Details

analyze198.0ms (1.4%)

Algorithm

1×

Search

Probability	Valid	Unknown	Precondition	Infinite	Domain	Can't	Iter
0%	0%	99.9%	0.1%	0%	0%	0%	0
0%	0%	99.9%	0.1%	0%	0%	0%	1
0%	0%	50%	0.1%	0%	50%	0%	2
0%	0%	50%	0.1%	0%	50%	0%	3
0%	0%	50%	0.1%	0%	50%	0%	4
25%	12.5%	37.5%	0.1%	0%	50%	0%	5
26.7%	12.5%	34.3%	0.1%	0%	53.1%	0%	6
37%	15.6%	26.5%	0.1%	1.6%	54.6%	1.6%	7
40.8%	15.6%	22.6%	0.1%	2.3%	57%	2.3%	8
49.4%	17.2%	17.6%	0.1%	3.5%	58.1%	3.5%	9
53.3%	17.2%	15%	0.1%	4.1%	59.5%	4.1%	10
59.5%	18%	12.2%	0.1%	4.8%	60.2%	4.8%	11
62.5%	18%	10.8%	0.1%	5.1%	60.9%	5.1%	12

Compiler

Compiled 19 to 16 computations (15.8% saved)

sample6.3s (43.8%)

Results

3.2s	8256×	body	256	valid
2.3s	1257×	body	1024	invalid
370.0ms	1569×	body	256	invalid
367.0ms	697×	body	512	invalid
79.0ms	479×	body	256	infinite
54.0ms	241×	body	256	unsamplable

Bogosity

preprocess6.0ms (0%)

Algorithm

2×	egg-herbie

Rules

26×	`rational_best-simplify-2`
8×	`rational_best-simplify-44`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	24	98
1	29	98
2	37	98
3	45	98
0	2	2

Stop Event

1×	saturated
1×	saturated

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

Compiler

Compiled 20 to 17 computations (15% saved)

simplify15.0ms (0.1%)

Algorithm

1×	egg-herbie

Rules

14×	`rational_best-simplify-2`
4×	`rational_best-simplify-44`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	17	49
1	20	49
2	24	49
3	28	49

Stop Event

1×

saturated

Counts

1 → 3

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

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

eval1.0ms (0%)

Compiler: Compiled 50 to 37 computations (26% saved)

prune1.0ms (0%)

Pruning

2 alts after pruning (2 fresh and 0 done)

	Pruned	Kept	Total
New	2	1	3
Fresh	0	1	1
Picked	0	0	0
Done	0	0	0
Total	2	2	4

Error

0.4b

Counts

4 → 1

Alt Table

Click to see full alt table

Status	Error	Program
▶	0.4b	(.f64 (/.f64 1 (sqrt.f64 k)) (pow.f64 (.f64 (*.f64 2 (PI.f64)) n) (/.f64 (-.f64 1 k) 2)))

Compiler

Compiled 18 to 15 computations (16.7% saved)

localize25.0ms (0.2%)

Local error

Found 4 expressions with local error:

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

Compiler

Compiled 56 to 38 computations (32.1% saved)

series53.0ms (0.4%)

Counts

4 → 48

Calls

18 calls:

Time	Variable		Point	Expression
22.0ms	n	@	0	(pow.f64 (.f64 (.f64 2 (PI.f64)) n) (/.f64 (-.f64 1 k) 2))
17.0ms	n	@	-inf	(pow.f64 (.f64 (.f64 2 (PI.f64)) n) (/.f64 (-.f64 1 k) 2))
6.0ms	n	@	inf	(pow.f64 (.f64 (.f64 2 (PI.f64)) n) (/.f64 (-.f64 1 k) 2))
1.0ms	k	@	0	(.f64 (/.f64 1 (sqrt.f64 k)) (pow.f64 (.f64 (*.f64 2 (PI.f64)) n) (/.f64 (-.f64 1 k) 2)))
1.0ms	k	@	-inf	(.f64 (/.f64 1 (sqrt.f64 k)) (pow.f64 (.f64 (*.f64 2 (PI.f64)) n) (/.f64 (-.f64 1 k) 2)))

rewrite132.0ms (0.9%)

Algorithm

1×	batch-egg-rewrite

Rules

840×	`rational_best-5`
840×	`rational_best-2`
840×	`rational_best-3`
840×	`rational_best-1`
838×	`rational_best-4`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	17	108
1	137	108
2	441	108
3	1867	108
4	7468	108

Stop Event

1×	node limit

Counts

4 → 57

Calls

Call 1

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

simplify241.0ms (1.7%)

Algorithm

1×	egg-herbie

Rules

1082×	`rational_best-simplify-44`
884×	`rational_best-simplify-49`
758×	`rational_best-simplify-132`
618×	`rational_best-simplify-50`
518×	`rational_best-simplify-24`

Iterations

Useful iterations: 4 (0.0ms)

Iter	Nodes	Cost
0	182	3951
1	346	3871
2	693	3831
3	2217	3831
4	3937	3767
5	7558	3767

Stop Event

1×	node limit

Counts

105 → 121

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)))
(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)))))
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(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)))))))
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(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 (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))))))))
(+.f64 (.f64 2 (.f64 (PI.f64) n)) 0)
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(-.f64 (.f64 2 (.f64 (PI.f64) n)) 0)
(-.f64 0 (neg.f64 (.f64 2 (.f64 (PI.f64) n))))
(/.f64 (.f64 2 (.f64 (PI.f64) n)) 1)
(/.f64 (.f64 2 (.f64 (PI.f64) n)) (/.f64 (.f64 (PI.f64) n) (.f64 (PI.f64) n)))
(/.f64 (.f64 (PI.f64) (.f64 n 4)) 2)
(pow.f64 (.f64 2 (.f64 (PI.f64) n)) 1)
(neg.f64 (neg.f64 (.f64 2 (.f64 (PI.f64) n))))
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(-.f64 (pow.f64 (.f64 2 (.f64 (PI.f64) n)) (/.f64 (-.f64 1 k) 2)) 0)
(-.f64 0 (neg.f64 (pow.f64 (.f64 2 (.f64 (PI.f64) n)) (/.f64 (-.f64 1 k) 2))))
(.f64 1 (pow.f64 (.f64 2 (*.f64 (PI.f64) n)) (/.f64 (-.f64 1 k) 2)))
(.f64 (pow.f64 (.f64 2 (*.f64 (PI.f64) n)) (/.f64 (-.f64 1 k) 2)) 1)
(.f64 (pow.f64 (.f64 2 (.f64 (PI.f64) n)) (/.f64 (-.f64 1 k) 2)) (/.f64 (pow.f64 (.f64 2 (.f64 (PI.f64) n)) (/.f64 (-.f64 1 k) 2)) (pow.f64 (.f64 2 (*.f64 (PI.f64) n)) (/.f64 (-.f64 1 k) 2))))
(.f64 (pow.f64 (.f64 2 (.f64 (PI.f64) n)) (/.f64 (-.f64 1 k) 2)) (.f64 (pow.f64 (.f64 2 (.f64 (PI.f64) n)) (/.f64 (-.f64 1 k) 2)) (/.f64 1 (pow.f64 (.f64 2 (.f64 (PI.f64) n)) (/.f64 (-.f64 1 k) 2)))))
(.f64 (pow.f64 (.f64 2 (.f64 (PI.f64) n)) (/.f64 (-.f64 1 k) 2)) (/.f64 1 (/.f64 (pow.f64 (.f64 2 (.f64 (PI.f64) n)) (/.f64 (-.f64 1 k) 2)) (pow.f64 (.f64 2 (*.f64 (PI.f64) n)) (/.f64 (-.f64 1 k) 2)))))
(.f64 (/.f64 (pow.f64 (.f64 2 (.f64 (PI.f64) n)) (/.f64 (-.f64 1 k) 2)) (pow.f64 (.f64 2 (.f64 (PI.f64) n)) (/.f64 (-.f64 1 k) 2))) (pow.f64 (.f64 2 (*.f64 (PI.f64) n)) (/.f64 (-.f64 1 k) 2)))
(.f64 (/.f64 1 (pow.f64 (.f64 2 (.f64 (PI.f64) n)) (/.f64 (-.f64 1 k) 2))) (pow.f64 (.f64 (.f64 2 (.f64 (PI.f64) n)) (.f64 2 (.f64 (PI.f64) n))) (/.f64 (-.f64 1 k) 2)))
(.f64 (pow.f64 (.f64 (.f64 2 (.f64 (PI.f64) n)) (.f64 2 (.f64 (PI.f64) n))) (/.f64 (-.f64 1 k) 2)) (/.f64 1 (pow.f64 (.f64 2 (.f64 (PI.f64) n)) (/.f64 (-.f64 1 k) 2))))
(.f64 (.f64 (pow.f64 (.f64 2 (.f64 (PI.f64) n)) (/.f64 (-.f64 1 k) 2)) (/.f64 1 (pow.f64 (.f64 2 (.f64 (PI.f64) n)) (/.f64 (-.f64 1 k) 2)))) (pow.f64 (.f64 2 (.f64 (PI.f64) n)) (/.f64 (-.f64 1 k) 2)))
(.f64 (/.f64 (/.f64 1 (pow.f64 (.f64 2 (.f64 (PI.f64) n)) (/.f64 (-.f64 1 k) 2))) (pow.f64 (.f64 (.f64 2 (.f64 (PI.f64) n)) (.f64 2 (.f64 (PI.f64) n))) (/.f64 (-.f64 1 k) 2))) (pow.f64 (.f64 (.f64 (.f64 2 (.f64 (PI.f64) n)) (.f64 2 (.f64 (PI.f64) n))) (.f64 (.f64 2 (.f64 (PI.f64) n)) (.f64 2 (*.f64 (PI.f64) n)))) (/.f64 (-.f64 1 k) 2)))
(.f64 (/.f64 (/.f64 (pow.f64 (.f64 2 (.f64 (PI.f64) n)) (/.f64 (-.f64 1 k) 2)) (pow.f64 (.f64 2 (.f64 (PI.f64) n)) (/.f64 (-.f64 1 k) 2))) (pow.f64 (.f64 2 (.f64 (PI.f64) n)) (/.f64 (-.f64 1 k) 2))) (pow.f64 (.f64 (.f64 2 (.f64 (PI.f64) n)) (.f64 2 (.f64 (PI.f64) n))) (/.f64 (-.f64 1 k) 2)))
(.f64 (/.f64 (.f64 (pow.f64 (.f64 2 (.f64 (PI.f64) n)) (/.f64 (-.f64 1 k) 2)) (/.f64 1 (pow.f64 (.f64 2 (.f64 (PI.f64) n)) (/.f64 (-.f64 1 k) 2)))) (pow.f64 (.f64 2 (.f64 (PI.f64) n)) (/.f64 (-.f64 1 k) 2))) (pow.f64 (.f64 (.f64 2 (.f64 (PI.f64) n)) (.f64 2 (*.f64 (PI.f64) n))) (/.f64 (-.f64 1 k) 2)))
(/.f64 (pow.f64 (.f64 2 (.f64 (PI.f64) n)) (/.f64 (-.f64 1 k) 2)) 1)
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(/.f64 (.f64 2 (pow.f64 (.f64 2 (*.f64 (PI.f64) n)) (/.f64 (-.f64 1 k) 2))) 2)
(neg.f64 (neg.f64 (pow.f64 (.f64 2 (.f64 (PI.f64) n)) (/.f64 (-.f64 1 k) 2))))
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(-.f64 0 (neg.f64 (/.f64 1 (sqrt.f64 k))))
(*.f64 1 (/.f64 1 (sqrt.f64 k)))
(*.f64 (/.f64 1 (sqrt.f64 k)) 1)
(*.f64 (/.f64 1 (sqrt.f64 k)) (/.f64 (/.f64 1 (sqrt.f64 k)) (/.f64 1 (sqrt.f64 k))))
(.f64 (/.f64 1 (sqrt.f64 k)) (.f64 (/.f64 1 (sqrt.f64 k)) (/.f64 1 (/.f64 1 (sqrt.f64 k)))))
(*.f64 (/.f64 1 (sqrt.f64 k)) (/.f64 1 (/.f64 (/.f64 1 (sqrt.f64 k)) (/.f64 1 (sqrt.f64 k)))))
(*.f64 (/.f64 (/.f64 1 (sqrt.f64 k)) (/.f64 1 (sqrt.f64 k))) (/.f64 1 (sqrt.f64 k)))
(.f64 (/.f64 1 (/.f64 1 (sqrt.f64 k))) (.f64 (/.f64 1 (sqrt.f64 k)) (/.f64 1 (sqrt.f64 k))))
(.f64 (.f64 (/.f64 1 (sqrt.f64 k)) (/.f64 1 (sqrt.f64 k))) (/.f64 1 (/.f64 1 (sqrt.f64 k))))
(.f64 (.f64 (/.f64 1 (sqrt.f64 k)) (/.f64 1 (/.f64 1 (sqrt.f64 k)))) (/.f64 1 (sqrt.f64 k)))
(.f64 (/.f64 (/.f64 1 (/.f64 1 (sqrt.f64 k))) (.f64 (/.f64 1 (sqrt.f64 k)) (/.f64 1 (sqrt.f64 k)))) (.f64 (.f64 (/.f64 1 (sqrt.f64 k)) (/.f64 1 (sqrt.f64 k))) (*.f64 (/.f64 1 (sqrt.f64 k)) (/.f64 1 (sqrt.f64 k)))))
(.f64 (/.f64 (/.f64 (/.f64 1 (sqrt.f64 k)) (/.f64 1 (sqrt.f64 k))) (/.f64 1 (sqrt.f64 k))) (.f64 (/.f64 1 (sqrt.f64 k)) (/.f64 1 (sqrt.f64 k))))
(.f64 (/.f64 (.f64 (/.f64 1 (sqrt.f64 k)) (/.f64 1 (/.f64 1 (sqrt.f64 k)))) (/.f64 1 (sqrt.f64 k))) (*.f64 (/.f64 1 (sqrt.f64 k)) (/.f64 1 (sqrt.f64 k))))
(pow.f64 (/.f64 1 (sqrt.f64 k)) 1)
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(+.f64 0 (.f64 (pow.f64 (.f64 2 (*.f64 (PI.f64) n)) (/.f64 (-.f64 1 k) 2)) (/.f64 1 (sqrt.f64 k))))
(-.f64 (.f64 (pow.f64 (.f64 2 (*.f64 (PI.f64) n)) (/.f64 (-.f64 1 k) 2)) (/.f64 1 (sqrt.f64 k))) 0)
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(/.f64 (.f64 (pow.f64 (.f64 2 (*.f64 (PI.f64) n)) (/.f64 (-.f64 1 k) 2)) (/.f64 1 (sqrt.f64 k))) 1)
(/.f64 (.f64 (pow.f64 (.f64 2 (.f64 (PI.f64) n)) (/.f64 (-.f64 1 k) 2)) (/.f64 1 (sqrt.f64 k))) (/.f64 (.f64 (pow.f64 (.f64 2 (.f64 (PI.f64) n)) (/.f64 (-.f64 1 k) 2)) (/.f64 1 (sqrt.f64 k))) (.f64 (pow.f64 (.f64 2 (*.f64 (PI.f64) n)) (/.f64 (-.f64 1 k) 2)) (/.f64 1 (sqrt.f64 k)))))
(/.f64 (.f64 (pow.f64 (.f64 2 (.f64 (PI.f64) n)) (/.f64 (-.f64 1 k) 2)) (.f64 2 (/.f64 1 (sqrt.f64 k)))) 2)
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(neg.f64 (neg.f64 (.f64 (pow.f64 (.f64 2 (*.f64 (PI.f64) n)) (/.f64 (-.f64 1 k) 2)) (/.f64 1 (sqrt.f64 k)))))

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))
(exp.f64 (.f64 1/2 (.f64 (-.f64 1 k) (+.f64 (log.f64 n) (log.f64 (*.f64 2 (PI.f64)))))))
(exp.f64 (.f64 (-.f64 1 k) (.f64 1/2 (+.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 (-.f64 1 k) (.f64 1/2 (+.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 (-.f64 1 k) (.f64 1/2 (+.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 (-.f64 1 k) (.f64 1/2 (+.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 (log.f64 (.f64 2 (PI.f64))) (.f64 -1 (log.f64 (/.f64 1 n)))))))
(exp.f64 (.f64 1/2 (.f64 (-.f64 1 k) (+.f64 (log.f64 (*.f64 2 (PI.f64))) (neg.f64 (log.f64 (/.f64 1 n)))))))
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(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 (log.f64 (.f64 2 (PI.f64))) (.f64 -1 (log.f64 (/.f64 1 n)))))))
(exp.f64 (.f64 1/2 (.f64 (-.f64 1 k) (+.f64 (log.f64 (*.f64 2 (PI.f64))) (neg.f64 (log.f64 (/.f64 1 n)))))))
(exp.f64 (.f64 (-.f64 1 k) (.f64 1/2 (+.f64 (log.f64 (*.f64 2 (PI.f64))) (neg.f64 (log.f64 (/.f64 1 n)))))))
(exp.f64 (.f64 1/2 (.f64 (-.f64 1 k) (+.f64 (.f64 -1 (log.f64 (/.f64 1 n))) (log.f64 (.f64 2 (PI.f64)))))))
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(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 (PI.f64) -2))))))
(exp.f64 (.f64 1/2 (.f64 (-.f64 1 k) (+.f64 (neg.f64 (log.f64 (/.f64 -1 n))) (log.f64 (*.f64 (PI.f64) -2))))))
(exp.f64 (.f64 (+.f64 (neg.f64 (log.f64 (/.f64 -1 n))) (log.f64 (.f64 (PI.f64) -2))) (*.f64 1/2 (-.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)))))))
(exp.f64 (.f64 1/2 (.f64 (-.f64 1 k) (+.f64 (.f64 -1 (log.f64 (/.f64 -1 n))) (log.f64 (.f64 (PI.f64) -2))))))
(exp.f64 (.f64 1/2 (.f64 (-.f64 1 k) (+.f64 (neg.f64 (log.f64 (/.f64 -1 n))) (log.f64 (*.f64 (PI.f64) -2))))))
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(exp.f64 (.f64 (+.f64 (neg.f64 (log.f64 (/.f64 -1 n))) (log.f64 (.f64 (PI.f64) -2))) (*.f64 1/2 (-.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)))))))
(exp.f64 (.f64 1/2 (.f64 (-.f64 1 k) (+.f64 (.f64 -1 (log.f64 (/.f64 -1 n))) (log.f64 (.f64 (PI.f64) -2))))))
(exp.f64 (.f64 1/2 (.f64 (-.f64 1 k) (+.f64 (neg.f64 (log.f64 (/.f64 -1 n))) (log.f64 (*.f64 (PI.f64) -2))))))
(exp.f64 (.f64 (+.f64 (neg.f64 (log.f64 (/.f64 -1 n))) (log.f64 (.f64 (PI.f64) -2))) (*.f64 1/2 (-.f64 1 k))))
(.f64 (sqrt.f64 2) (sqrt.f64 (.f64 n (PI.f64))))
(sqrt.f64 (.f64 2 (.f64 n (PI.f64))))
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(.f64 (PI.f64) (.f64 2 n))
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(.f64 2 (.f64 n (PI.f64)))
(.f64 (PI.f64) (.f64 2 n))
(neg.f64 (neg.f64 (.f64 2 (.f64 (PI.f64) n))))
(.f64 2 (.f64 n (PI.f64)))
(.f64 (PI.f64) (.f64 2 n))
(+.f64 (pow.f64 (.f64 2 (.f64 (PI.f64) n)) (/.f64 (-.f64 1 k) 2)) 0)
(pow.f64 (.f64 2 (.f64 n (PI.f64))) (/.f64 (-.f64 1 k) 2))
(pow.f64 (.f64 (PI.f64) (.f64 2 n)) (/.f64 (-.f64 1 k) 2))
(+.f64 0 (pow.f64 (.f64 2 (.f64 (PI.f64) n)) (/.f64 (-.f64 1 k) 2)))
(pow.f64 (.f64 2 (.f64 n (PI.f64))) (/.f64 (-.f64 1 k) 2))
(pow.f64 (.f64 (PI.f64) (.f64 2 n)) (/.f64 (-.f64 1 k) 2))
(-.f64 (pow.f64 (.f64 2 (.f64 (PI.f64) n)) (/.f64 (-.f64 1 k) 2)) 0)
(pow.f64 (.f64 2 (.f64 n (PI.f64))) (/.f64 (-.f64 1 k) 2))
(pow.f64 (.f64 (PI.f64) (.f64 2 n)) (/.f64 (-.f64 1 k) 2))
(-.f64 0 (neg.f64 (pow.f64 (.f64 2 (.f64 (PI.f64) n)) (/.f64 (-.f64 1 k) 2))))
(pow.f64 (.f64 2 (.f64 n (PI.f64))) (/.f64 (-.f64 1 k) 2))
(pow.f64 (.f64 (PI.f64) (.f64 2 n)) (/.f64 (-.f64 1 k) 2))
(.f64 1 (pow.f64 (.f64 2 (*.f64 (PI.f64) n)) (/.f64 (-.f64 1 k) 2)))
(pow.f64 (.f64 2 (.f64 n (PI.f64))) (/.f64 (-.f64 1 k) 2))
(pow.f64 (.f64 (PI.f64) (.f64 2 n)) (/.f64 (-.f64 1 k) 2))
(.f64 (pow.f64 (.f64 2 (*.f64 (PI.f64) n)) (/.f64 (-.f64 1 k) 2)) 1)
(pow.f64 (.f64 2 (.f64 n (PI.f64))) (/.f64 (-.f64 1 k) 2))
(pow.f64 (.f64 (PI.f64) (.f64 2 n)) (/.f64 (-.f64 1 k) 2))
(.f64 (pow.f64 (.f64 2 (.f64 (PI.f64) n)) (/.f64 (-.f64 1 k) 2)) (/.f64 (pow.f64 (.f64 2 (.f64 (PI.f64) n)) (/.f64 (-.f64 1 k) 2)) (pow.f64 (.f64 2 (*.f64 (PI.f64) n)) (/.f64 (-.f64 1 k) 2))))
(pow.f64 (.f64 2 (.f64 n (PI.f64))) (/.f64 (-.f64 1 k) 2))
(pow.f64 (.f64 (PI.f64) (.f64 2 n)) (/.f64 (-.f64 1 k) 2))
(.f64 (pow.f64 (.f64 2 (.f64 (PI.f64) n)) (/.f64 (-.f64 1 k) 2)) (.f64 (pow.f64 (.f64 2 (.f64 (PI.f64) n)) (/.f64 (-.f64 1 k) 2)) (/.f64 1 (pow.f64 (.f64 2 (.f64 (PI.f64) n)) (/.f64 (-.f64 1 k) 2)))))
(pow.f64 (.f64 2 (.f64 n (PI.f64))) (/.f64 (-.f64 1 k) 2))
(pow.f64 (.f64 (PI.f64) (.f64 2 n)) (/.f64 (-.f64 1 k) 2))
(.f64 (pow.f64 (.f64 2 (.f64 (PI.f64) n)) (/.f64 (-.f64 1 k) 2)) (/.f64 1 (/.f64 (pow.f64 (.f64 2 (.f64 (PI.f64) n)) (/.f64 (-.f64 1 k) 2)) (pow.f64 (.f64 2 (*.f64 (PI.f64) n)) (/.f64 (-.f64 1 k) 2)))))
(pow.f64 (.f64 2 (.f64 n (PI.f64))) (/.f64 (-.f64 1 k) 2))
(pow.f64 (.f64 (PI.f64) (.f64 2 n)) (/.f64 (-.f64 1 k) 2))
(.f64 (/.f64 (pow.f64 (.f64 2 (.f64 (PI.f64) n)) (/.f64 (-.f64 1 k) 2)) (pow.f64 (.f64 2 (.f64 (PI.f64) n)) (/.f64 (-.f64 1 k) 2))) (pow.f64 (.f64 2 (*.f64 (PI.f64) n)) (/.f64 (-.f64 1 k) 2)))
(pow.f64 (.f64 2 (.f64 n (PI.f64))) (/.f64 (-.f64 1 k) 2))
(pow.f64 (.f64 (PI.f64) (.f64 2 n)) (/.f64 (-.f64 1 k) 2))
(.f64 (/.f64 1 (pow.f64 (.f64 2 (.f64 (PI.f64) n)) (/.f64 (-.f64 1 k) 2))) (pow.f64 (.f64 (.f64 2 (.f64 (PI.f64) n)) (.f64 2 (.f64 (PI.f64) n))) (/.f64 (-.f64 1 k) 2)))
(pow.f64 (.f64 2 (.f64 n (PI.f64))) (/.f64 (-.f64 1 k) 2))
(pow.f64 (.f64 (PI.f64) (.f64 2 n)) (/.f64 (-.f64 1 k) 2))
(.f64 (pow.f64 (.f64 (.f64 2 (.f64 (PI.f64) n)) (.f64 2 (.f64 (PI.f64) n))) (/.f64 (-.f64 1 k) 2)) (/.f64 1 (pow.f64 (.f64 2 (.f64 (PI.f64) n)) (/.f64 (-.f64 1 k) 2))))
(pow.f64 (.f64 2 (.f64 n (PI.f64))) (/.f64 (-.f64 1 k) 2))
(pow.f64 (.f64 (PI.f64) (.f64 2 n)) (/.f64 (-.f64 1 k) 2))
(.f64 (.f64 (pow.f64 (.f64 2 (.f64 (PI.f64) n)) (/.f64 (-.f64 1 k) 2)) (/.f64 1 (pow.f64 (.f64 2 (.f64 (PI.f64) n)) (/.f64 (-.f64 1 k) 2)))) (pow.f64 (.f64 2 (.f64 (PI.f64) n)) (/.f64 (-.f64 1 k) 2)))
(pow.f64 (.f64 2 (.f64 n (PI.f64))) (/.f64 (-.f64 1 k) 2))
(pow.f64 (.f64 (PI.f64) (.f64 2 n)) (/.f64 (-.f64 1 k) 2))
(.f64 (/.f64 (/.f64 1 (pow.f64 (.f64 2 (.f64 (PI.f64) n)) (/.f64 (-.f64 1 k) 2))) (pow.f64 (.f64 (.f64 2 (.f64 (PI.f64) n)) (.f64 2 (.f64 (PI.f64) n))) (/.f64 (-.f64 1 k) 2))) (pow.f64 (.f64 (.f64 (.f64 2 (.f64 (PI.f64) n)) (.f64 2 (.f64 (PI.f64) n))) (.f64 (.f64 2 (.f64 (PI.f64) n)) (.f64 2 (*.f64 (PI.f64) n)))) (/.f64 (-.f64 1 k) 2)))
(pow.f64 (.f64 2 (.f64 n (PI.f64))) (/.f64 (-.f64 1 k) 2))
(pow.f64 (.f64 (PI.f64) (.f64 2 n)) (/.f64 (-.f64 1 k) 2))
(.f64 (/.f64 (/.f64 (pow.f64 (.f64 2 (.f64 (PI.f64) n)) (/.f64 (-.f64 1 k) 2)) (pow.f64 (.f64 2 (.f64 (PI.f64) n)) (/.f64 (-.f64 1 k) 2))) (pow.f64 (.f64 2 (.f64 (PI.f64) n)) (/.f64 (-.f64 1 k) 2))) (pow.f64 (.f64 (.f64 2 (.f64 (PI.f64) n)) (.f64 2 (.f64 (PI.f64) n))) (/.f64 (-.f64 1 k) 2)))
(pow.f64 (.f64 2 (.f64 n (PI.f64))) (/.f64 (-.f64 1 k) 2))
(pow.f64 (.f64 (PI.f64) (.f64 2 n)) (/.f64 (-.f64 1 k) 2))
(.f64 (/.f64 (.f64 (pow.f64 (.f64 2 (.f64 (PI.f64) n)) (/.f64 (-.f64 1 k) 2)) (/.f64 1 (pow.f64 (.f64 2 (.f64 (PI.f64) n)) (/.f64 (-.f64 1 k) 2)))) (pow.f64 (.f64 2 (.f64 (PI.f64) n)) (/.f64 (-.f64 1 k) 2))) (pow.f64 (.f64 (.f64 2 (.f64 (PI.f64) n)) (.f64 2 (*.f64 (PI.f64) n))) (/.f64 (-.f64 1 k) 2)))
(pow.f64 (.f64 2 (.f64 n (PI.f64))) (/.f64 (-.f64 1 k) 2))
(pow.f64 (.f64 (PI.f64) (.f64 2 n)) (/.f64 (-.f64 1 k) 2))
(/.f64 (pow.f64 (.f64 2 (.f64 (PI.f64) n)) (/.f64 (-.f64 1 k) 2)) 1)
(pow.f64 (.f64 2 (.f64 n (PI.f64))) (/.f64 (-.f64 1 k) 2))
(pow.f64 (.f64 (PI.f64) (.f64 2 n)) (/.f64 (-.f64 1 k) 2))
(/.f64 (pow.f64 (.f64 2 (.f64 (PI.f64) n)) (/.f64 (-.f64 1 k) 2)) (/.f64 (pow.f64 (.f64 2 (.f64 (PI.f64) n)) (/.f64 (-.f64 1 k) 2)) (pow.f64 (.f64 2 (.f64 (PI.f64) n)) (/.f64 (-.f64 1 k) 2))))
(pow.f64 (.f64 2 (.f64 n (PI.f64))) (/.f64 (-.f64 1 k) 2))
(pow.f64 (.f64 (PI.f64) (.f64 2 n)) (/.f64 (-.f64 1 k) 2))
(/.f64 (.f64 2 (pow.f64 (.f64 2 (*.f64 (PI.f64) n)) (/.f64 (-.f64 1 k) 2))) 2)
(pow.f64 (.f64 2 (.f64 n (PI.f64))) (/.f64 (-.f64 1 k) 2))
(pow.f64 (.f64 (PI.f64) (.f64 2 n)) (/.f64 (-.f64 1 k) 2))
(neg.f64 (neg.f64 (pow.f64 (.f64 2 (.f64 (PI.f64) n)) (/.f64 (-.f64 1 k) 2))))
(pow.f64 (.f64 2 (.f64 n (PI.f64))) (/.f64 (-.f64 1 k) 2))
(pow.f64 (.f64 (PI.f64) (.f64 2 n)) (/.f64 (-.f64 1 k) 2))
(+.f64 (/.f64 1 (sqrt.f64 k)) 0)
(/.f64 1 (sqrt.f64 k))
(+.f64 0 (/.f64 1 (sqrt.f64 k)))
(/.f64 1 (sqrt.f64 k))
(-.f64 (/.f64 1 (sqrt.f64 k)) 0)
(/.f64 1 (sqrt.f64 k))
(-.f64 0 (neg.f64 (/.f64 1 (sqrt.f64 k))))
(/.f64 1 (sqrt.f64 k))
(*.f64 1 (/.f64 1 (sqrt.f64 k)))
(/.f64 1 (sqrt.f64 k))
(*.f64 (/.f64 1 (sqrt.f64 k)) 1)
(/.f64 1 (sqrt.f64 k))
(*.f64 (/.f64 1 (sqrt.f64 k)) (/.f64 (/.f64 1 (sqrt.f64 k)) (/.f64 1 (sqrt.f64 k))))
(/.f64 1 (sqrt.f64 k))
(.f64 (/.f64 1 (sqrt.f64 k)) (.f64 (/.f64 1 (sqrt.f64 k)) (/.f64 1 (/.f64 1 (sqrt.f64 k)))))
(/.f64 1 (sqrt.f64 k))
(*.f64 (/.f64 1 (sqrt.f64 k)) (/.f64 1 (/.f64 (/.f64 1 (sqrt.f64 k)) (/.f64 1 (sqrt.f64 k)))))
(/.f64 1 (sqrt.f64 k))
(*.f64 (/.f64 (/.f64 1 (sqrt.f64 k)) (/.f64 1 (sqrt.f64 k))) (/.f64 1 (sqrt.f64 k)))
(/.f64 1 (sqrt.f64 k))
(.f64 (/.f64 1 (/.f64 1 (sqrt.f64 k))) (.f64 (/.f64 1 (sqrt.f64 k)) (/.f64 1 (sqrt.f64 k))))
(/.f64 1 (sqrt.f64 k))
(.f64 (.f64 (/.f64 1 (sqrt.f64 k)) (/.f64 1 (sqrt.f64 k))) (/.f64 1 (/.f64 1 (sqrt.f64 k))))
(/.f64 1 (sqrt.f64 k))
(.f64 (.f64 (/.f64 1 (sqrt.f64 k)) (/.f64 1 (/.f64 1 (sqrt.f64 k)))) (/.f64 1 (sqrt.f64 k)))
(/.f64 1 (sqrt.f64 k))
(.f64 (/.f64 (/.f64 1 (/.f64 1 (sqrt.f64 k))) (.f64 (/.f64 1 (sqrt.f64 k)) (/.f64 1 (sqrt.f64 k)))) (.f64 (.f64 (/.f64 1 (sqrt.f64 k)) (/.f64 1 (sqrt.f64 k))) (*.f64 (/.f64 1 (sqrt.f64 k)) (/.f64 1 (sqrt.f64 k)))))
(/.f64 1 (sqrt.f64 k))
(.f64 (/.f64 (/.f64 (/.f64 1 (sqrt.f64 k)) (/.f64 1 (sqrt.f64 k))) (/.f64 1 (sqrt.f64 k))) (.f64 (/.f64 1 (sqrt.f64 k)) (/.f64 1 (sqrt.f64 k))))
(/.f64 1 (sqrt.f64 k))
(.f64 (/.f64 (.f64 (/.f64 1 (sqrt.f64 k)) (/.f64 1 (/.f64 1 (sqrt.f64 k)))) (/.f64 1 (sqrt.f64 k))) (*.f64 (/.f64 1 (sqrt.f64 k)) (/.f64 1 (sqrt.f64 k))))
(/.f64 1 (sqrt.f64 k))
(pow.f64 (/.f64 1 (sqrt.f64 k)) 1)
(/.f64 1 (sqrt.f64 k))
(neg.f64 (neg.f64 (/.f64 1 (sqrt.f64 k))))
(/.f64 1 (sqrt.f64 k))
(+.f64 (.f64 (pow.f64 (.f64 2 (*.f64 (PI.f64) n)) (/.f64 (-.f64 1 k) 2)) (/.f64 1 (sqrt.f64 k))) 0)
(.f64 (pow.f64 (.f64 2 (*.f64 n (PI.f64))) (/.f64 (-.f64 1 k) 2)) (/.f64 1 (sqrt.f64 k)))
(.f64 (pow.f64 (.f64 (PI.f64) (*.f64 2 n)) (/.f64 (-.f64 1 k) 2)) (/.f64 1 (sqrt.f64 k)))
(+.f64 0 (.f64 (pow.f64 (.f64 2 (*.f64 (PI.f64) n)) (/.f64 (-.f64 1 k) 2)) (/.f64 1 (sqrt.f64 k))))
(.f64 (pow.f64 (.f64 2 (*.f64 n (PI.f64))) (/.f64 (-.f64 1 k) 2)) (/.f64 1 (sqrt.f64 k)))
(.f64 (pow.f64 (.f64 (PI.f64) (*.f64 2 n)) (/.f64 (-.f64 1 k) 2)) (/.f64 1 (sqrt.f64 k)))
(-.f64 (.f64 (pow.f64 (.f64 2 (*.f64 (PI.f64) n)) (/.f64 (-.f64 1 k) 2)) (/.f64 1 (sqrt.f64 k))) 0)
(.f64 (pow.f64 (.f64 2 (*.f64 n (PI.f64))) (/.f64 (-.f64 1 k) 2)) (/.f64 1 (sqrt.f64 k)))
(.f64 (pow.f64 (.f64 (PI.f64) (*.f64 2 n)) (/.f64 (-.f64 1 k) 2)) (/.f64 1 (sqrt.f64 k)))
(-.f64 0 (neg.f64 (.f64 (pow.f64 (.f64 2 (*.f64 (PI.f64) n)) (/.f64 (-.f64 1 k) 2)) (/.f64 1 (sqrt.f64 k)))))
(.f64 (pow.f64 (.f64 2 (*.f64 n (PI.f64))) (/.f64 (-.f64 1 k) 2)) (/.f64 1 (sqrt.f64 k)))
(.f64 (pow.f64 (.f64 (PI.f64) (*.f64 2 n)) (/.f64 (-.f64 1 k) 2)) (/.f64 1 (sqrt.f64 k)))
(/.f64 (.f64 (pow.f64 (.f64 2 (*.f64 (PI.f64) n)) (/.f64 (-.f64 1 k) 2)) (/.f64 1 (sqrt.f64 k))) 1)
(.f64 (pow.f64 (.f64 2 (*.f64 n (PI.f64))) (/.f64 (-.f64 1 k) 2)) (/.f64 1 (sqrt.f64 k)))
(.f64 (pow.f64 (.f64 (PI.f64) (*.f64 2 n)) (/.f64 (-.f64 1 k) 2)) (/.f64 1 (sqrt.f64 k)))
(/.f64 (.f64 (pow.f64 (.f64 2 (.f64 (PI.f64) n)) (/.f64 (-.f64 1 k) 2)) (/.f64 1 (sqrt.f64 k))) (/.f64 (.f64 (pow.f64 (.f64 2 (.f64 (PI.f64) n)) (/.f64 (-.f64 1 k) 2)) (/.f64 1 (sqrt.f64 k))) (.f64 (pow.f64 (.f64 2 (*.f64 (PI.f64) n)) (/.f64 (-.f64 1 k) 2)) (/.f64 1 (sqrt.f64 k)))))
(.f64 (pow.f64 (.f64 2 (*.f64 n (PI.f64))) (/.f64 (-.f64 1 k) 2)) (/.f64 1 (sqrt.f64 k)))
(.f64 (pow.f64 (.f64 (PI.f64) (*.f64 2 n)) (/.f64 (-.f64 1 k) 2)) (/.f64 1 (sqrt.f64 k)))
(/.f64 (.f64 (pow.f64 (.f64 2 (.f64 (PI.f64) n)) (/.f64 (-.f64 1 k) 2)) (.f64 2 (/.f64 1 (sqrt.f64 k)))) 2)
(.f64 (pow.f64 (.f64 2 (*.f64 n (PI.f64))) (/.f64 (-.f64 1 k) 2)) (/.f64 1 (sqrt.f64 k)))
(.f64 (pow.f64 (.f64 (PI.f64) (*.f64 2 n)) (/.f64 (-.f64 1 k) 2)) (/.f64 1 (sqrt.f64 k)))
(pow.f64 (.f64 (pow.f64 (.f64 2 (*.f64 (PI.f64) n)) (/.f64 (-.f64 1 k) 2)) (/.f64 1 (sqrt.f64 k))) 1)
(.f64 (pow.f64 (.f64 2 (*.f64 n (PI.f64))) (/.f64 (-.f64 1 k) 2)) (/.f64 1 (sqrt.f64 k)))
(.f64 (pow.f64 (.f64 (PI.f64) (*.f64 2 n)) (/.f64 (-.f64 1 k) 2)) (/.f64 1 (sqrt.f64 k)))
(neg.f64 (neg.f64 (.f64 (pow.f64 (.f64 2 (*.f64 (PI.f64) n)) (/.f64 (-.f64 1 k) 2)) (/.f64 1 (sqrt.f64 k)))))
(.f64 (pow.f64 (.f64 2 (*.f64 n (PI.f64))) (/.f64 (-.f64 1 k) 2)) (/.f64 1 (sqrt.f64 k)))
(.f64 (pow.f64 (.f64 (PI.f64) (*.f64 2 n)) (/.f64 (-.f64 1 k) 2)) (/.f64 1 (sqrt.f64 k)))

eval50.0ms (0.3%)

Compiler: Compiled 3275 to 2182 computations (33.4% saved)

prune252.0ms (1.7%)

Pruning

12 alts after pruning (11 fresh and 1 done)

	Pruned	Kept	Total
New	110	11	121
Fresh	0	0	0
Picked	0	1	1
Done	0	0	0
Total	110	12	122

Error

0.2b

Counts

122 → 12

Alt Table

Click to see full alt table

Status	Error	Program
▶	21.1b	(.f64 (/.f64 1 (sqrt.f64 k)) (pow.f64 (.f64 (/.f64 2 (.f64 n (PI.f64))) (.f64 n (.f64 (.f64 n (PI.f64)) (PI.f64)))) (/.f64 (-.f64 1 k) 2)))
✓	0.4b	(.f64 (/.f64 1 (sqrt.f64 k)) (pow.f64 (.f64 (*.f64 2 (PI.f64)) n) (/.f64 (-.f64 1 k) 2)))
	22.3b	(.f64 (/.f64 1 (sqrt.f64 k)) (+.f64 (.f64 (sqrt.f64 (.f64 n (PI.f64))) (+.f64 (.f64 (log.f64 (.f64 (PI.f64) (.f64 2 n))) (.f64 -1/2 (.f64 k (sqrt.f64 2)))) (sqrt.f64 2))) (.f64 1/8 (.f64 (sqrt.f64 (.f64 (PI.f64) (.f64 2 n))) (pow.f64 (.f64 k (log.f64 (.f64 (PI.f64) (*.f64 2 n)))) 2)))))
	22.2b	(.f64 (/.f64 1 (sqrt.f64 k)) (+.f64 (sqrt.f64 (.f64 2 (.f64 n (PI.f64)))) (.f64 -1/2 (.f64 (.f64 k (log.f64 (.f64 2 (.f64 n (PI.f64))))) (sqrt.f64 (.f64 2 (.f64 n (PI.f64))))))))
	42.6b	(.f64 (/.f64 1 (sqrt.f64 k)) (.f64 (pow.f64 (.f64 (.f64 2 (.f64 (PI.f64) n)) (.f64 2 (.f64 (PI.f64) n))) (/.f64 (-.f64 1 k) 2)) (/.f64 1 (pow.f64 (.f64 2 (*.f64 (PI.f64) n)) (/.f64 (-.f64 1 k) 2)))))
	22.0b	(.f64 (/.f64 1 (sqrt.f64 k)) (.f64 (pow.f64 (.f64 2 (.f64 (PI.f64) n)) (/.f64 (-.f64 1 k) 2)) (.f64 (pow.f64 (.f64 2 (.f64 (PI.f64) n)) (/.f64 (-.f64 1 k) 2)) (/.f64 1 (pow.f64 (.f64 2 (*.f64 (PI.f64) n)) (/.f64 (-.f64 1 k) 2))))))
▶	22.3b	(.f64 (/.f64 1 (sqrt.f64 k)) (.f64 (sqrt.f64 (.f64 n (PI.f64))) (+.f64 (.f64 (log.f64 (.f64 (PI.f64) (.f64 2 n))) (.f64 -1/2 (.f64 k (sqrt.f64 2)))) (sqrt.f64 2))))
	22.4b	(.f64 (/.f64 1 (sqrt.f64 k)) (.f64 (sqrt.f64 2) (sqrt.f64 (*.f64 n (PI.f64)))))
▶	22.3b	(.f64 (/.f64 1 (sqrt.f64 k)) (sqrt.f64 (.f64 (PI.f64) (*.f64 2 n))))
▶	3.4b	(.f64 (/.f64 1 (sqrt.f64 k)) (exp.f64 (.f64 1/2 (.f64 (-.f64 1 k) (log.f64 (.f64 2 (*.f64 n (PI.f64))))))))
▶	0.6b	(.f64 (.f64 (/.f64 1 (/.f64 1 (sqrt.f64 k))) (.f64 (/.f64 1 (sqrt.f64 k)) (/.f64 1 (sqrt.f64 k)))) (pow.f64 (.f64 (*.f64 2 (PI.f64)) n) (/.f64 (-.f64 1 k) 2)))
	3.7b	(.f64 (sqrt.f64 (/.f64 1 k)) (exp.f64 (.f64 (-.f64 1 k) (.f64 1/2 (+.f64 (log.f64 n) (log.f64 (.f64 2 (PI.f64))))))))

Compiler

Compiled 644 to 501 computations (22.2% saved)

localize36.0ms (0.3%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.3b	(/.f64 1 (/.f64 1 (sqrt.f64 k)))
	0.3b	(.f64 (.f64 2 (PI.f64)) n)
✓	0.4b	(.f64 (/.f64 1 (/.f64 1 (sqrt.f64 k))) (.f64 (/.f64 1 (sqrt.f64 k)) (/.f64 1 (sqrt.f64 k))))
✓	0.5b	(*.f64 (/.f64 1 (sqrt.f64 k)) (/.f64 1 (sqrt.f64 k)))

Compiler

Compiled 99 to 65 computations (34.3% saved)

series90.0ms (0.6%)

Counts

3 → 12

Calls

9 calls:

Time	Variable		Point	Expression
87.0ms	k	@	0	(.f64 (/.f64 1 (/.f64 1 (sqrt.f64 k))) (.f64 (/.f64 1 (sqrt.f64 k)) (/.f64 1 (sqrt.f64 k))))
1.0ms	k	@	-inf	(*.f64 (/.f64 1 (sqrt.f64 k)) (/.f64 1 (sqrt.f64 k)))
0.0ms	k	@	-inf	(/.f64 1 (/.f64 1 (sqrt.f64 k)))
0.0ms	k	@	0	(*.f64 (/.f64 1 (sqrt.f64 k)) (/.f64 1 (sqrt.f64 k)))
0.0ms	k	@	inf	(/.f64 1 (/.f64 1 (sqrt.f64 k)))

rewrite228.0ms (1.6%)

Algorithm

1×	batch-egg-rewrite

Rules

1204×	`rational_best-simplify-57`
782×	`rational_best-simplify-43`
760×	`rational_best-simplify-47`
598×	`rational_best-5`
596×	`rational_best-4`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	10	55
1	86	55
2	281	55
3	1211	55
4	5491	55

Stop Event

1×	node limit

Counts

3 → 100

Calls

Call 1

Inputs
(*.f64 (/.f64 1 (sqrt.f64 k)) (/.f64 1 (sqrt.f64 k)))
(.f64 (/.f64 1 (/.f64 1 (sqrt.f64 k))) (.f64 (/.f64 1 (sqrt.f64 k)) (/.f64 1 (sqrt.f64 k))))
(/.f64 1 (/.f64 1 (sqrt.f64 k)))

Outputs
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simplify496.0ms (3.4%)

Algorithm

1×	egg-herbie

Rules

1524×	`rational_best-simplify-80`
1464×	`rational_best-simplify-78`
1354×	`rational_best-simplify-24`
1262×	`rational_best-simplify-94`
1016×	`rational_best-simplify-135`

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	243	3634
1	558	3586
2	1156	3550
3	3730	3550
4	7467	3550

