Details

analyze107.0ms (0.7%)

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)

sample3.9s (26.2%)

Results

2.2s	8256×	body	256	valid
864.0ms	1396×	body	1024	invalid
367.0ms	643×	body	512	invalid
279.0ms	1565×	body	256	invalid
139.0ms	456×	body	256	infinite
71.0ms	249×	body	256	unsamplable

Bogosity

preprocess115.0ms (0.8%)

Algorithm

2×	egg-herbie

Rules

1174×	`rational_best_45_simplify-84`
1140×	`rational_best_45_simplify-71`
942×	`rational_best_45_simplify-1`
876×	`rational_best_45_simplify-73`
848×	`rational_best_45_simplify-25`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	24	98
1	48	98
2	146	98
3	558	98
4	2622	98
5	6350	98
0	2	2

Stop Event

1×	saturated
1×	node limit

Calls

Call 1

Inputs
0
1

Outputs
0
1

Call 2

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

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

simplify104.0ms (0.7%)

Algorithm

1×	egg-herbie

Rules

1528×	`rational_best_45_simplify-100`
1258×	`rational_best_45_simplify-91`
1000×	`rational_best_45_simplify-37`
850×	`rational_best_45_simplify-71`
644×	`rational_best_45_simplify-84`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	17	49
1	32	49
2	89	49
3	332	49
4	1554	49
5	5901	49

Stop Event

1×	node limit

Counts

1 → 4

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 (PI.f64) (*.f64 2 n)) (/.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 66 to 48 computations (27.3% saved)

prune1.0ms (0%)

Pruning

2 alts after pruning (2 fresh and 0 done)

	Pruned	Kept	Total
New	3	1	4
Fresh	0	1	1
Picked	0	0	0
Done	0	0	0
Total	3	2	5

Error

0.5b

Counts

5 → 1

Alt Table

Click to see full alt table

Status	Error	Program
▶	0.5b	(.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)

localize26.0ms (0.2%)

Local error

Found 4 expressions with local error:

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

Compiler

Compiled 56 to 38 computations (32.1% saved)

series57.0ms (0.4%)

Counts

4 → 48

Calls

18 calls:

Time	Variable		Point	Expression
26.0ms	n	@	0	(.f64 (/.f64 1 (sqrt.f64 k)) (pow.f64 (.f64 (*.f64 2 (PI.f64)) n) (/.f64 (-.f64 1 k) 2)))
17.0ms	n	@	-inf	(.f64 (/.f64 1 (sqrt.f64 k)) (pow.f64 (.f64 (*.f64 2 (PI.f64)) n) (/.f64 (-.f64 1 k) 2)))
7.0ms	n	@	inf	(.f64 (/.f64 1 (sqrt.f64 k)) (pow.f64 (.f64 (*.f64 2 (PI.f64)) n) (/.f64 (-.f64 1 k) 2)))
2.0ms	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)))

rewrite126.0ms (0.8%)

Algorithm

1×	batch-egg-rewrite

Rules

770×	`rational_best_45_simplify-73`
662×	`rational_best_45_simplify-100`
608×	`rational_best_45_simplify-71`
602×	`rational_best-4`
602×	`rational_best-2`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	17	108
1	98	108
2	288	108
3	1255	108
4	5620	108

Stop Event

1×	node limit

Counts

4 → 124

Calls

Call 1

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

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

simplify144.0ms (1%)

Algorithm

1×	egg-herbie

Rules

1372×	`rational_best_45_simplify-98`
1238×	`rational_best_45_simplify-25`
984×	`rational_best_45_simplify-100`
800×	`rational_best_45_simplify-37`
752×	`rational_best_45_simplify-91`

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	307	7674
1	1069	7606
2	4760	7590

Stop Event

1×	node limit

Counts

172 → 179

Calls

Call 1

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

eval85.0ms (0.6%)

Compiler: Compiled 5780 to 3737 computations (35.3% saved)

prune39.0ms (0.3%)

Pruning

9 alts after pruning (8 fresh and 1 done)

	Pruned	Kept	Total
New	171	8	179
Fresh	0	0	0
Picked	0	1	1
Done	0	0	0
Total	171	9	180

Error

0.3b

Counts

180 → 9

Alt Table

Click to see full alt table

Status	Error	Program
▶	0.5b	(.f64 (/.f64 1 (sqrt.f64 k)) (pow.f64 (.f64 (.f64 2 (.f64 (/.f64 n (.f64 2 (PI.f64))) (PI.f64))) (neg.f64 (.f64 (PI.f64) -2))) (/.f64 (-.f64 1 k) 2)))
✓	0.5b	(.f64 (/.f64 1 (sqrt.f64 k)) (pow.f64 (.f64 (*.f64 2 (PI.f64)) n) (/.f64 (-.f64 1 k) 2)))
▶	20.5b	(.f64 (/.f64 1 (sqrt.f64 k)) (+.f64 (.f64 (sqrt.f64 2) (sqrt.f64 (.f64 (PI.f64) n))) (+.f64 (.f64 (.f64 (pow.f64 (log.f64 (.f64 2 (.f64 (PI.f64) n))) 3) (.f64 (sqrt.f64 2) (pow.f64 k 3))) (.f64 (sqrt.f64 (.f64 (PI.f64) n)) -1/48)) (+.f64 (.f64 (.f64 k (.f64 (sqrt.f64 2) (log.f64 (.f64 2 (.f64 (PI.f64) n))))) (.f64 (sqrt.f64 (.f64 (PI.f64) n)) -1/2)) (.f64 (sqrt.f64 (.f64 (PI.f64) n)) (.f64 1/8 (.f64 (pow.f64 (log.f64 (.f64 2 (.f64 (PI.f64) n))) 2) (.f64 (sqrt.f64 2) (pow.f64 k 2)))))))))
	20.5b	(.f64 (/.f64 1 (sqrt.f64 k)) (+.f64 (.f64 (sqrt.f64 2) (sqrt.f64 (.f64 (PI.f64) n))) (+.f64 (.f64 (.f64 k (.f64 (sqrt.f64 2) (log.f64 (.f64 2 (.f64 (PI.f64) n))))) (.f64 (sqrt.f64 (.f64 (PI.f64) n)) -1/2)) (.f64 (sqrt.f64 (.f64 (PI.f64) n)) (.f64 1/8 (.f64 (pow.f64 (log.f64 (.f64 2 (.f64 (PI.f64) n))) 2) (*.f64 (sqrt.f64 2) (pow.f64 k 2))))))))
▶	20.5b	(.f64 (/.f64 1 (sqrt.f64 k)) (+.f64 (.f64 (sqrt.f64 2) (sqrt.f64 (.f64 (PI.f64) n))) (.f64 (.f64 k (.f64 (sqrt.f64 2) (log.f64 (.f64 2 (.f64 (PI.f64) n))))) (.f64 (sqrt.f64 (.f64 (PI.f64) n)) -1/2))))
	20.5b	(.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))))))
▶	20.6b	(.f64 (/.f64 1 (sqrt.f64 k)) (.f64 (sqrt.f64 2) (sqrt.f64 (*.f64 (PI.f64) n))))
	3.2b	(.f64 (/.f64 1 (sqrt.f64 k)) (exp.f64 (.f64 (-.f64 1 k) (.f64 1/2 (log.f64 (.f64 2 (*.f64 (PI.f64) n)))))))
▶	3.5b	(.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))))))

Compiler

Compiled 606 to 447 computations (26.2% saved)

localize66.0ms (0.4%)

Local error

Found 4 expressions with local error:

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

Compiler

Compiled 112 to 78 computations (30.4% saved)

series7.0ms (0%)

Counts

3 → 36

Calls

12 calls:

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

rewrite112.0ms (0.8%)

