls:

Time	Variable		Point	Expression
2.0ms	n	@	0	(exp.f64 (log.f64 (sqrt.f64 (/.f64 (pow.f64 (.f64 2 (.f64 (PI.f64) n)) (-.f64 1 k)) k))))
1.0ms	k	@	0	(exp.f64 (log.f64 (sqrt.f64 (/.f64 (pow.f64 (.f64 2 (.f64 (PI.f64) n)) (-.f64 1 k)) k))))
1.0ms	k	@	-inf	(exp.f64 (log.f64 (sqrt.f64 (/.f64 (pow.f64 (.f64 2 (.f64 (PI.f64) n)) (-.f64 1 k)) k))))
1.0ms	k	@	inf	(exp.f64 (log.f64 (sqrt.f64 (/.f64 (pow.f64 (.f64 2 (.f64 (PI.f64) n)) (-.f64 1 k)) k))))
0.0ms	n	@	inf	(exp.f64 (log.f64 (sqrt.f64 (/.f64 (pow.f64 (.f64 2 (.f64 (PI.f64) n)) (-.f64 1 k)) k))))

rewrite57.0ms (0.6%)

Algorithm

1×	batch-egg-rewrite

Rules

694×	`log-prod_binary64`
467×	`pow-unpow_binary64`
352×	`pow2_binary64`
240×	`pow1/3_binary64`
236×	`expm1-udef_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	14	19
1	283	19
2	3568	19

Stop Event

1×	node limit

Counts

1 → 50

Calls

Call 1

Inputs
(exp.f64 (log.f64 (sqrt.f64 (/.f64 (pow.f64 (.f64 2 (.f64 (PI.f64) n)) (-.f64 1 k)) k))))

Outputs

((#(struct:change #<rule egg-rr> (2) ((x +.f64 0 (sqrt.f64 (/.f64 (pow.f64 (*.f64 (PI.f64) (*.f64 n 2)) (-.f64 1 k)) k)))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (log.f64 (pow.f64 (cbrt.f64 (exp.f64 (sqrt.f64 (/.f64 (pow.f64 (*.f64 (PI.f64) (*.f64 n 2)) (-.f64 1 k)) k)))) 2)) (log.f64 (cbrt.f64 (exp.f64 (sqrt.f64 (/.f64 (pow.f64 (*.f64 (PI.f64) (*.f64 n 2)) (-.f64 1 k)) k))))))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (log.f64 (sqrt.f64 (exp.f64 (sqrt.f64 (/.f64 (pow.f64 (*.f64 (PI.f64) (*.f64 n 2)) (-.f64 1 k)) k))))) (log.f64 (sqrt.f64 (exp.f64 (sqrt.f64 (/.f64 (pow.f64 (*.f64 (PI.f64) (*.f64 n 2)) (-.f64 1 k)) k))))))))) (#(struct:change #<rule egg-rr> (2) ((x -.f64 (exp.f64 (log1p.f64 (sqrt.f64 (/.f64 (pow.f64 (*.f64 (PI.f64) (*.f64 n 2)) (-.f64 1 k)) k)))) 1)))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 1 (sqrt.f64 (/.f64 (pow.f64 (*.f64 (PI.f64) (*.f64 n 2)) (-.f64 1 k)) k)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (sqrt.f64 (/.f64 (pow.f64 (*.f64 (PI.f64) (*.f64 n 2)) (-.f64 1 k)) k)) 1)))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (cbrt.f64 (sqrt.f64 (/.f64 (pow.f64 (*.f64 (PI.f64) (*.f64 n 2)) (-.f64 1 k)) k))) (cbrt.f64 (/.f64 (pow.f64 (*.f64 (PI.f64) (*.f64 n 2)) (-.f64 1 k)) k)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (cbrt.f64 (/.f64 (pow.f64 (*.f64 (PI.f64) (*.f64 n 2)) (-.f64 1 k)) k)) (cbrt.f64 (sqrt.f64 (/.f64 (pow.f64 (*.f64 (PI.f64) (*.f64 n 2)) (-.f64 1 k)) k))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (pow.f64 (/.f64 (pow.f64 (*.f64 (PI.f64) (*.f64 n 2)) (-.f64 1 k)) k) 1/4) (pow.f64 (/.f64 (pow.f64 (*.f64 (PI.f64) (*.f64 n 2)) (-.f64 1 k)) k) 1/4))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (sqrt.f64 (pow.f64 (*.f64 (PI.f64) (*.f64 n 2)) (-.f64 1 k))) (sqrt.f64 (pow.f64 k -1)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (sqrt.f64 (pow.f64 (*.f64 (PI.f64) (*.f64 n 2)) (-.f64 1 k))) (/.f64 1 (sqrt.f64 k)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (sqrt.f64 (cbrt.f64 (pow.f64 (/.f64 (pow.f64 (*.f64 (PI.f64) (*.f64 n 2)) (-.f64 1 k)) k) 2))) (sqrt.f64 (cbrt.f64 (/.f64 (pow.f64 (*.f64 (PI.f64) (*.f64 n 2)) (-.f64 1 k)) k))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (pow.f64 1 1/2) (sqrt.f64 (/.f64 (pow.f64 (*.f64 (PI.f64) (*.f64 n 2)) (-.f64 1 k)) k)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (pow.f64 (E.f64) (*.f64 1/4 (log.f64 (/.f64 (pow.f64 (*.f64 (PI.f64) (*.f64 n 2)) (-.f64 1 k)) k)))) (pow.f64 (E.f64) (*.f64 1/4 (log.f64 (/.f64 (pow.f64 (*.f64 (PI.f64) (*.f64 n 2)) (-.f64 1 k)) k)))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (pow.f64 (E.f64) (log.f64 (cbrt.f64 (/.f64 (pow.f64 (*.f64 (PI.f64) (*.f64 n 2)) (-.f64 1 k)) k)))) (pow.f64 (E.f64) (log.f64 (cbrt.f64 (sqrt.f64 (/.f64 (pow.f64 (*.f64 (PI.f64) (*.f64 n 2)) (-.f64 1 k)) k))))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 1 (sqrt.f64 (/.f64 k (pow.f64 (*.f64 (PI.f64) (*.f64 n 2)) (-.f64 1 k)))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 1 (/.f64 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3/2) 1/3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (cbrt.f64 (sqrt.f64 (/.f64 (pow.f64 (*.f64 (PI.f64) (*.f64 n 2)) (-.f64 1 k)) k))) 3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (pow.f64 (/.f64 (pow.f64 (*.f64 (PI.f64) (*.f64 n 2)) (-.f64 1 k)) k) 1/4) 2)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (exp.f64 (sqrt.f64 (log.f64 (sqrt.f64 (/.f64 (pow.f64 (*.f64 (PI.f64) (*.f64 n 2)) (-.f64 1 k)) k))))) (sqrt.f64 (log.f64 (sqrt.f64 (/.f64 (pow.f64 (*.f64 (PI.f64) (*.f64 n 2)) (-.f64 1 k)) k)))))))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (exp.f64 (pow.f64 (cbrt.f64 (log.f64 (sqrt.f64 (/.f64 (pow.f64 (*.f64 (PI.f64) (*.f64 n 2)) (-.f64 1 k)) k)))) 2)) (cbrt.f64 (log.f64 (sqrt.f64 (/.f64 (pow.f64 (*.f64 (PI.f64) (*.f64 n 2)) (-.f64 1 k)) k)))))))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (sqrt.f64 (E.f64)) (log.f64 (/.f64 (pow.f64 (*.f64 (PI.f64) (*.f64 n 2)) (-.f64 1 k)) k)))))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (sqrt.f64 (/.f64 k (pow.f64 (*.f64 (PI.f64) (*.f64 n 2)) (-.f64 1 k)))) -1)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (/.f64 (sqrt.f64 k) (sqrt.f64 (pow.f64 (*.f64 (PI.f64) (*.f64 n 2)) (-.f64 1 k)))) -1)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (pow.f64 (E.f64) (cbrt.f64 (log.f64 (sqrt.f64 (/.f64 (pow.f64 (*.f64 (PI.f64) (*.f64 n 2)) (-.f64 1 k)) k))))) (pow.f64 (cbrt.f64 (log.f64 (sqrt.f64 (/.f64 (pow.f64 (*.f64 (PI.f64) (*.f64 n 2)) (-.f64 1 k)) k)))) 2))))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (pow.f64 (E.f64) (pow.f64 (cbrt.f64 (log.f64 (sqrt.f64 (/.f64 (pow.f64 (*.f64 (PI.f64) (*.f64 n 2)) (-.f64 1 k)) k)))) 2)) (cbrt.f64 (log.f64 (sqrt.f64 (/.f64 (pow.f64 (*.f64 (PI.f64) (*.f64 n 2)) (-.f64 1 k)) k)))))))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (pow.f64 (E.f64) (sqrt.f64 (log.f64 (sqrt.f64 (/.f64 (pow.f64 (*.f64 (PI.f64) (*.f64 n 2)) (-.f64 1 k)) k))))) (sqrt.f64 (log.f64 (sqrt.f64 (/.f64 (pow.f64 (*.f64 (PI.f64) (*.f64 n 2)) (-.f64 1 k)) k)))))))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (pow.f64 (exp.f64 (sqrt.f64 (log.f64 (sqrt.f64 (/.f64 (pow.f64 (*.f64 (PI.f64) (*.f64 n 2)) (-.f64 1 k)) k))))) 1) (sqrt.f64 (log.f64 (sqrt.f64 (/.f64 (pow.f64 (*.f64 (PI.f64) (*.f64 n 2)) (-.f64 1 k)) k)))))))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (pow.f64 (exp.f64 (sqrt.f64 (log.f64 (sqrt.f64 (/.f64 (pow.f64 (*.f64 (PI.f64) (*.f64 n 2)) (-.f64 1 k)) k))))) (cbrt.f64 (log.f64 (sqrt.f64 (/.f64 (pow.f64 (*.f64 (PI.f64) (*.f64 n 2)) (-.f64 1 k)) k))))) (cbrt.f64 (sqrt.f64 (log.f64 (sqrt.f64 (/.f64 (pow.f64 (*.f64 (PI.f64) (*.f64 n 2)) (-.f64 1 k)) k))))))))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (pow.f64 (exp.f64 (sqrt.f64 (log.f64 (sqrt.f64 (/.f64 (pow.f64 (*.f64 (PI.f64) (*.f64 n 2)) (-.f64 1 k)) k))))) (sqrt.f64 (sqrt.f64 (log.f64 (sqrt.f64 (/.f64 (pow.f64 (*.f64 (PI.f64) (*.f64 n 2)) (-.f64 1 k)) k)))))) (sqrt.f64 (sqrt.f64 (log.f64 (sqrt.f64 (/.f64 (pow.f64 (*.f64 (PI.f64) (*.f64 n 2)) (-.f64 1 k)) k))))))))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (pow.f64 (exp.f64 (sqrt.f64 (log.f64 (sqrt.f64 (/.f64 (pow.f64 (*.f64 (PI.f64) (*.f64 n 2)) (-.f64 1 k)) k))))) (sqrt.f64 (pow.f64 (cbrt.f64 (log.f64 (sqrt.f64 (/.f64 (pow.f64 (*.f64 (PI.f64) (*.f64 n 2)) (-.f64 1 k)) k)))) 2))) (sqrt.f64 (cbrt.f64 (log.f64 (sqrt.f64 (/.f64 (pow.f64 (*.f64 (PI.f64) (*.f64 n 2)) (-.f64 1 k)) k))))))))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (pow.f64 (exp.f64 (pow.f64 (cbrt.f64 (log.f64 (sqrt.f64 (/.f64 (pow.f64 (*.f64 (PI.f64) (*.f64 n 2)) (-.f64 1 k)) k)))) 2)) 1) (cbrt.f64 (log.f64 (sqrt.f64 (/.f64 (pow.f64 (*.f64 (PI.f64) (*.f64 n 2)) (-.f64 1 k)) k)))))))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (pow.f64 (exp.f64 (pow.f64 (cbrt.f64 (log.f64 (sqrt.f64 (/.f64 (pow.f64 (*.f64 (PI.f64) (*.f64 n 2)) (-.f64 1 k)) k)))) 2)) (pow.f64 (cbrt.f64 (cbrt.f64 (log.f64 (sqrt.f64 (/.f64 (pow.f64 (*.f64 (PI.f64) (*.f64 n 2)) (-.f64 1 k)) k))))) 2)) (cbrt.f64 (cbrt.f64 (log.f64 (sqrt.f64 (/.f64 (pow.f64 (*.f64 (PI.f64) (*.f64 n 2)) (-.f64 1 k)) k))))))))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (pow.f64 (exp.f64 (pow.f64 (cbrt.f64 (log.f64 (sqrt.f64 (/.f64 (pow.f64 (*.f64 (PI.f64) (*.f64 n 2)) (-.f64 1 k)) k)))) 2)) (cbrt.f64 (sqrt.f64 (log.f64 (sqrt.f64 (/.f64 (pow.f64 (*.f64 (PI.f64) (*.f64 n 2)) (-.f64 1 k)) k)))))) (cbrt.f64 (sqrt.f64 (log.f64 (sqrt.f64 (/.f64 (pow.f64 (*.f64 (PI.f64) (*.f64 n 2)) (-.f64 1 k)) k))))))))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (pow.f64 (exp.f64 (pow.f64 (cbrt.f64 (log.f64 (sqrt.f64 (/.f64 (pow.f64 (*.f64 (PI.f64) (*.f64 n 2)) (-.f64 1 k)) k)))) 2)) (cbrt.f64 (pow.f64 (cbrt.f64 (log.f64 (sqrt.f64 (/.f64 (pow.f64 (*.f64 (PI.f64) (*.f64 n 2)) (-.f64 1 k)) k)))) 2))) (cbrt.f64 (cbrt.f64 (log.f64 (sqrt.f64 (/.f64 (pow.f64 (*.f64 (PI.f64) (*.f64 n 2)) (-.f64 1 k)) k))))))))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (pow.f64 (exp.f64 (pow.f64 (cbrt.f64 (log.f64 (sqrt.f64 (/.f64 (pow.f64 (*.f64 (PI.f64) (*.f64 n 2)) (-.f64 1 k)) k)))) 2)) (sqrt.f64 (cbrt.f64 (log.f64 (sqrt.f64 (/.f64 (pow.f64 (*.f64 (PI.f64) (*.f64 n 2)) (-.f64 1 k)) k)))))) (sqrt.f64 (cbrt.f64 (log.f64 (sqrt.f64 (/.f64 (pow.f64 (*.f64 (PI.f64) (*.f64 n 2)) (-.f64 1 k)) k))))))))) (#(struct:change #<rule egg-rr> (2) ((x sqrt.f64 (/.f64 (pow.f64 (*.f64 (PI.f64) (*.f64 n 2)) (-.f64 1 k)) k))))) (#(struct:change #<rule egg-rr> (2) ((x fabs.f64 (sqrt.f64 (/.f64 (pow.f64 (*.f64 (PI.f64) (*.f64 n 2)) (-.f64 1 k)) k)))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (exp.f64 (sqrt.f64 (/.f64 (pow.f64 (*.f64 (PI.f64) (*.f64 n 2)) (-.f64 1 k)) k))))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (+.f64 1 (expm1.f64 (sqrt.f64 (/.f64 (pow.f64 (*.f64 (PI.f64) (*.f64 n 2)) (-.f64 1 k)) k)))))))) (#(struct:change #<rule egg-rr> (2) ((x cbrt.f64 (pow.f64 (/.f64 (pow.f64 (*.f64 (PI.f64) (*.f64 n 2)) (-.f64 1 k)) k) 3/2))))) (#(struct:change #<rule egg-rr> (2) ((x expm1.f64 (log1p.f64 (sqrt.f64 (/.f64 (pow.f64 (*.f64 (PI.f64) (*.f64 n 2)) (-.f64 1 k)) k))))))) (#(struct:change #<rule egg-rr> (2) ((x log1p.f64 (expm1.f64 (sqrt.f64 (/.f64 (pow.f64 (*.f64 (PI.f64) (*.f64 n 2)) (-.f64 1 k)) k))))))))

simplify33.0ms (0.3%)

Algorithm

1×	egg-herbie

Rules

543×	`exp-sum_binary64`
410×	`unsub-neg_binary64`
308×	`associate--r+_binary64`
308×	`fma-neg_binary64`
305×	`fma-def_binary64`

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	35	300
1	83	300
2	232	300
3	817	228
4	3324	228

Stop Event

1×	node limit

Counts

62 → 54

Calls

Call 1

Inputs
(sqrt.f64 (/.f64 (exp.f64 (.f64 (-.f64 1 k) (+.f64 (log.f64 n) (log.f64 (.f64 2 (PI.f64)))))) k))
(sqrt.f64 (/.f64 (exp.f64 (.f64 (-.f64 1 k) (+.f64 (log.f64 n) (log.f64 (.f64 2 (PI.f64)))))) k))
(sqrt.f64 (/.f64 (exp.f64 (.f64 (-.f64 1 k) (+.f64 (log.f64 n) (log.f64 (.f64 2 (PI.f64)))))) k))
(sqrt.f64 (/.f64 (exp.f64 (.f64 (-.f64 1 k) (+.f64 (log.f64 n) (log.f64 (.f64 2 (PI.f64)))))) k))
(sqrt.f64 (/.f64 (exp.f64 (.f64 (-.f64 1 k) (+.f64 (.f64 -1 (log.f64 (/.f64 1 n))) (log.f64 (*.f64 2 (PI.f64)))))) k))
(sqrt.f64 (/.f64 (exp.f64 (.f64 (-.f64 1 k) (+.f64 (.f64 -1 (log.f64 (/.f64 1 n))) (log.f64 (*.f64 2 (PI.f64)))))) k))
(sqrt.f64 (/.f64 (exp.f64 (.f64 (-.f64 1 k) (+.f64 (.f64 -1 (log.f64 (/.f64 1 n))) (log.f64 (*.f64 2 (PI.f64)))))) k))
(sqrt.f64 (/.f64 (exp.f64 (.f64 (-.f64 1 k) (+.f64 (.f64 -1 (log.f64 (/.f64 1 n))) (log.f64 (*.f64 2 (PI.f64)))))) k))
(sqrt.f64 (/.f64 (exp.f64 (.f64 (-.f64 1 k) (+.f64 (.f64 -1 (log.f64 (/.f64 -1 n))) (log.f64 (*.f64 -2 (PI.f64)))))) k))
(sqrt.f64 (/.f64 (exp.f64 (.f64 (-.f64 1 k) (+.f64 (.f64 -1 (log.f64 (/.f64 -1 n))) (log.f64 (*.f64 -2 (PI.f64)))))) k))
(sqrt.f64 (/.f64 (exp.f64 (.f64 (-.f64 1 k) (+.f64 (.f64 -1 (log.f64 (/.f64 -1 n))) (log.f64 (*.f64 -2 (PI.f64)))))) k))
(sqrt.f64 (/.f64 (exp.f64 (.f64 (-.f64 1 k) (+.f64 (.f64 -1 (log.f64 (/.f64 -1 n))) (log.f64 (*.f64 -2 (PI.f64)))))) k))

Outputs
(sqrt.f64 (/.f64 (exp.f64 (.f64 (-.f64 1 k) (+.f64 (log.f64 n) (log.f64 (.f64 2 (PI.f64)))))) k))
(sqrt.f64 (/.f64 (pow.f64 (exp.f64 (-.f64 1 k)) (+.f64 (log.f64 n) (log.f64 (*.f64 2 (PI.f64))))) k))
(sqrt.f64 (/.f64 (pow.f64 (.f64 2 (.f64 n (PI.f64))) (-.f64 1 k)) k))
(sqrt.f64 (/.f64 (exp.f64 (.f64 (-.f64 1 k) (+.f64 (log.f64 n) (log.f64 (.f64 2 (PI.f64)))))) k))
(sqrt.f64 (/.f64 (pow.f64 (exp.f64 (-.f64 1 k)) (+.f64 (log.f64 n) (log.f64 (*.f64 2 (PI.f64))))) k))
(sqrt.f64 (/.f64 (pow.f64 (.f64 2 (.f64 n (PI.f64))) (-.f64 1 k)) k))
(sqrt.f64 (/.f64 (exp.f64 (.f64 (-.f64 1 k) (+.f64 (log.f64 n) (log.f64 (.f64 2 (PI.f64)))))) k))
(sqrt.f64 (/.f64 (pow.f64 (exp.f64 (-.f64 1 k)) (+.f64 (log.f64 n) (log.f64 (*.f64 2 (PI.f64))))) k))
(sqrt.f64 (/.f64 (pow.f64 (.f64 2 (.f64 n (PI.f64))) (-.f64 1 k)) k))
(sqrt.f64 (/.f64 (exp.f64 (.f64 (-.f64 1 k) (+.f64 (log.f64 n) (log.f64 (.f64 2 (PI.f64)))))) k))
(sqrt.f64 (/.f64 (pow.f64 (exp.f64 (-.f64 1 k)) (+.f64 (log.f64 n) (log.f64 (*.f64 2 (PI.f64))))) k))
(sqrt.f64 (/.f64 (pow.f64 (.f64 2 (.f64 n (PI.f64))) (-.f64 1 k)) k))
(sqrt.f64 (/.f64 (exp.f64 (.f64 (-.f64 1 k) (+.f64 (.f64 -1 (log.f64 (/.f64 1 n))) (log.f64 (*.f64 2 (PI.f64)))))) k))
(sqrt.f64 (/.f64 (pow.f64 (exp.f64 (-.f64 1 k)) (+.f64 (log.f64 n) (log.f64 (*.f64 2 (PI.f64))))) k))
(sqrt.f64 (/.f64 (pow.f64 (.f64 2 (.f64 n (PI.f64))) (-.f64 1 k)) k))
(sqrt.f64 (/.f64 (exp.f64 (.f64 (-.f64 1 k) (+.f64 (.f64 -1 (log.f64 (/.f64 1 n))) (log.f64 (*.f64 2 (PI.f64)))))) k))
(sqrt.f64 (/.f64 (pow.f64 (exp.f64 (-.f64 1 k)) (+.f64 (log.f64 n) (log.f64 (*.f64 2 (PI.f64))))) k))
(sqrt.f64 (/.f64 (pow.f64 (.f64 2 (.f64 n (PI.f64))) (-.f64 1 k)) k))
(sqrt.f64 (/.f64 (exp.f64 (.f64 (-.f64 1 k) (+.f64 (.f64 -1 (log.f64 (/.f64 1 n))) (log.f64 (*.f64 2 (PI.f64)))))) k))
(sqrt.f64 (/.f64 (pow.f64 (exp.f64 (-.f64 1 k)) (+.f64 (log.f64 n) (log.f64 (*.f64 2 (PI.f64))))) k))
(sqrt.f64 (/.f64 (pow.f64 (.f64 2 (.f64 n (PI.f64))) (-.f64 1 k)) k))
(sqrt.f64 (/.f64 (exp.f64 (.f64 (-.f64 1 k) (+.f64 (.f64 -1 (log.f64 (/.f64 1 n))) (log.f64 (*.f64 2 (PI.f64)))))) k))
(sqrt.f64 (/.f64 (pow.f64 (exp.f64 (-.f64 1 k)) (+.f64 (log.f64 n) (log.f64 (*.f64 2 (PI.f64))))) k))
(sqrt.f64 (/.f64 (pow.f64 (.f64 2 (.f64 n (PI.f64))) (-.f64 1 k)) k))
(sqrt.f64 (/.f64 (exp.f64 (.f64 (-.f64 1 k) (+.f64 (.f64 -1 (log.f64 (/.f64 -1 n))) (log.f64 (*.f64 -2 (PI.f64)))))) k))
(sqrt.f64 (/.f64 (pow.f64 (exp.f64 (-.f64 1 k)) (+.f64 (log.f64 n) (log.f64 (*.f64 2 (PI.f64))))) k))
(sqrt.f64 (/.f64 (pow.f64 (.f64 2 (.f64 n (PI.f64))) (-.f64 1 k)) k))
(sqrt.f64 (/.f64 (exp.f64 (.f64 (-.f64 1 k) (+.f64 (.f64 -1 (log.f64 (/.f64 -1 n))) (log.f64 (*.f64 -2 (PI.f64)))))) k))
(sqrt.f64 (/.f64 (pow.f64 (exp.f64 (-.f64 1 k)) (+.f64 (log.f64 n) (log.f64 (*.f64 2 (PI.f64))))) k))
(sqrt.f64 (/.f64 (pow.f64 (.f64 2 (.f64 n (PI.f64))) (-.f64 1 k)) k))
(sqrt.f64 (/.f64 (exp.f64 (.f64 (-.f64 1 k) (+.f64 (.f64 -1 (log.f64 (/.f64 -1 n))) (log.f64 (*.f64 -2 (PI.f64)))))) k))
(sqrt.f64 (/.f64 (pow.f64 (exp.f64 (-.f64 1 k)) (+.f64 (log.f64 n) (log.f64 (*.f64 2 (PI.f64))))) k))
(sqrt.f64 (/.f64 (pow.f64 (.f64 2 (.f64 n (PI.f64))) (-.f64 1 k)) k))
(sqrt.f64 (/.f64 (exp.f64 (.f64 (-.f64 1 k) (+.f64 (.f64 -1 (log.f64 (/.f64 -1 n))) (log.f64 (*.f64 -2 (PI.f64)))))) k))
(sqrt.f64 (/.f64 (pow.f64 (exp.f64 (-.f64 1 k)) (+.f64 (log.f64 n) (log.f64 (*.f64 2 (PI.f64))))) k))
(sqrt.f64 (/.f64 (pow.f64 (.f64 2 (.f64 n (PI.f64))) (-.f64 1 k)) k))

localize43.0ms (0.5%)

Local error

Found 8 expressions with local error:

New	Error	Program
	0.6b	(pow.f64 (pow.f64 k -1/2) 3)
	0.4b	(pow.f64 (.f64 (.f64 2 (PI.f64)) n) (/.f64 (-.f64 1 k) 2))
	0.2b	(.f64 (.f64 2 (PI.f64)) n)
	0.2b	(.f64 (cbrt.f64 (pow.f64 (pow.f64 k -1/2) 3)) (pow.f64 (.f64 (*.f64 2 (PI.f64)) n) (/.f64 (-.f64 1 k) 2)))
	0.2b	(.f64 (.f64 2 (PI.f64)) n)
	0.4b	(pow.f64 (.f64 (.f64 2 (PI.f64)) n) (/.f64 (-.f64 1 k) 2))
✓	0.6b	(pow.f64 (pow.f64 k -1/2) 3)
✓	18.0b	(cbrt.f64 (pow.f64 (pow.f64 k -1/2) 3))

Compiler

Compiled 68 to 51 computations (25% saved)

series69.0ms (0.7%)

Counts

2 → 12

Calls

6 calls:

Time	Variable		Point	Expression
41.0ms	k	@	0	(pow.f64 (pow.f64 k -1/2) 3)
17.0ms	k	@	-inf	(pow.f64 (pow.f64 k -1/2) 3)
9.0ms	k	@	inf	(pow.f64 (pow.f64 k -1/2) 3)
1.0ms	k	@	0	(cbrt.f64 (pow.f64 (pow.f64 k -1/2) 3))
1.0ms	k	@	-inf	(cbrt.f64 (pow.f64 (pow.f64 k -1/2) 3))

rewrite43.0ms (0.5%)

Algorithm

1×	batch-egg-rewrite

Rules

536×	`pow1_binary64`
514×	`add-log-exp_binary64`
514×	`log1p-expm1-u_binary64`
514×	`expm1-log1p-u_binary64`
500×	`add-exp-log_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	7	8
1	156	8
2	1475	8

Stop Event

1×	node limit

Counts

2 → 46

Calls

Call 1

Inputs
(cbrt.f64 (pow.f64 (pow.f64 k -1/2) 3))
(pow.f64 (pow.f64 k -1/2) 3)

Outputs

((#(struct:change #<rule egg-rr> (2) ((x -.f64 (+.f64 1 (pow.f64 k -1/2)) 1)))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (pow.f64 k -1/2) 1)))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 1 (pow.f64 k -1/2))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (cbrt.f64 (pow.f64 k -1/2)) (cbrt.f64 (pow.f64 k -1)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (cbrt.f64 (pow.f64 k -1/2)) (pow.f64 (pow.f64 k -1) 1/3))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (cbrt.f64 (pow.f64 k -1)) (cbrt.f64 (pow.f64 k -1/2)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (pow.f64 k -1/4) (pow.f64 k -1/4))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (pow.f64 1 -1/2) (pow.f64 k -1/2))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (pow.f64 (pow.f64 (cbrt.f64 k) 2) -1/2) (pow.f64 (cbrt.f64 k) -1/2))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (pow.f64 (sqrt.f64 k) -1/2) (pow.f64 (sqrt.f64 k) -1/2))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (pow.f64 (pow.f64 k -1) 1/3) (cbrt.f64 (pow.f64 k -1/2)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (pow.f64 1 1/3) (pow.f64 k -1/2))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (pow.f64 (pow.f64 k -3/4) 1/3) (pow.f64 (pow.f64 k -3/4) 1/3))))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 k -1/2)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (pow.f64 k -1/2) 1)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (pow.f64 k -3/2) 1/3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (*.f64 k k) -1/4)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (cbrt.f64 (pow.f64 k -1/2)) 3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (pow.f64 k -1/4) 2)))) (#(struct:change #<rule egg-rr> (2) ((x sqrt.f64 (pow.f64 k -1))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (exp.f64 (pow.f64 k -1/2)))))) (#(struct:change #<rule egg-rr> (2) ((x expm1.f64 (log1p.f64 (pow.f64 k -1/2)))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (*.f64 -1/2 (log.f64 k)))))) (#(struct:change #<rule egg-rr> (2) ((x log1p.f64 (expm1.f64 (pow.f64 k -1/2)))))))

((#(struct:change #<rule egg-rr> (2) ((x -.f64 (+.f64 1 (pow.f64 k -3/2)) 1)))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (pow.f64 k -1/2) (pow.f64 k -1))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (pow.f64 k -3/2) 1)))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 1 (pow.f64 k -3/2))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (pow.f64 k -1) (pow.f64 k -1/2))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (cbrt.f64 (pow.f64 k -1)) (*.f64 (cbrt.f64 (pow.f64 k -1/2)) (pow.f64 k -1)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (pow.f64 k -1/4) (*.f64 (pow.f64 k -1/4) (pow.f64 k -1)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (pow.f64 k -3/4) (pow.f64 k -3/4))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (pow.f64 1 -3/2) (pow.f64 k -3/2))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (pow.f64 (pow.f64 (cbrt.f64 k) 2) -3/2) (pow.f64 (cbrt.f64 k) -3/2))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (pow.f64 (sqrt.f64 k) -3/2) (pow.f64 (sqrt.f64 k) -3/2))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (pow.f64 (cbrt.f64 (pow.f64 k -1)) 3) (pow.f64 k -1/2))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (pow.f64 (pow.f64 k -1/4) 3) (pow.f64 (pow.f64 k -1/4) 3))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (*.f64 (pow.f64 k -1) 1) (pow.f64 k -1/2))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (*.f64 (pow.f64 k -1) (cbrt.f64 (pow.f64 k -1))) (cbrt.f64 (pow.f64 k -1/2)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (*.f64 (pow.f64 k -1) (pow.f64 k -1/4)) (pow.f64 k -1/4))))) (#(struct:change #<rule egg-rr> (2) ((x sqrt.f64 (pow.f64 k -3))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (exp.f64 (pow.f64 k -3/2)))))) (#(struct:change #<rule egg-rr> (2) ((x cbrt.f64 (pow.f64 (pow.f64 k -3/2) 3))))) (#(struct:change #<rule egg-rr> (2) ((x expm1.f64 (log1p.f64 (pow.f64 k -3/2)))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (*.f64 (log.f64 k) -3/2))))) (#(struct:change #<rule egg-rr> (2) ((x log1p.f64 (expm1.f64 (pow.f64 k -3/2)))))))

simplify50.0ms (0.5%)

Algorithm

1×	egg-herbie

Rules

548×	`associate-l_binary64`
518×	`div-sub_binary64`
460×	`associate-r_binary64`
379×	`unswap-sqr_binary64`
256×	`exp-sum_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	17	108
1	46	108
2	97	108
3	259	108
4	988	108
5	5275	108

Stop Event

1×	node limit

Counts

58 → 48

Calls

Call 1

Inputs
(sqrt.f64 (/.f64 1 (pow.f64 k 3)))
(sqrt.f64 (/.f64 1 (pow.f64 k 3)))
(sqrt.f64 (/.f64 1 (pow.f64 k 3)))
(sqrt.f64 (/.f64 1 (pow.f64 k 3)))
(sqrt.f64 (/.f64 1 (pow.f64 k 3)))
(sqrt.f64 (/.f64 1 (pow.f64 k 3)))
(sqrt.f64 (/.f64 1 (pow.f64 k 3)))
(sqrt.f64 (/.f64 1 (pow.f64 k 3)))
(pow.f64 (exp.f64 (.f64 -1/2 (+.f64 (log.f64 -1) (.f64 -1 (log.f64 (/.f64 -1 k)))))) 3)
(pow.f64 (exp.f64 (.f64 -1/2 (+.f64 (log.f64 -1) (.f64 -1 (log.f64 (/.f64 -1 k)))))) 3)
(pow.f64 (exp.f64 (.f64 -1/2 (+.f64 (log.f64 -1) (.f64 -1 (log.f64 (/.f64 -1 k)))))) 3)
(pow.f64 (exp.f64 (.f64 -1/2 (+.f64 (log.f64 -1) (.f64 -1 (log.f64 (/.f64 -1 k)))))) 3)

Outputs
(sqrt.f64 (/.f64 1 (pow.f64 k 3)))
(sqrt.f64 (/.f64 1 (pow.f64 k 3)))
(sqrt.f64 (/.f64 1 (pow.f64 k 3)))
(sqrt.f64 (/.f64 1 (pow.f64 k 3)))
(sqrt.f64 (/.f64 1 (pow.f64 k 3)))
(sqrt.f64 (/.f64 1 (pow.f64 k 3)))
(sqrt.f64 (/.f64 1 (pow.f64 k 3)))
(sqrt.f64 (/.f64 1 (pow.f64 k 3)))
(pow.f64 (exp.f64 (.f64 -1/2 (+.f64 (log.f64 -1) (.f64 -1 (log.f64 (/.f64 -1 k)))))) 3)
(sqrt.f64 (/.f64 1 (pow.f64 k 3)))
(pow.f64 (exp.f64 (.f64 -1/2 (+.f64 (log.f64 -1) (.f64 -1 (log.f64 (/.f64 -1 k)))))) 3)
(sqrt.f64 (/.f64 1 (pow.f64 k 3)))
(pow.f64 (exp.f64 (.f64 -1/2 (+.f64 (log.f64 -1) (.f64 -1 (log.f64 (/.f64 -1 k)))))) 3)
(sqrt.f64 (/.f64 1 (pow.f64 k 3)))
(pow.f64 (exp.f64 (.f64 -1/2 (+.f64 (log.f64 -1) (.f64 -1 (log.f64 (/.f64 -1 k)))))) 3)
(sqrt.f64 (/.f64 1 (pow.f64 k 3)))

eval344.0ms (3.7%)

Compiler: Compiled 16173 to 11216 computations (30.6% saved)

prune144.0ms (1.5%)

Pruning

29 alts after pruning (28 fresh and 1 done)

	Pruned	Kept	Total
New	741	23	764
Fresh	12	5	17
Picked	1	0	1
Done	5	1	6
Total	759	29	788

Error

Counts

788 → 29

Alt Table

Click to see full alt table

Status	Error	Program
▶	0.3b	(/.f64 1 (/.f64 (sqrt.f64 k) (sqrt.f64 (/.f64 (.f64 n (.f64 2 (PI.f64))) (pow.f64 (.f64 n (.f64 2 (PI.f64))) k)))))
	33.3b	(sqrt.f64 (.f64 2 (.f64 (/.f64 (PI.f64) k) n)))
▶	33.3b	(sqrt.f64 (/.f64 (.f64 2 (.f64 n (PI.f64))) k))
	24.1b	(/.f64 (.f64 (sqrt.f64 2) (sqrt.f64 (.f64 n (PI.f64)))) (sqrt.f64 k))
	9.6b	(sqrt.f64 (/.f64 (.f64 (.f64 n (.f64 2 (PI.f64))) (pow.f64 (.f64 n (*.f64 2 (PI.f64))) (neg.f64 k))) k))
	0.7b	(.f64 (pow.f64 (pow.f64 k -1/4) 2) (pow.f64 (.f64 (*.f64 2 (PI.f64)) n) (/.f64 (-.f64 1 k) 2)))
▶	0.6b	(/.f64 1 (.f64 (sqrt.f64 k) (pow.f64 (pow.f64 (.f64 2 (*.f64 (PI.f64) n)) (-.f64 1 k)) -1/2)))
▶	11.8b	(sqrt.f64 (/.f64 (exp.f64 (.f64 (-.f64 1 k) (log.f64 (.f64 n (*.f64 2 (PI.f64)))))) k))
	24.0b	(/.f64 1 (/.f64 (sqrt.f64 k) (sqrt.f64 (.f64 2 (.f64 n (PI.f64))))))
	9.2b	(pow.f64 (/.f64 k (pow.f64 (.f64 2 (.f64 (PI.f64) n)) (-.f64 1 k))) -1/2)
	0.6b	(.f64 (pow.f64 k -1/2) (/.f64 1 (pow.f64 (pow.f64 (.f64 2 (*.f64 (PI.f64) n)) (-.f64 1 k)) -1/2)))
	19.1b	(pow.f64 (pow.f64 (/.f64 (pow.f64 (.f64 n (.f64 2 (PI.f64))) (-.f64 1 k)) k) 3/2) 1/3)
	0.5b	(.f64 (pow.f64 k -1/2) (pow.f64 (.f64 (*.f64 2 (PI.f64)) n) (/.f64 (-.f64 1 k) 2)))
	17.6b	(cbrt.f64 (pow.f64 (/.f64 (pow.f64 (.f64 (PI.f64) (.f64 n 2)) (-.f64 1 k)) k) 3/2))
	0.8b	(.f64 (.f64 (/.f64 1 (cbrt.f64 k)) (cbrt.f64 (pow.f64 k -1/2))) (pow.f64 (.f64 (.f64 2 (PI.f64)) n) (/.f64 (-.f64 1 k) 2)))
	14.7b	(.f64 (cbrt.f64 (exp.f64 (.f64 (log.f64 k) -3/2))) (pow.f64 (.f64 (.f64 2 (PI.f64)) n) (/.f64 (-.f64 1 k) 2)))
	11.7b	(exp.f64 (.f64 (log.f64 (/.f64 (pow.f64 (.f64 n (*.f64 2 (PI.f64))) (-.f64 1 k)) k)) 1/2))
✓	9.9b	(sqrt.f64 (/.f64 (pow.f64 (.f64 2 (.f64 (PI.f64) n)) (-.f64 1 k)) k))
	3.2b	(.f64 (exp.f64 (.f64 -1/2 (log.f64 k))) (pow.f64 (.f64 (.f64 2 (PI.f64)) n) (/.f64 (-.f64 1 k) 2)))
	13.0b	(.f64 (cbrt.f64 (.f64 (pow.f64 k -3/2) 1)) (pow.f64 (.f64 (.f64 2 (PI.f64)) n) (/.f64 (-.f64 1 k) 2)))
	0.7b	(/.f64 (pow.f64 (*.f64 2 (PI.f64)) (-.f64 1/2 (/.f64 k 2))) (/.f64 (sqrt.f64 k) (pow.f64 n (-.f64 1/2 (/.f64 k 2)))))
▶	9.9b	(sqrt.f64 (.f64 (pow.f64 (.f64 n (*.f64 2 (PI.f64))) (-.f64 1 k)) (/.f64 1 k)))
	9.2b	(/.f64 1 (sqrt.f64 (/.f64 k (pow.f64 (.f64 n (.f64 2 (PI.f64))) (-.f64 1 k)))))
	10.0b	(pow.f64 (pow.f64 (/.f64 (pow.f64 (.f64 (PI.f64) (.f64 n 2)) (-.f64 1 k)) k) 1/4) 2)
	9.6b	(sqrt.f64 (/.f64 (/.f64 (.f64 2 (PI.f64)) (/.f64 (pow.f64 (.f64 n (*.f64 2 (PI.f64))) k) n)) k))
	0.5b	(.f64 (sqrt.f64 (/.f64 1 k)) (pow.f64 (.f64 (*.f64 2 (PI.f64)) n) (/.f64 (-.f64 1 k) 2)))
	0.5b	(.f64 (pow.f64 k -1/2) (sqrt.f64 (pow.f64 (.f64 2 (*.f64 (PI.f64) n)) (-.f64 1 k))))
	9.6b	(sqrt.f64 (/.f64 (.f64 (pow.f64 (.f64 2 (PI.f64)) (-.f64 1 k)) (/.f64 n (pow.f64 n k))) k))
	0.5b	(/.f64 (pow.f64 (.f64 (PI.f64) (.f64 n 2)) (+.f64 1/2 (*.f64 k -1/2))) (sqrt.f64 k))

Compiler

Compiled 970 to 787 computations (18.9% saved)

localize46.0ms (0.5%)

Local error

Found 8 expressions with local error:

New	Error	Program
	0.2b	(/.f64 (sqrt.f64 k) (sqrt.f64 (/.f64 (.f64 n (.f64 2 (PI.f64))) (pow.f64 (.f64 n (.f64 2 (PI.f64))) k))))
	0.2b	(/.f64 1 (/.f64 (sqrt.f64 k) (sqrt.f64 (/.f64 (.f64 n (.f64 2 (PI.f64))) (pow.f64 (.f64 n (.f64 2 (PI.f64))) k)))))
	0.1b	(sqrt.f64 (/.f64 (.f64 n (.f64 2 (PI.f64))) (pow.f64 (.f64 n (.f64 2 (PI.f64))) k)))
	0.0b	(/.f64 (.f64 n (.f64 2 (PI.f64))) (pow.f64 (.f64 n (.f64 2 (PI.f64))) k))
✓	0.1b	(sqrt.f64 (/.f64 (.f64 n (.f64 2 (PI.f64))) (pow.f64 (.f64 n (.f64 2 (PI.f64))) k)))
✓	0.2b	(/.f64 1 (/.f64 (sqrt.f64 k) (sqrt.f64 (/.f64 (.f64 n (.f64 2 (PI.f64))) (pow.f64 (.f64 n (.f64 2 (PI.f64))) k)))))
✓	0.2b	(/.f64 (sqrt.f64 k) (sqrt.f64 (/.f64 (.f64 n (.f64 2 (PI.f64))) (pow.f64 (.f64 n (.f64 2 (PI.f64))) k))))
	0.2b	(.f64 n (.f64 2 (PI.f64)))

Compiler

Compiled 87 to 54 computations (37.9% saved)

series42.0ms (0.5%)

Counts

3 → 12

Calls

18 calls:

Time	Variable		Point	Expression
4.0ms	n	@	0	(/.f64 1 (/.f64 (sqrt.f64 k) (sqrt.f64 (/.f64 (.f64 n (.f64 2 (PI.f64))) (pow.f64 (.f64 n (.f64 2 (PI.f64))) k)))))
4.0ms	k	@	-inf	(/.f64 (sqrt.f64 k) (sqrt.f64 (/.f64 (.f64 n (.f64 2 (PI.f64))) (pow.f64 (.f64 n (.f64 2 (PI.f64))) k))))
3.0ms	k	@	0	(/.f64 (sqrt.f64 k) (sqrt.f64 (/.f64 (.f64 n (.f64 2 (PI.f64))) (pow.f64 (.f64 n (.f64 2 (PI.f64))) k))))
3.0ms	k	@	0	(/.f64 1 (/.f64 (sqrt.f64 k) (sqrt.f64 (/.f64 (.f64 n (.f64 2 (PI.f64))) (pow.f64 (.f64 n (.f64 2 (PI.f64))) k)))))
3.0ms	n	@	-inf	(/.f64 (sqrt.f64 k) (sqrt.f64 (/.f64 (.f64 n (.f64 2 (PI.f64))) (pow.f64 (.f64 n (.f64 2 (PI.f64))) k))))

rewrite81.0ms (0.9%)

Algorithm

1×	batch-egg-rewrite

Rules

853×	`log-prod_binary64`
259×	`pow1/3_binary64`
253×	`expm1-udef_binary64`
253×	`log1p-udef_binary64`
246×	`log-pow_binary64`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	14	78
1	304	54
2	4175	54

Stop Event

1×	node limit

Counts

3 → 122

Calls

Call 1

Inputs

(/.f64 (sqrt.f64 k) (sqrt.f64 (/.f64 (*.f64 n (*.f64 2 (PI.f64))) (pow.f64 (*.f64 n (*.f64 2 (PI.f64))) k))))

(/.f64 1 (/.f64 (sqrt.f64 k) (sqrt.f64 (/.f64 (*.f64 n (*.f64 2 (PI.f64))) (pow.f64 (*.f64 n (*.f64 2 (PI.f64))) k)))))

(sqrt.f64 (/.f64 (*.f64 n (*.f64 2 (PI.f64))) (pow.f64 (*.f64 n (*.f64 2 (PI.f64))) k)))

Outputs

((#(struct:change #<rule egg-rr> (2) ((x +.f64 0 (sqrt.f64 (*.f64 k (pow.f64 (*.f64 n (*.f64 2 (PI.f64))) (-.f64 k 1)))))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (log.f64 (*.f64 (cbrt.f64 (exp.f64 (sqrt.f64 (*.f64 k (pow.f64 (*.f64 n (*.f64 2 (PI.f64))) (-.f64 k 1)))))) (cbrt.f64 (exp.f64 (sqrt.f64 (*.f64 k (pow.f64 (*.f64 n (*.f64 2 (PI.f64))) (-.f64 k 1)))))))) (log.f64 (cbrt.f64 (exp.f64 (sqrt.f64 (*.f64 k (pow.f64 (*.f64 n (*.f64 2 (PI.f64))) (-.f64 k 1))))))))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (log.f64 (sqrt.f64 (exp.f64 (sqrt.f64 (*.f64 k (pow.f64 (*.f64 n (*.f64 2 (PI.f64))) (-.f64 k 1))))))) (log.f64 (sqrt.f64 (exp.f64 (sqrt.f64 (*.f64 k (pow.f64 (*.f64 n (*.f64 2 (PI.f64))) (-.f64 k 1))))))))))) (#(struct:change #<rule egg-rr> (2) ((x -.f64 (exp.f64 (log1p.f64 (sqrt.f64 (*.f64 k (pow.f64 (*.f64 n (*.f64 2 (PI.f64))) (-.f64 k 1)))))) 1)))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (sqrt.f64 k) (pow.f64 (pow.f64 (*.f64 n (*.f64 2 (PI.f64))) (-.f64 1 k)) -1/2))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (sqrt.f64 (*.f64 k (pow.f64 (*.f64 n (*.f64 2 (PI.f64))) (-.f64 k 1)))) 1)))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 1 (sqrt.f64 (*.f64 k (pow.f64 (*.f64 n (*.f64 2 (PI.f64))) (-.f64 k 1)))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (cbrt.f64 k) (*.f64 (cbrt.f64 (sqrt.f64 k)) (pow.f64 (pow.f64 (*.f64 n (*.f64 2 (PI.f64))) (-.f64 1 k)) -1/2)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (cbrt.f64 (sqrt.f64 (*.f64 k (pow.f64 (*.f64 n (*.f64 2 (PI.f64))) (-.f64 k 1))))) (cbrt.f64 (*.f64 k (pow.f64 (*.f64 n (*.f64 2 (PI.f64))) (-.f64 k 1)))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (cbrt.f64 (*.f64 k (pow.f64 (*.f64 n (*.f64 2 (PI.f64))) (-.f64 k 1)))) (cbrt.f64 (sqrt.f64 (*.f64 k (pow.f64 (*.f64 n (*.f64 2 (PI.f64))) (-.f64 k 1))))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (sqrt.f64 (sqrt.f64 (*.f64 k (pow.f64 (*.f64 n (*.f64 2 (PI.f64))) (-.f64 k 1))))) (sqrt.f64 (sqrt.f64 (*.f64 k (pow.f64 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(*.f64 n (*.f64 2 (PI.f64))) (-.f64 1 k))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (cbrt.f64 (sqrt.f64 (pow.f64 (*.f64 n (*.f64 2 (PI.f64))) (-.f64 1 k)))) (cbrt.f64 (pow.f64 (*.f64 n (*.f64 2 (PI.f64))) (-.f64 1 k))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (cbrt.f64 (pow.f64 (*.f64 n (*.f64 2 (PI.f64))) (-.f64 1 k))) (cbrt.f64 (sqrt.f64 (pow.f64 (*.f64 n (*.f64 2 (PI.f64))) (-.f64 1 k)))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (pow.f64 (pow.f64 (*.f64 n (*.f64 2 (PI.f64))) (-.f64 1 k)) 1/4) (pow.f64 (pow.f64 (*.f64 n (*.f64 2 (PI.f64))) (-.f64 1 k)) 1/4))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (sqrt.f64 (*.f64 n (*.f64 2 (PI.f64)))) (sqrt.f64 (pow.f64 (*.f64 n (*.f64 2 (PI.f64))) (neg.f64 k))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (sqrt.f64 (*.f64 n (*.f64 2 (PI.f64)))) (pow.f64 (pow.f64 (*.f64 n (*.f64 2 (PI.f64))) (neg.f64 k)) 1/2))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (sqrt.f64 (*.f64 n (*.f64 2 (PI.f64)))) (/.f64 1 (sqrt.f64 (pow.f64 (*.f64 n (*.f64 2 (PI.f64))) k))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (sqrt.f64 (pow.f64 (cbrt.f64 (pow.f64 (*.f64 n (*.f64 2 (PI.f64))) (-.f64 1 k))) 2)) (sqrt.f64 (cbrt.f64 (pow.f64 (*.f64 n (*.f64 2 (PI.f64))) (-.f64 1 k)))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (pow.f64 1 1/2) (sqrt.f64 (pow.f64 (*.f64 n (*.f64 2 (PI.f64))) (-.f64 1 k))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (pow.f64 (pow.f64 (cbrt.f64 (pow.f64 (*.f64 n (*.f64 2 (PI.f64))) (-.f64 1 k))) 2) 1/2) (pow.f64 (cbrt.f64 (pow.f64 (*.f64 n (*.f64 2 (PI.f64))) (-.f64 1 k))) 1/2))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 1 (sqrt.f64 (pow.f64 (*.f64 n (*.f64 2 (PI.f64))) (-.f64 k 1))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 1 (/.f64 (sqrt.f64 (pow.f64 (*.f64 n (*.f64 2 (PI.f64))) k)) (sqrt.f64 (*.f64 n (*.f64 2 (PI.f64))))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (sqrt.f64 (*.f64 n (*.f64 2 (PI.f64)))) (sqrt.f64 (pow.f64 (*.f64 n (*.f64 2 (PI.f64))) k)))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (sqrt.f64 n) (sqrt.f64 (*.f64 1/2 (/.f64 (pow.f64 (*.f64 n (*.f64 2 (PI.f64))) k) (PI.f64)))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (sqrt.f64 (*.f64 n (neg.f64 (*.f64 2 (PI.f64))))) (sqrt.f64 (neg.f64 (pow.f64 (*.f64 n (*.f64 2 (PI.f64))) k))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (neg.f64 (sqrt.f64 (*.f64 n (*.f64 2 (PI.f64))))) (neg.f64 (sqrt.f64 (pow.f64 (*.f64 n (*.f64 2 (PI.f64))) k))))))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (pow.f64 (*.f64 n (*.f64 2 (PI.f64))) (-.f64 1 k)) 1/2)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (sqrt.f64 (pow.f64 (*.f64 n (*.f64 2 (PI.f64))) (-.f64 1 k))) 1)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (pow.f64 (pow.f64 (*.f64 n (*.f64 2 (PI.f64))) (-.f64 1 k)) 3/2) 1/3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (cbrt.f64 (sqrt.f64 (pow.f64 (*.f64 n (*.f64 2 (PI.f64))) (-.f64 1 k)))) 3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (pow.f64 (pow.f64 (*.f64 n (*.f64 2 (PI.f64))) (-.f64 1 k)) 1/4) 2)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (sqrt.f64 (pow.f64 (*.f64 n (*.f64 2 (PI.f64))) (-.f64 k 1))) -1)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (/.f64 (sqrt.f64 (pow.f64 (*.f64 n (*.f64 2 (PI.f64))) k)) (sqrt.f64 (*.f64 n (*.f64 2 (PI.f64))))) -1)))) (#(struct:change #<rule egg-rr> (2) ((x fabs.f64 (sqrt.f64 (pow.f64 (*.f64 n (*.f64 2 (PI.f64))) (-.f64 1 k))))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (exp.f64 (sqrt.f64 (pow.f64 (*.f64 n (*.f64 2 (PI.f64))) (-.f64 1 k)))))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (+.f64 1 (expm1.f64 (sqrt.f64 (pow.f64 (*.f64 n (*.f64 2 (PI.f64))) (-.f64 1 k))))))))) (#(struct:change #<rule egg-rr> (2) ((x cbrt.f64 (pow.f64 (pow.f64 (*.f64 n (*.f64 2 (PI.f64))) (-.f64 1 k)) 3/2))))) (#(struct:change #<rule egg-rr> (2) ((x expm1.f64 (log1p.f64 (sqrt.f64 (pow.f64 (*.f64 n (*.f64 2 (PI.f64))) (-.f64 1 k)))))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (log.f64 (sqrt.f64 (pow.f64 (*.f64 n (*.f64 2 (PI.f64))) (-.f64 1 k)))))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (*.f64 (*.f64 (-.f64 1 k) (log.f64 (*.f64 n (*.f64 2 (PI.f64))))) 1/2))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (*.f64 (log.f64 (sqrt.f64 (pow.f64 (*.f64 n (*.f64 2 (PI.f64))) (-.f64 1 k)))) 1))))) (#(struct:change #<rule egg-rr> (2) ((x log1p.f64 (expm1.f64 (sqrt.f64 (pow.f64 (*.f64 n (*.f64 2 (PI.f64))) (-.f64 1 k)))))))))

simplify43.0ms (0.5%)

Algorithm

1×	egg-herbie

Rules

623×	`distribute-rgt-in_binary64`
621×	`distribute-lft-in_binary64`
566×	`fma-def_binary64`
400×	`associate--l+_binary64`
327×	`*-commutative_binary64`

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	73	749
1	245	618
2	991	583
3	5323	510

Stop Event

1×	node limit

Counts

134 → 131

Calls

Call 1

Inputs
(.f64 (sqrt.f64 2) (sqrt.f64 (.f64 n (PI.f64))))
(+.f64 (.f64 -1/2 (.f64 (.f64 (sqrt.f64 2) (.f64 k (log.f64 (.f64 2 (.f64 n (PI.f64)))))) (sqrt.f64 (.f64 n (PI.f64))))) (.f64 (sqrt.f64 2) (sqrt.f64 (*.f64 n (PI.f64)))))
(+.f64 (.f64 -1/2 (.f64 (.f64 (sqrt.f64 2) (.f64 k (log.f64 (.f64 2 (.f64 n (PI.f64)))))) (sqrt.f64 (.f64 n (PI.f64))))) (+.f64 (.f64 (sqrt.f64 2) (sqrt.f64 (.f64 n (PI.f64)))) (.f64 -1/2 (.f64 (.f64 (sqrt.f64 2) (.f64 (pow.f64 k 2) (+.f64 (.f64 -1 (.f64 n (.f64 (pow.f64 (log.f64 (.f64 2 (.f64 n (PI.f64)))) 2) (PI.f64)))) (+.f64 (pow.f64 (.f64 -1/2 (.f64 (sqrt.f64 (.f64 n (PI.f64))) (log.f64 (.f64 2 (.f64 n (PI.f64)))))) 2) (.f64 1/2 (.f64 n (.f64 (PI.f64) (pow.f64 (log.f64 (.f64 2 (.f64 n (PI.f64)))) 2)))))))) (sqrt.f64 (/.f64 1 (*.f64 n (PI.f64))))))))
(+.f64 (.f64 -1/2 (.f64 (.f64 (sqrt.f64 2) (.f64 k (log.f64 (.f64 2 (.f64 n (PI.f64)))))) (sqrt.f64 (.f64 n (PI.f64))))) (+.f64 (.f64 -1/2 (.f64 (.f64 (sqrt.f64 2) (.f64 (pow.f64 k 3) (+.f64 (.f64 -1/2 (.f64 n (.f64 (pow.f64 (log.f64 (.f64 2 (.f64 n (PI.f64)))) 3) (PI.f64)))) (+.f64 (.f64 1/6 (.f64 n (.f64 (PI.f64) (pow.f64 (log.f64 (.f64 2 (.f64 n (PI.f64)))) 3)))) (+.f64 (.f64 1/2 (.f64 (+.f64 (.f64 1/2 (.f64 n (.f64 (pow.f64 (log.f64 (.f64 2 (.f64 n (PI.f64)))) 2) (PI.f64)))) (+.f64 (.f64 -1 (.f64 n (.f64 (PI.f64) (pow.f64 (log.f64 (.f64 2 (.f64 n (PI.f64)))) 2)))) (pow.f64 (.f64 -1/2 (.f64 (sqrt.f64 (.f64 n (PI.f64))) (log.f64 (.f64 2 (.f64 n (PI.f64)))))) 2))) (log.f64 (.f64 2 (.f64 n (PI.f64)))))) (.f64 -1 (.f64 (+.f64 (.f64 1/2 (.f64 n (.f64 (pow.f64 (log.f64 (.f64 2 (.f64 n (PI.f64)))) 2) (PI.f64)))) (.f64 -1 (.f64 n (.f64 (PI.f64) (pow.f64 (log.f64 (.f64 2 (.f64 n (PI.f64)))) 2))))) (log.f64 (.f64 2 (.f64 n (PI.f64))))))))))) (sqrt.f64 (/.f64 1 (.f64 n (PI.f64)))))) (+.f64 (.f64 (sqrt.f64 2) (sqrt.f64 (.f64 n (PI.f64)))) (.f64 -1/2 (.f64 (.f64 (sqrt.f64 2) (.f64 (pow.f64 k 2) (+.f64 (.f64 -1 (.f64 n (.f64 (pow.f64 (log.f64 (.f64 2 (.f64 n (PI.f64)))) 2) (PI.f64)))) (+.f64 (pow.f64 (.f64 -1/2 (.f64 (sqrt.f64 (.f64 n (PI.f64))) (log.f64 (.f64 2 (.f64 n (PI.f64)))))) 2) (.f64 1/2 (.f64 n (.f64 (PI.f64) (pow.f64 (log.f64 (.f64 2 (.f64 n (PI.f64)))) 2)))))))) (sqrt.f64 (/.f64 1 (*.f64 n (PI.f64)))))))))
(.f64 (sqrt.f64 (/.f64 (.f64 n (PI.f64)) (pow.f64 (.f64 2 (.f64 n (PI.f64))) k))) (sqrt.f64 2))
(.f64 (sqrt.f64 (/.f64 (.f64 n (PI.f64)) (pow.f64 (.f64 2 (.f64 n (PI.f64))) k))) (sqrt.f64 2))
(.f64 (sqrt.f64 (/.f64 (.f64 n (PI.f64)) (pow.f64 (.f64 2 (.f64 n (PI.f64))) k))) (sqrt.f64 2))
(.f64 (sqrt.f64 (/.f64 (.f64 n (PI.f64)) (pow.f64 (.f64 2 (.f64 n (PI.f64))) k))) (sqrt.f64 2))
(.f64 (sqrt.f64 (/.f64 (.f64 n (PI.f64)) (pow.f64 (.f64 2 (.f64 n (PI.f64))) k))) (sqrt.f64 2))
(.f64 (sqrt.f64 (/.f64 (.f64 n (PI.f64)) (pow.f64 (.f64 2 (.f64 n (PI.f64))) k))) (sqrt.f64 2))
(.f64 (sqrt.f64 (/.f64 (.f64 n (PI.f64)) (pow.f64 (.f64 2 (.f64 n (PI.f64))) k))) (sqrt.f64 2))
(.f64 (sqrt.f64 (/.f64 (.f64 n (PI.f64)) (pow.f64 (.f64 2 (.f64 n (PI.f64))) k))) (sqrt.f64 2))