Stop Event

1×	node limit

Counts

112 → 126

Calls

Call 1

Inputs
(/.f64 1 k)
(/.f64 1 k)
(/.f64 1 k)
(/.f64 1 k)
(/.f64 1 k)
(/.f64 1 k)
(/.f64 1 k)
(/.f64 1 k)
(/.f64 -1 (*.f64 k (pow.f64 (sqrt.f64 -1) 2)))
(/.f64 -1 (*.f64 k (pow.f64 (sqrt.f64 -1) 2)))
(/.f64 -1 (*.f64 k (pow.f64 (sqrt.f64 -1) 2)))
(/.f64 -1 (*.f64 k (pow.f64 (sqrt.f64 -1) 2)))
(+.f64 (*.f64 (/.f64 1 (sqrt.f64 k)) (/.f64 1 (sqrt.f64 k))) 0)
(+.f64 0 (*.f64 (/.f64 1 (sqrt.f64 k)) (/.f64 1 (sqrt.f64 k))))
(-.f64 (*.f64 (/.f64 1 (sqrt.f64 k)) (/.f64 1 (sqrt.f64 k))) 0)
(-.f64 0 (neg.f64 (*.f64 (/.f64 1 (sqrt.f64 k)) (/.f64 1 (sqrt.f64 k)))))
(/.f64 (*.f64 (/.f64 1 (sqrt.f64 k)) (/.f64 1 (sqrt.f64 k))) 1)
(/.f64 (*.f64 (/.f64 1 (sqrt.f64 k)) (/.f64 1 (sqrt.f64 k))) (/.f64 (/.f64 1 (sqrt.f64 k)) (/.f64 1 (sqrt.f64 k))))
(/.f64 (.f64 (/.f64 1 (sqrt.f64 k)) (.f64 (/.f64 1 (sqrt.f64 k)) 2)) 2)
(pow.f64 (*.f64 (/.f64 1 (sqrt.f64 k)) (/.f64 1 (sqrt.f64 k))) 1)
(neg.f64 (neg.f64 (*.f64 (/.f64 1 (sqrt.f64 k)) (/.f64 1 (sqrt.f64 k)))))
(fabs.f64 (*.f64 (/.f64 1 (sqrt.f64 k)) (/.f64 1 (sqrt.f64 k))))
(fabs.f64 (neg.f64 (*.f64 (/.f64 1 (sqrt.f64 k)) (/.f64 1 (sqrt.f64 k)))))
(fabs.f64 (/.f64 (*.f64 (/.f64 1 (sqrt.f64 k)) (/.f64 1 (sqrt.f64 k))) (fabs.f64 (/.f64 (/.f64 1 (sqrt.f64 k)) (/.f64 1 (sqrt.f64 k))))))
(fabs.f64 (/.f64 (*.f64 (/.f64 1 (sqrt.f64 k)) (/.f64 1 (sqrt.f64 k))) (neg.f64 (/.f64 (/.f64 1 (sqrt.f64 k)) (/.f64 1 (sqrt.f64 k))))))
(fabs.f64 (.f64 (.f64 (/.f64 1 (sqrt.f64 k)) (*.f64 (/.f64 1 (sqrt.f64 k)) (/.f64 1 (sqrt.f64 k)))) (fabs.f64 (/.f64 1 (/.f64 1 (sqrt.f64 k))))))
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(fabs.f64 (.f64 (.f64 (/.f64 1 (sqrt.f64 k)) (.f64 (/.f64 1 (sqrt.f64 k)) (/.f64 1 (sqrt.f64 k)))) (fabs.f64 (.f64 (/.f64 1 (sqrt.f64 k)) (/.f64 (/.f64 1 (/.f64 1 (sqrt.f64 k))) (/.f64 1 (sqrt.f64 k)))))))
(fabs.f64 (.f64 (.f64 (/.f64 1 (sqrt.f64 k)) (neg.f64 (.f64 (/.f64 1 (sqrt.f64 k)) (/.f64 1 (sqrt.f64 k))))) (fabs.f64 (.f64 (/.f64 1 (sqrt.f64 k)) (/.f64 (/.f64 1 (/.f64 1 (sqrt.f64 k))) (/.f64 1 (sqrt.f64 k)))))))
(fabs.f64 (.f64 (.f64 (/.f64 1 (sqrt.f64 k)) (/.f64 (.f64 (/.f64 1 (sqrt.f64 k)) (/.f64 1 (sqrt.f64 k))) (fabs.f64 (/.f64 (/.f64 1 (sqrt.f64 k)) (/.f64 1 (sqrt.f64 k)))))) (fabs.f64 (.f64 (/.f64 1 (sqrt.f64 k)) (/.f64 (/.f64 1 (/.f64 1 (sqrt.f64 k))) (/.f64 1 (sqrt.f64 k)))))))
(fabs.f64 (.f64 (.f64 (/.f64 1 (sqrt.f64 k)) (.f64 (/.f64 1 (sqrt.f64 k)) (/.f64 1 (sqrt.f64 k)))) (fabs.f64 (.f64 (/.f64 1 (/.f64 1 (sqrt.f64 k))) (/.f64 (/.f64 1 (sqrt.f64 k)) (/.f64 1 (sqrt.f64 k)))))))
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(fabs.f64 (.f64 (.f64 (/.f64 1 (/.f64 1 (sqrt.f64 k))) (/.f64 1 (/.f64 1 (sqrt.f64 k)))) (.f64 (.f64 (/.f64 1 (sqrt.f64 k)) (/.f64 1 (sqrt.f64 k))) (*.f64 (/.f64 1 (sqrt.f64 k)) (/.f64 1 (sqrt.f64 k))))))
(fabs.f64 (.f64 (.f64 (/.f64 1 (/.f64 1 (sqrt.f64 k))) (/.f64 1 (/.f64 1 (sqrt.f64 k)))) (.f64 (.f64 (/.f64 1 (sqrt.f64 k)) (/.f64 1 (sqrt.f64 k))) (neg.f64 (*.f64 (/.f64 1 (sqrt.f64 k)) (/.f64 1 (sqrt.f64 k)))))))
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(fabs.f64 (*.f64 (/.f64 1 (sqrt.f64 k)) (fabs.f64 (/.f64 1 (sqrt.f64 k)))))
(fabs.f64 (.f64 (fabs.f64 (/.f64 1 (sqrt.f64 k))) (.f64 (/.f64 1 (/.f64 1 (sqrt.f64 k))) (neg.f64 (*.f64 (/.f64 1 (sqrt.f64 k)) (/.f64 1 (sqrt.f64 k)))))))
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(fabs.f64 (/.f64 (.f64 (.f64 (/.f64 1 (sqrt.f64 k)) 2) (neg.f64 (/.f64 1 (sqrt.f64 k)))) 2))
(fabs.f64 (/.f64 (.f64 (.f64 (/.f64 1 (sqrt.f64 k)) 2) (fabs.f64 (/.f64 1 (sqrt.f64 k)))) 2))
(fabs.f64 (/.f64 (.f64 (.f64 (/.f64 1 (sqrt.f64 k)) 2) (/.f64 1 (fabs.f64 (sqrt.f64 k)))) 2))
(fabs.f64 (/.f64 (.f64 (.f64 (/.f64 1 (sqrt.f64 k)) 2) (/.f64 (/.f64 1 (sqrt.f64 k)) (fabs.f64 (/.f64 (/.f64 1 (sqrt.f64 k)) (/.f64 1 (sqrt.f64 k)))))) 2))
(fabs.f64 (/.f64 (.f64 (.f64 (/.f64 1 (sqrt.f64 k)) 2) (.f64 (.f64 (/.f64 1 (sqrt.f64 k)) (/.f64 1 (sqrt.f64 k))) (fabs.f64 (/.f64 1 (/.f64 1 (sqrt.f64 k)))))) 2))
(fabs.f64 (/.f64 (.f64 (.f64 (/.f64 1 (sqrt.f64 k)) 2) (.f64 (neg.f64 (.f64 (/.f64 1 (sqrt.f64 k)) (/.f64 1 (sqrt.f64 k)))) (fabs.f64 (/.f64 1 (/.f64 1 (sqrt.f64 k)))))) 2))
(fabs.f64 (/.f64 (.f64 (.f64 (/.f64 1 (sqrt.f64 k)) 2) (.f64 (fabs.f64 (/.f64 1 (/.f64 1 (sqrt.f64 k)))) (/.f64 (.f64 (/.f64 1 (sqrt.f64 k)) (/.f64 1 (sqrt.f64 k))) (fabs.f64 (/.f64 (/.f64 1 (sqrt.f64 k)) (/.f64 1 (sqrt.f64 k))))))) 2))
(fabs.f64 (/.f64 (.f64 (.f64 (/.f64 1 (sqrt.f64 k)) 2) (.f64 (/.f64 1 (/.f64 1 (sqrt.f64 k))) (neg.f64 (.f64 (/.f64 1 (sqrt.f64 k)) (/.f64 1 (sqrt.f64 k)))))) 2))
(fabs.f64 (/.f64 (.f64 (.f64 (/.f64 1 (sqrt.f64 k)) 2) (.f64 (/.f64 1 (/.f64 1 (sqrt.f64 k))) (/.f64 (.f64 (/.f64 1 (sqrt.f64 k)) (/.f64 1 (sqrt.f64 k))) (fabs.f64 (/.f64 (/.f64 1 (sqrt.f64 k)) (/.f64 1 (sqrt.f64 k))))))) 2))
(fabs.f64 (/.f64 (.f64 (.f64 (/.f64 1 (sqrt.f64 k)) 2) (.f64 (.f64 (/.f64 1 (/.f64 1 (sqrt.f64 k))) (/.f64 1 (/.f64 1 (sqrt.f64 k)))) (.f64 (.f64 (/.f64 1 (sqrt.f64 k)) (/.f64 1 (sqrt.f64 k))) (/.f64 1 (/.f64 1 (/.f64 1 (sqrt.f64 k))))))) 2))
(fabs.f64 (/.f64 (.f64 (.f64 (/.f64 1 (sqrt.f64 k)) 2) (.f64 (.f64 (/.f64 1 (/.f64 1 (sqrt.f64 k))) (/.f64 1 (/.f64 1 (sqrt.f64 k)))) (.f64 (neg.f64 (.f64 (/.f64 1 (sqrt.f64 k)) (/.f64 1 (sqrt.f64 k)))) (/.f64 1 (/.f64 1 (/.f64 1 (sqrt.f64 k))))))) 2))
(fabs.f64 (/.f64 (.f64 (.f64 (/.f64 1 (sqrt.f64 k)) 2) (.f64 (.f64 (/.f64 1 (/.f64 1 (sqrt.f64 k))) (/.f64 1 (/.f64 1 (sqrt.f64 k)))) (.f64 (/.f64 1 (/.f64 1 (/.f64 1 (sqrt.f64 k)))) (/.f64 (.f64 (/.f64 1 (sqrt.f64 k)) (/.f64 1 (sqrt.f64 k))) (fabs.f64 (/.f64 (/.f64 1 (sqrt.f64 k)) (/.f64 1 (sqrt.f64 k)))))))) 2))
(fabs.f64 (/.f64 (.f64 (/.f64 1 (sqrt.f64 k)) (/.f64 1 (sqrt.f64 k))) (/.f64 (.f64 (/.f64 1 (sqrt.f64 k)) (/.f64 1 (sqrt.f64 k))) (neg.f64 (*.f64 (/.f64 1 (sqrt.f64 k)) (/.f64 1 (sqrt.f64 k)))))))
(fabs.f64 (/.f64 (.f64 (/.f64 1 (sqrt.f64 k)) (/.f64 1 (sqrt.f64 k))) (/.f64 (.f64 (/.f64 1 (sqrt.f64 k)) (/.f64 1 (sqrt.f64 k))) (/.f64 (*.f64 (/.f64 1 (sqrt.f64 k)) (/.f64 1 (sqrt.f64 k))) (fabs.f64 (/.f64 (/.f64 1 (sqrt.f64 k)) (/.f64 1 (sqrt.f64 k))))))))
(fabs.f64 (/.f64 (*.f64 (/.f64 1 (sqrt.f64 k)) (/.f64 1 (sqrt.f64 k))) (/.f64 (/.f64 1 (sqrt.f64 k)) (fabs.f64 (/.f64 1 (sqrt.f64 k))))))
(fabs.f64 (/.f64 (*.f64 (/.f64 1 (sqrt.f64 k)) (/.f64 1 (sqrt.f64 k))) (/.f64 (/.f64 (/.f64 1 (sqrt.f64 k)) (/.f64 1 (sqrt.f64 k))) (fabs.f64 (/.f64 (/.f64 (/.f64 1 (sqrt.f64 k)) (/.f64 1 (sqrt.f64 k))) (/.f64 (/.f64 1 (sqrt.f64 k)) (/.f64 1 (sqrt.f64 k))))))))
(fabs.f64 (/.f64 (*.f64 (/.f64 1 (sqrt.f64 k)) (/.f64 1 (sqrt.f64 k))) (/.f64 (neg.f64 (/.f64 1 (sqrt.f64 k))) (fabs.f64 (/.f64 1 (sqrt.f64 k))))))
(fabs.f64 (/.f64 (.f64 (/.f64 1 (sqrt.f64 k)) (/.f64 1 (sqrt.f64 k))) (/.f64 (.f64 (/.f64 1 (sqrt.f64 k)) 2) (*.f64 (fabs.f64 (/.f64 1 (sqrt.f64 k))) 2))))
(fabs.f64 (/.f64 (neg.f64 (*.f64 (/.f64 1 (sqrt.f64 k)) (/.f64 1 (sqrt.f64 k)))) (fabs.f64 (/.f64 (/.f64 1 (sqrt.f64 k)) (/.f64 1 (sqrt.f64 k))))))
(fabs.f64 (/.f64 (/.f64 (*.f64 (/.f64 1 (sqrt.f64 k)) (/.f64 1 (sqrt.f64 k))) (fabs.f64 (/.f64 (/.f64 1 (sqrt.f64 k)) (/.f64 1 (sqrt.f64 k))))) (fabs.f64 (/.f64 (/.f64 1 (sqrt.f64 k)) (/.f64 1 (sqrt.f64 k))))))
(fabs.f64 (/.f64 (*.f64 (/.f64 1 (sqrt.f64 k)) (/.f64 1 (sqrt.f64 k))) (neg.f64 (fabs.f64 (/.f64 (/.f64 1 (sqrt.f64 k)) (/.f64 1 (sqrt.f64 k)))))))
(fabs.f64 (-.f64 0 (/.f64 (*.f64 (/.f64 1 (sqrt.f64 k)) (/.f64 1 (sqrt.f64 k))) (neg.f64 (/.f64 (/.f64 1 (sqrt.f64 k)) (/.f64 1 (sqrt.f64 k)))))))
(fabs.f64 (-.f64 0 (.f64 (.f64 (/.f64 1 (sqrt.f64 k)) (*.f64 (/.f64 1 (sqrt.f64 k)) (/.f64 1 (sqrt.f64 k)))) (fabs.f64 (/.f64 1 (/.f64 1 (sqrt.f64 k)))))))
(fabs.f64 (-.f64 0 (.f64 (fabs.f64 (/.f64 1 (/.f64 1 (sqrt.f64 k)))) (.f64 (/.f64 1 (sqrt.f64 k)) (neg.f64 (*.f64 (/.f64 1 (sqrt.f64 k)) (/.f64 1 (sqrt.f64 k))))))))
(fabs.f64 (-.f64 0 (.f64 (fabs.f64 (/.f64 1 (/.f64 1 (sqrt.f64 k)))) (.f64 (/.f64 1 (sqrt.f64 k)) (/.f64 (*.f64 (/.f64 1 (sqrt.f64 k)) (/.f64 1 (sqrt.f64 k))) (fabs.f64 (/.f64 (/.f64 1 (sqrt.f64 k)) (/.f64 1 (sqrt.f64 k)))))))))
(fabs.f64 (-.f64 0 (.f64 (.f64 (/.f64 1 (sqrt.f64 k)) (.f64 (/.f64 1 (sqrt.f64 k)) (/.f64 1 (sqrt.f64 k)))) (fabs.f64 (.f64 (/.f64 1 (sqrt.f64 k)) (/.f64 (/.f64 1 (/.f64 1 (sqrt.f64 k))) (/.f64 1 (sqrt.f64 k))))))))
(fabs.f64 (-.f64 0 (.f64 (.f64 (/.f64 1 (sqrt.f64 k)) (neg.f64 (.f64 (/.f64 1 (sqrt.f64 k)) (/.f64 1 (sqrt.f64 k))))) (fabs.f64 (.f64 (/.f64 1 (sqrt.f64 k)) (/.f64 (/.f64 1 (/.f64 1 (sqrt.f64 k))) (/.f64 1 (sqrt.f64 k))))))))
(fabs.f64 (-.f64 0 (.f64 (.f64 (/.f64 1 (sqrt.f64 k)) (/.f64 (.f64 (/.f64 1 (sqrt.f64 k)) (/.f64 1 (sqrt.f64 k))) (fabs.f64 (/.f64 (/.f64 1 (sqrt.f64 k)) (/.f64 1 (sqrt.f64 k)))))) (fabs.f64 (.f64 (/.f64 1 (sqrt.f64 k)) (/.f64 (/.f64 1 (/.f64 1 (sqrt.f64 k))) (/.f64 1 (sqrt.f64 k))))))))
(fabs.f64 (-.f64 0 (.f64 (.f64 (/.f64 1 (sqrt.f64 k)) (.f64 (/.f64 1 (sqrt.f64 k)) (/.f64 1 (sqrt.f64 k)))) (fabs.f64 (.f64 (/.f64 1 (/.f64 1 (sqrt.f64 k))) (/.f64 (/.f64 1 (sqrt.f64 k)) (/.f64 1 (sqrt.f64 k))))))))
(fabs.f64 (-.f64 0 (.f64 (.f64 (/.f64 1 (sqrt.f64 k)) (neg.f64 (.f64 (/.f64 1 (sqrt.f64 k)) (/.f64 1 (sqrt.f64 k))))) (fabs.f64 (.f64 (/.f64 1 (/.f64 1 (sqrt.f64 k))) (/.f64 (/.f64 1 (sqrt.f64 k)) (/.f64 1 (sqrt.f64 k))))))))
(fabs.f64 (-.f64 0 (.f64 (.f64 (/.f64 1 (sqrt.f64 k)) (/.f64 (.f64 (/.f64 1 (sqrt.f64 k)) (/.f64 1 (sqrt.f64 k))) (fabs.f64 (/.f64 (/.f64 1 (sqrt.f64 k)) (/.f64 1 (sqrt.f64 k)))))) (fabs.f64 (.f64 (/.f64 1 (/.f64 1 (sqrt.f64 k))) (/.f64 (/.f64 1 (sqrt.f64 k)) (/.f64 1 (sqrt.f64 k))))))))
(fabs.f64 (-.f64 0 (.f64 (.f64 (/.f64 1 (/.f64 1 (sqrt.f64 k))) (/.f64 1 (/.f64 1 (sqrt.f64 k)))) (.f64 (.f64 (/.f64 1 (sqrt.f64 k)) (/.f64 1 (sqrt.f64 k))) (*.f64 (/.f64 1 (sqrt.f64 k)) (/.f64 1 (sqrt.f64 k)))))))
(fabs.f64 (-.f64 0 (.f64 (.f64 (/.f64 1 (/.f64 1 (sqrt.f64 k))) (/.f64 1 (/.f64 1 (sqrt.f64 k)))) (.f64 (.f64 (/.f64 1 (sqrt.f64 k)) (/.f64 1 (sqrt.f64 k))) (neg.f64 (*.f64 (/.f64 1 (sqrt.f64 k)) (/.f64 1 (sqrt.f64 k))))))))
(fabs.f64 (-.f64 0 (.f64 (.f64 (/.f64 1 (/.f64 1 (sqrt.f64 k))) (/.f64 1 (/.f64 1 (sqrt.f64 k)))) (.f64 (.f64 (/.f64 1 (sqrt.f64 k)) (/.f64 1 (sqrt.f64 k))) (/.f64 (*.f64 (/.f64 1 (sqrt.f64 k)) (/.f64 1 (sqrt.f64 k))) (fabs.f64 (/.f64 (/.f64 1 (sqrt.f64 k)) (/.f64 1 (sqrt.f64 k)))))))))
(fabs.f64 (-.f64 0 (*.f64 (/.f64 1 (sqrt.f64 k)) (fabs.f64 (/.f64 1 (sqrt.f64 k))))))
(fabs.f64 (-.f64 0 (.f64 (fabs.f64 (/.f64 1 (sqrt.f64 k))) (.f64 (/.f64 1 (/.f64 1 (sqrt.f64 k))) (neg.f64 (*.f64 (/.f64 1 (sqrt.f64 k)) (/.f64 1 (sqrt.f64 k))))))))
(fabs.f64 (-.f64 0 (.f64 (fabs.f64 (/.f64 1 (sqrt.f64 k))) (.f64 (/.f64 1 (/.f64 1 (sqrt.f64 k))) (/.f64 (*.f64 (/.f64 1 (sqrt.f64 k)) (/.f64 1 (sqrt.f64 k))) (fabs.f64 (/.f64 (/.f64 1 (sqrt.f64 k)) (/.f64 1 (sqrt.f64 k)))))))))
(fabs.f64 (-.f64 0 (.f64 (.f64 (/.f64 1 (sqrt.f64 k)) (/.f64 1 (/.f64 1 (sqrt.f64 k)))) (neg.f64 (*.f64 (/.f64 1 (sqrt.f64 k)) (/.f64 1 (sqrt.f64 k)))))))
(fabs.f64 (-.f64 0 (.f64 (.f64 (/.f64 1 (sqrt.f64 k)) (/.f64 1 (/.f64 1 (sqrt.f64 k)))) (/.f64 (*.f64 (/.f64 1 (sqrt.f64 k)) (/.f64 1 (sqrt.f64 k))) (fabs.f64 (/.f64 (/.f64 1 (sqrt.f64 k)) (/.f64 1 (sqrt.f64 k))))))))
(+.f64 (/.f64 1 (sqrt.f64 k)) 0)
(+.f64 0 (/.f64 1 (sqrt.f64 k)))
(-.f64 (/.f64 1 (sqrt.f64 k)) 0)
(-.f64 0 (neg.f64 (/.f64 1 (sqrt.f64 k))))
(/.f64 1 (sqrt.f64 k))
(/.f64 (/.f64 1 (sqrt.f64 k)) 1)
(/.f64 (/.f64 1 (sqrt.f64 k)) (/.f64 (/.f64 1 (sqrt.f64 k)) (/.f64 1 (sqrt.f64 k))))
(/.f64 (/.f64 1 (sqrt.f64 k)) (/.f64 (/.f64 (/.f64 1 (sqrt.f64 k)) (/.f64 1 (sqrt.f64 k))) (/.f64 (/.f64 1 (sqrt.f64 k)) (/.f64 1 (sqrt.f64 k)))))
(/.f64 (*.f64 (/.f64 1 (sqrt.f64 k)) 2) 2)
(pow.f64 (/.f64 1 (sqrt.f64 k)) 1)
(neg.f64 (neg.f64 (/.f64 1 (sqrt.f64 k))))
(+.f64 (/.f64 1 (/.f64 1 (sqrt.f64 k))) 0)
(+.f64 0 (/.f64 1 (/.f64 1 (sqrt.f64 k))))
(-.f64 (/.f64 1 (/.f64 1 (sqrt.f64 k))) 0)
(-.f64 0 (neg.f64 (/.f64 1 (/.f64 1 (sqrt.f64 k)))))
(*.f64 1 (/.f64 1 (/.f64 1 (sqrt.f64 k))))
(*.f64 (/.f64 1 (/.f64 1 (sqrt.f64 k))) 1)
(*.f64 (/.f64 1 (/.f64 1 (sqrt.f64 k))) (/.f64 (/.f64 1 (/.f64 1 (sqrt.f64 k))) (/.f64 1 (/.f64 1 (sqrt.f64 k)))))
(.f64 (/.f64 1 (/.f64 1 (sqrt.f64 k))) (.f64 (/.f64 1 (/.f64 1 (sqrt.f64 k))) (/.f64 1 (/.f64 1 (/.f64 1 (sqrt.f64 k))))))
(*.f64 (/.f64 1 (/.f64 1 (sqrt.f64 k))) (/.f64 1 (/.f64 (/.f64 1 (/.f64 1 (sqrt.f64 k))) (/.f64 1 (/.f64 1 (sqrt.f64 k))))))
(*.f64 (/.f64 (/.f64 1 (/.f64 1 (sqrt.f64 k))) (/.f64 1 (/.f64 1 (sqrt.f64 k)))) (/.f64 1 (/.f64 1 (sqrt.f64 k))))
(.f64 (.f64 (/.f64 1 (/.f64 1 (sqrt.f64 k))) (/.f64 1 (/.f64 1 (sqrt.f64 k)))) (/.f64 1 (/.f64 1 (/.f64 1 (sqrt.f64 k)))))
(.f64 (/.f64 1 (/.f64 1 (/.f64 1 (sqrt.f64 k)))) (.f64 (/.f64 1 (/.f64 1 (sqrt.f64 k))) (/.f64 1 (/.f64 1 (sqrt.f64 k)))))
(.f64 (.f64 (/.f64 1 (/.f64 1 (sqrt.f64 k))) (/.f64 1 (/.f64 1 (/.f64 1 (sqrt.f64 k))))) (/.f64 1 (/.f64 1 (sqrt.f64 k))))
(.f64 (/.f64 (/.f64 1 (/.f64 1 (/.f64 1 (sqrt.f64 k)))) (.f64 (/.f64 1 (/.f64 1 (sqrt.f64 k))) (/.f64 1 (/.f64 1 (sqrt.f64 k))))) (.f64 (.f64 (/.f64 1 (/.f64 1 (sqrt.f64 k))) (/.f64 1 (/.f64 1 (sqrt.f64 k)))) (*.f64 (/.f64 1 (/.f64 1 (sqrt.f64 k))) (/.f64 1 (/.f64 1 (sqrt.f64 k))))))
(.f64 (/.f64 (/.f64 (/.f64 1 (/.f64 1 (sqrt.f64 k))) (/.f64 1 (/.f64 1 (sqrt.f64 k)))) (/.f64 1 (/.f64 1 (sqrt.f64 k)))) (.f64 (/.f64 1 (/.f64 1 (sqrt.f64 k))) (/.f64 1 (/.f64 1 (sqrt.f64 k)))))
(.f64 (/.f64 (.f64 (/.f64 1 (/.f64 1 (sqrt.f64 k))) (/.f64 1 (/.f64 1 (/.f64 1 (sqrt.f64 k))))) (/.f64 1 (/.f64 1 (sqrt.f64 k)))) (*.f64 (/.f64 1 (/.f64 1 (sqrt.f64 k))) (/.f64 1 (/.f64 1 (sqrt.f64 k)))))
(.f64 (/.f64 (/.f64 1 (/.f64 (/.f64 1 (/.f64 1 (sqrt.f64 k))) (/.f64 1 (/.f64 1 (sqrt.f64 k))))) (/.f64 1 (/.f64 1 (sqrt.f64 k)))) (.f64 (/.f64 1 (/.f64 1 (sqrt.f64 k))) (/.f64 1 (/.f64 1 (sqrt.f64 k)))))
(pow.f64 (/.f64 1 (/.f64 1 (sqrt.f64 k))) 1)
(neg.f64 (neg.f64 (/.f64 1 (/.f64 1 (sqrt.f64 k)))))

Outputs
(/.f64 1 k)
(/.f64 1 k)
(/.f64 1 k)
(/.f64 1 k)
(/.f64 1 k)
(/.f64 1 k)
(/.f64 1 k)
(/.f64 1 k)
(/.f64 -1 (*.f64 k (pow.f64 (sqrt.f64 -1) 2)))
(/.f64 -1 (*.f64 1 k))
(/.f64 -1 k)
(/.f64 -1 (*.f64 k (pow.f64 (sqrt.f64 -1) 2)))
(/.f64 -1 (*.f64 1 k))
(/.f64 -1 k)
(/.f64 -1 (*.f64 k (pow.f64 (sqrt.f64 -1) 2)))
(/.f64 -1 (*.f64 1 k))
(/.f64 -1 k)
(/.f64 -1 (*.f64 k (pow.f64 (sqrt.f64 -1) 2)))
(/.f64 -1 (*.f64 1 k))
(/.f64 -1 k)
(+.f64 (*.f64 (/.f64 1 (sqrt.f64 k)) (/.f64 1 (sqrt.f64 k))) 0)
(*.f64 (/.f64 1 (sqrt.f64 k)) (/.f64 1 (sqrt.f64 k)))
(+.f64 0 (*.f64 (/.f64 1 (sqrt.f64 k)) (/.f64 1 (sqrt.f64 k))))
(*.f64 (/.f64 1 (sqrt.f64 k)) (/.f64 1 (sqrt.f64 k)))
(-.f64 (*.f64 (/.f64 1 (sqrt.f64 k)) (/.f64 1 (sqrt.f64 k))) 0)
(*.f64 (/.f64 1 (sqrt.f64 k)) (/.f64 1 (sqrt.f64 k)))
(-.f64 0 (neg.f64 (*.f64 (/.f64 1 (sqrt.f64 k)) (/.f64 1 (sqrt.f64 k)))))
(*.f64 (/.f64 1 (sqrt.f64 k)) (/.f64 1 (sqrt.f64 k)))
(/.f64 (*.f64 (/.f64 1 (sqrt.f64 k)) (/.f64 1 (sqrt.f64 k))) 1)
(*.f64 (/.f64 1 (sqrt.f64 k)) (/.f64 1 (sqrt.f64 k)))
(/.f64 (*.f64 (/.f64 1 (sqrt.f64 k)) (/.f64 1 (sqrt.f64 k))) (/.f64 (/.f64 1 (sqrt.f64 k)) (/.f64 1 (sqrt.f64 k))))
(*.f64 (/.f64 1 (sqrt.f64 k)) (/.f64 1 (sqrt.f64 k)))
(/.f64 (.f64 (/.f64 1 (sqrt.f64 k)) (.f64 (/.f64 1 (sqrt.f64 k)) 2)) 2)
(*.f64 (/.f64 1 (sqrt.f64 k)) (/.f64 1 (sqrt.f64 k)))
(pow.f64 (*.f64 (/.f64 1 (sqrt.f64 k)) (/.f64 1 (sqrt.f64 k))) 1)
(*.f64 (/.f64 1 (sqrt.f64 k)) (/.f64 1 (sqrt.f64 k)))
(neg.f64 (neg.f64 (*.f64 (/.f64 1 (sqrt.f64 k)) (/.f64 1 (sqrt.f64 k)))))
(*.f64 (/.f64 1 (sqrt.f64 k)) (/.f64 1 (sqrt.f64 k)))
(fabs.f64 (*.f64 (/.f64 1 (sqrt.f64 k)) (/.f64 1 (sqrt.f64 k))))
(*.f64 (/.f64 1 (sqrt.f64 k)) (/.f64 1 (sqrt.f64 k)))
(fabs.f64 (neg.f64 (*.f64 (/.f64 1 (sqrt.f64 k)) (/.f64 1 (sqrt.f64 k)))))
(*.f64 (/.f64 1 (sqrt.f64 k)) (/.f64 1 (sqrt.f64 k)))
(fabs.f64 (/.f64 (*.f64 (/.f64 1 (sqrt.f64 k)) (/.f64 1 (sqrt.f64 k))) (fabs.f64 (/.f64 (/.f64 1 (sqrt.f64 k)) (/.f64 1 (sqrt.f64 k))))))
(*.f64 (/.f64 1 (sqrt.f64 k)) (/.f64 1 (sqrt.f64 k)))
(fabs.f64 (/.f64 (*.f64 (/.f64 1 (sqrt.f64 k)) (/.f64 1 (sqrt.f64 k))) (neg.f64 (/.f64 (/.f64 1 (sqrt.f64 k)) (/.f64 1 (sqrt.f64 k))))))
(*.f64 (/.f64 1 (sqrt.f64 k)) (/.f64 1 (sqrt.f64 k)))
(fabs.f64 (.f64 (.f64 (/.f64 1 (sqrt.f64 k)) (*.f64 (/.f64 1 (sqrt.f64 k)) (/.f64 1 (sqrt.f64 k)))) (fabs.f64 (/.f64 1 (/.f64 1 (sqrt.f64 k))))))
(*.f64 (/.f64 1 (sqrt.f64 k)) (/.f64 1 (sqrt.f64 k)))
(fabs.f64 (.f64 (fabs.f64 (/.f64 1 (/.f64 1 (sqrt.f64 k)))) (.f64 (/.f64 1 (sqrt.f64 k)) (neg.f64 (*.f64 (/.f64 1 (sqrt.f64 k)) (/.f64 1 (sqrt.f64 k)))))))
(*.f64 (/.f64 1 (sqrt.f64 k)) (/.f64 1 (sqrt.f64 k)))
(fabs.f64 (.f64 (fabs.f64 (/.f64 1 (/.f64 1 (sqrt.f64 k)))) (.f64 (/.f64 1 (sqrt.f64 k)) (/.f64 (*.f64 (/.f64 1 (sqrt.f64 k)) (/.f64 1 (sqrt.f64 k))) (fabs.f64 (/.f64 (/.f64 1 (sqrt.f64 k)) (/.f64 1 (sqrt.f64 k))))))))
(*.f64 (/.f64 1 (sqrt.f64 k)) (/.f64 1 (sqrt.f64 k)))
(fabs.f64 (.f64 (.f64 (/.f64 1 (sqrt.f64 k)) (.f64 (/.f64 1 (sqrt.f64 k)) (/.f64 1 (sqrt.f64 k)))) (fabs.f64 (.f64 (/.f64 1 (sqrt.f64 k)) (/.f64 (/.f64 1 (/.f64 1 (sqrt.f64 k))) (/.f64 1 (sqrt.f64 k)))))))
(fabs.f64 (.f64 (.f64 (/.f64 1 (sqrt.f64 k)) (/.f64 1 (sqrt.f64 k))) (.f64 (/.f64 1 (sqrt.f64 k)) (.f64 (/.f64 1 (sqrt.f64 k)) (/.f64 (/.f64 1 (/.f64 1 (sqrt.f64 k))) (/.f64 1 (sqrt.f64 k)))))))
(fabs.f64 (.f64 (.f64 (/.f64 1 (sqrt.f64 k)) (neg.f64 (.f64 (/.f64 1 (sqrt.f64 k)) (/.f64 1 (sqrt.f64 k))))) (fabs.f64 (.f64 (/.f64 1 (sqrt.f64 k)) (/.f64 (/.f64 1 (/.f64 1 (sqrt.f64 k))) (/.f64 1 (sqrt.f64 k)))))))
(fabs.f64 (.f64 (.f64 (/.f64 1 (sqrt.f64 k)) (.f64 (/.f64 1 (sqrt.f64 k)) (/.f64 1 (sqrt.f64 k)))) (fabs.f64 (.f64 (/.f64 1 (sqrt.f64 k)) (/.f64 (/.f64 1 (/.f64 1 (sqrt.f64 k))) (/.f64 1 (sqrt.f64 k)))))))
(fabs.f64 (.f64 (.f64 (/.f64 1 (sqrt.f64 k)) (/.f64 1 (sqrt.f64 k))) (.f64 (/.f64 1 (sqrt.f64 k)) (.f64 (/.f64 1 (sqrt.f64 k)) (/.f64 (/.f64 1 (/.f64 1 (sqrt.f64 k))) (/.f64 1 (sqrt.f64 k)))))))
(fabs.f64 (.f64 (.f64 (/.f64 1 (sqrt.f64 k)) (/.f64 (.f64 (/.f64 1 (sqrt.f64 k)) (/.f64 1 (sqrt.f64 k))) (fabs.f64 (/.f64 (/.f64 1 (sqrt.f64 k)) (/.f64 1 (sqrt.f64 k)))))) (fabs.f64 (.f64 (/.f64 1 (sqrt.f64 k)) (/.f64 (/.f64 1 (/.f64 1 (sqrt.f64 k))) (/.f64 1 (sqrt.f64 k)))))))
(fabs.f64 (.f64 (.f64 (/.f64 1 (sqrt.f64 k)) (.f64 (/.f64 1 (sqrt.f64 k)) (/.f64 1 (sqrt.f64 k)))) (fabs.f64 (.f64 (/.f64 1 (sqrt.f64 k)) (/.f64 (/.f64 1 (/.f64 1 (sqrt.f64 k))) (/.f64 1 (sqrt.f64 k)))))))
(fabs.f64 (.f64 (.f64 (/.f64 1 (sqrt.f64 k)) (/.f64 1 (sqrt.f64 k))) (.f64 (/.f64 1 (sqrt.f64 k)) (.f64 (/.f64 1 (sqrt.f64 k)) (/.f64 (/.f64 1 (/.f64 1 (sqrt.f64 k))) (/.f64 1 (sqrt.f64 k)))))))
(fabs.f64 (.f64 (.f64 (/.f64 1 (sqrt.f64 k)) (.f64 (/.f64 1 (sqrt.f64 k)) (/.f64 1 (sqrt.f64 k)))) (fabs.f64 (.f64 (/.f64 1 (/.f64 1 (sqrt.f64 k))) (/.f64 (/.f64 1 (sqrt.f64 k)) (/.f64 1 (sqrt.f64 k)))))))
(*.f64 (/.f64 1 (sqrt.f64 k)) (/.f64 1 (sqrt.f64 k)))
(fabs.f64 (.f64 (.f64 (/.f64 1 (sqrt.f64 k)) (neg.f64 (.f64 (/.f64 1 (sqrt.f64 k)) (/.f64 1 (sqrt.f64 k))))) (fabs.f64 (.f64 (/.f64 1 (/.f64 1 (sqrt.f64 k))) (/.f64 (/.f64 1 (sqrt.f64 k)) (/.f64 1 (sqrt.f64 k)))))))
(*.f64 (/.f64 1 (sqrt.f64 k)) (/.f64 1 (sqrt.f64 k)))
(fabs.f64 (.f64 (.f64 (/.f64 1 (sqrt.f64 k)) (/.f64 (.f64 (/.f64 1 (sqrt.f64 k)) (/.f64 1 (sqrt.f64 k))) (fabs.f64 (/.f64 (/.f64 1 (sqrt.f64 k)) (/.f64 1 (sqrt.f64 k)))))) (fabs.f64 (.f64 (/.f64 1 (/.f64 1 (sqrt.f64 k))) (/.f64 (/.f64 1 (sqrt.f64 k)) (/.f64 1 (sqrt.f64 k)))))))
(*.f64 (/.f64 1 (sqrt.f64 k)) (/.f64 1 (sqrt.f64 k)))
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(fabs.f64 (-.f64 0 (.f64 (.f64 (/.f64 1 (sqrt.f64 k)) (/.f64 (.f64 (/.f64 1 (sqrt.f64 k)) (/.f64 1 (sqrt.f64 k))) (fabs.f64 (/.f64 (/.f64 1 (sqrt.f64 k)) (/.f64 1 (sqrt.f64 k)))))) (fabs.f64 (.f64 (/.f64 1 (/.f64 1 (sqrt.f64 k))) (/.f64 (/.f64 1 (sqrt.f64 k)) (/.f64 1 (sqrt.f64 k))))))))
(*.f64 (/.f64 1 (sqrt.f64 k)) (/.f64 1 (sqrt.f64 k)))
(fabs.f64 (-.f64 0 (.f64 (.f64 (/.f64 1 (/.f64 1 (sqrt.f64 k))) (/.f64 1 (/.f64 1 (sqrt.f64 k)))) (.f64 (.f64 (/.f64 1 (sqrt.f64 k)) (/.f64 1 (sqrt.f64 k))) (*.f64 (/.f64 1 (sqrt.f64 k)) (/.f64 1 (sqrt.f64 k)))))))
(*.f64 (/.f64 1 (sqrt.f64 k)) (/.f64 1 (sqrt.f64 k)))
(fabs.f64 (-.f64 0 (.f64 (.f64 (/.f64 1 (/.f64 1 (sqrt.f64 k))) (/.f64 1 (/.f64 1 (sqrt.f64 k)))) (.f64 (.f64 (/.f64 1 (sqrt.f64 k)) (/.f64 1 (sqrt.f64 k))) (neg.f64 (*.f64 (/.f64 1 (sqrt.f64 k)) (/.f64 1 (sqrt.f64 k))))))))
(*.f64 (/.f64 1 (sqrt.f64 k)) (/.f64 1 (sqrt.f64 k)))
(fabs.f64 (-.f64 0 (.f64 (.f64 (/.f64 1 (/.f64 1 (sqrt.f64 k))) (/.f64 1 (/.f64 1 (sqrt.f64 k)))) (.f64 (.f64 (/.f64 1 (sqrt.f64 k)) (/.f64 1 (sqrt.f64 k))) (/.f64 (*.f64 (/.f64 1 (sqrt.f64 k)) (/.f64 1 (sqrt.f64 k))) (fabs.f64 (/.f64 (/.f64 1 (sqrt.f64 k)) (/.f64 1 (sqrt.f64 k)))))))))
(*.f64 (/.f64 1 (sqrt.f64 k)) (/.f64 1 (sqrt.f64 k)))
(fabs.f64 (-.f64 0 (*.f64 (/.f64 1 (sqrt.f64 k)) (fabs.f64 (/.f64 1 (sqrt.f64 k))))))
(*.f64 (/.f64 1 (sqrt.f64 k)) (/.f64 1 (sqrt.f64 k)))
(fabs.f64 (-.f64 0 (.f64 (fabs.f64 (/.f64 1 (sqrt.f64 k))) (.f64 (/.f64 1 (/.f64 1 (sqrt.f64 k))) (neg.f64 (*.f64 (/.f64 1 (sqrt.f64 k)) (/.f64 1 (sqrt.f64 k))))))))
(*.f64 (/.f64 1 (sqrt.f64 k)) (/.f64 1 (sqrt.f64 k)))
(fabs.f64 (-.f64 0 (.f64 (fabs.f64 (/.f64 1 (sqrt.f64 k))) (.f64 (/.f64 1 (/.f64 1 (sqrt.f64 k))) (/.f64 (*.f64 (/.f64 1 (sqrt.f64 k)) (/.f64 1 (sqrt.f64 k))) (fabs.f64 (/.f64 (/.f64 1 (sqrt.f64 k)) (/.f64 1 (sqrt.f64 k)))))))))
(*.f64 (/.f64 1 (sqrt.f64 k)) (/.f64 1 (sqrt.f64 k)))
(fabs.f64 (-.f64 0 (.f64 (.f64 (/.f64 1 (sqrt.f64 k)) (/.f64 1 (/.f64 1 (sqrt.f64 k)))) (neg.f64 (*.f64 (/.f64 1 (sqrt.f64 k)) (/.f64 1 (sqrt.f64 k)))))))
(*.f64 (/.f64 1 (sqrt.f64 k)) (/.f64 1 (sqrt.f64 k)))
(fabs.f64 (-.f64 0 (.f64 (.f64 (/.f64 1 (sqrt.f64 k)) (/.f64 1 (/.f64 1 (sqrt.f64 k)))) (/.f64 (*.f64 (/.f64 1 (sqrt.f64 k)) (/.f64 1 (sqrt.f64 k))) (fabs.f64 (/.f64 (/.f64 1 (sqrt.f64 k)) (/.f64 1 (sqrt.f64 k))))))))
(fabs.f64 (.f64 (/.f64 (.f64 (/.f64 1 (sqrt.f64 k)) (/.f64 1 (sqrt.f64 k))) (fabs.f64 (/.f64 (/.f64 1 (sqrt.f64 k)) (/.f64 1 (sqrt.f64 k))))) (*.f64 (/.f64 1 (sqrt.f64 k)) (/.f64 1 (/.f64 1 (sqrt.f64 k))))))
(fabs.f64 (.f64 (/.f64 1 (sqrt.f64 k)) (/.f64 (/.f64 (.f64 (/.f64 1 (sqrt.f64 k)) (/.f64 1 (sqrt.f64 k))) (fabs.f64 (/.f64 (/.f64 1 (sqrt.f64 k)) (/.f64 1 (sqrt.f64 k))))) (/.f64 1 (sqrt.f64 k)))))
(+.f64 (/.f64 1 (sqrt.f64 k)) 0)
(/.f64 1 (sqrt.f64 k))
(+.f64 0 (/.f64 1 (sqrt.f64 k)))
(/.f64 1 (sqrt.f64 k))
(-.f64 (/.f64 1 (sqrt.f64 k)) 0)
(/.f64 1 (sqrt.f64 k))
(-.f64 0 (neg.f64 (/.f64 1 (sqrt.f64 k))))
(/.f64 1 (sqrt.f64 k))
(/.f64 1 (sqrt.f64 k))
(/.f64 (/.f64 1 (sqrt.f64 k)) 1)
(/.f64 1 (sqrt.f64 k))
(/.f64 (/.f64 1 (sqrt.f64 k)) (/.f64 (/.f64 1 (sqrt.f64 k)) (/.f64 1 (sqrt.f64 k))))
(/.f64 1 (sqrt.f64 k))
(/.f64 (/.f64 1 (sqrt.f64 k)) (/.f64 (/.f64 (/.f64 1 (sqrt.f64 k)) (/.f64 1 (sqrt.f64 k))) (/.f64 (/.f64 1 (sqrt.f64 k)) (/.f64 1 (sqrt.f64 k)))))
(.f64 (/.f64 1 (sqrt.f64 k)) (.f64 (/.f64 (/.f64 1 (sqrt.f64 k)) (/.f64 1 (sqrt.f64 k))) (/.f64 (/.f64 1 (sqrt.f64 k)) (/.f64 1 (sqrt.f64 k)))))
(/.f64 (*.f64 (/.f64 1 (sqrt.f64 k)) 2) 2)
(/.f64 1 (sqrt.f64 k))
(pow.f64 (/.f64 1 (sqrt.f64 k)) 1)
(/.f64 1 (sqrt.f64 k))
(neg.f64 (neg.f64 (/.f64 1 (sqrt.f64 k))))
(/.f64 1 (sqrt.f64 k))
(+.f64 (/.f64 1 (/.f64 1 (sqrt.f64 k))) 0)
(/.f64 1 (/.f64 1 (sqrt.f64 k)))
(+.f64 0 (/.f64 1 (/.f64 1 (sqrt.f64 k))))
(/.f64 1 (/.f64 1 (sqrt.f64 k)))
(-.f64 (/.f64 1 (/.f64 1 (sqrt.f64 k))) 0)
(/.f64 1 (/.f64 1 (sqrt.f64 k)))
(-.f64 0 (neg.f64 (/.f64 1 (/.f64 1 (sqrt.f64 k)))))
(/.f64 1 (/.f64 1 (sqrt.f64 k)))
(*.f64 1 (/.f64 1 (/.f64 1 (sqrt.f64 k))))
(/.f64 1 (/.f64 1 (sqrt.f64 k)))
(*.f64 (/.f64 1 (/.f64 1 (sqrt.f64 k))) 1)
(/.f64 1 (/.f64 1 (sqrt.f64 k)))
(*.f64 (/.f64 1 (/.f64 1 (sqrt.f64 k))) (/.f64 (/.f64 1 (/.f64 1 (sqrt.f64 k))) (/.f64 1 (/.f64 1 (sqrt.f64 k)))))
(/.f64 1 (/.f64 1 (sqrt.f64 k)))
(.f64 (/.f64 1 (/.f64 1 (sqrt.f64 k))) (.f64 (/.f64 1 (/.f64 1 (sqrt.f64 k))) (/.f64 1 (/.f64 1 (/.f64 1 (sqrt.f64 k))))))
(/.f64 1 (/.f64 1 (sqrt.f64 k)))
(*.f64 (/.f64 1 (/.f64 1 (sqrt.f64 k))) (/.f64 1 (/.f64 (/.f64 1 (/.f64 1 (sqrt.f64 k))) (/.f64 1 (/.f64 1 (sqrt.f64 k))))))
(/.f64 1 (/.f64 1 (sqrt.f64 k)))
(*.f64 (/.f64 (/.f64 1 (/.f64 1 (sqrt.f64 k))) (/.f64 1 (/.f64 1 (sqrt.f64 k)))) (/.f64 1 (/.f64 1 (sqrt.f64 k))))
(/.f64 1 (/.f64 1 (sqrt.f64 k)))
(.f64 (.f64 (/.f64 1 (/.f64 1 (sqrt.f64 k))) (/.f64 1 (/.f64 1 (sqrt.f64 k)))) (/.f64 1 (/.f64 1 (/.f64 1 (sqrt.f64 k)))))
(/.f64 1 (/.f64 1 (sqrt.f64 k)))
(.f64 (/.f64 1 (/.f64 1 (/.f64 1 (sqrt.f64 k)))) (.f64 (/.f64 1 (/.f64 1 (sqrt.f64 k))) (/.f64 1 (/.f64 1 (sqrt.f64 k)))))
(/.f64 1 (/.f64 1 (sqrt.f64 k)))
(.f64 (.f64 (/.f64 1 (/.f64 1 (sqrt.f64 k))) (/.f64 1 (/.f64 1 (/.f64 1 (sqrt.f64 k))))) (/.f64 1 (/.f64 1 (sqrt.f64 k))))
(/.f64 1 (/.f64 1 (sqrt.f64 k)))
(.f64 (/.f64 (/.f64 1 (/.f64 1 (/.f64 1 (sqrt.f64 k)))) (.f64 (/.f64 1 (/.f64 1 (sqrt.f64 k))) (/.f64 1 (/.f64 1 (sqrt.f64 k))))) (.f64 (.f64 (/.f64 1 (/.f64 1 (sqrt.f64 k))) (/.f64 1 (/.f64 1 (sqrt.f64 k)))) (*.f64 (/.f64 1 (/.f64 1 (sqrt.f64 k))) (/.f64 1 (/.f64 1 (sqrt.f64 k))))))
(/.f64 1 (/.f64 1 (sqrt.f64 k)))
(.f64 (/.f64 (/.f64 (/.f64 1 (/.f64 1 (sqrt.f64 k))) (/.f64 1 (/.f64 1 (sqrt.f64 k)))) (/.f64 1 (/.f64 1 (sqrt.f64 k)))) (.f64 (/.f64 1 (/.f64 1 (sqrt.f64 k))) (/.f64 1 (/.f64 1 (sqrt.f64 k)))))
(/.f64 1 (/.f64 1 (sqrt.f64 k)))
(.f64 (/.f64 (.f64 (/.f64 1 (/.f64 1 (sqrt.f64 k))) (/.f64 1 (/.f64 1 (/.f64 1 (sqrt.f64 k))))) (/.f64 1 (/.f64 1 (sqrt.f64 k)))) (*.f64 (/.f64 1 (/.f64 1 (sqrt.f64 k))) (/.f64 1 (/.f64 1 (sqrt.f64 k)))))
(/.f64 1 (/.f64 1 (sqrt.f64 k)))
(.f64 (/.f64 (/.f64 1 (/.f64 (/.f64 1 (/.f64 1 (sqrt.f64 k))) (/.f64 1 (/.f64 1 (sqrt.f64 k))))) (/.f64 1 (/.f64 1 (sqrt.f64 k)))) (.f64 (/.f64 1 (/.f64 1 (sqrt.f64 k))) (/.f64 1 (/.f64 1 (sqrt.f64 k)))))
(/.f64 1 (/.f64 1 (sqrt.f64 k)))
(pow.f64 (/.f64 1 (/.f64 1 (sqrt.f64 k))) 1)
(/.f64 1 (/.f64 1 (sqrt.f64 k)))
(neg.f64 (neg.f64 (/.f64 1 (/.f64 1 (sqrt.f64 k)))))
(/.f64 1 (/.f64 1 (sqrt.f64 k)))

localize15.0ms (0.1%)

Local error

Found 4 expressions with local error:

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

Compiler

Compiled 38 to 24 computations (36.8% saved)

series5.0ms (0%)

Counts

3 → 12

Calls

12 calls:

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

rewrite311.0ms (2.1%)

Algorithm

1×	batch-egg-rewrite

Rules

1376×	`rational_best-simplify-57`
746×	`rational_best-2`
746×	`rational_best-3`
746×	`rational_best-1`
744×	`rational_best-5`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	15	69
1	123	69
2	394	69
3	1656	69
4	6616	69

Stop Event

1×	node limit

Counts

3 → 41

Calls

Call 1

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

Outputs

((#(struct:change #<rule egg-rr> (2) ((x +.f64 (*.f64 (/.f64 1 (sqrt.f64 k)) (sqrt.f64 (*.f64 (PI.f64) (+.f64 n n)))) 0)))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 0 (*.f64 (/.f64 1 (sqrt.f64 k)) (sqrt.f64 (*.f64 (PI.f64) (+.f64 n n)))))))) (#(struct:change #<rule egg-rr> (2) ((x -.f64 (*.f64 (/.f64 1 (sqrt.f64 k)) (sqrt.f64 (*.f64 (PI.f64) (+.f64 n n)))) 0)))) (#(struct:change #<rule egg-rr> (2) ((x -.f64 0 (neg.f64 (*.f64 (/.f64 1 (sqrt.f64 k)) (sqrt.f64 (*.f64 (PI.f64) (+.f64 n n))))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (*.f64 (/.f64 1 (sqrt.f64 k)) (sqrt.f64 (*.f64 (PI.f64) (+.f64 n n)))) 1)))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (*.f64 (/.f64 1 (sqrt.f64 k)) (sqrt.f64 (*.f64 (PI.f64) (+.f64 n n)))) (/.f64 (*.f64 (/.f64 1 (sqrt.f64 k)) (sqrt.f64 (*.f64 (PI.f64) (+.f64 n n)))) (*.f64 (/.f64 1 (sqrt.f64 k)) (sqrt.f64 (*.f64 (PI.f64) (+.f64 n n))))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (*.f64 (/.f64 1 (sqrt.f64 k)) (*.f64 2 (sqrt.f64 (*.f64 (PI.f64) (+.f64 n n))))) 2)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (*.f64 (/.f64 1 (sqrt.f64 k)) (sqrt.f64 (*.f64 (PI.f64) (+.f64 n n)))) 1)))) (#(struct:change #<rule egg-rr> (2) ((x neg.f64 (neg.f64 (*.f64 (/.f64 1 (sqrt.f64 k)) (sqrt.f64 (*.f64 (PI.f64) (+.f64 n n))))))))))

((#(struct:change #<rule egg-rr> (2) ((x +.f64 (*.f64 (PI.f64) (+.f64 n n)) 0)))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 0 (*.f64 (PI.f64) (+.f64 n n)))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (*.f64 (PI.f64) n) (*.f64 (PI.f64) n))))) (#(struct:change #<rule egg-rr> (2) ((x -.f64 (*.f64 (PI.f64) (+.f64 n n)) 0)))) (#(struct:change #<rule egg-rr> (2) ((x -.f64 0 (neg.f64 (*.f64 (PI.f64) (+.f64 n n))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (*.f64 (PI.f64) (+.f64 n n)) 1)))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (*.f64 (PI.f64) (+.f64 n n)) (/.f64 (*.f64 (PI.f64) n) (*.f64 (PI.f64) n)))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (*.f64 (*.f64 (PI.f64) n) 4) 2)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (*.f64 (PI.f64) (+.f64 n n)) 1)))) (#(struct:change #<rule egg-rr> (2) ((x neg.f64 (neg.f64 (*.f64 (PI.f64) (+.f64 n n))))))))

((#(struct:change #<rule egg-rr> (2) ((x +.f64 (sqrt.f64 (*.f64 (PI.f64) (+.f64 n n))) 0)))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 0 (sqrt.f64 (*.f64 (PI.f64) (+.f64 n n))))))) (#(struct:change #<rule egg-rr> (2) ((x -.f64 (sqrt.f64 (*.f64 (PI.f64) (+.f64 n n))) 0)))) (#(struct:change #<rule egg-rr> (2) ((x -.f64 0 (neg.f64 (sqrt.f64 (*.f64 (PI.f64) (+.f64 n n)))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 1 (sqrt.f64 (*.f64 (PI.f64) (+.f64 n n))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (sqrt.f64 (*.f64 (PI.f64) (+.f64 n n))) 1)))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (sqrt.f64 (*.f64 (PI.f64) (+.f64 n n))) (/.f64 (sqrt.f64 (*.f64 (PI.f64) (+.f64 n n))) (sqrt.f64 (*.f64 (PI.f64) (+.f64 n n)))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (sqrt.f64 (*.f64 (PI.f64) (+.f64 n n))) (*.f64 (sqrt.f64 (*.f64 (PI.f64) (+.f64 n n))) (/.f64 1 (sqrt.f64 (*.f64 (PI.f64) (+.f64 n n))))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (sqrt.f64 (*.f64 (PI.f64) (+.f64 n n))) (/.f64 1 (/.f64 (sqrt.f64 (*.f64 (PI.f64) (+.f64 n n))) (sqrt.f64 (*.f64 (PI.f64) (+.f64 n n))))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (/.f64 (sqrt.f64 (*.f64 (PI.f64) (+.f64 n n))) (sqrt.f64 (*.f64 (PI.f64) (+.f64 n n)))) (sqrt.f64 (*.f64 (PI.f64) (+.f64 n n))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (/.f64 1 (sqrt.f64 (*.f64 (PI.f64) (+.f64 n n)))) (sqrt.f64 (*.f64 (*.f64 (PI.f64) n) (*.f64 (*.f64 (PI.f64) n) 4))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (sqrt.f64 (*.f64 (*.f64 (PI.f64) n) (*.f64 (*.f64 (PI.f64) n) 4))) (/.f64 1 (sqrt.f64 (*.f64 (PI.f64) (+.f64 n n)))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (*.f64 (sqrt.f64 (*.f64 (PI.f64) (+.f64 n n))) (/.f64 1 (sqrt.f64 (*.f64 (PI.f64) (+.f64 n n))))) (sqrt.f64 (*.f64 (PI.f64) (+.f64 n n))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (/.f64 (/.f64 1 (sqrt.f64 (*.f64 (PI.f64) (+.f64 n n)))) (sqrt.f64 (*.f64 (*.f64 (PI.f64) n) (*.f64 (*.f64 (PI.f64) n) 4)))) (sqrt.f64 (*.f64 (*.f64 (*.f64 (PI.f64) n) (*.f64 (*.f64 (PI.f64) n) 4)) (*.f64 (*.f64 (PI.f64) n) (*.f64 (*.f64 (PI.f64) n) 4)))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (/.f64 (/.f64 (sqrt.f64 (*.f64 (PI.f64) (+.f64 n n))) (sqrt.f64 (*.f64 (PI.f64) (+.f64 n n)))) (sqrt.f64 (*.f64 (PI.f64) (+.f64 n n)))) (sqrt.f64 (*.f64 (*.f64 (PI.f64) n) (*.f64 (*.f64 (PI.f64) n) 4))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (/.f64 (*.f64 (sqrt.f64 (*.f64 (PI.f64) (+.f64 n n))) (/.f64 1 (sqrt.f64 (*.f64 (PI.f64) (+.f64 n n))))) (sqrt.f64 (*.f64 (PI.f64) (+.f64 n n)))) (sqrt.f64 (*.f64 (*.f64 (PI.f64) n) (*.f64 (*.f64 (PI.f64) n) 4))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (/.f64 (/.f64 1 (/.f64 (sqrt.f64 (*.f64 (PI.f64) (+.f64 n n))) (sqrt.f64 (*.f64 (PI.f64) (+.f64 n n))))) (sqrt.f64 (*.f64 (PI.f64) (+.f64 n n)))) (sqrt.f64 (*.f64 (*.f64 (PI.f64) n) (*.f64 (*.f64 (PI.f64) n) 4))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (sqrt.f64 (*.f64 (PI.f64) (+.f64 n n))) 1)))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (sqrt.f64 (*.f64 (PI.f64) (+.f64 n n))) (/.f64 (sqrt.f64 (*.f64 (PI.f64) (+.f64 n n))) (sqrt.f64 (*.f64 (PI.f64) (+.f64 n n)))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (*.f64 2 (sqrt.f64 (*.f64 (PI.f64) (+.f64 n n)))) 2)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (sqrt.f64 (*.f64 (PI.f64) (+.f64 n n))) 1)))) (#(struct:change #<rule egg-rr> (2) ((x neg.f64 (neg.f64 (sqrt.f64 (*.f64 (PI.f64) (+.f64 n n)))))))))

simplify161.0ms (1.1%)

Algorithm

1×	egg-herbie

Rules

1092×	`rational_best-simplify-78`
1022×	`rational_best-simplify-47`
778×	`rational_best-simplify-43`
684×	`rational_best-simplify-1`
632×	`rational_best-simplify-132`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	81	1543
1	137	1543
2	291	1543
3	887	1543
4	2948	1543
5	5686	1543

Stop Event

1×	node limit

Counts

53 → 76

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 (.f64 (/.f64 1 (sqrt.f64 k)) (sqrt.f64 (.f64 (PI.f64) (+.f64 n n)))) 0)
(+.f64 0 (.f64 (/.f64 1 (sqrt.f64 k)) (sqrt.f64 (.f64 (PI.f64) (+.f64 n n)))))
(-.f64 (.f64 (/.f64 1 (sqrt.f64 k)) (sqrt.f64 (.f64 (PI.f64) (+.f64 n n)))) 0)
(-.f64 0 (neg.f64 (.f64 (/.f64 1 (sqrt.f64 k)) (sqrt.f64 (.f64 (PI.f64) (+.f64 n n))))))
(/.f64 (.f64 (/.f64 1 (sqrt.f64 k)) (sqrt.f64 (.f64 (PI.f64) (+.f64 n n)))) 1)
(/.f64 (.f64 (/.f64 1 (sqrt.f64 k)) (sqrt.f64 (.f64 (PI.f64) (+.f64 n n)))) (/.f64 (.f64 (/.f64 1 (sqrt.f64 k)) (sqrt.f64 (.f64 (PI.f64) (+.f64 n n)))) (.f64 (/.f64 1 (sqrt.f64 k)) (sqrt.f64 (.f64 (PI.f64) (+.f64 n n))))))
(/.f64 (.f64 (/.f64 1 (sqrt.f64 k)) (.f64 2 (sqrt.f64 (*.f64 (PI.f64) (+.f64 n n))))) 2)
(pow.f64 (.f64 (/.f64 1 (sqrt.f64 k)) (sqrt.f64 (.f64 (PI.f64) (+.f64 n n)))) 1)
(neg.f64 (neg.f64 (.f64 (/.f64 1 (sqrt.f64 k)) (sqrt.f64 (.f64 (PI.f64) (+.f64 n n))))))
(+.f64 (*.f64 (PI.f64) (+.f64 n n)) 0)
(+.f64 0 (*.f64 (PI.f64) (+.f64 n n)))
(+.f64 (.f64 (PI.f64) n) (.f64 (PI.f64) n))
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(/.f64 (sqrt.f64 (*.f64 (PI.f64) (+.f64 n n))) 1)
(sqrt.f64 (*.f64 (PI.f64) (+.f64 n n)))
(/.f64 (sqrt.f64 (.f64 (PI.f64) (+.f64 n n))) (/.f64 (sqrt.f64 (.f64 (PI.f64) (+.f64 n n))) (sqrt.f64 (*.f64 (PI.f64) (+.f64 n n)))))
(sqrt.f64 (*.f64 (PI.f64) (+.f64 n n)))
(/.f64 (.f64 2 (sqrt.f64 (.f64 (PI.f64) (+.f64 n n)))) 2)
(sqrt.f64 (*.f64 (PI.f64) (+.f64 n n)))
(pow.f64 (sqrt.f64 (*.f64 (PI.f64) (+.f64 n n))) 1)
(sqrt.f64 (*.f64 (PI.f64) (+.f64 n n)))
(neg.f64 (neg.f64 (sqrt.f64 (*.f64 (PI.f64) (+.f64 n n)))))
(sqrt.f64 (*.f64 (PI.f64) (+.f64 n n)))

localize193.0ms (1.3%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.2b	(.f64 (/.f64 1 (sqrt.f64 k)) (exp.f64 (.f64 1/2 (.f64 (-.f64 1 k) (log.f64 (.f64 2 (*.f64 n (PI.f64))))))))
	0.2b	(/.f64 1 (sqrt.f64 k))
✓	0.3b	(*.f64 n (PI.f64))
✓	3.1b	(exp.f64 (.f64 1/2 (.f64 (-.f64 1 k) (log.f64 (.f64 2 (.f64 n (PI.f64)))))))

Compiler

Compiled 84 to 52 computations (38.1% saved)

series5.0ms (0%)

Counts

3 → 32

Calls

15 calls:

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

rewrite65.0ms (0.4%)

Algorithm

1×	batch-egg-rewrite

Rules

1014×	`rational_best-5`
1014×	`rational_best-2`
1014×	`rational_best-3`
1014×	`rational_best-1`
1012×	`rational_best-4`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	20	107
1	166	103
2	539	103
3	2301	103

Stop Event

1×	node limit

Counts

3 → 33

Calls

Call 1

Inputs

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

(*.f64 n (PI.f64))

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

Outputs

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

((#(struct:change #<rule egg-rr> (2) ((x +.f64 (*.f64 n (PI.f64)) 0)))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 0 (*.f64 n (PI.f64)))))) (#(struct:change #<rule egg-rr> (2) ((x -.f64 (*.f64 n (PI.f64)) 0)))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (*.f64 n (PI.f64)) 1)))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (*.f64 n (PI.f64)) (/.f64 (*.f64 n (PI.f64)) (*.f64 n (PI.f64))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (*.f64 (PI.f64) (+.f64 n n)) 2)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (*.f64 n (PI.f64)) 1)))))

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

simplify244.0ms (1.7%)

Algorithm

1×	egg-herbie

Rules

1392×	`rational_best-simplify-80`
1192×	`rational_best-simplify-78`
1158×	`rational_best-simplify-47`
944×	`rational_best-simplify-82`
894×	`rational_best-simplify-43`

Iterations

Useful iterations: 4 (0.0ms)

Iter	Nodes	Cost
0	142	4133
1	255	4041
2	458	4001
3	975	3873
4	2817	3845
5	5640	3845

Stop Event

1×	node limit

Counts

65 → 113

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 1/8 (.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 (.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 k) (+.f64 (log.f64 (*.f64 2 (PI.f64))) (log.f64 n)))))
(exp.f64 (.f64 1/2 (.f64 (-.f64 1 k) (+.f64 (log.f64 (*.f64 2 (PI.f64))) (log.f64 n)))))
(exp.f64 (.f64 1/2 (.f64 (-.f64 1 k) (+.f64 (log.f64 (*.f64 2 (PI.f64))) (log.f64 n)))))
(exp.f64 (.f64 1/2 (.f64 (-.f64 1 k) (+.f64 (log.f64 (*.f64 2 (PI.f64))) (log.f64 n)))))
(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 (/.f64 1 k)) (exp.f64 (.f64 1/2 (.f64 (-.f64 1 k) (+.f64 (log.f64 n) (log.f64 (.f64 2 (PI.f64))))))))
(.f64 (sqrt.f64 (/.f64 1 k)) (exp.f64 (.f64 1/2 (.f64 (-.f64 1 k) (+.f64 (log.f64 n) (log.f64 (.f64 2 (PI.f64))))))))
(.f64 (sqrt.f64 (/.f64 1 k)) (exp.f64 (.f64 1/2 (.f64 (-.f64 1 k) (+.f64 (log.f64 n) (log.f64 (.f64 2 (PI.f64))))))))
(.f64 (sqrt.f64 (/.f64 1 k)) (exp.f64 (.f64 1/2 (.f64 (-.f64 1 k) (+.f64 (log.f64 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))))))))
(.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 (exp.f64 (.f64 (-.f64 1 k) (log.f64 (sqrt.f64 (.f64 (PI.f64) (+.f64 n n)))))) 0)
(+.f64 0 (exp.f64 (.f64 (-.f64 1 k) (log.f64 (sqrt.f64 (.f64 (PI.f64) (+.f64 n n)))))))
(-.f64 (exp.f64 (.f64 (-.f64 1 k) (log.f64 (sqrt.f64 (.f64 (PI.f64) (+.f64 n n)))))) 0)
(.f64 1 (exp.f64 (.f64 (-.f64 1 k) (log.f64 (sqrt.f64 (*.f64 (PI.f64) (+.f64 n n)))))))
(.f64 (exp.f64 (.f64 (-.f64 1 k) (log.f64 (sqrt.f64 (*.f64 (PI.f64) (+.f64 n n)))))) 1)
(.f64 (exp.f64 (.f64 (-.f64 1 k) (log.f64 (sqrt.f64 (.f64 (PI.f64) (+.f64 n n)))))) (/.f64 (exp.f64 (log.f64 (pow.f64 (.f64 (PI.f64) (+.f64 n n)) (-.f64 1 k)))) (exp.f64 (log.f64 (pow.f64 (*.f64 (PI.f64) (+.f64 n n)) (-.f64 1 k))))))
(.f64 (exp.f64 (.f64 (-.f64 1 k) (log.f64 (sqrt.f64 (.f64 (PI.f64) (+.f64 n n)))))) (.f64 (exp.f64 (.f64 (-.f64 1 k) (log.f64 (sqrt.f64 (.f64 (PI.f64) (+.f64 n n)))))) (exp.f64 (/.f64 (log.f64 (pow.f64 (*.f64 (PI.f64) (+.f64 n n)) (-.f64 1 k))) -2))))
(.f64 (exp.f64 (.f64 (-.f64 1 k) (log.f64 (sqrt.f64 (.f64 (PI.f64) (+.f64 n n)))))) (/.f64 1 (/.f64 (exp.f64 (log.f64 (pow.f64 (.f64 (PI.f64) (+.f64 n n)) (-.f64 1 k)))) (exp.f64 (log.f64 (pow.f64 (*.f64 (PI.f64) (+.f64 n n)) (-.f64 1 k)))))))
(.f64 (/.f64 (exp.f64 (log.f64 (pow.f64 (.f64 (PI.f64) (+.f64 n n)) (-.f64 1 k)))) (exp.f64 (log.f64 (pow.f64 (.f64 (PI.f64) (+.f64 n n)) (-.f64 1 k))))) (exp.f64 (.f64 (-.f64 1 k) (log.f64 (sqrt.f64 (*.f64 (PI.f64) (+.f64 n n)))))))
(.f64 (exp.f64 (/.f64 (log.f64 (pow.f64 (.f64 (PI.f64) (+.f64 n n)) (-.f64 1 k))) -2)) (exp.f64 (log.f64 (pow.f64 (*.f64 (PI.f64) (+.f64 n n)) (-.f64 1 k)))))
(.f64 (exp.f64 (log.f64 (pow.f64 (.f64 (PI.f64) (+.f64 n n)) (-.f64 1 k)))) (exp.f64 (/.f64 (log.f64 (pow.f64 (*.f64 (PI.f64) (+.f64 n n)) (-.f64 1 k))) -2)))
(.f64 (.f64 (exp.f64 (.f64 (-.f64 1 k) (log.f64 (sqrt.f64 (.f64 (PI.f64) (+.f64 n n)))))) (exp.f64 (/.f64 (log.f64 (pow.f64 (.f64 (PI.f64) (+.f64 n n)) (-.f64 1 k))) -2))) (exp.f64 (.f64 (-.f64 1 k) (log.f64 (sqrt.f64 (*.f64 (PI.f64) (+.f64 n n)))))))
(.f64 (/.f64 (exp.f64 (/.f64 (log.f64 (pow.f64 (.f64 (PI.f64) (+.f64 n n)) (-.f64 1 k))) -2)) (exp.f64 (log.f64 (pow.f64 (.f64 (PI.f64) (+.f64 n n)) (-.f64 1 k))))) (.f64 (exp.f64 (log.f64 (pow.f64 (.f64 (PI.f64) (+.f64 n n)) (-.f64 1 k)))) (exp.f64 (log.f64 (pow.f64 (.f64 (PI.f64) (+.f64 n n)) (-.f64 1 k))))))
(.f64 (/.f64 (/.f64 (exp.f64 (log.f64 (pow.f64 (.f64 (PI.f64) (+.f64 n n)) (-.f64 1 k)))) (exp.f64 (log.f64 (pow.f64 (.f64 (PI.f64) (+.f64 n n)) (-.f64 1 k))))) (exp.f64 (.f64 (-.f64 1 k) (log.f64 (sqrt.f64 (.f64 (PI.f64) (+.f64 n n))))))) (exp.f64 (log.f64 (pow.f64 (.f64 (PI.f64) (+.f64 n n)) (-.f64 1 k)))))
(.f64 (/.f64 (.f64 (exp.f64 (.f64 (-.f64 1 k) (log.f64 (sqrt.f64 (.f64 (PI.f64) (+.f64 n n)))))) (exp.f64 (/.f64 (log.f64 (pow.f64 (.f64 (PI.f64) (+.f64 n n)) (-.f64 1 k))) -2))) (exp.f64 (.f64 (-.f64 1 k) (log.f64 (sqrt.f64 (.f64 (PI.f64) (+.f64 n n))))))) (exp.f64 (log.f64 (pow.f64 (.f64 (PI.f64) (+.f64 n n)) (-.f64 1 k)))))
(/.f64 (exp.f64 (.f64 (-.f64 1 k) (log.f64 (sqrt.f64 (.f64 (PI.f64) (+.f64 n n)))))) 1)
(/.f64 (exp.f64 (.f64 (-.f64 1 k) (log.f64 (sqrt.f64 (.f64 (PI.f64) (+.f64 n n)))))) (/.f64 (exp.f64 (log.f64 (pow.f64 (.f64 (PI.f64) (+.f64 n n)) (-.f64 1 k)))) (exp.f64 (log.f64 (pow.f64 (.f64 (PI.f64) (+.f64 n n)) (-.f64 1 k))))))
(/.f64 (.f64 2 (exp.f64 (.f64 (-.f64 1 k) (log.f64 (sqrt.f64 (*.f64 (PI.f64) (+.f64 n n))))))) 2)
(pow.f64 (exp.f64 (.f64 (-.f64 1 k) (log.f64 (sqrt.f64 (.f64 (PI.f64) (+.f64 n n)))))) 1)
(+.f64 (*.f64 n (PI.f64)) 0)
(+.f64 0 (*.f64 n (PI.f64)))
(-.f64 (*.f64 n (PI.f64)) 0)
(/.f64 (*.f64 n (PI.f64)) 1)
(/.f64 (.f64 n (PI.f64)) (/.f64 (.f64 n (PI.f64)) (*.f64 n (PI.f64))))
(/.f64 (*.f64 (PI.f64) (+.f64 n n)) 2)
(pow.f64 (*.f64 n (PI.f64)) 1)
(+.f64 (.f64 (exp.f64 (.f64 (-.f64 1 k) (log.f64 (sqrt.f64 (*.f64 (PI.f64) (+.f64 n n)))))) (/.f64 1 (sqrt.f64 k))) 0)
(+.f64 0 (.f64 (exp.f64 (.f64 (-.f64 1 k) (log.f64 (sqrt.f64 (*.f64 (PI.f64) (+.f64 n n)))))) (/.f64 1 (sqrt.f64 k))))
(-.f64 (.f64 (exp.f64 (.f64 (-.f64 1 k) (log.f64 (sqrt.f64 (*.f64 (PI.f64) (+.f64 n n)))))) (/.f64 1 (sqrt.f64 k))) 0)
(/.f64 (.f64 (exp.f64 (.f64 (-.f64 1 k) (log.f64 (sqrt.f64 (*.f64 (PI.f64) (+.f64 n n)))))) (/.f64 1 (sqrt.f64 k))) 1)
(/.f64 (.f64 (exp.f64 (.f64 (-.f64 1 k) (log.f64 (sqrt.f64 (.f64 (PI.f64) (+.f64 n n)))))) (/.f64 1 (sqrt.f64 k))) (/.f64 (.f64 (exp.f64 (.f64 (-.f64 1 k) (log.f64 (sqrt.f64 (.f64 (PI.f64) (+.f64 n n)))))) (/.f64 1 (sqrt.f64 k))) (.f64 (exp.f64 (.f64 (-.f64 1 k) (log.f64 (sqrt.f64 (*.f64 (PI.f64) (+.f64 n n)))))) (/.f64 1 (sqrt.f64 k)))))
(/.f64 (.f64 (exp.f64 (.f64 (-.f64 1 k) (log.f64 (sqrt.f64 (.f64 (PI.f64) (+.f64 n n)))))) (.f64 2 (/.f64 1 (sqrt.f64 k)))) 2)
(pow.f64 (.f64 (exp.f64 (.f64 (-.f64 1 k) (log.f64 (sqrt.f64 (*.f64 (PI.f64) (+.f64 n n)))))) (/.f64 1 (sqrt.f64 k))) 1)