Algorithm

1×	batch-egg-rewrite

Rules

1086×	`rational_best_45_simplify-71`
1024×	`rational_best_45_simplify-91`
1016×	`rational_best-4`
1016×	`rational_best-2`
1016×	`rational_best-3`

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	23	119
1	144	119
2	466	109
3	2326	103

Stop Event

1×	node limit

Counts

3 → 87

Calls

Call 1

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

Inputs

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

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

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

Outputs
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simplify151.0ms (1%)

Algorithm

1×	egg-herbie

Rules

1032×	`rational_best_45_simplify-83`
894×	`rational_best_45_simplify-84`
814×	`rational_best_45_simplify-67`
736×	`rational_best_45_simplify-98`
610×	`rational_best_45_simplify-99`

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	215	6049
1	726	6033
2	2814	6025

Stop Event

1×	node limit

Counts

123 → 122

Calls

Call 1

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

localize21.0ms (0.1%)

Local error

Found 4 expressions with local error:

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

Compiler

Compiled 41 to 21 computations (48.8% saved)

series8.0ms (0.1%)

Counts

3 → 12

Calls

12 calls:

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

rewrite134.0ms (0.9%)

Algorithm

1×	batch-egg-rewrite

Rules

930×	`rational_best_45_simplify-100`
734×	`rational_best-4`
734×	`rational_best-2`
734×	`rational_best-3`
734×	`rational_best-1`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	16	71
1	98	71
2	328	71
3	1532	71
4	6820	71

Stop Event

1×	node limit

Counts

3 → 134

Calls

Call 1

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

Outputs

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simplify160.0ms (1.1%)

Algorithm

1×	egg-herbie

Rules

1728×	`rational_best_45_simplify-1`
846×	`rational_best_45_simplify-71`
822×	`rational_best_45_simplify-98`
708×	`rational_best_45_simplify-74`
594×	`rational_best_45_simplify-84`

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	261	5714
1	841	5714
2	2924	5674
3	7514	5674

Stop Event

1×	node limit

Counts

146 → 169

Calls

Call 1

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

localize44.0ms (0.3%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.3b	(.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))))))
✓	0.4b	(+.f64 (log.f64 (*.f64 2 (PI.f64))) (log.f64 n))
✓	1.0b	(log.f64 (*.f64 2 (PI.f64)))
✓	3.2b	(exp.f64 (.f64 (-.f64 1 k) (.f64 1/2 (+.f64 (log.f64 (*.f64 2 (PI.f64))) (log.f64 n)))))

Compiler

Compiled 89 to 62 computations (30.3% saved)

series195.0ms (1.3%)

Counts

4 → 48

Calls

15 calls:

Time	Variable		Point	Expression
105.0ms	n	@	-inf	(exp.f64 (.f64 (-.f64 1 k) (.f64 1/2 (+.f64 (log.f64 (*.f64 2 (PI.f64))) (log.f64 n)))))
64.0ms	n	@	inf	(exp.f64 (.f64 (-.f64 1 k) (.f64 1/2 (+.f64 (log.f64 (*.f64 2 (PI.f64))) (log.f64 n)))))
19.0ms	n	@	0	(exp.f64 (.f64 (-.f64 1 k) (.f64 1/2 (+.f64 (log.f64 (*.f64 2 (PI.f64))) (log.f64 n)))))
2.0ms	k	@	0	(.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))))))
1.0ms	k	@	-inf	(.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))))))

rewrite155.0ms (1%)

Algorithm

1×	batch-egg-rewrite

Rules

912×	`rational_best_45_simplify-100`
812×	`rational_best-4`
812×	`rational_best-2`
812×	`rational_best-3`
812×	`rational_best-1`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	21	142
1	126	142
2	383	142
3	1698	142
4	7823	142

Stop Event

1×	node limit

Counts

4 → 129

Calls

Call 1

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

Outputs
((#(struct:change #<rule egg-rr> (2) ((x +.f64 (exp.f64 (.f64 (+.f64 (log.f64 (.f64 2 (PI.f64))) (log.f64 n)) (.f64 -1/2 (+.f64 k -1)))) 0)))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 0 (exp.f64 (.f64 (+.f64 (log.f64 (.f64 2 (PI.f64))) (log.f64 n)) (.f64 -1/2 (+.f64 k -1)))))))) (#(struct:change #<rule egg-rr> (2) ((x -.f64 (exp.f64 (.f64 (+.f64 (log.f64 (.f64 2 (PI.f64))) (log.f64 n)) (.f64 -1/2 (+.f64 k -1)))) 0)))) (#(struct:change #<rule egg-rr> (2) ((x -.f64 0 (neg.f64 (exp.f64 (.f64 (+.f64 (log.f64 (.f64 2 (PI.f64))) (log.f64 n)) (.f64 -1/2 (+.f64 k -1))))))))) (#(struct:change #<rule egg-rr> (2) ((x .f64 1 (exp.f64 (.f64 (+.f64 (log.f64 (.f64 2 (PI.f64))) (log.f64 n)) (.f64 -1/2 (+.f64 k -1)))))))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (exp.f64 (.f64 (+.f64 (log.f64 (.f64 2 (PI.f64))) (log.f64 n)) (.f64 -1/2 (+.f64 k -1)))) 1)))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (exp.f64 (.f64 (+.f64 (log.f64 (.f64 2 (PI.f64))) (log.f64 n)) (.f64 -1/2 (+.f64 k -1)))) 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simplify204.0ms (1.4%)

Algorithm

1×	egg-herbie

Rules

1086×	`rational_best_45_simplify-100`
968×	`rational_best_45_simplify-80`
896×	`rational_best_45_simplify-37`
848×	`rational_best_45_simplify-91`
580×	`rational_best_45_simplify-73`

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	314	8871
1	1174	8815
2	4859	8807

Stop Event

1×	node limit

Counts

177 → 193

Calls

Call 1

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

localize113.0ms (0.8%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.3b	(.f64 (.f64 k (.f64 (sqrt.f64 2) (log.f64 (.f64 2 (.f64 (PI.f64) n))))) (.f64 (sqrt.f64 (*.f64 (PI.f64) n)) -1/2))
✓	0.5b	(.f64 (sqrt.f64 2) (log.f64 (.f64 2 (*.f64 (PI.f64) n))))
	0.5b	(.f64 (sqrt.f64 2) (sqrt.f64 (.f64 (PI.f64) n)))
✓	6.2b	(.f64 (/.f64 1 (sqrt.f64 k)) (+.f64 (.f64 (sqrt.f64 2) (sqrt.f64 (.f64 (PI.f64) n))) (.f64 (.f64 k (.f64 (sqrt.f64 2) (log.f64 (.f64 2 (.f64 (PI.f64) n))))) (.f64 (sqrt.f64 (.f64 (PI.f64) n)) -1/2))))

Compiler

Compiled 142 to 77 computations (45.8% saved)

series46.0ms (0.3%)

Counts

3 → 24

Calls

15 calls:

Time	Variable		Point	Expression
30.0ms	k	@	0	(.f64 (.f64 k (.f64 (sqrt.f64 2) (log.f64 (.f64 2 (.f64 (PI.f64) n))))) (.f64 (sqrt.f64 (*.f64 (PI.f64) n)) -1/2))
3.0ms	n	@	inf	(.f64 (/.f64 1 (sqrt.f64 k)) (+.f64 (.f64 (sqrt.f64 2) (sqrt.f64 (.f64 (PI.f64) n))) (.f64 (.f64 k (.f64 (sqrt.f64 2) (log.f64 (.f64 2 (.f64 (PI.f64) n))))) (.f64 (sqrt.f64 (.f64 (PI.f64) n)) -1/2))))
2.0ms	n	@	-inf	(.f64 (/.f64 1 (sqrt.f64 k)) (+.f64 (.f64 (sqrt.f64 2) (sqrt.f64 (.f64 (PI.f64) n))) (.f64 (.f64 k (.f64 (sqrt.f64 2) (log.f64 (.f64 2 (.f64 (PI.f64) n))))) (.f64 (sqrt.f64 (.f64 (PI.f64) n)) -1/2))))
2.0ms	n	@	0	(.f64 (/.f64 1 (sqrt.f64 k)) (+.f64 (.f64 (sqrt.f64 2) (sqrt.f64 (.f64 (PI.f64) n))) (.f64 (.f64 k (.f64 (sqrt.f64 2) (log.f64 (.f64 2 (.f64 (PI.f64) n))))) (.f64 (sqrt.f64 (.f64 (PI.f64) n)) -1/2))))
2.0ms	k	@	0	(.f64 (/.f64 1 (sqrt.f64 k)) (+.f64 (.f64 (sqrt.f64 2) (sqrt.f64 (.f64 (PI.f64) n))) (.f64 (.f64 k (.f64 (sqrt.f64 2) (log.f64 (.f64 2 (.f64 (PI.f64) n))))) (.f64 (sqrt.f64 (.f64 (PI.f64) n)) -1/2))))

rewrite86.0ms (0.6%)

Algorithm

1×	batch-egg-rewrite

Rules

1754×	`rational_best-4`
1754×	`rational_best-2`
1754×	`rational_best-3`
1754×	`rational_best-1`
884×	`rational_best_45_simplify-25`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	24	191
1	167	173
2	658	173
3	3559	173

Stop Event

1×	node limit

Counts

3 → 48

Calls

Call 1

Inputs

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

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

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

Outputs

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simplify182.0ms (1.2%)

Algorithm

1×	egg-herbie

Rules

1190×	`rational_best_45_simplify-67`
1088×	`rational_best_45_simplify-1`
842×	`rational_best_45_simplify-39`
746×	`rational_best_45_simplify-71`
642×	`rational_best_45_simplify-98`

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	153	4722
1	557	4706
2	2376	4698
3	5953	4698

Stop Event

1×	node limit

Counts

72 → 80

Calls

Call 1

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

localize231.0ms (1.6%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	1.4b	(.f64 (/.f64 1 (sqrt.f64 k)) (+.f64 (.f64 (sqrt.f64 2) (sqrt.f64 (.f64 (PI.f64) n))) (+.f64 (.f64 (.f64 (pow.f64 (log.f64 (.f64 2 (.f64 (PI.f64) n))) 3) (.f64 (sqrt.f64 2) (pow.f64 k 3))) (.f64 (sqrt.f64 (.f64 (PI.f64) n)) -1/48)) (+.f64 (.f64 (.f64 k (.f64 (sqrt.f64 2) (log.f64 (.f64 2 (.f64 (PI.f64) n))))) (.f64 (sqrt.f64 (.f64 (PI.f64) n)) -1/2)) (.f64 (sqrt.f64 (.f64 (PI.f64) n)) (.f64 1/8 (.f64 (pow.f64 (log.f64 (.f64 2 (.f64 (PI.f64) n))) 2) (.f64 (sqrt.f64 2) (pow.f64 k 2)))))))))
✓	1.8b	(.f64 (sqrt.f64 (.f64 (PI.f64) n)) (.f64 1/8 (.f64 (pow.f64 (log.f64 (.f64 2 (.f64 (PI.f64) n))) 2) (*.f64 (sqrt.f64 2) (pow.f64 k 2)))))
✓	5.0b	(+.f64 (.f64 (.f64 k (.f64 (sqrt.f64 2) (log.f64 (.f64 2 (.f64 (PI.f64) n))))) (.f64 (sqrt.f64 (.f64 (PI.f64) n)) -1/2)) (.f64 (sqrt.f64 (.f64 (PI.f64) n)) (.f64 1/8 (.f64 (pow.f64 (log.f64 (.f64 2 (.f64 (PI.f64) n))) 2) (.f64 (sqrt.f64 2) (pow.f64 k 2))))))
✓	12.0b	(+.f64 (.f64 (.f64 (pow.f64 (log.f64 (.f64 2 (.f64 (PI.f64) n))) 3) (.f64 (sqrt.f64 2) (pow.f64 k 3))) (.f64 (sqrt.f64 (.f64 (PI.f64) n)) -1/48)) (+.f64 (.f64 (.f64 k (.f64 (sqrt.f64 2) (log.f64 (.f64 2 (.f64 (PI.f64) n))))) (.f64 (sqrt.f64 (.f64 (PI.f64) n)) -1/2)) (.f64 (sqrt.f64 (.f64 (PI.f64) n)) (.f64 1/8 (.f64 (pow.f64 (log.f64 (.f64 2 (.f64 (PI.f64) n))) 2) (*.f64 (sqrt.f64 2) (pow.f64 k 2)))))))

Compiler

Compiled 473 to 294 computations (37.8% saved)

series41.0ms (0.3%)

Counts

4 → 36

Calls

24 calls:

Time	Variable		Point	Expression
5.0ms	n	@	0	(+.f64 (.f64 (.f64 (pow.f64 (log.f64 (.f64 2 (.f64 (PI.f64) n))) 3) (.f64 (sqrt.f64 2) (pow.f64 k 3))) (.f64 (sqrt.f64 (.f64 (PI.f64) n)) -1/48)) (+.f64 (.f64 (.f64 k (.f64 (sqrt.f64 2) (log.f64 (.f64 2 (.f64 (PI.f64) n))))) (.f64 (sqrt.f64 (.f64 (PI.f64) n)) -1/2)) (.f64 (sqrt.f64 (.f64 (PI.f64) n)) (.f64 1/8 (.f64 (pow.f64 (log.f64 (.f64 2 (.f64 (PI.f64) n))) 2) (*.f64 (sqrt.f64 2) (pow.f64 k 2)))))))
5.0ms	n	@	inf	(+.f64 (.f64 (.f64 (pow.f64 (log.f64 (.f64 2 (.f64 (PI.f64) n))) 3) (.f64 (sqrt.f64 2) (pow.f64 k 3))) (.f64 (sqrt.f64 (.f64 (PI.f64) n)) -1/48)) (+.f64 (.f64 (.f64 k (.f64 (sqrt.f64 2) (log.f64 (.f64 2 (.f64 (PI.f64) n))))) (.f64 (sqrt.f64 (.f64 (PI.f64) n)) -1/2)) (.f64 (sqrt.f64 (.f64 (PI.f64) n)) (.f64 1/8 (.f64 (pow.f64 (log.f64 (.f64 2 (.f64 (PI.f64) n))) 2) (*.f64 (sqrt.f64 2) (pow.f64 k 2)))))))
5.0ms	n	@	-inf	(+.f64 (.f64 (.f64 (pow.f64 (log.f64 (.f64 2 (.f64 (PI.f64) n))) 3) (.f64 (sqrt.f64 2) (pow.f64 k 3))) (.f64 (sqrt.f64 (.f64 (PI.f64) n)) -1/48)) (+.f64 (.f64 (.f64 k (.f64 (sqrt.f64 2) (log.f64 (.f64 2 (.f64 (PI.f64) n))))) (.f64 (sqrt.f64 (.f64 (PI.f64) n)) -1/2)) (.f64 (sqrt.f64 (.f64 (PI.f64) n)) (.f64 1/8 (.f64 (pow.f64 (log.f64 (.f64 2 (.f64 (PI.f64) n))) 2) (*.f64 (sqrt.f64 2) (pow.f64 k 2)))))))
4.0ms	n	@	-inf	(.f64 (/.f64 1 (sqrt.f64 k)) (+.f64 (.f64 (sqrt.f64 2) (sqrt.f64 (.f64 (PI.f64) n))) (+.f64 (.f64 (.f64 (pow.f64 (log.f64 (.f64 2 (.f64 (PI.f64) n))) 3) (.f64 (sqrt.f64 2) (pow.f64 k 3))) (.f64 (sqrt.f64 (.f64 (PI.f64) n)) -1/48)) (+.f64 (.f64 (.f64 k (.f64 (sqrt.f64 2) (log.f64 (.f64 2 (.f64 (PI.f64) n))))) (.f64 (sqrt.f64 (.f64 (PI.f64) n)) -1/2)) (.f64 (sqrt.f64 (.f64 (PI.f64) n)) (.f64 1/8 (.f64 (pow.f64 (log.f64 (.f64 2 (.f64 (PI.f64) n))) 2) (.f64 (sqrt.f64 2) (pow.f64 k 2)))))))))
3.0ms	n	@	0	(.f64 (/.f64 1 (sqrt.f64 k)) (+.f64 (.f64 (sqrt.f64 2) (sqrt.f64 (.f64 (PI.f64) n))) (+.f64 (.f64 (.f64 (pow.f64 (log.f64 (.f64 2 (.f64 (PI.f64) n))) 3) (.f64 (sqrt.f64 2) (pow.f64 k 3))) (.f64 (sqrt.f64 (.f64 (PI.f64) n)) -1/48)) (+.f64 (.f64 (.f64 k (.f64 (sqrt.f64 2) (log.f64 (.f64 2 (.f64 (PI.f64) n))))) (.f64 (sqrt.f64 (.f64 (PI.f64) n)) -1/2)) (.f64 (sqrt.f64 (.f64 (PI.f64) n)) (.f64 1/8 (.f64 (pow.f64 (log.f64 (.f64 2 (.f64 (PI.f64) n))) 2) (.f64 (sqrt.f64 2) (pow.f64 k 2)))))))))