Outputs
(.f64 (sqrt.f64 2) (sqrt.f64 (.f64 n (PI.f64))))
(+.f64 (.f64 -1/2 (.f64 (.f64 (sqrt.f64 2) (.f64 k (log.f64 (.f64 2 (.f64 n (PI.f64)))))) (sqrt.f64 (.f64 n (PI.f64))))) (.f64 (sqrt.f64 2) (sqrt.f64 (*.f64 n (PI.f64)))))
(fma.f64 -1/2 (.f64 (sqrt.f64 (.f64 n (PI.f64))) (.f64 (.f64 (sqrt.f64 2) k) (log.f64 (.f64 2 (.f64 n (PI.f64)))))) (.f64 (sqrt.f64 2) (sqrt.f64 (.f64 n (PI.f64)))))
(.f64 (sqrt.f64 (.f64 n (PI.f64))) (+.f64 (sqrt.f64 2) (.f64 -1/2 (.f64 (sqrt.f64 2) (.f64 k (log.f64 (.f64 n (*.f64 (PI.f64) 2))))))))
(.f64 (sqrt.f64 (.f64 n (PI.f64))) (fma.f64 -1/2 (.f64 k (.f64 (sqrt.f64 2) (log.f64 (.f64 2 (.f64 n (PI.f64)))))) (sqrt.f64 2)))
(+.f64 (.f64 -1/2 (.f64 (.f64 (sqrt.f64 2) (.f64 k (log.f64 (.f64 2 (.f64 n (PI.f64)))))) (sqrt.f64 (.f64 n (PI.f64))))) (+.f64 (.f64 (sqrt.f64 2) (sqrt.f64 (.f64 n (PI.f64)))) (.f64 -1/2 (.f64 (.f64 (sqrt.f64 2) (.f64 (pow.f64 k 2) (+.f64 (.f64 -1 (.f64 n (.f64 (pow.f64 (log.f64 (.f64 2 (.f64 n (PI.f64)))) 2) (PI.f64)))) (+.f64 (pow.f64 (.f64 -1/2 (.f64 (sqrt.f64 (.f64 n (PI.f64))) (log.f64 (.f64 2 (.f64 n (PI.f64)))))) 2) (.f64 1/2 (.f64 n (.f64 (PI.f64) (pow.f64 (log.f64 (.f64 2 (.f64 n (PI.f64)))) 2)))))))) (sqrt.f64 (/.f64 1 (*.f64 n (PI.f64))))))))
(fma.f64 -1/2 (.f64 (sqrt.f64 (.f64 n (PI.f64))) (.f64 (.f64 (sqrt.f64 2) k) (log.f64 (.f64 2 (.f64 n (PI.f64)))))) (fma.f64 (sqrt.f64 2) (sqrt.f64 (.f64 n (PI.f64))) (.f64 -1/2 (.f64 (sqrt.f64 2) (.f64 (.f64 (fma.f64 1/2 (.f64 (.f64 n (PI.f64)) (pow.f64 (log.f64 (.f64 2 (.f64 n (PI.f64)))) 2)) (fma.f64 -1 (.f64 (.f64 n (PI.f64)) (pow.f64 (log.f64 (.f64 2 (.f64 n (PI.f64)))) 2)) (pow.f64 (.f64 (.f64 -1/2 (sqrt.f64 (.f64 n (PI.f64)))) (log.f64 (.f64 2 (.f64 n (PI.f64))))) 2))) (.f64 k k)) (sqrt.f64 (/.f64 1 (.f64 n (PI.f64)))))))))
(+.f64 (.f64 (sqrt.f64 2) (.f64 (.f64 (.f64 (+.f64 (pow.f64 (.f64 (sqrt.f64 (.f64 n (PI.f64))) (.f64 (log.f64 (.f64 n (.f64 (PI.f64) 2))) -1/2)) 2) (.f64 (.f64 n (.f64 (PI.f64) (pow.f64 (log.f64 (.f64 n (.f64 (PI.f64) 2))) 2))) -1/2)) (.f64 k k)) (sqrt.f64 (/.f64 1 (.f64 n (PI.f64))))) -1/2)) (.f64 (sqrt.f64 (.f64 n (PI.f64))) (+.f64 (sqrt.f64 2) (.f64 -1/2 (.f64 (sqrt.f64 2) (.f64 k (log.f64 (.f64 n (*.f64 (PI.f64) 2)))))))))
(fma.f64 (sqrt.f64 (.f64 n (PI.f64))) (fma.f64 -1/2 (.f64 k (.f64 (sqrt.f64 2) (log.f64 (.f64 2 (.f64 n (PI.f64)))))) (sqrt.f64 2)) (.f64 (.f64 (fma.f64 (.f64 n (.f64 (PI.f64) (pow.f64 (log.f64 (.f64 2 (.f64 n (PI.f64)))) 2))) -1/2 (pow.f64 (.f64 (sqrt.f64 (.f64 n (PI.f64))) (.f64 -1/2 (log.f64 (.f64 2 (.f64 n (PI.f64)))))) 2)) (.f64 (sqrt.f64 2) (.f64 k k))) (*.f64 -1/2 (sqrt.f64 (/.f64 (/.f64 1 (PI.f64)) n)))))
(fma.f64 (sqrt.f64 (.f64 n (PI.f64))) (fma.f64 -1/2 (.f64 k (.f64 (sqrt.f64 2) (log.f64 (.f64 2 (.f64 n (PI.f64)))))) (sqrt.f64 2)) (.f64 (.f64 (.f64 (pow.f64 (log.f64 (.f64 2 (.f64 n (PI.f64)))) 2) (+.f64 (.f64 (.f64 n (PI.f64)) 1/4) (.f64 (.f64 n (PI.f64)) -1/2))) (.f64 (sqrt.f64 2) (.f64 k k))) (*.f64 -1/2 (sqrt.f64 (/.f64 (/.f64 1 (PI.f64)) n)))))
(+.f64 (.f64 -1/2 (.f64 (.f64 (sqrt.f64 2) (.f64 k (log.f64 (.f64 2 (.f64 n (PI.f64)))))) (sqrt.f64 (.f64 n (PI.f64))))) (+.f64 (.f64 -1/2 (.f64 (.f64 (sqrt.f64 2) (.f64 (pow.f64 k 3) (+.f64 (.f64 -1/2 (.f64 n (.f64 (pow.f64 (log.f64 (.f64 2 (.f64 n (PI.f64)))) 3) (PI.f64)))) (+.f64 (.f64 1/6 (.f64 n (.f64 (PI.f64) (pow.f64 (log.f64 (.f64 2 (.f64 n (PI.f64)))) 3)))) (+.f64 (.f64 1/2 (.f64 (+.f64 (.f64 1/2 (.f64 n (.f64 (pow.f64 (log.f64 (.f64 2 (.f64 n (PI.f64)))) 2) (PI.f64)))) (+.f64 (.f64 -1 (.f64 n (.f64 (PI.f64) (pow.f64 (log.f64 (.f64 2 (.f64 n (PI.f64)))) 2)))) (pow.f64 (.f64 -1/2 (.f64 (sqrt.f64 (.f64 n (PI.f64))) (log.f64 (.f64 2 (.f64 n (PI.f64)))))) 2))) (log.f64 (.f64 2 (.f64 n (PI.f64)))))) (.f64 -1 (.f64 (+.f64 (.f64 1/2 (.f64 n (.f64 (pow.f64 (log.f64 (.f64 2 (.f64 n (PI.f64)))) 2) (PI.f64)))) (.f64 -1 (.f64 n (.f64 (PI.f64) (pow.f64 (log.f64 (.f64 2 (.f64 n (PI.f64)))) 2))))) (log.f64 (.f64 2 (.f64 n (PI.f64))))))))))) (sqrt.f64 (/.f64 1 (.f64 n (PI.f64)))))) (+.f64 (.f64 (sqrt.f64 2) (sqrt.f64 (.f64 n (PI.f64)))) (.f64 -1/2 (.f64 (.f64 (sqrt.f64 2) (.f64 (pow.f64 k 2) (+.f64 (.f64 -1 (.f64 n (.f64 (pow.f64 (log.f64 (.f64 2 (.f64 n (PI.f64)))) 2) (PI.f64)))) (+.f64 (pow.f64 (.f64 -1/2 (.f64 (sqrt.f64 (.f64 n (PI.f64))) (log.f64 (.f64 2 (.f64 n (PI.f64)))))) 2) (.f64 1/2 (.f64 n (.f64 (PI.f64) (pow.f64 (log.f64 (.f64 2 (.f64 n (PI.f64)))) 2)))))))) (sqrt.f64 (/.f64 1 (*.f64 n (PI.f64)))))))))
(fma.f64 -1/2 (.f64 (sqrt.f64 (.f64 n (PI.f64))) (.f64 (.f64 (sqrt.f64 2) k) (log.f64 (.f64 2 (.f64 n (PI.f64)))))) (fma.f64 -1/2 (.f64 (sqrt.f64 (/.f64 1 (.f64 n (PI.f64)))) (.f64 (.f64 (sqrt.f64 2) (pow.f64 k 3)) (fma.f64 -1/2 (.f64 (.f64 n (PI.f64)) (pow.f64 (log.f64 (.f64 2 (.f64 n (PI.f64)))) 3)) (fma.f64 1/6 (.f64 (.f64 n (PI.f64)) (pow.f64 (log.f64 (.f64 2 (.f64 n (PI.f64)))) 3)) (fma.f64 1/2 (.f64 (log.f64 (.f64 2 (.f64 n (PI.f64)))) (fma.f64 1/2 (.f64 (.f64 n (PI.f64)) (pow.f64 (log.f64 (.f64 2 (.f64 n (PI.f64)))) 2)) (fma.f64 -1 (.f64 (.f64 n (PI.f64)) (pow.f64 (log.f64 (.f64 2 (.f64 n (PI.f64)))) 2)) (pow.f64 (.f64 (.f64 -1/2 (sqrt.f64 (.f64 n (PI.f64)))) (log.f64 (.f64 2 (.f64 n (PI.f64))))) 2)))) (neg.f64 (.f64 (log.f64 (.f64 2 (.f64 n (PI.f64)))) (fma.f64 1/2 (.f64 (.f64 n (PI.f64)) (pow.f64 (log.f64 (.f64 2 (.f64 n (PI.f64)))) 2)) (neg.f64 (.f64 (.f64 n (PI.f64)) (pow.f64 (log.f64 (.f64 2 (.f64 n (PI.f64)))) 2))))))))))) (fma.f64 (sqrt.f64 2) (sqrt.f64 (.f64 n (PI.f64))) (.f64 -1/2 (.f64 (sqrt.f64 2) (.f64 (.f64 (fma.f64 1/2 (.f64 (.f64 n (PI.f64)) (pow.f64 (log.f64 (.f64 2 (.f64 n (PI.f64)))) 2)) (fma.f64 -1 (.f64 (.f64 n (PI.f64)) (pow.f64 (log.f64 (.f64 2 (.f64 n (PI.f64)))) 2)) (pow.f64 (.f64 (.f64 -1/2 (sqrt.f64 (.f64 n (PI.f64)))) (log.f64 (.f64 2 (.f64 n (PI.f64))))) 2))) (.f64 k k)) (sqrt.f64 (/.f64 1 (*.f64 n (PI.f64))))))))))
(+.f64 (.f64 -1/2 (.f64 (sqrt.f64 (/.f64 1 (.f64 n (PI.f64)))) (.f64 (sqrt.f64 2) (.f64 (pow.f64 k 3) (+.f64 (.f64 (log.f64 (.f64 n (.f64 (PI.f64) 2))) (+.f64 (.f64 1/2 (+.f64 (pow.f64 (.f64 (sqrt.f64 (.f64 n (PI.f64))) (.f64 (log.f64 (.f64 n (.f64 (PI.f64) 2))) -1/2)) 2) (.f64 (.f64 n (.f64 (PI.f64) (pow.f64 (log.f64 (.f64 n (.f64 (PI.f64) 2))) 2))) -1/2))) (neg.f64 (.f64 (.f64 n (.f64 (PI.f64) (pow.f64 (log.f64 (.f64 n (.f64 (PI.f64) 2))) 2))) -1/2)))) (.f64 (.f64 n (.f64 (PI.f64) (pow.f64 (log.f64 (.f64 n (.f64 (PI.f64) 2))) 3))) -1/3)))))) (+.f64 (.f64 (sqrt.f64 2) (.f64 (.f64 (.f64 (+.f64 (pow.f64 (.f64 (sqrt.f64 (.f64 n (PI.f64))) (.f64 (log.f64 (.f64 n (.f64 (PI.f64) 2))) -1/2)) 2) (.f64 (.f64 n (.f64 (PI.f64) (pow.f64 (log.f64 (.f64 n (.f64 (PI.f64) 2))) 2))) -1/2)) (.f64 k k)) (sqrt.f64 (/.f64 1 (.f64 n (PI.f64))))) -1/2)) (.f64 (sqrt.f64 (.f64 n (PI.f64))) (+.f64 (sqrt.f64 2) (.f64 -1/2 (.f64 (sqrt.f64 2) (.f64 k (log.f64 (.f64 n (.f64 (PI.f64) 2))))))))))
(+.f64 (.f64 (sqrt.f64 (.f64 n (PI.f64))) (fma.f64 -1/2 (.f64 k (.f64 (sqrt.f64 2) (log.f64 (.f64 2 (.f64 n (PI.f64)))))) (sqrt.f64 2))) (.f64 (.f64 -1/2 (sqrt.f64 (/.f64 (/.f64 1 (PI.f64)) n))) (+.f64 (.f64 (fma.f64 (.f64 n (.f64 (PI.f64) (pow.f64 (log.f64 (.f64 2 (.f64 n (PI.f64)))) 2))) -1/2 (pow.f64 (.f64 (sqrt.f64 (.f64 n (PI.f64))) (.f64 -1/2 (log.f64 (.f64 2 (.f64 n (PI.f64)))))) 2)) (.f64 (sqrt.f64 2) (.f64 k k))) (.f64 (fma.f64 (log.f64 (.f64 2 (.f64 n (PI.f64)))) (fma.f64 1/2 (fma.f64 (.f64 n (.f64 (PI.f64) (pow.f64 (log.f64 (.f64 2 (.f64 n (PI.f64)))) 2))) -1/2 (pow.f64 (.f64 (sqrt.f64 (.f64 n (PI.f64))) (.f64 -1/2 (log.f64 (.f64 2 (.f64 n (PI.f64)))))) 2)) (.f64 (PI.f64) (.f64 (pow.f64 (log.f64 (.f64 2 (.f64 n (PI.f64)))) 2) (.f64 n 1/2)))) (.f64 (.f64 (PI.f64) (pow.f64 (log.f64 (.f64 2 (.f64 n (PI.f64)))) 3)) (.f64 n -1/3))) (*.f64 (sqrt.f64 2) (pow.f64 k 3))))))
(+.f64 (.f64 (sqrt.f64 (.f64 n (PI.f64))) (fma.f64 -1/2 (.f64 k (.f64 (sqrt.f64 2) (log.f64 (.f64 2 (.f64 n (PI.f64)))))) (sqrt.f64 2))) (.f64 -1/2 (.f64 (.f64 (sqrt.f64 2) (sqrt.f64 (/.f64 (/.f64 1 (PI.f64)) n))) (+.f64 (.f64 (pow.f64 k 3) (fma.f64 (log.f64 (.f64 2 (.f64 n (PI.f64)))) (.f64 1/2 (.f64 (pow.f64 (log.f64 (.f64 2 (.f64 n (PI.f64)))) 2) (+.f64 (.f64 (.f64 n (PI.f64)) 1/4) (.f64 (.f64 n (PI.f64)) 1/2)))) (.f64 (PI.f64) (.f64 (.f64 n (pow.f64 (log.f64 (.f64 2 (.f64 n (PI.f64)))) 3)) -1/3)))) (.f64 (.f64 (pow.f64 (log.f64 (.f64 2 (.f64 n (PI.f64)))) 2) (+.f64 (.f64 (.f64 n (PI.f64)) 1/4) (.f64 (.f64 n (PI.f64)) -1/2))) (.f64 k k))))))
(.f64 (sqrt.f64 (/.f64 (.f64 n (PI.f64)) (pow.f64 (.f64 2 (.f64 n (PI.f64))) k))) (sqrt.f64 2))
(.f64 (sqrt.f64 2) (sqrt.f64 (/.f64 n (/.f64 (pow.f64 (.f64 2 (*.f64 n (PI.f64))) k) (PI.f64)))))
(.f64 (sqrt.f64 2) (sqrt.f64 (/.f64 n (/.f64 (pow.f64 (.f64 n (*.f64 (PI.f64) 2)) k) (PI.f64)))))
(.f64 (sqrt.f64 2) (sqrt.f64 (.f64 (PI.f64) (/.f64 n (pow.f64 (.f64 2 (.f64 n (PI.f64))) k)))))
(.f64 (sqrt.f64 (/.f64 (.f64 n (PI.f64)) (pow.f64 (.f64 2 (.f64 n (PI.f64))) k))) (sqrt.f64 2))
(.f64 (sqrt.f64 2) (sqrt.f64 (/.f64 n (/.f64 (pow.f64 (.f64 2 (*.f64 n (PI.f64))) k) (PI.f64)))))
(.f64 (sqrt.f64 2) (sqrt.f64 (/.f64 n (/.f64 (pow.f64 (.f64 n (*.f64 (PI.f64) 2)) k) (PI.f64)))))
(.f64 (sqrt.f64 2) (sqrt.f64 (.f64 (PI.f64) (/.f64 n (pow.f64 (.f64 2 (.f64 n (PI.f64))) k)))))
(.f64 (sqrt.f64 (/.f64 (.f64 n (PI.f64)) (pow.f64 (.f64 2 (.f64 n (PI.f64))) k))) (sqrt.f64 2))
(.f64 (sqrt.f64 2) (sqrt.f64 (/.f64 n (/.f64 (pow.f64 (.f64 2 (*.f64 n (PI.f64))) k) (PI.f64)))))
(.f64 (sqrt.f64 2) (sqrt.f64 (/.f64 n (/.f64 (pow.f64 (.f64 n (*.f64 (PI.f64) 2)) k) (PI.f64)))))
(.f64 (sqrt.f64 2) (sqrt.f64 (.f64 (PI.f64) (/.f64 n (pow.f64 (.f64 2 (.f64 n (PI.f64))) k)))))
(.f64 (sqrt.f64 (/.f64 (.f64 n (PI.f64)) (pow.f64 (.f64 2 (.f64 n (PI.f64))) k))) (sqrt.f64 2))
(.f64 (sqrt.f64 2) (sqrt.f64 (/.f64 n (/.f64 (pow.f64 (.f64 2 (*.f64 n (PI.f64))) k) (PI.f64)))))
(.f64 (sqrt.f64 2) (sqrt.f64 (/.f64 n (/.f64 (pow.f64 (.f64 n (*.f64 (PI.f64) 2)) k) (PI.f64)))))
(.f64 (sqrt.f64 2) (sqrt.f64 (.f64 (PI.f64) (/.f64 n (pow.f64 (.f64 2 (.f64 n (PI.f64))) k)))))
(.f64 (sqrt.f64 (/.f64 (.f64 n (PI.f64)) (pow.f64 (.f64 2 (.f64 n (PI.f64))) k))) (sqrt.f64 2))
(.f64 (sqrt.f64 2) (sqrt.f64 (/.f64 n (/.f64 (pow.f64 (.f64 2 (*.f64 n (PI.f64))) k) (PI.f64)))))
(.f64 (sqrt.f64 2) (sqrt.f64 (/.f64 n (/.f64 (pow.f64 (.f64 n (*.f64 (PI.f64) 2)) k) (PI.f64)))))
(.f64 (sqrt.f64 2) (sqrt.f64 (.f64 (PI.f64) (/.f64 n (pow.f64 (.f64 2 (.f64 n (PI.f64))) k)))))
(.f64 (sqrt.f64 (/.f64 (.f64 n (PI.f64)) (pow.f64 (.f64 2 (.f64 n (PI.f64))) k))) (sqrt.f64 2))
(.f64 (sqrt.f64 2) (sqrt.f64 (/.f64 n (/.f64 (pow.f64 (.f64 2 (*.f64 n (PI.f64))) k) (PI.f64)))))
(.f64 (sqrt.f64 2) (sqrt.f64 (/.f64 n (/.f64 (pow.f64 (.f64 n (*.f64 (PI.f64) 2)) k) (PI.f64)))))
(.f64 (sqrt.f64 2) (sqrt.f64 (.f64 (PI.f64) (/.f64 n (pow.f64 (.f64 2 (.f64 n (PI.f64))) k)))))
(.f64 (sqrt.f64 (/.f64 (.f64 n (PI.f64)) (pow.f64 (.f64 2 (.f64 n (PI.f64))) k))) (sqrt.f64 2))
(.f64 (sqrt.f64 2) (sqrt.f64 (/.f64 n (/.f64 (pow.f64 (.f64 2 (*.f64 n (PI.f64))) k) (PI.f64)))))
(.f64 (sqrt.f64 2) (sqrt.f64 (/.f64 n (/.f64 (pow.f64 (.f64 n (*.f64 (PI.f64) 2)) k) (PI.f64)))))
(.f64 (sqrt.f64 2) (sqrt.f64 (.f64 (PI.f64) (/.f64 n (pow.f64 (.f64 2 (.f64 n (PI.f64))) k)))))
(.f64 (sqrt.f64 (/.f64 (.f64 n (PI.f64)) (pow.f64 (.f64 2 (.f64 n (PI.f64))) k))) (sqrt.f64 2))
(.f64 (sqrt.f64 2) (sqrt.f64 (/.f64 n (/.f64 (pow.f64 (.f64 2 (*.f64 n (PI.f64))) k) (PI.f64)))))
(.f64 (sqrt.f64 2) (sqrt.f64 (/.f64 n (/.f64 (pow.f64 (.f64 n (*.f64 (PI.f64) 2)) k) (PI.f64)))))
(.f64 (sqrt.f64 2) (sqrt.f64 (.f64 (PI.f64) (/.f64 n (pow.f64 (.f64 2 (.f64 n (PI.f64))) k)))))

localize13.0ms (0.1%)

Local error

Found 6 expressions with local error:

New	Error	Program
	9.1b	(sqrt.f64 (/.f64 (.f64 2 (.f64 n (PI.f64))) k))
	0.2b	(*.f64 n (PI.f64))
	0.2b	(/.f64 (.f64 2 (.f64 n (PI.f64))) k)
✓	0.2b	(/.f64 (.f64 2 (.f64 n (PI.f64))) k)
✓	0.2b	(*.f64 n (PI.f64))
✓	9.1b	(sqrt.f64 (/.f64 (.f64 2 (.f64 n (PI.f64))) k))

Compiler

Compiled 29 to 14 computations (51.7% saved)

series11.0ms (0.1%)

Counts

3 → 24

Calls

15 calls:

Time	Variable		Point	Expression
3.0ms	n	@	-inf	(sqrt.f64 (/.f64 (.f64 2 (.f64 n (PI.f64))) k))
1.0ms	n	@	0	(sqrt.f64 (/.f64 (.f64 2 (.f64 n (PI.f64))) k))
1.0ms	k	@	-inf	(sqrt.f64 (/.f64 (.f64 2 (.f64 n (PI.f64))) k))
1.0ms	n	@	inf	(sqrt.f64 (/.f64 (.f64 2 (.f64 n (PI.f64))) k))
1.0ms	k	@	0	(sqrt.f64 (/.f64 (.f64 2 (.f64 n (PI.f64))) k))

rewrite65.0ms (0.7%)

Algorithm

1×	batch-egg-rewrite

Rules

524×	`log-prod_binary64`
396×	`exp-prod_binary64`
353×	`prod-exp_binary64`
295×	`pow-prod-down_binary64`
240×	`pow2_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	9	29
1	189	29
2	2487	29

Stop Event

1×	node limit

Counts

3 → 159

Calls

Call 1

Inputs
(sqrt.f64 (/.f64 (.f64 2 (.f64 n (PI.f64))) k))
(*.f64 n (PI.f64))
(/.f64 (.f64 2 (.f64 n (PI.f64))) k)

Outputs

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simplify17.0ms (0.2%)

Algorithm

1×	egg-herbie

Rules

15×	`associate-/l*_binary64`
14×	`*-commutative_binary64`
11×	`associate-/r/_binary64`
10×	`associate-r_binary64`
8×	`associate-l_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	8	264
1	14	264
2	29	264
3	55	264
4	85	264
5	96	264

Stop Event

1×

saturated

Counts

183 → 160

Calls

Call 1

Inputs
(.f64 2 (/.f64 (.f64 n (PI.f64)) k))
(.f64 2 (/.f64 (.f64 n (PI.f64)) k))
(.f64 2 (/.f64 (.f64 n (PI.f64)) k))
(.f64 2 (/.f64 (.f64 n (PI.f64)) k))
(.f64 2 (/.f64 (.f64 n (PI.f64)) k))
(.f64 2 (/.f64 (.f64 n (PI.f64)) k))
(.f64 2 (/.f64 (.f64 n (PI.f64)) k))
(.f64 2 (/.f64 (.f64 n (PI.f64)) k))
(.f64 2 (/.f64 (.f64 n (PI.f64)) k))
(.f64 2 (/.f64 (.f64 n (PI.f64)) k))
(.f64 2 (/.f64 (.f64 n (PI.f64)) k))
(.f64 2 (/.f64 (.f64 n (PI.f64)) k))
(.f64 2 (/.f64 (.f64 n (PI.f64)) k))
(.f64 2 (/.f64 (.f64 n (PI.f64)) k))
(.f64 2 (/.f64 (.f64 n (PI.f64)) k))
(.f64 2 (/.f64 (.f64 n (PI.f64)) k))
(.f64 2 (/.f64 (.f64 n (PI.f64)) k))
(.f64 2 (/.f64 (.f64 n (PI.f64)) k))
(.f64 2 (/.f64 (.f64 n (PI.f64)) k))
(.f64 2 (/.f64 (.f64 n (PI.f64)) k))
(.f64 2 (/.f64 (.f64 n (PI.f64)) k))
(.f64 2 (/.f64 (.f64 n (PI.f64)) k))
(.f64 2 (/.f64 (.f64 n (PI.f64)) k))
(.f64 2 (/.f64 (.f64 n (PI.f64)) k))

Outputs
(.f64 2 (/.f64 (.f64 n (PI.f64)) k))
(*.f64 2 (/.f64 n (/.f64 k (PI.f64))))
(/.f64 (*.f64 n 2) (/.f64 k (PI.f64)))
(.f64 (/.f64 (.f64 2 n) k) (PI.f64))
(/.f64 (*.f64 2 (PI.f64)) (/.f64 k n))
(*.f64 2 (/.f64 (PI.f64) (/.f64 k n)))
(.f64 2 (/.f64 (.f64 n (PI.f64)) k))
(*.f64 2 (/.f64 n (/.f64 k (PI.f64))))
(/.f64 (*.f64 n 2) (/.f64 k (PI.f64)))
(.f64 (/.f64 (.f64 2 n) k) (PI.f64))
(/.f64 (*.f64 2 (PI.f64)) (/.f64 k n))
(*.f64 2 (/.f64 (PI.f64) (/.f64 k n)))
(.f64 2 (/.f64 (.f64 n (PI.f64)) k))
(*.f64 2 (/.f64 n (/.f64 k (PI.f64))))
(/.f64 (*.f64 n 2) (/.f64 k (PI.f64)))
(.f64 (/.f64 (.f64 2 n) k) (PI.f64))
(/.f64 (*.f64 2 (PI.f64)) (/.f64 k n))
(*.f64 2 (/.f64 (PI.f64) (/.f64 k n)))
(.f64 2 (/.f64 (.f64 n (PI.f64)) k))
(*.f64 2 (/.f64 n (/.f64 k (PI.f64))))
(/.f64 (*.f64 n 2) (/.f64 k (PI.f64)))
(.f64 (/.f64 (.f64 2 n) k) (PI.f64))
(/.f64 (*.f64 2 (PI.f64)) (/.f64 k n))
(*.f64 2 (/.f64 (PI.f64) (/.f64 k n)))
(.f64 2 (/.f64 (.f64 n (PI.f64)) k))
(*.f64 2 (/.f64 n (/.f64 k (PI.f64))))
(/.f64 (*.f64 n 2) (/.f64 k (PI.f64)))
(.f64 (/.f64 (.f64 2 n) k) (PI.f64))
(/.f64 (*.f64 2 (PI.f64)) (/.f64 k n))
(*.f64 2 (/.f64 (PI.f64) (/.f64 k n)))
(.f64 2 (/.f64 (.f64 n (PI.f64)) k))
(*.f64 2 (/.f64 n (/.f64 k (PI.f64))))
(/.f64 (*.f64 n 2) (/.f64 k (PI.f64)))
(.f64 (/.f64 (.f64 2 n) k) (PI.f64))
(/.f64 (*.f64 2 (PI.f64)) (/.f64 k n))
(*.f64 2 (/.f64 (PI.f64) (/.f64 k n)))
(.f64 2 (/.f64 (.f64 n (PI.f64)) k))
(*.f64 2 (/.f64 n (/.f64 k (PI.f64))))
(/.f64 (*.f64 n 2) (/.f64 k (PI.f64)))
(.f64 (/.f64 (.f64 2 n) k) (PI.f64))
(/.f64 (*.f64 2 (PI.f64)) (/.f64 k n))
(*.f64 2 (/.f64 (PI.f64) (/.f64 k n)))
(.f64 2 (/.f64 (.f64 n (PI.f64)) k))
(*.f64 2 (/.f64 n (/.f64 k (PI.f64))))
(/.f64 (*.f64 n 2) (/.f64 k (PI.f64)))
(.f64 (/.f64 (.f64 2 n) k) (PI.f64))
(/.f64 (*.f64 2 (PI.f64)) (/.f64 k n))
(*.f64 2 (/.f64 (PI.f64) (/.f64 k n)))
(.f64 2 (/.f64 (.f64 n (PI.f64)) k))
(*.f64 2 (/.f64 n (/.f64 k (PI.f64))))
(/.f64 (*.f64 n 2) (/.f64 k (PI.f64)))
(.f64 (/.f64 (.f64 2 n) k) (PI.f64))
(/.f64 (*.f64 2 (PI.f64)) (/.f64 k n))
(*.f64 2 (/.f64 (PI.f64) (/.f64 k n)))
(.f64 2 (/.f64 (.f64 n (PI.f64)) k))
(*.f64 2 (/.f64 n (/.f64 k (PI.f64))))
(/.f64 (*.f64 n 2) (/.f64 k (PI.f64)))
(.f64 (/.f64 (.f64 2 n) k) (PI.f64))
(/.f64 (*.f64 2 (PI.f64)) (/.f64 k n))
(*.f64 2 (/.f64 (PI.f64) (/.f64 k n)))
(.f64 2 (/.f64 (.f64 n (PI.f64)) k))
(*.f64 2 (/.f64 n (/.f64 k (PI.f64))))
(/.f64 (*.f64 n 2) (/.f64 k (PI.f64)))
(.f64 (/.f64 (.f64 2 n) k) (PI.f64))
(/.f64 (*.f64 2 (PI.f64)) (/.f64 k n))
(*.f64 2 (/.f64 (PI.f64) (/.f64 k n)))
(.f64 2 (/.f64 (.f64 n (PI.f64)) k))
(*.f64 2 (/.f64 n (/.f64 k (PI.f64))))
(/.f64 (*.f64 n 2) (/.f64 k (PI.f64)))
(.f64 (/.f64 (.f64 2 n) k) (PI.f64))
(/.f64 (*.f64 2 (PI.f64)) (/.f64 k n))
(*.f64 2 (/.f64 (PI.f64) (/.f64 k n)))
(.f64 2 (/.f64 (.f64 n (PI.f64)) k))
(*.f64 2 (/.f64 n (/.f64 k (PI.f64))))
(/.f64 (*.f64 n 2) (/.f64 k (PI.f64)))
(.f64 (/.f64 (.f64 2 n) k) (PI.f64))
(/.f64 (*.f64 2 (PI.f64)) (/.f64 k n))
(*.f64 2 (/.f64 (PI.f64) (/.f64 k n)))
(.f64 2 (/.f64 (.f64 n (PI.f64)) k))
(*.f64 2 (/.f64 n (/.f64 k (PI.f64))))
(/.f64 (*.f64 n 2) (/.f64 k (PI.f64)))
(.f64 (/.f64 (.f64 2 n) k) (PI.f64))
(/.f64 (*.f64 2 (PI.f64)) (/.f64 k n))
(*.f64 2 (/.f64 (PI.f64) (/.f64 k n)))
(.f64 2 (/.f64 (.f64 n (PI.f64)) k))
(*.f64 2 (/.f64 n (/.f64 k (PI.f64))))
(/.f64 (*.f64 n 2) (/.f64 k (PI.f64)))
(.f64 (/.f64 (.f64 2 n) k) (PI.f64))
(/.f64 (*.f64 2 (PI.f64)) (/.f64 k n))
(*.f64 2 (/.f64 (PI.f64) (/.f64 k n)))
(.f64 2 (/.f64 (.f64 n (PI.f64)) k))
(*.f64 2 (/.f64 n (/.f64 k (PI.f64))))
(/.f64 (*.f64 n 2) (/.f64 k (PI.f64)))
(.f64 (/.f64 (.f64 2 n) k) (PI.f64))
(/.f64 (*.f64 2 (PI.f64)) (/.f64 k n))
(*.f64 2 (/.f64 (PI.f64) (/.f64 k n)))
(.f64 2 (/.f64 (.f64 n (PI.f64)) k))
(*.f64 2 (/.f64 n (/.f64 k (PI.f64))))
(/.f64 (*.f64 n 2) (/.f64 k (PI.f64)))
(.f64 (/.f64 (.f64 2 n) k) (PI.f64))
(/.f64 (*.f64 2 (PI.f64)) (/.f64 k n))
(*.f64 2 (/.f64 (PI.f64) (/.f64 k n)))
(.f64 2 (/.f64 (.f64 n (PI.f64)) k))
(*.f64 2 (/.f64 n (/.f64 k (PI.f64))))
(/.f64 (*.f64 n 2) (/.f64 k (PI.f64)))
(.f64 (/.f64 (.f64 2 n) k) (PI.f64))
(/.f64 (*.f64 2 (PI.f64)) (/.f64 k n))
(*.f64 2 (/.f64 (PI.f64) (/.f64 k n)))
(.f64 2 (/.f64 (.f64 n (PI.f64)) k))
(*.f64 2 (/.f64 n (/.f64 k (PI.f64))))
(/.f64 (*.f64 n 2) (/.f64 k (PI.f64)))
(.f64 (/.f64 (.f64 2 n) k) (PI.f64))
(/.f64 (*.f64 2 (PI.f64)) (/.f64 k n))
(*.f64 2 (/.f64 (PI.f64) (/.f64 k n)))
(.f64 2 (/.f64 (.f64 n (PI.f64)) k))
(*.f64 2 (/.f64 n (/.f64 k (PI.f64))))
(/.f64 (*.f64 n 2) (/.f64 k (PI.f64)))
(.f64 (/.f64 (.f64 2 n) k) (PI.f64))
(/.f64 (*.f64 2 (PI.f64)) (/.f64 k n))
(*.f64 2 (/.f64 (PI.f64) (/.f64 k n)))
(.f64 2 (/.f64 (.f64 n (PI.f64)) k))
(*.f64 2 (/.f64 n (/.f64 k (PI.f64))))
(/.f64 (*.f64 n 2) (/.f64 k (PI.f64)))
(.f64 (/.f64 (.f64 2 n) k) (PI.f64))
(/.f64 (*.f64 2 (PI.f64)) (/.f64 k n))
(*.f64 2 (/.f64 (PI.f64) (/.f64 k n)))
(.f64 2 (/.f64 (.f64 n (PI.f64)) k))
(*.f64 2 (/.f64 n (/.f64 k (PI.f64))))
(/.f64 (*.f64 n 2) (/.f64 k (PI.f64)))
(.f64 (/.f64 (.f64 2 n) k) (PI.f64))
(/.f64 (*.f64 2 (PI.f64)) (/.f64 k n))
(*.f64 2 (/.f64 (PI.f64) (/.f64 k n)))
(.f64 2 (/.f64 (.f64 n (PI.f64)) k))
(*.f64 2 (/.f64 n (/.f64 k (PI.f64))))
(/.f64 (*.f64 n 2) (/.f64 k (PI.f64)))
(.f64 (/.f64 (.f64 2 n) k) (PI.f64))
(/.f64 (*.f64 2 (PI.f64)) (/.f64 k n))
(*.f64 2 (/.f64 (PI.f64) (/.f64 k n)))
(.f64 2 (/.f64 (.f64 n (PI.f64)) k))
(*.f64 2 (/.f64 n (/.f64 k (PI.f64))))
(/.f64 (*.f64 n 2) (/.f64 k (PI.f64)))
(.f64 (/.f64 (.f64 2 n) k) (PI.f64))
(/.f64 (*.f64 2 (PI.f64)) (/.f64 k n))
(*.f64 2 (/.f64 (PI.f64) (/.f64 k n)))

localize27.0ms (0.3%)

Local error

Found 8 expressions with local error:

New	Error	Program
	9.0b	(sqrt.f64 (.f64 (pow.f64 (.f64 n (*.f64 2 (PI.f64))) (-.f64 1 k)) (/.f64 1 k)))
	0.4b	(pow.f64 (.f64 n (.f64 2 (PI.f64))) (-.f64 1 k))
	0.2b	(.f64 n (.f64 2 (PI.f64)))
	0.2b	(.f64 (pow.f64 (.f64 n (*.f64 2 (PI.f64))) (-.f64 1 k)) (/.f64 1 k))
✓	0.2b	(.f64 (pow.f64 (.f64 n (*.f64 2 (PI.f64))) (-.f64 1 k)) (/.f64 1 k))
	0.2b	(.f64 n (.f64 2 (PI.f64)))
✓	0.4b	(pow.f64 (.f64 n (.f64 2 (PI.f64))) (-.f64 1 k))
✓	9.0b	(sqrt.f64 (.f64 (pow.f64 (.f64 n (*.f64 2 (PI.f64))) (-.f64 1 k)) (/.f64 1 k)))

Compiler

Compiled 57 to 39 computations (31.6% saved)

series6.0ms (0.1%)

Counts

3 → 60

Calls

18 calls:

Time	Variable		Point	Expression
1.0ms	k	@	0	(sqrt.f64 (.f64 (pow.f64 (.f64 n (*.f64 2 (PI.f64))) (-.f64 1 k)) (/.f64 1 k)))
1.0ms	k	@	-inf	(sqrt.f64 (.f64 (pow.f64 (.f64 n (*.f64 2 (PI.f64))) (-.f64 1 k)) (/.f64 1 k)))
0.0ms	k	@	inf	(sqrt.f64 (.f64 (pow.f64 (.f64 n (*.f64 2 (PI.f64))) (-.f64 1 k)) (/.f64 1 k)))
0.0ms	n	@	0	(sqrt.f64 (.f64 (pow.f64 (.f64 n (*.f64 2 (PI.f64))) (-.f64 1 k)) (/.f64 1 k)))
0.0ms	k	@	0	(pow.f64 (.f64 n (.f64 2 (PI.f64))) (-.f64 1 k))

rewrite70.0ms (0.7%)

Algorithm

1×	batch-egg-rewrite

Rules

700×	`log-prod_binary64`
519×	`pow-unpow_binary64`
349×	`pow2_binary64`
239×	`pow1/3_binary64`
235×	`expm1-udef_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	13	50
1	282	50
2	3610	50

Stop Event

1×	node limit

Counts

3 → 107

Calls

Call 1

Inputs

(sqrt.f64 (*.f64 (pow.f64 (*.f64 n (*.f64 2 (PI.f64))) (-.f64 1 k)) (/.f64 1 k)))

(pow.f64 (*.f64 n (*.f64 2 (PI.f64))) (-.f64 1 k))

(*.f64 (pow.f64 (*.f64 n (*.f64 2 (PI.f64))) (-.f64 1 k)) (/.f64 1 k))

Outputs

((#(struct:change #<rule egg-rr> (2) ((x +.f64 0 (sqrt.f64 (/.f64 (pow.f64 (*.f64 2 (*.f64 (PI.f64) n)) (-.f64 1 k)) k)))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (log.f64 (pow.f64 (cbrt.f64 (exp.f64 (sqrt.f64 (/.f64 (pow.f64 (*.f64 2 (*.f64 (PI.f64) n)) (-.f64 1 k)) k)))) 2)) (log.f64 (cbrt.f64 (exp.f64 (sqrt.f64 (/.f64 (pow.f64 (*.f64 2 (*.f64 (PI.f64) n)) (-.f64 1 k)) k))))))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (log.f64 (sqrt.f64 (exp.f64 (sqrt.f64 (/.f64 (pow.f64 (*.f64 2 (*.f64 (PI.f64) n)) (-.f64 1 k)) k))))) (log.f64 (sqrt.f64 (exp.f64 (sqrt.f64 (/.f64 (pow.f64 (*.f64 2 (*.f64 (PI.f64) n)) (-.f64 1 k)) k))))))))) (#(struct:change #<rule egg-rr> (2) ((x -.f64 (exp.f64 (log1p.f64 (sqrt.f64 (/.f64 (pow.f64 (*.f64 2 (*.f64 (PI.f64) n)) (-.f64 1 k)) k)))) 1)))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 1 (sqrt.f64 (/.f64 (pow.f64 (*.f64 2 (*.f64 (PI.f64) n)) (-.f64 1 k)) k)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (sqrt.f64 (/.f64 (pow.f64 (*.f64 2 (*.f64 (PI.f64) n)) (-.f64 1 k)) k)) 1)))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (cbrt.f64 (/.f64 (pow.f64 (*.f64 2 (*.f64 (PI.f64) n)) (-.f64 1 k)) k)) (cbrt.f64 (sqrt.f64 (/.f64 (pow.f64 (*.f64 2 (*.f64 (PI.f64) n)) (-.f64 1 k)) k))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (cbrt.f64 (sqrt.f64 (/.f64 (pow.f64 (*.f64 2 (*.f64 (PI.f64) n)) (-.f64 1 k)) k))) (cbrt.f64 (/.f64 (pow.f64 (*.f64 2 (*.f64 (PI.f64) n)) (-.f64 1 k)) k)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (pow.f64 k -1/2) (sqrt.f64 (pow.f64 (*.f64 2 (*.f64 (PI.f64) n)) (-.f64 1 k))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (pow.f64 (/.f64 (pow.f64 (*.f64 2 (*.f64 (PI.f64) n)) (-.f64 1 k)) k) 1/4) (pow.f64 (/.f64 (pow.f64 (*.f64 2 (*.f64 (PI.f64) n)) (-.f64 1 k)) k) 1/4))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (sqrt.f64 (pow.f64 (*.f64 2 (*.f64 (PI.f64) n)) (-.f64 1 k))) (pow.f64 k -1/2))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (sqrt.f64 (cbrt.f64 (pow.f64 (/.f64 (pow.f64 (*.f64 2 (*.f64 (PI.f64) n)) (-.f64 1 k)) k) 2))) (sqrt.f64 (cbrt.f64 (/.f64 (pow.f64 (*.f64 2 (*.f64 (PI.f64) n)) (-.f64 1 k)) k))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (pow.f64 1 1/2) (sqrt.f64 (/.f64 (pow.f64 (*.f64 2 (*.f64 (PI.f64) n)) (-.f64 1 k)) k)))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (sqrt.f64 (pow.f64 (*.f64 2 (*.f64 (PI.f64) n)) (-.f64 1 k))) (sqrt.f64 k))))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (/.f64 (pow.f64 (*.f64 2 (*.f64 (PI.f64) n)) (-.f64 1 k)) k) 1/2)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (sqrt.f64 (/.f64 (pow.f64 (*.f64 2 (*.f64 (PI.f64) n)) (-.f64 1 k)) k)) 1)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (pow.f64 (/.f64 (pow.f64 (*.f64 2 (*.f64 (PI.f64) n)) (-.f64 1 k)) k) 3/2) 1/3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (cbrt.f64 (sqrt.f64 (/.f64 (pow.f64 (*.f64 2 (*.f64 (PI.f64) n)) (-.f64 1 k)) k))) 3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (pow.f64 (/.f64 (pow.f64 (*.f64 2 (*.f64 (PI.f64) n)) (-.f64 1 k)) k) 1/4) 2)))) (#(struct:change #<rule egg-rr> (2) ((x fabs.f64 (sqrt.f64 (/.f64 (pow.f64 (*.f64 2 (*.f64 (PI.f64) n)) (-.f64 1 k)) k)))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (exp.f64 (sqrt.f64 (/.f64 (pow.f64 (*.f64 2 (*.f64 (PI.f64) n)) (-.f64 1 k)) k))))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (+.f64 1 (expm1.f64 (sqrt.f64 (/.f64 (pow.f64 (*.f64 2 (*.f64 (PI.f64) n)) (-.f64 1 k)) k)))))))) (#(struct:change #<rule egg-rr> (2) ((x cbrt.f64 (pow.f64 (/.f64 (pow.f64 (*.f64 2 (*.f64 (PI.f64) n)) (-.f64 1 k)) k) 3/2))))) (#(struct:change #<rule egg-rr> (2) ((x expm1.f64 (log1p.f64 (sqrt.f64 (/.f64 (pow.f64 (*.f64 2 (*.f64 (PI.f64) n)) (-.f64 1 k)) k))))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (log.f64 (sqrt.f64 (/.f64 (pow.f64 (*.f64 2 (*.f64 (PI.f64) n)) (-.f64 1 k)) k))))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (*.f64 (log.f64 (/.f64 (pow.f64 (*.f64 2 (*.f64 (PI.f64) n)) (-.f64 1 k)) k)) 1/2))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (*.f64 (log.f64 (sqrt.f64 (/.f64 (pow.f64 (*.f64 2 (*.f64 (PI.f64) n)) (-.f64 1 k)) k))) 1))))) (#(struct:change #<rule egg-rr> (2) ((x log1p.f64 (expm1.f64 (sqrt.f64 (/.f64 (pow.f64 (*.f64 2 (*.f64 (PI.f64) n)) (-.f64 1 k)) k))))))))

((#(struct:change #<rule egg-rr> (2) ((x +.f64 0 (pow.f64 (*.f64 2 (*.f64 (PI.f64) n)) (-.f64 1 k)))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (log.f64 (pow.f64 (cbrt.f64 (exp.f64 (pow.f64 (*.f64 2 (*.f64 (PI.f64) n)) (-.f64 1 k)))) 2)) (log.f64 (cbrt.f64 (exp.f64 (pow.f64 (*.f64 2 (*.f64 (PI.f64) n)) (-.f64 1 k))))))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (log.f64 (sqrt.f64 (exp.f64 (pow.f64 (*.f64 2 (*.f64 (PI.f64) n)) (-.f64 1 k))))) (log.f64 (sqrt.f64 (exp.f64 (pow.f64 (*.f64 2 (*.f64 (PI.f64) n)) (-.f64 1 k))))))))) (#(struct:change #<rule egg-rr> (2) ((x -.f64 (exp.f64 (log1p.f64 (pow.f64 (*.f64 2 (*.f64 (PI.f64) n)) (-.f64 1 k)))) 1)))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (*.f64 2 (*.f64 (PI.f64) n)) (pow.f64 (*.f64 2 (*.f64 (PI.f64) n)) (neg.f64 k)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (*.f64 2 (*.f64 (PI.f64) n)) (/.f64 1 (pow.f64 (*.f64 2 (*.f64 (PI.f64) n)) k)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (*.f64 2 (*.f64 (PI.f64) 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simplify56.0ms (0.6%)

Algorithm

1×	egg-herbie

Rules

580×	`associate-+l+_binary64`
475×	`associate-l_binary64`
439×	`fma-def_binary64`
400×	`associate-r_binary64`
330×	`distribute-lft-out_binary64`

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	84	1569
1	241	1477
2	774	1289
3	4236	1184

Stop Event

1×	node limit

Counts

167 → 142

Calls

Call 1

Inputs
(sqrt.f64 (/.f64 (exp.f64 (.f64 (-.f64 1 k) (+.f64 (log.f64 n) (log.f64 (.f64 2 (PI.f64)))))) k))
(sqrt.f64 (/.f64 (exp.f64 (.f64 (-.f64 1 k) (+.f64 (log.f64 n) (log.f64 (.f64 2 (PI.f64)))))) k))
(sqrt.f64 (/.f64 (exp.f64 (.f64 (-.f64 1 k) (+.f64 (log.f64 n) (log.f64 (.f64 2 (PI.f64)))))) k))
(sqrt.f64 (/.f64 (exp.f64 (.f64 (-.f64 1 k) (+.f64 (log.f64 n) (log.f64 (.f64 2 (PI.f64)))))) k))
(sqrt.f64 (/.f64 (exp.f64 (.f64 (-.f64 1 k) (+.f64 (.f64 -1 (log.f64 (/.f64 1 n))) (log.f64 (*.f64 2 (PI.f64)))))) k))
(sqrt.f64 (/.f64 (exp.f64 (.f64 (-.f64 1 k) (+.f64 (.f64 -1 (log.f64 (/.f64 1 n))) (log.f64 (*.f64 2 (PI.f64)))))) k))
(sqrt.f64 (/.f64 (exp.f64 (.f64 (-.f64 1 k) (+.f64 (.f64 -1 (log.f64 (/.f64 1 n))) (log.f64 (*.f64 2 (PI.f64)))))) k))
(sqrt.f64 (/.f64 (exp.f64 (.f64 (-.f64 1 k) (+.f64 (.f64 -1 (log.f64 (/.f64 1 n))) (log.f64 (*.f64 2 (PI.f64)))))) k))
(sqrt.f64 (/.f64 (exp.f64 (.f64 (-.f64 1 k) (+.f64 (.f64 -1 (log.f64 (/.f64 -1 n))) (log.f64 (*.f64 -2 (PI.f64)))))) k))
(sqrt.f64 (/.f64 (exp.f64 (.f64 (-.f64 1 k) (+.f64 (.f64 -1 (log.f64 (/.f64 -1 n))) (log.f64 (*.f64 -2 (PI.f64)))))) k))
(sqrt.f64 (/.f64 (exp.f64 (.f64 (-.f64 1 k) (+.f64 (.f64 -1 (log.f64 (/.f64 -1 n))) (log.f64 (*.f64 -2 (PI.f64)))))) k))
(sqrt.f64 (/.f64 (exp.f64 (.f64 (-.f64 1 k) (+.f64 (.f64 -1 (log.f64 (/.f64 -1 n))) (log.f64 (*.f64 -2 (PI.f64)))))) k))
(exp.f64 (.f64 (-.f64 1 k) (+.f64 (log.f64 n) (log.f64 (.f64 2 (PI.f64))))))
(exp.f64 (.f64 (-.f64 1 k) (+.f64 (log.f64 n) (log.f64 (.f64 2 (PI.f64))))))
(exp.f64 (.f64 (-.f64 1 k) (+.f64 (log.f64 n) (log.f64 (.f64 2 (PI.f64))))))
(exp.f64 (.f64 (-.f64 1 k) (+.f64 (log.f64 n) (log.f64 (.f64 2 (PI.f64))))))
(exp.f64 (.f64 (-.f64 1 k) (+.f64 (.f64 -1 (log.f64 (/.f64 1 n))) (log.f64 (*.f64 2 (PI.f64))))))
(exp.f64 (.f64 (-.f64 1 k) (+.f64 (.f64 -1 (log.f64 (/.f64 1 n))) (log.f64 (*.f64 2 (PI.f64))))))
(exp.f64 (.f64 (-.f64 1 k) (+.f64 (.f64 -1 (log.f64 (/.f64 1 n))) (log.f64 (*.f64 2 (PI.f64))))))
(exp.f64 (.f64 (-.f64 1 k) (+.f64 (.f64 -1 (log.f64 (/.f64 1 n))) (log.f64 (*.f64 2 (PI.f64))))))
(exp.f64 (.f64 (-.f64 1 k) (+.f64 (.f64 -1 (log.f64 (/.f64 -1 n))) (log.f64 (*.f64 -2 (PI.f64))))))
(exp.f64 (.f64 (-.f64 1 k) (+.f64 (.f64 -1 (log.f64 (/.f64 -1 n))) (log.f64 (*.f64 -2 (PI.f64))))))
(exp.f64 (.f64 (-.f64 1 k) (+.f64 (.f64 -1 (log.f64 (/.f64 -1 n))) (log.f64 (*.f64 -2 (PI.f64))))))
(exp.f64 (.f64 (-.f64 1 k) (+.f64 (.f64 -1 (log.f64 (/.f64 -1 n))) (log.f64 (*.f64 -2 (PI.f64))))))
(.f64 2 (.f64 n (PI.f64)))
(+.f64 (.f64 -2 (.f64 k (.f64 n (.f64 (PI.f64) (log.f64 (.f64 2 (.f64 n (PI.f64)))))))) (.f64 2 (.f64 n (PI.f64))))
(+.f64 (.f64 -2 (.f64 k (.f64 n (.f64 (PI.f64) (log.f64 (.f64 2 (.f64 n (PI.f64)))))))) (+.f64 (.f64 2 (.f64 n (PI.f64))) (.f64 (pow.f64 k 2) (.f64 n (.f64 (pow.f64 (log.f64 (.f64 2 (*.f64 n (PI.f64)))) 2) (PI.f64))))))
(+.f64 (.f64 -2 (.f64 k (.f64 n (.f64 (PI.f64) (log.f64 (.f64 2 (.f64 n (PI.f64)))))))) (+.f64 (.f64 -1/3 (.f64 (pow.f64 k 3) (.f64 n (.f64 (PI.f64) (pow.f64 (log.f64 (.f64 2 (.f64 n (PI.f64)))) 3))))) (+.f64 (.f64 2 (.f64 n (PI.f64))) (.f64 (pow.f64 k 2) (.f64 n (.f64 (pow.f64 (log.f64 (.f64 2 (*.f64 n (PI.f64)))) 2) (PI.f64)))))))
(pow.f64 (.f64 2 (.f64 n (PI.f64))) (-.f64 1 k))
(pow.f64 (.f64 2 (.f64 n (PI.f64))) (-.f64 1 k))
(pow.f64 (.f64 2 (.f64 n (PI.f64))) (-.f64 1 k))
(pow.f64 (.f64 2 (.f64 n (PI.f64))) (-.f64 1 k))
(pow.f64 (.f64 2 (.f64 n (PI.f64))) (+.f64 1 (*.f64 -1 k)))
(pow.f64 (.f64 2 (.f64 n (PI.f64))) (+.f64 1 (*.f64 -1 k)))
(pow.f64 (.f64 2 (.f64 n (PI.f64))) (+.f64 1 (*.f64 -1 k)))
(pow.f64 (.f64 2 (.f64 n (PI.f64))) (+.f64 1 (*.f64 -1 k)))
(/.f64 (exp.f64 (.f64 (-.f64 1 k) (+.f64 (log.f64 (.f64 2 (PI.f64))) (log.f64 n)))) k)
(/.f64 (exp.f64 (.f64 (-.f64 1 k) (+.f64 (log.f64 (.f64 2 (PI.f64))) (log.f64 n)))) k)
(/.f64 (exp.f64 (.f64 (-.f64 1 k) (+.f64 (log.f64 (.f64 2 (PI.f64))) (log.f64 n)))) k)
(/.f64 (exp.f64 (.f64 (-.f64 1 k) (+.f64 (log.f64 (.f64 2 (PI.f64))) (log.f64 n)))) k)
(/.f64 (exp.f64 (.f64 (-.f64 1 k) (+.f64 (.f64 -1 (log.f64 (/.f64 1 n))) (log.f64 (*.f64 2 (PI.f64)))))) k)
(/.f64 (exp.f64 (.f64 (-.f64 1 k) (+.f64 (.f64 -1 (log.f64 (/.f64 1 n))) (log.f64 (*.f64 2 (PI.f64)))))) k)
(/.f64 (exp.f64 (.f64 (-.f64 1 k) (+.f64 (.f64 -1 (log.f64 (/.f64 1 n))) (log.f64 (*.f64 2 (PI.f64)))))) k)
(/.f64 (exp.f64 (.f64 (-.f64 1 k) (+.f64 (.f64 -1 (log.f64 (/.f64 1 n))) (log.f64 (*.f64 2 (PI.f64)))))) k)
(/.f64 (exp.f64 (.f64 (-.f64 1 k) (+.f64 (.f64 -1 (log.f64 (/.f64 -1 n))) (log.f64 (*.f64 -2 (PI.f64)))))) k)
(/.f64 (exp.f64 (.f64 (-.f64 1 k) (+.f64 (.f64 -1 (log.f64 (/.f64 -1 n))) (log.f64 (*.f64 -2 (PI.f64)))))) k)
(/.f64 (exp.f64 (.f64 (-.f64 1 k) (+.f64 (.f64 -1 (log.f64 (/.f64 -1 n))) (log.f64 (*.f64 -2 (PI.f64)))))) k)
(/.f64 (exp.f64 (.f64 (-.f64 1 k) (+.f64 (.f64 -1 (log.f64 (/.f64 -1 n))) (log.f64 (*.f64 -2 (PI.f64)))))) k)
(.f64 2 (/.f64 (.f64 n (PI.f64)) k))
(+.f64 (.f64 2 (/.f64 (.f64 n (PI.f64)) k)) (.f64 -2 (.f64 n (.f64 (log.f64 (.f64 2 (*.f64 n (PI.f64)))) (PI.f64)))))
(+.f64 (.f64 2 (/.f64 (.f64 n (PI.f64)) k)) (+.f64 (.f64 k (.f64 n (.f64 (PI.f64) (pow.f64 (log.f64 (.f64 2 (.f64 n (PI.f64)))) 2)))) (.f64 -2 (.f64 n (.f64 (log.f64 (.f64 2 (.f64 n (PI.f64)))) (PI.f64))))))
(+.f64 (.f64 -1/3 (.f64 (pow.f64 k 2) (.f64 n (.f64 (PI.f64) (pow.f64 (log.f64 (.f64 2 (.f64 n (PI.f64)))) 3))))) (+.f64 (.f64 2 (/.f64 (.f64 n (PI.f64)) k)) (+.f64 (.f64 k (.f64 n (.f64 (PI.f64) (pow.f64 (log.f64 (.f64 2 (.f64 n (PI.f64)))) 2)))) (.f64 -2 (.f64 n (.f64 (log.f64 (.f64 2 (.f64 n (PI.f64)))) (PI.f64)))))))
(/.f64 (pow.f64 (.f64 2 (.f64 n (PI.f64))) (-.f64 1 k)) k)
(/.f64 (pow.f64 (.f64 2 (.f64 n (PI.f64))) (-.f64 1 k)) k)
(/.f64 (pow.f64 (.f64 2 (.f64 n (PI.f64))) (-.f64 1 k)) k)
(/.f64 (pow.f64 (.f64 2 (.f64 n (PI.f64))) (-.f64 1 k)) k)
(/.f64 (pow.f64 (.f64 2 (.f64 n (PI.f64))) (+.f64 1 (*.f64 -1 k))) k)
(/.f64 (pow.f64 (.f64 2 (.f64 n (PI.f64))) (+.f64 1 (*.f64 -1 k))) k)
(/.f64 (pow.f64 (.f64 2 (.f64 n (PI.f64))) (+.f64 1 (*.f64 -1 k))) k)
(/.f64 (pow.f64 (.f64 2 (.f64 n (PI.f64))) (+.f64 1 (*.f64 -1 k))) k)