Outputs
(.f64 (sqrt.f64 2) (sqrt.f64 (.f64 n (PI.f64))))
(sqrt.f64 (.f64 n (.f64 2 (PI.f64))))
(sqrt.f64 (*.f64 (PI.f64) (+.f64 n n)))
(sqrt.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 (sqrt.f64 2) (sqrt.f64 (*.f64 n (PI.f64)))))
(+.f64 (sqrt.f64 (.f64 n (.f64 2 (PI.f64)))) (.f64 (.f64 (sqrt.f64 2) (.f64 k (log.f64 (.f64 n (.f64 2 (PI.f64)))))) (.f64 -1/2 (sqrt.f64 (*.f64 n (PI.f64))))))
(+.f64 (sqrt.f64 (.f64 n (.f64 2 (PI.f64)))) (.f64 -1/2 (.f64 (.f64 k (log.f64 (.f64 n (.f64 2 (PI.f64))))) (sqrt.f64 (.f64 n (*.f64 2 (PI.f64)))))))
(.f64 (sqrt.f64 (.f64 n (PI.f64))) (+.f64 (.f64 (log.f64 (.f64 (PI.f64) (+.f64 n n))) (.f64 -1/2 (.f64 (sqrt.f64 2) k))) (sqrt.f64 2)))
(.f64 (sqrt.f64 (.f64 n (PI.f64))) (+.f64 (sqrt.f64 2) (.f64 (sqrt.f64 2) (.f64 k (.f64 -1/2 (log.f64 (.f64 2 (*.f64 n (PI.f64)))))))))
(.f64 (sqrt.f64 (.f64 n (PI.f64))) (+.f64 (sqrt.f64 2) (.f64 (sqrt.f64 2) (.f64 k (.f64 -1/2 (log.f64 (.f64 (PI.f64) (+.f64 n 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 (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 (.f64 (sqrt.f64 2) (pow.f64 (.f64 k (log.f64 (.f64 n (.f64 2 (PI.f64))))) 2)) (.f64 1/8 (sqrt.f64 (.f64 n (PI.f64))))) (+.f64 (sqrt.f64 (.f64 n (.f64 2 (PI.f64)))) (.f64 (.f64 (sqrt.f64 2) (.f64 k (log.f64 (.f64 n (.f64 2 (PI.f64)))))) (.f64 -1/2 (sqrt.f64 (.f64 n (PI.f64)))))))
(+.f64 (+.f64 (sqrt.f64 (.f64 n (.f64 2 (PI.f64)))) (.f64 -1/2 (.f64 (.f64 k (log.f64 (.f64 n (.f64 2 (PI.f64))))) (sqrt.f64 (.f64 n (.f64 2 (PI.f64))))))) (.f64 1/8 (.f64 (pow.f64 (.f64 k (log.f64 (.f64 n (.f64 2 (PI.f64))))) 2) (sqrt.f64 (.f64 n (.f64 2 (PI.f64)))))))
(+.f64 (sqrt.f64 (.f64 (PI.f64) (+.f64 n n))) (.f64 (sqrt.f64 (.f64 n (PI.f64))) (+.f64 (.f64 1/8 (.f64 (sqrt.f64 2) (pow.f64 (.f64 k (log.f64 (.f64 (PI.f64) (+.f64 n n)))) 2))) (.f64 (log.f64 (.f64 (PI.f64) (+.f64 n n))) (.f64 -1/2 (*.f64 (sqrt.f64 2) k))))))
(.f64 (sqrt.f64 (.f64 n (PI.f64))) (+.f64 (.f64 (sqrt.f64 2) (+.f64 (.f64 k (.f64 -1/2 (log.f64 (.f64 2 (.f64 n (PI.f64)))))) (.f64 1/8 (pow.f64 (.f64 k (log.f64 (.f64 2 (*.f64 n (PI.f64))))) 2)))) (sqrt.f64 2)))
(.f64 (sqrt.f64 (.f64 n (PI.f64))) (+.f64 (sqrt.f64 2) (.f64 (sqrt.f64 2) (+.f64 (.f64 1/8 (pow.f64 (.f64 k (log.f64 (.f64 (PI.f64) (+.f64 n n)))) 2)) (.f64 k (.f64 -1/2 (log.f64 (*.f64 (PI.f64) (+.f64 n 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 (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 (.f64 (.f64 (sqrt.f64 2) (pow.f64 (.f64 k (log.f64 (.f64 n (.f64 2 (PI.f64))))) 2)) (.f64 1/8 (sqrt.f64 (.f64 n (PI.f64))))) (.f64 (.f64 (sqrt.f64 2) (pow.f64 (.f64 k (log.f64 (.f64 n (.f64 2 (PI.f64))))) 3)) (.f64 -1/48 (sqrt.f64 (.f64 n (PI.f64)))))) (+.f64 (sqrt.f64 (.f64 n (.f64 2 (PI.f64)))) (.f64 (.f64 (sqrt.f64 2) (.f64 k (log.f64 (.f64 n (.f64 2 (PI.f64)))))) (.f64 -1/2 (sqrt.f64 (*.f64 n (PI.f64)))))))
(+.f64 (+.f64 (sqrt.f64 (.f64 n (.f64 2 (PI.f64)))) (.f64 -1/2 (.f64 (.f64 k (log.f64 (.f64 n (.f64 2 (PI.f64))))) (sqrt.f64 (.f64 n (.f64 2 (PI.f64))))))) (+.f64 (.f64 1/8 (.f64 (pow.f64 (.f64 k (log.f64 (.f64 n (.f64 2 (PI.f64))))) 2) (sqrt.f64 (.f64 n (.f64 2 (PI.f64)))))) (.f64 -1/48 (.f64 (pow.f64 (.f64 k (log.f64 (.f64 n (.f64 2 (PI.f64))))) 3) (sqrt.f64 (.f64 n (*.f64 2 (PI.f64))))))))
(+.f64 (.f64 (sqrt.f64 (.f64 n (PI.f64))) (+.f64 (.f64 (log.f64 (.f64 (PI.f64) (+.f64 n n))) (.f64 -1/2 (.f64 (sqrt.f64 2) k))) (sqrt.f64 2))) (.f64 (sqrt.f64 (.f64 n (PI.f64))) (+.f64 (.f64 (pow.f64 (.f64 k (log.f64 (.f64 (PI.f64) (+.f64 n n)))) 3) (.f64 -1/48 (sqrt.f64 2))) (.f64 1/8 (.f64 (sqrt.f64 2) (pow.f64 (.f64 k (log.f64 (.f64 (PI.f64) (+.f64 n n)))) 2))))))
(.f64 (sqrt.f64 (.f64 n (PI.f64))) (+.f64 (.f64 (sqrt.f64 2) (+.f64 (.f64 -1/48 (pow.f64 (.f64 k (log.f64 (.f64 2 (.f64 n (PI.f64))))) 3)) (.f64 1/8 (pow.f64 (.f64 k (log.f64 (.f64 2 (.f64 n (PI.f64))))) 2)))) (+.f64 (sqrt.f64 2) (.f64 (sqrt.f64 2) (.f64 k (.f64 -1/2 (log.f64 (.f64 2 (.f64 n (PI.f64))))))))))
(.f64 (sqrt.f64 (.f64 n (PI.f64))) (+.f64 (.f64 (sqrt.f64 2) (+.f64 (+.f64 (.f64 1/8 (pow.f64 (.f64 k (log.f64 (.f64 (PI.f64) (+.f64 n n)))) 2)) (.f64 -1/48 (pow.f64 (.f64 k (log.f64 (.f64 (PI.f64) (+.f64 n n)))) 3))) (.f64 k (.f64 -1/2 (log.f64 (.f64 (PI.f64) (+.f64 n n))))))) (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 (PI.f64) (+.f64 n n))))) (+.f64 (.f64 1/8 (pow.f64 (.f64 k (log.f64 (.f64 (PI.f64) (+.f64 n n)))) 2)) (.f64 -1/48 (pow.f64 (.f64 k (log.f64 (.f64 (PI.f64) (+.f64 n n)))) 3)))))))
(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 (log.f64 (.f64 n (.f64 2 (PI.f64)))) (+.f64 1 (*.f64 k -1)))))
(exp.f64 (.f64 (+.f64 1 (neg.f64 k)) (log.f64 (sqrt.f64 (.f64 n (*.f64 2 (PI.f64)))))))
(exp.f64 (.f64 (+.f64 1 (neg.f64 k)) (log.f64 (sqrt.f64 (.f64 (PI.f64) (+.f64 n n))))))
(exp.f64 (.f64 (+.f64 1 (neg.f64 k)) (log.f64 (sqrt.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 (log.f64 (.f64 n (.f64 2 (PI.f64)))) (+.f64 1 (*.f64 k -1)))))
(exp.f64 (.f64 (+.f64 1 (neg.f64 k)) (log.f64 (sqrt.f64 (.f64 n (*.f64 2 (PI.f64)))))))
(exp.f64 (.f64 (+.f64 1 (neg.f64 k)) (log.f64 (sqrt.f64 (.f64 (PI.f64) (+.f64 n n))))))
(exp.f64 (.f64 (+.f64 1 (neg.f64 k)) (log.f64 (sqrt.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 (log.f64 (.f64 n (.f64 2 (PI.f64)))) (+.f64 1 (*.f64 k -1)))))
(exp.f64 (.f64 (+.f64 1 (neg.f64 k)) (log.f64 (sqrt.f64 (.f64 n (*.f64 2 (PI.f64)))))))
(exp.f64 (.f64 (+.f64 1 (neg.f64 k)) (log.f64 (sqrt.f64 (.f64 (PI.f64) (+.f64 n n))))))
(exp.f64 (.f64 (+.f64 1 (neg.f64 k)) (log.f64 (sqrt.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 (log.f64 (.f64 n (.f64 2 (PI.f64)))) (+.f64 1 (*.f64 k -1)))))
(exp.f64 (.f64 (+.f64 1 (neg.f64 k)) (log.f64 (sqrt.f64 (.f64 n (*.f64 2 (PI.f64)))))))
(exp.f64 (.f64 (+.f64 1 (neg.f64 k)) (log.f64 (sqrt.f64 (.f64 (PI.f64) (+.f64 n n))))))
(exp.f64 (.f64 (+.f64 1 (neg.f64 k)) (log.f64 (sqrt.f64 (.f64 2 (*.f64 n (PI.f64)))))))
(exp.f64 (.f64 1/2 (.f64 (-.f64 1 k) (+.f64 (log.f64 (*.f64 2 (PI.f64))) (log.f64 n)))))
(exp.f64 (.f64 (+.f64 (log.f64 (.f64 2 (PI.f64))) (log.f64 n)) (*.f64 1/2 (-.f64 1 k))))
(exp.f64 (.f64 (-.f64 1 k) (.f64 1/2 (+.f64 (log.f64 (*.f64 2 (PI.f64))) (log.f64 n)))))
(exp.f64 (.f64 1/2 (.f64 (-.f64 1 k) (+.f64 (log.f64 (*.f64 2 (PI.f64))) (log.f64 n)))))
(exp.f64 (.f64 (+.f64 (log.f64 (.f64 2 (PI.f64))) (log.f64 n)) (*.f64 1/2 (-.f64 1 k))))
(exp.f64 (.f64 (-.f64 1 k) (.f64 1/2 (+.f64 (log.f64 (*.f64 2 (PI.f64))) (log.f64 n)))))
(exp.f64 (.f64 1/2 (.f64 (-.f64 1 k) (+.f64 (log.f64 (*.f64 2 (PI.f64))) (log.f64 n)))))
(exp.f64 (.f64 (+.f64 (log.f64 (.f64 2 (PI.f64))) (log.f64 n)) (*.f64 1/2 (-.f64 1 k))))
(exp.f64 (.f64 (-.f64 1 k) (.f64 1/2 (+.f64 (log.f64 (*.f64 2 (PI.f64))) (log.f64 n)))))
(exp.f64 (.f64 1/2 (.f64 (-.f64 1 k) (+.f64 (log.f64 (*.f64 2 (PI.f64))) (log.f64 n)))))
(exp.f64 (.f64 (+.f64 (log.f64 (.f64 2 (PI.f64))) (log.f64 n)) (*.f64 1/2 (-.f64 1 k))))
(exp.f64 (.f64 (-.f64 1 k) (.f64 1/2 (+.f64 (log.f64 (*.f64 2 (PI.f64))) (log.f64 n)))))
(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 (log.f64 (.f64 2 (PI.f64))) (.f64 -1 (log.f64 (/.f64 1 n)))))))
(exp.f64 (.f64 (+.f64 (log.f64 (.f64 2 (PI.f64))) (neg.f64 (log.f64 (/.f64 1 n)))) (*.f64 1/2 (-.f64 1 k))))
(exp.f64 (.f64 1/2 (.f64 (-.f64 1 k) (+.f64 (log.f64 (*.f64 2 (PI.f64))) (neg.f64 (log.f64 (/.f64 1 n)))))))
(exp.f64 (.f64 (-.f64 1 k) (.f64 1/2 (+.f64 (log.f64 (*.f64 2 (PI.f64))) (neg.f64 (log.f64 (/.f64 1 n)))))))
(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 (log.f64 (.f64 2 (PI.f64))) (.f64 -1 (log.f64 (/.f64 1 n)))))))
(exp.f64 (.f64 (+.f64 (log.f64 (.f64 2 (PI.f64))) (neg.f64 (log.f64 (/.f64 1 n)))) (*.f64 1/2 (-.f64 1 k))))
(exp.f64 (.f64 1/2 (.f64 (-.f64 1 k) (+.f64 (log.f64 (*.f64 2 (PI.f64))) (neg.f64 (log.f64 (/.f64 1 n)))))))
(exp.f64 (.f64 (-.f64 1 k) (.f64 1/2 (+.f64 (log.f64 (*.f64 2 (PI.f64))) (neg.f64 (log.f64 (/.f64 1 n)))))))
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(exp.f64 (.f64 (-.f64 1 k) (.f64 1/2 (+.f64 (log.f64 (*.f64 2 (PI.f64))) (neg.f64 (log.f64 (/.f64 1 n)))))))
(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 (log.f64 (.f64 2 (PI.f64))) (.f64 -1 (log.f64 (/.f64 1 n)))))))
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(exp.f64 (+.f64 (/.f64 (log.f64 (pow.f64 (.f64 (PI.f64) (+.f64 n n)) (-.f64 1 k))) -2) (.f64 (log.f64 (*.f64 (PI.f64) (+.f64 n n))) (-.f64 1 k))))
(.f64 (/.f64 (exp.f64 (/.f64 (log.f64 (pow.f64 (.f64 (PI.f64) (+.f64 n n)) (-.f64 1 k))) -2)) (exp.f64 (log.f64 (pow.f64 (.f64 (PI.f64) (+.f64 n n)) (-.f64 1 k))))) (.f64 (exp.f64 (log.f64 (pow.f64 (.f64 (PI.f64) (+.f64 n n)) (-.f64 1 k)))) (exp.f64 (log.f64 (pow.f64 (.f64 (PI.f64) (+.f64 n n)) (-.f64 1 k))))))
(.f64 (.f64 (pow.f64 (.f64 (PI.f64) (+.f64 n n)) (-.f64 1 k)) (exp.f64 (/.f64 (log.f64 (pow.f64 (.f64 (PI.f64) (+.f64 n n)) (-.f64 1 k))) -2))) (/.f64 (pow.f64 (.f64 (PI.f64) (+.f64 n n)) (-.f64 1 k)) (pow.f64 (.f64 (PI.f64) (+.f64 n n)) (-.f64 1 k))))
(.f64 (/.f64 (exp.f64 (/.f64 (log.f64 (pow.f64 (.f64 (PI.f64) (+.f64 n n)) (-.f64 1 k))) -2)) (pow.f64 (.f64 (PI.f64) (+.f64 n n)) (-.f64 1 k))) (pow.f64 (.f64 (.f64 (PI.f64) (+.f64 n n)) (.f64 (PI.f64) (+.f64 n n))) (-.f64 1 k)))
(.f64 (/.f64 (exp.f64 (/.f64 (log.f64 (pow.f64 (.f64 2 (.f64 n (PI.f64))) (-.f64 1 k))) -2)) (pow.f64 (.f64 2 (.f64 n (PI.f64))) (-.f64 1 k))) (pow.f64 (.f64 n (.f64 (.f64 2 (.f64 n (PI.f64))) (.f64 2 (PI.f64)))) (-.f64 1 k)))
(.f64 (/.f64 (exp.f64 (/.f64 (log.f64 (pow.f64 (.f64 (PI.f64) (+.f64 n n)) (-.f64 1 k))) -2)) (pow.f64 (.f64 (PI.f64) (+.f64 n n)) (-.f64 1 k))) (pow.f64 (.f64 (.f64 n (PI.f64)) (.f64 n (*.f64 (PI.f64) 4))) (-.f64 1 k)))
(.f64 (/.f64 (/.f64 (exp.f64 (log.f64 (pow.f64 (.f64 (PI.f64) (+.f64 n n)) (-.f64 1 k)))) (exp.f64 (log.f64 (pow.f64 (.f64 (PI.f64) (+.f64 n n)) (-.f64 1 k))))) (exp.f64 (.f64 (-.f64 1 k) (log.f64 (sqrt.f64 (.f64 (PI.f64) (+.f64 n n))))))) (exp.f64 (log.f64 (pow.f64 (.f64 (PI.f64) (+.f64 n n)) (-.f64 1 k)))))
(.f64 (pow.f64 (.f64 (PI.f64) (+.f64 n n)) (-.f64 1 k)) (/.f64 (/.f64 (pow.f64 (.f64 (PI.f64) (+.f64 n n)) (-.f64 1 k)) (pow.f64 (.f64 (PI.f64) (+.f64 n n)) (-.f64 1 k))) (exp.f64 (.f64 (-.f64 1 k) (log.f64 (sqrt.f64 (.f64 (PI.f64) (+.f64 n n))))))))
(.f64 (pow.f64 (.f64 2 (.f64 n (PI.f64))) (-.f64 1 k)) (/.f64 (/.f64 (pow.f64 (.f64 2 (.f64 n (PI.f64))) (-.f64 1 k)) (pow.f64 (.f64 2 (.f64 n (PI.f64))) (-.f64 1 k))) (exp.f64 (.f64 (-.f64 1 k) (log.f64 (sqrt.f64 (.f64 2 (.f64 n (PI.f64)))))))))
(.f64 (/.f64 (.f64 (exp.f64 (.f64 (-.f64 1 k) (log.f64 (sqrt.f64 (.f64 (PI.f64) (+.f64 n n)))))) (exp.f64 (/.f64 (log.f64 (pow.f64 (.f64 (PI.f64) (+.f64 n n)) (-.f64 1 k))) -2))) (exp.f64 (.f64 (-.f64 1 k) (log.f64 (sqrt.f64 (.f64 (PI.f64) (+.f64 n n))))))) (exp.f64 (log.f64 (pow.f64 (.f64 (PI.f64) (+.f64 n n)) (-.f64 1 k)))))
(.f64 (pow.f64 (.f64 (PI.f64) (+.f64 n n)) (-.f64 1 k)) (/.f64 (exp.f64 (+.f64 (.f64 (-.f64 1 k) (log.f64 (sqrt.f64 (.f64 (PI.f64) (+.f64 n n))))) (/.f64 (log.f64 (pow.f64 (.f64 (PI.f64) (+.f64 n n)) (-.f64 1 k))) -2))) (exp.f64 (.f64 (-.f64 1 k) (log.f64 (sqrt.f64 (*.f64 (PI.f64) (+.f64 n n))))))))
(.f64 (pow.f64 (.f64 2 (.f64 n (PI.f64))) (-.f64 1 k)) (/.f64 (exp.f64 (+.f64 (.f64 (-.f64 1 k) (log.f64 (sqrt.f64 (.f64 2 (.f64 n (PI.f64)))))) (/.f64 (log.f64 (pow.f64 (.f64 2 (.f64 n (PI.f64))) (-.f64 1 k))) -2))) (exp.f64 (.f64 (-.f64 1 k) (log.f64 (sqrt.f64 (.f64 2 (*.f64 n (PI.f64)))))))))
(/.f64 (exp.f64 (.f64 (-.f64 1 k) (log.f64 (sqrt.f64 (.f64 (PI.f64) (+.f64 n n)))))) 1)
(exp.f64 (.f64 (-.f64 1 k) (log.f64 (sqrt.f64 (.f64 (PI.f64) (+.f64 n n))))))
(exp.f64 (.f64 (-.f64 1 k) (log.f64 (sqrt.f64 (.f64 2 (*.f64 n (PI.f64)))))))
(/.f64 (exp.f64 (.f64 (-.f64 1 k) (log.f64 (sqrt.f64 (.f64 (PI.f64) (+.f64 n n)))))) (/.f64 (exp.f64 (log.f64 (pow.f64 (.f64 (PI.f64) (+.f64 n n)) (-.f64 1 k)))) (exp.f64 (log.f64 (pow.f64 (.f64 (PI.f64) (+.f64 n n)) (-.f64 1 k))))))
(/.f64 (exp.f64 (.f64 (-.f64 1 k) (log.f64 (sqrt.f64 (.f64 (PI.f64) (+.f64 n n)))))) (/.f64 (pow.f64 (.f64 (PI.f64) (+.f64 n n)) (-.f64 1 k)) (pow.f64 (.f64 (PI.f64) (+.f64 n n)) (-.f64 1 k))))
(/.f64 (exp.f64 (.f64 (-.f64 1 k) (log.f64 (sqrt.f64 (.f64 2 (.f64 n (PI.f64))))))) (/.f64 (pow.f64 (.f64 2 (.f64 n (PI.f64))) (-.f64 1 k)) (pow.f64 (.f64 2 (*.f64 n (PI.f64))) (-.f64 1 k))))
(/.f64 (.f64 2 (exp.f64 (.f64 (-.f64 1 k) (log.f64 (sqrt.f64 (*.f64 (PI.f64) (+.f64 n n))))))) 2)
(exp.f64 (.f64 (-.f64 1 k) (log.f64 (sqrt.f64 (.f64 (PI.f64) (+.f64 n n))))))
(exp.f64 (.f64 (-.f64 1 k) (log.f64 (sqrt.f64 (.f64 2 (*.f64 n (PI.f64)))))))
(pow.f64 (exp.f64 (.f64 (-.f64 1 k) (log.f64 (sqrt.f64 (.f64 (PI.f64) (+.f64 n n)))))) 1)
(exp.f64 (.f64 (-.f64 1 k) (log.f64 (sqrt.f64 (.f64 (PI.f64) (+.f64 n n))))))
(exp.f64 (.f64 (-.f64 1 k) (log.f64 (sqrt.f64 (.f64 2 (*.f64 n (PI.f64)))))))
(+.f64 (*.f64 n (PI.f64)) 0)
(*.f64 n (PI.f64))
(+.f64 0 (*.f64 n (PI.f64)))
(*.f64 n (PI.f64))
(-.f64 (*.f64 n (PI.f64)) 0)
(*.f64 n (PI.f64))
(/.f64 (*.f64 n (PI.f64)) 1)
(*.f64 n (PI.f64))
(/.f64 (.f64 n (PI.f64)) (/.f64 (.f64 n (PI.f64)) (*.f64 n (PI.f64))))
(*.f64 n (PI.f64))
(/.f64 (*.f64 (PI.f64) (+.f64 n n)) 2)
(*.f64 n (PI.f64))
(pow.f64 (*.f64 n (PI.f64)) 1)
(*.f64 n (PI.f64))
(+.f64 (.f64 (exp.f64 (.f64 (-.f64 1 k) (log.f64 (sqrt.f64 (*.f64 (PI.f64) (+.f64 n n)))))) (/.f64 1 (sqrt.f64 k))) 0)
(.f64 (exp.f64 (.f64 (-.f64 1 k) (log.f64 (sqrt.f64 (*.f64 (PI.f64) (+.f64 n n)))))) (/.f64 1 (sqrt.f64 k)))
(.f64 (exp.f64 (.f64 (-.f64 1 k) (log.f64 (sqrt.f64 (.f64 2 (.f64 n (PI.f64))))))) (/.f64 1 (sqrt.f64 k)))
(+.f64 0 (.f64 (exp.f64 (.f64 (-.f64 1 k) (log.f64 (sqrt.f64 (*.f64 (PI.f64) (+.f64 n n)))))) (/.f64 1 (sqrt.f64 k))))
(.f64 (exp.f64 (.f64 (-.f64 1 k) (log.f64 (sqrt.f64 (*.f64 (PI.f64) (+.f64 n n)))))) (/.f64 1 (sqrt.f64 k)))
(.f64 (exp.f64 (.f64 (-.f64 1 k) (log.f64 (sqrt.f64 (.f64 2 (.f64 n (PI.f64))))))) (/.f64 1 (sqrt.f64 k)))
(-.f64 (.f64 (exp.f64 (.f64 (-.f64 1 k) (log.f64 (sqrt.f64 (*.f64 (PI.f64) (+.f64 n n)))))) (/.f64 1 (sqrt.f64 k))) 0)
(.f64 (exp.f64 (.f64 (-.f64 1 k) (log.f64 (sqrt.f64 (*.f64 (PI.f64) (+.f64 n n)))))) (/.f64 1 (sqrt.f64 k)))
(.f64 (exp.f64 (.f64 (-.f64 1 k) (log.f64 (sqrt.f64 (.f64 2 (.f64 n (PI.f64))))))) (/.f64 1 (sqrt.f64 k)))
(/.f64 (.f64 (exp.f64 (.f64 (-.f64 1 k) (log.f64 (sqrt.f64 (*.f64 (PI.f64) (+.f64 n n)))))) (/.f64 1 (sqrt.f64 k))) 1)
(.f64 (exp.f64 (.f64 (-.f64 1 k) (log.f64 (sqrt.f64 (*.f64 (PI.f64) (+.f64 n n)))))) (/.f64 1 (sqrt.f64 k)))
(.f64 (exp.f64 (.f64 (-.f64 1 k) (log.f64 (sqrt.f64 (.f64 2 (.f64 n (PI.f64))))))) (/.f64 1 (sqrt.f64 k)))
(/.f64 (.f64 (exp.f64 (.f64 (-.f64 1 k) (log.f64 (sqrt.f64 (.f64 (PI.f64) (+.f64 n n)))))) (/.f64 1 (sqrt.f64 k))) (/.f64 (.f64 (exp.f64 (.f64 (-.f64 1 k) (log.f64 (sqrt.f64 (.f64 (PI.f64) (+.f64 n n)))))) (/.f64 1 (sqrt.f64 k))) (.f64 (exp.f64 (.f64 (-.f64 1 k) (log.f64 (sqrt.f64 (*.f64 (PI.f64) (+.f64 n n)))))) (/.f64 1 (sqrt.f64 k)))))
(.f64 (exp.f64 (.f64 (-.f64 1 k) (log.f64 (sqrt.f64 (*.f64 (PI.f64) (+.f64 n n)))))) (/.f64 1 (sqrt.f64 k)))
(.f64 (exp.f64 (.f64 (-.f64 1 k) (log.f64 (sqrt.f64 (.f64 2 (.f64 n (PI.f64))))))) (/.f64 1 (sqrt.f64 k)))
(/.f64 (.f64 (exp.f64 (.f64 (-.f64 1 k) (log.f64 (sqrt.f64 (.f64 (PI.f64) (+.f64 n n)))))) (.f64 2 (/.f64 1 (sqrt.f64 k)))) 2)
(.f64 (exp.f64 (.f64 (-.f64 1 k) (log.f64 (sqrt.f64 (*.f64 (PI.f64) (+.f64 n n)))))) (/.f64 1 (sqrt.f64 k)))
(.f64 (exp.f64 (.f64 (-.f64 1 k) (log.f64 (sqrt.f64 (.f64 2 (.f64 n (PI.f64))))))) (/.f64 1 (sqrt.f64 k)))
(pow.f64 (.f64 (exp.f64 (.f64 (-.f64 1 k) (log.f64 (sqrt.f64 (*.f64 (PI.f64) (+.f64 n n)))))) (/.f64 1 (sqrt.f64 k))) 1)
(.f64 (exp.f64 (.f64 (-.f64 1 k) (log.f64 (sqrt.f64 (*.f64 (PI.f64) (+.f64 n n)))))) (/.f64 1 (sqrt.f64 k)))
(.f64 (exp.f64 (.f64 (-.f64 1 k) (log.f64 (sqrt.f64 (.f64 2 (.f64 n (PI.f64))))))) (/.f64 1 (sqrt.f64 k)))

localize35.0ms (0.2%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.2b	(/.f64 2 (*.f64 n (PI.f64)))
	0.3b	(*.f64 n (PI.f64))
✓	0.3b	(.f64 (.f64 n (PI.f64)) (PI.f64))
✓	30.1b	(.f64 (/.f64 2 (.f64 n (PI.f64))) (.f64 n (.f64 (*.f64 n (PI.f64)) (PI.f64))))

Compiler

Compiled 97 to 41 computations (57.7% saved)

series3.0ms (0%)

Counts

3 → 24

Calls

9 calls:

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

rewrite117.0ms (0.8%)

Algorithm

1×	batch-egg-rewrite

Rules

1124×	`rational_best-simplify-57`
722×	`rational_best-simplify-47`
716×	`rational_best-simplify-43`
636×	`rational_best-5`
634×	`rational_best-4`

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	11	75
1	96	75
2	326	47
3	1430	47
4	6231	47

Stop Event

1×	node limit

Counts

3 → 38

Calls

Call 1

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

Outputs

((#(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 2 (*.f64 n (PI.f64))))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (*.f64 2 (*.f64 n (PI.f64))) 0)))) (#(struct:change #<rule egg-rr> (2) ((x -.f64 0 (neg.f64 (*.f64 2 (*.f64 n (PI.f64)))))))) (#(struct:change #<rule egg-rr> (2) ((x -.f64 (*.f64 2 (*.f64 n (PI.f64))) 0)))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (*.f64 2 (*.f64 n (PI.f64))) 1)))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (*.f64 2 (*.f64 n (PI.f64))) (/.f64 (*.f64 n (PI.f64)) (*.f64 n (PI.f64))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (*.f64 (PI.f64) (*.f64 n 4)) 2)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (*.f64 2 (*.f64 n (PI.f64))) 1)))) (#(struct:change #<rule egg-rr> (2) ((x neg.f64 (neg.f64 (*.f64 2 (*.f64 n (PI.f64)))))))))

((#(struct:change #<rule egg-rr> (2) ((x +.f64 (*.f64 n (*.f64 (PI.f64) (PI.f64))) 0)))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 0 (*.f64 n (*.f64 (PI.f64) (PI.f64))))))) (#(struct:change #<rule egg-rr> (2) ((x -.f64 (*.f64 n (*.f64 (PI.f64) (PI.f64))) 0)))) (#(struct:change #<rule egg-rr> (2) ((x -.f64 0 (neg.f64 (*.f64 n (*.f64 (PI.f64) (PI.f64)))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (*.f64 n (*.f64 (PI.f64) (PI.f64))) 1)))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (*.f64 n (*.f64 (PI.f64) (PI.f64))) (/.f64 (*.f64 n (*.f64 (PI.f64) (PI.f64))) (*.f64 n (*.f64 (PI.f64) (PI.f64)))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (*.f64 n (*.f64 (PI.f64) (*.f64 2 (PI.f64)))) 2)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (*.f64 n (*.f64 (PI.f64) (PI.f64))) 1)))) (#(struct:change #<rule egg-rr> (2) ((x neg.f64 (neg.f64 (*.f64 n (*.f64 (PI.f64) (PI.f64)))))))))

((#(struct:change #<rule egg-rr> (2) ((x +.f64 (/.f64 2 (*.f64 n (PI.f64))) 0)))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 0 (/.f64 2 (*.f64 n (PI.f64))))))) (#(struct:change #<rule egg-rr> (2) ((x -.f64 (/.f64 2 (*.f64 n (PI.f64))) 0)))) (#(struct:change #<rule egg-rr> (2) ((x -.f64 0 (neg.f64 (/.f64 2 (*.f64 n (PI.f64)))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (/.f64 2 (*.f64 n (PI.f64))) 1)))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (/.f64 2 (*.f64 n (PI.f64))) (/.f64 (/.f64 2 (*.f64 n (PI.f64))) (/.f64 2 (*.f64 n (PI.f64)))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (/.f64 2 (*.f64 n (PI.f64))) (*.f64 (/.f64 2 (*.f64 n (PI.f64))) (/.f64 1 (/.f64 2 (*.f64 n (PI.f64))))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (/.f64 2 (*.f64 n (PI.f64))) (/.f64 1 (/.f64 (/.f64 2 (*.f64 n (PI.f64))) (/.f64 2 (*.f64 n (PI.f64))))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 1 (/.f64 2 (*.f64 n (PI.f64))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (/.f64 (/.f64 2 (*.f64 n (PI.f64))) (/.f64 2 (*.f64 n (PI.f64)))) (/.f64 2 (*.f64 n (PI.f64))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (/.f64 1 (/.f64 2 (*.f64 n (PI.f64)))) (*.f64 (/.f64 2 (*.f64 n (PI.f64))) (/.f64 2 (*.f64 n (PI.f64)))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (*.f64 (/.f64 2 (*.f64 n (PI.f64))) (/.f64 2 (*.f64 n (PI.f64)))) (/.f64 1 (/.f64 2 (*.f64 n (PI.f64)))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (*.f64 (/.f64 2 (*.f64 n (PI.f64))) (/.f64 1 (/.f64 2 (*.f64 n (PI.f64))))) (/.f64 2 (*.f64 n (PI.f64))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (/.f64 (/.f64 1 (/.f64 2 (*.f64 n (PI.f64)))) (*.f64 (/.f64 2 (*.f64 n (PI.f64))) (/.f64 2 (*.f64 n (PI.f64))))) (*.f64 (*.f64 (/.f64 2 (*.f64 n (PI.f64))) (/.f64 2 (*.f64 n (PI.f64)))) (*.f64 (/.f64 2 (*.f64 n (PI.f64))) (/.f64 2 (*.f64 n (PI.f64))))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (/.f64 (/.f64 (/.f64 2 (*.f64 n (PI.f64))) (/.f64 2 (*.f64 n (PI.f64)))) (/.f64 2 (*.f64 n (PI.f64)))) (*.f64 (/.f64 2 (*.f64 n (PI.f64))) (/.f64 2 (*.f64 n (PI.f64)))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (/.f64 (*.f64 (/.f64 2 (*.f64 n (PI.f64))) (/.f64 1 (/.f64 2 (*.f64 n (PI.f64))))) (/.f64 2 (*.f64 n (PI.f64)))) (*.f64 (/.f64 2 (*.f64 n (PI.f64))) (/.f64 2 (*.f64 n (PI.f64)))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (/.f64 (/.f64 1 (/.f64 (/.f64 2 (*.f64 n (PI.f64))) (/.f64 2 (*.f64 n (PI.f64))))) (/.f64 2 (*.f64 n (PI.f64)))) (*.f64 (/.f64 2 (*.f64 n (PI.f64))) (/.f64 2 (*.f64 n (PI.f64)))))))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (/.f64 2 (*.f64 n (PI.f64))) 1)))) (#(struct:change #<rule egg-rr> (2) ((x neg.f64 (neg.f64 (/.f64 2 (*.f64 n (PI.f64)))))))))

simplify147.0ms (1%)

Algorithm

1×	egg-herbie

Rules

916×	`rational_best-simplify-49`
898×	`rational_best-simplify-50`
874×	`rational_best-simplify-2`
718×	`rational_best-simplify-82`
642×	`rational_best-simplify-80`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	75	978
1	153	976
2	319	976
3	1137	976
4	2349	976
5	4838	976

Stop Event

1×	node limit

Counts

62 → 49

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 n (pow.f64 (PI.f64) 2))
(*.f64 n (pow.f64 (PI.f64) 2))
(*.f64 n (pow.f64 (PI.f64) 2))
(*.f64 n (pow.f64 (PI.f64) 2))
(*.f64 n (pow.f64 (PI.f64) 2))
(*.f64 n (pow.f64 (PI.f64) 2))
(*.f64 n (pow.f64 (PI.f64) 2))
(*.f64 n (pow.f64 (PI.f64) 2))
(*.f64 n (pow.f64 (PI.f64) 2))
(*.f64 n (pow.f64 (PI.f64) 2))
(*.f64 n (pow.f64 (PI.f64) 2))
(*.f64 n (pow.f64 (PI.f64) 2))
(+.f64 (.f64 n (PI.f64)) (.f64 n (PI.f64)))
(+.f64 0 (.f64 2 (.f64 n (PI.f64))))
(+.f64 (.f64 2 (.f64 n (PI.f64))) 0)
(-.f64 0 (neg.f64 (.f64 2 (.f64 n (PI.f64)))))
(-.f64 (.f64 2 (.f64 n (PI.f64))) 0)
(/.f64 (.f64 2 (.f64 n (PI.f64))) 1)
(/.f64 (.f64 2 (.f64 n (PI.f64))) (/.f64 (.f64 n (PI.f64)) (.f64 n (PI.f64))))
(/.f64 (.f64 (PI.f64) (.f64 n 4)) 2)
(pow.f64 (.f64 2 (.f64 n (PI.f64))) 1)
(neg.f64 (neg.f64 (.f64 2 (.f64 n (PI.f64)))))
(+.f64 (.f64 n (.f64 (PI.f64) (PI.f64))) 0)
(+.f64 0 (.f64 n (.f64 (PI.f64) (PI.f64))))
(-.f64 (.f64 n (.f64 (PI.f64) (PI.f64))) 0)
(-.f64 0 (neg.f64 (.f64 n (.f64 (PI.f64) (PI.f64)))))
(/.f64 (.f64 n (.f64 (PI.f64) (PI.f64))) 1)
(/.f64 (.f64 n (.f64 (PI.f64) (PI.f64))) (/.f64 (.f64 n (.f64 (PI.f64) (PI.f64))) (.f64 n (.f64 (PI.f64) (PI.f64)))))
(/.f64 (.f64 n (.f64 (PI.f64) (*.f64 2 (PI.f64)))) 2)
(pow.f64 (.f64 n (.f64 (PI.f64) (PI.f64))) 1)
(neg.f64 (neg.f64 (.f64 n (.f64 (PI.f64) (PI.f64)))))
(+.f64 (/.f64 2 (*.f64 n (PI.f64))) 0)
(+.f64 0 (/.f64 2 (*.f64 n (PI.f64))))
(-.f64 (/.f64 2 (*.f64 n (PI.f64))) 0)
(-.f64 0 (neg.f64 (/.f64 2 (*.f64 n (PI.f64)))))
(.f64 (/.f64 2 (.f64 n (PI.f64))) 1)
(.f64 (/.f64 2 (.f64 n (PI.f64))) (/.f64 (/.f64 2 (.f64 n (PI.f64))) (/.f64 2 (.f64 n (PI.f64)))))
(.f64 (/.f64 2 (.f64 n (PI.f64))) (.f64 (/.f64 2 (.f64 n (PI.f64))) (/.f64 1 (/.f64 2 (*.f64 n (PI.f64))))))
(.f64 (/.f64 2 (.f64 n (PI.f64))) (/.f64 1 (/.f64 (/.f64 2 (.f64 n (PI.f64))) (/.f64 2 (.f64 n (PI.f64))))))
(.f64 1 (/.f64 2 (.f64 n (PI.f64))))
(.f64 (/.f64 (/.f64 2 (.f64 n (PI.f64))) (/.f64 2 (.f64 n (PI.f64)))) (/.f64 2 (.f64 n (PI.f64))))
(.f64 (/.f64 1 (/.f64 2 (.f64 n (PI.f64)))) (.f64 (/.f64 2 (.f64 n (PI.f64))) (/.f64 2 (*.f64 n (PI.f64)))))
(.f64 (.f64 (/.f64 2 (.f64 n (PI.f64))) (/.f64 2 (.f64 n (PI.f64)))) (/.f64 1 (/.f64 2 (*.f64 n (PI.f64)))))
(.f64 (.f64 (/.f64 2 (.f64 n (PI.f64))) (/.f64 1 (/.f64 2 (.f64 n (PI.f64))))) (/.f64 2 (*.f64 n (PI.f64))))
(.f64 (/.f64 (/.f64 1 (/.f64 2 (.f64 n (PI.f64)))) (.f64 (/.f64 2 (.f64 n (PI.f64))) (/.f64 2 (.f64 n (PI.f64))))) (.f64 (.f64 (/.f64 2 (.f64 n (PI.f64))) (/.f64 2 (.f64 n (PI.f64)))) (.f64 (/.f64 2 (.f64 n (PI.f64))) (/.f64 2 (.f64 n (PI.f64))))))
(.f64 (/.f64 (/.f64 (/.f64 2 (.f64 n (PI.f64))) (/.f64 2 (.f64 n (PI.f64)))) (/.f64 2 (.f64 n (PI.f64)))) (.f64 (/.f64 2 (.f64 n (PI.f64))) (/.f64 2 (*.f64 n (PI.f64)))))
(.f64 (/.f64 (.f64 (/.f64 2 (.f64 n (PI.f64))) (/.f64 1 (/.f64 2 (.f64 n (PI.f64))))) (/.f64 2 (.f64 n (PI.f64)))) (.f64 (/.f64 2 (.f64 n (PI.f64))) (/.f64 2 (.f64 n (PI.f64)))))
(.f64 (/.f64 (/.f64 1 (/.f64 (/.f64 2 (.f64 n (PI.f64))) (/.f64 2 (.f64 n (PI.f64))))) (/.f64 2 (.f64 n (PI.f64)))) (.f64 (/.f64 2 (.f64 n (PI.f64))) (/.f64 2 (*.f64 n (PI.f64)))))
(pow.f64 (/.f64 2 (*.f64 n (PI.f64))) 1)
(neg.f64 (neg.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))
(*.f64 n (pow.f64 (PI.f64) 2))
(*.f64 n (pow.f64 (PI.f64) 2))
(*.f64 n (pow.f64 (PI.f64) 2))
(*.f64 n (pow.f64 (PI.f64) 2))
(*.f64 n (pow.f64 (PI.f64) 2))
(*.f64 n (pow.f64 (PI.f64) 2))
(*.f64 n (pow.f64 (PI.f64) 2))
(*.f64 n (pow.f64 (PI.f64) 2))
(*.f64 n (pow.f64 (PI.f64) 2))
(*.f64 n (pow.f64 (PI.f64) 2))
(*.f64 n (pow.f64 (PI.f64) 2))
(*.f64 n (pow.f64 (PI.f64) 2))
(+.f64 (.f64 n (PI.f64)) (.f64 n (PI.f64)))
(*.f64 n (+.f64 (PI.f64) (PI.f64)))
(*.f64 (PI.f64) (+.f64 n n))
(+.f64 0 (.f64 2 (.f64 n (PI.f64))))
(.f64 2 (.f64 n (PI.f64)))
(.f64 (PI.f64) (.f64 2 n))
(+.f64 (.f64 2 (.f64 n (PI.f64))) 0)
(.f64 2 (.f64 n (PI.f64)))
(.f64 (PI.f64) (.f64 2 n))
(-.f64 0 (neg.f64 (.f64 2 (.f64 n (PI.f64)))))
(.f64 2 (.f64 n (PI.f64)))
(.f64 (PI.f64) (.f64 2 n))
(-.f64 (.f64 2 (.f64 n (PI.f64))) 0)
(.f64 2 (.f64 n (PI.f64)))
(.f64 (PI.f64) (.f64 2 n))
(/.f64 (.f64 2 (.f64 n (PI.f64))) 1)
(.f64 2 (.f64 n (PI.f64)))
(.f64 (PI.f64) (.f64 2 n))
(/.f64 (.f64 2 (.f64 n (PI.f64))) (/.f64 (.f64 n (PI.f64)) (.f64 n (PI.f64))))
(.f64 (/.f64 2 (.f64 n (PI.f64))) (.f64 (.f64 n (PI.f64)) (*.f64 n (PI.f64))))
(.f64 (.f64 n (PI.f64)) (.f64 (/.f64 2 (.f64 n (PI.f64))) (*.f64 n (PI.f64))))
(.f64 (.f64 (PI.f64) (.f64 2 n)) (/.f64 (.f64 n (PI.f64)) (*.f64 n (PI.f64))))
(.f64 n (.f64 (.f64 (PI.f64) (.f64 2 n)) (/.f64 (PI.f64) (*.f64 n (PI.f64)))))
(/.f64 (.f64 (PI.f64) (.f64 n 4)) 2)
(.f64 2 (.f64 n (PI.f64)))
(.f64 (PI.f64) (.f64 2 n))
(pow.f64 (.f64 2 (.f64 n (PI.f64))) 1)
(.f64 2 (.f64 n (PI.f64)))
(.f64 (PI.f64) (.f64 2 n))
(neg.f64 (neg.f64 (.f64 2 (.f64 n (PI.f64)))))
(.f64 2 (.f64 n (PI.f64)))
(.f64 (PI.f64) (.f64 2 n))
(+.f64 (.f64 n (.f64 (PI.f64) (PI.f64))) 0)
(.f64 n (.f64 (PI.f64) (PI.f64)))
(+.f64 0 (.f64 n (.f64 (PI.f64) (PI.f64))))
(.f64 n (.f64 (PI.f64) (PI.f64)))
(-.f64 (.f64 n (.f64 (PI.f64) (PI.f64))) 0)
(.f64 n (.f64 (PI.f64) (PI.f64)))
(-.f64 0 (neg.f64 (.f64 n (.f64 (PI.f64) (PI.f64)))))
(.f64 n (.f64 (PI.f64) (PI.f64)))
(/.f64 (.f64 n (.f64 (PI.f64) (PI.f64))) 1)
(.f64 n (.f64 (PI.f64) (PI.f64)))
(/.f64 (.f64 n (.f64 (PI.f64) (PI.f64))) (/.f64 (.f64 n (.f64 (PI.f64) (PI.f64))) (.f64 n (.f64 (PI.f64) (PI.f64)))))
(.f64 n (.f64 (PI.f64) (PI.f64)))
(/.f64 (.f64 n (.f64 (PI.f64) (*.f64 2 (PI.f64)))) 2)
(.f64 n (.f64 (PI.f64) (PI.f64)))
(pow.f64 (.f64 n (.f64 (PI.f64) (PI.f64))) 1)
(.f64 n (.f64 (PI.f64) (PI.f64)))
(neg.f64 (neg.f64 (.f64 n (.f64 (PI.f64) (PI.f64)))))
(.f64 n (.f64 (PI.f64) (PI.f64)))
(+.f64 (/.f64 2 (*.f64 n (PI.f64))) 0)
(/.f64 2 (*.f64 n (PI.f64)))
(+.f64 0 (/.f64 2 (*.f64 n (PI.f64))))
(/.f64 2 (*.f64 n (PI.f64)))
(-.f64 (/.f64 2 (*.f64 n (PI.f64))) 0)
(/.f64 2 (*.f64 n (PI.f64)))
(-.f64 0 (neg.f64 (/.f64 2 (*.f64 n (PI.f64)))))
(/.f64 2 (*.f64 n (PI.f64)))
(.f64 (/.f64 2 (.f64 n (PI.f64))) 1)
(/.f64 2 (*.f64 n (PI.f64)))
(.f64 (/.f64 2 (.f64 n (PI.f64))) (/.f64 (/.f64 2 (.f64 n (PI.f64))) (/.f64 2 (.f64 n (PI.f64)))))
(/.f64 2 (*.f64 n (PI.f64)))
(.f64 (/.f64 2 (.f64 n (PI.f64))) (.f64 (/.f64 2 (.f64 n (PI.f64))) (/.f64 1 (/.f64 2 (*.f64 n (PI.f64))))))
(/.f64 2 (*.f64 n (PI.f64)))
(.f64 (/.f64 2 (.f64 n (PI.f64))) (/.f64 1 (/.f64 (/.f64 2 (.f64 n (PI.f64))) (/.f64 2 (.f64 n (PI.f64))))))
(/.f64 2 (*.f64 n (PI.f64)))
(.f64 1 (/.f64 2 (.f64 n (PI.f64))))
(/.f64 2 (*.f64 n (PI.f64)))
(.f64 (/.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 (/.f64 1 (/.f64 2 (.f64 n (PI.f64)))) (.f64 (/.f64 2 (.f64 n (PI.f64))) (/.f64 2 (*.f64 n (PI.f64)))))
(/.f64 2 (*.f64 n (PI.f64)))
(.f64 (.f64 (/.f64 2 (.f64 n (PI.f64))) (/.f64 2 (.f64 n (PI.f64)))) (/.f64 1 (/.f64 2 (*.f64 n (PI.f64)))))
(/.f64 2 (*.f64 n (PI.f64)))
(.f64 (.f64 (/.f64 2 (.f64 n (PI.f64))) (/.f64 1 (/.f64 2 (.f64 n (PI.f64))))) (/.f64 2 (*.f64 n (PI.f64))))
(/.f64 2 (*.f64 n (PI.f64)))
(.f64 (/.f64 (/.f64 1 (/.f64 2 (.f64 n (PI.f64)))) (.f64 (/.f64 2 (.f64 n (PI.f64))) (/.f64 2 (.f64 n (PI.f64))))) (.f64 (.f64 (/.f64 2 (.f64 n (PI.f64))) (/.f64 2 (.f64 n (PI.f64)))) (.f64 (/.f64 2 (.f64 n (PI.f64))) (/.f64 2 (.f64 n (PI.f64))))))
(/.f64 2 (*.f64 n (PI.f64)))
(.f64 (/.f64 (/.f64 (/.f64 2 (.f64 n (PI.f64))) (/.f64 2 (.f64 n (PI.f64)))) (/.f64 2 (.f64 n (PI.f64)))) (.f64 (/.f64 2 (.f64 n (PI.f64))) (/.f64 2 (*.f64 n (PI.f64)))))
(/.f64 2 (*.f64 n (PI.f64)))
(.f64 (/.f64 (.f64 (/.f64 2 (.f64 n (PI.f64))) (/.f64 1 (/.f64 2 (.f64 n (PI.f64))))) (/.f64 2 (.f64 n (PI.f64)))) (.f64 (/.f64 2 (.f64 n (PI.f64))) (/.f64 2 (.f64 n (PI.f64)))))
(/.f64 2 (*.f64 n (PI.f64)))
(.f64 (/.f64 (/.f64 1 (/.f64 (/.f64 2 (.f64 n (PI.f64))) (/.f64 2 (.f64 n (PI.f64))))) (/.f64 2 (.f64 n (PI.f64)))) (.f64 (/.f64 2 (.f64 n (PI.f64))) (/.f64 2 (*.f64 n (PI.f64)))))
(/.f64 2 (*.f64 n (PI.f64)))
(pow.f64 (/.f64 2 (*.f64 n (PI.f64))) 1)
(/.f64 2 (*.f64 n (PI.f64)))
(neg.f64 (neg.f64 (/.f64 2 (*.f64 n (PI.f64)))))
(/.f64 2 (*.f64 n (PI.f64)))

localize54.0ms (0.4%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.3b	(.f64 (log.f64 (.f64 (PI.f64) (.f64 2 n))) (.f64 -1/2 (*.f64 k (sqrt.f64 2))))
✓	0.4b	(.f64 (sqrt.f64 (.f64 n (PI.f64))) (+.f64 (.f64 (log.f64 (.f64 (PI.f64) (.f64 2 n))) (.f64 -1/2 (*.f64 k (sqrt.f64 2)))) (sqrt.f64 2)))
✓	0.5b	(*.f64 k (sqrt.f64 2))
✓	4.8b	(.f64 (/.f64 1 (sqrt.f64 k)) (.f64 (sqrt.f64 (.f64 n (PI.f64))) (+.f64 (.f64 (log.f64 (.f64 (PI.f64) (.f64 2 n))) (.f64 -1/2 (.f64 k (sqrt.f64 2)))) (sqrt.f64 2))))

Compiler

Compiled 123 to 84 computations (31.7% saved)

series53.0ms (0.4%)

Counts

4 → 48

Calls

21 calls:

Time	Variable		Point	Expression
34.0ms	k	@	0	(.f64 (log.f64 (.f64 (PI.f64) (.f64 2 n))) (.f64 -1/2 (*.f64 k (sqrt.f64 2))))
3.0ms	k	@	0	(.f64 (sqrt.f64 (.f64 n (PI.f64))) (+.f64 (.f64 (log.f64 (.f64 (PI.f64) (.f64 2 n))) (.f64 -1/2 (*.f64 k (sqrt.f64 2)))) (sqrt.f64 2)))
2.0ms	k	@	-inf	(.f64 (/.f64 1 (sqrt.f64 k)) (.f64 (sqrt.f64 (.f64 n (PI.f64))) (+.f64 (.f64 (log.f64 (.f64 (PI.f64) (.f64 2 n))) (.f64 -1/2 (.f64 k (sqrt.f64 2)))) (sqrt.f64 2))))
2.0ms	n	@	-inf	(.f64 (/.f64 1 (sqrt.f64 k)) (.f64 (sqrt.f64 (.f64 n (PI.f64))) (+.f64 (.f64 (log.f64 (.f64 (PI.f64) (.f64 2 n))) (.f64 -1/2 (.f64 k (sqrt.f64 2)))) (sqrt.f64 2))))
1.0ms	k	@	0	(.f64 (/.f64 1 (sqrt.f64 k)) (.f64 (sqrt.f64 (.f64 n (PI.f64))) (+.f64 (.f64 (log.f64 (.f64 (PI.f64) (.f64 2 n))) (.f64 -1/2 (.f64 k (sqrt.f64 2)))) (sqrt.f64 2))))

rewrite368.0ms (2.5%)

Algorithm

1×	batch-egg-rewrite

Rules

1366×	`rational_best-simplify-47`
1322×	`rational_best-2`
1322×	`rational_best-3`
1322×	`rational_best-1`
1320×	`rational_best-4`

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	24	206
1	205	206
2	670	206
3	2943	198

Stop Event

1×	node limit

Counts

4 → 29

Calls

Call 1

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

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

simplify185.0ms (1.3%)

Algorithm

1×	egg-herbie

Rules

1304×	`rational_best-simplify-132`
1204×	`rational_best-simplify-80`
1074×	`rational_best-simplify-78`
1002×	`rational_best-simplify-76`
948×	`rational_best-simplify-43`

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	111	3651
1	227	3535
2	488	3445
3	1181	3445
4	3730	3445
5	7307	3445