rewrite211.0ms (1.4%)

Algorithm

1×	batch-egg-rewrite

Rules

972×	`rational_best_45_simplify-100`
876×	`rational_best_45_simplify-91`
738×	`rational_best_45_simplify-73`
720×	`rational_best-4`
720×	`rational_best-2`

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	41	672
1	301	618
2	1238	582
3	5859	582

Stop Event

1×	node limit

Counts

4 → 77

Calls

Call 1

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

Outputs
((#(struct:change #<rule egg-rr> (2) ((x -.f64 (.f64 (sqrt.f64 (.f64 (PI.f64) n)) (+.f64 (.f64 (.f64 (pow.f64 (log.f64 (.f64 2 (.f64 (PI.f64) n))) 3) (.f64 (sqrt.f64 2) (pow.f64 k 3))) -1/48) (+.f64 (.f64 (pow.f64 (log.f64 (.f64 2 (.f64 (PI.f64) n))) 2) (.f64 (sqrt.f64 2) (.f64 1/8 (pow.f64 k 2)))) (.f64 (.f64 (log.f64 (.f64 2 (.f64 (PI.f64) n))) (.f64 (sqrt.f64 2) k)) -1/2)))) 0)))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (sqrt.f64 (.f64 (PI.f64) n)) (+.f64 (.f64 (.f64 (pow.f64 (log.f64 (.f64 2 (.f64 (PI.f64) n))) 3) (.f64 (sqrt.f64 2) (pow.f64 k 3))) -1/48) (+.f64 (.f64 (pow.f64 (log.f64 (.f64 2 (.f64 (PI.f64) n))) 2) (.f64 (sqrt.f64 2) (.f64 1/8 (pow.f64 k 2)))) (.f64 (.f64 (log.f64 (.f64 2 (.f64 (PI.f64) n))) (.f64 (sqrt.f64 2) k)) -1/2))))))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (.f64 (sqrt.f64 (.f64 (PI.f64) n)) (+.f64 (.f64 (.f64 (pow.f64 (log.f64 (.f64 2 (.f64 (PI.f64) n))) 3) (.f64 (sqrt.f64 2) (pow.f64 k 3))) -1/48) (+.f64 (.f64 (pow.f64 (log.f64 (.f64 2 (.f64 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simplify250.0ms (1.7%)

Algorithm

1×	egg-herbie

Rules

1570×	`rational_best_45_simplify-83`
996×	`rational_best_45_simplify-25`
910×	`rational_best_45_simplify-100`
726×	`rational_best_45_simplify-37`
714×	`rational_best_45_simplify-91`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	228	17739
1	936	15957
2	4318	15957

Stop Event

1×	node limit

Counts

113 → 112

Calls

Call 1

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

eval563.0ms (3.8%)

Compiler: Compiled 36533 to 23830 computations (34.8% saved)

prune210.0ms (1.4%)

Pruning

12 alts after pruning (10 fresh and 2 done)

	Pruned	Kept	Total
New	761	8	769
Fresh	1	2	3
Picked	1	0	1
Done	3	2	5
Total	766	12	778

Error

0.1b

Counts

778 → 12

Alt Table

Click to see full alt table

Status	Error	Program
	20.5b	(/.f64 (.f64 (sqrt.f64 2) (.f64 (sqrt.f64 (*.f64 (PI.f64) n)) (/.f64 1 (sqrt.f64 k)))) 1)
▶	20.5b	(+.f64 (.f64 (/.f64 1 (sqrt.f64 k)) (.f64 (sqrt.f64 2) (sqrt.f64 (.f64 (PI.f64) n)))) (.f64 (/.f64 1 (sqrt.f64 k)) (.f64 (log.f64 (.f64 (PI.f64) (.f64 2 n))) (.f64 (.f64 (sqrt.f64 (.f64 (PI.f64) n)) -1/2) (*.f64 k (sqrt.f64 2))))))
▶	0.5b	(.f64 (/.f64 1 (sqrt.f64 k)) (pow.f64 (.f64 (.f64 2 (.f64 (.f64 (/.f64 n (.f64 2 (PI.f64))) (.f64 (/.f64 n (.f64 2 (PI.f64))) (/.f64 1 (/.f64 n (.f64 2 (PI.f64)))))) (PI.f64))) (neg.f64 (.f64 (PI.f64) -2))) (/.f64 (-.f64 1 k) 2)))
✓	0.5b	(.f64 (/.f64 1 (sqrt.f64 k)) (pow.f64 (.f64 (*.f64 2 (PI.f64)) n) (/.f64 (-.f64 1 k) 2)))
	20.5b	(.f64 (/.f64 1 (sqrt.f64 k)) (+.f64 (.f64 (sqrt.f64 2) (sqrt.f64 (.f64 (PI.f64) n))) (.f64 (sqrt.f64 (.f64 n (PI.f64))) (+.f64 (.f64 (sqrt.f64 2) (.f64 1/8 (.f64 (pow.f64 k 2) (pow.f64 (log.f64 (.f64 (PI.f64) (.f64 2 n))) 2)))) (.f64 -1/2 (.f64 k (.f64 (sqrt.f64 2) (log.f64 (.f64 (PI.f64) (*.f64 2 n))))))))))
	20.5b	(.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))))))
	20.5b	(.f64 (/.f64 1 (sqrt.f64 k)) (.f64 (sqrt.f64 (.f64 n (PI.f64))) (+.f64 (+.f64 (.f64 (.f64 (pow.f64 k 3) (pow.f64 (log.f64 (.f64 (PI.f64) (.f64 2 n))) 3)) (.f64 -1/48 (sqrt.f64 2))) (.f64 (sqrt.f64 2) (.f64 1/8 (.f64 (pow.f64 k 2) (pow.f64 (log.f64 (.f64 (PI.f64) (.f64 2 n))) 2))))) (+.f64 (sqrt.f64 2) (.f64 -1/2 (.f64 k (.f64 (sqrt.f64 2) (log.f64 (.f64 (PI.f64) (.f64 2 n))))))))))
✓	20.6b	(.f64 (/.f64 1 (sqrt.f64 k)) (.f64 (sqrt.f64 2) (sqrt.f64 (*.f64 (PI.f64) n))))
▶	3.2b	(.f64 (/.f64 1 (sqrt.f64 k)) (exp.f64 (.f64 (-.f64 1 k) (.f64 1/2 (log.f64 (.f64 2 (*.f64 (PI.f64) n)))))))
	23.5b	(.f64 (sqrt.f64 (/.f64 1 k)) (exp.f64 (.f64 1/2 (+.f64 (log.f64 (*.f64 2 (PI.f64))) (log.f64 n)))))
▶	20.3b	(.f64 (sqrt.f64 (.f64 (PI.f64) n)) (.f64 (/.f64 1 (sqrt.f64 k)) (+.f64 (sqrt.f64 2) (.f64 (sqrt.f64 2) (.f64 (.f64 -1/2 k) (log.f64 (.f64 2 (.f64 (PI.f64) n))))))))
▶	20.5b	(.f64 (sqrt.f64 (.f64 n (PI.f64))) (*.f64 (sqrt.f64 2) (/.f64 1 (sqrt.f64 k))))