Outputs
(sqrt.f64 (/.f64 (exp.f64 (.f64 (-.f64 1 k) (+.f64 (log.f64 n) (log.f64 (.f64 2 (PI.f64)))))) k))
(sqrt.f64 (/.f64 (pow.f64 (exp.f64 (-.f64 1 k)) (+.f64 (log.f64 n) (log.f64 (*.f64 2 (PI.f64))))) k))
(sqrt.f64 (/.f64 (pow.f64 (exp.f64 (-.f64 1 k)) (log.f64 (.f64 n (.f64 2 (PI.f64))))) k))
(sqrt.f64 (/.f64 (pow.f64 (.f64 n (.f64 2 (PI.f64))) (-.f64 1 k)) k))
(sqrt.f64 (/.f64 (exp.f64 (.f64 (-.f64 1 k) (+.f64 (log.f64 n) (log.f64 (.f64 2 (PI.f64)))))) k))
(sqrt.f64 (/.f64 (pow.f64 (exp.f64 (-.f64 1 k)) (+.f64 (log.f64 n) (log.f64 (*.f64 2 (PI.f64))))) k))
(sqrt.f64 (/.f64 (pow.f64 (exp.f64 (-.f64 1 k)) (log.f64 (.f64 n (.f64 2 (PI.f64))))) k))
(sqrt.f64 (/.f64 (pow.f64 (.f64 n (.f64 2 (PI.f64))) (-.f64 1 k)) k))
(sqrt.f64 (/.f64 (exp.f64 (.f64 (-.f64 1 k) (+.f64 (log.f64 n) (log.f64 (.f64 2 (PI.f64)))))) k))
(sqrt.f64 (/.f64 (pow.f64 (exp.f64 (-.f64 1 k)) (+.f64 (log.f64 n) (log.f64 (*.f64 2 (PI.f64))))) k))
(sqrt.f64 (/.f64 (pow.f64 (exp.f64 (-.f64 1 k)) (log.f64 (.f64 n (.f64 2 (PI.f64))))) k))
(sqrt.f64 (/.f64 (pow.f64 (.f64 n (.f64 2 (PI.f64))) (-.f64 1 k)) k))
(sqrt.f64 (/.f64 (exp.f64 (.f64 (-.f64 1 k) (+.f64 (log.f64 n) (log.f64 (.f64 2 (PI.f64)))))) k))
(sqrt.f64 (/.f64 (pow.f64 (exp.f64 (-.f64 1 k)) (+.f64 (log.f64 n) (log.f64 (*.f64 2 (PI.f64))))) k))
(sqrt.f64 (/.f64 (pow.f64 (exp.f64 (-.f64 1 k)) (log.f64 (.f64 n (.f64 2 (PI.f64))))) k))
(sqrt.f64 (/.f64 (pow.f64 (.f64 n (.f64 2 (PI.f64))) (-.f64 1 k)) k))
(sqrt.f64 (/.f64 (exp.f64 (.f64 (-.f64 1 k) (+.f64 (.f64 -1 (log.f64 (/.f64 1 n))) (log.f64 (*.f64 2 (PI.f64)))))) k))
(sqrt.f64 (/.f64 (pow.f64 (exp.f64 (-.f64 1 k)) (+.f64 (log.f64 n) (log.f64 (*.f64 2 (PI.f64))))) k))
(sqrt.f64 (/.f64 (pow.f64 (exp.f64 (-.f64 1 k)) (log.f64 (.f64 n (.f64 2 (PI.f64))))) k))
(sqrt.f64 (/.f64 (pow.f64 (.f64 n (.f64 2 (PI.f64))) (-.f64 1 k)) k))
(sqrt.f64 (/.f64 (exp.f64 (.f64 (-.f64 1 k) (+.f64 (.f64 -1 (log.f64 (/.f64 1 n))) (log.f64 (*.f64 2 (PI.f64)))))) k))
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(sqrt.f64 (/.f64 (pow.f64 (exp.f64 (-.f64 1 k)) (+.f64 (log.f64 n) (log.f64 (*.f64 2 (PI.f64))))) k))
(sqrt.f64 (/.f64 (pow.f64 (exp.f64 (-.f64 1 k)) (log.f64 (.f64 n (.f64 2 (PI.f64))))) k))
(sqrt.f64 (/.f64 (pow.f64 (.f64 n (.f64 2 (PI.f64))) (-.f64 1 k)) k))
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(sqrt.f64 (/.f64 (pow.f64 (exp.f64 (-.f64 1 k)) (+.f64 (log.f64 n) (log.f64 (*.f64 2 (PI.f64))))) k))
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(sqrt.f64 (/.f64 (pow.f64 (exp.f64 (-.f64 1 k)) (fma.f64 -1 (log.f64 (/.f64 -1 n)) (log.f64 (*.f64 (PI.f64) -2)))) k))
(sqrt.f64 (/.f64 (pow.f64 (exp.f64 (-.f64 1 k)) (-.f64 (log.f64 (*.f64 (PI.f64) -2)) (log.f64 (/.f64 -1 n)))) k))
(sqrt.f64 (/.f64 (pow.f64 (*.f64 -2 (/.f64 (PI.f64) (/.f64 -1 n))) (-.f64 1 k)) k))
(sqrt.f64 (/.f64 (exp.f64 (.f64 (-.f64 1 k) (+.f64 (.f64 -1 (log.f64 (/.f64 -1 n))) (log.f64 (*.f64 -2 (PI.f64)))))) k))
(sqrt.f64 (/.f64 (pow.f64 (exp.f64 (-.f64 1 k)) (fma.f64 -1 (log.f64 (/.f64 -1 n)) (log.f64 (*.f64 (PI.f64) -2)))) k))
(sqrt.f64 (/.f64 (pow.f64 (exp.f64 (-.f64 1 k)) (-.f64 (log.f64 (*.f64 (PI.f64) -2)) (log.f64 (/.f64 -1 n)))) k))
(sqrt.f64 (/.f64 (pow.f64 (*.f64 -2 (/.f64 (PI.f64) (/.f64 -1 n))) (-.f64 1 k)) k))
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(sqrt.f64 (/.f64 (pow.f64 (*.f64 -2 (/.f64 (PI.f64) (/.f64 -1 n))) (-.f64 1 k)) k))
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(pow.f64 (exp.f64 (-.f64 1 k)) (+.f64 (log.f64 n) (log.f64 (*.f64 2 (PI.f64)))))
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(pow.f64 (.f64 n (.f64 2 (PI.f64))) (-.f64 1 k))
(exp.f64 (.f64 (-.f64 1 k) (+.f64 (log.f64 n) (log.f64 (.f64 2 (PI.f64))))))
(pow.f64 (exp.f64 (-.f64 1 k)) (+.f64 (log.f64 n) (log.f64 (*.f64 2 (PI.f64)))))
(pow.f64 (exp.f64 (-.f64 1 k)) (log.f64 (.f64 n (.f64 2 (PI.f64)))))
(pow.f64 (.f64 n (.f64 2 (PI.f64))) (-.f64 1 k))
(exp.f64 (.f64 (-.f64 1 k) (+.f64 (log.f64 n) (log.f64 (.f64 2 (PI.f64))))))
(pow.f64 (exp.f64 (-.f64 1 k)) (+.f64 (log.f64 n) (log.f64 (*.f64 2 (PI.f64)))))
(pow.f64 (exp.f64 (-.f64 1 k)) (log.f64 (.f64 n (.f64 2 (PI.f64)))))
(pow.f64 (.f64 n (.f64 2 (PI.f64))) (-.f64 1 k))
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(pow.f64 (exp.f64 (-.f64 1 k)) (+.f64 (log.f64 n) (log.f64 (*.f64 2 (PI.f64)))))
(pow.f64 (exp.f64 (-.f64 1 k)) (log.f64 (.f64 n (.f64 2 (PI.f64)))))
(pow.f64 (.f64 n (.f64 2 (PI.f64))) (-.f64 1 k))
(exp.f64 (.f64 (-.f64 1 k) (+.f64 (.f64 -1 (log.f64 (/.f64 1 n))) (log.f64 (*.f64 2 (PI.f64))))))
(pow.f64 (exp.f64 (-.f64 1 k)) (+.f64 (log.f64 n) (log.f64 (*.f64 2 (PI.f64)))))
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(pow.f64 (.f64 n (.f64 2 (PI.f64))) (-.f64 1 k))
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(pow.f64 (exp.f64 (-.f64 1 k)) (+.f64 (log.f64 n) (log.f64 (*.f64 2 (PI.f64)))))
(pow.f64 (exp.f64 (-.f64 1 k)) (log.f64 (.f64 n (.f64 2 (PI.f64)))))
(pow.f64 (.f64 n (.f64 2 (PI.f64))) (-.f64 1 k))
(exp.f64 (.f64 (-.f64 1 k) (+.f64 (.f64 -1 (log.f64 (/.f64 1 n))) (log.f64 (*.f64 2 (PI.f64))))))
(pow.f64 (exp.f64 (-.f64 1 k)) (+.f64 (log.f64 n) (log.f64 (*.f64 2 (PI.f64)))))
(pow.f64 (exp.f64 (-.f64 1 k)) (log.f64 (.f64 n (.f64 2 (PI.f64)))))
(pow.f64 (.f64 n (.f64 2 (PI.f64))) (-.f64 1 k))
(exp.f64 (.f64 (-.f64 1 k) (+.f64 (.f64 -1 (log.f64 (/.f64 1 n))) (log.f64 (*.f64 2 (PI.f64))))))
(pow.f64 (exp.f64 (-.f64 1 k)) (+.f64 (log.f64 n) (log.f64 (*.f64 2 (PI.f64)))))
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(pow.f64 (.f64 n (.f64 2 (PI.f64))) (-.f64 1 k))
(exp.f64 (.f64 (-.f64 1 k) (+.f64 (.f64 -1 (log.f64 (/.f64 -1 n))) (log.f64 (*.f64 -2 (PI.f64))))))
(pow.f64 (exp.f64 (-.f64 1 k)) (fma.f64 -1 (log.f64 (/.f64 -1 n)) (log.f64 (*.f64 (PI.f64) -2))))
(pow.f64 (exp.f64 (-.f64 1 k)) (-.f64 (log.f64 (*.f64 (PI.f64) -2)) (log.f64 (/.f64 -1 n))))
(pow.f64 (*.f64 -2 (/.f64 (PI.f64) (/.f64 -1 n))) (-.f64 1 k))
(exp.f64 (.f64 (-.f64 1 k) (+.f64 (.f64 -1 (log.f64 (/.f64 -1 n))) (log.f64 (*.f64 -2 (PI.f64))))))
(pow.f64 (exp.f64 (-.f64 1 k)) (fma.f64 -1 (log.f64 (/.f64 -1 n)) (log.f64 (*.f64 (PI.f64) -2))))
(pow.f64 (exp.f64 (-.f64 1 k)) (-.f64 (log.f64 (*.f64 (PI.f64) -2)) (log.f64 (/.f64 -1 n))))
(pow.f64 (*.f64 -2 (/.f64 (PI.f64) (/.f64 -1 n))) (-.f64 1 k))
(exp.f64 (.f64 (-.f64 1 k) (+.f64 (.f64 -1 (log.f64 (/.f64 -1 n))) (log.f64 (*.f64 -2 (PI.f64))))))
(pow.f64 (exp.f64 (-.f64 1 k)) (fma.f64 -1 (log.f64 (/.f64 -1 n)) (log.f64 (*.f64 (PI.f64) -2))))
(pow.f64 (exp.f64 (-.f64 1 k)) (-.f64 (log.f64 (*.f64 (PI.f64) -2)) (log.f64 (/.f64 -1 n))))
(pow.f64 (*.f64 -2 (/.f64 (PI.f64) (/.f64 -1 n))) (-.f64 1 k))
(exp.f64 (.f64 (-.f64 1 k) (+.f64 (.f64 -1 (log.f64 (/.f64 -1 n))) (log.f64 (*.f64 -2 (PI.f64))))))
(pow.f64 (exp.f64 (-.f64 1 k)) (fma.f64 -1 (log.f64 (/.f64 -1 n)) (log.f64 (*.f64 (PI.f64) -2))))
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(pow.f64 (*.f64 -2 (/.f64 (PI.f64) (/.f64 -1 n))) (-.f64 1 k))
(.f64 2 (.f64 n (PI.f64)))
(.f64 n (.f64 2 (PI.f64)))
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(fma.f64 2 (.f64 n (PI.f64)) (.f64 (.f64 (.f64 k -2) (.f64 n (PI.f64))) (log.f64 (.f64 n (*.f64 2 (PI.f64))))))
(.f64 (PI.f64) (+.f64 (.f64 n 2) (.f64 (.f64 n (log.f64 (.f64 n (.f64 2 (PI.f64))))) (*.f64 k -2))))
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(fma.f64 -2 (.f64 k (.f64 (.f64 n (PI.f64)) (log.f64 (.f64 2 (.f64 n (PI.f64)))))) (fma.f64 2 (.f64 n (PI.f64)) (.f64 (.f64 k k) (.f64 (.f64 n (PI.f64)) (pow.f64 (log.f64 (.f64 2 (.f64 n (PI.f64)))) 2)))))
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(.f64 (PI.f64) (+.f64 (.f64 n 2) (.f64 k (.f64 n (.f64 (log.f64 (.f64 n (.f64 2 (PI.f64)))) (+.f64 (.f64 k (log.f64 (.f64 n (.f64 2 (PI.f64))))) -2))))))
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(fma.f64 -2 (.f64 k (.f64 (PI.f64) (.f64 n (log.f64 (.f64 n (.f64 2 (PI.f64))))))) (fma.f64 -1/3 (.f64 (.f64 n (PI.f64)) (.f64 (pow.f64 (log.f64 (.f64 n (.f64 2 (PI.f64)))) 3) (pow.f64 k 3))) (fma.f64 2 (.f64 n (PI.f64)) (.f64 k (.f64 (.f64 n (PI.f64)) (.f64 (pow.f64 (log.f64 (.f64 n (*.f64 2 (PI.f64)))) 2) k))))))
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(.f64 n (+.f64 (.f64 (PI.f64) (+.f64 2 (.f64 (.f64 -1/3 (pow.f64 k 3)) (pow.f64 (log.f64 (.f64 n (.f64 2 (PI.f64)))) 3)))) (.f64 k (.f64 (.f64 (PI.f64) (log.f64 (.f64 n (.f64 2 (PI.f64))))) (+.f64 -2 (.f64 k (log.f64 (.f64 n (.f64 2 (PI.f64))))))))))
(pow.f64 (.f64 2 (.f64 n (PI.f64))) (-.f64 1 k))
(pow.f64 (exp.f64 (-.f64 1 k)) (+.f64 (log.f64 n) (log.f64 (*.f64 2 (PI.f64)))))
(pow.f64 (exp.f64 (-.f64 1 k)) (log.f64 (.f64 n (.f64 2 (PI.f64)))))
(pow.f64 (.f64 n (.f64 2 (PI.f64))) (-.f64 1 k))
(pow.f64 (.f64 2 (.f64 n (PI.f64))) (-.f64 1 k))
(pow.f64 (exp.f64 (-.f64 1 k)) (+.f64 (log.f64 n) (log.f64 (*.f64 2 (PI.f64)))))
(pow.f64 (exp.f64 (-.f64 1 k)) (log.f64 (.f64 n (.f64 2 (PI.f64)))))
(pow.f64 (.f64 n (.f64 2 (PI.f64))) (-.f64 1 k))
(pow.f64 (.f64 2 (.f64 n (PI.f64))) (-.f64 1 k))
(pow.f64 (exp.f64 (-.f64 1 k)) (+.f64 (log.f64 n) (log.f64 (*.f64 2 (PI.f64)))))
(pow.f64 (exp.f64 (-.f64 1 k)) (log.f64 (.f64 n (.f64 2 (PI.f64)))))
(pow.f64 (.f64 n (.f64 2 (PI.f64))) (-.f64 1 k))
(pow.f64 (.f64 2 (.f64 n (PI.f64))) (-.f64 1 k))
(pow.f64 (exp.f64 (-.f64 1 k)) (+.f64 (log.f64 n) (log.f64 (*.f64 2 (PI.f64)))))
(pow.f64 (exp.f64 (-.f64 1 k)) (log.f64 (.f64 n (.f64 2 (PI.f64)))))
(pow.f64 (.f64 n (.f64 2 (PI.f64))) (-.f64 1 k))
(pow.f64 (.f64 2 (.f64 n (PI.f64))) (+.f64 1 (*.f64 -1 k)))
(pow.f64 (exp.f64 (-.f64 1 k)) (+.f64 (log.f64 n) (log.f64 (*.f64 2 (PI.f64)))))
(pow.f64 (exp.f64 (-.f64 1 k)) (log.f64 (.f64 n (.f64 2 (PI.f64)))))
(pow.f64 (.f64 n (.f64 2 (PI.f64))) (-.f64 1 k))
(pow.f64 (.f64 2 (.f64 n (PI.f64))) (+.f64 1 (*.f64 -1 k)))
(pow.f64 (exp.f64 (-.f64 1 k)) (+.f64 (log.f64 n) (log.f64 (*.f64 2 (PI.f64)))))
(pow.f64 (exp.f64 (-.f64 1 k)) (log.f64 (.f64 n (.f64 2 (PI.f64)))))
(pow.f64 (.f64 n (.f64 2 (PI.f64))) (-.f64 1 k))
(pow.f64 (.f64 2 (.f64 n (PI.f64))) (+.f64 1 (*.f64 -1 k)))
(pow.f64 (exp.f64 (-.f64 1 k)) (+.f64 (log.f64 n) (log.f64 (*.f64 2 (PI.f64)))))
(pow.f64 (exp.f64 (-.f64 1 k)) (log.f64 (.f64 n (.f64 2 (PI.f64)))))
(pow.f64 (.f64 n (.f64 2 (PI.f64))) (-.f64 1 k))
(pow.f64 (.f64 2 (.f64 n (PI.f64))) (+.f64 1 (*.f64 -1 k)))
(pow.f64 (exp.f64 (-.f64 1 k)) (+.f64 (log.f64 n) (log.f64 (*.f64 2 (PI.f64)))))
(pow.f64 (exp.f64 (-.f64 1 k)) (log.f64 (.f64 n (.f64 2 (PI.f64)))))
(pow.f64 (.f64 n (.f64 2 (PI.f64))) (-.f64 1 k))
(/.f64 (exp.f64 (.f64 (-.f64 1 k) (+.f64 (log.f64 (.f64 2 (PI.f64))) (log.f64 n)))) k)
(/.f64 (pow.f64 (exp.f64 (-.f64 1 k)) (+.f64 (log.f64 n) (log.f64 (*.f64 2 (PI.f64))))) k)
(/.f64 (pow.f64 (exp.f64 (-.f64 1 k)) (log.f64 (.f64 n (.f64 2 (PI.f64))))) k)
(/.f64 (pow.f64 (.f64 n (.f64 2 (PI.f64))) (-.f64 1 k)) k)
(/.f64 (exp.f64 (.f64 (-.f64 1 k) (+.f64 (log.f64 (.f64 2 (PI.f64))) (log.f64 n)))) k)
(/.f64 (pow.f64 (exp.f64 (-.f64 1 k)) (+.f64 (log.f64 n) (log.f64 (*.f64 2 (PI.f64))))) k)
(/.f64 (pow.f64 (exp.f64 (-.f64 1 k)) (log.f64 (.f64 n (.f64 2 (PI.f64))))) k)
(/.f64 (pow.f64 (.f64 n (.f64 2 (PI.f64))) (-.f64 1 k)) k)
(/.f64 (exp.f64 (.f64 (-.f64 1 k) (+.f64 (log.f64 (.f64 2 (PI.f64))) (log.f64 n)))) k)
(/.f64 (pow.f64 (exp.f64 (-.f64 1 k)) (+.f64 (log.f64 n) (log.f64 (*.f64 2 (PI.f64))))) k)
(/.f64 (pow.f64 (exp.f64 (-.f64 1 k)) (log.f64 (.f64 n (.f64 2 (PI.f64))))) k)
(/.f64 (pow.f64 (.f64 n (.f64 2 (PI.f64))) (-.f64 1 k)) k)
(/.f64 (exp.f64 (.f64 (-.f64 1 k) (+.f64 (log.f64 (.f64 2 (PI.f64))) (log.f64 n)))) k)
(/.f64 (pow.f64 (exp.f64 (-.f64 1 k)) (+.f64 (log.f64 n) (log.f64 (*.f64 2 (PI.f64))))) k)
(/.f64 (pow.f64 (exp.f64 (-.f64 1 k)) (log.f64 (.f64 n (.f64 2 (PI.f64))))) k)
(/.f64 (pow.f64 (.f64 n (.f64 2 (PI.f64))) (-.f64 1 k)) k)
(/.f64 (exp.f64 (.f64 (-.f64 1 k) (+.f64 (.f64 -1 (log.f64 (/.f64 1 n))) (log.f64 (*.f64 2 (PI.f64)))))) k)
(/.f64 (pow.f64 (exp.f64 (-.f64 1 k)) (+.f64 (log.f64 n) (log.f64 (*.f64 2 (PI.f64))))) k)
(/.f64 (pow.f64 (exp.f64 (-.f64 1 k)) (log.f64 (.f64 n (.f64 2 (PI.f64))))) k)
(/.f64 (pow.f64 (.f64 n (.f64 2 (PI.f64))) (-.f64 1 k)) k)
(/.f64 (exp.f64 (.f64 (-.f64 1 k) (+.f64 (.f64 -1 (log.f64 (/.f64 1 n))) (log.f64 (*.f64 2 (PI.f64)))))) k)
(/.f64 (pow.f64 (exp.f64 (-.f64 1 k)) (+.f64 (log.f64 n) (log.f64 (*.f64 2 (PI.f64))))) k)
(/.f64 (pow.f64 (exp.f64 (-.f64 1 k)) (log.f64 (.f64 n (.f64 2 (PI.f64))))) k)
(/.f64 (pow.f64 (.f64 n (.f64 2 (PI.f64))) (-.f64 1 k)) k)
(/.f64 (exp.f64 (.f64 (-.f64 1 k) (+.f64 (.f64 -1 (log.f64 (/.f64 1 n))) (log.f64 (*.f64 2 (PI.f64)))))) k)
(/.f64 (pow.f64 (exp.f64 (-.f64 1 k)) (+.f64 (log.f64 n) (log.f64 (*.f64 2 (PI.f64))))) k)
(/.f64 (pow.f64 (exp.f64 (-.f64 1 k)) (log.f64 (.f64 n (.f64 2 (PI.f64))))) k)
(/.f64 (pow.f64 (.f64 n (.f64 2 (PI.f64))) (-.f64 1 k)) k)
(/.f64 (exp.f64 (.f64 (-.f64 1 k) (+.f64 (.f64 -1 (log.f64 (/.f64 1 n))) (log.f64 (*.f64 2 (PI.f64)))))) k)
(/.f64 (pow.f64 (exp.f64 (-.f64 1 k)) (+.f64 (log.f64 n) (log.f64 (*.f64 2 (PI.f64))))) k)
(/.f64 (pow.f64 (exp.f64 (-.f64 1 k)) (log.f64 (.f64 n (.f64 2 (PI.f64))))) k)
(/.f64 (pow.f64 (.f64 n (.f64 2 (PI.f64))) (-.f64 1 k)) k)
(/.f64 (exp.f64 (.f64 (-.f64 1 k) (+.f64 (.f64 -1 (log.f64 (/.f64 -1 n))) (log.f64 (*.f64 -2 (PI.f64)))))) k)
(/.f64 (pow.f64 (exp.f64 (-.f64 1 k)) (fma.f64 -1 (log.f64 (/.f64 -1 n)) (log.f64 (*.f64 (PI.f64) -2)))) k)
(/.f64 (pow.f64 (exp.f64 (-.f64 1 k)) (-.f64 (log.f64 (*.f64 (PI.f64) -2)) (log.f64 (/.f64 -1 n)))) k)
(/.f64 (pow.f64 (*.f64 -2 (/.f64 (PI.f64) (/.f64 -1 n))) (-.f64 1 k)) k)
(/.f64 (exp.f64 (.f64 (-.f64 1 k) (+.f64 (.f64 -1 (log.f64 (/.f64 -1 n))) (log.f64 (*.f64 -2 (PI.f64)))))) k)
(/.f64 (pow.f64 (exp.f64 (-.f64 1 k)) (fma.f64 -1 (log.f64 (/.f64 -1 n)) (log.f64 (*.f64 (PI.f64) -2)))) k)
(/.f64 (pow.f64 (exp.f64 (-.f64 1 k)) (-.f64 (log.f64 (*.f64 (PI.f64) -2)) (log.f64 (/.f64 -1 n)))) k)
(/.f64 (pow.f64 (*.f64 -2 (/.f64 (PI.f64) (/.f64 -1 n))) (-.f64 1 k)) k)
(/.f64 (exp.f64 (.f64 (-.f64 1 k) (+.f64 (.f64 -1 (log.f64 (/.f64 -1 n))) (log.f64 (*.f64 -2 (PI.f64)))))) k)
(/.f64 (pow.f64 (exp.f64 (-.f64 1 k)) (fma.f64 -1 (log.f64 (/.f64 -1 n)) (log.f64 (*.f64 (PI.f64) -2)))) k)
(/.f64 (pow.f64 (exp.f64 (-.f64 1 k)) (-.f64 (log.f64 (*.f64 (PI.f64) -2)) (log.f64 (/.f64 -1 n)))) k)
(/.f64 (pow.f64 (*.f64 -2 (/.f64 (PI.f64) (/.f64 -1 n))) (-.f64 1 k)) k)
(/.f64 (exp.f64 (.f64 (-.f64 1 k) (+.f64 (.f64 -1 (log.f64 (/.f64 -1 n))) (log.f64 (*.f64 -2 (PI.f64)))))) k)
(/.f64 (pow.f64 (exp.f64 (-.f64 1 k)) (fma.f64 -1 (log.f64 (/.f64 -1 n)) (log.f64 (*.f64 (PI.f64) -2)))) k)
(/.f64 (pow.f64 (exp.f64 (-.f64 1 k)) (-.f64 (log.f64 (*.f64 (PI.f64) -2)) (log.f64 (/.f64 -1 n)))) k)
(/.f64 (pow.f64 (*.f64 -2 (/.f64 (PI.f64) (/.f64 -1 n))) (-.f64 1 k)) k)
(.f64 2 (/.f64 (.f64 n (PI.f64)) k))
(*.f64 2 (/.f64 n (/.f64 k (PI.f64))))
(*.f64 2 (/.f64 (PI.f64) (/.f64 k n)))
(.f64 2 (.f64 (/.f64 (PI.f64) k) n))
(+.f64 (.f64 2 (/.f64 (.f64 n (PI.f64)) k)) (.f64 -2 (.f64 n (.f64 (log.f64 (.f64 2 (*.f64 n (PI.f64)))) (PI.f64)))))
(fma.f64 2 (/.f64 n (/.f64 k (PI.f64))) (.f64 -2 (.f64 (.f64 n (PI.f64)) (log.f64 (.f64 2 (*.f64 n (PI.f64)))))))
(fma.f64 2 (/.f64 (PI.f64) (/.f64 k n)) (.f64 (.f64 -2 (.f64 n (PI.f64))) (log.f64 (.f64 n (*.f64 2 (PI.f64))))))
(fma.f64 (.f64 n (.f64 (PI.f64) -2)) (log.f64 (.f64 n (.f64 2 (PI.f64)))) (.f64 2 (.f64 (/.f64 (PI.f64) k) n)))
(.f64 (.f64 n (PI.f64)) (+.f64 (/.f64 2 k) (.f64 -2 (log.f64 (.f64 n (*.f64 2 (PI.f64)))))))
(+.f64 (.f64 2 (/.f64 (.f64 n (PI.f64)) k)) (+.f64 (.f64 k (.f64 n (.f64 (PI.f64) (pow.f64 (log.f64 (.f64 2 (.f64 n (PI.f64)))) 2)))) (.f64 -2 (.f64 n (.f64 (log.f64 (.f64 2 (.f64 n (PI.f64)))) (PI.f64))))))
(fma.f64 2 (/.f64 n (/.f64 k (PI.f64))) (fma.f64 k (.f64 (.f64 n (PI.f64)) (pow.f64 (log.f64 (.f64 2 (.f64 n (PI.f64)))) 2)) (.f64 -2 (.f64 (.f64 n (PI.f64)) (log.f64 (.f64 2 (*.f64 n (PI.f64))))))))
(fma.f64 2 (/.f64 (PI.f64) (/.f64 k n)) (fma.f64 k (.f64 n (.f64 (PI.f64) (pow.f64 (log.f64 (.f64 n (.f64 2 (PI.f64)))) 2))) (.f64 (.f64 -2 (.f64 n (PI.f64))) (log.f64 (.f64 n (*.f64 2 (PI.f64)))))))
(fma.f64 2 (.f64 (/.f64 (PI.f64) k) n) (.f64 (.f64 n (PI.f64)) (+.f64 (.f64 -2 (log.f64 (.f64 n (.f64 2 (PI.f64))))) (.f64 k (pow.f64 (log.f64 (.f64 n (*.f64 2 (PI.f64)))) 2)))))
(fma.f64 2 (.f64 (/.f64 (PI.f64) k) n) (.f64 n (.f64 (.f64 (PI.f64) (log.f64 (.f64 n (.f64 2 (PI.f64))))) (+.f64 (.f64 k (log.f64 (.f64 n (*.f64 2 (PI.f64))))) -2))))
(+.f64 (.f64 -1/3 (.f64 (pow.f64 k 2) (.f64 n (.f64 (PI.f64) (pow.f64 (log.f64 (.f64 2 (.f64 n (PI.f64)))) 3))))) (+.f64 (.f64 2 (/.f64 (.f64 n (PI.f64)) k)) (+.f64 (.f64 k (.f64 n (.f64 (PI.f64) (pow.f64 (log.f64 (.f64 2 (.f64 n (PI.f64)))) 2)))) (.f64 -2 (.f64 n (.f64 (log.f64 (.f64 2 (.f64 n (PI.f64)))) (PI.f64)))))))
(fma.f64 -1/3 (.f64 (.f64 k k) (.f64 (.f64 n (PI.f64)) (pow.f64 (log.f64 (.f64 2 (.f64 n (PI.f64)))) 3))) (fma.f64 2 (/.f64 n (/.f64 k (PI.f64))) (fma.f64 k (.f64 (.f64 n (PI.f64)) (pow.f64 (log.f64 (.f64 2 (.f64 n (PI.f64)))) 2)) (.f64 -2 (.f64 (.f64 n (PI.f64)) (log.f64 (.f64 2 (*.f64 n (PI.f64)))))))))
(fma.f64 -1/3 (.f64 n (.f64 (.f64 (PI.f64) (pow.f64 (log.f64 (.f64 n (.f64 2 (PI.f64)))) 3)) (.f64 k k))) (fma.f64 2 (/.f64 (PI.f64) (/.f64 k n)) (fma.f64 k (.f64 n (.f64 (PI.f64) (pow.f64 (log.f64 (.f64 n (.f64 2 (PI.f64)))) 2))) (.f64 (.f64 -2 (.f64 n (PI.f64))) (log.f64 (.f64 n (*.f64 2 (PI.f64))))))))
(fma.f64 (.f64 k k) (.f64 n (.f64 -1/3 (.f64 (PI.f64) (pow.f64 (log.f64 (.f64 n (.f64 2 (PI.f64)))) 3)))) (fma.f64 2 (.f64 (/.f64 (PI.f64) k) n) (.f64 (.f64 n (PI.f64)) (+.f64 (.f64 -2 (log.f64 (.f64 n (.f64 2 (PI.f64))))) (.f64 k (pow.f64 (log.f64 (.f64 n (*.f64 2 (PI.f64)))) 2))))))
(fma.f64 2 (.f64 (/.f64 (PI.f64) k) n) (.f64 (.f64 n (PI.f64)) (+.f64 (.f64 (log.f64 (.f64 n (.f64 2 (PI.f64)))) (+.f64 -2 (.f64 k (log.f64 (.f64 n (.f64 2 (PI.f64))))))) (.f64 (pow.f64 (log.f64 (.f64 n (.f64 2 (PI.f64)))) 3) (.f64 (.f64 k k) -1/3)))))
(/.f64 (pow.f64 (.f64 2 (.f64 n (PI.f64))) (-.f64 1 k)) k)
(/.f64 (pow.f64 (exp.f64 (-.f64 1 k)) (+.f64 (log.f64 n) (log.f64 (*.f64 2 (PI.f64))))) k)
(/.f64 (pow.f64 (exp.f64 (-.f64 1 k)) (log.f64 (.f64 n (.f64 2 (PI.f64))))) k)
(/.f64 (pow.f64 (.f64 n (.f64 2 (PI.f64))) (-.f64 1 k)) k)
(/.f64 (pow.f64 (.f64 2 (.f64 n (PI.f64))) (-.f64 1 k)) k)
(/.f64 (pow.f64 (exp.f64 (-.f64 1 k)) (+.f64 (log.f64 n) (log.f64 (*.f64 2 (PI.f64))))) k)
(/.f64 (pow.f64 (exp.f64 (-.f64 1 k)) (log.f64 (.f64 n (.f64 2 (PI.f64))))) k)
(/.f64 (pow.f64 (.f64 n (.f64 2 (PI.f64))) (-.f64 1 k)) k)
(/.f64 (pow.f64 (.f64 2 (.f64 n (PI.f64))) (-.f64 1 k)) k)
(/.f64 (pow.f64 (exp.f64 (-.f64 1 k)) (+.f64 (log.f64 n) (log.f64 (*.f64 2 (PI.f64))))) k)
(/.f64 (pow.f64 (exp.f64 (-.f64 1 k)) (log.f64 (.f64 n (.f64 2 (PI.f64))))) k)
(/.f64 (pow.f64 (.f64 n (.f64 2 (PI.f64))) (-.f64 1 k)) k)
(/.f64 (pow.f64 (.f64 2 (.f64 n (PI.f64))) (-.f64 1 k)) k)
(/.f64 (pow.f64 (exp.f64 (-.f64 1 k)) (+.f64 (log.f64 n) (log.f64 (*.f64 2 (PI.f64))))) k)
(/.f64 (pow.f64 (exp.f64 (-.f64 1 k)) (log.f64 (.f64 n (.f64 2 (PI.f64))))) k)
(/.f64 (pow.f64 (.f64 n (.f64 2 (PI.f64))) (-.f64 1 k)) k)
(/.f64 (pow.f64 (.f64 2 (.f64 n (PI.f64))) (+.f64 1 (*.f64 -1 k))) k)
(/.f64 (pow.f64 (exp.f64 (-.f64 1 k)) (+.f64 (log.f64 n) (log.f64 (*.f64 2 (PI.f64))))) k)
(/.f64 (pow.f64 (exp.f64 (-.f64 1 k)) (log.f64 (.f64 n (.f64 2 (PI.f64))))) k)
(/.f64 (pow.f64 (.f64 n (.f64 2 (PI.f64))) (-.f64 1 k)) k)
(/.f64 (pow.f64 (.f64 2 (.f64 n (PI.f64))) (+.f64 1 (*.f64 -1 k))) k)
(/.f64 (pow.f64 (exp.f64 (-.f64 1 k)) (+.f64 (log.f64 n) (log.f64 (*.f64 2 (PI.f64))))) k)
(/.f64 (pow.f64 (exp.f64 (-.f64 1 k)) (log.f64 (.f64 n (.f64 2 (PI.f64))))) k)
(/.f64 (pow.f64 (.f64 n (.f64 2 (PI.f64))) (-.f64 1 k)) k)
(/.f64 (pow.f64 (.f64 2 (.f64 n (PI.f64))) (+.f64 1 (*.f64 -1 k))) k)
(/.f64 (pow.f64 (exp.f64 (-.f64 1 k)) (+.f64 (log.f64 n) (log.f64 (*.f64 2 (PI.f64))))) k)
(/.f64 (pow.f64 (exp.f64 (-.f64 1 k)) (log.f64 (.f64 n (.f64 2 (PI.f64))))) k)
(/.f64 (pow.f64 (.f64 n (.f64 2 (PI.f64))) (-.f64 1 k)) k)
(/.f64 (pow.f64 (.f64 2 (.f64 n (PI.f64))) (+.f64 1 (*.f64 -1 k))) k)
(/.f64 (pow.f64 (exp.f64 (-.f64 1 k)) (+.f64 (log.f64 n) (log.f64 (*.f64 2 (PI.f64))))) k)
(/.f64 (pow.f64 (exp.f64 (-.f64 1 k)) (log.f64 (.f64 n (.f64 2 (PI.f64))))) k)
(/.f64 (pow.f64 (.f64 n (.f64 2 (PI.f64))) (-.f64 1 k)) k)

localize38.0ms (0.4%)

Local error

Found 8 expressions with local error:

New	Error	Program
	0.2b	(.f64 n (.f64 2 (PI.f64)))
	0.1b	(/.f64 (exp.f64 (.f64 (-.f64 1 k) (log.f64 (.f64 n (*.f64 2 (PI.f64)))))) k)
	0.1b	(.f64 (-.f64 1 k) (log.f64 (.f64 n (*.f64 2 (PI.f64)))))
	0.0b	(log.f64 (.f64 n (.f64 2 (PI.f64))))
✓	0.1b	(/.f64 (exp.f64 (.f64 (-.f64 1 k) (log.f64 (.f64 n (*.f64 2 (PI.f64)))))) k)
	0.2b	(.f64 n (.f64 2 (PI.f64)))
✓	3.6b	(exp.f64 (.f64 (-.f64 1 k) (log.f64 (.f64 n (*.f64 2 (PI.f64))))))
✓	9.0b	(sqrt.f64 (/.f64 (exp.f64 (.f64 (-.f64 1 k) (log.f64 (.f64 n (*.f64 2 (PI.f64)))))) k))

Compiler

Compiled 72 to 50 computations (30.6% saved)

series8.0ms (0.1%)

Counts

3 → 60

Calls

18 calls:

Time	Variable		Point	Expression
2.0ms	k	@	0	(sqrt.f64 (/.f64 (exp.f64 (.f64 (-.f64 1 k) (log.f64 (.f64 n (*.f64 2 (PI.f64)))))) k))
1.0ms	k	@	-inf	(/.f64 (exp.f64 (.f64 (-.f64 1 k) (log.f64 (.f64 n (*.f64 2 (PI.f64)))))) k)
1.0ms	k	@	-inf	(sqrt.f64 (/.f64 (exp.f64 (.f64 (-.f64 1 k) (log.f64 (.f64 n (*.f64 2 (PI.f64)))))) k))
0.0ms	k	@	inf	(sqrt.f64 (/.f64 (exp.f64 (.f64 (-.f64 1 k) (log.f64 (.f64 n (*.f64 2 (PI.f64)))))) k))
0.0ms	k	@	0	(exp.f64 (.f64 (-.f64 1 k) (log.f64 (.f64 n (*.f64 2 (PI.f64))))))

rewrite84.0ms (0.9%)

Algorithm

1×	batch-egg-rewrite

Rules

689×	`log-prod_binary64`
351×	`pow2_binary64`
263×	`pow-unpow_binary64`
248×	`pow1/3_binary64`
242×	`expm1-udef_binary64`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	14	62
1	285	50
2	3526	50

Stop Event

1×	node limit

Counts

3 → 158

Calls

Call 1

Inputs

(sqrt.f64 (/.f64 (exp.f64 (*.f64 (-.f64 1 k) (log.f64 (*.f64 n (*.f64 2 (PI.f64)))))) k))

(exp.f64 (*.f64 (-.f64 1 k) (log.f64 (*.f64 n (*.f64 2 (PI.f64))))))

(/.f64 (exp.f64 (*.f64 (-.f64 1 k) (log.f64 (*.f64 n (*.f64 2 (PI.f64)))))) k)

Outputs

((#(struct:change #<rule egg-rr> (2) ((x +.f64 0 (sqrt.f64 (/.f64 (pow.f64 (*.f64 n (*.f64 2 (PI.f64))) (-.f64 1 k)) k)))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (log.f64 (pow.f64 (cbrt.f64 (exp.f64 (sqrt.f64 (/.f64 (pow.f64 (*.f64 n (*.f64 2 (PI.f64))) (-.f64 1 k)) k)))) 2)) (log.f64 (cbrt.f64 (exp.f64 (sqrt.f64 (/.f64 (pow.f64 (*.f64 n (*.f64 2 (PI.f64))) (-.f64 1 k)) k))))))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (log.f64 (sqrt.f64 (exp.f64 (sqrt.f64 (/.f64 (pow.f64 (*.f64 n (*.f64 2 (PI.f64))) (-.f64 1 k)) k))))) (log.f64 (sqrt.f64 (exp.f64 (sqrt.f64 (/.f64 (pow.f64 (*.f64 n (*.f64 2 (PI.f64))) (-.f64 1 k)) k))))))))) (#(struct:change #<rule egg-rr> (2) ((x -.f64 (exp.f64 (log1p.f64 (sqrt.f64 (/.f64 (pow.f64 (*.f64 n (*.f64 2 (PI.f64))) (-.f64 1 k)) k)))) 1)))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 1 (sqrt.f64 (/.f64 (pow.f64 (*.f64 n (*.f64 2 (PI.f64))) (-.f64 1 k)) k)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (sqrt.f64 (/.f64 (pow.f64 (*.f64 n 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simplify56.0ms (0.6%)

Algorithm

1×	egg-herbie

Rules

584×	`associate-+l+_binary64`
474×	`associate-l_binary64`
439×	`fma-def_binary64`
401×	`associate-r_binary64`
330×	`distribute-lft-out_binary64`

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	84	1377
1	242	1349
2	776	1289
3	4232	1184

Stop Event

1×	node limit

Counts

218 → 192

Calls

Call 1

Inputs
(sqrt.f64 (/.f64 (exp.f64 (.f64 (-.f64 1 k) (+.f64 (log.f64 n) (log.f64 (.f64 2 (PI.f64)))))) k))
(sqrt.f64 (/.f64 (exp.f64 (.f64 (-.f64 1 k) (+.f64 (log.f64 n) (log.f64 (.f64 2 (PI.f64)))))) k))
(sqrt.f64 (/.f64 (exp.f64 (.f64 (-.f64 1 k) (+.f64 (log.f64 n) (log.f64 (.f64 2 (PI.f64)))))) k))
(sqrt.f64 (/.f64 (exp.f64 (.f64 (-.f64 1 k) (+.f64 (log.f64 n) (log.f64 (.f64 2 (PI.f64)))))) k))
(sqrt.f64 (/.f64 (exp.f64 (.f64 (-.f64 1 k) (+.f64 (.f64 -1 (log.f64 (/.f64 1 n))) (log.f64 (*.f64 2 (PI.f64)))))) k))
(sqrt.f64 (/.f64 (exp.f64 (.f64 (-.f64 1 k) (+.f64 (.f64 -1 (log.f64 (/.f64 1 n))) (log.f64 (*.f64 2 (PI.f64)))))) k))
(sqrt.f64 (/.f64 (exp.f64 (.f64 (-.f64 1 k) (+.f64 (.f64 -1 (log.f64 (/.f64 1 n))) (log.f64 (*.f64 2 (PI.f64)))))) k))
(sqrt.f64 (/.f64 (exp.f64 (.f64 (-.f64 1 k) (+.f64 (.f64 -1 (log.f64 (/.f64 1 n))) (log.f64 (*.f64 2 (PI.f64)))))) k))
(sqrt.f64 (/.f64 (exp.f64 (.f64 (-.f64 1 k) (+.f64 (.f64 -1 (log.f64 (/.f64 -1 n))) (log.f64 (*.f64 -2 (PI.f64)))))) k))
(sqrt.f64 (/.f64 (exp.f64 (.f64 (-.f64 1 k) (+.f64 (.f64 -1 (log.f64 (/.f64 -1 n))) (log.f64 (*.f64 -2 (PI.f64)))))) k))
(sqrt.f64 (/.f64 (exp.f64 (.f64 (-.f64 1 k) (+.f64 (.f64 -1 (log.f64 (/.f64 -1 n))) (log.f64 (*.f64 -2 (PI.f64)))))) k))
(sqrt.f64 (/.f64 (exp.f64 (.f64 (-.f64 1 k) (+.f64 (.f64 -1 (log.f64 (/.f64 -1 n))) (log.f64 (*.f64 -2 (PI.f64)))))) k))
(.f64 2 (.f64 n (PI.f64)))
(+.f64 (.f64 -2 (.f64 k (.f64 n (.f64 (PI.f64) (log.f64 (.f64 2 (.f64 n (PI.f64)))))))) (.f64 2 (.f64 n (PI.f64))))
(+.f64 (.f64 -2 (.f64 k (.f64 n (.f64 (PI.f64) (log.f64 (.f64 2 (.f64 n (PI.f64)))))))) (+.f64 (.f64 2 (.f64 n (PI.f64))) (.f64 (pow.f64 k 2) (.f64 n (.f64 (pow.f64 (log.f64 (.f64 2 (*.f64 n (PI.f64)))) 2) (PI.f64))))))
(+.f64 (.f64 -2 (.f64 k (.f64 n (.f64 (PI.f64) (log.f64 (.f64 2 (.f64 n (PI.f64)))))))) (+.f64 (.f64 -1/3 (.f64 (pow.f64 k 3) (.f64 n (.f64 (PI.f64) (pow.f64 (log.f64 (.f64 2 (.f64 n (PI.f64)))) 3))))) (+.f64 (.f64 2 (.f64 n (PI.f64))) (.f64 (pow.f64 k 2) (.f64 n (.f64 (pow.f64 (log.f64 (.f64 2 (*.f64 n (PI.f64)))) 2) (PI.f64)))))))
(pow.f64 (.f64 2 (.f64 n (PI.f64))) (-.f64 1 k))
(pow.f64 (.f64 2 (.f64 n (PI.f64))) (-.f64 1 k))
(pow.f64 (.f64 2 (.f64 n (PI.f64))) (-.f64 1 k))
(pow.f64 (.f64 2 (.f64 n (PI.f64))) (-.f64 1 k))
(pow.f64 (.f64 2 (.f64 n (PI.f64))) (+.f64 1 (*.f64 -1 k)))
(pow.f64 (.f64 2 (.f64 n (PI.f64))) (+.f64 1 (*.f64 -1 k)))
(pow.f64 (.f64 2 (.f64 n (PI.f64))) (+.f64 1 (*.f64 -1 k)))
(pow.f64 (.f64 2 (.f64 n (PI.f64))) (+.f64 1 (*.f64 -1 k)))
(exp.f64 (.f64 (-.f64 1 k) (+.f64 (log.f64 n) (log.f64 (.f64 2 (PI.f64))))))
(exp.f64 (.f64 (-.f64 1 k) (+.f64 (log.f64 n) (log.f64 (.f64 2 (PI.f64))))))
(exp.f64 (.f64 (-.f64 1 k) (+.f64 (log.f64 n) (log.f64 (.f64 2 (PI.f64))))))
(exp.f64 (.f64 (-.f64 1 k) (+.f64 (log.f64 n) (log.f64 (.f64 2 (PI.f64))))))
(exp.f64 (.f64 (-.f64 1 k) (+.f64 (.f64 -1 (log.f64 (/.f64 1 n))) (log.f64 (*.f64 2 (PI.f64))))))
(exp.f64 (.f64 (-.f64 1 k) (+.f64 (.f64 -1 (log.f64 (/.f64 1 n))) (log.f64 (*.f64 2 (PI.f64))))))
(exp.f64 (.f64 (-.f64 1 k) (+.f64 (.f64 -1 (log.f64 (/.f64 1 n))) (log.f64 (*.f64 2 (PI.f64))))))
(exp.f64 (.f64 (-.f64 1 k) (+.f64 (.f64 -1 (log.f64 (/.f64 1 n))) (log.f64 (*.f64 2 (PI.f64))))))
(exp.f64 (.f64 (-.f64 1 k) (+.f64 (.f64 -1 (log.f64 (/.f64 -1 n))) (log.f64 (*.f64 -2 (PI.f64))))))
(exp.f64 (.f64 (-.f64 1 k) (+.f64 (.f64 -1 (log.f64 (/.f64 -1 n))) (log.f64 (*.f64 -2 (PI.f64))))))
(exp.f64 (.f64 (-.f64 1 k) (+.f64 (.f64 -1 (log.f64 (/.f64 -1 n))) (log.f64 (*.f64 -2 (PI.f64))))))
(exp.f64 (.f64 (-.f64 1 k) (+.f64 (.f64 -1 (log.f64 (/.f64 -1 n))) (log.f64 (*.f64 -2 (PI.f64))))))
(.f64 2 (/.f64 (.f64 n (PI.f64)) k))
(+.f64 (.f64 2 (/.f64 (.f64 n (PI.f64)) k)) (.f64 -2 (.f64 n (.f64 (log.f64 (.f64 2 (*.f64 n (PI.f64)))) (PI.f64)))))
(+.f64 (.f64 2 (/.f64 (.f64 n (PI.f64)) k)) (+.f64 (.f64 k (.f64 n (.f64 (PI.f64) (pow.f64 (log.f64 (.f64 2 (.f64 n (PI.f64)))) 2)))) (.f64 -2 (.f64 n (.f64 (log.f64 (.f64 2 (.f64 n (PI.f64)))) (PI.f64))))))
(+.f64 (.f64 -1/3 (.f64 (pow.f64 k 2) (.f64 n (.f64 (PI.f64) (pow.f64 (log.f64 (.f64 2 (.f64 n (PI.f64)))) 3))))) (+.f64 (.f64 2 (/.f64 (.f64 n (PI.f64)) k)) (+.f64 (.f64 k (.f64 n (.f64 (PI.f64) (pow.f64 (log.f64 (.f64 2 (.f64 n (PI.f64)))) 2)))) (.f64 -2 (.f64 n (.f64 (log.f64 (.f64 2 (.f64 n (PI.f64)))) (PI.f64)))))))
(/.f64 (pow.f64 (.f64 2 (.f64 n (PI.f64))) (-.f64 1 k)) k)
(/.f64 (pow.f64 (.f64 2 (.f64 n (PI.f64))) (-.f64 1 k)) k)
(/.f64 (pow.f64 (.f64 2 (.f64 n (PI.f64))) (-.f64 1 k)) k)
(/.f64 (pow.f64 (.f64 2 (.f64 n (PI.f64))) (-.f64 1 k)) k)
(/.f64 (pow.f64 (.f64 2 (.f64 n (PI.f64))) (+.f64 1 (*.f64 -1 k))) k)
(/.f64 (pow.f64 (.f64 2 (.f64 n (PI.f64))) (+.f64 1 (*.f64 -1 k))) k)
(/.f64 (pow.f64 (.f64 2 (.f64 n (PI.f64))) (+.f64 1 (*.f64 -1 k))) k)
(/.f64 (pow.f64 (.f64 2 (.f64 n (PI.f64))) (+.f64 1 (*.f64 -1 k))) k)
(/.f64 (exp.f64 (.f64 (-.f64 1 k) (+.f64 (log.f64 (.f64 2 (PI.f64))) (log.f64 n)))) k)
(/.f64 (exp.f64 (.f64 (-.f64 1 k) (+.f64 (log.f64 (.f64 2 (PI.f64))) (log.f64 n)))) k)
(/.f64 (exp.f64 (.f64 (-.f64 1 k) (+.f64 (log.f64 (.f64 2 (PI.f64))) (log.f64 n)))) k)
(/.f64 (exp.f64 (.f64 (-.f64 1 k) (+.f64 (log.f64 (.f64 2 (PI.f64))) (log.f64 n)))) k)
(/.f64 (exp.f64 (.f64 (-.f64 1 k) (+.f64 (.f64 -1 (log.f64 (/.f64 1 n))) (log.f64 (*.f64 2 (PI.f64)))))) k)
(/.f64 (exp.f64 (.f64 (-.f64 1 k) (+.f64 (.f64 -1 (log.f64 (/.f64 1 n))) (log.f64 (*.f64 2 (PI.f64)))))) k)
(/.f64 (exp.f64 (.f64 (-.f64 1 k) (+.f64 (.f64 -1 (log.f64 (/.f64 1 n))) (log.f64 (*.f64 2 (PI.f64)))))) k)
(/.f64 (exp.f64 (.f64 (-.f64 1 k) (+.f64 (.f64 -1 (log.f64 (/.f64 1 n))) (log.f64 (*.f64 2 (PI.f64)))))) k)
(/.f64 (exp.f64 (.f64 (-.f64 1 k) (+.f64 (.f64 -1 (log.f64 (/.f64 -1 n))) (log.f64 (*.f64 -2 (PI.f64)))))) k)
(/.f64 (exp.f64 (.f64 (-.f64 1 k) (+.f64 (.f64 -1 (log.f64 (/.f64 -1 n))) (log.f64 (*.f64 -2 (PI.f64)))))) k)
(/.f64 (exp.f64 (.f64 (-.f64 1 k) (+.f64 (.f64 -1 (log.f64 (/.f64 -1 n))) (log.f64 (*.f64 -2 (PI.f64)))))) k)
(/.f64 (exp.f64 (.f64 (-.f64 1 k) (+.f64 (.f64 -1 (log.f64 (/.f64 -1 n))) (log.f64 (*.f64 -2 (PI.f64)))))) k)