Stop Event

1×	node limit

Counts

77 → 78

Calls

Call 1

Inputs
(*.f64 (sqrt.f64 2) k)
(*.f64 (sqrt.f64 2) k)
(*.f64 (sqrt.f64 2) k)
(*.f64 (sqrt.f64 2) k)
(*.f64 (sqrt.f64 2) k)
(*.f64 (sqrt.f64 2) k)
(*.f64 (sqrt.f64 2) k)
(*.f64 (sqrt.f64 2) k)
(*.f64 (sqrt.f64 2) k)
(*.f64 (sqrt.f64 2) k)
(*.f64 (sqrt.f64 2) k)
(*.f64 (sqrt.f64 2) k)
(.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 (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 -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 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 (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 -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 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 (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 -1/2 (.f64 (sqrt.f64 2) (.f64 k (+.f64 (log.f64 (.f64 2 (PI.f64))) (log.f64 n)))))
(.f64 -1/2 (.f64 (sqrt.f64 2) (.f64 k (+.f64 (log.f64 (.f64 2 (PI.f64))) (log.f64 n)))))
(.f64 -1/2 (.f64 (sqrt.f64 2) (.f64 k (+.f64 (log.f64 (.f64 2 (PI.f64))) (log.f64 n)))))
(.f64 -1/2 (.f64 (sqrt.f64 2) (.f64 k (+.f64 (log.f64 (.f64 2 (PI.f64))) (log.f64 n)))))
(.f64 -1/2 (.f64 (sqrt.f64 2) (.f64 k (+.f64 (.f64 -1 (log.f64 (/.f64 1 n))) (log.f64 (*.f64 2 (PI.f64)))))))
(.f64 -1/2 (.f64 (sqrt.f64 2) (.f64 k (+.f64 (.f64 -1 (log.f64 (/.f64 1 n))) (log.f64 (*.f64 2 (PI.f64)))))))
(.f64 -1/2 (.f64 (sqrt.f64 2) (.f64 k (+.f64 (.f64 -1 (log.f64 (/.f64 1 n))) (log.f64 (*.f64 2 (PI.f64)))))))
(.f64 -1/2 (.f64 (sqrt.f64 2) (.f64 k (+.f64 (.f64 -1 (log.f64 (/.f64 1 n))) (log.f64 (*.f64 2 (PI.f64)))))))
(.f64 -1/2 (.f64 (sqrt.f64 2) (.f64 k (+.f64 (.f64 -1 (log.f64 (/.f64 -1 n))) (log.f64 (*.f64 -2 (PI.f64)))))))
(.f64 -1/2 (.f64 (sqrt.f64 2) (.f64 k (+.f64 (.f64 -1 (log.f64 (/.f64 -1 n))) (log.f64 (*.f64 -2 (PI.f64)))))))
(.f64 -1/2 (.f64 (sqrt.f64 2) (.f64 k (+.f64 (.f64 -1 (log.f64 (/.f64 -1 n))) (log.f64 (*.f64 -2 (PI.f64)))))))
(.f64 -1/2 (.f64 (sqrt.f64 2) (.f64 k (+.f64 (.f64 -1 (log.f64 (/.f64 -1 n))) (log.f64 (*.f64 -2 (PI.f64)))))))
(.f64 -1/2 (.f64 k (.f64 (sqrt.f64 2) (log.f64 (.f64 2 (*.f64 n (PI.f64)))))))
(.f64 -1/2 (.f64 k (.f64 (sqrt.f64 2) (log.f64 (.f64 2 (*.f64 n (PI.f64)))))))
(.f64 -1/2 (.f64 k (.f64 (sqrt.f64 2) (log.f64 (.f64 2 (*.f64 n (PI.f64)))))))
(.f64 -1/2 (.f64 k (.f64 (sqrt.f64 2) (log.f64 (.f64 2 (*.f64 n (PI.f64)))))))
(.f64 -1/2 (.f64 k (.f64 (sqrt.f64 2) (log.f64 (.f64 2 (*.f64 n (PI.f64)))))))
(.f64 -1/2 (.f64 k (.f64 (sqrt.f64 2) (log.f64 (.f64 2 (*.f64 n (PI.f64)))))))
(.f64 -1/2 (.f64 k (.f64 (sqrt.f64 2) (log.f64 (.f64 2 (*.f64 n (PI.f64)))))))
(.f64 -1/2 (.f64 k (.f64 (sqrt.f64 2) (log.f64 (.f64 2 (*.f64 n (PI.f64)))))))
(.f64 -1/2 (.f64 k (.f64 (sqrt.f64 2) (log.f64 (.f64 2 (*.f64 n (PI.f64)))))))
(.f64 -1/2 (.f64 k (.f64 (sqrt.f64 2) (log.f64 (.f64 2 (*.f64 n (PI.f64)))))))
(.f64 -1/2 (.f64 k (.f64 (sqrt.f64 2) (log.f64 (.f64 2 (*.f64 n (PI.f64)))))))
(.f64 -1/2 (.f64 k (.f64 (sqrt.f64 2) (log.f64 (.f64 2 (*.f64 n (PI.f64)))))))
(+.f64 (.f64 (/.f64 1 (sqrt.f64 k)) (.f64 (sqrt.f64 (.f64 n (PI.f64))) (.f64 (sqrt.f64 2) (+.f64 (.f64 (log.f64 (.f64 (PI.f64) (+.f64 n n))) (*.f64 k -1/2)) 1)))) 0)
(+.f64 0 (.f64 (/.f64 1 (sqrt.f64 k)) (.f64 (sqrt.f64 (.f64 n (PI.f64))) (.f64 (sqrt.f64 2) (+.f64 (.f64 (log.f64 (.f64 (PI.f64) (+.f64 n n))) (*.f64 k -1/2)) 1)))))
(-.f64 (.f64 (/.f64 1 (sqrt.f64 k)) (.f64 (sqrt.f64 (.f64 n (PI.f64))) (.f64 (sqrt.f64 2) (+.f64 (.f64 (log.f64 (.f64 (PI.f64) (+.f64 n n))) (*.f64 k -1/2)) 1)))) 0)
(/.f64 (.f64 (/.f64 1 (sqrt.f64 k)) (.f64 (sqrt.f64 (.f64 n (PI.f64))) (.f64 (sqrt.f64 2) (+.f64 (.f64 (log.f64 (.f64 (PI.f64) (+.f64 n n))) (*.f64 k -1/2)) 1)))) 1)
(/.f64 (.f64 (/.f64 1 (sqrt.f64 k)) (.f64 (sqrt.f64 (.f64 n (PI.f64))) (.f64 (sqrt.f64 2) (+.f64 (.f64 (log.f64 (.f64 (PI.f64) (+.f64 n n))) (.f64 k -1/2)) 1)))) (/.f64 (.f64 (/.f64 1 (sqrt.f64 k)) (.f64 (sqrt.f64 (.f64 n (PI.f64))) (.f64 (sqrt.f64 2) (+.f64 (.f64 (log.f64 (.f64 (PI.f64) (+.f64 n n))) (.f64 k -1/2)) 1)))) (.f64 (/.f64 1 (sqrt.f64 k)) (.f64 (sqrt.f64 (.f64 n (PI.f64))) (.f64 (sqrt.f64 2) (+.f64 (.f64 (log.f64 (.f64 (PI.f64) (+.f64 n n))) (*.f64 k -1/2)) 1))))))
(/.f64 (.f64 (.f64 (sqrt.f64 2) (+.f64 (.f64 (log.f64 (.f64 (PI.f64) (+.f64 n n))) (.f64 k -1/2)) 1)) (.f64 (/.f64 1 (sqrt.f64 k)) (.f64 (sqrt.f64 (.f64 n (PI.f64))) 2))) 2)
(pow.f64 (.f64 (/.f64 1 (sqrt.f64 k)) (.f64 (sqrt.f64 (.f64 n (PI.f64))) (.f64 (sqrt.f64 2) (+.f64 (.f64 (log.f64 (.f64 (PI.f64) (+.f64 n n))) (*.f64 k -1/2)) 1)))) 1)
(+.f64 (*.f64 k (sqrt.f64 2)) 0)
(+.f64 0 (*.f64 k (sqrt.f64 2)))
(-.f64 (*.f64 k (sqrt.f64 2)) 0)
(/.f64 (*.f64 k (sqrt.f64 2)) 1)
(/.f64 (.f64 k (sqrt.f64 2)) (/.f64 (.f64 k (sqrt.f64 2)) (*.f64 k (sqrt.f64 2))))
(/.f64 (.f64 k (.f64 2 (sqrt.f64 2))) 2)
(pow.f64 (*.f64 k (sqrt.f64 2)) 1)
(+.f64 (.f64 (sqrt.f64 (.f64 n (PI.f64))) (.f64 (sqrt.f64 2) (+.f64 (.f64 (log.f64 (.f64 (PI.f64) (+.f64 n n))) (.f64 k -1/2)) 1))) 0)
(+.f64 0 (.f64 (sqrt.f64 (.f64 n (PI.f64))) (.f64 (sqrt.f64 2) (+.f64 (.f64 (log.f64 (.f64 (PI.f64) (+.f64 n n))) (.f64 k -1/2)) 1))))
(-.f64 (.f64 (sqrt.f64 (.f64 n (PI.f64))) (.f64 (sqrt.f64 2) (+.f64 (.f64 (log.f64 (.f64 (PI.f64) (+.f64 n n))) (.f64 k -1/2)) 1))) 0)
(/.f64 (.f64 (sqrt.f64 (.f64 n (PI.f64))) (.f64 (sqrt.f64 2) (+.f64 (.f64 (log.f64 (.f64 (PI.f64) (+.f64 n n))) (.f64 k -1/2)) 1))) 1)
(/.f64 (.f64 (sqrt.f64 (.f64 n (PI.f64))) (.f64 (sqrt.f64 2) (+.f64 (.f64 (log.f64 (.f64 (PI.f64) (+.f64 n n))) (.f64 k -1/2)) 1))) (/.f64 (.f64 (sqrt.f64 (.f64 n (PI.f64))) (.f64 (sqrt.f64 2) (+.f64 (.f64 (log.f64 (.f64 (PI.f64) (+.f64 n n))) (.f64 k -1/2)) 1))) (.f64 (sqrt.f64 (.f64 n (PI.f64))) (.f64 (sqrt.f64 2) (+.f64 (.f64 (log.f64 (.f64 (PI.f64) (+.f64 n n))) (.f64 k -1/2)) 1)))))
(/.f64 (.f64 (sqrt.f64 (.f64 n (PI.f64))) (.f64 2 (.f64 (sqrt.f64 2) (+.f64 (.f64 (log.f64 (.f64 (PI.f64) (+.f64 n n))) (*.f64 k -1/2)) 1)))) 2)
(pow.f64 (.f64 (sqrt.f64 (.f64 n (PI.f64))) (.f64 (sqrt.f64 2) (+.f64 (.f64 (log.f64 (.f64 (PI.f64) (+.f64 n n))) (.f64 k -1/2)) 1))) 1)
(+.f64 (.f64 (log.f64 (.f64 (PI.f64) (+.f64 n n))) (.f64 k (.f64 -1/2 (sqrt.f64 2)))) 0)
(+.f64 0 (.f64 (log.f64 (.f64 (PI.f64) (+.f64 n n))) (.f64 k (.f64 -1/2 (sqrt.f64 2)))))
(-.f64 (.f64 (log.f64 (.f64 (PI.f64) (+.f64 n n))) (.f64 k (.f64 -1/2 (sqrt.f64 2)))) 0)
(/.f64 (.f64 (log.f64 (.f64 (PI.f64) (+.f64 n n))) (.f64 k (.f64 -1/2 (sqrt.f64 2)))) 1)
(/.f64 (.f64 (log.f64 (.f64 (PI.f64) (+.f64 n n))) (.f64 k (.f64 -1/2 (sqrt.f64 2)))) (/.f64 (.f64 (log.f64 (.f64 (PI.f64) (+.f64 n n))) (.f64 k (sqrt.f64 2))) (.f64 (log.f64 (.f64 (PI.f64) (+.f64 n n))) (.f64 k (sqrt.f64 2)))))
(/.f64 (.f64 k (.f64 (log.f64 (*.f64 (PI.f64) (+.f64 n n))) (neg.f64 (sqrt.f64 2)))) 2)
(pow.f64 (.f64 (log.f64 (.f64 (PI.f64) (+.f64 n n))) (.f64 k (.f64 -1/2 (sqrt.f64 2)))) 1)
(log.f64 (pow.f64 (.f64 (PI.f64) (+.f64 n n)) (.f64 k (*.f64 -1/2 (sqrt.f64 2)))))

Outputs
(*.f64 (sqrt.f64 2) k)
(*.f64 (sqrt.f64 2) k)
(*.f64 (sqrt.f64 2) k)
(*.f64 (sqrt.f64 2) k)
(*.f64 (sqrt.f64 2) k)
(*.f64 (sqrt.f64 2) k)
(*.f64 (sqrt.f64 2) k)
(*.f64 (sqrt.f64 2) k)
(*.f64 (sqrt.f64 2) k)
(*.f64 (sqrt.f64 2) k)
(*.f64 (sqrt.f64 2) k)
(*.f64 (sqrt.f64 2) k)
(.f64 (sqrt.f64 2) (sqrt.f64 (.f64 n (PI.f64))))
(sqrt.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 (sqrt.f64 2) (sqrt.f64 (*.f64 n (PI.f64)))))
(+.f64 (sqrt.f64 (.f64 2 (.f64 n (PI.f64)))) (.f64 (.f64 (sqrt.f64 2) (.f64 k (log.f64 (.f64 2 (.f64 n (PI.f64)))))) (.f64 -1/2 (sqrt.f64 (*.f64 n (PI.f64))))))
(+.f64 (sqrt.f64 (.f64 2 (.f64 n (PI.f64)))) (.f64 -1/2 (.f64 (.f64 k (log.f64 (.f64 2 (.f64 n (PI.f64))))) (sqrt.f64 (.f64 2 (*.f64 n (PI.f64)))))))
(.f64 (sqrt.f64 (.f64 n (PI.f64))) (+.f64 (.f64 k (.f64 (sqrt.f64 2) (.f64 -1/2 (log.f64 (.f64 2 (*.f64 n (PI.f64))))))) (sqrt.f64 2)))
(.f64 (sqrt.f64 (.f64 n (PI.f64))) (+.f64 (sqrt.f64 2) (.f64 (sqrt.f64 2) (.f64 k (.f64 -1/2 (log.f64 (.f64 2 (*.f64 n (PI.f64)))))))))
(.f64 (sqrt.f64 (.f64 n (PI.f64))) (+.f64 (sqrt.f64 2) (.f64 k (.f64 (sqrt.f64 2) (.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 (sqrt.f64 2) (sqrt.f64 (*.f64 n (PI.f64)))))
(+.f64 (sqrt.f64 (.f64 2 (.f64 n (PI.f64)))) (.f64 (.f64 (sqrt.f64 2) (.f64 k (log.f64 (.f64 2 (.f64 n (PI.f64)))))) (.f64 -1/2 (sqrt.f64 (*.f64 n (PI.f64))))))
(+.f64 (sqrt.f64 (.f64 2 (.f64 n (PI.f64)))) (.f64 -1/2 (.f64 (.f64 k (log.f64 (.f64 2 (.f64 n (PI.f64))))) (sqrt.f64 (.f64 2 (*.f64 n (PI.f64)))))))
(.f64 (sqrt.f64 (.f64 n (PI.f64))) (+.f64 (.f64 k (.f64 (sqrt.f64 2) (.f64 -1/2 (log.f64 (.f64 2 (*.f64 n (PI.f64))))))) (sqrt.f64 2)))
(.f64 (sqrt.f64 (.f64 n (PI.f64))) (+.f64 (sqrt.f64 2) (.f64 (sqrt.f64 2) (.f64 k (.f64 -1/2 (log.f64 (.f64 2 (*.f64 n (PI.f64)))))))))
(.f64 (sqrt.f64 (.f64 n (PI.f64))) (+.f64 (sqrt.f64 2) (.f64 k (.f64 (sqrt.f64 2) (.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 (sqrt.f64 2) (sqrt.f64 (*.f64 n (PI.f64)))))
(+.f64 (sqrt.f64 (.f64 2 (.f64 n (PI.f64)))) (.f64 (.f64 (sqrt.f64 2) (.f64 k (log.f64 (.f64 2 (.f64 n (PI.f64)))))) (.f64 -1/2 (sqrt.f64 (*.f64 n (PI.f64))))))
(+.f64 (sqrt.f64 (.f64 2 (.f64 n (PI.f64)))) (.f64 -1/2 (.f64 (.f64 k (log.f64 (.f64 2 (.f64 n (PI.f64))))) (sqrt.f64 (.f64 2 (*.f64 n (PI.f64)))))))
(.f64 (sqrt.f64 (.f64 n (PI.f64))) (+.f64 (.f64 k (.f64 (sqrt.f64 2) (.f64 -1/2 (log.f64 (.f64 2 (*.f64 n (PI.f64))))))) (sqrt.f64 2)))
(.f64 (sqrt.f64 (.f64 n (PI.f64))) (+.f64 (sqrt.f64 2) (.f64 (sqrt.f64 2) (.f64 k (.f64 -1/2 (log.f64 (.f64 2 (*.f64 n (PI.f64)))))))))
(.f64 (sqrt.f64 (.f64 n (PI.f64))) (+.f64 (sqrt.f64 2) (.f64 k (.f64 (sqrt.f64 2) (.f64 -1/2 (log.f64 (.f64 2 (*.f64 n (PI.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) (.f64 k (log.f64 (.f64 2 (.f64 n (PI.f64)))))) (.f64 -1/2 (sqrt.f64 (*.f64 n (PI.f64)))))
(.f64 -1/2 (.f64 (.f64 k (log.f64 (.f64 2 (.f64 n (PI.f64))))) (sqrt.f64 (.f64 2 (*.f64 n (PI.f64))))))
(.f64 -1/2 (.f64 k (.f64 (log.f64 (.f64 2 (.f64 n (PI.f64)))) (sqrt.f64 (.f64 2 (*.f64 n (PI.f64)))))))
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eval211.0ms (1.5%)

Compiler: Compiled 16233 to 9634 computations (40.7% saved)

prune111.0ms (0.8%)

Pruning

18 alts after pruning (15 fresh and 3 done)

	Pruned	Kept	Total
New	501	13	514
Fresh	4	2	6
Picked	1	0	1
Done	2	3	5
Total	508	18	526

Error

0.1b

Counts

526 → 18

Alt Table

Click to see full alt table

Status	Error	Program
	22.3b	(/.f64 (.f64 (.f64 (sqrt.f64 2) (+.f64 (.f64 (log.f64 (.f64 (PI.f64) (+.f64 n n))) (.f64 k -1/2)) 1)) (.f64 (/.f64 1 (sqrt.f64 k)) (.f64 (sqrt.f64 (.f64 n (PI.f64))) 2))) 2)
	21.1b	(.f64 (/.f64 1 (sqrt.f64 k)) (pow.f64 (.f64 (/.f64 2 (.f64 n (PI.f64))) (.f64 (.f64 n (PI.f64)) (.f64 n (PI.f64)))) (/.f64 (-.f64 1 k) 2)))
▶	21.1b	(.f64 (/.f64 1 (sqrt.f64 k)) (pow.f64 (.f64 (/.f64 2 (.f64 n (PI.f64))) (.f64 n (*.f64 n (pow.f64 (PI.f64) 2)))) (/.f64 (-.f64 1 k) 2)))
✓	0.4b	(.f64 (/.f64 1 (sqrt.f64 k)) (pow.f64 (.f64 (*.f64 2 (PI.f64)) n) (/.f64 (-.f64 1 k) 2)))
	22.3b	(.f64 (/.f64 1 (sqrt.f64 k)) (+.f64 (.f64 (sqrt.f64 (.f64 n (PI.f64))) (+.f64 (.f64 (log.f64 (.f64 (PI.f64) (.f64 2 n))) (.f64 -1/2 (.f64 k (sqrt.f64 2)))) (sqrt.f64 2))) (.f64 1/8 (.f64 (sqrt.f64 (.f64 (PI.f64) (.f64 2 n))) (pow.f64 (.f64 k (log.f64 (.f64 (PI.f64) (*.f64 2 n)))) 2)))))
	22.2b	(.f64 (/.f64 1 (sqrt.f64 k)) (+.f64 (sqrt.f64 (.f64 n (.f64 2 (PI.f64)))) (.f64 -1/2 (.f64 (.f64 k (log.f64 (.f64 n (.f64 2 (PI.f64))))) (sqrt.f64 (.f64 n (.f64 2 (PI.f64))))))))
▶	24.6b	(.f64 (/.f64 1 (sqrt.f64 k)) (.f64 (pow.f64 (.f64 (PI.f64) (+.f64 n n)) (-.f64 1 k)) (exp.f64 (/.f64 (log.f64 (pow.f64 (.f64 (PI.f64) (+.f64 n n)) (-.f64 1 k))) -2))))
	43.8b	(.f64 (/.f64 1 (sqrt.f64 k)) (.f64 (/.f64 (exp.f64 (/.f64 (log.f64 (pow.f64 (.f64 (PI.f64) (+.f64 n n)) (-.f64 1 k))) -2)) (pow.f64 (.f64 (PI.f64) (+.f64 n n)) (-.f64 1 k))) (pow.f64 (.f64 (.f64 n (PI.f64)) (.f64 n (.f64 (PI.f64) 4))) (-.f64 1 k))))
	42.7b	(.f64 (/.f64 1 (sqrt.f64 k)) (.f64 (/.f64 1 (sqrt.f64 (.f64 (PI.f64) (+.f64 n n)))) (sqrt.f64 (.f64 (.f64 (PI.f64) n) (.f64 (*.f64 (PI.f64) n) 4)))))
	22.2b	(.f64 (/.f64 1 (sqrt.f64 k)) (.f64 (+.f64 1 (.f64 (log.f64 (.f64 (PI.f64) (+.f64 n n))) (.f64 k -1/2))) (sqrt.f64 (.f64 2 (*.f64 n (PI.f64))))))
	22.4b	(.f64 (/.f64 1 (sqrt.f64 k)) (.f64 (.f64 (sqrt.f64 (.f64 (PI.f64) (+.f64 n n))) (/.f64 1 (sqrt.f64 (.f64 (PI.f64) (+.f64 n n))))) (sqrt.f64 (.f64 (PI.f64) (+.f64 n n)))))
	22.3b	(.f64 (/.f64 1 (sqrt.f64 k)) (.f64 (sqrt.f64 (.f64 n (PI.f64))) (+.f64 (.f64 (sqrt.f64 2) (+.f64 (.f64 k (.f64 -1/2 (log.f64 (.f64 2 (.f64 n (PI.f64)))))) (.f64 1/8 (pow.f64 (.f64 k (log.f64 (.f64 2 (.f64 n (PI.f64))))) 2)))) (sqrt.f64 2))))
▶	22.4b	(.f64 (/.f64 1 (sqrt.f64 k)) (.f64 (sqrt.f64 2) (sqrt.f64 (*.f64 n (PI.f64)))))
✓	22.3b	(.f64 (/.f64 1 (sqrt.f64 k)) (sqrt.f64 (.f64 (PI.f64) (*.f64 2 n))))
✓	3.4b	(.f64 (/.f64 1 (sqrt.f64 k)) (exp.f64 (.f64 1/2 (.f64 (-.f64 1 k) (log.f64 (.f64 2 (*.f64 n (PI.f64))))))))
▶	0.6b	(.f64 (.f64 (/.f64 1 (/.f64 1 (sqrt.f64 k))) (/.f64 1 k)) (pow.f64 (.f64 (.f64 2 (PI.f64)) n) (/.f64 (-.f64 1 k) 2)))
	3.7b	(.f64 (sqrt.f64 (/.f64 1 k)) (exp.f64 (.f64 (-.f64 1 k) (.f64 1/2 (+.f64 (log.f64 (.f64 2 (PI.f64))) (log.f64 n))))))
▶	22.2b	(.f64 (sqrt.f64 (.f64 n (PI.f64))) (.f64 (/.f64 1 (sqrt.f64 k)) (.f64 (sqrt.f64 2) (+.f64 1 (.f64 (log.f64 (.f64 (PI.f64) (+.f64 n n))) (*.f64 k -1/2))))))

Compiler

Compiled 939 to 697 computations (25.8% saved)

localize37.0ms (0.3%)

Local error

Found 4 expressions with local error:

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

Compiler

Compiled 81 to 56 computations (30.9% saved)

series1.0ms (0%)

Counts

1 → 0

Calls

3 calls:

Time	Variable		Point	Expression
0.0ms	k	@	-inf	(*.f64 (/.f64 1 (/.f64 1 (sqrt.f64 k))) (/.f64 1 k))
0.0ms	k	@	0	(*.f64 (/.f64 1 (/.f64 1 (sqrt.f64 k))) (/.f64 1 k))
0.0ms	k	@	inf	(*.f64 (/.f64 1 (/.f64 1 (sqrt.f64 k))) (/.f64 1 k))

rewrite95.0ms (0.7%)

Algorithm

1×	batch-egg-rewrite

Rules

974×	`rational_best-simplify-57`
872×	`rational_best-simplify-80`
638×	`rational_best-simplify-78`
582×	`rational_best-simplify-43`
536×	`rational_best-simplify-44`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	10	29
1	80	29
2	255	29
3	1061	29
4	4823	29

Stop Event

1×	node limit

Counts

1 → 10

Calls

Call 1

Inputs
(*.f64 (/.f64 1 (/.f64 1 (sqrt.f64 k))) (/.f64 1 k))

Outputs

((#(struct:change #<rule egg-rr> (2) ((x +.f64 (*.f64 (/.f64 1 (/.f64 1 (sqrt.f64 k))) (/.f64 1 k)) 0)))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 0 (*.f64 (/.f64 1 (/.f64 1 (sqrt.f64 k))) (/.f64 1 k)))))) (#(struct:change #<rule egg-rr> (2) ((x -.f64 (*.f64 (/.f64 1 (/.f64 1 (sqrt.f64 k))) (/.f64 1 k)) 0)))) (#(struct:change #<rule egg-rr> (2) ((x -.f64 0 (neg.f64 (*.f64 (/.f64 1 (/.f64 1 (sqrt.f64 k))) (/.f64 1 k))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (*.f64 (/.f64 1 (/.f64 1 (sqrt.f64 k))) (/.f64 1 k)) 1)))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (*.f64 (/.f64 1 (/.f64 1 (sqrt.f64 k))) (/.f64 1 k)) (/.f64 (*.f64 (/.f64 1 (/.f64 1 (sqrt.f64 k))) (/.f64 1 k)) (*.f64 (/.f64 1 (/.f64 1 (sqrt.f64 k))) (/.f64 1 k))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (*.f64 (/.f64 1 (/.f64 1 (sqrt.f64 k))) (*.f64 (/.f64 1 k) 2)) 2)))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (*.f64 (neg.f64 (*.f64 (/.f64 1 (/.f64 1 (sqrt.f64 k))) (/.f64 1 k))) 2) -2)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (*.f64 (/.f64 1 (/.f64 1 (sqrt.f64 k))) (/.f64 1 k)) 1)))) (#(struct:change #<rule egg-rr> (2) ((x neg.f64 (neg.f64 (*.f64 (/.f64 1 (/.f64 1 (sqrt.f64 k))) (/.f64 1 k))))))))

simplify147.0ms (1%)

Algorithm

1×	egg-herbie

Rules

1574×	`rational_best-simplify-132`
1420×	`rational_best-simplify-80`
1286×	`rational_best-simplify-78`
1018×	`rational_best-simplify-82`
868×	`rational_best-simplify-47`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	28	290
1	46	290
2	92	290
3	229	290
4	1051	290
5	3047	290
6	5986	290

Stop Event

1×	node limit

Counts

10 → 11

Calls

Call 1

Inputs
(+.f64 (*.f64 (/.f64 1 (/.f64 1 (sqrt.f64 k))) (/.f64 1 k)) 0)
(+.f64 0 (*.f64 (/.f64 1 (/.f64 1 (sqrt.f64 k))) (/.f64 1 k)))
(-.f64 (*.f64 (/.f64 1 (/.f64 1 (sqrt.f64 k))) (/.f64 1 k)) 0)
(-.f64 0 (neg.f64 (*.f64 (/.f64 1 (/.f64 1 (sqrt.f64 k))) (/.f64 1 k))))
(/.f64 (*.f64 (/.f64 1 (/.f64 1 (sqrt.f64 k))) (/.f64 1 k)) 1)
(/.f64 (.f64 (/.f64 1 (/.f64 1 (sqrt.f64 k))) (/.f64 1 k)) (/.f64 (.f64 (/.f64 1 (/.f64 1 (sqrt.f64 k))) (/.f64 1 k)) (*.f64 (/.f64 1 (/.f64 1 (sqrt.f64 k))) (/.f64 1 k))))
(/.f64 (.f64 (/.f64 1 (/.f64 1 (sqrt.f64 k))) (.f64 (/.f64 1 k) 2)) 2)
(/.f64 (.f64 (neg.f64 (.f64 (/.f64 1 (/.f64 1 (sqrt.f64 k))) (/.f64 1 k))) 2) -2)
(pow.f64 (*.f64 (/.f64 1 (/.f64 1 (sqrt.f64 k))) (/.f64 1 k)) 1)
(neg.f64 (neg.f64 (*.f64 (/.f64 1 (/.f64 1 (sqrt.f64 k))) (/.f64 1 k))))

Outputs
(+.f64 (*.f64 (/.f64 1 (/.f64 1 (sqrt.f64 k))) (/.f64 1 k)) 0)
(*.f64 (/.f64 1 (/.f64 1 (sqrt.f64 k))) (/.f64 1 k))
(+.f64 0 (*.f64 (/.f64 1 (/.f64 1 (sqrt.f64 k))) (/.f64 1 k)))
(*.f64 (/.f64 1 (/.f64 1 (sqrt.f64 k))) (/.f64 1 k))
(-.f64 (*.f64 (/.f64 1 (/.f64 1 (sqrt.f64 k))) (/.f64 1 k)) 0)
(*.f64 (/.f64 1 (/.f64 1 (sqrt.f64 k))) (/.f64 1 k))
(-.f64 0 (neg.f64 (*.f64 (/.f64 1 (/.f64 1 (sqrt.f64 k))) (/.f64 1 k))))
(*.f64 (/.f64 1 (/.f64 1 (sqrt.f64 k))) (/.f64 1 k))
(/.f64 (*.f64 (/.f64 1 (/.f64 1 (sqrt.f64 k))) (/.f64 1 k)) 1)
(*.f64 (/.f64 1 (/.f64 1 (sqrt.f64 k))) (/.f64 1 k))
(/.f64 (.f64 (/.f64 1 (/.f64 1 (sqrt.f64 k))) (/.f64 1 k)) (/.f64 (.f64 (/.f64 1 (/.f64 1 (sqrt.f64 k))) (/.f64 1 k)) (*.f64 (/.f64 1 (/.f64 1 (sqrt.f64 k))) (/.f64 1 k))))
(*.f64 (/.f64 1 (/.f64 1 (sqrt.f64 k))) (/.f64 1 k))
(/.f64 (.f64 (/.f64 1 (/.f64 1 (sqrt.f64 k))) (.f64 (/.f64 1 k) 2)) 2)
(*.f64 (/.f64 1 (/.f64 1 (sqrt.f64 k))) (/.f64 1 k))
(/.f64 (.f64 (neg.f64 (.f64 (/.f64 1 (/.f64 1 (sqrt.f64 k))) (/.f64 1 k))) 2) -2)
(*.f64 (/.f64 1 (/.f64 1 (sqrt.f64 k))) (/.f64 1 k))
(pow.f64 (*.f64 (/.f64 1 (/.f64 1 (sqrt.f64 k))) (/.f64 1 k)) 1)
(*.f64 (/.f64 1 (/.f64 1 (sqrt.f64 k))) (/.f64 1 k))
(neg.f64 (neg.f64 (*.f64 (/.f64 1 (/.f64 1 (sqrt.f64 k))) (/.f64 1 k))))
(*.f64 (/.f64 1 (/.f64 1 (sqrt.f64 k))) (/.f64 1 k))

localize18.0ms (0.1%)

Local error

Found 4 expressions with local error:

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

Compiler

Compiled 41 to 21 computations (48.8% saved)

series3.0ms (0%)

Counts

2 → 0

Calls

9 calls:

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

rewrite116.0ms (0.8%)

Algorithm

1×	batch-egg-rewrite

Rules

810×	`rational_best-2`
810×	`rational_best-3`
810×	`rational_best-1`
808×	`rational_best-4`
808×	`exponential-1`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	16	54
1	133	54
2	425	54
3	1786	54
4	7062	54

Stop Event

1×	node limit

Counts

2 → 19

Calls

Call 1

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

Outputs

((#(struct:change #<rule egg-rr> (2) ((x +.f64 (sqrt.f64 (*.f64 (PI.f64) (+.f64 n n))) 0)))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 0 (sqrt.f64 (*.f64 (PI.f64) (+.f64 n n))))))) (#(struct:change #<rule egg-rr> (2) ((x -.f64 (sqrt.f64 (*.f64 (PI.f64) (+.f64 n n))) 0)))) (#(struct:change #<rule egg-rr> (2) ((x -.f64 0 (neg.f64 (sqrt.f64 (*.f64 (PI.f64) (+.f64 n n)))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (sqrt.f64 (*.f64 (PI.f64) (+.f64 n n))) 1)))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (sqrt.f64 (*.f64 (PI.f64) (+.f64 n n))) (/.f64 (sqrt.f64 (*.f64 (PI.f64) (+.f64 n n))) (sqrt.f64 (*.f64 (PI.f64) (+.f64 n n)))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (*.f64 2 (sqrt.f64 (*.f64 (PI.f64) (+.f64 n n)))) 2)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (sqrt.f64 (*.f64 (PI.f64) (+.f64 n n))) 1)))) (#(struct:change #<rule egg-rr> (2) ((x neg.f64 (neg.f64 (sqrt.f64 (*.f64 (PI.f64) (+.f64 n n)))))))) (#(struct:change #<rule egg-rr> (2) ((x sqrt.f64 (*.f64 (PI.f64) (+.f64 n n)))))))

((#(struct:change #<rule egg-rr> (2) ((x +.f64 (*.f64 (sqrt.f64 (*.f64 (PI.f64) (+.f64 n n))) (/.f64 1 (sqrt.f64 k))) 0)))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 0 (*.f64 (sqrt.f64 (*.f64 (PI.f64) (+.f64 n n))) (/.f64 1 (sqrt.f64 k))))))) (#(struct:change #<rule egg-rr> (2) ((x -.f64 (*.f64 (sqrt.f64 (*.f64 (PI.f64) (+.f64 n n))) (/.f64 1 (sqrt.f64 k))) 0)))) (#(struct:change #<rule egg-rr> (2) ((x -.f64 0 (neg.f64 (*.f64 (sqrt.f64 (*.f64 (PI.f64) (+.f64 n n))) (/.f64 1 (sqrt.f64 k)))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (*.f64 (sqrt.f64 (*.f64 (PI.f64) (+.f64 n n))) (/.f64 1 (sqrt.f64 k))) 1)))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (*.f64 (sqrt.f64 (*.f64 (PI.f64) (+.f64 n n))) (/.f64 1 (sqrt.f64 k))) (/.f64 (*.f64 (sqrt.f64 (*.f64 (PI.f64) (+.f64 n n))) (/.f64 1 (sqrt.f64 k))) (*.f64 (sqrt.f64 (*.f64 (PI.f64) (+.f64 n n))) (/.f64 1 (sqrt.f64 k)))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (*.f64 2 (*.f64 (sqrt.f64 (*.f64 (PI.f64) (+.f64 n n))) (/.f64 1 (sqrt.f64 k)))) 2)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (*.f64 (sqrt.f64 (*.f64 (PI.f64) (+.f64 n n))) (/.f64 1 (sqrt.f64 k))) 1)))) (#(struct:change #<rule egg-rr> (2) ((x neg.f64 (neg.f64 (*.f64 (sqrt.f64 (*.f64 (PI.f64) (+.f64 n n))) (/.f64 1 (sqrt.f64 k)))))))))

simplify159.0ms (1.1%)

Algorithm

1×	egg-herbie

Rules

1262×	`rational_best-simplify-2`
1196×	`rational_best-simplify-47`
1058×	`rational_best-simplify-80`
928×	`rational_best-simplify-78`
644×	`rational_best-simplify-82`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	40	505
1	71	505
2	146	505
3	402	505
4	1837	505
5	4964	505

Stop Event

1×	node limit

Counts

19 → 20

Calls

Call 1

Inputs
(+.f64 (sqrt.f64 (*.f64 (PI.f64) (+.f64 n n))) 0)
(+.f64 0 (sqrt.f64 (*.f64 (PI.f64) (+.f64 n n))))
(-.f64 (sqrt.f64 (*.f64 (PI.f64) (+.f64 n n))) 0)
(-.f64 0 (neg.f64 (sqrt.f64 (*.f64 (PI.f64) (+.f64 n n)))))
(/.f64 (sqrt.f64 (*.f64 (PI.f64) (+.f64 n n))) 1)
(/.f64 (sqrt.f64 (.f64 (PI.f64) (+.f64 n n))) (/.f64 (sqrt.f64 (.f64 (PI.f64) (+.f64 n n))) (sqrt.f64 (*.f64 (PI.f64) (+.f64 n n)))))
(/.f64 (.f64 2 (sqrt.f64 (.f64 (PI.f64) (+.f64 n n)))) 2)
(pow.f64 (sqrt.f64 (*.f64 (PI.f64) (+.f64 n n))) 1)
(neg.f64 (neg.f64 (sqrt.f64 (*.f64 (PI.f64) (+.f64 n n)))))
(sqrt.f64 (*.f64 (PI.f64) (+.f64 n n)))
(+.f64 (.f64 (sqrt.f64 (.f64 (PI.f64) (+.f64 n n))) (/.f64 1 (sqrt.f64 k))) 0)
(+.f64 0 (.f64 (sqrt.f64 (.f64 (PI.f64) (+.f64 n n))) (/.f64 1 (sqrt.f64 k))))
(-.f64 (.f64 (sqrt.f64 (.f64 (PI.f64) (+.f64 n n))) (/.f64 1 (sqrt.f64 k))) 0)
(-.f64 0 (neg.f64 (.f64 (sqrt.f64 (.f64 (PI.f64) (+.f64 n n))) (/.f64 1 (sqrt.f64 k)))))
(/.f64 (.f64 (sqrt.f64 (.f64 (PI.f64) (+.f64 n n))) (/.f64 1 (sqrt.f64 k))) 1)
(/.f64 (.f64 (sqrt.f64 (.f64 (PI.f64) (+.f64 n n))) (/.f64 1 (sqrt.f64 k))) (/.f64 (.f64 (sqrt.f64 (.f64 (PI.f64) (+.f64 n n))) (/.f64 1 (sqrt.f64 k))) (.f64 (sqrt.f64 (.f64 (PI.f64) (+.f64 n n))) (/.f64 1 (sqrt.f64 k)))))
(/.f64 (.f64 2 (.f64 (sqrt.f64 (*.f64 (PI.f64) (+.f64 n n))) (/.f64 1 (sqrt.f64 k)))) 2)
(pow.f64 (.f64 (sqrt.f64 (.f64 (PI.f64) (+.f64 n n))) (/.f64 1 (sqrt.f64 k))) 1)
(neg.f64 (neg.f64 (.f64 (sqrt.f64 (.f64 (PI.f64) (+.f64 n n))) (/.f64 1 (sqrt.f64 k)))))

Outputs
(+.f64 (sqrt.f64 (*.f64 (PI.f64) (+.f64 n n))) 0)
(sqrt.f64 (*.f64 (PI.f64) (+.f64 n n)))
(+.f64 0 (sqrt.f64 (*.f64 (PI.f64) (+.f64 n n))))
(sqrt.f64 (*.f64 (PI.f64) (+.f64 n n)))
(-.f64 (sqrt.f64 (*.f64 (PI.f64) (+.f64 n n))) 0)
(sqrt.f64 (*.f64 (PI.f64) (+.f64 n n)))
(-.f64 0 (neg.f64 (sqrt.f64 (*.f64 (PI.f64) (+.f64 n n)))))
(sqrt.f64 (*.f64 (PI.f64) (+.f64 n n)))
(/.f64 (sqrt.f64 (*.f64 (PI.f64) (+.f64 n n))) 1)
(sqrt.f64 (*.f64 (PI.f64) (+.f64 n n)))
(/.f64 (sqrt.f64 (.f64 (PI.f64) (+.f64 n n))) (/.f64 (sqrt.f64 (.f64 (PI.f64) (+.f64 n n))) (sqrt.f64 (*.f64 (PI.f64) (+.f64 n n)))))
(sqrt.f64 (*.f64 (PI.f64) (+.f64 n n)))
(/.f64 (.f64 2 (sqrt.f64 (.f64 (PI.f64) (+.f64 n n)))) 2)
(sqrt.f64 (*.f64 (PI.f64) (+.f64 n n)))
(pow.f64 (sqrt.f64 (*.f64 (PI.f64) (+.f64 n n))) 1)
(sqrt.f64 (*.f64 (PI.f64) (+.f64 n n)))
(neg.f64 (neg.f64 (sqrt.f64 (*.f64 (PI.f64) (+.f64 n n)))))
(sqrt.f64 (*.f64 (PI.f64) (+.f64 n n)))
(sqrt.f64 (*.f64 (PI.f64) (+.f64 n n)))
(+.f64 (.f64 (sqrt.f64 (.f64 (PI.f64) (+.f64 n n))) (/.f64 1 (sqrt.f64 k))) 0)
(.f64 (sqrt.f64 (.f64 (PI.f64) (+.f64 n n))) (/.f64 1 (sqrt.f64 k)))
(+.f64 0 (.f64 (sqrt.f64 (.f64 (PI.f64) (+.f64 n n))) (/.f64 1 (sqrt.f64 k))))
(.f64 (sqrt.f64 (.f64 (PI.f64) (+.f64 n n))) (/.f64 1 (sqrt.f64 k)))
(-.f64 (.f64 (sqrt.f64 (.f64 (PI.f64) (+.f64 n n))) (/.f64 1 (sqrt.f64 k))) 0)
(.f64 (sqrt.f64 (.f64 (PI.f64) (+.f64 n n))) (/.f64 1 (sqrt.f64 k)))
(-.f64 0 (neg.f64 (.f64 (sqrt.f64 (.f64 (PI.f64) (+.f64 n n))) (/.f64 1 (sqrt.f64 k)))))
(.f64 (sqrt.f64 (.f64 (PI.f64) (+.f64 n n))) (/.f64 1 (sqrt.f64 k)))
(/.f64 (.f64 (sqrt.f64 (.f64 (PI.f64) (+.f64 n n))) (/.f64 1 (sqrt.f64 k))) 1)
(.f64 (sqrt.f64 (.f64 (PI.f64) (+.f64 n n))) (/.f64 1 (sqrt.f64 k)))
(/.f64 (.f64 (sqrt.f64 (.f64 (PI.f64) (+.f64 n n))) (/.f64 1 (sqrt.f64 k))) (/.f64 (.f64 (sqrt.f64 (.f64 (PI.f64) (+.f64 n n))) (/.f64 1 (sqrt.f64 k))) (.f64 (sqrt.f64 (.f64 (PI.f64) (+.f64 n n))) (/.f64 1 (sqrt.f64 k)))))
(.f64 (sqrt.f64 (.f64 (PI.f64) (+.f64 n n))) (/.f64 1 (sqrt.f64 k)))
(/.f64 (.f64 2 (.f64 (sqrt.f64 (*.f64 (PI.f64) (+.f64 n n))) (/.f64 1 (sqrt.f64 k)))) 2)
(.f64 (sqrt.f64 (.f64 (PI.f64) (+.f64 n n))) (/.f64 1 (sqrt.f64 k)))
(pow.f64 (.f64 (sqrt.f64 (.f64 (PI.f64) (+.f64 n n))) (/.f64 1 (sqrt.f64 k))) 1)
(.f64 (sqrt.f64 (.f64 (PI.f64) (+.f64 n n))) (/.f64 1 (sqrt.f64 k)))
(neg.f64 (neg.f64 (.f64 (sqrt.f64 (.f64 (PI.f64) (+.f64 n n))) (/.f64 1 (sqrt.f64 k)))))
(.f64 (sqrt.f64 (.f64 (PI.f64) (+.f64 n n))) (/.f64 1 (sqrt.f64 k)))

localize66.0ms (0.5%)

Local error

Found 4 expressions with local error:

New	Error	Program
	0.2b	(/.f64 2 (*.f64 n (PI.f64)))
	0.3b	(*.f64 n (PI.f64))
✓	0.4b	(*.f64 n (pow.f64 (PI.f64) 2))
✓	30.1b	(.f64 (/.f64 2 (.f64 n (PI.f64))) (.f64 n (.f64 n (pow.f64 (PI.f64) 2))))

Compiler

Compiled 100 to 60 computations (40% saved)

series0.0ms (0%)

Counts

2 → 12

Calls

6 calls:

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

rewrite104.0ms (0.7%)

Algorithm

1×	batch-egg-rewrite

Rules

1194×	`rational_best-simplify-57`
684×	`rational_best-simplify-47`
680×	`rational_best-5`
678×	`rational_best-4`
678×	`rational_best-2`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	12	56
1	103	56
2	341	56
3	1442	56
4	5932	56

Stop Event

1×	node limit

Counts

2 → 18

Calls

Call 1

Inputs
(.f64 (/.f64 2 (.f64 n (PI.f64))) (.f64 n (.f64 n (pow.f64 (PI.f64) 2))))
(*.f64 n (pow.f64 (PI.f64) 2))

Outputs

((#(struct:change #<rule egg-rr> (2) ((x +.f64 (*.f64 (/.f64 2 (*.f64 n (PI.f64))) (*.f64 (pow.f64 (PI.f64) 2) (*.f64 n n))) 0)))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 0 (*.f64 (/.f64 2 (*.f64 n (PI.f64))) (*.f64 (pow.f64 (PI.f64) 2) (*.f64 n n))))))) (#(struct:change #<rule egg-rr> (2) ((x -.f64 (*.f64 (/.f64 2 (*.f64 n (PI.f64))) (*.f64 (pow.f64 (PI.f64) 2) (*.f64 n n))) 0)))) (#(struct:change #<rule egg-rr> (2) ((x -.f64 0 (neg.f64 (*.f64 (/.f64 2 (*.f64 n (PI.f64))) (*.f64 (pow.f64 (PI.f64) 2) (*.f64 n n)))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (*.f64 (/.f64 2 (*.f64 n (PI.f64))) (*.f64 (pow.f64 (PI.f64) 2) (*.f64 n n))) 1)))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (*.f64 (/.f64 2 (*.f64 n (PI.f64))) (*.f64 (pow.f64 (PI.f64) 2) (*.f64 n n))) (/.f64 (*.f64 (/.f64 2 (*.f64 n (PI.f64))) (*.f64 (pow.f64 (PI.f64) 2) (*.f64 n n))) (*.f64 (/.f64 2 (*.f64 n (PI.f64))) (*.f64 (pow.f64 (PI.f64) 2) (*.f64 n n)))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (*.f64 2 (*.f64 (/.f64 2 (*.f64 n (PI.f64))) (*.f64 (pow.f64 (PI.f64) 2) (*.f64 n n)))) 2)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (*.f64 (/.f64 2 (*.f64 n (PI.f64))) (*.f64 (pow.f64 (PI.f64) 2) (*.f64 n n))) 1)))) (#(struct:change #<rule egg-rr> (2) ((x neg.f64 (neg.f64 (*.f64 (/.f64 2 (*.f64 n (PI.f64))) (*.f64 (pow.f64 (PI.f64) 2) (*.f64 n n)))))))))

((#(struct:change #<rule egg-rr> (2) ((x +.f64 (*.f64 n (pow.f64 (PI.f64) 2)) 0)))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 0 (*.f64 n (pow.f64 (PI.f64) 2)))))) (#(struct:change #<rule egg-rr> (2) ((x -.f64 (*.f64 n (pow.f64 (PI.f64) 2)) 0)))) (#(struct:change #<rule egg-rr> (2) ((x -.f64 0 (neg.f64 (*.f64 n (pow.f64 (PI.f64) 2))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (*.f64 n (pow.f64 (PI.f64) 2)) 1)))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (*.f64 n (pow.f64 (PI.f64) 2)) (/.f64 (*.f64 n (pow.f64 (PI.f64) 2)) (*.f64 n (pow.f64 (PI.f64) 2))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (*.f64 2 (*.f64 n (pow.f64 (PI.f64) 2))) 2)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (*.f64 n (pow.f64 (PI.f64) 2)) 1)))) (#(struct:change #<rule egg-rr> (2) ((x neg.f64 (neg.f64 (*.f64 n (pow.f64 (PI.f64) 2))))))))

simplify151.0ms (1%)

Algorithm

1×	egg-herbie

Rules

1126×	`rational_best-simplify-132`
1124×	`rational_best-simplify-82`
1076×	`rational_best-simplify-44`
938×	`rational_best-simplify-80`
866×	`rational_best-simplify-78`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	41	684
1	81	684
2	189	684
3	547	684
4	3101	684
5	6167	684

Stop Event

1×	node limit

Counts

30 → 25

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 (.f64 (/.f64 2 (.f64 n (PI.f64))) (.f64 (pow.f64 (PI.f64) 2) (.f64 n n))) 0)
(+.f64 0 (.f64 (/.f64 2 (.f64 n (PI.f64))) (.f64 (pow.f64 (PI.f64) 2) (.f64 n n))))
(-.f64 (.f64 (/.f64 2 (.f64 n (PI.f64))) (.f64 (pow.f64 (PI.f64) 2) (.f64 n n))) 0)
(-.f64 0 (neg.f64 (.f64 (/.f64 2 (.f64 n (PI.f64))) (.f64 (pow.f64 (PI.f64) 2) (.f64 n n)))))
(/.f64 (.f64 (/.f64 2 (.f64 n (PI.f64))) (.f64 (pow.f64 (PI.f64) 2) (.f64 n n))) 1)
(/.f64 (.f64 (/.f64 2 (.f64 n (PI.f64))) (.f64 (pow.f64 (PI.f64) 2) (.f64 n n))) (/.f64 (.f64 (/.f64 2 (.f64 n (PI.f64))) (.f64 (pow.f64 (PI.f64) 2) (.f64 n n))) (.f64 (/.f64 2 (.f64 n (PI.f64))) (.f64 (pow.f64 (PI.f64) 2) (.f64 n n)))))
(/.f64 (.f64 2 (.f64 (/.f64 2 (.f64 n (PI.f64))) (.f64 (pow.f64 (PI.f64) 2) (*.f64 n n)))) 2)
(pow.f64 (.f64 (/.f64 2 (.f64 n (PI.f64))) (.f64 (pow.f64 (PI.f64) 2) (.f64 n n))) 1)
(neg.f64 (neg.f64 (.f64 (/.f64 2 (.f64 n (PI.f64))) (.f64 (pow.f64 (PI.f64) 2) (.f64 n n)))))
(+.f64 (*.f64 n (pow.f64 (PI.f64) 2)) 0)
(+.f64 0 (*.f64 n (pow.f64 (PI.f64) 2)))
(-.f64 (*.f64 n (pow.f64 (PI.f64) 2)) 0)
(-.f64 0 (neg.f64 (*.f64 n (pow.f64 (PI.f64) 2))))
(/.f64 (*.f64 n (pow.f64 (PI.f64) 2)) 1)
(/.f64 (.f64 n (pow.f64 (PI.f64) 2)) (/.f64 (.f64 n (pow.f64 (PI.f64) 2)) (*.f64 n (pow.f64 (PI.f64) 2))))
(/.f64 (.f64 2 (.f64 n (pow.f64 (PI.f64) 2))) 2)
(pow.f64 (*.f64 n (pow.f64 (PI.f64) 2)) 1)
(neg.f64 (neg.f64 (*.f64 n (pow.f64 (PI.f64) 2))))

Outputs
(.f64 2 (.f64 n (PI.f64)))
(.f64 (PI.f64) (.f64 2 n))
(.f64 n (.f64 2 (PI.f64)))
(.f64 2 (.f64 n (PI.f64)))
(.f64 (PI.f64) (.f64 2 n))
(.f64 n (.f64 2 (PI.f64)))
(.f64 2 (.f64 n (PI.f64)))
(.f64 (PI.f64) (.f64 2 n))
(.f64 n (.f64 2 (PI.f64)))
(.f64 2 (.f64 n (PI.f64)))
(.f64 (PI.f64) (.f64 2 n))
(.f64 n (.f64 2 (PI.f64)))
(.f64 2 (.f64 n (PI.f64)))
(.f64 (PI.f64) (.f64 2 n))
(.f64 n (.f64 2 (PI.f64)))
(.f64 2 (.f64 n (PI.f64)))
(.f64 (PI.f64) (.f64 2 n))
(.f64 n (.f64 2 (PI.f64)))
(.f64 2 (.f64 n (PI.f64)))
(.f64 (PI.f64) (.f64 2 n))
(.f64 n (.f64 2 (PI.f64)))
(.f64 2 (.f64 n (PI.f64)))
(.f64 (PI.f64) (.f64 2 n))
(.f64 n (.f64 2 (PI.f64)))
(.f64 2 (.f64 n (PI.f64)))
(.f64 (PI.f64) (.f64 2 n))
(.f64 n (.f64 2 (PI.f64)))
(.f64 2 (.f64 n (PI.f64)))
(.f64 (PI.f64) (.f64 2 n))
(.f64 n (.f64 2 (PI.f64)))
(.f64 2 (.f64 n (PI.f64)))
(.f64 (PI.f64) (.f64 2 n))
(.f64 n (.f64 2 (PI.f64)))
(.f64 2 (.f64 n (PI.f64)))
(.f64 (PI.f64) (.f64 2 n))
(.f64 n (.f64 2 (PI.f64)))
(+.f64 (.f64 (/.f64 2 (.f64 n (PI.f64))) (.f64 (pow.f64 (PI.f64) 2) (.f64 n n))) 0)
(.f64 (/.f64 2 (.f64 n (PI.f64))) (.f64 n (.f64 n (pow.f64 (PI.f64) 2))))
(.f64 n (.f64 (/.f64 2 (.f64 n (PI.f64))) (.f64 n (pow.f64 (PI.f64) 2))))
(.f64 (/.f64 2 (.f64 n (PI.f64))) (.f64 (pow.f64 (PI.f64) 2) (.f64 n n)))
(+.f64 0 (.f64 (/.f64 2 (.f64 n (PI.f64))) (.f64 (pow.f64 (PI.f64) 2) (.f64 n n))))
(.f64 (/.f64 2 (.f64 n (PI.f64))) (.f64 n (.f64 n (pow.f64 (PI.f64) 2))))
(.f64 n (.f64 (/.f64 2 (.f64 n (PI.f64))) (.f64 n (pow.f64 (PI.f64) 2))))
(.f64 (/.f64 2 (.f64 n (PI.f64))) (.f64 (pow.f64 (PI.f64) 2) (.f64 n n)))
(-.f64 (.f64 (/.f64 2 (.f64 n (PI.f64))) (.f64 (pow.f64 (PI.f64) 2) (.f64 n n))) 0)
(.f64 (/.f64 2 (.f64 n (PI.f64))) (.f64 n (.f64 n (pow.f64 (PI.f64) 2))))
(.f64 n (.f64 (/.f64 2 (.f64 n (PI.f64))) (.f64 n (pow.f64 (PI.f64) 2))))
(.f64 (/.f64 2 (.f64 n (PI.f64))) (.f64 (pow.f64 (PI.f64) 2) (.f64 n n)))
(-.f64 0 (neg.f64 (.f64 (/.f64 2 (.f64 n (PI.f64))) (.f64 (pow.f64 (PI.f64) 2) (.f64 n n)))))
(.f64 (/.f64 2 (.f64 n (PI.f64))) (.f64 n (.f64 n (pow.f64 (PI.f64) 2))))
(.f64 n (.f64 (/.f64 2 (.f64 n (PI.f64))) (.f64 n (pow.f64 (PI.f64) 2))))
(.f64 (/.f64 2 (.f64 n (PI.f64))) (.f64 (pow.f64 (PI.f64) 2) (.f64 n n)))
(/.f64 (.f64 (/.f64 2 (.f64 n (PI.f64))) (.f64 (pow.f64 (PI.f64) 2) (.f64 n n))) 1)
(.f64 (/.f64 2 (.f64 n (PI.f64))) (.f64 n (.f64 n (pow.f64 (PI.f64) 2))))
(.f64 n (.f64 (/.f64 2 (.f64 n (PI.f64))) (.f64 n (pow.f64 (PI.f64) 2))))
(.f64 (/.f64 2 (.f64 n (PI.f64))) (.f64 (pow.f64 (PI.f64) 2) (.f64 n n)))
(/.f64 (.f64 (/.f64 2 (.f64 n (PI.f64))) (.f64 (pow.f64 (PI.f64) 2) (.f64 n n))) (/.f64 (.f64 (/.f64 2 (.f64 n (PI.f64))) (.f64 (pow.f64 (PI.f64) 2) (.f64 n n))) (.f64 (/.f64 2 (.f64 n (PI.f64))) (.f64 (pow.f64 (PI.f64) 2) (.f64 n n)))))
(.f64 (/.f64 2 (.f64 n (PI.f64))) (.f64 n (.f64 n (pow.f64 (PI.f64) 2))))
(.f64 n (.f64 (/.f64 2 (.f64 n (PI.f64))) (.f64 n (pow.f64 (PI.f64) 2))))
(.f64 (/.f64 2 (.f64 n (PI.f64))) (.f64 (pow.f64 (PI.f64) 2) (.f64 n n)))
(/.f64 (.f64 2 (.f64 (/.f64 2 (.f64 n (PI.f64))) (.f64 (pow.f64 (PI.f64) 2) (*.f64 n n)))) 2)
(.f64 (/.f64 2 (.f64 n (PI.f64))) (.f64 n (.f64 n (pow.f64 (PI.f64) 2))))
(.f64 n (.f64 (/.f64 2 (.f64 n (PI.f64))) (.f64 n (pow.f64 (PI.f64) 2))))
(.f64 (/.f64 2 (.f64 n (PI.f64))) (.f64 (pow.f64 (PI.f64) 2) (.f64 n n)))
(pow.f64 (.f64 (/.f64 2 (.f64 n (PI.f64))) (.f64 (pow.f64 (PI.f64) 2) (.f64 n n))) 1)
(.f64 (/.f64 2 (.f64 n (PI.f64))) (.f64 n (.f64 n (pow.f64 (PI.f64) 2))))
(.f64 n (.f64 (/.f64 2 (.f64 n (PI.f64))) (.f64 n (pow.f64 (PI.f64) 2))))
(.f64 (/.f64 2 (.f64 n (PI.f64))) (.f64 (pow.f64 (PI.f64) 2) (.f64 n n)))
(neg.f64 (neg.f64 (.f64 (/.f64 2 (.f64 n (PI.f64))) (.f64 (pow.f64 (PI.f64) 2) (.f64 n n)))))
(.f64 (/.f64 2 (.f64 n (PI.f64))) (.f64 n (.f64 n (pow.f64 (PI.f64) 2))))
(.f64 n (.f64 (/.f64 2 (.f64 n (PI.f64))) (.f64 n (pow.f64 (PI.f64) 2))))
(.f64 (/.f64 2 (.f64 n (PI.f64))) (.f64 (pow.f64 (PI.f64) 2) (.f64 n n)))
(+.f64 (*.f64 n (pow.f64 (PI.f64) 2)) 0)
(*.f64 n (pow.f64 (PI.f64) 2))
(+.f64 0 (*.f64 n (pow.f64 (PI.f64) 2)))
(*.f64 n (pow.f64 (PI.f64) 2))
(-.f64 (*.f64 n (pow.f64 (PI.f64) 2)) 0)
(*.f64 n (pow.f64 (PI.f64) 2))
(-.f64 0 (neg.f64 (*.f64 n (pow.f64 (PI.f64) 2))))
(*.f64 n (pow.f64 (PI.f64) 2))
(/.f64 (*.f64 n (pow.f64 (PI.f64) 2)) 1)
(*.f64 n (pow.f64 (PI.f64) 2))
(/.f64 (.f64 n (pow.f64 (PI.f64) 2)) (/.f64 (.f64 n (pow.f64 (PI.f64) 2)) (*.f64 n (pow.f64 (PI.f64) 2))))
(*.f64 n (pow.f64 (PI.f64) 2))
(/.f64 (.f64 2 (.f64 n (pow.f64 (PI.f64) 2))) 2)
(*.f64 n (pow.f64 (PI.f64) 2))
(pow.f64 (*.f64 n (pow.f64 (PI.f64) 2)) 1)
(*.f64 n (pow.f64 (PI.f64) 2))
(neg.f64 (neg.f64 (*.f64 n (pow.f64 (PI.f64) 2))))
(*.f64 n (pow.f64 (PI.f64) 2))

localize38.0ms (0.3%)