Compiler

Compiled 698 to 559 computations (19.9% saved)

localize146.0ms (1%)

Local error

Found 4 expressions with local error:

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

Compiler

Compiled 221 to 155 computations (29.9% saved)

series3.0ms (0%)

Counts

2 → 24

Calls

9 calls:

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

rewrite80.0ms (0.5%)

Algorithm

1×	batch-egg-rewrite

Rules

1446×	`rational_best-4`
1446×	`rational_best-2`
1446×	`rational_best-3`
1446×	`rational_best-1`
958×	`rational_best_45_simplify-98`

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	26	196
1	172	104
2	618	94
3	3213	88

Stop Event

1×	node limit

Counts

2 → 25

Calls

Call 1

Inputs

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

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

Outputs

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

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

simplify198.0ms (1.3%)

Algorithm

1×	egg-herbie

Rules

1306×	`rational_best_45_simplify-100`
1220×	`rational_best_45_simplify-25`
1174×	`rational_best_45_simplify-67`
1010×	`rational_best_45_simplify-91`
966×	`rational_best_45_simplify-37`

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	104	2375
1	333	2359
2	1353	2135
3	6151	2135

Stop Event

1×	node limit

Counts

49 → 46

Calls

Call 1

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

localize76.0ms (0.5%)

Local error

Found 4 expressions with local error:

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

Compiler

Compiled 41 to 23 computations (43.9% saved)

series6.0ms (0%)

Counts

3 → 0

Calls

12 calls:

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

rewrite177.0ms (1.2%)

Algorithm

1×	batch-egg-rewrite

Rules

936×	`rational_best_45_simplify-100`
734×	`rational_best-4`
734×	`rational_best-2`
734×	`rational_best-3`
734×	`rational_best-1`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	16	69
1	98	69
2	328	69
3	1522	69
4	6842	69

Stop Event

1×	node limit

Counts

3 → 134

Calls

Call 1

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

Outputs

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simplify238.0ms (1.6%)

Algorithm

1×	egg-herbie

Rules

1726×	`rational_best_45_simplify-1`
818×	`rational_best_45_simplify-71`
810×	`rational_best_45_simplify-98`
710×	`rational_best_45_simplify-74`
592×	`rational_best_45_simplify-100`

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	259	5560
1	835	5560
2	2900	5520
3	7485	5520

Stop Event

1×	node limit

Counts

134 → 156

Calls

Call 1

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

localize36.0ms (0.2%)

Local error

Found 4 expressions with local error:

New	Error	Program
	0.2b	(*.f64 (PI.f64) n)
	0.3b	(/.f64 1 (sqrt.f64 k))
✓	0.3b	(.f64 (/.f64 1 (sqrt.f64 k)) (exp.f64 (.f64 (-.f64 1 k) (.f64 1/2 (log.f64 (.f64 2 (*.f64 (PI.f64) n)))))))
✓	3.2b	(exp.f64 (.f64 (-.f64 1 k) (.f64 1/2 (log.f64 (.f64 2 (.f64 (PI.f64) n))))))

Compiler

Compiled 82 to 51 computations (37.8% saved)

series5.0ms (0%)

Counts

2 → 36

Calls

12 calls:

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

rewrite98.0ms (0.7%)

Algorithm

1×	batch-egg-rewrite

Rules

1020×	`rational_best_45_simplify-100`
870×	`rational_best-4`
870×	`rational_best-2`
870×	`rational_best-3`
870×	`rational_best-1`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	20	98
1	124	98
2	404	98
3	1846	98

Stop Event

1×	node limit

Counts

2 → 61

Calls

Call 1

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

Outputs

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simplify295.0ms (2%)

Algorithm

1×	egg-herbie

Rules

1162×	`rational_best_45_simplify-1`
874×	`rational_best_45_simplify-83`
782×	`rational_best_45_simplify-84`
654×	`rational_best_45_simplify-67`
644×	`rational_best_45_simplify-98`

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	202	6365
1	699	6325
2	2712	6317
3	7416	6317

Stop Event

1×	node limit

Counts

97 → 124

Calls

Call 1

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

localize118.0ms (0.8%)

Local error

Found 4 expressions with local error:

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

Compiler

Compiled 123 to 78 computations (36.6% saved)

series18.0ms (0.1%)

Counts

4 → 60

Calls

24 calls:

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

rewrite155.0ms (1%)

Algorithm

1×	batch-egg-rewrite

Rules

1840×	`rational_best_45_simplify-71`
1556×	`rational_best-4`
1556×	`rational_best-2`
1556×	`rational_best-3`
1556×	`rational_best-1`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	23	224
1	155	216
2	599	216
3	3157	216

Stop Event

1×	node limit

Counts

4 → 68

Calls

Call 1

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

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

simplify217.0ms (1.5%)

Algorithm

1×	egg-herbie

Rules

1028×	`rational_best_45_simplify-71`
874×	`rational_best_45_simplify-100`
786×	`rational_best_45_simplify-98`
730×	`rational_best_45_simplify-84`
728×	`rational_best_45_simplify-37`

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	221	8140
1	844	8092
2	3650	8040

Stop Event

1×	node limit

Counts

128 → 141

Calls

Call 1

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

localize60.0ms (0.4%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.4b	(.f64 (log.f64 (.f64 (PI.f64) (.f64 2 n))) (.f64 (.f64 (sqrt.f64 (.f64 (PI.f64) n)) -1/2) (*.f64 k (sqrt.f64 2))))
✓	0.4b	(*.f64 k (sqrt.f64 2))
	0.5b	(.f64 (sqrt.f64 2) (sqrt.f64 (.f64 (PI.f64) n)))
✓	9.2b	(.f64 (/.f64 1 (sqrt.f64 k)) (.f64 (log.f64 (.f64 (PI.f64) (.f64 2 n))) (.f64 (.f64 (sqrt.f64 (.f64 (PI.f64) n)) -1/2) (.f64 k (sqrt.f64 2)))))

Compiler

Compiled 154 to 88 computations (42.9% saved)

series18.0ms (0.1%)

Counts

3 → 24

Calls

15 calls:

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

rewrite99.0ms (0.7%)

Algorithm

1×	batch-egg-rewrite

Rules

1774×	`rational_best-4`
1774×	`rational_best-2`
1774×	`rational_best-3`
1774×	`rational_best-1`
978×	`rational_best_45_simplify-25`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	23	145
1	159	145
2	641	145
3	3581	145