Outputs
(sqrt.f64 (/.f64 (exp.f64 (.f64 (-.f64 1 k) (+.f64 (log.f64 n) (log.f64 (.f64 2 (PI.f64)))))) k))
(sqrt.f64 (/.f64 (pow.f64 (exp.f64 (-.f64 1 k)) (+.f64 (log.f64 n) (log.f64 (*.f64 2 (PI.f64))))) k))
(sqrt.f64 (/.f64 (pow.f64 (exp.f64 (-.f64 1 k)) (log.f64 (.f64 n (.f64 2 (PI.f64))))) k))
(sqrt.f64 (/.f64 (pow.f64 (.f64 n (.f64 2 (PI.f64))) (-.f64 1 k)) k))
(sqrt.f64 (/.f64 (exp.f64 (.f64 (-.f64 1 k) (+.f64 (log.f64 n) (log.f64 (.f64 2 (PI.f64)))))) k))
(sqrt.f64 (/.f64 (pow.f64 (exp.f64 (-.f64 1 k)) (+.f64 (log.f64 n) (log.f64 (*.f64 2 (PI.f64))))) k))
(sqrt.f64 (/.f64 (pow.f64 (exp.f64 (-.f64 1 k)) (log.f64 (.f64 n (.f64 2 (PI.f64))))) k))
(sqrt.f64 (/.f64 (pow.f64 (.f64 n (.f64 2 (PI.f64))) (-.f64 1 k)) k))
(sqrt.f64 (/.f64 (exp.f64 (.f64 (-.f64 1 k) (+.f64 (log.f64 n) (log.f64 (.f64 2 (PI.f64)))))) k))
(sqrt.f64 (/.f64 (pow.f64 (exp.f64 (-.f64 1 k)) (+.f64 (log.f64 n) (log.f64 (*.f64 2 (PI.f64))))) k))
(sqrt.f64 (/.f64 (pow.f64 (exp.f64 (-.f64 1 k)) (log.f64 (.f64 n (.f64 2 (PI.f64))))) k))
(sqrt.f64 (/.f64 (pow.f64 (.f64 n (.f64 2 (PI.f64))) (-.f64 1 k)) k))
(sqrt.f64 (/.f64 (exp.f64 (.f64 (-.f64 1 k) (+.f64 (log.f64 n) (log.f64 (.f64 2 (PI.f64)))))) k))
(sqrt.f64 (/.f64 (pow.f64 (exp.f64 (-.f64 1 k)) (+.f64 (log.f64 n) (log.f64 (*.f64 2 (PI.f64))))) k))
(sqrt.f64 (/.f64 (pow.f64 (exp.f64 (-.f64 1 k)) (log.f64 (.f64 n (.f64 2 (PI.f64))))) k))
(sqrt.f64 (/.f64 (pow.f64 (.f64 n (.f64 2 (PI.f64))) (-.f64 1 k)) k))
(sqrt.f64 (/.f64 (exp.f64 (.f64 (-.f64 1 k) (+.f64 (.f64 -1 (log.f64 (/.f64 1 n))) (log.f64 (*.f64 2 (PI.f64)))))) k))
(sqrt.f64 (/.f64 (pow.f64 (exp.f64 (-.f64 1 k)) (+.f64 (log.f64 n) (log.f64 (*.f64 2 (PI.f64))))) k))
(sqrt.f64 (/.f64 (pow.f64 (exp.f64 (-.f64 1 k)) (log.f64 (.f64 n (.f64 2 (PI.f64))))) k))
(sqrt.f64 (/.f64 (pow.f64 (.f64 n (.f64 2 (PI.f64))) (-.f64 1 k)) k))
(sqrt.f64 (/.f64 (exp.f64 (.f64 (-.f64 1 k) (+.f64 (.f64 -1 (log.f64 (/.f64 1 n))) (log.f64 (*.f64 2 (PI.f64)))))) k))
(sqrt.f64 (/.f64 (pow.f64 (exp.f64 (-.f64 1 k)) (+.f64 (log.f64 n) (log.f64 (*.f64 2 (PI.f64))))) k))
(sqrt.f64 (/.f64 (pow.f64 (exp.f64 (-.f64 1 k)) (log.f64 (.f64 n (.f64 2 (PI.f64))))) k))
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(sqrt.f64 (/.f64 (pow.f64 (exp.f64 (-.f64 1 k)) (+.f64 (log.f64 n) (log.f64 (*.f64 2 (PI.f64))))) k))
(sqrt.f64 (/.f64 (pow.f64 (exp.f64 (-.f64 1 k)) (log.f64 (.f64 n (.f64 2 (PI.f64))))) k))
(sqrt.f64 (/.f64 (pow.f64 (.f64 n (.f64 2 (PI.f64))) (-.f64 1 k)) k))
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(sqrt.f64 (/.f64 (pow.f64 (exp.f64 (-.f64 1 k)) (fma.f64 -1 (log.f64 (/.f64 -1 n)) (log.f64 (*.f64 (PI.f64) -2)))) k))
(sqrt.f64 (/.f64 (pow.f64 (exp.f64 (-.f64 1 k)) (-.f64 (log.f64 (*.f64 (PI.f64) -2)) (log.f64 (/.f64 -1 n)))) k))
(sqrt.f64 (/.f64 (pow.f64 (/.f64 (*.f64 (PI.f64) -2) (/.f64 -1 n)) (-.f64 1 k)) k))
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(sqrt.f64 (/.f64 (pow.f64 (exp.f64 (-.f64 1 k)) (-.f64 (log.f64 (*.f64 (PI.f64) -2)) (log.f64 (/.f64 -1 n)))) k))
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(sqrt.f64 (/.f64 (pow.f64 (/.f64 (*.f64 (PI.f64) -2) (/.f64 -1 n)) (-.f64 1 k)) k))
(.f64 2 (.f64 n (PI.f64)))
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(fma.f64 2 (.f64 n (PI.f64)) (.f64 k (.f64 (.f64 -2 (.f64 n (PI.f64))) (log.f64 (.f64 n (*.f64 2 (PI.f64)))))))
(.f64 (PI.f64) (+.f64 (.f64 n 2) (.f64 -2 (.f64 (log.f64 (.f64 n (.f64 2 (PI.f64)))) (*.f64 k n)))))
(.f64 n (.f64 (PI.f64) (+.f64 2 (.f64 (.f64 k -2) (log.f64 (.f64 n (.f64 2 (PI.f64))))))))
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(fma.f64 -2 (.f64 k (.f64 (.f64 n (PI.f64)) (log.f64 (.f64 2 (.f64 n (PI.f64)))))) (fma.f64 2 (.f64 n (PI.f64)) (.f64 (.f64 k k) (.f64 n (.f64 (PI.f64) (pow.f64 (log.f64 (.f64 2 (.f64 n (PI.f64)))) 2))))))
(fma.f64 -2 (.f64 k (.f64 n (.f64 (PI.f64) (log.f64 (.f64 n (.f64 2 (PI.f64))))))) (fma.f64 2 (.f64 n (PI.f64)) (.f64 k (.f64 (.f64 n (PI.f64)) (.f64 (pow.f64 (log.f64 (.f64 n (.f64 2 (PI.f64)))) 2) k)))))
(fma.f64 n (.f64 2 (PI.f64)) (.f64 k (.f64 (.f64 n (PI.f64)) (+.f64 (.f64 -2 (log.f64 (.f64 n (.f64 2 (PI.f64))))) (.f64 k (pow.f64 (log.f64 (.f64 n (.f64 2 (PI.f64)))) 2))))))
(.f64 (PI.f64) (+.f64 (.f64 k (.f64 n (.f64 (log.f64 (.f64 n (.f64 2 (PI.f64)))) (+.f64 (.f64 k (log.f64 (.f64 n (.f64 2 (PI.f64))))) -2)))) (.f64 n 2)))
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(fma.f64 -2 (.f64 k (.f64 (.f64 n (PI.f64)) (log.f64 (.f64 2 (.f64 n (PI.f64)))))) (fma.f64 -1/3 (.f64 (pow.f64 k 3) (.f64 (.f64 n (PI.f64)) (pow.f64 (log.f64 (.f64 2 (.f64 n (PI.f64)))) 3))) (fma.f64 2 (.f64 n (PI.f64)) (.f64 (.f64 k k) (.f64 n (.f64 (PI.f64) (pow.f64 (log.f64 (.f64 2 (*.f64 n (PI.f64)))) 2)))))))
(fma.f64 -2 (.f64 k (.f64 n (.f64 (PI.f64) (log.f64 (.f64 n (.f64 2 (PI.f64))))))) (fma.f64 -1/3 (.f64 n (.f64 (.f64 (PI.f64) (pow.f64 (log.f64 (.f64 n (.f64 2 (PI.f64)))) 3)) (pow.f64 k 3))) (fma.f64 2 (.f64 n (PI.f64)) (.f64 k (.f64 (.f64 n (PI.f64)) (.f64 (pow.f64 (log.f64 (.f64 n (*.f64 2 (PI.f64)))) 2) k))))))
(fma.f64 -1/3 (.f64 n (.f64 (pow.f64 (log.f64 (.f64 n (.f64 2 (PI.f64)))) 3) (.f64 (PI.f64) (pow.f64 k 3)))) (fma.f64 n (.f64 2 (PI.f64)) (.f64 k (.f64 (.f64 n (PI.f64)) (+.f64 (.f64 -2 (log.f64 (.f64 n (.f64 2 (PI.f64))))) (.f64 k (pow.f64 (log.f64 (.f64 n (*.f64 2 (PI.f64)))) 2)))))))
(.f64 n (+.f64 (.f64 (PI.f64) (+.f64 2 (.f64 (.f64 -1/3 (pow.f64 k 3)) (pow.f64 (log.f64 (.f64 n (.f64 2 (PI.f64)))) 3)))) (.f64 k (.f64 (PI.f64) (.f64 (log.f64 (.f64 n (.f64 2 (PI.f64)))) (+.f64 (.f64 k (log.f64 (.f64 n (.f64 2 (PI.f64))))) -2))))))
(pow.f64 (.f64 2 (.f64 n (PI.f64))) (-.f64 1 k))
(pow.f64 (.f64 n (.f64 2 (PI.f64))) (-.f64 1 k))
(pow.f64 (.f64 2 (.f64 n (PI.f64))) (-.f64 1 k))
(pow.f64 (.f64 n (.f64 2 (PI.f64))) (-.f64 1 k))
(pow.f64 (.f64 2 (.f64 n (PI.f64))) (-.f64 1 k))
(pow.f64 (.f64 n (.f64 2 (PI.f64))) (-.f64 1 k))
(pow.f64 (.f64 2 (.f64 n (PI.f64))) (-.f64 1 k))
(pow.f64 (.f64 n (.f64 2 (PI.f64))) (-.f64 1 k))
(pow.f64 (.f64 2 (.f64 n (PI.f64))) (+.f64 1 (*.f64 -1 k)))
(pow.f64 (.f64 2 (.f64 n (PI.f64))) (-.f64 1 k))
(pow.f64 (.f64 n (.f64 2 (PI.f64))) (-.f64 1 k))
(pow.f64 (.f64 2 (.f64 n (PI.f64))) (+.f64 1 (*.f64 -1 k)))
(pow.f64 (.f64 2 (.f64 n (PI.f64))) (-.f64 1 k))
(pow.f64 (.f64 n (.f64 2 (PI.f64))) (-.f64 1 k))
(pow.f64 (.f64 2 (.f64 n (PI.f64))) (+.f64 1 (*.f64 -1 k)))
(pow.f64 (.f64 2 (.f64 n (PI.f64))) (-.f64 1 k))
(pow.f64 (.f64 n (.f64 2 (PI.f64))) (-.f64 1 k))
(pow.f64 (.f64 2 (.f64 n (PI.f64))) (+.f64 1 (*.f64 -1 k)))
(pow.f64 (.f64 2 (.f64 n (PI.f64))) (-.f64 1 k))
(pow.f64 (.f64 n (.f64 2 (PI.f64))) (-.f64 1 k))
(exp.f64 (.f64 (-.f64 1 k) (+.f64 (log.f64 n) (log.f64 (.f64 2 (PI.f64))))))
(pow.f64 (.f64 2 (.f64 n (PI.f64))) (-.f64 1 k))
(pow.f64 (.f64 n (.f64 2 (PI.f64))) (-.f64 1 k))
(exp.f64 (.f64 (-.f64 1 k) (+.f64 (log.f64 n) (log.f64 (.f64 2 (PI.f64))))))
(pow.f64 (.f64 2 (.f64 n (PI.f64))) (-.f64 1 k))
(pow.f64 (.f64 n (.f64 2 (PI.f64))) (-.f64 1 k))
(exp.f64 (.f64 (-.f64 1 k) (+.f64 (log.f64 n) (log.f64 (.f64 2 (PI.f64))))))
(pow.f64 (.f64 2 (.f64 n (PI.f64))) (-.f64 1 k))
(pow.f64 (.f64 n (.f64 2 (PI.f64))) (-.f64 1 k))
(exp.f64 (.f64 (-.f64 1 k) (+.f64 (log.f64 n) (log.f64 (.f64 2 (PI.f64))))))
(pow.f64 (.f64 2 (.f64 n (PI.f64))) (-.f64 1 k))
(pow.f64 (.f64 n (.f64 2 (PI.f64))) (-.f64 1 k))
(exp.f64 (.f64 (-.f64 1 k) (+.f64 (.f64 -1 (log.f64 (/.f64 1 n))) (log.f64 (*.f64 2 (PI.f64))))))
(pow.f64 (.f64 2 (.f64 n (PI.f64))) (-.f64 1 k))
(pow.f64 (.f64 n (.f64 2 (PI.f64))) (-.f64 1 k))
(exp.f64 (.f64 (-.f64 1 k) (+.f64 (.f64 -1 (log.f64 (/.f64 1 n))) (log.f64 (*.f64 2 (PI.f64))))))
(pow.f64 (.f64 2 (.f64 n (PI.f64))) (-.f64 1 k))
(pow.f64 (.f64 n (.f64 2 (PI.f64))) (-.f64 1 k))
(exp.f64 (.f64 (-.f64 1 k) (+.f64 (.f64 -1 (log.f64 (/.f64 1 n))) (log.f64 (*.f64 2 (PI.f64))))))
(pow.f64 (.f64 2 (.f64 n (PI.f64))) (-.f64 1 k))
(pow.f64 (.f64 n (.f64 2 (PI.f64))) (-.f64 1 k))
(exp.f64 (.f64 (-.f64 1 k) (+.f64 (.f64 -1 (log.f64 (/.f64 1 n))) (log.f64 (*.f64 2 (PI.f64))))))
(pow.f64 (.f64 2 (.f64 n (PI.f64))) (-.f64 1 k))
(pow.f64 (.f64 n (.f64 2 (PI.f64))) (-.f64 1 k))
(exp.f64 (.f64 (-.f64 1 k) (+.f64 (.f64 -1 (log.f64 (/.f64 -1 n))) (log.f64 (*.f64 -2 (PI.f64))))))
(pow.f64 (exp.f64 (-.f64 1 k)) (fma.f64 -1 (log.f64 (/.f64 -1 n)) (log.f64 (*.f64 (PI.f64) -2))))
(pow.f64 (exp.f64 (-.f64 1 k)) (-.f64 (log.f64 (*.f64 (PI.f64) -2)) (log.f64 (/.f64 -1 n))))
(pow.f64 (/.f64 (*.f64 (PI.f64) -2) (/.f64 -1 n)) (-.f64 1 k))
(exp.f64 (.f64 (-.f64 1 k) (+.f64 (.f64 -1 (log.f64 (/.f64 -1 n))) (log.f64 (*.f64 -2 (PI.f64))))))
(pow.f64 (exp.f64 (-.f64 1 k)) (fma.f64 -1 (log.f64 (/.f64 -1 n)) (log.f64 (*.f64 (PI.f64) -2))))
(pow.f64 (exp.f64 (-.f64 1 k)) (-.f64 (log.f64 (*.f64 (PI.f64) -2)) (log.f64 (/.f64 -1 n))))
(pow.f64 (/.f64 (*.f64 (PI.f64) -2) (/.f64 -1 n)) (-.f64 1 k))
(exp.f64 (.f64 (-.f64 1 k) (+.f64 (.f64 -1 (log.f64 (/.f64 -1 n))) (log.f64 (*.f64 -2 (PI.f64))))))
(pow.f64 (exp.f64 (-.f64 1 k)) (fma.f64 -1 (log.f64 (/.f64 -1 n)) (log.f64 (*.f64 (PI.f64) -2))))
(pow.f64 (exp.f64 (-.f64 1 k)) (-.f64 (log.f64 (*.f64 (PI.f64) -2)) (log.f64 (/.f64 -1 n))))
(pow.f64 (/.f64 (*.f64 (PI.f64) -2) (/.f64 -1 n)) (-.f64 1 k))
(exp.f64 (.f64 (-.f64 1 k) (+.f64 (.f64 -1 (log.f64 (/.f64 -1 n))) (log.f64 (*.f64 -2 (PI.f64))))))
(pow.f64 (exp.f64 (-.f64 1 k)) (fma.f64 -1 (log.f64 (/.f64 -1 n)) (log.f64 (*.f64 (PI.f64) -2))))
(pow.f64 (exp.f64 (-.f64 1 k)) (-.f64 (log.f64 (*.f64 (PI.f64) -2)) (log.f64 (/.f64 -1 n))))
(pow.f64 (/.f64 (*.f64 (PI.f64) -2) (/.f64 -1 n)) (-.f64 1 k))
(.f64 2 (/.f64 (.f64 n (PI.f64)) k))
(*.f64 2 (/.f64 n (/.f64 k (PI.f64))))
(.f64 2 (.f64 (PI.f64) (/.f64 n k)))
(+.f64 (.f64 2 (/.f64 (.f64 n (PI.f64)) k)) (.f64 -2 (.f64 n (.f64 (log.f64 (.f64 2 (*.f64 n (PI.f64)))) (PI.f64)))))
(fma.f64 2 (/.f64 n (/.f64 k (PI.f64))) (.f64 -2 (.f64 (.f64 n (PI.f64)) (log.f64 (.f64 2 (*.f64 n (PI.f64)))))))
(fma.f64 2 (/.f64 (.f64 n (PI.f64)) k) (.f64 (.f64 -2 (.f64 n (PI.f64))) (log.f64 (.f64 n (.f64 2 (PI.f64))))))
(fma.f64 n (.f64 (PI.f64) (.f64 -2 (log.f64 (.f64 n (.f64 2 (PI.f64)))))) (.f64 2 (/.f64 (.f64 n (PI.f64)) k)))
(.f64 (.f64 n (PI.f64)) (+.f64 (/.f64 2 k) (.f64 -2 (log.f64 (.f64 n (*.f64 2 (PI.f64)))))))
(+.f64 (.f64 2 (/.f64 (.f64 n (PI.f64)) k)) (+.f64 (.f64 k (.f64 n (.f64 (PI.f64) (pow.f64 (log.f64 (.f64 2 (.f64 n (PI.f64)))) 2)))) (.f64 -2 (.f64 n (.f64 (log.f64 (.f64 2 (.f64 n (PI.f64)))) (PI.f64))))))
(fma.f64 2 (/.f64 n (/.f64 k (PI.f64))) (fma.f64 k (.f64 n (.f64 (PI.f64) (pow.f64 (log.f64 (.f64 2 (.f64 n (PI.f64)))) 2))) (.f64 -2 (.f64 (.f64 n (PI.f64)) (log.f64 (.f64 2 (*.f64 n (PI.f64))))))))
(fma.f64 2 (/.f64 (.f64 n (PI.f64)) k) (fma.f64 (.f64 n -2) (.f64 (PI.f64) (log.f64 (.f64 n (.f64 2 (PI.f64))))) (.f64 (.f64 n (PI.f64)) (.f64 (pow.f64 (log.f64 (.f64 n (.f64 2 (PI.f64)))) 2) k))))
(fma.f64 2 (/.f64 (.f64 n (PI.f64)) k) (.f64 (.f64 n (PI.f64)) (+.f64 (.f64 -2 (log.f64 (.f64 n (.f64 2 (PI.f64))))) (.f64 k (pow.f64 (log.f64 (.f64 n (*.f64 2 (PI.f64)))) 2)))))
(fma.f64 2 (.f64 (PI.f64) (/.f64 n k)) (.f64 (.f64 n (PI.f64)) (.f64 (log.f64 (.f64 n (.f64 2 (PI.f64)))) (+.f64 (.f64 k (log.f64 (.f64 n (*.f64 2 (PI.f64))))) -2))))
(+.f64 (.f64 -1/3 (.f64 (pow.f64 k 2) (.f64 n (.f64 (PI.f64) (pow.f64 (log.f64 (.f64 2 (.f64 n (PI.f64)))) 3))))) (+.f64 (.f64 2 (/.f64 (.f64 n (PI.f64)) k)) (+.f64 (.f64 k (.f64 n (.f64 (PI.f64) (pow.f64 (log.f64 (.f64 2 (.f64 n (PI.f64)))) 2)))) (.f64 -2 (.f64 n (.f64 (log.f64 (.f64 2 (.f64 n (PI.f64)))) (PI.f64)))))))
(fma.f64 -1/3 (.f64 (.f64 k k) (.f64 (.f64 n (PI.f64)) (pow.f64 (log.f64 (.f64 2 (.f64 n (PI.f64)))) 3))) (fma.f64 2 (/.f64 n (/.f64 k (PI.f64))) (fma.f64 k (.f64 n (.f64 (PI.f64) (pow.f64 (log.f64 (.f64 2 (.f64 n (PI.f64)))) 2))) (.f64 -2 (.f64 (.f64 n (PI.f64)) (log.f64 (.f64 2 (*.f64 n (PI.f64)))))))))
(fma.f64 -1/3 (.f64 (.f64 n (PI.f64)) (.f64 (pow.f64 (log.f64 (.f64 n (.f64 2 (PI.f64)))) 3) (.f64 k k))) (fma.f64 2 (/.f64 (.f64 n (PI.f64)) k) (fma.f64 (.f64 n -2) (.f64 (PI.f64) (log.f64 (.f64 n (.f64 2 (PI.f64))))) (.f64 (.f64 n (PI.f64)) (.f64 (pow.f64 (log.f64 (.f64 n (.f64 2 (PI.f64)))) 2) k)))))
(fma.f64 (.f64 k k) (.f64 (pow.f64 (log.f64 (.f64 n (.f64 2 (PI.f64)))) 3) (.f64 (.f64 n (PI.f64)) -1/3)) (fma.f64 2 (/.f64 (.f64 n (PI.f64)) k) (.f64 (.f64 n (PI.f64)) (+.f64 (.f64 -2 (log.f64 (.f64 n (.f64 2 (PI.f64))))) (.f64 k (pow.f64 (log.f64 (.f64 n (*.f64 2 (PI.f64)))) 2))))))
(fma.f64 2 (.f64 (PI.f64) (/.f64 n k)) (.f64 (.f64 n (PI.f64)) (+.f64 (.f64 (log.f64 (.f64 n (.f64 2 (PI.f64)))) (+.f64 (.f64 k (log.f64 (.f64 n (.f64 2 (PI.f64))))) -2)) (.f64 (pow.f64 (log.f64 (.f64 n (.f64 2 (PI.f64)))) 3) (.f64 k (.f64 k -1/3))))))
(/.f64 (pow.f64 (.f64 2 (.f64 n (PI.f64))) (-.f64 1 k)) k)
(/.f64 (pow.f64 (.f64 n (.f64 2 (PI.f64))) (-.f64 1 k)) k)
(/.f64 (pow.f64 (.f64 2 (.f64 n (PI.f64))) (-.f64 1 k)) k)
(/.f64 (pow.f64 (.f64 n (.f64 2 (PI.f64))) (-.f64 1 k)) k)
(/.f64 (pow.f64 (.f64 2 (.f64 n (PI.f64))) (-.f64 1 k)) k)
(/.f64 (pow.f64 (.f64 n (.f64 2 (PI.f64))) (-.f64 1 k)) k)
(/.f64 (pow.f64 (.f64 2 (.f64 n (PI.f64))) (-.f64 1 k)) k)
(/.f64 (pow.f64 (.f64 n (.f64 2 (PI.f64))) (-.f64 1 k)) k)
(/.f64 (pow.f64 (.f64 2 (.f64 n (PI.f64))) (+.f64 1 (*.f64 -1 k))) k)
(/.f64 (pow.f64 (.f64 2 (.f64 n (PI.f64))) (-.f64 1 k)) k)
(/.f64 (pow.f64 (.f64 n (.f64 2 (PI.f64))) (-.f64 1 k)) k)
(/.f64 (pow.f64 (.f64 2 (.f64 n (PI.f64))) (+.f64 1 (*.f64 -1 k))) k)
(/.f64 (pow.f64 (.f64 2 (.f64 n (PI.f64))) (-.f64 1 k)) k)
(/.f64 (pow.f64 (.f64 n (.f64 2 (PI.f64))) (-.f64 1 k)) k)
(/.f64 (pow.f64 (.f64 2 (.f64 n (PI.f64))) (+.f64 1 (*.f64 -1 k))) k)
(/.f64 (pow.f64 (.f64 2 (.f64 n (PI.f64))) (-.f64 1 k)) k)
(/.f64 (pow.f64 (.f64 n (.f64 2 (PI.f64))) (-.f64 1 k)) k)
(/.f64 (pow.f64 (.f64 2 (.f64 n (PI.f64))) (+.f64 1 (*.f64 -1 k))) k)
(/.f64 (pow.f64 (.f64 2 (.f64 n (PI.f64))) (-.f64 1 k)) k)
(/.f64 (pow.f64 (.f64 n (.f64 2 (PI.f64))) (-.f64 1 k)) k)
(/.f64 (exp.f64 (.f64 (-.f64 1 k) (+.f64 (log.f64 (.f64 2 (PI.f64))) (log.f64 n)))) k)
(/.f64 (pow.f64 (.f64 2 (.f64 n (PI.f64))) (-.f64 1 k)) k)
(/.f64 (pow.f64 (.f64 n (.f64 2 (PI.f64))) (-.f64 1 k)) k)
(/.f64 (exp.f64 (.f64 (-.f64 1 k) (+.f64 (log.f64 (.f64 2 (PI.f64))) (log.f64 n)))) k)
(/.f64 (pow.f64 (.f64 2 (.f64 n (PI.f64))) (-.f64 1 k)) k)
(/.f64 (pow.f64 (.f64 n (.f64 2 (PI.f64))) (-.f64 1 k)) k)
(/.f64 (exp.f64 (.f64 (-.f64 1 k) (+.f64 (log.f64 (.f64 2 (PI.f64))) (log.f64 n)))) k)
(/.f64 (pow.f64 (.f64 2 (.f64 n (PI.f64))) (-.f64 1 k)) k)
(/.f64 (pow.f64 (.f64 n (.f64 2 (PI.f64))) (-.f64 1 k)) k)
(/.f64 (exp.f64 (.f64 (-.f64 1 k) (+.f64 (log.f64 (.f64 2 (PI.f64))) (log.f64 n)))) k)
(/.f64 (pow.f64 (.f64 2 (.f64 n (PI.f64))) (-.f64 1 k)) k)
(/.f64 (pow.f64 (.f64 n (.f64 2 (PI.f64))) (-.f64 1 k)) k)
(/.f64 (exp.f64 (.f64 (-.f64 1 k) (+.f64 (.f64 -1 (log.f64 (/.f64 1 n))) (log.f64 (*.f64 2 (PI.f64)))))) k)
(/.f64 (pow.f64 (.f64 2 (.f64 n (PI.f64))) (-.f64 1 k)) k)
(/.f64 (pow.f64 (.f64 n (.f64 2 (PI.f64))) (-.f64 1 k)) k)
(/.f64 (exp.f64 (.f64 (-.f64 1 k) (+.f64 (.f64 -1 (log.f64 (/.f64 1 n))) (log.f64 (*.f64 2 (PI.f64)))))) k)
(/.f64 (pow.f64 (.f64 2 (.f64 n (PI.f64))) (-.f64 1 k)) k)
(/.f64 (pow.f64 (.f64 n (.f64 2 (PI.f64))) (-.f64 1 k)) k)
(/.f64 (exp.f64 (.f64 (-.f64 1 k) (+.f64 (.f64 -1 (log.f64 (/.f64 1 n))) (log.f64 (*.f64 2 (PI.f64)))))) k)
(/.f64 (pow.f64 (.f64 2 (.f64 n (PI.f64))) (-.f64 1 k)) k)
(/.f64 (pow.f64 (.f64 n (.f64 2 (PI.f64))) (-.f64 1 k)) k)
(/.f64 (exp.f64 (.f64 (-.f64 1 k) (+.f64 (.f64 -1 (log.f64 (/.f64 1 n))) (log.f64 (*.f64 2 (PI.f64)))))) k)
(/.f64 (pow.f64 (.f64 2 (.f64 n (PI.f64))) (-.f64 1 k)) k)
(/.f64 (pow.f64 (.f64 n (.f64 2 (PI.f64))) (-.f64 1 k)) k)
(/.f64 (exp.f64 (.f64 (-.f64 1 k) (+.f64 (.f64 -1 (log.f64 (/.f64 -1 n))) (log.f64 (*.f64 -2 (PI.f64)))))) k)
(/.f64 (pow.f64 (exp.f64 (-.f64 1 k)) (fma.f64 -1 (log.f64 (/.f64 -1 n)) (log.f64 (*.f64 (PI.f64) -2)))) k)
(/.f64 (pow.f64 (exp.f64 (-.f64 1 k)) (-.f64 (log.f64 (*.f64 (PI.f64) -2)) (log.f64 (/.f64 -1 n)))) k)
(/.f64 (pow.f64 (/.f64 (*.f64 (PI.f64) -2) (/.f64 -1 n)) (-.f64 1 k)) k)
(/.f64 (exp.f64 (.f64 (-.f64 1 k) (+.f64 (.f64 -1 (log.f64 (/.f64 -1 n))) (log.f64 (*.f64 -2 (PI.f64)))))) k)
(/.f64 (pow.f64 (exp.f64 (-.f64 1 k)) (fma.f64 -1 (log.f64 (/.f64 -1 n)) (log.f64 (*.f64 (PI.f64) -2)))) k)
(/.f64 (pow.f64 (exp.f64 (-.f64 1 k)) (-.f64 (log.f64 (*.f64 (PI.f64) -2)) (log.f64 (/.f64 -1 n)))) k)
(/.f64 (pow.f64 (/.f64 (*.f64 (PI.f64) -2) (/.f64 -1 n)) (-.f64 1 k)) k)
(/.f64 (exp.f64 (.f64 (-.f64 1 k) (+.f64 (.f64 -1 (log.f64 (/.f64 -1 n))) (log.f64 (*.f64 -2 (PI.f64)))))) k)
(/.f64 (pow.f64 (exp.f64 (-.f64 1 k)) (fma.f64 -1 (log.f64 (/.f64 -1 n)) (log.f64 (*.f64 (PI.f64) -2)))) k)
(/.f64 (pow.f64 (exp.f64 (-.f64 1 k)) (-.f64 (log.f64 (*.f64 (PI.f64) -2)) (log.f64 (/.f64 -1 n)))) k)
(/.f64 (pow.f64 (/.f64 (*.f64 (PI.f64) -2) (/.f64 -1 n)) (-.f64 1 k)) k)
(/.f64 (exp.f64 (.f64 (-.f64 1 k) (+.f64 (.f64 -1 (log.f64 (/.f64 -1 n))) (log.f64 (*.f64 -2 (PI.f64)))))) k)
(/.f64 (pow.f64 (exp.f64 (-.f64 1 k)) (fma.f64 -1 (log.f64 (/.f64 -1 n)) (log.f64 (*.f64 (PI.f64) -2)))) k)
(/.f64 (pow.f64 (exp.f64 (-.f64 1 k)) (-.f64 (log.f64 (*.f64 (PI.f64) -2)) (log.f64 (/.f64 -1 n)))) k)
(/.f64 (pow.f64 (/.f64 (*.f64 (PI.f64) -2) (/.f64 -1 n)) (-.f64 1 k)) k)

localize32.0ms (0.3%)

Local error

Found 8 expressions with local error:

New	Error	Program
	0.2b	(*.f64 (PI.f64) n)
	0.2b	(.f64 (sqrt.f64 k) (pow.f64 (pow.f64 (.f64 2 (*.f64 (PI.f64) n)) (-.f64 1 k)) -1/2))
	0.2b	(/.f64 1 (.f64 (sqrt.f64 k) (pow.f64 (pow.f64 (.f64 2 (*.f64 (PI.f64) n)) (-.f64 1 k)) -1/2)))
	0.1b	(pow.f64 (pow.f64 (.f64 2 (.f64 (PI.f64) n)) (-.f64 1 k)) -1/2)
✓	0.2b	(/.f64 1 (.f64 (sqrt.f64 k) (pow.f64 (pow.f64 (.f64 2 (*.f64 (PI.f64) n)) (-.f64 1 k)) -1/2)))
✓	0.2b	(.f64 (sqrt.f64 k) (pow.f64 (pow.f64 (.f64 2 (*.f64 (PI.f64) n)) (-.f64 1 k)) -1/2))
	0.2b	(*.f64 (PI.f64) n)
	0.4b	(pow.f64 (.f64 2 (.f64 (PI.f64) n)) (-.f64 1 k))

Compiler

Compiled 71 to 42 computations (40.8% saved)

series9.0ms (0.1%)

Counts

2 → 24

Calls

12 calls:

Time	Variable		Point	Expression
2.0ms	k	@	0	(/.f64 1 (.f64 (sqrt.f64 k) (pow.f64 (pow.f64 (.f64 2 (*.f64 (PI.f64) n)) (-.f64 1 k)) -1/2)))
1.0ms	k	@	0	(.f64 (sqrt.f64 k) (pow.f64 (pow.f64 (.f64 2 (*.f64 (PI.f64) n)) (-.f64 1 k)) -1/2))
1.0ms	n	@	0	(.f64 (sqrt.f64 k) (pow.f64 (pow.f64 (.f64 2 (*.f64 (PI.f64) n)) (-.f64 1 k)) -1/2))
1.0ms	n	@	inf	(.f64 (sqrt.f64 k) (pow.f64 (pow.f64 (.f64 2 (*.f64 (PI.f64) n)) (-.f64 1 k)) -1/2))
1.0ms	n	@	-inf	(.f64 (sqrt.f64 k) (pow.f64 (pow.f64 (.f64 2 (*.f64 (PI.f64) n)) (-.f64 1 k)) -1/2))

rewrite60.0ms (0.6%)

Algorithm

1×	batch-egg-rewrite

Rules

777×	`log-prod_binary64`
408×	`pow2_binary64`
277×	`pow1/3_binary64`
275×	`expm1-udef_binary64`
274×	`log1p-udef_binary64`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	15	47
1	329	45
2	4102	45

Stop Event

1×	node limit

Counts

2 → 56

Calls

Call 1

Inputs
(.f64 (sqrt.f64 k) (pow.f64 (pow.f64 (.f64 2 (*.f64 (PI.f64) n)) (-.f64 1 k)) -1/2))
(/.f64 1 (.f64 (sqrt.f64 k) (pow.f64 (pow.f64 (.f64 2 (*.f64 (PI.f64) n)) (-.f64 1 k)) -1/2)))

Outputs

((#(struct:change #<rule egg-rr> (2) ((x +.f64 0 (*.f64 (sqrt.f64 k) (pow.f64 (*.f64 2 (*.f64 (PI.f64) n)) (*.f64 (-.f64 1 k) -1/2))))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (log.f64 (pow.f64 (cbrt.f64 (pow.f64 (exp.f64 (sqrt.f64 k)) (pow.f64 (*.f64 2 (*.f64 (PI.f64) n)) (*.f64 (-.f64 1 k) -1/2)))) 2)) (log.f64 (cbrt.f64 (pow.f64 (exp.f64 (sqrt.f64 k)) (pow.f64 (*.f64 2 (*.f64 (PI.f64) n)) (*.f64 (-.f64 1 k) -1/2))))))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (log.f64 (sqrt.f64 (pow.f64 (exp.f64 (sqrt.f64 k)) (pow.f64 (*.f64 2 (*.f64 (PI.f64) n)) (*.f64 (-.f64 1 k) -1/2))))) (log.f64 (sqrt.f64 (pow.f64 (exp.f64 (sqrt.f64 k)) (pow.f64 (*.f64 2 (*.f64 (PI.f64) n)) (*.f64 (-.f64 1 k) -1/2))))))))) (#(struct:change #<rule egg-rr> (2) ((x -.f64 (exp.f64 (log1p.f64 (*.f64 (sqrt.f64 k) (pow.f64 (*.f64 2 (*.f64 (PI.f64) n)) (*.f64 (-.f64 1 k) -1/2))))) 1)))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (sqrt.f64 k) (/.f64 1 (pow.f64 (*.f64 2 (*.f64 (PI.f64) n)) (*.f64 (-.f64 1 k) -1/2))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 1 (/.f64 (pow.f64 k -1/2) (pow.f64 (*.f64 2 (*.f64 (PI.f64) n)) (*.f64 (-.f64 1 k) -1/2))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (pow.f64 (*.f64 2 (*.f64 (PI.f64) n)) (*.f64 (-.f64 1 k) -1/2)) (pow.f64 k -1/2))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (*.f64 (sqrt.f64 k) (pow.f64 (*.f64 2 (*.f64 (PI.f64) n)) (*.f64 (-.f64 1 k) -1/2))) 1)))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (cbrt.f64 (*.f64 k (pow.f64 (pow.f64 (*.f64 2 (*.f64 (PI.f64) n)) (-.f64 1 k)) -1))) (cbrt.f64 (/.f64 (pow.f64 k -1/2) (pow.f64 (*.f64 2 (*.f64 (PI.f64) n)) (*.f64 (-.f64 1 k) -1/2)))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (*.f64 (pow.f64 k 1/4) (pow.f64 (*.f64 2 (*.f64 (PI.f64) n)) (*.f64 (-.f64 1 k) -1/4))) (/.f64 (sqrt.f64 (pow.f64 k -1/2)) (pow.f64 (*.f64 2 (*.f64 (PI.f64) n)) (*.f64 (-.f64 1 k) -1/4))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (*.f64 (sqrt.f64 k) (neg.f64 (pow.f64 (*.f64 2 (*.f64 (PI.f64) n)) (*.f64 (-.f64 1 k) -1/2)))) -1)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (*.f64 (sqrt.f64 k) (pow.f64 (*.f64 2 (*.f64 (PI.f64) n)) (*.f64 (-.f64 1 k) -1/2))) 1)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (/.f64 (pow.f64 k -1/2) (pow.f64 (*.f64 2 (*.f64 (PI.f64) n)) (*.f64 (-.f64 1 k) -1/2))) -1)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (pow.f64 (*.f64 (sqrt.f64 k) (pow.f64 (*.f64 2 (*.f64 (PI.f64) n)) (*.f64 (-.f64 1 k) -1/2))) 3) 1/3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (cbrt.f64 (*.f64 (sqrt.f64 k) (pow.f64 (*.f64 2 (*.f64 (PI.f64) n)) (*.f64 (-.f64 1 k) -1/2)))) 3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (*.f64 (pow.f64 k 1/4) (pow.f64 (*.f64 2 (*.f64 (PI.f64) n)) (*.f64 (-.f64 1 k) -1/4))) 2)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (*.f64 (pow.f64 k 3/2) (pow.f64 (pow.f64 (*.f64 2 (*.f64 (PI.f64) n)) (*.f64 (-.f64 1 k) -1/2)) 3)) 1/3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (*.f64 (pow.f64 (pow.f64 (*.f64 2 (*.f64 (PI.f64) n)) (*.f64 (-.f64 1 k) -1/2)) 3) (pow.f64 k 3/2)) 1/3)))) (#(struct:change #<rule egg-rr> (2) ((x sqrt.f64 (*.f64 k (pow.f64 (pow.f64 (*.f64 2 (*.f64 (PI.f64) n)) (-.f64 1 k)) -1)))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (pow.f64 (exp.f64 (sqrt.f64 k)) (pow.f64 (*.f64 2 (*.f64 (PI.f64) n)) (*.f64 (-.f64 1 k) -1/2))))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (+.f64 1 (expm1.f64 (*.f64 (sqrt.f64 k) (pow.f64 (*.f64 2 (*.f64 (PI.f64) n)) (*.f64 (-.f64 1 k) -1/2))))))))) (#(struct:change #<rule egg-rr> (2) ((x cbrt.f64 (pow.f64 (*.f64 (sqrt.f64 k) (pow.f64 (*.f64 2 (*.f64 (PI.f64) n)) (*.f64 (-.f64 1 k) -1/2))) 3))))) (#(struct:change #<rule egg-rr> (2) ((x cbrt.f64 (*.f64 (pow.f64 k 3/2) (pow.f64 (pow.f64 (*.f64 2 (*.f64 (PI.f64) n)) (*.f64 (-.f64 1 k) -1/2)) 3)))))) (#(struct:change #<rule egg-rr> (2) ((x cbrt.f64 (*.f64 (pow.f64 (pow.f64 (*.f64 2 (*.f64 (PI.f64) n)) (*.f64 (-.f64 1 k) -1/2)) 3) (pow.f64 k 3/2)))))) (#(struct:change #<rule egg-rr> (2) ((x expm1.f64 (log1p.f64 (*.f64 (sqrt.f64 k) (pow.f64 (*.f64 2 (*.f64 (PI.f64) n)) (*.f64 (-.f64 1 k) -1/2)))))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (log.f64 (*.f64 (sqrt.f64 k) (pow.f64 (*.f64 2 (*.f64 (PI.f64) n)) (*.f64 (-.f64 1 k) -1/2)))))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (*.f64 (log.f64 (*.f64 (sqrt.f64 k) (pow.f64 (*.f64 2 (*.f64 (PI.f64) n)) (*.f64 (-.f64 1 k) -1/2)))) 1))))) (#(struct:change #<rule egg-rr> (2) ((x log1p.f64 (expm1.f64 (*.f64 (sqrt.f64 k) (pow.f64 (*.f64 2 (*.f64 (PI.f64) n)) (*.f64 (-.f64 1 k) -1/2)))))))))

((#(struct:change #<rule egg-rr> (2) ((x +.f64 0 (/.f64 (pow.f64 k -1/2) (pow.f64 (*.f64 2 (*.f64 (PI.f64) n)) (*.f64 (-.f64 1 k) -1/2))))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (log.f64 (pow.f64 (cbrt.f64 (exp.f64 (/.f64 (pow.f64 k -1/2) (pow.f64 (*.f64 2 (*.f64 (PI.f64) n)) (*.f64 (-.f64 1 k) -1/2))))) 2)) (log.f64 (cbrt.f64 (exp.f64 (/.f64 (pow.f64 k -1/2) (pow.f64 (*.f64 2 (*.f64 (PI.f64) n)) (*.f64 (-.f64 1 k) -1/2)))))))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (log.f64 (sqrt.f64 (exp.f64 (/.f64 (pow.f64 k -1/2) (pow.f64 (*.f64 2 (*.f64 (PI.f64) n)) (*.f64 (-.f64 1 k) -1/2)))))) (log.f64 (sqrt.f64 (exp.f64 (/.f64 (pow.f64 k -1/2) (pow.f64 (*.f64 2 (*.f64 (PI.f64) n)) (*.f64 (-.f64 1 k) -1/2)))))))))) (#(struct:change #<rule egg-rr> (2) ((x -.f64 (exp.f64 (log1p.f64 (/.f64 (pow.f64 k -1/2) (pow.f64 (*.f64 2 (*.f64 (PI.f64) n)) (*.f64 (-.f64 1 k) -1/2))))) 1)))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 1 (/.f64 (pow.f64 k -1/2) (pow.f64 (*.f64 2 (*.f64 (PI.f64) n)) (*.f64 (-.f64 1 k) -1/2))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (/.f64 (pow.f64 k -1/2) (pow.f64 (*.f64 2 (*.f64 (PI.f64) n)) (*.f64 (-.f64 1 k) -1/2))) 1)))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (cbrt.f64 (/.f64 (pow.f64 k -1/2) (pow.f64 (*.f64 2 (*.f64 (PI.f64) n)) (*.f64 (-.f64 1 k) -1/2)))) (cbrt.f64 (/.f64 1 (*.f64 k (pow.f64 (pow.f64 (*.f64 2 (*.f64 (PI.f64) n)) (-.f64 1 k)) -1)))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (cbrt.f64 (/.f64 1 (*.f64 k (pow.f64 (pow.f64 (*.f64 2 (*.f64 (PI.f64) n)) (-.f64 1 k)) -1)))) (cbrt.f64 (/.f64 (pow.f64 k -1/2) (pow.f64 (*.f64 2 (*.f64 (PI.f64) n)) (*.f64 (-.f64 1 k) -1/2)))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (/.f64 (sqrt.f64 (pow.f64 k -1/2)) (pow.f64 (*.f64 2 (*.f64 (PI.f64) n)) (*.f64 (-.f64 1 k) -1/4))) (/.f64 (sqrt.f64 (pow.f64 k -1/2)) (pow.f64 (*.f64 2 (*.f64 (PI.f64) n)) (*.f64 (-.f64 1 k) -1/4))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 -1 (/.f64 1 (*.f64 (sqrt.f64 k) (neg.f64 (pow.f64 (*.f64 2 (*.f64 (PI.f64) n)) (*.f64 (-.f64 1 k) -1/2))))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (pow.f64 k -1/2) (/.f64 1 (pow.f64 (*.f64 2 (*.f64 (PI.f64) n)) (*.f64 (-.f64 1 k) -1/2))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (/.f64 1 (cbrt.f64 (*.f64 k (pow.f64 (pow.f64 (*.f64 2 (*.f64 (PI.f64) n)) (-.f64 1 k)) -1)))) (cbrt.f64 (/.f64 (pow.f64 k -1/2) (pow.f64 (*.f64 2 (*.f64 (PI.f64) n)) (*.f64 (-.f64 1 k) -1/2)))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (/.f64 1 (pow.f64 (*.f64 2 (*.f64 (PI.f64) n)) (*.f64 (-.f64 1 k) -1/2))) (pow.f64 k -1/2))))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (*.f64 (sqrt.f64 k) (pow.f64 (*.f64 2 (*.f64 (PI.f64) n)) (*.f64 (-.f64 1 k) -1/2))) -1)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (/.f64 (pow.f64 k -1/2) (pow.f64 (*.f64 2 (*.f64 (PI.f64) n)) (*.f64 (-.f64 1 k) -1/2))) 1)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (pow.f64 (/.f64 (pow.f64 k -1/2) (pow.f64 (*.f64 2 (*.f64 (PI.f64) n)) (*.f64 (-.f64 1 k) -1/2))) 3) 1/3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (cbrt.f64 (/.f64 (pow.f64 k -1/2) (pow.f64 (*.f64 2 (*.f64 (PI.f64) n)) (*.f64 (-.f64 1 k) -1/2)))) 3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (/.f64 (sqrt.f64 (pow.f64 k -1/2)) (pow.f64 (*.f64 2 (*.f64 (PI.f64) n)) (*.f64 (-.f64 1 k) -1/4))) 2)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (neg.f64 (*.f64 (sqrt.f64 k) (neg.f64 (pow.f64 (*.f64 2 (*.f64 (PI.f64) n)) (*.f64 (-.f64 1 k) -1/2))))) -1)))) (#(struct:change #<rule egg-rr> (2) ((x sqrt.f64 (/.f64 1 (*.f64 k (pow.f64 (pow.f64 (*.f64 2 (*.f64 (PI.f64) n)) (-.f64 1 k)) -1))))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (exp.f64 (/.f64 (pow.f64 k -1/2) (pow.f64 (*.f64 2 (*.f64 (PI.f64) n)) (*.f64 (-.f64 1 k) -1/2)))))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (+.f64 1 (expm1.f64 (/.f64 (pow.f64 k -1/2) (pow.f64 (*.f64 2 (*.f64 (PI.f64) n)) (*.f64 (-.f64 1 k) -1/2))))))))) (#(struct:change #<rule egg-rr> (2) ((x cbrt.f64 (pow.f64 (/.f64 (pow.f64 k -1/2) (pow.f64 (*.f64 2 (*.f64 (PI.f64) n)) (*.f64 (-.f64 1 k) -1/2))) 3))))) (#(struct:change #<rule egg-rr> (2) ((x expm1.f64 (log1p.f64 (/.f64 (pow.f64 k -1/2) (pow.f64 (*.f64 2 (*.f64 (PI.f64) n)) (*.f64 (-.f64 1 k) -1/2)))))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (log.f64 (/.f64 (pow.f64 k -1/2) (pow.f64 (*.f64 2 (*.f64 (PI.f64) n)) (*.f64 (-.f64 1 k) -1/2)))))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (*.f64 (log.f64 (*.f64 (sqrt.f64 k) (pow.f64 (*.f64 2 (*.f64 (PI.f64) n)) (*.f64 (-.f64 1 k) -1/2)))) -1))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (*.f64 (log.f64 (/.f64 (pow.f64 k -1/2) (pow.f64 (*.f64 2 (*.f64 (PI.f64) n)) (*.f64 (-.f64 1 k) -1/2)))) 1))))) (#(struct:change #<rule egg-rr> (2) ((x log1p.f64 (expm1.f64 (/.f64 (pow.f64 k -1/2) (pow.f64 (*.f64 2 (*.f64 (PI.f64) n)) (*.f64 (-.f64 1 k) -1/2)))))))))

simplify40.0ms (0.4%)

Algorithm

1×	egg-herbie

Rules

544×	`exp-sum_binary64`
410×	`unsub-neg_binary64`
308×	`fma-neg_binary64`
305×	`associate--r+_binary64`
305×	`fma-def_binary64`

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	44	600
1	96	600
2	247	600
3	835	456
4	3381	456

Stop Event

1×	node limit

Counts

80 → 64

Calls

Call 1

Inputs
(sqrt.f64 (/.f64 k (exp.f64 (.f64 (-.f64 1 k) (+.f64 (log.f64 (.f64 2 (PI.f64))) (log.f64 n))))))
(sqrt.f64 (/.f64 k (exp.f64 (.f64 (-.f64 1 k) (+.f64 (log.f64 (.f64 2 (PI.f64))) (log.f64 n))))))
(sqrt.f64 (/.f64 k (exp.f64 (.f64 (-.f64 1 k) (+.f64 (log.f64 (.f64 2 (PI.f64))) (log.f64 n))))))
(sqrt.f64 (/.f64 k (exp.f64 (.f64 (-.f64 1 k) (+.f64 (log.f64 (.f64 2 (PI.f64))) (log.f64 n))))))
(sqrt.f64 (/.f64 k (exp.f64 (.f64 (-.f64 1 k) (+.f64 (.f64 -1 (log.f64 (/.f64 1 n))) (log.f64 (*.f64 2 (PI.f64))))))))
(sqrt.f64 (/.f64 k (exp.f64 (.f64 (-.f64 1 k) (+.f64 (.f64 -1 (log.f64 (/.f64 1 n))) (log.f64 (*.f64 2 (PI.f64))))))))
(sqrt.f64 (/.f64 k (exp.f64 (.f64 (-.f64 1 k) (+.f64 (.f64 -1 (log.f64 (/.f64 1 n))) (log.f64 (*.f64 2 (PI.f64))))))))
(sqrt.f64 (/.f64 k (exp.f64 (.f64 (-.f64 1 k) (+.f64 (.f64 -1 (log.f64 (/.f64 1 n))) (log.f64 (*.f64 2 (PI.f64))))))))
(sqrt.f64 (/.f64 k (exp.f64 (.f64 (-.f64 1 k) (+.f64 (.f64 -1 (log.f64 (/.f64 -1 n))) (log.f64 (*.f64 -2 (PI.f64))))))))
(sqrt.f64 (/.f64 k (exp.f64 (.f64 (-.f64 1 k) (+.f64 (.f64 -1 (log.f64 (/.f64 -1 n))) (log.f64 (*.f64 -2 (PI.f64))))))))
(sqrt.f64 (/.f64 k (exp.f64 (.f64 (-.f64 1 k) (+.f64 (.f64 -1 (log.f64 (/.f64 -1 n))) (log.f64 (*.f64 -2 (PI.f64))))))))
(sqrt.f64 (/.f64 k (exp.f64 (.f64 (-.f64 1 k) (+.f64 (.f64 -1 (log.f64 (/.f64 -1 n))) (log.f64 (*.f64 -2 (PI.f64))))))))
(sqrt.f64 (/.f64 (exp.f64 (.f64 (-.f64 1 k) (+.f64 (log.f64 n) (log.f64 (.f64 2 (PI.f64)))))) k))
(sqrt.f64 (/.f64 (exp.f64 (.f64 (-.f64 1 k) (+.f64 (log.f64 n) (log.f64 (.f64 2 (PI.f64)))))) k))
(sqrt.f64 (/.f64 (exp.f64 (.f64 (-.f64 1 k) (+.f64 (log.f64 n) (log.f64 (.f64 2 (PI.f64)))))) k))
(sqrt.f64 (/.f64 (exp.f64 (.f64 (-.f64 1 k) (+.f64 (log.f64 n) (log.f64 (.f64 2 (PI.f64)))))) k))
(sqrt.f64 (/.f64 (exp.f64 (.f64 (-.f64 1 k) (+.f64 (.f64 -1 (log.f64 (/.f64 1 n))) (log.f64 (*.f64 2 (PI.f64)))))) k))
(sqrt.f64 (/.f64 (exp.f64 (.f64 (-.f64 1 k) (+.f64 (.f64 -1 (log.f64 (/.f64 1 n))) (log.f64 (*.f64 2 (PI.f64)))))) k))
(sqrt.f64 (/.f64 (exp.f64 (.f64 (-.f64 1 k) (+.f64 (.f64 -1 (log.f64 (/.f64 1 n))) (log.f64 (*.f64 2 (PI.f64)))))) k))
(sqrt.f64 (/.f64 (exp.f64 (.f64 (-.f64 1 k) (+.f64 (.f64 -1 (log.f64 (/.f64 1 n))) (log.f64 (*.f64 2 (PI.f64)))))) k))
(sqrt.f64 (/.f64 (exp.f64 (.f64 (-.f64 1 k) (+.f64 (.f64 -1 (log.f64 (/.f64 -1 n))) (log.f64 (*.f64 -2 (PI.f64)))))) k))
(sqrt.f64 (/.f64 (exp.f64 (.f64 (-.f64 1 k) (+.f64 (.f64 -1 (log.f64 (/.f64 -1 n))) (log.f64 (*.f64 -2 (PI.f64)))))) k))
(sqrt.f64 (/.f64 (exp.f64 (.f64 (-.f64 1 k) (+.f64 (.f64 -1 (log.f64 (/.f64 -1 n))) (log.f64 (*.f64 -2 (PI.f64)))))) k))
(sqrt.f64 (/.f64 (exp.f64 (.f64 (-.f64 1 k) (+.f64 (.f64 -1 (log.f64 (/.f64 -1 n))) (log.f64 (*.f64 -2 (PI.f64)))))) k))

Outputs
(sqrt.f64 (/.f64 k (exp.f64 (.f64 (-.f64 1 k) (+.f64 (log.f64 (.f64 2 (PI.f64))) (log.f64 n))))))
(sqrt.f64 (/.f64 k (pow.f64 (exp.f64 (-.f64 1 k)) (+.f64 (log.f64 (*.f64 2 (PI.f64))) (log.f64 n)))))
(sqrt.f64 (/.f64 k (pow.f64 (.f64 2 (.f64 n (PI.f64))) (-.f64 1 k))))
(sqrt.f64 (/.f64 k (exp.f64 (.f64 (-.f64 1 k) (+.f64 (log.f64 (.f64 2 (PI.f64))) (log.f64 n))))))
(sqrt.f64 (/.f64 k (pow.f64 (exp.f64 (-.f64 1 k)) (+.f64 (log.f64 (*.f64 2 (PI.f64))) (log.f64 n)))))
(sqrt.f64 (/.f64 k (pow.f64 (.f64 2 (.f64 n (PI.f64))) (-.f64 1 k))))
(sqrt.f64 (/.f64 k (exp.f64 (.f64 (-.f64 1 k) (+.f64 (log.f64 (.f64 2 (PI.f64))) (log.f64 n))))))
(sqrt.f64 (/.f64 k (pow.f64 (exp.f64 (-.f64 1 k)) (+.f64 (log.f64 (*.f64 2 (PI.f64))) (log.f64 n)))))
(sqrt.f64 (/.f64 k (pow.f64 (.f64 2 (.f64 n (PI.f64))) (-.f64 1 k))))
(sqrt.f64 (/.f64 k (exp.f64 (.f64 (-.f64 1 k) (+.f64 (log.f64 (.f64 2 (PI.f64))) (log.f64 n))))))
(sqrt.f64 (/.f64 k (pow.f64 (exp.f64 (-.f64 1 k)) (+.f64 (log.f64 (*.f64 2 (PI.f64))) (log.f64 n)))))
(sqrt.f64 (/.f64 k (pow.f64 (.f64 2 (.f64 n (PI.f64))) (-.f64 1 k))))
(sqrt.f64 (/.f64 k (exp.f64 (.f64 (-.f64 1 k) (+.f64 (.f64 -1 (log.f64 (/.f64 1 n))) (log.f64 (*.f64 2 (PI.f64))))))))
(sqrt.f64 (/.f64 k (pow.f64 (exp.f64 (-.f64 1 k)) (+.f64 (log.f64 (*.f64 2 (PI.f64))) (log.f64 n)))))
(sqrt.f64 (/.f64 k (pow.f64 (.f64 2 (.f64 n (PI.f64))) (-.f64 1 k))))
(sqrt.f64 (/.f64 k (exp.f64 (.f64 (-.f64 1 k) (+.f64 (.f64 -1 (log.f64 (/.f64 1 n))) (log.f64 (*.f64 2 (PI.f64))))))))
(sqrt.f64 (/.f64 k (pow.f64 (exp.f64 (-.f64 1 k)) (+.f64 (log.f64 (*.f64 2 (PI.f64))) (log.f64 n)))))
(sqrt.f64 (/.f64 k (pow.f64 (.f64 2 (.f64 n (PI.f64))) (-.f64 1 k))))
(sqrt.f64 (/.f64 k (exp.f64 (.f64 (-.f64 1 k) (+.f64 (.f64 -1 (log.f64 (/.f64 1 n))) (log.f64 (*.f64 2 (PI.f64))))))))
(sqrt.f64 (/.f64 k (pow.f64 (exp.f64 (-.f64 1 k)) (+.f64 (log.f64 (*.f64 2 (PI.f64))) (log.f64 n)))))
(sqrt.f64 (/.f64 k (pow.f64 (.f64 2 (.f64 n (PI.f64))) (-.f64 1 k))))
(sqrt.f64 (/.f64 k (exp.f64 (.f64 (-.f64 1 k) (+.f64 (.f64 -1 (log.f64 (/.f64 1 n))) (log.f64 (*.f64 2 (PI.f64))))))))
(sqrt.f64 (/.f64 k (pow.f64 (exp.f64 (-.f64 1 k)) (+.f64 (log.f64 (*.f64 2 (PI.f64))) (log.f64 n)))))
(sqrt.f64 (/.f64 k (pow.f64 (.f64 2 (.f64 n (PI.f64))) (-.f64 1 k))))
(sqrt.f64 (/.f64 k (exp.f64 (.f64 (-.f64 1 k) (+.f64 (.f64 -1 (log.f64 (/.f64 -1 n))) (log.f64 (*.f64 -2 (PI.f64))))))))
(sqrt.f64 (/.f64 k (pow.f64 (exp.f64 (-.f64 1 k)) (+.f64 (log.f64 (*.f64 2 (PI.f64))) (log.f64 n)))))
(sqrt.f64 (/.f64 k (pow.f64 (.f64 2 (.f64 n (PI.f64))) (-.f64 1 k))))
(sqrt.f64 (/.f64 k (exp.f64 (.f64 (-.f64 1 k) (+.f64 (.f64 -1 (log.f64 (/.f64 -1 n))) (log.f64 (*.f64 -2 (PI.f64))))))))
(sqrt.f64 (/.f64 k (pow.f64 (exp.f64 (-.f64 1 k)) (+.f64 (log.f64 (*.f64 2 (PI.f64))) (log.f64 n)))))
(sqrt.f64 (/.f64 k (pow.f64 (.f64 2 (.f64 n (PI.f64))) (-.f64 1 k))))
(sqrt.f64 (/.f64 k (exp.f64 (.f64 (-.f64 1 k) (+.f64 (.f64 -1 (log.f64 (/.f64 -1 n))) (log.f64 (*.f64 -2 (PI.f64))))))))
(sqrt.f64 (/.f64 k (pow.f64 (exp.f64 (-.f64 1 k)) (+.f64 (log.f64 (*.f64 2 (PI.f64))) (log.f64 n)))))
(sqrt.f64 (/.f64 k (pow.f64 (.f64 2 (.f64 n (PI.f64))) (-.f64 1 k))))
(sqrt.f64 (/.f64 k (exp.f64 (.f64 (-.f64 1 k) (+.f64 (.f64 -1 (log.f64 (/.f64 -1 n))) (log.f64 (*.f64 -2 (PI.f64))))))))
(sqrt.f64 (/.f64 k (pow.f64 (exp.f64 (-.f64 1 k)) (+.f64 (log.f64 (*.f64 2 (PI.f64))) (log.f64 n)))))
(sqrt.f64 (/.f64 k (pow.f64 (.f64 2 (.f64 n (PI.f64))) (-.f64 1 k))))
(sqrt.f64 (/.f64 (exp.f64 (.f64 (-.f64 1 k) (+.f64 (log.f64 n) (log.f64 (.f64 2 (PI.f64)))))) k))
(sqrt.f64 (/.f64 (pow.f64 (exp.f64 (-.f64 1 k)) (+.f64 (log.f64 (*.f64 2 (PI.f64))) (log.f64 n))) k))
(sqrt.f64 (/.f64 (pow.f64 (.f64 2 (.f64 n (PI.f64))) (-.f64 1 k)) k))
(sqrt.f64 (/.f64 (exp.f64 (.f64 (-.f64 1 k) (+.f64 (log.f64 n) (log.f64 (.f64 2 (PI.f64)))))) k))
(sqrt.f64 (/.f64 (pow.f64 (exp.f64 (-.f64 1 k)) (+.f64 (log.f64 (*.f64 2 (PI.f64))) (log.f64 n))) k))
(sqrt.f64 (/.f64 (pow.f64 (.f64 2 (.f64 n (PI.f64))) (-.f64 1 k)) k))
(sqrt.f64 (/.f64 (exp.f64 (.f64 (-.f64 1 k) (+.f64 (log.f64 n) (log.f64 (.f64 2 (PI.f64)))))) k))
(sqrt.f64 (/.f64 (pow.f64 (exp.f64 (-.f64 1 k)) (+.f64 (log.f64 (*.f64 2 (PI.f64))) (log.f64 n))) k))
(sqrt.f64 (/.f64 (pow.f64 (.f64 2 (.f64 n (PI.f64))) (-.f64 1 k)) k))
(sqrt.f64 (/.f64 (exp.f64 (.f64 (-.f64 1 k) (+.f64 (log.f64 n) (log.f64 (.f64 2 (PI.f64)))))) k))
(sqrt.f64 (/.f64 (pow.f64 (exp.f64 (-.f64 1 k)) (+.f64 (log.f64 (*.f64 2 (PI.f64))) (log.f64 n))) k))
(sqrt.f64 (/.f64 (pow.f64 (.f64 2 (.f64 n (PI.f64))) (-.f64 1 k)) k))
(sqrt.f64 (/.f64 (exp.f64 (.f64 (-.f64 1 k) (+.f64 (.f64 -1 (log.f64 (/.f64 1 n))) (log.f64 (*.f64 2 (PI.f64)))))) k))
(sqrt.f64 (/.f64 (pow.f64 (exp.f64 (-.f64 1 k)) (+.f64 (log.f64 (*.f64 2 (PI.f64))) (log.f64 n))) k))
(sqrt.f64 (/.f64 (pow.f64 (.f64 2 (.f64 n (PI.f64))) (-.f64 1 k)) k))
(sqrt.f64 (/.f64 (exp.f64 (.f64 (-.f64 1 k) (+.f64 (.f64 -1 (log.f64 (/.f64 1 n))) (log.f64 (*.f64 2 (PI.f64)))))) k))
(sqrt.f64 (/.f64 (pow.f64 (exp.f64 (-.f64 1 k)) (+.f64 (log.f64 (*.f64 2 (PI.f64))) (log.f64 n))) k))
(sqrt.f64 (/.f64 (pow.f64 (.f64 2 (.f64 n (PI.f64))) (-.f64 1 k)) k))
(sqrt.f64 (/.f64 (exp.f64 (.f64 (-.f64 1 k) (+.f64 (.f64 -1 (log.f64 (/.f64 1 n))) (log.f64 (*.f64 2 (PI.f64)))))) k))
(sqrt.f64 (/.f64 (pow.f64 (exp.f64 (-.f64 1 k)) (+.f64 (log.f64 (*.f64 2 (PI.f64))) (log.f64 n))) k))
(sqrt.f64 (/.f64 (pow.f64 (.f64 2 (.f64 n (PI.f64))) (-.f64 1 k)) k))
(sqrt.f64 (/.f64 (exp.f64 (.f64 (-.f64 1 k) (+.f64 (.f64 -1 (log.f64 (/.f64 1 n))) (log.f64 (*.f64 2 (PI.f64)))))) k))
(sqrt.f64 (/.f64 (pow.f64 (exp.f64 (-.f64 1 k)) (+.f64 (log.f64 (*.f64 2 (PI.f64))) (log.f64 n))) k))
(sqrt.f64 (/.f64 (pow.f64 (.f64 2 (.f64 n (PI.f64))) (-.f64 1 k)) k))
(sqrt.f64 (/.f64 (exp.f64 (.f64 (-.f64 1 k) (+.f64 (.f64 -1 (log.f64 (/.f64 -1 n))) (log.f64 (*.f64 -2 (PI.f64)))))) k))
(sqrt.f64 (/.f64 (pow.f64 (exp.f64 (-.f64 1 k)) (+.f64 (log.f64 (*.f64 2 (PI.f64))) (log.f64 n))) k))
(sqrt.f64 (/.f64 (pow.f64 (.f64 2 (.f64 n (PI.f64))) (-.f64 1 k)) k))
(sqrt.f64 (/.f64 (exp.f64 (.f64 (-.f64 1 k) (+.f64 (.f64 -1 (log.f64 (/.f64 -1 n))) (log.f64 (*.f64 -2 (PI.f64)))))) k))
(sqrt.f64 (/.f64 (pow.f64 (exp.f64 (-.f64 1 k)) (+.f64 (log.f64 (*.f64 2 (PI.f64))) (log.f64 n))) k))
(sqrt.f64 (/.f64 (pow.f64 (.f64 2 (.f64 n (PI.f64))) (-.f64 1 k)) k))
(sqrt.f64 (/.f64 (exp.f64 (.f64 (-.f64 1 k) (+.f64 (.f64 -1 (log.f64 (/.f64 -1 n))) (log.f64 (*.f64 -2 (PI.f64)))))) k))
(sqrt.f64 (/.f64 (pow.f64 (exp.f64 (-.f64 1 k)) (+.f64 (log.f64 (*.f64 2 (PI.f64))) (log.f64 n))) k))
(sqrt.f64 (/.f64 (pow.f64 (.f64 2 (.f64 n (PI.f64))) (-.f64 1 k)) k))
(sqrt.f64 (/.f64 (exp.f64 (.f64 (-.f64 1 k) (+.f64 (.f64 -1 (log.f64 (/.f64 -1 n))) (log.f64 (*.f64 -2 (PI.f64)))))) k))
(sqrt.f64 (/.f64 (pow.f64 (exp.f64 (-.f64 1 k)) (+.f64 (log.f64 (*.f64 2 (PI.f64))) (log.f64 n))) k))
(sqrt.f64 (/.f64 (pow.f64 (.f64 2 (.f64 n (PI.f64))) (-.f64 1 k)) k))

eval350.0ms (3.7%)

Compiler: Compiled 17135 to 11663 computations (31.9% saved)

prune173.0ms (1.8%)

Pruning

41 alts after pruning (37 fresh and 4 done)

	Pruned	Kept	Total
New	827	25	852
Fresh	11	12	23
Picked	1	0	1
Done	1	4	5
Total	840	41	881