Local error

Found 4 expressions with local error:

New	Error	Program
	0.3b	(*.f64 n (PI.f64))
✓	0.3b	(.f64 (log.f64 (.f64 (PI.f64) (+.f64 n n))) (*.f64 k -1/2))
✓	0.4b	(.f64 (sqrt.f64 (.f64 n (PI.f64))) (.f64 (/.f64 1 (sqrt.f64 k)) (.f64 (sqrt.f64 2) (+.f64 1 (.f64 (log.f64 (.f64 (PI.f64) (+.f64 n n))) (*.f64 k -1/2))))))
✓	0.6b	(.f64 (/.f64 1 (sqrt.f64 k)) (.f64 (sqrt.f64 2) (+.f64 1 (.f64 (log.f64 (.f64 (PI.f64) (+.f64 n n))) (*.f64 k -1/2)))))

Compiler

Compiled 122 to 57 computations (53.3% saved)

series14.0ms (0.1%)

Counts

3 → 36

Calls

18 calls:

Time	Variable		Point	Expression
4.0ms	n	@	-inf	(.f64 (sqrt.f64 (.f64 n (PI.f64))) (.f64 (/.f64 1 (sqrt.f64 k)) (.f64 (sqrt.f64 2) (+.f64 1 (.f64 (log.f64 (.f64 (PI.f64) (+.f64 n n))) (*.f64 k -1/2))))))
1.0ms	n	@	inf	(.f64 (sqrt.f64 (.f64 n (PI.f64))) (.f64 (/.f64 1 (sqrt.f64 k)) (.f64 (sqrt.f64 2) (+.f64 1 (.f64 (log.f64 (.f64 (PI.f64) (+.f64 n n))) (*.f64 k -1/2))))))
1.0ms	n	@	0	(.f64 (sqrt.f64 (.f64 n (PI.f64))) (.f64 (/.f64 1 (sqrt.f64 k)) (.f64 (sqrt.f64 2) (+.f64 1 (.f64 (log.f64 (.f64 (PI.f64) (+.f64 n n))) (*.f64 k -1/2))))))
1.0ms	k	@	-inf	(.f64 (/.f64 1 (sqrt.f64 k)) (.f64 (sqrt.f64 2) (+.f64 1 (.f64 (log.f64 (.f64 (PI.f64) (+.f64 n n))) (*.f64 k -1/2)))))
1.0ms	n	@	inf	(.f64 (/.f64 1 (sqrt.f64 k)) (.f64 (sqrt.f64 2) (+.f64 1 (.f64 (log.f64 (.f64 (PI.f64) (+.f64 n n))) (*.f64 k -1/2)))))

rewrite69.0ms (0.5%)

Algorithm

1×	batch-egg-rewrite

Rules

1314×	`rational_best-simplify-47`
1290×	`rational_best-4`
1290×	`rational_best-2`
1290×	`rational_best-3`
1290×	`rational_best-1`

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	24	175
1	203	175
2	658	171
3	2841	171

Stop Event

1×	node limit

Counts

3 → 22

Calls

Call 1

Inputs

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

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

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

Outputs

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

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

((#(struct:change #<rule egg-rr> (2) ((x +.f64 (*.f64 k (*.f64 (log.f64 (*.f64 2 (*.f64 (PI.f64) n))) -1/2)) 0)))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 0 (*.f64 k (*.f64 (log.f64 (*.f64 2 (*.f64 (PI.f64) n))) -1/2)))))) (#(struct:change #<rule egg-rr> (2) ((x -.f64 (*.f64 k (*.f64 (log.f64 (*.f64 2 (*.f64 (PI.f64) n))) -1/2)) 0)))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (*.f64 k (*.f64 (log.f64 (*.f64 2 (*.f64 (PI.f64) n))) -1/2)) 1)))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (*.f64 k (*.f64 (log.f64 (*.f64 2 (*.f64 (PI.f64) n))) -1/2)) (/.f64 (*.f64 k (neg.f64 (log.f64 (*.f64 2 (*.f64 (PI.f64) n))))) (*.f64 k (neg.f64 (log.f64 (*.f64 2 (*.f64 (PI.f64) n)))))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (*.f64 k (neg.f64 (log.f64 (*.f64 2 (*.f64 (PI.f64) n))))) 2)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (*.f64 k (*.f64 (log.f64 (*.f64 2 (*.f64 (PI.f64) n))) -1/2)) 1)))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (pow.f64 (*.f64 2 (*.f64 (PI.f64) n)) (*.f64 k -1/2)))))))

simplify153.0ms (1.1%)

Algorithm

1×	egg-herbie

Rules

1746×	`rational_best-simplify-47`
1738×	`rational_best-simplify-80`
1538×	`rational_best-simplify-78`
892×	`rational_best-simplify-132`
688×	`rational_best-simplify-76`

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	101	3084
1	190	3052
2	342	3004
3	738	3004
4	2887	3004
5	6493	3004

Stop Event

1×	node limit

Counts

58 → 65

Calls

Call 1

Inputs
(.f64 (sqrt.f64 (/.f64 1 k)) (.f64 (sqrt.f64 2) (+.f64 1 (.f64 -1/2 (.f64 k (+.f64 (log.f64 (*.f64 2 (PI.f64))) (log.f64 n)))))))
(.f64 (sqrt.f64 (/.f64 1 k)) (.f64 (sqrt.f64 2) (+.f64 1 (.f64 -1/2 (.f64 k (+.f64 (log.f64 (*.f64 2 (PI.f64))) (log.f64 n)))))))
(.f64 (sqrt.f64 (/.f64 1 k)) (.f64 (sqrt.f64 2) (+.f64 1 (.f64 -1/2 (.f64 k (+.f64 (log.f64 (*.f64 2 (PI.f64))) (log.f64 n)))))))
(.f64 (sqrt.f64 (/.f64 1 k)) (.f64 (sqrt.f64 2) (+.f64 1 (.f64 -1/2 (.f64 k (+.f64 (log.f64 (*.f64 2 (PI.f64))) (log.f64 n)))))))
(.f64 (sqrt.f64 (/.f64 1 k)) (.f64 (sqrt.f64 2) (+.f64 1 (.f64 -1/2 (.f64 k (+.f64 (.f64 -1 (log.f64 (/.f64 1 n))) (log.f64 (.f64 2 (PI.f64)))))))))
(.f64 (sqrt.f64 (/.f64 1 k)) (.f64 (sqrt.f64 2) (+.f64 1 (.f64 -1/2 (.f64 k (+.f64 (.f64 -1 (log.f64 (/.f64 1 n))) (log.f64 (.f64 2 (PI.f64)))))))))
(.f64 (sqrt.f64 (/.f64 1 k)) (.f64 (sqrt.f64 2) (+.f64 1 (.f64 -1/2 (.f64 k (+.f64 (.f64 -1 (log.f64 (/.f64 1 n))) (log.f64 (.f64 2 (PI.f64)))))))))
(.f64 (sqrt.f64 (/.f64 1 k)) (.f64 (sqrt.f64 2) (+.f64 1 (.f64 -1/2 (.f64 k (+.f64 (.f64 -1 (log.f64 (/.f64 1 n))) (log.f64 (.f64 2 (PI.f64)))))))))
(.f64 (sqrt.f64 (/.f64 1 k)) (.f64 (sqrt.f64 2) (+.f64 1 (.f64 -1/2 (.f64 k (+.f64 (.f64 -1 (log.f64 (/.f64 -1 n))) (log.f64 (.f64 -2 (PI.f64)))))))))
(.f64 (sqrt.f64 (/.f64 1 k)) (.f64 (sqrt.f64 2) (+.f64 1 (.f64 -1/2 (.f64 k (+.f64 (.f64 -1 (log.f64 (/.f64 -1 n))) (log.f64 (.f64 -2 (PI.f64)))))))))
(.f64 (sqrt.f64 (/.f64 1 k)) (.f64 (sqrt.f64 2) (+.f64 1 (.f64 -1/2 (.f64 k (+.f64 (.f64 -1 (log.f64 (/.f64 -1 n))) (log.f64 (.f64 -2 (PI.f64)))))))))
(.f64 (sqrt.f64 (/.f64 1 k)) (.f64 (sqrt.f64 2) (+.f64 1 (.f64 -1/2 (.f64 k (+.f64 (.f64 -1 (log.f64 (/.f64 -1 n))) (log.f64 (.f64 -2 (PI.f64)))))))))
(.f64 -1/2 (.f64 k (+.f64 (log.f64 n) (log.f64 (*.f64 2 (PI.f64))))))
(.f64 -1/2 (.f64 k (+.f64 (log.f64 n) (log.f64 (*.f64 2 (PI.f64))))))
(.f64 -1/2 (.f64 k (+.f64 (log.f64 n) (log.f64 (*.f64 2 (PI.f64))))))
(.f64 -1/2 (.f64 k (+.f64 (log.f64 n) (log.f64 (*.f64 2 (PI.f64))))))
(.f64 -1/2 (.f64 k (+.f64 (.f64 -1 (log.f64 (/.f64 1 n))) (log.f64 (.f64 2 (PI.f64))))))
(.f64 -1/2 (.f64 k (+.f64 (.f64 -1 (log.f64 (/.f64 1 n))) (log.f64 (.f64 2 (PI.f64))))))
(.f64 -1/2 (.f64 k (+.f64 (.f64 -1 (log.f64 (/.f64 1 n))) (log.f64 (.f64 2 (PI.f64))))))
(.f64 -1/2 (.f64 k (+.f64 (.f64 -1 (log.f64 (/.f64 1 n))) (log.f64 (.f64 2 (PI.f64))))))
(.f64 -1/2 (.f64 k (+.f64 (.f64 -1 (log.f64 (/.f64 -1 n))) (log.f64 (.f64 -2 (PI.f64))))))
(.f64 -1/2 (.f64 k (+.f64 (.f64 -1 (log.f64 (/.f64 -1 n))) (log.f64 (.f64 -2 (PI.f64))))))
(.f64 -1/2 (.f64 k (+.f64 (.f64 -1 (log.f64 (/.f64 -1 n))) (log.f64 (.f64 -2 (PI.f64))))))
(.f64 -1/2 (.f64 k (+.f64 (.f64 -1 (log.f64 (/.f64 -1 n))) (log.f64 (.f64 -2 (PI.f64))))))
(.f64 -1/2 (.f64 k (log.f64 (.f64 2 (.f64 n (PI.f64))))))
(.f64 -1/2 (.f64 k (log.f64 (.f64 2 (.f64 n (PI.f64))))))
(.f64 -1/2 (.f64 k (log.f64 (.f64 2 (.f64 n (PI.f64))))))
(.f64 -1/2 (.f64 k (log.f64 (.f64 2 (.f64 n (PI.f64))))))
(.f64 -1/2 (.f64 k (log.f64 (.f64 2 (.f64 n (PI.f64))))))
(.f64 -1/2 (.f64 k (log.f64 (.f64 2 (.f64 n (PI.f64))))))
(.f64 -1/2 (.f64 k (log.f64 (.f64 2 (.f64 n (PI.f64))))))
(.f64 -1/2 (.f64 k (log.f64 (.f64 2 (.f64 n (PI.f64))))))
(.f64 -1/2 (.f64 k (log.f64 (.f64 2 (.f64 n (PI.f64))))))
(.f64 -1/2 (.f64 k (log.f64 (.f64 2 (.f64 n (PI.f64))))))
(.f64 -1/2 (.f64 k (log.f64 (.f64 2 (.f64 n (PI.f64))))))
(.f64 -1/2 (.f64 k (log.f64 (.f64 2 (.f64 n (PI.f64))))))
(+.f64 (.f64 (/.f64 1 (sqrt.f64 k)) (.f64 (sqrt.f64 2) (+.f64 1 (.f64 k (.f64 (log.f64 (.f64 2 (.f64 (PI.f64) n))) -1/2))))) 0)
(+.f64 0 (.f64 (/.f64 1 (sqrt.f64 k)) (.f64 (sqrt.f64 2) (+.f64 1 (.f64 k (.f64 (log.f64 (.f64 2 (.f64 (PI.f64) n))) -1/2))))))
(-.f64 (.f64 (/.f64 1 (sqrt.f64 k)) (.f64 (sqrt.f64 2) (+.f64 1 (.f64 k (.f64 (log.f64 (.f64 2 (.f64 (PI.f64) n))) -1/2))))) 0)
(/.f64 (.f64 (/.f64 1 (sqrt.f64 k)) (.f64 (sqrt.f64 2) (+.f64 1 (.f64 k (.f64 (log.f64 (.f64 2 (.f64 (PI.f64) n))) -1/2))))) 1)
(/.f64 (.f64 (/.f64 1 (sqrt.f64 k)) (.f64 (sqrt.f64 2) (+.f64 1 (.f64 k (.f64 (log.f64 (.f64 2 (.f64 (PI.f64) n))) -1/2))))) (/.f64 (.f64 (/.f64 1 (sqrt.f64 k)) (.f64 (sqrt.f64 2) (+.f64 1 (.f64 k (.f64 (log.f64 (.f64 2 (.f64 (PI.f64) n))) -1/2))))) (.f64 (/.f64 1 (sqrt.f64 k)) (.f64 (sqrt.f64 2) (+.f64 1 (.f64 k (.f64 (log.f64 (.f64 2 (.f64 (PI.f64) n))) -1/2)))))))
(/.f64 (.f64 (.f64 (/.f64 1 (sqrt.f64 k)) (sqrt.f64 2)) (+.f64 1 (+.f64 1 (.f64 k (neg.f64 (log.f64 (.f64 2 (*.f64 (PI.f64) n)))))))) 2)
(pow.f64 (.f64 (/.f64 1 (sqrt.f64 k)) (.f64 (sqrt.f64 2) (+.f64 1 (.f64 k (.f64 (log.f64 (.f64 2 (.f64 (PI.f64) n))) -1/2))))) 1)
(+.f64 (.f64 (+.f64 1 (.f64 k (.f64 (log.f64 (.f64 2 (.f64 (PI.f64) n))) -1/2))) (.f64 (/.f64 1 (sqrt.f64 k)) (sqrt.f64 (.f64 2 (.f64 (PI.f64) n))))) 0)
(+.f64 0 (.f64 (+.f64 1 (.f64 k (.f64 (log.f64 (.f64 2 (.f64 (PI.f64) n))) -1/2))) (.f64 (/.f64 1 (sqrt.f64 k)) (sqrt.f64 (.f64 2 (.f64 (PI.f64) n))))))
(-.f64 (.f64 (+.f64 1 (.f64 k (.f64 (log.f64 (.f64 2 (.f64 (PI.f64) n))) -1/2))) (.f64 (/.f64 1 (sqrt.f64 k)) (sqrt.f64 (.f64 2 (.f64 (PI.f64) n))))) 0)
(/.f64 (.f64 (+.f64 1 (.f64 k (.f64 (log.f64 (.f64 2 (.f64 (PI.f64) n))) -1/2))) (.f64 (/.f64 1 (sqrt.f64 k)) (sqrt.f64 (.f64 2 (.f64 (PI.f64) n))))) 1)
(/.f64 (.f64 (+.f64 1 (.f64 k (.f64 (log.f64 (.f64 2 (.f64 (PI.f64) n))) -1/2))) (.f64 (/.f64 1 (sqrt.f64 k)) (sqrt.f64 (.f64 2 (.f64 (PI.f64) n))))) (/.f64 (.f64 (+.f64 1 (.f64 k (.f64 (log.f64 (.f64 2 (.f64 (PI.f64) n))) -1/2))) (.f64 (/.f64 1 (sqrt.f64 k)) (sqrt.f64 (.f64 2 (.f64 (PI.f64) n))))) (.f64 (+.f64 1 (.f64 k (.f64 (log.f64 (.f64 2 (.f64 (PI.f64) n))) -1/2))) (.f64 (/.f64 1 (sqrt.f64 k)) (sqrt.f64 (.f64 2 (.f64 (PI.f64) n)))))))
(/.f64 (.f64 (/.f64 1 (sqrt.f64 k)) (.f64 (sqrt.f64 (.f64 2 (.f64 (PI.f64) n))) (+.f64 1 (+.f64 1 (.f64 k (neg.f64 (log.f64 (.f64 2 (*.f64 (PI.f64) n))))))))) 2)
(pow.f64 (.f64 (+.f64 1 (.f64 k (.f64 (log.f64 (.f64 2 (.f64 (PI.f64) n))) -1/2))) (.f64 (/.f64 1 (sqrt.f64 k)) (sqrt.f64 (.f64 2 (.f64 (PI.f64) n))))) 1)
(+.f64 (.f64 k (.f64 (log.f64 (.f64 2 (.f64 (PI.f64) n))) -1/2)) 0)
(+.f64 0 (.f64 k (.f64 (log.f64 (.f64 2 (.f64 (PI.f64) n))) -1/2)))
(-.f64 (.f64 k (.f64 (log.f64 (.f64 2 (.f64 (PI.f64) n))) -1/2)) 0)
(/.f64 (.f64 k (.f64 (log.f64 (.f64 2 (.f64 (PI.f64) n))) -1/2)) 1)
(/.f64 (.f64 k (.f64 (log.f64 (.f64 2 (.f64 (PI.f64) n))) -1/2)) (/.f64 (.f64 k (neg.f64 (log.f64 (.f64 2 (.f64 (PI.f64) n))))) (.f64 k (neg.f64 (log.f64 (.f64 2 (.f64 (PI.f64) n)))))))
(/.f64 (.f64 k (neg.f64 (log.f64 (.f64 2 (*.f64 (PI.f64) n))))) 2)
(pow.f64 (.f64 k (.f64 (log.f64 (.f64 2 (.f64 (PI.f64) n))) -1/2)) 1)
(log.f64 (pow.f64 (.f64 2 (.f64 (PI.f64) n)) (*.f64 k -1/2)))

Outputs
(.f64 (sqrt.f64 (/.f64 1 k)) (.f64 (sqrt.f64 2) (+.f64 1 (.f64 -1/2 (.f64 k (+.f64 (log.f64 (*.f64 2 (PI.f64))) (log.f64 n)))))))
(.f64 (sqrt.f64 (/.f64 1 k)) (.f64 (sqrt.f64 2) (+.f64 1 (.f64 k (.f64 -1/2 (+.f64 (log.f64 (*.f64 2 (PI.f64))) (log.f64 n)))))))
(.f64 (+.f64 1 (.f64 (+.f64 (log.f64 (.f64 2 (PI.f64))) (log.f64 n)) (.f64 k -1/2))) (*.f64 (sqrt.f64 (/.f64 1 k)) (sqrt.f64 2)))
(.f64 (+.f64 1 (.f64 k (.f64 -1/2 (+.f64 (log.f64 (.f64 2 (PI.f64))) (log.f64 n))))) (sqrt.f64 (*.f64 2 (/.f64 1 k))))
(.f64 (+.f64 1 (.f64 k (.f64 -1/2 (+.f64 (log.f64 (.f64 2 (PI.f64))) (log.f64 n))))) (sqrt.f64 (*.f64 (/.f64 1 k) 2)))
(.f64 (sqrt.f64 (/.f64 1 k)) (.f64 (sqrt.f64 2) (+.f64 1 (.f64 -1/2 (.f64 k (+.f64 (log.f64 (*.f64 2 (PI.f64))) (log.f64 n)))))))
(.f64 (sqrt.f64 (/.f64 1 k)) (.f64 (sqrt.f64 2) (+.f64 1 (.f64 k (.f64 -1/2 (+.f64 (log.f64 (*.f64 2 (PI.f64))) (log.f64 n)))))))
(.f64 (+.f64 1 (.f64 (+.f64 (log.f64 (.f64 2 (PI.f64))) (log.f64 n)) (.f64 k -1/2))) (*.f64 (sqrt.f64 (/.f64 1 k)) (sqrt.f64 2)))
(.f64 (+.f64 1 (.f64 k (.f64 -1/2 (+.f64 (log.f64 (.f64 2 (PI.f64))) (log.f64 n))))) (sqrt.f64 (*.f64 2 (/.f64 1 k))))
(.f64 (+.f64 1 (.f64 k (.f64 -1/2 (+.f64 (log.f64 (.f64 2 (PI.f64))) (log.f64 n))))) (sqrt.f64 (*.f64 (/.f64 1 k) 2)))
(.f64 (sqrt.f64 (/.f64 1 k)) (.f64 (sqrt.f64 2) (+.f64 1 (.f64 -1/2 (.f64 k (+.f64 (log.f64 (*.f64 2 (PI.f64))) (log.f64 n)))))))
(.f64 (sqrt.f64 (/.f64 1 k)) (.f64 (sqrt.f64 2) (+.f64 1 (.f64 k (.f64 -1/2 (+.f64 (log.f64 (*.f64 2 (PI.f64))) (log.f64 n)))))))
(.f64 (+.f64 1 (.f64 (+.f64 (log.f64 (.f64 2 (PI.f64))) (log.f64 n)) (.f64 k -1/2))) (*.f64 (sqrt.f64 (/.f64 1 k)) (sqrt.f64 2)))
(.f64 (+.f64 1 (.f64 k (.f64 -1/2 (+.f64 (log.f64 (.f64 2 (PI.f64))) (log.f64 n))))) (sqrt.f64 (*.f64 2 (/.f64 1 k))))
(.f64 (+.f64 1 (.f64 k (.f64 -1/2 (+.f64 (log.f64 (.f64 2 (PI.f64))) (log.f64 n))))) (sqrt.f64 (*.f64 (/.f64 1 k) 2)))
(.f64 (sqrt.f64 (/.f64 1 k)) (.f64 (sqrt.f64 2) (+.f64 1 (.f64 -1/2 (.f64 k (+.f64 (log.f64 (*.f64 2 (PI.f64))) (log.f64 n)))))))
(.f64 (sqrt.f64 (/.f64 1 k)) (.f64 (sqrt.f64 2) (+.f64 1 (.f64 k (.f64 -1/2 (+.f64 (log.f64 (*.f64 2 (PI.f64))) (log.f64 n)))))))
(.f64 (+.f64 1 (.f64 (+.f64 (log.f64 (.f64 2 (PI.f64))) (log.f64 n)) (.f64 k -1/2))) (*.f64 (sqrt.f64 (/.f64 1 k)) (sqrt.f64 2)))
(.f64 (+.f64 1 (.f64 k (.f64 -1/2 (+.f64 (log.f64 (.f64 2 (PI.f64))) (log.f64 n))))) (sqrt.f64 (*.f64 2 (/.f64 1 k))))
(.f64 (+.f64 1 (.f64 k (.f64 -1/2 (+.f64 (log.f64 (.f64 2 (PI.f64))) (log.f64 n))))) (sqrt.f64 (*.f64 (/.f64 1 k) 2)))
(.f64 (sqrt.f64 (/.f64 1 k)) (.f64 (sqrt.f64 2) (+.f64 1 (.f64 -1/2 (.f64 k (+.f64 (.f64 -1 (log.f64 (/.f64 1 n))) (log.f64 (.f64 2 (PI.f64)))))))))
(.f64 (sqrt.f64 (/.f64 1 k)) (.f64 (sqrt.f64 2) (+.f64 1 (.f64 k (.f64 -1/2 (+.f64 (log.f64 (.f64 2 (PI.f64))) (.f64 -1 (log.f64 (/.f64 1 n)))))))))
(.f64 (+.f64 1 (.f64 (+.f64 (log.f64 (.f64 2 (PI.f64))) (neg.f64 (log.f64 (/.f64 1 n)))) (.f64 k -1/2))) (*.f64 (sqrt.f64 (/.f64 1 k)) (sqrt.f64 2)))
(.f64 (+.f64 1 (.f64 -1/2 (.f64 k (+.f64 (log.f64 (.f64 2 (PI.f64))) (neg.f64 (log.f64 (/.f64 1 n))))))) (sqrt.f64 (*.f64 2 (/.f64 1 k))))
(.f64 (+.f64 1 (.f64 -1/2 (.f64 k (+.f64 (log.f64 (.f64 2 (PI.f64))) (neg.f64 (log.f64 (/.f64 1 n))))))) (sqrt.f64 (*.f64 (/.f64 1 k) 2)))
(.f64 (+.f64 1 (.f64 (+.f64 (log.f64 (.f64 2 (PI.f64))) (neg.f64 (log.f64 (/.f64 1 n)))) (.f64 k -1/2))) (sqrt.f64 (*.f64 (/.f64 1 k) 2)))
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(.f64 (+.f64 1 (.f64 (log.f64 (.f64 2 (.f64 (PI.f64) n))) (.f64 k -1/2))) (.f64 (sqrt.f64 2) (/.f64 1 (sqrt.f64 k))))
(.f64 (sqrt.f64 2) (.f64 (/.f64 1 (sqrt.f64 k)) (+.f64 1 (.f64 k (.f64 -1/2 (log.f64 (.f64 2 (.f64 (PI.f64) n))))))))
(.f64 (+.f64 1 (.f64 -1/2 (.f64 k (log.f64 (.f64 2 (.f64 (PI.f64) n)))))) (.f64 (sqrt.f64 2) (/.f64 1 (sqrt.f64 k))))
(/.f64 (.f64 (/.f64 1 (sqrt.f64 k)) (.f64 (sqrt.f64 2) (+.f64 1 (.f64 k (.f64 (log.f64 (.f64 2 (.f64 (PI.f64) n))) -1/2))))) 1)
(.f64 (sqrt.f64 2) (.f64 (/.f64 1 (sqrt.f64 k)) (+.f64 1 (.f64 (log.f64 (.f64 2 (.f64 (PI.f64) n))) (.f64 k -1/2)))))
(.f64 (+.f64 1 (.f64 (log.f64 (.f64 2 (.f64 (PI.f64) n))) (.f64 k -1/2))) (.f64 (sqrt.f64 2) (/.f64 1 (sqrt.f64 k))))
(.f64 (sqrt.f64 2) (.f64 (/.f64 1 (sqrt.f64 k)) (+.f64 1 (.f64 k (.f64 -1/2 (log.f64 (.f64 2 (.f64 (PI.f64) n))))))))
(.f64 (+.f64 1 (.f64 -1/2 (.f64 k (log.f64 (.f64 2 (.f64 (PI.f64) n)))))) (.f64 (sqrt.f64 2) (/.f64 1 (sqrt.f64 k))))
(/.f64 (.f64 (/.f64 1 (sqrt.f64 k)) (.f64 (sqrt.f64 2) (+.f64 1 (.f64 k (.f64 (log.f64 (.f64 2 (.f64 (PI.f64) n))) -1/2))))) (/.f64 (.f64 (/.f64 1 (sqrt.f64 k)) (.f64 (sqrt.f64 2) (+.f64 1 (.f64 k (.f64 (log.f64 (.f64 2 (.f64 (PI.f64) n))) -1/2))))) (.f64 (/.f64 1 (sqrt.f64 k)) (.f64 (sqrt.f64 2) (+.f64 1 (.f64 k (.f64 (log.f64 (.f64 2 (.f64 (PI.f64) n))) -1/2)))))))
(.f64 (sqrt.f64 2) (.f64 (/.f64 1 (sqrt.f64 k)) (+.f64 1 (.f64 (log.f64 (.f64 2 (.f64 (PI.f64) n))) (.f64 k -1/2)))))
(.f64 (+.f64 1 (.f64 (log.f64 (.f64 2 (.f64 (PI.f64) n))) (.f64 k -1/2))) (.f64 (sqrt.f64 2) (/.f64 1 (sqrt.f64 k))))
(.f64 (sqrt.f64 2) (.f64 (/.f64 1 (sqrt.f64 k)) (+.f64 1 (.f64 k (.f64 -1/2 (log.f64 (.f64 2 (.f64 (PI.f64) n))))))))
(.f64 (+.f64 1 (.f64 -1/2 (.f64 k (log.f64 (.f64 2 (.f64 (PI.f64) n)))))) (.f64 (sqrt.f64 2) (/.f64 1 (sqrt.f64 k))))
(/.f64 (.f64 (.f64 (/.f64 1 (sqrt.f64 k)) (sqrt.f64 2)) (+.f64 1 (+.f64 1 (.f64 k (neg.f64 (log.f64 (.f64 2 (*.f64 (PI.f64) n)))))))) 2)
(.f64 (sqrt.f64 2) (.f64 (/.f64 1 (sqrt.f64 k)) (+.f64 1 (.f64 (log.f64 (.f64 2 (.f64 (PI.f64) n))) (.f64 k -1/2)))))
(.f64 (+.f64 1 (.f64 (log.f64 (.f64 2 (.f64 (PI.f64) n))) (.f64 k -1/2))) (.f64 (sqrt.f64 2) (/.f64 1 (sqrt.f64 k))))
(.f64 (sqrt.f64 2) (.f64 (/.f64 1 (sqrt.f64 k)) (+.f64 1 (.f64 k (.f64 -1/2 (log.f64 (.f64 2 (.f64 (PI.f64) n))))))))
(.f64 (+.f64 1 (.f64 -1/2 (.f64 k (log.f64 (.f64 2 (.f64 (PI.f64) n)))))) (.f64 (sqrt.f64 2) (/.f64 1 (sqrt.f64 k))))
(pow.f64 (.f64 (/.f64 1 (sqrt.f64 k)) (.f64 (sqrt.f64 2) (+.f64 1 (.f64 k (.f64 (log.f64 (.f64 2 (.f64 (PI.f64) n))) -1/2))))) 1)
(.f64 (sqrt.f64 2) (.f64 (/.f64 1 (sqrt.f64 k)) (+.f64 1 (.f64 (log.f64 (.f64 2 (.f64 (PI.f64) n))) (.f64 k -1/2)))))
(.f64 (+.f64 1 (.f64 (log.f64 (.f64 2 (.f64 (PI.f64) n))) (.f64 k -1/2))) (.f64 (sqrt.f64 2) (/.f64 1 (sqrt.f64 k))))
(.f64 (sqrt.f64 2) (.f64 (/.f64 1 (sqrt.f64 k)) (+.f64 1 (.f64 k (.f64 -1/2 (log.f64 (.f64 2 (.f64 (PI.f64) n))))))))
(.f64 (+.f64 1 (.f64 -1/2 (.f64 k (log.f64 (.f64 2 (.f64 (PI.f64) n)))))) (.f64 (sqrt.f64 2) (/.f64 1 (sqrt.f64 k))))
(+.f64 (.f64 (+.f64 1 (.f64 k (.f64 (log.f64 (.f64 2 (.f64 (PI.f64) n))) -1/2))) (.f64 (/.f64 1 (sqrt.f64 k)) (sqrt.f64 (.f64 2 (.f64 (PI.f64) n))))) 0)
(.f64 (/.f64 1 (sqrt.f64 k)) (.f64 (+.f64 1 (.f64 (log.f64 (.f64 2 (.f64 (PI.f64) n))) (.f64 k -1/2))) (sqrt.f64 (.f64 2 (.f64 (PI.f64) n)))))
(.f64 (/.f64 1 (sqrt.f64 k)) (.f64 (+.f64 1 (.f64 k (.f64 -1/2 (log.f64 (.f64 2 (.f64 (PI.f64) n)))))) (sqrt.f64 (.f64 2 (.f64 (PI.f64) n)))))
(.f64 (/.f64 1 (sqrt.f64 k)) (.f64 (+.f64 1 (.f64 -1/2 (.f64 k (log.f64 (.f64 2 (.f64 (PI.f64) n)))))) (sqrt.f64 (.f64 2 (.f64 (PI.f64) n)))))
(+.f64 0 (.f64 (+.f64 1 (.f64 k (.f64 (log.f64 (.f64 2 (.f64 (PI.f64) n))) -1/2))) (.f64 (/.f64 1 (sqrt.f64 k)) (sqrt.f64 (.f64 2 (.f64 (PI.f64) n))))))
(.f64 (/.f64 1 (sqrt.f64 k)) (.f64 (+.f64 1 (.f64 (log.f64 (.f64 2 (.f64 (PI.f64) n))) (.f64 k -1/2))) (sqrt.f64 (.f64 2 (.f64 (PI.f64) n)))))
(.f64 (/.f64 1 (sqrt.f64 k)) (.f64 (+.f64 1 (.f64 k (.f64 -1/2 (log.f64 (.f64 2 (.f64 (PI.f64) n)))))) (sqrt.f64 (.f64 2 (.f64 (PI.f64) n)))))
(.f64 (/.f64 1 (sqrt.f64 k)) (.f64 (+.f64 1 (.f64 -1/2 (.f64 k (log.f64 (.f64 2 (.f64 (PI.f64) n)))))) (sqrt.f64 (.f64 2 (.f64 (PI.f64) n)))))
(-.f64 (.f64 (+.f64 1 (.f64 k (.f64 (log.f64 (.f64 2 (.f64 (PI.f64) n))) -1/2))) (.f64 (/.f64 1 (sqrt.f64 k)) (sqrt.f64 (.f64 2 (.f64 (PI.f64) n))))) 0)
(.f64 (/.f64 1 (sqrt.f64 k)) (.f64 (+.f64 1 (.f64 (log.f64 (.f64 2 (.f64 (PI.f64) n))) (.f64 k -1/2))) (sqrt.f64 (.f64 2 (.f64 (PI.f64) n)))))
(.f64 (/.f64 1 (sqrt.f64 k)) (.f64 (+.f64 1 (.f64 k (.f64 -1/2 (log.f64 (.f64 2 (.f64 (PI.f64) n)))))) (sqrt.f64 (.f64 2 (.f64 (PI.f64) n)))))
(.f64 (/.f64 1 (sqrt.f64 k)) (.f64 (+.f64 1 (.f64 -1/2 (.f64 k (log.f64 (.f64 2 (.f64 (PI.f64) n)))))) (sqrt.f64 (.f64 2 (.f64 (PI.f64) n)))))
(/.f64 (.f64 (+.f64 1 (.f64 k (.f64 (log.f64 (.f64 2 (.f64 (PI.f64) n))) -1/2))) (.f64 (/.f64 1 (sqrt.f64 k)) (sqrt.f64 (.f64 2 (.f64 (PI.f64) n))))) 1)
(.f64 (/.f64 1 (sqrt.f64 k)) (.f64 (+.f64 1 (.f64 (log.f64 (.f64 2 (.f64 (PI.f64) n))) (.f64 k -1/2))) (sqrt.f64 (.f64 2 (.f64 (PI.f64) n)))))
(.f64 (/.f64 1 (sqrt.f64 k)) (.f64 (+.f64 1 (.f64 k (.f64 -1/2 (log.f64 (.f64 2 (.f64 (PI.f64) n)))))) (sqrt.f64 (.f64 2 (.f64 (PI.f64) n)))))
(.f64 (/.f64 1 (sqrt.f64 k)) (.f64 (+.f64 1 (.f64 -1/2 (.f64 k (log.f64 (.f64 2 (.f64 (PI.f64) n)))))) (sqrt.f64 (.f64 2 (.f64 (PI.f64) n)))))
(/.f64 (.f64 (+.f64 1 (.f64 k (.f64 (log.f64 (.f64 2 (.f64 (PI.f64) n))) -1/2))) (.f64 (/.f64 1 (sqrt.f64 k)) (sqrt.f64 (.f64 2 (.f64 (PI.f64) n))))) (/.f64 (.f64 (+.f64 1 (.f64 k (.f64 (log.f64 (.f64 2 (.f64 (PI.f64) n))) -1/2))) (.f64 (/.f64 1 (sqrt.f64 k)) (sqrt.f64 (.f64 2 (.f64 (PI.f64) n))))) (.f64 (+.f64 1 (.f64 k (.f64 (log.f64 (.f64 2 (.f64 (PI.f64) n))) -1/2))) (.f64 (/.f64 1 (sqrt.f64 k)) (sqrt.f64 (.f64 2 (.f64 (PI.f64) n)))))))
(.f64 (/.f64 1 (sqrt.f64 k)) (.f64 (+.f64 1 (.f64 (log.f64 (.f64 2 (.f64 (PI.f64) n))) (.f64 k -1/2))) (sqrt.f64 (.f64 2 (.f64 (PI.f64) n)))))
(.f64 (/.f64 1 (sqrt.f64 k)) (.f64 (+.f64 1 (.f64 k (.f64 -1/2 (log.f64 (.f64 2 (.f64 (PI.f64) n)))))) (sqrt.f64 (.f64 2 (.f64 (PI.f64) n)))))
(.f64 (/.f64 1 (sqrt.f64 k)) (.f64 (+.f64 1 (.f64 -1/2 (.f64 k (log.f64 (.f64 2 (.f64 (PI.f64) n)))))) (sqrt.f64 (.f64 2 (.f64 (PI.f64) n)))))
(/.f64 (.f64 (/.f64 1 (sqrt.f64 k)) (.f64 (sqrt.f64 (.f64 2 (.f64 (PI.f64) n))) (+.f64 1 (+.f64 1 (.f64 k (neg.f64 (log.f64 (.f64 2 (*.f64 (PI.f64) n))))))))) 2)
(.f64 (/.f64 1 (sqrt.f64 k)) (.f64 (+.f64 1 (.f64 (log.f64 (.f64 2 (.f64 (PI.f64) n))) (.f64 k -1/2))) (sqrt.f64 (.f64 2 (.f64 (PI.f64) n)))))
(.f64 (/.f64 1 (sqrt.f64 k)) (.f64 (+.f64 1 (.f64 k (.f64 -1/2 (log.f64 (.f64 2 (.f64 (PI.f64) n)))))) (sqrt.f64 (.f64 2 (.f64 (PI.f64) n)))))
(.f64 (/.f64 1 (sqrt.f64 k)) (.f64 (+.f64 1 (.f64 -1/2 (.f64 k (log.f64 (.f64 2 (.f64 (PI.f64) n)))))) (sqrt.f64 (.f64 2 (.f64 (PI.f64) n)))))
(pow.f64 (.f64 (+.f64 1 (.f64 k (.f64 (log.f64 (.f64 2 (.f64 (PI.f64) n))) -1/2))) (.f64 (/.f64 1 (sqrt.f64 k)) (sqrt.f64 (.f64 2 (.f64 (PI.f64) n))))) 1)
(.f64 (/.f64 1 (sqrt.f64 k)) (.f64 (+.f64 1 (.f64 (log.f64 (.f64 2 (.f64 (PI.f64) n))) (.f64 k -1/2))) (sqrt.f64 (.f64 2 (.f64 (PI.f64) n)))))
(.f64 (/.f64 1 (sqrt.f64 k)) (.f64 (+.f64 1 (.f64 k (.f64 -1/2 (log.f64 (.f64 2 (.f64 (PI.f64) n)))))) (sqrt.f64 (.f64 2 (.f64 (PI.f64) n)))))
(.f64 (/.f64 1 (sqrt.f64 k)) (.f64 (+.f64 1 (.f64 -1/2 (.f64 k (log.f64 (.f64 2 (.f64 (PI.f64) n)))))) (sqrt.f64 (.f64 2 (.f64 (PI.f64) n)))))
(+.f64 (.f64 k (.f64 (log.f64 (.f64 2 (.f64 (PI.f64) n))) -1/2)) 0)
(.f64 (log.f64 (.f64 2 (.f64 (PI.f64) n))) (.f64 k -1/2))
(.f64 k (.f64 -1/2 (log.f64 (.f64 2 (.f64 (PI.f64) n)))))
(.f64 -1/2 (.f64 k (log.f64 (.f64 2 (.f64 (PI.f64) n)))))
(+.f64 0 (.f64 k (.f64 (log.f64 (.f64 2 (.f64 (PI.f64) n))) -1/2)))
(.f64 (log.f64 (.f64 2 (.f64 (PI.f64) n))) (.f64 k -1/2))
(.f64 k (.f64 -1/2 (log.f64 (.f64 2 (.f64 (PI.f64) n)))))
(.f64 -1/2 (.f64 k (log.f64 (.f64 2 (.f64 (PI.f64) n)))))
(-.f64 (.f64 k (.f64 (log.f64 (.f64 2 (.f64 (PI.f64) n))) -1/2)) 0)
(.f64 (log.f64 (.f64 2 (.f64 (PI.f64) n))) (.f64 k -1/2))
(.f64 k (.f64 -1/2 (log.f64 (.f64 2 (.f64 (PI.f64) n)))))
(.f64 -1/2 (.f64 k (log.f64 (.f64 2 (.f64 (PI.f64) n)))))
(/.f64 (.f64 k (.f64 (log.f64 (.f64 2 (.f64 (PI.f64) n))) -1/2)) 1)
(.f64 (log.f64 (.f64 2 (.f64 (PI.f64) n))) (.f64 k -1/2))
(.f64 k (.f64 -1/2 (log.f64 (.f64 2 (.f64 (PI.f64) n)))))
(.f64 -1/2 (.f64 k (log.f64 (.f64 2 (.f64 (PI.f64) n)))))
(/.f64 (.f64 k (.f64 (log.f64 (.f64 2 (.f64 (PI.f64) n))) -1/2)) (/.f64 (.f64 k (neg.f64 (log.f64 (.f64 2 (.f64 (PI.f64) n))))) (.f64 k (neg.f64 (log.f64 (.f64 2 (.f64 (PI.f64) n)))))))
(/.f64 (.f64 (log.f64 (.f64 2 (.f64 (PI.f64) n))) (.f64 k -1/2)) (/.f64 (.f64 k (neg.f64 (log.f64 (.f64 2 (.f64 (PI.f64) n))))) (.f64 k (neg.f64 (log.f64 (.f64 2 (.f64 (PI.f64) n)))))))
(/.f64 (.f64 k (.f64 -1/2 (log.f64 (.f64 2 (.f64 (PI.f64) n))))) (/.f64 (.f64 k (neg.f64 (log.f64 (.f64 2 (.f64 (PI.f64) n))))) (.f64 k (neg.f64 (log.f64 (.f64 2 (.f64 (PI.f64) n)))))))
(/.f64 (.f64 -1/2 (.f64 k (log.f64 (.f64 2 (.f64 (PI.f64) n))))) (/.f64 (.f64 k (neg.f64 (log.f64 (.f64 2 (.f64 (PI.f64) n))))) (.f64 k (neg.f64 (log.f64 (.f64 2 (.f64 (PI.f64) n)))))))
(/.f64 (.f64 k (neg.f64 (log.f64 (.f64 2 (*.f64 (PI.f64) n))))) 2)
(.f64 (log.f64 (.f64 2 (.f64 (PI.f64) n))) (.f64 k -1/2))
(.f64 k (.f64 -1/2 (log.f64 (.f64 2 (.f64 (PI.f64) n)))))
(.f64 -1/2 (.f64 k (log.f64 (.f64 2 (.f64 (PI.f64) n)))))
(pow.f64 (.f64 k (.f64 (log.f64 (.f64 2 (.f64 (PI.f64) n))) -1/2)) 1)
(.f64 (log.f64 (.f64 2 (.f64 (PI.f64) n))) (.f64 k -1/2))
(.f64 k (.f64 -1/2 (log.f64 (.f64 2 (.f64 (PI.f64) n)))))
(.f64 -1/2 (.f64 k (log.f64 (.f64 2 (.f64 (PI.f64) n)))))
(log.f64 (pow.f64 (.f64 2 (.f64 (PI.f64) n)) (*.f64 k -1/2)))

localize42.0ms (0.3%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.2b	(log.f64 (pow.f64 (*.f64 (PI.f64) (+.f64 n n)) (-.f64 1 k)))
✓	0.3b	(*.f64 (PI.f64) (+.f64 n n))
✓	0.5b	(.f64 (pow.f64 (.f64 (PI.f64) (+.f64 n n)) (-.f64 1 k)) (exp.f64 (/.f64 (log.f64 (pow.f64 (*.f64 (PI.f64) (+.f64 n n)) (-.f64 1 k))) -2)))
✓	3.1b	(exp.f64 (/.f64 (log.f64 (pow.f64 (*.f64 (PI.f64) (+.f64 n n)) (-.f64 1 k))) -2))

Compiler

Compiled 119 to 57 computations (52.1% saved)

series124.0ms (0.9%)

Counts

4 → 84

Calls

21 calls:

Time	Variable		Point	Expression
57.0ms	k	@	-inf	(exp.f64 (/.f64 (log.f64 (pow.f64 (*.f64 (PI.f64) (+.f64 n n)) (-.f64 1 k))) -2))
18.0ms	k	@	inf	(exp.f64 (/.f64 (log.f64 (pow.f64 (*.f64 (PI.f64) (+.f64 n n)) (-.f64 1 k))) -2))
16.0ms	n	@	inf	(exp.f64 (/.f64 (log.f64 (pow.f64 (*.f64 (PI.f64) (+.f64 n n)) (-.f64 1 k))) -2))
13.0ms	n	@	-inf	(exp.f64 (/.f64 (log.f64 (pow.f64 (*.f64 (PI.f64) (+.f64 n n)) (-.f64 1 k))) -2))
13.0ms	n	@	0	(exp.f64 (/.f64 (log.f64 (pow.f64 (*.f64 (PI.f64) (+.f64 n n)) (-.f64 1 k))) -2))

rewrite139.0ms (1%)

Algorithm

1×	batch-egg-rewrite

Rules

828×	`rational_best-5`
826×	`rational_best-4`
826×	`rational_best-2`
826×	`rational_best-3`
826×	`rational_best-1`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	17	160
1	136	160
2	438	160
3	1826	160
4	7355	160

Stop Event

1×	node limit

Counts

4 → 62

Calls

Call 1

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

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

simplify237.0ms (1.6%)

Algorithm

1×	egg-herbie

Rules

1180×	`rational_best-simplify-78`
1056×	`rational_best-simplify-2`
646×	`rational_best-simplify-132`
630×	`rational_best-simplify-43`
534×	`rational_best-simplify-49`

Iterations

Useful iterations: 4 (0.0ms)

Iter	Nodes	Cost
0	255	7832
1	500	7590
2	1277	7578
3	2717	7578
4	5795	7574

Stop Event

1×	node limit

Counts

146 → 178

Calls

Call 1

Inputs
(exp.f64 (.f64 -1/2 (.f64 (-.f64 1 k) (+.f64 (log.f64 (*.f64 2 (PI.f64))) (log.f64 n)))))
(exp.f64 (.f64 -1/2 (.f64 (-.f64 1 k) (+.f64 (log.f64 (*.f64 2 (PI.f64))) (log.f64 n)))))
(exp.f64 (.f64 -1/2 (.f64 (-.f64 1 k) (+.f64 (log.f64 (*.f64 2 (PI.f64))) (log.f64 n)))))
(exp.f64 (.f64 -1/2 (.f64 (-.f64 1 k) (+.f64 (log.f64 (*.f64 2 (PI.f64))) (log.f64 n)))))
(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 (/.f64 1 (.f64 n (PI.f64)))) (sqrt.f64 1/2))
(+.f64 (.f64 1/2 (.f64 (.f64 k (.f64 (sqrt.f64 1/2) (log.f64 (.f64 2 (.f64 n (PI.f64)))))) (sqrt.f64 (/.f64 1 (.f64 n (PI.f64)))))) (.f64 (sqrt.f64 (/.f64 1 (*.f64 n (PI.f64)))) (sqrt.f64 1/2)))
(+.f64 (.f64 1/2 (.f64 (.f64 k (.f64 (sqrt.f64 1/2) (log.f64 (.f64 2 (.f64 n (PI.f64)))))) (sqrt.f64 (/.f64 1 (.f64 n (PI.f64)))))) (+.f64 (.f64 (.f64 (pow.f64 k 2) (.f64 (sqrt.f64 1/2) (+.f64 (.f64 1/8 (pow.f64 (log.f64 (.f64 2 (.f64 n (PI.f64)))) 2)) (.f64 -1/4 (+.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)))))) (sqrt.f64 (/.f64 1 (.f64 n (PI.f64))))) (.f64 (sqrt.f64 (/.f64 1 (.f64 n (PI.f64)))) (sqrt.f64 1/2))))
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(sqrt.f64 (/.f64 1 (pow.f64 (.f64 2 (.f64 n (PI.f64))) (-.f64 1 k))))
(sqrt.f64 (/.f64 1 (pow.f64 (.f64 2 (.f64 n (PI.f64))) (-.f64 1 k))))
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(.f64 (/.f64 (/.f64 (.f64 (-.f64 1 k) (log.f64 (.f64 (PI.f64) (+.f64 n n)))) (.f64 (-.f64 1 k) (log.f64 (.f64 (PI.f64) (+.f64 n n))))) (.f64 (-.f64 1 k) (log.f64 (.f64 (PI.f64) (+.f64 n n))))) (.f64 (.f64 (-.f64 1 k) (log.f64 (.f64 (PI.f64) (+.f64 n n)))) (.f64 (-.f64 1 k) (log.f64 (.f64 (PI.f64) (+.f64 n n))))))
(.f64 (/.f64 (.f64 (.f64 (-.f64 1 k) (log.f64 (.f64 (PI.f64) (+.f64 n n)))) (/.f64 1 (.f64 (-.f64 1 k) (log.f64 (.f64 (PI.f64) (+.f64 n n)))))) (.f64 (-.f64 1 k) (log.f64 (.f64 (PI.f64) (+.f64 n n))))) (.f64 (.f64 (-.f64 1 k) (log.f64 (.f64 (PI.f64) (+.f64 n n)))) (.f64 (-.f64 1 k) (log.f64 (*.f64 (PI.f64) (+.f64 n n))))))
(/.f64 (.f64 (-.f64 1 k) (log.f64 (.f64 (PI.f64) (+.f64 n n)))) 1)
(/.f64 (.f64 (-.f64 1 k) (log.f64 (.f64 (PI.f64) (+.f64 n n)))) (/.f64 (.f64 (-.f64 1 k) (log.f64 (.f64 (PI.f64) (+.f64 n n)))) (.f64 (-.f64 1 k) (log.f64 (.f64 (PI.f64) (+.f64 n n))))))
(/.f64 (.f64 (.f64 (-.f64 1 k) (log.f64 (*.f64 (PI.f64) (+.f64 n n)))) 2) 2)
(pow.f64 (.f64 (-.f64 1 k) (log.f64 (.f64 (PI.f64) (+.f64 n n)))) 1)
(neg.f64 (neg.f64 (.f64 (-.f64 1 k) (log.f64 (.f64 (PI.f64) (+.f64 n n))))))