Stop Event

1×	node limit

Counts

3 → 48

Calls

Call 1

Inputs

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

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

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

Outputs

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

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

simplify134.0ms (0.9%)

Algorithm

1×	egg-herbie

Rules

1120×	`rational_best_45_simplify-67`
1056×	`rational_best_45_simplify-1`
904×	`rational_best_45_simplify-98`
884×	`rational_best_45_simplify-71`
814×	`rational_best_45_simplify-39`

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	133	4152
1	496	4152
2	2336	4152
3	6036	4132

Stop Event

1×	node limit

Counts

72 → 79

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

eval611.0ms (4.1%)

Compiler: Compiled 30704 to 19416 computations (36.8% saved)

prune403.0ms (2.7%)

Pruning

13 alts after pruning (9 fresh and 4 done)

	Pruned	Kept	Total
New	773	5	778
Fresh	1	4	5
Picked	1	0	1
Done	2	4	6
Total	777	13	790

Error

0.1b

Counts

790 → 13

Alt Table

Click to see full alt table

Status	Error	Program
▶	0.5b	(.f64 (/.f64 1 (sqrt.f64 k)) (pow.f64 (.f64 (.f64 2 (.f64 (.f64 (/.f64 n (.f64 2 (PI.f64))) (.f64 (.f64 (/.f64 n (.f64 2 (PI.f64))) (.f64 (/.f64 n (.f64 2 (PI.f64))) (/.f64 1 (/.f64 n (.f64 2 (PI.f64)))))) (/.f64 1 (/.f64 n (.f64 2 (PI.f64)))))) (PI.f64))) (neg.f64 (.f64 (PI.f64) -2))) (/.f64 (-.f64 1 k) 2)))
✓	0.5b	(.f64 (/.f64 1 (sqrt.f64 k)) (pow.f64 (.f64 (*.f64 2 (PI.f64)) n) (/.f64 (-.f64 1 k) 2)))
▶	20.5b	(.f64 (/.f64 1 (sqrt.f64 k)) (+.f64 (.f64 (sqrt.f64 2) (sqrt.f64 (.f64 (PI.f64) n))) (.f64 (sqrt.f64 (.f64 n (PI.f64))) (+.f64 (.f64 (sqrt.f64 2) (.f64 1/8 (.f64 (pow.f64 k 2) (pow.f64 (log.f64 (.f64 (PI.f64) (.f64 2 n))) 2)))) (.f64 -1/2 (.f64 k (.f64 (sqrt.f64 2) (log.f64 (.f64 (PI.f64) (*.f64 2 n))))))))))
	20.5b	(.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))))))
	20.5b	(.f64 (/.f64 1 (sqrt.f64 k)) (.f64 (sqrt.f64 (.f64 n (PI.f64))) (+.f64 (+.f64 (.f64 (.f64 (pow.f64 k 3) (pow.f64 (log.f64 (.f64 (PI.f64) (.f64 2 n))) 3)) (.f64 -1/48 (sqrt.f64 2))) (.f64 (sqrt.f64 2) (.f64 1/8 (.f64 (pow.f64 k 2) (pow.f64 (log.f64 (.f64 (PI.f64) (.f64 2 n))) 2))))) (+.f64 (sqrt.f64 2) (.f64 -1/2 (.f64 k (.f64 (sqrt.f64 2) (log.f64 (.f64 (PI.f64) (.f64 2 n))))))))))
✓	20.6b	(.f64 (/.f64 1 (sqrt.f64 k)) (.f64 (sqrt.f64 2) (sqrt.f64 (*.f64 (PI.f64) n))))
✓	3.2b	(.f64 (/.f64 1 (sqrt.f64 k)) (exp.f64 (.f64 (-.f64 1 k) (.f64 1/2 (log.f64 (.f64 2 (*.f64 (PI.f64) n)))))))
	23.5b	(.f64 (sqrt.f64 (/.f64 1 k)) (exp.f64 (.f64 1/2 (+.f64 (log.f64 (*.f64 2 (PI.f64))) (log.f64 n)))))
	20.3b	(.f64 (sqrt.f64 (.f64 (PI.f64) n)) (.f64 (.f64 (sqrt.f64 2) (/.f64 1 (sqrt.f64 k))) (+.f64 1 (.f64 -1/2 (.f64 k (log.f64 (.f64 2 (.f64 n (PI.f64)))))))))
▶	20.3b	(.f64 (sqrt.f64 (.f64 (PI.f64) n)) (.f64 (.f64 (sqrt.f64 2) (+.f64 1 (.f64 (+.f64 (log.f64 (.f64 2 (PI.f64))) (log.f64 n)) (*.f64 -1/2 k)))) (sqrt.f64 (/.f64 1 k))))
✓	20.5b	(.f64 (sqrt.f64 (.f64 n (PI.f64))) (*.f64 (sqrt.f64 2) (/.f64 1 (sqrt.f64 k))))
▶	20.5b	(.f64 (sqrt.f64 2) (.f64 (/.f64 1 (sqrt.f64 k)) (sqrt.f64 (*.f64 n (PI.f64)))))
▶	20.3b	(.f64 (sqrt.f64 2) (.f64 (+.f64 1 (.f64 k (.f64 -1/2 (log.f64 (.f64 (PI.f64) (.f64 2 n)))))) (.f64 (/.f64 1 (sqrt.f64 k)) (sqrt.f64 (.f64 n (PI.f64))))))

Compiler

Compiled 720 to 582 computations (19.2% saved)

localize217.0ms (1.5%)

Local error

Found 4 expressions with local error:

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

Compiler

Compiled 351 to 247 computations (29.6% saved)

series3.0ms (0%)

Counts

2 → 24

Calls

9 calls:

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

rewrite74.0ms (0.5%)

Algorithm

1×	batch-egg-rewrite

Rules

1490×	`rational_best-4`
1490×	`rational_best-2`
1490×	`rational_best-3`
1490×	`rational_best-1`
960×	`rational_best_45_simplify-98`

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	28	288
1	195	104
2	750	94
3	3431	88

Stop Event

1×	node limit

Counts

2 → 25

Calls

Call 1

Inputs

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

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

Outputs

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

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

simplify124.0ms (0.8%)

Algorithm

1×	egg-herbie

Rules

1306×	`rational_best_45_simplify-100`
1216×	`rational_best_45_simplify-25`
1176×	`rational_best_45_simplify-67`
1008×	`rational_best_45_simplify-91`
966×	`rational_best_45_simplify-37`

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	104	2375
1	333	2359
2	1353	2135
3	6120	2135

Stop Event

1×	node limit

Counts

49 → 43

Calls

Call 1

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

localize29.0ms (0.2%)

Local error

Found 4 expressions with local error:

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

Compiler

Compiled 43 to 21 computations (51.2% saved)

series9.0ms (0.1%)

Counts

2 → 0

Calls

12 calls:

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

rewrite156.0ms (1%)

Algorithm

1×	batch-egg-rewrite

Rules

932×	`rational_best_45_simplify-100`
734×	`rational_best-4`
734×	`rational_best-2`
734×	`rational_best-3`
734×	`rational_best-1`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	16	68
1	98	68
2	328	68
3	1512	68
4	6856	68

Stop Event

1×	node limit

Counts

2 → 94

Calls

Call 1

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

Outputs

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simplify184.0ms (1.2%)

Algorithm

1×	egg-herbie

Rules

1218×	`rational_best_45_simplify-1`
1204×	`rational_best_45_simplify-74`
964×	`rational_best_45_simplify-39`
624×	`rational_best_45_simplify-71`
620×	`rational_best_45_simplify-98`

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	188	4944
1	611	4944
2	2156	4936
3	5636	4932

Stop Event

1×	node limit

Counts

94 → 109

Calls

Call 1

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

localize92.0ms (0.6%)