Error

Counts

881 → 41

Alt Table

Click to see full alt table

Status	Error	Program
	0.5b	(.f64 (sqrt.f64 (/.f64 1 k)) (pow.f64 (.f64 (*.f64 2 (PI.f64)) n) (/.f64 (-.f64 1 k) 2)))
	32.6b	(pow.f64 (*.f64 1/2 (/.f64 (/.f64 k n) (PI.f64))) -1/2)
	9.2b	(pow.f64 (.f64 k (pow.f64 (.f64 n (*.f64 2 (PI.f64))) (-.f64 k 1))) -1/2)
	35.6b	(pow.f64 (pow.f64 (/.f64 2 (/.f64 (/.f64 k n) (PI.f64))) 1/6) 3)
✓	0.3b	(/.f64 1 (/.f64 (sqrt.f64 k) (sqrt.f64 (/.f64 (.f64 n (.f64 2 (PI.f64))) (pow.f64 (.f64 n (.f64 2 (PI.f64))) k)))))
✓	33.3b	(sqrt.f64 (/.f64 (.f64 2 (.f64 n (PI.f64))) k))
	35.2b	(exp.f64 (*.f64 (log.f64 (/.f64 2 (/.f64 (/.f64 k n) (PI.f64)))) 1/2))
	33.6b	(pow.f64 (cbrt.f64 (/.f64 2 (/.f64 (/.f64 k n) (PI.f64)))) 3/2)
	24.1b	(/.f64 (.f64 (sqrt.f64 2) (sqrt.f64 (.f64 n (PI.f64)))) (sqrt.f64 k))
	0.7b	(.f64 (pow.f64 (pow.f64 k -1/4) 2) (pow.f64 (.f64 (*.f64 2 (PI.f64)) n) (/.f64 (-.f64 1 k) 2)))
	41.6b	(pow.f64 (pow.f64 (/.f64 2 (/.f64 (/.f64 k n) (PI.f64))) 3/2) 1/3)
✓	11.8b	(sqrt.f64 (/.f64 (exp.f64 (.f64 (-.f64 1 k) (log.f64 (.f64 n (*.f64 2 (PI.f64)))))) k))
	24.0b	(/.f64 1 (/.f64 (sqrt.f64 k) (sqrt.f64 (.f64 2 (.f64 n (PI.f64))))))
	49.0b	(pow.f64 (pow.f64 (/.f64 2 (/.f64 (/.f64 k n) (PI.f64))) 3) 1/6)
▶	24.0b	(/.f64 1 (.f64 (sqrt.f64 k) (pow.f64 (.f64 2 (*.f64 n (PI.f64))) -1/2)))
	19.1b	(pow.f64 (pow.f64 (/.f64 (pow.f64 (.f64 n (.f64 2 (PI.f64))) (-.f64 1 k)) k) 3/2) 1/3)
	33.3b	(sqrt.f64 (.f64 (/.f64 2 k) (.f64 n (PI.f64))))
	0.6b	(/.f64 1 (/.f64 (pow.f64 (.f64 2 (.f64 (PI.f64) n)) (*.f64 (-.f64 1 k) -1/2)) (pow.f64 k -1/2)))
	9.6b	(sqrt.f64 (/.f64 (/.f64 n (pow.f64 n k)) (/.f64 k (pow.f64 (*.f64 2 (PI.f64)) (-.f64 1 k)))))
	33.3b	(pow.f64 (/.f64 2 (/.f64 (/.f64 k n) (PI.f64))) 1/2)
	14.7b	(.f64 (cbrt.f64 (exp.f64 (.f64 (log.f64 k) -3/2))) (pow.f64 (.f64 (.f64 2 (PI.f64)) n) (/.f64 (-.f64 1 k) 2)))
	33.3b	(sqrt.f64 (.f64 (.f64 2 n) (*.f64 (PI.f64) (/.f64 1 k))))
	33.3b	(sqrt.f64 (*.f64 2 (/.f64 (PI.f64) (/.f64 k n))))
▶	11.7b	(exp.f64 (.f64 (log.f64 (/.f64 (pow.f64 (.f64 n (*.f64 2 (PI.f64))) (-.f64 1 k)) k)) 1/2))
▶	0.5b	(.f64 (pow.f64 k -1/2) (sqrt.f64 (pow.f64 (.f64 n (*.f64 2 (PI.f64))) (-.f64 1 k))))
✓	9.9b	(sqrt.f64 (/.f64 (pow.f64 (.f64 2 (.f64 (PI.f64) n)) (-.f64 1 k)) k))
	33.3b	(sqrt.f64 (.f64 2 (.f64 (PI.f64) (/.f64 n k))))
	13.0b	(.f64 (cbrt.f64 (.f64 (pow.f64 k -3/2) 1)) (pow.f64 (.f64 (.f64 2 (PI.f64)) n) (/.f64 (-.f64 1 k) 2)))
	3.2b	(.f64 (exp.f64 (.f64 -1/2 (log.f64 k))) (pow.f64 (.f64 (.f64 2 (PI.f64)) n) (/.f64 (-.f64 1 k) 2)))
▶	24.0b	(/.f64 (sqrt.f64 (.f64 n (.f64 (PI.f64) 2))) (sqrt.f64 k))
	9.6b	(sqrt.f64 (/.f64 (.f64 (pow.f64 (.f64 n (.f64 2 (PI.f64))) (neg.f64 k)) (.f64 n (*.f64 2 (PI.f64)))) k))
	9.9b	(sqrt.f64 (/.f64 1 (.f64 k (pow.f64 (.f64 n (*.f64 2 (PI.f64))) (-.f64 k 1)))))
	32.6b	(/.f64 (sqrt.f64 2) (sqrt.f64 (/.f64 (/.f64 k n) (PI.f64))))
	9.2b	(/.f64 1 (sqrt.f64 (/.f64 k (pow.f64 (.f64 n (.f64 2 (PI.f64))) (-.f64 1 k)))))
▶	33.3b	(sqrt.f64 (.f64 2 (.f64 (/.f64 (PI.f64) k) n)))
	9.6b	(sqrt.f64 (/.f64 (/.f64 (.f64 2 (PI.f64)) (/.f64 (pow.f64 (.f64 n (*.f64 2 (PI.f64))) k) n)) k))
	32.7b	(/.f64 1 (sqrt.f64 (*.f64 1/2 (/.f64 (/.f64 k n) (PI.f64)))))
	0.5b	(.f64 (/.f64 (pow.f64 k -1/2) (pow.f64 (.f64 2 (.f64 (PI.f64) n)) (.f64 (-.f64 1 k) -1/2))) 1)
	24.0b	(.f64 (sqrt.f64 (.f64 n (*.f64 (PI.f64) 2))) (pow.f64 k -1/2))
	0.5b	(/.f64 (pow.f64 (.f64 (PI.f64) (.f64 n 2)) (+.f64 1/2 (*.f64 k -1/2))) (sqrt.f64 k))
	40.2b	(cbrt.f64 (pow.f64 (/.f64 2 (/.f64 (/.f64 k n) (PI.f64))) 3/2))

Compiler

Compiled 1135 to 928 computations (18.2% saved)

localize31.0ms (0.3%)

Local error

Found 8 expressions with local error:

New	Error	Program
	0.4b	(pow.f64 (.f64 n (.f64 2 (PI.f64))) (-.f64 1 k))
	0.2b	(.f64 n (.f64 2 (PI.f64)))
	0.2b	(.f64 (pow.f64 k -1/2) (sqrt.f64 (pow.f64 (.f64 n (*.f64 2 (PI.f64))) (-.f64 1 k))))
	0.1b	(sqrt.f64 (pow.f64 (.f64 n (.f64 2 (PI.f64))) (-.f64 1 k)))
✓	0.1b	(sqrt.f64 (pow.f64 (.f64 n (.f64 2 (PI.f64))) (-.f64 1 k)))
✓	0.2b	(.f64 (pow.f64 k -1/2) (sqrt.f64 (pow.f64 (.f64 n (*.f64 2 (PI.f64))) (-.f64 1 k))))
	0.2b	(.f64 n (.f64 2 (PI.f64)))
	0.4b	(pow.f64 (.f64 n (.f64 2 (PI.f64))) (-.f64 1 k))

Compiler

Compiled 55 to 38 computations (30.9% saved)

series10.0ms (0.1%)

Counts

2 → 36

Calls

12 calls:

Time	Variable		Point	Expression
2.0ms	n	@	0	(sqrt.f64 (pow.f64 (.f64 n (.f64 2 (PI.f64))) (-.f64 1 k)))
2.0ms	k	@	0	(sqrt.f64 (pow.f64 (.f64 n (.f64 2 (PI.f64))) (-.f64 1 k)))
1.0ms	k	@	-inf	(.f64 (pow.f64 k -1/2) (sqrt.f64 (pow.f64 (.f64 n (*.f64 2 (PI.f64))) (-.f64 1 k))))
1.0ms	k	@	0	(.f64 (pow.f64 k -1/2) (sqrt.f64 (pow.f64 (.f64 n (*.f64 2 (PI.f64))) (-.f64 1 k))))
1.0ms	n	@	0	(.f64 (pow.f64 k -1/2) (sqrt.f64 (pow.f64 (.f64 n (*.f64 2 (PI.f64))) (-.f64 1 k))))

rewrite60.0ms (0.6%)

Algorithm

1×	batch-egg-rewrite

Rules

701×	`log-prod_binary64`
498×	`pow-unpow_binary64`
372×	`pow2_binary64`
253×	`pow1/3_binary64`
250×	`expm1-udef_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	14	38
1	298	38
2	3609	38

Stop Event

1×	node limit

Counts

2 → 59

Calls

Call 1

Inputs
(.f64 (pow.f64 k -1/2) (sqrt.f64 (pow.f64 (.f64 n (*.f64 2 (PI.f64))) (-.f64 1 k))))
(sqrt.f64 (pow.f64 (.f64 n (.f64 2 (PI.f64))) (-.f64 1 k)))

Outputs

((#(struct:change #<rule egg-rr> (2) ((x +.f64 0 (*.f64 (pow.f64 k -1/2) (sqrt.f64 (pow.f64 (*.f64 (PI.f64) (*.f64 n 2)) (-.f64 1 k)))))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (log.f64 (pow.f64 (cbrt.f64 (pow.f64 (exp.f64 (sqrt.f64 (pow.f64 (*.f64 (PI.f64) (*.f64 n 2)) (-.f64 1 k)))) (pow.f64 k -1/2))) 2)) (log.f64 (cbrt.f64 (pow.f64 (exp.f64 (sqrt.f64 (pow.f64 (*.f64 (PI.f64) (*.f64 n 2)) (-.f64 1 k)))) (pow.f64 k -1/2)))))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (log.f64 (sqrt.f64 (pow.f64 (exp.f64 (sqrt.f64 (pow.f64 (*.f64 (PI.f64) (*.f64 n 2)) (-.f64 1 k)))) (pow.f64 k -1/2)))) (log.f64 (sqrt.f64 (pow.f64 (exp.f64 (sqrt.f64 (pow.f64 (*.f64 (PI.f64) (*.f64 n 2)) (-.f64 1 k)))) (pow.f64 k -1/2)))))))) (#(struct:change #<rule egg-rr> (2) ((x -.f64 (exp.f64 (log1p.f64 (*.f64 (pow.f64 k -1/2) (sqrt.f64 (pow.f64 (*.f64 (PI.f64) (*.f64 n 2)) (-.f64 1 k)))))) 1)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (*.f64 (pow.f64 k -1/2) (sqrt.f64 (pow.f64 (*.f64 (PI.f64) (*.f64 n 2)) (-.f64 1 k)))) 1)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (*.f64 (pow.f64 (*.f64 (PI.f64) (*.f64 n 2)) (-.f64 1 k)) (pow.f64 k -1)) 1/2)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (pow.f64 (*.f64 (pow.f64 k -1/2) (sqrt.f64 (pow.f64 (*.f64 (PI.f64) (*.f64 n 2)) (-.f64 1 k)))) 3) 1/3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (cbrt.f64 (*.f64 (pow.f64 k -1/2) (sqrt.f64 (pow.f64 (*.f64 (PI.f64) (*.f64 n 2)) (-.f64 1 k))))) 3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (*.f64 (pow.f64 (pow.f64 (*.f64 (PI.f64) (*.f64 n 2)) (-.f64 1 k)) 1/4) (pow.f64 k -1/4)) 2)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (*.f64 (pow.f64 (pow.f64 k -1/2) 3) (pow.f64 (pow.f64 (*.f64 (PI.f64) (*.f64 n 2)) (-.f64 1 k)) 3/2)) 1/3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (*.f64 (pow.f64 (pow.f64 (*.f64 (PI.f64) (*.f64 n 2)) (-.f64 1 k)) 3/2) (pow.f64 (pow.f64 k -1/2) 3)) 1/3)))) (#(struct:change #<rule egg-rr> (2) ((x sqrt.f64 (*.f64 (pow.f64 (*.f64 (PI.f64) (*.f64 n 2)) (-.f64 1 k)) (pow.f64 k -1)))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (pow.f64 (exp.f64 (sqrt.f64 (pow.f64 (*.f64 (PI.f64) (*.f64 n 2)) (-.f64 1 k)))) (pow.f64 k -1/2)))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (+.f64 1 (expm1.f64 (*.f64 (pow.f64 k -1/2) (sqrt.f64 (pow.f64 (*.f64 (PI.f64) (*.f64 n 2)) (-.f64 1 k)))))))))) (#(struct:change #<rule egg-rr> (2) ((x cbrt.f64 (pow.f64 (*.f64 (pow.f64 k -1/2) (sqrt.f64 (pow.f64 (*.f64 (PI.f64) (*.f64 n 2)) (-.f64 1 k)))) 3))))) (#(struct:change #<rule egg-rr> (2) ((x cbrt.f64 (*.f64 (pow.f64 (pow.f64 k -1/2) 3) (pow.f64 (pow.f64 (*.f64 (PI.f64) (*.f64 n 2)) (-.f64 1 k)) 3/2)))))) (#(struct:change #<rule egg-rr> (2) ((x cbrt.f64 (*.f64 (pow.f64 (pow.f64 (*.f64 (PI.f64) (*.f64 n 2)) (-.f64 1 k)) 3/2) (pow.f64 (pow.f64 k -1/2) 3)))))) (#(struct:change #<rule egg-rr> (2) ((x expm1.f64 (log1p.f64 (*.f64 (pow.f64 k -1/2) (sqrt.f64 (pow.f64 (*.f64 (PI.f64) (*.f64 n 2)) (-.f64 1 k))))))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (fma.f64 -1/2 (log.f64 k) (log.f64 (sqrt.f64 (pow.f64 (*.f64 (PI.f64) (*.f64 n 2)) (-.f64 1 k))))))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (*.f64 (fma.f64 -1/2 (log.f64 k) (log.f64 (sqrt.f64 (pow.f64 (*.f64 (PI.f64) (*.f64 n 2)) (-.f64 1 k))))) 1))))) (#(struct:change #<rule egg-rr> (2) ((x log1p.f64 (expm1.f64 (*.f64 (pow.f64 k -1/2) (sqrt.f64 (pow.f64 (*.f64 (PI.f64) (*.f64 n 2)) (-.f64 1 k))))))))))

((#(struct:change #<rule egg-rr> (2) ((x +.f64 0 (sqrt.f64 (pow.f64 (*.f64 (PI.f64) (*.f64 n 2)) (-.f64 1 k))))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (log.f64 (pow.f64 (cbrt.f64 (exp.f64 (sqrt.f64 (pow.f64 (*.f64 (PI.f64) (*.f64 n 2)) (-.f64 1 k))))) 2)) (log.f64 (cbrt.f64 (exp.f64 (sqrt.f64 (pow.f64 (*.f64 (PI.f64) (*.f64 n 2)) (-.f64 1 k)))))))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (log.f64 (sqrt.f64 (exp.f64 (sqrt.f64 (pow.f64 (*.f64 (PI.f64) (*.f64 n 2)) (-.f64 1 k)))))) (log.f64 (sqrt.f64 (exp.f64 (sqrt.f64 (pow.f64 (*.f64 (PI.f64) (*.f64 n 2)) (-.f64 1 k)))))))))) (#(struct:change #<rule egg-rr> (2) ((x -.f64 (exp.f64 (log1p.f64 (sqrt.f64 (pow.f64 (*.f64 (PI.f64) (*.f64 n 2)) (-.f64 1 k))))) 1)))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 1 (sqrt.f64 (pow.f64 (*.f64 (PI.f64) (*.f64 n 2)) (-.f64 1 k))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (sqrt.f64 (pow.f64 (*.f64 (PI.f64) (*.f64 n 2)) (-.f64 1 k))) 1)))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (cbrt.f64 (pow.f64 (*.f64 (PI.f64) (*.f64 n 2)) (-.f64 1 k))) (cbrt.f64 (sqrt.f64 (pow.f64 (*.f64 (PI.f64) (*.f64 n 2)) (-.f64 1 k)))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (cbrt.f64 (sqrt.f64 (pow.f64 (*.f64 (PI.f64) (*.f64 n 2)) (-.f64 1 k)))) (cbrt.f64 (pow.f64 (*.f64 (PI.f64) (*.f64 n 2)) (-.f64 1 k))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (pow.f64 (pow.f64 (*.f64 (PI.f64) (*.f64 n 2)) (-.f64 1 k)) 1/4) (pow.f64 (pow.f64 (*.f64 (PI.f64) (*.f64 n 2)) (-.f64 1 k)) 1/4))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (sqrt.f64 (/.f64 n (pow.f64 n k))) (sqrt.f64 (pow.f64 (*.f64 2 (PI.f64)) (-.f64 1 k))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (sqrt.f64 (cbrt.f64 (pow.f64 (pow.f64 (*.f64 (PI.f64) (*.f64 n 2)) 2) (-.f64 1 k)))) (sqrt.f64 (cbrt.f64 (pow.f64 (*.f64 (PI.f64) (*.f64 n 2)) (-.f64 1 k)))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (sqrt.f64 (pow.f64 (*.f64 2 (PI.f64)) (-.f64 1 k))) (sqrt.f64 (/.f64 n (pow.f64 n k))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (pow.f64 1 (-.f64 1/2 (/.f64 k 2))) (sqrt.f64 (pow.f64 (*.f64 (PI.f64) (*.f64 n 2)) (-.f64 1 k))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (pow.f64 (pow.f64 (cbrt.f64 (*.f64 (PI.f64) (*.f64 n 2))) 2) (-.f64 1/2 (/.f64 k 2))) (pow.f64 (cbrt.f64 (*.f64 (PI.f64) (*.f64 n 2))) (-.f64 1/2 (/.f64 k 2))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (pow.f64 (sqrt.f64 (*.f64 (PI.f64) (*.f64 n 2))) (-.f64 1/2 (/.f64 k 2))) (pow.f64 (sqrt.f64 (*.f64 (PI.f64) (*.f64 n 2))) (-.f64 1/2 (/.f64 k 2))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (pow.f64 (*.f64 n 2) (-.f64 1/2 (/.f64 k 2))) (pow.f64 (PI.f64) (-.f64 1/2 (/.f64 k 2))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (pow.f64 1 1/2) (sqrt.f64 (pow.f64 (*.f64 (PI.f64) (*.f64 n 2)) (-.f64 1 k))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (sqrt.f64 (*.f64 (PI.f64) (*.f64 n 2))) (sqrt.f64 (pow.f64 (*.f64 (PI.f64) (*.f64 n 2)) k)))))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (*.f64 (PI.f64) (*.f64 n 2)) (-.f64 1/2 (/.f64 k 2)))))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (*.f64 (PI.f64) (*.f64 n 2)) (*.f64 (-.f64 1/2 (/.f64 k 2)) 1))))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (pow.f64 (*.f64 (PI.f64) (*.f64 n 2)) (-.f64 1 k)) 1/2)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (sqrt.f64 (pow.f64 (*.f64 (PI.f64) (*.f64 n 2)) (-.f64 1 k))) 1)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (pow.f64 (pow.f64 (*.f64 (PI.f64) (*.f64 n 2)) (-.f64 1 k)) 3/2) 1/3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (cbrt.f64 (sqrt.f64 (pow.f64 (*.f64 (PI.f64) (*.f64 n 2)) (-.f64 1 k)))) 3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (pow.f64 (pow.f64 (*.f64 (PI.f64) (*.f64 n 2)) (-.f64 1 k)) 1/4) 2)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (pow.f64 (sqrt.f64 (*.f64 (PI.f64) (*.f64 n 2))) (-.f64 1/2 (/.f64 k 2))) 2)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (pow.f64 (*.f64 (PI.f64) (*.f64 n 2)) (pow.f64 (cbrt.f64 (-.f64 1/2 (/.f64 k 2))) 2)) (cbrt.f64 (-.f64 1/2 (/.f64 k 2))))))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (pow.f64 (*.f64 (PI.f64) (*.f64 n 2)) (sqrt.f64 (-.f64 1/2 (/.f64 k 2)))) (sqrt.f64 (-.f64 1/2 (/.f64 k 2))))))) (#(struct:change #<rule egg-rr> (2) ((x fabs.f64 (sqrt.f64 (pow.f64 (*.f64 (PI.f64) (*.f64 n 2)) (-.f64 1 k))))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (exp.f64 (sqrt.f64 (pow.f64 (*.f64 (PI.f64) (*.f64 n 2)) (-.f64 1 k)))))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (+.f64 1 (expm1.f64 (sqrt.f64 (pow.f64 (*.f64 (PI.f64) (*.f64 n 2)) (-.f64 1 k))))))))) (#(struct:change #<rule egg-rr> (2) ((x cbrt.f64 (pow.f64 (pow.f64 (*.f64 (PI.f64) (*.f64 n 2)) (-.f64 1 k)) 3/2))))) (#(struct:change #<rule egg-rr> (2) ((x expm1.f64 (log1p.f64 (sqrt.f64 (pow.f64 (*.f64 (PI.f64) (*.f64 n 2)) (-.f64 1 k)))))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (log.f64 (sqrt.f64 (pow.f64 (*.f64 (PI.f64) (*.f64 n 2)) (-.f64 1 k)))))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (*.f64 (log.f64 (*.f64 (PI.f64) (*.f64 n 2))) (-.f64 1/2 (/.f64 k 2))))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (*.f64 (*.f64 (-.f64 1 k) (log.f64 (*.f64 (PI.f64) (*.f64 n 2)))) 1/2))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (*.f64 (log.f64 (sqrt.f64 (pow.f64 (*.f64 (PI.f64) (*.f64 n 2)) (-.f64 1 k)))) 1))))) (#(struct:change #<rule egg-rr> (2) ((x log1p.f64 (expm1.f64 (sqrt.f64 (pow.f64 (*.f64 (PI.f64) (*.f64 n 2)) (-.f64 1 k)))))))))

simplify54.0ms (0.6%)

Algorithm

1×	egg-herbie

Rules

390×	`associate-/r/_binary64`
286×	`cancel-sign-sub-inv_binary64`
284×	`associate-r_binary64`
271×	`associate-l_binary64`
269×	`fma-neg_binary64`

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	94	1186
1	263	1101
2	832	984
3	4243	933

Stop Event

1×	node limit

Counts

95 → 78

Calls

Call 1

Inputs
(sqrt.f64 (/.f64 (exp.f64 (.f64 (-.f64 1 k) (+.f64 (log.f64 n) (log.f64 (.f64 2 (PI.f64)))))) k))
(sqrt.f64 (/.f64 (exp.f64 (.f64 (-.f64 1 k) (+.f64 (log.f64 n) (log.f64 (.f64 2 (PI.f64)))))) k))
(sqrt.f64 (/.f64 (exp.f64 (.f64 (-.f64 1 k) (+.f64 (log.f64 n) (log.f64 (.f64 2 (PI.f64)))))) k))
(sqrt.f64 (/.f64 (exp.f64 (.f64 (-.f64 1 k) (+.f64 (log.f64 n) (log.f64 (.f64 2 (PI.f64)))))) k))
(sqrt.f64 (/.f64 (exp.f64 (.f64 (-.f64 1 k) (+.f64 (.f64 -1 (log.f64 (/.f64 1 n))) (log.f64 (*.f64 2 (PI.f64)))))) k))
(sqrt.f64 (/.f64 (exp.f64 (.f64 (-.f64 1 k) (+.f64 (.f64 -1 (log.f64 (/.f64 1 n))) (log.f64 (*.f64 2 (PI.f64)))))) k))
(sqrt.f64 (/.f64 (exp.f64 (.f64 (-.f64 1 k) (+.f64 (.f64 -1 (log.f64 (/.f64 1 n))) (log.f64 (*.f64 2 (PI.f64)))))) k))
(sqrt.f64 (/.f64 (exp.f64 (.f64 (-.f64 1 k) (+.f64 (.f64 -1 (log.f64 (/.f64 1 n))) (log.f64 (*.f64 2 (PI.f64)))))) k))
(sqrt.f64 (/.f64 (exp.f64 (.f64 (-.f64 1 k) (+.f64 (.f64 -1 (log.f64 (/.f64 -1 n))) (log.f64 (*.f64 -2 (PI.f64)))))) k))
(sqrt.f64 (/.f64 (exp.f64 (.f64 (-.f64 1 k) (+.f64 (.f64 -1 (log.f64 (/.f64 -1 n))) (log.f64 (*.f64 -2 (PI.f64)))))) k))
(sqrt.f64 (/.f64 (exp.f64 (.f64 (-.f64 1 k) (+.f64 (.f64 -1 (log.f64 (/.f64 -1 n))) (log.f64 (*.f64 -2 (PI.f64)))))) k))
(sqrt.f64 (/.f64 (exp.f64 (.f64 (-.f64 1 k) (+.f64 (.f64 -1 (log.f64 (/.f64 -1 n))) (log.f64 (*.f64 -2 (PI.f64)))))) k))
(sqrt.f64 (exp.f64 (.f64 (-.f64 1 k) (+.f64 (log.f64 (.f64 2 (PI.f64))) (log.f64 n)))))
(sqrt.f64 (exp.f64 (.f64 (-.f64 1 k) (+.f64 (log.f64 (.f64 2 (PI.f64))) (log.f64 n)))))
(sqrt.f64 (exp.f64 (.f64 (-.f64 1 k) (+.f64 (log.f64 (.f64 2 (PI.f64))) (log.f64 n)))))
(sqrt.f64 (exp.f64 (.f64 (-.f64 1 k) (+.f64 (log.f64 (.f64 2 (PI.f64))) (log.f64 n)))))
(sqrt.f64 (exp.f64 (.f64 (-.f64 1 k) (+.f64 (.f64 -1 (log.f64 (/.f64 1 n))) (log.f64 (*.f64 2 (PI.f64)))))))
(sqrt.f64 (exp.f64 (.f64 (-.f64 1 k) (+.f64 (.f64 -1 (log.f64 (/.f64 1 n))) (log.f64 (*.f64 2 (PI.f64)))))))
(sqrt.f64 (exp.f64 (.f64 (-.f64 1 k) (+.f64 (.f64 -1 (log.f64 (/.f64 1 n))) (log.f64 (*.f64 2 (PI.f64)))))))
(sqrt.f64 (exp.f64 (.f64 (-.f64 1 k) (+.f64 (.f64 -1 (log.f64 (/.f64 1 n))) (log.f64 (*.f64 2 (PI.f64)))))))
(sqrt.f64 (exp.f64 (.f64 (-.f64 1 k) (+.f64 (.f64 -1 (log.f64 (/.f64 -1 n))) (log.f64 (*.f64 -2 (PI.f64)))))))
(sqrt.f64 (exp.f64 (.f64 (-.f64 1 k) (+.f64 (.f64 -1 (log.f64 (/.f64 -1 n))) (log.f64 (*.f64 -2 (PI.f64)))))))
(sqrt.f64 (exp.f64 (.f64 (-.f64 1 k) (+.f64 (.f64 -1 (log.f64 (/.f64 -1 n))) (log.f64 (*.f64 -2 (PI.f64)))))))
(sqrt.f64 (exp.f64 (.f64 (-.f64 1 k) (+.f64 (.f64 -1 (log.f64 (/.f64 -1 n))) (log.f64 (*.f64 -2 (PI.f64)))))))
(.f64 (sqrt.f64 2) (sqrt.f64 (.f64 n (PI.f64))))
(+.f64 (.f64 (sqrt.f64 2) (sqrt.f64 (.f64 n (PI.f64)))) (.f64 -1 (.f64 (/.f64 (.f64 k (log.f64 (.f64 2 (.f64 n (PI.f64))))) (sqrt.f64 2)) (sqrt.f64 (.f64 n (PI.f64))))))
(+.f64 (.f64 1/2 (.f64 (/.f64 (.f64 (pow.f64 k 2) (-.f64 (.f64 n (.f64 (pow.f64 (log.f64 (.f64 2 (.f64 n (PI.f64)))) 2) (PI.f64))) (pow.f64 (.f64 -1 (.f64 (/.f64 (log.f64 (.f64 2 (.f64 n (PI.f64)))) (sqrt.f64 2)) (sqrt.f64 (.f64 n (PI.f64))))) 2))) (sqrt.f64 2)) (sqrt.f64 (/.f64 1 (.f64 n (PI.f64)))))) (+.f64 (.f64 (sqrt.f64 2) (sqrt.f64 (.f64 n (PI.f64)))) (.f64 -1 (.f64 (/.f64 (.f64 k (log.f64 (.f64 2 (.f64 n (PI.f64))))) (sqrt.f64 2)) (sqrt.f64 (*.f64 n (PI.f64)))))))
(+.f64 (.f64 1/2 (.f64 (/.f64 (.f64 (pow.f64 k 2) (-.f64 (.f64 n (.f64 (pow.f64 (log.f64 (.f64 2 (.f64 n (PI.f64)))) 2) (PI.f64))) (pow.f64 (.f64 -1 (.f64 (/.f64 (log.f64 (.f64 2 (.f64 n (PI.f64)))) (sqrt.f64 2)) (sqrt.f64 (.f64 n (PI.f64))))) 2))) (sqrt.f64 2)) (sqrt.f64 (/.f64 1 (.f64 n (PI.f64)))))) (+.f64 (.f64 (sqrt.f64 2) (sqrt.f64 (.f64 n (PI.f64)))) (+.f64 (.f64 -1 (.f64 (/.f64 (.f64 k (log.f64 (.f64 2 (.f64 n (PI.f64))))) (sqrt.f64 2)) (sqrt.f64 (.f64 n (PI.f64))))) (.f64 1/2 (.f64 (/.f64 (.f64 (pow.f64 k 3) (-.f64 (.f64 -1/3 (.f64 n (.f64 (pow.f64 (log.f64 (.f64 2 (.f64 n (PI.f64)))) 3) (PI.f64)))) (.f64 -1 (/.f64 (.f64 (-.f64 (.f64 n (.f64 (pow.f64 (log.f64 (.f64 2 (.f64 n (PI.f64)))) 2) (PI.f64))) (pow.f64 (.f64 -1 (.f64 (/.f64 (log.f64 (.f64 2 (.f64 n (PI.f64)))) (sqrt.f64 2)) (sqrt.f64 (.f64 n (PI.f64))))) 2)) (log.f64 (.f64 2 (.f64 n (PI.f64))))) (pow.f64 (sqrt.f64 2) 2))))) (sqrt.f64 2)) (sqrt.f64 (/.f64 1 (*.f64 n (PI.f64)))))))))
(sqrt.f64 (pow.f64 (.f64 2 (.f64 n (PI.f64))) (-.f64 1 k)))
(sqrt.f64 (pow.f64 (.f64 2 (.f64 n (PI.f64))) (-.f64 1 k)))
(sqrt.f64 (pow.f64 (.f64 2 (.f64 n (PI.f64))) (-.f64 1 k)))
(sqrt.f64 (pow.f64 (.f64 2 (.f64 n (PI.f64))) (-.f64 1 k)))
(sqrt.f64 (pow.f64 (.f64 2 (.f64 n (PI.f64))) (+.f64 1 (*.f64 -1 k))))
(sqrt.f64 (pow.f64 (.f64 2 (.f64 n (PI.f64))) (+.f64 1 (*.f64 -1 k))))
(sqrt.f64 (pow.f64 (.f64 2 (.f64 n (PI.f64))) (+.f64 1 (*.f64 -1 k))))
(sqrt.f64 (pow.f64 (.f64 2 (.f64 n (PI.f64))) (+.f64 1 (*.f64 -1 k))))

Outputs
(sqrt.f64 (/.f64 (exp.f64 (.f64 (-.f64 1 k) (+.f64 (log.f64 n) (log.f64 (.f64 2 (PI.f64)))))) k))
(sqrt.f64 (/.f64 (pow.f64 (exp.f64 (-.f64 1 k)) (+.f64 (log.f64 n) (log.f64 (*.f64 2 (PI.f64))))) k))
(sqrt.f64 (/.f64 (pow.f64 (exp.f64 (-.f64 1 k)) (log.f64 (.f64 2 (.f64 n (PI.f64))))) k))
(sqrt.f64 (/.f64 (pow.f64 (.f64 2 (.f64 n (PI.f64))) (-.f64 1 k)) k))
(sqrt.f64 (/.f64 (pow.f64 (.f64 n (.f64 2 (PI.f64))) (-.f64 1 k)) k))
(sqrt.f64 (/.f64 (exp.f64 (.f64 (-.f64 1 k) (+.f64 (log.f64 n) (log.f64 (.f64 2 (PI.f64)))))) k))
(sqrt.f64 (/.f64 (pow.f64 (exp.f64 (-.f64 1 k)) (+.f64 (log.f64 n) (log.f64 (*.f64 2 (PI.f64))))) k))
(sqrt.f64 (/.f64 (pow.f64 (exp.f64 (-.f64 1 k)) (log.f64 (.f64 2 (.f64 n (PI.f64))))) k))
(sqrt.f64 (/.f64 (pow.f64 (.f64 2 (.f64 n (PI.f64))) (-.f64 1 k)) k))
(sqrt.f64 (/.f64 (pow.f64 (.f64 n (.f64 2 (PI.f64))) (-.f64 1 k)) k))
(sqrt.f64 (/.f64 (exp.f64 (.f64 (-.f64 1 k) (+.f64 (log.f64 n) (log.f64 (.f64 2 (PI.f64)))))) k))
(sqrt.f64 (/.f64 (pow.f64 (exp.f64 (-.f64 1 k)) (+.f64 (log.f64 n) (log.f64 (*.f64 2 (PI.f64))))) k))
(sqrt.f64 (/.f64 (pow.f64 (exp.f64 (-.f64 1 k)) (log.f64 (.f64 2 (.f64 n (PI.f64))))) k))
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(fma.f64 (sqrt.f64 (.f64 n (PI.f64))) (-.f64 (sqrt.f64 2) (.f64 (log.f64 (.f64 2 (.f64 n (PI.f64)))) (/.f64 k (sqrt.f64 2)))) (.f64 (.f64 1/2 (sqrt.f64 (/.f64 1 (.f64 n (PI.f64))))) (+.f64 (.f64 (fma.f64 n (.f64 -1/3 (.f64 (PI.f64) (pow.f64 (log.f64 (.f64 2 (.f64 n (PI.f64)))) 3))) (.f64 (log.f64 (.f64 2 (.f64 n (PI.f64)))) (/.f64 (-.f64 (.f64 n (.f64 (PI.f64) (pow.f64 (log.f64 (.f64 2 (.f64 n (PI.f64)))) 2))) (pow.f64 (/.f64 (.f64 (log.f64 (.f64 2 (.f64 n (PI.f64)))) (neg.f64 (sqrt.f64 (.f64 n (PI.f64))))) (sqrt.f64 2)) 2)) 2))) (/.f64 (pow.f64 k 3) (sqrt.f64 2))) (.f64 (-.f64 (.f64 n (.f64 (PI.f64) (pow.f64 (log.f64 (.f64 2 (.f64 n (PI.f64)))) 2))) (pow.f64 (/.f64 (.f64 (log.f64 (.f64 2 (.f64 n (PI.f64)))) (neg.f64 (sqrt.f64 (.f64 n (PI.f64))))) (sqrt.f64 2)) 2)) (/.f64 k (/.f64 (sqrt.f64 2) k))))))
(fma.f64 (sqrt.f64 (.f64 n (PI.f64))) (-.f64 (sqrt.f64 2) (.f64 (log.f64 (.f64 n (.f64 2 (PI.f64)))) (/.f64 k (sqrt.f64 2)))) (.f64 (.f64 1/2 (sqrt.f64 (/.f64 1 (.f64 n (PI.f64))))) (.f64 (.f64 k k) (+.f64 (.f64 (/.f64 k (sqrt.f64 2)) (fma.f64 n (.f64 -1/3 (.f64 (PI.f64) (pow.f64 (log.f64 (.f64 n (.f64 2 (PI.f64)))) 3))) (.f64 (/.f64 (log.f64 (.f64 n (.f64 2 (PI.f64)))) 2) (-.f64 (.f64 n (.f64 (PI.f64) (pow.f64 (log.f64 (.f64 n (.f64 2 (PI.f64)))) 2))) (pow.f64 (.f64 (sqrt.f64 (.f64 n (PI.f64))) (/.f64 (neg.f64 (log.f64 (.f64 n (.f64 2 (PI.f64))))) (sqrt.f64 2))) 2))))) (/.f64 (-.f64 (.f64 n (.f64 (PI.f64) (pow.f64 (log.f64 (.f64 n (.f64 2 (PI.f64)))) 2))) (pow.f64 (.f64 (sqrt.f64 (.f64 n (PI.f64))) (/.f64 (neg.f64 (log.f64 (.f64 n (*.f64 2 (PI.f64))))) (sqrt.f64 2))) 2)) (sqrt.f64 2))))))
(sqrt.f64 (pow.f64 (.f64 2 (.f64 n (PI.f64))) (-.f64 1 k)))
(sqrt.f64 (pow.f64 (exp.f64 (-.f64 1 k)) (+.f64 (log.f64 n) (log.f64 (*.f64 2 (PI.f64))))))
(sqrt.f64 (pow.f64 (exp.f64 (-.f64 1 k)) (log.f64 (.f64 2 (.f64 n (PI.f64))))))
(sqrt.f64 (pow.f64 (.f64 n (.f64 2 (PI.f64))) (-.f64 1 k)))
(sqrt.f64 (pow.f64 (.f64 2 (.f64 n (PI.f64))) (-.f64 1 k)))
(sqrt.f64 (pow.f64 (exp.f64 (-.f64 1 k)) (+.f64 (log.f64 n) (log.f64 (*.f64 2 (PI.f64))))))
(sqrt.f64 (pow.f64 (exp.f64 (-.f64 1 k)) (log.f64 (.f64 2 (.f64 n (PI.f64))))))
(sqrt.f64 (pow.f64 (.f64 n (.f64 2 (PI.f64))) (-.f64 1 k)))
(sqrt.f64 (pow.f64 (.f64 2 (.f64 n (PI.f64))) (-.f64 1 k)))
(sqrt.f64 (pow.f64 (exp.f64 (-.f64 1 k)) (+.f64 (log.f64 n) (log.f64 (*.f64 2 (PI.f64))))))
(sqrt.f64 (pow.f64 (exp.f64 (-.f64 1 k)) (log.f64 (.f64 2 (.f64 n (PI.f64))))))
(sqrt.f64 (pow.f64 (.f64 n (.f64 2 (PI.f64))) (-.f64 1 k)))
(sqrt.f64 (pow.f64 (.f64 2 (.f64 n (PI.f64))) (-.f64 1 k)))
(sqrt.f64 (pow.f64 (exp.f64 (-.f64 1 k)) (+.f64 (log.f64 n) (log.f64 (*.f64 2 (PI.f64))))))
(sqrt.f64 (pow.f64 (exp.f64 (-.f64 1 k)) (log.f64 (.f64 2 (.f64 n (PI.f64))))))
(sqrt.f64 (pow.f64 (.f64 n (.f64 2 (PI.f64))) (-.f64 1 k)))
(sqrt.f64 (pow.f64 (.f64 2 (.f64 n (PI.f64))) (+.f64 1 (*.f64 -1 k))))
(sqrt.f64 (pow.f64 (exp.f64 (-.f64 1 k)) (+.f64 (log.f64 n) (log.f64 (*.f64 2 (PI.f64))))))
(sqrt.f64 (pow.f64 (exp.f64 (-.f64 1 k)) (log.f64 (.f64 2 (.f64 n (PI.f64))))))
(sqrt.f64 (pow.f64 (.f64 2 (.f64 n (PI.f64))) (-.f64 1 k)))
(sqrt.f64 (pow.f64 (.f64 n (.f64 2 (PI.f64))) (-.f64 1 k)))
(sqrt.f64 (pow.f64 (.f64 2 (.f64 n (PI.f64))) (+.f64 1 (*.f64 -1 k))))
(sqrt.f64 (pow.f64 (exp.f64 (-.f64 1 k)) (+.f64 (log.f64 n) (log.f64 (*.f64 2 (PI.f64))))))
(sqrt.f64 (pow.f64 (exp.f64 (-.f64 1 k)) (log.f64 (.f64 2 (.f64 n (PI.f64))))))
(sqrt.f64 (pow.f64 (.f64 2 (.f64 n (PI.f64))) (-.f64 1 k)))
(sqrt.f64 (pow.f64 (.f64 n (.f64 2 (PI.f64))) (-.f64 1 k)))
(sqrt.f64 (pow.f64 (.f64 2 (.f64 n (PI.f64))) (+.f64 1 (*.f64 -1 k))))
(sqrt.f64 (pow.f64 (exp.f64 (-.f64 1 k)) (+.f64 (log.f64 n) (log.f64 (*.f64 2 (PI.f64))))))
(sqrt.f64 (pow.f64 (exp.f64 (-.f64 1 k)) (log.f64 (.f64 2 (.f64 n (PI.f64))))))
(sqrt.f64 (pow.f64 (.f64 2 (.f64 n (PI.f64))) (-.f64 1 k)))
(sqrt.f64 (pow.f64 (.f64 n (.f64 2 (PI.f64))) (-.f64 1 k)))
(sqrt.f64 (pow.f64 (.f64 2 (.f64 n (PI.f64))) (+.f64 1 (*.f64 -1 k))))
(sqrt.f64 (pow.f64 (exp.f64 (-.f64 1 k)) (+.f64 (log.f64 n) (log.f64 (*.f64 2 (PI.f64))))))
(sqrt.f64 (pow.f64 (exp.f64 (-.f64 1 k)) (log.f64 (.f64 2 (.f64 n (PI.f64))))))
(sqrt.f64 (pow.f64 (.f64 2 (.f64 n (PI.f64))) (-.f64 1 k)))
(sqrt.f64 (pow.f64 (.f64 n (.f64 2 (PI.f64))) (-.f64 1 k)))

localize11.0ms (0.1%)

Local error

Found 6 expressions with local error:

New	Error	Program
	9.1b	(sqrt.f64 (.f64 2 (.f64 (/.f64 (PI.f64) k) n)))
	0.3b	(*.f64 (/.f64 (PI.f64) k) n)
	0.2b	(/.f64 (PI.f64) k)
✓	0.2b	(/.f64 (PI.f64) k)
✓	0.3b	(*.f64 (/.f64 (PI.f64) k) n)
✓	9.1b	(sqrt.f64 (.f64 2 (.f64 (/.f64 (PI.f64) k) n)))

Compiler

Compiled 29 to 11 computations (62.1% saved)

series6.0ms (0.1%)

Counts

3 → 24

Calls

15 calls:

Time	Variable		Point	Expression
1.0ms	k	@	0	(sqrt.f64 (.f64 2 (.f64 (/.f64 (PI.f64) k) n)))
0.0ms	k	@	-inf	(*.f64 (/.f64 (PI.f64) k) n)
0.0ms	k	@	-inf	(sqrt.f64 (.f64 2 (.f64 (/.f64 (PI.f64) k) n)))
0.0ms	k	@	inf	(sqrt.f64 (.f64 2 (.f64 (/.f64 (PI.f64) k) n)))
0.0ms	k	@	-inf	(/.f64 (PI.f64) k)

rewrite63.0ms (0.7%)

Algorithm

1×	batch-egg-rewrite

Rules

953×	`pow1_binary64`
882×	`add-log-exp_binary64`
882×	`log1p-expm1-u_binary64`
882×	`expm1-log1p-u_binary64`
862×	`add-exp-log_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	9	26
1	189	26
2	2390	26

Stop Event

1×	node limit

Counts

3 → 78

Calls

Call 1

Inputs
(sqrt.f64 (.f64 2 (.f64 (/.f64 (PI.f64) k) n)))
(*.f64 (/.f64 (PI.f64) k) n)
(/.f64 (PI.f64) k)

Outputs

((#(struct:change #<rule egg-rr> (2) ((x -.f64 (+.f64 1 (sqrt.f64 (*.f64 2 (*.f64 (/.f64 (PI.f64) k) n)))) 1)))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (sqrt.f64 (*.f64 2 (*.f64 (/.f64 (PI.f64) k) n))) 1)))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 1 (sqrt.f64 (*.f64 2 (*.f64 (/.f64 (PI.f64) k) n))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (cbrt.f64 (*.f64 2 (*.f64 (/.f64 (PI.f64) k) n))) (cbrt.f64 (sqrt.f64 (*.f64 2 (*.f64 (/.f64 (PI.f64) k) n)))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (cbrt.f64 (sqrt.f64 (*.f64 2 (*.f64 (/.f64 (PI.f64) k) n)))) (cbrt.f64 (*.f64 2 (*.f64 (/.f64 (PI.f64) k) n))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (sqrt.f64 2) (sqrt.f64 (*.f64 (/.f64 (PI.f64) k) n)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (pow.f64 (*.f64 2 (*.f64 (/.f64 (PI.f64) k) n)) 1/4) (pow.f64 (*.f64 2 (*.f64 (/.f64 (PI.f64) k) n)) 1/4))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (sqrt.f64 (*.f64 (/.f64 (PI.f64) k) n)) (sqrt.f64 2))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (sqrt.f64 (*.f64 2 (/.f64 (PI.f64) k))) (sqrt.f64 n))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (sqrt.f64 (pow.f64 (cbrt.f64 (*.f64 2 (*.f64 (/.f64 (PI.f64) k) n))) 2)) (sqrt.f64 (cbrt.f64 (*.f64 2 (*.f64 (/.f64 (PI.f64) k) n)))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (pow.f64 1 1/2) (sqrt.f64 (*.f64 2 (*.f64 (/.f64 (PI.f64) k) n))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (pow.f64 (pow.f64 (cbrt.f64 (*.f64 2 (*.f64 (/.f64 (PI.f64) k) n))) 2) 1/2) (pow.f64 (cbrt.f64 (*.f64 2 (*.f64 (/.f64 (PI.f64) k) n))) 1/2))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (pow.f64 (*.f64 2 (/.f64 (PI.f64) k)) 1/2) (sqrt.f64 n))))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (*.f64 2 (*.f64 (/.f64 (PI.f64) k) n)) 1/2)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (sqrt.f64 (*.f64 2 (*.f64 (/.f64 (PI.f64) k) n))) 1)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (pow.f64 (*.f64 2 (*.f64 (/.f64 (PI.f64) k) n)) 3/2) 1/3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (cbrt.f64 (sqrt.f64 (*.f64 2 (*.f64 (/.f64 (PI.f64) k) n)))) 3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (pow.f64 (*.f64 2 (*.f64 (/.f64 (PI.f64) k) n)) 1/4) 2)))) (#(struct:change #<rule egg-rr> (2) ((x fabs.f64 (sqrt.f64 (*.f64 2 (*.f64 (/.f64 (PI.f64) k) n))))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (exp.f64 (sqrt.f64 (*.f64 2 (*.f64 (/.f64 (PI.f64) k) n)))))))) (#(struct:change #<rule egg-rr> (2) ((x cbrt.f64 (pow.f64 (*.f64 2 (*.f64 (/.f64 (PI.f64) k) n)) 3/2))))) (#(struct:change #<rule egg-rr> (2) ((x expm1.f64 (log1p.f64 (sqrt.f64 (*.f64 2 (*.f64 (/.f64 (PI.f64) k) n)))))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (log.f64 (sqrt.f64 (*.f64 2 (*.f64 (/.f64 (PI.f64) k) n)))))))) (#(struct:change #<rule egg-rr> (2) ((x log1p.f64 (expm1.f64 (sqrt.f64 (*.f64 2 (*.f64 (/.f64 (PI.f64) k) n)))))))))

((#(struct:change #<rule egg-rr> (2) ((x -.f64 (+.f64 1 (*.f64 (/.f64 (PI.f64) k) n)) 1)))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (PI.f64) (/.f64 k n))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 n (/.f64 k (PI.f64)))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 1 (/.f64 k (*.f64 (PI.f64) n)))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (*.f64 (PI.f64) n) k)))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (neg.f64 (*.f64 (PI.f64) n)) (neg.f64 k))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (/.f64 (*.f64 (PI.f64) n) 1) k)))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (/.f64 (*.f64 (PI.f64) n) (pow.f64 (cbrt.f64 k) 2)) (cbrt.f64 k))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (/.f64 (*.f64 (PI.f64) n) (sqrt.f64 k)) (sqrt.f64 k))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (*.f64 (neg.f64 (PI.f64)) n) (neg.f64 k))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (*.f64 n (neg.f64 (PI.f64))) (neg.f64 k))))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (*.f64 (/.f64 (PI.f64) k) n) 1)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (pow.f64 (*.f64 (/.f64 (PI.f64) k) n) 3) 1/3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (cbrt.f64 (*.f64 (/.f64 (PI.f64) k) n)) 3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (sqrt.f64 (*.f64 (/.f64 (PI.f64) k) n)) 2)))) (#(struct:change #<rule egg-rr> (2) ((x sqrt.f64 (pow.f64 (*.f64 (/.f64 (PI.f64) k) n) 2))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (pow.f64 (exp.f64 (/.f64 (PI.f64) k)) n))))) (#(struct:change #<rule egg-rr> (2) ((x cbrt.f64 (pow.f64 (*.f64 (/.f64 (PI.f64) k) n) 3))))) (#(struct:change #<rule egg-rr> (2) ((x cbrt.f64 (*.f64 (pow.f64 (/.f64 (PI.f64) k) 3) (pow.f64 n 3)))))) (#(struct:change #<rule egg-rr> (2) ((x cbrt.f64 (*.f64 (pow.f64 n 3) (pow.f64 (/.f64 (PI.f64) k) 3)))))) (#(struct:change #<rule egg-rr> (2) ((x expm1.f64 (log1p.f64 (*.f64 (/.f64 (PI.f64) k) n)))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (log.f64 (*.f64 (/.f64 (PI.f64) k) n)))))) (#(struct:change #<rule egg-rr> (2) ((x log1p.f64 (expm1.f64 (*.f64 (/.f64 (PI.f64) k) n)))))))

((#(struct:change #<rule egg-rr> (2) ((x -.f64 (+.f64 1 (/.f64 (PI.f64) k)) 1)))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (PI.f64) (/.f64 1 k))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (/.f64 (PI.f64) k) 1)))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 1 (/.f64 (PI.f64) k))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (cbrt.f64 (/.f64 (PI.f64) k)) (pow.f64 (cbrt.f64 (/.f64 (PI.f64) k)) 2))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (pow.f64 (cbrt.f64 (/.f64 (PI.f64) k)) 2) (cbrt.f64 (/.f64 (PI.f64) k)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (cbrt.f64 (pow.f64 (PI.f64) 2)) (*.f64 (cbrt.f64 (PI.f64)) (/.f64 1 k)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (sqrt.f64 (/.f64 (PI.f64) k)) (sqrt.f64 (/.f64 (PI.f64) k)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (sqrt.f64 (PI.f64)) (*.f64 (sqrt.f64 (PI.f64)) (/.f64 1 k)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (neg.f64 (PI.f64)) (/.f64 1 (neg.f64 k)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (/.f64 1 k) (PI.f64))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (/.f64 (cbrt.f64 (pow.f64 (PI.f64) 2)) 1) (/.f64 (cbrt.f64 (PI.f64)) k))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (/.f64 (sqrt.f64 (PI.f64)) 1) (/.f64 (sqrt.f64 (PI.f64)) k))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (/.f64 1 (pow.f64 (cbrt.f64 k) 2)) (/.f64 (PI.f64) (cbrt.f64 k)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (/.f64 (cbrt.f64 (pow.f64 (PI.f64) 2)) (pow.f64 (cbrt.f64 k) 2)) (cbrt.f64 (/.f64 (PI.f64) k)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (/.f64 (sqrt.f64 (PI.f64)) (pow.f64 (cbrt.f64 k) 2)) (/.f64 (sqrt.f64 (PI.f64)) (cbrt.f64 k)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (/.f64 1 (sqrt.f64 k)) (/.f64 (PI.f64) (sqrt.f64 k)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (/.f64 (cbrt.f64 (pow.f64 (PI.f64) 2)) (sqrt.f64 k)) (/.f64 (cbrt.f64 (PI.f64)) (sqrt.f64 k)))))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (/.f64 (PI.f64) k) 1)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (pow.f64 (/.f64 (PI.f64) k) 3) 1/3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (cbrt.f64 (/.f64 (PI.f64) k)) 3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (sqrt.f64 (/.f64 (PI.f64) k)) 2)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (/.f64 k (PI.f64)) -1)))) (#(struct:change #<rule egg-rr> (2) ((x neg.f64 (/.f64 (PI.f64) (neg.f64 k)))))) (#(struct:change #<rule egg-rr> (2) ((x sqrt.f64 (pow.f64 (/.f64 (PI.f64) k) 2))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (exp.f64 (/.f64 (PI.f64) k)))))) (#(struct:change #<rule egg-rr> (2) ((x cbrt.f64 (pow.f64 (/.f64 (PI.f64) k) 3))))) (#(struct:change #<rule egg-rr> (2) ((x cbrt.f64 (/.f64 (pow.f64 (PI.f64) 3) (pow.f64 k 3)))))) (#(struct:change #<rule egg-rr> (2) ((x expm1.f64 (log1p.f64 (/.f64 (PI.f64) k)))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (log.f64 (/.f64 (PI.f64) k)))))) (#(struct:change #<rule egg-rr> (2) ((x log1p.f64 (expm1.f64 (/.f64 (PI.f64) k)))))))

simplify13.0ms (0.1%)

Algorithm

1×	egg-herbie

Rules

3×	`*-commutative_binary64`
2×	`associate-/l*_binary64`
2×	`associate-/r/_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	6	192
1	9	192
2	13	192
3	16	192
4	17	192

Stop Event

1×

saturated

Counts

102 → 80

Calls

Call 1

Inputs
(/.f64 (*.f64 n (PI.f64)) k)
(/.f64 (*.f64 n (PI.f64)) k)
(/.f64 (*.f64 n (PI.f64)) k)
(/.f64 (*.f64 n (PI.f64)) k)
(/.f64 (*.f64 n (PI.f64)) k)
(/.f64 (*.f64 n (PI.f64)) k)
(/.f64 (*.f64 n (PI.f64)) k)
(/.f64 (*.f64 n (PI.f64)) k)
(/.f64 (*.f64 n (PI.f64)) k)
(/.f64 (*.f64 n (PI.f64)) k)
(/.f64 (*.f64 n (PI.f64)) k)
(/.f64 (*.f64 n (PI.f64)) k)
(/.f64 (*.f64 n (PI.f64)) k)
(/.f64 (*.f64 n (PI.f64)) k)
(/.f64 (*.f64 n (PI.f64)) k)
(/.f64 (*.f64 n (PI.f64)) k)
(/.f64 (*.f64 n (PI.f64)) k)
(/.f64 (*.f64 n (PI.f64)) k)
(/.f64 (*.f64 n (PI.f64)) k)
(/.f64 (*.f64 n (PI.f64)) k)
(/.f64 (*.f64 n (PI.f64)) k)
(/.f64 (*.f64 n (PI.f64)) k)
(/.f64 (*.f64 n (PI.f64)) k)
(/.f64 (*.f64 n (PI.f64)) k)

Outputs
(/.f64 (*.f64 n (PI.f64)) k)
(/.f64 n (/.f64 k (PI.f64)))
(/.f64 (PI.f64) (/.f64 k n))
(*.f64 n (/.f64 (PI.f64) k))
(/.f64 (*.f64 n (PI.f64)) k)
(/.f64 n (/.f64 k (PI.f64)))
(/.f64 (PI.f64) (/.f64 k n))
(*.f64 n (/.f64 (PI.f64) k))
(/.f64 (*.f64 n (PI.f64)) k)
(/.f64 n (/.f64 k (PI.f64)))
(/.f64 (PI.f64) (/.f64 k n))
(*.f64 n (/.f64 (PI.f64) k))
(/.f64 (*.f64 n (PI.f64)) k)
(/.f64 n (/.f64 k (PI.f64)))
(/.f64 (PI.f64) (/.f64 k n))
(*.f64 n (/.f64 (PI.f64) k))
(/.f64 (*.f64 n (PI.f64)) k)
(/.f64 n (/.f64 k (PI.f64)))
(/.f64 (PI.f64) (/.f64 k n))
(*.f64 n (/.f64 (PI.f64) k))
(/.f64 (*.f64 n (PI.f64)) k)
(/.f64 n (/.f64 k (PI.f64)))
(/.f64 (PI.f64) (/.f64 k n))
(*.f64 n (/.f64 (PI.f64) k))
(/.f64 (*.f64 n (PI.f64)) k)
(/.f64 n (/.f64 k (PI.f64)))
(/.f64 (PI.f64) (/.f64 k n))
(*.f64 n (/.f64 (PI.f64) k))
(/.f64 (*.f64 n (PI.f64)) k)
(/.f64 n (/.f64 k (PI.f64)))
(/.f64 (PI.f64) (/.f64 k n))
(*.f64 n (/.f64 (PI.f64) k))
(/.f64 (*.f64 n (PI.f64)) k)
(/.f64 n (/.f64 k (PI.f64)))
(/.f64 (PI.f64) (/.f64 k n))
(*.f64 n (/.f64 (PI.f64) k))
(/.f64 (*.f64 n (PI.f64)) k)
(/.f64 n (/.f64 k (PI.f64)))
(/.f64 (PI.f64) (/.f64 k n))
(*.f64 n (/.f64 (PI.f64) k))
(/.f64 (*.f64 n (PI.f64)) k)
(/.f64 n (/.f64 k (PI.f64)))
(/.f64 (PI.f64) (/.f64 k n))
(*.f64 n (/.f64 (PI.f64) k))
(/.f64 (*.f64 n (PI.f64)) k)
(/.f64 n (/.f64 k (PI.f64)))
(/.f64 (PI.f64) (/.f64 k n))
(*.f64 n (/.f64 (PI.f64) k))
(/.f64 (*.f64 n (PI.f64)) k)
(/.f64 n (/.f64 k (PI.f64)))
(/.f64 (PI.f64) (/.f64 k n))
(*.f64 n (/.f64 (PI.f64) k))
(/.f64 (*.f64 n (PI.f64)) k)
(/.f64 n (/.f64 k (PI.f64)))
(/.f64 (PI.f64) (/.f64 k n))
(*.f64 n (/.f64 (PI.f64) k))
(/.f64 (*.f64 n (PI.f64)) k)
(/.f64 n (/.f64 k (PI.f64)))
(/.f64 (PI.f64) (/.f64 k n))
(*.f64 n (/.f64 (PI.f64) k))
(/.f64 (*.f64 n (PI.f64)) k)
(/.f64 n (/.f64 k (PI.f64)))
(/.f64 (PI.f64) (/.f64 k n))
(*.f64 n (/.f64 (PI.f64) k))
(/.f64 (*.f64 n (PI.f64)) k)
(/.f64 n (/.f64 k (PI.f64)))
(/.f64 (PI.f64) (/.f64 k n))
(*.f64 n (/.f64 (PI.f64) k))
(/.f64 (*.f64 n (PI.f64)) k)
(/.f64 n (/.f64 k (PI.f64)))
(/.f64 (PI.f64) (/.f64 k n))
(*.f64 n (/.f64 (PI.f64) k))
(/.f64 (*.f64 n (PI.f64)) k)
(/.f64 n (/.f64 k (PI.f64)))
(/.f64 (PI.f64) (/.f64 k n))
(*.f64 n (/.f64 (PI.f64) k))
(/.f64 (*.f64 n (PI.f64)) k)
(/.f64 n (/.f64 k (PI.f64)))
(/.f64 (PI.f64) (/.f64 k n))
(*.f64 n (/.f64 (PI.f64) k))
(/.f64 (*.f64 n (PI.f64)) k)
(/.f64 n (/.f64 k (PI.f64)))
(/.f64 (PI.f64) (/.f64 k n))
(*.f64 n (/.f64 (PI.f64) k))
(/.f64 (*.f64 n (PI.f64)) k)
(/.f64 n (/.f64 k (PI.f64)))
(/.f64 (PI.f64) (/.f64 k n))
(*.f64 n (/.f64 (PI.f64) k))
(/.f64 (*.f64 n (PI.f64)) k)
(/.f64 n (/.f64 k (PI.f64)))
(/.f64 (PI.f64) (/.f64 k n))
(*.f64 n (/.f64 (PI.f64) k))
(/.f64 (*.f64 n (PI.f64)) k)
(/.f64 n (/.f64 k (PI.f64)))
(/.f64 (PI.f64) (/.f64 k n))
(*.f64 n (/.f64 (PI.f64) k))

localize15.0ms (0.2%)