Outputs
(exp.f64 (.f64 -1/2 (.f64 (-.f64 1 k) (+.f64 (log.f64 (*.f64 2 (PI.f64))) (log.f64 n)))))
(exp.f64 (.f64 -1/2 (.f64 (-.f64 1 k) (+.f64 (log.f64 (*.f64 2 (PI.f64))) (log.f64 n)))))
(exp.f64 (.f64 -1/2 (.f64 (-.f64 1 k) (+.f64 (log.f64 (*.f64 2 (PI.f64))) (log.f64 n)))))
(exp.f64 (.f64 -1/2 (.f64 (-.f64 1 k) (+.f64 (log.f64 (*.f64 2 (PI.f64))) (log.f64 n)))))
(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 (log.f64 (.f64 2 (PI.f64))) (.f64 -1 (log.f64 (/.f64 1 n)))))))
(exp.f64 (.f64 (+.f64 (log.f64 (.f64 2 (PI.f64))) (neg.f64 (log.f64 (/.f64 1 n)))) (*.f64 -1/2 (-.f64 1 k))))
(exp.f64 (.f64 -1/2 (.f64 (-.f64 1 k) (+.f64 (log.f64 (*.f64 2 (PI.f64))) (neg.f64 (log.f64 (/.f64 1 n)))))))
(exp.f64 (.f64 (-.f64 1 k) (.f64 -1/2 (+.f64 (log.f64 (*.f64 2 (PI.f64))) (neg.f64 (log.f64 (/.f64 1 n)))))))
(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 (log.f64 (.f64 2 (PI.f64))) (.f64 -1 (log.f64 (/.f64 1 n)))))))
(exp.f64 (.f64 (+.f64 (log.f64 (.f64 2 (PI.f64))) (neg.f64 (log.f64 (/.f64 1 n)))) (*.f64 -1/2 (-.f64 1 k))))
(exp.f64 (.f64 -1/2 (.f64 (-.f64 1 k) (+.f64 (log.f64 (*.f64 2 (PI.f64))) (neg.f64 (log.f64 (/.f64 1 n)))))))
(exp.f64 (.f64 (-.f64 1 k) (.f64 -1/2 (+.f64 (log.f64 (*.f64 2 (PI.f64))) (neg.f64 (log.f64 (/.f64 1 n)))))))
(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 (log.f64 (.f64 2 (PI.f64))) (.f64 -1 (log.f64 (/.f64 1 n)))))))
(exp.f64 (.f64 (+.f64 (log.f64 (.f64 2 (PI.f64))) (neg.f64 (log.f64 (/.f64 1 n)))) (*.f64 -1/2 (-.f64 1 k))))
(exp.f64 (.f64 -1/2 (.f64 (-.f64 1 k) (+.f64 (log.f64 (*.f64 2 (PI.f64))) (neg.f64 (log.f64 (/.f64 1 n)))))))
(exp.f64 (.f64 (-.f64 1 k) (.f64 -1/2 (+.f64 (log.f64 (*.f64 2 (PI.f64))) (neg.f64 (log.f64 (/.f64 1 n)))))))
(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 (log.f64 (.f64 2 (PI.f64))) (.f64 -1 (log.f64 (/.f64 1 n)))))))
(exp.f64 (.f64 (+.f64 (log.f64 (.f64 2 (PI.f64))) (neg.f64 (log.f64 (/.f64 1 n)))) (*.f64 -1/2 (-.f64 1 k))))
(exp.f64 (.f64 -1/2 (.f64 (-.f64 1 k) (+.f64 (log.f64 (*.f64 2 (PI.f64))) (neg.f64 (log.f64 (/.f64 1 n)))))))
(exp.f64 (.f64 (-.f64 1 k) (.f64 -1/2 (+.f64 (log.f64 (*.f64 2 (PI.f64))) (neg.f64 (log.f64 (/.f64 1 n)))))))
(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 (PI.f64) -2))))))
(exp.f64 (.f64 (-.f64 1 k) (.f64 -1/2 (+.f64 (neg.f64 (log.f64 (/.f64 -1 n))) (log.f64 (*.f64 (PI.f64) -2))))))
(exp.f64 (.f64 -1/2 (.f64 (-.f64 1 k) (+.f64 (neg.f64 (log.f64 (/.f64 -1 n))) (log.f64 (*.f64 (PI.f64) -2))))))
(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 (PI.f64) -2))))))
(exp.f64 (.f64 (-.f64 1 k) (.f64 -1/2 (+.f64 (neg.f64 (log.f64 (/.f64 -1 n))) (log.f64 (*.f64 (PI.f64) -2))))))
(exp.f64 (.f64 -1/2 (.f64 (-.f64 1 k) (+.f64 (neg.f64 (log.f64 (/.f64 -1 n))) (log.f64 (*.f64 (PI.f64) -2))))))
(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 (PI.f64) -2))))))
(exp.f64 (.f64 (-.f64 1 k) (.f64 -1/2 (+.f64 (neg.f64 (log.f64 (/.f64 -1 n))) (log.f64 (*.f64 (PI.f64) -2))))))
(exp.f64 (.f64 -1/2 (.f64 (-.f64 1 k) (+.f64 (neg.f64 (log.f64 (/.f64 -1 n))) (log.f64 (*.f64 (PI.f64) -2))))))
(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 (PI.f64) -2))))))
(exp.f64 (.f64 (-.f64 1 k) (.f64 -1/2 (+.f64 (neg.f64 (log.f64 (/.f64 -1 n))) (log.f64 (*.f64 (PI.f64) -2))))))
(exp.f64 (.f64 -1/2 (.f64 (-.f64 1 k) (+.f64 (neg.f64 (log.f64 (/.f64 -1 n))) (log.f64 (*.f64 (PI.f64) -2))))))
(.f64 (sqrt.f64 (/.f64 1 (.f64 n (PI.f64)))) (sqrt.f64 1/2))
(sqrt.f64 (.f64 1/2 (/.f64 1 (.f64 (PI.f64) n))))
(sqrt.f64 (.f64 (/.f64 1 (.f64 (PI.f64) n)) 1/2))
(+.f64 (.f64 1/2 (.f64 (.f64 k (.f64 (sqrt.f64 1/2) (log.f64 (.f64 2 (.f64 n (PI.f64)))))) (sqrt.f64 (/.f64 1 (.f64 n (PI.f64)))))) (.f64 (sqrt.f64 (/.f64 1 (*.f64 n (PI.f64)))) (sqrt.f64 1/2)))
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(.f64 (/.f64 (exp.f64 (neg.f64 (/.f64 (.f64 (-.f64 1 k) (log.f64 (.f64 (PI.f64) (+.f64 n n)))) -2))) (exp.f64 (.f64 2 (/.f64 (.f64 (-.f64 1 k) (log.f64 (.f64 (PI.f64) (+.f64 n n)))) -2)))) (exp.f64 (.f64 (/.f64 (.f64 (-.f64 1 k) (log.f64 (*.f64 (PI.f64) (+.f64 n n)))) -2) 4)))
(.f64 (/.f64 (/.f64 (exp.f64 (/.f64 (.f64 (-.f64 1 k) (log.f64 (.f64 (PI.f64) (+.f64 n n)))) -2)) (exp.f64 (/.f64 (.f64 (-.f64 1 k) (log.f64 (.f64 (PI.f64) (+.f64 n n)))) -2))) (exp.f64 (/.f64 (.f64 (-.f64 1 k) (log.f64 (.f64 (PI.f64) (+.f64 n n)))) -2))) (exp.f64 (.f64 (/.f64 (.f64 (-.f64 1 k) (log.f64 (.f64 (PI.f64) (+.f64 n n)))) -2) 2)))
(.f64 (exp.f64 (.f64 2 (/.f64 (.f64 (-.f64 1 k) (log.f64 (.f64 (PI.f64) (+.f64 n n)))) -2))) (/.f64 (/.f64 (exp.f64 (/.f64 (.f64 (-.f64 1 k) (log.f64 (.f64 (PI.f64) (+.f64 n n)))) -2)) (exp.f64 (/.f64 (.f64 (-.f64 1 k) (log.f64 (.f64 (PI.f64) (+.f64 n n)))) -2))) (exp.f64 (/.f64 (.f64 (-.f64 1 k) (log.f64 (.f64 (PI.f64) (+.f64 n n)))) -2))))
(.f64 (/.f64 (exp.f64 (+.f64 (neg.f64 (/.f64 (.f64 (-.f64 1 k) (log.f64 (.f64 (PI.f64) (+.f64 n n)))) -2)) (/.f64 (.f64 (-.f64 1 k) (log.f64 (.f64 (PI.f64) (+.f64 n n)))) -2))) (exp.f64 (/.f64 (.f64 (-.f64 1 k) (log.f64 (.f64 (PI.f64) (+.f64 n n)))) -2))) (exp.f64 (.f64 (/.f64 (.f64 (-.f64 1 k) (log.f64 (.f64 (PI.f64) (+.f64 n n)))) -2) 2)))
(.f64 (exp.f64 (.f64 2 (/.f64 (.f64 (-.f64 1 k) (log.f64 (.f64 (PI.f64) (+.f64 n n)))) -2))) (/.f64 (exp.f64 (+.f64 (/.f64 (.f64 (-.f64 1 k) (log.f64 (.f64 (PI.f64) (+.f64 n n)))) -2) (neg.f64 (/.f64 (.f64 (-.f64 1 k) (log.f64 (.f64 (PI.f64) (+.f64 n n)))) -2)))) (exp.f64 (/.f64 (.f64 (-.f64 1 k) (log.f64 (.f64 (PI.f64) (+.f64 n n)))) -2))))
(/.f64 (exp.f64 (/.f64 (.f64 (-.f64 1 k) (log.f64 (.f64 (PI.f64) (+.f64 n n)))) -2)) 1)
(exp.f64 (/.f64 (.f64 (-.f64 1 k) (log.f64 (.f64 (PI.f64) (+.f64 n n)))) -2))
(/.f64 (exp.f64 (/.f64 (.f64 (-.f64 1 k) (log.f64 (.f64 (PI.f64) (+.f64 n n)))) -2)) (/.f64 (exp.f64 (/.f64 (.f64 (-.f64 1 k) (log.f64 (.f64 (PI.f64) (+.f64 n n)))) -2)) (exp.f64 (/.f64 (.f64 (-.f64 1 k) (log.f64 (.f64 (PI.f64) (+.f64 n n)))) -2))))
(exp.f64 (/.f64 (.f64 (-.f64 1 k) (log.f64 (.f64 (PI.f64) (+.f64 n n)))) -2))
(/.f64 (.f64 (exp.f64 (/.f64 (.f64 (-.f64 1 k) (log.f64 (*.f64 (PI.f64) (+.f64 n n)))) -2)) 2) 2)
(exp.f64 (/.f64 (.f64 (-.f64 1 k) (log.f64 (.f64 (PI.f64) (+.f64 n n)))) -2))
(pow.f64 (exp.f64 (/.f64 (.f64 (-.f64 1 k) (log.f64 (.f64 (PI.f64) (+.f64 n n)))) -2)) 1)
(exp.f64 (/.f64 (.f64 (-.f64 1 k) (log.f64 (.f64 (PI.f64) (+.f64 n n)))) -2))
(neg.f64 (neg.f64 (exp.f64 (/.f64 (.f64 (-.f64 1 k) (log.f64 (.f64 (PI.f64) (+.f64 n n)))) -2))))
(exp.f64 (/.f64 (.f64 (-.f64 1 k) (log.f64 (.f64 (PI.f64) (+.f64 n n)))) -2))
(+.f64 (.f64 (pow.f64 (.f64 (PI.f64) (+.f64 n n)) (-.f64 1 k)) (exp.f64 (/.f64 (.f64 (-.f64 1 k) (log.f64 (.f64 (PI.f64) (+.f64 n n)))) -2))) 0)
(.f64 (exp.f64 (/.f64 (.f64 (-.f64 1 k) (log.f64 (.f64 (PI.f64) (+.f64 n n)))) -2)) (pow.f64 (.f64 (PI.f64) (+.f64 n n)) (-.f64 1 k)))
(+.f64 0 (.f64 (pow.f64 (.f64 (PI.f64) (+.f64 n n)) (-.f64 1 k)) (exp.f64 (/.f64 (.f64 (-.f64 1 k) (log.f64 (.f64 (PI.f64) (+.f64 n n)))) -2))))
(.f64 (exp.f64 (/.f64 (.f64 (-.f64 1 k) (log.f64 (.f64 (PI.f64) (+.f64 n n)))) -2)) (pow.f64 (.f64 (PI.f64) (+.f64 n n)) (-.f64 1 k)))
(-.f64 (.f64 (pow.f64 (.f64 (PI.f64) (+.f64 n n)) (-.f64 1 k)) (exp.f64 (/.f64 (.f64 (-.f64 1 k) (log.f64 (.f64 (PI.f64) (+.f64 n n)))) -2))) 0)
(.f64 (exp.f64 (/.f64 (.f64 (-.f64 1 k) (log.f64 (.f64 (PI.f64) (+.f64 n n)))) -2)) (pow.f64 (.f64 (PI.f64) (+.f64 n n)) (-.f64 1 k)))
(-.f64 0 (neg.f64 (.f64 (pow.f64 (.f64 (PI.f64) (+.f64 n n)) (-.f64 1 k)) (exp.f64 (/.f64 (.f64 (-.f64 1 k) (log.f64 (.f64 (PI.f64) (+.f64 n n)))) -2)))))
(.f64 (exp.f64 (/.f64 (.f64 (-.f64 1 k) (log.f64 (.f64 (PI.f64) (+.f64 n n)))) -2)) (pow.f64 (.f64 (PI.f64) (+.f64 n n)) (-.f64 1 k)))
(/.f64 (.f64 (pow.f64 (.f64 (PI.f64) (+.f64 n n)) (-.f64 1 k)) (exp.f64 (/.f64 (.f64 (-.f64 1 k) (log.f64 (.f64 (PI.f64) (+.f64 n n)))) -2))) 1)
(.f64 (exp.f64 (/.f64 (.f64 (-.f64 1 k) (log.f64 (.f64 (PI.f64) (+.f64 n n)))) -2)) (pow.f64 (.f64 (PI.f64) (+.f64 n n)) (-.f64 1 k)))
(/.f64 (.f64 (pow.f64 (.f64 (PI.f64) (+.f64 n n)) (-.f64 1 k)) (exp.f64 (/.f64 (.f64 (-.f64 1 k) (log.f64 (.f64 (PI.f64) (+.f64 n n)))) -2))) (/.f64 (.f64 (pow.f64 (.f64 (PI.f64) (+.f64 n n)) (-.f64 1 k)) (exp.f64 (/.f64 (.f64 (-.f64 1 k) (log.f64 (.f64 (PI.f64) (+.f64 n n)))) -2))) (.f64 (pow.f64 (.f64 (PI.f64) (+.f64 n n)) (-.f64 1 k)) (exp.f64 (/.f64 (.f64 (-.f64 1 k) (log.f64 (.f64 (PI.f64) (+.f64 n n)))) -2)))))
(.f64 (exp.f64 (/.f64 (.f64 (-.f64 1 k) (log.f64 (.f64 (PI.f64) (+.f64 n n)))) -2)) (pow.f64 (.f64 (PI.f64) (+.f64 n n)) (-.f64 1 k)))
(/.f64 (.f64 (exp.f64 (/.f64 (.f64 (-.f64 1 k) (log.f64 (.f64 (PI.f64) (+.f64 n n)))) -2)) (.f64 (pow.f64 (*.f64 (PI.f64) (+.f64 n n)) (-.f64 1 k)) 2)) 2)
(.f64 (exp.f64 (/.f64 (.f64 (-.f64 1 k) (log.f64 (.f64 (PI.f64) (+.f64 n n)))) -2)) (pow.f64 (.f64 (PI.f64) (+.f64 n n)) (-.f64 1 k)))
(pow.f64 (.f64 (pow.f64 (.f64 (PI.f64) (+.f64 n n)) (-.f64 1 k)) (exp.f64 (/.f64 (.f64 (-.f64 1 k) (log.f64 (.f64 (PI.f64) (+.f64 n n)))) -2))) 1)
(.f64 (exp.f64 (/.f64 (.f64 (-.f64 1 k) (log.f64 (.f64 (PI.f64) (+.f64 n n)))) -2)) (pow.f64 (.f64 (PI.f64) (+.f64 n n)) (-.f64 1 k)))
(neg.f64 (neg.f64 (.f64 (pow.f64 (.f64 (PI.f64) (+.f64 n n)) (-.f64 1 k)) (exp.f64 (/.f64 (.f64 (-.f64 1 k) (log.f64 (.f64 (PI.f64) (+.f64 n n)))) -2)))))
(.f64 (exp.f64 (/.f64 (.f64 (-.f64 1 k) (log.f64 (.f64 (PI.f64) (+.f64 n n)))) -2)) (pow.f64 (.f64 (PI.f64) (+.f64 n n)) (-.f64 1 k)))
(+.f64 (*.f64 (PI.f64) (+.f64 n n)) 0)
(*.f64 (PI.f64) (+.f64 n n))
(+.f64 0 (*.f64 (PI.f64) (+.f64 n n)))
(*.f64 (PI.f64) (+.f64 n n))
(-.f64 (*.f64 (PI.f64) (+.f64 n n)) 0)
(*.f64 (PI.f64) (+.f64 n n))
(-.f64 0 (neg.f64 (*.f64 (PI.f64) (+.f64 n n))))
(*.f64 (PI.f64) (+.f64 n n))
(/.f64 (*.f64 (PI.f64) (+.f64 n n)) 1)
(*.f64 (PI.f64) (+.f64 n n))
(/.f64 (.f64 (PI.f64) (+.f64 n n)) (/.f64 (.f64 (PI.f64) (.f64 n 4)) (.f64 (PI.f64) (*.f64 n 4))))
(/.f64 (.f64 (PI.f64) (.f64 n 4)) 2)
(pow.f64 (*.f64 (PI.f64) (+.f64 n n)) 1)
(*.f64 (PI.f64) (+.f64 n n))
(neg.f64 (neg.f64 (*.f64 (PI.f64) (+.f64 n n))))
(*.f64 (PI.f64) (+.f64 n n))
(+.f64 (.f64 (-.f64 1 k) (log.f64 (.f64 (PI.f64) (+.f64 n n)))) 0)
(.f64 (-.f64 1 k) (log.f64 (.f64 (PI.f64) (+.f64 n n))))
(+.f64 0 (.f64 (-.f64 1 k) (log.f64 (.f64 (PI.f64) (+.f64 n n)))))
(.f64 (-.f64 1 k) (log.f64 (.f64 (PI.f64) (+.f64 n n))))
(-.f64 (.f64 (-.f64 1 k) (log.f64 (.f64 (PI.f64) (+.f64 n n)))) 0)
(.f64 (-.f64 1 k) (log.f64 (.f64 (PI.f64) (+.f64 n n))))
(-.f64 0 (neg.f64 (.f64 (-.f64 1 k) (log.f64 (.f64 (PI.f64) (+.f64 n n))))))
(.f64 (-.f64 1 k) (log.f64 (.f64 (PI.f64) (+.f64 n n))))
(.f64 1 (.f64 (-.f64 1 k) (log.f64 (*.f64 (PI.f64) (+.f64 n n)))))
(.f64 (-.f64 1 k) (log.f64 (.f64 (PI.f64) (+.f64 n n))))
(.f64 (-.f64 1 k) (log.f64 (.f64 (PI.f64) (+.f64 n n))))
(.f64 (.f64 (-.f64 1 k) (log.f64 (*.f64 (PI.f64) (+.f64 n n)))) 1)
(.f64 (-.f64 1 k) (log.f64 (.f64 (PI.f64) (+.f64 n n))))
(.f64 (.f64 (-.f64 1 k) (log.f64 (.f64 (PI.f64) (+.f64 n n)))) (/.f64 (.f64 (-.f64 1 k) (log.f64 (.f64 (PI.f64) (+.f64 n n)))) (.f64 (-.f64 1 k) (log.f64 (*.f64 (PI.f64) (+.f64 n n))))))
(.f64 (-.f64 1 k) (log.f64 (.f64 (PI.f64) (+.f64 n n))))
(.f64 (.f64 (-.f64 1 k) (log.f64 (.f64 (PI.f64) (+.f64 n n)))) (.f64 (.f64 (-.f64 1 k) (log.f64 (.f64 (PI.f64) (+.f64 n n)))) (/.f64 1 (.f64 (-.f64 1 k) (log.f64 (.f64 (PI.f64) (+.f64 n n)))))))
(.f64 (-.f64 1 k) (log.f64 (.f64 (PI.f64) (+.f64 n n))))
(.f64 (.f64 (-.f64 1 k) (log.f64 (.f64 (PI.f64) (+.f64 n n)))) (/.f64 1 (/.f64 (.f64 (-.f64 1 k) (log.f64 (.f64 (PI.f64) (+.f64 n n)))) (.f64 (-.f64 1 k) (log.f64 (*.f64 (PI.f64) (+.f64 n n)))))))
(.f64 (-.f64 1 k) (log.f64 (.f64 (PI.f64) (+.f64 n n))))
(.f64 (/.f64 (.f64 (-.f64 1 k) (log.f64 (.f64 (PI.f64) (+.f64 n n)))) (.f64 (-.f64 1 k) (log.f64 (.f64 (PI.f64) (+.f64 n n))))) (.f64 (-.f64 1 k) (log.f64 (*.f64 (PI.f64) (+.f64 n n)))))
(.f64 (-.f64 1 k) (log.f64 (.f64 (PI.f64) (+.f64 n n))))
(.f64 (/.f64 1 (.f64 (-.f64 1 k) (log.f64 (.f64 (PI.f64) (+.f64 n n))))) (.f64 (.f64 (-.f64 1 k) (log.f64 (.f64 (PI.f64) (+.f64 n n)))) (.f64 (-.f64 1 k) (log.f64 (.f64 (PI.f64) (+.f64 n n))))))
(.f64 (-.f64 1 k) (log.f64 (.f64 (PI.f64) (+.f64 n n))))
(.f64 (.f64 (.f64 (-.f64 1 k) (log.f64 (.f64 (PI.f64) (+.f64 n n)))) (.f64 (-.f64 1 k) (log.f64 (.f64 (PI.f64) (+.f64 n n))))) (/.f64 1 (.f64 (-.f64 1 k) (log.f64 (.f64 (PI.f64) (+.f64 n n))))))
(.f64 (-.f64 1 k) (log.f64 (.f64 (PI.f64) (+.f64 n n))))
(.f64 (.f64 (.f64 (-.f64 1 k) (log.f64 (.f64 (PI.f64) (+.f64 n n)))) (/.f64 1 (.f64 (-.f64 1 k) (log.f64 (.f64 (PI.f64) (+.f64 n n)))))) (.f64 (-.f64 1 k) (log.f64 (.f64 (PI.f64) (+.f64 n n)))))
(.f64 (-.f64 1 k) (log.f64 (.f64 (PI.f64) (+.f64 n n))))
(.f64 (log.f64 (.f64 (PI.f64) (+.f64 n n))) (-.f64 1 k))
(.f64 (-.f64 1 k) (log.f64 (.f64 (PI.f64) (+.f64 n n))))
(.f64 (/.f64 (/.f64 1 (.f64 (-.f64 1 k) (log.f64 (.f64 (PI.f64) (+.f64 n n))))) (.f64 (.f64 (-.f64 1 k) (log.f64 (.f64 (PI.f64) (+.f64 n n)))) (.f64 (-.f64 1 k) (log.f64 (.f64 (PI.f64) (+.f64 n n)))))) (.f64 (.f64 (.f64 (-.f64 1 k) (log.f64 (.f64 (PI.f64) (+.f64 n n)))) (.f64 (-.f64 1 k) (log.f64 (.f64 (PI.f64) (+.f64 n n))))) (.f64 (.f64 (-.f64 1 k) (log.f64 (.f64 (PI.f64) (+.f64 n n)))) (.f64 (-.f64 1 k) (log.f64 (*.f64 (PI.f64) (+.f64 n n)))))))
(.f64 (-.f64 1 k) (log.f64 (.f64 (PI.f64) (+.f64 n n))))
(.f64 (/.f64 (/.f64 (.f64 (-.f64 1 k) (log.f64 (.f64 (PI.f64) (+.f64 n n)))) (.f64 (-.f64 1 k) (log.f64 (.f64 (PI.f64) (+.f64 n n))))) (.f64 (-.f64 1 k) (log.f64 (.f64 (PI.f64) (+.f64 n n))))) (.f64 (.f64 (-.f64 1 k) (log.f64 (.f64 (PI.f64) (+.f64 n n)))) (.f64 (-.f64 1 k) (log.f64 (.f64 (PI.f64) (+.f64 n n))))))
(.f64 (-.f64 1 k) (log.f64 (.f64 (PI.f64) (+.f64 n n))))
(.f64 (/.f64 (.f64 (.f64 (-.f64 1 k) (log.f64 (.f64 (PI.f64) (+.f64 n n)))) (/.f64 1 (.f64 (-.f64 1 k) (log.f64 (.f64 (PI.f64) (+.f64 n n)))))) (.f64 (-.f64 1 k) (log.f64 (.f64 (PI.f64) (+.f64 n n))))) (.f64 (.f64 (-.f64 1 k) (log.f64 (.f64 (PI.f64) (+.f64 n n)))) (.f64 (-.f64 1 k) (log.f64 (*.f64 (PI.f64) (+.f64 n n))))))
(.f64 (-.f64 1 k) (log.f64 (.f64 (PI.f64) (+.f64 n n))))
(/.f64 (.f64 (-.f64 1 k) (log.f64 (.f64 (PI.f64) (+.f64 n n)))) 1)
(.f64 (-.f64 1 k) (log.f64 (.f64 (PI.f64) (+.f64 n n))))
(/.f64 (.f64 (-.f64 1 k) (log.f64 (.f64 (PI.f64) (+.f64 n n)))) (/.f64 (.f64 (-.f64 1 k) (log.f64 (.f64 (PI.f64) (+.f64 n n)))) (.f64 (-.f64 1 k) (log.f64 (.f64 (PI.f64) (+.f64 n n))))))
(.f64 (-.f64 1 k) (log.f64 (.f64 (PI.f64) (+.f64 n n))))
(/.f64 (.f64 (.f64 (-.f64 1 k) (log.f64 (*.f64 (PI.f64) (+.f64 n n)))) 2) 2)
(.f64 (-.f64 1 k) (log.f64 (.f64 (PI.f64) (+.f64 n n))))
(pow.f64 (.f64 (-.f64 1 k) (log.f64 (.f64 (PI.f64) (+.f64 n n)))) 1)
(.f64 (-.f64 1 k) (log.f64 (.f64 (PI.f64) (+.f64 n n))))
(neg.f64 (neg.f64 (.f64 (-.f64 1 k) (log.f64 (.f64 (PI.f64) (+.f64 n n))))))
(.f64 (-.f64 1 k) (log.f64 (.f64 (PI.f64) (+.f64 n n))))

eval237.0ms (1.6%)

Compiler: Compiled 17005 to 10593 computations (37.7% saved)

prune109.0ms (0.8%)

Pruning

26 alts after pruning (19 fresh and 7 done)

	Pruned	Kept	Total
New	464	12	476
Fresh	3	7	10
Picked	1	0	1
Done	0	7	7
Total	468	26	494

Error

0.0b

Counts

494 → 26

Alt Table

Click to see full alt table

Status	Error	Program
	22.2b	(/.f64 (.f64 (/.f64 1 (sqrt.f64 k)) (.f64 (sqrt.f64 (.f64 2 (.f64 (PI.f64) n))) (+.f64 1 (+.f64 1 (.f64 k (neg.f64 (log.f64 (.f64 2 (*.f64 (PI.f64) n))))))))) 2)
	22.1b	(/.f64 (.f64 (+.f64 1 (.f64 k (.f64 (log.f64 (.f64 2 (.f64 (PI.f64) n))) -1/2))) (.f64 (/.f64 1 (sqrt.f64 k)) (sqrt.f64 (.f64 2 (.f64 (PI.f64) n))))) 1)
	22.3b	(/.f64 (.f64 (.f64 (sqrt.f64 2) (+.f64 (.f64 (log.f64 (.f64 (PI.f64) (+.f64 n n))) (.f64 k -1/2)) 1)) (.f64 (/.f64 1 (sqrt.f64 k)) (.f64 (sqrt.f64 (.f64 n (PI.f64))) 2))) 2)
✓	21.1b	(.f64 (/.f64 1 (sqrt.f64 k)) (pow.f64 (.f64 (/.f64 2 (.f64 n (PI.f64))) (.f64 n (*.f64 n (pow.f64 (PI.f64) 2)))) (/.f64 (-.f64 1 k) 2)))
✓	0.4b	(.f64 (/.f64 1 (sqrt.f64 k)) (pow.f64 (.f64 (*.f64 2 (PI.f64)) n) (/.f64 (-.f64 1 k) 2)))
▶	0.5b	(.f64 (/.f64 1 (sqrt.f64 k)) (pow.f64 (.f64 n (.f64 (/.f64 2 (.f64 n (PI.f64))) (*.f64 n (pow.f64 (PI.f64) 2)))) (/.f64 (-.f64 1 k) 2)))
	22.3b	(.f64 (/.f64 1 (sqrt.f64 k)) (+.f64 (.f64 (sqrt.f64 (.f64 n (PI.f64))) (+.f64 (.f64 (log.f64 (.f64 (PI.f64) (.f64 2 n))) (.f64 -1/2 (.f64 k (sqrt.f64 2)))) (sqrt.f64 2))) (.f64 1/8 (.f64 (sqrt.f64 (.f64 (PI.f64) (.f64 2 n))) (pow.f64 (.f64 k (log.f64 (.f64 (PI.f64) (*.f64 2 n)))) 2)))))
▶	1.9b	(.f64 (/.f64 1 (sqrt.f64 k)) (.f64 (pow.f64 (.f64 (PI.f64) (+.f64 n n)) (-.f64 1 k)) (.f64 (sqrt.f64 (/.f64 1 (*.f64 n (PI.f64)))) (sqrt.f64 1/2))))
	24.6b	(.f64 (/.f64 1 (sqrt.f64 k)) (.f64 (pow.f64 (.f64 (PI.f64) (+.f64 n n)) (-.f64 1 k)) (.f64 (exp.f64 (.f64 (/.f64 (.f64 (-.f64 1 k) (log.f64 (.f64 (PI.f64) (+.f64 n n)))) -2) 2)) (exp.f64 (neg.f64 (/.f64 (.f64 (-.f64 1 k) (log.f64 (*.f64 (PI.f64) (+.f64 n n)))) -2))))))
	24.6b	(.f64 (/.f64 1 (sqrt.f64 k)) (.f64 (pow.f64 (.f64 (PI.f64) (+.f64 n n)) (-.f64 1 k)) (exp.f64 (/.f64 (.f64 (-.f64 1 k) (log.f64 (*.f64 (PI.f64) (+.f64 n n)))) -2))))
	43.8b	(.f64 (/.f64 1 (sqrt.f64 k)) (.f64 (/.f64 (exp.f64 (/.f64 (log.f64 (pow.f64 (.f64 (PI.f64) (+.f64 n n)) (-.f64 1 k))) -2)) (pow.f64 (.f64 (PI.f64) (+.f64 n n)) (-.f64 1 k))) (pow.f64 (.f64 (.f64 n (PI.f64)) (.f64 n (.f64 (PI.f64) 4))) (-.f64 1 k))))
	42.7b	(.f64 (/.f64 1 (sqrt.f64 k)) (.f64 (/.f64 1 (sqrt.f64 (.f64 (PI.f64) (+.f64 n n)))) (sqrt.f64 (.f64 (.f64 (PI.f64) n) (.f64 (*.f64 (PI.f64) n) 4)))))
▶	22.2b	(.f64 (/.f64 1 (sqrt.f64 k)) (.f64 (+.f64 1 (.f64 (log.f64 (.f64 (PI.f64) (+.f64 n n))) (.f64 k -1/2))) (sqrt.f64 (.f64 2 (*.f64 n (PI.f64))))))
	22.3b	(.f64 (/.f64 1 (sqrt.f64 k)) (.f64 (sqrt.f64 (.f64 n (PI.f64))) (+.f64 (.f64 (sqrt.f64 2) (+.f64 (.f64 k (.f64 -1/2 (log.f64 (.f64 2 (.f64 n (PI.f64)))))) (.f64 1/8 (pow.f64 (.f64 k (log.f64 (.f64 2 (.f64 n (PI.f64))))) 2)))) (sqrt.f64 2))))
✓	22.4b	(.f64 (/.f64 1 (sqrt.f64 k)) (.f64 (sqrt.f64 2) (sqrt.f64 (*.f64 n (PI.f64)))))
✓	22.3b	(.f64 (/.f64 1 (sqrt.f64 k)) (sqrt.f64 (.f64 (PI.f64) (*.f64 2 n))))
✓	3.4b	(.f64 (/.f64 1 (sqrt.f64 k)) (exp.f64 (.f64 1/2 (.f64 (-.f64 1 k) (log.f64 (.f64 2 (*.f64 n (PI.f64))))))))
✓	0.6b	(.f64 (.f64 (/.f64 1 (/.f64 1 (sqrt.f64 k))) (/.f64 1 k)) (pow.f64 (.f64 (.f64 2 (PI.f64)) n) (/.f64 (-.f64 1 k) 2)))
▶	42.7b	(.f64 (.f64 (/.f64 1 (/.f64 1 (sqrt.f64 k))) (/.f64 1 k)) (.f64 (pow.f64 (.f64 (.f64 2 (.f64 (PI.f64) n)) (.f64 2 (.f64 (PI.f64) n))) (/.f64 (-.f64 1 k) 2)) (/.f64 1 (pow.f64 (.f64 2 (.f64 (PI.f64) n)) (/.f64 (-.f64 1 k) 2)))))
	22.5b	(.f64 (.f64 (/.f64 1 (/.f64 1 (sqrt.f64 k))) (/.f64 1 k)) (.f64 (sqrt.f64 2) (sqrt.f64 (.f64 n (PI.f64)))))
▶	22.5b	(.f64 (.f64 (/.f64 1 (/.f64 1 (sqrt.f64 k))) (/.f64 1 k)) (sqrt.f64 (.f64 (PI.f64) (.f64 2 n))))
	3.4b	(.f64 (.f64 (/.f64 1 (/.f64 1 (sqrt.f64 k))) (/.f64 1 k)) (exp.f64 (.f64 1/2 (.f64 (-.f64 1 k) (log.f64 (.f64 2 (.f64 n (PI.f64))))))))
	3.7b	(.f64 (sqrt.f64 (/.f64 1 k)) (exp.f64 (.f64 (-.f64 1 k) (.f64 1/2 (+.f64 (log.f64 (.f64 2 (PI.f64))) (log.f64 n))))))
✓	22.2b	(.f64 (sqrt.f64 (.f64 n (PI.f64))) (.f64 (/.f64 1 (sqrt.f64 k)) (.f64 (sqrt.f64 2) (+.f64 1 (.f64 (log.f64 (.f64 (PI.f64) (+.f64 n n))) (*.f64 k -1/2))))))
	22.2b	(.f64 (sqrt.f64 (.f64 n (PI.f64))) (.f64 (+.f64 1 (.f64 (+.f64 (log.f64 (.f64 2 (PI.f64))) (log.f64 n)) (.f64 k -1/2))) (*.f64 (sqrt.f64 (/.f64 1 k)) (sqrt.f64 2))))
	22.1b	(.f64 (sqrt.f64 (.f64 n (PI.f64))) (.f64 (+.f64 1 (.f64 k (.f64 -1/2 (+.f64 (log.f64 (.f64 2 (PI.f64))) (log.f64 n))))) (sqrt.f64 (*.f64 (/.f64 1 k) 2))))

Compiler

Compiled 1316 to 1010 computations (23.3% saved)

localize40.0ms (0.3%)

Local error

Found 4 expressions with local error:

New	Error	Program
	0.3b	(*.f64 n (PI.f64))
✓	0.3b	(.f64 n (.f64 (/.f64 2 (.f64 n (PI.f64))) (.f64 n (pow.f64 (PI.f64) 2))))
✓	0.4b	(.f64 (/.f64 2 (.f64 n (PI.f64))) (*.f64 n (pow.f64 (PI.f64) 2)))
	0.4b	(*.f64 n (pow.f64 (PI.f64) 2))

Compiler

Compiled 104 to 62 computations (40.4% saved)

series1.0ms (0%)

Counts

2 → 24

Calls

6 calls:

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

rewrite107.0ms (0.7%)

Algorithm

1×	batch-egg-rewrite

Rules

1220×	`rational_best-simplify-57`
712×	`rational_best-simplify-47`
700×	`rational_best-5`
698×	`rational_best-4`
698×	`rational_best-2`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	12	76
1	105	76
2	351	76
3	1485	76
4	6087	76

Stop Event

1×	node limit

Counts

2 → 18

Calls

Call 1

Inputs
(.f64 (/.f64 2 (.f64 n (PI.f64))) (*.f64 n (pow.f64 (PI.f64) 2)))
(.f64 n (.f64 (/.f64 2 (.f64 n (PI.f64))) (.f64 n (pow.f64 (PI.f64) 2))))

Outputs

((#(struct:change #<rule egg-rr> (2) ((x +.f64 (*.f64 n (*.f64 (/.f64 2 (*.f64 n (PI.f64))) (pow.f64 (PI.f64) 2))) 0)))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 0 (*.f64 n (*.f64 (/.f64 2 (*.f64 n (PI.f64))) (pow.f64 (PI.f64) 2))))))) (#(struct:change #<rule egg-rr> (2) ((x -.f64 (*.f64 n (*.f64 (/.f64 2 (*.f64 n (PI.f64))) (pow.f64 (PI.f64) 2))) 0)))) (#(struct:change #<rule egg-rr> (2) ((x -.f64 0 (neg.f64 (*.f64 n (*.f64 (/.f64 2 (*.f64 n (PI.f64))) (pow.f64 (PI.f64) 2)))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (*.f64 n (*.f64 (/.f64 2 (*.f64 n (PI.f64))) (pow.f64 (PI.f64) 2))) 1)))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (*.f64 n (*.f64 (/.f64 2 (*.f64 n (PI.f64))) (pow.f64 (PI.f64) 2))) (/.f64 (*.f64 n (*.f64 (/.f64 2 (*.f64 n (PI.f64))) (pow.f64 (PI.f64) 2))) (*.f64 n (*.f64 (/.f64 2 (*.f64 n (PI.f64))) (pow.f64 (PI.f64) 2)))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (*.f64 2 (*.f64 n (*.f64 (/.f64 2 (*.f64 n (PI.f64))) (pow.f64 (PI.f64) 2)))) 2)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (*.f64 n (*.f64 (/.f64 2 (*.f64 n (PI.f64))) (pow.f64 (PI.f64) 2))) 1)))) (#(struct:change #<rule egg-rr> (2) ((x neg.f64 (neg.f64 (*.f64 n (*.f64 (/.f64 2 (*.f64 n (PI.f64))) (pow.f64 (PI.f64) 2)))))))))

((#(struct:change #<rule egg-rr> (2) ((x +.f64 (*.f64 (/.f64 2 (*.f64 n (PI.f64))) (*.f64 (pow.f64 (PI.f64) 2) (*.f64 n n))) 0)))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 0 (*.f64 (/.f64 2 (*.f64 n (PI.f64))) (*.f64 (pow.f64 (PI.f64) 2) (*.f64 n n))))))) (#(struct:change #<rule egg-rr> (2) ((x -.f64 (*.f64 (/.f64 2 (*.f64 n (PI.f64))) (*.f64 (pow.f64 (PI.f64) 2) (*.f64 n n))) 0)))) (#(struct:change #<rule egg-rr> (2) ((x -.f64 0 (neg.f64 (*.f64 (/.f64 2 (*.f64 n (PI.f64))) (*.f64 (pow.f64 (PI.f64) 2) (*.f64 n n)))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (*.f64 (/.f64 2 (*.f64 n (PI.f64))) (*.f64 (pow.f64 (PI.f64) 2) (*.f64 n n))) 1)))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (*.f64 (/.f64 2 (*.f64 n (PI.f64))) (*.f64 (pow.f64 (PI.f64) 2) (*.f64 n n))) (/.f64 (*.f64 (/.f64 2 (*.f64 n (PI.f64))) (*.f64 (pow.f64 (PI.f64) 2) (*.f64 n n))) (*.f64 (/.f64 2 (*.f64 n (PI.f64))) (*.f64 (pow.f64 (PI.f64) 2) (*.f64 n n)))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (*.f64 2 (*.f64 (/.f64 2 (*.f64 n (PI.f64))) (*.f64 (pow.f64 (PI.f64) 2) (*.f64 n n)))) 2)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (*.f64 (/.f64 2 (*.f64 n (PI.f64))) (*.f64 (pow.f64 (PI.f64) 2) (*.f64 n n))) 1)))) (#(struct:change #<rule egg-rr> (2) ((x neg.f64 (neg.f64 (*.f64 (/.f64 2 (*.f64 n (PI.f64))) (*.f64 (pow.f64 (PI.f64) 2) (*.f64 n n)))))))))

simplify188.0ms (1.3%)

Algorithm

1×	egg-herbie

Rules

1364×	`rational_best-simplify-132`
1308×	`rational_best-simplify-44`
1140×	`rational_best-simplify-80`
1068×	`rational_best-simplify-78`
1068×	`rational_best-simplify-76`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	43	972
1	87	972
2	212	972
3	596	972
4	3628	972
5	7302	972

Stop Event

1×	node limit

Counts

42 → 25

Calls

Call 1

Inputs
(*.f64 2 (PI.f64))
(*.f64 2 (PI.f64))
(*.f64 2 (PI.f64))
(*.f64 2 (PI.f64))
(*.f64 2 (PI.f64))
(*.f64 2 (PI.f64))
(*.f64 2 (PI.f64))
(*.f64 2 (PI.f64))
(*.f64 2 (PI.f64))
(*.f64 2 (PI.f64))
(*.f64 2 (PI.f64))
(*.f64 2 (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 (.f64 n (.f64 (/.f64 2 (*.f64 n (PI.f64))) (pow.f64 (PI.f64) 2))) 0)
(+.f64 0 (.f64 n (.f64 (/.f64 2 (*.f64 n (PI.f64))) (pow.f64 (PI.f64) 2))))
(-.f64 (.f64 n (.f64 (/.f64 2 (*.f64 n (PI.f64))) (pow.f64 (PI.f64) 2))) 0)
(-.f64 0 (neg.f64 (.f64 n (.f64 (/.f64 2 (*.f64 n (PI.f64))) (pow.f64 (PI.f64) 2)))))
(/.f64 (.f64 n (.f64 (/.f64 2 (*.f64 n (PI.f64))) (pow.f64 (PI.f64) 2))) 1)
(/.f64 (.f64 n (.f64 (/.f64 2 (.f64 n (PI.f64))) (pow.f64 (PI.f64) 2))) (/.f64 (.f64 n (.f64 (/.f64 2 (.f64 n (PI.f64))) (pow.f64 (PI.f64) 2))) (.f64 n (.f64 (/.f64 2 (*.f64 n (PI.f64))) (pow.f64 (PI.f64) 2)))))
(/.f64 (.f64 2 (.f64 n (.f64 (/.f64 2 (.f64 n (PI.f64))) (pow.f64 (PI.f64) 2)))) 2)
(pow.f64 (.f64 n (.f64 (/.f64 2 (*.f64 n (PI.f64))) (pow.f64 (PI.f64) 2))) 1)
(neg.f64 (neg.f64 (.f64 n (.f64 (/.f64 2 (*.f64 n (PI.f64))) (pow.f64 (PI.f64) 2)))))
(+.f64 (.f64 (/.f64 2 (.f64 n (PI.f64))) (.f64 (pow.f64 (PI.f64) 2) (.f64 n n))) 0)
(+.f64 0 (.f64 (/.f64 2 (.f64 n (PI.f64))) (.f64 (pow.f64 (PI.f64) 2) (.f64 n n))))
(-.f64 (.f64 (/.f64 2 (.f64 n (PI.f64))) (.f64 (pow.f64 (PI.f64) 2) (.f64 n n))) 0)
(-.f64 0 (neg.f64 (.f64 (/.f64 2 (.f64 n (PI.f64))) (.f64 (pow.f64 (PI.f64) 2) (.f64 n n)))))
(/.f64 (.f64 (/.f64 2 (.f64 n (PI.f64))) (.f64 (pow.f64 (PI.f64) 2) (.f64 n n))) 1)
(/.f64 (.f64 (/.f64 2 (.f64 n (PI.f64))) (.f64 (pow.f64 (PI.f64) 2) (.f64 n n))) (/.f64 (.f64 (/.f64 2 (.f64 n (PI.f64))) (.f64 (pow.f64 (PI.f64) 2) (.f64 n n))) (.f64 (/.f64 2 (.f64 n (PI.f64))) (.f64 (pow.f64 (PI.f64) 2) (.f64 n n)))))
(/.f64 (.f64 2 (.f64 (/.f64 2 (.f64 n (PI.f64))) (.f64 (pow.f64 (PI.f64) 2) (*.f64 n n)))) 2)
(pow.f64 (.f64 (/.f64 2 (.f64 n (PI.f64))) (.f64 (pow.f64 (PI.f64) 2) (.f64 n n))) 1)
(neg.f64 (neg.f64 (.f64 (/.f64 2 (.f64 n (PI.f64))) (.f64 (pow.f64 (PI.f64) 2) (.f64 n n)))))

Outputs
(*.f64 2 (PI.f64))
(*.f64 2 (PI.f64))
(*.f64 2 (PI.f64))
(*.f64 2 (PI.f64))
(*.f64 2 (PI.f64))
(*.f64 2 (PI.f64))
(*.f64 2 (PI.f64))
(*.f64 2 (PI.f64))
(*.f64 2 (PI.f64))
(*.f64 2 (PI.f64))
(*.f64 2 (PI.f64))
(*.f64 2 (PI.f64))
(.f64 2 (.f64 n (PI.f64)))
(.f64 2 (.f64 (PI.f64) n))
(.f64 (PI.f64) (.f64 2 n))
(.f64 2 (.f64 n (PI.f64)))
(.f64 2 (.f64 (PI.f64) n))
(.f64 (PI.f64) (.f64 2 n))
(.f64 2 (.f64 n (PI.f64)))
(.f64 2 (.f64 (PI.f64) n))
(.f64 (PI.f64) (.f64 2 n))
(.f64 2 (.f64 n (PI.f64)))
(.f64 2 (.f64 (PI.f64) n))
(.f64 (PI.f64) (.f64 2 n))
(.f64 2 (.f64 n (PI.f64)))
(.f64 2 (.f64 (PI.f64) n))
(.f64 (PI.f64) (.f64 2 n))
(.f64 2 (.f64 n (PI.f64)))
(.f64 2 (.f64 (PI.f64) n))
(.f64 (PI.f64) (.f64 2 n))
(.f64 2 (.f64 n (PI.f64)))
(.f64 2 (.f64 (PI.f64) n))
(.f64 (PI.f64) (.f64 2 n))
(.f64 2 (.f64 n (PI.f64)))
(.f64 2 (.f64 (PI.f64) n))
(.f64 (PI.f64) (.f64 2 n))
(.f64 2 (.f64 n (PI.f64)))
(.f64 2 (.f64 (PI.f64) n))
(.f64 (PI.f64) (.f64 2 n))
(.f64 2 (.f64 n (PI.f64)))
(.f64 2 (.f64 (PI.f64) n))
(.f64 (PI.f64) (.f64 2 n))
(.f64 2 (.f64 n (PI.f64)))
(.f64 2 (.f64 (PI.f64) n))
(.f64 (PI.f64) (.f64 2 n))
(.f64 2 (.f64 n (PI.f64)))
(.f64 2 (.f64 (PI.f64) n))
(.f64 (PI.f64) (.f64 2 n))
(+.f64 (.f64 n (.f64 (/.f64 2 (*.f64 n (PI.f64))) (pow.f64 (PI.f64) 2))) 0)
(.f64 n (.f64 (/.f64 2 (*.f64 (PI.f64) n)) (pow.f64 (PI.f64) 2)))
(+.f64 0 (.f64 n (.f64 (/.f64 2 (*.f64 n (PI.f64))) (pow.f64 (PI.f64) 2))))
(.f64 n (.f64 (/.f64 2 (*.f64 (PI.f64) n)) (pow.f64 (PI.f64) 2)))
(-.f64 (.f64 n (.f64 (/.f64 2 (*.f64 n (PI.f64))) (pow.f64 (PI.f64) 2))) 0)
(.f64 n (.f64 (/.f64 2 (*.f64 (PI.f64) n)) (pow.f64 (PI.f64) 2)))
(-.f64 0 (neg.f64 (.f64 n (.f64 (/.f64 2 (*.f64 n (PI.f64))) (pow.f64 (PI.f64) 2)))))
(.f64 n (.f64 (/.f64 2 (*.f64 (PI.f64) n)) (pow.f64 (PI.f64) 2)))
(/.f64 (.f64 n (.f64 (/.f64 2 (*.f64 n (PI.f64))) (pow.f64 (PI.f64) 2))) 1)
(.f64 n (.f64 (/.f64 2 (*.f64 (PI.f64) n)) (pow.f64 (PI.f64) 2)))
(/.f64 (.f64 n (.f64 (/.f64 2 (.f64 n (PI.f64))) (pow.f64 (PI.f64) 2))) (/.f64 (.f64 n (.f64 (/.f64 2 (.f64 n (PI.f64))) (pow.f64 (PI.f64) 2))) (.f64 n (.f64 (/.f64 2 (*.f64 n (PI.f64))) (pow.f64 (PI.f64) 2)))))
(.f64 n (.f64 (/.f64 2 (*.f64 (PI.f64) n)) (pow.f64 (PI.f64) 2)))
(/.f64 (.f64 2 (.f64 n (.f64 (/.f64 2 (.f64 n (PI.f64))) (pow.f64 (PI.f64) 2)))) 2)
(.f64 n (.f64 (/.f64 2 (*.f64 (PI.f64) n)) (pow.f64 (PI.f64) 2)))
(pow.f64 (.f64 n (.f64 (/.f64 2 (*.f64 n (PI.f64))) (pow.f64 (PI.f64) 2))) 1)
(.f64 n (.f64 (/.f64 2 (*.f64 (PI.f64) n)) (pow.f64 (PI.f64) 2)))
(neg.f64 (neg.f64 (.f64 n (.f64 (/.f64 2 (*.f64 n (PI.f64))) (pow.f64 (PI.f64) 2)))))
(.f64 n (.f64 (/.f64 2 (*.f64 (PI.f64) n)) (pow.f64 (PI.f64) 2)))
(+.f64 (.f64 (/.f64 2 (.f64 n (PI.f64))) (.f64 (pow.f64 (PI.f64) 2) (.f64 n n))) 0)
(.f64 (/.f64 2 (.f64 (PI.f64) n)) (.f64 (pow.f64 (PI.f64) 2) (.f64 n n)))
(.f64 (/.f64 2 (.f64 (PI.f64) n)) (.f64 n (.f64 n (pow.f64 (PI.f64) 2))))
(+.f64 0 (.f64 (/.f64 2 (.f64 n (PI.f64))) (.f64 (pow.f64 (PI.f64) 2) (.f64 n n))))
(.f64 (/.f64 2 (.f64 (PI.f64) n)) (.f64 (pow.f64 (PI.f64) 2) (.f64 n n)))
(.f64 (/.f64 2 (.f64 (PI.f64) n)) (.f64 n (.f64 n (pow.f64 (PI.f64) 2))))
(-.f64 (.f64 (/.f64 2 (.f64 n (PI.f64))) (.f64 (pow.f64 (PI.f64) 2) (.f64 n n))) 0)
(.f64 (/.f64 2 (.f64 (PI.f64) n)) (.f64 (pow.f64 (PI.f64) 2) (.f64 n n)))
(.f64 (/.f64 2 (.f64 (PI.f64) n)) (.f64 n (.f64 n (pow.f64 (PI.f64) 2))))
(-.f64 0 (neg.f64 (.f64 (/.f64 2 (.f64 n (PI.f64))) (.f64 (pow.f64 (PI.f64) 2) (.f64 n n)))))
(.f64 (/.f64 2 (.f64 (PI.f64) n)) (.f64 (pow.f64 (PI.f64) 2) (.f64 n n)))
(.f64 (/.f64 2 (.f64 (PI.f64) n)) (.f64 n (.f64 n (pow.f64 (PI.f64) 2))))
(/.f64 (.f64 (/.f64 2 (.f64 n (PI.f64))) (.f64 (pow.f64 (PI.f64) 2) (.f64 n n))) 1)
(.f64 (/.f64 2 (.f64 (PI.f64) n)) (.f64 (pow.f64 (PI.f64) 2) (.f64 n n)))
(.f64 (/.f64 2 (.f64 (PI.f64) n)) (.f64 n (.f64 n (pow.f64 (PI.f64) 2))))
(/.f64 (.f64 (/.f64 2 (.f64 n (PI.f64))) (.f64 (pow.f64 (PI.f64) 2) (.f64 n n))) (/.f64 (.f64 (/.f64 2 (.f64 n (PI.f64))) (.f64 (pow.f64 (PI.f64) 2) (.f64 n n))) (.f64 (/.f64 2 (.f64 n (PI.f64))) (.f64 (pow.f64 (PI.f64) 2) (.f64 n n)))))
(.f64 (/.f64 2 (.f64 (PI.f64) n)) (.f64 (pow.f64 (PI.f64) 2) (.f64 n n)))
(.f64 (/.f64 2 (.f64 (PI.f64) n)) (.f64 n (.f64 n (pow.f64 (PI.f64) 2))))
(/.f64 (.f64 2 (.f64 (/.f64 2 (.f64 n (PI.f64))) (.f64 (pow.f64 (PI.f64) 2) (*.f64 n n)))) 2)
(.f64 (/.f64 2 (.f64 (PI.f64) n)) (.f64 (pow.f64 (PI.f64) 2) (.f64 n n)))
(.f64 (/.f64 2 (.f64 (PI.f64) n)) (.f64 n (.f64 n (pow.f64 (PI.f64) 2))))
(pow.f64 (.f64 (/.f64 2 (.f64 n (PI.f64))) (.f64 (pow.f64 (PI.f64) 2) (.f64 n n))) 1)
(.f64 (/.f64 2 (.f64 (PI.f64) n)) (.f64 (pow.f64 (PI.f64) 2) (.f64 n n)))
(.f64 (/.f64 2 (.f64 (PI.f64) n)) (.f64 n (.f64 n (pow.f64 (PI.f64) 2))))
(neg.f64 (neg.f64 (.f64 (/.f64 2 (.f64 n (PI.f64))) (.f64 (pow.f64 (PI.f64) 2) (.f64 n n)))))
(.f64 (/.f64 2 (.f64 (PI.f64) n)) (.f64 (pow.f64 (PI.f64) 2) (.f64 n n)))
(.f64 (/.f64 2 (.f64 (PI.f64) n)) (.f64 n (.f64 n (pow.f64 (PI.f64) 2))))

localize24.0ms (0.2%)

Local error

Found 4 expressions with local error:

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

Compiler

Compiled 63 to 42 computations (33.3% saved)

series2.0ms (0%)

Counts

1 → 0

Calls

6 calls:

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

rewrite52.0ms (0.4%)

Algorithm

1×	batch-egg-rewrite

Rules

932×	`rational_best-2`
932×	`rational_best-3`
932×	`rational_best-1`
930×	`rational_best-5`
930×	`rational_best-simplify-47`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	18	53
1	148	53
2	478	53
3	2038	53

Stop Event

1×	node limit

Counts

1 → 7

Calls

Call 1

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

Outputs

((#(struct:change #<rule egg-rr> (2) ((x +.f64 (*.f64 (/.f64 1 (/.f64 1 (sqrt.f64 k))) (*.f64 (/.f64 1 k) (sqrt.f64 (*.f64 (PI.f64) (+.f64 n n))))) 0)))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 0 (*.f64 (/.f64 1 (/.f64 1 (sqrt.f64 k))) (*.f64 (/.f64 1 k) (sqrt.f64 (*.f64 (PI.f64) (+.f64 n n))))))))) (#(struct:change #<rule egg-rr> (2) ((x -.f64 (*.f64 (/.f64 1 (/.f64 1 (sqrt.f64 k))) (*.f64 (/.f64 1 k) (sqrt.f64 (*.f64 (PI.f64) (+.f64 n n))))) 0)))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (*.f64 (/.f64 1 (/.f64 1 (sqrt.f64 k))) (*.f64 (/.f64 1 k) (sqrt.f64 (*.f64 (PI.f64) (+.f64 n n))))) 1)))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (*.f64 (/.f64 1 (/.f64 1 (sqrt.f64 k))) (*.f64 (/.f64 1 k) (sqrt.f64 (*.f64 (PI.f64) (+.f64 n n))))) (/.f64 (*.f64 (/.f64 1 (/.f64 1 (sqrt.f64 k))) (*.f64 (/.f64 1 k) (sqrt.f64 (*.f64 (PI.f64) (+.f64 n n))))) (*.f64 (/.f64 1 (/.f64 1 (sqrt.f64 k))) (*.f64 (/.f64 1 k) (sqrt.f64 (*.f64 (PI.f64) (+.f64 n n)))))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (*.f64 (*.f64 (/.f64 1 (/.f64 1 (sqrt.f64 k))) (sqrt.f64 (*.f64 (PI.f64) (+.f64 n n)))) (*.f64 (/.f64 1 k) 2)) 2)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (*.f64 (/.f64 1 (/.f64 1 (sqrt.f64 k))) (*.f64 (/.f64 1 k) (sqrt.f64 (*.f64 (PI.f64) (+.f64 n n))))) 1)))))

simplify139.0ms (1%)

Algorithm

1×	egg-herbie

Rules

1604×	`rational_best-simplify-132`
1456×	`rational_best-simplify-80`
1320×	`rational_best-simplify-78`
1136×	`rational_best-simplify-82`
902×	`rational_best-simplify-2`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	30	371
1	45	371
2	97	371
3	257	371
4	1166	371
5	2857	371
6	5532	371

Stop Event

1×	node limit

Counts

7 → 9

Calls

Call 1

Inputs
(+.f64 (.f64 (/.f64 1 (/.f64 1 (sqrt.f64 k))) (.f64 (/.f64 1 k) (sqrt.f64 (*.f64 (PI.f64) (+.f64 n n))))) 0)
(+.f64 0 (.f64 (/.f64 1 (/.f64 1 (sqrt.f64 k))) (.f64 (/.f64 1 k) (sqrt.f64 (*.f64 (PI.f64) (+.f64 n n))))))
(-.f64 (.f64 (/.f64 1 (/.f64 1 (sqrt.f64 k))) (.f64 (/.f64 1 k) (sqrt.f64 (*.f64 (PI.f64) (+.f64 n n))))) 0)
(/.f64 (.f64 (/.f64 1 (/.f64 1 (sqrt.f64 k))) (.f64 (/.f64 1 k) (sqrt.f64 (*.f64 (PI.f64) (+.f64 n n))))) 1)
(/.f64 (.f64 (/.f64 1 (/.f64 1 (sqrt.f64 k))) (.f64 (/.f64 1 k) (sqrt.f64 (.f64 (PI.f64) (+.f64 n n))))) (/.f64 (.f64 (/.f64 1 (/.f64 1 (sqrt.f64 k))) (.f64 (/.f64 1 k) (sqrt.f64 (.f64 (PI.f64) (+.f64 n n))))) (.f64 (/.f64 1 (/.f64 1 (sqrt.f64 k))) (.f64 (/.f64 1 k) (sqrt.f64 (*.f64 (PI.f64) (+.f64 n n)))))))
(/.f64 (.f64 (.f64 (/.f64 1 (/.f64 1 (sqrt.f64 k))) (sqrt.f64 (.f64 (PI.f64) (+.f64 n n)))) (.f64 (/.f64 1 k) 2)) 2)
(pow.f64 (.f64 (/.f64 1 (/.f64 1 (sqrt.f64 k))) (.f64 (/.f64 1 k) (sqrt.f64 (*.f64 (PI.f64) (+.f64 n n))))) 1)

Outputs
(+.f64 (.f64 (/.f64 1 (/.f64 1 (sqrt.f64 k))) (.f64 (/.f64 1 k) (sqrt.f64 (*.f64 (PI.f64) (+.f64 n n))))) 0)
(.f64 (/.f64 1 (/.f64 1 (sqrt.f64 k))) (.f64 (/.f64 1 k) (sqrt.f64 (*.f64 (PI.f64) (+.f64 n n)))))
(.f64 (sqrt.f64 (.f64 (PI.f64) (+.f64 n n))) (*.f64 (/.f64 1 (/.f64 1 (sqrt.f64 k))) (/.f64 1 k)))
(+.f64 0 (.f64 (/.f64 1 (/.f64 1 (sqrt.f64 k))) (.f64 (/.f64 1 k) (sqrt.f64 (*.f64 (PI.f64) (+.f64 n n))))))
(.f64 (/.f64 1 (/.f64 1 (sqrt.f64 k))) (.f64 (/.f64 1 k) (sqrt.f64 (*.f64 (PI.f64) (+.f64 n n)))))
(.f64 (sqrt.f64 (.f64 (PI.f64) (+.f64 n n))) (*.f64 (/.f64 1 (/.f64 1 (sqrt.f64 k))) (/.f64 1 k)))
(-.f64 (.f64 (/.f64 1 (/.f64 1 (sqrt.f64 k))) (.f64 (/.f64 1 k) (sqrt.f64 (*.f64 (PI.f64) (+.f64 n n))))) 0)
(.f64 (/.f64 1 (/.f64 1 (sqrt.f64 k))) (.f64 (/.f64 1 k) (sqrt.f64 (*.f64 (PI.f64) (+.f64 n n)))))
(.f64 (sqrt.f64 (.f64 (PI.f64) (+.f64 n n))) (*.f64 (/.f64 1 (/.f64 1 (sqrt.f64 k))) (/.f64 1 k)))
(/.f64 (.f64 (/.f64 1 (/.f64 1 (sqrt.f64 k))) (.f64 (/.f64 1 k) (sqrt.f64 (*.f64 (PI.f64) (+.f64 n n))))) 1)
(.f64 (/.f64 1 (/.f64 1 (sqrt.f64 k))) (.f64 (/.f64 1 k) (sqrt.f64 (*.f64 (PI.f64) (+.f64 n n)))))
(.f64 (sqrt.f64 (.f64 (PI.f64) (+.f64 n n))) (*.f64 (/.f64 1 (/.f64 1 (sqrt.f64 k))) (/.f64 1 k)))
(/.f64 (.f64 (/.f64 1 (/.f64 1 (sqrt.f64 k))) (.f64 (/.f64 1 k) (sqrt.f64 (.f64 (PI.f64) (+.f64 n n))))) (/.f64 (.f64 (/.f64 1 (/.f64 1 (sqrt.f64 k))) (.f64 (/.f64 1 k) (sqrt.f64 (.f64 (PI.f64) (+.f64 n n))))) (.f64 (/.f64 1 (/.f64 1 (sqrt.f64 k))) (.f64 (/.f64 1 k) (sqrt.f64 (*.f64 (PI.f64) (+.f64 n n)))))))
(.f64 (/.f64 1 (/.f64 1 (sqrt.f64 k))) (.f64 (/.f64 1 k) (sqrt.f64 (*.f64 (PI.f64) (+.f64 n n)))))
(.f64 (sqrt.f64 (.f64 (PI.f64) (+.f64 n n))) (*.f64 (/.f64 1 (/.f64 1 (sqrt.f64 k))) (/.f64 1 k)))
(/.f64 (.f64 (.f64 (/.f64 1 (/.f64 1 (sqrt.f64 k))) (sqrt.f64 (.f64 (PI.f64) (+.f64 n n)))) (.f64 (/.f64 1 k) 2)) 2)
(.f64 (/.f64 1 (/.f64 1 (sqrt.f64 k))) (.f64 (/.f64 1 k) (sqrt.f64 (*.f64 (PI.f64) (+.f64 n n)))))
(.f64 (sqrt.f64 (.f64 (PI.f64) (+.f64 n n))) (*.f64 (/.f64 1 (/.f64 1 (sqrt.f64 k))) (/.f64 1 k)))
(pow.f64 (.f64 (/.f64 1 (/.f64 1 (sqrt.f64 k))) (.f64 (/.f64 1 k) (sqrt.f64 (*.f64 (PI.f64) (+.f64 n n))))) 1)
(.f64 (/.f64 1 (/.f64 1 (sqrt.f64 k))) (.f64 (/.f64 1 k) (sqrt.f64 (*.f64 (PI.f64) (+.f64 n n)))))
(.f64 (sqrt.f64 (.f64 (PI.f64) (+.f64 n n))) (*.f64 (/.f64 1 (/.f64 1 (sqrt.f64 k))) (/.f64 1 k)))

localize35.0ms (0.2%)

Local error

Found 4 expressions with local error:

New	Error	Program
	0.3b	(*.f64 (PI.f64) (+.f64 n n))
	0.3b	(*.f64 n (PI.f64))
	0.3b	(.f64 (log.f64 (.f64 (PI.f64) (+.f64 n n))) (*.f64 k -1/2))
✓	4.8b	(.f64 (/.f64 1 (sqrt.f64 k)) (.f64 (+.f64 1 (.f64 (log.f64 (.f64 (PI.f64) (+.f64 n n))) (.f64 k -1/2))) (sqrt.f64 (.f64 2 (*.f64 n (PI.f64))))))

Compiler

Compiled 110 to 49 computations (55.5% saved)

series5.0ms (0%)

Counts

1 → 0

Calls

6 calls:

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

rewrite57.0ms (0.4%)

Algorithm

1×	batch-egg-rewrite

Rules

1184×	`rational_best-5`
1184×	`rational_best-2`
1184×	`rational_best-3`
1184×	`rational_best-1`
1184×	`rational_best-simplify-47`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	23	77
1	195	77
2	630	77
3	2676	77

Stop Event

1×	node limit

Counts

1 → 7

Calls

Call 1

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

Outputs

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

simplify140.0ms (1%)

Algorithm

1×	egg-herbie

Rules

1604×	`rational_best-simplify-132`
1392×	`rational_best-simplify-80`
1256×	`rational_best-simplify-78`
1136×	`rational_best-simplify-82`
890×	`rational_best-simplify-2`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	37	543
1	66	543
2	124	543
3	278	543
4	1181	543
5	2891	543
6	5502	543