Local error

Found 4 expressions with local error:

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

Compiler

Compiled 123 to 76 computations (38.2% saved)

series14.0ms (0.1%)

Counts

2 → 24

Calls

12 calls:

Time	Variable		Point	Expression
5.0ms	n	@	-inf	(.f64 (sqrt.f64 2) (.f64 (+.f64 1 (.f64 k (.f64 -1/2 (log.f64 (.f64 (PI.f64) (.f64 2 n)))))) (.f64 (/.f64 1 (sqrt.f64 k)) (sqrt.f64 (.f64 n (PI.f64))))))
2.0ms	n	@	0	(.f64 (sqrt.f64 2) (.f64 (+.f64 1 (.f64 k (.f64 -1/2 (log.f64 (.f64 (PI.f64) (.f64 2 n)))))) (.f64 (/.f64 1 (sqrt.f64 k)) (sqrt.f64 (.f64 n (PI.f64))))))
2.0ms	n	@	inf	(.f64 (sqrt.f64 2) (.f64 (+.f64 1 (.f64 k (.f64 -1/2 (log.f64 (.f64 (PI.f64) (.f64 2 n)))))) (.f64 (/.f64 1 (sqrt.f64 k)) (sqrt.f64 (.f64 n (PI.f64))))))
1.0ms	k	@	-inf	(.f64 (sqrt.f64 2) (.f64 (+.f64 1 (.f64 k (.f64 -1/2 (log.f64 (.f64 (PI.f64) (.f64 2 n)))))) (.f64 (/.f64 1 (sqrt.f64 k)) (sqrt.f64 (.f64 n (PI.f64))))))
1.0ms	k	@	inf	(.f64 (sqrt.f64 2) (.f64 (+.f64 1 (.f64 k (.f64 -1/2 (log.f64 (.f64 (PI.f64) (.f64 2 n)))))) (.f64 (/.f64 1 (sqrt.f64 k)) (sqrt.f64 (.f64 n (PI.f64))))))

rewrite188.0ms (1.3%)

Algorithm

1×	batch-egg-rewrite

Rules

1566×	`rational_best-4`
1566×	`rational_best-2`
1566×	`rational_best-3`
1566×	`rational_best-1`
776×	`rational_best_45_simplify-84`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	24	112
1	164	112
2	628	112
3	3269	112

Stop Event

1×	node limit

Counts

2 → 51

Calls

Call 1

Inputs

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

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

Outputs

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simplify226.0ms (1.5%)

Algorithm

1×	egg-herbie

Rules

1312×	`rational_best_45_simplify-67`
978×	`rational_best_45_simplify-1`
762×	`rational_best_45_simplify-39`
692×	`rational_best_45_simplify-71`
548×	`rational_best_45_simplify-98`

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	154	4771
1	536	4755
2	2122	4743
3	5355	4743

Stop Event

1×	node limit

Counts

75 → 77

Calls

Call 1

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

localize305.0ms (2%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.3b	(.f64 (sqrt.f64 (.f64 (PI.f64) n)) (.f64 (.f64 (sqrt.f64 2) (+.f64 1 (.f64 (+.f64 (log.f64 (.f64 2 (PI.f64))) (log.f64 n)) (*.f64 -1/2 k)))) (sqrt.f64 (/.f64 1 k))))
	0.4b	(+.f64 (log.f64 (*.f64 2 (PI.f64))) (log.f64 n))
✓	0.4b	(.f64 (.f64 (sqrt.f64 2) (+.f64 1 (.f64 (+.f64 (log.f64 (.f64 2 (PI.f64))) (log.f64 n)) (*.f64 -1/2 k)))) (sqrt.f64 (/.f64 1 k)))
	1.0b	(log.f64 (*.f64 2 (PI.f64)))

Compiler

Compiled 130 to 88 computations (32.3% saved)

series26.0ms (0.2%)

Counts

2 → 12

Calls

12 calls:

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

rewrite199.0ms (1.3%)

Algorithm

1×	batch-egg-rewrite

Rules

1598×	`rational_best-4`
1598×	`rational_best-2`
1598×	`rational_best-3`
1598×	`rational_best-1`
778×	`rational_best_45_simplify-98`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	25	152
1	164	152
2	598	152
3	3166	152

Stop Event

1×	node limit

Counts

2 → 62

Calls

Call 1

Inputs

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

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

Outputs

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simplify225.0ms (1.5%)

Algorithm

1×	egg-herbie

Rules

968×	`rational_best_45_simplify-1`
914×	`rational_best_45_simplify-71`
750×	`rational_best_45_simplify-39`
710×	`rational_best_45_simplify-83`
590×	`rational_best_45_simplify-98`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	179	6066
1	665	6050
2	2538	6050
3	6574	6050

Stop Event

1×	node limit

Counts

74 → 83

Calls

Call 1

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

localize215.0ms (1.4%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.5b	(.f64 (sqrt.f64 2) (log.f64 (.f64 (PI.f64) (*.f64 2 n))))
	0.5b	(.f64 (sqrt.f64 2) (sqrt.f64 (.f64 (PI.f64) n)))
✓	0.5b	(pow.f64 (log.f64 (.f64 (PI.f64) (.f64 2 n))) 2)
✓	0.8b	(.f64 (/.f64 1 (sqrt.f64 k)) (+.f64 (.f64 (sqrt.f64 2) (sqrt.f64 (.f64 (PI.f64) n))) (.f64 (sqrt.f64 (.f64 n (PI.f64))) (+.f64 (.f64 (sqrt.f64 2) (.f64 1/8 (.f64 (pow.f64 k 2) (pow.f64 (log.f64 (.f64 (PI.f64) (.f64 2 n))) 2)))) (.f64 -1/2 (.f64 k (.f64 (sqrt.f64 2) (log.f64 (.f64 (PI.f64) (*.f64 2 n))))))))))

Compiler

Compiled 299 to 209 computations (30.1% saved)

series14.0ms (0.1%)

Counts

3 → 24

Calls

12 calls:

Time	Variable		Point	Expression
3.0ms	n	@	-inf	(.f64 (/.f64 1 (sqrt.f64 k)) (+.f64 (.f64 (sqrt.f64 2) (sqrt.f64 (.f64 (PI.f64) n))) (.f64 (sqrt.f64 (.f64 n (PI.f64))) (+.f64 (.f64 (sqrt.f64 2) (.f64 1/8 (.f64 (pow.f64 k 2) (pow.f64 (log.f64 (.f64 (PI.f64) (.f64 2 n))) 2)))) (.f64 -1/2 (.f64 k (.f64 (sqrt.f64 2) (log.f64 (.f64 (PI.f64) (*.f64 2 n))))))))))
2.0ms	k	@	-inf	(.f64 (/.f64 1 (sqrt.f64 k)) (+.f64 (.f64 (sqrt.f64 2) (sqrt.f64 (.f64 (PI.f64) n))) (.f64 (sqrt.f64 (.f64 n (PI.f64))) (+.f64 (.f64 (sqrt.f64 2) (.f64 1/8 (.f64 (pow.f64 k 2) (pow.f64 (log.f64 (.f64 (PI.f64) (.f64 2 n))) 2)))) (.f64 -1/2 (.f64 k (.f64 (sqrt.f64 2) (log.f64 (.f64 (PI.f64) (*.f64 2 n))))))))))
2.0ms	n	@	inf	(.f64 (/.f64 1 (sqrt.f64 k)) (+.f64 (.f64 (sqrt.f64 2) (sqrt.f64 (.f64 (PI.f64) n))) (.f64 (sqrt.f64 (.f64 n (PI.f64))) (+.f64 (.f64 (sqrt.f64 2) (.f64 1/8 (.f64 (pow.f64 k 2) (pow.f64 (log.f64 (.f64 (PI.f64) (.f64 2 n))) 2)))) (.f64 -1/2 (.f64 k (.f64 (sqrt.f64 2) (log.f64 (.f64 (PI.f64) (*.f64 2 n))))))))))
2.0ms	n	@	0	(.f64 (/.f64 1 (sqrt.f64 k)) (+.f64 (.f64 (sqrt.f64 2) (sqrt.f64 (.f64 (PI.f64) n))) (.f64 (sqrt.f64 (.f64 n (PI.f64))) (+.f64 (.f64 (sqrt.f64 2) (.f64 1/8 (.f64 (pow.f64 k 2) (pow.f64 (log.f64 (.f64 (PI.f64) (.f64 2 n))) 2)))) (.f64 -1/2 (.f64 k (.f64 (sqrt.f64 2) (log.f64 (.f64 (PI.f64) (*.f64 2 n))))))))))
1.0ms	k	@	inf	(.f64 (/.f64 1 (sqrt.f64 k)) (+.f64 (.f64 (sqrt.f64 2) (sqrt.f64 (.f64 (PI.f64) n))) (.f64 (sqrt.f64 (.f64 n (PI.f64))) (+.f64 (.f64 (sqrt.f64 2) (.f64 1/8 (.f64 (pow.f64 k 2) (pow.f64 (log.f64 (.f64 (PI.f64) (.f64 2 n))) 2)))) (.f64 -1/2 (.f64 k (.f64 (sqrt.f64 2) (log.f64 (.f64 (PI.f64) (*.f64 2 n))))))))))