Local error

Found 6 expressions with local error:

New	Error	Program
	0.4b	(/.f64 (sqrt.f64 (.f64 n (.f64 (PI.f64) 2))) (sqrt.f64 k))
	0.2b	(.f64 n (.f64 (PI.f64) 2))
	0.1b	(sqrt.f64 (.f64 n (.f64 (PI.f64) 2)))
✓	0.1b	(sqrt.f64 (.f64 n (.f64 (PI.f64) 2)))
✓	0.2b	(.f64 n (.f64 (PI.f64) 2))
✓	0.4b	(/.f64 (sqrt.f64 (.f64 n (.f64 (PI.f64) 2))) (sqrt.f64 k))

Compiler

Compiled 31 to 19 computations (38.7% saved)

series5.0ms (0.1%)

Counts

3 → 12

Calls

12 calls:

Time	Variable		Point	Expression
1.0ms	k	@	-inf	(/.f64 (sqrt.f64 (.f64 n (.f64 (PI.f64) 2))) (sqrt.f64 k))
1.0ms	n	@	0	(/.f64 (sqrt.f64 (.f64 n (.f64 (PI.f64) 2))) (sqrt.f64 k))
0.0ms	k	@	0	(/.f64 (sqrt.f64 (.f64 n (.f64 (PI.f64) 2))) (sqrt.f64 k))
0.0ms	n	@	inf	(/.f64 (sqrt.f64 (.f64 n (.f64 (PI.f64) 2))) (sqrt.f64 k))
0.0ms	n	@	-inf	(/.f64 (sqrt.f64 (.f64 n (.f64 (PI.f64) 2))) (sqrt.f64 k))

rewrite64.0ms (0.7%)

Algorithm

1×	batch-egg-rewrite

Rules

546×	`log-prod_binary64`
399×	`exp-prod_binary64`
324×	`pow-prod-down_binary64`
255×	`pow2_binary64`
203×	`pow-unpow_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	10	31
1	208	31
2	2622	31

Stop Event

1×	node limit

Counts

3 → 130

Calls

Call 1

Inputs
(/.f64 (sqrt.f64 (.f64 n (.f64 (PI.f64) 2))) (sqrt.f64 k))
(.f64 n (.f64 (PI.f64) 2))
(sqrt.f64 (.f64 n (.f64 (PI.f64) 2)))

Outputs

((#(struct:change #<rule egg-rr> (2) ((x +.f64 0 (sqrt.f64 (/.f64 (*.f64 (PI.f64) 2) (/.f64 k n))))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (log.f64 (pow.f64 (cbrt.f64 (exp.f64 (sqrt.f64 (/.f64 (*.f64 (PI.f64) 2) (/.f64 k n))))) 2)) (log.f64 (cbrt.f64 (exp.f64 (sqrt.f64 (/.f64 (*.f64 (PI.f64) 2) (/.f64 k n)))))))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (log.f64 (sqrt.f64 (exp.f64 (sqrt.f64 (/.f64 (*.f64 (PI.f64) 2) (/.f64 k n)))))) (log.f64 (sqrt.f64 (exp.f64 (sqrt.f64 (/.f64 (*.f64 (PI.f64) 2) (/.f64 k n)))))))))) (#(struct:change #<rule egg-rr> (2) ((x -.f64 (exp.f64 (log1p.f64 (sqrt.f64 (/.f64 (*.f64 (PI.f64) 2) (/.f64 k n))))) 1)))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (sqrt.f64 (*.f64 (PI.f64) (*.f64 2 n))) (pow.f64 k -1/2))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (sqrt.f64 (/.f64 (*.f64 (PI.f64) 2) (/.f64 k n))) 1)))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 1 (sqrt.f64 (/.f64 (*.f64 (PI.f64) 2) (/.f64 k n))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (cbrt.f64 (*.f64 (PI.f64) (*.f64 2 n))) (*.f64 (pow.f64 (*.f64 (PI.f64) (*.f64 2 n)) 1/6) (pow.f64 k -1/2)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (pow.f64 (/.f64 (*.f64 (PI.f64) 2) (/.f64 k n)) 1/6) (cbrt.f64 (/.f64 (*.f64 (PI.f64) 2) (/.f64 k n))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (cbrt.f64 (/.f64 (*.f64 (PI.f64) 2) (/.f64 k n))) (pow.f64 (/.f64 (*.f64 (PI.f64) 2) (/.f64 k n)) 1/6))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (sqrt.f64 n) (*.f64 (sqrt.f64 (*.f64 (PI.f64) 2)) (pow.f64 k -1/2)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (pow.f64 (/.f64 (*.f64 (PI.f64) 2) (/.f64 k n)) 1/4) (pow.f64 (/.f64 (*.f64 (PI.f64) 2) (/.f64 k n)) 1/4))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (pow.f64 (*.f64 (PI.f64) (*.f64 2 n)) 1/4) (*.f64 (pow.f64 (*.f64 (PI.f64) (*.f64 2 n)) 1/4) (pow.f64 k -1/2)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (neg.f64 (sqrt.f64 (*.f64 (PI.f64) (*.f64 2 n)))) (/.f64 1 (neg.f64 (sqrt.f64 k))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (pow.f64 k -1/2) (sqrt.f64 (*.f64 (PI.f64) (*.f64 2 n))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (/.f64 (cbrt.f64 (*.f64 (PI.f64) (*.f64 2 n))) (cbrt.f64 k)) (pow.f64 (/.f64 (*.f64 (PI.f64) 2) (/.f64 k n)) 1/6))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (/.f64 (cbrt.f64 (*.f64 (PI.f64) (*.f64 2 n))) 1) (/.f64 (pow.f64 (*.f64 (PI.f64) (*.f64 2 n)) 1/6) (sqrt.f64 k)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (/.f64 (sqrt.f64 n) 1) (/.f64 (sqrt.f64 (*.f64 (PI.f64) 2)) (sqrt.f64 k)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (/.f64 (pow.f64 (*.f64 (PI.f64) (*.f64 2 n)) 1/4) 1) (/.f64 (pow.f64 (*.f64 (PI.f64) (*.f64 2 n)) 1/4) (sqrt.f64 k)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (/.f64 1 (cbrt.f64 k)) (/.f64 (sqrt.f64 (*.f64 (PI.f64) (*.f64 2 n))) (pow.f64 k 1/6)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (/.f64 (sqrt.f64 n) (cbrt.f64 k)) (/.f64 (sqrt.f64 (*.f64 (PI.f64) 2)) (pow.f64 k 1/6)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (/.f64 (pow.f64 (*.f64 (PI.f64) (*.f64 2 n)) 1/4) (cbrt.f64 k)) (/.f64 (pow.f64 (*.f64 (PI.f64) (*.f64 2 n)) 1/4) (pow.f64 k 1/6)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (pow.f64 k -1/4) (/.f64 (sqrt.f64 (*.f64 (PI.f64) (*.f64 2 n))) (pow.f64 k 1/4)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (/.f64 (cbrt.f64 (*.f64 (PI.f64) (*.f64 2 n))) (pow.f64 k 1/4)) (/.f64 (pow.f64 (*.f64 (PI.f64) (*.f64 2 n)) 1/6) (pow.f64 k 1/4)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (/.f64 (sqrt.f64 n) (pow.f64 k 1/4)) (/.f64 (sqrt.f64 (*.f64 (PI.f64) 2)) (pow.f64 k 1/4)))))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (sqrt.f64 (/.f64 (*.f64 (PI.f64) 2) (/.f64 k n))) 1)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (/.f64 (*.f64 (PI.f64) 2) (/.f64 k n)) 1/2)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (pow.f64 (/.f64 (*.f64 (PI.f64) 2) (/.f64 k n)) 3/2) 1/3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (pow.f64 (/.f64 (*.f64 (PI.f64) 2) (/.f64 k n)) 1/6) 3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (pow.f64 (/.f64 (*.f64 (PI.f64) 2) (/.f64 k n)) 1/4) 2)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (sqrt.f64 (/.f64 k (*.f64 (PI.f64) (*.f64 2 n)))) -1)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (exp.f64 1) (log.f64 (sqrt.f64 (/.f64 (*.f64 (PI.f64) 2) (/.f64 k n)))))))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (/.f64 (pow.f64 (*.f64 (PI.f64) (*.f64 2 n)) 3/2) (pow.f64 k 3/2)) 1/3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (/.f64 (sqrt.f64 (/.f64 k (*.f64 (PI.f64) (*.f64 2 n)))) 1) -1)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (exp.f64 (pow.f64 (cbrt.f64 (log.f64 (sqrt.f64 (/.f64 (*.f64 (PI.f64) 2) (/.f64 k n))))) 2)) (cbrt.f64 (log.f64 (sqrt.f64 (/.f64 (*.f64 (PI.f64) 2) (/.f64 k n))))))))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (exp.f64 (sqrt.f64 (log.f64 (sqrt.f64 (/.f64 (*.f64 (PI.f64) 2) (/.f64 k n)))))) (sqrt.f64 (log.f64 (sqrt.f64 (/.f64 (*.f64 (PI.f64) 2) (/.f64 k n))))))))) (#(struct:change #<rule egg-rr> (2) ((x neg.f64 (/.f64 (sqrt.f64 (*.f64 (PI.f64) (*.f64 2 n))) (neg.f64 (sqrt.f64 k))))))) (#(struct:change #<rule egg-rr> (2) ((x sqrt.f64 (/.f64 (*.f64 (PI.f64) 2) (/.f64 k n)))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (exp.f64 (sqrt.f64 (/.f64 (*.f64 (PI.f64) 2) (/.f64 k n)))))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (+.f64 1 (expm1.f64 (sqrt.f64 (/.f64 (*.f64 (PI.f64) 2) (/.f64 k n))))))))) (#(struct:change #<rule egg-rr> (2) ((x cbrt.f64 (pow.f64 (/.f64 (*.f64 (PI.f64) 2) (/.f64 k n)) 3/2))))) (#(struct:change #<rule egg-rr> (2) ((x cbrt.f64 (/.f64 (pow.f64 (*.f64 (PI.f64) (*.f64 2 n)) 3/2) (pow.f64 k 3/2)))))) (#(struct:change #<rule egg-rr> (2) ((x expm1.f64 (log1p.f64 (sqrt.f64 (/.f64 (*.f64 (PI.f64) 2) (/.f64 k n)))))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (log.f64 (sqrt.f64 (/.f64 (*.f64 (PI.f64) 2) (/.f64 k n)))))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (*.f64 (log.f64 (sqrt.f64 (/.f64 (*.f64 (PI.f64) 2) (/.f64 k n)))) 1))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (*.f64 (log.f64 (/.f64 (*.f64 (PI.f64) 2) (/.f64 k n))) 1/2))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (*.f64 (log.f64 (pow.f64 (/.f64 (*.f64 (PI.f64) 2) (/.f64 k n)) 3/2)) 1/3))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (*.f64 (log.f64 (pow.f64 (/.f64 (*.f64 (PI.f64) 2) (/.f64 k n)) 1/6)) 3))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (*.f64 (log.f64 (pow.f64 (/.f64 (*.f64 (PI.f64) 2) (/.f64 k n)) 1/4)) 2))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (*.f64 (log.f64 (sqrt.f64 (/.f64 k (*.f64 (PI.f64) (*.f64 2 n))))) -1))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (*.f64 (*.f64 (log.f64 (sqrt.f64 (/.f64 (*.f64 (PI.f64) 2) (/.f64 k n)))) 1) 1))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (-.f64 (*.f64 (log.f64 (*.f64 (PI.f64) (*.f64 2 n))) 1/2) (log.f64 (sqrt.f64 k))))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (-.f64 (*.f64 (log.f64 (sqrt.f64 (*.f64 (PI.f64) (*.f64 2 n)))) 1) (log.f64 (sqrt.f64 k))))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (-.f64 (log.f64 (sqrt.f64 (*.f64 (PI.f64) (*.f64 2 n)))) (*.f64 (log.f64 k) 1/2)))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (-.f64 (*.f64 (log.f64 (*.f64 (PI.f64) (*.f64 2 n))) 1/2) (*.f64 (log.f64 k) 1/2)))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (-.f64 (*.f64 (log.f64 (sqrt.f64 (*.f64 (PI.f64) (*.f64 2 n)))) 1) (*.f64 (log.f64 k) 1/2)))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (-.f64 (log.f64 (sqrt.f64 (*.f64 (PI.f64) (*.f64 2 n)))) (*.f64 (log.f64 (sqrt.f64 k)) 1)))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (-.f64 (*.f64 (log.f64 (*.f64 (PI.f64) (*.f64 2 n))) 1/2) (*.f64 (log.f64 (sqrt.f64 k)) 1)))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (-.f64 (*.f64 (log.f64 (sqrt.f64 (*.f64 (PI.f64) (*.f64 2 n)))) 1) (*.f64 (log.f64 (sqrt.f64 k)) 1)))))) (#(struct:change #<rule egg-rr> (2) ((x log1p.f64 (expm1.f64 (sqrt.f64 (/.f64 (*.f64 (PI.f64) 2) (/.f64 k n)))))))))

((#(struct:change #<rule egg-rr> (2) ((x +.f64 (*.f64 n (PI.f64)) (*.f64 n (PI.f64)))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 0 (*.f64 (PI.f64) (*.f64 2 n)))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (log.f64 (pow.f64 (cbrt.f64 (pow.f64 (exp.f64 n) (*.f64 (PI.f64) 2))) 2)) (log.f64 (cbrt.f64 (pow.f64 (exp.f64 n) (*.f64 (PI.f64) 2)))))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (log.f64 (sqrt.f64 (pow.f64 (exp.f64 n) (*.f64 (PI.f64) 2)))) (log.f64 (sqrt.f64 (pow.f64 (exp.f64 n) (*.f64 (PI.f64) 2)))))))) (#(struct:change #<rule egg-rr> (2) ((x -.f64 (exp.f64 (log1p.f64 (*.f64 (PI.f64) (*.f64 2 n)))) 1)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (*.f64 (PI.f64) (*.f64 2 n)) 1)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (sqrt.f64 (*.f64 (PI.f64) (*.f64 2 n))) 2)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (pow.f64 (*.f64 (PI.f64) (*.f64 2 n)) 2) 1/2)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (pow.f64 (*.f64 (PI.f64) (*.f64 2 n)) 3) 1/3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (pow.f64 (*.f64 (PI.f64) (*.f64 2 n)) 3/2) 2/3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (cbrt.f64 (*.f64 (PI.f64) (*.f64 2 n))) 3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (pow.f64 (*.f64 (PI.f64) (*.f64 2 n)) 1/6) 6)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (pow.f64 (*.f64 (PI.f64) (*.f64 2 n)) 1/4) 4)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (exp.f64 1) (log.f64 (*.f64 (PI.f64) (*.f64 2 n))))))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (exp.f64 (pow.f64 (cbrt.f64 (log.f64 (*.f64 (PI.f64) (*.f64 2 n)))) 2)) (cbrt.f64 (log.f64 (*.f64 (PI.f64) (*.f64 2 n)))))))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (exp.f64 (sqrt.f64 (log.f64 (*.f64 (PI.f64) (*.f64 2 n))))) (sqrt.f64 (log.f64 (*.f64 (PI.f64) (*.f64 2 n)))))))) (#(struct:change #<rule egg-rr> (2) ((x sqrt.f64 (pow.f64 (*.f64 (PI.f64) (*.f64 2 n)) 2))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (pow.f64 (exp.f64 n) (*.f64 (PI.f64) 2)))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (+.f64 1 (expm1.f64 (*.f64 (PI.f64) (*.f64 2 n)))))))) (#(struct:change #<rule egg-rr> (2) ((x cbrt.f64 (pow.f64 (*.f64 (PI.f64) (*.f64 2 n)) 3))))) (#(struct:change #<rule egg-rr> (2) ((x expm1.f64 (log1p.f64 (*.f64 (PI.f64) (*.f64 2 n))))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (log.f64 (*.f64 (PI.f64) (*.f64 2 n))))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (*.f64 (log.f64 (*.f64 (PI.f64) (*.f64 2 n))) 1))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (*.f64 (log.f64 (sqrt.f64 (*.f64 (PI.f64) (*.f64 2 n)))) 2))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (*.f64 (log.f64 (pow.f64 (*.f64 (PI.f64) (*.f64 2 n)) 2)) 1/2))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (*.f64 (log.f64 (pow.f64 (*.f64 (PI.f64) (*.f64 2 n)) 3)) 1/3))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (*.f64 (log.f64 (cbrt.f64 (*.f64 (PI.f64) (*.f64 2 n)))) 3))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (*.f64 (*.f64 (log.f64 (*.f64 (PI.f64) (*.f64 2 n))) 1) 1))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (*.f64 (*.f64 (log.f64 (*.f64 (PI.f64) (*.f64 2 n))) 1/2) 2))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (*.f64 (*.f64 (log.f64 (sqrt.f64 (*.f64 (PI.f64) (*.f64 2 n)))) 1) 2))))) (#(struct:change #<rule egg-rr> (2) ((x log1p.f64 (expm1.f64 (*.f64 (PI.f64) (*.f64 2 n))))))))

((#(struct:change #<rule egg-rr> (2) ((x +.f64 0 (sqrt.f64 (*.f64 (PI.f64) (*.f64 2 n))))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (log.f64 (pow.f64 (cbrt.f64 (exp.f64 (sqrt.f64 (*.f64 (PI.f64) (*.f64 2 n))))) 2)) (log.f64 (cbrt.f64 (exp.f64 (sqrt.f64 (*.f64 (PI.f64) (*.f64 2 n)))))))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (log.f64 (sqrt.f64 (exp.f64 (sqrt.f64 (*.f64 (PI.f64) (*.f64 2 n)))))) (log.f64 (sqrt.f64 (exp.f64 (sqrt.f64 (*.f64 (PI.f64) (*.f64 2 n)))))))))) (#(struct:change #<rule egg-rr> (2) ((x -.f64 (exp.f64 (log1p.f64 (sqrt.f64 (*.f64 (PI.f64) (*.f64 2 n))))) 1)))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (sqrt.f64 (*.f64 (PI.f64) (*.f64 2 n))) 1)))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 1 (sqrt.f64 (*.f64 (PI.f64) (*.f64 2 n))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (cbrt.f64 (*.f64 (PI.f64) (*.f64 2 n))) (pow.f64 (*.f64 (PI.f64) (*.f64 2 n)) 1/6))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (pow.f64 (*.f64 (PI.f64) (*.f64 2 n)) 1/6) (cbrt.f64 (*.f64 (PI.f64) (*.f64 2 n))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (sqrt.f64 (*.f64 (PI.f64) 2)) (sqrt.f64 n))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (sqrt.f64 n) (sqrt.f64 (*.f64 (PI.f64) 2)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (pow.f64 (*.f64 (PI.f64) (*.f64 2 n)) 1/4) (pow.f64 (*.f64 (PI.f64) (*.f64 2 n)) 1/4))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (sqrt.f64 (*.f64 n (PI.f64))) (sqrt.f64 2))))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (*.f64 (PI.f64) (*.f64 2 n)) 1/2)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (sqrt.f64 (*.f64 (PI.f64) (*.f64 2 n))) 1)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (pow.f64 (*.f64 (PI.f64) (*.f64 2 n)) 2) 1/4)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (pow.f64 (*.f64 (PI.f64) (*.f64 2 n)) 3) 1/6)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (pow.f64 (*.f64 (PI.f64) (*.f64 2 n)) 3/2) 1/3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (cbrt.f64 (*.f64 (PI.f64) (*.f64 2 n))) 3/2)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (pow.f64 (*.f64 (PI.f64) (*.f64 2 n)) 1/6) 3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (pow.f64 (*.f64 (PI.f64) (*.f64 2 n)) 1/4) 2)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (exp.f64 1/2) (log.f64 (*.f64 (PI.f64) (*.f64 2 n))))))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (exp.f64 1) (log.f64 (sqrt.f64 (*.f64 (PI.f64) (*.f64 2 n)))))))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (exp.f64 (pow.f64 (cbrt.f64 (log.f64 (sqrt.f64 (*.f64 (PI.f64) (*.f64 2 n))))) 2)) (cbrt.f64 (log.f64 (sqrt.f64 (*.f64 (PI.f64) (*.f64 2 n))))))))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (exp.f64 (sqrt.f64 (log.f64 (sqrt.f64 (*.f64 (PI.f64) (*.f64 2 n)))))) (sqrt.f64 (log.f64 (sqrt.f64 (*.f64 (PI.f64) (*.f64 2 n))))))))) (#(struct:change #<rule egg-rr> (2) ((x fabs.f64 (sqrt.f64 (*.f64 (PI.f64) (*.f64 2 n))))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (exp.f64 (sqrt.f64 (*.f64 (PI.f64) (*.f64 2 n)))))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (+.f64 1 (expm1.f64 (sqrt.f64 (*.f64 (PI.f64) (*.f64 2 n))))))))) (#(struct:change #<rule egg-rr> (2) ((x cbrt.f64 (pow.f64 (*.f64 (PI.f64) (*.f64 2 n)) 3/2))))) (#(struct:change #<rule egg-rr> (2) ((x expm1.f64 (log1p.f64 (sqrt.f64 (*.f64 (PI.f64) (*.f64 2 n)))))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (log.f64 (sqrt.f64 (*.f64 (PI.f64) (*.f64 2 n)))))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (*.f64 (log.f64 (*.f64 (PI.f64) (*.f64 2 n))) 1/2))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (*.f64 (log.f64 (sqrt.f64 (*.f64 (PI.f64) (*.f64 2 n)))) 1))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (*.f64 (log.f64 (pow.f64 (*.f64 (PI.f64) (*.f64 2 n)) 3/2)) 1/3))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (*.f64 (log.f64 (pow.f64 (*.f64 (PI.f64) (*.f64 2 n)) 1/6)) 3))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (*.f64 (*.f64 1/4 (log.f64 (*.f64 (PI.f64) (*.f64 2 n)))) 2))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (*.f64 (*.f64 (log.f64 (*.f64 (PI.f64) (*.f64 2 n))) 1) 1/2))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (*.f64 (*.f64 (log.f64 (*.f64 (PI.f64) (*.f64 2 n))) 1/2) 1))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (*.f64 (*.f64 (log.f64 (sqrt.f64 (*.f64 (PI.f64) (*.f64 2 n)))) 1) 1))))) (#(struct:change #<rule egg-rr> (2) ((x log1p.f64 (expm1.f64 (sqrt.f64 (*.f64 (PI.f64) (*.f64 2 n)))))))))

simplify13.0ms (0.1%)

Algorithm

1×	egg-herbie

Rules

5×	`*-commutative_binary64`
3×	`associate-r_binary64`
3×	`associate-l_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	6	96
1	10	96
2	17	96
3	19	96

Stop Event

1×

saturated

Counts

142 → 132

Calls

Call 1

Inputs
(.f64 2 (.f64 n (PI.f64)))
(.f64 2 (.f64 n (PI.f64)))
(.f64 2 (.f64 n (PI.f64)))
(.f64 2 (.f64 n (PI.f64)))
(.f64 2 (.f64 n (PI.f64)))
(.f64 2 (.f64 n (PI.f64)))
(.f64 2 (.f64 n (PI.f64)))
(.f64 2 (.f64 n (PI.f64)))
(.f64 2 (.f64 n (PI.f64)))
(.f64 2 (.f64 n (PI.f64)))
(.f64 2 (.f64 n (PI.f64)))
(.f64 2 (.f64 n (PI.f64)))

Outputs
(.f64 2 (.f64 n (PI.f64)))
(.f64 (PI.f64) (.f64 2 n))
(.f64 2 (.f64 n (PI.f64)))
(.f64 (PI.f64) (.f64 2 n))
(.f64 2 (.f64 n (PI.f64)))
(.f64 (PI.f64) (.f64 2 n))
(.f64 2 (.f64 n (PI.f64)))
(.f64 (PI.f64) (.f64 2 n))
(.f64 2 (.f64 n (PI.f64)))
(.f64 (PI.f64) (.f64 2 n))
(.f64 2 (.f64 n (PI.f64)))
(.f64 (PI.f64) (.f64 2 n))
(.f64 2 (.f64 n (PI.f64)))
(.f64 (PI.f64) (.f64 2 n))
(.f64 2 (.f64 n (PI.f64)))
(.f64 (PI.f64) (.f64 2 n))
(.f64 2 (.f64 n (PI.f64)))
(.f64 (PI.f64) (.f64 2 n))
(.f64 2 (.f64 n (PI.f64)))
(.f64 (PI.f64) (.f64 2 n))
(.f64 2 (.f64 n (PI.f64)))
(.f64 (PI.f64) (.f64 2 n))
(.f64 2 (.f64 n (PI.f64)))
(.f64 (PI.f64) (.f64 2 n))

localize27.0ms (0.3%)

Local error

Found 8 expressions with local error:

New	Error	Program
	0.3b	(.f64 (sqrt.f64 k) (pow.f64 (.f64 2 (*.f64 n (PI.f64))) -1/2))
	0.3b	(/.f64 1 (.f64 (sqrt.f64 k) (pow.f64 (.f64 2 (*.f64 n (PI.f64))) -1/2)))
	0.2b	(*.f64 n (PI.f64))
	0.1b	(pow.f64 (.f64 2 (.f64 n (PI.f64))) -1/2)
✓	0.1b	(pow.f64 (.f64 2 (.f64 n (PI.f64))) -1/2)
	0.2b	(*.f64 n (PI.f64))
✓	0.3b	(/.f64 1 (.f64 (sqrt.f64 k) (pow.f64 (.f64 2 (*.f64 n (PI.f64))) -1/2)))
✓	0.3b	(.f64 (sqrt.f64 k) (pow.f64 (.f64 2 (*.f64 n (PI.f64))) -1/2))

Compiler

Compiled 47 to 26 computations (44.7% saved)

series22.0ms (0.2%)

Counts

3 → 12

Calls

15 calls:

Time	Variable		Point	Expression
8.0ms	k	@	-inf	(.f64 (sqrt.f64 k) (pow.f64 (.f64 2 (*.f64 n (PI.f64))) -1/2))
2.0ms	n	@	0	(pow.f64 (.f64 2 (.f64 n (PI.f64))) -1/2)
1.0ms	n	@	0	(.f64 (sqrt.f64 k) (pow.f64 (.f64 2 (*.f64 n (PI.f64))) -1/2))
1.0ms	k	@	-inf	(/.f64 1 (.f64 (sqrt.f64 k) (pow.f64 (.f64 2 (*.f64 n (PI.f64))) -1/2)))
1.0ms	k	@	0	(.f64 (sqrt.f64 k) (pow.f64 (.f64 2 (*.f64 n (PI.f64))) -1/2))

rewrite61.0ms (0.7%)

Algorithm

1×	batch-egg-rewrite

Rules

616×	`log-prod_binary64`
369×	`pow-prod-down_binary64`
321×	`pow2_binary64`
235×	`pow-unpow_binary64`
232×	`pow-to-exp_binary64`

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	13	46
1	270	44
2	3128	41

Stop Event

1×	node limit

Counts

3 → 99

Calls

Call 1

Inputs
(.f64 (sqrt.f64 k) (pow.f64 (.f64 2 (*.f64 n (PI.f64))) -1/2))
(/.f64 1 (.f64 (sqrt.f64 k) (pow.f64 (.f64 2 (*.f64 n (PI.f64))) -1/2)))
(pow.f64 (.f64 2 (.f64 n (PI.f64))) -1/2)

Outputs

((#(struct:change #<rule egg-rr> (2) ((x +.f64 0 (/.f64 (sqrt.f64 k) (sqrt.f64 (*.f64 2 (*.f64 n (PI.f64))))))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (log.f64 (pow.f64 (cbrt.f64 (exp.f64 (/.f64 (sqrt.f64 k) (sqrt.f64 (*.f64 2 (*.f64 n (PI.f64))))))) 2)) (log.f64 (cbrt.f64 (exp.f64 (/.f64 (sqrt.f64 k) (sqrt.f64 (*.f64 2 (*.f64 n (PI.f64)))))))))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (log.f64 (sqrt.f64 (exp.f64 (/.f64 (sqrt.f64 k) (sqrt.f64 (*.f64 2 (*.f64 n (PI.f64)))))))) (log.f64 (sqrt.f64 (exp.f64 (/.f64 (sqrt.f64 k) (sqrt.f64 (*.f64 2 (*.f64 n (PI.f64)))))))))))) (#(struct:change #<rule egg-rr> (2) ((x -.f64 (exp.f64 (log1p.f64 (/.f64 (sqrt.f64 k) (sqrt.f64 (*.f64 2 (*.f64 n (PI.f64))))))) 1)))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (sqrt.f64 k) (sqrt.f64 (*.f64 2 (*.f64 n (PI.f64)))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (pow.f64 (*.f64 2 (*.f64 n (PI.f64))) -1/2) (pow.f64 k -1/2))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (/.f64 (sqrt.f64 k) (sqrt.f64 (*.f64 2 (*.f64 n (PI.f64))))) 1)))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 1 (/.f64 (sqrt.f64 (*.f64 2 (*.f64 n (PI.f64)))) (sqrt.f64 k)))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (cbrt.f64 (*.f64 k (*.f64 1/2 (pow.f64 (*.f64 n (PI.f64)) -1)))) (cbrt.f64 (/.f64 (sqrt.f64 (*.f64 2 (*.f64 n (PI.f64)))) (sqrt.f64 k))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (*.f64 (pow.f64 k 1/4) (pow.f64 (*.f64 2 (*.f64 n (PI.f64))) -1/4)) (sqrt.f64 (/.f64 (sqrt.f64 (*.f64 2 (*.f64 n (PI.f64)))) (sqrt.f64 k))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (neg.f64 (/.f64 (sqrt.f64 k) (sqrt.f64 (*.f64 2 (*.f64 n (PI.f64)))))) -1)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (/.f64 (sqrt.f64 k) (sqrt.f64 (*.f64 2 (*.f64 n (PI.f64))))) 1)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (/.f64 (sqrt.f64 (*.f64 2 (*.f64 n (PI.f64)))) (sqrt.f64 k)) -1)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (*.f64 k (*.f64 1/2 (pow.f64 (*.f64 n (PI.f64)) -1))) 1/2)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (*.f64 (pow.f64 k 3/2) (pow.f64 (*.f64 2 (*.f64 n (PI.f64))) -3/2)) 1/3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (pow.f64 (/.f64 (sqrt.f64 k) (sqrt.f64 (*.f64 2 (*.f64 n (PI.f64))))) -3) -1/3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (*.f64 (pow.f64 k 1/6) (pow.f64 (*.f64 2 (*.f64 n (PI.f64))) -1/6)) 3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (cbrt.f64 (/.f64 (sqrt.f64 (*.f64 2 (*.f64 n (PI.f64)))) (sqrt.f64 k))) -3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (*.f64 (pow.f64 k 1/4) (pow.f64 (*.f64 2 (*.f64 n (PI.f64))) -1/4)) 2)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (sqrt.f64 (/.f64 (sqrt.f64 (*.f64 2 (*.f64 n (PI.f64)))) (sqrt.f64 k))) -2)))) (#(struct:change #<rule egg-rr> (2) ((x sqrt.f64 (*.f64 k (*.f64 1/2 (pow.f64 (*.f64 n (PI.f64)) -1))))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (exp.f64 (/.f64 (sqrt.f64 k) (sqrt.f64 (*.f64 2 (*.f64 n (PI.f64)))))))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (+.f64 1 (expm1.f64 (/.f64 (sqrt.f64 k) (sqrt.f64 (*.f64 2 (*.f64 n (PI.f64))))))))))) (#(struct:change #<rule egg-rr> (2) ((x cbrt.f64 (*.f64 (pow.f64 k 3/2) (pow.f64 (*.f64 2 (*.f64 n (PI.f64))) -3/2)))))) (#(struct:change #<rule egg-rr> (2) ((x expm1.f64 (log1p.f64 (/.f64 (sqrt.f64 k) (sqrt.f64 (*.f64 2 (*.f64 n (PI.f64)))))))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (log.f64 (/.f64 (sqrt.f64 k) (sqrt.f64 (*.f64 2 (*.f64 n (PI.f64)))))))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (*.f64 (log.f64 (/.f64 (sqrt.f64 k) (sqrt.f64 (*.f64 2 (*.f64 n (PI.f64)))))) 1))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (*.f64 (log.f64 (*.f64 (pow.f64 k 3/2) (pow.f64 (*.f64 2 (*.f64 n (PI.f64))) -3/2))) 1/3))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (*.f64 (log.f64 (*.f64 (pow.f64 k 1/6) (pow.f64 (*.f64 2 (*.f64 n (PI.f64))) -1/6))) 3))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (*.f64 (log.f64 (*.f64 (pow.f64 k 1/4) (pow.f64 (*.f64 2 (*.f64 n (PI.f64))) -1/4))) 2))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (*.f64 (*.f64 (log.f64 (/.f64 (sqrt.f64 k) (sqrt.f64 (*.f64 2 (*.f64 n (PI.f64)))))) 1) 1))))) (#(struct:change #<rule egg-rr> (2) ((x log1p.f64 (expm1.f64 (/.f64 (sqrt.f64 k) (sqrt.f64 (*.f64 2 (*.f64 n (PI.f64)))))))))))

((#(struct:change #<rule egg-rr> (2) ((x +.f64 0 (/.f64 (sqrt.f64 (*.f64 2 (*.f64 n (PI.f64)))) (sqrt.f64 k)))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (log.f64 (pow.f64 (cbrt.f64 (exp.f64 (/.f64 (sqrt.f64 (*.f64 2 (*.f64 n (PI.f64)))) (sqrt.f64 k)))) 2)) (log.f64 (cbrt.f64 (exp.f64 (/.f64 (sqrt.f64 (*.f64 2 (*.f64 n (PI.f64)))) (sqrt.f64 k))))))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (log.f64 (sqrt.f64 (exp.f64 (/.f64 (sqrt.f64 (*.f64 2 (*.f64 n (PI.f64)))) (sqrt.f64 k))))) (log.f64 (sqrt.f64 (exp.f64 (/.f64 (sqrt.f64 (*.f64 2 (*.f64 n (PI.f64)))) (sqrt.f64 k))))))))) (#(struct:change #<rule egg-rr> (2) ((x -.f64 (exp.f64 (log1p.f64 (/.f64 (sqrt.f64 (*.f64 2 (*.f64 n (PI.f64)))) (sqrt.f64 k)))) 1)))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 1 (/.f64 (sqrt.f64 (*.f64 2 (*.f64 n (PI.f64)))) (sqrt.f64 k)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (/.f64 (sqrt.f64 (*.f64 2 (*.f64 n (PI.f64)))) (sqrt.f64 k)) 1)))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (cbrt.f64 (/.f64 (sqrt.f64 (*.f64 2 (*.f64 n (PI.f64)))) (sqrt.f64 k))) (cbrt.f64 (/.f64 (pow.f64 k -1) (*.f64 1/2 (pow.f64 (*.f64 n (PI.f64)) -1)))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (cbrt.f64 (/.f64 (pow.f64 k -1) (*.f64 1/2 (pow.f64 (*.f64 n (PI.f64)) -1)))) (cbrt.f64 (/.f64 (sqrt.f64 (*.f64 2 (*.f64 n (PI.f64)))) (sqrt.f64 k))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (sqrt.f64 (*.f64 2 (*.f64 n (PI.f64)))) (pow.f64 k -1/2))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (sqrt.f64 (/.f64 (sqrt.f64 (*.f64 2 (*.f64 n (PI.f64)))) (sqrt.f64 k))) (sqrt.f64 (/.f64 (sqrt.f64 (*.f64 2 (*.f64 n (PI.f64)))) (sqrt.f64 k))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 -1 (/.f64 1 (neg.f64 (/.f64 (sqrt.f64 k) (sqrt.f64 (*.f64 2 (*.f64 n (PI.f64))))))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (pow.f64 k -1/2) (sqrt.f64 (*.f64 2 (*.f64 n (PI.f64)))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (/.f64 1 (cbrt.f64 (*.f64 k (*.f64 1/2 (pow.f64 (*.f64 n (PI.f64)) -1))))) (cbrt.f64 (/.f64 (sqrt.f64 (*.f64 2 (*.f64 n (PI.f64)))) (sqrt.f64 k))))))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (/.f64 (sqrt.f64 k) (sqrt.f64 (*.f64 2 (*.f64 n (PI.f64))))) -1)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (/.f64 (sqrt.f64 (*.f64 2 (*.f64 n (PI.f64)))) (sqrt.f64 k)) 1)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (*.f64 k (*.f64 1/2 (pow.f64 (*.f64 n (PI.f64)) -1))) -1/2)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (*.f64 (pow.f64 k 3/2) (pow.f64 (*.f64 2 (*.f64 n (PI.f64))) -3/2)) -1/3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (/.f64 (pow.f64 k -1) (*.f64 1/2 (pow.f64 (*.f64 n (PI.f64)) -1))) 1/2)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (pow.f64 (/.f64 (sqrt.f64 k) (sqrt.f64 (*.f64 2 (*.f64 n (PI.f64))))) -3) 1/3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (*.f64 (pow.f64 k 1/6) (pow.f64 (*.f64 2 (*.f64 n (PI.f64))) -1/6)) -3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (cbrt.f64 (/.f64 (sqrt.f64 (*.f64 2 (*.f64 n (PI.f64)))) (sqrt.f64 k))) 3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (*.f64 (pow.f64 k 1/4) (pow.f64 (*.f64 2 (*.f64 n (PI.f64))) -1/4)) -2)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (sqrt.f64 (/.f64 (sqrt.f64 (*.f64 2 (*.f64 n (PI.f64)))) (sqrt.f64 k))) 2)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (neg.f64 (neg.f64 (/.f64 (sqrt.f64 k) (sqrt.f64 (*.f64 2 (*.f64 n (PI.f64))))))) -1)))) (#(struct:change #<rule egg-rr> (2) ((x sqrt.f64 (/.f64 (pow.f64 k -1) (*.f64 1/2 (pow.f64 (*.f64 n (PI.f64)) -1))))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (exp.f64 (/.f64 (sqrt.f64 (*.f64 2 (*.f64 n (PI.f64)))) (sqrt.f64 k))))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (+.f64 1 (expm1.f64 (/.f64 (sqrt.f64 (*.f64 2 (*.f64 n (PI.f64)))) (sqrt.f64 k)))))))) (#(struct:change #<rule egg-rr> (2) ((x cbrt.f64 (pow.f64 (/.f64 (sqrt.f64 k) (sqrt.f64 (*.f64 2 (*.f64 n (PI.f64))))) -3))))) (#(struct:change #<rule egg-rr> (2) ((x expm1.f64 (log1p.f64 (/.f64 (sqrt.f64 (*.f64 2 (*.f64 n (PI.f64)))) (sqrt.f64 k))))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (log.f64 (/.f64 (sqrt.f64 (*.f64 2 (*.f64 n (PI.f64)))) (sqrt.f64 k))))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (*.f64 (log.f64 (/.f64 (sqrt.f64 k) (sqrt.f64 (*.f64 2 (*.f64 n (PI.f64)))))) -1))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (*.f64 (log.f64 (/.f64 (sqrt.f64 (*.f64 2 (*.f64 n (PI.f64)))) (sqrt.f64 k))) 1))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (*.f64 (*.f64 3 (log.f64 (/.f64 (sqrt.f64 (*.f64 2 (*.f64 n (PI.f64)))) (sqrt.f64 k)))) 1/3))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (*.f64 (log.f64 (cbrt.f64 (/.f64 (sqrt.f64 (*.f64 2 (*.f64 n (PI.f64)))) (sqrt.f64 k)))) 3))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (*.f64 (log.f64 (sqrt.f64 (/.f64 (sqrt.f64 (*.f64 2 (*.f64 n (PI.f64)))) (sqrt.f64 k)))) 2))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (*.f64 (*.f64 (log.f64 (/.f64 (sqrt.f64 k) (sqrt.f64 (*.f64 2 (*.f64 n (PI.f64)))))) 1) -1))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (*.f64 (*.f64 (log.f64 (/.f64 (sqrt.f64 k) (sqrt.f64 (*.f64 2 (*.f64 n (PI.f64)))))) -1) 1))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (*.f64 (*.f64 (log.f64 (/.f64 (sqrt.f64 (*.f64 2 (*.f64 n (PI.f64)))) (sqrt.f64 k))) 1) 1))))) (#(struct:change #<rule egg-rr> (2) ((x log1p.f64 (expm1.f64 (/.f64 (sqrt.f64 (*.f64 2 (*.f64 n (PI.f64)))) (sqrt.f64 k))))))))

((#(struct:change #<rule egg-rr> (2) ((x +.f64 0 (pow.f64 (*.f64 2 (*.f64 n (PI.f64))) -1/2))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (log.f64 (pow.f64 (cbrt.f64 (exp.f64 (pow.f64 (*.f64 2 (*.f64 n (PI.f64))) -1/2))) 2)) (log.f64 (cbrt.f64 (exp.f64 (pow.f64 (*.f64 2 (*.f64 n (PI.f64))) -1/2)))))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (log.f64 (sqrt.f64 (exp.f64 (pow.f64 (*.f64 2 (*.f64 n (PI.f64))) -1/2)))) (log.f64 (sqrt.f64 (exp.f64 (pow.f64 (*.f64 2 (*.f64 n (PI.f64))) -1/2)))))))) (#(struct:change #<rule egg-rr> (2) ((x -.f64 (exp.f64 (log1p.f64 (pow.f64 (*.f64 2 (*.f64 n (PI.f64))) -1/2))) 1)))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (pow.f64 (*.f64 2 (*.f64 n (PI.f64))) -1/2) 1)))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 1 (pow.f64 (*.f64 2 (*.f64 n (PI.f64))) -1/2))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (pow.f64 (*.f64 2 (*.f64 n (PI.f64))) -1/6) (cbrt.f64 (*.f64 1/2 (pow.f64 (*.f64 n (PI.f64)) -1))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (cbrt.f64 (*.f64 1/2 (pow.f64 (*.f64 n (PI.f64)) -1))) (pow.f64 (*.f64 2 (*.f64 n (PI.f64))) -1/6))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (pow.f64 2 -1/2) (pow.f64 (*.f64 n (PI.f64)) -1/2))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (pow.f64 (*.f64 n (PI.f64)) -1/2) (pow.f64 2 -1/2))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (pow.f64 (*.f64 2 (*.f64 n (PI.f64))) -1/4) (pow.f64 (*.f64 2 (*.f64 n (PI.f64))) -1/4))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (pow.f64 (cbrt.f64 (*.f64 2 (*.f64 n (PI.f64)))) -1) (pow.f64 (*.f64 2 (*.f64 n (PI.f64))) -1/6))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (pow.f64 (*.f64 2 n) -1/2) (pow.f64 (PI.f64) -1/2))))) (#(struct:change #<rule egg-rr> (2) ((x sqrt.f64 (*.f64 1/2 (pow.f64 (*.f64 n (PI.f64)) -1)))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (exp.f64 (pow.f64 (*.f64 2 (*.f64 n (PI.f64))) -1/2)))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (+.f64 1 (expm1.f64 (pow.f64 (*.f64 2 (*.f64 n (PI.f64))) -1/2))))))) (#(struct:change #<rule egg-rr> (2) ((x cbrt.f64 (pow.f64 (*.f64 2 (*.f64 n (PI.f64))) -3/2))))) (#(struct:change #<rule egg-rr> (2) ((x expm1.f64 (log1p.f64 (pow.f64 (*.f64 2 (*.f64 n (PI.f64))) -1/2)))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (*.f64 -1/2 (log.f64 (*.f64 2 (*.f64 n (PI.f64))))))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (*.f64 (*.f64 -1/2 (log.f64 (*.f64 2 (*.f64 n (PI.f64))))) 1))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (*.f64 (log.f64 (*.f64 (pow.f64 (*.f64 n (PI.f64)) 2) 4)) -1/4))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (*.f64 (log.f64 (pow.f64 (*.f64 2 (*.f64 n (PI.f64))) -3/2)) 1/3))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (*.f64 (log.f64 (pow.f64 (*.f64 2 (*.f64 n (PI.f64))) -1/6)) 3))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (*.f64 (*.f64 -1/4 (log.f64 (*.f64 2 (*.f64 n (PI.f64))))) 2))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (*.f64 (*.f64 (log.f64 (*.f64 2 (*.f64 n (PI.f64)))) 1) -1/2))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (*.f64 (*.f64 (*.f64 -1/2 (log.f64 (*.f64 2 (*.f64 n (PI.f64))))) 1) 1))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (*.f64 (*.f64 (log.f64 (*.f64 2 (*.f64 n (PI.f64)))) -1/4) 2))))) (#(struct:change #<rule egg-rr> (2) ((x log1p.f64 (expm1.f64 (pow.f64 (*.f64 2 (*.f64 n (PI.f64))) -1/2)))))))

simplify33.0ms (0.3%)

Algorithm

1×	egg-herbie

Rules

556×	`times-frac_binary64`
523×	`fma-def_binary64`
458×	`unswap-sqr_binary64`
317×	`exp-sum_binary64`
288×	`fma-neg_binary64`

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	28	204
1	74	204
2	169	168
3	439	132
4	1083	132
5	2868	132

Stop Event

1×	node limit

Counts

111 → 103

Calls

Call 1

Inputs
(exp.f64 (.f64 -1/2 (+.f64 (log.f64 n) (log.f64 (.f64 2 (PI.f64))))))
(exp.f64 (.f64 -1/2 (+.f64 (log.f64 n) (log.f64 (.f64 2 (PI.f64))))))
(exp.f64 (.f64 -1/2 (+.f64 (log.f64 n) (log.f64 (.f64 2 (PI.f64))))))
(exp.f64 (.f64 -1/2 (+.f64 (log.f64 n) (log.f64 (.f64 2 (PI.f64))))))
(exp.f64 (.f64 -1/2 (+.f64 (.f64 -1 (log.f64 (/.f64 1 n))) (log.f64 (*.f64 2 (PI.f64))))))
(exp.f64 (.f64 -1/2 (+.f64 (.f64 -1 (log.f64 (/.f64 1 n))) (log.f64 (*.f64 2 (PI.f64))))))
(exp.f64 (.f64 -1/2 (+.f64 (.f64 -1 (log.f64 (/.f64 1 n))) (log.f64 (*.f64 2 (PI.f64))))))
(exp.f64 (.f64 -1/2 (+.f64 (.f64 -1 (log.f64 (/.f64 1 n))) (log.f64 (*.f64 2 (PI.f64))))))
(exp.f64 (.f64 -1/2 (+.f64 (.f64 -1 (log.f64 (/.f64 -1 n))) (log.f64 (*.f64 -2 (PI.f64))))))
(exp.f64 (.f64 -1/2 (+.f64 (.f64 -1 (log.f64 (/.f64 -1 n))) (log.f64 (*.f64 -2 (PI.f64))))))
(exp.f64 (.f64 -1/2 (+.f64 (.f64 -1 (log.f64 (/.f64 -1 n))) (log.f64 (*.f64 -2 (PI.f64))))))
(exp.f64 (.f64 -1/2 (+.f64 (.f64 -1 (log.f64 (/.f64 -1 n))) (log.f64 (*.f64 -2 (PI.f64))))))

Outputs
(exp.f64 (.f64 -1/2 (+.f64 (log.f64 n) (log.f64 (.f64 2 (PI.f64))))))
(pow.f64 (exp.f64 -1/2) (+.f64 (log.f64 n) (log.f64 (*.f64 2 (PI.f64)))))
(.f64 (pow.f64 n -1/2) (pow.f64 (.f64 2 (PI.f64)) -1/2))
(pow.f64 (.f64 2 (.f64 n (PI.f64))) -1/2)
(exp.f64 (.f64 -1/2 (+.f64 (log.f64 n) (log.f64 (.f64 2 (PI.f64))))))
(pow.f64 (exp.f64 -1/2) (+.f64 (log.f64 n) (log.f64 (*.f64 2 (PI.f64)))))
(.f64 (pow.f64 n -1/2) (pow.f64 (.f64 2 (PI.f64)) -1/2))
(pow.f64 (.f64 2 (.f64 n (PI.f64))) -1/2)
(exp.f64 (.f64 -1/2 (+.f64 (log.f64 n) (log.f64 (.f64 2 (PI.f64))))))
(pow.f64 (exp.f64 -1/2) (+.f64 (log.f64 n) (log.f64 (*.f64 2 (PI.f64)))))
(.f64 (pow.f64 n -1/2) (pow.f64 (.f64 2 (PI.f64)) -1/2))
(pow.f64 (.f64 2 (.f64 n (PI.f64))) -1/2)
(exp.f64 (.f64 -1/2 (+.f64 (log.f64 n) (log.f64 (.f64 2 (PI.f64))))))
(pow.f64 (exp.f64 -1/2) (+.f64 (log.f64 n) (log.f64 (*.f64 2 (PI.f64)))))
(.f64 (pow.f64 n -1/2) (pow.f64 (.f64 2 (PI.f64)) -1/2))
(pow.f64 (.f64 2 (.f64 n (PI.f64))) -1/2)
(exp.f64 (.f64 -1/2 (+.f64 (.f64 -1 (log.f64 (/.f64 1 n))) (log.f64 (*.f64 2 (PI.f64))))))
(pow.f64 (exp.f64 -1/2) (+.f64 (log.f64 n) (log.f64 (*.f64 2 (PI.f64)))))
(.f64 (pow.f64 n -1/2) (pow.f64 (.f64 2 (PI.f64)) -1/2))
(pow.f64 (.f64 2 (.f64 n (PI.f64))) -1/2)
(exp.f64 (.f64 -1/2 (+.f64 (.f64 -1 (log.f64 (/.f64 1 n))) (log.f64 (*.f64 2 (PI.f64))))))
(pow.f64 (exp.f64 -1/2) (+.f64 (log.f64 n) (log.f64 (*.f64 2 (PI.f64)))))
(.f64 (pow.f64 n -1/2) (pow.f64 (.f64 2 (PI.f64)) -1/2))
(pow.f64 (.f64 2 (.f64 n (PI.f64))) -1/2)
(exp.f64 (.f64 -1/2 (+.f64 (.f64 -1 (log.f64 (/.f64 1 n))) (log.f64 (*.f64 2 (PI.f64))))))
(pow.f64 (exp.f64 -1/2) (+.f64 (log.f64 n) (log.f64 (*.f64 2 (PI.f64)))))
(.f64 (pow.f64 n -1/2) (pow.f64 (.f64 2 (PI.f64)) -1/2))
(pow.f64 (.f64 2 (.f64 n (PI.f64))) -1/2)
(exp.f64 (.f64 -1/2 (+.f64 (.f64 -1 (log.f64 (/.f64 1 n))) (log.f64 (*.f64 2 (PI.f64))))))
(pow.f64 (exp.f64 -1/2) (+.f64 (log.f64 n) (log.f64 (*.f64 2 (PI.f64)))))
(.f64 (pow.f64 n -1/2) (pow.f64 (.f64 2 (PI.f64)) -1/2))
(pow.f64 (.f64 2 (.f64 n (PI.f64))) -1/2)
(exp.f64 (.f64 -1/2 (+.f64 (.f64 -1 (log.f64 (/.f64 -1 n))) (log.f64 (*.f64 -2 (PI.f64))))))
(pow.f64 (exp.f64 -1/2) (+.f64 (log.f64 n) (log.f64 (*.f64 2 (PI.f64)))))
(.f64 (pow.f64 n -1/2) (pow.f64 (.f64 2 (PI.f64)) -1/2))
(pow.f64 (.f64 2 (.f64 n (PI.f64))) -1/2)
(exp.f64 (.f64 -1/2 (+.f64 (.f64 -1 (log.f64 (/.f64 -1 n))) (log.f64 (*.f64 -2 (PI.f64))))))
(pow.f64 (exp.f64 -1/2) (+.f64 (log.f64 n) (log.f64 (*.f64 2 (PI.f64)))))
(.f64 (pow.f64 n -1/2) (pow.f64 (.f64 2 (PI.f64)) -1/2))
(pow.f64 (.f64 2 (.f64 n (PI.f64))) -1/2)
(exp.f64 (.f64 -1/2 (+.f64 (.f64 -1 (log.f64 (/.f64 -1 n))) (log.f64 (*.f64 -2 (PI.f64))))))
(pow.f64 (exp.f64 -1/2) (+.f64 (log.f64 n) (log.f64 (*.f64 2 (PI.f64)))))
(.f64 (pow.f64 n -1/2) (pow.f64 (.f64 2 (PI.f64)) -1/2))
(pow.f64 (.f64 2 (.f64 n (PI.f64))) -1/2)
(exp.f64 (.f64 -1/2 (+.f64 (.f64 -1 (log.f64 (/.f64 -1 n))) (log.f64 (*.f64 -2 (PI.f64))))))
(pow.f64 (exp.f64 -1/2) (+.f64 (log.f64 n) (log.f64 (*.f64 2 (PI.f64)))))
(.f64 (pow.f64 n -1/2) (pow.f64 (.f64 2 (PI.f64)) -1/2))
(pow.f64 (.f64 2 (.f64 n (PI.f64))) -1/2)

localize38.0ms (0.4%)

Local error

Found 8 expressions with local error:

New	Error	Program
	3.2b	(exp.f64 (.f64 (log.f64 (/.f64 (pow.f64 (.f64 n (*.f64 2 (PI.f64))) (-.f64 1 k)) k)) 1/2))
	0.4b	(pow.f64 (.f64 n (.f64 2 (PI.f64))) (-.f64 1 k))
	0.2b	(.f64 n (.f64 2 (PI.f64)))
	0.1b	(/.f64 (pow.f64 (.f64 n (.f64 2 (PI.f64))) (-.f64 1 k)) k)
	0.2b	(.f64 n (.f64 2 (PI.f64)))
	0.4b	(pow.f64 (.f64 n (.f64 2 (PI.f64))) (-.f64 1 k))
✓	3.2b	(exp.f64 (.f64 (log.f64 (/.f64 (pow.f64 (.f64 n (*.f64 2 (PI.f64))) (-.f64 1 k)) k)) 1/2))
✓	9.4b	(log.f64 (/.f64 (pow.f64 (.f64 n (.f64 2 (PI.f64))) (-.f64 1 k)) k))

Compiler

Compiled 80 to 55 computations (31.3% saved)

series171.0ms (1.8%)

Counts

2 → 36

Calls

12 calls:

Time	Variable		Point	Expression
87.0ms	n	@	-inf	(log.f64 (/.f64 (pow.f64 (.f64 n (.f64 2 (PI.f64))) (-.f64 1 k)) k))
21.0ms	n	@	0	(log.f64 (/.f64 (pow.f64 (.f64 n (.f64 2 (PI.f64))) (-.f64 1 k)) k))
20.0ms	n	@	inf	(log.f64 (/.f64 (pow.f64 (.f64 n (.f64 2 (PI.f64))) (-.f64 1 k)) k))
18.0ms	k	@	inf	(log.f64 (/.f64 (pow.f64 (.f64 n (.f64 2 (PI.f64))) (-.f64 1 k)) k))
17.0ms	k	@	-inf	(log.f64 (/.f64 (pow.f64 (.f64 n (.f64 2 (PI.f64))) (-.f64 1 k)) k))

rewrite81.0ms (0.9%)

Algorithm

1×	batch-egg-rewrite

Rules

769×	`log-prod_binary64`
393×	`pow2_binary64`
267×	`pow1/3_binary64`
264×	`expm1-udef_binary64`
263×	`log1p-udef_binary64`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	15	39
1	314	38
2	3951	38

Stop Event

1×	node limit

Counts

2 → 135

Calls

Call 1

Inputs
(log.f64 (/.f64 (pow.f64 (.f64 n (.f64 2 (PI.f64))) (-.f64 1 k)) k))
(exp.f64 (.f64 (log.f64 (/.f64 (pow.f64 (.f64 n (*.f64 2 (PI.f64))) (-.f64 1 k)) k)) 1/2))

Outputs

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(PI.f64) n)) (-.f64 1 k)) k) 1/2)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (sqrt.f64 (/.f64 (pow.f64 (*.f64 2 (*.f64 (PI.f64) n)) (-.f64 1 k)) k)) 1)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (exp.f64 1/2) (log.f64 (/.f64 (pow.f64 (*.f64 2 (*.f64 (PI.f64) n)) (-.f64 1 k)) k)))))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (E.f64) (log.f64 (sqrt.f64 (/.f64 (pow.f64 (*.f64 2 (*.f64 (PI.f64) n)) (-.f64 1 k)) k))))))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (pow.f64 (sqrt.f64 (/.f64 (pow.f64 (*.f64 2 (*.f64 (PI.f64) n)) (-.f64 1 k)) k)) 3) 1/3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (cbrt.f64 (sqrt.f64 (/.f64 (pow.f64 (*.f64 2 (*.f64 (PI.f64) n)) (-.f64 1 k)) k))) 3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (pow.f64 (/.f64 (pow.f64 (*.f64 2 (*.f64 (PI.f64) n)) (-.f64 1 k)) k) 1/4) 2)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (exp.f64 (sqrt.f64 (log.f64 (sqrt.f64 (/.f64 (pow.f64 (*.f64 2 (*.f64 (PI.f64) n)) (-.f64 1 k)) k))))) (sqrt.f64 (log.f64 (sqrt.f64 (/.f64 (pow.f64 (*.f64 2 (*.f64 (PI.f64) n)) (-.f64 1 k)) k)))))))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (exp.f64 (cbrt.f64 (pow.f64 (log.f64 (sqrt.f64 (/.f64 (pow.f64 (*.f64 2 (*.f64 (PI.f64) n)) (-.f64 1 k)) k))) 2))) (cbrt.f64 (log.f64 (sqrt.f64 (/.f64 (pow.f64 (*.f64 2 (*.f64 (PI.f64) n)) (-.f64 1 k)) k)))))))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (sqrt.f64 (/.f64 k (pow.f64 (*.f64 2 (*.f64 (PI.f64) n)) (-.f64 1 k)))) -1)))) (#(struct:change #<rule egg-rr> (2) ((x sqrt.f64 (/.f64 (pow.f64 (*.f64 2 (*.f64 (PI.f64) n)) (-.f64 1 k)) k))))) (#(struct:change #<rule egg-rr> (2) ((x fabs.f64 (sqrt.f64 (/.f64 (pow.f64 (*.f64 2 (*.f64 (PI.f64) n)) (-.f64 1 k)) k)))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (exp.f64 (sqrt.f64 (/.f64 (pow.f64 (*.f64 2 (*.f64 (PI.f64) n)) (-.f64 1 k)) k))))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (+.f64 1 (expm1.f64 (sqrt.f64 (/.f64 (pow.f64 (*.f64 2 (*.f64 (PI.f64) n)) (-.f64 1 k)) k)))))))) (#(struct:change #<rule egg-rr> (2) ((x cbrt.f64 (pow.f64 (sqrt.f64 (/.f64 (pow.f64 (*.f64 2 (*.f64 (PI.f64) n)) (-.f64 1 k)) k)) 3))))) (#(struct:change #<rule egg-rr> (2) ((x expm1.f64 (log1p.f64 (sqrt.f64 (/.f64 (pow.f64 (*.f64 2 (*.f64 (PI.f64) n)) (-.f64 1 k)) k))))))) (#(struct:change #<rule egg-rr> (2) ((x log1p.f64 (expm1.f64 (sqrt.f64 (/.f64 (pow.f64 (*.f64 2 (*.f64 (PI.f64) n)) (-.f64 1 k)) k))))))))

simplify49.0ms (0.5%)

Algorithm

1×	egg-herbie

Rules

652×	`cancel-sign-sub-inv_binary64`
432×	`fma-def_binary64`
424×	`fma-neg_binary64`
382×	`associate-l_binary64`
337×	`associate-r_binary64`

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	83	927
1	249	834
2	896	772
3	5465	732