Stop Event

1×	node limit

Counts

7 → 12

Calls

Call 1

Inputs
(+.f64 (.f64 (/.f64 1 (sqrt.f64 k)) (.f64 (+.f64 1 (log.f64 (pow.f64 (.f64 n (.f64 (PI.f64) 2)) (.f64 k -1/2)))) (sqrt.f64 (.f64 n (*.f64 (PI.f64) 2))))) 0)
(+.f64 0 (.f64 (/.f64 1 (sqrt.f64 k)) (.f64 (+.f64 1 (log.f64 (pow.f64 (.f64 n (.f64 (PI.f64) 2)) (.f64 k -1/2)))) (sqrt.f64 (.f64 n (*.f64 (PI.f64) 2))))))
(-.f64 (.f64 (/.f64 1 (sqrt.f64 k)) (.f64 (+.f64 1 (log.f64 (pow.f64 (.f64 n (.f64 (PI.f64) 2)) (.f64 k -1/2)))) (sqrt.f64 (.f64 n (*.f64 (PI.f64) 2))))) 0)
(/.f64 (.f64 (/.f64 1 (sqrt.f64 k)) (.f64 (+.f64 1 (log.f64 (pow.f64 (.f64 n (.f64 (PI.f64) 2)) (.f64 k -1/2)))) (sqrt.f64 (.f64 n (*.f64 (PI.f64) 2))))) 1)
(/.f64 (.f64 (/.f64 1 (sqrt.f64 k)) (.f64 (+.f64 1 (log.f64 (pow.f64 (.f64 n (.f64 (PI.f64) 2)) (.f64 k -1/2)))) (sqrt.f64 (.f64 n (.f64 (PI.f64) 2))))) (/.f64 (.f64 (/.f64 1 (sqrt.f64 k)) (.f64 (+.f64 1 (log.f64 (pow.f64 (.f64 n (.f64 (PI.f64) 2)) (.f64 k -1/2)))) (sqrt.f64 (.f64 n (.f64 (PI.f64) 2))))) (.f64 (/.f64 1 (sqrt.f64 k)) (.f64 (+.f64 1 (log.f64 (pow.f64 (.f64 n (.f64 (PI.f64) 2)) (.f64 k -1/2)))) (sqrt.f64 (.f64 n (*.f64 (PI.f64) 2)))))))
(/.f64 (.f64 (/.f64 1 (sqrt.f64 k)) (.f64 (sqrt.f64 (.f64 n (.f64 (PI.f64) 2))) (+.f64 1 (+.f64 1 (.f64 (log.f64 (.f64 n (*.f64 (PI.f64) 2))) (neg.f64 k)))))) 2)
(pow.f64 (.f64 (/.f64 1 (sqrt.f64 k)) (.f64 (+.f64 1 (log.f64 (pow.f64 (.f64 n (.f64 (PI.f64) 2)) (.f64 k -1/2)))) (sqrt.f64 (.f64 n (*.f64 (PI.f64) 2))))) 1)

Outputs
(+.f64 (.f64 (/.f64 1 (sqrt.f64 k)) (.f64 (+.f64 1 (log.f64 (pow.f64 (.f64 n (.f64 (PI.f64) 2)) (.f64 k -1/2)))) (sqrt.f64 (.f64 n (*.f64 (PI.f64) 2))))) 0)
(.f64 (/.f64 1 (sqrt.f64 k)) (.f64 (+.f64 1 (log.f64 (pow.f64 (.f64 n (.f64 (PI.f64) 2)) (.f64 k -1/2)))) (sqrt.f64 (.f64 n (*.f64 (PI.f64) 2)))))
(+.f64 0 (.f64 (/.f64 1 (sqrt.f64 k)) (.f64 (+.f64 1 (log.f64 (pow.f64 (.f64 n (.f64 (PI.f64) 2)) (.f64 k -1/2)))) (sqrt.f64 (.f64 n (*.f64 (PI.f64) 2))))))
(.f64 (/.f64 1 (sqrt.f64 k)) (.f64 (+.f64 1 (log.f64 (pow.f64 (.f64 n (.f64 (PI.f64) 2)) (.f64 k -1/2)))) (sqrt.f64 (.f64 n (*.f64 (PI.f64) 2)))))
(-.f64 (.f64 (/.f64 1 (sqrt.f64 k)) (.f64 (+.f64 1 (log.f64 (pow.f64 (.f64 n (.f64 (PI.f64) 2)) (.f64 k -1/2)))) (sqrt.f64 (.f64 n (*.f64 (PI.f64) 2))))) 0)
(.f64 (/.f64 1 (sqrt.f64 k)) (.f64 (+.f64 1 (log.f64 (pow.f64 (.f64 n (.f64 (PI.f64) 2)) (.f64 k -1/2)))) (sqrt.f64 (.f64 n (*.f64 (PI.f64) 2)))))
(/.f64 (.f64 (/.f64 1 (sqrt.f64 k)) (.f64 (+.f64 1 (log.f64 (pow.f64 (.f64 n (.f64 (PI.f64) 2)) (.f64 k -1/2)))) (sqrt.f64 (.f64 n (*.f64 (PI.f64) 2))))) 1)
(.f64 (/.f64 1 (sqrt.f64 k)) (.f64 (+.f64 1 (log.f64 (pow.f64 (.f64 n (.f64 (PI.f64) 2)) (.f64 k -1/2)))) (sqrt.f64 (.f64 n (*.f64 (PI.f64) 2)))))
(/.f64 (.f64 (/.f64 1 (sqrt.f64 k)) (.f64 (+.f64 1 (log.f64 (pow.f64 (.f64 n (.f64 (PI.f64) 2)) (.f64 k -1/2)))) (sqrt.f64 (.f64 n (.f64 (PI.f64) 2))))) (/.f64 (.f64 (/.f64 1 (sqrt.f64 k)) (.f64 (+.f64 1 (log.f64 (pow.f64 (.f64 n (.f64 (PI.f64) 2)) (.f64 k -1/2)))) (sqrt.f64 (.f64 n (.f64 (PI.f64) 2))))) (.f64 (/.f64 1 (sqrt.f64 k)) (.f64 (+.f64 1 (log.f64 (pow.f64 (.f64 n (.f64 (PI.f64) 2)) (.f64 k -1/2)))) (sqrt.f64 (.f64 n (*.f64 (PI.f64) 2)))))))
(.f64 (/.f64 1 (sqrt.f64 k)) (.f64 (+.f64 1 (log.f64 (pow.f64 (.f64 n (.f64 (PI.f64) 2)) (.f64 k -1/2)))) (sqrt.f64 (.f64 n (*.f64 (PI.f64) 2)))))
(/.f64 (.f64 (/.f64 1 (sqrt.f64 k)) (.f64 (sqrt.f64 (.f64 n (.f64 (PI.f64) 2))) (+.f64 1 (+.f64 1 (.f64 (log.f64 (.f64 n (*.f64 (PI.f64) 2))) (neg.f64 k)))))) 2)
(/.f64 (.f64 (/.f64 1 (sqrt.f64 k)) (.f64 (sqrt.f64 (.f64 n (.f64 (PI.f64) 2))) (+.f64 (.f64 (log.f64 (.f64 n (*.f64 (PI.f64) 2))) (neg.f64 k)) 2))) 2)
(/.f64 (.f64 (/.f64 1 (sqrt.f64 k)) (.f64 (sqrt.f64 (.f64 n (.f64 (PI.f64) 2))) (+.f64 2 (.f64 (log.f64 (.f64 n (*.f64 (PI.f64) 2))) (neg.f64 k))))) 2)
(/.f64 (.f64 (+.f64 2 (.f64 (log.f64 (.f64 n (.f64 (PI.f64) 2))) (neg.f64 k))) (.f64 (/.f64 1 (sqrt.f64 k)) (sqrt.f64 (.f64 n (*.f64 (PI.f64) 2))))) 2)
(/.f64 (.f64 (/.f64 1 (sqrt.f64 k)) (.f64 (sqrt.f64 (.f64 n (.f64 (PI.f64) 2))) (+.f64 2 (.f64 k (neg.f64 (log.f64 (.f64 n (*.f64 (PI.f64) 2)))))))) 2)
(pow.f64 (.f64 (/.f64 1 (sqrt.f64 k)) (.f64 (+.f64 1 (log.f64 (pow.f64 (.f64 n (.f64 (PI.f64) 2)) (.f64 k -1/2)))) (sqrt.f64 (.f64 n (*.f64 (PI.f64) 2))))) 1)
(.f64 (/.f64 1 (sqrt.f64 k)) (.f64 (+.f64 1 (log.f64 (pow.f64 (.f64 n (.f64 (PI.f64) 2)) (.f64 k -1/2)))) (sqrt.f64 (.f64 n (*.f64 (PI.f64) 2)))))

localize34.0ms (0.2%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.2b	(/.f64 1 (*.f64 n (PI.f64)))
	0.3b	(*.f64 (PI.f64) (+.f64 n n))
	0.3b	(*.f64 n (PI.f64))
✓	0.5b	(.f64 (sqrt.f64 (/.f64 1 (.f64 n (PI.f64)))) (sqrt.f64 1/2))

Compiler

Compiled 101 to 52 computations (48.5% saved)

series2.0ms (0%)

Counts

2 → 0

Calls

6 calls:

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

rewrite106.0ms (0.7%)

Algorithm

1×	batch-egg-rewrite

Rules

1250×	`rational_best-simplify-57`
688×	`rational_best-simplify-44`
680×	`rational_best-simplify-43`
612×	`rational_best-4`
612×	`rational_best-2`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	13	40
1	106	40
2	329	40
3	1382	40
4	5857	40

Stop Event

1×	node limit

Counts

2 → 38

Calls

Call 1

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

Outputs

((#(struct:change #<rule egg-rr> (2) ((x +.f64 (sqrt.f64 (*.f64 (/.f64 1 (*.f64 n (PI.f64))) 1/2)) 0)))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 0 (sqrt.f64 (*.f64 (/.f64 1 (*.f64 n (PI.f64))) 1/2)))))) (#(struct:change #<rule egg-rr> (2) ((x -.f64 (sqrt.f64 (*.f64 (/.f64 1 (*.f64 n (PI.f64))) 1/2)) 0)))) (#(struct:change #<rule egg-rr> (2) ((x -.f64 0 (neg.f64 (sqrt.f64 (*.f64 (/.f64 1 (*.f64 n (PI.f64))) 1/2))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (sqrt.f64 (*.f64 (/.f64 1 (*.f64 n (PI.f64))) 1/2)) 1)))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (sqrt.f64 (*.f64 (/.f64 1 (*.f64 n (PI.f64))) 1/2)) (/.f64 (sqrt.f64 (*.f64 (/.f64 1 (*.f64 n (PI.f64))) 1/2)) (sqrt.f64 (*.f64 (/.f64 1 (*.f64 n (PI.f64))) 1/2))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (*.f64 (sqrt.f64 (*.f64 (/.f64 1 (*.f64 n (PI.f64))) 1/2)) 2) 2)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (sqrt.f64 (*.f64 (/.f64 1 (*.f64 n (PI.f64))) 1/2)) 1)))) (#(struct:change #<rule egg-rr> (2) ((x neg.f64 (neg.f64 (sqrt.f64 (*.f64 (/.f64 1 (*.f64 n (PI.f64))) 1/2))))))) (#(struct:change #<rule egg-rr> (2) ((x sqrt.f64 (*.f64 (/.f64 1 (*.f64 n (PI.f64))) 1/2))))))

((#(struct:change #<rule egg-rr> (2) ((x +.f64 (/.f64 1 (*.f64 n (PI.f64))) 0)))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 0 (/.f64 1 (*.f64 n (PI.f64))))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (*.f64 (/.f64 1 (*.f64 n (PI.f64))) 1/2) (*.f64 (/.f64 1 (*.f64 n (PI.f64))) 1/2))))) (#(struct:change #<rule egg-rr> (2) ((x -.f64 (/.f64 1 (*.f64 n (PI.f64))) 0)))) (#(struct:change #<rule egg-rr> (2) ((x -.f64 0 (neg.f64 (/.f64 1 (*.f64 n (PI.f64)))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 1 (/.f64 1 (*.f64 n (PI.f64))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (/.f64 1 (*.f64 n (PI.f64))) 1)))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (/.f64 1 (*.f64 n (PI.f64))) (/.f64 (/.f64 1 (*.f64 n (PI.f64))) (/.f64 1 (*.f64 n (PI.f64)))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (/.f64 1 (*.f64 n (PI.f64))) (*.f64 (/.f64 1 (*.f64 n (PI.f64))) (/.f64 1 (/.f64 1 (*.f64 n (PI.f64))))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (/.f64 1 (*.f64 n (PI.f64))) (/.f64 1 (/.f64 (/.f64 1 (*.f64 n (PI.f64))) (/.f64 1 (*.f64 n (PI.f64))))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (/.f64 (/.f64 1 (*.f64 n (PI.f64))) (/.f64 1 (*.f64 n (PI.f64)))) (/.f64 1 (*.f64 n (PI.f64))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (*.f64 (/.f64 1 (*.f64 n (PI.f64))) 1/2) 2)))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 1/2 (*.f64 (/.f64 1 (*.f64 n (PI.f64))) 2))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (/.f64 1 (/.f64 1 (*.f64 n (PI.f64)))) (*.f64 (/.f64 1 (*.f64 n (PI.f64))) (/.f64 1 (*.f64 n (PI.f64)))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (/.f64 1 (/.f64 1 (*.f64 n (PI.f64)))) (+.f64 (*.f64 (/.f64 1 (*.f64 n (PI.f64))) (*.f64 (/.f64 1 (*.f64 n (PI.f64))) 1/2)) (*.f64 (/.f64 1 (*.f64 n (PI.f64))) (*.f64 (/.f64 1 (*.f64 n (PI.f64))) 1/2))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (*.f64 (/.f64 1 (*.f64 n (PI.f64))) (/.f64 1 (*.f64 n (PI.f64)))) (/.f64 1 (/.f64 1 (*.f64 n (PI.f64)))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (*.f64 (/.f64 1 (*.f64 n (PI.f64))) (/.f64 1 (/.f64 1 (*.f64 n (PI.f64))))) (/.f64 1 (*.f64 n (PI.f64))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (/.f64 1 (/.f64 (/.f64 1 (*.f64 n (PI.f64))) (/.f64 1 (*.f64 n (PI.f64))))) (*.f64 (/.f64 1 (*.f64 n (PI.f64))) (*.f64 (/.f64 (/.f64 1 (*.f64 n (PI.f64))) (/.f64 1 (*.f64 n (PI.f64)))) (/.f64 (/.f64 1 (*.f64 n (PI.f64))) (/.f64 1 (*.f64 n (PI.f64)))))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (/.f64 (/.f64 1 (*.f64 n (PI.f64))) 1/2) 1/2)))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (/.f64 1 (*.f64 (/.f64 1 (*.f64 n (PI.f64))) 1/2)) (+.f64 (*.f64 (/.f64 1 (*.f64 n (PI.f64))) (*.f64 (*.f64 (/.f64 1 (*.f64 n (PI.f64))) 1/2) 1/2)) (*.f64 (/.f64 1 (*.f64 n (PI.f64))) (*.f64 (*.f64 (/.f64 1 (*.f64 n (PI.f64))) 1/2) 1/2))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (/.f64 (/.f64 1 (/.f64 1 (*.f64 n (PI.f64)))) (*.f64 (/.f64 1 (*.f64 n (PI.f64))) (/.f64 1 (*.f64 n (PI.f64))))) (*.f64 (/.f64 1 (*.f64 n (PI.f64))) (*.f64 (/.f64 1 (*.f64 n (PI.f64))) (*.f64 (/.f64 1 (*.f64 n (PI.f64))) (/.f64 1 (*.f64 n (PI.f64)))))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (/.f64 (/.f64 (/.f64 1 (*.f64 n (PI.f64))) (/.f64 1 (*.f64 n (PI.f64)))) (/.f64 1 (*.f64 n (PI.f64)))) (*.f64 (/.f64 1 (*.f64 n (PI.f64))) (/.f64 1 (*.f64 n (PI.f64)))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (/.f64 (*.f64 (/.f64 1 (*.f64 n (PI.f64))) (/.f64 1 (/.f64 1 (*.f64 n (PI.f64))))) (/.f64 1 (*.f64 n (PI.f64)))) (*.f64 (/.f64 1 (*.f64 n (PI.f64))) (/.f64 1 (*.f64 n (PI.f64)))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (/.f64 (*.f64 (/.f64 1 (*.f64 n (PI.f64))) 2) 1/2) 1/4)))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (/.f64 (/.f64 1 (/.f64 (/.f64 1 (*.f64 n (PI.f64))) (/.f64 1 (*.f64 n (PI.f64))))) (/.f64 1 (*.f64 n (PI.f64)))) (*.f64 (/.f64 1 (*.f64 n (PI.f64))) (/.f64 1 (*.f64 n (PI.f64)))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (/.f64 2 (*.f64 (/.f64 1 (*.f64 n (PI.f64))) 1/2)) (*.f64 (/.f64 1 (*.f64 n (PI.f64))) (*.f64 (*.f64 (/.f64 1 (*.f64 n (PI.f64))) 1/2) 1/2)))))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (/.f64 1 (*.f64 n (PI.f64))) 1)))) (#(struct:change #<rule egg-rr> (2) ((x neg.f64 (neg.f64 (/.f64 1 (*.f64 n (PI.f64)))))))))

simplify222.0ms (1.5%)

Algorithm

1×	egg-herbie

Rules

1668×	`rational_best-simplify-132`
966×	`rational_best-simplify-2`
670×	`rational_best-simplify-50`
578×	`rational_best-simplify-80`
576×	`rational_best-simplify-24`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	79	682
1	155	682
2	400	682
3	1231	682
4	2709	682
5	7018	682

Stop Event

1×	node limit

Counts

38 → 40

Calls

Call 1

Inputs
(+.f64 (sqrt.f64 (.f64 (/.f64 1 (.f64 n (PI.f64))) 1/2)) 0)
(+.f64 0 (sqrt.f64 (.f64 (/.f64 1 (.f64 n (PI.f64))) 1/2)))
(-.f64 (sqrt.f64 (.f64 (/.f64 1 (.f64 n (PI.f64))) 1/2)) 0)
(-.f64 0 (neg.f64 (sqrt.f64 (.f64 (/.f64 1 (.f64 n (PI.f64))) 1/2))))
(/.f64 (sqrt.f64 (.f64 (/.f64 1 (.f64 n (PI.f64))) 1/2)) 1)
(/.f64 (sqrt.f64 (.f64 (/.f64 1 (.f64 n (PI.f64))) 1/2)) (/.f64 (sqrt.f64 (.f64 (/.f64 1 (.f64 n (PI.f64))) 1/2)) (sqrt.f64 (.f64 (/.f64 1 (.f64 n (PI.f64))) 1/2))))
(/.f64 (.f64 (sqrt.f64 (.f64 (/.f64 1 (*.f64 n (PI.f64))) 1/2)) 2) 2)
(pow.f64 (sqrt.f64 (.f64 (/.f64 1 (.f64 n (PI.f64))) 1/2)) 1)
(neg.f64 (neg.f64 (sqrt.f64 (.f64 (/.f64 1 (.f64 n (PI.f64))) 1/2))))
(sqrt.f64 (.f64 (/.f64 1 (.f64 n (PI.f64))) 1/2))
(+.f64 (/.f64 1 (*.f64 n (PI.f64))) 0)
(+.f64 0 (/.f64 1 (*.f64 n (PI.f64))))
(+.f64 (.f64 (/.f64 1 (.f64 n (PI.f64))) 1/2) (.f64 (/.f64 1 (.f64 n (PI.f64))) 1/2))
(-.f64 (/.f64 1 (*.f64 n (PI.f64))) 0)
(-.f64 0 (neg.f64 (/.f64 1 (*.f64 n (PI.f64)))))
(.f64 1 (/.f64 1 (.f64 n (PI.f64))))
(.f64 (/.f64 1 (.f64 n (PI.f64))) 1)
(.f64 (/.f64 1 (.f64 n (PI.f64))) (/.f64 (/.f64 1 (.f64 n (PI.f64))) (/.f64 1 (.f64 n (PI.f64)))))
(.f64 (/.f64 1 (.f64 n (PI.f64))) (.f64 (/.f64 1 (.f64 n (PI.f64))) (/.f64 1 (/.f64 1 (*.f64 n (PI.f64))))))
(.f64 (/.f64 1 (.f64 n (PI.f64))) (/.f64 1 (/.f64 (/.f64 1 (.f64 n (PI.f64))) (/.f64 1 (.f64 n (PI.f64))))))
(.f64 (/.f64 (/.f64 1 (.f64 n (PI.f64))) (/.f64 1 (.f64 n (PI.f64)))) (/.f64 1 (.f64 n (PI.f64))))
(.f64 (.f64 (/.f64 1 (*.f64 n (PI.f64))) 1/2) 2)
(.f64 1/2 (.f64 (/.f64 1 (*.f64 n (PI.f64))) 2))
(.f64 (/.f64 1 (/.f64 1 (.f64 n (PI.f64)))) (.f64 (/.f64 1 (.f64 n (PI.f64))) (/.f64 1 (*.f64 n (PI.f64)))))
(.f64 (/.f64 1 (/.f64 1 (.f64 n (PI.f64)))) (+.f64 (.f64 (/.f64 1 (.f64 n (PI.f64))) (.f64 (/.f64 1 (.f64 n (PI.f64))) 1/2)) (.f64 (/.f64 1 (.f64 n (PI.f64))) (.f64 (/.f64 1 (.f64 n (PI.f64))) 1/2))))
(.f64 (.f64 (/.f64 1 (.f64 n (PI.f64))) (/.f64 1 (.f64 n (PI.f64)))) (/.f64 1 (/.f64 1 (*.f64 n (PI.f64)))))
(.f64 (.f64 (/.f64 1 (.f64 n (PI.f64))) (/.f64 1 (/.f64 1 (.f64 n (PI.f64))))) (/.f64 1 (*.f64 n (PI.f64))))
(.f64 (/.f64 1 (/.f64 (/.f64 1 (.f64 n (PI.f64))) (/.f64 1 (.f64 n (PI.f64))))) (.f64 (/.f64 1 (.f64 n (PI.f64))) (.f64 (/.f64 (/.f64 1 (.f64 n (PI.f64))) (/.f64 1 (.f64 n (PI.f64)))) (/.f64 (/.f64 1 (.f64 n (PI.f64))) (/.f64 1 (.f64 n (PI.f64)))))))
(.f64 (/.f64 (/.f64 1 (.f64 n (PI.f64))) 1/2) 1/2)
(.f64 (/.f64 1 (.f64 (/.f64 1 (.f64 n (PI.f64))) 1/2)) (+.f64 (.f64 (/.f64 1 (.f64 n (PI.f64))) (.f64 (.f64 (/.f64 1 (.f64 n (PI.f64))) 1/2) 1/2)) (.f64 (/.f64 1 (.f64 n (PI.f64))) (.f64 (.f64 (/.f64 1 (*.f64 n (PI.f64))) 1/2) 1/2))))
(.f64 (/.f64 (/.f64 1 (/.f64 1 (.f64 n (PI.f64)))) (.f64 (/.f64 1 (.f64 n (PI.f64))) (/.f64 1 (.f64 n (PI.f64))))) (.f64 (/.f64 1 (.f64 n (PI.f64))) (.f64 (/.f64 1 (.f64 n (PI.f64))) (.f64 (/.f64 1 (.f64 n (PI.f64))) (/.f64 1 (.f64 n (PI.f64)))))))
(.f64 (/.f64 (/.f64 (/.f64 1 (.f64 n (PI.f64))) (/.f64 1 (.f64 n (PI.f64)))) (/.f64 1 (.f64 n (PI.f64)))) (.f64 (/.f64 1 (.f64 n (PI.f64))) (/.f64 1 (*.f64 n (PI.f64)))))
(.f64 (/.f64 (.f64 (/.f64 1 (.f64 n (PI.f64))) (/.f64 1 (/.f64 1 (.f64 n (PI.f64))))) (/.f64 1 (.f64 n (PI.f64)))) (.f64 (/.f64 1 (.f64 n (PI.f64))) (/.f64 1 (.f64 n (PI.f64)))))
(.f64 (/.f64 (.f64 (/.f64 1 (*.f64 n (PI.f64))) 2) 1/2) 1/4)
(.f64 (/.f64 (/.f64 1 (/.f64 (/.f64 1 (.f64 n (PI.f64))) (/.f64 1 (.f64 n (PI.f64))))) (/.f64 1 (.f64 n (PI.f64)))) (.f64 (/.f64 1 (.f64 n (PI.f64))) (/.f64 1 (*.f64 n (PI.f64)))))
(.f64 (/.f64 2 (.f64 (/.f64 1 (.f64 n (PI.f64))) 1/2)) (.f64 (/.f64 1 (.f64 n (PI.f64))) (.f64 (.f64 (/.f64 1 (.f64 n (PI.f64))) 1/2) 1/2)))
(pow.f64 (/.f64 1 (*.f64 n (PI.f64))) 1)
(neg.f64 (neg.f64 (/.f64 1 (*.f64 n (PI.f64)))))

Outputs
(+.f64 (sqrt.f64 (.f64 (/.f64 1 (.f64 n (PI.f64))) 1/2)) 0)
(sqrt.f64 (.f64 (/.f64 1 (.f64 n (PI.f64))) 1/2))
(+.f64 0 (sqrt.f64 (.f64 (/.f64 1 (.f64 n (PI.f64))) 1/2)))
(sqrt.f64 (.f64 (/.f64 1 (.f64 n (PI.f64))) 1/2))
(-.f64 (sqrt.f64 (.f64 (/.f64 1 (.f64 n (PI.f64))) 1/2)) 0)
(sqrt.f64 (.f64 (/.f64 1 (.f64 n (PI.f64))) 1/2))
(-.f64 0 (neg.f64 (sqrt.f64 (.f64 (/.f64 1 (.f64 n (PI.f64))) 1/2))))
(sqrt.f64 (.f64 (/.f64 1 (.f64 n (PI.f64))) 1/2))
(/.f64 (sqrt.f64 (.f64 (/.f64 1 (.f64 n (PI.f64))) 1/2)) 1)
(sqrt.f64 (.f64 (/.f64 1 (.f64 n (PI.f64))) 1/2))
(/.f64 (sqrt.f64 (.f64 (/.f64 1 (.f64 n (PI.f64))) 1/2)) (/.f64 (sqrt.f64 (.f64 (/.f64 1 (.f64 n (PI.f64))) 1/2)) (sqrt.f64 (.f64 (/.f64 1 (.f64 n (PI.f64))) 1/2))))
(sqrt.f64 (.f64 (/.f64 1 (.f64 n (PI.f64))) 1/2))
(/.f64 (.f64 (sqrt.f64 (.f64 (/.f64 1 (*.f64 n (PI.f64))) 1/2)) 2) 2)
(sqrt.f64 (.f64 (/.f64 1 (.f64 n (PI.f64))) 1/2))
(pow.f64 (sqrt.f64 (.f64 (/.f64 1 (.f64 n (PI.f64))) 1/2)) 1)
(sqrt.f64 (.f64 (/.f64 1 (.f64 n (PI.f64))) 1/2))
(neg.f64 (neg.f64 (sqrt.f64 (.f64 (/.f64 1 (.f64 n (PI.f64))) 1/2))))
(sqrt.f64 (.f64 (/.f64 1 (.f64 n (PI.f64))) 1/2))
(sqrt.f64 (.f64 (/.f64 1 (.f64 n (PI.f64))) 1/2))
(+.f64 (/.f64 1 (*.f64 n (PI.f64))) 0)
(/.f64 1 (*.f64 n (PI.f64)))
(+.f64 0 (/.f64 1 (*.f64 n (PI.f64))))
(/.f64 1 (*.f64 n (PI.f64)))
(+.f64 (.f64 (/.f64 1 (.f64 n (PI.f64))) 1/2) (.f64 (/.f64 1 (.f64 n (PI.f64))) 1/2))
(/.f64 1 (*.f64 n (PI.f64)))
(-.f64 (/.f64 1 (*.f64 n (PI.f64))) 0)
(/.f64 1 (*.f64 n (PI.f64)))
(-.f64 0 (neg.f64 (/.f64 1 (*.f64 n (PI.f64)))))
(/.f64 1 (*.f64 n (PI.f64)))
(.f64 1 (/.f64 1 (.f64 n (PI.f64))))
(/.f64 1 (*.f64 n (PI.f64)))
(.f64 (/.f64 1 (.f64 n (PI.f64))) 1)
(/.f64 1 (*.f64 n (PI.f64)))
(.f64 (/.f64 1 (.f64 n (PI.f64))) (/.f64 (/.f64 1 (.f64 n (PI.f64))) (/.f64 1 (.f64 n (PI.f64)))))
(/.f64 1 (*.f64 n (PI.f64)))
(.f64 (/.f64 1 (.f64 n (PI.f64))) (.f64 (/.f64 1 (.f64 n (PI.f64))) (/.f64 1 (/.f64 1 (*.f64 n (PI.f64))))))
(/.f64 1 (*.f64 n (PI.f64)))
(.f64 (/.f64 1 (.f64 n (PI.f64))) (/.f64 1 (/.f64 (/.f64 1 (.f64 n (PI.f64))) (/.f64 1 (.f64 n (PI.f64))))))
(/.f64 1 (*.f64 n (PI.f64)))
(.f64 (/.f64 (/.f64 1 (.f64 n (PI.f64))) (/.f64 1 (.f64 n (PI.f64)))) (/.f64 1 (.f64 n (PI.f64))))
(/.f64 1 (*.f64 n (PI.f64)))
(.f64 (.f64 (/.f64 1 (*.f64 n (PI.f64))) 1/2) 2)
(/.f64 1 (*.f64 n (PI.f64)))
(.f64 1/2 (.f64 (/.f64 1 (*.f64 n (PI.f64))) 2))
(/.f64 1 (*.f64 n (PI.f64)))
(.f64 (/.f64 1 (/.f64 1 (.f64 n (PI.f64)))) (.f64 (/.f64 1 (.f64 n (PI.f64))) (/.f64 1 (*.f64 n (PI.f64)))))
(/.f64 1 (*.f64 n (PI.f64)))
(.f64 (/.f64 1 (/.f64 1 (.f64 n (PI.f64)))) (+.f64 (.f64 (/.f64 1 (.f64 n (PI.f64))) (.f64 (/.f64 1 (.f64 n (PI.f64))) 1/2)) (.f64 (/.f64 1 (.f64 n (PI.f64))) (.f64 (/.f64 1 (.f64 n (PI.f64))) 1/2))))
(/.f64 1 (*.f64 n (PI.f64)))
(.f64 (.f64 (/.f64 1 (.f64 n (PI.f64))) (/.f64 1 (.f64 n (PI.f64)))) (/.f64 1 (/.f64 1 (*.f64 n (PI.f64)))))
(/.f64 1 (*.f64 n (PI.f64)))
(.f64 (.f64 (/.f64 1 (.f64 n (PI.f64))) (/.f64 1 (/.f64 1 (.f64 n (PI.f64))))) (/.f64 1 (*.f64 n (PI.f64))))
(/.f64 1 (*.f64 n (PI.f64)))
(.f64 (/.f64 1 (/.f64 (/.f64 1 (.f64 n (PI.f64))) (/.f64 1 (.f64 n (PI.f64))))) (.f64 (/.f64 1 (.f64 n (PI.f64))) (.f64 (/.f64 (/.f64 1 (.f64 n (PI.f64))) (/.f64 1 (.f64 n (PI.f64)))) (/.f64 (/.f64 1 (.f64 n (PI.f64))) (/.f64 1 (.f64 n (PI.f64)))))))
(/.f64 1 (*.f64 n (PI.f64)))
(.f64 (/.f64 (/.f64 1 (.f64 n (PI.f64))) 1/2) 1/2)
(.f64 1/2 (/.f64 (/.f64 1 (.f64 n (PI.f64))) 1/2))
(.f64 (/.f64 1 (.f64 (/.f64 1 (.f64 n (PI.f64))) 1/2)) (+.f64 (.f64 (/.f64 1 (.f64 n (PI.f64))) (.f64 (.f64 (/.f64 1 (.f64 n (PI.f64))) 1/2) 1/2)) (.f64 (/.f64 1 (.f64 n (PI.f64))) (.f64 (.f64 (/.f64 1 (*.f64 n (PI.f64))) 1/2) 1/2))))
(/.f64 1 (*.f64 n (PI.f64)))
(.f64 (/.f64 (/.f64 1 (/.f64 1 (.f64 n (PI.f64)))) (.f64 (/.f64 1 (.f64 n (PI.f64))) (/.f64 1 (.f64 n (PI.f64))))) (.f64 (/.f64 1 (.f64 n (PI.f64))) (.f64 (/.f64 1 (.f64 n (PI.f64))) (.f64 (/.f64 1 (.f64 n (PI.f64))) (/.f64 1 (.f64 n (PI.f64)))))))
(/.f64 1 (*.f64 n (PI.f64)))
(.f64 (/.f64 (/.f64 (/.f64 1 (.f64 n (PI.f64))) (/.f64 1 (.f64 n (PI.f64)))) (/.f64 1 (.f64 n (PI.f64)))) (.f64 (/.f64 1 (.f64 n (PI.f64))) (/.f64 1 (*.f64 n (PI.f64)))))
(/.f64 1 (*.f64 n (PI.f64)))
(.f64 (/.f64 (.f64 (/.f64 1 (.f64 n (PI.f64))) (/.f64 1 (/.f64 1 (.f64 n (PI.f64))))) (/.f64 1 (.f64 n (PI.f64)))) (.f64 (/.f64 1 (.f64 n (PI.f64))) (/.f64 1 (.f64 n (PI.f64)))))
(/.f64 1 (*.f64 n (PI.f64)))
(.f64 (/.f64 (.f64 (/.f64 1 (*.f64 n (PI.f64))) 2) 1/2) 1/4)
(/.f64 1 (*.f64 n (PI.f64)))
(.f64 (/.f64 (/.f64 1 (/.f64 (/.f64 1 (.f64 n (PI.f64))) (/.f64 1 (.f64 n (PI.f64))))) (/.f64 1 (.f64 n (PI.f64)))) (.f64 (/.f64 1 (.f64 n (PI.f64))) (/.f64 1 (*.f64 n (PI.f64)))))
(/.f64 1 (*.f64 n (PI.f64)))
(.f64 (/.f64 2 (.f64 (/.f64 1 (.f64 n (PI.f64))) 1/2)) (.f64 (/.f64 1 (.f64 n (PI.f64))) (.f64 (.f64 (/.f64 1 (.f64 n (PI.f64))) 1/2) 1/2)))
(/.f64 1 (*.f64 n (PI.f64)))
(pow.f64 (/.f64 1 (*.f64 n (PI.f64))) 1)
(/.f64 1 (*.f64 n (PI.f64)))
(neg.f64 (neg.f64 (/.f64 1 (*.f64 n (PI.f64)))))
(/.f64 1 (*.f64 n (PI.f64)))

localize62.0ms (0.4%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.3b	(*.f64 (PI.f64) n)
	0.4b	(*.f64 (/.f64 1 (/.f64 1 (sqrt.f64 k))) (/.f64 1 k))
✓	0.5b	(.f64 (pow.f64 (.f64 (.f64 2 (.f64 (PI.f64) n)) (.f64 2 (.f64 (PI.f64) n))) (/.f64 (-.f64 1 k) 2)) (/.f64 1 (pow.f64 (.f64 2 (.f64 (PI.f64) n)) (/.f64 (-.f64 1 k) 2))))
✓	19.8b	(pow.f64 (.f64 (.f64 2 (.f64 (PI.f64) n)) (.f64 2 (*.f64 (PI.f64) n))) (/.f64 (-.f64 1 k) 2))

Compiler

Compiled 173 to 109 computations (37% saved)

series25.0ms (0.2%)

Counts

3 → 60

Calls

15 calls:

Time	Variable		Point	Expression
12.0ms	n	@	0	(pow.f64 (.f64 (.f64 2 (.f64 (PI.f64) n)) (.f64 2 (*.f64 (PI.f64) n))) (/.f64 (-.f64 1 k) 2))
6.0ms	n	@	inf	(pow.f64 (.f64 (.f64 2 (.f64 (PI.f64) n)) (.f64 2 (*.f64 (PI.f64) n))) (/.f64 (-.f64 1 k) 2))
2.0ms	k	@	0	(.f64 (pow.f64 (.f64 (.f64 2 (.f64 (PI.f64) n)) (.f64 2 (.f64 (PI.f64) n))) (/.f64 (-.f64 1 k) 2)) (/.f64 1 (pow.f64 (.f64 2 (.f64 (PI.f64) n)) (/.f64 (-.f64 1 k) 2))))
1.0ms	k	@	0	(pow.f64 (.f64 (.f64 2 (.f64 (PI.f64) n)) (.f64 2 (*.f64 (PI.f64) n))) (/.f64 (-.f64 1 k) 2))
1.0ms	n	@	inf	(.f64 (pow.f64 (.f64 (.f64 2 (.f64 (PI.f64) n)) (.f64 2 (.f64 (PI.f64) n))) (/.f64 (-.f64 1 k) 2)) (/.f64 1 (pow.f64 (.f64 2 (.f64 (PI.f64) n)) (/.f64 (-.f64 1 k) 2))))

rewrite76.0ms (0.5%)

Algorithm

1×	batch-egg-rewrite

Rules

876×	`rational_best-2`
876×	`rational_best-3`
876×	`rational_best-1`
874×	`rational_best-5`
872×	`rational_best-4`

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	17	159
1	143	159
2	484	89
3	2084	89

Stop Event

1×	node limit

Counts

3 → 73

Calls

Call 1

Inputs

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

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

(*.f64 (PI.f64) n)

Outputs

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((#(struct:change #<rule egg-rr> (2) ((x +.f64 (pow.f64 (*.f64 2 (*.f64 (PI.f64) n)) (/.f64 (-.f64 1 k) 2)) 0)))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 0 (pow.f64 (*.f64 2 (*.f64 (PI.f64) n)) (/.f64 (-.f64 1 k) 2)))))) (#(struct:change #<rule egg-rr> (2) ((x -.f64 (pow.f64 (*.f64 2 (*.f64 (PI.f64) n)) (/.f64 (-.f64 1 k) 2)) 0)))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (pow.f64 (*.f64 2 (*.f64 (PI.f64) n)) (/.f64 (-.f64 1 k) 2)) 1)))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (pow.f64 (*.f64 2 (*.f64 (PI.f64) n)) (/.f64 (-.f64 1 k) 2)) (/.f64 (pow.f64 (*.f64 2 (*.f64 (PI.f64) n)) (/.f64 (-.f64 1 k) 2)) (pow.f64 (*.f64 2 (*.f64 (PI.f64) n)) (/.f64 (-.f64 1 k) 2))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (*.f64 2 (pow.f64 (*.f64 2 (*.f64 (PI.f64) n)) (/.f64 (-.f64 1 k) 2))) 2)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (*.f64 2 (*.f64 (PI.f64) n)) (/.f64 (-.f64 1 k) 2))))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (pow.f64 (*.f64 2 (*.f64 (PI.f64) n)) (/.f64 (-.f64 1 k) 2)) 1)))))

((#(struct:change #<rule egg-rr> (2) ((x +.f64 (*.f64 (PI.f64) n) 0)))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 0 (*.f64 (PI.f64) n))))) (#(struct:change #<rule egg-rr> (2) ((x -.f64 (*.f64 (PI.f64) n) 0)))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (*.f64 (PI.f64) n) 1)))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (*.f64 (PI.f64) n) (/.f64 (*.f64 (PI.f64) n) (*.f64 (PI.f64) n)))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (*.f64 2 (*.f64 (PI.f64) n)) 2)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (*.f64 (PI.f64) n) 1)))))

simplify180.0ms (1.2%)

Algorithm

1×	egg-herbie

Rules

1210×	`rational_best-simplify-2`
1126×	`rational_best-simplify-132`
1000×	`rational_best-simplify-129`
918×	`rational_best-simplify-47`
490×	`rational_best-simplify-44`

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	309	8981
1	685	8873
2	1365	8715
3	2420	8549
4	3601	8549

Stop Event

1×	node limit

Counts

133 → 159

Calls

Call 1

Inputs
(exp.f64 (.f64 1/2 (.f64 (-.f64 1 k) (+.f64 (log.f64 (.f64 4 (pow.f64 (PI.f64) 2))) (.f64 2 (log.f64 n))))))
(exp.f64 (.f64 1/2 (.f64 (-.f64 1 k) (+.f64 (log.f64 (.f64 4 (pow.f64 (PI.f64) 2))) (.f64 2 (log.f64 n))))))
(exp.f64 (.f64 1/2 (.f64 (-.f64 1 k) (+.f64 (log.f64 (.f64 4 (pow.f64 (PI.f64) 2))) (.f64 2 (log.f64 n))))))
(exp.f64 (.f64 1/2 (.f64 (-.f64 1 k) (+.f64 (log.f64 (.f64 4 (pow.f64 (PI.f64) 2))) (.f64 2 (log.f64 n))))))
(exp.f64 (.f64 1/2 (.f64 (-.f64 1 k) (+.f64 (log.f64 (.f64 4 (pow.f64 (PI.f64) 2))) (.f64 -2 (log.f64 (/.f64 1 n)))))))
(exp.f64 (.f64 1/2 (.f64 (-.f64 1 k) (+.f64 (log.f64 (.f64 4 (pow.f64 (PI.f64) 2))) (.f64 -2 (log.f64 (/.f64 1 n)))))))
(exp.f64 (.f64 1/2 (.f64 (-.f64 1 k) (+.f64 (log.f64 (.f64 4 (pow.f64 (PI.f64) 2))) (.f64 -2 (log.f64 (/.f64 1 n)))))))
(exp.f64 (.f64 1/2 (.f64 (-.f64 1 k) (+.f64 (log.f64 (.f64 4 (pow.f64 (PI.f64) 2))) (.f64 -2 (log.f64 (/.f64 1 n)))))))
(exp.f64 (.f64 1/2 (.f64 (-.f64 1 k) (+.f64 (log.f64 (.f64 4 (pow.f64 (PI.f64) 2))) (.f64 -2 (log.f64 (/.f64 -1 n)))))))
(exp.f64 (.f64 1/2 (.f64 (-.f64 1 k) (+.f64 (log.f64 (.f64 4 (pow.f64 (PI.f64) 2))) (.f64 -2 (log.f64 (/.f64 -1 n)))))))
(exp.f64 (.f64 1/2 (.f64 (-.f64 1 k) (+.f64 (log.f64 (.f64 4 (pow.f64 (PI.f64) 2))) (.f64 -2 (log.f64 (/.f64 -1 n)))))))
(exp.f64 (.f64 1/2 (.f64 (-.f64 1 k) (+.f64 (log.f64 (.f64 4 (pow.f64 (PI.f64) 2))) (.f64 -2 (log.f64 (/.f64 -1 n)))))))
(.f64 2 (.f64 n (PI.f64)))
(+.f64 (.f64 -1 (.f64 k (.f64 n (.f64 (log.f64 (.f64 4 (.f64 (pow.f64 n 2) (pow.f64 (PI.f64) 2)))) (PI.f64))))) (.f64 2 (.f64 n (PI.f64))))
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(+.f64 (.f64 -1 (.f64 k (.f64 n (.f64 (log.f64 (.f64 4 (.f64 (pow.f64 n 2) (pow.f64 (PI.f64) 2)))) (PI.f64))))) (+.f64 (.f64 2 (.f64 n (PI.f64))) (+.f64 (.f64 -1/24 (.f64 (pow.f64 k 3) (.f64 n (.f64 (pow.f64 (log.f64 (.f64 4 (.f64 (pow.f64 n 2) (pow.f64 (PI.f64) 2)))) 3) (PI.f64))))) (.f64 1/4 (.f64 (pow.f64 k 2) (.f64 n (.f64 (pow.f64 (log.f64 (.f64 4 (.f64 (pow.f64 n 2) (pow.f64 (PI.f64) 2)))) 2) (PI.f64))))))))
(exp.f64 (.f64 1/2 (.f64 (-.f64 1 k) (log.f64 (.f64 4 (.f64 (pow.f64 n 2) (pow.f64 (PI.f64) 2)))))))
(exp.f64 (.f64 1/2 (.f64 (-.f64 1 k) (log.f64 (.f64 4 (.f64 (pow.f64 n 2) (pow.f64 (PI.f64) 2)))))))
(exp.f64 (.f64 1/2 (.f64 (-.f64 1 k) (log.f64 (.f64 4 (.f64 (pow.f64 n 2) (pow.f64 (PI.f64) 2)))))))
(exp.f64 (.f64 1/2 (.f64 (-.f64 1 k) (log.f64 (.f64 4 (.f64 (pow.f64 n 2) (pow.f64 (PI.f64) 2)))))))
(exp.f64 (.f64 1/2 (.f64 (log.f64 (.f64 4 (.f64 (pow.f64 n 2) (pow.f64 (PI.f64) 2)))) (+.f64 1 (*.f64 -1 k)))))
(exp.f64 (.f64 1/2 (.f64 (log.f64 (.f64 4 (.f64 (pow.f64 n 2) (pow.f64 (PI.f64) 2)))) (+.f64 1 (*.f64 -1 k)))))
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(/.f64 (exp.f64 (.f64 1/2 (.f64 (-.f64 1 k) (+.f64 (log.f64 (.f64 4 (pow.f64 (PI.f64) 2))) (.f64 2 (log.f64 n)))))) (exp.f64 (.f64 1/2 (.f64 (-.f64 1 k) (+.f64 (log.f64 (*.f64 2 (PI.f64))) (log.f64 n))))))
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(/.f64 (exp.f64 (.f64 1/2 (.f64 (-.f64 1 k) (+.f64 (log.f64 (.f64 4 (pow.f64 (PI.f64) 2))) (.f64 2 (log.f64 n)))))) (exp.f64 (.f64 1/2 (.f64 (-.f64 1 k) (+.f64 (log.f64 (*.f64 2 (PI.f64))) (log.f64 n))))))
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(fabs.f64 (.f64 (/.f64 (pow.f64 (.f64 2 (.f64 (PI.f64) n)) (/.f64 (-.f64 1 k) 2)) (fabs.f64 (/.f64 (pow.f64 (.f64 2 (.f64 (PI.f64) n)) (/.f64 (-.f64 1 k) 2)) (pow.f64 (.f64 2 (.f64 (PI.f64) n)) (/.f64 (-.f64 1 k) 2))))) (/.f64 (pow.f64 (.f64 2 (.f64 (PI.f64) n)) (/.f64 (-.f64 1 k) 2)) (fabs.f64 (/.f64 (pow.f64 (.f64 2 (.f64 (PI.f64) n)) (/.f64 (-.f64 1 k) 2)) (pow.f64 (.f64 2 (*.f64 (PI.f64) n)) (/.f64 (-.f64 1 k) 2)))))))
(fabs.f64 (/.f64 (neg.f64 (pow.f64 (.f64 (PI.f64) (.f64 n (.f64 (PI.f64) (.f64 n 4)))) (/.f64 (-.f64 1 k) 2))) (fabs.f64 (/.f64 (pow.f64 (.f64 2 (.f64 (PI.f64) n)) (/.f64 (-.f64 1 k) 2)) (pow.f64 (.f64 2 (.f64 (PI.f64) n)) (/.f64 (-.f64 1 k) 2))))))
(fabs.f64 (/.f64 (pow.f64 (.f64 (PI.f64) (.f64 n (.f64 (PI.f64) (.f64 n 4)))) (/.f64 (-.f64 1 k) 2)) (neg.f64 (/.f64 (pow.f64 (.f64 2 (.f64 (PI.f64) n)) (/.f64 (-.f64 1 k) 2)) (pow.f64 (.f64 2 (.f64 (PI.f64) n)) (/.f64 (-.f64 1 k) 2))))))
(fabs.f64 (.f64 (fabs.f64 (/.f64 (pow.f64 (.f64 2 (.f64 (PI.f64) n)) (/.f64 (-.f64 1 k) 2)) (pow.f64 (.f64 2 (.f64 (PI.f64) n)) (/.f64 (-.f64 1 k) 2)))) (pow.f64 (.f64 (PI.f64) (.f64 n (.f64 (PI.f64) (*.f64 n 4)))) (/.f64 (-.f64 1 k) 2))))
(fabs.f64 (.f64 (fabs.f64 (/.f64 (pow.f64 (.f64 2 (.f64 (PI.f64) n)) (/.f64 (-.f64 1 k) 2)) (pow.f64 (.f64 2 (.f64 (PI.f64) n)) (/.f64 (-.f64 1 k) 2)))) (neg.f64 (pow.f64 (.f64 (PI.f64) (.f64 n (.f64 (PI.f64) (*.f64 n 4)))) (/.f64 (-.f64 1 k) 2)))))
(fabs.f64 (.f64 (fabs.f64 (/.f64 (pow.f64 (.f64 2 (.f64 (PI.f64) n)) (/.f64 (-.f64 1 k) 2)) (pow.f64 (.f64 2 (.f64 (PI.f64) n)) (/.f64 (-.f64 1 k) 2)))) (.f64 1 (/.f64 (pow.f64 (.f64 (PI.f64) (.f64 n (.f64 (PI.f64) (.f64 n 4)))) (/.f64 (-.f64 1 k) 2)) (fabs.f64 (/.f64 (pow.f64 (.f64 2 (.f64 (PI.f64) n)) (/.f64 (-.f64 1 k) 2)) (pow.f64 (.f64 2 (.f64 (PI.f64) n)) (/.f64 (-.f64 1 k) 2))))))))
(fabs.f64 (.f64 1 (.f64 (/.f64 (pow.f64 (.f64 2 (.f64 (PI.f64) n)) (/.f64 (-.f64 1 k) 2)) (pow.f64 (.f64 2 (.f64 (PI.f64) n)) (/.f64 (-.f64 1 k) 2))) (neg.f64 (pow.f64 (.f64 (PI.f64) (.f64 n (.f64 (PI.f64) (.f64 n 4)))) (/.f64 (-.f64 1 k) 2))))))
(fabs.f64 (.f64 1 (.f64 (/.f64 (pow.f64 (.f64 2 (.f64 (PI.f64) n)) (/.f64 (-.f64 1 k) 2)) (pow.f64 (.f64 2 (.f64 (PI.f64) n)) (/.f64 (-.f64 1 k) 2))) (/.f64 (pow.f64 (.f64 (PI.f64) (.f64 n (.f64 (PI.f64) (.f64 n 4)))) (/.f64 (-.f64 1 k) 2)) (fabs.f64 (/.f64 (pow.f64 (.f64 2 (.f64 (PI.f64) n)) (/.f64 (-.f64 1 k) 2)) (pow.f64 (.f64 2 (.f64 (PI.f64) n)) (/.f64 (-.f64 1 k) 2))))))))
(fabs.f64 (.f64 (.f64 (/.f64 (pow.f64 (.f64 2 (.f64 (PI.f64) n)) (/.f64 (-.f64 1 k) 2)) (pow.f64 (.f64 2 (.f64 (PI.f64) n)) (/.f64 (-.f64 1 k) 2))) (/.f64 (pow.f64 (.f64 2 (.f64 (PI.f64) n)) (/.f64 (-.f64 1 k) 2)) (pow.f64 (.f64 2 (.f64 (PI.f64) n)) (/.f64 (-.f64 1 k) 2)))) (.f64 (/.f64 1 (/.f64 (pow.f64 (.f64 2 (.f64 (PI.f64) n)) (/.f64 (-.f64 1 k) 2)) (pow.f64 (.f64 2 (.f64 (PI.f64) n)) (/.f64 (-.f64 1 k) 2)))) (pow.f64 (.f64 (PI.f64) (.f64 n (.f64 (PI.f64) (*.f64 n 4)))) (/.f64 (-.f64 1 k) 2)))))
(fabs.f64 (.f64 (.f64 (/.f64 (pow.f64 (.f64 2 (.f64 (PI.f64) n)) (/.f64 (-.f64 1 k) 2)) (pow.f64 (.f64 2 (.f64 (PI.f64) n)) (/.f64 (-.f64 1 k) 2))) (/.f64 (pow.f64 (.f64 2 (.f64 (PI.f64) n)) (/.f64 (-.f64 1 k) 2)) (pow.f64 (.f64 2 (.f64 (PI.f64) n)) (/.f64 (-.f64 1 k) 2)))) (.f64 (/.f64 1 (/.f64 (pow.f64 (.f64 2 (.f64 (PI.f64) n)) (/.f64 (-.f64 1 k) 2)) (pow.f64 (.f64 2 (.f64 (PI.f64) n)) (/.f64 (-.f64 1 k) 2)))) (neg.f64 (pow.f64 (.f64 (PI.f64) (.f64 n (.f64 (PI.f64) (*.f64 n 4)))) (/.f64 (-.f64 1 k) 2))))))
(fabs.f64 (.f64 (.f64 (/.f64 (pow.f64 (.f64 2 (.f64 (PI.f64) n)) (/.f64 (-.f64 1 k) 2)) (pow.f64 (.f64 2 (.f64 (PI.f64) n)) (/.f64 (-.f64 1 k) 2))) (/.f64 (pow.f64 (.f64 2 (.f64 (PI.f64) n)) (/.f64 (-.f64 1 k) 2)) (pow.f64 (.f64 2 (.f64 (PI.f64) n)) (/.f64 (-.f64 1 k) 2)))) (.f64 (/.f64 1 (/.f64 (pow.f64 (.f64 2 (.f64 (PI.f64) n)) (/.f64 (-.f64 1 k) 2)) (pow.f64 (.f64 2 (.f64 (PI.f64) n)) (/.f64 (-.f64 1 k) 2)))) (/.f64 (pow.f64 (.f64 (PI.f64) (.f64 n (.f64 (PI.f64) (.f64 n 4)))) (/.f64 (-.f64 1 k) 2)) (fabs.f64 (/.f64 (pow.f64 (.f64 2 (.f64 (PI.f64) n)) (/.f64 (-.f64 1 k) 2)) (pow.f64 (.f64 2 (*.f64 (PI.f64) n)) (/.f64 (-.f64 1 k) 2))))))))
(fabs.f64 (.f64 (fabs.f64 (/.f64 1 (pow.f64 (.f64 2 (.f64 (PI.f64) n)) (/.f64 (-.f64 1 k) 2)))) (.f64 (pow.f64 (.f64 (PI.f64) (.f64 n (.f64 (PI.f64) (.f64 n 4)))) (/.f64 (-.f64 1 k) 2)) (pow.f64 (.f64 2 (.f64 (PI.f64) n)) (/.f64 (-.f64 1 k) 2)))))
(fabs.f64 (.f64 (fabs.f64 (/.f64 1 (pow.f64 (.f64 2 (.f64 (PI.f64) n)) (/.f64 (-.f64 1 k) 2)))) (.f64 (pow.f64 (.f64 2 (.f64 (PI.f64) n)) (/.f64 (-.f64 1 k) 2)) (neg.f64 (pow.f64 (.f64 (PI.f64) (.f64 n (.f64 (PI.f64) (.f64 n 4)))) (/.f64 (-.f64 1 k) 2))))))
(fabs.f64 (.f64 (fabs.f64 (/.f64 1 (pow.f64 (.f64 2 (.f64 (PI.f64) n)) (/.f64 (-.f64 1 k) 2)))) (.f64 (pow.f64 (.f64 2 (.f64 (PI.f64) n)) (/.f64 (-.f64 1 k) 2)) (/.f64 (pow.f64 (.f64 (PI.f64) (.f64 n (.f64 (PI.f64) (.f64 n 4)))) (/.f64 (-.f64 1 k) 2)) (fabs.f64 (/.f64 (pow.f64 (.f64 2 (.f64 (PI.f64) n)) (/.f64 (-.f64 1 k) 2)) (pow.f64 (.f64 2 (.f64 (PI.f64) n)) (/.f64 (-.f64 1 k) 2))))))))
(fabs.f64 (.f64 (pow.f64 (.f64 (PI.f64) (.f64 n (.f64 (PI.f64) (.f64 n 4)))) (/.f64 (-.f64 1 k) 2)) (.f64 (/.f64 1 (pow.f64 (.f64 (PI.f64) (.f64 n (.f64 (PI.f64) (.f64 n 4)))) (/.f64 (-.f64 1 k) 2))) (neg.f64 (pow.f64 (.f64 (PI.f64) (.f64 n (.f64 (PI.f64) (.f64 n 4)))) (/.f64 (-.f64 1 k) 2))))))
(fabs.f64 (.f64 (pow.f64 (.f64 (PI.f64) (.f64 n (.f64 (PI.f64) (.f64 n 4)))) (/.f64 (-.f64 1 k) 2)) (.f64 (/.f64 1 (pow.f64 (.f64 (PI.f64) (.f64 n (.f64 (PI.f64) (.f64 n 4)))) (/.f64 (-.f64 1 k) 2))) (/.f64 (pow.f64 (.f64 (PI.f64) (.f64 n (.f64 (PI.f64) (.f64 n 4)))) (/.f64 (-.f64 1 k) 2)) (fabs.f64 (/.f64 (pow.f64 (.f64 2 (.f64 (PI.f64) n)) (/.f64 (-.f64 1 k) 2)) (pow.f64 (.f64 2 (.f64 (PI.f64) n)) (/.f64 (-.f64 1 k) 2))))))))
(+.f64 (pow.f64 (.f64 2 (.f64 (PI.f64) n)) (/.f64 (-.f64 1 k) 2)) 0)
(+.f64 0 (pow.f64 (.f64 2 (.f64 (PI.f64) n)) (/.f64 (-.f64 1 k) 2)))
(-.f64 (pow.f64 (.f64 2 (.f64 (PI.f64) n)) (/.f64 (-.f64 1 k) 2)) 0)
(/.f64 (pow.f64 (.f64 2 (.f64 (PI.f64) n)) (/.f64 (-.f64 1 k) 2)) 1)
(/.f64 (pow.f64 (.f64 2 (.f64 (PI.f64) n)) (/.f64 (-.f64 1 k) 2)) (/.f64 (pow.f64 (.f64 2 (.f64 (PI.f64) n)) (/.f64 (-.f64 1 k) 2)) (pow.f64 (.f64 2 (.f64 (PI.f64) n)) (/.f64 (-.f64 1 k) 2))))
(/.f64 (.f64 2 (pow.f64 (.f64 2 (*.f64 (PI.f64) n)) (/.f64 (-.f64 1 k) 2))) 2)
(pow.f64 (.f64 2 (.f64 (PI.f64) n)) (/.f64 (-.f64 1 k) 2))
(pow.f64 (pow.f64 (.f64 2 (.f64 (PI.f64) n)) (/.f64 (-.f64 1 k) 2)) 1)
(+.f64 (*.f64 (PI.f64) n) 0)
(+.f64 0 (*.f64 (PI.f64) n))
(-.f64 (*.f64 (PI.f64) n) 0)
(/.f64 (*.f64 (PI.f64) n) 1)
(/.f64 (.f64 (PI.f64) n) (/.f64 (.f64 (PI.f64) n) (*.f64 (PI.f64) n)))
(/.f64 (.f64 2 (.f64 (PI.f64) n)) 2)
(pow.f64 (*.f64 (PI.f64) n) 1)