rewrite215.0ms (1.4%)

Algorithm

1×	batch-egg-rewrite

Rules

1202×	`rational_best_45_simplify-98`
1172×	`rational_best_45_simplify-25`
710×	`rational_best_45_simplify-100`
548×	`rational_best-4`
548×	`rational_best-2`

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	34	215
1	243	197
2	948	187
3	4945	187

Stop Event

1×	node limit

Counts

3 → 56

Calls

Call 1

Inputs

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

(pow.f64 (log.f64 (*.f64 (PI.f64) (*.f64 2 n))) 2)

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

Outputs

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simplify160.0ms (1.1%)

Algorithm

1×	egg-herbie

Rules

1254×	`rational_best_45_simplify-71`
916×	`rational_best_45_simplify-1`
704×	`rational_best_45_simplify-39`
594×	`rational_best_45_simplify-83`
542×	`rational_best_45_simplify-84`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	172	6180
1	574	6148
2	2354	6148
3	6459	6148

Stop Event

1×	node limit

Counts

80 → 78

Calls

Call 1

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

eval814.0ms (5.5%)

Compiler: Compiled 36697 to 23984 computations (34.6% saved)

prune240.0ms (1.6%)

Pruning

13 alts after pruning (7 fresh and 6 done)

	Pruned	Kept	Total
New	779	4	783
Fresh	1	3	4
Picked	1	0	1
Done	2	6	8
Total	783	13	796

Error

0.1b

Counts

796 → 13

Alt Table

Click to see full alt table

Status	Error	Program
✓	0.5b	(.f64 (/.f64 1 (sqrt.f64 k)) (pow.f64 (.f64 (*.f64 2 (PI.f64)) n) (/.f64 (-.f64 1 k) 2)))
	20.5b	(.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))))))
	20.5b	(.f64 (/.f64 1 (sqrt.f64 k)) (.f64 (sqrt.f64 (.f64 n (PI.f64))) (+.f64 (+.f64 (.f64 (.f64 (pow.f64 k 3) (pow.f64 (log.f64 (.f64 (PI.f64) (.f64 2 n))) 3)) (.f64 -1/48 (sqrt.f64 2))) (.f64 (sqrt.f64 2) (.f64 1/8 (.f64 (pow.f64 k 2) (pow.f64 (log.f64 (.f64 (PI.f64) (.f64 2 n))) 2))))) (+.f64 (sqrt.f64 2) (.f64 -1/2 (.f64 k (.f64 (sqrt.f64 2) (log.f64 (.f64 (PI.f64) (.f64 2 n))))))))))
✓	20.6b	(.f64 (/.f64 1 (sqrt.f64 k)) (.f64 (sqrt.f64 2) (sqrt.f64 (*.f64 (PI.f64) n))))
✓	3.2b	(.f64 (/.f64 1 (sqrt.f64 k)) (exp.f64 (.f64 (-.f64 1 k) (.f64 1/2 (log.f64 (.f64 2 (*.f64 (PI.f64) n)))))))
	20.3b	(.f64 (+.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) (sqrt.f64 (*.f64 (PI.f64) n)))))
	20.3b	(.f64 (+.f64 1 (.f64 -1/2 (.f64 k (+.f64 (log.f64 (.f64 2 (PI.f64))) (log.f64 n))))) (.f64 (sqrt.f64 2) (.f64 (sqrt.f64 (/.f64 1 k)) (sqrt.f64 (*.f64 (PI.f64) n)))))
	20.3b	(.f64 (+.f64 1 (.f64 -1/2 (.f64 k (log.f64 (.f64 2 (.f64 n (PI.f64))))))) (.f64 (sqrt.f64 2) (.f64 (/.f64 1 (sqrt.f64 k)) (sqrt.f64 (.f64 n (PI.f64))))))
	23.5b	(.f64 (sqrt.f64 (/.f64 1 k)) (exp.f64 (.f64 1/2 (+.f64 (log.f64 (*.f64 2 (PI.f64))) (log.f64 n)))))
	20.5b	(.f64 (sqrt.f64 (.f64 (PI.f64) n)) (.f64 (/.f64 1 (sqrt.f64 k)) (+.f64 (sqrt.f64 2) (.f64 (sqrt.f64 2) (+.f64 (.f64 (pow.f64 (log.f64 (.f64 2 (.f64 (PI.f64) n))) 2) (.f64 1/8 (pow.f64 k 2))) (.f64 k (.f64 (log.f64 (.f64 2 (.f64 (PI.f64) n))) -1/2)))))))
✓	20.3b	(.f64 (sqrt.f64 (.f64 (PI.f64) n)) (.f64 (.f64 (sqrt.f64 2) (+.f64 1 (.f64 (+.f64 (log.f64 (.f64 2 (PI.f64))) (log.f64 n)) (*.f64 -1/2 k)))) (sqrt.f64 (/.f64 1 k))))
✓	20.5b	(.f64 (sqrt.f64 (.f64 n (PI.f64))) (*.f64 (sqrt.f64 2) (/.f64 1 (sqrt.f64 k))))
✓	20.5b	(.f64 (sqrt.f64 2) (.f64 (/.f64 1 (sqrt.f64 k)) (sqrt.f64 (*.f64 n (PI.f64)))))

Compiler

Compiled 359 to 292 computations (18.7% saved)

regimes73.0ms (0.5%)

Accuracy

Total -23.6b remaining (-4862.1%)

Threshold costs -23.6b (-4862.1%)

Counts

26 → 1

Calls

Call 1

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

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

Calls

4 calls:

16.0ms	k
14.0ms	n
13.0ms	(.f64 (.f64 2 (PI.f64)) 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
0.5b	1	`k`
0.5b	1	`n`
0.5b	1	`(.f64 (/.f64 1 (sqrt.f64 k)) (pow.f64 (.f64 (*.f64 2 (PI.f64)) n) (/.f64 (-.f64 1 k) 2)))`
0.5b	1	`(.f64 (.f64 2 (PI.f64)) n)`

Compiler

Compiled 839 to 557 computations (33.6% saved)

simplify2.0ms (0%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	17	49

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)))

Outputs
(.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)

soundness0.0ms (0%)

end17.0ms (0.1%)

Compiler: Compiled 18 to 15 computations (16.7% saved)