Stop Event

1×	node limit

Counts

171 → 153

Calls

Call 1

Inputs
(log.f64 (/.f64 (exp.f64 (.f64 (-.f64 1 k) (+.f64 (log.f64 n) (log.f64 (.f64 2 (PI.f64)))))) k))
(log.f64 (/.f64 (exp.f64 (.f64 (-.f64 1 k) (+.f64 (log.f64 n) (log.f64 (.f64 2 (PI.f64)))))) k))
(log.f64 (/.f64 (exp.f64 (.f64 (-.f64 1 k) (+.f64 (log.f64 n) (log.f64 (.f64 2 (PI.f64)))))) k))
(log.f64 (/.f64 (exp.f64 (.f64 (-.f64 1 k) (+.f64 (log.f64 n) (log.f64 (.f64 2 (PI.f64)))))) k))
(log.f64 (/.f64 (exp.f64 (.f64 (-.f64 1 k) (+.f64 (.f64 -1 (log.f64 (/.f64 1 n))) (log.f64 (*.f64 2 (PI.f64)))))) k))
(log.f64 (/.f64 (exp.f64 (.f64 (-.f64 1 k) (+.f64 (.f64 -1 (log.f64 (/.f64 1 n))) (log.f64 (*.f64 2 (PI.f64)))))) k))
(log.f64 (/.f64 (exp.f64 (.f64 (-.f64 1 k) (+.f64 (.f64 -1 (log.f64 (/.f64 1 n))) (log.f64 (*.f64 2 (PI.f64)))))) k))
(log.f64 (/.f64 (exp.f64 (.f64 (-.f64 1 k) (+.f64 (.f64 -1 (log.f64 (/.f64 1 n))) (log.f64 (*.f64 2 (PI.f64)))))) k))
(log.f64 (/.f64 (exp.f64 (.f64 (-.f64 1 k) (+.f64 (.f64 -1 (log.f64 (/.f64 -1 n))) (log.f64 (*.f64 -2 (PI.f64)))))) k))
(log.f64 (/.f64 (exp.f64 (.f64 (-.f64 1 k) (+.f64 (.f64 -1 (log.f64 (/.f64 -1 n))) (log.f64 (*.f64 -2 (PI.f64)))))) k))
(log.f64 (/.f64 (exp.f64 (.f64 (-.f64 1 k) (+.f64 (.f64 -1 (log.f64 (/.f64 -1 n))) (log.f64 (*.f64 -2 (PI.f64)))))) k))
(log.f64 (/.f64 (exp.f64 (.f64 (-.f64 1 k) (+.f64 (.f64 -1 (log.f64 (/.f64 -1 n))) (log.f64 (*.f64 -2 (PI.f64)))))) k))
(+.f64 (.f64 -1 (log.f64 k)) (log.f64 (.f64 2 (*.f64 n (PI.f64)))))
(+.f64 (.f64 -1 (log.f64 k)) (+.f64 (.f64 -1 (.f64 k (log.f64 (.f64 2 (.f64 n (PI.f64)))))) (log.f64 (.f64 2 (*.f64 n (PI.f64))))))
(+.f64 (.f64 -1 (log.f64 k)) (+.f64 (.f64 1/2 (.f64 (pow.f64 k 2) (+.f64 (.f64 -1 (pow.f64 (log.f64 (.f64 2 (.f64 n (PI.f64)))) 2)) (pow.f64 (log.f64 (.f64 2 (.f64 n (PI.f64)))) 2)))) (+.f64 (.f64 -1 (.f64 k (log.f64 (.f64 2 (.f64 n (PI.f64)))))) (log.f64 (.f64 2 (.f64 n (PI.f64)))))))
(+.f64 (.f64 -1 (log.f64 k)) (+.f64 (.f64 1/6 (.f64 (pow.f64 k 3) (+.f64 (.f64 -2 (pow.f64 (log.f64 (.f64 2 (.f64 n (PI.f64)))) 3)) (+.f64 (.f64 3 (pow.f64 (log.f64 (.f64 2 (.f64 n (PI.f64)))) 3)) (.f64 -1 (pow.f64 (log.f64 (.f64 2 (.f64 n (PI.f64)))) 3)))))) (+.f64 (.f64 1/2 (.f64 (pow.f64 k 2) (+.f64 (.f64 -1 (pow.f64 (log.f64 (.f64 2 (.f64 n (PI.f64)))) 2)) (pow.f64 (log.f64 (.f64 2 (.f64 n (PI.f64)))) 2)))) (+.f64 (.f64 -1 (.f64 k (log.f64 (.f64 2 (.f64 n (PI.f64)))))) (log.f64 (.f64 2 (*.f64 n (PI.f64))))))))
(+.f64 (log.f64 (pow.f64 (.f64 2 (.f64 n (PI.f64))) (-.f64 1 k))) (log.f64 (/.f64 1 k)))
(+.f64 (log.f64 (pow.f64 (.f64 2 (.f64 n (PI.f64))) (-.f64 1 k))) (log.f64 (/.f64 1 k)))
(+.f64 (log.f64 (pow.f64 (.f64 2 (.f64 n (PI.f64))) (-.f64 1 k))) (log.f64 (/.f64 1 k)))
(+.f64 (log.f64 (pow.f64 (.f64 2 (.f64 n (PI.f64))) (-.f64 1 k))) (log.f64 (/.f64 1 k)))
(+.f64 (log.f64 (.f64 -1 (pow.f64 (.f64 2 (.f64 n (PI.f64))) (+.f64 1 (.f64 -1 k))))) (log.f64 (/.f64 -1 k)))
(+.f64 (log.f64 (.f64 -1 (pow.f64 (.f64 2 (.f64 n (PI.f64))) (+.f64 1 (.f64 -1 k))))) (log.f64 (/.f64 -1 k)))
(+.f64 (log.f64 (.f64 -1 (pow.f64 (.f64 2 (.f64 n (PI.f64))) (+.f64 1 (.f64 -1 k))))) (log.f64 (/.f64 -1 k)))
(+.f64 (log.f64 (.f64 -1 (pow.f64 (.f64 2 (.f64 n (PI.f64))) (+.f64 1 (.f64 -1 k))))) (log.f64 (/.f64 -1 k)))
(sqrt.f64 (/.f64 (exp.f64 (.f64 (-.f64 1 k) (+.f64 (log.f64 n) (log.f64 (.f64 2 (PI.f64)))))) k))
(sqrt.f64 (/.f64 (exp.f64 (.f64 (-.f64 1 k) (+.f64 (log.f64 n) (log.f64 (.f64 2 (PI.f64)))))) k))
(sqrt.f64 (/.f64 (exp.f64 (.f64 (-.f64 1 k) (+.f64 (log.f64 n) (log.f64 (.f64 2 (PI.f64)))))) k))
(sqrt.f64 (/.f64 (exp.f64 (.f64 (-.f64 1 k) (+.f64 (log.f64 n) (log.f64 (.f64 2 (PI.f64)))))) k))
(sqrt.f64 (/.f64 (exp.f64 (.f64 (-.f64 1 k) (+.f64 (.f64 -1 (log.f64 (/.f64 1 n))) (log.f64 (*.f64 2 (PI.f64)))))) k))
(sqrt.f64 (/.f64 (exp.f64 (.f64 (-.f64 1 k) (+.f64 (.f64 -1 (log.f64 (/.f64 1 n))) (log.f64 (*.f64 2 (PI.f64)))))) k))
(sqrt.f64 (/.f64 (exp.f64 (.f64 (-.f64 1 k) (+.f64 (.f64 -1 (log.f64 (/.f64 1 n))) (log.f64 (*.f64 2 (PI.f64)))))) k))
(sqrt.f64 (/.f64 (exp.f64 (.f64 (-.f64 1 k) (+.f64 (.f64 -1 (log.f64 (/.f64 1 n))) (log.f64 (*.f64 2 (PI.f64)))))) k))
(sqrt.f64 (/.f64 (exp.f64 (.f64 (-.f64 1 k) (+.f64 (.f64 -1 (log.f64 (/.f64 -1 n))) (log.f64 (*.f64 -2 (PI.f64)))))) k))
(sqrt.f64 (/.f64 (exp.f64 (.f64 (-.f64 1 k) (+.f64 (.f64 -1 (log.f64 (/.f64 -1 n))) (log.f64 (*.f64 -2 (PI.f64)))))) k))
(sqrt.f64 (/.f64 (exp.f64 (.f64 (-.f64 1 k) (+.f64 (.f64 -1 (log.f64 (/.f64 -1 n))) (log.f64 (*.f64 -2 (PI.f64)))))) k))
(sqrt.f64 (/.f64 (exp.f64 (.f64 (-.f64 1 k) (+.f64 (.f64 -1 (log.f64 (/.f64 -1 n))) (log.f64 (*.f64 -2 (PI.f64)))))) k))

Outputs
(log.f64 (/.f64 (exp.f64 (.f64 (-.f64 1 k) (+.f64 (log.f64 n) (log.f64 (.f64 2 (PI.f64)))))) k))
(log.f64 (/.f64 (pow.f64 (exp.f64 (-.f64 1 k)) (+.f64 (log.f64 n) (log.f64 (*.f64 2 (PI.f64))))) k))
(-.f64 (.f64 (-.f64 1 k) (log.f64 (.f64 2 (*.f64 n (PI.f64))))) (log.f64 k))
(log.f64 (/.f64 (pow.f64 (.f64 2 (.f64 n (PI.f64))) (-.f64 1 k)) k))
(log.f64 (/.f64 (exp.f64 (.f64 (-.f64 1 k) (+.f64 (log.f64 n) (log.f64 (.f64 2 (PI.f64)))))) k))
(log.f64 (/.f64 (pow.f64 (exp.f64 (-.f64 1 k)) (+.f64 (log.f64 n) (log.f64 (*.f64 2 (PI.f64))))) k))
(-.f64 (.f64 (-.f64 1 k) (log.f64 (.f64 2 (*.f64 n (PI.f64))))) (log.f64 k))
(log.f64 (/.f64 (pow.f64 (.f64 2 (.f64 n (PI.f64))) (-.f64 1 k)) k))
(log.f64 (/.f64 (exp.f64 (.f64 (-.f64 1 k) (+.f64 (log.f64 n) (log.f64 (.f64 2 (PI.f64)))))) k))
(log.f64 (/.f64 (pow.f64 (exp.f64 (-.f64 1 k)) (+.f64 (log.f64 n) (log.f64 (*.f64 2 (PI.f64))))) k))
(-.f64 (.f64 (-.f64 1 k) (log.f64 (.f64 2 (*.f64 n (PI.f64))))) (log.f64 k))
(log.f64 (/.f64 (pow.f64 (.f64 2 (.f64 n (PI.f64))) (-.f64 1 k)) k))
(log.f64 (/.f64 (exp.f64 (.f64 (-.f64 1 k) (+.f64 (log.f64 n) (log.f64 (.f64 2 (PI.f64)))))) k))
(log.f64 (/.f64 (pow.f64 (exp.f64 (-.f64 1 k)) (+.f64 (log.f64 n) (log.f64 (*.f64 2 (PI.f64))))) k))
(-.f64 (.f64 (-.f64 1 k) (log.f64 (.f64 2 (*.f64 n (PI.f64))))) (log.f64 k))
(log.f64 (/.f64 (pow.f64 (.f64 2 (.f64 n (PI.f64))) (-.f64 1 k)) k))
(log.f64 (/.f64 (exp.f64 (.f64 (-.f64 1 k) (+.f64 (.f64 -1 (log.f64 (/.f64 1 n))) (log.f64 (*.f64 2 (PI.f64)))))) k))
(log.f64 (/.f64 (pow.f64 (exp.f64 (-.f64 1 k)) (+.f64 (log.f64 n) (log.f64 (*.f64 2 (PI.f64))))) k))
(-.f64 (.f64 (-.f64 1 k) (log.f64 (.f64 2 (*.f64 n (PI.f64))))) (log.f64 k))
(log.f64 (/.f64 (pow.f64 (.f64 2 (.f64 n (PI.f64))) (-.f64 1 k)) k))
(log.f64 (/.f64 (exp.f64 (.f64 (-.f64 1 k) (+.f64 (.f64 -1 (log.f64 (/.f64 1 n))) (log.f64 (*.f64 2 (PI.f64)))))) k))
(log.f64 (/.f64 (pow.f64 (exp.f64 (-.f64 1 k)) (+.f64 (log.f64 n) (log.f64 (*.f64 2 (PI.f64))))) k))
(-.f64 (.f64 (-.f64 1 k) (log.f64 (.f64 2 (*.f64 n (PI.f64))))) (log.f64 k))
(log.f64 (/.f64 (pow.f64 (.f64 2 (.f64 n (PI.f64))) (-.f64 1 k)) k))
(log.f64 (/.f64 (exp.f64 (.f64 (-.f64 1 k) (+.f64 (.f64 -1 (log.f64 (/.f64 1 n))) (log.f64 (*.f64 2 (PI.f64)))))) k))
(log.f64 (/.f64 (pow.f64 (exp.f64 (-.f64 1 k)) (+.f64 (log.f64 n) (log.f64 (*.f64 2 (PI.f64))))) k))
(-.f64 (.f64 (-.f64 1 k) (log.f64 (.f64 2 (*.f64 n (PI.f64))))) (log.f64 k))
(log.f64 (/.f64 (pow.f64 (.f64 2 (.f64 n (PI.f64))) (-.f64 1 k)) k))
(log.f64 (/.f64 (exp.f64 (.f64 (-.f64 1 k) (+.f64 (.f64 -1 (log.f64 (/.f64 1 n))) (log.f64 (*.f64 2 (PI.f64)))))) k))
(log.f64 (/.f64 (pow.f64 (exp.f64 (-.f64 1 k)) (+.f64 (log.f64 n) (log.f64 (*.f64 2 (PI.f64))))) k))
(-.f64 (.f64 (-.f64 1 k) (log.f64 (.f64 2 (*.f64 n (PI.f64))))) (log.f64 k))
(log.f64 (/.f64 (pow.f64 (.f64 2 (.f64 n (PI.f64))) (-.f64 1 k)) k))
(log.f64 (/.f64 (exp.f64 (.f64 (-.f64 1 k) (+.f64 (.f64 -1 (log.f64 (/.f64 -1 n))) (log.f64 (*.f64 -2 (PI.f64)))))) k))
(log.f64 (/.f64 (pow.f64 (exp.f64 (-.f64 1 k)) (fma.f64 -1 (log.f64 (/.f64 -1 n)) (log.f64 (*.f64 (PI.f64) -2)))) k))
(-.f64 (.f64 (-.f64 1 k) (-.f64 (log.f64 (.f64 (PI.f64) -2)) (log.f64 (/.f64 -1 n)))) (log.f64 k))
(log.f64 (/.f64 (pow.f64 (*.f64 -2 (/.f64 (PI.f64) (/.f64 -1 n))) (-.f64 1 k)) k))
(log.f64 (/.f64 (exp.f64 (.f64 (-.f64 1 k) (+.f64 (.f64 -1 (log.f64 (/.f64 -1 n))) (log.f64 (*.f64 -2 (PI.f64)))))) k))
(log.f64 (/.f64 (pow.f64 (exp.f64 (-.f64 1 k)) (fma.f64 -1 (log.f64 (/.f64 -1 n)) (log.f64 (*.f64 (PI.f64) -2)))) k))
(-.f64 (.f64 (-.f64 1 k) (-.f64 (log.f64 (.f64 (PI.f64) -2)) (log.f64 (/.f64 -1 n)))) (log.f64 k))
(log.f64 (/.f64 (pow.f64 (*.f64 -2 (/.f64 (PI.f64) (/.f64 -1 n))) (-.f64 1 k)) k))
(log.f64 (/.f64 (exp.f64 (.f64 (-.f64 1 k) (+.f64 (.f64 -1 (log.f64 (/.f64 -1 n))) (log.f64 (*.f64 -2 (PI.f64)))))) k))
(log.f64 (/.f64 (pow.f64 (exp.f64 (-.f64 1 k)) (fma.f64 -1 (log.f64 (/.f64 -1 n)) (log.f64 (*.f64 (PI.f64) -2)))) k))
(-.f64 (.f64 (-.f64 1 k) (-.f64 (log.f64 (.f64 (PI.f64) -2)) (log.f64 (/.f64 -1 n)))) (log.f64 k))
(log.f64 (/.f64 (pow.f64 (*.f64 -2 (/.f64 (PI.f64) (/.f64 -1 n))) (-.f64 1 k)) k))
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(log.f64 (/.f64 (pow.f64 (exp.f64 (-.f64 1 k)) (fma.f64 -1 (log.f64 (/.f64 -1 n)) (log.f64 (*.f64 (PI.f64) -2)))) k))
(-.f64 (.f64 (-.f64 1 k) (-.f64 (log.f64 (.f64 (PI.f64) -2)) (log.f64 (/.f64 -1 n)))) (log.f64 k))
(log.f64 (/.f64 (pow.f64 (*.f64 -2 (/.f64 (PI.f64) (/.f64 -1 n))) (-.f64 1 k)) k))
(+.f64 (.f64 -1 (log.f64 k)) (log.f64 (.f64 2 (*.f64 n (PI.f64)))))
(fma.f64 -1 (log.f64 k) (log.f64 (.f64 2 (.f64 n (PI.f64)))))
(-.f64 (log.f64 (.f64 2 (.f64 n (PI.f64)))) (log.f64 k))
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(log.f64 (/.f64 (pow.f64 (exp.f64 (-.f64 1 k)) (+.f64 (log.f64 n) (log.f64 (*.f64 2 (PI.f64))))) k))
(-.f64 (.f64 (-.f64 1 k) (log.f64 (.f64 2 (*.f64 n (PI.f64))))) (log.f64 k))
(log.f64 (/.f64 (pow.f64 (.f64 2 (.f64 n (PI.f64))) (-.f64 1 k)) k))
(+.f64 (.f64 -1 (log.f64 k)) (+.f64 (.f64 1/2 (.f64 (pow.f64 k 2) (+.f64 (.f64 -1 (pow.f64 (log.f64 (.f64 2 (.f64 n (PI.f64)))) 2)) (pow.f64 (log.f64 (.f64 2 (.f64 n (PI.f64)))) 2)))) (+.f64 (.f64 -1 (.f64 k (log.f64 (.f64 2 (.f64 n (PI.f64)))))) (log.f64 (.f64 2 (.f64 n (PI.f64)))))))
(log.f64 (/.f64 (pow.f64 (exp.f64 (-.f64 1 k)) (+.f64 (log.f64 n) (log.f64 (*.f64 2 (PI.f64))))) k))
(-.f64 (.f64 (-.f64 1 k) (log.f64 (.f64 2 (*.f64 n (PI.f64))))) (log.f64 k))
(log.f64 (/.f64 (pow.f64 (.f64 2 (.f64 n (PI.f64))) (-.f64 1 k)) k))
(+.f64 (.f64 -1 (log.f64 k)) (+.f64 (.f64 1/6 (.f64 (pow.f64 k 3) (+.f64 (.f64 -2 (pow.f64 (log.f64 (.f64 2 (.f64 n (PI.f64)))) 3)) (+.f64 (.f64 3 (pow.f64 (log.f64 (.f64 2 (.f64 n (PI.f64)))) 3)) (.f64 -1 (pow.f64 (log.f64 (.f64 2 (.f64 n (PI.f64)))) 3)))))) (+.f64 (.f64 1/2 (.f64 (pow.f64 k 2) (+.f64 (.f64 -1 (pow.f64 (log.f64 (.f64 2 (.f64 n (PI.f64)))) 2)) (pow.f64 (log.f64 (.f64 2 (.f64 n (PI.f64)))) 2)))) (+.f64 (.f64 -1 (.f64 k (log.f64 (.f64 2 (.f64 n (PI.f64)))))) (log.f64 (.f64 2 (*.f64 n (PI.f64))))))))
(log.f64 (/.f64 (pow.f64 (exp.f64 (-.f64 1 k)) (+.f64 (log.f64 n) (log.f64 (*.f64 2 (PI.f64))))) k))
(-.f64 (.f64 (-.f64 1 k) (log.f64 (.f64 2 (*.f64 n (PI.f64))))) (log.f64 k))
(log.f64 (/.f64 (pow.f64 (.f64 2 (.f64 n (PI.f64))) (-.f64 1 k)) k))
(+.f64 (log.f64 (pow.f64 (.f64 2 (.f64 n (PI.f64))) (-.f64 1 k))) (log.f64 (/.f64 1 k)))
(log.f64 (/.f64 (pow.f64 (exp.f64 (-.f64 1 k)) (+.f64 (log.f64 n) (log.f64 (*.f64 2 (PI.f64))))) k))
(-.f64 (.f64 (-.f64 1 k) (log.f64 (.f64 2 (*.f64 n (PI.f64))))) (log.f64 k))
(log.f64 (/.f64 (pow.f64 (.f64 2 (.f64 n (PI.f64))) (-.f64 1 k)) k))
(+.f64 (log.f64 (pow.f64 (.f64 2 (.f64 n (PI.f64))) (-.f64 1 k))) (log.f64 (/.f64 1 k)))
(log.f64 (/.f64 (pow.f64 (exp.f64 (-.f64 1 k)) (+.f64 (log.f64 n) (log.f64 (*.f64 2 (PI.f64))))) k))
(-.f64 (.f64 (-.f64 1 k) (log.f64 (.f64 2 (*.f64 n (PI.f64))))) (log.f64 k))
(log.f64 (/.f64 (pow.f64 (.f64 2 (.f64 n (PI.f64))) (-.f64 1 k)) k))
(+.f64 (log.f64 (pow.f64 (.f64 2 (.f64 n (PI.f64))) (-.f64 1 k))) (log.f64 (/.f64 1 k)))
(log.f64 (/.f64 (pow.f64 (exp.f64 (-.f64 1 k)) (+.f64 (log.f64 n) (log.f64 (*.f64 2 (PI.f64))))) k))
(-.f64 (.f64 (-.f64 1 k) (log.f64 (.f64 2 (*.f64 n (PI.f64))))) (log.f64 k))
(log.f64 (/.f64 (pow.f64 (.f64 2 (.f64 n (PI.f64))) (-.f64 1 k)) k))
(+.f64 (log.f64 (pow.f64 (.f64 2 (.f64 n (PI.f64))) (-.f64 1 k))) (log.f64 (/.f64 1 k)))
(log.f64 (/.f64 (pow.f64 (exp.f64 (-.f64 1 k)) (+.f64 (log.f64 n) (log.f64 (*.f64 2 (PI.f64))))) k))
(-.f64 (.f64 (-.f64 1 k) (log.f64 (.f64 2 (*.f64 n (PI.f64))))) (log.f64 k))
(log.f64 (/.f64 (pow.f64 (.f64 2 (.f64 n (PI.f64))) (-.f64 1 k)) k))
(+.f64 (log.f64 (.f64 -1 (pow.f64 (.f64 2 (.f64 n (PI.f64))) (+.f64 1 (.f64 -1 k))))) (log.f64 (/.f64 -1 k)))
(+.f64 (log.f64 (neg.f64 (pow.f64 (.f64 2 (.f64 n (PI.f64))) (-.f64 1 k)))) (log.f64 (/.f64 -1 k)))
(+.f64 (log.f64 (.f64 -1 (pow.f64 (.f64 2 (.f64 n (PI.f64))) (+.f64 1 (.f64 -1 k))))) (log.f64 (/.f64 -1 k)))
(+.f64 (log.f64 (neg.f64 (pow.f64 (.f64 2 (.f64 n (PI.f64))) (-.f64 1 k)))) (log.f64 (/.f64 -1 k)))
(+.f64 (log.f64 (.f64 -1 (pow.f64 (.f64 2 (.f64 n (PI.f64))) (+.f64 1 (.f64 -1 k))))) (log.f64 (/.f64 -1 k)))
(+.f64 (log.f64 (neg.f64 (pow.f64 (.f64 2 (.f64 n (PI.f64))) (-.f64 1 k)))) (log.f64 (/.f64 -1 k)))
(+.f64 (log.f64 (.f64 -1 (pow.f64 (.f64 2 (.f64 n (PI.f64))) (+.f64 1 (.f64 -1 k))))) (log.f64 (/.f64 -1 k)))
(+.f64 (log.f64 (neg.f64 (pow.f64 (.f64 2 (.f64 n (PI.f64))) (-.f64 1 k)))) (log.f64 (/.f64 -1 k)))
(sqrt.f64 (/.f64 (exp.f64 (.f64 (-.f64 1 k) (+.f64 (log.f64 n) (log.f64 (.f64 2 (PI.f64)))))) k))
(sqrt.f64 (/.f64 (pow.f64 (exp.f64 (-.f64 1 k)) (+.f64 (log.f64 n) (log.f64 (*.f64 2 (PI.f64))))) k))
(sqrt.f64 (/.f64 (pow.f64 (exp.f64 (-.f64 1 k)) (log.f64 (.f64 2 (.f64 n (PI.f64))))) k))
(sqrt.f64 (/.f64 (pow.f64 (.f64 2 (.f64 n (PI.f64))) (-.f64 1 k)) k))
(sqrt.f64 (/.f64 (exp.f64 (.f64 (-.f64 1 k) (+.f64 (log.f64 n) (log.f64 (.f64 2 (PI.f64)))))) k))
(sqrt.f64 (/.f64 (pow.f64 (exp.f64 (-.f64 1 k)) (+.f64 (log.f64 n) (log.f64 (*.f64 2 (PI.f64))))) k))
(sqrt.f64 (/.f64 (pow.f64 (exp.f64 (-.f64 1 k)) (log.f64 (.f64 2 (.f64 n (PI.f64))))) k))
(sqrt.f64 (/.f64 (pow.f64 (.f64 2 (.f64 n (PI.f64))) (-.f64 1 k)) k))
(sqrt.f64 (/.f64 (exp.f64 (.f64 (-.f64 1 k) (+.f64 (log.f64 n) (log.f64 (.f64 2 (PI.f64)))))) k))
(sqrt.f64 (/.f64 (pow.f64 (exp.f64 (-.f64 1 k)) (+.f64 (log.f64 n) (log.f64 (*.f64 2 (PI.f64))))) k))
(sqrt.f64 (/.f64 (pow.f64 (exp.f64 (-.f64 1 k)) (log.f64 (.f64 2 (.f64 n (PI.f64))))) k))
(sqrt.f64 (/.f64 (pow.f64 (.f64 2 (.f64 n (PI.f64))) (-.f64 1 k)) k))
(sqrt.f64 (/.f64 (exp.f64 (.f64 (-.f64 1 k) (+.f64 (log.f64 n) (log.f64 (.f64 2 (PI.f64)))))) k))
(sqrt.f64 (/.f64 (pow.f64 (exp.f64 (-.f64 1 k)) (+.f64 (log.f64 n) (log.f64 (*.f64 2 (PI.f64))))) k))
(sqrt.f64 (/.f64 (pow.f64 (exp.f64 (-.f64 1 k)) (log.f64 (.f64 2 (.f64 n (PI.f64))))) k))
(sqrt.f64 (/.f64 (pow.f64 (.f64 2 (.f64 n (PI.f64))) (-.f64 1 k)) k))
(sqrt.f64 (/.f64 (exp.f64 (.f64 (-.f64 1 k) (+.f64 (.f64 -1 (log.f64 (/.f64 1 n))) (log.f64 (*.f64 2 (PI.f64)))))) k))
(sqrt.f64 (/.f64 (pow.f64 (exp.f64 (-.f64 1 k)) (+.f64 (log.f64 n) (log.f64 (*.f64 2 (PI.f64))))) k))
(sqrt.f64 (/.f64 (pow.f64 (exp.f64 (-.f64 1 k)) (log.f64 (.f64 2 (.f64 n (PI.f64))))) k))
(sqrt.f64 (/.f64 (pow.f64 (.f64 2 (.f64 n (PI.f64))) (-.f64 1 k)) k))
(sqrt.f64 (/.f64 (exp.f64 (.f64 (-.f64 1 k) (+.f64 (.f64 -1 (log.f64 (/.f64 1 n))) (log.f64 (*.f64 2 (PI.f64)))))) k))
(sqrt.f64 (/.f64 (pow.f64 (exp.f64 (-.f64 1 k)) (+.f64 (log.f64 n) (log.f64 (*.f64 2 (PI.f64))))) k))
(sqrt.f64 (/.f64 (pow.f64 (exp.f64 (-.f64 1 k)) (log.f64 (.f64 2 (.f64 n (PI.f64))))) k))
(sqrt.f64 (/.f64 (pow.f64 (.f64 2 (.f64 n (PI.f64))) (-.f64 1 k)) k))
(sqrt.f64 (/.f64 (exp.f64 (.f64 (-.f64 1 k) (+.f64 (.f64 -1 (log.f64 (/.f64 1 n))) (log.f64 (*.f64 2 (PI.f64)))))) k))
(sqrt.f64 (/.f64 (pow.f64 (exp.f64 (-.f64 1 k)) (+.f64 (log.f64 n) (log.f64 (*.f64 2 (PI.f64))))) k))
(sqrt.f64 (/.f64 (pow.f64 (exp.f64 (-.f64 1 k)) (log.f64 (.f64 2 (.f64 n (PI.f64))))) k))
(sqrt.f64 (/.f64 (pow.f64 (.f64 2 (.f64 n (PI.f64))) (-.f64 1 k)) k))
(sqrt.f64 (/.f64 (exp.f64 (.f64 (-.f64 1 k) (+.f64 (.f64 -1 (log.f64 (/.f64 1 n))) (log.f64 (*.f64 2 (PI.f64)))))) k))
(sqrt.f64 (/.f64 (pow.f64 (exp.f64 (-.f64 1 k)) (+.f64 (log.f64 n) (log.f64 (*.f64 2 (PI.f64))))) k))
(sqrt.f64 (/.f64 (pow.f64 (exp.f64 (-.f64 1 k)) (log.f64 (.f64 2 (.f64 n (PI.f64))))) k))
(sqrt.f64 (/.f64 (pow.f64 (.f64 2 (.f64 n (PI.f64))) (-.f64 1 k)) k))
(sqrt.f64 (/.f64 (exp.f64 (.f64 (-.f64 1 k) (+.f64 (.f64 -1 (log.f64 (/.f64 -1 n))) (log.f64 (*.f64 -2 (PI.f64)))))) k))
(sqrt.f64 (/.f64 (pow.f64 (exp.f64 (-.f64 1 k)) (fma.f64 -1 (log.f64 (/.f64 -1 n)) (log.f64 (*.f64 (PI.f64) -2)))) k))
(sqrt.f64 (/.f64 (pow.f64 (exp.f64 (-.f64 1 k)) (-.f64 (log.f64 (*.f64 (PI.f64) -2)) (log.f64 (/.f64 -1 n)))) k))
(sqrt.f64 (/.f64 (pow.f64 (*.f64 -2 (/.f64 (PI.f64) (/.f64 -1 n))) (-.f64 1 k)) k))
(sqrt.f64 (/.f64 (exp.f64 (.f64 (-.f64 1 k) (+.f64 (.f64 -1 (log.f64 (/.f64 -1 n))) (log.f64 (*.f64 -2 (PI.f64)))))) k))
(sqrt.f64 (/.f64 (pow.f64 (exp.f64 (-.f64 1 k)) (fma.f64 -1 (log.f64 (/.f64 -1 n)) (log.f64 (*.f64 (PI.f64) -2)))) k))
(sqrt.f64 (/.f64 (pow.f64 (exp.f64 (-.f64 1 k)) (-.f64 (log.f64 (*.f64 (PI.f64) -2)) (log.f64 (/.f64 -1 n)))) k))
(sqrt.f64 (/.f64 (pow.f64 (*.f64 -2 (/.f64 (PI.f64) (/.f64 -1 n))) (-.f64 1 k)) k))
(sqrt.f64 (/.f64 (exp.f64 (.f64 (-.f64 1 k) (+.f64 (.f64 -1 (log.f64 (/.f64 -1 n))) (log.f64 (*.f64 -2 (PI.f64)))))) k))
(sqrt.f64 (/.f64 (pow.f64 (exp.f64 (-.f64 1 k)) (fma.f64 -1 (log.f64 (/.f64 -1 n)) (log.f64 (*.f64 (PI.f64) -2)))) k))
(sqrt.f64 (/.f64 (pow.f64 (exp.f64 (-.f64 1 k)) (-.f64 (log.f64 (*.f64 (PI.f64) -2)) (log.f64 (/.f64 -1 n)))) k))
(sqrt.f64 (/.f64 (pow.f64 (*.f64 -2 (/.f64 (PI.f64) (/.f64 -1 n))) (-.f64 1 k)) k))
(sqrt.f64 (/.f64 (exp.f64 (.f64 (-.f64 1 k) (+.f64 (.f64 -1 (log.f64 (/.f64 -1 n))) (log.f64 (*.f64 -2 (PI.f64)))))) k))
(sqrt.f64 (/.f64 (pow.f64 (exp.f64 (-.f64 1 k)) (fma.f64 -1 (log.f64 (/.f64 -1 n)) (log.f64 (*.f64 (PI.f64) -2)))) k))
(sqrt.f64 (/.f64 (pow.f64 (exp.f64 (-.f64 1 k)) (-.f64 (log.f64 (*.f64 (PI.f64) -2)) (log.f64 (/.f64 -1 n)))) k))
(sqrt.f64 (/.f64 (pow.f64 (*.f64 -2 (/.f64 (PI.f64) (/.f64 -1 n))) (-.f64 1 k)) k))

eval312.0ms (3.3%)

Compiler: Compiled 13835 to 9223 computations (33.3% saved)

prune140.0ms (1.5%)

Pruning

43 alts after pruning (36 fresh and 7 done)

	Pruned	Kept	Total
New	713	15	728
Fresh	11	21	32
Picked	0	1	1
Done	2	6	8
Total	726	43	769

Error

Counts

769 → 43

Alt Table

Click to see full alt table

Status	Error	Program
	13.7b	(sqrt.f64 (.f64 2 (.f64 (-.f64 (+.f64 1 (/.f64 (PI.f64) k)) 1) n)))
	9.2b	(pow.f64 (.f64 k (pow.f64 (.f64 n (*.f64 2 (PI.f64))) (-.f64 k 1))) -1/2)
	0.5b	(.f64 (sqrt.f64 (/.f64 1 k)) (pow.f64 (.f64 (*.f64 2 (PI.f64)) n) (/.f64 (-.f64 1 k) 2)))
	32.6b	(pow.f64 (*.f64 1/2 (/.f64 (/.f64 k n) (PI.f64))) -1/2)
	41.6b	(pow.f64 (pow.f64 (.f64 2 (.f64 (/.f64 (PI.f64) k) n)) 3/2) 1/3)
	24.1b	(/.f64 (pow.f64 (pow.f64 (.f64 (PI.f64) (.f64 2 n)) 1/4) 2) (sqrt.f64 k))
	24.0b	(.f64 (sqrt.f64 (.f64 2 (*.f64 n (PI.f64)))) (pow.f64 k -1/2))
	35.6b	(pow.f64 (pow.f64 (/.f64 2 (/.f64 (/.f64 k n) (PI.f64))) 1/6) 3)
	35.2b	(exp.f64 (.f64 (log.f64 (/.f64 (.f64 (PI.f64) 2) (/.f64 k n))) 1/2))
	24.0b	(.f64 (pow.f64 k -1/2) (.f64 (sqrt.f64 2) (sqrt.f64 (*.f64 n (PI.f64)))))
✓	33.3b	(sqrt.f64 (/.f64 (.f64 2 (.f64 n (PI.f64))) k))
	33.6b	(pow.f64 (cbrt.f64 (/.f64 2 (/.f64 (/.f64 k n) (PI.f64)))) 3/2)
	24.1b	(/.f64 (.f64 (sqrt.f64 2) (sqrt.f64 (.f64 n (PI.f64)))) (sqrt.f64 k))
✓	11.8b	(sqrt.f64 (/.f64 (exp.f64 (.f64 (-.f64 1 k) (log.f64 (.f64 n (*.f64 2 (PI.f64)))))) k))
	33.3b	(sqrt.f64 (.f64 2 (/.f64 1 (/.f64 k (.f64 (PI.f64) n)))))
	19.1b	(pow.f64 (pow.f64 (/.f64 (pow.f64 (.f64 n (.f64 2 (PI.f64))) (-.f64 1 k)) k) 3/2) 1/3)
	33.3b	(sqrt.f64 (*.f64 2 (/.f64 n (/.f64 k (PI.f64)))))
	33.3b	(sqrt.f64 (.f64 (/.f64 2 k) (.f64 n (PI.f64))))
	0.6b	(/.f64 1 (/.f64 (pow.f64 (.f64 2 (.f64 (PI.f64) n)) (*.f64 (-.f64 1 k) -1/2)) (pow.f64 k -1/2)))
	0.2b	(.f64 (pow.f64 k -1/2) (sqrt.f64 (.f64 (pow.f64 (*.f64 2 (PI.f64)) (-.f64 1 k)) (/.f64 n (pow.f64 n k)))))
	9.6b	(sqrt.f64 (/.f64 (/.f64 n (pow.f64 n k)) (/.f64 k (pow.f64 (*.f64 2 (PI.f64)) (-.f64 1 k)))))
	33.3b	(pow.f64 (/.f64 2 (/.f64 (/.f64 k n) (PI.f64))) 1/2)
	33.2b	(.f64 (sqrt.f64 (.f64 (/.f64 (PI.f64) k) n)) (sqrt.f64 2))
✓	11.7b	(exp.f64 (.f64 (log.f64 (/.f64 (pow.f64 (.f64 n (*.f64 2 (PI.f64))) (-.f64 1 k)) k)) 1/2))
✓	0.5b	(.f64 (pow.f64 k -1/2) (sqrt.f64 (pow.f64 (.f64 n (*.f64 2 (PI.f64))) (-.f64 1 k))))
✓	9.9b	(sqrt.f64 (/.f64 (pow.f64 (.f64 2 (.f64 (PI.f64) n)) (-.f64 1 k)) k))
	3.2b	(.f64 (exp.f64 (.f64 -1/2 (log.f64 k))) (pow.f64 (.f64 (.f64 2 (PI.f64)) n) (/.f64 (-.f64 1 k) 2)))
	24.1b	(/.f64 (.f64 (sqrt.f64 n) (sqrt.f64 (.f64 (PI.f64) 2))) (sqrt.f64 k))
✓	24.0b	(/.f64 (sqrt.f64 (.f64 n (.f64 (PI.f64) 2))) (sqrt.f64 k))
	9.6b	(sqrt.f64 (/.f64 (.f64 (pow.f64 (.f64 n (.f64 2 (PI.f64))) (neg.f64 k)) (.f64 n (*.f64 2 (PI.f64)))) k))
	9.9b	(sqrt.f64 (/.f64 1 (.f64 k (pow.f64 (.f64 n (*.f64 2 (PI.f64))) (-.f64 k 1)))))
	33.3b	(sqrt.f64 (.f64 2 (.f64 (PI.f64) (/.f64 n k))))
	32.6b	(/.f64 (sqrt.f64 2) (sqrt.f64 (/.f64 (/.f64 k n) (PI.f64))))
	26.2b	(.f64 (/.f64 1 (cbrt.f64 k)) (/.f64 (sqrt.f64 (.f64 (PI.f64) (*.f64 2 n))) (pow.f64 k 1/6)))
	9.2b	(/.f64 1 (sqrt.f64 (/.f64 k (pow.f64 (.f64 n (.f64 2 (PI.f64))) (-.f64 1 k)))))
✓	33.3b	(sqrt.f64 (.f64 2 (.f64 (/.f64 (PI.f64) k) n)))
	9.6b	(sqrt.f64 (/.f64 (/.f64 (.f64 2 (PI.f64)) (/.f64 (pow.f64 (.f64 n (*.f64 2 (PI.f64))) k) n)) k))
	32.7b	(/.f64 1 (sqrt.f64 (*.f64 1/2 (/.f64 (/.f64 k n) (PI.f64)))))
	0.5b	(.f64 (/.f64 (pow.f64 k -1/2) (pow.f64 (.f64 2 (.f64 (PI.f64) n)) (.f64 (-.f64 1 k) -1/2))) 1)
	33.3b	(sqrt.f64 (.f64 2 (.f64 (*.f64 (/.f64 1 k) (PI.f64)) n)))
	24.2b	(.f64 (sqrt.f64 (.f64 2 (/.f64 (PI.f64) k))) (sqrt.f64 n))
	26.1b	(/.f64 (.f64 (pow.f64 (.f64 (PI.f64) (.f64 2 n)) 1/6) (cbrt.f64 (.f64 (PI.f64) (*.f64 2 n)))) (sqrt.f64 k))
	0.5b	(/.f64 (pow.f64 (.f64 (PI.f64) (.f64 n 2)) (+.f64 1/2 (*.f64 k -1/2))) (sqrt.f64 k))

Compiler

Compiled 609 to 495 computations (18.7% saved)

regimes299.0ms (3.2%)

Counts

87 → 1

Calls

Call 1

Inputs
(sqrt.f64 (*.f64 2 (/.f64 n (/.f64 k (PI.f64)))))
(sqrt.f64 (.f64 (/.f64 2 k) (.f64 n (PI.f64))))
(sqrt.f64 (*.f64 2 (/.f64 (PI.f64) (/.f64 k n))))
(sqrt.f64 (.f64 2 (.f64 (PI.f64) (/.f64 n k))))
(sqrt.f64 (.f64 2 (.f64 (/.f64 (PI.f64) k) n)))
(sqrt.f64 (.f64 2 (.f64 (/.f64 (PI.f64) k) n)))
(sqrt.f64 (/.f64 (.f64 2 (.f64 n (PI.f64))) k))
(pow.f64 (*.f64 1/2 (/.f64 (/.f64 k n) (PI.f64))) -1/2)
(pow.f64 (/.f64 2 (/.f64 (/.f64 k n) (PI.f64))) 1/2)
(sqrt.f64 (.f64 2 (/.f64 1 (/.f64 k (.f64 (PI.f64) n)))))
(sqrt.f64 (.f64 2 (.f64 (*.f64 (/.f64 1 k) (PI.f64)) n)))
(sqrt.f64 (.f64 (.f64 2 n) (*.f64 (PI.f64) (/.f64 1 k))))
(/.f64 1 (sqrt.f64 (*.f64 1/2 (/.f64 (/.f64 k n) (PI.f64)))))
(sqrt.f64 (.f64 2 (.f64 (-.f64 (+.f64 1 (/.f64 (PI.f64) k)) 1) n)))
(.f64 (sqrt.f64 (.f64 (/.f64 (PI.f64) k) n)) (sqrt.f64 2))
(.f64 (sqrt.f64 (.f64 2 (/.f64 (PI.f64) k))) (sqrt.f64 n))
(/.f64 (sqrt.f64 (.f64 n (.f64 (PI.f64) 2))) (sqrt.f64 k))
(/.f64 (sqrt.f64 2) (sqrt.f64 (/.f64 (/.f64 k n) (PI.f64))))
(.f64 (sqrt.f64 (.f64 2 (*.f64 n (PI.f64)))) (pow.f64 k -1/2))
(pow.f64 (cbrt.f64 (/.f64 2 (/.f64 (/.f64 k n) (PI.f64)))) 3/2)
(.f64 (sqrt.f64 (.f64 n (*.f64 (PI.f64) 2))) (pow.f64 k -1/2))
(cbrt.f64 (pow.f64 (/.f64 2 (/.f64 (/.f64 k n) (PI.f64))) 3/2))
(pow.f64 (pow.f64 (.f64 2 (.f64 (/.f64 (PI.f64) k) n)) 3/2) 1/3)
(exp.f64 (.f64 (log.f64 (/.f64 (.f64 (PI.f64) 2) (/.f64 k n))) 1/2))
(pow.f64 (pow.f64 (/.f64 2 (/.f64 (/.f64 k n) (PI.f64))) 1/6) 3)
(exp.f64 (*.f64 (log.f64 (/.f64 2 (/.f64 (/.f64 k n) (PI.f64)))) 1/2))
(pow.f64 (pow.f64 (/.f64 2 (/.f64 (/.f64 k n) (PI.f64))) 3/2) 1/3)
(pow.f64 (pow.f64 (/.f64 2 (/.f64 (/.f64 k n) (PI.f64))) 3) 1/6)
(/.f64 1 (/.f64 (sqrt.f64 k) (sqrt.f64 (.f64 2 (.f64 n (PI.f64))))))
(/.f64 1 (.f64 (sqrt.f64 k) (pow.f64 (.f64 2 (*.f64 n (PI.f64))) -1/2)))
(sqrt.f64 (/.f64 (pow.f64 (.f64 2 (.f64 (PI.f64) n)) (-.f64 1 k)) k))
(pow.f64 (.f64 k (pow.f64 (.f64 n (*.f64 2 (PI.f64))) (-.f64 k 1))) -1/2)
(pow.f64 (/.f64 k (pow.f64 (.f64 2 (.f64 (PI.f64) n)) (-.f64 1 k))) -1/2)
(sqrt.f64 (/.f64 1 (.f64 k (pow.f64 (.f64 n (*.f64 2 (PI.f64))) (-.f64 k 1)))))
(sqrt.f64 (.f64 (pow.f64 (.f64 n (*.f64 2 (PI.f64))) (-.f64 1 k)) (/.f64 1 k)))
(/.f64 1 (sqrt.f64 (/.f64 k (pow.f64 (.f64 n (.f64 2 (PI.f64))) (-.f64 1 k)))))
(/.f64 (pow.f64 (.f64 (PI.f64) (.f64 n 2)) (+.f64 1/2 (*.f64 k -1/2))) (sqrt.f64 k))
(.f64 (pow.f64 k -1/2) (pow.f64 (.f64 (*.f64 2 (PI.f64)) n) (/.f64 (-.f64 1 k) 2)))
(.f64 (sqrt.f64 (/.f64 1 k)) (pow.f64 (.f64 (*.f64 2 (PI.f64)) n) (/.f64 (-.f64 1 k) 2)))
(.f64 (/.f64 1 (sqrt.f64 k)) (pow.f64 (.f64 (*.f64 2 (PI.f64)) n) (/.f64 (-.f64 1 k) 2)))
(/.f64 1 (/.f64 (pow.f64 (.f64 2 (.f64 (PI.f64) n)) (*.f64 (-.f64 1 k) -1/2)) (pow.f64 k -1/2)))
(.f64 (/.f64 (pow.f64 k -1/2) (pow.f64 (.f64 2 (.f64 (PI.f64) n)) (.f64 (-.f64 1 k) -1/2))) 1)
(/.f64 (.f64 (sqrt.f64 n) (sqrt.f64 (.f64 (PI.f64) 2))) (sqrt.f64 k))
(/.f64 (.f64 (sqrt.f64 2) (sqrt.f64 (.f64 n (PI.f64)))) (sqrt.f64 k))
(/.f64 (.f64 (sqrt.f64 2) (sqrt.f64 (.f64 n (PI.f64)))) (sqrt.f64 k))
(.f64 (pow.f64 k -1/2) (.f64 (sqrt.f64 2) (sqrt.f64 (*.f64 n (PI.f64)))))
(/.f64 (pow.f64 (pow.f64 (.f64 (PI.f64) (.f64 2 n)) 1/4) 2) (sqrt.f64 k))
(.f64 (/.f64 1 (sqrt.f64 k)) (.f64 (sqrt.f64 2) (sqrt.f64 (*.f64 n (PI.f64)))))
(/.f64 (pow.f64 (.f64 2 (.f64 (PI.f64) n)) (fma.f64 k -1/2 1/2)) (sqrt.f64 k))
(.f64 (pow.f64 k -1/2) (sqrt.f64 (pow.f64 (.f64 n (*.f64 2 (PI.f64))) (-.f64 1 k))))
(sqrt.f64 (/.f64 (exp.f64 (.f64 (-.f64 1 k) (log.f64 (.f64 n (*.f64 2 (PI.f64)))))) k))
(cbrt.f64 (pow.f64 (/.f64 (pow.f64 (.f64 (PI.f64) (.f64 n 2)) (-.f64 1 k)) k) 3/2))
(.f64 (pow.f64 k -1/2) (sqrt.f64 (pow.f64 (.f64 2 (*.f64 (PI.f64) n)) (-.f64 1 k))))
(.f64 (/.f64 1 (cbrt.f64 k)) (/.f64 (sqrt.f64 (.f64 (PI.f64) (*.f64 2 n))) (pow.f64 k 1/6)))
(pow.f64 (pow.f64 (/.f64 (pow.f64 (.f64 n (.f64 2 (PI.f64))) (-.f64 1 k)) k) 3/2) 1/3)
(exp.f64 (.f64 (log.f64 (/.f64 (pow.f64 (.f64 n (*.f64 2 (PI.f64))) (-.f64 1 k)) k)) 1/2))
(pow.f64 (pow.f64 (/.f64 (pow.f64 (.f64 (PI.f64) (.f64 n 2)) (-.f64 1 k)) k) 1/4) 2)
(.f64 (sqrt.f64 (/.f64 1 k)) (sqrt.f64 (pow.f64 (.f64 n (*.f64 2 (PI.f64))) (-.f64 1 k))))
(/.f64 1 (/.f64 (sqrt.f64 k) (sqrt.f64 (pow.f64 (.f64 2 (.f64 (PI.f64) n)) (-.f64 1 k)))))
(sqrt.f64 (/.f64 (/.f64 n (pow.f64 n k)) (/.f64 k (pow.f64 (*.f64 2 (PI.f64)) (-.f64 1 k)))))
(/.f64 1 (.f64 (sqrt.f64 k) (pow.f64 (pow.f64 (.f64 2 (*.f64 (PI.f64) n)) (-.f64 1 k)) -1/2)))
(sqrt.f64 (/.f64 (/.f64 (.f64 2 (PI.f64)) (/.f64 (pow.f64 (.f64 n (*.f64 2 (PI.f64))) k) n)) k))
(sqrt.f64 (/.f64 (.f64 (pow.f64 (.f64 2 (PI.f64)) (-.f64 1 k)) (/.f64 n (pow.f64 n k))) k))
(sqrt.f64 (/.f64 (.f64 (pow.f64 (.f64 n (.f64 2 (PI.f64))) (neg.f64 k)) (.f64 n (*.f64 2 (PI.f64)))) k))
(sqrt.f64 (/.f64 (.f64 (.f64 n (.f64 2 (PI.f64))) (pow.f64 (.f64 n (*.f64 2 (PI.f64))) (neg.f64 k))) k))
(.f64 (pow.f64 (pow.f64 k -1/4) 2) (pow.f64 (.f64 (*.f64 2 (PI.f64)) n) (/.f64 (-.f64 1 k) 2)))
(.f64 (pow.f64 k -1/2) (/.f64 1 (pow.f64 (pow.f64 (.f64 2 (*.f64 (PI.f64) n)) (-.f64 1 k)) -1/2)))
(.f64 (exp.f64 (.f64 -1/2 (log.f64 k))) (pow.f64 (.f64 (.f64 2 (PI.f64)) n) (/.f64 (-.f64 1 k) 2)))
(.f64 (cbrt.f64 (.f64 (pow.f64 k -3/2) 1)) (pow.f64 (.f64 (.f64 2 (PI.f64)) n) (/.f64 (-.f64 1 k) 2)))
(.f64 (/.f64 1 (sqrt.f64 k)) (exp.f64 (.f64 1/2 (.f64 (-.f64 1 k) (log.f64 (.f64 2 (*.f64 n (PI.f64))))))))
(/.f64 (pow.f64 (*.f64 2 (PI.f64)) (-.f64 1/2 (/.f64 k 2))) (/.f64 (sqrt.f64 k) (pow.f64 n (-.f64 1/2 (/.f64 k 2)))))
(exp.f64 (log.f64 (sqrt.f64 (/.f64 (pow.f64 (.f64 2 (.f64 (PI.f64) n)) (-.f64 1 k)) k))))
(pow.f64 (cbrt.f64 (sqrt.f64 (/.f64 (pow.f64 (.f64 2 (.f64 (PI.f64) n)) (-.f64 1 k)) k))) 3)
(pow.f64 (pow.f64 (sqrt.f64 (/.f64 (pow.f64 (.f64 2 (.f64 (PI.f64) n)) (-.f64 1 k)) k)) 3) 1/3)
(/.f64 (.f64 (pow.f64 (.f64 (PI.f64) (.f64 2 n)) 1/6) (cbrt.f64 (.f64 (PI.f64) (*.f64 2 n)))) (sqrt.f64 k))
(.f64 (expm1.f64 (log1p.f64 (pow.f64 k -1/2))) (pow.f64 (.f64 (*.f64 2 (PI.f64)) n) (/.f64 (-.f64 1 k) 2)))
(/.f64 (exp.f64 (.f64 (+.f64 1/2 (.f64 -1/2 k)) (+.f64 (log.f64 n) (log.f64 (*.f64 2 (PI.f64)))))) (sqrt.f64 k))
(.f64 (pow.f64 k -1/2) (sqrt.f64 (.f64 (pow.f64 (*.f64 2 (PI.f64)) (-.f64 1 k)) (/.f64 n (pow.f64 n k)))))
(.f64 (cbrt.f64 (exp.f64 (.f64 (log.f64 k) -3/2))) (pow.f64 (.f64 (.f64 2 (PI.f64)) n) (/.f64 (-.f64 1 k) 2)))
(.f64 (pow.f64 k -1/4) (/.f64 (pow.f64 (.f64 n (*.f64 2 (PI.f64))) (fma.f64 k -1/2 1/2)) (pow.f64 k 1/4)))
(.f64 (/.f64 1 (sqrt.f64 k)) (pow.f64 (exp.f64 (log.f64 (.f64 2 (*.f64 (PI.f64) n)))) (/.f64 (-.f64 1 k) 2)))
(.f64 (cbrt.f64 (pow.f64 (pow.f64 k -1/2) 3)) (pow.f64 (.f64 (*.f64 2 (PI.f64)) n) (/.f64 (-.f64 1 k) 2)))
(/.f64 1 (/.f64 (sqrt.f64 k) (sqrt.f64 (/.f64 (.f64 n (.f64 2 (PI.f64))) (pow.f64 (.f64 n (.f64 2 (PI.f64))) k)))))
(/.f64 (.f64 (sqrt.f64 (.f64 n (.f64 2 (PI.f64)))) (pow.f64 (.f64 n (.f64 2 (PI.f64))) (.f64 k -1/2))) (sqrt.f64 k))
(.f64 (.f64 (/.f64 1 (cbrt.f64 k)) (cbrt.f64 (pow.f64 k -1/2))) (pow.f64 (.f64 (.f64 2 (PI.f64)) n) (/.f64 (-.f64 1 k) 2)))
(.f64 (/.f64 1 (sqrt.f64 k)) (/.f64 (sqrt.f64 (.f64 2 (.f64 (PI.f64) n))) (pow.f64 (.f64 2 (*.f64 (PI.f64) n)) (/.f64 k 2))))
(/.f64 (.f64 (sqrt.f64 (.f64 n (PI.f64))) (fma.f64 (.f64 (.f64 -1/2 k) (sqrt.f64 2)) (log.f64 (.f64 2 (.f64 n (PI.f64)))) (sqrt.f64 2))) (sqrt.f64 k))

Outputs
(.f64 (pow.f64 k -1/2) (sqrt.f64 (.f64 (pow.f64 (*.f64 2 (PI.f64)) (-.f64 1 k)) (/.f64 n (pow.f64 n k)))))

Calls

5 calls:

66.0ms	k
65.0ms	(.f64 (.f64 2 (PI.f64)) n)
53.0ms	n
52.0ms	(.f64 (.f64 2 (PI.f64)) n)
25.0ms	(.f64 (/.f64 1 (sqrt.f64 k)) (pow.f64 (.f64 (*.f64 2 (PI.f64)) n) (/.f64 (-.f64 1 k) 2)))

Results

Error	Segments	Branch
0.2b	1	`k`
0.2b	1	`n`
0.2b	1	`(.f64 (/.f64 1 (sqrt.f64 k)) (pow.f64 (.f64 (*.f64 2 (PI.f64)) n) (/.f64 (-.f64 1 k) 2)))`
0.2b	1	`(.f64 (.f64 2 (PI.f64)) n)`
0.2b	1	`(.f64 (.f64 2 (PI.f64)) n)`

Compiler

Compiled 1224 to 795 computations (35% saved)

regimes313.0ms (3.3%)