Outputs
(exp.f64 (.f64 1/2 (.f64 (-.f64 1 k) (+.f64 (log.f64 (.f64 4 (pow.f64 (PI.f64) 2))) (.f64 2 (log.f64 n))))))
(exp.f64 (.f64 (+.f64 (log.f64 (.f64 4 (pow.f64 (PI.f64) 2))) (.f64 2 (log.f64 n))) (.f64 1/2 (-.f64 1 k))))
(exp.f64 (.f64 (-.f64 1 k) (.f64 1/2 (+.f64 (log.f64 (.f64 4 (pow.f64 (PI.f64) 2))) (.f64 2 (log.f64 n))))))
(exp.f64 (.f64 1/2 (.f64 (-.f64 1 k) (+.f64 (log.f64 (.f64 4 (pow.f64 (PI.f64) 2))) (.f64 2 (log.f64 n))))))
(exp.f64 (.f64 (+.f64 (log.f64 (.f64 4 (pow.f64 (PI.f64) 2))) (.f64 2 (log.f64 n))) (.f64 1/2 (-.f64 1 k))))
(exp.f64 (.f64 (-.f64 1 k) (.f64 1/2 (+.f64 (log.f64 (.f64 4 (pow.f64 (PI.f64) 2))) (.f64 2 (log.f64 n))))))
(exp.f64 (.f64 1/2 (.f64 (-.f64 1 k) (+.f64 (log.f64 (.f64 4 (pow.f64 (PI.f64) 2))) (.f64 2 (log.f64 n))))))
(exp.f64 (.f64 (+.f64 (log.f64 (.f64 4 (pow.f64 (PI.f64) 2))) (.f64 2 (log.f64 n))) (.f64 1/2 (-.f64 1 k))))
(exp.f64 (.f64 (-.f64 1 k) (.f64 1/2 (+.f64 (log.f64 (.f64 4 (pow.f64 (PI.f64) 2))) (.f64 2 (log.f64 n))))))
(exp.f64 (.f64 1/2 (.f64 (-.f64 1 k) (+.f64 (log.f64 (.f64 4 (pow.f64 (PI.f64) 2))) (.f64 2 (log.f64 n))))))
(exp.f64 (.f64 (+.f64 (log.f64 (.f64 4 (pow.f64 (PI.f64) 2))) (.f64 2 (log.f64 n))) (.f64 1/2 (-.f64 1 k))))
(exp.f64 (.f64 (-.f64 1 k) (.f64 1/2 (+.f64 (log.f64 (.f64 4 (pow.f64 (PI.f64) 2))) (.f64 2 (log.f64 n))))))
(exp.f64 (.f64 1/2 (.f64 (-.f64 1 k) (+.f64 (log.f64 (.f64 4 (pow.f64 (PI.f64) 2))) (.f64 -2 (log.f64 (/.f64 1 n)))))))
(exp.f64 (.f64 (+.f64 (log.f64 (.f64 4 (pow.f64 (PI.f64) 2))) (.f64 -2 (log.f64 (/.f64 1 n)))) (.f64 1/2 (-.f64 1 k))))
(exp.f64 (.f64 (-.f64 1 k) (.f64 1/2 (+.f64 (log.f64 (.f64 4 (pow.f64 (PI.f64) 2))) (.f64 -2 (log.f64 (/.f64 1 n)))))))
(exp.f64 (.f64 1/2 (.f64 (-.f64 1 k) (+.f64 (log.f64 (.f64 4 (pow.f64 (PI.f64) 2))) (.f64 -2 (log.f64 (/.f64 1 n)))))))
(exp.f64 (.f64 (+.f64 (log.f64 (.f64 4 (pow.f64 (PI.f64) 2))) (.f64 -2 (log.f64 (/.f64 1 n)))) (.f64 1/2 (-.f64 1 k))))
(exp.f64 (.f64 (-.f64 1 k) (.f64 1/2 (+.f64 (log.f64 (.f64 4 (pow.f64 (PI.f64) 2))) (.f64 -2 (log.f64 (/.f64 1 n)))))))
(exp.f64 (.f64 1/2 (.f64 (-.f64 1 k) (+.f64 (log.f64 (.f64 4 (pow.f64 (PI.f64) 2))) (.f64 -2 (log.f64 (/.f64 1 n)))))))
(exp.f64 (.f64 (+.f64 (log.f64 (.f64 4 (pow.f64 (PI.f64) 2))) (.f64 -2 (log.f64 (/.f64 1 n)))) (.f64 1/2 (-.f64 1 k))))
(exp.f64 (.f64 (-.f64 1 k) (.f64 1/2 (+.f64 (log.f64 (.f64 4 (pow.f64 (PI.f64) 2))) (.f64 -2 (log.f64 (/.f64 1 n)))))))
(exp.f64 (.f64 1/2 (.f64 (-.f64 1 k) (+.f64 (log.f64 (.f64 4 (pow.f64 (PI.f64) 2))) (.f64 -2 (log.f64 (/.f64 1 n)))))))
(exp.f64 (.f64 (+.f64 (log.f64 (.f64 4 (pow.f64 (PI.f64) 2))) (.f64 -2 (log.f64 (/.f64 1 n)))) (.f64 1/2 (-.f64 1 k))))
(exp.f64 (.f64 (-.f64 1 k) (.f64 1/2 (+.f64 (log.f64 (.f64 4 (pow.f64 (PI.f64) 2))) (.f64 -2 (log.f64 (/.f64 1 n)))))))
(exp.f64 (.f64 1/2 (.f64 (-.f64 1 k) (+.f64 (log.f64 (.f64 4 (pow.f64 (PI.f64) 2))) (.f64 -2 (log.f64 (/.f64 -1 n)))))))
(exp.f64 (.f64 (+.f64 (log.f64 (.f64 4 (pow.f64 (PI.f64) 2))) (.f64 -2 (log.f64 (/.f64 -1 n)))) (.f64 1/2 (-.f64 1 k))))
(exp.f64 (.f64 1/2 (.f64 (-.f64 1 k) (+.f64 (log.f64 (.f64 4 (pow.f64 (PI.f64) 2))) (.f64 -2 (log.f64 (/.f64 -1 n)))))))
(exp.f64 (.f64 (+.f64 (log.f64 (.f64 4 (pow.f64 (PI.f64) 2))) (.f64 -2 (log.f64 (/.f64 -1 n)))) (.f64 1/2 (-.f64 1 k))))
(exp.f64 (.f64 1/2 (.f64 (-.f64 1 k) (+.f64 (log.f64 (.f64 4 (pow.f64 (PI.f64) 2))) (.f64 -2 (log.f64 (/.f64 -1 n)))))))
(exp.f64 (.f64 (+.f64 (log.f64 (.f64 4 (pow.f64 (PI.f64) 2))) (.f64 -2 (log.f64 (/.f64 -1 n)))) (.f64 1/2 (-.f64 1 k))))
(exp.f64 (.f64 1/2 (.f64 (-.f64 1 k) (+.f64 (log.f64 (.f64 4 (pow.f64 (PI.f64) 2))) (.f64 -2 (log.f64 (/.f64 -1 n)))))))
(exp.f64 (.f64 (+.f64 (log.f64 (.f64 4 (pow.f64 (PI.f64) 2))) (.f64 -2 (log.f64 (/.f64 -1 n)))) (.f64 1/2 (-.f64 1 k))))
(.f64 2 (.f64 n (PI.f64)))
(.f64 2 (.f64 (PI.f64) n))
(.f64 (PI.f64) (.f64 2 n))
(+.f64 (.f64 -1 (.f64 k (.f64 n (.f64 (log.f64 (.f64 4 (.f64 (pow.f64 n 2) (pow.f64 (PI.f64) 2)))) (PI.f64))))) (.f64 2 (.f64 n (PI.f64))))
(+.f64 (.f64 k (.f64 -1 (.f64 n (.f64 (PI.f64) (log.f64 (.f64 4 (pow.f64 (.f64 (PI.f64) n) 2))))))) (.f64 2 (.f64 (PI.f64) n)))
(+.f64 (.f64 (.f64 (PI.f64) (.f64 n (log.f64 (.f64 4 (pow.f64 (.f64 (PI.f64) n) 2))))) (neg.f64 k)) (.f64 (PI.f64) (*.f64 2 n)))
(.f64 n (+.f64 (.f64 (PI.f64) 2) (.f64 -1 (.f64 k (.f64 (PI.f64) (log.f64 (.f64 4 (pow.f64 (*.f64 (PI.f64) n) 2))))))))
(.f64 n (+.f64 (.f64 (PI.f64) 2) (neg.f64 (.f64 k (.f64 (PI.f64) (log.f64 (.f64 4 (pow.f64 (.f64 (PI.f64) n) 2))))))))
(+.f64 (.f64 -1 (.f64 k (.f64 n (.f64 (log.f64 (.f64 4 (.f64 (pow.f64 n 2) (pow.f64 (PI.f64) 2)))) (PI.f64))))) (+.f64 (.f64 2 (.f64 n (PI.f64))) (.f64 1/4 (.f64 (pow.f64 k 2) (.f64 n (.f64 (pow.f64 (log.f64 (.f64 4 (.f64 (pow.f64 n 2) (pow.f64 (PI.f64) 2)))) 2) (PI.f64)))))))
(+.f64 (.f64 k (.f64 -1 (.f64 n (.f64 (PI.f64) (log.f64 (.f64 4 (pow.f64 (.f64 (PI.f64) n) 2))))))) (+.f64 (.f64 1/4 (.f64 n (.f64 (pow.f64 k 2) (.f64 (PI.f64) (pow.f64 (log.f64 (.f64 4 (pow.f64 (.f64 (PI.f64) n) 2))) 2))))) (.f64 2 (.f64 (PI.f64) n))))
(+.f64 (.f64 (PI.f64) (.f64 2 n)) (+.f64 (.f64 (.f64 (PI.f64) (.f64 n (log.f64 (.f64 4 (pow.f64 (.f64 (PI.f64) n) 2))))) (neg.f64 k)) (.f64 (.f64 (pow.f64 (log.f64 (.f64 4 (pow.f64 (.f64 (PI.f64) n) 2))) 2) (.f64 (PI.f64) n)) (*.f64 1/4 (pow.f64 k 2)))))
(+.f64 (.f64 (.f64 (log.f64 (.f64 4 (pow.f64 (.f64 (PI.f64) n) 2))) (.f64 (PI.f64) n)) (neg.f64 k)) (.f64 n (+.f64 (.f64 1/4 (.f64 (PI.f64) (pow.f64 (.f64 k (log.f64 (.f64 4 (pow.f64 (.f64 (PI.f64) n) 2)))) 2))) (.f64 (PI.f64) 2))))
(.f64 n (+.f64 (.f64 1/4 (.f64 (PI.f64) (pow.f64 (.f64 k (log.f64 (.f64 4 (pow.f64 (.f64 (PI.f64) n) 2)))) 2))) (+.f64 (.f64 (PI.f64) 2) (neg.f64 (.f64 k (.f64 (PI.f64) (log.f64 (.f64 4 (pow.f64 (*.f64 (PI.f64) n) 2)))))))))
(.f64 n (+.f64 (.f64 (PI.f64) 2) (+.f64 (.f64 1/4 (.f64 (PI.f64) (pow.f64 (.f64 k (log.f64 (.f64 4 (pow.f64 (.f64 (PI.f64) n) 2)))) 2))) (neg.f64 (.f64 k (.f64 (PI.f64) (log.f64 (.f64 4 (pow.f64 (*.f64 (PI.f64) n) 2)))))))))
(+.f64 (.f64 -1 (.f64 k (.f64 n (.f64 (log.f64 (.f64 4 (.f64 (pow.f64 n 2) (pow.f64 (PI.f64) 2)))) (PI.f64))))) (+.f64 (.f64 2 (.f64 n (PI.f64))) (+.f64 (.f64 -1/24 (.f64 (pow.f64 k 3) (.f64 n (.f64 (pow.f64 (log.f64 (.f64 4 (.f64 (pow.f64 n 2) (pow.f64 (PI.f64) 2)))) 3) (PI.f64))))) (.f64 1/4 (.f64 (pow.f64 k 2) (.f64 n (.f64 (pow.f64 (log.f64 (.f64 4 (.f64 (pow.f64 n 2) (pow.f64 (PI.f64) 2)))) 2) (PI.f64))))))))
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(fabs.f64 (.f64 (fabs.f64 (/.f64 (pow.f64 (.f64 2 (.f64 (PI.f64) n)) (/.f64 (-.f64 1 k) 2)) (pow.f64 (.f64 2 (.f64 (PI.f64) n)) (/.f64 (-.f64 1 k) 2)))) (pow.f64 (.f64 (PI.f64) (.f64 n (.f64 (PI.f64) (*.f64 n 4)))) (/.f64 (-.f64 1 k) 2))))
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(fabs.f64 (.f64 (fabs.f64 (/.f64 (pow.f64 (.f64 2 (.f64 (PI.f64) n)) (/.f64 (-.f64 1 k) 2)) (pow.f64 (.f64 2 (.f64 (PI.f64) n)) (/.f64 (-.f64 1 k) 2)))) (.f64 1 (/.f64 (pow.f64 (.f64 (PI.f64) (.f64 n (.f64 (PI.f64) (.f64 n 4)))) (/.f64 (-.f64 1 k) 2)) (fabs.f64 (/.f64 (pow.f64 (.f64 2 (.f64 (PI.f64) n)) (/.f64 (-.f64 1 k) 2)) (pow.f64 (.f64 2 (.f64 (PI.f64) n)) (/.f64 (-.f64 1 k) 2))))))))
(pow.f64 (.f64 (PI.f64) (.f64 (PI.f64) (.f64 n (.f64 4 n)))) (/.f64 (-.f64 1 k) 2))
(pow.f64 (.f64 n (.f64 (PI.f64) (.f64 (PI.f64) (.f64 4 n)))) (/.f64 (-.f64 1 k) 2))
(pow.f64 (.f64 (PI.f64) (.f64 (PI.f64) (.f64 4 (.f64 n n)))) (/.f64 (-.f64 1 k) 2))
(pow.f64 (.f64 (PI.f64) (.f64 (.f64 4 n) (.f64 (PI.f64) n))) (/.f64 (-.f64 1 k) 2))
(fabs.f64 (.f64 1 (.f64 (/.f64 (pow.f64 (.f64 2 (.f64 (PI.f64) n)) (/.f64 (-.f64 1 k) 2)) (pow.f64 (.f64 2 (.f64 (PI.f64) n)) (/.f64 (-.f64 1 k) 2))) (neg.f64 (pow.f64 (.f64 (PI.f64) (.f64 n (.f64 (PI.f64) (.f64 n 4)))) (/.f64 (-.f64 1 k) 2))))))
(pow.f64 (.f64 (PI.f64) (.f64 (PI.f64) (.f64 n (.f64 4 n)))) (/.f64 (-.f64 1 k) 2))
(pow.f64 (.f64 n (.f64 (PI.f64) (.f64 (PI.f64) (.f64 4 n)))) (/.f64 (-.f64 1 k) 2))
(pow.f64 (.f64 (PI.f64) (.f64 (PI.f64) (.f64 4 (.f64 n n)))) (/.f64 (-.f64 1 k) 2))
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(fabs.f64 (.f64 1 (.f64 (/.f64 (pow.f64 (.f64 2 (.f64 (PI.f64) n)) (/.f64 (-.f64 1 k) 2)) (pow.f64 (.f64 2 (.f64 (PI.f64) n)) (/.f64 (-.f64 1 k) 2))) (/.f64 (pow.f64 (.f64 (PI.f64) (.f64 n (.f64 (PI.f64) (.f64 n 4)))) (/.f64 (-.f64 1 k) 2)) (fabs.f64 (/.f64 (pow.f64 (.f64 2 (.f64 (PI.f64) n)) (/.f64 (-.f64 1 k) 2)) (pow.f64 (.f64 2 (.f64 (PI.f64) n)) (/.f64 (-.f64 1 k) 2))))))))
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(pow.f64 (.f64 n (.f64 (PI.f64) (.f64 (PI.f64) (.f64 4 n)))) (/.f64 (-.f64 1 k) 2))
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(pow.f64 (.f64 (PI.f64) (.f64 (.f64 4 n) (.f64 (PI.f64) n))) (/.f64 (-.f64 1 k) 2))
(fabs.f64 (.f64 (.f64 (/.f64 (pow.f64 (.f64 2 (.f64 (PI.f64) n)) (/.f64 (-.f64 1 k) 2)) (pow.f64 (.f64 2 (.f64 (PI.f64) n)) (/.f64 (-.f64 1 k) 2))) (/.f64 (pow.f64 (.f64 2 (.f64 (PI.f64) n)) (/.f64 (-.f64 1 k) 2)) (pow.f64 (.f64 2 (.f64 (PI.f64) n)) (/.f64 (-.f64 1 k) 2)))) (.f64 (/.f64 1 (/.f64 (pow.f64 (.f64 2 (.f64 (PI.f64) n)) (/.f64 (-.f64 1 k) 2)) (pow.f64 (.f64 2 (.f64 (PI.f64) n)) (/.f64 (-.f64 1 k) 2)))) (pow.f64 (.f64 (PI.f64) (.f64 n (.f64 (PI.f64) (*.f64 n 4)))) (/.f64 (-.f64 1 k) 2)))))
(pow.f64 (.f64 (PI.f64) (.f64 (PI.f64) (.f64 n (.f64 4 n)))) (/.f64 (-.f64 1 k) 2))
(pow.f64 (.f64 n (.f64 (PI.f64) (.f64 (PI.f64) (.f64 4 n)))) (/.f64 (-.f64 1 k) 2))
(pow.f64 (.f64 (PI.f64) (.f64 (PI.f64) (.f64 4 (.f64 n n)))) (/.f64 (-.f64 1 k) 2))
(pow.f64 (.f64 (PI.f64) (.f64 (.f64 4 n) (.f64 (PI.f64) n))) (/.f64 (-.f64 1 k) 2))
(fabs.f64 (.f64 (.f64 (/.f64 (pow.f64 (.f64 2 (.f64 (PI.f64) n)) (/.f64 (-.f64 1 k) 2)) (pow.f64 (.f64 2 (.f64 (PI.f64) n)) (/.f64 (-.f64 1 k) 2))) (/.f64 (pow.f64 (.f64 2 (.f64 (PI.f64) n)) (/.f64 (-.f64 1 k) 2)) (pow.f64 (.f64 2 (.f64 (PI.f64) n)) (/.f64 (-.f64 1 k) 2)))) (.f64 (/.f64 1 (/.f64 (pow.f64 (.f64 2 (.f64 (PI.f64) n)) (/.f64 (-.f64 1 k) 2)) (pow.f64 (.f64 2 (.f64 (PI.f64) n)) (/.f64 (-.f64 1 k) 2)))) (neg.f64 (pow.f64 (.f64 (PI.f64) (.f64 n (.f64 (PI.f64) (*.f64 n 4)))) (/.f64 (-.f64 1 k) 2))))))
(pow.f64 (.f64 (PI.f64) (.f64 (PI.f64) (.f64 n (.f64 4 n)))) (/.f64 (-.f64 1 k) 2))
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(pow.f64 (.f64 (PI.f64) (.f64 (.f64 4 n) (.f64 (PI.f64) n))) (/.f64 (-.f64 1 k) 2))
(fabs.f64 (.f64 (.f64 (/.f64 (pow.f64 (.f64 2 (.f64 (PI.f64) n)) (/.f64 (-.f64 1 k) 2)) (pow.f64 (.f64 2 (.f64 (PI.f64) n)) (/.f64 (-.f64 1 k) 2))) (/.f64 (pow.f64 (.f64 2 (.f64 (PI.f64) n)) (/.f64 (-.f64 1 k) 2)) (pow.f64 (.f64 2 (.f64 (PI.f64) n)) (/.f64 (-.f64 1 k) 2)))) (.f64 (/.f64 1 (/.f64 (pow.f64 (.f64 2 (.f64 (PI.f64) n)) (/.f64 (-.f64 1 k) 2)) (pow.f64 (.f64 2 (.f64 (PI.f64) n)) (/.f64 (-.f64 1 k) 2)))) (/.f64 (pow.f64 (.f64 (PI.f64) (.f64 n (.f64 (PI.f64) (.f64 n 4)))) (/.f64 (-.f64 1 k) 2)) (fabs.f64 (/.f64 (pow.f64 (.f64 2 (.f64 (PI.f64) n)) (/.f64 (-.f64 1 k) 2)) (pow.f64 (.f64 2 (*.f64 (PI.f64) n)) (/.f64 (-.f64 1 k) 2))))))))
(pow.f64 (.f64 (PI.f64) (.f64 (PI.f64) (.f64 n (.f64 4 n)))) (/.f64 (-.f64 1 k) 2))
(pow.f64 (.f64 n (.f64 (PI.f64) (.f64 (PI.f64) (.f64 4 n)))) (/.f64 (-.f64 1 k) 2))
(pow.f64 (.f64 (PI.f64) (.f64 (PI.f64) (.f64 4 (.f64 n n)))) (/.f64 (-.f64 1 k) 2))
(pow.f64 (.f64 (PI.f64) (.f64 (.f64 4 n) (.f64 (PI.f64) n))) (/.f64 (-.f64 1 k) 2))
(fabs.f64 (.f64 (fabs.f64 (/.f64 1 (pow.f64 (.f64 2 (.f64 (PI.f64) n)) (/.f64 (-.f64 1 k) 2)))) (.f64 (pow.f64 (.f64 (PI.f64) (.f64 n (.f64 (PI.f64) (.f64 n 4)))) (/.f64 (-.f64 1 k) 2)) (pow.f64 (.f64 2 (.f64 (PI.f64) n)) (/.f64 (-.f64 1 k) 2)))))
(pow.f64 (.f64 (PI.f64) (.f64 (PI.f64) (.f64 n (.f64 4 n)))) (/.f64 (-.f64 1 k) 2))
(pow.f64 (.f64 n (.f64 (PI.f64) (.f64 (PI.f64) (.f64 4 n)))) (/.f64 (-.f64 1 k) 2))
(pow.f64 (.f64 (PI.f64) (.f64 (PI.f64) (.f64 4 (.f64 n n)))) (/.f64 (-.f64 1 k) 2))
(pow.f64 (.f64 (PI.f64) (.f64 (.f64 4 n) (.f64 (PI.f64) n))) (/.f64 (-.f64 1 k) 2))
(fabs.f64 (.f64 (fabs.f64 (/.f64 1 (pow.f64 (.f64 2 (.f64 (PI.f64) n)) (/.f64 (-.f64 1 k) 2)))) (.f64 (pow.f64 (.f64 2 (.f64 (PI.f64) n)) (/.f64 (-.f64 1 k) 2)) (neg.f64 (pow.f64 (.f64 (PI.f64) (.f64 n (.f64 (PI.f64) (.f64 n 4)))) (/.f64 (-.f64 1 k) 2))))))
(pow.f64 (.f64 (PI.f64) (.f64 (PI.f64) (.f64 n (.f64 4 n)))) (/.f64 (-.f64 1 k) 2))
(pow.f64 (.f64 n (.f64 (PI.f64) (.f64 (PI.f64) (.f64 4 n)))) (/.f64 (-.f64 1 k) 2))
(pow.f64 (.f64 (PI.f64) (.f64 (PI.f64) (.f64 4 (.f64 n n)))) (/.f64 (-.f64 1 k) 2))
(pow.f64 (.f64 (PI.f64) (.f64 (.f64 4 n) (.f64 (PI.f64) n))) (/.f64 (-.f64 1 k) 2))
(fabs.f64 (.f64 (fabs.f64 (/.f64 1 (pow.f64 (.f64 2 (.f64 (PI.f64) n)) (/.f64 (-.f64 1 k) 2)))) (.f64 (pow.f64 (.f64 2 (.f64 (PI.f64) n)) (/.f64 (-.f64 1 k) 2)) (/.f64 (pow.f64 (.f64 (PI.f64) (.f64 n (.f64 (PI.f64) (.f64 n 4)))) (/.f64 (-.f64 1 k) 2)) (fabs.f64 (/.f64 (pow.f64 (.f64 2 (.f64 (PI.f64) n)) (/.f64 (-.f64 1 k) 2)) (pow.f64 (.f64 2 (.f64 (PI.f64) n)) (/.f64 (-.f64 1 k) 2))))))))
(pow.f64 (.f64 (PI.f64) (.f64 (PI.f64) (.f64 n (.f64 4 n)))) (/.f64 (-.f64 1 k) 2))
(pow.f64 (.f64 n (.f64 (PI.f64) (.f64 (PI.f64) (.f64 4 n)))) (/.f64 (-.f64 1 k) 2))
(pow.f64 (.f64 (PI.f64) (.f64 (PI.f64) (.f64 4 (.f64 n n)))) (/.f64 (-.f64 1 k) 2))
(pow.f64 (.f64 (PI.f64) (.f64 (.f64 4 n) (.f64 (PI.f64) n))) (/.f64 (-.f64 1 k) 2))
(fabs.f64 (.f64 (pow.f64 (.f64 (PI.f64) (.f64 n (.f64 (PI.f64) (.f64 n 4)))) (/.f64 (-.f64 1 k) 2)) (.f64 (/.f64 1 (pow.f64 (.f64 (PI.f64) (.f64 n (.f64 (PI.f64) (.f64 n 4)))) (/.f64 (-.f64 1 k) 2))) (neg.f64 (pow.f64 (.f64 (PI.f64) (.f64 n (.f64 (PI.f64) (.f64 n 4)))) (/.f64 (-.f64 1 k) 2))))))
(pow.f64 (.f64 (PI.f64) (.f64 (PI.f64) (.f64 n (.f64 4 n)))) (/.f64 (-.f64 1 k) 2))
(pow.f64 (.f64 n (.f64 (PI.f64) (.f64 (PI.f64) (.f64 4 n)))) (/.f64 (-.f64 1 k) 2))
(pow.f64 (.f64 (PI.f64) (.f64 (PI.f64) (.f64 4 (.f64 n n)))) (/.f64 (-.f64 1 k) 2))
(pow.f64 (.f64 (PI.f64) (.f64 (.f64 4 n) (.f64 (PI.f64) n))) (/.f64 (-.f64 1 k) 2))
(fabs.f64 (.f64 (pow.f64 (.f64 (PI.f64) (.f64 n (.f64 (PI.f64) (.f64 n 4)))) (/.f64 (-.f64 1 k) 2)) (.f64 (/.f64 1 (pow.f64 (.f64 (PI.f64) (.f64 n (.f64 (PI.f64) (.f64 n 4)))) (/.f64 (-.f64 1 k) 2))) (/.f64 (pow.f64 (.f64 (PI.f64) (.f64 n (.f64 (PI.f64) (.f64 n 4)))) (/.f64 (-.f64 1 k) 2)) (fabs.f64 (/.f64 (pow.f64 (.f64 2 (.f64 (PI.f64) n)) (/.f64 (-.f64 1 k) 2)) (pow.f64 (.f64 2 (.f64 (PI.f64) n)) (/.f64 (-.f64 1 k) 2))))))))
(fabs.f64 (.f64 (pow.f64 (.f64 (PI.f64) (.f64 (PI.f64) (.f64 n (.f64 4 n)))) (/.f64 (-.f64 1 k) 2)) (.f64 (/.f64 1 (pow.f64 (.f64 (PI.f64) (.f64 (PI.f64) (.f64 n (.f64 4 n)))) (/.f64 (-.f64 1 k) 2))) (/.f64 (pow.f64 (.f64 (PI.f64) (.f64 (PI.f64) (.f64 n (.f64 4 n)))) (/.f64 (-.f64 1 k) 2)) (fabs.f64 (/.f64 (pow.f64 (.f64 2 (.f64 (PI.f64) n)) (/.f64 (-.f64 1 k) 2)) (pow.f64 (.f64 2 (.f64 (PI.f64) n)) (/.f64 (-.f64 1 k) 2))))))))
(fabs.f64 (.f64 (/.f64 1 (pow.f64 (.f64 n (.f64 (PI.f64) (.f64 (PI.f64) (.f64 4 n)))) (/.f64 (-.f64 1 k) 2))) (.f64 (pow.f64 (.f64 n (.f64 (PI.f64) (.f64 (PI.f64) (.f64 4 n)))) (/.f64 (-.f64 1 k) 2)) (/.f64 (pow.f64 (.f64 n (.f64 (PI.f64) (.f64 (PI.f64) (.f64 4 n)))) (/.f64 (-.f64 1 k) 2)) (fabs.f64 (/.f64 (pow.f64 (.f64 (PI.f64) (.f64 2 n)) (/.f64 (-.f64 1 k) 2)) (pow.f64 (.f64 (PI.f64) (.f64 2 n)) (/.f64 (-.f64 1 k) 2))))))))
(fabs.f64 (.f64 (pow.f64 (.f64 n (.f64 (PI.f64) (.f64 (PI.f64) (.f64 4 n)))) (/.f64 (-.f64 1 k) 2)) (/.f64 (/.f64 (pow.f64 (.f64 n (.f64 (PI.f64) (.f64 (PI.f64) (.f64 4 n)))) (/.f64 (-.f64 1 k) 2)) (fabs.f64 (/.f64 (pow.f64 (.f64 (PI.f64) (.f64 2 n)) (/.f64 (-.f64 1 k) 2)) (pow.f64 (.f64 (PI.f64) (.f64 2 n)) (/.f64 (-.f64 1 k) 2))))) (pow.f64 (.f64 n (.f64 (PI.f64) (.f64 (PI.f64) (*.f64 4 n)))) (/.f64 (-.f64 1 k) 2)))))
(fabs.f64 (.f64 (.f64 (pow.f64 (.f64 (PI.f64) (.f64 2 n)) (/.f64 (-.f64 1 k) 2)) (/.f64 1 (pow.f64 (.f64 (PI.f64) (.f64 2 n)) (/.f64 (-.f64 1 k) 2)))) (/.f64 (pow.f64 (.f64 (PI.f64) (.f64 (PI.f64) (.f64 4 (.f64 n n)))) (/.f64 (-.f64 1 k) 2)) (fabs.f64 (/.f64 (pow.f64 (.f64 (PI.f64) (.f64 2 n)) (/.f64 (-.f64 1 k) 2)) (pow.f64 (.f64 (PI.f64) (.f64 2 n)) (/.f64 (-.f64 1 k) 2)))))))
(fabs.f64 (.f64 (.f64 (pow.f64 (.f64 (PI.f64) (.f64 2 n)) (/.f64 (-.f64 1 k) 2)) (/.f64 1 (pow.f64 (.f64 (PI.f64) (.f64 2 n)) (/.f64 (-.f64 1 k) 2)))) (/.f64 (pow.f64 (.f64 (PI.f64) (.f64 (.f64 4 n) (.f64 (PI.f64) n))) (/.f64 (-.f64 1 k) 2)) (fabs.f64 (/.f64 (pow.f64 (.f64 (PI.f64) (.f64 2 n)) (/.f64 (-.f64 1 k) 2)) (pow.f64 (.f64 (PI.f64) (.f64 2 n)) (/.f64 (-.f64 1 k) 2)))))))
(+.f64 (pow.f64 (.f64 2 (.f64 (PI.f64) n)) (/.f64 (-.f64 1 k) 2)) 0)
(pow.f64 (.f64 2 (.f64 (PI.f64) n)) (/.f64 (-.f64 1 k) 2))
(pow.f64 (.f64 (PI.f64) (.f64 2 n)) (/.f64 (-.f64 1 k) 2))
(+.f64 0 (pow.f64 (.f64 2 (.f64 (PI.f64) n)) (/.f64 (-.f64 1 k) 2)))
(pow.f64 (.f64 2 (.f64 (PI.f64) n)) (/.f64 (-.f64 1 k) 2))
(pow.f64 (.f64 (PI.f64) (.f64 2 n)) (/.f64 (-.f64 1 k) 2))
(-.f64 (pow.f64 (.f64 2 (.f64 (PI.f64) n)) (/.f64 (-.f64 1 k) 2)) 0)
(pow.f64 (.f64 2 (.f64 (PI.f64) n)) (/.f64 (-.f64 1 k) 2))
(pow.f64 (.f64 (PI.f64) (.f64 2 n)) (/.f64 (-.f64 1 k) 2))
(/.f64 (pow.f64 (.f64 2 (.f64 (PI.f64) n)) (/.f64 (-.f64 1 k) 2)) 1)
(pow.f64 (.f64 2 (.f64 (PI.f64) n)) (/.f64 (-.f64 1 k) 2))
(pow.f64 (.f64 (PI.f64) (.f64 2 n)) (/.f64 (-.f64 1 k) 2))
(/.f64 (pow.f64 (.f64 2 (.f64 (PI.f64) n)) (/.f64 (-.f64 1 k) 2)) (/.f64 (pow.f64 (.f64 2 (.f64 (PI.f64) n)) (/.f64 (-.f64 1 k) 2)) (pow.f64 (.f64 2 (.f64 (PI.f64) n)) (/.f64 (-.f64 1 k) 2))))
(pow.f64 (.f64 2 (.f64 (PI.f64) n)) (/.f64 (-.f64 1 k) 2))
(pow.f64 (.f64 (PI.f64) (.f64 2 n)) (/.f64 (-.f64 1 k) 2))
(/.f64 (.f64 2 (pow.f64 (.f64 2 (*.f64 (PI.f64) n)) (/.f64 (-.f64 1 k) 2))) 2)
(pow.f64 (.f64 2 (.f64 (PI.f64) n)) (/.f64 (-.f64 1 k) 2))
(pow.f64 (.f64 (PI.f64) (.f64 2 n)) (/.f64 (-.f64 1 k) 2))
(pow.f64 (.f64 2 (.f64 (PI.f64) n)) (/.f64 (-.f64 1 k) 2))
(pow.f64 (.f64 (PI.f64) (.f64 2 n)) (/.f64 (-.f64 1 k) 2))
(pow.f64 (pow.f64 (.f64 2 (.f64 (PI.f64) n)) (/.f64 (-.f64 1 k) 2)) 1)
(pow.f64 (.f64 2 (.f64 (PI.f64) n)) (/.f64 (-.f64 1 k) 2))
(pow.f64 (.f64 (PI.f64) (.f64 2 n)) (/.f64 (-.f64 1 k) 2))
(+.f64 (*.f64 (PI.f64) n) 0)
(*.f64 (PI.f64) n)
(+.f64 0 (*.f64 (PI.f64) n))
(*.f64 (PI.f64) n)
(-.f64 (*.f64 (PI.f64) n) 0)
(*.f64 (PI.f64) n)
(/.f64 (*.f64 (PI.f64) n) 1)
(*.f64 (PI.f64) n)
(/.f64 (.f64 (PI.f64) n) (/.f64 (.f64 (PI.f64) n) (*.f64 (PI.f64) n)))
(*.f64 (PI.f64) n)
(/.f64 (.f64 2 (.f64 (PI.f64) n)) 2)
(*.f64 (PI.f64) n)
(pow.f64 (*.f64 (PI.f64) n) 1)
(*.f64 (PI.f64) n)

eval259.0ms (1.8%)

Compiler: Compiled 18845 to 12756 computations (32.3% saved)

prune88.0ms (0.6%)

Pruning

29 alts after pruning (19 fresh and 10 done)

	Pruned	Kept	Total
New	404	8	412
Fresh	3	11	14
Picked	1	0	1
Done	1	10	11
Total	409	29	438

Error

0.0b

Counts

438 → 29

Alt Table

Click to see full alt table

Status	Error	Program
	22.2b	(/.f64 (.f64 (/.f64 1 (sqrt.f64 k)) (.f64 (sqrt.f64 (.f64 n (.f64 (PI.f64) 2))) (+.f64 1 (+.f64 1 (.f64 (log.f64 (.f64 n (*.f64 (PI.f64) 2))) (neg.f64 k)))))) 2)
	22.1b	(/.f64 (.f64 (+.f64 2 (.f64 (log.f64 (.f64 n (.f64 (PI.f64) 2))) (neg.f64 k))) (.f64 (/.f64 1 (sqrt.f64 k)) (sqrt.f64 (.f64 n (*.f64 (PI.f64) 2))))) 2)
	22.4b	(/.f64 (.f64 (.f64 (/.f64 1 (/.f64 1 (sqrt.f64 k))) (sqrt.f64 (.f64 (PI.f64) (+.f64 n n)))) (.f64 (/.f64 1 k) 2)) 2)
	22.3b	(/.f64 (.f64 (.f64 (sqrt.f64 2) (+.f64 (.f64 (log.f64 (.f64 (PI.f64) (+.f64 n n))) (.f64 k -1/2)) 1)) (.f64 (/.f64 1 (sqrt.f64 k)) (.f64 (sqrt.f64 (.f64 n (PI.f64))) 2))) 2)
	27.9b	(.f64 (/.f64 1 (/.f64 1 (sqrt.f64 k))) (.f64 (/.f64 1 k) (sqrt.f64 (*.f64 (PI.f64) (+.f64 n n)))))
✓	21.1b	(.f64 (/.f64 1 (sqrt.f64 k)) (pow.f64 (.f64 (/.f64 2 (.f64 n (PI.f64))) (.f64 n (*.f64 n (pow.f64 (PI.f64) 2)))) (/.f64 (-.f64 1 k) 2)))
✓	0.4b	(.f64 (/.f64 1 (sqrt.f64 k)) (pow.f64 (.f64 (*.f64 2 (PI.f64)) n) (/.f64 (-.f64 1 k) 2)))
	0.5b	(.f64 (/.f64 1 (sqrt.f64 k)) (pow.f64 (.f64 n (.f64 n (.f64 (/.f64 2 (*.f64 (PI.f64) n)) (pow.f64 (PI.f64) 2)))) (/.f64 (-.f64 1 k) 2)))
	22.3b	(.f64 (/.f64 1 (sqrt.f64 k)) (+.f64 (.f64 (sqrt.f64 (.f64 n (PI.f64))) (+.f64 (.f64 (log.f64 (.f64 (PI.f64) (.f64 2 n))) (.f64 -1/2 (.f64 k (sqrt.f64 2)))) (sqrt.f64 2))) (.f64 1/8 (.f64 (sqrt.f64 (.f64 (PI.f64) (.f64 2 n))) (pow.f64 (.f64 k (log.f64 (.f64 (PI.f64) (*.f64 2 n)))) 2)))))
✓	1.9b	(.f64 (/.f64 1 (sqrt.f64 k)) (.f64 (pow.f64 (.f64 (PI.f64) (+.f64 n n)) (-.f64 1 k)) (.f64 (sqrt.f64 (/.f64 1 (*.f64 n (PI.f64)))) (sqrt.f64 1/2))))
	24.6b	(.f64 (/.f64 1 (sqrt.f64 k)) (.f64 (pow.f64 (.f64 (PI.f64) (+.f64 n n)) (-.f64 1 k)) (.f64 (exp.f64 (.f64 (/.f64 (.f64 (-.f64 1 k) (log.f64 (.f64 (PI.f64) (+.f64 n n)))) -2) 2)) (exp.f64 (neg.f64 (/.f64 (.f64 (-.f64 1 k) (log.f64 (*.f64 (PI.f64) (+.f64 n n)))) -2))))))
	24.6b	(.f64 (/.f64 1 (sqrt.f64 k)) (.f64 (pow.f64 (.f64 (PI.f64) (+.f64 n n)) (-.f64 1 k)) (exp.f64 (/.f64 (.f64 (-.f64 1 k) (log.f64 (*.f64 (PI.f64) (+.f64 n n)))) -2))))
	43.8b	(.f64 (/.f64 1 (sqrt.f64 k)) (.f64 (/.f64 (exp.f64 (/.f64 (log.f64 (pow.f64 (.f64 (PI.f64) (+.f64 n n)) (-.f64 1 k))) -2)) (pow.f64 (.f64 (PI.f64) (+.f64 n n)) (-.f64 1 k))) (pow.f64 (.f64 (.f64 n (PI.f64)) (.f64 n (.f64 (PI.f64) 4))) (-.f64 1 k))))
✓	22.2b	(.f64 (/.f64 1 (sqrt.f64 k)) (.f64 (+.f64 1 (.f64 (log.f64 (.f64 (PI.f64) (+.f64 n n))) (.f64 k -1/2))) (sqrt.f64 (.f64 2 (*.f64 n (PI.f64))))))
	22.3b	(.f64 (/.f64 1 (sqrt.f64 k)) (.f64 (sqrt.f64 (.f64 n (PI.f64))) (+.f64 (.f64 (sqrt.f64 2) (+.f64 (.f64 k (.f64 -1/2 (log.f64 (.f64 2 (.f64 n (PI.f64)))))) (.f64 1/8 (pow.f64 (.f64 k (log.f64 (.f64 2 (.f64 n (PI.f64))))) 2)))) (sqrt.f64 2))))
✓	22.4b	(.f64 (/.f64 1 (sqrt.f64 k)) (.f64 (sqrt.f64 2) (sqrt.f64 (*.f64 n (PI.f64)))))
✓	22.3b	(.f64 (/.f64 1 (sqrt.f64 k)) (sqrt.f64 (.f64 (PI.f64) (*.f64 2 n))))
✓	3.4b	(.f64 (/.f64 1 (sqrt.f64 k)) (exp.f64 (.f64 1/2 (.f64 (-.f64 1 k) (log.f64 (.f64 2 (*.f64 n (PI.f64))))))))
✓	0.6b	(.f64 (.f64 (/.f64 1 (/.f64 1 (sqrt.f64 k))) (/.f64 1 k)) (pow.f64 (.f64 (.f64 2 (PI.f64)) n) (/.f64 (-.f64 1 k) 2)))
	24.9b	(.f64 (.f64 (/.f64 1 (/.f64 1 (sqrt.f64 k))) (/.f64 1 k)) (/.f64 (exp.f64 (.f64 (-.f64 1 k) (.f64 1/2 (+.f64 (log.f64 (.f64 4 (pow.f64 (PI.f64) 2))) (.f64 2 (log.f64 n)))))) (exp.f64 (.f64 (+.f64 (log.f64 n) (log.f64 (.f64 (PI.f64) 2))) (*.f64 1/2 (-.f64 1 k))))))
	23.2b	(.f64 (.f64 (/.f64 1 (/.f64 1 (sqrt.f64 k))) (/.f64 1 k)) (.f64 (.f64 (PI.f64) (.f64 2 n)) (/.f64 1 (pow.f64 (.f64 2 (*.f64 (PI.f64) n)) (/.f64 (-.f64 1 k) 2)))))
	22.5b	(.f64 (.f64 (/.f64 1 (/.f64 1 (sqrt.f64 k))) (/.f64 1 k)) (.f64 (sqrt.f64 2) (sqrt.f64 (.f64 n (PI.f64)))))
	25.5b	(.f64 (.f64 (/.f64 1 (/.f64 1 (sqrt.f64 k))) (/.f64 1 k)) (.f64 (exp.f64 (.f64 (-.f64 1 k) (.f64 1/2 (+.f64 (log.f64 (.f64 4 (pow.f64 (PI.f64) 2))) (.f64 2 (log.f64 n)))))) (/.f64 1 (pow.f64 (.f64 2 (*.f64 (PI.f64) n)) (/.f64 (-.f64 1 k) 2)))))
✓	22.5b	(.f64 (.f64 (/.f64 1 (/.f64 1 (sqrt.f64 k))) (/.f64 1 k)) (sqrt.f64 (.f64 (PI.f64) (.f64 2 n))))
	3.4b	(.f64 (.f64 (/.f64 1 (/.f64 1 (sqrt.f64 k))) (/.f64 1 k)) (exp.f64 (.f64 1/2 (.f64 (-.f64 1 k) (log.f64 (.f64 2 (.f64 n (PI.f64))))))))
	3.7b	(.f64 (sqrt.f64 (/.f64 1 k)) (exp.f64 (.f64 (-.f64 1 k) (.f64 1/2 (+.f64 (log.f64 (.f64 2 (PI.f64))) (log.f64 n))))))
✓	22.2b	(.f64 (sqrt.f64 (.f64 n (PI.f64))) (.f64 (/.f64 1 (sqrt.f64 k)) (.f64 (sqrt.f64 2) (+.f64 1 (.f64 (log.f64 (.f64 (PI.f64) (+.f64 n n))) (*.f64 k -1/2))))))
	22.2b	(.f64 (sqrt.f64 (.f64 n (PI.f64))) (.f64 (+.f64 1 (.f64 (+.f64 (log.f64 (.f64 2 (PI.f64))) (log.f64 n)) (.f64 k -1/2))) (*.f64 (sqrt.f64 (/.f64 1 k)) (sqrt.f64 2))))
	22.1b	(.f64 (sqrt.f64 (.f64 n (PI.f64))) (.f64 (+.f64 1 (.f64 k (.f64 -1/2 (+.f64 (log.f64 (.f64 2 (PI.f64))) (log.f64 n))))) (sqrt.f64 (*.f64 (/.f64 1 k) 2))))

Compiler

Compiled 823 to 649 computations (21.1% saved)

regimes90.0ms (0.6%)

Accuracy

Total -45.0b remaining (-10215.5%)

Threshold costs -45.0b (-10215.5%)

Counts

45 → 1

Calls

Call 1

Inputs
(.f64 (/.f64 1 (sqrt.f64 k)) (sqrt.f64 (.f64 (PI.f64) (*.f64 2 n))))
(.f64 (/.f64 1 (sqrt.f64 k)) (pow.f64 (.f64 (*.f64 2 (PI.f64)) n) (/.f64 (-.f64 1 k) 2)))
(.f64 (.f64 (/.f64 1 (/.f64 1 (sqrt.f64 k))) (/.f64 1 k)) (sqrt.f64 (.f64 (PI.f64) (.f64 2 n))))
(.f64 (/.f64 1 (/.f64 1 (sqrt.f64 k))) (.f64 (/.f64 1 k) (sqrt.f64 (*.f64 (PI.f64) (+.f64 n n)))))
(/.f64 (.f64 (.f64 (/.f64 1 (/.f64 1 (sqrt.f64 k))) (sqrt.f64 (.f64 (PI.f64) (+.f64 n n)))) (.f64 (/.f64 1 k) 2)) 2)
(.f64 (.f64 (/.f64 1 (/.f64 1 (sqrt.f64 k))) (/.f64 1 k)) (pow.f64 (.f64 (.f64 2 (PI.f64)) n) (/.f64 (-.f64 1 k) 2)))
(.f64 (/.f64 1 (sqrt.f64 k)) (.f64 (sqrt.f64 2) (sqrt.f64 (*.f64 n (PI.f64)))))
(.f64 (.f64 (/.f64 1 (/.f64 1 (sqrt.f64 k))) (/.f64 1 k)) (.f64 (sqrt.f64 2) (sqrt.f64 (.f64 n (PI.f64)))))
(.f64 (/.f64 1 (sqrt.f64 k)) (exp.f64 (.f64 1/2 (.f64 (-.f64 1 k) (log.f64 (.f64 2 (*.f64 n (PI.f64))))))))
(.f64 (.f64 (/.f64 1 (/.f64 1 (sqrt.f64 k))) (/.f64 1 k)) (exp.f64 (.f64 1/2 (.f64 (-.f64 1 k) (log.f64 (.f64 2 (.f64 n (PI.f64))))))))
(.f64 (.f64 (/.f64 1 (/.f64 1 (sqrt.f64 k))) (/.f64 1 k)) (.f64 (.f64 (PI.f64) (.f64 2 n)) (/.f64 1 (pow.f64 (.f64 2 (*.f64 (PI.f64) n)) (/.f64 (-.f64 1 k) 2)))))
(.f64 (sqrt.f64 (/.f64 1 k)) (exp.f64 (.f64 (-.f64 1 k) (.f64 1/2 (+.f64 (log.f64 n) (log.f64 (.f64 2 (PI.f64))))))))
(.f64 (sqrt.f64 (/.f64 1 k)) (exp.f64 (.f64 (-.f64 1 k) (.f64 1/2 (+.f64 (log.f64 (.f64 2 (PI.f64))) (log.f64 n))))))
(.f64 (/.f64 1 (sqrt.f64 k)) (.f64 (+.f64 1 (.f64 (log.f64 (.f64 (PI.f64) (+.f64 n n))) (.f64 k -1/2))) (sqrt.f64 (.f64 2 (*.f64 n (PI.f64))))))
(.f64 (/.f64 1 (sqrt.f64 k)) (pow.f64 (.f64 n (.f64 n (.f64 (/.f64 2 (*.f64 (PI.f64) n)) (pow.f64 (PI.f64) 2)))) (/.f64 (-.f64 1 k) 2)))
(.f64 (/.f64 1 (sqrt.f64 k)) (pow.f64 (.f64 n (.f64 (/.f64 2 (.f64 n (PI.f64))) (*.f64 n (pow.f64 (PI.f64) 2)))) (/.f64 (-.f64 1 k) 2)))
(.f64 (/.f64 1 (sqrt.f64 k)) (pow.f64 (.f64 (/.f64 2 (.f64 n (PI.f64))) (.f64 n (*.f64 n (pow.f64 (PI.f64) 2)))) (/.f64 (-.f64 1 k) 2)))
(.f64 (/.f64 1 (sqrt.f64 k)) (pow.f64 (.f64 (/.f64 2 (.f64 n (PI.f64))) (.f64 n (.f64 (.f64 n (PI.f64)) (PI.f64)))) (/.f64 (-.f64 1 k) 2)))
(.f64 (/.f64 1 (sqrt.f64 k)) (pow.f64 (.f64 (/.f64 2 (.f64 n (PI.f64))) (.f64 (.f64 n (PI.f64)) (.f64 n (PI.f64)))) (/.f64 (-.f64 1 k) 2)))
(/.f64 (.f64 (+.f64 2 (.f64 (log.f64 (.f64 n (.f64 (PI.f64) 2))) (neg.f64 k))) (.f64 (/.f64 1 (sqrt.f64 k)) (sqrt.f64 (.f64 n (*.f64 (PI.f64) 2))))) 2)
(/.f64 (.f64 (+.f64 1 (.f64 k (.f64 (log.f64 (.f64 2 (.f64 (PI.f64) n))) -1/2))) (.f64 (/.f64 1 (sqrt.f64 k)) (sqrt.f64 (.f64 2 (.f64 (PI.f64) n))))) 1)
(/.f64 (.f64 (/.f64 1 (sqrt.f64 k)) (.f64 (sqrt.f64 (.f64 2 (.f64 (PI.f64) n))) (+.f64 1 (+.f64 1 (.f64 k (neg.f64 (log.f64 (.f64 2 (*.f64 (PI.f64) n))))))))) 2)
(/.f64 (.f64 (/.f64 1 (sqrt.f64 k)) (.f64 (sqrt.f64 (.f64 n (.f64 (PI.f64) 2))) (+.f64 1 (+.f64 1 (.f64 (log.f64 (.f64 n (*.f64 (PI.f64) 2))) (neg.f64 k)))))) 2)
(.f64 (.f64 (/.f64 1 (/.f64 1 (sqrt.f64 k))) (.f64 (/.f64 1 (sqrt.f64 k)) (/.f64 1 (sqrt.f64 k)))) (pow.f64 (.f64 (*.f64 2 (PI.f64)) n) (/.f64 (-.f64 1 k) 2)))
(.f64 (/.f64 1 (sqrt.f64 k)) (.f64 (/.f64 1 (sqrt.f64 (.f64 (PI.f64) (+.f64 n n)))) (sqrt.f64 (.f64 (.f64 (PI.f64) n) (.f64 (*.f64 (PI.f64) n) 4)))))
(.f64 (/.f64 1 (sqrt.f64 k)) (.f64 (pow.f64 (.f64 (PI.f64) (+.f64 n n)) (-.f64 1 k)) (.f64 (sqrt.f64 (/.f64 1 (*.f64 n (PI.f64)))) (sqrt.f64 1/2))))
(.f64 (sqrt.f64 (.f64 n (PI.f64))) (.f64 (+.f64 1 (.f64 k (.f64 -1/2 (+.f64 (log.f64 (.f64 2 (PI.f64))) (log.f64 n))))) (sqrt.f64 (*.f64 (/.f64 1 k) 2))))
(.f64 (sqrt.f64 (.f64 n (PI.f64))) (.f64 (/.f64 1 (sqrt.f64 k)) (.f64 (sqrt.f64 2) (+.f64 1 (.f64 (log.f64 (.f64 (PI.f64) (+.f64 n n))) (*.f64 k -1/2))))))
(.f64 (/.f64 1 (sqrt.f64 k)) (.f64 (pow.f64 (.f64 (PI.f64) (+.f64 n n)) (-.f64 1 k)) (exp.f64 (/.f64 (.f64 (-.f64 1 k) (log.f64 (*.f64 (PI.f64) (+.f64 n n)))) -2))))
(/.f64 (.f64 (.f64 (sqrt.f64 2) (+.f64 (.f64 (log.f64 (.f64 (PI.f64) (+.f64 n n))) (.f64 k -1/2)) 1)) (.f64 (/.f64 1 (sqrt.f64 k)) (.f64 (sqrt.f64 (.f64 n (PI.f64))) 2))) 2)
(.f64 (/.f64 1 (sqrt.f64 k)) (.f64 (pow.f64 (.f64 (.f64 2 (.f64 (PI.f64) n)) (.f64 2 (.f64 (PI.f64) n))) (/.f64 (-.f64 1 k) 2)) (/.f64 1 (pow.f64 (.f64 2 (*.f64 (PI.f64) n)) (/.f64 (-.f64 1 k) 2)))))
(.f64 (.f64 (/.f64 1 (/.f64 1 (sqrt.f64 k))) (/.f64 1 k)) (.f64 (pow.f64 (.f64 (.f64 2 (.f64 (PI.f64) n)) (.f64 2 (.f64 (PI.f64) n))) (/.f64 (-.f64 1 k) 2)) (/.f64 1 (pow.f64 (.f64 2 (.f64 (PI.f64) n)) (/.f64 (-.f64 1 k) 2)))))
(.f64 (sqrt.f64 (.f64 n (PI.f64))) (.f64 (+.f64 1 (.f64 (+.f64 (log.f64 (.f64 2 (PI.f64))) (log.f64 n)) (.f64 k -1/2))) (*.f64 (sqrt.f64 (/.f64 1 k)) (sqrt.f64 2))))
(.f64 (/.f64 1 (sqrt.f64 k)) (.f64 (sqrt.f64 (.f64 n (PI.f64))) (+.f64 (.f64 (log.f64 (.f64 (PI.f64) (.f64 2 n))) (.f64 -1/2 (.f64 k (sqrt.f64 2)))) (sqrt.f64 2))))
(.f64 (/.f64 1 (sqrt.f64 k)) (.f64 (.f64 (sqrt.f64 (.f64 (PI.f64) (+.f64 n n))) (/.f64 1 (sqrt.f64 (.f64 (PI.f64) (+.f64 n n))))) (sqrt.f64 (.f64 (PI.f64) (+.f64 n n)))))
(.f64 (/.f64 1 (sqrt.f64 k)) (.f64 (pow.f64 (.f64 (PI.f64) (+.f64 n n)) (-.f64 1 k)) (exp.f64 (/.f64 (log.f64 (pow.f64 (.f64 (PI.f64) (+.f64 n n)) (-.f64 1 k))) -2))))
(.f64 (/.f64 1 (sqrt.f64 k)) (+.f64 (sqrt.f64 (.f64 2 (.f64 n (PI.f64)))) (.f64 -1/2 (.f64 (.f64 k (log.f64 (.f64 2 (.f64 n (PI.f64))))) (sqrt.f64 (.f64 2 (.f64 n (PI.f64))))))))
(.f64 (/.f64 1 (sqrt.f64 k)) (+.f64 (sqrt.f64 (.f64 n (.f64 2 (PI.f64)))) (.f64 -1/2 (.f64 (.f64 k (log.f64 (.f64 n (.f64 2 (PI.f64))))) (sqrt.f64 (.f64 n (.f64 2 (PI.f64))))))))
(.f64 (/.f64 1 (sqrt.f64 k)) (.f64 (pow.f64 (.f64 2 (.f64 (PI.f64) n)) (/.f64 (-.f64 1 k) 2)) (.f64 (pow.f64 (.f64 2 (.f64 (PI.f64) n)) (/.f64 (-.f64 1 k) 2)) (/.f64 1 (pow.f64 (.f64 2 (*.f64 (PI.f64) n)) (/.f64 (-.f64 1 k) 2))))))
(.f64 (.f64 (/.f64 1 (/.f64 1 (sqrt.f64 k))) (/.f64 1 k)) (.f64 (exp.f64 (.f64 (-.f64 1 k) (.f64 1/2 (+.f64 (log.f64 (.f64 4 (pow.f64 (PI.f64) 2))) (.f64 2 (log.f64 n)))))) (/.f64 1 (pow.f64 (.f64 2 (*.f64 (PI.f64) n)) (/.f64 (-.f64 1 k) 2)))))
(.f64 (/.f64 1 (sqrt.f64 k)) (.f64 (pow.f64 (.f64 (PI.f64) (+.f64 n n)) (-.f64 1 k)) (.f64 (exp.f64 (.f64 (/.f64 (.f64 (-.f64 1 k) (log.f64 (.f64 (PI.f64) (+.f64 n n)))) -2) 2)) (exp.f64 (neg.f64 (/.f64 (.f64 (-.f64 1 k) (log.f64 (*.f64 (PI.f64) (+.f64 n n)))) -2))))))
(.f64 (/.f64 1 (sqrt.f64 k)) (.f64 (sqrt.f64 (.f64 n (PI.f64))) (+.f64 (.f64 (sqrt.f64 2) (+.f64 (.f64 k (.f64 -1/2 (log.f64 (.f64 2 (.f64 n (PI.f64)))))) (.f64 1/8 (pow.f64 (.f64 k (log.f64 (.f64 2 (.f64 n (PI.f64))))) 2)))) (sqrt.f64 2))))
(.f64 (/.f64 1 (sqrt.f64 k)) (.f64 (/.f64 (exp.f64 (/.f64 (log.f64 (pow.f64 (.f64 (PI.f64) (+.f64 n n)) (-.f64 1 k))) -2)) (pow.f64 (.f64 (PI.f64) (+.f64 n n)) (-.f64 1 k))) (pow.f64 (.f64 (.f64 n (PI.f64)) (.f64 n (.f64 (PI.f64) 4))) (-.f64 1 k))))
(.f64 (.f64 (/.f64 1 (/.f64 1 (sqrt.f64 k))) (/.f64 1 k)) (/.f64 (exp.f64 (.f64 (-.f64 1 k) (.f64 1/2 (+.f64 (log.f64 (.f64 4 (pow.f64 (PI.f64) 2))) (.f64 2 (log.f64 n)))))) (exp.f64 (.f64 (+.f64 (log.f64 n) (log.f64 (.f64 (PI.f64) 2))) (*.f64 1/2 (-.f64 1 k))))))
(.f64 (/.f64 1 (sqrt.f64 k)) (+.f64 (.f64 (sqrt.f64 (.f64 n (PI.f64))) (+.f64 (.f64 (log.f64 (.f64 (PI.f64) (.f64 2 n))) (.f64 -1/2 (.f64 k (sqrt.f64 2)))) (sqrt.f64 2))) (.f64 1/8 (.f64 (sqrt.f64 (.f64 (PI.f64) (.f64 2 n))) (pow.f64 (.f64 k (log.f64 (.f64 (PI.f64) (*.f64 2 n)))) 2)))))

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

Calls

4 calls:

19.0ms	k
18.0ms	(.f64 (.f64 2 (PI.f64)) n)
18.0ms	n
10.0ms	(.f64 (/.f64 1 (sqrt.f64 k)) (pow.f64 (.f64 (*.f64 2 (PI.f64)) n) (/.f64 (-.f64 1 k) 2)))

Results

Error	Segments	Branch
0.4b	1	`k`
0.4b	1	`n`
0.4b	1	`(.f64 (/.f64 1 (sqrt.f64 k)) (pow.f64 (.f64 (*.f64 2 (PI.f64)) n) (/.f64 (-.f64 1 k) 2)))`
0.4b	1	`(.f64 (.f64 2 (PI.f64)) n)`

Compiler

Compiled 1253 to 789 computations (37% saved)

simplify2.0ms (0%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	21	84

Stop Event

1×	fuel
1×	saturated

Calls

Call 1

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

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)) (sqrt.f64 (.f64 (PI.f64) (*.f64 2 n))))

Compiler

Compiled 31 to 26 computations (16.1% saved)

soundness0.0ms (0%)

end21.0ms (0.1%)

Compiler: Compiled 29 to 22 computations (24.1% saved)