Counts

77 → 1

Calls

Call 1

Inputs
(sqrt.f64 (*.f64 2 (/.f64 n (/.f64 k (PI.f64)))))
(sqrt.f64 (.f64 (/.f64 2 k) (.f64 n (PI.f64))))
(sqrt.f64 (*.f64 2 (/.f64 (PI.f64) (/.f64 k n))))
(sqrt.f64 (.f64 2 (.f64 (PI.f64) (/.f64 n k))))
(sqrt.f64 (.f64 2 (.f64 (/.f64 (PI.f64) k) n)))
(sqrt.f64 (.f64 2 (.f64 (/.f64 (PI.f64) k) n)))
(sqrt.f64 (/.f64 (.f64 2 (.f64 n (PI.f64))) k))
(pow.f64 (*.f64 1/2 (/.f64 (/.f64 k n) (PI.f64))) -1/2)
(pow.f64 (/.f64 2 (/.f64 (/.f64 k n) (PI.f64))) 1/2)
(sqrt.f64 (.f64 2 (/.f64 1 (/.f64 k (.f64 (PI.f64) n)))))
(sqrt.f64 (.f64 2 (.f64 (*.f64 (/.f64 1 k) (PI.f64)) n)))
(sqrt.f64 (.f64 (.f64 2 n) (*.f64 (PI.f64) (/.f64 1 k))))
(/.f64 1 (sqrt.f64 (*.f64 1/2 (/.f64 (/.f64 k n) (PI.f64)))))
(sqrt.f64 (.f64 2 (.f64 (-.f64 (+.f64 1 (/.f64 (PI.f64) k)) 1) n)))
(.f64 (sqrt.f64 (.f64 (/.f64 (PI.f64) k) n)) (sqrt.f64 2))
(.f64 (sqrt.f64 (.f64 2 (/.f64 (PI.f64) k))) (sqrt.f64 n))
(/.f64 (sqrt.f64 (.f64 n (.f64 (PI.f64) 2))) (sqrt.f64 k))
(/.f64 (sqrt.f64 2) (sqrt.f64 (/.f64 (/.f64 k n) (PI.f64))))
(.f64 (sqrt.f64 (.f64 2 (*.f64 n (PI.f64)))) (pow.f64 k -1/2))
(pow.f64 (cbrt.f64 (/.f64 2 (/.f64 (/.f64 k n) (PI.f64)))) 3/2)
(.f64 (sqrt.f64 (.f64 n (*.f64 (PI.f64) 2))) (pow.f64 k -1/2))
(cbrt.f64 (pow.f64 (/.f64 2 (/.f64 (/.f64 k n) (PI.f64))) 3/2))
(pow.f64 (pow.f64 (.f64 2 (.f64 (/.f64 (PI.f64) k) n)) 3/2) 1/3)
(exp.f64 (.f64 (log.f64 (/.f64 (.f64 (PI.f64) 2) (/.f64 k n))) 1/2))
(pow.f64 (pow.f64 (/.f64 2 (/.f64 (/.f64 k n) (PI.f64))) 1/6) 3)
(exp.f64 (*.f64 (log.f64 (/.f64 2 (/.f64 (/.f64 k n) (PI.f64)))) 1/2))
(pow.f64 (pow.f64 (/.f64 2 (/.f64 (/.f64 k n) (PI.f64))) 3/2) 1/3)
(pow.f64 (pow.f64 (/.f64 2 (/.f64 (/.f64 k n) (PI.f64))) 3) 1/6)
(/.f64 1 (/.f64 (sqrt.f64 k) (sqrt.f64 (.f64 2 (.f64 n (PI.f64))))))
(/.f64 1 (.f64 (sqrt.f64 k) (pow.f64 (.f64 2 (*.f64 n (PI.f64))) -1/2)))
(sqrt.f64 (/.f64 (pow.f64 (.f64 2 (.f64 (PI.f64) n)) (-.f64 1 k)) k))
(pow.f64 (.f64 k (pow.f64 (.f64 n (*.f64 2 (PI.f64))) (-.f64 k 1))) -1/2)
(pow.f64 (/.f64 k (pow.f64 (.f64 2 (.f64 (PI.f64) n)) (-.f64 1 k))) -1/2)
(sqrt.f64 (/.f64 1 (.f64 k (pow.f64 (.f64 n (*.f64 2 (PI.f64))) (-.f64 k 1)))))
(sqrt.f64 (.f64 (pow.f64 (.f64 n (*.f64 2 (PI.f64))) (-.f64 1 k)) (/.f64 1 k)))
(/.f64 1 (sqrt.f64 (/.f64 k (pow.f64 (.f64 n (.f64 2 (PI.f64))) (-.f64 1 k)))))
(/.f64 (pow.f64 (.f64 (PI.f64) (.f64 n 2)) (+.f64 1/2 (*.f64 k -1/2))) (sqrt.f64 k))
(.f64 (pow.f64 k -1/2) (pow.f64 (.f64 (*.f64 2 (PI.f64)) n) (/.f64 (-.f64 1 k) 2)))
(.f64 (sqrt.f64 (/.f64 1 k)) (pow.f64 (.f64 (*.f64 2 (PI.f64)) n) (/.f64 (-.f64 1 k) 2)))
(.f64 (/.f64 1 (sqrt.f64 k)) (pow.f64 (.f64 (*.f64 2 (PI.f64)) n) (/.f64 (-.f64 1 k) 2)))
(/.f64 1 (/.f64 (pow.f64 (.f64 2 (.f64 (PI.f64) n)) (*.f64 (-.f64 1 k) -1/2)) (pow.f64 k -1/2)))
(.f64 (/.f64 (pow.f64 k -1/2) (pow.f64 (.f64 2 (.f64 (PI.f64) n)) (.f64 (-.f64 1 k) -1/2))) 1)
(/.f64 (.f64 (sqrt.f64 n) (sqrt.f64 (.f64 (PI.f64) 2))) (sqrt.f64 k))
(/.f64 (.f64 (sqrt.f64 2) (sqrt.f64 (.f64 n (PI.f64)))) (sqrt.f64 k))
(/.f64 (.f64 (sqrt.f64 2) (sqrt.f64 (.f64 n (PI.f64)))) (sqrt.f64 k))
(.f64 (pow.f64 k -1/2) (.f64 (sqrt.f64 2) (sqrt.f64 (*.f64 n (PI.f64)))))
(/.f64 (pow.f64 (pow.f64 (.f64 (PI.f64) (.f64 2 n)) 1/4) 2) (sqrt.f64 k))
(.f64 (/.f64 1 (sqrt.f64 k)) (.f64 (sqrt.f64 2) (sqrt.f64 (*.f64 n (PI.f64)))))
(/.f64 (pow.f64 (.f64 2 (.f64 (PI.f64) n)) (fma.f64 k -1/2 1/2)) (sqrt.f64 k))
(.f64 (pow.f64 k -1/2) (sqrt.f64 (pow.f64 (.f64 n (*.f64 2 (PI.f64))) (-.f64 1 k))))
(sqrt.f64 (/.f64 (exp.f64 (.f64 (-.f64 1 k) (log.f64 (.f64 n (*.f64 2 (PI.f64)))))) k))
(cbrt.f64 (pow.f64 (/.f64 (pow.f64 (.f64 (PI.f64) (.f64 n 2)) (-.f64 1 k)) k) 3/2))
(.f64 (pow.f64 k -1/2) (sqrt.f64 (pow.f64 (.f64 2 (*.f64 (PI.f64) n)) (-.f64 1 k))))
(.f64 (/.f64 1 (cbrt.f64 k)) (/.f64 (sqrt.f64 (.f64 (PI.f64) (*.f64 2 n))) (pow.f64 k 1/6)))
(pow.f64 (pow.f64 (/.f64 (pow.f64 (.f64 n (.f64 2 (PI.f64))) (-.f64 1 k)) k) 3/2) 1/3)
(exp.f64 (.f64 (log.f64 (/.f64 (pow.f64 (.f64 n (*.f64 2 (PI.f64))) (-.f64 1 k)) k)) 1/2))
(pow.f64 (pow.f64 (/.f64 (pow.f64 (.f64 (PI.f64) (.f64 n 2)) (-.f64 1 k)) k) 1/4) 2)
(.f64 (sqrt.f64 (/.f64 1 k)) (sqrt.f64 (pow.f64 (.f64 n (*.f64 2 (PI.f64))) (-.f64 1 k))))
(/.f64 1 (/.f64 (sqrt.f64 k) (sqrt.f64 (pow.f64 (.f64 2 (.f64 (PI.f64) n)) (-.f64 1 k)))))
(sqrt.f64 (/.f64 (/.f64 n (pow.f64 n k)) (/.f64 k (pow.f64 (*.f64 2 (PI.f64)) (-.f64 1 k)))))
(/.f64 1 (.f64 (sqrt.f64 k) (pow.f64 (pow.f64 (.f64 2 (*.f64 (PI.f64) n)) (-.f64 1 k)) -1/2)))
(sqrt.f64 (/.f64 (/.f64 (.f64 2 (PI.f64)) (/.f64 (pow.f64 (.f64 n (*.f64 2 (PI.f64))) k) n)) k))
(sqrt.f64 (/.f64 (.f64 (pow.f64 (.f64 2 (PI.f64)) (-.f64 1 k)) (/.f64 n (pow.f64 n k))) k))
(sqrt.f64 (/.f64 (.f64 (pow.f64 (.f64 n (.f64 2 (PI.f64))) (neg.f64 k)) (.f64 n (*.f64 2 (PI.f64)))) k))
(sqrt.f64 (/.f64 (.f64 (.f64 n (.f64 2 (PI.f64))) (pow.f64 (.f64 n (*.f64 2 (PI.f64))) (neg.f64 k))) k))
(.f64 (pow.f64 (pow.f64 k -1/4) 2) (pow.f64 (.f64 (*.f64 2 (PI.f64)) n) (/.f64 (-.f64 1 k) 2)))
(.f64 (pow.f64 k -1/2) (/.f64 1 (pow.f64 (pow.f64 (.f64 2 (*.f64 (PI.f64) n)) (-.f64 1 k)) -1/2)))
(.f64 (exp.f64 (.f64 -1/2 (log.f64 k))) (pow.f64 (.f64 (.f64 2 (PI.f64)) n) (/.f64 (-.f64 1 k) 2)))
(.f64 (cbrt.f64 (.f64 (pow.f64 k -3/2) 1)) (pow.f64 (.f64 (.f64 2 (PI.f64)) n) (/.f64 (-.f64 1 k) 2)))
(.f64 (/.f64 1 (sqrt.f64 k)) (exp.f64 (.f64 1/2 (.f64 (-.f64 1 k) (log.f64 (.f64 2 (*.f64 n (PI.f64))))))))
(/.f64 (pow.f64 (*.f64 2 (PI.f64)) (-.f64 1/2 (/.f64 k 2))) (/.f64 (sqrt.f64 k) (pow.f64 n (-.f64 1/2 (/.f64 k 2)))))
(exp.f64 (log.f64 (sqrt.f64 (/.f64 (pow.f64 (.f64 2 (.f64 (PI.f64) n)) (-.f64 1 k)) k))))
(pow.f64 (cbrt.f64 (sqrt.f64 (/.f64 (pow.f64 (.f64 2 (.f64 (PI.f64) n)) (-.f64 1 k)) k))) 3)
(pow.f64 (pow.f64 (sqrt.f64 (/.f64 (pow.f64 (.f64 2 (.f64 (PI.f64) n)) (-.f64 1 k)) k)) 3) 1/3)
(/.f64 (.f64 (pow.f64 (.f64 (PI.f64) (.f64 2 n)) 1/6) (cbrt.f64 (.f64 (PI.f64) (*.f64 2 n)))) (sqrt.f64 k))
(.f64 (expm1.f64 (log1p.f64 (pow.f64 k -1/2))) (pow.f64 (.f64 (*.f64 2 (PI.f64)) n) (/.f64 (-.f64 1 k) 2)))
(/.f64 (exp.f64 (.f64 (+.f64 1/2 (.f64 -1/2 k)) (+.f64 (log.f64 n) (log.f64 (*.f64 2 (PI.f64)))))) (sqrt.f64 k))

Outputs
(.f64 (pow.f64 k -1/2) (sqrt.f64 (pow.f64 (.f64 n (*.f64 2 (PI.f64))) (-.f64 1 k))))

Calls

5 calls:

75.0ms	k
58.0ms	n
46.0ms	(.f64 (.f64 2 (PI.f64)) n)
46.0ms	(.f64 (.f64 2 (PI.f64)) n)
25.0ms	(.f64 (/.f64 1 (sqrt.f64 k)) (pow.f64 (.f64 (*.f64 2 (PI.f64)) n) (/.f64 (-.f64 1 k) 2)))

Results

Error	Segments	Branch
0.5b	1	`k`
0.5b	1	`n`
0.5b	1	`(.f64 (/.f64 1 (sqrt.f64 k)) (pow.f64 (.f64 (*.f64 2 (PI.f64)) n) (/.f64 (-.f64 1 k) 2)))`
0.5b	1	`(.f64 (.f64 2 (PI.f64)) n)`
0.5b	1	`(.f64 (.f64 2 (PI.f64)) n)`

Compiler

Compiled 1031 to 669 computations (35.1% saved)

regimes138.0ms (1.5%)

Counts

49 → 1

Calls

Call 1

Inputs
(sqrt.f64 (*.f64 2 (/.f64 n (/.f64 k (PI.f64)))))
(sqrt.f64 (.f64 (/.f64 2 k) (.f64 n (PI.f64))))
(sqrt.f64 (*.f64 2 (/.f64 (PI.f64) (/.f64 k n))))
(sqrt.f64 (.f64 2 (.f64 (PI.f64) (/.f64 n k))))
(sqrt.f64 (.f64 2 (.f64 (/.f64 (PI.f64) k) n)))
(sqrt.f64 (.f64 2 (.f64 (/.f64 (PI.f64) k) n)))
(sqrt.f64 (/.f64 (.f64 2 (.f64 n (PI.f64))) k))
(pow.f64 (*.f64 1/2 (/.f64 (/.f64 k n) (PI.f64))) -1/2)
(pow.f64 (/.f64 2 (/.f64 (/.f64 k n) (PI.f64))) 1/2)
(sqrt.f64 (.f64 2 (/.f64 1 (/.f64 k (.f64 (PI.f64) n)))))
(sqrt.f64 (.f64 2 (.f64 (*.f64 (/.f64 1 k) (PI.f64)) n)))
(sqrt.f64 (.f64 (.f64 2 n) (*.f64 (PI.f64) (/.f64 1 k))))
(/.f64 1 (sqrt.f64 (*.f64 1/2 (/.f64 (/.f64 k n) (PI.f64)))))
(sqrt.f64 (.f64 2 (.f64 (-.f64 (+.f64 1 (/.f64 (PI.f64) k)) 1) n)))
(.f64 (sqrt.f64 (.f64 (/.f64 (PI.f64) k) n)) (sqrt.f64 2))
(.f64 (sqrt.f64 (.f64 2 (/.f64 (PI.f64) k))) (sqrt.f64 n))
(/.f64 (sqrt.f64 (.f64 n (.f64 (PI.f64) 2))) (sqrt.f64 k))
(/.f64 (sqrt.f64 2) (sqrt.f64 (/.f64 (/.f64 k n) (PI.f64))))
(.f64 (sqrt.f64 (.f64 2 (*.f64 n (PI.f64)))) (pow.f64 k -1/2))
(pow.f64 (cbrt.f64 (/.f64 2 (/.f64 (/.f64 k n) (PI.f64)))) 3/2)
(.f64 (sqrt.f64 (.f64 n (*.f64 (PI.f64) 2))) (pow.f64 k -1/2))
(cbrt.f64 (pow.f64 (/.f64 2 (/.f64 (/.f64 k n) (PI.f64))) 3/2))
(pow.f64 (pow.f64 (.f64 2 (.f64 (/.f64 (PI.f64) k) n)) 3/2) 1/3)
(exp.f64 (.f64 (log.f64 (/.f64 (.f64 (PI.f64) 2) (/.f64 k n))) 1/2))
(pow.f64 (pow.f64 (/.f64 2 (/.f64 (/.f64 k n) (PI.f64))) 1/6) 3)
(exp.f64 (*.f64 (log.f64 (/.f64 2 (/.f64 (/.f64 k n) (PI.f64)))) 1/2))
(pow.f64 (pow.f64 (/.f64 2 (/.f64 (/.f64 k n) (PI.f64))) 3/2) 1/3)
(pow.f64 (pow.f64 (/.f64 2 (/.f64 (/.f64 k n) (PI.f64))) 3) 1/6)
(/.f64 1 (/.f64 (sqrt.f64 k) (sqrt.f64 (.f64 2 (.f64 n (PI.f64))))))
(/.f64 1 (.f64 (sqrt.f64 k) (pow.f64 (.f64 2 (*.f64 n (PI.f64))) -1/2)))
(sqrt.f64 (/.f64 (pow.f64 (.f64 2 (.f64 (PI.f64) n)) (-.f64 1 k)) k))
(pow.f64 (.f64 k (pow.f64 (.f64 n (*.f64 2 (PI.f64))) (-.f64 k 1))) -1/2)
(pow.f64 (/.f64 k (pow.f64 (.f64 2 (.f64 (PI.f64) n)) (-.f64 1 k))) -1/2)
(sqrt.f64 (/.f64 1 (.f64 k (pow.f64 (.f64 n (*.f64 2 (PI.f64))) (-.f64 k 1)))))
(sqrt.f64 (.f64 (pow.f64 (.f64 n (*.f64 2 (PI.f64))) (-.f64 1 k)) (/.f64 1 k)))
(/.f64 1 (sqrt.f64 (/.f64 k (pow.f64 (.f64 n (.f64 2 (PI.f64))) (-.f64 1 k)))))
(/.f64 (pow.f64 (.f64 (PI.f64) (.f64 n 2)) (+.f64 1/2 (*.f64 k -1/2))) (sqrt.f64 k))
(.f64 (pow.f64 k -1/2) (pow.f64 (.f64 (*.f64 2 (PI.f64)) n) (/.f64 (-.f64 1 k) 2)))
(.f64 (sqrt.f64 (/.f64 1 k)) (pow.f64 (.f64 (*.f64 2 (PI.f64)) n) (/.f64 (-.f64 1 k) 2)))
(.f64 (/.f64 1 (sqrt.f64 k)) (pow.f64 (.f64 (*.f64 2 (PI.f64)) n) (/.f64 (-.f64 1 k) 2)))
(/.f64 1 (/.f64 (pow.f64 (.f64 2 (.f64 (PI.f64) n)) (*.f64 (-.f64 1 k) -1/2)) (pow.f64 k -1/2)))
(.f64 (/.f64 (pow.f64 k -1/2) (pow.f64 (.f64 2 (.f64 (PI.f64) n)) (.f64 (-.f64 1 k) -1/2))) 1)
(/.f64 (.f64 (sqrt.f64 n) (sqrt.f64 (.f64 (PI.f64) 2))) (sqrt.f64 k))
(/.f64 (.f64 (sqrt.f64 2) (sqrt.f64 (.f64 n (PI.f64)))) (sqrt.f64 k))
(/.f64 (.f64 (sqrt.f64 2) (sqrt.f64 (.f64 n (PI.f64)))) (sqrt.f64 k))
(.f64 (pow.f64 k -1/2) (.f64 (sqrt.f64 2) (sqrt.f64 (*.f64 n (PI.f64)))))
(/.f64 (pow.f64 (pow.f64 (.f64 (PI.f64) (.f64 2 n)) 1/4) 2) (sqrt.f64 k))
(.f64 (/.f64 1 (sqrt.f64 k)) (.f64 (sqrt.f64 2) (sqrt.f64 (*.f64 n (PI.f64)))))
(/.f64 (pow.f64 (.f64 2 (.f64 (PI.f64) n)) (fma.f64 k -1/2 1/2)) (sqrt.f64 k))

Outputs
(.f64 (sqrt.f64 (/.f64 1 k)) (pow.f64 (.f64 (*.f64 2 (PI.f64)) n) (/.f64 (-.f64 1 k) 2)))

Calls

4 calls:

49.0ms	k
29.0ms	(.f64 (.f64 2 (PI.f64)) n)
28.0ms	n
14.0ms	(.f64 (/.f64 1 (sqrt.f64 k)) (pow.f64 (.f64 (*.f64 2 (PI.f64)) n) (/.f64 (-.f64 1 k) 2)))

Results

Error	Segments	Branch
0.5b	1	`k`
0.5b	1	`n`
0.5b	1	`(.f64 (/.f64 1 (sqrt.f64 k)) (pow.f64 (.f64 (*.f64 2 (PI.f64)) n) (/.f64 (-.f64 1 k) 2)))`
0.5b	1	`(.f64 (.f64 2 (PI.f64)) n)`

Compiler

Compiled 577 to 357 computations (38.1% saved)

regimes97.0ms (1%)

Counts

38 → 1

Calls

Call 1

Inputs
(sqrt.f64 (*.f64 2 (/.f64 n (/.f64 k (PI.f64)))))
(sqrt.f64 (.f64 (/.f64 2 k) (.f64 n (PI.f64))))
(sqrt.f64 (*.f64 2 (/.f64 (PI.f64) (/.f64 k n))))
(sqrt.f64 (.f64 2 (.f64 (PI.f64) (/.f64 n k))))
(sqrt.f64 (.f64 2 (.f64 (/.f64 (PI.f64) k) n)))
(sqrt.f64 (.f64 2 (.f64 (/.f64 (PI.f64) k) n)))
(sqrt.f64 (/.f64 (.f64 2 (.f64 n (PI.f64))) k))
(pow.f64 (*.f64 1/2 (/.f64 (/.f64 k n) (PI.f64))) -1/2)
(pow.f64 (/.f64 2 (/.f64 (/.f64 k n) (PI.f64))) 1/2)
(sqrt.f64 (.f64 2 (/.f64 1 (/.f64 k (.f64 (PI.f64) n)))))
(sqrt.f64 (.f64 2 (.f64 (*.f64 (/.f64 1 k) (PI.f64)) n)))
(sqrt.f64 (.f64 (.f64 2 n) (*.f64 (PI.f64) (/.f64 1 k))))
(/.f64 1 (sqrt.f64 (*.f64 1/2 (/.f64 (/.f64 k n) (PI.f64)))))
(sqrt.f64 (.f64 2 (.f64 (-.f64 (+.f64 1 (/.f64 (PI.f64) k)) 1) n)))
(.f64 (sqrt.f64 (.f64 (/.f64 (PI.f64) k) n)) (sqrt.f64 2))
(.f64 (sqrt.f64 (.f64 2 (/.f64 (PI.f64) k))) (sqrt.f64 n))
(/.f64 (sqrt.f64 (.f64 n (.f64 (PI.f64) 2))) (sqrt.f64 k))
(/.f64 (sqrt.f64 2) (sqrt.f64 (/.f64 (/.f64 k n) (PI.f64))))
(.f64 (sqrt.f64 (.f64 2 (*.f64 n (PI.f64)))) (pow.f64 k -1/2))
(pow.f64 (cbrt.f64 (/.f64 2 (/.f64 (/.f64 k n) (PI.f64)))) 3/2)
(.f64 (sqrt.f64 (.f64 n (*.f64 (PI.f64) 2))) (pow.f64 k -1/2))
(cbrt.f64 (pow.f64 (/.f64 2 (/.f64 (/.f64 k n) (PI.f64))) 3/2))
(pow.f64 (pow.f64 (.f64 2 (.f64 (/.f64 (PI.f64) k) n)) 3/2) 1/3)
(exp.f64 (.f64 (log.f64 (/.f64 (.f64 (PI.f64) 2) (/.f64 k n))) 1/2))
(pow.f64 (pow.f64 (/.f64 2 (/.f64 (/.f64 k n) (PI.f64))) 1/6) 3)
(exp.f64 (*.f64 (log.f64 (/.f64 2 (/.f64 (/.f64 k n) (PI.f64)))) 1/2))
(pow.f64 (pow.f64 (/.f64 2 (/.f64 (/.f64 k n) (PI.f64))) 3/2) 1/3)
(pow.f64 (pow.f64 (/.f64 2 (/.f64 (/.f64 k n) (PI.f64))) 3) 1/6)
(/.f64 1 (/.f64 (sqrt.f64 k) (sqrt.f64 (.f64 2 (.f64 n (PI.f64))))))
(/.f64 1 (.f64 (sqrt.f64 k) (pow.f64 (.f64 2 (*.f64 n (PI.f64))) -1/2)))
(sqrt.f64 (/.f64 (pow.f64 (.f64 2 (.f64 (PI.f64) n)) (-.f64 1 k)) k))
(pow.f64 (.f64 k (pow.f64 (.f64 n (*.f64 2 (PI.f64))) (-.f64 k 1))) -1/2)
(pow.f64 (/.f64 k (pow.f64 (.f64 2 (.f64 (PI.f64) n)) (-.f64 1 k))) -1/2)
(sqrt.f64 (/.f64 1 (.f64 k (pow.f64 (.f64 n (*.f64 2 (PI.f64))) (-.f64 k 1)))))
(sqrt.f64 (.f64 (pow.f64 (.f64 n (*.f64 2 (PI.f64))) (-.f64 1 k)) (/.f64 1 k)))
(/.f64 1 (sqrt.f64 (/.f64 k (pow.f64 (.f64 n (.f64 2 (PI.f64))) (-.f64 1 k)))))
(/.f64 (pow.f64 (.f64 (PI.f64) (.f64 n 2)) (+.f64 1/2 (*.f64 k -1/2))) (sqrt.f64 k))
(.f64 (pow.f64 k -1/2) (pow.f64 (.f64 (*.f64 2 (PI.f64)) n) (/.f64 (-.f64 1 k) 2)))

Outputs
(.f64 (pow.f64 k -1/2) (pow.f64 (.f64 (*.f64 2 (PI.f64)) n) (/.f64 (-.f64 1 k) 2)))

Calls

3 calls:

45.0ms	n
20.0ms	k
20.0ms	(.f64 (.f64 2 (PI.f64)) n)

Results

Error	Segments	Branch
0.5b	1	`k`
0.5b	1	`n`
0.5b	1	`(.f64 (.f64 2 (PI.f64)) n)`

Compiler

Compiled 415 to 254 computations (38.8% saved)

regimes54.0ms (0.6%)

Counts

37 → 1

Calls

Call 1

Inputs
(sqrt.f64 (*.f64 2 (/.f64 n (/.f64 k (PI.f64)))))
(sqrt.f64 (.f64 (/.f64 2 k) (.f64 n (PI.f64))))
(sqrt.f64 (*.f64 2 (/.f64 (PI.f64) (/.f64 k n))))
(sqrt.f64 (.f64 2 (.f64 (PI.f64) (/.f64 n k))))
(sqrt.f64 (.f64 2 (.f64 (/.f64 (PI.f64) k) n)))
(sqrt.f64 (.f64 2 (.f64 (/.f64 (PI.f64) k) n)))
(sqrt.f64 (/.f64 (.f64 2 (.f64 n (PI.f64))) k))
(pow.f64 (*.f64 1/2 (/.f64 (/.f64 k n) (PI.f64))) -1/2)
(pow.f64 (/.f64 2 (/.f64 (/.f64 k n) (PI.f64))) 1/2)
(sqrt.f64 (.f64 2 (/.f64 1 (/.f64 k (.f64 (PI.f64) n)))))
(sqrt.f64 (.f64 2 (.f64 (*.f64 (/.f64 1 k) (PI.f64)) n)))
(sqrt.f64 (.f64 (.f64 2 n) (*.f64 (PI.f64) (/.f64 1 k))))
(/.f64 1 (sqrt.f64 (*.f64 1/2 (/.f64 (/.f64 k n) (PI.f64)))))
(sqrt.f64 (.f64 2 (.f64 (-.f64 (+.f64 1 (/.f64 (PI.f64) k)) 1) n)))
(.f64 (sqrt.f64 (.f64 (/.f64 (PI.f64) k) n)) (sqrt.f64 2))
(.f64 (sqrt.f64 (.f64 2 (/.f64 (PI.f64) k))) (sqrt.f64 n))
(/.f64 (sqrt.f64 (.f64 n (.f64 (PI.f64) 2))) (sqrt.f64 k))
(/.f64 (sqrt.f64 2) (sqrt.f64 (/.f64 (/.f64 k n) (PI.f64))))
(.f64 (sqrt.f64 (.f64 2 (*.f64 n (PI.f64)))) (pow.f64 k -1/2))
(pow.f64 (cbrt.f64 (/.f64 2 (/.f64 (/.f64 k n) (PI.f64)))) 3/2)
(.f64 (sqrt.f64 (.f64 n (*.f64 (PI.f64) 2))) (pow.f64 k -1/2))
(cbrt.f64 (pow.f64 (/.f64 2 (/.f64 (/.f64 k n) (PI.f64))) 3/2))
(pow.f64 (pow.f64 (.f64 2 (.f64 (/.f64 (PI.f64) k) n)) 3/2) 1/3)
(exp.f64 (.f64 (log.f64 (/.f64 (.f64 (PI.f64) 2) (/.f64 k n))) 1/2))
(pow.f64 (pow.f64 (/.f64 2 (/.f64 (/.f64 k n) (PI.f64))) 1/6) 3)
(exp.f64 (*.f64 (log.f64 (/.f64 2 (/.f64 (/.f64 k n) (PI.f64)))) 1/2))
(pow.f64 (pow.f64 (/.f64 2 (/.f64 (/.f64 k n) (PI.f64))) 3/2) 1/3)
(pow.f64 (pow.f64 (/.f64 2 (/.f64 (/.f64 k n) (PI.f64))) 3) 1/6)
(/.f64 1 (/.f64 (sqrt.f64 k) (sqrt.f64 (.f64 2 (.f64 n (PI.f64))))))
(/.f64 1 (.f64 (sqrt.f64 k) (pow.f64 (.f64 2 (*.f64 n (PI.f64))) -1/2)))
(sqrt.f64 (/.f64 (pow.f64 (.f64 2 (.f64 (PI.f64) n)) (-.f64 1 k)) k))
(pow.f64 (.f64 k (pow.f64 (.f64 n (*.f64 2 (PI.f64))) (-.f64 k 1))) -1/2)
(pow.f64 (/.f64 k (pow.f64 (.f64 2 (.f64 (PI.f64) n)) (-.f64 1 k))) -1/2)
(sqrt.f64 (/.f64 1 (.f64 k (pow.f64 (.f64 n (*.f64 2 (PI.f64))) (-.f64 k 1)))))
(sqrt.f64 (.f64 (pow.f64 (.f64 n (*.f64 2 (PI.f64))) (-.f64 1 k)) (/.f64 1 k)))
(/.f64 1 (sqrt.f64 (/.f64 k (pow.f64 (.f64 n (.f64 2 (PI.f64))) (-.f64 1 k)))))
(/.f64 (pow.f64 (.f64 (PI.f64) (.f64 n 2)) (+.f64 1/2 (*.f64 k -1/2))) (sqrt.f64 k))

Outputs
(/.f64 (pow.f64 (.f64 (PI.f64) (.f64 n 2)) (+.f64 1/2 (*.f64 k -1/2))) (sqrt.f64 k))

Calls

2 calls:

21.0ms	n
21.0ms	k

Results

Error	Segments	Branch
0.5b	1	`k`
0.5b	1	`n`

Compiler

Compiled 393 to 237 computations (39.7% saved)

regimes107.0ms (1.1%)

Counts

36 → 2

Calls

Call 1

Inputs
(sqrt.f64 (*.f64 2 (/.f64 n (/.f64 k (PI.f64)))))
(sqrt.f64 (.f64 (/.f64 2 k) (.f64 n (PI.f64))))
(sqrt.f64 (*.f64 2 (/.f64 (PI.f64) (/.f64 k n))))
(sqrt.f64 (.f64 2 (.f64 (PI.f64) (/.f64 n k))))
(sqrt.f64 (.f64 2 (.f64 (/.f64 (PI.f64) k) n)))
(sqrt.f64 (.f64 2 (.f64 (/.f64 (PI.f64) k) n)))
(sqrt.f64 (/.f64 (.f64 2 (.f64 n (PI.f64))) k))
(pow.f64 (*.f64 1/2 (/.f64 (/.f64 k n) (PI.f64))) -1/2)
(pow.f64 (/.f64 2 (/.f64 (/.f64 k n) (PI.f64))) 1/2)
(sqrt.f64 (.f64 2 (/.f64 1 (/.f64 k (.f64 (PI.f64) n)))))
(sqrt.f64 (.f64 2 (.f64 (*.f64 (/.f64 1 k) (PI.f64)) n)))
(sqrt.f64 (.f64 (.f64 2 n) (*.f64 (PI.f64) (/.f64 1 k))))
(/.f64 1 (sqrt.f64 (*.f64 1/2 (/.f64 (/.f64 k n) (PI.f64)))))
(sqrt.f64 (.f64 2 (.f64 (-.f64 (+.f64 1 (/.f64 (PI.f64) k)) 1) n)))
(.f64 (sqrt.f64 (.f64 (/.f64 (PI.f64) k) n)) (sqrt.f64 2))
(.f64 (sqrt.f64 (.f64 2 (/.f64 (PI.f64) k))) (sqrt.f64 n))
(/.f64 (sqrt.f64 (.f64 n (.f64 (PI.f64) 2))) (sqrt.f64 k))
(/.f64 (sqrt.f64 2) (sqrt.f64 (/.f64 (/.f64 k n) (PI.f64))))
(.f64 (sqrt.f64 (.f64 2 (*.f64 n (PI.f64)))) (pow.f64 k -1/2))
(pow.f64 (cbrt.f64 (/.f64 2 (/.f64 (/.f64 k n) (PI.f64)))) 3/2)
(.f64 (sqrt.f64 (.f64 n (*.f64 (PI.f64) 2))) (pow.f64 k -1/2))
(cbrt.f64 (pow.f64 (/.f64 2 (/.f64 (/.f64 k n) (PI.f64))) 3/2))
(pow.f64 (pow.f64 (.f64 2 (.f64 (/.f64 (PI.f64) k) n)) 3/2) 1/3)
(exp.f64 (.f64 (log.f64 (/.f64 (.f64 (PI.f64) 2) (/.f64 k n))) 1/2))
(pow.f64 (pow.f64 (/.f64 2 (/.f64 (/.f64 k n) (PI.f64))) 1/6) 3)
(exp.f64 (*.f64 (log.f64 (/.f64 2 (/.f64 (/.f64 k n) (PI.f64)))) 1/2))
(pow.f64 (pow.f64 (/.f64 2 (/.f64 (/.f64 k n) (PI.f64))) 3/2) 1/3)
(pow.f64 (pow.f64 (/.f64 2 (/.f64 (/.f64 k n) (PI.f64))) 3) 1/6)
(/.f64 1 (/.f64 (sqrt.f64 k) (sqrt.f64 (.f64 2 (.f64 n (PI.f64))))))
(/.f64 1 (.f64 (sqrt.f64 k) (pow.f64 (.f64 2 (*.f64 n (PI.f64))) -1/2)))
(sqrt.f64 (/.f64 (pow.f64 (.f64 2 (.f64 (PI.f64) n)) (-.f64 1 k)) k))
(pow.f64 (.f64 k (pow.f64 (.f64 n (*.f64 2 (PI.f64))) (-.f64 k 1))) -1/2)
(pow.f64 (/.f64 k (pow.f64 (.f64 2 (.f64 (PI.f64) n)) (-.f64 1 k))) -1/2)
(sqrt.f64 (/.f64 1 (.f64 k (pow.f64 (.f64 n (*.f64 2 (PI.f64))) (-.f64 k 1)))))
(sqrt.f64 (.f64 (pow.f64 (.f64 n (*.f64 2 (PI.f64))) (-.f64 1 k)) (/.f64 1 k)))
(/.f64 1 (sqrt.f64 (/.f64 k (pow.f64 (.f64 n (.f64 2 (PI.f64))) (-.f64 1 k)))))

Outputs
(.f64 (sqrt.f64 (.f64 2 (*.f64 n (PI.f64)))) (pow.f64 k -1/2))
(pow.f64 (.f64 k (pow.f64 (.f64 n (*.f64 2 (PI.f64))) (-.f64 k 1))) -1/2)

Calls

2 calls:

53.0ms	n
42.0ms	k

Results

Error	Segments	Branch
0.5b	2	`k`
7.7b	3	`n`

Compiler

Compiled 379 to 228 computations (39.8% saved)

bsearch33.0ms (0.4%)

Algorithm

1×	binary-search

Steps

Time	Left	Right
33.0ms	1.3230474388299305e-17	4.8017754247521106e-17

Compiler

Compiled 23 to 19 computations (17.4% saved)

regimes159.0ms (1.7%)

Counts

31 → 2

Calls

Call 1

Inputs
(sqrt.f64 (*.f64 2 (/.f64 n (/.f64 k (PI.f64)))))
(sqrt.f64 (.f64 (/.f64 2 k) (.f64 n (PI.f64))))
(sqrt.f64 (*.f64 2 (/.f64 (PI.f64) (/.f64 k n))))
(sqrt.f64 (.f64 2 (.f64 (PI.f64) (/.f64 n k))))
(sqrt.f64 (.f64 2 (.f64 (/.f64 (PI.f64) k) n)))
(sqrt.f64 (.f64 2 (.f64 (/.f64 (PI.f64) k) n)))
(sqrt.f64 (/.f64 (.f64 2 (.f64 n (PI.f64))) k))
(pow.f64 (*.f64 1/2 (/.f64 (/.f64 k n) (PI.f64))) -1/2)
(pow.f64 (/.f64 2 (/.f64 (/.f64 k n) (PI.f64))) 1/2)
(sqrt.f64 (.f64 2 (/.f64 1 (/.f64 k (.f64 (PI.f64) n)))))
(sqrt.f64 (.f64 2 (.f64 (*.f64 (/.f64 1 k) (PI.f64)) n)))
(sqrt.f64 (.f64 (.f64 2 n) (*.f64 (PI.f64) (/.f64 1 k))))
(/.f64 1 (sqrt.f64 (*.f64 1/2 (/.f64 (/.f64 k n) (PI.f64)))))
(sqrt.f64 (.f64 2 (.f64 (-.f64 (+.f64 1 (/.f64 (PI.f64) k)) 1) n)))
(.f64 (sqrt.f64 (.f64 (/.f64 (PI.f64) k) n)) (sqrt.f64 2))
(.f64 (sqrt.f64 (.f64 2 (/.f64 (PI.f64) k))) (sqrt.f64 n))
(/.f64 (sqrt.f64 (.f64 n (.f64 (PI.f64) 2))) (sqrt.f64 k))
(/.f64 (sqrt.f64 2) (sqrt.f64 (/.f64 (/.f64 k n) (PI.f64))))
(.f64 (sqrt.f64 (.f64 2 (*.f64 n (PI.f64)))) (pow.f64 k -1/2))
(pow.f64 (cbrt.f64 (/.f64 2 (/.f64 (/.f64 k n) (PI.f64)))) 3/2)
(.f64 (sqrt.f64 (.f64 n (*.f64 (PI.f64) 2))) (pow.f64 k -1/2))
(cbrt.f64 (pow.f64 (/.f64 2 (/.f64 (/.f64 k n) (PI.f64))) 3/2))
(pow.f64 (pow.f64 (.f64 2 (.f64 (/.f64 (PI.f64) k) n)) 3/2) 1/3)
(exp.f64 (.f64 (log.f64 (/.f64 (.f64 (PI.f64) 2) (/.f64 k n))) 1/2))
(pow.f64 (pow.f64 (/.f64 2 (/.f64 (/.f64 k n) (PI.f64))) 1/6) 3)
(exp.f64 (*.f64 (log.f64 (/.f64 2 (/.f64 (/.f64 k n) (PI.f64)))) 1/2))
(pow.f64 (pow.f64 (/.f64 2 (/.f64 (/.f64 k n) (PI.f64))) 3/2) 1/3)
(pow.f64 (pow.f64 (/.f64 2 (/.f64 (/.f64 k n) (PI.f64))) 3) 1/6)
(/.f64 1 (/.f64 (sqrt.f64 k) (sqrt.f64 (.f64 2 (.f64 n (PI.f64))))))
(/.f64 1 (.f64 (sqrt.f64 k) (pow.f64 (.f64 2 (*.f64 n (PI.f64))) -1/2)))
(sqrt.f64 (/.f64 (pow.f64 (.f64 2 (.f64 (PI.f64) n)) (-.f64 1 k)) k))

Outputs
(.f64 (sqrt.f64 (.f64 2 (*.f64 n (PI.f64)))) (pow.f64 k -1/2))
(sqrt.f64 (/.f64 (pow.f64 (.f64 2 (.f64 (PI.f64) n)) (-.f64 1 k)) k))

Calls

2 calls:

79.0ms	n
65.0ms	k

Results

Error	Segments	Branch
0.5b	2	`k`
8.4b	3	`n`

Compiler

Compiled 311 to 181 computations (41.8% saved)

bsearch47.0ms (0.5%)

Algorithm

1×	binary-search

Steps

Time	Left	Right
47.0ms	1.3230474388299305e-17	4.8017754247521106e-17

Compiler

Compiled 23 to 19 computations (17.4% saved)

regimes177.0ms (1.9%)

Counts

30 → 2

Calls

Call 1

Inputs
(sqrt.f64 (*.f64 2 (/.f64 n (/.f64 k (PI.f64)))))
(sqrt.f64 (.f64 (/.f64 2 k) (.f64 n (PI.f64))))
(sqrt.f64 (*.f64 2 (/.f64 (PI.f64) (/.f64 k n))))
(sqrt.f64 (.f64 2 (.f64 (PI.f64) (/.f64 n k))))
(sqrt.f64 (.f64 2 (.f64 (/.f64 (PI.f64) k) n)))
(sqrt.f64 (.f64 2 (.f64 (/.f64 (PI.f64) k) n)))
(sqrt.f64 (/.f64 (.f64 2 (.f64 n (PI.f64))) k))
(pow.f64 (*.f64 1/2 (/.f64 (/.f64 k n) (PI.f64))) -1/2)
(pow.f64 (/.f64 2 (/.f64 (/.f64 k n) (PI.f64))) 1/2)
(sqrt.f64 (.f64 2 (/.f64 1 (/.f64 k (.f64 (PI.f64) n)))))
(sqrt.f64 (.f64 2 (.f64 (*.f64 (/.f64 1 k) (PI.f64)) n)))
(sqrt.f64 (.f64 (.f64 2 n) (*.f64 (PI.f64) (/.f64 1 k))))
(/.f64 1 (sqrt.f64 (*.f64 1/2 (/.f64 (/.f64 k n) (PI.f64)))))
(sqrt.f64 (.f64 2 (.f64 (-.f64 (+.f64 1 (/.f64 (PI.f64) k)) 1) n)))
(.f64 (sqrt.f64 (.f64 (/.f64 (PI.f64) k) n)) (sqrt.f64 2))
(.f64 (sqrt.f64 (.f64 2 (/.f64 (PI.f64) k))) (sqrt.f64 n))
(/.f64 (sqrt.f64 (.f64 n (.f64 (PI.f64) 2))) (sqrt.f64 k))
(/.f64 (sqrt.f64 2) (sqrt.f64 (/.f64 (/.f64 k n) (PI.f64))))
(.f64 (sqrt.f64 (.f64 2 (*.f64 n (PI.f64)))) (pow.f64 k -1/2))
(pow.f64 (cbrt.f64 (/.f64 2 (/.f64 (/.f64 k n) (PI.f64)))) 3/2)
(.f64 (sqrt.f64 (.f64 n (*.f64 (PI.f64) 2))) (pow.f64 k -1/2))
(cbrt.f64 (pow.f64 (/.f64 2 (/.f64 (/.f64 k n) (PI.f64))) 3/2))
(pow.f64 (pow.f64 (.f64 2 (.f64 (/.f64 (PI.f64) k) n)) 3/2) 1/3)
(exp.f64 (.f64 (log.f64 (/.f64 (.f64 (PI.f64) 2) (/.f64 k n))) 1/2))
(pow.f64 (pow.f64 (/.f64 2 (/.f64 (/.f64 k n) (PI.f64))) 1/6) 3)
(exp.f64 (*.f64 (log.f64 (/.f64 2 (/.f64 (/.f64 k n) (PI.f64)))) 1/2))
(pow.f64 (pow.f64 (/.f64 2 (/.f64 (/.f64 k n) (PI.f64))) 3/2) 1/3)
(pow.f64 (pow.f64 (/.f64 2 (/.f64 (/.f64 k n) (PI.f64))) 3) 1/6)
(/.f64 1 (/.f64 (sqrt.f64 k) (sqrt.f64 (.f64 2 (.f64 n (PI.f64))))))
(/.f64 1 (.f64 (sqrt.f64 k) (pow.f64 (.f64 2 (*.f64 n (PI.f64))) -1/2)))

Outputs
(.f64 (sqrt.f64 (.f64 2 (*.f64 n (PI.f64)))) (pow.f64 k -1/2))
(sqrt.f64 (.f64 2 (.f64 (-.f64 (+.f64 1 (/.f64 (PI.f64) k)) 1) n)))

Calls

2 calls:

105.0ms	k
61.0ms	n

Results

Error	Segments	Branch
4.4b	2	`k`
11.9b	3	`n`

Compiler

Compiled 299 to 174 computations (41.8% saved)

bsearch32.0ms (0.3%)

Algorithm

1×	binary-search

Steps

Time	Left	Right
31.0ms	1.3230474388299305e-17	4.8017754247521106e-17

Compiler

Compiled 23 to 19 computations (17.4% saved)

regimes76.0ms (0.8%)

Counts

18 → 2

Calls

Call 1

Inputs
(sqrt.f64 (*.f64 2 (/.f64 n (/.f64 k (PI.f64)))))
(sqrt.f64 (.f64 (/.f64 2 k) (.f64 n (PI.f64))))
(sqrt.f64 (*.f64 2 (/.f64 (PI.f64) (/.f64 k n))))
(sqrt.f64 (.f64 2 (.f64 (PI.f64) (/.f64 n k))))
(sqrt.f64 (.f64 2 (.f64 (/.f64 (PI.f64) k) n)))
(sqrt.f64 (.f64 2 (.f64 (/.f64 (PI.f64) k) n)))
(sqrt.f64 (/.f64 (.f64 2 (.f64 n (PI.f64))) k))
(pow.f64 (*.f64 1/2 (/.f64 (/.f64 k n) (PI.f64))) -1/2)
(pow.f64 (/.f64 2 (/.f64 (/.f64 k n) (PI.f64))) 1/2)
(sqrt.f64 (.f64 2 (/.f64 1 (/.f64 k (.f64 (PI.f64) n)))))
(sqrt.f64 (.f64 2 (.f64 (*.f64 (/.f64 1 k) (PI.f64)) n)))
(sqrt.f64 (.f64 (.f64 2 n) (*.f64 (PI.f64) (/.f64 1 k))))
(/.f64 1 (sqrt.f64 (*.f64 1/2 (/.f64 (/.f64 k n) (PI.f64)))))
(sqrt.f64 (.f64 2 (.f64 (-.f64 (+.f64 1 (/.f64 (PI.f64) k)) 1) n)))
(.f64 (sqrt.f64 (.f64 (/.f64 (PI.f64) k) n)) (sqrt.f64 2))
(.f64 (sqrt.f64 (.f64 2 (/.f64 (PI.f64) k))) (sqrt.f64 n))
(/.f64 (sqrt.f64 (.f64 n (.f64 (PI.f64) 2))) (sqrt.f64 k))
(/.f64 (sqrt.f64 2) (sqrt.f64 (/.f64 (/.f64 k n) (PI.f64))))

Outputs
(/.f64 (sqrt.f64 (.f64 n (.f64 (PI.f64) 2))) (sqrt.f64 k))
(sqrt.f64 (.f64 2 (.f64 (-.f64 (+.f64 1 (/.f64 (PI.f64) k)) 1) n)))

Calls

2 calls:

44.0ms	k
26.0ms	n

Results

Error	Segments	Branch
4.4b	2	`k`
11.9b	3	`n`

Compiler

Compiled 170 to 101 computations (40.6% saved)

bsearch34.0ms (0.4%)

Algorithm

1×	binary-search

Steps

Time	Left	Right
34.0ms	1.6644590962652856e-13	2.13364313926662e-13

Compiler

Compiled 23 to 19 computations (17.4% saved)

regimes46.0ms (0.5%)

Counts

16 → 2

Calls

Call 1

Inputs
(sqrt.f64 (*.f64 2 (/.f64 n (/.f64 k (PI.f64)))))
(sqrt.f64 (.f64 (/.f64 2 k) (.f64 n (PI.f64))))
(sqrt.f64 (*.f64 2 (/.f64 (PI.f64) (/.f64 k n))))
(sqrt.f64 (.f64 2 (.f64 (PI.f64) (/.f64 n k))))
(sqrt.f64 (.f64 2 (.f64 (/.f64 (PI.f64) k) n)))
(sqrt.f64 (.f64 2 (.f64 (/.f64 (PI.f64) k) n)))
(sqrt.f64 (/.f64 (.f64 2 (.f64 n (PI.f64))) k))
(pow.f64 (*.f64 1/2 (/.f64 (/.f64 k n) (PI.f64))) -1/2)
(pow.f64 (/.f64 2 (/.f64 (/.f64 k n) (PI.f64))) 1/2)
(sqrt.f64 (.f64 2 (/.f64 1 (/.f64 k (.f64 (PI.f64) n)))))
(sqrt.f64 (.f64 2 (.f64 (*.f64 (/.f64 1 k) (PI.f64)) n)))
(sqrt.f64 (.f64 (.f64 2 n) (*.f64 (PI.f64) (/.f64 1 k))))
(/.f64 1 (sqrt.f64 (*.f64 1/2 (/.f64 (/.f64 k n) (PI.f64)))))
(sqrt.f64 (.f64 2 (.f64 (-.f64 (+.f64 1 (/.f64 (PI.f64) k)) 1) n)))
(.f64 (sqrt.f64 (.f64 (/.f64 (PI.f64) k) n)) (sqrt.f64 2))
(.f64 (sqrt.f64 (.f64 2 (/.f64 (PI.f64) k))) (sqrt.f64 n))

Outputs
(.f64 (sqrt.f64 (.f64 2 (/.f64 (PI.f64) k))) (sqrt.f64 n))
(sqrt.f64 (.f64 2 (.f64 (-.f64 (+.f64 1 (/.f64 (PI.f64) k)) 1) n)))

Calls

2 calls:

25.0ms	n
17.0ms	k

Results

Error	Segments	Branch
4.6b	2	`k`
11.9b	3	`n`

Compiler

Compiled 152 to 91 computations (40.1% saved)

bsearch50.0ms (0.5%)

Algorithm

1×	binary-search

Steps

Time	Left	Right
50.0ms	1.3230474388299305e-17	4.8017754247521106e-17

Compiler

Compiled 23 to 19 computations (17.4% saved)

regimes24.0ms (0.3%)

Counts

15 → 1

Calls

Call 1

Inputs
(sqrt.f64 (*.f64 2 (/.f64 n (/.f64 k (PI.f64)))))
(sqrt.f64 (.f64 (/.f64 2 k) (.f64 n (PI.f64))))
(sqrt.f64 (*.f64 2 (/.f64 (PI.f64) (/.f64 k n))))
(sqrt.f64 (.f64 2 (.f64 (PI.f64) (/.f64 n k))))
(sqrt.f64 (.f64 2 (.f64 (/.f64 (PI.f64) k) n)))
(sqrt.f64 (.f64 2 (.f64 (/.f64 (PI.f64) k) n)))
(sqrt.f64 (/.f64 (.f64 2 (.f64 n (PI.f64))) k))
(pow.f64 (*.f64 1/2 (/.f64 (/.f64 k n) (PI.f64))) -1/2)
(pow.f64 (/.f64 2 (/.f64 (/.f64 k n) (PI.f64))) 1/2)
(sqrt.f64 (.f64 2 (/.f64 1 (/.f64 k (.f64 (PI.f64) n)))))
(sqrt.f64 (.f64 2 (.f64 (*.f64 (/.f64 1 k) (PI.f64)) n)))
(sqrt.f64 (.f64 (.f64 2 n) (*.f64 (PI.f64) (/.f64 1 k))))
(/.f64 1 (sqrt.f64 (*.f64 1/2 (/.f64 (/.f64 k n) (PI.f64)))))
(sqrt.f64 (.f64 2 (.f64 (-.f64 (+.f64 1 (/.f64 (PI.f64) k)) 1) n)))
(.f64 (sqrt.f64 (.f64 (/.f64 (PI.f64) k) n)) (sqrt.f64 2))

Outputs
(sqrt.f64 (.f64 2 (.f64 (-.f64 (+.f64 1 (/.f64 (PI.f64) k)) 1) n)))

Calls

2 calls:

10.0ms	n
9.0ms	k

Results

Error	Segments	Branch
13.7b	1	`k`
13.7b	1	`n`

Compiler

Compiled 143 to 86 computations (39.9% saved)

regimes21.0ms (0.2%)

Counts

13 → 1

Calls

Call 1

Inputs
(sqrt.f64 (*.f64 2 (/.f64 n (/.f64 k (PI.f64)))))
(sqrt.f64 (.f64 (/.f64 2 k) (.f64 n (PI.f64))))
(sqrt.f64 (*.f64 2 (/.f64 (PI.f64) (/.f64 k n))))
(sqrt.f64 (.f64 2 (.f64 (PI.f64) (/.f64 n k))))
(sqrt.f64 (.f64 2 (.f64 (/.f64 (PI.f64) k) n)))
(sqrt.f64 (.f64 2 (.f64 (/.f64 (PI.f64) k) n)))
(sqrt.f64 (/.f64 (.f64 2 (.f64 n (PI.f64))) k))
(pow.f64 (*.f64 1/2 (/.f64 (/.f64 k n) (PI.f64))) -1/2)
(pow.f64 (/.f64 2 (/.f64 (/.f64 k n) (PI.f64))) 1/2)
(sqrt.f64 (.f64 2 (/.f64 1 (/.f64 k (.f64 (PI.f64) n)))))
(sqrt.f64 (.f64 2 (.f64 (*.f64 (/.f64 1 k) (PI.f64)) n)))
(sqrt.f64 (.f64 (.f64 2 n) (*.f64 (PI.f64) (/.f64 1 k))))
(/.f64 1 (sqrt.f64 (*.f64 1/2 (/.f64 (/.f64 k n) (PI.f64)))))

Outputs
(pow.f64 (*.f64 1/2 (/.f64 (/.f64 k n) (PI.f64))) -1/2)

Calls

2 calls:

9.0ms	k
8.0ms	n

Results

Error	Segments	Branch
32.6b	1	`k`
32.6b	1	`n`

Compiler

Compiled 122 to 74 computations (39.3% saved)

regimes14.0ms (0.2%)

Counts

7 → 1

Calls

Call 1

Inputs
(sqrt.f64 (*.f64 2 (/.f64 n (/.f64 k (PI.f64)))))
(sqrt.f64 (.f64 (/.f64 2 k) (.f64 n (PI.f64))))
(sqrt.f64 (*.f64 2 (/.f64 (PI.f64) (/.f64 k n))))
(sqrt.f64 (.f64 2 (.f64 (PI.f64) (/.f64 n k))))
(sqrt.f64 (.f64 2 (.f64 (/.f64 (PI.f64) k) n)))
(sqrt.f64 (.f64 2 (.f64 (/.f64 (PI.f64) k) n)))
(sqrt.f64 (/.f64 (.f64 2 (.f64 n (PI.f64))) k))

Outputs
(sqrt.f64 (.f64 2 (.f64 (/.f64 (PI.f64) k) n)))

Calls

2 calls:

7.0ms	k
5.0ms	n

Results

Error	Segments	Branch
33.3b	1	`k`
33.3b	1	`n`

Compiler

Compiled 64 to 39 computations (39.1% saved)

regimes9.0ms (0.1%)

Accuracy

Total -0.1b remaining (-0.4%)

Threshold costs -0.1b (-0.4%)

Counts

4 → 1

Calls

Call 1

Inputs
(sqrt.f64 (*.f64 2 (/.f64 n (/.f64 k (PI.f64)))))
(sqrt.f64 (.f64 (/.f64 2 k) (.f64 n (PI.f64))))
(sqrt.f64 (*.f64 2 (/.f64 (PI.f64) (/.f64 k n))))
(sqrt.f64 (.f64 2 (.f64 (PI.f64) (/.f64 n k))))

Outputs
(sqrt.f64 (*.f64 2 (/.f64 n (/.f64 k (PI.f64)))))

Calls

2 calls:

4.0ms	k
4.0ms	n

Results

Error	Segments	Branch
33.3b	1	`k`
33.3b	1	`n`

Compiler

Compiled 40 to 27 computations (32.5% saved)

simplify11.0ms (0.1%)

Algorithm

1×	egg-herbie

Rules

25×	`*-commutative_binary64`
6×	`+-commutative_binary64`
4×	`sub-neg_binary64`
1×	`neg-sub0_binary64`
1×	`neg-mul-1_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	83	383
1	115	383
2	120	383
3	122	383
4	123	383

Stop Event

1×

saturated

Calls

Call 1

Inputs
(.f64 (pow.f64 k -1/2) (sqrt.f64 (.f64 (pow.f64 (*.f64 2 (PI.f64)) (-.f64 1 k)) (/.f64 n (pow.f64 n k)))))
(.f64 (pow.f64 k -1/2) (sqrt.f64 (pow.f64 (.f64 n (*.f64 2 (PI.f64))) (-.f64 1 k))))
(.f64 (sqrt.f64 (/.f64 1 k)) (pow.f64 (.f64 (*.f64 2 (PI.f64)) n) (/.f64 (-.f64 1 k) 2)))
(.f64 (pow.f64 k -1/2) (pow.f64 (.f64 (*.f64 2 (PI.f64)) n) (/.f64 (-.f64 1 k) 2)))
(/.f64 (pow.f64 (.f64 (PI.f64) (.f64 n 2)) (+.f64 1/2 (*.f64 k -1/2))) (sqrt.f64 k))
(if (<=.f64 k 8587068825411497/649037107316853453566312041152512) (.f64 (sqrt.f64 (.f64 2 (.f64 n (PI.f64)))) (pow.f64 k -1/2)) (pow.f64 (.f64 k (pow.f64 (.f64 n (.f64 2 (PI.f64))) (-.f64 k 1))) -1/2))
(if (<=.f64 k 8587068825411497/649037107316853453566312041152512) (.f64 (sqrt.f64 (.f64 2 (.f64 n (PI.f64)))) (pow.f64 k -1/2)) (sqrt.f64 (/.f64 (pow.f64 (.f64 2 (*.f64 (PI.f64) n)) (-.f64 1 k)) k)))
(if (<=.f64 k 8587068825411497/649037107316853453566312041152512) (.f64 (sqrt.f64 (.f64 2 (.f64 n (PI.f64)))) (pow.f64 k -1/2)) (sqrt.f64 (.f64 2 (*.f64 (-.f64 (+.f64 1 (/.f64 (PI.f64) k)) 1) n))))
(if (<=.f64 k 13187203577725160/79228162514264337593543950336) (/.f64 (sqrt.f64 (.f64 n (.f64 (PI.f64) 2))) (sqrt.f64 k)) (sqrt.f64 (.f64 2 (.f64 (-.f64 (+.f64 1 (/.f64 (PI.f64) k)) 1) n))))
(if (<=.f64 k 8587068825411497/649037107316853453566312041152512) (.f64 (sqrt.f64 (.f64 2 (/.f64 (PI.f64) k))) (sqrt.f64 n)) (sqrt.f64 (.f64 2 (.f64 (-.f64 (+.f64 1 (/.f64 (PI.f64) k)) 1) n))))
(sqrt.f64 (.f64 2 (.f64 (-.f64 (+.f64 1 (/.f64 (PI.f64) k)) 1) n)))
(pow.f64 (*.f64 1/2 (/.f64 (/.f64 k n) (PI.f64))) -1/2)
(sqrt.f64 (.f64 2 (.f64 (/.f64 (PI.f64) k) n)))
(sqrt.f64 (*.f64 2 (/.f64 n (/.f64 k (PI.f64)))))

Outputs
(.f64 (pow.f64 k -1/2) (sqrt.f64 (.f64 (pow.f64 (*.f64 2 (PI.f64)) (-.f64 1 k)) (/.f64 n (pow.f64 n k)))))
(.f64 (pow.f64 k -1/2) (sqrt.f64 (pow.f64 (.f64 n (*.f64 2 (PI.f64))) (-.f64 1 k))))
(.f64 (pow.f64 k -1/2) (sqrt.f64 (pow.f64 (.f64 (*.f64 2 (PI.f64)) n) (-.f64 1 k))))
(.f64 (sqrt.f64 (/.f64 1 k)) (pow.f64 (.f64 (*.f64 2 (PI.f64)) n) (/.f64 (-.f64 1 k) 2)))
(.f64 (pow.f64 k -1/2) (pow.f64 (.f64 (*.f64 2 (PI.f64)) n) (/.f64 (-.f64 1 k) 2)))
(/.f64 (pow.f64 (.f64 (PI.f64) (.f64 n 2)) (+.f64 1/2 (*.f64 k -1/2))) (sqrt.f64 k))
(/.f64 (pow.f64 (.f64 (PI.f64) (.f64 2 n)) (+.f64 1/2 (*.f64 k -1/2))) (sqrt.f64 k))
(if (<=.f64 k 8587068825411497/649037107316853453566312041152512) (.f64 (sqrt.f64 (.f64 2 (.f64 n (PI.f64)))) (pow.f64 k -1/2)) (pow.f64 (.f64 k (pow.f64 (.f64 n (.f64 2 (PI.f64))) (-.f64 k 1))) -1/2))
(if (<=.f64 k 8587068825411497/649037107316853453566312041152512) (.f64 (pow.f64 k -1/2) (sqrt.f64 (.f64 2 (.f64 (PI.f64) n)))) (pow.f64 (.f64 k (pow.f64 (.f64 (.f64 2 (PI.f64)) n) (+.f64 k -1))) -1/2))
(if (<=.f64 k 8587068825411497/649037107316853453566312041152512) (.f64 (sqrt.f64 (.f64 2 (.f64 n (PI.f64)))) (pow.f64 k -1/2)) (sqrt.f64 (/.f64 (pow.f64 (.f64 2 (*.f64 (PI.f64) n)) (-.f64 1 k)) k)))
(if (<=.f64 k 8587068825411497/649037107316853453566312041152512) (.f64 (pow.f64 k -1/2) (sqrt.f64 (.f64 2 (.f64 (PI.f64) n)))) (sqrt.f64 (/.f64 (pow.f64 (.f64 2 (*.f64 (PI.f64) n)) (-.f64 1 k)) k)))
(if (<=.f64 k 8587068825411497/649037107316853453566312041152512) (.f64 (sqrt.f64 (.f64 2 (.f64 n (PI.f64)))) (pow.f64 k -1/2)) (sqrt.f64 (.f64 2 (*.f64 (-.f64 (+.f64 1 (/.f64 (PI.f64) k)) 1) n))))
(if (<=.f64 k 8587068825411497/649037107316853453566312041152512) (.f64 (pow.f64 k -1/2) (sqrt.f64 (.f64 2 (.f64 (PI.f64) n)))) (sqrt.f64 (.f64 2 (*.f64 n (+.f64 (+.f64 1 (/.f64 (PI.f64) k)) -1)))))
(if (<=.f64 k 13187203577725160/79228162514264337593543950336) (/.f64 (sqrt.f64 (.f64 n (.f64 (PI.f64) 2))) (sqrt.f64 k)) (sqrt.f64 (.f64 2 (.f64 (-.f64 (+.f64 1 (/.f64 (PI.f64) k)) 1) n))))
(if (<=.f64 k 1648400447215645/9903520314283042199192993792) (/.f64 (sqrt.f64 (.f64 (.f64 2 (PI.f64)) n)) (sqrt.f64 k)) (sqrt.f64 (.f64 2 (.f64 n (+.f64 (+.f64 1 (/.f64 (PI.f64) k)) -1)))))
(if (<=.f64 k 8587068825411497/649037107316853453566312041152512) (.f64 (sqrt.f64 (.f64 2 (/.f64 (PI.f64) k))) (sqrt.f64 n)) (sqrt.f64 (.f64 2 (.f64 (-.f64 (+.f64 1 (/.f64 (PI.f64) k)) 1) n))))
(if (<=.f64 k 8587068825411497/649037107316853453566312041152512) (.f64 (sqrt.f64 (.f64 2 (/.f64 (PI.f64) k))) (sqrt.f64 n)) (sqrt.f64 (.f64 2 (.f64 n (+.f64 (+.f64 1 (/.f64 (PI.f64) k)) -1)))))
(sqrt.f64 (.f64 2 (.f64 (-.f64 (+.f64 1 (/.f64 (PI.f64) k)) 1) n)))
(sqrt.f64 (.f64 2 (.f64 n (+.f64 (+.f64 1 (/.f64 (PI.f64) k)) -1))))
(pow.f64 (*.f64 1/2 (/.f64 (/.f64 k n) (PI.f64))) -1/2)
(sqrt.f64 (.f64 2 (.f64 (/.f64 (PI.f64) k) n)))
(sqrt.f64 (.f64 2 (.f64 n (/.f64 (PI.f64) k))))
(sqrt.f64 (*.f64 2 (/.f64 n (/.f64 k (PI.f64)))))

end150.0ms (1.6%)

Stop Event

1×

fuel

Compiler

Compiled 516 to 378 computations (26.7% saved)